LMFDB - Embedded newform 1.106.a.a.1.4

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			1.4
Root			$-9.82818e12$ 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)

$f(q)$	$=$	$q-2.56214e15 q^{2} +7.24197e24 q^{3} -3.40003e31 q^{4} -1.17115e36 q^{5} -1.85549e40 q^{6} -1.82598e44 q^{7} +1.91046e47 q^{8} -7.27906e49 q^{9} +O(q^{10})$	\(q-2.56214e15 q^{2} +7.24197e24 q^{3} -3.40003e31 q^{4} -1.17115e36 q^{5} -1.85549e40 q^{6} -1.82598e44 q^{7} +1.91046e47 q^{8} -7.27906e49 q^{9} +3.00065e51 q^{10} +6.21211e54 q^{11} -2.46229e56 q^{12} +9.87817e57 q^{13} +4.67841e59 q^{14} -8.48143e60 q^{15} +8.89729e62 q^{16} +1.10681e64 q^{17} +1.86500e65 q^{18} +1.61722e67 q^{19} +3.98194e67 q^{20} -1.32237e69 q^{21} -1.59163e70 q^{22} -2.39949e71 q^{23} +1.38355e72 q^{24} -2.32803e73 q^{25} -2.53092e73 q^{26} -1.43411e75 q^{27} +6.20838e75 q^{28} +4.95038e76 q^{29} +2.17306e76 q^{30} +8.41659e76 q^{31} -1.00294e79 q^{32} +4.49879e79 q^{33} -2.83579e79 q^{34} +2.13850e80 q^{35} +2.47490e81 q^{36} +2.33838e82 q^{37} -4.14355e82 q^{38} +7.15374e82 q^{39} -2.23744e83 q^{40} +3.56271e84 q^{41} +3.38809e84 q^{42} -2.88851e85 q^{43} -2.11214e86 q^{44} +8.52488e85 q^{45} +6.14782e86 q^{46} +8.77673e86 q^{47} +6.44339e87 q^{48} -2.10199e88 q^{49} +5.96474e88 q^{50} +8.01546e88 q^{51} -3.35860e89 q^{52} -1.32848e90 q^{53} +3.67438e90 q^{54} -7.27532e90 q^{55} -3.48846e91 q^{56} +1.17119e92 q^{57} -1.26835e92 q^{58} +9.30110e92 q^{59} +2.88371e92 q^{60} -9.36850e93 q^{61} -2.15645e92 q^{62} +1.32914e94 q^{63} -1.03951e94 q^{64} -1.15688e94 q^{65} -1.15265e95 q^{66} -4.39312e95 q^{67} -3.76317e95 q^{68} -1.73770e96 q^{69} -5.47912e95 q^{70} -2.93219e97 q^{71} -1.39064e97 q^{72} -6.72839e97 q^{73} -5.99126e97 q^{74} -1.68595e98 q^{75} -5.49860e98 q^{76} -1.13432e99 q^{77} -1.83289e98 q^{78} -7.95646e99 q^{79} -1.04201e99 q^{80} -1.26970e99 q^{81} -9.12816e99 q^{82} +6.25680e100 q^{83} +4.49609e100 q^{84} -1.29624e100 q^{85} +7.40076e100 q^{86} +3.58505e101 q^{87} +1.18680e102 q^{88} +3.11302e102 q^{89} -2.18419e101 q^{90} -1.80373e102 q^{91} +8.15832e102 q^{92} +6.09527e101 q^{93} -2.24872e102 q^{94} -1.89401e103 q^{95} -7.26323e103 q^{96} -3.96647e104 q^{97} +5.38558e103 q^{98} -4.52184e104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.56214e15	−0.402279	−0.201140	−	0.979563i	$-0.564464\pi$
$2$	−2.56214e15	−0.402279	−0.201140	+	0.979563i	$0.564464\pi$
$3$	7.24197e24	0.647129	0.323564	−	0.946206i	$-0.395119\pi$
$3$	7.24197e24	0.647129	0.323564	+	0.946206i	$0.395119\pi$
$4$	−3.40003e31	−0.838171
$5$	−1.17115e36	−0.235878	−0.117939	−	0.993021i	$-0.537629\pi$
$5$	−1.17115e36	−0.235878	−0.117939	+	0.993021i	$0.537629\pi$
$6$	−1.85549e40	−0.260326
$7$	−1.82598e44	−0.783156	−0.391578	−	0.920145i	$-0.628071\pi$
$7$	−1.82598e44	−0.783156	−0.391578	+	0.920145i	$0.628071\pi$
$8$	1.91046e47	0.739458
$9$	−7.27906e49	−0.581224
$10$	3.00065e51	0.0948888
$11$	6.21211e54	1.31863	0.659316	−	0.751866i	$-0.270846\pi$
$11$	6.21211e54	1.31863	0.659316	+	0.751866i	$0.270846\pi$
$12$	−2.46229e56	−0.542405
$13$	9.87817e57	0.325575	0.162787	−	0.986661i	$-0.447952\pi$
$13$	9.87817e57	0.325575	0.162787	+	0.986661i	$0.447952\pi$
$14$	4.67841e59	0.315048
$15$	−8.48143e60	−0.152643
$16$	8.89729e62	0.540703
$17$	1.10681e64	0.278935	0.139468	−	0.990227i	$-0.455461\pi$
$17$	1.10681e64	0.278935	0.139468	+	0.990227i	$0.455461\pi$
$18$	1.86500e65	0.233814
$19$	1.61722e67	1.18633	0.593165	−	0.805081i	$-0.297878\pi$
$19$	1.61722e67	1.18633	0.593165	+	0.805081i	$0.297878\pi$
$20$	3.98194e67	0.197706
$21$	−1.32237e69	−0.506803
$22$	−1.59163e70	−0.530458
$23$	−2.39949e71	−0.775188	−0.387594	−	0.921830i	$-0.626694\pi$
$23$	−2.39949e71	−0.775188	−0.387594	+	0.921830i	$0.626694\pi$
$24$	1.38355e72	0.478525
$25$	−2.32803e73	−0.944362
$26$	−2.53092e73	−0.130972
$27$	−1.43411e75	−1.02326
$28$	6.20838e75	0.656419
$29$	4.95038e76	0.829360	0.414680	−	0.909967i	$-0.363893\pi$
$29$	4.95038e76	0.829360	0.414680	+	0.909967i	$0.363893\pi$
$30$	2.17306e76	0.0614053
$31$	8.41659e76	0.0425253	0.0212627	−	0.999774i	$-0.493231\pi$
$31$	8.41659e76	0.0425253	0.0212627	+	0.999774i	$0.493231\pi$
$32$	−1.00294e79	−0.956972
$33$	4.49879e79	0.853324
$34$	−2.83579e79	−0.112210
$35$	2.13850e80	0.184729
$36$	2.47490e81	0.487166
$37$	2.33838e82	1.09226	0.546129	−	0.837701i	$-0.316101\pi$
$37$	2.33838e82	1.09226	0.546129	+	0.837701i	$0.316101\pi$
$38$	−4.14355e82	−0.477236
$39$	7.15374e82	0.210689
$40$	−2.23744e83	−0.174422
$41$	3.56271e84	0.759676	0.379838	−	0.925053i	$-0.375980\pi$
$41$	3.56271e84	0.759676	0.379838	+	0.925053i	$0.375980\pi$
$42$	3.38809e84	0.203876
$43$	−2.88851e85	−0.505336	−0.252668	−	0.967553i	$-0.581308\pi$
$43$	−2.88851e85	−0.505336	−0.252668	+	0.967553i	$0.581308\pi$
$44$	−2.11214e86	−1.10524
$45$	8.52488e85	0.137098
$46$	6.14782e86	0.311842
$47$	8.77673e86	0.143944	0.0719722	−	0.997407i	$-0.477071\pi$
$47$	8.77673e86	0.143944	0.0719722	+	0.997407i	$0.477071\pi$
$48$	6.44339e87	0.349904
$49$	−2.10199e88	−0.386666
$50$	5.96474e88	0.379897
$51$	8.01546e88	0.180507
$52$	−3.35860e89	−0.272887
$53$	−1.32848e90	−0.397074	−0.198537	−	0.980093i	$-0.563619\pi$
$53$	−1.32848e90	−0.397074	−0.198537	+	0.980093i	$0.563619\pi$
$54$	3.67438e90	0.411635
$55$	−7.27532e90	−0.311036
$56$	−3.48846e91	−0.579111
$57$	1.17119e92	0.767709
$58$	−1.26835e92	−0.333634
$59$	9.30110e92	0.997250	0.498625	−	0.866818i	$-0.333839\pi$
$59$	9.30110e92	0.997250	0.498625	+	0.866818i	$0.333839\pi$
$60$	2.88371e92	0.127941
$61$	−9.36850e93	−1.74523	−0.872617	−	0.488406i	$-0.837579\pi$
$61$	−9.36850e93	−1.74523	−0.872617	+	0.488406i	$0.837579\pi$
$62$	−2.15645e92	−0.0171070
$63$	1.32914e94	0.455190
$64$	−1.03951e94	−0.155733
$65$	−1.15688e94	−0.0767959
$66$	−1.15265e95	−0.343275
$67$	−4.39312e95	−0.594081	−0.297040	−	0.954865i	$-0.596000\pi$
$67$	−4.39312e95	−0.594081	−0.297040	+	0.954865i	$0.596000\pi$
$68$	−3.76317e95	−0.233796
$69$	−1.73770e96	−0.501647
$70$	−5.47912e95	−0.0743128
$71$	−2.93219e97	−1.88855	−0.944276	−	0.329154i	$-0.893236\pi$
$71$	−2.93219e97	−1.88855	−0.944276	+	0.329154i	$0.893236\pi$
$72$	−1.39064e97	−0.429791
$73$	−6.72839e97	−1.00800	−0.504000	−	0.863703i	$-0.668139\pi$
$73$	−6.72839e97	−1.00800	−0.504000	+	0.863703i	$0.668139\pi$
$74$	−5.99126e97	−0.439393
$75$	−1.68595e98	−0.611124
$76$	−5.49860e98	−0.994349
$77$	−1.13432e99	−1.03269
$78$	−1.83289e98	−0.0847557
$79$	−7.95646e99	−1.88494	−0.942470	−	0.334290i	$-0.891503\pi$
$79$	−7.95646e99	−1.88494	−0.942470	+	0.334290i	$0.891503\pi$
$80$	−1.04201e99	−0.127540
$81$	−1.26970e99	−0.0809539
$82$	−9.12816e99	−0.305602
$83$	6.25680e100	1.10854	0.554272	−	0.832336i	$-0.312997\pi$
$83$	6.25680e100	1.10854	0.554272	+	0.832336i	$0.312997\pi$
$84$	4.49609e100	0.424788
$85$	−1.29624e100	−0.0657947
$86$	7.40076e100	0.203286
$87$	3.58505e101	0.536703
$88$	1.18680e102	0.975073
$89$	3.11302e102	1.41321	0.706606	−	0.707607i	$-0.250225\pi$
$89$	3.11302e102	1.41321	0.706606	+	0.707607i	$0.250225\pi$
$90$	−2.18419e101	−0.0551517
$91$	−1.80373e102	−0.254976
$92$	8.15832e102	0.649740
$93$	6.09527e101	0.0275193
$94$	−2.24872e102	−0.0579059
$95$	−1.89401e103	−0.279829
$96$	−7.26323e103	−0.619284
$97$	−3.96647e104	−1.96285	−0.981427	−	0.191838i	$-0.938555\pi$
$97$	−3.96647e104	−1.96285	−0.981427	+	0.191838i	$0.938555\pi$
$98$	5.38558e103	0.155548
$99$	−4.52184e104	−0.766421
$100$	7.91537e104	0.791537
$101$	−1.19764e105	−0.710319	−0.355160	−	0.934806i	$-0.615573\pi$
$101$	−1.19764e105	−0.710319	−0.355160	+	0.934806i	$0.615573\pi$
$102$	−2.05367e104	−0.0726142
$103$	1.60564e105	0.340169	0.170085	−	0.985429i	$-0.445596\pi$
$103$	1.60564e105	0.340169	0.170085	+	0.985429i	$0.445596\pi$
$104$	1.88718e105	0.240749
$105$	1.54869e105	0.119544
$106$	3.40374e105	0.159734
$107$	4.52744e106	1.29779	0.648895	−	0.760878i	$-0.275231\pi$
$107$	4.52744e106	1.29779	0.648895	+	0.760878i	$0.275231\pi$
$108$	4.87601e106	0.857664
$109$	−1.52154e106	−0.164965	−0.0824826	−	0.996593i	$-0.526285\pi$
$109$	−1.52154e106	−0.164965	−0.0824826	+	0.996593i	$0.526285\pi$
$110$	1.86404e106	0.125123
$111$	1.69345e107	0.706832
$112$	−1.62463e107	−0.423455
$113$	−9.69099e107	−1.58398	−0.791990	−	0.610534i	$-0.790955\pi$
$113$	−9.69099e107	−1.58398	−0.791990	+	0.610534i	$0.790955\pi$
$114$	−3.00074e107	−0.308833
$115$	2.81016e107	0.182850
$116$	−1.68314e108	−0.695146
$117$	−7.19038e107	−0.189232
$118$	−2.38307e108	−0.401173
$119$	−2.02101e108	−0.218450
$120$	−1.62034e108	−0.112873
$121$	1.63965e109	0.738789
$122$	2.40034e109	0.702071
$123$	2.58011e109	0.491608
$124$	−2.86166e108	−0.0356435
$125$	5.61358e109	0.458632
$126$	−3.40544e109	−0.183113
$127$	9.27636e109	0.329369	0.164684	−	0.986346i	$-0.447339\pi$
$127$	9.27636e109	0.329369	0.164684	+	0.986346i	$0.447339\pi$
$128$	4.33473e110	1.01962
$129$	−2.09185e110	−0.327017
$130$	2.96409e109	0.0308934
$131$	−2.18559e111	−1.52344	−0.761721	−	0.647905i	$-0.775645\pi$
$131$	−2.18559e111	−1.52344	−0.761721	+	0.647905i	$0.775645\pi$
$132$	−1.52960e111	−0.715232
$133$	−2.95301e111	−0.929083
$134$	1.12558e111	0.238986
$135$	1.67956e111	0.241364
$136$	2.11451e111	0.206261
$137$	−3.76107e111	−0.249736	−0.124868	−	0.992173i	$-0.539851\pi$
$137$	−3.76107e111	−0.249736	−0.124868	+	0.992173i	$0.539851\pi$
$138$	4.45223e111	0.201802
$139$	3.64309e112	1.13030	0.565149	−	0.824989i	$-0.308819\pi$
$139$	3.64309e112	1.13030	0.565149	+	0.824989i	$0.308819\pi$
$140$	−7.27094e111	−0.154835
$141$	6.35608e111	0.0931506
$142$	7.51268e112	0.759725
$143$	6.13643e112	0.429313
$144$	−6.47639e112	−0.314270
$145$	−5.79763e112	−0.195628
$146$	1.72391e113	0.405498
$147$	−1.52225e113	−0.250223
$148$	−7.95057e113	−0.915500
$149$	−6.94410e113	−0.561483	−0.280742	−	0.959783i	$-0.590580\pi$
$149$	−6.94410e113	−0.561483	−0.280742	+	0.959783i	$0.590580\pi$
$150$	4.31964e113	0.245842
$151$	−4.13611e114	−1.66074	−0.830372	−	0.557210i	$-0.811872\pi$
$151$	−4.13611e114	−1.66074	−0.830372	+	0.557210i	$0.811872\pi$
$152$	3.08964e114	0.877242
$153$	−8.05652e113	−0.162124
$154$	2.90628e114	0.415432
$155$	−9.85710e112	−0.0100308
$156$	−2.43229e114	−0.176593
$157$	2.62565e115	1.36303	0.681515	−	0.731804i	$-0.261321\pi$
$157$	2.62565e115	1.36303	0.681515	+	0.731804i	$0.261321\pi$
$158$	2.03855e115	0.758272
$159$	−9.62079e114	−0.256958
$160$	1.17459e115	0.225729
$161$	4.38141e115	0.607094
$162$	3.25315e114	0.0325661
$163$	−2.06745e116	−1.49825	−0.749126	−	0.662428i	$-0.769526\pi$
$163$	−2.06745e116	−1.49825	−0.749126	+	0.662428i	$0.769526\pi$
$164$	−1.21133e116	−0.636739
$165$	−5.26876e115	−0.201280
$166$	−1.60308e116	−0.445944
$167$	6.33450e116	1.28558	0.642788	−	0.766044i	$-0.277778\pi$
$167$	6.33450e116	1.28558	0.642788	+	0.766044i	$0.277778\pi$
$168$	−2.52633e116	−0.374760
$169$	−8.22982e116	−0.894001
$170$	3.32114e115	0.0264678
$171$	−1.17719e117	−0.689524
$172$	9.82101e116	0.423558
$173$	4.01565e117	1.27742	0.638712	−	0.769446i	$-0.279468\pi$
$173$	4.01565e117	1.27742	0.638712	+	0.769446i	$0.279468\pi$
$174$	−9.18538e116	−0.215904
$175$	4.25093e117	0.739583
$176$	5.52710e117	0.712988
$177$	6.73583e117	0.645349
$178$	−7.97600e117	−0.568506
$179$	−1.42554e118	−0.757175	−0.378587	−	0.925566i	$-0.623590\pi$
$179$	−1.42554e118	−0.757175	−0.378587	+	0.925566i	$0.623590\pi$
$180$	−2.89848e117	−0.114912
$181$	1.74104e117	0.0516041	0.0258021	−	0.999667i	$-0.491786\pi$
$181$	1.74104e117	0.0516041	0.0258021	+	0.999667i	$0.491786\pi$
$182$	4.62141e117	0.102571
$183$	−6.78463e118	−1.12939
$184$	−4.58412e118	−0.573219
$185$	−2.73860e118	−0.257640
$186$	−1.56169e117	−0.0110705
$187$	6.87561e118	0.367813
$188$	−2.98411e118	−0.120650
$189$	2.61865e119	0.801369
$190$	4.85272e118	0.112570
$191$	3.92171e119	0.690595	0.345297	−	0.938493i	$-0.387778\pi$
$191$	3.92171e119	0.690595	0.345297	+	0.938493i	$0.387778\pi$
$192$	−7.52810e118	−0.100779
$193$	5.37554e118	0.0547852	0.0273926	−	0.999625i	$-0.491280\pi$
$193$	5.37554e118	0.0547852	0.0273926	+	0.999625i	$0.491280\pi$
$194$	1.01626e120	0.789615
$195$	−8.37810e118	−0.0496968
$196$	7.14681e119	0.324092
$197$	−4.45142e120	−1.54533	−0.772667	−	0.634812i	$-0.781078\pi$
$197$	−4.45142e120	−1.54533	−0.772667	+	0.634812i	$0.781078\pi$
$198$	1.15856e120	0.308315
$199$	1.12654e120	0.230122	0.115061	−	0.993358i	$-0.463294\pi$
$199$	1.12654e120	0.230122	0.115061	+	0.993358i	$0.463294\pi$
$200$	−4.44761e120	−0.698316
$201$	−3.18148e120	−0.384447
$202$	3.06851e120	0.285747
$203$	−9.03928e120	−0.649519
$204$	−2.72528e120	−0.151296
$205$	−4.17247e120	−0.179191
$206$	−4.11388e120	−0.136843
$207$	1.74660e121	0.450558
$208$	8.78889e120	0.176039
$209$	1.00464e122	1.56433
$210$	−3.96796e120	−0.0480899
$211$	1.16814e122	1.10323	0.551615	−	0.834099i	$-0.314012\pi$
$211$	1.16814e122	1.10323	0.551615	+	0.834099i	$0.314012\pi$
$212$	4.51686e121	0.332816
$213$	−2.12348e122	−1.22214
$214$	−1.15999e122	−0.522074
$215$	3.38288e121	0.119198
$216$	−2.73981e122	−0.756655
$217$	−1.53685e121	−0.0333040
$218$	3.89839e121	0.0663620
$219$	−4.87268e122	−0.652306
$220$	2.47363e122	0.260702
$221$	1.09332e122	0.0908142
$222$	−4.33885e122	−0.284344
$223$	−2.12569e123	−1.10026	−0.550130	−	0.835079i	$-0.685422\pi$
$223$	−2.12569e123	−1.10026	−0.550130	+	0.835079i	$0.685422\pi$
$224$	1.83134e123	0.749459
$225$	1.69459e123	0.548886
$226$	2.48296e123	0.637202
$227$	5.43051e123	1.10531	0.552654	−	0.833411i	$-0.313615\pi$
$227$	5.43051e123	1.10531	0.552654	+	0.833411i	$0.313615\pi$
$228$	−3.98207e123	−0.643472
$229$	3.86165e123	0.495919	0.247959	−	0.968770i	$-0.420240\pi$
$229$	3.86165e123	0.495919	0.247959	+	0.968770i	$0.420240\pi$
$230$	−7.20002e122	−0.0735567
$231$	−8.21470e123	−0.668286
$232$	9.45749e123	0.613277
$233$	−2.50053e123	−0.129374	−0.0646868	−	0.997906i	$-0.520605\pi$
$233$	−2.50053e123	−0.129374	−0.0646868	+	0.997906i	$0.520605\pi$
$234$	1.84227e123	0.0761241
$235$	−1.02789e123	−0.0339533
$236$	−3.16240e124	−0.835866
$237$	−5.76204e124	−1.21980
$238$	5.17809e123	0.0878779
$239$	2.77950e124	0.378509	0.189255	−	0.981928i	$-0.439393\pi$
$239$	2.77950e124	0.378509	0.189255	+	0.981928i	$0.439393\pi$
$240$	−7.54617e123	−0.0825347
$241$	−7.57110e124	−0.665678	−0.332839	−	0.942984i	$-0.608007\pi$
$241$	−7.57110e124	−0.665678	−0.332839	+	0.942984i	$0.608007\pi$
$242$	−4.20102e124	−0.297199
$243$	1.70408e125	0.970868
$244$	3.18531e125	1.46280
$245$	2.46174e124	0.0912060
$246$	−6.61059e124	−0.197764
$247$	1.59752e125	0.386239
$248$	1.60796e124	0.0314457
$249$	4.53116e125	0.717370
$250$	−1.43828e125	−0.184498
$251$	−6.06940e125	−0.631357	−0.315679	−	0.948866i	$-0.602232\pi$
$251$	−6.06940e125	−0.631357	−0.315679	+	0.948866i	$0.602232\pi$
$252$	−4.51912e125	−0.381527
$253$	−1.49059e126	−1.02219
$254$	−2.37673e125	−0.132498
$255$	−9.38731e124	−0.0425776
$256$	−6.88941e125	−0.254439
$257$	2.79612e126	0.841525	0.420762	−	0.907171i	$-0.361763\pi$
$257$	2.79612e126	0.841525	0.420762	+	0.907171i	$0.361763\pi$
$258$	5.35961e125	0.131552
$259$	−4.26984e126	−0.855409
$260$	3.93343e125	0.0643681
$261$	−3.60341e126	−0.482044
$262$	5.59979e126	0.612849
$263$	2.58860e126	0.231946	0.115973	−	0.993252i	$-0.463001\pi$
$263$	2.58860e126	0.231946	0.115973	+	0.993252i	$0.463001\pi$
$264$	8.59476e126	0.630998
$265$	1.55585e126	0.0936609
$266$	7.56603e126	0.373751
$267$	2.25444e127	0.914530
$268$	1.49367e127	0.497941
$269$	−3.07299e127	−0.842493	−0.421247	−	0.906946i	$-0.638407\pi$
$269$	−3.07299e127	−0.842493	−0.421247	+	0.906946i	$0.638407\pi$
$270$	−4.30325e126	−0.0970955
$271$	−6.80647e127	−1.26484	−0.632418	−	0.774627i	$-0.717937\pi$
$271$	−6.80647e127	−1.26484	−0.632418	+	0.774627i	$0.717937\pi$
$272$	9.84758e126	0.150821
$273$	−1.30626e127	−0.165002
$274$	9.63637e126	0.100464
$275$	−1.44620e128	−1.24526
$276$	5.90823e127	0.420466
$277$	4.37682e127	0.257615	0.128807	−	0.991670i	$-0.458885\pi$
$277$	4.37682e127	0.257615	0.128807	+	0.991670i	$0.458885\pi$
$278$	−9.33409e127	−0.454695
$279$	−6.12649e126	−0.0247167
$280$	4.08551e127	0.136600
$281$	3.24288e127	0.0899184	0.0449592	−	0.998989i	$-0.485684\pi$
$281$	3.24288e127	0.0899184	0.0449592	+	0.998989i	$0.485684\pi$
$282$	−1.62851e127	−0.0374726
$283$	5.75459e128	1.09958	0.549789	−	0.835303i	$-0.314708\pi$
$283$	5.75459e128	1.09958	0.549789	+	0.835303i	$0.314708\pi$
$284$	9.96953e128	1.58293
$285$	−1.37164e128	−0.181086
$286$	−1.57224e128	−0.172704
$287$	−6.50544e128	−0.594945
$288$	7.30043e128	0.556215
$289$	−1.45198e129	−0.922195
$290$	1.48543e128	0.0786970
$291$	−2.87250e129	−1.27022
$292$	2.28767e129	0.844878
$293$	−2.15304e129	−0.664512	−0.332256	−	0.943189i	$-0.607810\pi$
$293$	−2.15304e129	−0.664512	−0.332256	+	0.943189i	$0.607810\pi$
$294$	3.90022e128	0.100659
$295$	−1.08930e129	−0.235229
$296$	4.46739e129	0.807679
$297$	−8.90884e129	−1.34930
$298$	1.77917e129	0.225873
$299$	−2.37025e129	−0.252382
$300$	5.73228e129	0.512226
$301$	5.27436e129	0.395757
$302$	1.05973e130	0.668083
$303$	−8.67326e129	−0.459668
$304$	1.43889e130	0.641452
$305$	1.09719e130	0.411662
$306$	2.06419e129	0.0652191
$307$	−1.55007e130	−0.412654	−0.206327	−	0.978483i	$-0.566151\pi$
$307$	−1.55007e130	−0.412654	−0.206327	+	0.978483i	$0.566151\pi$
$308$	3.85671e130	0.865575
$309$	1.16280e130	0.220133
$310$	2.52552e128	0.00403518
$311$	−1.05354e131	−1.42145	−0.710724	−	0.703471i	$-0.751633\pi$
$311$	−1.05354e131	−1.42145	−0.710724	+	0.703471i	$0.751633\pi$
$312$	1.36669e130	0.155795
$313$	−1.51544e131	−1.46036	−0.730181	−	0.683253i	$-0.760564\pi$
$313$	−1.51544e131	−1.46036	−0.730181	+	0.683253i	$0.760564\pi$
$314$	−6.72729e130	−0.548319
$315$	−1.55662e130	−0.107369
$316$	2.70522e131	1.57990
$317$	−3.01876e131	−1.49354	−0.746770	−	0.665083i	$-0.768396\pi$
$317$	−3.01876e131	−1.49354	−0.746770	+	0.665083i	$0.768396\pi$
$318$	2.46498e130	0.103369
$319$	3.07523e131	1.09362
$320$	1.21742e130	0.0367340
$321$	3.27876e131	0.839837
$322$	−1.12258e131	−0.244221
$323$	1.78995e131	0.330910
$324$	4.31702e130	0.0678532
$325$	−2.29967e131	−0.307460
$326$	5.29708e131	0.602716
$327$	−1.10189e131	−0.106754
$328$	6.80642e131	0.561749
$329$	−1.60261e131	−0.112731
$330$	1.34993e131	0.0809709
$331$	−1.11942e132	−0.572828	−0.286414	−	0.958106i	$-0.592463\pi$
$331$	−1.11942e132	−0.572828	−0.286414	+	0.958106i	$0.592463\pi$
$332$	−2.12733e132	−0.929150
$333$	−1.70212e132	−0.634847
$334$	−1.62299e132	−0.517160
$335$	5.14500e131	0.140131
$336$	−1.17655e132	−0.274030
$337$	6.42673e132	1.28062	0.640310	−	0.768117i	$-0.278806\pi$
$337$	6.42673e132	1.28062	0.640310	+	0.768117i	$0.278806\pi$
$338$	2.10859e132	0.359638
$339$	−7.01818e132	−1.02504
$340$	4.40724e131	0.0551472
$341$	5.22848e131	0.0560752
$342$	3.01611e132	0.277381
$343$	1.37645e133	1.08598
$344$	−5.51838e132	−0.373675
$345$	2.03511e132	0.118327
$346$	−1.02886e133	−0.513881
$347$	2.99641e133	1.28619	0.643093	−	0.765788i	$-0.277651\pi$
$347$	2.99641e133	1.28619	0.643093	+	0.765788i	$0.277651\pi$
$348$	−1.21893e133	−0.449849
$349$	4.87919e133	1.54886	0.774431	−	0.632659i	$-0.218036\pi$
$349$	4.87919e133	1.54886	0.774431	+	0.632659i	$0.218036\pi$
$350$	−1.08915e133	−0.297519
$351$	−1.41664e133	−0.333146
$352$	−6.23035e133	−1.26189
$353$	−5.34299e133	−0.932421	−0.466210	−	0.884674i	$-0.654381\pi$
$353$	−5.34299e133	−0.932421	−0.466210	+	0.884674i	$0.654381\pi$
$354$	−1.72581e133	−0.259611
$355$	3.43404e133	0.445468
$356$	−1.05844e134	−1.18451
$357$	−1.46361e133	−0.141365
$358$	3.65244e133	0.304596
$359$	7.64396e133	0.550630	0.275315	−	0.961354i	$-0.411218\pi$
$359$	7.64396e133	0.550630	0.275315	+	0.961354i	$0.411218\pi$
$360$	1.62864e133	0.101378
$361$	7.57057e133	0.407381
$362$	−4.46079e132	−0.0207593
$363$	1.18743e134	0.478091
$364$	6.13274e133	0.213713
$365$	7.87995e133	0.237765
$366$	1.73832e134	0.454330
$367$	2.15324e134	0.487669	0.243834	−	0.969817i	$-0.421595\pi$
$367$	2.15324e134	0.487669	0.243834	+	0.969817i	$0.421595\pi$
$368$	−2.13489e134	−0.419146
$369$	−2.59332e134	−0.441542
$370$	7.01667e133	0.103643
$371$	2.42577e134	0.310971
$372$	−2.07241e133	−0.0230659
$373$	−1.48002e135	−1.43072	−0.715358	−	0.698758i	$-0.753737\pi$
$373$	−1.48002e135	−1.43072	−0.715358	+	0.698758i	$0.753737\pi$
$374$	−1.76163e134	−0.147963
$375$	4.06534e134	0.296794
$376$	1.67676e134	0.106441
$377$	4.89006e134	0.270019
$378$	−6.70934e134	−0.322374
$379$	−3.14867e135	−1.31695	−0.658474	−	0.752604i	$-0.728798\pi$
$379$	−3.14867e135	−1.31695	−0.658474	+	0.752604i	$0.728798\pi$
$380$	6.43969e134	0.234545
$381$	6.71791e134	0.213144
$382$	−1.00479e135	−0.277812
$383$	2.26604e135	0.546176	0.273088	−	0.961989i	$-0.411955\pi$
$383$	2.26604e135	0.546176	0.273088	+	0.961989i	$0.411955\pi$
$384$	3.13919e135	0.659825
$385$	1.32846e135	0.243590
$386$	−1.37729e134	−0.0220389
$387$	2.10256e135	0.293713
$388$	1.34861e136	1.64521
$389$	−7.51665e135	−0.801070	−0.400535	−	0.916281i	$-0.631176\pi$
$389$	−7.51665e135	−0.801070	−0.400535	+	0.916281i	$0.631176\pi$
$390$	2.14659e134	0.0199920
$391$	−2.65577e135	−0.216227
$392$	−4.01576e135	−0.285923
$393$	−1.58280e136	−0.985863
$394$	1.14052e136	0.621656
$395$	9.31821e135	0.444616
$396$	1.53744e136	0.642392
$397$	−4.62294e136	−1.69206	−0.846031	−	0.533133i	$-0.821014\pi$
$397$	−4.62294e136	−1.69206	−0.846031	+	0.533133i	$0.821014\pi$
$398$	−2.88634e135	−0.0925733
$399$	−2.13856e136	−0.601236
$400$	−2.07132e136	−0.510619
$401$	−1.12123e136	−0.242446	−0.121223	−	0.992625i	$-0.538682\pi$
$401$	−1.12123e136	−0.242446	−0.121223	+	0.992625i	$0.538682\pi$
$402$	8.15139e135	0.154655
$403$	8.31405e134	0.0138452
$404$	4.07200e136	0.595369
$405$	1.48701e135	0.0190952
$406$	2.31599e136	0.261288
$407$	1.45263e137	1.44029
$408$	1.53132e136	0.133477
$409$	8.99941e136	0.689827	0.344914	−	0.938634i	$-0.387908\pi$
$409$	8.99941e136	0.689827	0.344914	+	0.938634i	$0.387908\pi$
$410$	1.06905e136	0.0720848
$411$	−2.72375e136	−0.161611
$412$	−5.45923e136	−0.285120
$413$	−1.69836e137	−0.781003
$414$	−4.47503e136	−0.181250
$415$	−7.32766e136	−0.261481
$416$	−9.90717e136	−0.311566
$417$	2.63831e137	0.731448
$418$	−2.57402e137	−0.629299
$419$	2.61797e137	0.564584	0.282292	−	0.959329i	$-0.408905\pi$
$419$	2.61797e137	0.564584	0.282292	+	0.959329i	$0.408905\pi$
$420$	−5.26559e136	−0.100198
$421$	−4.32460e137	−0.726333	−0.363166	−	0.931724i	$-0.618304\pi$
$421$	−4.32460e137	−0.726333	−0.363166	+	0.931724i	$0.618304\pi$
$422$	−2.99294e137	−0.443807
$423$	−6.38864e136	−0.0836640
$424$	−2.53800e137	−0.293619
$425$	−2.57668e137	−0.263416
$426$	5.44066e137	0.491640
$427$	1.71067e138	1.36679
$428$	−1.53934e138	−1.08777
$429$	4.44398e137	0.277821
$430$	−8.66740e136	−0.0479507
$431$	2.80133e138	1.37185	0.685926	−	0.727672i	$-0.259397\pi$
$431$	2.80133e138	1.37185	0.685926	+	0.727672i	$0.259397\pi$
$432$	−1.27597e138	−0.553277
$433$	3.15333e138	1.21103	0.605516	−	0.795833i	$-0.292967\pi$
$433$	3.15333e138	1.21103	0.605516	+	0.795833i	$0.292967\pi$
$434$	3.93763e136	0.0133975
$435$	−4.19863e137	−0.126596
$436$	5.17328e137	0.138269
$437$	−3.88051e138	−0.919630
$438$	1.24845e138	0.262409
$439$	−2.85338e138	−0.532075	−0.266037	−	0.963963i	$-0.585714\pi$
$439$	−2.85338e138	−0.532075	−0.266037	+	0.963963i	$0.585714\pi$
$440$	−1.38992e138	−0.229998
$441$	1.53005e138	0.224740
$442$	−2.80124e137	−0.0365327
$443$	−8.53493e138	−0.988564	−0.494282	−	0.869302i	$-0.664569\pi$
$443$	−8.53493e138	−0.988564	−0.494282	+	0.869302i	$0.664569\pi$
$444$	−5.75778e138	−0.592446
$445$	−3.64582e138	−0.333346
$446$	5.44632e138	0.442612
$447$	−5.02889e138	−0.363352
$448$	1.89812e138	0.121963
$449$	1.33416e139	0.762563	0.381282	−	0.924459i	$-0.375483\pi$
$449$	1.33416e139	0.762563	0.381282	+	0.924459i	$0.375483\pi$
$450$	−4.34177e138	−0.220805
$451$	2.21320e139	1.00173
$452$	3.29496e139	1.32765
$453$	−2.99536e139	−1.07471
$454$	−1.39137e139	−0.444643
$455$	2.11244e138	0.0601432
$456$	2.23751e139	0.567689
$457$	5.91284e139	1.33720	0.668599	−	0.743623i	$-0.266894\pi$
$457$	5.91284e139	1.33720	0.668599	+	0.743623i	$0.266894\pi$
$458$	−9.89409e138	−0.199498
$459$	−1.58728e139	−0.285422
$460$	−9.55462e138	−0.153259
$461$	−3.82087e139	−0.546844	−0.273422	−	0.961894i	$-0.588155\pi$
$461$	−3.82087e139	−0.546844	−0.273422	+	0.961894i	$0.588155\pi$
$462$	2.10472e139	0.268838
$463$	−1.58389e140	−1.80602	−0.903012	−	0.429616i	$-0.858649\pi$
$463$	−1.58389e140	−1.80602	−0.903012	+	0.429616i	$0.858649\pi$
$464$	4.40449e139	0.448437
$465$	−7.13848e137	−0.00649121
$466$	6.40669e138	0.0520443
$467$	−1.90647e140	−1.38386	−0.691932	−	0.721962i	$-0.743240\pi$
$467$	−1.90647e140	−1.38386	−0.691932	+	0.721962i	$0.743240\pi$
$468$	2.44475e139	0.158609
$469$	8.02173e139	0.465258
$470$	2.63359e138	0.0136587
$471$	1.90149e140	0.882056
$472$	1.77694e140	0.737425
$473$	−1.79438e140	−0.666351
$474$	1.47631e140	0.490700
$475$	−3.76495e140	−1.12033
$476$	6.87147e139	0.183099
$477$	9.67007e139	0.230789
$478$	−7.12146e139	−0.152266
$479$	6.06845e140	1.16269	0.581344	−	0.813658i	$-0.302527\pi$
$479$	6.06845e140	1.16269	0.581344	+	0.813658i	$0.302527\pi$
$480$	8.50633e139	0.146075
$481$	2.30990e140	0.355611
$482$	1.93982e140	0.267788
$483$	3.17300e140	0.392868
$484$	−5.57487e140	−0.619232
$485$	4.64533e140	0.462994
$486$	−4.36608e140	−0.390560
$487$	−6.06707e140	−0.487201	−0.243601	−	0.969876i	$-0.578329\pi$
$487$	−6.06707e140	−0.487201	−0.243601	+	0.969876i	$0.578329\pi$
$488$	−1.78981e141	−1.29053
$489$	−1.49724e141	−0.969562
$490$	−6.30732e139	−0.0366903
$491$	8.94476e140	0.467509	0.233755	−	0.972296i	$-0.424899\pi$
$491$	8.94476e140	0.467509	0.233755	+	0.972296i	$0.424899\pi$
$492$	−8.77243e140	−0.412052
$493$	5.47911e140	0.231338
$494$	−4.09307e140	−0.155376
$495$	5.29575e140	0.180782
$496$	7.48849e139	0.0229935
$497$	5.35412e141	1.47903
$498$	−1.16094e141	−0.288583
$499$	6.99369e140	0.156469	0.0782344	−	0.996935i	$-0.475072\pi$
$499$	6.99369e140	0.156469	0.0782344	+	0.996935i	$0.475072\pi$
$500$	−1.90863e141	−0.384412
$501$	4.58742e141	0.831933
$502$	1.55506e141	0.253982
$503$	−9.78558e140	−0.143968	−0.0719842	−	0.997406i	$-0.522933\pi$
$503$	−9.78558e140	−0.143968	−0.0719842	+	0.997406i	$0.522933\pi$
$504$	2.53927e141	0.336594
$505$	1.40261e141	0.167549
$506$	3.81909e141	0.411205
$507$	−5.96001e141	−0.578534
$508$	−3.15399e141	−0.276067
$509$	−6.84286e141	−0.540199	−0.270100	−	0.962832i	$-0.587057\pi$
$509$	−6.84286e141	−0.540199	−0.270100	+	0.962832i	$0.587057\pi$
$510$	2.40516e140	0.0171281
$511$	1.22859e142	0.789422
$512$	−1.58186e142	−0.917264
$513$	−2.31927e142	−1.21392
$514$	−7.16404e141	−0.338528
$515$	−1.88045e141	−0.0802384
$516$	7.11235e141	0.274096
$517$	5.45220e141	0.189810
$518$	1.09399e142	0.344113
$519$	2.90812e142	0.826658
$520$	−2.21018e141	−0.0567873
$521$	−6.61502e142	−1.53656	−0.768282	−	0.640111i	$-0.778888\pi$
$521$	−6.61502e142	−1.53656	−0.768282	+	0.640111i	$0.778888\pi$
$522$	9.23243e141	0.193916
$523$	2.02789e142	0.385218	0.192609	−	0.981276i	$-0.438305\pi$
$523$	2.02789e142	0.385218	0.192609	+	0.981276i	$0.438305\pi$
$524$	7.43107e142	1.27691
$525$	3.07851e142	0.478605
$526$	−6.63234e141	−0.0933072
$527$	9.31554e140	0.0118618
$528$	4.00271e142	0.461395
$529$	−3.82372e142	−0.399083
$530$	−3.98629e141	−0.0376778
$531$	−6.77033e142	−0.579626
$532$	1.00403e143	0.778731
$533$	3.51931e142	0.247331
$534$	−5.77619e142	−0.367896
$535$	−5.30231e142	−0.306120
$536$	−8.39287e142	−0.439298
$537$	−1.03237e143	−0.489990
$538$	7.87342e142	0.338918
$539$	−1.30578e143	−0.509870
$540$	−5.71054e142	−0.202304
$541$	−2.71630e143	−0.873214	−0.436607	−	0.899652i	$-0.643820\pi$
$541$	−2.71630e143	−0.873214	−0.436607	+	0.899652i	$0.643820\pi$
$542$	1.74391e143	0.508817
$543$	1.26086e142	0.0333945
$544$	−1.11006e143	−0.266933
$545$	1.78195e142	0.0389116
$546$	3.34681e142	0.0663770
$547$	−1.10405e142	−0.0198909	−0.00994546	−	0.999951i	$-0.503166\pi$
$547$	−1.10405e142	−0.0198909	−0.00994546	+	0.999951i	$0.503166\pi$
$548$	1.27877e143	0.209322
$549$	6.81939e143	1.01437
$550$	3.70536e143	0.500944
$551$	8.00586e143	0.983896
$552$	−3.31981e143	−0.370947
$553$	1.45283e144	1.47620
$554$	−1.12140e143	−0.103633
$555$	−1.98328e143	−0.166726
$556$	−1.23866e144	−0.947383
$557$	−2.49231e144	−1.73462	−0.867308	−	0.497771i	$-0.834152\pi$
$557$	−2.49231e144	−1.73462	−0.867308	+	0.497771i	$0.834152\pi$
$558$	1.56969e142	0.00994303
$559$	−2.85332e143	−0.164524
$560$	1.90268e143	0.0998837
$561$	4.97929e143	0.238022
$562$	−8.30869e142	−0.0361723
$563$	−5.67998e143	−0.225245	−0.112623	−	0.993638i	$-0.535925\pi$
$563$	−5.67998e143	−0.225245	−0.112623	+	0.993638i	$0.535925\pi$
$564$	−2.16108e143	−0.0780762
$565$	1.13496e144	0.373626
$566$	−1.47440e144	−0.442338
$567$	2.31845e143	0.0633996
$568$	−5.60184e144	−1.39651
$569$	5.71338e144	1.29867	0.649336	−	0.760502i	$-0.275047\pi$
$569$	5.71338e144	1.29867	0.649336	+	0.760502i	$0.275047\pi$
$570$	3.51432e143	0.0728470
$571$	−1.15237e144	−0.217869	−0.108934	−	0.994049i	$-0.534744\pi$
$571$	−1.15237e144	−0.217869	−0.108934	+	0.994049i	$0.534744\pi$
$572$	−2.08640e144	−0.359838
$573$	2.84009e144	0.446904
$574$	1.66678e144	0.239334
$575$	5.58608e144	0.732058
$576$	7.56666e143	0.0905157
$577$	6.44279e144	0.703629	0.351815	−	0.936070i	$-0.385565\pi$
$577$	6.44279e144	0.703629	0.351815	+	0.936070i	$0.385565\pi$
$578$	3.72016e144	0.370980
$579$	3.89295e143	0.0354531
$580$	1.97121e144	0.163970
$581$	−1.14248e145	−0.868163
$582$	7.35975e144	0.510983
$583$	−8.25265e144	−0.523594
$584$	−1.28543e145	−0.745375
$585$	8.42102e143	0.0446356
$586$	5.51639e144	0.267319
$587$	−1.50682e145	−0.667670	−0.333835	−	0.942632i	$-0.608343\pi$
$587$	−1.50682e145	−0.667670	−0.333835	+	0.942632i	$0.608343\pi$
$588$	5.17570e144	0.209729
$589$	1.36115e144	0.0504491
$590$	2.79093e144	0.0946278
$591$	−3.22371e145	−1.00003
$592$	2.08053e145	0.590587
$593$	−6.35659e145	−1.65140	−0.825702	−	0.564107i	$-0.809220\pi$
$593$	−6.35659e145	−1.65140	−0.825702	+	0.564107i	$0.809220\pi$
$594$	2.28257e145	0.542794
$595$	2.36690e144	0.0515275
$596$	2.36101e145	0.470619
$597$	8.15833e144	0.148919
$598$	6.07292e144	0.101528
$599$	4.32195e145	0.661868	0.330934	−	0.943654i	$-0.392636\pi$
$599$	4.32195e145	0.661868	0.330934	+	0.943654i	$0.392636\pi$
$600$	−3.22094e145	−0.451900
$601$	6.55679e145	0.842910	0.421455	−	0.906849i	$-0.361519\pi$
$601$	6.55679e145	0.842910	0.421455	+	0.906849i	$0.361519\pi$
$602$	−1.35136e145	−0.159205
$603$	3.19778e145	0.345294
$604$	1.40629e146	1.39199
$605$	−1.92028e145	−0.174264
$606$	2.22221e145	0.184915
$607$	2.18967e145	0.167098	0.0835492	−	0.996504i	$-0.473374\pi$
$607$	2.18967e145	0.167098	0.0835492	+	0.996504i	$0.473374\pi$
$608$	−1.62197e146	−1.13529
$609$	−6.54622e145	−0.420322
$610$	−2.81116e145	−0.165603
$611$	8.66980e144	0.0468647
$612$	2.73924e145	0.135888
$613$	−2.25524e146	−1.02688	−0.513438	−	0.858127i	$-0.671628\pi$
$613$	−2.25524e146	−1.02688	−0.513438	+	0.858127i	$0.671628\pi$
$614$	3.97148e145	0.166002
$615$	−3.02169e145	−0.115960
$616$	−2.16707e146	−0.763635
$617$	−2.13544e146	−0.691060	−0.345530	−	0.938408i	$-0.612301\pi$
$617$	−2.13544e146	−0.691060	−0.345530	+	0.938408i	$0.612301\pi$
$618$	−2.97926e145	−0.0885550
$619$	2.66610e146	0.727977	0.363989	−	0.931403i	$-0.381415\pi$
$619$	2.66610e146	0.727977	0.363989	+	0.931403i	$0.381415\pi$
$620$	3.35144e144	0.00840752
$621$	3.44112e146	0.793216
$622$	2.69932e146	0.571819
$623$	−5.68432e146	−1.10677
$624$	6.36489e145	0.113920
$625$	5.08160e146	0.836180
$626$	3.88276e146	0.587474
$627$	7.27555e146	1.01232
$628$	−8.92729e146	−1.14245
$629$	2.58814e146	0.304669
$630$	3.98829e145	0.0431924
$631$	1.72070e146	0.171460	0.0857302	−	0.996318i	$-0.472678\pi$
$631$	1.72070e146	0.171460	0.0857302	+	0.996318i	$0.472678\pi$
$632$	−1.52005e147	−1.39383
$633$	8.45964e146	0.713932
$634$	7.73447e146	0.600820
$635$	−1.08640e146	−0.0776908
$636$	3.27110e146	0.215375
$637$	−2.07638e146	−0.125889
$638$	−7.87916e146	−0.439941
$639$	2.13436e147	1.09767
$640$	−5.07662e146	−0.240506
$641$	−4.25546e147	−1.85738	−0.928689	−	0.370859i	$-0.879063\pi$
$641$	−4.25546e147	−1.85738	−0.928689	+	0.370859i	$0.879063\pi$
$642$	−8.40063e146	−0.337849
$643$	3.00504e146	0.111372	0.0556858	−	0.998448i	$-0.482265\pi$
$643$	3.00504e146	0.111372	0.0556858	+	0.998448i	$0.482265\pi$
$644$	−1.48969e147	−0.508848
$645$	2.44987e146	0.0771362
$646$	−4.58611e146	−0.133118
$647$	−2.99856e147	−0.802486	−0.401243	−	0.915972i	$-0.631422\pi$
$647$	−2.99856e147	−0.802486	−0.401243	+	0.915972i	$0.631422\pi$
$648$	−2.42571e146	−0.0598620
$649$	5.77795e147	1.31500
$650$	5.89207e146	0.123685
$651$	−1.11298e146	−0.0215520
$652$	7.02937e147	1.25579
$653$	−6.59787e146	−0.108758	−0.0543791	−	0.998520i	$-0.517318\pi$
$653$	−6.59787e146	−0.108758	−0.0543791	+	0.998520i	$0.517318\pi$
$654$	2.82320e146	0.0429448
$655$	2.55966e147	0.359346
$656$	3.16985e147	0.410759
$657$	4.89764e147	0.585875
$658$	4.10611e146	0.0453494
$659$	−1.06461e148	−1.08569	−0.542844	−	0.839834i	$-0.682652\pi$
$659$	−1.06461e148	−1.08569	−0.542844	+	0.839834i	$0.682652\pi$
$660$	1.79139e147	0.168707
$661$	−1.04052e148	−0.905051	−0.452526	−	0.891751i	$-0.649477\pi$
$661$	−1.04052e148	−0.905051	−0.452526	+	0.891751i	$0.649477\pi$
$662$	2.86811e147	0.230437
$663$	7.91781e146	0.0587685
$664$	1.19534e148	0.819722
$665$	3.45842e147	0.219150
$666$	4.36108e147	0.255386
$667$	−1.18784e148	−0.642910
$668$	−2.15375e148	−1.07753
$669$	−1.53942e148	−0.712010
$670$	−1.31822e147	−0.0563716
$671$	−5.81982e148	−2.30132
$672$	1.32625e148	0.484996
$673$	4.95268e148	1.67513	0.837567	−	0.546335i	$-0.183977\pi$
$673$	4.95268e148	1.67513	0.837567	+	0.546335i	$0.183977\pi$
$674$	−1.64662e148	−0.515167
$675$	3.33865e148	0.966323
$676$	2.79816e148	0.749326
$677$	−6.34338e148	−1.57187	−0.785934	−	0.618311i	$-0.787817\pi$
$677$	−6.34338e148	−1.57187	−0.785934	+	0.618311i	$0.787817\pi$
$678$	1.79815e148	0.412352
$679$	7.24268e148	1.53722
$680$	−2.47641e147	−0.0486524
$681$	3.93276e148	0.715277
$682$	−1.33961e147	−0.0225579
$683$	−4.16276e148	−0.649074	−0.324537	−	0.945873i	$-0.605209\pi$
$683$	−4.16276e148	−0.649074	−0.324537	+	0.945873i	$0.605209\pi$
$684$	4.00247e148	0.577940
$685$	4.40478e147	0.0589073
$686$	−3.52666e148	−0.436866
$687$	2.79660e148	0.320923
$688$	−2.56999e148	−0.273236
$689$	−1.31229e148	−0.129277
$690$	−5.21423e147	−0.0476006
$691$	3.41789e148	0.289175	0.144587	−	0.989492i	$-0.453815\pi$
$691$	3.41789e148	0.289175	0.144587	+	0.989492i	$0.453815\pi$
$692$	−1.36533e149	−1.07070
$693$	8.25678e148	0.600227
$694$	−7.67721e148	−0.517406
$695$	−4.26660e148	−0.266612
$696$	6.84909e148	0.396869
$697$	3.94324e148	0.211901
$698$	−1.25011e149	−0.623075
$699$	−1.81087e148	−0.0837214
$700$	−1.44533e149	−0.619897
$701$	−2.33245e149	−0.928146	−0.464073	−	0.885797i	$-0.653612\pi$
$701$	−2.33245e149	−0.928146	−0.464073	+	0.885797i	$0.653612\pi$
$702$	3.62962e148	0.134018
$703$	3.78169e149	1.29578
$704$	−6.45756e148	−0.205354
$705$	−7.44392e147	−0.0219722
$706$	1.36895e149	0.375094
$707$	2.18686e149	0.556291
$708$	−2.29020e149	−0.540913
$709$	−3.10165e148	−0.0680244	−0.0340122	−	0.999421i	$-0.510829\pi$
$709$	−3.10165e148	−0.0680244	−0.0340122	+	0.999421i	$0.510829\pi$
$710$	−8.79847e148	−0.179203
$711$	5.79156e149	1.09557
$712$	5.94731e149	1.04501
$713$	−2.01955e148	−0.0329651
$714$	3.74996e148	0.0568683
$715$	−7.18668e148	−0.101265
$716$	4.84688e149	0.634642
$717$	2.01290e149	0.244944
$718$	−1.95849e149	−0.221507
$719$	−1.69695e150	−1.78403	−0.892015	−	0.452005i	$-0.850709\pi$
$719$	−1.69695e150	−1.78403	−0.892015	+	0.452005i	$0.850709\pi$
$720$	7.58483e148	0.0741293
$721$	−2.93187e149	−0.266406
$722$	−1.93969e149	−0.163881
$723$	−5.48297e149	−0.430779
$724$	−5.91959e148	−0.0432531
$725$	−1.15246e150	−0.783216
$726$	−3.04236e149	−0.192326
$727$	−8.19359e148	−0.0481856	−0.0240928	−	0.999710i	$-0.507670\pi$
$727$	−8.19359e148	−0.0481856	−0.0240928	+	0.999710i	$0.507670\pi$
$728$	−3.44596e149	−0.188544
$729$	1.39310e150	0.709231
$730$	−2.01895e149	−0.0956480
$731$	−3.19702e149	−0.140956
$732$	2.30679e150	0.946623
$733$	1.32500e150	0.506126	0.253063	−	0.967450i	$-0.418562\pi$
$733$	1.32500e150	0.506126	0.253063	+	0.967450i	$0.418562\pi$
$734$	−5.51691e149	−0.196179
$735$	1.78279e149	0.0590220
$736$	2.40653e150	0.741833
$737$	−2.72905e150	−0.783373
$738$	6.64445e149	0.177623
$739$	5.43053e149	0.135210	0.0676051	−	0.997712i	$-0.478464\pi$
$739$	5.43053e149	0.135210	0.0676051	+	0.997712i	$0.478464\pi$
$740$	9.31131e149	0.215946
$741$	1.15692e150	0.249946
$742$	−6.21516e149	−0.125097
$743$	3.72400e150	0.698388	0.349194	−	0.937051i	$-0.386455\pi$
$743$	3.72400e150	0.698388	0.349194	+	0.937051i	$0.386455\pi$
$744$	1.16448e149	0.0203494
$745$	8.13258e149	0.132441
$746$	3.79201e150	0.575548
$747$	−4.55437e150	−0.644313
$748$	−2.33773e150	−0.308290
$749$	−8.26701e150	−1.01637
$750$	−1.04160e150	−0.119394
$751$	−7.26582e150	−0.776583	−0.388292	−	0.921537i	$-0.626935\pi$
$751$	−7.26582e150	−0.776583	−0.388292	+	0.921537i	$0.626935\pi$
$752$	7.80891e149	0.0778312
$753$	−4.39544e150	−0.408569
$754$	−1.25290e150	−0.108623
$755$	4.84401e150	0.391733
$756$	−8.90348e150	−0.671685
$757$	6.80097e150	0.478671	0.239336	−	0.970937i	$-0.423070\pi$
$757$	6.80097e150	0.478671	0.239336	+	0.970937i	$0.423070\pi$
$758$	8.06732e150	0.529781
$759$	−1.07948e151	−0.661487
$760$	−3.61843e150	−0.206922
$761$	3.21674e151	1.71681	0.858405	−	0.512973i	$-0.171456\pi$
$761$	3.21674e151	1.71681	0.858405	+	0.512973i	$0.171456\pi$
$762$	−1.72122e150	−0.0857434
$763$	2.77830e150	0.129194
$764$	−1.33339e151	−0.578837
$765$	9.43539e149	0.0382415
$766$	−5.80591e150	−0.219715
$767$	9.18779e150	0.324679
$768$	−4.98929e150	−0.164655
$769$	1.66173e151	0.512185	0.256093	−	0.966652i	$-0.417565\pi$
$769$	1.66173e151	0.512185	0.256093	+	0.966652i	$0.417565\pi$
$770$	−3.40369e150	−0.0979912
$771$	2.02494e151	0.544575
$772$	−1.82770e150	−0.0459194
$773$	7.47787e151	1.75531	0.877656	−	0.479291i	$-0.159106\pi$
$773$	7.47787e151	1.75531	0.877656	+	0.479291i	$0.159106\pi$
$774$	−5.38706e150	−0.118155
$775$	−1.95941e150	−0.0401593
$776$	−7.57778e151	−1.45145
$777$	−3.09220e151	−0.553560
$778$	1.92587e151	0.322254
$779$	5.76170e151	0.901227
$780$	2.84858e150	0.0416545
$781$	−1.82151e152	−2.49030
$782$	6.80445e150	0.0869838
$783$	−7.09937e151	−0.848648
$784$	−1.87020e151	−0.209071
$785$	−3.07503e151	−0.321509
$786$	4.05535e151	0.396592
$787$	−2.94929e151	−0.269801	−0.134900	−	0.990859i	$-0.543071\pi$
$787$	−2.94929e151	−0.269801	−0.134900	+	0.990859i	$0.543071\pi$
$788$	1.51350e152	1.29525
$789$	1.87465e151	0.150099
$790$	−2.38745e151	−0.178860
$791$	1.76955e152	1.24050
$792$	−8.63879e151	−0.566736
$793$	−9.25436e151	−0.568204
$794$	1.18446e152	0.680682
$795$	1.12674e151	0.0606107
$796$	−3.83025e151	−0.192882
$797$	3.01507e152	1.42146	0.710731	−	0.703464i	$-0.248364\pi$
$797$	3.01507e152	1.42146	0.710731	+	0.703464i	$0.248364\pi$
$798$	5.47929e151	0.241865
$799$	9.71414e150	0.0401512
$800$	2.33486e152	0.903727
$801$	−2.26599e152	−0.821393
$802$	2.87275e151	0.0975310
$803$	−4.17975e152	−1.32918
$804$	1.08171e152	0.322232
$805$	−5.13129e151	−0.143200
$806$	−2.13017e150	−0.00556962
$807$	−2.22545e152	−0.545202
$808$	−2.28804e152	−0.525251
$809$	4.42609e151	0.0952188	0.0476094	−	0.998866i	$-0.484840\pi$
$809$	4.42609e151	0.0952188	0.0476094	+	0.998866i	$0.484840\pi$
$810$	−3.80992e150	−0.00768162
$811$	1.17673e152	0.222373	0.111186	−	0.993800i	$-0.464535\pi$
$811$	1.17673e152	0.222373	0.111186	+	0.993800i	$0.464535\pi$
$812$	3.07338e152	0.544408
$813$	−4.92922e152	−0.818512
$814$	−3.72184e152	−0.579397
$815$	2.42129e152	0.353405
$816$	7.13159e151	0.0976007
$817$	−4.67136e152	−0.599495
$818$	−2.30577e152	−0.277503
$819$	1.31295e152	0.148198
$820$	1.41865e152	0.150193
$821$	9.52380e152	0.945789	0.472895	−	0.881119i	$-0.343209\pi$
$821$	9.52380e152	0.945789	0.472895	+	0.881119i	$0.343209\pi$
$822$	6.97863e151	0.0650129
$823$	2.93577e152	0.256585	0.128292	−	0.991736i	$-0.459050\pi$
$823$	2.93577e152	0.256585	0.128292	+	0.991736i	$0.459050\pi$
$824$	3.06752e152	0.251541
$825$	−1.04733e153	−0.805847
$826$	4.35144e152	0.314181
$827$	4.85556e152	0.329003	0.164502	−	0.986377i	$-0.447398\pi$
$827$	4.85556e152	0.329003	0.164502	+	0.986377i	$0.447398\pi$
$828$	−5.93850e152	−0.377645
$829$	3.22510e153	1.92500	0.962500	−	0.271282i	$-0.0874477\pi$
$829$	3.22510e153	1.92500	0.962500	+	0.271282i	$0.0874477\pi$
$830$	1.87745e152	0.105188
$831$	3.16968e152	0.166710
$832$	−1.02685e152	−0.0507027
$833$	−2.32649e152	−0.107855
$834$	−6.75972e152	−0.294246
$835$	−7.41865e152	−0.303239
$836$	−3.41579e153	−1.31118
$837$	−1.20703e152	−0.0435143
$838$	−6.70760e152	−0.227120
$839$	4.24065e152	0.134874	0.0674372	−	0.997724i	$-0.478518\pi$
$839$	4.24065e152	0.134874	0.0674372	+	0.997724i	$0.478518\pi$
$840$	2.95871e152	0.0883976
$841$	−1.11216e153	−0.312162
$842$	1.10802e153	0.292189
$843$	2.34848e152	0.0581888
$844$	−3.97171e153	−0.924696
$845$	9.63835e152	0.210875
$846$	1.63686e152	0.0336563
$847$	−2.99397e153	−0.578587
$848$	−1.18198e153	−0.214699
$849$	4.16745e153	0.711569
$850$	6.60181e152	0.105967
$851$	−5.61092e153	−0.846705
$852$	7.21990e153	1.02436
$853$	−2.26454e152	−0.0302103	−0.0151052	−	0.999886i	$-0.504808\pi$
$853$	−2.26454e152	−0.0302103	−0.0151052	+	0.999886i	$0.504808\pi$
$854$	−4.38296e153	−0.549832
$855$	1.37866e153	0.162644
$856$	8.64949e153	0.959661
$857$	1.27702e154	1.33262	0.666309	−	0.745675i	$-0.267873\pi$
$857$	1.27702e154	1.33262	0.666309	+	0.745675i	$0.267873\pi$
$858$	−1.13861e153	−0.111762
$859$	1.34385e154	1.24083	0.620414	−	0.784275i	$-0.286965\pi$
$859$	1.34385e154	1.24083	0.620414	+	0.784275i	$0.286965\pi$
$860$	−1.15019e153	−0.0999080
$861$	−4.71122e153	−0.385006
$862$	−7.17738e153	−0.551867
$863$	−3.76062e153	−0.272078	−0.136039	−	0.990703i	$-0.543437\pi$
$863$	−3.76062e153	−0.272078	−0.136039	+	0.990703i	$0.543437\pi$
$864$	1.43832e154	0.979227
$865$	−4.70293e153	−0.301316
$866$	−8.07928e153	−0.487173
$867$	−1.05152e154	−0.596779
$868$	5.22534e152	0.0279144
$869$	−4.94264e154	−2.48554
$870$	1.07575e153	0.0509271
$871$	−4.33959e153	−0.193418
$872$	−2.90684e153	−0.121985
$873$	2.88722e154	1.14086
$874$	9.94239e153	0.369948
$875$	−1.02503e154	−0.359181
$876$	1.65672e154	0.546745
$877$	4.57524e153	0.142212	0.0711058	−	0.997469i	$-0.477347\pi$
$877$	4.57524e153	0.142212	0.0711058	+	0.997469i	$0.477347\pi$
$878$	7.31076e153	0.214043
$879$	−1.55923e154	−0.430025
$880$	−6.47306e153	−0.168178
$881$	−3.46430e154	−0.847969	−0.423985	−	0.905669i	$-0.639369\pi$
$881$	−3.46430e154	−0.847969	−0.423985	+	0.905669i	$0.639369\pi$
$882$	−3.92020e153	−0.0904081
$883$	7.08435e154	1.53944	0.769720	−	0.638381i	$-0.220396\pi$
$883$	7.08435e154	1.53944	0.769720	+	0.638381i	$0.220396\pi$
$884$	−3.71733e153	−0.0761179
$885$	−7.88867e153	−0.152224
$886$	2.18677e154	0.397679
$887$	−3.38114e153	−0.0579525	−0.0289763	−	0.999580i	$-0.509225\pi$
$887$	−3.38114e153	−0.0579525	−0.0289763	+	0.999580i	$0.509225\pi$
$888$	3.23527e154	0.522672
$889$	−1.69384e154	−0.257947
$890$	9.34109e153	0.134098
$891$	−7.88752e153	−0.106748
$892$	7.22741e154	0.922206
$893$	1.41939e154	0.170766
$894$	1.28847e154	0.146169
$895$	1.66952e154	0.178601
$896$	−7.91512e154	−0.798522
$897$	−1.71653e154	−0.163323
$898$	−3.41831e154	−0.306763
$899$	4.16653e153	0.0352688
$900$	−5.76165e154	−0.460061
$901$	−1.47037e154	−0.110758
$902$	−5.67052e154	−0.402976
$903$	3.81967e154	0.256106
$904$	−1.85142e155	−1.17129
$905$	−2.03902e153	−0.0121723
$906$	7.67452e154	0.432335
$907$	7.45945e154	0.396574	0.198287	−	0.980144i	$-0.436462\pi$
$907$	7.45945e154	0.396574	0.198287	+	0.980144i	$0.436462\pi$
$908$	−1.84639e155	−0.926438
$909$	8.71768e154	0.412855
$910$	−5.41237e153	−0.0241944
$911$	−2.85703e155	−1.20559	−0.602796	−	0.797895i	$-0.705947\pi$
$911$	−2.85703e155	−1.20559	−0.602796	+	0.797895i	$0.705947\pi$
$912$	1.04204e155	0.415102
$913$	3.88680e155	1.46176
$914$	−1.51495e155	−0.537927
$915$	7.94583e154	0.266398
$916$	−1.31297e155	−0.415665
$917$	3.99084e155	1.19309
$918$	4.06683e154	0.114819
$919$	5.08138e155	1.35493	0.677465	−	0.735555i	$-0.263078\pi$
$919$	5.08138e155	1.35493	0.677465	+	0.735555i	$0.263078\pi$
$920$	5.36870e154	0.135210
$921$	−1.12255e155	−0.267040
$922$	9.78958e154	0.219984
$923$	−2.89647e155	−0.614865
$924$	2.79302e155	0.560139
$925$	−5.44383e155	−1.03149
$926$	4.05815e155	0.726526
$927$	−1.16876e155	−0.197715
$928$	−4.96491e155	−0.793674
$929$	1.26997e155	0.191853	0.0959267	−	0.995388i	$-0.469419\pi$
$929$	1.26997e155	0.191853	0.0959267	+	0.995388i	$0.469419\pi$
$930$	1.82898e153	0.00261128
$931$	−3.39938e155	−0.458714
$932$	8.50186e154	0.108437
$933$	−7.62971e155	−0.919860
$934$	4.88464e155	0.556700
$935$	−8.05237e154	−0.0867590
$936$	−1.37369e155	−0.139929
$937$	−6.80517e155	−0.655406	−0.327703	−	0.944781i	$-0.606275\pi$
$937$	−6.80517e155	−0.655406	−0.327703	+	0.944781i	$0.606275\pi$
$938$	−2.05528e155	−0.187164
$939$	−1.09748e156	−0.945043
$940$	3.49484e154	0.0284587
$941$	1.63427e156	1.25855	0.629274	−	0.777184i	$-0.283352\pi$
$941$	1.63427e156	1.25855	0.629274	+	0.777184i	$0.283352\pi$
$942$	−4.87188e155	−0.354833
$943$	−8.54869e155	−0.588892
$944$	8.27546e155	0.539216
$945$	−3.06683e155	−0.189025
$946$	4.59744e155	0.268059
$947$	3.35162e156	1.84876	0.924380	−	0.381472i	$-0.124583\pi$
$947$	3.35162e156	1.84876	0.924380	+	0.381472i	$0.124583\pi$
$948$	1.95911e156	1.02240
$949$	−6.64642e155	−0.328179
$950$	9.64631e155	0.450684
$951$	−2.18617e156	−0.966513
$952$	−3.86105e155	−0.161535
$953$	1.15047e156	0.455508	0.227754	−	0.973719i	$-0.426862\pi$
$953$	1.15047e156	0.455508	0.227754	+	0.973719i	$0.426862\pi$
$954$	−2.47761e155	−0.0928416
$955$	−4.59291e155	−0.162896
$956$	−9.45037e155	−0.317256
$957$	2.22707e156	0.707713
$958$	−1.55482e156	−0.467725
$959$	6.86763e155	0.195583
$960$	8.81654e154	0.0237716
$961$	−3.91014e156	−0.998192
$962$	−5.91827e155	−0.143055
$963$	−3.29555e156	−0.754307
$964$	2.57419e156	0.557952
$965$	−6.29556e154	−0.0129226
$966$	−8.12967e155	−0.158043
$967$	2.29280e156	0.422159	0.211079	−	0.977469i	$-0.432302\pi$
$967$	2.29280e156	0.422159	0.211079	+	0.977469i	$0.432302\pi$
$968$	3.13249e156	0.546303
$969$	1.29628e156	0.214141
$970$	−1.19020e156	−0.186253
$971$	−4.42509e156	−0.656013	−0.328006	−	0.944676i	$-0.606377\pi$
$971$	−4.42509e156	−0.656013	−0.328006	+	0.944676i	$0.606377\pi$
$972$	−5.79391e156	−0.813754
$973$	−6.65220e156	−0.885199
$974$	1.55447e156	0.195991
$975$	−1.66541e156	−0.198966
$976$	−8.33542e156	−0.943652
$977$	5.67880e156	0.609244	0.304622	−	0.952473i	$-0.401470\pi$
$977$	5.67880e156	0.609244	0.304622	+	0.952473i	$0.401470\pi$
$978$	3.83613e156	0.390035
$979$	1.93385e157	1.86351
$980$	−8.36999e155	−0.0764462
$981$	1.10754e156	0.0958817
$982$	−2.29177e156	−0.188069
$983$	1.60539e157	1.24888	0.624441	−	0.781072i	$-0.285327\pi$
$983$	1.60539e157	1.24888	0.624441	+	0.781072i	$0.285327\pi$
$984$	4.92919e156	0.363524
$985$	5.21329e156	0.364510
$986$	−1.40382e156	−0.0930624
$987$	−1.16061e156	−0.0729515
$988$	−5.43161e156	−0.323735
$989$	6.93094e156	0.391730
$990$	−1.35684e156	−0.0727247
$991$	−1.04972e157	−0.533591	−0.266795	−	0.963753i	$-0.585965\pi$
$991$	−1.04972e157	−0.533591	−0.266795	+	0.963753i	$0.585965\pi$
$992$	−8.44130e155	−0.0406955
$993$	−8.10682e156	−0.370693
$994$	−1.37180e157	−0.594984
$995$	−1.31934e156	−0.0542807
$996$	−1.54061e157	−0.601279
$997$	1.20849e157	0.447451	0.223726	−	0.974652i	$-0.428178\pi$
$997$	1.20849e157	0.447451	0.223726	+	0.974652i	$0.428178\pi$
$998$	−1.79188e156	−0.0629441
$999$	−3.35349e157	−1.11766

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.106.a.a.1.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.106.a.a.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.56214e15 q^{2} +7.24197e24 q^{3} -3.40003e31 q^{4} -1.17115e36 q^{5} -1.85549e40 q^{6} -1.82598e44 q^{7} +1.91046e47 q^{8} -7.27906e49 q^{9} +O(q^{10})\)	\(q-2.56214e15 q^{2} +7.24197e24 q^{3} -3.40003e31 q^{4} -1.17115e36 q^{5} -1.85549e40 q^{6} -1.82598e44 q^{7} +1.91046e47 q^{8} -7.27906e49 q^{9} +3.00065e51 q^{10} +6.21211e54 q^{11} -2.46229e56 q^{12} +9.87817e57 q^{13} +4.67841e59 q^{14} -8.48143e60 q^{15} +8.89729e62 q^{16} +1.10681e64 q^{17} +1.86500e65 q^{18} +1.61722e67 q^{19} +3.98194e67 q^{20} -1.32237e69 q^{21} -1.59163e70 q^{22} -2.39949e71 q^{23} +1.38355e72 q^{24} -2.32803e73 q^{25} -2.53092e73 q^{26} -1.43411e75 q^{27} +6.20838e75 q^{28} +4.95038e76 q^{29} +2.17306e76 q^{30} +8.41659e76 q^{31} -1.00294e79 q^{32} +4.49879e79 q^{33} -2.83579e79 q^{34} +2.13850e80 q^{35} +2.47490e81 q^{36} +2.33838e82 q^{37} -4.14355e82 q^{38} +7.15374e82 q^{39} -2.23744e83 q^{40} +3.56271e84 q^{41} +3.38809e84 q^{42} -2.88851e85 q^{43} -2.11214e86 q^{44} +8.52488e85 q^{45} +6.14782e86 q^{46} +8.77673e86 q^{47} +6.44339e87 q^{48} -2.10199e88 q^{49} +5.96474e88 q^{50} +8.01546e88 q^{51} -3.35860e89 q^{52} -1.32848e90 q^{53} +3.67438e90 q^{54} -7.27532e90 q^{55} -3.48846e91 q^{56} +1.17119e92 q^{57} -1.26835e92 q^{58} +9.30110e92 q^{59} +2.88371e92 q^{60} -9.36850e93 q^{61} -2.15645e92 q^{62} +1.32914e94 q^{63} -1.03951e94 q^{64} -1.15688e94 q^{65} -1.15265e95 q^{66} -4.39312e95 q^{67} -3.76317e95 q^{68} -1.73770e96 q^{69} -5.47912e95 q^{70} -2.93219e97 q^{71} -1.39064e97 q^{72} -6.72839e97 q^{73} -5.99126e97 q^{74} -1.68595e98 q^{75} -5.49860e98 q^{76} -1.13432e99 q^{77} -1.83289e98 q^{78} -7.95646e99 q^{79} -1.04201e99 q^{80} -1.26970e99 q^{81} -9.12816e99 q^{82} +6.25680e100 q^{83} +4.49609e100 q^{84} -1.29624e100 q^{85} +7.40076e100 q^{86} +3.58505e101 q^{87} +1.18680e102 q^{88} +3.11302e102 q^{89} -2.18419e101 q^{90} -1.80373e102 q^{91} +8.15832e102 q^{92} +6.09527e101 q^{93} -2.24872e102 q^{94} -1.89401e103 q^{95} -7.26323e103 q^{96} -3.96647e104 q^{97} +5.38558e103 q^{98} -4.52184e104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 91\!\cdots\!20 q^{2}+ \cdots + 31\!\cdots\!84 q^{9}+O(q^{10}) \) 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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