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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_361.196', 'a10': [-0.00918581424472636, -0.9999578095183124], 'a2': [0.7419142528352816, -0.670494773611149], 'a3': [-0.0459135704399718, -0.9989454159509686], 'a4': [0.10087351712026821, -0.9948992579873537], 'a5': [0.6636513986016214, -0.7480419915580354], 'a6': [-0.7038516128259115, -0.710347032880664], 'a7': [-0.9622680003092504, 0.272103464845335], 'a8': [-0.59223525266498, -0.8057651056609781], 'a9': [-0.9957838880989075, 0.09173030144190346], 'algebraic': True, 'analytic_conductor': 1.6764769519433462, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '361.196', 'coeff_info': ['x^171 - 1', '0.999325023492064 + 0.0367355062927724*I', '\\\\zeta_{171}'], 'conductor': 361, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_361.35', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^151', 'a^127', 'a^131', 'a^148', 'a^107', 'a^78', 'a^111', 'a^83', 'a^128', 'a^12', 'a^87', 'a^89', 'a^58', 'a^104', 'a^91', 'a^97', 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'st_group': 'mu(171)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.784071925801482314912747856934-1.13786178918848935193888040435*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.73514513901', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.04784326528', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.79395649118', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6764769519433462, 'bad_primes': [19], 'central_character': '361.196', 'conductor': 361, 'conductor_radical': 19, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/361/196'], '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': '1-19e2-361.196-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': '1-19e2-361.196-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6764769519433462, 'root_angle': 0.4755309325946445, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.73514513901', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_361.196', 'Lhash_array': ['dirichlet_L_361.196'], 'label': '1-19e2-361.196-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/361/196'}