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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_308.223', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.8090169943749475, 0.5877852522924731], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.30901699437494745, -0.9510565162951535], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.30901699437494745, -0.9510565162951535], 'algebraic': True, 'analytic_conductor': 1.4303459866995862, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]], [11, [1]]], 'bad_primes': [2, 7, 11], 'central_character': '308.223', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 308, 'conductor_radical': 154, 'conjugate': 'dirichlet_L_308.279', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^14', 0, 'a^7', 0, 0, 0, 'a^8', 0, 0, 0, 'a^3', 0, 'a^11', 0, 'a^7', 0, 'a^14', 0, 0, 0, 'a^5', 0, 'a^4', 0, 'a^12', 0, 'a^6', 0, 'a^8', 0, 0, 0, 0, 0, 'a^6', 0, 'a^7', 0, 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'197.824987204624825907355611405691', '198.40151499286012016223176471482', '198.96525092804198024502950201312', '199.95001735573292689437358679548'], 'prelabel': '1-308-308.223-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4303459866995862, 'root_angle': -0.8075674742043435, 'root_number': '-0.822761021268750033178975733422-0.568387457532978515621493932108*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.403783737102', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.579959102040469628983052771320-0.0510482589987831721126793370510*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.16733890168', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.88482683848', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.85366349887', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.4303459866995862, 'bad_primes': [2, 7, 11], 'central_character': '308.223', 'conductor': 308, 'conductor_radical': 154, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/308/223'], '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': '1-308-308.223-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': '1-308-308.223-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4303459866995862, 'root_angle': -0.40378373710217175, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.16733890168', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_308.223', 'Lhash_array': ['dirichlet_L_308.223'], 'label': '1-308-308.223-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/308/223'}