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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 1, 'A4': -1, 'A5': -1, 'A6': -1, 'A7': 0, 'A8': 3, 'A9': 1, 'Lhash': '2270854068250249189', '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': [0.0, 0], 'a8': [1.0606601717798212, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 3104.7034061904146, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [5, [1, 1]], [7, [1]], [23, [1]]], 'bad_primes': [3, 5, 7, 23], 'central_character': '388815.1', 'coefficient_field': '1.1.1.1', 'conductor': 388815, 'conductor_radical': 2415, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, -1], [1, 1], [1], [1, 4, 11], [1, -6, 13], [1, 2, 17], [1, 0, 19], [1], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, -12, 59], [1, -10, 61], [1, 4, 67], [1, -4, 71], [1, -2, 73], [1, 0, 79], [1, 0, 83], [1, 10, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 19, 'label': '2-388815-1.1-c1-0-19', 'leading_term': '1.51748292615', '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': 0, 'origin': 'EllipticCurve/Q/388815/bb', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.517482926153226, 0.8721967418487221, -0.4105844098041868, -0.8473057163641655, 0.3223800454870588, 1.745325777681793, 1.230196057976456, -0.9663322118129968, -1.658244985535802, 0.8825023709757879, 3.588435120075962, 2.516096298999435, -0.897542915657034, -1.692549020626167, 0.545733033880103, 1.007330008249973, -1.585835015324551, -2.317347233214643, 0.6192289137911781, 1.719299043502497, -1.479221184055879, -2.456781166238667, 2.413381774260494, 5.312781982863311, 0.0144927788803713, -6.032237006690355, -4.115494344456156, 0.8771077098189766, 0.4533350167469946, -2.528948971417999, -1.529446703094441, 1.148537506164856, 0.9753460314951169, -0.05230114408698358, 0.08533115280126163, -0.6388259954901245, -1.323383053246916, 0.7541311892253783, 2.415427612076288, 0.410964231617815, -0.9393373190749768, 0.7158410837033333, 0.3790182598294533, -1.818978838046674, -0.1904345625513348, 1.504239998963283, -3.192777550017043, -6.112509114875969, 0.9655517575602441, 7.152958541789654, 2.679585419846472, -2.59545747528079, -1.04570425992949, -0.03115434220699488, -1.434286545337856, 0.5410299164813023, 1.855010136024378, -1.560952763305138, -0.9312826160702292, 5.484007071585019, 5.962183390093214, 0.4772785835291534, -0.4290489362386948, 0.9936700267223965, -1.007514413581591, -0.8740768504967357, 1.449275535247993, -2.17942327188214, -6.941625458478154, -3.882177719681395, 0.2235728376292835, -1.055154871017326, -1.56662653919327, 0.1167429127009183, -0.2217713444333542, 0.02371023712634726, 1.406275826068847, -0.2609275175587164, -1.358241316715332, 0.6847506227397177, -0.6728848637183327, -3.678571334405003, -1.280778230531878, 0.661351295533128, -0.7270398770533661, 3.232819872762365, 7.292240842442923, 1.127814447486146, -3.378125387304644, 1.547995319444586, 1.273286547005873, -4.999727871509419, -3.324557243837564, 0.9674491298125589, -0.09186893484633502, 1.199157247626664, 1.80015258033895, -5.84797972484883, -8.397296659045676, 0.2300332688734945, 3.817136335992273, -0.04131127034343497, -0.3214153415640889, 0.2798375878252024, -1.40456271850456, -0.3997645907205719, 0.7105342603609417, -0.2723685166913638, 0.712459231221726, 0.5505833049551905, -1.937197716465495, -0.3327559240902077, 1.737720402401406, -0.2337938864625706, 0.1076195003745197, 0.6792998085590796, -1.702110917166482, 3.755916886904277, 12.4339997035468, 7.328620540375241, -0.8525371787691597], 'positive_zeros': ['0.4167844445620186', '0.9509106957713767', '1.643749160640780', '2.184378742046898', '2.929181891552874', '3.442622416558415', '3.862133541868539', '4.453280542321301', '4.901623853985601', '5.396697964466754', '6.000465442018271', '6.690465001200377', '7.034590366926673', '7.624534882493532', '8.218527878295463', '8.401674869071615', '8.592123446386949', '9.183436973136858', '9.788659818597682', '10.15499273461315', '10.53931049106239', '11.01440424146721', '11.36530325241693', '11.97483223045103', '12.59387005975657', '13.12202365977822', '13.24300655510039', '13.70764244717237', '14.14840184731022', '14.54198012947487', '15.28034435449712', '15.55192488189888', '15.89983100579099', '16.32485774546392', '16.65428415669130', '17.46565693513117', '17.62765179903413', '18.22280735188627', '18.43960837600261', '18.74612728256920', '19.22531042964617', '19.66376154769644', '19.95109152899493'], 'prelabel': '2-388815-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.719865453807536, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2270854068250249189, 'z1': {'__RealLiteral__': 0, 'data': '0.4167844445620186', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9509106957713767', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.643749160640780', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3104.7034061904146, 'bad_primes': [3, 5, 7, 23], 'central_character': '1.1', 'conductor': 388815, 'conductor_radical': 2415, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, -1, -1, -1, 0, 3, 1, 1, -4, -1, 6, 0, -1, -1, -2, -1, 0, 1, 0, 4, 0, 3, 1, -6, 1, 0, 6, 1, 0, -5, -4, 2, 0, -1, -2, 0, 6, -3, -6, 0, -4, 4, -1, 0, 0, -1, 0, -1, -2, -6, -6, -1, 4, 0, 0, -6, 12, 1, 10, 0, 0, 7, -6, 4, -4, 2, 0, 0, 4, 3, 2, 2, 1, 0, 0, -6, 0, 1, 1, 6, 0, 0, 2, 4, 6, -12, -10, 1, 0, 0, 0, 0, 0, -5, -2, 0, -4, -1], 'euler11': [1, 4, 11], 'euler13': [1, -6, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 2], 'euler23': [1, 0, 0], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, 6, 53], 'euler59': [1, -12, 59], 'euler61': [1, -10, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -4, 71], 'euler73': [1, -2, 73], 'euler79': [1, 0, 79], 'euler83': [1, 0, 83], 'euler89': [1, 10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 2], [1, -1, 0], [1, 1, 0], [1, 0, 0], [1, 4, 11], [1, -6, 13], [1, 2, 17], [1, 0, 19], [1, 0, 0], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, -12, 59], [1, -10, 61], [1, 4, 67], [1, -4, 71], [1, -2, 73], [1, 0, 79], [1, 0, 83], [1, 10, 89], [1, 2, 97]], 'index': 19, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/388815/bb'], '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': '2-388815-1.1-c1-0-19', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-388815-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.719865453807536, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2270854068250249189, 'z1': {'__RealLiteral__': 0, 'data': '0.4167844445620186', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2270854068250249189', 'Lhash_array': ['2270854068250249189'], 'label': '2-388815-1.1-c1-0-19', 'type': 'ECQ', 'url': 'EllipticCurve/Q/388815/bb'}