-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '232448975813400891541947793309,716952824930272380745834248283,1722695167113842173813100364217,2431533205312128885005054402499', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67153.79168657961, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 0, 2, 0, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '2016.1', 'coefficient_field': '1.1.1.1', 'conductor': 16518176833536, 'conductor_radical': 42, 'degree': 8, 'euler_factors': [[1], [1], [1, 0, -4, 0, 54, 0, -100, 0, 625], [1, 0, 2, 0, 1], [1, 0, 40, 0, 642, 0, 4840, 0, 14641], [1, 8, 76, 344, 1654, 4472, 12844, 17576, 28561], [1, 0, -68, 0, 1734, 0, -19652, 0, 83521], [1, 0, -76, 0, 2166, 0, -27436, 0, 130321], [1, 0, -8, 0, 1074, 0, -4232, 0, 279841], [1, 0, 80, 0, 3282, 0, 67280, 0, 707281], [1, 0, -92, 0, 4038, 0, -88412, 0, 923521], [1, 0, 148, 0, 8214, 0, 202612, 0, 1874161], [1, 0, -148, 0, 8838, 0, -248788, 0, 2825761], [1, 0, -140, 0, 8598, 0, -258860, 0, 3418801], [1, 0, 172, 0, 11814, 0, 379948, 0, 4879681], [1, 0, -176, 0, 13362, 0, -494384, 0, 7890481], [1, 0, 220, 0, 19062, 0, 765820, 0, 12117361], [1, 56, 1420, 21224, 204214, 1294664, 5283820, 12710936, 13845841], [1, 0, -68, 0, 10134, 0, -305252, 0, 20151121], [1, 0, 184, 0, 18546, 0, 927544, 0, 25411681], [1, 24, 508, 6120, 64806, 446760, 2707132, 9336408, 28398241], [1, 0, 76, 0, 13926, 0, 474316, 0, 38950081], [1, 0, 76, 0, 15222, 0, 523564, 0, 47458321], [1, 0, -212, 0, 27078, 0, -1679252, 0, 62742241], [1, 56, 1564, 27272, 323014, 2645384, 14715676, 51109688, 88529281], [1, 0, -148, 0, 25878, 0, -1509748, 0, 104060401], [1, 0, 100, 0, 23718, 0, 1060900, 0, 112550881], [1, 0, 392, 0, 61314, 0, 4488008, 0, 131079601], [1, -48, 1300, -22608, 280374, -2464272, 15445300, -62161392, 141158161], [1, 0, -352, 0, 56514, 0, -4494688, 0, 163047361]], 'euler_factors_factorization': [[1], [1], [[[1, 0, -2, 0, 25], 2]], [[[1, 0, 1], 2]], [[[1, 0, 20, 0, 121], 2]], [[[1, 2, 13], 4]], [[[1, 0, -17], 4]], [[[1, 0, -19], 4]], [[[1, 0, -4, 0, 529], 2]], [[[1, 0, 40, 0, 841], 2]], [[[1, 0, -46, 0, 961], 2]], [[[1, 0, 37], 4]], [[[1, 0, -74, 0, 1681], 2]], [[[1, 0, -70, 0, 1849], 2]], [[[1, 0, 86, 0, 2209], 2]], [[[1, 0, -88, 0, 2809], 2]], [[[1, 0, 110, 0, 3481], 2]], [[[1, 14, 61], 4]], [[[1, 0, -34, 0, 4489], 2]], [[[1, 0, 92, 0, 5041], 2]], [[[1, 6, 73], 4]], [[[1, 0, 38, 0, 6241], 2]], [[[1, 0, 38, 0, 6889], 2]], [[[1, 0, -106, 0, 7921], 2]], [[[1, 14, 97], 4]], [[[1, 0, -74, 0, 10201], 2]], [[[1, 0, 50, 0, 10609], 2]], [[[1, 0, 196, 0, 11449], 2]], [[[1, -12, 109], 4]], [[[1, 0, -176, 0, 12769], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 3, 'label': '8-2016e4-1.1-c1e4-0-3', 'leading_term': '0.64864258305458766556458715103671204146263209784405961072864776142369488794005863179448972', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2016/2/h/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0146484375', 'prec': 40}, 'plot_values': [0.6486425830545874, 0.64404000484397, 0.6301669569004792, 0.6071747185977073, 0.5752920623077099, 0.5347775599861984, 0.4859524392854165, 0.42922032634750457, 0.36506340844651736, 0.2940615440999695, 0.21686174480429543, 0.13418373248818033, 0.04681789140543267, -0.044375521982078954, -0.1384660332932284, -0.2344547382259673, -0.3312734739379161, -0.4277946180118282, -0.5228343553175753, -0.6151543597148238, -0.7034698968131494, -0.7864595227281075, -0.8627707674413903, -0.9310263139396917, -0.9898388936399092, -1.0378220678989774, -1.0735987700158487, -1.0958164225860192, -1.1031621407606162, -1.0943750437486253, -1.0682649597669822, -1.0237290352182125, -0.9597649418168451, -0.8754860226444524, -0.77014941439732, -0.6431666453259609, -0.4941141772099881, -0.3227514507136229, -0.12905044256932086, 0.08680255147656178, 0.3244007873923437, 0.583102713857339, 0.8620073992008658, 1.1599634107383796, 1.4755718630566155, 1.8071823781048133, 2.1528787545461356, 2.510501260947394, 2.8776631985175625, 3.25176019467432, 3.6299734173433844, 4.009305697628408, 4.38661027202687, 4.758616442494079, 5.1219566363068125, 5.473207948258917, 5.808930515585092, 6.125712611740355, 6.420215374249033, 6.689210384555429, 6.929625199196912, 7.138600722019046, 7.313539488269785, 7.452133229156019, 7.5524115151271705, 7.6127835486463695, 7.63208756537584, 7.609602319403728, 7.545076224886185, 7.4387369110236445, 7.2913391828851255, 7.104153567244301, 6.878940338590627, 6.617938346398038, 6.323903570818661, 6.000048997535885, 5.649968765946398, 5.277612926537136, 4.887304968274761, 4.483617846828006, 4.071283720816917, 3.6551571551804325, 3.240187583005318, 2.8312729936458494, 2.433175017007924, 2.0504724754900097, 1.687496574748154, 1.3482125700863885, 1.0361537040628368, 0.7543686203391341, 0.5053690946892864, 0.29106125579252917, 0.11270960880409772, -0.02908867281184622, -0.13441140592618087, -0.20402264428956032, -0.2393623312912809, -0.2425143503631777, -0.21616443125724646, -0.16355403772591773, -0.08840776834946198, 0.005150138437477897, 0.11268009654666193, 0.229526536093148, 0.35093200265603725, 0.4721466945680652, 0.5885401614116461, 0.6957234941609108, 0.7896609809043745, 0.8667719144852769, 0.9240440125927276, 0.9591214881263261, 0.9703738494890465, 0.9569572744288357, 0.9188822363548733, 0.8570255518919796, 0.7731269591134144, 0.6697805854872247, 0.5504182960951237, 0.41923307411171384, 0.2810940981507124, 0.1414552077369334, 0.006252144576794079, -0.11824650393433409, -0.2255885294429402, -0.3092889274089164, -0.3629863348212881, -0.38062035687793494, -0.35659773585738574, -0.28595003603844216, -0.16448325498197108, 0.011078509951538381, 0.2429696118676804, 0.532282186693209, 0.8788978809007824, 1.2814284307877422, 1.7371841842977527, 2.2421877158406276, 2.79123937552001, 3.3779585494575963, 3.9948690133927403, 4.633542273708154, 5.284802394524123, 5.938847027901142, 6.585432624976765, 7.2140926872568985, 7.8144516888236515, 8.376375640707158, 8.890161460386832, 9.346758252267824, 9.7381277929112, 10.057336791561308, 10.2986253907712, 10.45757896933509, 10.531461126506722, 10.519110932459128, 10.420862173673392, 10.238622273752496, 9.976077903142688, 9.638353137153334, 9.231817328193957, 8.76406407287659, 8.243891444965096, 7.680849167704016, 7.084990812388292, 6.466748799910624, 5.836754834139735, 5.205423763859941, 4.582731854488065, 3.9780240301271794, 3.3998525824299923, 2.8557031890969373, 2.3518554429131595, 1.8932642194564204, 1.4835234022818917, 1.1247932438624764, 0.8177935410251552, 0.5618607263937306, 0.3550604366839652, 0.19429799068138665, 0.07547161640559369, -0.006326958464516435, -0.05659445112098721, -0.08119559274429838, -0.08612563024138996, -0.07727210525877189, -0.06019028032978655, -0.039893005580035105, -0.020664107308370216, -0.005904131850637184, 0.0019875476040035972, 0.0016885315214703357, -0.0070155013393389054, -0.023245342743101614, -0.045090812556258526, -0.0697183801271234, -0.09351811625116942, -0.11228880566671239, -0.12145991478997195, -0.11632690714690437, -0.0923013856020131, -0.045171441609835876, 0.02863844189583228, 0.13183822036097145, 0.26605964594613885, 0.4316722256146372, 0.6276569330081607, 0.8515236402180211, 1.0992666574410763, 1.3653898198316705, 1.6430488773399066, 1.9241718874490705, 2.199630635935471, 2.4595152315490583, 2.693548802273736, 2.891343829529221, 3.0427180288490536, 3.1381171966952293, 3.169154889921216, 3.1288395866182612, 3.0118621797208105, 2.8149488580746924, 2.537305528629772, 2.180622788694895, 1.749127842652227, 1.2496746181941996, 0.6918820260385999, 0.08779892877697351, -0.5483797857007302, -1.2005519705528778, -1.8509777922937314, -2.480900119683881, -3.0710600994797717, -3.602189187222483, -4.055597294260754, -4.413810464212456, -4.661090952029593, -4.783968835802564, -4.771855396435307, -4.6173810057049325, -4.316664369377751, -3.8696002424627474, -3.2801601178740944, -2.556247270456453, -1.709532189548519, -0.7552849144212735, 0.2877805863329801, 1.398129770120123, 2.5520092109834454, 3.7240121008084066, 4.887618207400405, 6.016075521278643, 7.083184348014958, 8.06397884362995, 8.93540620169802, 9.677077719950445, 10.271832592984305, 10.70621934856086, 10.970969527131482, 11.061223402788954, 10.97661427128873, 10.72130049926075, 10.303947875491012, 9.737332027057882, 9.037904824155195, 8.225308437281427, 7.321884705043902, 6.351877141307702, 5.340647357303187, 4.313898534390337, 3.2970458471808177, 2.314371322881966, 1.388222542128469, 0.5384516018462828, -0.21804278050615145, -0.8678491466260958, -1.4014165935666543, -1.8130886073456167, -2.1011800692275, -2.267983443025841, -2.3194582941997557, -2.2648305185133113, -2.1162322908760953, -1.8881696487806088, -1.5968247818122128, -1.2594410692967573, -0.8936877768037718, -0.5169592032036305, -0.14576591106674222, 0.20481449422886147, 0.5217116820751619, 0.7942077791571335, 1.0141785547342002, 1.1763157553847796, 1.2782650904211457, 1.3204443163738577, 1.3058531542458827, 1.2398420234549097, 1.1297840340083543, 0.9845416671765923, 0.8139894234177576, 0.628503473859616, 0.43847512334257965, 0.2537638108057208, 0.08323651947768908, -0.06561589077812778, -0.1869814269152377, -0.2769687242019536, -0.3337156161558882, -0.35738690398611683, -0.350099043250625, -0.315713678679176, -0.2595290598585901, -0.18792366474832728, -0.10795596841713417, -0.02687753821791551, 0.048339469599837134, 0.1114481624368856, 0.15736134798317858, 0.18252813808900273, 0.18521743504395052, 0.1657168432389629, 0.1264415476623565, 0.07190594816846302, 0.008588766518960069, -0.055304789266856974, -0.11018967955470649, -0.14554053839283917, -0.15039061959588335, -0.1138789251189003, -0.025842320471143536, 0.12262273463669474, 0.33863130632839655, 0.6270228737533059, 0.9899564433677505, 1.4266359760078344, 1.9331182999531398, 2.5022575214651717, 3.123896065367363, 3.7850615326503, 4.470255708623973, 5.161988155333559, 5.841600624975778, 6.489729520014179, 7.086923673779966, 7.614566639228409, 8.055851797941378, 8.396131444859284, 8.62350235992246, 8.729497926112414, 8.709695302037572, 8.563598000376672, 8.294763766750163, 7.910729311038428, 7.423045834173455, 6.846598928998237, 6.1989885542579035, 5.49985485574937, 4.7704177696147285, 4.032437656174709, 3.307202197484894, 2.6147834642791237, 1.9734615268496405, 1.3988041890314917, 0.9030282467980715, 0.4946556789303227, 0.1782875435433886, -0.04559342547419355, -0.18050032786040465, -0.23364532615043776, -0.21551409326287535, -0.1392488381223108, -0.01991125631018719, 0.12631281341392006, 0.2830091737394596, 0.4344427059633986, 0.5663947629627148, 0.6669514583185185, 0.7272347063642615, 0.741920200456444, 0.7095805760069503, 0.6328708909257494, 0.5185482030146532, 0.37719426583697546, 0.2227594969025103, 0.07195633273745251, -0.056492580033588084, -0.14279343757649798, -0.16707570152553142, -0.11041342426105563, 0.04416199629149484, 0.3106867494989936, 0.6993859820331108, 1.215949063248441, 1.8610701487095784, 2.6300783357898103, 3.5127696818416863, 4.493602298960763, 5.552290473010583, 6.664218326233369, 7.801165135258082, 8.932419486586596, 10.026228586029406, 11.050625951343758, 11.97463856927101, 12.769530457691644, 13.410460097427025, 13.87706398273233, 14.154127273279464, 14.232192166104758, 14.108683849032001, 13.787589425281935, 13.278847333807443, 12.598108553962074, 11.766960967033416, 10.811362603053412, 9.760196782143758, 8.644444783494045, 7.496596113868994, 6.348580767098905, 5.230438536329031, 4.169554067843406, 3.1898243234471986, 2.3104052903997365, 1.5452131059158105, 0.9027845620884379, 0.3861301839460085, -0.007167988584485638, -0.28441148860269266, -0.45710462593848417, -0.5401434571556724, -0.5507746472081481, -0.5074559031770515, -0.42873293898673404, -0.3321344760732563, -0.23310172548843955, -0.14407663984243183, -0.07377913397345967, -0.026699159796820183, -0.002828766562246812, 0.0023409064517430026, -0.0024399979435187767, -0.004693797078736515, 0.0110492177053187, 0.06232631685110903, 0.16766720544367988, 0.34544597844234143, 0.6127019820119315, 0.9839606998795627, 1.4701596954592635, 2.0778449940864823, 2.808408391042946, 3.6575234179216713, 4.614953742014833, 5.66495123602565, 6.786397369744339, 7.953280103443069, 9.135605327756457, 10.30113262646418, 11.416172158089786, 12.446629121715096, 13.359463416433538, 14.125073732248632, 14.717855067794797, 15.116771754740553, 15.306505050222938, 15.279417021149353, 15.034851270197988, 14.578649777971684, 13.923349491735372, 13.088878589855499, 12.100515384613121, 10.987536251627628, 9.782497614359244, 8.52063288118918, 7.237521879768395, 5.9676025859675095, 4.743170486145778, 3.5934673147776826, 2.5432223072639344, 1.6118843530331852, 0.81319775059569, 0.1549972718294288, -0.3608404296283316, -0.7380598213633791, -0.9854699750860505, -1.1162584056904952, -1.1469602539900616, -1.0963795810974009, -0.9845312870075247, -0.831629313500426, -0.6569267566190665, -0.4777915534901673, -0.30899494450192516, -0.16217192261801966, -0.04542435162232771, 0.03677219227567544, 0.08343863802788791, 0.09677641629933592, 0.0816463912951899, 0.0449058244634785, -0.005342577917824333, -0.06055153110647448, -0.11253533465954883, -0.15419935974921142, -0.18016522506387736, -0.18727377260864983, -0.1748690621070359, -0.14488667196512997, -0.10174837263684308, -0.0520927174921675, -0.00425008750434586, 0.032407371832000306, 0.04819628370560667, 0.03391254947907397, -0.018326753141205535, -0.11432440237428727, -0.25714716687107475, -0.446628043692271, -0.6790485327360024, -0.9470208107504472, -1.239616970743929, -1.5428488186463383, -1.8402199240756625, -2.1134540246087044, -2.3435022660835467, -2.511811073432579, -2.601263229611614, -2.5971941149229134, -2.4885131659993975, -2.2687980736615465, -1.9367106529324896, -1.4963499717741255, -0.9574457428359318, -0.3354184481576985, 0.34936842246059546, 1.0724753140622068, 1.8063621533332954, 2.521500186548045, 3.1880174668505235, 3.7772244646665003, 4.263035962591677, 4.623457071350721, 4.841930799573591, 4.908280941606575, 4.81945830629611, 4.580125093443726, 4.202534021746625, 3.7060871446836896, 3.1166322658102144, 2.46546745481728, 1.7877921448640528, 1.1210306043697011, 0.5029833888148583, -0.02996291058705273, -0.44473356152813015, -0.7133707017262493, -0.8145383987744952, -0.7346693741846917, -0.46885157773609887, -0.02128887087309704, 0.5948135591146472, 1.3576916605537772, 2.237945793729621, 3.199917123584533, 4.203210196464591, 5.2047454346510476, 6.1609825770720255, 7.029689120473368, 7.771842839968804, 8.354298181156881, 8.75114272717587, 8.944300598629502, 8.92465917417454, 8.693577501750516, 8.261685972128204, 7.647988057443594, 6.879632071025504, 5.990812476559278, 5.020023861596368, 4.008275719036816, 2.9976150663666483, 2.0286172568550014, 1.1380542441794195, 0.357491758631256, -0.2882810108645744, -0.7826414167043477, -1.117730232767118, -1.2945122303346062, -1.322711453266684, -1.220123997039104, -1.011339956201643, -0.7262787204541828, -0.3984535771328854, -0.06298325268772668, 0.24543056266715618, 0.4944366556509357, 0.6558600014523563, 0.707338864325048, 0.6334752978507665, 0.4266370338973109, 0.08737648909768951, -0.37564292366204954, -0.9462458413934148, -1.601647652161895, -2.3137468009547844, -3.0508863824882457, -3.7795332294406947, -4.466044707298722, -5.078575471660178, -5.589074811545258, -5.97451485433989, -6.218031872742002, -6.3098019854132685, -6.247717324649662, -6.037125606297901, -5.690358523074726, -5.2259370396495415, -4.667504089331156, -4.042334086787692, -3.379730340403435, -2.709374338720947, -2.0594714242502, -1.4553869432862874, -0.9184535919815767, -0.4648515269944805, -0.10445791557484488, 0.1590242867180861, 0.32783135583853357, 0.4099016663434018, 0.4185239556455989, 0.3707164367957396, 0.28586872717482736, 0.18454640921298318, 0.08724825273065297, 0.012632719801575824, -0.023699653606814634, -0.010095328359418577, 0.06039721903519218, 0.18950892037149034, 0.3737908424604809, 0.604959995857035, 0.8704042652170267, 1.1541969648605384, 1.4383306786441583, 1.7039833755641463, 1.9327726610554414, 2.10821250501113, 2.2169397627036678, 2.2496761321384757, 2.201922638038191, 2.074418343710772, 1.8731845780614327, 1.6091766827011433, 1.297607403924372, 0.957001978000722, 0.6079649224785854, 0.27175129236016365, -0.031197423088087255, -0.2826979319183507, -0.4681759723055647, -0.577778602052091, -0.6073114772225517, -0.5587408554050504, -0.4401458328660583, -0.2655313470860725, -0.0543260920133387, 0.169909098863591, 0.3809930956472039, 0.5512936339439997, 0.6534821887913761, 0.6628862990123994, 0.5586560478267423, 0.32495470970320056, -0.04719051614209749, -0.5589777826019232, -1.204131568470511, -1.968680348236881, -2.830724116741026, -3.7621757549162167, -4.730183584231343, -5.697987144228669, -6.627258149918144, -7.480521482210778, -8.222626359304112, -8.822150846012002, -9.254286383031824, -9.501771020787942, -9.555136014063491, -9.413475439283287, -9.085253237287647, -8.587119671096044, -7.942635955024529, -7.181288110621762, -6.337144825356625, -5.446491352822046, -4.545803059965838, -3.6698908773153347, -2.850141843407023, -2.112776127856794, -1.4775926311478689, -0.9571345956095229, -0.5562814757871919, -0.27237351113486163, -0.09576826010168703, -0.01079242207251543, 0.0029293942552951363, -0.031174489531034376, -0.0883571331546952, -0.14434576452599998, -0.17709398875340873, -0.16828599110230827, -0.10457916832621837, 0.02148891273733806, 0.21113472279524279, 0.459342994491084, 0.7552296707713928, 1.0828944384566792, 1.422986053452046, 1.7540086591392556, 2.053775730970985, 2.3011690097160766, 2.478390194298445, 2.5719463571619894, 2.5735075713791606, 2.480866417013501, 2.298989381019956, 2.0392102666318928, 1.7184006193698362, 1.3582136447982978, 0.9841512484243489, 0.6232671960467243, 0.30226520350826475, 0.04581007920097466, -0.12522228547083522, -0.19561483536691715, -0.15701651090859148, -0.008734899215395631, 0.24173898784363496, 0.5789437973287906, 0.9802461144020597, 1.4170364694147595, 1.8562237571369737, 2.2623671895354227, 2.5999651560496435, 2.835724095965875, 2.940812674464327, 2.892939175844709, 2.67803070590704, 2.2914897612986183, 1.7389707199314959, 1.036304670702536, 0.20894129961688912, -0.7091484713905113, -1.677341879980395, -2.650629326939824, -3.5819946511679728, -4.425195716864229, -5.137950681309529, -5.68421382192537, -6.0362919896961715, -6.176971296357351, -6.101168090621112, -5.815989807293114, -5.340573437584255, -4.705454629149913, -3.9512868286446814, -3.126277338569463, -2.2835981497627813, -1.478485385267719, -0.7651957618660683, -0.19371188189445424, 0.19312475301170473, 0.3620980211524869, 0.2917892023472715, -0.026145812152554047, -0.5864591012859363, -1.370393221332144, -2.3464829842397745, -3.472407899490618, -4.6971758518476765, -5.963774138965205, -7.212632519530134, -8.384677263076496, -9.424209809022035, -10.28206860018635, -10.918903273124252, -11.30646210888533, -11.428688706907778, -11.282799818816995, -10.879776403842357, -10.242624816677283, -9.404775781121568, -8.408253480854345, -7.30162435280607, -6.136497375274823, -4.96457845259442, -3.834977075718567, -2.7918590670146877, -1.8718767358549757, -1.1024862269056697, -0.5009516985376311, -0.07390463666039437, 0.18247691677367742, 0.2815840291858496, 0.2450106844292019, 0.10072088199330531, -0.11916337295149884, -0.3806125449580381, -0.6500016024203255, -0.8963944357326298, -1.093335914808101, -1.2202966760977687, -1.2638067003211484, -1.2179648342877893, -1.084262975085604, -0.8710884358133721, -0.5927571092364152, -0.268041123798796, 0.081436771218717, 0.4328765803055164, 0.7640767753600655, 1.055242298282215, 1.2902006093391059, 1.4573529400682779, 1.550335602166551, 1.5685374360149473, 1.516631819090603, 1.4037940103782662, 1.2428474488345267, 1.0493409616374656, 0.8398862226985389, 0.6306972309041855, 0.4364133017279509, 0.2690737044463288, 0.1370895120277891, 0.04476816436190769, -0.007760978298548865, -0.024302570083454215, -0.011983969915145215, 0.01969847582679795, 0.06004040215049316, 0.09842134534156166, 0.12562868391882864, 0.1350688925509639, 0.12377920157410816, 0.09315518978577846, 0.04926964158279865, 0.0027874809861794035, -0.031531943012179105, -0.03576494850571835, 0.009879793981381843, 0.12553462881347593, 0.3299642648141242, 0.6387834067950308, 1.0628555452594817, 1.6068493038531653, 2.2681126252711463, 3.0362361214707674, 3.892900138098529, 4.812096751817009, 5.761214193536558, 6.7031414961963165, 7.597637947095617, 8.403256089514812, 9.080286258529723, 9.593759128369575, 9.914753768511323, 10.022325620965766, 9.90551256042839, 9.56476978813052, 9.011355058010476, 8.267166308184802, 7.363624699645619, 6.3406493448955175, 5.243794026273322, 4.121517837874525, 3.0224559069361367, 1.9931210769846475, 1.0747052567481385, 0.30026403010990094, -0.30700789299154413, -0.7348008695225579, -0.9820761442348908, -1.0587852234995385, -0.9855205014308616, -0.7938662140040512, -0.5230390158738518], 'positive_zeros': ['0.18336990947785650624021473923389', '0.56557605447525627040454183607479', '1.35896686894928774431925936306698', '1.47874488893559954389493611207165', '1.78781076218911119458511871536715', '1.91814148541747434332632901685782', '2.64997537838759852476012929644329', '2.77783392857995085703289123041403', '2.80212292510036994662328863547798', '2.95393654252162424218046187239708', '3.32725408469917901749656852368193', '3.59958093013743889585048963707456', '4.00924234978420940382886947876374', '4.22470355973473536538549117116650', '4.46101054022409817401880442905250', '4.61929811004212363961206708831059', '4.74802571157142289038999913583555', '4.83705498833167358416491705276218', '5.37244848859719355475287577929046', '5.45134145812226616470449838335857', '5.64739558181282096177381646038698', '5.70958883213699101794291930541827', '6.25456939991234159985501383387315', '6.43441876828900572970375733727693', '6.45395562642449660141746778740959', '6.48206157586021002695001319933240', '7.06454845603752847662683550309455', '7.25827716433049915597682272226513', '7.33741453208251919975745664479276', '7.48679082250974263271284539309537', '7.53996416472029429360829836427350', '7.82957903175270038131401809991093', '8.114324781043737924608546505940418', '8.203704512559838155648909425584051', '8.562388125035950299082070839179166', '8.704012257788808466940264483272283', '8.806786070206760093486480569352842', '9.175104463484998582447294120007170', '9.334171452299861624061307629047078', '9.637055315887257287363720956340077'], 'prelabel': '8-2016e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.0122114908726, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 439642030075492415, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.18336990947785650624021473923', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.56557605447525627040454183607', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.35896686894928774431925936307', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 67153.79168657961, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 16518176833536, 'conductor_radical': 42, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0], 'euler11': [1, 0, 40, 0, 642, 0, 4840, 0, 14641], 'euler13': [1, 8, 76, 344, 1654, 4472, 12844, 17576, 28561], 'euler17': [1, 0, -68, 0, 1734, 0, -19652, 0, 83521], 'euler19': [1, 0, -76, 0, 2166, 0, -27436, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -8, 0, 1074, 0, -4232, 0, 279841], 'euler29': [1, 0, 80, 0, 3282, 0, 67280, 0, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, -92, 0, 4038, 0, -88412, 0, 923521], 'euler37': [1, 0, 148, 0, 8214, 0, 202612, 0, 1874161], 'euler41': [1, 0, -148, 0, 8838, 0, -248788, 0, 2825761], 'euler43': [1, 0, -140, 0, 8598, 0, -258860, 0, 3418801], 'euler47': [1, 0, 172, 0, 11814, 0, 379948, 0, 4879681], 'euler5': [1, 0, -4, 0, 54, 0, -100, 0, 625], 'euler53': [1, 0, -176, 0, 13362, 0, -494384, 0, 7890481], 'euler59': [1, 0, 220, 0, 19062, 0, 765820, 0, 12117361], 'euler61': [1, 56, 1420, 21224, 204214, 1294664, 5283820, 12710936, 13845841], 'euler67': [1, 0, -68, 0, 10134, 0, -305252, 0, 20151121], 'euler7': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler71': [1, 0, 184, 0, 18546, 0, 927544, 0, 25411681], 'euler73': [1, 24, 508, 6120, 64806, 446760, 2707132, 9336408, 28398241], 'euler79': [1, 0, 76, 0, 13926, 0, 474316, 0, 38950081], 'euler83': [1, 0, 76, 0, 15222, 0, 523564, 0, 47458321], 'euler89': [1, 0, -212, 0, 27078, 0, -1679252, 0, 62742241], 'euler97': [1, 56, 1564, 27272, 323014, 2645384, 14715676, 51109688, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -4, 0, 54, 0, -100, 0, 625], [1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, 40, 0, 642, 0, 4840, 0, 14641], [1, 8, 76, 344, 1654, 4472, 12844, 17576, 28561], [1, 0, -68, 0, 1734, 0, -19652, 0, 83521], [1, 0, -76, 0, 2166, 0, -27436, 0, 130321], [1, 0, -8, 0, 1074, 0, -4232, 0, 279841], [1, 0, 80, 0, 3282, 0, 67280, 0, 707281], [1, 0, -92, 0, 4038, 0, -88412, 0, 923521], [1, 0, 148, 0, 8214, 0, 202612, 0, 1874161], [1, 0, -148, 0, 8838, 0, -248788, 0, 2825761], [1, 0, -140, 0, 8598, 0, -258860, 0, 3418801], [1, 0, 172, 0, 11814, 0, 379948, 0, 4879681], [1, 0, -176, 0, 13362, 0, -494384, 0, 7890481], [1, 0, 220, 0, 19062, 0, 765820, 0, 12117361], [1, 56, 1420, 21224, 204214, 1294664, 5283820, 12710936, 13845841], [1, 0, -68, 0, 10134, 0, -305252, 0, 20151121], [1, 0, 184, 0, 18546, 0, 927544, 0, 25411681], [1, 24, 508, 6120, 64806, 446760, 2707132, 9336408, 28398241], [1, 0, 76, 0, 13926, 0, 474316, 0, 38950081], [1, 0, 76, 0, 15222, 0, 523564, 0, 47458321], [1, 0, -212, 0, 27078, 0, -1679252, 0, 62742241], [1, 56, 1564, 27272, 323014, 2645384, 14715676, 51109688, 88529281]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2016/2/h/a'], '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': '8-2016e4-1.1-c1e4-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-2016e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.0122114908726, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 439642030075492415, 'z1': {'__RealLiteral__': 0, 'data': '0.18336990947785650624021473923', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '232448975813400891541947793309,716952824930272380745834248283,1722695167113842173813100364217,2431533205312128885005054402499', 'Lhash_array': ['232448975813400891541947793309', '716952824930272380745834248283', '1722695167113842173813100364217', '2431533205312128885005054402499'], 'factors': ['2-2016-12.11-c1-0-1', '2-2016-12.11-c1-0-6', '2-2016-12.11-c1-0-19', '2-2016-12.11-c1-0-23'], 'label': '8-2016e4-1.1-c1e4-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2016/2/h/a'}