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lfunc_lfunctions • Show schema
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{'Lhash': '2748610550371441137804488631056', 'a10': [-1.5462012557187128, -1.615320920688479], 'a2': [-0.25881904510252074, -0.9659258262890683], 'a3': [0.9659258262890683, 0.25881904510252074], 'a4': [-0.8660254037844386, 0.5], 'a5': [1.9604665275794735, -1.075439907312576], 'a6': [-4.400336302403101e-61, -1.0], 'a7': [-1.5285631655136713, -2.1595125952480165], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6768584424468889, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.25881904510252074, 0.9659258262890683]]], [3, [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]]], [5, [[1.0, 0], [-1.9604665275794735, 1.075439907312576]]], [7, [[1.0, 0], [1.5285631655136713, 2.1595125952480165]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '210.103', 'coefficient_field': 'CDF', 'conductor': 210, 'conductor_radical': 210, 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'3.73906282589903083937683315606067', '5.65189647578177810448058018737210', '6.32884405002945171716543360931589', '7.40746710895612195176442180502187', '8.816096784473200067353091663393651', '9.263987510609683967870982362408413', '10.29471938737382343159517970105661', '11.59639904886651443655256864958417', '12.83388027702011954595230832713067'], 'prelabel': '2-210-35.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2949356904676343, 'root_angle': 0.3607792209192292, 'root_number': '0.42356300615613013 + 0.9058666457133644*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.18038961046', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.16827140686603852223399571930', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.73906282589903083937683315606', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.65189647578177810448058018737', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6768584424468889, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.33', 'conductor': 210, 'conductor_radical': 210, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/210/2/u/b/103/2'], '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': '2-210-35.33-c1-0-7', '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': '2-210-35.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2949356904676343, 'root_angle': 0.1803896104596146, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.16827140686603852223399571930', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2748610550371441137804488631056', 'Lhash_array': ['2748610550371441137804488631056'], 'label': '2-210-35.33-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/210/2/u/b/103/2'}