-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '926887545996604203718969817554', 'a10': [5.029975905552078, 0.0], 'a2': [0.0, -2.7210864666445014], 'a3': [1.0, 0.0], 'a4': [-5.4043115589558575, 0.0], 'a5': [0.0, 1.848517482707845], 'a6': [0.0, -2.7210864666445014], 'a7': [0.0, 5.017151007498971], 'a8': [0.0, 9.263426111316228], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.760953935202308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [157, [[1.0, 0], [-11.525620043939568, -4.915290693615026]]]], 'bad_primes': [3, 157], 'central_character': '471.313', 'coefficient_field': 'CDF', 'conductor': 471, 'conductor_radical': 471, 'conjugate': '2477852907020542754528108805683', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.7210864666445014], [-2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, -1.848517482707845], [-5.0, 0]], [[1.0, 0], [0, -5.017151007498971], [-7.0, 0]], [[1.0, 0], [1.3806897277207877, 0], [11.0, 0]], [[1.0, 0], [1.0308646938115027, 0], [13.0, 0]], [[1.0, 0], [-5.758500084590937, 0], [17.0, 0]], [[1.0, 0], [5.929928779182099, 0], [19.0, 0]], [[1.0, 0], [0, -2.891161496474575], [-23.0, 0]], [[1.0, 0], [0, -1.6309866217117208], [-29.0, 0]], [[1.0, 0], [7.310618506902887, 0], [31.0, 0]], [[1.0, 0], [-6.341483200714389, 0], [37.0, 0]], [[1.0, 0], [0, -6.984182784586817], [-41.0, 0]], [[1.0, 0], [0, 1.292054225124156], [-43.0, 0]], [[1.0, 0], [-6.080987727132281, 0], [47.0, 0]], [[1.0, 0], [0, -5.57361426508266], [-53.0, 0]], [[1.0, 0], [0, 3.4180437361485523], [-59.0, 0]], [[1.0, 0], [0, 10.684104991213946], [-61.0, 0]], [[1.0, 0], [-12.189312845632502, 0], [67.0, 0]], [[1.0, 0], [3.1933036236148453, 0], [71.0, 0]], [[1.0, 0], [0, -5.10378595151767], [-73.0, 0]], [[1.0, 0], [0, 7.115624116380474], [-79.0, 0]], [[1.0, 0], [0, 12.998589760140987], [-83.0, 0]], [[1.0, 0], [2.522581895281302, 0], [89.0, 0]], [[1.0, 0], [0, 13.931577855777691], [-97.0, 0]], [[1.0, 0], [-19.301165266576287, 0], [101.0, 0]], [[1.0, 0], [0, -18.706568841349085], [-103.0, 0]], [[1.0, 0], [0, 0.7885834833090501], [-107.0, 0]], [[1.0, 0], [-9.661091472405094, 0], [109.0, 0]], [[1.0, 0], [-6.319785287292554, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-471-157.156-c1-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/471/2/b/b/313/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2104218286849864, 1.1022649137799754, 0.9689575335590569, 0.7995437196473837, 0.580870196032335, 0.29900152426170107, -0.059281892914339246, -0.5050077541959997, -1.0455911440355843, -1.6834918398654017, -2.4150026923225916, -3.22926370894023, -4.107628822144924, -5.0235255309889535, -5.942937922932953, -6.825610290094371, -7.627012932576102, -8.3010371714117, -8.803298932315204, -9.09483798790507, -9.145913858865702, -8.939531767441784, -8.474295381110105, -7.766188330227644, -6.848941172100495, -5.7727469235871895, -4.6012421567097554, -3.406860212072776, -2.264869427637046, -1.2466076939225423, -0.41258714246469236, 0.1937583804883092, 0.5508985102617618, 0.6619093406524141, 0.5545526816594004, 0.27851457587825773, -0.10006636669366786, -0.5062810436960734, -0.8655023773232079, -1.1127104305513318, -1.2008646944176753, -1.1071350536195836, -0.8360174482630957, -0.41873914039133847, 0.09113912657948883, 0.6254565117565168, 1.1115179503825954, 1.48306692420267, 1.6905094286355444, 1.708751959667735, 1.5413039053654602, 1.219828083404093, 0.7990342672210676, 0.3475932461661713, -0.0635265310606447, -0.3733642728509846, -0.5417486430206383, -0.5565327596375667, -0.435781302430684, -0.22424920632000306, 0.015476909740483021, 0.21575697390027057, 0.3183138823891655, 0.28750841054406717, 0.11969219412123498, -0.15359543815694915, -0.4697798338161233, -0.746564081012286, -0.8987306663290895, -0.8574585072261509, -0.58834295939718, -0.10414737675625807, 0.5310575307540065, 1.208334976629525, 1.7909425787371875, 2.1398917619415183, 2.1439052700757735, 1.748285775142533, 0.9767586612192212, -0.058970484828441465, -1.1654125765247967, -2.090049212887585, -2.5583437446606205, -2.319733803904272, -1.1950805267134748, 0.8829661257220204, 3.8446996369783597, 7.4791006706371315, 11.45311258631496, 15.35283987498865, 18.74094276461317, 21.221193976488863, 22.499360773878863, 22.429717153139432, 21.038657150145664, 18.52075107800941, 15.207483999336246, 11.513922033265784, 7.872685724103101, 4.667025272702677, 2.1749626895674083, 0.5343057306592146, -0.2657593951248083, -0.36601949443452586, 0.0036463557074846256, 0.5782826086124974, 1.1135629858168063, 1.4318169827869138, 1.4494868689348985, 1.18145940690943, 0.7229440852037486, 0.21452136791101312, -0.2004529423501847, -0.41552870639497724, -0.38848504836837044, -0.15017490821084314, 0.20651055592083373, 0.5539838062976995, 0.7660190202382344, 0.7528669132353204, 0.4861587945127162, 0.007091737794417092, -0.5841787751052662, -1.1550313230717577, -1.575608741147819, -1.7532600862651362, -1.656809797968572, -1.3239423253631786, -0.8495356564715377, -0.3580160382091204, 0.032665179613028096, 0.24527590225476376, 0.26580561025684524, 0.14726363642954887, -0.007088250868638393, -0.07705230322029621, 0.033707796252600446, 0.3612166786522351, 0.8604666988323144, 1.4080783540615351, 1.829804125953372, 1.9472566671240488, 1.6321879336784282, 0.8533882055187755, -0.29806470378610245, -1.614773086139989, -2.8120079232849924, -3.5925923829756017, -3.7228089426106634, -3.1001005833757658, -1.7938080567799166, -0.045726353576177346, 1.773236150565528, 3.242804237678057, 3.99194184064833, 3.792612171113974, 2.624603277977374, 0.693185674437183, -1.6076984172183806, -3.780572406050972, -5.339164769307293, -5.925619382386985, -5.401196125391059, -3.886959687892139, -1.7426446564540792, 0.5130005164953723, 2.3223355001601225, 3.220789895542266, 2.948491962123397, 1.5139507674269501, -0.8061713958510658, -3.5313142343450163, -6.089428830799717, -7.949675345065861, -8.742686270175172, -8.339224854755424, -6.869079211609466, -4.677564877977757, -2.232922555040224, -0.00997269764871933, 1.619525458689618, 2.462483831085545, 2.5290247657509966, 2.003368011986034, 1.1730177057101288, 0.33878026742232953, -0.2680588641332396, -0.5388866947828257, -0.4987808771513153, -0.27607299394833273, -0.04339192201000239, 0.04911234595088703, -0.0734357208826733, -0.3879497262726843, -0.786450163799294, -1.1186627145079568, -1.2484355744383935, -1.1041511757858482, -0.7057992190441935, -0.15958158973307013, 0.3779036405942868, 0.7534118491689009, 0.8700282428803748, 0.7207836084349467, 0.39081826716602225, 0.026781258065514974, -0.21636850566286017, -0.23272418243911688, -0.006412178794931229, 0.37934070718360186, 0.7698839840124424, 0.9954323624508064, 0.93699358138981, 0.5781308249657479, 0.02199926040038602, -0.5361476616253474, -0.875677315977171, -0.8366141135947522, -0.39602954502938886, 0.2941273693512094, 0.9267337394989339, 1.1183207963900654, 0.5288855702319982, -1.0112551998790857, -3.4078837672659175, -6.276947749399107, -9.003231624219568, -10.876239274393646, -11.271665032186064, -9.830231295266126, -6.582330932467333, -1.9787239313897942, 3.1881382529453086, 7.957336818007184, 11.424957266587082, 12.963048404968808, 12.373126584197092, 9.931950030170363, 6.316369393958578, 2.4273242662608845, -0.8391249834005757, -2.8116032609108723, -3.195454358924298, -2.118569183918527, -0.06336008073005882, 2.290560016978602, 4.264317333574453, 5.36056791247565, 5.37756677226539, 4.429380733018237, 2.87446944050819, 1.1819073846671195, -0.2189543151052524, -1.058209699547252, -1.280764090488912, -1.0268146739964321, -0.5519120113960604], 'positive_zeros': ['0.73118534857296340902690699436951', '3.82922255242176687414533562418320', '4.46880158761889284247348270846196', '5.47857416870875336280350898778483', '6.72897219732108392575212774135988', '7.49167082929471118075855234659765', '8.059293895552010644459484478011113', '8.897149268091588213565820781793018', '9.868342081837263966722702241304154', '10.57850828217246152298466819849573'], 'prelabel': '2-471-157.156-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9393179046258269, 'root_angle': 0.12831457282306227, 'root_number': '0.9198446192425308 + 0.39228290359199136*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0641572864115', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73118534857296340902690699437', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.82922255242176687414533562418', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.46880158761889284247348270846', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.760953935202308, 'bad_primes': [3, 157], 'central_character': '157.156', 'conductor': 471, 'conductor_radical': 471, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/471/2/b/b/313/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-471-157.156-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-471-157.156-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9393179046258269, 'root_angle': 0.06415728641153114, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.73118534857296340902690699437', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '926887545996604203718969817554', 'Lhash_array': ['926887545996604203718969817554'], 'label': '2-471-157.156-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/471/2/b/b/313/1'}