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lfunc_lfunctions • Show schema
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{'Lhash': '2518632990256341040838396005539', 'a10': [-1.2143197433775352, 0.0], 'a2': [1.2143197433775352, 0.0], 'a3': [2.9032119259115534, 0.0], 'a4': [-0.525427560843517, 0.0], 'a5': [-1.0, 0.0], 'a6': [3.525427560843517, 0.0], 'a7': [1.525427560843517, 0.0], 'a8': [-3.066676547602054, 0.0], 'a9': [5.4286394867550705, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.57709404994842, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.0, 0]]], [29, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 29], 'central_character': '4205.1', 'coefficient_field': 'CDF', 'conductor': 4205, 'conductor_radical': 145, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2143197433775352, 0], [2.0, 0]], [[1.0, 0], [-2.9032119259115534, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.525427560843517, 0], [7.0, 0]], [[1.0, 0], [4.903211925911553, 0], [11.0, 0]], [[1.0, 0], [6.4286394867550705, 0], [13.0, 0]], [[1.0, 0], 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'4.31522064007672728190090361480254', '4.82164686105692823699127435319511', '5.37090459241885913174232389589682', '6.83820624517000479484291550357942', '7.44494593997879591809928467339932', '8.101926118374928217031855706400850'], 'prelabel': '2-4205-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.794574535714285, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98685110061312099981051352536', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78918519951561115477274122299', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.21697391197670304149041584058', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.57709404994842, 'bad_primes': [5, 29], 'central_character': '1.1', 'conductor': 4205, 'conductor_radical': 145, 'degree': 2, 'index': 259, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4205/2/a/e/1/3'], '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': '2-4205-1.1-c1-0-259', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4205-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.794574535714285, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.98685110061312099981051352536', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2518632990256341040838396005539', 'Lhash_array': ['2518632990256341040838396005539'], 'factors': ['2-4205-1.1-c1-0-259'], 'label': '2-4205-1.1-c1-0-259', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4205/2/a/e/1/3'}