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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3328.163', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.4127070298043947, -0.9108638249211758], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.881921264348355, -0.47139673682599764], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.3214394653031616, 0.9469301294951057], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.6593458151000688, 0.7518398074789774], 'algebraic': True, 'analytic_conductor': 15.455167025117607, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [13, [1]]], 'bad_primes': [2, 13], 'central_character': '3328.163', 'coeff_info': ['x^192 - 1', '0.999464587476366 + 0.0327190828217761*I', '\\\\zeta_{192}'], 'conductor': 3328, 'conductor_radical': 26, 'conjugate': 'dirichlet_L_3328.3083', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^131', 0, 'a^177', 0, 'a^58', 0, 'a^70', 0, 'a^197', 0, 0, 0, 'a^308', 0, 'a^316', 0, 'a^295', 0, 'a^189', 0, 'a^206', 0, 'a^162', 0, 'a^9', 0, 'a^251', 0, 'a^216', 0, 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'199.36036591918256662651451396039', '199.69491207758364361321012050145'], 'prelabel': '1-3328-3328.163-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.455167025117607, 'root_angle': 0.02624003475646636, 'root_number': '0.986439535551346891420343605622+0.164125082486629789060667710677*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(192)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.04049140462770930577694339120-0.159021690167668342526736296202*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.943321910193', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.74069054443', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.41573733647', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.455167025117607, 'bad_primes': [2, 13], 'central_character': '3328.163', 'conductor': 3328, 'conductor_radical': 26, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3328/163'], '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': '1-3328-3328.163-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': '1-3328-3328.163-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.455167025117607, 'root_angle': 0.02624003475646636, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.943321910193', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3328.163', 'Lhash_array': ['dirichlet_L_3328.163'], 'factors': ['1-3328-3328.163-r0-0-0'], 'label': '1-3328-3328.163-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3328/163'}
Lfunction data - 1-3328-3328.163-r0-0-0