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hmf_forms • Show schema
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{'deg': 2, 'dimension': 5, 'disc': 157, 'field_bad_primes': [157], 'field_label': '2.2.157.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.157.1-9.3-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [3], 'level_ideal': '[9,9,w + 5]', 'level_label': '9.3', 'level_norm': 9, 'parallel_weight': 2, 'short_label': '9.3-d', 'weight': '[2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[3,3,-w + 7]', -1]], 'hecke_eigenvalues': ['e', 0, '-5/3*e^4 - 3*e^3 + 13*e^2 + 35/3*e - 41/3', 'e^4 + 2*e^3 - 7*e^2 - 8*e + 6', '-e^4 - 2*e^3 + 7*e^2 + 8*e - 6', 'e^4 + 2*e^3 - 8*e^2 - 9*e + 9', 'e^4 + 2*e^3 - 8*e^2 - 9*e + 9', '3*e^4 + 5*e^3 - 23*e^2 - 18*e + 22', '-3*e^4 - 5*e^3 + 23*e^2 + 18*e - 22', '-1/3*e^4 + 4*e^2 - 5/3*e - 19/3', '-1/3*e^4 + 4*e^2 - 5/3*e - 19/3', '8/3*e^4 + 4*e^3 - 21*e^2 - 41/3*e + 41/3', '7/3*e^4 + 3*e^3 - 20*e^2 - 25/3*e + 58/3', '7/3*e^4 + 3*e^3 - 20*e^2 - 25/3*e + 58/3', '1/3*e^4 - 4*e^2 - 4/3*e + 10/3', '1/3*e^4 - 4*e^2 - 4/3*e + 10/3', '4*e^4 + 7*e^3 - 31*e^2 - 24*e + 28', '-4*e^4 - 7*e^3 + 31*e^2 + 24*e - 28', '-3*e^4 - 5*e^3 + 24*e^2 + 21*e - 18', '3*e^4 + 6*e^3 - 22*e^2 - 26*e + 17', '3*e^4 + 6*e^3 - 22*e^2 - 26*e + 17', '2*e^4 + 4*e^3 - 17*e^2 - 19*e + 24', '-2*e^4 - 4*e^3 + 17*e^2 + 19*e - 24', '4*e^4 + 6*e^3 - 33*e^2 - 23*e + 33', '-4*e^4 - 6*e^3 + 33*e^2 + 23*e - 33', '-4*e^2 - 5*e + 14', '4*e^2 + 5*e - 14', '-19/3*e^4 - 10*e^3 + 49*e^2 + 112/3*e - 130/3', '-19/3*e^4 - 10*e^3 + 49*e^2 + 112/3*e - 130/3', '-7*e^4 - 10*e^3 + 57*e^2 + 34*e - 50', '7*e^4 + 10*e^3 - 57*e^2 - 34*e + 50', '-25/3*e^4 - 14*e^3 + 66*e^2 + 163/3*e - 190/3', '-25/3*e^4 - 14*e^3 + 66*e^2 + 163/3*e - 190/3', '-12*e^4 - 20*e^3 + 92*e^2 + 70*e - 80', '-6*e^4 - 9*e^3 + 47*e^2 + 29*e - 42', '6*e^4 + 9*e^3 - 47*e^2 - 29*e + 42', '-8*e^4 - 14*e^3 + 64*e^2 + 56*e - 65', '8*e^4 + 14*e^3 - 64*e^2 - 56*e + 65', '-e^3 + 3*e^2 + 12*e - 10', '-e^3 + 3*e^2 + 12*e - 10', '-3*e^4 - 6*e^3 + 21*e^2 + 19*e - 8', '3*e^4 + 6*e^3 - 21*e^2 - 19*e + 8', '9*e^4 + 15*e^3 - 70*e^2 - 50*e + 62', '9*e^4 + 15*e^3 - 70*e^2 - 50*e + 62', '6*e^4 + 9*e^3 - 47*e^2 - 24*e + 50', '-6*e^4 - 9*e^3 + 47*e^2 + 24*e - 50', '-e^4 + e^3 + 10*e^2 - 6*e - 5', 'e^4 - e^3 - 10*e^2 + 6*e + 5', '-3*e^4 - 7*e^3 + 22*e^2 + 28*e - 22', '3*e^4 + 7*e^3 - 22*e^2 - 28*e + 22', '12*e^4 + 22*e^3 - 89*e^2 - 84*e + 81', '-12*e^4 - 22*e^3 + 89*e^2 + 84*e - 81', '26/3*e^4 + 17*e^3 - 67*e^2 - 209/3*e + 221/3', '26/3*e^4 + 17*e^3 - 67*e^2 - 209/3*e + 221/3', '-6*e^4 - 13*e^3 + 43*e^2 + 60*e - 41', '6*e^4 + 13*e^3 - 43*e^2 - 60*e + 41', '10/3*e^4 + 5*e^3 - 22*e^2 - 43/3*e - 5/3', '10/3*e^4 + 5*e^3 - 22*e^2 - 43/3*e - 5/3', '7*e^4 + 11*e^3 - 59*e^2 - 49*e + 74', '-7*e^4 - 11*e^3 + 59*e^2 + 49*e - 74', '-46/3*e^4 - 27*e^3 + 119*e^2 + 304/3*e - 370/3', '-46/3*e^4 - 27*e^3 + 119*e^2 + 304/3*e - 370/3', 'e^4 - 9*e^2 + 7*e + 15', '-e^4 + 9*e^2 - 7*e - 15', '-9*e^4 - 15*e^3 + 66*e^2 + 48*e - 60', '-9*e^4 - 15*e^3 + 66*e^2 + 48*e - 60', '-2*e^3 - e^2 + 18*e - 10', '2*e^3 + e^2 - 18*e + 10', '3*e^4 + 6*e^3 - 19*e^2 - 20*e + 12', '3*e^4 + 6*e^3 - 19*e^2 - 20*e + 12', '6*e^4 + 13*e^3 - 47*e^2 - 59*e + 49', '-6*e^4 - 13*e^3 + 47*e^2 + 59*e - 49', '4*e^4 + 9*e^3 - 30*e^2 - 33*e + 47', '-4*e^4 - 9*e^3 + 30*e^2 + 33*e - 47', '8*e^4 + 14*e^3 - 60*e^2 - 43*e + 47', '-8*e^4 - 14*e^3 + 60*e^2 + 43*e - 47', '8*e^4 + 14*e^3 - 59*e^2 - 47*e + 39', '-8*e^4 - 14*e^3 + 59*e^2 + 47*e - 39', '13*e^4 + 22*e^3 - 98*e^2 - 72*e + 72', '13*e^4 + 22*e^3 - 98*e^2 - 72*e + 72', 'e^4 + 4*e^3 - 3*e^2 - 26*e - 5', '-e^4 - 4*e^3 + 3*e^2 + 26*e + 5', '-e^3 - 8*e^2 + 25', 'e^3 + 8*e^2 - 25', 'e^4 + e^3 - 2*e^2 + 12*e - 20', 'e^4 + e^3 - 2*e^2 + 12*e - 20', '-25/3*e^4 - 14*e^3 + 61*e^2 + 151/3*e - 187/3', '-25/3*e^4 - 14*e^3 + 61*e^2 + 151/3*e - 187/3', '10/3*e^4 + 4*e^3 - 27*e^2 - 22/3*e - 8/3', '-47/3*e^4 - 23*e^3 + 124*e^2 + 242/3*e - 329/3', '-47/3*e^4 - 23*e^3 + 124*e^2 + 242/3*e - 329/3', '12*e^4 + 22*e^3 - 91*e^2 - 80*e + 90', '-12*e^4 - 22*e^3 + 91*e^2 + 80*e - 90', '-12*e^4 - 20*e^3 + 89*e^2 + 67*e - 79', '-12*e^4 - 20*e^3 + 89*e^2 + 67*e - 79', '35/3*e^4 + 19*e^3 - 94*e^2 - 215/3*e + 275/3', '35/3*e^4 + 19*e^3 - 94*e^2 - 215/3*e + 275/3', '10*e^4 + 22*e^3 - 69*e^2 - 92*e + 76', '-10*e^4 - 22*e^3 + 69*e^2 + 92*e - 76', '4*e^2 + 2*e - 29', '4*e^2 + 2*e - 29', '-4*e^4 - 11*e^3 + 27*e^2 + 55*e - 15', '4*e^4 + 11*e^3 - 27*e^2 - 55*e + 15', '11/3*e^4 + 5*e^3 - 30*e^2 - 29/3*e + 134/3', '11/3*e^4 + 5*e^3 - 30*e^2 - 29/3*e + 134/3', '-3*e^4 - 10*e^3 + 21*e^2 + 48*e - 36', '-3*e^4 - 10*e^3 + 21*e^2 + 48*e - 36', '5*e^4 + 6*e^3 - 40*e^2 - 25*e + 25', '-5*e^4 - 6*e^3 + 40*e^2 + 25*e - 25', '4*e^4 + 8*e^3 - 27*e^2 - 26*e + 35', '-4*e^4 - 8*e^3 + 27*e^2 + 26*e - 35', '-e^4 + 15*e^2 - 4*e - 45', 'e^4 - 15*e^2 + 4*e + 45', '-11*e^4 - 20*e^3 + 91*e^2 + 90*e - 100', '11*e^4 + 20*e^3 - 91*e^2 - 90*e + 100', '35/3*e^4 + 21*e^3 - 87*e^2 - 233/3*e + 278/3', '35/3*e^4 + 21*e^3 - 87*e^2 - 233/3*e + 278/3', '-11*e^4 - 23*e^3 + 81*e^2 + 101*e - 88', '11*e^4 + 23*e^3 - 81*e^2 - 101*e + 88', '9*e^4 + 11*e^3 - 77*e^2 - 28*e + 78', '9*e^4 + 11*e^3 - 77*e^2 - 28*e + 78', '-14*e^4 - 21*e^3 + 113*e^2 + 65*e - 110', '-14*e^4 - 21*e^3 + 113*e^2 + 65*e - 110', '-31/3*e^4 - 16*e^3 + 81*e^2 + 124/3*e - 265/3', '-31/3*e^4 - 16*e^3 + 81*e^2 + 124/3*e - 265/3', '-56/3*e^4 - 34*e^3 + 145*e^2 + 401/3*e - 455/3', '-56/3*e^4 - 34*e^3 + 145*e^2 + 401/3*e - 455/3', '-5*e^4 - 5*e^3 + 44*e^2 + 6*e - 44', '5*e^4 + 5*e^3 - 44*e^2 - 6*e + 44', '-14/3*e^4 - 10*e^3 + 33*e^2 + 155/3*e - 128/3', '-14/3*e^4 - 10*e^3 + 33*e^2 + 155/3*e - 128/3', '7*e^4 + 15*e^3 - 47*e^2 - 68*e + 35', '-7*e^4 - 15*e^3 + 47*e^2 + 68*e - 35', '-e^4 + 2*e^3 + 12*e^2 - 17*e - 20', 'e^4 - 2*e^3 - 12*e^2 + 17*e + 20', '20*e^4 + 32*e^3 - 161*e^2 - 126*e + 164', '-20*e^4 - 32*e^3 + 161*e^2 + 126*e - 164', '-e^4 + 8*e^2 - 2*e + 18', 'e^4 - 8*e^2 + 2*e - 18', '-8/3*e^4 - 2*e^3 + 17*e^2 - 13/3*e - 5/3', '-8/3*e^4 - 2*e^3 + 17*e^2 - 13/3*e - 5/3', '-11/3*e^4 - 4*e^3 + 29*e^2 + 8/3*e - 194/3', '34/3*e^4 + 14*e^3 - 94*e^2 - 130/3*e + 280/3', '34/3*e^4 + 14*e^3 - 94*e^2 - 130/3*e + 280/3', '-5*e^4 - 11*e^3 + 30*e^2 + 46*e - 8', '-5*e^4 - 11*e^3 + 30*e^2 + 46*e - 8', '-23*e^4 - 40*e^3 + 179*e^2 + 137*e - 176', '23*e^4 + 40*e^3 - 179*e^2 - 137*e + 176', '-20*e^4 - 32*e^3 + 162*e^2 + 114*e - 153', '20*e^4 + 32*e^3 - 162*e^2 - 114*e + 153', 'e^4 + e^3 - 10*e^2 - 7*e + 36', '-e^4 - e^3 + 10*e^2 + 7*e - 36', '9*e^4 + 13*e^3 - 75*e^2 - 45*e + 85', '-9*e^4 - 13*e^3 + 75*e^2 + 45*e - 85', '-11*e^4 - 20*e^3 + 80*e^2 + 68*e - 57', '-11*e^4 - 20*e^3 + 80*e^2 + 68*e - 57', '-e^4 - 3*e^3 + 4*e^2 + e + 25', 'e^4 + 3*e^3 - 4*e^2 - e - 25', '10*e^4 + 18*e^3 - 71*e^2 - 66*e + 56', '10*e^4 + 18*e^3 - 71*e^2 - 66*e + 56'], 'hecke_polynomial': 'x^5 + x^4 - 9*x^3 - x^2 + 12*x - 5', 'label': '2.2.157.1-9.3-d'}
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hmf_fields • Show schema
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{'degree': 2, 'discriminant': 157, 'ideals': ['[1, 1, 1]', '[3, 3, w + 6]', '[3, 3, -w + 7]', '[4, 2, 2]', '[9, 3, 3]', '[9, 9, -w + 6]', '[9, 9, -w - 5]', '[11, 11, -3*w - 17]', '[11, 11, 3*w - 20]', '[12, 6, 2*w + 12]', '[12, 6, -2*w + 14]', '[13, 13, 2*w - 13]', '[13, 13, 2*w + 11]', '[16, 4, 4]', '[17, 17, w + 7]', '[17, 17, -w + 8]', '[19, 19, -w - 4]', '[19, 19, -w + 5]', '[25, 5, 5]', '[27, 9, 3*w + 18]', '[27, 9, -3*w + 21]', '[27, 27, -w - 3]', '[27, 27, -w + 4]', '[31, 31, -6*w - 35]', '[31, 31, -6*w + 41]', '[33, 33, -w - 2]', '[33, 33, -w - 8]', '[33, 33, -w + 9]', '[33, 33, w - 3]', '[36, 6, 6]', '[36, 18, -2*w + 12]', '[36, 18, -2*w - 10]', '[37, 37, -w - 1]', '[37, 37, w - 2]', '[39, 39, w]', '[39, 39, 2*w - 15]', '[39, 39, -2*w - 13]', '[39, 39, w - 1]', '[44, 22, -6*w - 34]', '[44, 22, 6*w - 40]', '[47, 47, 3*w + 16]', '[47, 47, -3*w + 19]', '[48, 12, 4*w + 24]', '[48, 12, -4*w + 28]', '[49, 7, -7]', '[51, 51, w + 9]', '[51, 51, -5*w + 33]', '[51, 51, -5*w - 28]', '[51, 51, -w + 10]', '[52, 26, 4*w - 26]', '[52, 26, 4*w + 22]', '[57, 57, 7*w + 41]', '[57, 57, -2*w + 11]', '[57, 57, -2*w - 9]', '[57, 57, -7*w + 48]', '[64, 8, 8]', '[67, 67, 3*w - 22]', '[67, 67, -3*w - 19]', '[68, 34, 2*w + 14]', '[68, 34, -2*w + 16]', '[71, 71, -w - 10]', '[71, 71, w - 11]', '[75, 15, 5*w + 30]', '[75, 15, -5*w + 35]', '[76, 38, -2*w - 8]', '[76, 38, -2*w + 10]', '[81, 9, 9]', '[81, 27, -3*w + 18]', '[81, 27, -3*w - 15]', '[81, 81, -10*w - 57]', '[81, 81, -10*w + 67]', '[89, 89, -8*w - 47]', '[89, 89, 8*w - 55]', '[93, 93, -w - 11]', '[93, 93, 2*w - 9]', '[93, 93, -2*w - 7]', '[93, 93, -w + 12]', '[99, 33, -9*w - 51]', '[99, 33, 9*w - 60]', '[99, 99, 4*w + 21]', '[99, 99, 2*w - 17]', '[99, 99, 2*w + 15]', '[99, 99, -4*w + 25]', '[100, 10, 10]', '[101, 101, 4*w - 29]', '[101, 101, -4*w - 25]', '[108, 18, 6*w + 36]', '[108, 18, -6*w + 42]', '[108, 54, -2*w - 6]', '[108, 54, -2*w + 8]', '[109, 109, -3*w - 20]', '[109, 109, 3*w - 23]', '[111, 111, 8*w - 53]', '[111, 111, -5*w + 32]', '[111, 111, 5*w + 27]', '[111, 111, -8*w - 45]', '[113, 113, 3*w - 17]', '[113, 113, -3*w - 14]', '[117, 39, 6*w - 39]', '[117, 39, 6*w + 33]', '[117, 117, -w - 12]', '[117, 117, 7*w + 39]', '[117, 117, 7*w - 46]', '[117, 117, w - 13]', '[121, 11, 11]', '[121, 121, -2*w + 7]', '[121, 121, -2*w - 5]', '[124, 62, -12*w - 70]', '[124, 62, -12*w + 82]', '[127, 127, -9*w - 53]', '[127, 127, 9*w - 62]', '[132, 66, -2*w - 4]', '[132, 66, -2*w - 16]', '[132, 66, -2*w + 18]', '[132, 66, 2*w - 6]', '[141, 141, 5*w - 36]', '[141, 141, 2*w - 5]', '[141, 141, -2*w - 3]', '[141, 141, 5*w + 31]', '[143, 143, -w - 13]', '[143, 143, -3*w - 13]', '[143, 143, 3*w - 16]', '[143, 143, -w + 14]', '[144, 12, 12]', '[144, 36, -4*w + 24]', '[144, 36, -4*w - 20]', '[147, 21, -7*w - 42]', '[147, 21, 7*w - 49]', '[148, 74, -2*w - 2]', '[148, 74, 2*w - 4]', '[153, 51, 3*w + 21]', '[153, 51, -3*w + 24]', '[153, 153, -13*w - 74]', '[153, 153, -2*w + 3]', '[153, 153, -2*w - 1]', '[153, 153, -13*w + 87]', '[156, 78, 2*w]', '[156, 78, 4*w - 30]', '[156, 78, -4*w - 26]', '[156, 78, 2*w - 2]', '[157, 157, 2*w - 1]', '[167, 167, 2*w - 19]', '[167, 167, -2*w - 17]', '[169, 13, 13]', '[169, 169, -5*w - 26]', '[169, 169, -5*w + 31]', '[171, 57, -3*w - 12]', '[171, 57, -3*w + 15]', '[171, 171, w + 14]', '[171, 171, 10*w + 59]', '[171, 171, -10*w + 69]', '[171, 171, -w + 15]', '[173, 173, 13*w - 89]', '[173, 173, -13*w - 76]', '[176, 44, -12*w - 68]', '[176, 44, 12*w - 80]', '[187, 187, -6*w + 43]', '[187, 187, 4*w - 23]', '[187, 187, -4*w - 19]', '[187, 187, -6*w - 37]', '[188, 94, 6*w + 32]', '[188, 94, -6*w + 38]', '[192, 24, 8*w + 48]', '[192, 24, -8*w + 56]', '[193, 193, 11*w - 73]', '[193, 193, -11*w - 62]', '[196, 14, -14]', '[197, 197, 3*w - 14]', '[197, 197, -3*w - 11]', '[199, 199, 3*w - 25]', '[199, 199, -3*w - 22]', '[201, 201, -w - 15]', '[201, 201, 7*w - 45]', '[201, 201, 7*w + 38]', '[201, 201, w - 16]', '[204, 102, 2*w + 18]', '[204, 102, -10*w + 66]', '[204, 102, -10*w - 56]', '[204, 102, -2*w + 20]', '[208, 52, 8*w - 52]', '[208, 52, 8*w + 44]', '[209, 209, 9*w + 50]', '[209, 209, 5*w + 32]', '[209, 209, 5*w - 37]', '[209, 209, -9*w + 59]', '[213, 213, -4*w - 27]', '[213, 213, -17*w - 99]', '[213, 213, 17*w - 116]', '[213, 213, 4*w - 31]', '[221, 221, -11*w - 65]', '[221, 221, 3*w + 10]', '[221, 221, 3*w - 13]', '[221, 221, 11*w - 76]', '[225, 15, 15]', '[225, 45, -5*w + 30]', '[225, 45, -5*w - 25]', '[228, 114, 14*w + 82]', '[228, 114, -4*w + 22]', '[228, 114, -4*w - 18]', '[228, 114, -14*w + 96]', '[233, 233, -w - 16]', '[233, 233, w - 17]', '[239, 239, 7*w - 50]', '[239, 239, -7*w - 43]', '[243, 27, 9*w + 54]', '[243, 27, -9*w + 63]', '[243, 81, -3*w - 9]', '[243, 81, -3*w + 12]', '[243, 243, -2*w + 21]', '[243, 243, 2*w + 19]', '[247, 247, 16*w + 91]', '[247, 247, -3*w - 23]', '[247, 247, 3*w - 26]', '[247, 247, 16*w - 107]', '[256, 16, 16]', '[257, 257, 6*w + 31]', '[257, 257, -6*w + 37]', '[263, 263, 3*w - 11]', '[263, 263, -3*w - 8]', '[267, 267, -w - 17]', '[267, 267, 4*w + 17]', '[267, 267, 4*w - 21]', '[267, 267, w - 18]', '[268, 134, 6*w - 44]', '[268, 134, -6*w - 38]', '[272, 68, 4*w + 28]', '[272, 68, -4*w + 32]', '[275, 55, -15*w - 85]', '[275, 55, 15*w - 100]', '[277, 277, -12*w - 71]', '[277, 277, 12*w - 83]', '[279, 93, -18*w - 105]', '[279, 93, -18*w + 123]', '[279, 279, -5*w + 29]', '[279, 279, 5*w - 38]', '[279, 279, 5*w + 33]', '[279, 279, 5*w + 24]', '[281, 281, -3*w - 7]', '[281, 281, 3*w - 10]', '[283, 283, -7*w + 44]', '[283, 283, 7*w + 37]', '[284, 142, -2*w - 20]', '[284, 142, 2*w - 22]', '[289, 17, 17]', '[289, 289, -15*w + 103]', '[289, 289, 15*w + 88]', '[297, 99, -3*w - 6]', '[297, 99, -3*w - 24]', '[297, 99, -3*w + 27]', '[297, 99, 3*w - 9]', '[297, 297, 8*w - 57]', '[297, 297, -14*w + 93]', '[297, 297, 14*w + 79]', '[297, 297, 8*w + 49]', '[300, 30, 10*w + 60]', '[300, 30, -10*w + 70]', '[303, 303, -w - 18]', '[303, 303, 8*w + 43]', '[303, 303, 8*w - 51]', '[303, 303, w - 19]', '[304, 76, -4*w - 16]', '[304, 76, -4*w + 20]', '[311, 311, 3*w - 8]', '[311, 311, -3*w - 5]', '[313, 313, -13*w - 73]', '[313, 313, 13*w - 86]', '[317, 317, -9*w + 58]', '[317, 317, 9*w + 49]', '[323, 323, -3*w - 4]', '[323, 323, -12*w + 79]', '[323, 323, -12*w - 67]', '[323, 323, -3*w + 7]', '[324, 18, 18]', '[324, 54, -6*w + 36]', '[324, 54, -6*w - 30]', '[324, 162, -20*w - 114]', '[324, 162, -20*w + 134]', '[325, 65, 10*w - 65]', '[325, 65, 10*w + 55]', '[327, 327, 11*w + 61]', '[327, 327, 2*w - 23]', '[327, 327, -2*w - 21]', '[327, 327, 11*w - 72]', '[331, 331, -5*w - 23]', '[331, 331, 5*w - 28]', '[333, 111, -3*w - 3]', '[333, 111, 3*w - 6]', '[333, 333, -4*w + 33]', '[333, 333, 7*w + 44]', '[333, 333, 7*w - 51]', '[333, 333, -4*w - 29]', '[339, 339, 35*w - 236]', '[339, 339, -4*w + 19]', '[339, 339, 4*w + 15]', '[339, 339, -35*w - 201]', '[341, 341, -w - 19]', '[341, 341, -3*w + 5]', '[341, 341, -3*w - 2]', '[341, 341, w - 20]', '[347, 347, -3*w - 1]', '[347, 347, 3*w - 4]', '[349, 349, 3*w - 28]', '[349, 349, -3*w - 25]', '[351, 117, 3*w]', '[351, 117, 6*w - 45]', '[351, 117, -6*w - 39]', '[351, 117, 3*w - 3]', '[351, 351, -5*w - 34]', '[351, 351, 19*w - 130]', '[351, 351, -19*w - 111]', '[351, 351, 5*w - 39]', '[353, 353, 3*w - 2]', '[353, 353, 3*w - 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1]', '[37, 37, w - 2]', '[47, 47, 3*w + 16]', '[47, 47, -3*w + 19]', '[49, 7, -7]', '[67, 67, 3*w - 22]', '[67, 67, -3*w - 19]', '[71, 71, -w - 10]', '[71, 71, w - 11]', '[89, 89, -8*w - 47]', '[89, 89, 8*w - 55]', '[101, 101, 4*w - 29]', '[101, 101, -4*w - 25]', '[109, 109, -3*w - 20]', '[109, 109, 3*w - 23]', '[113, 113, 3*w - 17]', '[113, 113, -3*w - 14]', '[127, 127, -9*w - 53]', '[127, 127, 9*w - 62]', '[157, 157, 2*w - 1]', '[167, 167, 2*w - 19]', '[167, 167, -2*w - 17]', '[173, 173, 13*w - 89]', '[173, 173, -13*w - 76]', '[193, 193, 11*w - 73]', '[193, 193, -11*w - 62]', '[197, 197, 3*w - 14]', '[197, 197, -3*w - 11]', '[199, 199, 3*w - 25]', '[199, 199, -3*w - 22]', '[233, 233, -w - 16]', '[233, 233, w - 17]', '[239, 239, 7*w - 50]', '[239, 239, -7*w - 43]', '[257, 257, 6*w + 31]', '[257, 257, -6*w + 37]', '[263, 263, 3*w - 11]', '[263, 263, -3*w - 8]', '[277, 277, -12*w - 71]', '[277, 277, 12*w - 83]', '[281, 281, -3*w - 7]', '[281, 281, 3*w - 10]', '[283, 283, -7*w + 44]', '[283, 283, 7*w + 37]', '[311, 311, 3*w - 8]', '[311, 311, -3*w - 5]', '[313, 313, -13*w - 73]', '[313, 313, 13*w - 86]', '[317, 317, -9*w + 58]', '[317, 317, 9*w + 49]', '[331, 331, -5*w - 23]', '[331, 331, 5*w - 28]', '[347, 347, -3*w - 1]', '[347, 347, 3*w - 4]', '[349, 349, 3*w - 28]', '[349, 349, -3*w - 25]', '[353, 353, 3*w - 2]', '[353, 353, 3*w - 1]', '[389, 389, 6*w - 35]', '[389, 389, 6*w + 29]', '[419, 419, 2*w - 25]', '[419, 419, -2*w - 23]', '[431, 431, 10*w - 71]', '[431, 431, -10*w - 61]', '[457, 457, 27*w + 157]', '[457, 457, 27*w - 184]', '[461, 461, -4*w - 31]', '[461, 461, 4*w - 35]', '[467, 467, -w - 22]', '[467, 467, w - 23]', '[487, 487, 8*w + 41]', '[487, 487, -8*w + 49]', '[523, 523, -6*w - 41]', '[523, 523, 6*w - 47]', '[529, 23, -23]', '[547, 547, 4*w - 11]', '[547, 547, -4*w - 7]', '[557, 557, 28*w - 191]', '[557, 557, -28*w - 163]', '[571, 571, 20*w - 133]', '[571, 571, -20*w - 113]', '[577, 577, -3*w - 29]', '[577, 577, 3*w - 32]', '[593, 593, 19*w - 131]', '[593, 593, -19*w - 112]', '[601, 601, 5*w - 22]', '[601, 601, -5*w - 17]', '[617, 617, -18*w - 101]', '[617, 617, 18*w - 119]', '[619, 619, -4*w - 1]', '[619, 619, 4*w - 5]', '[631, 631, 17*w - 112]', '[631, 631, -17*w - 95]', '[641, 641, 15*w + 83]', '[641, 641, 15*w - 98]', '[647, 647, -17*w - 101]', '[647, 647, 17*w - 118]', '[653, 653, -11*w - 68]', '[653, 653, 11*w - 79]', '[659, 659, 5*w - 43]', '[659, 659, -5*w - 38]', '[661, 661, -25*w - 142]', '[661, 661, 25*w - 167]', '[677, 677, 13*w - 92]', '[677, 677, -13*w - 79]', '[709, 709, 5*w - 19]', '[709, 709, -5*w - 14]', '[727, 727, -9*w - 58]', '[727, 727, 9*w - 67]', '[733, 733, 7*w - 38]', '[733, 733, -7*w - 31]', '[739, 739, -18*w - 107]', '[739, 739, 18*w - 125]', '[743, 743, 2*w - 31]', '[743, 743, -2*w - 29]', '[769, 769, -3*w - 32]', '[769, 769, 3*w - 35]', '[773, 773, -w - 28]', '[773, 773, w - 29]', '[797, 797, 21*w - 139]', '[797, 797, -21*w - 118]', '[821, 821, -15*w + 97]', '[821, 821, 15*w + 82]', '[827, 827, 9*w - 53]', '[827, 827, -9*w - 44]', '[829, 829, -19*w - 106]', '[829, 829, 19*w - 125]', '[841, 29, -29]', '[853, 853, 9*w - 68]', '[853, 853, -9*w - 59]', '[907, 907, 3*w - 37]', '[907, 907, -3*w - 34]', '[911, 911, 5*w - 46]', '[911, 911, -5*w - 41]', '[929, 929, -6*w - 19]', '[929, 929, 6*w - 25]', '[941, 941, -20*w - 119]', '[941, 941, 20*w - 139]', '[953, 953, -w - 31]', '[953, 953, w - 32]', '[967, 967, 11*w + 56]', '[967, 967, -11*w + 67]', '[977, 977, 16*w - 113]', '[977, 977, -16*w - 97]', '[991, 991, -8*w - 35]', '[991, 991, 8*w - 43]']}
-
nf_fields • Show schema
Hide schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-39, -1, 1], 'conductor': 157, 'degree': 2, 'dirichlet_group': [1, 156], 'disc_abs': 157, 'disc_rad': 157, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [[1, 2]]], [5, [[2, 1]]], [7, [[2, 1]]], [11, [[1, 2]]], [13, [[1, 2]]], [17, [[1, 2]]], [19, [[1, 2]]], [23, [[2, 1]]], [29, [[2, 1]]], [31, [[1, 2]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[2, 1]]], [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': 12.529964086141668, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.157.1', 'local_algs': ['157.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [157], 'rd': 12.5299640861, 'regulator': {'__RealLiteral__': 0, 'data': '5.36131420646', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 17 a + 98 \\)'], 'used_grh': False, 'zk': ['1', 'a']}