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lfunc_lfunctions • Show schema
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{'Lhash': '1384591324978862987427902555055', 'a10': [0.0, 0.0], 'a2': [0.7071067811865476, 0.7071067811865476], 'a3': [0.0, 0.0], 'a4': [0.0, 1.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, -1.0], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [0.0, 3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.58578819202164, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-4.242640687119285, -1.0]]]], 'bad_primes': [2, 5, 19], 'central_character': '950.493', 'coefficient_field': 'CDF', 'conductor': 950, 'conductor_radical': 190, 'conjugate': '1835657167641171669267283117515', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0, -3.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 1.0], [0, -7.0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [-4.242640687119285, 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'4.30845811282412531923279970749794', '5.53988068858311242324984151069482', '6.36513902269706337491651665571513', '7.10996802837178866673510985506599', '8.480261320899370882769845778311285', '9.267625998531578727949606906721877', '9.694250279172984659403977935370864'], 'prelabel': '2-950-95.18-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7542309619967678, 'root_angle': -0.352526657795312, 'root_number': '0.44690370283833863 - 0.8945820702369246*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.176263328898', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09224996598398599062437472727', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37226409512794249815340943665', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68913073477991881696100971166', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.58578819202164, 'bad_primes': [2, 5, 19], 'central_character': '95.18', 'conductor': 950, 'conductor_radical': 190, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/950/2/f/a/493/2'], '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': '2-950-95.18-c1-0-18', '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': '2-950-95.18-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7542309619967678, 'root_angle': -0.176263328897656, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09224996598398599062437472727', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1384591324978862987427902555055', 'Lhash_array': ['1384591324978862987427902555055'], 'label': '2-950-95.18-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/950/2/f/a/493/2'}