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lfunc_lfunctions • Show schema
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{'Lhash': '1771818984107415061682728160712', 'a10': 0, 'a2': 0, 'a3': -14, 'a4': 0, 'a5': 56, 'a6': 0, 'a7': 49, 'a8': 0, 'a9': -47, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 71.85195127621535, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -49]]], 'bad_primes': [2, 7], 'central_character': '448.1', 'coefficient_field': '1.1.1.1', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1], [1, 14, 243], [1, -56, 3125], [1, -49], [1, -232, 161051], [1, -140, 371293], [1, 1722, 1419857], [1, 98, 2476099], [1, 1824, 6436343], [1, 3418, 20511149], [1, -7644, 28629151], [1, -10398, 69343957], [1, 17962, 115856201], [1, -10880, 147008443], [1, 9324, 229345007], [1, 2262, 418195493], [1, 2730, 714924299], [1, 25648, 844596301], [1, 48404, 1350125107], [1, -58560, 1804229351], [1, -68082, 2073071593], [1, 31784, 3077056399], [1, 20538, 3939040643], [1, 50582, 5584059449], [1, 58506, 8587340257], 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1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 43, 'label': '2-448-1.1-c5-0-43', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/448/6/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.0884199572899712e-60, 0.22259866351640722, 0.441555469917657, 0.6532802077977101, 0.8542855531998466, 1.0412374955259294, 1.211004520477125, 1.360705101234828, 1.4877530225239635, 1.5899000325986719, 1.6652752877796426, 1.7124210254550418, 1.7303238771248641, 1.7184412159102838, 1.676721925751839, 1.6056209849659269, 1.506107277394627, 1.3796640822388175, 1.228281750575102, 1.054442153796575, 0.8610945874861761, 0.6516229335874598, 0.42980402354205893, 0.19975730394041033, -0.03411391795117778, -0.26718918156199856, -0.4947048657888417, -0.7118345933202109, 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'9.056049294397904300488206588404368', '9.913071822640726152024743688613568'], 'prelabel': '2-448-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.476553030342897, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 306217744281463870, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39771872769074897531002236466', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51011321749267820896969986293', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.19023577693847241362096888082', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 71.85195127621535, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 0, -14, 0, 56, 0, 49, 0, -47, 0, 232, 0, 140, 0, -784, 0, -1722, 0, -98, 0, -686, 0, -1824, 0, 11, 0, 4060, 0, -3418, 0, 7644, 0, -3248, 0, 2744, 0, 10398, 0, -1960, 0, -17962, 0, 10880, 0, -2632, 0, -9324, 0, 2401, 0, 24108, 0, -2262, 0, 12992, 0, 1372, 0, -2730, 0, -25648, 0, -2303, 0, 7840, 0, -48404, 0, 25536, 0, 58560, 0, 68082, 0, -154, 0, 11368, 0, -31784, 0, -45419, 0, -20538, 0, -96432, 0, 47852, 0, -50582, 0, 6860, 0, -107016, 0, -5488, 0, -58506, 0, -10904, 0], 'euler11': [1, -232, 161051], 'euler13': [1, -140, 371293], 'euler17': [1, 1722, 1419857], 'euler19': [1, 98, 2476099], 'euler2': [1, 0, 0], 'euler23': [1, 1824, 6436343], 'euler29': [1, 3418, 20511149], 'euler3': [1, 14, 243], 'euler31': [1, -7644, 28629151], 'euler37': [1, -10398, 69343957], 'euler41': [1, 17962, 115856201], 'euler43': [1, -10880, 147008443], 'euler47': [1, 9324, 229345007], 'euler5': [1, -56, 3125], 'euler53': [1, 2262, 418195493], 'euler59': [1, 2730, 714924299], 'euler61': [1, 25648, 844596301], 'euler67': [1, 48404, 1350125107], 'euler7': [1, -49, 0], 'euler71': [1, -58560, 1804229351], 'euler73': [1, -68082, 2073071593], 'euler79': [1, 31784, 3077056399], 'euler83': [1, 20538, 3939040643], 'euler89': [1, 50582, 5584059449], 'euler97': [1, 58506, 8587340257], 'euler_factors': [[1, 0, 0], [1, 14, 243], [1, -56, 3125], [1, -49, 0], [1, -232, 161051], [1, -140, 371293], [1, 1722, 1419857], [1, 98, 2476099], [1, 1824, 6436343], [1, 3418, 20511149], [1, -7644, 28629151], [1, -10398, 69343957], [1, 17962, 115856201], [1, -10880, 147008443], [1, 9324, 229345007], [1, 2262, 418195493], [1, 2730, 714924299], [1, 25648, 844596301], [1, 48404, 1350125107], [1, -58560, 1804229351], [1, -68082, 2073071593], [1, 31784, 3077056399], [1, 20538, 3939040643], [1, 50582, 5584059449], [1, 58506, 8587340257]], 'index': 43, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/448/6/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/448/6/a/c'], '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': '2-448-1.1-c5-0-43', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-448-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.476553030342897, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 306217744281463870, 'z1': {'__RealLiteral__': 0, 'data': '1.39771872769074897531002236466', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20372302
{'Lhash': '1771818984107415061682728160712', 'Lhash_array': ['1771818984107415061682728160712'], 'label': '2-448-1.1-c5-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/6/a/c'}
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id: 24586559
{'Lhash': '1771818984107415061682728160712', 'Lhash_array': ['1771818984107415061682728160712'], 'label': '2-448-1.1-c5-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/6/a/c/1/1'}