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lfunc_lfunctions • Show schema
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{'Lhash': '1112043530107885316352784945670', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.606153953490637, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]], [17, [1, -1]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.1', 'coefficient_field': '1.1.1.1', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, -4, 5], [1], [1, 3, 11], [1, -5, 13], [1, -1], [1, 6, 19], [1, 4, 23], [1, -8, 29], [1, 0, 31], [1, 8, 37], [1, -8, 41], [1, -10, 43], [1, -2, 47], [1, -3, 53], [1, 2, 59], [1, -8, 61], [1, -14, 67], [1, -7, 71], [1, -8, 73], [1, -15, 79], [1, 12, 83], [1, 1, 89], [1, 18, 97], [1, -6, 101], [1, 4, 103], [1, -1, 107], [1, 8, 109], [1, 8, 113]], 'euler_factors_factorization': [[1], [[[1, 1, 3], 1]], [[[1, -4, 5], 1]], [1], [[[1, 3, 11], 1]], [[[1, -5, 13], 1]], [[[1, -1], 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-0.9089285688213417, -0.9526906971063144, -0.876325771062135, -0.6916814571629046, -0.41626276523013966, -0.07217296947600581, 0.3152042776410278, 0.7187058017984752, 1.1109856076359559, 1.4661140124223788, 1.7610849590840776, 1.9771419825724896], 'positive_zeros': ['0.877247665806075906579844897195062', '2.10933951911823627095213212569207', '2.74021814560234606035472977390723', '4.02612867331051694119474885613845', '5.17372327145834137805046453831305', '5.65155783123102046970331334827798', '6.26639307836174474805434261591988', '6.71433346291073231637249834347245', '8.152865808465919495805947046936728', '8.592745901478006067413909081133355'], 'prelabel': '2-3332-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.158115348990427, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1787678177966855210, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.877247665806075906579844897195', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.10933951911823627095213212569', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.74021814560234606035472977391', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.606153953490637, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 4, 0, 0, 0, -2, 0, -3, 0, 5, 0, -4, 0, 1, 0, -6, 0, 0, 0, -4, 0, 11, 0, 5, 0, 8, 0, 0, 0, 3, 0, 0, 0, -8, 0, -5, 0, 8, 0, 10, 0, -8, 0, 2, 0, 0, 0, -1, 0, 3, 0, -12, 0, 6, 0, -2, 0, 8, 0, 0, 0, 20, 0, 14, 0, 4, 0, 7, 0, 8, 0, -11, 0, 0, 0, 15, 0, 1, 0, -12, 0, 4, 0, -8, 0, -1, 0, 0, 0, 0, 0, -24, 0, -18, 0, 6, 0], 'euler11': [1, 3, 11], 'euler13': [1, -5, 13], 'euler17': [1, -1, 0], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -8, 29], 'euler3': [1, 1, 3], 'euler31': [1, 0, 31], 'euler37': [1, 8, 37], 'euler41': [1, -8, 41], 'euler43': [1, -10, 43], 'euler47': [1, -2, 47], 'euler5': [1, -4, 5], 'euler53': [1, -3, 53], 'euler59': [1, 2, 59], 'euler61': [1, -8, 61], 'euler67': [1, -14, 67], 'euler7': [1, 0, 0], 'euler71': [1, -7, 71], 'euler73': [1, -8, 73], 'euler79': [1, -15, 79], 'euler83': [1, 12, 83], 'euler89': [1, 1, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, -4, 5], [1, 0, 0], [1, 3, 11], [1, -5, 13], [1, -1, 0], [1, 6, 19], [1, 4, 23], [1, -8, 29], [1, 0, 31], [1, 8, 37], [1, -8, 41], [1, -10, 43], [1, -2, 47], [1, -3, 53], [1, 2, 59], [1, -8, 61], [1, -14, 67], [1, -7, 71], [1, -8, 73], [1, -15, 79], [1, 12, 83], [1, 1, 89], [1, 18, 97]], 'index': 17, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3332/c', 'ModularForm/GL2/Q/holomorphic/3332/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/3332/2/a/c'], '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': '2-3332-1.1-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': '2-3332-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.158115348990427, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1787678177966855210, 'z1': {'__RealLiteral__': 0, 'data': '0.877247665806075906579844897195', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20484613
{'Lhash': '1112043530107885316352784945670', 'Lhash_array': ['1112043530107885316352784945670'], 'label': '2-3332-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/2/a/c'}
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id: 24561141
{'Lhash': '1112043530107885316352784945670', 'Lhash_array': ['1112043530107885316352784945670'], 'label': '2-3332-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/2/a/c/1/1'}
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id: 37701
{'Lhash': '1787678177966855210', 'Lhash_array': ['1787678177966855210'], 'label': '2-3332-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3332/c'}