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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_837.220', 'a10': [0.6691306063588582, 0.7431448254773942], 'a2': [0.848048096156426, -0.5299192642332049], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.4383711467890774, -0.898794046299167], 'a5': [0.17364817766693036, 0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.24192189559966773, -0.9702957262759965], 'a8': [-0.10452846326765347, -0.9945218953682733], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 89.94814205310114, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.220', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.331', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^82', 0, 'a^74', 'a^20', 0, 'a^64', 'a^66', 0, 'a^12', 'a^19', 0, 'a^23', 'a^56', 0, 'a^58', 'a^81', 0, 'a^42', 'a^4', 0, 'a^11', 'a^11', 0, 'a^40', 'a^15', 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'195.03911897593623600968095847074', '195.513324027900907078422004679986', '196.13597905571795708320953695842', '196.86494677901429220112472054037', '197.6306683893124697001661054359', '198.12423829368029308974354168607', '198.36154297348219606068157271124', '199.65736696545812093343213427701'], 'prelabel': '1-837-837.220-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 89.94814205310114, 'root_angle': 0.3509175086827006, 'root_number': '0.451420345775928128761212343542+0.892311420648386348577915143401*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.175458754341', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.57052938193227445475741973023-0.149549492564999171126047319582*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.29930265403', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.205952532', 'prec': 37}, 'z3': {'__RealLiteral__': 0, 'data': '3.32346776886', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.94814205310114, 'bad_primes': [3, 31], 'central_character': '837.220', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/220'], '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': '1-837-837.220-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': '1-837-837.220-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 89.94814205310114, 'root_angle': 0.1754587543413503, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29930265403', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_837.220', 'Lhash_array': ['dirichlet_L_837.220'], 'label': '1-837-837.220-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/220'}