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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2580.2183', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8660254037844386, 0.5], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 11.981469628847185, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [43, [1]]], 'bad_primes': [2, 3, 5, 43], 'central_character': '2580.2183', 'coeff_info': ['x^84 - 1', '0.997203797181180 + 0.0747300935864243*I', '\\\\zeta_{84}'], 'conductor': 2580, 'conductor_radical': 1290, 'conjugate': 'dirichlet_L_2580.2567', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^91', 0, 0, 0, 'a^96', 0, 'a^73', 0, 0, 0, 'a^25', 0, 'a^86', 0, 0, 0, 'a^89', 0, 0, 0, 0, 0, 'a^22', 0, 'a^50', 0, 0, 0, 0, 0, 'a^77', 0, 0, 0, 'a^78', 0, 0, 0, 0, 0, 'a^51', 0, 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'194.05028435424876236595977036256', '194.81833839356419324045551808521', '195.257207963700851877032225648469', '195.699741372612596708054610043613', '196.18232277605177532303976629747', '196.98187701506607675761763198906', '197.453610679058476363903847140816', '197.88540274016778667790056851211', '198.75133122836767225082724568056', '199.12590880215658887476531811535', '199.43311186035566383447665446173'], 'prelabel': '1-2580-2580.2183-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.981469628847185, 'root_angle': 0.12556236635097295, 'root_number': '0.704603844310408618177752470890+0.709600889643603429400351119688*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.125562366351', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(84)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.31372799396661265349688256221+0.209139258678381393611763209609*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.15543113998', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.76269669219', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.83319668008', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 11.981469628847185, 'bad_primes': [2, 3, 5, 43], 'central_character': '2580.2183', 'conductor': 2580, 'conductor_radical': 1290, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2580/2183'], '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': '1-2580-2580.2183-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': '1-2580-2580.2183-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.981469628847185, 'root_angle': 0.12556236635097295, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15543113998', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2580.2183', 'Lhash_array': ['dirichlet_L_2580.2183'], 'factors': ['1-2580-2580.2183-r0-0-0'], 'label': '1-2580-2580.2183-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2580/2183'}
Lfunction data - 1-2580-2580.2183-r0-0-0