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lfunc_lfunctions • Show schema
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{'Lhash': '481621284512272655613536794752', 'a10': [-5.0769756569633895, -4.260088401254009], 'a2': [0.32614009210243955, 1.37609325277156], 'a3': [-1.1872037755329314, 2.755094770667672], 'a4': [-1.7872652806468246, 0.8975983604009243], 'a5': [-3.7590421067699538, 2.798503161241631], 'a6': [-4.178462073358666, -0.7351562429192843], 'a7': [1.0337981928111812, -0.6799397677656203], 'a8': [-1.8180779106881748, -2.1667008816788074], 'a9': [-6.181094390720706, -6.541717827375392], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.41418028263681, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.32614009210243955, -1.37609325277156]]], [3, [[1.0, 0], [1.1872037755329314, -2.755094770667672]]]], 'bad_primes': [2, 3], 'central_character': '162.5', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '4254838093854163990630506154603', 'degree': 2, 'euler_factors': [[[1.0, 0], 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2.100995069636483, 'root_angle': 0.789644861593677, 'root_number': '-0.7894707002028474 + 0.6137882481126743*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.394822430797', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37993220247405788032882113091', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.15022842218353781080498431944', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.01897963890798918863078977792', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.41418028263681, 'bad_primes': [2, 3], 'central_character': '81.5', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/3/h/a/5/13'], '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': '2-162-81.5-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-162-81.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.100995069636483, 'root_angle': 0.3948224307968385, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37993220247405788032882113091', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '481621284512272655613536794752', 'Lhash_array': ['481621284512272655613536794752'], 'label': '2-162-81.5-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/3/h/a/5/13'}