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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_55.49', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.8090169943749475, -0.5877852522924731], 'a3': [-0.30901699437494745, -0.9510565162951535], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.8090169943749475, -0.5877852522924731], 'a7': [-0.30901699437494745, 0.9510565162951535], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [-0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 0.2554189261963547, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]]], 'bad_primes': [5, 11], 'central_character': '55.49', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 55, 'conductor_radical': 55, 'conjugate': 'dirichlet_L_55.9', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 'a^7', 'a^8', 0, 'a^6', 'a^3', 'a^7', 'a^4', 0, 0, 'a^5', 'a^9', 'a^2', 0, 'a^6', 'a^1', 'a^3', 'a^2', 0, 'a^0', 0, 'a^5', 'a^4', 0, 'a^8', 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'197.45833539376890760050415771145', '199.04479310304114863839984387206', '199.92185684859497668801117636991'], 'prelabel': '1-55-55.49-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2554189261963547, 'root_angle': -0.25728286993039323, 'root_number': '-0.0457436533399285543029207132605-0.998953211206168776295316442835*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25728286993', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.08509167791619262554986162447-0.717111604565652472064655898791*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.70537787625', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.29308429218', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.49354600265', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.2554189261963547, 'bad_primes': [5, 11], 'central_character': '55.49', 'conductor': 55, 'conductor_radical': 55, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/55/49'], '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': '1-55-55.49-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': '1-55-55.49-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2554189261963547, 'root_angle': -0.25728286993039323, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70537787625', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_55.49', 'Lhash_array': ['dirichlet_L_55.49'], 'factors': ['1-55-55.49-r0-0-0'], 'label': '1-55-55.49-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/55/49'}
Lfunction data - 1-55-55.49-r0-0-0