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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-3509, -11253, -4356, 13904, 9900, -4653, -4122, 531, 639, -19, -42, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 11078561287986328125, 'disc_rad': 165, 'disc_sign': 1, 'frobs': [[2, [[12, 1]]], [3, [0]], [5, [0]], [7, [[12, 1]]], [11, [0]], [13, [[12, 1]]], [17, [[4, 3]]], [19, [[2, 6]]], [23, [[12, 1]]], [29, [[3, 2], [1, 6]]], [31, [[3, 2], [1, 6]]], [37, [[4, 3]]], [41, [[6, 2]]], [43, [[12, 1]]], [47, [[12, 1]]], [53, [[4, 3]]], [59, [[3, 2], [1, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [194, 81, 72], 'galois_label': '12T73', 'galt': 73, 'grd': 118.99821203205568, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.12.11078561287986328125.1', 'local_algs': ['3.2.6.18a4.5', '5.3.4.9a1.1', '11.2.3.4a1.1', '11.6.1.0a1.1'], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 3, 'r2': 0, 'ramps': [3, 5, 11], 'rd': 38.6402813871, 'regulator': {'__RealLiteral__': 0, 'data': '387641.416817', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '1.4.-4.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{91725}{462239} a^{11} - \\frac{267422}{1386717} a^{10} - \\frac{3767616}{462239} a^{9} + \\frac{1926596}{462239} a^{8} + \\frac{56789486}{462239} a^{7} - \\frac{20089291}{1386717} a^{6} - \\frac{372047599}{462239} a^{5} - \\frac{63392780}{462239} a^{4} + \\frac{2914230638}{1386717} a^{3} + \\frac{325816700}{462239} a^{2} - \\frac{2155859662}{1386717} a - \\frac{986800807}{1386717} \\)', '\\( \\frac{700081}{5084629} a^{11} - \\frac{2096185}{15253887} a^{10} - \\frac{28690711}{5084629} a^{9} + \\frac{1388162}{462239} a^{8} + \\frac{431667573}{5084629} a^{7} - \\frac{172055399}{15253887} a^{6} - \\frac{256743691}{462239} a^{5} - \\frac{41260912}{462239} a^{4} + \\frac{22106167114}{15253887} a^{3} + \\frac{220554873}{462239} a^{2} - \\frac{1488207145}{1386717} a - \\frac{676833763}{1386717} \\)', '\\( \\frac{234357}{5084629} a^{11} - \\frac{705758}{15253887} a^{10} - \\frac{28748215}{15253887} a^{9} + \\frac{462763}{462239} a^{8} + \\frac{143935736}{5084629} a^{7} - \\frac{54185986}{15253887} a^{6} - \\frac{85513226}{462239} a^{5} - \\frac{14814646}{462239} a^{4} + \\frac{7360787483}{15253887} a^{3} + \\frac{76925464}{462239} a^{2} - \\frac{496764740}{1386717} a - \\frac{77647019}{462239} \\)', '\\( \\frac{184231732}{472870497} a^{11} - \\frac{184661129}{472870497} a^{10} - \\frac{7546546489}{472870497} a^{9} + \\frac{1344747947}{157623499} a^{8} + \\frac{113510529511}{472870497} a^{7} - \\frac{15140961029}{472870497} a^{6} - \\frac{247521381718}{157623499} a^{5} - \\frac{120015037397}{472870497} a^{4} + \\frac{1937246069329}{472870497} a^{3} + \\frac{58260774343}{42988227} a^{2} - \\frac{43411490566}{14329409} a - \\frac{59379083921}{42988227} \\)', '\\( \\frac{24912122}{472870497} a^{11} - \\frac{7697255}{157623499} a^{10} - \\frac{1028661896}{472870497} a^{9} + \\frac{165105616}{157623499} a^{8} + \\frac{15569800787}{472870497} a^{7} - \\frac{535807136}{157623499} a^{6} - \\frac{34120717270}{157623499} a^{5} - \\frac{17630340736}{472870497} a^{4} + \\frac{89442377128}{157623499} a^{3} + \\frac{8053902449}{42988227} a^{2} - \\frac{18177092789}{42988227} a - \\frac{8275003061}{42988227} \\)', '\\( \\frac{9183695}{157623499} a^{11} - \\frac{2307514}{42988227} a^{10} - \\frac{1137997247}{472870497} a^{9} + \\frac{536815799}{472870497} a^{8} + \\frac{17240319155}{472870497} a^{7} - \\frac{1567562863}{472870497} a^{6} - \\frac{113503422946}{472870497} a^{5} - \\frac{20934403348}{472870497} a^{4} + \\frac{298003927682}{472870497} a^{3} + \\frac{9148112698}{42988227} a^{2} - \\frac{20159404960}{42988227} a - \\frac{9235426108}{42988227} \\)', '\\( \\frac{60731384}{472870497} a^{11} - \\frac{60094132}{472870497} a^{10} - \\frac{2490808568}{472870497} a^{9} + \\frac{1308248171}{472870497} a^{8} + \\frac{37495794770}{472870497} a^{7} - \\frac{4774331554}{472870497} a^{6} - \\frac{245372667610}{472870497} a^{5} - \\frac{40500545347}{472870497} a^{4} + \\frac{639881695991}{472870497} a^{3} + \\frac{6448150479}{14329409} a^{2} - \\frac{14326889772}{14329409} a - \\frac{19623925783}{42988227} \\)', '\\( \\frac{57319751}{472870497} a^{11} - \\frac{18229179}{157623499} a^{10} - \\frac{2359367278}{472870497} a^{9} + \\frac{393069669}{157623499} a^{8} + \\frac{35615980885}{472870497} a^{7} - \\frac{1325251047}{157623499} a^{6} - \\frac{77874989279}{157623499} a^{5} - \\frac{40338850097}{472870497} a^{4} + \\frac{203620565310}{157623499} a^{3} + \\frac{18609816983}{42988227} a^{2} - \\frac{41159114530}{42988227} a - \\frac{18806063533}{42988227} \\)', '\\( \\frac{43508254}{472870497} a^{11} - \\frac{17453576}{157623499} a^{10} - \\frac{1747364063}{472870497} a^{9} + \\frac{1204299658}{472870497} a^{8} + \\frac{25883961236}{472870497} a^{7} - \\frac{558160385}{42988227} a^{6} - \\frac{167506344854}{472870497} a^{5} - \\frac{17138578279}{472870497} a^{4} + \\frac{434283537047}{472870497} a^{3} + \\frac{3955796609}{14329409} a^{2} - \\frac{29149109345}{42988227} a - \\frac{12765446611}{42988227} \\)', '\\( \\frac{93957037}{472870497} a^{11} - \\frac{34638205}{157623499} a^{10} - \\frac{1269176985}{157623499} a^{9} + \\frac{778257957}{157623499} a^{8} + \\frac{56771011534}{472870497} a^{7} - \\frac{3481810720}{157623499} a^{6} - \\frac{122971037242}{157623499} a^{5} - \\frac{50396588744}{472870497} a^{4} + \\frac{319474417753}{157623499} a^{3} + \\frac{28166810527}{42988227} a^{2} - \\frac{64415048152}{42988227} a - \\frac{9757374221}{14329409} \\)', '\\( \\frac{81569182}{472870497} a^{11} - \\frac{26079941}{157623499} a^{10} - \\frac{304351753}{42988227} a^{9} + \\frac{554349584}{157623499} a^{8} + \\frac{50410198222}{472870497} a^{7} - \\frac{1718860164}{157623499} a^{6} - \\frac{109907873916}{157623499} a^{5} - \\frac{61156815815}{472870497} a^{4} + \\frac{286268233357}{157623499} a^{3} + \\frac{27130972687}{42988227} a^{2} - \\frac{57759728617}{42988227} a - \\frac{27065774024}{42988227} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/3*a^6 + 1/3*a^3 + 1/3', '1/3*a^7 + 1/3*a^4 + 1/3*a', '1/3*a^8 + 1/3*a^5 + 1/3*a^2', '1/33*a^9 + 2/33*a^7 + 1/11*a^6 + 4/11*a^5 + 14/33*a^4 + 1/11*a^3 + 1/3*a + 1/3', '1/33*a^10 + 2/33*a^8 + 1/11*a^7 + 1/33*a^6 + 14/33*a^5 + 1/11*a^4 - 1/3*a^3 + 1/3*a^2 + 1/3*a - 1/3', '1/472870497*a^11 - 2952715/472870497*a^10 - 2423141/472870497*a^9 - 2704330/42988227*a^8 - 9007430/472870497*a^7 + 5389723/157623499*a^6 - 194282939/472870497*a^5 + 49918450/472870497*a^4 + 32046226/157623499*a^3 - 6398629/14329409*a^2 - 8146100/42988227*a + 9313030/42988227']}
Number field data - 12.12.11078561287986328125.1