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lfunc_lfunctions • Show schema
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{'Lhash': '2138891315656126955386103236795', 'a10': [2.843065319231943, 1.6414445273822513], 'a2': [-0.5, 0.8660254037844386], 'a3': [-1.7223854147914457, 0.1827251567620057], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, -3.2828890547645027], 'a6': [0.702948079729332, -1.5829921026981923], 'a7': [-0.20383690572476088, 2.6378875100854007], 'a8': [1.0, 0.0], 'a9': [2.9332230341726007, -0.6294462898447183], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [1.7223854147914457, -0.1827251567620057]]], [7, [[1.0, 0], [0.20383690572476088, -2.6378875100854007]]], [13, [[1.0, 0], [-3.605334695333547, -0.03951878824255847]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.251', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '267967776257074292173633887010', 'degree': 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'7.48969769720563743985214897234702', '8.305375748960281157955725839032861', '9.804862445508370487002123458313871', '10.66096253843872665347137863176456', '10.94460665802989277271206181916037'], 'prelabel': '2-546-273.251-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.6569784345347448, 'root_number': '-0.47341372865766257 + 0.8808401906807211*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.328489217267', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68728773943785321007340405421', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.39736722750849468205600421097', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09517336699224355643020182410', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.251', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/q/i/251/1'], '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': '2-546-273.251-c1-0-19', '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': '2-546-273.251-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.3284892172673724, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68728773943785321007340405421', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2138891315656126955386103236795', 'Lhash_array': ['2138891315656126955386103236795'], 'label': '2-546-273.251-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/q/i/251/1'}