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lfunc_lfunctions • Show schema
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{'Lhash': '1364352019643646242844129916705', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.847069993022323, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, -1]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'euler_factors': [[1], [1], [1, -2, 5], [1, 0, 7], [1, 0, 11], [1, -6, 13], [1, -6, 17], [1, -1], [1, -4, 23], [1, 2, 29], [1, 8, 31], [1, 10, 37], [1, -2, 41], [1, -4, 43], [1, -12, 47], [1, -6, 53], [1, 12, 59], [1, 2, 61], [1, -4, 67], [1, 0, 71], [1, -10, 73], [1, 0, 79], [1, -16, 83], [1, -2, 89], [1, -10, 97], [1, -10, 101], [1, 8, 103], [1, -4, 107], [1, 10, 109], [1, 6, 113]], 'euler_factors_factorization': [[1], [1], [[[1, -2, 5], 1]], [[[1, 0, 7], 1]], [[[1, 0, 11], 1]], [[[1, -6, 13], 1]], [[[1, -6, 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1.1099129493824242, 1.5936557664909035, 2.0679393407043873, 2.4912081560100874, 2.824072928622017, 3.032547086228189, 3.0909254777021617, 2.9840698731938655, 2.7089089114312683, 2.2750192237781253, 1.7042250855405257, 1.0292306897975803, 0.2913760009093097, -0.46232199599985585], 'positive_zeros': ['1.07628396925620245570845051253048', '1.95255670636420425042320954208735', '3.25148783575260438600086430314841', '3.84859941092912106278451327058144', '5.22523151161492305197654101067557', '5.69178884171323828176864961556391', '6.39584814801769229586264060019174', '7.33667434445098454643296446244942', '8.062008804214737453511932083588107', '9.092693734190788229037074202447569'], 'prelabel': '2-2736-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1543816632100312673, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07628396925620245570845051253', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95255670636420425042320954209', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.25148783575260438600086430315', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.847069993022323, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 1, 0, 0, 0, 4, 0, -1, 0, 0, 0, -2, 0, -8, 0, 0, 0, 0, 0, -10, 0, 0, 0, 2, 0, 4, 0, 0, 0, 12, 0, -7, 0, 0, 0, 6, 0, 0, 0, 0, 0, -12, 0, -2, 0, 0, 0, 12, 0, 4, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 12, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 10, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -6, 13], 'euler17': [1, -6, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, 10, 37], 'euler41': [1, -2, 41], 'euler43': [1, -4, 43], 'euler47': [1, -12, 47], 'euler5': [1, -2, 5], 'euler53': [1, -6, 53], 'euler59': [1, 12, 59], 'euler61': [1, 2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, -10, 73], 'euler79': [1, 0, 79], 'euler83': [1, -16, 83], 'euler89': [1, -2, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -2, 5], [1, 0, 7], [1, 0, 11], [1, -6, 13], [1, -6, 17], [1, -1, 0], [1, -4, 23], [1, 2, 29], [1, 8, 31], [1, 10, 37], [1, -2, 41], [1, -4, 43], [1, -12, 47], [1, -6, 53], [1, 12, 59], [1, 2, 61], [1, -4, 67], [1, 0, 71], [1, -10, 73], [1, 0, 79], [1, -16, 83], [1, -2, 89], [1, -10, 97]], 'index': 17, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2736/s', 'ModularForm/GL2/Q/holomorphic/2736/2/a/s/1/1', 'ModularForm/GL2/Q/holomorphic/2736/2/a/s'], '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': '2-2736-1.1-c1-0-17', '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': '2-2736-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1543816632100312673, 'z1': {'__RealLiteral__': 0, 'data': '1.07628396925620245570845051253', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20220981
{'Lhash': '1364352019643646242844129916705', 'Lhash_array': ['1364352019643646242844129916705'], 'label': '2-2736-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/a/s'}
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id: 24558584
{'Lhash': '1364352019643646242844129916705', 'Lhash_array': ['1364352019643646242844129916705'], 'label': '2-2736-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/a/s/1/1'}
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id: 92272
{'Lhash': '1543816632100312673', 'Lhash_array': ['1543816632100312673'], 'label': '2-2736-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2736/s'}