-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 1, 'A2': 1, 'A3': 1, 'A4': -1, 'A5': 1, 'A6': 1, 'A7': 4, 'A8': -3, 'A9': -2, 'Lhash': '59144743369780241', 'a10': [0.31622776601683794, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [-0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.4082482904638631, 0], 'a7': [1.5118578920369088, 0], 'a8': [-1.0606601717798212, 0], 'a9': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 1314.0262007023928, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[43, [1]], [89, [1, -1]]], 'bad_primes': [43, 89], 'central_character': '164561.1', 'coefficient_field': '1.1.1.1', 'conductor': 164561, 'conductor_radical': 3827, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, -1, 3], [1, -1, 5], [1, -4, 7], [1, 2, 11], [1, -2, 13], [1, -3, 17], [1, -5, 19], [1, -7, 23], [1, 0, 29], [1, 9, 31], [1, -2, 37], [1, 0, 41], [1], [1, 12, 47], [1, 3, 53], [1, -4, 59], [1, 6, 61], [1, -12, 67], [1, -10, 71], [1, 7, 73], [1, 6, 79], [1, -12, 83], [1, -1], [1, -9, 97]], 'gamma_factors': [[], [0]], 'index': 2, 'label': '2-164561-1.1-c1-0-2', 'leading_term': '13.4473177902', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/164561/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 3.059505194879544, 4.42431988281396, 3.213812311950008, 0.3841004294106549, -1.534184226034567, -0.7585140117944021, 1.58771028464654, 2.521329666877613, 0.8320800116198512, -1.271665599435039, -1.127000791141357, 0.6546040093489905, 1.238411241515818, 0.05885409061248495, -0.2821957638527184, 1.559542502470849, 3.103325925064593, 1.958931619365084, -0.1841849514034201, -0.5238400357689437, 0.1185623765564912, -0.413082072592698, -0.5781788224760653, 2.094525633395565, 4.486100186153628, 1.201250458331218, -5.477768811501212, -7.053433677975422, -1.7912727825951, 2.517385169245801, 1.413525613039956, -0.2285270372128534, 1.133762179669621, 1.501611779843007, -1.167107785340402, -2.117245273154127, -0.009965881042396797, -0.419546426741072, -3.632641362909236, -1.952958176700925, 5.171569464498661, 7.772325532231087, 2.778000087309847, -0.7648416037813992, 1.056404334611759, 1.365489665395724, -1.704982841441885, -1.29982412800321, 2.901525398648926, 3.301178426010053, -0.4998550477857401, -1.768127157327079, -0.157627129575919, -0.1606468374224274, -0.8891296123249617, 0.1109724393808808, 0.660673240342125, -0.02713120086906251, 0.2823153512360142, -0.2523788959229259, -3.224467280172398, -2.741904900635064, 2.713241414745445, 2.803239747529581, -5.092248420981044, -7.561254307903306, -0.1300220274352876, 4.082486582692015, 0.4876806717826602, -0.7566644551363035, 1.757553288081414, 0.633875459084609, -1.392808215952556, 0.3226355346860152, -0.8378227499737879, -5.977418138141191, -3.900344106374251, 4.76832958453324, 6.096488960716638, 0.1746714446980521, -1.226602384225104, 1.249962239099881, 0.7332183403262854, -0.1285289391760046, 0.8483016657729775, 0.02603751519255473, -0.3548227461790735, 2.808579960982895, 3.283786777770056, -1.037613665511252, -2.255371989155924, 0.08726270925938114, -0.2969355117959547, -0.7623757572218763, 1.724249493690615, 1.39774078173422, -1.351947178524051, 0.009099036580809407, 1.449301352603538, -1.566189078956287, -1.56316090615858, 2.390545145833707, 1.271609739032278, -1.418576386827947, 2.137937838760414, 4.07340170361688, -0.3182481926911202, -1.249794905694461, 1.25285673248033, -0.6841485063539336, -0.8079555582021268, 4.271686932762676, 2.497661280453389, -4.549514841536651, -2.358914787837112, 3.138865110994157, -0.1262986780943405, -2.335349211675218, 3.455120754115208, 5.237049978659115], 'positive_zeros': ['1.034828437743972', '1.584441878088868', '2.334162845756546', '2.909133076067920', '3.511773266405766', '3.809978751521974', '4.721272054891493', '5.177173007087387', '5.378429988412966', '5.832550691347391', '6.545721715530421', '7.324972988418656', '7.913718071762976', '8.087621311896879', '8.652540804859988', '9.251378773433749', '9.456356265847952', '10.07578430689845', '10.89244570336737', '11.14667274016407', '11.61568642850704', '12.08171556214329', '12.71600218860068', '13.28576674964887', '13.45636762139405', '13.97946863530072', '14.48445772178384', '14.63392089476169', '14.96718831731681', '15.63051058180946', '16.10102247413393', '16.75393725257250', '17.28147751619832', '17.57744492278593', '18.05195409470232', '18.46019223835600', '18.69530904783039', '19.36193691961181'], 'prelabel': '2-164561-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 36.249499316575296, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 59144743369780241, 'z1': {'__RealLiteral__': 0, 'data': '1.034828437743972', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.584441878088868', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.334162845756546', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1314.0262007023928, 'bad_primes': [43, 89], 'central_character': '1.1', 'conductor': 164561, 'conductor_radical': 3827, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, -1, 1, 1, 4, -3, -2, 1, -2, -1, 2, 4, 1, -1, 3, -2, 5, -1, 4, -2, 7, -3, -4, 2, -5, -4, 0, 1, -9, 5, -2, 3, 4, 2, 2, 5, 2, -3, 0, 4, 0, 2, -2, 7, -12, -1, 9, -4, 3, -2, -3, -5, -2, -12, 5, 0, 4, -1, -6, -9, -8, 7, 2, -2, 12, -3, 7, 4, 10, 6, -7, 2, -4, -5, -8, 2, -6, -1, 1, 0, 12, -4, 3, 0, 0, 6, 1, -2, 8, -7, -9, -12, 5, 5, 9, 9, 4, 4], 'euler11': [1, 2, 11], 'euler13': [1, -2, 13], 'euler17': [1, -3, 17], 'euler19': [1, -5, 19], 'euler2': [1, -1, 2], 'euler23': [1, -7, 23], 'euler29': [1, 0, 29], 'euler3': [1, -1, 3], 'euler31': [1, 9, 31], 'euler37': [1, -2, 37], 'euler41': [1, 0, 41], 'euler43': [1, 0, 0], 'euler47': [1, 12, 47], 'euler5': [1, -1, 5], 'euler53': [1, 3, 53], 'euler59': [1, -4, 59], 'euler61': [1, 6, 61], 'euler67': [1, -12, 67], 'euler7': [1, -4, 7], 'euler71': [1, -10, 71], 'euler73': [1, 7, 73], 'euler79': [1, 6, 79], 'euler83': [1, -12, 83], 'euler89': [1, -1, 0], 'euler97': [1, -9, 97], 'euler_factors': [[1, -1, 2], [1, -1, 3], [1, -1, 5], [1, -4, 7], [1, 2, 11], [1, -2, 13], [1, -3, 17], [1, -5, 19], [1, -7, 23], [1, 0, 29], [1, 9, 31], [1, -2, 37], [1, 0, 41], [1, 0, 0], [1, 12, 47], [1, 3, 53], [1, -4, 59], [1, 6, 61], [1, -12, 67], [1, -10, 71], [1, 7, 73], [1, 6, 79], [1, -12, 83], [1, -1, 0], [1, -9, 97]], 'index': 2, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/164561/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, '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': '2-164561-1.1-c1-0-2', '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': '2-164561-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 36.249499316575296, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 59144743369780241, 'z1': {'__RealLiteral__': 0, 'data': '1.034828437743972', 'prec': 57}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '59144743369780241', 'Lhash_array': ['59144743369780241'], 'label': '2-164561-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/164561/b'}