LMFDB - Embedded newform 1.106.a.a.1.7

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			1.7
Root			$4.91848e13$ 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)

$f(q)$	$=$	$q+5.93573e15 q^{2} +1.55541e25 q^{3} -5.33194e30 q^{4} +1.46253e36 q^{5} +9.23248e40 q^{6} +8.76445e43 q^{7} -2.72431e47 q^{8} +1.16692e50 q^{9} +O(q^{10})$	\(q+5.93573e15 q^{2} +1.55541e25 q^{3} -5.33194e30 q^{4} +1.46253e36 q^{5} +9.23248e40 q^{6} +8.76445e43 q^{7} -2.72431e47 q^{8} +1.16692e50 q^{9} +8.68120e51 q^{10} -7.28669e54 q^{11} -8.29334e55 q^{12} -4.19396e58 q^{13} +5.20234e59 q^{14} +2.27483e61 q^{15} -1.40079e63 q^{16} +8.65740e63 q^{17} +6.92655e65 q^{18} -9.21112e66 q^{19} -7.79814e66 q^{20} +1.36323e69 q^{21} -4.32518e70 q^{22} -1.62076e69 q^{23} -4.23741e72 q^{24} -2.25129e73 q^{25} -2.48942e74 q^{26} -1.32898e74 q^{27} -4.67316e74 q^{28} +9.56136e76 q^{29} +1.35028e77 q^{30} -1.52589e78 q^{31} +2.73642e78 q^{32} -1.13338e80 q^{33} +5.13880e79 q^{34} +1.28183e80 q^{35} -6.22198e80 q^{36} -2.78360e82 q^{37} -5.46747e82 q^{38} -6.52332e83 q^{39} -3.98439e83 q^{40} +5.59619e84 q^{41} +8.09176e84 q^{42} +2.87167e84 q^{43} +3.88522e85 q^{44} +1.70667e86 q^{45} -9.62038e84 q^{46} +8.04149e87 q^{47} -2.17879e88 q^{48} -4.66803e88 q^{49} -1.33630e89 q^{50} +1.34658e89 q^{51} +2.23620e89 q^{52} +5.94866e90 q^{53} -7.88847e89 q^{54} -1.06570e91 q^{55} -2.38771e91 q^{56} -1.43271e92 q^{57} +5.67537e92 q^{58} -1.24710e93 q^{59} -1.21293e92 q^{60} +3.83239e93 q^{61} -9.05730e93 q^{62} +1.02275e94 q^{63} +7.30653e94 q^{64} -6.13380e94 q^{65} -6.72742e95 q^{66} -7.25169e95 q^{67} -4.61608e94 q^{68} -2.52094e94 q^{69} +7.60859e95 q^{70} -3.02377e96 q^{71} -3.17906e97 q^{72} -1.13078e98 q^{73} -1.65227e98 q^{74} -3.50167e98 q^{75} +4.91132e97 q^{76} -6.38639e98 q^{77} -3.87206e99 q^{78} +1.66730e99 q^{79} -2.04869e99 q^{80} -1.66813e100 q^{81} +3.32175e100 q^{82} -3.34613e100 q^{83} -7.26866e99 q^{84} +1.26617e100 q^{85} +1.70454e100 q^{86} +1.48718e102 q^{87} +1.98512e102 q^{88} +3.73253e101 q^{89} +1.01303e102 q^{90} -3.67578e102 q^{91} +8.64179e99 q^{92} -2.37339e103 q^{93} +4.77321e103 q^{94} -1.34716e103 q^{95} +4.25625e103 q^{96} -2.81285e104 q^{97} -2.77082e104 q^{98} -8.50302e104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.93573e15	0.931964	0.465982	−	0.884794i	$-0.345701\pi$
$2$	5.93573e15	0.931964	0.465982	+	0.884794i	$0.345701\pi$
$3$	1.55541e25	1.38988	0.694942	−	0.719066i	$-0.255430\pi$
$3$	1.55541e25	1.38988	0.694942	+	0.719066i	$0.255430\pi$
$4$	−5.33194e30	−0.131443
$5$	1.46253e36	0.294564	0.147282	−	0.989095i	$-0.452947\pi$
$5$	1.46253e36	0.294564	0.147282	+	0.989095i	$0.452947\pi$
$6$	9.23248e40	1.29532
$7$	8.76445e43	0.375905	0.187952	−	0.982178i	$-0.439815\pi$
$7$	8.76445e43	0.375905	0.187952	+	0.982178i	$0.439815\pi$
$8$	−2.72431e47	−1.05446
$9$	1.16692e50	0.931775
$10$	8.68120e51	0.274524
$11$	−7.28669e54	−1.54673	−0.773365	−	0.633961i	$-0.781428\pi$
$11$	−7.28669e54	−1.54673	−0.773365	+	0.633961i	$0.781428\pi$
$12$	−8.29334e55	−0.182690
$13$	−4.19396e58	−1.38229	−0.691144	−	0.722717i	$-0.742893\pi$
$13$	−4.19396e58	−1.38229	−0.691144	+	0.722717i	$0.742893\pi$
$14$	5.20234e59	0.350330
$15$	2.27483e61	0.409410
$16$	−1.40079e63	−0.851280
$17$	8.65740e63	0.218182	0.109091	−	0.994032i	$-0.465206\pi$
$17$	8.65740e63	0.218182	0.109091	+	0.994032i	$0.465206\pi$
$18$	6.92655e65	0.868381
$19$	−9.21112e66	−0.675692	−0.337846	−	0.941201i	$-0.609698\pi$
$19$	−9.21112e66	−0.675692	−0.337846	+	0.941201i	$0.609698\pi$
$20$	−7.79814e66	−0.0387183
$21$	1.36323e69	0.522463
$22$	−4.32518e70	−1.44150
$23$	−1.62076e69	−0.00523609	−0.00261804	−	0.999997i	$-0.500833\pi$
$23$	−1.62076e69	−0.00523609	−0.00261804	+	0.999997i	$0.500833\pi$
$24$	−4.23741e72	−1.46558
$25$	−2.25129e73	−0.913232
$26$	−2.48942e74	−1.28824
$27$	−1.32898e74	−0.0948246
$28$	−4.67316e74	−0.0494099
$29$	9.56136e76	1.60186	0.800931	−	0.598757i	$-0.204338\pi$
$29$	9.56136e76	1.60186	0.800931	+	0.598757i	$0.204338\pi$
$30$	1.35028e77	0.381556
$31$	−1.52589e78	−0.770967	−0.385483	−	0.922715i	$-0.625965\pi$
$31$	−1.52589e78	−0.770967	−0.385483	+	0.922715i	$0.625965\pi$
$32$	2.73642e78	0.261101
$33$	−1.13338e80	−2.14977
$34$	5.13880e79	0.203338
$35$	1.28183e80	0.110728
$36$	−6.22198e80	−0.122475
$37$	−2.78360e82	−1.30022	−0.650109	−	0.759841i	$-0.725277\pi$
$37$	−2.78360e82	−1.30022	−0.650109	+	0.759841i	$0.725277\pi$
$38$	−5.46747e82	−0.629721
$39$	−6.52332e83	−1.92122
$40$	−3.98439e83	−0.310608
$41$	5.59619e84	1.19327	0.596636	−	0.802512i	$-0.296503\pi$
$41$	5.59619e84	1.19327	0.596636	+	0.802512i	$0.296503\pi$
$42$	8.09176e84	0.486917
$43$	2.87167e84	0.0502389	0.0251195	−	0.999684i	$-0.492003\pi$
$43$	2.87167e84	0.0502389	0.0251195	+	0.999684i	$0.492003\pi$
$44$	3.88522e85	0.203306
$45$	1.70667e86	0.274468
$46$	−9.62038e84	−0.00487985
$47$	8.04149e87	1.31886	0.659431	−	0.751765i	$-0.270797\pi$
$47$	8.04149e87	1.31886	0.659431	+	0.751765i	$0.270797\pi$
$48$	−2.17879e88	−1.18318
$49$	−4.66803e88	−0.858696
$50$	−1.33630e89	−0.851099
$51$	1.34658e89	0.303248
$52$	2.23620e89	0.181691
$53$	5.94866e90	1.77802	0.889008	−	0.457892i	$-0.151395\pi$
$53$	5.94866e90	1.77802	0.889008	+	0.457892i	$0.151395\pi$
$54$	−7.88847e89	−0.0883732
$55$	−1.06570e91	−0.455612
$56$	−2.38771e91	−0.396378
$57$	−1.43271e92	−0.939133
$58$	5.67537e92	1.49288
$59$	−1.24710e93	−1.33712	−0.668559	−	0.743659i	$-0.733089\pi$
$59$	−1.24710e93	−1.33712	−0.668559	+	0.743659i	$0.733089\pi$
$60$	−1.21293e92	−0.0538139
$61$	3.83239e93	0.713927	0.356963	−	0.934118i	$-0.383812\pi$
$61$	3.83239e93	0.713927	0.356963	+	0.934118i	$0.383812\pi$
$62$	−9.05730e93	−0.718513
$63$	1.02275e94	0.350259
$64$	7.30653e94	1.09462
$65$	−6.13380e94	−0.407173
$66$	−6.72742e95	−2.00351
$67$	−7.25169e95	−0.980646	−0.490323	−	0.871541i	$-0.663121\pi$
$67$	−7.25169e95	−0.980646	−0.490323	+	0.871541i	$0.663121\pi$
$68$	−4.61608e94	−0.0286784
$69$	−2.52094e94	−0.00727755
$70$	7.60859e95	0.103195
$71$	−3.02377e96	−0.194754	−0.0973768	−	0.995248i	$-0.531045\pi$
$71$	−3.02377e96	−0.194754	−0.0973768	+	0.995248i	$0.531045\pi$
$72$	−3.17906e97	−0.982523
$73$	−1.13078e98	−1.69405	−0.847026	−	0.531551i	$-0.821609\pi$
$73$	−1.13078e98	−1.69405	−0.847026	+	0.531551i	$0.821609\pi$
$74$	−1.65227e98	−1.21176
$75$	−3.50167e98	−1.26929
$76$	4.91132e97	0.0888146
$77$	−6.38639e98	−0.581423
$78$	−3.87206e99	−1.79051
$79$	1.66730e99	0.394994	0.197497	−	0.980303i	$-0.436719\pi$
$79$	1.66730e99	0.394994	0.197497	+	0.980303i	$0.436719\pi$
$80$	−2.04869e99	−0.250757
$81$	−1.66813e100	−1.06357
$82$	3.32175e100	1.11209
$83$	−3.34613e100	−0.592847	−0.296423	−	0.955057i	$-0.595794\pi$
$83$	−3.34613e100	−0.592847	−0.296423	+	0.955057i	$0.595794\pi$
$84$	−7.26866e99	−0.0686739
$85$	1.26617e100	0.0642687
$86$	1.70454e100	0.0468209
$87$	1.48718e102	2.22640
$88$	1.98512e102	1.63097
$89$	3.73253e101	0.169445	0.0847224	−	0.996405i	$-0.473000\pi$
$89$	3.73253e101	0.169445	0.0847224	+	0.996405i	$0.473000\pi$
$90$	1.01303e102	0.255794
$91$	−3.67578e102	−0.519608
$92$	8.64179e99	0.000688245 0
$93$	−2.37339e103	−1.07155
$94$	4.77321e103	1.22913
$95$	−1.34716e103	−0.199035
$96$	4.25625e103	0.362900
$97$	−2.81285e104	−1.39197	−0.695986	−	0.718055i	$-0.745033\pi$
$97$	−2.81285e104	−1.39197	−0.695986	+	0.718055i	$0.745033\pi$
$98$	−2.77082e104	−0.800274
$99$	−8.50302e104	−1.44120
$100$	1.20038e104	0.120038
$101$	2.44200e104	0.144835	0.0724175	−	0.997374i	$-0.476929\pi$
$101$	2.44200e104	0.144835	0.0724175	+	0.997374i	$0.476929\pi$
$102$	7.99293e104	0.282616
$103$	−5.07710e105	−1.07563	−0.537814	−	0.843064i	$-0.680750\pi$
$103$	−5.07710e105	−1.07563	−0.537814	+	0.843064i	$0.680750\pi$
$104$	1.14256e106	1.45757
$105$	1.99377e105	0.153899
$106$	3.53096e106	1.65705
$107$	−8.73746e105	−0.250459	−0.125230	−	0.992128i	$-0.539967\pi$
$107$	−8.73746e105	−0.250459	−0.125230	+	0.992128i	$0.539967\pi$
$108$	7.08605e104	0.0124640
$109$	1.52768e107	1.65631	0.828156	−	0.560497i	$-0.189390\pi$
$109$	1.52768e107	1.65631	0.828156	+	0.560497i	$0.189390\pi$
$110$	−6.32572e106	−0.424614
$111$	−4.32963e107	−1.80715
$112$	−1.22771e107	−0.320000
$113$	1.04871e108	1.71411	0.857054	−	0.515227i	$-0.172292\pi$
$113$	1.04871e108	1.71411	0.857054	+	0.515227i	$0.172292\pi$
$114$	−8.50415e107	−0.875238
$115$	−2.37041e105	−0.00154237
$116$	−5.09806e107	−0.210553
$117$	−4.89404e108	−1.28798
$118$	−7.40243e108	−1.24615
$119$	7.58774e107	0.0820157
$120$	−6.19735e108	−0.431708
$121$	3.09021e109	1.39237
$122$	2.27481e109	0.665354
$123$	8.70435e109	1.65851
$124$	8.13598e108	0.101338
$125$	−6.89801e109	−0.563570
$126$	6.07074e109	0.326428
$127$	−1.89039e110	−0.671208	−0.335604	−	0.942003i	$-0.608940\pi$
$127$	−1.89039e110	−0.671208	−0.335604	+	0.942003i	$0.608940\pi$
$128$	3.22693e110	0.759043
$129$	4.46661e109	0.0698262
$130$	−3.64086e110	−0.379470
$131$	−1.66200e111	−1.15848	−0.579240	−	0.815157i	$-0.696650\pi$
$131$	−1.66200e111	−1.15848	−0.579240	+	0.815157i	$0.696650\pi$
$132$	6.04310e110	0.282572
$133$	−8.07305e110	−0.253996
$134$	−4.30441e111	−0.913927
$135$	−1.94368e110	−0.0279320
$136$	−2.35854e111	−0.230065
$137$	1.41306e112	0.938276	0.469138	−	0.883125i	$-0.344565\pi$
$137$	1.41306e112	0.938276	0.469138	+	0.883125i	$0.344565\pi$
$138$	−1.49636e110	−0.00678242
$139$	−2.16214e112	−0.670821	−0.335410	−	0.942072i	$-0.608875\pi$
$139$	−2.16214e112	−0.670821	−0.335410	+	0.942072i	$0.608875\pi$
$140$	−6.83464e110	−0.0145544
$141$	1.25078e113	1.83306
$142$	−1.79483e112	−0.181503
$143$	3.05601e113	2.13803
$144$	−1.63461e113	−0.793202
$145$	1.39838e113	0.471851
$146$	−6.71199e113	−1.57880
$147$	−7.26069e113	−1.19349
$148$	1.48420e113	0.170904
$149$	−5.65399e113	−0.457169	−0.228584	−	0.973524i	$-0.573410\pi$
$149$	−5.65399e113	−0.457169	−0.228584	+	0.973524i	$0.573410\pi$
$150$	−2.07850e114	−1.18293
$151$	2.64543e114	1.06220	0.531100	−	0.847309i	$-0.321779\pi$
$151$	2.64543e114	1.06220	0.531100	+	0.847309i	$0.321779\pi$
$152$	2.50939e114	0.712493
$153$	1.01025e114	0.203297
$154$	−3.79079e114	−0.541865
$155$	−2.23167e114	−0.227099
$156$	3.47820e114	0.252530
$157$	−1.17083e115	−0.607801	−0.303901	−	0.952704i	$-0.598289\pi$
$157$	−1.17083e115	−0.607801	−0.303901	+	0.952704i	$0.598289\pi$
$158$	9.89662e114	0.368120
$159$	9.25258e115	2.47123
$160$	4.00210e114	0.0769111
$161$	−1.42051e113	−0.00196827
$162$	−9.90156e115	−0.991210
$163$	1.03779e115	0.0752071	0.0376035	−	0.999293i	$-0.488028\pi$
$163$	1.03779e115	0.0752071	0.0376035	+	0.999293i	$0.488028\pi$
$164$	−2.98386e115	−0.156847
$165$	−1.65760e116	−0.633247
$166$	−1.98617e116	−0.552512
$167$	−3.53472e116	−0.717364	−0.358682	−	0.933460i	$-0.616774\pi$
$167$	−3.53472e116	−0.717364	−0.358682	+	0.933460i	$0.616774\pi$
$168$	−3.71386e116	−0.550919
$169$	8.38371e116	0.910719
$170$	7.51566e115	0.0598961
$171$	−1.07487e117	−0.629593
$172$	−1.53116e115	−0.00660353
$173$	2.29574e117	0.730302	0.365151	−	0.930948i	$-0.381017\pi$
$173$	2.29574e117	0.730302	0.365151	+	0.930948i	$0.381017\pi$
$174$	8.82751e117	2.07493
$175$	−1.97313e117	−0.343288
$176$	1.02071e118	1.31670
$177$	−1.93975e118	−1.85844
$178$	2.21553e117	0.157916
$179$	−6.76216e117	−0.359171	−0.179586	−	0.983742i	$-0.557476\pi$
$179$	−6.76216e117	−0.359171	−0.179586	+	0.983742i	$0.557476\pi$
$180$	−9.09984e116	−0.0360767
$181$	−1.36028e118	−0.403184	−0.201592	−	0.979470i	$-0.564612\pi$
$181$	−1.36028e118	−0.403184	−0.201592	+	0.979470i	$0.564612\pi$
$182$	−2.18184e118	−0.484256
$183$	5.96093e118	0.992275
$184$	4.41545e116	0.00552127
$185$	−4.07111e118	−0.382998
$186$	−1.40878e119	−0.998650
$187$	−6.30838e118	−0.337469
$188$	−4.28768e118	−0.173355
$189$	−1.16478e118	−0.0356450
$190$	−7.99636e118	−0.185493
$191$	6.87230e119	1.21018	0.605091	−	0.796157i	$-0.293137\pi$
$191$	6.87230e119	1.21018	0.605091	+	0.796157i	$0.293137\pi$
$192$	1.13646e120	1.52139
$193$	1.79504e120	1.82943	0.914714	−	0.404103i	$-0.132416\pi$
$193$	1.79504e120	1.82943	0.914714	+	0.404103i	$0.132416\pi$
$194$	−1.66963e120	−1.29727
$195$	−9.54056e119	−0.565922
$196$	2.48897e119	0.112869
$197$	7.42365e119	0.257715	0.128858	−	0.991663i	$-0.458869\pi$
$197$	7.42365e119	0.257715	0.128858	+	0.991663i	$0.458869\pi$
$198$	−5.04716e120	−1.34315
$199$	−4.51807e120	−0.922926	−0.461463	−	0.887160i	$-0.652675\pi$
$199$	−4.51807e120	−0.922926	−0.461463	+	0.887160i	$0.652675\pi$
$200$	6.13321e120	0.962970
$201$	−1.12793e121	−1.36298
$202$	1.44950e120	0.134981
$203$	8.38001e120	0.602147
$204$	−7.17988e119	−0.0398596
$205$	8.18461e120	0.351496
$206$	−3.01363e121	−1.00245
$207$	−1.89130e119	−0.00487886
$208$	5.87484e121	1.17671
$209$	6.71186e121	1.04511
$210$	1.18345e121	0.143429
$211$	−3.56693e120	−0.0336872	−0.0168436	−	0.999858i	$-0.505362\pi$
$211$	−3.56693e120	−0.0336872	−0.0168436	+	0.999858i	$0.505362\pi$
$212$	−3.17179e121	−0.233707
$213$	−4.70320e121	−0.270685
$214$	−5.18632e121	−0.233419
$215$	4.19991e120	0.0147986
$216$	3.62055e121	0.0999892
$217$	−1.33736e122	−0.289810
$218$	9.06792e122	1.54362
$219$	−1.75882e123	−2.35454
$220$	5.68226e121	0.0598867
$221$	−3.63088e122	−0.301590
$222$	−2.56995e123	−1.68420
$223$	2.69470e123	1.39478	0.697388	−	0.716694i	$-0.254345\pi$
$223$	2.69470e123	1.39478	0.697388	+	0.716694i	$0.254345\pi$
$224$	2.39832e122	0.0981491
$225$	−2.62709e123	−0.850927
$226$	6.22487e123	1.59749
$227$	7.89252e123	1.60642	0.803208	−	0.595698i	$-0.203125\pi$
$227$	7.89252e123	1.60642	0.803208	+	0.595698i	$0.203125\pi$
$228$	7.63910e122	0.123442
$229$	7.09479e123	0.911123	0.455561	−	0.890204i	$-0.349439\pi$
$229$	7.09479e123	0.911123	0.455561	+	0.890204i	$0.349439\pi$
$230$	−1.40701e121	−0.00143743
$231$	−9.93343e123	−0.808110
$232$	−2.60481e124	−1.68911
$233$	7.64294e123	0.395434	0.197717	−	0.980259i	$-0.436647\pi$
$233$	7.64294e123	0.395434	0.197717	+	0.980259i	$0.436647\pi$
$234$	−2.90497e124	−1.20035
$235$	1.17609e124	0.388490
$236$	6.64945e123	0.175754
$237$	2.59333e124	0.548996
$238$	4.50388e123	0.0764357
$239$	−8.75129e124	−1.19174	−0.595871	−	0.803080i	$-0.703193\pi$
$239$	−8.75129e124	−1.19174	−0.595871	+	0.803080i	$0.703193\pi$
$240$	−3.18655e124	−0.348523
$241$	6.50591e124	0.572023	0.286011	−	0.958226i	$-0.407671\pi$
$241$	6.50591e124	0.572023	0.286011	+	0.958226i	$0.407671\pi$
$242$	1.83426e125	1.29764
$243$	−2.42818e125	−1.38341
$244$	−2.04341e124	−0.0938404
$245$	−6.82714e124	−0.252941
$246$	5.16667e125	1.54567
$247$	3.86311e125	0.934000
$248$	4.15701e125	0.812957
$249$	−5.20459e125	−0.823988
$250$	−4.09447e125	−0.525227
$251$	−1.04222e125	−0.108415	−0.0542077	−	0.998530i	$-0.517263\pi$
$251$	−1.04222e125	−0.108415	−0.0542077	+	0.998530i	$0.517263\pi$
$252$	−5.45322e124	−0.0460389
$253$	1.18100e124	0.00809882
$254$	−1.12209e126	−0.625542
$255$	1.96942e125	0.0893260
$256$	−1.04846e126	−0.387216
$257$	−3.16211e126	−0.951675	−0.475838	−	0.879533i	$-0.657855\pi$
$257$	−3.16211e126	−0.951675	−0.475838	+	0.879533i	$0.657855\pi$
$258$	2.65126e125	0.0650756
$259$	−2.43967e126	−0.488758
$260$	3.27051e125	0.0535198
$261$	1.11574e127	1.49257
$262$	−9.86519e126	−1.07966
$263$	2.05656e126	0.184274	0.0921371	−	0.995746i	$-0.470630\pi$
$263$	2.05656e126	0.184274	0.0921371	+	0.995746i	$0.470630\pi$
$264$	3.08767e127	2.26686
$265$	8.70010e126	0.523740
$266$	−4.79194e126	−0.236715
$267$	5.80561e126	0.235508
$268$	3.86656e126	0.128899
$269$	−3.70566e127	−1.01595	−0.507974	−	0.861373i	$-0.669605\pi$
$269$	−3.70566e127	−1.01595	−0.507974	+	0.861373i	$0.669605\pi$
$270$	−1.15371e126	−0.0260316
$271$	−8.71045e127	−1.61865	−0.809324	−	0.587362i	$-0.800167\pi$
$271$	−8.71045e127	−1.61865	−0.809324	+	0.587362i	$0.800167\pi$
$272$	−1.21272e127	−0.185734
$273$	−5.71733e127	−0.722195
$274$	8.38754e127	0.874440
$275$	1.64045e128	1.41252
$276$	1.34415e125	0.000956580 0
$277$	−6.76019e127	−0.397897	−0.198949	−	0.980010i	$-0.563753\pi$
$277$	−6.76019e127	−0.397897	−0.198949	+	0.980010i	$0.563753\pi$
$278$	−1.28339e128	−0.625181
$279$	−1.78060e128	−0.718368
$280$	−3.49210e127	−0.116759
$281$	−1.03457e128	−0.286866	−0.143433	−	0.989660i	$-0.545814\pi$
$281$	−1.03457e128	−0.286866	−0.143433	+	0.989660i	$0.545814\pi$
$282$	7.42429e128	1.70835
$283$	−1.78925e128	−0.341887	−0.170943	−	0.985281i	$-0.554682\pi$
$283$	−1.78925e128	−0.341887	−0.170943	+	0.985281i	$0.554682\pi$
$284$	1.61226e127	0.0255989
$285$	−2.09538e128	−0.276635
$286$	1.81396e129	1.99256
$287$	4.90475e128	0.448557
$288$	3.19320e128	0.243288
$289$	−1.49953e129	−0.952397
$290$	8.30041e128	0.439749
$291$	−4.37513e129	−1.93468
$292$	6.02924e128	0.222671
$293$	−1.69501e129	−0.523145	−0.261572	−	0.965184i	$-0.584241\pi$
$293$	−1.69501e129	−0.523145	−0.261572	+	0.965184i	$0.584241\pi$
$294$	−4.30975e129	−1.11229
$295$	−1.82392e129	−0.393868
$296$	7.58339e129	1.37103
$297$	9.68388e128	0.146668
$298$	−3.35606e129	−0.426065
$299$	6.79740e127	0.00723778
$300$	1.86707e129	0.166838
$301$	2.51686e128	0.0188850
$302$	1.57025e130	0.989932
$303$	3.79830e129	0.201304
$304$	1.29028e130	0.575203
$305$	5.60500e129	0.210297
$306$	5.99659e129	0.189465
$307$	4.16550e129	0.110893	0.0554463	−	0.998462i	$-0.482342\pi$
$307$	4.16550e129	0.110893	0.0554463	+	0.998462i	$0.482342\pi$
$308$	3.40518e129	0.0764237
$309$	−7.89696e130	−1.49500
$310$	−1.32466e130	−0.211648
$311$	−7.28115e130	−0.982381	−0.491190	−	0.871052i	$-0.663438\pi$
$311$	−7.28115e130	−0.982381	−0.491190	+	0.871052i	$0.663438\pi$
$312$	1.77715e131	2.02586
$313$	−1.68114e131	−1.62004	−0.810019	−	0.586403i	$-0.800543\pi$
$313$	−1.68114e131	−1.62004	−0.810019	+	0.586403i	$0.800543\pi$
$314$	−6.94972e130	−0.566449
$315$	1.49580e130	0.103174
$316$	−8.88993e129	−0.0519190
$317$	1.20789e131	0.597609	0.298804	−	0.954314i	$-0.403412\pi$
$317$	1.20789e131	0.597609	0.298804	+	0.954314i	$0.403412\pi$
$318$	5.49208e131	2.30310
$319$	−6.96707e131	−2.47765
$320$	1.06860e131	0.322435
$321$	−1.35903e131	−0.348109
$322$	−8.43174e128	−0.00183436
$323$	−7.97444e130	−0.147424
$324$	8.89437e130	0.139798
$325$	9.44182e131	1.26235
$326$	6.16002e130	0.0700903
$327$	2.37617e132	2.30208
$328$	−1.52457e132	−1.25826
$329$	7.04793e131	0.495766
$330$	−9.83907e131	−0.590164
$331$	−1.75907e132	−0.900146	−0.450073	−	0.892992i	$-0.648602\pi$
$331$	−1.75907e132	−0.900146	−0.450073	+	0.892992i	$0.648602\pi$
$332$	1.78414e131	0.0779253
$333$	−3.24825e132	−1.21151
$334$	−2.09811e132	−0.668558
$335$	−1.06058e132	−0.288863
$336$	−1.90959e132	−0.444763
$337$	−5.46915e132	−1.08981	−0.544904	−	0.838498i	$-0.683434\pi$
$337$	−5.46915e132	−1.08981	−0.544904	+	0.838498i	$0.683434\pi$
$338$	4.97634e132	0.848757
$339$	1.63117e133	2.38241
$340$	−6.75116e130	−0.00844764
$341$	1.11187e133	1.19248
$342$	−6.38013e132	−0.586758
$343$	−8.85579e132	−0.698692
$344$	−7.82331e131	−0.0529751
$345$	−3.68696e130	−0.00214371
$346$	1.36269e133	0.680615
$347$	1.69890e133	0.729238	0.364619	−	0.931157i	$-0.381199\pi$
$347$	1.69890e133	0.729238	0.364619	+	0.931157i	$0.381199\pi$
$348$	−7.92957e132	−0.292644
$349$	−1.33296e133	−0.423137	−0.211568	−	0.977363i	$-0.567857\pi$
$349$	−1.33296e133	−0.423137	−0.211568	+	0.977363i	$0.567857\pi$
$350$	−1.17120e133	−0.319932
$351$	5.57369e132	0.131075
$352$	−1.99394e133	−0.403853
$353$	4.25860e133	0.743181	0.371591	−	0.928397i	$-0.378812\pi$
$353$	4.25860e133	0.743181	0.371591	+	0.928397i	$0.378812\pi$
$354$	−1.15138e134	−1.73200
$355$	−4.42236e132	−0.0573675
$356$	−1.99016e132	−0.0222722
$357$	1.18020e133	0.113992
$358$	−4.01383e133	−0.334735
$359$	1.29130e134	0.930187	0.465093	−	0.885262i	$-0.346021\pi$
$359$	1.29130e134	0.930187	0.465093	+	0.885262i	$0.346021\pi$
$360$	−4.64948e133	−0.289416
$361$	−1.00990e134	−0.543441
$362$	−8.07426e133	−0.375753
$363$	4.80653e134	1.93524
$364$	1.95990e133	0.0682986
$365$	−1.65380e134	−0.499008
$366$	3.53825e134	0.924765
$367$	−4.52119e134	−1.02396	−0.511982	−	0.858996i	$-0.671088\pi$
$367$	−4.52119e134	−1.02396	−0.511982	+	0.858996i	$0.671088\pi$
$368$	2.27034e132	0.00445738
$369$	6.53033e134	1.11186
$370$	−2.41650e134	−0.356941
$371$	5.21367e134	0.668364
$372$	1.26548e134	0.140848
$373$	2.53939e134	0.245480	0.122740	−	0.992439i	$-0.460832\pi$
$373$	2.53939e134	0.245480	0.122740	+	0.992439i	$0.460832\pi$
$374$	−3.74448e134	−0.314509
$375$	−1.07292e135	−0.783297
$376$	−2.19075e135	−1.39069
$377$	−4.01000e135	−2.21423
$378$	−6.91381e133	−0.0332199
$379$	4.23774e135	1.77246	0.886228	−	0.463250i	$-0.153317\pi$
$379$	4.23774e135	1.77246	0.886228	+	0.463250i	$0.153317\pi$
$380$	7.18296e133	0.0261616
$381$	−2.94033e135	−0.932901
$382$	4.07921e135	1.12785
$383$	1.40505e135	0.338653	0.169327	−	0.985560i	$-0.445841\pi$
$383$	1.40505e135	0.338653	0.169327	+	0.985560i	$0.445841\pi$
$384$	5.01919e135	1.05498
$385$	−9.34030e134	−0.171266
$386$	1.06549e136	1.70496
$387$	3.35102e134	0.0468114
$388$	1.49980e135	0.182964
$389$	−1.50971e136	−1.60894	−0.804468	−	0.593996i	$-0.797549\pi$
$389$	−1.50971e136	−1.60894	−0.804468	+	0.593996i	$0.797549\pi$
$390$	−5.66302e135	−0.527420
$391$	−1.40316e133	−0.00114242
$392$	1.27171e136	0.905464
$393$	−2.58509e136	−1.61015
$394$	4.40648e135	0.240182
$395$	2.43848e135	0.116351
$396$	4.53376e135	0.189436
$397$	3.01792e136	1.10460	0.552301	−	0.833645i	$-0.313750\pi$
$397$	3.01792e136	1.10460	0.552301	+	0.833645i	$0.313750\pi$
$398$	−2.68181e136	−0.860134
$399$	−1.25569e136	−0.353024
$400$	3.15357e136	0.777416
$401$	−7.19899e136	−1.55665	−0.778326	−	0.627860i	$-0.783931\pi$
$401$	−7.19899e136	−1.55665	−0.778326	+	0.627860i	$0.783931\pi$
$402$	−6.69511e136	−1.27025
$403$	6.39954e136	1.06570
$404$	−1.30206e135	−0.0190375
$405$	−2.43969e136	−0.313290
$406$	4.97415e136	0.561180
$407$	2.02832e137	2.01109
$408$	−3.66849e136	−0.319764
$409$	−1.05041e137	−0.805163	−0.402581	−	0.915384i	$-0.631887\pi$
$409$	−1.05041e137	−0.805163	−0.402581	+	0.915384i	$0.631887\pi$
$410$	4.85816e136	0.327581
$411$	2.19788e137	1.30409
$412$	2.70708e136	0.141383
$413$	−1.09301e137	−0.502629
$414$	−1.12263e135	−0.00454692
$415$	−4.89382e136	−0.174632
$416$	−1.14764e137	−0.360917
$417$	−3.36301e137	−0.932363
$418$	3.98398e137	0.974008
$419$	−5.13603e137	−1.10762	−0.553811	−	0.832643i	$-0.686827\pi$
$419$	−5.13603e137	−1.10762	−0.553811	+	0.832643i	$0.686827\pi$
$420$	−1.06307e136	−0.0202289
$421$	−3.41684e137	−0.573871	−0.286935	−	0.957950i	$-0.592636\pi$
$421$	−3.41684e137	−0.573871	−0.286935	+	0.957950i	$0.592636\pi$
$422$	−2.11723e136	−0.0313953
$423$	9.38382e137	1.22888
$424$	−1.62060e138	−1.87485
$425$	−1.94903e137	−0.199251
$426$	−2.79169e137	−0.252269
$427$	3.35888e137	0.268368
$428$	4.65877e136	0.0329210
$429$	4.75334e138	2.97161
$430$	2.49295e136	0.0137918
$431$	2.04799e138	1.00293	0.501466	−	0.865177i	$-0.332794\pi$
$431$	2.04799e138	1.00293	0.501466	+	0.865177i	$0.332794\pi$
$432$	1.86162e137	0.0807223
$433$	−3.08552e138	−1.18499	−0.592494	−	0.805575i	$-0.701857\pi$
$433$	−3.08552e138	−1.18499	−0.592494	+	0.805575i	$0.701857\pi$
$434$	−7.93822e137	−0.270092
$435$	2.17505e138	0.655818
$436$	−8.14552e137	−0.217710
$437$	1.49290e136	0.00353798
$438$	−1.04399e139	−2.19434
$439$	2.64684e138	0.493561	0.246780	−	0.969071i	$-0.420627\pi$
$439$	2.64684e138	0.493561	0.246780	+	0.969071i	$0.420627\pi$
$440$	2.90330e138	0.480426
$441$	−5.44724e138	−0.800111
$442$	−2.15519e138	−0.281072
$443$	1.00847e138	0.116806	0.0584032	−	0.998293i	$-0.481399\pi$
$443$	1.00847e138	0.116806	0.0584032	+	0.998293i	$0.481399\pi$
$444$	2.30854e138	0.237537
$445$	5.45895e137	0.0499124
$446$	1.59950e139	1.29988
$447$	−8.79426e138	−0.635411
$448$	6.40377e138	0.411472
$449$	−4.95920e137	−0.0283452	−0.0141726	−	0.999900i	$-0.504511\pi$
$449$	−4.95920e137	−0.0283452	−0.0141726	+	0.999900i	$0.504511\pi$
$450$	−1.55937e139	−0.793033
$451$	−4.07777e139	−1.84567
$452$	−5.59167e138	−0.225307
$453$	4.11472e139	1.47633
$454$	4.68479e139	1.49712
$455$	−5.37594e138	−0.153058
$456$	3.90313e139	0.990282
$457$	−1.67962e139	−0.379848	−0.189924	−	0.981799i	$-0.560824\pi$
$457$	−1.67962e139	−0.379848	−0.189924	+	0.981799i	$0.560824\pi$
$458$	4.21128e139	0.849134
$459$	−1.15055e138	−0.0206890
$460$	1.26389e136	0.000202732 0
$461$	2.43974e139	0.349176	0.174588	−	0.984642i	$-0.444141\pi$
$461$	2.43974e139	0.349176	0.174588	+	0.984642i	$0.444141\pi$
$462$	−5.89622e139	−0.753130
$463$	−8.04930e139	−0.917817	−0.458909	−	0.888484i	$-0.651759\pi$
$463$	−8.04930e139	−0.917817	−0.458909	+	0.888484i	$0.651759\pi$
$464$	−1.33934e140	−1.36363
$465$	−3.47116e139	−0.315642
$466$	4.53664e139	0.368531
$467$	−6.71585e139	−0.487489	−0.243744	−	0.969840i	$-0.578376\pi$
$467$	−6.71585e139	−0.487489	−0.243744	+	0.969840i	$0.578376\pi$
$468$	2.60947e139	0.169295
$469$	−6.35571e139	−0.368629
$470$	6.98098e139	0.362059
$471$	−1.82112e140	−0.844773
$472$	3.39748e140	1.40994
$473$	−2.09250e139	−0.0777060
$474$	1.53933e140	0.511644
$475$	2.07369e140	0.617063
$476$	−4.04574e138	−0.0107803
$477$	6.94163e140	1.65671
$478$	−5.19453e140	−1.11066
$479$	−7.93981e140	−1.52123	−0.760616	−	0.649202i	$-0.775103\pi$
$479$	−7.93981e140	−1.52123	−0.760616	+	0.649202i	$0.775103\pi$
$480$	6.22490e139	0.106897
$481$	1.16743e141	1.79728
$482$	3.86173e140	0.533105
$483$	−2.20947e138	−0.00273566
$484$	−1.64768e140	−0.183017
$485$	−4.11389e140	−0.410026
$486$	−1.44130e141	−1.28929
$487$	−6.81986e140	−0.547652	−0.273826	−	0.961779i	$-0.588289\pi$
$487$	−6.81986e140	−0.547652	−0.273826	+	0.961779i	$0.588289\pi$
$488$	−1.04406e141	−0.752810
$489$	1.61418e140	0.104529
$490$	−4.05241e140	−0.235732
$491$	7.17413e140	0.374965	0.187483	−	0.982268i	$-0.439967\pi$
$491$	7.17413e140	0.374965	0.187483	+	0.982268i	$0.439967\pi$
$492$	−4.64111e140	−0.217999
$493$	8.27766e140	0.349498
$494$	2.29304e141	0.870455
$495$	−1.24359e141	−0.424528
$496$	2.13745e141	0.656309
$497$	−2.65017e140	−0.0732088
$498$	−3.08930e141	−0.767927
$499$	5.28030e141	1.18135	0.590677	−	0.806908i	$-0.298861\pi$
$499$	5.28030e141	1.18135	0.590677	+	0.806908i	$0.298861\pi$
$500$	3.67798e140	0.0740771
$501$	−5.49792e141	−0.997052
$502$	−6.18636e140	−0.101039
$503$	6.45019e141	0.948971	0.474486	−	0.880263i	$-0.342634\pi$
$503$	6.45019e141	0.948971	0.474486	+	0.880263i	$0.342634\pi$
$504$	−2.78627e141	−0.369335
$505$	3.57150e140	0.0426632
$506$	7.01008e139	0.00754781
$507$	1.30401e142	1.26579
$508$	1.00795e141	0.0882253
$509$	5.45984e141	0.431019	0.215509	−	0.976502i	$-0.430859\pi$
$509$	5.45984e141	0.431019	0.215509	+	0.976502i	$0.430859\pi$
$510$	1.16899e141	0.0832486
$511$	−9.91064e141	−0.636802
$512$	−1.93134e142	−1.11991
$513$	1.22414e141	0.0640722
$514$	−1.87695e142	−0.886927
$515$	−7.42543e141	−0.316841
$516$	−2.38157e140	−0.00917814
$517$	−5.85959e142	−2.03992
$518$	−1.44812e142	−0.455505
$519$	3.57081e142	1.01503
$520$	1.67104e142	0.429349
$521$	4.91559e142	1.14181	0.570906	−	0.821015i	$-0.306592\pi$
$521$	4.91559e142	1.14181	0.570906	+	0.821015i	$0.306592\pi$
$522$	6.62273e142	1.39103
$523$	2.21300e142	0.420381	0.210190	−	0.977660i	$-0.432592\pi$
$523$	2.21300e142	0.420381	0.210190	+	0.977660i	$0.432592\pi$
$524$	8.86169e141	0.152273
$525$	−3.06902e142	−0.477130
$526$	1.22072e142	0.171737
$527$	−1.32103e142	−0.168211
$528$	1.58762e143	1.83006
$529$	−9.58100e142	−0.999973
$530$	5.16414e142	0.488107
$531$	−1.45527e143	−1.24589
$532$	4.30450e141	0.0333858
$533$	−2.34702e143	−1.64945
$534$	3.44605e142	0.219485
$535$	−1.27788e142	−0.0737764
$536$	1.97558e143	1.03406
$537$	−1.05179e143	−0.499206
$538$	−2.19958e143	−0.946827
$539$	3.40145e143	1.32817
$540$	1.03636e141	0.00367145
$541$	6.21110e142	0.199670	0.0998348	−	0.995004i	$-0.468169\pi$
$541$	6.21110e142	0.199670	0.0998348	+	0.995004i	$0.468169\pi$
$542$	−5.17028e143	−1.50852
$543$	−2.11579e143	−0.560379
$544$	2.36903e142	0.0569676
$545$	2.23429e143	0.487891
$546$	−3.39365e143	−0.673060
$547$	9.88009e143	1.78003	0.890013	−	0.455936i	$-0.150695\pi$
$547$	9.88009e143	1.78003	0.890013	+	0.455936i	$0.150695\pi$
$548$	−7.53435e142	−0.123329
$549$	4.47212e143	0.665219
$550$	9.73724e143	1.31642
$551$	−8.80709e143	−1.08236
$552$	6.86782e141	0.00767392
$553$	1.46129e143	0.148480
$554$	−4.01267e143	−0.370826
$555$	−6.33223e143	−0.532323
$556$	1.15284e143	0.0881744
$557$	2.14551e144	1.49325	0.746626	−	0.665244i	$-0.231672\pi$
$557$	2.14551e144	1.49325	0.746626	+	0.665244i	$0.231672\pi$
$558$	−1.05692e144	−0.669493
$559$	−1.20437e143	−0.0694446
$560$	−1.79557e143	−0.0942607
$561$	−9.81210e143	−0.469042
$562$	−6.14094e143	−0.267349
$563$	−9.74563e143	−0.386473	−0.193237	−	0.981152i	$-0.561898\pi$
$563$	−9.74563e143	−0.386473	−0.193237	+	0.981152i	$0.561898\pi$
$564$	−6.66909e143	−0.240943
$565$	1.53378e144	0.504915
$566$	−1.06205e144	−0.318626
$567$	−1.46202e144	−0.399801
$568$	8.23768e143	0.205361
$569$	−3.93707e144	−0.894909	−0.447454	−	0.894307i	$-0.647669\pi$
$569$	−3.93707e144	−0.894909	−0.447454	+	0.894307i	$0.647669\pi$
$570$	−1.24376e144	−0.257814
$571$	−1.88688e144	−0.356738	−0.178369	−	0.983964i	$-0.557082\pi$
$571$	−1.88688e144	−0.356738	−0.178369	+	0.983964i	$0.557082\pi$
$572$	−1.62945e144	−0.281027
$573$	1.06892e145	1.68201
$574$	2.91133e144	0.418039
$575$	3.64880e142	0.00478176
$576$	8.52617e144	1.01994
$577$	1.05199e145	1.14889	0.574446	−	0.818542i	$-0.305217\pi$
$577$	1.05199e145	1.14889	0.574446	+	0.818542i	$0.305217\pi$
$578$	−8.90079e144	−0.887600
$579$	2.79202e145	2.54269
$580$	−7.45609e143	−0.0620213
$581$	−2.93270e144	−0.222854
$582$	−2.59696e145	−1.80305
$583$	−4.33460e145	−2.75011
$584$	3.08058e145	1.78632
$585$	−7.15769e144	−0.379393
$586$	−1.00611e145	−0.487552
$587$	−3.35704e145	−1.48750	−0.743748	−	0.668460i	$-0.766954\pi$
$587$	−3.35704e145	−1.48750	−0.743748	+	0.668460i	$0.766954\pi$
$588$	3.87136e144	0.156875
$589$	1.40552e145	0.520936
$590$	−1.08263e145	−0.367071
$591$	1.15468e145	0.358194
$592$	3.89923e145	1.10685
$593$	9.74195e143	0.0253090	0.0126545	−	0.999920i	$-0.495972\pi$
$593$	9.74195e143	0.0253090	0.0126545	+	0.999920i	$0.495972\pi$
$594$	5.74809e144	0.136689
$595$	1.10973e144	0.0241589
$596$	3.01468e144	0.0600914
$597$	−7.02744e145	−1.28276
$598$	4.03475e143	0.00674535
$599$	7.73768e145	1.18496	0.592478	−	0.805586i	$-0.298150\pi$
$599$	7.73768e145	1.18496	0.592478	+	0.805586i	$0.298150\pi$
$600$	9.53963e145	1.33842
$601$	−7.70795e145	−0.990899	−0.495449	−	0.868637i	$-0.664997\pi$
$601$	−7.70795e145	−0.990899	−0.495449	+	0.868637i	$0.664997\pi$
$602$	1.49394e144	0.0176002
$603$	−8.46218e145	−0.913741
$604$	−1.41053e145	−0.139618
$605$	4.51953e145	0.410144
$606$	2.25457e145	0.187608
$607$	2.37938e146	1.81576	0.907880	−	0.419231i	$-0.137700\pi$
$607$	2.37938e146	1.81576	0.907880	+	0.419231i	$0.137700\pi$
$608$	−2.52055e145	−0.176424
$609$	1.30343e146	0.836914
$610$	3.32698e145	0.195990
$611$	−3.37257e146	−1.82305
$612$	−5.38661e144	−0.0267218
$613$	−4.21329e146	−1.91843	−0.959217	−	0.282672i	$-0.908779\pi$
$613$	−4.21329e146	−1.91843	−0.959217	+	0.282672i	$0.908779\pi$
$614$	2.47253e145	0.103348
$615$	1.27304e146	0.488538
$616$	1.73985e146	0.613090
$617$	−2.51057e146	−0.812457	−0.406228	−	0.913772i	$-0.633156\pi$
$617$	−2.51057e146	−0.812457	−0.406228	+	0.913772i	$0.633156\pi$
$618$	−4.68742e146	−1.39328
$619$	4.37224e146	1.19384	0.596919	−	0.802302i	$-0.296392\pi$
$619$	4.37224e146	1.19384	0.596919	+	0.802302i	$0.296392\pi$
$620$	1.18991e145	0.0298505
$621$	2.15396e143	0.000496510 0
$622$	−4.32190e146	−0.915544
$623$	3.27136e145	0.0636950
$624$	9.13777e146	1.63550
$625$	4.54100e146	0.747224
$626$	−9.97877e146	−1.50982
$627$	1.04397e147	1.45258
$628$	6.24279e145	0.0798909
$629$	−2.40988e146	−0.283685
$630$	8.87865e145	0.0961542
$631$	1.17893e147	1.17475	0.587375	−	0.809315i	$-0.300161\pi$
$631$	1.17893e147	1.17475	0.587375	+	0.809315i	$0.300161\pi$
$632$	−4.54223e146	−0.416507
$633$	−5.54803e145	−0.0468213
$634$	7.16972e146	0.556950
$635$	−2.76476e146	−0.197714
$636$	−4.93342e146	−0.324825
$637$	1.95775e147	1.18696
$638$	−4.13547e147	−2.30908
$639$	−3.52851e146	−0.181467
$640$	4.71949e146	0.223587
$641$	−1.42300e147	−0.621096	−0.310548	−	0.950558i	$-0.600513\pi$
$641$	−1.42300e147	−0.621096	−0.310548	+	0.950558i	$0.600513\pi$
$642$	−8.06684e146	−0.324425
$643$	−3.56269e147	−1.32039	−0.660195	−	0.751095i	$-0.729526\pi$
$643$	−3.56269e147	−1.32039	−0.660195	+	0.751095i	$0.729526\pi$
$644$	7.57406e143	0.000258714 0
$645$	6.53257e145	0.0205683
$646$	−4.73341e146	−0.137394
$647$	−2.08851e147	−0.558934	−0.279467	−	0.960155i	$-0.590158\pi$
$647$	−2.08851e147	−0.558934	−0.279467	+	0.960155i	$0.590158\pi$
$648$	4.54450e147	1.12150
$649$	9.08722e147	2.06816
$650$	5.60441e147	1.17646
$651$	−2.08014e147	−0.402802
$652$	−5.53342e145	−0.00988541
$653$	−7.12364e147	−1.17425	−0.587124	−	0.809497i	$-0.699740\pi$
$653$	−7.12364e147	−1.17425	−0.587124	+	0.809497i	$0.699740\pi$
$654$	1.41043e148	2.14546
$655$	−2.43073e147	−0.341247
$656$	−7.83906e147	−1.01581
$657$	−1.31953e148	−1.57848
$658$	4.18346e147	0.462036
$659$	2.60531e147	0.265690	0.132845	−	0.991137i	$-0.457589\pi$
$659$	2.60531e147	0.265690	0.132845	+	0.991137i	$0.457589\pi$
$660$	8.83824e146	0.0832356
$661$	1.69983e148	1.47852	0.739262	−	0.673418i	$-0.235175\pi$
$661$	1.69983e148	1.47852	0.739262	+	0.673418i	$0.235175\pi$
$662$	−1.04413e148	−0.838903
$663$	−5.64750e147	−0.419175
$664$	9.11587e147	0.625136
$665$	−1.18071e147	−0.0748181
$666$	−1.92807e148	−1.12909
$667$	−1.54967e146	−0.00838749
$668$	1.88469e147	0.0942922
$669$	4.19135e148	1.93858
$670$	−6.29533e147	−0.269210
$671$	−2.79255e148	−1.10425
$672$	3.73037e147	0.136416
$673$	−5.70050e148	−1.92807	−0.964033	−	0.265783i	$-0.914369\pi$
$673$	−5.70050e148	−1.92807	−0.964033	+	0.265783i	$0.914369\pi$
$674$	−3.24634e148	−1.01566
$675$	2.99192e147	0.0865969
$676$	−4.47015e147	−0.119707
$677$	−1.15809e148	−0.286971	−0.143486	−	0.989652i	$-0.545831\pi$
$677$	−1.15809e148	−0.286971	−0.143486	+	0.989652i	$0.545831\pi$
$678$	9.68221e148	2.22032
$679$	−2.46531e148	−0.523249
$680$	−3.44944e147	−0.0677690
$681$	1.22761e149	2.23273
$682$	6.59977e148	1.11135
$683$	−4.36434e148	−0.680506	−0.340253	−	0.940334i	$-0.610513\pi$
$683$	−4.36434e148	−0.680506	−0.340253	+	0.940334i	$0.610513\pi$
$684$	5.73114e147	0.0827553
$685$	2.06665e148	0.276383
$686$	−5.25656e148	−0.651156
$687$	1.10353e149	1.26635
$688$	−4.02259e147	−0.0427674
$689$	−2.49484e149	−2.45773
$690$	−2.18848e146	−0.00199786
$691$	9.93176e148	0.840289	0.420144	−	0.907457i	$-0.361979\pi$
$691$	9.93176e148	0.840289	0.420144	+	0.907457i	$0.361979\pi$
$692$	−1.22408e148	−0.0959927
$693$	−7.45243e148	−0.541755
$694$	1.00842e149	0.679624
$695$	−3.16220e148	−0.197600
$696$	−4.05154e149	−2.34766
$697$	4.84484e148	0.260351
$698$	−7.91206e148	−0.394348
$699$	1.18879e149	0.549608
$700$	1.05206e148	0.0451226
$701$	8.46981e148	0.337037	0.168519	−	0.985698i	$-0.446102\pi$
$701$	8.46981e148	0.337037	0.168519	+	0.985698i	$0.446102\pi$
$702$	3.30839e148	0.122157
$703$	2.56401e149	0.878547
$704$	−5.32404e149	−1.69308
$705$	1.82931e149	0.539955
$706$	2.52779e149	0.692619
$707$	2.14028e148	0.0544441
$708$	1.03426e149	0.244278
$709$	5.21147e149	1.14296	0.571482	−	0.820615i	$-0.306369\pi$
$709$	5.21147e149	1.14296	0.571482	+	0.820615i	$0.306369\pi$
$710$	−2.62500e148	−0.0534645
$711$	1.94561e149	0.368046
$712$	−1.01686e149	−0.178673
$713$	2.47311e147	0.00403685
$714$	7.00536e148	0.106237
$715$	4.46951e149	0.629786
$716$	3.60554e148	0.0472104
$717$	−1.36118e150	−1.65638
$718$	7.66483e149	0.866901
$719$	−1.22999e150	−1.29311	−0.646553	−	0.762869i	$-0.723790\pi$
$719$	−1.22999e150	−1.29311	−0.646553	+	0.762869i	$0.723790\pi$
$720$	−2.39067e149	−0.233649
$721$	−4.44980e149	−0.404333
$722$	−5.99452e149	−0.506467
$723$	1.01193e150	0.795045
$724$	7.25294e148	0.0529955
$725$	−2.15254e150	−1.46287
$726$	2.85303e150	1.80357
$727$	6.70077e149	0.394065	0.197033	−	0.980397i	$-0.436870\pi$
$727$	6.70077e149	0.394065	0.197033	+	0.980397i	$0.436870\pi$
$728$	1.00139e150	0.547908
$729$	−1.68770e150	−0.859213
$730$	−9.81650e149	−0.465057
$731$	2.48612e148	0.0109612
$732$	−3.17834e149	−0.130427
$733$	3.97348e149	0.151779	0.0758897	−	0.997116i	$-0.475820\pi$
$733$	3.97348e149	0.151779	0.0758897	+	0.997116i	$0.475820\pi$
$734$	−2.68366e150	−0.954297
$735$	−1.06190e150	−0.351559
$736$	−4.43508e147	−0.00136715
$737$	5.28408e150	1.51679
$738$	3.87623e150	1.03622
$739$	−6.00249e150	−1.49451	−0.747254	−	0.664538i	$-0.768628\pi$
$739$	−6.00249e150	−1.49451	−0.747254	+	0.664538i	$0.768628\pi$
$740$	2.17069e149	0.0503423
$741$	6.00871e150	1.29815
$742$	3.09469e150	0.622892
$743$	−2.11116e148	−0.00395922	−0.00197961	−	0.999998i	$-0.500630\pi$
$743$	−2.11116e148	−0.00395922	−0.00197961	+	0.999998i	$0.500630\pi$
$744$	6.46584e150	1.12991
$745$	−8.26915e149	−0.134666
$746$	1.50731e150	0.228779
$747$	−3.90468e150	−0.552400
$748$	3.36359e149	0.0443578
$749$	−7.65791e149	−0.0941488
$750$	−6.36857e150	−0.730004
$751$	−1.19849e151	−1.28097	−0.640483	−	0.767972i	$-0.721266\pi$
$751$	−1.19849e151	−1.28097	−0.640483	+	0.767972i	$0.721266\pi$
$752$	−1.12644e151	−1.12272
$753$	−1.62108e150	−0.150685
$754$	−2.38023e151	−2.06359
$755$	3.86902e150	0.312886
$756$	6.21053e148	0.00468527
$757$	1.35251e151	0.951933	0.475966	−	0.879464i	$-0.342098\pi$
$757$	1.35251e151	0.951933	0.475966	+	0.879464i	$0.342098\pi$
$758$	2.51540e151	1.65187
$759$	1.83693e149	0.0112564
$760$	3.67007e150	0.209875
$761$	1.16327e151	0.620848	0.310424	−	0.950598i	$-0.399529\pi$
$761$	1.16327e151	0.620848	0.310424	+	0.950598i	$0.399529\pi$
$762$	−1.74530e151	−0.869430
$763$	1.33893e151	0.622615
$764$	−3.66427e150	−0.159069
$765$	1.47753e150	0.0598840
$766$	8.33997e150	0.315613
$767$	5.23028e151	1.84828
$768$	−1.63078e151	−0.538185
$769$	9.66156e149	0.0297793	0.0148896	−	0.999889i	$-0.495260\pi$
$769$	9.66156e149	0.0297793	0.0148896	+	0.999889i	$0.495260\pi$
$770$	−5.54415e150	−0.159614
$771$	−4.91838e151	−1.32272
$772$	−9.57105e150	−0.240465
$773$	4.94920e150	0.116175	0.0580873	−	0.998312i	$-0.481500\pi$
$773$	4.94920e150	0.116175	0.0580873	+	0.998312i	$0.481500\pi$
$774$	1.98907e150	0.0436265
$775$	3.43523e151	0.704071
$776$	7.66307e151	1.46779
$777$	−3.79469e151	−0.679317
$778$	−8.96121e151	−1.49947
$779$	−5.15472e151	−0.806285
$780$	5.08697e150	0.0743863
$781$	2.20333e151	0.301231
$782$	−8.32875e148	−0.00106470
$783$	−1.27069e151	−0.151896
$784$	6.53891e151	0.730991
$785$	−1.71237e151	−0.179037
$786$	−1.53444e152	−1.50060
$787$	−3.96812e151	−0.363004	−0.181502	−	0.983391i	$-0.558096\pi$
$787$	−3.96812e151	−0.363004	−0.181502	+	0.983391i	$0.558096\pi$
$788$	−3.95825e150	−0.0338748
$789$	3.19879e151	0.256120
$790$	1.44741e151	0.108435
$791$	9.19139e151	0.644341
$792$	2.31648e152	1.51970
$793$	−1.60729e152	−0.986852
$794$	1.79135e152	1.02945
$795$	1.35322e152	0.727938
$796$	2.40901e151	0.121312
$797$	−2.62714e152	−1.23857	−0.619287	−	0.785165i	$-0.712578\pi$
$797$	−2.62714e152	−1.23857	−0.619287	+	0.785165i	$0.712578\pi$
$798$	−7.45342e151	−0.329006
$799$	6.96185e151	0.287752
$800$	−6.16047e151	−0.238446
$801$	4.35558e151	0.157884
$802$	−4.27312e152	−1.45074
$803$	8.23963e152	2.62024
$804$	6.01407e151	0.179154
$805$	−2.07754e149	−0.000579782 0
$806$	3.79859e152	0.993192
$807$	−5.76382e152	−1.41205
$808$	−6.65275e151	−0.152723
$809$	1.80159e152	0.387578	0.193789	−	0.981043i	$-0.437922\pi$
$809$	1.80159e152	0.387578	0.193789	+	0.981043i	$0.437922\pi$
$810$	−1.44814e152	−0.291975
$811$	−7.80264e152	−1.47451	−0.737253	−	0.675617i	$-0.763877\pi$
$811$	−7.80264e152	−1.47451	−0.737253	+	0.675617i	$0.763877\pi$
$812$	−4.46817e151	−0.0791477
$813$	−1.35483e153	−2.24973
$814$	1.20396e153	1.87426
$815$	1.51780e151	0.0221533
$816$	−1.88627e152	−0.258149
$817$	−2.64513e151	−0.0339460
$818$	−6.23493e152	−0.750383
$819$	−4.28935e152	−0.484158
$820$	−4.36399e151	−0.0462015
$821$	3.35866e152	0.333542	0.166771	−	0.985996i	$-0.446666\pi$
$821$	3.35866e152	0.333542	0.166771	+	0.985996i	$0.446666\pi$
$822$	1.30460e153	1.21537
$823$	−8.67106e152	−0.757846	−0.378923	−	0.925428i	$-0.623705\pi$
$823$	−8.67106e152	−0.757846	−0.378923	+	0.925428i	$0.623705\pi$
$824$	1.38316e153	1.13421
$825$	2.55156e153	1.96324
$826$	−6.48783e152	−0.468432
$827$	2.50977e153	1.70057	0.850284	−	0.526324i	$-0.176430\pi$
$827$	2.50977e153	1.70057	0.850284	+	0.526324i	$0.176430\pi$
$828$	1.00843e150	0.000641289 0
$829$	8.67655e152	0.517886	0.258943	−	0.965893i	$-0.416626\pi$
$829$	8.67655e152	0.517886	0.258943	+	0.965893i	$0.416626\pi$
$830$	−2.90484e152	−0.162750
$831$	−1.05149e153	−0.553031
$832$	−3.06433e153	−1.51308
$833$	−4.04130e152	−0.187352
$834$	−1.99619e153	−0.868929
$835$	−5.16964e152	−0.211310
$836$	−3.57873e152	−0.137372
$837$	2.02788e152	0.0731066
$838$	−3.04861e153	−1.03226
$839$	1.69754e152	0.0539904	0.0269952	−	0.999636i	$-0.491406\pi$
$839$	1.69754e152	0.0539904	0.0269952	+	0.999636i	$0.491406\pi$
$840$	−5.43163e152	−0.162281
$841$	5.57918e153	1.56596
$842$	−2.02814e153	−0.534827
$843$	−1.60918e153	−0.398710
$844$	1.90187e151	0.00442794
$845$	1.22614e153	0.268265
$846$	5.56998e153	1.14527
$847$	2.70840e153	0.523400
$848$	−8.33279e153	−1.51359
$849$	−2.78301e153	−0.475183
$850$	−1.15689e153	−0.185695
$851$	4.51155e151	0.00680806
$852$	2.50772e152	0.0355795
$853$	5.71396e153	0.762278	0.381139	−	0.924518i	$-0.375532\pi$
$853$	5.71396e153	0.762278	0.381139	+	0.924518i	$0.375532\pi$
$854$	1.99374e153	0.250110
$855$	−1.57203e153	−0.185456
$856$	2.38035e153	0.264100
$857$	−1.55632e154	−1.62407	−0.812035	−	0.583609i	$-0.801640\pi$
$857$	−1.55632e154	−1.62407	−0.812035	+	0.583609i	$0.801640\pi$
$858$	2.82145e154	2.76943
$859$	−9.58283e153	−0.884815	−0.442408	−	0.896814i	$-0.645876\pi$
$859$	−9.58283e153	−0.884815	−0.442408	+	0.896814i	$0.645876\pi$
$860$	−2.23937e151	−0.00194517
$861$	7.62889e153	0.623441
$862$	1.21563e154	0.934697
$863$	5.02429e153	0.363503	0.181751	−	0.983345i	$-0.441823\pi$
$863$	5.02429e153	0.363503	0.181751	+	0.983345i	$0.441823\pi$
$864$	−3.63665e152	−0.0247588
$865$	3.35760e153	0.215121
$866$	−1.83148e154	−1.10437
$867$	−2.33238e154	−1.32372
$868$	7.13074e152	0.0380933
$869$	−1.21491e154	−0.610949
$870$	1.29105e154	0.611199
$871$	3.04133e154	1.35553
$872$	−4.16188e154	−1.74652
$873$	−3.28239e154	−1.29701
$874$	8.86146e151	0.00329727
$875$	−6.04572e153	−0.211849
$876$	9.37792e153	0.309486
$877$	2.68630e154	0.834981	0.417490	−	0.908681i	$-0.362910\pi$
$877$	2.68630e154	0.834981	0.417490	+	0.908681i	$0.362910\pi$
$878$	1.57109e154	0.459981
$879$	−2.63643e154	−0.727110
$880$	1.49282e154	0.387853
$881$	−5.37696e151	−0.00131614	−0.000658069	−	1.00000i	$-0.500209\pi$
$881$	−5.37696e151	−0.00131614	−0.000658069		1.00000i	$0.500209\pi$
$882$	−3.23333e154	−0.745675
$883$	2.65925e154	0.577861	0.288930	−	0.957350i	$-0.406700\pi$
$883$	2.65925e154	0.577861	0.288930	+	0.957350i	$0.406700\pi$
$884$	1.93596e153	0.0396418
$885$	−2.83694e154	−0.547430
$886$	5.98600e153	0.108859
$887$	4.10224e154	0.703122	0.351561	−	0.936165i	$-0.385651\pi$
$887$	4.10224e154	0.703122	0.351561	+	0.936165i	$0.385651\pi$
$888$	1.17953e155	1.90558
$889$	−1.65683e154	−0.252310
$890$	3.24028e153	0.0465166
$891$	1.21551e155	1.64506
$892$	−1.43680e154	−0.183333
$893$	−7.40712e154	−0.891144
$894$	−5.22004e154	−0.592180
$895$	−9.88988e153	−0.105799
$896$	2.82823e154	0.285328
$897$	1.05727e153	0.0100597
$898$	−2.94365e153	−0.0264167
$899$	−1.45896e155	−1.23498
$900$	1.40075e154	0.111848
$901$	5.14999e154	0.387931
$902$	−2.42045e155	−1.72010
$903$	3.91474e153	0.0262480
$904$	−2.85701e155	−1.80746
$905$	−1.98946e154	−0.118764
$906$	2.44238e155	1.37589
$907$	−4.27645e154	−0.227353	−0.113677	−	0.993518i	$-0.536263\pi$
$907$	−4.27645e154	−0.227353	−0.113677	+	0.993518i	$0.536263\pi$
$908$	−4.20825e154	−0.211151
$909$	2.84963e154	0.134954
$910$	−3.19101e154	−0.142645
$911$	4.52642e155	1.91003	0.955015	−	0.296556i	$-0.0958383\pi$
$911$	4.52642e155	1.91003	0.955015	+	0.296556i	$0.0958383\pi$
$912$	2.00691e155	0.799465
$913$	2.43822e155	0.916974
$914$	−9.96974e154	−0.354004
$915$	8.71806e154	0.292289
$916$	−3.78290e154	−0.119760
$917$	−1.45665e155	−0.435478
$918$	−6.82937e153	−0.0192814
$919$	−5.60391e155	−1.49426	−0.747132	−	0.664676i	$-0.768569\pi$
$919$	−5.60391e155	−1.49426	−0.747132	+	0.664676i	$0.768569\pi$
$920$	6.45773e152	0.00162637
$921$	6.47905e154	0.154128
$922$	1.44816e155	0.325419
$923$	1.26816e155	0.269206
$924$	5.29645e154	0.106220
$925$	6.26669e155	1.18740
$926$	−4.77785e155	−0.855373
$927$	−5.92460e155	−1.00224
$928$	2.61639e155	0.418248
$929$	8.70215e155	1.31462	0.657312	−	0.753619i	$-0.271693\pi$
$929$	8.70215e155	1.31462	0.657312	+	0.753619i	$0.271693\pi$
$930$	−2.06038e155	−0.294167
$931$	4.29978e155	0.580214
$932$	−4.07517e154	−0.0519769
$933$	−1.13252e156	−1.36539
$934$	−3.98634e155	−0.454322
$935$	−9.22621e154	−0.0994063
$936$	1.33329e156	1.35813
$937$	−8.48069e155	−0.816775	−0.408388	−	0.912809i	$-0.633909\pi$
$937$	−8.48069e155	−0.816775	−0.408388	+	0.912809i	$0.633909\pi$
$938$	−3.77258e155	−0.343549
$939$	−2.61485e156	−2.25166
$940$	−6.27087e154	−0.0510641
$941$	1.20312e156	0.926517	0.463258	−	0.886223i	$-0.346680\pi$
$941$	1.20312e156	0.926517	0.463258	+	0.886223i	$0.346680\pi$
$942$	−1.08096e156	−0.787298
$943$	−9.07007e153	−0.00624808
$944$	1.74692e156	1.13826
$945$	−1.70353e154	−0.0104998
$946$	−1.24205e155	−0.0724193
$947$	−9.05317e155	−0.499375	−0.249687	−	0.968326i	$-0.580328\pi$
$947$	−9.05317e155	−0.499375	−0.249687	+	0.968326i	$0.580328\pi$
$948$	−1.38275e155	−0.0721614
$949$	4.74244e156	2.34167
$950$	1.23089e156	0.575081
$951$	1.87876e156	0.830606
$952$	−2.06713e155	−0.0864826
$953$	−3.42515e155	−0.135613	−0.0678067	−	0.997698i	$-0.521600\pi$
$953$	−3.42515e155	−0.135613	−0.0678067	+	0.997698i	$0.521600\pi$
$954$	4.12036e156	1.54400
$955$	1.00510e156	0.356476
$956$	4.66614e155	0.156646
$957$	−1.08366e157	−3.44364
$958$	−4.71285e156	−1.41773
$959$	1.23847e156	0.352702
$960$	1.66211e156	0.448147
$961$	−1.58887e156	−0.405610
$962$	6.92956e156	1.67500
$963$	−1.01960e156	−0.233372
$964$	−3.46891e155	−0.0751881
$965$	2.62530e156	0.538884
$966$	−1.31148e154	−0.00254954
$967$	−9.59776e156	−1.76718	−0.883588	−	0.468265i	$-0.844879\pi$
$967$	−9.59776e156	−1.76718	−0.883588	+	0.468265i	$0.844879\pi$
$968$	−8.41868e156	−1.46821
$969$	−1.24035e156	−0.204902
$970$	−2.44189e156	−0.382129
$971$	8.31538e156	1.23274	0.616372	−	0.787455i	$-0.288602\pi$
$971$	8.31538e156	1.23274	0.616372	+	0.787455i	$0.288602\pi$
$972$	1.29469e156	0.181839
$973$	−1.89500e156	−0.252165
$974$	−4.04808e156	−0.510392
$975$	1.46859e157	1.75452
$976$	−5.36836e156	−0.607752
$977$	2.36789e156	0.254037	0.127018	−	0.991900i	$-0.459459\pi$
$977$	2.36789e156	0.254037	0.127018	+	0.991900i	$0.459459\pi$
$978$	9.58134e155	0.0974174
$979$	−2.71978e156	−0.262085
$980$	3.64019e155	0.0332472
$981$	1.78269e157	1.54331
$982$	4.25837e156	0.349454
$983$	1.74866e157	1.36033	0.680167	−	0.733057i	$-0.261907\pi$
$983$	1.74866e157	1.36033	0.680167	+	0.733057i	$0.261907\pi$
$984$	−2.37133e157	−1.74884
$985$	1.08573e156	0.0759138
$986$	4.91339e156	0.325719
$987$	1.09624e157	0.689057
$988$	−2.05979e156	−0.122767
$989$	−4.65428e153	−0.000263055 0
$990$	−7.38164e156	−0.395645
$991$	−1.15467e157	−0.586938	−0.293469	−	0.955969i	$-0.594810\pi$
$991$	−1.15467e157	−0.586938	−0.293469	+	0.955969i	$0.594810\pi$
$992$	−4.17549e156	−0.201300
$993$	−2.73607e157	−1.25110
$994$	−1.57307e156	−0.0682280
$995$	−6.60783e156	−0.271861
$996$	2.77506e156	0.108307
$997$	−2.03200e157	−0.752364	−0.376182	−	0.926546i	$-0.622763\pi$
$997$	−2.03200e157	−0.752364	−0.376182	+	0.926546i	$0.622763\pi$
$998$	3.13425e157	1.10098
$999$	3.69935e156	0.123293

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.106.a.a.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.106.a.a.1.7	✓	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)

\(f(q)\)	\(=\)	\(q+5.93573e15 q^{2} +1.55541e25 q^{3} -5.33194e30 q^{4} +1.46253e36 q^{5} +9.23248e40 q^{6} +8.76445e43 q^{7} -2.72431e47 q^{8} +1.16692e50 q^{9} +O(q^{10})\)	\(q+5.93573e15 q^{2} +1.55541e25 q^{3} -5.33194e30 q^{4} +1.46253e36 q^{5} +9.23248e40 q^{6} +8.76445e43 q^{7} -2.72431e47 q^{8} +1.16692e50 q^{9} +8.68120e51 q^{10} -7.28669e54 q^{11} -8.29334e55 q^{12} -4.19396e58 q^{13} +5.20234e59 q^{14} +2.27483e61 q^{15} -1.40079e63 q^{16} +8.65740e63 q^{17} +6.92655e65 q^{18} -9.21112e66 q^{19} -7.79814e66 q^{20} +1.36323e69 q^{21} -4.32518e70 q^{22} -1.62076e69 q^{23} -4.23741e72 q^{24} -2.25129e73 q^{25} -2.48942e74 q^{26} -1.32898e74 q^{27} -4.67316e74 q^{28} +9.56136e76 q^{29} +1.35028e77 q^{30} -1.52589e78 q^{31} +2.73642e78 q^{32} -1.13338e80 q^{33} +5.13880e79 q^{34} +1.28183e80 q^{35} -6.22198e80 q^{36} -2.78360e82 q^{37} -5.46747e82 q^{38} -6.52332e83 q^{39} -3.98439e83 q^{40} +5.59619e84 q^{41} +8.09176e84 q^{42} +2.87167e84 q^{43} +3.88522e85 q^{44} +1.70667e86 q^{45} -9.62038e84 q^{46} +8.04149e87 q^{47} -2.17879e88 q^{48} -4.66803e88 q^{49} -1.33630e89 q^{50} +1.34658e89 q^{51} +2.23620e89 q^{52} +5.94866e90 q^{53} -7.88847e89 q^{54} -1.06570e91 q^{55} -2.38771e91 q^{56} -1.43271e92 q^{57} +5.67537e92 q^{58} -1.24710e93 q^{59} -1.21293e92 q^{60} +3.83239e93 q^{61} -9.05730e93 q^{62} +1.02275e94 q^{63} +7.30653e94 q^{64} -6.13380e94 q^{65} -6.72742e95 q^{66} -7.25169e95 q^{67} -4.61608e94 q^{68} -2.52094e94 q^{69} +7.60859e95 q^{70} -3.02377e96 q^{71} -3.17906e97 q^{72} -1.13078e98 q^{73} -1.65227e98 q^{74} -3.50167e98 q^{75} +4.91132e97 q^{76} -6.38639e98 q^{77} -3.87206e99 q^{78} +1.66730e99 q^{79} -2.04869e99 q^{80} -1.66813e100 q^{81} +3.32175e100 q^{82} -3.34613e100 q^{83} -7.26866e99 q^{84} +1.26617e100 q^{85} +1.70454e100 q^{86} +1.48718e102 q^{87} +1.98512e102 q^{88} +3.73253e101 q^{89} +1.01303e102 q^{90} -3.67578e102 q^{91} +8.64179e99 q^{92} -2.37339e103 q^{93} +4.77321e103 q^{94} -1.34716e103 q^{95} +4.25625e103 q^{96} -2.81285e104 q^{97} -2.77082e104 q^{98} -8.50302e104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 91\!\cdots\!20 q^{2}+ \cdots + 31\!\cdots\!84 q^{9}+O(q^{10}) \) 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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