LMFDB - Embedded newform 1512.2.q.d.793.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(793,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1512.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.q (of order $3$, degree $2$, not minimal)

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:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			793.5
Character	$\chi$	$=$	1512.793
Dual form			1512.2.q.d.1369.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.234085 - 0.405446i) q^{5} +(0.212345 - 2.63722i) q^{7} +O(q^{10})$	$q+(-0.234085 - 0.405446i) q^{5} +(0.212345 - 2.63722i) q^{7} +(-0.674293 + 1.16791i) q^{11} +(-3.16486 + 5.48171i) q^{13} +(2.47120 + 4.28024i) q^{17} +(2.38910 - 4.13804i) q^{19} +(3.81399 + 6.60603i) q^{23} +(2.39041 - 4.14031i) q^{25} +(1.80565 + 3.12747i) q^{29} +6.49878 q^{31} +(-1.11896 + 0.531237i) q^{35} +(5.24214 - 9.07966i) q^{37} +(0.0251630 - 0.0435837i) q^{41} +(-0.431869 - 0.748019i) q^{43} +10.9883 q^{47} +(-6.90982 - 1.12000i) q^{49} +(-5.84976 - 10.1321i) q^{53} +0.631366 q^{55} +3.87784 q^{59} +3.74462 q^{61} +2.96338 q^{65} -2.64871 q^{67} +7.04562 q^{71} +(-3.30117 - 5.71779i) q^{73} +(2.93685 + 2.02626i) q^{77} +3.17902 q^{79} +(-4.90272 - 8.49176i) q^{83} +(1.15694 - 2.00388i) q^{85} +(-5.30709 + 9.19214i) q^{89} +(13.7844 + 9.51045i) q^{91} -2.23701 q^{95} +(6.97792 + 12.0861i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{5} + 5 q^{7}+O(q^{10}) $ 22 * q - q^5 + 5 * q^7	$ 22 q - q^{5} + 5 q^{7} - 3 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} - 22 q^{25} + 7 q^{29} - 12 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} + 34 q^{47} - 25 q^{49} - q^{53} + 2 q^{55} - 42 q^{59} - 62 q^{61} - 6 q^{65} + 52 q^{67} + 32 q^{71} + 17 q^{73} + q^{77} + 32 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} - 48 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q - q^5 + 5 * q^7 - 3 * q^11 + 7 * q^13 + q^17 + 13 * q^19 - 22 * q^25 + 7 * q^29 - 12 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 + 34 * q^47 - 25 * q^49 - q^53 + 2 * q^55 - 42 * q^59 - 62 * q^61 - 6 * q^65 + 52 * q^67 + 32 * q^71 + 17 * q^73 + q^77 + 32 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 - 48 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.234085	−	0.405446i	−0.104686	−	0.181321i	0.808924	−	0.587913i	$-0.200050\pi$
$5$	−0.234085	−	0.405446i	−0.104686	−	0.181321i	−0.913610	+	0.406592i	$0.866717\pi$
$6$		0			0
$7$	0.212345	−	2.63722i	0.0802590	−	0.996774i
$7$	0.212345	−	2.63722i	0.0802590	−	0.996774i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.674293	+	1.16791i	−0.203307	+	0.352138i	−0.949592	−	0.313489i	$-0.898502\pi$
$11$	−0.674293	+	1.16791i	−0.203307	+	0.352138i	0.746285	+	0.665626i	$0.231836\pi$
$12$		0			0
$13$	−3.16486	+	5.48171i	−0.877775	+	1.52035i	−0.0239988	+	0.999712i	$0.507640\pi$
$13$	−3.16486	+	5.48171i	−0.877775	+	1.52035i	−0.853777	+	0.520640i	$0.825694\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.47120	+	4.28024i	0.599353	+	1.03811i	0.992917	+	0.118813i	$0.0379089\pi$
$17$	2.47120	+	4.28024i	0.599353	+	1.03811i	−0.393563	+	0.919298i	$0.628758\pi$
$18$		0			0
$19$	2.38910	−	4.13804i	0.548097	−	0.949332i	−0.450308	−	0.892873i	$-0.648686\pi$
$19$	2.38910	−	4.13804i	0.548097	−	0.949332i	0.998405	−	0.0564585i	$-0.0179809\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.81399	+	6.60603i	0.795273	+	1.37745i	0.922666	+	0.385600i	$0.126006\pi$
$23$	3.81399	+	6.60603i	0.795273	+	1.37745i	−0.127393	+	0.991852i	$0.540661\pi$
$24$		0			0
$25$	2.39041	−	4.14031i	0.478082	−	0.828062i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.80565	+	3.12747i	0.335300	+	0.580757i	0.983542	−	0.180677i	$-0.0578290\pi$
$29$	1.80565	+	3.12747i	0.335300	+	0.580757i	−0.648242	+	0.761434i	$0.724496\pi$
$30$		0			0
$31$	6.49878			1.16721			0.583607	−	0.812036i	$-0.301641\pi$
$31$	6.49878			1.16721			0.583607	+	0.812036i	$0.301641\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.11896	+	0.531237i	−0.189138	+	0.0897954i
$36$		0			0
$37$	5.24214	−	9.07966i	0.861803	−	1.49269i	−0.00838383	−	0.999965i	$-0.502669\pi$
$37$	5.24214	−	9.07966i	0.861803	−	1.49269i	0.870187	−	0.492722i	$-0.163998\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.0251630	−	0.0435837i	0.00392981	−	0.00680662i	−0.864054	−	0.503399i	$-0.832082\pi$
$41$	0.0251630	−	0.0435837i	0.00392981	−	0.00680662i	0.867984	+	0.496593i	$0.165416\pi$
$42$		0			0
$43$	−0.431869	−	0.748019i	−0.0658594	−	0.114072i	0.831215	−	0.555950i	$-0.187646\pi$
$43$	−0.431869	−	0.748019i	−0.0658594	−	0.114072i	−0.897075	+	0.441879i	$0.854312\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	10.9883			1.60282			0.801408	−	0.598118i	$-0.204085\pi$
$47$	10.9883			1.60282			0.801408	+	0.598118i	$0.204085\pi$
$48$		0			0
$49$	−6.90982	−	1.12000i	−0.987117	−	0.160000i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.84976	−	10.1321i	−0.803526	−	1.39175i	−0.917282	−	0.398239i	$-0.869622\pi$
$53$	−5.84976	−	10.1321i	−0.803526	−	1.39175i	0.113756	−	0.993509i	$-0.463712\pi$
$54$		0			0
$55$	0.631366			0.0851334
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.87784			0.504852			0.252426	−	0.967616i	$-0.418772\pi$
$59$	3.87784			0.504852			0.252426	+	0.967616i	$0.418772\pi$
$60$		0			0
$61$	3.74462			0.479450			0.239725	−	0.970841i	$-0.422943\pi$
$61$	3.74462			0.479450			0.239725	+	0.970841i	$0.422943\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.96338			0.367562
$66$		0			0
$67$	−2.64871			−0.323592			−0.161796	−	0.986824i	$-0.551729\pi$
$67$	−2.64871			−0.323592			−0.161796	+	0.986824i	$0.551729\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	7.04562			0.836161			0.418081	−	0.908410i	$-0.362703\pi$
$71$	7.04562			0.836161			0.418081	+	0.908410i	$0.362703\pi$
$72$		0			0
$73$	−3.30117	−	5.71779i	−0.386373	−	0.669217i	0.605586	−	0.795780i	$-0.292939\pi$
$73$	−3.30117	−	5.71779i	−0.386373	−	0.669217i	−0.991959	+	0.126563i	$0.959605\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.93685	+	2.02626i	0.334685	+	0.230913i
$78$		0			0
$79$	3.17902			0.357667			0.178834	−	0.983879i	$-0.442768\pi$
$79$	3.17902			0.357667			0.178834	+	0.983879i	$0.442768\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.90272	−	8.49176i	−0.538143	−	0.932092i	−0.999004	−	0.0446192i	$-0.985793\pi$
$83$	−4.90272	−	8.49176i	−0.538143	−	0.932092i	0.460861	−	0.887472i	$-0.347541\pi$
$84$		0			0
$85$	1.15694	−	2.00388i	0.125488	−	0.217351i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.30709	+	9.19214i	−0.562550	+	0.974365i	0.434723	+	0.900564i	$0.356846\pi$
$89$	−5.30709	+	9.19214i	−0.562550	+	0.974365i	−0.997273	+	0.0738011i	$0.976487\pi$
$90$		0			0
$91$	13.7844	+	9.51045i	1.44500	+	0.996966i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.23701			−0.229512
$96$		0			0
$97$	6.97792	+	12.0861i	0.708500	+	1.22716i	0.965413	+	0.260724i	$0.0839611\pi$
$97$	6.97792	+	12.0861i	0.708500	+	1.22716i	−0.256913	+	0.966434i	$0.582706\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.12472	−	3.68013i	0.211418	−	0.366187i	−0.740741	−	0.671791i	$-0.765525\pi$
$101$	2.12472	−	3.68013i	0.211418	−	0.366187i	0.952159	+	0.305604i	$0.0988585\pi$
$102$		0			0
$103$	4.47820	+	7.75647i	0.441250	+	0.764268i	0.997783	−	0.0665580i	$-0.0212017\pi$
$103$	4.47820	+	7.75647i	0.441250	+	0.764268i	−0.556532	+	0.830826i	$0.687868\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.810731	−	1.40423i	0.0783763	−	0.135752i	−0.824173	−	0.566338i	$-0.808360\pi$
$107$	0.810731	−	1.40423i	0.0783763	−	0.135752i	0.902550	+	0.430586i	$0.141693\pi$
$108$		0			0
$109$	2.97644	+	5.15534i	0.285091	+	0.493792i	0.972631	−	0.232354i	$-0.0746428\pi$
$109$	2.97644	+	5.15534i	0.285091	+	0.493792i	−0.687540	+	0.726146i	$0.741309\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.14346	+	7.17669i	−0.389784	+	0.675126i	−0.992420	−	0.122890i	$-0.960784\pi$
$113$	−4.14346	+	7.17669i	−0.389784	+	0.675126i	0.602636	+	0.798016i	$0.294117\pi$
$114$		0			0
$115$	1.78559	−	3.09274i	0.166508	−	0.288399i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	11.8127	−	5.60819i	1.08287	−	0.514102i
$120$		0			0
$121$	4.59066	+	7.95125i	0.417333	+	0.722841i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.57908			−0.409565
$126$		0			0
$127$	8.12368			0.720860			0.360430	−	0.932786i	$-0.382630\pi$
$127$	8.12368			0.720860			0.360430	+	0.932786i	$0.382630\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.74823	+	16.8844i	0.851707	+	1.47520i	0.879667	+	0.475591i	$0.157766\pi$
$131$	9.74823	+	16.8844i	0.851707	+	1.47520i	−0.0279597	+	0.999609i	$0.508901\pi$
$132$		0			0
$133$	−10.4056	−	7.17927i	−0.902280	−	0.622521i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.55175	+	13.0800i	−0.645189	+	1.11750i	0.339069	+	0.940762i	$0.389888\pi$
$137$	−7.55175	+	13.0800i	−0.645189	+	1.11750i	−0.984258	+	0.176739i	$0.943445\pi$
$138$		0			0
$139$	−2.18826	+	3.79017i	−0.185605	+	0.321478i	−0.943780	−	0.330573i	$-0.892758\pi$
$139$	−2.18826	+	3.79017i	−0.185605	+	0.321478i	0.758175	+	0.652051i	$0.226091\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.26809	−	7.39255i	−0.356916	−	0.618196i
$144$		0			0
$145$	0.845348	−	1.46419i	0.0702023	−	0.121594i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.87820	−	10.1813i	−0.481561	−	0.834087i	0.518215	−	0.855250i	$-0.326597\pi$
$149$	−5.87820	−	10.1813i	−0.481561	−	0.834087i	−0.999776	+	0.0211627i	$0.993263\pi$
$150$		0			0
$151$	2.57153	−	4.45401i	0.209268	−	0.362462i	−0.742216	−	0.670160i	$-0.766225\pi$
$151$	2.57153	−	4.45401i	0.209268	−	0.362462i	0.951484	+	0.307698i	$0.0995586\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.52126	−	2.63490i	−0.122191	−	0.211641i
$156$		0			0
$157$	−12.0889			−0.964803			−0.482401	−	0.875950i	$-0.660235\pi$
$157$	−12.0889			−0.964803			−0.482401	+	0.875950i	$0.660235\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	18.2314	−	8.65557i	1.43684	−	0.682154i
$162$		0			0
$163$	−2.74663	+	4.75730i	−0.215133	+	0.372621i	−0.953314	−	0.301982i	$-0.902352\pi$
$163$	−2.74663	+	4.75730i	−0.215133	+	0.372621i	0.738181	+	0.674603i	$0.235685\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.59378	−	6.22461i	0.278095	−	0.481675i	−0.692816	−	0.721114i	$-0.743630\pi$
$167$	3.59378	−	6.22461i	0.278095	−	0.481675i	0.970911	+	0.239440i	$0.0769637\pi$
$168$		0			0
$169$	−13.5327	−	23.4394i	−1.04098	−	1.80303i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.95902			0.605113			0.302557	−	0.953131i	$-0.402160\pi$
$173$	7.95902			0.605113			0.302557	+	0.953131i	$0.402160\pi$
$174$		0			0
$175$	−10.4113	−	7.18320i	−0.787020	−	0.542999i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.168821	−	0.292406i	−0.0126182	−	0.0218554i	0.859647	−	0.510888i	$-0.170683\pi$
$179$	−0.168821	−	0.292406i	−0.0126182	−	0.0218554i	−0.872266	+	0.489032i	$0.837350\pi$
$180$		0			0
$181$	7.05801			0.524618			0.262309	−	0.964984i	$-0.415516\pi$
$181$	7.05801			0.524618			0.262309	+	0.964984i	$0.415516\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.90842			−0.360874
$186$		0			0
$187$	−6.66524			−0.487411
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−17.7187			−1.28208			−0.641039	−	0.767508i	$-0.721496\pi$
$191$	−17.7187			−1.28208			−0.641039	+	0.767508i	$0.721496\pi$
$192$		0			0
$193$	−16.8024			−1.20946			−0.604732	−	0.796429i	$-0.706720\pi$
$193$	−16.8024			−1.20946			−0.604732	+	0.796429i	$0.706720\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.97545			−0.425733			−0.212867	−	0.977081i	$-0.568280\pi$
$197$	−5.97545			−0.425733			−0.212867	+	0.977081i	$0.568280\pi$
$198$		0			0
$199$	6.26093	+	10.8443i	0.443826	+	0.768729i	0.997970	−	0.0636923i	$-0.0202876\pi$
$199$	6.26093	+	10.8443i	0.443826	+	0.768729i	−0.554144	+	0.832421i	$0.686954\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	8.63124	−	4.09778i	0.605794	−	0.287607i
$204$		0			0
$205$	−0.0235611			−0.00164558
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.22190	+	5.58050i	0.222864	+	0.386011i
$210$		0			0
$211$	1.17688	−	2.03842i	0.0810198	−	0.140330i	−0.822668	−	0.568521i	$-0.807516\pi$
$211$	1.17688	−	2.03842i	0.0810198	−	0.140330i	0.903688	+	0.428191i	$0.140849\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.202188	+	0.350199i	−0.0137891	+	0.0238834i
$216$		0			0
$217$	1.37999	−	17.1387i	0.0936795	−	1.16345i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−31.2840			−2.10439
$222$		0			0
$223$	5.30709	+	9.19215i	0.355389	+	0.615552i	0.987184	−	0.159583i	$-0.0510150\pi$
$223$	5.30709	+	9.19215i	0.355389	+	0.615552i	−0.631795	+	0.775135i	$0.717682\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.637749	−	1.10461i	0.0423289	−	0.0733158i	−0.844085	−	0.536210i	$-0.819856\pi$
$227$	0.637749	−	1.10461i	0.0423289	−	0.0733158i	0.886414	+	0.462894i	$0.153189\pi$
$228$		0			0
$229$	6.73313	+	11.6621i	0.444938	+	0.770655i	0.998048	−	0.0624532i	$-0.0198924\pi$
$229$	6.73313	+	11.6621i	0.444938	+	0.770655i	−0.553110	+	0.833108i	$0.686559\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.98509	+	17.2947i	−0.654145	+	1.13301i	0.327963	+	0.944691i	$0.393638\pi$
$233$	−9.98509	+	17.2947i	−0.654145	+	1.13301i	−0.982107	+	0.188321i	$0.939695\pi$
$234$		0			0
$235$	−2.57220	−	4.45519i	−0.167792	−	0.290624i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	14.1092	−	24.4379i	0.912650	−	1.58076i	0.102345	−	0.994749i	$-0.467365\pi$
$239$	14.1092	−	24.4379i	0.912650	−	1.58076i	0.810305	−	0.586008i	$-0.199301\pi$
$240$		0			0
$241$	8.67622	−	15.0277i	0.558884	−	0.968016i	−0.438706	−	0.898631i	$-0.644563\pi$
$241$	8.67622	−	15.0277i	0.558884	−	0.968016i	0.997590	−	0.0693852i	$-0.0221038\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.16338	+	3.06374i	0.0743257	+	0.195735i
$246$		0			0
$247$	15.1223	+	26.1927i	0.962212	+	1.66660i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.29051			−0.397054			−0.198527	−	0.980095i	$-0.563616\pi$
$251$	−6.29051			−0.397054			−0.198527	+	0.980095i	$0.563616\pi$
$252$		0			0
$253$	−10.2870			−0.646738
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.06819	−	5.31426i	−0.191388	−	0.331494i	0.754322	−	0.656504i	$-0.227966\pi$
$257$	−3.06819	−	5.31426i	−0.191388	−	0.331494i	−0.945711	+	0.325010i	$0.894632\pi$
$258$		0			0
$259$	−22.8319	−	15.7527i	−1.41870	−	0.978825i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.93957	−	5.09148i	0.181262	−	0.313954i	−0.761049	−	0.648695i	$-0.775315\pi$
$263$	2.93957	−	5.09148i	0.181262	−	0.313954i	0.942310	+	0.334740i	$0.108649\pi$
$264$		0			0
$265$	−2.73868	+	4.74352i	−0.168235	+	0.291392i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	15.4633	+	26.7832i	0.942812	+	1.63300i	0.760074	+	0.649837i	$0.225163\pi$
$269$	15.4633	+	26.7832i	0.942812	+	1.63300i	0.182738	+	0.983162i	$0.441504\pi$
$270$		0			0
$271$	5.44528	−	9.43150i	0.330777	−	0.572923i	−0.651887	−	0.758316i	$-0.726022\pi$
$271$	5.44528	−	9.43150i	0.330777	−	0.572923i	0.982664	+	0.185393i	$0.0593558\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.22367	+	5.58356i	0.194395	+	0.336701i
$276$		0			0
$277$	−9.79498	+	16.9654i	−0.588524	+	1.01935i	0.405903	+	0.913916i	$0.366957\pi$
$277$	−9.79498	+	16.9654i	−0.588524	+	1.01935i	−0.994426	+	0.105436i	$0.966376\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.142477	+	0.246777i	0.00849944	+	0.0147215i	0.870244	−	0.492621i	$-0.163961\pi$
$281$	0.142477	+	0.246777i	0.00849944	+	0.0147215i	−0.861744	+	0.507343i	$0.830628\pi$
$282$		0			0
$283$	2.84269			0.168981			0.0844903	−	0.996424i	$-0.473074\pi$
$283$	2.84269			0.168981			0.0844903	+	0.996424i	$0.473074\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.109596	−	0.0756152i	−0.00646926	−	0.00446342i
$288$		0			0
$289$	−3.71364	+	6.43221i	−0.218449	+	0.378365i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.45979	−	2.52842i	0.0852816	−	0.147712i	−0.820230	−	0.572034i	$-0.806154\pi$
$293$	1.45979	−	2.52842i	0.0852816	−	0.147712i	0.905511	+	0.424322i	$0.139488\pi$
$294$		0			0
$295$	−0.907743	−	1.57226i	−0.0528509	−	0.0915404i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−48.2831			−2.79228
$300$		0			0
$301$	−2.06439	+	0.980094i	−0.118990	+	0.0564917i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.876558	−	1.51824i	−0.0501916	−	0.0869344i
$306$		0			0
$307$	−4.12553			−0.235457			−0.117728	−	0.993046i	$-0.537561\pi$
$307$	−4.12553			−0.235457			−0.117728	+	0.993046i	$0.537561\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−15.3917			−0.872781			−0.436390	−	0.899757i	$-0.643743\pi$
$311$	−15.3917			−0.872781			−0.436390	+	0.899757i	$0.643743\pi$
$312$		0			0
$313$	−20.7240			−1.17139			−0.585694	−	0.810533i	$-0.699178\pi$
$313$	−20.7240			−1.17139			−0.585694	+	0.810533i	$0.699178\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.488292			0.0274252			0.0137126	−	0.999906i	$-0.495635\pi$
$317$	0.488292			0.0274252			0.0137126	+	0.999906i	$0.495635\pi$
$318$		0			0
$319$	−4.87014			−0.272675
$320$		0			0
$321$		0			0
$322$		0			0
$323$	23.6157			1.31402
$324$		0			0
$325$	15.1306	+	26.2070i	0.839297	+	1.45370i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.33333	−	28.9787i	0.128640	−	1.59764i
$330$		0			0
$331$	−18.9573			−1.04199			−0.520993	−	0.853561i	$-0.674438\pi$
$331$	−18.9573			−1.04199			−0.520993	+	0.853561i	$0.674438\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.620023	+	1.07391i	0.0338755	+	0.0586740i
$336$		0			0
$337$	11.6202	−	20.1268i	0.632993	−	1.09638i	−0.353944	−	0.935267i	$-0.615160\pi$
$337$	11.6202	−	20.1268i	0.632993	−	1.09638i	0.986937	−	0.161109i	$-0.0515071\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−4.38208	+	7.58998i	−0.237303	+	0.411020i
$342$		0			0
$343$	−4.42096	+	17.9849i	−0.238709	+	0.971091i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−18.1888			−0.976425			−0.488212	−	0.872725i	$-0.662351\pi$
$347$	−18.1888			−0.976425			−0.488212	+	0.872725i	$0.662351\pi$
$348$		0			0
$349$	−9.40155	−	16.2840i	−0.503253	−	0.871661i	−0.999993	−	0.00376081i	$-0.998803\pi$
$349$	−9.40155	−	16.2840i	−0.503253	−	0.871661i	0.496740	−	0.867900i	$-0.334530\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.95997	+	10.3230i	−0.317217	+	0.549436i	−0.979906	−	0.199458i	$-0.936082\pi$
$353$	−5.95997	+	10.3230i	−0.317217	+	0.549436i	0.662689	+	0.748895i	$0.269415\pi$
$354$		0			0
$355$	−1.64927	−	2.85662i	−0.0875342	−	0.151614i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	17.3849	−	30.1115i	0.917540	−	1.58923i	0.114400	−	0.993435i	$-0.463505\pi$
$359$	17.3849	−	30.1115i	0.917540	−	1.58923i	0.803140	−	0.595791i	$-0.203161\pi$
$360$		0			0
$361$	−1.91559	−	3.31790i	−0.100821	−	0.174626i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.54551	+	2.67689i	−0.0808954	+	0.140115i
$366$		0			0
$367$	14.4431	−	25.0161i	0.753922	−	1.30583i	−0.191987	−	0.981398i	$-0.561493\pi$
$367$	14.4431	−	25.0161i	0.753922	−	1.30583i	0.945909	−	0.324433i	$-0.105174\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−27.9626	+	13.2756i	−1.45175	+	0.689233i
$372$		0			0
$373$	−7.15472	−	12.3923i	−0.370457	−	0.641651i	0.619179	−	0.785250i	$-0.287466\pi$
$373$	−7.15472	−	12.3923i	−0.370457	−	0.641651i	−0.989636	+	0.143599i	$0.954132\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−22.8585			−1.17727
$378$		0			0
$379$	1.15511			0.0593340			0.0296670	−	0.999560i	$-0.490555\pi$
$379$	1.15511			0.0593340			0.0296670	+	0.999560i	$0.490555\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	16.9131	+	29.2944i	0.864219	+	1.49687i	0.867820	+	0.496878i	$0.165521\pi$
$383$	16.9131	+	29.2944i	0.864219	+	1.49687i	−0.00360069	+	0.999994i	$0.501146\pi$
$384$		0			0
$385$	0.134068	−	1.66505i	0.00683272	−	0.0848587i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	9.66080	−	16.7330i	0.489822	−	0.848397i	−0.510109	−	0.860110i	$-0.670395\pi$
$389$	9.66080	−	16.7330i	0.489822	−	0.848397i	0.999931	+	0.0117128i	$0.00372838\pi$
$390$		0			0
$391$	−18.8503	+	32.6496i	−0.953299	+	1.65116i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.744159	−	1.28892i	−0.0374427	−	0.0648526i
$396$		0			0
$397$	−6.18190	+	10.7074i	−0.310261	+	0.537387i	−0.978419	−	0.206632i	$-0.933750\pi$
$397$	−6.18190	+	10.7074i	−0.310261	+	0.537387i	0.668158	+	0.744019i	$0.267083\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−15.2568	−	26.4256i	−0.761889	−	1.31963i	−0.941876	−	0.335961i	$-0.890939\pi$
$401$	−15.2568	−	26.4256i	−0.761889	−	1.31963i	0.179987	−	0.983669i	$-0.442394\pi$
$402$		0			0
$403$	−20.5677	+	35.6244i	−1.02455	+	1.77458i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.06948	+	12.2447i	0.350421	+	0.606947i
$408$		0			0
$409$	−5.25446			−0.259816			−0.129908	−	0.991526i	$-0.541468\pi$
$409$	−5.25446			−0.259816			−0.129908	+	0.991526i	$0.541468\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.823443	−	10.2267i	0.0405190	−	0.503224i
$414$		0			0
$415$	−2.29530	+	3.97558i	−0.112672	+	0.195154i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−15.2824	+	26.4699i	−0.746594	+	1.29314i	0.202852	+	0.979209i	$0.434979\pi$
$419$	−15.2824	+	26.4699i	−0.746594	+	1.29314i	−0.949446	+	0.313930i	$0.898354\pi$
$420$		0			0
$421$	3.11608	+	5.39721i	0.151869	+	0.263044i	0.931914	−	0.362678i	$-0.118138\pi$
$421$	3.11608	+	5.39721i	0.151869	+	0.263044i	−0.780046	+	0.625722i	$0.784804\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	23.6287			1.14616
$426$		0			0
$427$	0.795154	−	9.87538i	0.0384802	−	0.477903i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−14.8142	−	25.6590i	−0.713576	−	1.23595i	−0.963506	−	0.267686i	$-0.913741\pi$
$431$	−14.8142	−	25.6590i	−0.713576	−	1.23595i	0.249930	−	0.968264i	$-0.419592\pi$
$432$		0			0
$433$	7.36815			0.354091			0.177045	−	0.984203i	$-0.443346\pi$
$433$	7.36815			0.354091			0.177045	+	0.984203i	$0.443346\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	36.4480			1.74355
$438$		0			0
$439$	10.4427			0.498403			0.249201	−	0.968452i	$-0.419832\pi$
$439$	10.4427			0.498403			0.249201	+	0.968452i	$0.419832\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.66664			−0.269230			−0.134615	−	0.990898i	$-0.542980\pi$
$443$	−5.66664			−0.269230			−0.134615	+	0.990898i	$0.542980\pi$
$444$		0			0
$445$	4.96923			0.235564
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−11.4794			−0.541748			−0.270874	−	0.962615i	$-0.587313\pi$
$449$	−11.4794			−0.541748			−0.270874	+	0.962615i	$0.587313\pi$
$450$		0			0
$451$	0.0339345	+	0.0587763i	0.00159791	+	0.00276767i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.629261	−	7.81508i	0.0295002	−	0.366377i
$456$		0			0
$457$	19.5872			0.916251			0.458126	−	0.888887i	$-0.348521\pi$
$457$	19.5872			0.916251			0.458126	+	0.888887i	$0.348521\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−17.3028	−	29.9693i	−0.805871	−	1.39581i	−0.915701	−	0.401859i	$-0.868364\pi$
$461$	−17.3028	−	29.9693i	−0.805871	−	1.39581i	0.109830	−	0.993950i	$-0.464969\pi$
$462$		0			0
$463$	6.91882	−	11.9837i	0.321545	−	0.556932i	−0.659262	−	0.751913i	$-0.729131\pi$
$463$	6.91882	−	11.9837i	0.321545	−	0.556932i	0.980807	+	0.194981i	$0.0624646\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.71088	+	6.42743i	−0.171719	+	0.297426i	−0.939021	−	0.343860i	$-0.888265\pi$
$467$	−3.71088	+	6.42743i	−0.171719	+	0.297426i	0.767302	+	0.641286i	$0.221599\pi$
$468$		0			0
$469$	−0.562442	+	6.98523i	−0.0259712	+	0.322548i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.16482			0.0535587
$474$		0			0
$475$	−11.4218	−	19.7832i	−0.524070	−	0.907716i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.89577	+	6.74767i	−0.178002	+	0.308309i	−0.941196	−	0.337860i	$-0.890297\pi$
$479$	−3.89577	+	6.74767i	−0.178002	+	0.308309i	0.763194	+	0.646170i	$0.223630\pi$
$480$		0			0
$481$	33.1813	+	57.4718i	1.51294	+	2.62049i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.26684	−	5.65834i	0.148340	−	0.256932i
$486$		0			0
$487$	−1.04434	−	1.80886i	−0.0473238	−	0.0819672i	0.841393	−	0.540423i	$-0.181736\pi$
$487$	−1.04434	−	1.80886i	−0.0473238	−	0.0819672i	−0.888717	+	0.458456i	$0.848403\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	16.8767	−	29.2312i	0.761633	−	1.31919i	−0.180375	−	0.983598i	$-0.557731\pi$
$491$	16.8767	−	29.2312i	0.761633	−	1.31919i	0.942008	−	0.335590i	$-0.108936\pi$
$492$		0			0
$493$	−8.92422	+	15.4572i	−0.401927	+	0.696157i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.49611	−	18.5808i	0.0671095	−	0.833464i
$498$		0			0
$499$	−20.9098	−	36.2169i	−0.936052	−	1.62129i	−0.772747	−	0.634714i	$-0.781118\pi$
$499$	−20.9098	−	36.2169i	−0.936052	−	1.62129i	−0.163304	−	0.986576i	$-0.552215\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−6.54978			−0.292040			−0.146020	−	0.989282i	$-0.546646\pi$
$503$	−6.54978			−0.292040			−0.146020	+	0.989282i	$0.546646\pi$
$504$		0			0
$505$	−1.98946			−0.0885299
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6.30653	−	10.9232i	−0.279532	−	0.484164i	0.691736	−	0.722150i	$-0.256846\pi$
$509$	−6.30653	−	10.9232i	−0.279532	−	0.484164i	−0.971269	+	0.237986i	$0.923513\pi$
$510$		0			0
$511$	−15.7800	+	7.49175i	−0.698068	+	0.331415i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2.09656	−	3.63134i	0.0923853	−	0.160016i
$516$		0			0
$517$	−7.40936	+	12.8334i	−0.325863	+	0.564412i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−10.2688	−	17.7861i	−0.449883	−	0.779221i	0.548495	−	0.836154i	$-0.315201\pi$
$521$	−10.2688	−	17.7861i	−0.449883	−	0.779221i	−0.998378	+	0.0569331i	$0.981868\pi$
$522$		0			0
$523$	14.4579	−	25.0419i	0.632202	−	1.09501i	−0.354899	−	0.934905i	$-0.615485\pi$
$523$	14.4579	−	25.0419i	0.632202	−	1.09501i	0.987101	−	0.160101i	$-0.0511820\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	16.0598	+	27.8163i	0.699574	+	1.21170i
$528$		0			0
$529$	−17.5931	+	30.4721i	−0.764917	+	1.32488i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.159275	+	0.275873i	0.00689897	+	0.0119494i
$534$		0			0
$535$	−0.759119			−0.0328196
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.96730	−	7.31483i	0.257030	−	0.315072i
$540$		0			0
$541$	3.29262	−	5.70299i	0.141561	−	0.245191i	−0.786524	−	0.617560i	$-0.788121\pi$
$541$	3.29262	−	5.70299i	0.141561	−	0.245191i	0.928085	+	0.372369i	$0.121455\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.39348	−	2.41357i	0.0596900	−	0.103386i
$546$		0			0
$547$	4.46777	+	7.73840i	0.191028	+	0.330870i	0.945591	−	0.325357i	$-0.105485\pi$
$547$	4.46777	+	7.73840i	0.191028	+	0.330870i	−0.754563	+	0.656227i	$0.772151\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	17.2555			0.735108
$552$		0			0
$553$	0.675050	−	8.38376i	0.0287060	−	0.356514i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.93523	+	5.08396i	0.124370	+	0.215414i	0.921486	−	0.388411i	$-0.126976\pi$
$557$	2.93523	+	5.08396i	0.124370	+	0.215414i	−0.797117	+	0.603825i	$0.793642\pi$
$558$		0			0
$559$	5.46723			0.231239
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−27.5972			−1.16308			−0.581541	−	0.813517i	$-0.697550\pi$
$563$	−27.5972			−1.16308			−0.581541	+	0.813517i	$0.697550\pi$
$564$		0			0
$565$	3.87968			0.163220
$566$		0			0
$567$		0			0
$568$		0			0
$569$	27.9202			1.17048			0.585238	−	0.810862i	$-0.301001\pi$
$569$	27.9202			1.17048			0.585238	+	0.810862i	$0.301001\pi$
$570$		0			0
$571$	−31.7974			−1.33068			−0.665339	−	0.746541i	$-0.731713\pi$
$571$	−31.7974			−1.33068			−0.665339	+	0.746541i	$0.731713\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	36.4680			1.52082
$576$		0			0
$577$	13.7476	+	23.8115i	0.572320	+	0.991287i	0.996327	+	0.0856281i	$0.0272897\pi$
$577$	13.7476	+	23.8115i	0.572320	+	0.991287i	−0.424007	+	0.905659i	$0.639377\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−23.4357	+	11.1263i	−0.972276	+	0.461599i
$582$		0			0
$583$	15.7778			0.653449
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.12422	+	12.3395i	0.294048	+	0.509306i	0.974763	−	0.223242i	$-0.0716641\pi$
$587$	7.12422	+	12.3395i	0.294048	+	0.509306i	−0.680715	+	0.732548i	$0.738331\pi$
$588$		0			0
$589$	15.5262	−	26.8922i	0.639747	−	1.10807i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−15.4636	+	26.7838i	−0.635015	+	1.09988i	0.351498	+	0.936189i	$0.385673\pi$
$593$	−15.4636	+	26.7838i	−0.635015	+	1.09988i	−0.986512	+	0.163689i	$0.947661\pi$
$594$		0			0
$595$	−5.03898	−	3.47661i	−0.206578	−	0.142527i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−36.5315			−1.49264			−0.746318	−	0.665589i	$-0.768180\pi$
$599$	−36.5315			−1.49264			−0.746318	+	0.665589i	$0.768180\pi$
$600$		0			0
$601$	7.11575	+	12.3248i	0.290257	+	0.502741i	0.973871	−	0.227104i	$-0.0729257\pi$
$601$	7.11575	+	12.3248i	0.290257	+	0.502741i	−0.683613	+	0.729845i	$0.739592\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.14920	−	3.72253i	0.0873776	−	0.151342i
$606$		0			0
$607$	14.6729	+	25.4141i	0.595553	+	1.03153i	0.993469	+	0.114106i	$0.0364003\pi$
$607$	14.6729	+	25.4141i	0.595553	+	1.03153i	−0.397916	+	0.917422i	$0.630266\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−34.7766	+	60.2349i	−1.40691	+	2.43684i
$612$		0			0
$613$	−3.79264	−	6.56905i	−0.153183	−	0.265321i	0.779213	−	0.626760i	$-0.215619\pi$
$613$	−3.79264	−	6.56905i	−0.153183	−	0.265321i	−0.932396	+	0.361438i	$0.882286\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	10.4367	−	18.0769i	0.420165	−	0.727748i	−0.575790	−	0.817598i	$-0.695305\pi$
$617$	10.4367	−	18.0769i	0.420165	−	0.727748i	0.995955	+	0.0898500i	$0.0286388\pi$
$618$		0			0
$619$	12.6300	−	21.8758i	0.507642	−	0.879262i	−0.492319	−	0.870415i	$-0.663851\pi$
$619$	12.6300	−	21.8758i	0.507642	−	0.879262i	0.999961	−	0.00884679i	$-0.00281606\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	23.1147	+	15.9478i	0.926072	+	0.638937i
$624$		0			0
$625$	−10.8802	−	18.8450i	−0.435206	−	0.753799i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	51.8175			2.06610
$630$		0			0
$631$	−34.0114			−1.35397			−0.676986	−	0.735996i	$-0.736714\pi$
$631$	−34.0114			−1.35397			−0.676986	+	0.735996i	$0.736714\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.90163	−	3.29372i	−0.0754638	−	0.130707i
$636$		0			0
$637$	28.0082	−	34.3329i	1.10972	−	1.36032i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.64947	−	4.58902i	0.104648	−	0.181255i	−0.808946	−	0.587882i	$-0.799962\pi$
$641$	2.64947	−	4.58902i	0.104648	−	0.181255i	0.913594	+	0.406627i	$0.133295\pi$
$642$		0			0
$643$	19.4304	−	33.6544i	0.766260	−	1.32720i	−0.173318	−	0.984866i	$-0.555449\pi$
$643$	19.4304	−	33.6544i	0.766260	−	1.32720i	0.939578	−	0.342335i	$-0.111218\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.11420	−	7.12601i	−0.161746	−	0.280152i	0.773749	−	0.633492i	$-0.218379\pi$
$647$	−4.11420	−	7.12601i	−0.161746	−	0.280152i	−0.935495	+	0.353340i	$0.885046\pi$
$648$		0			0
$649$	−2.61480	+	4.52897i	−0.102640	+	0.177778i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	21.0164	+	36.4015i	0.822436	+	1.42450i	0.903863	+	0.427821i	$0.140719\pi$
$653$	21.0164	+	36.4015i	0.822436	+	1.42450i	−0.0814277	+	0.996679i	$0.525948\pi$
$654$		0			0
$655$	4.56382	−	7.90477i	0.178323	−	0.308865i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7.33484	−	12.7043i	−0.285725	−	0.494890i	0.687060	−	0.726601i	$-0.258901\pi$
$659$	−7.33484	−	12.7043i	−0.285725	−	0.494890i	−0.972785	+	0.231711i	$0.925568\pi$
$660$		0			0
$661$	5.86605			0.228163			0.114081	−	0.993471i	$-0.463608\pi$
$661$	5.86605			0.228163			0.114081	+	0.993471i	$0.463608\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.475018	+	5.89947i	−0.0184204	+	0.228771i
$666$		0			0
$667$	−13.7734	+	23.8563i	−0.533310	+	0.923720i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.52497	+	4.37338i	−0.0974754	+	0.168832i
$672$		0			0
$673$	9.42591	+	16.3261i	0.363342	+	0.629327i	0.988509	−	0.151165i	$-0.0483023\pi$
$673$	9.42591	+	16.3261i	0.363342	+	0.629327i	−0.625167	+	0.780491i	$0.714969\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−29.9144			−1.14970			−0.574852	−	0.818257i	$-0.694941\pi$
$677$	−29.9144			−1.14970			−0.574852	+	0.818257i	$0.694941\pi$
$678$		0			0
$679$	33.3554	−	15.8358i	1.28006	−	0.607724i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−12.8525	−	22.2612i	−0.491788	−	0.851802i	0.508167	−	0.861258i	$-0.330323\pi$
$683$	−12.8525	−	22.2612i	−0.491788	−	0.851802i	−0.999955	+	0.00945677i	$0.996990\pi$
$684$		0			0
$685$	7.07099			0.270169
$686$		0			0
$687$		0			0
$688$		0			0
$689$	74.0547			2.82126
$690$		0			0
$691$	38.4020			1.46088			0.730440	−	0.682976i	$-0.239315\pi$
$691$	38.4020			1.46088			0.730440	+	0.682976i	$0.239315\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.04895			0.0777210
$696$		0			0
$697$	0.248731			0.00942137
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−11.5694			−0.436972			−0.218486	−	0.975840i	$-0.570112\pi$
$701$	−11.5694			−0.436972			−0.218486	+	0.975840i	$0.570112\pi$
$702$		0			0
$703$	−25.0480	−	43.3844i	−0.944703	−	1.63627i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.25413	−	6.38482i	−0.348037	−	0.240126i
$708$		0			0
$709$	52.0550			1.95497			0.977483	−	0.211013i	$-0.0676763\pi$
$709$	52.0550			1.95497			0.977483	+	0.211013i	$0.0676763\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	24.7863	+	42.9311i	0.928254	+	1.60778i
$714$		0			0
$715$	−1.99819	+	3.46096i	−0.0747280	+	0.129433i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.416175	+	0.720836i	−0.0155207	+	0.0268827i	−0.873681	−	0.486498i	$-0.838274\pi$
$719$	−0.416175	+	0.720836i	−0.0155207	+	0.0268827i	0.858161	+	0.513381i	$0.171607\pi$
$720$		0			0
$721$	21.4064	−	10.1629i	0.797217	−	0.378488i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	17.2649			0.641203
$726$		0			0
$727$	10.7029	+	18.5379i	0.396948	+	0.687534i	0.993348	−	0.115154i	$-0.0367361\pi$
$727$	10.7029	+	18.5379i	0.396948	+	0.687534i	−0.596400	+	0.802687i	$0.703403\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.13447	−	3.69701i	0.0789461	−	0.136739i
$732$		0			0
$733$	3.72620	+	6.45396i	0.137630	+	0.238383i	0.926599	−	0.376051i	$-0.122718\pi$
$733$	3.72620	+	6.45396i	0.137630	+	0.238383i	−0.788969	+	0.614433i	$0.789385\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.78601	−	3.09346i	0.0657885	−	0.113949i
$738$		0			0
$739$	−17.9473	−	31.0857i	−0.660203	−	1.14351i	−0.980562	−	0.196210i	$-0.937137\pi$
$739$	−17.9473	−	31.0857i	−0.660203	−	1.14351i	0.320358	−	0.947296i	$-0.396197\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−16.8379	+	29.1641i	−0.617723	+	1.06993i	0.372177	+	0.928162i	$0.378611\pi$
$743$	−16.8379	+	29.1641i	−0.617723	+	1.06993i	−0.989900	+	0.141766i	$0.954722\pi$
$744$		0			0
$745$	−2.75199	+	4.76659i	−0.100825	+	0.174634i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.53110	−	2.43625i	−0.129023	−	0.0890188i
$750$		0			0
$751$	−7.51689	−	13.0196i	−0.274295	−	0.475093i	0.695662	−	0.718369i	$-0.255111\pi$
$751$	−7.51689	−	13.0196i	−0.274295	−	0.475093i	−0.969957	+	0.243276i	$0.921778\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.40782			−0.0876295
$756$		0			0
$757$	−34.2548			−1.24501			−0.622507	−	0.782615i	$-0.713886\pi$
$757$	−34.2548			−1.24501			−0.622507	+	0.782615i	$0.713886\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	21.1043	+	36.5538i	0.765031	+	1.32507i	0.940230	+	0.340540i	$0.110610\pi$
$761$	21.1043	+	36.5538i	0.765031	+	1.32507i	−0.175199	+	0.984533i	$0.556057\pi$
$762$		0			0
$763$	14.2278	−	6.75480i	0.515081	−	0.244540i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−12.2728	+	21.2572i	−0.443147	+	0.767553i
$768$		0			0
$769$	22.2741	−	38.5799i	0.803226	−	1.39123i	−0.114256	−	0.993451i	$-0.536448\pi$
$769$	22.2741	−	38.5799i	0.803226	−	1.39123i	0.917482	−	0.397777i	$-0.130218\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	9.61003	+	16.6451i	0.345649	+	0.598681i	0.985471	−	0.169841i	$-0.0543256\pi$
$773$	9.61003	+	16.6451i	0.345649	+	0.598681i	−0.639823	+	0.768523i	$0.720992\pi$
$774$		0			0
$775$	15.5347	−	26.9069i	0.558024	−	0.966526i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.120234	−	0.208251i	−0.00430783	−	0.00746138i
$780$		0			0
$781$	−4.75081	+	8.22864i	−0.169997	+	0.294444i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.82984	+	4.90142i	0.101001	+	0.174939i
$786$		0			0
$787$	−40.3502			−1.43833			−0.719165	−	0.694839i	$-0.755476\pi$
$787$	−40.3502			−1.43833			−0.719165	+	0.694839i	$0.755476\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	18.0466	+	12.4512i	0.641665	+	0.442712i
$792$		0			0
$793$	−11.8512	+	20.5269i	−0.420849	+	0.728932i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−22.4965	+	38.9651i	−0.796867	+	1.38021i	0.124780	+	0.992184i	$0.460177\pi$
$797$	−22.4965	+	38.9651i	−0.796867	+	1.38021i	−0.921647	+	0.388029i	$0.873156\pi$
$798$		0			0
$799$	27.1544	+	47.0328i	0.960653	+	1.66390i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.90381			0.314209
$804$		0			0
$805$	−7.77706	−	5.36573i	−0.274105	−	0.189117i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−16.8858	−	29.2470i	−0.593672	−	1.02827i	−0.993733	−	0.111782i	$-0.964344\pi$
$809$	−16.8858	−	29.2470i	−0.593672	−	1.02827i	0.400061	−	0.916489i	$-0.368989\pi$
$810$		0			0
$811$	−31.7254			−1.11403			−0.557014	−	0.830503i	$-0.688053\pi$
$811$	−31.7254			−1.11403			−0.557014	+	0.830503i	$0.688053\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	2.57178			0.0900854
$816$		0			0
$817$	−4.12711			−0.144389
$818$		0			0
$819$		0			0
$820$		0			0
$821$	11.7504			0.410093			0.205046	−	0.978752i	$-0.434265\pi$
$821$	11.7504			0.410093			0.205046	+	0.978752i	$0.434265\pi$
$822$		0			0
$823$	−8.50742			−0.296550			−0.148275	−	0.988946i	$-0.547372\pi$
$823$	−8.50742			−0.296550			−0.148275	+	0.988946i	$0.547372\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.9662			0.485651			0.242825	−	0.970070i	$-0.421926\pi$
$827$	13.9662			0.485651			0.242825	+	0.970070i	$0.421926\pi$
$828$		0			0
$829$	−18.5484	−	32.1267i	−0.644212	−	1.11581i	−0.984483	−	0.175480i	$-0.943852\pi$
$829$	−18.5484	−	32.1267i	−0.644212	−	1.11581i	0.340271	−	0.940327i	$-0.389481\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−12.2817	−	32.3434i	−0.425534	−	1.12063i
$834$		0			0
$835$	−3.36499			−0.116450
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.32105	+	2.28813i	0.0456077	+	0.0789949i	0.887928	−	0.459982i	$-0.152144\pi$
$839$	1.32105	+	2.28813i	0.0456077	+	0.0789949i	−0.842320	+	0.538977i	$0.818811\pi$
$840$		0			0
$841$	7.97928	−	13.8205i	0.275148	−	0.476570i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.33561	+	10.9736i	−0.217952	+	0.377503i
$846$		0			0
$847$	21.9440	−	10.4181i	0.754004	−	0.357972i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	79.9740			2.74147
$852$		0			0
$853$	17.3405	+	30.0346i	0.593726	+	1.02836i	0.993725	+	0.111848i	$0.0356771\pi$
$853$	17.3405	+	30.0346i	0.593726	+	1.02836i	−0.399999	+	0.916516i	$0.630990\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	11.8611	−	20.5441i	0.405169	−	0.701773i	−0.589172	−	0.808008i	$-0.700546\pi$
$857$	11.8611	−	20.5441i	0.405169	−	0.701773i	0.994341	+	0.106234i	$0.0338793\pi$
$858$		0			0
$859$	10.9075	+	18.8923i	0.372158	+	0.644597i	0.989897	−	0.141786i	$-0.0452845\pi$
$859$	10.9075	+	18.8923i	0.372158	+	0.644597i	−0.617739	+	0.786383i	$0.711951\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	14.6899	−	25.4436i	0.500049	−	0.866111i	−0.499951	−	0.866054i	$-0.666649\pi$
$863$	14.6899	−	25.4436i	0.500049	−	0.866111i	1.00000		5.68129e-5i	$-1.80841e-5\pi$
$864$		0			0
$865$	−1.86308	−	3.22696i	−0.0633467	−	0.109720i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.14359	+	3.71280i	−0.0727162	+	0.125948i
$870$		0			0
$871$	8.38282	−	14.5195i	0.284041	−	0.491973i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.972346	+	12.0760i	−0.0328713	+	0.408244i
$876$		0			0
$877$	2.81065	+	4.86818i	0.0949087	+	0.164387i	0.909571	−	0.415550i	$-0.136411\pi$
$877$	2.81065	+	4.86818i	0.0949087	+	0.164387i	−0.814662	+	0.579936i	$0.803077\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−2.75442			−0.0927987			−0.0463994	−	0.998923i	$-0.514775\pi$
$881$	−2.75442			−0.0927987			−0.0463994	+	0.998923i	$0.514775\pi$
$882$		0			0
$883$	33.8917			1.14055			0.570274	−	0.821455i	$-0.306837\pi$
$883$	33.8917			1.14055			0.570274	+	0.821455i	$0.306837\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−27.8447	−	48.2284i	−0.934932	−	1.61935i	−0.774755	−	0.632261i	$-0.782127\pi$
$887$	−27.8447	−	48.2284i	−0.934932	−	1.61935i	−0.160177	−	0.987088i	$-0.551206\pi$
$888$		0			0
$889$	1.72503	−	21.4239i	0.0578555	−	0.718535i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	26.2523	−	45.4702i	0.878498	−	1.52160i
$894$		0			0
$895$	−0.0790366	+	0.136895i	−0.00264190	+	0.00457591i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	11.7345	+	20.3247i	0.391367	+	0.677868i
$900$		0			0
$901$	28.9118	−	50.0767i	0.963192	−	1.66830i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.65217	−	2.86164i	−0.0549200	−	0.0951243i
$906$		0			0
$907$	−26.7313	+	46.2999i	−0.887597	+	1.53736i	−0.0448901	+	0.998992i	$0.514294\pi$
$907$	−26.7313	+	46.2999i	−0.887597	+	1.53736i	−0.842707	+	0.538372i	$0.819040\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−9.77060	−	16.9232i	−0.323714	−	0.560690i	0.657537	−	0.753422i	$-0.271598\pi$
$911$	−9.77060	−	16.9232i	−0.323714	−	0.560690i	−0.981251	+	0.192732i	$0.938265\pi$
$912$		0			0
$913$	13.2235			0.437633
$914$		0			0
$915$		0			0
$916$		0			0
$917$	46.5979	−	22.1229i	1.53880	−	0.730561i
$918$		0			0
$919$	0.0878895	−	0.152229i	0.00289921	−	0.00502157i	−0.864572	−	0.502509i	$-0.832410\pi$
$919$	0.0878895	−	0.152229i	0.00289921	−	0.00502157i	0.867471	+	0.497487i	$0.165744\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−22.2984	+	38.6220i	−0.733962	+	1.27126i
$924$		0			0
$925$	−25.0617	−	43.4082i	−0.824025	−	1.42725i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	24.6016			0.807152			0.403576	−	0.914946i	$-0.367767\pi$
$929$	24.6016			0.807152			0.403576	+	0.914946i	$0.367767\pi$
$930$		0			0
$931$	−21.1429	+	25.9173i	−0.692929	+	0.849406i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.56023	+	2.70240i	0.0510250	+	0.0883779i
$936$		0			0
$937$	−28.5655			−0.933195			−0.466598	−	0.884470i	$-0.654520\pi$
$937$	−28.5655			−0.933195			−0.466598	+	0.884470i	$0.654520\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−37.5604			−1.22443			−0.612217	−	0.790689i	$-0.709722\pi$
$941$	−37.5604			−1.22443			−0.612217	+	0.790689i	$0.709722\pi$
$942$		0			0
$943$	0.383887			0.0125011
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.66763			−0.314156			−0.157078	−	0.987586i	$-0.550207\pi$
$947$	−9.66763			−0.314156			−0.157078	+	0.987586i	$0.550207\pi$
$948$		0			0
$949$	41.7910			1.35659
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−58.1964			−1.88517			−0.942583	−	0.333971i	$-0.891611\pi$
$953$	−58.1964			−1.88517			−0.942583	+	0.333971i	$0.891611\pi$
$954$		0			0
$955$	4.14767	+	7.18397i	0.134215	+	0.232468i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	32.8912	+	22.6931i	1.06211	+	0.732797i
$960$		0			0
$961$	11.2341			0.362390
$962$		0			0
$963$		0			0
$964$		0			0
$965$	3.93319	+	6.81248i	0.126614	+	0.219301i
$966$		0			0
$967$	7.97991	−	13.8216i	0.256617	−	0.444473i	−0.708717	−	0.705493i	$-0.750726\pi$
$967$	7.97991	−	13.8216i	0.256617	−	0.444473i	0.965333	+	0.261020i	$0.0840589\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.67394	−	2.89935i	0.0537193	−	0.0930445i	−0.837915	−	0.545800i	$-0.816226\pi$
$971$	1.67394	−	2.89935i	0.0537193	−	0.0930445i	0.891635	+	0.452756i	$0.149559\pi$
$972$		0			0
$973$	9.53083	+	6.57573i	0.305544	+	0.210808i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−23.8803			−0.763999			−0.382000	−	0.924162i	$-0.624764\pi$
$977$	−23.8803			−0.763999			−0.382000	+	0.924162i	$0.624764\pi$
$978$		0			0
$979$	−7.15706	−	12.3964i	−0.228741	−	0.396190i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18.8786	−	32.6988i	0.602135	−	1.04293i	−0.390362	−	0.920661i	$-0.627650\pi$
$983$	18.8786	−	32.6988i	0.602135	−	1.04293i	0.992497	−	0.122267i	$-0.0390165\pi$
$984$		0			0
$985$	1.39876	+	2.42272i	0.0445682	+	0.0771944i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.29429	−	5.70588i	0.104752	−	0.181436i
$990$		0			0
$991$	−1.08487	−	1.87904i	−0.0344619	−	0.0596898i	0.848280	−	0.529548i	$-0.177638\pi$
$991$	−1.08487	−	1.87904i	−0.0344619	−	0.0596898i	−0.882742	+	0.469858i	$0.844305\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.93117	−	5.07694i	0.0929245	−	0.160950i
$996$		0			0
$997$	4.34727	−	7.52969i	0.137679	−	0.238468i	−0.788938	−	0.614472i	$-0.789369\pi$
$997$	4.34727	−	7.52969i	0.137679	−	0.238468i	0.926618	+	0.376005i	$0.122702\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.q.d.793.5		22
3.2	odd	2		504.2.q.c.121.1	yes	22
4.3	odd	2		3024.2.q.l.2305.5		22
7.4	even	3		1512.2.t.c.361.7		22
9.2	odd	6		504.2.t.c.457.7	yes	22
9.7	even	3		1512.2.t.c.289.7		22
12.11	even	2		1008.2.q.l.625.11		22
21.11	odd	6		504.2.t.c.193.7	yes	22
28.11	odd	6		3024.2.t.k.1873.7		22
36.7	odd	6		3024.2.t.k.289.7		22
36.11	even	6		1008.2.t.l.961.5		22
63.11	odd	6		504.2.q.c.25.1	✓	22
63.25	even	3	inner	1512.2.q.d.1369.5		22
84.11	even	6		1008.2.t.l.193.5		22
252.11	even	6		1008.2.q.l.529.11		22
252.151	odd	6		3024.2.q.l.2881.5		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.1	✓	22	63.11	odd	6
504.2.q.c.121.1	yes	22	3.2	odd	2
504.2.t.c.193.7	yes	22	21.11	odd	6
504.2.t.c.457.7	yes	22	9.2	odd	6
1008.2.q.l.529.11		22	252.11	even	6
1008.2.q.l.625.11		22	12.11	even	2
1008.2.t.l.193.5		22	84.11	even	6
1008.2.t.l.961.5		22	36.11	even	6
1512.2.q.d.793.5		22	1.1	even	1	trivial
1512.2.q.d.1369.5		22	63.25	even	3	inner
1512.2.t.c.289.7		22	9.7	even	3
1512.2.t.c.361.7		22	7.4	even	3
3024.2.q.l.2305.5		22	4.3	odd	2
3024.2.q.l.2881.5		22	252.151	odd	6
3024.2.t.k.289.7		22	36.7	odd	6
3024.2.t.k.1873.7		22	28.11	odd	6

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.234085 - 0.405446i) q^{5} +(0.212345 - 2.63722i) q^{7} +O(q^{10})\)	\(q+(-0.234085 - 0.405446i) q^{5} +(0.212345 - 2.63722i) q^{7} +(-0.674293 + 1.16791i) q^{11} +(-3.16486 + 5.48171i) q^{13} +(2.47120 + 4.28024i) q^{17} +(2.38910 - 4.13804i) q^{19} +(3.81399 + 6.60603i) q^{23} +(2.39041 - 4.14031i) q^{25} +(1.80565 + 3.12747i) q^{29} +6.49878 q^{31} +(-1.11896 + 0.531237i) q^{35} +(5.24214 - 9.07966i) q^{37} +(0.0251630 - 0.0435837i) q^{41} +(-0.431869 - 0.748019i) q^{43} +10.9883 q^{47} +(-6.90982 - 1.12000i) q^{49} +(-5.84976 - 10.1321i) q^{53} +0.631366 q^{55} +3.87784 q^{59} +3.74462 q^{61} +2.96338 q^{65} -2.64871 q^{67} +7.04562 q^{71} +(-3.30117 - 5.71779i) q^{73} +(2.93685 + 2.02626i) q^{77} +3.17902 q^{79} +(-4.90272 - 8.49176i) q^{83} +(1.15694 - 2.00388i) q^{85} +(-5.30709 + 9.19214i) q^{89} +(13.7844 + 9.51045i) q^{91} -2.23701 q^{95} +(6.97792 + 12.0861i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{5} + 5 q^{7}+O(q^{10}) \) 22 * q - q^5 + 5 * q^7	\( 22 q - q^{5} + 5 q^{7} - 3 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} - 22 q^{25} + 7 q^{29} - 12 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} + 34 q^{47} - 25 q^{49} - q^{53} + 2 q^{55} - 42 q^{59} - 62 q^{61} - 6 q^{65} + 52 q^{67} + 32 q^{71} + 17 q^{73} + q^{77} + 32 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} - 48 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q - q^5 + 5 * q^7 - 3 * q^11 + 7 * q^13 + q^17 + 13 * q^19 - 22 * q^25 + 7 * q^29 - 12 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 + 34 * q^47 - 25 * q^49 - q^53 + 2 * q^55 - 42 * q^59 - 62 * q^61 - 6 * q^65 + 52 * q^67 + 32 * q^71 + 17 * q^73 + q^77 + 32 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 - 48 * q^95 + 19 * q^97

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