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lfunc_lfunctions • Show schema
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{'Lhash': '2125035046130575355234193620832', 'a10': [0.3284861043058889, -1.8164662665015359], 'a2': [0.8060875540404192, 1.1619909015225267], 'a3': [0.8660254037844386, 0.5], 'a4': [-0.7004457104422686, 1.8733328072510302], 'a5': [-0.922964357120589, -0.922964357120589], 'a6': [0.11709684871220118, 1.4093574167050997], 'a7': [-0.7572678456511461, 2.8261620749083036], 'a8': [-2.7414162470178622, 0.6961587179562566], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2456662715319746, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8060875540404192, -1.1619909015225267]]], [3, [[1.0, 0], [-0.8660254037844386, -0.5]]], [13, [[1.0, 0], [1.1150993561164662, 3.4287830823761136]]]], 'bad_primes': [2, 3, 13], 'central_character': '156.7', 'coefficient_field': 'CDF', 'conductor': 156, 'conductor_radical': 78, 'conjugate': '3875150758901375713028847579019', 'degree': 2, 'euler_factors': 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'4.21279934659059444244537417655014', '6.36955839445900720125847697917525', '7.16649554097056479511995821490022', '8.819887524186037127503866618165159', '9.828118330048824361140818336874334', '10.76577094859876928297734336711082', '11.89684367653380870820071511365216', '12.55945453011186421401938570436233'], 'prelabel': '2-156-52.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1160942036996584, 'root_angle': -0.4944007470543947, 'root_number': '0.01758966476364549 - 0.9998452898791406*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.247200373527', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67635707011694025500925682234', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.65681015801774233509223706860', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.21279934659059444244537417655', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2456662715319746, 'bad_primes': [2, 3, 13], 'central_character': '52.7', 'conductor': 156, 'conductor_radical': 78, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/156/2/w/c/7/5'], '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': '2-156-52.7-c1-0-5', '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': '2-156-52.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1160942036996584, 'root_angle': -0.24720037352719734, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67635707011694025500925682234', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2125035046130575355234193620832', 'Lhash_array': ['2125035046130575355234193620832'], 'label': '2-156-52.7-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/156/2/w/c/7/5'}