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lfunc_lfunctions • Show schema
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{'Lhash': '1583791321444058583325648457294', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.7459592127163204, 1.2920392567987464], 'a4': [0, 0], 'a5': [-0.5, -0.8660254037844386], 'a6': [0, 0], 'a7': [2.848637442707416, 0], 'a8': [0, 0], 'a9': [0.38708970592729514, -0.6704590377529708], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, 0.8660254037844386]]], [19, [[1.0, 0], [-3.360694492710967, -2.7759201225291363]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.881', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'conjugate': '1341691344945666622928729988444', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7459592127163204, -1.2920392567987464], [-1.5, 2.598076211353316]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-2.848637442707416, 0], [7.0, 0]], [[1.0, 0], 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'7.76535428393878696439868655284511', '8.506109334995253785468837355620394', '9.214353119792764857612028910926200'], 'prelabel': '2-1520-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': -0.045821326464422406, 'root_number': '0.98965679875648425069113406598918808316863704545084628012 - 0.14345529155478243589884033556929378259145194878305772613*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.022910663232211203', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24939105551554254026306767424', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18170088007259169205682767218', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24765723229919047175921915060', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '19.7', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/q/o/881/3'], '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': '2-1520-19.7-c1-0-23', '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': '2-1520-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': -0.022910663232211203, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24939105551554254026306767424', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1583791321444058583325648457294', 'Lhash_array': ['1583791321444058583325648457294'], 'label': '2-1520-19.7-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/q/o/881/3'}