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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2668.163', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.8727450898448561, -0.48817620604828127], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.10182298670383538, -0.994802532857004], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9333365210373668, -0.3590026998475987], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.523367983696612, -0.8521067736154565], 'algebraic': True, 'analytic_conductor': 12.390139910761352, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [23, [1]], [29, [1]]], 'bad_primes': [2, 23, 29], 'central_character': '2668.163', 'coeff_info': ['x^308 - 1', '0.999791928189206 + 0.0203985373914054*I', '\\\\zeta_{308}'], 'conductor': 2668, 'conductor_radical': 1334, 'conjugate': 'dirichlet_L_2668.311', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^283', 0, 'a^226', 0, 'a^290', 0, 'a^258', 0, 'a^351', 0, 'a^106', 0, 'a^201', 0, 'a^273', 0, 'a^431', 0, 'a^265', 0, 0, 0, 'a^144', 0, 'a^233', 0, 0, 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0, 'data': '-0.238836637029', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(308)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.48358777861476549699825465966-0.604879626879092890225506900206*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.795075739862', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.74729982777', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.10309567331', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 12.390139910761352, 'bad_primes': [2, 23, 29], 'central_character': '2668.163', 'conductor': 2668, 'conductor_radical': 1334, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2668/163'], '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': '1-2668-2668.163-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': '1-2668-2668.163-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.390139910761352, 'root_angle': -0.23883663702931032, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.795075739862', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2668.163', 'Lhash_array': ['dirichlet_L_2668.163'], 'factors': ['1-2668-2668.163-r0-0-0'], 'label': '1-2668-2668.163-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2668/163'}
Lfunction data - 1-2668-2668.163-r0-0-0