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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4235.3023', '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': '4235.3023', 'coeff_info': ['x^220 - 1', '0.999592192828189 + 0.0285560507936963*I', '\\\\zeta_{220}'], 'conductor': 4235, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_4235.2722', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^57', 'a^121', 'a^114', 0, 'a^178', 0, 'a^171', 'a^22', 0, 0, 'a^15', 'a^37', 0, 0, 'a^8', 'a^43', 'a^79', 'a^56', 0, 0, 0, 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'193.21272457599747055068837463834', '193.7341205309266962636812963292', '194.23500426038425620520534753752', '194.80483304599473336527056044573', '195.254562327808964477028044662182', '195.61130101545432245735221799046', '196.13463079597002603921934163185', '196.78838054788712936796435316065', '197.22040514561122930495695091823', '197.78321036477877538836790506670', '198.35469133753839669096511304429', '199.024466430093390903286295136207', '199.39047975798244707569072866475', '199.7248135131474355435112870375'], 'prelabel': '1-4235-4235.3023-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': 0.847758750973977, 'root_number': '-0.887787875353473078023454983463+0.460252852653154284888756825553*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, '0.631985765764936064779046730824+0.450931089540910403448962929852*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.05544886577', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.56487724997', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.07066077381', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 19.66725731711931, 'bad_primes': [5, 7, 11], 'central_character': '4235.3023', 'conductor': 4235, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4235/3023'], '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': '1-4235-4235.3023-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': '1-4235-4235.3023-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': 0.4238793754869885, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05544886577', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4235.3023', 'Lhash_array': ['dirichlet_L_4235.3023'], 'label': '1-4235-4235.3023-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4235/3023'}
Lfunction data - 1-4235-4235.3023-r0-0-0