LMFDB - Embedded newform 1.106.a.a.1.5

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			1.5
Root			$1.99379e13$ 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)

$f(q)$	$=$	$q+1.72418e15 q^{2} -1.28608e25 q^{3} -3.75920e31 q^{4} -7.91382e36 q^{5} -2.21743e40 q^{6} +2.76433e44 q^{7} -1.34757e47 q^{8} +4.01631e49 q^{9} +O(q^{10})$	\(q+1.72418e15 q^{2} -1.28608e25 q^{3} -3.75920e31 q^{4} -7.91382e36 q^{5} -2.21743e40 q^{6} +2.76433e44 q^{7} -1.34757e47 q^{8} +4.01631e49 q^{9} -1.36449e52 q^{10} -6.07175e54 q^{11} +4.83463e56 q^{12} +2.29543e58 q^{13} +4.76621e59 q^{14} +1.01778e62 q^{15} +1.29257e63 q^{16} -1.76894e64 q^{17} +6.92484e64 q^{18} +1.67507e67 q^{19} +2.97496e68 q^{20} -3.55515e69 q^{21} -1.04688e70 q^{22} +4.70564e71 q^{23} +1.73308e72 q^{24} +3.79766e73 q^{25} +3.95773e73 q^{26} +1.09411e75 q^{27} -1.03917e76 q^{28} -2.66735e76 q^{29} +1.75484e77 q^{30} -3.05391e78 q^{31} +7.69500e78 q^{32} +7.80875e79 q^{33} -3.04998e79 q^{34} -2.18764e81 q^{35} -1.50981e81 q^{36} +8.35117e81 q^{37} +2.88812e82 q^{38} -2.95210e83 q^{39} +1.06644e84 q^{40} -4.13967e84 q^{41} -6.12972e84 q^{42} +2.16424e85 q^{43} +2.28250e86 q^{44} -3.17843e86 q^{45} +8.11337e86 q^{46} -2.62376e87 q^{47} -1.66234e88 q^{48} +2.20535e88 q^{49} +6.54785e88 q^{50} +2.27500e89 q^{51} -8.62898e89 q^{52} -2.71935e90 q^{53} +1.88645e90 q^{54} +4.80507e91 q^{55} -3.72512e91 q^{56} -2.15427e92 q^{57} -4.59900e91 q^{58} +1.20365e93 q^{59} -3.82604e93 q^{60} +7.31250e93 q^{61} -5.26549e93 q^{62} +1.11024e94 q^{63} -3.91652e94 q^{64} -1.81656e95 q^{65} +1.34637e95 q^{66} -2.41093e95 q^{67} +6.64982e95 q^{68} -6.05182e96 q^{69} -3.77189e96 q^{70} -9.07767e96 q^{71} -5.41224e96 q^{72} -9.30512e97 q^{73} +1.43989e97 q^{74} -4.88409e98 q^{75} -6.29692e98 q^{76} -1.67843e99 q^{77} -5.08996e98 q^{78} +5.92503e99 q^{79} -1.02292e100 q^{80} -1.91011e100 q^{81} -7.13754e99 q^{82} -1.53405e99 q^{83} +1.33645e101 q^{84} +1.39991e101 q^{85} +3.73155e100 q^{86} +3.43042e101 q^{87} +8.18209e101 q^{88} +2.87836e102 q^{89} -5.48019e101 q^{90} +6.34533e102 q^{91} -1.76894e103 q^{92} +3.92757e103 q^{93} -4.52384e102 q^{94} -1.32562e104 q^{95} -9.89637e103 q^{96} +8.84441e103 q^{97} +3.80242e103 q^{98} -2.43860e104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.72418e15	0.270712	0.135356	−	0.990797i	$-0.456782\pi$
$2$	1.72418e15	0.270712	0.135356	+	0.990797i	$0.456782\pi$
$3$	−1.28608e25	−1.14922	−0.574608	−	0.818429i	$-0.694845\pi$
$3$	−1.28608e25	−1.14922	−0.574608	+	0.818429i	$0.694845\pi$
$4$	−3.75920e31	−0.926715
$5$	−7.91382e36	−1.59390	−0.796949	−	0.604046i	$-0.793554\pi$
$5$	−7.91382e36	−1.59390	−0.796949	+	0.604046i	$0.793554\pi$
$6$	−2.21743e40	−0.311107
$7$	2.76433e44	1.18561	0.592807	−	0.805345i	$-0.298020\pi$
$7$	2.76433e44	1.18561	0.592807	+	0.805345i	$0.298020\pi$
$8$	−1.34757e47	−0.521586
$9$	4.01631e49	0.320697
$10$	−1.36449e52	−0.431488
$11$	−6.07175e54	−1.28884	−0.644419	−	0.764673i	$-0.722901\pi$
$11$	−6.07175e54	−1.28884	−0.644419	+	0.764673i	$0.722901\pi$
$12$	4.83463e56	1.06500
$13$	2.29543e58	0.756550	0.378275	−	0.925693i	$-0.376517\pi$
$13$	2.29543e58	0.756550	0.378275	+	0.925693i	$0.376517\pi$
$14$	4.76621e59	0.320960
$15$	1.01778e62	1.83173
$16$	1.29257e63	0.785515
$17$	−1.76894e64	−0.445806	−0.222903	−	0.974841i	$-0.571553\pi$
$17$	−1.76894e64	−0.445806	−0.222903	+	0.974841i	$0.571553\pi$
$18$	6.92484e64	0.0868167
$19$	1.67507e67	1.22876	0.614382	−	0.789008i	$-0.289405\pi$
$19$	1.67507e67	1.22876	0.614382	+	0.789008i	$0.289405\pi$
$20$	2.97496e68	1.47709
$21$	−3.55515e69	−1.36253
$22$	−1.04688e70	−0.348904
$23$	4.70564e71	1.52022	0.760111	−	0.649793i	$-0.225144\pi$
$23$	4.70564e71	1.52022	0.760111	+	0.649793i	$0.225144\pi$
$24$	1.73308e72	0.599414
$25$	3.79766e73	1.54051
$26$	3.95773e73	0.204807
$27$	1.09411e75	0.780666
$28$	−1.03917e76	−1.09873
$29$	−2.66735e76	−0.446874	−0.223437	−	0.974718i	$-0.571728\pi$
$29$	−2.66735e76	−0.446874	−0.223437	+	0.974718i	$0.571728\pi$
$30$	1.75484e77	0.495873
$31$	−3.05391e78	−1.54300	−0.771502	−	0.636227i	$-0.780494\pi$
$31$	−3.05391e78	−1.54300	−0.771502	+	0.636227i	$0.780494\pi$
$32$	7.69500e78	0.734234
$33$	7.80875e79	1.48115
$34$	−3.04998e79	−0.120685
$35$	−2.18764e81	−1.88975
$36$	−1.50981e81	−0.297195
$37$	8.35117e81	0.390083	0.195041	−	0.980795i	$-0.437516\pi$
$37$	8.35117e81	0.390083	0.195041	+	0.980795i	$0.437516\pi$
$38$	2.88812e82	0.332642
$39$	−2.95210e83	−0.869439
$40$	1.06644e84	0.831354
$41$	−4.13967e84	−0.882700	−0.441350	−	0.897335i	$-0.645500\pi$
$41$	−4.13967e84	−0.882700	−0.441350	+	0.897335i	$0.645500\pi$
$42$	−6.12972e84	−0.368853
$43$	2.16424e85	0.378628	0.189314	−	0.981917i	$-0.439374\pi$
$43$	2.16424e85	0.378628	0.189314	+	0.981917i	$0.439374\pi$
$44$	2.28250e86	1.19438
$45$	−3.17843e86	−0.511159
$46$	8.11337e86	0.411543
$47$	−2.62376e87	−0.430316	−0.215158	−	0.976579i	$-0.569027\pi$
$47$	−2.62376e87	−0.430316	−0.215158	+	0.976579i	$0.569027\pi$
$48$	−1.66234e88	−0.902727
$49$	2.20535e88	0.405680
$50$	6.54785e88	0.417036
$51$	2.27500e89	0.512327
$52$	−8.62898e89	−0.701106
$53$	−2.71935e90	−0.812796	−0.406398	−	0.913696i	$-0.633215\pi$
$53$	−2.71935e90	−0.812796	−0.406398	+	0.913696i	$0.633215\pi$
$54$	1.88645e90	0.211336
$55$	4.80507e91	2.05428
$56$	−3.72512e91	−0.618399
$57$	−2.15427e92	−1.41212
$58$	−4.59900e91	−0.120974
$59$	1.20365e93	1.29053	0.645266	−	0.763958i	$-0.276746\pi$
$59$	1.20365e93	1.29053	0.645266	+	0.763958i	$0.276746\pi$
$60$	−3.82604e93	−1.69749
$61$	7.31250e93	1.36223	0.681114	−	0.732178i	$-0.261496\pi$
$61$	7.31250e93	1.36223	0.681114	+	0.732178i	$0.261496\pi$
$62$	−5.26549e93	−0.417710
$63$	1.11024e94	0.380223
$64$	−3.91652e94	−0.586749
$65$	−1.81656e95	−1.20586
$66$	1.34637e95	0.400966
$67$	−2.41093e95	−0.326030	−0.163015	−	0.986624i	$-0.552122\pi$
$67$	−2.41093e95	−0.326030	−0.163015	+	0.986624i	$0.552122\pi$
$68$	6.64982e95	0.413135
$69$	−6.05182e96	−1.74706
$70$	−3.77189e96	−0.511578
$71$	−9.07767e96	−0.584671	−0.292335	−	0.956316i	$-0.594432\pi$
$71$	−9.07767e96	−0.584671	−0.292335	+	0.956316i	$0.594432\pi$
$72$	−5.41224e96	−0.167271
$73$	−9.30512e97	−1.39403	−0.697014	−	0.717057i	$-0.745489\pi$
$73$	−9.30512e97	−1.39403	−0.697014	+	0.717057i	$0.745489\pi$
$74$	1.43989e97	0.105600
$75$	−4.88409e98	−1.77038
$76$	−6.29692e98	−1.13871
$77$	−1.67843e99	−1.52806
$78$	−5.08996e98	−0.235368
$79$	5.92503e99	1.40368	0.701840	−	0.712335i	$-0.252362\pi$
$79$	5.92503e99	1.40368	0.701840	+	0.712335i	$0.252362\pi$
$80$	−1.02292e100	−1.25203
$81$	−1.91011e100	−1.21785
$82$	−7.13754e99	−0.238958
$83$	−1.53405e99	−0.0271793	−0.0135897	−	0.999908i	$-0.504326\pi$
$83$	−1.53405e99	−0.0271793	−0.0135897	+	0.999908i	$0.504326\pi$
$84$	1.33645e101	1.26267
$85$	1.39991e101	0.710569
$86$	3.73155e100	0.102499
$87$	3.43042e101	0.513555
$88$	8.18209e101	0.672239
$89$	2.87836e102	1.30668	0.653342	−	0.757063i	$-0.273366\pi$
$89$	2.87836e102	1.30668	0.653342	+	0.757063i	$0.273366\pi$
$90$	−5.48019e101	−0.138377
$91$	6.34533e102	0.896976
$92$	−1.76894e103	−1.40881
$93$	3.92757e103	1.77324
$94$	−4.52384e102	−0.116492
$95$	−1.32562e104	−1.95853
$96$	−9.89637e103	−0.843794
$97$	8.84441e103	0.437676	0.218838	−	0.975761i	$-0.429773\pi$
$97$	8.84441e103	0.437676	0.218838	+	0.975761i	$0.429773\pi$
$98$	3.80242e103	0.109822
$99$	−2.43860e104	−0.413327
$100$	−1.42762e105	−1.42762
$101$	−1.30055e105	−0.771357	−0.385679	−	0.922633i	$-0.626033\pi$
$101$	−1.30055e105	−0.771357	−0.385679	+	0.922633i	$0.626033\pi$
$102$	3.92251e104	0.138693
$103$	4.74349e105	1.00495	0.502475	−	0.864592i	$-0.332423\pi$
$103$	4.74349e105	1.00495	0.502475	+	0.864592i	$0.332423\pi$
$104$	−3.09324e105	−0.394606
$105$	2.81348e106	2.17173
$106$	−4.68865e105	−0.220034
$107$	2.56647e106	0.735679	0.367839	−	0.929889i	$-0.380098\pi$
$107$	2.56647e106	0.735679	0.367839	+	0.929889i	$0.380098\pi$
$108$	−4.11300e106	−0.723454
$109$	5.73392e106	0.621671	0.310836	−	0.950464i	$-0.399391\pi$
$109$	5.73392e106	0.621671	0.310836	+	0.950464i	$0.399391\pi$
$110$	8.28482e106	0.556118
$111$	−1.07403e107	−0.448289
$112$	3.57309e107	0.931317
$113$	−4.20335e107	−0.687032	−0.343516	−	0.939147i	$-0.611618\pi$
$113$	−4.20335e107	−0.687032	−0.343516	+	0.939147i	$0.611618\pi$
$114$	−3.71435e107	−0.382277
$115$	−3.72396e108	−2.42308
$116$	1.00271e108	0.414125
$117$	9.21915e107	0.242624
$118$	2.07531e108	0.349363
$119$	−4.88995e108	−0.528553
$120$	−1.37152e109	−0.955406
$121$	1.46724e109	0.661103
$122$	1.26081e109	0.368772
$123$	5.32394e109	1.01441
$124$	1.14803e110	1.42992
$125$	−1.05449e110	−0.861522
$126$	1.91426e109	0.102931
$127$	4.07032e110	1.44522	0.722610	−	0.691256i	$-0.242942\pi$
$127$	4.07032e110	1.44522	0.722610	+	0.691256i	$0.242942\pi$
$128$	−3.79674e110	−0.893074
$129$	−2.78339e110	−0.435125
$130$	−3.13208e110	−0.326442
$131$	−6.75209e110	−0.470647	−0.235323	−	0.971917i	$-0.575615\pi$
$131$	−6.75209e110	−0.470647	−0.235323	+	0.971917i	$0.575615\pi$
$132$	−2.93547e111	−1.37261
$133$	4.63045e111	1.45684
$134$	−4.15689e110	−0.0882604
$135$	−8.65862e111	−1.24430
$136$	2.38377e111	0.232526
$137$	−1.29262e112	−0.858303	−0.429152	−	0.903232i	$-0.641187\pi$
$137$	−1.29262e112	−0.858303	−0.429152	+	0.903232i	$0.641187\pi$
$138$	−1.04344e112	−0.472952
$139$	5.20344e112	1.61441	0.807204	−	0.590273i	$-0.200980\pi$
$139$	5.20344e112	1.61441	0.807204	+	0.590273i	$0.200980\pi$
$140$	8.22379e112	1.75126
$141$	3.37437e112	0.494526
$142$	−1.56516e112	−0.158278
$143$	−1.39373e113	−0.975070
$144$	5.19135e112	0.251913
$145$	2.11089e113	0.712272
$146$	−1.60437e113	−0.377381
$147$	−2.83625e113	−0.466213
$148$	−3.13937e113	−0.361495
$149$	−5.94493e113	−0.480693	−0.240347	−	0.970687i	$-0.577261\pi$
$149$	−5.94493e113	−0.480693	−0.240347	+	0.970687i	$0.577261\pi$
$150$	−8.42105e113	−0.479264
$151$	−1.55664e113	−0.0625026	−0.0312513	−	0.999512i	$-0.509949\pi$
$151$	−1.55664e113	−0.0625026	−0.0312513	+	0.999512i	$0.509949\pi$
$152$	−2.25727e114	−0.640906
$153$	−7.10462e113	−0.142969
$154$	−2.89393e114	−0.413666
$155$	2.41681e115	2.45939
$156$	1.10975e115	0.805722
$157$	−2.92893e115	−1.52047	−0.760233	−	0.649651i	$-0.774915\pi$
$157$	−2.92893e115	−1.52047	−0.760233	+	0.649651i	$0.774915\pi$
$158$	1.02158e115	0.379993
$159$	3.49729e115	0.934078
$160$	−6.08968e115	−1.17029
$161$	1.30080e116	1.80240
$162$	−3.29337e115	−0.329687
$163$	−4.30034e115	−0.311640	−0.155820	−	0.987785i	$-0.549802\pi$
$163$	−4.30034e115	−0.311640	−0.155820	+	0.987785i	$0.549802\pi$
$164$	1.55619e116	0.818011
$165$	−6.17970e116	−2.36081
$166$	−2.64497e114	−0.00735778
$167$	−5.37632e116	−1.09111	−0.545557	−	0.838074i	$-0.683682\pi$
$167$	−5.37632e116	−1.09111	−0.545557	+	0.838074i	$0.683682\pi$
$168$	4.79080e116	0.710674
$169$	−3.93661e116	−0.427632
$170$	2.41370e116	0.192360
$171$	6.72759e116	0.394062
$172$	−8.13583e116	−0.350880
$173$	3.98690e117	1.26828	0.634139	−	0.773219i	$-0.281355\pi$
$173$	3.98690e117	1.26828	0.634139	+	0.773219i	$0.281355\pi$
$174$	5.91467e116	0.139026
$175$	1.04980e118	1.82645
$176$	−7.84816e117	−1.01240
$177$	−1.54799e118	−1.48310
$178$	4.96282e117	0.353735
$179$	2.27492e118	1.20832	0.604160	−	0.796863i	$-0.293509\pi$
$179$	2.27492e118	1.20832	0.604160	+	0.796863i	$0.293509\pi$
$180$	1.19484e118	0.473699
$181$	−2.97655e118	−0.882242	−0.441121	−	0.897448i	$-0.645419\pi$
$181$	−2.97655e118	−0.882242	−0.441121	+	0.897448i	$0.645419\pi$
$182$	1.09405e118	0.242823
$183$	−9.40445e118	−1.56549
$184$	−6.34116e118	−0.792926
$185$	−6.60896e118	−0.621752
$186$	6.77184e118	0.480039
$187$	1.07406e119	0.574571
$188$	9.86326e118	0.398780
$189$	3.02449e119	0.925568
$190$	−2.28561e119	−0.530197
$191$	−3.30349e119	−0.581730	−0.290865	−	0.956764i	$-0.593943\pi$
$191$	−3.30349e119	−0.581730	−0.290865	+	0.956764i	$0.593943\pi$
$192$	5.03696e119	0.674301
$193$	5.23171e119	0.533194	0.266597	−	0.963808i	$-0.414101\pi$
$193$	5.23171e119	0.533194	0.266597	+	0.963808i	$0.414101\pi$
$194$	1.52494e119	0.118484
$195$	2.33624e120	1.38580
$196$	−8.29035e119	−0.375949
$197$	−1.35909e120	−0.471814	−0.235907	−	0.971776i	$-0.575806\pi$
$197$	−1.35909e120	−0.471814	−0.235907	+	0.971776i	$0.575806\pi$
$198$	−4.20459e119	−0.111893
$199$	−6.37670e120	−1.30259	−0.651297	−	0.758823i	$-0.725775\pi$
$199$	−6.37670e120	−1.30259	−0.651297	+	0.758823i	$0.725775\pi$
$200$	−5.11759e120	−0.803509
$201$	3.10065e120	0.374679
$202$	−2.24239e120	−0.208816
$203$	−7.37345e120	−0.529820
$204$	−8.55219e120	−0.474781
$205$	3.27606e121	1.40693
$206$	8.17864e120	0.272052
$207$	1.88993e121	0.487531
$208$	2.96700e121	0.594282
$209$	−1.01706e122	−1.58368
$210$	4.85095e121	0.587914
$211$	3.13721e121	0.296288	0.148144	−	0.988966i	$-0.452670\pi$
$211$	3.13721e121	0.296288	0.148144	+	0.988966i	$0.452670\pi$
$212$	1.02226e122	0.753230
$213$	1.16746e122	0.671913
$214$	4.42506e121	0.199157
$215$	−1.71274e122	−0.603494
$216$	−1.47439e122	−0.407184
$217$	−8.44202e122	−1.82941
$218$	9.88632e121	0.168294
$219$	1.19671e123	1.60204
$220$	−1.80632e123	−1.90373
$221$	−4.06048e122	−0.337274
$222$	−1.85181e122	−0.121357
$223$	4.92657e122	0.255000	0.127500	−	0.991839i	$-0.459305\pi$
$223$	4.92657e122	0.255000	0.127500	+	0.991839i	$0.459305\pi$
$224$	2.12715e123	0.870518
$225$	1.52526e123	0.494038
$226$	−7.24733e122	−0.185988
$227$	4.08331e123	0.831104	0.415552	−	0.909569i	$-0.363588\pi$
$227$	4.08331e123	0.831104	0.415552	+	0.909569i	$0.363588\pi$
$228$	8.09834e123	1.30863
$229$	−1.31242e124	−1.68543	−0.842716	−	0.538359i	$-0.819045\pi$
$229$	−1.31242e124	−1.68543	−0.842716	+	0.538359i	$0.819045\pi$
$230$	−6.42078e123	−0.655958
$231$	2.15860e124	1.75607
$232$	3.59443e123	0.233083
$233$	−1.99296e124	−1.03113	−0.515565	−	0.856850i	$-0.672418\pi$
$233$	−1.99296e124	−1.03113	−0.515565	+	0.856850i	$0.672418\pi$
$234$	1.58955e123	0.0656812
$235$	2.07640e124	0.685879
$236$	−4.52476e124	−1.19596
$237$	−7.62005e124	−1.61313
$238$	−8.43116e123	−0.143086
$239$	−8.89501e124	−1.21131	−0.605657	−	0.795726i	$-0.707090\pi$
$239$	−8.89501e124	−1.21131	−0.605657	+	0.795726i	$0.707090\pi$
$240$	1.31555e125	1.43885
$241$	1.87728e125	1.65057	0.825284	−	0.564718i	$-0.191015\pi$
$241$	1.87728e125	1.65057	0.825284	+	0.564718i	$0.191015\pi$
$242$	2.52979e124	0.178969
$243$	1.08631e125	0.618908
$244$	−2.74892e125	−1.26240
$245$	−1.74527e125	−0.646612
$246$	9.17944e124	0.274614
$247$	3.84500e125	0.929622
$248$	4.11534e125	0.804809
$249$	1.97290e124	0.0312349
$250$	−1.81813e125	−0.233225
$251$	1.01406e126	1.05485	0.527426	−	0.849601i	$-0.323157\pi$
$251$	1.01406e126	1.05485	0.527426	+	0.849601i	$0.323157\pi$
$252$	−4.17362e125	−0.352358
$253$	−2.85715e126	−1.95932
$254$	7.01798e125	0.391239
$255$	−1.80039e126	−0.816597
$256$	9.34104e125	0.344983
$257$	−4.56506e126	−1.37391	−0.686954	−	0.726701i	$-0.741053\pi$
$257$	−4.56506e126	−1.37391	−0.686954	+	0.726701i	$0.741053\pi$
$258$	−4.79906e125	−0.117794
$259$	2.30854e126	0.462487
$260$	6.82881e126	1.11749
$261$	−1.07129e126	−0.143311
$262$	−1.16418e126	−0.127410
$263$	1.42574e127	1.27751	0.638756	−	0.769410i	$-0.279449\pi$
$263$	1.42574e127	1.27751	0.638756	+	0.769410i	$0.279449\pi$
$264$	−1.05228e127	−0.772548
$265$	2.15204e127	1.29551
$266$	7.98373e126	0.394385
$267$	−3.70180e127	−1.50166
$268$	9.06318e126	0.302137
$269$	1.86088e127	0.510179	0.255089	−	0.966917i	$-0.417895\pi$
$269$	1.86088e127	0.510179	0.255089	+	0.966917i	$0.417895\pi$
$270$	−1.49290e127	−0.336848
$271$	4.04456e127	0.751595	0.375797	−	0.926702i	$-0.377369\pi$
$271$	4.04456e127	0.751595	0.375797	+	0.926702i	$0.377369\pi$
$272$	−2.28648e127	−0.350187
$273$	−8.16059e127	−1.03082
$274$	−2.22871e127	−0.232353
$275$	−2.30584e128	−1.98547
$276$	2.27500e128	1.61903
$277$	−1.03896e128	−0.611519	−0.305760	−	0.952109i	$-0.598910\pi$
$277$	−1.03896e128	−0.611519	−0.305760	+	0.952109i	$0.598910\pi$
$278$	8.97167e127	0.437040
$279$	−1.22654e128	−0.494837
$280$	2.94799e128	0.985665
$281$	1.51367e128	0.419710	0.209855	−	0.977732i	$-0.432701\pi$
$281$	1.51367e128	0.419710	0.209855	+	0.977732i	$0.432701\pi$
$282$	5.81802e127	0.133874
$283$	−5.26985e128	−1.00696	−0.503478	−	0.864008i	$-0.667947\pi$
$283$	−5.26985e128	−1.00696	−0.503478	+	0.864008i	$0.667947\pi$
$284$	3.41248e128	0.541823
$285$	1.70485e129	2.25077
$286$	−2.40304e128	−0.263964
$287$	−1.14434e129	−1.04654
$288$	3.09055e128	0.235467
$289$	−1.26156e129	−0.801257
$290$	3.63956e128	0.192821
$291$	−1.13746e129	−0.502985
$292$	3.49798e129	1.29187
$293$	−8.63812e128	−0.266606	−0.133303	−	0.991075i	$-0.542558\pi$
$293$	−8.63812e128	−0.266606	−0.133303	+	0.991075i	$0.542558\pi$
$294$	−4.89021e128	−0.126210
$295$	−9.52545e129	−2.05698
$296$	−1.12537e129	−0.203461
$297$	−6.64319e129	−1.00615
$298$	−1.02501e129	−0.130130
$299$	1.08015e130	1.15012
$300$	1.83603e130	1.64064
$301$	5.98269e129	0.448906
$302$	−2.68393e128	−0.0169202
$303$	1.67261e130	0.886456
$304$	2.16514e130	0.965213
$305$	−5.78698e130	−2.17125
$306$	−1.22497e129	−0.0387034
$307$	−1.83896e130	−0.489562	−0.244781	−	0.969578i	$-0.578716\pi$
$307$	−1.83896e130	−0.489562	−0.244781	+	0.969578i	$0.578716\pi$
$308$	6.30957e130	1.41608
$309$	−6.10051e130	−1.15490
$310$	4.16701e130	0.665788
$311$	1.34727e130	0.181776	0.0908878	−	0.995861i	$-0.471030\pi$
$311$	1.34727e130	0.181776	0.0908878	+	0.995861i	$0.471030\pi$
$312$	3.97815e130	0.453487
$313$	−1.30348e131	−1.25611	−0.628056	−	0.778168i	$-0.716149\pi$
$313$	−1.30348e131	−1.25611	−0.628056	+	0.778168i	$0.716149\pi$
$314$	−5.05000e130	−0.411609
$315$	−8.78624e130	−0.606037
$316$	−2.22734e131	−1.30081
$317$	1.73457e131	0.858183	0.429091	−	0.903261i	$-0.358834\pi$
$317$	1.73457e131	0.858183	0.429091	+	0.903261i	$0.358834\pi$
$318$	6.02997e130	0.252866
$319$	1.61955e131	0.575948
$320$	3.09947e131	0.935218
$321$	−3.30069e131	−0.845454
$322$	2.24281e131	0.487931
$323$	−2.96310e131	−0.547790
$324$	7.18047e131	1.12860
$325$	8.71725e131	1.16547
$326$	−7.41456e130	−0.0843648
$327$	−7.37428e131	−0.714434
$328$	5.57848e131	0.460404
$329$	−7.25295e131	−0.510188
$330$	−1.06549e132	−0.639100
$331$	−6.66098e131	−0.340854	−0.170427	−	0.985370i	$-0.554515\pi$
$331$	−6.66098e131	−0.340854	−0.170427	+	0.985370i	$0.554515\pi$
$332$	5.76679e130	0.0251875
$333$	3.35409e131	0.125098
$334$	−9.26975e131	−0.295378
$335$	1.90797e132	0.519659
$336$	−4.59527e132	−1.07028
$337$	−4.68436e132	−0.933427	−0.466713	−	0.884409i	$-0.654562\pi$
$337$	−4.68436e132	−0.933427	−0.466713	+	0.884409i	$0.654562\pi$
$338$	−6.78743e131	−0.115765
$339$	5.40584e132	0.789548
$340$	−5.26254e132	−0.658495
$341$	1.85426e133	1.98868
$342$	1.15996e132	0.106677
$343$	−8.93110e132	−0.704634
$344$	−2.91646e132	−0.197487
$345$	4.78930e133	2.78464
$346$	6.87413e132	0.343339
$347$	−2.93933e133	−1.26169	−0.630843	−	0.775911i	$-0.717291\pi$
$347$	−2.93933e133	−1.26169	−0.630843	+	0.775911i	$0.717291\pi$
$348$	−1.28957e133	−0.475919
$349$	−2.97134e133	−0.943230	−0.471615	−	0.881804i	$-0.656329\pi$
$349$	−2.97134e133	−0.943230	−0.471615	+	0.881804i	$0.656329\pi$
$350$	1.81004e133	0.494443
$351$	2.51146e133	0.590613
$352$	−4.67221e133	−0.946309
$353$	−3.13067e133	−0.546343	−0.273171	−	0.961965i	$-0.588073\pi$
$353$	−3.13067e133	−0.546343	−0.273171	+	0.961965i	$0.588073\pi$
$354$	−2.66901e133	−0.401494
$355$	7.18390e133	0.931906
$356$	−1.08204e134	−1.21092
$357$	6.28886e133	0.607422
$358$	3.92237e133	0.327107
$359$	−9.32496e133	−0.671721	−0.335860	−	0.941912i	$-0.609027\pi$
$359$	−9.32496e133	−0.671721	−0.335860	+	0.941912i	$0.609027\pi$
$360$	4.28315e133	0.266613
$361$	9.47505e133	0.509863
$362$	−5.13211e133	−0.238834
$363$	−1.88698e134	−0.759750
$364$	−2.38534e134	−0.831241
$365$	7.36390e134	2.22194
$366$	−1.62150e134	−0.423799
$367$	7.95942e134	1.80266	0.901329	−	0.433136i	$-0.142593\pi$
$367$	7.95942e134	1.80266	0.901329	+	0.433136i	$0.142593\pi$
$368$	6.08236e134	1.19416
$369$	−1.66262e134	−0.283080
$370$	−1.13950e134	−0.168316
$371$	−7.51718e134	−0.963661
$372$	−1.47645e135	−1.64329
$373$	−1.34599e135	−1.30115	−0.650574	−	0.759443i	$-0.725472\pi$
$373$	−1.34599e135	−1.30115	−0.650574	+	0.759443i	$0.725472\pi$
$374$	1.85187e134	0.155544
$375$	1.35616e135	0.990075
$376$	3.53569e134	0.224446
$377$	−6.12271e134	−0.338083
$378$	5.21478e134	0.250563
$379$	−2.25026e135	−0.941182	−0.470591	−	0.882351i	$-0.655959\pi$
$379$	−2.25026e135	−0.941182	−0.470591	+	0.882351i	$0.655959\pi$
$380$	4.98327e135	1.81500
$381$	−5.23476e135	−1.66087
$382$	−5.69582e134	−0.157481
$383$	−5.53878e135	−1.33499	−0.667495	−	0.744614i	$-0.732634\pi$
$383$	−5.53878e135	−1.33499	−0.667495	+	0.744614i	$0.732634\pi$
$384$	4.88291e135	1.02634
$385$	1.32828e136	2.43558
$386$	9.02041e134	0.144342
$387$	8.69227e134	0.121425
$388$	−3.32479e135	−0.405601
$389$	4.13994e135	0.441204	0.220602	−	0.975364i	$-0.429198\pi$
$389$	4.13994e135	0.441204	0.220602	+	0.975364i	$0.429198\pi$
$390$	4.02810e135	0.375153
$391$	−8.32401e135	−0.677724
$392$	−2.97185e135	−0.211597
$393$	8.68371e135	0.540875
$394$	−2.34332e135	−0.127726
$395$	−4.68896e136	−2.23732
$396$	9.16720e135	0.383036
$397$	2.52452e136	0.924012	0.462006	−	0.886877i	$-0.347130\pi$
$397$	2.52452e136	0.924012	0.462006	+	0.886877i	$0.347130\pi$
$398$	−1.09946e136	−0.352628
$399$	−5.95512e136	−1.67422
$400$	4.90873e136	1.21010
$401$	−8.02537e135	−0.173534	−0.0867672	−	0.996229i	$-0.527654\pi$
$401$	−8.02537e135	−0.173534	−0.0867672	+	0.996229i	$0.527654\pi$
$402$	5.34608e135	0.101430
$403$	−7.01003e136	−1.16736
$404$	4.88904e136	0.714828
$405$	1.51162e137	1.94113
$406$	−1.27132e136	−0.143429
$407$	−5.07062e136	−0.502753
$408$	−3.06571e136	−0.267222
$409$	−3.44614e136	−0.264155	−0.132077	−	0.991239i	$-0.542165\pi$
$409$	−3.44614e136	−0.264155	−0.132077	+	0.991239i	$0.542165\pi$
$410$	5.64852e136	0.380875
$411$	1.66241e137	0.986376
$412$	−1.78318e137	−0.931301
$413$	3.32728e137	1.53007
$414$	3.25858e136	0.131981
$415$	1.21402e136	0.0433211
$416$	1.76633e137	0.555485
$417$	−6.69203e137	−1.85530
$418$	−1.75360e137	−0.428721
$419$	−1.84518e137	−0.397926	−0.198963	−	0.980007i	$-0.563757\pi$
$419$	−1.84518e137	−0.397926	−0.198963	+	0.980007i	$0.563757\pi$
$420$	−1.05764e138	−2.01257
$421$	6.84171e137	1.14909	0.574546	−	0.818473i	$-0.305179\pi$
$421$	6.84171e137	1.14909	0.574546	+	0.818473i	$0.305179\pi$
$422$	5.40911e136	0.0802088
$423$	−1.05378e137	−0.138001
$424$	3.66450e137	0.423942
$425$	−6.71784e137	−0.686769
$426$	2.01291e137	0.181895
$427$	2.02142e138	1.61508
$428$	−9.64789e137	−0.681765
$429$	1.79244e138	1.12057
$430$	−2.95308e137	−0.163373
$431$	7.02164e137	0.343860	0.171930	−	0.985109i	$-0.445000\pi$
$431$	7.02164e137	0.343860	0.171930	+	0.985109i	$0.445000\pi$
$432$	1.41422e138	0.613225
$433$	−7.67228e137	−0.294652	−0.147326	−	0.989088i	$-0.547067\pi$
$433$	−7.67228e137	−0.294652	−0.147326	+	0.989088i	$0.547067\pi$
$434$	−1.45556e138	−0.495243
$435$	−2.71477e138	−0.818555
$436$	−2.15550e138	−0.576112
$437$	7.88227e138	1.86800
$438$	2.06335e138	0.433692
$439$	−1.85235e138	−0.345411	−0.172705	−	0.984974i	$-0.555251\pi$
$439$	−1.85235e138	−0.345411	−0.172705	+	0.984974i	$0.555251\pi$
$440$	−6.47515e138	−1.07148
$441$	8.85736e137	0.130100
$442$	−7.00101e137	−0.0913043
$443$	−6.11745e138	−0.708557	−0.354278	−	0.935140i	$-0.615273\pi$
$443$	−6.11745e138	−0.708557	−0.354278	+	0.935140i	$0.615273\pi$
$444$	4.03748e138	0.415436
$445$	−2.27788e139	−2.08272
$446$	8.49431e137	0.0690316
$447$	7.64565e138	0.552420
$448$	−1.08266e139	−0.695657
$449$	2.64878e139	1.51396	0.756979	−	0.653440i	$-0.226675\pi$
$449$	2.64878e139	1.51396	0.756979	+	0.653440i	$0.226675\pi$
$450$	2.62982e138	0.133742
$451$	2.51351e139	1.13766
$452$	1.58012e139	0.636683
$453$	2.00196e138	0.0718290
$454$	7.04037e138	0.224990
$455$	−5.02157e139	−1.42969
$456$	2.90302e139	0.736539
$457$	−3.40764e139	−0.770642	−0.385321	−	0.922783i	$-0.625909\pi$
$457$	−3.40764e139	−0.770642	−0.385321	+	0.922783i	$0.625909\pi$
$458$	−2.26286e139	−0.456267
$459$	−1.93543e139	−0.348025
$460$	1.39991e140	2.24551
$461$	1.76000e139	0.251891	0.125946	−	0.992037i	$-0.459804\pi$
$461$	1.76000e139	0.251891	0.125946	+	0.992037i	$0.459804\pi$
$462$	3.72182e139	0.475391
$463$	−3.51403e139	−0.400685	−0.200342	−	0.979726i	$-0.564205\pi$
$463$	−3.51403e139	−0.400685	−0.200342	+	0.979726i	$0.564205\pi$
$464$	−3.44773e139	−0.351026
$465$	−3.10820e140	−2.82637
$466$	−3.43623e139	−0.279140
$467$	5.51524e139	0.400339	0.200170	−	0.979761i	$-0.435851\pi$
$467$	5.51524e139	0.400339	0.200170	+	0.979761i	$0.435851\pi$
$468$	−3.46566e139	−0.224843
$469$	−6.66462e139	−0.386546
$470$	3.58009e139	0.185676
$471$	3.76683e140	1.74734
$472$	−1.62200e140	−0.673123
$473$	−1.31408e140	−0.487989
$474$	−1.31383e140	−0.436695
$475$	6.36134e140	1.89293
$476$	1.83823e140	0.489818
$477$	−1.09217e140	−0.260661
$478$	−1.53366e140	−0.327918
$479$	1.76670e140	0.338493	0.169246	−	0.985574i	$-0.445867\pi$
$479$	1.76670e140	0.338493	0.169246	+	0.985574i	$0.445867\pi$
$480$	7.83181e140	1.34492
$481$	1.91695e140	0.295117
$482$	3.23676e140	0.446829
$483$	−1.67292e141	−2.07134
$484$	−5.51565e140	−0.612654
$485$	−6.99931e140	−0.697612
$486$	1.87300e140	0.167546
$487$	7.86002e140	0.631180	0.315590	−	0.948896i	$-0.397798\pi$
$487$	7.86002e140	0.631180	0.315590	+	0.948896i	$0.397798\pi$
$488$	−9.85408e140	−0.710518
$489$	5.53057e140	0.358142
$490$	−3.00917e140	−0.175046
$491$	8.16969e140	0.426999	0.213500	−	0.976943i	$-0.431514\pi$
$491$	8.16969e140	0.426999	0.213500	+	0.976943i	$0.431514\pi$
$492$	−2.00138e141	−0.940072
$493$	4.71839e140	0.199219
$494$	6.62948e140	0.251660
$495$	1.92987e141	0.658801
$496$	−3.94739e141	−1.21205
$497$	−2.50937e141	−0.693193
$498$	3.40164e139	0.00845567
$499$	3.10828e141	0.695411	0.347706	−	0.937604i	$-0.386961\pi$
$499$	3.10828e141	0.695411	0.347706	+	0.937604i	$0.386961\pi$
$500$	3.96404e141	0.798386
$501$	6.91437e141	1.25393
$502$	1.74842e141	0.285562
$503$	−1.58808e141	−0.233643	−0.116821	−	0.993153i	$-0.537271\pi$
$503$	−1.58808e141	−0.233643	−0.116821	+	0.993153i	$0.537271\pi$
$504$	−1.49612e141	−0.198319
$505$	1.02923e142	1.22946
$506$	−4.92624e141	−0.530412
$507$	5.06279e141	0.491442
$508$	−1.53012e142	−1.33931
$509$	−4.45459e141	−0.351661	−0.175831	−	0.984420i	$-0.556261\pi$
$509$	−4.45459e141	−0.351661	−0.175831	+	0.984420i	$0.556261\pi$
$510$	−3.10420e141	−0.221063
$511$	−2.57224e142	−1.65278
$512$	1.70120e142	0.986465
$513$	1.83272e142	0.959254
$514$	−7.87099e141	−0.371934
$515$	−3.75391e142	−1.60179
$516$	1.04633e142	0.403237
$517$	1.59308e142	0.554607
$518$	3.98034e141	0.125201
$519$	−5.12746e142	−1.45753
$520$	2.44793e142	0.628961
$521$	4.14489e142	0.962792	0.481396	−	0.876503i	$-0.340130\pi$
$521$	4.14489e142	0.962792	0.481396	+	0.876503i	$0.340130\pi$
$522$	−1.84710e141	−0.0387962
$523$	4.05731e142	0.770725	0.385362	−	0.922765i	$-0.374076\pi$
$523$	4.05731e142	0.770725	0.385362	+	0.922765i	$0.374076\pi$
$524$	2.53825e142	0.436155
$525$	−1.35012e143	−2.09899
$526$	2.45824e142	0.345838
$527$	5.40219e142	0.687880
$528$	1.00934e143	1.16347
$529$	1.25618e143	1.31108
$530$	3.71051e142	0.350712
$531$	4.83422e142	0.413870
$532$	−1.74068e143	−1.35008
$533$	−9.50231e142	−0.667807
$534$	−6.38258e142	−0.406518
$535$	−2.03106e143	−1.17260
$536$	3.24889e142	0.170053
$537$	−2.92572e143	−1.38862
$538$	3.20849e142	0.138112
$539$	−1.33903e143	−0.522855
$540$	3.25495e143	1.15311
$541$	1.47517e143	0.474225	0.237112	−	0.971482i	$-0.423799\pi$
$541$	1.47517e143	0.474225	0.237112	+	0.971482i	$0.423799\pi$
$542$	6.97356e142	0.203466
$543$	3.82808e143	1.01389
$544$	−1.36120e143	−0.327326
$545$	−4.53772e143	−0.990881
$546$	−1.40703e143	−0.279056
$547$	−5.05802e142	−0.0911268	−0.0455634	−	0.998961i	$-0.514508\pi$
$547$	−5.05802e142	−0.0911268	−0.0455634	+	0.998961i	$0.514508\pi$
$548$	4.85922e143	0.795402
$549$	2.93693e143	0.436863
$550$	−3.97569e143	−0.537492
$551$	−4.46800e143	−0.549103
$552$	8.15523e143	0.911244
$553$	1.63787e144	1.66422
$554$	−1.79135e143	−0.165546
$555$	8.49964e143	0.714528
$556$	−1.95608e144	−1.49610
$557$	7.98264e143	0.555583	0.277792	−	0.960641i	$-0.410398\pi$
$557$	7.98264e143	0.555583	0.277792	+	0.960641i	$0.410398\pi$
$558$	−2.11478e143	−0.133959
$559$	4.96786e143	0.286451
$560$	−2.82768e144	−1.48443
$561$	−1.38132e144	−0.660306
$562$	2.60984e143	0.113621
$563$	3.83728e143	0.152171	0.0760856	−	0.997101i	$-0.475758\pi$
$563$	3.83728e143	0.152171	0.0760856	+	0.997101i	$0.475758\pi$
$564$	−1.26849e144	−0.458284
$565$	3.32645e144	1.09506
$566$	−9.08618e143	−0.272596
$567$	−5.28017e144	−1.44390
$568$	1.22328e144	0.304956
$569$	−7.81233e144	−1.77577	−0.887884	−	0.460067i	$-0.847825\pi$
$569$	−7.81233e144	−1.77577	−0.887884	+	0.460067i	$0.847825\pi$
$570$	2.93947e144	0.609311
$571$	5.50316e144	1.04044	0.520220	−	0.854033i	$-0.325850\pi$
$571$	5.50316e144	1.04044	0.520220	+	0.854033i	$0.325850\pi$
$572$	5.23930e144	0.903612
$573$	4.24855e144	0.668533
$574$	−1.97305e144	−0.283312
$575$	1.78704e145	2.34192
$576$	−1.57300e144	−0.188169
$577$	−6.56179e144	−0.716625	−0.358312	−	0.933602i	$-0.616648\pi$
$577$	−6.56179e144	−0.716625	−0.358312	+	0.933602i	$0.616648\pi$
$578$	−2.17516e144	−0.216910
$579$	−6.72839e144	−0.612755
$580$	−7.93527e144	−0.660073
$581$	−4.24061e143	−0.0322242
$582$	−1.96119e144	−0.136164
$583$	1.65112e145	1.04756
$584$	1.25393e145	0.727105
$585$	−7.29586e144	−0.386717
$586$	−1.48937e144	−0.0721734
$587$	−1.42844e145	−0.632939	−0.316469	−	0.948603i	$-0.602497\pi$
$587$	−1.42844e145	−0.632939	−0.316469	+	0.948603i	$0.602497\pi$
$588$	1.06620e145	0.432047
$589$	−5.11551e145	−1.89599
$590$	−1.64236e145	−0.556850
$591$	1.74790e145	0.542216
$592$	1.07945e145	0.306416
$593$	−5.51029e145	−1.43154	−0.715769	−	0.698337i	$-0.753924\pi$
$593$	−5.51029e145	−1.43154	−0.715769	+	0.698337i	$0.753924\pi$
$594$	−1.14541e145	−0.272378
$595$	3.86981e145	0.842460
$596$	2.23482e145	0.445465
$597$	8.20093e145	1.49696
$598$	1.86237e145	0.311353
$599$	−1.15611e146	−1.77048	−0.885238	−	0.465138i	$-0.846005\pi$
$599$	−1.15611e146	−1.77048	−0.885238	+	0.465138i	$0.846005\pi$
$600$	6.58162e145	0.923406
$601$	1.32026e146	1.69727	0.848633	−	0.528982i	$-0.177426\pi$
$601$	1.32026e146	1.69727	0.848633	+	0.528982i	$0.177426\pi$
$602$	1.03152e145	0.121524
$603$	−9.68305e144	−0.104557
$604$	5.85172e144	0.0579221
$605$	−1.16115e146	−1.05373
$606$	2.88389e145	0.239975
$607$	−1.59602e146	−1.21796	−0.608980	−	0.793185i	$-0.708421\pi$
$607$	−1.59602e146	−1.21796	−0.608980	+	0.793185i	$0.708421\pi$
$608$	1.28897e146	0.902201
$609$	9.48283e145	0.608878
$610$	−9.97780e145	−0.587785
$611$	−6.02266e145	−0.325555
$612$	2.67077e145	0.132491
$613$	6.35553e145	0.289386	0.144693	−	0.989477i	$-0.453781\pi$
$613$	6.35553e145	0.289386	0.144693	+	0.989477i	$0.453781\pi$
$614$	−3.17070e145	−0.132530
$615$	−4.21327e146	−1.61687
$616$	2.26180e146	0.797016
$617$	3.62889e146	1.17436	0.587182	−	0.809455i	$-0.300237\pi$
$617$	3.62889e146	1.17436	0.587182	+	0.809455i	$0.300237\pi$
$618$	−1.05184e146	−0.312647
$619$	−4.93925e146	−1.34866	−0.674329	−	0.738431i	$-0.735567\pi$
$619$	−4.93925e146	−1.34866	−0.674329	+	0.738431i	$0.735567\pi$
$620$	−9.08526e146	−2.27915
$621$	5.14851e146	1.18679
$622$	2.32295e145	0.0492089
$623$	7.95676e146	1.54922
$624$	−3.81579e146	−0.682958
$625$	−1.01691e146	−0.167333
$626$	−2.24744e146	−0.340045
$627$	1.30802e147	1.81999
$628$	1.10104e147	1.40904
$629$	−1.47727e146	−0.173901
$630$	−1.51491e146	−0.164062
$631$	1.66165e147	1.65576	0.827882	−	0.560903i	$-0.189546\pi$
$631$	1.66165e147	1.65576	0.827882	+	0.560903i	$0.189546\pi$
$632$	−7.98436e146	−0.732139
$633$	−4.03469e146	−0.340499
$634$	2.99071e146	0.232321
$635$	−3.22118e147	−2.30353
$636$	−1.31470e147	−0.865624
$637$	5.06222e146	0.306917
$638$	2.79240e146	0.155916
$639$	−3.64587e146	−0.187502
$640$	3.00467e147	1.42347
$641$	−1.30831e147	−0.571037	−0.285519	−	0.958373i	$-0.592166\pi$
$641$	−1.30831e147	−0.571037	−0.285519	+	0.958373i	$0.592166\pi$
$642$	−5.69098e146	−0.228875
$643$	8.82411e146	0.327035	0.163518	−	0.986540i	$-0.447716\pi$
$643$	8.82411e146	0.327035	0.163518	+	0.986540i	$0.447716\pi$
$644$	−4.88995e147	−1.67031
$645$	2.20272e147	0.693545
$646$	−5.10893e146	−0.148294
$647$	−1.73337e147	−0.463893	−0.231946	−	0.972729i	$-0.574509\pi$
$647$	−1.73337e147	−0.463893	−0.231946	+	0.972729i	$0.574509\pi$
$648$	2.57399e147	0.635213
$649$	−7.30826e147	−1.66329
$650$	1.50301e147	0.315509
$651$	1.08571e148	2.10238
$652$	1.61658e147	0.288801
$653$	4.30837e147	0.710184	0.355092	−	0.934831i	$-0.384450\pi$
$653$	4.30837e147	0.710184	0.355092	+	0.934831i	$0.384450\pi$
$654$	−1.27146e147	−0.193406
$655$	5.34348e147	0.750163
$656$	−5.35081e147	−0.693374
$657$	−3.73722e147	−0.447061
$658$	−1.25054e147	−0.138114
$659$	−1.06978e148	−1.09096	−0.545482	−	0.838123i	$-0.683653\pi$
$659$	−1.06978e148	−1.09096	−0.545482	+	0.838123i	$0.683653\pi$
$660$	2.32308e148	2.18780
$661$	3.16357e147	0.275170	0.137585	−	0.990490i	$-0.456066\pi$
$661$	3.16357e147	0.275170	0.137585	+	0.990490i	$0.456066\pi$
$662$	−1.14847e147	−0.0922734
$663$	5.22210e147	0.387601
$664$	2.06723e146	0.0141763
$665$	−3.66445e148	−2.32206
$666$	5.78305e146	0.0338657
$667$	−1.25516e148	−0.679348
$668$	2.02107e148	1.01115
$669$	−6.33596e147	−0.293050
$670$	3.28968e147	0.140678
$671$	−4.43997e148	−1.75569
$672$	−2.73569e148	−1.00041
$673$	4.25179e148	1.43807	0.719037	−	0.694972i	$-0.244583\pi$
$673$	4.25179e148	1.43807	0.719037	+	0.694972i	$0.244583\pi$
$674$	−8.07668e147	−0.252690
$675$	4.15507e148	1.20263
$676$	1.47985e148	0.396293
$677$	9.84342e147	0.243916	0.121958	−	0.992535i	$-0.461083\pi$
$677$	9.84342e147	0.243916	0.121958	+	0.992535i	$0.461083\pi$
$678$	9.32064e147	0.213740
$679$	2.44489e148	0.518915
$680$	−1.88647e148	−0.370623
$681$	−5.25146e148	−0.955118
$682$	3.19708e148	0.538361
$683$	−5.19588e148	−0.810163	−0.405082	−	0.914281i	$-0.632757\pi$
$683$	−5.19588e148	−0.810163	−0.405082	+	0.914281i	$0.632757\pi$
$684$	−2.52904e148	−0.365183
$685$	1.02295e149	1.36805
$686$	−1.53988e148	−0.190753
$687$	1.68788e149	1.93693
$688$	2.79743e148	0.297418
$689$	−6.24206e148	−0.614920
$690$	8.25762e148	0.753837
$691$	1.83656e148	0.155385	0.0776924	−	0.996977i	$-0.475245\pi$
$691$	1.83656e148	0.155385	0.0776924	+	0.996977i	$0.475245\pi$
$692$	−1.49875e149	−1.17533
$693$	−6.74111e148	−0.490046
$694$	−5.06794e148	−0.341554
$695$	−4.11790e149	−2.57320
$696$	−4.62272e148	−0.267863
$697$	7.32284e148	0.393513
$698$	−5.12313e148	−0.255344
$699$	2.56311e149	1.18499
$700$	−3.94640e149	−1.69260
$701$	4.14109e149	1.64785	0.823927	−	0.566696i	$-0.191779\pi$
$701$	4.14109e149	1.64785	0.823927	+	0.566696i	$0.191779\pi$
$702$	4.33021e148	0.159886
$703$	1.39888e149	0.479320
$704$	2.37802e149	0.756224
$705$	−2.67041e149	−0.788224
$706$	−5.39784e148	−0.147902
$707$	−3.59516e149	−0.914531
$708$	5.81919e149	1.37441
$709$	7.22005e149	1.58348	0.791740	−	0.610858i	$-0.209175\pi$
$709$	7.22005e149	1.58348	0.791740	+	0.610858i	$0.209175\pi$
$710$	1.23864e149	0.252278
$711$	2.37967e149	0.450156
$712$	−3.87878e149	−0.681547
$713$	−1.43706e150	−2.34571
$714$	1.08431e149	0.164437
$715$	1.10297e150	1.55416
$716$	−8.55188e149	−1.11977
$717$	1.14397e150	1.39206
$718$	−1.60779e149	−0.181843
$719$	−3.81074e149	−0.400629	−0.200314	−	0.979732i	$-0.564196\pi$
$719$	−3.81074e149	−0.400629	−0.200314	+	0.979732i	$0.564196\pi$
$720$	−4.10834e149	−0.401523
$721$	1.31126e150	1.19148
$722$	1.63367e149	0.138026
$723$	−2.41432e150	−1.89686
$724$	1.11894e150	0.817587
$725$	−1.01297e150	−0.688415
$726$	−3.25350e149	−0.205674
$727$	−2.71636e150	−1.59746	−0.798731	−	0.601689i	$-0.794495\pi$
$727$	−2.71636e150	−1.59746	−0.798731	+	0.601689i	$0.794495\pi$
$728$	−8.55074e149	−0.467850
$729$	9.95070e149	0.506592
$730$	1.26967e150	0.601507
$731$	−3.82842e149	−0.168794
$732$	3.53532e150	1.45077
$733$	−3.94863e150	−1.50830	−0.754151	−	0.656701i	$-0.771951\pi$
$733$	−3.94863e150	−1.50830	−0.754151	+	0.656701i	$0.771951\pi$
$734$	1.37235e150	0.488002
$735$	2.24456e150	0.743097
$736$	3.62099e150	1.11620
$737$	1.46386e150	0.420200
$738$	−2.86666e149	−0.0766332
$739$	1.16910e148	0.00291083	0.00145542	−	0.999999i	$-0.499537\pi$
$739$	1.16910e148	0.00291083	0.00145542	+	0.999999i	$0.499537\pi$
$740$	2.48444e150	0.576187
$741$	−4.94497e150	−1.06834
$742$	−1.29610e150	−0.260875
$743$	4.78469e150	0.897307	0.448654	−	0.893706i	$-0.351904\pi$
$743$	4.78469e150	0.897307	0.448654	+	0.893706i	$0.351904\pi$
$744$	−5.29265e150	−0.924899
$745$	4.70471e150	0.766176
$746$	−2.32072e150	−0.352237
$747$	−6.16120e148	−0.00871633
$748$	−4.03760e150	−0.532464
$749$	7.09458e150	0.872231
$750$	2.33826e150	0.268026
$751$	−6.26686e150	−0.669813	−0.334906	−	0.942251i	$-0.608705\pi$
$751$	−6.26686e150	−0.669813	−0.334906	+	0.942251i	$0.608705\pi$
$752$	−3.39139e150	−0.338019
$753$	−1.30416e151	−1.21225
$754$	−1.05567e150	−0.0915232
$755$	1.23190e150	0.0996229
$756$	−1.13697e151	−0.857737
$757$	−1.16053e151	−0.816815	−0.408408	−	0.912800i	$-0.633916\pi$
$757$	−1.16053e151	−0.816815	−0.408408	+	0.912800i	$0.633916\pi$
$758$	−3.87985e150	−0.254790
$759$	3.67452e151	2.25168
$760$	1.78636e151	1.02154
$761$	−2.34237e151	−1.25015	−0.625074	−	0.780566i	$-0.714931\pi$
$761$	−2.34237e151	−1.25015	−0.625074	+	0.780566i	$0.714931\pi$
$762$	−9.02567e150	−0.449618
$763$	1.58505e151	0.737062
$764$	1.24185e151	0.539098
$765$	5.62247e150	0.227878
$766$	−9.54985e150	−0.361399
$767$	2.76289e151	0.976353
$768$	−1.20133e151	−0.396459
$769$	−2.06829e151	−0.637499	−0.318749	−	0.947839i	$-0.603263\pi$
$769$	−2.06829e151	−0.637499	−0.318749	+	0.947839i	$0.603263\pi$
$770$	2.29020e151	0.659341
$771$	5.87103e151	1.57892
$772$	−1.96671e151	−0.494118
$773$	6.81430e151	1.59955	0.799775	−	0.600300i	$-0.204952\pi$
$773$	6.81430e151	1.59955	0.799775	+	0.600300i	$0.204952\pi$
$774$	1.49870e150	0.0328712
$775$	−1.15977e152	−2.37702
$776$	−1.19184e151	−0.228286
$777$	−2.96896e151	−0.531498
$778$	7.13800e150	0.119439
$779$	−6.93423e151	−1.08463
$780$	−8.78239e151	−1.28424
$781$	5.51174e151	0.753546
$782$	−1.43521e151	−0.183468
$783$	−2.91839e151	−0.348859
$784$	2.85056e151	0.318667
$785$	2.31790e152	2.42347
$786$	1.49723e151	0.146421
$787$	−3.75742e151	−0.343729	−0.171865	−	0.985121i	$-0.554979\pi$
$787$	−3.75742e151	−0.343729	−0.171865	+	0.985121i	$0.554979\pi$
$788$	5.10909e151	0.437237
$789$	−1.83362e152	−1.46814
$790$	−8.08461e151	−0.605671
$791$	−1.16195e152	−0.814555
$792$	3.28618e151	0.215585
$793$	1.67853e152	1.03059
$794$	4.35274e151	0.250142
$795$	−2.76769e152	−1.48882
$796$	2.39713e152	1.20713
$797$	2.91172e152	1.37274	0.686369	−	0.727253i	$-0.259203\pi$
$797$	2.91172e152	1.37274	0.686369	+	0.727253i	$0.259203\pi$
$798$	−1.02677e152	−0.453233
$799$	4.64129e151	0.191837
$800$	2.92230e152	1.13110
$801$	1.15604e152	0.419050
$802$	−1.38372e151	−0.0469779
$803$	5.64984e152	1.79668
$804$	−1.16560e152	−0.347221
$805$	−1.02943e153	−2.87284
$806$	−1.20866e152	−0.316019
$807$	−2.39323e152	−0.586306
$808$	1.75258e152	0.402329
$809$	−4.11093e152	−0.884387	−0.442194	−	0.896920i	$-0.645800\pi$
$809$	−4.11093e152	−0.884387	−0.442194	+	0.896920i	$0.645800\pi$
$810$	2.60631e152	0.525488
$811$	−4.85458e152	−0.917396	−0.458698	−	0.888592i	$-0.651684\pi$
$811$	−4.85458e152	−0.917396	−0.458698	+	0.888592i	$0.651684\pi$
$812$	2.77183e152	0.490992
$813$	−5.20163e152	−0.863745
$814$	−8.74267e151	−0.136102
$815$	3.40321e152	0.496723
$816$	2.94059e152	0.402441
$817$	3.62526e152	0.465244
$818$	−5.94176e151	−0.0715100
$819$	2.54848e152	0.287658
$820$	−1.23154e153	−1.30383
$821$	3.03410e152	0.301310	0.150655	−	0.988586i	$-0.451862\pi$
$821$	3.03410e152	0.301310	0.150655	+	0.988586i	$0.451862\pi$
$822$	2.86630e152	0.267024
$823$	4.02257e152	0.351571	0.175785	−	0.984429i	$-0.443754\pi$
$823$	4.02257e152	0.351571	0.175785	+	0.984429i	$0.443754\pi$
$824$	−6.39217e152	−0.524167
$825$	2.96550e153	2.28173
$826$	5.73684e152	0.414210
$827$	−8.19205e151	−0.0555077	−0.0277539	−	0.999615i	$-0.508835\pi$
$827$	−8.19205e151	−0.0555077	−0.0277539	+	0.999615i	$0.508835\pi$
$828$	−7.10463e152	−0.451803
$829$	−1.29914e153	−0.775433	−0.387716	−	0.921779i	$-0.626736\pi$
$829$	−1.29914e153	−0.775433	−0.387716	+	0.921779i	$0.626736\pi$
$830$	2.09318e151	0.0117275
$831$	1.33618e153	0.702768
$832$	−8.99010e152	−0.443905
$833$	−3.90114e152	−0.180854
$834$	−1.15383e153	−0.502254
$835$	4.25472e153	1.73913
$836$	3.82334e153	1.46762
$837$	−3.34132e153	−1.20457
$838$	−3.18142e152	−0.107724
$839$	−5.26860e153	−1.67568	−0.837842	−	0.545913i	$-0.816183\pi$
$839$	−5.26860e153	−1.67568	−0.837842	+	0.545913i	$0.816183\pi$
$840$	−3.79135e153	−1.13274
$841$	−2.85131e153	−0.800303
$842$	1.17963e153	0.311073
$843$	−1.94670e153	−0.482338
$844$	−1.17934e153	−0.274574
$845$	3.11536e153	0.681602
$846$	−1.81691e152	−0.0373586
$847$	4.05594e153	0.783812
$848$	−3.51494e153	−0.638463
$849$	6.77745e153	1.15721
$850$	−1.15828e153	−0.185917
$851$	3.92976e153	0.593013
$852$	−4.38872e153	−0.622672
$853$	9.25670e153	1.23490	0.617450	−	0.786610i	$-0.288166\pi$
$853$	9.25670e153	1.23490	0.617450	+	0.786610i	$0.288166\pi$
$854$	3.48529e153	0.437221
$855$	−5.32409e153	−0.628094
$856$	−3.45849e153	−0.383720
$857$	−1.01455e154	−1.05871	−0.529357	−	0.848399i	$-0.677567\pi$
$857$	−1.01455e154	−1.05871	−0.529357	+	0.848399i	$0.677567\pi$
$858$	3.09050e153	0.303351
$859$	1.04057e154	0.960794	0.480397	−	0.877051i	$-0.340493\pi$
$859$	1.04057e154	0.960794	0.480397	+	0.877051i	$0.340493\pi$
$860$	6.43854e153	0.559267
$861$	1.47171e154	1.20270
$862$	1.21066e153	0.0930872
$863$	−1.59859e154	−1.15656	−0.578282	−	0.815837i	$-0.696277\pi$
$863$	−1.59859e154	−1.15656	−0.578282	+	0.815837i	$0.696277\pi$
$864$	8.41921e153	0.573191
$865$	−3.15516e154	−2.02151
$866$	−1.32284e153	−0.0797660
$867$	1.62247e154	0.920818
$868$	3.17352e154	1.69534
$869$	−3.59753e154	−1.80912
$870$	−4.68076e153	−0.221593
$871$	−5.53412e153	−0.246658
$872$	−7.72684e153	−0.324255
$873$	3.55219e153	0.140362
$874$	1.35905e154	0.505690
$875$	−2.91496e154	−1.02143
$876$	−4.49868e154	−1.48463
$877$	1.92505e154	0.598362	0.299181	−	0.954196i	$-0.403287\pi$
$877$	1.92505e154	0.598362	0.299181	+	0.954196i	$0.403287\pi$
$878$	−3.19379e153	−0.0935070
$879$	1.11093e154	0.306387
$880$	6.21089e154	1.61367
$881$	−4.86159e154	−1.18999	−0.594995	−	0.803729i	$-0.702846\pi$
$881$	−4.86159e154	−1.18999	−0.594995	+	0.803729i	$0.702846\pi$
$882$	1.52717e153	0.0352198
$883$	−5.99705e154	−1.30317	−0.651584	−	0.758576i	$-0.725895\pi$
$883$	−5.99705e154	−1.30317	−0.651584	+	0.758576i	$0.725895\pi$
$884$	1.52642e154	0.312557
$885$	1.22505e155	2.36391
$886$	−1.05476e154	−0.191815
$887$	1.04076e154	0.178386	0.0891932	−	0.996014i	$-0.471571\pi$
$887$	1.04076e154	0.178386	0.0891932	+	0.996014i	$0.471571\pi$
$888$	1.44732e154	0.233821
$889$	1.12517e155	1.71347
$890$	−3.92749e154	−0.563818
$891$	1.15977e155	1.56961
$892$	−1.85200e154	−0.236312
$893$	−4.39499e154	−0.528757
$894$	1.31825e154	0.149547
$895$	−1.80033e155	−1.92594
$896$	−1.04955e155	−1.05884
$897$	−1.38915e155	−1.32174
$898$	4.56698e154	0.409847
$899$	8.14584e154	0.689529
$900$	−5.73375e154	−0.457833
$901$	4.81037e154	0.362349
$902$	4.33374e154	0.307978
$903$	−7.69421e154	−0.515890
$904$	5.66429e154	0.358346
$905$	2.35559e155	1.40620
$906$	3.45174e153	0.0194450
$907$	−1.16482e155	−0.619262	−0.309631	−	0.950857i	$-0.600206\pi$
$907$	−1.16482e155	−0.619262	−0.309631	+	0.950857i	$0.600206\pi$
$908$	−1.53500e155	−0.770196
$909$	−5.22342e154	−0.247372
$910$	−8.65810e154	−0.387034
$911$	−1.37817e155	−0.581551	−0.290776	−	0.956791i	$-0.593913\pi$
$911$	−1.37817e155	−0.581551	−0.290776	+	0.956791i	$0.593913\pi$
$912$	−2.78454e155	−1.10924
$913$	9.31435e153	0.0350297
$914$	−5.87538e154	−0.208622
$915$	7.44251e155	2.49524
$916$	4.93366e155	1.56191
$917$	−1.86650e155	−0.558005
$918$	−3.33702e154	−0.0942147
$919$	4.43843e154	0.118349	0.0591746	−	0.998248i	$-0.481153\pi$
$919$	4.43843e154	0.118349	0.0591746	+	0.998248i	$0.481153\pi$
$920$	5.01827e155	1.26384
$921$	2.36505e155	0.562612
$922$	3.03455e154	0.0681901
$923$	−2.08371e155	−0.442333
$924$	−8.11461e155	−1.62738
$925$	3.17149e155	0.600927
$926$	−6.05882e154	−0.108470
$927$	1.90513e155	0.322284
$928$	−2.05253e155	−0.328110
$929$	−7.19518e155	−1.08697	−0.543484	−	0.839419i	$-0.682895\pi$
$929$	−7.19518e155	−1.08697	−0.543484	+	0.839419i	$0.682895\pi$
$930$	−5.35911e155	−0.765134
$931$	3.69411e155	0.498485
$932$	7.49196e155	0.955564
$933$	−1.73270e155	−0.208899
$934$	9.50927e154	0.108377
$935$	−8.49990e155	−0.915808
$936$	−1.24234e155	−0.126549
$937$	−1.14815e156	−1.10579	−0.552894	−	0.833252i	$-0.686476\pi$
$937$	−1.14815e156	−1.10579	−0.552894	+	0.833252i	$0.686476\pi$
$938$	−1.14910e155	−0.104643
$939$	1.67638e156	1.44354
$940$	−7.80560e155	−0.635615
$941$	7.99074e155	0.615364	0.307682	−	0.951489i	$-0.400447\pi$
$941$	7.99074e155	0.615364	0.307682	+	0.951489i	$0.400447\pi$
$942$	6.49469e155	0.473027
$943$	−1.94798e156	−1.34190
$944$	1.55580e156	1.01373
$945$	−2.39353e156	−1.47526
$946$	−2.26570e155	−0.132105
$947$	2.63160e156	1.45160	0.725798	−	0.687908i	$-0.241471\pi$
$947$	2.63160e156	1.45160	0.725798	+	0.687908i	$0.241471\pi$
$948$	2.86453e156	1.49491
$949$	−2.13592e156	−1.05465
$950$	1.09681e156	0.512439
$951$	−2.23079e156	−0.986238
$952$	6.58952e155	0.275686
$953$	2.53066e156	1.00197	0.500987	−	0.865455i	$-0.332970\pi$
$953$	2.53066e156	1.00197	0.500987	+	0.865455i	$0.332970\pi$
$954$	−1.88310e155	−0.0705642
$955$	2.61432e156	0.927218
$956$	3.34381e156	1.12254
$957$	−2.08287e156	−0.661889
$958$	3.04612e155	0.0916342
$959$	−3.57323e156	−1.01762
$960$	−3.98616e156	−1.07477
$961$	5.40913e156	1.38086
$962$	3.30517e155	0.0798918
$963$	1.03077e156	0.235930
$964$	−7.05706e156	−1.52961
$965$	−4.14028e156	−0.849856
$966$	−2.88443e156	−0.560738
$967$	−6.77596e156	−1.24762	−0.623808	−	0.781578i	$-0.714415\pi$
$967$	−6.77596e156	−1.24762	−0.623808	+	0.781578i	$0.714415\pi$
$968$	−1.97720e156	−0.344822
$969$	3.81078e156	0.629529
$970$	−1.20681e156	−0.188852
$971$	6.47134e156	0.959366	0.479683	−	0.877442i	$-0.340752\pi$
$971$	6.47134e156	0.959366	0.479683	+	0.877442i	$0.340752\pi$
$972$	−4.08367e156	−0.573551
$973$	1.43840e157	1.91406
$974$	1.35521e156	0.170868
$975$	−1.12111e157	−1.33938
$976$	9.45191e156	1.07005
$977$	5.82573e156	0.625009	0.312504	−	0.949916i	$-0.398832\pi$
$977$	5.82573e156	0.625009	0.312504	+	0.949916i	$0.398832\pi$
$978$	9.53571e155	0.0969534
$979$	−1.74767e157	−1.68410
$980$	6.56083e156	0.599225
$981$	2.30292e156	0.199368
$982$	1.40860e156	0.115594
$983$	1.53172e157	1.19157	0.595784	−	0.803144i	$-0.296841\pi$
$983$	1.53172e157	1.19157	0.595784	+	0.803144i	$0.296841\pi$
$984$	−7.17436e156	−0.529103
$985$	1.07556e157	0.752024
$986$	8.13536e155	0.0539311
$987$	9.32787e156	0.586316
$988$	−1.44541e157	−0.861495
$989$	1.01841e157	0.575598
$990$	3.32744e156	0.178346
$991$	−3.06213e157	−1.55653	−0.778263	−	0.627939i	$-0.783899\pi$
$991$	−3.06213e157	−1.55653	−0.778263	+	0.627939i	$0.783899\pi$
$992$	−2.34998e157	−1.13293
$993$	8.56654e156	0.391715
$994$	−4.32661e156	−0.187656
$995$	5.04640e157	2.07620
$996$	−7.41654e155	−0.0289458
$997$	−4.11854e157	−1.52492	−0.762461	−	0.647034i	$-0.776009\pi$
$997$	−4.11854e157	−1.52492	−0.762461	+	0.647034i	$0.776009\pi$
$998$	5.35924e156	0.188256
$999$	9.13713e156	0.304524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.106.a.a.1.5	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.106.a.a.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.72418e15 q^{2} -1.28608e25 q^{3} -3.75920e31 q^{4} -7.91382e36 q^{5} -2.21743e40 q^{6} +2.76433e44 q^{7} -1.34757e47 q^{8} +4.01631e49 q^{9} +O(q^{10})\)	\(q+1.72418e15 q^{2} -1.28608e25 q^{3} -3.75920e31 q^{4} -7.91382e36 q^{5} -2.21743e40 q^{6} +2.76433e44 q^{7} -1.34757e47 q^{8} +4.01631e49 q^{9} -1.36449e52 q^{10} -6.07175e54 q^{11} +4.83463e56 q^{12} +2.29543e58 q^{13} +4.76621e59 q^{14} +1.01778e62 q^{15} +1.29257e63 q^{16} -1.76894e64 q^{17} +6.92484e64 q^{18} +1.67507e67 q^{19} +2.97496e68 q^{20} -3.55515e69 q^{21} -1.04688e70 q^{22} +4.70564e71 q^{23} +1.73308e72 q^{24} +3.79766e73 q^{25} +3.95773e73 q^{26} +1.09411e75 q^{27} -1.03917e76 q^{28} -2.66735e76 q^{29} +1.75484e77 q^{30} -3.05391e78 q^{31} +7.69500e78 q^{32} +7.80875e79 q^{33} -3.04998e79 q^{34} -2.18764e81 q^{35} -1.50981e81 q^{36} +8.35117e81 q^{37} +2.88812e82 q^{38} -2.95210e83 q^{39} +1.06644e84 q^{40} -4.13967e84 q^{41} -6.12972e84 q^{42} +2.16424e85 q^{43} +2.28250e86 q^{44} -3.17843e86 q^{45} +8.11337e86 q^{46} -2.62376e87 q^{47} -1.66234e88 q^{48} +2.20535e88 q^{49} +6.54785e88 q^{50} +2.27500e89 q^{51} -8.62898e89 q^{52} -2.71935e90 q^{53} +1.88645e90 q^{54} +4.80507e91 q^{55} -3.72512e91 q^{56} -2.15427e92 q^{57} -4.59900e91 q^{58} +1.20365e93 q^{59} -3.82604e93 q^{60} +7.31250e93 q^{61} -5.26549e93 q^{62} +1.11024e94 q^{63} -3.91652e94 q^{64} -1.81656e95 q^{65} +1.34637e95 q^{66} -2.41093e95 q^{67} +6.64982e95 q^{68} -6.05182e96 q^{69} -3.77189e96 q^{70} -9.07767e96 q^{71} -5.41224e96 q^{72} -9.30512e97 q^{73} +1.43989e97 q^{74} -4.88409e98 q^{75} -6.29692e98 q^{76} -1.67843e99 q^{77} -5.08996e98 q^{78} +5.92503e99 q^{79} -1.02292e100 q^{80} -1.91011e100 q^{81} -7.13754e99 q^{82} -1.53405e99 q^{83} +1.33645e101 q^{84} +1.39991e101 q^{85} +3.73155e100 q^{86} +3.43042e101 q^{87} +8.18209e101 q^{88} +2.87836e102 q^{89} -5.48019e101 q^{90} +6.34533e102 q^{91} -1.76894e103 q^{92} +3.92757e103 q^{93} -4.52384e102 q^{94} -1.32562e104 q^{95} -9.89637e103 q^{96} +8.84441e103 q^{97} +3.80242e103 q^{98} -2.43860e104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 91\!\cdots\!20 q^{2}+ \cdots + 31\!\cdots\!84 q^{9}+O(q^{10}) \) 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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