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lfunc_lfunctions • Show schema
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{'Lhash': '1918411295791954866592435079779', 'a10': [0.8055117703103548, 0.5920758621384056], 'a2': [-0.26278708405611173, 0.36169539142817075], 'a3': [2.647930102192325, -0.8603646444502988], 'a4': [0.5562674841162311, 1.7120152781304212], 'a5': [0.012372492993238678, -2.236033747826077], 'a6': [-0.3846519034941132, 1.1838368309269567], 'a7': [0.0, 4.3243614278122875], 'a8': [-1.615804813875054, -0.5250068092959502], 'a9': [3.844255521551325, -2.793015124926467], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-0.012372492993238678, 2.236033747826077]]], [19, [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]]]], 'bad_primes': [5, 19], 'central_character': '475.134', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '2484928742909331697654141952286', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.26278708405611173, 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'data': '-0.0782387355966', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51335967138465575178449618317', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07912058217488582457784872335', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57261171709917307932723989389', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '25.9', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/n/b/134/10'], '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': '2-475-25.9-c1-0-24', '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': '2-475-25.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.07823873559660433, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51335967138465575178449618317', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1918411295791954866592435079779', 'Lhash_array': ['1918411295791954866592435079779'], 'label': '2-475-25.9-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/n/b/134/10'}