LMFDB - Embedded newform 1.82.a.a.1.4

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			1.4
Root			$-3.17952e9$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.81039e11 q^{2} -1.66183e18 q^{3} -2.27266e24 q^{4} +2.26484e28 q^{5} -6.33221e29 q^{6} -1.01850e33 q^{7} -1.78727e36 q^{8} -4.40665e38 q^{9} +O(q^{10})$	\(q+3.81039e11 q^{2} -1.66183e18 q^{3} -2.27266e24 q^{4} +2.26484e28 q^{5} -6.33221e29 q^{6} -1.01850e33 q^{7} -1.78727e36 q^{8} -4.40665e38 q^{9} +8.62992e39 q^{10} +2.49459e42 q^{11} +3.77677e42 q^{12} -4.84484e44 q^{13} -3.88090e44 q^{14} -3.76378e46 q^{15} +4.81394e48 q^{16} -5.05995e49 q^{17} -1.67910e50 q^{18} +5.69767e51 q^{19} -5.14722e52 q^{20} +1.69258e51 q^{21} +9.50534e53 q^{22} -1.40607e55 q^{23} +2.97013e54 q^{24} +9.93602e55 q^{25} -1.84607e56 q^{26} +1.46921e57 q^{27} +2.31472e57 q^{28} +3.83527e58 q^{29} -1.43414e58 q^{30} -2.12645e60 q^{31} +6.15564e60 q^{32} -4.14558e60 q^{33} -1.92804e61 q^{34} -2.30675e61 q^{35} +1.00148e63 q^{36} -5.54853e63 q^{37} +2.17103e63 q^{38} +8.05129e62 q^{39} -4.04788e64 q^{40} -2.25758e65 q^{41} +6.44938e62 q^{42} -1.09927e66 q^{43} -5.66935e66 q^{44} -9.98036e66 q^{45} -5.35768e66 q^{46} -7.15986e67 q^{47} -7.99994e66 q^{48} -2.82716e68 q^{49} +3.78601e67 q^{50} +8.40877e67 q^{51} +1.10107e69 q^{52} +6.78492e69 q^{53} +5.59825e68 q^{54} +5.64985e70 q^{55} +1.82034e69 q^{56} -9.46855e69 q^{57} +1.46139e70 q^{58} -3.00068e69 q^{59} +8.55379e70 q^{60} -3.61060e72 q^{61} -8.10261e71 q^{62} +4.48819e71 q^{63} -9.29385e72 q^{64} -1.09728e73 q^{65} -1.57962e72 q^{66} +1.41697e74 q^{67} +1.14996e74 q^{68} +2.33665e73 q^{69} -8.78961e72 q^{70} +4.91356e74 q^{71} +7.87586e74 q^{72} -3.62528e75 q^{73} -2.11421e75 q^{74} -1.65120e74 q^{75} -1.29489e76 q^{76} -2.54075e75 q^{77} +3.06785e74 q^{78} -3.03962e76 q^{79} +1.09028e77 q^{80} +1.92961e77 q^{81} -8.60227e76 q^{82} +6.46937e77 q^{83} -3.84666e75 q^{84} -1.14600e78 q^{85} -4.18865e77 q^{86} -6.37357e76 q^{87} -4.45849e78 q^{88} -4.68721e78 q^{89} -3.80290e78 q^{90} +4.93449e77 q^{91} +3.19553e79 q^{92} +3.53380e78 q^{93} -2.72818e79 q^{94} +1.29043e80 q^{95} -1.02296e79 q^{96} +4.00926e80 q^{97} -1.07726e80 q^{98} -1.09928e81 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.81039e11	0.245050	0.122525	−	0.992465i	$-0.460901\pi$
$2$	3.81039e11	0.245050	0.122525	+	0.992465i	$0.460901\pi$
$3$	−1.66183e18	−0.0789178	−0.0394589	−	0.999221i	$-0.512563\pi$
$3$	−1.66183e18	−0.0789178	−0.0394589	+	0.999221i	$0.512563\pi$
$4$	−2.27266e24	−0.939951
$5$	2.26484e28	1.11366	0.556830	−	0.830627i	$-0.312018\pi$
$5$	2.26484e28	1.11366	0.556830	+	0.830627i	$0.312018\pi$
$6$	−6.33221e29	−0.0193388
$7$	−1.01850e33	−0.0604634	−0.0302317	−	0.999543i	$-0.509625\pi$
$7$	−1.01850e33	−0.0604634	−0.0302317	+	0.999543i	$0.509625\pi$
$8$	−1.78727e36	−0.475384
$9$	−4.40665e38	−0.993772
$10$	8.62992e39	0.272902
$11$	2.49459e42	1.66186	0.830931	−	0.556375i	$-0.187808\pi$
$11$	2.49459e42	1.66186	0.830931	+	0.556375i	$0.187808\pi$
$12$	3.77677e42	0.0741789
$13$	−4.84484e44	−0.372026	−0.186013	−	0.982547i	$-0.559557\pi$
$13$	−4.84484e44	−0.372026	−0.186013	+	0.982547i	$0.559557\pi$
$14$	−3.88090e44	−0.0148165
$15$	−3.76378e46	−0.0878876
$16$	4.81394e48	0.823458
$17$	−5.05995e49	−0.742959	−0.371480	−	0.928441i	$-0.621149\pi$
$17$	−5.05995e49	−0.742959	−0.371480	+	0.928441i	$0.621149\pi$
$18$	−1.67910e50	−0.243524
$19$	5.69767e51	0.925074	0.462537	−	0.886600i	$-0.346939\pi$
$19$	5.69767e51	0.925074	0.462537	+	0.886600i	$0.346939\pi$
$20$	−5.14722e52	−1.04679
$21$	1.69258e51	0.00477164
$22$	9.50534e53	0.407239
$23$	−1.40607e55	−0.995476	−0.497738	−	0.867327i	$-0.665836\pi$
$23$	−1.40607e55	−0.995476	−0.497738	+	0.867327i	$0.665836\pi$
$24$	2.97013e54	0.0375163
$25$	9.93602e55	0.240238
$26$	−1.84607e56	−0.0911650
$27$	1.46921e57	0.157344
$28$	2.31472e57	0.0568326
$29$	3.83527e58	0.227341	0.113670	−	0.993519i	$-0.463739\pi$
$29$	3.83527e58	0.227341	0.113670	+	0.993519i	$0.463739\pi$
$30$	−1.43414e58	−0.0215368
$31$	−2.12645e60	−0.846267	−0.423134	−	0.906067i	$-0.639070\pi$
$31$	−2.12645e60	−0.846267	−0.423134	+	0.906067i	$0.639070\pi$
$32$	6.15564e60	0.677172
$33$	−4.14558e60	−0.131151
$34$	−1.92804e61	−0.182062
$35$	−2.30675e61	−0.0673356
$36$	1.00148e63	0.934097
$37$	−5.54853e63	−1.70612	−0.853058	−	0.521817i	$-0.825255\pi$
$37$	−5.54853e63	−1.70612	−0.853058	+	0.521817i	$0.825255\pi$
$38$	2.17103e63	0.226689
$39$	8.05129e62	0.0293595
$40$	−4.04788e64	−0.529416
$41$	−2.25758e65	−1.08617	−0.543085	−	0.839678i	$-0.682744\pi$
$41$	−2.25758e65	−1.08617	−0.543085	+	0.839678i	$0.682744\pi$
$42$	6.44938e62	0.00116929
$43$	−1.09927e66	−0.768480	−0.384240	−	0.923233i	$-0.625537\pi$
$43$	−1.09927e66	−0.768480	−0.384240	+	0.923233i	$0.625537\pi$
$44$	−5.66935e66	−1.56207
$45$	−9.98036e66	−1.10672
$46$	−5.35768e66	−0.243941
$47$	−7.15986e67	−1.36440	−0.682199	−	0.731167i	$-0.738976\pi$
$47$	−7.15986e67	−1.36440	−0.682199	+	0.731167i	$0.738976\pi$
$48$	−7.99994e66	−0.0649855
$49$	−2.82716e68	−0.996344
$50$	3.78601e67	0.0588703
$51$	8.40877e67	0.0586327
$52$	1.10107e69	0.349687
$53$	6.78492e69	0.996258	0.498129	−	0.867103i	$-0.334021\pi$
$53$	6.78492e69	0.996258	0.498129	+	0.867103i	$0.334021\pi$
$54$	5.59825e68	0.0385572
$55$	5.64985e70	1.85075
$56$	1.82034e69	0.0287433
$57$	−9.46855e69	−0.0730048
$58$	1.46139e70	0.0557098
$59$	−3.00068e69	−0.00572418	−0.00286209	−	0.999996i	$-0.500911\pi$
$59$	−3.00068e69	−0.00572418	−0.00286209	+	0.999996i	$0.500911\pi$
$60$	8.55379e70	0.0826100
$61$	−3.61060e72	−1.78534	−0.892669	−	0.450713i	$-0.851170\pi$
$61$	−3.61060e72	−1.78534	−0.892669	+	0.450713i	$0.851170\pi$
$62$	−8.10261e71	−0.207378
$63$	4.48819e71	0.0600868
$64$	−9.29385e72	−0.657517
$65$	−1.09728e73	−0.414311
$66$	−1.57962e72	−0.0321384
$67$	1.41697e74	1.56795	0.783974	−	0.620794i	$-0.213190\pi$
$67$	1.41697e74	1.56795	0.783974	+	0.620794i	$0.213190\pi$
$68$	1.14996e74	0.698345
$69$	2.33665e73	0.0785608
$70$	−8.78961e72	−0.0165006
$71$	4.91356e74	0.519318	0.259659	−	0.965700i	$-0.416390\pi$
$71$	4.91356e74	0.519318	0.259659	+	0.965700i	$0.416390\pi$
$72$	7.87586e74	0.472424
$73$	−3.62528e75	−1.24384	−0.621922	−	0.783080i	$-0.713648\pi$
$73$	−3.62528e75	−1.24384	−0.621922	+	0.783080i	$0.713648\pi$
$74$	−2.11421e75	−0.418083
$75$	−1.65120e74	−0.0189591
$76$	−1.29489e76	−0.869524
$77$	−2.54075e75	−0.100482
$78$	3.06785e74	0.00719454
$79$	−3.03962e76	−0.425522	−0.212761	−	0.977104i	$-0.568246\pi$
$79$	−3.03962e76	−0.425522	−0.212761	+	0.977104i	$0.568246\pi$
$80$	1.09028e77	0.917052
$81$	1.92961e77	0.981355
$82$	−8.60227e76	−0.266166
$83$	6.46937e77	1.22518	0.612589	−	0.790402i	$-0.290128\pi$
$83$	6.46937e77	1.22518	0.612589	+	0.790402i	$0.290128\pi$
$84$	−3.84666e75	−0.00448510
$85$	−1.14600e78	−0.827404
$86$	−4.18865e77	−0.188316
$87$	−6.37357e76	−0.0179413
$88$	−4.45849e78	−0.790023
$89$	−4.68721e78	−0.525557	−0.262778	−	0.964856i	$-0.584639\pi$
$89$	−4.68721e78	−0.525557	−0.262778	+	0.964856i	$0.584639\pi$
$90$	−3.80290e78	−0.271202
$91$	4.93449e77	0.0224940
$92$	3.19553e79	0.935698
$93$	3.53380e78	0.0667856
$94$	−2.72818e79	−0.334345
$95$	1.29043e80	1.03022
$96$	−1.02296e79	−0.0534410
$97$	4.00926e80	1.37661	0.688303	−	0.725424i	$-0.258356\pi$
$97$	4.00926e80	1.37661	0.688303	+	0.725424i	$0.258356\pi$
$98$	−1.07726e80	−0.244154
$99$	−1.09928e81	−1.65151
$100$	−2.25812e80	−0.225812
$101$	−6.81104e79	−0.0455196	−0.0227598	−	0.999741i	$-0.507245\pi$
$101$	−6.81104e79	−0.0455196	−0.0227598	+	0.999741i	$0.507245\pi$
$102$	3.20407e79	0.0143679
$103$	−3.12239e81	−0.943147	−0.471573	−	0.881827i	$-0.656314\pi$
$103$	−3.12239e81	−0.943147	−0.471573	+	0.881827i	$0.656314\pi$
$104$	8.65902e80	0.176856
$105$	3.83342e79	0.00531398
$106$	2.58532e81	0.244133
$107$	2.91468e82	1.88169	0.940844	−	0.338841i	$-0.110035\pi$
$107$	2.91468e82	1.88169	0.940844	+	0.338841i	$0.110035\pi$
$108$	−3.33901e81	−0.147896
$109$	−2.02990e82	−0.619015	−0.309508	−	0.950897i	$-0.600164\pi$
$109$	−2.02990e82	−0.619015	−0.309508	+	0.950897i	$0.600164\pi$
$110$	2.15281e82	0.453526
$111$	9.22071e81	0.134643
$112$	−4.90302e81	−0.0497890
$113$	−9.08790e82	−0.643853	−0.321926	−	0.946765i	$-0.604330\pi$
$113$	−9.08790e82	−0.643853	−0.321926	+	0.946765i	$0.604330\pi$
$114$	−3.60788e81	−0.0178898
$115$	−3.18453e83	−1.10862
$116$	−8.71628e82	−0.213689
$117$	2.13495e83	0.369709
$118$	−1.14338e81	−0.00140271
$119$	5.15358e82	0.0449218
$120$	6.72687e82	0.0417804
$121$	3.96973e84	1.76179
$122$	−1.37578e84	−0.437497
$123$	3.75172e83	0.0857182
$124$	4.83271e84	0.795449
$125$	−7.11681e84	−0.846116
$126$	1.71017e83	0.0147243
$127$	−1.25212e85	−0.782700	−0.391350	−	0.920242i	$-0.627992\pi$
$127$	−1.25212e85	−0.782700	−0.391350	+	0.920242i	$0.627992\pi$
$128$	−1.84247e85	−0.838297
$129$	1.82680e84	0.0606468
$130$	−4.18106e84	−0.101527
$131$	2.28191e85	0.406267	0.203134	−	0.979151i	$-0.434887\pi$
$131$	2.28191e85	0.406267	0.203134	+	0.979151i	$0.434887\pi$
$132$	9.42149e84	0.123275
$133$	−5.80310e84	−0.0559331
$134$	5.39921e85	0.384225
$135$	3.32752e85	0.175228
$136$	9.04348e85	0.353191
$137$	4.46253e86	1.29538	0.647692	−	0.761902i	$-0.275734\pi$
$137$	4.46253e86	1.29538	0.647692	+	0.761902i	$0.275734\pi$
$138$	8.90355e84	0.0192513
$139$	−1.12979e87	−1.82347	−0.911736	−	0.410776i	$-0.865258\pi$
$139$	−1.12979e87	−1.82347	−0.911736	+	0.410776i	$0.865258\pi$
$140$	5.24246e85	0.0632922
$141$	1.18984e86	0.107675
$142$	1.87226e86	0.127259
$143$	−1.20859e87	−0.618257
$144$	−2.12133e87	−0.818329
$145$	8.68629e86	0.253180
$146$	−1.38137e87	−0.304803
$147$	4.69826e86	0.0786293
$148$	1.26099e88	1.60366
$149$	8.03546e87	0.777977	0.388989	−	0.921243i	$-0.372825\pi$
$149$	8.03546e87	0.777977	0.388989	+	0.921243i	$0.372825\pi$
$150$	−6.29170e85	−0.00464592
$151$	−8.85019e87	−0.499328	−0.249664	−	0.968333i	$-0.580320\pi$
$151$	−8.85019e87	−0.499328	−0.249664	+	0.968333i	$0.580320\pi$
$152$	−1.01833e88	−0.439766
$153$	2.22974e88	0.738332
$154$	−9.68123e86	−0.0246230
$155$	−4.81608e88	−0.942454
$156$	−1.82979e87	−0.0275965
$157$	−8.25728e88	−0.961394	−0.480697	−	0.876887i	$-0.659616\pi$
$157$	−8.25728e88	−0.961394	−0.480697	+	0.876887i	$0.659616\pi$
$158$	−1.15821e88	−0.104274
$159$	−1.12754e88	−0.0786225
$160$	1.39416e89	0.754140
$161$	1.43209e88	0.0601898
$162$	7.35256e88	0.240481
$163$	−1.06134e89	−0.270556	−0.135278	−	0.990808i	$-0.543193\pi$
$163$	−1.06134e89	−0.270556	−0.135278	+	0.990808i	$0.543193\pi$
$164$	5.13073e89	1.02095
$165$	−9.38907e88	−0.146057
$166$	2.46508e89	0.300229
$167$	4.67762e89	0.446692	0.223346	−	0.974739i	$-0.428302\pi$
$167$	4.67762e89	0.446692	0.223346	+	0.974739i	$0.428302\pi$
$168$	−3.02509e87	−0.00226836
$169$	−1.46122e90	−0.861596
$170$	−4.36670e89	−0.202755
$171$	−2.51076e90	−0.919312
$172$	2.49827e90	0.722334
$173$	−5.69207e90	−1.30138	−0.650688	−	0.759345i	$-0.725519\pi$
$173$	−5.69207e90	−1.30138	−0.650688	+	0.759345i	$0.725519\pi$
$174$	−2.42857e88	−0.00439650
$175$	−1.01199e89	−0.0145256
$176$	1.20088e91	1.36847
$177$	4.98662e87	0.000451740 0
$178$	−1.78601e90	−0.128787
$179$	5.72532e90	0.329043	0.164521	−	0.986374i	$-0.447392\pi$
$179$	5.72532e90	0.329043	0.164521	+	0.986374i	$0.447392\pi$
$180$	2.26820e91	1.04027
$181$	−1.24555e91	−0.456437	−0.228218	−	0.973610i	$-0.573290\pi$
$181$	−1.24555e91	−0.456437	−0.228218	+	0.973610i	$0.573290\pi$
$182$	1.88023e89	0.00551214
$183$	6.00019e90	0.140895
$184$	2.51303e91	0.473234
$185$	−1.25665e92	−1.90003
$186$	1.34652e90	0.0163658
$187$	−1.26225e92	−1.23470
$188$	1.62719e92	1.28247
$189$	−1.49639e90	−0.00951356
$190$	4.91704e91	0.252455
$191$	−1.62959e92	−0.676438	−0.338219	−	0.941067i	$-0.609825\pi$
$191$	−1.62959e92	−0.676438	−0.338219	+	0.941067i	$0.609825\pi$
$192$	1.54448e91	0.0518898
$193$	1.86011e92	0.506370	0.253185	−	0.967418i	$-0.418522\pi$
$193$	1.86011e92	0.506370	0.253185	+	0.967418i	$0.418522\pi$
$194$	1.52768e92	0.337337
$195$	1.82349e91	0.0326965
$196$	6.42518e92	0.936514
$197$	8.05894e92	0.955863	0.477932	−	0.878397i	$-0.341387\pi$
$197$	8.05894e92	0.955863	0.477932	+	0.878397i	$0.341387\pi$
$198$	−4.18867e92	−0.404703
$199$	−1.90732e93	−1.50270	−0.751352	−	0.659902i	$-0.770598\pi$
$199$	−1.90732e93	−1.50270	−0.751352	+	0.659902i	$0.770598\pi$
$200$	−1.77583e92	−0.114206
$201$	−2.35476e92	−0.123739
$202$	−2.59527e91	−0.0111546
$203$	−3.90624e91	−0.0137458
$204$	−1.91103e92	−0.0551119
$205$	−5.11307e93	−1.20962
$206$	−1.18975e93	−0.231118
$207$	6.19607e93	0.989276
$208$	−2.33228e93	−0.306348
$209$	1.42133e94	1.53735
$210$	1.46068e91	0.00130219
$211$	1.47294e94	1.08329	0.541647	−	0.840606i	$-0.317801\pi$
$211$	1.47294e94	1.08329	0.541647	+	0.840606i	$0.317801\pi$
$212$	−1.54198e94	−0.936433
$213$	−8.16549e92	−0.0409834
$214$	1.11060e94	0.461107
$215$	−2.48968e94	−0.855826
$216$	−2.62587e93	−0.0747990
$217$	2.16580e93	0.0511682
$218$	−7.73470e93	−0.151690
$219$	6.02459e93	0.0981614
$220$	−1.28402e95	−1.73961
$221$	2.45147e94	0.276400
$222$	3.51345e93	0.0329942
$223$	1.49057e95	1.16683	0.583413	−	0.812176i	$-0.301717\pi$
$223$	1.49057e95	1.16683	0.583413	+	0.812176i	$0.301717\pi$
$224$	−6.26955e93	−0.0409441
$225$	−4.37846e94	−0.238742
$226$	−3.46284e94	−0.157776
$227$	3.64384e95	1.38839	0.694196	−	0.719786i	$-0.255760\pi$
$227$	3.64384e95	1.38839	0.694196	+	0.719786i	$0.255760\pi$
$228$	2.15188e94	0.0686209
$229$	3.52400e94	0.0941238	0.0470619	−	0.998892i	$-0.485014\pi$
$229$	3.52400e94	0.0941238	0.0470619	+	0.998892i	$0.485014\pi$
$230$	−1.21343e95	−0.271667
$231$	4.22229e93	0.00792981
$232$	−6.85466e94	−0.108074
$233$	−2.36242e94	−0.0312927	−0.0156463	−	0.999878i	$-0.504981\pi$
$233$	−2.36242e94	−0.0312927	−0.0156463	+	0.999878i	$0.504981\pi$
$234$	8.13499e94	0.0905972
$235$	−1.62159e96	−1.51947
$236$	6.81953e93	0.00538045
$237$	5.05133e94	0.0335813
$238$	1.96371e94	0.0110081
$239$	−1.84588e96	−0.873150	−0.436575	−	0.899668i	$-0.643809\pi$
$239$	−1.84588e96	−0.873150	−0.436575	+	0.899668i	$0.643809\pi$
$240$	−1.81186e95	−0.0723718
$241$	4.81468e96	1.62509	0.812544	−	0.582900i	$-0.198082\pi$
$241$	4.81468e96	1.62509	0.812544	+	0.582900i	$0.198082\pi$
$242$	1.51262e96	0.431725
$243$	−9.72153e95	−0.234791
$244$	8.20566e96	1.67813
$245$	−6.40307e96	−1.10959
$246$	1.42955e95	0.0210052
$247$	−2.76043e96	−0.344152
$248$	3.80054e96	0.402302
$249$	−1.07510e96	−0.0966884
$250$	−2.71178e96	−0.207341
$251$	−2.67769e95	−0.0174171	−0.00870853	−	0.999962i	$-0.502772\pi$
$251$	−2.67769e95	−0.0174171	−0.00870853	+	0.999962i	$0.502772\pi$
$252$	−1.02001e96	−0.0564786
$253$	−3.50757e97	−1.65434
$254$	−4.77106e96	−0.191800
$255$	1.90445e96	0.0652969
$256$	1.54506e97	0.452092
$257$	3.01397e97	0.753092	0.376546	−	0.926398i	$-0.377112\pi$
$257$	3.01397e97	0.753092	0.376546	+	0.926398i	$0.377112\pi$
$258$	6.96082e95	0.0148615
$259$	5.65121e96	0.103157
$260$	2.49375e97	0.389432
$261$	−1.69007e97	−0.225925
$262$	8.69497e96	0.0995556
$263$	2.11768e97	0.207803	0.103902	−	0.994588i	$-0.466867\pi$
$263$	2.11768e97	0.207803	0.103902	+	0.994588i	$0.466867\pi$
$264$	7.40925e96	0.0623469
$265$	1.53668e98	1.10949
$266$	−2.21121e96	−0.0137064
$267$	7.78934e96	0.0414758
$268$	−3.22030e98	−1.47379
$269$	−2.78485e98	−1.09606	−0.548029	−	0.836459i	$-0.684622\pi$
$269$	−2.78485e98	−1.09606	−0.548029	+	0.836459i	$0.684622\pi$
$270$	1.26791e97	0.0429396
$271$	1.47348e98	0.429622	0.214811	−	0.976656i	$-0.431086\pi$
$271$	1.47348e98	0.429622	0.214811	+	0.976656i	$0.431086\pi$
$272$	−2.43583e98	−0.611796
$273$	−8.20028e95	−0.00177518
$274$	1.70040e98	0.317434
$275$	2.47863e98	0.399243
$276$	−5.31042e97	−0.0738433
$277$	2.61114e98	0.313617	0.156808	−	0.987629i	$-0.449880\pi$
$277$	2.61114e98	0.313617	0.156808	+	0.987629i	$0.449880\pi$
$278$	−4.30495e98	−0.446841
$279$	9.37054e98	0.840997
$280$	4.12278e97	0.0320103
$281$	2.82065e99	1.89558	0.947791	−	0.318893i	$-0.103311\pi$
$281$	2.82065e99	1.89558	0.947791	+	0.318893i	$0.103311\pi$
$282$	4.53377e97	0.0263858
$283$	−2.85819e99	−1.44125	−0.720626	−	0.693324i	$-0.756146\pi$
$283$	−2.85819e99	−1.44125	−0.720626	+	0.693324i	$0.756146\pi$
$284$	−1.11669e99	−0.488133
$285$	−2.14448e98	−0.0813026
$286$	−4.60519e98	−0.151504
$287$	2.29936e98	0.0656735
$288$	−2.71258e99	−0.672955
$289$	−2.07803e99	−0.448012
$290$	3.30981e98	0.0620418
$291$	−6.66271e98	−0.108639
$292$	8.23903e99	1.16915
$293$	−6.85926e99	−0.847498	−0.423749	−	0.905780i	$-0.639286\pi$
$293$	−6.85926e99	−0.847498	−0.423749	+	0.905780i	$0.639286\pi$
$294$	1.79022e98	0.0192681
$295$	−6.79607e97	−0.00637479
$296$	9.91671e99	0.811061
$297$	3.66507e99	0.261484
$298$	3.06182e99	0.190643
$299$	6.81221e99	0.370343
$300$	3.75261e98	0.0178206
$301$	1.11961e99	0.0464649
$302$	−3.37226e99	−0.122360
$303$	1.13188e98	0.00359231
$304$	2.74282e100	0.761759
$305$	−8.17743e100	−1.98826
$306$	8.49618e99	0.180928
$307$	−4.64178e100	−0.866125	−0.433063	−	0.901364i	$-0.642567\pi$
$307$	−4.64178e100	−0.866125	−0.433063	+	0.901364i	$0.642567\pi$
$308$	5.77426e99	0.0944479
$309$	5.18887e99	0.0744311
$310$	−1.83511e100	−0.230948
$311$	5.57540e100	0.615857	0.307929	−	0.951409i	$-0.400364\pi$
$311$	5.57540e100	0.615857	0.307929	+	0.951409i	$0.400364\pi$
$312$	−1.43898e99	−0.0139571
$313$	8.58275e99	0.0731275	0.0365638	−	0.999331i	$-0.488359\pi$
$313$	8.58275e99	0.0731275	0.0365638	+	0.999331i	$0.488359\pi$
$314$	−3.14634e100	−0.235589
$315$	1.01650e100	0.0669163
$316$	6.90803e100	0.399970
$317$	3.25887e101	1.66022	0.830112	−	0.557597i	$-0.188277\pi$
$317$	3.25887e101	1.66022	0.830112	+	0.557597i	$0.188277\pi$
$318$	−4.29635e99	−0.0192664
$319$	9.56743e100	0.377809
$320$	−2.10491e101	−0.732250
$321$	−4.84369e100	−0.148499
$322$	5.45683e99	0.0147495
$323$	−2.88299e101	−0.687292
$324$	−4.38535e101	−0.922425
$325$	−4.81385e100	−0.0893750
$326$	−4.04413e100	−0.0662997
$327$	3.37334e100	0.0488514
$328$	4.03491e101	0.516348
$329$	7.29234e100	0.0824961
$330$	−3.57760e100	−0.0357913
$331$	−9.42082e101	−0.833787	−0.416893	−	0.908955i	$-0.636881\pi$
$331$	−9.42082e101	−0.833787	−0.416893	+	0.908955i	$0.636881\pi$
$332$	−1.47027e102	−1.15161
$333$	2.44504e102	1.69549
$334$	1.78236e101	0.109462
$335$	3.20922e102	1.74616
$336$	8.14797e99	0.00392924
$337$	−1.00942e102	−0.431582	−0.215791	−	0.976440i	$-0.569233\pi$
$337$	−1.00942e102	−0.431582	−0.215791	+	0.976440i	$0.569233\pi$
$338$	−5.56781e101	−0.211134
$339$	1.51025e101	0.0508115
$340$	2.60447e102	0.777719
$341$	−5.30463e102	−1.40638
$342$	−9.56697e101	−0.225277
$343$	5.76952e101	0.120706
$344$	1.96469e102	0.365324
$345$	5.29215e101	0.0874900
$346$	−2.16890e102	−0.318902
$347$	−7.31979e102	−0.957536	−0.478768	−	0.877942i	$-0.658916\pi$
$347$	−7.31979e102	−0.957536	−0.478768	+	0.877942i	$0.658916\pi$
$348$	1.44850e101	0.0168639
$349$	−8.19063e102	−0.848961	−0.424480	−	0.905437i	$-0.639543\pi$
$349$	−8.19063e102	−0.848961	−0.424480	+	0.905437i	$0.639543\pi$
$350$	−3.85607e100	−0.00355950
$351$	−7.11808e101	−0.0585362
$352$	1.53558e103	1.12537
$353$	1.05641e103	0.690169	0.345084	−	0.938572i	$-0.387850\pi$
$353$	1.05641e103	0.690169	0.345084	+	0.938572i	$0.387850\pi$
$354$	1.90009e99	0.000110699 0
$355$	1.11284e103	0.578343
$356$	1.06524e103	0.493997
$357$	−8.56437e100	−0.00354513
$358$	2.18157e102	0.0806318
$359$	−2.70416e103	−0.892705	−0.446352	−	0.894857i	$-0.647277\pi$
$359$	−2.70416e103	−0.892705	−0.446352	+	0.894857i	$0.647277\pi$
$360$	1.78376e103	0.526119
$361$	−5.47171e102	−0.144239
$362$	−4.74605e102	−0.111850
$363$	−6.59701e102	−0.139036
$364$	−1.12144e102	−0.0211432
$365$	−8.21068e103	−1.38522
$366$	2.28630e102	0.0345263
$367$	8.97978e102	0.121420	0.0607100	−	0.998155i	$-0.480664\pi$
$367$	8.97978e102	0.121420	0.0607100	+	0.998155i	$0.480664\pi$
$368$	−6.76875e103	−0.819732
$369$	9.94838e103	1.07941
$370$	−4.78834e103	−0.465602
$371$	−6.91047e102	−0.0602371
$372$	−8.03113e102	−0.0627752
$373$	2.10477e104	1.47569	0.737847	−	0.674968i	$-0.235843\pi$
$373$	2.10477e104	1.47569	0.737847	+	0.674968i	$0.235843\pi$
$374$	−4.80966e103	−0.302562
$375$	1.18269e103	0.0667737
$376$	1.27966e104	0.648613
$377$	−1.85813e103	−0.0845768
$378$	−5.70184e101	−0.00233130
$379$	2.56191e104	0.941186	0.470593	−	0.882351i	$-0.344040\pi$
$379$	2.56191e104	0.941186	0.470593	+	0.882351i	$0.344040\pi$
$380$	−2.93271e104	−0.968354
$381$	2.08081e103	0.0617690
$382$	−6.20939e103	−0.165761
$383$	−2.88384e104	−0.692501	−0.346251	−	0.938142i	$-0.612545\pi$
$383$	−2.88384e104	−0.692501	−0.346251	+	0.938142i	$0.612545\pi$
$384$	3.06188e103	0.0661566
$385$	−5.75439e103	−0.111903
$386$	7.08774e103	0.124086
$387$	4.84411e104	0.763694
$388$	−9.11170e104	−1.29394
$389$	−1.01152e105	−1.29424	−0.647119	−	0.762389i	$-0.724026\pi$
$389$	−1.01152e105	−1.29424	−0.647119	+	0.762389i	$0.724026\pi$
$390$	6.94820e102	0.00801228
$391$	7.11466e104	0.739598
$392$	5.05289e104	0.473646
$393$	−3.79215e103	−0.0320617
$394$	3.07077e104	0.234234
$395$	−6.88426e104	−0.473887
$396$	2.49828e105	1.55234
$397$	1.75711e105	0.985787	0.492893	−	0.870090i	$-0.335939\pi$
$397$	1.75711e105	0.985787	0.492893	+	0.870090i	$0.335939\pi$
$398$	−7.26762e104	−0.368237
$399$	9.64376e102	0.00441412
$400$	4.78314e104	0.197826
$401$	−3.67465e105	−1.37363	−0.686814	−	0.726833i	$-0.740991\pi$
$401$	−3.67465e105	−1.37363	−0.686814	+	0.726833i	$0.740991\pi$
$402$	−8.97256e103	−0.0303222
$403$	1.03023e105	0.314834
$404$	1.54792e104	0.0427861
$405$	4.37026e105	1.09290
$406$	−1.48843e103	−0.00336840
$407$	−1.38413e106	−2.83533
$408$	−1.50287e104	−0.0278731
$409$	−2.52614e103	−0.00424291	−0.00212145	−	0.999998i	$-0.500675\pi$
$409$	−2.52614e103	−0.00424291	−0.00212145	+	0.999998i	$0.500675\pi$
$410$	−1.94828e105	−0.296418
$411$	−7.41596e104	−0.102229
$412$	7.09613e105	0.886511
$413$	3.05621e102	0.000346103 0
$414$	2.36094e105	0.242422
$415$	1.46521e106	1.36443
$416$	−2.98231e105	−0.251926
$417$	1.87752e105	0.143905
$418$	5.41583e105	0.376726
$419$	−7.52345e105	−0.475061	−0.237530	−	0.971380i	$-0.576338\pi$
$419$	−7.52345e105	−0.475061	−0.237530	+	0.971380i	$0.576338\pi$
$420$	−8.71207e103	−0.00499488
$421$	−1.21436e106	−0.632299	−0.316149	−	0.948709i	$-0.602390\pi$
$421$	−1.21436e106	−0.632299	−0.316149	+	0.948709i	$0.602390\pi$
$422$	5.61248e105	0.265461
$423$	3.15510e106	1.35590
$424$	−1.21265e106	−0.473605
$425$	−5.02758e105	−0.178487
$426$	−3.11137e104	−0.0100430
$427$	3.67741e105	0.107948
$428$	−6.62407e106	−1.76869
$429$	2.00847e105	0.0487915
$430$	−9.48663e105	−0.209720
$431$	−4.71152e106	−0.948052	−0.474026	−	0.880511i	$-0.657200\pi$
$431$	−4.71152e106	−0.948052	−0.474026	+	0.880511i	$0.657200\pi$
$432$	7.07268e105	0.129566
$433$	8.26628e106	1.37896	0.689478	−	0.724307i	$-0.257840\pi$
$433$	8.26628e106	1.37896	0.689478	+	0.724307i	$0.257840\pi$
$434$	8.25255e104	0.0125387
$435$	−1.44351e105	−0.0199805
$436$	4.61327e106	0.581844
$437$	−8.01134e106	−0.920889
$438$	2.29560e105	0.0240544
$439$	1.49322e107	1.42662	0.713312	−	0.700847i	$-0.247194\pi$
$439$	1.49322e107	1.42662	0.713312	+	0.700847i	$0.247194\pi$
$440$	−1.00978e107	−0.879817
$441$	1.24583e107	0.990139
$442$	9.34103e105	0.0677319
$443$	8.94391e106	0.591802	0.295901	−	0.955219i	$-0.404380\pi$
$443$	8.94391e106	0.591802	0.295901	+	0.955219i	$0.404380\pi$
$444$	−2.09555e106	−0.126558
$445$	−1.06158e107	−0.585291
$446$	5.67966e106	0.285930
$447$	−1.33536e106	−0.0613963
$448$	9.46583e105	0.0397557
$449$	−2.67493e107	−1.02645	−0.513223	−	0.858255i	$-0.671549\pi$
$449$	−2.67493e107	−1.02645	−0.513223	+	0.858255i	$0.671549\pi$
$450$	−1.66836e106	−0.0585037
$451$	−5.63174e107	−1.80507
$452$	2.06537e107	0.605190
$453$	1.47075e106	0.0394059
$454$	1.38844e107	0.340225
$455$	1.11758e106	0.0250506
$456$	1.69228e106	0.0347054
$457$	−3.40179e106	−0.0638412	−0.0319206	−	0.999490i	$-0.510162\pi$
$457$	−3.40179e106	−0.0638412	−0.0319206	+	0.999490i	$0.510162\pi$
$458$	1.34278e106	0.0230650
$459$	−7.43412e106	−0.116900
$460$	7.23737e107	1.04205
$461$	1.03862e108	1.36953	0.684764	−	0.728765i	$-0.259905\pi$
$461$	1.03862e108	1.36953	0.684764	+	0.728765i	$0.259905\pi$
$462$	1.60885e105	0.00194320
$463$	−8.59685e107	−0.951282	−0.475641	−	0.879639i	$-0.657784\pi$
$463$	−8.59685e107	−0.951282	−0.475641	+	0.879639i	$0.657784\pi$
$464$	1.84628e107	0.187206
$465$	8.00350e106	0.0743764
$466$	−9.00175e105	−0.00766826
$467$	4.96067e107	0.387442	0.193721	−	0.981057i	$-0.437944\pi$
$467$	4.96067e107	0.387442	0.193721	+	0.981057i	$0.437944\pi$
$468$	−4.85202e107	−0.347509
$469$	−1.44319e107	−0.0948034
$470$	−6.17890e107	−0.372347
$471$	1.37222e107	0.0758711
$472$	5.36302e105	0.00272119
$473$	−2.74223e108	−1.27711
$474$	1.92475e106	0.00822909
$475$	5.66122e107	0.222238
$476$	−1.17123e107	−0.0422243
$477$	−2.98987e108	−0.990053
$478$	−7.03352e107	−0.213965
$479$	5.17027e108	1.44519	0.722596	−	0.691271i	$-0.242949\pi$
$479$	5.17027e108	1.44519	0.722596	+	0.691271i	$0.242949\pi$
$480$	−2.31685e107	−0.0595151
$481$	2.68818e108	0.634720
$482$	1.83458e108	0.398227
$483$	−2.37989e106	−0.00475005
$484$	−9.02185e108	−1.65599
$485$	9.08035e108	1.53307
$486$	−3.70428e107	−0.0575354
$487$	4.08219e107	0.0583405	0.0291702	−	0.999574i	$-0.490714\pi$
$487$	4.08219e107	0.0583405	0.0291702	+	0.999574i	$0.490714\pi$
$488$	6.45310e108	0.848722
$489$	1.76377e107	0.0213517
$490$	−2.43982e108	−0.271904
$491$	4.69644e108	0.481913	0.240956	−	0.970536i	$-0.422539\pi$
$491$	4.69644e108	0.481913	0.240956	+	0.970536i	$0.422539\pi$
$492$	−8.52638e107	−0.0805709
$493$	−1.94063e108	−0.168905
$494$	−1.05183e108	−0.0843343
$495$	−2.48969e109	−1.83922
$496$	−1.02366e109	−0.696865
$497$	−5.00448e107	−0.0313997
$498$	−4.09654e107	−0.0236935
$499$	−2.47888e108	−0.132186	−0.0660928	−	0.997813i	$-0.521053\pi$
$499$	−2.47888e108	−0.132186	−0.0660928	+	0.997813i	$0.521053\pi$
$500$	1.61741e109	0.795307
$501$	−7.77341e107	−0.0352520
$502$	−1.02030e107	−0.00426805
$503$	2.00713e109	0.774591	0.387295	−	0.921956i	$-0.373409\pi$
$503$	2.00713e109	0.774591	0.387295	+	0.921956i	$0.373409\pi$
$504$	−8.02159e107	−0.0285643
$505$	−1.54259e108	−0.0506933
$506$	−1.33652e109	−0.405397
$507$	2.42829e108	0.0679953
$508$	2.84565e109	0.735699
$509$	1.97892e109	0.472452	0.236226	−	0.971698i	$-0.424089\pi$
$509$	1.97892e109	0.472452	0.236226	+	0.971698i	$0.424089\pi$
$510$	7.25670e107	0.0160010
$511$	3.69236e108	0.0752069
$512$	5.04356e109	0.949082
$513$	8.37106e108	0.145555
$514$	1.14844e109	0.184545
$515$	−7.07171e109	−1.05034
$516$	−4.15170e108	−0.0570050
$517$	−1.78609e110	−2.26744
$518$	2.15333e108	0.0252787
$519$	9.45924e108	0.102702
$520$	1.96113e109	0.196957
$521$	7.75473e109	0.720508	0.360254	−	0.932854i	$-0.382690\pi$
$521$	7.75473e109	0.720508	0.360254	+	0.932854i	$0.382690\pi$
$522$	−6.43982e108	−0.0553629
$523$	−3.77994e109	−0.300723	−0.150361	−	0.988631i	$-0.548044\pi$
$523$	−3.77994e109	−0.300723	−0.150361	+	0.988631i	$0.548044\pi$
$524$	−5.18601e109	−0.381871
$525$	1.68175e107	0.00114633
$526$	8.06917e108	0.0509221
$527$	1.07598e110	0.628742
$528$	−1.99566e109	−0.107997
$529$	−1.80109e108	−0.00902777
$530$	5.85533e109	0.271881
$531$	1.32230e108	0.00568853
$532$	1.31885e109	0.0525743
$533$	1.09376e110	0.404084
$534$	2.96804e108	0.0101636
$535$	6.60128e110	2.09556
$536$	−2.53251e110	−0.745378
$537$	−9.51450e108	−0.0259673
$538$	−1.06113e110	−0.268589
$539$	−7.05260e110	−1.65579
$540$	−7.56233e109	−0.164706
$541$	3.40813e110	0.688696	0.344348	−	0.938842i	$-0.388100\pi$
$541$	3.40813e110	0.688696	0.344348	+	0.938842i	$0.388100\pi$
$542$	5.61452e109	0.105279
$543$	2.06990e109	0.0360210
$544$	−3.11472e110	−0.503112
$545$	−4.59740e110	−0.689373
$546$	−3.12462e107	−0.000435006 0
$547$	−4.52897e110	−0.585480	−0.292740	−	0.956192i	$-0.594567\pi$
$547$	−4.52897e110	−0.585480	−0.292740	+	0.956192i	$0.594567\pi$
$548$	−1.01418e111	−1.21760
$549$	1.59106e111	1.77422
$550$	9.44453e109	0.0978344
$551$	2.18521e110	0.210307
$552$	−4.17622e109	−0.0373466
$553$	3.09587e109	0.0257285
$554$	9.94945e109	0.0768517
$555$	2.08834e110	0.149946
$556$	2.56764e111	1.71397
$557$	−1.10823e111	−0.687852	−0.343926	−	0.938997i	$-0.611757\pi$
$557$	−1.10823e111	−0.687852	−0.343926	+	0.938997i	$0.611757\pi$
$558$	3.57054e110	0.206086
$559$	5.32580e110	0.285895
$560$	−1.11046e110	−0.0554480
$561$	2.09764e110	0.0974395
$562$	1.07477e111	0.464512
$563$	−2.04352e111	−0.821845	−0.410922	−	0.911670i	$-0.634793\pi$
$563$	−2.04352e111	−0.821845	−0.410922	+	0.911670i	$0.634793\pi$
$564$	−2.70411e110	−0.101209
$565$	−2.05827e111	−0.717033
$566$	−1.08908e111	−0.353179
$567$	−1.96532e110	−0.0593360
$568$	−8.78184e110	−0.246876
$569$	−2.62420e111	−0.686990	−0.343495	−	0.939155i	$-0.611611\pi$
$569$	−2.62420e111	−0.686990	−0.343495	+	0.939155i	$0.611611\pi$
$570$	−8.17128e109	−0.0199232
$571$	−2.69607e110	−0.0612306	−0.0306153	−	0.999531i	$-0.509747\pi$
$571$	−2.69607e110	−0.0612306	−0.0306153	+	0.999531i	$0.509747\pi$
$572$	2.74671e111	0.581131
$573$	2.70811e110	0.0533831
$574$	8.76145e109	0.0160933
$575$	−1.39708e111	−0.239151
$576$	4.09547e111	0.653422
$577$	2.27120e111	0.337781	0.168890	−	0.985635i	$-0.445982\pi$
$577$	2.27120e111	0.337781	0.168890	+	0.985635i	$0.445982\pi$
$578$	−7.91810e110	−0.109785
$579$	−3.09119e110	−0.0399616
$580$	−1.97410e111	−0.237977
$581$	−6.58908e110	−0.0740784
$582$	−2.53875e110	−0.0266219
$583$	1.69256e112	1.65564
$584$	6.47934e111	0.591304
$585$	4.83533e111	0.411731
$586$	−2.61364e111	−0.207679
$587$	−1.53407e112	−1.13763	−0.568816	−	0.822465i	$-0.692598\pi$
$587$	−1.53407e112	−1.13763	−0.568816	+	0.822465i	$0.692598\pi$
$588$	−1.06775e111	−0.0739077
$589$	−1.21158e112	−0.782860
$590$	−2.58957e109	−0.00156214
$591$	−1.33926e111	−0.0754347
$592$	−2.67103e112	−1.40491
$593$	2.37317e112	1.16577	0.582886	−	0.812554i	$-0.301924\pi$
$593$	2.37317e112	1.16577	0.582886	+	0.812554i	$0.301924\pi$
$594$	1.39653e111	0.0640767
$595$	1.16720e111	0.0500276
$596$	−1.82619e112	−0.731260
$597$	3.16963e111	0.118590
$598$	2.59571e111	0.0907525
$599$	−4.76363e111	−0.155651	−0.0778254	−	0.996967i	$-0.524798\pi$
$599$	−4.76363e111	−0.155651	−0.0778254	+	0.996967i	$0.524798\pi$
$600$	2.95113e110	0.00901286
$601$	7.77739e111	0.222033	0.111017	−	0.993819i	$-0.464589\pi$
$601$	7.77739e111	0.222033	0.111017	+	0.993819i	$0.464589\pi$
$602$	4.26616e110	0.0113862
$603$	−6.24409e112	−1.55818
$604$	2.01135e112	0.469344
$605$	8.99080e112	1.96203
$606$	4.31289e109	0.000880293 0
$607$	6.09984e112	1.16460	0.582299	−	0.812974i	$-0.302153\pi$
$607$	6.09984e112	1.16460	0.582299	+	0.812974i	$0.302153\pi$
$608$	3.50728e112	0.626434
$609$	6.49150e109	0.00108479
$610$	−3.11592e112	−0.487222
$611$	3.46884e112	0.507592
$612$	−5.06745e112	−0.693996
$613$	−9.85750e112	−1.26362	−0.631812	−	0.775122i	$-0.717688\pi$
$613$	−9.85750e112	−1.26362	−0.631812	+	0.775122i	$0.717688\pi$
$614$	−1.76870e112	−0.212244
$615$	8.49704e111	0.0954609
$616$	4.54100e111	0.0477675
$617$	−1.56188e112	−0.153851	−0.0769254	−	0.997037i	$-0.524510\pi$
$617$	−1.56188e112	−0.153851	−0.0769254	+	0.997037i	$0.524510\pi$
$618$	1.97716e111	0.0182393
$619$	−1.58169e113	−1.36663	−0.683313	−	0.730125i	$-0.739462\pi$
$619$	−1.58169e113	−1.36663	−0.683313	+	0.730125i	$0.739462\pi$
$620$	1.09453e113	0.885860
$621$	−2.06581e112	−0.156632
$622$	2.12444e112	0.150916
$623$	4.77395e111	0.0317769
$624$	3.87584e111	0.0241763
$625$	−2.02279e113	−1.18252
$626$	3.27036e111	0.0179199
$627$	−2.36201e112	−0.121324
$628$	1.87660e113	0.903663
$629$	2.80753e113	1.26757
$630$	3.87327e111	0.0163978
$631$	1.41887e113	0.563319	0.281660	−	0.959514i	$-0.409115\pi$
$631$	1.41887e113	0.563319	0.281660	+	0.959514i	$0.409115\pi$
$632$	5.43262e112	0.202287
$633$	−2.44778e112	−0.0854912
$634$	1.24175e113	0.406837
$635$	−2.83585e113	−0.871662
$636$	2.56251e112	0.0739013
$637$	1.36972e113	0.370666
$638$	3.64556e112	0.0925820
$639$	−2.16523e113	−0.516083
$640$	−4.17291e113	−0.933578
$641$	4.66631e113	0.979995	0.489997	−	0.871724i	$-0.336998\pi$
$641$	4.66631e113	0.979995	0.489997	+	0.871724i	$0.336998\pi$
$642$	−1.84563e112	−0.0363896
$643$	−4.43227e113	−0.820506	−0.410253	−	0.911972i	$-0.634560\pi$
$643$	−4.43227e113	−0.820506	−0.410253	+	0.911972i	$0.634560\pi$
$644$	−3.25466e112	−0.0565755
$645$	4.13742e112	0.0675399
$646$	−1.09853e113	−0.168421
$647$	−2.70448e113	−0.389457	−0.194729	−	0.980857i	$-0.562383\pi$
$647$	−2.70448e113	−0.389457	−0.194729	+	0.980857i	$0.562383\pi$
$648$	−3.44873e113	−0.466521
$649$	−7.48547e111	−0.00951281
$650$	−1.83426e112	−0.0219013
$651$	−3.59919e111	−0.00403808
$652$	2.41207e113	0.254310
$653$	3.70480e113	0.367097	0.183549	−	0.983011i	$-0.441241\pi$
$653$	3.70480e113	0.367097	0.183549	+	0.983011i	$0.441241\pi$
$654$	1.28537e112	0.0119710
$655$	5.16817e113	0.452443
$656$	−1.08679e114	−0.894415
$657$	1.59753e114	1.23610
$658$	2.77866e112	0.0202156
$659$	1.09752e114	0.750850	0.375425	−	0.926853i	$-0.377497\pi$
$659$	1.09752e114	0.750850	0.375425	+	0.926853i	$0.377497\pi$
$660$	2.13382e113	0.137287
$661$	8.29343e113	0.501851	0.250926	−	0.968006i	$-0.419265\pi$
$661$	8.29343e113	0.501851	0.250926	+	0.968006i	$0.419265\pi$
$662$	−3.58970e113	−0.204319
$663$	−4.07391e112	−0.0218129
$664$	−1.15625e114	−0.582430
$665$	−1.31431e113	−0.0622904
$666$	9.31656e113	0.415479
$667$	−5.39268e113	−0.226312
$668$	−1.06307e114	−0.419868
$669$	−2.47707e113	−0.0920834
$670$	1.22284e114	0.427896
$671$	−9.00695e114	−2.96699
$672$	1.04189e112	0.00323122
$673$	5.00689e114	1.46204	0.731018	−	0.682358i	$-0.239045\pi$
$673$	5.00689e114	1.46204	0.731018	+	0.682358i	$0.239045\pi$
$674$	−3.84630e113	−0.105759
$675$	1.45981e113	0.0378001
$676$	3.32086e114	0.809858
$677$	−5.80519e114	−1.33345	−0.666723	−	0.745305i	$-0.732304\pi$
$677$	−5.80519e114	−1.33345	−0.666723	+	0.745305i	$0.732304\pi$
$678$	5.75465e112	0.0124513
$679$	−4.08345e113	−0.0832342
$680$	2.04820e114	0.393335
$681$	−6.05544e113	−0.109569
$682$	−2.02127e114	−0.344633
$683$	6.44494e114	1.03557	0.517786	−	0.855510i	$-0.326756\pi$
$683$	6.44494e114	1.03557	0.517786	+	0.855510i	$0.326756\pi$
$684$	5.70611e114	0.864108
$685$	1.01069e115	1.44262
$686$	2.19841e113	0.0295789
$687$	−5.85629e112	−0.00742804
$688$	−5.29183e114	−0.632811
$689$	−3.28718e114	−0.370634
$690$	2.01651e113	0.0214394
$691$	−1.15361e115	−1.15664	−0.578322	−	0.815809i	$-0.696292\pi$
$691$	−1.15361e115	−1.15664	−0.578322	+	0.815809i	$0.696292\pi$
$692$	1.29361e115	1.22323
$693$	1.11962e114	0.0998560
$694$	−2.78912e114	−0.234644
$695$	−2.55880e115	−2.03073
$696$	1.13913e113	0.00852899
$697$	1.14233e115	0.806980
$698$	−3.12095e114	−0.208038
$699$	3.92594e112	0.00246955
$700$	2.29991e113	0.0136534
$701$	2.13331e115	1.19529	0.597646	−	0.801760i	$-0.296103\pi$
$701$	2.13331e115	1.19529	0.597646	+	0.801760i	$0.296103\pi$
$702$	−2.71226e113	−0.0143443
$703$	−3.16137e115	−1.57828
$704$	−2.31843e115	−1.09270
$705$	2.69481e114	0.119914
$706$	4.02532e114	0.169126
$707$	6.93708e112	0.00275227
$708$	−1.13329e112	−0.000424614 0
$709$	4.92402e115	1.74240	0.871200	−	0.490929i	$-0.163343\pi$
$709$	4.92402e115	1.74240	0.871200	+	0.490929i	$0.163343\pi$
$710$	4.24036e114	0.141723
$711$	1.33945e115	0.422872
$712$	8.37730e114	0.249841
$713$	2.98995e115	0.842439
$714$	−3.26335e112	−0.000868734 0
$715$	−2.73726e115	−0.688528
$716$	−1.30117e115	−0.309284
$717$	3.06754e114	0.0689071
$718$	−1.03039e115	−0.218757
$719$	3.15572e115	0.633255	0.316628	−	0.948550i	$-0.397449\pi$
$719$	3.15572e115	0.633255	0.316628	+	0.948550i	$0.397449\pi$
$720$	−4.80448e115	−0.911341
$721$	3.18017e114	0.0570258
$722$	−2.08493e114	−0.0353456
$723$	−8.00116e114	−0.128248
$724$	2.83072e115	0.429028
$725$	3.81074e114	0.0546160
$726$	−2.51371e114	−0.0340708
$727$	−1.09326e116	−1.40145	−0.700726	−	0.713430i	$-0.747140\pi$
$727$	−1.09326e116	−1.40145	−0.700726	+	0.713430i	$0.747140\pi$
$728$	−8.81925e113	−0.0106933
$729$	−8.39484e115	−0.962826
$730$	−3.12859e115	−0.339447
$731$	5.56226e115	0.570950
$732$	−1.36364e115	−0.132434
$733$	4.79348e115	0.440494	0.220247	−	0.975444i	$-0.429314\pi$
$733$	4.79348e115	0.440494	0.220247	+	0.975444i	$0.429314\pi$
$734$	3.42164e114	0.0297539
$735$	1.06408e115	0.0875663
$736$	−8.65529e115	−0.674109
$737$	3.53476e116	2.60571
$738$	3.79072e115	0.264508
$739$	−1.65197e116	−1.09120	−0.545599	−	0.838047i	$-0.683698\pi$
$739$	−1.65197e116	−1.09120	−0.545599	+	0.838047i	$0.683698\pi$
$740$	2.85595e116	1.78594
$741$	4.58736e114	0.0271597
$742$	−2.63315e114	−0.0147611
$743$	−3.23015e116	−1.71465	−0.857324	−	0.514777i	$-0.827875\pi$
$743$	−3.23015e116	−1.71465	−0.857324	+	0.514777i	$0.827875\pi$
$744$	−6.31585e114	−0.0317488
$745$	1.81990e116	0.866402
$746$	8.01997e115	0.361618
$747$	−2.85082e116	−1.21755
$748$	2.86866e116	1.16055
$749$	−2.96861e115	−0.113773
$750$	4.50651e114	0.0163629
$751$	−1.87932e116	−0.646523	−0.323261	−	0.946310i	$-0.604779\pi$
$751$	−1.87932e116	−0.646523	−0.323261	+	0.946310i	$0.604779\pi$
$752$	−3.44671e116	−1.12352
$753$	4.44986e113	0.00137452
$754$	−7.08019e114	−0.0207255
$755$	−2.00443e116	−0.556082
$756$	3.40080e114	0.00894228
$757$	3.86465e114	0.00963224	0.00481612	−	0.999988i	$-0.498467\pi$
$757$	3.86465e114	0.00963224	0.00481612	+	0.999988i	$0.498467\pi$
$758$	9.76185e115	0.230637
$759$	5.82899e115	0.130557
$760$	−2.30635e116	−0.489749
$761$	1.38900e116	0.279655	0.139828	−	0.990176i	$-0.455345\pi$
$761$	1.38900e116	0.279655	0.139828	+	0.990176i	$0.455345\pi$
$762$	7.92869e114	0.0151365
$763$	2.06746e115	0.0374278
$764$	3.70352e116	0.635819
$765$	5.05001e116	0.822251
$766$	−1.09885e116	−0.169697
$767$	1.45378e114	0.00212955
$768$	−2.56763e115	−0.0356782
$769$	4.07365e116	0.536990	0.268495	−	0.963281i	$-0.413474\pi$
$769$	4.07365e116	0.536990	0.268495	+	0.963281i	$0.413474\pi$
$770$	−2.19265e115	−0.0274217
$771$	−5.00870e115	−0.0594324
$772$	−4.22740e116	−0.475963
$773$	1.12721e117	1.20431	0.602153	−	0.798380i	$-0.294310\pi$
$773$	1.12721e117	1.20431	0.602153	+	0.798380i	$0.294310\pi$
$774$	1.84579e116	0.187143
$775$	−2.11285e116	−0.203306
$776$	−7.16562e116	−0.654417
$777$	−9.39133e114	−0.00814097
$778$	−3.85427e116	−0.317153
$779$	−1.28630e117	−1.00479
$780$	−4.14418e115	−0.0307331
$781$	1.22573e117	0.863035
$782$	2.71096e116	0.181238
$783$	5.63481e115	0.0357708
$784$	−1.36098e117	−0.820447
$785$	−1.87014e117	−1.07067
$786$	−1.44495e115	−0.00785672
$787$	1.20280e117	0.621180	0.310590	−	0.950544i	$-0.399473\pi$
$787$	1.20280e117	0.621180	0.310590	+	0.950544i	$0.399473\pi$
$788$	−1.83152e117	−0.898464
$789$	−3.51922e115	−0.0163994
$790$	−2.62317e116	−0.116126
$791$	9.25607e115	0.0389295
$792$	1.96470e117	0.785103
$793$	1.74928e117	0.664193
$794$	6.69526e116	0.241567
$795$	−2.55369e116	−0.0875587
$796$	4.33469e117	1.41247
$797$	−1.92384e117	−0.595808	−0.297904	−	0.954596i	$-0.596288\pi$
$797$	−1.92384e117	−0.595808	−0.297904	+	0.954596i	$0.596288\pi$
$798$	3.67464e114	0.00108168
$799$	3.62285e117	1.01369
$800$	6.11626e116	0.162683
$801$	2.06549e117	0.522283
$802$	−1.40018e117	−0.336607
$803$	−9.04358e117	−2.06710
$804$	5.35158e116	0.116309
$805$	3.24346e116	0.0670310
$806$	3.92559e116	0.0771499
$807$	4.62793e116	0.0864986
$808$	1.21732e116	0.0216393
$809$	1.06556e117	0.180162	0.0900808	−	0.995934i	$-0.471287\pi$
$809$	1.06556e117	0.180162	0.0900808	+	0.995934i	$0.471287\pi$
$810$	1.66524e117	0.267814
$811$	−7.46805e117	−1.14252	−0.571259	−	0.820770i	$-0.693545\pi$
$811$	−7.46805e117	−1.14252	−0.571259	+	0.820770i	$0.693545\pi$
$812$	8.87757e115	0.0129204
$813$	−2.44866e116	−0.0339049
$814$	−5.27407e117	−0.694797
$815$	−2.40377e117	−0.301308
$816$	4.04793e116	0.0482816
$817$	−6.26329e117	−0.710901
$818$	−9.62557e114	−0.00103972
$819$	−2.17446e116	−0.0223539
$820$	1.16203e118	1.13699
$821$	3.94100e117	0.367036	0.183518	−	0.983016i	$-0.441251\pi$
$821$	3.94100e117	0.367036	0.183518	+	0.983016i	$0.441251\pi$
$822$	−2.82577e116	−0.0250512
$823$	1.58564e118	1.33817	0.669085	−	0.743186i	$-0.266686\pi$
$823$	1.58564e118	1.33817	0.669085	+	0.743186i	$0.266686\pi$
$824$	5.58054e117	0.448357
$825$	−4.11905e116	−0.0315074
$826$	1.16453e114	8.48125e−5 0
$827$	1.11417e118	0.772645	0.386322	−	0.922364i	$-0.373745\pi$
$827$	1.11417e118	0.772645	0.386322	+	0.922364i	$0.373745\pi$
$828$	−1.40816e118	−0.929871
$829$	−1.88133e118	−1.18306	−0.591529	−	0.806284i	$-0.701476\pi$
$829$	−1.88133e118	−1.18306	−0.591529	+	0.806284i	$0.701476\pi$
$830$	5.58301e117	0.334354
$831$	−4.33926e116	−0.0247500
$832$	4.50273e117	0.244614
$833$	1.43053e118	0.740243
$834$	7.15408e116	0.0352638
$835$	1.05941e118	0.497463
$836$	−3.23021e118	−1.44503
$837$	−3.12420e117	−0.133155
$838$	−2.86673e117	−0.116413
$839$	2.30700e118	0.892666	0.446333	−	0.894867i	$-0.352730\pi$
$839$	2.30700e118	0.892666	0.446333	+	0.894867i	$0.352730\pi$
$840$	−6.85135e115	−0.00252618
$841$	−2.69893e118	−0.948316
$842$	−4.62718e117	−0.154945
$843$	−4.68743e117	−0.149595
$844$	−3.34750e118	−1.01824
$845$	−3.30943e118	−0.959525
$846$	1.20221e118	0.332263
$847$	−4.04319e117	−0.106524
$848$	3.26622e118	0.820376
$849$	4.74982e117	0.113741
$850$	−1.91570e117	−0.0437383
$851$	7.80165e118	1.69840
$852$	1.85574e117	0.0385224
$853$	3.16499e118	0.626523	0.313262	−	0.949667i	$-0.398578\pi$
$853$	3.16499e118	0.626523	0.313262	+	0.949667i	$0.398578\pi$
$854$	1.40123e117	0.0264525
$855$	−5.68648e118	−1.02380
$856$	−5.20931e118	−0.894525
$857$	2.71295e118	0.444343	0.222172	−	0.975008i	$-0.428686\pi$
$857$	2.71295e118	0.444343	0.222172	+	0.975008i	$0.428686\pi$
$858$	7.65303e116	0.0119563
$859$	9.25294e118	1.37898	0.689488	−	0.724297i	$-0.257836\pi$
$859$	9.25294e118	1.37898	0.689488	+	0.724297i	$0.257836\pi$
$860$	5.65819e118	0.804434
$861$	−3.82114e116	−0.00518281
$862$	−1.79527e118	−0.232320
$863$	2.28392e117	0.0281996	0.0140998	−	0.999901i	$-0.495512\pi$
$863$	2.28392e117	0.0281996	0.0140998	+	0.999901i	$0.495512\pi$
$864$	9.04392e117	0.106549
$865$	−1.28916e119	−1.44929
$866$	3.14977e118	0.337913
$867$	3.45333e117	0.0353561
$868$	−4.92214e117	−0.0480955
$869$	−7.58261e118	−0.707160
$870$	−5.50034e116	−0.00489620
$871$	−6.86500e118	−0.583318
$872$	3.62797e118	0.294270
$873$	−1.76674e119	−1.36803
$874$	−3.05263e118	−0.225664
$875$	7.24850e117	0.0511590
$876$	−1.36919e118	−0.0922669
$877$	8.70438e118	0.560085	0.280043	−	0.959988i	$-0.409651\pi$
$877$	8.70438e118	0.560085	0.280043	+	0.959988i	$0.409651\pi$
$878$	5.68973e118	0.349594
$879$	1.13989e118	0.0668827
$880$	2.71980e119	1.52401
$881$	−1.61438e119	−0.863938	−0.431969	−	0.901888i	$-0.642181\pi$
$881$	−1.61438e119	−0.863938	−0.431969	+	0.901888i	$0.642181\pi$
$882$	4.74710e118	0.242633
$883$	9.06279e118	0.442439	0.221219	−	0.975224i	$-0.428996\pi$
$883$	9.06279e118	0.442439	0.221219	+	0.975224i	$0.428996\pi$
$884$	−5.57135e118	−0.259803
$885$	1.12939e116	0.000503085 0
$886$	3.40798e118	0.145021
$887$	2.19271e119	0.891404	0.445702	−	0.895181i	$-0.352954\pi$
$887$	2.19271e119	0.891404	0.445702	+	0.895181i	$0.352954\pi$
$888$	−1.64799e118	−0.0640072
$889$	1.27529e118	0.0473247
$890$	−4.04503e118	−0.143425
$891$	4.81358e119	1.63088
$892$	−3.38757e119	−1.09676
$893$	−4.07945e119	−1.26217
$894$	−5.08822e117	−0.0150451
$895$	1.29669e119	0.366442
$896$	1.87657e118	0.0506862
$897$	−1.13207e118	−0.0292267
$898$	−1.01925e119	−0.251530
$899$	−8.15554e118	−0.192391
$900$	9.95075e118	0.224406
$901$	−3.43313e119	−0.740179
$902$	−2.14591e119	−0.442331
$903$	−1.86061e117	−0.00366691
$904$	1.62425e119	0.306078
$905$	−2.82098e119	−0.508315
$906$	5.60412e117	0.00965641
$907$	2.81849e119	0.464431	0.232216	−	0.972664i	$-0.425403\pi$
$907$	2.81849e119	0.464431	0.232216	+	0.972664i	$0.425403\pi$
$908$	−8.28122e119	−1.30502
$909$	3.00139e118	0.0452361
$910$	4.25843e117	0.00613865
$911$	4.14570e119	0.571615	0.285808	−	0.958287i	$-0.407738\pi$
$911$	4.14570e119	0.571615	0.285808	+	0.958287i	$0.407738\pi$
$912$	−4.55810e118	−0.0601164
$913$	1.61384e120	2.03608
$914$	−1.29621e118	−0.0156443
$915$	1.35895e119	0.156909
$916$	−8.00887e118	−0.0884717
$917$	−2.32414e118	−0.0245643
$918$	−2.83269e118	−0.0286464
$919$	−4.86484e119	−0.470750	−0.235375	−	0.971905i	$-0.575632\pi$
$919$	−4.86484e119	−0.470750	−0.235375	+	0.971905i	$0.575632\pi$
$920$	5.69161e119	0.527021
$921$	7.71384e118	0.0683527
$922$	3.95756e119	0.335602
$923$	−2.38054e119	−0.193200
$924$	−9.59583e117	−0.00745363
$925$	−5.51304e119	−0.409874
$926$	−3.27573e119	−0.233111
$927$	1.37593e120	0.937273
$928$	2.36086e119	0.153949
$929$	−1.01757e120	−0.635225	−0.317613	−	0.948221i	$-0.602881\pi$
$929$	−1.01757e120	−0.635225	−0.317613	+	0.948221i	$0.602881\pi$
$930$	3.04964e118	0.0182259
$931$	−1.61082e120	−0.921692
$932$	5.36899e118	0.0294136
$933$	−9.26535e118	−0.0486021
$934$	1.89021e119	0.0949426
$935$	−2.85879e120	−1.37503
$936$	−3.81573e119	−0.175754
$937$	−2.90798e120	−1.28274	−0.641368	−	0.767233i	$-0.721633\pi$
$937$	−2.90798e120	−1.28274	−0.641368	+	0.767233i	$0.721633\pi$
$938$	−5.49912e118	−0.0232315
$939$	−1.42631e118	−0.00577107
$940$	3.68533e120	1.42823
$941$	2.46055e120	0.913383	0.456692	−	0.889625i	$-0.349034\pi$
$941$	2.46055e120	0.913383	0.456692	+	0.889625i	$0.349034\pi$
$942$	5.22868e118	0.0185922
$943$	3.17433e120	1.08126
$944$	−1.44451e118	−0.00471362
$945$	−3.38910e118	−0.0105949
$946$	−1.04490e120	−0.312955
$947$	1.13269e120	0.325039	0.162519	−	0.986705i	$-0.448038\pi$
$947$	1.13269e120	0.325039	0.162519	+	0.986705i	$0.448038\pi$
$948$	−1.14800e119	−0.0315648
$949$	1.75639e120	0.462743
$950$	2.15714e119	0.0544594
$951$	−5.41568e119	−0.131021
$952$	−9.21083e118	−0.0213551
$953$	1.13612e120	0.252442	0.126221	−	0.992002i	$-0.459715\pi$
$953$	1.13612e120	0.252442	0.126221	+	0.992002i	$0.459715\pi$
$954$	−1.13926e120	−0.242612
$955$	−3.69077e120	−0.753322
$956$	4.19506e120	0.820718
$957$	−1.58994e119	−0.0298159
$958$	1.97007e120	0.354144
$959$	−4.54511e119	−0.0783233
$960$	3.49800e119	0.0577876
$961$	−1.79208e120	−0.283832
$962$	1.02430e120	0.155538
$963$	−1.28440e121	−1.86997
$964$	−1.09421e121	−1.52750
$965$	4.21286e120	0.563924
$966$	−9.06830e117	−0.00116400
$967$	3.96069e120	0.487527	0.243763	−	0.969835i	$-0.421618\pi$
$967$	3.96069e120	0.487527	0.243763	+	0.969835i	$0.421618\pi$
$968$	−7.09496e120	−0.837526
$969$	4.79104e119	0.0542396
$970$	3.45996e120	0.375678
$971$	1.43446e121	1.49386	0.746930	−	0.664902i	$-0.231527\pi$
$971$	1.43446e121	1.49386	0.746930	+	0.664902i	$0.231527\pi$
$972$	2.20938e120	0.220692
$973$	1.15070e120	0.110253
$974$	1.55547e119	0.0142963
$975$	7.99978e118	0.00705328
$976$	−1.73812e121	−1.47015
$977$	1.72213e121	1.39745	0.698725	−	0.715390i	$-0.253751\pi$
$977$	1.72213e121	1.39745	0.698725	+	0.715390i	$0.253751\pi$
$978$	6.72064e118	0.00523223
$979$	−1.16927e121	−0.873403
$980$	1.45520e121	1.04296
$981$	8.94506e120	0.615160
$982$	1.78953e120	0.118093
$983$	−1.40198e121	−0.887817	−0.443908	−	0.896072i	$-0.646408\pi$
$983$	−1.40198e121	−0.887817	−0.443908	+	0.896072i	$0.646408\pi$
$984$	−6.70532e119	−0.0407491
$985$	1.82522e121	1.06451
$986$	−7.39455e119	−0.0413901
$987$	−1.21186e119	−0.00651041
$988$	6.27352e120	0.323486
$989$	1.54566e121	0.765004
$990$	−9.48667e120	−0.450701
$991$	−1.84277e121	−0.840406	−0.420203	−	0.907430i	$-0.638041\pi$
$991$	−1.84277e121	−0.840406	−0.420203	+	0.907430i	$0.638041\pi$
$992$	−1.30897e121	−0.573069
$993$	1.56558e120	0.0658007
$994$	−1.90690e119	−0.00769449
$995$	−4.31977e121	−1.67350
$996$	2.44333e120	0.0908823
$997$	−1.86505e120	−0.0666097	−0.0333048	−	0.999445i	$-0.510603\pi$
$997$	−1.86505e120	−0.0666097	−0.0333048	+	0.999445i	$0.510603\pi$
$998$	−9.44550e119	−0.0323920
$999$	−8.15195e120	−0.268447

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.82.a.a.1.4	✓	6
3.2	odd	2		9.82.a.b.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.82.a.a.1.4	✓	6	1.1	even	1	trivial
9.82.a.b.1.3		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)

\(f(q)\)	\(=\)	\(q+3.81039e11 q^{2} -1.66183e18 q^{3} -2.27266e24 q^{4} +2.26484e28 q^{5} -6.33221e29 q^{6} -1.01850e33 q^{7} -1.78727e36 q^{8} -4.40665e38 q^{9} +O(q^{10})\)	\(q+3.81039e11 q^{2} -1.66183e18 q^{3} -2.27266e24 q^{4} +2.26484e28 q^{5} -6.33221e29 q^{6} -1.01850e33 q^{7} -1.78727e36 q^{8} -4.40665e38 q^{9} +8.62992e39 q^{10} +2.49459e42 q^{11} +3.77677e42 q^{12} -4.84484e44 q^{13} -3.88090e44 q^{14} -3.76378e46 q^{15} +4.81394e48 q^{16} -5.05995e49 q^{17} -1.67910e50 q^{18} +5.69767e51 q^{19} -5.14722e52 q^{20} +1.69258e51 q^{21} +9.50534e53 q^{22} -1.40607e55 q^{23} +2.97013e54 q^{24} +9.93602e55 q^{25} -1.84607e56 q^{26} +1.46921e57 q^{27} +2.31472e57 q^{28} +3.83527e58 q^{29} -1.43414e58 q^{30} -2.12645e60 q^{31} +6.15564e60 q^{32} -4.14558e60 q^{33} -1.92804e61 q^{34} -2.30675e61 q^{35} +1.00148e63 q^{36} -5.54853e63 q^{37} +2.17103e63 q^{38} +8.05129e62 q^{39} -4.04788e64 q^{40} -2.25758e65 q^{41} +6.44938e62 q^{42} -1.09927e66 q^{43} -5.66935e66 q^{44} -9.98036e66 q^{45} -5.35768e66 q^{46} -7.15986e67 q^{47} -7.99994e66 q^{48} -2.82716e68 q^{49} +3.78601e67 q^{50} +8.40877e67 q^{51} +1.10107e69 q^{52} +6.78492e69 q^{53} +5.59825e68 q^{54} +5.64985e70 q^{55} +1.82034e69 q^{56} -9.46855e69 q^{57} +1.46139e70 q^{58} -3.00068e69 q^{59} +8.55379e70 q^{60} -3.61060e72 q^{61} -8.10261e71 q^{62} +4.48819e71 q^{63} -9.29385e72 q^{64} -1.09728e73 q^{65} -1.57962e72 q^{66} +1.41697e74 q^{67} +1.14996e74 q^{68} +2.33665e73 q^{69} -8.78961e72 q^{70} +4.91356e74 q^{71} +7.87586e74 q^{72} -3.62528e75 q^{73} -2.11421e75 q^{74} -1.65120e74 q^{75} -1.29489e76 q^{76} -2.54075e75 q^{77} +3.06785e74 q^{78} -3.03962e76 q^{79} +1.09028e77 q^{80} +1.92961e77 q^{81} -8.60227e76 q^{82} +6.46937e77 q^{83} -3.84666e75 q^{84} -1.14600e78 q^{85} -4.18865e77 q^{86} -6.37357e76 q^{87} -4.45849e78 q^{88} -4.68721e78 q^{89} -3.80290e78 q^{90} +4.93449e77 q^{91} +3.19553e79 q^{92} +3.53380e78 q^{93} -2.72818e79 q^{94} +1.29043e80 q^{95} -1.02296e79 q^{96} +4.00926e80 q^{97} -1.07726e80 q^{98} -1.09928e81 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 460872026640 q^{2} - 15\!\cdots\!60 q^{3}+ \cdots + 11\!\cdots\!98 q^{9}+O(q^{10}) \) 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

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