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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1001.125', 'a10': [1.0, 0.0], 'a2': [-0.9510565162951535, 0.30901699437494745], 'a3': [0.8090169943749475, 0.5877852522924731], 'a4': [0.8090169943749475, -0.5877852522924731], 'a5': [-0.9510565162951535, -0.30901699437494745], 'a6': [-0.9510565162951535, -0.30901699437494745], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.5877852522924731, 0.8090169943749475], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 4.648624456773655, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]], [13, [1]]], 'bad_primes': [7, 11, 13], 'central_character': '1001.125', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 1001, 'conductor_radical': 1001, 'conjugate': 'dirichlet_L_1001.993', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 'a^2', 'a^18', 'a^11', 'a^11', 0, 'a^7', 'a^4', 'a^0', 0, 'a^0', 0, 0, 'a^13', 'a^16', 'a^16', 'a^13', 'a^7', 'a^9', 0, 0, 'a^10', 'a^9', 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'189.56144073713468930190888522246', '190.39091920930687473316172711201', '190.87689321098042576801383268088', '191.37005706197620388231484299090', '191.84036151868187751324273171950', '192.44058840048901863128132163307', '192.7973169916082047593477926843', '193.78373691128514445610702263781', '194.18434858380846845385839273176', '195.33538450937629286817673939443', '195.87422409882479950348424015671', '196.34160488033204381173682505784', '196.87943061145970394639924016448', '197.80760825864919276100495259768', '198.07658370495981463853220809401', '198.57382316265768181187774854152', '199.240030086765755286848626999553', '199.72290086891987216652543702456'], 'prelabel': '1-1001-1001.125-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': 0.813983953298844, 'root_number': '-0.834050622872210759847534332413+0.551687917654970273962339708450*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.406991976649', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.637285955114313404376034655987+0.276661275426962092257238372799*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.30689112667', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.49964164913', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.47169413406', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.648624456773655, 'bad_primes': [7, 11, 13], 'central_character': '1001.125', 'conductor': 1001, 'conductor_radical': 1001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1001/125'], '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': '1-1001-1001.125-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': '1-1001-1001.125-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': 0.406991976649422, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30689112667', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1001.125', 'Lhash_array': ['dirichlet_L_1001.125'], 'label': '1-1001-1001.125-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1001/125'}