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lfunc_lfunctions • Show schema
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{'Lhash': '1400660399849385953195213612513', 'a10': [1.0614141018680863, -1.8384231523056134], 'a2': [-1.0614141018680863, 1.8384231523056134], 'a3': [0.0, 0.0], 'a4': [-1.2531997912888722, -2.1706057105470395], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.7335336111914176, -1.2705174836430095], 'a8': [1.0749993162562603, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [-1.7667850056770464, 3.1430034590682143]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.451', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '956923000379988168447599571119', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0614141018680863, -1.8384231523056134], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.7335336111914176, 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'10.60321896016353712209046775911456'], 'prelabel': '2-585-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.2516159135013692, 'root_number': '0.7035080278391503 - 0.7106873115272773*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.125807956751', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10492623093241095047129026657', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.55963128393530351015437525547', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.45962494245081517311096089939', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '13.9', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/j/i/451/1'], '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': '2-585-13.9-c1-0-8', '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': '2-585-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.1258079567506846, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10492623093241095047129026657', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1400660399849385953195213612513', 'Lhash_array': ['1400660399849385953195213612513'], 'label': '2-585-13.9-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/j/i/451/1'}