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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_207.193', 'a10': [-0.6548607339452851, 0.7557495743542583], 'a2': [0.0475819158237423, 0.998867339183008], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9954719225730846, 0.09505604330418266], 'a5': [0.7237340381050702, 0.690079011482112], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9819286972627067, -0.18925124436041021], 'a8': [-0.14231483827328514, -0.9898214418809327], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.9613039585935531, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]]], 'bad_primes': [3, 23], 'central_character': '207.193', 'coeff_info': ['x^33 - 1', '0.981928697262707 + 0.189251244360410*I', '\\\\zeta_{33}'], 'conductor': 207, 'conductor_radical': 69, 'conjugate': 'dirichlet_L_207.133', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 0, 'a^16', 'a^4', 0, 'a^32', 'a^24', 0, 'a^12', 'a^14', 0, 'a^1', 'a^7', 0, 'a^32', 'a^6', 0, 'a^27', 'a^20', 0, 'a^22', 0, 0, 'a^8', 'a^9', 0, 'a^15', 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.296833225326', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(33)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.946398501094827496977778851919+0.694067659563776700528011447274*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.72209904702', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.49875095229', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.93313074805', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9613039585935531, 'bad_primes': [3, 23], 'central_character': '207.193', 'conductor': 207, 'conductor_radical': 69, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/207/193'], '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': '1-207-207.193-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': '1-207-207.193-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9613039585935531, 'root_angle': 0.2968332253256105, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72209904702', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_207.193', 'Lhash_array': ['dirichlet_L_207.193'], 'factors': ['1-207-207.193-r0-0-0'], 'label': '1-207-207.193-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/207/193'}