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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_693.95', 'a10': [0.5, 0.8660254037844386], 'a2': [0.6691306063588582, -0.7431448254773942], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.10452846326765347, -0.9945218953682733], 'a5': [-0.30901699437494745, 0.9510565162951535], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.218278470074069, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '693.95', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 693, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_693.569', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^26', 0, 'a^22', 'a^9', 0, 0, 'a^18', 0, 'a^5', 0, 0, 'a^11', 0, 0, 'a^14', 'a^14', 0, 'a^13', 'a^1', 0, 0, 'a^15', 0, 'a^18', 'a^7', 0, 0, 'a^22', 0, 'a^16', 'a^10', 0, 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'199.14884198346381328382004993175', '199.71891459012646842779709240412'], 'prelabel': '1-693-693.95-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.218278470074069, 'root_angle': 0.3399580275515731, 'root_number': '-0.535604109621299229165474434582+0.844469204741520031762468992380*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.339958027552', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.899258283536634912748636202794-0.238382091751994960279932769771*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.96055008834', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.51171339578', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.87376887226', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.218278470074069, 'bad_primes': [3, 7, 11], 'central_character': '693.95', 'conductor': 693, 'conductor_radical': 231, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/693/95'], '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': '1-693-693.95-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': '1-693-693.95-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.218278470074069, 'root_angle': 0.3399580275515731, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96055008834', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_693.95', 'Lhash_array': ['dirichlet_L_693.95'], 'factors': ['1-693-693.95-r0-0-0'], 'label': '1-693-693.95-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/693/95'}
Lfunction data - 1-693-693.95-r0-0-0