-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_287.97', 'a10': [0.8090169943749475, -0.5877852522924731], 'a2': [0.9510565162951535, 0.30901699437494745], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [0.8090169943749475, 0.5877852522924731], 'a5': [0.5877852522924731, -0.8090169943749475], 'a6': [-0.8910065241883679, 0.4539904997395468], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.5877852522924731, 0.8090169943749475], 'a9': [2.9010907910729803e-30, -1.0], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.97', 'coeff_info': ['x^40 - 1', '0.987688340595138 + 0.156434465040231*I', '\\\\zeta_{40}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.216', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^15', 'a^4', 'a^34', 'a^17', 0, 'a^6', 'a^30', 'a^36', 'a^31', 'a^19', 'a^7', 0, 'a^9', 'a^8', 'a^1', 'a^32', 'a^33', 'a^38', 0, 'a^33', 'a^12', 'a^21', 'a^28', 'a^9', 'a^5', 0, 'a^19', 'a^11', 'a^16', 'a^10', 'a^6', 'a^3', 0, 'a^34', 'a^24', 'a^35', 'a^22', 'a^0', 0, 0, 'a^2', 'a^35', 'a^24', 'a^14', 'a^17', 'a^23', 0, 'a^30', 'a^16', 'a^11', 'a^39', 'a^7', 'a^25', 0, 'a^8', 'a^21', 'a^12', 'a^13', 'a^38', 'a^18', 0, 'a^12', 'a^1', 'a^8', 'a^29', 'a^5', 'a^27', 0, 'a^11', 'a^36', 'a^30', 'a^26', 'a^3', 'a^37', 0, 'a^24', 'a^15', 'a^2', 'a^20', 0, 'a^20', 0, 'a^35', 'a^4', 'a^34', 'a^37', 'a^23', 'a^26', 0, 'a^16', 'a^31', 'a^19', 'a^27', 'a^25', 'a^29', 0, 'a^21', 'a^32'], 'euler_factors': [[1, 'a^2'], [1, 'a^15'], [1, 'a^34'], [0], [1, 'a^31'], [1, 'a^7'], [1, 'a^1'], [1, 'a^33'], [1, 'a^12'], [1, 'a^19'], [1, 'a^16'], [1, 'a^24'], [0], [1, 'a^2'], [1, 'a^17'], [1, 'a^39'], [1, 'a^12'], [1, 'a^38'], [1, 'a^29'], [1, 'a^11'], [1, 'a^30'], [1, 'a^15'], [1, 'a^20'], [1, 'a^23'], [1, 'a^29'], [1, 'a^33']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-287-287.97-r0-0-0', 'leading_term': '1.89606103993573407029958495108+0.740887388291790552730308450270*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/287/97', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.035672269618076, 2.36892568482049, 2.7045638344595417, 2.4081796255569516, 1.23063124757744, -0.6059333788528852, -2.4966899596165666, -3.7101207024171132, -3.7478296136208478, -2.6336633502622604, -0.9458028613095697, 0.47211339316297973, 0.9841282726025897, 0.5335393056198684, -0.3465770233548566, -0.9224846002769693, -0.7997554831739637, -0.22049014302375905, 0.1374929164674769, -0.24842388397821488, -1.2075898733468855, -1.860762976403793, -1.2377015930539792, 0.8785028443613546, 3.554050554232745, 5.17615519892471, 4.566309019392584, 1.9397019552519534, -1.0798721031934382, -2.520696989220331, -1.4774223767753278, 1.2000697271486018, 3.527605297934554, 3.8836859361045057, 2.2167544630081624, -0.007779369243798332, -1.0730049076374126, -0.425440590238138, 0.9567694076229882, 1.5357034182172282, 0.6406000135845923, -0.9418275465617156, -1.746523006721106, -1.0478042413075428, 0.4235035561859802, 1.160228497820441, 0.32667727553104464, -1.415279299336903, -2.522719021989189, -2.0549460575435834, -0.5681810474702295, 0.490143724220412, 0.30343174455016053, -0.4401733794690853, -0.3063013676675909, 1.171332099747283, 2.6012874160510484, 1.789830715182102, -2.053685913316208, -7.072313996130763, -9.890348255628663, -8.331028448431052, -3.3215429671861765, 1.8041703467123777, 4.028554316626742, 2.945454174961321, 0.6207468627943822, -0.639417674781776, -0.3363696364871032, 0.25944922317136504, -0.09565493039070534, -1.1457766301425676, -1.5476040094814523, -0.5705866530696893, 0.9377454163173894, 1.4765713285756135, 0.6688509096931283, -0.19716407014403942, 0.38999737948845853, 2.291306083981505, 3.6155478912158756, 2.720611205286362, 0.21847916530075848, -1.347771501234488, -0.0667553199070023, 3.1686852604029836, 5.312782336437605, 4.158038669229333, 0.6072548651809687, -2.202230933084791, -2.0572569838599026, 0.2036329681561319, 1.8141718489835412, 1.1702101433371026, -0.5053570285015754, -0.698430943641063, 1.437675623198591, 4.026783858089824, 4.474758568056124, 2.26311898454228, -0.5684403019610595, -1.6871262739715096, -0.8432111363085403, 0.25884832651747014, 0.20979665838598785, -0.5330801727863133, -0.5615456654111222, 0.4026920491563142, 1.0195857653517635, 0.14740896888671945, -1.3591149128496884, -1.3918478847718472, 0.7007239218467636, 2.7211399214811434, 1.6533085791290174, -2.7910028089506627, -7.180559435206064, -7.474363135668273, -3.1619037731967006, 2.0549005860035763, 3.902588264195599, 1.6507142639303336, -1.619334723837268, -2.6020297381813946, -1.0680719243505843, 0.5917916112579683, 0.548323722074009, -0.5349380556951118, -0.8723202429333732, -0.09789949436129955, 0.39881423897096335, -0.3487864609320987, -1.2374985439798218, -0.34636919889112555, 2.392212967248139, 4.628332130418271, 4.143752197419526, 1.5085795106234792, -0.5179339020371376, -0.2479442405663256, 1.0045833061986973, 0.7650881953097731, -1.2811267400400033, -2.7676379752060516, -1.7593627013974977, 0.37974706295816496, 0.22160350840878504, -3.5395791838984585, -7.996053031956398, -8.853111022843878, -5.120473566949525, -0.22482707506937333, 1.7659993746988643, 0.3885674196932182, -1.3219898556747287, -0.7933426232874381, 1.2244597750570603, 2.1209356210935786, 0.9382899323275915, -0.6158747831418782, -0.6542381064738924, 0.44744622647773524, 0.8481989725098207, -0.043417641661170264, -0.7950842641960081, -0.1557997784942918, 0.9763594267776599, 0.8107318116297287, -0.4372176559764636, -0.25766628533382563, 2.804226039499561, 6.310289238702358, 5.825330969179014, 0.006308614777857373, -7.135984463486073, -9.957427208747617, -6.924121326893704, -1.829484688045838, 0.7392139428452655, 0.15836777901685997, -0.6548449562648513, 0.36942066301686705, 1.960639729534872, 1.7748539324645394, -0.08563268246887372, -1.1711717760136562, -0.1228530055744864, 1.3851943981097037, 0.9064944713299121, -1.398022447889497, -2.8841848877390808, -1.8952985975541579, 0.13153655718342827, 0.7380174748608958, -0.2301667411016752, -0.6577668075458921, 0.5565266485561671, 1.6885728608537005, 0.5773053197873438, -2.043509471668825, -3.149516617193315, -1.5271572348158455, 0.20811095298316842, -1.1171710589022283, -4.632557530706173, -5.777679006058852, -1.7707402704925443, 4.5114877118119985, 7.370487889474287, 4.629967010102499, -0.16633544117617094, -2.156436016402995, -0.5058294279518656, 1.6314066428833482, 1.6667540871929105, 0.3939484380947647, -0.05225734290695042, 0.5272037976860985, 0.5796929395151632, -0.3518418430763746, -0.76126235110782, 0.30225559114306416, 1.2764364698421446, 0.05714780166395748, -2.6236960540608876, -3.5236210843111753, -1.089356286378369, 2.0910806597491614, 2.3603202551076703, -0.15777165478194088, -1.5444973000922178, 0.7064233491392741, 4.079023157430845, 4.042013128152532, -0.06350642358048135, -3.983734513405406, -3.7756784336359175, -0.47610805302546666, 1.714748031956918, 0.9686852422818574, -0.36405420245424486, 0.3352536641374685, 2.14997891656322, 2.19177222262466, 0.01199094600069856, -1.5745067372974098, -0.4036957782955154, 2.0049317317484667, 2.568025002916214, 0.8182649865527277, -0.7351650855964463, -0.31970225145767833, 0.8214811307499319, 0.6997320603202344, -0.3256772604794611, -0.44862033565747617, 0.17300503086402444, -0.8269416840366244, -4.023299618463156, -5.832768039462764, -2.306671381293787, 5.0919276955028465, 9.7747757918921, 7.1199279626362655, -0.11463474621695213, -4.95673074959455, -4.065981058232406, -0.5871390003921865, 0.8385338319797238, -0.263443283448817, -0.9384647782453301, 0.23875862615776114, 1.3944560590235764, 0.7152506357888594, -0.6534091537262244, -0.5110552899608161, 0.8889010753205902, 1.2445270341315424, -0.1363369780260803, -1.1978709470292086, -0.4555240459771238, 0.31723246616508305, -1.4882241509240555, -5.034621767545891, -6.455911007914923, -3.9682050276261753, -0.527126091621255, 0.06706315193991585, -1.6445863408615113, -1.7144428231124453, 1.338034581137223, 4.103583713900216, 2.949306412686126, -0.7672732594271581, -2.45704565366732, -0.6914557564898586, 0.80472400332531, -1.5436424822386219, -5.972590407856194, -7.541156494600344, -4.569456140798199, -0.5168443477895882, 0.8458272883936981, -0.09922650694231537, -0.5248237133270376, 0.32467598730467284, 0.6163666318956466, -0.49970569283636135, -1.3089477723091953, -0.41337928772311905, 0.7792388442040307, 0.2311096601425479, -1.225374281196863, -0.9356825355308989, 1.1318652594226424, 1.610208169226459, -1.2865522798161908, -4.075191970051331, -1.8800999975653894, 4.585513837822361, 8.77522762853308, 6.033739716539557, -0.5998669867363465, -4.208050971188442, -2.3077061246065056, 1.148208943233947, 1.8253071286044937, 0.19632515876522325, -0.6323327180792497, 0.00432825669709406, 0.09154776834131462, -0.9919534255185469, -1.1650017576612064, 0.7329041574005554, 2.3977820115542463, 1.0953942832756423, -2.0856268327083924, -3.4179261842037567, -1.702174971593708, 0.2071498911218932, -0.2491836197117493, -1.7315235694305406, -1.500859945919415, 0.11953575108462403, 0.49392484623962357, -0.5104489799673322, 0.4006032749884112, 4.748572736263537, 8.693318918125449, 7.367684656380472, 1.7782326407042592, -1.7573971692894292, 0.41324946116319294, 4.647808427065277, 5.086785280511703, 1.3083521065614359, -1.8471168768557997, -1.3273074904614957, 0.489816808612213, 0.07975025307358657, -2.066349942615558, -2.8095225261389345, -1.3451257787536215, 0.0164861875333971, -0.17520173846452158, -0.5524529647782478, 0.15182030643043862, 0.6583815717955417, -0.4663206453423759, -1.680997272585915, -0.4939786646840629, 1.9295517700568463, 1.3653612692381556, -3.2757160438069794, -7.137086395478718, -5.1754813196859875, 0.8839122295126767, 4.400569620003761, 2.332541536128679, -1.315016430158385, -1.6198735850003412, 0.6362993888944659, 1.0875555853924272, -1.2434046453740617, -2.7103553087601266, -0.9093249837267979, 1.6636056447225975, 1.582861301192752, -0.3516412958462273, -0.6957962736346492, 1.1062135347183457, 1.9837278644076586, 0.24122279577488898, -1.7400131688138563, -1.271535870286472, 0.526520122569236, 0.7476371805337106, -0.5840819437813991, -0.768076186019979, 0.874095854868431, 1.6915068507875068, 0.09109269696926427, -1.6196342819715404, -0.98761763406364, 0.13606270523582065, -1.687254204516345, -4.997581089152028, -3.722776311483078, 4.521748423370687, 13.57598695655285, 15.174315931060002, 8.737140883049715, 1.4974878537771616, -0.7389672411328126, 0.5437053552395436, 0.8728753054798898, -0.5130790670077239, -1.0788003839625628, -0.0997536599908942, 0.34599571292158654, -0.6375500642823305, -1.1876934601730094, -0.23198114952219526, 0.1946209356089209, -1.7253434816807476, -3.9857033669932544, -3.3196365373958745, -0.3683562242247249, 0.9572735708892103, -0.5826877287924419, -1.6430738063505395, 0.19095702867023612, 2.0295663454522517, -0.16506734254708813, -4.836542028188404, -6.190910306050316, -2.323371746754833, 1.8746875843559574, 1.5576459955863415, -1.532323780246279, -2.3084905437427166, -0.03498742431838279, 1.1995337468074923, -0.6324213128017928, -2.320613846244867, -0.7292151620848174, 2.0427728955555144, 1.7897559532900158, -1.3977797906383471, -3.367765569603196, -2.069517904246244, 0.00012142827053402823, 0.22594619675256752, -0.44772732182157643, -0.08440057814252477, 0.5943840115355858, -0.10250362678923682, -1.1562393596972151, -0.2870486508484826, 1.4310523397622794, 0.2841028820690701, -3.7444986031794603, -5.106525683586979, 0.06007454775379305, 7.395861058676142, 8.960849041635248, 3.5355443801942963, -1.8822464802308643, -1.5518984199965702, 2.045391764822357, 2.9985273123683864, 0.4786658604260008, -1.3636092431727678, -0.4807501019537303, 0.5394514305445598, -0.5083387482102597, -1.8757731106072355, -1.266634112265668, 0.18518216813867205, 0.18779342230301158, -0.43202167156300153, 0.82812321440839, 3.249729167151387, 3.214530037703855, -0.04601079582666317, -2.585506449032024, -1.3682770000197548, 1.2306187422304236, 1.2722990219928851, -0.6562367520225738, -0.8962222310518086, 0.8178028750435493, 0.7988043122028983, -1.9748563016180378, -3.09981287110711, 0.6923523538164659, 5.515324966498363, 4.987856320385127, -0.592030447512257, -4.312251632842285, -2.15678349337991, 1.9264467027374066, 2.3300004048971394, -0.5305529184275033, -2.118926228984598, -0.9663443649074763, 0.21511409889548713, -0.10313074067879731, -0.0653194722306535, 1.5049038448963281, 2.531815931687716, 1.222973343836082, -0.6428818726563714, -0.6313716721072222, 0.27648039997760904, -0.19895023734800266, -0.8918978404363502, 1.2940697283794527, 5.202539665790056, 5.365574563927607, 0.02999252928333899, -4.729999517212845, -2.5119482402811197, 4.302869807405264, 7.393932866203437, 3.5876739039095358, -1.650553337846658, -2.574886983518711, -0.37642996133878254, 0.5199744208944617, -0.38468679738243267, -0.3689748649937834, 0.6476884136094296, -0.200989758048371, -3.1642630624079846, -4.498924683738301, -2.1917342928025945, 0.5961224133519563, 0.27150510803650907, -1.837976803582973, -2.0569312719906225, -0.31097684885506566, 0.33419521712876676, -0.7749740224516701, -1.0007501558188325, 0.46805291199765814, 0.8259832195093195, -1.228123323930824, -2.4267681695908885, -0.18908694028669715, 2.0363814766110964, -0.7955453428070519, -6.930331748201137, -9.06388584907581, -4.608281965368772, 0.2968592489185206, -0.5034633200673703, -4.5945468970801535, -5.126430161512667, -0.8877902208200403, 2.7366739724885205, 2.1714554699425856, -0.04811025868133983, -0.4806732514805815, 0.16188096498172763, -0.3113579617923151, -1.2093336888017412, -0.6682746933408836, 0.458679097892715, 0.1620114964962967, -0.5269495478109147, 1.032493347949621, 3.747530735184653, 3.294020549527647, -0.9620488267512962, -3.821032075311566, -1.5210623605619062, 2.4862313387749873, 2.7694028984600476, 0.25420391839909107, 0.38976034341669286, 4.0220810856051, 5.723802783075501, 2.403821114760606, -1.605035170383049, -1.1414712439746317, 2.06818688899753, 2.6280461480660766, -0.05000569749235989, -1.5892835496087367, -0.2507539872671927, 0.5860578892065209, -1.3538463068745796, -3.265291744904122, -2.1072645838346657, 0.2435167234475169, 0.2143437477457188, -1.5811774879556149, -1.7225280354733177, 0.12616278632587083, 0.9990576579778828, 0.010800486980433786, -0.4108914414814275, 0.5862733695867003, 0.5215082412477233, -1.428027852819757, -1.9743342649740283, 0.34584998955547175, 0.4372122128371867, -6.929281895363347, -17.63824267455814, -21.15536850027292, -13.65443420325356, -2.9366680799645715, 1.8810215837755235, 0.8716065647305082, 0.0015375598834671033, 1.3347977830467115, 1.876966401670014, 0.4016109744569239, -0.42591871078269633, 0.7095644744329722, 1.384474507866791, 0.07550601121441047, -0.9133502839771448, 0.3031869670272391, 1.4761354839136243, 0.046739851743189245, -2.0302785392639375, -1.2879240301051433, 1.23667911725738, 1.5775363874719033, -0.2916929296221319, -0.2384734124798331, 2.67688525503423, 3.8223807312677938, 0.3917206662249947, -3.4100692555235463, -2.5367393992251044, 0.9858657212335897, 1.4180372644095862], 'positive_zeros': ['1.46610208172458995482604136996', '3.315175228943662799822110157054', '4.25274630176230580010579100653', '5.445264429291843209251909854692', '5.8146115495942141967271989884', '7.07767089941079544698500047622', '8.62905310767481631151337929634', '9.5569324955538457756298162583', '10.93620210126037886094337914825', '11.65958003284997390249580844688', '12.6265107512919325669301719323', '13.65820113453647599343774997617', '14.438549218793434653312972248339', '15.75456807170440109465774670626', '16.37179316712699458752520544820', '16.96283951585443028581170698696', '17.98379877152171727449137674759', '19.56400947243385396130768316111', '20.731220566127709997821443022205', '21.39319787560375177860527488198', '21.83920913523847191469682193949', '22.92610438734042623907819079436', '23.95226558891823388833132643243', '24.272447301046868841935902638932', '25.65275260315312416658261732307', '26.25775479803150842611861029745', '27.551920491246593718123207958967', '28.41133638275258417334537202587', '29.271722273591968044111572103475', '29.82308916714298414658257628671', '31.177356942122619570160173722741', '32.088662552547152452242959090507', '32.59167704520424865227853036859', '33.32372970982796446953559968543', '34.09230572078157071894812402995', '34.914695361045038815552358751236', '35.76099021229478072256743486500', '37.05186689722795729478478399449', '37.958696183675053254875930850059', '38.922308943589280510110608376806', '39.53594335452592740479203693196', '40.34641653786767672046521997714', '40.83728606703107598178221896796', '41.61157975822333817096681274093', '43.008139621263242014723072178269', '43.497849569419701003170390229334', '44.19792241252192301423400767630', '45.24543273968403850163835368965', '45.65513190912754449907616626369', '47.20592781995727443296813085242', '47.86848331670769819432233793452', '48.565594775316957621118218158259', '49.54148698297241467325393957080', '50.19080831150466836121210023570', '50.925697831817965429455862171695', '51.60175709449871135000521288467', '52.38754913116364214202325162969', '52.85502806015130395807096465182', '54.06276303836377168684564170106', '55.47758693078823614252471648795', '55.97647961096740418739869978717', '56.49252086843479925419878358841', '57.4861886113998531143753732876', '58.14667140303870852535275801279', '58.88570721358568011258264655577', '59.97547157436911982532921474101', '60.56175372736753751440163811560', '61.13989178128953372207626313958', '61.94814560052266604590056707292', '63.05170698115595638656302328333', '63.28095259863762919015215404670', '64.46222193775621315474243202319', '65.612157699022694838550126238643', '66.31183145811601496518245952824', '67.33675734761108797284040631341', '67.54719730064063708455158085028', '68.33235612666549377579867357793', '68.99668999262072491249321706971', '69.69492861213663126119284030148', '70.72029631772822987755831661142', '71.54443667862293253535022643745', '72.123204427101425257229065453008', '73.12097210714134522294816894171', '74.107511681040900535350240352739', '74.87832519098878365241593541335', '75.24519136608916685159374956206', '76.25152064855481672923937755972', '76.92700926319055339153802203401', '77.93964324018189593541780568516', '78.51705444151251852112176512438', '79.26941276146253437003064970678', '79.887083270910675248358106353189', '80.15883721637725590447783482486', '81.35417189628980654159083410829', '82.49499719765526023415444141332', '83.50578682599864006174193447161', '84.00569400711450783783666390300', '84.641529744376353283792369616983', '85.45917517816626980498792853176', '86.05889646544883697487568558662', '86.84964501044979775087579294135', '87.6157859953366669581114044438', '87.92961293224934397439963145258', '89.461070520658165115158692001377', '89.7054067465410706532997345287', '90.510894613852768779441398115205', '91.49627719151232181390699635368', '92.27864617950859111750369440063', '92.673604730412143410817521462875', '94.12142570668907543759809216027', '94.66013617671181360921835099819', '95.21030389318088581340375948373', '95.82313432321072293531574448781', '96.649144318251820549687073719973', '97.23557551192994413812171598458', '97.96217675997285596877639381989', '98.64022799456129091846166949976', '99.47635491227185166139675975875', '100.59522606401665759449953034860', '101.44299316858209590936911244070', '102.225949932990192620401004754063', '102.81063292889182062572574142551', '103.16239297565793443094799493738', '103.96496612037151086033322301764', '104.79798394202605082167258689189', '105.87903811220222961823665744272', '106.192812043205710503919297586051', '107.161570949740376565132443620455', '107.655164218459488428380548719284', '108.0749896800576847252509884767', '109.482803037569589385874961797172', '109.96906267334511274871305132686', '111.03585332402027633020582658030', '111.7688939065620869932816941875', '112.201419647942848533277885245928', '113.42871954545070463960436760940', '113.65686770049555261109439525741', '114.32677686507697380778502020074', '114.90872865816568265967585155040', '115.68580646626265142458564596369', '116.363456591978039488217410842283', '117.45447157639658102566254451005', '118.30676591356853047146608420808', '118.97399238998349001230324045059', '119.54337857981558201024639017445', '120.408207103507593463246999576311', '121.18877510481751911478400276805', '121.70424342787402707029828027545', '122.53024114736696581502396822754', '123.3362648691031935088398391458', '123.93131620825249781759451118902', '124.54044750030215717978900863949', '125.32505477086930427865032250830', '126.15711344932629021657636952001', '126.3344127609883880401736529358', '127.353321795216324203813057837674', '128.866817062901217561846132521182', '129.26449975659968072363967423721', '129.89444604640236816149931907044', '130.65396703817756123506309670512', '131.08061493584922915646711614', '131.94003123920819838854690154773', '132.24857296997365119511040357864', '133.48138185474244383293457143374', '133.97362393763267487756251487195', '134.66520004198634820662521984202', '135.30026482890262589869495164817', '136.39566174307633785798459964374', '137.03296105618773721070129382517', '137.816857137684756863809930507345', '138.35909747112484355792237705423', '139.13679551520051607553921856689', '139.87398932994609005647283236535', '140.93747092628302445042116220663', '141.345005134414591257539355055667', '141.90463111182636828989159239004', '142.47510721938406030850707564532', '143.17140261204342414531928485572', '143.77685017640556433454110660344', '144.685036439609540835125430483091', '145.79824992395882355273773809310', '146.38636579053165217197192685625', '147.24025378340528100058150915130', '147.9112484514042353688803227570', '148.34003518000861206041650579921', '149.3212211574961287188933280188', '149.75899727660238360228120485910', '150.179959013156170794330376770623', '151.24616008743278362778685529020', '152.02464400741443348954492322314', '152.70347534209584031916777804389', '153.29467158228798944812387840528', '153.85914101283199285354866224329', '154.647409317858969770344488315908', '155.59421376412782493529976300221', '156.400693304558054004025462288', '157.13302324569235418628996839958', '158.02249347444583222221399074033', '158.38370161315320189726886960847', '158.7710519374695781268942391425', '159.86873679893469602516203197762', '160.50297584877499136278009617423', '160.87958676244203908594567549785', '161.43740877626538304677343772131', '162.501444108691656250249683325193', '163.24511497106287028950395997367', '164.25755201248299621462062713547', '165.06138018136639674963927531229', '165.50534925861220207315279336464', '166.0454716841057146770622110378', '166.533760146247939671513169891594', '167.71935550339365707897709342519', '168.16776656556756379099900755998', '169.126647981564688294412221504631', '169.49552558324537996632403031116', '170.22166723412315485864747373991', '170.77795768952799395447389204822', '171.5806184229467832288030774310', '172.13960800187169031266528582487', '173.40450910779651199840769799505', '173.70169819553907221512550329520', '174.74435142053804703409628626434', '175.61577587093997530783636633823', '176.14602112756584732340792280849', '176.45716903330031885532168468045', '177.34864673444919280854000397747', '177.8626012352602693839611203998', '178.29791735858758587327954440530', '179.31162173065741830520847642092', '180.10742505333266502625860919406', '180.982989760823051110136989789656', '181.1896924817242801595476620293', '182.34771728272777551251846722225', '182.92528564087727412765489593044', '183.744595635587738345939633794391', '184.419305932274258625704684876781', '184.82606041159336764640583506843', '185.89315242597465950109926433010', '186.29250925215827440072986801647', '187.166745464064572837337342116090', '187.81539936352773924847795584983', '188.27394185025190192626143782017', '188.85023793042210060330593270276', '189.645612395417182161280548354419', '190.03557766730321079422277090258', '191.69112748063969922028722973643', '192.395658990628028290802300456434', '192.49900208459677705747762329441', '193.5183678266620346921057759896', '193.907914704104247855202222716379', '194.701300041861227909892556271254', '195.26017875768414837735057883116', '195.94345511152843064560370481172', '196.71699395069433953706048258826', '197.4482152861771510976745721339', '197.84790716237532418793583213226', '198.775710592932925216767428435802', '199.59109141188312531851736878953'], 'prelabel': '1-287-287.97-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.2371457015461025, 'root_number': '0.735077601323224656445063458047+0.677982979161641187589478612761*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.118572850773', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(40)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.60451468731202744511055280089+0.461170322241469065192613519048*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.46610208172', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.31517522894', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.25274630176', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.97', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/97'], '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': '1-287-287.97-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': '1-287-287.97-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.11857285077305126, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46610208172', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_287.97', 'Lhash_array': ['dirichlet_L_287.97'], 'label': '1-287-287.97-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/97'}
Lfunction data - 1-287-287.97-r0-0-0