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lfunc_lfunctions • Show schema
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{'Lhash': '1359405434105359044974246635385', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [21.35755975068582, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 69.386246166751, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-3.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1176.1', 'coefficient_field': 'CDF', 'conductor': 1176, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [-21.35755975068582, 0], [125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-31.35755975068582, 0], [1331.0, 0]], [[1.0, 0], [84.71511950137163, 0], [2197.0, 0]], [[1.0, 0], [-16.07267925205746, 0], [4913.0, 0]], [[1.0, 0], [20.0, 0], [6859.0, 0]], [[1.0, 0], [80.7877987534291, 0], [12167.0, 0]], [[1.0, 0], [-102.0, 0], 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'5.16724276032225045010682939806927', '6.11981081410916523755818810393916', '6.77591550613549412981129215370443', '7.76170822180029035495302287593879', '8.847035982021804425222343869863918', '9.509599816015690414425847846567606'], 'prelabel': '2-1176-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.329840704764466, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07238180131071605084645991421', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22789930601882573389399924082', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.71780340321345677952077662760', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 69.386246166751, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1176, 'conductor_radical': 42, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1176/4/a/w/1/2'], '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': '2-1176-1.1-c3-0-30', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1176-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.329840704764466, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07238180131071605084645991421', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1359405434105359044974246635385', 'Lhash_array': ['1359405434105359044974246635385'], 'label': '2-1176-1.1-c3-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1176/4/a/w/1/2'}