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  • lfunc_lfunctions • Show schema
    {'Lhash': '334970123440693737056700039699,1025129901805078021877927495075,1115852247743594399490945812787', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 380137.2649529088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 3, 3, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '9072.1', 'coefficient_field': '1.1.1.1', 'conductor': 746636341248, 'conductor_radical': 42, 'degree': 6, 'euler_factors': [[1], [1], [1, -3, 9, -18, 45, -75, 125], [1, 3, 3, 1], [1, 6, 36, 126, 396, 726, 1331], [1, -3, 3, 34, 39, -507, 2197], [1, -3, 27, -114, 459, -867, 4913], [1, 0, 9, 56, 171, 0, 6859], [1, -6, 45, -180, 1035, -3174, 12167], [1, -3, 51, -210, 1479, -2523, 24389], [1, 6, 105, 380, 3255, 5766, 29791], [1, -15, 186, -1235, 6882, -20535, 50653], [1, 12, 123, 912, 5043, 20172, 68921], [1, 12, 84, 380, 3612, 22188, 79507], [1, 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'5.70914753648950583723172091883818', '6.13055349884249246890422173344205', '6.46494991836705844270774626486872', '6.54199186418154863981745514726172', '6.80040908828266490278950233222826', '7.00932321174860742636095057352756', '7.13389743997473677684154313539763', '7.58315003100174115095043938718433', '7.71208910670643612868055624523118', '7.928882683453306244043141893492542'], 'prelabel': '6-9072e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.511185858251809, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 199445668463827448, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.26424483479941972698299773125', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.808684902307080792313719998769', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '0.880252214247912605781906273632', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 380137.2649529088, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 746636341248, 'conductor_radical': 42, 'degree': 6, 'dirichlet_coefficients': [1, 0, 0, 0, 3, 0, -3, 0, 0, 0, -6, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 3, 0, -6, 0, 0, 0, -9, 0, 15, 0, 0, 0, -12, 0, -12, 0, 0, 0, 0, 0, 6, 0, 0, 0, 12, 0, -18, 0, 0, 0, 18, 0, -3, 0, 0, 0, 9, 0, -6, 0, 0, 0, 0, 0, 9, 0, 0, 0, 18, 0, -6, 0, 0, 0, -12, 0, 9, 0, 0, 0, 15, 0, -9, 0, 0, 0, 0, 0, 12, 0, 0, 0], 'euler11': [1, 6, 36, 126, 396, 726, 1331], 'euler13': [1, -3, 3, 34, 39, -507, 2197], 'euler17': [1, -3, 27, -114, 459, -867, 4913], 'euler19': [1, 0, 9, 56, 171, 0, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, -6, 45, -180, 1035, -3174, 12167], 'euler29': [1, -3, 51, -210, 1479, -2523, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, 6, 105, 380, 3255, 5766, 29791], 'euler37': [1, -15, 186, -1235, 6882, -20535, 50653], 'euler41': [1, 12, 123, 912, 5043, 20172, 68921], 'euler43': [1, 12, 84, 380, 3612, 22188, 79507], 'euler47': [1, 0, 117, 24, 5499, 0, 103823], 'euler5': [1, -3, 9, -18, 45, -75, 125], 'euler53': [1, -12, 180, -1266, 9540, -33708, 148877], 'euler59': [1, -18, 189, -1572, 11151, -62658, 205379], 'euler61': [1, 3, 105, 178, 6405, 11163, 226981], 'euler67': [1, 6, 132, 542, 8844, 26934, 300763], 'euler7': [1, 3, 3, 1, 0, 0, 0], 'euler71': [1, 0, 132, 108, 9372, 0, 357911], 'euler73': [1, -9, 207, -1298, 15111, -47961, 389017], 'euler79': [1, 6, 168, 686, 13272, 37446, 493039], 'euler83': [1, 12, 249, 1920, 20667, 82668, 571787], 'euler89': [1, -15, 315, -2622, 28035, -118815, 704969], 'euler97': [1, -12, 291, -2144, 28227, -112908, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, -3, 9, -18, 45, -75, 125], [1, 3, 3, 1, 0, 0, 0], [1, 6, 36, 126, 396, 726, 1331], [1, -3, 3, 34, 39, -507, 2197], [1, -3, 27, -114, 459, -867, 4913], [1, 0, 9, 56, 171, 0, 6859], [1, -6, 45, -180, 1035, -3174, 12167], [1, -3, 51, -210, 1479, -2523, 24389], [1, 6, 105, 380, 3255, 5766, 29791], [1, -15, 186, -1235, 6882, -20535, 50653], [1, 12, 123, 912, 5043, 20172, 68921], [1, 12, 84, 380, 3612, 22188, 79507], [1, 0, 117, 24, 5499, 0, 103823], [1, -12, 180, -1266, 9540, -33708, 148877], [1, -18, 189, -1572, 11151, -62658, 205379], [1, 3, 105, 178, 6405, 11163, 226981], [1, 6, 132, 542, 8844, 26934, 300763], [1, 0, 132, 108, 9372, 0, 357911], [1, -9, 207, -1298, 15111, -47961, 389017], [1, 6, 168, 686, 13272, 37446, 493039], [1, 12, 249, 1920, 20667, 82668, 571787], [1, -15, 315, -2622, 28035, -118815, 704969], [1, -12, 291, -2144, 28227, -112908, 912673]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9072/2/a/cb'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '6-9072e3-1.1-c1e3-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-9072e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.511185858251809, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 199445668463827448, 'z1': {'__RealLiteral__': 0, 'data': '0.26424483479941972698299773125', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '334970123440693737056700039699,1025129901805078021877927495075,1115852247743594399490945812787', 'Lhash_array': ['334970123440693737056700039699', '1025129901805078021877927495075', '1115852247743594399490945812787'], 'factors': ['2-9072-1.1-c1-0-2', '2-9072-1.1-c1-0-47', '2-9072-1.1-c1-0-55'], 'label': '6-9072e3-1.1-c1e3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9072/2/a/cb'}