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lfunc_lfunctions • Show schema
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{'Lhash': '4658339895169879819369284508026', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.25552128646809735, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '32.1', 'coefficient_field': '1.1.1.1', 'conductor': 32, 'conductor_radical': 2, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, 2, 5], [1, 0, 7], [1, 0, 11], [1, -6, 13], [1, -2, 17], [1, 0, 19], [1, 0, 23], [1, 10, 29], [1, 0, 31], [1, 2, 37], [1, -10, 41], [1, 0, 43], [1, 0, 47], [1, -14, 53], [1, 0, 59], [1, 10, 61], [1, 0, 67], [1, 0, 71], [1, 6, 73], [1, 0, 79], [1, 0, 83], [1, -10, 89], [1, -18, 97], [1, 2, 101], [1, 0, 103], [1, 0, 107], [1, -6, 109], [1, 14, 113]], 'euler_factors_factorization': [[1], [[[1, 0, 3], 1]], [[[1, 2, 5], 1]], [[[1, 0, 7], 1]], [[[1, 0, 11], 1]], [[[1, -6, 13], 1]], [[[1, -2, 17], 1]], [[[1, 0, 19], 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0.22795055349514443, 0.7947026930963288, 1.2321610154709486, 1.4322616434509643, 1.3291437154867003, 0.9120376561272512, 0.22858107622077595], 'positive_zeros': ['3.67478222653086463350186782835361', '5.87146418848833687506982135025618', '7.77199473906097062385997282225311', '8.955386231165229198073332132052119', '10.90769214371221130983350005998246', '11.76661268274493420855693255102103', '13.27687552535142704095990346642387', '14.57652563978276046331230069556564', '15.74882074786535250024495459074091', '16.73856366990991880815681244917426'], 'prelabel': '2-2e5-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.5054911339164094, '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': 1485208795141819780, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.67478222653086463350186782835', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.87146418848833687506982135026', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.77199473906097062385997282225', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.25552128646809735, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 32, 'conductor_radical': 2, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 10, 0, 0, 0, 6, 0, 0, 0, -7, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, -4, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -6, 13], 'euler17': [1, -2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 10, 29], 'euler3': [1, 0, 3], 'euler31': [1, 0, 31], 'euler37': [1, 2, 37], 'euler41': [1, -10, 41], 'euler43': [1, 0, 43], 'euler47': [1, 0, 47], 'euler5': [1, 2, 5], 'euler53': [1, -14, 53], 'euler59': [1, 0, 59], 'euler61': [1, 10, 61], 'euler67': [1, 0, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 6, 73], 'euler79': [1, 0, 79], 'euler83': [1, 0, 83], 'euler89': [1, -10, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, 2, 5], [1, 0, 7], [1, 0, 11], [1, -6, 13], [1, -2, 17], [1, 0, 19], [1, 0, 23], [1, 10, 29], [1, 0, 31], [1, 2, 37], [1, -10, 41], [1, 0, 43], [1, 0, 47], [1, -14, 53], [1, 0, 59], [1, 10, 61], [1, 0, 67], [1, 0, 71], [1, 6, 73], [1, 0, 79], [1, 0, 83], [1, -10, 89], [1, -18, 97]], 'index': 0, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/32/a', 'ModularForm/GL2/Q/holomorphic/32/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/32/2/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': '2-2e5-1.1-c1-0-0', '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': '2-2e5-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.5054911339164094, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1485208795141819780, 'z1': {'__RealLiteral__': 0, 'data': '3.67478222653086463350186782835', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9955711
{'Lhash': '4658339895169879819369284508026', 'Lhash_array': ['4658339895169879819369284508026'], 'label': '2-2e5-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/32/2/a/a'}
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id: 24545951
{'Lhash': '4658339895169879819369284508026', 'Lhash_array': ['4658339895169879819369284508026'], 'label': '2-2e5-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/32/2/a/a/1/1'}
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id: 22123
{'Lhash': '1485208795141819780', 'Lhash_array': ['1485208795141819780'], 'label': '2-2e5-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32/a'}