Formats: - HTML - YAML - JSON - 2026-09-22T05:45:03.920384
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '691072606724542739750539792160', 'a10': [-992.7057677897538, 1719.4168267785255], 'a2': [3.2419831266210335, -0.5716490962248759], 'a3': [0, 0], 'a4': [-230.37763901711176, 83.85060324275277], 'a5': [-387.666922335987, 462.00344742385306], 'a6': [0, 0], 'a7': [-3862.1525072472177, -1405.7085528345706], 'a8': [-1428.7910383163378, 824.9128905876624], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.997667414951316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '81.71', 'coefficient_field': 'CDF', 'conductor': 81, 'conductor_radical': 3, 'conjugate': '462985039681724984222007884368', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.2419831266210335, 0.5716490962248759], [240.56131092119256, -87.55715669137119]], [[1.0, 0], [0, 0]], [[1.0, 0], [387.666922335987, -462.00344742385306], [-67831.31940114466, -384690.52852039377]], [[1.0, 0], [3862.1525072472177, 1405.7085528345706], [4416093.771736728, 3705542.6551085715]], [[1.0, 0], [11423.308992504923, 13613.769531131487], [-37223029.05237238, 211102287.9358213]], [[1.0, 0], [882.8590467743727, -5006.942461256521], [-766536139.0720687, -278996338.1115711]], [[1.0, 0], [23746.870820285047, 13710.262260502841], [3487878720.5, 6041183154.544328]], [[1.0, 0], [-92857.3304680529, -160833.61422588112], [-8491781520.5, 14708197040.280493]], [[1.0, 0], [-88410.20276682898, -242905.03575126716], [-59989695109.68213, 50337331040.971756]], [[1.0, 0], [-234351.4420074766, 41322.48219385328], [470077862834.0719, -171094349859.07288]], [[1.0, 0], [618503.4441610442, -225116.84346574827], [653352439817.6583, -548227791279.77313]], [[1.0, 0], [-779021.964997424, 1349305.6235876821], [-1756239726960.5, -3041896437366.4785]], [[1.0, 0], [3822740.350258322, 674052.2639934698], [7503375315332.232, 2731005271308.713]], [[1.0, 0], [1196755.5552296806, -1004197.1450025858], [2029634678411.5232, -11510630252140.908]], [[1.0, 0], [407155.4983143011, -1118650.537825337], [-18240503830755.055, -15305600036874.33]], [[1.0, 0], [0, 12994358.45269401], [-62259690411361.0, 0]], [[1.0, 0], [-13826817.060106229, 16478158.90552451], [-25496837916028.266, -144599753330910.6]], [[1.0, 0], [-13973073.566360286, -5085782.859367033], [146856321826837.75, 123227085480951.48]], [[1.0, 0], [1061765.3706678585, -6021570.643368285], [-381578800139647.2, -138883325277843.8]], [[1.0, 0], [30739509.014430836, 17747463.80423857], [322876765622880.5, 559238962642337.3]], [[1.0, 0], [-6899192.544616763, -11949752.01847664], [-403230045947040.5, 698414926718607.0]], [[1.0, 0], [7762973.439876117, 44026010.13574457], [-1425615953598486.8, 518881772604876.7]], [[1.0, 0], [-45744158.39724704, 8065929.335236345], [2116462390394479.0, -770329312047485.1]], [[1.0, 0], [-3601260.0518485946, 2079188.4603566315], [1968294402851040.5, -3409185909991446.0]], [[1.0, 0], [108572424.40113081, -91103081.27101198], [1360956061249139.0, -7718365367460768.0]], [[1.0, 0], [40702161.23924736, -111828268.92783329], [-8295163620405137.0, -6960468734437142.0]], [[1.0, 0], [27760812.759507455, 23294087.747684233], [2199723161559485.8, 12475249974344302]], [[1.0, 0], [0, 186648853.82305157], [-17181861798319200, 0]], [[1.0, 0], [-105605805.81226866, 0], [19925626416901920, 0]], [[1.0, 0], [187684587.66526577, -223673781.62464345], [-4616339895274354.0, -26180564521245364]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 22968459, 'index': 8, 'label': '2-3e4-27.14-c8-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/81/9/f/a/71/13', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [0.6024890917968021, 0.621877052272456, 0.54281565815325, 0.36986026674344086, 0.11180685158153628, -0.21863019614034349, -0.6052981197794844, -1.0292337475747555, -1.4694245935554315, -1.9036829560408817, -2.309606954505877, -2.6655962788818686, -2.951884365112294, -3.1515432371605496, -3.251412936189012, -3.2429049088218216, -3.122628564376762, -2.892792992989186, -2.561341997171238, -2.14179037524694, -1.6527428044483528, -1.117093403743072, -0.5609234794391315, -0.01213609666039377, 0.5011123187697227, 0.9521027261903323, 1.3172684174047615, 1.577823199585443, 1.7211854607511563, 1.742082284994473, 1.6432282600090755, 1.4354935036451246, 1.137504447773662, 0.7746579435615139, 0.37757231289265303, -0.01995473784880705, -0.38336540377544803, -0.6799805588578516, -0.8816669604523912, -0.9673208578045037, -0.924950815147473, -0.7531555865970553, -0.4618251286152443, -0.0719436698699425, 0.38555929637116726, 0.8718854991481237, 1.3432627350235882, 1.7544659384973793, 2.0626988872233354, 2.231515122140006, 2.2344257459587538, 2.0578414109504193, 1.7030292491723953, 1.186832910545507, 0.5410019860588766, -0.18990088160485705, -0.9519109601615221, -1.686148896942317, -2.334018410928038, -2.8426499329762214, -3.170067383913908, -3.289545982850104, -3.1926743614733173, -2.890734354313413, -2.414160679610008, -1.8100284115721563, -1.1377215460577759, -0.4631401502542557, 0.14801615347164898, 0.637216354753291, 0.9595763838517174, 1.0891144435985565, 1.02214148440643, 0.7783151828744677, 0.39912130746587066, -0.05617526713105084, -0.5167757743547152, -0.9081828958096803, -1.1608016719299417, -1.2183463453531165, -1.0450638220066029, -0.6308710104260561, 0.006296496111635451, 0.821329969386327, 1.746029333991687, 2.6960736893021804, 3.5801644448025876, 4.31032470319878, 4.812148710860951, 5.0337465853050105, 4.952236764550097, 4.576897100825627, 3.948470604282159, 3.1345906881552104, 2.2217867484189235, 1.3049902456374345, 0.47582131140001177, -0.1888570226823203, -0.6366114337904272, -0.8460147391281474, -0.8291721834402656, -0.6297582355118568, -0.3167212660154993, 0.025586220502868833, 0.3095736993245782, 0.4572332990987098, 0.41182522835089225, 0.14673722673973585, -0.3298287614231162, -0.975138368651592, -1.7172820779151128, -2.4649823057213194, -3.1205526673682726, -3.594202085713125, -3.8176117335438247, -3.754743900112591, -3.4081779611874814, -2.8198736579899775, -2.0660574221974555, -1.2468022359315691, -0.4716964829454017, 0.15635551849815257, 0.5567962655653025, 0.6841272894842344, 0.5356192731058962, 0.15266251815071233, -0.38466684609602536, -0.9692124076960047, -1.4829186117105684, -1.8152179364445964, -1.8808224426713178, -1.6341103115290783, -1.0777340685224577, -0.26390648719127024, 0.7120732790640036, 1.7252728077122954, 2.639640100299294, 3.3287877562064603, 3.6958044600476625, 3.688905943561462, 3.310311948130542, 2.6167549414922124, 1.7113398131394368, 0.7278759691570279, -0.1899344568783774, -0.9111606778391285, -1.338478310262248, -1.423705813492332, -1.1753709568507145, -0.6569061704873578, 0.024385194835981765, 0.7358864772153267, 1.3427264578786071, 1.7314780431609473, 1.8304355027188288, 1.6229018683479215, 1.1510408122843345, 0.5094246452758373, -0.17081853774800482, -0.7446935511812354, -1.0790396147739718, -1.0768008124021091, -0.6955664213190598, 0.04301094219173946, 1.0547811041917197, 2.205608925062365, 3.3328579166408456, 4.272236694769814, 4.8853753499934465, 5.08328230552856, 4.841483697028842, 4.204070163553957, 3.275829830741818, 2.203786648999967, 1.151401663441415, 0.2700694597254788, -0.3269140282459403, -0.5831423407863121, -0.5071791119857232, -0.16843118467157897, 0.3183981438729548, 0.8173154486027931, 1.1988979643931057, 1.366612605748394, 1.2764305515907073, 0.945811476924314, 0.4501557018705583, -0.09274010556655896, -0.5473025497141373, -0.7890898482411438, -0.7322366830236045, -0.3498319936484826, 0.3171094551937265, 1.1642592714671844, 2.0416926058034877, 2.7815933332258185, 3.2307353799029457, 3.2814100608670462, 2.8945800241690973, 2.110395189480272, 1.0435719310216351, -0.1359287996432985, -1.2335557092134053, -2.0664406377969047, -2.4983089903707976, -2.4661358219237024, -1.993126670788327, -1.1851935781882297, -0.21131670131873592, 0.7286027432433644, 1.4422313605764652, 1.782094526327536, 1.6742509118360263, 1.1325564199931952, 0.25555241950402785, -0.7935057291183875, -1.81953072455323, -2.6347683527861, -3.0962613056950823, -3.133899224821235, -2.7632171781898536, -2.080223006965668, -1.2392680681643962, -0.4185552047362414, 0.21945298314694145, 0.5642836835513777, 0.582509513769081, 0.3260279339173292, -0.07851727680510037, -0.4572421899829584, -0.6278477387768513, -0.4416023037540604, 0.18053635374379248, 1.2256205566577343, 2.5854092658833245, 4.073286771746258, 5.45833702753437, 6.509790019672617, 7.0427239873355925, 6.955486297263095, 6.250909885221084, 5.036736098680442, 3.5050141203689056, 1.894702518720735, 0.4452843375061007, -0.6488669446917045, -1.2738055123324332, -1.4137036988502456, -1.1474611737355678, -0.62540338931836, -0.03161073451235739, 0.45943887636474645, 0.7220329227333776, 0.7053418046617076, 0.4406846425599864, 0.02852202530134111, -0.39150913499401063], 'positive_zeros': ['0.54516016211416707587357095626669', '2.87783425602871505835491470900235', '4.36855517334169756368100582257066', '5.39567016504951829839695249628216', '6.84341012426552291103208241176482', '8.467781296136203684396413320772633', '9.360054145296662078185785322179846', '10.24892910900828900891821714749151', '12.08543061010236590318891675108764', '12.86529582147472922632565935154888'], 'prelabel': '2-3e4-27.14-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.744359617481423, 'root_angle': 0.033271879495158606, 'root_number': '0.9782278078932305 + 0.20753398725125713*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.033271879495158606', 'prec': 57}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.54516016211416707587357095626669', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.87783425602871505835491470900235', 'prec': 110}, 'z3': {'__RealLiteral__': 0, 'data': '4.36855517334169756368100582257066', 'prec': 110}}