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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2601.178', 'a10': [0.04618345864573959, -0.9989329748023724], 'a2': [-0.9881654720812594, 0.15339165487868536], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9529420004271566, -0.3031526741130435], 'a5': [-0.1988648813328366, 0.9800269174734318], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.01539935528900683, 0.9998814228980769], 'a8': [-0.8951632913550623, 0.44573835577653825], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 12.078993218849428, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [17, [1]]], 'bad_primes': [3, 17], 'central_character': '2601.178', 'coeff_info': ['x^408 - 1', '0.999881422898077 + 0.0153993552890068*I', '\\\\zeta_{408}'], 'conductor': 2601, 'conductor_radical': 51, 'conjugate': 'dirichlet_L_2601.1885', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^194', 0, 'a^388', 'a^115', 0, 'a^101', 'a^174', 0, 'a^309', 'a^65', 0, 'a^4', 'a^295', 0, 'a^368', 0, 0, 'a^282', 'a^95', 0, 'a^259', 'a^169', 0, 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12.078993218849428, 'root_angle': 0.9525182622068435, 'root_number': '-0.988895026813548951933472316558+0.148615698845816081534285649692*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.476259131103', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(408)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.593778266315801147245896524077+0.332752666356519612157559739583*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.30270227586', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.19518362515', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.85182189873', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 12.078993218849428, 'bad_primes': [3, 17], 'central_character': '2601.178', 'conductor': 2601, 'conductor_radical': 51, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2601/178'], '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': '1-51e2-2601.178-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': '1-51e2-2601.178-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.078993218849428, 'root_angle': 0.4762591311034218, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30270227586', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2601.178', 'Lhash_array': ['dirichlet_L_2601.178'], 'label': '1-51e2-2601.178-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2601/178'}
Lfunction data - 1-51e2-2601.178-r0-0-0