-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -4, 'A5': 6, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -2, 'Lhash': '409437620317032020,448699003308363115', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-2.0, 0], 'a5': [2.6832815729997477, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 38.69270830911013, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[19, [1, 0, -1]], [41, [1, 6, 41]]], 'bad_primes': [19, 41], 'central_character': '606841.1', 'coefficient_field': '1.1.1.1', 'conductor': 606841, 'conductor_radical': 779, 'degree': 4, 'euler_factors': [[1, 0, 4, 0, 4], [1, 0, 2, 0, 9], [1, -6, 19, -30, 25], [1, 0, 13, 0, 49], [1, 0, 13, 0, 121], [1, 0, 10, 0, 169], [1, 0, 25, 0, 289], [1, 0, -1], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 8, 78, 248, 961], [1, -4, 78, -148, 1369], [1, 6, 41], [1, 2, 87, 86, 1849], [1, 0, 85, 0, 2209], [1, 0, -38, 0, 2809], [1, 12, 154, 708, 3481], [1, 2, 123, 122, 3721], [1, 0, 118, 0, 4489], [1, 0, 106, 0, 5041], [1, 14, 195, 1022, 5329], [1, 0, 94, 0, 6241], [1, -24, 310, -1992, 6889], [1, 0, 34, 0, 7921], [1, 0, 130, 0, 9409], [1, 0, 166, 0, 10201], [1, -28, 402, -2884, 10609], [1, 36, 538, 3852, 11449], [1, 0, -38, 0, 11881], [1, -12, 262, -1356, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 1, 'label': '4-779e2-1.1-c1e2-0-1', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/2.2.41.1/361.1/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.048828125', 'prec': 37}, 'plot_values': [-1.6672165275591064e-74, 0.18897627175396098, 0.37763518210307906, 0.5655638408670202, 0.752162875109428, 0.9365645713477834, 1.1175645190300387, 1.2935709630105072, 1.4625757695263717, 1.622150472077708, 1.769470260874979, 1.901367985413326, 2.0144192347296763, 2.105058335848792, 2.1697236750150997, 2.2050291244482265, 2.20795659667378, 2.176062918561437, 2.107692409838664, 2.0021848779516387, 1.8600673307058244, 1.6832166981256032, 1.4749803853610204, 1.2402416813324584, 0.9854180362654629, 0.718382077609946, 0.44829799763137934, 0.18536960310404724, -0.05949920879850436, -0.27512563977711524, -0.4505393373665672, -0.5755266237428276, -0.6412047373360454, -0.6405981905347415, -0.5691853006148294, -0.42538030254331505, -0.2109155879855788, 0.06891014108318572, 0.40514843470308487, 0.7853069843952557, 1.1936610465911184, 1.611776045100865, 2.019234690585579, 2.394548496297888, 2.716219717871558, 2.963906392653551, 3.1196312793758185, 3.168966106397095, 3.102116585980649, 2.914831980217606, 2.6090662466191525, 2.193326307179787, 1.6826567934616852, 1.0982293568377708, 0.46652752649127904, -0.18185602064811185, -0.8137655701781822, -1.3953006564228456, -1.8938106579071794, -2.279949538410755, -2.529660560956486, -2.6259547330704245, -2.5603498335154, -2.3338497699824465, -1.9573666826814642, -1.45151984148836, -0.845784412166097, -0.1770072913909986, 0.512646482879087, 1.1782081037761087, 1.7747311092357383, 2.2602480358968777, 2.5986556415968134, 2.7623198462924186, 2.7342001433137466, 2.509317776305858, 2.0954316567634095, 1.5128386998577652, 0.793277629849742, -0.022017059053082752, -0.8849965810312619, -1.7440381243110843, -2.547515967147513, -3.2474401183686754, -3.802883570864948, -4.182925929706581, -4.36887078983662, -4.355545507121777, -4.15156165635299, -3.7784973919259857, -3.269052516680417, -2.664315723926989, -2.010363249965844, -1.3544714577941872, -0.7412661546419246, -0.20914398592197916, 0.21271636021584656, 0.5064828554909148, 0.6667425981898047, 0.7004168475827484, 0.6255249854243103, 0.46891407292575954, 0.2631730922929048, 0.043035076131774, -0.1583730039835071, -0.3130503611504736, -0.4010460105239211, -0.4124732187155737, -0.34839029794879106, -0.22043817181615102, -0.04925602465414563, 0.1381698268957803, 0.3119459956303143, 0.443125263551579, 0.5075359420830564, 0.4891341787431307, 0.3824593258839091, 0.1938543159397553, -0.05876282936385505, -0.34763486723932446, -0.6382958283280348, -0.8938142034261991, -1.079718685043473, -1.1690669133139457, -1.1470617501154503, -1.0146269297875292, -0.7904279363899647, -0.5109609282240719, -0.22852156253838535, -0.007089284890891112, 0.08360132701859117, -0.024692557114251112, -0.390836430171214, -1.0565972159270451, -2.039934144122154, -3.3301051803579678, -4.885258207105828, -6.632960787416014, -8.47384414076159, -10.288222184843773, -11.94522697258115, -13.313711770609645, -14.273945295033467, -14.728983159015364, -14.61457495466389, -13.906556177262432, -12.624879497488687, -10.833743096832443, -8.637646826853093, -6.1736128553019975, -3.6002040441771044, -1.0843176599289337, 1.213014732645949, 3.150458525846805, 4.618483474797072, 5.548542672616906, 5.918399261594354, 5.753060870373166, 5.12122917592424, 4.127635355826355, 2.902060944700867, 1.5861899182424801, 0.31966220433760584, -0.773225137733159, -1.5948050572075725, -2.0821844000950294, -2.2114701497228912, -1.997745280345344, -1.49093709309121, -0.7681754870221738, 0.07638074185157635, 0.9430092472242219, 1.737827481384962, 2.3828286654164885, 2.8234478955836844, 3.0328875180069996, 3.0128493935942355, 2.7907743411718906, 2.414118895221528, 1.9425524636627483, 1.4391898041706017, 0.9620558954768869, 0.5569037102488812, 0.25228190819213, 0.0574103604971642, -0.03698650861599482, -0.05515914379306051, -0.03077077980845427, -0.00021731013657065704, 0.0041059668183412385, -0.040459475367807946, -0.14297744208929652, -0.29751896677092593, -0.4844188248654432, -0.673962978214117, -0.8318955121246804, -0.9258349389568432, -0.9315270459154488, -0.837862755691736, -0.6497591912870263, -0.3883197543185549, -0.0881111524115315, 0.2081387651464121, 0.45667855462256624, 0.6206172296922581, 0.6772735682783807, 0.6237074211653608, 0.4793491247182256, 0.2850252061609838, 0.0981963812814221, -0.015192553917155661, 0.008714257144970506, 0.22011446878385477, 0.6446901117727217, 1.2752173623560363, 2.067188823676125, 2.9395392685795776, 3.7809162869524062, 4.461173098948959, 4.846983851876868, 4.819802003184068, 4.293902728677254, 3.2320513245154014, 1.6564671158596111, -0.34679088864314495, -2.6311475806077884, -5.000731964411479, -7.228654506622916, -9.080526972067547, -10.34062121907669, -10.837576261022797, -10.466456951813841, -9.20427401796279, -7.116770302562216, -4.355284976731371, -1.14370421475282, 2.2432581755856797, 5.508094918118694, 8.361660043408827, 10.553800847938602, 11.899831389240877, 12.299684039008476, 11.747457293584162, 10.330258386215705, 8.216565701355385, 5.635634615829064, 2.850569528082221, 0.12843882653721697, -2.288880887855223, -4.209618684736973, -5.509898228921299, -6.142514313070595, -6.1360314545412855, -5.584817165456002, -4.631780876476631, -3.4464710554953237, -2.201672127404223], 'positive_zeros': ['1.35486074388197716928380982193862', '1.79554652871898727064930174154583', '2.67183638730115156824697116427592', '3.28403235558794973310569727230370', '3.85615252208514256878324668323871', '4.66113670445354521481725901186497', '5.03912355415234199771433602491991', '5.38402383492515633625005346052310', '5.75116326140982635046813181963760', '6.30092624798927176107946148011650', '6.39084306102520193435942181608554', '7.39532327685859741640586695459627', '7.923460562946246199886108427468690', '8.296499449630110216369102611507149'], 'prelabel': '4-779e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.494062212026345, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 858136623625395135, 'z1': {'__RealLiteral__': 0, 'data': '1.35486074388197716928380982193862', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.79554652871898727064930174154583', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.67183638730115156824697116427592', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 38.69270830911013, 'bad_primes': [19, 41], 'central_character': '1.1', 'conductor': 606841, 'conductor_radical': 779, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -4, 6, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, -24, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 8, 4, 0, 0, 0, -6, 0, -2, 0, -12, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, -2, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 72, -5, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -68], 'euler11': [1, 0, 13, 0, 121], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 0, 25, 0, 289], 'euler19': [1, 0, -1, 0, 0], 'euler2': [1, 0, 4, 0, 4], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 2, 0, 9], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 6, 41, 0, 0], 'euler43': [1, 2, 87, 86, 1849], 'euler47': [1, 0, 85, 0, 2209], 'euler5': [1, -6, 19, -30, 25], 'euler53': [1, 0, -38, 0, 2809], 'euler59': [1, 12, 154, 708, 3481], 'euler61': [1, 2, 123, 122, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, 13, 0, 49], 'euler71': [1, 0, 106, 0, 5041], 'euler73': [1, 14, 195, 1022, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, -24, 310, -1992, 6889], 'euler89': [1, 0, 34, 0, 7921], 'euler97': [1, 0, 130, 0, 9409], 'euler_factors': [[1, 0, 4, 0, 4], [1, 0, 2, 0, 9], [1, -6, 19, -30, 25], [1, 0, 13, 0, 49], [1, 0, 13, 0, 121], [1, 0, 10, 0, 169], [1, 0, 25, 0, 289], [1, 0, -1, 0, 0], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 8, 78, 248, 961], [1, -4, 78, -148, 1369], [1, 6, 41, 0, 0], [1, 2, 87, 86, 1849], [1, 0, 85, 0, 2209], [1, 0, -38, 0, 2809], [1, 12, 154, 708, 3481], [1, 2, 123, 122, 3721], [1, 0, 118, 0, 4489], [1, 0, 106, 0, 5041], [1, 14, 195, 1022, 5329], [1, 0, 94, 0, 6241], [1, -24, 310, -1992, 6889], [1, 0, 34, 0, 7921], [1, 0, 130, 0, 9409]], 'index': 1, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.41.1/361.1/a', 'ModularForm/GL2/TotallyReal/2.2.41.1/holomorphic/2.2.41.1-361.1-a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-779e2-1.1-c1e2-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-779e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.494062212026345, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 858136623625395135, 'z1': {'__RealLiteral__': 0, 'data': '1.35486074388197716928380982193862', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9538117
{'Lhash': '409437620317032020,448699003308363115', 'Lhash_array': ['409437620317032020', '448699003308363115'], 'label': '4-779e2-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.41.1/holomorphic/2.2.41.1-361.1-a'}
-
id: 9538020
{'Lhash': '409437620317032020,448699003308363115', 'Lhash_array': ['409437620317032020', '448699003308363115'], 'label': '4-779e2-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.41.1/361.1/a'}