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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_93.20', 'a10': [-0.10452846326765347, -0.9945218953682733], 'a2': [0.8090169943749475, -0.5877852522924731], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [0.5, -0.8660254037844386], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9781476007338057, 0.20791169081775934], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 9.994238005900128, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '93.20', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 93, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_93.14', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^27', 0, 'a^24', 'a^25', 0, 'a^14', 'a^21', 0, 'a^22', 'a^19', 0, 'a^28', 'a^11', 0, 'a^18', 'a^11', 0, 'a^2', 'a^19', 0, 'a^16', 'a^21', 0, 'a^20', 'a^25', 0, 'a^8', 'a^27', 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'-0.729138917602148691595205707111-0.684365720092676048197912016948*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.380039597151', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.23299797911303508808667353228-0.991629835092646892044514259231*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.809405691901', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.57610832815', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.96852695221', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.994238005900128, 'bad_primes': [3, 31], 'central_character': '93.20', 'conductor': 93, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/93/20'], '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': '1-93-93.20-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-93-93.20-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.994238005900128, 'root_angle': -0.3800395971509206, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.809405691901', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_93.20', 'Lhash_array': ['dirichlet_L_93.20'], 'label': '1-93-93.20-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/93/20'}