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lfunc_lfunctions • Show schema
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{'Lhash': '875165361244511252330088327626', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [4.154371394578272, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.144268834604052, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.91226177783285, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 23, 29], 'central_character': '8004.1', 'coefficient_field': 'CDF', 'conductor': 8004, 'conductor_radical': 4002, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.154371394578272, 0], [5.0, 0]], [[1.0, 0], [4.144268834604052, 0], [7.0, 0]], [[1.0, 0], [-0.22913467024416076, 0], [11.0, 0]], [[1.0, 0], [4.103232768345379, 0], [13.0, 0]], [[1.0, 0], [-6.385565369800157, 0], [17.0, 0]], [[1.0, 0], [2.892034160262216, 0], 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'5.86793332476945793330792410576684', '6.33234303810638309181672507773459', '6.86467552317700987218721310720512', '7.61979700856925993043626625161414'], 'prelabel': '2-8004-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.994514480431745, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69038373908941894931825389365', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.77376919841295182462719975837', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.71155203316148887155414304824', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.91226177783285, 'bad_primes': [2, 3, 23, 29], 'central_character': '1.1', 'conductor': 8004, 'conductor_radical': 4002, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8004/2/a/i/1/16'], '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': '2-8004-1.1-c1-0-28', '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': '2-8004-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.994514480431745, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.69038373908941894931825389365', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '875165361244511252330088327626', 'Lhash_array': ['875165361244511252330088327626'], 'label': '2-8004-1.1-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8004/2/a/i/1/16'}