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lfunc_lfunctions • Show schema
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{'Lhash': '1890747198721790016582530820817', 'a10': [4.587603438035308, 61.45949090890292], 'a2': [-4.459622877623749, -3.240105679459301], 'a3': [0.0, 0.0], 'a4': [6.9178154415611335, 21.290846697709455], 'a5': [-7.226698529190536, -8.530816395175513], 'a6': [0.0, 0.0], 'a7': [-10.269624424724428, 0.0], 'a8': [24.506350401415567, -75.42279118668486], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [7.226698529190536, 8.530816395175513]]]], 'bad_primes': [3, 5], 'central_character': '225.91', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '318897495311797751141622689698', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.459622877623749, 3.240105679459301], [2.4721359549995796, 7.608452130361228]], [[1.0, 0], [0, 0]], [[1.0, 0], [7.226698529190536, 8.530816395175513]], [[1.0, 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-4.411651996845526, -1.3952422617037614, 1.3271002280168813, 3.256114629258423], 'positive_zeros': ['1.49153654672776356766793140633815', '3.73521983858448574886029987694846', '5.90302492041356016229250821814836', '6.52120393613172643525782982415898', '7.39944268969057075776517543593071', '8.471817710340210739928771360038911', '9.154915164313788178439675706090324', '10.22713320459807379673360542635526', '11.06607330002596690640613924164548', '11.83853317504896113220866556668044'], 'prelabel': '2-15e2-25.16-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.8074321026624336, 'root_number': '-0.8225192217796885 - 0.5687373117731381*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.403716051331', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49153654672776356766793140634', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.73521983858448574886029987695', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.90302492041356016229250821815', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '25.16', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/h/d/91/1'], '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': '2-15e2-25.16-c3-0-22', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15e2-25.16-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.4037160513312168, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.49153654672776356766793140634', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1890747198721790016582530820817', 'Lhash_array': ['1890747198721790016582530820817'], 'label': '2-15e2-25.16-c3-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/h/d/91/1'}