LMFDB - Embedded newform 1.82.a.a.1.5

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			1.5
Root			$-1.13941e10$ 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)

$f(q)$	$=$	$q+1.56393e12 q^{2} +3.91464e19 q^{3} +2.80371e22 q^{4} -1.92800e28 q^{5} +6.12224e31 q^{6} -2.38829e34 q^{7} -3.73751e36 q^{8} +1.08902e39 q^{9} +O(q^{10})$	\(q+1.56393e12 q^{2} +3.91464e19 q^{3} +2.80371e22 q^{4} -1.92800e28 q^{5} +6.12224e31 q^{6} -2.38829e34 q^{7} -3.73751e36 q^{8} +1.08902e39 q^{9} -3.01526e40 q^{10} -1.58267e41 q^{11} +1.09755e42 q^{12} -8.55032e44 q^{13} -3.73513e46 q^{14} -7.54741e47 q^{15} -5.91301e48 q^{16} -3.20005e49 q^{17} +1.70315e51 q^{18} -6.82724e51 q^{19} -5.40554e50 q^{20} -9.34931e53 q^{21} -2.47519e53 q^{22} +7.90383e54 q^{23} -1.46310e56 q^{24} -4.18734e55 q^{25} -1.33721e57 q^{26} +2.52725e58 q^{27} -6.69608e56 q^{28} -1.55020e58 q^{29} -1.18037e60 q^{30} +1.98005e60 q^{31} -2.10807e59 q^{32} -6.19560e60 q^{33} -5.00467e61 q^{34} +4.60462e62 q^{35} +3.05328e61 q^{36} -2.31493e63 q^{37} -1.06774e64 q^{38} -3.34714e64 q^{39} +7.20591e64 q^{40} +2.84678e65 q^{41} -1.46217e66 q^{42} -1.94265e66 q^{43} -4.43735e63 q^{44} -2.09962e67 q^{45} +1.23611e67 q^{46} -4.81398e67 q^{47} -2.31473e68 q^{48} +2.86641e68 q^{49} -6.54872e67 q^{50} -1.25271e69 q^{51} -2.39726e67 q^{52} +3.25315e69 q^{53} +3.95245e70 q^{54} +3.05139e69 q^{55} +8.92627e70 q^{56} -2.67262e71 q^{57} -2.42441e70 q^{58} +5.77888e71 q^{59} -2.11607e70 q^{60} -2.57200e72 q^{61} +3.09666e72 q^{62} -2.60089e73 q^{63} +1.39671e73 q^{64} +1.64850e73 q^{65} -9.68950e72 q^{66} +7.40069e73 q^{67} -8.97201e71 q^{68} +3.09407e74 q^{69} +7.20132e74 q^{70} -1.55130e74 q^{71} -4.07021e75 q^{72} +3.73048e75 q^{73} -3.62040e75 q^{74} -1.63919e75 q^{75} -1.91416e74 q^{76} +3.77989e75 q^{77} -5.23471e76 q^{78} -9.43898e76 q^{79} +1.14003e77 q^{80} +5.06429e77 q^{81} +4.45217e77 q^{82} -7.99636e77 q^{83} -2.62127e76 q^{84} +6.16969e77 q^{85} -3.03818e78 q^{86} -6.06847e77 q^{87} +5.91526e77 q^{88} +5.72264e78 q^{89} -3.28366e79 q^{90} +2.04207e79 q^{91} +2.21600e77 q^{92} +7.75118e79 q^{93} -7.52874e79 q^{94} +1.31629e80 q^{95} -8.25235e78 q^{96} -4.74987e79 q^{97} +4.48287e80 q^{98} -1.72355e80 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.56393e12	1.00578	0.502891	−	0.864350i	$-0.332270\pi$
$2$	1.56393e12	1.00578	0.502891	+	0.864350i	$0.332270\pi$
$3$	3.91464e19	1.85901	0.929504	−	0.368812i	$-0.120236\pi$
$3$	3.91464e19	1.85901	0.929504	+	0.368812i	$0.120236\pi$
$4$	2.80371e22	0.0115959
$5$	−1.92800e28	−0.948028	−0.474014	−	0.880517i	$-0.657195\pi$
$5$	−1.92800e28	−0.948028	−0.474014	+	0.880517i	$0.657195\pi$
$6$	6.12224e31	1.86976
$7$	−2.38829e34	−1.41781	−0.708903	−	0.705306i	$-0.750810\pi$
$7$	−2.38829e34	−1.41781	−0.708903	+	0.705306i	$0.750810\pi$
$8$	−3.73751e36	−0.994118
$9$	1.08902e39	2.45591
$10$	−3.01526e40	−0.953508
$11$	−1.58267e41	−0.105436	−0.0527178	−	0.998609i	$-0.516788\pi$
$11$	−1.58267e41	−0.105436	−0.0527178	+	0.998609i	$0.516788\pi$
$12$	1.09755e42	0.0215568
$13$	−8.55032e44	−0.656563	−0.328282	−	0.944580i	$-0.606469\pi$
$13$	−8.55032e44	−0.656563	−0.328282	+	0.944580i	$0.606469\pi$
$14$	−3.73513e46	−1.42600
$15$	−7.54741e47	−1.76239
$16$	−5.91301e48	−1.01146
$17$	−3.20005e49	−0.469868	−0.234934	−	0.972011i	$-0.575487\pi$
$17$	−3.20005e49	−0.469868	−0.234934	+	0.972011i	$0.575487\pi$
$18$	1.70315e51	2.47011
$19$	−6.82724e51	−1.10847	−0.554236	−	0.832360i	$-0.686989\pi$
$19$	−6.82724e51	−1.10847	−0.554236	+	0.832360i	$0.686989\pi$
$20$	−5.40554e50	−0.0109932
$21$	−9.34931e53	−2.63571
$22$	−2.47519e53	−0.106045
$23$	7.90383e54	0.559578	0.279789	−	0.960062i	$-0.409736\pi$
$23$	7.90383e54	0.559578	0.279789	+	0.960062i	$0.409736\pi$
$24$	−1.46310e56	−1.84807
$25$	−4.18734e55	−0.101244
$26$	−1.33721e57	−0.660359
$27$	2.52725e58	2.70655
$28$	−6.69608e56	−0.0164407
$29$	−1.55020e58	−0.0918900	−0.0459450	−	0.998944i	$-0.514630\pi$
$29$	−1.55020e58	−0.0918900	−0.0459450	+	0.998944i	$0.514630\pi$
$30$	−1.18037e60	−1.77258
$31$	1.98005e60	0.788001	0.394001	−	0.919110i	$-0.371091\pi$
$31$	1.98005e60	0.788001	0.394001	+	0.919110i	$0.371091\pi$
$32$	−2.10807e59	−0.0231906
$33$	−6.19560e60	−0.196006
$34$	−5.00467e61	−0.472584
$35$	4.60462e62	1.34412
$36$	3.05328e61	0.0284784
$37$	−2.31493e63	−0.711818	−0.355909	−	0.934521i	$-0.615829\pi$
$37$	−2.31493e63	−0.711818	−0.355909	+	0.934521i	$0.615829\pi$
$38$	−1.06774e64	−1.11488
$39$	−3.34714e64	−1.22056
$40$	7.20591e64	0.942452
$41$	2.84678e65	1.36964	0.684822	−	0.728710i	$-0.259880\pi$
$41$	2.84678e65	1.36964	0.684822	+	0.728710i	$0.259880\pi$
$42$	−1.46217e66	−2.65095
$43$	−1.94265e66	−1.35807	−0.679036	−	0.734105i	$-0.737602\pi$
$43$	−1.94265e66	−1.35807	−0.679036	+	0.734105i	$0.737602\pi$
$44$	−4.43735e63	−0.00122262
$45$	−2.09962e67	−2.32827
$46$	1.23611e67	0.562813
$47$	−4.81398e67	−0.917362	−0.458681	−	0.888601i	$-0.651678\pi$
$47$	−4.81398e67	−0.917362	−0.458681	+	0.888601i	$0.651678\pi$
$48$	−2.31473e68	−1.88031
$49$	2.86641e68	1.01018
$50$	−6.54872e67	−0.101829
$51$	−1.25271e69	−0.873488
$52$	−2.39726e67	−0.00761342
$53$	3.25315e69	0.477674	0.238837	−	0.971060i	$-0.423234\pi$
$53$	3.25315e69	0.477674	0.238837	+	0.971060i	$0.423234\pi$
$54$	3.95245e70	2.72219
$55$	3.05139e69	0.0999559
$56$	8.92627e70	1.40947
$57$	−2.67262e71	−2.06066
$58$	−2.42441e70	−0.0924212
$59$	5.77888e71	1.10239	0.551197	−	0.834375i	$-0.314171\pi$
$59$	5.77888e71	1.10239	0.551197	+	0.834375i	$0.314171\pi$
$60$	−2.11607e70	−0.0204364
$61$	−2.57200e72	−1.27178	−0.635892	−	0.771778i	$-0.719368\pi$
$61$	−2.57200e72	−1.27178	−0.635892	+	0.771778i	$0.719368\pi$
$62$	3.09666e72	0.792557
$63$	−2.60089e73	−3.48201
$64$	1.39671e73	0.988137
$65$	1.64850e73	0.622440
$66$	−9.68950e72	−0.197139
$67$	7.40069e73	0.818923	0.409461	−	0.912328i	$-0.365717\pi$
$67$	7.40069e73	0.818923	0.409461	+	0.912328i	$0.365717\pi$
$68$	−8.97201e71	−0.00544852
$69$	3.09407e74	1.04026
$70$	7.20132e74	1.35189
$71$	−1.55130e74	−0.163958	−0.0819789	−	0.996634i	$-0.526124\pi$
$71$	−1.55130e74	−0.163958	−0.0819789	+	0.996634i	$0.526124\pi$
$72$	−4.07021e75	−2.44146
$73$	3.73048e75	1.27994	0.639968	−	0.768401i	$-0.278947\pi$
$73$	3.73048e75	1.27994	0.639968	+	0.768401i	$0.278947\pi$
$74$	−3.62040e75	−0.715933
$75$	−1.63919e75	−0.188213
$76$	−1.91416e74	−0.0128537
$77$	3.77989e75	0.149487
$78$	−5.23471e76	−1.22761
$79$	−9.43898e76	−1.32138	−0.660690	−	0.750659i	$-0.729736\pi$
$79$	−9.43898e76	−1.32138	−0.660690	+	0.750659i	$0.729736\pi$
$80$	1.14003e77	0.958893
$81$	5.06429e77	2.57558
$82$	4.45217e77	1.37756
$83$	−7.99636e77	−1.51436	−0.757181	−	0.653205i	$-0.773424\pi$
$83$	−7.99636e77	−1.51436	−0.757181	+	0.653205i	$0.773424\pi$
$84$	−2.62127e76	−0.0305634
$85$	6.16969e77	0.445448
$86$	−3.03818e78	−1.36592
$87$	−6.06847e77	−0.170824
$88$	5.91526e77	0.104815
$89$	5.72264e78	0.641654	0.320827	−	0.947138i	$-0.396039\pi$
$89$	5.72264e78	0.641654	0.320827	+	0.947138i	$0.396039\pi$
$90$	−3.28366e79	−2.34173
$91$	2.04207e79	0.930879
$92$	2.21600e77	0.00648879
$93$	7.75118e79	1.46490
$94$	−7.52874e79	−0.922666
$95$	1.31629e80	1.05086
$96$	−8.25235e78	−0.0431114
$97$	−4.74987e79	−0.163090	−0.0815448	−	0.996670i	$-0.525985\pi$
$97$	−4.74987e79	−0.163090	−0.0815448	+	0.996670i	$0.525985\pi$
$98$	4.48287e80	1.01602
$99$	−1.72355e80	−0.258940
$100$	−1.17401e78	−0.00117401
$101$	−2.46714e81	−1.64884	−0.824418	−	0.565981i	$-0.808498\pi$
$101$	−2.46714e81	−1.64884	−0.824418	+	0.565981i	$0.808498\pi$
$102$	−1.95915e81	−0.878538
$103$	−4.06048e81	−1.22651	−0.613253	−	0.789887i	$-0.710139\pi$
$103$	−4.06048e81	−1.22651	−0.613253	+	0.789887i	$0.710139\pi$
$104$	3.19569e81	0.652701
$105$	1.80254e82	2.49873
$106$	5.08771e81	0.480435
$107$	−1.28964e82	−0.832578	−0.416289	−	0.909232i	$-0.636670\pi$
$107$	−1.28964e82	−0.832578	−0.416289	+	0.909232i	$0.636670\pi$
$108$	7.08567e80	0.0313848
$109$	1.24376e82	0.379284	0.189642	−	0.981853i	$-0.439267\pi$
$109$	1.24376e82	0.379284	0.189642	+	0.981853i	$0.439267\pi$
$110$	4.77217e81	0.100534
$111$	−9.06214e82	−1.32328
$112$	1.41220e83	1.43406
$113$	1.55164e83	1.09929	0.549646	−	0.835397i	$-0.314762\pi$
$113$	1.55164e83	1.09929	0.549646	+	0.835397i	$0.314762\pi$
$114$	−4.17980e83	−2.07257
$115$	−1.52386e83	−0.530495
$116$	−4.34630e80	−0.00106554
$117$	−9.31143e83	−1.61246
$118$	9.03778e83	1.10877
$119$	7.64266e83	0.666182
$120$	2.82085e84	1.75202
$121$	−2.22819e84	−0.988883
$122$	−4.02244e84	−1.27914
$123$	1.11441e85	2.54618
$124$	5.55148e82	0.00913756
$125$	8.78132e84	1.04401
$126$	−4.06762e85	−3.50214
$127$	6.04361e84	0.377786	0.188893	−	0.981998i	$-0.439510\pi$
$127$	6.04361e84	0.377786	0.188893	+	0.981998i	$0.439510\pi$
$128$	2.23533e85	1.01704
$129$	−7.60479e85	−2.52467
$130$	2.57814e85	0.626038
$131$	4.16820e85	0.742097	0.371049	−	0.928613i	$-0.378998\pi$
$131$	4.16820e85	0.742097	0.371049	+	0.928613i	$0.378998\pi$
$132$	−1.73706e83	−0.00227285
$133$	1.63055e86	1.57160
$134$	1.15742e86	0.823657
$135$	−4.87253e86	−2.56588
$136$	1.19602e86	0.467104
$137$	2.58998e85	0.0751819	0.0375909	−	0.999293i	$-0.488032\pi$
$137$	2.58998e85	0.0751819	0.0375909	+	0.999293i	$0.488032\pi$
$138$	4.83891e86	1.04627
$139$	6.24948e86	1.00866	0.504330	−	0.863511i	$-0.331740\pi$
$139$	6.24948e86	1.00866	0.504330	+	0.863511i	$0.331740\pi$
$140$	1.29100e85	0.0155862
$141$	−1.88450e87	−1.70538
$142$	−2.42613e86	−0.164906
$143$	1.35324e86	0.0692251
$144$	−6.43936e87	−2.48406
$145$	2.98878e86	0.0871143
$146$	5.83422e87	1.28734
$147$	1.12210e88	1.87792
$148$	−6.49040e85	−0.00825414
$149$	5.67560e85	0.00549501	0.00274750	−	0.999996i	$-0.499125\pi$
$149$	5.67560e85	0.00549501	0.00274750	+	0.999996i	$0.499125\pi$
$150$	−2.56359e87	−0.189301
$151$	−1.40793e87	−0.0794357	−0.0397178	−	0.999211i	$-0.512646\pi$
$151$	−1.40793e87	−0.0794357	−0.0397178	+	0.999211i	$0.512646\pi$
$152$	2.55169e88	1.10195
$153$	−3.48491e88	−1.15395
$154$	5.91149e87	0.150352
$155$	−3.81752e88	−0.747047
$156$	−9.38441e86	−0.0141534
$157$	−3.20170e87	−0.0372774	−0.0186387	−	0.999826i	$-0.505933\pi$
$157$	−3.20170e87	−0.0372774	−0.0186387	+	0.999826i	$0.505933\pi$
$158$	−1.47619e89	−1.32902
$159$	1.27349e89	0.887999
$160$	4.06435e87	0.0219853
$161$	−1.88767e89	−0.793373
$162$	7.92022e89	2.59047
$163$	−2.57931e89	−0.657516	−0.328758	−	0.944414i	$-0.606630\pi$
$163$	−2.57931e89	−0.657516	−0.328758	+	0.944414i	$0.606630\pi$
$164$	7.98154e87	0.0158822
$165$	1.19451e89	0.185819
$166$	−1.25058e90	−1.52312
$167$	3.27541e89	0.312787	0.156393	−	0.987695i	$-0.450013\pi$
$167$	3.27541e89	0.312787	0.156393	+	0.987695i	$0.450013\pi$
$168$	3.49432e90	2.62021
$169$	−9.64865e89	−0.568925
$170$	9.64898e89	0.448023
$171$	−7.43497e90	−2.72230
$172$	−5.44663e88	−0.0157480
$173$	−3.79756e90	−0.868235	−0.434117	−	0.900856i	$-0.642940\pi$
$173$	−3.79756e90	−0.868235	−0.434117	+	0.900856i	$0.642940\pi$
$174$	−9.49068e89	−0.171812
$175$	1.00006e90	0.143544
$176$	9.35836e89	0.106644
$177$	2.26222e91	2.04936
$178$	8.94983e90	0.645364
$179$	4.97996e90	0.286206	0.143103	−	0.989708i	$-0.454292\pi$
$179$	4.97996e90	0.286206	0.143103	+	0.989708i	$0.454292\pi$
$180$	−5.88671e89	−0.0269983
$181$	−1.79235e91	−0.656812	−0.328406	−	0.944537i	$-0.606511\pi$
$181$	−1.79235e91	−0.656812	−0.328406	+	0.944537i	$0.606511\pi$
$182$	3.19366e91	0.936261
$183$	−1.00685e92	−2.36426
$184$	−2.95407e91	−0.556286
$185$	4.46319e91	0.674823
$186$	1.21223e92	1.47337
$187$	5.06463e90	0.0495408
$188$	−1.34970e90	−0.0106376
$189$	−6.03581e92	−3.83736
$190$	2.05859e92	1.05694
$191$	2.44953e92	1.01679	0.508395	−	0.861124i	$-0.330239\pi$
$191$	2.44953e92	1.01679	0.508395	+	0.861124i	$0.330239\pi$
$192$	5.46762e92	1.83695
$193$	−4.95465e92	−1.34878	−0.674392	−	0.738374i	$-0.735594\pi$
$193$	−4.95465e92	−1.34878	−0.674392	+	0.738374i	$0.735594\pi$
$194$	−7.42848e91	−0.164033
$195$	6.45328e92	1.15712
$196$	8.03657e90	0.0117139
$197$	7.70778e92	0.914213	0.457107	−	0.889412i	$-0.348886\pi$
$197$	7.70778e92	0.914213	0.457107	+	0.889412i	$0.348886\pi$
$198$	−2.69553e92	−0.260437
$199$	−1.98497e93	−1.56388	−0.781942	−	0.623351i	$-0.785771\pi$
$199$	−1.98497e93	−1.56388	−0.781942	+	0.623351i	$0.785771\pi$
$200$	1.56502e92	0.100648
$201$	2.89711e93	1.52238
$202$	−3.85844e93	−1.65837
$203$	3.70233e92	0.130282
$204$	−3.51222e91	−0.0101288
$205$	−5.48858e93	−1.29846
$206$	−6.35032e93	−1.23360
$207$	8.60739e93	1.37427
$208$	5.05581e93	0.664088
$209$	1.08053e93	0.116872
$210$	2.81906e94	2.51317
$211$	−5.82704e93	−0.428557	−0.214278	−	0.976773i	$-0.568740\pi$
$211$	−5.82704e93	−0.428557	−0.214278	+	0.976773i	$0.568740\pi$
$212$	9.12088e91	0.00553904
$213$	−6.07277e93	−0.304799
$214$	−2.01691e94	−0.837392
$215$	3.74543e94	1.28749
$216$	−9.44562e94	−2.69063
$217$	−4.72893e94	−1.11723
$218$	1.94516e94	0.381477
$219$	1.46035e95	2.37941
$220$	8.55520e91	0.00115907
$221$	2.73615e94	0.308498
$222$	−1.41726e95	−1.33093
$223$	−1.14102e95	−0.893192	−0.446596	−	0.894736i	$-0.647364\pi$
$223$	−1.14102e95	−0.893192	−0.446596	+	0.894736i	$0.647364\pi$
$224$	5.03469e93	0.0328797
$225$	−4.56008e94	−0.248645
$226$	2.42666e95	1.10565
$227$	2.34171e95	0.892250	0.446125	−	0.894971i	$-0.352804\pi$
$227$	2.34171e95	0.892250	0.446125	+	0.894971i	$0.352804\pi$
$228$	−7.49325e93	−0.0238951
$229$	4.19863e95	1.12143	0.560713	−	0.828011i	$-0.310527\pi$
$229$	4.19863e95	1.12143	0.560713	+	0.828011i	$0.310527\pi$
$230$	−2.38321e95	−0.533562
$231$	1.47969e95	0.277898
$232$	5.79388e94	0.0913495
$233$	−6.11187e95	−0.809579	−0.404789	−	0.914410i	$-0.632655\pi$
$233$	−6.11187e95	−0.809579	−0.404789	+	0.914410i	$0.632655\pi$
$234$	−1.45625e96	−1.62178
$235$	9.28133e95	0.869685
$236$	1.62023e94	0.0127832
$237$	−3.69502e96	−2.45646
$238$	1.19526e96	0.670033
$239$	2.76350e96	1.30721	0.653605	−	0.756836i	$-0.273256\pi$
$239$	2.76350e96	1.30721	0.653605	+	0.756836i	$0.273256\pi$
$240$	4.46279e96	1.78259
$241$	−5.28476e96	−1.78375	−0.891876	−	0.452279i	$-0.850611\pi$
$241$	−5.28476e96	−1.78375	−0.891876	+	0.452279i	$0.850611\pi$
$242$	−3.48474e96	−0.994600
$243$	8.61840e96	2.08148
$244$	−7.21115e94	−0.0147474
$245$	−5.52642e96	−0.957674
$246$	1.74287e97	2.56090
$247$	5.83751e96	0.727781
$248$	−7.40045e96	−0.783367
$249$	−3.13029e97	−2.81521
$250$	1.37334e97	1.05005
$251$	−2.30311e97	−1.49806	−0.749029	−	0.662538i	$-0.769480\pi$
$251$	−2.30311e97	−1.49806	−0.749029	+	0.662538i	$0.769480\pi$
$252$	−7.29213e95	−0.0403769
$253$	−1.25092e96	−0.0589994
$254$	9.45181e96	0.379970
$255$	2.41521e97	0.828091
$256$	1.18873e96	0.0347829
$257$	5.56463e97	1.39042	0.695208	−	0.718809i	$-0.255312\pi$
$257$	5.56463e97	1.39042	0.695208	+	0.718809i	$0.255312\pi$
$258$	−1.18934e98	−2.53926
$259$	5.52874e97	1.00922
$260$	4.62191e95	0.00721773
$261$	−1.68819e97	−0.225674
$262$	6.51879e97	0.746388
$263$	−2.12212e97	−0.208239	−0.104120	−	0.994565i	$-0.533202\pi$
$263$	−2.12212e97	−0.208239	−0.104120	+	0.994565i	$0.533202\pi$
$264$	2.31561e97	0.194853
$265$	−6.27206e97	−0.452848
$266$	2.55006e98	1.58068
$267$	2.24021e98	1.19284
$268$	2.07494e96	0.00949611
$269$	−3.69321e98	−1.45357	−0.726785	−	0.686865i	$-0.758986\pi$
$269$	−3.69321e98	−1.45357	−0.726785	+	0.686865i	$0.758986\pi$
$270$	−7.62031e98	−2.58072
$271$	−5.67133e98	−1.65359	−0.826797	−	0.562500i	$-0.809839\pi$
$271$	−5.67133e98	−1.65359	−0.826797	+	0.562500i	$0.809839\pi$
$272$	1.89219e98	0.475253
$273$	7.99396e98	1.73051
$274$	4.05055e97	0.0756165
$275$	6.62719e96	0.0106747
$276$	8.67486e96	0.0120627
$277$	2.74564e98	0.329771	0.164886	−	0.986313i	$-0.447274\pi$
$277$	2.74564e98	0.329771	0.164886	+	0.986313i	$0.447274\pi$
$278$	9.77377e98	1.01449
$279$	2.15630e99	1.93526
$280$	−1.72098e99	−1.33621
$281$	4.51021e98	0.303104	0.151552	−	0.988449i	$-0.451573\pi$
$281$	4.51021e98	0.303104	0.151552	+	0.988449i	$0.451573\pi$
$282$	−2.94723e99	−1.71524
$283$	−3.88881e98	−0.196095	−0.0980475	−	0.995182i	$-0.531260\pi$
$283$	−3.88881e98	−0.196095	−0.0980475	+	0.995182i	$0.531260\pi$
$284$	−4.34939e96	−0.00190123
$285$	5.15280e99	1.95356
$286$	2.11637e98	0.0696253
$287$	−6.79894e99	−1.94189
$288$	−2.29572e98	−0.0569539
$289$	−3.61431e99	−0.779224
$290$	4.67425e98	0.0876179
$291$	−1.85940e99	−0.303185
$292$	1.04592e98	0.0148420
$293$	3.39457e99	0.419417	0.209709	−	0.977764i	$-0.432748\pi$
$293$	3.39457e99	0.419417	0.209709	+	0.977764i	$0.432748\pi$
$294$	1.75488e100	1.88878
$295$	−1.11417e100	−1.04510
$296$	8.65210e99	0.707631
$297$	−3.99981e99	−0.285366
$298$	8.87627e97	0.00552677
$299$	−6.75803e99	−0.367398
$300$	−4.59582e97	−0.00218249
$301$	4.63963e100	1.92548
$302$	−2.20191e99	−0.0798949
$303$	−9.65796e100	−3.06520
$304$	4.03695e100	1.12118
$305$	4.95881e100	1.20569
$306$	−5.45016e100	−1.16062
$307$	7.75380e100	1.44681	0.723403	−	0.690426i	$-0.242577\pi$
$307$	7.75380e100	1.44681	0.723403	+	0.690426i	$0.242577\pi$
$308$	1.05977e98	0.00173343
$309$	−1.58953e101	−2.28008
$310$	−5.97035e100	−0.751366
$311$	−1.53402e101	−1.69447	−0.847235	−	0.531218i	$-0.821735\pi$
$311$	−1.53402e101	−1.69447	−0.847235	+	0.531218i	$0.821735\pi$
$312$	1.25100e101	1.21338
$313$	6.55157e100	0.558213	0.279106	−	0.960260i	$-0.409962\pi$
$313$	6.55157e100	0.558213	0.279106	+	0.960260i	$0.409962\pi$
$314$	−5.00725e99	−0.0374929
$315$	5.01450e101	3.30104
$316$	−2.64641e99	−0.0153225
$317$	−3.33535e100	−0.169919	−0.0849593	−	0.996384i	$-0.527076\pi$
$317$	−3.33535e100	−0.169919	−0.0849593	+	0.996384i	$0.527076\pi$
$318$	1.99166e101	0.893133
$319$	2.45346e99	0.00968848
$320$	−2.69285e101	−0.936781
$321$	−5.04847e101	−1.54777
$322$	−2.95219e101	−0.797959
$323$	2.18475e101	0.520835
$324$	1.41988e100	0.0298661
$325$	3.58031e100	0.0664729
$326$	−4.03388e101	−0.661317
$327$	4.86889e101	0.705092
$328$	−1.06399e102	−1.36159
$329$	1.14972e102	1.30064
$330$	1.86813e101	0.186893
$331$	8.00025e101	0.708060	0.354030	−	0.935234i	$-0.384811\pi$
$331$	8.00025e101	0.708060	0.354030	+	0.935234i	$0.384811\pi$
$332$	−2.24195e100	−0.0175603
$333$	−2.52100e102	−1.74816
$334$	5.12252e101	0.314595
$335$	−1.42685e102	−0.776361
$336$	5.52826e102	2.66592
$337$	−8.78587e101	−0.375642	−0.187821	−	0.982203i	$-0.560142\pi$
$337$	−8.78587e101	−0.375642	−0.187821	+	0.982203i	$0.560142\pi$
$338$	−1.50898e102	−0.572214
$339$	6.07411e102	2.04359
$340$	1.72980e100	0.00516535
$341$	−3.13377e101	−0.0830834
$342$	−1.16278e103	−2.73804
$343$	−6.89583e100	−0.0144270
$344$	7.26069e102	1.35008
$345$	−5.96535e102	−0.986194
$346$	−5.93913e102	−0.873254
$347$	3.53536e102	0.462477	0.231239	−	0.972897i	$-0.425722\pi$
$347$	3.53536e102	0.462477	0.231239	+	0.972897i	$0.425722\pi$
$348$	−1.70142e100	−0.00198085
$349$	8.29319e102	0.859591	0.429796	−	0.902926i	$-0.358586\pi$
$349$	8.29319e102	0.859591	0.429796	+	0.902926i	$0.358586\pi$
$350$	1.56403e102	0.144374
$351$	−2.16088e103	−1.77702
$352$	3.33639e100	0.00244511
$353$	−6.04486e102	−0.394921	−0.197461	−	0.980311i	$-0.563269\pi$
$353$	−6.04486e102	−0.394921	−0.197461	+	0.980311i	$0.563269\pi$
$354$	3.53797e103	2.06121
$355$	2.99090e102	0.155436
$356$	1.60446e101	0.00744053
$357$	2.99183e103	1.23844
$358$	7.78833e102	0.287860
$359$	−5.70102e103	−1.88203	−0.941016	−	0.338361i	$-0.890127\pi$
$359$	−5.70102e103	−1.88203	−0.941016	+	0.338361i	$0.890127\pi$
$360$	7.84734e103	2.31458
$361$	8.67608e102	0.228708
$362$	−2.80312e103	−0.660609
$363$	−8.72257e103	−1.83834
$364$	5.72536e101	0.0107944
$365$	−7.19234e103	−1.21342
$366$	−1.57464e104	−2.37792
$367$	9.58383e103	1.29588	0.647938	−	0.761693i	$-0.275632\pi$
$367$	9.58383e103	1.29588	0.647938	+	0.761693i	$0.275632\pi$
$368$	−4.67354e103	−0.565991
$369$	3.10019e104	3.36372
$370$	6.98013e103	0.678724
$371$	−7.76947e103	−0.677249
$372$	2.17320e102	0.0169868
$373$	−2.02968e104	−1.42305	−0.711526	−	0.702660i	$-0.751995\pi$
$373$	−2.02968e104	−1.42305	−0.711526	+	0.702660i	$0.751995\pi$
$374$	7.92075e102	0.0498272
$375$	3.43757e104	1.94082
$376$	1.79923e104	0.911967
$377$	1.32547e103	0.0603316
$378$	−9.43961e104	−3.85955
$379$	3.03789e104	1.11605	0.558026	−	0.829824i	$-0.311559\pi$
$379$	3.03789e104	1.11605	0.558026	+	0.829824i	$0.311559\pi$
$380$	3.69049e102	0.0121856
$381$	2.36586e104	0.702307
$382$	3.83090e104	1.02267
$383$	−1.32063e104	−0.317125	−0.158563	−	0.987349i	$-0.550686\pi$
$383$	−1.32063e104	−0.317125	−0.158563	+	0.987349i	$0.550686\pi$
$384$	8.75052e104	1.89069
$385$	−7.28760e103	−0.141718
$386$	−7.74875e104	−1.35658
$387$	−2.11558e105	−3.33530
$388$	−1.33172e102	−0.00189117
$389$	7.65743e103	0.0979770	0.0489885	−	0.998799i	$-0.484400\pi$
$389$	7.65743e103	0.0979770	0.0489885	+	0.998799i	$0.484400\pi$
$390$	1.00925e105	1.16381
$391$	−2.52927e104	−0.262927
$392$	−1.07132e105	−1.00423
$393$	1.63170e105	1.37956
$394$	1.20545e105	0.919498
$395$	1.81983e105	1.25271
$396$	−4.83234e102	−0.00300264
$397$	−1.57567e105	−0.883996	−0.441998	−	0.897016i	$-0.645730\pi$
$397$	−1.57567e105	−0.883996	−0.441998	+	0.897016i	$0.645730\pi$
$398$	−3.10436e105	−1.57293
$399$	6.38300e105	2.92161
$400$	2.47598e104	0.102404
$401$	−4.32161e105	−1.61547	−0.807735	−	0.589546i	$-0.799307\pi$
$401$	−4.32161e105	−1.61547	−0.807735	+	0.589546i	$0.799307\pi$
$402$	4.53088e105	1.53118
$403$	−1.69300e105	−0.517373
$404$	−6.91713e103	−0.0191197
$405$	−9.76394e105	−2.44172
$406$	5.79019e104	0.131035
$407$	3.66378e104	0.0750510
$408$	4.68200e105	0.868350
$409$	6.40070e104	0.107506	0.0537531	−	0.998554i	$-0.482882\pi$
$409$	6.40070e104	0.107506	0.0537531	+	0.998554i	$0.482882\pi$
$410$	−8.58378e105	−1.30597
$411$	1.01388e105	0.139764
$412$	−1.13844e104	−0.0142224
$413$	−1.38017e106	−1.56298
$414$	1.34614e106	1.38222
$415$	1.54169e106	1.43566
$416$	1.80247e104	0.0152261
$417$	2.44645e106	1.87511
$418$	1.68988e105	0.117548
$419$	−1.78898e106	−1.12963	−0.564816	−	0.825217i	$-0.691053\pi$
$419$	−1.78898e106	−1.12963	−0.564816	+	0.825217i	$0.691053\pi$
$420$	5.05381e104	0.0289749
$421$	1.94480e106	1.01263	0.506314	−	0.862349i	$-0.331008\pi$
$421$	1.94480e106	1.01263	0.506314	+	0.862349i	$0.331008\pi$
$422$	−9.11310e105	−0.431034
$423$	−5.24250e106	−2.25296
$424$	−1.21587e106	−0.474864
$425$	1.33997e105	0.0475712
$426$	−9.49742e105	−0.306561
$427$	6.14270e106	1.80314
$428$	−3.61577e104	−0.00965447
$429$	5.29743e105	0.128690
$430$	5.85760e106	1.29493
$431$	−5.20354e106	−1.04706	−0.523528	−	0.852009i	$-0.675384\pi$
$431$	−5.20354e106	−1.04706	−0.523528	+	0.852009i	$0.675384\pi$
$432$	−1.49437e107	−2.73757
$433$	1.02158e107	1.70417	0.852084	−	0.523406i	$-0.175339\pi$
$433$	1.02158e107	1.70417	0.852084	+	0.523406i	$0.175339\pi$
$434$	−7.39574e106	−1.12369
$435$	1.17000e106	0.161946
$436$	3.48715e104	0.00439813
$437$	−5.39614e106	−0.620276
$438$	2.28389e107	2.39317
$439$	−1.91431e107	−1.82894	−0.914469	−	0.404655i	$-0.867392\pi$
$439$	−1.91431e107	−1.82894	−0.914469	+	0.404655i	$0.867392\pi$
$440$	−1.14046e106	−0.0993680
$441$	3.12156e107	2.48090
$442$	4.27915e106	0.310281
$443$	2.19161e107	1.45015	0.725075	−	0.688670i	$-0.241805\pi$
$443$	2.19161e107	1.45015	0.725075	+	0.688670i	$0.241805\pi$
$444$	−2.54076e105	−0.0153445
$445$	−1.10332e107	−0.608306
$446$	−1.78447e107	−0.898356
$447$	2.22180e105	0.0102153
$448$	−3.33575e107	−1.40099
$449$	−2.93038e107	−1.12447	−0.562235	−	0.826978i	$-0.690058\pi$
$449$	−2.93038e107	−1.12447	−0.562235	+	0.826978i	$0.690058\pi$
$450$	−7.13166e106	−0.250083
$451$	−4.50552e106	−0.144409
$452$	4.35034e105	0.0127473
$453$	−5.51155e106	−0.147671
$454$	3.66229e107	0.897409
$455$	−3.93710e107	−0.882499
$456$	9.98895e107	2.04854
$457$	−3.40317e107	−0.638672	−0.319336	−	0.947642i	$-0.603460\pi$
$457$	−3.40317e107	−0.638672	−0.319336	+	0.947642i	$0.603460\pi$
$458$	6.56637e107	1.12791
$459$	−8.08733e107	−1.27172
$460$	−4.27245e105	−0.00615155
$461$	2.11500e107	0.278883	0.139442	−	0.990230i	$-0.455469\pi$
$461$	2.11500e107	0.278883	0.139442	+	0.990230i	$0.455469\pi$
$462$	2.31414e107	0.279505
$463$	1.38708e108	1.53487	0.767436	−	0.641125i	$-0.221532\pi$
$463$	1.38708e108	1.53487	0.767436	+	0.641125i	$0.221532\pi$
$464$	9.16634e106	0.0929432
$465$	−1.49442e108	−1.38877
$466$	−9.55855e107	−0.814259
$467$	2.33227e108	1.82156	0.910782	−	0.412888i	$-0.135480\pi$
$467$	2.33227e108	1.82156	0.910782	+	0.412888i	$0.135480\pi$
$468$	−2.61065e106	−0.0186979
$469$	−1.76750e108	−1.16107
$470$	1.45154e108	0.874713
$471$	−1.25335e107	−0.0692989
$472$	−2.15986e108	−1.09591
$473$	3.07459e107	0.143189
$474$	−5.77877e108	−2.47066
$475$	2.85880e107	0.112226
$476$	2.14278e106	0.00772495
$477$	3.54273e108	1.17312
$478$	4.32194e108	1.31477
$479$	2.96776e108	0.829546	0.414773	−	0.909925i	$-0.363861\pi$
$479$	2.96776e108	0.829546	0.414773	+	0.909925i	$0.363861\pi$
$480$	1.59105e107	0.0408708
$481$	1.97934e108	0.467353
$482$	−8.26501e108	−1.79407
$483$	−7.38954e108	−1.47489
$484$	−6.24720e106	−0.0114670
$485$	9.15773e107	0.154614
$486$	1.34786e109	2.09351
$487$	5.10610e108	0.729737	0.364869	−	0.931059i	$-0.381114\pi$
$487$	5.10610e108	0.729737	0.364869	+	0.931059i	$0.381114\pi$
$488$	9.61290e108	1.26430
$489$	−1.00971e109	−1.22233
$490$	−8.64296e108	−0.963211
$491$	3.12833e108	0.321006	0.160503	−	0.987035i	$-0.448688\pi$
$491$	3.12833e108	0.321006	0.160503	+	0.987035i	$0.448688\pi$
$492$	3.12449e107	0.0295251
$493$	4.96071e107	0.0431762
$494$	9.12947e108	0.731989
$495$	3.32301e108	0.245483
$496$	−1.17080e109	−0.797033
$497$	3.70495e108	0.232460
$498$	−4.89556e109	−2.83148
$499$	−2.04358e109	−1.08973	−0.544865	−	0.838524i	$-0.683419\pi$
$499$	−2.04358e109	−1.08973	−0.544865	+	0.838524i	$0.683419\pi$
$500$	2.46203e107	0.0121062
$501$	1.28221e109	0.581473
$502$	−3.60191e109	−1.50672
$503$	1.45113e109	0.560018	0.280009	−	0.959997i	$-0.409662\pi$
$503$	1.45113e109	0.560018	0.280009	+	0.959997i	$0.409662\pi$
$504$	9.72085e109	3.46152
$505$	4.75663e109	1.56314
$506$	−1.95635e108	−0.0593405
$507$	−3.77710e109	−1.05764
$508$	1.69445e107	0.00438075
$509$	7.81037e109	1.86467	0.932334	−	0.361598i	$-0.117769\pi$
$509$	7.81037e109	1.86467	0.932334	+	0.361598i	$0.117769\pi$
$510$	3.77723e109	0.832878
$511$	−8.90947e109	−1.81470
$512$	−5.21879e109	−0.982056
$513$	−1.72541e110	−3.00013
$514$	8.70271e109	1.39845
$515$	7.82858e109	1.16276
$516$	−2.13216e108	−0.0292757
$517$	7.61895e108	0.0967227
$518$	8.64659e109	1.01505
$519$	−1.48661e110	−1.61406
$520$	−6.16128e109	−0.618779
$521$	4.76883e109	0.443082	0.221541	−	0.975151i	$-0.428891\pi$
$521$	4.76883e109	0.443082	0.221541	+	0.975151i	$0.428891\pi$
$522$	−2.64022e109	−0.226978
$523$	2.46701e109	0.196269	0.0981347	−	0.995173i	$-0.468712\pi$
$523$	2.46701e109	0.196269	0.0981347	+	0.995173i	$0.468712\pi$
$524$	1.16864e108	0.00860526
$525$	3.91488e109	0.266849
$526$	−3.31886e109	−0.209443
$527$	−6.33626e109	−0.370257
$528$	3.66346e109	0.198252
$529$	−1.37035e110	−0.686873
$530$	−9.80908e109	−0.455466
$531$	6.29329e110	2.70738
$532$	4.57157e108	0.0182240
$533$	−2.43409e110	−0.899258
$534$	3.50354e110	1.19974
$535$	2.48642e110	0.789307
$536$	−2.76602e110	−0.814106
$537$	1.94948e110	0.532059
$538$	−5.77593e110	−1.46197
$539$	−4.53659e109	−0.106508
$540$	−1.36611e109	−0.0297536
$541$	7.51723e110	1.51904	0.759519	−	0.650485i	$-0.225434\pi$
$541$	7.51723e110	1.51904	0.759519	+	0.650485i	$0.225434\pi$
$542$	−8.86959e110	−1.66315
$543$	−7.01642e110	−1.22102
$544$	6.74594e108	0.0108965
$545$	−2.39797e110	−0.359572
$546$	1.25020e111	1.74052
$547$	7.64074e110	0.987753	0.493877	−	0.869532i	$-0.335579\pi$
$547$	7.64074e110	0.987753	0.493877	+	0.869532i	$0.335579\pi$
$548$	7.26154e107	0.000871799 0
$549$	−2.80095e111	−3.12339
$550$	1.03645e109	0.0107364
$551$	1.05836e110	0.101857
$552$	−1.15641e111	−1.03414
$553$	2.25431e111	1.87346
$554$	4.29400e110	0.331678
$555$	1.74718e111	1.25450
$556$	1.75217e109	0.0116963
$557$	−7.81954e110	−0.485340	−0.242670	−	0.970109i	$-0.578023\pi$
$557$	−7.81954e110	−0.485340	−0.242670	+	0.970109i	$0.578023\pi$
$558$	3.37231e111	1.94645
$559$	1.66103e111	0.891660
$560$	−2.72272e111	−1.35953
$561$	1.98262e110	0.0920967
$562$	7.05368e110	0.304856
$563$	−8.86900e110	−0.356685	−0.178342	−	0.983968i	$-0.557073\pi$
$563$	−8.86900e110	−0.356685	−0.178342	+	0.983968i	$0.557073\pi$
$564$	−5.28359e109	−0.0197754
$565$	−2.99155e111	−1.04216
$566$	−6.08185e110	−0.197229
$567$	−1.20950e112	−3.65168
$568$	5.79799e110	0.162993
$569$	9.86466e109	0.0258247	0.0129124	−	0.999917i	$-0.495890\pi$
$569$	9.86466e109	0.0258247	0.0129124	+	0.999917i	$0.495890\pi$
$570$	8.05864e111	1.96485
$571$	1.70758e111	0.387810	0.193905	−	0.981020i	$-0.437885\pi$
$571$	1.70758e111	0.387810	0.193905	+	0.981020i	$0.437885\pi$
$572$	3.79408e108	0.000802725 0
$573$	9.58903e111	1.89022
$574$	−1.06331e112	−1.95312
$575$	−3.30960e110	−0.0566537
$576$	1.52104e112	2.42677
$577$	1.48752e111	0.221229	0.110615	−	0.993863i	$-0.464718\pi$
$577$	1.48752e111	0.221229	0.110615	+	0.993863i	$0.464718\pi$
$578$	−5.65254e111	−0.783729
$579$	−1.93957e112	−2.50740
$580$	8.37965e108	0.00101017
$581$	1.90976e112	2.14707
$582$	−2.90798e111	−0.304938
$583$	−5.14867e110	−0.0503638
$584$	−1.39427e112	−1.27241
$585$	1.79524e112	1.52866
$586$	5.30888e111	0.421842
$587$	6.52767e111	0.484078	0.242039	−	0.970267i	$-0.422184\pi$
$587$	6.52767e111	0.484078	0.242039	+	0.970267i	$0.422184\pi$
$588$	3.14603e110	0.0217762
$589$	−1.35183e112	−0.873477
$590$	−1.74248e112	−1.05114
$591$	3.01732e112	1.69953
$592$	1.36882e112	0.719976
$593$	−2.55079e112	−1.25303	−0.626513	−	0.779411i	$-0.715518\pi$
$593$	−2.55079e112	−1.25303	−0.626513	+	0.779411i	$0.715518\pi$
$594$	−6.25543e111	−0.287016
$595$	−1.47350e112	−0.631559
$596$	1.59127e108	6.37193e−5 0
$597$	−7.77045e112	−2.90727
$598$	−1.05691e112	−0.369522
$599$	1.79162e112	0.585411	0.292705	−	0.956203i	$-0.405445\pi$
$599$	1.79162e112	0.585411	0.292705	+	0.956203i	$0.405445\pi$
$600$	6.12651e111	0.187106
$601$	2.81748e112	0.804350	0.402175	−	0.915563i	$-0.368254\pi$
$601$	2.81748e112	0.804350	0.402175	+	0.915563i	$0.368254\pi$
$602$	7.25607e112	1.93662
$603$	8.05947e112	2.01120
$604$	−3.94743e109	−0.000921125 0
$605$	4.29594e112	0.937489
$606$	−1.51044e113	−3.08292
$607$	−2.82075e112	−0.538547	−0.269273	−	0.963064i	$-0.586784\pi$
$607$	−2.82075e112	−0.538547	−0.269273	+	0.963064i	$0.586784\pi$
$608$	1.43923e111	0.0257061
$609$	1.44933e112	0.242196
$610$	7.75526e112	1.21266
$611$	4.11610e112	0.602306
$612$	−9.77066e110	−0.0133811
$613$	2.74764e112	0.352217	0.176109	−	0.984371i	$-0.443649\pi$
$613$	2.74764e112	0.352217	0.176109	+	0.984371i	$0.443649\pi$
$614$	1.21264e113	1.45517
$615$	−2.14858e113	−2.41385
$616$	−1.41274e112	−0.148608
$617$	−9.38674e112	−0.924625	−0.462313	−	0.886717i	$-0.652980\pi$
$617$	−9.38674e112	−0.924625	−0.462313	+	0.886717i	$0.652980\pi$
$618$	−2.48592e113	−2.29326
$619$	1.67031e113	1.44320	0.721598	−	0.692312i	$-0.243408\pi$
$619$	1.67031e113	1.44320	0.721598	+	0.692312i	$0.243408\pi$
$620$	−1.07032e111	−0.00866266
$621$	1.99750e113	1.51452
$622$	−2.39910e113	−1.70427
$623$	−1.36673e113	−0.909741
$624$	1.97917e113	1.23455
$625$	−1.51985e113	−0.888506
$626$	1.02462e113	0.561440
$627$	4.22988e112	0.217267
$628$	−8.97665e109	−0.000432263 0
$629$	7.40791e112	0.334460
$630$	7.84235e113	3.32012
$631$	−3.81210e113	−1.51347	−0.756737	−	0.653720i	$-0.773207\pi$
$631$	−3.81210e113	−1.51347	−0.756737	+	0.653720i	$0.773207\pi$
$632$	3.52783e113	1.31361
$633$	−2.28108e113	−0.796691
$634$	−5.21626e112	−0.170901
$635$	−1.16521e113	−0.358151
$636$	3.57050e111	0.0102971
$637$	−2.45087e113	−0.663244
$638$	3.83704e111	0.00974449
$639$	−1.68939e113	−0.402666
$640$	−4.30971e113	−0.964182
$641$	3.45863e113	0.726363	0.363181	−	0.931718i	$-0.381691\pi$
$641$	3.45863e113	0.726363	0.363181	+	0.931718i	$0.381691\pi$
$642$	−7.89548e113	−1.55672
$643$	3.92122e113	0.725899	0.362950	−	0.931809i	$-0.381770\pi$
$643$	3.92122e113	0.725899	0.362950	+	0.931809i	$0.381770\pi$
$644$	−5.29247e111	−0.00919984
$645$	1.46620e114	2.39345
$646$	3.41681e113	0.523846
$647$	4.31703e113	0.621672	0.310836	−	0.950463i	$-0.399391\pi$
$647$	4.31703e113	0.621672	0.310836	+	0.950463i	$0.399391\pi$
$648$	−1.89279e114	−2.56043
$649$	−9.14607e112	−0.116232
$650$	5.59937e112	0.0668572
$651$	−1.85121e114	−2.07695
$652$	−7.23164e111	−0.00762446
$653$	5.70426e113	0.565218	0.282609	−	0.959235i	$-0.408800\pi$
$653$	5.70426e113	0.565218	0.282609	+	0.959235i	$0.408800\pi$
$654$	7.61462e113	0.709168
$655$	−8.03627e113	−0.703529
$656$	−1.68330e114	−1.38534
$657$	4.06255e114	3.14341
$658$	1.79808e114	1.30816
$659$	−1.52696e114	−1.04465	−0.522324	−	0.852747i	$-0.674935\pi$
$659$	−1.52696e114	−1.04465	−0.522324	+	0.852747i	$0.674935\pi$
$660$	3.34905e111	0.00215473
$661$	1.43598e114	0.868939	0.434470	−	0.900686i	$-0.356936\pi$
$661$	1.43598e114	0.868939	0.434470	+	0.900686i	$0.356936\pi$
$662$	1.25119e114	0.712153
$663$	1.07110e114	0.573500
$664$	2.98865e114	1.50545
$665$	−3.14368e114	−1.48992
$666$	−3.94268e114	−1.75827
$667$	−1.22525e113	−0.0514196
$668$	9.18329e111	0.00362703
$669$	−4.46667e114	−1.66045
$670$	−2.23150e114	−0.780849
$671$	4.07064e113	0.134091
$672$	1.97090e113	0.0611237
$673$	2.12684e114	0.621047	0.310524	−	0.950566i	$-0.399496\pi$
$673$	2.12684e114	0.621047	0.310524	+	0.950566i	$0.399496\pi$
$674$	−1.37405e114	−0.377813
$675$	−1.05825e114	−0.274021
$676$	−2.70520e112	−0.00659718
$677$	−2.60216e114	−0.597713	−0.298857	−	0.954298i	$-0.596605\pi$
$677$	−2.60216e114	−0.597713	−0.298857	+	0.954298i	$0.596605\pi$
$678$	9.49950e114	2.05541
$679$	1.13441e114	0.231230
$680$	−2.30593e114	−0.442828
$681$	9.16697e114	1.65870
$682$	−4.90100e113	−0.0835637
$683$	−1.14716e115	−1.84325	−0.921624	−	0.388084i	$-0.873137\pi$
$683$	−1.14716e115	−1.84325	−0.921624	+	0.388084i	$0.873137\pi$
$684$	−2.08455e113	−0.0315675
$685$	−4.99347e113	−0.0712745
$686$	−1.07846e113	−0.0145104
$687$	1.64361e115	2.08474
$688$	1.14869e115	1.37364
$689$	−2.78155e114	−0.313623
$690$	−9.32941e114	−0.991896
$691$	−1.28895e115	−1.29234	−0.646170	−	0.763194i	$-0.723630\pi$
$691$	−1.28895e115	−1.29234	−0.646170	+	0.763194i	$0.723630\pi$
$692$	−1.06472e113	−0.0100679
$693$	4.11635e114	0.367127
$694$	5.52907e114	0.465151
$695$	−1.20490e115	−0.956237
$696$	2.26810e114	0.169819
$697$	−9.10984e114	−0.643552
$698$	1.29700e115	0.864561
$699$	−2.39258e115	−1.50501
$700$	2.80388e112	0.00166452
$701$	3.94817e114	0.221216	0.110608	−	0.993864i	$-0.464720\pi$
$701$	3.94817e114	0.221216	0.110608	+	0.993864i	$0.464720\pi$
$702$	−3.37947e115	−1.78729
$703$	1.58046e115	0.789030
$704$	−2.21053e114	−0.104185
$705$	3.63331e115	1.61675
$706$	−9.45376e114	−0.397204
$707$	5.89225e115	2.33773
$708$	6.34261e113	0.0237641
$709$	5.25234e114	0.185858	0.0929288	−	0.995673i	$-0.470377\pi$
$709$	5.25234e114	0.185858	0.0929288	+	0.995673i	$0.470377\pi$
$710$	4.67756e114	0.156335
$711$	−1.02792e116	−3.24519
$712$	−2.13884e115	−0.637880
$713$	1.56500e115	0.440948
$714$	4.67902e115	1.24560
$715$	−2.60903e114	−0.0656273
$716$	1.39624e113	0.00331880
$717$	1.08181e116	2.43011
$718$	−8.91601e115	−1.89291
$719$	−3.09564e115	−0.621199	−0.310599	−	0.950541i	$-0.600530\pi$
$719$	−3.09564e115	−0.621199	−0.310599	+	0.950541i	$0.600530\pi$
$720$	1.24151e116	2.35496
$721$	9.69761e115	1.73895
$722$	1.35688e115	0.230030
$723$	−2.06879e116	−3.31601
$724$	−5.02523e113	−0.00761631
$725$	6.49121e113	0.00930328
$726$	−1.36415e116	−1.84897
$727$	−8.85677e114	−0.113535	−0.0567677	−	0.998387i	$-0.518079\pi$
$727$	−8.85677e114	−0.113535	−0.0567677	+	0.998387i	$0.518079\pi$
$728$	−7.63225e115	−0.925404
$729$	1.12815e116	1.29391
$730$	−1.12483e116	−1.22043
$731$	6.21659e115	0.638115
$732$	−2.82291e114	−0.0274156
$733$	−3.53718e115	−0.325047	−0.162523	−	0.986705i	$-0.551963\pi$
$733$	−3.53718e115	−0.325047	−0.162523	+	0.986705i	$0.551963\pi$
$734$	1.49885e116	1.30337
$735$	−2.16340e116	−1.78032
$736$	−1.66618e114	−0.0129769
$737$	−1.17129e115	−0.0863436
$738$	4.84849e116	3.38317
$739$	2.26661e116	1.49719	0.748594	−	0.663029i	$-0.230729\pi$
$739$	2.26661e116	1.49719	0.748594	+	0.663029i	$0.230729\pi$
$740$	1.25135e114	0.00782516
$741$	2.28517e116	1.35295
$742$	−1.21509e116	−0.681164
$743$	7.67500e115	0.407410	0.203705	−	0.979032i	$-0.434702\pi$
$743$	7.67500e115	0.407410	0.203705	+	0.979032i	$0.434702\pi$
$744$	−2.89701e116	−1.45628
$745$	−1.09425e114	−0.00520942
$746$	−3.17429e116	−1.43128
$747$	−8.70816e116	−3.71913
$748$	1.41998e113	0.000574468 0
$749$	3.08004e116	1.18044
$750$	5.37614e116	1.95204
$751$	3.77305e116	1.29800	0.649001	−	0.760787i	$-0.275187\pi$
$751$	3.77305e116	1.29800	0.649001	+	0.760787i	$0.275187\pi$
$752$	2.84651e116	0.927877
$753$	−9.01584e116	−2.78490
$754$	2.07294e115	0.0606804
$755$	2.71449e115	0.0753072
$756$	−1.69227e115	−0.0444975
$757$	−3.29108e116	−0.820267	−0.410134	−	0.912025i	$-0.634518\pi$
$757$	−3.29108e116	−0.820267	−0.410134	+	0.912025i	$0.634518\pi$
$758$	4.75106e116	1.12250
$759$	−4.89689e115	−0.109680
$760$	−4.91965e116	−1.04468
$761$	1.07592e116	0.216622	0.108311	−	0.994117i	$-0.465456\pi$
$761$	1.07592e116	0.216622	0.108311	+	0.994117i	$0.465456\pi$
$762$	3.70004e116	0.706367
$763$	−2.97047e116	−0.537751
$764$	6.86776e114	0.0117906
$765$	6.71888e116	1.09398
$766$	−2.06538e116	−0.318959
$767$	−4.94112e116	−0.723791
$768$	4.65347e115	0.0646617
$769$	9.26857e116	1.22179	0.610894	−	0.791712i	$-0.290810\pi$
$769$	9.26857e116	1.22179	0.610894	+	0.791712i	$0.290810\pi$
$770$	−1.13973e116	−0.142537
$771$	2.17835e117	2.58479
$772$	−1.38914e115	−0.0156403
$773$	2.42790e115	0.0259395	0.0129697	−	0.999916i	$-0.495871\pi$
$773$	2.42790e115	0.0259395	0.0129697	+	0.999916i	$0.495871\pi$
$774$	−3.30863e117	−3.35459
$775$	−8.29114e115	−0.0797802
$776$	1.77527e116	0.162130
$777$	2.16430e117	1.87615
$778$	1.19757e116	0.0985434
$779$	−1.94357e117	−1.51821
$780$	1.80931e115	0.0134178
$781$	2.45520e115	0.0172870
$782$	−3.95561e116	−0.264448
$783$	−3.91774e116	−0.248705
$784$	−1.69491e117	−1.02175
$785$	6.17287e115	0.0353400
$786$	2.55187e117	1.38754
$787$	−1.32932e117	−0.686520	−0.343260	−	0.939240i	$-0.611531\pi$
$787$	−1.32932e117	−0.686520	−0.343260	+	0.939240i	$0.611531\pi$
$788$	2.16104e115	0.0106011
$789$	−8.30734e116	−0.387118
$790$	2.84610e117	1.25995
$791$	−3.70577e117	−1.55858
$792$	6.44181e116	0.257417
$793$	2.19915e117	0.835006
$794$	−2.46425e117	−0.889106
$795$	−2.45529e117	−0.841848
$796$	−5.56528e115	−0.0181346
$797$	2.26174e117	0.700457	0.350228	−	0.936664i	$-0.386104\pi$
$797$	2.26174e117	0.700457	0.350228	+	0.936664i	$0.386104\pi$
$798$	9.98259e117	2.93850
$799$	1.54050e117	0.431039
$800$	8.82722e114	0.00234790
$801$	6.23204e117	1.57584
$802$	−6.75871e117	−1.62481
$803$	−5.90412e116	−0.134951
$804$	8.12264e115	0.0176534
$805$	3.63941e117	0.752139
$806$	−2.64775e117	−0.520364
$807$	−1.44576e118	−2.70220
$808$	9.22095e117	1.63914
$809$	−5.92877e117	−1.00242	−0.501209	−	0.865326i	$-0.667111\pi$
$809$	−5.92877e117	−1.00242	−0.501209	+	0.865326i	$0.667111\pi$
$810$	−1.52701e118	−2.45584
$811$	1.14257e118	1.74799	0.873997	−	0.485931i	$-0.161519\pi$
$811$	1.14257e118	1.74799	0.873997	+	0.485931i	$0.161519\pi$
$812$	1.03802e115	0.00151074
$813$	−2.22012e118	−3.07404
$814$	5.72992e116	0.0754848
$815$	4.97291e117	0.623343
$816$	7.40726e117	0.883499
$817$	1.32630e118	1.50538
$818$	1.00103e117	0.108128
$819$	2.22384e118	2.28616
$820$	−1.53884e116	−0.0150568
$821$	−1.25595e118	−1.16970	−0.584850	−	0.811141i	$-0.698847\pi$
$821$	−1.25595e118	−1.16970	−0.584850	+	0.811141i	$0.698847\pi$
$822$	1.58565e117	0.140572
$823$	−4.90534e117	−0.413977	−0.206988	−	0.978343i	$-0.566366\pi$
$823$	−4.90534e117	−0.413977	−0.206988	+	0.978343i	$0.566366\pi$
$824$	1.51761e118	1.21929
$825$	2.59431e116	0.0198443
$826$	−2.15849e118	−1.57202
$827$	−3.08704e116	−0.0214077	−0.0107038	−	0.999943i	$-0.503407\pi$
$827$	−3.08704e116	−0.0214077	−0.0107038	+	0.999943i	$0.503407\pi$
$828$	2.41326e116	0.0159359
$829$	−2.29643e118	−1.44409	−0.722047	−	0.691844i	$-0.756798\pi$
$829$	−2.29643e118	−1.44409	−0.722047	+	0.691844i	$0.756798\pi$
$830$	2.41111e118	1.44396
$831$	1.07482e118	0.613048
$832$	−1.19423e118	−0.648774
$833$	−9.17266e117	−0.474649
$834$	3.82608e118	1.88595
$835$	−6.31498e117	−0.296531
$836$	3.02949e115	0.00135524
$837$	5.00407e118	2.13276
$838$	−2.79784e118	−1.13616
$839$	−1.33498e118	−0.516552	−0.258276	−	0.966071i	$-0.583154\pi$
$839$	−1.33498e118	−0.516552	−0.258276	+	0.966071i	$0.583154\pi$
$840$	−6.73703e118	−2.48403
$841$	−2.82199e118	−0.991556
$842$	3.04154e118	1.01848
$843$	1.76559e118	0.563472
$844$	−1.63373e116	−0.00496949
$845$	1.86026e118	0.539357
$846$	−8.19892e118	−2.26598
$847$	5.32157e118	1.40205
$848$	−1.92359e118	−0.483148
$849$	−1.52233e118	−0.364542
$850$	2.09563e117	0.0478462
$851$	−1.82969e118	−0.398317
$852$	−1.70263e116	−0.00353441
$853$	−4.31034e118	−0.853249	−0.426625	−	0.904429i	$-0.640297\pi$
$853$	−4.31034e118	−0.853249	−0.426625	+	0.904429i	$0.640297\pi$
$854$	9.60678e118	1.81357
$855$	1.43346e119	2.58082
$856$	4.82004e118	0.827682
$857$	9.71669e117	0.159146	0.0795729	−	0.996829i	$-0.474644\pi$
$857$	9.71669e117	0.159146	0.0795729	+	0.996829i	$0.474644\pi$
$858$	8.28483e117	0.129434
$859$	3.21532e118	0.479183	0.239591	−	0.970874i	$-0.422987\pi$
$859$	3.21532e118	0.479183	0.239591	+	0.970874i	$0.422987\pi$
$860$	1.05011e117	0.0149296
$861$	−2.66154e119	−3.60999
$862$	−8.13799e118	−1.05311
$863$	8.11311e118	1.00173	0.500865	−	0.865526i	$-0.333015\pi$
$863$	8.11311e118	1.00173	0.500865	+	0.865526i	$0.333015\pi$
$864$	−5.32762e117	−0.0627664
$865$	7.32168e118	0.823111
$866$	1.59768e119	1.71402
$867$	−1.41487e119	−1.44858
$868$	−1.32585e117	−0.0129553
$869$	1.49388e118	0.139321
$870$	1.82980e118	0.162882
$871$	−6.32783e118	−0.537674
$872$	−4.64858e118	−0.377053
$873$	−5.17268e118	−0.400534
$874$	−8.43920e118	−0.623861
$875$	−2.09724e119	−1.48020
$876$	4.09439e117	0.0275913
$877$	1.38571e119	0.891639	0.445819	−	0.895123i	$-0.352912\pi$
$877$	1.38571e119	0.891639	0.445819	+	0.895123i	$0.352912\pi$
$878$	−2.99385e119	−1.83951
$879$	1.32885e119	0.779700
$880$	−1.80429e118	−0.101101
$881$	2.88620e119	1.54455	0.772274	−	0.635289i	$-0.219119\pi$
$881$	2.88620e119	1.54455	0.772274	+	0.635289i	$0.219119\pi$
$882$	4.88192e119	2.49524
$883$	1.87269e119	0.914232	0.457116	−	0.889407i	$-0.348882\pi$
$883$	1.87269e119	0.914232	0.457116	+	0.889407i	$0.348882\pi$
$884$	7.67135e116	0.00357730
$885$	−4.36156e119	−1.94285
$886$	3.42754e119	1.45853
$887$	−2.20296e119	−0.895572	−0.447786	−	0.894141i	$-0.647787\pi$
$887$	−2.20296e119	−0.895572	−0.447786	+	0.894141i	$0.647787\pi$
$888$	3.38699e119	1.31549
$889$	−1.44339e119	−0.535627
$890$	−1.72552e119	−0.611823
$891$	−8.01512e118	−0.271558
$892$	−3.19908e117	−0.0103573
$893$	3.28662e119	1.01687
$894$	3.47474e117	0.0102743
$895$	−9.60135e118	−0.271331
$896$	−5.33862e119	−1.44197
$897$	−2.64552e119	−0.682996
$898$	−4.58293e119	−1.13097
$899$	−3.06947e118	−0.0724095
$900$	−1.27851e117	−0.00288326
$901$	−1.04102e119	−0.224443
$902$	−7.04633e118	−0.145244
$903$	1.81625e120	3.57949
$904$	−5.79926e119	−1.09283
$905$	3.45565e119	0.622676
$906$	−8.61970e118	−0.148525
$907$	1.17862e120	1.94214	0.971069	−	0.238798i	$-0.0767533\pi$
$907$	1.17862e120	1.94214	0.971069	+	0.238798i	$0.0767533\pi$
$908$	6.56548e117	0.0103464
$909$	−2.68675e120	−4.04939
$910$	−6.15736e119	−0.887601
$911$	−7.70017e119	−1.06171	−0.530855	−	0.847463i	$-0.678129\pi$
$911$	−7.70017e119	−1.06171	−0.530855	+	0.847463i	$0.678129\pi$
$912$	1.58032e120	2.08427
$913$	1.26556e119	0.159668
$914$	−5.32233e119	−0.642364
$915$	1.94120e120	2.24138
$916$	1.17717e118	0.0130039
$917$	−9.95488e119	−1.05215
$918$	−1.26480e120	−1.27907
$919$	8.06001e119	0.779933	0.389967	−	0.920829i	$-0.372487\pi$
$919$	8.06001e119	0.779933	0.389967	+	0.920829i	$0.372487\pi$
$920$	5.69543e119	0.527375
$921$	3.03534e120	2.68963
$922$	3.30772e119	0.280495
$923$	1.32641e119	0.107649
$924$	4.14862e117	0.00322247
$925$	9.69342e118	0.0720671
$926$	2.16931e120	1.54375
$927$	−4.42192e120	−3.01219
$928$	3.26793e117	0.00213098
$929$	5.26281e119	0.328535	0.164267	−	0.986416i	$-0.447474\pi$
$929$	5.26281e119	0.328535	0.164267	+	0.986416i	$0.447474\pi$
$930$	−2.33718e120	−1.39680
$931$	−1.95697e120	−1.11975
$932$	−1.71359e118	−0.00938776
$933$	−6.00512e120	−3.15003
$934$	3.64751e120	1.83209
$935$	−9.76459e118	−0.0469660
$936$	3.48016e120	1.60298
$937$	3.47611e118	0.0153335	0.00766673	−	0.999971i	$-0.497560\pi$
$937$	3.47611e118	0.0153335	0.00766673	+	0.999971i	$0.497560\pi$
$938$	−2.76426e120	−1.16779
$939$	2.56470e120	1.03772
$940$	2.60221e118	0.0100847
$941$	−7.54819e119	−0.280197	−0.140098	−	0.990138i	$-0.544742\pi$
$941$	−7.54819e119	−0.280197	−0.140098	+	0.990138i	$0.544742\pi$
$942$	−1.96016e119	−0.0696996
$943$	2.25005e120	0.766422
$944$	−3.41706e120	−1.11503
$945$	1.16370e121	3.63792
$946$	4.80845e119	0.144017
$947$	−3.26959e120	−0.938250	−0.469125	−	0.883132i	$-0.655431\pi$
$947$	−3.26959e120	−0.938250	−0.469125	+	0.883132i	$0.655431\pi$
$948$	−1.03598e119	−0.0284847
$949$	−3.18968e120	−0.840359
$950$	4.47097e119	0.112875
$951$	−1.30567e120	−0.315880
$952$	−2.85645e120	−0.662263
$953$	6.16270e120	1.36933	0.684666	−	0.728857i	$-0.259948\pi$
$953$	6.16270e120	1.36933	0.684666	+	0.728857i	$0.259948\pi$
$954$	5.54059e120	1.17991
$955$	−4.72268e120	−0.963945
$956$	7.74806e118	0.0151582
$957$	9.60440e118	0.0180110
$958$	4.64138e120	0.834342
$959$	−6.18563e119	−0.106593
$960$	−1.05415e121	−1.74148
$961$	−2.39330e120	−0.379054
$962$	3.09556e120	0.470055
$963$	−1.40444e121	−2.04474
$964$	−1.48169e119	−0.0206842
$965$	9.55255e120	1.27868
$966$	−1.15567e121	−1.48341
$967$	−9.04508e119	−0.111337	−0.0556686	−	0.998449i	$-0.517729\pi$
$967$	−9.04508e119	−0.111337	−0.0556686	+	0.998449i	$0.517729\pi$
$968$	8.32789e120	0.983067
$969$	8.55252e120	0.968236
$970$	1.43221e120	0.155507
$971$	−5.16605e120	−0.537997	−0.268998	−	0.963141i	$-0.586693\pi$
$971$	−5.16605e120	−0.537997	−0.268998	+	0.963141i	$0.586693\pi$
$972$	2.41635e119	0.0241366
$973$	−1.49256e121	−1.43008
$974$	7.98560e120	0.733956
$975$	1.40156e120	0.123574
$976$	1.52083e121	1.28636
$977$	2.45665e121	1.99348	0.996742	−	0.0806580i	$-0.0257022\pi$
$977$	2.45665e121	1.99348	0.996742	+	0.0806580i	$0.0257022\pi$
$978$	−1.57912e121	−1.22939
$979$	−9.05706e119	−0.0676532
$980$	−1.54945e119	−0.0111051
$981$	1.35448e121	0.931487
$982$	4.89251e120	0.322861
$983$	−5.44000e120	−0.344494	−0.172247	−	0.985054i	$-0.555103\pi$
$983$	−5.44000e120	−0.344494	−0.172247	+	0.985054i	$0.555103\pi$
$984$	−4.16513e121	−2.53120
$985$	−1.48606e121	−0.866699
$986$	7.75823e119	0.0434258
$987$	4.50074e121	2.41790
$988$	1.63667e119	0.00843925
$989$	−1.53544e121	−0.759947
$990$	5.19696e120	0.246902
$991$	−6.39891e120	−0.291826	−0.145913	−	0.989297i	$-0.546612\pi$
$991$	−6.39891e120	−0.291826	−0.145913	+	0.989297i	$0.546612\pi$
$992$	−4.17408e119	−0.0182742
$993$	3.13181e121	1.31629
$994$	5.79430e120	0.233804
$995$	3.82702e121	1.48261
$996$	−8.77641e119	−0.0326448
$997$	−3.98545e121	−1.42339	−0.711694	−	0.702490i	$-0.752072\pi$
$997$	−3.98545e121	−1.42339	−0.711694	+	0.702490i	$0.752072\pi$
$998$	−3.19602e121	−1.09603
$999$	−5.85042e121	−1.92657

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.56393e12 q^{2} +3.91464e19 q^{3} +2.80371e22 q^{4} -1.92800e28 q^{5} +6.12224e31 q^{6} -2.38829e34 q^{7} -3.73751e36 q^{8} +1.08902e39 q^{9} +O(q^{10})\)	\(q+1.56393e12 q^{2} +3.91464e19 q^{3} +2.80371e22 q^{4} -1.92800e28 q^{5} +6.12224e31 q^{6} -2.38829e34 q^{7} -3.73751e36 q^{8} +1.08902e39 q^{9} -3.01526e40 q^{10} -1.58267e41 q^{11} +1.09755e42 q^{12} -8.55032e44 q^{13} -3.73513e46 q^{14} -7.54741e47 q^{15} -5.91301e48 q^{16} -3.20005e49 q^{17} +1.70315e51 q^{18} -6.82724e51 q^{19} -5.40554e50 q^{20} -9.34931e53 q^{21} -2.47519e53 q^{22} +7.90383e54 q^{23} -1.46310e56 q^{24} -4.18734e55 q^{25} -1.33721e57 q^{26} +2.52725e58 q^{27} -6.69608e56 q^{28} -1.55020e58 q^{29} -1.18037e60 q^{30} +1.98005e60 q^{31} -2.10807e59 q^{32} -6.19560e60 q^{33} -5.00467e61 q^{34} +4.60462e62 q^{35} +3.05328e61 q^{36} -2.31493e63 q^{37} -1.06774e64 q^{38} -3.34714e64 q^{39} +7.20591e64 q^{40} +2.84678e65 q^{41} -1.46217e66 q^{42} -1.94265e66 q^{43} -4.43735e63 q^{44} -2.09962e67 q^{45} +1.23611e67 q^{46} -4.81398e67 q^{47} -2.31473e68 q^{48} +2.86641e68 q^{49} -6.54872e67 q^{50} -1.25271e69 q^{51} -2.39726e67 q^{52} +3.25315e69 q^{53} +3.95245e70 q^{54} +3.05139e69 q^{55} +8.92627e70 q^{56} -2.67262e71 q^{57} -2.42441e70 q^{58} +5.77888e71 q^{59} -2.11607e70 q^{60} -2.57200e72 q^{61} +3.09666e72 q^{62} -2.60089e73 q^{63} +1.39671e73 q^{64} +1.64850e73 q^{65} -9.68950e72 q^{66} +7.40069e73 q^{67} -8.97201e71 q^{68} +3.09407e74 q^{69} +7.20132e74 q^{70} -1.55130e74 q^{71} -4.07021e75 q^{72} +3.73048e75 q^{73} -3.62040e75 q^{74} -1.63919e75 q^{75} -1.91416e74 q^{76} +3.77989e75 q^{77} -5.23471e76 q^{78} -9.43898e76 q^{79} +1.14003e77 q^{80} +5.06429e77 q^{81} +4.45217e77 q^{82} -7.99636e77 q^{83} -2.62127e76 q^{84} +6.16969e77 q^{85} -3.03818e78 q^{86} -6.06847e77 q^{87} +5.91526e77 q^{88} +5.72264e78 q^{89} -3.28366e79 q^{90} +2.04207e79 q^{91} +2.21600e77 q^{92} +7.75118e79 q^{93} -7.52874e79 q^{94} +1.31629e80 q^{95} -8.25235e78 q^{96} -4.74987e79 q^{97} +4.48287e80 q^{98} -1.72355e80 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 460872026640 q^{2} - 15\!\cdots\!60 q^{3}+ \cdots + 11\!\cdots\!98 q^{9}+O(q^{10}) \) 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

Representations

Groups

Database

Properties

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