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lfunc_lfunctions • Show schema
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{'Lhash': '847846524017882834287209386051', 'a10': [-3.8832540853410533, -1.7889167972995788e-60], 'a2': [1.3345395441411443, 2.3114902951622702], 'a3': [0.0, 0.0], 'a4': [-2.561991589752906, 4.437499602016192], 'a5': [-0.7274520456117617, 1.2599839030694837], 'a6': [0.0, 0.0], 'a7': [-0.5, -0.8660254037844386], 'a8': [-8.338158176564576, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.5275177946066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [3, 7], 'central_character': '567.190', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'conjugate': '3748723568077864326837849504645', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3345395441411443, -2.3114902951622702], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7274520456117617, -1.2599839030694837], [-2.5, -4.330127018922194]], 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'10.22764884526164391701088068254589'], 'prelabel': '2-567-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.7777777777777778, 'root_number': '-0.7660444431189779 + 0.6427876096865395*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.388888888889', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66883297642523537982502379660', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28240781966629604498926252264', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24142057702453439162492181676', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.5275177946066, 'bad_primes': [3, 7], 'central_character': '9.4', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/f/l/190/3'], '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': '2-567-9.4-c1-0-3', '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': '2-567-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.3888888888888889, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66883297642523537982502379660', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '847846524017882834287209386051', 'Lhash_array': ['847846524017882834287209386051'], 'label': '2-567-9.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/f/l/190/3'}