LMFDB - Embedded newform 1.106.a.a.1.1

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			1.1
Root			$-7.21371e13$ 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)

$f(q)$	$=$	$q-1.15346e16 q^{2} +2.00325e25 q^{3} +9.24825e31 q^{4} -4.02660e36 q^{5} -2.31067e41 q^{6} -1.49411e43 q^{7} -5.98851e47 q^{8} +2.76064e50 q^{9} +O(q^{10})$	\(q-1.15346e16 q^{2} +2.00325e25 q^{3} +9.24825e31 q^{4} -4.02660e36 q^{5} -2.31067e41 q^{6} -1.49411e43 q^{7} -5.98851e47 q^{8} +2.76064e50 q^{9} +4.64453e52 q^{10} -4.19278e54 q^{11} +1.85266e57 q^{12} +4.35724e58 q^{13} +1.72340e59 q^{14} -8.06629e61 q^{15} +3.15598e63 q^{16} -5.45067e64 q^{17} -3.18429e66 q^{18} +5.82286e66 q^{19} -3.72391e68 q^{20} -2.99307e68 q^{21} +4.83621e70 q^{22} -5.38565e70 q^{23} -1.19965e73 q^{24} -8.43836e72 q^{25} -5.02591e74 q^{26} +3.02144e75 q^{27} -1.38179e75 q^{28} -5.63591e76 q^{29} +9.30415e77 q^{30} +1.44648e78 q^{31} -1.21107e79 q^{32} -8.39919e79 q^{33} +6.28714e80 q^{34} +6.01618e79 q^{35} +2.55311e82 q^{36} -2.11238e81 q^{37} -6.71645e82 q^{38} +8.72864e83 q^{39} +2.41134e84 q^{40} -5.42415e84 q^{41} +3.45239e84 q^{42} -3.33535e85 q^{43} -3.87759e86 q^{44} -1.11160e87 q^{45} +6.21214e86 q^{46} +2.06871e87 q^{47} +6.32221e88 q^{48} -5.41386e88 q^{49} +9.73333e88 q^{50} -1.09190e90 q^{51} +4.02969e90 q^{52} -1.52093e90 q^{53} -3.48512e91 q^{54} +1.68827e91 q^{55} +8.94748e90 q^{56} +1.16646e92 q^{57} +6.50081e92 q^{58} +1.70773e93 q^{59} -7.45991e93 q^{60} +2.17269e93 q^{61} -1.66846e94 q^{62} -4.12469e93 q^{63} +1.16707e94 q^{64} -1.75449e95 q^{65} +9.68814e95 q^{66} +8.39741e94 q^{67} -5.04092e96 q^{68} -1.07888e96 q^{69} -6.93944e95 q^{70} +1.45834e97 q^{71} -1.65321e98 q^{72} +3.40172e97 q^{73} +2.43655e97 q^{74} -1.69041e98 q^{75} +5.38513e98 q^{76} +6.26447e97 q^{77} -1.00682e100 q^{78} -3.48037e99 q^{79} -1.27079e100 q^{80} +2.59537e100 q^{81} +6.25655e100 q^{82} -4.88553e100 q^{83} -2.76807e100 q^{84} +2.19477e101 q^{85} +3.84720e101 q^{86} -1.12901e102 q^{87} +2.51085e102 q^{88} -3.37399e102 q^{89} +1.28219e103 q^{90} -6.51020e101 q^{91} -4.98078e102 q^{92} +2.89766e103 q^{93} -2.38617e103 q^{94} -2.34464e103 q^{95} -2.42608e104 q^{96} -3.41463e104 q^{97} +6.24468e104 q^{98} -1.15748e105 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.15346e16	−1.81104	−0.905521	−	0.424302i	$-0.860519\pi$
$2$	−1.15346e16	−1.81104	−0.905521	+	0.424302i	$0.860519\pi$
$3$	2.00325e25	1.79007	0.895033	−	0.446000i	$-0.147152\pi$
$3$	2.00325e25	1.79007	0.895033	+	0.446000i	$0.147152\pi$
$4$	9.24825e31	2.27987
$5$	−4.02660e36	−0.810987	−0.405493	−	0.914098i	$-0.632900\pi$
$5$	−4.02660e36	−0.810987	−0.405493	+	0.914098i	$0.632900\pi$
$6$	−2.31067e41	−3.24188
$7$	−1.49411e43	−0.0640819	−0.0320409	−	0.999487i	$-0.510201\pi$
$7$	−1.49411e43	−0.0640819	−0.0320409	+	0.999487i	$0.510201\pi$
$8$	−5.98851e47	−2.31790
$9$	2.76064e50	2.20434
$10$	4.64453e52	1.46873
$11$	−4.19278e54	−0.889993	−0.444996	−	0.895532i	$-0.646795\pi$
$11$	−4.19278e54	−0.889993	−0.444996	+	0.895532i	$0.646795\pi$
$12$	1.85266e57	4.08112
$13$	4.35724e58	1.43610	0.718052	−	0.695990i	$-0.245034\pi$
$13$	4.35724e58	1.43610	0.718052	+	0.695990i	$0.245034\pi$
$14$	1.72340e59	0.116055
$15$	−8.06629e61	−1.45172
$16$	3.15598e63	1.91794
$17$	−5.45067e64	−1.37367	−0.686833	−	0.726815i	$-0.741000\pi$
$17$	−5.45067e64	−1.37367	−0.686833	+	0.726815i	$0.741000\pi$
$18$	−3.18429e66	−3.99214
$19$	5.82286e66	0.427142	0.213571	−	0.976928i	$-0.431490\pi$
$19$	5.82286e66	0.427142	0.213571	+	0.976928i	$0.431490\pi$
$20$	−3.72391e68	−1.84894
$21$	−2.99307e68	−0.114711
$22$	4.83621e70	1.61181
$23$	−5.38565e70	−0.173991	−0.0869954	−	0.996209i	$-0.527727\pi$
$23$	−5.38565e70	−0.173991	−0.0869954	+	0.996209i	$0.527727\pi$
$24$	−1.19965e73	−4.14919
$25$	−8.43836e72	−0.342301
$26$	−5.02591e74	−2.60084
$27$	3.02144e75	2.15584
$28$	−1.38179e75	−0.146098
$29$	−5.63591e76	−0.944211	−0.472106	−	0.881542i	$-0.656506\pi$
$29$	−5.63591e76	−0.944211	−0.472106	+	0.881542i	$0.656506\pi$
$30$	9.30415e77	2.62912
$31$	1.44648e78	0.730841	0.365421	−	0.930843i	$-0.380925\pi$
$31$	1.44648e78	0.730841	0.365421	+	0.930843i	$0.380925\pi$
$32$	−1.21107e79	−1.15557
$33$	−8.39919e79	−1.59315
$34$	6.28714e80	2.48777
$35$	6.01618e79	0.0519695
$36$	2.55311e82	5.02560
$37$	−2.11238e81	−0.0986693	−0.0493347	−	0.998782i	$-0.515710\pi$
$37$	−2.11238e81	−0.0986693	−0.0493347	+	0.998782i	$0.515710\pi$
$38$	−6.71645e82	−0.773572
$39$	8.72864e83	2.57072
$40$	2.41134e84	1.87978
$41$	−5.42415e84	−1.15659	−0.578295	−	0.815828i	$-0.696282\pi$
$41$	−5.42415e84	−1.15659	−0.578295	+	0.815828i	$0.696282\pi$
$42$	3.45239e84	0.207746
$43$	−3.33535e85	−0.583509	−0.291755	−	0.956493i	$-0.594239\pi$
$43$	−3.33535e85	−0.583509	−0.291755	+	0.956493i	$0.594239\pi$
$44$	−3.87759e86	−2.02907
$45$	−1.11160e87	−1.78769
$46$	6.21214e86	0.315105
$47$	2.06871e87	0.339282	0.169641	−	0.985506i	$-0.445739\pi$
$47$	2.06871e87	0.339282	0.169641	+	0.985506i	$0.445739\pi$
$48$	6.32221e88	3.43324
$49$	−5.41386e88	−0.995894
$50$	9.73333e88	0.619921
$51$	−1.09190e90	−2.45895
$52$	4.02969e90	3.27413
$53$	−1.52093e90	−0.454596	−0.227298	−	0.973825i	$-0.572989\pi$
$53$	−1.52093e90	−0.454596	−0.227298	+	0.973825i	$0.572989\pi$
$54$	−3.48512e91	−3.90432
$55$	1.68827e91	0.721772
$56$	8.94748e90	0.148535
$57$	1.16646e92	0.764613
$58$	6.50081e92	1.71001
$59$	1.70773e93	1.83100	0.915499	−	0.402320i	$-0.131796\pi$
$59$	1.70773e93	1.83100	0.915499	+	0.402320i	$0.131796\pi$
$60$	−7.45991e93	−3.30973
$61$	2.17269e93	0.404745	0.202372	−	0.979309i	$-0.435135\pi$
$61$	2.17269e93	0.404745	0.202372	+	0.979309i	$0.435135\pi$
$62$	−1.66846e94	−1.32358
$63$	−4.12469e93	−0.141258
$64$	1.16707e94	0.174843
$65$	−1.75449e95	−1.16466
$66$	9.68814e95	2.88525
$67$	8.39741e94	0.113558	0.0567791	−	0.998387i	$-0.481917\pi$
$67$	8.39741e94	0.113558	0.0567791	+	0.998387i	$0.481917\pi$
$68$	−5.04092e96	−3.13178
$69$	−1.07888e96	−0.311455
$70$	−6.93944e95	−0.0941190
$71$	1.45834e97	0.939278	0.469639	−	0.882859i	$-0.344384\pi$
$71$	1.45834e97	0.939278	0.469639	+	0.882859i	$0.344384\pi$
$72$	−1.65321e98	−5.10943
$73$	3.40172e97	0.509622	0.254811	−	0.966991i	$-0.417987\pi$
$73$	3.40172e97	0.509622	0.254811	+	0.966991i	$0.417987\pi$
$74$	2.43655e97	0.178694
$75$	−1.69041e98	−0.612741
$76$	5.38513e98	0.973829
$77$	6.26447e97	0.0570324
$78$	−1.00682e100	−4.65568
$79$	−3.48037e99	−0.824523	−0.412261	−	0.911066i	$-0.635261\pi$
$79$	−3.48037e99	−0.824523	−0.412261	+	0.911066i	$0.635261\pi$
$80$	−1.27079e100	−1.55542
$81$	2.59537e100	1.65476
$82$	6.25655e100	2.09463
$83$	−4.88553e100	−0.865589	−0.432795	−	0.901493i	$-0.642472\pi$
$83$	−4.88553e100	−0.865589	−0.432795	+	0.901493i	$0.642472\pi$
$84$	−2.76807e100	−0.261526
$85$	2.19477e101	1.11403
$86$	3.84720e101	1.05676
$87$	−1.12901e102	−1.69020
$88$	2.51085e102	2.06291
$89$	−3.37399e102	−1.53168	−0.765841	−	0.643030i	$-0.777677\pi$
$89$	−3.37399e102	−1.53168	−0.765841	+	0.643030i	$0.777677\pi$
$90$	1.28219e103	3.23757
$91$	−6.51020e101	−0.0920282
$92$	−4.98078e102	−0.396677
$93$	2.89766e103	1.30825
$94$	−2.38617e103	−0.614454
$95$	−2.34464e103	−0.346407
$96$	−2.42608e104	−2.06854
$97$	−3.41463e104	−1.68977	−0.844885	−	0.534948i	$-0.820331\pi$
$97$	−3.41463e104	−1.68977	−0.844885	+	0.534948i	$0.820331\pi$
$98$	6.24468e104	1.80360
$99$	−1.15748e105	−1.96184
$100$	−7.80401e104	−0.780401
$101$	9.40507e104	0.557814	0.278907	−	0.960318i	$-0.410028\pi$
$101$	9.40507e104	0.557814	0.278907	+	0.960318i	$0.410028\pi$
$102$	1.25947e106	4.45327
$103$	−7.48693e105	−1.58617	−0.793084	−	0.609112i	$-0.791526\pi$
$103$	−7.48693e105	−1.58617	−0.793084	+	0.609112i	$0.791526\pi$
$104$	−2.60934e106	−3.32874
$105$	1.20519e105	0.0930289
$106$	1.75433e106	0.823291
$107$	1.11641e106	0.320020	0.160010	−	0.987115i	$-0.448847\pi$
$107$	1.11641e106	0.320020	0.160010	+	0.987115i	$0.448847\pi$
$108$	2.79431e107	4.91504
$109$	−6.08327e106	−0.659548	−0.329774	−	0.944060i	$-0.606973\pi$
$109$	−6.08327e106	−0.659548	−0.329774	+	0.944060i	$0.606973\pi$
$110$	−1.94735e107	−1.30716
$111$	−4.23163e106	−0.176625
$112$	−4.71537e106	−0.122905
$113$	−1.91150e107	−0.312432	−0.156216	−	0.987723i	$-0.549930\pi$
$113$	−1.91150e107	−0.312432	−0.156216	+	0.987723i	$0.549930\pi$
$114$	−1.34547e108	−1.38475
$115$	2.16859e107	0.141104
$116$	−5.21223e108	−2.15268
$117$	1.20288e109	3.16566
$118$	−1.96980e109	−3.31601
$119$	8.14389e107	0.0880271
$120$	4.83050e109	3.36494
$121$	−4.61438e108	−0.207913
$122$	−2.50611e109	−0.733009
$123$	−1.08659e110	−2.07037
$124$	1.33774e110	1.66622
$125$	1.33241e110	1.08859
$126$	4.75768e109	0.255824
$127$	7.03101e109	0.249645	0.124822	−	0.992179i	$-0.460164\pi$
$127$	7.03101e109	0.249645	0.124822	+	0.992179i	$0.460164\pi$
$128$	3.56652e110	0.838921
$129$	−6.68154e110	−1.04452
$130$	2.02374e111	2.10925
$131$	−1.77240e111	−1.23543	−0.617717	−	0.786401i	$-0.711942\pi$
$131$	−1.77240e111	−1.23543	−0.617717	+	0.786401i	$0.711942\pi$
$132$	−7.76778e111	−3.63217
$133$	−8.69999e109	−0.0273721
$134$	−9.68609e110	−0.205658
$135$	−1.21662e112	−1.74836
$136$	3.26414e112	3.18402
$137$	1.65935e112	1.10181	0.550907	−	0.834567i	$-0.314282\pi$
$137$	1.65935e112	1.10181	0.550907	+	0.834567i	$0.314282\pi$
$138$	1.24445e112	0.564058
$139$	−2.84779e112	−0.883551	−0.441775	−	0.897126i	$-0.645651\pi$
$139$	−2.84779e112	−0.883551	−0.441775	+	0.897126i	$0.645651\pi$
$140$	5.56392e111	0.118484
$141$	4.14413e112	0.607338
$142$	−1.68213e113	−1.70107
$143$	−1.82690e113	−1.27812
$144$	8.71251e113	4.22778
$145$	2.26936e113	0.765743
$146$	−3.92375e113	−0.922946
$147$	−1.08453e114	−1.78272
$148$	−1.95359e113	−0.224953
$149$	−1.97570e114	−1.59750	−0.798752	−	0.601661i	$-0.794506\pi$
$149$	−1.97570e114	−1.59750	−0.798752	+	0.601661i	$0.794506\pi$
$150$	1.94983e114	1.10970
$151$	3.99582e114	1.60441	0.802207	−	0.597046i	$-0.203659\pi$
$151$	3.99582e114	1.60441	0.802207	+	0.597046i	$0.203659\pi$
$152$	−3.48703e114	−0.990072
$153$	−1.50473e115	−3.02802
$154$	−7.22583e113	−0.103288
$155$	−5.82439e114	−0.592702
$156$	8.07247e115	5.86091
$157$	−3.24507e115	−1.68458	−0.842290	−	0.539024i	$-0.818793\pi$
$157$	−3.24507e115	−1.68458	−0.842290	+	0.539024i	$0.818793\pi$
$158$	4.01447e115	1.49325
$159$	−3.04680e115	−0.813756
$160$	4.87650e115	0.937150
$161$	8.04674e113	0.0111497
$162$	−2.99366e116	−2.99684
$163$	1.98748e116	1.44030	0.720150	−	0.693818i	$-0.244073\pi$
$163$	1.98748e116	1.44030	0.720150	+	0.693818i	$0.244073\pi$
$164$	−5.01639e116	−2.63687
$165$	3.38202e116	1.29202
$166$	5.63527e116	1.56762
$167$	−6.79873e116	−1.37979	−0.689895	−	0.723910i	$-0.742343\pi$
$167$	−6.79873e116	−1.37979	−0.689895	+	0.723910i	$0.742343\pi$
$168$	1.79240e116	0.265888
$169$	9.77997e116	1.06239
$170$	−2.53158e117	−2.01755
$171$	1.60748e117	0.941565
$172$	−3.08462e117	−1.33033
$173$	−3.33164e117	−1.05983	−0.529917	−	0.848049i	$-0.677777\pi$
$173$	−3.33164e117	−1.05983	−0.529917	+	0.848049i	$0.677777\pi$
$174$	1.30227e118	3.06102
$175$	1.26078e116	0.0219353
$176$	−1.32323e118	−1.70695
$177$	3.42100e118	3.27761
$178$	3.89177e118	2.77394
$179$	−1.92920e118	−1.02469	−0.512345	−	0.858780i	$-0.671223\pi$
$179$	−1.92920e118	−1.02469	−0.512345	+	0.858780i	$0.671223\pi$
$180$	−1.02804e119	−4.07569
$181$	−3.92801e118	−1.16425	−0.582126	−	0.813099i	$-0.697779\pi$
$181$	−3.92801e118	−1.16425	−0.582126	+	0.813099i	$0.697779\pi$
$182$	7.50926e117	0.166667
$183$	4.35244e118	0.724520
$184$	3.22520e118	0.403293
$185$	8.50573e117	0.0800195
$186$	−3.34233e119	−2.36930
$187$	2.28535e119	1.22255
$188$	1.91319e119	0.773520
$189$	−4.51436e118	−0.138150
$190$	2.70445e119	0.627357
$191$	5.36723e119	0.945145	0.472573	−	0.881292i	$-0.343325\pi$
$191$	5.36723e119	0.945145	0.472573	+	0.881292i	$0.343325\pi$
$192$	2.33793e119	0.312980
$193$	−1.23058e120	−1.25416	−0.627079	−	0.778956i	$-0.715750\pi$
$193$	−1.23058e120	−1.25416	−0.627079	+	0.778956i	$0.715750\pi$
$194$	3.93865e120	3.06024
$195$	−3.51468e120	−2.08482
$196$	−5.00688e120	−2.27051
$197$	−3.21266e120	−1.11529	−0.557644	−	0.830080i	$-0.688295\pi$
$197$	−3.21266e120	−1.11529	−0.557644	+	0.830080i	$0.688295\pi$
$198$	1.33510e121	3.55298
$199$	−2.12151e120	−0.433369	−0.216685	−	0.976242i	$-0.569524\pi$
$199$	−2.12151e120	−0.433369	−0.216685	+	0.976242i	$0.569524\pi$
$200$	5.05332e120	0.793418
$201$	1.68221e120	0.203277
$202$	−1.08484e121	−1.01023
$203$	8.42066e119	0.0605068
$204$	−1.00982e122	−5.60610
$205$	2.18409e121	0.937979
$206$	8.63588e121	2.87262
$207$	−1.48678e121	−0.383534
$208$	1.37514e122	2.75436
$209$	−2.44140e121	−0.380153
$210$	−1.39014e121	−0.168479
$211$	1.16118e122	1.09665	0.548327	−	0.836264i	$-0.315265\pi$
$211$	1.16118e122	1.09665	0.548327	+	0.836264i	$0.315265\pi$
$212$	−1.40659e122	−1.03642
$213$	2.92141e122	1.68137
$214$	−1.28774e122	−0.579570
$215$	1.34301e122	0.473218
$216$	−1.80939e123	−4.99702
$217$	−2.16120e121	−0.0468336
$218$	7.01682e122	1.19447
$219$	6.81449e122	0.912257
$220$	1.56135e123	1.64555
$221$	−2.37499e123	−1.97273
$222$	4.88102e122	0.319874
$223$	7.24098e122	0.374793	0.187397	−	0.982284i	$-0.439995\pi$
$223$	7.24098e122	0.374793	0.187397	+	0.982284i	$0.439995\pi$
$224$	1.80947e122	0.0740510
$225$	−2.32953e123	−0.754546
$226$	2.20484e123	0.565828
$227$	−2.60705e123	−0.530630	−0.265315	−	0.964162i	$-0.585476\pi$
$227$	−2.60705e123	−0.530630	−0.265315	+	0.964162i	$0.585476\pi$
$228$	1.07878e124	1.74322
$229$	−3.82412e123	−0.491098	−0.245549	−	0.969384i	$-0.578968\pi$
$229$	−3.82412e123	−0.491098	−0.245549	+	0.969384i	$0.578968\pi$
$230$	−2.50138e123	−0.255546
$231$	1.25493e123	0.102092
$232$	3.37507e124	2.18859
$233$	2.49183e124	1.28923	0.644617	−	0.764505i	$-0.277017\pi$
$233$	2.49183e124	1.28923	0.644617	+	0.764505i	$0.277017\pi$
$234$	−1.38747e125	−5.73313
$235$	−8.32986e123	−0.275153
$236$	1.57935e125	4.17444
$237$	−6.97204e124	−1.47595
$238$	−9.39366e123	−0.159421
$239$	−7.40706e123	−0.100869	−0.0504343	−	0.998727i	$-0.516061\pi$
$239$	−7.40706e123	−0.100869	−0.0504343	+	0.998727i	$0.516061\pi$
$240$	−2.54570e125	−2.78431
$241$	−4.19382e124	−0.368735	−0.184368	−	0.982857i	$-0.559024\pi$
$241$	−4.19382e124	−0.368735	−0.184368	+	0.982857i	$0.559024\pi$
$242$	5.32251e124	0.376539
$243$	1.41521e125	0.806290
$244$	2.00936e125	0.922765
$245$	2.17995e125	0.807656
$246$	1.25334e126	3.74953
$247$	2.53716e125	0.613421
$248$	−8.66225e125	−1.69402
$249$	−9.78693e125	−1.54946
$250$	−1.53689e126	−1.97148
$251$	2.46814e125	0.256744	0.128372	−	0.991726i	$-0.459025\pi$
$251$	2.46814e125	0.256744	0.128372	+	0.991726i	$0.459025\pi$
$252$	−3.81462e125	−0.322050
$253$	2.25809e125	0.154851
$254$	−8.10999e125	−0.452117
$255$	4.39667e126	1.99418
$256$	−4.58726e126	−1.69416
$257$	1.85222e126	0.557448	0.278724	−	0.960371i	$-0.410089\pi$
$257$	1.85222e126	0.557448	0.278724	+	0.960371i	$0.410089\pi$
$258$	7.70690e126	1.89167
$259$	3.15613e124	0.00632291
$260$	−1.62260e127	−2.65528
$261$	−1.55587e127	−2.08136
$262$	2.04440e127	2.23742
$263$	−1.47726e127	−1.32367	−0.661834	−	0.749650i	$-0.730222\pi$
$263$	−1.47726e127	−1.32367	−0.661834	+	0.749650i	$0.730222\pi$
$264$	5.02986e127	3.69275
$265$	6.12417e126	0.368671
$266$	1.00351e126	0.0495719
$267$	−6.75894e127	−2.74181
$268$	7.76614e126	0.258898
$269$	4.07814e127	1.11807	0.559033	−	0.829145i	$-0.311172\pi$
$269$	4.07814e127	1.11807	0.559033	+	0.829145i	$0.311172\pi$
$270$	1.40332e128	3.16635
$271$	−2.10498e127	−0.391165	−0.195582	−	0.980687i	$-0.562660\pi$
$271$	−2.10498e127	−0.391165	−0.195582	+	0.980687i	$0.562660\pi$
$272$	−1.72022e128	−2.63461
$273$	−1.30415e127	−0.164737
$274$	−1.91400e128	−1.99543
$275$	3.53802e127	0.304645
$276$	−9.97775e127	−0.710077
$277$	−1.88787e128	−1.11118	−0.555590	−	0.831456i	$-0.687508\pi$
$277$	−1.88787e128	−1.11118	−0.555590	+	0.831456i	$0.687508\pi$
$278$	3.28482e128	1.60015
$279$	3.99320e128	1.61102
$280$	−3.60280e127	−0.120460
$281$	1.51465e128	0.419982	0.209991	−	0.977703i	$-0.432657\pi$
$281$	1.51465e128	0.419982	0.209991	+	0.977703i	$0.432657\pi$
$282$	−4.78010e128	−1.09991
$283$	−9.04953e127	−0.172917	−0.0864586	−	0.996255i	$-0.527555\pi$
$283$	−9.04953e127	−0.172917	−0.0864586	+	0.996255i	$0.527555\pi$
$284$	1.34871e129	2.14143
$285$	−4.69689e128	−0.620091
$286$	2.10726e129	2.31473
$287$	8.10427e127	0.0741164
$288$	−3.34333e129	−2.54726
$289$	1.39650e129	0.886960
$290$	−2.61762e129	−1.38679
$291$	−6.84036e129	−3.02480
$292$	3.14599e129	1.16187
$293$	6.96245e128	0.214888	0.107444	−	0.994211i	$-0.465733\pi$
$293$	6.96245e128	0.214888	0.107444	+	0.994211i	$0.465733\pi$
$294$	1.25096e130	3.22857
$295$	−6.87634e129	−1.48491
$296$	1.26500e129	0.228705
$297$	−1.26683e130	−1.91868
$298$	2.27889e130	2.89314
$299$	−2.34666e129	−0.249869
$300$	−1.56334e130	−1.39697
$301$	4.98338e128	0.0373923
$302$	−4.60903e130	−2.90566
$303$	1.88407e130	0.998525
$304$	1.83768e130	0.819233
$305$	−8.74856e129	−0.328243
$306$	1.73565e131	5.48387
$307$	4.13248e129	0.110014	0.0550068	−	0.998486i	$-0.482482\pi$
$307$	4.13248e129	0.110014	0.0550068	+	0.998486i	$0.482482\pi$
$308$	5.79354e129	0.130026
$309$	−1.49982e131	−2.83935
$310$	6.71821e130	1.07341
$311$	−3.52591e130	−0.475719	−0.237859	−	0.971300i	$-0.576446\pi$
$311$	−3.52591e130	−0.475719	−0.237859	+	0.971300i	$0.576446\pi$
$312$	−5.22716e131	−5.95867
$313$	1.39264e131	1.34202	0.671011	−	0.741447i	$-0.265860\pi$
$313$	1.39264e131	1.34202	0.671011	+	0.741447i	$0.265860\pi$
$314$	3.74306e131	3.05084
$315$	1.66085e130	0.114558
$316$	−3.21873e131	−1.87981
$317$	−2.13768e131	−1.05762	−0.528812	−	0.848739i	$-0.677362\pi$
$317$	−2.13768e131	−1.05762	−0.528812	+	0.848739i	$0.677362\pi$
$318$	3.51436e131	1.47375
$319$	2.36301e131	0.840341
$320$	−4.69932e130	−0.141795
$321$	2.23646e131	0.572857
$322$	−9.28161e129	−0.0201925
$323$	−3.17385e131	−0.586751
$324$	2.40026e132	3.77264
$325$	−3.67680e131	−0.491579
$326$	−2.29248e132	−2.60844
$327$	−1.21863e132	−1.18063
$328$	3.24826e132	2.68086
$329$	−3.09087e130	−0.0217418
$330$	−3.90103e132	−2.33990
$331$	1.84900e132	0.946166	0.473083	−	0.881018i	$-0.343141\pi$
$331$	1.84900e132	0.946166	0.473083	+	0.881018i	$0.343141\pi$
$332$	−4.51826e132	−1.97343
$333$	−5.83153e131	−0.217500
$334$	7.84207e132	2.49886
$335$	−3.38130e131	−0.0920941
$336$	−9.44606e131	−0.220008
$337$	1.77864e132	0.354421	0.177210	−	0.984173i	$-0.443293\pi$
$337$	1.77864e132	0.354421	0.177210	+	0.984173i	$0.443293\pi$
$338$	−1.12808e133	−1.92404
$339$	−3.82921e132	−0.559275
$340$	2.02978e133	2.53983
$341$	−6.06477e132	−0.650443
$342$	−1.85417e133	−1.70521
$343$	1.62111e132	0.127901
$344$	1.99738e133	1.35251
$345$	4.34422e132	0.252586
$346$	3.84292e133	1.91940
$347$	1.92289e133	0.825387	0.412694	−	0.910870i	$-0.364588\pi$
$347$	1.92289e133	0.825387	0.412694	+	0.910870i	$0.364588\pi$
$348$	−1.04414e134	−3.85344
$349$	2.67204e133	0.848220	0.424110	−	0.905611i	$-0.360587\pi$
$349$	2.67204e133	0.848220	0.424110	+	0.905611i	$0.360587\pi$
$350$	−1.45427e132	−0.0397257
$351$	1.31652e134	3.09601
$352$	5.07776e133	1.02845
$353$	7.63262e133	1.33199	0.665996	−	0.745955i	$-0.268007\pi$
$353$	7.63262e133	1.33199	0.665996	+	0.745955i	$0.268007\pi$
$354$	−3.94599e134	−5.93588
$355$	−5.87214e133	−0.761742
$356$	−3.12035e134	−3.49204
$357$	1.63142e133	0.157574
$358$	2.22526e134	1.85576
$359$	−3.74967e133	−0.270106	−0.135053	−	0.990838i	$-0.543120\pi$
$359$	−3.74967e133	−0.270106	−0.135053	+	0.990838i	$0.543120\pi$
$360$	6.65682e134	4.14368
$361$	−1.51930e134	−0.817549
$362$	4.53080e134	2.10851
$363$	−9.24376e133	−0.372178
$364$	−6.02079e133	−0.209812
$365$	−1.36974e134	−0.413297
$366$	−5.02037e134	−1.31213
$367$	8.36768e134	1.89512	0.947560	−	0.319578i	$-0.103541\pi$
$367$	8.36768e134	1.89512	0.947560	+	0.319578i	$0.103541\pi$
$368$	−1.69970e134	−0.333704
$369$	−1.49741e135	−2.54951
$370$	−9.81103e133	−0.144919
$371$	2.27243e133	0.0291313
$372$	2.67983e135	2.98265
$373$	−3.45717e134	−0.334200	−0.167100	−	0.985940i	$-0.553440\pi$
$373$	−3.45717e134	−0.334200	−0.167100	+	0.985940i	$0.553440\pi$
$374$	−2.63606e135	−2.21409
$375$	2.66916e135	1.94864
$376$	−1.23885e135	−0.786422
$377$	−2.45570e135	−1.35599
$378$	5.20714e134	0.250196
$379$	8.50571e134	0.355756	0.177878	−	0.984053i	$-0.443077\pi$
$379$	8.50571e134	0.355756	0.177878	+	0.984053i	$0.443077\pi$
$380$	−2.16838e135	−0.789762
$381$	1.40849e135	0.446880
$382$	−6.19090e135	−1.71170
$383$	5.56925e135	1.34234	0.671168	−	0.741305i	$-0.265793\pi$
$383$	5.56925e135	1.34234	0.671168	+	0.741305i	$0.265793\pi$
$384$	7.14462e135	1.50172
$385$	−2.52246e134	−0.0462525
$386$	1.41943e136	2.27133
$387$	−9.20770e135	−1.28625
$388$	−3.15794e136	−3.85246
$389$	−3.38533e135	−0.360784	−0.180392	−	0.983595i	$-0.557737\pi$
$389$	−3.38533e135	−0.360784	−0.180392	+	0.983595i	$0.557737\pi$
$390$	4.05405e136	3.77569
$391$	2.93554e135	0.239005
$392$	3.24210e136	2.30838
$393$	−3.55056e136	−2.21151
$394$	3.70568e136	2.01983
$395$	1.40141e136	0.668677
$396$	−1.07046e137	−4.47275
$397$	−4.90612e136	−1.79571	−0.897856	−	0.440290i	$-0.854876\pi$
$397$	−4.90612e136	−1.79571	−0.897856	+	0.440290i	$0.854876\pi$
$398$	2.44708e136	0.784849
$399$	−1.74282e135	−0.0489978
$400$	−2.66313e136	−0.656512
$401$	1.98317e136	0.428826	0.214413	−	0.976743i	$-0.431216\pi$
$401$	1.98317e136	0.428826	0.214413	+	0.976743i	$0.431216\pi$
$402$	−1.94036e136	−0.368142
$403$	6.30266e136	1.04956
$404$	8.69804e136	1.27174
$405$	−1.04505e137	−1.34199
$406$	−9.71291e135	−0.109580
$407$	8.85677e135	0.0878150
$408$	6.53888e137	5.69960
$409$	−1.84011e137	−1.41049	−0.705246	−	0.708963i	$-0.749163\pi$
$409$	−1.84011e137	−1.41049	−0.705246	+	0.708963i	$0.749163\pi$
$410$	−2.51926e137	−1.69872
$411$	3.32409e137	1.97232
$412$	−6.92410e137	−3.61626
$413$	−2.55153e136	−0.117334
$414$	1.71495e137	0.694597
$415$	1.96721e137	0.701981
$416$	−5.27693e137	−1.65952
$417$	−5.70484e137	−1.58161
$418$	2.81606e137	0.688474
$419$	4.70201e137	1.01402	0.507011	−	0.861940i	$-0.330750\pi$
$419$	4.70201e137	1.01402	0.507011	+	0.861940i	$0.330750\pi$
$420$	1.11459e137	0.212094
$421$	1.06651e138	1.79124	0.895622	−	0.444817i	$-0.146731\pi$
$421$	1.06651e138	1.79124	0.895622	+	0.444817i	$0.146731\pi$
$422$	−1.33937e138	−1.98609
$423$	5.71095e137	0.747892
$424$	9.10809e137	1.05371
$425$	4.59947e137	0.470207
$426$	−3.36973e138	−3.04503
$427$	−3.24623e136	−0.0259368
$428$	1.03249e138	0.729604
$429$	−3.65973e138	−2.28792
$430$	−1.54911e138	−0.857017
$431$	2.22553e138	1.08987	0.544937	−	0.838477i	$-0.316554\pi$
$431$	2.22553e138	1.08987	0.544937	+	0.838477i	$0.316554\pi$
$432$	9.53560e138	4.13477
$433$	2.56876e138	0.986525	0.493263	−	0.869880i	$-0.335804\pi$
$433$	2.56876e138	0.986525	0.493263	+	0.869880i	$0.335804\pi$
$434$	2.49286e137	0.0848177
$435$	4.54609e138	1.37073
$436$	−5.62597e138	−1.50368
$437$	−3.13599e137	−0.0743189
$438$	−7.86025e138	−1.65213
$439$	−1.19025e138	−0.221947	−0.110973	−	0.993823i	$-0.535397\pi$
$439$	−1.19025e138	−0.221947	−0.110973	+	0.993823i	$0.535397\pi$
$440$	−1.01102e139	−1.67299
$441$	−1.49457e139	−2.19528
$442$	2.73946e139	3.57269
$443$	−1.45385e138	−0.168393	−0.0841963	−	0.996449i	$-0.526832\pi$
$443$	−1.45385e138	−0.168393	−0.0841963	+	0.996449i	$0.526832\pi$
$444$	−3.91352e138	−0.402681
$445$	1.35857e139	1.24217
$446$	−8.35219e138	−0.678766
$447$	−3.95782e139	−2.85964
$448$	−1.74373e137	−0.0112042
$449$	−1.37731e138	−0.0787227	−0.0393613	−	0.999225i	$-0.512532\pi$
$449$	−1.37731e138	−0.0787227	−0.0393613	+	0.999225i	$0.512532\pi$
$450$	2.68702e139	1.36651
$451$	2.27423e139	1.02936
$452$	−1.76780e139	−0.712306
$453$	8.00463e139	2.87201
$454$	3.00713e139	0.960993
$455$	2.62140e138	0.0746336
$456$	−6.98538e139	−1.77229
$457$	3.38698e139	0.765970	0.382985	−	0.923755i	$-0.374896\pi$
$457$	3.38698e139	0.765970	0.382985	+	0.923755i	$0.374896\pi$
$458$	4.41097e139	0.889399
$459$	−1.64689e140	−2.96141
$460$	2.00556e139	0.321699
$461$	2.63171e139	0.376651	0.188325	−	0.982107i	$-0.439694\pi$
$461$	2.63171e139	0.376651	0.188325	+	0.982107i	$0.439694\pi$
$462$	−1.44751e139	−0.184892
$463$	1.79225e139	0.204360	0.102180	−	0.994766i	$-0.467418\pi$
$463$	1.79225e139	0.204360	0.102180	+	0.994766i	$0.467418\pi$
$464$	−1.77868e140	−1.81094
$465$	−1.16677e140	−1.06098
$466$	−2.87423e140	−2.33486
$467$	1.27444e140	0.925087	0.462543	−	0.886597i	$-0.346937\pi$
$467$	1.27444e140	0.925087	0.462543	+	0.886597i	$0.346937\pi$
$468$	1.11245e141	7.21728
$469$	−1.25466e138	−0.00727702
$470$	9.60817e139	0.498314
$471$	−6.50067e140	−3.01551
$472$	−1.02267e141	−4.24407
$473$	1.39844e140	0.519319
$474$	8.04198e140	2.67301
$475$	−4.91354e139	−0.146211
$476$	7.53168e139	0.200690
$477$	−4.19873e140	−1.00208
$478$	8.54375e139	0.182677
$479$	2.18412e140	0.418467	0.209233	−	0.977866i	$-0.432903\pi$
$479$	2.18412e140	0.418467	0.209233	+	0.977866i	$0.432903\pi$
$480$	9.76885e140	1.67756
$481$	−9.20417e139	−0.141699
$482$	4.83741e140	0.667795
$483$	1.61196e139	0.0199586
$484$	−4.26750e140	−0.474015
$485$	1.37494e141	1.37038
$486$	−1.63239e141	−1.46023
$487$	−6.62572e140	−0.532062	−0.266031	−	0.963964i	$-0.585712\pi$
$487$	−6.62572e140	−0.532062	−0.266031	+	0.963964i	$0.585712\pi$
$488$	−1.30112e141	−0.938157
$489$	3.98141e141	2.57823
$490$	−2.51449e141	−1.46270
$491$	−1.37473e141	−0.718518	−0.359259	−	0.933238i	$-0.616971\pi$
$491$	−1.37473e141	−0.718518	−0.359259	+	0.933238i	$0.616971\pi$
$492$	−1.00491e142	−4.72018
$493$	3.07195e141	1.29703
$494$	−2.92652e141	−1.11093
$495$	4.66070e141	1.59103
$496$	4.56505e141	1.40171
$497$	−2.17891e140	−0.0601907
$498$	1.12888e142	2.80614
$499$	3.23152e141	0.722983	0.361491	−	0.932375i	$-0.382268\pi$
$499$	3.23152e141	0.722983	0.361491	+	0.932375i	$0.382268\pi$
$500$	1.23225e142	2.48184
$501$	−1.36195e142	−2.46991
$502$	−2.84691e141	−0.464974
$503$	−9.98096e141	−1.46843	−0.734215	−	0.678917i	$-0.762450\pi$
$503$	−9.98096e141	−1.46843	−0.734215	+	0.678917i	$0.762450\pi$
$504$	2.47008e141	0.327422
$505$	−3.78705e141	−0.452380
$506$	−2.60461e141	−0.280441
$507$	1.95917e142	1.90176
$508$	6.50245e141	0.569157
$509$	−9.19610e141	−0.725972	−0.362986	−	0.931795i	$-0.618243\pi$
$509$	−9.19610e141	−0.725972	−0.362986	+	0.931795i	$0.618243\pi$
$510$	−5.07139e142	−3.61154
$511$	−5.08254e140	−0.0326575
$512$	3.84448e142	2.22928
$513$	1.75934e142	0.920851
$514$	−2.13647e142	−1.00956
$515$	3.01469e142	1.28636
$516$	−6.17925e142	−2.38137
$517$	−8.67363e141	−0.301959
$518$	−3.64047e140	−0.0114511
$519$	−6.67411e142	−1.89717
$520$	1.05068e143	2.69957
$521$	−3.87902e142	−0.901034	−0.450517	−	0.892768i	$-0.648760\pi$
$521$	−3.87902e142	−0.901034	−0.450517	+	0.892768i	$0.648760\pi$
$522$	1.79464e143	3.76943
$523$	3.97356e142	0.754815	0.377408	−	0.926047i	$-0.376816\pi$
$523$	3.97356e142	0.754815	0.377408	+	0.926047i	$0.376816\pi$
$524$	−1.63916e143	−2.81663
$525$	2.52566e141	0.0392656
$526$	1.70396e143	2.39722
$527$	−7.88427e142	−1.00393
$528$	−2.65076e143	−3.05556
$529$	−9.29121e142	−0.969727
$530$	−7.06400e142	−0.667678
$531$	4.71442e143	4.03613
$532$	−8.04597e141	−0.0624048
$533$	−2.36343e143	−1.66098
$534$	7.79618e143	4.96553
$535$	−4.49536e142	−0.259532
$536$	−5.02880e142	−0.263216
$537$	−3.86466e143	−1.83426
$538$	−4.70398e143	−2.02486
$539$	2.26991e143	0.886338
$540$	−1.12516e144	−3.98603
$541$	2.44851e143	0.787129	0.393564	−	0.919297i	$-0.371242\pi$
$541$	2.44851e143	0.787129	0.393564	+	0.919297i	$0.371242\pi$
$542$	2.42801e143	0.708416
$543$	−7.86877e143	−2.08409
$544$	6.60114e143	1.58737
$545$	2.44949e143	0.534884
$546$	1.50429e143	0.298345
$547$	−3.00103e142	−0.0540675	−0.0270337	−	0.999635i	$-0.508606\pi$
$547$	−3.00103e142	−0.0540675	−0.0270337	+	0.999635i	$0.508606\pi$
$548$	1.53461e144	2.51199
$549$	5.99801e143	0.892193
$550$	−4.08097e143	−0.551725
$551$	−3.28171e143	−0.403313
$552$	6.46088e143	0.721921
$553$	5.20005e142	0.0528370
$554$	2.17759e144	2.01239
$555$	1.70391e143	0.143240
$556$	−2.63371e144	−2.01438
$557$	−5.76286e143	−0.401089	−0.200544	−	0.979685i	$-0.564271\pi$
$557$	−5.76286e143	−0.401089	−0.200544	+	0.979685i	$0.564271\pi$
$558$	−4.60601e144	−2.91762
$559$	−1.45329e144	−0.837980
$560$	1.89869e143	0.0996744
$561$	4.57812e144	2.18845
$562$	−1.74709e144	−0.760605
$563$	−2.14485e144	−0.850564	−0.425282	−	0.905061i	$-0.639825\pi$
$563$	−2.14485e144	−0.850564	−0.425282	+	0.905061i	$0.639825\pi$
$564$	3.83260e144	1.38465
$565$	7.69686e143	0.253379
$566$	1.04383e144	0.313160
$567$	−3.87776e143	−0.106040
$568$	−8.73325e144	−2.17715
$569$	4.55830e144	1.03612	0.518059	−	0.855345i	$-0.326655\pi$
$569$	4.55830e144	1.03612	0.518059	+	0.855345i	$0.326655\pi$
$570$	5.41768e144	1.12301
$571$	8.13053e144	1.53717	0.768587	−	0.639745i	$-0.220960\pi$
$571$	8.13053e144	1.53717	0.768587	+	0.639745i	$0.220960\pi$
$572$	−1.68956e145	−2.91395
$573$	1.07519e145	1.69187
$574$	−9.34796e143	−0.134228
$575$	4.54461e143	0.0595572
$576$	3.22185e144	0.385412
$577$	6.19944e143	0.0677052	0.0338526	−	0.999427i	$-0.489222\pi$
$577$	6.19944e143	0.0677052	0.0338526	+	0.999427i	$0.489222\pi$
$578$	−1.61081e145	−1.60632
$579$	−2.46516e145	−2.24503
$580$	2.09876e145	1.74579
$581$	7.29951e143	0.0554686
$582$	7.89009e145	5.47804
$583$	6.37692e144	0.404587
$584$	−2.03712e145	−1.18125
$585$	−4.84351e145	−2.56730
$586$	−8.03092e144	−0.389171
$587$	1.70804e145	0.756828	0.378414	−	0.925636i	$-0.376470\pi$
$587$	1.70804e145	0.756828	0.378414	+	0.925636i	$0.376470\pi$
$588$	−1.00300e146	−4.06436
$589$	8.42264e144	0.312173
$590$	7.93159e145	2.68924
$591$	−6.43575e145	−1.99644
$592$	−6.66663e144	−0.189242
$593$	2.00221e145	0.520160	0.260080	−	0.965587i	$-0.416251\pi$
$593$	2.00221e145	0.520160	0.260080	+	0.965587i	$0.416251\pi$
$594$	1.46123e146	3.47481
$595$	−3.27922e144	−0.0713888
$596$	−1.82718e146	−3.64210
$597$	−4.24991e145	−0.775759
$598$	2.70678e145	0.452523
$599$	−7.83512e144	−0.119988	−0.0599940	−	0.998199i	$-0.519108\pi$
$599$	−7.83512e144	−0.119988	−0.0599940	+	0.998199i	$0.519108\pi$
$600$	1.01231e146	1.42027
$601$	7.00949e144	0.0901108	0.0450554	−	0.998984i	$-0.485654\pi$
$601$	7.00949e144	0.0901108	0.0450554	+	0.998984i	$0.485654\pi$
$602$	−5.74813e144	−0.0677191
$603$	2.31822e145	0.250320
$604$	3.69544e146	3.65786
$605$	1.85803e145	0.168615
$606$	−2.17320e146	−1.80837
$607$	2.12280e146	1.61996	0.809978	−	0.586460i	$-0.199479\pi$
$607$	2.12280e146	1.61996	0.809978	+	0.586460i	$0.199479\pi$
$608$	−7.05190e145	−0.493592
$609$	1.68687e145	0.108311
$610$	1.00911e146	0.594461
$611$	9.01386e145	0.487245
$612$	−1.39161e147	−6.90350
$613$	−2.40584e146	−1.09545	−0.547725	−	0.836658i	$-0.684506\pi$
$613$	−2.40584e146	−1.09545	−0.547725	+	0.836658i	$0.684506\pi$
$614$	−4.76666e145	−0.199239
$615$	4.37528e146	1.67904
$616$	−3.75149e145	−0.132195
$617$	−2.96563e146	−0.959723	−0.479861	−	0.877344i	$-0.659313\pi$
$617$	−2.96563e146	−0.959723	−0.479861	+	0.877344i	$0.659313\pi$
$618$	1.72998e147	5.14217
$619$	−3.44019e146	−0.939340	−0.469670	−	0.882842i	$-0.655627\pi$
$619$	−3.44019e146	−0.939340	−0.469670	+	0.882842i	$0.655627\pi$
$620$	−5.38655e146	−1.35128
$621$	−1.62724e146	−0.375097
$622$	4.06700e146	0.861547
$623$	5.04111e145	0.0981530
$624$	2.75474e147	4.93048
$625$	−3.28489e146	−0.540530
$626$	−1.60635e147	−2.43046
$627$	−4.89073e146	−0.680500
$628$	−3.00112e147	−3.84062
$629$	1.15139e146	0.135539
$630$	−1.91573e146	−0.207470
$631$	8.24712e146	0.821790	0.410895	−	0.911683i	$-0.365216\pi$
$631$	8.24712e146	0.821790	0.410895	+	0.911683i	$0.365216\pi$
$632$	2.08422e147	1.91116
$633$	2.32613e147	1.96308
$634$	2.46573e147	1.91540
$635$	−2.83111e146	−0.202458
$636$	−2.81775e147	−1.85526
$637$	−2.35895e147	−1.43021
$638$	−2.72565e147	−1.52189
$639$	4.02594e147	2.07048
$640$	−1.43610e147	−0.680353
$641$	2.02276e147	0.882871	0.441436	−	0.897293i	$-0.354469\pi$
$641$	2.02276e147	0.882871	0.441436	+	0.897293i	$0.354469\pi$
$642$	−2.57967e147	−1.03747
$643$	−2.37322e147	−0.879553	−0.439776	−	0.898107i	$-0.644942\pi$
$643$	−2.37322e147	−0.879553	−0.439776	+	0.898107i	$0.644942\pi$
$644$	7.44183e145	0.0254198
$645$	2.69039e147	0.847091
$646$	3.66091e147	1.06263
$647$	5.29062e146	0.141590	0.0707949	−	0.997491i	$-0.477446\pi$
$647$	5.29062e146	0.141590	0.0707949	+	0.997491i	$0.477446\pi$
$648$	−1.55424e148	−3.83557
$649$	−7.16013e147	−1.62957
$650$	4.24105e147	0.890271
$651$	−4.32941e146	−0.0838353
$652$	1.83807e148	3.28370
$653$	−4.21757e146	−0.0695218	−0.0347609	−	0.999396i	$-0.511067\pi$
$653$	−4.21757e146	−0.0695218	−0.0347609	+	0.999396i	$0.511067\pi$
$654$	1.40564e148	2.13818
$655$	7.13677e147	1.00192
$656$	−1.71185e148	−2.21827
$657$	9.39091e147	1.12338
$658$	3.56520e146	0.0393754
$659$	−1.62818e148	−1.66042	−0.830212	−	0.557448i	$-0.811781\pi$
$659$	−1.62818e148	−1.66042	−0.830212	+	0.557448i	$0.811781\pi$
$660$	3.12778e148	2.94564
$661$	6.87944e147	0.598380	0.299190	−	0.954194i	$-0.403284\pi$
$661$	6.87944e147	0.598380	0.299190	+	0.954194i	$0.403284\pi$
$662$	−2.13275e148	−1.71355
$663$	−4.75769e148	−3.53131
$664$	2.92570e148	2.00635
$665$	3.50314e146	0.0221984
$666$	6.72644e147	0.393902
$667$	3.03530e147	0.164284
$668$	−6.28763e148	−3.14574
$669$	1.45055e148	0.670905
$670$	3.90020e147	0.166786
$671$	−9.10961e147	−0.360220
$672$	3.62482e147	0.132556
$673$	−4.65685e147	−0.157508	−0.0787538	−	0.996894i	$-0.525094\pi$
$673$	−4.65685e147	−0.157508	−0.0787538	+	0.996894i	$0.525094\pi$
$674$	−2.05160e148	−0.641871
$675$	−2.54960e148	−0.737946
$676$	9.04477e148	2.42212
$677$	6.98042e148	1.72972	0.864861	−	0.502012i	$-0.167407\pi$
$677$	6.98042e148	1.72972	0.864861	+	0.502012i	$0.167407\pi$
$678$	4.41685e148	1.01287
$679$	5.10183e147	0.108284
$680$	−1.31434e149	−2.58220
$681$	−5.22257e148	−0.949863
$682$	6.99548e148	1.17798
$683$	8.39022e148	1.30824	0.654118	−	0.756392i	$-0.273040\pi$
$683$	8.39022e148	1.30824	0.654118	+	0.756392i	$0.273040\pi$
$684$	1.48664e149	2.14665
$685$	−6.68154e148	−0.893556
$686$	−1.86989e148	−0.231633
$687$	−7.66065e148	−0.879098
$688$	−1.05263e149	−1.11913
$689$	−6.62705e148	−0.652847
$690$	−5.01089e148	−0.457444
$691$	1.77282e149	1.49992	0.749959	−	0.661484i	$-0.230073\pi$
$691$	1.77282e149	1.49992	0.749959	+	0.661484i	$0.230073\pi$
$692$	−3.08119e149	−2.41629
$693$	1.72939e148	0.125719
$694$	−2.21798e149	−1.49481
$695$	1.14669e149	0.716548
$696$	6.76110e149	3.91771
$697$	2.95652e149	1.58877
$698$	−3.08210e149	−1.53616
$699$	4.99175e149	2.30782
$700$	1.16600e148	0.0500096
$701$	−2.47268e149	−0.983948	−0.491974	−	0.870610i	$-0.663725\pi$
$701$	−2.47268e149	−0.983948	−0.491974	+	0.870610i	$0.663725\pi$
$702$	−1.51855e150	−5.60700
$703$	−1.23001e148	−0.0421458
$704$	−4.89326e148	−0.155609
$705$	−1.66868e149	−0.492543
$706$	−8.80394e149	−2.41229
$707$	−1.40522e148	−0.0357458
$708$	3.16383e150	7.47252
$709$	−6.59385e149	−1.44614	−0.723072	−	0.690772i	$-0.757271\pi$
$709$	−6.59385e149	−1.44614	−0.723072	+	0.690772i	$0.757271\pi$
$710$	6.77329e149	1.37955
$711$	−9.60803e149	−1.81753
$712$	2.02052e150	3.55028
$713$	−7.79022e148	−0.127160
$714$	−1.88178e149	−0.285374
$715$	7.35619e149	1.03654
$716$	−1.78417e150	−2.33616
$717$	−1.48382e149	−0.180561
$718$	4.32510e149	0.489173
$719$	6.21958e149	0.653875	0.326937	−	0.945046i	$-0.393983\pi$
$719$	6.21958e149	0.653875	0.326937	+	0.945046i	$0.393983\pi$
$720$	−3.50818e150	−3.42867
$721$	1.11863e149	0.101645
$722$	1.75245e150	1.48062
$723$	−8.40126e149	−0.660061
$724$	−3.63272e150	−2.65434
$725$	4.75579e149	0.323204
$726$	1.06623e150	0.674030
$727$	−2.32064e149	−0.136474	−0.0682372	−	0.997669i	$-0.521737\pi$
$727$	−2.32064e149	−0.136474	−0.0682372	+	0.997669i	$0.521737\pi$
$728$	3.89864e149	0.213312
$729$	−4.15335e149	−0.211448
$730$	1.57994e150	0.748497
$731$	1.81799e150	0.801547
$732$	4.02524e150	1.65181
$733$	−1.28759e150	−0.491833	−0.245917	−	0.969291i	$-0.579089\pi$
$733$	−1.28759e150	−0.491833	−0.245917	+	0.969291i	$0.579089\pi$
$734$	−9.65180e150	−3.43214
$735$	4.36698e150	1.44576
$736$	6.52240e149	0.201058
$737$	−3.52085e149	−0.101066
$738$	1.72721e151	4.61727
$739$	−7.51915e150	−1.87213	−0.936064	−	0.351830i	$-0.885559\pi$
$739$	−7.51915e150	−1.87213	−0.936064	+	0.351830i	$0.885559\pi$
$740$	7.86632e149	0.182434
$741$	5.08257e150	1.09806
$742$	−2.62116e149	−0.0527580
$743$	−8.03286e150	−1.50646	−0.753229	−	0.657758i	$-0.771505\pi$
$743$	−8.03286e150	−1.50646	−0.753229	+	0.657758i	$0.771505\pi$
$744$	−1.73526e151	−3.03240
$745$	7.95536e150	1.29555
$746$	3.98771e150	0.605250
$747$	−1.34872e151	−1.90805
$748$	2.11355e151	2.78726
$749$	−1.66805e149	−0.0205075
$750$	−3.07877e151	−3.52907
$751$	6.97978e150	0.746010	0.373005	−	0.927829i	$-0.378327\pi$
$751$	6.97978e150	0.746010	0.373005	+	0.927829i	$0.378327\pi$
$752$	6.52879e150	0.650723
$753$	4.94431e150	0.459589
$754$	2.83256e151	2.45575
$755$	−1.60896e151	−1.30116
$756$	−4.17500e150	−0.314965
$757$	−1.00145e151	−0.704851	−0.352426	−	0.935840i	$-0.614643\pi$
$757$	−1.00145e151	−0.704851	−0.352426	+	0.935840i	$0.614643\pi$
$758$	−9.81101e150	−0.644288
$759$	4.52351e150	0.277193
$760$	1.40409e151	0.802935
$761$	−3.09059e151	−1.64948	−0.824741	−	0.565511i	$-0.808679\pi$
$761$	−3.09059e151	−1.64948	−0.824741	+	0.565511i	$0.808679\pi$
$762$	−1.62463e151	−0.809318
$763$	9.08907e149	0.0422650
$764$	4.96375e151	2.15481
$765$	6.05896e151	2.45569
$766$	−6.42392e151	−2.43103
$767$	7.44098e151	2.62950
$768$	−9.18942e151	−3.03266
$769$	2.69582e150	0.0830917	0.0415459	−	0.999137i	$-0.486772\pi$
$769$	2.69582e150	0.0830917	0.0415459	+	0.999137i	$0.486772\pi$
$770$	2.90956e150	0.0837652
$771$	3.71046e151	0.997869
$772$	−1.13807e152	−2.85932
$773$	3.50661e151	0.823122	0.411561	−	0.911382i	$-0.364984\pi$
$773$	3.50661e151	0.823122	0.411561	+	0.911382i	$0.364984\pi$
$774$	1.06207e152	2.32945
$775$	−1.22059e151	−0.250167
$776$	2.04485e152	3.91672
$777$	6.32251e149	0.0113184
$778$	3.90485e151	0.653394
$779$	−3.15841e151	−0.494028
$780$	−3.25046e152	−4.75312
$781$	−6.11448e151	−0.835951
$782$	−3.38603e151	−0.432849
$783$	−1.70286e152	−2.03557
$784$	−1.70860e152	−1.91006
$785$	1.30666e152	1.36617
$786$	4.09544e152	4.00513
$787$	1.02568e152	0.938289	0.469145	−	0.883121i	$-0.344562\pi$
$787$	1.02568e152	0.938289	0.469145	+	0.883121i	$0.344562\pi$
$788$	−2.97115e152	−2.54271
$789$	−2.95931e152	−2.36945
$790$	−1.61647e152	−1.21100
$791$	2.85599e150	0.0200213
$792$	6.93155e152	4.54735
$793$	9.46693e151	0.581255
$794$	5.65902e152	3.25211
$795$	1.22682e152	0.659945
$796$	−1.96202e152	−0.988025
$797$	6.06121e151	0.285757	0.142879	−	0.989740i	$-0.454364\pi$
$797$	6.06121e151	0.285757	0.142879	+	0.989740i	$0.454364\pi$
$798$	2.01028e151	0.0887371
$799$	−1.12758e152	−0.466061
$800$	1.02195e152	0.395552
$801$	−9.31437e152	−3.37634
$802$	−2.28751e152	−0.776621
$803$	−1.42627e152	−0.453560
$804$	1.55575e152	0.463444
$805$	−3.24010e150	−0.00904222
$806$	−7.26987e152	−1.90080
$807$	8.16953e152	2.00141
$808$	−5.63223e152	−1.29296
$809$	2.40237e152	0.516823	0.258412	−	0.966035i	$-0.416801\pi$
$809$	2.40237e152	0.516823	0.258412	+	0.966035i	$0.416801\pi$
$810$	1.20543e153	2.43040
$811$	8.16006e152	1.54205	0.771025	−	0.636805i	$-0.219744\pi$
$811$	8.16006e152	1.54205	0.771025	+	0.636805i	$0.219744\pi$
$812$	7.78764e151	0.137948
$813$	−4.21680e152	−0.700211
$814$	−1.02159e152	−0.159037
$815$	−8.00278e152	−1.16806
$816$	−3.44603e153	−4.71612
$817$	−1.94213e152	−0.249241
$818$	2.12250e153	2.55446
$819$	−1.79723e152	−0.202861
$820$	2.01990e153	2.13847
$821$	9.67277e152	0.960583	0.480292	−	0.877109i	$-0.340531\pi$
$821$	9.67277e152	0.960583	0.480292	+	0.877109i	$0.340531\pi$
$822$	−3.83421e153	−3.57195
$823$	6.39371e152	0.558807	0.279403	−	0.960174i	$-0.409863\pi$
$823$	6.39371e152	0.558807	0.279403	+	0.960174i	$0.409863\pi$
$824$	4.48355e153	3.67658
$825$	7.08754e152	0.545335
$826$	2.94309e152	0.212496
$827$	−1.35582e153	−0.918675	−0.459338	−	0.888262i	$-0.651913\pi$
$827$	−1.35582e153	−0.918675	−0.459338	+	0.888262i	$0.651913\pi$
$828$	−1.37501e153	−0.874409
$829$	−1.59964e151	−0.00954791	−0.00477396	−	0.999989i	$-0.501520\pi$
$829$	−1.59964e151	−0.00954791	−0.00477396	+	0.999989i	$0.501520\pi$
$830$	−2.26910e153	−1.27132
$831$	−3.78187e153	−1.98909
$832$	5.08520e152	0.251092
$833$	2.95092e153	1.36803
$834$	6.58031e153	2.86437
$835$	2.73758e153	1.11899
$836$	−2.25787e153	−0.866701
$837$	4.37045e153	1.57558
$838$	−5.42359e153	−1.83644
$839$	−2.91785e153	−0.928025	−0.464012	−	0.885829i	$-0.653591\pi$
$839$	−2.91785e153	−0.928025	−0.464012	+	0.885829i	$0.653591\pi$
$840$	−7.21730e152	−0.215631
$841$	−3.86438e152	−0.108465
$842$	−1.23018e154	−3.24402
$843$	3.03422e153	0.751795
$844$	1.07389e154	2.50023
$845$	−3.93801e153	−0.861588
$846$	−6.58736e153	−1.35446
$847$	6.89439e151	0.0133235
$848$	−4.80001e153	−0.871887
$849$	−1.81285e153	−0.309533
$850$	−5.30531e153	−0.851564
$851$	1.13766e152	0.0171676
$852$	2.70179e154	3.83330
$853$	−1.89242e153	−0.252460	−0.126230	−	0.992001i	$-0.540288\pi$
$853$	−1.89242e153	−0.252460	−0.126230	+	0.992001i	$0.540288\pi$
$854$	3.74440e152	0.0469726
$855$	−6.47269e153	−0.763597
$856$	−6.68566e153	−0.741774
$857$	1.69723e154	1.77111	0.885557	−	0.464531i	$-0.153777\pi$
$857$	1.69723e154	1.77111	0.885557	+	0.464531i	$0.153777\pi$
$858$	4.22136e154	4.14352
$859$	−1.63155e154	−1.50646	−0.753232	−	0.657755i	$-0.771506\pi$
$859$	−1.63155e154	−1.50646	−0.753232	+	0.657755i	$0.771506\pi$
$860$	1.24205e154	1.07888
$861$	1.62349e153	0.132673
$862$	−2.56706e154	−1.97381
$863$	−1.13157e153	−0.0818682	−0.0409341	−	0.999162i	$-0.513033\pi$
$863$	−1.13157e153	−0.0818682	−0.0409341	+	0.999162i	$0.513033\pi$
$864$	−3.65918e154	−2.49122
$865$	1.34152e154	0.859512
$866$	−2.96296e154	−1.78664
$867$	2.79754e154	1.58772
$868$	−1.99873e153	−0.106775
$869$	1.45924e154	0.733819
$870$	−5.24374e154	−2.48245
$871$	3.65896e153	0.163081
$872$	3.64297e154	1.52876
$873$	−9.42656e154	−3.72482
$874$	3.61724e153	0.134595
$875$	−1.99077e153	−0.0697587
$876$	6.30221e154	2.07983
$877$	1.22909e154	0.382038	0.191019	−	0.981586i	$-0.438821\pi$
$877$	1.22909e154	0.382038	0.191019	+	0.981586i	$0.438821\pi$
$878$	1.37290e154	0.401955
$879$	1.39475e154	0.384663
$880$	5.32813e154	1.38431
$881$	−7.81284e153	−0.191238	−0.0956189	−	0.995418i	$-0.530483\pi$
$881$	−7.81284e153	−0.191238	−0.0956189	+	0.995418i	$0.530483\pi$
$882$	1.72393e155	3.97575
$883$	1.14392e154	0.248575	0.124288	−	0.992246i	$-0.460335\pi$
$883$	1.14392e154	0.248575	0.124288	+	0.992246i	$0.460335\pi$
$884$	−2.19645e155	−4.49756
$885$	−1.37750e155	−2.65810
$886$	1.67696e154	0.304966
$887$	8.81345e154	1.51062	0.755311	−	0.655367i	$-0.227486\pi$
$887$	8.81345e154	1.51062	0.755311	+	0.655367i	$0.227486\pi$
$888$	2.53411e154	0.409398
$889$	−1.05051e153	−0.0159977
$890$	−1.56706e155	−2.24963
$891$	−1.08818e155	−1.47273
$892$	6.69664e154	0.854481
$893$	1.20458e154	0.144922
$894$	4.56519e155	5.17892
$895$	7.76812e154	0.831010
$896$	−5.32876e153	−0.0537596
$897$	−4.70094e154	−0.447282
$898$	1.58868e154	0.142570
$899$	−8.15222e154	−0.690068
$900$	−2.15441e155	−1.72027
$901$	8.29007e154	0.624463
$902$	−2.62324e155	−1.86421
$903$	9.98294e153	0.0669348
$904$	1.14470e155	0.724187
$905$	1.58165e155	0.944193
$906$	−9.23303e155	−5.20132
$907$	2.85448e155	1.51756	0.758778	−	0.651349i	$-0.225797\pi$
$907$	2.85448e155	1.51756	0.758778	+	0.651349i	$0.225797\pi$
$908$	−2.41107e155	−1.20977
$909$	2.59640e155	1.22961
$910$	−3.02368e154	−0.135165
$911$	3.07697e155	1.29840	0.649199	−	0.760619i	$-0.275104\pi$
$911$	3.07697e155	1.29840	0.649199	+	0.760619i	$0.275104\pi$
$912$	3.68133e155	1.46648
$913$	2.04840e155	0.770368
$914$	−3.90675e155	−1.38720
$915$	−1.75255e155	−0.587576
$916$	−3.53664e155	−1.11964
$917$	2.64816e154	0.0791689
$918$	1.89962e156	5.36323
$919$	−6.63998e155	−1.77053	−0.885263	−	0.465092i	$-0.846021\pi$
$919$	−6.63998e155	−1.77053	−0.885263	+	0.465092i	$0.846021\pi$
$920$	−1.29866e155	−0.327065
$921$	8.27839e154	0.196932
$922$	−3.03557e155	−0.682130
$923$	6.35432e155	1.34890
$924$	1.16059e155	0.232756
$925$	1.78251e154	0.0337746
$926$	−2.06729e155	−0.370104
$927$	−2.06687e156	−3.49645
$928$	6.82548e155	1.09110
$929$	1.50933e155	0.228014	0.114007	−	0.993480i	$-0.463631\pi$
$929$	1.50933e155	0.228014	0.114007	+	0.993480i	$0.463631\pi$
$930$	1.34583e156	1.92147
$931$	−3.15242e155	−0.425388
$932$	2.30450e156	2.93929
$933$	−7.06327e155	−0.851568
$934$	−1.47001e156	−1.67537
$935$	−9.20219e155	−0.991474
$936$	−7.20344e156	−7.33767
$937$	1.05238e156	1.01355	0.506773	−	0.862079i	$-0.330838\pi$
$937$	1.05238e156	1.01355	0.506773	+	0.862079i	$0.330838\pi$
$938$	1.44721e154	0.0131790
$939$	2.78980e156	2.40231
$940$	−7.70366e155	−0.627314
$941$	−2.16414e156	−1.66660	−0.833298	−	0.552825i	$-0.813550\pi$
$941$	−2.16414e156	−1.66660	−0.833298	+	0.552825i	$0.813550\pi$
$942$	7.49828e156	5.46121
$943$	2.92126e155	0.201236
$944$	5.38955e156	3.51174
$945$	1.81776e155	0.112038
$946$	−1.61305e156	−0.940508
$947$	1.62005e156	0.893625	0.446813	−	0.894628i	$-0.352559\pi$
$947$	1.62005e156	0.893625	0.446813	+	0.894628i	$0.352559\pi$
$948$	−6.44792e156	−3.36498
$949$	1.48221e156	0.731870
$950$	5.66758e155	0.264794
$951$	−4.28230e156	−1.89322
$952$	−4.87698e155	−0.204038
$953$	−1.07207e156	−0.424470	−0.212235	−	0.977219i	$-0.568074\pi$
$953$	−1.07207e156	−0.424470	−0.212235	+	0.977219i	$0.568074\pi$
$954$	4.84307e156	1.81481
$955$	−2.16117e156	−0.766500
$956$	−6.85023e155	−0.229967
$957$	4.73371e156	1.50427
$958$	−2.51929e156	−0.757861
$959$	−2.47925e155	−0.0706062
$960$	−9.41391e155	−0.253823
$961$	−1.82492e156	−0.465871
$962$	1.06167e156	0.256623
$963$	3.08202e156	0.705432
$964$	−3.87855e156	−0.840669
$965$	4.95507e156	1.01711
$966$	−1.85934e155	−0.0361459
$967$	1.63853e156	0.301692	0.150846	−	0.988557i	$-0.451800\pi$
$967$	1.63853e156	0.301692	0.150846	+	0.988557i	$0.451800\pi$
$968$	2.76333e156	0.481921
$969$	−6.35801e156	−1.05032
$970$	−1.58594e157	−2.48182
$971$	1.42295e156	0.210951	0.105475	−	0.994422i	$-0.466364\pi$
$971$	1.42295e156	0.210951	0.105475	+	0.994422i	$0.466364\pi$
$972$	1.30882e157	1.83824
$973$	4.25491e155	0.0566196
$974$	7.64251e156	0.963587
$975$	−7.36555e156	−0.879959
$976$	6.85696e156	0.776276
$977$	−1.83385e157	−1.96743	−0.983715	−	0.179733i	$-0.942477\pi$
$977$	−1.83385e157	−1.96743	−0.983715	+	0.179733i	$0.942477\pi$
$978$	−4.59241e157	−4.66928
$979$	1.41464e157	1.36319
$980$	2.01607e157	1.84135
$981$	−1.67937e157	−1.45386
$982$	1.58569e157	1.30127
$983$	2.13639e157	1.66196	0.830980	−	0.556303i	$-0.187780\pi$
$983$	2.13639e157	1.66196	0.830980	+	0.556303i	$0.187780\pi$
$984$	6.50707e157	4.79891
$985$	1.29361e157	0.904484
$986$	−3.54337e157	−2.34898
$987$	−6.19178e155	−0.0389193
$988$	2.34643e157	1.39852
$989$	1.79630e156	0.101525
$990$	−5.37593e157	−2.88142
$991$	1.35147e157	0.686973	0.343487	−	0.939158i	$-0.388392\pi$
$991$	1.35147e157	0.686973	0.343487	+	0.939158i	$0.388392\pi$
$992$	−1.75179e157	−0.844537
$993$	3.70401e157	1.69370
$994$	2.51329e156	0.109008
$995$	8.54247e156	0.351457
$996$	−9.05120e157	−3.53257
$997$	−4.76047e156	−0.176260	−0.0881301	−	0.996109i	$-0.528089\pi$
$997$	−4.76047e156	−0.176260	−0.0881301	+	0.996109i	$0.528089\pi$
$998$	−3.72743e157	−1.30935
$999$	−6.38244e156	−0.212715

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.106.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-1.15346e16 q^{2} +2.00325e25 q^{3} +9.24825e31 q^{4} -4.02660e36 q^{5} -2.31067e41 q^{6} -1.49411e43 q^{7} -5.98851e47 q^{8} +2.76064e50 q^{9} +O(q^{10})\)	\(q-1.15346e16 q^{2} +2.00325e25 q^{3} +9.24825e31 q^{4} -4.02660e36 q^{5} -2.31067e41 q^{6} -1.49411e43 q^{7} -5.98851e47 q^{8} +2.76064e50 q^{9} +4.64453e52 q^{10} -4.19278e54 q^{11} +1.85266e57 q^{12} +4.35724e58 q^{13} +1.72340e59 q^{14} -8.06629e61 q^{15} +3.15598e63 q^{16} -5.45067e64 q^{17} -3.18429e66 q^{18} +5.82286e66 q^{19} -3.72391e68 q^{20} -2.99307e68 q^{21} +4.83621e70 q^{22} -5.38565e70 q^{23} -1.19965e73 q^{24} -8.43836e72 q^{25} -5.02591e74 q^{26} +3.02144e75 q^{27} -1.38179e75 q^{28} -5.63591e76 q^{29} +9.30415e77 q^{30} +1.44648e78 q^{31} -1.21107e79 q^{32} -8.39919e79 q^{33} +6.28714e80 q^{34} +6.01618e79 q^{35} +2.55311e82 q^{36} -2.11238e81 q^{37} -6.71645e82 q^{38} +8.72864e83 q^{39} +2.41134e84 q^{40} -5.42415e84 q^{41} +3.45239e84 q^{42} -3.33535e85 q^{43} -3.87759e86 q^{44} -1.11160e87 q^{45} +6.21214e86 q^{46} +2.06871e87 q^{47} +6.32221e88 q^{48} -5.41386e88 q^{49} +9.73333e88 q^{50} -1.09190e90 q^{51} +4.02969e90 q^{52} -1.52093e90 q^{53} -3.48512e91 q^{54} +1.68827e91 q^{55} +8.94748e90 q^{56} +1.16646e92 q^{57} +6.50081e92 q^{58} +1.70773e93 q^{59} -7.45991e93 q^{60} +2.17269e93 q^{61} -1.66846e94 q^{62} -4.12469e93 q^{63} +1.16707e94 q^{64} -1.75449e95 q^{65} +9.68814e95 q^{66} +8.39741e94 q^{67} -5.04092e96 q^{68} -1.07888e96 q^{69} -6.93944e95 q^{70} +1.45834e97 q^{71} -1.65321e98 q^{72} +3.40172e97 q^{73} +2.43655e97 q^{74} -1.69041e98 q^{75} +5.38513e98 q^{76} +6.26447e97 q^{77} -1.00682e100 q^{78} -3.48037e99 q^{79} -1.27079e100 q^{80} +2.59537e100 q^{81} +6.25655e100 q^{82} -4.88553e100 q^{83} -2.76807e100 q^{84} +2.19477e101 q^{85} +3.84720e101 q^{86} -1.12901e102 q^{87} +2.51085e102 q^{88} -3.37399e102 q^{89} +1.28219e103 q^{90} -6.51020e101 q^{91} -4.98078e102 q^{92} +2.89766e103 q^{93} -2.38617e103 q^{94} -2.34464e103 q^{95} -2.42608e104 q^{96} -3.41463e104 q^{97} +6.24468e104 q^{98} -1.15748e105 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 91\!\cdots\!20 q^{2}+ \cdots + 31\!\cdots\!84 q^{9}+O(q^{10}) \) 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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