#This file contains data about the mod 2 cohomology of groups of order
#dividing 64. The results come from computations by Jon Carlson, with
#additional information on Steenrod operations in some cases obtained
#by P. Guillot.

#The file unstable_algebras.sage contains functions to work
#conveniently with all this.

gap_to_hall= {(16, 6): (16, 11), (64, 91): (64, 126), (64, 245): (64, 187), (64, 186): (64, 134), (16, 9): (16, 14), (64, 78): (64, 151), (64, 51): (64, 42), (64, 248): (64, 21), (64, 173): (64, 189), (32, 44): (32, 45), (64, 113): (64, 98), (64, 38): (64, 138), (64, 235): (64, 161), (64, 261): (64, 12), (32, 31): (32, 39), (64, 100): (64, 115), (64, 41): (64, 248), (64, 158): (64, 212), (64, 264): (64, 103), (8, 5): (8, 1), (32, 2): (32, 18), (64, 23): (64, 128), (64, 220): (64, 177), (64, 129): (64, 203), (64, 85): (64, 31), (64, 26): (64, 9), (64, 207): (64, 74), (64, 180): (64, 199), (16, 3): (16, 9), (64, 88): (64, 94), (64, 13): (64, 235), (64, 242): (64, 183), (64, 167): (64, 193), (32, 38): (32, 17), (64, 75): (64, 146), (64, 48): (64, 141), (64, 229): (64, 159), (64, 170): (64, 232), (32, 41): (32, 25), (64, 126): (64, 35), (64, 35): (64, 253), (64, 232): (64, 163), (64, 258): (64, 242), (32, 28): (32, 36), (64, 97): (64, 53), (64, 214): (64, 79), (64, 155): (64, 207), (8, 2): (8, 2), (32, 15): (32, 32), (64, 20): (64, 60), (64, 217): (64, 172), (64, 142): (64, 208), (64, 82): (64, 153), (64, 7): (64, 63), (64, 204): (64, 72), (64, 177): (64, 225), (32, 48): (32, 10), (64, 69): (64, 91), (64, 10): (64, 239), (64, 255): (64, 111), (64, 164): (64, 215), (32, 35): (32, 35), (64, 72): (64, 87), (64, 61): (64, 83), (64, 226): (64, 154), (32, 22): (32, 11), (64, 123): (64, 117), (64, 32): (64, 250), (64, 149): (64, 229), (32, 25): (32, 14), (64, 110): (64, 52), (64, 211): (64, 69), (64, 152): (64, 257), (32, 12): (32, 21), (64, 17): (64, 37), (64, 198): (64, 27), (64, 139): (64, 260), (64, 95): (64, 47), (64, 4): (64, 131), (64, 201): (64, 107), (64, 190): (64, 244), (16, 13): (16, 8), (64, 66): (64, 86), (64, 55): (64, 5), (64, 252): (64, 45), (64, 161): (64, 213), (32, 32): (32, 40), (64, 117): (64, 100), (64, 58): (64, 28), (64, 239): (64, 156), (32, 19): (32, 50), (64, 120): (64, 57), (64, 45): (64, 67), (64, 146): (64, 196), (32, 6): (32, 46), (64, 107): (64, 49), (64, 208): (64, 75), (64, 133): (64, 218), (32, 9): (32, 27), (64, 30): (64, 133), (64, 195): (64, 20), (64, 136): (64, 262), (16, 7): (16, 12), (64, 92): (64, 124), (64, 1): (64, 11), (64, 246): (64, 4), (64, 187): (64, 135), (16, 10): (16, 2), (64, 79): (64, 149), (64, 52): (64, 265), (64, 249): (64, 109), (64, 174): (64, 188), (32, 45): (32, 2), (64, 114): (64, 102), (64, 39): (64, 139), (64, 236): (64, 166), (64, 262): (64, 13), (32, 16): (32, 6), (64, 101): (64, 51), (64, 42): (64, 247), (64, 159): (64, 221), (64, 265): (64, 104), (32, 3): (32, 5), (64, 104): (64, 95), (64, 221): (64, 176), (64, 130): (64, 217), (64, 86): (64, 32), (64, 27): (64, 39), (64, 192): (64, 3), (64, 181): (64, 190), (16, 4): (16, 10), (64, 89): (64, 96), (64, 14): (64, 236), (64, 243): (64, 185), (64, 184): (64, 26), (32, 39): (32, 23), (64, 76): (64, 145), (64, 49): (64, 143), (64, 230): (64, 155), (64, 171): (64, 231), (32, 42): (32, 26), (64, 127): (64, 101), (64, 36): (64, 254), (64, 233): (64, 167), (64, 259): (64, 243), (32, 29): (32, 37), (64, 98): (64, 114), (64, 215): (64, 169), (64, 156): (64, 210), (8, 3): (8, 4), (64, 21): (64, 59), (64, 218): (64, 171), (64, 143): (64, 211), (64, 83): (64, 6), (64, 24): (64, 129), (64, 205): (64, 73), (64, 178): (64, 226), (32, 49): (32, 42), (64, 70): (64, 88), (64, 11): (64, 240), (64, 240): (64, 165), (64, 165): (64, 216), (32, 36): (32, 4), (64, 73): (64, 144), (64, 62): (64, 89), (64, 227): (64, 157), (64, 168): (64, 194), (32, 51): (32, 1), (32, 23): (32, 12), (64, 124): (64, 58), (64, 33): (64, 251), (64, 150): (64, 228), (64, 256): (64, 112), (32, 26): (32, 15), (64, 111): (64, 121), (64, 212): (64, 70), (64, 153): (64, 256), (32, 13): (32, 30), (64, 18): (64, 180), (64, 199): (64, 106), (64, 140): (64, 205), (64, 80): (64, 148), (64, 5): (64, 132), (64, 202): (64, 68), (64, 191): (64, 245), (16, 14): (16, 1), (64, 67): (64, 84), (64, 8): (64, 237), (64, 253): (64, 46), (64, 162): (64, 214), (32, 33): (32, 41), (64, 118): (64, 55), (64, 59): (64, 29), (64, 224): (64, 173), (32, 20): (32, 51), (64, 121): (64, 118), (64, 46): (64, 246), (64, 147): (64, 195), (32, 7): (32, 47), (64, 108): (64, 54), (64, 209): (64, 76), (64, 134): (64, 261), (32, 10): (32, 28), (64, 31): (64, 66), (64, 196): (64, 18), (64, 137): (64, 264), (64, 93): (64, 125), (64, 2): (64, 8), (64, 247): (64, 17), (64, 188): (64, 136), (16, 11): (16, 6), (64, 64): (64, 93), (64, 53): (64, 266), (64, 250): (64, 43), (64, 175): (64, 192), (32, 46): (32, 8), (64, 115): (64, 34), (64, 56): (64, 22), (64, 237): (64, 168), (64, 263): (64, 14), (32, 50): (32, 43), (32, 17): (32, 22), (64, 102): (64, 120), (64, 43): (64, 249), (64, 144): (64, 219), (64, 266): (64, 105), (32, 4): (32, 19), (64, 105): (64, 97), (64, 222): (64, 179), (64, 131): (64, 202), (64, 87): (64, 24), (64, 28): (64, 182), (64, 193): (64, 15), (64, 182): (64, 227), (16, 5): (16, 4), (64, 90): (64, 123), (64, 15): (64, 65), (64, 244): (64, 186), (64, 185): (64, 36), (16, 8): (16, 13), (64, 77): (64, 150), (64, 50): (64, 10), (64, 231): (64, 158), (64, 172): (64, 233), (32, 43): (32, 44), (64, 112): (64, 33), (64, 37): (64, 255), (64, 234): (64, 164), (64, 260): (64, 2), (32, 30): (32, 38), (64, 99): (64, 113), (64, 40): (64, 142), (64, 157): (64, 209), (8, 4): (8, 5), (32, 1): (32, 7), (64, 22): (64, 61), (64, 219): (64, 175), (64, 128): (64, 201), (64, 84): (64, 23), (64, 25): (64, 130), (64, 206): (64, 77), (64, 179): (64, 191), (16, 2): (16, 3), (64, 71): (64, 85), (64, 12): (64, 234), (64, 241): (64, 184), (64, 166): (64, 224), (32, 37): (32, 13), (64, 74): (64, 147), (64, 63): (64, 90), (64, 228): (64, 160), (64, 169): (64, 200), (32, 40): (32, 24), (64, 125): (64, 122), (64, 34): (64, 252), (64, 151): (64, 230), (64, 257): (64, 241), (16, 1): (16, 5), (32, 27): (32, 33), (64, 96): (64, 48), (64, 213): (64, 78), (64, 154): (64, 258), (8, 1): (8, 3), (32, 14): (32, 29), (64, 19): (64, 181), (64, 216): (64, 170), (64, 141): (64, 206), (64, 81): (64, 152), (64, 6): (64, 62), (64, 203): (64, 71), (64, 176): (64, 198), (64, 68): (64, 92), (64, 9): (64, 238), (64, 254): (64, 110), (64, 163): (64, 223), (32, 34): (32, 34), (64, 119): (64, 56), (64, 60): (64, 81), (64, 225): (64, 174), (32, 21): (32, 3), (64, 122): (64, 119), (64, 47): (64, 140), (64, 148): (64, 197), (32, 24): (32, 16), (64, 109): (64, 116), (64, 210): (64, 80), (64, 135): (64, 263), (32, 11): (32, 31), (64, 16): (64, 64), (64, 197): (64, 19), (64, 138): (64, 259), (64, 94): (64, 127), (64, 3): (64, 38), (64, 200): (64, 108), (64, 189): (64, 137), (16, 12): (16, 7), (64, 65): (64, 82), (64, 54): (64, 267), (64, 251): (64, 44), (64, 160): (64, 222), (32, 47): (32, 9), (64, 116): (64, 99), (64, 57): (64, 30), (64, 238): (64, 162), (32, 18): (32, 49), (64, 103): (64, 25), (64, 44): (64, 41), (64, 145): (64, 220), (64, 267): (64, 1), (32, 5): (32, 20), (64, 106): (64, 50), (64, 223): (64, 178), (64, 132): (64, 204), (32, 8): (32, 48), (64, 29): (64, 40), (64, 194): (64, 16), (64, 183): (64, 7)}











mod2_cohomology= {
(8,1) : {'gap_number': 5, 'degrees': [1, 1, 1], 'names': ['z', 'y', 'x'], 'relations': []},
(8,2) : {'gap_number': 2, 'degrees': [1, 1, 2], 'names': ['z', 'y', 'x'], 'relations': ['z**2']},
(8,3) : {'gap_number': 1, 'degrees': [1, 2], 'names': ['z', 'y'], 'relations': ['z**2']},
(8,4) : {'gap_number': 3, 'degrees': [1, 1, 2], 'names': ['z', 'y', 'x'], 'relations': ['z*y']},
(8,5) : {'gap_number': 4, 'degrees': [1, 1, 4], 'names': ['z', 'y', 'x'], 'relations': ['z**2 + z*y + y**2', 'y**3']},
(16,1) : {'gap_number': 14, 'degrees': [1, 1, 1, 1], 'names': ['z', 'y', 'x', 'w'], 'relations': []},
(16,2) : {'gap_number': 10, 'degrees': [1, 1, 1, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2']},
(16,3) : {'gap_number': 2, 'degrees': [1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2', 'y**2']},
(16,4) : {'gap_number': 5, 'degrees': [1, 1, 2], 'names': ['z', 'y', 'x'], 'relations': ['z**2']},
(16,5) : {'gap_number': 1, 'degrees': [1, 2], 'names': ['z', 'y'], 'relations': ['z**2']},
(16,6) : {'gap_number': 11, 'degrees': [1, 1, 1, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z*y']},
(16,7) : {'gap_number': 12, 'degrees': [1, 1, 1, 4], 'names': ['z', 'y', 'x', 'w'], 'relations': ['y**2 + y*x + x**2', 'x**3']},
(16,8) : {'gap_number': 13, 'degrees': [1, 1, 1, 4], 'names': ['z', 'y', 'x', 'w'], 'relations': ['y**2 + z*x + x**2', 'z**2*x + z*x**2']},
(16,9) : {'gap_number': 3, 'degrees': [1, 1, 2, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2', 'z*y', 'z*x', 'y**2*w + x**2']},
(16,10) : {'gap_number': 4, 'degrees': [1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2 + y**2', 'z*y']},
(16,11) : {'gap_number': 6, 'degrees': [1, 1, 3, 4], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2', 'z*y**2', 'z*x', 'x**2']},
(16,12) : {'gap_number': 7, 'degrees': [1, 1, 2], 'names': ['z', 'y', 'x'], 'relations': ['z**2 + z*y']},
(16,13) : {'gap_number': 8, 'degrees': [1, 1, 3, 4], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z*y', 'y**3', 'y*x', 'z**2*w + x**2']},
(16,14) : {'gap_number': 9, 'degrees': [1, 1, 4], 'names': ['z', 'y', 'x'], 'relations': ['z*y', 'z**3 + y**3']},
(32,1) : {'gap_number': 51, 'degrees': [1, 1, 1, 1, 1], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': []},
(32,2) : {'gap_number': 45, 'degrees': [1, 1, 1, 1, 2], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2']},
(32,3) : {'gap_number': 21, 'degrees': [1, 1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2', 'y**2']},
(32,4) : {'gap_number': 36, 'degrees': [1, 1, 1, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2']},
(32,5) : {'gap_number': 3, 'degrees': [1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2', 'y**2']},
(32,6) : {'gap_number': 16, 'degrees': [1, 1, 2], 'names': ['z', 'y', 'x'], 'relations': ['z**2']},
(32,7) : {'gap_number': 1, 'degrees': [1, 2], 'names': ['z', 'y'], 'relations': ['z**2']},
(32,8) : {'gap_number': 46, 'degrees': [1, 1, 1, 1, 2], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z*w + w**2']},
(32,9) : {'gap_number': 47, 'degrees': [1, 1, 1, 1, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2 + z*w + w**2', 'w**3']},
(32,10) : {'gap_number': 48, 'degrees': [1, 1, 1, 1, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['x**2 + y*w', 'y**2*w + y*w**2']},
(32,11) : {'gap_number': 22, 'degrees': [1, 1, 1, 2, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2', 'z*x', 'z*v', 'x**2*w + v**2']},
(32,12) : {'gap_number': 23, 'degrees': [1, 1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2 + y**2', 'z*y']},
(32,13) : {'gap_number': 37, 'degrees': [1, 1, 1, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2', 'z*x**2', 'z*w', 'w**2']},
(32,14) : {'gap_number': 25, 'degrees': [1, 1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2', 'y*x']},
(32,15) : {'gap_number': 26, 'degrees': [1, 1, 1, 2, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2', 'y**2 + y*x + x**2', 'x**3']},
(32,16) : {'gap_number': 24, 'degrees': [1, 1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2', 'z*y + x**2', 'y*x**2', 'z*v', 'y**4*w + v**2']},
(32,17) : {'gap_number': 38, 'degrees': [1, 1, 1, 4], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2 + y**2', 'y**2*x + z*x**2']},
(32,18) : {'gap_number': 2, 'degrees': [1, 1, 2, 2, 2, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z**2', 'z*y', 'y**2', 'z*x', 'y*x + z*v', 'y*v', 'x**2', 'x*v', 'v**2']},
(32,19) : {'gap_number': 4, 'degrees': [1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2', 'y**2']},
(32,20) : {'gap_number': 5, 'degrees': [1, 1, 2, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2', 'z*y', 'z*w', 'w**2']},
(32,21) : {'gap_number': 12, 'degrees': [1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2', 'z*y + y**2']},
(32,22) : {'gap_number': 17, 'degrees': [1, 1, 3, 4], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2', 'z*y**2', 'z*x', 'y**6 + x**2']},
(32,23) : {'gap_number': 39, 'degrees': [1, 1, 1, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2 + z*y']},
(32,24) : {'gap_number': 40, 'degrees': [1, 1, 1, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z*y', 'y**3', 'y*w', 'z**2*v + w**2']},
(32,25) : {'gap_number': 41, 'degrees': [1, 1, 1, 4], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z*y + y**2', 'z**3']},
(32,26) : {'gap_number': 42, 'degrees': [1, 1, 1, 4], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z*y', 'z*x**2 + y*x**2']},
(32,27) : {'gap_number': 9, 'degrees': [1, 1, 2, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2', 'z*y', 'z*x', 'y**2*w + x**2']},
(32,28) : {'gap_number': 10, 'degrees': [1, 1, 2, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2', 'z*y', 'y**3', 'z*x', 'y**2*x + y*v', 'y**2*w + x**2', 'z*v + y*v', 'x*v', 'v**2']},
(32,29) : {'gap_number': 14, 'degrees': [1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2', 'z*y + y**2']},
(32,30) : {'gap_number': 13, 'degrees': [1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2 + y**2', 'z*y']},
(32,31) : {'gap_number': 11, 'degrees': [1, 1, 2, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2', 'z*y', 'y**3 + y*x', 'z*w', 'y**2*w + y*v', 'x*w + z*v + y*v', 'w**2', 'w*v', 'v**2']},
(32,32) : {'gap_number': 15, 'degrees': [1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2 + y**2', 'z*y', 'z*x + y*x', 'z*w + y*w', 'x**3 + w**2']},
(32,33) : {'gap_number': 27, 'degrees': [1, 1, 1, 2, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z*x + x**2', 'y*x', 'x*w', 'z*y*w + z**2*v + x**2*v + y**2*u + w**2']},
(32,34) : {'gap_number': 34, 'degrees': [1, 1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z*y + y**2', 'z*x + x**2']},
(32,35) : {'gap_number': 35, 'degrees': [1, 1, 1, 2, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2 + z*y + y**2', 'y*x + x**2', 'y**3']},
(32,36) : {'gap_number': 28, 'degrees': [1, 1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z*y + y**2', 'z*x']},
(32,37) : {'gap_number': 29, 'degrees': [1, 1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2 + z*y + y**2', 'z*x', 'y**3', 'z*v', 'x**2*u + v**2']},
(32,38) : {'gap_number': 30, 'degrees': [1, 1, 1, 2, 3, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z**2 + y*x', 'z*x', 'y**2*x', 'z*v + y*u', 'x*v', 'z*u', 'z*y**3*w + v*u', 'y**4*w + y**3*u + y*x*t + v**2', 'x**2*t + u**2']},
(32,39) : {'gap_number': 31, 'degrees': [1, 1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2 + z*x + y*x + x**2', 'z*y', 'y*x**2 + x**3', 'z*v', 'y**2*u + v**2']},
(32,40) : {'gap_number': 32, 'degrees': [1, 1, 1, 3, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z**2 + z*x + x**2', 'y**2 + z*x + y*x + x**2', 'z*x**2', 'x**3', 'z*w + x*v', 'x*w + z*v + x*v', 'z*x*v', 'z*x*u + z*x*t + x**2*t + v**2', 'x**2*u + z*x*t + w*v', 'w**2 + w*v + v**2']},
(32,41) : {'gap_number': 33, 'degrees': [1, 1, 1, 3, 3, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'], 'relations': ['z*y + z*x + x**2', 'y**2 + z*x + y*x', 'y*x**2', 'z*x**2 + x**3', 'y*w + y*v + x*u', 'x*w + y*v', 'z*v + x*u', 'x*v + y*u + x*u', 'y*x*u', 'z**2*t + z*x*s + x**2*s + v**2 + v*u + u**2', 'z*x*t + y*x*s + w*v + v*u', 'y*x*t + z*x*s + x**2*s + w*v + v**2 + v*u', 'x**2*t + z*x*s + v**2 + v*u', 'z**2*s + y*x*s + w**2 + v*u + u**2']},
(32,42) : {'gap_number': 49, 'degrees': [1, 1, 1, 1, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z*x + z*w + y*w + x*w + w**2', 'z*y*w + y**2*w + y*x*w + y*w**2']},
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(64,135) : {'gap_number': 187, 'degrees': [1, 1, 1, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2 + z*y', 'z*y**2', 'z*w', 'z*y*v + y**2*v + w**2']},
(64,136) : {'gap_number': 188, 'degrees': [1, 1, 1, 4], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z*x + y*x + x**2', 'z**3 + z**2*y + z*y**2 + y**3']},
(64,137) : {'gap_number': 189, 'degrees': [1, 1, 1, 4], 'names': ['z', 'y', 'x', 'w'], 'relations': ['y*x', 'z**2*y + z**2*x']},
(64,138) : {'gap_number': 38, 'degrees': [1, 1, 2, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2 + y**2', 'z*y + y**2', 'z*x + y*x', 'y**2*v + x**2']},
(64,139) : {'gap_number': 39, 'degrees': [1, 1, 2, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2 + y**2', 'z*y + y**2', 'y**3', 'z*x + y*x', 'y**2*x + z*v', 'y**2*w + x**2 + z*v', 'y*v', 'x*v', 'v**2']},
(64,140) : {'gap_number': 47, 'degrees': [1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2', 'z*y + y**2']},
(64,141) : {'gap_number': 48, 'degrees': [1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2 + y**2', 'z*y']},
(64,142) : {'gap_number': 40, 'degrees': [1, 1, 2, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2', 'z*y', 'z*x', 'z*w + y*w', 'y**4 + x**2', 'x*w + y*v', 'z*v + y*v', 'y*w**2 + x*v', 'w**3 + v**2']},
(64,143) : {'gap_number': 49, 'degrees': [1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2', 'z*y + y**2', 'z*x', 'z*w', 'x**3 + w**2']},
(64,144) : {'gap_number': 73, 'degrees': [1, 1, 1, 2, 2, 2, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'], 'relations': ['z*y + y**2', 'z*x', 'y*x', 'y*v + y*u', 'x*v', 'z*u + y*u', 'y**2*w + y**2*u + y**2*s + v*u', 'x**2*t + v*u + u**2', 'z**2*s + y**2*s + v**2 + v*u']},
(64,145) : {'gap_number': 76, 'degrees': [1, 1, 1, 2, 2, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'], 'relations': ['z**2 + z*y + y**2', 'z*x', 'y*x + x**2', 'y**3', 'x*v', 'y**2*w + x**2*w + y**2*v + z*y*u + y**2*u + v**2 + y*t + x*t', 'z*y*v + y**2*v + y*t + x*t', 'z*t', 'z*v**2 + x**2*t + v*t', 'x**2*s + t**2']},
(64,146) : {'gap_number': 75, 'degrees': [1, 1, 1, 2, 2, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z*y + y**2', 'z*x', 'y*x + x**2', 'x*v', 'y**2*w + x**2*w + y**2*v + z**2*t + v**2']},
(64,147) : {'gap_number': 74, 'degrees': [1, 1, 1, 2, 2, 2, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r'], 'relations': ['z*y', 'y**2 + y*x + x**2', 'z*x', 'x**3', 'z*w', 'y*w + x*t', 'x*w + y*t + x*t', 'y*x*v + x**2*u + y*x*t + w*t', 'x**2*v + y*x*u + x**2*u + w*t + t**2 + z*s + x*s', 'x**2*t + x*s', 'w**2 + w*t + t**2 + z*s', 'y*s + x*s', 'x*t**2 + w*s', 'z**2*r + s**2']},
(64,148) : {'gap_number': 80, 'degrees': [1, 1, 1, 2, 2, 2, 3], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z**2 + y*x', 'z*y', 'z*x + y*x + x**2', 'y*x*v + x*t', 'z*t', 'y**4*u + y**2*v**2 + t**2']},
(64,149) : {'gap_number': 79, 'degrees': [1, 1, 1, 2, 2, 3, 3, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r'], 'relations': ['z**2 + y*x + x**2', 'z*y + y**2', 'z*x', 'x**3', 'z*u + x*t + x*s', 'y*u + x*t + z*s + x*s', 'x*u', 'z*t', 'y*t + x*s', 'y*s', 'y**2*r + t**2 + t*s + s**2', 'y*x*r + t*s', 'x**2*r + t**2', 'u**2 + t**2 + t*s', 'u*t', 'u*s + s**2']},
(64,150) : {'gap_number': 77, 'degrees': [1, 1, 1, 2, 2, 2, 3], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z*y + y*x + x**2', 'y**2 + y*x + x**2', 'z*x', 'y*x*u + x*t', 'y*t', 'z**2*u**2 + x**2*u**2 + z**3*t + x*u*t + t**2']},
(64,151) : {'gap_number': 78, 'degrees': [1, 1, 1, 2, 2, 2, 3], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z**2 + y*x', 'z*y + y**2', 'z*x', 'z*t', 'y*t', 'x**4*v + t**2']},
(64,152) : {'gap_number': 81, 'degrees': [1, 1, 1, 2, 2, 3, 3, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r'], 'relations': ['z**2 + y*x + x**2', 'z*y + y**2 + y*x + x**2', 'z*x', 'x**3', 'z*u + y*s', 'y*u + z*s + y*s', 'x*u', 'z*t', 'y*t + x*s', 'x*t + y*s + x*s', 'y**2*r + u*s', 'y*x*r + t*s', 'x**2*r + u*s + t*s + s**2', 'u**2 + u*s + s**2', 'u*t', 't**2 + u*s + t*s + s**2']},
(64,153) : {'gap_number': 82, 'degrees': [1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q', 'p', 'n', 'm', 'k', 'j', 'i', 'h', 'g', 'f', 'e'], 'relations': ['z**2 + y*x', 'z*y + z*x + x**2', 'y**2 + z*x + y*x', 'z*x**2', 'y*x**2', 'x**3', 'z*w + x*v', 'y*w + z*v', 'x*w + y*v + x*v', 'z*x*v + x*u + z*q', 'y*x*v + x*s + z*r + z*q + y*q + z*p', 'x**2*v + x*u + z*r + x*q', 'w**2 + x*s + z*r + z*q + y*q + y*p', 'w*v + x*u + x*s + z*q + y*q + x*q + y*p + x*p', 'v**2 + x*s + y*q + x*q + z*p + y*p + x*p', 'z*u + y*q', 'y*u + z*r', 'z*t + z*r + z*q + y*q + x*p', 'y*t + x*s + y*q', 'x*t + x*s + z*r + x*q + z*p + y*p + x*p', 'z*s + x*q + y*p', 'y*s + x*s + z*r + y*q + x*p', 'y*r + z*q + y*q', 'x*r + y*q', 'z*x*q + y*m + x*m + z*k + y*k + x*k + z*i + y*i', 'y*x*q + x**2*q + z*x*p + z*m + y*m + x*m + z*k + y*k + z*i + x*i', 'x**2*q + z*x*p', 'z*x*p + y*m + x*m + z*k + y*k + x*k + z*i + y*i', 'y*x*p + z*m + x*k + y*i + x*i', 'x**2*p + z*m + y*m + z*k + x*k + y*i', 'w*u + z*m + y*i', 'v*u + z*m + y*m + x*m + y*k + x*i', 'w*t + z*m + x*m + z*k + y*k + x*i', 'v*t + z*m + y*k + x*k + z*i + x*i', 'w*s + z*m + x*m + y*k + x*k + z*i + y*i + x*i', 'v*s + z*m + z*k + x*k + y*i', 'w*r + z*m + y*m + x*k + z*i + y*i', 'v*r + z*m + x*m + z*i + y*i', 'w*q + y*k + x*k + y*i + x*i', 'v*q + x*m + y*k + z*i + y*i', 'w*p + z*k + x*k + x*i', 'v*p + y*m + x*m + x*k + y*i', 'z*x*n + q*p + p**2 + w*i + z*g + x*g + z*f + y*f + x*f + x*e', 'y*x*n + u*p + q*p + w*k + v*i + y*g + x*g + z*f + z*e', 'x**2*n + u*p + q*p + p**2 + w*m + w*i + y*e + x*e', 'x**2*k + y*x*i + x**2*i + q*p + v*m + w*k + w*i + v*i + z*g + x*g + z*f + y*f     + x*f', 'z*x*k + x**2*i + u*p + q*p + w*i + y*g + x*g + z*f', 'y*x*k + z*x*i + u*p + q*p + v*k + x*g + y*f', 'x**2*i + q*p + p**2 + v*m + v*k + w*i + v*i + y*g + z*f + y*f', 'z*x*i + u*p + w*m + v*m + w*k + v*k + w*i + v*i + z*g + x*g + z*f + y*f +     x*f', 'y*x*i + u*p + p**2 + v*k + v*i + z*g + x*g + z*f + y*f + x*f', 'z*x*j + p**2 + v*m + y*g + x*g + z*f + y*f + x*f + y*e + x*e', 'y*x*j + q*p + p**2 + v*k + x*g + y*f + x*f + x*e', 'x**2*j + p**2 + w*m + w*k + w*i + v*i + x*g + z*f + x*f + z*e + y*e + x*e', 'z*x*h + u*p + q*p + p**2 + w*k + y*g + y*f + x*f + x*e', 'y*x*h + u*p + p**2 + w*i + v*i + z*g + x*g + x*f + z*e', 'x**2*h + v*m + v*k + w*i + z*g + y*g + x*g + y*f + x*f + y*e + x*e', 'u**2 + v*m + w*k + z*f + x*f + y*e', 'u*t + q*p + p**2 + v*m + w*k + v*k + w*i + v*i + y*g + x*g + z*f + x*f + y*e     + x*e', 't**2 + u*p + w*m + v*m + w*k + v*k + w*i + v*i + y*g + z*e + x*e', 'u*s + q*p + p**2 + v*m + v*k + z*g + x*g + y*f + x*f + x*e', 't*s + q*p + w*m + w*k + v*i + z*g + y*g + x*g + z*f + y*f + z*e + y*e', 's**2 + u*p + q*p + p**2 + v*m + w*k + v*i + y*f + x*f + z*e + y*e + x*e', 'u*r + u*p + w*k + v*k + v*i + z*f + y*f + z*e + x*e', 't*r + u*p + q*p + p**2 + w*m + v*m + w*k + v*k + z*g + y*g + x*g + z*f + x*f     + x*e', 's*r + p**2 + w*m + v*m + v*i + z*g + y*g + x*g + y*f + x*f + z*e', 'r**2 + v*m + v*k + w*i + v*i + z*g + y*g + z*f + z*e + y*e', 'u*q + p**2 + w*m + v*k + v*i + y*g + z*f + z*e', 't*q + u*p + q*p + p**2 + v*k + w*i + v*i + y*g + z*f + x*f + z*e + y*e + x*e', 's*q + u*p + q*p + p**2 + w*m + v*k + z*g + y*g + x*g + y*e + x*e', 'r*q + v*m + w*k + z*f + x*f + y*e', 'q**2 + u*p + w*i + z*g + y*g + z*f + y*f + x*f + x*e', 't*p + q*p + v*m + z*g + y*g + y*f + x*f', 's*p + p**2 + w*m + w*k + v*k', 'r*p + p**2 + w*m + w*i + z*g + y*g + x*g + x*f', 'z*x*e + x**2*e + r*k + p*k + t*i + s*i + w*g + v*g + w*f + v*f + v*e', 'y*x*e + x**2*e + r*k + p*k + t*i + s*i + w*g + v*g + w*f + v*f + v*e', 'x**2*e + r*k + p*k + u*i + t*i + p*i + v*g + w*f + v*f', 'z*v*n + s*i + r*i + q*i + v*g + w*f + v*f + v*e', 'y*v*n + r*k + u*i + r*i + q*i + w*g + v*g + v*e', 'x*v*n + r*k + t*i + r*i + p*i + v*f', 'z*v*j + r*k + p*k + u*i + q*i + p*i + w*f + v*f', 'y*v*j + u*i + t*i + r*i + w*g + w*e', 'x*v*j + r*k + p*k + q*i + v*g + w*f + v*f + v*e', 'z*v*h + r*k + p*k + s*i + q*i + p*i + v*g + w*f + v*f + w*e', 'y*v*h + t*i + r*i + q*i + v*e', 'x*v*h + u*i + s*i + p*i + w*g + v*g + w*e + v*e', 'u*m + p*k + u*i + t*i + s*i + r*i + q*i + p*i + v*g + w*f + w*e', 't*m + t*i + s*i + r*i + w*g + v*g + w*f + v*f + v*e', 's*m + p*k + u*i + q*i + p*i + w*g + v*g + w*f + w*e + v*e', 'r*m + u*i + t*i + s*i + q*i + p*i + w*g + v*g + w*f + v*f + v*e', 'q*m + r*i + q*i + p*i + w*g + v*f + w*e + v*e', 'p*m + p*k + s*i + r*i + w*g + v*f + w*e + v*e', 'u*k + u*i + t*i + s*i + p*i + w*g + v*g + w*f + v*f + v*e', 't*k + r*k + u*i + t*i + r*i', 's*k + r*k + p*k + u*i + s*i + q*i + p*i', 'q*k + p*k + u*i + t*i + s*i + p*i + v*g + w*f + w*e', 'z*q*n + z*p*i + x*v*g + y*v*f + y*v*e + m*k + k**2 + i**2 + u*g + t*g + q*g +     u*f + s*f + q*f + q*e', 'y*q*n + x*q*n + z*p*n + z*p*i + y*p*i + x*p*i + x*p*h + z*v*g + y*v*g +     y*v*f + y*v*e + x*v*e + m*k + k**2 + k*i + i**2 + u*g + r*g + q*g + q*f +     t*e + s*e + r*e + q*e + p*e', 'x*q*n + x*p*i + x*p*h + y*v*g + x*v*g + z*v*f + x*v*f + z*v*e + m**2 + k*i +     r*g + q*g + t*f + s*f + r*e + q*e + p*e', 'z*p*i + x*v*g + y*v*f + m*k + u*g + t*g + r*g + s*f + q*f', 'z*p*n + y*p*i + x*p*h + z*v*g + z*v*f + y*v*f + k**2 + m*i + k*i + u*g + t*g     + s*g + q*g + p*g + s*f + q*f', 'x*p*i + y*v*g + x*v*g + z*v*f + y*v*f + x*v*f + z*v*e + y*v*e + m**2 + k**2 +     k*i + i**2 + u*g + q*g + t*f + p*f + s*e + r*e + q*e', 'y*p*i + x*p*h + z*v*g + z*v*f + y*v*f + z*v*e + y*v*e + x*v*e + m**2 + m*k +     k*i + s*g + p*g + t*f + r*f + q*f + p*f + s*e + r*e + q*e + p*e', 'y*p*n + x*v*f + x*v*e + i**2 + s*g + q*g + u*f + s*f + q*f + u*e + t*e + s*e', 'x*p*n + y*v*f + x*v*f + z*v*e + y*v*e + x*v*e + m**2 + k**2 + m*i + i**2 + r*g     + q*g + u*f + s*f + r*f + q*f + u*e + t*e + r*e + q*e + p*e', 'x*v*g + z*v*f + z*v*e + y*v*e + m**2 + m*k + m*i + r*g + q*g + p*g + t*f +     r*f + q*f + p*f', 'z*v*g + y*v*e + k*i + i**2 + u*g + s*g + r*g + q*g + p*g + t*f + r*f + p*e', 'y*v*g + x*v*f + z*v*e + m**2 + m*k + k**2 + m*i + k*i + u*g + t*g + r*g + q*g     + s*f + r*f + q*f + p*f + u*e + t*e + r*e + q*e', 'z*v*f + y*v*f + x*v*f + z*v*e + y*v*e + m*k + m*i + u*g + u*f + q*f', 'z*q*j + y*v*f + z*v*e + y*v*e + x*v*e + m*k + k**2 + k*i + i**2 + u*g + s*g +     s*f + q*f + p*f + r*e + q*e', 'y*q*j + x*q*j + z*p*j + x*p*h + x*v*f + z*v*e + x*v*e + m**2 + m*i + i**2 +     t*g + q*g + p*g + u*f + s*f + r*f + t*e + s*e + r*e', 'x*q*j + y*v*f + x*v*f + y*v*e + x*v*e + m**2 + m*k + k*i + i**2 + u*g + t*g +     p*g + u*f + t*f + s*f + r*f + q*f + p*f + u*e + r*e + q*e', 'z*p*j + x*p*h + y*v*f + x*v*f + z*v*e + y*v*e + m*i + u*g + t*g + p*g + t*f     + s*f + p*f + u*e + t*e + r*e + q*e', 'y*p*j + y*v*f + z*v*e + x*v*e + m*k + k**2 + k*i + u*g + q*g + p*g + t*f +     s*f + r*f + q*f + p*f + u*e + t*e + r*e + q*e', 'x*p*j + x*p*h + y*v*f + m*k + t*g + r*g + q*g + p*g + u*f + q*f + u*e + t*e     + r*e + q*e', 'z*q*h + x*v*f + z*v*e + y*v*e + k*i + i**2 + s*g + r*g + q*g + p*g + t*f +     r*f + q*e + p*e', 'y*q*h + x*q*h + z*p*h + x*p*h + z*v*e + y*v*e + x*v*e + m**2 + m*i + k*i +     u*g + p*g + u*f + t*f + r*f + p*f + u*e + s*e', 'x*q*h + x*p*h + z*v*e + x*v*e + m*k + k*i + u*g + s*g + r*g + u*f + q*f +     s*e + p*e', 'z*p*h + x*v*f + m*k + k*i + i**2 + t*g + r*g + p*g + t*f + s*f + r*f + q*f', 'y*p*h + z*v*e + m**2 + k**2 + m*i + k*i + i**2 + p*g + u*f + t*f + s*f + p*f', 'y*n*i + x*n*i + z*k*h + x*k*h + z*i*h + y*i*h + x*p*f + y*q*e + x*q*e +     y*p*e + k*g + i*g + i*e', 'z*n*k + x*n*i + z*i*h + x*i*h + y*p*f + y*q*e + y*p*e + x*p*e + k*g + m*f +     k*f + k*e + i*e', 'y*n*k + x*n*k + z*n*i + z*j*i + z*i*h + z*p*f + y*p*f + x*p*f + z*q*e +     y*q*e + y*p*e + x*p*e + k*g + i*g + k*f + i*f + i*e', 'x*n*i + y*k*h + x*k*h + y*i*h + z*p*f + x*p*f + x*s*e + z*q*e + z*p*e +     y*p*e + k*g + i*g + m*e + k*e + i*e', 'z*n*i + z*k*h + y*k*h + x*k*h + z*i*h + y*i*h + y*p*e + x*p*e + m*g + k*g', 'x*k*j + z*j*i + x*j*i + y*k*h + z*q*e + y*q*e + x*q*e + z*p*e + i*g + i*e', 'z*k*j + z*j*i + y*j*i + x*j*i + z*p*f + x*s*e + z*q*e + y*q*e + x*q*e + k*g     + i*g + i*f', 'y*k*j + z*j*i + y*j*i + y*k*h + x*k*h + z*i*h + y*i*h + x*i*h + x*p*f +     x*s*e + z*q*e + x*q*e + y*p*e + k*g + i*f', 'x*j*i + z*k*h + z*i*h + x*i*h + z*p*f + x*s*e + x*q*e + x*p*e + i*f + m*e +     i*e', 'v*n*i + w*j*i + z*k*g + y*k*g + x*k*g + z*j*g + y*j*g + z*i*g + x*i*g +     z*h*g + y*n*f + x*n*f + y*k*f + y*j*f + y*i*f + z*h*f + y*k*e + x*k*e +     z*i*e + y*i*e + x*i*e + g**2 + g*f + f**2 + g*e + f*e', 'v*j*i + z*k*g + y*k*g + x*k*g + z*j*g + z*i*g + y*i*g + y*h*g + x*h*g +     y*n*f + x*n*f + z*k*f + z*i*f + x*h*f + z*n*e + x*n*e + z*k*e + z*j*e +     y*j*e + z*i*e + y*i*e + x*i*e + g*f + f**2 + g*e + f*e', 'w*j*i + y*k*g + x*j*g + z*h*g + y*h*g + y*n*f + x*n*f + z*k*f + y*j*f +     x*i*f + z*h*f + y*h*f + x*h*f + z*n*e + x*n*e + z*k*e + y*k*e + z*j*e +     y*j*e + x*i*e + z*h*e + g**2 + g*f + f**2 + f*e + e**2', 'z*k*g + y*k*g + x*k*g + y*i*g + x*i*g + y*k*f + z*i*f + y*i*f + x*i*f +     x*h*f + z*n*e + y*n*e + x*n*e + y*k*e + x*k*e + y*j*e + x*j*e + y*i*e +     x*i*e + z*h*e + g*f + e**2', 'z*i*g + y*i*g + x*i*g + x*h*g + y*n*e + x*n*e + z*k*e + x*j*e + z*i*e +     y*i*e + x*i*e + g**2 + g*e + f*e', 'x*k*g + y*i*g + x*i*g + x*h*g + y*n*f + x*n*f + z*k*f + x*j*f + y*h*f +     x*h*f + z*n*e + x*n*e + y*k*e + z*j*e + y*j*e + y*i*e + g**2 + g*f + f**2     + f*e']},
(64,154) : {'gap_number': 226, 'degrees': [1, 1, 1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2 + z*w', 'y*x']},
(64,155) : {'gap_number': 230, 'degrees': [1, 1, 1, 1, 2, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2 + z*w + w**2', 'y*x', 'w**3']},
(64,156) : {'gap_number': 239, 'degrees': [1, 1, 1, 1, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2 + z*y + y**2', 'x**2 + x*w + w**2', 'y**3', 'w**3']},
(64,157) : {'gap_number': 227, 'degrees': [1, 1, 1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z*y + y**2 + z*x', 'y*w', 'z*x**2', 'y*u', 'w**2*t + u**2']},
(64,158) : {'gap_number': 231, 'degrees': [1, 1, 1, 1, 2, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z*y', 'x**2 + z*w + y*w + x*w + w**2', 'z**2*w + y**2*w + w**3']},
(64,159) : {'gap_number': 229, 'degrees': [1, 1, 1, 1, 2, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2 + z*w + x*w + w**2', 'y*x', 'x**2*w + w**3']},
(64,160) : {'gap_number': 228, 'degrees': [1, 1, 1, 1, 2, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2 + y**2 + y*x', 'z*w + w**2', 'y**2*x + y*x**2']},
(64,161) : {'gap_number': 235, 'degrees': [1, 1, 1, 1, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['y**2 + z*w + w**2', 'y*x + x**2 + z*w + w**2', 'z*y*w + y*w**2', 'z**2*w + z*w**2', 'z*w*v + w**2*v', 'z*w*u + w**2*u + z**2*t + v**2']},
(64,162) : {'gap_number': 238, 'degrees': [1, 1, 1, 1, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2 + z*y + y**2', 'x**2 + z*w + x*w + w**2', 'y**3', 'z*y*w + y**2*w + w**3']},
(64,163) : {'gap_number': 232, 'degrees': [1, 1, 1, 1, 3, 4, 4, 4, 4, 6], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q'], 'relations': ['y**2 + z*w + y*w', 'y*x + z*w + w**2', 'z**2*w', 'x*w**2 + w**3', 'y*w**4 + y*w*v + w*s', 'w**5 + z*y*v + y*w*v + y*s', 'z**2*v + z*x*v + y*w*v + w**2*v + x*u + z*s + y*s + w*s', 'z*w*v + y*w*v + w**2*v', 'y*u', 'w*u', 'z*x**2*v + y*w**2*v + x**2*u + z**2*t + x**2*t + w**2*t + z*x*s + y*w*s + w**2*s +     z**2*r + z*w*r + y*w*r + v**2', 'z**2*y*t + z**2*x*t + x**3*t + z*x*w*t + x**2*w*t + y*w**2*t + w**3*t + z*x*w*r +     w**3*r + z*v**2 + y*v**2 + x*v**2 + v*u + v*s + z*q + x*q', 'z*x**2*t + x**3*t + z*x*w*t + x**2*w*t + z*x*w*r + w**3*r + z*v**2 + y*v**2 +     x*v**2 + v*s + x*q', 'y*q', 'w*q', 'x**4*t + w**4*t + z*x*v**2 + x**2*v**2 + y*w*v**2 + x*w*v**2 + w**2*v**2 + z*v*u +     x*v*u + x*v*s + w*v*s + x**2*q + u*s', 'z*v*u + z*x*q + u**2 + u*s', 'y*w**3*s + z*y*v**2 + y*w*v**2 + x*w*v**2 + z*v*s + x*v*s + z*x*q + x**2*q + u**2     + s**2', 'z*y*v*t + y*w*v*t + x*w*v*t + z*x**2*q + x*u**2 + z*u*t + x*u*s + x*t*s +     w*t*s + z*u*r + v*q', 'x**2*u**2 + z**2*u*t + z*x*u*s + z*y*t*s + z*x*t*s + z**2*u*r + z*x*u*r + u*q +     s*q', 'w**3*v*t + z*x*u*t + z**2*t**2 + x**2*t**2 + w**2*t**2 + z*x*t*s + y*w*t*s +     w**2*t*s + z**2*t*r + z*w*t*r + y*w*t*r + v**2*t + u*q', 'x*v*u**2 + u**2*r + q**2']},
(64,164) : {'gap_number': 234, 'degrees': [1, 1, 1, 1, 3, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'], 'relations': ['z**2 + y*x', 'z*x + y*x + z*w + w**2', 'z*y*w + y*x*w + z*w**2 + y*w**2', 'x*w**2 + w**3', 'z*v + x*u', 'y*v + z*u', 'y*x*u + x**2*u', 'y*x**5 + x**2*t + y*x*s + v**2', 'y*x**4*w + z*w**5 + z*w*t + w**2*t + z*y*s + y**2*s + v*u + u**2', 'y*x*t + x**2*t + y**2*s + y*x*s + v**2 + u**2']},
(64,165) : {'gap_number': 240, 'degrees': [1, 1, 1, 1, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z**2 + y**2 + z*w + w**2', 'y*x + x**2 + z*w + w**2', 'z*y*w + y*w**2', 'y**2*w + w**3', 'z*w*v + w**2*v', 'z*y**2*v + y**2*u + y**2*t + z*w*t + w**2*t + v**2']},
(64,166) : {'gap_number': 236, 'degrees': [1, 1, 1, 1, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z**2 + y*x + x**2', 'z*y + z*w + w**2', 'y*x*w + x**2*w + z*w**2', 'z*w**2 + y*w**2 + w**3', 'z*w*v + w**2*v', 'y**2*u + y*x*t + x**2*t + v**2']},
(64,167) : {'gap_number': 233, 'degrees': [1, 1, 1, 1, 4, 4, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'], 'relations': ['z**2 + y*x + x**2', 'y**2 + z*w', 'y*x**2 + z*x*w', 'y*x*w + x**2*w + z*w**2', 'y*v', 'w*v + y*t', 'z*t', 'y*w**3*u + v*t', 'w**4*u + t**2', 'x**4*s + z*x**2*w*s + v**2']},
(64,168) : {'gap_number': 237, 'degrees': [1, 1, 1, 1, 4, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z**2 + y*x + x**2', 'z*y + y*x + x**2 + z*w + w**2', 'z*x**2 + y*x**2 + x**3 + z*x*w + y*x*w + x**2*w + z*w**2 + x*w**2', 'y*w**2 + w**3', 'z*v', 'y**4*v + y**4*u + v**2']},
(64,169) : {'gap_number': 215, 'degrees': [1, 1, 1, 1, 2, 3, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'], 'relations': ['z*y + z*x + y*w', 'y*x', 'z*x*w', 'z*u + w*u + z*t', 'x*u', 'y*t', 'z**2*w**2*v + y*w**2*u + y**2*s + u**2', 'z*w**3*v + y*w**2*u + y**2*s + u**2 + u*t', 'w**4*v + y*w**2*u + x**2*w*t + x*w**2*t + y**2*s + x**2*s + u**2 + t**2']},
(64,170) : {'gap_number': 216, 'degrees': [1, 1, 1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z*x + x**2 + y*w', 'z*w + w**2', 'y**2*w', 'w*u', 'y**4*v + z*y**2*u + z**2*t + w**2*t + u**2']},
(64,171) : {'gap_number': 218, 'degrees': [1, 1, 1, 1, 2, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2 + y*x + x**2 + z*w', 'y*w', 'y**2*x + y*x**2 + x**2*w']},
(64,172) : {'gap_number': 217, 'degrees': [1, 1, 1, 1, 2, 5, 5, 8], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'], 'relations': ['y**2 + z*x + y*w + w**2', 'y*x', 'z**2*x + z*x*w + x*w**2 + w**3', 'z**2*w**3 + z*w**4 + x*w**4 + w**5', 'x*u', 'y*t', 'y*w*u + w**2*u + z**2*t + w**2*t', 'z**8*v + w**8*v + z**4*y*u + z*x*s + y*w*s + w**2*s + u**2', 'z**6*y*w*v + z**6*w**2*v + w**8*v + u*t', 'x**2*s + t**2']},
(64,173) : {'gap_number': 224, 'degrees': [1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 6], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q', 'p', 'n'], 'relations': ['z**2 + z*w + w**2', 'z*x + y*w', 'y**2*w + y*x*w + x*w**2', 'w**3', 'z*v + z*q', 'x*v + y*u', 'w*v + z*t', 'z*u + z*t', 'x*u + y*t', 'w*u + z*t', 'w*t + w*q', 'z*s', 'y*s + z*q', 'x*s + w*q', 'w*s', 'z*w**2*r + y*x*w*p + w*n', 'x*w**2*p + z*n + w*n', 'y**4*t + y**2*x**2*t + v**2 + v*t + t**2 + q**2', 'z*y**3*p + u*s + t*s + s*q', 'y**4*p + v**2', 'y**3*x*p + v*u', 'y**2*x**2*p + v*t', 'y*x**3*p + u*t', 'x**4*p + t**2', 'x*w*n + u*s', 'x**3*w*p + t*s', 'y**2*n + v**2 + v*t + u*s + t*s + v*q + s*q', 'y*x*n + v*u + u*t + u*s + u*q', 'x**2*n + v*t + t**2 + t*s + t*q', 'u**2 + v*t', 'v*s + u*s + t*s + s*q', 's**2', 'y**2*v*t + y**2*t**2 + x**2*t*p + x**2*q*p + x*w*q*p + v*n + s*n + q*n', 'y**2*v*p + x**2*t*p + z*y*q*p + y**2*q*p + x**2*q*p + x*w*q*p + v*n + t*n', 'y**2*u*p + y*x*t*p + y*x*q*p + u*n + s*n', 'y**2*t*p + x**2*t*p + x**2*q*p + x*w*q*p + t*n', 'y*w*q*p + s*n', 'v**2*p + t**2*p + q**2*p + n**2']},
(64,174) : {'gap_number': 225, 'degrees': [1, 1, 1, 1, 4, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z*y + x*w + w**2', 'y**2 + y*x + x**2', 'x**3', 'z*x*w + y*x*w + x**2*w + z*w**2 + y*w**2 + x*w**2', 'y*v', 'z**4*t + v**2']},
(64,175) : {'gap_number': 219, 'degrees': [1, 1, 1, 1, 3, 3, 4, 4, 4, 6], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q'], 'relations': ['z*y + y*w + w**2', 'y*x + z*w + y*w + w**2', 'z*x*w', 'z*w**2 + y*w**2 + w**3', 'y*v + w*v + y*u', 'x*v + z*u', 'z*w*u', 'y*w*u + w**2*u + y*r', 'w*r', 'w**3*u + z**2*t + x**2*t + w**2*t + w**2*s + v**2 + u**2', 'y**2*t + x**2*t + w**2*t + y**2*s + w**2*s + y**2*r + u**2', 'z*x*t + x**2*t + y*w*t + w**2*t + y*w*s + w**2*s + v*u + u**2', 'x**3*w*u + z*v*u + z*u**2 + w*u**2 + u*r + x*q', 'z*v**2 + z*v*u + w*v*u + v*r + z*q', 'y*q', 'w*q', 'z**5*u + z**4*x*u + z**3*x**2*u + z**2*x**3*u + z**4*s + z**3*x*r + z**2*x**2*r +     z*v*r + z*u*r + z**2*q + z*x*q + r**2', 'x**2*w*u**2 + x*w*u*t + w**2*u*t + w**2*u*s + v**2*u + v*u**2 + y*t*r + x*t*r +     y*s*r + u*q', 'z**2*v*t + x**2*u*t + w**2*u*t + w**2*u*s + v**2*u + u**3 + z*t*r + v*q', 'z**3*v*s + z**2*x*u*r + z*x**2*u*r + z**3*x*q + z*x**3*q + z*v*q + z*u*q + r*q', 'z*v*t*r + z*u*t*r + t*r**2 + v**2*q + v*u*q + q**2']},
(64,176) : {'gap_number': 221, 'degrees': [1, 1, 1, 1, 3, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'], 'relations': ['z**2 + z*y + x**2', 'y*x + z*w + w**2', 'z*x*w + x*w**2', 'x**2*w + z*w**2 + y*w**2', 'z*y**2*w + z*w**3 + y*w**3 + w**4 + x*v + z*u', 'z*v + y*v + x*u', 'z*w*u + w**2*u', 'y**3*v + y**2*w*v + x*w**2*v + w**3*v + y*w**2*u + x*w**2*u + w**3*u + y**2*t +     z*y*s + v**2 + u**2', 'z*x**2*u + z*y*t + y**2*t + x**2*s + u**2', 'x**3*u + z*w*t + w**2*t + z*x*s + v*u']},
(64,177) : {'gap_number': 220, 'degrees': [1, 1, 1, 1, 4, 4, 4, 4, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q'], 'relations': ['z**2 + x*w + w**2', 'y*x + z*w', 'z*y*w + z*x*w + z*w**2 + x*w**2 + w**3', 'x**2*w + x*w**2', 'z*v + x*r', 'y*v + w*r', 'w*v + w*t + y*r', 'z*u + w*r', 'y*u + z*t', 'x*u + w*t + y*r', 'w*u + w*t + y*r', 'x*t + w*t + y*r', 'z*r', 'z*x**3*s + v*r', 'x**4*s + x**4*r + v**2', 'y*w**3*s + u*r', 'w**4*s + w**4*r + v*t + r**2', 'z*y**3*q + v*t + u*t + r**2', 'y**4*q + v*t + t**2', 'y**3*w*q + u*r + t*r', 'y**2*w**2*q + r**2', 'v*u + v*t + r**2', 'u**2 + v*t']},
(64,178) : {'gap_number': 223, 'degrees': [1, 1, 1, 1, 4, 4, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'], 'relations': ['y**2 + z*w + y*w', 'z*x + y*x + x**2 + y*w', 'z**2*w', 'z*y*w + y*w**2', 'y*u + z*t', 'w*u', 'y*t', 'z**4*v + z**4*u + z**4*t + z**4*s + u**2', 'z**3*y*v + z**4*t + z**3*y*s + u*t', 'w**4*v + t**2']},
(64,179) : {'gap_number': 222, 'degrees': [1, 1, 1, 1, 4, 4, 5], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z*y + y*x + x**2', 'y**2 + z*x + y*w + w**2', 'z*x**2 + y*x**2 + x**3', 'y*x**2 + z*x*w + x**2*w + z*w**2 + x*w**2 + w**3', 'z*x*u + x*t', 'y*x*u + x**2*u + y*t', 'z**6*v + z**2*u**2 + t**2']},
(64,180) : {'gap_number': 18, 'degrees': [1, 1, 2, 2, 2, 2, 3, 3, 5, 5, 6, 6, 8], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q', 'p', 'n', 'm'], 'relations': ['z**2', 'z*y', 'y**2', 'z*x', 'y*x + z*v', 'y*w + z*u', 'y*v', 'x**2', 'x*w + z*t', 'x*v', 'w*v + z*s', 'v**2', 'x*u + y*t', 'v*u + y*s', 'z*w*u + v*s', 'z*u**2 + v*s', 'x*t + v*s', 'v*t + x*s', 'w**2*u + s**2 + y*q', 'w*u**2 + z*w*s + z*u*s + t**2 + z*q', 'z*u*t + z*u*s + z*q', 'y*u*t + z*u*s + y*q', 'z*r + z*q', 'y*r + z*q', 'u**2*t + w*u*s + y*s**2 + u*r + w*q + u*q', 'z*t*s + y*s**2 + v*q + z*p + y*n', 'y*t*s + y*s**2 + v*q', 'x*r + v*q + y*n', 'v*r + v*q + y*n', 'x*q + v*q + y*n', 'y*p', 'z*n', 'z*w**2*t + u*t**2 + w*s**2 + z*u*q + t*r + t*q + w*n', 'w*t**2 + w*t*s + v*s**2 + z*u*q + y*u*q + s*r + w*p + u*p', 'y*u*q + t*q + s*q + u*p + u*n', 'u*t*s + u*s**2 + s*q + u*p', 'x*p', 'v*p', 'x*n', 'v*n', 'w**2*q + w*u*q + y*u*n + t*p + s*p + t*n + s*n', 't**2*s + s**3 + y*s*q + t*p + s*n', 't*s**2 + s**3 + w*u*q + y*u*n + t*p + t*n + s*n', 'y*s**3 + u*s*r + u*s*q + u**2*n + r*q + q**2', 'u*t*r + u*s*r + w*s*q + v*s*q + u*s*q + w*u*n + u**2*n + q**2', 'u*t*q + w*s*q + v*s*q + r**2 + r*q + q**2', 't**2*r + s**2*r + u*t*p + w*s*p + w*t*n + u*t*n + z*v*m + q*n', 't*s*r + s**2*r + u*t*p + u*t*n + z*v*m + r*p + r*n + q*n', 't**2*q + s**2*q + u*t*p + w*s*p + w*t*n + u*s*n + r*n + q*n', 'u*t*p + w*s*p + w*t*n + u*t*n + q*p + r*n + q*n', 'w*r*q + t**2*p + t*s*p + s**2*p + t**2*n + t*s*n + s**2*n + n**2', 't**2*p + s**2*p + p*n', 'p**2']},
(64,181) : {'gap_number': 19, 'degrees': [1, 1, 2, 2, 2, 2, 3, 3, 5, 5, 6, 6, 8], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q', 'p', 'n', 'm'], 'relations': ['z**2', 'z*y', 'y**2', 'z*x', 'y*x + z*v', 'z*w + y*w + z*v + z*u', 'y*v', 'x**2', 'x*w + z*t', 'x*v', 'w*v + z*s', 'v**2', 'x*u + z*t + y*t', 'v*u + z*s + y*s', 'y*w**2 + y*u**2 + v*s', 'y*w*u', 'z*u**2 + y*u**2 + x*t + v*s', 'v*t + x*s', 'w**3 + u**3 + y*w*s + z*u*s + y*u*s + s**2 + z*r + z*q', 'w**2*u + w*u**2 + u**3 + y*w*s + y*u*s + t**2 + s**2 + z*r', 'y*w*t + z*u*s + z*r', 'z*u*t + z*u*s + z*q', 'y*u*t + z*u*s + z*r + y*r', 'y*q', 'z*s**2 + y*p + y*n', 'w*u*t + u**2*t + w*u*s + u*r + w*q + v*q + u*q', 'z*t**2 + v*q + y*p + z*n', 'z*t*s + v*q + y*n', 'y*t*s + v*r', 'x*r + v*q + y*p + y*n', 'x*q + z*n + y*n', 'z*p + y*p', 'w*u**3 + u*t**2 + u*t*s + y*u*r + t*r + s*r + w*p + v*p + u*p', 'u**4 + u*t*s + v*s**2 + u*s**2 + t*r + s*r + s*q + w*p + v*n + u*n', 'x*t*s + z*u*r + z*u*q + x*n', 'y*w*r + z*u*r + v*n', 'z*u*r + z*u*q + v*p + x*n + v*n', 'w*t*s + w*s**2 + z*u*q + t*r + w*n + v*n + u*n', 't*q + v*p + x*n + v*n + u*n', 'x*p + v*p', 'w*u**2*s + u**3*s + y*u*s**2 + t**2*s + s**3 + y*s*r + w**2*q + w*u*q + u**2*q +     y*w*p + y*w*n + z*u*n + s*p + t*n + s*n', 'u**3*s + y*u*s**2 + t**3 + t**2*s + t*s**2 + s**3 + u**2*r + w**2*q + z*s*q + y*w*p     + z*u*n + t*p + s*p', 't**2*s + t*s**2 + w**2*r + w*u*r + u**2*r + y*s*r + w**2*q + w*u*q + u**2*q +     z*s*q + y*w*p + z*u*n + t*n', 'w*s*q + w*u*p + w*u*n + z*s*n + y*s*n + q**2', 'w**2*s**2 + w*t*r + u*t*r + w*s*r + v*s*r + u*s*q + w**2*p + u**2*p + w*u*n +     u**2*n + z*t*n + y*t*n + z*s*n + r**2 + r*q', 'w*u*s**2 + w*t*r + u*t*r + w*s*r + w**2*p + w*u*n + y*t*n + y*s*n + r*q + q**2', 'u**3*r + y*u*s*r + w*u**2*q + s**2*r + u*t*p + w*s*p + x*t*n + u*t*n + w*s*n +     z*v*m + r*p + q*p', 'w*s**3 + y*u*s*r + u**3*q + t**2*r + t*s*r + u*t*p + u*s*p + u*t*n + v*s*n +     r*p + q*p + r*n', 'w*t*p + v*s*p + x*t*n + w*t*n + w*s*n + v*s*n + z*v*m + q*n', 'w*u**2*q + u**3*q + s**2*q + w*s*p + v*s*p + w*t*n + x*s*n + w*s*n + v*s*n +     z*v*m + q*p + q*n', 'w*q**2 + t**2*p + t**2*n + t*s*n + z*q*n + p**2', 'w**2*s*r + y*s**2*r + u**2*s*q + w*u**2*n + w*r**2 + w*r*q + t*s*p + s**2*p +     y*r*p + t*s*n + z*q*n + p**2 + p*n + n**2', 'y*s**2*r + u**2*s*q + w*u**2*n + w*r**2 + w*r*q + u*r*q + u*q**2 + s**2*p + y*r*p     + t**2*n + t*s*n + y*r*n + z*q*n + n**2']},
(64,182) : {'gap_number': 28, 'degrees': [1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2', 'y**2', 'y*x', 'y*w', 'w**2']},
(64,183) : {'gap_number': 242, 'degrees': [1, 1, 1, 1, 3, 3, 4, 4, 6], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r'], 'relations': ['z*y + z*w + x*w', 'y*x + z*w', 'z*x*w + x**2*w + z*w**2', 'x**2*w + x*w**2', 'z*w*v + x*w*u', 'x*w*v + x*w*u', 'z*w*u', 'y**3*v + z**2*x*v + y*w**2*v + z**3*u + y**2*w*u + y*w**2*u + y**2*t + x**2*t +     z**2*s + y**2*s + x**2*s + w**2*s + u**2', 'z*x**2*v + x**3*v + y**2*w*v + x**3*u + y**2*w*u + y*w**2*u + z**2*t + y**2*t +     w**2*t + x**2*s + w**2*s + v**2 + u**2', 'x*w**2*t + z*w**2*s + x*w**2*s + z*r', 'z*w**2*t + z*w**2*s + x*w**2*s + z*r + x*r', 'y**2*w*t + y*w**2*t + y**2*w*s + w**3*s + w*v*u + z*r + x*r + w*r', 'y**3*t + y*w**2*t + y**3*s + y**2*w*s + z*w**2*s + y*w**2*s + x*w**2*s + w**3*s +     y*v*u + w*v*u + y*r + x*r + w*r', 'z**2*x*v**2 + z**3*v*u + x**2*v*t + y**2*u*t + y*w*u*t + z**2*v*s + x**2*v*s +     y**2*u*s + w**2*u*s + v*u**2 + u*r', 'z**2*x*v*u + y**2*w*v*u + z**3*u**2 + y**2*w*u**2 + y*w**2*u**2 + y**2*v*t + y*w*v*t     + y**2*u*t + x**2*u*t + w**2*u*t + y**2*v*s + w**2*v*s + z**2*u*s + x**2*u*s +     x*w*u*s + w**2*u*s + u**3 + v*r', 'y**2*t*r + y*w*t*r + y**2*s*r + w**2*s*r + v*u*r + r**2']},
(64,184) : {'gap_number': 241, 'degrees': [1, 1, 1, 1, 3, 3, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r'], 'relations': ['z*x + x**2 + y*w', 'y*x + z*w + y*w + w**2', 'z*y*w + y**2*w + y*w**2', 'y**2*w', 'z*v + w*v + x*u', 'y*v + x*t', 'x*v + w*v + x*u + w*t', 'w*u + x*t + w*t', 'z*w*t + y*w*t + w**2*t', 'z*y**2*u + y**3*t + z**2*s + x**2*s + w**2*s + y**2*r + v**2 + u**2', 'y**3*u + z*y**2*t + y**3*t + y**2*s + z*w*s + x*w*s + w**2*s + z**2*r + y**2*r +     x**2*r + z*w*r + y*w*r + x*w*r + v**2 + v*u + v*t + t**2', 'x**3*u + x**2*s + z*w*s + y*w*s + w**2*s + x**2*r + y*w*r + x*w*r + v**2 + v*t', 'x**3*t + x*w**2*t + z*w*s + y*w*s + w**2*s + y*w*r + x*w*r + w**2*r + v*t', 'y*w**2*t + z*w*s + x*w*s + w**2*s + z*w*r + y*w*r + x*w*r + v**2 + v*u + v*t']},
(64,185) : {'gap_number': 243, 'degrees': [1, 1, 1, 1, 4, 4, 4, 4, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q'], 'relations': ['y**2 + y*x + z*w + y*w', 'z*x + y*w + x*w', 'z**2*w + y*w**2 + x*w**2', 'z*y*w + z*w**2 + y*w**2', 'z*v + w*t + x*s', 'y*v + x*t + w*t', 'x*v + x*u + x*t + w*t', 'z*u + z*s + y*s + x*s', 'y*u + y*s', 'w*u + w*t + x*s', 'z*t + z*s', 'y*t + x*t + y*s', 'w*s', 'w**4*t + w**4*q + v**2 + u**2 + t**2', 'z**3*y*s + z**4*r + s**2', 'z**3*y*r + v*s + u*s + t*s', 'y*x**3*r + x**4*r + x**3*w*r + u**2 + v*s + t*s', 'y*x**2*w*r + x**3*w*r + v*s + t*s + s**2', 'y*x**3*q + t**2 + t*s', 'y*x**2*w*q + t*s + s**2', 'x*w**3*q + v*t + t**2 + s**2', 'v*u + u**2 + v*t + t**2 + t*s + s**2', 'u*t + v*s + u*s']},
(64,186) : {'gap_number': 244, 'degrees': [1, 1, 1, 1, 4, 4, 5, 5, 5], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r'], 'relations': ['z**2 + y*x + x**2 + z*w + y*w', 'z*x + y*x + z*w', 'x**3 + z*y*w + y**2*w + y*w**2', 'z*y*w + y*x*w', 'z*w*v + z*s', 'y*w*v + z*y*u + x*w*u + x*t + y*s + z*r + x*r + w*r', 'x*w*v + x*s', 'w**2*v + x*t + w*s', 'x**2*u + y*w*u + x*w*u + x*t + x*r + w*r', 'z*w*u + y*w*u + x*w*u + x*t + w*r', 'z*t', 'y*t', 'z*y**5*v + w*v*s + z*u*s + y*u*s + x*u*s + s**2 + s*r', 'y**6*v + y**5*s + y**2*u**2 + y*x*u**2 + x*w*u**2 + x*u*t + w*u*r + r**2', 'x*w**4*s + x*u*t + t*r', 'w**5*s + t**2', 'x*v*t + w*v*s + s**2', 'w*v*t + x*u*t + t*s + t*r']},
(64,187) : {'gap_number': 245, 'degrees': [1, 1, 1, 1, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 9, 9, 9, 9, 9, 9, 11, 11], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q', 'p', 'o', 'n', 'm', 'l', 'k', 'j', 'i', 'h', 'g', 'f', 'e', 'd', 'c', 'b', 'a'], 'relations': ['z**2 + y*x + x**2 + z*w + w**2', 'y**2 + z*x + z*w + y*w + w**2', 'y**2*x + y*x**2 + y*x*w + x**2*w + w**3', 'x**3 + y**2*w + y*x*w + y*w**2', 'x*w**4 + w**5 + z*v + w*v + y*u + x*u + w*u + x*s', 'x*w**4 + w**5 + x*v + z*u + y*u + x*u + x*t + x*s + w*s', 'x*w**4 + x*v + x*u + w*u + z*t + y*s', 'x*w**4 + w**5 + x*v + x*u + x*t + z*s + x*s', 'y*x**3*w + x*w**4 + w**5 + x*v + w*v + y*u + x*u + w*u + x*t + y*s + x*s', 'y*x**2*w**2 + x*w**4 + w**5 + x*v + y*u + x*u + w*t', 'y*x*w**3 + x*w**4 + w**5 + y*u + x*t + y*s', 'y*w**4 + w**5 + x*u + y*t + x*t + y*s + w*s', 'w**5 + y*v + x*v + w*v + y*u + x*u + y*t + x*t + x*s + w*s', 'x**3*w**2 + x*w**4 + w**5', 'x**2*w**3 + x*w**4', 'w**3*v + z*r + w*q + x*o + x*n + w*n', 'w**3*v + w**3*u + w**3*t + x*r + z*q + w*p + x*o + x*k', 'w**3*u + w**3*t + x*q + z*p + w*p + x*o + x*n + w*n + x*m + x*k', 'w**3*u + w**3*s + x*r + w*r + w*q + x*p + w*p + z*o + w*o + x*n + x*l + w*l', 'w*p + x*o + z*n', 'w**3*v + w**3*u + w**3*t + w**3*s + x*q + w*q + x*p + x*o + x*n + z*m + x*k +     w*k', 'w**3*v + w**3*t + x*q + w*q + x*p + w*o + x*m + z*l + x*l', 'w**3*v + w**3*u + w**3*t + w**3*s + x*r + x*q + w*q + x*p + w*p + x*o + x*n +     w*m + x*l + z*k + x*k + w*k', 'w**3*u + w**3*t + w**3*s + y*r + x*r + w*r + x*q + x*o + w*o + w*n + x*m', 'w**3*v + w**3*u + w**3*s + w*r + y*q + x*q + x*p + w*p + w*o + w*n + x*m + x*l     + w*l', 'w**3*u + w*q + y*p + w*n + w*l + w*k', 'w**3*s + x*r + x*q + x*p + w*p + y*o + w*o + x*n + w*k', 'w**3*v + w**3*u + w**3*s + w*r + x*p + w*p + w*o + y*n + w*m + x*l + w*l', 'x*r + x*q + w*q + x*p + w*p + x*o + w*o + y*m + x*m', 'w**3*t + w*r + w*q + w*p + w*o + w*n + x*m + y*l + x*l + w*k', 'w**3*u + w**3*s + x*r + w*q + w*o + w*n + w*m + y*k + x*k + w*k', 'w**3*v + x**2*w*t + w*r + w*q + w*n + x*m', 'x*w**2*u + w**3*u + w**3*t + x*r + w*n + w*k', 'w**3*u + x*w**2*t + w**3*t + w**3*s + x*r + w*q + x*n + x*m + w*m + x*k + w*k', 'w**3*u + x*w**2*s + w**3*s + w*r + x*q + x*n + w*n + w*k', 'w**2*p + w**2*o + x*w*n + w**2*n + w**2*m + w**2*l + w**2*k + v*u + v*t + u*s', 'w**2*r + w**2*q + w**2*n + x*w*m + u*t + v*s + t*s', 'w**4*v + w**2*r + w**2*p + w**2*n + x*w*l + v*u + v*s', 'w**2*r + w**2*p + w**2*o + w**2*n + w**2*l + x*w*k + w**2*k + t*s', 'w**4*u + w**4*t + v*u + v*s + u*s + t*s', 'w**4*s + v*u + v*t + v*s + u*s', 'v**2', 'u**2', 't**2', 's**2', 'w**3*r + w**3*m', 'z*y*j + t*n + s*n + s*m + s*l + t*k + s*k + x*e + w*d + y*c + x*c', 'z*y*i + t*q + s*p + s*n + s*m + t*l + s*k + y*f', 'z*w*j + w**2*i + s*r + t*q + s*q + s*o + s*n + s*m + t*l + s*k + w*e + w*c', 'z*w*i + t*q + s*q + s*p + t*n + s*n + s*m + s*l + t*k + w*f', 'w**2*i + s*r + s*p + s*o + s*n + z*h + x*h + w*g + y*f + x*e + w*e + w*d +     y*c + x*c + w*c', 's*o + t*k + s*k + z*g + x*g + w*g + x*f + w*f + w*e + x*d + x*c + w*c', 'w**2*i + s*r + s*n + s*l + t*k + s*k + x*h + x*g + z*f + x*f + w*f + x*d +     x*c', 'w**2*i + s*r + t*q + s*o + s*l + t*k + s*k + w*f + z*e + x*e + w*e + w*d +     y*c + x*c + w*c', 'w**2*j + w**2*i + s*r + t*q + s*l + s*k + x*g + w*g + x*f + x*e + z*d + x*d +     w*d', 'w**2*j + w**2*i + s*r + t*q + s*q + s*o + s*n + t*l + s*k + x*g + w*g + x*d +     z*c + y*c + x*c', 'y**2*j + w**2*j + w**2*i + t*q + s*q + s*o + t*n + s*n + s*m + s*l + s*k + x*e     + w*e + w*d + x*c', 'w**2*j + y**2*i + t*q + s*p + s*o + t*l + s*k + w*h + w*g + x*f + w*e', 'y*x*j + w**2*j + s*o + t*n + s*n + s*m + s*l + t*k + w*g + x*e + w*e + w*c', 'w**2*j + y*x*i + s*q + t*k + x*h + x*g + w*g + x*f + x*e + w*e + w*c', 'y*w*j + w**2*j + w**2*i + s*r + s*q + t*n + s*n + t*l + w*e', 'w**2*j + y*w*i + w**2*i + s*r + t*q + s*p + s*o + s*n + s*l + t*k + s*k + w*h     + w*g + w*f + w*e', 'w**2*i + s*q + s*n + s*m + t*l + s*l + s*k + y*h + x*h + x*g + y*f + w*f +     y*c', 's*q + s*p + s*o + t*n + s*n + s*m + s*k + x*h + w*h + y*g + x*g + w*g + x*f     + w*f + x*e + w*d + y*c + x*c', 'w**2*j + w**2*i + s*r + t*q + s*p + s*n + t*l + w*h + w*g + w*f + y*e + x*e +     w*e + w*d + x*c', 'w**2*i + s*r + t*q + s*p + s*o + s*n + t*l + s*l + x*h + x*g + w*g + x*f +     y*d + w*d + y*c + x*c + w*c', 'x**2*j + w**2*j + w**2*i + s*r + s*o + s*n + s*l + x*g + w*e + x*d + w*d + w*c', 'w**2*j + x**2*i + t*q + s*q + t*l + s*l + w*g + x*e + w*e + x*d + x*c + w*c', 'x*w*j + w**2*i + s*r + s*p + s*m + s*l + s*k + w*g + w*d', 'w**2*j + x*w*i + w**2*i + t*q + s*p + s*o + t*n + s*m + s*l + w*e + w*d + w*c', 'w**4*n + s*r + t*q + s*q + t*n + s*n + s*m + t*k + s*k', 'w**4*m + s*r + s*m + t*k', 'w**4*l + s*r + t*q + s*q + s*p + s*n + s*m + t*l + s*l', 'w**4*k + s*m + t*l + t*k', 'v*r + t*q + s*q + s*p + s*o + t*l + t*k', 'v*q + s*q + s*o + t*n + s*n + t*l + s*l + t*k + s*k', 's*r + v*p + s*p + t*n + s*m + t*l + t*k', 's*r + t*q + s*q + v*o + s*o + t*n + s*n + s*m + t*l + s*l + s*k', 's*r + s*q + s*p + v*n + s*m + t*l + t*k + s*k', 's*q + s*o + t*n + v*m + t*l + t*k', 's*r + s*q + s*o + v*l + s*l + t*k + s*k', 't*q + s*p + t*n + s*n + t*l + s*l + v*k + t*k', 'u*r + t*q + s*o + t*n + s*l + t*k', 'u*q + t*q + s*q + s*n + s*m + t*l + s*l + t*k + s*k', 's*r + u*p + s*p + t*n + s*n + s*m + t*l + t*k', 'u*o + t*l + t*k + s*k', 's*r + s*p + s*o + u*n + s*n + s*m + t*l', 't*q + s*o + u*m + s*m + t*k', 's*r + s*q + s*p + s*n + u*l + t*l + s*l + t*k + s*k', 't*q + s*o + s*n + s*m + t*l + u*k + t*k', 't*r + s*r + t*q + s*q + s*p + s*o + s*n + s*m + s*l + s*k', 's*r + t*p + s*o + t*n + s*n', 's*q + t*o + s*n + t*k', 's*p + s*o + s*n + t*m + t*k', 'w**3*h + w**3*f + w**3*e + w**3*d + w**3*c + p*n + o*n + o*m + n*m + p*l + o*l +     m*l + p*k + n*k + m*k + l*k + z*b + w*b', 'w**3*d + w**3*c + o*m + p*l + n*l + n*k + m*k + l*k + w*b + z*a + w*a', 'w**3*g + w**3*d + w**3*c + p*n + o*n + p*m + n*m + m**2 + p*l + o*l + m*l + l**2     + n*k + y*b + w*b + w*a', 'w**3*c + p*n + p*m + o*m + p*l + n*l + l**2 + m*k + y*a', 'x**2*w*f + w**3*c + o*n + o*m + p*l + o*l + l**2 + p*k + l*k + w*b', 'w**3*h + w**3*f + x**2*w*d + w**3*d + p*n + p*m + o*m + n*m + m**2 + n*l + n*k +     w*a', 'x*w**2*h + w**3*h + w**3*f + w**3*e + w**3*d + p*n + o*n + m**2 + o*l + n*l + n*k     + m*k + w*b + w*a', 'x*w**2*g + w**3*d + w**3*c + o*n + p*m + n*m + p*l + n*k + m*k + l*k + k**2 +     w*b + w*a', 'w**3*h + w**3*g + x*w**2*f + w**3*e + w**3*d + w**3*c + p*n + p*m + n*m + p*l +     o*l + l**2 + p*k + l*k + w*b + w*a', 'w**3*g + x*w**2*e + w**3*d + w**3*c + p*n + p*m + o*m + m**2 + o*l + l**2 + p*k +     m*k + l*k + w*b + w*a', 'w**3*e + x*w**2*d + o*l + n*l + l**2 + n*k + k**2 + w*b + w*a', 'w**3*d + x*w**2*c + p*n + o*n + p*m + o*m + n*m + m**2 + n*l + m*l + l**2 + p*k     + n*k + m*k + l*k + k**2', 'w**3*h + w**3*c + o*n + p*m + m**2 + o*l + m*l + k**2 + x*b + w*b', 'w**3*g + w**3*f + p*m + o*m + m**2 + p*l + o*l + p*k + k**2 + x*a', 'w**4*j + w**3*h + w**3*g + w**3*c + p*n + o*n + o*m + m**2 + o*l + p*k + n*k +     l*k + k**2 + w*b + w*a', 'w**4*i + w**3*e + p*n + p*m + o*m + n*m + n*l + p*k + l*k + w*b', 'w**2*s*r + p*n + p*m + o*m + n*m + m**2 + p*l + n*l + l**2', 'w**2*s*q + p*n + p*m + o*m + m**2 + p*l + o*l + n*k + m*k', 'w**2*s*p + p*n + o*m + m**2 + o*l + n*l + m*l + l**2 + n*k + m*k + l*k + k**2', 'w**2*s*o + p*n + o*m + n*m + m**2 + p*l + o*l + n*l + p*k + n*k + l*k', 'w**2*s*n + o*n + o*m + n*m + m**2 + o*l + l**2 + n*k + l*k + k**2', 'w**2*s*m + p*m + o*m + p*l + n*l + l**2 + n*k + m*k + l*k', 'w**2*s*l + o*m + p*l + o*l + n*l + l**2 + p*k + m*k + l*k + k**2', 'w**2*s*k + p*m + o*m + n*m + m**2 + p*l + p*k + n*k + k**2', 'r**2 + n*m + n*l + l**2 + n*k + l*k', 'r*q + m**2 + p*l + o*l + n*l + m*l + p*k + m*k + l*k + k**2', 'r*p + p*n + p*m + p*l + m*l + m*k + l*k', 'r*o + p*n + o*m + n*m + m**2 + n*l + l**2 + n*k + l*k + k**2', 'r*n + p*n + o*n + p*m + o*m + n*m + l**2 + n*k + l*k + k**2', 'o*n + r*m + p*m + n*m + p*l + n*l + l**2', 'p*n + o*n + p*m + o*m + m**2 + r*l + o*l + l**2 + l*k + k**2', 'p*n + p*m + p*l + l**2 + r*k + p*k + n*k + m*k + k**2', 'q**2 + k**2', 'q*p + o*n + p*m + o*m + n*m + o*l + n*l + m*k + l*k + k**2', 'q*o + o*n + p*m + o*m + m**2 + p*l + o*l + l**2 + p*k + m*k + l*k + k**2', 'q*n + p*n + m**2 + p*l + o*l + m*l + l**2 + p*k + n*k + m*k + k**2', 'p*n + q*m + m**2 + p*l + o*l + n*l + p*k + n*k + m*k + k**2', 'o*n + p*m + m**2 + q*l + p*l + l**2 + m*k + l*k', 'p*n + p*m + o*m + n*m + p*l + o*l + m*l + l**2 + q*k + p*k + m*k + k**2', 'p**2 + n*m + m**2 + n*l + n*k + l*k', 'p*o + p*n + o*n + p*m + o*m + n*m + p*l + m*l + p*k + k**2', 'o**2 + l**2', 'm**2 + m*l + o*k + m*k + k**2', 'n**2 + m**2 + k**2', 'w*l**2 + w*m*k + w*l*k + x*u*j + v*h + t*h + v*g + u*g + t*g + v*f + t*f +     t*e + s*e + v*d + t*d', 'w*m**2 + w*l**2 + w*m*k + x*u*i + v*h + s*h + v*g + t*f + v*e + u*e + t*e +     s*e + v*d + s*d + v*c + u*c + s*c', 'w*m**2 + w*m*l + w*l**2 + w*l*k + w*k**2 + x*t*j + v*h + u*h + t*h + u*g + s*g     + t*f + t*e + s*e + t*d + s*d + u*c + t*c + s*c', 'w*m**2 + w*l**2 + w*l*k + w*k**2 + x*t*i + v*h + t*h + v*g + s*g + v*f + u*f +     t*f + s*f + v*e + t*e + s*e + v*d + u*d + t*d + v*c + t*c', 'w*m**2 + w*l**2 + x*s*j + v*h + u*h + u*g + t*g + s*g + v*f + t*f + v*e + u*c', 'w*m**2 + w*l**2 + w*m*k + w*k**2 + x*s*i + t*h + v*g + u*g + t*g + v*f + u*f +     s*f + u*e + t*d', 'w**4*g + w*m**2 + w*k**2 + s*h + t*g + s*g + v*f + u*f + s*f + s*e + v*d + t*d     + s*d + v*c + t*c + s*c', 'w**4*f + w*m*l + w*l**2 + v*h + t*h + s*h + v*g + u*g + t*g + v*f + t*f + s*f     + u*d + s*d + v*c + t*c', 'w**4*e + w*m*k + w*l*k + w*k**2 + u*h + t*h + v*g + u*g + t*g + v*f + u*f +     t*f + v*e + t*e + s*e + v*d + s*c', 'w**4*c + w*m*l + w*k**2 + v*h + u*h + t*h + s*h + u*g + t*g + s*g + v*f + u*f     + t*f + t*e + s*e + u*d + t*d + v*c + u*c + t*c', 'w*m*l + w*l**2 + w*m*k + w**2*b + v*h + t*h + s*h + v*g + s*g + v*f + t*f +     s*f + v*e + t*e + s*e + v*d + u*d + t*d + s*d + t*c', 'w*m**2 + w*l**2 + w*m*k + w*k**2 + w**2*a + u*h + s*h + v*g + u*g + u*f + s*f +     u*e + s*e + u*d + t*d + v*c + s*c', 'w*l**2 + w*k**2 + w*v*j + v*h + u*h + s*h + v*g + u*g + t*g + s*g + v*f + t*f     + v*e + u*e + t*e + s*e + u*d + s*d + v*c + t*c + s*c', 'w*m**2 + w*m*l + w*m*k + w*v*i + u*h + v*g + t*g + u*f + t*f + v*e + u*e +     t*e + v*d + u*d + s*d', 'w*m**2 + w*m*l + w*l**2 + w*k**2 + w*u*j + u*h + t*h + s*h + u*f + s*f + v*e +     u*e + t*e + t*d + u*c + s*c', 'w*m*l + w*k**2 + w*u*i + v*h + u*h + t*h + s*h + t*g + v*f + u*f + t*f + t*e     + t*d + s*d + s*c', 'w*m*l + w*l**2 + w*l*k + w*k**2 + w*t*j + u*h + v*g + s*f + s*e + s*d + v*c +     u*c + t*c + s*c', 'w*m**2 + w*m*l + w*l**2 + w*m*k + w*l*k + w*k**2 + w*t*i + v*h + u*h + t*h +     s*h + v*g + t*g + s*g + u*f + t*f + s*f + v*e + u*e + t*e + s*e + s*d +     v*c + t*c', 'w*l**2 + w*m*k + w*l*k + w*s*j + v*h + u*h + t*h + v*g + u*f + t*f + s*f +     v*e + u*e + s*e + t*d + u*c + s*c', 'w*m**2 + w*m*k + w*l*k + w*k**2 + w*s*i + v*h + u*h + s*h + v*g + t*g + v*f +     u*f + t*f + s*f + u*e + s*d + v*c + s*c', 'w*o*n + w*m**2 + w*m*l + w*l**2 + s*h + v*g + t*g + v*f + s*f + u*e + t*e +     s*e + v*d + u*d + v*c + u*c + s*c', 'w*o*m + w*m*l + w*l*k + w*k**2 + u*h + s*h + v*g + u*g + t*g + v*f + v*e +     t*e + s*d + s*c', 'w*n*m + w*l**2 + w*k**2 + v*h + u*h + u*g + s*g + t*f + v*e + u*d + t*d + v*c', 'w*n*l + w*l*k + w*k**2 + u*h + s*h + v*g + u*f + s*e + v*d + u*d + s*d + s*c', 'x*p*j + p*h + n*h + k*h + p*g + o*g + n*g + l*g + k*g + p*f + l*f + k*f +     q*e + l*e + n*d + m*d + l*d + k*d + p*c + o*c + l*c + k*c', 'x*p*i + n*h + m*h + k*h + o*g + m*g + l*g + p*f + m*f + l*f + k*f + q*e +     o*e + n*e + m*e + q*d + n*d + m*d + l*d + p*c + o*c + k*c', 'x*o*j + o*h + k*h + p*g + l*g + p*f + n*f + m*e + k*e + l*d + k*d + n*c +     k*c', 'x*o*i + n*h + l*h + k*h + p*g + n*g + k*g + p*f + n*f + k*f + m*e + r*d +     p*d + k*d + p*c + o*c + n*c + l*c + k*c', 'x*m*j + p*h + n*h + k*h + o*g + n*g + m*g + n*f + q*e + o*e + m*e + k*e +     r*d + p*d + o*d + n*d + k*d + p*c + m*c', 'x*m*i + p*h + o*h + k*h + o*g + l*g + k*f + q*e + o*e + n*e + m*e + l*e +     q*d + p*d + o*d + k*d + p*c + o*c + n*c + m*c + l*c', 'x*l*j + p*h + o*h + m*h + p*g + p*f + n*f + m*f + m*e + r*d + p*d + o*d +     m*d + l*d + q*c + p*c + k*c', 'x*l*i + p*h + o*h + n*h + l*h + n*g + m*g + l*g + k*g + p*f + l*f + o*e +     m*e + l*e + k*e + m*d + o*c + m*c + l*c', 'x*k*j + p*h + n*h + m*h + k*h + p*g + o*g + n*g + m*g + k*g + o*f + m*f +     l*f + k*f + p*e + n*e + l*e + k*e + r*d + n*d + l*d + q*c + p*c + n*c +     k*c', 'x*k*i + p*h + o*h + l*h + p*g + o*g + n*g + m*g + p*f + n*f + m*f + k*f +     q*e + p*e + l*e + k*e + q*d + p*d + o*d + l*d + k*d + p*c + n*c + m*c +     l*c + k*c', 'w**2*u*e + p*h + o*h + n*h + o*g + n*g + k*g + n*f + k*f + o*e + l*e + k*e +     r*d + p*d + n*d + l*d + k*d + o*c + l*c', 'w**2*u*d + p*h + o*h + n*h + l*h + k*h + o*g + p*f + l*f + p*e + o*e + m*e +     k*e + r*d + p*d + l*d + k*d + n*c + m*c', 'w**2*t*h + o*h + n*h + l*h + k*h + o*g + l*g + p*f + m*f + k*f + n*e + m*e +     k*e + q*d + p*d + o*d + n*d + k*d + p*c + n*c + m*c + l*c + k*c', 'w**2*t*g + p*h + o*h + n*h + k*h + o*g + m*g + k*g + p*f + o*f + n*f + m*f +     l*f + q*e + r*d + q*d + n*d + l*d + k*d + q*c + o*c + m*c', 'w**2*t*f + n*h + m*h + k*h + o*g + k*g + l*f + k*f + q*e + p*e + o*e + l*e +     k*e + k*d + n*c + m*c', 'w**2*t*e + p*h + o*h + n*h + l*h + m*g + k*g + o*f + m*f + o*e + l*e + k*e +     r*d + p*d + k*d + l*c', 'w**2*t*d + p*h + o*h + n*h + p*g + n*g + m*g + l*g + p*f + o*f + m*f + l*f +     p*e + n*e + m*e + l*e + r*d + o*d + m*d + l*d + o*c + n*c + m*c + l*c', 'w**2*t*c + o*h + n*h + m*h + l*h + o*g + n*g + l*g + o*f + n*f + l*f + k*f +     p*e + n*e + l*e + q*d + p*d + o*d + n*d + m*d + l*d + k*d + k*c', 'w**2*s*h + o*h + n*h + m*h + l*h + o*g + l*g + p*f + m*f + l*f + p*e + o*e +     n*e + k*e + q*d + o*d + m*d + l*d + k*d + p*c + o*c + m*c + l*c + k*c', 'w**2*s*g + o*h + m*h + l*h + n*g + m*g + l*g + p*f + l*f + k*f + o*e + m*e +     l*e + r*d + p*d + o*d + n*d + l*d + k*d + p*c + o*c + n*c + l*c', 'w**2*s*f + p*h + n*h + m*h + o*g + n*g + l*g + k*g + m*f + k*f + q*e + o*e +     m*e + l*e + k*e + r*d + o*d + n*d + m*d + l*d + k*d + p*c + o*c + n*c +     l*c', 'w**2*s*e + o*h + m*h + l*h + o*g + n*g + o*f + n*f + n*e + l*e + r*d + o*d +     l*d + q*c + p*c + n*c + k*c', 'w**2*s*d + o*h + n*h + l*h + k*h + p*g + o*g + n*g + l*g + k*g + p*f + m*f +     l*f + o*e + n*e + m*e + r*d + n*d + m*d + p*c + o*c + n*c + m*c + l*c +     k*c', 'w**2*s*c + p*h + n*h + l*h + m*g + l*g + p*f + o*f + q*e + p*e + n*e + m*e +     l*e + k*e + r*d + o*d + k*d + o*c', 'w*r*j + n*h + m*h + k*h + m*g + l*g + p*f + o*f + m*f + l*f + o*e + n*e +     m*e + l*e + q*d + p*d + n*d + l*d + q*c + p*c + o*c + m*c + k*c', 'w*r*i + p*h + o*h + m*h + k*h + o*g + k*g + p*f + o*f + q*e + o*e + n*e +     m*e + l*e + q*d + p*d + o*d + l*d + k*d + q*c + o*c', 'w*q*j + o*h + m*h + l*h + p*g + l*g + p*f + n*f + m*f + p*e + n*e + l*e +     k*e + r*d + q*d + p*d + n*d + m*d + l*d + p*c + o*c + n*c + k*c', 'w*q*i + p*h + n*h + p*g + o*g + n*g + m*g + l*g + o*f + n*f + m*f + p*e +     o*e + r*d + p*d + o*d + n*d + l*d + o*c + m*c + k*c', 'w*p*j + p*h + m*h + n*g + k*g + p*f + n*f + m*f + q*e + p*e + o*e + n*e +     m*e + l*e + m*d + k*d + p*c + n*c + l*c', 'w*p*i + n*h + k*h + n*g + m*g + l*g + n*f + m*f + l*f + k*f + q*e + o*e +     n*e + m*e + k*e + q*d + p*d + o*d + l*d + k*d + q*c + p*c + m*c', 'w*o*j + n*h + m*h + k*h + p*g + n*g + m*g + l*g + n*f + k*f + q*e + p*e +     o*e + n*e + m*e + k*e + m*d + q*c + o*c + m*c + l*c', 'w*o*i + m*h + l*h + o*g + n*g + k*g + o*f + n*f + l*f + k*f + q*e + p*e +     o*e + n*e + m*e + k*e + r*d + o*d + m*d + q*c + m*c + l*c + k*c', 'w*n*j + p*h + n*h + k*h + p*g + o*g + n*g + l*g + k*g + o*f + m*f + k*f +     m*e + q*d + p*d + n*d + m*d + l*d + q*c + p*c + l*c', 'w*n*i + p*h + o*h + n*h + m*h + k*h + m*g + l*g + k*g + k*f + p*e + m*e +     o*d + m*d + l*d + n*c + m*c + k*c', 'w*m*j + p*h + p*g + m*g + l*g + k*g + p*f + n*f + l*f + p*e + o*e + n*e +     r*d + p*d + o*d + q*c + o*c + n*c + m*c', 'w*m*i + o*h + m*h + p*g + n*g + m*g + k*g + p*f + o*f + n*f + m*f + p*e +     o*e + n*e + m*e + r*d + p*d + m*d + q*c + m*c', 'w*l*j + p*h + o*h + n*h + l*h + k*h + p*g + o*g + o*f + m*f + l*f + k*f +     q*e + p*e + n*e + m*e + l*e + k*e + r*d + q*d + p*d + o*d + n*d + m*d +     l*d + k*d + p*c + o*c + n*c + l*c + k*c', 'w*l*i + p*h + l*h + o*g + n*g + m*g + l*g + n*f + m*f + k*f + q*e + p*e +     o*e + q*d + o*d + n*d + l*d + k*d + p*c + n*c + m*c + k*c', 'w*k*j + p*h + o*h + n*h + l*h + k*h + o*g + n*g + m*g + l*g + p*f + o*f +     n*f + l*f + k*f + q*e + m*e + r*d + q*d + p*d + n*d + p*c + o*c + n*c', 'w*k*i + o*h + n*h + m*h + l*h + k*h + o*g + n*g + l*g + o*f + n*f + m*f +     l*f + k*f + o*e + l*e + p*d + o*d + k*d + q*c + o*c + l*c', 'p*h + o*h + k*h + l*g + k*g + m*f + l*f + q*e + p*e + o*e + n*e + l*e + r*d     + q*d + n*d + m*d + q*c + k*c + v*b', 'o*h + l*h + p*g + n*g + o*f + n*f + l*f + q*e + o*e + l*e + n*d + m*d + p*c     + m*c + l*c + v*a', 'k*h + p*g + o*g + m*g + n*f + m*f + l*f + k*f + o*e + n*e + m*e + p*d + o*d     + m*d + l*d + n*c + m*c + l*c + u*b', 'p*h + n*h + l*h + k*h + o*g + n*g + l*g + p*f + o*f + l*f + q*e + o*e + m*e     + l*e + r*d + o*d + n*d + m*d + k*d + q*c + p*c + o*c + l*c + u*a', 'm*h + k*h + n*g + m*f + m*e + r*d + q*d + n*d + m*d + l*d + k*d + q*c + o*c     + m*c + l*c + k*c + t*b', 'p*h + l*h + k*h + p*g + n*f + l*f + k*f + p*e + m*e + k*e + q*d + n*d + m*d     + k*d + p*c + k*c + t*a', 'o*h + k*h + o*g + k*g + o*f + m*f + k*f + p*e + q*d + o*d + k*d + p*c + o*c     + k*c + s*b', 'n*h + l*h + p*g + n*g + l*g + o*f + p*e + n*e + r*d + o*d + n*d + m*d + k*d     + n*c + l*c + s*a', 'r*h + p*h + o*h + m*h + l*h + k*h + p*g + n*g + l*g + p*f + k*f + q*e + n*e     + m*e + q*d + p*d + o*d + l*d + o*c + n*c + k*c', 'p*h + o*h + m*h + r*g + p*g + o*g + n*g + m*g + n*f + m*f + l*f + k*f + q*e     + n*e + m*e + k*e + r*d + q*d + p*d + n*d + m*d + l*d + q*c + p*c + o*c     + l*c + k*c', 'p*h + o*h + m*h + k*h + p*g + n*g + k*g + r*f + n*f + o*e + n*e + r*d + p*d     + o*d + n*d + k*d + q*c + p*c + o*c + l*c', 'p*h + o*h + l*h + k*h + m*g + l*g + m*f + k*f + r*e + q*e + p*e + n*e + r*d     + p*d + o*d + m*d + l*d + q*c + o*c + n*c', 'p*h + o*h + l*h + k*h + p*g + o*g + n*g + m*g + l*g + n*f + k*f + p*e + o*e     + k*e + p*d + n*d + m*d + l*d + k*d + r*c + p*c + n*c + l*c + k*c', 'q*h + p*h + n*h + k*h + m*g + l*g + o*f + n*f + q*e + p*e + l*e + k*e + q*d     + p*d + o*d + n*d + m*d + l*d + k*d + q*c + p*c + o*c', 'm*h + k*h + q*g + p*g + n*g + l*g + p*f + k*f + p*e + m*e + l*e + q*d + p*d     + o*d + n*d + m*d + l*d + k*d + q*c + o*c + n*c + m*c', 'o*h + m*h + l*h + p*g + k*g + q*f + p*f + o*f + n*f + k*f + q*e + o*e + m*e     + l*e + k*e + o*d + n*d + m*d + q*c + k*c', 'w**2*m*h + o*b + m*b + k*b + q*a + l*a + k*a', 'w**2*m*d + o*b + n*b + m*b + l*b + k*b + p*a + o*a + m*a + l*a', 'w**2*m*c + k*b + p*a + n*a + m*a', 'w**2*l*h + q*b + p*b + k*b + q*a + n*a + m*a', 'w**2*l*g + q*b + m*b + l*b + k*b + q*a + p*a + n*a + m*a + l*a', 'w**2*l*f + q*b + o*b + n*b + l*b + p*a + o*a', 'w**2*l*e + q*b + p*b + o*b + n*b + m*b + p*a + m*a', 'w**2*l*d + q*b + p*b + o*b + m*b + l*b + k*b + k*a', 'w**2*l*c + o*b + n*b + m*b + l*b + q*a + p*a + o*a + k*a', 'w**2*k*g + q*b + p*b + o*b + m*b + l*b + k*b + n*a + k*a', 'w**2*k*f + p*b + m*b + l*b + q*a + o*a + m*a + l*a + k*a', 'w**2*k*e + o*b + m*b + k*b + p*a + n*a + m*a + l*a + k*a', 'w**2*k*d + q*b + p*b + o*b + o*a + l*a + k*a', 'w**2*k*c + q*b + n*b + m*b + q*a + o*a + n*a + k*a', 'r*b + q*b + p*b + n*b + l*b + o*a', 'q*b + r*a + p*a + o*a + m*a + l*a', 'm**2*l + m**2*k + m*l*k + l*k**2 + k**3 + s*r*j + s*o*j + s*m*j + s*k*j + s*r*i     + s*p*i + s*m*i + s*k*i + w*i*f + y*j*c + h*g + g**2 + g*f + h*e + g*e +     h*d + f*d + e*d + d**2 + g*c + f*c + e*c + c**2', 'm**2*l + m**2*k + n*l*k + m*l*k + m*k**2 + l*k**2 + s*p*j + s*o*j + s*n*j +     s*m*j + s*l*j + s*k*j + s*q*i + s*p*i + s*o*i + s*l*i + y*i*f + w*i*f +     w*i*e + w*i*c + h*g + h*f + g*f + f**2 + h*e + f*e + e**2 + h*d + g*d +     e*d + d**2 + h*c + f*c', 'm**2*l + m**2*k + m*l*k + l*k**2 + k**3 + s*r*j + s*p*j + s*o*j + s*n*j + s*l*j     + s*r*i + s*p*i + s*m*i + s*k*i + w*i*f + y*i*c + h*g + g**2 + g*f + h*e     + g*e + h*d + f*d + e*d + d**2 + h*c + e*c + c**2', 'm**3 + m**2*l + n*l*k + m*k**2 + l*k**2 + k**3 + s*q*j + s*p*j + s*n*j + s*k*j +     s*r*i + s*o*i + s*k*i + x*j*g + w*i*c + h**2 + h*g + f**2 + e**2 + h*d +     f*d + e*d + d**2 + h*c + g*c + c**2', 'm**3 + m**2*l + m**2*k + s*n*j + s*m*j + s*l*j + s*q*i + s*p*i + s*m*i + x*j*d     + h**2 + g*f + h*e + g*e + e**2 + h*d + g*d + f*d + g*c + e*c + d*c', 'm**2*k + n*l*k + m*k**2 + s*r*j + s*q*j + s*o*j + s*m*j + x*j*c + w*i*c + g*c     + d*c', 'n*l*k + l*k**2 + s*q*j + s*p*j + s*n*j + s*m*j + s*q*i + s*n*i + s*l*i +     x*i*h + w*i*e + h**2 + g**2 + g*f + h*e + f*d + g*c + f*c + c**2', 'n*l*k + m*l*k + s*r*j + s*o*j + s*l*j + s*k*j + s*r*i + s*q*i + s*o*i +     s*n*i + s*l*i + s*k*i + x*i*g + w*i*f + w*i*e + w*i*c + h**2 + g**2 + f**2     + h*e + g*e + f*e + f*d + e*d + d**2 + e*c + c**2', 'm**3 + m**2*l + m**2*k + n*l*k + m*l*k + l*k**2 + k**3 + s*p*j + s*o*j + s*n*j +     s*m*j + s*l*j + s*k*j + s*q*i + s*p*i + s*m*i + x*i*f + w*i*f + w*i*e +     w*i*c + h*g + h*e + f*e + e**2 + h*d + g*d + f*d + e*d + d**2 + h*c', 'm**2*l + n*l*k + m*l*k + m*k**2 + k**3 + s*p*j + s*m*j + s*l*j + s*o*i + s*l*i     + w*i*f + x*i*e + w*i*e + w*i*c + h**2 + h*g + g*f + g*e + f*e + g*d +     f*d + e*d + e*c + c**2', 'm**2*l + l*k**2 + s*m*j + s*r*i + s*q*i + s*o*i + s*l*i + w*i*e + x*i*d + h*g     + g**2 + h*e + h*d + f*c + d*c', 'm**2*l + m*l*k + l*k**2 + s*q*j + s*o*j + s*n*j + s*r*i + s*p*i + s*m*i +     s*k*i + w*i*f + x*i*c + h*g + g**2 + g*f + h*e + g*e + h*d + f*d + e*d +     d**2 + g*c + f*c + e*c + d*c', 'm*l*k + m*k**2 + k**3 + s*r*j + s*q*j + s*o*j + s*m*j + s*r*i + s*q*i + s*m*i     + s*k*i + w*j*h + w*i*f + w*i*c + h**2 + g*f + f**2 + h*e + e**2 + e*d +     d**2 + f*c + c**2', 'm**2*l + m*l*k + l*k**2 + s*p*j + s*o*j + s*n*j + s*m*j + s*l*i + s*k*i +     w*j*g + w*i*f + w*i*e + h*g + h*e + f*e + e**2 + h*d + h*c + e*c', 'n*l*k + m*l*k + m*k**2 + k**3 + s*p*j + s*o*j + s*n*j + s*m*j + s*l*j + s*k*j     + s*q*i + s*p*i + s*o*i + s*n*i + s*l*i + w*j*f + w*i*e + w*i*c + h*g +     h*e + e**2 + h*d + g*d + e*d + d**2 + h*c + f*c', 'm**3 + m**2*l + m**2*k + s*r*j + s*p*j + s*o*j + s*k*j + s*q*i + s*p*i + s*n*i     + s*m*i + s*k*i + w*i*f + w*j*e + w*i*c + h**2 + h*g + g*f + g*e + f*e +     e**2 + g*d + f*d + c**2', 'm**3 + m**2*l + m*l*k + k**3 + s*q*j + s*o*j + s*n*j + s*m*j + s*k*j + s*p*i +     s*m*i + s*l*i + s*k*i + w*i*e + w*j*d + h**2 + h*g + g**2 + g*f + g*e +     e**2 + f*d + e*d + g*c + f*c + e*c + d*c', 'm**2*l + m*l*k + l*k**2 + s*r*j + s*q*j + s*o*j + s*k*j + s*r*i + s*p*i +     s*m*i + s*k*i + w*i*f + w*j*c + w*i*c + h*g + g**2 + g*f + h*e + g*e +     h*d + f*d + e*d + d**2 + g*c + f*c + c**2', 'm**3 + m**2*k + m*l*k + m*k**2 + l*k**2 + s*q*j + s*m*j + s*k*j + s*q*i + s*p*i     + s*o*i + s*l*i + w*i*h + w*i*f + w*i*e + w*i*c + g**2 + f**2 + h*e + e**2     + h*d + f*d + e*d + d**2 + h*c + g*c', 'm**2*k + m*l*k + m*k**2 + s*r*j + s*p*j + s*o*j + s*n*j + s*l*j + s*r*i +     s*q*i + s*o*i + s*l*i + s*k*i + w*i*g + w*i*c + h**2 + h*g + g**2 + f**2 +     e**2 + h*d + g*d + f*d + e*d + d**2 + h*c + g*c + c**2', 'm**2*l + m**2*k + m*l*k + k**3 + s*p*j + s*o*j + s*n*j + s*r*i + s*k*i + w*i*d     + h**2 + g*f + h*e + g*e + e**2 + h*d + f*d + d**2 + g*c + e*c + d*c', 'w**2*f*d + o*n*j + n*m*j + m**2*j + n*l*j + m*l*j + l**2*j + n*k*j + m*k*j +     l*k*j + n*m*i + p*l*i + o*l*i + n*l*i + m*l*i + l**2*i + p*k*i + n*k*i +     l*k*i + k**2*i + h*b + e*b + d*b + e*a + d*a', 'w**2*f*c + o*n*j + o*m*j + n*m*j + m**2*j + n*l*j + m*l*j + p*k*j + m*k*j +     l*k*j + k**2*j + o*n*i + p*l*i + o*l*i + m*l*i + l**2*i + n*k*i + m*k*i +     k**2*i + g*b + e*b + f*a', 'w**2*d**2 + o*n*j + n*m*j + n*l*j + p*k*j + k**2*j + o*n*i + o*m*i + p*l*i +     o*l*i + l**2*i + n*k*i + m*k*i + l*k*i + k**2*i + h*b + c*b + g*a', 'w**2*c**2 + o*n*j + o*m*j + o*l*j + p*k*j + m**2*i + p*l*i + o*l*i + n*k*i +     l*k*i + k**2*i + h*b + g*b + e*b + d*b + f*a + e*a', 'o*m*j + n*m*j + o*l*j + m*l*j + l**2*j + n*k*j + m*k*j + k**2*j + p*n*i +     o*n*i + n*m*i + m**2*i + p*l*i + l**2*i + n*k*i + m*k*i + w*j*b + h*b +     g*b + f*b + e*b + d*b + c*b + g*a + f*a + d*a + c*a', 'o*m*j + o*l*j + m*l*j + p*k*j + n*k*j + o*n*i + m**2*i + p*l*i + p*k*i +     n*k*i + m*k*i + k**2*i + w*j*a + c*b + h*a + d*a', 'm**2*j + n*l*j + m*l*j + m*k*j + k**2*j + p*n*i + o*n*i + p*l*i + n*l*i +     n*k*i + l*k*i + k**2*i + w*i*b + h*b + g*b + e*b + d*b + c*b + f*a + d*a', 'o*n*j + o*m*j + m*l*j + l*k*j + k**2*j + p*n*i + n*m*i + m**2*i + p*l*i +     m*l*i + l**2*i + n*k*i + k**2*i + w*i*a + h*b + e*b + d*b + c*b + f*a', 'p*n*j + n*m*j + o*l*j + m*l*j + l*k*j + k**2*j + o*m*i + p*l*i + o*l*i +     p*k*i + m*k*i + l*k*i + h*b + d*b + h*a + g*a + e*a + d*a + c*a', 'p*m*j + m**2*j + o*l*j + n*l*j + m*l*j + l**2*j + n*k*j + m*k*j + l*k*j +     k**2*j + o*n*i + m**2*i + p*l*i + m*l*i + n*k*i + l*k*i + h*b + g*b + e*b     + d*b + c*b + h*a + d*a', 'o*n*j + o*m*j + n*l*j + m*l*j + p*k*j + l*k*j + k**2*j + p*m*i + m**2*i +     n*k*i + m*k*i + h*b + g*b + h*a + e*a + c*a', 'o*n*j + o*m*j + p*l*j + n*l*j + m*l*j + l**2*j + p*k*j + n*m*i + m**2*i +     p*l*i + o*l*i + p*k*i + n*k*i + f*b + e*b + d*b + c*b + f*a', 'b**2', 'b*a', 'a**2']},
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(64,189) : {'gap_number': 173, 'degrees': [1, 1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z*y + y*x', 'z*x + y*x', 'z**3 + x**3', 'z*v + x*v', 'x**6 + x**3*v + y**2*u + v**2']},
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(64,191) : {'gap_number': 179, 'degrees': [1, 1, 1, 3, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z**2 + z*y + z*x + y*x', 'y**2 + y*x + x**2', 'z*y*x + y*x**2', 'x**3', 'z*w + y*w', 'z*v + x*v', 'y*x*w + y*x*v', 'y*x**2*v + w*v', 'z*y*u + z*x*u + x**2*u + y*x*t + w**2 + v**2', 'z*y*t + z*x*t + y*x*t + x**2*t + w**2']},
(64,192) : {'gap_number': 175, 'degrees': [1, 1, 1, 2, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z*y + y**2', 'z*x + x**2', 'z**3']},
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(64,194) : {'gap_number': 168, 'degrees': [1, 1, 1, 3, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z**2 + z*x + y*x + x**2', 'z*y', 'y**3', 'y*x**2 + x**3', 'z*w', 'y*v', 'y**2*w + z*x*v + x**2*v', 'y**2*u + w**2', 'z*x*t + y*x*t + x**2*t + v**2', 'w*v']},
(64,195) : {'gap_number': 147, 'degrees': [1, 1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2 + z*y + y*x + x**2', 'y**2 + y*x']},
(64,196) : {'gap_number': 146, 'degrees': [1, 1, 1, 2, 3, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['y**2 + y*x', 'z*x', 'y*x**2', 'y*v + z*u', 'x*v', 'y*u', 'z**2*t + v**2', 'z*y*t + v*u', 'y*x*t + x**2*t + u**2']},
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(64,198) : {'gap_number': 176, 'degrees': [1, 1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2 + z*y + z*x', 'y*x', 'z*y**2 + y**3 + z*x**2', 'z*v + y*v', 'y**6 + y**3*v + x**3*v + z*y*u + z*x*u + x**2*u + v**2']},
(64,199) : {'gap_number': 180, 'degrees': [1, 1, 1, 3, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z**2 + z*x + x**2', 'z*y + y**2 + z*x + x**2', 'x**3', 'y**2*x + z*x**2 + y*x**2', 'z*w + y*v', 'y*w + z*v + y*v', 'y**2*v + z*x*v + x**2*v', 'y**2*u + z*x*t + x**2*t + w*v + v**2', 'z*x*u + x**2*u + y**2*t + z*x*t + x**2*t + v**2', 'w**2 + w*v + v**2']},
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(64,201) : {'gap_number': 128, 'degrees': [1, 1, 1, 2, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z*y + y**2', 'y*x', 'y*w', 'z*x*w + x**2*v + w**2']},
(64,202) : {'gap_number': 131, 'degrees': [1, 1, 1, 2, 2, 3, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r'], 'relations': ['z*x', 'y*x', 'x**3', 'x*w', 'z*y*w + y**2*v + w**2', 'y*u + z*t', 'x*u', 'x*t', 'w*u + z*s', 'w*t + y*s', 'x*s', 'y*v*t + z*y*s + w*s', 'z**2*r + u**2', 'z*y*r + u*t', 'y**2*r + t**2', 'z*w*r + u*s', 'y*w*r + t*s', 'w**2*r + s**2']},
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(64,204) : {'gap_number': 132, 'degrees': [1, 1, 1, 2, 2, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z*x', 'y*x + x**2', 'y**3', 'x*w', 'z**2*y**2 + z*y*w + y**2*v + x**2*v + w**2']},
(64,205) : {'gap_number': 140, 'degrees': [1, 1, 1, 2, 2], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2 + z*y', 'z*x + x**2']},
(64,206) : {'gap_number': 141, 'degrees': [1, 1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z*y + y**2', 'z*x', 'x**3', 'x*v', 'z**2*u + v**2']},
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(64,208) : {'gap_number': 142, 'degrees': [1, 1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z*y + y**2', 'y*x + x**2', 'y**3', 'y*v', 'z**3*v + z**2*u + y**2*u + v**2']},
(64,209) : {'gap_number': 157, 'degrees': [1, 1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2 + z*x + x**2', 'z*y + z*x + x**2', 'x**3', 'z*x*w + x**2*w + z*v', 'z*w*v + y**2*u + z*x*u + x**2*u + v**2']},
(64,210) : {'gap_number': 156, 'degrees': [1, 1, 1, 3, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z**2 + z*y + y**2', 'z*x', 'y**3', 'x**3', 'z*w', 'x*v', 'x**2*w + z*y*v + y**2*v', 'x**2*u + w**2', 'z*y*t + y**2*t + v**2', 'w*v']},
(64,211) : {'gap_number': 143, 'degrees': [1, 1, 1, 2, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2 + z*y', 'z*x + x**2', 'y**3']},
(64,212) : {'gap_number': 158, 'degrees': [1, 1, 1, 3, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z**2 + z*x + x**2', 'z*y + z*x + x**2', 'y**3', 'x**3', 'z*w', 'y*w + z*v + y*v', 'y**2*v', 'y**2*u + z*x*t + x**2*t + v**2', 'z*x*u + x**2*u + z*x*t + x**2*t + w*v + v**2', 'w**2 + w*v']},
(64,213) : {'gap_number': 161, 'degrees': [1, 1, 1, 2, 3, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['y**2 + z*x + x**2', 'y*x', 'z**2*x + x**3', 'z*v + x*v + y*u', 'y*v', 'x*u', 'z**2*y*u + z*x*t + v**2 + u**2', 'x**2*t + v**2', 'v*u']},
(64,214) : {'gap_number': 162, 'degrees': [1, 1, 1, 2, 3, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['y**2 + z*x + x**2', 'y*x', 'z**2*x + x**3', 'z**2*w + x**2*w + z*v + y*v + z*u + x*u', 'z*y*w + y*v + y*u', 'x*v', 'z**2*y*v + z*x*t + x**2*t + v**2', 'z*w*v + v**2 + v*u', 'y*w*v + z*w*u + x*w*u + x**2*t + v*u + u**2']},
(64,215) : {'gap_number': 164, 'degrees': [1, 1, 1, 3, 3, 3, 3, 4, 4, 5], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q'], 'relations': ['z*y + y*x + x**2', 'y**2 + y*x', 'z*x**2', 'x**3', 'y*w', 'x*w + z*v', 'y*v + x*v', 'z*u + x*t', 'y*u', 'x*u + y*t', 'x**2*v + x**2*t', 'z**3*v + x**2*s + w**2 + v**2', 'y*x*s + v**2', 'z**2*r + u**2 + t**2', 'z*x*r + u*t', 'y*x*r + x**2*r + u**2', 'w*v', 'w*u + x*q', 'v*u', 'w*t + z*q + x*q', 'v*t + x*q', 'y*q', 'z**2*x*q + y*t*s + w*q', 'z*w*r + u*q + t*q', 'z*v*r + u*q', 'v*q', 'w**2*r + q**2']},
(64,216) : {'gap_number': 165, 'degrees': [1, 1, 1, 3, 3, 3, 3, 4, 4, 5], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q'], 'relations': ['y**2 + z*x', 'y*x + x**2', 'z**2*x', 'x**3', 'y*w + z*u + x*u + z*t + y*t', 'x*w', 'y*v + z*u', 'x*v + x*u + y*t', 'y*u + x*u + y*t', 'x*t', 'x**2*u + z*y*t', 'z**3*u + z**3*t + z*x*r + w*v + u**2 + v*t + t**2 + z*q + y*q', 'z**2*s + x**2*s + z**2*r + z*x*r + v**2 + u**2', 'z*y*s + x**2*s + z*y*r + u**2 + v*t + t**2 + y*q', 'z*x*s + x**2*s + z*x*r + u**2', 'x**2*r + u**2 + t**2', 'w**2 + w*v + v*t + t**2 + z*q + y*q', 'w*u + t**2 + y*q', 'v*u + u**2 + v*t + t**2 + y*q', 'w*t + t**2 + y*q', 'u*t + t**2', 'x*q', 'z**2*y*q + y*t*r + w*q + t*q', 'z*w*s + z*t*s + z*w*r + z*t*r + w*q + v*q', 'z*u*s + x*u*s + z*t*s + z*u*r + x*u*r + z*t*r + t*q', 'u*q + t*q', 'w*v*s + v*t*s + w*v*r + v*t*r + z*s*q + y*s*q + z*r*q + y*r*q + q**2']},
(64,217) : {'gap_number': 130, 'degrees': [1, 1, 1, 2, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z*y + y*x', 'z*x + x**2', 'y**2*x', 'z*w + x*w', 'y*x*w + x**2*v + x*u', 'y*x*v + y*u', 'w**2 + x*u', 'x*w*v + y*x*u + w*u', 'z**3*u + x**3*u + y*w*u + x*v*u + z**2*t + x**2*t + u**2']},
(64,218) : {'gap_number': 133, 'degrees': [1, 1, 1, 2, 2, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z*x + x**2', 'y*x', 'z**3 + z*y**2', 'x*w', 'z**2*y**2 + z*y**3 + z*y*w + z**2*v + x**2*v + w**2']},
(64,219) : {'gap_number': 144, 'degrees': [1, 1, 1, 2, 3, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z*y', 'z*x + x**2', 'x**3', 'z*v', 'x*v + y*u', 'x*u', 'z**4*w + z**3*u + z**2*t + x**2*t + u**2', 'y**2*t + v**2', 'y*x*t + v*u']},
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(64,221) : {'gap_number': 159, 'degrees': [1, 1, 1, 3, 3, 3, 3, 4, 4, 5], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q'], 'relations': ['z**2 + z*x + x**2', 'z*y', 'z*x**2', 'x**3', 'z*w', 'x*w + y*v', 'z*v + x*t', 'x*v + z*t + x*t', 'z*u', 'x*u + y*t', 'z*x*t', 'y**2*s + u**2', 'z*x*s + z*x*r + x**2*r + t**2', 'y*x*s + u*t', 'x**2*s + z*x*r + v*t', 'y**2*r + w**2', 'y*x*r + w*v', 'v**2 + v*t + t**2', 'w*u + y*q', 'v*u + x*q', 'w*t + x*q', 'z*q', 'y*w*s + u*q', 'y*v*s + t*q', 'y*u*r + w*q', 'y*t*r + v*q', 'u**2*r + q**2']},
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(64,241) : {'gap_number': 257, 'degrees': [1, 1, 1, 1, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z*w + w**2', 'z*y*x + y**2*x + z*x**2 + y*x**2']},
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(64,245) : {'gap_number': 191, 'degrees': [1, 1, 1, 5, 5, 8], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['y*x', 'y**3 + z**2*x', 'z**4*x', 'x*w', 'y*v', 'y**2*w + z**2*v', 'z**4*y*w + y**2*u + w**2', 'x**2*u + v**2', 'w*v']},
(64,246) : {'gap_number': 46, 'degrees': [1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2', 'z*y + y**2', 'y*x', 'y*w', 'z*x*w + y**2*v + w**2']},
(64,247) : {'gap_number': 42, 'degrees': [1, 1, 2, 2, 3, 3, 4, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'], 'relations': ['z**2', 'z*y', 'z*x', 'z*w', 'y**2*x + w**2', 'x*w + y*v', 'z*v', 'z*u', 'y*x**2 + w*v', 'w*u + y*t', 'z*t', 'x**3 + v**2', 'y*x*u + w*t', 'y**2*s + u**2 + w*t', 'v*u + x*t', 'x**2*u + v*t', 'y*x*t + y*w*s + u*t', 'y*v*t + w**2*s + t**2']},
(64,248) : {'gap_number': 41, 'degrees': [1, 1, 2, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z**2', 'z*y', 'y*x', 'z*w', 'x*w + z*v', 'w**2', 'y*v', 'w*v', 'z*x*v + v**2']},
(64,249) : {'gap_number': 43, 'degrees': [1, 1, 2, 2, 3, 5, 5, 6, 8], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r'], 'relations': ['z**2', 'z*y', 'y**3 + z*w', 'z*x', 'y**2*x + z*v', 'y**2*w + x**2 + z*v', 'x*w + y*v', 'z*w**2', 'y*w**2 + y**2*v + x*v', 'z*w*v + y*w*v + y*u', 'w**3 + y*x*v + y*w*v + v**2', 'z*u', 'z*t', 'w**2*v + y**2*u + y**2*t + w*u', 'y*v**2 + x*u', 'x*t + y*s', 'z*s', 'w*v**2 + y*x*u + y**2*s + v*u', 'y*w*t + y**2*s + x*s', 'v*t + w*s', 'w**2*t + y*x*s + y*w*s + v*s', 'y**2*v*u + w*v*u + y*v*s + y**2*r + u**2 + t**2', 'x**2*s + y*v*s + y**2*r + t**2', 'w**2*s + y*v*s + y**2*r + u*t + t**2', 'y*t**2 + w*v*s + z*w*r + u*s', 'x*v*s + w*v*s + y*x*r + u*s + t*s', 'y*u*s + x**2*r + s**2']},
(64,250) : {'gap_number': 32, 'degrees': [1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q', 'p'], 'relations': ['z**2', 'z*y', 'y*x', 'z*w', 'z*v', 'x*w', 'z*u', 'y*u', 'z*t', 'z*s', 'y*v**2 + v*t + w*s + y*q', 'w*u', 'x*t', 'x*s', 'z*q', 'y**2*w*v + y**3*s + w**3 + y*w*t + t**2', 'w**2*v + y*v*t + y*v*s + t*s + y*p', 'x*v**2 + x*q', 'w*v**2 + y*v*s + y**2*r + s**2', 'u**2 + x*q', 'u*t', 'u*s', 'z*p', 'y**3*r + y*s**2 + y*w*r + t*q + s*q + w*p + v*p', 'v**2*u + u*q', 'v**2*t + w*v*s + y*w*r + s*q + v*p', 'x*p', 'v**4 + v*t*s + w*s**2 + w**2*r + w*v*q + y*s*q + q**2', 'y**2*s**2 + y**2*w*r + v*t**2 + w*t*s + v*t*s + w*s**2 + w**2*q + t*p', 'y**2*v*r + v*t*s + w*s**2 + y*t*r + w*v*q + y*s*q + s*p', 'u*p', 'v**3*s + y*w**2*r + y*w*v*r + y**2*t*r + w*t*r + v*t*q + w*s*q + w*v*p + y*s*p     + q*p', 'w**3*r + y*w*t*r + y*v*t*r + y*w*s*r + y*v*s*q + y**2*r*q + t**2*r + w*q**2 +     v*t*p + w*s*p + p**2']},
(64,251) : {'gap_number': 33, 'degrees': [1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q', 'p', 'n', 'm', 'k', 'j', 'i', 'h', 'g', 'f'], 'relations': ['z**2', 'z*y', 'y**3', 'y*x', 'z*w', 'y**2*w + y*u', 'x*w', 'z*v + y*u', 'z*u', 'z*t', 'y**2*v', 'y**2*t', 'x*v + x*t', 'x*u + x*t', 'w*u', 'z*s', 'y*s', 'z*r', 'w**3 + y*w*t + t**2 + x*s + x*r + y*p', 'y**2*r + y*p', 'v**2 + x*s + x*r + w*r + y*n', 'v*u + x*s + x*r + y*p', 'u**2 + x*s + x*r', 'u*t + x*s + x*r', 'w*s', 'z*q', 'y*q', 'z*p', 'z*n', 'y*v*t + w*q', 'y*w*r + w*q + w*p', 'y**2*n', 'v*s + x*n + z*m', 'u*s + x*n + z*m', 't*s + x*n + z*m', 'u*r + t*r + w*q + w*n + y*k', 'x*q + z*m', 'x*p + x*n + z*m', 'y*m', 'z*k', 'y*w**2*v + u*p + t*p + y*j', 'x**2*s + x**2*r + s*r + u*p', 'x**2*r + u*p + x*k', 'w**2*r + t*p + t*n + y*i', 'y*v*r + v*p + u*p + y*j', 'y*w*n + y**2*k + y*j', 'y**2*k + u*p + u*n', 's**2 + s*r + u*p', 'v*q + u*p + u*n + y*j', 'u*q', 't*q + u*p + t*p + y*j', 'w*m', 'z*j', 'z*i', 'x*t*r + t*m + x*j + z*h + z*g', 'w**2*p + w**2*n + y*w*k + y**2*i + u*k + t*k + w*j + w*i + y*h + y*g', 'y*r**2 + r*q + y*h + y*g', 'y*w*k + r*q + u*k + t*k + w*i + y*h + y*g', 'y**2*i', 'x**2*n + s*n + t*m + x*j', 'y*v*n + r*q', 'z*x*m + z*h + z*g', 's*q', 's*p + s*n', 'r*p + s*n + t*m + u*k + x*j + z*h + y*h + z*g + y*g', 'v*m + t*m', 'u*m + t*m', 'x*i + z*h + z*g', 'x*s*r + x*r**2 + w*v*n + y*v*k + y*w*j + y*w*i + y**2*h + y**2*g + s*m + r*m +     v*j + u*i + y*f', 'w*t*p + w*v*n + w*t*n + y*v*k + y*w*j + y*w*i + q*n + v*j + t*j + u*i + y*f', 'x*r**2 + w*v*n + y*v*k + y*w*j + y*w*i + y**2*h + y**2*g + p**2 + s*m + r*m +     s*k + v*j + y*f', 'w*v*n + y*v*k + y*w*j + y*w*i + y**2*h + y**2*g + v*j + u*j + u*i + y*f', 'w*r**2 + y**2*g + q*n + p*n + n**2', 'w*v*p + y*w*j + q*n', 'w*t*n + y*w*i + y**2*h + p**2 + n**2 + v*j + t*j + u*i + w*h + w*g', 'y*v*k + y*w*i + y**2*h + y**2*g + p**2 + p*n + y*f', 'x*t*n + p**2 + s*m + r*m + u*j + u*i', 'y**2*h + y**2*g + u*i', 'y*r*n + p**2 + q*n + p*n', 'x**2*m + x**2*k + r*m + u*j + x*h + x*g', 'w**2*k + p**2 + q*n + p*n + u*i + t*i', 'q**2', 'q*p', 'z*f', 'x**4*t + z*x*h + y*w*h + n*m + q*k + n*k + s*j + r*i + u*h + u*g + x*f', 'v*r**2 + w*r*n + x*t*m + x*t*k + y*v*j + y*t*j + y*w*h + y*w*g + q*k + s*j +     v*h + v*g', 't*r**2 + w*r*n + x*t*m + x*t*k + y*v*j + y*w*h + p*k + n*k + s*j + r*i + u*h     + u*g', 'x**2*j + z*x*h + y*w*h + z*x*g + q*k + n*k + s*j + r*i + u*h + u*g', 't**2*n + x*t*m + w*v*k + x*t*k + w**2*j + w**2*i + q*k + p*k + s*j + t*h + t*g     + w*f', 'v*t*n + w*r*n + x*t*m + w*v*k + x*t*k + w**2*i + y*t*i + y*w*h + q*k + n*k +     s*j + r*i + u*h + u*g + w*f', 'x*r*n + p*m + s*j', 'y*r*k + y*w*h + p*k + n*k + r*i', 'z*x*g + p*m + n*m', 'y*v*i + q*k', 'q*m + p*m + n*m', 's*i', 'x**3*k + x**2*g + m**2 + m*k + u*f', 'y*w**2*j + w*v*j + w*v*i + w*t*i + y*w*f + p*j + n*j + q*i + p*i + u*f + t*f', 't**2*k + x*s*k + x*r*k + y*r*j + w*t*i + y*r*i + y*t*h + y*t*g + y*w*f + p*i', 'x*n**2 + x*s*k + x*r*k + x*t*j + m*k + s*h + s*g + u*f', 'r**3 + x*r*m + w*v*i + w*t*i + w**2*g + y*t*g + k**2 + q*j + q*i + n*i + s*h +     s*g + u*f + t*f', 'v*r*n + x*r*m + w*v*i + y*v*h + y*v*g + y*u*g + y*t*g + m*k + q*j + n*j +     q*i + p*i + n*i + v*f + u*f', 'w*n**2 + x*s*m + y*p*k + y*r*j + y*v*h + y*t*h + y*v*g + y*u*g + y*t*g + n*j     + s*h + s*g + u*f', 'y*r*j + y*t*h + y*t*g + q*j', 'y*p*k + y*r*i + q*i + p*i', 'x*s*k + x*r*k + x*t*j + w*t*i + y*v*h + y*t*h + w**2*g + y*v*g + y*u*g +     y*t*g + m*k + k**2 + q*j + p*j + n*j + q*i + r*h + r*g + v*f + t*f', 'x*s*m + y*t*h + y*t*g + p*j + s*h + s*g + u*f', 'x*r*k + x*t*j + w*t*i + y*v*h + w**2*g + y*v*g + y*u*g + k**2 + q*j + n*j +     q*i + s*h + r*h + s*g + r*g + v*f + t*f', 'w*r*k + y*t*h + p*i + n*i', 'x**2*t*k + t*r*m + s*f', 'v*n**2 + x*n*m + z*m**2 + v*r*k + w*p*k + x*n*k + x*s*j + y*n*j + v*t*i +     t**2*i + w*r*i + y*n*i + x*t*g + w*t*g + w**2*f + y*v*f + y*t*f + m*j +     k*j + m*i + k*i + r*f', 'w*p*k + y*v*f + m*i + q*h + q*g', 'y*k**2 + v*t*j + x*s*j + x*r*j + y*n*j + w*r*i + w*v*h + w*v*g + w*t*g +     y*v*f + y*t*f + m*i + k*i + p*h + n*h + p*g + n*g', 'x*n*m + z*m**2 + x*n*k + x*t*g + m*j + m*i + s*f', 'r**2*n + v*t*j + v*t*i + t**2*i + w*v*h + w*v*g + x*t*g + w**2*f + y*v*f + m*j     + m*i + q*h + n*h + q*g + n*g + s*f', 'z*m**2 + m*i', 't*r*k + x*n*k + x*r*j + y*n*j + w*r*i + y*n*i + p*h + p*g', 'u*n*k + t*n*k + w*k**2 + w*q*j + w*p*j + w*q*i + w*n*i + y*k*i + y*p*h +     y*n*h + y*n*g + i**2 + q*f', 'w*k**2 + y*k*i + y*p*h + i**2', 'w*q*i + w*n*i + y*n*h + y*n*g + y*r*f + j*i', 'v*n*k + t*n*k + w*q*j + w*p*i + w*r*h + y*p*h + y*n*h + w*r*g + y*n*g + p*f     + n*f', 't*n*m + x*m*k + t*r*j + w*q*j + w*n*j + w*p*i + w*n*i + x*r*h + y*p*h +     y*n*h + x*r*g + y*p*g + y*n*g + x*t*f + j*i + q*f + p*f', 't*n*k + x*m*k + w*p*j + w*n*j + w*p*i + x*r*h + x*s*g + x*t*f + y*r*f + j**2     + j*i', 'x*m**2 + t*r*j + w*q*j + w*n*j + w*p*i + w*n*i + x*r*h + y*p*h + y*n*h +     x*s*g + x*r*g + y*p*g + y*n*g + y*r*f + j*i + m*h + m*g', 'r**2*k + x*k**2 + t*r*j + w*p*j + x*n*j + w*p*i + y*k*i + x*s*h + w*r*h +     y*p*h + y*n*h + x*r*g + w*r*g + y*n*g + x*t*f + y*r*f + j**2 + j*i + k*h     + k*g + p*f + n*f', 'v*k**2 + t*k**2 + x*m*j + y*j**2 + t*p*i + y*i**2 + t*r*h + w*q*h + z*m*h +     t*r*g + w*p*g + x*n*g + x*s*f + y*n*f + j*h + i*h + j*g + i*g + k*f', 'x**2*t*h + r**2*j + v*n*j + u*n*j + x*m*j + x*k*j + y*j**2 + t*p*i + v*n*i +     t*n*i + y*i**2 + w*q*h + x*n*h + w*n*h + x*n*g + w*n*g + w*r*f + j*h +     j*g + m*f', 't*m**2 + s*r*j + r**2*j + v*n*j + u*n*j + y*j**2 + t*p*i + v*n*i + t*n*i +     y*i**2 + w*q*h + w*n*h + z*m*h + x*n*g + w*n*g + w*r*f + j*h + j*g', 'r**2*i + t*p*i + v*n*i + y*j*i + y*i**2 + z*m*h + z*m*g + i*h + i*g', 'r*m**2 + r*k**2 + s*n*j + r*n*j + t*k*j + x*j**2 + s*r*h + v*p*h + u*p*h +     u*n*h + x*m*h + x*k*h + w*k*h + y*i*h + v*p*g + u*p*g + u*n*g + t*n*g +     x*m*g + x*k*g + w*k*g + y*j*g + x*n*f + w*n*f + y*k*f + h**2 + g**2', 'v*k*i + w*i**2 + u*p*h + t*p*h + v*n*h + u*n*h + y*j*h + u*p*g + t*p*g +     v*n*g + u*n*g + v*r*f + t*r*f + w*p*f + w*n*f + i*f', 'r*k**2 + s*n*j + r*n*j + t*m*j + x*j**2 + w*j*i + r**2*h + v*p*h + u*p*h +     t*p*h + s*r*g + r**2*g + v*p*g + t*p*g + t*n*g + y*j*g + y*i*g + v*r*f +     x*n*f + j*f', 'u*j**2 + t*m*h + x*j*h + z*h**2 + s*n*g + z*h*g + s*r*f + r**2*f + t*p*f +     v*n*f + x*m*f + x*k*f + y*j*f + y*i*f + h*f + g*f', 'x**2*k*g + k**3 + n*m*j + p*k*j + n*k*j + r*i**2 + r*m*h + r*k*h + u*i*h +     w*h**2 + q*n*g + p*n*g + s*m*g + s*k*g + r*k*g + u*j*g + u*i*g + t*i*g +     w*g**2 + r*q*f + t*m*f + v*k*f + u*k*f + w*i*f + f**2']},
(64,252) : {'gap_number': 34, 'degrees': [1, 1, 2, 2, 2, 3, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'], 'relations': ['z**2', 'z*y', 'y*x + y*w', 'z*w + y*w', 'z*v', 'x*w + w**2', 'z*u', 'y*u', 'z*t', 'x*u + w*u + x*t', 'w*t', 'x*v**2 + u**2', 'w*v**2 + u**2 + u*t', 'y*v*t + y**2*s + u*t + t**2']},
(64,253) : {'gap_number': 35, 'degrees': [1, 1, 2, 2, 2, 3, 5, 5, 6, 6, 7, 8], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q', 'p', 'n'], 'relations': ['z**2', 'z*y', 'y**3 + z*w + z*v', 'y*x + z*v', 'y*w + z*v', 'y**2*v + y*u', 'x*w + w**2', 'z*u', 'y**2*u', 'w**3 + x*v**2 + u**2', 'y*v*u + y*s', 'z*t', 'z*s', 'z*v**3 + w*t + w*s + y*r', 'w**2*u + v**2*u + w*s + v*s + y*r + y*q', 'x*v*u + v**2*u + x*s + w*s + v*s + z*r + y*r + y*q', 'w*v*u + v**2*u + v*s + y*r', 'y**2*t + y*r + y*q', 'x*t + w*t + z*r + y*q', 'z*q + y*q', 'w**2*v**2 + w*v**3 + w*u**2 + y*v*s + u*t + w*r + w*q + y*p', 'w*u**2 + v*u**2 + u*s', 'x*v**3 + w*v**3 + y*v*s + u*t + u*s + y*p', 'y*v*t + y*p', 'x*q + w*q', 'z*p', 'w*v*t + w**2*s + w*v*s + u*q + w*p', 'x**2*s + w**2*s + x*v*s + z*x*r + y**2*p + u*r + u*q + x*p + w*p', 'y*v**2*s + y**2*n + t**2 + t*s', 'w*u*s + v*u*s + s**2', 'v*u*t + v*u*s + t*s + s**2', 'x*u*s + v*u*s + w**2*r + v**2*r + u*p', 'y*v**2*q + w*u*q + v*u*q + y*u*p + t*q', 'w*u*q + v*u*q + z*w*n + s*q', 'u**2*t + w*u*r + v*u*r + w**2*p + w*v*p + y*u*p + z*w*n + z*v*n + t*r + s*r +     t*q + s*q', 'z*x**2*r + w*u*r + v*u*r + y*u*p + z*x*n + z*w*n + s*r + t*q + s*q', 'x**5*v + w*v**5 + x**3*r + x**2*v*r + y*v**2*p + v*t**2 + u**2*r + x*u*p + v*u*p +     x**2*n + w**2*n + y*u*n + r**2 + r*q + s*p', 'w*u*p + v*u*p + s*p', 'w*v**2*r + v**3*q + y*v**2*p + w*s**2 + u**2*q + v*u*p + w**2*n + y*u*n + q**2 +     t*p + s*p', 'w**2*v*q + v**3*q + y*v**2*p + w*s**2 + u**2*q + y*u*n + t*p', 'w*v**2*q + v**3*q + y*v**2*p + w*s**2 + u**2*q + y*u*n + r*q + q**2 + t*p', 'v**2*u*r + v**2*u*q + u*t*s + w*s*r + v*s*r + v*t*q + w*s*q + y*q**2 + y*s*p +     w*u*n + q*p', 'x**3*p + x**2*v*p + u*s**2 + x*s*r + v*s*r + z*r**2 + y*q**2 + x*u*n + w*u*n +     r*p + q*p', 'v**2*t**2 + x*v*s**2 + x**2*u*p + u*s*r + w*r*q + v*r*q + w*q**2 + v*q**2 + w*s*p     + u**2*n + y*s*n + p**2']},
(64,254) : {'gap_number': 36, 'degrees': [1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 6, 7, 8], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q', 'p', 'n', 'm'], 'relations': ['z**2', 'z*y', 'z*x', 'y*x + y*w', 'z*w + y*w', 'x**2 + z*u', 'x*w + z*t', 'w**2 + z*u + z*t', 'z*v + z*u', 'y*u + z*t', 'x*v', 'w*v + w*t', 'x*u', 'w*u + w*t', 'x*t + w*t', 'z*s', 'y**2*s + y*q', 'v**2 + x*s + y*q', 'v*u + x*s', 'u**2 + x*s', 'u*t + w*s', 't**2 + x*s + w*s + y*r + y*q', 'z*r', 'z*q', 'y*v*t + v*s + u*s + w*q + y*p', 'x*r + w*q', 'w*r + w*q', 'x*q', 'z*p', 'y**3*q + y**2*p + v*r + v*q + t*q + x*p + y*n', 'y*v*s + v*q + x*p', 'y*t*s + t*q + w*p', 'u*r + w*p', 'u*q + x*p', 'z*n', 'w*t*s + w*n', 'y*s**2 + s*q + u*p + w*n', 'y*t*q + s*q + v*p', 'x*n', 'y**5*r + y**2*t*r + v*t*s + y*s*r + y*t*p + y**2*m + r**2 + q**2', 'y**2*v*q + v*t*s + w*s**2 + y*s*r + y*v*p + q**2 + v*n', 'w*s**2 + y*s*r + r*q', 'x*s**2 + u*n', 'y*s*q + q**2 + u*n', 'u*s**2 + w*t*p + y*s*p + q*p', 't*s**2 + v*t*r + v*t*q + y*q**2 + y*s*p + y*w*m + r*p + q*p + s*n', 'x*s*p + y*s*n + q*n', 'y**2*v*n + y**2*t*n + t*s*r + y*r*p + y*q*p + y*s*n + y*v*m + z*t*m + r*n +     q*n', 's**3 + t*s*q + v*t*p + y*s*n + z*u*m + p**2 + q*n', 's**2*r + v*r*q + t*q**2 + u*s*p + t*s*p + v*t*n + w*s*n + p*n', 'y*v*q**2 + s*q**2 + v*r*p + v*q*p + t*q*p + v*s*n + y*q*m + n**2']},
(64,255) : {'gap_number': 37, 'degrees': [1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q', 'p', 'n'], 'relations': ['z**2', 'z*y', 'y**3 + y*w', 'z*x', 'y*x + z*w + y*w', 'y**2*w', 'x**2 + z*v', 'x*w + z*v + y*v + y*u', 'w**2 + y*v + y*u', 'z*u', 'y**2*u + w*u', 'x*v', 'x*u + w*u', 'z*t', 'y**2*t + y*s', 'v**2 + x*t', 'v*u + y*s', 'u**2 + y*s', 'z*s', 'z*r', 'y**2*s + w*s + x*r + w*r', 'y**2*r + w*s + x*r', 'u*t + w*s + y*q', 'x*s', 'z*q', 'y*v*t + u*s', 'y*w*r + u*s + u*r + y*p', 'y**2*q + u*r + y*p', 'v*s + x*q', 'v*r + u*r + x*q + w*q', 'z*p', 'w*v*t + y**2*p + w*p', 'y*t**2 + y**2*p + u*q + x*p', 'y*w*q + x*p + w*p', 't*s + v*q + w*p', 'x*t**2 + s*r + v*p', 'w*t**2 + y*u*q + v*p + u*p', 'y*t*r + y*u*q + u*p', 'y**2*n + r**2 + v*p', 's**2 + s*r + v*p', 'v*t**2 + w*v*q + y*u*p + s*q', 'w*u*q + y*u*p + z*w*n + s*q + r*q + t*p', 't**3 + w*u*p + z*v*n + y*u*n + q**2 + r*p', 'x*t*q + w*u*p + y*u*n + r*p', 'w*t*q + y*r*q + w*u*p + s*p', 't**2*r + v*t*q + y*s*p + q*p', 'x*q**2 + v*t*p + y*s*n + p**2']},
(64,256) : {'gap_number': 153, 'degrees': [1, 1, 1, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u'], 'relations': ['z*y + y*x + x**2', 'z*x + y*x + x**2', 'x*w', 'x*v', 'w**3 + z*w*v + y*w*v + z**2*u + y**2*u + x**2*u + v**2']},
(64,257) : {'gap_number': 152, 'degrees': [1, 1, 1, 2, 4, 5, 5, 5, 8, 8], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q'], 'relations': ['z**2 + z*y + x**2', 'y*x', 'z*y**2 + x*w', 'x*w**2', 'z*v', 'x*v', 'z*y*w**2 + y**2*w**2 + w*v + z*t + y*t + y*s', 'z*u + x*s', 'y*u', 'x*u + z*s', 'x*t', 'z*y*t + w*u', 'y**2*w*v + y**3*s + w**2*v + z*w*t + y*w*t + y*w*s + v**2', 'z*w**4 + y*w**4 + y**2*w*s + v*t + v*s', 'y**2*w*t + y**2*w*s + w**2*u + v*s + y*r', 'v*u', 'z*r', 'x*r', 'y**2*w**4 + w**3*v + y*w**2*s + u**2 + u*t + t*s + s**2 + w*r', 'w**5 + y*w**2*t + y**2*q + t**2', 'z*w**2*t + y*w**2*t + u**2 + t*s + s**2 + w*r', 'z*y*q + y**2*q + u**2 + s**2', 'z*x*q + u*s', 'x**2*q + u**2', 'y*w**3*s + y**2*t**2 + y**2*w*r + w*u*t + v*r', 'y*w*t*s + y*w*s**2 + y*v*q + s*r', 'w**4*s + z*w*t**2 + y*w*t**2 + t*r + s*r', 'u*r', 'y*t**2*s + y*w*t*r + w**2*v*q + z*w*t*q + y*w*t*q + y*w*s*q + r**2']},
(64,258) : {'gap_number': 154, 'degrees': [1, 1, 1, 2, 5, 5, 8], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z*y + y**2', 'z*x', 'z**3 + x*w', 'x*w**2', 'x*v', 'z*u', 'z**2*v + w*u', 'z**2*w**4 + v*u', 'w**5 + z*w**2*v + y*w**2*u + z**2*t + v**2 + v*u', 'x**2*t + u**2']},
(64,259) : {'gap_number': 138, 'degrees': [1, 1, 1, 2, 2, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'], 'relations': ['z*y', 'y*x', 'x*w + z*u', 'z*v + z*u', 'x*v + z*u', 'v**2 + w*u + y*t', 'z*t', 'x*t', 'w**2*u + w*u**2 + y*w*t + y*v*t + y*u*t + y**2*s + t**2']},
(64,260) : {'gap_number': 139, 'degrees': [1, 1, 1, 2, 2, 3, 5, 5, 5, 8], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q'], 'relations': ['z*y', 'y*x', 'y**3', 'x*w + z*v', 'y**2*w + z*u', 'z**2*v + z*x*v', 'y**2*v + x*u', 'z*w*v + z*v**2', 'y**2*u', 'z*x*v**2 + x*t + x*s + z*r + x*r', 'w**2*v + w*v**2 + y*w*u + y*v*u + u**2 + y*r', 'z*v*u + x*s + x*r', 'x*v*u + y*s', 'y*t', 'z*s + x*s + z*r + x*r', 'y*w*v**2 + z*v**3 + y*u**2 + v*t + w*s', 'y**2*r', 'y*w*v*u + x*v*s + y*w*r + x*v*r + u*t', 'y*v**2*u + y*v*s + y*w*r + y*v*r + u*t + u*s', 'z*w*r + z*v*r', 'y*v*u**2 + w*v*t + v**2*t + y*u*r', 'z**4*w**3 + z**5*r + z**3*w*t + x**3*v*t + z*x**2*v*r + x*v**2*t + x*v**2*s +     z*v**2*r + x*v**2*r + z**2*q + t**2', 'x**2*v**4 + z**3*x**2*r + x**3*v*t + x*v**2*t + z*v**2*r + y*v**2*r + v*u*t + x**2*q     + s*r', 'z**4*x*r + x**3*v*t + x*v**2*s + z*v**2*r + x*v**2*r + z*x*q + t*s', 'w*v*u**2 + x*v**2*s + y*v**2*r + x*v**2*r + y**2*q + t*s + t*r + s*r + r**2', 'y*w*v*r + v*u*t + w*u*s + t*s + t*r', 'y*v**2*s + x*v**2*s + y*v**2*r + x*v**2*r + v*u*t + s**2 + s*r']},
(64,261) : {'gap_number': 134, 'degrees': [1, 1, 1, 2, 2, 3, 4], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z*x', 'y*x + x**2', 'x*w', 'z*v', 'z*y*w + y**2*w + w**2', 'w*v + y*u + x*u', 'z*u', 'y**2*u + x**2*u + w*u', 'y*v*u + x**2*t + u**2']},
(64,262) : {'gap_number': 136, 'degrees': [1, 1, 1, 2, 2, 5, 5, 5, 6, 8], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's', 'r', 'q'], 'relations': ['z*y', 'y*x', 'y**3 + x*v', 'y*w', 'z**2*w + z*x*w + w**2', 'x*v**2', 'y**2*v**2 + y*s', 'w**2*v + z*t + x*s', 'w*v**2 + z*u', 'x*u', 'y*t', 'z**2*u + w*u', 'y**2*u + w*u + v*t', 'z**2*t + z*x*s + w*t + x*r', 'w*s + z*r', 'y*r', 'z**2*r + z*x*r + w*r', 'z**5*s + z**2*x**3*s + z*x**4*s + x**5*s + z**3*v*s + z*w*v*t + y*v**2*s + z**2*q +     x**2*q + u*t + t**2 + s**2', 'z**4*x*s + z**2*x**3*s + z*x**4*s + w*v*r + z*x*q + t*s', 'z**3*x**2*s + z*x**4*s + x**5*s + z*w*v*t + x**2*q + t**2', 'z*v**2*u + y*v**2*s + v**2*r + y**2*q + u**2 + u*s', 'y*v**2*u + v**2*r + u*s', 'z*v**2*t + u*t', 'z*x**4*r + x*w**2*r + z*t*s + x*s**2 + x*w*q + t*r', 'x**3*w*r + z*w**2*r + x*w**2*r + z*u*t + z*w*q + x*w*q + t*r + s*r', 'z*u*s + u*r', 'z*s*r + x*s*r + r**2']},
(64,263) : {'gap_number': 135, 'degrees': [1, 1, 1, 2, 2, 3, 5, 8], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'], 'relations': ['z*x', 'y*x', 'z**2*y + z*w + y*w', 'x*v', 'z**4 + z**2*w + y**2*w + v**2 + z*u + y*u', 'z*y*v + z*u + y*u', 'w*v + z*u', 'y**3*w + z*w**2 + y*w**2 + y*v**2 + y**2*u + v*u', 'z*y**2*w', 'y**2*w**2 + x**2*w**2 + z*y**2*u + y*w*u + y*v*u + u**2 + x*t', 'z*y**2*u + y*w*u + y*t', 'z*w*u + z*t', 'z*u**2 + v*t', 'x**2*w**4 + w**2*u**2 + x**2*s + t**2']},
(64,264) : {'gap_number': 137, 'degrees': [1, 1, 1, 2, 2, 5, 8], 'names': ['z', 'y', 'x', 'w', 'v', 'u', 't'], 'relations': ['z*y', 'y**2 + y*x', 'z*x**2 + x**3 + z*v', 'y*w', 'x**4 + z*x*w + x**2*w + z**2*v + w**2', 'z**2*x*v + x**3*v', 'z*x*w*v + x**2*w*v + w*v**2 + y*u + x*u', 'z*u', 'y*x**2*v**2 + y*x*u + x**2*u + w*u', 'x**2*v**4 + x*v**2*u + y*x*t + u**2']},
(64,265) : {'gap_number': 52, 'degrees': [1, 1, 2], 'names': ['z', 'y', 'x'], 'relations': ['z*y']},
(64,266) : {'gap_number': 53, 'degrees': [1, 1, 3, 4], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2 + z*y', 'z*y**2 + y**3', 'z*x + y*x', 'y**3*x + z*y*w + x**2']},
(64,267) : {'gap_number': 54, 'degrees': [1, 1, 4], 'names': ['z', 'y', 'x'], 'relations': ['z**2 + z*y', 'y**3']},
}

















unstable_cohomology= {
(8,5) : {'steenrod': [['z**2'], ['y**2'], ['x**2']], 'degrees': [1, 1, 1], 'names': ['z', 'y', 'x'], 'relations': []},
(8,2) : {'steenrod': [['0', 'z**2'], ['y**2'], ['x**2']], 'degrees': [2, 1, 1], 'names': ['z', 'y', 'x'], 'relations': ['y**2 + x**2']},
(8,1) : {'steenrod': [['z**2'], ['0', 'y**2']], 'degrees': [1, 2], 'names': ['z', 'y'], 'relations': ['z**2']},
(8,3) : {'steenrod': [['z*x', 'z**2'], ['y**2'], ['x**2']], 'degrees': [2, 1, 1], 'names': ['z', 'y', 'x'], 'relations': ['y**2 + y*x']},
(8,4) : {'steenrod': [['0', '0', '0', 'z**2'], ['y**2'], ['x**2']], 'degrees': [4, 1, 1], 'names': ['z', 'y', 'x'], 'relations': ['y**2 + y*x + x**2', 'y**2*x + y*x**2']},
(16,14) : {'steenrod': [['z**2'], ['y**2'], ['x**2'], ['w**2']], 'degrees': [1, 1, 1, 1], 'names': ['z', 'y', 'x', 'w'], 'relations': []},
(16,10) : {'steenrod': [['z**2'], ['y**2'], ['x**2'], ['0', 'w**2']], 'degrees': [1, 1, 1, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2 + x**2']},
(16,2) : {'steenrod': [['0', 'z**2'], ['y**2'], ['x**2'], ['0', 'w**2']], 'degrees': [2, 1, 1, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['x**2', 'y**2']},
(16,5) : {'steenrod': [['0', 'z**2'], ['y**2'], ['x**2']], 'degrees': [2, 1, 1], 'names': ['z', 'y', 'x'], 'relations': ['y**2 + x**2']},
(16,1) : {'steenrod': [['z**2'], ['0', 'y**2']], 'degrees': [1, 2], 'names': ['z', 'y'], 'relations': ['z**2']},
(16,11) : {'steenrod': [['z**2'], ['y**2'], ['x**2'], ['z*w + x*w', 'w**2']], 'degrees': [1, 1, 1, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z*y + y**2 + z*x + y*x']},
(16,12) : {'steenrod': [['z**2'], ['0', '0', '0', 'y**2'], ['x**2'], ['w**2']], 'degrees': [1, 4, 1, 1], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2 + z*x + x**2 + z*w + x*w + w**2', 'z**2*x + z*x**2 + z**2*w + x**2*w + z*w**2 + x*w**2']},
(16,13) : {'steenrod': [['0', 'z*w**2', '0', 'z**2'], ['y**2'], ['x**2'], ['w**2']], 'degrees': [4, 1, 1, 1], 'names': ['z', 'y', 'x', 'w'], 'relations': ['y**2 + y*x + x**2 + y*w + x*w', 'y**2*x + y*x**2 + y**2*w + x**2*w + y*w**2 + x*w**2']},
(16,3) : {'steenrod': [['z*x', 'z**2'], ['y*w', 'y**2'], ['x**2'], ['w**2'], ['0', 'v**2']], 'degrees': [2, 2, 1, 1, 2], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['x**2 + w**2', 'x**2 + x*w', 'z*x + y*x + z*w + y*w + x*v + w*v', 'z**2 + y**2 + x**2*v + v**2']},
(16,4) : {'steenrod': [['0', 'z**2'], ['y*w', 'y**2'], ['x**2'], ['w**2']], 'degrees': [2, 2, 1, 1], 'names': ['z', 'y', 'x', 'w'], 'relations': ['w**2', 'x**2 + x*w']},
(16,7) : {'steenrod': [['z**2'], ['y**2'], ['z*x', 'x**2']], 'degrees': [1, 1, 2], 'names': ['z', 'y', 'x'], 'relations': ['z*y + y**2']},
(16,9) : {'steenrod': [['z**2'], ['y**2'], ['0', '0', '0', 'x**2']], 'degrees': [1, 1, 4], 'names': ['z', 'y', 'x'], 'relations': ['z*y + y**2', 'z**3']},
(32,51) : {'steenrod': [['z**2'], ['y**2'], ['x**2'], ['w**2'], ['v**2']], 'degrees': [1, 1, 1, 1, 1], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': []},
(32,45) : {'steenrod': [['z**2'], ['y**2'], ['x**2'], ['0', 'w**2'], ['v**2']], 'degrees': [1, 1, 1, 2, 1], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['y**2 + x**2 + v**2']},
(32,21) : {'steenrod': [['z**2'], ['y**2'], ['0', 'x**2'], ['0', 'w**2'], ['v**2']], 'degrees': [1, 1, 2, 2, 1], 'names': ['z', 'y', 'x', 'w', 'v'], 'relations': ['z**2 + y**2', 'z**2 + v**2']},
(32,36) : {'steenrod': [['z**2'], ['y**2'], ['x**2'], ['0', 'w**2']], 'degrees': [1, 1, 1, 2], 'names': ['z', 'y', 'x', 'w'], 'relations': ['z**2 + x**2']},
(32,16) : {'steenrod': [['0', 'z**2'], ['y**2'], ['x**2']], 'degrees': [2, 1, 1], 'names': ['z', 'y', 'x'], 'relations': ['y**2 + x**2']},
(32,1) : {'steenrod': [['z**2'], ['0', 'y**2']], 'degrees': [1, 2], 'names': ['z', 'y'], 'relations': ['z**2']},
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}