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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4235.1028', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.057088810862767986, 0.9983691039261356], 'a3': [0.9510565162951535, -0.30901699437494745], 'a4': [-0.9934817353485502, 0.11399140989054063], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.362807705350641, 0.9318640292114523], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.17052219263262378, -0.985353835847693], 'a9': [0.8090169943749475, -0.5877852522924731], 'algebraic': True, 'analytic_conductor': 19.66725731711931, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.1028', 'coeff_info': ['x^220 - 1', '0.999592192828189 + 0.0285560507936963*I', '\\\\zeta_{220}'], 'conductor': 4235, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_4235.482', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^53', 'a^209', 'a^106', 0, 'a^42', 0, 'a^159', 'a^198', 0, 0, 'a^95', 'a^73', 0, 0, 'a^212', 'a^67', 'a^31', 'a^164', 0, 0, 0, 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'193.02003713630312582997243660471', '194.02429487650968484245415853960', '194.57816832414456792973514239533', '194.977056425111446291730770773409', '195.58413618175794058969922568227', '196.041768127247139260450781678912', '196.669908434588435432370825711692', '196.90210824608476295623766558005', '197.4316672761951255918418919963', '198.07518061007140557027576356824', '198.505526580933265451811112372878', '198.797814166058978430113994758949', '199.5332151921672636821100623268'], 'prelabel': '1-4235-4235.1028-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': -0.2001751333235437, 'root_number': '0.808693473926354154831329660213-0.588230282482060891683599053717*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(220)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.16439148572879448679411612720+0.301553832347769066458457606466*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.371572653', 'prec': 37}, 'z2': {'__RealLiteral__': 0, 'data': '1.67642970572', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.45028821889', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.66725731711931, 'bad_primes': [5, 7, 11], 'central_character': '4235.1028', 'conductor': 4235, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4235/1028'], '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': '1-4235-4235.1028-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': '1-4235-4235.1028-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': -0.10008756666177185, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.371572653', 'prec': 37}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4235.1028', 'Lhash_array': ['dirichlet_L_4235.1028'], 'label': '1-4235-4235.1028-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4235/1028'}