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lfunc_lfunctions • Show schema
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{'Lhash': '2878577556645347278512271402587', 'a10': 0, 'a2': 2, 'a3': 0, 'a4': 2, 'a5': 0, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '225.1', 'coefficient_field': '1.1.1.1', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, -2, 2], [1], [1], [1, -3, 7], [1, 2, 11], [1, 1, 13], [1, -2, 17], [1, 5, 19], [1, -6, 23], [1, 10, 29], [1, 3, 31], [1, 2, 37], [1, -8, 41], [1, 1, 43], [1, -2, 47], [1, 4, 53], [1, -10, 59], [1, -7, 61], [1, -3, 67], [1, -8, 71], [1, -14, 73], [1, 0, 79], [1, -6, 83], [1, 0, 89], [1, 17, 97], [1, 12, 101], [1, -4, 103], [1, -12, 107], [1, -5, 109], [1, 4, 113]], 'euler_factors_factorization': [[[[1, -2, 2], 1]], [1], [1], [[[1, -3, 7], 1]], [[[1, 2, 11], 1]], [[[1, 1, 13], 1]], [[[1, -2, 17], 1]], [[[1, 5, 19], 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-0.5659491166101738, -0.37843816766725813, -0.06766744874883705, 0.20669180710117938, 0.2930966704435994, 0.10079411238613066, -0.36658356512765145], 'positive_zeros': ['2.27079729708413704097834802657905', '3.78545707329788062312381068332996', '4.92213034669592094010306499373611', '5.60694328736998842121660037612863', '6.99182605075727565742724929802103', '8.102126663118456650752904190011748', '9.294135845295806835405725735271406', '10.84373752796776504705892968640759', '11.37636969058177948973372420564676', '12.58033395895800211021523424017459'], 'prelabel': '2-15e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.3403857823323886, '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': 1813732781413488101, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.27079729708413704097834802658', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.78545707329788062312381068333', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.92213034669592094010306499374', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 2, 0, 0, 3, 0, 0, 0, -2, 0, -1, 6, 0, -4, 2, 0, -5, 0, 0, -4, 6, 0, 0, -2, 0, 6, -10, 0, -3, -8, 0, 4, 0, 0, -2, -10, 0, 0, 8, 0, -1, -4, 0, 12, 2, 0, 2, 0, 0, -2, -4, 0, 0, 0, 0, -20, 10, 0, 7, -6, 0, -8, 0, 0, 3, 4, 0, 0, 8, 0, 14, -4, 0, -10, -6, 0, 0, 0, 0, 16, 6, 0, 0, -2, 0, 0, 0, 0, -3, 12, 0, 4, 0, 0, -17, 4, 0, 0], 'euler11': [1, 2, 11], 'euler13': [1, 1, 13], 'euler17': [1, -2, 17], 'euler19': [1, 5, 19], 'euler2': [1, -2, 2], 'euler23': [1, -6, 23], 'euler29': [1, 10, 29], 'euler3': [1, 0, 0], 'euler31': [1, 3, 31], 'euler37': [1, 2, 37], 'euler41': [1, -8, 41], 'euler43': [1, 1, 43], 'euler47': [1, -2, 47], 'euler5': [1, 0, 0], 'euler53': [1, 4, 53], 'euler59': [1, -10, 59], 'euler61': [1, -7, 61], 'euler67': [1, -3, 67], 'euler7': [1, -3, 7], 'euler71': [1, -8, 71], 'euler73': [1, -14, 73], 'euler79': [1, 0, 79], 'euler83': [1, -6, 83], 'euler89': [1, 0, 89], 'euler97': [1, 17, 97], 'euler_factors': [[1, -2, 2], [1, 0, 0], [1, 0, 0], [1, -3, 7], [1, 2, 11], [1, 1, 13], [1, -2, 17], [1, 5, 19], [1, -6, 23], [1, 10, 29], [1, 3, 31], [1, 2, 37], [1, -8, 41], [1, 1, 43], [1, -2, 47], [1, 4, 53], [1, -10, 59], [1, -7, 61], [1, -3, 67], [1, -8, 71], [1, -14, 73], [1, 0, 79], [1, -6, 83], [1, 0, 89], [1, 17, 97]], 'index': 4, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/225/e', 'ModularForm/GL2/Q/holomorphic/225/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/225/2/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': '2-15e2-1.1-c1-0-4', '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': '2-15e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1813732781413488101, 'z1': {'__RealLiteral__': 0, 'data': '2.27079729708413704097834802658', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10064046
{'Lhash': '2878577556645347278512271402587', 'Lhash_array': ['2878577556645347278512271402587'], 'label': '2-15e2-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/a/e'}
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id: 24548403
{'Lhash': '2878577556645347278512271402587', 'Lhash_array': ['2878577556645347278512271402587'], 'label': '2-15e2-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/a/e/1/1'}
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id: 22040
{'Lhash': '1813732781413488101', 'Lhash_array': ['1813732781413488101'], 'label': '2-15e2-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/225/e'}