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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_712.421', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9369497249997617, -0.3494641795990983], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9898214418809327, 0.14231483827328514], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8005412409243604, -0.599277666511347], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.7557495743542583, 0.6548607339452851], 'algebraic': True, 'analytic_conductor': 76.51502645377302, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [89, [1]]], 'bad_primes': [2, 89], 'central_character': '712.421', 'coeff_info': ['x^88 - 1', '0.997452114610254 + 0.0713391831992323*I', '\\\\zeta_{88}'], 'conductor': 712, 'conductor_radical': 178, 'conjugate': 'dirichlet_L_712.597', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^49', 0, 'a^130', 0, 'a^53', 0, 'a^10', 0, 'a^112', 0, 'a^71', 0, 'a^3', 0, 'a^30', 0, 'a^131', 0, 'a^102', 0, 'a^21', 0, 'a^84', 0, 'a^59', 0, 'a^75', 0, 'a^67', 0, 'a^73', 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'198.14168987827233153727391408631', '198.462978965674634257096164870688', '199.269831846792413345421397226319', '199.69286931803382601594568328267'], 'prelabel': '1-712-712.421-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 76.51502645377302, 'root_angle': -0.850269446704502, 'root_number': '-0.891390504147452421222004165557-0.453236107471316331619971222826*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.425134723352', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(88)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.544987631717858083538811076173-0.0314324159276272033321254249438*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0605191159773', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.10939913312', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.60178799104', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 76.51502645377302, 'bad_primes': [2, 89], 'central_character': '712.421', 'conductor': 712, 'conductor_radical': 178, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/712/421'], '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': '1-712-712.421-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-712-712.421-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 76.51502645377302, 'root_angle': -0.425134723352251, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0605191159773', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_712.421', 'Lhash_array': ['dirichlet_L_712.421'], 'label': '1-712-712.421-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/712/421'}
Lfunction data - 1-712-712.421-r1-0-0