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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_967.64', 'a10': [0.7374604040411934, 0.6753903704313526], 'a2': [0.27917848281287244, -0.9602392278668388], 'a3': [-0.9574697646386026, -0.2885336198831931], 'a4': [-0.8441187494686053, -0.5361562615465363], 'a5': [-0.442653251076912, 0.8966928678823315], 'a6': [-0.5443662566012645, 0.8388476492629197], 'a7': [-0.6386260144683744, -0.7695172601340659], 'a8': [-0.7504980663939613, 0.6608726445684715], 'a9': [0.8334967003942021, 0.5525244342397698], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.64', 'coeff_info': ['x^161 - 1', '0.999238582475670 + 0.0390160901682098*I', '\\\\zeta_{161}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.136', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^128', 'a^88', 'a^95', 'a^52', 'a^55', 'a^103', 'a^62', 'a^15', 'a^19', 'a^130', 'a^22', 'a^31', 'a^70', 'a^140', 'a^29', 'a^136', 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[1, 'a^43'], [1, 'a^101'], [1, 'a^53'], [1, 'a^69'], [1, 'a^75']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-967-967.64-r0-0-0', 'leading_term': '-0.125410420170686960264731956960-0.320390162278115015942386522190*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/967/64', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.3440605027781959, 0.24227470992761102, 0.7860460037693292, 0.8625524827316086, 0.12738912501236793, -1.127310675815241, -2.036736513386279, -1.806722755210422, -0.4435332409339709, 1.1084104881460126, 1.6865055782610974, 0.9603786100357272, -0.1679011402301646, -0.33610622524187017, 0.9224132038081708, 2.553948486090361, 2.871943365773902, 1.2564418642953858, -1.0352546264919753, -1.9666249090419679, -0.821151520048086, 0.8587404424125744, 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4.490729120579545, 'root_angle': 0.38123955161726625, 'root_number': '-0.734277945178413466015318910573+0.678848951700278335633509339721*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.381239551617', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(161)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.504161518781238099805748975448-0.377699162345334958367854824267*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.184701766759', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.28504901725', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.58242519684', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.490729120579545, 'bad_primes': [967], 'central_character': '967.64', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/64'], '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': '1-967-967.64-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': '1-967-967.64-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': 0.38123955161726625, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.184701766759', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_967.64', 'Lhash_array': ['dirichlet_L_967.64'], 'factors': ['1-967-967.64-r0-0-0'], 'label': '1-967-967.64-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/64'}
Lfunction data - 1-967-967.64-r0-0-0