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hmf_forms • Show schema
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{'deg': 2, 'dimension': 1, 'disc': 89, 'field_bad_primes': [89], 'field_label': '2.2.89.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.89.1-2.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2], 'level_ideal': '[2, 2, -w - 4]', 'level_label': '2.1', 'level_norm': 2, 'parallel_weight': 2, 'short_label': '2.1-a', 'weight': '[2, 2]'}
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hmf_hecke • Show schema
Hide schema
{'AL_eigenvalues': [['[2, 2, -w - 4]', 1]], 'hecke_eigenvalues': [-1, 2, -2, 3, -4, 5, 0, 2, 7, -7, -7, -1, -11, -6, 8, -2, -3, -13, 4, -6, 1, -4, -1, -2, -2, 18, -7, 15, 0, -7, 8, 9, 14, 17, 22, 2, 22, -14, 6, 6, 4, 9, -4, -14, -21, 9, -22, 13, -16, 24, 15, 0, -8, 12, -24, 16, 25, 20, -20, -10, -7, 8, -4, 11, 13, 8, 5, -20, -18, -33, 18, -17, -32, -12, -2, -8, -18, -16, 19, -3, 27, 5, -10, 6, -4, 30, -30, -30, 30, -9, -19, 12, 27, 14, 4, 38, -22, 14, 9, -6, 44, -29, -8, 12, -25, -10, -33, -8, -1, -36, -10, 20, -20, 10, 12, 32, -19, -14, -30, 20, -9, 41, -22, 13, -18, 52, 26, -14, 0, -35, -2, 18, 38, 8, 19, -6, 22, 47, 6, 26, -40, 40, 7, 12, 4, 54, 8, -8, 22, -17, 8, -23, -33, -5, 5, 37, 17, 12, -3, -18, -22, -52, 48, -22, 36, 16, -57, 48, 4, 54, 51, -54, 20, 10, -52, -37, 26, -54, 25, -10, -14, -14, -58, 12, -4, 66, 6, 16, -54, -24, 30, 10, -34, 26, -22, 33, 12, -53, -28, -18, -14, 6, -45, -20, -48, -48, 18, 8, -16, -54, -24, 31, 31, 24, -61, -4, 66, -28, -8, 30, -60, 46, -54, 0, -30, 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hmf_fields • Show schema
Hide schema
{'degree': 2, 'discriminant': 89, 'ideals': ['[1, 1, 1]', '[2, 2, -w - 4]', '[2, 2, -w + 5]', '[4, 2, 2]', '[4, 4, -5*w - 21]', '[4, 4, -5*w + 26]', '[5, 5, 4*w - 21]', '[5, 5, -4*w - 17]', '[8, 4, -2*w - 8]', '[8, 4, -2*w + 10]', '[8, 8, -w + 6]', '[8, 8, w + 5]', '[9, 3, 3]', '[10, 10, -3*w - 13]', '[10, 10, w + 3]', '[10, 10, w - 4]', '[10, 10, 3*w - 16]', '[11, 11, 2*w - 11]', '[11, 11, -2*w - 9]', '[16, 4, 4]', '[16, 8, -10*w - 42]', '[16, 8, -10*w + 52]', '[16, 16, -w - 2]', '[16, 16, -w + 3]', '[17, 17, -6*w - 25]', '[17, 17, -6*w + 31]', '[18, 6, -3*w - 12]', '[18, 6, -3*w + 15]', '[20, 10, 8*w - 42]', '[20, 10, -8*w - 34]', '[20, 20, w + 1]', '[20, 20, -w - 6]', '[20, 20, w - 7]', '[20, 20, w - 2]', '[22, 22, w]', '[22, 22, 13*w - 68]', '[22, 22, -13*w - 55]', '[22, 22, w - 1]', '[25, 5, 5]', '[25, 25, -2*w + 9]', '[25, 25, -2*w - 7]', '[32, 8, -4*w - 16]', '[32, 8, -4*w + 20]', '[32, 16, -2*w + 12]', '[32, 16, 2*w + 10]', '[32, 32, -7*w + 37]', '[32, 32, 7*w + 30]', '[34, 34, w + 7]', '[34, 34, -7*w - 29]', '[34, 34, -7*w + 36]', '[34, 34, -w + 8]', '[36, 6, 6]', '[36, 12, -15*w - 63]', '[36, 12, -15*w + 78]', '[40, 20, -6*w - 26]', '[40, 20, 2*w + 6]', '[40, 20, 2*w - 8]', '[40, 20, 6*w - 32]', '[40, 40, 11*w - 57]', '[40, 40, -3*w - 14]', '[40, 40, 3*w - 17]', '[40, 40, 11*w + 46]', '[44, 22, 4*w - 22]', '[44, 22, -4*w - 18]', '[44, 44, 3*w - 14]', '[44, 44, 5*w - 27]', '[44, 44, -5*w - 22]', '[44, 44, 3*w + 11]', '[45, 15, 12*w - 63]', '[45, 15, -12*w - 51]', '[47, 47, 24*w + 101]', '[47, 47, 24*w - 125]', '[49, 7, -7]', '[50, 10, -5*w - 20]', '[50, 10, -5*w + 25]', '[50, 50, w + 8]', '[50, 50, 17*w + 72]', '[50, 50, -17*w + 89]', '[50, 50, -w + 9]', '[53, 53, 2*w - 7]', '[53, 53, -2*w - 5]', '[55, 55, -8*w - 33]', '[55, 55, -2*w + 13]', '[55, 55, 2*w + 11]', '[55, 55, -8*w + 41]', '[64, 8, 8]', '[64, 16, -20*w - 84]', '[64, 16, -20*w + 104]', '[64, 32, -2*w - 4]', '[64, 32, -2*w + 6]', '[64, 64, -11*w + 58]', '[64, 64, 11*w + 47]', '[67, 67, 4*w - 19]', '[67, 67, 4*w + 15]', '[68, 34, -12*w - 50]', '[68, 34, -12*w + 62]', '[68, 68, w + 9]', '[68, 68, -3*w - 10]', '[68, 68, -3*w + 13]', '[68, 68, -w + 10]', '[71, 71, 16*w - 83]', '[71, 71, 16*w + 67]', '[72, 12, -6*w - 24]', '[72, 12, -6*w + 30]', '[72, 24, -3*w + 18]', '[72, 24, 3*w + 15]', '[73, 73, 2*w - 5]', '[73, 73, -2*w - 3]', '[79, 79, 10*w + 43]', '[79, 79, 10*w - 53]', '[80, 20, 16*w - 84]', '[80, 20, -16*w - 68]', '[80, 40, 2*w + 2]', '[80, 40, -2*w - 12]', '[80, 40, 2*w - 14]', '[80, 40, 2*w - 4]', '[80, 80, 9*w + 37]', '[80, 80, 29*w + 122]', '[80, 80, 29*w - 151]', '[80, 80, 9*w - 46]', '[81, 9, 9]', '[85, 85, -4*w - 19]', '[85, 85, 2*w - 3]', '[85, 85, 2*w + 1]', '[85, 85, 4*w - 23]', '[88, 44, 2*w]', '[88, 44, 26*w - 136]', '[88, 44, -26*w - 110]', '[88, 44, 2*w - 2]', '[88, 88, -w - 10]', '[88, 88, -21*w - 89]', '[88, 88, 21*w - 110]', '[88, 88, w - 11]', '[89, 89, 2*w - 1]', '[90, 30, -9*w - 39]', '[90, 30, 3*w + 9]', '[90, 30, 3*w - 12]', '[90, 30, 9*w - 48]', '[94, 94, 5*w - 24]', '[94, 94, 5*w - 28]', '[94, 94, -5*w - 23]', '[94, 94, 5*w + 19]', '[97, 97, 8*w - 43]', '[97, 97, 8*w + 35]', '[98, 14, 7*w + 28]', '[98, 14, 7*w - 35]', '[99, 33, 6*w - 33]', '[99, 33, -6*w - 27]', '[100, 10, 10]', '[100, 20, -25*w - 105]', '[100, 20, -25*w + 130]', '[100, 50, -4*w + 18]', '[100, 50, -4*w - 14]', '[100, 100, 7*w + 31]', '[100, 100, -13*w + 67]', '[100, 100, -13*w - 54]', '[100, 100, -7*w + 38]', '[106, 106, 15*w - 79]', '[106, 106, -3*w + 19]', '[106, 106, -3*w - 16]', '[106, 106, 15*w + 64]', '[107, 107, 2*w - 15]', '[107, 107, -2*w - 13]', '[109, 109, 10*w + 41]', '[109, 109, 10*w - 51]', '[110, 110, w + 11]', '[110, 110, -21*w + 109]', '[110, 110, -3*w + 11]', '[110, 110, -17*w - 71]', '[110, 110, -17*w + 88]', '[110, 110, -3*w - 8]', '[110, 110, -21*w - 88]', '[110, 110, -w + 12]', '[121, 11, 11]', '[121, 121, -34*w - 143]', '[121, 121, -34*w + 177]', '[125, 25, 20*w - 105]', '[125, 25, -20*w - 85]', '[125, 125, 6*w - 29]', '[125, 125, 6*w + 23]', '[128, 16, -8*w - 32]', '[128, 16, -8*w + 40]', '[128, 32, -4*w + 24]', '[128, 32, 4*w + 20]', '[128, 64, -14*w + 74]', '[128, 64, 14*w + 60]', '[128, 128, -3*w - 7]', '[128, 128, -3*w + 10]', '[131, 131, -4*w - 13]', '[131, 131, 4*w - 17]', '[134, 134, -w - 12]', '[134, 134, 43*w - 224]', '[134, 134, 43*w + 181]', '[134, 134, w - 13]', '[136, 68, 2*w + 14]', '[136, 68, -14*w - 58]', '[136, 68, -14*w + 72]', '[136, 68, -2*w + 16]', '[136, 136, 25*w + 106]', '[136, 136, -5*w - 18]', '[136, 136, -5*w + 23]', '[136, 136, -25*w + 131]', '[139, 139, -30*w + 157]', '[139, 139, 52*w - 271]', '[142, 142, 11*w + 45]', '[142, 142, -3*w - 17]', '[142, 142, 3*w - 20]', '[142, 142, 11*w - 56]', '[144, 12, 12]', '[144, 24, -30*w - 126]', '[144, 24, -30*w + 156]', '[144, 48, -3*w - 6]', '[144, 48, -3*w + 9]', '[146, 146, -5*w - 24]', '[146, 146, 13*w + 56]', '[146, 146, 13*w - 69]', '[146, 146, -5*w + 29]', '[153, 51, -18*w - 75]', '[153, 51, -18*w + 93]', '[157, 157, 26*w - 135]', '[157, 157, 26*w + 109]', '[158, 158, -19*w + 100]', '[158, 158, 3*w - 8]', '[158, 158, -3*w - 5]', '[158, 158, -19*w - 81]', '[160, 40, -12*w - 52]', '[160, 40, 4*w + 12]', '[160, 40, 4*w - 16]', '[160, 40, 12*w - 64]', '[160, 80, 22*w - 114]', '[160, 80, -6*w - 28]', '[160, 80, 6*w - 34]', '[160, 80, 22*w + 92]', '[160, 160, -w - 13]', '[160, 160, 7*w - 34]', '[160, 160, 7*w + 27]', '[160, 160, w - 14]', '[162, 18, -9*w - 36]', '[162, 18, -9*w + 45]', '[167, 167, 2*w - 17]', '[167, 167, -2*w - 15]', '[169, 13, -13]', '[170, 170, 39*w + 164]', '[170, 170, 11*w - 59]', '[170, 170, 7*w - 39]', '[170, 170, 3*w + 4]', '[170, 170, 3*w - 7]', '[170, 170, -7*w - 32]', '[170, 170, -11*w - 48]', '[170, 170, 39*w - 203]', '[173, 173, 4*w - 25]', '[173, 173, -4*w - 21]', '[176, 44, 8*w - 44]', '[176, 44, -8*w - 36]', '[176, 88, 6*w - 28]', '[176, 88, 10*w - 54]', '[176, 88, -10*w - 44]', '[176, 88, 6*w + 22]', '[176, 176, 5*w - 22]', '[176, 176, 15*w - 77]', '[176, 176, 15*w + 62]', '[176, 176, 5*w + 17]', '[178, 178, -9*w - 40]', '[178, 178, 9*w - 49]', '[179, 179, 12*w + 49]', '[179, 179, 12*w - 61]', '[180, 30, 24*w - 126]', '[180, 30, -24*w - 102]', '[180, 60, 3*w + 3]', '[180, 60, -3*w - 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171]', '[9629, 9629, 38*w + 131]', '[9629, 9629, 38*w - 169]', '[9661, 9661, -148*w + 779]', '[9661, 9661, 148*w + 631]', '[9679, 9679, 40*w - 181]', '[9679, 9679, 40*w + 141]', '[9697, 9697, 192*w + 815]', '[9697, 9697, -192*w + 1007]', '[9719, 9719, 72*w + 289]', '[9719, 9719, 72*w - 361]', '[9721, 9721, 350*w - 1823]', '[9721, 9721, 350*w + 1473]', '[9733, 9733, 82*w + 333]', '[9733, 9733, 82*w - 415]', '[9743, 9743, 112*w + 463]', '[9743, 9743, 112*w - 575]', '[9769, 9769, -40*w + 233]', '[9769, 9769, -40*w - 193]', '[9781, 9781, 28*w + 151]', '[9781, 9781, 28*w - 179]', '[9791, 9791, 24*w - 67]', '[9791, 9791, -24*w - 43]', '[9811, 9811, 220*w + 923]', '[9811, 9811, 220*w - 1143]', '[9829, 9829, 50*w + 189]', '[9829, 9829, 50*w - 239]', '[9839, 9839, 170*w + 723]', '[9839, 9839, -170*w + 893]', '[9857, 9857, 26*w - 85]', '[9857, 9857, -26*w - 59]', '[9859, 9859, 68*w - 339]', '[9859, 9859, 68*w + 271]', '[9871, 9871, 90*w + 391]', '[9871, 9871, 90*w - 481]', '[9883, 9883, 148*w - 765]', '[9883, 9883, 148*w + 617]', '[9887, 9887, 122*w - 645]', '[9887, 9887, 122*w + 523]', '[9901, 9901, 106*w + 437]', '[9901, 9901, 106*w - 543]', '[9923, 9923, 26*w - 171]', '[9923, 9923, -26*w - 145]', '[9929, 9929, -16*w - 117]', '[9929, 9929, 16*w - 133]', '[9967, 9967, 22*w - 155]', '[9967, 9967, -22*w - 133]', '[9973, 9973, -36*w - 179]', '[9973, 9973, -36*w + 215]']}
-
nf_fields • Show schema
Hide schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-22, -1, 1], 'conductor': 89, 'degree': 2, 'dirichlet_group': [1, 88], 'disc_abs': 89, 'disc_rad': 89, 'disc_sign': 1, 'frobs': [[2, [[1, 2]]], [3, [[2, 1]]], [5, [[1, 2]]], [7, [[2, 1]]], [11, [[1, 2]]], [13, [[2, 1]]], [17, [[1, 2]]], [19, [[2, 1]]], [23, [[2, 1]]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[2, 1]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[1, 2]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1], 'galois_label': '2T1', 'galt': 1, 'grd': 9.433981132056603, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.89.1', 'local_algs': ['89.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [89], 'rd': 9.43398113206, 'regulator': {'__RealLiteral__': 0, 'data': '6.90775627898', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 106 a + 447 \\)'], 'used_grh': False, 'zk': ['1', 'a']}