LMFDB - Embedded newform 1.106.a.a.1.8

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			1.8
Root			$7.96777e13$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.03267e16 q^{2} -2.77402e24 q^{3} +6.60762e31 q^{4} -1.38808e36 q^{5} -2.86465e40 q^{6} -3.04428e43 q^{7} +2.63449e47 q^{8} -1.17542e50 q^{9} +O(q^{10})$	\(q+1.03267e16 q^{2} -2.77402e24 q^{3} +6.60762e31 q^{4} -1.38808e36 q^{5} -2.86465e40 q^{6} -3.04428e43 q^{7} +2.63449e47 q^{8} -1.17542e50 q^{9} -1.43343e52 q^{10} +4.98478e54 q^{11} -1.83297e56 q^{12} +2.40158e58 q^{13} -3.14374e59 q^{14} +3.85057e60 q^{15} +4.01897e61 q^{16} -3.48835e64 q^{17} -1.21382e66 q^{18} -1.66529e67 q^{19} -9.17192e67 q^{20} +8.44489e67 q^{21} +5.14764e70 q^{22} -2.46240e70 q^{23} -7.30812e71 q^{24} -2.27251e73 q^{25} +2.48005e74 q^{26} +6.73472e74 q^{27} -2.01154e75 q^{28} -7.76434e76 q^{29} +3.97637e76 q^{30} +1.96420e78 q^{31} -1.02717e79 q^{32} -1.38279e79 q^{33} -3.60231e80 q^{34} +4.22571e79 q^{35} -7.76670e81 q^{36} -3.69942e82 q^{37} -1.71969e83 q^{38} -6.66204e82 q^{39} -3.65688e83 q^{40} -4.85828e84 q^{41} +8.72080e83 q^{42} +9.79144e85 q^{43} +3.29376e86 q^{44} +1.63157e86 q^{45} -2.54285e86 q^{46} -3.79881e87 q^{47} -1.11487e86 q^{48} -5.34351e88 q^{49} -2.34676e89 q^{50} +9.67674e88 q^{51} +1.58687e90 q^{52} +1.90979e90 q^{53} +6.95475e90 q^{54} -6.91929e90 q^{55} -8.02011e90 q^{56} +4.61954e91 q^{57} -8.01801e92 q^{58} -2.84039e92 q^{59} +2.54431e92 q^{60} +3.64939e93 q^{61} +2.02837e94 q^{62} +3.57829e93 q^{63} -1.07703e95 q^{64} -3.33360e94 q^{65} -1.42797e95 q^{66} -4.96150e95 q^{67} -2.30497e96 q^{68} +6.83075e94 q^{69} +4.36377e95 q^{70} +1.33111e97 q^{71} -3.09662e97 q^{72} -8.83827e97 q^{73} -3.82028e98 q^{74} +6.30400e97 q^{75} -1.10036e99 q^{76} -1.51751e98 q^{77} -6.87970e98 q^{78} -1.15100e99 q^{79} -5.57867e97 q^{80} +1.28523e100 q^{81} -5.01700e100 q^{82} -5.00947e100 q^{83} +5.58006e99 q^{84} +4.84211e100 q^{85} +1.01113e102 q^{86} +2.15384e101 q^{87} +1.31323e102 q^{88} +6.61147e101 q^{89} +1.68488e102 q^{90} -7.31109e101 q^{91} -1.62706e102 q^{92} -5.44873e102 q^{93} -3.92292e103 q^{94} +2.31155e103 q^{95} +2.84940e103 q^{96} +1.82524e104 q^{97} -5.51809e104 q^{98} -5.85919e104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 91\!\cdots\!20 q^{2}+ \cdots + 31\!\cdots\!84 q^{9}+O(q^{10}) $ 8 * q - 9175032489175920 * q^2 - 3552367551392844422995680 * q^3 + 120400994563419904822151366840576 * q^4 + 748366724871512021371292499759044400 * q^5 - 132475226406122000574502252920799787081664 * q^6 + 70538552172860257833295679508195640805531200 * q^7 - 706397877636490430592988742663067828802762076160 * q^8 + 317686049104616976165951103806454636773011694234984 * q^9	$ 8 q - 91\!\cdots\!20 q^{2}+ \cdots - 25\!\cdots\!32 q^{99}+O(q^{100}) $ 8 * q - 9175032489175920 * q^2 - 3552367551392844422995680 * q^3 + 120400994563419904822151366840576 * q^4 + 748366724871512021371292499759044400 * q^5 - 132475226406122000574502252920799787081664 * q^6 + 70538552172860257833295679508195640805531200 * q^7 - 706397877636490430592988742663067828802762076160 * q^8 + 317686049104616976165951103806454636773011694234984 * q^9 + 44171640525838765855893406263279104758565541661288800 * q^10 - 9131055394382837373664474069991492435117703171343284384 * q^11 + 1527166610615675905236013736606832949994468355519571829760 * q^12 + 4027585984285071020829060873004471073659148035689891664240 * q^13 - 160479473931693657661766690342904266858167662972048261318528 * q^14 - 85128562811603808162187988771451472214709069164574920929377600 * q^15 + 889182208997906282405898151302671436269823882827077347193192448 * q^16 - 47501502884916058924984340290257937633075778259367096814503394160 * q^17 - 2631080775730316510475478098580289149623650642713560969940755311280 * q^18 - 18490664070300440944092597449321411045310230817014503422448283738720 * q^19 - 433265654737251440411002845299403120817887965583462605623471811443200 * q^20 + 3435707407505559395644737215619994347818097875706879454950102719283456 * q^21 + 61667954680464912832813918015747124830645650785532527356368764542445760 * q^22 + 356123479312529060531796005710488420903589988587191444144805952706144960 * q^23 - 8553895157762497374674387748794258238227739674467572965053160752231464960 * q^24 + 36710330225103772037154153143396858524815591923552301173280524244928235000 * q^25 - 178290299429521612994896681862440451353112938442078389560127528645835464224 * q^26 + 4108583825736723245642984497148380325909672596193180989676962467681728811840 * q^27 - 10197863837452248524370326511788692919181508212113555118341665631868445276160 * q^28 - 132808057928545728770070628075237950532883381334274325807559945373631525579280 * q^29 + 368843646251862307061952875207762300737776646306173378951277228159200294844800 * q^30 + 2123150329739540390115408696476884203950374929670685127189943125782378108098816 * q^31 + 10156626912480412308164375397145246760285661187761787998479811379273048947425280 * q^32 - 110453822927144134530855124481163271865404195805770611489444997754143335676114560 * q^33 + 626514570831444006665132709400608888132203790316575476126972954148191421104888352 * q^34 - 180124138596474130911007456858429985683613480525844149859433273467968580724675200 * q^35 + 16221855297378912428170473077312544781163834427405933513071046969489436648368930048 * q^36 - 23010049861253897057830375004531412092720779537210279421336409908255568411112521680 * q^37 + 81514285558726303526499020366236482021009949677570093462995405282915730851685437760 * q^38 + 973250204883059182004683876455057324018758755152662643519744443013209490499392320448 * q^39 + 1620603767802466493396978076732241543088378147649587002013209944275991354096540672000 * q^40 - 9194436894335705500488956082645864740213392167963146808356372625255538188465570116784 * q^41 - 9987175533659763810738086904398668829743024019181589555089340923029980612539996188160 * q^42 + 3032382926300215248368351846801184405080019611637638159804034319071519733367501308000 * q^43 - 61413740744912033848381562467905778729130346597543024132573739224535613780500625691648 * q^44 - 728055588424370630925028219171725592820104067843765840180299922436159334808200708678800 * q^45 - 1937857727868547524263658836001472070613971220638572213222135000017628068861666423993984 * q^46 - 193114845358989650895015242618332478679741488577861492750207342621672434970683481651840 * q^47 + 47504655695285299018807413925656103836145592812920588522461073427843872384146136331714560 * q^48 + 9009795911083753626429293565600536034814214101588418291494061693709008119369143800410056 * q^49 + 124085104852024153585775552318382585485956095474767588057564984609967735836202360766470000 * q^50 - 1021523462097644786402134875264470962590383726411120471709206304906745531337979847222893504 * q^51 + 2601002607846544407071841678151669268750253239046498757166255249010956826575867860287884800 * q^52 - 508977518161307968273832984082037167871777334860039281483640147609506187672311865310329680 * q^53 - 33215015372693850873232010101241869628048359784733721234902490207672455295016159119447797120 * q^54 + 18450671784502163418133731529996697688391744925805957647904016734511230779675351655763828800 * q^55 + 77907763278563265290300076439200648252399491244631034718538984366849741317596223703232839680 * q^56 - 17514494370932414539251899866861034389141458703710767594438206182965846210727691039357326720 * q^57 + 521188643454307966215167554048547429862263982605454645813054246139388891719965181350028489440 * q^58 - 800548783090069547249411402735852579353665443321854402294237928007339127684491029048409334560 * q^59 - 4945597330350911740055109354650466378405725800344464689989883069207313581778154248500120627200 * q^60 + 9301780115240647873952088718367909265400456376594614456607735293030740558435392467259218034416 * q^61 - 24958988483741760731654226022541604930667635314913646027823754011402485431605464535556971159040 * q^62 - 69917019353683231050173137254943101675489279093995056831426882673091272292662113138105940233920 * q^63 - 97451971150817117830440198299734679886485437857461550467094176739811166528413095345956746952704 * q^64 - 361156613980852842706992602837566394553099687955520933659145529501075901774183231590989074101600 * q^65 + 156882494260210220362013449528635783983344936752786747375982538482579620426751742603199124015872 * q^66 - 1104667221349188765660578837514456152306124133482553297212406551469220909847432127137057601268960 * q^67 - 9721401068443204036258202986739714019478462517573215331908850090837288931485135338678529805012480 * q^68 - 15109507425538340400955372418178718530943009113130778845692031950392404855615907056642892252773632 * q^69 - 42141974870106016058865849455224368290398026088671930674752184932090288769297201065857297686150400 * q^70 - 50469870302247936824042683436030531088994086024328522294948330069784198912349909975813351349301184 * q^71 - 312770283013563627062551283668577288708985871414226238388562703871210081634250694390516261706772480 * q^72 - 309796921364548112330210024475355394269902333254274320239737341959226533985104691513778940551838640 * q^73 - 925823752396046652342642416972554390081562347656534041993730400149451972597268102227614960148886688 * q^74 - 2035970471601402025465859080535649095398414802703074791592862122373110362938204069403415245277940000 * q^75 - 3130569503520776632201267436445813580876068550759173850078744887758531600111432515821247207535037440 * q^76 - 5943612343311427733153258808379776193285399172298997030946865449540200274638852351419681744544800000 * q^77 - 21269159569550168394975895479661937627684008715929340977029750772463946126724250407354989139174454400 * q^78 - 15393227887174294584948162208020437185460179522932597986148734991937027143223423856935347902468612480 * q^79 - 36135869014387530593279194332920203124385252019916366550807261806779025414796891084911471716850073600 * q^80 - 16813579079052539310958564290225362908835005641306645336831720897045685008922728854885093229369750072 * q^81 + 40683812685771158034068852888314888590966014976906157199478748314343833251276146968126649606561452960 * q^82 - 27748711091393049888979586421607112972809560782068769478686312453860122910561653683460280801656090720 * q^83 + 243729273671324707074190479881332236879714714008146405350632616637128634259974190017728217778172076032 * q^84 + 1114476595266646322768819965977266122931255323002065012571315493969146685766458335643036439956923496800 * q^85 + 2001948212296635436448279509615999770689923972184784294781573198292641086063207267886445869810840226496 * q^86 + 2452094134677213482937709450778797624299131398431787829024781103485568458306913143764742103712037328320 * q^87 + 6587629213482246089116430616322572992490320338289310595388533189153014205464262604258615522799278407680 * q^88 + 4561891385239988132989403179389372513149936713239528905622804144400695279296267497385381892983137482960 * q^89 + 27831127206069462137128463558919625443225864994138363209261172284208865542079088020097519776839212242400 * q^90 + 27533535014530695422075480606590604897330716562374502844003945844898533709216751249129046131797307879296 * q^91 + 11219382355167481799152672023779859908676464262842813795936572357113636635896010169112116501983056189440 * q^92 - 1816432822902220399473532579920329564793343562884883929779919263741160765335835765675399623257440680960 * q^93 - 145721137880009419474465571784854076810270560388958588104991210830700849472154051473896292058236218084608 * q^94 - 197505250338784881028096044265210353994741936910104745900078290549992685412473006655125953841487400936000 * q^95 - 722643410665348223758010527434181844660741784808619153000544243764286894029121981921039078126765698187264 * q^96 - 765925425726897926053834041674103560846690860133522436616120766353705349104461208876007591285452102784240 * q^97 - 1378222404256086778845054197358441766991528993251977664562346500406878280455090891540290251693972016377840 * q^98 - 2543675383725234370604494641035024609729543664951752733885226452347175058619125118596469912791508615603232 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.03267e16	1.62139	0.810695	−	0.585469i	$-0.199090\pi$
$2$	1.03267e16	1.62139	0.810695	+	0.585469i	$0.199090\pi$
$3$	−2.77402e24	−0.247881	−0.123941	−	0.992290i	$-0.539553\pi$
$3$	−2.77402e24	−0.247881	−0.123941	+	0.992290i	$0.539553\pi$
$4$	6.60762e31	1.62890
$5$	−1.38808e36	−0.279570	−0.139785	−	0.990182i	$-0.544641\pi$
$5$	−1.38808e36	−0.279570	−0.139785	+	0.990182i	$0.544641\pi$
$6$	−2.86465e40	−0.401912
$7$	−3.04428e43	−0.130568	−0.0652841	−	0.997867i	$-0.520795\pi$
$7$	−3.04428e43	−0.130568	−0.0652841	+	0.997867i	$0.520795\pi$
$8$	2.63449e47	1.01970
$9$	−1.17542e50	−0.938555
$10$	−1.43343e52	−0.453291
$11$	4.98478e54	1.05811	0.529055	−	0.848588i	$-0.322547\pi$
$11$	4.98478e54	1.05811	0.529055	+	0.848588i	$0.322547\pi$
$12$	−1.83297e56	−0.403775
$13$	2.40158e58	0.791538	0.395769	−	0.918350i	$-0.370478\pi$
$13$	2.40158e58	0.791538	0.395769	+	0.918350i	$0.370478\pi$
$14$	−3.14374e59	−0.211702
$15$	3.85057e60	0.0693001
$16$	4.01897e61	0.0244240
$17$	−3.48835e64	−0.879126	−0.439563	−	0.898212i	$-0.644867\pi$
$17$	−3.48835e64	−0.879126	−0.439563	+	0.898212i	$0.644867\pi$
$18$	−1.21382e66	−1.52176
$19$	−1.66529e67	−1.22159	−0.610794	−	0.791789i	$-0.709150\pi$
$19$	−1.66529e67	−1.22159	−0.610794	+	0.791789i	$0.709150\pi$
$20$	−9.17192e67	−0.455392
$21$	8.44489e67	0.0323654
$22$	5.14764e70	1.71561
$23$	−2.46240e70	−0.0795513	−0.0397757	−	0.999209i	$-0.512664\pi$
$23$	−2.46240e70	−0.0795513	−0.0397757	+	0.999209i	$0.512664\pi$
$24$	−7.30812e71	−0.252764
$25$	−2.27251e73	−0.921841
$26$	2.48005e74	1.28339
$27$	6.73472e74	0.480532
$28$	−2.01154e75	−0.212683
$29$	−7.76434e76	−1.30080	−0.650399	−	0.759593i	$-0.725398\pi$
$29$	−7.76434e76	−1.30080	−0.650399	+	0.759593i	$0.725398\pi$
$30$	3.97637e76	0.112362
$31$	1.96420e78	0.992422	0.496211	−	0.868202i	$-0.334724\pi$
$31$	1.96420e78	0.992422	0.496211	+	0.868202i	$0.334724\pi$
$32$	−1.02717e79	−0.980097
$33$	−1.38279e79	−0.262286
$34$	−3.60231e80	−1.42541
$35$	4.22571e79	0.0365029
$36$	−7.76670e81	−1.52882
$37$	−3.69942e82	−1.72800	−0.863998	−	0.503494i	$-0.832047\pi$
$37$	−3.69942e82	−1.72800	−0.863998	+	0.503494i	$0.832047\pi$
$38$	−1.71969e83	−1.98067
$39$	−6.66204e82	−0.196207
$40$	−3.65688e83	−0.285077
$41$	−4.85828e84	−1.03593	−0.517964	−	0.855402i	$-0.673310\pi$
$41$	−4.85828e84	−1.03593	−0.517964	+	0.855402i	$0.673310\pi$
$42$	8.72080e83	0.0524769
$43$	9.79144e85	1.71298	0.856491	−	0.516162i	$-0.172640\pi$
$43$	9.79144e85	1.71298	0.856491	+	0.516162i	$0.172640\pi$
$44$	3.29376e86	1.72356
$45$	1.63157e86	0.262391
$46$	−2.54285e86	−0.128984
$47$	−3.79881e87	−0.623031	−0.311516	−	0.950241i	$-0.600837\pi$
$47$	−3.79881e87	−0.623031	−0.311516	+	0.950241i	$0.600837\pi$
$48$	−1.11487e86	−0.00605424
$49$	−5.34351e88	−0.982952
$50$	−2.34676e89	−1.49466
$51$	9.67674e88	0.217919
$52$	1.58687e90	1.28934
$53$	1.90979e90	0.570823	0.285412	−	0.958405i	$-0.407870\pi$
$53$	1.90979e90	0.570823	0.285412	+	0.958405i	$0.407870\pi$
$54$	6.95475e90	0.779129
$55$	−6.91929e90	−0.295815
$56$	−8.02011e90	−0.133140
$57$	4.61954e91	0.302809
$58$	−8.01801e92	−2.10910
$59$	−2.84039e92	−0.304542	−0.152271	−	0.988339i	$-0.548659\pi$
$59$	−2.84039e92	−0.304542	−0.152271	+	0.988339i	$0.548659\pi$
$60$	2.54431e92	0.112883
$61$	3.64939e93	0.679835	0.339917	−	0.940455i	$-0.389601\pi$
$61$	3.64939e93	0.679835	0.339917	+	0.940455i	$0.389601\pi$
$62$	2.02837e94	1.60910
$63$	3.57829e93	0.122545
$64$	−1.07703e95	−1.61354
$65$	−3.33360e94	−0.221290
$66$	−1.42797e95	−0.425267
$67$	−4.96150e95	−0.670944	−0.335472	−	0.942050i	$-0.608896\pi$
$67$	−4.96150e95	−0.670944	−0.335472	+	0.942050i	$0.608896\pi$
$68$	−2.30497e96	−1.43201
$69$	6.83075e94	0.0197193
$70$	4.36377e95	0.0591854
$71$	1.33111e97	0.857336	0.428668	−	0.903462i	$-0.358983\pi$
$71$	1.33111e97	0.857336	0.428668	+	0.903462i	$0.358983\pi$
$72$	−3.09662e97	−0.957043
$73$	−8.83827e97	−1.32409	−0.662044	−	0.749465i	$-0.730311\pi$
$73$	−8.83827e97	−1.32409	−0.662044	+	0.749465i	$0.730311\pi$
$74$	−3.82028e98	−2.80176
$75$	6.30400e97	0.228507
$76$	−1.10036e99	−1.98985
$77$	−1.51751e98	−0.138155
$78$	−6.87970e98	−0.318129
$79$	−1.15100e99	−0.272679	−0.136340	−	0.990662i	$-0.543534\pi$
$79$	−1.15100e99	−0.272679	−0.136340	+	0.990662i	$0.543534\pi$
$80$	−5.57867e97	−0.00682820
$81$	1.28523e100	0.819440
$82$	−5.01700e100	−1.67964
$83$	−5.00947e100	−0.887548	−0.443774	−	0.896139i	$-0.646361\pi$
$83$	−5.00947e100	−0.887548	−0.443774	+	0.896139i	$0.646361\pi$
$84$	5.58006e99	0.0527201
$85$	4.84211e100	0.245777
$86$	1.01113e102	2.77741
$87$	2.15384e101	0.322443
$88$	1.31323e102	1.07895
$89$	6.61147e101	0.300139	0.150070	−	0.988675i	$-0.452050\pi$
$89$	6.61147e101	0.300139	0.150070	+	0.988675i	$0.452050\pi$
$90$	1.68488e102	0.425439
$91$	−7.31109e101	−0.103350
$92$	−1.62706e102	−0.129581
$93$	−5.44873e102	−0.246003
$94$	−3.92292e103	−1.01018
$95$	2.31155e103	0.341519
$96$	2.84940e103	0.242948
$97$	1.82524e104	0.903239	0.451620	−	0.892211i	$-0.350846\pi$
$97$	1.82524e104	0.903239	0.451620	+	0.892211i	$0.350846\pi$
$98$	−5.51809e104	−1.59375
$99$	−5.85919e104	−0.993093
$100$	−1.50159e105	−1.50159
$101$	−1.19154e105	−0.706705	−0.353353	−	0.935490i	$-0.614958\pi$
$101$	−1.19154e105	−0.706705	−0.353353	+	0.935490i	$0.614958\pi$
$102$	9.99290e104	0.353332
$103$	5.84658e105	1.23865	0.619324	−	0.785136i	$-0.287407\pi$
$103$	5.84658e105	1.23865	0.619324	+	0.785136i	$0.287407\pi$
$104$	6.32694e105	0.807130
$105$	−1.17222e104	−0.00904839
$106$	1.97218e106	0.925527
$107$	3.82326e106	1.09594	0.547969	−	0.836499i	$-0.315401\pi$
$107$	3.82326e106	1.09594	0.547969	+	0.836499i	$0.315401\pi$
$108$	4.45005e106	0.782740
$109$	−1.46820e107	−1.59183	−0.795913	−	0.605411i	$-0.793009\pi$
$109$	−1.46820e107	−1.59183	−0.795913	+	0.605411i	$0.793009\pi$
$110$	−7.14536e106	−0.479632
$111$	1.02623e107	0.428338
$112$	−1.22349e105	−0.00318899
$113$	1.89904e107	0.310396	0.155198	−	0.987883i	$-0.450399\pi$
$113$	1.89904e107	0.310396	0.155198	+	0.987883i	$0.450399\pi$
$114$	4.77047e107	0.490971
$115$	3.41802e106	0.0222401
$116$	−5.13038e108	−2.11887
$117$	−2.82286e108	−0.742902
$118$	−2.93319e108	−0.493782
$119$	1.06195e108	0.114786
$120$	1.01443e108	0.0706652
$121$	2.65426e108	0.119595
$122$	3.76862e109	1.10228
$123$	1.34770e109	0.256787
$124$	1.29787e110	1.61656
$125$	6.57632e109	0.537288
$126$	3.69520e109	0.198694
$127$	−1.05260e110	−0.373739	−0.186869	−	0.982385i	$-0.559834\pi$
$127$	−1.05260e110	−0.373739	−0.186869	+	0.982385i	$0.559834\pi$
$128$	−6.95552e110	−1.63609
$129$	−2.71617e110	−0.424616
$130$	−3.44251e110	−0.358797
$131$	2.13428e111	1.48768	0.743838	−	0.668360i	$-0.233003\pi$
$131$	2.13428e111	1.48768	0.743838	+	0.668360i	$0.233003\pi$
$132$	−9.13695e110	−0.427238
$133$	5.06959e110	0.159500
$134$	−5.12360e111	−1.08786
$135$	−9.34835e110	−0.134342
$136$	−9.19000e111	−0.896443
$137$	−4.09322e111	−0.271791	−0.135895	−	0.990723i	$-0.543391\pi$
$137$	−4.09322e111	−0.271791	−0.135895	+	0.990723i	$0.543391\pi$
$138$	7.05392e110	0.0319727
$139$	4.93193e112	1.53017	0.765085	−	0.643930i	$-0.222697\pi$
$139$	4.93193e112	1.53017	0.765085	+	0.643930i	$0.222697\pi$
$140$	2.79219e111	0.0594597
$141$	1.05380e112	0.154438
$142$	1.37460e113	1.39007
$143$	1.19714e113	0.837533
$144$	−4.72396e111	−0.0229232
$145$	1.07775e113	0.363663
$146$	−9.12703e113	−2.14686
$147$	1.48230e113	0.243655
$148$	−2.44443e114	−2.81474
$149$	1.21380e114	0.981446	0.490723	−	0.871316i	$-0.336733\pi$
$149$	1.21380e114	0.981446	0.490723	+	0.871316i	$0.336733\pi$
$150$	6.50996e113	0.370499
$151$	2.65500e114	1.06604	0.533021	−	0.846102i	$-0.321057\pi$
$151$	2.65500e114	1.06604	0.533021	+	0.846102i	$0.321057\pi$
$152$	−4.38717e114	−1.24565
$153$	4.10026e114	0.825108
$154$	−1.56709e114	−0.224004
$155$	−2.72647e114	−0.277451
$156$	−4.40202e114	−0.319603
$157$	3.38855e115	1.75907	0.879533	−	0.475839i	$-0.157855\pi$
$157$	3.38855e115	1.75907	0.879533	+	0.475839i	$0.157855\pi$
$158$	−1.18860e115	−0.442119
$159$	−5.29779e114	−0.141497
$160$	1.42580e115	0.274006
$161$	7.49623e113	0.0103869
$162$	1.32722e116	1.32863
$163$	1.30750e116	0.947531	0.473766	−	0.880651i	$-0.342894\pi$
$163$	1.30750e116	0.947531	0.473766	+	0.880651i	$0.342894\pi$
$164$	−3.21017e116	−1.68743
$165$	1.91943e115	0.0733271
$166$	−5.17313e116	−1.43906
$167$	−8.47344e116	−1.71967	−0.859835	−	0.510572i	$-0.829434\pi$
$167$	−8.47344e116	−1.71967	−0.859835	+	0.510572i	$0.829434\pi$
$168$	2.22480e115	0.0330029
$169$	−3.43799e116	−0.373468
$170$	5.00031e116	0.398500
$171$	1.95740e117	1.14653
$172$	6.46981e117	2.79028
$173$	−5.65562e117	−1.79912	−0.899560	−	0.436798i	$-0.856112\pi$
$173$	−5.65562e117	−1.79912	−0.899560	+	0.436798i	$0.856112\pi$
$174$	2.22421e117	0.522806
$175$	6.91816e116	0.120363
$176$	2.00337e116	0.0258432
$177$	7.87931e116	0.0754904
$178$	6.82747e117	0.486642
$179$	−2.82664e118	−1.50137	−0.750683	−	0.660662i	$-0.770276\pi$
$179$	−2.82664e118	−1.50137	−0.750683	+	0.660662i	$0.770276\pi$
$180$	1.07808e118	0.427411
$181$	−1.03605e117	−0.0307083	−0.0153542	−	0.999882i	$-0.504888\pi$
$181$	−1.03605e117	−0.0307083	−0.0153542	+	0.999882i	$0.504888\pi$
$182$	−7.54995e117	−0.167570
$183$	−1.01235e118	−0.168518
$184$	−6.48716e117	−0.0811183
$185$	5.13510e118	0.483096
$186$	−5.62674e118	−0.398867
$187$	−1.73887e119	−0.930211
$188$	−2.51011e119	−1.01486
$189$	−2.05024e118	−0.0627421
$190$	2.38708e119	0.553735
$191$	1.02181e120	1.79937	0.899685	−	0.436540i	$-0.143796\pi$
$191$	1.02181e120	1.79937	0.899685	+	0.436540i	$0.143796\pi$
$192$	2.98771e119	0.399967
$193$	3.21850e119	0.328016	0.164008	−	0.986459i	$-0.447558\pi$
$193$	3.21850e119	0.328016	0.164008	+	0.986459i	$0.447558\pi$
$194$	1.88487e120	1.46450
$195$	9.24747e118	0.0548537
$196$	−3.53079e120	−1.60113
$197$	1.33975e120	0.465100	0.232550	−	0.972584i	$-0.425293\pi$
$197$	1.33975e120	0.465100	0.232550	+	0.972584i	$0.425293\pi$
$198$	−6.05062e120	−1.61019
$199$	1.61212e120	0.329315	0.164657	−	0.986351i	$-0.447348\pi$
$199$	1.61212e120	0.329315	0.164657	+	0.986351i	$0.447348\pi$
$200$	−5.98690e120	−0.939999
$201$	1.37633e120	0.166314
$202$	−1.23047e121	−1.14584
$203$	2.36368e120	0.169843
$204$	6.39402e120	0.354969
$205$	6.74369e120	0.289614
$206$	6.03760e121	2.00833
$207$	2.89434e120	0.0746633
$208$	9.65190e119	0.0193325
$209$	−8.30109e121	−1.29257
$210$	−1.21052e120	−0.0146710
$211$	−5.16909e121	−0.488186	−0.244093	−	0.969752i	$-0.578490\pi$
$211$	−5.16909e121	−0.488186	−0.244093	+	0.969752i	$0.578490\pi$
$212$	1.26191e122	0.929817
$213$	−3.69253e121	−0.212518
$214$	3.94817e122	1.77694
$215$	−1.35913e122	−0.478898
$216$	1.77425e122	0.489997
$217$	−5.97957e121	−0.129579
$218$	−1.51617e123	−2.58097
$219$	2.45176e122	0.328217
$220$	−4.57201e122	−0.481855
$221$	−8.37755e122	−0.695862
$222$	1.05975e123	0.694503
$223$	−1.13362e123	−0.586765	−0.293382	−	0.955995i	$-0.594781\pi$
$223$	−1.13362e123	−0.586765	−0.293382	+	0.955995i	$0.594781\pi$
$224$	3.12700e122	0.127969
$225$	2.67115e123	0.865198
$226$	1.96108e123	0.503272
$227$	3.47011e123	0.706295	0.353147	−	0.935568i	$-0.385111\pi$
$227$	3.47011e123	0.706295	0.353147	+	0.935568i	$0.385111\pi$
$228$	3.05242e123	0.493247
$229$	8.38603e123	1.07695	0.538473	−	0.842643i	$-0.319002\pi$
$229$	8.38603e123	1.07695	0.538473	+	0.842643i	$0.319002\pi$
$230$	3.52969e122	0.0360599
$231$	4.20960e122	0.0342461
$232$	−2.04550e124	−1.32642
$233$	−1.19820e124	−0.619930	−0.309965	−	0.950748i	$-0.600317\pi$
$233$	−1.19820e124	−0.619930	−0.309965	+	0.950748i	$0.600317\pi$
$234$	−2.91508e124	−1.20453
$235$	5.27306e123	0.174181
$236$	−1.87682e124	−0.496070
$237$	3.19289e123	0.0675921
$238$	1.09664e124	0.186113
$239$	1.34965e125	1.83795	0.918973	−	0.394320i	$-0.129020\pi$
$239$	1.34965e125	1.83795	0.918973	+	0.394320i	$0.129020\pi$
$240$	1.54753e122	0.00169258
$241$	−1.84320e125	−1.62061	−0.810305	−	0.586008i	$-0.800699\pi$
$241$	−1.84320e125	−1.62061	−0.810305	+	0.586008i	$0.800699\pi$
$242$	2.74098e124	0.193910
$243$	−1.19996e125	−0.683656
$244$	2.41138e125	1.10739
$245$	7.41723e124	0.274804
$246$	1.39173e125	0.416352
$247$	−3.99932e125	−0.966933
$248$	5.17465e125	1.01197
$249$	1.38964e125	0.220007
$250$	6.79118e125	0.871154
$251$	−5.04861e125	−0.525172	−0.262586	−	0.964909i	$-0.584575\pi$
$251$	−5.04861e125	−0.525172	−0.262586	+	0.964909i	$0.584575\pi$
$252$	2.36440e125	0.199615
$253$	−1.22745e125	−0.0841740
$254$	−1.08699e126	−0.605976
$255$	−1.34321e125	−0.0609235
$256$	−2.81379e126	−1.03919
$257$	−4.52195e126	−1.36093	−0.680467	−	0.732779i	$-0.738223\pi$
$257$	−4.52195e126	−1.36093	−0.680467	+	0.732779i	$0.738223\pi$
$258$	−2.80491e126	−0.688468
$259$	1.12621e126	0.225621
$260$	−2.20271e126	−0.360460
$261$	9.12632e126	1.22087
$262$	2.20401e127	2.41210
$263$	8.08828e126	0.724735	0.362367	−	0.932035i	$-0.381969\pi$
$263$	8.08828e126	0.724735	0.362367	+	0.932035i	$0.381969\pi$
$264$	−3.64294e126	−0.267452
$265$	−2.65094e126	−0.159585
$266$	5.23522e126	0.258612
$267$	−1.83403e126	−0.0743989
$268$	−3.27837e127	−1.09290
$269$	−1.02359e127	−0.280628	−0.140314	−	0.990107i	$-0.544811\pi$
$269$	−1.02359e127	−0.280628	−0.140314	+	0.990107i	$0.544811\pi$
$270$	−9.65377e126	−0.217821
$271$	1.97338e127	0.366710	0.183355	−	0.983047i	$-0.441304\pi$
$271$	1.97338e127	0.366710	0.183355	+	0.983047i	$0.441304\pi$
$272$	−1.40196e126	−0.0214717
$273$	2.02811e126	0.0256184
$274$	−4.22695e127	−0.440679
$275$	−1.13280e128	−0.975408
$276$	4.51350e126	0.0321208
$277$	−6.48997e127	−0.381992	−0.190996	−	0.981591i	$-0.561172\pi$
$277$	−6.48997e127	−0.381992	−0.190996	+	0.981591i	$0.561172\pi$
$278$	5.09306e128	2.48100
$279$	−2.30875e128	−0.931442
$280$	1.11326e127	0.0372219
$281$	−1.98290e128	−0.549818	−0.274909	−	0.961470i	$-0.588648\pi$
$281$	−1.98290e128	−0.549818	−0.274909	+	0.961470i	$0.588648\pi$
$282$	1.08823e128	0.250404
$283$	−7.67388e128	−1.46632	−0.733158	−	0.680059i	$-0.761954\pi$
$283$	−7.67388e128	−1.46632	−0.733158	+	0.680059i	$0.761954\pi$
$284$	8.79547e128	1.39652
$285$	−6.41230e127	−0.0846562
$286$	1.23625e129	1.35797
$287$	1.47899e128	0.135259
$288$	1.20735e129	0.919875
$289$	−3.57623e128	−0.227137
$290$	1.11297e129	0.589640
$291$	−5.06324e128	−0.223896
$292$	−5.83999e129	−2.15681
$293$	−4.81415e129	−1.48583	−0.742916	−	0.669385i	$-0.766558\pi$
$293$	−4.81415e129	−1.48583	−0.742916	+	0.669385i	$0.766558\pi$
$294$	1.53073e129	0.395060
$295$	3.94270e128	0.0851408
$296$	−9.74607e129	−1.76204
$297$	3.35711e129	0.508455
$298$	1.25345e130	1.59131
$299$	−5.91366e128	−0.0629679
$300$	4.16544e129	0.372216
$301$	−2.98079e129	−0.223661
$302$	2.74174e130	1.72847
$303$	3.30537e129	0.175179
$304$	−6.69274e128	−0.0298360
$305$	−5.06565e129	−0.190061
$306$	4.23422e130	1.33782
$307$	−6.76464e130	−1.80086	−0.900430	−	0.435001i	$-0.856748\pi$
$307$	−6.76464e130	−1.80086	−0.900430	+	0.435001i	$0.856748\pi$
$308$	−1.00271e130	−0.225042
$309$	−1.62185e130	−0.307038
$310$	−2.81555e130	−0.449856
$311$	−1.62681e130	−0.219491	−0.109746	−	0.993960i	$-0.535004\pi$
$311$	−1.62681e130	−0.219491	−0.109746	+	0.993960i	$0.535004\pi$
$312$	−1.75511e130	−0.200072
$313$	−1.22308e131	−1.17863	−0.589315	−	0.807903i	$-0.700602\pi$
$313$	−1.22308e131	−1.17863	−0.589315	+	0.807903i	$0.700602\pi$
$314$	3.49926e131	2.85213
$315$	−4.96696e129	−0.0342600
$316$	−7.60535e130	−0.444168
$317$	−8.81854e130	−0.436300	−0.218150	−	0.975915i	$-0.570002\pi$
$317$	−8.81854e130	−0.436300	−0.218150	+	0.975915i	$0.570002\pi$
$318$	−5.47088e130	−0.229421
$319$	−3.87036e131	−1.37639
$320$	1.49501e131	0.451098
$321$	−1.06058e131	−0.271663
$322$	7.74115e129	0.0168412
$323$	5.80909e131	1.07393
$324$	8.49231e131	1.33479
$325$	−5.45763e131	−0.729672
$326$	1.35022e132	1.53632
$327$	4.07283e131	0.394584
$328$	−1.27991e132	−1.05633
$329$	1.15646e131	0.0813480
$330$	1.98214e131	0.118892
$331$	−4.77509e131	−0.244350	−0.122175	−	0.992509i	$-0.538987\pi$
$331$	−4.77509e131	−0.244350	−0.122175	+	0.992509i	$0.538987\pi$
$332$	−3.31007e132	−1.44573
$333$	4.34835e132	1.62182
$334$	−8.75028e132	−2.78825
$335$	6.88697e131	0.187575
$336$	3.39398e129	0.000790491 0
$337$	−7.27203e131	−0.144906	−0.0724529	−	0.997372i	$-0.523083\pi$
$337$	−7.27203e131	−0.144906	−0.0724529	+	0.997372i	$0.523083\pi$
$338$	−3.55032e132	−0.605537
$339$	−5.26797e131	−0.0769413
$340$	3.19948e132	0.400347
$341$	9.79110e132	1.05009
$342$	2.02135e133	1.85897
$343$	3.28164e132	0.258910
$344$	2.57954e133	1.74672
$345$	−9.48165e130	−0.00551292
$346$	−5.84040e133	−2.91707
$347$	−3.89677e132	−0.167266	−0.0836328	−	0.996497i	$-0.526652\pi$
$347$	−3.89677e132	−0.167266	−0.0836328	+	0.996497i	$0.526652\pi$
$348$	1.42318e133	0.525229
$349$	−3.25515e133	−1.03332	−0.516662	−	0.856190i	$-0.672825\pi$
$349$	−3.25515e133	−1.03332	−0.516662	+	0.856190i	$0.672825\pi$
$350$	7.14419e132	0.195155
$351$	1.61740e133	0.380359
$352$	−5.12023e133	−1.03705
$353$	6.25734e133	1.09199	0.545994	−	0.837789i	$-0.316152\pi$
$353$	6.25734e133	1.09199	0.545994	+	0.837789i	$0.316152\pi$
$354$	8.13674e132	0.122399
$355$	−1.84769e133	−0.239685
$356$	4.36861e133	0.488898
$357$	−2.94587e132	−0.0284533
$358$	−2.91899e134	−2.43430
$359$	1.08453e134	0.781236	0.390618	−	0.920553i	$-0.372261\pi$
$359$	1.08453e134	0.781236	0.390618	+	0.920553i	$0.372261\pi$
$360$	4.29836e133	0.267560
$361$	9.14826e133	0.492278
$362$	−1.06990e133	−0.0497902
$363$	−7.36298e132	−0.0296453
$364$	−4.83089e133	−0.168347
$365$	1.22682e134	0.370175
$366$	−1.04542e134	−0.273234
$367$	4.80224e134	1.08762	0.543808	−	0.839210i	$-0.316982\pi$
$367$	4.80224e134	1.08762	0.543808	+	0.839210i	$0.316982\pi$
$368$	−9.89633e131	−0.00194296
$369$	5.71050e134	0.972276
$370$	5.30287e134	0.783286
$371$	−5.81392e133	−0.0745314
$372$	−3.60031e134	−0.400715
$373$	−3.40674e134	−0.329325	−0.164663	−	0.986350i	$-0.552654\pi$
$373$	−3.40674e134	−0.329325	−0.164663	+	0.986350i	$0.552654\pi$
$374$	−1.79568e135	−1.50823
$375$	−1.82429e134	−0.133184
$376$	−1.00079e135	−0.635304
$377$	−1.86467e135	−1.02963
$378$	−2.11722e134	−0.101729
$379$	−2.63938e135	−1.10394	−0.551968	−	0.833865i	$-0.686123\pi$
$379$	−2.63938e135	−1.10394	−0.551968	+	0.833865i	$0.686123\pi$
$380$	1.52739e135	0.556302
$381$	2.91994e134	0.0926429
$382$	1.05520e136	2.91748
$383$	−3.06697e133	−0.00739220	−0.00369610	−	0.999993i	$-0.501177\pi$
$383$	−3.06697e133	−0.00739220	−0.00369610	+	0.999993i	$0.501177\pi$
$384$	1.92947e135	0.405555
$385$	2.10643e134	0.0386240
$386$	3.32365e135	0.531841
$387$	−1.15090e136	−1.60773
$388$	1.20605e136	1.47129
$389$	−3.94802e135	−0.420751	−0.210376	−	0.977621i	$-0.567469\pi$
$389$	−3.94802e135	−0.420751	−0.210376	+	0.977621i	$0.567469\pi$
$390$	9.54959e134	0.0889392
$391$	8.58971e134	0.0699356
$392$	−1.40774e136	−1.00231
$393$	−5.92054e135	−0.368767
$394$	1.38352e136	0.754109
$395$	1.59768e135	0.0762328
$396$	−3.87153e136	−1.61765
$397$	−2.49919e135	−0.0914740	−0.0457370	−	0.998954i	$-0.514564\pi$
$397$	−2.49919e135	−0.0914740	−0.0457370	+	0.998954i	$0.514564\pi$
$398$	1.66479e136	0.533947
$399$	−1.40632e135	−0.0395372
$400$	−9.13317e134	−0.0225150
$401$	2.08911e136	0.451734	0.225867	−	0.974158i	$-0.427479\pi$
$401$	2.08911e136	0.451734	0.225867	+	0.974158i	$0.427479\pi$
$402$	1.42130e136	0.269660
$403$	4.71719e136	0.785540
$404$	−7.87327e136	−1.15115
$405$	−1.78400e136	−0.229091
$406$	2.44091e136	0.275381
$407$	−1.84408e137	−1.82841
$408$	2.54933e136	0.222212
$409$	1.89309e137	1.45110	0.725551	−	0.688168i	$-0.241585\pi$
$409$	1.89309e137	1.45110	0.725551	+	0.688168i	$0.241585\pi$
$410$	6.96402e136	0.469578
$411$	1.13547e136	0.0673719
$412$	3.86320e137	2.01764
$413$	8.64695e135	0.0397635
$414$	2.98891e136	0.121058
$415$	6.95356e136	0.248131
$416$	−2.46684e137	−0.775784
$417$	−1.36813e137	−0.379300
$418$	−8.57230e137	−2.09577
$419$	−3.76420e136	−0.0811777	−0.0405889	−	0.999176i	$-0.512923\pi$
$419$	−3.76420e136	−0.0811777	−0.0405889	+	0.999176i	$0.512923\pi$
$420$	−7.74559e135	−0.0147390
$421$	−6.26646e137	−1.05248	−0.526238	−	0.850337i	$-0.676398\pi$
$421$	−6.26646e137	−1.05248	−0.526238	+	0.850337i	$0.676398\pi$
$422$	−5.33797e137	−0.791539
$423$	4.46518e137	0.584749
$424$	5.03131e137	0.582068
$425$	7.92731e137	0.810414
$426$	−3.81317e137	−0.344574
$427$	−1.11097e137	−0.0887648
$428$	2.52627e138	1.78518
$429$	−3.32089e137	−0.207609
$430$	−1.40354e138	−0.776480
$431$	2.82998e138	1.38588	0.692941	−	0.720994i	$-0.256314\pi$
$431$	2.82998e138	1.38588	0.692941	+	0.720994i	$0.256314\pi$
$432$	2.70667e136	0.0117365
$433$	3.83279e138	1.47198	0.735988	−	0.676994i	$-0.236718\pi$
$433$	3.83279e138	1.47198	0.735988	+	0.676994i	$0.236718\pi$
$434$	−6.17493e137	−0.210098
$435$	−2.98971e137	−0.0901454
$436$	−9.70134e138	−2.59293
$437$	4.10060e137	0.0971790
$438$	2.53186e138	0.532168
$439$	−7.85880e138	−1.46544	−0.732722	−	0.680529i	$-0.761750\pi$
$439$	−7.85880e138	−1.46544	−0.732722	+	0.680529i	$0.761750\pi$
$440$	−1.82288e138	−0.301642
$441$	6.28084e138	0.922554
$442$	−8.65126e138	−1.12826
$443$	1.56157e139	1.80870	0.904349	−	0.426794i	$-0.140357\pi$
$443$	1.56157e139	1.80870	0.904349	+	0.426794i	$0.140357\pi$
$444$	6.78091e138	0.697722
$445$	−9.17726e137	−0.0839098
$446$	−1.17066e139	−0.951374
$447$	−3.36709e138	−0.243282
$448$	3.27879e138	0.210677
$449$	−2.40110e139	−1.37239	−0.686196	−	0.727417i	$-0.740721\pi$
$449$	−2.40110e139	−1.37239	−0.686196	+	0.727417i	$0.740721\pi$
$450$	2.75842e139	1.40282
$451$	−2.42175e139	−1.09613
$452$	1.25481e139	0.505604
$453$	−7.36501e138	−0.264252
$454$	3.58348e139	1.14518
$455$	1.01484e138	0.0288934
$456$	1.21701e139	0.308774
$457$	5.92334e138	0.133957	0.0669786	−	0.997754i	$-0.478664\pi$
$457$	5.92334e138	0.133957	0.0669786	+	0.997754i	$0.478664\pi$
$458$	8.66001e139	1.74615
$459$	−2.34930e139	−0.422448
$460$	2.25849e138	0.0362270
$461$	−1.13272e140	−1.62115	−0.810577	−	0.585632i	$-0.800846\pi$
$461$	−1.13272e140	−1.62115	−0.810577	+	0.585632i	$0.800846\pi$
$462$	4.34713e138	0.0555263
$463$	4.89305e139	0.557928	0.278964	−	0.960302i	$-0.410009\pi$
$463$	4.89305e139	0.557928	0.278964	+	0.960302i	$0.410009\pi$
$464$	−3.12047e138	−0.0317706
$465$	7.56328e138	0.0687750
$466$	−1.23734e140	−1.00515
$467$	−1.36004e140	−0.987221	−0.493610	−	0.869683i	$-0.664323\pi$
$467$	−1.36004e140	−0.987221	−0.493610	+	0.869683i	$0.664323\pi$
$468$	−1.86524e140	−1.21012
$469$	1.51042e139	0.0876038
$470$	5.44534e139	0.282415
$471$	−9.39991e139	−0.436040
$472$	−7.48298e139	−0.310541
$473$	4.88082e140	1.81252
$474$	3.29721e139	0.109593
$475$	3.78438e140	1.12611
$476$	7.01696e139	0.186975
$477$	−2.24479e140	−0.535749
$478$	1.39375e141	2.98003
$479$	2.16327e140	0.414473	0.207237	−	0.978291i	$-0.433553\pi$
$479$	2.16327e140	0.414473	0.207237	+	0.978291i	$0.433553\pi$
$480$	−3.95520e139	−0.0679209
$481$	−8.88446e140	−1.36777
$482$	−1.90342e141	−2.62764
$483$	−2.07947e138	−0.00257471
$484$	1.75384e140	0.194808
$485$	−2.53358e140	−0.252518
$486$	−1.23916e141	−1.10847
$487$	1.52760e141	1.22670	0.613349	−	0.789812i	$-0.289822\pi$
$487$	1.52760e141	1.22670	0.613349	+	0.789812i	$0.289822\pi$
$488$	9.61426e140	0.693226
$489$	−3.62704e140	−0.234875
$490$	7.65956e140	0.445564
$491$	−2.51656e141	−1.31531	−0.657656	−	0.753318i	$-0.728452\pi$
$491$	−2.51656e141	−1.31531	−0.657656	+	0.753318i	$0.728452\pi$
$492$	8.90507e140	0.418282
$493$	2.70847e141	1.14356
$494$	−4.12999e141	−1.56778
$495$	8.13304e140	0.277639
$496$	7.89406e139	0.0242389
$497$	−4.05227e140	−0.111941
$498$	1.43504e141	0.356716
$499$	−1.66340e141	−0.372150	−0.186075	−	0.982536i	$-0.559577\pi$
$499$	−1.66340e141	−0.372150	−0.186075	+	0.982536i	$0.559577\pi$
$500$	4.34538e141	0.875191
$501$	2.35055e141	0.426274
$502$	−5.21356e141	−0.851509
$503$	5.11786e141	0.752956	0.376478	−	0.926426i	$-0.377135\pi$
$503$	5.11786e141	0.752956	0.376478	+	0.926426i	$0.377135\pi$
$504$	9.42696e140	0.124959
$505$	1.65396e141	0.197573
$506$	−1.26756e141	−0.136479
$507$	9.53707e140	0.0925757
$508$	−6.95518e141	−0.608785
$509$	2.08898e142	1.64912	0.824558	−	0.565778i	$-0.191424\pi$
$509$	2.08898e142	1.64912	0.824558	+	0.565778i	$0.191424\pi$
$510$	−1.38710e141	−0.0987808
$511$	2.69062e141	0.172884
$512$	−8.42315e140	−0.0488429
$513$	−1.12152e142	−0.587012
$514$	−4.66969e142	−2.20660
$515$	−8.11554e141	−0.346288
$516$	−1.79474e142	−0.691659
$517$	−1.89362e142	−0.659235
$518$	1.16300e142	0.365820
$519$	1.56888e142	0.445968
$520$	−8.78231e141	−0.225649
$521$	−7.88634e140	−0.0183187	−0.00915936	−	0.999958i	$-0.502916\pi$
$521$	−7.88634e140	−0.0183187	−0.00915936	+	0.999958i	$0.502916\pi$
$522$	9.42449e142	1.97950
$523$	−3.47386e142	−0.659893	−0.329947	−	0.944000i	$-0.607031\pi$
$523$	−3.47386e142	−0.659893	−0.329947	+	0.944000i	$0.607031\pi$
$524$	1.41025e143	2.42328
$525$	−1.91911e141	−0.0298358
$526$	8.35253e142	1.17508
$527$	−6.85180e142	−0.872464
$528$	−5.55740e140	−0.00640605
$529$	−9.52063e142	−0.993672
$530$	−2.73755e142	−0.258749
$531$	3.33864e142	0.285830
$532$	3.34979e142	0.259811
$533$	−1.16676e143	−0.819977
$534$	−1.89396e142	−0.120630
$535$	−5.30701e142	−0.306391
$536$	−1.30710e143	−0.684160
$537$	7.84117e142	0.372161
$538$	−1.05703e143	−0.455007
$539$	−2.66362e143	−1.04007
$540$	−6.17703e142	−0.218830
$541$	2.80623e143	0.902126	0.451063	−	0.892492i	$-0.351045\pi$
$541$	2.80623e143	0.902126	0.451063	+	0.892492i	$0.351045\pi$
$542$	2.03785e143	0.594580
$543$	2.87403e141	0.00761202
$544$	3.58313e143	0.861629
$545$	2.03799e143	0.445026
$546$	2.09437e142	0.0415375
$547$	1.36569e143	0.246047	0.123024	−	0.992404i	$-0.460741\pi$
$547$	1.36569e143	0.246047	0.123024	+	0.992404i	$0.460741\pi$
$548$	−2.70464e143	−0.442721
$549$	−4.28955e143	−0.638062
$550$	−1.16981e144	−1.58152
$551$	1.29298e144	1.58904
$552$	1.79955e142	0.0201077
$553$	3.50395e142	0.0356032
$554$	−6.70200e143	−0.619358
$555$	−1.42449e143	−0.119750
$556$	3.25883e144	2.49250
$557$	5.17009e143	0.359833	0.179916	−	0.983682i	$-0.442417\pi$
$557$	5.17009e143	0.359833	0.179916	+	0.983682i	$0.442417\pi$
$558$	−2.38418e144	−1.51023
$559$	2.35150e144	1.35589
$560$	1.69830e141	0.000891545 0
$561$	4.82365e143	0.230582
$562$	−2.04768e144	−0.891469
$563$	−4.74938e144	−1.88342	−0.941709	−	0.336429i	$-0.890781\pi$
$563$	−4.74938e144	−1.88342	−0.941709	+	0.336429i	$0.890781\pi$
$564$	6.96309e143	0.251564
$565$	−2.63602e143	−0.0867772
$566$	−7.92460e144	−2.37747
$567$	−3.91260e143	−0.106993
$568$	3.50679e144	0.874224
$569$	1.10238e144	0.250574	0.125287	−	0.992121i	$-0.460015\pi$
$569$	1.10238e144	0.250574	0.125287	+	0.992121i	$0.460015\pi$
$570$	−6.62180e143	−0.137261
$571$	4.01955e144	0.759944	0.379972	−	0.924998i	$-0.375934\pi$
$571$	4.01955e144	0.759944	0.379972	+	0.924998i	$0.375934\pi$
$572$	7.91023e144	1.36426
$573$	−2.83454e144	−0.446030
$574$	1.52732e144	0.219308
$575$	5.59584e143	0.0733337
$576$	1.26596e145	1.51440
$577$	1.09495e144	0.119582	0.0597909	−	0.998211i	$-0.480957\pi$
$577$	1.09495e144	0.119582	0.0597909	+	0.998211i	$0.480957\pi$
$578$	−3.69307e144	−0.368278
$579$	−8.92818e143	−0.0813090
$580$	7.12139e144	0.592373
$581$	1.52502e144	0.115885
$582$	−5.22866e144	−0.363023
$583$	9.51988e144	0.603993
$584$	−2.32843e145	−1.35017
$585$	3.91836e144	0.207693
$586$	−4.97144e145	−2.40911
$587$	2.23123e144	0.0988652	0.0494326	−	0.998777i	$-0.484259\pi$
$587$	2.23123e144	0.0988652	0.0494326	+	0.998777i	$0.484259\pi$
$588$	9.79448e144	0.396891
$589$	−3.27095e145	−1.21233
$590$	4.07151e144	0.138046
$591$	−3.71649e144	−0.115290
$592$	−1.48679e144	−0.0422045
$593$	4.65023e145	1.20810	0.604050	−	0.796946i	$-0.293553\pi$
$593$	4.65023e145	1.20810	0.604050	+	0.796946i	$0.293553\pi$
$594$	3.46679e145	0.824403
$595$	−1.47407e144	−0.0320906
$596$	8.02030e145	1.59868
$597$	−4.47206e144	−0.0816310
$598$	−6.10687e144	−0.102095
$599$	−6.28831e145	−0.962999	−0.481499	−	0.876446i	$-0.659908\pi$
$599$	−6.28831e145	−0.962999	−0.481499	+	0.876446i	$0.659908\pi$
$600$	1.66078e145	0.233008
$601$	−1.30706e146	−1.68029	−0.840147	−	0.542359i	$-0.817531\pi$
$601$	−1.30706e146	−1.68029	−0.840147	+	0.542359i	$0.817531\pi$
$602$	−3.07817e145	−0.362641
$603$	5.83183e145	0.629717
$604$	1.75432e146	1.73648
$605$	−3.68433e144	−0.0334350
$606$	3.41336e145	0.284033
$607$	−1.74931e146	−1.33494	−0.667469	−	0.744638i	$-0.732622\pi$
$607$	−1.74931e146	−1.33494	−0.667469	+	0.744638i	$0.732622\pi$
$608$	1.71054e146	1.19728
$609$	−6.55690e144	−0.0421008
$610$	−5.23115e145	−0.308163
$611$	−9.12315e145	−0.493153
$612$	2.70929e146	1.34402
$613$	2.63791e146	1.20112	0.600558	−	0.799581i	$-0.294945\pi$
$613$	2.63791e146	1.20112	0.600558	+	0.799581i	$0.294945\pi$
$614$	−6.98565e146	−2.91989
$615$	−1.87071e145	−0.0717900
$616$	−3.99785e145	−0.140877
$617$	−1.82675e146	−0.591164	−0.295582	−	0.955317i	$-0.595513\pi$
$617$	−1.82675e146	−0.591164	−0.295582	+	0.955317i	$0.595513\pi$
$618$	−1.67484e146	−0.497828
$619$	3.49692e146	0.954832	0.477416	−	0.878677i	$-0.341574\pi$
$619$	3.49692e146	0.954832	0.477416	+	0.878677i	$0.341574\pi$
$620$	−1.80155e146	−0.451941
$621$	−1.65836e145	−0.0382269
$622$	−1.67997e146	−0.355881
$623$	−2.01271e145	−0.0391886
$624$	−2.67746e144	−0.00479216
$625$	4.68933e146	0.771631
$626$	−1.26304e147	−1.91102
$627$	2.30274e146	0.320405
$628$	2.23902e147	2.86535
$629$	1.29049e147	1.51913
$630$	−5.12924e145	−0.0555487
$631$	8.83472e146	0.880342	0.440171	−	0.897914i	$-0.354918\pi$
$631$	8.83472e146	0.880342	0.440171	+	0.897914i	$0.354918\pi$
$632$	−3.03229e146	−0.278050
$633$	1.43392e146	0.121012
$634$	−9.10666e146	−0.707413
$635$	1.46110e146	0.104486
$636$	−3.50058e146	−0.230484
$637$	−1.28329e147	−0.778044
$638$	−3.99681e147	−2.23166
$639$	−1.56461e147	−0.804656
$640$	9.65483e146	0.457400
$641$	−1.21859e147	−0.531875	−0.265937	−	0.963990i	$-0.585681\pi$
$641$	−1.21859e147	−0.531875	−0.265937	+	0.963990i	$0.585681\pi$
$642$	−1.09523e147	−0.440471
$643$	1.50782e147	0.558822	0.279411	−	0.960172i	$-0.409861\pi$
$643$	1.50782e147	0.558822	0.279411	+	0.960172i	$0.409861\pi$
$644$	4.95323e145	0.0169192
$645$	3.77026e146	0.118710
$646$	5.99888e147	1.74126
$647$	−1.59600e146	−0.0427128	−0.0213564	−	0.999772i	$-0.506798\pi$
$647$	−1.59600e146	−0.0427128	−0.0213564	+	0.999772i	$0.506798\pi$
$648$	3.38592e147	0.835581
$649$	−1.41587e147	−0.322239
$650$	−5.63594e147	−1.18308
$651$	1.65874e146	0.0321201
$652$	8.63948e147	1.54344
$653$	−6.07906e147	−1.00206	−0.501030	−	0.865430i	$-0.667046\pi$
$653$	−6.07906e147	−1.00206	−0.501030	+	0.865430i	$0.667046\pi$
$654$	4.20590e147	0.639774
$655$	−2.96256e147	−0.415909
$656$	−1.95253e146	−0.0253015
$657$	1.03886e148	1.24273
$658$	1.19425e147	0.131897
$659$	−7.04451e147	−0.718401	−0.359200	−	0.933260i	$-0.616951\pi$
$659$	−7.04451e147	−0.718401	−0.359200	+	0.933260i	$0.616951\pi$
$660$	1.26828e147	0.119443
$661$	−5.89028e147	−0.512341	−0.256171	−	0.966632i	$-0.582461\pi$
$661$	−5.89028e147	−0.512341	−0.256171	+	0.966632i	$0.582461\pi$
$662$	−4.93110e147	−0.396186
$663$	2.32395e147	0.172491
$664$	−1.31974e148	−0.905031
$665$	−7.03702e146	−0.0445915
$666$	4.49042e148	2.62960
$667$	1.91189e147	0.103480
$668$	−5.59893e148	−2.80118
$669$	3.14470e147	0.145448
$670$	7.11198e147	0.304133
$671$	1.81914e148	0.719340
$672$	−8.67435e146	−0.0317213
$673$	−1.13637e148	−0.384350	−0.192175	−	0.981361i	$-0.561554\pi$
$673$	−1.13637e148	−0.384350	−0.192175	+	0.981361i	$0.561554\pi$
$674$	−7.50961e147	−0.234949
$675$	−1.53047e148	−0.442974
$676$	−2.27170e148	−0.608343
$677$	−1.55016e148	−0.384123	−0.192062	−	0.981383i	$-0.561517\pi$
$677$	−1.55016e148	−0.384123	−0.192062	+	0.981383i	$0.561517\pi$
$678$	−5.44008e147	−0.124752
$679$	−5.55652e147	−0.117934
$680$	1.27565e148	0.250618
$681$	−9.62616e147	−0.175077
$682$	1.01110e149	1.70261
$683$	3.44980e148	0.537907	0.268954	−	0.963153i	$-0.413322\pi$
$683$	3.44980e148	0.537907	0.268954	+	0.963153i	$0.413322\pi$
$684$	1.29338e149	1.86758
$685$	5.68172e147	0.0759845
$686$	3.38885e148	0.419795
$687$	−2.32630e148	−0.266955
$688$	3.93515e147	0.0418378
$689$	4.58651e148	0.451828
$690$	−9.79143e146	−0.00893858
$691$	−1.05892e149	−0.895915	−0.447957	−	0.894055i	$-0.647848\pi$
$691$	−1.05892e149	−0.895915	−0.447957	+	0.894055i	$0.647848\pi$
$692$	−3.73702e149	−2.93059
$693$	1.78370e148	0.129666
$694$	−4.02408e148	−0.271203
$695$	−6.84592e148	−0.427789
$696$	5.67427e148	0.328795
$697$	1.69474e149	0.910712
$698$	−3.36150e149	−1.67542
$699$	3.32382e148	0.153669
$700$	4.57126e148	0.196060
$701$	−1.63990e149	−0.652561	−0.326280	−	0.945273i	$-0.605795\pi$
$701$	−1.63990e149	−0.652561	−0.326280	+	0.945273i	$0.605795\pi$
$702$	1.67024e149	0.616710
$703$	6.16059e149	2.11090
$704$	−5.36878e149	−1.70730
$705$	−1.46276e148	−0.0431761
$706$	6.46177e149	1.77054
$707$	3.62739e148	0.0922732
$708$	5.20635e148	0.122967
$709$	4.35222e149	0.954516	0.477258	−	0.878763i	$-0.341631\pi$
$709$	4.35222e149	0.954516	0.477258	+	0.878763i	$0.341631\pi$
$710$	−1.90806e149	−0.388623
$711$	1.35290e149	0.255924
$712$	1.74178e149	0.306051
$713$	−4.83664e148	−0.0789485
$714$	−3.04212e148	−0.0461338
$715$	−1.66173e149	−0.234149
$716$	−1.86774e150	−2.44558
$717$	−3.74397e149	−0.455593
$718$	1.11996e150	1.26669
$719$	−4.96405e149	−0.521878	−0.260939	−	0.965355i	$-0.584032\pi$
$719$	−4.96405e149	−0.521878	−0.260939	+	0.965355i	$0.584032\pi$
$720$	6.55725e147	0.00640864
$721$	−1.77986e149	−0.161728
$722$	9.44714e149	0.798174
$723$	5.11309e149	0.401719
$724$	−6.84583e148	−0.0500209
$725$	1.76446e150	1.19913
$726$	−7.60354e148	−0.0480666
$727$	−2.41824e150	−1.42214	−0.711072	−	0.703119i	$-0.751790\pi$
$727$	−2.41824e150	−1.42214	−0.711072	+	0.703119i	$0.751790\pi$
$728$	−1.92610e149	−0.105385
$729$	−1.27671e150	−0.649974
$730$	1.26691e150	0.600198
$731$	−3.41559e150	−1.50593
$732$	−6.68921e149	−0.274500
$733$	−2.05795e150	−0.786096	−0.393048	−	0.919518i	$-0.628579\pi$
$733$	−2.05795e150	−0.786096	−0.393048	+	0.919518i	$0.628579\pi$
$734$	4.95914e150	1.76345
$735$	−2.05756e149	−0.0681187
$736$	2.52931e149	0.0779680
$737$	−2.47320e150	−0.709931
$738$	5.89706e150	1.57644
$739$	2.20246e150	0.548372	0.274186	−	0.961677i	$-0.411592\pi$
$739$	2.20246e150	0.548372	0.274186	+	0.961677i	$0.411592\pi$
$740$	3.39308e150	0.786916
$741$	1.10942e150	0.239685
$742$	−6.00387e149	−0.120844
$743$	4.42483e150	0.829819	0.414910	−	0.909863i	$-0.363813\pi$
$743$	4.42483e150	0.829819	0.414910	+	0.909863i	$0.363813\pi$
$744$	−1.43546e150	−0.250849
$745$	−1.68485e150	−0.274383
$746$	−3.51804e150	−0.533964
$747$	5.88821e150	0.833012
$748$	−1.14898e151	−1.51522
$749$	−1.16391e150	−0.143095
$750$	−1.88389e150	−0.215943
$751$	2.63233e150	0.281348	0.140674	−	0.990056i	$-0.455073\pi$
$751$	2.63233e150	0.281348	0.140674	+	0.990056i	$0.455073\pi$
$752$	−1.52673e149	−0.0152169
$753$	1.40050e150	0.130180
$754$	−1.92559e151	−1.66943
$755$	−3.68535e150	−0.298033
$756$	−1.35472e150	−0.102201
$757$	−2.55196e150	−0.179614	−0.0898072	−	0.995959i	$-0.528625\pi$
$757$	−2.55196e150	−0.179614	−0.0898072	+	0.995959i	$0.528625\pi$
$758$	−2.72562e151	−1.78991
$759$	3.40498e149	0.0208652
$760$	6.08976e150	0.348246
$761$	3.67649e151	1.96218	0.981091	−	0.193549i	$-0.0619997\pi$
$761$	3.67649e151	1.96218	0.981091	+	0.193549i	$0.0619997\pi$
$762$	3.01533e150	0.150210
$763$	4.46962e150	0.207842
$764$	6.75176e151	2.93100
$765$	−5.69149e150	−0.230675
$766$	−3.16717e149	−0.0119856
$767$	−6.82144e150	−0.241057
$768$	7.80552e150	0.257595
$769$	−8.16388e150	−0.251631	−0.125815	−	0.992054i	$-0.540155\pi$
$769$	−8.16388e150	−0.251631	−0.125815	+	0.992054i	$0.540155\pi$
$770$	2.17524e150	0.0626246
$771$	1.25440e151	0.337350
$772$	2.12666e151	0.534306
$773$	−3.70048e151	−0.868630	−0.434315	−	0.900761i	$-0.643009\pi$
$773$	−3.70048e151	−0.868630	−0.434315	+	0.900761i	$0.643009\pi$
$774$	−1.18850e152	−2.60675
$775$	−4.46367e151	−0.914855
$776$	4.80856e151	0.921032
$777$	−3.12412e150	−0.0559273
$778$	−4.07701e151	−0.682202
$779$	8.09042e151	1.26548
$780$	6.11037e150	0.0893514
$781$	6.63530e151	0.907155
$782$	8.87034e150	0.113393
$783$	−5.22907e151	−0.625074
$784$	−2.14754e150	−0.0240076
$785$	−4.70359e151	−0.491781
$786$	−6.11397e151	−0.597915
$787$	1.07166e151	0.0980352	0.0490176	−	0.998798i	$-0.484391\pi$
$787$	1.07166e151	0.0980352	0.0490176	+	0.998798i	$0.484391\pi$
$788$	8.85255e151	0.757603
$789$	−2.24370e151	−0.179648
$790$	1.64988e151	0.123603
$791$	−5.78120e150	−0.0405278
$792$	−1.54360e152	−1.01266
$793$	8.76431e151	0.538115
$794$	−2.58084e151	−0.148315
$795$	7.35377e150	0.0395581
$796$	1.06523e152	0.536422
$797$	5.71590e151	0.269478	0.134739	−	0.990881i	$-0.456980\pi$
$797$	5.71590e151	0.269478	0.134739	+	0.990881i	$0.456980\pi$
$798$	−1.45226e151	−0.0641052
$799$	1.32516e152	0.547723
$800$	2.33426e152	0.903494
$801$	−7.77122e151	−0.281697
$802$	2.15737e152	0.732436
$803$	−4.40569e152	−1.40103
$804$	9.09427e151	0.270910
$805$	−1.04054e150	−0.00290385
$806$	4.87130e152	1.27367
$807$	2.83945e151	0.0695623
$808$	−3.13911e152	−0.720626
$809$	9.92211e151	0.213455	0.106728	−	0.994288i	$-0.465963\pi$
$809$	9.92211e151	0.213455	0.106728	+	0.994288i	$0.465963\pi$
$810$	−1.84229e152	−0.371445
$811$	−4.56922e152	−0.863471	−0.431735	−	0.902000i	$-0.642099\pi$
$811$	−4.56922e152	−0.863471	−0.431735	+	0.902000i	$0.642099\pi$
$812$	1.56183e152	0.276657
$813$	−5.47420e151	−0.0909006
$814$	−1.90433e153	−2.96456
$815$	−1.81492e152	−0.264901
$816$	3.88906e150	0.00532244
$817$	−1.63056e153	−2.09256
$818$	1.95494e153	2.35280
$819$	8.59357e151	0.0969993
$820$	4.45597e152	0.471754
$821$	1.02228e153	1.01520	0.507602	−	0.861592i	$-0.330532\pi$
$821$	1.02228e153	1.01520	0.507602	+	0.861592i	$0.330532\pi$
$822$	1.17256e152	0.109236
$823$	1.57311e153	1.37489	0.687443	−	0.726238i	$-0.258733\pi$
$823$	1.57311e153	1.37489	0.687443	+	0.726238i	$0.258733\pi$
$824$	1.54027e153	1.26305
$825$	3.14241e152	0.241785
$826$	8.92945e151	0.0644722
$827$	−3.06424e152	−0.207627	−0.103813	−	0.994597i	$-0.533104\pi$
$827$	−3.06424e152	−0.207627	−0.103813	+	0.994597i	$0.533104\pi$
$828$	1.91247e152	0.121619
$829$	−1.45148e153	−0.866360	−0.433180	−	0.901307i	$-0.642609\pi$
$829$	−1.45148e153	−0.866360	−0.433180	+	0.901307i	$0.642609\pi$
$830$	7.18074e152	0.402318
$831$	1.80033e152	0.0946888
$832$	−2.58659e153	−1.27718
$833$	1.86400e153	0.864139
$834$	−1.41283e153	−0.614994
$835$	1.17618e153	0.480767
$836$	−5.48505e153	−2.10548
$837$	1.32283e153	0.476890
$838$	−3.88719e152	−0.131621
$839$	1.03463e153	0.329064	0.164532	−	0.986372i	$-0.447389\pi$
$839$	1.03463e153	0.329064	0.164532	+	0.986372i	$0.447389\pi$
$840$	−3.08820e151	−0.00922662
$841$	2.46571e153	0.692073
$842$	−6.47119e153	−1.70647
$843$	5.50061e152	0.136290
$844$	−3.41554e153	−0.795207
$845$	4.77222e152	0.104410
$846$	4.61106e153	0.948106
$847$	−8.08031e151	−0.0156153
$848$	7.67538e151	0.0139418
$849$	2.12875e153	0.363472
$850$	8.18631e153	1.31400
$851$	9.10945e152	0.137464
$852$	−2.43988e153	−0.346171
$853$	8.89160e152	0.118619	0.0593097	−	0.998240i	$-0.481110\pi$
$853$	8.89160e152	0.118619	0.0593097	+	0.998240i	$0.481110\pi$
$854$	−1.14727e153	−0.143922
$855$	−2.71704e153	−0.320534
$856$	1.00723e154	1.11753
$857$	−1.49289e154	−1.55788	−0.778942	−	0.627096i	$-0.784243\pi$
$857$	−1.49289e154	−1.55788	−0.778942	+	0.627096i	$0.784243\pi$
$858$	−3.42938e153	−0.336615
$859$	3.27076e153	0.302000	0.151000	−	0.988534i	$-0.451751\pi$
$859$	3.27076e153	0.302000	0.151000	+	0.988534i	$0.451751\pi$
$860$	−8.98063e153	−0.780078
$861$	−4.10276e152	−0.0335283
$862$	2.92244e154	2.24706
$863$	−1.47873e154	−1.06985	−0.534925	−	0.844899i	$-0.679660\pi$
$863$	−1.47873e154	−1.06985	−0.534925	+	0.844899i	$0.679660\pi$
$864$	−6.91772e153	−0.470968
$865$	7.85047e153	0.502979
$866$	3.95802e154	2.38665
$867$	9.92054e152	0.0563031
$868$	−3.95107e153	−0.211071
$869$	−5.73747e153	−0.288524
$870$	−3.08739e153	−0.146161
$871$	−1.19155e154	−0.531077
$872$	−3.86797e154	−1.62318
$873$	−2.14541e154	−0.847740
$874$	4.23457e153	0.157565
$875$	−2.00202e153	−0.0701527
$876$	1.62003e154	0.534634
$877$	−4.01870e154	−1.24913	−0.624565	−	0.780973i	$-0.714724\pi$
$877$	−4.01870e154	−1.24913	−0.624565	+	0.780973i	$0.714724\pi$
$878$	−8.11556e154	−2.37605
$879$	1.33546e154	0.368310
$880$	−2.78085e152	−0.00722498
$881$	7.65040e154	1.87262	0.936308	−	0.351180i	$-0.114219\pi$
$881$	7.65040e154	1.87262	0.936308	+	0.351180i	$0.114219\pi$
$882$	6.48605e154	1.49582
$883$	3.55919e154	0.773418	0.386709	−	0.922202i	$-0.373612\pi$
$883$	3.55919e154	0.773418	0.386709	+	0.922202i	$0.373612\pi$
$884$	−5.53557e154	−1.13349
$885$	−1.09371e153	−0.0211048
$886$	1.61259e155	2.93260
$887$	−7.16354e154	−1.22783	−0.613914	−	0.789373i	$-0.710406\pi$
$887$	−7.16354e154	−1.22783	−0.613914	+	0.789373i	$0.710406\pi$
$888$	2.70358e154	0.436776
$889$	3.20441e153	0.0487984
$890$	−9.47710e153	−0.136050
$891$	6.40659e154	0.867057
$892$	−7.49056e154	−0.955783
$893$	6.32610e154	0.761088
$894$	−3.47710e154	−0.394455
$895$	3.92361e154	0.419737
$896$	2.11745e154	0.213621
$897$	1.64046e153	0.0156086
$898$	−2.47955e155	−2.22518
$899$	−1.52507e155	−1.29094
$900$	1.76499e155	1.40932
$901$	−6.66200e154	−0.501826
$902$	−2.50087e155	−1.77725
$903$	8.26877e153	0.0554414
$904$	5.00299e154	0.316510
$905$	1.43812e153	0.00858512
$906$	−7.60564e154	−0.428455
$907$	−5.78217e154	−0.307403	−0.153701	−	0.988117i	$-0.549119\pi$
$907$	−5.78217e154	−0.307403	−0.153701	+	0.988117i	$0.549119\pi$
$908$	2.29292e155	1.15049
$909$	1.40056e155	0.663281
$910$	1.04800e154	0.0468475
$911$	3.54703e155	1.49675	0.748377	−	0.663274i	$-0.230834\pi$
$911$	3.54703e155	1.49675	0.748377	+	0.663274i	$0.230834\pi$
$912$	1.85658e153	0.00739579
$913$	−2.49711e155	−0.939122
$914$	6.11686e154	0.217197
$915$	1.40522e154	0.0471126
$916$	5.54117e155	1.75424
$917$	−6.49734e154	−0.194243
$918$	−2.42606e155	−0.684953
$919$	−2.75804e155	−0.735421	−0.367710	−	0.929940i	$-0.619858\pi$
$919$	−2.75804e155	−0.735421	−0.367710	+	0.929940i	$0.619858\pi$
$920$	9.00472e153	0.0226782
$921$	1.87652e155	0.446400
$922$	−1.16973e156	−2.62852
$923$	3.19677e155	0.678614
$924$	2.78154e154	0.0557837
$925$	8.40698e155	1.59294
$926$	5.05292e155	0.904618
$927$	−6.87216e155	−1.16254
$928$	7.97531e155	1.27491
$929$	−4.30019e155	−0.649625	−0.324812	−	0.945778i	$-0.605301\pi$
$929$	−4.30019e155	−0.649625	−0.324812	+	0.945778i	$0.605301\pi$
$930$	7.81039e154	0.111511
$931$	8.89847e155	1.20076
$932$	−7.91723e155	−1.00981
$933$	4.51282e154	0.0544079
$934$	−1.40447e156	−1.60067
$935$	2.41369e155	0.260059
$936$	−7.43678e155	−0.757535
$937$	−1.31573e155	−0.126718	−0.0633589	−	0.997991i	$-0.520181\pi$
$937$	−1.31573e155	−0.126718	−0.0633589	+	0.997991i	$0.520181\pi$
$938$	1.55977e155	0.142040
$939$	3.39285e155	0.292161
$940$	3.48424e155	0.283724
$941$	−1.44411e156	−1.11210	−0.556051	−	0.831148i	$-0.687684\pi$
$941$	−1.44411e156	−1.11210	−0.556051	+	0.831148i	$0.687684\pi$
$942$	−9.70701e155	−0.706990
$943$	1.19630e155	0.0824095
$944$	−1.14155e154	−0.00743813
$945$	2.84590e154	0.0175408
$946$	5.04029e156	2.93880
$947$	−2.81570e156	−1.55314	−0.776572	−	0.630028i	$-0.783043\pi$
$947$	−2.81570e156	−1.55314	−0.776572	+	0.630028i	$0.783043\pi$
$948$	2.10974e155	0.110101
$949$	−2.12258e156	−1.04807
$950$	3.90803e156	1.82586
$951$	2.44628e155	0.108151
$952$	2.79769e155	0.117047
$953$	1.37104e156	0.542842	0.271421	−	0.962461i	$-0.412506\pi$
$953$	1.37104e156	0.542842	0.271421	+	0.962461i	$0.412506\pi$
$954$	−2.31813e156	−0.868658
$955$	−1.41836e156	−0.503049
$956$	8.91800e156	2.99384
$957$	1.07364e156	0.341180
$958$	2.23395e156	0.672022
$959$	1.24609e155	0.0354872
$960$	−4.14719e155	−0.111819
$961$	−5.91443e154	−0.0150985
$962$	−9.17473e156	−2.21770
$963$	−4.49392e156	−1.02860
$964$	−1.21792e157	−2.63982
$965$	−4.46754e155	−0.0917032
$966$	−2.14741e154	−0.00417461
$967$	−3.40133e155	−0.0626266	−0.0313133	−	0.999510i	$-0.509969\pi$
$967$	−3.40133e155	−0.0626266	−0.0313133	+	0.999510i	$0.509969\pi$
$968$	6.99262e155	0.121950
$969$	−1.61145e156	−0.266207
$970$	−2.61635e156	−0.409431
$971$	1.34108e157	1.98812	0.994062	−	0.108811i	$-0.0347044\pi$
$971$	1.34108e157	1.98812	0.994062	+	0.108811i	$0.0347044\pi$
$972$	−7.92888e156	−1.11361
$973$	−1.50142e156	−0.199791
$974$	1.57750e157	1.98896
$975$	1.51396e156	0.180872
$976$	1.46668e155	0.0166043
$977$	1.30307e157	1.39798	0.698991	−	0.715130i	$-0.253633\pi$
$977$	1.30307e157	1.39798	0.698991	+	0.715130i	$0.253633\pi$
$978$	−3.74554e156	−0.380824
$979$	3.29567e156	0.317580
$980$	4.90102e156	0.447629
$981$	1.72575e157	1.49402
$982$	−2.59878e157	−2.13263
$983$	−1.96199e157	−1.52629	−0.763145	−	0.646227i	$-0.776346\pi$
$983$	−1.96199e157	−1.52629	−0.763145	+	0.646227i	$0.776346\pi$
$984$	3.55049e156	0.261846
$985$	−1.85968e156	−0.130028
$986$	2.79696e157	1.85416
$987$	−3.20805e155	−0.0201647
$988$	−2.64260e157	−1.57504
$989$	−2.41105e156	−0.136270
$990$	8.39876e156	0.450161
$991$	2.45550e157	1.24817	0.624085	−	0.781356i	$-0.285472\pi$
$991$	2.45550e157	1.24817	0.624085	+	0.781356i	$0.285472\pi$
$992$	−2.01757e157	−0.972670
$993$	1.32462e156	0.0605698
$994$	−4.18466e156	−0.181499
$995$	−2.23776e156	−0.0920664
$996$	9.18219e156	0.358370
$997$	−8.88450e156	−0.328955	−0.164478	−	0.986381i	$-0.552594\pi$
$997$	−8.88450e156	−0.328955	−0.164478	+	0.986381i	$0.552594\pi$
$998$	−1.71775e157	−0.603400
$999$	−2.49146e157	−0.830357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.106.a.a.1.8	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.106.a.a.1.8	✓	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 106 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+1.03267e16 q^{2} -2.77402e24 q^{3} +6.60762e31 q^{4} -1.38808e36 q^{5} -2.86465e40 q^{6} -3.04428e43 q^{7} +2.63449e47 q^{8} -1.17542e50 q^{9} +O(q^{10})\)	\(q+1.03267e16 q^{2} -2.77402e24 q^{3} +6.60762e31 q^{4} -1.38808e36 q^{5} -2.86465e40 q^{6} -3.04428e43 q^{7} +2.63449e47 q^{8} -1.17542e50 q^{9} -1.43343e52 q^{10} +4.98478e54 q^{11} -1.83297e56 q^{12} +2.40158e58 q^{13} -3.14374e59 q^{14} +3.85057e60 q^{15} +4.01897e61 q^{16} -3.48835e64 q^{17} -1.21382e66 q^{18} -1.66529e67 q^{19} -9.17192e67 q^{20} +8.44489e67 q^{21} +5.14764e70 q^{22} -2.46240e70 q^{23} -7.30812e71 q^{24} -2.27251e73 q^{25} +2.48005e74 q^{26} +6.73472e74 q^{27} -2.01154e75 q^{28} -7.76434e76 q^{29} +3.97637e76 q^{30} +1.96420e78 q^{31} -1.02717e79 q^{32} -1.38279e79 q^{33} -3.60231e80 q^{34} +4.22571e79 q^{35} -7.76670e81 q^{36} -3.69942e82 q^{37} -1.71969e83 q^{38} -6.66204e82 q^{39} -3.65688e83 q^{40} -4.85828e84 q^{41} +8.72080e83 q^{42} +9.79144e85 q^{43} +3.29376e86 q^{44} +1.63157e86 q^{45} -2.54285e86 q^{46} -3.79881e87 q^{47} -1.11487e86 q^{48} -5.34351e88 q^{49} -2.34676e89 q^{50} +9.67674e88 q^{51} +1.58687e90 q^{52} +1.90979e90 q^{53} +6.95475e90 q^{54} -6.91929e90 q^{55} -8.02011e90 q^{56} +4.61954e91 q^{57} -8.01801e92 q^{58} -2.84039e92 q^{59} +2.54431e92 q^{60} +3.64939e93 q^{61} +2.02837e94 q^{62} +3.57829e93 q^{63} -1.07703e95 q^{64} -3.33360e94 q^{65} -1.42797e95 q^{66} -4.96150e95 q^{67} -2.30497e96 q^{68} +6.83075e94 q^{69} +4.36377e95 q^{70} +1.33111e97 q^{71} -3.09662e97 q^{72} -8.83827e97 q^{73} -3.82028e98 q^{74} +6.30400e97 q^{75} -1.10036e99 q^{76} -1.51751e98 q^{77} -6.87970e98 q^{78} -1.15100e99 q^{79} -5.57867e97 q^{80} +1.28523e100 q^{81} -5.01700e100 q^{82} -5.00947e100 q^{83} +5.58006e99 q^{84} +4.84211e100 q^{85} +1.01113e102 q^{86} +2.15384e101 q^{87} +1.31323e102 q^{88} +6.61147e101 q^{89} +1.68488e102 q^{90} -7.31109e101 q^{91} -1.62706e102 q^{92} -5.44873e102 q^{93} -3.92292e103 q^{94} +2.31155e103 q^{95} +2.84940e103 q^{96} +1.82524e104 q^{97} -5.51809e104 q^{98} -5.85919e104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 91\!\cdots\!20 q^{2}+ \cdots + 31\!\cdots\!84 q^{9}+O(q^{10}) \) 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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