Formats: - HTML - YAML - JSON - 2025-12-18T21:45:43.043747
Query: /api/lfunc_search/?_offset=0
Show schema

{'algebraic': True, 'analytic_conductor': 12.997833714117988, 'bad_primes': [7], 'central_character': '1.1', 'conductor': 49, 'conductor_radical': 7, 'degree': 4, 'dirichlet_coefficients': [1, -6, -86, -804, -2238, 516, -4802, 6792, -10466, 13428, 35316, 69144, -26530, 28812, 192468, 390896, -463920, 62796, -925426, 1799352, 412972, -211896, 778128, -584112, 1592058, 159180, 743470, 3860808, -10003584, -1154808, 2467260, -4007904, -3037176, 2783520, 10746876, 8414664, 30735552, 5552556, 2281580, -15200496, -19103448, -2477832, 4065100, -28394064, 23422908, -4668768, -82195020, -33617056, 17294403, -9552348, 39897120, 21330120, -55189812, -4460820, -79037208, -32615184, 79586636, 60021504, -7069218, -154744272, 44316386, -14803560, 50257732, -114406464, 59374140, 18223056, -241921336, 372991680, -66919008, -64481256, 206493816, -71085072, -499153188, -184413312, -136916988, 744042504, -169587432, -13689480, 468535096, -874825248, -118839749, 114620688, 444023958, -332029488, 1038252960, -24390600, 860308224, 239866272, 636267396, -140537448, 127397060, -625614912, -212184360, 493170120, 2071103388, 344679744, -1632716064, -103766418, -369617256, -1280014632], 'euler11': [1, -35316, 2892681078, -83273280655356, 5559917313492231481], 'euler13': [1, 26530, -1541163822, 281337368365690, 112455406951957393129], 'euler17': [1, 463920, 273833245726, 55015287664488240, 14063084452067724991009], 'euler19': [1, 925426, 858791487510, 298623585404828854, 104127350297911241532841], 'euler2': [1, 6, 840, 3072, 262144], 'euler23': [1, -778128, 3473691840430, -1401527318158881264, 3244150909895248285300369], 'euler29': [1, 10003584, 52302031706070, 145123453369867514496, 210457284365172120330305161], 'euler3': [1, 86, 17862, 1692738, 387420489], 'euler31': [1, -2467260, 49371575832542, -65233422172137131460, 699053619999045038539170241], 'euler37': [1, -30735552, 484209298874630, -3994445811482058477504, 16890053810563300749953435929], 'euler41': [1, 19103448, 602984827739166, 6254123759834445477528, 107178930967531784356353269521], 'euler43': [1, -4065100, 797231337676374, -2043089226784460479300, 252599333573498060811820806649], 'euler47': [1, 82195020, 3721245520696702, 91986951619291395620340, 1252453015827223091648143056289], 'euler5': [1, 2238, 3416586, 4371093750, 3814697265625], 'euler53': [1, 55189812, 3123778356606670, 182113332276004461468996, 10888439761782913818722623349689], 'euler59': [1, 7069218, 16866494212382134, 61240605975160230567702, 75047496554032956760519149093721], 'euler61': [1, -44316386, 21654336818123658, -518242292190429626534426, 136753052840548005895349735207881], 'euler67': [1, 241921336, 59516583718815510, 6581841149081627028289192, 740195513856780056217081017732809], 'euler7': [1, 4802, 5764801, 0, 0], 'euler71': [1, -206493816, 58491352612128526, -9467431871231282012692296, 2102085018129621311776010144838961], 'euler73': [1, 499153188, 178474458263805254, 29385940188050354732056644, 3465863721549107204083472585375569], 'euler79': [1, -468535096, 239633073722978334, -56154679029469288424023624, 14364405059580771582276370834385761], 'euler83': [1, -444023958, 333438010641681622, -83005952053423638664975074, 34946659039493167390823397237402409], 'euler89': [1, -636267396, 801539802340191990, -222920356658886359638945764, 122749609618842355502421774953773681], 'euler97': [1, 1632716064, 2180562419544849758, 1241241461817034856731545888, 577951262543040979328274795306257089], 'euler_factors': [[1, 6, 840, 3072, 262144], [1, 86, 17862, 1692738, 387420489], [1, 2238, 3416586, 4371093750, 3814697265625], [1, 4802, 5764801, 0, 0], [1, -35316, 2892681078, -83273280655356, 5559917313492231481], [1, 26530, -1541163822, 281337368365690, 112455406951957393129], [1, 463920, 273833245726, 55015287664488240, 14063084452067724991009], [1, 925426, 858791487510, 298623585404828854, 104127350297911241532841], [1, -778128, 3473691840430, -1401527318158881264, 3244150909895248285300369], [1, 10003584, 52302031706070, 145123453369867514496, 210457284365172120330305161], [1, -2467260, 49371575832542, -65233422172137131460, 699053619999045038539170241], [1, -30735552, 484209298874630, -3994445811482058477504, 16890053810563300749953435929], [1, 19103448, 602984827739166, 6254123759834445477528, 107178930967531784356353269521], [1, -4065100, 797231337676374, -2043089226784460479300, 252599333573498060811820806649], [1, 82195020, 3721245520696702, 91986951619291395620340, 1252453015827223091648143056289], [1, 55189812, 3123778356606670, 182113332276004461468996, 10888439761782913818722623349689], [1, 7069218, 16866494212382134, 61240605975160230567702, 75047496554032956760519149093721], [1, -44316386, 21654336818123658, -518242292190429626534426, 136753052840548005895349735207881], [1, 241921336, 59516583718815510, 6581841149081627028289192, 740195513856780056217081017732809], [1, -206493816, 58491352612128526, -9467431871231282012692296, 2102085018129621311776010144838961], [1, 499153188, 178474458263805254, 29385940188050354732056644, 3465863721549107204083472585375569], [1, -468535096, 239633073722978334, -56154679029469288424023624, 14364405059580771582276370834385761], [1, -444023958, 333438010641681622, -83005952053423638664975074, 34946659039493167390823397237402409], [1, -636267396, 801539802340191990, -222920356658886359638945764, 122749609618842355502421774953773681], [1, 1632716064, 2180562419544849758, 1241241461817034856731545888, 577951262543040979328274795306257089]], 'id': 9639349, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7/10/a/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-7e2-1.1-c9e2-0-0', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9, 9], 'order_of_vanishing': 2, 'prelabel': '4-7e2-1.1-c9e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8987498132052874, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c9e2-0', 'trace_hash': 231594098602202499, 'z1': {'__RealLiteral__': 0, 'data': '3.79837678420596625160071144778', 'prec': 103}}