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lfunc_lfunctions • Show schema
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{'Lhash': '2180799825353278534971526034571', 'a10': [8207.262604092422, 20911.764069279394], 'a2': [4.02560917576191, 17.637346200227835], 'a3': [-44.08859436980665, -40.90823731495012], 'a4': [166.42560861532579, -80.14634902873648], 'a5': [1227.8947683933409, -185.07535773924855], 'a6': [544.0292939233154, -942.2863778810047], 'a7': [-1047.1995142163582, -1813.8027642841794], 'a8': [7858.640566322523, 9854.423578115613], 'a9': [-1200.592158772519, -16020.78897719192], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.14654095504655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-12687598.4057996, 18482896.38097867]]]], 'bad_primes': [43], 'central_character': '43.10', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '945154309436940025174283724279', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.02560917576191, -17.637346200227835], [-461.2960603660386, 222.14847442818976]], 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0.22929582716624541, 'root_number': '0.7515722030533046 + 0.6596508346069171*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.11464791358312272', 'prec': 64}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72034772433401175645762261180621', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.81521252493729140390463910625324', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.72310374106378117241489800056491', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.14654095504655, 'bad_primes': [43], 'central_character': '43.10', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/10/g/a/10/22'], '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': '2-43-43.10-c9-0-22', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-43-43.10-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.706011151181705, 'root_angle': 0.11464791358312271, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72034772433401175645762261180621', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '2180799825353278534971526034571', 'Lhash_array': ['2180799825353278534971526034571'], 'label': '2-43-43.10-c9-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/10/g/a/10/22'}