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'11.02586450709934580027793378522677', '11.60895642450622763200767859345997', '12.65656296573071284450520735566011', '13.00499652022815517299775094807483', '13.22507792103989415095560813895415'], 'prelabel': '4-45e2-1.1-c9e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.814209449886274, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c9e2-0', 'trace_hash': 1180707416357399883, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45105038198193150584580212025', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46626957077382352071554309710', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.02883950645134132259172977111', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 537.1553728793658, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 2025, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, -19, 0, 429, 1250, 0, -11872, -19171, 0, -23750, -35488, 0, 143676, 225568, 0, 316109, -385156, 0, -403296, 536250, 0, 674272, -223704, 0, 1171875, -2729844, 0, -5093088, 74572, 0, -5027128, -6502275, 0, 7317964, -14840000, 0, 5373628, 7662624, 0, -23963750, -14211332, 0, 27748920, -15224352, 0, 4250376, -95966440, 0, 28708610, -22265625, 0, 61637004, 64305596, 0, -44360000, 227598112, 0, -1416868, -187863136, 0, 154080060, 95515432, 0, 219074349, 179595000, 0, 33592376, -165231924, 0, 281960000, 228270976, 0, -33122316, -102098932, 0, -173013984, 421313536, 0, -932406760, 395136250, 0, 270015308, -207040152, 0, -481445000, -527229480, 0, 680340448, -224518164, 0, -1705721472, -95969016, 0, 1823362360, -504120000, 0, 387134596, -545463590, 0, 502734375], 'euler11': [1, 35488, 526013014, 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34946659039493167390823397237402409], 'euler89': [1, 224518164, 610925899926766678, 78661376506047372181836276, 122749609618842355502421774953773681], 'euler97': [1, -387134596, -734969029248610362, -294311743758887408838947332, 577951262543040979328274795306257089], 'euler_factors': [[1, 19, -68, 9728, 262144], [1, 0, 0, 0, 0], [1, -1250, 390625, 0, 0], [1, 11872, 112235774, 479078022304, 1628413597910449], [1, 35488, 526013014, 83678847658208, 5559917313492231481], [1, -143676, 24105149134, -1523612051915148, 112455406951957393129], [1, 385156, 268539949078, 45674832160078532, 14063084452067724991009], [1, 403296, 684929514838, 130138657763479584, 104127350297911241532841], [1, 223704, -1375273107794, 402925054979918952, 3244150909895248285300369], [1, -74572, 28833430018078, -1081826889712503068, 210457284365172120330305161], [1, 5027128, 52415931233342, 132915364873329682888, 699053619999045038539170241], [1, -5373628, 231061724951934, -698366043891540029356, 16890053810563300749953435929], [1, 14211332, 443988635955862, 4652533360474798566052, 107178930967531784356353269521], [1, -27748920, 1170232974699430, -13946402181226501459560, 252599333573498060811820806649], [1, 95966440, 4320659216802910, 107398967399188303139480, 1252453015827223091648143056289], [1, -64305596, 6611083028543086, -212193264429936876636268, 10888439761782913818722623349689], [1, 187863136, 23071633420288438, 1627457561647404142428704, 75047496554032956760519149093721], [1, -154080060, 23302683905802238, -1801834731632650015328460, 136753052840548005895349735207881], [1, -33592376, -10819815556424362, -913932133097272866524072, 740195513856780056217081017732809], [1, -228270976, 45777616900481806, -10465882007137061512624256, 2102085018129621311776010144838961], [1, 33122316, 68371107952007926, 1949963298372649627046508, 3465863721549107204083472585375569], [1, 932406760, 453226630902929438, 111750438290982163135436440, 14364405059580771582276370834385761], [1, 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'4-45e2-1.1-c9e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.814209449886274, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c9e2-0', 'trace_hash': 1180707416357399883, 'z1': {'__RealLiteral__': 0, 'data': '1.45105038198193150584580212025', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1839424887680797022765633361516,3126368101716055078396411486098', 'Lhash_array': ['1839424887680797022765633361516', '3126368101716055078396411486098'], 'label': '4-45e2-1.1-c9e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/10/a/e'}