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hmf_forms • Show schema
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{'deg': 2, 'dimension': 4, 'disc': 328, 'field_bad_primes': [2, 41], 'field_label': '2.2.328.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.328.1-1.1-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [], 'level_ideal': '[1, 1, 1]', 'level_label': '1.1', 'level_norm': 1, 'parallel_weight': 2, 'short_label': '1.1-d', 'weight': '[2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [], 'hecke_eigenvalues': ['1/2*e^3 + e^2 + 2*e - 1', 'e', '1/2*e^3 + e^2 + e - 2', '1/6*e^3 + 2/3*e^2 - 1/3*e + 2/3', '-2/3*e^3 - 5/3*e^2 - 5/3*e + 10/3', '1/6*e^3 + 2/3*e^2 + 2/3*e - 4/3', '-1/6*e^3 - 2/3*e^2 - 2/3*e - 2/3', '-1/6*e^3 - 2/3*e^2 + 7/3*e - 2/3', '5/3*e^3 + 11/3*e^2 + 11/3*e - 22/3', 'e^3 + 3*e^2 + 4*e - 2', '-e^2', -4, '4/3*e^3 + 10/3*e^2 + 10/3*e - 20/3', '-1/3*e^3 - 4/3*e^2 + 2/3*e - 4/3', '-e^3 - e^2 - 4*e + 2', '-2*e^3 - 5*e^2 - 8*e + 4', '-e^3 - 2*e^2 - 4*e + 2', -4, '4/3*e^3 + 10/3*e^2 + 10/3*e - 20/3', '-1/3*e^3 - 4/3*e^2 + 2/3*e - 4/3', '-7/6*e^3 - 14/3*e^2 - 23/3*e - 14/3', '-1/3*e^3 + 5/3*e^2 + 5/3*e - 10/3', 'e^3 + e^2 - 2*e - 6', '-e^3 - e^2 + 2*e + 4', '-5/6*e^3 - 10/3*e^2 - 4/3*e - 10/3', '11/6*e^3 + 16/3*e^2 + 16/3*e - 32/3', 'e^3 + e^2 - 2*e - 6', '-e^3 - e^2 + 2*e + 4', '-10/3*e^3 - 22/3*e^2 - 22/3*e + 44/3', '1/3*e^3 + 4/3*e^2 - 14/3*e + 4/3', '2*e^3 + 2*e^2 - 4*e - 4', '-2*e^3 - 2*e^2 + 4*e + 16', '-2*e^3 - 8*e^2 - 8*e + 4', '2*e^3 + 8*e^2 + 8*e - 4', '7/6*e^3 + 14/3*e^2 + 38/3*e + 14/3', '17/6*e^3 + 10/3*e^2 + 10/3*e - 20/3', '7/6*e^3 + 14/3*e^2 + 14/3*e - 28/3', '-7/6*e^3 - 14/3*e^2 - 14/3*e - 14/3', '2/3*e^3 + 8/3*e^2 + 5/3*e + 8/3', '-7/6*e^3 - 11/3*e^2 - 11/3*e + 22/3', '8/3*e^3 + 14/3*e^2 + 14/3*e - 28/3', '1/3*e^3 + 4/3*e^2 + 22/3*e + 4/3', '2/3*e^3 - 1/3*e^2 - 1/3*e + 2/3', '5/6*e^3 + 10/3*e^2 + 19/3*e + 10/3', 'e^3 + e^2 - 2*e - 24', '-e^3 - e^2 + 2*e - 14', '-14/3*e^3 - 17/3*e^2 - 17/3*e + 34/3', '-11/6*e^3 - 22/3*e^2 - 61/3*e - 22/3', '-2/3*e^3 - 8/3*e^2 - 26/3*e - 8/3', '-7/3*e^3 - 10/3*e^2 - 10/3*e + 20/3', 'e^3 - 2*e^2 + 4*e - 2', '5*e^3 + 14*e^2 + 20*e - 10', '-e^3 - e^2 - 4*e + 2', '-2*e^3 - 5*e^2 - 8*e + 4', -4, '16/3*e^3 + 22/3*e^2 + 22/3*e - 44/3', '5/3*e^3 + 20/3*e^2 + 62/3*e + 20/3', '5/6*e^3 + 4/3*e^2 + 4/3*e - 8/3', '1/6*e^3 + 2/3*e^2 + 8/3*e + 2/3', '-2/3*e^3 - 8/3*e^2 - 35/3*e - 8/3', '-23/6*e^3 - 19/3*e^2 - 19/3*e + 38/3', '-6*e^2', '6*e^3 + 18*e^2 + 24*e - 12', '29/6*e^3 + 43/3*e^2 + 43/3*e - 86/3', '-7/3*e^3 - 28/3*e^2 - 13/3*e - 28/3', '-2*e^3 - 12*e^2 - 8*e + 4', '6*e^3 + 20*e^2 + 24*e - 12', '-5*e^3 - 5*e^2 + 10*e + 28', '5*e^3 + 5*e^2 - 10*e - 22', '4*e^3 + 13*e^2 + 16*e - 8', '-e^3 - 7*e^2 - 4*e + 2', '10/3*e^3 + 40/3*e^2 + 58/3*e + 40/3', '-1/3*e^3 - 22/3*e^2 - 22/3*e + 44/3', '3*e^3 + 3*e^2 - 6*e - 12', '-3*e^3 - 3*e^2 + 6*e + 18', 0, 0, '1/6*e^3 + 2/3*e^2 + 2/3*e - 4/3', '-1/6*e^3 - 2/3*e^2 - 2/3*e - 2/3', '6*e^3 + 14*e^2 + 24*e - 12', '4*e^3 + 6*e^2 + 16*e - 8', 'e^3 - 2*e^2 + 4*e - 2', '5*e^3 + 14*e^2 + 20*e - 10', -18, -18, '-e^3 - e^2 + 2*e - 26', 'e^3 + e^2 - 2*e - 36', '-13/6*e^3 - 26/3*e^2 - 71/3*e - 26/3', '-16/3*e^3 - 19/3*e^2 - 19/3*e + 38/3', '23/6*e^3 + 40/3*e^2 + 40/3*e - 80/3', '-17/6*e^3 - 34/3*e^2 - 28/3*e - 34/3', '1/3*e^3 + 4/3*e^2 - 23/3*e + 4/3', '-29/6*e^3 - 31/3*e^2 - 31/3*e + 62/3', '-17/6*e^3 - 34/3*e^2 - 46/3*e - 34/3', '5/6*e^3 + 22/3*e^2 + 22/3*e - 44/3', '19/6*e^3 + 38/3*e^2 + 71/3*e + 38/3', '7/3*e^3 - 5/3*e^2 - 5/3*e + 10/3', '-2*e^3 - 2*e^2 + 4*e + 4', '2*e^3 + 2*e^2 - 4*e - 16', '-8/3*e^3 - 32/3*e^2 - 77/3*e - 32/3', '-29/6*e^3 - 13/3*e^2 - 13/3*e + 26/3', '7/6*e^3 + 14/3*e^2 + 65/3*e + 14/3', '22/3*e^3 + 37/3*e^2 + 37/3*e - 74/3', '6*e^3 + 20*e^2 + 24*e - 12', '-2*e^3 - 12*e^2 - 8*e + 4', '-2*e^3 - 14*e^2 - 8*e + 4', '8*e^3 + 26*e^2 + 32*e - 16', '-4*e^3 - 4*e^2 + 8*e + 26', '4*e^3 + 4*e^2 - 8*e - 14', -16, -16, '-13/6*e^3 - 26/3*e^2 - 89/3*e - 26/3', '-25/3*e^3 - 37/3*e^2 - 37/3*e + 74/3', -24, -24, '-4/3*e^3 - 16/3*e^2 + 26/3*e - 16/3', '25/3*e^3 + 58/3*e^2 + 58/3*e - 116/3', '-11/6*e^3 - 22/3*e^2 - 25/3*e - 22/3', '4/3*e^3 + 19/3*e^2 + 19/3*e - 38/3', '13/3*e^3 + 1/3*e^2 + 1/3*e - 2/3', '25/6*e^3 + 50/3*e^2 + 101/3*e + 50/3', '-11/6*e^3 + 5/3*e^2 + 5/3*e - 10/3', '-8/3*e^3 - 32/3*e^2 - 59/3*e - 32/3', '-1/6*e^3 - 2/3*e^2 - 38/3*e - 2/3', '-35/6*e^3 - 34/3*e^2 - 34/3*e + 68/3', '-2*e^3 - 2*e^2 + 4*e + 40', '2*e^3 + 2*e^2 - 4*e + 20', '11/3*e^3 + 26/3*e^2 + 26/3*e - 52/3', '-2/3*e^3 - 8/3*e^2 + 10/3*e - 8/3', '-4*e^3 - 4*e^2 + 8*e + 44', '4*e^3 + 4*e^2 - 8*e + 4', 2, 2, '-17/3*e^3 - 38/3*e^2 - 38/3*e + 76/3', '2/3*e^3 + 8/3*e^2 - 22/3*e + 8/3', '-10/3*e^3 - 40/3*e^2 - 115/3*e - 40/3', '-55/6*e^3 - 35/3*e^2 - 35/3*e + 70/3', '2*e^3 - 2*e^2 + 8*e - 4', '8*e^3 + 22*e^2 + 32*e - 16', '10*e^3 + 24*e^2 + 40*e - 20', '6*e^3 + 8*e^2 + 24*e - 12', '7*e^3 + 24*e^2 + 28*e - 14', '-3*e^3 - 16*e^2 - 12*e + 6', '1/3*e^3 + 4/3*e^2 - 59/3*e + 4/3', '-65/6*e^3 - 67/3*e^2 - 67/3*e + 134/3', '-2*e^3 - 8*e + 4', '-6*e^3 - 16*e^2 - 24*e + 12', '-2*e^3 - 6*e^2 - 8*e + 4', '2*e^2', '-11/6*e^3 - 22/3*e^2 - 79/3*e - 22/3', '-23/3*e^3 - 35/3*e^2 - 35/3*e + 70/3', '4*e^3 + 18*e^2 + 16*e - 8', '-6*e^3 - 22*e^2 - 24*e + 12', '-4/3*e^3 - 34/3*e^2 - 34/3*e + 68/3', '13/3*e^3 + 52/3*e^2 + 70/3*e + 52/3'], 'hecke_polynomial': 'x^4 + 2*x^3 + 2*x^2 - 4*x + 4', 'label': '2.2.328.1-1.1-d'}
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hmf_fields • Show schema
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{'degree': 2, 'discriminant': 328, 'ideals': ['[1, 1, 1]', '[2, 2, w]', '[3, 3, w + 1]', '[3, 3, w + 2]', '[4, 2, 2]', '[6, 6, w + 2]', '[6, 6, w + 4]', '[8, 4, 2*w]', '[9, 3, 3]', '[9, 9, w + 1]', '[9, 9, w + 8]', '[11, 11, w + 4]', '[11, 11, w + 7]', '[12, 6, 2*w + 2]', '[12, 6, 2*w + 4]', '[13, 13, w + 2]', '[13, 13, w + 11]', '[16, 4, 4]', '[18, 6, 3*w]', '[18, 18, -w - 8]', '[18, 18, -w + 8]', '[19, 19, w + 5]', '[19, 19, w + 14]', '[22, 22, w + 4]', '[22, 22, w + 18]', '[23, 23, w + 6]', '[23, 23, w + 17]', '[24, 12, 2*w + 4]', '[24, 12, 2*w + 8]', '[25, 5, -5]', '[26, 26, w + 2]', '[26, 26, w + 24]', '[27, 9, 3*w + 3]', '[27, 9, 3*w + 6]', '[27, 27, w + 1]', '[27, 27, w + 26]', '[29, 29, w + 13]', '[29, 29, w + 16]', '[31, 31, w + 12]', '[31, 31, w + 19]', '[32, 8, 4*w]', '[33, 33, w + 4]', '[33, 33, -w - 7]', '[33, 33, -w + 7]', '[33, 33, w + 29]', '[36, 6, 6]', '[36, 18, 2*w + 2]', '[36, 18, 2*w + 16]', '[38, 38, w + 14]', '[38, 38, w + 24]', '[39, 39, w + 2]', '[39, 39, -w - 11]', '[39, 39, w - 11]', '[39, 39, w + 37]', '[41, 41, w]', '[44, 22, 2*w + 8]', '[44, 22, 2*w + 14]', '[46, 46, -w - 6]', '[46, 46, w - 6]', '[48, 12, 4*w + 4]', '[48, 12, 4*w + 8]', '[49, 7, -7]', '[50, 10, 5*w]', '[52, 26, 2*w + 4]', '[52, 26, 2*w + 22]', '[53, 53, w + 20]', '[53, 53, w + 33]', '[54, 18, 3*w + 6]', '[54, 18, 3*w + 12]', '[54, 54, w + 26]', '[54, 54, w + 28]', '[57, 57, w + 5]', '[57, 57, w + 14]', '[57, 57, w + 43]', '[57, 57, w - 5]', '[58, 58, w + 16]', '[58, 58, w + 42]', '[62, 62, -w - 12]', '[62, 62, -w + 12]', '[64, 8, 8]', '[66, 66, w + 4]', '[66, 66, w + 26]', '[66, 66, w + 40]', '[66, 66, w - 4]', '[67, 67, w + 22]', '[67, 67, w + 45]', '[69, 69, w + 17]', '[69, 69, w + 29]', '[69, 69, w + 40]', '[69, 69, w + 52]', '[72, 12, 6*w]', '[72, 36, -2*w - 16]', '[72, 36, -2*w + 16]', '[73, 73, -w - 3]', '[73, 73, w - 3]', '[75, 15, 5*w + 5]', '[75, 15, 5*w + 10]', '[76, 38, 2*w + 10]', '[76, 38, 2*w + 28]', '[78, 78, w + 2]', '[78, 78, w + 28]', '[78, 78, w + 50]', '[78, 78, w - 2]', '[81, 9, 9]', '[81, 27, 3*w + 3]', '[81, 27, 3*w + 24]', '[81, 81, w + 1]', '[81, 81, w - 1]', '[82, 82, -w]', '[87, 87, 4*w - 35]', '[87, 87, w + 16]', '[87, 87, w + 71]', '[87, 87, 4*w + 35]', '[88, 44, 2*w + 8]', '[88, 44, 2*w + 36]', '[92, 46, 2*w + 12]', '[92, 46, 2*w + 34]', '[93, 93, w + 19]', '[93, 93, w + 43]', '[93, 93, w + 50]', '[93, 93, w + 74]', '[96, 24, 4*w + 8]', '[96, 24, 4*w + 16]', '[98, 14, 7*w]', '[99, 33, 3*w + 12]', '[99, 33, 3*w + 21]', '[99, 99, w + 26]', '[99, 99, w + 37]', '[99, 99, w + 62]', '[99, 99, w + 73]', '[100, 10, -10]', '[101, 101, w + 48]', '[101, 101, w + 53]', '[103, 103, 2*w - 15]', '[103, 103, -2*w - 15]', '[104, 52, 2*w + 4]', '[104, 52, 2*w + 48]', '[106, 106, w + 20]', '[106, 106, w + 86]', '[108, 18, 6*w + 6]', '[108, 18, 6*w + 12]', '[108, 54, 2*w + 2]', '[108, 54, 2*w + 52]', '[109, 109, w + 54]', '[109, 109, w + 55]', '[113, 113, 2*w - 21]', '[113, 113, -2*w - 21]', '[114, 114, -w - 14]', '[114, 114, w + 52]', '[114, 114, w + 62]', '[114, 114, w - 14]', '[116, 58, 2*w + 26]', '[116, 58, 2*w + 32]', '[117, 39, 3*w + 6]', '[117, 39, 3*w + 33]', '[117, 117, w + 28]', '[117, 117, w + 37]', '[117, 117, w + 80]', '[117, 117, w + 89]', '[121, 11, 11]', '[121, 121, w + 18]', '[121, 121, w + 103]', '[123, 123, w + 41]', '[123, 123, w + 82]', '[124, 62, 2*w + 24]', '[124, 62, 2*w + 38]', '[127, 127, w + 35]', '[127, 127, w + 92]', '[128, 16, 8*w]', '[132, 66, 2*w + 8]', '[132, 66, -2*w - 14]', '[132, 66, -2*w + 14]', '[132, 66, 2*w + 58]', '[134, 134, w + 22]', '[134, 134, w + 112]', '[138, 138, w + 40]', '[138, 138, w + 52]', '[138, 138, w + 86]', '[138, 138, w + 98]', '[143, 143, w + 15]', '[143, 143, w + 37]', '[143, 143, w + 106]', '[143, 143, -w + 15]', '[144, 12, 12]', '[144, 36, 4*w + 4]', '[144, 36, 4*w + 32]', '[146, 146, w + 70]', '[146, 146, w + 76]', '[147, 21, 7*w + 7]', '[147, 21, 7*w + 14]', '[149, 149, w + 23]', '[149, 149, w + 126]', '[150, 30, 5*w + 10]', '[150, 30, 5*w + 20]', '[152, 76, 2*w + 28]', '[152, 76, 2*w + 48]', '[156, 78, 2*w + 4]', '[156, 78, -2*w - 22]', '[156, 78, 2*w - 22]', '[156, 78, 2*w + 74]', '[157, 157, w + 32]', '[157, 157, w + 125]', '[159, 159, w + 20]', '[159, 159, -2*w + 13]', '[159, 159, 2*w + 13]', '[159, 159, w + 139]', '[162, 18, 9*w]', '[162, 54, -3*w - 24]', '[162, 54, -3*w + 24]', '[162, 162, w + 80]', '[162, 162, w + 82]', '[164, 82, 2*w]', '[169, 13, 13]', '[169, 169, w + 63]', '[169, 169, w + 106]', '[171, 57, 3*w + 15]', '[171, 57, 3*w + 42]', '[171, 171, w + 62]', '[171, 171, w + 71]', '[171, 171, w + 100]', '[171, 171, w + 109]', '[174, 174, -w - 16]', '[174, 174, w + 74]', '[174, 174, w + 100]', '[174, 174, w - 16]', '[176, 44, 4*w + 16]', '[176, 44, 4*w + 28]', '[179, 179, w + 34]', '[179, 179, w + 145]', '[181, 181, w + 25]', '[181, 181, w + 156]', '[184, 92, -2*w - 12]', '[184, 92, 2*w - 12]', '[186, 186, w + 50]', '[186, 186, w + 74]', '[186, 186, w + 112]', '[186, 186, w + 136]', '[192, 24, 8*w + 8]', '[192, 24, 8*w + 16]', '[196, 14, -14]', '[198, 66, 3*w + 12]', '[198, 66, 3*w + 54]', '[198, 198, w + 26]', '[198, 198, w + 62]', '[198, 198, w + 136]', '[198, 198, w + 172]', '[200, 20, 10*w]', '[201, 201, w + 22]', '[201, 201, 2*w - 23]', '[201, 201, -2*w - 23]', '[201, 201, w + 179]', '[202, 202, w + 48]', '[202, 202, w + 154]', '[206, 206, w + 44]', '[206, 206, w + 162]', '[207, 69, 3*w + 18]', '[207, 69, 3*w + 51]', '[207, 207, -w - 17]', '[207, 207, 7*w + 65]', '[207, 207, 7*w - 65]', '[207, 207, -w + 17]', '[208, 52, 4*w + 8]', '[208, 52, 4*w + 44]', '[209, 209, -3*w + 23]', '[209, 209, w + 81]', '[209, 209, w + 128]', '[209, 209, -3*w - 23]', '[211, 211, w + 90]', '[211, 211, w + 121]', '[212, 106, 2*w + 40]', '[212, 106, 2*w + 66]', '[216, 36, 6*w + 12]', '[216, 36, 6*w + 24]', '[216, 108, 2*w + 52]', '[216, 108, 2*w + 56]', '[218, 218, w + 54]', '[218, 218, w + 164]', '[219, 219, w + 70]', '[219, 219, w + 76]', '[219, 219, w + 143]', '[219, 219, w + 149]', '[223, 223, -4*w - 33]', '[223, 223, 4*w - 33]', '[225, 15, 15]', '[225, 45, 5*w + 5]', '[225, 45, 5*w + 40]', '[226, 226, w + 46]', '[226, 226, w + 180]', '[227, 227, w + 38]', '[227, 227, w + 189]', '[228, 114, 2*w + 10]', '[228, 114, 2*w + 28]', '[228, 114, 2*w + 86]', '[228, 114, 2*w - 10]', '[229, 229, w + 51]', '[229, 229, w + 178]', '[232, 116, 2*w + 32]', '[232, 116, 2*w + 84]', '[234, 78, 3*w + 6]', '[234, 78, 3*w + 72]', '[234, 234, w + 28]', '[234, 234, w + 80]', '[234, 234, w + 154]', '[234, 234, w + 206]', '[241, 241, w + 75]', '[241, 241, w + 166]', '[242, 22, 11*w]', '[242, 242, -w - 18]', '[242, 242, w - 18]', '[243, 27, 9*w + 9]', '[243, 27, 9*w + 18]', '[243, 81, 3*w + 3]', '[243, 81, 3*w + 78]', '[243, 243, w + 80]', '[243, 243, w + 163]', '[246, 246, w + 82]', '[246, 246, w + 164]', '[247, 247, w + 24]', '[247, 247, -2*w + 9]', '[247, 247, -2*w - 9]', '[247, 247, w + 223]', '[248, 124, -2*w - 24]', '[248, 124, -2*w + 24]', '[253, 253, w + 29]', '[253, 253, w + 40]', '[253, 253, w + 213]', '[253, 253, w + 224]', '[254, 254, -5*w + 48]', '[254, 254, -5*w - 48]', '[256, 16, 16]', '[261, 87, 3*w + 39]', '[261, 87, 3*w + 48]', '[261, 261, w + 71]', '[261, 261, w + 100]', '[261, 261, w + 161]', '[261, 261, w + 190]', '[264, 132, 2*w + 8]', '[264, 132, 2*w + 52]', '[264, 132, 2*w + 80]', '[264, 132, 2*w - 8]', '[268, 134, 2*w + 44]', '[268, 134, 2*w + 90]', '[271, 271, w + 95]', '[271, 271, w + 176]', '[275, 55, 5*w + 20]', '[275, 55, 5*w + 35]', '[276, 138, 2*w + 34]', '[276, 138, 2*w + 58]', '[276, 138, 2*w + 80]', '[276, 138, 2*w + 104]', '[279, 93, 3*w + 36]', '[279, 93, 3*w + 57]', '[279, 279, -w - 19]', '[279, 279, 2*w - 7]', '[279, 279, -2*w - 7]', '[279, 279, -w + 19]', '[286, 286, -3*w - 32]', '[286, 286, w + 128]', '[286, 286, w + 158]', '[286, 286, 3*w - 32]', '[288, 24, 12*w]', '[288, 72, -4*w - 32]', '[288, 72, -4*w + 32]', '[289, 17, -17]', '[292, 146, -2*w - 6]', '[292, 146, 2*w - 6]', '[293, 293, w + 31]', '[293, 293, w + 262]', '[294, 42, 7*w + 14]', '[294, 42, 7*w + 28]', '[297, 99, 3*w + 12]', '[297, 99, -3*w - 21]', '[297, 99, -3*w + 21]', '[297, 99, 3*w + 87]', '[297, 297, w + 26]', '[297, 297, 2*w - 25]', '[297, 297, -2*w - 25]', '[297, 297, w + 271]', '[298, 298, w + 126]', '[298, 298, w + 172]', '[299, 299, w + 63]', '[299, 299, w + 132]', '[299, 299, w + 167]', '[299, 299, w + 236]', '[300, 30, 10*w + 10]', '[300, 30, 10*w + 20]', '[303, 303, w + 53]', '[303, 303, 2*w - 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nf_fields • Show schema
Hide schema
{'class_group': [4], 'class_number': 4, 'cm': False, 'coeffs': [-82, 0, 1], 'conductor': 328, 'degree': 2, 'dirichlet_group': [1, 245], 'disc_abs': 328, 'disc_rad': 82, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[1, 2]]], [5, [[2, 1]]], [7, [[2, 1]]], [11, [[1, 2]]], [13, [[1, 2]]], [17, [[2, 1]]], [19, [[1, 2]]], [23, [[1, 2]]], [29, [[1, 2]]], [31, [[1, 2]]], [37, [[2, 1]]], [41, [0]], [43, [[2, 1]]], [47, [[2, 1]]], [53, [[1, 2]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 18.110770276274835, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.328.1', 'local_algs': ['2.2.3.1', '41.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 41], 'rd': 18.1107702763, 'regulator': {'__RealLiteral__': 0, 'data': '2.89344398589', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 9 \\)'], 'used_grh': False, 'zk': ['1', 'a']}