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lfunc_lfunctions • Show schema
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{'Lhash': '2572007365695277247873104771509,3802367330539273659400178365225', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.011620418016144782, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1, -1, 1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '216.1', 'coefficient_field': '1.1.1.1', 'conductor': 46656, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1, -1, 1], [1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 1, 0, 1, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, 4, 6, 4, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1]], 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'4.34688403368470327698843044605607', '4.80359899466792150821964388886538', '5.60946620480892776908866980381557', '5.85262563460310281494664278878045', '6.45581861224275953103461660851256', '7.27330252395249658553950690551183', '7.78871758008494411283579834539534', '8.440327092698017982364765255790247', '8.628332674260032220341229115632012', '9.666611710270148306101285950825077', '9.785940083012428641225926651121382', '10.45068527584334776278651051759561', '10.89885766179764084292457815164961', '11.50416066905037812463826442050946', '12.05278273691497617937970632253139', '12.43047215731515122245881153187262', '12.89328439347955743801991004717465'], 'prelabel': '4-6e6-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.3283261225195591, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e2-0', 'trace_hash': 422578371568114731, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.02895605873748635540766396231', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.99953893435201362555814620289', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.54587282395174421740539371584', 'prec': 100}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.011620418016144782, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 46656, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, 2, 0, -2, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 1, 0, 1, -4, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0], 'euler11': [1, 1, 0, 1, 1], 'euler13': [1, 0, 1, 0, 1], 'euler17': [1, -2, 3, -2, 1], 'euler19': [1, 2, 3, 2, 1], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, 0, 1, 0, 1], 'euler29': [1, 0, 1, 0, 1], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 1, 0, 1], 'euler37': [1, 0, -2, 0, 1], 'euler41': [1, 1, 0, 1, 1], 'euler43': [1, -1, 0, -1, 1], 'euler47': [1, 0, 1, 0, 1], 'euler5': [1, 0, 1, 0, 1], 'euler53': [1, 0, -2, 0, 1], 'euler59': [1, 1, 0, 1, 1], 'euler61': [1, 0, 1, 0, 1], 'euler67': [1, -1, 0, -1, 1], 'euler7': [1, 0, 1, 0, 1], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, 2, 3, 2, 1], 'euler79': [1, 0, 1, 0, 1], 'euler83': [1, -2, 3, -2, 1], 'euler89': [1, 4, 6, 4, 1], 'euler97': [1, -1, 0, -1, 1], 'euler_factors': [[1, -1, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 1, 0, 1, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, 4, 6, 4, 1], [1, -1, 0, -1, 1]], 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/216/1/p/a', 'ArtinRepresentation/2.216.12t18.a'], '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': '4-6e6-1.1-c0e2-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-6e6-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.3283261225195591, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 422578371568114731, 'z1': {'__RealLiteral__': 0, 'data': '2.02895605873748635540766396231', 'prec': 100}}
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lfunc_instances • Show schema
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id: 19806838
{'Lhash': '2572007365695277247873104771509,3802367330539273659400178365225', 'Lhash_array': ['2572007365695277247873104771509', '3802367330539273659400178365225'], 'factors': ['2-6e3-72.67-c0-0-0', '2-6e3-72.43-c0-0-0'], 'label': '4-6e6-1.1-c0e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/216/1/p/a'}
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id: 24602953
{'Lhash': '2572007365695277247873104771509,3802367330539273659400178365225', 'Lhash_array': ['2572007365695277247873104771509', '3802367330539273659400178365225'], 'factors': ['2-6e3-72.67-c0-0-0', '2-6e3-72.43-c0-0-0'], 'label': '4-6e6-1.1-c0e2-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.216.12t18.a'}