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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_23.14', 'a10': [0.6548607339452851, -0.7557495743542583], 'a2': [0.8412535328311812, -0.5406408174555976], 'a3': [-0.14231483827328514, 0.9898214418809327], 'a4': [0.41541501300188644, -0.9096319953545183], 'a5': [0.9594929736144974, -0.28173255684142967], 'a6': [0.41541501300188644, 0.9096319953545183], 'a7': [0.6548607339452851, 0.7557495743542583], 'a8': [-0.14231483827328514, -0.9898214418809327], 'a9': [-0.9594929736144974, -0.28173255684142967], 'algebraic': True, 'analytic_conductor': 2.4716932702763756, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.14', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.5', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^20', 'a^6', 'a^18', 'a^21', 'a^4', 'a^3', 'a^16', 'a^12', 'a^19', 'a^13', 'a^2', 'a^8', 'a^1', 'a^5', 'a^14', 'a^15', 'a^10', 'a^7', 'a^17', 'a^9', 'a^11', 0, 'a^0', 'a^20', 'a^6', 'a^18', 'a^21', 'a^4', 'a^3', 'a^16', 'a^12', 'a^19', 'a^13', 'a^2', 'a^8', 'a^1', 'a^5', 'a^14', 'a^15', 'a^10', 'a^7', 'a^17', 'a^9', 'a^11', 0, 'a^0', 'a^20', 'a^6', 'a^18', 'a^21', 'a^4', 'a^3', 'a^16', 'a^12', 'a^19', 'a^13', 'a^2', 'a^8', 'a^1', 'a^5', 'a^14', 'a^15', 'a^10', 'a^7', 'a^17', 'a^9', 'a^11', 0, 'a^0', 'a^20', 'a^6', 'a^18', 'a^21', 'a^4', 'a^3', 'a^16', 'a^12', 'a^19', 'a^13', 'a^2', 'a^8', 'a^1', 'a^5', 'a^14', 'a^15', 'a^10', 'a^7', 'a^17', 'a^9', 'a^11', 0, 'a^0', 'a^20', 'a^6', 'a^18', 'a^21', 'a^4', 'a^3', 'a^16'], 'euler_factors': [[1, 'a^20'], [1, 'a^6'], [1, 'a^21'], [1, 'a^3'], [1, 'a^13'], [1, 'a^8'], [1, 'a^15'], [1, 'a^7'], [0], [1, 'a^4'], [1, 'a^16'], [1, 'a^1'], [1, 'a^10'], [1, 'a^17'], [1, 'a^0'], [1, 'a^3'], [1, 'a^8'], [1, 'a^5'], [1, 'a^9'], [1, 'a^20'], [1, 'a^18'], [1, 'a^19'], [1, 'a^1'], [1, 'a^17'], [1, 'a^21'], [1, 'a^12']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-23-23.14-r1-0-0', 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'193.512049776041381161452087879987', '194.079580892286438314126823059382', '195.4343747278554254000958246054', '196.21729359822568840410438274718', '197.29190866413151347042085687516', '198.17570297403320877229750340018', '199.57638053743013547699584374586'], 'prelabel': '1-23-23.14-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4716932702763756, 'root_angle': -0.05099742260757029, 'root_number': '0.987193305749012352407808798515-0.159528608983896725759522636067*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0254987113038', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.68374103656625157306608682546-0.125244753395362212773114722736*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.4737123724', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '4.74635317214', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.80015224207', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4716932702763756, 'bad_primes': [23], 'central_character': '23.14', 'conductor': 23, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/23/14'], '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': '1-23-23.14-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': '1-23-23.14-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4716932702763756, 'root_angle': -0.025498711303785147, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.4737123724', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_23.14', 'Lhash_array': ['dirichlet_L_23.14'], 'label': '1-23-23.14-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/23/14'}