LMFDB - Embedded newform 1.106.a.a.1.2

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			1.2
Root			$-5.83850e13$ 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)

$f(q)$	$=$	$q-9.55432e15 q^{2} -1.37857e25 q^{3} +5.07201e31 q^{4} -2.80039e36 q^{5} +1.31713e41 q^{6} -2.78207e44 q^{7} -9.70270e46 q^{8} +6.48087e49 q^{9} +O(q^{10})$	\(q-9.55432e15 q^{2} -1.37857e25 q^{3} +5.07201e31 q^{4} -2.80039e36 q^{5} +1.31713e41 q^{6} -2.78207e44 q^{7} -9.70270e46 q^{8} +6.48087e49 q^{9} +2.67558e52 q^{10} +6.08520e53 q^{11} -6.99212e56 q^{12} -5.49066e58 q^{13} +2.65807e60 q^{14} +3.86053e61 q^{15} -1.13043e63 q^{16} -2.90311e64 q^{17} -6.19203e65 q^{18} -1.56027e67 q^{19} -1.42036e68 q^{20} +3.83527e69 q^{21} -5.81399e69 q^{22} +5.72406e71 q^{23} +1.33759e72 q^{24} -1.68097e73 q^{25} +5.24595e74 q^{26} +8.33042e74 q^{27} -1.41107e76 q^{28} -1.76595e76 q^{29} -3.68848e77 q^{30} +1.61443e78 q^{31} +1.47363e79 q^{32} -8.38888e78 q^{33} +2.77372e80 q^{34} +7.79087e80 q^{35} +3.28711e81 q^{36} +1.96604e82 q^{37} +1.49073e83 q^{38} +7.56926e83 q^{39} +2.71714e83 q^{40} +1.17183e83 q^{41} -3.66434e85 q^{42} +1.98821e84 q^{43} +3.08642e85 q^{44} -1.81490e86 q^{45} -5.46895e87 q^{46} +1.10467e88 q^{47} +1.55837e88 q^{48} +2.30371e88 q^{49} +1.60605e89 q^{50} +4.00214e89 q^{51} -2.78487e90 q^{52} -7.34914e89 q^{53} -7.95915e90 q^{54} -1.70409e90 q^{55} +2.69936e91 q^{56} +2.15094e92 q^{57} +1.68724e92 q^{58} -1.37917e93 q^{59} +1.95807e93 q^{60} +1.74942e93 q^{61} -1.54248e94 q^{62} -1.80302e94 q^{63} -9.49400e94 q^{64} +1.53760e95 q^{65} +8.01500e94 q^{66} +1.25972e96 q^{67} -1.47246e96 q^{68} -7.89102e96 q^{69} -7.44364e96 q^{70} -1.81563e97 q^{71} -6.28820e96 q^{72} -2.37938e97 q^{73} -1.87841e98 q^{74} +2.31734e98 q^{75} -7.91371e98 q^{76} -1.69294e98 q^{77} -7.23191e99 q^{78} +8.68206e98 q^{79} +3.16563e99 q^{80} -1.96005e100 q^{81} -1.11961e99 q^{82} +2.69773e100 q^{83} +1.94526e101 q^{84} +8.12984e100 q^{85} -1.89960e100 q^{86} +2.43448e101 q^{87} -5.90429e100 q^{88} -5.78519e101 q^{89} +1.73401e102 q^{90} +1.52754e103 q^{91} +2.90325e103 q^{92} -2.22561e103 q^{93} -1.05543e104 q^{94} +4.36937e103 q^{95} -2.03151e104 q^{96} +1.53726e103 q^{97} -2.20103e104 q^{98} +3.94374e103 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.55432e15	−1.50012	−0.750058	−	0.661372i	$-0.769974\pi$
$2$	−9.55432e15	−1.50012	−0.750058	+	0.661372i	$0.769974\pi$
$3$	−1.37857e25	−1.23186	−0.615932	−	0.787799i	$-0.711220\pi$
$3$	−1.37857e25	−1.23186	−0.615932	+	0.787799i	$0.711220\pi$
$4$	5.07201e31	1.25035
$5$	−2.80039e36	−0.564018	−0.282009	−	0.959412i	$-0.591001\pi$
$5$	−2.80039e36	−0.564018	−0.282009	+	0.959412i	$0.591001\pi$
$6$	1.31713e41	1.84794
$7$	−2.78207e44	−1.19322	−0.596610	−	0.802531i	$-0.703486\pi$
$7$	−2.78207e44	−1.19322	−0.596610	+	0.802531i	$0.703486\pi$
$8$	−9.70270e46	−0.375551
$9$	6.48087e49	0.517490
$10$	2.67558e52	0.846093
$11$	6.08520e53	0.129169	0.0645846	−	0.997912i	$-0.479428\pi$
$11$	6.08520e53	0.129169	0.0645846	+	0.997912i	$0.479428\pi$
$12$	−6.99212e56	−1.54026
$13$	−5.49066e58	−1.80967	−0.904834	−	0.425764i	$-0.860005\pi$
$13$	−5.49066e58	−1.80967	−0.904834	+	0.425764i	$0.860005\pi$
$14$	2.65807e60	1.78997
$15$	3.86053e61	0.694794
$16$	−1.13043e63	−0.686978
$17$	−2.90311e64	−0.731636	−0.365818	−	0.930686i	$-0.619211\pi$
$17$	−2.90311e64	−0.731636	−0.365818	+	0.930686i	$0.619211\pi$
$18$	−6.19203e65	−0.776295
$19$	−1.56027e67	−1.14455	−0.572277	−	0.820061i	$-0.693940\pi$
$19$	−1.56027e67	−1.14455	−0.572277	+	0.820061i	$0.693940\pi$
$20$	−1.42036e68	−0.705219
$21$	3.83527e69	1.46988
$22$	−5.81399e69	−0.193769
$23$	5.72406e71	1.84924	0.924620	−	0.380892i	$-0.124383\pi$
$23$	5.72406e71	1.84924	0.924620	+	0.380892i	$0.124383\pi$
$24$	1.33759e72	0.462627
$25$	−1.68097e73	−0.681883
$26$	5.24595e74	2.71471
$27$	8.33042e74	0.594387
$28$	−1.41107e76	−1.49194
$29$	−1.76595e76	−0.295857	−0.147929	−	0.988998i	$-0.547261\pi$
$29$	−1.76595e76	−0.295857	−0.147929	+	0.988998i	$0.547261\pi$
$30$	−3.68848e77	−1.04227
$31$	1.61443e78	0.815700	0.407850	−	0.913049i	$-0.366279\pi$
$31$	1.61443e78	0.815700	0.407850	+	0.913049i	$0.366279\pi$
$32$	1.47363e79	1.40610
$33$	−8.38888e78	−0.159119
$34$	2.77372e80	1.09754
$35$	7.79087e80	0.672998
$36$	3.28711e81	0.647042
$37$	1.96604e82	0.918335	0.459168	−	0.888350i	$-0.348148\pi$
$37$	1.96604e82	0.918335	0.459168	+	0.888350i	$0.348148\pi$
$38$	1.49073e83	1.71696
$39$	7.56926e83	2.22927
$40$	2.71714e83	0.211817
$41$	1.17183e83	0.0249870	0.0124935	−	0.999922i	$-0.496023\pi$
$41$	1.17183e83	0.0249870	0.0124935	+	0.999922i	$0.496023\pi$
$42$	−3.66434e85	−2.20500
$43$	1.98821e84	0.0347831	0.0173915	−	0.999849i	$-0.494464\pi$
$43$	1.98821e84	0.0347831	0.0173915	+	0.999849i	$0.494464\pi$
$44$	3.08642e85	0.161506
$45$	−1.81490e86	−0.291874
$46$	−5.46895e87	−2.77407
$47$	1.10467e88	1.81173	0.905866	−	0.423564i	$-0.139221\pi$
$47$	1.10467e88	1.81173	0.905866	+	0.423564i	$0.139221\pi$
$48$	1.55837e88	0.846264
$49$	2.30371e88	0.423773
$50$	1.60605e89	1.02290
$51$	4.00214e89	0.901276
$52$	−2.78487e90	−2.26271
$53$	−7.34914e89	−0.219661	−0.109831	−	0.993950i	$-0.535031\pi$
$53$	−7.34914e89	−0.219661	−0.109831	+	0.993950i	$0.535031\pi$
$54$	−7.95915e90	−0.891650
$55$	−1.70409e90	−0.0728538
$56$	2.69936e91	0.448114
$57$	2.15094e92	1.40993
$58$	1.68724e92	0.443820
$59$	−1.37917e93	−1.47872	−0.739360	−	0.673310i	$-0.764872\pi$
$59$	−1.37917e93	−1.47872	−0.739360	+	0.673310i	$0.764872\pi$
$60$	1.95807e93	0.868734
$61$	1.74942e93	0.325894	0.162947	−	0.986635i	$-0.447900\pi$
$61$	1.74942e93	0.325894	0.162947	+	0.986635i	$0.447900\pi$
$62$	−1.54248e94	−1.22365
$63$	−1.80302e94	−0.617479
$64$	−9.49400e94	−1.42233
$65$	1.53760e95	1.02069
$66$	8.01500e94	0.238697
$67$	1.25972e96	1.70352	0.851762	−	0.523929i	$-0.175534\pi$
$67$	1.25972e96	1.70352	0.851762	+	0.523929i	$0.175534\pi$
$68$	−1.47246e96	−0.914799
$69$	−7.89102e96	−2.27801
$70$	−7.44364e96	−1.00957
$71$	−1.81563e97	−1.16940	−0.584702	−	0.811248i	$-0.698788\pi$
$71$	−1.81563e97	−1.16940	−0.584702	+	0.811248i	$0.698788\pi$
$72$	−6.28820e96	−0.194344
$73$	−2.37938e97	−0.356462	−0.178231	−	0.983989i	$-0.557037\pi$
$73$	−2.37938e97	−0.356462	−0.178231	+	0.983989i	$0.557037\pi$
$74$	−1.87841e98	−1.37761
$75$	2.31734e98	0.839988
$76$	−7.91371e98	−1.43109
$77$	−1.69294e98	−0.154127
$78$	−7.23191e99	−3.34416
$79$	8.68206e98	0.205684	0.102842	−	0.994698i	$-0.467206\pi$
$79$	8.68206e98	0.205684	0.102842	+	0.994698i	$0.467206\pi$
$80$	3.16563e99	0.387468
$81$	−1.96005e100	−1.24969
$82$	−1.11961e99	−0.0374834
$83$	2.69773e100	0.477968	0.238984	−	0.971023i	$-0.423186\pi$
$83$	2.69773e100	0.477968	0.238984	+	0.971023i	$0.423186\pi$
$84$	1.94526e101	1.83787
$85$	8.12984e100	0.412656
$86$	−1.89960e100	−0.0521787
$87$	2.43448e101	0.364456
$88$	−5.90429e100	−0.0485096
$89$	−5.78519e101	−0.262629	−0.131314	−	0.991341i	$-0.541920\pi$
$89$	−5.78519e101	−0.262629	−0.131314	+	0.991341i	$0.541920\pi$
$90$	1.73401e102	0.437845
$91$	1.52754e103	2.15933
$92$	2.90325e103	2.31219
$93$	−2.22561e103	−1.00483
$94$	−1.05543e104	−2.71781
$95$	4.36937e103	0.645549
$96$	−2.03151e104	−1.73212
$97$	1.53726e103	0.0760730	0.0380365	−	0.999276i	$-0.487890\pi$
$97$	1.53726e103	0.0760730	0.0380365	+	0.999276i	$0.487890\pi$
$98$	−2.20103e104	−0.635708
$99$	3.94374e103	0.0668438
$100$	−8.52591e104	−0.852591
$101$	2.28689e105	1.35635	0.678177	−	0.734898i	$-0.262770\pi$
$101$	2.28689e105	1.35635	0.678177	+	0.734898i	$0.262770\pi$
$102$	−3.82377e105	−1.35202
$103$	3.42402e105	0.725408	0.362704	−	0.931904i	$-0.381854\pi$
$103$	3.42402e105	0.725408	0.362704	+	0.931904i	$0.381854\pi$
$104$	5.32743e105	0.679622
$105$	−1.07403e106	−0.829042
$106$	7.02160e105	0.329517
$107$	2.13857e106	0.613020	0.306510	−	0.951867i	$-0.400839\pi$
$107$	2.13857e106	0.613020	0.306510	+	0.951867i	$0.400839\pi$
$108$	4.22520e106	0.743191
$109$	1.63899e107	1.77699	0.888495	−	0.458886i	$-0.151751\pi$
$109$	1.63899e107	1.77699	0.888495	+	0.458886i	$0.151751\pi$
$110$	1.62815e106	0.109289
$111$	−2.71032e107	−1.13126
$112$	3.14492e107	0.819716
$113$	−1.62565e107	−0.265711	−0.132855	−	0.991135i	$-0.542415\pi$
$113$	−1.62565e107	−0.265711	−0.132855	+	0.991135i	$0.542415\pi$
$114$	−2.05508e108	−2.11506
$115$	−1.60296e108	−1.04301
$116$	−8.95690e107	−0.369924
$117$	−3.55843e108	−0.936485
$118$	1.31770e109	2.21825
$119$	8.07664e108	0.873002
$120$	−3.74576e108	−0.260930
$121$	−2.18235e109	−0.983315
$122$	−1.67145e109	−0.488879
$123$	−1.61546e108	−0.0307806
$124$	8.18842e109	1.01991
$125$	1.16109e110	0.948613
$126$	1.72266e110	0.926290
$127$	−3.88074e109	−0.137790	−0.0688952	−	0.997624i	$-0.521947\pi$
$127$	−3.88074e109	−0.137790	−0.0688952	+	0.997624i	$0.521947\pi$
$128$	3.09310e110	0.727564
$129$	−2.74088e109	−0.0428480
$130$	−1.46907e111	−1.53115
$131$	−1.57108e111	−1.09510	−0.547552	−	0.836772i	$-0.684440\pi$
$131$	−1.57108e111	−1.09510	−0.547552	+	0.836772i	$0.684440\pi$
$132$	−4.25485e110	−0.198954
$133$	4.34078e111	1.36570
$134$	−1.20358e112	−2.55548
$135$	−2.33284e111	−0.335245
$136$	2.81680e111	0.274766
$137$	−1.76329e111	−0.117083	−0.0585416	−	0.998285i	$-0.518645\pi$
$137$	−1.76329e111	−0.117083	−0.0585416	+	0.998285i	$0.518645\pi$
$138$	7.53933e112	3.41728
$139$	−2.53726e112	−0.787207	−0.393603	−	0.919280i	$-0.628772\pi$
$139$	−2.53726e112	−0.787207	−0.393603	+	0.919280i	$0.628772\pi$
$140$	3.95154e112	0.841481
$141$	−1.52286e113	−2.23181
$142$	1.73471e113	1.75424
$143$	−3.34118e112	−0.233753
$144$	−7.32615e112	−0.355504
$145$	4.94534e112	0.166869
$146$	2.27333e113	0.534734
$147$	−3.17582e113	−0.522031
$148$	9.97177e113	1.14824
$149$	−8.32260e113	−0.672945	−0.336473	−	0.941693i	$-0.609234\pi$
$149$	−8.32260e113	−0.672945	−0.336473	+	0.941693i	$0.609234\pi$
$150$	−2.21406e114	−1.26008
$151$	−4.51522e114	−1.81296	−0.906482	−	0.422245i	$-0.861242\pi$
$151$	−4.51522e114	−1.81296	−0.906482	+	0.422245i	$0.861242\pi$
$152$	1.51388e114	0.429838
$153$	−1.88147e114	−0.378614
$154$	1.61749e114	0.231209
$155$	−4.52104e114	−0.460070
$156$	3.83914e115	2.78736
$157$	2.88320e115	1.49673	0.748364	−	0.663288i	$-0.230839\pi$
$157$	2.88320e115	1.49673	0.748364	+	0.663288i	$0.230839\pi$
$158$	−8.29511e114	−0.308550
$159$	1.01313e115	0.270593
$160$	−4.12675e115	−0.793065
$161$	−1.59247e116	−2.20655
$162$	1.87269e116	1.87469
$163$	−5.49862e115	−0.398478	−0.199239	−	0.979951i	$-0.563847\pi$
$163$	−5.49862e115	−0.398478	−0.199239	+	0.979951i	$0.563847\pi$
$164$	5.94356e114	0.0312424
$165$	2.34921e115	0.0897460
$166$	−2.57750e116	−0.717008
$167$	−6.07691e116	−1.23330	−0.616649	−	0.787238i	$-0.711510\pi$
$167$	−6.07691e116	−1.23330	−0.616649	+	0.787238i	$0.711510\pi$
$168$	−3.72125e116	−0.552016
$169$	2.09418e117	2.27490
$170$	−7.76751e116	−0.619032
$171$	−1.01119e117	−0.592295
$172$	1.00842e116	0.0434909
$173$	1.52150e117	0.484006	0.242003	−	0.970275i	$-0.422196\pi$
$173$	1.52150e117	0.484006	0.242003	+	0.970275i	$0.422196\pi$
$174$	−2.32598e117	−0.546726
$175$	4.67657e117	0.813636
$176$	−6.87887e116	−0.0887365
$177$	1.90128e118	1.82158
$178$	5.52735e117	0.393973
$179$	−1.41887e117	−0.0753629	−0.0376814	−	0.999290i	$-0.511997\pi$
$179$	−1.41887e117	−0.0753629	−0.0376814	+	0.999290i	$0.511997\pi$
$180$	−9.20518e117	−0.364944
$181$	2.12802e118	0.630741	0.315370	−	0.948969i	$-0.397871\pi$
$181$	2.12802e118	0.630741	0.315370	+	0.948969i	$0.397871\pi$
$182$	−1.45946e119	−3.23925
$183$	−2.41169e118	−0.401458
$184$	−5.55389e118	−0.694483
$185$	−5.50567e118	−0.517958
$186$	2.12641e119	1.50736
$187$	−1.76660e118	−0.0945049
$188$	5.60289e119	2.26530
$189$	−2.31758e119	−0.709234
$190$	−4.17463e119	−0.968399
$191$	3.26522e119	0.574991	0.287495	−	0.957782i	$-0.407177\pi$
$191$	3.26522e119	0.574991	0.287495	+	0.957782i	$0.407177\pi$
$192$	1.30881e120	1.75212
$193$	−1.01008e120	−1.02943	−0.514713	−	0.857362i	$-0.672102\pi$
$193$	−1.01008e120	−1.02943	−0.514713	+	0.857362i	$0.672102\pi$
$194$	−1.46874e119	−0.114118
$195$	−2.11969e120	−1.25735
$196$	1.16844e120	0.529863
$197$	3.20363e120	1.11215	0.556077	−	0.831130i	$-0.312306\pi$
$197$	3.20363e120	1.11215	0.556077	+	0.831130i	$0.312306\pi$
$198$	−3.76798e119	−0.100273
$199$	3.54060e120	0.723253	0.361627	−	0.932323i	$-0.382221\pi$
$199$	3.54060e120	0.723253	0.361627	+	0.932323i	$0.382221\pi$
$200$	1.63100e120	0.256082
$201$	−1.73662e121	−2.09851
$202$	−2.18497e121	−2.03469
$203$	4.91298e120	0.353023
$204$	2.02989e121	1.12691
$205$	−3.28159e119	−0.0140931
$206$	−3.27142e121	−1.08820
$207$	3.70969e121	0.956962
$208$	6.20679e121	1.24320
$209$	−9.49457e120	−0.147841
$210$	1.02616e122	1.24366
$211$	−3.74411e121	−0.353606	−0.176803	−	0.984246i	$-0.556576\pi$
$211$	−3.74411e121	−0.353606	−0.176803	+	0.984246i	$0.556576\pi$
$212$	−3.72750e121	−0.274653
$213$	2.50297e122	1.44055
$214$	−2.04325e122	−0.919601
$215$	−5.56776e120	−0.0196183
$216$	−8.08276e121	−0.223222
$217$	−4.49145e122	−0.973310
$218$	−1.56594e123	−2.66569
$219$	3.28014e122	0.439112
$220$	−8.64319e121	−0.0910926
$221$	1.59400e123	1.32402
$222$	2.58952e123	1.69703
$223$	1.59180e123	0.823918	0.411959	−	0.911202i	$-0.364845\pi$
$223$	1.59180e123	0.823918	0.411959	+	0.911202i	$0.364845\pi$
$224$	−4.09974e123	−1.67778
$225$	−1.08942e123	−0.352868
$226$	1.55320e123	0.398597
$227$	−6.30732e123	−1.28377	−0.641885	−	0.766801i	$-0.721847\pi$
$227$	−6.30732e123	−1.28377	−0.641885	+	0.766801i	$0.721847\pi$
$228$	1.09096e124	1.76291
$229$	−8.73627e123	−1.12192	−0.560962	−	0.827842i	$-0.689569\pi$
$229$	−8.73627e123	−1.12192	−0.560962	+	0.827842i	$0.689569\pi$
$230$	1.53152e124	1.56463
$231$	2.33384e123	0.189864
$232$	1.71344e123	0.111109
$233$	−2.69610e123	−0.139492	−0.0697461	−	0.997565i	$-0.522219\pi$
$233$	−2.69610e123	−0.139492	−0.0697461	+	0.997565i	$0.522219\pi$
$234$	3.39984e124	1.40484
$235$	−3.09350e124	−1.02185
$236$	−6.99515e124	−1.84891
$237$	−1.19688e124	−0.253375
$238$	−7.71668e124	−1.30960
$239$	4.10469e124	0.558972	0.279486	−	0.960150i	$-0.409836\pi$
$239$	4.10469e124	0.558972	0.279486	+	0.960150i	$0.409836\pi$
$240$	−4.36405e124	−0.477309
$241$	−4.83839e124	−0.425409	−0.212704	−	0.977117i	$-0.568227\pi$
$241$	−4.83839e124	−0.425409	−0.212704	+	0.977117i	$0.568227\pi$
$242$	2.08509e125	1.47509
$243$	1.65879e125	0.945066
$244$	8.87306e124	0.407481
$245$	−6.45128e124	−0.239016
$246$	1.54346e124	0.0461744
$247$	8.56693e125	2.07126
$248$	−1.56643e125	−0.306337
$249$	−3.71901e125	−0.588792
$250$	−1.10934e126	−1.42303
$251$	2.38736e125	0.248341	0.124170	−	0.992261i	$-0.460373\pi$
$251$	2.38736e125	0.248341	0.124170	+	0.992261i	$0.460373\pi$
$252$	−9.14495e125	−0.772063
$253$	3.48321e125	0.238865
$254$	3.70778e125	0.206701
$255$	−1.12076e126	−0.508337
$256$	8.95976e125	0.330901
$257$	−1.73877e126	−0.523302	−0.261651	−	0.965163i	$-0.584267\pi$
$257$	−1.73877e126	−0.523302	−0.261651	+	0.965163i	$0.584267\pi$
$258$	2.61873e125	0.0642770
$259$	−5.46965e126	−1.09578
$260$	7.79873e126	1.27621
$261$	−1.14449e126	−0.153103
$262$	1.50106e127	1.64278
$263$	−8.47350e126	−0.759252	−0.379626	−	0.925140i	$-0.623947\pi$
$263$	−8.47350e126	−0.759252	−0.379626	+	0.925140i	$0.623947\pi$
$264$	8.13948e125	0.0597572
$265$	2.05805e126	0.123893
$266$	−4.14732e127	−2.04871
$267$	7.97529e126	0.323523
$268$	6.38934e127	2.13000
$269$	5.38318e127	1.47586	0.737928	−	0.674880i	$-0.235805\pi$
$269$	5.38318e127	1.47586	0.737928	+	0.674880i	$0.235805\pi$
$270$	2.22887e127	0.502907
$271$	−6.18683e127	−1.14969	−0.574845	−	0.818263i	$-0.694937\pi$
$271$	−6.18683e127	−1.14969	−0.574845	+	0.818263i	$0.694937\pi$
$272$	3.28175e127	0.502618
$273$	−2.10582e128	−2.66000
$274$	1.68470e127	0.175638
$275$	−1.02291e127	−0.0880783
$276$	−4.00234e128	−2.84831
$277$	5.28238e127	0.310915	0.155458	−	0.987843i	$-0.450315\pi$
$277$	5.28238e127	0.310915	0.155458	+	0.987843i	$0.450315\pi$
$278$	2.42418e128	1.18090
$279$	1.04629e128	0.422117
$280$	−7.55925e127	−0.252745
$281$	4.88641e128	1.35490	0.677451	−	0.735568i	$-0.263085\pi$
$281$	4.88641e128	1.35490	0.677451	+	0.735568i	$0.263085\pi$
$282$	1.45499e129	3.34797
$283$	−4.29397e128	−0.820486	−0.410243	−	0.911976i	$-0.634556\pi$
$283$	−4.29397e128	−0.820486	−0.410243	+	0.911976i	$0.634556\pi$
$284$	−9.20891e128	−1.46216
$285$	−6.02348e128	−0.795229
$286$	3.19227e128	0.350657
$287$	−3.26012e127	−0.0298149
$288$	9.55043e128	0.727641
$289$	−7.31674e128	−0.464709
$290$	−4.72493e128	−0.250323
$291$	−2.11922e128	−0.0937116
$292$	−1.20682e129	−0.445701
$293$	−4.25875e129	−1.31441	−0.657207	−	0.753710i	$-0.728262\pi$
$293$	−4.25875e129	−1.31441	−0.657207	+	0.753710i	$0.728262\pi$
$294$	3.03428e129	0.783106
$295$	3.86220e129	0.834026
$296$	−1.90759e129	−0.344881
$297$	5.06923e128	0.0767765
$298$	7.95167e129	1.00950
$299$	−3.14289e130	−3.34651
$300$	1.17536e130	1.05028
$301$	−5.53133e128	−0.0415039
$302$	4.31398e130	2.71966
$303$	−3.15264e130	−1.67084
$304$	1.76377e130	0.786283
$305$	−4.89905e129	−0.183810
$306$	1.79761e130	0.567965
$307$	3.47475e130	0.925036	0.462518	−	0.886610i	$-0.346946\pi$
$307$	3.47475e130	0.925036	0.462518	+	0.886610i	$0.346946\pi$
$308$	−8.58663e129	−0.192713
$309$	−4.72026e130	−0.893605
$310$	4.31954e130	0.690158
$311$	4.08993e130	0.551817	0.275908	−	0.961184i	$-0.411021\pi$
$311$	4.08993e130	0.551817	0.275908	+	0.961184i	$0.411021\pi$
$312$	−7.34423e130	−0.837202
$313$	−1.00853e131	−0.971873	−0.485937	−	0.873994i	$-0.661521\pi$
$313$	−1.00853e131	−0.971873	−0.485937	+	0.873994i	$0.661521\pi$
$314$	−2.75470e131	−2.24527
$315$	5.04916e130	0.348270
$316$	4.40355e130	0.257176
$317$	7.79846e130	0.385832	0.192916	−	0.981215i	$-0.438206\pi$
$317$	7.79846e130	0.385832	0.192916	+	0.981215i	$0.438206\pi$
$318$	−9.67977e130	−0.405921
$319$	−1.07461e130	−0.0382157
$320$	2.65869e131	0.802221
$321$	−2.94816e131	−0.755157
$322$	1.52150e132	3.31008
$323$	4.52964e131	0.837396
$324$	−9.94140e131	−1.56255
$325$	9.22965e131	1.23398
$326$	5.25355e131	0.597763
$327$	−2.25946e132	−2.18901
$328$	−1.13700e130	−0.00938387
$329$	−3.07326e132	−2.16179
$330$	−2.24451e131	−0.134629
$331$	1.33736e132	0.684353	0.342176	−	0.939636i	$-0.388836\pi$
$331$	1.33736e132	0.684353	0.342176	+	0.939636i	$0.388836\pi$
$332$	1.36829e132	0.597627
$333$	1.27416e132	0.475229
$334$	5.80608e132	1.85009
$335$	−3.52772e132	−0.960819
$336$	−4.33549e132	−1.00978
$337$	5.42067e132	1.08015	0.540074	−	0.841618i	$-0.318396\pi$
$337$	5.42067e132	1.08015	0.540074	+	0.841618i	$0.318396\pi$
$338$	−2.00085e133	−3.41261
$339$	2.24108e132	0.327320
$340$	4.12347e132	0.515964
$341$	9.82414e131	0.105363
$342$	9.66125e132	0.888511
$343$	8.71476e132	0.687566
$344$	−1.92910e131	−0.0130628
$345$	2.20979e133	1.28484
$346$	−1.45369e133	−0.726066
$347$	1.25222e132	0.0537506	0.0268753	−	0.999639i	$-0.491444\pi$
$347$	1.25222e132	0.0537506	0.0268753	+	0.999639i	$0.491444\pi$
$348$	1.23477e133	0.455697
$349$	4.47790e133	1.42148	0.710738	−	0.703457i	$-0.248361\pi$
$349$	4.47790e133	1.42148	0.710738	+	0.703457i	$0.248361\pi$
$350$	−4.46815e133	−1.22055
$351$	−4.57396e133	−1.07564
$352$	8.96736e132	0.181625
$353$	5.25259e133	0.916645	0.458323	−	0.888786i	$-0.348450\pi$
$353$	5.25259e133	0.916645	0.458323	+	0.888786i	$0.348450\pi$
$354$	−1.81654e134	−2.73259
$355$	5.08448e133	0.659565
$356$	−2.93425e133	−0.328377
$357$	−1.11342e134	−1.07542
$358$	1.35563e133	0.113053
$359$	1.00745e134	0.725712	0.362856	−	0.931845i	$-0.381802\pi$
$359$	1.00745e134	0.725712	0.362856	+	0.931845i	$0.381802\pi$
$360$	1.76094e133	0.109613
$361$	5.76093e133	0.310002
$362$	−2.03318e134	−0.946185
$363$	3.00852e134	1.21131
$364$	7.74770e134	2.69991
$365$	6.66318e133	0.201051
$366$	2.30421e134	0.602233
$367$	−8.02021e134	−1.81643	−0.908213	−	0.418509i	$-0.862553\pi$
$367$	−8.02021e134	−1.81643	−0.908213	+	0.418509i	$0.862553\pi$
$368$	−6.47063e134	−1.27039
$369$	7.59451e132	0.0129305
$370$	5.26029e134	0.776997
$371$	2.04458e134	0.262104
$372$	−1.12883e135	−1.25639
$373$	4.43980e134	0.429190	0.214595	−	0.976703i	$-0.431157\pi$
$373$	4.43980e134	0.429190	0.214595	+	0.976703i	$0.431157\pi$
$374$	1.68787e134	0.141768
$375$	−1.60064e135	−1.16856
$376$	−1.07183e135	−0.680397
$377$	9.69621e134	0.535404
$378$	2.21429e135	1.06393
$379$	−6.75431e133	−0.0282502	−0.0141251	−	0.999900i	$-0.504496\pi$
$379$	−6.75431e133	−0.0282502	−0.0141251	+	0.999900i	$0.504496\pi$
$380$	2.21615e135	0.807161
$381$	5.34987e134	0.169739
$382$	−3.11970e135	−0.862553
$383$	−5.34001e135	−1.28708	−0.643541	−	0.765412i	$-0.722535\pi$
$383$	−5.34001e135	−1.28708	−0.643541	+	0.765412i	$0.722535\pi$
$384$	−4.26406e135	−0.896260
$385$	4.74090e134	0.0869306
$386$	9.65059e135	1.54426
$387$	1.28853e134	0.0179999
$388$	7.79699e134	0.0951177
$389$	1.35889e136	1.44820	0.724102	−	0.689693i	$-0.242254\pi$
$389$	1.35889e136	1.44820	0.724102	+	0.689693i	$0.242254\pi$
$390$	2.02522e136	1.88617
$391$	−1.66176e136	−1.35297
$392$	−2.23522e135	−0.159148
$393$	2.16584e136	1.34902
$394$	−3.06085e136	−1.66836
$395$	−2.43131e135	−0.116010
$396$	2.00027e135	0.0835779
$397$	−4.74251e136	−1.73583	−0.867914	−	0.496715i	$-0.834539\pi$
$397$	−4.74251e136	−1.73583	−0.867914	+	0.496715i	$0.834539\pi$
$398$	−3.38280e136	−1.08496
$399$	−5.98406e136	−1.68236
$400$	1.90021e136	0.468439
$401$	−1.79524e135	−0.0388189	−0.0194094	−	0.999812i	$-0.506179\pi$
$401$	−1.79524e135	−0.0388189	−0.0194094	+	0.999812i	$0.506179\pi$
$402$	1.65922e137	3.14801
$403$	−8.86430e136	−1.47615
$404$	1.15991e137	1.69591
$405$	5.48891e136	0.704851
$406$	−4.69401e136	−0.529575
$407$	1.19637e136	0.118621
$408$	−3.88316e136	−0.338475
$409$	−3.15143e136	−0.241565	−0.120783	−	0.992679i	$-0.538540\pi$
$409$	−3.15143e136	−0.241565	−0.120783	+	0.992679i	$0.538540\pi$
$410$	3.13534e135	0.0211413
$411$	2.43082e136	0.144231
$412$	1.73667e137	0.907013
$413$	3.83693e137	1.76444
$414$	−3.54436e137	−1.43555
$415$	−7.55470e136	−0.269583
$416$	−8.09123e137	−2.54457
$417$	3.49780e137	0.969732
$418$	9.07141e136	0.221779
$419$	−4.51580e137	−0.973864	−0.486932	−	0.873440i	$-0.661884\pi$
$419$	−4.51580e137	−0.973864	−0.486932	+	0.873440i	$0.661884\pi$
$420$	−5.44747e137	−1.03659
$421$	6.83262e137	1.14757	0.573783	−	0.819008i	$-0.305475\pi$
$421$	6.83262e137	1.14757	0.573783	+	0.819008i	$0.305475\pi$
$422$	3.57724e137	0.530450
$423$	7.15921e137	0.937553
$424$	7.13066e136	0.0824939
$425$	4.88005e137	0.498890
$426$	−2.39142e138	−2.16099
$427$	−4.86699e137	−0.388863
$428$	1.08468e138	0.766488
$429$	4.60605e137	0.287953
$430$	5.31961e136	0.0294297
$431$	1.34945e137	0.0660846	0.0330423	−	0.999454i	$-0.489480\pi$
$431$	1.34945e137	0.0660846	0.0330423	+	0.999454i	$0.489480\pi$
$432$	−9.41693e137	−0.408331
$433$	1.24017e138	0.476286	0.238143	−	0.971230i	$-0.423461\pi$
$433$	1.24017e138	0.476286	0.238143	+	0.971230i	$0.423461\pi$
$434$	4.29128e138	1.46008
$435$	−6.81749e137	−0.205560
$436$	8.31298e138	2.22186
$437$	−8.93109e138	−2.11655
$438$	−3.13394e138	−0.658720
$439$	6.09549e138	1.13664	0.568318	−	0.822809i	$-0.307594\pi$
$439$	6.09549e138	1.13664	0.568318	+	0.822809i	$0.307594\pi$
$440$	1.65343e137	0.0273603
$441$	1.49300e138	0.219298
$442$	−1.52296e139	−1.98618
$443$	−6.29540e138	−0.729168	−0.364584	−	0.931171i	$-0.618789\pi$
$443$	−6.29540e138	−0.729168	−0.364584	+	0.931171i	$0.618789\pi$
$444$	−1.37468e139	−1.41447
$445$	1.62008e138	0.148127
$446$	−1.52086e139	−1.23597
$447$	1.14733e139	0.828977
$448$	2.64129e139	1.69715
$449$	−3.53370e137	−0.0201975	−0.0100987	−	0.999949i	$-0.503215\pi$
$449$	−3.53370e137	−0.0201975	−0.0100987	+	0.999949i	$0.503215\pi$
$450$	1.04086e139	0.529342
$451$	7.13085e136	0.00322755
$452$	−8.24533e138	−0.332231
$453$	6.22454e139	2.23333
$454$	6.02621e139	1.92580
$455$	−4.27771e139	−1.21790
$456$	−2.08700e139	−0.529502
$457$	−7.29371e139	−1.64948	−0.824742	−	0.565510i	$-0.808679\pi$
$457$	−7.29371e139	−1.64948	−0.824742	+	0.565510i	$0.808679\pi$
$458$	8.34691e139	1.68302
$459$	−2.41841e139	−0.434875
$460$	−8.13024e139	−1.30412
$461$	−1.26835e140	−1.81526	−0.907632	−	0.419768i	$-0.862112\pi$
$461$	−1.26835e140	−1.81526	−0.907632	+	0.419768i	$0.862112\pi$
$462$	−2.22983e139	−0.284818
$463$	1.37630e140	1.56932	0.784660	−	0.619927i	$-0.212838\pi$
$463$	1.37630e140	1.56932	0.784660	+	0.619927i	$0.212838\pi$
$464$	1.99627e139	0.203248
$465$	6.23257e139	0.566744
$466$	2.57594e139	0.209254
$467$	1.53938e140	1.11740	0.558700	−	0.829370i	$-0.311300\pi$
$467$	1.53938e140	1.11740	0.558700	+	0.829370i	$0.311300\pi$
$468$	−1.80484e140	−1.17093
$469$	−3.50464e140	−2.03268
$470$	2.95563e140	1.53289
$471$	−3.97469e140	−1.84377
$472$	1.33816e140	0.555334
$473$	1.20987e138	0.00449290
$474$	1.14354e140	0.380091
$475$	2.62277e140	0.780452
$476$	4.09648e140	1.09156
$477$	−4.76289e139	−0.113673
$478$	−3.92175e140	−0.838523
$479$	1.64056e140	0.314323	0.157162	−	0.987573i	$-0.449766\pi$
$479$	1.64056e140	0.314323	0.157162	+	0.987573i	$0.449766\pi$
$480$	5.68901e140	0.976949
$481$	−1.07949e141	−1.66188
$482$	4.62276e140	0.638163
$483$	2.19533e141	2.71817
$484$	−1.10689e141	−1.22949
$485$	−4.30492e139	−0.0429066
$486$	−1.58486e141	−1.41771
$487$	−6.86441e140	−0.551230	−0.275615	−	0.961268i	$-0.588881\pi$
$487$	−6.86441e140	−0.551230	−0.275615	+	0.961268i	$0.588881\pi$
$488$	−1.69741e140	−0.122390
$489$	7.58023e140	0.490871
$490$	6.16376e140	0.358551
$491$	−1.07369e141	−0.561176	−0.280588	−	0.959828i	$-0.590529\pi$
$491$	−1.07369e141	−0.561176	−0.280588	+	0.959828i	$0.590529\pi$
$492$	−8.19361e139	−0.0384864
$493$	5.12673e140	0.216460
$494$	−8.18511e141	−3.10713
$495$	−1.10440e140	−0.0377011
$496$	−1.82500e141	−0.560368
$497$	5.05121e141	1.39536
$498$	3.55326e141	0.883256
$499$	7.22628e141	1.61673	0.808363	−	0.588685i	$-0.200354\pi$
$499$	7.22628e141	1.61673	0.808363	+	0.588685i	$0.200354\pi$
$500$	5.88905e141	1.18610
$501$	8.37745e141	1.51926
$502$	−2.28096e141	−0.372540
$503$	−2.57863e140	−0.0379376	−0.0189688	−	0.999820i	$-0.506038\pi$
$503$	−2.57863e140	−0.0379376	−0.0189688	+	0.999820i	$0.506038\pi$
$504$	1.74942e141	0.231895
$505$	−6.40419e141	−0.765009
$506$	−3.32797e141	−0.358325
$507$	−2.88697e142	−2.80237
$508$	−1.96831e141	−0.172286
$509$	8.55017e141	0.674981	0.337490	−	0.941329i	$-0.390422\pi$
$509$	8.55017e141	0.674981	0.337490	+	0.941329i	$0.390422\pi$
$510$	1.07080e142	0.762564
$511$	6.61958e141	0.425337
$512$	−2.11076e142	−1.22395
$513$	−1.29977e142	−0.680308
$514$	1.66127e142	0.785013
$515$	−9.58861e141	−0.409144
$516$	−1.39018e141	−0.0535749
$517$	6.72213e141	0.234020
$518$	5.22587e142	1.64379
$519$	−2.09749e142	−0.596230
$520$	−1.49189e142	−0.383319
$521$	−2.86534e141	−0.0665572	−0.0332786	−	0.999446i	$-0.510595\pi$
$521$	−2.86534e141	−0.0665572	−0.0332786	+	0.999446i	$0.510595\pi$
$522$	1.09348e142	0.229672
$523$	4.48660e142	0.852272	0.426136	−	0.904659i	$-0.359874\pi$
$523$	4.48660e142	0.852272	0.426136	+	0.904659i	$0.359874\pi$
$524$	−7.96854e142	−1.36926
$525$	−6.44698e142	−1.00229
$526$	8.09585e142	1.13897
$527$	−4.68687e142	−0.596796
$528$	9.48300e141	0.109311
$529$	2.31836e143	2.41969
$530$	−1.96632e142	−0.185854
$531$	−8.93820e142	−0.765223
$532$	2.20165e143	1.70760
$533$	−6.43415e141	−0.0452181
$534$	−7.61984e142	−0.485322
$535$	−5.98882e142	−0.345754
$536$	−1.22227e143	−0.639759
$537$	1.95601e142	0.0928368
$538$	−5.14326e143	−2.21395
$539$	1.40185e142	0.0547384
$540$	−1.18322e143	−0.419173
$541$	−1.97481e143	−0.634847	−0.317424	−	0.948284i	$-0.602818\pi$
$541$	−1.97481e143	−0.634847	−0.317424	+	0.948284i	$0.602818\pi$
$542$	5.91109e143	1.72467
$543$	−2.93363e143	−0.776987
$544$	−4.27812e143	−1.02875
$545$	−4.58981e143	−1.00226
$546$	2.01197e144	3.99031
$547$	−1.18448e143	−0.213399	−0.106700	−	0.994291i	$-0.534028\pi$
$547$	−1.18448e143	−0.213399	−0.106700	+	0.994291i	$0.534028\pi$
$548$	−8.94344e142	−0.146395
$549$	1.13377e143	0.168647
$550$	9.77316e142	0.132128
$551$	2.75535e143	0.338624
$552$	7.65642e143	0.855509
$553$	−2.41541e143	−0.245426
$554$	−5.04695e143	−0.466409
$555$	7.58995e143	0.638054
$556$	−1.28690e144	−0.984282
$557$	1.54722e144	1.07685	0.538423	−	0.842675i	$-0.319020\pi$
$557$	1.54722e144	1.07685	0.538423	+	0.842675i	$0.319020\pi$
$558$	−9.99661e143	−0.633224
$559$	−1.09166e143	−0.0629458
$560$	−8.80700e143	−0.462335
$561$	2.43538e143	0.116417
$562$	−4.66863e144	−2.03251
$563$	1.70654e144	0.676748	0.338374	−	0.941012i	$-0.390123\pi$
$563$	1.70654e144	0.676748	0.338374	+	0.941012i	$0.390123\pi$
$564$	−7.72397e144	−2.79054
$565$	4.55246e143	0.149866
$566$	4.10260e144	1.23082
$567$	5.45299e144	1.49116
$568$	1.76165e144	0.439170
$569$	−2.55776e144	−0.581388	−0.290694	−	0.956816i	$-0.593886\pi$
$569$	−2.55776e144	−0.581388	−0.290694	+	0.956816i	$0.593886\pi$
$570$	5.75502e144	1.19294
$571$	7.49648e144	1.41730	0.708650	−	0.705561i	$-0.249305\pi$
$571$	7.49648e144	1.41730	0.708650	+	0.705561i	$0.249305\pi$
$572$	−1.69465e144	−0.292273
$573$	−4.50134e144	−0.708311
$574$	3.11482e143	0.0447259
$575$	−9.62199e144	−1.26097
$576$	−6.15294e144	−0.736042
$577$	−2.51068e144	−0.274196	−0.137098	−	0.990557i	$-0.543778\pi$
$577$	−2.51068e144	−0.274196	−0.137098	+	0.990557i	$0.543778\pi$
$578$	6.99064e144	0.697117
$579$	1.39246e145	1.26811
$580$	2.50828e144	0.208644
$581$	−7.50527e144	−0.570321
$582$	2.02477e144	0.140578
$583$	−4.47210e143	−0.0283735
$584$	2.30864e144	0.133869
$585$	9.96499e144	0.528195
$586$	4.06895e145	1.97177
$587$	−1.70386e145	−0.754978	−0.377489	−	0.926014i	$-0.623212\pi$
$587$	−1.70386e145	−0.754978	−0.377489	+	0.926014i	$0.623212\pi$
$588$	−1.61078e145	−0.652720
$589$	−2.51895e145	−0.933612
$590$	−3.69007e145	−1.25114
$591$	−4.41643e145	−1.37002
$592$	−2.22246e145	−0.630876
$593$	3.57082e145	0.927675	0.463838	−	0.885920i	$-0.346472\pi$
$593$	3.57082e145	0.927675	0.463838	+	0.885920i	$0.346472\pi$
$594$	−4.84330e144	−0.115174
$595$	−2.26178e145	−0.492389
$596$	−4.22123e145	−0.841415
$597$	−4.88097e145	−0.890950
$598$	3.00282e146	5.02015
$599$	4.04087e145	0.618823	0.309412	−	0.950928i	$-0.399868\pi$
$599$	4.04087e145	0.618823	0.309412	+	0.950928i	$0.399868\pi$
$600$	−2.24844e145	−0.315458
$601$	−4.23700e145	−0.544689	−0.272345	−	0.962200i	$-0.587799\pi$
$601$	−4.23700e145	−0.544689	−0.272345	+	0.962200i	$0.587799\pi$
$602$	5.28481e144	0.0622606
$603$	8.16411e145	0.881556
$604$	−2.29012e146	−2.26683
$605$	6.11144e145	0.554608
$606$	3.01213e146	2.50646
$607$	1.81602e146	1.38584	0.692920	−	0.721014i	$-0.256324\pi$
$607$	1.81602e146	1.38584	0.692920	+	0.721014i	$0.256324\pi$
$608$	−2.29927e146	−1.60935
$609$	−6.77288e145	−0.434876
$610$	4.68070e145	0.275737
$611$	−6.06536e146	−3.27863
$612$	−9.54283e145	−0.473399
$613$	1.35963e146	0.619079	0.309539	−	0.950887i	$-0.399825\pi$
$613$	1.35963e146	0.619079	0.309539	+	0.950887i	$0.399825\pi$
$614$	−3.31988e146	−1.38766
$615$	4.52390e144	0.0173608
$616$	1.64261e145	0.0578826
$617$	5.10995e146	1.65366	0.826829	−	0.562453i	$-0.190142\pi$
$617$	5.10995e146	1.65366	0.826829	+	0.562453i	$0.190142\pi$
$618$	4.50988e146	1.34051
$619$	−2.66391e146	−0.727378	−0.363689	−	0.931520i	$-0.618483\pi$
$619$	−2.66391e146	−0.727378	−0.363689	+	0.931520i	$0.618483\pi$
$620$	−2.29308e146	−0.575248
$621$	4.76839e146	1.09916
$622$	−3.90764e146	−0.827789
$623$	1.60948e146	0.313374
$624$	−8.55649e146	−1.53146
$625$	8.92418e145	0.146848
$626$	9.63578e146	1.45792
$627$	1.30889e146	0.182120
$628$	1.46236e147	1.87143
$629$	−5.70762e146	−0.671887
$630$	−4.82413e146	−0.522445
$631$	−3.13753e146	−0.312641	−0.156321	−	0.987706i	$-0.549963\pi$
$631$	−3.13753e146	−0.312641	−0.156321	+	0.987706i	$0.549963\pi$
$632$	−8.42394e145	−0.0772447
$633$	5.16152e146	0.435595
$634$	−7.45090e146	−0.578792
$635$	1.08676e146	0.0777163
$636$	5.13861e146	0.338335
$637$	−1.26489e147	−0.766888
$638$	1.02672e146	0.0573279
$639$	−1.17669e147	−0.605154
$640$	−8.66190e146	−0.410359
$641$	2.34806e147	1.02486	0.512428	−	0.858730i	$-0.328746\pi$
$641$	2.34806e147	1.02486	0.512428	+	0.858730i	$0.328746\pi$
$642$	2.81677e147	1.13282
$643$	2.81374e147	1.04282	0.521409	−	0.853307i	$-0.325407\pi$
$643$	2.81374e147	1.04282	0.521409	+	0.853307i	$0.325407\pi$
$644$	−8.07704e147	−2.75895
$645$	7.67555e145	0.0241671
$646$	−4.32776e147	−1.25619
$647$	2.99199e147	0.800728	0.400364	−	0.916356i	$-0.368884\pi$
$647$	2.99199e147	0.800728	0.400364	+	0.916356i	$0.368884\pi$
$648$	1.90178e147	0.469323
$649$	−8.39251e146	−0.191005
$650$	−8.81830e147	−1.85112
$651$	6.19178e147	1.19899
$652$	−2.78891e147	−0.498236
$653$	−1.01216e148	−1.66843	−0.834214	−	0.551441i	$-0.814078\pi$
$653$	−1.01216e148	−1.66843	−0.834214	+	0.551441i	$0.814078\pi$
$654$	2.15876e148	3.28377
$655$	4.39964e147	0.617659
$656$	−1.32467e146	−0.0171655
$657$	−1.54204e147	−0.184465
$658$	2.93629e148	3.24294
$659$	3.85253e146	0.0392881	0.0196441	−	0.999807i	$-0.493747\pi$
$659$	3.85253e146	0.0392881	0.0196441	+	0.999807i	$0.493747\pi$
$660$	1.19152e147	0.112214
$661$	−2.48731e146	−0.0216348	−0.0108174	−	0.999941i	$-0.503443\pi$
$661$	−2.48731e146	−0.0216348	−0.0108174	+	0.999941i	$0.503443\pi$
$662$	−1.27776e148	−1.02661
$663$	−2.19744e148	−1.63101
$664$	−2.61753e147	−0.179501
$665$	−1.21559e148	−0.770282
$666$	−1.21738e148	−0.712899
$667$	−1.01084e148	−0.547111
$668$	−3.08222e148	−1.54205
$669$	−2.19441e148	−1.01496
$670$	3.37049e148	1.44134
$671$	1.06456e147	0.0420955
$672$	5.65178e148	2.06680
$673$	3.07607e148	1.04041	0.520206	−	0.854041i	$-0.325855\pi$
$673$	3.07607e148	1.04041	0.520206	+	0.854041i	$0.325855\pi$
$674$	−5.17908e148	−1.62035
$675$	−1.40032e148	−0.405303
$676$	1.06217e149	2.84441
$677$	−5.19092e148	−1.28629	−0.643146	−	0.765744i	$-0.722371\pi$
$677$	−5.19092e148	−1.28629	−0.643146	+	0.765744i	$0.722371\pi$
$678$	−2.14119e148	−0.491018
$679$	−4.27675e147	−0.0907718
$680$	−7.88814e147	−0.154973
$681$	8.69508e148	1.58143
$682$	−9.38630e147	−0.158057
$683$	1.89336e148	0.295221	0.147610	−	0.989046i	$-0.452842\pi$
$683$	1.89336e148	0.295221	0.147610	+	0.989046i	$0.452842\pi$
$684$	−5.12878e148	−0.740574
$685$	4.93791e147	0.0660371
$686$	−8.32636e148	−1.03143
$687$	1.20436e149	1.38206
$688$	−2.24752e147	−0.0238952
$689$	4.03517e148	0.397514
$690$	−2.11131e149	−1.92741
$691$	5.38718e148	0.455789	0.227894	−	0.973686i	$-0.426816\pi$
$691$	5.38718e148	0.455789	0.227894	+	0.973686i	$0.426816\pi$
$692$	7.71706e148	0.605176
$693$	−1.09718e148	−0.0797593
$694$	−1.19641e148	−0.0806321
$695$	7.10533e148	0.443999
$696$	−2.36210e148	−0.136872
$697$	−3.40196e147	−0.0182814
$698$	−4.27833e149	−2.13238
$699$	3.71676e148	0.171835
$700$	2.37196e149	1.01733
$701$	−2.86338e149	−1.13942	−0.569708	−	0.821847i	$-0.692944\pi$
$701$	−2.86338e149	−1.13942	−0.569708	+	0.821847i	$0.692944\pi$
$702$	4.37010e149	1.61359
$703$	−3.06755e149	−1.05108
$704$	−5.77729e148	−0.183721
$705$	4.26461e149	1.25878
$706$	−5.01849e149	−1.37507
$707$	−6.36228e149	−1.61843
$708$	9.64330e149	2.27761
$709$	4.90339e149	1.07540	0.537699	−	0.843137i	$-0.319294\pi$
$709$	4.90339e149	1.07540	0.537699	+	0.843137i	$0.319294\pi$
$710$	−4.85787e149	−0.989424
$711$	5.62673e148	0.106439
$712$	5.61320e148	0.0986303
$713$	9.24111e149	1.50843
$714$	1.06380e150	1.61326
$715$	9.35661e148	0.131841
$716$	−7.19651e148	−0.0942298
$717$	−5.65860e149	−0.688578
$718$	−9.62548e149	−1.08865
$719$	−6.37999e149	−0.670738	−0.335369	−	0.942087i	$-0.608861\pi$
$719$	−6.37999e149	−0.670738	−0.335369	+	0.942087i	$0.608861\pi$
$720$	2.05161e149	0.200511
$721$	−9.52586e149	−0.865571
$722$	−5.50418e149	−0.465039
$723$	6.67007e149	0.524046
$724$	1.07934e150	0.788645
$725$	2.96850e149	0.201740
$726$	−2.87444e150	−1.81711
$727$	−1.08800e150	−0.639841	−0.319921	−	0.947444i	$-0.603656\pi$
$727$	−1.08800e150	−0.639841	−0.319921	+	0.947444i	$0.603656\pi$
$728$	−1.48213e150	−0.810938
$729$	1.67944e149	0.0855004
$730$	−6.36621e149	−0.301600
$731$	−5.77199e148	−0.0254486
$732$	−1.22321e150	−0.501962
$733$	1.12535e150	0.429863	0.214932	−	0.976629i	$-0.431047\pi$
$733$	1.12535e150	0.429863	0.214932	+	0.976629i	$0.431047\pi$
$734$	7.66276e150	2.72485
$735$	8.89354e149	0.294435
$736$	8.43517e150	2.60021
$737$	7.66568e149	0.220043
$738$	−7.25603e148	−0.0193973
$739$	3.16267e150	0.787446	0.393723	−	0.919229i	$-0.371187\pi$
$739$	3.16267e150	0.787446	0.393723	+	0.919229i	$0.371187\pi$
$740$	−2.79248e150	−0.647628
$741$	−1.18101e151	−2.55151
$742$	−1.95346e150	−0.393187
$743$	−6.22279e150	−1.16701	−0.583503	−	0.812111i	$-0.698318\pi$
$743$	−6.22279e150	−1.16701	−0.583503	+	0.812111i	$0.698318\pi$
$744$	2.15944e150	0.377365
$745$	2.33065e150	0.379554
$746$	−4.24192e150	−0.643834
$747$	1.74837e150	0.247344
$748$	−8.96022e149	−0.118164
$749$	−5.94963e150	−0.731467
$750$	1.52930e151	1.75298
$751$	1.24977e151	1.33577	0.667886	−	0.744264i	$-0.267199\pi$
$751$	1.24977e151	1.33577	0.667886	+	0.744264i	$0.267199\pi$
$752$	−1.24874e151	−1.24462
$753$	−3.29115e150	−0.305922
$754$	−9.26407e150	−0.803167
$755$	1.26444e151	1.02254
$756$	−1.17548e151	−0.886789
$757$	1.28207e151	0.902357	0.451178	−	0.892434i	$-0.351004\pi$
$757$	1.28207e151	0.902357	0.451178	+	0.892434i	$0.351004\pi$
$758$	6.45328e149	0.0423786
$759$	−4.80185e150	−0.294249
$760$	−4.23947e150	−0.242436
$761$	−1.91799e151	−1.02365	−0.511826	−	0.859089i	$-0.671031\pi$
$761$	−1.91799e151	−1.02365	−0.511826	+	0.859089i	$0.671031\pi$
$762$	−5.11143e150	−0.254628
$763$	−4.55978e151	−2.12034
$764$	1.65613e151	0.718939
$765$	5.26885e150	0.213545
$766$	5.10201e151	1.93077
$767$	7.57254e151	2.67599
$768$	−1.23517e151	−0.407625
$769$	−4.55055e150	−0.140259	−0.0701296	−	0.997538i	$-0.522341\pi$
$769$	−4.55055e150	−0.140259	−0.0701296	+	0.997538i	$0.522341\pi$
$770$	−4.52961e150	−0.130406
$771$	2.39701e151	0.644637
$772$	−5.12312e151	−1.28714
$773$	4.52563e151	1.06232	0.531160	−	0.847272i	$-0.321756\pi$
$773$	4.52563e151	1.06232	0.531160	+	0.847272i	$0.321756\pi$
$774$	−1.23111e150	−0.0270019
$775$	−2.71381e151	−0.556212
$776$	−1.49156e150	−0.0285693
$777$	7.54029e151	1.34985
$778$	−1.29832e152	−2.17247
$779$	−1.82838e150	−0.0285989
$780$	−1.07511e152	−1.57212
$781$	−1.10485e151	−0.151051
$782$	1.58770e152	2.02961
$783$	−1.47111e151	−0.175854
$784$	−2.60417e151	−0.291123
$785$	−8.07409e151	−0.844183
$786$	−2.06931e152	−2.02368
$787$	−1.16926e152	−1.06964	−0.534819	−	0.844967i	$-0.679620\pi$
$787$	−1.16926e152	−1.06964	−0.534819	+	0.844967i	$0.679620\pi$
$788$	1.62488e152	1.39058
$789$	1.16813e152	0.935296
$790$	2.32295e151	0.174028
$791$	4.52267e151	0.317052
$792$	−3.82650e150	−0.0251032
$793$	−9.60546e151	−0.589761
$794$	4.53114e152	2.60394
$795$	−2.83716e151	−0.152619
$796$	1.79580e152	0.904318
$797$	−1.15487e152	−0.544468	−0.272234	−	0.962231i	$-0.587762\pi$
$797$	−1.15487e152	−0.544468	−0.272234	+	0.962231i	$0.587762\pi$
$798$	5.71736e152	2.52374
$799$	−3.20697e152	−1.32553
$800$	−2.47714e152	−0.958794
$801$	−3.74931e151	−0.135908
$802$	1.71523e151	0.0582328
$803$	−1.44790e151	−0.0460439
$804$	−8.80815e152	−2.62387
$805$	4.45954e152	1.24453
$806$	8.46923e152	2.21439
$807$	−7.42108e152	−1.81805
$808$	−2.21890e152	−0.509380
$809$	−4.63963e152	−0.998127	−0.499064	−	0.866565i	$-0.666323\pi$
$809$	−4.63963e152	−0.998127	−0.499064	+	0.866565i	$0.666323\pi$
$810$	−5.24427e152	−1.05736
$811$	8.65154e151	0.163493	0.0817464	−	0.996653i	$-0.473950\pi$
$811$	8.65154e151	0.163493	0.0817464	+	0.996653i	$0.473950\pi$
$812$	2.49187e152	0.441401
$813$	8.52898e152	1.41626
$814$	−1.14305e152	−0.177945
$815$	1.53983e152	0.224749
$816$	−4.52412e152	−0.619157
$817$	−3.10214e151	−0.0398111
$818$	3.01098e152	0.362376
$819$	9.89979e152	1.11743
$820$	−1.66443e151	−0.0176213
$821$	−5.99650e152	−0.595501	−0.297750	−	0.954644i	$-0.596236\pi$
$821$	−5.99650e152	−0.595501	−0.297750	+	0.954644i	$0.596236\pi$
$822$	−2.32248e152	−0.216363
$823$	9.52116e152	0.832144	0.416072	−	0.909332i	$-0.363406\pi$
$823$	9.52116e152	0.832144	0.416072	+	0.909332i	$0.363406\pi$
$824$	−3.32223e152	−0.272428
$825$	1.41015e152	0.108501
$826$	−3.66593e153	−2.64686
$827$	1.42933e153	0.968488	0.484244	−	0.874933i	$-0.339095\pi$
$827$	1.42933e153	0.968488	0.484244	+	0.874933i	$0.339095\pi$
$828$	1.88156e153	1.19654
$829$	−8.24532e152	−0.492147	−0.246073	−	0.969251i	$-0.579140\pi$
$829$	−8.24532e152	−0.492147	−0.246073	+	0.969251i	$0.579140\pi$
$830$	7.21800e152	0.404406
$831$	−7.28213e152	−0.383005
$832$	5.21284e153	2.57395
$833$	−6.68791e152	−0.310047
$834$	−3.34190e153	−1.45471
$835$	1.70177e153	0.695603
$836$	−4.81566e152	−0.184853
$837$	1.34489e153	0.484842
$838$	4.31453e153	1.46091
$839$	−1.00004e153	−0.318063	−0.159031	−	0.987274i	$-0.550837\pi$
$839$	−1.00004e153	−0.318063	−0.159031	+	0.987274i	$0.550837\pi$
$840$	1.04210e153	0.311347
$841$	−3.25093e153	−0.912468
$842$	−6.52810e153	−1.72148
$843$	−6.73625e153	−1.66906
$844$	−1.89902e153	−0.442131
$845$	−5.86452e153	−1.28308
$846$	−6.84014e153	−1.40644
$847$	6.07145e153	1.17331
$848$	8.30766e152	0.150903
$849$	5.91954e153	1.01073
$850$	−4.66255e153	−0.748393
$851$	1.12537e154	1.69822
$852$	1.26951e154	1.80118
$853$	7.56898e153	1.00975	0.504874	−	0.863193i	$-0.331539\pi$
$853$	7.56898e153	1.00975	0.504874	+	0.863193i	$0.331539\pi$
$854$	4.65008e153	0.583340
$855$	2.83173e153	0.334065
$856$	−2.07499e153	−0.230220
$857$	−2.02420e153	−0.211232	−0.105616	−	0.994407i	$-0.533681\pi$
$857$	−2.02420e153	−0.211232	−0.105616	+	0.994407i	$0.533681\pi$
$858$	−4.40077e153	−0.431962
$859$	−1.23650e154	−1.14171	−0.570853	−	0.821053i	$-0.693387\pi$
$859$	−1.23650e154	−1.14171	−0.570853	+	0.821053i	$0.693387\pi$
$860$	−2.82398e152	−0.0245297
$861$	4.49430e152	0.0367280
$862$	−1.28931e153	−0.0991345
$863$	1.07223e154	0.775748	0.387874	−	0.921712i	$-0.373210\pi$
$863$	1.07223e154	0.775748	0.387874	+	0.921712i	$0.373210\pi$
$864$	1.22760e154	0.835766
$865$	−4.26079e153	−0.272989
$866$	−1.18490e154	−0.714484
$867$	1.00866e154	0.572458
$868$	−2.27807e154	−1.21698
$869$	5.28321e152	0.0265680
$870$	6.51364e153	0.308364
$871$	−6.91672e154	−3.08281
$872$	−1.59026e154	−0.667350
$873$	9.96277e152	0.0393670
$874$	8.53305e154	3.17507
$875$	−3.23022e154	−1.13190
$876$	1.66369e154	0.549043
$877$	1.27536e154	0.396420	0.198210	−	0.980160i	$-0.436487\pi$
$877$	1.27536e154	0.396420	0.198210	+	0.980160i	$0.436487\pi$
$878$	−5.82382e154	−1.70508
$879$	5.87099e154	1.61918
$880$	1.92635e153	0.0500490
$881$	−1.17829e154	−0.288414	−0.144207	−	0.989548i	$-0.546063\pi$
$881$	−1.17829e154	−0.288414	−0.144207	+	0.989548i	$0.546063\pi$
$882$	−1.42646e154	−0.328973
$883$	1.02733e154	0.223241	0.111621	−	0.993751i	$-0.464396\pi$
$883$	1.02733e154	0.223241	0.111621	+	0.993751i	$0.464396\pi$
$884$	8.08479e154	1.65548
$885$	−5.32432e154	−1.02741
$886$	6.01482e154	1.09384
$887$	−3.44753e154	−0.590906	−0.295453	−	0.955357i	$-0.595471\pi$
$887$	−3.44753e154	−0.590906	−0.295453	+	0.955357i	$0.595471\pi$
$888$	2.62974e154	0.424847
$889$	1.07965e154	0.164414
$890$	−1.54787e154	−0.222208
$891$	−1.19273e154	−0.161422
$892$	8.07365e154	1.03018
$893$	−1.72358e155	−2.07362
$894$	−1.09619e155	−1.24356
$895$	3.97338e153	0.0425060
$896$	−8.60522e154	−0.868143
$897$	4.33270e155	4.12245
$898$	3.37621e153	0.0302985
$899$	−2.85100e154	−0.241331
$900$	−5.52553e154	−0.441207
$901$	2.13354e154	0.160712
$902$	−6.81304e152	−0.00484170
$903$	7.62532e153	0.0511271
$904$	1.57732e154	0.0997879
$905$	−5.95929e154	−0.355750
$906$	−5.94713e155	−3.35025
$907$	1.66663e155	0.886048	0.443024	−	0.896510i	$-0.353906\pi$
$907$	1.66663e155	0.886048	0.443024	+	0.896510i	$0.353906\pi$
$908$	−3.19908e155	−1.60516
$909$	1.48210e155	0.701900
$910$	4.08706e155	1.82700
$911$	−3.43117e155	−1.44786	−0.723931	−	0.689873i	$-0.757666\pi$
$911$	−3.43117e155	−1.44786	−0.723931	+	0.689873i	$0.757666\pi$
$912$	−2.43148e155	−0.968594
$913$	1.64163e154	0.0617388
$914$	6.96864e155	2.47442
$915$	6.75368e154	0.226429
$916$	−4.43105e155	−1.40279
$917$	4.37085e155	1.30670
$918$	2.31063e155	0.652363
$919$	−1.14534e155	−0.305401	−0.152700	−	0.988273i	$-0.548797\pi$
$919$	−1.14534e155	−0.305401	−0.152700	+	0.988273i	$0.548797\pi$
$920$	1.55531e155	0.391701
$921$	−4.79018e155	−1.13952
$922$	1.21182e156	2.72311
$923$	9.96902e155	2.11623
$924$	1.18373e155	0.237396
$925$	−3.30485e155	−0.626197
$926$	−1.31496e156	−2.35416
$927$	2.21907e155	0.375391
$928$	−2.60235e155	−0.416004
$929$	−2.98166e155	−0.450436	−0.225218	−	0.974308i	$-0.572309\pi$
$929$	−2.98166e155	−0.450436	−0.225218	+	0.974308i	$0.572309\pi$
$930$	−5.95479e155	−0.850182
$931$	−3.59441e155	−0.485030
$932$	−1.36746e155	−0.174414
$933$	−5.63825e155	−0.679764
$934$	−1.47077e156	−1.67623
$935$	4.94717e154	0.0533025
$936$	3.45264e155	0.351697
$937$	−1.80246e156	−1.73595	−0.867976	−	0.496605i	$-0.834580\pi$
$937$	−1.80246e156	−1.73595	−0.867976	+	0.496605i	$0.834580\pi$
$938$	3.34844e156	3.04925
$939$	1.39032e156	1.19722
$940$	−1.56903e156	−1.27767
$941$	−1.52494e156	−1.17435	−0.587176	−	0.809460i	$-0.699760\pi$
$941$	−1.52494e156	−1.17435	−0.587176	+	0.809460i	$0.699760\pi$
$942$	3.79755e156	2.76586
$943$	6.70765e154	0.0462069
$944$	1.55905e156	1.01585
$945$	6.49012e155	0.400021
$946$	−1.15594e154	−0.00673988
$947$	−2.42446e156	−1.33734	−0.668670	−	0.743559i	$-0.733136\pi$
$947$	−2.42446e156	−1.33734	−0.668670	+	0.743559i	$0.733136\pi$
$948$	−6.07060e155	−0.316806
$949$	1.30644e156	0.645077
$950$	−2.50588e156	−1.17077
$951$	−1.07507e156	−0.475292
$952$	−7.83653e155	−0.327857
$953$	4.23514e156	1.67683	0.838417	−	0.545029i	$-0.183481\pi$
$953$	4.23514e156	1.67683	0.838417	+	0.545029i	$0.183481\pi$
$954$	4.55061e155	0.170522
$955$	−9.14390e155	−0.324306
$956$	2.08190e156	0.698910
$957$	1.48143e155	0.0470765
$958$	−1.56744e156	−0.471521
$959$	4.90560e155	0.139706
$960$	−3.66519e156	−0.988227
$961$	−1.31083e156	−0.334633
$962$	1.03137e157	2.49302
$963$	1.38598e156	0.317231
$964$	−2.45404e156	−0.531909
$965$	2.82861e156	0.580616
$966$	−2.09749e157	−4.07757
$967$	2.95182e156	0.543500	0.271750	−	0.962368i	$-0.412398\pi$
$967$	2.95182e156	0.543500	0.271750	+	0.962368i	$0.412398\pi$
$968$	2.11747e156	0.369285
$969$	−6.24442e156	−1.03156
$970$	4.11306e155	0.0643648
$971$	−2.93287e156	−0.434794	−0.217397	−	0.976083i	$-0.569757\pi$
$971$	−2.93287e156	−0.434794	−0.217397	+	0.976083i	$0.569757\pi$
$972$	8.41341e156	1.18166
$973$	7.05884e156	0.939310
$974$	6.55847e156	0.826909
$975$	−1.27237e157	−1.52010
$976$	−1.97759e156	−0.223882
$977$	1.11036e157	1.19123	0.595617	−	0.803268i	$-0.296907\pi$
$977$	1.11036e157	1.19123	0.595617	+	0.803268i	$0.296907\pi$
$978$	−7.24239e156	−0.736363
$979$	−3.52040e155	−0.0339235
$980$	−3.27210e156	−0.298853
$981$	1.06221e157	0.919574
$982$	1.02583e157	0.841829
$983$	−2.45904e157	−1.91296	−0.956480	−	0.291799i	$-0.905746\pi$
$983$	−2.45904e157	−1.91296	−0.956480	+	0.291799i	$0.905746\pi$
$984$	1.56743e155	0.0115597
$985$	−8.97141e156	−0.627276
$986$	−4.89824e156	−0.324715
$987$	4.23670e157	2.66304
$988$	4.34516e157	2.58980
$989$	1.13806e156	0.0643222
$990$	1.05518e156	0.0565560
$991$	−6.63369e156	−0.337201	−0.168600	−	0.985684i	$-0.553925\pi$
$991$	−6.63369e156	−0.337201	−0.168600	+	0.985684i	$0.553925\pi$
$992$	2.37908e157	1.14695
$993$	−1.84365e157	−0.843030
$994$	−4.82608e157	−2.09319
$995$	−9.91506e156	−0.407928
$996$	−1.88629e157	−0.736195
$997$	5.95950e156	0.220655	0.110328	−	0.993895i	$-0.464810\pi$
$997$	5.95950e156	0.220655	0.110328	+	0.993895i	$0.464810\pi$
$998$	−6.90422e157	−2.42528
$999$	1.63779e157	0.545847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.106.a.a.1.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.106.a.a.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-9.55432e15 q^{2} -1.37857e25 q^{3} +5.07201e31 q^{4} -2.80039e36 q^{5} +1.31713e41 q^{6} -2.78207e44 q^{7} -9.70270e46 q^{8} +6.48087e49 q^{9} +O(q^{10})\)	\(q-9.55432e15 q^{2} -1.37857e25 q^{3} +5.07201e31 q^{4} -2.80039e36 q^{5} +1.31713e41 q^{6} -2.78207e44 q^{7} -9.70270e46 q^{8} +6.48087e49 q^{9} +2.67558e52 q^{10} +6.08520e53 q^{11} -6.99212e56 q^{12} -5.49066e58 q^{13} +2.65807e60 q^{14} +3.86053e61 q^{15} -1.13043e63 q^{16} -2.90311e64 q^{17} -6.19203e65 q^{18} -1.56027e67 q^{19} -1.42036e68 q^{20} +3.83527e69 q^{21} -5.81399e69 q^{22} +5.72406e71 q^{23} +1.33759e72 q^{24} -1.68097e73 q^{25} +5.24595e74 q^{26} +8.33042e74 q^{27} -1.41107e76 q^{28} -1.76595e76 q^{29} -3.68848e77 q^{30} +1.61443e78 q^{31} +1.47363e79 q^{32} -8.38888e78 q^{33} +2.77372e80 q^{34} +7.79087e80 q^{35} +3.28711e81 q^{36} +1.96604e82 q^{37} +1.49073e83 q^{38} +7.56926e83 q^{39} +2.71714e83 q^{40} +1.17183e83 q^{41} -3.66434e85 q^{42} +1.98821e84 q^{43} +3.08642e85 q^{44} -1.81490e86 q^{45} -5.46895e87 q^{46} +1.10467e88 q^{47} +1.55837e88 q^{48} +2.30371e88 q^{49} +1.60605e89 q^{50} +4.00214e89 q^{51} -2.78487e90 q^{52} -7.34914e89 q^{53} -7.95915e90 q^{54} -1.70409e90 q^{55} +2.69936e91 q^{56} +2.15094e92 q^{57} +1.68724e92 q^{58} -1.37917e93 q^{59} +1.95807e93 q^{60} +1.74942e93 q^{61} -1.54248e94 q^{62} -1.80302e94 q^{63} -9.49400e94 q^{64} +1.53760e95 q^{65} +8.01500e94 q^{66} +1.25972e96 q^{67} -1.47246e96 q^{68} -7.89102e96 q^{69} -7.44364e96 q^{70} -1.81563e97 q^{71} -6.28820e96 q^{72} -2.37938e97 q^{73} -1.87841e98 q^{74} +2.31734e98 q^{75} -7.91371e98 q^{76} -1.69294e98 q^{77} -7.23191e99 q^{78} +8.68206e98 q^{79} +3.16563e99 q^{80} -1.96005e100 q^{81} -1.11961e99 q^{82} +2.69773e100 q^{83} +1.94526e101 q^{84} +8.12984e100 q^{85} -1.89960e100 q^{86} +2.43448e101 q^{87} -5.90429e100 q^{88} -5.78519e101 q^{89} +1.73401e102 q^{90} +1.52754e103 q^{91} +2.90325e103 q^{92} -2.22561e103 q^{93} -1.05543e104 q^{94} +4.36937e103 q^{95} -2.03151e104 q^{96} +1.53726e103 q^{97} -2.20103e104 q^{98} +3.94374e103 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 91\!\cdots\!20 q^{2}+ \cdots + 31\!\cdots\!84 q^{9}+O(q^{10}) \) 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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