LMFDB - Embedded newform 1.82.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,82,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, 82, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 82);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 82 $
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:	$41.5501285538$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 27\!\cdots\!00 $ x^6 - 3x^5 - 457312410974129060102x^4 - 374381904318715551718938507366x^3 + 44188779498690494552956207183337235151045x^2 + 43570916530513802078515169165814719895908350666425*x - 274514886475906972833021199940770859283985201013623777350000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{58}\cdot 3^{26}\cdot 5^{7}\cdot 7^{3}\cdot 13 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.12136e10$ 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)

$f(q)$	$=$	$q-1.69157e12 q^{2} +1.74109e19 q^{3} +4.43572e23 q^{4} -9.34342e27 q^{5} -2.94518e31 q^{6} +1.25454e34 q^{7} +3.33964e36 q^{8} -1.40288e38 q^{9} +O(q^{10})$	\(q-1.69157e12 q^{2} +1.74109e19 q^{3} +4.43572e23 q^{4} -9.34342e27 q^{5} -2.94518e31 q^{6} +1.25454e34 q^{7} +3.33964e36 q^{8} -1.40288e38 q^{9} +1.58051e40 q^{10} -1.22907e42 q^{11} +7.72297e42 q^{12} -2.40644e44 q^{13} -2.12214e46 q^{14} -1.62677e47 q^{15} -6.72174e48 q^{16} +5.23327e49 q^{17} +2.37308e50 q^{18} +4.30835e51 q^{19} -4.14448e51 q^{20} +2.18426e53 q^{21} +2.07907e54 q^{22} +2.46610e55 q^{23} +5.81460e55 q^{24} -3.26291e56 q^{25} +4.07066e56 q^{26} -1.01630e58 q^{27} +5.56478e57 q^{28} -1.43069e59 q^{29} +2.75180e59 q^{30} +3.22118e60 q^{31} +3.29557e60 q^{32} -2.13992e61 q^{33} -8.85246e61 q^{34} -1.17217e62 q^{35} -6.22280e61 q^{36} +3.75151e63 q^{37} -7.28790e63 q^{38} -4.18981e63 q^{39} -3.12037e64 q^{40} -2.79637e65 q^{41} -3.69483e65 q^{42} -1.62171e66 q^{43} -5.45183e65 q^{44} +1.31077e66 q^{45} -4.17159e67 q^{46} -7.84999e67 q^{47} -1.17031e68 q^{48} -1.26367e68 q^{49} +5.51945e68 q^{50} +9.11157e68 q^{51} -1.06743e68 q^{52} -1.22433e69 q^{53} +1.71914e70 q^{54} +1.14838e70 q^{55} +4.18970e70 q^{56} +7.50121e70 q^{57} +2.42011e71 q^{58} -6.83628e71 q^{59} -7.21590e70 q^{60} -2.07281e72 q^{61} -5.44887e72 q^{62} -1.75997e72 q^{63} +1.06775e73 q^{64} +2.24843e72 q^{65} +3.61984e73 q^{66} -9.39505e73 q^{67} +2.32133e73 q^{68} +4.29370e74 q^{69} +1.98281e74 q^{70} +1.00405e75 q^{71} -4.68513e74 q^{72} -1.94604e75 q^{73} -6.34595e75 q^{74} -5.68100e75 q^{75} +1.91106e75 q^{76} -1.54192e76 q^{77} +7.08738e75 q^{78} +5.95779e76 q^{79} +6.28041e76 q^{80} -1.14739e77 q^{81} +4.73026e77 q^{82} -2.52276e77 q^{83} +9.68875e76 q^{84} -4.88966e77 q^{85} +2.74325e78 q^{86} -2.49095e78 q^{87} -4.10467e78 q^{88} -1.28946e79 q^{89} -2.21727e78 q^{90} -3.01896e78 q^{91} +1.09389e79 q^{92} +5.60835e79 q^{93} +1.32788e80 q^{94} -4.02547e79 q^{95} +5.73787e79 q^{96} -4.38321e80 q^{97} +2.13759e80 q^{98} +1.72425e80 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 460872026640 q^{2} - 15\!\cdots\!60 q^{3}+ \cdots + 11\!\cdots\!98 q^{9}+O(q^{10}) $ 6 * q - 460872026640 * q^2 - 15648291925893129960 * q^3 + 4493950976700073762513152 * q^4 - 18364304155649862126617790300 * q^5 + 79543552376002656592687080272832 * q^6 - 31430760593927655842892725138869200 * q^7 - 5498145101596630185016447889074360320 * q^8 + 1187896030123132129876714384590115355598 * q^9	$ 6 q - 460872026640 q^{2} - 15\!\cdots\!60 q^{3}+ \cdots - 63\!\cdots\!24 q^{99}+O(q^{100}) $ 6 * q - 460872026640 * q^2 - 15648291925893129960 * q^3 + 4493950976700073762513152 * q^4 - 18364304155649862126617790300 * q^5 + 79543552376002656592687080272832 * q^6 - 31430760593927655842892725138869200 * q^7 - 5498145101596630185016447889074360320 * q^8 + 1187896030123132129876714384590115355598 * q^9 - 66472312087527710620452553569669697173600 * q^10 - 2302475295973581620809306061775551681990328 * q^11 - 53870867926220164150329513348046663235681280 * q^12 + 1313253814255449492724146018729804193778100180 * q^13 + 41225372723246048337281629784765672712004401024 * q^14 - 156056001993392003275961063842210281482861266800 * q^15 + 2799490233261278434402974316306719898117729222656 * q^16 + 2377848571505238562780180385684069414829577769580 * q^17 + 506306622204276540508620731115428014111485052430640 * q^18 - 17422016964741760630179674590582970665727618619375240 * q^19 + 148672889698640611477740875719636714144962866333222400 * q^20 - 114072752249915469711576730788399479267919883382138688 * q^21 - 1258034178625689345497738618244246726621220713529586880 * q^22 + 10526595063181453314046018770874462030150898790798283920 * q^23 - 12327611736558023893782629055720670133074337356786974720 * q^24 + 411037910011361515508644334216291479522821661187695496250 * q^25 - 3180570114716540139250277986112641638356676984048903123168 * q^26 + 14621431460046183096199709161966291993457773283863231280880 * q^27 - 82116517748637002885903417761702653442063276903193852344320 * q^28 + 155464359052154485146727469597467543970919715236853926245940 * q^29 + 164012983787559943750248070451087782537372525868704541558400 * q^30 + 1259277021063335018777245090979655984137503836933555134668992 * q^31 - 13036312845125683749178794475020758767431562303480221102243840 * q^32 + 21091354949357251433966784004957297352147245536782330440814880 * q^33 + 11899550405754031112224464347628728246396477955985557631122144 * q^34 - 232034356615504837711196063040035766391492406317925929510437600 * q^35 - 2071479648832132808682929357240066191852277967275841354377712384 * q^36 + 414692688584236378963319357622814947056491742931883680122973540 * q^37 - 2455417714037465297201999851134772037590829998762172946918415680 * q^38 - 92285563929532296901251298670288831485071753513924535804838199984 * q^39 - 258059824285668605758122263287555971608050642150708772544789504000 * q^40 - 250252788823194090638944408016236187978548863949167831014660870148 * q^41 - 3774470339882908627686770098374833879180889302300694800640098910720 * q^42 - 5362516930786214192203446564720631507618558180640993338648106782200 * q^43 - 17252465656682175267213991915222412585785021276568609411813835518976 * q^44 - 62055994195911488597384173133359170181530078929941731114719230089900 * q^45 - 123763409427226200113215389587151615608344054530127843046255996688768 * q^46 - 230717394511751791462615349254196337530205542984846694602934639341280 * q^47 - 691982889190309031684460851104240936972943285356349640319551063982080 * q^48 - 148965540042877735285285650175007198234557699456949204802064464556458 * q^49 - 1416105420952806525015169807922957339416756851287952031511031347670000 * q^50 + 723978686772453055369497103847414979467127084371963703072714225585072 * q^51 + 12562371185881747636341658298037576485393840750032566447999727917043200 * q^52 + 25898990256961205776642859216859182171010424056472082121008236344959940 * q^53 + 60731909939285801872082597253734783721512219559188195805336458971800960 * q^54 + 70427859302095658379065386305135120838252257009889309990749877277396400 * q^55 + 350275852246953465289512615368698332984392220622408793911163576939151360 * q^56 + 303622382725256536236947985463289143154200643659779472092208351796091360 * q^57 - 312514134877257928766126367534026770462807935435519457753987287493386720 * q^58 - 38532453307459913471042984274454520116124717672121643571528434328282520 * q^59 - 5854438714408546634435977504160054633094179506942282108438463374797465600 * q^60 - 4585192544270629640163935422584783189092178505653567017169797728495170828 * q^61 - 11745445982868867354760701788812677993661414140303262885466836339630318080 * q^62 - 35632339418998518169074915366562958999484559616578607415025802007025188240 * q^63 - 24049189879736877632355406073912155582619770074517134096672197458230509568 * q^64 + 40108571425620140080303901416556158312567794172295521521551039993118238200 * q^65 + 46637466443959380664183766096173047575934541297502070623350605582042365184 * q^66 + 278606964486964374833906544600580027758780739521508130980859112605565987480 * q^67 + 591059149620766869951154898169335214276013402788475417448362648514550551040 * q^68 + 783789679110178241786835392836945981604400905715238386162022702382323722816 * q^69 + 2635837114104224632390936486964777102611174135296488988531978806621369068800 * q^70 - 554281436103188717611008447226924711986842423491780222553301787426789861968 * q^71 - 3169897304032072056282604590226317130165389286798806197352424269626436341760 * q^72 - 1159677538409433721867557656635958525415325708297922475676033828300683142980 * q^73 - 14870996314347354169518203977127998385153668929299472477677600807989626002016 * q^74 - 40272209656064989140640078595938035284494253817756477276130430269166782335000 * q^75 - 56365824164857229782022127848008365902008884166434980738114640515976798612480 * q^76 - 22951272837324694774527636903423616359482790364245898655274441101674154673600 * q^77 + 29994870322699852265351947769035786178441787146653937638111333726813935158400 * q^78 + 76488528596848273963909721387433081359345259080220208993600380062891411190240 * q^79 + 326185463863660018876021371340485226979224823762794013840530768719064527667200 * q^80 + 713659220427214109967671419496287178348529210497808359051350032218775138774486 * q^81 + 836977463852743303549437738986542975894462808796250502348000478828556860551520 * q^82 + 440718478462773776637617020819789880594300172591745821478345102532528865997560 * q^83 + 2327207348086698397722806131221331490656683214148360655124465557042000906952704 * q^84 + 1165607138975709364402518400492567424057357396402879557680723771041190675179400 * q^85 - 10339197506820945136003281093027314178240703830345630490304599234644673765234368 * q^86 - 13777097629225807302706950021773234863450868385225572161845501405567814463584560 * q^87 - 9603847126452588175246186358824265187739652448840879006569656469218022549667840 * q^88 - 18886228493337874501351816155449414708824427288664596668607356717228138798590180 * q^89 - 27536035459180423419106541648329015873635894588277179325118018321007646877848800 * q^90 - 14576226325987997036142564032100430704897317032265698214767987870608618538920288 * q^91 + 66364414655655668275929797141498084164407535259475789695165805684452941775738880 * q^92 + 130065128543178746783515152749840115744191801626425494555088565985583783043572480 * q^93 + 331286952814608158700187065887753978184064043063622410298763861434514546852072704 * q^94 + 267699559747800180626411366716842325842865933645649558098598518850783266973922000 * q^95 + 495554087106091786297185708372687557293322071836937974888325742175573190348111872 * q^96 + 113832498161281214584608062040287314379413598012089688107897449655058469975263820 * q^97 - 858118355318723523117883130491863373979750018711838274840266757637744872892872080 * q^98 - 630632406390824053363198011181718527371969259570962092705191903378628178893256024 * 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 $

$2$	−1.69157e12	−1.08787	−0.543934	−	0.839128i	$-0.683066\pi$
$2$	−1.69157e12	−1.08787	−0.543934	+	0.839128i	$0.683066\pi$
$3$	1.74109e19	0.826817	0.413409	−	0.910546i	$-0.364338\pi$
$3$	1.74109e19	0.826817	0.413409	+	0.910546i	$0.364338\pi$
$4$	4.43572e23	0.183457
$5$	−9.34342e27	−0.459432	−0.229716	−	0.973258i	$-0.573780\pi$
$5$	−9.34342e27	−0.459432	−0.229716	+	0.973258i	$0.573780\pi$
$6$	−2.94518e31	−0.899468
$7$	1.25454e34	0.744754	0.372377	−	0.928082i	$-0.378543\pi$
$7$	1.25454e34	0.744754	0.372377	+	0.928082i	$0.378543\pi$
$8$	3.33964e36	0.888291
$9$	−1.40288e38	−0.316373
$10$	1.58051e40	0.499801
$11$	−1.22907e42	−0.818794	−0.409397	−	0.912356i	$-0.634261\pi$
$11$	−1.22907e42	−0.818794	−0.409397	+	0.912356i	$0.634261\pi$
$12$	7.72297e42	0.151685
$13$	−2.40644e44	−0.184786	−0.0923929	−	0.995723i	$-0.529452\pi$
$13$	−2.40644e44	−0.184786	−0.0923929	+	0.995723i	$0.529452\pi$
$14$	−2.12214e46	−0.810194
$15$	−1.62677e47	−0.379866
$16$	−6.72174e48	−1.14980
$17$	5.23327e49	0.768408	0.384204	−	0.923248i	$-0.374476\pi$
$17$	5.23327e49	0.768408	0.384204	+	0.923248i	$0.374476\pi$
$18$	2.37308e50	0.344173
$19$	4.30835e51	0.699504	0.349752	−	0.936842i	$-0.386266\pi$
$19$	4.30835e51	0.699504	0.349752	+	0.936842i	$0.386266\pi$
$20$	−4.14448e51	−0.0842860
$21$	2.18426e53	0.615775
$22$	2.07907e54	0.890740
$23$	2.46610e55	1.74596	0.872979	−	0.487758i	$-0.162185\pi$
$23$	2.46610e55	1.74596	0.872979	+	0.487758i	$0.162185\pi$
$24$	5.81460e55	0.734454
$25$	−3.26291e56	−0.788923
$26$	4.07066e56	0.201022
$27$	−1.01630e58	−1.08840
$28$	5.56478e57	0.136630
$29$	−1.43069e59	−0.848059	−0.424029	−	0.905648i	$-0.639385\pi$
$29$	−1.43069e59	−0.848059	−0.424029	+	0.905648i	$0.639385\pi$
$30$	2.75180e59	0.413244
$31$	3.22118e60	1.28194	0.640968	−	0.767568i	$-0.278533\pi$
$31$	3.22118e60	1.28194	0.640968	+	0.767568i	$0.278533\pi$
$32$	3.29557e60	0.362540
$33$	−2.13992e61	−0.676993
$34$	−8.85246e61	−0.835926
$35$	−1.17217e62	−0.342164
$36$	−6.22280e61	−0.0580409
$37$	3.75151e63	1.15355	0.576774	−	0.816903i	$-0.304311\pi$
$37$	3.75151e63	1.15355	0.576774	+	0.816903i	$0.304311\pi$
$38$	−7.28790e63	−0.760968
$39$	−4.18981e63	−0.152784
$40$	−3.12037e64	−0.408109
$41$	−2.79637e65	−1.34539	−0.672695	−	0.739920i	$-0.734863\pi$
$41$	−2.79637e65	−1.34539	−0.672695	+	0.739920i	$0.734863\pi$
$42$	−3.69483e65	−0.669882
$43$	−1.62171e66	−1.13371	−0.566854	−	0.823818i	$-0.691840\pi$
$43$	−1.62171e66	−1.13371	−0.566854	+	0.823818i	$0.691840\pi$
$44$	−5.45183e65	−0.150214
$45$	1.31077e66	0.145352
$46$	−4.17159e67	−1.89937
$47$	−7.84999e67	−1.49591	−0.747955	−	0.663749i	$-0.768964\pi$
$47$	−7.84999e67	−1.49591	−0.747955	+	0.663749i	$0.768964\pi$
$48$	−1.17031e68	−0.950675
$49$	−1.26367e68	−0.445341
$50$	5.51945e68	0.858244
$51$	9.11157e68	0.635333
$52$	−1.06743e68	−0.0339002
$53$	−1.22433e69	−0.179774	−0.0898870	−	0.995952i	$-0.528651\pi$
$53$	−1.22433e69	−0.179774	−0.0898870	+	0.995952i	$0.528651\pi$
$54$	1.71914e70	1.18404
$55$	1.14838e70	0.376180
$56$	4.18970e70	0.661558
$57$	7.50121e70	0.578362
$58$	2.42011e71	0.922576
$59$	−6.83628e71	−1.30411	−0.652054	−	0.758173i	$-0.726092\pi$
$59$	−6.83628e71	−1.30411	−0.652054	+	0.758173i	$0.726092\pi$
$60$	−7.21590e70	−0.0696891
$61$	−2.07281e72	−1.02495	−0.512474	−	0.858703i	$-0.671271\pi$
$61$	−2.07281e72	−1.02495	−0.512474	+	0.858703i	$0.671271\pi$
$62$	−5.44887e72	−1.39458
$63$	−1.75997e72	−0.235620
$64$	1.06775e73	0.755404
$65$	2.24843e72	0.0848964
$66$	3.61984e73	0.736479
$67$	−9.39505e73	−1.03961	−0.519804	−	0.854286i	$-0.673995\pi$
$67$	−9.39505e73	−1.03961	−0.519804	+	0.854286i	$0.673995\pi$
$68$	2.32133e73	0.140970
$69$	4.29370e74	1.44359
$70$	1.98281e74	0.372229
$71$	1.00405e75	1.06119	0.530594	−	0.847626i	$-0.321969\pi$
$71$	1.00405e75	1.06119	0.530594	+	0.847626i	$0.321969\pi$
$72$	−4.68513e74	−0.281032
$73$	−1.94604e75	−0.667692	−0.333846	−	0.942628i	$-0.608346\pi$
$73$	−1.94604e75	−0.667692	−0.333846	+	0.942628i	$0.608346\pi$
$74$	−6.34595e75	−1.25491
$75$	−5.68100e75	−0.652295
$76$	1.91106e75	0.128329
$77$	−1.54192e76	−0.609800
$78$	7.08738e75	0.166209
$79$	5.95779e76	0.834042	0.417021	−	0.908897i	$-0.363074\pi$
$79$	5.95779e76	0.834042	0.417021	+	0.908897i	$0.363074\pi$
$80$	6.28041e76	0.528255
$81$	−1.14739e77	−0.583534
$82$	4.73026e77	1.46361
$83$	−2.52276e77	−0.477764	−0.238882	−	0.971049i	$-0.576781\pi$
$83$	−2.52276e77	−0.477764	−0.238882	+	0.971049i	$0.576781\pi$
$84$	9.68875e76	0.112968
$85$	−4.88966e77	−0.353031
$86$	2.74325e78	1.23332
$87$	−2.49095e78	−0.701189
$88$	−4.10467e78	−0.727327
$89$	−1.28946e79	−1.44582	−0.722908	−	0.690945i	$-0.757195\pi$
$89$	−1.28946e79	−1.44582	−0.722908	+	0.690945i	$0.757195\pi$
$90$	−2.21727e78	−0.158124
$91$	−3.01896e78	−0.137620
$92$	1.09389e79	0.320308
$93$	5.60835e79	1.05993
$94$	1.32788e80	1.62735
$95$	−4.02547e79	−0.321374
$96$	5.73787e79	0.299755
$97$	−4.38321e80	−1.50500	−0.752501	−	0.658591i	$-0.771153\pi$
$97$	−4.38321e80	−1.50500	−0.752501	+	0.658591i	$0.771153\pi$
$98$	2.13759e80	0.484473
$99$	1.72425e80	0.259045
$100$	−1.44733e80	−0.144733
$101$	−8.29691e80	−0.554499	−0.277250	−	0.960798i	$-0.589423\pi$
$101$	−8.29691e80	−0.554499	−0.277250	+	0.960798i	$0.589423\pi$
$102$	−1.54129e81	−0.691158
$103$	5.00186e80	0.151086	0.0755429	−	0.997143i	$-0.475931\pi$
$103$	5.00186e80	0.151086	0.0755429	+	0.997143i	$0.475931\pi$
$104$	−8.03663e80	−0.164143
$105$	−2.04084e81	−0.282907
$106$	2.07105e81	0.195570
$107$	1.63787e82	1.05739	0.528696	−	0.848811i	$-0.322681\pi$
$107$	1.63787e82	1.05739	0.528696	+	0.848811i	$0.322681\pi$
$108$	−4.50801e81	−0.199675
$109$	4.41655e82	1.34682	0.673411	−	0.739269i	$-0.264829\pi$
$109$	4.41655e82	1.34682	0.673411	+	0.739269i	$0.264829\pi$
$110$	−1.94256e82	−0.409234
$111$	6.53170e82	0.953774
$112$	−8.43267e82	−0.856319
$113$	−1.28535e83	−0.910636	−0.455318	−	0.890329i	$-0.650474\pi$
$113$	−1.28535e83	−0.910636	−0.455318	+	0.890329i	$0.650474\pi$
$114$	−1.26889e83	−0.629182
$115$	−2.30418e83	−0.802148
$116$	−6.34613e82	−0.155582
$117$	3.37595e82	0.0584613
$118$	1.15641e84	1.41870
$119$	6.56533e83	0.572275
$120$	−5.43283e83	−0.337431
$121$	−7.42616e83	−0.329577
$122$	3.50632e84	1.11501
$123$	−4.86872e84	−1.11239
$124$	1.42883e84	0.235180
$125$	6.91302e84	0.821887
$126$	2.97712e84	0.256324
$127$	−3.28155e84	−0.205129	−0.102565	−	0.994726i	$-0.532705\pi$
$127$	−3.28155e84	−0.205129	−0.102565	+	0.994726i	$0.532705\pi$
$128$	−2.60299e85	−1.18432
$129$	−2.82354e85	−0.937369
$130$	−3.80339e84	−0.0923561
$131$	−7.50537e81	−0.000133624 0	−6.68120e−5	−	1.00000i	$-0.500021\pi$
$131$	−7.50537e81	−0.000133624 0	−6.68120e−5		1.00000i	$0.500021\pi$
$132$	−9.49211e84	−0.124199
$133$	5.40499e85	0.520959
$134$	1.58924e86	1.13096
$135$	9.49570e85	0.500045
$136$	1.74772e86	0.682570
$137$	−1.55472e85	−0.0451305	−0.0225652	−	0.999745i	$-0.507183\pi$
$137$	−1.55472e85	−0.0451305	−0.0225652	+	0.999745i	$0.507183\pi$
$138$	−7.26311e86	−1.57043
$139$	7.32420e86	1.18212	0.591059	−	0.806629i	$-0.298710\pi$
$139$	7.32420e86	1.18212	0.591059	+	0.806629i	$0.298710\pi$
$140$	−5.19940e85	−0.0627723
$141$	−1.36675e87	−1.23684
$142$	−1.69843e87	−1.15443
$143$	2.95769e86	0.151301
$144$	9.42982e86	0.363766
$145$	1.33675e87	0.389625
$146$	3.29187e87	0.726360
$147$	−2.20016e87	−0.368216
$148$	1.66406e87	0.211627
$149$	−5.08889e87	−0.492696	−0.246348	−	0.969181i	$-0.579231\pi$
$149$	−5.08889e87	−0.492696	−0.246348	+	0.969181i	$0.579231\pi$
$150$	9.60984e87	0.709611
$151$	8.98336e85	0.00506842	0.00253421	−	0.999997i	$-0.499193\pi$
$151$	8.98336e85	0.00506842	0.00253421	+	0.999997i	$0.499193\pi$
$152$	1.43883e88	0.621363
$153$	−7.34167e87	−0.243104
$154$	2.60827e88	0.663382
$155$	−3.00968e88	−0.588962
$156$	−1.85848e87	−0.0280293
$157$	−1.23342e89	−1.43607	−0.718035	−	0.696007i	$-0.754958\pi$
$157$	−1.23342e89	−1.43607	−0.718035	+	0.696007i	$0.754958\pi$
$158$	−1.00780e89	−0.907328
$159$	−2.13167e88	−0.148640
$160$	−3.07919e88	−0.166562
$161$	3.09382e89	1.30031
$162$	1.94089e89	0.634809
$163$	4.18107e89	1.06583	0.532917	−	0.846168i	$-0.321096\pi$
$163$	4.18107e89	1.06583	0.532917	+	0.846168i	$0.321096\pi$
$164$	−1.24039e89	−0.246821
$165$	1.99942e89	0.311032
$166$	4.26743e89	0.519744
$167$	−1.67565e90	−1.60017	−0.800087	−	0.599884i	$-0.795213\pi$
$167$	−1.67565e90	−1.60017	−0.800087	+	0.599884i	$0.795213\pi$
$168$	7.29463e89	0.546988
$169$	−1.63803e90	−0.965854
$170$	8.27123e89	0.384051
$171$	−6.04412e89	−0.221305
$172$	−7.19346e89	−0.207987
$173$	−3.00523e90	−0.687085	−0.343542	−	0.939137i	$-0.611627\pi$
$173$	−3.00523e90	−0.687085	−0.343542	+	0.939137i	$0.611627\pi$
$174$	4.21363e90	0.762802
$175$	−4.09344e90	−0.587553
$176$	8.26152e90	0.941449
$177$	−1.19026e91	−1.07826
$178$	2.18122e91	1.57286
$179$	−5.46416e90	−0.314033	−0.157017	−	0.987596i	$-0.550188\pi$
$179$	−5.46416e90	−0.314033	−0.157017	+	0.987596i	$0.550188\pi$
$180$	5.81422e89	0.0266658
$181$	1.58639e91	0.581338	0.290669	−	0.956824i	$-0.406122\pi$
$181$	1.58639e91	0.581338	0.290669	+	0.956824i	$0.406122\pi$
$182$	5.10680e90	0.149712
$183$	−3.60894e91	−0.847444
$184$	8.23589e91	1.55092
$185$	−3.50519e91	−0.529977
$186$	−9.48695e91	−1.15306
$187$	−6.43208e91	−0.629167
$188$	−3.48203e91	−0.274435
$189$	−1.27498e92	−0.810590
$190$	6.80939e91	0.349613
$191$	−6.99207e91	−0.290238	−0.145119	−	0.989414i	$-0.546357\pi$
$191$	−6.99207e91	−0.290238	−0.145119	+	0.989414i	$0.546357\pi$
$192$	1.85904e92	0.624581
$193$	4.60274e92	1.25298	0.626492	−	0.779428i	$-0.284490\pi$
$193$	4.60274e92	1.25298	0.626492	+	0.779428i	$0.284490\pi$
$194$	7.41453e92	1.63724
$195$	3.91472e91	0.0701938
$196$	−5.60529e91	−0.0817010
$197$	−1.57642e93	−1.86978	−0.934888	−	0.354944i	$-0.884500\pi$
$197$	−1.57642e93	−1.86978	−0.934888	+	0.354944i	$0.884500\pi$
$198$	−2.91669e92	−0.281806
$199$	1.49362e93	1.17676	0.588382	−	0.808583i	$-0.299765\pi$
$199$	1.49362e93	1.17676	0.588382	+	0.808583i	$0.299765\pi$
$200$	−1.08969e93	−0.700793
$201$	−1.63576e93	−0.859565
$202$	1.40348e93	0.603222
$203$	−1.79485e93	−0.631595
$204$	4.04164e92	0.116556
$205$	2.61276e93	0.618114
$206$	−8.46101e92	−0.164361
$207$	−3.45965e93	−0.552374
$208$	1.61754e93	0.212467
$209$	−5.29529e93	−0.572750
$210$	3.45224e93	0.307765
$211$	2.31712e94	1.70415	0.852076	−	0.523417i	$-0.175343\pi$
$211$	2.31712e94	1.70415	0.852076	+	0.523417i	$0.175343\pi$
$212$	−5.43080e92	−0.0329808
$213$	1.74814e94	0.877408
$214$	−2.77058e94	−1.15030
$215$	1.51523e94	0.520861
$216$	−3.39407e94	−0.966816
$217$	4.04109e94	0.954727
$218$	−7.47092e94	−1.46516
$219$	−3.38822e94	−0.552059
$220$	5.09388e93	0.0690128
$221$	−1.25935e94	−0.141991
$222$	−1.10489e95	−1.03758
$223$	1.25417e95	0.981769	0.490884	−	0.871225i	$-0.336674\pi$
$223$	1.25417e95	0.981769	0.490884	+	0.871225i	$0.336674\pi$
$224$	4.13441e94	0.270003
$225$	4.57748e94	0.249594
$226$	2.17427e95	0.990652
$227$	2.47658e95	0.943638	0.471819	−	0.881695i	$-0.343598\pi$
$227$	2.47658e95	0.943638	0.471819	+	0.881695i	$0.343598\pi$
$228$	3.32733e94	0.106105
$229$	−3.05408e95	−0.815724	−0.407862	−	0.913044i	$-0.633726\pi$
$229$	−3.05408e95	−0.815724	−0.407862	+	0.913044i	$0.633726\pi$
$230$	3.89770e95	0.872631
$231$	−2.68462e95	−0.504193
$232$	−4.77798e95	−0.753323
$233$	−1.07793e96	−1.42782	−0.713911	−	0.700237i	$-0.753078\pi$
$233$	−1.07793e96	−1.42782	−0.713911	+	0.700237i	$0.753078\pi$
$234$	−5.71067e94	−0.0635982
$235$	7.33457e95	0.687268
$236$	−3.03238e95	−0.239248
$237$	1.03730e96	0.689601
$238$	−1.11057e96	−0.622559
$239$	1.41758e96	0.670553	0.335276	−	0.942120i	$-0.391170\pi$
$239$	1.41758e96	0.670553	0.335276	+	0.942120i	$0.391170\pi$
$240$	1.09347e96	0.436770
$241$	−4.78381e96	−1.61467	−0.807334	−	0.590094i	$-0.799091\pi$
$241$	−4.78381e96	−1.61467	−0.807334	+	0.590094i	$0.799091\pi$
$242$	1.25619e96	0.358536
$243$	2.50884e96	0.605924
$244$	−9.19441e95	−0.188034
$245$	1.18070e96	0.204604
$246$	8.23580e96	1.21013
$247$	−1.03678e96	−0.129258
$248$	1.07576e97	1.13873
$249$	−4.39234e96	−0.395023
$250$	−1.16939e97	−0.894105
$251$	−1.18391e97	−0.770074	−0.385037	−	0.922901i	$-0.625811\pi$
$251$	−1.18391e97	−0.770074	−0.385037	+	0.922901i	$0.625811\pi$
$252$	−7.80673e95	−0.0432262
$253$	−3.03102e97	−1.42958
$254$	5.55098e96	0.223154
$255$	−8.51333e96	−0.291892
$256$	1.82150e97	0.532980
$257$	−2.24434e97	−0.560785	−0.280393	−	0.959885i	$-0.590465\pi$
$257$	−2.24434e97	−0.560785	−0.280393	+	0.959885i	$0.590465\pi$
$258$	4.77623e97	1.01973
$259$	4.70641e97	0.859110
$260$	9.97342e95	0.0155748
$261$	2.00709e97	0.268303
$262$	1.26959e94	0.000145365 0
$263$	1.23149e98	1.20844	0.604219	−	0.796818i	$-0.293485\pi$
$263$	1.23149e98	1.20844	0.604219	+	0.796818i	$0.293485\pi$
$264$	−7.14658e97	−0.601367
$265$	1.14395e97	0.0825938
$266$	−9.14294e97	−0.566734
$267$	−2.24506e98	−1.19542
$268$	−4.16738e97	−0.190723
$269$	1.48666e98	0.585119	0.292560	−	0.956247i	$-0.405493\pi$
$269$	1.48666e98	0.585119	0.292560	+	0.956247i	$0.405493\pi$
$270$	−1.60627e98	−0.543983
$271$	1.71520e98	0.500102	0.250051	−	0.968233i	$-0.419553\pi$
$271$	1.71520e98	0.500102	0.250051	+	0.968233i	$0.419553\pi$
$272$	−3.51767e98	−0.883516
$273$	−5.25627e97	−0.113787
$274$	2.62993e97	0.0490960
$275$	4.01036e98	0.645965
$276$	1.90456e98	0.264836
$277$	1.38140e99	1.65916	0.829579	−	0.558389i	$-0.188581\pi$
$277$	1.38140e99	1.65916	0.829579	+	0.558389i	$0.188581\pi$
$278$	−1.23894e99	−1.28599
$279$	−4.51894e98	−0.405571
$280$	−3.91462e98	−0.303941
$281$	−3.89154e98	−0.261526	−0.130763	−	0.991414i	$-0.541743\pi$
$281$	−3.89154e98	−0.261526	−0.130763	+	0.991414i	$0.541743\pi$
$282$	2.31196e99	1.34552
$283$	1.53533e99	0.774196	0.387098	−	0.922038i	$-0.373477\pi$
$283$	1.53533e99	0.774196	0.387098	+	0.922038i	$0.373477\pi$
$284$	4.45368e98	0.194682
$285$	−7.00870e98	−0.265718
$286$	−5.00315e98	−0.164596
$287$	−3.50815e99	−1.00198
$288$	−4.62330e98	−0.114698
$289$	−1.89963e99	−0.409550
$290$	−2.26121e99	−0.423860
$291$	−7.63155e99	−1.24436
$292$	−8.63209e98	−0.122493
$293$	5.11212e99	0.631630	0.315815	−	0.948821i	$-0.397722\pi$
$293$	5.11212e99	0.631630	0.315815	+	0.948821i	$0.397722\pi$
$294$	3.72174e99	0.400570
$295$	6.38743e99	0.599148
$296$	1.25287e100	1.02469
$297$	1.24911e100	0.891175
$298$	8.60824e99	0.535988
$299$	−5.93451e99	−0.322628
$300$	−2.51993e99	−0.119668
$301$	−2.03450e100	−0.844334
$302$	−1.51960e98	−0.00551377
$303$	−1.44456e100	−0.458469
$304$	−2.89596e100	−0.804290
$305$	1.93672e100	0.470893
$306$	1.24190e100	0.264465
$307$	−4.84455e100	−0.903960	−0.451980	−	0.892028i	$-0.649282\pi$
$307$	−4.84455e100	−0.903960	−0.451980	+	0.892028i	$0.649282\pi$
$308$	−6.83952e99	−0.111872
$309$	8.70866e99	0.124920
$310$	5.09111e100	0.640713
$311$	−2.74849e100	−0.303598	−0.151799	−	0.988411i	$-0.548507\pi$
$311$	−2.74849e100	−0.303598	−0.151799	+	0.988411i	$0.548507\pi$
$312$	−1.39925e100	−0.135717
$313$	−7.72165e100	−0.657907	−0.328954	−	0.944346i	$-0.606696\pi$
$313$	−7.72165e100	−0.657907	−0.328954	+	0.944346i	$0.606696\pi$
$314$	2.08643e101	1.56226
$315$	1.64441e100	0.108251
$316$	2.64271e100	0.153011
$317$	−9.40410e100	−0.479090	−0.239545	−	0.970885i	$-0.576998\pi$
$317$	−9.40410e100	−0.479090	−0.239545	+	0.970885i	$0.576998\pi$
$318$	3.60588e100	0.161701
$319$	1.75842e101	0.694385
$320$	−9.97641e100	−0.347057
$321$	2.85167e101	0.874270
$322$	−5.23342e101	−1.41456
$323$	2.25468e101	0.537504
$324$	−5.08949e100	−0.107054
$325$	7.85198e100	0.145782
$326$	−7.07259e101	−1.15949
$327$	7.68959e101	1.11357
$328$	−9.33886e101	−1.19510
$329$	−9.84810e101	−1.11409
$330$	−3.38217e101	−0.338362
$331$	1.15510e102	1.02232	0.511160	−	0.859486i	$-0.329216\pi$
$331$	1.15510e102	1.02232	0.511160	+	0.859486i	$0.329216\pi$
$332$	−1.11903e101	−0.0876491
$333$	−5.26293e101	−0.364952
$334$	2.83449e102	1.74078
$335$	8.77819e101	0.477628
$336$	−1.46820e102	−0.708019
$337$	3.41253e102	1.45903	0.729517	−	0.683962i	$-0.239745\pi$
$337$	3.41253e102	1.45903	0.729517	+	0.683962i	$0.239745\pi$
$338$	2.77086e102	1.05072
$339$	−2.23791e102	−0.752930
$340$	−2.16892e101	−0.0647660
$341$	−3.95907e102	−1.04964
$342$	1.02241e102	0.240750
$343$	−5.14512e102	−1.07642
$344$	−5.41594e102	−1.00706
$345$	−4.01178e102	−0.663230
$346$	5.08357e102	0.747457
$347$	−1.88420e102	−0.246481	−0.123241	−	0.992377i	$-0.539329\pi$
$347$	−1.88420e102	−0.246481	−0.123241	+	0.992377i	$0.539329\pi$
$348$	−1.10492e102	−0.128638
$349$	1.25276e103	1.29849	0.649243	−	0.760581i	$-0.275086\pi$
$349$	1.25276e103	1.29849	0.649243	+	0.760581i	$0.275086\pi$
$350$	6.92436e102	0.639181
$351$	2.44566e102	0.201121
$352$	−4.05050e102	−0.296846
$353$	−1.82582e103	−1.19284	−0.596422	−	0.802671i	$-0.703411\pi$
$353$	−1.82582e103	−1.19284	−0.596422	+	0.802671i	$0.703411\pi$
$354$	2.01341e103	1.17300
$355$	−9.38126e102	−0.487543
$356$	−5.71969e102	−0.265245
$357$	1.14308e103	0.473167
$358$	9.24304e102	0.341627
$359$	2.87142e103	0.947919	0.473959	−	0.880547i	$-0.342824\pi$
$359$	2.87142e103	0.947919	0.473959	+	0.880547i	$0.342824\pi$
$360$	4.37751e102	0.129115
$361$	−1.93732e103	−0.510694
$362$	−2.68350e103	−0.632419
$363$	−1.29296e103	−0.272500
$364$	−1.33913e102	−0.0252473
$365$	1.81827e103	0.306759
$366$	6.10480e103	0.921907
$367$	−1.10758e104	−1.49762	−0.748808	−	0.662787i	$-0.769374\pi$
$367$	−1.10758e104	−1.49762	−0.748808	+	0.662787i	$0.769374\pi$
$368$	−1.65765e104	−2.00750
$369$	3.92298e103	0.425646
$370$	5.92929e103	0.576545
$371$	−1.53597e103	−0.133887
$372$	2.48771e103	0.194451
$373$	1.30887e104	0.917678	0.458839	−	0.888519i	$-0.348265\pi$
$373$	1.30887e104	0.917678	0.458839	+	0.888519i	$0.348265\pi$
$374$	1.08803e104	0.684451
$375$	1.20362e104	0.679551
$376$	−2.62161e104	−1.32880
$377$	3.44286e103	0.156709
$378$	2.15673e104	0.881816
$379$	2.85715e104	1.04965	0.524826	−	0.851209i	$-0.324130\pi$
$379$	2.85715e104	1.04965	0.524826	+	0.851209i	$0.324130\pi$
$380$	−1.78559e103	−0.0589584
$381$	−5.71346e103	−0.169605
$382$	1.18276e104	0.315741
$383$	−6.28789e104	−1.50992	−0.754961	−	0.655769i	$-0.772344\pi$
$383$	−6.28789e104	−1.50992	−0.754961	+	0.655769i	$0.772344\pi$
$384$	−4.53204e104	−0.979217
$385$	1.44068e104	0.280161
$386$	−7.78588e104	−1.36308
$387$	2.27507e104	0.358675
$388$	−1.94427e104	−0.276103
$389$	2.00764e103	0.0256878	0.0128439	−	0.999918i	$-0.495912\pi$
$389$	2.00764e103	0.0256878	0.0128439	+	0.999918i	$0.495912\pi$
$390$	−6.62204e103	−0.0763616
$391$	1.29058e105	1.34161
$392$	−4.22021e104	−0.395593
$393$	−1.30675e101	−0.000110483 0
$394$	2.66663e105	2.03407
$395$	−5.56662e104	−0.383185
$396$	7.64828e103	0.0475236
$397$	1.06166e104	0.0595621	0.0297811	−	0.999556i	$-0.490519\pi$
$397$	1.06166e104	0.0595621	0.0297811	+	0.999556i	$0.490519\pi$
$398$	−2.52656e105	−1.28016
$399$	9.41055e104	0.430737
$400$	2.19324e105	0.907104
$401$	−4.58486e105	−1.71388	−0.856938	−	0.515420i	$-0.827636\pi$
$401$	−4.58486e105	−1.71388	−0.856938	+	0.515420i	$0.827636\pi$
$402$	2.76701e105	0.935094
$403$	−7.75156e104	−0.236884
$404$	−3.68028e104	−0.101727
$405$	1.07205e105	0.268094
$406$	3.03612e105	0.687092
$407$	−4.61088e105	−0.944519
$408$	3.04294e105	0.564360
$409$	−5.26287e105	−0.883951	−0.441976	−	0.897027i	$-0.645722\pi$
$409$	−5.26287e105	−0.883951	−0.441976	+	0.897027i	$0.645722\pi$
$410$	−4.41969e105	−0.672427
$411$	−2.70691e104	−0.0373147
$412$	2.21868e104	0.0277177
$413$	−8.57637e105	−0.971240
$414$	5.85226e105	0.600911
$415$	2.35712e105	0.219500
$416$	−7.93057e104	−0.0669923
$417$	1.27521e106	0.977395
$418$	8.95737e105	0.623076
$419$	1.53701e106	0.970530	0.485265	−	0.874367i	$-0.338723\pi$
$419$	1.53701e106	0.970530	0.485265	+	0.874367i	$0.338723\pi$
$420$	−9.05261e104	−0.0519012
$421$	2.96710e106	1.54492	0.772462	−	0.635061i	$-0.219025\pi$
$421$	2.96710e106	1.54492	0.772462	+	0.635061i	$0.219025\pi$
$422$	−3.91958e106	−1.85389
$423$	1.10126e106	0.473266
$424$	−4.08883e105	−0.159692
$425$	−1.70757e106	−0.606214
$426$	−2.95710e106	−0.954504
$427$	−2.60042e106	−0.763334
$428$	7.26513e105	0.193986
$429$	5.14959e105	0.125099
$430$	−2.56313e106	−0.566628
$431$	−2.14220e106	−0.431052	−0.215526	−	0.976498i	$-0.569147\pi$
$431$	−2.14220e106	−0.431052	−0.215526	+	0.976498i	$0.569147\pi$
$432$	6.83129e106	1.25144
$433$	−1.02877e106	−0.171616	−0.0858082	−	0.996312i	$-0.527347\pi$
$433$	−1.02877e106	−0.171616	−0.0858082	+	0.996312i	$0.527347\pi$
$434$	−6.83580e106	−1.03862
$435$	2.32740e106	0.322149
$436$	1.95906e106	0.247084
$437$	1.06248e107	1.22130
$438$	5.73143e106	0.600567
$439$	1.19074e106	0.113764	0.0568818	−	0.998381i	$-0.481884\pi$
$439$	1.19074e106	0.113764	0.0568818	+	0.998381i	$0.481884\pi$
$440$	3.83516e106	0.334157
$441$	1.77278e106	0.140894
$442$	2.13029e106	0.154467
$443$	−1.86890e107	−1.23662	−0.618309	−	0.785935i	$-0.712182\pi$
$443$	−1.86890e107	−1.23662	−0.618309	+	0.785935i	$0.712182\pi$
$444$	2.89728e106	0.174977
$445$	1.20480e107	0.664253
$446$	−2.12152e107	−1.06803
$447$	−8.86020e106	−0.407370
$448$	1.33953e107	0.562591
$449$	−2.31011e107	−0.886455	−0.443227	−	0.896409i	$-0.646167\pi$
$449$	−2.31011e107	−0.886455	−0.443227	+	0.896409i	$0.646167\pi$
$450$	−7.74315e106	−0.271526
$451$	3.43694e107	1.10160
$452$	−5.70146e106	−0.167063
$453$	1.56408e105	0.00419065
$454$	−4.18932e107	−1.02655
$455$	2.82074e106	0.0632269
$456$	2.50514e107	0.513754
$457$	−3.89090e106	−0.0730203	−0.0365101	−	0.999333i	$-0.511624\pi$
$457$	−3.89090e106	−0.0730203	−0.0365101	+	0.999333i	$0.511624\pi$
$458$	5.16620e107	0.887400
$459$	−5.31856e107	−0.836335
$460$	−1.02207e107	−0.147160
$461$	−7.47217e107	−0.985279	−0.492639	−	0.870234i	$-0.663968\pi$
$461$	−7.47217e107	−0.985279	−0.492639	+	0.870234i	$0.663968\pi$
$462$	4.54123e107	0.548496
$463$	8.92911e107	0.988047	0.494024	−	0.869448i	$-0.335526\pi$
$463$	8.92911e107	0.988047	0.494024	+	0.869448i	$0.335526\pi$
$464$	9.61671e107	0.975098
$465$	−5.24012e107	−0.486964
$466$	1.82339e108	1.55328
$467$	7.80671e107	0.609726	0.304863	−	0.952396i	$-0.401389\pi$
$467$	7.80671e107	0.609726	0.304863	+	0.952396i	$0.401389\pi$
$468$	1.49748e106	0.0107251
$469$	−1.17864e108	−0.774252
$470$	−1.24070e108	−0.747657
$471$	−2.14749e108	−1.18737
$472$	−2.28307e108	−1.15843
$473$	1.99320e108	0.928273
$474$	−1.75468e108	−0.750195
$475$	−1.40578e108	−0.551855
$476$	2.91220e107	0.104988
$477$	1.71760e107	0.0568757
$478$	−2.39794e108	−0.729473
$479$	4.50563e108	1.25941	0.629706	−	0.776834i	$-0.283175\pi$
$479$	4.50563e108	1.25941	0.629706	+	0.776834i	$0.283175\pi$
$480$	−5.36114e107	−0.137717
$481$	−9.02776e107	−0.213159
$482$	8.09216e108	1.75655
$483$	5.38660e108	1.07512
$484$	−3.29404e107	−0.0604632
$485$	4.09542e108	0.691446
$486$	−4.24388e108	−0.659165
$487$	−6.34024e108	−0.906114	−0.453057	−	0.891482i	$-0.649667\pi$
$487$	−6.34024e108	−0.906114	−0.453057	+	0.891482i	$0.649667\pi$
$488$	−6.92245e108	−0.910452
$489$	7.27960e108	0.881249
$490$	−1.99724e108	−0.222582
$491$	4.82876e108	0.495490	0.247745	−	0.968825i	$-0.420310\pi$
$491$	4.82876e108	0.495490	0.247745	+	0.968825i	$0.420310\pi$
$492$	−2.15963e108	−0.204076
$493$	−7.48717e108	−0.651655
$494$	1.75379e108	0.140616
$495$	−1.61104e108	−0.119013
$496$	−2.16519e109	−1.47397
$497$	1.25962e109	0.790324
$498$	7.42997e108	0.429733
$499$	−6.72667e107	−0.0358697	−0.0179349	−	0.999839i	$-0.505709\pi$
$499$	−6.72667e107	−0.0358697	−0.0179349	+	0.999839i	$0.505709\pi$
$500$	3.06642e108	0.150781
$501$	−2.91746e109	−1.32305
$502$	2.00267e109	0.837739
$503$	−3.90960e108	−0.150879	−0.0754395	−	0.997150i	$-0.524036\pi$
$503$	−3.90960e108	−0.150879	−0.0754395	+	0.997150i	$0.524036\pi$
$504$	−5.87767e108	−0.209299
$505$	7.75215e108	0.254754
$506$	5.12720e109	1.55519
$507$	−2.85196e109	−0.798585
$508$	−1.45560e108	−0.0376324
$509$	2.41958e109	0.577657	0.288828	−	0.957381i	$-0.406734\pi$
$509$	2.41958e109	0.577657	0.288828	+	0.957381i	$0.406734\pi$
$510$	1.44009e109	0.317540
$511$	−2.44138e109	−0.497266
$512$	3.21245e109	0.604508
$513$	−4.37857e109	−0.761340
$514$	3.79646e109	0.610061
$515$	−4.67344e108	−0.0694136
$516$	−1.25244e109	−0.171967
$517$	9.64822e109	1.22484
$518$	−7.96123e109	−0.934599
$519$	−5.23236e109	−0.568093
$520$	7.50896e108	0.0754127
$521$	−1.38894e110	−1.29049	−0.645246	−	0.763975i	$-0.723245\pi$
$521$	−1.38894e110	−1.29049	−0.645246	+	0.763975i	$0.723245\pi$
$522$	−3.39514e109	−0.291878
$523$	−1.99372e109	−0.158616	−0.0793079	−	0.996850i	$-0.525271\pi$
$523$	−1.99372e109	−0.158616	−0.0793079	+	0.996850i	$0.525271\pi$
$524$	−3.32917e105	−2.45143e−5 0
$525$	−7.12703e109	−0.485799
$526$	−2.08316e110	−1.31462
$527$	1.68573e110	0.985050
$528$	1.43840e110	0.778407
$529$	4.08660e110	2.04837
$530$	−1.93507e109	−0.0898512
$531$	9.59051e109	0.412585
$532$	2.39750e109	0.0955735
$533$	6.72928e109	0.248609
$534$	3.79769e110	1.30046
$535$	−1.53033e110	−0.485800
$536$	−3.13761e110	−0.923474
$537$	−9.51358e109	−0.259648
$538$	−2.51480e110	−0.636533
$539$	1.55315e110	0.364643
$540$	4.21203e109	0.0917369
$541$	−9.17656e110	−1.85435	−0.927173	−	0.374634i	$-0.877768\pi$
$541$	−9.17656e110	−1.85435	−0.927173	+	0.374634i	$0.877768\pi$
$542$	−2.90139e110	−0.544045
$543$	2.76205e110	0.480660
$544$	1.72466e110	0.278579
$545$	−4.12657e110	−0.618772
$546$	8.89138e109	0.123785
$547$	1.07546e111	1.39029	0.695146	−	0.718868i	$-0.255340\pi$
$547$	1.07546e111	1.39029	0.695146	+	0.718868i	$0.255340\pi$
$548$	−6.89632e108	−0.00827951
$549$	2.90791e110	0.324266
$550$	−6.78382e110	−0.702725
$551$	−6.16390e110	−0.593221
$552$	1.43394e111	1.28233
$553$	7.47427e110	0.621157
$554$	−2.33673e111	−1.80494
$555$	−6.10284e110	−0.438194
$556$	3.24881e110	0.216868
$557$	2.28270e111	1.41682	0.708409	−	0.705803i	$-0.249413\pi$
$557$	2.28270e111	1.41682	0.708409	+	0.705803i	$0.249413\pi$
$558$	7.64412e110	0.441207
$559$	3.90254e110	0.209493
$560$	7.87900e110	0.393420
$561$	−1.11988e111	−0.520206
$562$	6.58283e110	0.284506
$563$	−7.12053e110	−0.286367	−0.143183	−	0.989696i	$-0.545734\pi$
$563$	−7.12053e110	−0.286367	−0.143183	+	0.989696i	$0.545734\pi$
$564$	−6.06252e110	−0.226908
$565$	1.20096e111	0.418375
$566$	−2.59713e111	−0.842224
$567$	−1.43944e111	−0.434590
$568$	3.35317e111	0.942644
$569$	−4.85305e111	−1.27048	−0.635240	−	0.772315i	$-0.719099\pi$
$569$	−4.85305e111	−1.27048	−0.635240	+	0.772315i	$0.719099\pi$
$570$	1.18557e111	0.289066
$571$	−5.06575e111	−1.15049	−0.575243	−	0.817982i	$-0.695093\pi$
$571$	−5.06575e111	−1.15049	−0.575243	+	0.817982i	$0.695093\pi$
$572$	1.31195e110	0.0277573
$573$	−1.21738e111	−0.239974
$574$	5.93429e111	1.09003
$575$	−8.04666e111	−1.37743
$576$	−1.49793e111	−0.238990
$577$	7.76525e111	1.15487	0.577437	−	0.816435i	$-0.304053\pi$
$577$	7.76525e111	1.15487	0.577437	+	0.816435i	$0.304053\pi$
$578$	3.21337e111	0.445536
$579$	8.01377e111	1.03599
$580$	5.92946e110	0.0714794
$581$	−3.16489e111	−0.355816
$582$	1.29093e112	1.35370
$583$	1.50480e111	0.147198
$584$	−6.49907e111	−0.593104
$585$	−3.15429e110	−0.0268590
$586$	−8.64753e111	−0.687130
$587$	1.41330e112	1.04807	0.524037	−	0.851695i	$-0.324425\pi$
$587$	1.41330e112	1.04807	0.524037	+	0.851695i	$0.324425\pi$
$588$	−9.75930e110	−0.0675518
$589$	1.38780e112	0.896720
$590$	−1.08048e112	−0.651794
$591$	−2.74468e112	−1.54596
$592$	−2.52167e112	−1.32635
$593$	1.13526e111	0.0557674	0.0278837	−	0.999611i	$-0.491123\pi$
$593$	1.13526e111	0.0557674	0.0278837	+	0.999611i	$0.491123\pi$
$594$	−2.11296e112	−0.969481
$595$	−6.13426e111	−0.262921
$596$	−2.25729e111	−0.0903886
$597$	2.60051e112	0.972969
$598$	1.00387e112	0.350977
$599$	4.76205e112	1.55599	0.777996	−	0.628269i	$-0.216236\pi$
$599$	4.76205e112	1.55599	0.777996	+	0.628269i	$0.216236\pi$
$600$	−1.89725e112	−0.579428
$601$	−1.39830e112	−0.399194	−0.199597	−	0.979878i	$-0.563963\pi$
$601$	−1.39830e112	−0.399194	−0.199597	+	0.979878i	$0.563963\pi$
$602$	3.44150e112	0.918524
$603$	1.31802e112	0.328904
$604$	3.98477e109	0.000929837 0
$605$	6.93857e111	0.151418
$606$	2.44359e112	0.498754
$607$	−3.61455e112	−0.690100	−0.345050	−	0.938584i	$-0.612138\pi$
$607$	−3.61455e112	−0.690100	−0.345050	+	0.938584i	$0.612138\pi$
$608$	1.41985e112	0.253598
$609$	−3.12499e112	−0.522214
$610$	−3.27610e112	−0.512270
$611$	1.88905e112	0.276423
$612$	−3.25656e111	−0.0445991
$613$	−5.69675e112	−0.730261	−0.365130	−	0.930956i	$-0.618976\pi$
$613$	−5.69675e112	−0.730261	−0.365130	+	0.930956i	$0.618976\pi$
$614$	8.19492e112	0.983389
$615$	4.54905e112	0.511068
$616$	−5.14946e112	−0.541680
$617$	1.15372e113	1.13645	0.568227	−	0.822872i	$-0.307630\pi$
$617$	1.15372e113	1.13645	0.568227	+	0.822872i	$0.307630\pi$
$618$	−1.47313e112	−0.135897
$619$	−6.00781e112	−0.519093	−0.259546	−	0.965731i	$-0.583573\pi$
$619$	−6.00781e112	−0.519093	−0.259546	+	0.965731i	$0.583573\pi$
$620$	−1.33501e112	−0.108049
$621$	−2.50629e113	−1.90030
$622$	4.64928e112	0.330275
$623$	−1.61768e113	−1.07678
$624$	2.81628e112	0.175671
$625$	7.03594e112	0.411322
$626$	1.30617e113	0.715716
$627$	−9.21955e112	−0.473559
$628$	−5.47111e112	−0.263457
$629$	1.96326e113	0.886396
$630$	−2.78165e112	−0.117763
$631$	−3.03315e112	−0.120422	−0.0602108	−	0.998186i	$-0.519177\pi$
$631$	−3.03315e112	−0.120422	−0.0602108	+	0.998186i	$0.519177\pi$
$632$	1.98969e113	0.740872
$633$	4.03430e113	1.40902
$634$	1.59077e113	0.521187
$635$	3.06609e112	0.0942429
$636$	−9.45549e111	−0.0272691
$637$	3.04094e112	0.0822927
$638$	−2.97450e113	−0.755399
$639$	−1.40857e113	−0.335732
$640$	2.43209e113	0.544114
$641$	−3.76259e113	−0.790200	−0.395100	−	0.918638i	$-0.629290\pi$
$641$	−3.76259e113	−0.790200	−0.395100	+	0.918638i	$0.629290\pi$
$642$	−4.82382e113	−0.951091
$643$	−4.06599e113	−0.752699	−0.376350	−	0.926478i	$-0.622821\pi$
$643$	−4.06599e113	−0.752699	−0.376350	+	0.926478i	$0.622821\pi$
$644$	1.37233e113	0.238551
$645$	2.63815e113	0.430657
$646$	−3.81395e113	−0.584734
$647$	−5.91371e113	−0.851602	−0.425801	−	0.904817i	$-0.640008\pi$
$647$	−5.91371e113	−0.851602	−0.425801	+	0.904817i	$0.640008\pi$
$648$	−3.83186e113	−0.518348
$649$	8.40230e113	1.06780
$650$	−1.32822e113	−0.158591
$651$	7.03589e113	0.789385
$652$	1.85460e113	0.195535
$653$	4.17662e113	0.413849	0.206924	−	0.978357i	$-0.433655\pi$
$653$	4.17662e113	0.413849	0.206924	+	0.978357i	$0.433655\pi$
$654$	−1.30075e114	−1.21142
$655$	7.01259e109	6.13911e−5 0
$656$	1.87965e114	1.54693
$657$	2.73007e113	0.211240
$658$	1.66588e114	1.21198
$659$	−8.63890e113	−0.591016	−0.295508	−	0.955340i	$-0.595489\pi$
$659$	−8.63890e113	−0.591016	−0.295508	+	0.955340i	$0.595489\pi$
$660$	8.86888e112	0.0570610
$661$	1.56098e114	0.944581	0.472291	−	0.881443i	$-0.343427\pi$
$661$	1.56098e114	0.944581	0.472291	+	0.881443i	$0.343427\pi$
$662$	−1.95394e114	−1.11215
$663$	−2.19264e113	−0.117400
$664$	−8.42511e113	−0.424393
$665$	−5.05011e113	−0.239345
$666$	8.90263e113	0.397020
$667$	−3.52822e114	−1.48067
$668$	−7.43273e113	−0.293563
$669$	2.18362e114	0.811743
$670$	−1.48490e114	−0.519597
$671$	2.54764e114	0.839221
$672$	7.19837e113	0.223243
$673$	7.13265e112	0.0208277	0.0104138	−	0.999946i	$-0.496685\pi$
$673$	7.13265e112	0.0208277	0.0104138	+	0.999946i	$0.496685\pi$
$674$	−5.77255e114	−1.58724
$675$	3.31609e114	0.858664
$676$	−7.26586e113	−0.177193
$677$	−1.11004e113	−0.0254974	−0.0127487	−	0.999919i	$-0.504058\pi$
$677$	−1.11004e113	−0.0254974	−0.0127487	+	0.999919i	$0.504058\pi$
$678$	3.78559e114	0.819088
$679$	−5.49890e114	−1.12086
$680$	−1.63297e114	−0.313594
$681$	4.31194e114	0.780216
$682$	6.69706e114	1.14187
$683$	−1.00164e115	−1.60943	−0.804716	−	0.593660i	$-0.797682\pi$
$683$	−1.00164e115	−1.60943	−0.804716	+	0.593660i	$0.797682\pi$
$684$	−2.68100e113	−0.0405999
$685$	1.45264e113	0.0207344
$686$	8.70335e114	1.17101
$687$	−5.31741e114	−0.674454
$688$	1.09007e115	1.30354
$689$	2.94628e113	0.0332197
$690$	6.78623e114	0.721506
$691$	4.50925e114	0.452109	0.226055	−	0.974115i	$-0.427417\pi$
$691$	4.50925e114	0.452109	0.226055	+	0.974115i	$0.427417\pi$
$692$	−1.33303e114	−0.126051
$693$	2.16313e114	0.192925
$694$	3.18727e114	0.268139
$695$	−6.84331e114	−0.543102
$696$	−8.31888e114	−0.622860
$697$	−1.46341e115	−1.03381
$698$	−2.11913e115	−1.41258
$699$	−1.87676e115	−1.18055
$700$	−1.81573e114	−0.107791
$701$	8.96807e114	0.502481	0.251240	−	0.967925i	$-0.419162\pi$
$701$	8.96807e114	0.502481	0.251240	+	0.967925i	$0.419162\pi$
$702$	−4.13701e114	−0.218793
$703$	1.61628e115	0.806912
$704$	−1.31234e115	−0.618520
$705$	1.27701e115	0.568245
$706$	3.08852e115	1.29766
$707$	−1.04088e115	−0.412965
$708$	−5.27964e114	−0.197814
$709$	4.23525e115	1.49867	0.749335	−	0.662191i	$-0.230373\pi$
$709$	4.23525e115	1.49867	0.749335	+	0.662191i	$0.230373\pi$
$710$	1.58691e115	0.530383
$711$	−8.35809e114	−0.263869
$712$	−4.30634e115	−1.28430
$713$	7.94376e115	2.23821
$714$	−1.93361e115	−0.514743
$715$	−2.76349e114	−0.0695126
$716$	−2.42375e114	−0.0576117
$717$	2.46813e115	0.554425
$718$	−4.85721e115	−1.03121
$719$	−3.83707e115	−0.769980	−0.384990	−	0.922921i	$-0.625795\pi$
$719$	−3.83707e115	−0.769980	−0.384990	+	0.922921i	$0.625795\pi$
$720$	−8.81068e114	−0.167126
$721$	6.27501e114	0.112522
$722$	3.27713e115	0.555568
$723$	−8.32902e115	−1.33504
$724$	7.03680e114	0.106651
$725$	4.66820e115	0.669053
$726$	2.18713e115	0.296444
$727$	−1.04070e116	−1.33409	−0.667043	−	0.745019i	$-0.732440\pi$
$727$	−1.04070e116	−1.33409	−0.667043	+	0.745019i	$0.732440\pi$
$728$	−1.00822e115	−0.122247
$729$	9.45591e115	1.08452
$730$	−3.07573e115	−0.333713
$731$	−8.48685e115	−0.871150
$732$	−1.60083e115	−0.155470
$733$	−5.64569e115	−0.518807	−0.259404	−	0.965769i	$-0.583526\pi$
$733$	−5.64569e115	−0.518807	−0.259404	+	0.965769i	$0.583526\pi$
$734$	1.87356e116	1.62921
$735$	2.05570e115	0.169170
$736$	8.12721e115	0.632980
$737$	1.15472e116	0.851224
$738$	−6.63601e115	−0.463046
$739$	−1.99965e116	−1.32086	−0.660428	−	0.750890i	$-0.729625\pi$
$739$	−1.99965e116	−1.32086	−0.660428	+	0.750890i	$0.729625\pi$
$740$	−1.55480e115	−0.0972280
$741$	−1.80512e115	−0.106873
$742$	2.59821e115	0.145652
$743$	2.16743e116	1.15053	0.575266	−	0.817966i	$-0.304898\pi$
$743$	2.16743e116	1.15053	0.575266	+	0.817966i	$0.304898\pi$
$744$	1.87299e116	0.941524
$745$	4.75476e115	0.226360
$746$	−2.21406e116	−0.998313
$747$	3.53914e115	0.151152
$748$	−2.85309e115	−0.115425
$749$	2.05477e116	0.787498
$750$	−2.03601e116	−0.739262
$751$	−5.13869e116	−1.76781	−0.883903	−	0.467670i	$-0.845093\pi$
$751$	−5.13869e116	−1.76781	−0.883903	+	0.467670i	$0.845093\pi$
$752$	5.27656e116	1.72000
$753$	−2.06129e116	−0.636710
$754$	−5.82385e115	−0.170479
$755$	−8.39353e113	−0.00232859
$756$	−5.65547e115	−0.148709
$757$	1.52248e116	0.379462	0.189731	−	0.981836i	$-0.439238\pi$
$757$	1.52248e116	0.379462	0.189731	+	0.981836i	$0.439238\pi$
$758$	−4.83309e116	−1.14188
$759$	−5.27727e116	−1.18200
$760$	−1.34436e116	−0.285474
$761$	−1.42159e116	−0.286217	−0.143109	−	0.989707i	$-0.545710\pi$
$761$	−1.42159e116	−0.286217	−0.143109	+	0.989707i	$0.545710\pi$
$762$	9.66474e115	0.184507
$763$	5.54073e116	1.00305
$764$	−3.10149e115	−0.0532463
$765$	6.85963e115	0.111690
$766$	1.06364e117	1.64260
$767$	1.64511e116	0.240981
$768$	3.17139e116	0.440677
$769$	1.22375e117	1.61315	0.806577	−	0.591129i	$-0.201317\pi$
$769$	1.22375e117	1.61315	0.806577	+	0.591129i	$0.201317\pi$
$770$	−2.43702e116	−0.304779
$771$	−3.90759e116	−0.463667
$772$	2.04165e116	0.229869
$773$	5.37256e116	0.574000	0.287000	−	0.957931i	$-0.407342\pi$
$773$	5.37256e116	0.574000	0.287000	+	0.957931i	$0.407342\pi$
$774$	−3.84845e116	−0.390191
$775$	−1.05104e117	−1.01135
$776$	−1.46384e117	−1.33688
$777$	8.19426e116	0.710327
$778$	−3.39607e115	−0.0279449
$779$	−1.20477e117	−0.941106
$780$	1.73646e115	0.0128775
$781$	−1.23405e117	−0.868894
$782$	−2.18311e117	−1.45949
$783$	1.45400e117	0.923027
$784$	8.49407e116	0.512054
$785$	1.15244e117	0.659776
$786$	2.21046e113	0.000120191 0
$787$	−3.33890e115	−0.0172435	−0.00862177	−	0.999963i	$-0.502744\pi$
$787$	−3.33890e115	−0.0172435	−0.00862177	+	0.999963i	$0.502744\pi$
$788$	−6.99255e116	−0.343024
$789$	2.14414e117	0.999158
$790$	9.41635e116	0.416855
$791$	−1.61252e117	−0.678200
$792$	5.75837e116	0.230107
$793$	4.98809e116	0.189396
$794$	−1.79588e116	−0.0647957
$795$	1.99171e116	0.0682900
$796$	6.62526e116	0.215886
$797$	1.54851e117	0.479571	0.239786	−	0.970826i	$-0.422923\pi$
$797$	1.54851e117	0.479571	0.239786	+	0.970826i	$0.422923\pi$
$798$	−1.59186e117	−0.468586
$799$	−4.10811e117	−1.14947
$800$	−1.07531e117	−0.286016
$801$	1.80896e117	0.457418
$802$	7.75564e117	1.86447
$803$	2.39183e117	0.546702
$804$	−7.25577e116	−0.157693
$805$	−2.89068e117	−0.597403
$806$	1.31123e117	0.257698
$807$	2.58840e117	0.483787
$808$	−2.77087e117	−0.492557
$809$	−7.40169e117	−1.25146	−0.625729	−	0.780041i	$-0.715198\pi$
$809$	−7.40169e117	−1.25146	−0.625729	+	0.780041i	$0.715198\pi$
$810$	−1.81346e117	−0.291651
$811$	−6.40061e117	−0.979213	−0.489606	−	0.871944i	$-0.662859\pi$
$811$	−6.40061e117	−0.979213	−0.489606	+	0.871944i	$0.662859\pi$
$812$	−7.96145e116	−0.115871
$813$	2.98631e117	0.413493
$814$	7.79965e117	1.02751
$815$	−3.90655e117	−0.489677
$816$	−6.12456e117	−0.730506
$817$	−6.98691e117	−0.793034
$818$	8.90253e117	0.961623
$819$	4.23525e116	0.0435393
$820$	1.15895e117	0.113397
$821$	−2.13728e117	−0.199051	−0.0995253	−	0.995035i	$-0.531732\pi$
$821$	−2.13728e117	−0.199051	−0.0995253	+	0.995035i	$0.531732\pi$
$822$	4.57893e116	0.0405934
$823$	−4.16508e117	−0.351504	−0.175752	−	0.984435i	$-0.556236\pi$
$823$	−4.16508e117	−0.351504	−0.175752	+	0.984435i	$0.556236\pi$
$824$	1.67044e117	0.134208
$825$	6.98238e117	0.534095
$826$	1.45076e118	1.05658
$827$	9.80109e117	0.679675	0.339837	−	0.940484i	$-0.389628\pi$
$827$	9.80109e117	0.679675	0.339837	+	0.940484i	$0.389628\pi$
$828$	−1.53461e117	−0.101337
$829$	5.19162e117	0.326471	0.163235	−	0.986587i	$-0.447807\pi$
$829$	5.19162e117	0.326471	0.163235	+	0.986587i	$0.447807\pi$
$830$	−3.98724e117	−0.238787
$831$	2.40513e118	1.37182
$832$	−2.56946e117	−0.139588
$833$	−6.61313e117	−0.342204
$834$	−2.15711e118	−1.06328
$835$	1.56563e118	0.735170
$836$	−2.34884e117	−0.105075
$837$	−3.27368e118	−1.39526
$838$	−2.59997e118	−1.05581
$839$	2.83635e118	1.09749	0.548746	−	0.835989i	$-0.315106\pi$
$839$	2.83635e118	1.09749	0.548746	+	0.835989i	$0.315106\pi$
$840$	−6.81569e117	−0.251303
$841$	−7.99153e117	−0.280797
$842$	−5.01907e118	−1.68067
$843$	−6.77551e117	−0.216234
$844$	1.02781e118	0.312639
$845$	1.53049e118	0.443744
$846$	−1.86287e118	−0.514851
$847$	−9.31639e117	−0.245454
$848$	8.22965e117	0.206704
$849$	2.67314e118	0.640119
$850$	2.88848e118	0.659481
$851$	9.25160e118	2.01405
$852$	7.75425e117	0.160967
$853$	−6.31035e118	−1.24916	−0.624580	−	0.780961i	$-0.714730\pi$
$853$	−6.31035e118	−1.24916	−0.624580	+	0.780961i	$0.714730\pi$
$854$	4.39880e118	0.830407
$855$	5.64727e117	0.101674
$856$	5.46990e118	0.939272
$857$	−2.58673e118	−0.423670	−0.211835	−	0.977305i	$-0.567944\pi$
$857$	−2.58673e118	−0.423670	−0.211835	+	0.977305i	$0.567944\pi$
$858$	−8.71092e117	−0.136091
$859$	−8.01078e118	−1.19385	−0.596927	−	0.802295i	$-0.703612\pi$
$859$	−8.01078e118	−1.19385	−0.596927	+	0.802295i	$0.703612\pi$
$860$	6.72115e117	0.0955557
$861$	−6.10799e118	−0.828458
$862$	3.62368e118	0.468928
$863$	2.32314e118	0.286838	0.143419	−	0.989662i	$-0.454190\pi$
$863$	2.32314e118	0.286838	0.143419	+	0.989662i	$0.454190\pi$
$864$	−3.34928e118	−0.394589
$865$	2.80791e118	0.315668
$866$	1.74024e118	0.186696
$867$	−3.30742e118	−0.338623
$868$	1.79251e118	0.175151
$869$	−7.32257e118	−0.682909
$870$	−3.93697e118	−0.350455
$871$	2.26086e118	0.192105
$872$	1.47497e119	1.19637
$873$	6.14914e118	0.476143
$874$	−1.79727e119	−1.32862
$875$	8.67264e118	0.612104
$876$	−1.50292e118	−0.101279
$877$	−2.89611e119	−1.86351	−0.931753	−	0.363092i	$-0.881721\pi$
$877$	−2.89611e119	−1.86351	−0.931753	+	0.363092i	$0.881721\pi$
$878$	−2.01422e118	−0.123760
$879$	8.90064e118	0.522242
$880$	−7.71909e118	−0.432532
$881$	1.78861e118	0.0957176	0.0478588	−	0.998854i	$-0.484760\pi$
$881$	1.78861e118	0.0957176	0.0478588	+	0.998854i	$0.484760\pi$
$882$	−2.99880e118	−0.153274
$883$	2.47851e118	0.120999	0.0604994	−	0.998168i	$-0.480731\pi$
$883$	2.47851e118	0.120999	0.0604994	+	0.998168i	$0.480731\pi$
$884$	−5.58613e117	−0.0260492
$885$	1.11211e119	0.495386
$886$	3.16139e119	1.34528
$887$	2.63326e119	1.07050	0.535250	−	0.844694i	$-0.320217\pi$
$887$	2.63326e119	1.07050	0.535250	+	0.844694i	$0.320217\pi$
$888$	2.18135e119	0.847229
$889$	−4.11682e118	−0.152771
$890$	−2.03800e119	−0.722620
$891$	1.41022e119	0.477794
$892$	5.56314e118	0.180112
$893$	−3.38205e119	−1.04640
$894$	1.49877e119	0.443164
$895$	5.10540e118	0.144277
$896$	−3.26555e119	−0.882028
$897$	−1.03325e119	−0.266754
$898$	3.90773e119	0.964346
$899$	−4.60850e119	−1.08716
$900$	2.03044e118	0.0457898
$901$	−6.40726e118	−0.138140
$902$	−5.81385e119	−1.19839
$903$	−3.54224e119	−0.698110
$904$	−4.29261e119	−0.808910
$905$	−1.48223e119	−0.267085
$906$	−2.64576e117	−0.00455888
$907$	1.08334e120	1.78513	0.892566	−	0.450918i	$-0.148903\pi$
$907$	1.08334e120	1.78513	0.892566	+	0.450918i	$0.148903\pi$
$908$	1.09854e119	0.173117
$909$	1.16396e119	0.175429
$910$	−4.77150e118	−0.0687826
$911$	5.73361e119	0.790559	0.395279	−	0.918561i	$-0.370648\pi$
$911$	5.73361e119	0.790559	0.395279	+	0.918561i	$0.370648\pi$
$912$	−5.04212e119	−0.665001
$913$	3.10066e119	0.391190
$914$	6.58174e118	0.0794364
$915$	3.37199e119	0.389343
$916$	−1.35470e119	−0.149650
$917$	−9.41577e115	−9.95171e−5 0
$918$	8.99674e119	0.909822
$919$	1.60979e120	1.55772	0.778862	−	0.627195i	$-0.215797\pi$
$919$	1.60979e120	1.55772	0.778862	+	0.627195i	$0.215797\pi$
$920$	−7.69514e119	−0.712541
$921$	−8.43478e119	−0.747410
$922$	1.26397e120	1.07185
$923$	−2.41618e119	−0.196092
$924$	−1.19082e119	−0.0924978
$925$	−1.22408e120	−0.910061
$926$	−1.51042e120	−1.07487
$927$	−7.01702e118	−0.0477995
$928$	−4.71493e119	−0.307455
$929$	−7.05190e119	−0.440220	−0.220110	−	0.975475i	$-0.570642\pi$
$929$	−7.05190e119	−0.440220	−0.220110	+	0.975475i	$0.570642\pi$
$930$	8.86405e119	0.529752
$931$	−5.44434e119	−0.311518
$932$	−4.78137e119	−0.261944
$933$	−4.78536e119	−0.251020
$934$	−1.32056e120	−0.663301
$935$	6.00976e119	0.289059
$936$	1.12745e119	0.0519306
$937$	3.61872e120	1.59625	0.798127	−	0.602489i	$-0.205824\pi$
$937$	3.61872e120	1.59625	0.798127	+	0.602489i	$0.205824\pi$
$938$	1.99376e120	0.842284
$939$	−1.34441e120	−0.543969
$940$	3.25341e119	0.126084
$941$	−3.06542e120	−1.13792	−0.568959	−	0.822366i	$-0.692654\pi$
$941$	−3.06542e120	−1.13792	−0.568959	+	0.822366i	$0.692654\pi$
$942$	3.63265e120	1.29170
$943$	−6.89613e120	−2.34899
$944$	4.59517e120	1.49946
$945$	1.19127e120	0.372411
$946$	−3.37165e120	−1.00984
$947$	6.08781e119	0.174698	0.0873488	−	0.996178i	$-0.472161\pi$
$947$	6.08781e119	0.174698	0.0873488	+	0.996178i	$0.472161\pi$
$948$	4.60119e119	0.126512
$949$	4.68302e119	0.123380
$950$	2.37797e120	0.600345
$951$	−1.63733e120	−0.396120
$952$	2.19258e120	0.508346
$953$	4.90917e120	1.09080	0.545401	−	0.838175i	$-0.316377\pi$
$953$	4.90917e120	1.09080	0.545401	+	0.838175i	$0.316377\pi$
$954$	−2.90544e119	−0.0618733
$955$	6.53299e119	0.133345
$956$	6.28799e119	0.123018
$957$	3.06156e120	0.574129
$958$	−7.62162e120	−1.37007
$959$	−1.95046e119	−0.0336111
$960$	−1.73698e120	−0.286952
$961$	4.06211e120	0.643360
$962$	1.52711e120	0.231889
$963$	−2.29774e120	−0.334531
$964$	−2.12196e120	−0.296222
$965$	−4.30054e120	−0.575661
$966$	−9.11184e120	−1.16959
$967$	−8.58734e120	−1.05703	−0.528514	−	0.848924i	$-0.677251\pi$
$967$	−8.58734e120	−1.05703	−0.528514	+	0.848924i	$0.677251\pi$
$968$	−2.48007e120	−0.292760
$969$	3.92559e120	0.444418
$970$	−6.92771e120	−0.752202
$971$	−4.10198e120	−0.427184	−0.213592	−	0.976923i	$-0.568516\pi$
$971$	−4.10198e120	−0.427184	−0.213592	+	0.976923i	$0.568516\pi$
$972$	1.11285e120	0.111161
$973$	9.18848e120	0.880387
$974$	1.07250e121	0.985732
$975$	1.36710e120	0.120535
$976$	1.39329e121	1.17849
$977$	1.76972e121	1.43606	0.718032	−	0.696011i	$-0.245043\pi$
$977$	1.76972e121	1.43606	0.718032	+	0.696011i	$0.245043\pi$
$978$	−1.23140e121	−0.958683
$979$	1.58484e121	1.18382
$980$	5.23726e119	0.0375360
$981$	−6.19591e120	−0.426098
$982$	−8.16820e120	−0.539028
$983$	1.56603e121	0.991703	0.495851	−	0.868407i	$-0.334856\pi$
$983$	1.56603e121	0.991703	0.495851	+	0.868407i	$0.334856\pi$
$984$	−1.62598e121	−0.988127
$985$	1.47291e121	0.859034
$986$	1.26651e121	0.708914
$987$	−1.71464e121	−0.921145
$988$	−4.59885e119	−0.0237134
$989$	−3.99931e121	−1.97941
$990$	2.72519e120	0.129471
$991$	−1.05972e121	−0.483292	−0.241646	−	0.970364i	$-0.577687\pi$
$991$	−1.05972e121	−0.483292	−0.241646	+	0.970364i	$0.577687\pi$
$992$	1.06156e121	0.464754
$993$	2.01113e121	0.845271
$994$	−2.13074e121	−0.859768
$995$	−1.39555e121	−0.540642
$996$	−1.94832e120	−0.0724698
$997$	4.58369e120	0.163705	0.0818524	−	0.996644i	$-0.473916\pi$
$997$	4.58369e120	0.163705	0.0818524	+	0.996644i	$0.473916\pi$
$998$	1.13787e120	0.0390216
$999$	−3.81265e121	−1.25552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.82.a.a.1.2	✓	6
3.2	odd	2		9.82.a.b.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.82.a.a.1.2	✓	6	1.1	even	1	trivial
9.82.a.b.1.5		6	3.2	odd	2

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:	\( k \)	\(=\)	\( 82 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-1.69157e12 q^{2} +1.74109e19 q^{3} +4.43572e23 q^{4} -9.34342e27 q^{5} -2.94518e31 q^{6} +1.25454e34 q^{7} +3.33964e36 q^{8} -1.40288e38 q^{9} +O(q^{10})\)	\(q-1.69157e12 q^{2} +1.74109e19 q^{3} +4.43572e23 q^{4} -9.34342e27 q^{5} -2.94518e31 q^{6} +1.25454e34 q^{7} +3.33964e36 q^{8} -1.40288e38 q^{9} +1.58051e40 q^{10} -1.22907e42 q^{11} +7.72297e42 q^{12} -2.40644e44 q^{13} -2.12214e46 q^{14} -1.62677e47 q^{15} -6.72174e48 q^{16} +5.23327e49 q^{17} +2.37308e50 q^{18} +4.30835e51 q^{19} -4.14448e51 q^{20} +2.18426e53 q^{21} +2.07907e54 q^{22} +2.46610e55 q^{23} +5.81460e55 q^{24} -3.26291e56 q^{25} +4.07066e56 q^{26} -1.01630e58 q^{27} +5.56478e57 q^{28} -1.43069e59 q^{29} +2.75180e59 q^{30} +3.22118e60 q^{31} +3.29557e60 q^{32} -2.13992e61 q^{33} -8.85246e61 q^{34} -1.17217e62 q^{35} -6.22280e61 q^{36} +3.75151e63 q^{37} -7.28790e63 q^{38} -4.18981e63 q^{39} -3.12037e64 q^{40} -2.79637e65 q^{41} -3.69483e65 q^{42} -1.62171e66 q^{43} -5.45183e65 q^{44} +1.31077e66 q^{45} -4.17159e67 q^{46} -7.84999e67 q^{47} -1.17031e68 q^{48} -1.26367e68 q^{49} +5.51945e68 q^{50} +9.11157e68 q^{51} -1.06743e68 q^{52} -1.22433e69 q^{53} +1.71914e70 q^{54} +1.14838e70 q^{55} +4.18970e70 q^{56} +7.50121e70 q^{57} +2.42011e71 q^{58} -6.83628e71 q^{59} -7.21590e70 q^{60} -2.07281e72 q^{61} -5.44887e72 q^{62} -1.75997e72 q^{63} +1.06775e73 q^{64} +2.24843e72 q^{65} +3.61984e73 q^{66} -9.39505e73 q^{67} +2.32133e73 q^{68} +4.29370e74 q^{69} +1.98281e74 q^{70} +1.00405e75 q^{71} -4.68513e74 q^{72} -1.94604e75 q^{73} -6.34595e75 q^{74} -5.68100e75 q^{75} +1.91106e75 q^{76} -1.54192e76 q^{77} +7.08738e75 q^{78} +5.95779e76 q^{79} +6.28041e76 q^{80} -1.14739e77 q^{81} +4.73026e77 q^{82} -2.52276e77 q^{83} +9.68875e76 q^{84} -4.88966e77 q^{85} +2.74325e78 q^{86} -2.49095e78 q^{87} -4.10467e78 q^{88} -1.28946e79 q^{89} -2.21727e78 q^{90} -3.01896e78 q^{91} +1.09389e79 q^{92} +5.60835e79 q^{93} +1.32788e80 q^{94} -4.02547e79 q^{95} +5.73787e79 q^{96} -4.38321e80 q^{97} +2.13759e80 q^{98} +1.72425e80 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 460872026640 q^{2} - 15\!\cdots\!60 q^{3}+ \cdots + 11\!\cdots\!98 q^{9}+O(q^{10}) \) 6 * q - 460872026640 * q^2 - 15648291925893129960 * q^3 + 4493950976700073762513152 * q^4 - 18364304155649862126617790300 * q^5 + 79543552376002656592687080272832 * q^6 - 31430760593927655842892725138869200 * q^7 - 5498145101596630185016447889074360320 * q^8 + 1187896030123132129876714384590115355598 * q^9	\( 6 q - 460872026640 q^{2} - 15\!\cdots\!60 q^{3}+ \cdots - 63\!\cdots\!24 q^{99}+O(q^{100}) \) 6 * q - 460872026640 * q^2 - 15648291925893129960 * q^3 + 4493950976700073762513152 * q^4 - 18364304155649862126617790300 * q^5 + 79543552376002656592687080272832 * q^6 - 31430760593927655842892725138869200 * q^7 - 5498145101596630185016447889074360320 * q^8 + 1187896030123132129876714384590115355598 * q^9 - 66472312087527710620452553569669697173600 * q^10 - 2302475295973581620809306061775551681990328 * q^11 - 53870867926220164150329513348046663235681280 * q^12 + 1313253814255449492724146018729804193778100180 * q^13 + 41225372723246048337281629784765672712004401024 * q^14 - 156056001993392003275961063842210281482861266800 * q^15 + 2799490233261278434402974316306719898117729222656 * q^16 + 2377848571505238562780180385684069414829577769580 * q^17 + 506306622204276540508620731115428014111485052430640 * q^18 - 17422016964741760630179674590582970665727618619375240 * q^19 + 148672889698640611477740875719636714144962866333222400 * q^20 - 114072752249915469711576730788399479267919883382138688 * q^21 - 1258034178625689345497738618244246726621220713529586880 * q^22 + 10526595063181453314046018770874462030150898790798283920 * q^23 - 12327611736558023893782629055720670133074337356786974720 * q^24 + 411037910011361515508644334216291479522821661187695496250 * q^25 - 3180570114716540139250277986112641638356676984048903123168 * q^26 + 14621431460046183096199709161966291993457773283863231280880 * q^27 - 82116517748637002885903417761702653442063276903193852344320 * q^28 + 155464359052154485146727469597467543970919715236853926245940 * q^29 + 164012983787559943750248070451087782537372525868704541558400 * q^30 + 1259277021063335018777245090979655984137503836933555134668992 * q^31 - 13036312845125683749178794475020758767431562303480221102243840 * q^32 + 21091354949357251433966784004957297352147245536782330440814880 * q^33 + 11899550405754031112224464347628728246396477955985557631122144 * q^34 - 232034356615504837711196063040035766391492406317925929510437600 * q^35 - 2071479648832132808682929357240066191852277967275841354377712384 * q^36 + 414692688584236378963319357622814947056491742931883680122973540 * q^37 - 2455417714037465297201999851134772037590829998762172946918415680 * q^38 - 92285563929532296901251298670288831485071753513924535804838199984 * q^39 - 258059824285668605758122263287555971608050642150708772544789504000 * q^40 - 250252788823194090638944408016236187978548863949167831014660870148 * q^41 - 3774470339882908627686770098374833879180889302300694800640098910720 * q^42 - 5362516930786214192203446564720631507618558180640993338648106782200 * q^43 - 17252465656682175267213991915222412585785021276568609411813835518976 * q^44 - 62055994195911488597384173133359170181530078929941731114719230089900 * q^45 - 123763409427226200113215389587151615608344054530127843046255996688768 * q^46 - 230717394511751791462615349254196337530205542984846694602934639341280 * q^47 - 691982889190309031684460851104240936972943285356349640319551063982080 * q^48 - 148965540042877735285285650175007198234557699456949204802064464556458 * q^49 - 1416105420952806525015169807922957339416756851287952031511031347670000 * q^50 + 723978686772453055369497103847414979467127084371963703072714225585072 * q^51 + 12562371185881747636341658298037576485393840750032566447999727917043200 * q^52 + 25898990256961205776642859216859182171010424056472082121008236344959940 * q^53 + 60731909939285801872082597253734783721512219559188195805336458971800960 * q^54 + 70427859302095658379065386305135120838252257009889309990749877277396400 * q^55 + 350275852246953465289512615368698332984392220622408793911163576939151360 * q^56 + 303622382725256536236947985463289143154200643659779472092208351796091360 * q^57 - 312514134877257928766126367534026770462807935435519457753987287493386720 * q^58 - 38532453307459913471042984274454520116124717672121643571528434328282520 * q^59 - 5854438714408546634435977504160054633094179506942282108438463374797465600 * q^60 - 4585192544270629640163935422584783189092178505653567017169797728495170828 * q^61 - 11745445982868867354760701788812677993661414140303262885466836339630318080 * q^62 - 35632339418998518169074915366562958999484559616578607415025802007025188240 * q^63 - 24049189879736877632355406073912155582619770074517134096672197458230509568 * q^64 + 40108571425620140080303901416556158312567794172295521521551039993118238200 * q^65 + 46637466443959380664183766096173047575934541297502070623350605582042365184 * q^66 + 278606964486964374833906544600580027758780739521508130980859112605565987480 * q^67 + 591059149620766869951154898169335214276013402788475417448362648514550551040 * q^68 + 783789679110178241786835392836945981604400905715238386162022702382323722816 * q^69 + 2635837114104224632390936486964777102611174135296488988531978806621369068800 * q^70 - 554281436103188717611008447226924711986842423491780222553301787426789861968 * q^71 - 3169897304032072056282604590226317130165389286798806197352424269626436341760 * q^72 - 1159677538409433721867557656635958525415325708297922475676033828300683142980 * q^73 - 14870996314347354169518203977127998385153668929299472477677600807989626002016 * q^74 - 40272209656064989140640078595938035284494253817756477276130430269166782335000 * q^75 - 56365824164857229782022127848008365902008884166434980738114640515976798612480 * q^76 - 22951272837324694774527636903423616359482790364245898655274441101674154673600 * q^77 + 29994870322699852265351947769035786178441787146653937638111333726813935158400 * q^78 + 76488528596848273963909721387433081359345259080220208993600380062891411190240 * q^79 + 326185463863660018876021371340485226979224823762794013840530768719064527667200 * q^80 + 713659220427214109967671419496287178348529210497808359051350032218775138774486 * q^81 + 836977463852743303549437738986542975894462808796250502348000478828556860551520 * q^82 + 440718478462773776637617020819789880594300172591745821478345102532528865997560 * q^83 + 2327207348086698397722806131221331490656683214148360655124465557042000906952704 * q^84 + 1165607138975709364402518400492567424057357396402879557680723771041190675179400 * q^85 - 10339197506820945136003281093027314178240703830345630490304599234644673765234368 * q^86 - 13777097629225807302706950021773234863450868385225572161845501405567814463584560 * q^87 - 9603847126452588175246186358824265187739652448840879006569656469218022549667840 * q^88 - 18886228493337874501351816155449414708824427288664596668607356717228138798590180 * q^89 - 27536035459180423419106541648329015873635894588277179325118018321007646877848800 * q^90 - 14576226325987997036142564032100430704897317032265698214767987870608618538920288 * q^91 + 66364414655655668275929797141498084164407535259475789695165805684452941775738880 * q^92 + 130065128543178746783515152749840115744191801626425494555088565985583783043572480 * q^93 + 331286952814608158700187065887753978184064043063622410298763861434514546852072704 * q^94 + 267699559747800180626411366716842325842865933645649558098598518850783266973922000 * q^95 + 495554087106091786297185708372687557293322071836937974888325742175573190348111872 * q^96 + 113832498161281214584608062040287314379413598012089688107897449655058469975263820 * q^97 - 858118355318723523117883130491863373979750018711838274840266757637744872892872080 * q^98 - 630632406390824053363198011181718527371969259570962092705191903378628178893256024 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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