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hmf_forms • Show schema
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{'deg': 2, 'dimension': 2, 'disc': 321, 'field_bad_primes': [3, 107], 'field_label': '2.2.321.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.321.1-4.1-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [2], 'level_ideal': '[4, 2, 2]', 'level_label': '4.1', 'level_norm': 4, 'parallel_weight': 2, 'short_label': '4.1-d', 'weight': '[2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[2, 2, w]', '-1/3*e - 1'], ['[2, 2, w + 1]', '-1/3*e']], 'hecke_eigenvalues': ['1/3*e + 1', '1/3*e', -2, 'e', 'e + 3', '4/3*e + 4', '-4/3*e', '-2*e', '-2*e - 6', '2/3*e', '-2/3*e - 2', '2/3*e', '-2/3*e - 2', 14, 9, -9, '10/3*e + 10', '-10/3*e', '-2*e', '-2*e - 6', -1, -1, 0, '-2*e - 6', '-2*e', -22, '7*e', '7*e + 21', '17/3*e', '-17/3*e - 17', 2, 2, '4*e + 12', '4*e', '7*e + 21', '7*e', '4*e', '4*e + 12', '-2*e - 6', '-2*e', 5, 5, '-25/3*e', '25/3*e + 25', '-8/3*e - 8', '8/3*e', '-19/3*e', '19/3*e + 19', -18, 18, '-2*e', '-2*e - 6', '-7/3*e', '7/3*e + 7', -18, 18, '4/3*e + 4', '-4/3*e', '10*e', '10*e + 30', '1/3*e + 1', '-1/3*e', 9, -9, '10/3*e + 10', '-10/3*e', '31/3*e + 31', '-31/3*e', 'e', 'e + 3', 36, -36, '10*e', '10*e + 30', '-22/3*e', '22/3*e + 22', -27, 27, 2, 2, 0, 0, '-5*e - 15', '-5*e', '-28/3*e', '28/3*e + 28', 8, 8, -9, 9, '-8*e - 24', '-8*e', '1/3*e + 1', '-1/3*e', 5, 5, '4*e', '4*e + 12', '-5*e - 15', '-5*e', '4*e + 12', '4*e', -37, '10/3*e + 10', '-10/3*e', '-2*e', '-2*e - 6', '13*e', '13*e + 39', '14/3*e', '-14/3*e - 14', '29/3*e', '-29/3*e - 29', '-8*e', '-8*e - 24', '10*e + 30', '10*e', '-8*e', '-8*e - 24', '-22/3*e', '22/3*e + 22', 18, -18, -45, 45, 14, 14, '-28/3*e', '28/3*e + 28', '-5*e', '-5*e - 15', '-8*e - 24', '-8*e', '19/3*e + 19', '-19/3*e', 27, -27, '-8*e', '-8*e - 24', 38, 38, '13*e + 39', '13*e', '-5*e', '-5*e - 15', -22, '-22/3*e', '22/3*e + 22', '-8*e', '-8*e - 24', '-16/3*e', '16/3*e + 16', '-2*e - 6', '-2*e', 36, -36, '4*e + 12', '4*e', '38/3*e', '-38/3*e - 38', -27, 27, 0, 0, 62, '-49/3*e', '49/3*e + 49', '4*e + 12', '4*e', '10*e', '10*e + 30', '-8/3*e - 8', '8/3*e'], 'hecke_polynomial': 'x^2 + 3*x + 9', 'label': '2.2.321.1-4.1-d'}
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hmf_fields • Show schema
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{'degree': 2, 'discriminant': 321, 'ideals': ['[1, 1, 1]', '[2, 2, w]', '[2, 2, w + 1]', '[3, 3, -2*w + 19]', '[4, 2, 2]', '[4, 4, w]', '[4, 4, w + 3]', '[5, 5, w]', '[5, 5, w + 4]', '[6, 6, w + 1]', '[6, 6, w + 4]', '[8, 4, 2*w]', '[8, 4, 2*w + 2]', '[8, 8, -w - 8]', '[8, 8, -w + 9]', '[9, 3, 3]', '[10, 10, -w + 10]', '[10, 10, w + 4]', '[10, 10, w + 5]', '[10, 10, w + 9]', '[12, 6, -4*w + 38]', '[12, 12, w + 4]', '[12, 12, w + 7]', '[13, 13, w + 1]', '[13, 13, w + 11]', '[15, 15, w + 4]', '[15, 15, w + 10]', '[16, 4, 4]', '[16, 8, 2*w]', '[16, 8, 2*w + 6]', '[16, 16, w]', '[16, 16, w + 15]', '[17, 17, w + 3]', '[17, 17, w + 13]', '[18, 6, 3*w]', '[18, 6, 3*w + 3]', '[19, 19, w + 6]', '[19, 19, w + 12]', '[20, 10, 2*w]', '[20, 10, 2*w + 8]', '[20, 20, w]', '[20, 20, -3*w + 28]', '[20, 20, -3*w - 25]', '[20, 20, w + 19]', '[24, 12, 2*w + 2]', '[24, 12, 2*w + 8]', '[24, 24, -w - 7]', '[24, 24, -w + 8]', '[25, 5, 5]', '[25, 25, w + 5]', '[25, 25, w + 19]', '[26, 26, 5*w - 47]', '[26, 26, w + 11]', '[26, 26, w + 14]', '[26, 26, 5*w + 42]', '[27, 9, -6*w + 57]', '[30, 30, w + 4]', '[30, 30, w + 10]', '[30, 30, -w + 11]', '[30, 30, w + 25]', '[32, 8, 4*w]', '[32, 8, 4*w + 4]', '[32, 16, -2*w - 16]', '[32, 16, -2*w + 18]', '[32, 32, w + 15]', '[32, 32, w + 16]', '[34, 34, w + 3]', '[34, 34, 3*w - 29]', '[34, 34, -3*w - 26]', '[34, 34, w + 30]', '[36, 6, 6]', '[36, 12, 3*w]', '[36, 12, 3*w + 9]', '[37, 37, w + 2]', '[37, 37, w + 34]', '[38, 38, -w - 6]', '[38, 38, w + 12]', '[38, 38, w + 25]', '[38, 38, w - 7]', '[39, 39, w + 1]', '[39, 39, w + 37]', '[40, 20, -2*w + 20]', '[40, 20, 2*w + 8]', '[40, 20, 2*w + 10]', '[40, 20, 2*w + 18]', '[40, 40, w]', '[40, 40, w + 15]', '[40, 40, w + 24]', '[40, 40, w + 39]', '[45, 15, 3*w]', '[45, 15, 3*w + 12]', '[48, 12, -8*w + 76]', '[48, 24, 2*w + 8]', '[48, 24, 2*w + 14]', '[48, 48, w + 16]', '[48, 48, w + 31]', '[49, 7, -7]', '[50, 10, 5*w]', '[50, 10, 5*w + 5]', '[50, 50, -w - 5]', '[50, 50, w + 19]', '[50, 50, w + 30]', '[50, 50, -w + 6]', '[51, 51, w + 13]', '[51, 51, w + 37]', '[52, 26, 2*w + 2]', '[52, 26, 2*w + 22]', '[52, 52, -w - 11]', '[52, 52, w + 24]', '[52, 52, w + 27]', '[52, 52, w - 12]', '[54, 18, 3*w + 3]', '[54, 18, 3*w + 12]', '[57, 57, w + 25]', '[57, 57, w + 31]', '[59, 59, -4*w - 33]', '[59, 59, 4*w - 37]', '[60, 30, 2*w + 8]', '[60, 30, 2*w + 20]', '[60, 60, -w - 4]', '[60, 60, w + 19]', '[60, 60, w + 40]', '[60, 60, -w + 5]', '[61, 61, w + 28]', '[61, 61, w + 32]', '[64, 8, 8]', '[64, 16, 4*w]', '[64, 16, 4*w + 12]', '[64, 32, 2*w]', '[64, 32, 2*w + 30]', '[64, 64, -5*w + 48]', '[64, 64, 5*w + 43]', '[65, 65, w + 14]', '[65, 65, 2*w - 17]', '[65, 65, 2*w + 15]', '[65, 65, w + 50]', '[68, 34, 2*w + 6]', '[68, 34, 2*w + 26]', '[68, 68, w + 3]', '[68, 68, w + 20]', '[68, 68, w + 47]', '[68, 68, w - 4]', '[71, 71, w + 22]', '[71, 71, w + 48]', '[72, 12, 6*w]', '[72, 12, 6*w + 6]', '[72, 24, -3*w - 24]', '[72, 24, -3*w + 27]', '[74, 74, -w - 2]', '[74, 74, w + 34]', '[74, 74, w + 39]', '[74, 74, w - 3]', '[75, 15, -10*w + 95]', '[75, 75, w + 19]', '[75, 75, w + 55]', '[76, 38, 2*w + 12]', '[76, 38, 2*w + 24]', '[76, 76, -w - 12]', '[76, 76, w + 31]', '[76, 76, w + 44]', '[76, 76, -w + 13]', '[78, 78, w + 1]', '[78, 78, w + 37]', '[78, 78, w + 40]', '[78, 78, w - 2]', '[79, 79, 2*w - 21]', '[79, 79, 2*w + 19]', '[80, 20, 4*w]', '[80, 20, 4*w + 16]', '[80, 40, 2*w]', '[80, 40, -6*w + 56]', '[80, 40, -6*w - 50]', '[80, 40, 2*w + 38]', '[80, 80, -w]', '[80, 80, w + 15]', '[80, 80, w + 64]', '[80, 80, -w + 1]', '[81, 9, 9]', '[85, 85, w + 20]', '[85, 85, -4*w - 35]', '[85, 85, 4*w - 39]', '[85, 85, w + 64]', '[90, 30, -3*w + 30]', '[90, 30, 3*w + 12]', '[90, 30, 3*w + 15]', '[90, 30, 3*w + 27]', '[95, 95, w + 25]', '[95, 95, -8*w - 67]', '[95, 95, 8*w - 75]', '[95, 95, w + 69]', '[96, 24, 4*w + 4]', '[96, 24, 4*w + 16]', '[96, 48, -2*w - 14]', '[96, 48, -2*w + 16]', '[96, 96, w + 16]', '[96, 96, w + 79]', '[98, 14, 7*w]', '[98, 14, 7*w + 7]', '[100, 10, 10]', '[100, 20, 5*w]', '[100, 20, 5*w + 15]', '[100, 50, 2*w + 10]', '[100, 50, 2*w + 38]', '[100, 100, -7*w + 67]', '[100, 100, w + 44]', '[100, 100, w + 55]', '[100, 100, 7*w + 60]', '[102, 102, -w - 13]', '[102, 102, w + 37]', '[102, 102, w + 64]', '[102, 102, w - 14]', '[104, 52, 10*w - 94]', '[104, 52, 2*w + 22]', '[104, 52, 2*w + 28]', '[104, 52, 10*w + 84]', '[104, 104, w + 24]', '[104, 104, w + 40]', '[104, 104, w + 63]', '[104, 104, w + 79]', '[107, 107, 12*w - 113]', '[108, 18, -12*w + 114]', '[108, 36, 3*w + 12]', '[108, 36, 3*w + 21]', '[111, 111, w + 34]', '[111, 111, w + 76]', '[113, 113, w + 17]', '[113, 113, w + 95]', '[114, 114, w + 25]', '[114, 114, 31*w - 293]', '[114, 114, -5*w + 46]', '[114, 114, w + 88]', '[117, 39, 3*w + 3]', '[117, 39, 3*w + 33]', '[118, 118, w + 23]', '[118, 118, w + 35]', '[118, 118, w + 82]', '[118, 118, w + 94]', '[120, 60, 2*w + 8]', '[120, 60, 2*w + 20]', '[120, 60, -2*w + 22]', '[120, 60, 2*w + 50]', '[120, 120, w + 40]', '[120, 120, w + 55]', '[120, 120, w + 64]', '[120, 120, w + 79]', '[121, 11, -11]', '[122, 122, w + 28]', '[122, 122, -3*w + 26]', '[122, 122, 3*w + 23]', '[122, 122, w + 93]', '[125, 25, 5*w]', '[125, 25, 5*w + 20]', '[125, 125, -2*w + 15]', '[125, 125, -2*w - 13]', '[128, 16, 8*w]', '[128, 16, 8*w + 8]', '[128, 32, -4*w - 32]', '[128, 32, -4*w + 36]', '[128, 64, 2*w + 30]', '[128, 64, 2*w + 32]', '[128, 128, w + 47]', '[128, 128, w + 80]', '[130, 130, -w - 14]', '[130, 130, w + 24]', '[130, 130, w + 40]', '[130, 130, w + 50]', '[130, 130, w + 79]', '[130, 130, w + 89]', '[130, 130, w + 105]', '[130, 130, w - 15]', '[131, 131, w + 18]', '[131, 131, w + 112]', '[135, 45, 3*w + 12]', '[135, 45, 3*w + 30]', '[136, 68, 2*w + 6]', '[136, 68, 6*w - 58]', '[136, 68, -6*w - 52]', '[136, 68, 2*w + 60]', '[136, 136, w + 47]', '[136, 136, w + 64]', '[136, 136, w + 71]', '[136, 136, w + 88]', '[142, 142, 9*w - 86]', '[142, 142, w + 48]', '[142, 142, w + 93]', '[142, 142, -9*w - 77]', '[144, 12, 12]', '[144, 24, 6*w]', '[144, 24, 6*w + 18]', '[144, 48, 3*w]', '[144, 48, 3*w + 45]', '[147, 21, 14*w - 133]', '[148, 74, 2*w + 4]', '[148, 74, 2*w + 68]', '[148, 148, -3*w + 31]', '[148, 148, w + 71]', '[148, 148, w + 76]', '[148, 148, -3*w - 28]', '[150, 30, 5*w + 5]', '[150, 30, 5*w + 20]', '[150, 150, w + 19]', '[150, 150, -7*w + 65]', '[150, 150, -7*w - 58]', '[150, 150, w + 130]', '[151, 151, w + 43]', '[151, 151, w + 107]', '[152, 76, -2*w - 12]', '[152, 76, 2*w + 24]', '[152, 76, 2*w + 50]', '[152, 76, 2*w - 14]', '[152, 152, w + 31]', '[152, 152, w + 63]', '[152, 152, w + 88]', '[152, 152, w + 120]', '[153, 51, 3*w + 9]', '[153, 51, 3*w + 39]', '[156, 78, 2*w + 2]', '[156, 78, 2*w + 74]', '[156, 156, -5*w - 44]', '[156, 156, w + 76]', '[156, 156, w + 79]', '[156, 156, 5*w - 49]', '[158, 158, w + 29]', '[158, 158, w + 49]', '[158, 158, w + 108]', '[158, 158, w + 128]', '[160, 40, -4*w + 40]', '[160, 40, 4*w + 16]', '[160, 40, 4*w + 20]', '[160, 40, 4*w + 36]', '[160, 80, 2*w]', '[160, 80, 2*w + 30]', '[160, 80, 2*w + 48]', '[160, 80, 2*w + 78]', '[160, 160, w + 15]', '[160, 160, w + 79]', '[160, 160, w + 80]', '[160, 160, -w + 16]', '[162, 18, 9*w]', '[162, 18, 9*w + 9]', '[163, 163, 2*w - 23]', '[163, 163, -2*w - 21]', '[167, 167, w + 66]', '[167, 167, w + 100]', '[169, 13, 13]', '[169, 169, w + 27]', '[169, 169, w + 141]', '[170, 170, w + 20]', '[170, 170, w + 30]', '[170, 170, w + 54]', '[170, 170, 3*w + 22]', '[170, 170, 3*w - 25]', '[170, 170, w + 115]', '[170, 170, w + 139]', '[170, 170, w + 149]', '[171, 57, 3*w + 18]', '[171, 57, 3*w + 36]', '[173, 173, w + 59]', '[173, 173, w + 113]', '[177, 177, -2*w + 13]', '[177, 177, 2*w + 11]', '[179, 179, w + 60]', '[179, 179, w + 118]', '[180, 30, 6*w]', '[180, 30, 6*w + 24]', '[180, 60, 3*w]', '[180, 60, -9*w + 84]', '[180, 60, -9*w - 75]', '[180, 60, 3*w + 57]', '[183, 183, w + 28]', '[183, 183, w + 154]', '[185, 185, w + 34]', '[185, 185, -6*w - 49]', '[185, 185, 6*w - 55]', '[185, 185, w + 150]', '[190, 190, 23*w + 195]', '[190, 190, w + 44]', '[190, 190, w + 50]', '[190, 190, w + 69]', '[190, 190, w + 120]', '[190, 190, w + 139]', '[190, 190, w + 145]', '[190, 190, 23*w - 218]', '[191, 191, w + 21]', '[191, 191, w + 169]', '[192, 24, -16*w + 152]', '[192, 48, 4*w + 16]', '[192, 48, 4*w + 28]', '[192, 96, 2*w + 32]', '[192, 96, 2*w + 62]', '[192, 192, w + 16]', '[192, 192, -w + 17]', '[193, 193, 32*w - 303]', '[193, 193, 8*w - 77]', '[195, 195, 4*w - 35]', '[195, 195, w + 79]', '[195, 195, w + 115]', '[195, 195, 4*w + 31]', '[196, 14, 14]', '[196, 28, 7*w]', '[196, 28, 7*w + 21]', '[199, 199, w + 45]', '[199, 199, w + 153]', '[200, 20, 10*w]', '[200, 20, 10*w + 10]', '[200, 40, -5*w - 40]', '[200, 40, -5*w + 45]', '[200, 100, -2*w - 10]', '[200, 100, 2*w + 38]', '[200, 100, 2*w + 60]', '[200, 100, -2*w + 12]', '[200, 200, w + 55]', '[200, 200, w + 80]', '[200, 200, w + 119]', '[200, 200, w + 144]', '[204, 102, 2*w + 26]', '[204, 102, 2*w + 74]', '[204, 204, 11*w + 92]', '[204, 204, w + 88]', '[204, 204, w + 115]', '[204, 204, 11*w - 103]', '[208, 52, 4*w + 4]', '[208, 52, 4*w + 44]', '[208, 104, -2*w - 22]', '[208, 104, 2*w + 48]', '[208, 104, 2*w + 54]', '[208, 104, 2*w - 24]', '[208, 208, w + 63]', '[208, 208, -3*w - 29]', '[208, 208, 3*w - 32]', '[208, 208, w + 144]', '[213, 213, w + 22]', '[213, 213, w + 190]', '[214, 214, w + 53]', '[214, 214, w + 160]', '[216, 36, 6*w + 6]', '[216, 36, 6*w + 24]', '[216, 72, -3*w - 21]', '[216, 72, -3*w + 24]', '[221, 221, w + 37]', '[221, 221, -2*w + 11]', '[221, 221, -2*w - 9]', '[221, 221, w + 183]', '[222, 222, w + 34]', '[222, 222, -13*w + 122]', '[222, 222, 23*w - 217]', '[222, 222, w + 187]', '[223, 223, w + 52]', '[223, 223, w + 170]', '[225, 15, 15]', '[225, 75, 3*w + 15]', '[225, 75, 3*w + 57]', '[226, 226, -w - 17]', '[226, 226, w + 95]', '[226, 226, w + 130]', '[226, 226, w - 18]', '[228, 114, 2*w + 50]', '[228, 114, 2*w + 62]', '[228, 228, w + 31]', '[228, 228, 7*w - 68]', '[228, 228, 7*w + 61]', '[228, 228, w + 196]', '[234, 78, 15*w - 141]', '[234, 78, 3*w + 33]', '[234, 78, 3*w + 42]', '[234, 78, 15*w + 126]', '[236, 118, -8*w - 66]', '[236, 118, 8*w - 74]', '[236, 236, w + 23]', '[236, 236, w + 35]', '[236, 236, w + 200]', '[236, 236, w + 212]', '[237, 237, -4*w + 41]', '[237, 237, -4*w - 37]', '[240, 60, 4*w + 16]', '[240, 60, 4*w + 40]', '[240, 120, -2*w - 8]', '[240, 120, 2*w + 38]', '[240, 120, 2*w + 80]', '[240, 120, -2*w + 10]', '[240, 240, w + 64]', '[240, 240, -17*w - 143]', '[240, 240, -17*w + 160]', '[240, 240, w + 175]', '[241, 241, w + 85]', '[241, 241, w + 155]', '[242, 22, 11*w]', '[242, 22, 11*w + 11]', '[243, 27, -18*w + 171]', '[244, 122, 2*w + 56]', '[244, 122, 2*w + 64]', '[244, 244, 13*w - 124]', '[244, 244, w + 32]', '[244, 244, w + 211]', '[244, 244, 13*w + 111]', '[245, 35, 7*w]', '[245, 35, 7*w + 28]', '[247, 247, 6*w + 53]', '[247, 247, w + 63]', '[247, 247, w + 183]', '[247, 247, 6*w - 59]', '[250, 50, -5*w + 50]', '[250, 50, 5*w + 20]', '[250, 50, 5*w + 25]', '[250, 50, 5*w + 45]', '[250, 250, w + 55]', '[250, 250, w + 69]', '[250, 250, w + 180]', '[250, 250, w + 194]', '[255, 255, w + 64]', '[255, 255, 2*w - 25]', '[255, 255, -2*w - 23]', '[255, 255, w + 190]', '[256, 16, 16]', '[256, 32, 8*w]', '[256, 32, 8*w + 24]', '[256, 64, 4*w]', '[256, 64, 4*w + 60]', '[256, 128, -10*w + 96]', '[256, 128, 10*w + 86]', '[256, 256, w + 80]', '[256, 256, w + 175]', '[257, 257, 2*w - 9]', '[257, 257, -2*w - 7]', '[260, 130, 2*w + 28]', '[260, 130, 4*w - 34]', '[260, 130, 4*w + 30]', '[260, 130, 2*w + 100]', '[260, 260, w + 24]', '[260, 260, w + 40]', '[260, 260, 3*w - 23]', '[260, 260, w + 115]', '[260, 260, w + 144]', '[260, 260, 3*w + 20]', '[260, 260, w + 219]', '[260, 260, w + 235]', '[262, 262, -w - 18]', '[262, 262, w + 112]', '[262, 262, w + 149]', '[262, 262, w - 19]', '[269, 269, w + 101]', '[269, 269, w + 167]', '[270, 90, 3*w + 12]', '[270, 90, 3*w + 30]', '[270, 90, -3*w + 33]', '[270, 90, 3*w + 75]', '[271, 271, w + 104]', '[271, 271, w + 166]', '[272, 68, 4*w + 12]', '[272, 68, 4*w + 52]', '[272, 136, 2*w + 6]', '[272, 136, 2*w + 40]', '[272, 136, 2*w + 94]', '[272, 136, 2*w - 8]', '[272, 272, 7*w + 57]', '[272, 272, w + 64]', '[272, 272, w + 207]', '[272, 272, 7*w - 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869]', '[1910, 1910, w + 169]', '[1910, 1910, w + 360]', '[1910, 1910, 19*w - 174]', '[1910, 1910, w + 785]', '[1910, 1910, w + 1124]', '[1910, 1910, 19*w + 155]', '[1910, 1910, w + 1549]', '[1910, 1910, w + 1740]', '[1911, 273, 7*w + 7]', '[1911, 273, 7*w + 259]', '[1913, 1913, w + 62]', '[1913, 1913, w + 1850]', '[1916, 958, 2*w + 386]', '[1916, 958, 2*w + 570]', '[1916, 1916, w + 672]', '[1916, 1916, 5*w - 12]', '[1916, 1916, -5*w - 7]', '[1916, 1916, w + 1243]', '[1917, 639, 3*w + 66]', '[1917, 639, 3*w + 570]', '[1920, 240, 8*w + 32]', '[1920, 240, 8*w + 80]', '[1920, 240, -8*w + 88]', '[1920, 240, 8*w + 200]', '[1920, 480, 4*w + 160]', '[1920, 480, 4*w + 220]', '[1920, 480, 4*w + 256]', '[1920, 480, 4*w + 316]', '[1920, 960, 2*w + 158]', '[1920, 960, -26*w + 250]', '[1920, 960, 26*w + 224]', '[1920, 960, 2*w + 800]', '[1920, 1920, w + 175]', '[1920, 1920, 7*w + 73]', '[1920, 1920, -7*w + 80]', '[1920, 1920, w + 1744]', '[1921, 1921, w + 547]', '[1921, 1921, 40*w + 341]', '[1921, 1921, -40*w + 381]', '[1921, 1921, w + 1373]', '[1922, 62, 31*w]', '[1922, 62, 31*w + 31]', '[1923, 1923, w + 784]', '[1923, 1923, w + 1138]', '[1924, 962, 2*w + 152]', '[1924, 962, 32*w + 274]', '[1924, 962, 32*w - 306]', '[1924, 962, 2*w + 808]', '[1924, 1924, -57*w - 484]', '[1924, 1924, w + 219]', '[1924, 1924, w + 404]', '[1924, 1924, w + 700]', '[1924, 1924, w + 1223]', '[1924, 1924, w + 1519]', '[1924, 1924, w + 1704]', '[1924, 1924, -57*w + 541]', '[1926, 642, 3*w + 159]', '[1926, 642, 3*w + 480]', '[1928, 964, 2*w + 170]', '[1928, 964, 6*w - 34]', '[1928, 964, -6*w - 28]', '[1928, 964, 2*w + 792]', '[1928, 1928, w + 567]', '[1928, 1928, w + 808]', '[1928, 1928, w + 1119]', '[1928, 1928, w + 1360]', '[1929, 1929, w + 694]', '[1929, 1929, w + 1234]', '[1930, 1930, w + 274]', '[1930, 1930, w + 304]', '[1930, 1930, -3*w - 50]', '[1930, 1930, -17*w - 150]', '[1930, 1930, 17*w - 167]', '[1930, 1930, 3*w - 53]', '[1930, 1930, w + 1625]', '[1930, 1930, w + 1655]', '[1931, 1931, w + 340]', '[1931, 1931, w + 1590]', '[1934, 1934, -5*w - 6]', '[1934, 1934, w + 578]', '[1934, 1934, w + 1355]', '[1934, 1934, 5*w - 11]', '[1936, 44, 44]', '[1936, 88, 22*w]', '[1936, 88, 22*w + 66]', '[1936, 176, 11*w]', '[1936, 176, 11*w + 165]', '[1938, 1938, w + 88]', '[1938, 1938, 13*w - 131]', '[1938, 1938, w + 829]', '[1938, 1938, w + 880]', '[1938, 1938, w + 1057]', '[1938, 1938, w + 1108]', '[1938, 1938, 13*w + 118]', '[1938, 1938, w + 1849]', '[1941, 1941, 10*w - 83]', '[1941, 1941, 10*w + 73]', '[1942, 1942, w + 176]', '[1942, 1942, 29*w - 278]', '[1942, 1942, 89*w - 843]', '[1942, 1942, w + 1765]', '[1944, 108, 18*w + 18]', '[1944, 108, 18*w + 72]', '[1944, 216, -9*w - 63]', '[1944, 216, -9*w + 72]', '[1945, 1945, w + 445]', '[1945, 1945, w + 834]', '[1945, 1945, w + 1110]', '[1945, 1945, w + 1499]', '[1950, 390, 5*w + 5]', '[1950, 390, 5*w + 185]', '[1950, 390, 5*w + 200]', '[1950, 390, 5*w - 10]', '[1950, 1950, 37*w + 310]', '[1950, 1950, w + 469]', '[1950, 1950, w + 505]', '[1950, 1950, w + 544]', '[1950, 1950, w + 1405]', '[1950, 1950, w + 1444]', '[1950, 1950, w + 1480]', '[1950, 1950, 37*w - 347]', '[1951, 1951, w + 279]', '[1951, 1951, w + 1671]', '[1952, 488, 4*w + 112]', '[1952, 488, -12*w + 104]', '[1952, 488, 12*w + 92]', '[1952, 488, 4*w + 372]', '[1952, 976, 2*w + 64]', '[1952, 976, 2*w + 430]', '[1952, 976, 2*w + 544]', '[1952, 976, 2*w + 910]', '[1952, 1952, 7*w - 48]', '[1952, 1952, w + 943]', '[1952, 1952, w + 1008]', '[1952, 1952, -7*w - 41]', '[1956, 978, 160*w - 1514]', '[1956, 978, 16*w - 158]', '[1956, 1956, w + 559]', '[1956, 1956, w + 907]', '[1956, 1956, w + 1048]', '[1956, 1956, w + 1396]', '[1960, 140, 14*w - 140]', '[1960, 140, 14*w + 56]', '[1960, 140, 14*w + 70]', '[1960, 140, -14*w - 126]', '[1960, 280, 7*w]', '[1960, 280, 7*w + 105]', '[1960, 280, 7*w + 168]', '[1960, 280, 7*w + 273]', '[1963, 1963, -118*w - 999]', '[1963, 1963, w + 560]', '[1963, 1963, w + 1402]', '[1963, 1963, -118*w + 1117]', '[1964, 982, 2*w + 198]', '[1964, 982, 2*w + 782]', '[1964, 1964, w + 99]', '[1964, 1964, 5*w - 9]', '[1964, 1964, -5*w - 4]', '[1964, 1964, w + 1864]', '[1965, 1965, w + 280]', '[1965, 1965, -4*w - 55]', '[1965, 1965, 4*w - 59]', '[1965, 1965, w + 1684]', '[1966, 1966, -15*w - 134]', '[1966, 1966, w + 842]', '[1966, 1966, w + 1123]', '[1966, 1966, 15*w - 149]', '[1975, 395, 10*w - 105]', '[1975, 395, 10*w + 95]', '[1975, 1975, w + 444]', '[1975, 1975, w + 819]', '[1975, 1975, w + 1155]', '[1975, 1975, w + 1530]', '[1976, 988, 2*w + 100]', '[1976, 988, 18*w + 146]', '[1976, 988, 2*w + 366]', '[1976, 988, 2*w + 392]', '[1976, 988, 2*w + 594]', '[1976, 988, 2*w + 620]', '[1976, 988, -18*w + 164]', '[1976, 988, 2*w + 886]', '[1976, 1976, w + 63]', '[1976, 1976, w + 183]', '[1976, 1976, -25*w + 232]', '[1976, 1976, -5*w - 3]', '[1976, 1976, 5*w - 8]', '[1976, 1976, 25*w + 207]', '[1976, 1976, w + 1792]', '[1976, 1976, w + 1912]', '[1977, 1977, 122*w - 1153]', '[1977, 1977, -22*w + 203]', '[1983, 1983, 2*w - 49]', '[1983, 1983, -2*w - 47]', '[1985, 1985, w + 109]', '[1985, 1985, w + 684]', '[1985, 1985, w + 1300]', '[1985, 1985, w + 1875]', '[1986, 1986, w + 199]', '[1986, 1986, 5*w - 7]', '[1986, 1986, -5*w - 2]', '[1986, 1986, w + 1786]', '[1987, 1987, w + 614]', '[1987, 1987, w + 1372]', '[1989, 663, 3*w + 111]', '[1989, 663, -6*w + 33]', '[1989, 663, -6*w - 27]', '[1989, 663, 3*w + 549]', '[1990, 1990, -w - 45]', '[1990, 1990, w + 244]', '[1990, 1990, w + 750]', '[1990, 1990, w + 949]', '[1990, 1990, w + 1040]', '[1990, 1990, w + 1239]', '[1990, 1990, w + 1745]', '[1990, 1990, w - 46]', '[1994, 1994, -5*w - 1]', '[1994, 1994, w + 597]', '[1994, 1994, w + 1396]', '[1994, 1994, 5*w - 6]', '[1997, 1997, w + 911]', '[1997, 1997, w + 1085]', '[1998, 666, 3*w + 102]', '[1998, 666, -39*w + 366]', '[1998, 666, 69*w - 651]', '[1998, 666, 3*w + 561]', '[2000, 100, 20*w]', '[2000, 100, 20*w + 80]', '[2000, 200, 10*w]', '[2000, 200, -30*w + 280]', '[2000, 200, -30*w - 250]', '[2000, 200, 10*w + 190]', '[2000, 400, -5*w]', '[2000, 400, 5*w + 75]', '[2000, 400, 5*w + 320]', '[2000, 400, -5*w + 5]', '[2000, 500, -8*w + 60]', '[2000, 500, -8*w - 52]', '[2000, 1000, 2*w + 110]', '[2000, 1000, 2*w + 360]', '[2000, 1000, 2*w + 638]', '[2000, 1000, 2*w + 888]', '[2000, 2000, w + 319]', '[2000, 2000, w + 944]', '[2000, 2000, w + 1055]', '[2000, 2000, w + 1680]', '[2003, 2003, w + 456]', '[2003, 2003, w + 1546]', '[2004, 1002, 2*w + 200]', '[2004, 1002, 2*w + 800]', '[2004, 2004, w + 100]', '[2004, 2004, 5*w - 4]', '[2004, 2004, 5*w - 1]', '[2004, 2004, w + 1903]', '[2005, 2005, w + 699]', '[2005, 2005, w + 904]', '[2005, 2005, w + 1100]', '[2005, 2005, w + 1305]', '[2006, 2006, w + 200]', '[2006, 2006, w + 377]', '[2006, 2006, -13*w - 101]', '[2006, 2006, -5*w + 2]', '[2006, 2006, 5*w - 3]', '[2006, 2006, 13*w - 114]', '[2006, 2006, w + 1628]', '[2006, 2006, w + 1805]', '[2007, 669, 3*w + 156]', '[2007, 669, 3*w + 510]', '[2011, 2011, 6*w - 73]', '[2011, 2011, -6*w - 67]', '[2022, 2022, -163*w + 1541]', '[2022, 2022, w + 883]', '[2022, 2022, w + 1138]', '[2022, 2022, 17*w - 154]', '[2025, 45, 45]', '[2025, 225, 9*w + 45]', '[2025, 225, 9*w + 171]', '[2026, 2026, 5*w - 66]', '[2026, 2026, w + 620]', '[2026, 2026, w + 1405]', '[2026, 2026, -5*w - 61]', '[2028, 78, -52*w + 494]', '[2028, 156, 13*w + 52]', '[2028, 156, 13*w + 91]', '[2028, 1014, 2*w + 392]', '[2028, 1014, 2*w + 620]', '[2028, 2028, w + 196]', '[2028, 2028, -37*w + 353]', '[2028, 2028, 37*w + 316]', '[2028, 2028, w + 1831]', '[2033, 2033, w + 481]', '[2033, 2033, w + 1551]', '[2034, 678, -3*w - 51]', '[2034, 678, 3*w + 285]', '[2034, 678, 3*w + 390]', '[2034, 678, 3*w - 54]', '[2039, 2039, w + 278]', '[2039, 2039, w + 1760]', '[2040, 1020, 14*w - 124]', '[2040, 1020, 2*w + 230]', '[2040, 1020, 2*w + 278]', '[2040, 1020, 2*w + 380]', '[2040, 1020, 2*w + 638]', '[2040, 1020, 2*w + 740]', '[2040, 1020, 2*w + 788]', '[2040, 1020, 14*w + 110]', '[2040, 2040, w + 64]', '[2040, 2040, w + 319]', '[2040, 2040, 7*w + 40]', '[2040, 2040, 41*w + 344]', '[2040, 2040, 41*w - 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103]', '[2062, 2062, w + 1583]', '[2073, 2073, w + 91]', '[2073, 2073, w + 1981]', '[2074, 2074, w + 394]', '[2074, 2074, w + 455]', '[2074, 2074, 7*w - 81]', '[2074, 2074, w + 642]', '[2074, 2074, w + 1431]', '[2074, 2074, 7*w + 74]', '[2074, 2074, w + 1618]', '[2074, 2074, w + 1679]', '[2076, 1038, 2*w + 464]', '[2076, 1038, 2*w + 572]', '[2076, 2076, -43*w + 404]', '[2076, 2076, w + 751]', '[2076, 2076, w + 1324]', '[2076, 2076, 65*w - 613]', '[2078, 2078, 9*w - 71]', '[2078, 2078, w + 815]', '[2078, 2078, w + 1262]', '[2078, 2078, 9*w + 62]', '[2080, 520, -4*w - 56]', '[2080, 520, 4*w + 96]', '[2080, 520, 4*w + 160]', '[2080, 520, 4*w + 200]', '[2080, 520, 4*w + 316]', '[2080, 520, 4*w + 356]', '[2080, 520, 4*w + 420]', '[2080, 520, 4*w - 60]', '[2080, 1040, -2*w - 48]', '[2080, 1040, 42*w - 400]', '[2080, 1040, 2*w + 158]', '[2080, 1040, 2*w + 288]', '[2080, 1040, 2*w + 750]', '[2080, 1040, 2*w + 880]', '[2080, 1040, -42*w - 358]', '[2080, 1040, 2*w - 50]', '[2080, 2080, 47*w - 447]', '[2080, 2080, w + 144]', '[2080, 2080, w + 495]', '[2080, 2080, w + 560]', '[2080, 2080, w + 1519]', '[2080, 2080, w + 1584]', '[2080, 2080, w + 1935]', '[2080, 2080, -47*w - 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275]', '[9880, 9880, w + 4135]', '[9880, 9880, w + 5744]', '[9880, 9880, 27*w + 248]', '[9880, 9880, w + 6719]', '[9880, 9880, w + 7359]', '[9880, 9880, -41*w - 360]', '[9880, 9880, w + 7840]', '[9880, 9880, w + 8695]', '[9880, 9880, w + 9335]', '[9882, 1098, 9*w + 252]', '[9882, 1098, -27*w + 234]', '[9882, 1098, 27*w + 207]', '[9882, 1098, 9*w + 837]', '[9883, 9883, w + 314]', '[9883, 9883, w + 9568]', '[9885, 9885, w + 1159]', '[9885, 9885, w + 2794]', '[9885, 9885, w + 7090]', '[9885, 9885, w + 8725]', '[9886, 9886, w + 1767]', '[9886, 9886, w + 3175]', '[9886, 9886, w + 6710]', '[9886, 9886, w + 8118]', '[9887, 9887, w + 2649]', '[9887, 9887, w + 7237]', '[9892, 4946, 2*w + 344]', '[9892, 4946, 2*w + 4600]', '[9892, 9892, 109*w - 1036]', '[9892, 9892, w + 2300]', '[9892, 9892, w + 7591]', '[9892, 9892, 109*w + 927]', '[9899, 9899, 20*w - 159]', '[9899, 9899, w + 2571]', '[9899, 9899, w + 7327]', '[9899, 9899, -20*w - 139]', '[9901, 9901, w + 867]', '[9901, 9901, w + 9033]', '[9902, 9902, w + 385]', '[9902, 9902, 13*w - 67]', '[9902, 9902, -13*w - 54]', '[9902, 9902, w + 9516]', '[9914, 9914, w + 1219]', '[9914, 9914, w + 3737]', '[9914, 9914, w + 6176]', '[9914, 9914, w + 8694]', '[9915, 9915, w + 1015]', '[9915, 9915, w + 2950]', '[9915, 9915, w + 6964]', '[9915, 9915, w + 8899]', '[9924, 4962, 2*w + 1298]', '[9924, 4962, 2*w + 3662]', '[9924, 9924, 49*w + 403]', '[9924, 9924, w + 4312]', '[9924, 9924, w + 5611]', '[9924, 9924, 49*w - 452]', '[9925, 1985, 20*w + 195]', '[9925, 1985, -20*w + 215]', '[9925, 9925, w + 2094]', '[9925, 9925, w + 2669]', '[9925, 9925, w + 7255]', '[9925, 9925, w + 7830]', '[9930, 9930, w + 199]', '[9930, 9930, 73*w + 625]', '[9930, 9930, w + 2779]', '[9930, 9930, w + 4765]', '[9930, 9930, w + 5164]', '[9930, 9930, w + 7150]', '[9930, 9930, 73*w - 698]', '[9930, 9930, w + 9730]', '[9931, 9931, -10*w - 129]', '[9931, 9931, 10*w - 139]', '[9932, 4966, -152*w + 1434]', '[9932, 4966, 2*w + 1952]', '[9932, 4966, 2*w + 3012]', '[9932, 4966, -152*w - 1282]', '[9932, 9932, w + 976]', '[9932, 9932, w + 1740]', '[9932, 9932, -63*w + 587]', '[9932, 9932, w + 4223]', '[9932, 9932, w + 5708]', '[9932, 9932, -63*w - 524]', '[9932, 9932, w + 8191]', '[9932, 9932, w + 8955]', '[9934, 9934, w + 622]', '[9934, 9934, w + 4344]', '[9934, 9934, w + 5589]', '[9934, 9934, w + 9311]', '[9935, 9935, -16*w + 111]', '[9935, 9935, w + 3359]', '[9935, 9935, w + 6575]', '[9935, 9935, 16*w + 95]', '[9938, 9938, 41*w - 374]', '[9938, 9938, w + 3038]', '[9938, 9938, w + 6899]', '[9938, 9938, -41*w - 333]', '[9941, 9941, -22*w - 159]', '[9941, 9941, 22*w - 181]', '[9942, 9942, w + 508]', '[9942, 9942, w + 4462]', '[9942, 9942, w + 5479]', '[9942, 9942, w + 9433]', '[9943, 9943, w + 581]', '[9943, 9943, w + 1374]', '[9943, 9943, w + 8568]', '[9943, 9943, w + 9361]', '[9945, 3315, 3*w + 315]', '[9945, 3315, 3*w + 345]', '[9945, 3315, -24*w + 249]', '[9945, 3315, 3*w + 1437]', '[9945, 3315, 3*w + 1875]', '[9945, 3315, 24*w + 225]', '[9945, 3315, 3*w + 2967]', '[9945, 3315, 3*w + 2997]', '[9946, 9946, w + 315]', '[9946, 9946, w + 4657]', '[9946, 9946, w + 5288]', '[9946, 9946, w + 9630]', '[9949, 9949, w + 4542]', '[9949, 9949, w + 5406]', '[9950, 1990, 5*w + 225]', '[9950, 1990, 55*w + 455]', '[9950, 1990, 55*w - 510]', '[9950, 1990, 5*w + 1760]', '[9950, 9950, w + 244]', '[9950, 9950, w + 1944]', '[9950, 9950, w + 3030]', '[9950, 9950, 21*w - 170]', '[9950, 9950, 21*w + 149]', '[9950, 9950, w + 6919]', '[9950, 9950, w + 8005]', '[9950, 9950, w + 9705]', '[9952, 2488, -4*w - 104]', '[9952, 2488, 4*w + 1136]', '[9952, 2488, 4*w + 1348]', '[9952, 2488, 4*w - 108]', '[9952, 4976, 2*w + 1296]', '[9952, 4976, 2*w + 1918]', '[9952, 4976, 2*w + 3056]', '[9952, 4976, 2*w + 3678]', '[9952, 9952, w + 1839]', '[9952, 9952, 89*w - 848]', '[9952, 9952, -89*w - 759]', '[9952, 9952, w + 8112]', '[9953, 9953, 14*w - 83]', '[9953, 9953, w + 4405]', '[9953, 9953, w + 5547]', '[9953, 9953, -14*w - 69]', '[9956, 4978, 12*w - 46]', '[9956, 4978, 2*w + 1608]', '[9956, 4978, 2*w + 3368]', '[9956, 4978, -12*w - 34]', '[9956, 9956, w + 411]', '[9956, 9956, 25*w + 188]', '[9956, 9956, w + 1684]', '[9956, 9956, w + 2900]', '[9956, 9956, w + 7055]', '[9956, 9956, w + 8271]', '[9956, 9956, 25*w - 213]', '[9956, 9956, w + 9544]', '[9967, 9967, 46*w - 447]', '[9967, 9967, -46*w - 401]', '[9969, 9969, w + 4294]', '[9969, 9969, w + 5674]', '[9970, 9970, w + 399]', '[9970, 9970, w + 1594]', '[9970, 9970, w + 3390]', '[9970, 9970, -61*w - 525]', '[9970, 9970, -61*w + 586]', '[9970, 9970, w + 6579]', '[9970, 9970, w + 8375]', '[9970, 9970, w + 9570]', '[9971, 767, -52*w - 429]', '[9971, 767, 52*w - 481]', '[9971, 9971, w + 141]', '[9971, 9971, w + 4873]', '[9971, 9971, w + 5097]', '[9971, 9971, w + 9829]', '[9984, 624, 16*w + 16]', '[9984, 624, 16*w + 592]', '[9984, 1248, -40*w - 352]', '[9984, 1248, 8*w + 608]', '[9984, 1248, 8*w + 632]', '[9984, 1248, 40*w - 392]', '[9984, 2496, 28*w - 284]', '[9984, 2496, 4*w + 1084]', '[9984, 2496, 4*w + 1408]', '[9984, 2496, -28*w - 256]', '[9984, 4992, 2*w + 1952]', '[9984, 4992, 2*w + 2336]', '[9984, 4992, 2*w + 2654]', '[9984, 4992, 2*w + 3038]', '[9984, 9984, w + 3664]', '[9984, 9984, -5*w - 107]', '[9984, 9984, 5*w - 112]', '[9984, 9984, w + 6319]', '[9985, 9985, w + 1085]', '[9985, 9985, 104*w + 885]', '[9985, 9985, 104*w - 989]', '[9985, 9985, w + 8899]', '[9990, 3330, -3*w - 102]', '[9990, 3330, 3*w + 435]', '[9990, 3330, 3*w + 1227]', '[9990, 3330, 3*w + 1560]', '[9990, 3330, 3*w + 1767]', '[9990, 3330, 3*w + 2100]', '[9990, 3330, 3*w + 2892]', '[9990, 3330, -3*w + 105]', '[9993, 9993, -8*w - 119]', '[9993, 9993, 8*w - 127]', '[9996, 714, 14*w + 182]', '[9996, 714, 14*w + 518]', '[9996, 1428, -77*w - 644]', '[9996, 1428, 7*w + 616]', '[9996, 1428, 7*w + 805]', '[9996, 1428, -77*w + 721]', '[10000, 100, 100]', '[10000, 200, 50*w]', '[10000, 200, 50*w + 150]', '[10000, 400, 25*w]', '[10000, 400, 25*w + 375]', '[10000, 500, 20*w + 100]', '[10000, 500, 20*w + 380]', '[10000, 1000, -70*w + 670]', '[10000, 1000, 10*w + 440]', '[10000, 1000, 10*w + 550]', '[10000, 1000, 70*w + 600]', '[10000, 2000, 5*w + 400]', '[10000, 2000, 15*w + 160]', '[10000, 2000, -15*w + 175]', '[10000, 2000, 5*w + 1595]', '[10000, 2500, 4*w + 720]', '[10000, 2500, 4*w + 1776]', '[10000, 5000, 2*w + 360]', '[10000, 5000, -22*w + 232]', '[10000, 5000, 22*w + 210]', '[10000, 5000, 2*w + 4638]', '[10000, 10000, 13*w + 147]', '[10000, 10000, w + 2944]', '[10000, 10000, w + 7055]', '[10000, 10000, -13*w + 160]'], 'label': '2.2.321.1', 'narrow_class_no': 6, 'primes': ['[2, 2, w]', '[2, 2, w + 1]', '[3, 3, -2*w + 19]', '[5, 5, w]', '[5, 5, w + 4]', '[13, 13, w + 1]', '[13, 13, w + 11]', '[17, 17, w + 3]', '[17, 17, w + 13]', '[19, 19, w + 6]', '[19, 19, w + 12]', '[37, 37, w + 2]', '[37, 37, w + 34]', '[49, 7, -7]', '[59, 59, -4*w - 33]', '[59, 59, 4*w - 37]', '[61, 61, w + 28]', '[61, 61, w + 32]', '[71, 71, w + 22]', '[71, 71, w + 48]', '[79, 79, 2*w - 21]', '[79, 79, 2*w + 19]', '[107, 107, 12*w - 113]', '[113, 113, w + 17]', '[113, 113, w + 95]', '[121, 11, -11]', '[131, 131, w + 18]', '[131, 131, w + 112]', '[151, 151, w + 43]', '[151, 151, w + 107]', '[163, 163, 2*w - 23]', '[163, 163, -2*w - 21]', '[167, 167, w + 66]', '[167, 167, w + 100]', '[173, 173, w + 59]', '[173, 173, w + 113]', '[179, 179, w + 60]', '[179, 179, w + 118]', '[191, 191, w + 21]', '[191, 191, w + 169]', '[193, 193, 32*w - 303]', '[193, 193, 8*w - 77]', '[199, 199, w + 45]', '[199, 199, w + 153]', '[223, 223, w + 52]', '[223, 223, w + 170]', '[241, 241, w + 85]', '[241, 241, w + 155]', '[257, 257, 2*w - 9]', '[257, 257, -2*w - 7]', '[269, 269, w + 101]', '[269, 269, w + 167]', '[271, 271, w + 104]', '[271, 271, w + 166]', '[281, 281, -10*w + 93]', '[281, 281, 38*w - 359]', '[283, 283, w + 98]', '[283, 283, w + 184]', '[311, 311, w + 26]', '[311, 311, w + 284]', '[313, 313, w + 36]', '[313, 313, w + 276]', '[317, 317, 2*w - 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71]', '[647, 647, 8*w + 63]', '[659, 659, 4*w - 27]', '[659, 659, -4*w - 23]', '[661, 661, 44*w - 417]', '[661, 661, 20*w - 191]', '[691, 691, w + 91]', '[691, 691, w + 599]', '[701, 701, w + 38]', '[701, 701, w + 662]', '[719, 719, w + 303]', '[719, 719, w + 415]', '[727, 727, w + 295]', '[727, 727, w + 431]', '[773, 773, -6*w - 43]', '[773, 773, 6*w - 49]', '[809, 809, w + 220]', '[809, 809, w + 588]', '[811, 811, -10*w - 89]', '[811, 811, 10*w - 99]', '[821, 821, w + 41]', '[821, 821, w + 779]', '[827, 827, w + 177]', '[827, 827, w + 649]', '[841, 29, -29]', '[859, 859, w + 318]', '[859, 859, w + 540]', '[863, 863, w + 42]', '[863, 863, w + 820]', '[883, 883, w + 173]', '[883, 883, w + 709]', '[887, 887, w + 73]', '[887, 887, w + 813]', '[911, 911, 8*w - 69]', '[911, 911, 8*w + 61]', '[929, 929, w + 251]', '[929, 929, w + 677]', '[937, 937, w + 372]', '[937, 937, w + 564]', '[947, 947, 12*w + 97]', '[947, 947, 12*w - 109]', '[953, 953, 6*w - 47]', '[953, 953, -6*w - 41]', '[961, 31, -31]', '[967, 967, w + 388]', '[967, 967, w + 578]', '[971, 971, w + 176]', '[971, 971, w + 794]', '[983, 983, w + 140]', '[983, 983, w + 842]', '[997, 997, w + 399]', '[997, 997, w + 597]']}
-
nf_fields • Show schema
Hide schema
{'class_group': [3], 'class_number': 3, 'cm': False, 'coeffs': [-80, -1, 1], 'conductor': 321, 'degree': 2, 'dirichlet_group': [1, 320], 'disc_abs': 321, 'disc_rad': 321, 'disc_sign': 1, 'frobs': [[2, [[1, 2]]], [3, [0]], [5, [[1, 2]]], [7, [[2, 1]]], [11, [[2, 1]]], [13, [[1, 2]]], [17, [[1, 2]]], [19, [[1, 2]]], [23, [[2, 1]]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[2, 1]]], [53, [[2, 1]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 17.916472867168917, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.321.1', 'local_algs': ['3.2.1.2', '107.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [3, 107], 'rd': 17.9164728672, 'regulator': {'__RealLiteral__': 0, 'data': '6.06377980031', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 24 a + 203 \\)'], 'used_grh': False, 'zk': ['1', 'a']}