LMFDB - Embedded newform 2.88.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,88,Mod(1,2)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 88, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 88);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 88 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$95.8667262922$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2 x^{3} + \cdots + 13\!\cdots\!68 $ x^4 - 2x^3 - 281103089248735483936525960163617359x^2 - 12802046688892212650602531506830185803155982810145588*x + 13431538901013885043865389957038837902382364731827315409437340098095268
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 17\cdot 29 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.13103e17$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.79609e12 q^{2} -3.08348e20 q^{3} +7.73713e25 q^{4} +1.64822e30 q^{5} +2.71226e33 q^{6} -1.87890e36 q^{7} -6.80565e38 q^{8} -2.28179e41 q^{9} +O(q^{10})$	\(q-8.79609e12 q^{2} -3.08348e20 q^{3} +7.73713e25 q^{4} +1.64822e30 q^{5} +2.71226e33 q^{6} -1.87890e36 q^{7} -6.80565e38 q^{8} -2.28179e41 q^{9} -1.44979e43 q^{10} -1.23253e45 q^{11} -2.38573e46 q^{12} -1.24695e48 q^{13} +1.65269e49 q^{14} -5.08225e50 q^{15} +5.98631e51 q^{16} +1.26826e53 q^{17} +2.00708e54 q^{18} +8.44016e54 q^{19} +1.27524e56 q^{20} +5.79355e56 q^{21} +1.08415e58 q^{22} +7.04395e58 q^{23} +2.09851e59 q^{24} -3.74573e60 q^{25} +1.09683e61 q^{26} +1.70035e62 q^{27} -1.45373e62 q^{28} +3.70240e62 q^{29} +4.47039e63 q^{30} -1.30049e65 q^{31} -5.26561e64 q^{32} +3.80050e65 q^{33} -1.11557e66 q^{34} -3.09683e66 q^{35} -1.76545e67 q^{36} -7.32150e67 q^{37} -7.42404e67 q^{38} +3.84495e68 q^{39} -1.12172e69 q^{40} +1.01206e70 q^{41} -5.09606e69 q^{42} +6.22049e70 q^{43} -9.53626e70 q^{44} -3.76088e71 q^{45} -6.19593e71 q^{46} -4.55852e72 q^{47} -1.84587e72 q^{48} -2.98531e73 q^{49} +3.29478e73 q^{50} -3.91065e73 q^{51} -9.64781e73 q^{52} -9.26314e74 q^{53} -1.49564e75 q^{54} -2.03148e75 q^{55} +1.27871e75 q^{56} -2.60251e75 q^{57} -3.25667e75 q^{58} -7.26201e75 q^{59} -3.93220e76 q^{60} +3.50860e77 q^{61} +1.14392e78 q^{62} +4.28725e77 q^{63} +4.63168e77 q^{64} -2.05524e78 q^{65} -3.34295e78 q^{66} -1.42319e79 q^{67} +9.81267e78 q^{68} -2.17199e79 q^{69} +2.72400e79 q^{70} -1.26444e80 q^{71} +1.55291e80 q^{72} -1.17707e81 q^{73} +6.44006e80 q^{74} +1.15499e81 q^{75} +6.53025e80 q^{76} +2.31580e81 q^{77} -3.38205e81 q^{78} +4.54614e82 q^{79} +9.86673e81 q^{80} +2.13307e82 q^{81} -8.90221e82 q^{82} -2.90044e83 q^{83} +4.48254e82 q^{84} +2.09036e83 q^{85} -5.47160e83 q^{86} -1.14163e83 q^{87} +8.38818e83 q^{88} +7.03621e84 q^{89} +3.30811e84 q^{90} +2.34289e84 q^{91} +5.45000e84 q^{92} +4.01005e85 q^{93} +4.00971e85 q^{94} +1.39112e85 q^{95} +1.62364e85 q^{96} +3.12790e85 q^{97} +2.62590e86 q^{98} +2.81238e86 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 35184372088832 q^{2} + 40\!\cdots\!28 q^{3}+ \cdots + 82\!\cdots\!48 q^{9}+O(q^{10}) $ 4 * q - 35184372088832 * q^2 + 403237985254067182128 * q^3 + 309485009821345068724781056 * q^4 - 4037922390733497835169570162760 * q^5 - 3546918828382512738768149884698624 * q^6 + 8582179387397492406597229487230375904 * q^7 - 2722258935367507707706996859454145691648 * q^8 + 820135434884318664352221575507492568732948 * q^9	$ 4 q - 35184372088832 q^{2} + 40\!\cdots\!28 q^{3}+ \cdots + 22\!\cdots\!76 q^{99}+O(q^{100}) $ 4 * q - 35184372088832 * q^2 + 403237985254067182128 * q^3 + 309485009821345068724781056 * q^4 - 4037922390733497835169570162760 * q^5 - 3546918828382512738768149884698624 * q^6 + 8582179387397492406597229487230375904 * q^7 - 2722258935367507707706996859454145691648 * q^8 + 820135434884318664352221575507492568732948 * q^9 + 35517940965348365626859729845107910854574080 * q^10 + 2970616434026495781757184460756379040517208848 * q^11 + 31199027956673594964608194726311446315419041792 * q^12 - 1767394568818848613362028589161957028533441611112 * q^13 - 75489648224824411010546555477731971328955260076032 * q^14 + 3370976843124805373452544557684295582910726697502880 * q^15 + 23945242826029513411849172299223580994042798784118784 * q^16 - 702353032002195299447255515013113779135644499293109816 * q^17 - 7213987576051478951188874632704563580254297738585309184 * q^18 + 38051210330377980576900552965948384772060949611758270960 * q^19 - 312419112688496434410317985513745659312699567327821168640 * q^20 - 2960768946346244712423575885216855505816696171119080255872 * q^21 - 26129818486996871127304316256231512888117802859237038096384 * q^22 + 267410844513343534387094489566271409098947974355011539188128 * q^23 - 274429552109368924814832586348763817236857825346144736116736 * q^24 + 26866935732372298920001618987293695975686810093231631671755100 * q^25 + 15546167034275791140382436144471296993092547711081656715575296 * q^26 + 98351974670575379028284146601861806526822489553847883125490400 * q^27 + 664013967999314535695892002534007752932295679741402958744518656 * q^28 - 936377285291713459807588765220376016646503474372565915415382440 * q^29 - 29651425887834852403903990749669038123824799034099618745983959040 * q^30 + 119463507882721430244886842916392661099853847057206322986794525568 * q^31 - 210624583337114373395836055367340864637790190801098222508621955072 * q^32 - 975951433415384517573045287992141578476030063995050605617360966464 * q^33 + 6177962603921142192805661314942895498269819437765021241050270793728 * q^34 + 14105085028850567766840711566409137394874532315214531645239547531840 * q^35 + 63454905780001617731151046382612710619432714548573512194720658358272 * q^36 + 182087106643248709136261820106869557597167548749803025400276539121464 * q^37 - 334701985673606721323645108291715305922613643471269213861286961479680 * q^38 - 5157167650299694789254850025641525408739411563899847457339313757250784 * q^39 + 2748067577123698321827685975535901419950085077291708477942376033157120 * q^40 + 5499251594717860286021866958065054045901150247706209838765933372175208 * q^41 + 26043199069326335451693431452427559455621627547084532573326442418405376 * q^42 - 157807090931211109929865823295822094205785343123733495078770527721821552 * q^43 + 229840314065034778104010119086398472312972227124835062038272769756495872 * q^44 - 1370445036354823659067923168385609449595471872659192002945296358462825320 * q^45 - 2352170663486569504369914341681047401963148037857733129248014646193946624 * q^46 - 11700969700600051870794491472787906623524149540240126773037581150641555136 * q^47 + 2413907868396886727226140291242059049083751312718584875630451012128473088 * q^48 + 45608750768809825384693277965554885824930550141562503946687984691665533732 * q^49 - 236324065923630760668657815178197122585685320681456781276991408990637260800 * q^50 - 914883468555652107825206155517190576830844787740672822262980556765469169312 * q^51 - 136745531372273324016576733538944106078280970896210682631976284458024173568 * q^52 - 3205407327892231366350098762423033970241498041998526172742677864692608514312 * q^53 - 865113118120226050927175001395744751092084611954848335836798017458090803200 * q^54 - 10009926131406218736826424103970095109094189414661383153140158173941128709920 * q^55 - 5840728630567416793561662980979737449788739679624018831289026246209278312448 * q^56 + 24760562583447132282306921710743074800398451150699602451361304490068034752320 * q^57 + 8236461705308510473577685400040524235406303263089755599489781422351733227520 * q^58 - 81401388903576961577929700275194040780233584053778446123485310614164754536880 * q^59 + 260816700350501796503049467891128405126358446664151554703502613334842482360320 * q^60 + 908111889319782669823282318823295371554753169091641506977419705876741077882328 * q^61 - 1050812128095696376586514967647428079039044942828517372626320439677738647814144 * q^62 + 7137835102413627130280079665652016586382162073538425059614697312278117344350048 * q^63 + 1852673427797059126777135760139006525652319754650249024631321344126610074238976 * q^64 + 11407211919915638593357605065156231994296813060854399078385375214171172364857680 * q^65 + 8584559593478959280621500012652850349171438888492092327918713325137577495232512 * q^66 - 65059771693644954593974794228917141656005263924052931483321156753263176566322896 * q^67 - 54341933751812724902023253670568124974314494093364989057139191298059718491111424 * q^68 - 144323666676858272713465642347149842097884989245184653886655055101689375583845504 * q^69 - 124069639999923005500646624090308971041908232841505948959254386145464972707102720 * q^70 - 183272612160344892942190287282961718510131375557583525213035115209249713064136992 * q^71 - 558155253956338317275929527602177423655680841848067355296117578760944212116504576 * q^72 + 354182538046550765754528347144724476790476600029207619306415675742769571814637288 * q^73 - 1601655128178723932025775974507397068426901430503198065737820251919877020961472512 * q^74 + 710386439551323791969874648476083944602337020291621916942901745237698809202501200 * q^75 + 2944069800702774064027323538684509525361173924971530627370715914294143730780733440 * q^76 + 39316760279456924611775164190833990669200449799501752350802186925973327788597118848 * q^77 + 45362926383157972415756683406366951526581873158623352931657948697548800307937411072 * q^78 + 15689408650300008287770111864298279692820798574497171271867094782550105530843081920 * q^79 - 24172258039693807695503348146758763873414302432021545297363850106765398076513320960 * q^80 - 196590592451401107987710944406206415161857917104016937408869683425180184810203702876 * q^81 - 48371928579663987252349183028740936842481506637169603120359663272770590191611019264 * q^82 + 111926752599709260117886233216331177095176580206068162806299107496899925996223203568 * q^83 - 229078401609675258913891688255885614430188449105962531942162006259872232223914590208 * q^84 - 891497844731417844264766892389844899904478293183670323386186444763703698463839596560 * q^85 + 1388085851394969400976659588554077855842466084275351230019781346209556380442549026816 * q^86 + 2027498154029213080175869882525768385333184769847411190333977363043382754362186713120 * q^87 - 2021696782769547651193529032558892722193566089333659035337753899891686714980356325376 * q^88 - 1111763274969003683091618237538433748811411444468148051875571331333583253595104867160 * q^89 + 12054562021600253271129669326554918303828197627410649510778436683009490086217184706560 * q^90 + 79630263055292573954918630151432006426386375686727482380289693283976606755116980321088 * q^91 + 20689911960136575706111408504507326985128933416561732998791094227623959804415198625792 * q^92 + 121552396376548026998325328889505560359171182104366398760596365823334350324441379006976 * q^93 + 102922817936515347171258282828953462563508237397083710417081191671708730834331304460288 * q^94 + 360329377379389097240594968925389763617374668200294178024200943546627617266362721242400 * q^95 - 21232958157458842504504822471050360495135888697596704547293213652627233307394314338304 * q^96 + 84654632295309208342666811638631082612402959416215649507302559581340331556342797429384 * q^97 - 401178814389151860471251451603139889379513741986404607571754642978513123633817249120256 * q^98 + 2203878007770692926523827334498155512549713414229081953932986276578630523661724303178576 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−8.79609e12	−0.707107
$2$	−8.79609e12	−0.707107
$3$	−3.08348e20	−0.542335	−0.271167	−	0.962532i	$-0.587410\pi$
$3$	−3.08348e20	−0.542335	−0.271167	+	0.962532i	$0.587410\pi$
$4$	7.73713e25	0.500000
$5$	1.64822e30	0.648364	0.324182	−	0.945995i	$-0.394911\pi$
$5$	1.64822e30	0.648364	0.324182	+	0.945995i	$0.394911\pi$
$6$	2.71226e33	0.383488
$7$	−1.87890e36	−0.325191	−0.162595	−	0.986693i	$-0.551987\pi$
$7$	−1.87890e36	−0.325191	−0.162595	+	0.986693i	$0.551987\pi$
$8$	−6.80565e38	−0.353553
$9$	−2.28179e41	−0.705873
$10$	−1.44979e43	−0.458462
$11$	−1.23253e45	−0.616903	−0.308451	−	0.951240i	$-0.599811\pi$
$11$	−1.23253e45	−0.616903	−0.308451	+	0.951240i	$0.599811\pi$
$12$	−2.38573e46	−0.271167
$13$	−1.24695e48	−0.435826	−0.217913	−	0.975968i	$-0.569925\pi$
$13$	−1.24695e48	−0.435826	−0.217913	+	0.975968i	$0.569925\pi$
$14$	1.65269e49	0.229945
$15$	−5.08225e50	−0.351630
$16$	5.98631e51	0.250000
$17$	1.26826e53	0.379035	0.189517	−	0.981877i	$-0.439308\pi$
$17$	1.26826e53	0.379035	0.189517	+	0.981877i	$0.439308\pi$
$18$	2.00708e54	0.499128
$19$	8.44016e54	0.199788	0.0998939	−	0.994998i	$-0.468150\pi$
$19$	8.44016e54	0.199788	0.0998939	+	0.994998i	$0.468150\pi$
$20$	1.27524e56	0.324182
$21$	5.79355e56	0.176362
$22$	1.08415e58	0.436216
$23$	7.04395e58	0.409879	0.204939	−	0.978775i	$-0.434300\pi$
$23$	7.04395e58	0.409879	0.204939	+	0.978775i	$0.434300\pi$
$24$	2.09851e59	0.191744
$25$	−3.74573e60	−0.579624
$26$	1.09683e61	0.308176
$27$	1.70035e62	0.925154
$28$	−1.45373e62	−0.162595
$29$	3.70240e62	0.0899851	0.0449926	−	0.998987i	$-0.485674\pi$
$29$	3.70240e62	0.0899851	0.0449926	+	0.998987i	$0.485674\pi$
$30$	4.47039e63	0.248640
$31$	−1.30049e65	−1.73730	−0.868648	−	0.495429i	$-0.835011\pi$
$31$	−1.30049e65	−1.73730	−0.868648	+	0.495429i	$0.835011\pi$
$32$	−5.26561e64	−0.176777
$33$	3.80050e65	0.334568
$34$	−1.11557e66	−0.268018
$35$	−3.09683e66	−0.210842
$36$	−1.76545e67	−0.352937
$37$	−7.32150e67	−0.444452	−0.222226	−	0.974995i	$-0.571332\pi$
$37$	−7.32150e67	−0.444452	−0.222226	+	0.974995i	$0.571332\pi$
$38$	−7.42404e67	−0.141271
$39$	3.84495e68	0.236364
$40$	−1.12172e69	−0.229231
$41$	1.01206e70	0.706497	0.353249	−	0.935529i	$-0.385077\pi$
$41$	1.01206e70	0.706497	0.353249	+	0.935529i	$0.385077\pi$
$42$	−5.09606e69	−0.124707
$43$	6.22049e70	0.546949	0.273475	−	0.961879i	$-0.411827\pi$
$43$	6.22049e70	0.546949	0.273475	+	0.961879i	$0.411827\pi$
$44$	−9.53626e70	−0.308451
$45$	−3.76088e71	−0.457663
$46$	−6.19593e71	−0.289828
$47$	−4.55852e72	−0.836694	−0.418347	−	0.908287i	$-0.637390\pi$
$47$	−4.55852e72	−0.836694	−0.418347	+	0.908287i	$0.637390\pi$
$48$	−1.84587e72	−0.135584
$49$	−2.98531e73	−0.894251
$50$	3.29478e73	0.409856
$51$	−3.91065e73	−0.205564
$52$	−9.64781e73	−0.217913
$53$	−9.26314e74	−0.913604	−0.456802	−	0.889568i	$-0.651005\pi$
$53$	−9.26314e74	−0.913604	−0.456802	+	0.889568i	$0.651005\pi$
$54$	−1.49564e75	−0.654183
$55$	−2.03148e75	−0.399977
$56$	1.27871e75	0.114972
$57$	−2.60251e75	−0.108352
$58$	−3.25667e75	−0.0636291
$59$	−7.26201e75	−0.0674519	−0.0337260	−	0.999431i	$-0.510737\pi$
$59$	−7.26201e75	−0.0674519	−0.0337260	+	0.999431i	$0.510737\pi$
$60$	−3.93220e76	−0.175815
$61$	3.50860e77	0.764339	0.382170	−	0.924092i	$-0.375177\pi$
$61$	3.50860e77	0.764339	0.382170	+	0.924092i	$0.375177\pi$
$62$	1.14392e78	1.22845
$63$	4.28725e77	0.229543
$64$	4.63168e77	0.125000
$65$	−2.05524e78	−0.282574
$66$	−3.34295e78	−0.236575
$67$	−1.42319e79	−0.523613	−0.261807	−	0.965120i	$-0.584318\pi$
$67$	−1.42319e79	−0.523613	−0.261807	+	0.965120i	$0.584318\pi$
$68$	9.81267e78	0.189517
$69$	−2.17199e79	−0.222292
$70$	2.72400e79	0.149088
$71$	−1.26444e80	−0.373386	−0.186693	−	0.982418i	$-0.559777\pi$
$71$	−1.26444e80	−0.373386	−0.186693	+	0.982418i	$0.559777\pi$
$72$	1.55291e80	0.249564
$73$	−1.17707e81	−1.03814	−0.519071	−	0.854731i	$-0.673722\pi$
$73$	−1.17707e81	−1.03814	−0.519071	+	0.854731i	$0.673722\pi$
$74$	6.44006e80	0.314275
$75$	1.15499e81	0.314350
$76$	6.53025e80	0.0998939
$77$	2.31580e81	0.200611
$78$	−3.38205e81	−0.167134
$79$	4.54614e82	1.29082	0.645408	−	0.763838i	$-0.276687\pi$
$79$	4.54614e82	1.29082	0.645408	+	0.763838i	$0.276687\pi$
$80$	9.86673e81	0.162091
$81$	2.13307e82	0.204130
$82$	−8.90221e82	−0.499569
$83$	−2.90044e83	−0.960653	−0.480327	−	0.877090i	$-0.659482\pi$
$83$	−2.90044e83	−0.960653	−0.480327	+	0.877090i	$0.659482\pi$
$84$	4.48254e82	0.0881811
$85$	2.09036e83	0.245753
$86$	−5.47160e83	−0.386752
$87$	−1.14163e83	−0.0488021
$88$	8.38818e83	0.218108
$89$	7.03621e84	1.11911	0.559556	−	0.828793i	$-0.310972\pi$
$89$	7.03621e84	1.11911	0.559556	+	0.828793i	$0.310972\pi$
$90$	3.30811e84	0.323616
$91$	2.34289e84	0.141727
$92$	5.45000e84	0.204939
$93$	4.01005e85	0.942196
$94$	4.00971e85	0.591632
$95$	1.39112e85	0.129535
$96$	1.62364e85	0.0958721
$97$	3.12790e85	0.117674	0.0588372	−	0.998268i	$-0.481261\pi$
$97$	3.12790e85	0.117674	0.0588372	+	0.998268i	$0.481261\pi$
$98$	2.62590e86	0.632331
$99$	2.81238e86	0.435455
$100$	−2.89812e86	−0.289812
$101$	2.74359e87	1.77967	0.889834	−	0.456284i	$-0.150820\pi$
$101$	2.74359e87	1.77967	0.889834	+	0.456284i	$0.150820\pi$
$102$	3.43985e86	0.145356
$103$	6.16647e87	1.70458	0.852290	−	0.523070i	$-0.175213\pi$
$103$	6.16647e87	1.70458	0.852290	+	0.523070i	$0.175213\pi$
$104$	8.48630e86	0.154088
$105$	9.54902e86	0.114347
$106$	8.14795e87	0.646016
$107$	2.75753e88	1.45320	0.726600	−	0.687061i	$-0.241099\pi$
$107$	2.75753e88	1.45320	0.726600	+	0.687061i	$0.241099\pi$
$108$	1.31558e88	0.462577
$109$	5.94360e88	1.39958	0.699789	−	0.714349i	$-0.253277\pi$
$109$	5.94360e88	1.39958	0.699789	+	0.714349i	$0.253277\pi$
$110$	1.78691e88	0.282827
$111$	2.25757e88	0.241042
$112$	−1.12477e88	−0.0812977
$113$	−2.20232e89	−1.08135	−0.540677	−	0.841230i	$-0.681832\pi$
$113$	−2.20232e89	−1.08135	−0.540677	+	0.841230i	$0.681832\pi$
$114$	2.28919e88	0.0766163
$115$	1.16100e89	0.265751
$116$	2.86460e88	0.0449926
$117$	2.84528e89	0.307638
$118$	6.38773e88	0.0476957
$119$	−2.38292e89	−0.123259
$120$	3.45880e89	0.124320
$121$	−2.47262e90	−0.619431
$122$	−3.08620e90	−0.540469
$123$	−3.12069e90	−0.383158
$124$	−1.00621e91	−0.868648
$125$	−1.68251e91	−1.02417
$126$	−3.77110e90	−0.162312
$127$	−4.41124e91	−1.34617	−0.673083	−	0.739567i	$-0.735030\pi$
$127$	−4.41124e91	−1.34617	−0.673083	+	0.739567i	$0.735030\pi$
$128$	−4.07407e90	−0.0883883
$129$	−1.91808e91	−0.296629
$130$	1.80781e91	0.199810
$131$	1.37600e91	0.108973	0.0544864	−	0.998515i	$-0.482648\pi$
$131$	1.37600e91	0.108973	0.0544864	+	0.998515i	$0.482648\pi$
$132$	2.94049e91	0.167284
$133$	−1.58582e91	−0.0649691
$134$	1.25186e92	0.370250
$135$	2.80254e92	0.599836
$136$	−8.63131e91	−0.134009
$137$	7.02458e92	0.793005	0.396502	−	0.918034i	$-0.370224\pi$
$137$	7.02458e92	0.793005	0.396502	+	0.918034i	$0.370224\pi$
$138$	1.91050e92	0.157184
$139$	1.35236e93	0.812734	0.406367	−	0.913710i	$-0.366795\pi$
$139$	1.35236e93	0.812734	0.406367	+	0.913710i	$0.366795\pi$
$140$	−2.39605e92	−0.105421
$141$	1.40561e93	0.453768
$142$	1.11221e93	0.264024
$143$	1.53691e93	0.268862
$144$	−1.36595e93	−0.176468
$145$	6.10236e92	0.0583431
$146$	1.03536e94	0.734078
$147$	9.20515e93	0.484983
$148$	−5.66473e93	−0.222226
$149$	−5.80147e93	−0.169799	−0.0848996	−	0.996390i	$-0.527057\pi$
$149$	−5.80147e93	−0.169799	−0.0848996	+	0.996390i	$0.527057\pi$
$150$	−1.01594e94	−0.222279
$151$	−3.57638e94	−0.586066	−0.293033	−	0.956102i	$-0.594665\pi$
$151$	−3.57638e94	−0.586066	−0.293033	+	0.956102i	$0.594665\pi$
$152$	−5.74407e93	−0.0706356
$153$	−2.89390e94	−0.267551
$154$	−2.03700e94	−0.141853
$155$	−2.14349e95	−1.12640
$156$	2.97489e94	0.118182
$157$	−4.90088e95	−1.47448	−0.737240	−	0.675631i	$-0.763871\pi$
$157$	−4.90088e95	−1.47448	−0.737240	+	0.675631i	$0.763871\pi$
$158$	−3.99883e95	−0.912745
$159$	2.85628e95	0.495479
$160$	−8.67887e94	−0.114616
$161$	−1.32349e95	−0.133289
$162$	−1.87627e95	−0.144342
$163$	2.57015e96	1.51285	0.756427	−	0.654078i	$-0.226943\pi$
$163$	2.57015e96	1.51285	0.756427	+	0.654078i	$0.226943\pi$
$164$	7.83047e95	0.353249
$165$	6.26404e95	0.216922
$166$	2.55125e96	0.679284
$167$	4.74188e96	0.972264	0.486132	−	0.873885i	$-0.338407\pi$
$167$	4.74188e96	0.972264	0.486132	+	0.873885i	$0.338407\pi$
$168$	−3.94289e95	−0.0623534
$169$	−6.63111e96	−0.810056
$170$	−1.83870e96	−0.173773
$171$	−1.92587e96	−0.141025
$172$	4.81287e96	0.273475
$173$	3.34845e97	1.47856	0.739279	−	0.673399i	$-0.235166\pi$
$173$	3.34845e97	1.47856	0.739279	+	0.673399i	$0.235166\pi$
$174$	1.00419e96	0.0345083
$175$	7.03785e96	0.188488
$176$	−7.37832e96	−0.154226
$177$	2.23923e96	0.0365815
$178$	−6.18912e97	−0.791332
$179$	3.75796e97	0.376569	0.188285	−	0.982114i	$-0.439707\pi$
$179$	3.75796e97	0.376569	0.188285	+	0.982114i	$0.439707\pi$
$180$	−2.90984e97	−0.228831
$181$	−1.49385e98	−0.923187	−0.461593	−	0.887092i	$-0.652722\pi$
$181$	−1.49385e98	−0.923187	−0.461593	+	0.887092i	$0.652722\pi$
$182$	−2.06083e97	−0.100216
$183$	−1.08187e98	−0.414528
$184$	−4.79387e97	−0.144914
$185$	−1.20674e98	−0.288167
$186$	−3.52727e98	−0.666233
$187$	−1.56317e98	−0.233828
$188$	−3.52698e98	−0.418347
$189$	−3.19478e98	−0.300851
$190$	−1.22364e98	−0.0915952
$191$	1.58558e99	0.944576	0.472288	−	0.881444i	$-0.343428\pi$
$191$	1.58558e99	0.944576	0.472288	+	0.881444i	$0.343428\pi$
$192$	−1.42817e98	−0.0677918
$193$	3.46556e99	1.31229	0.656147	−	0.754633i	$-0.272185\pi$
$193$	3.46556e99	1.31229	0.656147	+	0.754633i	$0.272185\pi$
$194$	−2.75133e98	−0.0832083
$195$	6.33731e98	0.153250
$196$	−2.30977e99	−0.447125
$197$	1.20705e100	1.87260	0.936300	−	0.351201i	$-0.114227\pi$
$197$	1.20705e100	1.87260	0.936300	+	0.351201i	$0.114227\pi$
$198$	−2.47380e99	−0.307913
$199$	1.03786e100	1.03760	0.518800	−	0.854896i	$-0.326379\pi$
$199$	1.03786e100	1.03760	0.518800	+	0.854896i	$0.326379\pi$
$200$	2.54921e99	0.204928
$201$	4.38840e99	0.283973
$202$	−2.41329e100	−1.25842
$203$	−6.95643e98	−0.0292623
$204$	−3.02572e99	−0.102782
$205$	1.66810e100	0.458067
$206$	−5.42408e100	−1.20532
$207$	−1.60728e100	−0.289323
$208$	−7.46463e99	−0.108957
$209$	−1.04028e100	−0.123250
$210$	−8.39941e99	−0.0808554
$211$	3.40477e100	0.266564	0.133282	−	0.991078i	$-0.457448\pi$
$211$	3.40477e100	0.266564	0.133282	+	0.991078i	$0.457448\pi$
$212$	−7.16701e100	−0.456802
$213$	3.89887e100	0.202500
$214$	−2.42555e101	−1.02757
$215$	1.02527e101	0.354622
$216$	−1.15720e101	−0.327091
$217$	2.44349e101	0.564953
$218$	−5.22805e101	−0.989651
$219$	3.62947e101	0.563021
$220$	−1.57178e101	−0.199989
$221$	−1.58145e101	−0.165193
$222$	−1.98578e101	−0.170442
$223$	1.66553e102	1.17568	0.587841	−	0.808977i	$-0.299978\pi$
$223$	1.66553e102	1.17568	0.587841	+	0.808977i	$0.299978\pi$
$224$	9.89355e100	0.0574861
$225$	8.54698e101	0.409141
$226$	1.93718e102	0.764632
$227$	2.74644e102	0.894634	0.447317	−	0.894375i	$-0.352380\pi$
$227$	2.74644e102	0.894634	0.447317	+	0.894375i	$0.352380\pi$
$228$	−2.01359e101	−0.0541759
$229$	5.03261e102	1.11931	0.559655	−	0.828726i	$-0.310934\pi$
$229$	5.03261e102	1.11931	0.559655	+	0.828726i	$0.310934\pi$
$230$	−1.02122e102	−0.187914
$231$	−7.14074e101	−0.108798
$232$	−2.51973e101	−0.0318146
$233$	−1.42438e103	−1.49157	−0.745784	−	0.666187i	$-0.767925\pi$
$233$	−1.42438e103	−1.49157	−0.745784	+	0.666187i	$0.767925\pi$
$234$	−2.50273e102	−0.217533
$235$	−7.51342e102	−0.542482
$236$	−5.61871e101	−0.0337260
$237$	−1.40180e103	−0.700054
$238$	2.09604e102	0.0871570
$239$	−9.52589e102	−0.330063	−0.165032	−	0.986288i	$-0.552773\pi$
$239$	−9.52589e102	−0.330063	−0.165032	+	0.986288i	$0.552773\pi$
$240$	−3.04239e102	−0.0879075
$241$	−2.68017e102	−0.0646280	−0.0323140	−	0.999478i	$-0.510288\pi$
$241$	−2.68017e102	−0.0646280	−0.0323140	+	0.999478i	$0.510288\pi$
$242$	2.17494e103	0.438004
$243$	−6.15424e103	−1.03586
$244$	2.71465e103	0.382170
$245$	−4.92043e103	−0.579800
$246$	2.74498e103	0.270934
$247$	−1.05245e103	−0.0870727
$248$	8.85069e103	0.614227
$249$	8.94346e103	0.520995
$250$	1.47995e104	0.724198
$251$	3.06179e103	0.125941	0.0629707	−	0.998015i	$-0.479943\pi$
$251$	3.06179e103	0.125941	0.0629707	+	0.998015i	$0.479943\pi$
$252$	3.31710e103	0.114772
$253$	−8.68190e103	−0.252855
$254$	3.88017e104	0.951883
$255$	−6.44560e103	−0.133280
$256$	3.58359e103	0.0625000
$257$	−3.27657e104	−0.482313	−0.241156	−	0.970486i	$-0.577527\pi$
$257$	−3.27657e104	−0.482313	−0.241156	+	0.970486i	$0.577527\pi$
$258$	1.68716e104	0.209749
$259$	1.37563e104	0.144532
$260$	−1.59017e104	−0.141287
$261$	−8.44811e103	−0.0635181
$262$	−1.21035e104	−0.0770555
$263$	1.65003e105	0.890056	0.445028	−	0.895517i	$-0.353194\pi$
$263$	1.65003e105	0.890056	0.445028	+	0.895517i	$0.353194\pi$
$264$	−2.58648e104	−0.118287
$265$	−1.52677e105	−0.592348
$266$	1.39490e104	0.0459401
$267$	−2.16960e105	−0.606933
$268$	−1.10114e105	−0.261807
$269$	−7.09618e105	−1.43483	−0.717415	−	0.696646i	$-0.754675\pi$
$269$	−7.09618e105	−1.43483	−0.717415	+	0.696646i	$0.754675\pi$
$270$	−2.46514e105	−0.424148
$271$	2.75466e105	0.403557	0.201778	−	0.979431i	$-0.435328\pi$
$271$	2.75466e105	0.403557	0.201778	+	0.979431i	$0.435328\pi$
$272$	7.59218e104	0.0947587
$273$	−7.22427e104	−0.0768632
$274$	−6.17889e105	−0.560739
$275$	4.61674e105	0.357572
$276$	−1.68050e105	−0.111146
$277$	3.90215e105	0.220513	0.110256	−	0.993903i	$-0.464833\pi$
$277$	3.90215e105	0.220513	0.110256	+	0.993903i	$0.464833\pi$
$278$	−1.18955e106	−0.574690
$279$	2.96745e106	1.22631
$280$	2.10759e105	0.0745439
$281$	6.04182e106	1.82997	0.914983	−	0.403491i	$-0.132203\pi$
$281$	6.04182e106	1.82997	0.914983	+	0.403491i	$0.132203\pi$
$282$	−1.23639e106	−0.320863
$283$	6.83233e106	1.52005	0.760027	−	0.649892i	$-0.225186\pi$
$283$	6.83233e106	1.52005	0.760027	+	0.649892i	$0.225186\pi$
$284$	−9.78309e105	−0.186693
$285$	−4.28950e105	−0.0702514
$286$	−1.35188e106	−0.190114
$287$	−1.90156e106	−0.229746
$288$	1.20150e106	0.124782
$289$	−9.58735e106	−0.856332
$290$	−5.36769e105	−0.0412548
$291$	−9.64482e105	−0.0638189
$292$	−9.10712e106	−0.519071
$293$	−4.95573e106	−0.243426	−0.121713	−	0.992565i	$-0.538839\pi$
$293$	−4.95573e106	−0.243426	−0.121713	+	0.992565i	$0.538839\pi$
$294$	−8.09693e106	−0.342935
$295$	−1.19694e106	−0.0437334
$296$	4.98275e106	0.157138
$297$	−2.09573e107	−0.570730
$298$	5.10303e106	0.120066
$299$	−8.78346e106	−0.178636
$300$	8.93631e106	0.157175
$301$	−1.16877e107	−0.177863
$302$	3.14582e107	0.414411
$303$	−8.45981e107	−0.965176
$304$	5.05254e106	0.0499469
$305$	5.78293e107	0.495570
$306$	2.54550e107	0.189187
$307$	1.81673e107	0.117158	0.0585788	−	0.998283i	$-0.481343\pi$
$307$	1.81673e107	0.117158	0.0585788	+	0.998283i	$0.481343\pi$
$308$	1.79176e107	0.100305
$309$	−1.90142e108	−0.924452
$310$	1.88543e108	0.796485
$311$	8.21224e107	0.301568	0.150784	−	0.988567i	$-0.451820\pi$
$311$	8.21224e107	0.301568	0.150784	+	0.988567i	$0.451820\pi$
$312$	−2.61674e107	−0.0835671
$313$	3.06511e108	0.851663	0.425831	−	0.904802i	$-0.359982\pi$
$313$	3.06511e108	0.851663	0.425831	+	0.904802i	$0.359982\pi$
$314$	4.31086e108	1.04262
$315$	7.06631e107	0.148828
$316$	3.51741e108	0.645408
$317$	−3.79659e108	−0.607177	−0.303588	−	0.952803i	$-0.598185\pi$
$317$	−3.79659e108	−0.607177	−0.303588	+	0.952803i	$0.598185\pi$
$318$	−2.51241e108	−0.350357
$319$	−4.56333e107	−0.0555121
$320$	7.63401e107	0.0810455
$321$	−8.50279e108	−0.788120
$322$	1.16415e108	0.0942494
$323$	1.07043e108	0.0757265
$324$	1.65039e108	0.102065
$325$	4.67074e108	0.252615
$326$	−2.26072e109	−1.06975
$327$	−1.83270e109	−0.759040
$328$	−6.88776e108	−0.249785
$329$	8.56498e108	0.272085
$330$	−5.50990e108	−0.153387
$331$	−2.59813e109	−0.634080	−0.317040	−	0.948412i	$-0.602689\pi$
$331$	−2.59813e109	−0.634080	−0.317040	+	0.948412i	$0.602689\pi$
$332$	−2.24411e109	−0.480327
$333$	1.67061e109	0.313727
$334$	−4.17100e109	−0.687495
$335$	−2.34573e109	−0.339492
$336$	3.46820e108	0.0440905
$337$	1.45980e110	1.63077	0.815383	−	0.578923i	$-0.196527\pi$
$337$	1.45980e110	1.63077	0.815383	+	0.578923i	$0.196527\pi$
$338$	5.83279e109	0.572796
$339$	6.79081e109	0.586455
$340$	1.61734e109	0.122876
$341$	1.60290e110	1.07174
$342$	1.69401e109	0.0997196
$343$	1.18815e110	0.615993
$344$	−4.23345e109	−0.193376
$345$	−3.57991e109	−0.144126
$346$	−2.94533e110	−1.04550
$347$	1.78209e110	0.557953	0.278977	−	0.960298i	$-0.410005\pi$
$347$	1.78209e110	0.557953	0.278977	+	0.960298i	$0.410005\pi$
$348$	−8.83294e108	−0.0244010
$349$	−1.03854e110	−0.253231	−0.126616	−	0.991952i	$-0.540411\pi$
$349$	−1.03854e110	−0.253231	−0.126616	+	0.991952i	$0.540411\pi$
$350$	−6.19056e109	−0.133281
$351$	−2.12025e110	−0.403206
$352$	6.49004e109	0.109054
$353$	−3.68925e110	−0.547946	−0.273973	−	0.961737i	$-0.588338\pi$
$353$	−3.68925e110	−0.547946	−0.273973	+	0.961737i	$0.588338\pi$
$354$	−1.96965e109	−0.0258670
$355$	−2.08406e110	−0.242090
$356$	5.44400e110	0.559556
$357$	7.34771e109	0.0668474
$358$	−3.30553e110	−0.266275
$359$	−1.21926e111	−0.869939	−0.434970	−	0.900445i	$-0.643241\pi$
$359$	−1.21926e111	−0.869939	−0.434970	+	0.900445i	$0.643241\pi$
$360$	2.55952e110	0.161808
$361$	−1.71346e111	−0.960085
$362$	1.31401e111	0.652791
$363$	7.62427e110	0.335939
$364$	1.81272e110	0.0708633
$365$	−1.94006e111	−0.673094
$366$	9.51624e110	0.293115
$367$	−4.80519e110	−0.131443	−0.0657215	−	0.997838i	$-0.520935\pi$
$367$	−4.80519e110	−0.131443	−0.0657215	+	0.997838i	$0.520935\pi$
$368$	4.21673e110	0.102470
$369$	−2.30932e111	−0.498698
$370$	1.06146e111	0.203765
$371$	1.74045e111	0.297096
$372$	3.10262e111	0.471098
$373$	3.28592e111	0.443938	0.221969	−	0.975054i	$-0.428752\pi$
$373$	3.28592e111	0.443938	0.221969	+	0.975054i	$0.428752\pi$
$374$	1.37498e111	0.165341
$375$	5.18800e111	0.555443
$376$	3.10237e111	0.295816
$377$	−4.61671e110	−0.0392179
$378$	2.81016e111	0.212734
$379$	1.58160e112	1.06731	0.533657	−	0.845701i	$-0.320817\pi$
$379$	1.58160e112	1.06731	0.533657	+	0.845701i	$0.320817\pi$
$380$	1.07633e111	0.0647676
$381$	1.36020e112	0.730073
$382$	−1.39469e112	−0.667916
$383$	−3.34578e112	−1.43005	−0.715024	−	0.699100i	$-0.753584\pi$
$383$	−3.34578e112	−1.43005	−0.715024	+	0.699100i	$0.753584\pi$
$384$	1.25623e111	0.0479361
$385$	3.81694e111	0.130069
$386$	−3.04834e112	−0.927932
$387$	−1.41939e112	−0.386077
$388$	2.42009e111	0.0588372
$389$	−5.08854e112	−1.10608	−0.553038	−	0.833156i	$-0.686532\pi$
$389$	−5.08854e112	−1.10608	−0.553038	+	0.833156i	$0.686532\pi$
$390$	−5.57436e111	−0.108364
$391$	8.93355e111	0.155358
$392$	2.03169e112	0.316165
$393$	−4.24289e111	−0.0590997
$394$	−1.06173e113	−1.32413
$395$	7.49302e112	0.836919
$396$	2.17598e112	0.217728
$397$	3.54813e112	0.318135	0.159068	−	0.987268i	$-0.449151\pi$
$397$	3.54813e112	0.318135	0.159068	+	0.987268i	$0.449151\pi$
$398$	−9.12911e112	−0.733694
$399$	4.88985e111	0.0352350
$400$	−2.24231e112	−0.144906
$401$	2.25631e113	1.30803	0.654016	−	0.756481i	$-0.273083\pi$
$401$	2.25631e113	1.30803	0.654016	+	0.756481i	$0.273083\pi$
$402$	−3.86008e112	−0.200800
$403$	1.62165e113	0.757159
$404$	2.12275e113	0.889834
$405$	3.51576e112	0.132351
$406$	6.11894e111	0.0206916
$407$	9.02398e112	0.274184
$408$	2.66145e112	0.0726778
$409$	−1.02892e113	−0.252590	−0.126295	−	0.991993i	$-0.540309\pi$
$409$	−1.02892e113	−0.252590	−0.126295	+	0.991993i	$0.540309\pi$
$410$	−1.46728e113	−0.323902
$411$	−2.16602e113	−0.430074
$412$	4.77107e113	0.852290
$413$	1.36446e112	0.0219347
$414$	1.41378e113	0.204582
$415$	−4.78055e113	−0.622853
$416$	6.56596e112	0.0770439
$417$	−4.16998e113	−0.440774
$418$	9.15037e112	0.0871506
$419$	−1.89388e114	−1.62571	−0.812855	−	0.582466i	$-0.802088\pi$
$419$	−1.89388e114	−1.62571	−0.812855	+	0.582466i	$0.802088\pi$
$420$	7.38819e112	0.0571734
$421$	−2.53620e112	−0.0176975	−0.00884877	−	0.999961i	$-0.502817\pi$
$421$	−2.53620e112	−0.0176975	−0.00884877	+	0.999961i	$0.502817\pi$
$422$	−2.99487e113	−0.188489
$423$	1.04016e114	0.590600
$424$	6.30417e113	0.323008
$425$	−4.75056e113	−0.219698
$426$	−3.42948e113	−0.143189
$427$	−6.59230e113	−0.248556
$428$	2.13353e114	0.726600
$429$	−4.73903e113	−0.145813
$430$	−9.01838e113	−0.250756
$431$	−4.26293e114	−1.07139	−0.535695	−	0.844412i	$-0.679950\pi$
$431$	−4.26293e114	−1.07139	−0.535695	+	0.844412i	$0.679950\pi$
$432$	1.01788e114	0.231288
$433$	2.41130e113	0.0495482	0.0247741	−	0.999693i	$-0.492113\pi$
$433$	2.41130e113	0.0495482	0.0247741	+	0.999693i	$0.492113\pi$
$434$	−2.14932e114	−0.399482
$435$	−1.88165e113	−0.0316415
$436$	4.59864e114	0.699789
$437$	5.94521e113	0.0818888
$438$	−3.19252e114	−0.398116
$439$	1.43906e115	1.62507	0.812537	−	0.582910i	$-0.198086\pi$
$439$	1.43906e115	1.62507	0.812537	+	0.582910i	$0.198086\pi$
$440$	1.38255e114	0.141413
$441$	6.81185e114	0.631228
$442$	1.39106e114	0.116809
$443$	1.24905e115	0.950646	0.475323	−	0.879811i	$-0.342331\pi$
$443$	1.24905e115	0.950646	0.475323	+	0.879811i	$0.342331\pi$
$444$	1.74671e114	0.120521
$445$	1.15972e115	0.725592
$446$	−1.46501e115	−0.831332
$447$	1.78888e114	0.0920879
$448$	−8.70245e113	−0.0406488
$449$	−2.79216e115	−1.18365	−0.591827	−	0.806065i	$-0.701593\pi$
$449$	−2.79216e115	−1.18365	−0.591827	+	0.806065i	$0.701593\pi$
$450$	−7.51801e114	−0.289307
$451$	−1.24740e115	−0.435840
$452$	−1.70396e115	−0.540677
$453$	1.10277e115	0.317844
$454$	−2.41580e115	−0.632602
$455$	3.86159e114	0.0918904
$456$	1.77118e114	0.0383081
$457$	−3.76927e115	−0.741144	−0.370572	−	0.928804i	$-0.620838\pi$
$457$	−3.76927e115	−0.741144	−0.370572	+	0.928804i	$0.620838\pi$
$458$	−4.42673e115	−0.791471
$459$	2.15648e115	0.350666
$460$	8.98277e114	0.132875
$461$	−4.02304e115	−0.541457	−0.270728	−	0.962656i	$-0.587264\pi$
$461$	−4.02304e115	−0.541457	−0.270728	+	0.962656i	$0.587264\pi$
$462$	6.28106e114	0.0769320
$463$	8.67698e114	0.0967376	0.0483688	−	0.998830i	$-0.484598\pi$
$463$	8.67698e114	0.0967376	0.0483688	+	0.998830i	$0.484598\pi$
$464$	2.21637e114	0.0224963
$465$	6.60942e115	0.610886
$466$	1.25290e116	1.05470
$467$	−4.99482e115	−0.383033	−0.191516	−	0.981489i	$-0.561341\pi$
$467$	−4.99482e115	−0.383033	−0.191516	+	0.981489i	$0.561341\pi$
$468$	2.20143e115	0.153819
$469$	2.67404e115	0.170274
$470$	6.60887e115	0.383593
$471$	1.51118e116	0.799662
$472$	4.94227e114	0.0238479
$473$	−7.66696e115	−0.337414
$474$	1.23303e116	0.495013
$475$	−3.16146e115	−0.115802
$476$	−1.84370e115	−0.0616293
$477$	2.11366e116	0.644889
$478$	8.37906e115	0.233390
$479$	−5.93364e116	−1.50913	−0.754564	−	0.656227i	$-0.772152\pi$
$479$	−5.93364e116	−1.50913	−0.754564	+	0.656227i	$0.772152\pi$
$480$	2.67612e115	0.0621600
$481$	9.12954e115	0.193704
$482$	2.35750e115	0.0456989
$483$	4.08095e115	0.0722871
$484$	−1.91309e116	−0.309716
$485$	5.15545e115	0.0762958
$486$	5.41333e116	0.732464
$487$	−2.82011e116	−0.348945	−0.174472	−	0.984662i	$-0.555822\pi$
$487$	−2.82011e116	−0.348945	−0.174472	+	0.984662i	$0.555822\pi$
$488$	−2.38783e116	−0.270235
$489$	−7.92501e116	−0.820473
$490$	4.32805e116	0.409981
$491$	−1.55288e117	−1.34615	−0.673073	−	0.739576i	$-0.735026\pi$
$491$	−1.55288e117	−1.34615	−0.673073	+	0.739576i	$0.735026\pi$
$492$	−2.41451e116	−0.191579
$493$	4.69560e115	0.0341075
$494$	9.25741e115	0.0615697
$495$	4.63541e116	0.282333
$496$	−7.78515e116	−0.434324
$497$	2.37574e116	0.121422
$498$	−7.86675e116	−0.368399
$499$	3.64060e117	1.56243	0.781213	−	0.624264i	$-0.214601\pi$
$499$	3.64060e117	1.56243	0.781213	+	0.624264i	$0.214601\pi$
$500$	−1.30178e117	−0.512086
$501$	−1.46215e117	−0.527293
$502$	−2.69318e116	−0.0890540
$503$	1.85863e116	0.0563617	0.0281809	−	0.999603i	$-0.491029\pi$
$503$	1.85863e116	0.0563617	0.0281809	+	0.999603i	$0.491029\pi$
$504$	−2.91775e116	−0.0811559
$505$	4.52202e117	1.15387
$506$	7.63668e116	0.178796
$507$	2.04469e117	0.439321
$508$	−3.41303e117	−0.673083
$509$	2.26271e117	0.409644	0.204822	−	0.978799i	$-0.434339\pi$
$509$	2.26271e117	0.409644	0.204822	+	0.978799i	$0.434339\pi$
$510$	5.66961e116	0.0942433
$511$	2.21159e117	0.337594
$512$	−3.15216e116	−0.0441942
$513$	1.43512e117	0.184834
$514$	2.88210e117	0.341047
$515$	1.01637e118	1.10519
$516$	−1.48404e117	−0.148315
$517$	5.61852e117	0.516159
$518$	−1.21002e117	−0.102199
$519$	−1.03249e118	−0.801873
$520$	1.39873e117	0.0999049
$521$	−1.50142e118	−0.986420	−0.493210	−	0.869910i	$-0.664177\pi$
$521$	−1.50142e118	−0.986420	−0.493210	+	0.869910i	$0.664177\pi$
$522$	7.43104e116	0.0449141
$523$	−2.40900e118	−1.33972	−0.669858	−	0.742489i	$-0.733645\pi$
$523$	−2.40900e118	−1.33972	−0.669858	+	0.742489i	$0.733645\pi$
$524$	1.06463e117	0.0544864
$525$	−2.17011e117	−0.102224
$526$	−1.45138e118	−0.629365
$527$	−1.64936e118	−0.658496
$528$	2.27509e117	0.0836419
$529$	−2.45722e118	−0.831999
$530$	1.34296e118	0.418853
$531$	1.65704e117	0.0476125
$532$	−1.22697e117	−0.0324846
$533$	−1.26199e118	−0.307910
$534$	1.90840e118	0.429166
$535$	4.54500e118	0.942202
$536$	9.68576e117	0.185125
$537$	−1.15876e118	−0.204227
$538$	6.24187e118	1.01458
$539$	3.67949e118	0.551666
$540$	2.16836e118	0.299918
$541$	−5.50079e117	−0.0702011	−0.0351006	−	0.999384i	$-0.511175\pi$
$541$	−5.50079e117	−0.0702011	−0.0351006	+	0.999384i	$0.511175\pi$
$542$	−2.42303e118	−0.285358
$543$	4.60627e118	0.500676
$544$	−6.67815e117	−0.0670046
$545$	9.79634e118	0.907436
$546$	6.35453e117	0.0543505
$547$	−1.30991e119	−1.03465	−0.517325	−	0.855789i	$-0.673072\pi$
$547$	−1.30991e119	−1.03465	−0.517325	+	0.855789i	$0.673072\pi$
$548$	5.43501e118	0.396502
$549$	−8.00589e118	−0.539527
$550$	−4.06093e118	−0.252841
$551$	3.12489e117	0.0179779
$552$	1.47818e118	0.0785919
$553$	−8.54173e118	−0.419761
$554$	−3.43236e118	−0.155926
$555$	3.72097e118	0.156283
$556$	1.04634e119	0.406367
$557$	3.67961e119	1.32160	0.660802	−	0.750560i	$-0.270216\pi$
$557$	3.67961e119	1.32160	0.660802	+	0.750560i	$0.270216\pi$
$558$	−2.61020e119	−0.867133
$559$	−7.75664e118	−0.238375
$560$	−1.85386e118	−0.0527105
$561$	4.82001e118	0.126813
$562$	−5.31445e119	−1.29398
$563$	−5.43587e118	−0.122505	−0.0612525	−	0.998122i	$-0.519509\pi$
$563$	−5.43587e118	−0.122505	−0.0612525	+	0.998122i	$0.519509\pi$
$564$	1.08754e119	0.226884
$565$	−3.62989e119	−0.701111
$566$	−6.00978e119	−1.07484
$567$	−4.00782e118	−0.0663813
$568$	8.60530e118	0.132012
$569$	6.38919e119	0.907951	0.453976	−	0.891014i	$-0.350005\pi$
$569$	6.38919e119	0.907951	0.453976	+	0.891014i	$0.350005\pi$
$570$	3.77308e118	0.0496752
$571$	4.00620e119	0.488722	0.244361	−	0.969684i	$-0.421422\pi$
$571$	4.00620e119	0.488722	0.244361	+	0.969684i	$0.421422\pi$
$572$	1.18912e119	0.134431
$573$	−4.88911e119	−0.512276
$574$	1.67263e119	0.162455
$575$	−2.63848e119	−0.237576
$576$	−1.05685e119	−0.0882342
$577$	1.14781e120	0.888635	0.444318	−	0.895869i	$-0.353446\pi$
$577$	1.14781e120	0.888635	0.444318	+	0.895869i	$0.353446\pi$
$578$	8.43312e119	0.605518
$579$	−1.06860e120	−0.711702
$580$	4.72147e118	0.0291716
$581$	5.44962e119	0.312396
$582$	8.48367e118	0.0451268
$583$	1.14171e120	0.563605
$584$	8.01071e119	0.367039
$585$	4.68963e119	0.199461
$586$	4.35911e119	0.172128
$587$	3.25913e120	1.19493	0.597467	−	0.801893i	$-0.296174\pi$
$587$	3.25913e120	1.19493	0.597467	+	0.801893i	$0.296174\pi$
$588$	7.12214e119	0.242492
$589$	−1.09764e120	−0.347091
$590$	1.05284e119	0.0309242
$591$	−3.72193e120	−1.01558
$592$	−4.38288e119	−0.111113
$593$	−3.95172e120	−0.930908	−0.465454	−	0.885072i	$-0.654109\pi$
$593$	−3.95172e120	−0.930908	−0.465454	+	0.885072i	$0.654109\pi$
$594$	1.84343e120	0.403567
$595$	−3.92757e119	−0.0799165
$596$	−4.48867e119	−0.0848996
$597$	−3.20022e120	−0.562726
$598$	7.72601e119	0.126315
$599$	−5.10729e120	−0.776468	−0.388234	−	0.921561i	$-0.626915\pi$
$599$	−5.10729e120	−0.776468	−0.388234	+	0.921561i	$0.626915\pi$
$600$	−7.86047e119	−0.111140
$601$	−1.03717e121	−1.36399	−0.681995	−	0.731357i	$-0.738888\pi$
$601$	−1.03717e121	−1.36399	−0.681995	+	0.731357i	$0.738888\pi$
$602$	1.02806e120	0.125768
$603$	3.24743e120	0.369604
$604$	−2.76709e120	−0.293033
$605$	−4.07540e120	−0.401617
$606$	7.44133e120	0.682482
$607$	4.36069e120	0.372260	0.186130	−	0.982525i	$-0.440405\pi$
$607$	4.36069e120	0.372260	0.186130	+	0.982525i	$0.440405\pi$
$608$	−4.44426e119	−0.0353178
$609$	2.14501e119	0.0158700
$610$	−5.08672e120	−0.350421
$611$	5.68424e120	0.364653
$612$	−2.23905e120	−0.133775
$613$	1.98226e121	1.10314	0.551568	−	0.834130i	$-0.314030\pi$
$613$	1.98226e121	1.10314	0.551568	+	0.834130i	$0.314030\pi$
$614$	−1.59801e120	−0.0828429
$615$	−5.14356e120	−0.248426
$616$	−1.57605e120	−0.0709267
$617$	3.24628e121	1.36139	0.680694	−	0.732568i	$-0.261678\pi$
$617$	3.24628e121	1.36139	0.680694	+	0.732568i	$0.261678\pi$
$618$	1.67251e121	0.653687
$619$	2.97143e121	1.08249	0.541244	−	0.840866i	$-0.317954\pi$
$619$	2.97143e121	1.08249	0.541244	+	0.840866i	$0.317954\pi$
$620$	−1.65845e121	−0.563200
$621$	1.19772e121	0.379201
$622$	−7.22357e120	−0.213241
$623$	−1.32203e121	−0.363925
$624$	2.30171e120	0.0590909
$625$	−3.52518e120	−0.0844113
$626$	−2.69610e121	−0.602217
$627$	3.20768e120	0.0668425
$628$	−3.79187e121	−0.737240
$629$	−9.28554e120	−0.168463
$630$	−6.21559e120	−0.105237
$631$	2.22809e120	0.0352091	0.0176046	−	0.999845i	$-0.494396\pi$
$631$	2.22809e120	0.0352091	0.0176046	+	0.999845i	$0.494396\pi$
$632$	−3.09394e121	−0.456372
$633$	−1.04986e121	−0.144567
$634$	3.33951e121	0.429339
$635$	−7.27067e121	−0.872806
$636$	2.20994e121	0.247740
$637$	3.72253e121	0.389738
$638$	4.01395e120	0.0392530
$639$	2.88518e121	0.263563
$640$	−6.71495e120	−0.0573078
$641$	−1.10191e122	−0.878661	−0.439330	−	0.898326i	$-0.644784\pi$
$641$	−1.10191e122	−0.878661	−0.439330	+	0.898326i	$0.644784\pi$
$642$	7.47913e121	0.557285
$643$	3.31211e121	0.230636	0.115318	−	0.993329i	$-0.463211\pi$
$643$	3.31211e121	0.230636	0.115318	+	0.993329i	$0.463211\pi$
$644$	−1.02400e121	−0.0666444
$645$	−3.16141e121	−0.192324
$646$	−9.41559e120	−0.0535468
$647$	−2.05699e122	−1.09369	−0.546846	−	0.837233i	$-0.684172\pi$
$647$	−2.05699e122	−1.09369	−0.546846	+	0.837233i	$0.684172\pi$
$648$	−1.45169e121	−0.0721710
$649$	8.95066e120	0.0416113
$650$	−4.10843e121	−0.178626
$651$	−7.53446e121	−0.306393
$652$	1.98855e122	0.756427
$653$	2.28387e120	0.00812735	0.00406367	−	0.999992i	$-0.498706\pi$
$653$	2.28387e120	0.00812735	0.00406367	+	0.999992i	$0.498706\pi$
$654$	1.61206e122	0.536722
$655$	2.26795e121	0.0706541
$656$	6.05853e121	0.176624
$657$	2.68582e122	0.732797
$658$	−7.53384e121	−0.192393
$659$	6.74143e122	1.61152	0.805761	−	0.592241i	$-0.201757\pi$
$659$	6.74143e122	1.61152	0.805761	+	0.592241i	$0.201757\pi$
$660$	4.84656e121	0.108461
$661$	−3.29987e122	−0.691407	−0.345704	−	0.938344i	$-0.612360\pi$
$661$	−3.29987e122	−0.691407	−0.345704	+	0.938344i	$0.612360\pi$
$662$	2.28534e122	0.448362
$663$	4.87639e121	0.0895900
$664$	1.97394e122	0.339642
$665$	−2.61377e121	−0.0421236
$666$	−1.46949e122	−0.221838
$667$	2.60796e121	0.0368830
$668$	3.66885e122	0.486132
$669$	−5.13562e122	−0.637613
$670$	2.06333e122	0.240057
$671$	−4.32446e122	−0.471523
$672$	−3.05066e121	−0.0311767
$673$	−7.79724e122	−0.746940	−0.373470	−	0.927642i	$-0.621832\pi$
$673$	−7.79724e122	−0.746940	−0.373470	+	0.927642i	$0.621832\pi$
$674$	−1.28405e123	−1.15313
$675$	−6.36905e122	−0.536242
$676$	−5.13058e122	−0.405028
$677$	1.09917e123	0.813688	0.406844	−	0.913498i	$-0.366629\pi$
$677$	1.09917e123	0.813688	0.406844	+	0.913498i	$0.366629\pi$
$678$	−5.97326e122	−0.414687
$679$	−5.87699e121	−0.0382666
$680$	−1.42263e122	−0.0868867
$681$	−8.46861e122	−0.485191
$682$	−1.40992e123	−0.757837
$683$	2.19920e123	1.10908	0.554541	−	0.832156i	$-0.312894\pi$
$683$	2.19920e123	1.10908	0.554541	+	0.832156i	$0.312894\pi$
$684$	−1.49007e122	−0.0705124
$685$	1.15780e123	0.514156
$686$	−1.04510e123	−0.435573
$687$	−1.55180e123	−0.607040
$688$	3.72378e122	0.136737
$689$	1.15507e123	0.398173
$690$	3.14892e122	0.101912
$691$	3.35554e123	1.01969	0.509844	−	0.860267i	$-0.329703\pi$
$691$	3.35554e123	1.01969	0.509844	+	0.860267i	$0.329703\pi$
$692$	2.59074e123	0.739279
$693$	−5.28417e122	−0.141606
$694$	−1.56754e123	−0.394533
$695$	2.22898e123	0.526948
$696$	7.76953e121	0.0172541
$697$	1.28356e123	0.267787
$698$	9.13509e122	0.179061
$699$	4.39205e123	0.808929
$700$	5.44527e122	0.0942442
$701$	−1.94249e123	−0.315954	−0.157977	−	0.987443i	$-0.550497\pi$
$701$	−1.94249e123	−0.315954	−0.157977	+	0.987443i	$0.550497\pi$
$702$	1.86499e123	0.285110
$703$	−6.17946e122	−0.0887961
$704$	−5.70870e122	−0.0771128
$705$	2.31675e123	0.294207
$706$	3.24510e123	0.387456
$707$	−5.15492e123	−0.578732
$708$	1.73252e122	0.0182908
$709$	−1.16737e124	−1.15903	−0.579516	−	0.814961i	$-0.696758\pi$
$709$	−1.16737e124	−1.15903	−0.579516	+	0.814961i	$0.696758\pi$
$710$	1.83316e123	0.171184
$711$	−1.03733e124	−0.911153
$712$	−4.78860e123	−0.395666
$713$	−9.16060e123	−0.712081
$714$	−6.46312e122	−0.0472683
$715$	2.53315e123	0.174321
$716$	2.90758e123	0.188285
$717$	2.93729e123	0.179005
$718$	1.07247e124	0.615140
$719$	−1.74714e123	−0.0943236	−0.0471618	−	0.998887i	$-0.515018\pi$
$719$	−1.74714e123	−0.0943236	−0.0471618	+	0.998887i	$0.515018\pi$
$720$	−2.25138e123	−0.114416
$721$	−1.15862e124	−0.554313
$722$	1.50717e124	0.678883
$723$	8.26425e122	0.0350500
$724$	−1.15581e124	−0.461593
$725$	−1.38682e123	−0.0521576
$726$	−6.70638e123	−0.237545
$727$	−1.55581e124	−0.519049	−0.259525	−	0.965736i	$-0.583566\pi$
$727$	−1.55581e124	−0.519049	−0.259525	+	0.965736i	$0.583566\pi$
$728$	−1.59449e123	−0.0501079
$729$	1.20812e124	0.357653
$730$	1.70650e124	0.475950
$731$	7.88919e123	0.207313
$732$	−8.37058e123	−0.207264
$733$	7.77484e122	0.0181413	0.00907066	−	0.999959i	$-0.497113\pi$
$733$	7.77484e122	0.0181413	0.00907066	+	0.999959i	$0.497113\pi$
$734$	4.22669e123	0.0929442
$735$	1.51721e124	0.314446
$736$	−3.70907e123	−0.0724571
$737$	1.75413e124	0.323018
$738$	2.03130e124	0.352632
$739$	4.94872e124	0.809952	0.404976	−	0.914327i	$-0.367280\pi$
$739$	4.94872e124	0.809952	0.404976	+	0.914327i	$0.367280\pi$
$740$	−9.33670e123	−0.144083
$741$	3.24520e123	0.0472225
$742$	−1.53092e124	−0.210078
$743$	5.12556e124	0.663328	0.331664	−	0.943398i	$-0.392390\pi$
$743$	5.12556e124	0.663328	0.331664	+	0.943398i	$0.392390\pi$
$744$	−2.72910e124	−0.333117
$745$	−9.56208e123	−0.110092
$746$	−2.89032e124	−0.313912
$747$	6.61820e124	0.678099
$748$	−1.20944e124	−0.116914
$749$	−5.18111e124	−0.472567
$750$	−4.56341e124	−0.392758
$751$	2.33707e125	1.89817	0.949085	−	0.315019i	$-0.102011\pi$
$751$	2.33707e125	1.89817	0.949085	+	0.315019i	$0.102011\pi$
$752$	−2.72887e124	−0.209174
$753$	−9.44098e123	−0.0683024
$754$	4.06090e123	0.0277312
$755$	−5.89464e124	−0.379984
$756$	−2.47184e124	−0.150426
$757$	−2.24632e125	−1.29063	−0.645313	−	0.763918i	$-0.723273\pi$
$757$	−2.24632e125	−1.29063	−0.645313	+	0.763918i	$0.723273\pi$
$758$	−1.39119e125	−0.754704
$759$	2.67705e124	0.137132
$760$	−9.46747e123	−0.0457976
$761$	−4.15593e125	−1.89861	−0.949304	−	0.314360i	$-0.898210\pi$
$761$	−4.15593e125	−1.89861	−0.949304	+	0.314360i	$0.898210\pi$
$762$	−1.19644e125	−0.516239
$763$	−1.11674e125	−0.455130
$764$	1.22678e125	0.472288
$765$	−4.76977e124	−0.173470
$766$	2.94298e125	1.01120
$767$	9.05536e123	0.0293973
$768$	−1.10500e124	−0.0338959
$769$	7.51848e124	0.217939	0.108969	−	0.994045i	$-0.465245\pi$
$769$	7.51848e124	0.217939	0.108969	+	0.994045i	$0.465245\pi$
$770$	−3.35742e124	−0.0919726
$771$	1.01033e125	0.261575
$772$	2.68135e125	0.656147
$773$	2.09810e125	0.485310	0.242655	−	0.970113i	$-0.421982\pi$
$773$	2.09810e125	0.485310	0.242655	+	0.970113i	$0.421982\pi$
$774$	1.24851e125	0.272998
$775$	4.87130e125	1.00698
$776$	−2.12874e124	−0.0416042
$777$	−4.24175e124	−0.0783845
$778$	4.47592e125	0.782114
$779$	8.54198e124	0.141149
$780$	4.90325e124	0.0766248
$781$	1.55846e125	0.230343
$782$	−7.85803e124	−0.109855
$783$	6.29537e124	0.0832501
$784$	−1.78710e125	−0.223563
$785$	−8.07770e125	−0.956000
$786$	3.73208e124	0.0417898
$787$	−9.36024e124	−0.0991714	−0.0495857	−	0.998770i	$-0.515790\pi$
$787$	−9.36024e124	−0.0991714	−0.0495857	+	0.998770i	$0.515790\pi$
$788$	9.33911e125	0.936300
$789$	−5.08785e125	−0.482708
$790$	−6.59093e125	−0.591791
$791$	4.13793e125	0.351646
$792$	−1.91401e125	−0.153957
$793$	−4.37505e125	−0.333119
$794$	−3.12097e125	−0.224956
$795$	4.70776e125	0.321251
$796$	8.03005e125	0.518800
$797$	−1.44626e126	−0.884726	−0.442363	−	0.896836i	$-0.645860\pi$
$797$	−1.44626e126	−0.884726	−0.442363	+	0.896836i	$0.645860\pi$
$798$	−4.30115e124	−0.0249149
$799$	−5.78137e125	−0.317136
$800$	1.97236e125	0.102464
$801$	−1.60552e126	−0.789951
$802$	−1.98467e126	−0.924918
$803$	1.45077e126	0.640433
$804$	3.39536e125	0.141987
$805$	−2.18139e125	−0.0864197
$806$	−1.42642e126	−0.535392
$807$	2.18810e126	0.778158
$808$	−1.86719e126	−0.629208
$809$	−6.98055e124	−0.0222910	−0.0111455	−	0.999938i	$-0.503548\pi$
$809$	−6.98055e124	−0.0222910	−0.0111455	+	0.999938i	$0.503548\pi$
$810$	−3.09250e125	−0.0935861
$811$	3.32370e126	0.953267	0.476634	−	0.879102i	$-0.341857\pi$
$811$	3.32370e126	0.953267	0.476634	+	0.879102i	$0.341857\pi$
$812$	−5.38228e124	−0.0146312
$813$	−8.49397e125	−0.218863
$814$	−7.93758e125	−0.193877
$815$	4.23615e126	0.980880
$816$	−2.34104e125	−0.0513909
$817$	5.25019e125	0.109274
$818$	9.05045e125	0.178608
$819$	−5.34599e125	−0.100041
$820$	1.29063e126	0.229034
$821$	−5.14653e126	−0.866137	−0.433069	−	0.901361i	$-0.642569\pi$
$821$	−5.14653e126	−0.866137	−0.433069	+	0.901361i	$0.642569\pi$
$822$	1.90525e126	0.304108
$823$	1.24437e127	1.88390	0.941949	−	0.335756i	$-0.108992\pi$
$823$	1.24437e127	1.88390	0.941949	+	0.335756i	$0.108992\pi$
$824$	−4.19668e126	−0.602660
$825$	−1.42356e126	−0.193924
$826$	−1.20019e125	−0.0155102
$827$	6.20830e126	0.761172	0.380586	−	0.924745i	$-0.375722\pi$
$827$	6.20830e126	0.761172	0.380586	+	0.924745i	$0.375722\pi$
$828$	−1.24358e126	−0.144661
$829$	−5.44639e126	−0.601155	−0.300578	−	0.953757i	$-0.597179\pi$
$829$	−5.44639e126	−0.601155	−0.300578	+	0.953757i	$0.597179\pi$
$830$	4.20501e126	0.440423
$831$	−1.20322e126	−0.119592
$832$	−5.77548e125	−0.0544783
$833$	−3.78614e126	−0.338952
$834$	3.66796e126	0.311674
$835$	7.81564e126	0.630381
$836$	−8.04875e125	−0.0616248
$837$	−2.21129e127	−1.60727
$838$	1.66588e127	1.14955
$839$	9.56845e126	0.626897	0.313449	−	0.949605i	$-0.398516\pi$
$839$	9.56845e126	0.626897	0.313449	+	0.949605i	$0.398516\pi$
$840$	−6.49872e125	−0.0404277
$841$	−1.67917e127	−0.991903
$842$	2.23087e125	0.0125140
$843$	−1.86299e127	−0.992454
$844$	2.63431e126	0.133282
$845$	−1.09295e127	−0.525211
$846$	−9.14933e126	−0.417617
$847$	4.64579e126	0.201433
$848$	−5.54521e126	−0.228401
$849$	−2.10674e127	−0.824378
$850$	4.17863e126	0.155350
$851$	−5.15723e126	−0.182172
$852$	3.01660e126	0.101250
$853$	4.07674e126	0.130026	0.0650130	−	0.997884i	$-0.479291\pi$
$853$	4.07674e126	0.130026	0.0650130	+	0.997884i	$0.479291\pi$
$854$	5.79865e126	0.175756
$855$	−3.17424e126	−0.0914354
$856$	−1.87667e127	−0.513784
$857$	−3.53956e127	−0.921050	−0.460525	−	0.887647i	$-0.652339\pi$
$857$	−3.53956e127	−0.921050	−0.460525	+	0.887647i	$0.652339\pi$
$858$	4.16849e126	0.103106
$859$	6.45228e127	1.51709	0.758543	−	0.651623i	$-0.225911\pi$
$859$	6.45228e127	1.51709	0.758543	+	0.651623i	$0.225911\pi$
$860$	7.93265e126	0.177311
$861$	5.86345e126	0.124599
$862$	3.74972e127	0.757586
$863$	7.93055e127	1.52347	0.761735	−	0.647889i	$-0.224348\pi$
$863$	7.93055e127	1.52347	0.761735	+	0.647889i	$0.224348\pi$
$864$	−8.95338e126	−0.163546
$865$	5.51897e127	0.958644
$866$	−2.12100e126	−0.0350359
$867$	2.95624e127	0.464419
$868$	1.89056e127	0.282476
$869$	−5.60327e127	−0.796308
$870$	1.65512e126	0.0223739
$871$	1.77465e127	0.228204
$872$	−4.04501e127	−0.494826
$873$	−7.13721e126	−0.0830632
$874$	−5.22946e126	−0.0579041
$875$	3.16127e127	0.333051
$876$	2.80817e127	0.281510
$877$	6.22030e126	0.0593375	0.0296688	−	0.999560i	$-0.490555\pi$
$877$	6.22030e126	0.0593375	0.0296688	+	0.999560i	$0.490555\pi$
$878$	−1.26581e128	−1.14910
$879$	1.52809e127	0.132018
$880$	−1.21611e127	−0.0999943
$881$	−2.35799e128	−1.84540	−0.922700	−	0.385519i	$-0.874022\pi$
$881$	−2.35799e128	−1.84540	−0.922700	+	0.385519i	$0.874022\pi$
$882$	−5.99176e127	−0.446345
$883$	2.18292e128	1.54791	0.773957	−	0.633238i	$-0.218274\pi$
$883$	2.18292e128	1.54791	0.773957	+	0.633238i	$0.218274\pi$
$884$	−1.22359e127	−0.0825967
$885$	3.69073e126	0.0237181
$886$	−1.09868e128	−0.672209
$887$	−1.86746e128	−1.08786	−0.543930	−	0.839131i	$-0.683064\pi$
$887$	−1.86746e128	−1.08786	−0.543930	+	0.839131i	$0.683064\pi$
$888$	−1.53642e127	−0.0852211
$889$	8.28826e127	0.437761
$890$	−1.02010e128	−0.513071
$891$	−2.62908e127	−0.125929
$892$	1.28864e128	0.587841
$893$	−3.84746e127	−0.167161
$894$	−1.57351e127	−0.0651160
$895$	6.19392e127	0.244154
$896$	7.65476e126	0.0287431
$897$	2.70837e127	0.0968804
$898$	2.45601e128	0.836969
$899$	−4.81495e127	−0.156331
$900$	6.61291e127	0.204571
$901$	−1.17481e128	−0.346288
$902$	1.09723e128	0.308185
$903$	3.60387e127	0.0964612
$904$	1.49882e128	0.382316
$905$	−2.46219e128	−0.598561
$906$	−9.70008e127	−0.224749
$907$	7.50442e128	1.65730	0.828648	−	0.559769i	$-0.189110\pi$
$907$	7.50442e128	1.65730	0.828648	+	0.559769i	$0.189110\pi$
$908$	2.12496e128	0.447317
$909$	−6.26030e128	−1.25622
$910$	−3.39669e127	−0.0649763
$911$	−5.05217e128	−0.921358	−0.460679	−	0.887567i	$-0.652394\pi$
$911$	−5.05217e128	−0.921358	−0.460679	+	0.887567i	$0.652394\pi$
$912$	−1.55794e127	−0.0270879
$913$	3.57489e128	0.592630
$914$	3.31549e128	0.524068
$915$	−1.78316e128	−0.268765
$916$	3.89380e128	0.559655
$917$	−2.58537e127	−0.0354370
$918$	−1.89686e128	−0.247958
$919$	1.29999e129	1.62074	0.810371	−	0.585917i	$-0.199266\pi$
$919$	1.29999e129	1.62074	0.810371	+	0.585917i	$0.199266\pi$
$920$	−7.90133e127	−0.0939571
$921$	−5.60185e127	−0.0635386
$922$	3.53870e128	0.382868
$923$	1.57669e128	0.162731
$924$	−5.52488e127	−0.0543991
$925$	2.74244e128	0.257615
$926$	−7.63235e127	−0.0684038
$927$	−1.40706e129	−1.20322
$928$	−1.94954e127	−0.0159073
$929$	−1.69426e129	−1.31915	−0.659577	−	0.751637i	$-0.729264\pi$
$929$	−1.69426e129	−1.31915	−0.659577	+	0.751637i	$0.729264\pi$
$930$	−5.81371e128	−0.431961
$931$	−2.51965e128	−0.178660
$932$	−1.10206e129	−0.745784
$933$	−2.53223e128	−0.163551
$934$	4.39349e128	0.270845
$935$	−2.57644e128	−0.151605
$936$	−1.93640e128	−0.108766
$937$	1.57515e129	0.844595	0.422298	−	0.906457i	$-0.361224\pi$
$937$	1.57515e129	0.844595	0.422298	+	0.906457i	$0.361224\pi$
$938$	−2.35211e128	−0.120402
$939$	−9.45123e128	−0.461886
$940$	−5.81323e128	−0.271241
$941$	1.46784e129	0.653930	0.326965	−	0.945036i	$-0.393974\pi$
$941$	1.46784e129	0.653930	0.326965	+	0.945036i	$0.393974\pi$
$942$	−1.32925e129	−0.565446
$943$	7.12894e128	0.289578
$944$	−4.34727e127	−0.0168630
$945$	−5.26568e128	−0.195061
$946$	6.74393e128	0.238588
$947$	−5.37176e128	−0.181507	−0.0907533	−	0.995873i	$-0.528927\pi$
$947$	−5.37176e128	−0.181507	−0.0907533	+	0.995873i	$0.528927\pi$
$948$	−1.08459e129	−0.350027
$949$	1.46774e129	0.452450
$950$	2.78085e128	0.0818843
$951$	1.17067e129	0.329293
$952$	1.62173e128	0.0435785
$953$	3.70641e129	0.951509	0.475754	−	0.879578i	$-0.342175\pi$
$953$	3.70641e129	0.951509	0.475754	+	0.879578i	$0.342175\pi$
$954$	−1.85919e129	−0.456005
$955$	2.61338e129	0.612429
$956$	−7.37030e128	−0.165032
$957$	1.40710e128	0.0301061
$958$	5.21928e129	1.06711
$959$	−1.31985e129	−0.257878
$960$	−2.35394e128	−0.0439538
$961$	1.13092e130	2.01820
$962$	−8.03043e128	−0.136969
$963$	−6.29210e129	−1.02577
$964$	−2.07368e128	−0.0323140
$965$	5.71200e129	0.850844
$966$	−3.58964e128	−0.0511147
$967$	−2.80599e129	−0.381974	−0.190987	−	0.981593i	$-0.561169\pi$
$967$	−2.80599e129	−0.381974	−0.190987	+	0.981593i	$0.561169\pi$
$968$	1.68278e129	0.219002
$969$	−3.30065e128	−0.0410691
$970$	−4.53478e128	−0.0539493
$971$	−1.48204e130	−1.68587	−0.842936	−	0.538013i	$-0.819175\pi$
$971$	−1.48204e130	−1.68587	−0.842936	+	0.538013i	$0.819175\pi$
$972$	−4.76161e129	−0.517930
$973$	−2.54095e129	−0.264294
$974$	2.48060e129	0.246741
$975$	−1.44022e129	−0.137002
$976$	2.10036e129	0.191085
$977$	−1.47031e130	−1.27937	−0.639683	−	0.768639i	$-0.720934\pi$
$977$	−1.47031e130	−1.27937	−0.639683	+	0.768639i	$0.720934\pi$
$978$	6.97091e129	0.580162
$979$	−8.67236e129	−0.690383
$980$	−3.80700e129	−0.289900
$981$	−1.35621e130	−0.987925
$982$	1.36593e130	0.951869
$983$	−1.98713e130	−1.32480	−0.662398	−	0.749152i	$-0.730461\pi$
$983$	−1.98713e130	−1.32480	−0.662398	+	0.749152i	$0.730461\pi$
$984$	2.12383e129	0.135467
$985$	1.98948e130	1.21413
$986$	−4.13029e128	−0.0241177
$987$	−2.64100e129	−0.147561
$988$	−8.14290e128	−0.0435364
$989$	4.38169e129	0.224183
$990$	−4.07735e129	−0.199640
$991$	2.24431e130	1.05167	0.525835	−	0.850587i	$-0.323753\pi$
$991$	2.24431e130	1.05167	0.525835	+	0.850587i	$0.323753\pi$
$992$	6.84789e129	0.307114
$993$	8.01131e129	0.343883
$994$	−2.08973e129	−0.0858582
$995$	1.71062e130	0.672742
$996$	6.91967e129	0.260498
$997$	1.76550e130	0.636251	0.318125	−	0.948049i	$-0.396947\pi$
$997$	1.76550e130	0.636251	0.318125	+	0.948049i	$0.396947\pi$
$998$	−3.20231e130	−1.10480
$999$	−1.24491e130	−0.411187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.88.a.b.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.88.a.b.1.2	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 88 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-8.79609e12 q^{2} -3.08348e20 q^{3} +7.73713e25 q^{4} +1.64822e30 q^{5} +2.71226e33 q^{6} -1.87890e36 q^{7} -6.80565e38 q^{8} -2.28179e41 q^{9} +O(q^{10})\)	\(q-8.79609e12 q^{2} -3.08348e20 q^{3} +7.73713e25 q^{4} +1.64822e30 q^{5} +2.71226e33 q^{6} -1.87890e36 q^{7} -6.80565e38 q^{8} -2.28179e41 q^{9} -1.44979e43 q^{10} -1.23253e45 q^{11} -2.38573e46 q^{12} -1.24695e48 q^{13} +1.65269e49 q^{14} -5.08225e50 q^{15} +5.98631e51 q^{16} +1.26826e53 q^{17} +2.00708e54 q^{18} +8.44016e54 q^{19} +1.27524e56 q^{20} +5.79355e56 q^{21} +1.08415e58 q^{22} +7.04395e58 q^{23} +2.09851e59 q^{24} -3.74573e60 q^{25} +1.09683e61 q^{26} +1.70035e62 q^{27} -1.45373e62 q^{28} +3.70240e62 q^{29} +4.47039e63 q^{30} -1.30049e65 q^{31} -5.26561e64 q^{32} +3.80050e65 q^{33} -1.11557e66 q^{34} -3.09683e66 q^{35} -1.76545e67 q^{36} -7.32150e67 q^{37} -7.42404e67 q^{38} +3.84495e68 q^{39} -1.12172e69 q^{40} +1.01206e70 q^{41} -5.09606e69 q^{42} +6.22049e70 q^{43} -9.53626e70 q^{44} -3.76088e71 q^{45} -6.19593e71 q^{46} -4.55852e72 q^{47} -1.84587e72 q^{48} -2.98531e73 q^{49} +3.29478e73 q^{50} -3.91065e73 q^{51} -9.64781e73 q^{52} -9.26314e74 q^{53} -1.49564e75 q^{54} -2.03148e75 q^{55} +1.27871e75 q^{56} -2.60251e75 q^{57} -3.25667e75 q^{58} -7.26201e75 q^{59} -3.93220e76 q^{60} +3.50860e77 q^{61} +1.14392e78 q^{62} +4.28725e77 q^{63} +4.63168e77 q^{64} -2.05524e78 q^{65} -3.34295e78 q^{66} -1.42319e79 q^{67} +9.81267e78 q^{68} -2.17199e79 q^{69} +2.72400e79 q^{70} -1.26444e80 q^{71} +1.55291e80 q^{72} -1.17707e81 q^{73} +6.44006e80 q^{74} +1.15499e81 q^{75} +6.53025e80 q^{76} +2.31580e81 q^{77} -3.38205e81 q^{78} +4.54614e82 q^{79} +9.86673e81 q^{80} +2.13307e82 q^{81} -8.90221e82 q^{82} -2.90044e83 q^{83} +4.48254e82 q^{84} +2.09036e83 q^{85} -5.47160e83 q^{86} -1.14163e83 q^{87} +8.38818e83 q^{88} +7.03621e84 q^{89} +3.30811e84 q^{90} +2.34289e84 q^{91} +5.45000e84 q^{92} +4.01005e85 q^{93} +4.00971e85 q^{94} +1.39112e85 q^{95} +1.62364e85 q^{96} +3.12790e85 q^{97} +2.62590e86 q^{98} +2.81238e86 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 35184372088832 q^{2} + 40\!\cdots\!28 q^{3}+ \cdots + 82\!\cdots\!48 q^{9}+O(q^{10}) \) 4 * q - 35184372088832 * q^2 + 403237985254067182128 * q^3 + 309485009821345068724781056 * q^4 - 4037922390733497835169570162760 * q^5 - 3546918828382512738768149884698624 * q^6 + 8582179387397492406597229487230375904 * q^7 - 2722258935367507707706996859454145691648 * q^8 + 820135434884318664352221575507492568732948 * q^9	\( 4 q - 35184372088832 q^{2} + 40\!\cdots\!28 q^{3}+ \cdots + 22\!\cdots\!76 q^{99}+O(q^{100}) \) 4 * q - 35184372088832 * q^2 + 403237985254067182128 * q^3 + 309485009821345068724781056 * q^4 - 4037922390733497835169570162760 * q^5 - 3546918828382512738768149884698624 * q^6 + 8582179387397492406597229487230375904 * q^7 - 2722258935367507707706996859454145691648 * q^8 + 820135434884318664352221575507492568732948 * q^9 + 35517940965348365626859729845107910854574080 * q^10 + 2970616434026495781757184460756379040517208848 * q^11 + 31199027956673594964608194726311446315419041792 * q^12 - 1767394568818848613362028589161957028533441611112 * q^13 - 75489648224824411010546555477731971328955260076032 * q^14 + 3370976843124805373452544557684295582910726697502880 * q^15 + 23945242826029513411849172299223580994042798784118784 * q^16 - 702353032002195299447255515013113779135644499293109816 * q^17 - 7213987576051478951188874632704563580254297738585309184 * q^18 + 38051210330377980576900552965948384772060949611758270960 * q^19 - 312419112688496434410317985513745659312699567327821168640 * q^20 - 2960768946346244712423575885216855505816696171119080255872 * q^21 - 26129818486996871127304316256231512888117802859237038096384 * q^22 + 267410844513343534387094489566271409098947974355011539188128 * q^23 - 274429552109368924814832586348763817236857825346144736116736 * q^24 + 26866935732372298920001618987293695975686810093231631671755100 * q^25 + 15546167034275791140382436144471296993092547711081656715575296 * q^26 + 98351974670575379028284146601861806526822489553847883125490400 * q^27 + 664013967999314535695892002534007752932295679741402958744518656 * q^28 - 936377285291713459807588765220376016646503474372565915415382440 * q^29 - 29651425887834852403903990749669038123824799034099618745983959040 * q^30 + 119463507882721430244886842916392661099853847057206322986794525568 * q^31 - 210624583337114373395836055367340864637790190801098222508621955072 * q^32 - 975951433415384517573045287992141578476030063995050605617360966464 * q^33 + 6177962603921142192805661314942895498269819437765021241050270793728 * q^34 + 14105085028850567766840711566409137394874532315214531645239547531840 * q^35 + 63454905780001617731151046382612710619432714548573512194720658358272 * q^36 + 182087106643248709136261820106869557597167548749803025400276539121464 * q^37 - 334701985673606721323645108291715305922613643471269213861286961479680 * q^38 - 5157167650299694789254850025641525408739411563899847457339313757250784 * q^39 + 2748067577123698321827685975535901419950085077291708477942376033157120 * q^40 + 5499251594717860286021866958065054045901150247706209838765933372175208 * q^41 + 26043199069326335451693431452427559455621627547084532573326442418405376 * q^42 - 157807090931211109929865823295822094205785343123733495078770527721821552 * q^43 + 229840314065034778104010119086398472312972227124835062038272769756495872 * q^44 - 1370445036354823659067923168385609449595471872659192002945296358462825320 * q^45 - 2352170663486569504369914341681047401963148037857733129248014646193946624 * q^46 - 11700969700600051870794491472787906623524149540240126773037581150641555136 * q^47 + 2413907868396886727226140291242059049083751312718584875630451012128473088 * q^48 + 45608750768809825384693277965554885824930550141562503946687984691665533732 * q^49 - 236324065923630760668657815178197122585685320681456781276991408990637260800 * q^50 - 914883468555652107825206155517190576830844787740672822262980556765469169312 * q^51 - 136745531372273324016576733538944106078280970896210682631976284458024173568 * q^52 - 3205407327892231366350098762423033970241498041998526172742677864692608514312 * q^53 - 865113118120226050927175001395744751092084611954848335836798017458090803200 * q^54 - 10009926131406218736826424103970095109094189414661383153140158173941128709920 * q^55 - 5840728630567416793561662980979737449788739679624018831289026246209278312448 * q^56 + 24760562583447132282306921710743074800398451150699602451361304490068034752320 * q^57 + 8236461705308510473577685400040524235406303263089755599489781422351733227520 * q^58 - 81401388903576961577929700275194040780233584053778446123485310614164754536880 * q^59 + 260816700350501796503049467891128405126358446664151554703502613334842482360320 * q^60 + 908111889319782669823282318823295371554753169091641506977419705876741077882328 * q^61 - 1050812128095696376586514967647428079039044942828517372626320439677738647814144 * q^62 + 7137835102413627130280079665652016586382162073538425059614697312278117344350048 * q^63 + 1852673427797059126777135760139006525652319754650249024631321344126610074238976 * q^64 + 11407211919915638593357605065156231994296813060854399078385375214171172364857680 * q^65 + 8584559593478959280621500012652850349171438888492092327918713325137577495232512 * q^66 - 65059771693644954593974794228917141656005263924052931483321156753263176566322896 * q^67 - 54341933751812724902023253670568124974314494093364989057139191298059718491111424 * q^68 - 144323666676858272713465642347149842097884989245184653886655055101689375583845504 * q^69 - 124069639999923005500646624090308971041908232841505948959254386145464972707102720 * q^70 - 183272612160344892942190287282961718510131375557583525213035115209249713064136992 * q^71 - 558155253956338317275929527602177423655680841848067355296117578760944212116504576 * q^72 + 354182538046550765754528347144724476790476600029207619306415675742769571814637288 * q^73 - 1601655128178723932025775974507397068426901430503198065737820251919877020961472512 * q^74 + 710386439551323791969874648476083944602337020291621916942901745237698809202501200 * q^75 + 2944069800702774064027323538684509525361173924971530627370715914294143730780733440 * q^76 + 39316760279456924611775164190833990669200449799501752350802186925973327788597118848 * q^77 + 45362926383157972415756683406366951526581873158623352931657948697548800307937411072 * q^78 + 15689408650300008287770111864298279692820798574497171271867094782550105530843081920 * q^79 - 24172258039693807695503348146758763873414302432021545297363850106765398076513320960 * q^80 - 196590592451401107987710944406206415161857917104016937408869683425180184810203702876 * q^81 - 48371928579663987252349183028740936842481506637169603120359663272770590191611019264 * q^82 + 111926752599709260117886233216331177095176580206068162806299107496899925996223203568 * q^83 - 229078401609675258913891688255885614430188449105962531942162006259872232223914590208 * q^84 - 891497844731417844264766892389844899904478293183670323386186444763703698463839596560 * q^85 + 1388085851394969400976659588554077855842466084275351230019781346209556380442549026816 * q^86 + 2027498154029213080175869882525768385333184769847411190333977363043382754362186713120 * q^87 - 2021696782769547651193529032558892722193566089333659035337753899891686714980356325376 * q^88 - 1111763274969003683091618237538433748811411444468148051875571331333583253595104867160 * q^89 + 12054562021600253271129669326554918303828197627410649510778436683009490086217184706560 * q^90 + 79630263055292573954918630151432006426386375686727482380289693283976606755116980321088 * q^91 + 20689911960136575706111408504507326985128933416561732998791094227623959804415198625792 * q^92 + 121552396376548026998325328889505560359171182104366398760596365823334350324441379006976 * q^93 + 102922817936515347171258282828953462563508237397083710417081191671708730834331304460288 * q^94 + 360329377379389097240594968925389763617374668200294178024200943546627617266362721242400 * q^95 - 21232958157458842504504822471050360495135888697596704547293213652627233307394314338304 * q^96 + 84654632295309208342666811638631082612402959416215649507302559581340331556342797429384 * q^97 - 401178814389151860471251451603139889379513741986404607571754642978513123633817249120256 * q^98 + 2203878007770692926523827334498155512549713414229081953932986276578630523661724303178576 * q^99

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