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lfunc_lfunctions • Show schema
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{'Lhash': '1870643924927697476605123489966,2250444942470222397127084603373', 'a10': 2, 'a2': 2, 'a3': 3, 'a4': 3, 'a5': 1, 'a6': 6, 'a7': 0, 'a8': 4, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 49.60110872313537, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1, -3, 3]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '882.1', 'coefficient_field': '1.1.1.1', 'conductor': 777924, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, -3, 3], [1, -1, -4, -5, 25], [1], [1, -2, -7, -22, 121], [1, -2, -9, -26, 169], [1, 0, -17, 0, 289], [1, 7, 30, 133, 361], [1, 3, -14, 69, 529], [1, -8, 35, -232, 841], [1, 8, 78, 248, 961], [1, -6, -1, -222, 1369], [1, 12, 103, 492, 1681], [1, -8, 21, -344, 1849], [1, -16, 158, -752, 2209], [1, 4, -37, 212, 2809], [1, 8, 134, 472, 3481], [1, 26, 291, 1586, 3721], [1, 4, 138, 268, 4489], [1, 10, 167, 710, 5041], [1, 14, 123, 1022, 5329], [1, 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0.4797392277062226], 'positive_zeros': ['1.47567785996464988209168649709522', '1.77528803446710747546397883838004', '2.71671479382720217630510662210361', '2.80455990106201792401222549282975', '3.51325462622673589719819883675311', '4.03548871328453566246913551667347', '4.52277536523174472076842759038720', '4.60337356946091157326254310396014', '5.63479974483130136865129532210347', '6.02099304768654761605733423057642', '6.41835757670828001597970539844760', '6.81944051310264722369827652064377', '7.53520605461868283020667092819678', '7.57213595954818906173831958355185', '8.278154589518946319447741292518760', '8.763741754387745562606186147564715', '9.080708600348825569685490039945175', '9.198450010536496057141673274142982', '10.20146749885659175990741130289895', '10.24928735491817010990957004318278'], 'prelabel': '4-882e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 269009224531260289, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47567785996464988209168649710', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.77528803446710747546397883838', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.71671479382720217630510662210', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 49.60110872313537, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 777924, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 2, 3, 3, 1, 6, 0, 4, 6, 2, 2, 9, 2, 0, 3, 5, 0, 12, -7, 3, 0, 4, -3, 12, 5, 4, 9, 0, 8, 6, -8, 6, 6, 0, 0, 18, 6, -14, 6, 4, -12, 0, 8, 6, 6, -6, 16, 15, 0, 10, 0, 6, -4, 18, 2, 0, -21, 16, -8, 9, -26, -16, 0, 7, 2, 12, -4, 0, -9, 0, -10, 24, -14, 12, 15, -21, 0, 12, -22, 5, 9, -24, 12, 0, 0, 16, 24, 8, 14, 12, 0, -9, -24, 32, -7, 18, -2, 0, 12, 15], 'euler11': [1, -2, -7, -22, 121], 'euler13': [1, -2, -9, -26, 169], 'euler17': [1, 0, -17, 0, 289], 'euler19': [1, 7, 30, 133, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, 3, -14, 69, 529], 'euler29': [1, -8, 35, -232, 841], 'euler3': [1, -3, 3, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, -6, -1, -222, 1369], 'euler41': [1, 12, 103, 492, 1681], 'euler43': [1, -8, 21, -344, 1849], 'euler47': [1, -16, 158, -752, 2209], 'euler5': [1, -1, -4, -5, 25], 'euler53': [1, 4, -37, 212, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, 26, 291, 1586, 3721], 'euler67': [1, 4, 138, 268, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 10, 167, 710, 5041], 'euler73': [1, 14, 123, 1022, 5329], 'euler79': [1, 22, 279, 1738, 6241], 'euler83': [1, -12, 61, -996, 6889], 'euler89': [1, -14, 107, -1246, 7921], 'euler97': [1, 2, -93, 194, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, -3, 3, 0, 0], [1, -1, -4, -5, 25], [1, 0, 0, 0, 0], [1, -2, -7, -22, 121], [1, -2, -9, -26, 169], [1, 0, -17, 0, 289], [1, 7, 30, 133, 361], [1, 3, -14, 69, 529], [1, -8, 35, -232, 841], [1, 8, 78, 248, 961], [1, -6, -1, -222, 1369], [1, 12, 103, 492, 1681], [1, -8, 21, -344, 1849], [1, -16, 158, -752, 2209], [1, 4, -37, 212, 2809], [1, 8, 134, 472, 3481], [1, 26, 291, 1586, 3721], [1, 4, 138, 268, 4489], [1, 10, 167, 710, 5041], [1, 14, 123, 1022, 5329], [1, 22, 279, 1738, 6241], [1, -12, 61, -996, 6889], [1, -14, 107, -1246, 7921], [1, 2, -93, 194, 9409]], 'index': 52, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/2/e/j'], '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': '4-882e2-1.1-c1e2-0-52', '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': '4-882e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 269009224531260289, 'z1': {'__RealLiteral__': 0, 'data': '1.47567785996464988209168649710', 'prec': 103}}
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{'Lhash': '1870643924927697476605123489966,2250444942470222397127084603373', 'Lhash_array': ['1870643924927697476605123489966', '2250444942470222397127084603373'], 'label': '4-882e2-1.1-c1e2-0-52', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/2/e/j'}