LMFDB - Embedded newform 9.82.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,82,Mod(1,9)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 82, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 82);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 82 $
Character orbit:	$[\chi]$	$=$	9.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:	$373.951156984$
Analytic rank:	$0$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{58}\cdot 3^{34}\cdot 5^{7}\cdot 7^{3}\cdot 13 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.17952e9$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.81039e11 q^{2} -2.27266e24 q^{4} -2.26484e28 q^{5} -1.01850e33 q^{7} +1.78727e36 q^{8} +O(q^{10})$	\(q-3.81039e11 q^{2} -2.27266e24 q^{4} -2.26484e28 q^{5} -1.01850e33 q^{7} +1.78727e36 q^{8} +8.62992e39 q^{10} -2.49459e42 q^{11} -4.84484e44 q^{13} +3.88090e44 q^{14} +4.81394e48 q^{16} +5.05995e49 q^{17} +5.69767e51 q^{19} +5.14722e52 q^{20} +9.50534e53 q^{22} +1.40607e55 q^{23} +9.93602e55 q^{25} +1.84607e56 q^{26} +2.31472e57 q^{28} -3.83527e58 q^{29} -2.12645e60 q^{31} -6.15564e60 q^{32} -1.92804e61 q^{34} +2.30675e61 q^{35} -5.54853e63 q^{37} -2.17103e63 q^{38} -4.04788e64 q^{40} +2.25758e65 q^{41} -1.09927e66 q^{43} +5.66935e66 q^{44} -5.35768e66 q^{46} +7.15986e67 q^{47} -2.82716e68 q^{49} -3.78601e67 q^{50} +1.10107e69 q^{52} -6.78492e69 q^{53} +5.64985e70 q^{55} -1.82034e69 q^{56} +1.46139e70 q^{58} +3.00068e69 q^{59} -3.61060e72 q^{61} +8.10261e71 q^{62} -9.29385e72 q^{64} +1.09728e73 q^{65} +1.41697e74 q^{67} -1.14996e74 q^{68} -8.78961e72 q^{70} -4.91356e74 q^{71} -3.62528e75 q^{73} +2.11421e75 q^{74} -1.29489e76 q^{76} +2.54075e75 q^{77} -3.03962e76 q^{79} -1.09028e77 q^{80} -8.60227e76 q^{82} -6.46937e77 q^{83} -1.14600e78 q^{85} +4.18865e77 q^{86} -4.45849e78 q^{88} +4.68721e78 q^{89} +4.93449e77 q^{91} -3.19553e79 q^{92} -2.72818e79 q^{94} -1.29043e80 q^{95} +4.00926e80 q^{97} +1.07726e80 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 460872026640 q^{2} + 44\!\cdots\!52 q^{4}+ \cdots + 54\!\cdots\!20 q^{8}+O(q^{10}) $ 6 * q + 460872026640 * q^2 + 4493950976700073762513152 * q^4 + 18364304155649862126617790300 * q^5 - 31430760593927655842892725138869200 * q^7 + 5498145101596630185016447889074360320 * q^8	$ 6 q + 460872026640 q^{2} + 44\!\cdots\!52 q^{4}+ \cdots + 85\!\cdots\!80 q^{98}+O(q^{100}) $ 6 * q + 460872026640 * q^2 + 4493950976700073762513152 * q^4 + 18364304155649862126617790300 * q^5 - 31430760593927655842892725138869200 * q^7 + 5498145101596630185016447889074360320 * q^8 - 66472312087527710620452553569669697173600 * q^10 + 2302475295973581620809306061775551681990328 * q^11 + 1313253814255449492724146018729804193778100180 * q^13 - 41225372723246048337281629784765672712004401024 * q^14 + 2799490233261278434402974316306719898117729222656 * q^16 - 2377848571505238562780180385684069414829577769580 * q^17 - 17422016964741760630179674590582970665727618619375240 * q^19 - 148672889698640611477740875719636714144962866333222400 * q^20 - 1258034178625689345497738618244246726621220713529586880 * q^22 - 10526595063181453314046018770874462030150898790798283920 * q^23 + 411037910011361515508644334216291479522821661187695496250 * q^25 + 3180570114716540139250277986112641638356676984048903123168 * q^26 - 82116517748637002885903417761702653442063276903193852344320 * q^28 - 155464359052154485146727469597467543970919715236853926245940 * q^29 + 1259277021063335018777245090979655984137503836933555134668992 * q^31 + 13036312845125683749178794475020758767431562303480221102243840 * q^32 + 11899550405754031112224464347628728246396477955985557631122144 * q^34 + 232034356615504837711196063040035766391492406317925929510437600 * q^35 + 414692688584236378963319357622814947056491742931883680122973540 * q^37 + 2455417714037465297201999851134772037590829998762172946918415680 * q^38 - 258059824285668605758122263287555971608050642150708772544789504000 * q^40 + 250252788823194090638944408016236187978548863949167831014660870148 * q^41 - 5362516930786214192203446564720631507618558180640993338648106782200 * q^43 + 17252465656682175267213991915222412585785021276568609411813835518976 * q^44 - 123763409427226200113215389587151615608344054530127843046255996688768 * q^46 + 230717394511751791462615349254196337530205542984846694602934639341280 * q^47 - 148965540042877735285285650175007198234557699456949204802064464556458 * q^49 + 1416105420952806525015169807922957339416756851287952031511031347670000 * q^50 + 12562371185881747636341658298037576485393840750032566447999727917043200 * q^52 - 25898990256961205776642859216859182171010424056472082121008236344959940 * q^53 + 70427859302095658379065386305135120838252257009889309990749877277396400 * q^55 - 350275852246953465289512615368698332984392220622408793911163576939151360 * q^56 - 312514134877257928766126367534026770462807935435519457753987287493386720 * q^58 + 38532453307459913471042984274454520116124717672121643571528434328282520 * q^59 - 4585192544270629640163935422584783189092178505653567017169797728495170828 * q^61 + 11745445982868867354760701788812677993661414140303262885466836339630318080 * q^62 - 24049189879736877632355406073912155582619770074517134096672197458230509568 * q^64 - 40108571425620140080303901416556158312567794172295521521551039993118238200 * q^65 + 278606964486964374833906544600580027758780739521508130980859112605565987480 * q^67 - 591059149620766869951154898169335214276013402788475417448362648514550551040 * q^68 + 2635837114104224632390936486964777102611174135296488988531978806621369068800 * q^70 + 554281436103188717611008447226924711986842423491780222553301787426789861968 * q^71 - 1159677538409433721867557656635958525415325708297922475676033828300683142980 * q^73 + 14870996314347354169518203977127998385153668929299472477677600807989626002016 * q^74 - 56365824164857229782022127848008365902008884166434980738114640515976798612480 * q^76 + 22951272837324694774527636903423616359482790364245898655274441101674154673600 * q^77 + 76488528596848273963909721387433081359345259080220208993600380062891411190240 * q^79 - 326185463863660018876021371340485226979224823762794013840530768719064527667200 * q^80 + 836977463852743303549437738986542975894462808796250502348000478828556860551520 * q^82 - 440718478462773776637617020819789880594300172591745821478345102532528865997560 * q^83 + 1165607138975709364402518400492567424057357396402879557680723771041190675179400 * q^85 + 10339197506820945136003281093027314178240703830345630490304599234644673765234368 * q^86 - 9603847126452588175246186358824265187739652448840879006569656469218022549667840 * q^88 + 18886228493337874501351816155449414708824427288664596668607356717228138798590180 * q^89 - 14576226325987997036142564032100430704897317032265698214767987870608618538920288 * q^91 - 66364414655655668275929797141498084164407535259475789695165805684452941775738880 * q^92 + 331286952814608158700187065887753978184064043063622410298763861434514546852072704 * q^94 - 267699559747800180626411366716842325842865933645649558098598518850783266973922000 * q^95 + 113832498161281214584608062040287314379413598012089688107897449655058469975263820 * q^97 + 858118355318723523117883130491863373979750018711838274840266757637744872892872080 * q^98

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	$-0.539099\pi$
$2$	−3.81039e11	−0.245050	−0.122525	+	0.992465i	$0.539099\pi$
$3$	0	0
$3$	0	0
$4$	−2.27266e24	−0.939951
$5$	−2.26484e28	−1.11366	−0.556830	−	0.830627i	$-0.687982\pi$
$5$	−2.26484e28	−1.11366	−0.556830	+	0.830627i	$0.687982\pi$
$6$	0	0
$7$	−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
$9$	0	0
$10$	8.62992e39	0.272902
$11$	−2.49459e42	−1.66186	−0.830931	−	0.556375i	$-0.812192\pi$
$11$	−2.49459e42	−1.66186	−0.830931	+	0.556375i	$0.812192\pi$
$12$	0	0
$13$	−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
$15$	0	0
$16$	4.81394e48	0.823458
$17$	5.05995e49	0.742959	0.371480	−	0.928441i	$-0.378851\pi$
$17$	5.05995e49	0.742959	0.371480	+	0.928441i	$0.378851\pi$
$18$	0	0
$19$	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
$21$	0	0
$22$	9.50534e53	0.407239
$23$	1.40607e55	0.995476	0.497738	−	0.867327i	$-0.334164\pi$
$23$	1.40607e55	0.995476	0.497738	+	0.867327i	$0.334164\pi$
$24$	0	0
$25$	9.93602e55	0.240238
$26$	1.84607e56	0.0911650
$27$	0	0
$28$	2.31472e57	0.0568326
$29$	−3.83527e58	−0.227341	−0.113670	−	0.993519i	$-0.536261\pi$
$29$	−3.83527e58	−0.227341	−0.113670	+	0.993519i	$0.536261\pi$
$30$	0	0
$31$	−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
$33$	0	0
$34$	−1.92804e61	−0.182062
$35$	2.30675e61	0.0673356
$36$	0	0
$37$	−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
$39$	0	0
$40$	−4.04788e64	−0.529416
$41$	2.25758e65	1.08617	0.543085	−	0.839678i	$-0.317256\pi$
$41$	2.25758e65	1.08617	0.543085	+	0.839678i	$0.317256\pi$
$42$	0	0
$43$	−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
$45$	0	0
$46$	−5.35768e66	−0.243941
$47$	7.15986e67	1.36440	0.682199	−	0.731167i	$-0.261024\pi$
$47$	7.15986e67	1.36440	0.682199	+	0.731167i	$0.261024\pi$
$48$	0	0
$49$	−2.82716e68	−0.996344
$50$	−3.78601e67	−0.0588703
$51$	0	0
$52$	1.10107e69	0.349687
$53$	−6.78492e69	−0.996258	−0.498129	−	0.867103i	$-0.665979\pi$
$53$	−6.78492e69	−0.996258	−0.498129	+	0.867103i	$0.665979\pi$
$54$	0	0
$55$	5.64985e70	1.85075
$56$	−1.82034e69	−0.0287433
$57$	0	0
$58$	1.46139e70	0.0557098
$59$	3.00068e69	0.00572418	0.00286209	−	0.999996i	$-0.499089\pi$
$59$	3.00068e69	0.00572418	0.00286209	+	0.999996i	$0.499089\pi$
$60$	0	0
$61$	−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
$63$	0	0
$64$	−9.29385e72	−0.657517
$65$	1.09728e73	0.414311
$66$	0	0
$67$	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
$69$	0	0
$70$	−8.78961e72	−0.0165006
$71$	−4.91356e74	−0.519318	−0.259659	−	0.965700i	$-0.583610\pi$
$71$	−4.91356e74	−0.519318	−0.259659	+	0.965700i	$0.583610\pi$
$72$	0	0
$73$	−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
$75$	0	0
$76$	−1.29489e76	−0.869524
$77$	2.54075e75	0.100482
$78$	0	0
$79$	−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
$81$	0	0
$82$	−8.60227e76	−0.266166
$83$	−6.46937e77	−1.22518	−0.612589	−	0.790402i	$-0.709872\pi$
$83$	−6.46937e77	−1.22518	−0.612589	+	0.790402i	$0.709872\pi$
$84$	0	0
$85$	−1.14600e78	−0.827404
$86$	4.18865e77	0.188316
$87$	0	0
$88$	−4.45849e78	−0.790023
$89$	4.68721e78	0.525557	0.262778	−	0.964856i	$-0.415361\pi$
$89$	4.68721e78	0.525557	0.262778	+	0.964856i	$0.415361\pi$
$90$	0	0
$91$	4.93449e77	0.0224940
$92$	−3.19553e79	−0.935698
$93$	0	0
$94$	−2.72818e79	−0.334345
$95$	−1.29043e80	−1.03022
$96$	0	0
$97$	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
$99$	0	0
$100$	−2.25812e80	−0.225812
$101$	6.81104e79	0.0455196	0.0227598	−	0.999741i	$-0.492755\pi$
$101$	6.81104e79	0.0455196	0.0227598	+	0.999741i	$0.492755\pi$
$102$	0	0
$103$	−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
$105$	0	0
$106$	2.58532e81	0.244133
$107$	−2.91468e82	−1.88169	−0.940844	−	0.338841i	$-0.889965\pi$
$107$	−2.91468e82	−1.88169	−0.940844	+	0.338841i	$0.889965\pi$
$108$	0	0
$109$	−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
$111$	0	0
$112$	−4.90302e81	−0.0497890
$113$	9.08790e82	0.643853	0.321926	−	0.946765i	$-0.395670\pi$
$113$	9.08790e82	0.643853	0.321926	+	0.946765i	$0.395670\pi$
$114$	0	0
$115$	−3.18453e83	−1.10862
$116$	8.71628e82	0.213689
$117$	0	0
$118$	−1.14338e81	−0.00140271
$119$	−5.15358e82	−0.0449218
$120$	0	0
$121$	3.96973e84	1.76179
$122$	1.37578e84	0.437497
$123$	0	0
$124$	4.83271e84	0.795449
$125$	7.11681e84	0.846116
$126$	0	0
$127$	−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
$129$	0	0
$130$	−4.18106e84	−0.101527
$131$	−2.28191e85	−0.406267	−0.203134	−	0.979151i	$-0.565113\pi$
$131$	−2.28191e85	−0.406267	−0.203134	+	0.979151i	$0.565113\pi$
$132$	0	0
$133$	−5.80310e84	−0.0559331
$134$	−5.39921e85	−0.384225
$135$	0	0
$136$	9.04348e85	0.353191
$137$	−4.46253e86	−1.29538	−0.647692	−	0.761902i	$-0.724266\pi$
$137$	−4.46253e86	−1.29538	−0.647692	+	0.761902i	$0.724266\pi$
$138$	0	0
$139$	−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
$141$	0	0
$142$	1.87226e86	0.127259
$143$	1.20859e87	0.618257
$144$	0	0
$145$	8.68629e86	0.253180
$146$	1.38137e87	0.304803
$147$	0	0
$148$	1.26099e88	1.60366
$149$	−8.03546e87	−0.777977	−0.388989	−	0.921243i	$-0.627175\pi$
$149$	−8.03546e87	−0.777977	−0.388989	+	0.921243i	$0.627175\pi$
$150$	0	0
$151$	−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
$153$	0	0
$154$	−9.68123e86	−0.0246230
$155$	4.81608e88	0.942454
$156$	0	0
$157$	−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
$159$	0	0
$160$	1.39416e89	0.754140
$161$	−1.43209e88	−0.0601898
$162$	0	0
$163$	−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
$165$	0	0
$166$	2.46508e89	0.300229
$167$	−4.67762e89	−0.446692	−0.223346	−	0.974739i	$-0.571698\pi$
$167$	−4.67762e89	−0.446692	−0.223346	+	0.974739i	$0.571698\pi$
$168$	0	0
$169$	−1.46122e90	−0.861596
$170$	4.36670e89	0.202755
$171$	0	0
$172$	2.49827e90	0.722334
$173$	5.69207e90	1.30138	0.650688	−	0.759345i	$-0.274481\pi$
$173$	5.69207e90	1.30138	0.650688	+	0.759345i	$0.274481\pi$
$174$	0	0
$175$	−1.01199e89	−0.0145256
$176$	−1.20088e91	−1.36847
$177$	0	0
$178$	−1.78601e90	−0.128787
$179$	−5.72532e90	−0.329043	−0.164521	−	0.986374i	$-0.552608\pi$
$179$	−5.72532e90	−0.329043	−0.164521	+	0.986374i	$0.552608\pi$
$180$	0	0
$181$	−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
$183$	0	0
$184$	2.51303e91	0.473234
$185$	1.25665e92	1.90003
$186$	0	0
$187$	−1.26225e92	−1.23470
$188$	−1.62719e92	−1.28247
$189$	0	0
$190$	4.91704e91	0.252455
$191$	1.62959e92	0.676438	0.338219	−	0.941067i	$-0.390175\pi$
$191$	1.62959e92	0.676438	0.338219	+	0.941067i	$0.390175\pi$
$192$	0	0
$193$	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
$195$	0	0
$196$	6.42518e92	0.936514
$197$	−8.05894e92	−0.955863	−0.477932	−	0.878397i	$-0.658613\pi$
$197$	−8.05894e92	−0.955863	−0.477932	+	0.878397i	$0.658613\pi$
$198$	0	0
$199$	−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
$201$	0	0
$202$	−2.59527e91	−0.0111546
$203$	3.90624e91	0.0137458
$204$	0	0
$205$	−5.11307e93	−1.20962
$206$	1.18975e93	0.231118
$207$	0	0
$208$	−2.33228e93	−0.306348
$209$	−1.42133e94	−1.53735
$210$	0	0
$211$	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
$213$	0	0
$214$	1.11060e94	0.461107
$215$	2.48968e94	0.855826
$216$	0	0
$217$	2.16580e93	0.0511682
$218$	7.73470e93	0.151690
$219$	0	0
$220$	−1.28402e95	−1.73961
$221$	−2.45147e94	−0.276400
$222$	0	0
$223$	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
$225$	0	0
$226$	−3.46284e94	−0.157776
$227$	−3.64384e95	−1.38839	−0.694196	−	0.719786i	$-0.744240\pi$
$227$	−3.64384e95	−1.38839	−0.694196	+	0.719786i	$0.744240\pi$
$228$	0	0
$229$	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
$231$	0	0
$232$	−6.85466e94	−0.108074
$233$	2.36242e94	0.0312927	0.0156463	−	0.999878i	$-0.495019\pi$
$233$	2.36242e94	0.0312927	0.0156463	+	0.999878i	$0.495019\pi$
$234$	0	0
$235$	−1.62159e96	−1.51947
$236$	−6.81953e93	−0.00538045
$237$	0	0
$238$	1.96371e94	0.0110081
$239$	1.84588e96	0.873150	0.436575	−	0.899668i	$-0.356191\pi$
$239$	1.84588e96	0.873150	0.436575	+	0.899668i	$0.356191\pi$
$240$	0	0
$241$	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
$243$	0	0
$244$	8.20566e96	1.67813
$245$	6.40307e96	1.10959
$246$	0	0
$247$	−2.76043e96	−0.344152
$248$	−3.80054e96	−0.402302
$249$	0	0
$250$	−2.71178e96	−0.207341
$251$	2.67769e95	0.0174171	0.00870853	−	0.999962i	$-0.497228\pi$
$251$	2.67769e95	0.0174171	0.00870853	+	0.999962i	$0.497228\pi$
$252$	0	0
$253$	−3.50757e97	−1.65434
$254$	4.77106e96	0.191800
$255$	0	0
$256$	1.54506e97	0.452092
$257$	−3.01397e97	−0.753092	−0.376546	−	0.926398i	$-0.622888\pi$
$257$	−3.01397e97	−0.753092	−0.376546	+	0.926398i	$0.622888\pi$
$258$	0	0
$259$	5.65121e96	0.103157
$260$	−2.49375e97	−0.389432
$261$	0	0
$262$	8.69497e96	0.0995556
$263$	−2.11768e97	−0.207803	−0.103902	−	0.994588i	$-0.533133\pi$
$263$	−2.11768e97	−0.207803	−0.103902	+	0.994588i	$0.533133\pi$
$264$	0	0
$265$	1.53668e98	1.10949
$266$	2.21121e96	0.0137064
$267$	0	0
$268$	−3.22030e98	−1.47379
$269$	2.78485e98	1.09606	0.548029	−	0.836459i	$-0.315378\pi$
$269$	2.78485e98	1.09606	0.548029	+	0.836459i	$0.315378\pi$
$270$	0	0
$271$	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
$273$	0	0
$274$	1.70040e98	0.317434
$275$	−2.47863e98	−0.399243
$276$	0	0
$277$	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
$279$	0	0
$280$	4.12278e97	0.0320103
$281$	−2.82065e99	−1.89558	−0.947791	−	0.318893i	$-0.896689\pi$
$281$	−2.82065e99	−1.89558	−0.947791	+	0.318893i	$0.896689\pi$
$282$	0	0
$283$	−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
$285$	0	0
$286$	−4.60519e98	−0.151504
$287$	−2.29936e98	−0.0656735
$288$	0	0
$289$	−2.07803e99	−0.448012
$290$	−3.30981e98	−0.0620418
$291$	0	0
$292$	8.23903e99	1.16915
$293$	6.85926e99	0.847498	0.423749	−	0.905780i	$-0.360714\pi$
$293$	6.85926e99	0.847498	0.423749	+	0.905780i	$0.360714\pi$
$294$	0	0
$295$	−6.79607e97	−0.00637479
$296$	−9.91671e99	−0.811061
$297$	0	0
$298$	3.06182e99	0.190643
$299$	−6.81221e99	−0.370343
$300$	0	0
$301$	1.11961e99	0.0464649
$302$	3.37226e99	0.122360
$303$	0	0
$304$	2.74282e100	0.761759
$305$	8.17743e100	1.98826
$306$	0	0
$307$	−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
$309$	0	0
$310$	−1.83511e100	−0.230948
$311$	−5.57540e100	−0.615857	−0.307929	−	0.951409i	$-0.599636\pi$
$311$	−5.57540e100	−0.615857	−0.307929	+	0.951409i	$0.599636\pi$
$312$	0	0
$313$	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
$315$	0	0
$316$	6.90803e100	0.399970
$317$	−3.25887e101	−1.66022	−0.830112	−	0.557597i	$-0.811723\pi$
$317$	−3.25887e101	−1.66022	−0.830112	+	0.557597i	$0.811723\pi$
$318$	0	0
$319$	9.56743e100	0.377809
$320$	2.10491e101	0.732250
$321$	0	0
$322$	5.45683e99	0.0147495
$323$	2.88299e101	0.687292
$324$	0	0
$325$	−4.81385e100	−0.0893750
$326$	4.04413e100	0.0662997
$327$	0	0
$328$	4.03491e101	0.516348
$329$	−7.29234e100	−0.0824961
$330$	0	0
$331$	−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
$333$	0	0
$334$	1.78236e101	0.109462
$335$	−3.20922e102	−1.74616
$336$	0	0
$337$	−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
$339$	0	0
$340$	2.60447e102	0.777719
$341$	5.30463e102	1.40638
$342$	0	0
$343$	5.76952e101	0.120706
$344$	−1.96469e102	−0.365324
$345$	0	0
$346$	−2.16890e102	−0.318902
$347$	7.31979e102	0.957536	0.478768	−	0.877942i	$-0.341084\pi$
$347$	7.31979e102	0.957536	0.478768	+	0.877942i	$0.341084\pi$
$348$	0	0
$349$	−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
$351$	0	0
$352$	1.53558e103	1.12537
$353$	−1.05641e103	−0.690169	−0.345084	−	0.938572i	$-0.612150\pi$
$353$	−1.05641e103	−0.690169	−0.345084	+	0.938572i	$0.612150\pi$
$354$	0	0
$355$	1.11284e103	0.578343
$356$	−1.06524e103	−0.493997
$357$	0	0
$358$	2.18157e102	0.0806318
$359$	2.70416e103	0.892705	0.446352	−	0.894857i	$-0.352723\pi$
$359$	2.70416e103	0.892705	0.446352	+	0.894857i	$0.352723\pi$
$360$	0	0
$361$	−5.47171e102	−0.144239
$362$	4.74605e102	0.111850
$363$	0	0
$364$	−1.12144e102	−0.0211432
$365$	8.21068e103	1.38522
$366$	0	0
$367$	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
$369$	0	0
$370$	−4.78834e103	−0.465602
$371$	6.91047e102	0.0602371
$372$	0	0
$373$	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
$375$	0	0
$376$	1.27966e104	0.648613
$377$	1.85813e103	0.0845768
$378$	0	0
$379$	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
$381$	0	0
$382$	−6.20939e103	−0.165761
$383$	2.88384e104	0.692501	0.346251	−	0.938142i	$-0.387455\pi$
$383$	2.88384e104	0.692501	0.346251	+	0.938142i	$0.387455\pi$
$384$	0	0
$385$	−5.75439e103	−0.111903
$386$	−7.08774e103	−0.124086
$387$	0	0
$388$	−9.11170e104	−1.29394
$389$	1.01152e105	1.29424	0.647119	−	0.762389i	$-0.275974\pi$
$389$	1.01152e105	1.29424	0.647119	+	0.762389i	$0.275974\pi$
$390$	0	0
$391$	7.11466e104	0.739598
$392$	−5.05289e104	−0.473646
$393$	0	0
$394$	3.07077e104	0.234234
$395$	6.88426e104	0.473887
$396$	0	0
$397$	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
$399$	0	0
$400$	4.78314e104	0.197826
$401$	3.67465e105	1.37363	0.686814	−	0.726833i	$-0.259009\pi$
$401$	3.67465e105	1.37363	0.686814	+	0.726833i	$0.259009\pi$
$402$	0	0
$403$	1.03023e105	0.314834
$404$	−1.54792e104	−0.0427861
$405$	0	0
$406$	−1.48843e103	−0.00336840
$407$	1.38413e106	2.83533
$408$	0	0
$409$	−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
$411$	0	0
$412$	7.09613e105	0.886511
$413$	−3.05621e102	−0.000346103 0
$414$	0	0
$415$	1.46521e106	1.36443
$416$	2.98231e105	0.251926
$417$	0	0
$418$	5.41583e105	0.376726
$419$	7.52345e105	0.475061	0.237530	−	0.971380i	$-0.423662\pi$
$419$	7.52345e105	0.475061	0.237530	+	0.971380i	$0.423662\pi$
$420$	0	0
$421$	−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
$423$	0	0
$424$	−1.21265e106	−0.473605
$425$	5.02758e105	0.178487
$426$	0	0
$427$	3.67741e105	0.107948
$428$	6.62407e106	1.76869
$429$	0	0
$430$	−9.48663e105	−0.209720
$431$	4.71152e106	0.948052	0.474026	−	0.880511i	$-0.342800\pi$
$431$	4.71152e106	0.948052	0.474026	+	0.880511i	$0.342800\pi$
$432$	0	0
$433$	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
$435$	0	0
$436$	4.61327e106	0.581844
$437$	8.01134e106	0.920889
$438$	0	0
$439$	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
$441$	0	0
$442$	9.34103e105	0.0677319
$443$	−8.94391e106	−0.591802	−0.295901	−	0.955219i	$-0.595620\pi$
$443$	−8.94391e106	−0.591802	−0.295901	+	0.955219i	$0.595620\pi$
$444$	0	0
$445$	−1.06158e107	−0.585291
$446$	−5.67966e106	−0.285930
$447$	0	0
$448$	9.46583e105	0.0397557
$449$	2.67493e107	1.02645	0.513223	−	0.858255i	$-0.328451\pi$
$449$	2.67493e107	1.02645	0.513223	+	0.858255i	$0.328451\pi$
$450$	0	0
$451$	−5.63174e107	−1.80507
$452$	−2.06537e107	−0.605190
$453$	0	0
$454$	1.38844e107	0.340225
$455$	−1.11758e106	−0.0250506
$456$	0	0
$457$	−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
$459$	0	0
$460$	7.23737e107	1.04205
$461$	−1.03862e108	−1.36953	−0.684764	−	0.728765i	$-0.740095\pi$
$461$	−1.03862e108	−1.36953	−0.684764	+	0.728765i	$0.740095\pi$
$462$	0	0
$463$	−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
$465$	0	0
$466$	−9.00175e105	−0.00766826
$467$	−4.96067e107	−0.387442	−0.193721	−	0.981057i	$-0.562056\pi$
$467$	−4.96067e107	−0.387442	−0.193721	+	0.981057i	$0.562056\pi$
$468$	0	0
$469$	−1.44319e107	−0.0948034
$470$	6.17890e107	0.372347
$471$	0	0
$472$	5.36302e105	0.00272119
$473$	2.74223e108	1.27711
$474$	0	0
$475$	5.66122e107	0.222238
$476$	1.17123e107	0.0422243
$477$	0	0
$478$	−7.03352e107	−0.213965
$479$	−5.17027e108	−1.44519	−0.722596	−	0.691271i	$-0.757051\pi$
$479$	−5.17027e108	−1.44519	−0.722596	+	0.691271i	$0.757051\pi$
$480$	0	0
$481$	2.68818e108	0.634720
$482$	−1.83458e108	−0.398227
$483$	0	0
$484$	−9.02185e108	−1.65599
$485$	−9.08035e108	−1.53307
$486$	0	0
$487$	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
$489$	0	0
$490$	−2.43982e108	−0.271904
$491$	−4.69644e108	−0.481913	−0.240956	−	0.970536i	$-0.577461\pi$
$491$	−4.69644e108	−0.481913	−0.240956	+	0.970536i	$0.577461\pi$
$492$	0	0
$493$	−1.94063e108	−0.168905
$494$	1.05183e108	0.0843343
$495$	0	0
$496$	−1.02366e109	−0.696865
$497$	5.00448e107	0.0313997
$498$	0	0
$499$	−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
$501$	0	0
$502$	−1.02030e107	−0.00426805
$503$	−2.00713e109	−0.774591	−0.387295	−	0.921956i	$-0.626591\pi$
$503$	−2.00713e109	−0.774591	−0.387295	+	0.921956i	$0.626591\pi$
$504$	0	0
$505$	−1.54259e108	−0.0506933
$506$	1.33652e109	0.405397
$507$	0	0
$508$	2.84565e109	0.735699
$509$	−1.97892e109	−0.472452	−0.236226	−	0.971698i	$-0.575911\pi$
$509$	−1.97892e109	−0.472452	−0.236226	+	0.971698i	$0.575911\pi$
$510$	0	0
$511$	3.69236e108	0.0752069
$512$	−5.04356e109	−0.949082
$513$	0	0
$514$	1.14844e109	0.184545
$515$	7.07171e109	1.05034
$516$	0	0
$517$	−1.78609e110	−2.26744
$518$	−2.15333e108	−0.0252787
$519$	0	0
$520$	1.96113e109	0.196957
$521$	−7.75473e109	−0.720508	−0.360254	−	0.932854i	$-0.617310\pi$
$521$	−7.75473e109	−0.720508	−0.360254	+	0.932854i	$0.617310\pi$
$522$	0	0
$523$	−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
$525$	0	0
$526$	8.06917e108	0.0509221
$527$	−1.07598e110	−0.628742
$528$	0	0
$529$	−1.80109e108	−0.00902777
$530$	−5.85533e109	−0.271881
$531$	0	0
$532$	1.31885e109	0.0525743
$533$	−1.09376e110	−0.404084
$534$	0	0
$535$	6.60128e110	2.09556
$536$	2.53251e110	0.745378
$537$	0	0
$538$	−1.06113e110	−0.268589
$539$	7.05260e110	1.65579
$540$	0	0
$541$	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
$543$	0	0
$544$	−3.11472e110	−0.503112
$545$	4.59740e110	0.689373
$546$	0	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
$549$	0	0
$550$	9.44453e109	0.0978344
$551$	−2.18521e110	−0.210307
$552$	0	0
$553$	3.09587e109	0.0257285
$554$	−9.94945e109	−0.0768517
$555$	0	0
$556$	2.56764e111	1.71397
$557$	1.10823e111	0.687852	0.343926	−	0.938997i	$-0.388243\pi$
$557$	1.10823e111	0.687852	0.343926	+	0.938997i	$0.388243\pi$
$558$	0	0
$559$	5.32580e110	0.285895
$560$	1.11046e110	0.0554480
$561$	0	0
$562$	1.07477e111	0.464512
$563$	2.04352e111	0.821845	0.410922	−	0.911670i	$-0.365207\pi$
$563$	2.04352e111	0.821845	0.410922	+	0.911670i	$0.365207\pi$
$564$	0	0
$565$	−2.05827e111	−0.717033
$566$	1.08908e111	0.353179
$567$	0	0
$568$	−8.78184e110	−0.246876
$569$	2.62420e111	0.686990	0.343495	−	0.939155i	$-0.388389\pi$
$569$	2.62420e111	0.686990	0.343495	+	0.939155i	$0.388389\pi$
$570$	0	0
$571$	−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
$573$	0	0
$574$	8.76145e109	0.0160933
$575$	1.39708e111	0.239151
$576$	0	0
$577$	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
$579$	0	0
$580$	−1.97410e111	−0.237977
$581$	6.58908e110	0.0740784
$582$	0	0
$583$	1.69256e112	1.65564
$584$	−6.47934e111	−0.591304
$585$	0	0
$586$	−2.61364e111	−0.207679
$587$	1.53407e112	1.13763	0.568816	−	0.822465i	$-0.307402\pi$
$587$	1.53407e112	1.13763	0.568816	+	0.822465i	$0.307402\pi$
$588$	0	0
$589$	−1.21158e112	−0.782860
$590$	2.58957e109	0.00156214
$591$	0	0
$592$	−2.67103e112	−1.40491
$593$	−2.37317e112	−1.16577	−0.582886	−	0.812554i	$-0.698076\pi$
$593$	−2.37317e112	−1.16577	−0.582886	+	0.812554i	$0.698076\pi$
$594$	0	0
$595$	1.16720e111	0.0500276
$596$	1.82619e112	0.731260
$597$	0	0
$598$	2.59571e111	0.0907525
$599$	4.76363e111	0.155651	0.0778254	−	0.996967i	$-0.475202\pi$
$599$	4.76363e111	0.155651	0.0778254	+	0.996967i	$0.475202\pi$
$600$	0	0
$601$	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
$603$	0	0
$604$	2.01135e112	0.469344
$605$	−8.99080e112	−1.96203
$606$	0	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
$609$	0	0
$610$	−3.11592e112	−0.487222
$611$	−3.46884e112	−0.507592
$612$	0	0
$613$	−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
$615$	0	0
$616$	4.54100e111	0.0477675
$617$	1.56188e112	0.153851	0.0769254	−	0.997037i	$-0.475490\pi$
$617$	1.56188e112	0.153851	0.0769254	+	0.997037i	$0.475490\pi$
$618$	0	0
$619$	−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
$621$	0	0
$622$	2.12444e112	0.150916
$623$	−4.77395e111	−0.0317769
$624$	0	0
$625$	−2.02279e113	−1.18252
$626$	−3.27036e111	−0.0179199
$627$	0	0
$628$	1.87660e113	0.903663
$629$	−2.80753e113	−1.26757
$630$	0	0
$631$	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
$633$	0	0
$634$	1.24175e113	0.406837
$635$	2.83585e113	0.871662
$636$	0	0
$637$	1.36972e113	0.370666
$638$	−3.64556e112	−0.0925820
$639$	0	0
$640$	−4.17291e113	−0.933578
$641$	−4.66631e113	−0.979995	−0.489997	−	0.871724i	$-0.663002\pi$
$641$	−4.66631e113	−0.979995	−0.489997	+	0.871724i	$0.663002\pi$
$642$	0	0
$643$	−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
$645$	0	0
$646$	−1.09853e113	−0.168421
$647$	2.70448e113	0.389457	0.194729	−	0.980857i	$-0.437617\pi$
$647$	2.70448e113	0.389457	0.194729	+	0.980857i	$0.437617\pi$
$648$	0	0
$649$	−7.48547e111	−0.00951281
$650$	1.83426e112	0.0219013
$651$	0	0
$652$	2.41207e113	0.254310
$653$	−3.70480e113	−0.367097	−0.183549	−	0.983011i	$-0.558759\pi$
$653$	−3.70480e113	−0.367097	−0.183549	+	0.983011i	$0.558759\pi$
$654$	0	0
$655$	5.16817e113	0.452443
$656$	1.08679e114	0.894415
$657$	0	0
$658$	2.77866e112	0.0202156
$659$	−1.09752e114	−0.750850	−0.375425	−	0.926853i	$-0.622503\pi$
$659$	−1.09752e114	−0.750850	−0.375425	+	0.926853i	$0.622503\pi$
$660$	0	0
$661$	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
$663$	0	0
$664$	−1.15625e114	−0.582430
$665$	1.31431e113	0.0622904
$666$	0	0
$667$	−5.39268e113	−0.226312
$668$	1.06307e114	0.419868
$669$	0	0
$670$	1.22284e114	0.427896
$671$	9.00695e114	2.96699
$672$	0	0
$673$	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
$675$	0	0
$676$	3.32086e114	0.809858
$677$	5.80519e114	1.33345	0.666723	−	0.745305i	$-0.267696\pi$
$677$	5.80519e114	1.33345	0.666723	+	0.745305i	$0.267696\pi$
$678$	0	0
$679$	−4.08345e113	−0.0832342
$680$	−2.04820e114	−0.393335
$681$	0	0
$682$	−2.02127e114	−0.344633
$683$	−6.44494e114	−1.03557	−0.517786	−	0.855510i	$-0.673244\pi$
$683$	−6.44494e114	−1.03557	−0.517786	+	0.855510i	$0.673244\pi$
$684$	0	0
$685$	1.01069e115	1.44262
$686$	−2.19841e113	−0.0295789
$687$	0	0
$688$	−5.29183e114	−0.632811
$689$	3.28718e114	0.370634
$690$	0	0
$691$	−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
$693$	0	0
$694$	−2.78912e114	−0.234644
$695$	2.55880e115	2.03073
$696$	0	0
$697$	1.14233e115	0.806980
$698$	3.12095e114	0.208038
$699$	0	0
$700$	2.29991e113	0.0136534
$701$	−2.13331e115	−1.19529	−0.597646	−	0.801760i	$-0.703897\pi$
$701$	−2.13331e115	−1.19529	−0.597646	+	0.801760i	$0.703897\pi$
$702$	0	0
$703$	−3.16137e115	−1.57828
$704$	2.31843e115	1.09270
$705$	0	0
$706$	4.02532e114	0.169126
$707$	−6.93708e112	−0.00275227
$708$	0	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
$711$	0	0
$712$	8.37730e114	0.249841
$713$	−2.98995e115	−0.842439
$714$	0	0
$715$	−2.73726e115	−0.688528
$716$	1.30117e115	0.309284
$717$	0	0
$718$	−1.03039e115	−0.218757
$719$	−3.15572e115	−0.633255	−0.316628	−	0.948550i	$-0.602551\pi$
$719$	−3.15572e115	−0.633255	−0.316628	+	0.948550i	$0.602551\pi$
$720$	0	0
$721$	3.18017e114	0.0570258
$722$	2.08493e114	0.0353456
$723$	0	0
$724$	2.83072e115	0.429028
$725$	−3.81074e114	−0.0546160
$726$	0	0
$727$	−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
$729$	0	0
$730$	−3.12859e115	−0.339447
$731$	−5.56226e115	−0.570950
$732$	0	0
$733$	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
$735$	0	0
$736$	−8.65529e115	−0.674109
$737$	−3.53476e116	−2.60571
$738$	0	0
$739$	−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
$741$	0	0
$742$	−2.63315e114	−0.0147611
$743$	3.23015e116	1.71465	0.857324	−	0.514777i	$-0.172125\pi$
$743$	3.23015e116	1.71465	0.857324	+	0.514777i	$0.172125\pi$
$744$	0	0
$745$	1.81990e116	0.866402
$746$	−8.01997e115	−0.361618
$747$	0	0
$748$	2.86866e116	1.16055
$749$	2.96861e115	0.113773
$750$	0	0
$751$	−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
$753$	0	0
$754$	−7.08019e114	−0.0207255
$755$	2.00443e116	0.556082
$756$	0	0
$757$	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
$759$	0	0
$760$	−2.30635e116	−0.489749
$761$	−1.38900e116	−0.279655	−0.139828	−	0.990176i	$-0.544655\pi$
$761$	−1.38900e116	−0.279655	−0.139828	+	0.990176i	$0.544655\pi$
$762$	0	0
$763$	2.06746e115	0.0374278
$764$	−3.70352e116	−0.635819
$765$	0	0
$766$	−1.09885e116	−0.169697
$767$	−1.45378e114	−0.00212955
$768$	0	0
$769$	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
$771$	0	0
$772$	−4.22740e116	−0.475963
$773$	−1.12721e117	−1.20431	−0.602153	−	0.798380i	$-0.705690\pi$
$773$	−1.12721e117	−1.20431	−0.602153	+	0.798380i	$0.705690\pi$
$774$	0	0
$775$	−2.11285e116	−0.203306
$776$	7.16562e116	0.654417
$777$	0	0
$778$	−3.85427e116	−0.317153
$779$	1.28630e117	1.00479
$780$	0	0
$781$	1.22573e117	0.863035
$782$	−2.71096e116	−0.181238
$783$	0	0
$784$	−1.36098e117	−0.820447
$785$	1.87014e117	1.07067
$786$	0	0
$787$	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
$789$	0	0
$790$	−2.62317e116	−0.116126
$791$	−9.25607e115	−0.0389295
$792$	0	0
$793$	1.74928e117	0.664193
$794$	−6.69526e116	−0.241567
$795$	0	0
$796$	4.33469e117	1.41247
$797$	1.92384e117	0.595808	0.297904	−	0.954596i	$-0.403712\pi$
$797$	1.92384e117	0.595808	0.297904	+	0.954596i	$0.403712\pi$
$798$	0	0
$799$	3.62285e117	1.01369
$800$	−6.11626e116	−0.162683
$801$	0	0
$802$	−1.40018e117	−0.336607
$803$	9.04358e117	2.06710
$804$	0	0
$805$	3.24346e116	0.0670310
$806$	−3.92559e116	−0.0771499
$807$	0	0
$808$	1.21732e116	0.0216393
$809$	−1.06556e117	−0.180162	−0.0900808	−	0.995934i	$-0.528713\pi$
$809$	−1.06556e117	−0.180162	−0.0900808	+	0.995934i	$0.528713\pi$
$810$	0	0
$811$	−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
$813$	0	0
$814$	−5.27407e117	−0.694797
$815$	2.40377e117	0.301308
$816$	0	0
$817$	−6.26329e117	−0.710901
$818$	9.62557e114	0.00103972
$819$	0	0
$820$	1.16203e118	1.13699
$821$	−3.94100e117	−0.367036	−0.183518	−	0.983016i	$-0.558749\pi$
$821$	−3.94100e117	−0.367036	−0.183518	+	0.983016i	$0.558749\pi$
$822$	0	0
$823$	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
$825$	0	0
$826$	1.16453e114	8.48125e−5 0
$827$	−1.11417e118	−0.772645	−0.386322	−	0.922364i	$-0.626255\pi$
$827$	−1.11417e118	−0.772645	−0.386322	+	0.922364i	$0.626255\pi$
$828$	0	0
$829$	−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
$831$	0	0
$832$	4.50273e117	0.244614
$833$	−1.43053e118	−0.740243
$834$	0	0
$835$	1.05941e118	0.497463
$836$	3.23021e118	1.44503
$837$	0	0
$838$	−2.86673e117	−0.116413
$839$	−2.30700e118	−0.892666	−0.446333	−	0.894867i	$-0.647270\pi$
$839$	−2.30700e118	−0.892666	−0.446333	+	0.894867i	$0.647270\pi$
$840$	0	0
$841$	−2.69893e118	−0.948316
$842$	4.62718e117	0.154945
$843$	0	0
$844$	−3.34750e118	−1.01824
$845$	3.30943e118	0.959525
$846$	0	0
$847$	−4.04319e117	−0.106524
$848$	−3.26622e118	−0.820376
$849$	0	0
$850$	−1.91570e117	−0.0437383
$851$	−7.80165e118	−1.69840
$852$	0	0
$853$	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
$855$	0	0
$856$	−5.20931e118	−0.894525
$857$	−2.71295e118	−0.444343	−0.222172	−	0.975008i	$-0.571314\pi$
$857$	−2.71295e118	−0.444343	−0.222172	+	0.975008i	$0.571314\pi$
$858$	0	0
$859$	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
$861$	0	0
$862$	−1.79527e118	−0.232320
$863$	−2.28392e117	−0.0281996	−0.0140998	−	0.999901i	$-0.504488\pi$
$863$	−2.28392e117	−0.0281996	−0.0140998	+	0.999901i	$0.504488\pi$
$864$	0	0
$865$	−1.28916e119	−1.44929
$866$	−3.14977e118	−0.337913
$867$	0	0
$868$	−4.92214e117	−0.0480955
$869$	7.58261e118	0.707160
$870$	0	0
$871$	−6.86500e118	−0.583318
$872$	−3.62797e118	−0.294270
$873$	0	0
$874$	−3.05263e118	−0.225664
$875$	−7.24850e117	−0.0511590
$876$	0	0
$877$	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
$879$	0	0
$880$	2.71980e119	1.52401
$881$	1.61438e119	0.863938	0.431969	−	0.901888i	$-0.357819\pi$
$881$	1.61438e119	0.863938	0.431969	+	0.901888i	$0.357819\pi$
$882$	0	0
$883$	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
$885$	0	0
$886$	3.40798e118	0.145021
$887$	−2.19271e119	−0.891404	−0.445702	−	0.895181i	$-0.647046\pi$
$887$	−2.19271e119	−0.891404	−0.445702	+	0.895181i	$0.647046\pi$
$888$	0	0
$889$	1.27529e118	0.0473247
$890$	4.04503e118	0.143425
$891$	0	0
$892$	−3.38757e119	−1.09676
$893$	4.07945e119	1.26217
$894$	0	0
$895$	1.29669e119	0.366442
$896$	−1.87657e118	−0.0506862
$897$	0	0
$898$	−1.01925e119	−0.251530
$899$	8.15554e118	0.192391
$900$	0	0
$901$	−3.43313e119	−0.740179
$902$	2.14591e119	0.442331
$903$	0	0
$904$	1.62425e119	0.306078
$905$	2.82098e119	0.508315
$906$	0	0
$907$	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
$909$	0	0
$910$	4.25843e117	0.00613865
$911$	−4.14570e119	−0.571615	−0.285808	−	0.958287i	$-0.592262\pi$
$911$	−4.14570e119	−0.571615	−0.285808	+	0.958287i	$0.592262\pi$
$912$	0	0
$913$	1.61384e120	2.03608
$914$	1.29621e118	0.0156443
$915$	0	0
$916$	−8.00887e118	−0.0884717
$917$	2.32414e118	0.0245643
$918$	0	0
$919$	−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
$921$	0	0
$922$	3.95756e119	0.335602
$923$	2.38054e119	0.193200
$924$	0	0
$925$	−5.51304e119	−0.409874
$926$	3.27573e119	0.233111
$927$	0	0
$928$	2.36086e119	0.153949
$929$	1.01757e120	0.635225	0.317613	−	0.948221i	$-0.397119\pi$
$929$	1.01757e120	0.635225	0.317613	+	0.948221i	$0.397119\pi$
$930$	0	0
$931$	−1.61082e120	−0.921692
$932$	−5.36899e118	−0.0294136
$933$	0	0
$934$	1.89021e119	0.0949426
$935$	2.85879e120	1.37503
$936$	0	0
$937$	−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
$939$	0	0
$940$	3.68533e120	1.42823
$941$	−2.46055e120	−0.913383	−0.456692	−	0.889625i	$-0.650966\pi$
$941$	−2.46055e120	−0.913383	−0.456692	+	0.889625i	$0.650966\pi$
$942$	0	0
$943$	3.17433e120	1.08126
$944$	1.44451e118	0.00471362
$945$	0	0
$946$	−1.04490e120	−0.312955
$947$	−1.13269e120	−0.325039	−0.162519	−	0.986705i	$-0.551962\pi$
$947$	−1.13269e120	−0.325039	−0.162519	+	0.986705i	$0.551962\pi$
$948$	0	0
$949$	1.75639e120	0.462743
$950$	−2.15714e119	−0.0544594
$951$	0	0
$952$	−9.21083e118	−0.0213551
$953$	−1.13612e120	−0.252442	−0.126221	−	0.992002i	$-0.540285\pi$
$953$	−1.13612e120	−0.252442	−0.126221	+	0.992002i	$0.540285\pi$
$954$	0	0
$955$	−3.69077e120	−0.753322
$956$	−4.19506e120	−0.820718
$957$	0	0
$958$	1.97007e120	0.354144
$959$	4.54511e119	0.0783233
$960$	0	0
$961$	−1.79208e120	−0.283832
$962$	−1.02430e120	−0.155538
$963$	0	0
$964$	−1.09421e121	−1.52750
$965$	−4.21286e120	−0.563924
$966$	0	0
$967$	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
$969$	0	0
$970$	3.45996e120	0.375678
$971$	−1.43446e121	−1.49386	−0.746930	−	0.664902i	$-0.768473\pi$
$971$	−1.43446e121	−1.49386	−0.746930	+	0.664902i	$0.768473\pi$
$972$	0	0
$973$	1.15070e120	0.110253
$974$	−1.55547e119	−0.0142963
$975$	0	0
$976$	−1.73812e121	−1.47015
$977$	−1.72213e121	−1.39745	−0.698725	−	0.715390i	$-0.746249\pi$
$977$	−1.72213e121	−1.39745	−0.698725	+	0.715390i	$0.746249\pi$
$978$	0	0
$979$	−1.16927e121	−0.873403
$980$	−1.45520e121	−1.04296
$981$	0	0
$982$	1.78953e120	0.118093
$983$	1.40198e121	0.887817	0.443908	−	0.896072i	$-0.353592\pi$
$983$	1.40198e121	0.887817	0.443908	+	0.896072i	$0.353592\pi$
$984$	0	0
$985$	1.82522e121	1.06451
$986$	7.39455e119	0.0413901
$987$	0	0
$988$	6.27352e120	0.323486
$989$	−1.54566e121	−0.765004
$990$	0	0
$991$	−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
$993$	0	0
$994$	−1.90690e119	−0.00769449
$995$	4.31977e121	1.67350
$996$	0	0
$997$	−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
$999$	0	0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 82 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-3.81039e11 q^{2} -2.27266e24 q^{4} -2.26484e28 q^{5} -1.01850e33 q^{7} +1.78727e36 q^{8} +O(q^{10})\)	\(q-3.81039e11 q^{2} -2.27266e24 q^{4} -2.26484e28 q^{5} -1.01850e33 q^{7} +1.78727e36 q^{8} +8.62992e39 q^{10} -2.49459e42 q^{11} -4.84484e44 q^{13} +3.88090e44 q^{14} +4.81394e48 q^{16} +5.05995e49 q^{17} +5.69767e51 q^{19} +5.14722e52 q^{20} +9.50534e53 q^{22} +1.40607e55 q^{23} +9.93602e55 q^{25} +1.84607e56 q^{26} +2.31472e57 q^{28} -3.83527e58 q^{29} -2.12645e60 q^{31} -6.15564e60 q^{32} -1.92804e61 q^{34} +2.30675e61 q^{35} -5.54853e63 q^{37} -2.17103e63 q^{38} -4.04788e64 q^{40} +2.25758e65 q^{41} -1.09927e66 q^{43} +5.66935e66 q^{44} -5.35768e66 q^{46} +7.15986e67 q^{47} -2.82716e68 q^{49} -3.78601e67 q^{50} +1.10107e69 q^{52} -6.78492e69 q^{53} +5.64985e70 q^{55} -1.82034e69 q^{56} +1.46139e70 q^{58} +3.00068e69 q^{59} -3.61060e72 q^{61} +8.10261e71 q^{62} -9.29385e72 q^{64} +1.09728e73 q^{65} +1.41697e74 q^{67} -1.14996e74 q^{68} -8.78961e72 q^{70} -4.91356e74 q^{71} -3.62528e75 q^{73} +2.11421e75 q^{74} -1.29489e76 q^{76} +2.54075e75 q^{77} -3.03962e76 q^{79} -1.09028e77 q^{80} -8.60227e76 q^{82} -6.46937e77 q^{83} -1.14600e78 q^{85} +4.18865e77 q^{86} -4.45849e78 q^{88} +4.68721e78 q^{89} +4.93449e77 q^{91} -3.19553e79 q^{92} -2.72818e79 q^{94} -1.29043e80 q^{95} +4.00926e80 q^{97} +1.07726e80 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 460872026640 q^{2} + 44\!\cdots\!52 q^{4}+ \cdots + 54\!\cdots\!20 q^{8}+O(q^{10}) \) 6 * q + 460872026640 * q^2 + 4493950976700073762513152 * q^4 + 18364304155649862126617790300 * q^5 - 31430760593927655842892725138869200 * q^7 + 5498145101596630185016447889074360320 * q^8	\( 6 q + 460872026640 q^{2} + 44\!\cdots\!52 q^{4}+ \cdots + 85\!\cdots\!80 q^{98}+O(q^{100}) \) 6 * q + 460872026640 * q^2 + 4493950976700073762513152 * q^4 + 18364304155649862126617790300 * q^5 - 31430760593927655842892725138869200 * q^7 + 5498145101596630185016447889074360320 * q^8 - 66472312087527710620452553569669697173600 * q^10 + 2302475295973581620809306061775551681990328 * q^11 + 1313253814255449492724146018729804193778100180 * q^13 - 41225372723246048337281629784765672712004401024 * q^14 + 2799490233261278434402974316306719898117729222656 * q^16 - 2377848571505238562780180385684069414829577769580 * q^17 - 17422016964741760630179674590582970665727618619375240 * q^19 - 148672889698640611477740875719636714144962866333222400 * q^20 - 1258034178625689345497738618244246726621220713529586880 * q^22 - 10526595063181453314046018770874462030150898790798283920 * q^23 + 411037910011361515508644334216291479522821661187695496250 * q^25 + 3180570114716540139250277986112641638356676984048903123168 * q^26 - 82116517748637002885903417761702653442063276903193852344320 * q^28 - 155464359052154485146727469597467543970919715236853926245940 * q^29 + 1259277021063335018777245090979655984137503836933555134668992 * q^31 + 13036312845125683749178794475020758767431562303480221102243840 * q^32 + 11899550405754031112224464347628728246396477955985557631122144 * q^34 + 232034356615504837711196063040035766391492406317925929510437600 * q^35 + 414692688584236378963319357622814947056491742931883680122973540 * q^37 + 2455417714037465297201999851134772037590829998762172946918415680 * q^38 - 258059824285668605758122263287555971608050642150708772544789504000 * q^40 + 250252788823194090638944408016236187978548863949167831014660870148 * q^41 - 5362516930786214192203446564720631507618558180640993338648106782200 * q^43 + 17252465656682175267213991915222412585785021276568609411813835518976 * q^44 - 123763409427226200113215389587151615608344054530127843046255996688768 * q^46 + 230717394511751791462615349254196337530205542984846694602934639341280 * q^47 - 148965540042877735285285650175007198234557699456949204802064464556458 * q^49 + 1416105420952806525015169807922957339416756851287952031511031347670000 * q^50 + 12562371185881747636341658298037576485393840750032566447999727917043200 * q^52 - 25898990256961205776642859216859182171010424056472082121008236344959940 * q^53 + 70427859302095658379065386305135120838252257009889309990749877277396400 * q^55 - 350275852246953465289512615368698332984392220622408793911163576939151360 * q^56 - 312514134877257928766126367534026770462807935435519457753987287493386720 * q^58 + 38532453307459913471042984274454520116124717672121643571528434328282520 * q^59 - 4585192544270629640163935422584783189092178505653567017169797728495170828 * q^61 + 11745445982868867354760701788812677993661414140303262885466836339630318080 * q^62 - 24049189879736877632355406073912155582619770074517134096672197458230509568 * q^64 - 40108571425620140080303901416556158312567794172295521521551039993118238200 * q^65 + 278606964486964374833906544600580027758780739521508130980859112605565987480 * q^67 - 591059149620766869951154898169335214276013402788475417448362648514550551040 * q^68 + 2635837114104224632390936486964777102611174135296488988531978806621369068800 * q^70 + 554281436103188717611008447226924711986842423491780222553301787426789861968 * q^71 - 1159677538409433721867557656635958525415325708297922475676033828300683142980 * q^73 + 14870996314347354169518203977127998385153668929299472477677600807989626002016 * q^74 - 56365824164857229782022127848008365902008884166434980738114640515976798612480 * q^76 + 22951272837324694774527636903423616359482790364245898655274441101674154673600 * q^77 + 76488528596848273963909721387433081359345259080220208993600380062891411190240 * q^79 - 326185463863660018876021371340485226979224823762794013840530768719064527667200 * q^80 + 836977463852743303549437738986542975894462808796250502348000478828556860551520 * q^82 - 440718478462773776637617020819789880594300172591745821478345102532528865997560 * q^83 + 1165607138975709364402518400492567424057357396402879557680723771041190675179400 * q^85 + 10339197506820945136003281093027314178240703830345630490304599234644673765234368 * q^86 - 9603847126452588175246186358824265187739652448840879006569656469218022549667840 * q^88 + 18886228493337874501351816155449414708824427288664596668607356717228138798590180 * q^89 - 14576226325987997036142564032100430704897317032265698214767987870608618538920288 * q^91 - 66364414655655668275929797141498084164407535259475789695165805684452941775738880 * q^92 + 331286952814608158700187065887753978184064043063622410298763861434514546852072704 * q^94 - 267699559747800180626411366716842325842865933645649558098598518850783266973922000 * q^95 + 113832498161281214584608062040287314379413598012089688107897449655058469975263820 * q^97 + 858118355318723523117883130491863373979750018711838274840266757637744872892872080 * q^98

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