LMFDB - Embedded newform 1.106.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,106,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, 106, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 106);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 106 $
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:	$69.8187388595$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + \cdots + 48\!\cdots\!00 $ x^8 - x^7 - 10474462181102127261436928504x^6 - 6240865696604065178236747119353100133696x^5 + 32365663931605915811787141090666978113929529159769319936x^4 - 88741241336529855013349956862774730900060182109823885915459384913920x^3 - 32407505137182079391452708433863594692033598408124447196829319910118382841945292800x^2 + 214043885851451477460187594158307222184507667040597404032319249160871059741580610298216611840000x + 4856561902148750128808276554189976865031329612189319452104503000400130936617616805069859831987090718720000000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{111}\cdot 3^{44}\cdot 5^{13}\cdot 7^{7}\cdot 11\cdot 13^{3}\cdot 17 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-4.32050e13$ 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)

$f(q)$	$=$	$q-7.36840e15 q^{2} -8.33754e23 q^{3} +1.37285e31 q^{4} +6.83377e36 q^{5} +6.14343e39 q^{6} +4.41963e44 q^{7} +1.97741e47 q^{8} -1.24542e50 q^{9} +O(q^{10})$	\(q-7.36840e15 q^{2} -8.33754e23 q^{3} +1.37285e31 q^{4} +6.83377e36 q^{5} +6.14343e39 q^{6} +4.41963e44 q^{7} +1.97741e47 q^{8} -1.24542e50 q^{9} -5.03539e52 q^{10} -4.48414e54 q^{11} -1.14462e55 q^{12} +1.91848e58 q^{13} -3.25656e60 q^{14} -5.69768e60 q^{15} -2.01393e63 q^{16} +1.58211e64 q^{17} +9.17672e65 q^{18} -2.66912e67 q^{19} +9.38173e67 q^{20} -3.68489e68 q^{21} +3.30409e70 q^{22} -2.81725e71 q^{23} -1.64867e71 q^{24} +2.20485e73 q^{25} -1.41362e74 q^{26} +2.08254e74 q^{27} +6.06749e75 q^{28} -4.39751e76 q^{29} +4.19828e76 q^{30} +4.22496e77 q^{31} +6.81810e78 q^{32} +3.73867e78 q^{33} -1.16576e80 q^{34} +3.02028e81 q^{35} -1.70977e81 q^{36} +1.25411e82 q^{37} +1.96671e83 q^{38} -1.59954e82 q^{39} +1.35132e84 q^{40} -2.50078e84 q^{41} +2.71517e84 q^{42} -6.45716e85 q^{43} -6.15605e85 q^{44} -8.51089e86 q^{45} +2.07586e87 q^{46} -3.82379e87 q^{47} +1.67912e87 q^{48} +1.40970e89 q^{49} -1.62462e89 q^{50} -1.31909e88 q^{51} +2.63379e89 q^{52} -3.23348e90 q^{53} -1.53450e90 q^{54} -3.06436e91 q^{55} +8.73942e91 q^{56} +2.22539e91 q^{57} +3.24026e92 q^{58} -3.76398e92 q^{59} -7.82206e91 q^{60} -9.74654e92 q^{61} -3.11312e93 q^{62} -5.50428e94 q^{63} +3.14561e94 q^{64} +1.31105e95 q^{65} -2.75480e94 q^{66} -4.90505e95 q^{67} +2.17199e95 q^{68} +2.34889e95 q^{69} -2.22546e97 q^{70} -2.06839e96 q^{71} -2.46270e97 q^{72} -4.35765e97 q^{73} -9.24075e97 q^{74} -1.83830e97 q^{75} -3.66429e98 q^{76} -1.98183e99 q^{77} +1.17861e98 q^{78} -6.86400e99 q^{79} -1.37627e100 q^{80} +1.54236e100 q^{81} +1.84267e100 q^{82} +1.96175e100 q^{83} -5.05880e99 q^{84} +1.08117e101 q^{85} +4.75790e101 q^{86} +3.66644e100 q^{87} -8.86698e101 q^{88} +1.19123e102 q^{89} +6.27116e102 q^{90} +8.47900e102 q^{91} -3.86765e102 q^{92} -3.52258e101 q^{93} +2.81752e103 q^{94} -1.82401e104 q^{95} -5.68462e102 q^{96} +1.02974e104 q^{97} -1.03872e105 q^{98} +5.58462e104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 91\!\cdots\!20 q^{2}+ \cdots + 31\!\cdots\!84 q^{9}+O(q^{10}) $ 8 * q - 9175032489175920 * q^2 - 3552367551392844422995680 * q^3 + 120400994563419904822151366840576 * q^4 + 748366724871512021371292499759044400 * q^5 - 132475226406122000574502252920799787081664 * q^6 + 70538552172860257833295679508195640805531200 * q^7 - 706397877636490430592988742663067828802762076160 * q^8 + 317686049104616976165951103806454636773011694234984 * q^9	$ 8 q - 91\!\cdots\!20 q^{2}+ \cdots - 25\!\cdots\!32 q^{99}+O(q^{100}) $ 8 * q - 9175032489175920 * q^2 - 3552367551392844422995680 * q^3 + 120400994563419904822151366840576 * q^4 + 748366724871512021371292499759044400 * q^5 - 132475226406122000574502252920799787081664 * q^6 + 70538552172860257833295679508195640805531200 * q^7 - 706397877636490430592988742663067828802762076160 * q^8 + 317686049104616976165951103806454636773011694234984 * q^9 + 44171640525838765855893406263279104758565541661288800 * q^10 - 9131055394382837373664474069991492435117703171343284384 * q^11 + 1527166610615675905236013736606832949994468355519571829760 * q^12 + 4027585984285071020829060873004471073659148035689891664240 * q^13 - 160479473931693657661766690342904266858167662972048261318528 * q^14 - 85128562811603808162187988771451472214709069164574920929377600 * q^15 + 889182208997906282405898151302671436269823882827077347193192448 * q^16 - 47501502884916058924984340290257937633075778259367096814503394160 * q^17 - 2631080775730316510475478098580289149623650642713560969940755311280 * q^18 - 18490664070300440944092597449321411045310230817014503422448283738720 * q^19 - 433265654737251440411002845299403120817887965583462605623471811443200 * q^20 + 3435707407505559395644737215619994347818097875706879454950102719283456 * q^21 + 61667954680464912832813918015747124830645650785532527356368764542445760 * q^22 + 356123479312529060531796005710488420903589988587191444144805952706144960 * q^23 - 8553895157762497374674387748794258238227739674467572965053160752231464960 * q^24 + 36710330225103772037154153143396858524815591923552301173280524244928235000 * q^25 - 178290299429521612994896681862440451353112938442078389560127528645835464224 * q^26 + 4108583825736723245642984497148380325909672596193180989676962467681728811840 * q^27 - 10197863837452248524370326511788692919181508212113555118341665631868445276160 * q^28 - 132808057928545728770070628075237950532883381334274325807559945373631525579280 * q^29 + 368843646251862307061952875207762300737776646306173378951277228159200294844800 * q^30 + 2123150329739540390115408696476884203950374929670685127189943125782378108098816 * q^31 + 10156626912480412308164375397145246760285661187761787998479811379273048947425280 * q^32 - 110453822927144134530855124481163271865404195805770611489444997754143335676114560 * q^33 + 626514570831444006665132709400608888132203790316575476126972954148191421104888352 * q^34 - 180124138596474130911007456858429985683613480525844149859433273467968580724675200 * q^35 + 16221855297378912428170473077312544781163834427405933513071046969489436648368930048 * q^36 - 23010049861253897057830375004531412092720779537210279421336409908255568411112521680 * q^37 + 81514285558726303526499020366236482021009949677570093462995405282915730851685437760 * q^38 + 973250204883059182004683876455057324018758755152662643519744443013209490499392320448 * q^39 + 1620603767802466493396978076732241543088378147649587002013209944275991354096540672000 * q^40 - 9194436894335705500488956082645864740213392167963146808356372625255538188465570116784 * q^41 - 9987175533659763810738086904398668829743024019181589555089340923029980612539996188160 * q^42 + 3032382926300215248368351846801184405080019611637638159804034319071519733367501308000 * q^43 - 61413740744912033848381562467905778729130346597543024132573739224535613780500625691648 * q^44 - 728055588424370630925028219171725592820104067843765840180299922436159334808200708678800 * q^45 - 1937857727868547524263658836001472070613971220638572213222135000017628068861666423993984 * q^46 - 193114845358989650895015242618332478679741488577861492750207342621672434970683481651840 * q^47 + 47504655695285299018807413925656103836145592812920588522461073427843872384146136331714560 * q^48 + 9009795911083753626429293565600536034814214101588418291494061693709008119369143800410056 * q^49 + 124085104852024153585775552318382585485956095474767588057564984609967735836202360766470000 * q^50 - 1021523462097644786402134875264470962590383726411120471709206304906745531337979847222893504 * q^51 + 2601002607846544407071841678151669268750253239046498757166255249010956826575867860287884800 * q^52 - 508977518161307968273832984082037167871777334860039281483640147609506187672311865310329680 * q^53 - 33215015372693850873232010101241869628048359784733721234902490207672455295016159119447797120 * q^54 + 18450671784502163418133731529996697688391744925805957647904016734511230779675351655763828800 * q^55 + 77907763278563265290300076439200648252399491244631034718538984366849741317596223703232839680 * q^56 - 17514494370932414539251899866861034389141458703710767594438206182965846210727691039357326720 * q^57 + 521188643454307966215167554048547429862263982605454645813054246139388891719965181350028489440 * q^58 - 800548783090069547249411402735852579353665443321854402294237928007339127684491029048409334560 * q^59 - 4945597330350911740055109354650466378405725800344464689989883069207313581778154248500120627200 * q^60 + 9301780115240647873952088718367909265400456376594614456607735293030740558435392467259218034416 * q^61 - 24958988483741760731654226022541604930667635314913646027823754011402485431605464535556971159040 * q^62 - 69917019353683231050173137254943101675489279093995056831426882673091272292662113138105940233920 * q^63 - 97451971150817117830440198299734679886485437857461550467094176739811166528413095345956746952704 * q^64 - 361156613980852842706992602837566394553099687955520933659145529501075901774183231590989074101600 * q^65 + 156882494260210220362013449528635783983344936752786747375982538482579620426751742603199124015872 * q^66 - 1104667221349188765660578837514456152306124133482553297212406551469220909847432127137057601268960 * q^67 - 9721401068443204036258202986739714019478462517573215331908850090837288931485135338678529805012480 * q^68 - 15109507425538340400955372418178718530943009113130778845692031950392404855615907056642892252773632 * q^69 - 42141974870106016058865849455224368290398026088671930674752184932090288769297201065857297686150400 * q^70 - 50469870302247936824042683436030531088994086024328522294948330069784198912349909975813351349301184 * q^71 - 312770283013563627062551283668577288708985871414226238388562703871210081634250694390516261706772480 * q^72 - 309796921364548112330210024475355394269902333254274320239737341959226533985104691513778940551838640 * q^73 - 925823752396046652342642416972554390081562347656534041993730400149451972597268102227614960148886688 * q^74 - 2035970471601402025465859080535649095398414802703074791592862122373110362938204069403415245277940000 * q^75 - 3130569503520776632201267436445813580876068550759173850078744887758531600111432515821247207535037440 * q^76 - 5943612343311427733153258808379776193285399172298997030946865449540200274638852351419681744544800000 * q^77 - 21269159569550168394975895479661937627684008715929340977029750772463946126724250407354989139174454400 * q^78 - 15393227887174294584948162208020437185460179522932597986148734991937027143223423856935347902468612480 * q^79 - 36135869014387530593279194332920203124385252019916366550807261806779025414796891084911471716850073600 * q^80 - 16813579079052539310958564290225362908835005641306645336831720897045685008922728854885093229369750072 * q^81 + 40683812685771158034068852888314888590966014976906157199478748314343833251276146968126649606561452960 * q^82 - 27748711091393049888979586421607112972809560782068769478686312453860122910561653683460280801656090720 * q^83 + 243729273671324707074190479881332236879714714008146405350632616637128634259974190017728217778172076032 * q^84 + 1114476595266646322768819965977266122931255323002065012571315493969146685766458335643036439956923496800 * q^85 + 2001948212296635436448279509615999770689923972184784294781573198292641086063207267886445869810840226496 * q^86 + 2452094134677213482937709450778797624299131398431787829024781103485568458306913143764742103712037328320 * q^87 + 6587629213482246089116430616322572992490320338289310595388533189153014205464262604258615522799278407680 * q^88 + 4561891385239988132989403179389372513149936713239528905622804144400695279296267497385381892983137482960 * q^89 + 27831127206069462137128463558919625443225864994138363209261172284208865542079088020097519776839212242400 * q^90 + 27533535014530695422075480606590604897330716562374502844003945844898533709216751249129046131797307879296 * q^91 + 11219382355167481799152672023779859908676464262842813795936572357113636635896010169112116501983056189440 * q^92 - 1816432822902220399473532579920329564793343562884883929779919263741160765335835765675399623257440680960 * q^93 - 145721137880009419474465571784854076810270560388958588104991210830700849472154051473896292058236218084608 * q^94 - 197505250338784881028096044265210353994741936910104745900078290549992685412473006655125953841487400936000 * q^95 - 722643410665348223758010527434181844660741784808619153000544243764286894029121981921039078126765698187264 * q^96 - 765925425726897926053834041674103560846690860133522436616120766353705349104461208876007591285452102784240 * q^97 - 1378222404256086778845054197358441766991528993251977664562346500406878280455090891540290251693972016377840 * q^98 - 2543675383725234370604494641035024609729543664951752733885226452347175058619125118596469912791508615603232 * 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 $

$2$	−7.36840e15	−1.15691	−0.578453	−	0.815715i	$-0.696344\pi$
$2$	−7.36840e15	−1.15691	−0.578453	+	0.815715i	$0.696344\pi$
$3$	−8.33754e23	−0.0745027	−0.0372514	−	0.999306i	$-0.511860\pi$
$3$	−8.33754e23	−0.0745027	−0.0372514	+	0.999306i	$0.511860\pi$
$4$	1.37285e31	0.338433
$5$	6.83377e36	1.37637	0.688185	−	0.725535i	$-0.258408\pi$
$5$	6.83377e36	1.37637	0.688185	+	0.725535i	$0.258408\pi$
$6$	6.14343e39	0.0861927
$7$	4.41963e44	1.89557	0.947784	−	0.318914i	$-0.103318\pi$
$7$	4.41963e44	1.89557	0.947784	+	0.318914i	$0.103318\pi$
$8$	1.97741e47	0.765371
$9$	−1.24542e50	−0.994449
$10$	−5.03539e52	−1.59233
$11$	−4.48414e54	−0.951839	−0.475919	−	0.879489i	$-0.657885\pi$
$11$	−4.48414e54	−0.951839	−0.475919	+	0.879489i	$0.657885\pi$
$12$	−1.14462e55	−0.0252142
$13$	1.91848e58	0.632313	0.316157	−	0.948707i	$-0.397607\pi$
$13$	1.91848e58	0.632313	0.316157	+	0.948707i	$0.397607\pi$
$14$	−3.25656e60	−2.19300
$15$	−5.69768e60	−0.102543
$16$	−2.01393e63	−1.22390
$17$	1.58211e64	0.398719	0.199360	−	0.979926i	$-0.436114\pi$
$17$	1.58211e64	0.398719	0.199360	+	0.979926i	$0.436114\pi$
$18$	9.17672e65	1.15049
$19$	−2.66912e67	−1.95796	−0.978979	−	0.203960i	$-0.934619\pi$
$19$	−2.66912e67	−1.95796	−0.978979	+	0.203960i	$0.934619\pi$
$20$	9.38173e67	0.465809
$21$	−3.68489e68	−0.141225
$22$	3.30409e70	1.10119
$23$	−2.81725e71	−0.910151	−0.455075	−	0.890453i	$-0.650388\pi$
$23$	−2.81725e71	−0.910151	−0.455075	+	0.890453i	$0.650388\pi$
$24$	−1.64867e71	−0.0570222
$25$	2.20485e73	0.894394
$26$	−1.41362e74	−0.731528
$27$	2.08254e74	0.148592
$28$	6.06749e75	0.641523
$29$	−4.39751e76	−0.736736	−0.368368	−	0.929680i	$-0.620083\pi$
$29$	−4.39751e76	−0.736736	−0.368368	+	0.929680i	$0.620083\pi$
$30$	4.19828e76	0.118633
$31$	4.22496e77	0.213468	0.106734	−	0.994288i	$-0.465961\pi$
$31$	4.22496e77	0.213468	0.106734	+	0.994288i	$0.465961\pi$
$32$	6.81810e78	0.650563
$33$	3.73867e78	0.0709146
$34$	−1.16576e80	−0.461281
$35$	3.02028e81	2.60900
$36$	−1.70977e81	−0.336555
$37$	1.25411e82	0.585792	0.292896	−	0.956144i	$-0.405381\pi$
$37$	1.25411e82	0.585792	0.292896	+	0.956144i	$0.405381\pi$
$38$	1.96671e83	2.26518
$39$	−1.59954e82	−0.0471091
$40$	1.35132e84	1.05343
$41$	−2.50078e84	−0.533240	−0.266620	−	0.963802i	$-0.585907\pi$
$41$	−2.50078e84	−0.533240	−0.266620	+	0.963802i	$0.585907\pi$
$42$	2.71517e84	0.163384
$43$	−6.45716e85	−1.12966	−0.564830	−	0.825207i	$-0.691058\pi$
$43$	−6.45716e85	−1.12966	−0.564830	+	0.825207i	$0.691058\pi$
$44$	−6.15605e85	−0.322134
$45$	−8.51089e86	−1.36873
$46$	2.07586e87	1.05296
$47$	−3.82379e87	−0.627129	−0.313564	−	0.949567i	$-0.601523\pi$
$47$	−3.82379e87	−0.627129	−0.313564	+	0.949567i	$0.601523\pi$
$48$	1.67912e87	0.0911836
$49$	1.40970e89	2.59318
$50$	−1.62462e89	−1.03473
$51$	−1.31909e88	−0.0297057
$52$	2.63379e89	0.213996
$53$	−3.23348e90	−0.966467	−0.483234	−	0.875491i	$-0.660538\pi$
$53$	−3.23348e90	−0.966467	−0.483234	+	0.875491i	$0.660538\pi$
$54$	−1.53450e90	−0.171907
$55$	−3.06436e91	−1.31008
$56$	8.73942e91	1.45081
$57$	2.22539e91	0.145873
$58$	3.24026e92	0.852334
$59$	−3.76398e92	−0.403568	−0.201784	−	0.979430i	$-0.564674\pi$
$59$	−3.76398e92	−0.403568	−0.201784	+	0.979430i	$0.564674\pi$
$60$	−7.82206e91	−0.0347041
$61$	−9.74654e92	−0.181566	−0.0907829	−	0.995871i	$-0.528937\pi$
$61$	−9.74654e92	−0.181566	−0.0907829	+	0.995871i	$0.528937\pi$
$62$	−3.11312e93	−0.246963
$63$	−5.50428e94	−1.88505
$64$	3.14561e94	0.471256
$65$	1.31105e95	0.870297
$66$	−2.75480e94	−0.0820416
$67$	−4.90505e95	−0.663309	−0.331655	−	0.943401i	$-0.607607\pi$
$67$	−4.90505e95	−0.663309	−0.331655	+	0.943401i	$0.607607\pi$
$68$	2.17199e95	0.134940
$69$	2.34889e95	0.0678087
$70$	−2.22546e97	−3.01837
$71$	−2.06839e96	−0.133220	−0.0666098	−	0.997779i	$-0.521218\pi$
$71$	−2.06839e96	−0.133220	−0.0666098	+	0.997779i	$0.521218\pi$
$72$	−2.46270e97	−0.761123
$73$	−4.35765e97	−0.652833	−0.326417	−	0.945226i	$-0.605841\pi$
$73$	−4.35765e97	−0.652833	−0.326417	+	0.945226i	$0.605841\pi$
$74$	−9.24075e97	−0.677707
$75$	−1.83830e97	−0.0666348
$76$	−3.66429e98	−0.662638
$77$	−1.98183e99	−1.80427
$78$	1.17861e98	0.0545008
$79$	−6.86400e99	−1.62613	−0.813064	−	0.582174i	$-0.802202\pi$
$79$	−6.86400e99	−1.62613	−0.813064	+	0.582174i	$0.802202\pi$
$80$	−1.37627e100	−1.68453
$81$	1.54236e100	0.983379
$82$	1.84267e100	0.616910
$83$	1.96175e100	0.347572	0.173786	−	0.984783i	$-0.444400\pi$
$83$	1.96175e100	0.347572	0.173786	+	0.984783i	$0.444400\pi$
$84$	−5.05880e99	−0.0477952
$85$	1.08117e101	0.548785
$86$	4.75790e101	1.30691
$87$	3.66644e100	0.0548888
$88$	−8.86698e101	−0.728510
$89$	1.19123e102	0.540780	0.270390	−	0.962751i	$-0.412847\pi$
$89$	1.19123e102	0.540780	0.270390	+	0.962751i	$0.412847\pi$
$90$	6.27116e102	1.58349
$91$	8.47900e102	1.19859
$92$	−3.86765e102	−0.308025
$93$	−3.52258e101	−0.0159040
$94$	2.81752e103	0.725530
$95$	−1.82401e104	−2.69487
$96$	−5.68462e102	−0.0484687
$97$	1.02974e104	0.509580	0.254790	−	0.966996i	$-0.417994\pi$
$97$	1.02974e104	0.509580	0.254790	+	0.966996i	$0.417994\pi$
$98$	−1.03872e105	−3.00006
$99$	5.58462e104	0.946555
$100$	3.02693e104	0.302693
$101$	3.13638e104	0.186019	0.0930094	−	0.995665i	$-0.470351\pi$
$101$	3.13638e104	0.186019	0.0930094	+	0.995665i	$0.470351\pi$
$102$	9.71956e103	0.0343667
$103$	−3.39113e105	−0.718439	−0.359219	−	0.933253i	$-0.616957\pi$
$103$	−3.39113e105	−0.718439	−0.359219	+	0.933253i	$0.616957\pi$
$104$	3.79363e105	0.483954
$105$	−2.51817e105	−0.194378
$106$	2.38256e106	1.11811
$107$	1.15787e106	0.331904	0.165952	−	0.986134i	$-0.446930\pi$
$107$	1.15787e106	0.331904	0.165952	+	0.986134i	$0.446930\pi$
$108$	2.85901e105	0.0502885
$109$	1.01283e107	1.09811	0.549055	−	0.835786i	$-0.314988\pi$
$109$	1.01283e107	1.09811	0.549055	+	0.835786i	$0.314988\pi$
$110$	2.25794e107	1.51564
$111$	−1.04562e106	−0.0436431
$112$	−8.90082e107	−2.31998
$113$	4.58630e106	0.0749626	0.0374813	−	0.999297i	$-0.488067\pi$
$113$	4.58630e106	0.0749626	0.0374813	+	0.999297i	$0.488067\pi$
$114$	−1.63975e107	−0.168762
$115$	−1.92524e108	−1.25270
$116$	−6.03711e107	−0.249336
$117$	−2.38931e108	−0.628804
$118$	2.77345e108	0.466891
$119$	6.99233e108	0.755799
$120$	−1.12666e108	−0.0784837
$121$	−2.08629e108	−0.0940030
$122$	7.18164e108	0.210055
$123$	2.08504e108	0.0397279
$124$	5.80023e108	0.0722448
$125$	−1.77910e109	−0.145353
$126$	4.05578e110	2.18082
$127$	2.26248e110	0.803320	0.401660	−	0.915789i	$-0.368433\pi$
$127$	2.26248e110	0.803320	0.401660	+	0.915789i	$0.368433\pi$
$128$	−5.08356e110	−1.19576
$129$	5.38369e109	0.0841628
$130$	−9.66033e110	−1.00685
$131$	9.11375e110	0.635264	0.317632	−	0.948214i	$-0.397112\pi$
$131$	9.11375e110	0.635264	0.317632	+	0.948214i	$0.397112\pi$
$132$	5.13263e109	0.0239999
$133$	−1.17965e112	−3.71144
$134$	3.61424e111	0.767387
$135$	1.42316e111	0.204517
$136$	3.12847e111	0.305168
$137$	1.96095e112	1.30208	0.651039	−	0.759044i	$-0.274333\pi$
$137$	1.96095e112	1.30208	0.651039	+	0.759044i	$0.274333\pi$
$138$	−1.73076e111	−0.0784484
$139$	−5.25948e111	−0.163180	−0.0815899	−	0.996666i	$-0.526000\pi$
$139$	−5.25948e111	−0.163180	−0.0815899	+	0.996666i	$0.526000\pi$
$140$	4.14638e112	0.882973
$141$	3.18810e111	0.0467228
$142$	1.52407e112	0.154123
$143$	−8.60276e112	−0.601860
$144$	2.50818e113	1.21710
$145$	−3.00515e113	−1.01402
$146$	3.21089e113	0.755267
$147$	−1.17534e113	−0.193199
$148$	1.72170e113	0.198252
$149$	−1.63050e114	−1.31838	−0.659190	−	0.751976i	$-0.729101\pi$
$149$	−1.63050e114	−1.31838	−0.659190	+	0.751976i	$0.729101\pi$
$150$	1.35454e113	0.0770902
$151$	−1.72555e114	−0.692846	−0.346423	−	0.938078i	$-0.612604\pi$
$151$	−1.72555e114	−0.692846	−0.346423	+	0.938078i	$0.612604\pi$
$152$	−5.27793e114	−1.49856
$153$	−1.97038e114	−0.396506
$154$	1.46029e115	2.08738
$155$	2.88724e114	0.293812
$156$	−2.19593e113	−0.0159433
$157$	9.78183e113	0.0507795	0.0253897	−	0.999678i	$-0.491917\pi$
$157$	9.78183e113	0.0507795	0.0253897	+	0.999678i	$0.491917\pi$
$158$	5.05767e115	1.88128
$159$	2.69593e114	0.0720044
$160$	4.65933e115	0.895415
$161$	−1.24512e116	−1.72525
$162$	−1.13647e116	−1.13768
$163$	7.23022e115	0.523965	0.261983	−	0.965073i	$-0.415624\pi$
$163$	7.23022e115	0.523965	0.261983	+	0.965073i	$0.415624\pi$
$164$	−3.43319e115	−0.180466
$165$	2.55492e115	0.0976047
$166$	−1.44550e116	−0.402108
$167$	−3.73133e115	−0.0757268	−0.0378634	−	0.999283i	$-0.512055\pi$
$167$	−3.73133e115	−0.0757268	−0.0378634	+	0.999283i	$0.512055\pi$
$168$	−7.28653e115	−0.108089
$169$	−5.52501e116	−0.600180
$170$	−7.96652e116	−0.634893
$171$	3.32416e117	1.94709
$172$	−8.86471e116	−0.382315
$173$	−3.68706e117	−1.17290	−0.586449	−	0.809986i	$-0.699474\pi$
$173$	−3.68706e117	−1.17290	−0.586449	+	0.809986i	$0.699474\pi$
$174$	−2.70158e116	−0.0635012
$175$	9.74464e117	1.69538
$176$	9.03073e117	1.16495
$177$	3.13823e116	0.0300669
$178$	−8.77746e117	−0.625632
$179$	2.91163e118	1.54651	0.773253	−	0.634098i	$-0.218628\pi$
$179$	2.91163e118	1.54651	0.773253	+	0.634098i	$0.218628\pi$
$180$	−1.16842e118	−0.463224
$181$	−5.31349e118	−1.57491	−0.787454	−	0.616374i	$-0.788601\pi$
$181$	−5.31349e118	−1.57491	−0.787454	+	0.616374i	$0.788601\pi$
$182$	−6.24767e118	−1.38666
$183$	8.12622e116	0.0135271
$184$	−5.57085e118	−0.696603
$185$	8.57027e118	0.806267
$186$	2.59558e117	0.0183994
$187$	−7.09438e118	−0.379516
$188$	−5.24949e118	−0.212241
$189$	9.20405e118	0.281666
$190$	1.34401e120	3.11772
$191$	−6.62984e119	−1.16749	−0.583743	−	0.811939i	$-0.698412\pi$
$191$	−6.62984e119	−1.16749	−0.583743	+	0.811939i	$0.698412\pi$
$192$	−2.62267e118	−0.0351098
$193$	−2.46353e119	−0.251072	−0.125536	−	0.992089i	$-0.540065\pi$
$193$	−2.46353e119	−0.251072	−0.125536	+	0.992089i	$0.540065\pi$
$194$	−7.58756e119	−0.589537
$195$	−1.09309e119	−0.0648395
$196$	1.93530e120	0.877617
$197$	3.61918e120	1.25641	0.628207	−	0.778046i	$-0.283789\pi$
$197$	3.61918e120	1.25641	0.628207	+	0.778046i	$0.283789\pi$
$198$	−4.11497e120	−1.09508
$199$	−6.75502e120	−1.37988	−0.689938	−	0.723868i	$-0.742362\pi$
$199$	−6.75502e120	−1.37988	−0.689938	+	0.723868i	$0.742362\pi$
$200$	4.35989e120	0.684543
$201$	4.08960e119	0.0494184
$202$	−2.31101e120	−0.215206
$203$	−1.94354e121	−1.39653
$204$	−1.81091e119	−0.0100534
$205$	−1.70898e121	−0.733936
$206$	2.49872e121	0.831166
$207$	3.50864e121	0.905099
$208$	−3.86369e121	−0.773886
$209$	1.19687e122	1.86366
$210$	1.85549e121	0.224877
$211$	1.13421e122	1.07118	0.535592	−	0.844477i	$-0.320089\pi$
$211$	1.13421e122	1.07118	0.535592	+	0.844477i	$0.320089\pi$
$212$	−4.43908e121	−0.327085
$213$	1.72452e120	0.00992522
$214$	−8.53167e121	−0.383982
$215$	−4.41268e122	−1.55483
$216$	4.11803e121	0.113728
$217$	1.86728e122	0.404644
$218$	−7.46295e122	−1.27041
$219$	3.63321e121	0.0486379
$220$	−4.20690e122	−0.443375
$221$	3.03524e122	0.252115
$222$	7.70452e121	0.0504910
$223$	1.67124e123	0.865035	0.432517	−	0.901626i	$-0.357625\pi$
$223$	1.67124e123	0.865035	0.432517	+	0.901626i	$0.357625\pi$
$224$	3.01335e123	1.23319
$225$	−2.74596e123	−0.889429
$226$	−3.37937e122	−0.0867247
$227$	−4.72016e123	−0.960725	−0.480363	−	0.877070i	$-0.659495\pi$
$227$	−4.72016e123	−0.960725	−0.480363	+	0.877070i	$0.659495\pi$
$228$	3.05512e122	0.0493684
$229$	8.23914e123	1.05808	0.529040	−	0.848597i	$-0.322552\pi$
$229$	8.23914e123	1.05808	0.529040	+	0.848597i	$0.322552\pi$
$230$	1.41859e124	1.44926
$231$	1.65236e123	0.134423
$232$	−8.69567e123	−0.563876
$233$	−1.55779e124	−0.805977	−0.402988	−	0.915205i	$-0.632029\pi$
$233$	−1.55779e124	−0.805977	−0.402988	+	0.915205i	$0.632029\pi$
$234$	1.76054e124	0.727467
$235$	−2.61309e124	−0.863161
$236$	−5.16738e123	−0.136581
$237$	5.72289e123	0.121151
$238$	−5.15223e124	−0.874389
$239$	−1.18903e125	−1.61921	−0.809607	−	0.586972i	$-0.800320\pi$
$239$	−1.18903e125	−1.61921	−0.809607	+	0.586972i	$0.800320\pi$
$240$	1.14747e124	0.125502
$241$	1.11462e125	0.980017	0.490009	−	0.871718i	$-0.336994\pi$
$241$	1.11462e125	0.980017	0.490009	+	0.871718i	$0.336994\pi$
$242$	1.53726e124	0.108753
$243$	−3.89405e124	−0.221856
$244$	−1.33805e124	−0.0614479
$245$	9.63356e125	3.56917
$246$	−1.53634e124	−0.0459614
$247$	−5.12066e125	−1.23804
$248$	8.35447e124	0.163383
$249$	−1.63562e124	−0.0258951
$250$	1.31091e125	0.168160
$251$	−1.11133e126	−1.15604	−0.578019	−	0.816023i	$-0.696174\pi$
$251$	−1.11133e126	−1.15604	−0.578019	+	0.816023i	$0.696174\pi$
$252$	−7.55655e125	−0.637962
$253$	1.26329e126	0.866317
$254$	−1.66708e126	−0.929367
$255$	−9.01434e124	−0.0408860
$256$	2.46976e126	0.912129
$257$	−5.66215e126	−1.70409	−0.852044	−	0.523470i	$-0.824637\pi$
$257$	−5.66215e126	−1.70409	−0.852044	+	0.523470i	$0.824637\pi$
$258$	−3.96692e125	−0.0973685
$259$	5.54269e126	1.11041
$260$	1.79987e126	0.294537
$261$	5.47672e126	0.732646
$262$	−6.71538e126	−0.734941
$263$	−9.17187e126	−0.821828	−0.410914	−	0.911674i	$-0.634790\pi$
$263$	−9.17187e126	−0.821828	−0.410914	+	0.911674i	$0.634790\pi$
$264$	7.39288e125	0.0542760
$265$	−2.20969e127	−1.33022
$266$	8.69215e127	4.29379
$267$	−9.93194e125	−0.0402896
$268$	−6.73389e126	−0.224486
$269$	−4.82313e127	−1.32231	−0.661156	−	0.750248i	$-0.729934\pi$
$269$	−4.82313e127	−1.32231	−0.661156	+	0.750248i	$0.729934\pi$
$270$	−1.04864e127	−0.236608
$271$	6.98433e127	1.29789	0.648943	−	0.760837i	$-0.275211\pi$
$271$	6.98433e127	1.29789	0.648943	+	0.760837i	$0.275211\pi$
$272$	−3.18624e127	−0.487991
$273$	−7.06940e126	−0.0892984
$274$	−1.44491e128	−1.50638
$275$	−9.88687e127	−0.851319
$276$	3.22467e126	0.0229487
$277$	−1.33380e128	−0.785058	−0.392529	−	0.919740i	$-0.628400\pi$
$277$	−1.33380e128	−0.785058	−0.392529	+	0.919740i	$0.628400\pi$
$278$	3.87540e127	0.188784
$279$	−5.26183e127	−0.212284
$280$	5.97232e128	1.99685
$281$	1.71423e128	0.475321	0.237660	−	0.971348i	$-0.423619\pi$
$281$	1.71423e128	0.475321	0.237660	+	0.971348i	$0.423619\pi$
$282$	−2.34912e127	−0.0540539
$283$	4.21932e128	0.806221	0.403111	−	0.915151i	$-0.367929\pi$
$283$	4.21932e128	0.806221	0.403111	+	0.915151i	$0.367929\pi$
$284$	−2.83958e127	−0.0450859
$285$	1.52078e128	0.200776
$286$	6.33885e128	0.696296
$287$	−1.10525e129	−1.01079
$288$	−8.49137e128	−0.646952
$289$	−1.32417e129	−0.841023
$290$	2.21432e129	1.17313
$291$	−8.58552e127	−0.0379651
$292$	−5.98239e128	−0.220941
$293$	−3.79428e129	−1.17106	−0.585530	−	0.810651i	$-0.699114\pi$
$293$	−3.79428e129	−1.17106	−0.585530	+	0.810651i	$0.699114\pi$
$294$	8.66039e128	0.223513
$295$	−2.57222e129	−0.555459
$296$	2.47988e129	0.448348
$297$	−9.33839e128	−0.141436
$298$	1.20141e130	1.52524
$299$	−5.40484e129	−0.575500
$300$	−2.52371e128	−0.0225514
$301$	−2.85383e130	−2.14135
$302$	1.27145e130	0.801559
$303$	−2.61497e128	−0.0138589
$304$	5.37540e130	2.39634
$305$	−6.66056e129	−0.249902
$306$	1.45185e130	0.458720
$307$	2.81819e130	0.750249	0.375125	−	0.926974i	$-0.377600\pi$
$307$	2.81819e130	0.750249	0.375125	+	0.926974i	$0.377600\pi$
$308$	−2.72075e130	−0.610627
$309$	2.82737e129	0.0535256
$310$	−2.12743e130	−0.339913
$311$	−1.12349e131	−1.51583	−0.757914	−	0.652355i	$-0.773781\pi$
$311$	−1.12349e131	−1.51583	−0.757914	+	0.652355i	$0.773781\pi$
$312$	−3.16295e129	−0.0360559
$313$	9.89355e130	0.953398	0.476699	−	0.879067i	$-0.341833\pi$
$313$	9.89355e130	0.953398	0.476699	+	0.879067i	$0.341833\pi$
$314$	−7.20764e129	−0.0587471
$315$	−3.76150e131	−2.59452
$316$	−9.42323e130	−0.550336
$317$	2.02522e131	1.00198	0.500992	−	0.865452i	$-0.332969\pi$
$317$	2.02522e131	1.00198	0.500992	+	0.865452i	$0.332969\pi$
$318$	−1.98647e130	−0.0833024
$319$	1.97190e131	0.701253
$320$	2.14964e131	0.648622
$321$	−9.65381e129	−0.0247278
$322$	9.17454e131	1.99596
$323$	−4.22282e131	−0.780675
$324$	2.11742e131	0.332808
$325$	4.22997e131	0.565537
$326$	−5.32752e131	−0.606179
$327$	−8.44453e130	−0.0818122
$328$	−4.94506e131	−0.408127
$329$	−1.68998e132	−1.18876
$330$	−1.88257e131	−0.112920
$331$	2.08449e132	1.06667	0.533336	−	0.845904i	$-0.320938\pi$
$331$	2.08449e132	1.06667	0.533336	+	0.845904i	$0.320938\pi$
$332$	2.69319e131	0.117630
$333$	−1.56188e132	−0.582541
$334$	2.74940e131	0.0876088
$335$	−3.35200e132	−0.912959
$336$	7.42110e131	0.172845
$337$	−1.43308e132	−0.285563	−0.142781	−	0.989754i	$-0.545605\pi$
$337$	−1.43308e132	−0.285563	−0.142781	+	0.989754i	$0.545605\pi$
$338$	4.07105e132	0.694352
$339$	−3.82385e130	−0.00558491
$340$	1.48429e132	0.185727
$341$	−1.89453e132	−0.203188
$342$	−2.44937e133	−2.25260
$343$	3.82776e133	3.01997
$344$	−1.27684e133	−0.864609
$345$	1.60518e132	0.0933299
$346$	2.71677e133	1.35693
$347$	1.61500e133	0.693228	0.346614	−	0.938008i	$-0.387331\pi$
$347$	1.61500e133	0.693228	0.346614	+	0.938008i	$0.387331\pi$
$348$	5.03347e131	0.0185762
$349$	3.42631e133	1.08766	0.543829	−	0.839196i	$-0.316974\pi$
$349$	3.42631e133	1.08766	0.543829	+	0.839196i	$0.316974\pi$
$350$	−7.18024e133	−1.96140
$351$	3.99532e132	0.0939566
$352$	−3.05733e133	−0.619231
$353$	−4.49817e133	−0.784990	−0.392495	−	0.919754i	$-0.628388\pi$
$353$	−4.49817e133	−0.784990	−0.392495	+	0.919754i	$0.628388\pi$
$354$	−2.31238e132	−0.0347846
$355$	−1.41349e133	−0.183359
$356$	1.63538e133	0.183018
$357$	−5.82988e132	−0.0563091
$358$	−2.14540e134	−1.78916
$359$	−2.93840e132	−0.0211667	−0.0105833	−	0.999944i	$-0.503369\pi$
$359$	−2.93840e132	−0.0211667	−0.0105833	+	0.999944i	$0.503369\pi$
$360$	−1.68295e134	−1.04759
$361$	5.26583e134	2.83360
$362$	3.91519e134	1.82202
$363$	1.73945e132	0.00700348
$364$	1.16404e134	0.405644
$365$	−2.97792e134	−0.898540
$366$	−5.98772e132	−0.0156496
$367$	−2.14897e134	−0.486700	−0.243350	−	0.969939i	$-0.578246\pi$
$367$	−2.14897e134	−0.486700	−0.243350	+	0.969939i	$0.578246\pi$
$368$	5.67373e134	1.11393
$369$	3.11451e134	0.530281
$370$	−6.31492e134	−0.932776
$371$	−1.42908e135	−1.83200
$372$	−4.83597e132	−0.00538244
$373$	8.60799e134	0.832124	0.416062	−	0.909336i	$-0.363410\pi$
$373$	8.60799e134	0.832124	0.416062	+	0.909336i	$0.363410\pi$
$374$	5.22743e134	0.439065
$375$	1.48333e133	0.0108292
$376$	−7.56120e134	−0.479986
$377$	−8.43655e134	−0.465848
$378$	−6.78191e134	−0.325861
$379$	9.16019e134	0.383130	0.191565	−	0.981480i	$-0.438644\pi$
$379$	9.16019e134	0.383130	0.191565	+	0.981480i	$0.438644\pi$
$380$	−2.50409e135	−0.912035
$381$	−1.88635e134	−0.0598496
$382$	4.88513e135	1.35067
$383$	3.16438e135	0.762699	0.381349	−	0.924431i	$-0.375459\pi$
$383$	3.16438e135	0.762699	0.381349	+	0.924431i	$0.375459\pi$
$384$	4.23844e134	0.0890875
$385$	−1.35434e136	−2.48335
$386$	1.81523e135	0.290467
$387$	8.04185e135	1.12339
$388$	1.41368e135	0.172459
$389$	1.36629e136	1.45609	0.728045	−	0.685529i	$-0.240429\pi$
$389$	1.36629e136	1.45609	0.728045	+	0.685529i	$0.240429\pi$
$390$	8.05434e134	0.0750133
$391$	−4.45718e135	−0.362895
$392$	2.78755e136	1.98474
$393$	−7.59863e134	−0.0473289
$394$	−2.66675e136	−1.45355
$395$	−4.69070e136	−2.23815
$396$	7.66684e135	0.320346
$397$	−4.44670e136	−1.62756	−0.813778	−	0.581176i	$-0.802593\pi$
$397$	−4.44670e136	−1.62756	−0.813778	+	0.581176i	$0.802593\pi$
$398$	4.97737e136	1.59639
$399$	9.83540e135	0.276513
$400$	−4.44041e136	−1.09465
$401$	−2.66460e136	−0.576171	−0.288086	−	0.957605i	$-0.593019\pi$
$401$	−2.66460e136	−0.576171	−0.288086	+	0.957605i	$0.593019\pi$
$402$	−3.01338e135	−0.0571724
$403$	8.10552e135	0.134979
$404$	4.30578e135	0.0629549
$405$	1.05401e137	1.35349
$406$	1.43208e137	1.61566
$407$	−5.62359e136	−0.557580
$408$	−2.60837e135	−0.0227358
$409$	2.73574e136	0.209701	0.104851	−	0.994488i	$-0.466564\pi$
$409$	2.73574e136	0.209701	0.104851	+	0.994488i	$0.466564\pi$
$410$	1.25924e137	0.849096
$411$	−1.63495e136	−0.0970084
$412$	−4.65550e136	−0.243144
$413$	−1.66354e137	−0.764990
$414$	−2.58531e137	−1.04712
$415$	1.34062e137	0.478387
$416$	1.30804e137	0.411360
$417$	4.38512e135	0.0121573
$418$	−8.81901e137	−2.15608
$419$	6.16363e137	1.32923	0.664616	−	0.747186i	$-0.268595\pi$
$419$	6.16363e137	1.32923	0.664616	+	0.747186i	$0.268595\pi$
$420$	−3.45706e136	−0.0657839
$421$	4.88353e137	0.820207	0.410104	−	0.912039i	$-0.365492\pi$
$421$	4.88353e137	0.820207	0.410104	+	0.912039i	$0.365492\pi$
$422$	−8.35730e137	−1.23926
$423$	4.76221e137	0.623648
$424$	−6.39391e137	−0.739706
$425$	3.48831e137	0.356612
$426$	−1.27070e136	−0.0114826
$427$	−4.30761e137	−0.344170
$428$	1.58958e137	0.112327
$429$	7.17258e136	0.0448402
$430$	3.25144e138	1.79879
$431$	−2.78682e138	−1.36475	−0.682375	−	0.731002i	$-0.739053\pi$
$431$	−2.78682e138	−1.36475	−0.682375	+	0.731002i	$0.739053\pi$
$432$	−4.19408e137	−0.181861
$433$	3.64338e138	1.39923	0.699617	−	0.714518i	$-0.253354\pi$
$433$	3.64338e138	1.39923	0.699617	+	0.714518i	$0.253354\pi$
$434$	−1.37589e138	−0.468135
$435$	2.50556e137	0.0755473
$436$	1.39046e138	0.371637
$437$	7.51956e138	1.78204
$438$	−2.67709e137	−0.0562695
$439$	−1.56099e138	−0.291080	−0.145540	−	0.989352i	$-0.546492\pi$
$439$	−1.56099e138	−0.291080	−0.145540	+	0.989352i	$0.546492\pi$
$440$	−6.05949e138	−1.00270
$441$	−1.75566e139	−2.57878
$442$	−2.23649e138	−0.291674
$443$	1.04375e138	0.120893	0.0604467	−	0.998171i	$-0.480747\pi$
$443$	1.04375e138	0.120893	0.0604467	+	0.998171i	$0.480747\pi$
$444$	−1.43547e137	−0.0147703
$445$	8.14060e138	0.744313
$446$	−1.23144e139	−1.00076
$447$	1.35943e138	0.0982229
$448$	1.39025e139	0.893297
$449$	−1.68684e139	−0.964142	−0.482071	−	0.876132i	$-0.660115\pi$
$449$	−1.68684e139	−0.964142	−0.482071	+	0.876132i	$0.660115\pi$
$450$	2.02333e139	1.02899
$451$	1.12139e139	0.507559
$452$	6.29630e137	0.0253698
$453$	1.43868e138	0.0516190
$454$	3.47800e139	1.11147
$455$	5.79435e139	1.64971
$456$	4.40050e138	0.111647
$457$	−4.28923e139	−0.970015	−0.485008	−	0.874510i	$-0.661183\pi$
$457$	−4.28923e139	−0.970015	−0.485008	+	0.874510i	$0.661183\pi$
$458$	−6.07092e139	−1.22410
$459$	3.29479e138	0.0592464
$460$	−2.64306e139	−0.423957
$461$	−3.43285e139	−0.491311	−0.245656	−	0.969357i	$-0.579003\pi$
$461$	−3.43285e139	−0.491311	−0.245656	+	0.969357i	$0.579003\pi$
$462$	−1.21752e139	−0.155515
$463$	−7.65195e139	−0.872510	−0.436255	−	0.899823i	$-0.643695\pi$
$463$	−7.65195e139	−0.872510	−0.436255	+	0.899823i	$0.643695\pi$
$464$	8.85626e139	0.901688
$465$	−2.40725e138	−0.0218898
$466$	1.14784e140	0.932440
$467$	−7.91580e139	−0.574590	−0.287295	−	0.957842i	$-0.592756\pi$
$467$	−7.91580e139	−0.574590	−0.287295	+	0.957842i	$0.592756\pi$
$468$	−3.28016e139	−0.212808
$469$	−2.16785e140	−1.25735
$470$	1.92543e140	0.998597
$471$	−8.15564e137	−0.00378321
$472$	−7.44293e139	−0.308879
$473$	2.89548e140	1.07525
$474$	−4.21685e139	−0.140160
$475$	−5.88500e140	−1.75119
$476$	9.59941e139	0.255788
$477$	4.02703e140	0.961103
$478$	8.76127e140	1.87328
$479$	−1.70702e140	−0.327057	−0.163529	−	0.986539i	$-0.552288\pi$
$479$	−1.70702e140	−0.327057	−0.163529	+	0.986539i	$0.552288\pi$
$480$	−3.88474e139	−0.0667109
$481$	2.40598e140	0.370404
$482$	−8.21300e140	−1.13379
$483$	1.03812e140	0.128536
$484$	−2.86415e139	−0.0318138
$485$	7.03703e140	0.701371
$486$	2.86929e140	0.256667
$487$	7.74854e140	0.622228	0.311114	−	0.950373i	$-0.399298\pi$
$487$	7.74854e140	0.622228	0.311114	+	0.950373i	$0.399298\pi$
$488$	−1.92729e140	−0.138965
$489$	−6.02823e139	−0.0390368
$490$	−7.09839e141	−4.12920
$491$	−6.91335e140	−0.361335	−0.180668	−	0.983544i	$-0.557826\pi$
$491$	−6.91335e140	−0.361335	−0.180668	+	0.983544i	$0.557826\pi$
$492$	2.86244e139	0.0134452
$493$	−6.95732e140	−0.293750
$494$	3.77311e141	1.43230
$495$	3.81640e141	1.30281
$496$	−8.50876e140	−0.261263
$497$	−9.14151e140	−0.252527
$498$	1.20519e140	0.0299582
$499$	3.99593e141	0.894003	0.447001	−	0.894533i	$-0.352492\pi$
$499$	3.99593e141	0.894003	0.447001	+	0.894533i	$0.352492\pi$
$500$	−2.44243e140	−0.0491923
$501$	3.11102e139	0.00564185
$502$	8.18871e141	1.33743
$503$	1.07217e142	1.57741	0.788705	−	0.614772i	$-0.210752\pi$
$503$	1.07217e142	1.57741	0.788705	+	0.614772i	$0.210752\pi$
$504$	−1.08842e142	−1.44276
$505$	2.14333e141	0.256031
$506$	−9.30845e141	−1.00225
$507$	4.60650e140	0.0447150
$508$	3.10604e141	0.271870
$509$	−1.71358e142	−1.35276	−0.676381	−	0.736552i	$-0.736453\pi$
$509$	−1.71358e142	−1.35276	−0.676381	+	0.736552i	$0.736453\pi$
$510$	6.64212e140	0.0473013
$511$	−1.92592e142	−1.23749
$512$	2.42321e141	0.140513
$513$	−5.55853e141	−0.290937
$514$	4.17210e142	1.97147
$515$	−2.31742e142	−0.988837
$516$	7.39099e140	0.0284835
$517$	1.71464e142	0.596925
$518$	−4.08408e142	−1.28464
$519$	3.07410e141	0.0873841
$520$	2.59248e142	0.666100
$521$	5.71915e142	1.32847	0.664234	−	0.747525i	$-0.268758\pi$
$521$	5.71915e142	1.32847	0.664234	+	0.747525i	$0.268758\pi$
$522$	−4.03547e142	−0.847603
$523$	−3.96164e142	−0.752552	−0.376276	−	0.926508i	$-0.622796\pi$
$523$	−3.96164e142	−0.752552	−0.376276	+	0.926508i	$0.622796\pi$
$524$	1.25118e142	0.214995
$525$	−8.12463e141	−0.126311
$526$	6.75820e142	0.950779
$527$	6.68433e141	0.0851139
$528$	−7.52941e141	−0.0867921
$529$	−1.64439e142	−0.171625
$530$	1.62819e143	1.53894
$531$	4.68772e142	0.401328
$532$	−1.61948e143	−1.25608
$533$	−4.79771e142	−0.337175
$534$	7.31825e141	0.0466113
$535$	7.91264e142	0.456823
$536$	−9.69928e142	−0.507678
$537$	−2.42758e142	−0.115219
$538$	3.55387e143	1.52979
$539$	−6.32129e143	−2.46829
$540$	1.95378e142	0.0692155
$541$	−3.06037e143	−0.983823	−0.491912	−	0.870645i	$-0.663702\pi$
$541$	−3.06037e143	−0.983823	−0.491912	+	0.870645i	$0.663702\pi$
$542$	−5.14633e143	−1.50153
$543$	4.43015e142	0.117335
$544$	1.07869e143	0.259392
$545$	6.92146e143	1.51141
$546$	5.20902e142	0.103310
$547$	3.58490e143	0.645865	0.322933	−	0.946422i	$-0.395331\pi$
$547$	3.58490e143	0.645865	0.322933	+	0.946422i	$0.395331\pi$
$548$	2.69209e143	0.440667
$549$	1.21385e143	0.180558
$550$	7.28504e143	0.984897
$551$	1.17375e144	1.44250
$552$	4.64472e142	0.0518988
$553$	−3.03364e144	−3.08244
$554$	9.82795e143	0.908239
$555$	−7.14550e142	−0.0600691
$556$	−7.22048e142	−0.0552255
$557$	2.76592e144	1.92505	0.962524	−	0.271198i	$-0.0874199\pi$
$557$	2.76592e144	1.92505	0.962524	+	0.271198i	$0.0874199\pi$
$558$	3.87713e143	0.245592
$559$	−1.23880e144	−0.714299
$560$	−6.08262e144	−3.19315
$561$	5.91497e142	0.0282750
$562$	−1.26311e144	−0.549902
$563$	1.21160e144	0.480473	0.240237	−	0.970714i	$-0.422775\pi$
$563$	1.21160e144	0.480473	0.240237	+	0.970714i	$0.422775\pi$
$564$	4.37678e142	0.0158126
$565$	3.13417e143	0.103176
$566$	−3.10896e144	−0.932723
$567$	6.81665e144	1.86406
$568$	−4.09004e143	−0.101962
$569$	3.93949e144	0.895459	0.447730	−	0.894169i	$-0.352233\pi$
$569$	3.93949e144	0.895459	0.447730	+	0.894169i	$0.352233\pi$
$570$	−1.12057e144	−0.232279
$571$	−2.37657e144	−0.449320	−0.224660	−	0.974437i	$-0.572127\pi$
$571$	−2.37657e144	−0.449320	−0.224660	+	0.974437i	$0.572127\pi$
$572$	−1.18103e144	−0.203690
$573$	5.52766e143	0.0869809
$574$	8.14395e144	1.16939
$575$	−6.21161e144	−0.814033
$576$	−3.91760e144	−0.468640
$577$	−6.30933e143	−0.0689054	−0.0344527	−	0.999406i	$-0.510969\pi$
$577$	−6.30933e143	−0.0689054	−0.0344527	+	0.999406i	$0.510969\pi$
$578$	9.75703e144	0.972985
$579$	2.05398e143	0.0187056
$580$	−4.12562e144	−0.343178
$581$	8.67023e144	0.658846
$582$	6.32616e143	0.0439221
$583$	1.44994e145	0.919921
$584$	−8.61685e144	−0.499660
$585$	−1.63280e145	−0.865466
$586$	2.79578e145	1.35481
$587$	−4.42324e145	−1.95993	−0.979963	−	0.199179i	$-0.936172\pi$
$587$	−4.42324e145	−1.95993	−0.979963	+	0.199179i	$0.936172\pi$
$588$	−1.61357e144	−0.0653849
$589$	−1.12769e145	−0.417962
$590$	1.89531e145	0.642614
$591$	−3.01750e144	−0.0936063
$592$	−2.52568e145	−0.716949
$593$	−5.28905e145	−1.37406	−0.687031	−	0.726628i	$-0.741086\pi$
$593$	−5.28905e145	−1.37406	−0.687031	+	0.726628i	$0.741086\pi$
$594$	6.88090e144	0.163628
$595$	4.77840e145	1.04026
$596$	−2.23842e145	−0.446184
$597$	5.63203e144	0.102805
$598$	3.98250e145	0.665800
$599$	−7.53160e145	−1.15340	−0.576699	−	0.816957i	$-0.695659\pi$
$599$	−7.53160e145	−1.15340	−0.576699	+	0.816957i	$0.695659\pi$
$600$	−3.63508e144	−0.0510003
$601$	1.21435e146	1.56111	0.780553	−	0.625090i	$-0.214938\pi$
$601$	1.21435e146	1.56111	0.780553	+	0.625090i	$0.214938\pi$
$602$	2.10282e146	2.47734
$603$	6.10883e145	0.659628
$604$	−2.36891e145	−0.234482
$605$	−1.42572e145	−0.129383
$606$	1.92681e144	0.0160335
$607$	−1.55972e146	−1.19026	−0.595130	−	0.803630i	$-0.702899\pi$
$607$	−1.55972e146	−1.19026	−0.595130	+	0.803630i	$0.702899\pi$
$608$	−1.81983e146	−1.27377
$609$	1.62043e145	0.104045
$610$	4.90777e145	0.289113
$611$	−7.33589e145	−0.396542
$612$	−2.70503e145	−0.134191
$613$	1.58307e146	0.720816	0.360408	−	0.932795i	$-0.382638\pi$
$613$	1.58307e146	0.720816	0.360408	+	0.932795i	$0.382638\pi$
$614$	−2.07655e146	−0.867968
$615$	1.42487e145	0.0546802
$616$	−3.91888e146	−1.38094
$617$	−4.02502e146	−1.30256	−0.651279	−	0.758838i	$-0.725767\pi$
$617$	−4.02502e146	−1.30256	−0.651279	+	0.758838i	$0.725767\pi$
$618$	−2.08332e145	−0.0619242
$619$	6.53348e146	1.78396	0.891981	−	0.452073i	$-0.149315\pi$
$619$	6.53348e146	1.78396	0.891981	+	0.452073i	$0.149315\pi$
$620$	3.96374e145	0.0994356
$621$	−5.86702e145	−0.135241
$622$	8.27834e146	1.75367
$623$	5.26480e146	1.02508
$624$	3.22137e145	0.0576566
$625$	−6.65117e146	−1.09445
$626$	−7.28996e146	−1.10299
$627$	−9.97895e145	−0.138848
$628$	1.34290e145	0.0171855
$629$	1.98413e146	0.233567
$630$	2.77162e147	3.00162
$631$	−9.04534e146	−0.901329	−0.450664	−	0.892693i	$-0.648813\pi$
$631$	−9.04534e146	−0.901329	−0.450664	+	0.892693i	$0.648813\pi$
$632$	−1.35729e147	−1.24459
$633$	−9.45651e145	−0.0798061
$634$	−1.49226e147	−1.15920
$635$	1.54612e147	1.10567
$636$	3.70110e145	0.0243687
$637$	2.70449e147	1.63970
$638$	−1.45298e147	−0.811285
$639$	2.57600e146	0.132480
$640$	−3.47399e147	−1.64581
$641$	1.32664e147	0.579039	0.289520	−	0.957172i	$-0.406504\pi$
$641$	1.32664e147	0.579039	0.289520	+	0.957172i	$0.406504\pi$
$642$	7.11331e145	0.0286077
$643$	−2.59325e147	−0.961100	−0.480550	−	0.876967i	$-0.659563\pi$
$643$	−2.59325e147	−0.961100	−0.480550	+	0.876967i	$0.659563\pi$
$644$	−1.70936e147	−0.583883
$645$	3.67909e146	0.115839
$646$	3.11154e147	0.903169
$647$	−5.34417e147	−1.43023	−0.715115	−	0.699007i	$-0.753626\pi$
$647$	−5.34417e147	−1.43023	−0.715115	+	0.699007i	$0.753626\pi$
$648$	3.04987e147	0.752650
$649$	1.68782e147	0.384132
$650$	−3.11681e147	−0.654274
$651$	−1.55685e146	−0.0301471
$652$	9.92600e146	0.177327
$653$	6.55280e146	0.108015	0.0540076	−	0.998541i	$-0.482800\pi$
$653$	6.55280e146	0.108015	0.0540076	+	0.998541i	$0.482800\pi$
$654$	6.22226e146	0.0946491
$655$	6.22813e147	0.874358
$656$	5.03639e147	0.652631
$657$	5.42709e147	0.649210
$658$	1.24524e148	1.37529
$659$	−6.28428e147	−0.640872	−0.320436	−	0.947270i	$-0.603829\pi$
$659$	−6.28428e147	−0.640872	−0.320436	+	0.947270i	$0.603829\pi$
$660$	3.50752e146	0.0330327
$661$	1.52889e148	1.32984	0.664920	−	0.746914i	$-0.268465\pi$
$661$	1.52889e148	1.32984	0.664920	+	0.746914i	$0.268465\pi$
$662$	−1.53594e148	−1.23404
$663$	−2.53065e146	−0.0187833
$664$	3.87919e147	0.266021
$665$	−8.06147e148	−5.10832
$666$	1.15086e148	0.673945
$667$	1.23889e148	0.670540
$668$	−5.12256e146	−0.0256285
$669$	−1.39340e147	−0.0644474
$670$	2.46989e148	1.05621
$671$	4.37049e147	0.172821
$672$	−2.51239e147	−0.0918757
$673$	−4.68333e148	−1.58403	−0.792016	−	0.610501i	$-0.790968\pi$
$673$	−4.68333e148	−1.58403	−0.792016	+	0.610501i	$0.790968\pi$
$674$	1.05595e148	0.330370
$675$	4.59169e147	0.132900
$676$	−7.58501e147	−0.203121
$677$	5.48314e148	1.35870	0.679351	−	0.733814i	$-0.262261\pi$
$677$	5.48314e148	1.35870	0.679351	+	0.733814i	$0.262261\pi$
$678$	2.81756e146	0.00646123
$679$	4.55109e148	0.965944
$680$	2.13792e148	0.420024
$681$	3.93545e147	0.0715766
$682$	1.39597e148	0.235069
$683$	−5.85471e148	−0.912890	−0.456445	−	0.889752i	$-0.650877\pi$
$683$	−5.85471e148	−0.912890	−0.456445	+	0.889752i	$0.650877\pi$
$684$	4.56357e148	0.658960
$685$	1.34007e149	1.79214
$686$	−2.82045e149	−3.49383
$687$	−6.86942e147	−0.0788299
$688$	1.30043e149	1.38259
$689$	−6.20338e148	−0.611110
$690$	−1.18276e148	−0.107974
$691$	−5.99911e147	−0.0507562	−0.0253781	−	0.999678i	$-0.508079\pi$
$691$	−5.99911e147	−0.0507562	−0.0253781	+	0.999678i	$0.508079\pi$
$692$	−5.06178e148	−0.396948
$693$	2.46820e149	1.79426
$694$	−1.19000e149	−0.802000
$695$	−3.59421e148	−0.224596
$696$	7.25005e147	0.0420103
$697$	−3.95650e148	−0.212613
$698$	−2.52464e149	−1.25832
$699$	1.29881e148	0.0600475
$700$	1.33779e149	0.573775
$701$	5.70124e148	0.226868	0.113434	−	0.993546i	$-0.463815\pi$
$701$	5.70124e148	0.226868	0.113434	+	0.993546i	$0.463815\pi$
$702$	−2.94391e148	−0.108699
$703$	−3.34735e149	−1.14696
$704$	−1.41054e149	−0.448559
$705$	2.17868e148	0.0643079
$706$	3.31443e149	0.908161
$707$	1.38617e149	0.352611
$708$	4.30832e147	0.0101756
$709$	−6.68298e146	−0.00146569	−0.000732846	−	1.00000i	$-0.500233\pi$
$709$	−6.68298e146	−0.00146569	−0.000732846		1.00000i	$0.500233\pi$
$710$	1.04151e149	0.212130
$711$	8.54853e149	1.61710
$712$	2.35555e149	0.413897
$713$	−1.19028e149	−0.194289
$714$	4.29569e148	0.0651444
$715$	−5.87893e149	−0.828382
$716$	3.99722e149	0.523389
$717$	9.91362e148	0.120636
$718$	2.16513e148	0.0244879
$719$	5.00706e149	0.526400	0.263200	−	0.964741i	$-0.415222\pi$
$719$	5.00706e149	0.526400	0.263200	+	0.964741i	$0.415222\pi$
$720$	1.71403e150	1.67518
$721$	−1.49875e150	−1.36185
$722$	−3.88007e150	−3.27821
$723$	−9.29323e148	−0.0730140
$724$	−7.29462e149	−0.533001
$725$	−9.69585e149	−0.658932
$726$	−1.28170e148	−0.00810237
$727$	6.05190e149	0.355906	0.177953	−	0.984039i	$-0.443053\pi$
$727$	6.05190e149	0.355906	0.177953	+	0.984039i	$0.443053\pi$
$728$	1.67664e150	0.917368
$729$	−1.89913e150	−0.966850
$730$	2.19425e150	1.03953
$731$	−1.02159e150	−0.450417
$732$	1.11561e148	0.00457804
$733$	4.46401e150	1.70516	0.852582	−	0.522594i	$-0.175036\pi$
$733$	4.46401e150	1.70516	0.852582	+	0.522594i	$0.175036\pi$
$734$	1.58344e150	0.563066
$735$	−8.03202e149	−0.265913
$736$	−1.92083e150	−0.592110
$737$	2.19949e150	0.631364
$738$	−2.29490e150	−0.613485
$739$	3.56099e150	0.886621	0.443311	−	0.896368i	$-0.353804\pi$
$739$	3.56099e150	0.886621	0.443311	+	0.896368i	$0.353804\pi$
$740$	1.17657e150	0.272868
$741$	4.26937e149	0.0922376
$742$	1.05300e151	2.11946
$743$	−6.98622e150	−1.31018	−0.655088	−	0.755553i	$-0.727368\pi$
$743$	−6.98622e150	−1.31018	−0.655088	+	0.755553i	$0.727368\pi$
$744$	−6.96558e148	−0.0121724
$745$	−1.11424e151	−1.81458
$746$	−6.34271e150	−0.962690
$747$	−2.44320e150	−0.345643
$748$	−9.73952e149	−0.128441
$749$	5.11737e150	0.629146
$750$	−1.09298e149	−0.0125284
$751$	1.18621e150	0.126784	0.0633920	−	0.997989i	$-0.479808\pi$
$751$	1.18621e150	0.126784	0.0633920	+	0.997989i	$0.479808\pi$
$752$	7.70084e150	0.767541
$753$	9.26575e149	0.0861280
$754$	6.21639e150	0.538942
$755$	−1.17920e151	−0.953613
$756$	1.26358e150	0.0953252
$757$	−5.00625e150	−0.352354	−0.176177	−	0.984359i	$-0.556373\pi$
$757$	−5.00625e150	−0.352354	−0.176177	+	0.984359i	$0.556373\pi$
$758$	−6.74959e150	−0.443245
$759$	−1.05328e150	−0.0645430
$760$	−3.60682e151	−2.06258
$761$	2.83818e151	1.51476	0.757382	−	0.652972i	$-0.226478\pi$
$761$	2.83818e151	1.51476	0.757382	+	0.652972i	$0.226478\pi$
$762$	1.38994e150	0.0692404
$763$	4.47635e151	2.08154
$764$	−9.10177e150	−0.395116
$765$	−1.34651e151	−0.545739
$766$	−2.33164e151	−0.882371
$767$	−7.22114e150	−0.255181
$768$	−2.05917e150	−0.0679561
$769$	3.01681e151	0.929853	0.464927	−	0.885349i	$-0.346081\pi$
$769$	3.01681e151	0.929853	0.464927	+	0.885349i	$0.346081\pi$
$770$	9.97928e151	2.87300
$771$	4.72084e150	0.126959
$772$	−3.38205e150	−0.0849713
$773$	−2.17459e151	−0.510452	−0.255226	−	0.966881i	$-0.582150\pi$
$773$	−2.17459e151	−0.510452	−0.255226	+	0.966881i	$0.582150\pi$
$774$	−5.92556e151	−1.29966
$775$	9.31541e150	0.190925
$776$	2.03622e151	0.390018
$777$	−4.62124e150	−0.0827285
$778$	−1.00674e152	−1.68456
$779$	6.67487e151	1.04406
$780$	−1.50065e150	−0.0219438
$781$	9.27493e150	0.126804
$782$	3.28423e151	0.419835
$783$	−9.15797e150	−0.109473
$784$	−2.83903e152	−3.17378
$785$	6.68468e150	0.0698914
$786$	5.59897e150	0.0547551
$787$	−1.84640e152	−1.68909	−0.844544	−	0.535486i	$-0.820128\pi$
$787$	−1.84640e152	−1.68909	−0.844544	+	0.535486i	$0.820128\pi$
$788$	4.96858e151	0.425212
$789$	7.64708e150	0.0612284
$790$	3.45629e152	2.58933
$791$	2.02698e151	0.142097
$792$	1.10431e152	0.724466
$793$	−1.86986e151	−0.114806
$794$	3.27650e152	1.88293
$795$	1.84234e151	0.0991047
$796$	−9.27362e151	−0.466996
$797$	−7.49684e151	−0.353440	−0.176720	−	0.984261i	$-0.556549\pi$
$797$	−7.49684e151	−0.353440	−0.176720	+	0.984261i	$0.556549\pi$
$798$	−7.24711e151	−0.319899
$799$	−6.04964e151	−0.250048
$800$	1.50329e152	0.581859
$801$	−1.48358e152	−0.537778
$802$	1.96338e152	0.666577
$803$	1.95403e152	0.621392
$804$	5.61441e150	0.0167248
$805$	−8.50886e152	−2.37459
$806$	−5.97247e151	−0.156158
$807$	4.02130e151	0.0985159
$808$	6.20190e151	0.142373
$809$	7.83353e152	1.68523	0.842617	−	0.538513i	$-0.181014\pi$
$809$	7.83353e152	1.68523	0.842617	+	0.538513i	$0.181014\pi$
$810$	−7.76637e152	−1.56587
$811$	−7.46411e152	−1.41053	−0.705267	−	0.708942i	$-0.749173\pi$
$811$	−7.46411e152	−1.41053	−0.705267	+	0.708942i	$0.749173\pi$
$812$	−2.66818e152	−0.472633
$813$	−5.82321e151	−0.0966961
$814$	4.14368e152	0.645068
$815$	4.94097e152	0.721170
$816$	2.65654e151	0.0363566
$817$	1.72349e153	2.21183
$818$	−2.01580e152	−0.242605
$819$	−1.05599e153	−1.19194
$820$	−2.34617e152	−0.248388
$821$	−1.02758e153	−1.02047	−0.510233	−	0.860036i	$-0.670441\pi$
$821$	−1.02758e153	−1.02047	−0.510233	+	0.860036i	$0.670441\pi$
$822$	1.20470e152	0.112230
$823$	9.91017e152	0.866143	0.433072	−	0.901359i	$-0.357430\pi$
$823$	9.91017e152	0.866143	0.433072	+	0.901359i	$0.357430\pi$
$824$	−6.70564e152	−0.549872
$825$	8.24322e151	0.0634256
$826$	1.22576e153	0.885023
$827$	5.69334e152	0.385770	0.192885	−	0.981221i	$-0.438216\pi$
$827$	5.69334e152	0.385770	0.192885	+	0.981221i	$0.438216\pi$
$828$	4.81684e152	0.306316
$829$	−2.36891e152	−0.141396	−0.0706979	−	0.997498i	$-0.522523\pi$
$829$	−2.36891e152	−0.141396	−0.0706979	+	0.997498i	$0.522523\pi$
$830$	−9.87820e152	−0.553450
$831$	1.11206e152	0.0584890
$832$	6.03481e152	0.297981
$833$	2.23029e153	1.03395
$834$	−3.23113e151	−0.0140649
$835$	−2.54991e152	−0.104228
$836$	1.64312e153	0.630725
$837$	8.79864e151	0.0317197
$838$	−4.54161e153	−1.53780
$839$	2.95617e152	0.0940214	0.0470107	−	0.998894i	$-0.485031\pi$
$839$	2.95617e152	0.0940214	0.0470107	+	0.998894i	$0.485031\pi$
$840$	−4.97945e152	−0.148771
$841$	−1.62898e153	−0.457221
$842$	−3.59838e153	−0.948904
$843$	−1.42924e152	−0.0354127
$844$	1.55710e153	0.362524
$845$	−3.77567e153	−0.826070
$846$	−3.50899e153	−0.721502
$847$	−9.22062e152	−0.178189
$848$	6.51199e153	1.18286
$849$	−3.51787e152	−0.0600657
$850$	−2.57032e153	−0.412567
$851$	−3.53312e153	−0.533159
$852$	2.36751e151	0.00335903
$853$	6.28821e153	0.838886	0.419443	−	0.907782i	$-0.362225\pi$
$853$	6.28821e153	0.838886	0.419443	+	0.907782i	$0.362225\pi$
$854$	3.17402e153	0.398173
$855$	2.27165e154	2.67992
$856$	2.28959e153	0.254030
$857$	−3.80402e153	−0.396962	−0.198481	−	0.980105i	$-0.563601\pi$
$857$	−3.80402e153	−0.396962	−0.198481	+	0.980105i	$0.563601\pi$
$858$	−5.28505e152	−0.0518760
$859$	6.93239e153	0.640091	0.320046	−	0.947402i	$-0.396302\pi$
$859$	6.93239e153	0.640091	0.320046	+	0.947402i	$0.396302\pi$
$860$	−6.05794e153	−0.526206
$861$	9.21510e152	0.0753069
$862$	2.05344e154	1.57889
$863$	−2.25684e154	−1.63280	−0.816401	−	0.577486i	$-0.804034\pi$
$863$	−2.25684e154	−1.63280	−0.816401	+	0.577486i	$0.804034\pi$
$864$	1.41989e153	0.0966684
$865$	−2.51965e154	−1.61434
$866$	−2.68459e154	−1.61878
$867$	1.10403e153	0.0626585
$868$	2.56349e153	0.136945
$869$	3.07791e154	1.54781
$870$	−1.84620e153	−0.0874012
$871$	−9.41026e153	−0.419419
$872$	2.00278e154	0.840462
$873$	−1.28246e154	−0.506752
$874$	−5.54071e154	−2.06165
$875$	−7.86296e153	−0.275526
$876$	4.98785e152	0.0164607
$877$	9.58540e153	0.297942	0.148971	−	0.988842i	$-0.452404\pi$
$877$	9.58540e153	0.297942	0.148971	+	0.988842i	$0.452404\pi$
$878$	1.15020e154	0.336752
$879$	3.16350e153	0.0872472
$880$	6.17140e154	1.60340
$881$	−4.25775e154	−1.04219	−0.521093	−	0.853500i	$-0.674475\pi$
$881$	−4.25775e154	−1.04219	−0.521093	+	0.853500i	$0.674475\pi$
$882$	1.29364e155	2.98341
$883$	−5.65508e154	−1.22886	−0.614429	−	0.788972i	$-0.710614\pi$
$883$	−5.65508e154	−1.22886	−0.614429	+	0.788972i	$0.710614\pi$
$884$	4.16693e153	0.0853242
$885$	2.14460e153	0.0413832
$886$	−7.69079e153	−0.139862
$887$	−8.11925e154	−1.39164	−0.695819	−	0.718218i	$-0.744958\pi$
$887$	−8.11925e154	−1.39164	−0.695819	+	0.718218i	$0.744958\pi$
$888$	−2.06761e153	−0.0334032
$889$	9.99932e154	1.52275
$890$	−5.99832e154	−0.861101
$891$	−6.91614e154	−0.936018
$892$	2.29436e154	0.292757
$893$	1.02061e155	1.22789
$894$	−1.00168e154	−0.113635
$895$	1.98974e155	2.12856
$896$	−2.24675e155	−2.26665
$897$	4.50631e153	0.0428764
$898$	1.24293e155	1.11542
$899$	−1.85793e154	−0.157270
$900$	−3.76978e154	−0.301013
$901$	−5.11571e154	−0.385349
$902$	−8.26282e154	−0.587198
$903$	2.37939e154	0.159536
$904$	9.06899e153	0.0573742
$905$	−3.63112e155	−2.16765
$906$	−1.06008e154	−0.0597183
$907$	2.73085e155	1.45183	0.725914	−	0.687785i	$-0.241417\pi$
$907$	2.73085e155	1.45183	0.725914	+	0.687785i	$0.241417\pi$
$908$	−6.48006e154	−0.325141
$909$	−3.90610e154	−0.184986
$910$	−4.26951e155	−1.90856
$911$	3.00572e155	1.26833	0.634167	−	0.773196i	$-0.281343\pi$
$911$	3.00572e155	1.26833	0.634167	+	0.773196i	$0.281343\pi$
$912$	−4.48177e154	−0.178534
$913$	−8.79678e154	−0.330832
$914$	3.16047e155	1.12222
$915$	5.55327e153	0.0186184
$916$	1.13111e155	0.358090
$917$	4.02795e155	1.20419
$918$	−2.42774e154	−0.0685426
$919$	4.20926e155	1.12238	0.561192	−	0.827686i	$-0.310343\pi$
$919$	4.20926e155	1.12238	0.561192	+	0.827686i	$0.310343\pi$
$920$	−3.80699e155	−0.958784
$921$	−2.34968e154	−0.0558956
$922$	2.52946e155	0.568401
$923$	−3.96816e154	−0.0842365
$924$	2.26844e154	0.0454934
$925$	2.76512e155	0.523929
$926$	5.63827e155	1.00941
$927$	4.22336e155	0.714451
$928$	−2.99826e155	−0.479293
$929$	−2.46842e155	−0.372901	−0.186451	−	0.982464i	$-0.559698\pi$
$929$	−2.46842e155	−0.372901	−0.186451	+	0.982464i	$0.559698\pi$
$930$	1.77376e154	0.0253244
$931$	−3.76265e156	−5.07733
$932$	−2.13861e155	−0.272769
$933$	9.36717e154	0.112933
$934$	5.83268e155	0.664748
$935$	−4.84814e155	−0.522355
$936$	−4.72464e155	−0.481268
$937$	1.82249e156	1.75524	0.877621	−	0.479356i	$-0.159130\pi$
$937$	1.82249e156	1.75524	0.877621	+	0.479356i	$0.159130\pi$
$938$	1.59736e156	1.45463
$939$	−8.24879e154	−0.0710308
$940$	−3.58738e155	−0.292122
$941$	−1.54822e156	−1.19228	−0.596138	−	0.802882i	$-0.703299\pi$
$941$	−1.54822e156	−1.19228	−0.596138	+	0.802882i	$0.703299\pi$
$942$	6.00940e153	0.00437682
$943$	7.04531e155	0.485329
$944$	7.58038e155	0.493925
$945$	6.28984e155	0.387677
$946$	−2.13351e156	−1.24397
$947$	2.52207e156	1.39118	0.695589	−	0.718440i	$-0.255144\pi$
$947$	2.52207e156	1.39118	0.695589	+	0.718440i	$0.255144\pi$
$948$	7.85666e154	0.0410015
$949$	−8.36009e155	−0.412795
$950$	4.33631e156	2.02596
$951$	−1.68853e155	−0.0746505
$952$	1.38267e156	0.578467
$953$	−3.92414e155	−0.155370	−0.0776850	−	0.996978i	$-0.524753\pi$
$953$	−3.92414e155	−0.155370	−0.0776850	+	0.996978i	$0.524753\pi$
$954$	−2.96727e156	−1.11191
$955$	−4.53068e156	−1.60689
$956$	−1.63236e156	−0.547996
$957$	−1.64408e155	−0.0522453
$958$	1.25780e156	0.378375
$959$	8.66669e156	2.46818
$960$	−1.79227e155	−0.0483241
$961$	−3.73872e156	−0.954431
$962$	−1.77282e156	−0.428523
$963$	−1.44203e156	−0.330062
$964$	1.53021e156	0.331671
$965$	−1.68352e156	−0.345569
$966$	−7.64931e155	−0.148704
$967$	3.51079e156	0.646421	0.323210	−	0.946327i	$-0.395238\pi$
$967$	3.51079e156	0.646421	0.323210	+	0.946327i	$0.395238\pi$
$968$	−4.12544e155	−0.0719472
$969$	3.52080e155	0.0581624
$970$	−5.18516e156	−0.811421
$971$	−4.15598e156	−0.616118	−0.308059	−	0.951367i	$-0.599679\pi$
$971$	−4.15598e156	−0.616118	−0.308059	+	0.951367i	$0.599679\pi$
$972$	−5.34594e155	−0.0750836
$973$	−2.32450e156	−0.309318
$974$	−5.70943e156	−0.719860
$975$	−3.52676e155	−0.0421341
$976$	1.96288e156	0.222218
$977$	1.31466e157	1.41042	0.705209	−	0.708999i	$-0.250853\pi$
$977$	1.31466e157	1.41042	0.705209	+	0.708999i	$0.250853\pi$
$978$	4.44184e155	0.0451620
$979$	−5.34165e156	−0.514735
$980$	1.32254e157	1.20793
$981$	−1.26140e157	−1.09202
$982$	5.09403e156	0.418031
$983$	1.46640e156	0.114076	0.0570378	−	0.998372i	$-0.481834\pi$
$983$	1.46640e156	0.114076	0.0570378	+	0.998372i	$0.481834\pi$
$984$	4.12297e155	0.0304066
$985$	2.47326e157	1.72929
$986$	5.12643e156	0.339842
$987$	1.40903e156	0.0885662
$988$	−7.02989e156	−0.418995
$989$	1.81914e157	1.02816
$990$	−2.81208e157	−1.50723
$991$	1.77420e157	0.901854	0.450927	−	0.892561i	$-0.351093\pi$
$991$	1.77420e157	0.901854	0.450927	+	0.892561i	$0.351093\pi$
$992$	2.88062e156	0.138875
$993$	−1.73795e156	−0.0794699
$994$	6.73583e156	0.292150
$995$	−4.61623e157	−1.89922
$996$	−2.24546e155	−0.00876375
$997$	−5.26632e156	−0.194990	−0.0974948	−	0.995236i	$-0.531083\pi$
$997$	−5.26632e156	−0.194990	−0.0974948	+	0.995236i	$0.531083\pi$
$998$	−2.94436e157	−1.03428
$999$	2.61172e156	0.0870440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.106.a.a.1.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.106.a.a.1.3	✓	8	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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 106 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-7.36840e15 q^{2} -8.33754e23 q^{3} +1.37285e31 q^{4} +6.83377e36 q^{5} +6.14343e39 q^{6} +4.41963e44 q^{7} +1.97741e47 q^{8} -1.24542e50 q^{9} +O(q^{10})\)	\(q-7.36840e15 q^{2} -8.33754e23 q^{3} +1.37285e31 q^{4} +6.83377e36 q^{5} +6.14343e39 q^{6} +4.41963e44 q^{7} +1.97741e47 q^{8} -1.24542e50 q^{9} -5.03539e52 q^{10} -4.48414e54 q^{11} -1.14462e55 q^{12} +1.91848e58 q^{13} -3.25656e60 q^{14} -5.69768e60 q^{15} -2.01393e63 q^{16} +1.58211e64 q^{17} +9.17672e65 q^{18} -2.66912e67 q^{19} +9.38173e67 q^{20} -3.68489e68 q^{21} +3.30409e70 q^{22} -2.81725e71 q^{23} -1.64867e71 q^{24} +2.20485e73 q^{25} -1.41362e74 q^{26} +2.08254e74 q^{27} +6.06749e75 q^{28} -4.39751e76 q^{29} +4.19828e76 q^{30} +4.22496e77 q^{31} +6.81810e78 q^{32} +3.73867e78 q^{33} -1.16576e80 q^{34} +3.02028e81 q^{35} -1.70977e81 q^{36} +1.25411e82 q^{37} +1.96671e83 q^{38} -1.59954e82 q^{39} +1.35132e84 q^{40} -2.50078e84 q^{41} +2.71517e84 q^{42} -6.45716e85 q^{43} -6.15605e85 q^{44} -8.51089e86 q^{45} +2.07586e87 q^{46} -3.82379e87 q^{47} +1.67912e87 q^{48} +1.40970e89 q^{49} -1.62462e89 q^{50} -1.31909e88 q^{51} +2.63379e89 q^{52} -3.23348e90 q^{53} -1.53450e90 q^{54} -3.06436e91 q^{55} +8.73942e91 q^{56} +2.22539e91 q^{57} +3.24026e92 q^{58} -3.76398e92 q^{59} -7.82206e91 q^{60} -9.74654e92 q^{61} -3.11312e93 q^{62} -5.50428e94 q^{63} +3.14561e94 q^{64} +1.31105e95 q^{65} -2.75480e94 q^{66} -4.90505e95 q^{67} +2.17199e95 q^{68} +2.34889e95 q^{69} -2.22546e97 q^{70} -2.06839e96 q^{71} -2.46270e97 q^{72} -4.35765e97 q^{73} -9.24075e97 q^{74} -1.83830e97 q^{75} -3.66429e98 q^{76} -1.98183e99 q^{77} +1.17861e98 q^{78} -6.86400e99 q^{79} -1.37627e100 q^{80} +1.54236e100 q^{81} +1.84267e100 q^{82} +1.96175e100 q^{83} -5.05880e99 q^{84} +1.08117e101 q^{85} +4.75790e101 q^{86} +3.66644e100 q^{87} -8.86698e101 q^{88} +1.19123e102 q^{89} +6.27116e102 q^{90} +8.47900e102 q^{91} -3.86765e102 q^{92} -3.52258e101 q^{93} +2.81752e103 q^{94} -1.82401e104 q^{95} -5.68462e102 q^{96} +1.02974e104 q^{97} -1.03872e105 q^{98} +5.58462e104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 91\!\cdots\!20 q^{2}+ \cdots + 31\!\cdots\!84 q^{9}+O(q^{10}) \) 8 * q - 9175032489175920 * q^2 - 3552367551392844422995680 * q^3 + 120400994563419904822151366840576 * q^4 + 748366724871512021371292499759044400 * q^5 - 132475226406122000574502252920799787081664 * q^6 + 70538552172860257833295679508195640805531200 * q^7 - 706397877636490430592988742663067828802762076160 * q^8 + 317686049104616976165951103806454636773011694234984 * q^9	\( 8 q - 91\!\cdots\!20 q^{2}+ \cdots - 25\!\cdots\!32 q^{99}+O(q^{100}) \) 8 * q - 9175032489175920 * q^2 - 3552367551392844422995680 * q^3 + 120400994563419904822151366840576 * q^4 + 748366724871512021371292499759044400 * q^5 - 132475226406122000574502252920799787081664 * q^6 + 70538552172860257833295679508195640805531200 * q^7 - 706397877636490430592988742663067828802762076160 * q^8 + 317686049104616976165951103806454636773011694234984 * q^9 + 44171640525838765855893406263279104758565541661288800 * q^10 - 9131055394382837373664474069991492435117703171343284384 * q^11 + 1527166610615675905236013736606832949994468355519571829760 * q^12 + 4027585984285071020829060873004471073659148035689891664240 * q^13 - 160479473931693657661766690342904266858167662972048261318528 * q^14 - 85128562811603808162187988771451472214709069164574920929377600 * q^15 + 889182208997906282405898151302671436269823882827077347193192448 * q^16 - 47501502884916058924984340290257937633075778259367096814503394160 * q^17 - 2631080775730316510475478098580289149623650642713560969940755311280 * q^18 - 18490664070300440944092597449321411045310230817014503422448283738720 * q^19 - 433265654737251440411002845299403120817887965583462605623471811443200 * q^20 + 3435707407505559395644737215619994347818097875706879454950102719283456 * q^21 + 61667954680464912832813918015747124830645650785532527356368764542445760 * q^22 + 356123479312529060531796005710488420903589988587191444144805952706144960 * q^23 - 8553895157762497374674387748794258238227739674467572965053160752231464960 * q^24 + 36710330225103772037154153143396858524815591923552301173280524244928235000 * q^25 - 178290299429521612994896681862440451353112938442078389560127528645835464224 * q^26 + 4108583825736723245642984497148380325909672596193180989676962467681728811840 * q^27 - 10197863837452248524370326511788692919181508212113555118341665631868445276160 * q^28 - 132808057928545728770070628075237950532883381334274325807559945373631525579280 * q^29 + 368843646251862307061952875207762300737776646306173378951277228159200294844800 * q^30 + 2123150329739540390115408696476884203950374929670685127189943125782378108098816 * q^31 + 10156626912480412308164375397145246760285661187761787998479811379273048947425280 * q^32 - 110453822927144134530855124481163271865404195805770611489444997754143335676114560 * q^33 + 626514570831444006665132709400608888132203790316575476126972954148191421104888352 * q^34 - 180124138596474130911007456858429985683613480525844149859433273467968580724675200 * q^35 + 16221855297378912428170473077312544781163834427405933513071046969489436648368930048 * q^36 - 23010049861253897057830375004531412092720779537210279421336409908255568411112521680 * q^37 + 81514285558726303526499020366236482021009949677570093462995405282915730851685437760 * q^38 + 973250204883059182004683876455057324018758755152662643519744443013209490499392320448 * q^39 + 1620603767802466493396978076732241543088378147649587002013209944275991354096540672000 * q^40 - 9194436894335705500488956082645864740213392167963146808356372625255538188465570116784 * q^41 - 9987175533659763810738086904398668829743024019181589555089340923029980612539996188160 * q^42 + 3032382926300215248368351846801184405080019611637638159804034319071519733367501308000 * q^43 - 61413740744912033848381562467905778729130346597543024132573739224535613780500625691648 * q^44 - 728055588424370630925028219171725592820104067843765840180299922436159334808200708678800 * q^45 - 1937857727868547524263658836001472070613971220638572213222135000017628068861666423993984 * q^46 - 193114845358989650895015242618332478679741488577861492750207342621672434970683481651840 * q^47 + 47504655695285299018807413925656103836145592812920588522461073427843872384146136331714560 * q^48 + 9009795911083753626429293565600536034814214101588418291494061693709008119369143800410056 * q^49 + 124085104852024153585775552318382585485956095474767588057564984609967735836202360766470000 * q^50 - 1021523462097644786402134875264470962590383726411120471709206304906745531337979847222893504 * q^51 + 2601002607846544407071841678151669268750253239046498757166255249010956826575867860287884800 * q^52 - 508977518161307968273832984082037167871777334860039281483640147609506187672311865310329680 * q^53 - 33215015372693850873232010101241869628048359784733721234902490207672455295016159119447797120 * q^54 + 18450671784502163418133731529996697688391744925805957647904016734511230779675351655763828800 * q^55 + 77907763278563265290300076439200648252399491244631034718538984366849741317596223703232839680 * q^56 - 17514494370932414539251899866861034389141458703710767594438206182965846210727691039357326720 * q^57 + 521188643454307966215167554048547429862263982605454645813054246139388891719965181350028489440 * q^58 - 800548783090069547249411402735852579353665443321854402294237928007339127684491029048409334560 * q^59 - 4945597330350911740055109354650466378405725800344464689989883069207313581778154248500120627200 * q^60 + 9301780115240647873952088718367909265400456376594614456607735293030740558435392467259218034416 * q^61 - 24958988483741760731654226022541604930667635314913646027823754011402485431605464535556971159040 * q^62 - 69917019353683231050173137254943101675489279093995056831426882673091272292662113138105940233920 * q^63 - 97451971150817117830440198299734679886485437857461550467094176739811166528413095345956746952704 * q^64 - 361156613980852842706992602837566394553099687955520933659145529501075901774183231590989074101600 * q^65 + 156882494260210220362013449528635783983344936752786747375982538482579620426751742603199124015872 * q^66 - 1104667221349188765660578837514456152306124133482553297212406551469220909847432127137057601268960 * q^67 - 9721401068443204036258202986739714019478462517573215331908850090837288931485135338678529805012480 * q^68 - 15109507425538340400955372418178718530943009113130778845692031950392404855615907056642892252773632 * q^69 - 42141974870106016058865849455224368290398026088671930674752184932090288769297201065857297686150400 * q^70 - 50469870302247936824042683436030531088994086024328522294948330069784198912349909975813351349301184 * q^71 - 312770283013563627062551283668577288708985871414226238388562703871210081634250694390516261706772480 * q^72 - 309796921364548112330210024475355394269902333254274320239737341959226533985104691513778940551838640 * q^73 - 925823752396046652342642416972554390081562347656534041993730400149451972597268102227614960148886688 * q^74 - 2035970471601402025465859080535649095398414802703074791592862122373110362938204069403415245277940000 * q^75 - 3130569503520776632201267436445813580876068550759173850078744887758531600111432515821247207535037440 * q^76 - 5943612343311427733153258808379776193285399172298997030946865449540200274638852351419681744544800000 * q^77 - 21269159569550168394975895479661937627684008715929340977029750772463946126724250407354989139174454400 * q^78 - 15393227887174294584948162208020437185460179522932597986148734991937027143223423856935347902468612480 * q^79 - 36135869014387530593279194332920203124385252019916366550807261806779025414796891084911471716850073600 * q^80 - 16813579079052539310958564290225362908835005641306645336831720897045685008922728854885093229369750072 * q^81 + 40683812685771158034068852888314888590966014976906157199478748314343833251276146968126649606561452960 * q^82 - 27748711091393049888979586421607112972809560782068769478686312453860122910561653683460280801656090720 * q^83 + 243729273671324707074190479881332236879714714008146405350632616637128634259974190017728217778172076032 * q^84 + 1114476595266646322768819965977266122931255323002065012571315493969146685766458335643036439956923496800 * q^85 + 2001948212296635436448279509615999770689923972184784294781573198292641086063207267886445869810840226496 * q^86 + 2452094134677213482937709450778797624299131398431787829024781103485568458306913143764742103712037328320 * q^87 + 6587629213482246089116430616322572992490320338289310595388533189153014205464262604258615522799278407680 * q^88 + 4561891385239988132989403179389372513149936713239528905622804144400695279296267497385381892983137482960 * q^89 + 27831127206069462137128463558919625443225864994138363209261172284208865542079088020097519776839212242400 * q^90 + 27533535014530695422075480606590604897330716562374502844003945844898533709216751249129046131797307879296 * q^91 + 11219382355167481799152672023779859908676464262842813795936572357113636635896010169112116501983056189440 * q^92 - 1816432822902220399473532579920329564793343562884883929779919263741160765335835765675399623257440680960 * q^93 - 145721137880009419474465571784854076810270560388958588104991210830700849472154051473896292058236218084608 * q^94 - 197505250338784881028096044265210353994741936910104745900078290549992685412473006655125953841487400936000 * q^95 - 722643410665348223758010527434181844660741784808619153000544243764286894029121981921039078126765698187264 * q^96 - 765925425726897926053834041674103560846690860133522436616120766353705349104461208876007591285452102784240 * q^97 - 1378222404256086778845054197358441766991528993251977664562346500406878280455090891540290251693972016377840 * q^98 - 2543675383725234370604494641035024609729543664951752733885226452347175058619125118596469912791508615603232 * q^99

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