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lfunc_lfunctions • Show schema
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{'Lhash': '954548324977131771157939080467', 'a10': [142.69912968534823, -172.15387996511774], 'a2': [-3.23606797749979, 2.3511410091698925], 'a3': [2.3332183524938443, -7.180907712105473], 'a4': [4.944271909999159, -15.216904260722456], 'a5': [-54.15888319159653, 13.849742648836575], 'a6': [9.332873409975377, 28.72363084842189], 'a7': [54.59986013379121, 0.0], 'a8': [19.777087639996637, 60.867617042889826], 'a9': [150.46960194375046, 109.32256498417283], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.019190990649033, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [3.23606797749979, -2.3511410091698925]]], [5, [[1.0, 0], [54.15888319159653, -13.849742648836575]]]], 'bad_primes': [2, 5], 'central_character': '50.11', 'coefficient_field': 'CDF', 'conductor': 50, 'conductor_radical': 10, 'conjugate': '1963938328247614456561037443376', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.23606797749979, 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{'__RealLiteral__': 0, 'data': '-0.199691726858', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75300585571866072195584200975', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.27330047831288987793524281032', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.73346361233709691608322217834', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.019190990649033, 'bad_primes': [2, 5], 'central_character': '25.11', 'conductor': 50, 'conductor_radical': 10, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/50/6/d/a/11/4'], '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': '2-50-25.11-c5-0-3', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-50-25.11-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8318176125324586, 'root_angle': -0.19969172685799993, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75300585571866072195584200975', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '954548324977131771157939080467', 'Lhash_array': ['954548324977131771157939080467'], 'label': '2-50-25.11-c5-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/6/d/a/11/4'}