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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.488', 'a10': [0.9135454576426009, -0.4067366430758002], 'a2': [-0.5591929034707468, -0.8290375725550417], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.374606593415912, 0.9271838545667874], 'a5': [-0.17364817766693036, 0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.848048096156426, 0.5299192642332049], 'a8': [0.9781476007338057, -0.20791169081775934], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.488', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.554', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^59', 0, 'a^28', 'a^25', 0, 'a^8', 'a^87', 0, 'a^84', 'a^38', 0, 'a^31', 'a^67', 0, 'a^56', 'a^12', 0, 'a^24', 'a^53', 0, 'a^7', 'a^82', 0, 'a^50', 'a^0', 0, 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'194.57129681702985975936544343166', '195.2005650892867549000403235208', '195.67904864568148672770366190366', '196.514726878529405578636609783553', '197.42055478543378304547988015533', '197.99071291502987255023179915054', '198.68602369687972183690394402937', '198.85148476116687468359042128480', '199.48014453425205948175385148439'], 'prelabel': '1-837-837.488-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.564752943879093, 'root_number': '-0.202027210867164923909249048587+0.979379908957312682565814728547*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.28237647194', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.741543601436514747363083494907+0.110764034967298781223264617366*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.60240448962', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.34606790959', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.26025615731', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.488', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/488'], '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': '1-837-837.488-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': '1-837-837.488-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.2823764719395465, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60240448962', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.488', 'Lhash_array': ['dirichlet_L_837.488'], 'label': '1-837-837.488-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/488'}
Lfunction data - 1-837-837.488-r0-0-0