LMFDB - Embedded newform 1.106.a.a.1.6

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			1.6
Root			$3.47548e13$ 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)

$f(q)$	$=$	$q+3.85781e15 q^{2} -1.61266e25 q^{3} -2.56821e31 q^{4} +9.75211e36 q^{5} -6.22135e40 q^{6} -2.29314e44 q^{7} -2.55568e47 q^{8} +1.34832e50 q^{9} +O(q^{10})$	\(q+3.85781e15 q^{2} -1.61266e25 q^{3} -2.56821e31 q^{4} +9.75211e36 q^{5} -6.22135e40 q^{6} -2.29314e44 q^{7} -2.55568e47 q^{8} +1.34832e50 q^{9} +3.76218e52 q^{10} +1.09890e54 q^{11} +4.14166e56 q^{12} -1.87317e58 q^{13} -8.84652e59 q^{14} -1.57269e62 q^{15} +5.58564e61 q^{16} +5.30626e64 q^{17} +5.20155e65 q^{18} +1.09214e67 q^{19} -2.50455e68 q^{20} +3.69807e69 q^{21} +4.23934e69 q^{22} -8.50723e70 q^{23} +4.12146e72 q^{24} +7.04517e73 q^{25} -7.22635e73 q^{26} -1.54734e74 q^{27} +5.88928e75 q^{28} -5.56149e76 q^{29} -6.06713e77 q^{30} +1.17118e78 q^{31} +1.05826e79 q^{32} -1.77215e79 q^{33} +2.04706e80 q^{34} -2.23630e81 q^{35} -3.46276e81 q^{36} -2.00039e82 q^{37} +4.21327e82 q^{38} +3.02080e83 q^{39} -2.49233e84 q^{40} -1.54764e84 q^{41} +1.42665e85 q^{42} +5.42589e84 q^{43} -2.82220e85 q^{44} +1.31489e87 q^{45} -3.28193e86 q^{46} -1.19813e88 q^{47} -9.00775e86 q^{48} -1.77677e87 q^{49} +2.71789e89 q^{50} -8.55722e89 q^{51} +4.81070e89 q^{52} +1.16973e90 q^{53} -5.96936e89 q^{54} +1.07166e91 q^{55} +5.86054e91 q^{56} -1.76126e92 q^{57} -2.14552e92 q^{58} -1.35533e93 q^{59} +4.03899e93 q^{60} +9.28542e92 q^{61} +4.51820e93 q^{62} -3.09188e94 q^{63} +3.85597e94 q^{64} -1.82674e95 q^{65} -6.83664e94 q^{66} -5.61369e94 q^{67} -1.36276e96 q^{68} +1.37193e96 q^{69} -8.62722e96 q^{70} -1.67163e97 q^{71} -3.44587e97 q^{72} +8.53517e97 q^{73} -7.71713e97 q^{74} -1.13615e99 q^{75} -2.80485e98 q^{76} -2.51993e98 q^{77} +1.16537e99 q^{78} -4.40194e99 q^{79} +5.44717e98 q^{80} -1.43905e100 q^{81} -5.97051e99 q^{82} -2.96634e99 q^{83} -9.49742e100 q^{84} +5.17473e101 q^{85} +2.09321e100 q^{86} +8.96882e101 q^{87} -2.80844e101 q^{88} +2.97381e101 q^{89} +5.07261e102 q^{90} +4.29545e102 q^{91} +2.18484e102 q^{92} -1.88872e103 q^{93} -4.62216e103 q^{94} +1.06507e104 q^{95} -1.70661e104 q^{96} -1.35845e104 q^{97} -6.85446e102 q^{98} +1.48166e104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.85781e15	0.605712	0.302856	−	0.953036i	$-0.402060\pi$
$2$	3.85781e15	0.605712	0.302856	+	0.953036i	$0.402060\pi$
$3$	−1.61266e25	−1.44105	−0.720523	−	0.693431i	$-0.756098\pi$
$3$	−1.61266e25	−1.44105	−0.720523	+	0.693431i	$0.756098\pi$
$4$	−2.56821e31	−0.633113
$5$	9.75211e36	1.96414	0.982072	−	0.188508i	$-0.0603651\pi$
$5$	9.75211e36	1.96414	0.982072	+	0.188508i	$0.0603651\pi$
$6$	−6.22135e40	−0.872859
$7$	−2.29314e44	−0.983522	−0.491761	−	0.870730i	$-0.663647\pi$
$7$	−2.29314e44	−0.983522	−0.491761	+	0.870730i	$0.663647\pi$
$8$	−2.55568e47	−0.989196
$9$	1.34832e50	1.07661
$10$	3.76218e52	1.18971
$11$	1.09890e54	0.233261	0.116630	−	0.993175i	$-0.462791\pi$
$11$	1.09890e54	0.233261	0.116630	+	0.993175i	$0.462791\pi$
$12$	4.14166e56	0.912345
$13$	−1.87317e58	−0.617379	−0.308689	−	0.951163i	$-0.599890\pi$
$13$	−1.87317e58	−0.617379	−0.308689	+	0.951163i	$0.599890\pi$
$14$	−8.84652e59	−0.595731
$15$	−1.57269e62	−2.83042
$16$	5.58564e61	0.0339448
$17$	5.30626e64	1.33727	0.668637	−	0.743589i	$-0.266878\pi$
$17$	5.30626e64	1.33727	0.668637	+	0.743589i	$0.266878\pi$
$18$	5.20155e65	0.652118
$19$	1.09214e67	0.801151	0.400576	−	0.916264i	$-0.368810\pi$
$19$	1.09214e67	0.801151	0.400576	+	0.916264i	$0.368810\pi$
$20$	−2.50455e68	−1.24352
$21$	3.69807e69	1.41730
$22$	4.23934e69	0.141289
$23$	−8.50723e70	−0.274838	−0.137419	−	0.990513i	$-0.543881\pi$
$23$	−8.50723e70	−0.274838	−0.137419	+	0.990513i	$0.543881\pi$
$24$	4.12146e72	1.42548
$25$	7.04517e73	2.85786
$26$	−7.22635e73	−0.373954
$27$	−1.54734e74	−0.110405
$28$	5.88928e75	0.622681
$29$	−5.56149e76	−0.931744	−0.465872	−	0.884852i	$-0.654259\pi$
$29$	−5.56149e76	−0.931744	−0.465872	+	0.884852i	$0.654259\pi$
$30$	−6.06713e77	−1.71442
$31$	1.17118e78	0.591747	0.295873	−	0.955227i	$-0.404389\pi$
$31$	1.17118e78	0.591747	0.295873	+	0.955227i	$0.404389\pi$
$32$	1.05826e79	1.00976
$33$	−1.77215e79	−0.336140
$34$	2.04706e80	0.810003
$35$	−2.23630e81	−1.93178
$36$	−3.46276e81	−0.681619
$37$	−2.00039e82	−0.934382	−0.467191	−	0.884157i	$-0.654734\pi$
$37$	−2.00039e82	−0.934382	−0.467191	+	0.884157i	$0.654734\pi$
$38$	4.21327e82	0.485267
$39$	3.02080e83	0.889672
$40$	−2.49233e84	−1.94292
$41$	−1.54764e84	−0.330003	−0.165002	−	0.986293i	$-0.552763\pi$
$41$	−1.54764e84	−0.330003	−0.165002	+	0.986293i	$0.552763\pi$
$42$	1.42665e85	0.858476
$43$	5.42589e84	0.0949243	0.0474621	−	0.998873i	$-0.484887\pi$
$43$	5.42589e84	0.0949243	0.0474621	+	0.998873i	$0.484887\pi$
$44$	−2.82220e85	−0.147680
$45$	1.31489e87	2.11463
$46$	−3.28193e86	−0.166473
$47$	−1.19813e88	−1.96502	−0.982509	−	0.186217i	$-0.940377\pi$
$47$	−1.19813e88	−1.96502	−0.982509	+	0.186217i	$0.940377\pi$
$48$	−9.00775e86	−0.0489161
$49$	−1.77677e87	−0.0326842
$50$	2.71789e89	1.73104
$51$	−8.55722e89	−1.92707
$52$	4.81070e89	0.390871
$53$	1.16973e90	0.349624	0.174812	−	0.984602i	$-0.444068\pi$
$53$	1.16973e90	0.349624	0.174812	+	0.984602i	$0.444068\pi$
$54$	−5.96936e89	−0.0668737
$55$	1.07166e91	0.458158
$56$	5.86054e91	0.972896
$57$	−1.76126e92	−1.15450
$58$	−2.14552e92	−0.564369
$59$	−1.35533e93	−1.45317	−0.726583	−	0.687078i	$-0.758893\pi$
$59$	−1.35533e93	−1.45317	−0.726583	+	0.687078i	$0.758893\pi$
$60$	4.03899e93	1.79198
$61$	9.28542e92	0.172976	0.0864879	−	0.996253i	$-0.472436\pi$
$61$	9.28542e92	0.172976	0.0864879	+	0.996253i	$0.472436\pi$
$62$	4.51820e93	0.358428
$63$	−3.09188e94	−1.05887
$64$	3.85597e94	0.577677
$65$	−1.82674e95	−1.21262
$66$	−6.83664e94	−0.203604
$67$	−5.61369e94	−0.0759139	−0.0379569	−	0.999279i	$-0.512085\pi$
$67$	−5.61369e94	−0.0759139	−0.0379569	+	0.999279i	$0.512085\pi$
$68$	−1.36276e96	−0.846646
$69$	1.37193e96	0.396054
$70$	−8.62722e96	−1.17010
$71$	−1.67163e97	−1.07665	−0.538327	−	0.842736i	$-0.680943\pi$
$71$	−1.67163e97	−1.07665	−0.538327	+	0.842736i	$0.680943\pi$
$72$	−3.44587e97	−1.06498
$73$	8.53517e97	1.27868	0.639340	−	0.768924i	$-0.279208\pi$
$73$	8.53517e97	1.27868	0.639340	+	0.768924i	$0.279208\pi$
$74$	−7.71713e97	−0.565966
$75$	−1.13615e99	−4.11831
$76$	−2.80485e98	−0.507219
$77$	−2.51993e98	−0.229417
$78$	1.16537e99	0.538885
$79$	−4.40194e99	−1.04285	−0.521425	−	0.853297i	$-0.674599\pi$
$79$	−4.40194e99	−1.04285	−0.521425	+	0.853297i	$0.674599\pi$
$80$	5.44717e98	0.0666725
$81$	−1.43905e100	−0.917516
$82$	−5.97051e99	−0.199887
$83$	−2.96634e99	−0.0525559	−0.0262779	−	0.999655i	$-0.508365\pi$
$83$	−2.96634e99	−0.0525559	−0.0262779	+	0.999655i	$0.508365\pi$
$84$	−9.49742e100	−0.897312
$85$	5.17473e101	2.62660
$86$	2.09321e100	0.0574968
$87$	8.96882e101	1.34269
$88$	−2.80844e101	−0.230741
$89$	2.97381e101	0.135001	0.0675006	−	0.997719i	$-0.478498\pi$
$89$	2.97381e101	0.135001	0.0675006	+	0.997719i	$0.478498\pi$
$90$	5.07261e102	1.28085
$91$	4.29545e102	0.607206
$92$	2.18484e102	0.174003
$93$	−1.88872e103	−0.852735
$94$	−4.62216e103	−1.19023
$95$	1.06507e104	1.57358
$96$	−1.70661e104	−1.45511
$97$	−1.35845e104	−0.672245	−0.336122	−	0.941818i	$-0.609116\pi$
$97$	−1.35845e104	−0.672245	−0.336122	+	0.941818i	$0.609116\pi$
$98$	−6.85446e102	−0.0197972
$99$	1.48166e104	0.251132
$100$	−1.80935e105	−1.80935
$101$	2.13987e104	0.126916	0.0634579	−	0.997985i	$-0.479787\pi$
$101$	2.13987e104	0.126916	0.0634579	+	0.997985i	$0.479787\pi$
$102$	−3.30121e105	−1.16725
$103$	2.64790e105	0.560980	0.280490	−	0.959857i	$-0.409503\pi$
$103$	2.64790e105	0.560980	0.280490	+	0.959857i	$0.409503\pi$
$104$	4.78723e105	0.610709
$105$	3.60640e106	2.78378
$106$	4.51258e105	0.211771
$107$	−3.56766e106	−1.02267	−0.511334	−	0.859382i	$-0.670849\pi$
$107$	−3.56766e106	−1.02267	−0.511334	+	0.859382i	$0.670849\pi$
$108$	3.97391e105	0.0698989
$109$	1.04589e106	0.113395	0.0566976	−	0.998391i	$-0.481943\pi$
$109$	1.04589e106	0.113395	0.0566976	+	0.998391i	$0.481943\pi$
$110$	4.13425e106	0.277512
$111$	3.22596e107	1.34649
$112$	−1.28087e106	−0.0333855
$113$	−8.97870e107	−1.46756	−0.733778	−	0.679389i	$-0.762245\pi$
$113$	−8.97870e107	−1.46756	−0.733778	+	0.679389i	$0.762245\pi$
$114$	−6.79459e107	−0.699292
$115$	−8.29634e107	−0.539821
$116$	1.42831e108	0.589899
$117$	−2.52563e108	−0.664679
$118$	−5.22862e108	−0.880201
$119$	−1.21680e109	−1.31524
$120$	4.01929e109	2.79984
$121$	−2.09862e109	−0.945589
$122$	3.58214e108	0.104773
$123$	2.49583e109	0.475550
$124$	−3.00785e109	−0.374643
$125$	4.46644e110	3.64910
$126$	−1.19279e110	−0.641373
$127$	−2.54759e110	−0.904554	−0.452277	−	0.891878i	$-0.649388\pi$
$127$	−2.54759e110	−0.904554	−0.452277	+	0.891878i	$0.649388\pi$
$128$	−2.80524e110	−0.659851
$129$	−8.75014e109	−0.136790
$130$	−7.04721e110	−0.734499
$131$	5.81963e110	0.405651	0.202825	−	0.979215i	$-0.434988\pi$
$131$	5.81963e110	0.405651	0.202825	+	0.979215i	$0.434988\pi$
$132$	4.55127e110	0.212814
$133$	−2.50444e111	−0.787950
$134$	−2.16566e110	−0.0459819
$135$	−1.50899e111	−0.216852
$136$	−1.35611e112	−1.32283
$137$	1.10293e112	0.732348	0.366174	−	0.930546i	$-0.380668\pi$
$137$	1.10293e112	0.732348	0.366174	+	0.930546i	$0.380668\pi$
$138$	5.29265e111	0.239895
$139$	−2.42594e112	−0.752666	−0.376333	−	0.926484i	$-0.622815\pi$
$139$	−2.42594e112	−0.752666	−0.376333	+	0.926484i	$0.622815\pi$
$140$	5.74328e112	1.22303
$141$	1.93218e113	2.83168
$142$	−6.44882e112	−0.652142
$143$	−2.05843e112	−0.144010
$144$	7.53121e111	0.0365455
$145$	−5.42363e113	−1.83008
$146$	3.29271e113	0.774512
$147$	2.86534e112	0.0470995
$148$	5.13742e113	0.591569
$149$	−6.88442e113	−0.556658	−0.278329	−	0.960486i	$-0.589781\pi$
$149$	−6.88442e113	−0.556658	−0.278329	+	0.960486i	$0.589781\pi$
$150$	−4.38305e114	−2.49451
$151$	1.52326e114	0.611622	0.305811	−	0.952092i	$-0.401072\pi$
$151$	1.52326e114	0.611622	0.305811	+	0.952092i	$0.401072\pi$
$152$	−2.79116e114	−0.792496
$153$	7.15453e114	1.43973
$154$	−9.72143e113	−0.138961
$155$	1.14215e115	1.16228
$156$	−7.75805e114	−0.563263
$157$	1.53277e115	0.795693	0.397846	−	0.917452i	$-0.369758\pi$
$157$	1.53277e115	0.795693	0.397846	+	0.917452i	$0.369758\pi$
$158$	−1.69818e115	−0.631666
$159$	−1.88637e115	−0.503824
$160$	1.03202e116	1.98331
$161$	1.95083e115	0.270309
$162$	−5.55160e115	−0.555750
$163$	−4.71155e115	−0.341440	−0.170720	−	0.985320i	$-0.554609\pi$
$163$	−4.71155e115	−0.341440	−0.170720	+	0.985320i	$0.554609\pi$
$164$	3.97467e115	0.208929
$165$	−1.72822e116	−0.660226
$166$	−1.14436e115	−0.0318337
$167$	−5.58290e116	−1.13304	−0.566520	−	0.824048i	$-0.691711\pi$
$167$	−5.58290e116	−1.13304	−0.566520	+	0.824048i	$0.691711\pi$
$168$	−9.45109e116	−1.40199
$169$	−5.69682e116	−0.618843
$170$	1.99631e117	1.59096
$171$	1.47255e117	0.862531
$172$	−1.39348e116	−0.0600978
$173$	5.19513e117	1.65263	0.826316	−	0.563207i	$-0.190433\pi$
$173$	5.19513e117	1.65263	0.826316	+	0.563207i	$0.190433\pi$
$174$	3.46000e117	0.813281
$175$	−1.61556e118	−2.81077
$176$	6.13805e115	0.00791800
$177$	2.18570e118	2.09408
$178$	1.14724e117	0.0817719
$179$	5.93619e117	0.315300	0.157650	−	0.987495i	$-0.449608\pi$
$179$	5.93619e117	0.315300	0.157650	+	0.987495i	$0.449608\pi$
$180$	−3.37692e118	−1.33880
$181$	−1.51713e118	−0.449673	−0.224837	−	0.974396i	$-0.572185\pi$
$181$	−1.51713e118	−0.449673	−0.224837	+	0.974396i	$0.572185\pi$
$182$	1.65711e118	0.367792
$183$	−1.49743e118	−0.249266
$184$	2.17418e118	0.271869
$185$	−1.95080e119	−1.83526
$186$	−7.28634e118	−0.516512
$187$	5.83105e118	0.311934
$188$	3.07705e119	1.24408
$189$	3.54828e118	0.108586
$190$	4.10883e119	0.953134
$191$	−1.97568e119	−0.347908	−0.173954	−	0.984754i	$-0.555654\pi$
$191$	−1.97568e119	−0.347908	−0.173954	+	0.984754i	$0.555654\pi$
$192$	−6.21839e119	−0.832460
$193$	1.10407e120	1.12523	0.562613	−	0.826721i	$-0.309796\pi$
$193$	1.10407e120	1.12523	0.562613	+	0.826721i	$0.309796\pi$
$194$	−5.24064e119	−0.407187
$195$	2.94591e120	1.74744
$196$	4.56313e118	0.0206928
$197$	−9.83716e119	−0.341502	−0.170751	−	0.985314i	$-0.554619\pi$
$197$	−9.83716e119	−0.341502	−0.170751	+	0.985314i	$0.554619\pi$
$198$	5.71598e119	0.152114
$199$	−4.76500e120	−0.973367	−0.486684	−	0.873578i	$-0.661794\pi$
$199$	−4.76500e120	−0.973367	−0.486684	+	0.873578i	$0.661794\pi$
$200$	−1.80052e121	−2.82698
$201$	9.05299e119	0.109395
$202$	8.25522e119	0.0768744
$203$	1.27533e121	0.916391
$204$	2.19767e121	1.22006
$205$	−1.50928e121	−0.648174
$206$	1.02151e121	0.339792
$207$	−1.14704e121	−0.295895
$208$	−1.04629e120	−0.0209568
$209$	1.20015e121	0.186877
$210$	1.39128e122	1.68617
$211$	−1.39237e122	−1.31500	−0.657499	−	0.753455i	$-0.728386\pi$
$211$	−1.39237e122	−1.31500	−0.657499	+	0.753455i	$0.728386\pi$
$212$	−3.00410e121	−0.221351
$213$	2.69577e122	1.55151
$214$	−1.37634e122	−0.619443
$215$	5.29139e121	0.186445
$216$	3.95452e121	0.109212
$217$	−2.68569e122	−0.581996
$218$	4.03485e121	0.0686849
$219$	−1.37644e123	−1.84264
$220$	−2.75224e122	−0.290066
$221$	−9.93955e122	−0.825605
$222$	1.24451e123	0.815584
$223$	1.74645e123	0.903965	0.451983	−	0.892027i	$-0.350717\pi$
$223$	1.74645e123	0.903965	0.451983	+	0.892027i	$0.350717\pi$
$224$	−2.42673e123	−0.993118
$225$	9.49912e123	3.07681
$226$	−3.46381e123	−0.888917
$227$	−5.34039e123	−1.08696	−0.543482	−	0.839421i	$-0.682894\pi$
$227$	−5.34039e123	−1.08696	−0.543482	+	0.839421i	$0.682894\pi$
$228$	4.52328e123	0.730927
$229$	5.63117e123	0.723162	0.361581	−	0.932341i	$-0.382237\pi$
$229$	5.63117e123	0.723162	0.361581	+	0.932341i	$0.382237\pi$
$230$	−3.20057e123	−0.326976
$231$	4.06380e123	0.330601
$232$	1.42134e124	0.921678
$233$	5.69834e122	0.0294824	0.0147412	−	0.999891i	$-0.495308\pi$
$233$	5.69834e122	0.0294824	0.0147412	+	0.999891i	$0.495308\pi$
$234$	−9.74341e123	−0.402604
$235$	−1.16843e125	−3.85958
$236$	3.48078e124	0.920019
$237$	7.09885e124	1.50279
$238$	−4.69420e124	−0.796656
$239$	−4.34877e124	−0.592211	−0.296105	−	0.955155i	$-0.595688\pi$
$239$	−4.34877e124	−0.592211	−0.296105	+	0.955155i	$0.595688\pi$
$240$	−8.78446e123	−0.0960782
$241$	1.14521e125	1.00691	0.503455	−	0.864021i	$-0.332062\pi$
$241$	1.14521e125	1.00691	0.503455	+	0.864021i	$0.332062\pi$
$242$	−8.09609e124	−0.572755
$243$	2.51449e125	1.43259
$244$	−2.38469e124	−0.109513
$245$	−1.73273e124	−0.0641965
$246$	9.62843e124	0.288046
$247$	−2.04577e125	−0.494614
$248$	−2.99317e125	−0.585354
$249$	4.78371e124	0.0757355
$250$	1.72307e126	2.21031
$251$	−2.90548e125	−0.302237	−0.151119	−	0.988516i	$-0.548288\pi$
$251$	−2.90548e125	−0.302237	−0.151119	+	0.988516i	$0.548288\pi$
$252$	7.94061e125	0.670387
$253$	−9.34858e124	−0.0641089
$254$	−9.82813e125	−0.547899
$255$	−8.34509e126	−3.78505
$256$	−2.64637e126	−0.977357
$257$	5.72367e126	1.72261	0.861303	−	0.508092i	$-0.169649\pi$
$257$	5.72367e126	1.72261	0.861303	+	0.508092i	$0.169649\pi$
$258$	−3.37564e125	−0.0828555
$259$	4.58718e126	0.918985
$260$	4.69145e126	0.767726
$261$	−7.49866e126	−1.00313
$262$	2.24510e126	0.245708
$263$	1.04359e127	0.935090	0.467545	−	0.883969i	$-0.345139\pi$
$263$	1.04359e127	0.935090	0.467545	+	0.883969i	$0.345139\pi$
$264$	4.52906e126	0.332508
$265$	1.14073e127	0.686711
$266$	−9.66164e126	−0.477271
$267$	−4.79575e126	−0.194543
$268$	1.44171e126	0.0480621
$269$	2.31236e127	0.633960	0.316980	−	0.948432i	$-0.397331\pi$
$269$	2.31236e127	0.633960	0.316980	+	0.948432i	$0.397331\pi$
$270$	−5.82139e126	−0.131350
$271$	−6.16932e127	−1.14644	−0.573218	−	0.819403i	$-0.694305\pi$
$271$	−6.16932e127	−1.14644	−0.573218	+	0.819403i	$0.694305\pi$
$272$	2.96389e126	0.0453935
$273$	−6.92712e127	−0.875012
$274$	4.25489e127	0.443592
$275$	7.74193e127	0.666627
$276$	−3.52341e127	−0.250747
$277$	−3.05677e128	−1.79918	−0.899592	−	0.436732i	$-0.856136\pi$
$277$	−3.05677e128	−1.79918	−0.899592	+	0.436732i	$0.856136\pi$
$278$	−9.35881e127	−0.455899
$279$	1.57913e128	0.637083
$280$	5.71527e128	1.91091
$281$	−6.05535e128	−1.67903	−0.839513	−	0.543340i	$-0.817159\pi$
$281$	−6.05535e128	−1.67903	−0.839513	+	0.543340i	$0.817159\pi$
$282$	7.45399e128	1.71518
$283$	4.58881e128	0.876824	0.438412	−	0.898774i	$-0.355541\pi$
$283$	4.58881e128	0.876824	0.438412	+	0.898774i	$0.355541\pi$
$284$	4.29309e128	0.681643
$285$	−1.71760e129	−2.26760
$286$	−7.94102e127	−0.0872288
$287$	3.54897e128	0.324566
$288$	1.42686e129	1.08712
$289$	1.24117e129	0.788303
$290$	−2.09233e129	−1.10850
$291$	2.19072e129	0.968736
$292$	−2.19201e129	−0.809549
$293$	−2.26596e129	−0.699361	−0.349681	−	0.936869i	$-0.613710\pi$
$293$	−2.26596e129	−0.699361	−0.349681	+	0.936869i	$0.613710\pi$
$294$	1.10539e128	0.0285287
$295$	−1.32174e130	−2.85423
$296$	5.11236e129	0.924287
$297$	−1.70038e128	−0.0257532
$298$	−2.65588e129	−0.337175
$299$	1.59355e129	0.169679
$300$	2.91787e130	2.60735
$301$	−1.24423e129	−0.0933601
$302$	5.87644e129	0.370467
$303$	−3.45089e129	−0.182891
$304$	6.10030e128	0.0271949
$305$	9.05524e129	0.339749
$306$	2.76008e130	0.872061
$307$	−6.45251e130	−1.71777	−0.858883	−	0.512171i	$-0.828841\pi$
$307$	−6.45251e130	−1.71777	−0.858883	+	0.512171i	$0.828841\pi$
$308$	6.47172e129	0.145247
$309$	−4.27017e130	−0.808398
$310$	4.40620e130	0.704004
$311$	−2.67741e130	−0.361239	−0.180620	−	0.983553i	$-0.557810\pi$
$311$	−2.67741e130	−0.361239	−0.180620	+	0.983553i	$0.557810\pi$
$312$	−7.72020e130	−0.880060
$313$	1.88529e131	1.81678	0.908388	−	0.418129i	$-0.137314\pi$
$313$	1.88529e131	1.81678	0.908388	+	0.418129i	$0.137314\pi$
$314$	5.91314e130	0.481961
$315$	−3.01524e131	−2.07978
$316$	1.13051e131	0.660241
$317$	−3.65781e131	−1.80971	−0.904857	−	0.425715i	$-0.860023\pi$
$317$	−3.65781e131	−1.80971	−0.904857	+	0.425715i	$0.860023\pi$
$318$	−7.27728e130	−0.305172
$319$	−6.11152e130	−0.217339
$320$	3.76038e131	1.13464
$321$	5.75343e131	1.47371
$322$	7.52593e130	0.163730
$323$	5.79519e131	1.07136
$324$	3.69579e131	0.580891
$325$	−1.31968e132	−1.76438
$326$	−1.81763e131	−0.206815
$327$	−1.68667e131	−0.163408
$328$	3.95528e131	0.326438
$329$	2.74748e132	1.93264
$330$	−6.66716e131	−0.399907
$331$	−2.35018e132	−1.20263	−0.601313	−	0.799014i	$-0.705355\pi$
$331$	−2.35018e132	−1.20263	−0.601313	+	0.799014i	$0.705355\pi$
$332$	7.61819e130	0.0332738
$333$	−2.69716e132	−1.00597
$334$	−2.15378e132	−0.686296
$335$	−5.47453e131	−0.149106
$336$	2.06561e131	0.0481100
$337$	−7.74707e131	−0.154372	−0.0771858	−	0.997017i	$-0.524593\pi$
$337$	−7.74707e131	−0.154372	−0.0771858	+	0.997017i	$0.524593\pi$
$338$	−2.19773e132	−0.374841
$339$	1.44796e133	2.11482
$340$	−1.32898e133	−1.66293
$341$	1.28701e132	0.138031
$342$	5.68083e132	0.522446
$343$	1.28734e133	1.01567
$344$	−1.38669e132	−0.0938987
$345$	1.33792e133	0.777907
$346$	2.00418e133	1.00102
$347$	1.77869e133	0.763490	0.381745	−	0.924268i	$-0.375323\pi$
$347$	1.77869e133	0.763490	0.381745	+	0.924268i	$0.375323\pi$
$348$	−2.30338e133	−0.850072
$349$	−4.31176e133	−1.36873	−0.684367	−	0.729137i	$-0.739921\pi$
$349$	−4.31176e133	−1.36873	−0.684367	+	0.729137i	$0.739921\pi$
$350$	−6.23252e133	−1.70252
$351$	2.89844e132	0.0681618
$352$	1.16292e133	0.235537
$353$	2.59573e133	0.452989	0.226494	−	0.974012i	$-0.427274\pi$
$353$	2.59573e133	0.452989	0.226494	+	0.974012i	$0.427274\pi$
$354$	8.43201e133	1.26841
$355$	−1.63019e134	−2.11470
$356$	−7.63737e132	−0.0854710
$357$	1.96229e134	1.89532
$358$	2.29007e133	0.190981
$359$	−5.41344e133	−0.389955	−0.194977	−	0.980808i	$-0.562463\pi$
$359$	−5.41344e133	−0.389955	−0.194977	+	0.980808i	$0.562463\pi$
$360$	−3.36045e134	−2.09178
$361$	−6.65581e133	−0.358156
$362$	−5.85279e133	−0.272372
$363$	3.38437e134	1.36264
$364$	−1.10316e134	−0.384430
$365$	8.32359e134	2.51151
$366$	−5.77679e133	−0.150983
$367$	4.27460e134	0.968115	0.484058	−	0.875036i	$-0.339163\pi$
$367$	4.27460e134	0.968115	0.484058	+	0.875036i	$0.339163\pi$
$368$	−4.75183e132	−0.00932933
$369$	−2.08671e134	−0.355286
$370$	−7.52583e134	−1.11164
$371$	−2.68235e134	−0.343863
$372$	4.85064e134	0.539877
$373$	9.25400e134	0.894573	0.447287	−	0.894391i	$-0.352390\pi$
$373$	9.25400e134	0.894573	0.447287	+	0.894391i	$0.352390\pi$
$374$	2.24951e134	0.188942
$375$	−7.20287e135	−5.25853
$376$	3.06204e135	1.94379
$377$	1.04176e135	0.575239
$378$	1.36886e134	0.0657718
$379$	6.72747e134	0.281380	0.140690	−	0.990054i	$-0.455068\pi$
$379$	6.72747e134	0.281380	0.140690	+	0.990054i	$0.455068\pi$
$380$	−2.73532e135	−0.996251
$381$	4.10841e135	1.30350
$382$	−7.62179e134	−0.210732
$383$	−2.11776e135	−0.510437	−0.255218	−	0.966883i	$-0.582147\pi$
$383$	−2.11776e135	−0.510437	−0.255218	+	0.966883i	$0.582147\pi$
$384$	4.52390e135	0.950876
$385$	−2.45747e135	−0.450608
$386$	4.25931e135	0.681563
$387$	7.31582e134	0.102197
$388$	3.48879e135	0.425607
$389$	2.05445e135	0.218949	0.109474	−	0.993990i	$-0.465083\pi$
$389$	2.05445e135	0.218949	0.109474	+	0.993990i	$0.465083\pi$
$390$	1.13648e136	1.05845
$391$	−4.51416e135	−0.367534
$392$	4.54087e134	0.0323311
$393$	−9.38511e135	−0.584562
$394$	−3.79499e135	−0.206852
$395$	−4.29282e136	−2.04831
$396$	−3.80523e135	−0.158995
$397$	5.61029e135	0.205345	0.102672	−	0.994715i	$-0.467261\pi$
$397$	5.61029e135	0.205345	0.102672	+	0.994715i	$0.467261\pi$
$398$	−1.83825e136	−0.589580
$399$	4.03881e136	1.13547
$400$	3.93517e135	0.0970095
$401$	3.23792e136	0.700142	0.350071	−	0.936723i	$-0.386157\pi$
$401$	3.23792e136	0.700142	0.350071	+	0.936723i	$0.386157\pi$
$402$	3.49247e135	0.0662621
$403$	−2.19383e136	−0.365332
$404$	−5.49564e135	−0.0803520
$405$	−1.40338e137	−1.80213
$406$	4.91998e136	0.555069
$407$	−2.19823e136	−0.217955
$408$	2.18695e137	1.90625
$409$	1.96494e137	1.50617	0.753087	−	0.657921i	$-0.228564\pi$
$409$	1.96494e137	1.50617	0.753087	+	0.657921i	$0.228564\pi$
$410$	−5.82251e136	−0.392607
$411$	−1.77865e137	−1.05535
$412$	−6.80037e136	−0.355164
$413$	3.10797e137	1.42922
$414$	−4.42508e136	−0.179227
$415$	−2.89281e136	−0.103227
$416$	−1.98230e137	−0.623403
$417$	3.91222e137	1.08463
$418$	4.62996e136	0.113194
$419$	−5.84636e137	−1.26081	−0.630405	−	0.776267i	$-0.717111\pi$
$419$	−5.84636e137	−1.26081	−0.630405	+	0.776267i	$0.717111\pi$
$420$	−9.26199e137	−1.76245
$421$	1.86699e137	0.313568	0.156784	−	0.987633i	$-0.449887\pi$
$421$	1.86699e137	0.313568	0.156784	+	0.987633i	$0.449887\pi$
$422$	−5.37150e137	−0.796511
$423$	−1.61546e138	−2.11557
$424$	−2.98945e137	−0.345846
$425$	3.73835e138	3.82174
$426$	1.03998e138	0.939767
$427$	−2.12928e137	−0.170125
$428$	9.16250e137	0.647465
$429$	3.31955e137	0.207526
$430$	2.04132e137	0.112932
$431$	−1.43316e138	−0.701842	−0.350921	−	0.936405i	$-0.614131\pi$
$431$	−1.43316e138	−0.701842	−0.350921	+	0.936405i	$0.614131\pi$
$432$	−8.64290e135	−0.00374768
$433$	−3.38800e138	−1.30115	−0.650577	−	0.759441i	$-0.725473\pi$
$433$	−3.38800e138	−1.30115	−0.650577	+	0.759441i	$0.725473\pi$
$434$	−1.03609e138	−0.352522
$435$	8.74649e138	2.63723
$436$	−2.68607e137	−0.0717920
$437$	−9.29109e137	−0.220187
$438$	−5.31003e138	−1.11611
$439$	4.59945e138	0.857668	0.428834	−	0.903383i	$-0.358925\pi$
$439$	4.59945e138	0.857668	0.428834	+	0.903383i	$0.358925\pi$
$440$	−2.73882e138	−0.453208
$441$	−2.39565e137	−0.0351883
$442$	−3.83449e138	−0.500079
$443$	−9.97115e138	−1.15491	−0.577457	−	0.816421i	$-0.695955\pi$
$443$	−9.97115e138	−1.15491	−0.577457	+	0.816421i	$0.695955\pi$
$444$	−8.28494e138	−0.852478
$445$	2.90009e138	0.265162
$446$	6.73749e138	0.547543
$447$	1.11023e139	0.802170
$448$	−8.84230e138	−0.568158
$449$	−1.45874e139	−0.833767	−0.416884	−	0.908960i	$-0.636878\pi$
$449$	−1.45874e139	−0.833767	−0.416884	+	0.908960i	$0.636878\pi$
$450$	3.66458e139	1.86366
$451$	−1.70070e138	−0.0769768
$452$	2.30592e139	0.929129
$453$	−2.45650e139	−0.881376
$454$	−2.06022e139	−0.658388
$455$	4.18897e139	1.19264
$456$	4.50121e139	1.14202
$457$	−6.69538e139	−1.51417	−0.757085	−	0.653317i	$-0.773377\pi$
$457$	−6.69538e139	−1.51417	−0.757085	+	0.653317i	$0.773377\pi$
$458$	2.17240e139	0.438028
$459$	−8.21062e138	−0.147642
$460$	2.13067e139	0.341768
$461$	−3.68396e138	−0.0527250	−0.0263625	−	0.999652i	$-0.508392\pi$
$461$	−3.68396e138	−0.0527250	−0.0263625	+	0.999652i	$0.508392\pi$
$462$	1.56774e139	0.200249
$463$	9.52994e136	0.00108665	0.000543323	−	1.00000i	$-0.499827\pi$
$463$	9.52994e136	0.00108665	0.000543323		1.00000i	$0.499827\pi$
$464$	−3.10645e138	−0.0316279
$465$	−1.84190e140	−1.67489
$466$	2.19831e138	0.0178578
$467$	7.58015e138	0.0550226	0.0275113	−	0.999621i	$-0.491242\pi$
$467$	7.58015e138	0.0550226	0.0275113	+	0.999621i	$0.491242\pi$
$468$	6.48635e139	0.420817
$469$	1.28730e139	0.0746630
$470$	−4.50758e140	−2.33779
$471$	−2.47184e140	−1.14663
$472$	3.46380e140	1.43747
$473$	5.96251e138	0.0221421
$474$	2.73860e140	0.910261
$475$	7.69432e140	2.28958
$476$	3.12501e140	0.832695
$477$	1.57716e140	0.376410
$478$	−1.67767e140	−0.358709
$479$	3.21066e140	0.615148	0.307574	−	0.951524i	$-0.400483\pi$
$479$	3.21066e140	0.615148	0.307574	+	0.951524i	$0.400483\pi$
$480$	−1.66431e141	−2.85804
$481$	3.74708e140	0.576868
$482$	4.41801e140	0.609898
$483$	−3.14603e140	−0.389528
$484$	5.38971e140	0.598665
$485$	−1.32477e141	−1.32039
$486$	9.70044e140	0.867736
$487$	−1.74855e141	−1.40413	−0.702064	−	0.712114i	$-0.747738\pi$
$487$	−1.74855e141	−1.40413	−0.702064	+	0.712114i	$0.747738\pi$
$488$	−2.37306e140	−0.171107
$489$	7.59815e140	0.492031
$490$	−6.68454e139	−0.0388846
$491$	1.62859e141	0.851205	0.425603	−	0.904910i	$-0.360062\pi$
$491$	1.62859e141	0.851205	0.425603	+	0.904910i	$0.360062\pi$
$492$	−6.40981e140	−0.301077
$493$	−2.95108e141	−1.24600
$494$	−7.89219e140	−0.299594
$495$	1.44493e141	0.493259
$496$	6.54180e139	0.0200867
$497$	3.83328e141	1.05891
$498$	1.84547e140	0.0458739
$499$	9.87635e140	0.220962	0.110481	−	0.993878i	$-0.464761\pi$
$499$	9.87635e140	0.220962	0.110481	+	0.993878i	$0.464761\pi$
$500$	−1.14708e142	−2.31029
$501$	9.00334e141	1.63276
$502$	−1.12088e141	−0.183069
$503$	6.48833e141	0.954583	0.477291	−	0.878745i	$-0.341619\pi$
$503$	6.48833e141	0.954583	0.477291	+	0.878745i	$0.341619\pi$
$504$	7.90187e141	1.04743
$505$	2.08682e141	0.249281
$506$	−3.60651e140	−0.0388315
$507$	9.18706e141	0.891782
$508$	6.54275e141	0.572685
$509$	−1.90504e142	−1.50390	−0.751952	−	0.659218i	$-0.770888\pi$
$509$	−1.90504e142	−1.50390	−0.751952	+	0.659218i	$0.770888\pi$
$510$	−3.21938e142	−2.29265
$511$	−1.95724e142	−1.25761
$512$	1.17017e141	0.0678541
$513$	−1.68992e141	−0.0884513
$514$	2.20809e142	1.04340
$515$	2.58226e142	1.10185
$516$	2.24722e141	0.0866037
$517$	−1.31662e142	−0.458361
$518$	1.76965e142	0.556640
$519$	−8.37800e142	−2.38152
$520$	4.66856e142	1.19952
$521$	2.44040e141	0.0566865	0.0283433	−	0.999598i	$-0.490977\pi$
$521$	2.44040e141	0.0566865	0.0283433	+	0.999598i	$0.490977\pi$
$522$	−2.89284e142	−0.607607
$523$	−6.77418e142	−1.28682	−0.643410	−	0.765522i	$-0.722481\pi$
$523$	−6.77418e142	−1.28682	−0.643410	+	0.765522i	$0.722481\pi$
$524$	−1.49460e142	−0.256823
$525$	2.60535e143	4.05045
$526$	4.02598e142	0.566396
$527$	6.21461e142	0.791328
$528$	−9.89861e140	−0.0114102
$529$	−8.85753e142	−0.924464
$530$	4.40072e142	0.415949
$531$	−1.82742e143	−1.56450
$532$	6.43192e142	0.498861
$533$	2.89900e142	0.203737
$534$	−1.85011e142	−0.117837
$535$	−3.47922e143	−2.00867
$536$	1.43468e142	0.0750937
$537$	−9.57308e142	−0.454362
$538$	8.92067e142	0.383997
$539$	−1.95249e141	−0.00762394
$540$	3.87540e142	0.137292
$541$	−5.98871e142	−0.192521	−0.0962603	−	0.995356i	$-0.530688\pi$
$541$	−5.98871e142	−0.192521	−0.0962603	+	0.995356i	$0.530688\pi$
$542$	−2.38001e143	−0.694410
$543$	2.44662e143	0.648000
$544$	5.61539e143	1.35032
$545$	1.01996e143	0.222725
$546$	−2.67235e143	−0.530005
$547$	1.51335e143	0.272649	0.136324	−	0.990664i	$-0.456471\pi$
$547$	1.51335e143	0.272649	0.136324	+	0.990664i	$0.456471\pi$
$548$	−2.83255e143	−0.463659
$549$	1.25197e143	0.186228
$550$	2.98669e143	0.403784
$551$	−6.07393e143	−0.746468
$552$	−3.50622e143	−0.391775
$553$	1.00943e144	1.02567
$554$	−1.17925e144	−1.08979
$555$	3.14599e144	2.64469
$556$	6.23032e143	0.476523
$557$	−1.80980e144	−1.25960	−0.629800	−	0.776757i	$-0.716863\pi$
$557$	−1.80980e144	−1.25960	−0.629800	+	0.776757i	$0.716863\pi$
$558$	6.09197e143	0.385889
$559$	−1.01636e143	−0.0586042
$560$	−1.24911e143	−0.0655739
$561$	−9.40352e143	−0.449511
$562$	−2.33604e144	−1.01701
$563$	3.46251e144	1.37309	0.686546	−	0.727086i	$-0.259126\pi$
$563$	3.46251e144	1.37309	0.686546	+	0.727086i	$0.259126\pi$
$564$	−4.96225e144	−1.79277
$565$	−8.75612e144	−2.88249
$566$	1.77028e144	0.531103
$567$	3.29996e144	0.902397
$568$	4.27215e144	1.06502
$569$	2.15493e144	0.489823	0.244912	−	0.969545i	$-0.421241\pi$
$569$	2.15493e144	0.489823	0.244912	+	0.969545i	$0.421241\pi$
$570$	−6.62616e144	−1.37351
$571$	8.75199e144	1.65467	0.827334	−	0.561710i	$-0.189856\pi$
$571$	8.75199e144	1.65467	0.827334	+	0.561710i	$0.189856\pi$
$572$	5.28648e143	0.0911748
$573$	3.18610e144	0.501351
$574$	1.36912e144	0.196593
$575$	−5.99348e144	−0.785448
$576$	5.19907e144	0.621936
$577$	6.97485e144	0.761737	0.380868	−	0.924629i	$-0.375625\pi$
$577$	6.97485e144	0.761737	0.380868	+	0.924629i	$0.375625\pi$
$578$	4.78818e144	0.477484
$579$	−1.78050e145	−1.62150
$580$	1.39290e145	1.15865
$581$	6.80225e143	0.0516899
$582$	8.45140e144	0.586775
$583$	1.28541e144	0.0815535
$584$	−2.18132e145	−1.26487
$585$	−2.46302e145	−1.30553
$586$	−8.74164e144	−0.423612
$587$	2.14596e145	0.950872	0.475436	−	0.879750i	$-0.342290\pi$
$587$	2.14596e145	0.950872	0.475436	+	0.879750i	$0.342290\pi$
$588$	−7.35879e143	−0.0298193
$589$	1.27910e145	0.474079
$590$	−5.09901e145	−1.72884
$591$	1.58640e145	0.492120
$592$	−1.11735e144	−0.0317174
$593$	2.86896e145	0.745338	0.372669	−	0.927964i	$-0.378443\pi$
$593$	2.86896e145	0.745338	0.372669	+	0.927964i	$0.378443\pi$
$594$	−6.55973e143	−0.0155990
$595$	−1.18664e146	−2.58332
$596$	1.76807e145	0.352427
$597$	7.68435e145	1.40267
$598$	6.14762e144	0.102777
$599$	−4.36997e145	−0.669221	−0.334611	−	0.942356i	$-0.608605\pi$
$599$	−4.36997e145	−0.669221	−0.334611	+	0.942356i	$0.608605\pi$
$600$	2.90363e146	4.07381
$601$	−2.07766e145	−0.267094	−0.133547	−	0.991042i	$-0.542637\pi$
$601$	−2.07766e145	−0.267094	−0.133547	+	0.991042i	$0.542637\pi$
$602$	−4.80002e144	−0.0565494
$603$	−7.56903e144	−0.0817300
$604$	−3.91205e145	−0.387226
$605$	−2.04660e146	−1.85727
$606$	−1.33129e145	−0.110780
$607$	1.34388e145	0.102555	0.0512773	−	0.998684i	$-0.483671\pi$
$607$	1.34388e145	0.102555	0.0512773	+	0.998684i	$0.483671\pi$
$608$	1.15576e146	0.808968
$609$	−2.05668e146	−1.32056
$610$	3.49334e145	0.205790
$611$	2.24430e146	1.21316
$612$	−1.83743e146	−0.911511
$613$	3.61034e146	1.64389	0.821946	−	0.569565i	$-0.192888\pi$
$613$	3.61034e146	1.64389	0.821946	+	0.569565i	$0.192888\pi$
$614$	−2.48926e146	−1.04047
$615$	2.43396e146	0.934049
$616$	6.44015e145	0.226939
$617$	−4.17702e146	−1.35175	−0.675873	−	0.737018i	$-0.736233\pi$
$617$	−4.17702e146	−1.35175	−0.675873	+	0.737018i	$0.736233\pi$
$618$	−1.64735e146	−0.489657
$619$	−6.25468e146	−1.70784	−0.853918	−	0.520408i	$-0.825780\pi$
$619$	−6.25468e146	−1.70784	−0.853918	+	0.520408i	$0.825780\pi$
$620$	−2.93328e146	−0.735852
$621$	1.31636e145	0.0303435
$622$	−1.03290e146	−0.218807
$623$	−6.81937e145	−0.132777
$624$	1.68731e145	0.0301997
$625$	2.61895e147	4.30950
$626$	7.27311e146	1.10044
$627$	−1.93544e146	−0.269299
$628$	−3.93648e146	−0.503763
$629$	−1.06146e147	−1.24952
$630$	−1.16322e147	−1.25975
$631$	1.39055e147	1.38562	0.692810	−	0.721120i	$-0.256372\pi$
$631$	1.39055e147	1.38562	0.692810	+	0.721120i	$0.256372\pi$
$632$	1.12500e147	1.03158
$633$	2.24542e147	1.89497
$634$	−1.41111e147	−1.09617
$635$	−2.48444e147	−1.77667
$636$	4.84461e146	0.318977
$637$	3.32820e145	0.0201785
$638$	−2.35771e146	−0.131645
$639$	−2.25388e147	−1.15914
$640$	−2.73569e147	−1.29604
$641$	−2.86145e147	−1.24893	−0.624467	−	0.781051i	$-0.714684\pi$
$641$	−2.86145e147	−1.24893	−0.624467	+	0.781051i	$0.714684\pi$
$642$	2.21957e147	0.892645
$643$	4.77165e147	1.76845	0.884225	−	0.467062i	$-0.154687\pi$
$643$	4.77165e147	1.76845	0.884225	+	0.467062i	$0.154687\pi$
$644$	−5.01014e146	−0.171136
$645$	−8.53323e146	−0.268676
$646$	2.23567e147	0.648935
$647$	−2.58902e147	−0.692883	−0.346442	−	0.938071i	$-0.612610\pi$
$647$	−2.58902e147	−0.692883	−0.346442	+	0.938071i	$0.612610\pi$
$648$	3.67776e147	0.907603
$649$	−1.48937e147	−0.338967
$650$	−5.09108e147	−1.06871
$651$	4.33112e147	0.838683
$652$	1.21003e147	0.216170
$653$	−2.82440e147	−0.465569	−0.232785	−	0.972528i	$-0.574784\pi$
$653$	−2.82440e147	−0.465569	−0.232785	+	0.972528i	$0.574784\pi$
$654$	−6.50685e146	−0.0989781
$655$	5.67537e147	0.796756
$656$	−8.64457e145	−0.0112019
$657$	1.15081e148	1.37665
$658$	1.05993e148	1.17062
$659$	−1.00022e148	−1.02003	−0.510014	−	0.860166i	$-0.670360\pi$
$659$	−1.00022e148	−1.02003	−0.510014	+	0.860166i	$0.670360\pi$
$660$	4.43844e147	0.417998
$661$	−1.30786e148	−1.13759	−0.568793	−	0.822481i	$-0.692589\pi$
$661$	−1.30786e148	−1.13759	−0.568793	+	0.822481i	$0.692589\pi$
$662$	−9.06653e147	−0.728445
$663$	1.60292e148	1.18974
$664$	7.58103e146	0.0519881
$665$	−2.44235e148	−1.54765
$666$	−1.04051e148	−0.609327
$667$	4.73129e147	0.256079
$668$	1.43381e148	0.717342
$669$	−2.81644e148	−1.30266
$670$	−2.11197e147	−0.0903151
$671$	1.02037e147	0.0403485
$672$	3.91350e148	1.43113
$673$	−2.79605e148	−0.945701	−0.472851	−	0.881143i	$-0.656775\pi$
$673$	−2.79605e148	−0.945701	−0.472851	+	0.881143i	$0.656775\pi$
$674$	−2.98867e147	−0.0935048
$675$	−1.09013e148	−0.315522
$676$	1.46306e148	0.391798
$677$	−2.29011e148	−0.567480	−0.283740	−	0.958901i	$-0.591575\pi$
$677$	−2.29011e148	−0.567480	−0.283740	+	0.958901i	$0.591575\pi$
$678$	5.58596e148	1.28097
$679$	3.11512e148	0.661168
$680$	−1.32250e149	−2.59822
$681$	8.61225e148	1.56637
$682$	4.96505e147	0.0836072
$683$	5.95955e148	0.929238	0.464619	−	0.885511i	$-0.346191\pi$
$683$	5.95955e148	0.929238	0.464619	+	0.885511i	$0.346191\pi$
$684$	−3.78182e148	−0.546080
$685$	1.07559e149	1.43844
$686$	4.96631e148	0.615202
$687$	−9.08119e148	−1.04211
$688$	3.03071e146	0.00322219
$689$	−2.19110e148	−0.215850
$690$	5.16145e148	0.471188
$691$	1.11983e149	0.947446	0.473723	−	0.880674i	$-0.342910\pi$
$691$	1.11983e149	0.947446	0.473723	+	0.880674i	$0.342910\pi$
$692$	−1.33422e149	−1.04630
$693$	−3.39767e148	−0.246994
$694$	6.86186e148	0.462455
$695$	−2.36580e149	−1.47834
$696$	−2.29214e149	−1.32818
$697$	−8.21220e148	−0.441305
$698$	−1.66339e149	−0.829059
$699$	−9.18950e147	−0.0424854
$700$	4.14909e149	1.77953
$701$	−3.90688e149	−1.55466	−0.777328	−	0.629095i	$-0.783426\pi$
$701$	−3.90688e149	−1.55466	−0.777328	+	0.629095i	$0.783426\pi$
$702$	1.11816e148	0.0412864
$703$	−2.18471e149	−0.748581
$704$	4.23732e148	0.134749
$705$	1.88428e150	5.56183
$706$	1.00138e149	0.274381
$707$	−4.90703e148	−0.124824
$708$	−5.61333e149	−1.32579
$709$	2.40986e149	0.528524	0.264262	−	0.964451i	$-0.414872\pi$
$709$	2.40986e149	0.528524	0.264262	+	0.964451i	$0.414872\pi$
$710$	−6.28896e149	−1.28090
$711$	−5.93521e149	−1.12275
$712$	−7.60011e148	−0.133543
$713$	−9.96352e148	−0.162634
$714$	7.57016e149	1.14802
$715$	−2.00740e149	−0.282857
$716$	−1.52454e149	−0.199620
$717$	7.01310e149	0.853403
$718$	−2.08840e149	−0.236200
$719$	1.40303e150	1.47503	0.737513	−	0.675333i	$-0.236000\pi$
$719$	1.40303e150	1.47503	0.737513	+	0.675333i	$0.236000\pi$
$720$	7.34451e148	0.0717806
$721$	−6.07202e149	−0.551736
$722$	−2.56769e149	−0.216940
$723$	−1.84684e150	−1.45100
$724$	3.89630e149	0.284694
$725$	−3.91817e150	−2.66279
$726$	1.30563e150	0.825366
$727$	1.97966e150	1.16422	0.582109	−	0.813111i	$-0.302228\pi$
$727$	1.97966e150	1.16422	0.582109	+	0.813111i	$0.302228\pi$
$728$	−1.09778e150	−0.600646
$729$	−2.25281e150	−1.14691
$730$	3.21108e150	1.52125
$731$	2.87912e149	0.126940
$732$	3.84571e149	0.157814
$733$	−1.03662e150	−0.395970	−0.197985	−	0.980205i	$-0.563440\pi$
$733$	−1.03662e150	−0.395970	−0.197985	+	0.980205i	$0.563440\pi$
$734$	1.64906e150	0.586399
$735$	2.79431e149	0.0925101
$736$	−9.00282e149	−0.277520
$737$	−6.16888e148	−0.0177077
$738$	−8.05015e149	−0.215201
$739$	4.27280e150	1.06385	0.531924	−	0.846792i	$-0.321469\pi$
$739$	4.27280e150	1.06385	0.531924	+	0.846792i	$0.321469\pi$
$740$	5.01007e150	1.16193
$741$	3.29914e150	0.712762
$742$	−1.03480e150	−0.208282
$743$	−6.15028e150	−1.15341	−0.576703	−	0.816954i	$-0.695661\pi$
$743$	−6.15028e150	−1.15341	−0.576703	+	0.816954i	$0.695661\pi$
$744$	4.82698e150	0.843522
$745$	−6.71376e150	−1.09336
$746$	3.57002e150	0.541854
$747$	−3.99957e149	−0.0565824
$748$	−1.49754e150	−0.197489
$749$	8.18115e150	1.00582
$750$	−2.77873e151	−3.18515
$751$	7.08228e149	0.0756966	0.0378483	−	0.999283i	$-0.487950\pi$
$751$	7.08228e149	0.0756966	0.0378483	+	0.999283i	$0.487950\pi$
$752$	−6.69232e149	−0.0667022
$753$	4.68557e150	0.435538
$754$	4.01893e150	0.348429
$755$	1.48550e151	1.20131
$756$	−9.11274e149	−0.0687472
$757$	−2.59698e151	−1.82782	−0.913911	−	0.405914i	$-0.866953\pi$
$757$	−2.59698e151	−1.82782	−0.913911	+	0.405914i	$0.866953\pi$
$758$	2.59533e150	0.170435
$759$	1.50761e150	0.0923839
$760$	−2.72197e151	−1.55658
$761$	−4.79193e150	−0.255750	−0.127875	−	0.991790i	$-0.540816\pi$
$761$	−4.79193e150	−0.255750	−0.127875	+	0.991790i	$0.540816\pi$
$762$	1.58495e151	0.789548
$763$	−2.39838e150	−0.111527
$764$	5.07396e150	0.220265
$765$	6.97717e151	2.82783
$766$	−8.16994e150	−0.309178
$767$	2.53877e151	0.897155
$768$	4.26771e151	1.40842
$769$	2.80525e151	0.864648	0.432324	−	0.901718i	$-0.357694\pi$
$769$	2.80525e151	0.864648	0.432324	+	0.901718i	$0.357694\pi$
$770$	−9.48044e150	−0.272939
$771$	−9.23036e151	−2.48235
$772$	−2.83550e151	−0.712395
$773$	−5.28505e151	−1.24058	−0.620291	−	0.784371i	$-0.712986\pi$
$773$	−5.28505e151	−1.24058	−0.620291	+	0.784371i	$0.712986\pi$
$774$	2.82231e150	0.0619019
$775$	8.25118e151	1.69113
$776$	3.47177e151	0.664982
$777$	−7.39758e151	−1.32430
$778$	7.92569e150	0.132620
$779$	−1.69024e151	−0.264383
$780$	−7.56573e151	−1.10633
$781$	−1.83695e151	−0.251141
$782$	−1.74148e151	−0.222620
$783$	8.60555e150	0.102869
$784$	−9.92441e148	−0.00110946
$785$	1.49477e152	1.56285
$786$	−3.62060e151	−0.354076
$787$	8.59116e151	0.785920	0.392960	−	0.919555i	$-0.371451\pi$
$787$	8.59116e151	0.785920	0.392960	+	0.919555i	$0.371451\pi$
$788$	2.52639e151	0.216209
$789$	−1.68296e152	−1.34751
$790$	−1.65609e152	−1.24068
$791$	2.05894e152	1.44337
$792$	−3.78666e151	−0.248419
$793$	−1.73932e151	−0.106792
$794$	2.16434e151	0.124380
$795$	−1.83961e152	−0.989583
$796$	1.22375e152	0.616251
$797$	2.78075e152	1.31099	0.655497	−	0.755198i	$-0.272459\pi$
$797$	2.78075e152	1.31099	0.655497	+	0.755198i	$0.272459\pi$
$798$	1.55810e152	0.687770
$799$	−6.35759e152	−2.62777
$800$	7.45559e152	2.88574
$801$	4.00964e151	0.145344
$802$	1.24913e152	0.424084
$803$	9.37929e151	0.298266
$804$	−2.32500e151	−0.0692596
$805$	1.90247e152	0.530926
$806$	−8.46338e151	−0.221286
$807$	−3.72907e152	−0.913565
$808$	−5.46883e151	−0.125545
$809$	−8.78756e152	−1.89048	−0.945238	−	0.326383i	$-0.894170\pi$
$809$	−8.78756e152	−1.89048	−0.945238	+	0.326383i	$0.894170\pi$
$810$	−5.41398e152	−1.09157
$811$	−2.90293e152	−0.548583	−0.274291	−	0.961647i	$-0.588443\pi$
$811$	−2.90293e152	−0.548583	−0.274291	+	0.961647i	$0.588443\pi$
$812$	−3.27532e152	−0.580179
$813$	9.94904e152	1.65207
$814$	−8.48034e151	−0.132018
$815$	−4.59476e152	−0.670638
$816$	−4.77975e151	−0.0654142
$817$	5.92584e151	0.0760487
$818$	7.58036e152	0.912308
$819$	5.79163e152	0.653727
$820$	3.87614e152	0.410367
$821$	1.45710e153	1.44701	0.723507	−	0.690318i	$-0.242529\pi$
$821$	1.45710e153	1.44701	0.723507	+	0.690318i	$0.242529\pi$
$822$	−6.86170e152	−0.639236
$823$	−1.16445e153	−1.01772	−0.508861	−	0.860849i	$-0.669933\pi$
$823$	−1.16445e153	−1.01772	−0.508861	+	0.860849i	$0.669933\pi$
$824$	−6.76719e152	−0.554919
$825$	−1.24851e153	−0.960640
$826$	1.19900e153	0.865697
$827$	1.68034e153	1.13856	0.569282	−	0.822142i	$-0.307221\pi$
$827$	1.68034e153	1.13856	0.569282	+	0.822142i	$0.307221\pi$
$828$	2.94585e152	0.187335
$829$	−5.29417e152	−0.315999	−0.157999	−	0.987439i	$-0.550504\pi$
$829$	−5.29417e152	−0.315999	−0.157999	+	0.987439i	$0.550504\pi$
$830$	−1.11599e152	−0.0625260
$831$	4.92955e153	2.59271
$832$	−7.22290e152	−0.356646
$833$	−9.42803e151	−0.0437077
$834$	1.50926e153	0.656972
$835$	−5.44450e153	−2.22545
$836$	−3.08224e152	−0.118314
$837$	−1.81222e152	−0.0653319
$838$	−2.25542e153	−0.763688
$839$	9.42582e152	0.299789	0.149895	−	0.988702i	$-0.452107\pi$
$839$	9.42582e152	0.299789	0.149895	+	0.988702i	$0.452107\pi$
$840$	−9.21680e153	−2.75371
$841$	−4.69765e152	−0.131853
$842$	7.20249e152	0.189932
$843$	9.76524e153	2.41955
$844$	3.57590e153	0.832543
$845$	−5.55560e153	−1.21550
$846$	−6.23214e153	−1.28142
$847$	4.81245e153	0.930008
$848$	6.53366e151	0.0118679
$849$	−7.40021e153	−1.26354
$850$	1.44219e154	2.31488
$851$	1.70178e153	0.256804
$852$	−6.92331e153	−0.982280
$853$	−5.92490e153	−0.790418	−0.395209	−	0.918591i	$-0.629328\pi$
$853$	−5.92490e153	−0.790418	−0.395209	+	0.918591i	$0.629328\pi$
$854$	−8.21436e152	−0.103047
$855$	1.43605e154	1.69414
$856$	9.11780e153	1.01162
$857$	5.88114e153	0.613718	0.306859	−	0.951755i	$-0.400722\pi$
$857$	5.88114e153	0.613718	0.306859	+	0.951755i	$0.400722\pi$
$858$	1.28062e153	0.125701
$859$	−9.47543e153	−0.874898	−0.437449	−	0.899243i	$-0.644118\pi$
$859$	−9.47543e153	−0.874898	−0.437449	+	0.899243i	$0.644118\pi$
$860$	−1.35894e153	−0.118041
$861$	−5.72329e153	−0.467714
$862$	−5.52888e153	−0.425114
$863$	−1.91728e154	−1.38713	−0.693567	−	0.720392i	$-0.743962\pi$
$863$	−1.91728e154	−1.38713	−0.693567	+	0.720392i	$0.743962\pi$
$864$	−1.63749e153	−0.111482
$865$	5.06635e154	3.24601
$866$	−1.30703e154	−0.788124
$867$	−2.00158e154	−1.13598
$868$	6.89742e153	0.368469
$869$	−4.83728e153	−0.243256
$870$	3.37423e154	1.59740
$871$	1.05154e153	0.0468676
$872$	−2.67296e153	−0.112170
$873$	−1.83162e154	−0.723749
$874$	−3.58433e153	−0.133370
$875$	−1.02422e155	−3.58897
$876$	3.53498e154	1.16660
$877$	−5.33567e154	−1.65848	−0.829240	−	0.558893i	$-0.811226\pi$
$877$	−5.33567e154	−1.65848	−0.829240	+	0.558893i	$0.811226\pi$
$878$	1.77438e154	0.519500
$879$	3.65423e154	1.00781
$880$	5.98589e152	0.0155521
$881$	−2.42473e154	−0.593510	−0.296755	−	0.954954i	$-0.595904\pi$
$881$	−2.42473e154	−0.593510	−0.296755	+	0.954954i	$0.595904\pi$
$882$	−9.24198e152	−0.0213140
$883$	1.13732e154	0.247142	0.123571	−	0.992336i	$-0.460565\pi$
$883$	1.13732e154	0.247142	0.123571	+	0.992336i	$0.460565\pi$
$884$	2.55269e154	0.522701
$885$	2.13151e155	4.11307
$886$	−3.84668e154	−0.699546
$887$	3.65900e154	0.627152	0.313576	−	0.949563i	$-0.398473\pi$
$887$	3.65900e154	0.627152	0.313576	+	0.949563i	$0.398473\pi$
$888$	−8.24452e154	−1.33194
$889$	5.84199e154	0.889649
$890$	1.11880e154	0.160612
$891$	−1.58137e154	−0.214020
$892$	−4.48526e154	−0.572312
$893$	−1.30853e155	−1.57428
$894$	4.28304e154	0.485884
$895$	5.78904e154	0.619294
$896$	6.43281e154	0.648978
$897$	−2.56986e154	−0.244516
$898$	−5.62754e154	−0.505023
$899$	−6.51353e154	−0.551356
$900$	−2.43957e155	−1.94797
$901$	6.20687e154	0.467543
$902$	−6.56099e153	−0.0466258
$903$	2.00653e154	0.134536
$904$	2.29467e155	1.45170
$905$	−1.47952e155	−0.883222
$906$	−9.47672e154	−0.533860
$907$	−1.41609e155	−0.752852	−0.376426	−	0.926447i	$-0.622847\pi$
$907$	−1.41609e155	−0.752852	−0.376426	+	0.926447i	$0.622847\pi$
$908$	1.37152e155	0.688171
$909$	2.88522e154	0.136639
$910$	1.61603e155	0.722396
$911$	1.60586e155	0.677632	0.338816	−	0.940853i	$-0.389974\pi$
$911$	1.60586e155	0.677632	0.338816	+	0.940853i	$0.389974\pi$
$912$	−9.83774e153	−0.0391892
$913$	−3.25971e153	−0.0122592
$914$	−2.58295e155	−0.917151
$915$	−1.46031e155	−0.489594
$916$	−1.44620e155	−0.457843
$917$	−1.33452e155	−0.398967
$918$	−3.16750e154	−0.0894285
$919$	7.22092e155	1.92543	0.962716	−	0.270514i	$-0.0871936\pi$
$919$	7.22092e155	1.92543	0.962716	+	0.270514i	$0.0871936\pi$
$920$	2.12028e155	0.533989
$921$	1.04057e156	2.47538
$922$	−1.42120e154	−0.0319362
$923$	3.13125e155	0.664703
$924$	−1.04367e155	−0.209308
$925$	−1.40931e156	−2.67033
$926$	3.67647e152	0.000658194 0
$927$	3.57021e155	0.603959
$928$	−5.88548e155	−0.940835
$929$	−2.41990e155	−0.365572	−0.182786	−	0.983153i	$-0.558512\pi$
$929$	−2.41990e155	−0.365572	−0.182786	+	0.983153i	$0.558512\pi$
$930$	−7.10572e155	−1.01450
$931$	−1.94049e154	−0.0261850
$932$	−1.46345e154	−0.0186657
$933$	4.31777e155	0.520563
$934$	2.92428e154	0.0333279
$935$	5.68650e155	0.612682
$936$	6.45471e155	0.657498
$937$	−9.71475e155	−0.935628	−0.467814	−	0.883827i	$-0.654958\pi$
$937$	−9.71475e155	−0.935628	−0.467814	+	0.883827i	$0.654958\pi$
$938$	4.96616e154	0.0452243
$939$	−3.04034e156	−2.61806
$940$	3.00077e156	2.44355
$941$	4.90410e155	0.377663	0.188832	−	0.982010i	$-0.439530\pi$
$941$	4.90410e155	0.377663	0.188832	+	0.982010i	$0.439530\pi$
$942$	−9.53590e155	−0.694528
$943$	1.31662e155	0.0906974
$944$	−7.57040e154	−0.0493275
$945$	3.46032e155	0.213278
$946$	2.30022e154	0.0134117
$947$	−1.95961e156	−1.08093	−0.540464	−	0.841367i	$-0.681751\pi$
$947$	−1.95961e156	−1.08093	−0.540464	+	0.841367i	$0.681751\pi$
$948$	−1.82313e156	−0.951438
$949$	−1.59878e156	−0.789430
$950$	2.96832e156	1.38683
$951$	5.89882e156	2.60788
$952$	3.10976e156	1.30103
$953$	5.58969e155	0.221315	0.110657	−	0.993859i	$-0.464704\pi$
$953$	5.58969e155	0.221315	0.110657	+	0.993859i	$0.464704\pi$
$954$	6.08439e155	0.227996
$955$	−1.92670e156	−0.683341
$956$	1.11686e156	0.374936
$957$	9.85583e155	0.313196
$958$	1.23861e156	0.372603
$959$	−2.52917e156	−0.720280
$960$	−6.06424e156	−1.63507
$961$	−2.54555e156	−0.649836
$962$	1.44555e156	0.349416
$963$	−4.81033e156	−1.10102
$964$	−2.94114e156	−0.637488
$965$	1.07670e157	2.21010
$966$	−1.21368e156	−0.235942
$967$	−9.52983e156	−1.75467	−0.877335	−	0.479879i	$-0.840681\pi$
$967$	−9.52983e156	−1.75467	−0.877335	+	0.479879i	$0.840681\pi$
$968$	5.36341e156	0.935373
$969$	−9.34569e156	−1.54388
$970$	−5.11073e156	−0.799773
$971$	6.33625e156	0.939340	0.469670	−	0.882842i	$-0.344373\pi$
$971$	6.33625e156	0.939340	0.469670	+	0.882842i	$0.344373\pi$
$972$	−6.45775e156	−0.906990
$973$	5.56302e156	0.740264
$974$	−6.74556e156	−0.850497
$975$	2.12820e157	2.54256
$976$	5.18650e154	0.00587163
$977$	3.04048e156	0.326195	0.163098	−	0.986610i	$-0.447851\pi$
$977$	3.04048e156	0.326195	0.163098	+	0.986610i	$0.447851\pi$
$978$	2.93122e156	0.298029
$979$	3.26792e155	0.0314905
$980$	4.45001e155	0.0406436
$981$	1.41019e156	0.122083
$982$	6.28280e156	0.515585
$983$	2.40548e157	1.87129	0.935646	−	0.352939i	$-0.114818\pi$
$983$	2.40548e157	1.87129	0.935646	+	0.352939i	$0.114818\pi$
$984$	−6.37854e156	−0.470412
$985$	−9.59330e156	−0.670758
$986$	−1.13847e157	−0.754716
$987$	−4.43077e157	−2.78502
$988$	5.25396e156	0.313147
$989$	−4.61593e155	−0.0260888
$990$	5.57428e156	0.298773
$991$	1.87572e157	0.953455	0.476728	−	0.879051i	$-0.341823\pi$
$991$	1.87572e157	0.953455	0.476728	+	0.879051i	$0.341823\pi$
$992$	1.23941e157	0.597520
$993$	3.79004e157	1.73304
$994$	1.47881e157	0.641396
$995$	−4.64688e157	−1.91183
$996$	−1.22856e156	−0.0479491
$997$	1.53697e157	0.569076	0.284538	−	0.958665i	$-0.408160\pi$
$997$	1.53697e157	0.569076	0.284538	+	0.958665i	$0.408160\pi$
$998$	3.81011e156	0.133839
$999$	3.09529e156	0.103161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.106.a.a.1.6	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.106.a.a.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+3.85781e15 q^{2} -1.61266e25 q^{3} -2.56821e31 q^{4} +9.75211e36 q^{5} -6.22135e40 q^{6} -2.29314e44 q^{7} -2.55568e47 q^{8} +1.34832e50 q^{9} +O(q^{10})\)	\(q+3.85781e15 q^{2} -1.61266e25 q^{3} -2.56821e31 q^{4} +9.75211e36 q^{5} -6.22135e40 q^{6} -2.29314e44 q^{7} -2.55568e47 q^{8} +1.34832e50 q^{9} +3.76218e52 q^{10} +1.09890e54 q^{11} +4.14166e56 q^{12} -1.87317e58 q^{13} -8.84652e59 q^{14} -1.57269e62 q^{15} +5.58564e61 q^{16} +5.30626e64 q^{17} +5.20155e65 q^{18} +1.09214e67 q^{19} -2.50455e68 q^{20} +3.69807e69 q^{21} +4.23934e69 q^{22} -8.50723e70 q^{23} +4.12146e72 q^{24} +7.04517e73 q^{25} -7.22635e73 q^{26} -1.54734e74 q^{27} +5.88928e75 q^{28} -5.56149e76 q^{29} -6.06713e77 q^{30} +1.17118e78 q^{31} +1.05826e79 q^{32} -1.77215e79 q^{33} +2.04706e80 q^{34} -2.23630e81 q^{35} -3.46276e81 q^{36} -2.00039e82 q^{37} +4.21327e82 q^{38} +3.02080e83 q^{39} -2.49233e84 q^{40} -1.54764e84 q^{41} +1.42665e85 q^{42} +5.42589e84 q^{43} -2.82220e85 q^{44} +1.31489e87 q^{45} -3.28193e86 q^{46} -1.19813e88 q^{47} -9.00775e86 q^{48} -1.77677e87 q^{49} +2.71789e89 q^{50} -8.55722e89 q^{51} +4.81070e89 q^{52} +1.16973e90 q^{53} -5.96936e89 q^{54} +1.07166e91 q^{55} +5.86054e91 q^{56} -1.76126e92 q^{57} -2.14552e92 q^{58} -1.35533e93 q^{59} +4.03899e93 q^{60} +9.28542e92 q^{61} +4.51820e93 q^{62} -3.09188e94 q^{63} +3.85597e94 q^{64} -1.82674e95 q^{65} -6.83664e94 q^{66} -5.61369e94 q^{67} -1.36276e96 q^{68} +1.37193e96 q^{69} -8.62722e96 q^{70} -1.67163e97 q^{71} -3.44587e97 q^{72} +8.53517e97 q^{73} -7.71713e97 q^{74} -1.13615e99 q^{75} -2.80485e98 q^{76} -2.51993e98 q^{77} +1.16537e99 q^{78} -4.40194e99 q^{79} +5.44717e98 q^{80} -1.43905e100 q^{81} -5.97051e99 q^{82} -2.96634e99 q^{83} -9.49742e100 q^{84} +5.17473e101 q^{85} +2.09321e100 q^{86} +8.96882e101 q^{87} -2.80844e101 q^{88} +2.97381e101 q^{89} +5.07261e102 q^{90} +4.29545e102 q^{91} +2.18484e102 q^{92} -1.88872e103 q^{93} -4.62216e103 q^{94} +1.06507e104 q^{95} -1.70661e104 q^{96} -1.35845e104 q^{97} -6.85446e102 q^{98} +1.48166e104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 91\!\cdots\!20 q^{2}+ \cdots + 31\!\cdots\!84 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more