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lfunc_lfunctions • Show schema
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{'Lhash': '142553705874561995553522025599', 'a10': [-1.734198434871343, -1.4903997076267768], 'a2': [0.0, 1.0226177682794484], 'a3': [-1.9706271517178129, -1.9706271517178129], 'a4': [0.9542528999991604, 0.0], 'a5': [-1.4574357632513761, 1.6958422674281588], 'a6': [2.015198340000556, -2.015198340000556], 'a7': [0.9635738700418889, 0.0], 'a8': [0.0, 3.02107150753023], 'a9': [0.0, 4.7667427421749204], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.747358970798196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.4574357632513761, -1.6958422674281588]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 13], 'central_character': '845.408', 'coefficient_field': 'CDF', 'conductor': 845, 'conductor_radical': 65, 'conjugate': '2253957614560251098846325589442', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0226177682794484], [-2.0, 0]], [[1.0, 0], [1.9706271517178129, 1.9706271517178129], [0, 3.0]], [[1.0, 0], 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0, 'data': '0.497885648947', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.11245504545881684419442684407', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.81451616194069955192002821659', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52149404740169573274284977525', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.747358970798196, 'bad_primes': [5, 13], 'central_character': '65.18', 'conductor': 845, 'conductor_radical': 65, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/845/2/f/e/408/8'], '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': '2-845-65.18-c1-0-4', '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': '2-845-65.18-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 0.49788564894740084, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.11245504545881684419442684407', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '142553705874561995553522025599', 'Lhash_array': ['142553705874561995553522025599'], 'label': '2-845-65.18-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/845/2/f/e/408/8'}