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lfunc_lfunctions • Show schema
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{'Lhash': '748853088922303048785850655179,2126554745434663582123719728711', 'a10': 1, 'a2': -1, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 1, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2811510862799622, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 1]], [3, [1]], [7, [1, -1, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.1', 'coefficient_field': '1.1.1.1', 'conductor': 5143824, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, 1, 1], [1], [1, 1, 0, 1, 1], [1, -1, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 4, 6, 4, 1], [1, -2, 3, -2, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 2, 3, 2, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, 1, 0, 1, 1], [1, -4, 6, 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'5.08253181733135584145480783250994', '5.99987358125071482286251452212089', '6.59549761355052160381798194967822', '6.98831923034405337640474694243152', '7.09678196668526935685427506809631', '7.46314202071736085099869323404342', '7.952754639453290614692009359621347', '8.426778567277041829403347678834409', '8.804816752549850898130288785366881', '8.911380546109075490693015780755868', '9.144276481330495505466488822654258'], 'prelabel': '4-2268e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.063898232281476, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 1534103994462235805, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59074092560479883092033320852', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.67755590148562703536005320934', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.72010137694663409963575000526', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2811510862799622, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 5143824, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 0, -1, 0, 1, 1, 0, 1, 1, 0, 0, -1, 0, -1, -4, 0, 2, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 4, -1, 0, -2, -2, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, -2, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 4, 0, 0, 1, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0], 'euler11': [1, -1, 0, -1, 1], 'euler13': [1, 0, 1, 0, 1], 'euler17': [1, 4, 6, 4, 1], 'euler19': [1, -2, 3, -2, 1], 'euler2': [1, 1, 1, 0, 0], 'euler23': [1, -1, 0, -1, 1], 'euler29': [1, 0, 1, 0, 1], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 1, 0, 1, 1], 'euler37': [1, 2, 3, 2, 1], 'euler41': [1, 1, 0, 1, 1], 'euler43': [1, 0, 1, 0, 1], 'euler47': [1, 0, 1, 0, 1], 'euler5': [1, 1, 0, 1, 1], 'euler53': [1, 0, -2, 0, 1], 'euler59': [1, 0, 1, 0, 1], 'euler61': [1, 0, 1, 0, 1], 'euler67': [1, 0, 1, 0, 1], 'euler7': [1, -1, 1, 0, 0], 'euler71': [1, 2, 3, 2, 1], 'euler73': [1, 0, -2, 0, 1], 'euler79': [1, 0, 1, 0, 1], 'euler83': [1, 0, 1, 0, 1], 'euler89': [1, -2, 3, -2, 1], 'euler97': [1, 0, 1, 0, 1], 'euler_factors': [[1, 1, 1, 0, 0], [1, 0, 0, 0, 0], [1, 1, 0, 1, 1], [1, -1, 1, 0, 0], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 4, 6, 4, 1], [1, -2, 3, -2, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 2, 3, 2, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, 0, 1, 0, 1]], 'index': 3, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2268/1/s/a', 'ArtinRepresentation/2.2268.12t18.b'], 'is_instance_Artin': True, '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': '4-2268e2-1.1-c0e2-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-2268e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.063898232281476, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 1534103994462235805, 'z1': {'__RealLiteral__': 0, 'data': '0.59074092560479883092033320852', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24606083
{'Lhash': '748853088922303048785850655179,2126554745434663582123719728711', 'Lhash_array': ['748853088922303048785850655179', '2126554745434663582123719728711'], 'factors': ['2-2268-252.167-c0-0-2', '2-2268-252.83-c0-0-13'], 'label': '4-2268e2-1.1-c0e2-0-3', 'type': 'Artin', 'url': 'ArtinRepresentation/2.2268.12t18.b'}
-
id: 19854092
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