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lfunc_lfunctions • Show schema
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{'Lhash': '1182345071046791752830510626607,2039491319159085572379663780888', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': 6, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 477.2944672800165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, -8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, -4, 11, -20, 25], [1, -6, 23, -42, 49], [1, -8, 38, -88, 121], [1, 5, 12, 65, 169], [1, 0, -17, 0, 289], [1, -8, 19], [1, 4, -7, 92, 529], [1, -8, 35, -232, 841], [1, 2, 63, 62, 961], [1, 10, 99, 370, 1369], [1, -8, 23, -328, 1681], [1, 5, -18, 215, 1849], [1, -8, 17, -376, 2209], [1, -4, -37, -212, 2809], [1, 12, 85, 708, 3481], [1, -1, -60, -61, 3721], [1, -3, -58, -201, 4489], [1, 16, 185, 1136, 5041], [1, -15, 152, -1095, 5329], [1, 7, -30, 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'3.31222740790048070237403236387748', '4.13608802513676338527472232413277', '4.20094931029252274647204638510282', '4.90668742092623487607894746039803', '5.19549848884685461009015931337676', '5.34167253995475635532829145136364', '6.08866185893380106237319383681622', '6.13993357742049147799532149301553', '6.73556085055988780283667544223242', '7.26598114923559937606200382407935', '7.32817658501532653875286554677730', '8.029850932224612115333896879654832', '8.131730964228801101711620765473152', '8.843196246827819270476044869075599', '9.241431494376915632436297351459303'], 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1791509478060225151, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.932705803029573658256122849041', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.54929220257768350982780903308', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.60887496822223174216876199303', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 477.2944672800165, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, 6, 0, 0, 0, 8, 0, -5, 0, 0, 0, 0, 0, 8, 0, 0, 0, -4, 0, 5, 0, 0, 0, 8, 0, -2, 0, 0, 0, 24, 0, -10, 0, 0, 0, 8, 0, -5, 0, 0, 0, 8, 0, 13, 0, 0, 0, 4, 0, 32, 0, 0, 0, -12, 0, 1, 0, 0, 0, -20, 0, 3, 0, 0, 0, -16, 0, 15, 0, 0, 0, 48, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, -30, 0, 0, 0, 32, 0, 2, 0, 0, 0], 'euler11': [1, -8, 38, -88, 121], 'euler13': [1, 5, 12, 65, 169], 'euler17': [1, 0, -17, 0, 289], 'euler19': [1, -8, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 4, -7, 92, 529], 'euler29': [1, -8, 35, -232, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 2, 63, 62, 961], 'euler37': [1, 10, 99, 370, 1369], 'euler41': [1, -8, 23, -328, 1681], 'euler43': [1, 5, -18, 215, 1849], 'euler47': [1, -8, 17, -376, 2209], 'euler5': [1, -4, 11, -20, 25], 'euler53': [1, -4, -37, -212, 2809], 'euler59': [1, 12, 85, 708, 3481], 'euler61': [1, -1, -60, -61, 3721], 'euler67': [1, -3, -58, -201, 4489], 'euler7': [1, -6, 23, -42, 49], 'euler71': [1, 16, 185, 1136, 5041], 'euler73': [1, -15, 152, -1095, 5329], 'euler79': [1, 7, -30, 553, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 12, 55, 1068, 7921], 'euler97': [1, -2, -93, -194, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -4, 11, -20, 25], [1, -6, 23, -42, 49], [1, -8, 38, -88, 121], [1, 5, 12, 65, 169], [1, 0, -17, 0, 289], [1, -8, 19, 0, 0], [1, 4, -7, 92, 529], [1, -8, 35, -232, 841], [1, 2, 63, 62, 961], [1, 10, 99, 370, 1369], [1, -8, 23, -328, 1681], [1, 5, -18, 215, 1849], [1, -8, 17, -376, 2209], [1, -4, -37, -212, 2809], [1, 12, 85, 708, 3481], [1, -1, -60, -61, 3721], [1, -3, -58, -201, 4489], [1, 16, 185, 1136, 5041], [1, -15, 152, -1095, 5329], [1, 7, -30, 553, 6241], [1, 0, 166, 0, 6889], [1, 12, 55, 1068, 7921], [1, -2, -93, -194, 9409]], 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/s/r'], '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': '4-2736e2-1.1-c1e2-0-38', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1791509478060225151, 'z1': {'__RealLiteral__': 0, 'data': '0.932705803029573658256122849041', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1182345071046791752830510626607,2039491319159085572379663780888', 'Lhash_array': ['1182345071046791752830510626607', '2039491319159085572379663780888'], 'label': '4-2736e2-1.1-c1e2-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/s/r'}