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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3328.1107', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.528067850650368, 0.8492021815265789], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.6343932841636455, 0.773010453362737], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9978589232386035, -0.06540312923014306], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.4422886902190013, 0.8968727415326883], 'algebraic': True, 'analytic_conductor': 15.455167025117607, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [13, [1]]], 'bad_primes': [2, 13], 'central_character': '3328.1107', 'coeff_info': ['x^192 - 1', '0.999464587476366 + 0.0327190828217761*I', '\\\\zeta_{192}'], 'conductor': 3328, 'conductor_radical': 26, 'conjugate': 'dirichlet_L_3328.475', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^223', 0, 'a^261', 0, 'a^290', 0, 'a^254', 0, 'a^169', 0, 0, 0, 'a^100', 0, 'a^44', 0, 'a^179', 0, 'a^129', 0, 'a^166', 0, 'a^138', 0, 'a^93', 0, 'a^247', 0, 'a^216', 0, 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False, 'root_analytic_conductor': 15.455167025117607, 'root_angle': 0.21594746524353367, 'root_number': '0.212329680511067923388253388445+0.977198089833411321162361806454*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, '1.02154504746037359458715169615+0.436673484922240858843072905040*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.768157204921', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.27881846452', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.12619497753', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.455167025117607, 'bad_primes': [2, 13], 'central_character': '3328.1107', 'conductor': 3328, 'conductor_radical': 26, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3328/1107'], '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': '1-3328-3328.1107-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': '1-3328-3328.1107-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.455167025117607, 'root_angle': 0.21594746524353367, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.768157204921', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3328.1107', 'Lhash_array': ['dirichlet_L_3328.1107'], 'factors': ['1-3328-3328.1107-r0-0-0'], 'label': '1-3328-3328.1107-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3328/1107'}
Lfunction data - 1-3328-3328.1107-r0-0-0