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lfunc_lfunctions • Show schema
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{'Lhash': '519173951206083099278610085273,796440758229042242380546060647,1673773454748541741920215528339,2125557604926748902578127669220', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.4231959368982676, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 2, 0, 1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '2500.1', 'coefficient_field': '1.1.1.1', 'conductor': 39062500000000, 'conductor_radical': 10, 'degree': 8, 'euler_factors': [[1, 0, 2, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, -2, 3, -4, 5, -4, 3, -2, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 4, 0, 6, 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'prec': 10}, 'spectral_label': 'c0e4-0', 'trace_hash': 203220362289456063, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40955603311560012748092629782', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.62828097749147127048723355992', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.32037444264783487904565903411', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4231959368982676, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 39062500000000, 'conductor_radical': 10, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler13': [1, 0, -1, 0, 1, 0, -1, 0, 1], 'euler17': [1, 0, -1, 0, 1, 0, -1, 0, 1], 'euler19': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler2': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler23': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler29': [1, -2, 3, -4, 5, -4, 3, -2, 1], 'euler3': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler31': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler37': [1, 0, -1, 0, 1, 0, -1, 0, 1], 'euler41': [1, 2, 3, 4, 5, 4, 3, 2, 1], 'euler43': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler47': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -1, 0, 1, 0, -1, 0, 1], 'euler59': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler61': [1, 2, 3, 4, 5, 4, 3, 2, 1], 'euler67': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler7': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler71': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler73': [1, 0, -1, 0, 1, 0, -1, 0, 1], 'euler79': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler83': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler89': [1, -2, 3, -4, 5, -4, 3, -2, 1], 'euler97': [1, 0, -1, 0, 1, 0, -1, 0, 1], 'euler_factors': [[1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, -2, 3, -4, 5, -4, 3, -2, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, -2, 3, -4, 5, -4, 3, -2, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2500/1/d/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '8-50e8-1.1-c0e4-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '8-50e8-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.116988151943657, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e4-0', 'trace_hash': 203220362289456063, 'z1': {'__RealLiteral__': 0, 'data': '0.40955603311560012748092629782', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '519173951206083099278610085273,796440758229042242380546060647,1673773454748541741920215528339,2125557604926748902578127669220', 'Lhash_array': ['519173951206083099278610085273', '796440758229042242380546060647', '1673773454748541741920215528339', '2125557604926748902578127669220'], 'label': '8-50e8-1.1-c0e4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2500/1/d/a'}