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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_179.124', 'a10': [0.9900485105144543, -0.14072649653889052], 'a2': [-0.6352455960455385, 0.7723101920243889], 'a3': [0.4897757402062284, -0.8718484526025386], 'a4': [-0.19292606540949683, -0.9812132965291546], 'a5': [-0.7376084637406223, -0.6752286680956305], 'a6': [0.36220956382968256, 0.9320966859024395], 'a7': [-0.994398216007982, 0.105698571419593], 'a8': [0.8803564628730913, 0.4743126587785523], 'a9': [-0.5202394486108822, -0.8540204424421264], 'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'analytic_normalization': 0, 'bad_lfactors': [[179, [1]]], 'bad_primes': [179], 'central_character': '179.124', 'coeff_info': ['x^89 - 1', '0.997509025150764 + 0.0705389590423110*I', '\\\\zeta_{89}'], 'conductor': 179, 'conductor_radical': 179, 'conjugate': 'dirichlet_L_179.13', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^32', 'a^74', 'a^64', 'a^55', 'a^17', 'a^43', 'a^7', 'a^59', 'a^87', 'a^35', 'a^49', 'a^88', 'a^75', 'a^40', 'a^39', 'a^61', 'a^2', 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0.8312725052572271, 'root_angle': -0.8587084243374596, 'root_number': '-0.903091964592855591869702183163-0.429447206869268695664666436963*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.429354212169', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(89)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.518867989911606913487406703973-0.114089962447715929636212360267*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.235334203719', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.9551937716', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.74826719873', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'bad_primes': [179], 'central_character': '179.124', 'conductor': 179, 'conductor_radical': 179, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/179/124'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-179-179.124-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-179-179.124-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8312725052572271, 'root_angle': -0.4293542121687298, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.235334203719', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_179.124', 'Lhash_array': ['dirichlet_L_179.124'], 'label': '1-179-179.124-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/179/124'}