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lfunc_lfunctions • Show schema
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{'Lhash': '488686499660733262649651754082', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -5.196152422706632], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 31.176914536239792], 'a8': [0.0, 0.0], 'a9': [-27.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.328366721102203, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 5.196152422706632]]]], 'bad_primes': [2, 3], 'central_character': '192.191', 'coefficient_field': 'CDF', 'conductor': 192, 'conductor_radical': 6, 'conjugate': '2342693778171423147523611312634', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 5.196152422706632]], [[1.0, 0], [0, 0], [-125.0, 0]], [[1.0, 0], [0, -31.176914536239792], [-343.0, 0]], [[1.0, 0], [0, 0], [1331.0, 0]], [[1.0, 0], [70.0, 0], [2197.0, 0]], [[1.0, 0], [0, 0], [-4913.0, 0]], [[1.0, 0], [0, -155.88457268119896], [-6859.0, 0]], [[1.0, 0], [0, 0], 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'rational': False, 'root_analytic_conductor': 3.365763913452963, 'root_angle': -0.5, 'root_number': '6.123233995736766e-17 - 1.0*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.38550567449165372010776371804', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88471476683056850439371472394', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29923251272244425073223636634', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.328366721102203, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 192, 'conductor_radical': 6, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/4/c/a/191/1'], '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': '2-192-12.11-c3-0-2', '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': '2-192-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.365763913452963, 'root_angle': -0.25, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.38550567449165372010776371804', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '488686499660733262649651754082', 'Lhash_array': ['488686499660733262649651754082'], 'label': '2-192-12.11-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/4/c/a/191/1'}