LMFDB - Embedded newform 1.98.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,98,Mod(1,1)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 98, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 98);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 98 $
Character orbit:	$[\chi]$	$=$	1.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:	$59.5852992940$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} + \cdots - 60\!\cdots\!00 $ x^7 - x^6 - 276087571804405990752665088x^5 - 120083887007184048105302098667336699968x^4 + 19373155893793813105741918625198082602849023860244480x^3 + 17598423525325549028964286424215233146805218189713573416303513600x^2 - 58411389055962077878580852277509525104521481793026738328029906710656876544000*x - 6001611580367435872109665775701806052295874267155389813520177925124906158334928977920000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{83}\cdot 3^{30}\cdot 5^{10}\cdot 7^{8}\cdot 11^{2}\cdot 19 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.21527e13$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.80945e14 q^{2} +1.62851e23 q^{3} +1.79040e29 q^{4} -5.19758e33 q^{5} +9.46076e37 q^{6} -7.14729e40 q^{7} +1.19582e43 q^{8} +7.43249e45 q^{9} +O(q^{10})$	\(q+5.80945e14 q^{2} +1.62851e23 q^{3} +1.79040e29 q^{4} -5.19758e33 q^{5} +9.46076e37 q^{6} -7.14729e40 q^{7} +1.19582e43 q^{8} +7.43249e45 q^{9} -3.01951e48 q^{10} -5.76894e50 q^{11} +2.91569e52 q^{12} +1.05855e54 q^{13} -4.15218e55 q^{14} -8.46433e56 q^{15} -2.14230e58 q^{16} -4.74193e59 q^{17} +4.31787e60 q^{18} -1.19343e61 q^{19} -9.30577e62 q^{20} -1.16395e64 q^{21} -3.35144e65 q^{22} +1.47380e66 q^{23} +1.94740e66 q^{24} -3.60940e67 q^{25} +6.14957e68 q^{26} -1.89812e69 q^{27} -1.27965e70 q^{28} -1.17673e71 q^{29} -4.91731e71 q^{30} +9.54912e71 q^{31} -1.43404e73 q^{32} -9.39480e73 q^{33} -2.75480e74 q^{34} +3.71486e74 q^{35} +1.33072e75 q^{36} +1.79614e76 q^{37} -6.93314e75 q^{38} +1.72386e77 q^{39} -6.21535e76 q^{40} -5.94728e77 q^{41} -6.76188e78 q^{42} +1.56674e79 q^{43} -1.03287e80 q^{44} -3.86310e79 q^{45} +8.56198e80 q^{46} +2.24254e81 q^{47} -3.48877e81 q^{48} -4.32158e81 q^{49} -2.09686e82 q^{50} -7.72230e82 q^{51} +1.89523e83 q^{52} +1.09991e83 q^{53} -1.10270e84 q^{54} +2.99846e84 q^{55} -8.54684e83 q^{56} -1.94351e84 q^{57} -6.83616e85 q^{58} -4.65431e85 q^{59} -1.51546e86 q^{60} -3.66482e86 q^{61} +5.54751e86 q^{62} -5.31222e86 q^{63} -4.93639e87 q^{64} -5.50188e87 q^{65} -5.45786e88 q^{66} -1.40795e88 q^{67} -8.48997e88 q^{68} +2.40011e89 q^{69} +2.15813e89 q^{70} -7.30927e89 q^{71} +8.88789e88 q^{72} -7.23237e89 q^{73} +1.04346e91 q^{74} -5.87796e90 q^{75} -2.13671e90 q^{76} +4.12323e91 q^{77} +1.00147e92 q^{78} +2.50159e91 q^{79} +1.11348e92 q^{80} -4.50984e92 q^{81} -3.45504e92 q^{82} -1.80342e93 q^{83} -2.08393e93 q^{84} +2.46466e93 q^{85} +9.10189e93 q^{86} -1.91632e94 q^{87} -6.89859e93 q^{88} +4.69345e93 q^{89} -2.24425e94 q^{90} -7.56574e94 q^{91} +2.63870e95 q^{92} +1.55509e95 q^{93} +1.30279e96 q^{94} +6.20293e94 q^{95} -2.33536e96 q^{96} +1.90672e96 q^{97} -2.51060e96 q^{98} -4.28776e96 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots + 34\!\cdots\!51 q^{9}+O(q^{10}) $ 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9	$ 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots - 13\!\cdots\!28 q^{99}+O(q^{100}) $ 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9 + 2369114123959441270700616822719459966510786272800 * q^10 - 211379321299339211995860033669883746379479318698796 * q^11 + 29500590587146562092031430274877546417191966208812032 * q^12 - 883667637845783834437332163606692334928033653755299614 * q^13 + 24884922778173528138085777326574033504771595080747613568 * q^14 - 1421739776861319561135033238174867421082029896683725376600 * q^15 - 31468671341370205538262999960370611414173356196203424841728 * q^16 + 163250436637003263661570089512096377905088225334685131721342 * q^17 - 7054606772048003028382413409749231596837718873737440667537424 * q^18 + 133084372359310898958448501523235681541051727436663191570359820 * q^19 - 1318696260534044061297364386263469065025874939722479973417331200 * q^20 - 8226961344750528298533572507576209983448935264598913374247505696 * q^21 - 193421584410477868290586506488587370358898549812529751083484246976 * q^22 + 925260914184001305416523826357059292226482310773339215111132964776 * q^23 + 1719359518493251306391725804700467921422689016189510541760687554560 * q^24 - 15111829774373494694703308579556617230149980669179989285410298974375 * q^25 + 252570839996871764139482603418038366978372757286009959646749464447904 * q^26 - 16291464003153760806194022590188439733978909915063668620863256233960 * q^27 + 2270023864280230580582797832096861251181573169347509612847861972977664 * q^28 - 119228645746988213289933973286594685848645193803889692652451844737975470 * q^29 + 350448354156350400480979435069989695492221249186335731168327070817564800 * q^30 + 1783283666881858864849681148885200501497581294973934227348751364131906784 * q^31 - 5665372498136527985720301619489703024215195383428523596691479514791804928 * q^32 + 31524650657546522511070078635079454480923539002999356172307109465073458512 * q^33 - 360491523041063125717708388027762293189396999595568175085448186659598970272 * q^34 + 1278268341035082746531666145800358760269267683649420892787253371588938750800 * q^35 - 216561481226385812264597126278375191173372906326221899147967914271513631488 * q^36 - 4532061622841943284542390241171859851726205146853788500539269747469617514358 * q^37 - 2979582210919721773595405461863152858097797783237497905501709239616681227840 * q^38 + 43268347489134056222423767530379619668087154910038087692852374564634305176712 * q^39 - 252514831298472678734291758335102132215188475493571956673272319739362987008000 * q^40 + 123663386655433999860484853403953500874113711440208020678841289201379470695974 * q^41 + 3296122851141924824443574220618174749418258893075867148421980920155200276985344 * q^42 - 6595249409358954185694714287710218939626711013706300289026511229489118746183244 * q^43 + 31427981619155317050453798326367420934595218826815326227502736274099059309390848 * q^44 - 252057107931731391251960224707597558538839631727412739243273361199825466582835550 * q^45 + 333743461536679365083903174537100831945624746347277312419032904840551699600111744 * q^46 + 1582413179705462665936960636748613012540566075462612818643843634715630112826042192 * q^47 - 5861556434117332280930374286873664455351210291383528056190272983552191849213722624 * q^48 + 4345635008055985505106601346877321132027699788278385269907095782368403364891488399 * q^49 - 26742593205970009143775889336520990050133941492259748319418427757724876722706030000 * q^50 + 7043565089506559965061572069632281800522096763383079376468682406398600422146676984 * q^51 + 45800222007571685487736059984048709986270205428489770979037497696929384027946163712 * q^52 - 653999931744204429821742741003701830521617657540517458768483866216741544701292475654 * q^53 - 1692275654206728716605786947196644220317392594111136065941704729626944069981837438080 * q^54 - 2797264930804680667438884831689324464716285797264284803651188210713133784740241832200 * q^55 - 13571511538900847480549793700693331801076437559096966169392506220987757777557857402880 * q^56 - 32156245276763940566100505959698139630384956043693169857398532690693294678041975751120 * q^57 - 110275012470967940484400158535846043036245771061355495516009955997986614502808104491360 * q^58 - 289716843512018767811919727809674339112407721830489506743846640027004030301179845118940 * q^59 - 910863091257112962110410128770927709732237428874631129572443550789630933691032398899200 * q^60 - 1779644273771380099149369471014727845406783738447834645166296866716596067825339549188046 * q^61 - 4893410323209515393605311670149478112622973098189152140516775294151722525768562137565696 * q^62 - 12773855755538157144284595252262546905649007916763284311597736303148976241726684562602024 * q^63 - 24329532034212074257236420324752039539459926287390018025638252399891746834835822530789376 * q^64 - 40979880706222898178317998710539228015340375450212825952623031288613904725454054500850100 * q^65 - 142841613731497146561089386918878946227924637814625892149907766833242924230825872606056192 * q^66 - 183094181851902905703789039636502649221241410347877100016575616698548103898875205122783908 * q^67 - 250132580738896836682574414547500843555901286243235420681429272583107380144497499057716736 * q^68 - 372244836961332226973480986215431578494847115740354696097669790201492502675456308855459168 * q^69 - 587389541033882485666068522391834191601610745639266949076956170254929472707526921059782400 * q^70 - 36618527208607574135274147674246343687098099724640001025727994874106062220116534447931656 * q^71 + 2495502705800463241319297965149724088435827677064467496346161624547668625438549984339128320 * q^72 + 5937141741627411574629383951784847225959103237898806939243808260531064318159784943464907526 * q^73 + 25603418812897773069861990064614106209712057876935905208225093500026599325689360114519970848 * q^74 + 43416229043729585532262686371625117245611844558141193068941674421259839404159894884059222500 * q^75 + 64491781461168277038374423376126180174707623388661413952117963143585395013082375272839869440 * q^76 + 122801524700573133455664123216977109508839271312008866744292206338517188364407357732160152224 * q^77 + 256518622739178273010532892375526005382856863147760611859324715551823107217212845963281985152 * q^78 + 155279975164311735091235448536513906273532801204307686975280157544842456609207922540776901680 * q^79 + 343037548751841740038666995050634479050946344382038763901789904170114217394648666813900390400 * q^80 - 799336653019442009471583631583081099983526554777301855450568718504605547656753900698628831153 * q^81 - 2054599455199243418451530458808296516745297582440826399667363552358055209069956455679452833056 * q^82 - 2745080838526935126539434486643898932954125805020264508203796620734019354440308801326974021684 * q^83 - 12055830667015300843296227009204563031159870111997209215974794552386444770918151507927520305152 * q^84 - 16156906986132970771716277890961343081101351325821342812927748903601690598916612215092853170700 * q^85 - 16073101085057033129856695763368798351047883803740227513388827997968391823543719379002604387776 * q^86 - 44931373084677669249994770736329381356923858000626008622029156778901658182110994195783000791480 * q^87 - 20900444501134905678673788524771632932447417317035512416151379720801969394444956958395302789120 * q^88 + 8652425236627243255051028260917634407304730072980172181544783646255542601500269383337979350390 * q^89 + 169914380219009102880054256907856294069041898142575788262717672760376053145875718225670932330400 * q^90 + 235279610532724372901602846332263408075886672274330172793822218199845308058643167074949650230544 * q^91 + 622950794384614085632156625042963081233986358617743991991586248417198315809579918444522808891392 * q^92 + 1619655729334717431421579797164299646702152339363664709672746834797775058100318492643375449441152 * q^93 + 1784387548746436753701888750274366538460858609156963702431495773056050960861585984793528939671808 * q^94 + 1109691419127482658877926123378178695834970817464791602098716148821958373905367930889408748989000 * q^95 + 2773817117979873680694700349927475687549477810523157816910439588411515192104026991177258420404224 * q^96 - 462826972284038426621245345324758076530452205891330025493894671876723283114629445572915788984658 * q^97 - 10100804559243313775965110405631054964918520327952856127425837778067309219959758215138751854831056 * q^98 - 13792894935722775136702660269810636953813664741795563019740674282913700184659028566406972539495228 * 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 $

$2$	5.80945e14	1.45942	0.729709	−	0.683757i	$-0.239655\pi$
$2$	5.80945e14	1.45942	0.729709	+	0.683757i	$0.239655\pi$
$3$	1.62851e23	1.17872	0.589360	−	0.807871i	$-0.299380\pi$
$3$	1.62851e23	1.17872	0.589360	+	0.807871i	$0.299380\pi$
$4$	1.79040e29	1.12990
$5$	−5.19758e33	−0.654269	−0.327134	−	0.944978i	$-0.606083\pi$
$5$	−5.19758e33	−0.654269	−0.327134	+	0.944978i	$0.606083\pi$
$6$	9.46076e37	1.72025
$7$	−7.14729e40	−0.736015	−0.368007	−	0.929823i	$-0.619960\pi$
$7$	−7.14729e40	−0.736015	−0.368007	+	0.929823i	$0.619960\pi$
$8$	1.19582e43	0.189583
$9$	7.43249e45	0.389379
$10$	−3.01951e48	−0.954852
$11$	−5.76894e50	−1.79288	−0.896440	−	0.443166i	$-0.853855\pi$
$11$	−5.76894e50	−1.79288	−0.896440	+	0.443166i	$0.853855\pi$
$12$	2.91569e52	1.33184
$13$	1.05855e54	0.996454	0.498227	−	0.867047i	$-0.333985\pi$
$13$	1.05855e54	0.996454	0.498227	+	0.867047i	$0.333985\pi$
$14$	−4.15218e55	−1.07415
$15$	−8.46433e56	−0.771199
$16$	−2.14230e58	−0.853222
$17$	−4.74193e59	−0.998120	−0.499060	−	0.866567i	$-0.666321\pi$
$17$	−4.74193e59	−0.998120	−0.499060	+	0.866567i	$0.666321\pi$
$18$	4.31787e60	0.568267
$19$	−1.19343e61	−0.114090	−0.0570448	−	0.998372i	$-0.518168\pi$
$19$	−1.19343e61	−0.114090	−0.0570448	+	0.998372i	$0.518168\pi$
$20$	−9.30577e62	−0.739260
$21$	−1.16395e64	−0.867555
$22$	−3.35144e65	−2.61656
$23$	1.47380e66	1.33241	0.666207	−	0.745767i	$-0.267917\pi$
$23$	1.47380e66	1.33241	0.666207	+	0.745767i	$0.267917\pi$
$24$	1.94740e66	0.223465
$25$	−3.60940e67	−0.571932
$26$	6.14957e68	1.45424
$27$	−1.89812e69	−0.719751
$28$	−1.27965e70	−0.831626
$29$	−1.17673e71	−1.39436	−0.697180	−	0.716896i	$-0.745562\pi$
$29$	−1.17673e71	−1.39436	−0.697180	+	0.716896i	$0.745562\pi$
$30$	−4.91731e71	−1.12550
$31$	9.54912e71	0.445575	0.222788	−	0.974867i	$-0.428484\pi$
$31$	9.54912e71	0.445575	0.222788	+	0.974867i	$0.428484\pi$
$32$	−1.43404e73	−1.43479
$33$	−9.39480e73	−2.11330
$34$	−2.75480e74	−1.45668
$35$	3.71486e74	0.481552
$36$	1.33072e75	0.439961
$37$	1.79614e76	1.57238	0.786188	−	0.617988i	$-0.212052\pi$
$37$	1.79614e76	1.57238	0.786188	+	0.617988i	$0.212052\pi$
$38$	−6.93314e75	−0.166504
$39$	1.72386e77	1.17454
$40$	−6.21535e76	−0.124038
$41$	−5.94728e77	−0.358345	−0.179172	−	0.983818i	$-0.557342\pi$
$41$	−5.94728e77	−0.358345	−0.179172	+	0.983818i	$0.557342\pi$
$42$	−6.76188e78	−1.26613
$43$	1.56674e79	0.937080	0.468540	−	0.883442i	$-0.344780\pi$
$43$	1.56674e79	0.937080	0.468540	+	0.883442i	$0.344780\pi$
$44$	−1.03287e80	−2.02578
$45$	−3.86310e79	−0.254759
$46$	8.56198e80	1.94455
$47$	2.24254e81	1.79471	0.897355	−	0.441310i	$-0.145486\pi$
$47$	2.24254e81	1.79471	0.897355	+	0.441310i	$0.145486\pi$
$48$	−3.48877e81	−1.00571
$49$	−4.32158e81	−0.458282
$50$	−2.09686e82	−0.834689
$51$	−7.72230e82	−1.17650
$52$	1.89523e83	1.12590
$53$	1.09991e83	0.259404	0.129702	−	0.991553i	$-0.458598\pi$
$53$	1.09991e83	0.259404	0.129702	+	0.991553i	$0.458598\pi$
$54$	−1.10270e84	−1.05042
$55$	2.99846e84	1.17303
$56$	−8.54684e83	−0.139536
$57$	−1.94351e84	−0.134480
$58$	−6.83616e85	−2.03495
$59$	−4.65431e85	−0.604690	−0.302345	−	0.953199i	$-0.597769\pi$
$59$	−4.65431e85	−0.604690	−0.302345	+	0.953199i	$0.597769\pi$
$60$	−1.51546e86	−0.871381
$61$	−3.66482e86	−0.945270	−0.472635	−	0.881258i	$-0.656697\pi$
$61$	−3.66482e86	−0.945270	−0.472635	+	0.881258i	$0.656697\pi$
$62$	5.54751e86	0.650281
$63$	−5.31222e86	−0.286589
$64$	−4.93639e87	−1.24074
$65$	−5.50188e87	−0.651949
$66$	−5.45786e88	−3.08419
$67$	−1.40795e88	−0.383672	−0.191836	−	0.981427i	$-0.561444\pi$
$67$	−1.40795e88	−0.383672	−0.191836	+	0.981427i	$0.561444\pi$
$68$	−8.48997e88	−1.12778
$69$	2.40011e89	1.57054
$70$	2.15813e89	0.702785
$71$	−7.30927e89	−1.19631	−0.598156	−	0.801380i	$-0.704100\pi$
$71$	−7.30927e89	−1.19631	−0.598156	+	0.801380i	$0.704100\pi$
$72$	8.88789e88	0.0738197
$73$	−7.23237e89	−0.307696	−0.153848	−	0.988095i	$-0.549167\pi$
$73$	−7.23237e89	−0.307696	−0.153848	+	0.988095i	$0.549167\pi$
$74$	1.04346e91	2.29475
$75$	−5.87796e90	−0.674148
$76$	−2.13671e90	−0.128910
$77$	4.12323e91	1.31959
$78$	1.00147e92	1.71415
$79$	2.50159e91	0.230835	0.115418	−	0.993317i	$-0.463179\pi$
$79$	2.50159e91	0.230835	0.115418	+	0.993317i	$0.463179\pi$
$80$	1.11348e92	0.558237
$81$	−4.50984e92	−1.23776
$82$	−3.45504e92	−0.522975
$83$	−1.80342e93	−1.51638	−0.758190	−	0.652033i	$-0.773916\pi$
$83$	−1.80342e93	−1.51638	−0.758190	+	0.652033i	$0.773916\pi$
$84$	−2.08393e93	−0.980253
$85$	2.46466e93	0.653039
$86$	9.10189e93	1.36759
$87$	−1.91632e94	−1.64356
$88$	−6.89859e93	−0.339900
$89$	4.69345e93	0.133683	0.0668417	−	0.997764i	$-0.478708\pi$
$89$	4.69345e93	0.133683	0.0668417	+	0.997764i	$0.478708\pi$
$90$	−2.24425e94	−0.371800
$91$	−7.56574e94	−0.733405
$92$	2.63870e95	1.50550
$93$	1.55509e95	0.525208
$94$	1.30279e96	2.61923
$95$	6.20293e94	0.0746452
$96$	−2.33536e96	−1.69122
$97$	1.90672e96	0.835329	0.417664	−	0.908601i	$-0.362849\pi$
$97$	1.90672e96	0.835329	0.417664	+	0.908601i	$0.362849\pi$
$98$	−2.51060e96	−0.668826
$99$	−4.28776e96	−0.698110
$100$	−6.46228e96	−0.646228
$101$	7.76230e96	0.479075	0.239538	−	0.970887i	$-0.423004\pi$
$101$	7.76230e96	0.479075	0.239538	+	0.970887i	$0.423004\pi$
$102$	−4.48623e97	−1.71701
$103$	2.20969e97	0.526897	0.263448	−	0.964673i	$-0.415140\pi$
$103$	2.20969e97	0.526897	0.263448	+	0.964673i	$0.415140\pi$
$104$	1.26583e97	0.188911
$105$	6.04971e97	0.567614
$106$	6.38984e97	0.378578
$107$	−1.94773e98	−0.731841	−0.365920	−	0.930646i	$-0.619246\pi$
$107$	−1.94773e98	−0.731841	−0.365920	+	0.930646i	$0.619246\pi$
$108$	−3.39841e98	−0.813249
$109$	2.04416e98	0.312845	0.156422	−	0.987690i	$-0.450004\pi$
$109$	2.04416e98	0.312845	0.156422	+	0.987690i	$0.450004\pi$
$110$	1.74194e99	1.71193
$111$	2.92504e99	1.85339
$112$	1.53117e99	0.627984
$113$	−6.20044e99	−1.65241	−0.826205	−	0.563370i	$-0.809505\pi$
$113$	−6.20044e99	−1.65241	−0.826205	+	0.563370i	$0.809505\pi$
$114$	−1.12907e99	−0.196262
$115$	−7.66021e99	−0.871757
$116$	−2.10683e100	−1.57549
$117$	7.86764e99	0.387999
$118$	−2.70390e100	−0.882496
$119$	3.38920e100	0.734631
$120$	−1.01218e100	−0.146206
$121$	2.29271e101	2.21442
$122$	−2.12906e101	−1.37954
$123$	−9.68522e100	−0.422388
$124$	1.70968e101	0.503457
$125$	5.15615e101	1.02847
$126$	−3.08610e101	−0.418253
$127$	7.55132e101	0.697497	0.348749	−	0.937216i	$-0.386607\pi$
$127$	7.55132e101	0.697497	0.348749	+	0.937216i	$0.386607\pi$
$128$	−5.95434e101	−0.375967
$129$	2.55146e102	1.10455
$130$	−3.19629e102	−0.951467
$131$	3.29245e102	0.675867	0.337933	−	0.941170i	$-0.390272\pi$
$131$	3.29245e102	0.675867	0.337933	+	0.941170i	$0.390272\pi$
$132$	−1.68205e103	−2.38783
$133$	8.52977e101	0.0839716
$134$	−8.17941e102	−0.559937
$135$	9.86566e102	0.470910
$136$	−5.67048e102	−0.189227
$137$	−7.54798e103	−1.76556	−0.882781	−	0.469784i	$-0.844332\pi$
$137$	−7.54798e103	−1.76556	−0.882781	+	0.469784i	$0.844332\pi$
$138$	1.39433e104	2.29208
$139$	1.04374e104	1.20886	0.604429	−	0.796659i	$-0.293401\pi$
$139$	1.04374e104	1.20886	0.604429	+	0.796659i	$0.293401\pi$
$140$	6.65110e103	0.544107
$141$	3.65201e104	2.11546
$142$	−4.24628e104	−1.74592
$143$	−6.10670e104	−1.78652
$144$	−1.59227e104	−0.332227
$145$	6.11616e104	0.912286
$146$	−4.20161e104	−0.449057
$147$	−7.03775e104	−0.540186
$148$	3.21581e105	1.77663
$149$	−1.15832e105	−0.461629	−0.230815	−	0.972998i	$-0.574139\pi$
$149$	−1.15832e105	−0.461629	−0.230815	+	0.972998i	$0.574139\pi$
$150$	−3.41477e105	−0.983864
$151$	−6.18810e105	−1.29174	−0.645870	−	0.763447i	$-0.723505\pi$
$151$	−6.18810e105	−1.29174	−0.645870	+	0.763447i	$0.723505\pi$
$152$	−1.42712e104	−0.0216295
$153$	−3.52444e105	−0.388647
$154$	2.39537e106	1.92583
$155$	−4.96323e105	−0.291526
$156$	3.08640e106	1.32712
$157$	−4.62201e105	−0.145780	−0.0728900	−	0.997340i	$-0.523222\pi$
$157$	−4.62201e105	−0.145780	−0.0728900	+	0.997340i	$0.523222\pi$
$158$	1.45329e106	0.336885
$159$	1.79121e106	0.305764
$160$	7.45357e106	0.938739
$161$	−1.05337e107	−0.980677
$162$	−2.61997e107	−1.80641
$163$	−1.23935e107	−0.634010	−0.317005	−	0.948424i	$-0.602677\pi$
$163$	−1.23935e107	−0.634010	−0.317005	+	0.948424i	$0.602677\pi$
$164$	−1.06480e107	−0.404895
$165$	4.88303e107	1.38267
$166$	−1.04768e108	−2.21303
$167$	1.14523e108	1.80777	0.903884	−	0.427777i	$-0.140703\pi$
$167$	1.14523e108	1.80777	0.903884	+	0.427777i	$0.140703\pi$
$168$	−1.39186e107	−0.164474
$169$	−7.98835e105	−0.00707867
$170$	1.43183e108	0.953057
$171$	−8.87013e106	−0.0444241
$172$	2.80510e108	1.05881
$173$	9.59378e107	0.273372	0.136686	−	0.990614i	$-0.456355\pi$
$173$	9.59378e107	0.273372	0.136686	+	0.990614i	$0.456355\pi$
$174$	−1.11328e109	−2.39864
$175$	2.57974e108	0.420951
$176$	1.23588e109	1.52972
$177$	−7.57960e108	−0.712759
$178$	2.72664e108	0.195100
$179$	5.91656e108	0.322625	0.161312	−	0.986903i	$-0.448427\pi$
$179$	5.91656e108	0.322625	0.161312	+	0.986903i	$0.448427\pi$
$180$	−6.91650e108	−0.287853
$181$	−1.14400e109	−0.363929	−0.181965	−	0.983305i	$-0.558246\pi$
$181$	−1.14400e109	−0.363929	−0.181965	+	0.983305i	$0.558246\pi$
$182$	−4.39528e109	−1.07035
$183$	−5.96821e109	−1.11421
$184$	1.76240e109	0.252603
$185$	−9.33558e109	−1.02876
$186$	9.03419e109	0.766499
$187$	2.73559e110	1.78951
$188$	4.01505e110	2.02785
$189$	1.35664e110	0.529747
$190$	3.60356e109	0.108939
$191$	−6.34699e110	−1.48748	−0.743738	−	0.668471i	$-0.766949\pi$
$191$	−6.34699e110	−1.48748	−0.743738	+	0.668471i	$0.766949\pi$
$192$	−8.03897e110	−1.46248
$193$	6.48750e109	0.0917377	0.0458689	−	0.998947i	$-0.485394\pi$
$193$	6.48750e109	0.0917377	0.0458689	+	0.998947i	$0.485394\pi$
$194$	1.10770e111	1.21909
$195$	−8.95989e110	−0.768465
$196$	−7.73737e110	−0.517814
$197$	−4.96074e110	−0.259379	−0.129689	−	0.991555i	$-0.541398\pi$
$197$	−4.96074e110	−0.259379	−0.129689	+	0.991555i	$0.541398\pi$
$198$	−2.49095e111	−1.01883
$199$	3.90550e111	1.25113	0.625565	−	0.780172i	$-0.284869\pi$
$199$	3.90550e111	1.25113	0.625565	+	0.780172i	$0.284869\pi$
$200$	−4.31618e110	−0.108429
$201$	−2.29287e111	−0.452241
$202$	4.50947e111	0.699171
$203$	8.41045e111	1.02627
$204$	−1.38260e112	−1.32934
$205$	3.09115e111	0.234454
$206$	1.28371e112	0.768963
$207$	1.09540e112	0.518815
$208$	−2.26773e112	−0.850197
$209$	6.88481e111	0.204549
$210$	3.51454e112	0.828387
$211$	1.93935e112	0.363041	0.181521	−	0.983387i	$-0.441898\pi$
$211$	1.93935e112	0.363041	0.181521	+	0.983387i	$0.441898\pi$
$212$	1.96928e112	0.293101
$213$	−1.19032e113	−1.41011
$214$	−1.13153e113	−1.06806
$215$	−8.14326e112	−0.613102
$216$	−2.26981e112	−0.136453
$217$	−6.82503e112	−0.327950
$218$	1.18754e113	0.456572
$219$	−1.17780e113	−0.362687
$220$	5.36845e113	1.32540
$221$	−5.01956e113	−0.994581
$222$	1.69928e114	2.70487
$223$	3.72463e113	0.476758	0.238379	−	0.971172i	$-0.423384\pi$
$223$	3.72463e113	0.476758	0.238379	+	0.971172i	$0.423384\pi$
$224$	1.02495e114	1.05603
$225$	−2.68268e113	−0.222698
$226$	−3.60211e114	−2.41156
$227$	−1.86629e114	−1.00861	−0.504307	−	0.863524i	$-0.668252\pi$
$227$	−1.86629e114	−1.00861	−0.504307	+	0.863524i	$0.668252\pi$
$228$	−3.47967e113	−0.151949
$229$	2.25589e114	0.796705	0.398353	−	0.917232i	$-0.369582\pi$
$229$	2.25589e114	0.796705	0.398353	+	0.917232i	$0.369582\pi$
$230$	−4.45016e114	−1.27226
$231$	6.71474e114	1.55542
$232$	−1.40715e114	−0.264347
$233$	3.48285e113	0.0531096	0.0265548	−	0.999647i	$-0.491546\pi$
$233$	3.48285e113	0.0531096	0.0265548	+	0.999647i	$0.491546\pi$
$234$	4.57066e114	0.566252
$235$	−1.16558e115	−1.17422
$236$	−8.33309e114	−0.683241
$237$	4.07387e114	0.272090
$238$	1.96894e115	1.07213
$239$	−2.83338e115	−1.25895	−0.629473	−	0.777023i	$-0.716729\pi$
$239$	−2.83338e115	−1.25895	−0.629473	+	0.777023i	$0.716729\pi$
$240$	1.81332e115	0.658004
$241$	9.69225e112	0.00287474	0.00143737	−	0.999999i	$-0.499542\pi$
$241$	9.69225e112	0.00287474	0.00143737	+	0.999999i	$0.499542\pi$
$242$	1.33194e116	3.23176
$243$	−3.72118e115	−0.739225
$244$	−6.56151e115	−1.06806
$245$	2.24618e115	0.299840
$246$	−5.62658e115	−0.616441
$247$	−1.26330e115	−0.113685
$248$	1.14190e115	0.0844736
$249$	−2.93689e116	−1.78739
$250$	2.99544e116	1.50096
$251$	−1.66692e116	−0.688238	−0.344119	−	0.938926i	$-0.611822\pi$
$251$	−1.66692e116	−0.688238	−0.344119	+	0.938926i	$0.611822\pi$
$252$	−9.51101e115	−0.323818
$253$	−8.50229e116	−2.38886
$254$	4.38690e116	1.01794
$255$	4.01373e116	0.769750
$256$	4.36288e116	0.692046
$257$	1.50051e117	1.97008	0.985038	−	0.172337i	$-0.0551317\pi$
$257$	1.50051e117	1.97008	0.985038	+	0.172337i	$0.0551317\pi$
$258$	1.48225e117	1.61201
$259$	−1.28375e117	−1.15729
$260$	−9.85059e116	−0.736639
$261$	−8.74605e116	−0.542935
$262$	1.91273e117	0.986373
$263$	−3.21862e117	−1.37980	−0.689899	−	0.723905i	$-0.742345\pi$
$263$	−3.21862e117	−1.37980	−0.689899	+	0.723905i	$0.742345\pi$
$264$	−1.12344e117	−0.400646
$265$	−5.71685e116	−0.169720
$266$	4.95532e116	0.122550
$267$	7.64335e116	0.157575
$268$	−2.52080e117	−0.433512
$269$	−9.90826e116	−0.142237	−0.0711184	−	0.997468i	$-0.522657\pi$
$269$	−9.90826e116	−0.142237	−0.0711184	+	0.997468i	$0.522657\pi$
$270$	5.73140e117	0.687255
$271$	1.88089e117	0.188518	0.0942590	−	0.995548i	$-0.469952\pi$
$271$	1.88089e117	0.188518	0.0942590	+	0.995548i	$0.469952\pi$
$272$	1.01587e118	0.851618
$273$	−1.23209e118	−0.864479
$274$	−4.38496e118	−2.57669
$275$	2.08224e118	1.02541
$276$	4.29716e118	1.77456
$277$	−3.82013e118	−1.32376	−0.661880	−	0.749610i	$-0.730241\pi$
$277$	−3.82013e118	−1.32376	−0.661880	+	0.749610i	$0.730241\pi$
$278$	6.06356e118	1.76423
$279$	7.09737e117	0.173498
$280$	4.44229e117	0.0912941
$281$	−1.43114e118	−0.247415	−0.123707	−	0.992319i	$-0.539478\pi$
$281$	−1.43114e118	−0.247415	−0.123707	+	0.992319i	$0.539478\pi$
$282$	2.12161e119	3.08734
$283$	−1.55838e119	−1.90999	−0.954995	−	0.296621i	$-0.904140\pi$
$283$	−1.55838e119	−1.90999	−0.954995	+	0.296621i	$0.904140\pi$
$284$	−1.30865e119	−1.35172
$285$	1.01016e118	0.0879858
$286$	−3.54765e119	−2.60728
$287$	4.25069e118	0.263747
$288$	−1.06585e119	−0.558678
$289$	−8.47790e116	−0.00375615
$290$	3.55315e119	1.33141
$291$	3.10512e119	0.984618
$292$	−1.29489e119	−0.347667
$293$	2.93290e119	0.667142	0.333571	−	0.942725i	$-0.391746\pi$
$293$	2.93290e119	0.667142	0.333571	+	0.942725i	$0.391746\pi$
$294$	−4.08854e119	−0.788358
$295$	2.41912e119	0.395630
$296$	2.14785e119	0.298096
$297$	1.09502e120	1.29043
$298$	−6.72918e119	−0.673710
$299$	1.56009e120	1.32769
$300$	−1.05239e120	−0.761722
$301$	−1.11979e120	−0.689705
$302$	−3.59494e120	−1.88519
$303$	1.26410e120	0.564695
$304$	2.55668e119	0.0973437
$305$	1.90482e120	0.618461
$306$	−2.04750e120	−0.567199
$307$	−6.57031e120	−1.55373	−0.776863	−	0.629669i	$-0.783190\pi$
$307$	−6.57031e120	−1.55373	−0.776863	+	0.629669i	$0.783190\pi$
$308$	7.38225e120	1.49100
$309$	3.59851e120	0.621063
$310$	−2.88336e120	−0.425459
$311$	4.96160e120	0.626244	0.313122	−	0.949713i	$-0.398625\pi$
$311$	4.96160e120	0.626244	0.313122	+	0.949713i	$0.398625\pi$
$312$	2.06142e120	0.222673
$313$	−1.65467e121	−1.53042	−0.765212	−	0.643779i	$-0.777366\pi$
$313$	−1.65467e121	−1.53042	−0.765212	+	0.643779i	$0.777366\pi$
$314$	−2.68513e120	−0.212754
$315$	2.76107e120	0.187506
$316$	4.47885e120	0.260822
$317$	4.69666e120	0.234647	0.117323	−	0.993094i	$-0.462569\pi$
$317$	4.69666e120	0.234647	0.117323	+	0.993094i	$0.462569\pi$
$318$	1.04059e121	0.446238
$319$	6.78850e121	2.49992
$320$	2.56573e121	0.811777
$321$	−3.17191e121	−0.862635
$322$	−6.11950e121	−1.43122
$323$	5.65915e120	0.113875
$324$	−8.07443e121	−1.39855
$325$	−3.82072e121	−0.569904
$326$	−7.19995e121	−0.925286
$327$	3.32894e121	0.368756
$328$	−7.11185e120	−0.0679362
$329$	−1.60281e122	−1.32093
$330$	2.83677e122	2.01789
$331$	1.43264e122	0.879994	0.439997	−	0.897999i	$-0.354979\pi$
$331$	1.43264e122	0.879994	0.439997	+	0.897999i	$0.354979\pi$
$332$	−3.22884e122	−1.71336
$333$	1.33498e122	0.612250
$334$	6.65314e122	2.63829
$335$	7.31794e121	0.251024
$336$	2.49353e122	0.740217
$337$	−4.66879e122	−1.19993	−0.599963	−	0.800028i	$-0.704818\pi$
$337$	−4.66879e122	−1.19993	−0.599963	+	0.800028i	$0.704818\pi$
$338$	−4.64079e120	−0.0103308
$339$	−1.00975e123	−1.94773
$340$	4.41273e122	0.737871
$341$	−5.50883e122	−0.798863
$342$	−5.15305e121	−0.0648334
$343$	9.82863e122	1.07332
$344$	1.87353e122	0.177655
$345$	−1.24748e123	−1.02756
$346$	5.57346e122	0.398964
$347$	1.52298e123	0.947794	0.473897	−	0.880580i	$-0.342847\pi$
$347$	1.52298e123	0.947794	0.473897	+	0.880580i	$0.342847\pi$
$348$	−3.43099e123	−1.85706
$349$	−1.39112e123	−0.655136	−0.327568	−	0.944828i	$-0.606229\pi$
$349$	−1.39112e123	−0.655136	−0.327568	+	0.944828i	$0.606229\pi$
$350$	1.49869e123	0.614343
$351$	−2.00925e123	−0.717199
$352$	8.27292e123	2.57241
$353$	−3.28231e123	−0.889418	−0.444709	−	0.895675i	$-0.646693\pi$
$353$	−3.28231e123	−0.889418	−0.444709	+	0.895675i	$0.646693\pi$
$354$	−4.40333e123	−1.04021
$355$	3.79905e123	0.782709
$356$	8.40317e122	0.151049
$357$	5.51935e123	0.865924
$358$	3.43720e123	0.470844
$359$	−3.45698e122	−0.0413634	−0.0206817	−	0.999786i	$-0.506584\pi$
$359$	−3.45698e122	−0.0413634	−0.0206817	+	0.999786i	$0.506584\pi$
$360$	−4.61955e122	−0.0482980
$361$	−1.07996e124	−0.986984
$362$	−6.64603e123	−0.531125
$363$	3.73371e124	2.61017
$364$	−1.35457e124	−0.828677
$365$	3.75908e123	0.201316
$366$	−3.46720e124	−1.62610
$367$	−3.96529e123	−0.162919	−0.0814593	−	0.996677i	$-0.525958\pi$
$367$	−3.96529e123	−0.162919	−0.0814593	+	0.996677i	$0.525958\pi$
$368$	−3.15734e124	−1.13685
$369$	−4.42031e123	−0.139532
$370$	−5.42345e124	−1.50139
$371$	−7.86135e123	−0.190925
$372$	2.78423e124	0.593434
$373$	4.73757e124	0.886498	0.443249	−	0.896399i	$-0.353826\pi$
$373$	4.73757e124	0.886498	0.443249	+	0.896399i	$0.353826\pi$
$374$	1.58923e125	2.61164
$375$	8.39686e124	1.21227
$376$	2.68166e124	0.340247
$377$	−1.24563e125	−1.38942
$378$	7.88135e124	0.773123
$379$	−1.09064e125	−0.941193	−0.470596	−	0.882349i	$-0.655961\pi$
$379$	−1.09064e125	−0.941193	−0.470596	+	0.882349i	$0.655961\pi$
$380$	1.11057e124	0.0843419
$381$	1.22974e125	0.822153
$382$	−3.68725e125	−2.17085
$383$	6.19469e124	0.321277	0.160638	−	0.987013i	$-0.448645\pi$
$383$	6.19469e124	0.321277	0.160638	+	0.987013i	$0.448645\pi$
$384$	−9.69672e124	−0.443160
$385$	−2.14308e125	−0.863364
$386$	3.76888e124	0.133884
$387$	1.16448e125	0.364880
$388$	3.41380e125	0.943841
$389$	5.76337e125	1.40644	0.703220	−	0.710972i	$-0.251745\pi$
$389$	5.76337e125	1.40644	0.703220	+	0.710972i	$0.251745\pi$
$390$	−5.20520e125	−1.12151
$391$	−6.98868e125	−1.32991
$392$	−5.16782e124	−0.0868826
$393$	5.36180e125	0.796657
$394$	−2.88191e125	−0.378542
$395$	−1.30022e125	−0.151028
$396$	−7.67682e125	−0.788796
$397$	5.08950e125	0.462738	0.231369	−	0.972866i	$-0.425679\pi$
$397$	5.08950e125	0.462738	0.231369	+	0.972866i	$0.425679\pi$
$398$	2.26888e126	1.82592
$399$	1.38908e125	0.0989790
$400$	7.73243e125	0.487985
$401$	−1.13668e126	−0.635533	−0.317766	−	0.948169i	$-0.602933\pi$
$401$	−1.13668e126	−0.635533	−0.317766	+	0.948169i	$0.602933\pi$
$402$	−1.33203e126	−0.660009
$403$	1.01082e126	0.443995
$404$	1.38976e126	0.541309
$405$	2.34403e126	0.809830
$406$	4.88601e126	1.49776
$407$	−1.03618e127	−2.81908
$408$	−9.23445e125	−0.223045
$409$	−6.20420e126	−1.33078	−0.665389	−	0.746497i	$-0.731734\pi$
$409$	−6.20420e126	−1.33078	−0.665389	+	0.746497i	$0.731734\pi$
$410$	1.79579e126	0.342166
$411$	−1.22920e127	−2.08110
$412$	3.95623e126	0.595342
$413$	3.32657e126	0.445061
$414$	6.36368e126	0.757168
$415$	9.37340e126	0.992121
$416$	−1.51800e127	−1.42970
$417$	1.69975e127	1.42490
$418$	3.99969e126	0.298522
$419$	−6.36234e126	−0.422899	−0.211450	−	0.977389i	$-0.567818\pi$
$419$	−6.36234e126	−0.422899	−0.211450	+	0.977389i	$0.567818\pi$
$420$	1.08314e127	0.641349
$421$	4.23408e126	0.223397	0.111698	−	0.993742i	$-0.464371\pi$
$421$	4.23408e126	0.223397	0.111698	+	0.993742i	$0.464371\pi$
$422$	1.12665e127	0.529830
$423$	1.66677e127	0.698822
$424$	1.31528e126	0.0491785
$425$	1.71155e127	0.570857
$426$	−6.91512e127	−2.05795
$427$	2.61936e127	0.695733
$428$	−3.48723e127	−0.826909
$429$	−9.94483e127	−2.10581
$430$	−4.73078e127	−0.894773
$431$	2.86163e127	0.483577	0.241788	−	0.970329i	$-0.422266\pi$
$431$	2.86163e127	0.483577	0.241788	+	0.970329i	$0.422266\pi$
$432$	4.06636e127	0.614107
$433$	9.31655e127	1.25774	0.628872	−	0.777509i	$-0.283517\pi$
$433$	9.31655e127	1.25774	0.628872	+	0.777509i	$0.283517\pi$
$434$	−3.96497e127	−0.478616
$435$	9.96025e127	1.07533
$436$	3.65987e127	0.353485
$437$	−1.75888e127	−0.152015
$438$	−6.84237e127	−0.529313
$439$	4.77870e126	0.0330964	0.0165482	−	0.999863i	$-0.494732\pi$
$439$	4.77870e126	0.0330964	0.0165482	+	0.999863i	$0.494732\pi$
$440$	3.58560e127	0.222386
$441$	−3.21201e127	−0.178445
$442$	−2.91609e128	−1.45151
$443$	−1.23338e128	−0.550196	−0.275098	−	0.961416i	$-0.588710\pi$
$443$	−1.23338e128	−0.550196	−0.275098	+	0.961416i	$0.588710\pi$
$444$	5.23699e128	2.09415
$445$	−2.43946e127	−0.0874648
$446$	2.16381e128	0.695789
$447$	−1.88633e128	−0.544131
$448$	3.52818e128	0.913203
$449$	6.26534e128	1.45545	0.727725	−	0.685869i	$-0.240578\pi$
$449$	6.26534e128	1.45545	0.727725	+	0.685869i	$0.240578\pi$
$450$	−1.55849e128	−0.325010
$451$	3.43095e128	0.642469
$452$	−1.11013e129	−1.86706
$453$	−1.00774e129	−1.52260
$454$	−1.08421e129	−1.47199
$455$	3.93236e128	0.479844
$456$	−2.32408e127	−0.0254951
$457$	−1.07131e129	−1.05677	−0.528386	−	0.849004i	$-0.677203\pi$
$457$	−1.07131e129	−1.05677	−0.528386	+	0.849004i	$0.677203\pi$
$458$	1.31055e129	1.16273
$459$	9.00078e128	0.718398
$460$	−1.37149e129	−0.985002
$461$	−3.95142e128	−0.255422	−0.127711	−	0.991811i	$-0.540763\pi$
$461$	−3.95142e128	−0.255422	−0.127711	+	0.991811i	$0.540763\pi$
$462$	3.90089e129	2.27001
$463$	−1.49616e129	−0.783969	−0.391984	−	0.919972i	$-0.628211\pi$
$463$	−1.49616e129	−0.783969	−0.391984	+	0.919972i	$0.628211\pi$
$464$	2.52092e129	1.18970
$465$	−8.08269e128	−0.343627
$466$	2.02335e128	0.0775092
$467$	4.11978e129	1.42235	0.711174	−	0.703017i	$-0.248164\pi$
$467$	4.11978e129	1.42235	0.711174	+	0.703017i	$0.248164\pi$
$468$	1.40862e129	0.438401
$469$	1.00630e129	0.282388
$470$	−6.77137e129	−1.71368
$471$	−7.52700e128	−0.171834
$472$	−5.56569e128	−0.114639
$473$	−9.03843e129	−1.68007
$474$	2.36669e129	0.397093
$475$	4.30755e128	0.0652515
$476$	6.06803e129	0.830062
$477$	8.17504e128	0.101006
$478$	−1.64604e130	−1.83733
$479$	−1.35340e130	−1.36506	−0.682532	−	0.730856i	$-0.739121\pi$
$479$	−1.35340e130	−1.36506	−0.682532	+	0.730856i	$0.739121\pi$
$480$	1.21382e130	1.10651
$481$	1.90130e130	1.56680
$482$	5.63066e127	0.00419544
$483$	−1.71543e130	−1.15594
$484$	4.10488e130	2.50208
$485$	−9.91033e129	−0.546530
$486$	−2.16180e130	−1.07884
$487$	2.48775e130	1.12370	0.561852	−	0.827238i	$-0.310089\pi$
$487$	2.48775e130	1.12370	0.561852	+	0.827238i	$0.310089\pi$
$488$	−4.38245e129	−0.179207
$489$	−2.01830e130	−0.747320
$490$	1.30491e130	0.437592
$491$	−4.38925e129	−0.133333	−0.0666665	−	0.997775i	$-0.521236\pi$
$491$	−4.38925e129	−0.133333	−0.0666665	+	0.997775i	$0.521236\pi$
$492$	−1.73404e130	−0.477258
$493$	5.57999e130	1.39174
$494$	−7.33906e129	−0.165914
$495$	2.22860e130	0.456751
$496$	−2.04571e130	−0.380175
$497$	5.22415e130	0.880503
$498$	−1.70617e131	−2.60855
$499$	−3.55420e130	−0.493021	−0.246510	−	0.969140i	$-0.579284\pi$
$499$	−3.55420e130	−0.493021	−0.246510	+	0.969140i	$0.579284\pi$
$500$	9.23159e130	1.16207
$501$	1.86502e131	2.13085
$502$	−9.68387e130	−1.00443
$503$	−8.92475e130	−0.840521	−0.420261	−	0.907403i	$-0.638061\pi$
$503$	−8.92475e130	−0.840521	−0.420261	+	0.907403i	$0.638061\pi$
$504$	−6.35243e129	−0.0543324
$505$	−4.03452e130	−0.313444
$506$	−4.93936e131	−3.48635
$507$	−1.30091e129	−0.00834377
$508$	1.35199e131	0.788104
$509$	1.97808e131	1.04817	0.524085	−	0.851666i	$-0.324407\pi$
$509$	1.97808e131	1.04817	0.524085	+	0.851666i	$0.324407\pi$
$510$	2.33176e131	1.12339
$511$	5.16919e130	0.226469
$512$	3.47809e131	1.38595
$513$	2.26527e130	0.0821160
$514$	8.71714e131	2.87517
$515$	−1.14850e131	−0.344732
$516$	4.56814e131	1.24804
$517$	−1.29371e132	−3.21770
$518$	−7.45789e131	−1.68897
$519$	1.56236e131	0.322229
$520$	−6.57924e130	−0.123599
$521$	−3.34022e131	−0.571670	−0.285835	−	0.958279i	$-0.592271\pi$
$521$	−3.34022e131	−0.571670	−0.285835	+	0.958279i	$0.592271\pi$
$522$	−5.08097e131	−0.792369
$523$	1.61863e131	0.230046	0.115023	−	0.993363i	$-0.463306\pi$
$523$	1.61863e131	0.230046	0.115023	+	0.993363i	$0.463306\pi$
$524$	5.89481e131	0.763664
$525$	4.20115e131	0.496183
$526$	−1.86984e132	−2.01370
$527$	−4.52813e131	−0.444738
$528$	2.01265e132	1.80312
$529$	9.48607e131	0.775329
$530$	−3.32117e131	−0.247692
$531$	−3.45931e131	−0.235454
$532$	1.52717e131	0.0948798
$533$	−6.29547e131	−0.357074
$534$	4.44036e131	0.229968
$535$	1.01235e132	0.478821
$536$	−1.68365e131	−0.0727377
$537$	9.63520e131	0.380284
$538$	−5.75615e131	−0.207583
$539$	2.49310e132	0.821644
$540$	1.76635e132	0.532083
$541$	−5.87111e132	−1.61679	−0.808394	−	0.588641i	$-0.799663\pi$
$541$	−5.87111e132	−1.61679	−0.808394	+	0.588641i	$0.799663\pi$
$542$	1.09269e132	0.275127
$543$	−1.86303e132	−0.428970
$544$	6.80015e132	1.43209
$545$	−1.06247e132	−0.204685
$546$	−7.15777e132	−1.26164
$547$	7.80647e132	1.25913	0.629563	−	0.776949i	$-0.283234\pi$
$547$	7.80647e132	1.25913	0.629563	+	0.776949i	$0.283234\pi$
$548$	−1.35139e133	−1.99491
$549$	−2.72388e132	−0.368068
$550$	1.20967e133	1.49650
$551$	1.40434e132	0.159082
$552$	2.87009e132	0.297749
$553$	−1.78796e132	−0.169898
$554$	−2.21928e133	−1.93192
$555$	−1.52031e133	−1.21261
$556$	1.86872e133	1.36589
$557$	−1.08981e133	−0.730088	−0.365044	−	0.930990i	$-0.618946\pi$
$557$	−1.08981e133	−0.730088	−0.365044	+	0.930990i	$0.618946\pi$
$558$	4.12318e132	0.253206
$559$	1.65847e133	0.933758
$560$	−7.95837e132	−0.410870
$561$	4.45495e133	2.10933
$562$	−8.31413e132	−0.361082
$563$	−1.63334e133	−0.650758	−0.325379	−	0.945584i	$-0.605492\pi$
$563$	−1.63334e133	−0.650758	−0.325379	+	0.945584i	$0.605492\pi$
$564$	6.53856e133	2.39026
$565$	3.22273e133	1.08112
$566$	−9.05332e133	−2.78748
$567$	3.22331e133	0.911012
$568$	−8.74054e132	−0.226800
$569$	2.54954e133	0.607459	0.303730	−	0.952758i	$-0.401768\pi$
$569$	2.54954e133	0.607459	0.303730	+	0.952758i	$0.401768\pi$
$570$	5.86844e132	0.128408
$571$	3.10057e132	0.0623146	0.0311573	−	0.999514i	$-0.490081\pi$
$571$	3.10057e132	0.0623146	0.0311573	+	0.999514i	$0.490081\pi$
$572$	−1.09334e134	−2.01860
$573$	−1.03362e134	−1.75332
$574$	2.46942e133	0.384918
$575$	−5.31955e133	−0.762051
$576$	−3.66897e133	−0.483118
$577$	2.35450e133	0.285018	0.142509	−	0.989794i	$-0.454483\pi$
$577$	2.35450e133	0.285018	0.142509	+	0.989794i	$0.454483\pi$
$578$	−4.92519e131	−0.00548179
$579$	1.05650e133	0.108133
$580$	1.09504e134	1.03079
$581$	1.28895e134	1.11608
$582$	1.80390e134	1.43697
$583$	−6.34530e133	−0.465079
$584$	−8.64858e132	−0.0583340
$585$	−4.08927e133	−0.253855
$586$	1.70385e134	0.973639
$587$	−8.16435e133	−0.429511	−0.214755	−	0.976668i	$-0.568895\pi$
$587$	−8.16435e133	−0.429511	−0.214755	+	0.976668i	$0.568895\pi$
$588$	−1.26004e134	−0.610358
$589$	−1.13962e133	−0.0508355
$590$	1.40537e134	0.577389
$591$	−8.07863e133	−0.305735
$592$	−3.84788e134	−1.34159
$593$	−3.69984e134	−1.18858	−0.594292	−	0.804249i	$-0.702568\pi$
$593$	−3.69984e134	−1.18858	−0.594292	+	0.804249i	$0.702568\pi$
$594$	6.36144e134	1.88327
$595$	−1.76156e134	−0.480646
$596$	−2.07385e134	−0.521596
$597$	6.36016e134	1.47473
$598$	9.06326e134	1.93766
$599$	−5.58734e134	−1.10155	−0.550775	−	0.834654i	$-0.685668\pi$
$599$	−5.58734e134	−1.10155	−0.550775	+	0.834654i	$0.685668\pi$
$600$	−7.02895e133	−0.127807
$601$	−2.81713e134	−0.472493	−0.236247	−	0.971693i	$-0.575917\pi$
$601$	−2.81713e134	−0.472493	−0.236247	+	0.971693i	$0.575917\pi$
$602$	−6.50539e134	−1.00657
$603$	−1.04646e134	−0.149394
$604$	−1.10792e135	−1.45954
$605$	−1.19166e135	−1.44882
$606$	7.34372e134	0.824127
$607$	2.09397e134	0.216929	0.108465	−	0.994100i	$-0.465407\pi$
$607$	2.09397e134	0.216929	0.108465	+	0.994100i	$0.465407\pi$
$608$	1.71143e134	0.163695
$609$	1.36965e135	1.20968
$610$	1.10660e135	0.902593
$611$	2.37383e135	1.78835
$612$	−6.31016e134	−0.439134
$613$	2.80652e134	0.180441	0.0902204	−	0.995922i	$-0.471243\pi$
$613$	2.80652e134	0.180441	0.0902204	+	0.995922i	$0.471243\pi$
$614$	−3.81698e135	−2.26754
$615$	5.03397e134	0.276355
$616$	4.93063e134	0.250171
$617$	2.41135e135	1.13092	0.565458	−	0.824777i	$-0.308700\pi$
$617$	2.41135e135	1.13092	0.565458	+	0.824777i	$0.308700\pi$
$618$	2.09053e135	0.906392
$619$	3.55769e134	0.142617	0.0713087	−	0.997454i	$-0.477282\pi$
$619$	3.55769e134	0.142617	0.0713087	+	0.997454i	$0.477282\pi$
$620$	−8.88619e134	−0.329396
$621$	−2.79746e135	−0.959006
$622$	2.88242e135	0.913952
$623$	−3.35455e134	−0.0983929
$624$	−3.69303e135	−1.00214
$625$	−4.02101e134	−0.100961
$626$	−9.61273e135	−2.23353
$627$	1.12120e135	0.241106
$628$	−8.27526e134	−0.164717
$629$	−8.51717e135	−1.56942
$630$	1.60403e135	0.273650
$631$	1.14878e136	1.81473	0.907367	−	0.420338i	$-0.138089\pi$
$631$	1.14878e136	1.81473	0.907367	+	0.420338i	$0.138089\pi$
$632$	2.99144e134	0.0437625
$633$	3.15825e135	0.427924
$634$	2.72850e135	0.342448
$635$	−3.92486e135	−0.456351
$636$	3.20699e135	0.345484
$637$	−4.57460e135	−0.456657
$638$	3.94374e136	3.64843
$639$	−5.43261e135	−0.465819
$640$	3.09482e135	0.245984
$641$	−4.34208e135	−0.319951	−0.159976	−	0.987121i	$-0.551142\pi$
$641$	−4.34208e135	−0.319951	−0.159976	+	0.987121i	$0.551142\pi$
$642$	−1.84270e136	−1.25895
$643$	9.80684e135	0.621294	0.310647	−	0.950525i	$-0.399454\pi$
$643$	9.80684e135	0.621294	0.310647	+	0.950525i	$0.399454\pi$
$644$	−1.88596e136	−1.10807
$645$	−1.32614e136	−0.722676
$646$	3.28765e135	0.166191
$647$	−9.88248e135	−0.463456	−0.231728	−	0.972781i	$-0.574438\pi$
$647$	−9.88248e135	−0.463456	−0.231728	+	0.972781i	$0.574438\pi$
$648$	−5.39293e135	−0.234659
$649$	2.68504e136	1.08414
$650$	−2.21963e136	−0.831729
$651$	−1.11147e136	−0.386561
$652$	−2.21894e136	−0.716370
$653$	6.46443e136	1.93750	0.968748	−	0.248049i	$-0.0797893\pi$
$653$	6.46443e136	1.93750	0.968748	+	0.248049i	$0.0797893\pi$
$654$	1.93393e136	0.538170
$655$	−1.71128e136	−0.442199
$656$	1.27409e136	0.305748
$657$	−5.37545e135	−0.119810
$658$	−9.31143e136	−1.92779
$659$	−2.78484e136	−0.535621	−0.267811	−	0.963472i	$-0.586300\pi$
$659$	−2.78484e136	−0.535621	−0.267811	+	0.963472i	$0.586300\pi$
$660$	8.74258e136	1.56228
$661$	−3.15747e136	−0.524285	−0.262143	−	0.965029i	$-0.584429\pi$
$661$	−3.15747e136	−0.524285	−0.262143	+	0.965029i	$0.584429\pi$
$662$	8.32285e136	1.28428
$663$	−8.17442e136	−1.17233
$664$	−2.15655e136	−0.287480
$665$	−4.43342e135	−0.0549400
$666$	7.75548e136	0.893529
$667$	−1.73427e137	−1.85787
$668$	2.05042e137	2.04260
$669$	6.06561e136	0.561963
$670$	4.25132e136	0.366350
$671$	2.11422e137	1.69476
$672$	1.66915e137	1.24476
$673$	−1.55040e137	−1.07575	−0.537876	−	0.843024i	$-0.680773\pi$
$673$	−1.55040e137	−1.07575	−0.537876	+	0.843024i	$0.680773\pi$
$674$	−2.71231e137	−1.75119
$675$	6.85109e136	0.411649
$676$	−1.43024e135	−0.00799822
$677$	1.63602e137	0.851604	0.425802	−	0.904816i	$-0.359992\pi$
$677$	1.63602e137	0.851604	0.425802	+	0.904816i	$0.359992\pi$
$678$	−5.86608e137	−2.84255
$679$	−1.36279e137	−0.614815
$680$	2.94728e136	0.123805
$681$	−3.03928e137	−1.18887
$682$	−3.20033e137	−1.16588
$683$	1.68242e137	0.570859	0.285430	−	0.958400i	$-0.407864\pi$
$683$	1.68242e137	0.570859	0.285430	+	0.958400i	$0.407864\pi$
$684$	−1.58811e136	−0.0501949
$685$	3.92312e137	1.15515
$686$	5.70989e137	1.56642
$687$	3.67375e137	0.939092
$688$	−3.35643e137	−0.799538
$689$	1.16430e137	0.258484
$690$	−7.24714e137	−1.49964
$691$	6.99090e137	1.34849	0.674245	−	0.738508i	$-0.264469\pi$
$691$	6.99090e137	1.34849	0.674245	+	0.738508i	$0.264469\pi$
$692$	1.71767e137	0.308884
$693$	3.06459e137	0.513819
$694$	8.84766e137	1.38323
$695$	−5.42493e137	−0.790918
$696$	−2.29157e137	−0.311591
$697$	2.82016e137	0.357671
$698$	−8.08163e137	−0.956117
$699$	5.67187e136	0.0626013
$700$	4.61878e137	0.475634
$701$	−2.94894e137	−0.283363	−0.141681	−	0.989912i	$-0.545251\pi$
$701$	−2.94894e137	−0.283363	−0.141681	+	0.989912i	$0.545251\pi$
$702$	−1.16726e138	−1.04669
$703$	−2.14356e137	−0.179392
$704$	2.84777e138	2.22450
$705$	−1.89816e138	−1.38408
$706$	−1.90684e138	−1.29803
$707$	−5.54794e137	−0.352606
$708$	−1.35705e138	−0.805349
$709$	−1.16348e138	−0.644788	−0.322394	−	0.946606i	$-0.604488\pi$
$709$	−1.16348e138	−0.644788	−0.322394	+	0.946606i	$0.604488\pi$
$710$	2.20704e138	1.14230
$711$	1.85930e137	0.0898824
$712$	5.61251e136	0.0253441
$713$	1.40735e138	0.593691
$714$	3.20644e138	1.26375
$715$	3.17401e138	1.16887
$716$	1.05930e138	0.364535
$717$	−4.61420e138	−1.48394
$718$	−2.00831e137	−0.0603665
$719$	−1.87813e138	−0.527684	−0.263842	−	0.964566i	$-0.584990\pi$
$719$	−1.87813e138	−0.527684	−0.263842	+	0.964566i	$0.584990\pi$
$720$	8.27593e137	0.217366
$721$	−1.57933e138	−0.387804
$722$	−6.27399e138	−1.44042
$723$	1.57840e136	0.00338851
$724$	−2.04823e138	−0.411205
$725$	4.24730e138	0.797479
$726$	2.16908e139	3.80934
$727$	−2.39883e138	−0.394077	−0.197039	−	0.980396i	$-0.563132\pi$
$727$	−2.39883e138	−0.394077	−0.197039	+	0.980396i	$0.563132\pi$
$728$	−9.04723e137	−0.139041
$729$	2.54841e138	0.366425
$730$	2.18382e138	0.293804
$731$	−7.42938e138	−0.935319
$732$	−1.06855e139	−1.25895
$733$	−4.36487e137	−0.0481314	−0.0240657	−	0.999710i	$-0.507661\pi$
$733$	−4.36487e137	−0.0481314	−0.0240657	+	0.999710i	$0.507661\pi$
$734$	−2.30361e138	−0.237766
$735$	3.65793e138	0.353427
$736$	−2.11350e139	−1.91174
$737$	8.12239e138	0.687877
$738$	−2.56795e138	−0.203636
$739$	−6.08027e137	−0.0451510	−0.0225755	−	0.999745i	$-0.507187\pi$
$739$	−6.08027e137	−0.0451510	−0.0225755	+	0.999745i	$0.507187\pi$
$740$	−1.67145e139	−1.16239
$741$	−2.05730e138	−0.134003
$742$	−4.56701e138	−0.278639
$743$	4.71092e138	0.269245	0.134623	−	0.990897i	$-0.457018\pi$
$743$	4.71092e138	0.269245	0.134623	+	0.990897i	$0.457018\pi$
$744$	1.85960e138	0.0995706
$745$	6.02045e138	0.302030
$746$	2.75227e139	1.29377
$747$	−1.34039e139	−0.590447
$748$	4.89782e139	2.02197
$749$	1.39210e139	0.538646
$750$	4.87811e139	1.76921
$751$	3.47103e139	1.18011	0.590054	−	0.807364i	$-0.299107\pi$
$751$	3.47103e139	1.18011	0.590054	+	0.807364i	$0.299107\pi$
$752$	−4.80420e139	−1.53129
$753$	−2.71460e139	−0.811239
$754$	−7.23640e139	−2.02774
$755$	3.21631e139	0.845145
$756$	2.42894e139	0.598563
$757$	3.25016e139	0.751198	0.375599	−	0.926782i	$-0.377437\pi$
$757$	3.25016e139	0.751198	0.375599	+	0.926782i	$0.377437\pi$
$758$	−6.33600e139	−1.37359
$759$	−1.38461e140	−2.81579
$760$	7.41756e137	0.0141515
$761$	5.29421e139	0.947644	0.473822	−	0.880621i	$-0.342874\pi$
$761$	5.29421e139	0.947644	0.473822	+	0.880621i	$0.342874\pi$
$762$	7.14412e139	1.19987
$763$	−1.46102e139	−0.230259
$764$	−1.13637e140	−1.68070
$765$	1.83186e139	0.254280
$766$	3.59877e139	0.468877
$767$	−4.92680e139	−0.602546
$768$	7.10501e139	0.815728
$769$	9.09061e139	0.979864	0.489932	−	0.871761i	$-0.337022\pi$
$769$	9.09061e139	0.979864	0.489932	+	0.871761i	$0.337022\pi$
$770$	−1.24501e140	−1.26001
$771$	2.44360e140	2.32217
$772$	1.16152e139	0.103655
$773$	−2.36440e140	−1.98160	−0.990799	−	0.135342i	$-0.956787\pi$
$773$	−2.36440e140	−1.98160	−0.990799	+	0.135342i	$0.956787\pi$
$774$	6.76497e139	0.532512
$775$	−3.44666e139	−0.254839
$776$	2.28008e139	0.158364
$777$	−2.09061e140	−1.36412
$778$	3.34820e140	2.05258
$779$	7.09764e138	0.0408834
$780$	−1.60418e140	−0.868291
$781$	4.21668e140	2.14484
$782$	−4.06003e140	−1.94090
$783$	2.23358e140	1.00359
$784$	9.25814e139	0.391016
$785$	2.40233e139	0.0953793
$786$	3.11491e140	1.16266
$787$	−3.96482e140	−1.39139	−0.695695	−	0.718337i	$-0.744904\pi$
$787$	−3.96482e140	−1.39139	−0.695695	+	0.718337i	$0.744904\pi$
$788$	−8.88172e139	−0.293073
$789$	−5.24156e140	−1.62640
$790$	−7.55357e139	−0.220414
$791$	4.43163e140	1.21620
$792$	−5.12737e139	−0.132350
$793$	−3.87939e140	−0.941919
$794$	2.95672e140	0.675329
$795$	−9.30997e139	−0.200052
$796$	6.99242e140	1.41366
$797$	−6.88825e140	−1.31033	−0.655165	−	0.755486i	$-0.727401\pi$
$797$	−6.88825e140	−1.31033	−0.655165	+	0.755486i	$0.727401\pi$
$798$	8.06981e139	0.144452
$799$	−1.06340e141	−1.79134
$800$	5.17604e140	0.820603
$801$	3.48841e139	0.0520535
$802$	−6.60351e140	−0.927508
$803$	4.17231e140	0.551662
$804$	−4.10516e140	−0.510989
$805$	5.47498e140	0.641626
$806$	5.87230e140	0.647975
$807$	−1.61357e140	−0.167657
$808$	9.28228e139	0.0908246
$809$	1.41935e141	1.30793	0.653967	−	0.756523i	$-0.273104\pi$
$809$	1.41935e141	1.30793	0.653967	+	0.756523i	$0.273104\pi$
$810$	1.36175e141	1.18188
$811$	2.06491e141	1.68806	0.844032	−	0.536293i	$-0.180176\pi$
$811$	2.06491e141	1.68806	0.844032	+	0.536293i	$0.180176\pi$
$812$	1.50581e141	1.15959
$813$	3.06305e140	0.222210
$814$	−6.01964e141	−4.11422
$815$	6.44164e140	0.414813
$816$	1.65435e141	1.00382
$817$	−1.86979e140	−0.106911
$818$	−3.60430e141	−1.94216
$819$	−5.62323e140	−0.285573
$820$	5.53440e140	0.264910
$821$	−1.50810e141	−0.680434	−0.340217	−	0.940347i	$-0.610501\pi$
$821$	−1.50810e141	−0.680434	−0.340217	+	0.940347i	$0.610501\pi$
$822$	−7.14096e141	−3.03720
$823$	−1.16847e140	−0.0468517	−0.0234258	−	0.999726i	$-0.507457\pi$
$823$	−1.16847e140	−0.0468517	−0.0234258	+	0.999726i	$0.507457\pi$
$824$	2.64238e140	0.0998908
$825$	3.39096e141	1.20867
$826$	1.93255e141	0.649530
$827$	1.96275e141	0.622081	0.311040	−	0.950397i	$-0.399323\pi$
$827$	1.96275e141	0.622081	0.311040	+	0.950397i	$0.399323\pi$
$828$	1.96121e141	0.586210
$829$	4.38312e141	1.23563	0.617816	−	0.786323i	$-0.288018\pi$
$829$	4.38312e141	1.23563	0.617816	+	0.786323i	$0.288018\pi$
$830$	5.44543e141	1.44792
$831$	−6.22113e141	−1.56034
$832$	−5.22540e141	−1.23634
$833$	2.04927e141	0.457421
$834$	9.87459e141	2.07953
$835$	−5.95241e141	−1.18277
$836$	1.23266e141	0.231120
$837$	−1.81254e141	−0.320703
$838$	−3.69617e141	−0.617187
$839$	−3.13805e141	−0.494543	−0.247272	−	0.968946i	$-0.579534\pi$
$839$	−3.13805e141	−0.494543	−0.247272	+	0.968946i	$0.579534\pi$
$840$	7.23433e140	0.107610
$841$	6.72493e141	0.944239
$842$	2.45977e141	0.326030
$843$	−2.33063e141	−0.291632
$844$	3.47221e141	0.410202
$845$	4.15201e139	0.00463136
$846$	9.68299e141	1.01987
$847$	−1.63867e142	−1.62984
$848$	−2.35633e141	−0.221329
$849$	−2.53784e142	−2.25134
$850$	9.94318e141	0.833120
$851$	2.64715e142	2.09506
$852$	−2.13116e142	−1.59329
$853$	2.04478e142	1.44417	0.722084	−	0.691805i	$-0.243184\pi$
$853$	2.04478e142	1.44417	0.722084	+	0.691805i	$0.243184\pi$
$854$	1.52170e142	1.01537
$855$	4.61032e140	0.0290653
$856$	−2.32913e141	−0.138745
$857$	−2.81479e142	−1.58444	−0.792219	−	0.610236i	$-0.791074\pi$
$857$	−2.81479e142	−1.58444	−0.792219	+	0.610236i	$0.791074\pi$
$858$	−5.77740e142	−3.07326
$859$	1.42795e142	0.717868	0.358934	−	0.933363i	$-0.383140\pi$
$859$	1.42795e142	0.717868	0.358934	+	0.933363i	$0.383140\pi$
$860$	−1.45797e142	−0.692746
$861$	6.92231e141	0.310884
$862$	1.66245e142	0.705741
$863$	1.15899e142	0.465110	0.232555	−	0.972583i	$-0.425291\pi$
$863$	1.15899e142	0.465110	0.232555	+	0.972583i	$0.425291\pi$
$864$	2.72199e142	1.03269
$865$	−4.98645e141	−0.178859
$866$	5.41240e142	1.83557
$867$	−1.38064e140	−0.00442745
$868$	−1.22196e142	−0.370552
$869$	−1.44315e142	−0.413860
$870$	5.78636e142	1.56936
$871$	−1.49038e142	−0.382311
$872$	2.44444e141	0.0593101
$873$	1.41717e142	0.325260
$874$	−1.02181e142	−0.221853
$875$	−3.68525e142	−0.756966
$876$	−2.10874e142	−0.409802
$877$	2.04337e142	0.375721	0.187861	−	0.982196i	$-0.439845\pi$
$877$	2.04337e142	0.375721	0.187861	+	0.982196i	$0.439845\pi$
$878$	2.77616e141	0.0483014
$879$	4.77627e142	0.786373
$880$	−6.42361e142	−1.00085
$881$	7.94028e141	0.117086	0.0585429	−	0.998285i	$-0.481355\pi$
$881$	7.94028e141	0.117086	0.0585429	+	0.998285i	$0.481355\pi$
$882$	−1.86600e142	−0.260427
$883$	−1.29445e143	−1.70998	−0.854989	−	0.518646i	$-0.826436\pi$
$883$	−1.29445e143	−1.70998	−0.854989	+	0.518646i	$0.826436\pi$
$884$	−8.98703e142	−1.12378
$885$	3.93956e142	0.466336
$886$	−7.16527e142	−0.802966
$887$	3.36952e142	0.357497	0.178748	−	0.983895i	$-0.442795\pi$
$887$	3.36952e142	0.357497	0.178748	+	0.983895i	$0.442795\pi$
$888$	3.49780e142	0.351371
$889$	−5.39715e142	−0.513368
$890$	−1.41719e142	−0.127648
$891$	2.60170e143	2.21916
$892$	6.66859e142	0.538690
$893$	−2.67631e142	−0.204758
$894$	−1.09586e143	−0.794115
$895$	−3.07518e142	−0.211083
$896$	4.25574e142	0.276717
$897$	2.54063e143	1.56497
$898$	3.63982e143	2.12411
$899$	−1.12368e143	−0.621292
$900$	−4.80308e142	−0.251628
$901$	−5.21568e142	−0.258916
$902$	1.99319e143	0.937632
$903$	−1.82360e143	−0.812969
$904$	−7.41458e142	−0.313269
$905$	5.94606e142	0.238107
$906$	−5.85441e143	−2.22211
$907$	−2.14396e143	−0.771372	−0.385686	−	0.922630i	$-0.626035\pi$
$907$	−2.14396e143	−0.771372	−0.385686	+	0.922630i	$0.626035\pi$
$908$	−3.34141e143	−1.13964
$909$	5.76932e142	0.186542
$910$	2.28448e143	0.700294
$911$	−1.63615e143	−0.475534	−0.237767	−	0.971322i	$-0.576415\pi$
$911$	−1.63615e143	−0.475534	−0.237767	+	0.971322i	$0.576415\pi$
$912$	4.16359e142	0.114741
$913$	1.04038e144	2.71869
$914$	−6.22374e143	−1.54227
$915$	3.10203e143	0.728992
$916$	4.03896e143	0.900200
$917$	−2.35321e143	−0.497448
$918$	5.22895e143	1.04844
$919$	−2.84470e143	−0.541046	−0.270523	−	0.962714i	$-0.587197\pi$
$919$	−2.84470e143	−0.541046	−0.270523	+	0.962714i	$0.587197\pi$
$920$	−9.16020e142	−0.165271
$921$	−1.06998e144	−1.83141
$922$	−2.29555e143	−0.372767
$923$	−7.73720e143	−1.19207
$924$	1.20221e144	1.75748
$925$	−6.48298e143	−0.899292
$926$	−8.69183e143	−1.14414
$927$	1.64235e143	0.205163
$928$	1.68749e144	2.00062
$929$	8.93629e143	1.00553	0.502765	−	0.864423i	$-0.332316\pi$
$929$	8.93629e143	1.00553	0.502765	+	0.864423i	$0.332316\pi$
$930$	−4.69559e143	−0.501496
$931$	5.15749e142	0.0522852
$932$	6.23571e142	0.0600087
$933$	8.08004e143	0.738165
$934$	2.39337e144	2.07580
$935$	−1.42185e144	−1.17082
$936$	9.40824e142	0.0735580
$937$	1.50749e144	1.11914	0.559571	−	0.828783i	$-0.310966\pi$
$937$	1.50749e144	1.11914	0.559571	+	0.828783i	$0.310966\pi$
$938$	5.84607e143	0.412122
$939$	−2.69466e144	−1.80394
$940$	−2.08686e144	−1.32676
$941$	9.16279e143	0.553262	0.276631	−	0.960976i	$-0.410782\pi$
$941$	9.16279e143	0.553262	0.276631	+	0.960976i	$0.410782\pi$
$942$	−4.37277e143	−0.250777
$943$	−8.76512e143	−0.477464
$944$	9.97095e143	0.515935
$945$	−7.05127e143	−0.346597
$946$	−5.25083e144	−2.45193
$947$	6.11306e143	0.271197	0.135598	−	0.990764i	$-0.456704\pi$
$947$	6.11306e143	0.271197	0.135598	+	0.990764i	$0.456704\pi$
$948$	7.29387e143	0.307435
$949$	−7.65580e143	−0.306605
$950$	2.50245e143	0.0952293
$951$	7.64857e143	0.276583
$952$	4.05286e143	0.139274
$953$	−8.83941e143	−0.288681	−0.144340	−	0.989528i	$-0.546106\pi$
$953$	−8.83941e143	−0.288681	−0.144340	+	0.989528i	$0.546106\pi$
$954$	4.74925e143	0.147411
$955$	3.29890e144	0.973209
$956$	−5.07289e144	−1.42249
$957$	1.10552e145	2.94670
$958$	−7.86249e144	−1.99220
$959$	5.39476e144	1.29948
$960$	4.17832e144	0.956857
$961$	−3.68102e144	−0.801463
$962$	1.10455e145	2.28662
$963$	−1.44765e144	−0.284963
$964$	1.73530e142	0.00324817
$965$	−3.37193e143	−0.0600211
$966$	−9.96568e144	−1.68700
$967$	5.00806e144	0.806279	0.403139	−	0.915139i	$-0.367919\pi$
$967$	5.00806e144	0.806279	0.403139	+	0.915139i	$0.367919\pi$
$968$	2.74166e144	0.419816
$969$	9.21600e143	0.134227
$970$	−5.75735e144	−0.797616
$971$	−1.17752e145	−1.55180	−0.775902	−	0.630853i	$-0.782705\pi$
$971$	−1.17752e145	−1.55180	−0.775902	+	0.630853i	$0.782705\pi$
$972$	−6.66241e144	−0.835252
$973$	−7.45993e144	−0.889737
$974$	1.44524e145	1.63995
$975$	−6.22209e144	−0.671757
$976$	7.85117e144	0.806525
$977$	6.85312e144	0.669888	0.334944	−	0.942238i	$-0.391283\pi$
$977$	6.85312e144	0.669888	0.334944	+	0.942238i	$0.391283\pi$
$978$	−1.17252e145	−1.09065
$979$	−2.70763e144	−0.239678
$980$	4.02156e144	0.338790
$981$	1.51932e144	0.121815
$982$	−2.54991e144	−0.194589
$983$	−1.01485e145	−0.737152	−0.368576	−	0.929598i	$-0.620155\pi$
$983$	−1.01485e145	−0.737152	−0.368576	+	0.929598i	$0.620155\pi$
$984$	−1.15817e144	−0.0800777
$985$	2.57838e144	0.169703
$986$	3.24166e145	2.03113
$987$	−2.61020e145	−1.55701
$988$	−2.26181e144	−0.128453
$989$	2.30907e145	1.24858
$990$	1.29469e145	0.666592
$991$	−9.22135e143	−0.0452087	−0.0226044	−	0.999744i	$-0.507196\pi$
$991$	−9.22135e143	−0.0452087	−0.0226044	+	0.999744i	$0.507196\pi$
$992$	−1.36939e145	−0.639308
$993$	2.33308e145	1.03727
$994$	3.03494e145	1.28502
$995$	−2.02992e145	−0.818575
$996$	−5.25821e145	−2.01957
$997$	−6.29694e144	−0.230364	−0.115182	−	0.993344i	$-0.536745\pi$
$997$	−6.29694e144	−0.230364	−0.115182	+	0.993344i	$0.536745\pi$
$998$	−2.06479e145	−0.719524
$999$	−3.40929e145	−1.13172

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.98.a.a.1.7	✓	7
3.2	odd	2		9.98.a.a.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.98.a.a.1.7	✓	7	1.1	even	1	trivial
9.98.a.a.1.1		7	3.2	odd	2

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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 98 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+5.80945e14 q^{2} +1.62851e23 q^{3} +1.79040e29 q^{4} -5.19758e33 q^{5} +9.46076e37 q^{6} -7.14729e40 q^{7} +1.19582e43 q^{8} +7.43249e45 q^{9} +O(q^{10})\)	\(q+5.80945e14 q^{2} +1.62851e23 q^{3} +1.79040e29 q^{4} -5.19758e33 q^{5} +9.46076e37 q^{6} -7.14729e40 q^{7} +1.19582e43 q^{8} +7.43249e45 q^{9} -3.01951e48 q^{10} -5.76894e50 q^{11} +2.91569e52 q^{12} +1.05855e54 q^{13} -4.15218e55 q^{14} -8.46433e56 q^{15} -2.14230e58 q^{16} -4.74193e59 q^{17} +4.31787e60 q^{18} -1.19343e61 q^{19} -9.30577e62 q^{20} -1.16395e64 q^{21} -3.35144e65 q^{22} +1.47380e66 q^{23} +1.94740e66 q^{24} -3.60940e67 q^{25} +6.14957e68 q^{26} -1.89812e69 q^{27} -1.27965e70 q^{28} -1.17673e71 q^{29} -4.91731e71 q^{30} +9.54912e71 q^{31} -1.43404e73 q^{32} -9.39480e73 q^{33} -2.75480e74 q^{34} +3.71486e74 q^{35} +1.33072e75 q^{36} +1.79614e76 q^{37} -6.93314e75 q^{38} +1.72386e77 q^{39} -6.21535e76 q^{40} -5.94728e77 q^{41} -6.76188e78 q^{42} +1.56674e79 q^{43} -1.03287e80 q^{44} -3.86310e79 q^{45} +8.56198e80 q^{46} +2.24254e81 q^{47} -3.48877e81 q^{48} -4.32158e81 q^{49} -2.09686e82 q^{50} -7.72230e82 q^{51} +1.89523e83 q^{52} +1.09991e83 q^{53} -1.10270e84 q^{54} +2.99846e84 q^{55} -8.54684e83 q^{56} -1.94351e84 q^{57} -6.83616e85 q^{58} -4.65431e85 q^{59} -1.51546e86 q^{60} -3.66482e86 q^{61} +5.54751e86 q^{62} -5.31222e86 q^{63} -4.93639e87 q^{64} -5.50188e87 q^{65} -5.45786e88 q^{66} -1.40795e88 q^{67} -8.48997e88 q^{68} +2.40011e89 q^{69} +2.15813e89 q^{70} -7.30927e89 q^{71} +8.88789e88 q^{72} -7.23237e89 q^{73} +1.04346e91 q^{74} -5.87796e90 q^{75} -2.13671e90 q^{76} +4.12323e91 q^{77} +1.00147e92 q^{78} +2.50159e91 q^{79} +1.11348e92 q^{80} -4.50984e92 q^{81} -3.45504e92 q^{82} -1.80342e93 q^{83} -2.08393e93 q^{84} +2.46466e93 q^{85} +9.10189e93 q^{86} -1.91632e94 q^{87} -6.89859e93 q^{88} +4.69345e93 q^{89} -2.24425e94 q^{90} -7.56574e94 q^{91} +2.63870e95 q^{92} +1.55509e95 q^{93} +1.30279e96 q^{94} +6.20293e94 q^{95} -2.33536e96 q^{96} +1.90672e96 q^{97} -2.51060e96 q^{98} -4.28776e96 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots + 34\!\cdots\!51 q^{9}+O(q^{10}) \) 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9	\( 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots - 13\!\cdots\!28 q^{99}+O(q^{100}) \) 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9 + 2369114123959441270700616822719459966510786272800 * q^10 - 211379321299339211995860033669883746379479318698796 * q^11 + 29500590587146562092031430274877546417191966208812032 * q^12 - 883667637845783834437332163606692334928033653755299614 * q^13 + 24884922778173528138085777326574033504771595080747613568 * q^14 - 1421739776861319561135033238174867421082029896683725376600 * q^15 - 31468671341370205538262999960370611414173356196203424841728 * q^16 + 163250436637003263661570089512096377905088225334685131721342 * q^17 - 7054606772048003028382413409749231596837718873737440667537424 * q^18 + 133084372359310898958448501523235681541051727436663191570359820 * q^19 - 1318696260534044061297364386263469065025874939722479973417331200 * q^20 - 8226961344750528298533572507576209983448935264598913374247505696 * q^21 - 193421584410477868290586506488587370358898549812529751083484246976 * q^22 + 925260914184001305416523826357059292226482310773339215111132964776 * q^23 + 1719359518493251306391725804700467921422689016189510541760687554560 * q^24 - 15111829774373494694703308579556617230149980669179989285410298974375 * q^25 + 252570839996871764139482603418038366978372757286009959646749464447904 * q^26 - 16291464003153760806194022590188439733978909915063668620863256233960 * q^27 + 2270023864280230580582797832096861251181573169347509612847861972977664 * q^28 - 119228645746988213289933973286594685848645193803889692652451844737975470 * q^29 + 350448354156350400480979435069989695492221249186335731168327070817564800 * q^30 + 1783283666881858864849681148885200501497581294973934227348751364131906784 * q^31 - 5665372498136527985720301619489703024215195383428523596691479514791804928 * q^32 + 31524650657546522511070078635079454480923539002999356172307109465073458512 * q^33 - 360491523041063125717708388027762293189396999595568175085448186659598970272 * q^34 + 1278268341035082746531666145800358760269267683649420892787253371588938750800 * q^35 - 216561481226385812264597126278375191173372906326221899147967914271513631488 * q^36 - 4532061622841943284542390241171859851726205146853788500539269747469617514358 * q^37 - 2979582210919721773595405461863152858097797783237497905501709239616681227840 * q^38 + 43268347489134056222423767530379619668087154910038087692852374564634305176712 * q^39 - 252514831298472678734291758335102132215188475493571956673272319739362987008000 * q^40 + 123663386655433999860484853403953500874113711440208020678841289201379470695974 * q^41 + 3296122851141924824443574220618174749418258893075867148421980920155200276985344 * q^42 - 6595249409358954185694714287710218939626711013706300289026511229489118746183244 * q^43 + 31427981619155317050453798326367420934595218826815326227502736274099059309390848 * q^44 - 252057107931731391251960224707597558538839631727412739243273361199825466582835550 * q^45 + 333743461536679365083903174537100831945624746347277312419032904840551699600111744 * q^46 + 1582413179705462665936960636748613012540566075462612818643843634715630112826042192 * q^47 - 5861556434117332280930374286873664455351210291383528056190272983552191849213722624 * q^48 + 4345635008055985505106601346877321132027699788278385269907095782368403364891488399 * q^49 - 26742593205970009143775889336520990050133941492259748319418427757724876722706030000 * q^50 + 7043565089506559965061572069632281800522096763383079376468682406398600422146676984 * q^51 + 45800222007571685487736059984048709986270205428489770979037497696929384027946163712 * q^52 - 653999931744204429821742741003701830521617657540517458768483866216741544701292475654 * q^53 - 1692275654206728716605786947196644220317392594111136065941704729626944069981837438080 * q^54 - 2797264930804680667438884831689324464716285797264284803651188210713133784740241832200 * q^55 - 13571511538900847480549793700693331801076437559096966169392506220987757777557857402880 * q^56 - 32156245276763940566100505959698139630384956043693169857398532690693294678041975751120 * q^57 - 110275012470967940484400158535846043036245771061355495516009955997986614502808104491360 * q^58 - 289716843512018767811919727809674339112407721830489506743846640027004030301179845118940 * q^59 - 910863091257112962110410128770927709732237428874631129572443550789630933691032398899200 * q^60 - 1779644273771380099149369471014727845406783738447834645166296866716596067825339549188046 * q^61 - 4893410323209515393605311670149478112622973098189152140516775294151722525768562137565696 * q^62 - 12773855755538157144284595252262546905649007916763284311597736303148976241726684562602024 * q^63 - 24329532034212074257236420324752039539459926287390018025638252399891746834835822530789376 * q^64 - 40979880706222898178317998710539228015340375450212825952623031288613904725454054500850100 * q^65 - 142841613731497146561089386918878946227924637814625892149907766833242924230825872606056192 * q^66 - 183094181851902905703789039636502649221241410347877100016575616698548103898875205122783908 * q^67 - 250132580738896836682574414547500843555901286243235420681429272583107380144497499057716736 * q^68 - 372244836961332226973480986215431578494847115740354696097669790201492502675456308855459168 * q^69 - 587389541033882485666068522391834191601610745639266949076956170254929472707526921059782400 * q^70 - 36618527208607574135274147674246343687098099724640001025727994874106062220116534447931656 * q^71 + 2495502705800463241319297965149724088435827677064467496346161624547668625438549984339128320 * q^72 + 5937141741627411574629383951784847225959103237898806939243808260531064318159784943464907526 * q^73 + 25603418812897773069861990064614106209712057876935905208225093500026599325689360114519970848 * q^74 + 43416229043729585532262686371625117245611844558141193068941674421259839404159894884059222500 * q^75 + 64491781461168277038374423376126180174707623388661413952117963143585395013082375272839869440 * q^76 + 122801524700573133455664123216977109508839271312008866744292206338517188364407357732160152224 * q^77 + 256518622739178273010532892375526005382856863147760611859324715551823107217212845963281985152 * q^78 + 155279975164311735091235448536513906273532801204307686975280157544842456609207922540776901680 * q^79 + 343037548751841740038666995050634479050946344382038763901789904170114217394648666813900390400 * q^80 - 799336653019442009471583631583081099983526554777301855450568718504605547656753900698628831153 * q^81 - 2054599455199243418451530458808296516745297582440826399667363552358055209069956455679452833056 * q^82 - 2745080838526935126539434486643898932954125805020264508203796620734019354440308801326974021684 * q^83 - 12055830667015300843296227009204563031159870111997209215974794552386444770918151507927520305152 * q^84 - 16156906986132970771716277890961343081101351325821342812927748903601690598916612215092853170700 * q^85 - 16073101085057033129856695763368798351047883803740227513388827997968391823543719379002604387776 * q^86 - 44931373084677669249994770736329381356923858000626008622029156778901658182110994195783000791480 * q^87 - 20900444501134905678673788524771632932447417317035512416151379720801969394444956958395302789120 * q^88 + 8652425236627243255051028260917634407304730072980172181544783646255542601500269383337979350390 * q^89 + 169914380219009102880054256907856294069041898142575788262717672760376053145875718225670932330400 * q^90 + 235279610532724372901602846332263408075886672274330172793822218199845308058643167074949650230544 * q^91 + 622950794384614085632156625042963081233986358617743991991586248417198315809579918444522808891392 * q^92 + 1619655729334717431421579797164299646702152339363664709672746834797775058100318492643375449441152 * q^93 + 1784387548746436753701888750274366538460858609156963702431495773056050960861585984793528939671808 * q^94 + 1109691419127482658877926123378178695834970817464791602098716148821958373905367930889408748989000 * q^95 + 2773817117979873680694700349927475687549477810523157816910439588411515192104026991177258420404224 * q^96 - 462826972284038426621245345324758076530452205891330025493894671876723283114629445572915788984658 * q^97 - 10100804559243313775965110405631054964918520327952856127425837778067309219959758215138751854831056 * q^98 - 13792894935722775136702660269810636953813664741795563019740674282913700184659028566406972539495228 * q^99

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