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lfunc_lfunctions • Show schema
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{'Lhash': '7093992141337772911981812309558', 'a10': [3.449489742783178, -15.348469228349535], 'a2': [-2.224744871391589, -2.224744871391589], 'a3': [1.224744871391589, -1.224744871391589], 'a4': [0.0, 5.898979485566356], 'a5': [2.6742346141747673, 4.224744871391589], 'a6': [-5.449489742783178, 1.384462132401308e-60], 'a7': [-1.449489742783178, -1.449489742783178], 'a8': [4.224744871391589, -4.224744871391589], 'a9': [0.0, -3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4087203965404454, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.224744871391589, 1.224744871391589]]], [5, [[1.0, 0], [-2.6742346141747673, -4.224744871391589]]]], 'bad_primes': [3, 5], 'central_character': '15.7', 'coefficient_field': 'CDF', 'conductor': 15, 'conductor_radical': 15, 'conjugate': '3270928991659949998136674786600', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.224744871391589, 2.224744871391589], [0, 4.0]], [[1.0, 0], 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0.9452283779352676*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.197080541375', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '5.59617306224645946076413331450', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.77350152759057367301298746720', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '9.082219061602929262321369428557', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4087203965404454, 'bad_primes': [3, 5], 'central_character': '5.2', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/15/3/f/a/7/1'], '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': '2-15-5.2-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': '2-15-5.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6393124404705772, 'root_angle': 0.19708054137514794, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '5.59617306224645946076413331450', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '7093992141337772911981812309558', 'Lhash_array': ['7093992141337772911981812309558'], 'label': '2-15-5.2-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/15/3/f/a/7/1'}