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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_229.99', 'a10': [-0.45153335831088937, -0.892254238618394], 'a2': [0.08257934547233232, 0.9965844930066698], 'a3': [-0.2985148110016945, 0.9544050018795074], 'a4': [-0.9863613034027223, 0.1645945902807339], 'a5': [-0.9264940672148018, 0.3763093719478355], 'a6': [-0.9757963826274356, -0.2186810912063758], 'a7': [-0.027554342368161996, 0.9996203070249514], 'a8': [-0.24548548714079915, -0.9694002659393304], 'a9': [-0.8217778152252452, -0.5698080575102662], 'algebraic': True, 'analytic_conductor': 1.063471529072095, 'analytic_normalization': 0, 'bad_lfactors': [[229, [1]]], 'bad_primes': [229], 'central_character': '229.99', 'coeff_info': ['x^114 - 1', '0.998481516433316 + 0.0550877603558654*I', '\\\\zeta_{114}'], 'conductor': 229, 'conductor_radical': 229, 'conjugate': 'dirichlet_L_229.192', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^27', 'a^34', 'a^54', 'a^50', 'a^61', 'a^29', 'a^81', 'a^68', 'a^77', 'a^78', 'a^88', 'a^69', 'a^56', 'a^84', 'a^108', 'a^12', 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[1, 'a^52'], [1, 'a^75']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-229-229.99-r0-0-0', 'leading_term': '-0.158571080494221961728711115961+0.110895117403385108613281700233*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/229/99', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.19350068380503335, -0.8257200955096053, -2.017584927281089, -3.746446691829108, -5.638839829697691, -7.111188078732651, -7.585116460969046, -6.751497528835815, -4.770126355653014, -2.2772258011252213, -0.14784398786971648, 0.9046073131829332, 0.6901207198275241, -0.35338373706411247, -1.4083948851208947, -1.763804098464765, -1.2520810057524405, -0.34732091124809705, 0.16886937402557936, -0.22481659262627482, -1.3750950588089859, -2.5108570285803435, -2.7733540067944102, -1.8646206515142842, 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'198.57902146466846960740400576759', '199.38884944139294167320238238487', '199.66590337287396177362776089548'], 'prelabel': '1-229-229.99-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.063471529072095, 'root_angle': -0.38851819278303995, 'root_number': '0.343114254774606810488572704607-0.939293675146631766965891373606*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.194259096392', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(114)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.319106171291107468206988039809+0.456258026135513901121750329660*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.15345876405', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.96896023772', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.46608016603', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.063471529072095, 'bad_primes': [229], 'central_character': '229.99', 'conductor': 229, 'conductor_radical': 229, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/229/99'], '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': '1-229-229.99-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': '1-229-229.99-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.063471529072095, 'root_angle': -0.19425909639151998, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.15345876405', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_229.99', 'Lhash_array': ['dirichlet_L_229.99'], 'label': '1-229-229.99-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/229/99'}
Lfunction data - 1-229-229.99-r0-0-0