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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_621.11', 'a10': [-0.9283679330160726, -0.3716624556603275], 'a2': [-0.9679487013963562, -0.2511479871810792], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8738493770697849, 0.4861967361004687], 'a5': [0.9919548128307953, 0.12659245357374926], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.4722710747726827, 0.8814533634475821], 'a8': [-0.7237340381050702, -0.690079011482112], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.8839118757806594, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]]], 'bad_primes': [3, 23], 'central_character': '621.11', 'coeff_info': ['x^198 - 1', '0.999496542383185 + 0.0317279334980676*I', '\\\\zeta_{198}'], 'conductor': 621, 'conductor_radical': 69, 'conjugate': 'dirichlet_L_621.113', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^107', 0, 'a^16', 'a^4', 0, 'a^65', 'a^123', 0, 'a^111', 'a^14', 0, 'a^100', 'a^172', 0, 'a^32', 'a^138', 0, 'a^159', 'a^20', 0, 'a^121', 0, 0, 'a^8', 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'prelabel': '1-621-621.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8839118757806594, 'root_angle': 0.05420263153898067, 'root_number': '0.942566035368235573543809668357+0.334019863137218361836305716579*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.054202631539', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(198)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.846717663684374504154483997597+0.0368805676280931061624248632651*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.0853974496', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.49830893317', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.73982829504', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8839118757806594, 'bad_primes': [3, 23], 'central_character': '621.11', 'conductor': 621, 'conductor_radical': 69, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/621/11'], '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': '1-621-621.11-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': '1-621-621.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8839118757806594, 'root_angle': 0.05420263153898067, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.0853974496', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_621.11', 'Lhash_array': ['dirichlet_L_621.11'], 'factors': ['1-621-621.11-r0-0-0'], 'label': '1-621-621.11-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/621/11'}