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lfunc_lfunctions • Show schema
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{'Lhash': '2111265697744344900538117964710', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.85490444289385, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [19, [1, 1]]], 'bad_primes': [2, 19], 'central_character': '608.1', 'coefficient_field': '1.1.1.1', 'conductor': 608, 'conductor_radical': 38, 'degree': 2, 'euler_factors': [[1], [1, -3, 3], [1, 0, 5], [1, 1, 7], [1, -2, 11], [1, 1, 13], [1, -3, 17], [1, 1], [1, -3, 23], [1, -3, 29], [1, -8, 31], [1, 10, 37], [1, 12, 41], [1, -8, 43], [1, 8, 47], [1, 9, 53], [1, 5, 59], [1, -10, 61], [1, -7, 67], [1, 10, 71], [1, -1, 73], [1, 14, 79], [1, -6, 83], [1, 4, 89], [1, 6, 97], [1, -10, 101], [1, -14, 103], [1, -5, 107], [1, -9, 109], [1, -2, 113]], 'euler_factors_factorization': [[1], [[[1, -3, 3], 1]], [[[1, 0, 5], 1]], [[[1, 1, 7], 1]], [[[1, -2, 11], 1]], [[[1, 1, 13], 1]], [[[1, -3, 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1.7362748123901097, 1.772227328902114, 1.3895702293496586, 0.7511114967534358, 0.11765895110444952, -0.2589708424919528, -0.23890930180800274, 0.1475171261281179], 'positive_zeros': ['1.66549496948467502043296521631140', '2.94857221124987493994611399801079', '3.66834687648261549407687934910815', '4.82665740673161335065260299640417', '6.39357456655427571414069968223724', '7.28048593381483137900855724231201', '8.197820813644998743406881037051484', '8.796590556881761178241246784033804', '9.752900189125497232452224011820323', '10.15555477800038159845119846558880'], 'prelabel': '2-608-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.203384769597414, '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': 265043389064013348, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66549496948467502043296521631', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94857221124987493994611399801', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.66834687648261549407687934911', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.85490444289385, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 608, 'conductor_radical': 38, 'degree': 2, 'dirichlet_coefficients': [1, 0, 3, 0, 0, 0, -1, 0, 6, 0, 2, 0, -1, 0, 0, 0, 3, 0, -1, 0, -3, 0, 3, 0, -5, 0, 9, 0, 3, 0, 8, 0, 6, 0, 0, 0, -10, 0, -3, 0, -12, 0, 8, 0, 0, 0, -8, 0, -6, 0, 9, 0, -9, 0, 0, 0, -3, 0, -5, 0, 10, 0, -6, 0, 0, 0, 7, 0, 9, 0, -10, 0, 1, 0, -15, 0, -2, 0, -14, 0, 9, 0, 6, 0, 0, 0, 9, 0, -4, 0, 1, 0, 24, 0, 0, 0, -6, 0, 12, 0], 'euler11': [1, -2, 11], 'euler13': [1, 1, 13], 'euler17': [1, -3, 17], 'euler19': [1, 1, 0], 'euler2': [1, 0, 0], 'euler23': [1, -3, 23], 'euler29': [1, -3, 29], 'euler3': [1, -3, 3], 'euler31': [1, -8, 31], 'euler37': [1, 10, 37], 'euler41': [1, 12, 41], 'euler43': [1, -8, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 5], 'euler53': [1, 9, 53], 'euler59': [1, 5, 59], 'euler61': [1, -10, 61], 'euler67': [1, -7, 67], 'euler7': [1, 1, 7], 'euler71': [1, 10, 71], 'euler73': [1, -1, 73], 'euler79': [1, 14, 79], 'euler83': [1, -6, 83], 'euler89': [1, 4, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, -3, 3], [1, 0, 5], [1, 1, 7], [1, -2, 11], [1, 1, 13], [1, -3, 17], [1, 1, 0], [1, -3, 23], [1, -3, 29], [1, -8, 31], [1, 10, 37], [1, 12, 41], [1, -8, 43], [1, 8, 47], [1, 9, 53], [1, 5, 59], [1, -10, 61], [1, -7, 67], [1, 10, 71], [1, -1, 73], [1, 14, 79], [1, -6, 83], [1, 4, 89], [1, 6, 97]], 'index': 9, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/608/f', 'ModularForm/GL2/Q/holomorphic/608/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/608/2/a/f'], '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': '2-608-1.1-c1-0-9', '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': '2-608-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.203384769597414, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 265043389064013348, 'z1': {'__RealLiteral__': 0, 'data': '1.66549496948467502043296521631', 'prec': 103}}
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lfunc_instances • Show schema
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id: 12152182
{'Lhash': '2111265697744344900538117964710', 'Lhash_array': ['2111265697744344900538117964710'], 'label': '2-608-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/608/2/a/f'}
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id: 24549919
{'Lhash': '2111265697744344900538117964710', 'Lhash_array': ['2111265697744344900538117964710'], 'label': '2-608-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/608/2/a/f/1/1'}
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id: 95898
{'Lhash': '265043389064013348', 'Lhash_array': ['265043389064013348'], 'label': '2-608-1.1-c1-0-9', 'type': 'ECQ', 'url': 'EllipticCurve/Q/608/f'}