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lfunc_lfunctions • Show schema
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{'Lhash': '1957266624506733029729586215659', 'a10': 0, 'a2': 1, 'a3': -1, 'a4': 1, 'a5': 0, 'a6': -1, 'a7': 0, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.826704231553327, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [59, [1, 1]]], 'bad_primes': [2, 3, 59], 'central_character': '354.1', 'coefficient_field': '1.1.1.1', 'conductor': 354, 'conductor_radical': 354, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1, 0, 5], [1, 0, 7], [1, -4, 11], [1, -4, 13], [1, -6, 17], [1, 4, 19], [1, 4, 23], [1, 0, 29], [1, -2, 31], [1, 8, 37], [1, -6, 41], [1, -4, 43], [1, 4, 47], [1, -4, 53], [1, 1], [1, 0, 61], [1, 16, 67], [1, 14, 71], [1, -2, 73], [1, 8, 79], [1, 4, 83], [1, -14, 89], [1, 10, 97], [1, -10, 101], [1, 6, 103], [1, -8, 107], [1, -12, 109], [1, -2, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 1], 1]], [[[1, 0, 5], 1]], [[[1, 0, 7], 1]], [[[1, -4, 11], 1]], [[[1, -4, 13], 1]], [[[1, -6, 17], 1]], [[[1, 4, 19], 1]], [[[1, 4, 23], 1]], [[[1, 0, 29], 1]], [[[1, -2, 31], 1]], [[[1, 8, 37], 1]], [[[1, -6, 41], 1]], [[[1, -4, 43], 1]], [[[1, 4, 47], 1]], [[[1, -4, 53], 1]], [[[1, 1], 1]], [[[1, 0, 61], 1]], [[[1, 16, 67], 1]], [[[1, 14, 71], 1]], [[[1, -2, 73], 1]], [[[1, 8, 79], 1]], [[[1, 4, 83], 1]], [[[1, -14, 89], 1]], [[[1, 10, 97], 1]], [[[1, -10, 101], 1]], [[[1, 6, 103], 1]], [[[1, -8, 107], 1]], [[[1, -12, 109], 1]], [[[1, -2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-354-1.1-c1-0-3', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/354/2/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8409783331201197, 1.8417998966957378, 1.8423559717823161, 1.837224184361958, 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-2.1897614779428984, -1.429825974792316, -0.2713324220084274, 0.9888160646155575, 2.0186969064665474, 2.551010827585409, 2.4631409373434328, 1.812242498458406, 0.8141842932094155], 'positive_zeros': ['1.54401112116725562678022616809798', '3.50805659982399413447420234647026', '4.36796421890856096558774242233181', '5.80228630342277487853618653006395', '6.28217746208683326257101326743595', '7.48440393090391762911408213576773', '8.628238308702649889360069262550763', '9.856175284535481399715124392166811', '10.73797373102496691707175534992648', '11.71776516013665861790392197541831'], 'prelabel': '2-354-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.6812805332701997, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1599516717612380460, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54401112116725562678022616810', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.50805659982399413447420234647', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.36796421890856096558774242233', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.826704231553327, 'bad_primes': [2, 3, 59], 'central_character': '1.1', 'conductor': 354, 'conductor_radical': 354, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 0, -1, 0, 1, 1, 0, 4, -1, 4, 0, 0, 1, 6, 1, -4, 0, 0, 4, -4, -1, -5, 4, -1, 0, 0, 0, 2, 1, -4, 6, 0, 1, -8, -4, -4, 0, 6, 0, 4, 4, 0, -4, -4, -1, -7, -5, -6, 4, 4, -1, 0, 0, 4, 0, -1, 0, 0, 2, 0, 1, 0, -4, -16, 6, 4, 0, -14, 1, 2, -8, 5, -4, 0, -4, -8, 0, 1, 6, -4, 0, 0, 4, 0, 4, 14, 0, 0, -4, -2, -4, 0, -1, -10, -7, 4, -5], 'euler11': [1, -4, 11], 'euler13': [1, -4, 13], 'euler17': [1, -6, 17], 'euler19': [1, 4, 19], 'euler2': [1, -1, 0], 'euler23': [1, 4, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, -2, 31], 'euler37': [1, 8, 37], 'euler41': [1, -6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 4, 47], 'euler5': [1, 0, 5], 'euler53': [1, -4, 53], 'euler59': [1, 1, 0], 'euler61': [1, 0, 61], 'euler67': [1, 16, 67], 'euler7': [1, 0, 7], 'euler71': [1, 14, 71], 'euler73': [1, -2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 4, 83], 'euler89': [1, -14, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, 0, 5], [1, 0, 7], [1, -4, 11], [1, -4, 13], [1, -6, 17], [1, 4, 19], [1, 4, 23], [1, 0, 29], [1, -2, 31], [1, 8, 37], [1, -6, 41], [1, -4, 43], [1, 4, 47], [1, -4, 53], [1, 1, 0], [1, 0, 61], [1, 16, 67], [1, 14, 71], [1, -2, 73], [1, 8, 79], [1, 4, 83], [1, -14, 89], [1, 10, 97]], 'index': 3, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/354/e', 'ModularForm/GL2/Q/holomorphic/354/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/354/2/a/e'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-354-1.1-c1-0-3', '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': '2-354-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.6812805332701997, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1599516717612380460, 'z1': {'__RealLiteral__': 0, 'data': '1.54401112116725562678022616810', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10383706
{'Lhash': '1957266624506733029729586215659', 'Lhash_array': ['1957266624506733029729586215659'], 'label': '2-354-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/354/2/a/e'}
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id: 24549085
{'Lhash': '1957266624506733029729586215659', 'Lhash_array': ['1957266624506733029729586215659'], 'label': '2-354-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/354/2/a/e/1/1'}
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id: 93519
{'Lhash': '1599516717612380460', 'Lhash_array': ['1599516717612380460'], 'label': '2-354-1.1-c1-0-3', 'type': 'ECQ', 'url': 'EllipticCurve/Q/354/e'}