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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_311.121', 'a10': [0.6889669190756865, -0.72479278722912], 'a2': [0.5289640103269625, 0.8486442574947509], 'a3': [0.5289640103269625, -0.8486442574947509], 'a4': [-0.4403941515576343, 0.8978045395707417], 'a5': [-0.25065253225872053, -0.9680771188662043], 'a6': [1.0, 0.0], 'a7': [0.9189578116202306, -0.39435585511331855], 'a8': [-0.9948693233918952, 0.10116832198743218], 'a9': [-0.4403941515576343, -0.8978045395707417], 'algebraic': True, 'analytic_conductor': 1.4442779281284783, 'analytic_normalization': 0, 'bad_lfactors': [[311, [1]]], 'bad_primes': [311], 'central_character': '311.121', 'coeff_info': ['x^31 - 1', '0.979529941252494 + 0.201298520088660*I', '\\\\zeta_{31}'], 'conductor': 311, 'conductor_radical': 311, 'conjugate': 'dirichlet_L_311.18', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^26', 'a^10', 'a^22', 'a^0', 'a^29', 'a^15', 'a^21', 'a^27', 'a^18', 'a^5', 'a^21', 'a^3', 'a^17', 'a^20', 'a^27', 'a^26', 'a^9', 'a^1', 'a^24', 'a^23', 'a^15', 'a^10', 'a^13', 'a^26', 'a^16', 'a^8', 'a^28', 'a^22', 'a^4', 'a^25', 'a^13', 'a^1', 'a^20', 'a^0', 'a^2', 'a^14', 'a^16', 'a^6', 'a^12', 'a^29', 'a^29', 'a^28', 'a^12', 'a^20', 'a^28', 'a^15', 'a^27', 'a^18', 'a^22', 'a^0', 'a^29', 'a^21', 'a^9', 'a^13', 'a^4', 'a^2', 'a^29', 'a^27', 'a^9', 'a^9', 'a^19', 'a^30', 'a^12', 'a^18', 'a^19', 'a^6', 'a^10', 'a^25', 'a^6', 'a^5', 'a^30', 'a^7', 'a^8', 'a^19', 'a^16', 'a^21', 'a^12', 'a^11', 'a^11', 'a^17', 'a^14', 'a^3', 'a^18', 'a^3', 'a^23', 'a^2', 'a^2', 'a^17', 'a^19', 'a^25', 'a^30', 'a^2', 'a^0', 'a^20', 'a^6', 'a^1', 'a^8', 'a^23'], 'euler_factors': [[1, 'a^5'], [1, 'a^26'], [1, 'a^22'], [1, 'a^29'], [1, 'a^18'], [1, 'a^21'], [1, 'a^27'], [1, 'a^9'], [1, 'a^15'], [1, 'a^28'], [1, 'a^4'], [1, 'a^2'], [1, 'a^12'], [1, 'a^29'], [1, 'a^28'], [1, 'a^29'], [1, 'a^29'], [1, 'a^9'], [1, 'a^19'], [1, 'a^6'], [1, 'a^30'], [1, 'a^12'], [1, 'a^14'], [1, 'a^2'], [1, 'a^6'], [1, 'a^20']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-311-311.121-r0-0-0', 'leading_term': '1.48551198077183893610531629042-0.715859493665222157387259083918*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/311/121', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.6489998968123982, 1.347082591150171, 0.7863451245429196, -0.34008494932024463, -1.7757794608903483, -2.92531337562903, -3.1814060491046736, -2.277049555685734, -0.5070773100402052, 1.3403886172274166, 2.3651878993904214, 2.067722479269736, 0.6805751074418928, -0.9307343407930264, -1.790148397856146, -1.4466536095131324, -0.28726211100844057, 0.7270402758351936, 0.7548737499821868, -0.2923742132774215, -1.66831335124206, -2.3591095320997617, -1.8828123932130054, -0.6744360237570535, 0.29665723685549317, 0.3995584369692843, -0.0373043963513489, 0.03653045115370238, 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'191.90749578268302528330530658867', '192.66888163921653309101051141051', '193.729862590649092072020730526458', '194.43530061072938777891678205837', '195.02737565839078081782880701826', '195.82511564324913409175054423656', '196.18255010870307487801332851958', '196.61745032189446631740921837856', '197.3843121395026620141339551844', '198.27780903067596728654172011112', '198.60629400713803776776782694207', '199.54115037027940120175600890927'], 'prelabel': '1-311-311.121-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4442779281284783, 'root_angle': -0.2858793763530797, 'root_number': '0.623084223045489472713824431678-0.782154748749759062329853721980*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.142939688177', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(31)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.40830644325469534288755871054-0.165555602346046275458546456751*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.85652749845', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.58056515973', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.87564315873', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.4442779281284783, 'bad_primes': [311], 'central_character': '311.121', 'conductor': 311, 'conductor_radical': 311, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/311/121'], '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': '1-311-311.121-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': '1-311-311.121-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4442779281284783, 'root_angle': -0.14293968817653985, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.85652749845', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_311.121', 'Lhash_array': ['dirichlet_L_311.121'], 'label': '1-311-311.121-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/311/121'}
Lfunction data - 1-311-311.121-r0-0-0