-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 0, 'Lhash': '1368668413894833942263194188928', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.98650550050003, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [31, [1, -1, 29, 31]]], 'bad_primes': [2, 3, 31], 'central_character': '642816.1', 'coefficient_field': '1.1.1.1', 'conductor': 642816, 'conductor_radical': 186, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, 8, 0, 25], [1, 4, 14, 28, 49], [1, 0, -6, 0, 121], [1, -2, 26, -26, 169], [1, 0, 14, 0, 289], [1, 2, 14, 38, 361], [1, 0, 2, 0, 529], [1, 0, -34, 0, 841], [1, -1, 29, 31], [1, -16, 134, -592, 1369], [1, 0, 8, 0, 1681], [1, -2, 62, -86, 1849], [1, 0, 86, 0, 2209], [1, 0, -74, 0, 2809], [1, 0, -30, 0, 3481], [1, 4, 62, 244, 3721], [1, -2, 134, -134, 4489], [1, 0, 14, 0, 5041], [1, 10, 90, 730, 5329], [1, -10, 62, -790, 6241], [1, 0, 22, 0, 6889], [1, 0, -78, 0, 7921], [1, -12, 166, -1164, 9409], [1, 0, 8, 0, 10201], [1, 2, 198, 206, 10609], [1, 0, -62, 0, 11449], [1, -8, 198, -872, 11881], [1, 0, -116, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 5, 'label': '4-642816-1.1-c1e2-0-5', '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/2.0.3.1/71424.1/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.9020023279895075e-75, 0.15913983914763405, 0.31754128025256634, 0.47438449558664914, 0.6286905574781869, 0.7792512445005246, 0.9245699498706809, 1.0628171654300373, 1.191803784078221, 1.3089751349390435, 1.4114282179866717, 1.4959540190643177, 1.5591060471617908, 1.5972953354663328, 1.6069110876958308, 1.5844649451872053, 1.5267555256005119, 1.431048483339629, 1.2952659225334726, 1.118177627725849, 0.8995853497520969, 0.6404903882450504, 0.34323404604142216, 0.011600291607378693, -0.34912975713698263, -0.7321810462967168, -1.1293535055242043, -1.5311625093214114, -1.9270538960299262, -2.3056931526618927, -2.655324483162908, -2.964191256644473, -3.2210049780166403, -3.4154456733356238, -3.538672703556435, -3.583821798452168, -3.5464618240944117, -3.4249837322699688, -3.220894520713235, -2.9389910324825967, -2.587392135537909, -2.1774132469071055, -1.7232741862246561, -1.2416397283459697, -0.7510016216911996, -0.27092078285146537, 0.17884169250618426, 0.5792667792422143, 0.9130471413383326, 1.1655322379969892, 1.3255936359660918, 1.3863549479642976, 1.345733980396881, 1.2067514666204895, 0.9775711232088846, 0.6712493817664553, 0.30518944326298214, -0.09968754878207906, -0.5200224595675924, -0.9312989237135785, -1.3092577572799802, -1.6313640636044737, -1.8782365677931983, -2.0349445653315263, -2.09207986578998, -2.0465196711229843, -1.901811429254349, -1.66813184466288, -1.3617984116356006, -1.0043415974044996, -0.6211772725773514, -0.2399499958427278, 0.11135402305651398, 0.4064023635275289, 0.6224824934205166, 0.7422940051001179, 0.755425971183502, 0.6593927378993951, 0.4601263895357712, 0.1718585161378331, -0.18363413461284916, -0.5783987291339487, -0.9802203685745113, -1.3549650105165898, -1.6691948842991033, -1.8928691738423435, -2.0019246029745563, -1.9805274509378241, -1.82280175634666, -1.5338681050494511, -1.1300721681688979, -0.6383394479264158, -0.09465866309251157, 0.4582339689585143, 0.9738291129556453, 1.4052761115123555, 1.7090230241817106, 1.8483854860854423, 1.7967559917472764, 1.5401795541932601, 1.0790595217419319, 0.4288168242721185, -0.38059674303803026, -1.3063409944642634, -2.295400515387596, -3.288191162284614, -4.222800959309715, -5.039543157114261, -5.685460656094435, -6.1184117514907435, -6.3103894570244705, -6.249780026425609, -5.942347417869381, -5.41083335520157, -4.693179071320212, -3.8394948681607697, -2.9080165742582027, -1.9603832454643806, -1.0566385976048034, -0.25039233114206344, 0.41542775002151355, 0.9118471022009946, 1.2258359193528579, 1.3608304810949796, 1.335728395321541, 1.1824450903330364, 0.9422578371245898, 0.661284494682428, 0.3855346543519295, 0.1560209749444757, 0.00442189047295542, -0.05025843740607784, -0.0036782493412242834, 0.13343071849598767, 0.3364981032472551, 0.5698967339331394, 0.7910094092013518, 0.9551775059563995, 1.0210243229610463, 0.9555913899111601, 0.7387281079744943, 0.36623594742223825, -0.14861612642756855, -0.7754283268554816, -1.468892723737359, -2.172735852325565, -2.825025415999549, -3.3643262499085176, -3.7360806168498613, -3.898540381701101, -3.8276011992837073, -3.5199818876034374, -2.994348417661299, -2.290187094591566, -1.4644653265522594, -0.5863567428301774, 0.2694752745124584, 1.03036968616973, 1.6331634422760026, 2.0308922606234234, 2.1979573626239706, 2.1331604876385604, 1.8602207451958321, 1.4256471924260212, 0.8941235967232537, 0.3418363660875824, -0.1515874059347884, -0.5116947506536451, -0.6774542186669786, -0.6082311951682353, -0.2887023025680931, 0.2688736998673705, 1.0253347362174317, 1.9182325023427969, 2.8680518206845935, 3.7864010947147033, 4.585310963048346, 5.186637807534081, 5.530537878983295, 5.582062736981404, 5.335120622277706, 4.813331737197892, 4.067647805980303, 3.1709696973937525, 2.210339873746159, 1.2775688768391387, 0.4593429515212182, -0.17207051361291753, -0.5664621766565083, -0.7007902852083983, -0.5811743331468286, -0.24154712850671053, 0.2608690348208699, 0.8527203849584611, 1.4534568543637516, 1.9849718547887856, 2.3807858859507545, 2.5936651781078637, 2.6007545166108414, 2.405606392192286, 2.036871097874155, 1.5438282028148973, 0.9893377172884443, 0.4411191217685033, -0.037514373595997394, -0.39626008211231245, -0.6046363298374886, -0.6560872306672999, -0.5688111827278775, -0.3831636488333503, -0.15593315010820402, 0.04779226011099795, 0.16411728045339116, 0.13993623857267123, -0.058663332316806184, -0.4403626995626763, -0.985828917559441, -1.6486688818092106, -2.3601207542269003, -3.036987855458959, -3.5918759941107803, -3.944461801160204, -4.0323437984469255, -3.8200371799938226, -3.3048716660260276, -2.5189186403057895, -1.526565728259513, -0.4179129725208063, 0.7012863770323274, 1.7219479693072288, 2.544722587472044, 3.0921513636007796, 3.318331265710776, 3.214796891028155, 2.8117854841805685, 2.174632861624432, 1.3956750031594654, 0.5826219292394486, -0.15515175747265483, -0.7206572647602818, -1.0418655607558525, -1.0811502210535133, -0.8403282435075672, -0.3605861285750773, 0.28275956643166167, 0.9900385516949052, 1.6503046391988825, 2.1560279798133095, 2.4174808444588587, 2.3749151449219053, 2.006903088289717, 1.3337067097288673, 0.41519402969276087, -0.6564567000212688, -1.7683248018727848, -2.8010691584536627, -3.6441088773205657], 'positive_zeros': ['1.07968900393248515568336532822412', '2.13709908204565879061311657832907', '2.66060254344099039468031185130956', '3.35947576185604253054432810716570', '3.72667983816738567189367602637893', '4.32047437272777619982830123463546', '4.76020604081410974366295945357102', '5.59450261257392722087181604637820', '6.09576207798146178760399124922032', '6.18928493594399354864216985347836', '6.64385060314854380354660188701614', '7.29735708140565541171730422604613', '7.76577671354675230852365993518270', '7.995316380054213649664934308657120'], 'prelabel': '4-642816-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.5302312952251995, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 925359012550926636, 'z1': {'__RealLiteral__': 0, 'data': '1.07968900393248515568336532822412', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.13709908204565879061311657832907', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.66060254344099039468031185130956', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 40.98650550050003, 'bad_primes': [2, 3, 31], 'central_character': '1.1', 'conductor': 642816, 'conductor_radical': 186, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 12, 0, 0, 0], 'euler11': [1, 0, -6, 0, 121], 'euler13': [1, -2, 26, -26, 169], 'euler17': [1, 0, 14, 0, 289], 'euler19': [1, 2, 14, 38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 2, 0, 529], 'euler29': [1, 0, -34, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -1, 29, 31, 0], 'euler37': [1, -16, 134, -592, 1369], 'euler41': [1, 0, 8, 0, 1681], 'euler43': [1, -2, 62, -86, 1849], 'euler47': [1, 0, 86, 0, 2209], 'euler5': [1, 0, 8, 0, 25], 'euler53': [1, 0, -74, 0, 2809], 'euler59': [1, 0, -30, 0, 3481], 'euler61': [1, 4, 62, 244, 3721], 'euler67': [1, -2, 134, -134, 4489], 'euler7': [1, 4, 14, 28, 49], 'euler71': [1, 0, 14, 0, 5041], 'euler73': [1, 10, 90, 730, 5329], 'euler79': [1, -10, 62, -790, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 0, -78, 0, 7921], 'euler97': [1, -12, 166, -1164, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 8, 0, 25], [1, 4, 14, 28, 49], [1, 0, -6, 0, 121], [1, -2, 26, -26, 169], [1, 0, 14, 0, 289], [1, 2, 14, 38, 361], [1, 0, 2, 0, 529], [1, 0, -34, 0, 841], [1, -1, 29, 31, 0], [1, -16, 134, -592, 1369], [1, 0, 8, 0, 1681], [1, -2, 62, -86, 1849], [1, 0, 86, 0, 2209], [1, 0, -74, 0, 2809], [1, 0, -30, 0, 3481], [1, 4, 62, 244, 3721], [1, -2, 134, -134, 4489], [1, 0, 14, 0, 5041], [1, 10, 90, 730, 5329], [1, -10, 62, -790, 6241], [1, 0, 22, 0, 6889], [1, 0, -78, 0, 7921], [1, -12, 166, -1164, 9409]], 'index': 5, 'instance_types': ['BMF', 'ECNF', 'BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/71424.1/c', 'EllipticCurve/2.0.3.1/71424.1/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/71424.2/b', 'EllipticCurve/2.0.3.1/71424.2/b'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-642816-1.1-c1e2-0-5', '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': '4-642816-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.5302312952251995, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 925359012550926636, 'z1': {'__RealLiteral__': 0, 'data': '1.07968900393248515568336532822412', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9796652
{'Lhash': '1368668413894833942263194188928', 'Lhash_array': ['1368668413894833942263194188928'], 'label': '4-642816-1.1-c1e2-0-5', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/71424.2/b'}
-
id: 9796297
{'Lhash': '1368668413894833942263194188928', 'Lhash_array': ['1368668413894833942263194188928'], 'label': '4-642816-1.1-c1e2-0-5', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/71424.2/b'}
-
id: 9796228
{'Lhash': '1368668413894833942263194188928', 'Lhash_array': ['1368668413894833942263194188928'], 'label': '4-642816-1.1-c1e2-0-5', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/71424.1/c'}
-
id: 9796018
{'Lhash': '1368668413894833942263194188928', 'Lhash_array': ['1368668413894833942263194188928'], 'label': '4-642816-1.1-c1e2-0-5', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/71424.1/c'}