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lfunc_lfunctions • Show schema
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{'Lhash': '1568712403417359705297603513580', 'a10': [-81.5662503256755, -208.19929588691994], 'a2': [2.3511410091698925, 3.23606797749979], 'a3': [22.558166342070127, 7.329592555436797], 'a4': [-4.944271909999159, 15.216904260722456], 'a5': [-54.095051903911134, -14.096998244773983], 'a6': [29.318370221747188, 90.23266536828051], 'a7': [0.0, 229.53875423672562], 'a8': [-60.867617042889826, 19.777087639996637], 'a9': [258.55681205467874, 187.85251986321327], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.019190990649033, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.3511410091698925, -3.23606797749979]]], [5, [[1.0, 0], [54.095051903911134, 14.096998244773983]]]], 'bad_primes': [2, 5], 'central_character': '50.39', 'coefficient_field': 'CDF', 'conductor': 50, 'conductor_radical': 10, 'conjugate': '3544303761038218191182405986878', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.3511410091698925, 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{'__RealLiteral__': 0, 'data': '-0.288854214891', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23749588659124743028264334606', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.32050060209214033353914396714', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.12703508766755777244092431773', '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': '25.14', 'conductor': 50, 'conductor_radical': 10, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/50/6/e/a/39/12'], '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': '2-50-25.14-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': '2-50-25.14-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8318176125324586, 'root_angle': -0.2888542148914417, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23749588659124743028264334606', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1568712403417359705297603513580', 'Lhash_array': ['1568712403417359705297603513580'], 'label': '2-50-25.14-c5-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/6/e/a/39/12'}