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lfunc_lfunctions • Show schema
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{'Lhash': '994823523225203409371270039601', 'a10': [3.2752957490651133, 0.0], 'a2': [-1.0, 0.0], 'a3': [-1.7911209485565363, 0.0], 'a4': [1.0, 0.0], 'a5': [-3.2752957490651133, 0.0], 'a6': [1.7911209485565363, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [0.20811425235806588, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 61.8201812448753, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [79, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7, 79], 'central_character': '7742.1', 'coefficient_field': 'CDF', 'conductor': 7742, 'conductor_radical': 1106, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [1.7911209485565363, 0], [3.0, 0]], [[1.0, 0], [3.2752957490651133, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.66788688938574, 0], [11.0, 0]], [[1.0, 0], [3.6156369125656194, 0], [13.0, 0]], [[1.0, 0], [-2.9699342860971805, 0], [17.0, 0]], [[1.0, 0], 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'4.60992316097354487009298403834261', '5.51605926131131645640261804197031', '6.38979994110086092832190632661840', '6.76056016207730060964291991945744', '7.64015866748904608222548586837906'], 'prelabel': '2-7742-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.862581080337124, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78477738506659022325976445336', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.03231015204319745801612064952', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17602266061067149348296997912', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 61.8201812448753, 'bad_primes': [2, 7, 79], 'central_character': '1.1', 'conductor': 7742, 'conductor_radical': 1106, 'degree': 2, 'index': 86, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7742/2/a/bk/1/4'], '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': '2-7742-1.1-c1-0-86', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-7742-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.862581080337124, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78477738506659022325976445336', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '994823523225203409371270039601', 'Lhash_array': ['994823523225203409371270039601'], 'factors': ['2-7742-1.1-c1-0-86'], 'label': '2-7742-1.1-c1-0-86', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7742/2/a/bk/1/4'}