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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.576', 'a10': [0.16113406059086408, 0.9869325278444823], 'a2': [-0.9594929736144974, 0.28173255684142967], 'a3': [-0.9781476007338057, 0.20791169081775934], 'a4': [0.8412535328311812, -0.5406408174555976], 'a5': [0.12344402555269474, -0.992351536782881], 'a6': [0.8799502578106532, -0.4750658309949949], 'a7': [0.5800569095711982, -0.8145759520503357], 'a8': [-0.6548607339452851, 0.7557495743542583], 'a9': [0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 17.41957076659139, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.576', 'coeff_info': ['x^165 - 1', '0.999275047800474 + 0.0380707084693900*I', '\\\\zeta_{165}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.267', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^75', 'a^77', 'a^150', 'a^127', 'a^152', 'a^140', 'a^60', 'a^154', 'a^37', 0, 'a^62', 'a^106', 'a^50', 'a^39', 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'194.66568440588896896335191756250', '195.56115430622546476918774688550', '195.8662922224219452254334402385', '196.29497475483610475447027701668', '197.09007175632153296392189641691', '197.41494371683129244157564336020', '198.277919315811694763060077403285', '198.678964485593948987714116514836', '199.139109664082099714058950392650', '199.46439212913219499170924054529'], 'prelabel': '1-3751-3751.576-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.05930435242581576, 'root_number': '0.931376628476504711221591455310-0.364057105311431757867483865608*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(165)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.627645375844290466830888254554-0.0748028427124571101358793475958*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.880979910465', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '0.989899467421', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '2.13179689958', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.576', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/576'], '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': '1-3751-3751.576-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': '1-3751-3751.576-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.05930435242581576, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.880979910465', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.576', 'Lhash_array': ['dirichlet_L_3751.576'], 'factors': ['1-3751-3751.576-r0-0-0'], 'label': '1-3751-3751.576-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/576'}
Lfunction data - 1-3751-3751.576-r0-0-0