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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1074305025479773584', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2752.9224600856637, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [13, [1]], [17, [1, 1]]], 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '344760.1', 'coefficient_field': '1.1.1.1', 'conductor': 344760, 'conductor_radical': 6630, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1, 0, 7], [1, -4, 11], [1], [1, 1], [1, 6, 19], [1, -4, 23], [1, 6, 29], [1, -4, 31], [1, -6, 37], [1, -2, 41], [1, 4, 43], [1, 2, 47], [1, 6, 53], [1, -10, 59], [1, 2, 61], [1, -6, 67], [1, -4, 71], [1, -14, 73], [1, 8, 79], [1, -6, 83], [1, 0, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 21, 'label': '2-344760-1.1-c1-0-21', 'leading_term': '4.164631724', '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/344760/cq', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.16463172400017, 2.961314308561383, 0.1865934120293969, -2.008180952429967, -1.769490644230576, 0.3192205039123062, 1.560436130131962, 0.5361839582822758, -0.8037217641408408, -0.02955641756204662, 1.696693997494634, 1.151290799171854, -1.47228665468405, -2.314245521165089, -0.2198289142516152, 0.9824840533169287, -0.8547446949676043, -2.083710322910173, -0.02174727067972418, 1.324729488023628, -1.627839959298803, -4.353362010279447, -1.513381291542119, 2.98992263288928, 2.526015674321038, -0.6713569134790817, -0.801937784379256, 0.1318970660263399, -2.25508991950106, -4.210253262616527, -1.009794838944956, 2.537860913989147, 0.9209815511428783, -1.499661573057632, -0.03119688560586053, 1.189392018083381, -0.7012666162217279, -1.24583732011611, 0.3088186681955146, -0.6643559705913294, -2.034918725800469, 1.492167972196082, 5.040643344544448, 2.308223565682946, -0.7114550664444652, 1.3052845052962, 1.180925814238746, -3.947450775092439, -4.667072767350175, 0.554604110014297, 1.799990515038039, -1.346803006536513, -1.156351732511266, 0.2149053743176144, -1.926655195144665, -2.310900178177532, 1.257955531139145, 2.05633056142116, 0.06720838410902771, 0.3654745118146494, -0.2232598521507269, -3.219316950546353, -1.622149425159671, 2.474420662820797, -0.4500138406251148, -5.363445812614465, -2.753703003559028, 0.8907042164177578, -0.3797679232260063, 0.2522554845891794, 2.283663611548062, -1.372512586214095, -4.269409754937851, -0.0480804653957762, 1.973847852695219, -1.520271063984988, -1.585333713121891, 0.5135007264933695, -1.222561921932454, -1.600738753807078, 0.5451522395465765, -1.649106901505527, -4.172563478349236, -1.24536431422302, 0.2272600571678668, -1.174884850252448, 1.284107044600657, 3.020277557234678, -0.04742839597091313, 0.4538840957758036, 3.131932089806877, -0.531340686361009, -2.648466967811175, 2.020157227417481, 1.146018793999654, -5.050478478283549, -3.773656118214313, 0.08994303122748774, -1.659772365359027, -1.840851686755861, 0.6124542634455163, -0.3139208452371687, -0.2980001484564828, 1.600799072981359, -0.2875483650075723, -0.4251902082245356, 3.909317475625609, 3.121065726131154, -0.4665985953320042, 0.8230974564165763, -0.1607868840451775, -3.876622107359181, -1.074020886935537, 1.064266629677618, -3.043560350030295, -1.359724263223479, 4.185629631158994, 1.548287137675102, -1.476582886247487, 1.381455742195801, 1.339733402440633], 'positive_zeros': ['0.5162121916260201', '1.213764316618406', '1.827895638926886', '2.254106133788752', '2.864563243081467', '3.522990750263863', '3.911455038331088', '4.501975993061706', '4.896338788084991', '5.572553087377397', '6.186060537544002', '6.640825157250412', '6.787470526118940', '7.552591245138554', '8.068545797716248', '8.503172579853842', '8.922986130038432', '9.436321871852002', '9.670173280945511', '10.17532221547350', '10.89117854183520', '11.13333217167358', '11.56789913979025', '12.22221650683280', '12.64020555406029', '13.14498360166231', '13.30466419108158', '13.91536509611739', '14.51624909655561', '14.65349936153755', '14.97682509257197', '15.58206732570266', '15.98147254084298', '16.64672272271595', '16.94837607218163', '17.22614927773033', '17.68585948911383', '18.25232434535954', '18.64792661792847', '19.14879715061653', '19.37555449835403', '19.91132844657135'], 'prelabel': '2-344760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 52.46829957303423, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1074305025479773584, 'z1': {'__RealLiteral__': 0, 'data': '0.5162121916260201', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.213764316618406', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.827895638926886', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2752.9224600856637, 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '1.1', 'conductor': 344760, 'conductor_radical': 6630, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 4, 0, 0, 0, 1, 0, -1, 0, -6, 0, 0, 0, 4, 0, 1, 0, 1, 0, -6, 0, 4, 0, 4, 0, 0, 0, 6, 0, 0, 0, 2, 0, -4, 0, 1, 0, -2, 0, -7, 0, -1, 0, -6, 0, 4, 0, -6, 0, 10, 0, -2, 0, 0, 0, 0, 0, 6, 0, 4, 0, 4, 0, 14, 0, 1, 0, 0, 0, -8, 0, 1, 0, 6, 0, -1, 0, -6, 0, 0, 0, 0, 0, 4, 0, -6, 0, 10, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 0, 0], 'euler17': [1, 1, 0], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -6, 37], 'euler41': [1, -2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 2, 47], 'euler5': [1, -1, 0], 'euler53': [1, 6, 53], 'euler59': [1, -10, 59], 'euler61': [1, 2, 61], 'euler67': [1, -6, 67], 'euler7': [1, 0, 7], 'euler71': [1, -4, 71], 'euler73': [1, -14, 73], 'euler79': [1, 8, 79], 'euler83': [1, -6, 83], 'euler89': [1, 0, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 0, 7], [1, -4, 11], [1, 0, 0], [1, 1, 0], [1, 6, 19], [1, -4, 23], [1, 6, 29], [1, -4, 31], [1, -6, 37], [1, -2, 41], [1, 4, 43], [1, 2, 47], [1, 6, 53], [1, -10, 59], [1, 2, 61], [1, -6, 67], [1, -4, 71], [1, -14, 73], [1, 8, 79], [1, -6, 83], [1, 0, 89], [1, -10, 97]], 'index': 21, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/344760/cq'], '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': '2-344760-1.1-c1-0-21', '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': '2-344760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 52.46829957303423, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1074305025479773584, 'z1': {'__RealLiteral__': 0, 'data': '0.5162121916260201', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1074305025479773584', 'Lhash_array': ['1074305025479773584'], 'label': '2-344760-1.1-c1-0-21', 'type': 'ECQ', 'url': 'EllipticCurve/Q/344760/cq'}