-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1203417067667613926832797369600', 'a10': [-0.6705284454417363, 2.4521127877463704], 'a2': [1.4011504128017025, 0.1917746612710317], 'a3': [0.0, 0.0], 'a4': [1.9264449585887622, 0.5374102916096254], 'a5': [-0.2346290544287736, 1.7821846051421701], 'a6': [0.0, 0.0], 'a7': [-0.9270518227024962, 3.45980450357505], 'a8': [2.5961774723294004, 1.1224359813233564], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.899074734638629, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.4011504128017025, -0.1917746612710317]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '864.611', 'coefficient_field': 'CDF', 'conductor': 864, 'conductor_radical': 6, 'conjugate': '2778816142848379327822030997984', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4011504128017025, -0.1917746612710317]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.2346290544287736, -1.7821846051421701], [-4.8296291314453415, -1.294095225512604]], [[1.0, 0], [0.9270518227024962, -3.45980450357505], [-6.06217782649107, -3.5]], [[1.0, 0], [0.29612721714481244, 0.22722640559032045], [2.8470094961277286, 10.62518408917975]], [[1.0, 0], [1.8239759575403391, 2.377051747318904], [-3.36464758633277, 12.557035741757888]], [[1.0, 0], [1.7449025377384102, 0], [17.0, 0]], [[1.0, 0], [-5.204457440062082, -2.1557568564672738], [13.435028842544403, 13.435028842544403]], [[1.0, 0], [6.630806291881461, -1.7767191910768447], [19.91858428704209, -11.5]], [[1.0, 0], [5.673388316885746, -0.7469157417011605], [28.01184896238298, -7.505752307973102]], [[1.0, 0], [-2.7137025960345516, -1.5667569243211348], [15.5, 26.846787517317598]], [[1.0, 0], [-0.8451014641624662, -2.040255416362386], [-26.16295090390226, 26.16295090390226]], [[1.0, 0], [0.24742105716105733, 0.9233879561874693], [-35.50704155516198, 20.5]], [[1.0, 0], [-7.076746043042872, 9.222595000447075], [-11.129218939408393, -41.53481053042994]], [[1.0, 0], [-6.777793737076975, 3.913161038613151], [23.5, -40.703193977868615]], [[1.0, 0], [0.09245914497150713, 0.22321612175563266], [-37.476659402887016, 37.476659402887016]], [[1.0, 0], [-11.548196782400144, -1.5203489490337074], [56.98962375105503, 15.270323661048725]], [[1.0, 0], [0.2736383357504343, 2.0784895141756268], [-58.92147540363317, 15.787961751253766]], [[1.0, 0], [-9.30320926305802, -12.124178360468548], [-17.34087602186889, 64.71703036136758]], [[1.0, 0], [-6.981632424841108, 6.981632424841108], [0, -71.0]], [[1.0, 0], [-3.0782044707610647, -3.0782044707610647], [0, 73.0]], [[1.0, 0], [6.741662591820386, 11.67690213651939], [-39.5, 68.41600689897065]], [[1.0, 0], [3.5952591957571673, -0.47332485259548324], [80.17184358199266, -21.481980743509222]], [[1.0, 0], [8.067560941695726, 8.067560941695726], [0, 89.0]], [[1.0, 0], [-3.420134117104404, -5.923846059524553], [-48.5, 84.00446416709055]], [[1.0, 0], [5.793944297616125, 4.445849826407654], [26.140723555354597, 97.55850845519589]], [[1.0, 0], [17.207204102655112, -4.610656443303938], [89.20061658979718, -51.5]], [[1.0, 0], [-10.244244940666867, 4.243305190696178], [75.66042558696059, -75.66042558696059]], [[1.0, 0], [-4.357213644223006, 10.51924427404028], [-77.07463914933368, -77.07463914933368]], [[1.0, 0], [-1.1875124669729729, 2.056831927418647], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-864-288.131-c1-0-17', '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/864/2/bn/a/611/44', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.6607116985653567, 2.39088841109919, 2.111502259360297, 1.812164357873078, 1.482811386439256, 1.1164743913548372, 0.7114184746153687, 0.2724774412507395, -0.18843185129062642, -0.652587870817236, -1.0955147347902492, -1.488779499900731, -1.8024710118521898, -2.00822012642497, -2.082527207347636, -2.010069913822971, -1.786593355657526, -1.4209550298451008, -0.9359238950775529, -0.3674252696947162, 0.2379193044065959, 0.8268965912957759, 1.3451467948957876, 1.7434030699521277, 1.983776403259946, 2.0452139590774645, 1.9272507367373282, 1.651302917002073, 1.2590195970645899, 0.8075973317249816, 0.3624242687166145, -0.012108020177616795, -0.2623854148770252, -0.354453489845655, -0.2804745465868675, -0.06145312756944463, 0.2546012684211522, 0.5992228807141188, 0.8941005280261018, 1.0643160766317925, 1.0521481317946673, 0.8290448845961146, 0.40343212027091285, -0.17747856827135192, -0.8328164841434063, -1.459865984412247, -1.9510441162584848, -2.2133799806870873, -2.187071754137193, -1.8595047038986248, -1.2715978084663395, -0.514494410934299, 0.28372353478037377, 0.9797065413241415, 1.4414956420802525, 1.5754391216386878, 1.3481075350005625, 0.7984079393637945, 0.03656788158498164, -0.7710526819076553, -1.429637489844947, -1.7517414711149528, -1.5949042905739497, -0.8937577810708267, 0.3201933496610174, 1.9160351977910293, 3.6800005691653985, 5.3492636090029215, 6.657504565732743, 7.384010339461677, 7.396807723075335, 6.68093599845842, 5.345462784358782, 3.606834734488162, 1.7508836900475648, 0.08031507085584673, -1.142193467348615, -1.743841718623402, -1.6741325707277708, -1.012843153226895, 0.04849636461261174, 1.2480376534988056, 2.3093655181811705, 2.9996957686014696, 3.177928186721212, 2.8220481635235233, 2.0298799634464912, 0.9931650664595734, -0.04897392540338018, -0.8663431692659904, -1.2906113970931412, -1.2524912306162888, -0.79453400273012, -0.05677409959219833, 0.7609347416567492, 1.4503223709577013, 1.8468743856304917, 1.8696293879301915, 1.5386185188309487, 0.9657180362546574, 0.3215969570253743, -0.21226794161591075, -0.49353728340971936, -0.45734624785693045, -0.13251598765656536, 0.36891206111486874, 0.886032135399195, 1.257795555040955, 1.3723143733530259, 1.2024514036792555, 0.8169099592343168, 0.3627322675197341, 0.023232280874021242, -0.03731772221458095, 0.27342893816740627, 0.9411535645236132, 1.839496391926862, 2.757305644390609, 3.452465416118686, 3.718217634964662, 3.4435110489760605, 2.649646434297459, 1.4914037572687284, 0.2204984277364498, -0.8799815752332523, -1.5726374093122089, -1.7325565248527288, -1.3839579353461138, -0.6945868703261545, 0.07248387065236847, 0.6374811141634951, 0.79118350113278, 0.46521256111639825, -0.23670596945506348, -1.0583734695588085, -1.6592161203341764, -1.7139969951314071, -1.0169351723334086, 0.44001237684323824, 2.439381911261388, 4.572603626156323, 6.3311415258210415, 7.232519643188489, 6.948386686280425, 5.39960589959904, 2.791009963906103, -0.42588251029841956, -3.654429234257925, -6.293116352057313, -7.877849915204958, -8.18865587069554, -7.2927275283446225, -5.513291527486557, -3.3343038791427366, -1.2686320737685288, 0.2729942568964589, 1.0761745605101265, 1.1557049615965598, 0.721213285424767, 0.08955869576885284, -0.4267400096258388, -0.619724003370181, -0.4444218399443951, -0.019222367921770414, 0.4291306103449278, 0.6555566956209147, 0.4904630163673754, -0.09442237899355721, -0.9702253547996271, -1.8902090327970658, -2.570762958762483, -2.7866929303622263, -2.4485392986832832, -1.6355670474599906, -0.5728529499983759, 0.4403416321726198, 1.1272445783585907, 1.3230001471896538, 1.0267776605935712, 0.3989266303119946, -0.2959101098220423, -0.7804038476519249, -0.8595744699820091, -0.4866260285385745, 0.22311776731268507, 1.03495603278153, 1.6791863331684638, 1.9472405961949135, 1.7651862788871977, 1.217811747923625, 0.5138719586083614, -0.09573549393757938, -0.4175171475996532, -0.39577062322368917, -0.14251687768642757, 0.09708491598389768, 0.034726182770731064, -0.545817795333736, -1.6895990534943757, -3.225807045595805, -4.798583467589248, -5.968641493773405, -6.355235263821063, -5.7714710526383906, -4.304974818862316, -2.311758410617261, -0.31915026118301026, 1.1352348498862217, 1.6779605933751194, 1.229680205633285, 0.04449323206378412, -1.359022331204862, -2.357337219573893, -2.4232615951602066, -1.3043951070112652, 0.8805600769791978, 3.6616145362197723, 6.350089860944369, 8.243562165683043, 8.83835164564921, 7.981549051736418, 5.913892559083659, 3.1904027344877877, 0.5056777904035021, -1.5183258275753515, -2.5127992080447115, -2.4535541879275735, -1.6371553180956708, -0.5547310815937455, 0.2894724359392254, 0.5506477989819433, 0.14846489556935316, -0.7282574548950201, -1.7135289212203944, -2.4149169588087913, -2.565489604349641, -2.121091232767193, -1.268998566157776, -0.34781633116373645, 0.28845644844982005, 0.4091271922197962, -0.004698616652280439, -0.7548204422510981, -1.5046776283930705, -1.9108974006902788, -1.7566068133282091, -1.0352946939150154, 0.04655600859428968, 1.1483549910586957, 1.9246990393504602, 2.1547504315778645, 1.821752169102976, 1.1125241463456554, 0.3382708503671867, -0.19109764069519863, -0.2888059857338363, 0.03928619172879536], 'positive_zeros': ['0.949328677358689540300431993384334', '2.45109371825368122303505603584235', '3.87030438738669361630986250735361', '4.40170737206044434832512896082669', '5.33931892892000261444382662305823', '6.45490319577320879114368982613033', '7.25559523162208741355568278405661', '7.971165786251156931126468765179108', '9.381821546870661852513143521529588', '9.994837854026850329742298055832376'], 'prelabel': '2-864-288.131-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6266089801564734, 'root_angle': -0.49965185491083985, 'root_number': '0.0010937298364273502 - 0.9999994018773436*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.249825927455', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.949328677358689540300431993384', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.45109371825368122303505603584', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87030438738669361630986250735', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.899074734638629, 'bad_primes': [2, 3], 'central_character': '288.131', 'conductor': 864, 'conductor_radical': 6, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/864/2/bn/a/611/44'], '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': '2-864-288.131-c1-0-17', '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': '2-864-288.131-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6266089801564734, 'root_angle': -0.24982592745541993, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.949328677358689540300431993384', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1203417067667613926832797369600', 'Lhash_array': ['1203417067667613926832797369600'], 'label': '2-864-288.131-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/864/2/bn/a/611/44'}