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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_389.171', 'a10': [0.6659152250116811, 0.746027421143246], 'a2': [0.8989517410853953, 0.43804767685668233], 'a3': [-0.9372067050063436, -0.34877441432988227], 'a4': [0.6162284656009273, 0.7875674435774543], 'a5': [0.9254212296427042, 0.3789400318343067], 'a6': [-0.6897237772781042, -0.7240725868704215], 'a7': [-0.48118594449080504, -0.8766185526353477], 'a8': [0.2089675630312751, 0.9779225723955707], 'a9': [0.7567128158176952, 0.6537474392892525], 'algebraic': True, 'analytic_conductor': 1.8065084052796723, 'analytic_normalization': 0, 'bad_lfactors': [[389, [1]]], 'bad_primes': [389], 'central_character': '389.171', 'coeff_info': ['x^97 - 1', '0.997902826237712 + 0.0647298183744357*I', '\\\\zeta_{97}'], 'conductor': 389, 'conductor_radical': 389, 'conjugate': 'dirichlet_L_389.91', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^54', 'a^14', 'a^6', 'a^61', 'a^65', 'a^21', 'a^11', 'a^13', 'a^40', 'a^68', 'a^30', 'a^72', 'a^60', 'a^28', 'a^13', 'a^18', 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'0.259029813765477140901505260467+0.965869326348353516801563411495*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.208298604108', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(97)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.35719447783697795472153177477+0.508786208775809849599486957472*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.60964532531', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.85036732478', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.26141792461', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8065084052796723, 'bad_primes': [389], 'central_character': '389.171', 'conductor': 389, 'conductor_radical': 389, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/389/171'], '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': '1-389-389.171-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': '1-389-389.171-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8065084052796723, 'root_angle': 0.20829860410815698, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60964532531', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_389.171', 'Lhash_array': ['dirichlet_L_389.171'], 'label': '1-389-389.171-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/389/171'}