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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.1094', 'a10': [-0.7619494932706709, 0.647636448715302], 'a2': [-0.14231483827328514, 0.9898214418809327], 'a3': [-0.10452846326765347, 0.9945218953682733], 'a4': [-0.9594929736144974, -0.28173255684142967], 'a5': [0.749481162389254, 0.6620256696108185], 'a6': [-0.9695231451106913, -0.2449997369277637], 'a7': [-0.8888354486549235, -0.4582265217274104], 'a8': [0.41541501300188644, -0.9096319953545183], 'a9': [-0.9781476007338057, -0.20791169081775934], 'algebraic': True, 'analytic_conductor': 17.41957076659139, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.1094', 'coeff_info': ['x^165 - 1', '0.999275047800474 + 0.0380707084693900*I', '\\\\zeta_{165}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.3727', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^45', 'a^44', 'a^90', 'a^19', 'a^89', 'a^95', 'a^135', 'a^88', 'a^64', 0, 'a^134', 'a^112', 'a^140', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-3751-3751.1094-r0-0-0', 'leading_term': '-0.319980742910877540904917600216+0.332278883615654273730390049781*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/3751/1094', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.4612991787665165, -1.6072401633843336, -2.6691490471674983, -2.0325879110402134, 1.3961984162430388, 6.320329813917724, 9.446215835129406, 8.297258874630922, 3.854195125065422, -0.05257621920017525, -0.47254258989440745, 1.7054970776411777, 3.036729279322236, 1.6718091745565213, -0.617233243179258, -1.0063606258629136, 0.6398442852074747, 1.8274812290499727, 1.0669907584452023, -0.1416456786054106, 0.18430136603232167, 1.306804919079013, 0.8562743799044011, -1.2375994536277821, -2.0915516054151433, 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'193.598283175073571986058675365558', '194.162756742464267584202025261829', '194.66482409073377510338460793427', '194.98856487042738649046005396263', '195.87267700292314362009159404474', '196.51429918422749086770410527899', '197.20265829920869183110330084470', '197.344704652464178252745688996143', '197.69410103065904554494627531672', '198.40274570061075184447903405111', '198.95594452050662920890355747444', '199.292709458184002394942463102189', '199.86967324739176760652219982789'], 'prelabel': '1-3751-3751.1094-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.2560009171610561, 'root_number': '-0.0376959412676296084303755172275-0.999289255427049720397280691660*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(165)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.483674819137094845022301937098+0.573283542420531603501756809397*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.14857925941', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.80570105835', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.21121388003', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.1094', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/1094'], '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': '1-3751-3751.1094-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': '1-3751-3751.1094-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.2560009171610561, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14857925941', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.1094', 'Lhash_array': ['dirichlet_L_3751.1094'], 'factors': ['1-3751-3751.1094-r0-0-0'], 'label': '1-3751-3751.1094-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/1094'}
Lfunction data - 1-3751-3751.1094-r0-0-0