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lfunc_lfunctions • Show schema
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{'Lhash': '3035383384864359127169332604450', 'a10': [0.3838890905986631, -0.2216384697960988], 'a2': [-0.9659258262890683, -0.25881904510252074], 'a3': [1.7302233594747358, -0.07954323558895118], 'a4': [0.8660254037844386, 0.5], 'a5': [-0.3134441299292625, 0.3134441299292625], 'a6': [-1.691854732444779, -0.3709818921513629], 'a7': [-0.0745867472220269, -0.2783615302039012], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [2.987345747344081, -0.27525512860841095], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9659258262890683, 0.25881904510252074]]], [3, [[1.0, 0], [-1.7302233594747358, 0.07954323558895118]]], [13, [[1.0, 0], [1.7914386565624116, 3.129017024526051]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.11', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': 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'4.44211712062665931512074477068528', '6.60858545746184867538943732661406', '7.77532382286985354468170950158091', '8.895108233900281771634528627451375', '9.646254299324990271718437160140286', '11.00719039803608678476597237265962', '12.32927337919761791092082365973575', '13.64708313608005216943725208744103', '14.55299505727916212341205562331461'], 'prelabel': '2-78-39.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': 0.05757338380934899, 'root_number': '0.9836871834526647 + 0.17988753461805954*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0287866919047', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.39449528467691720530944554359', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.44211712062665931512074477069', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.60858545746184867538943732661', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'bad_primes': [2, 3, 13], 'central_character': '39.11', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/2/k/a/11/2'], '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': '2-78-39.11-c1-0-1', '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': '2-78-39.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': 0.028786691904674495, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.39449528467691720530944554359', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3035383384864359127169332604450', 'Lhash_array': ['3035383384864359127169332604450'], 'label': '2-78-39.11-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/k/a/11/2'}