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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_967.677', 'a10': [-0.8923315129986835, 0.4513806275301149], 'a2': [0.38943349913604447, -0.9210545856520429], 'a3': [0.9998096274980727, -0.019511759586594398], 'a4': [-0.6966830995013129, -0.7173790203715493], 'a5': [-0.7632499803575472, -0.6461032947479868], 'a6': [0.3713879660651067, -0.9284777749962695], 'a7': [0.9982870823553307, -0.05850556556842369], 'a8': [-0.9320569735915272, 0.3623117414318825], 'a9': [0.9992385824756699, -0.03901609016820979], 'algebraic': True, 'analytic_conductor': 103.91858227640239, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.677', 'coeff_info': ['x^322 - 1', '0.999809627498073 + 0.0195117595865944*I', '\\\\zeta_{322}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.10', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^262', 'a^321', 'a^202', 'a^197', 'a^261', 'a^319', 'a^142', 'a^320', 'a^137', 'a^90', 'a^201', 'a^71', 'a^259', 'a^196', 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'199.5330273285398643068749106190'], 'prelabel': '1-967-967.677-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 103.91858227640239, 'root_angle': -0.29264905971441807, 'root_number': '0.606310024055670095872630130471-0.795228366401509063816806782142*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.146324529857', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(322)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.50884871452098465345082553212-0.787672128378477717088451491063*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.983502218219', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.80659009237', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.66900258214', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 103.91858227640239, 'bad_primes': [967], 'central_character': '967.677', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/677'], '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': '1-967-967.677-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-967-967.677-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 103.91858227640239, 'root_angle': -0.14632452985720903, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.983502218219', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_967.677', 'Lhash_array': ['dirichlet_L_967.677'], 'label': '1-967-967.677-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/677'}
Lfunction data - 1-967-967.677-r1-0-0