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lfunc_lfunctions • Show schema
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{'Lhash': '704284853768952415984700906256', 'a10': [1.693134064383196, 5.106526905434899], 'a2': [-2.0403734063742727, -1.2749668080941188], 'a3': [2.3402596851406914, -0.6710586661914539], 'a4': [1.660840982119493, 3.4052286458919276], 'a5': [-1.7215160577419506, -1.4270187325107588], 'a6': [-5.63058115124891, -1.6145431642611416], 'a7': [-2.03229939716648, 3.520045812083944], 'a8': [0.449834232722706, -4.279886834109404], 'a9': [2.482351371954876, -1.5511452930046734], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.7215160577419506, 1.4270187325107588]]], [19, [[1.0, 0], [-2.7050998421100236, -3.417957700764643]]]], 'bad_primes': [5, 19], 'central_character': '475.6', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '2092065914644690179994684883040', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.14321338552616317, 'root_number': '0.9004827143709544 - 0.4348918039226748*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0716066927631', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55558278727762373083123904187', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04230265676980159732381988158', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.63520371568314988652688139925', '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': '475.6', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/bc/a/6/5'], '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': '2-475-475.6-c1-0-8', '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': '2-475-475.6-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.07160669276308158, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55558278727762373083123904187', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '704284853768952415984700906256', 'Lhash_array': ['704284853768952415984700906256'], 'label': '2-475-475.6-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/bc/a/6/5'}