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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_967.22', 'a10': [0.8334967003942021, -0.5525244342397698], 'a2': [-0.8074849976626273, -0.5898881068048302], 'a3': [-0.7241419573240463, -0.6896509447850405], 'a4': [0.3040640429004265, 0.9526515930890199], 'a5': [-0.3471084886925121, 0.9378249821142537], 'a6': [0.17791687654180785, 0.984045519801603], 'a7': [-0.982262866609439, -0.18750909545994704], 'a8': [0.3164306917211476, -0.9486156320327407], 'a9': [0.04876314871420185, 0.9988103700540342], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.22', 'coeff_info': ['x^483 - 1', '0.999915388507649 + 0.0130082983359933*I', '\\\\zeta_{483}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.44', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^290', 'a^300', 'a^97', 'a^148', 'a^107', 'a^256', 'a^387', 'a^117', 'a^438', 'a^48', 'a^397', 'a^274', 'a^63', 'a^448', 'a^194', 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'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': -0.753280903050521, 'root_number': '-0.714357425179995827961198116185-0.699781015097013519016360358575*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.376640451525', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(483)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.392326158290574819355290639689-0.0834167214254780710154276917835*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.146684815791', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.6308257134', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.57836671475', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.490729120579545, 'bad_primes': [967], 'central_character': '967.22', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/22'], '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': '1-967-967.22-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': '1-967-967.22-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': -0.3766404515252605, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.146684815791', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_967.22', 'Lhash_array': ['dirichlet_L_967.22'], 'label': '1-967-967.22-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/22'}