-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2000549635631717201095126659328', 'a10': 1, 'a2': -1, 'a3': -1, 'a4': 1, 'a5': -1, 'a6': 1, 'a7': 0, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.426087387979079, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1, 1]], [31, [1, 1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.1', 'coefficient_field': '1.1.1.1', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, 1], [1, 0, 7], [1, 4, 11], [1, -6, 13], [1, -2, 17], [1, 4, 19], [1, 4, 23], [1, -2, 29], [1, 1], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, -2, 53], [1, 4, 59], [1, 6, 61], [1, -16, 67], [1, 12, 71], [1, 6, 73], [1, 16, 79], [1, 12, 83], [1, 18, 89], [1, 14, 97], [1, -2, 101], [1, -8, 103], [1, -4, 107], [1, -6, 109], [1, 10, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 1], 1]], [[[1, 1], 1]], [[[1, 0, 7], 1]], [[[1, 4, 11], 1]], [[[1, -6, 13], 1]], [[[1, -2, 17], 1]], [[[1, 4, 19], 1]], [[[1, 4, 23], 1]], [[[1, -2, 29], 1]], [[[1, 1], 1]], [[[1, 2, 37], 1]], [[[1, 6, 41], 1]], [[[1, 4, 43], 1]], [[[1, 0, 47], 1]], [[[1, -2, 53], 1]], [[[1, 4, 59], 1]], [[[1, 6, 61], 1]], [[[1, -16, 67], 1]], [[[1, 12, 71], 1]], [[[1, 6, 73], 1]], [[[1, 16, 79], 1]], [[[1, 12, 83], 1]], [[[1, 18, 89], 1]], [[[1, 14, 97], 1]], [[[1, -2, 101], 1]], [[[1, -8, 103], 1]], [[[1, -4, 107], 1]], [[[1, -6, 109], 1]], [[[1, 10, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-930-1.1-c1-0-15', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/930/2/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-6.981439815023373e-119, 0.1912221270542871, 0.3817654601115051, 0.5691089519764793, 0.7475058504815244, 0.9073453161435383, 1.0353311538479992, 1.1154105904799951, 1.1303348897591106, 1.0637185841180055, 0.9024391304931066, 0.6391702643243891, 0.2747807361798083, -0.17972451918594015, -0.7020708603095068, -1.2587208160236913, -1.8062812669904498, -2.2944391853972212, -2.67036989032379, -2.8843413657988735, -2.89600819679535, -2.6806835370137767, -2.2347355715632893, -1.5792127666616598, -0.7608879311425979, 0.14986237450736486, 1.0645672408365272, 1.8853236408337222, 2.5158699217670066, 2.873851890748565, 2.90269737691717, 2.581340844573736, 1.930117480806969, 1.011504416863928, -0.07499018213751234, -1.2036657542795524, -2.2381567293829137, -3.0497470450732203, -3.5359147071294683, -3.636242224220621, -3.342968893249175, -2.704080105183635, -1.817876088599291, -0.8193017758867712, 0.14025640070456077, 0.9167405027037286, 1.3969424595224484, 1.5177226610199455, 1.2773488784600322, 0.7365521546619591, 0.008609895733472147, -0.7602574423064287, -1.4170080659448436, -1.8298376272801853, -1.9129651990562724, -1.6432814245617369, -1.0653209820396343, -0.28314014591957853, 0.5597800381453482, 1.3090131381089312, 1.8305709169242206, 2.0388466229568043, 1.9151818904925768, 1.5128054860320457, 0.9465787232542835, 0.36915868967636706, -0.061801951968577996, -0.21863105085326076, -0.03320431181857886, 0.48564179936234325, 1.2512078053882376, 2.1153991273429953, 2.899546719206411, 3.433170064610346, 3.592173945912849, 3.32773006520754, 2.6788768096906415, 1.7653730832760048, 0.7618345481095364, -0.14135163730639355, -0.781467919254093, -1.0610020292123394, -0.970044527308419, -0.5876522090658448, -0.06123337508507133, 0.43155940345114235, 0.7293650100237347, 0.7304863081459866, 0.4217889184361849, -0.11500054860565467, -0.7222777743126841, -1.2070604355738856, -1.3933947997606282, -1.173368894739129, -0.542991393698345, 0.3876706623552964, 1.4145801422176547, 2.2868262101773675, 2.7701439515857698, 2.7111984894224617, 2.0856799349882724, 1.0163300274879308, -0.24605620684611576, -1.3764097635503332, -2.052496526371775, -2.037106753446355, -1.2446182908287764, 0.2259916581185575, 2.1020210172213316, 3.991464988678332, 5.469524816372011, 6.177059954425186, 5.906984786708964, 4.656800652300095, 2.6333566267084083, 0.2076827240015856, -2.169626870326667, -4.0717924179012375, -5.192281928335122, -5.410220828251086, -4.808678315936931, -3.642030862832541, -2.2619718015687638, -1.0225589418509546, -0.18998953725274986, 0.11893467740266944, -0.04599865377800566, -0.49860886309948227, -0.9836030544023844, -1.2603204023665935, -1.1780049596959565, -0.7206157942714971, -0.008539866157980953, 0.7423941105055816, 1.2913466854588838, 1.4502545340552337, 1.1447542212137154, 0.43929232211114716, -0.4814088194948524, -1.368750640836988, -1.9868286502755232, -2.184992670958038, -1.943276361104949, -1.3759805686381898, -0.6919280613478045, -0.12386239297115056, 0.15030129451758562, 0.06853095452600187, -0.2926318439803783, -0.7423579004165016, -1.0401524200941448, -0.9805742702832135, -0.47036031837707526, 0.42837895160198003, 1.5051497733101298, 2.458649365281236, 2.9886229607139754, 2.8935911923705944, 2.1426788426503944, 0.8966667737484764, -0.5312592412194586, -1.7654046713190599, -2.481519794239069, -2.5091728413139243, -1.8890378135794046, -0.8647099578962216, 0.19102513001118732, 0.8943347615416362, 0.9765174586480524, 0.3777622823838189, -0.723100118256344, -1.9550099382794495, -2.8653144715022614, -3.061583064724456, -2.3403940091881443, -0.76162553727384, 1.3570205701711517, 3.5257287672717346, 5.223372116569879, 6.050155402699661, 5.844305260936306, 4.725827089698106, 3.0533092103958754, 1.3075883095096417, -0.06023874712111247, -0.7673058403177415, -0.77917682643394, -0.30610782937362546, 0.2825046332465082, 0.5961296067129771, 0.3666058477893775, -0.4517605008432534, -1.6598917549464367, -2.877563117916325, -3.6718740178882037, -3.707192437590114, -2.8654856240767503, -1.2955892421980313, 0.6261734848936751, 2.4115699715074936, 3.6138039953026064, 3.9672317782974207, 3.4666313455127407, 2.359843858669331, 1.0572317090396344, -0.010216778233093252, -0.535013779102452, -0.43022548343244793, 0.15288136513642697, 0.8908026070213051, 1.4122203105076134, 1.435550401119989, 0.8703864631385444, -0.15267261966124224, -1.3330105716863825, -2.3116397421115464, -2.801607394050687, -2.6890351566859296, -2.068174546174148, -1.1988182622560302, -0.4035334240647283, 0.05538675240270272, 0.07204783425732092, -0.27042606117198736, -0.7427336793167105, -1.0703093000232071, -1.0520562561158084, -0.6491828830134176, -0.007513494490813271, 0.5976155857103652, 0.874046416049931, 0.6394066173601547, -0.0894497950459215, -1.082748674970613, -1.9701337669830048, -2.3756422911113337, -2.0657774961007123, -1.053057807231981, 0.38859362534834163, 1.8085544378902076, 2.738193047477083, 2.867371457043656, 2.1724405107979012, 0.944033760394998, -0.3019905012805412, -1.0039607776201658, -0.7623284248424745, 0.49956082137435937, 2.4838029079990265, 4.599953266572645, 6.157285519175232, 6.602607658429287, 5.719968447112073, 3.719567812698059, 1.1809543029001714, -1.1330187946322798, -2.5285058914132184], 'positive_zeros': ['1.57815539650400176474671017268634', '3.10480934248580644535871888257442', '4.24169339874599851066555478594303', '5.48060746581028390822206046994885', '6.25138957092509924889691275064526', '7.16684503196615188101272461746620', '8.227015448372590527813033245190293', '8.511058036317142446114338783876062', '9.853371630582686648789462375202378'], 'prelabel': '2-930-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 2022489124566281697, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57815539650400176474671017269', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10480934248580644535871888257', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24169339874599851066555478594', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.426087387979079, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, -1, 1, 0, -1, 1, 1, -4, -1, 6, 0, 1, 1, 2, -1, -4, -1, 0, 4, -4, 1, 1, -6, -1, 0, 2, -1, -1, -1, 4, -2, 0, 1, -2, 4, -6, 1, -6, 0, -4, -4, -1, 4, 0, -1, -7, -1, -2, 6, 2, 1, 4, 0, 4, -2, -4, 1, -6, 1, 0, 1, -6, -4, 16, 2, 4, 0, -12, -1, -6, 2, -1, -4, 0, 6, -16, -1, 1, 6, -12, 0, -2, 4, -2, 4, -18, 1, 0, -4, 1, 0, 4, 1, -14, 7, -4, 1], 'euler11': [1, 4, 11], 'euler13': [1, -6, 13], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 4, 23], 'euler29': [1, -2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 1, 0], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, -2, 53], 'euler59': [1, 4, 59], 'euler61': [1, 6, 61], 'euler67': [1, -16, 67], 'euler7': [1, 0, 7], 'euler71': [1, 12, 71], 'euler73': [1, 6, 73], 'euler79': [1, 16, 79], 'euler83': [1, 12, 83], 'euler89': [1, 18, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 1, 0], [1, 0, 7], [1, 4, 11], [1, -6, 13], [1, -2, 17], [1, 4, 19], [1, 4, 23], [1, -2, 29], [1, 1, 0], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, -2, 53], [1, 4, 59], [1, 6, 61], [1, -16, 67], [1, 12, 71], [1, 6, 73], [1, 16, 79], [1, 12, 83], [1, 18, 89], [1, 14, 97]], 'index': 15, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/930/b', 'ModularForm/GL2/Q/holomorphic/930/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/930/2/a/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-930-1.1-c1-0-15', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-930-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2022489124566281697, 'z1': {'__RealLiteral__': 0, 'data': '1.57815539650400176474671017269', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 17863098
{'Lhash': '2000549635631717201095126659328', 'Lhash_array': ['2000549635631717201095126659328'], 'label': '2-930-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/a/b'}
-
id: 24551081
{'Lhash': '2000549635631717201095126659328', 'Lhash_array': ['2000549635631717201095126659328'], 'label': '2-930-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/a/b/1/1'}
-
id: 40596
{'Lhash': '2022489124566281697', 'Lhash_array': ['2022489124566281697'], 'label': '2-930-1.1-c1-0-15', 'type': 'ECQ', 'url': 'EllipticCurve/Q/930/b'}