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lfunc_lfunctions • Show schema
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{'Lhash': '2957138762022815088891980586987', 'a10': 0, 'a2': -2, 'a3': 0, 'a4': 2, 'a5': 0, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5730529198192242, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[197, [1, 1]]], 'bad_primes': [197], 'central_character': '197.1', 'coefficient_field': '1.1.1.1', 'conductor': 197, 'conductor_radical': 197, 'degree': 2, 'euler_factors': [[1, 2, 2], [1, 0, 3], [1, 0, 5], [1, 3, 7], [1, -4, 11], [1, 2, 13], [1, 8, 17], [1, 3, 19], [1, 3, 23], [1, -7, 29], [1, 10, 31], [1, -7, 37], [1, -9, 41], [1, -1, 43], [1, 11, 47], [1, -10, 53], [1, 0, 59], [1, -5, 61], [1, 10, 67], [1, -8, 71], [1, -6, 73], [1, -2, 79], [1, 7, 83], [1, 8, 89], [1, 2, 97], [1, 15, 101], [1, 4, 103], [1, 9, 107], [1, -13, 109], [1, 4, 113]], 'euler_factors_factorization': [[[[1, 2, 2], 1]], [[[1, 0, 3], 1]], [[[1, 0, 5], 1]], [[[1, 3, 7], 1]], [[[1, -4, 11], 1]], [[[1, 2, 13], 1]], 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1.108393607950446, 2.348072736601828, 2.5868486194136264, 1.8098910930219612, 0.23551377738102783, -1.7352738463335182, -3.614385146451697, -4.944301042327082, -5.408637545570201], 'positive_zeros': ['2.33277116067346011831864956690002', '4.15785519193072071590213469433070', '6.17591940844279569664203110179463', '6.92472041340395206972505718476572', '8.282753935470816342481418791481203', '9.141663261808505731463150219631335', '9.670505384884660391398822501320586', '10.87939044119722991367373344739338', '11.63768790626971835185556947748821'], 'prelabel': '2-197-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.254214064591537, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1531726400669359020, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.33277116067346011831864956690', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.15785519193072071590213469433', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.17591940844279569664203110179', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5730529198192242, 'bad_primes': [197], 'central_character': '1.1', 'conductor': 197, 'conductor_radical': 197, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 2, 0, 0, -3, 0, -3, 0, 4, 0, -2, 6, 0, -4, -8, 6, -3, 0, 0, -8, -3, 0, -5, 4, 0, -6, 7, 0, -10, 8, 0, 16, 0, -6, 7, 6, 0, 0, 9, 0, 1, 8, 0, 6, -11, 0, 2, 10, 0, -4, 10, 0, 0, 0, 0, -14, 0, 0, 5, 20, 9, -8, 0, 0, -10, -16, 0, 0, 8, 0, 6, -14, 0, -6, -12, 0, 2, 0, 9, -18, -7, 0, 0, -2, 0, 0, -8, 0, 6, -6, 0, 22, 0, 0, -2, -4, -12, -10], 'euler11': [1, -4, 11], 'euler13': [1, 2, 13], 'euler17': [1, 8, 17], 'euler19': [1, 3, 19], 'euler2': [1, 2, 2], 'euler23': [1, 3, 23], 'euler29': [1, -7, 29], 'euler3': [1, 0, 3], 'euler31': [1, 10, 31], 'euler37': [1, -7, 37], 'euler41': [1, -9, 41], 'euler43': [1, -1, 43], 'euler47': [1, 11, 47], 'euler5': [1, 0, 5], 'euler53': [1, -10, 53], 'euler59': [1, 0, 59], 'euler61': [1, -5, 61], 'euler67': [1, 10, 67], 'euler7': [1, 3, 7], 'euler71': [1, -8, 71], 'euler73': [1, -6, 73], 'euler79': [1, -2, 79], 'euler83': [1, 7, 83], 'euler89': [1, 8, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 2, 2], [1, 0, 3], [1, 0, 5], [1, 3, 7], [1, -4, 11], [1, 2, 13], [1, 8, 17], [1, 3, 19], [1, 3, 23], [1, -7, 29], [1, 10, 31], [1, -7, 37], [1, -9, 41], [1, -1, 43], [1, 11, 47], [1, -10, 53], [1, 0, 59], [1, -5, 61], [1, 10, 67], [1, -8, 71], [1, -6, 73], [1, -2, 79], [1, 7, 83], [1, 8, 89], [1, 2, 97]], 'index': 8, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/197/a', 'ModularForm/GL2/Q/holomorphic/197/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/197/2/a/a'], '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': '2-197-1.1-c1-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-197-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.254214064591537, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1531726400669359020, 'z1': {'__RealLiteral__': 0, 'data': '2.33277116067346011831864956690', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10027878
{'Lhash': '2957138762022815088891980586987', 'Lhash_array': ['2957138762022815088891980586987'], 'factors': ['2-197-1.1-c1-0-8'], 'label': '2-197-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/197/2/a/a'}
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id: 24548008
{'Lhash': '2957138762022815088891980586987', 'Lhash_array': ['2957138762022815088891980586987'], 'factors': ['2-197-1.1-c1-0-8'], 'label': '2-197-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/197/2/a/a/1/1'}
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id: 21974
{'Lhash': '1531726400669359020', 'Lhash_array': ['1531726400669359020'], 'factors': ['2-197-1.1-c1-0-8'], 'label': '2-197-1.1-c1-0-8', 'type': 'ECQ', 'url': 'EllipticCurve/Q/197/a'}