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lfunc_lfunctions • Show schema
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{'Lhash': '1332442653590513402389536328951', 'a10': 2, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': 2, 'a6': 0, 'a7': -2, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.290492294873506, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '3042.1', 'coefficient_field': '1.1.1.1', 'conductor': 3042, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, -2, 5], [1, 2, 7], [1, 0, 11], [1], [1, 2, 17], [1, -6, 19], [1, -4, 23], [1, -10, 29], [1, 10, 31], [1, -8, 37], [1, -10, 41], [1, 4, 43], [1, -12, 47], [1, -6, 53], [1, 4, 59], [1, -2, 61], [1, -2, 67], [1, 0, 71], [1, 4, 73], [1, 0, 79], [1, 4, 83], [1, -6, 89], [1, -12, 97], [1, -2, 101], [1, -16, 103], [1, 8, 107], [1, 4, 109], [1, 14, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [1], [[[1, -2, 5], 1]], [[[1, 2, 7], 1]], [[[1, 0, 11], 1]], [1], [[[1, 2, 17], 1]], [[[1, -6, 19], 1]], [[[1, -4, 23], 1]], [[[1, -10, 29], 1]], [[[1, 10, 31], 1]], [[[1, -8, 37], 1]], [[[1, -10, 41], 1]], [[[1, 4, 43], 1]], [[[1, -12, 47], 1]], [[[1, -6, 53], 1]], [[[1, 4, 59], 1]], [[[1, -2, 61], 1]], [[[1, -2, 67], 1]], [[[1, 0, 71], 1]], [[[1, 4, 73], 1]], [[[1, 0, 79], 1]], [[[1, 4, 83], 1]], [[[1, -6, 89], 1]], [[[1, -12, 97], 1]], [[[1, -2, 101], 1]], [[[1, -16, 103], 1]], [[[1, 8, 107], 1]], [[[1, 4, 109], 1]], [[[1, 14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-3042-1.1-c1-0-22', 'leading_term': '3.37722236240950101261695954826000000000000000000000000000000000000000000000000000000000000', '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/3042/2/a/n', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': 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'1.05111191786649945850127259101', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34513957051456022215968764679', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.02995086886666391737100473760', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.290492294873506, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 3042, 'conductor_radical': 78, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 2, 0, -2, 1, 0, 2, 0, 0, 0, -2, 0, 1, -2, 0, 6, 2, 0, 0, 4, 0, -1, 0, 0, -2, 10, 0, -10, 1, 0, -2, -4, 0, 8, 6, 0, 2, 10, 0, -4, 0, 0, 4, 12, 0, -3, -1, 0, 0, 6, 0, 0, -2, 0, 10, -4, 0, 2, -10, 0, 1, 0, 0, 2, -2, 0, -4, 0, 0, -4, 8, 0, 6, 0, 0, 0, 2, 0, 10, -4, 0, -4, -4, 0, 0, 6, 0, 0, 4, 0, 12, 12, 0, 12, -3, 0, -1], 'euler11': [1, 0, 11], 'euler13': [1, 0, 0], 'euler17': [1, 2, 17], 'euler19': [1, -6, 19], 'euler2': [1, -1, 0], 'euler23': [1, -4, 23], 'euler29': [1, -10, 29], 'euler3': [1, 0, 0], 'euler31': [1, 10, 31], 'euler37': [1, -8, 37], 'euler41': [1, -10, 41], 'euler43': [1, 4, 43], 'euler47': [1, -12, 47], 'euler5': [1, -2, 5], 'euler53': [1, -6, 53], 'euler59': [1, 4, 59], 'euler61': [1, -2, 61], 'euler67': [1, -2, 67], 'euler7': [1, 2, 7], 'euler71': [1, 0, 71], 'euler73': [1, 4, 73], 'euler79': [1, 0, 79], 'euler83': [1, 4, 83], 'euler89': [1, -6, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, -2, 5], [1, 2, 7], [1, 0, 11], [1, 0, 0], [1, 2, 17], [1, -6, 19], [1, -4, 23], [1, -10, 29], [1, 10, 31], [1, -8, 37], [1, -10, 41], [1, 4, 43], [1, -12, 47], [1, -6, 53], [1, 4, 59], [1, -2, 61], [1, -2, 67], [1, 0, 71], [1, 4, 73], [1, 0, 79], [1, 4, 83], [1, -6, 89], [1, -12, 97]], 'index': 22, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3042/n', 'ModularForm/GL2/Q/holomorphic/3042/2/a/n/1/1', 'ModularForm/GL2/Q/holomorphic/3042/2/a/n'], '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': '2-3042-1.1-c1-0-22', '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': '2-3042-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.928538555684992, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1452917491409852034, 'z1': {'__RealLiteral__': 0, 'data': '1.05111191786649945850127259101', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20081112
{'Lhash': '1332442653590513402389536328951', 'Lhash_array': ['1332442653590513402389536328951'], 'label': '2-3042-1.1-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3042/2/a/n'}
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id: 24559864
{'Lhash': '1332442653590513402389536328951', 'Lhash_array': ['1332442653590513402389536328951'], 'label': '2-3042-1.1-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3042/2/a/n/1/1'}
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id: 25572
{'Lhash': '1452917491409852034', 'Lhash_array': ['1452917491409852034'], 'label': '2-3042-1.1-c1-0-22', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3042/n'}