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lfunc_lfunctions • Show schema
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{'Lhash': '3211721421228254859100931295790', 'a10': [0.28672114686383093, -0.20173831437696252], 'a2': [0.0, -0.15678479744322704], 'a3': [0.0, -2.5638725190086307], 'a4': [1.9754185272906863, 0.0], 'a5': [1.2867211468638309, 1.828756049945817], 'a6': [-0.4019762335630244, 0.0], 'a7': [0.0, 1.0936395808830033], 'a8': [0.0, -0.6232851885533222], 'a9': [-3.5734422937276618, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1578308293085662, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.2867211468638309, -1.828756049945817]]], [29, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 29], 'central_character': '145.59', 'coefficient_field': 'CDF', 'conductor': 145, 'conductor_radical': 145, 'conjugate': '2505717034657923613398577649753', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.15678479744322704], [-2.0, 0]], [[1.0, 0], [0, 2.5638725190086307], [-3.0, 0]], [[1.0, 0], [-1.2867211468638309, -1.828756049945817]], 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'4.37802160209999028080511191461558', '5.27257905593781178201918173056388', '6.64669000630911676622173170837200', '8.170860650825783090267545135126756', '9.342434829249614183120278973941785', '10.23393874058491752016333589198125', '10.94148642932433863704871027290865', '12.05401848290328304994721366999194', '13.33398270687392890820488891156394'], 'prelabel': '2-145-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0760254780015974, 'root_angle': 0.15241557006214873, 'root_number': '0.5754391904948032 + 0.8178445683885696*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.152415570062', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.53360146766783568950618752460', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.37802160209999028080511191462', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.27257905593781178201918173056', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1578308293085662, 'bad_primes': [5, 29], 'central_character': '5.4', 'conductor': 145, 'conductor_radical': 145, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/145/2/b/c/59/3'], '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': '2-145-5.4-c1-0-9', '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': '2-145-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0760254780015974, 'root_angle': 0.15241557006214873, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.53360146766783568950618752460', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3211721421228254859100931295790', 'Lhash_array': ['3211721421228254859100931295790'], 'factors': ['2-145-5.4-c1-0-9'], 'label': '2-145-5.4-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/145/2/b/c/59/3'}