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lfunc_lfunctions • Show schema
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{'Lhash': '1671441490350495135624218838303', 'a10': [0.0, 0.0], 'a2': [1.3790081313599358, 2.388512147566025], 'a3': [0.7459592127163204, 1.2920392567987464], 'a4': [-2.803326852713644, 4.855504539122186], 'a5': [0.0, 0.0], 'a6': [-2.0573676399973233, 3.563465282323439], 'a7': [2.848637442707416, 0.0], 'a8': [-9.947209573567344, 0.0], 'a9': [0.38708970592729514, -0.6704590377529708], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [3.360694492710967, 2.7759201225291363]]]], 'bad_primes': [5, 19], 'central_character': '475.26', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '3817521670427490239370120803610', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3790081313599358, -2.388512147566025], [-1.0, 1.7320508075688772]], [[1.0, 0], [-0.7459592127163204, -1.2920392567987464], [-1.5, 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'8.048120363819779116714166283563368', '8.877667489640092717035089331127266', '10.12489801073201901230512390366187', '10.72594481772830030218598826837950'], 'prelabel': '2-475-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.4770893367677888, 'root_number': '-0.9896567987564843 + 0.14345529155478262*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.477089336768', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31853484710184866130905223205', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18149085859799448519180150318', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30192200281287034265994479783', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '19.7', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/e/e/26/4'], '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': '2-475-19.7-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': '2-475-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.4770893367677888, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31853484710184866130905223205', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1671441490350495135624218838303', 'Lhash_array': ['1671441490350495135624218838303'], 'factors': ['2-475-19.7-c1-0-5'], 'label': '2-475-19.7-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/e/e/26/4'}