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lfunc_lfunctions • Show schema
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{'Lhash': '2703719934254792294666451070551', 'a10': [0.0, 0.0], 'a2': [0.4953607011555205, 0.2859966341581015], 'a3': [1.708275716987816, 0.2859966341581015], 'a4': [-0.8364118505004741, -1.4487078211195252], 'a5': [0.0, 0.0], 'a6': [0.7644185821842711, 0.630232598497209], 'a7': [1.2366901064133569, 0.7140033658418985], 'a8': [0.0, -2.100830432684745], 'a9': [2.836411850500474, 0.977122210545066], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.708275716987816, -0.2859966341581015]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.124', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '2374767013382032654242075298375', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.4953607011555205, -0.2859966341581015], [1.0, 1.7320508075688772]], [[1.0, 0], [-1.708275716987816, -0.2859966341581015]], 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'11.38861859389619236624472679248386', '12.52812579412671848286397462564435'], 'prelabel': '2-15e2-45.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.013574373000611293, 'root_number': '0.9990908333669992 + 0.04263222586301293*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00678718650031', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.13285895480032997415493496905', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.64853079067432313172858473617', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.32883913078736191418348335676', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '45.34', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/k/b/124/4'], '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': '2-15e2-45.34-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': '2-15e2-45.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.0067871865003056465, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.13285895480032997415493496905', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2703719934254792294666451070551', 'Lhash_array': ['2703719934254792294666451070551'], 'label': '2-15e2-45.34-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/k/b/124/4'}