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lfunc_lfunctions • Show schema
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{'Lhash': '1863163426401926699875067625949', 'a10': [-0.6962426866527464, 0.0], 'a2': [1.0536771612163032, 0.0], 'a3': [2.278553219892704, 0.0], 'a4': [-0.8897644399311527, 0.0], 'a5': [-0.6607742032189865, 0.0], 'a6': [2.400859488416811, 0.0], 'a7': [3.155923558783142, 0.0], 'a8': [-3.044878791650477, 0.0], 'a9': [2.191804775883409, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.849294518691866, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[983, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [983], 'central_character': '983.1', 'coefficient_field': 'CDF', 'conductor': 983, 'conductor_radical': 983, 'conjugate': '1863163426401926699875067625949', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0536771612163032, 0], [2.0, 0]], [[1.0, 0], [-2.278553219892704, 0], [3.0, 0]], [[1.0, 0], [0.6607742032189865, 0], [5.0, 0]], [[1.0, 0], [-3.155923558783142, 0], [7.0, 0]], [[1.0, 0], [-2.391058245881305, 0], [11.0, 0]], [[1.0, 0], 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'3.79305841733673664137787366893370', '4.41730188960701406847212448941591', '5.44832856484579355246405552990149', '6.55449581799082001689688453440182', '7.77281588044116134307468711004997', '8.448880571204551881989550536801538', '8.919957946285284100583425814208583', '9.683826904172161190884027781544404'], 'prelabel': '2-983-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8016592438574444, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46977678712610590285330131420', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88034291934486793191037056494', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79305841733673664137787366893', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.849294518691866, 'bad_primes': [983], 'central_character': '1.1', 'conductor': 983, 'conductor_radical': 983, 'degree': 2, 'index': 43, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/983/2/a/b/1/34'], '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': '2-983-1.1-c1-0-43', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-983-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8016592438574444, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46977678712610590285330131420', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1863163426401926699875067625949', 'Lhash_array': ['1863163426401926699875067625949'], 'label': '2-983-1.1-c1-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/983/2/a/b/1/34'}