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  • lfunc_lfunctions • Show schema
    {'Lhash': '2182387157101768192701150019417', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [3.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.4913325430639492, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [13, [[1.0, 0], [-3.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 13], 'central_character': '312.289', 'coefficient_field': 'CDF', 'conductor': 312, 'conductor_radical': 78, 'conjugate': '1819067632283813036383266553652', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-3.0, 0], [5.0, 0]], [[1.0, 0], [0, 0], [-3.5, -6.06217782649107]], [[1.0, 0], [0, 0], [-5.5, 9.526279441628825]], [[1.0, 0], [-3.5, 0.8660254037844386]], [[1.0, 0], [-0.5, 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-2.4314348111831405, -1.057864055111836, 0.2953271897159257], 'positive_zeros': ['1.72159990829401135929287508890362', '3.38751374332310410175321206839754', '4.82361483187115110582129798380745', '5.88394477089614038455528081751278', '6.52662889645244401370877893506433', '8.100508021663300914241474255790006', '9.214684869125839839883750657889377', '9.861212634020860723693032357807935', '10.71888246329299168417625582925315', '11.59068624652272287960495516094609'], 'prelabel': '2-312-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5783955597580568, 'root_angle': 0.08537428472590003, 'root_number': '0.8595425350987749 + 0.5110642135348272*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0853742847259', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72159990829401135929287508890', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.38751374332310410175321206840', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.82361483187115110582129798381', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 2.4913325430639492, 'bad_primes': [2, 3, 13], 'central_character': '13.3', 'conductor': 312, 'conductor_radical': 78, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/312/2/q/a/289/1'], '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': '2-312-13.3-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': '2-312-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5783955597580568, 'root_angle': 0.08537428472590003, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72159990829401135929287508890', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '2182387157101768192701150019417', 'Lhash_array': ['2182387157101768192701150019417'], 'factors': ['2-312-13.3-c1-0-5'], 'label': '2-312-13.3-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/312/2/q/a/289/1'}