LMFDB - Embedded newform 2268.2.k.g.1621.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(1297,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2268.1297");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.k (of order $3$, degree $2$, 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:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 $ x^16 - 9x^14 + 31x^12 - 282x^10 + 1695x^8 - 3318x^6 + 4606x^4 - 4116*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1621.2
Root			$-2.40332 - 0.123797i$ of defining polynomial
Character	$\chi$	$=$	2268.1621
Dual form			2268.2.k.g.1297.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15101 - 1.99360i) q^{5} +(-0.271847 - 2.63175i) q^{7} +O(q^{10})$	$q+(-1.15101 - 1.99360i) q^{5} +(-0.271847 - 2.63175i) q^{7} +(2.23145 - 3.86499i) q^{11} -2.84296 q^{13} +(0.115312 - 0.199726i) q^{17} +(-1.49360 - 2.58700i) q^{19} +(-0.400294 - 0.693329i) q^{23} +(-0.149635 + 0.259175i) q^{25} +7.65502 q^{29} +(-2.64324 + 4.57822i) q^{31} +(-4.93376 + 3.57112i) q^{35} +(-1.69333 - 2.93293i) q^{37} -1.79939 q^{41} -9.71719 q^{43} +(2.88818 + 5.00247i) q^{47} +(-6.85220 + 1.43087i) q^{49} +(4.31905 - 7.48081i) q^{53} -10.2737 q^{55} +(-4.17793 + 7.23638i) q^{59} +(6.58675 + 11.4086i) q^{61} +(3.27227 + 5.66774i) q^{65} +(3.76545 - 6.52195i) q^{67} -8.59672 q^{71} +(-2.29287 + 3.97137i) q^{73} +(-10.7783 - 4.82194i) q^{77} +(-4.83657 - 8.37718i) q^{79} +16.9304 q^{83} -0.530900 q^{85} +(-0.944450 - 1.63584i) q^{89} +(0.772852 + 7.48196i) q^{91} +(-3.43829 + 5.95530i) q^{95} -15.4159 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{7}+O(q^{10}) $ 16 * q + 6 * q^7	$ 16 q + 6 q^{7} - 20 q^{13} + 8 q^{19} - 8 q^{31} - 4 q^{37} + 20 q^{43} + 10 q^{49} - 32 q^{55} + 28 q^{61} + 18 q^{67} - 20 q^{79} + 76 q^{85} - 2 q^{91} - 84 q^{97}+O(q^{100}) $ 16 * q + 6 * q^7 - 20 * q^13 + 8 * q^19 - 8 * q^31 - 4 * q^37 + 20 * q^43 + 10 * q^49 - 32 * q^55 + 28 * q^61 + 18 * q^67 - 20 * q^79 + 76 * q^85 - 2 * q^91 - 84 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$5$	−1.15101	−	1.99360i	−0.514746	−	0.891566i	−0.999854	−	0.0171118i	$-0.994553\pi$
$5$	−1.15101	−	1.99360i	−0.514746	−	0.891566i	0.485108	−	0.874454i	$-0.338780\pi$
$6$		0			0
$7$	−0.271847	−	2.63175i	−0.102749	−	0.994707i
$7$	−0.271847	−	2.63175i	−0.102749	−	0.994707i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.23145	−	3.86499i	0.672809	−	1.16534i	−0.304295	−	0.952578i	$-0.598421\pi$
$11$	2.23145	−	3.86499i	0.672809	−	1.16534i	0.977104	−	0.212761i	$-0.0682457\pi$
$12$		0			0
$13$	−2.84296			−0.788496			−0.394248	−	0.919004i	$-0.628995\pi$
$13$	−2.84296			−0.788496			−0.394248	+	0.919004i	$0.628995\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.115312	−	0.199726i	0.0279673	−	0.0484408i	−0.851703	−	0.524025i	$-0.824430\pi$
$17$	0.115312	−	0.199726i	0.0279673	−	0.0484408i	0.879670	+	0.475584i	$0.157763\pi$
$18$		0			0
$19$	−1.49360	−	2.58700i	−0.342656	−	0.593498i	0.642269	−	0.766479i	$-0.277993\pi$
$19$	−1.49360	−	2.58700i	−0.342656	−	0.593498i	−0.984925	+	0.172982i	$0.944660\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.400294	−	0.693329i	−0.0834670	−	0.144569i	0.821270	−	0.570540i	$-0.193266\pi$
$23$	−0.400294	−	0.693329i	−0.0834670	−	0.144569i	−0.904737	+	0.425971i	$0.859933\pi$
$24$		0			0
$25$	−0.149635	+	0.259175i	−0.0299269	+	0.0518349i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	7.65502			1.42150			0.710750	−	0.703444i	$-0.248356\pi$
$29$	7.65502			1.42150			0.710750	+	0.703444i	$0.248356\pi$
$30$		0			0
$31$	−2.64324	+	4.57822i	−0.474739	+	0.822273i	−0.999582	−	0.0289268i	$-0.990791\pi$
$31$	−2.64324	+	4.57822i	−0.474739	+	0.822273i	0.524842	+	0.851200i	$0.324124\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.93376	+	3.57112i	−0.833958	+	0.603629i
$36$		0			0
$37$	−1.69333	−	2.93293i	−0.278382	−	0.482171i	0.692601	−	0.721321i	$-0.256465\pi$
$37$	−1.69333	−	2.93293i	−0.278382	−	0.482171i	−0.970983	+	0.239150i	$0.923131\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.79939			−0.281018			−0.140509	−	0.990079i	$-0.544874\pi$
$41$	−1.79939			−0.281018			−0.140509	+	0.990079i	$0.544874\pi$
$42$		0			0
$43$	−9.71719			−1.48186			−0.740929	−	0.671584i	$-0.765614\pi$
$43$	−9.71719			−1.48186			−0.740929	+	0.671584i	$0.765614\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.88818	+	5.00247i	0.421284	+	0.729686i	0.996065	−	0.0886214i	$-0.0282461\pi$
$47$	2.88818	+	5.00247i	0.421284	+	0.729686i	−0.574781	+	0.818307i	$0.694913\pi$
$48$		0			0
$49$	−6.85220	+	1.43087i	−0.978885	+	0.204410i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.31905	−	7.48081i	0.593267	−	1.02757i	−0.400522	−	0.916287i	$-0.631171\pi$
$53$	4.31905	−	7.48081i	0.593267	−	1.02757i	0.993789	−	0.111281i	$-0.0354954\pi$
$54$		0			0
$55$	−10.2737			−1.38530
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.17793	+	7.23638i	−0.543920	+	0.942097i	0.454754	+	0.890617i	$0.349727\pi$
$59$	−4.17793	+	7.23638i	−0.543920	+	0.942097i	−0.998674	+	0.0514798i	$0.983606\pi$
$60$		0			0
$61$	6.58675	+	11.4086i	0.843347	+	1.46072i	0.887049	+	0.461675i	$0.152751\pi$
$61$	6.58675	+	11.4086i	0.843347	+	1.46072i	−0.0437026	+	0.999045i	$0.513915\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.27227	+	5.66774i	0.405875	+	0.702997i
$66$		0			0
$67$	3.76545	−	6.52195i	0.460023	−	0.796783i	−0.538939	−	0.842345i	$-0.681175\pi$
$67$	3.76545	−	6.52195i	0.460023	−	0.796783i	0.998962	+	0.0455620i	$0.0145078\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.59672			−1.02024			−0.510122	−	0.860102i	$-0.670400\pi$
$71$	−8.59672			−1.02024			−0.510122	+	0.860102i	$0.670400\pi$
$72$		0			0
$73$	−2.29287	+	3.97137i	−0.268360	+	0.464814i	−0.968439	−	0.249252i	$-0.919815\pi$
$73$	−2.29287	+	3.97137i	−0.268360	+	0.464814i	0.700078	+	0.714066i	$0.253148\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−10.7783	−	4.82194i	−1.22830	−	0.549511i
$78$		0			0
$79$	−4.83657	−	8.37718i	−0.544156	−	0.942506i	−0.998659	−	0.0517612i	$-0.983517\pi$
$79$	−4.83657	−	8.37718i	−0.544156	−	0.942506i	0.454503	−	0.890745i	$-0.349817\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	16.9304			1.85835			0.929177	−	0.369634i	$-0.120517\pi$
$83$	16.9304			1.85835			0.929177	+	0.369634i	$0.120517\pi$
$84$		0			0
$85$	−0.530900			−0.0575842
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.944450	−	1.63584i	−0.100111	−	0.173398i	0.811619	−	0.584187i	$-0.198587\pi$
$89$	−0.944450	−	1.63584i	−0.100111	−	0.173398i	−0.911730	+	0.410789i	$0.865253\pi$
$90$		0			0
$91$	0.772852	+	7.48196i	0.0810169	+	0.784323i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.43829	+	5.95530i	−0.352762	+	0.611001i
$96$		0			0
$97$	−15.4159			−1.56525			−0.782624	−	0.622494i	$-0.786119\pi$
$97$	−15.4159			−1.56525			−0.782624	+	0.622494i	$0.786119\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.40744	+	2.43775i	−0.140045	+	0.242566i	−0.927513	−	0.373790i	$-0.878058\pi$
$101$	−1.40744	+	2.43775i	−0.140045	+	0.242566i	0.787468	+	0.616355i	$0.211391\pi$
$102$		0			0
$103$	−2.55832	−	4.43114i	−0.252079	−	0.436614i	0.712019	−	0.702160i	$-0.247781\pi$
$103$	−2.55832	−	4.43114i	−0.252079	−	0.436614i	−0.964098	+	0.265547i	$0.914448\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.29487	+	2.24278i	0.125180	+	0.216818i	0.921803	−	0.387658i	$-0.126716\pi$
$107$	1.29487	+	2.24278i	0.125180	+	0.216818i	−0.796623	+	0.604476i	$0.793383\pi$
$108$		0			0
$109$	−8.76728	+	15.1854i	−0.839753	+	1.45450i	0.0503474	+	0.998732i	$0.483967\pi$
$109$	−8.76728	+	15.1854i	−0.839753	+	1.45450i	−0.890101	+	0.455764i	$0.849366\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−16.4342			−1.54600			−0.773001	−	0.634405i	$-0.781245\pi$
$113$	−16.4342			−1.54600			−0.773001	+	0.634405i	$0.781245\pi$
$114$		0			0
$115$	−0.921482	+	1.59605i	−0.0859286	+	0.148833i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.556977	−	0.249177i	−0.0510580	−	0.0228420i
$120$		0			0
$121$	−4.45878	−	7.72283i	−0.405344	−	0.702076i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−10.8211			−0.967873
$126$		0			0
$127$	8.13145			0.721549			0.360775	−	0.932653i	$-0.382512\pi$
$127$	8.13145			0.721549			0.360775	+	0.932653i	$0.382512\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.25591	−	10.8356i	−0.546582	−	0.946707i	−0.998506	−	0.0546508i	$-0.982595\pi$
$131$	−6.25591	−	10.8356i	−0.546582	−	0.946707i	0.451924	−	0.892057i	$-0.350738\pi$
$132$		0			0
$133$	−6.40229	+	4.63405i	−0.555149	+	0.401823i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.09668	−	14.0239i	0.691746	−	1.19814i	−0.279519	−	0.960140i	$-0.590175\pi$
$137$	8.09668	−	14.0239i	0.691746	−	1.19814i	0.971265	−	0.237999i	$-0.0764916\pi$
$138$		0			0
$139$	−6.14424			−0.521148			−0.260574	−	0.965454i	$-0.583912\pi$
$139$	−6.14424			−0.521148			−0.260574	+	0.965454i	$0.583912\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.34394	+	10.9880i	−0.530507	+	0.918866i
$144$		0			0
$145$	−8.81098	−	15.2611i	−0.731712	−	1.26736i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.85927	+	6.68446i	0.316164	+	0.547612i	0.979684	−	0.200546i	$-0.0642717\pi$
$149$	3.85927	+	6.68446i	0.316164	+	0.547612i	−0.663520	+	0.748158i	$0.730938\pi$
$150$		0			0
$151$	7.45878	−	12.9190i	0.606987	−	1.05133i	−0.384747	−	0.923022i	$-0.625711\pi$
$151$	7.45878	−	12.9190i	0.606987	−	1.05133i	0.991734	−	0.128310i	$-0.0409553\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	12.1695			0.977481
$156$		0			0
$157$	0.128610	−	0.222759i	0.0102642	−	0.0177781i	−0.860848	−	0.508863i	$-0.830066\pi$
$157$	0.128610	−	0.222759i	0.0102642	−	0.0177781i	0.871112	+	0.491085i	$0.163399\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.71585	+	1.24195i	−0.135228	+	0.0978795i
$162$		0			0
$163$	−6.28748	−	10.8902i	−0.492473	−	0.852989i	0.507489	−	0.861658i	$-0.330574\pi$
$163$	−6.28748	−	10.8902i	−0.492473	−	0.852989i	−0.999962	+	0.00866931i	$0.997240\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	21.6939			1.67873			0.839363	−	0.543572i	$-0.182928\pi$
$167$	21.6939			1.67873			0.839363	+	0.543572i	$0.182928\pi$
$168$		0			0
$169$	−4.91756			−0.378274
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.88024	+	11.9169i	0.523095	+	0.906026i	0.999639	+	0.0268759i	$0.00855590\pi$
$173$	6.88024	+	11.9169i	0.523095	+	0.906026i	−0.476544	+	0.879151i	$0.658111\pi$
$174$		0			0
$175$	0.722760	+	0.323345i	0.0546355	+	0.0244425i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.448262	−	0.776412i	0.0335046	−	0.0580317i	−0.848787	−	0.528735i	$-0.822666\pi$
$179$	0.448262	−	0.776412i	0.0335046	−	0.0580317i	0.882292	+	0.470703i	$0.156000\pi$
$180$		0			0
$181$	−17.4613			−1.29788			−0.648942	−	0.760838i	$-0.724788\pi$
$181$	−17.4613			−1.29788			−0.648942	+	0.760838i	$0.724788\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.89807	+	6.75165i	−0.286592	+	0.496391i
$186$		0			0
$187$	−0.514627	−	0.891361i	−0.0376333	−	0.0651827i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.734511	−	1.27221i	−0.0531474	−	0.0920540i	0.838228	−	0.545320i	$-0.183592\pi$
$191$	−0.734511	−	1.27221i	−0.0531474	−	0.0920540i	−0.891375	+	0.453266i	$0.850259\pi$
$192$		0			0
$193$	−3.25165	+	5.63202i	−0.234059	+	0.405402i	−0.958999	−	0.283410i	$-0.908534\pi$
$193$	−3.25165	+	5.63202i	−0.234059	+	0.405402i	0.724940	+	0.688812i	$0.241868\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	11.9521			0.851552			0.425776	−	0.904828i	$-0.360001\pi$
$197$	11.9521			0.851552			0.425776	+	0.904828i	$0.360001\pi$
$198$		0			0
$199$	9.73886	−	16.8682i	0.690369	−	1.19575i	−0.281348	−	0.959606i	$-0.590781\pi$
$199$	9.73886	−	16.8682i	0.690369	−	1.19575i	0.971717	−	0.236149i	$-0.0758852\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.08100	−	20.1461i	−0.146057	−	1.41398i
$204$		0			0
$205$	2.07112	+	3.58728i	0.144653	+	0.250546i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−13.3316			−0.922168
$210$		0			0
$211$	−12.8722			−0.886160			−0.443080	−	0.896482i	$-0.646114\pi$
$211$	−12.8722			−0.886160			−0.443080	+	0.896482i	$0.646114\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	11.1846	+	19.3722i	0.762780	+	1.32117i
$216$		0			0
$217$	12.7673	+	5.71176i	0.866700	+	0.387739i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.327828	+	0.567815i	−0.0220521	+	0.0381954i
$222$		0			0
$223$	9.84663			0.659379			0.329690	−	0.944089i	$-0.393056\pi$
$223$	9.84663			0.659379			0.329690	+	0.944089i	$0.393056\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	12.2254	−	21.1750i	0.811426	−	1.40543i	−0.100439	−	0.994943i	$-0.532025\pi$
$227$	12.2254	−	21.1750i	0.811426	−	1.40543i	0.911866	−	0.410489i	$-0.134642\pi$
$228$		0			0
$229$	11.0018	+	19.0557i	0.727022	+	1.25924i	0.958136	+	0.286312i	$0.0924293\pi$
$229$	11.0018	+	19.0557i	0.727022	+	1.25924i	−0.231115	+	0.972926i	$0.574237\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.8179	−	18.7372i	−0.708706	−	1.22752i	−0.965337	−	0.261006i	$-0.915946\pi$
$233$	−10.8179	−	18.7372i	−0.708706	−	1.22752i	0.256631	−	0.966510i	$-0.417388\pi$
$234$		0			0
$235$	6.64863	−	11.5158i	0.433709	−	0.751206i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−17.7272			−1.14668			−0.573338	−	0.819319i	$-0.694352\pi$
$239$	−17.7272			−1.14668			−0.573338	+	0.819319i	$0.694352\pi$
$240$		0			0
$241$	−2.15887	+	3.73927i	−0.139065	+	0.240868i	−0.927143	−	0.374708i	$-0.877743\pi$
$241$	−2.15887	+	3.73927i	−0.139065	+	0.240868i	0.788078	+	0.615575i	$0.211076\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	10.7395	+	12.0136i	0.686122	+	0.767522i
$246$		0			0
$247$	4.24626	+	7.35473i	0.270183	+	0.467971i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−10.2938			−0.649741			−0.324870	−	0.945759i	$-0.605321\pi$
$251$	−10.2938			−0.649741			−0.324870	+	0.945759i	$0.605321\pi$
$252$		0			0
$253$	−3.57295			−0.224629
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.89568	+	10.2116i	0.367763	+	0.636983i	0.989215	−	0.146468i	$-0.0467906\pi$
$257$	5.89568	+	10.2116i	0.367763	+	0.636983i	−0.621453	+	0.783452i	$0.713457\pi$
$258$		0			0
$259$	−7.25841	+	5.25373i	−0.451016	+	0.326451i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.59359	−	4.49223i	0.159928	−	0.277003i	−0.774915	−	0.632066i	$-0.782207\pi$
$263$	2.59359	−	4.49223i	0.159928	−	0.277003i	0.934842	+	0.355063i	$0.115541\pi$
$264$		0			0
$265$	−19.8850			−1.22153
$266$		0			0
$267$		0			0
$268$		0			0
$269$	14.6103	−	25.3058i	0.890805	−	1.54292i	0.0518936	−	0.998653i	$-0.483474\pi$
$269$	14.6103	−	25.3058i	0.890805	−	1.54292i	0.838912	−	0.544268i	$-0.183192\pi$
$270$		0			0
$271$	10.2801	+	17.8056i	0.624470	+	1.08161i	0.988643	+	0.150283i	$0.0480184\pi$
$271$	10.2801	+	17.8056i	0.624470	+	1.08161i	−0.364173	+	0.931331i	$0.618648\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.667805	+	1.15667i	0.0402702	+	0.0697500i
$276$		0			0
$277$	5.97833	−	10.3548i	0.359203	−	0.622158i	−0.628625	−	0.777709i	$-0.716382\pi$
$277$	5.97833	−	10.3548i	0.359203	−	0.622158i	0.987828	+	0.155550i	$0.0497151\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−29.8332			−1.77970			−0.889850	−	0.456254i	$-0.849191\pi$
$281$	−29.8332			−1.77970			−0.889850	+	0.456254i	$0.849191\pi$
$282$		0			0
$283$	4.78547	−	8.28868i	0.284467	−	0.492711i	−0.688013	−	0.725698i	$-0.741517\pi$
$283$	4.78547	−	8.28868i	0.284467	−	0.492711i	0.972480	+	0.232988i	$0.0748502\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.489161	+	4.73555i	0.0288742	+	0.279531i
$288$		0			0
$289$	8.47341	+	14.6764i	0.498436	+	0.863316i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	14.8203			0.865810			0.432905	−	0.901440i	$-0.357489\pi$
$293$	14.8203			0.865810			0.432905	+	0.901440i	$0.357489\pi$
$294$		0			0
$295$	19.2353			1.11992
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.13802	+	1.97111i	0.0658134	+	0.113992i
$300$		0			0
$301$	2.64159	+	25.5732i	0.152259	+	1.47401i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	15.1628	−	26.2627i	0.868219	−	1.50380i
$306$		0			0
$307$	−5.88207			−0.335708			−0.167854	−	0.985812i	$-0.553684\pi$
$307$	−5.88207			−0.335708			−0.167854	+	0.985812i	$0.553684\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.11753	−	14.0600i	0.460303	−	0.797268i	−0.538673	−	0.842515i	$-0.681074\pi$
$311$	8.11753	−	14.0600i	0.460303	−	0.797268i	0.998976	+	0.0452468i	$0.0144074\pi$
$312$		0			0
$313$	−8.84480	−	15.3196i	−0.499937	−	0.865917i	0.500063	−	0.865989i	$-0.333310\pi$
$313$	−8.84480	−	15.3196i	−0.499937	−	0.865917i	−1.00000		7.22344e-5i	$0.999977\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.64009	−	4.57276i	−0.148282	−	0.256832i	0.782311	−	0.622889i	$-0.214041\pi$
$317$	−2.64009	−	4.57276i	−0.148282	−	0.256832i	−0.930593	+	0.366057i	$0.880708\pi$
$318$		0			0
$319$	17.0818	−	29.5866i	0.956398	−	1.65653i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.688922			−0.0383326
$324$		0			0
$325$	0.425406	−	0.736824i	0.0235973	−	0.0408716i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	12.3801	−	8.96087i	0.682537	−	0.494029i
$330$		0			0
$331$	7.80358	+	13.5162i	0.428923	+	0.742917i	0.996778	−	0.0802120i	$-0.0255597\pi$
$331$	7.80358	+	13.5162i	0.428923	+	0.742917i	−0.567855	+	0.823129i	$0.692226\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−17.3362			−0.947180
$336$		0			0
$337$	7.54369			0.410931			0.205466	−	0.978664i	$-0.434129\pi$
$337$	7.54369			0.410931			0.205466	+	0.978664i	$0.434129\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	11.7965	+	20.4322i	0.638818	+	1.10646i
$342$		0			0
$343$	5.62843	+	17.6443i	0.303907	+	0.952702i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.4502	+	23.2963i	−0.722042	+	1.25061i	0.238138	+	0.971231i	$0.423463\pi$
$347$	−13.4502	+	23.2963i	−0.722042	+	1.25061i	−0.960180	+	0.279382i	$0.909870\pi$
$348$		0			0
$349$	−14.0020			−0.749510			−0.374755	−	0.927124i	$-0.622273\pi$
$349$	−14.0020			−0.749510			−0.374755	+	0.927124i	$0.622273\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−15.1655	+	26.2675i	−0.807180	+	1.39808i	0.107630	+	0.994191i	$0.465674\pi$
$353$	−15.1655	+	26.2675i	−0.807180	+	1.39808i	−0.914810	+	0.403885i	$0.867659\pi$
$354$		0			0
$355$	9.89489	+	17.1384i	0.525166	+	0.909614i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.99876	−	12.1222i	−0.369381	−	0.639786i	0.620088	−	0.784532i	$-0.287097\pi$
$359$	−6.99876	−	12.1222i	−0.369381	−	0.639786i	−0.989469	+	0.144746i	$0.953763\pi$
$360$		0			0
$361$	5.03830	−	8.72659i	0.265174	−	0.459294i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	10.5564			0.552550
$366$		0			0
$367$	1.25165	−	2.16792i	0.0653356	−	0.113165i	−0.831507	−	0.555514i	$-0.812522\pi$
$367$	1.25165	−	2.16792i	0.0653356	−	0.113165i	0.896843	+	0.442349i	$0.145855\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−20.8617	−	9.33301i	−1.08309	−	0.484546i
$372$		0			0
$373$	−8.80311	−	15.2474i	−0.455808	−	0.789482i	0.542926	−	0.839780i	$-0.317316\pi$
$373$	−8.80311	−	15.2474i	−0.455808	−	0.789482i	−0.998734	+	0.0502980i	$0.983983\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−21.7629			−1.12085
$378$		0			0
$379$	10.5474			0.541781			0.270891	−	0.962610i	$-0.412682\pi$
$379$	10.5474			0.541781			0.270891	+	0.962610i	$0.412682\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−10.8418	−	18.7786i	−0.553992	−	0.959542i	−0.997981	−	0.0635100i	$-0.979771\pi$
$383$	−10.8418	−	18.7786i	−0.553992	−	0.959542i	0.443989	−	0.896032i	$-0.353563\pi$
$384$		0			0
$385$	2.79287	+	27.0377i	0.142338	+	1.37797i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.96652	+	12.0664i	−0.353217	+	0.611790i	−0.986811	−	0.161876i	$-0.948246\pi$
$389$	−6.96652	+	12.0664i	−0.353217	+	0.611790i	0.633594	+	0.773665i	$0.281579\pi$
$390$		0			0
$391$	−0.184635			−0.00933738
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−11.1338	+	19.2844i	−0.560204	+	0.970303i
$396$		0			0
$397$	13.9542	+	24.1694i	0.700342	+	1.21303i	0.968346	+	0.249610i	$0.0803025\pi$
$397$	13.9542	+	24.1694i	0.700342	+	1.21303i	−0.268004	+	0.963418i	$0.586364\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	17.4525	+	30.2285i	0.871534	+	1.50954i	0.860410	+	0.509603i	$0.170208\pi$
$401$	17.4525	+	30.2285i	0.871534	+	1.50954i	0.0111242	+	0.999938i	$0.496459\pi$
$402$		0			0
$403$	7.51463	−	13.0157i	0.374330	−	0.648359i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−15.1143			−0.749190
$408$		0			0
$409$	10.3369	−	17.9041i	0.511128	−	0.885300i	−0.488789	−	0.872402i	$-0.662561\pi$
$409$	10.3369	−	17.9041i	0.511128	−	0.885300i	0.999917	−	0.0128979i	$-0.00410563\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	20.1801	+	9.02806i	0.992998	+	0.444242i
$414$		0			0
$415$	−19.4870	−	33.7525i	−0.956581	−	1.65685i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	39.9719			1.95275			0.976376	−	0.216076i	$-0.0693260\pi$
$419$	39.9719			1.95275			0.976376	+	0.216076i	$0.0693260\pi$
$420$		0			0
$421$	25.0165			1.21923			0.609614	−	0.792699i	$-0.291325\pi$
$421$	25.0165			1.21923			0.609614	+	0.792699i	$0.291325\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.0345093	+	0.0597719i	0.00167395	+	0.00289936i
$426$		0			0
$427$	28.2339	−	20.4361i	1.36634	−	0.988970i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−7.05181	+	12.2141i	−0.339674	+	0.588332i	−0.984371	−	0.176106i	$-0.943650\pi$
$431$	−7.05181	+	12.2141i	−0.339674	+	0.588332i	0.644698	+	0.764438i	$0.276983\pi$
$432$		0			0
$433$	1.58941			0.0763821			0.0381911	−	0.999270i	$-0.487840\pi$
$433$	1.58941			0.0763821			0.0381911	+	0.999270i	$0.487840\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.19576	+	2.07112i	−0.0572009	+	0.0990749i
$438$		0			0
$439$	12.1884	+	21.1109i	0.581721	+	1.00757i	0.995276	+	0.0970905i	$0.0309536\pi$
$439$	12.1884	+	21.1109i	0.581721	+	1.00757i	−0.413555	+	0.910479i	$0.635713\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.28200	−	16.0769i	−0.441001	−	0.763836i	0.556763	−	0.830671i	$-0.312043\pi$
$443$	−9.28200	−	16.0769i	−0.441001	−	0.763836i	−0.997764	+	0.0668352i	$0.978710\pi$
$444$		0			0
$445$	−2.17414	+	3.76572i	−0.103064	+	0.178512i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	21.4616			1.01284			0.506418	−	0.862288i	$-0.330969\pi$
$449$	21.4616			1.01284			0.506418	+	0.862288i	$0.330969\pi$
$450$		0			0
$451$	−4.01527	+	6.95465i	−0.189072	+	0.327482i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	14.0265	−	10.1526i	0.657573	−	0.475959i
$456$		0			0
$457$	−7.56371	−	13.1007i	−0.353816	−	0.612827i	0.633099	−	0.774071i	$-0.281783\pi$
$457$	−7.56371	−	13.1007i	−0.353816	−	0.612827i	−0.986915	+	0.161244i	$0.948449\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−33.0769			−1.54055			−0.770273	−	0.637714i	$-0.779880\pi$
$461$	−33.0769			−1.54055			−0.770273	+	0.637714i	$0.779880\pi$
$462$		0			0
$463$	26.8446			1.24758			0.623788	−	0.781594i	$-0.285593\pi$
$463$	26.8446			1.24758			0.623788	+	0.781594i	$0.285593\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.93579	+	10.2811i	0.274675	+	0.475752i	0.970053	−	0.242893i	$-0.0780963\pi$
$467$	5.93579	+	10.2811i	0.274675	+	0.475752i	−0.695378	+	0.718644i	$0.744763\pi$
$468$		0			0
$469$	−18.1878	−	8.13674i	−0.839833	−	0.375720i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−21.6835	+	37.5569i	−0.997007	+	1.72687i
$474$		0			0
$475$	0.893978			0.0410185
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8.71973	−	15.1030i	0.398415	−	0.690075i	−0.595116	−	0.803640i	$-0.702894\pi$
$479$	8.71973	−	15.1030i	0.398415	−	0.690075i	0.993531	+	0.113565i	$0.0362271\pi$
$480$		0			0
$481$	4.81407	+	8.33822i	0.219503	+	0.380190i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	17.7438	+	30.7332i	0.805706	+	1.39552i
$486$		0			0
$487$	18.3889	−	31.8504i	0.833279	−	1.44328i	−0.0621458	−	0.998067i	$-0.519794\pi$
$487$	18.3889	−	31.8504i	0.833279	−	1.44328i	0.895424	−	0.445214i	$-0.146872\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.08099			0.409819			0.204910	−	0.978781i	$-0.434310\pi$
$491$	9.08099			0.409819			0.204910	+	0.978781i	$0.434310\pi$
$492$		0			0
$493$	0.882716	−	1.52891i	0.0397555	−	0.0688586i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.33700	+	22.6244i	0.104829	+	1.01484i
$498$		0			0
$499$	−3.41261	−	5.91082i	−0.152769	−	0.264604i	0.779475	−	0.626433i	$-0.215486\pi$
$499$	−3.41261	−	5.91082i	−0.152769	−	0.264604i	−0.932245	+	0.361829i	$0.882153\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−4.09211			−0.182458			−0.0912291	−	0.995830i	$-0.529080\pi$
$503$	−4.09211			−0.182458			−0.0912291	+	0.995830i	$0.529080\pi$
$504$		0			0
$505$	6.47989			0.288351
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−14.3991	−	24.9400i	−0.638228	−	1.10544i	−0.985821	−	0.167798i	$-0.946334\pi$
$509$	−14.3991	−	24.9400i	−0.638228	−	1.10544i	0.347593	−	0.937646i	$-0.386999\pi$
$510$		0			0
$511$	11.0750	+	4.95466i	0.489927	+	0.219181i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−5.88929	+	10.2006i	−0.259513	+	0.449490i
$516$		0			0
$517$	25.7794			1.13378
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5.92170	−	10.2567i	0.259434	−	0.449353i	−0.706656	−	0.707557i	$-0.749797\pi$
$521$	5.92170	−	10.2567i	0.259434	−	0.449353i	0.966090	+	0.258204i	$0.0831306\pi$
$522$		0			0
$523$	6.86664	+	11.8934i	0.300257	+	0.520061i	0.976194	−	0.216899i	$-0.0695942\pi$
$523$	6.86664	+	11.8934i	0.300257	+	0.520061i	−0.675937	+	0.736959i	$0.736261\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.609594	+	1.05585i	0.0265543	+	0.0459935i
$528$		0			0
$529$	11.1795	−	19.3635i	0.486067	−	0.841892i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.11561			0.221582
$534$		0			0
$535$	2.98081	−	5.16291i	0.128872	−	0.223212i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−9.76008	+	29.6766i	−0.420396	+	1.27826i
$540$		0			0
$541$	21.7425	+	37.6592i	0.934784	+	1.61909i	0.775019	+	0.631938i	$0.217740\pi$
$541$	21.7425	+	37.6592i	0.934784	+	1.61909i	0.159765	+	0.987155i	$0.448926\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	40.3648			1.72904
$546$		0			0
$547$	22.0614			0.943279			0.471640	−	0.881791i	$-0.343662\pi$
$547$	22.0614			0.943279			0.471640	+	0.881791i	$0.343662\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−11.4336	−	19.8035i	−0.487086	−	0.843657i
$552$		0			0
$553$	−20.7318	+	15.0059i	−0.881607	+	0.638117i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	16.0925	−	27.8730i	0.681862	−	1.18102i	−0.292551	−	0.956250i	$-0.594504\pi$
$557$	16.0925	−	27.8730i	0.681862	−	1.18102i	0.974412	−	0.224769i	$-0.0721627\pi$
$558$		0			0
$559$	27.6256			1.16844
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.69369	−	2.93355i	0.0713804	−	0.123635i	−0.828126	−	0.560542i	$-0.810593\pi$
$563$	1.69369	−	2.93355i	0.0713804	−	0.123635i	0.899507	+	0.436907i	$0.143926\pi$
$564$		0			0
$565$	18.9159	+	32.7633i	0.795798	+	1.37836i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−20.1737	−	34.9419i	−0.845726	−	1.46484i	−0.884989	−	0.465611i	$-0.845835\pi$
$569$	−20.1737	−	34.9419i	−0.845726	−	1.46484i	0.0392637	−	0.999229i	$-0.487499\pi$
$570$		0			0
$571$	5.21928	−	9.04006i	0.218420	−	0.378315i	−0.735905	−	0.677085i	$-0.763243\pi$
$571$	5.21928	−	9.04006i	0.218420	−	0.378315i	0.954325	+	0.298770i	$0.0965763\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.239591			0.00999164
$576$		0			0
$577$	5.55156	−	9.61559i	0.231114	−	0.400302i	−0.727022	−	0.686614i	$-0.759096\pi$
$577$	5.55156	−	9.61559i	0.231114	−	0.400302i	0.958136	+	0.286312i	$0.0924295\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.60249	−	44.5566i	−0.190943	−	1.84852i
$582$		0			0
$583$	−19.2755	−	33.3862i	−0.798310	−	1.38271i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−40.7750			−1.68296			−0.841482	−	0.540285i	$-0.818316\pi$
$587$	−40.7750			−1.68296			−0.841482	+	0.540285i	$0.818316\pi$
$588$		0			0
$589$	15.7918			0.650689
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−14.7930	−	25.6221i	−0.607474	−	1.05218i	−0.991655	−	0.128918i	$-0.958850\pi$
$593$	−14.7930	−	25.6221i	−0.607474	−	1.05218i	0.384182	−	0.923258i	$-0.374484\pi$
$594$		0			0
$595$	0.144324	+	1.39720i	0.00591669	+	0.0572794i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−9.17760	+	15.8961i	−0.374987	+	0.649496i	−0.990325	−	0.138767i	$-0.955686\pi$
$599$	−9.17760	+	15.8961i	−0.374987	+	0.649496i	0.615338	+	0.788263i	$0.289019\pi$
$600$		0			0
$601$	−31.8499			−1.29919			−0.649593	−	0.760282i	$-0.725061\pi$
$601$	−31.8499			−1.29919			−0.649593	+	0.760282i	$0.725061\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−10.2642	+	17.7781i	−0.417298	+	0.722781i
$606$		0			0
$607$	−11.8452	−	20.5164i	−0.480780	−	0.832736i	0.518977	−	0.854788i	$-0.326313\pi$
$607$	−11.8452	−	20.5164i	−0.480780	−	0.832736i	−0.999757	+	0.0220527i	$0.992980\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8.21099	−	14.2219i	−0.332181	−	0.575354i
$612$		0			0
$613$	13.3159	−	23.0638i	0.537824	−	0.931539i	−0.461197	−	0.887298i	$-0.652580\pi$
$613$	13.3159	−	23.0638i	0.537824	−	0.931539i	0.999021	−	0.0442411i	$-0.0140870\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.44965			0.380429			0.190214	−	0.981743i	$-0.439082\pi$
$617$	9.44965			0.380429			0.190214	+	0.981743i	$0.439082\pi$
$618$		0			0
$619$	18.0474	−	31.2589i	0.725385	−	1.25640i	−0.233431	−	0.972373i	$-0.574995\pi$
$619$	18.0474	−	31.2589i	0.725385	−	1.25640i	0.958815	−	0.284030i	$-0.0916714\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.04836	+	2.93025i	−0.162194	+	0.117398i
$624$		0			0
$625$	13.2034	+	22.8689i	0.528136	+	0.914758i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−0.781045			−0.0311423
$630$		0			0
$631$	0.0100579			0.000400401			0.000200200	−	1.00000i	$-0.499936\pi$
$631$	0.0100579			0.000400401			0.000200200		1.00000i	$0.499936\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−9.35935	−	16.2109i	−0.371415	−	0.643309i
$636$		0			0
$637$	19.4805	−	4.06790i	0.771847	−	0.161176i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−2.45227	+	4.24745i	−0.0968587	+	0.167764i	−0.910383	−	0.413767i	$-0.864213\pi$
$641$	−2.45227	+	4.24745i	−0.0968587	+	0.167764i	0.813524	+	0.581531i	$0.197546\pi$
$642$		0			0
$643$	−44.1311			−1.74036			−0.870180	−	0.492734i	$-0.835998\pi$
$643$	−44.1311			−1.74036			−0.870180	+	0.492734i	$0.835998\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	24.8813	−	43.0957i	0.978186	−	1.69427i	0.309192	−	0.950999i	$-0.399941\pi$
$647$	24.8813	−	43.0957i	0.978186	−	1.69427i	0.668993	−	0.743268i	$-0.266725\pi$
$648$		0			0
$649$	18.6457	+	32.2953i	0.731908	+	1.26770i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	6.98578	+	12.0997i	0.273375	+	0.473499i	0.969724	−	0.244205i	$-0.0785268\pi$
$653$	6.98578	+	12.0997i	0.273375	+	0.473499i	−0.696349	+	0.717703i	$0.745193\pi$
$654$		0			0
$655$	−14.4012	+	24.9436i	−0.562702	+	0.974628i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	25.9654			1.01147			0.505733	−	0.862690i	$-0.331222\pi$
$659$	25.9654			1.01147			0.505733	+	0.862690i	$0.331222\pi$
$660$		0			0
$661$	−12.7681	+	22.1150i	−0.496622	+	0.860174i	−0.999992	−	0.00389626i	$-0.998760\pi$
$661$	−12.7681	+	22.1150i	−0.496622	+	0.860174i	0.503370	+	0.864071i	$0.332093\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	16.6075	+	7.42979i	0.644013	+	0.288115i
$666$		0			0
$667$	−3.06425	−	5.30744i	−0.118648	−	0.205505i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	58.7921			2.26964
$672$		0			0
$673$	−5.42943			−0.209289			−0.104645	−	0.994510i	$-0.533371\pi$
$673$	−5.42943			−0.209289			−0.104645	+	0.994510i	$0.533371\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.07571	−	12.2555i	−0.271942	−	0.471017i	0.697417	−	0.716665i	$-0.254332\pi$
$677$	−7.07571	−	12.2555i	−0.271942	−	0.471017i	−0.969359	+	0.245648i	$0.920999\pi$
$678$		0			0
$679$	4.19077	+	40.5708i	0.160827	+	1.55696i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.553330	−	0.958397i	0.0211726	−	0.0366720i	−0.855245	−	0.518224i	$-0.826593\pi$
$683$	0.553330	−	0.958397i	0.0211726	−	0.0366720i	0.876418	+	0.481552i	$0.159927\pi$
$684$		0			0
$685$	−37.2773			−1.42429
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−12.2789	+	21.2677i	−0.467789	+	0.810234i
$690$		0			0
$691$	−11.4539	−	19.8387i	−0.435725	−	0.754698i	0.561629	−	0.827389i	$-0.310175\pi$
$691$	−11.4539	−	19.8387i	−0.435725	−	0.754698i	−0.997355	+	0.0726910i	$0.976841\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.07207	+	12.2492i	0.268259	+	0.464638i
$696$		0			0
$697$	−0.207492	+	0.359387i	−0.00785932	+	0.0136127i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	11.4056			0.430782			0.215391	−	0.976528i	$-0.430897\pi$
$701$	11.4056			0.430782			0.215391	+	0.976528i	$0.430897\pi$
$702$		0			0
$703$	−5.05832	+	8.76127i	−0.190778	+	0.330438i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.79816	+	3.04133i	0.255671	+	0.114381i
$708$		0			0
$709$	18.5336	+	32.1011i	0.696042	+	1.20558i	0.969828	+	0.243790i	$0.0783908\pi$
$709$	18.5336	+	32.1011i	0.696042	+	1.20558i	−0.273786	+	0.961791i	$0.588276\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.23229			0.158500
$714$		0			0
$715$	29.2077			1.09231
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.459342	+	0.795604i	0.0171306	+	0.0296710i	0.874464	−	0.485091i	$-0.161214\pi$
$719$	0.459342	+	0.795604i	0.0171306	+	0.0296710i	−0.857333	+	0.514762i	$0.827880\pi$
$720$		0			0
$721$	−10.9662	+	7.93745i	−0.408402	+	0.295606i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.14545	+	1.98399i	−0.0425411	+	0.0736834i
$726$		0			0
$727$	−14.6887			−0.544772			−0.272386	−	0.962188i	$-0.587813\pi$
$727$	−14.6887			−0.544772			−0.272386	+	0.962188i	$0.587813\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.12051	+	1.94078i	−0.0414435	+	0.0717823i
$732$		0			0
$733$	11.4312	+	19.7994i	0.422220	+	0.731307i	0.996156	−	0.0875931i	$-0.0279175\pi$
$733$	11.4312	+	19.7994i	0.422220	+	0.731307i	−0.573936	+	0.818900i	$0.694584\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.8049	−	29.1069i	−0.619015	−	1.07217i
$738$		0			0
$739$	19.6692	−	34.0681i	0.723544	−	1.25321i	−0.236027	−	0.971746i	$-0.575845\pi$
$739$	19.6692	−	34.0681i	0.723544	−	1.25321i	0.959571	−	0.281468i	$-0.0908212\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	21.7327			0.797294			0.398647	−	0.917104i	$-0.369480\pi$
$743$	21.7327			0.797294			0.398647	+	0.917104i	$0.369480\pi$
$744$		0			0
$745$	8.88410	−	15.3877i	0.325488	−	0.563762i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	5.55043	−	4.01746i	0.202808	−	0.146795i
$750$		0			0
$751$	−10.3071	−	17.8525i	−0.376113	−	0.651446i	0.614380	−	0.789010i	$-0.289406\pi$
$751$	−10.3071	−	17.8525i	−0.376113	−	0.651446i	−0.990493	+	0.137564i	$0.956073\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−34.3404			−1.24978
$756$		0			0
$757$	17.8453			0.648600			0.324300	−	0.945954i	$-0.394871\pi$
$757$	17.8453			0.648600			0.324300	+	0.945954i	$0.394871\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−16.9714	−	29.3953i	−0.615211	−	1.06558i	−0.990347	−	0.138607i	$-0.955737\pi$
$761$	−16.9714	−	29.3953i	−0.615211	−	1.06558i	0.375136	−	0.926970i	$-0.377596\pi$
$762$		0			0
$763$	42.3475	+	18.9452i	1.53308	+	0.685861i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	11.8777	−	20.5728i	0.428879	−	0.742840i
$768$		0			0
$769$	−40.6903			−1.46733			−0.733665	−	0.679511i	$-0.762192\pi$
$769$	−40.6903			−1.46733			−0.733665	+	0.679511i	$0.762192\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−2.17562	+	3.76829i	−0.0782517	+	0.135536i	−0.902496	−	0.430699i	$-0.858267\pi$
$773$	−2.17562	+	3.76829i	−0.0782517	+	0.135536i	0.824244	+	0.566235i	$0.191600\pi$
$774$		0			0
$775$	−0.791039	−	1.37012i	−0.0284150	−	0.0492162i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.68758	+	4.65503i	0.0962926	+	0.166784i
$780$		0			0
$781$	−19.1832	+	33.2263i	−0.686429	+	1.18893i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.592124			−0.0211338
$786$		0			0
$787$	−18.8110	+	32.5816i	−0.670539	+	1.16141i	0.307213	+	0.951641i	$0.400604\pi$
$787$	−18.8110	+	32.5816i	−0.670539	+	1.16141i	−0.977751	+	0.209767i	$0.932730\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	4.46760	+	43.2508i	0.158850	+	1.53782i
$792$		0			0
$793$	−18.7259	−	32.4342i	−0.664976	−	1.15177i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−44.3141			−1.56968			−0.784842	−	0.619696i	$-0.787256\pi$
$797$	−44.3141			−1.56968			−0.784842	+	0.619696i	$0.787256\pi$
$798$		0			0
$799$	1.33217			0.0471287
$800$		0			0
$801$		0			0
$802$		0			0
$803$	10.2329	+	17.7239i	0.361110	+	0.625462i
$804$		0			0
$805$	4.45091	+	1.99123i	0.156874	+	0.0701815i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	9.78609	−	16.9500i	0.344061	−	0.595931i	−0.641122	−	0.767439i	$-0.721531\pi$
$809$	9.78609	−	16.9500i	0.344061	−	0.595931i	0.985183	+	0.171508i	$0.0548641\pi$
$810$		0			0
$811$	−4.15430			−0.145877			−0.0729386	−	0.997336i	$-0.523238\pi$
$811$	−4.15430			−0.145877			−0.0729386	+	0.997336i	$0.523238\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−14.4739	+	25.0695i	−0.506997	+	0.878145i
$816$		0			0
$817$	14.5136	+	25.1383i	0.507767	+	0.879479i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	14.3771	+	24.9019i	0.501764	+	0.869081i	0.999998	+	0.00203808i	$0.000648743\pi$
$821$	14.3771	+	24.9019i	0.501764	+	0.869081i	−0.498234	+	0.867043i	$0.666018\pi$
$822$		0			0
$823$	10.5441	−	18.2628i	0.367543	−	0.636603i	−0.621638	−	0.783305i	$-0.713532\pi$
$823$	10.5441	−	18.2628i	0.367543	−	0.636603i	0.989181	+	0.146702i	$0.0468658\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	56.8422			1.97660			0.988299	−	0.152530i	$-0.0487420\pi$
$827$	56.8422			1.97660			0.988299	+	0.152530i	$0.0487420\pi$
$828$		0			0
$829$	−8.97588	+	15.5467i	−0.311745	+	0.539959i	−0.978740	−	0.205104i	$-0.934247\pi$
$829$	−8.97588	+	15.5467i	−0.311745	+	0.539959i	0.666995	+	0.745062i	$0.267580\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.504359	+	1.53356i	−0.0174750	+	0.0531347i
$834$		0			0
$835$	−24.9698	−	43.2490i	−0.864117	−	1.49669i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−8.76938			−0.302753			−0.151376	−	0.988476i	$-0.548371\pi$
$839$	−8.76938			−0.302753			−0.151376	+	0.988476i	$0.548371\pi$
$840$		0			0
$841$	29.5993			1.02066
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.66014	+	9.80366i	0.194715	+	0.337256i
$846$		0			0
$847$	−19.1124	+	13.8338i	−0.656711	+	0.475336i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.35566	+	2.34807i	−0.0464714	+	0.0804908i
$852$		0			0
$853$	−32.1038			−1.09921			−0.549607	−	0.835423i	$-0.685223\pi$
$853$	−32.1038			−1.09921			−0.549607	+	0.835423i	$0.685223\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.25126	+	10.8275i	−0.213539	+	0.369861i	−0.952820	−	0.303537i	$-0.901832\pi$
$857$	−6.25126	+	10.8275i	−0.213539	+	0.369861i	0.739281	+	0.673398i	$0.235166\pi$
$858$		0			0
$859$	−3.78438	−	6.55474i	−0.129121	−	0.223645i	0.794215	−	0.607637i	$-0.207882\pi$
$859$	−3.78438	−	6.55474i	−0.129121	−	0.223645i	−0.923336	+	0.383992i	$0.874549\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.268987	−	0.465899i	−0.00915642	−	0.0158594i	0.861411	−	0.507909i	$-0.169581\pi$
$863$	−0.268987	−	0.465899i	−0.00915642	−	0.0158594i	−0.870567	+	0.492049i	$0.836248\pi$
$864$		0			0
$865$	15.8384	−	27.4329i	0.538522	−	0.932747i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−43.1703			−1.46445
$870$		0			0
$871$	−10.7050	+	18.5417i	−0.362726	+	0.628260i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.94170	+	28.4785i	0.0994476	+	0.962750i
$876$		0			0
$877$	−13.3537	−	23.1292i	−0.450921	−	0.781019i	0.547522	−	0.836791i	$-0.315571\pi$
$877$	−13.3537	−	23.1292i	−0.450921	−	0.781019i	−0.998443	+	0.0557726i	$0.982238\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−33.6239			−1.13282			−0.566408	−	0.824125i	$-0.691667\pi$
$881$	−33.6239			−1.13282			−0.566408	+	0.824125i	$0.691667\pi$
$882$		0			0
$883$	7.20109			0.242336			0.121168	−	0.992632i	$-0.461336\pi$
$883$	7.20109			0.242336			0.121168	+	0.992632i	$0.461336\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.39373	−	4.14606i	−0.0803736	−	0.139211i	0.823037	−	0.567988i	$-0.192278\pi$
$887$	−2.39373	−	4.14606i	−0.0803736	−	0.139211i	−0.903410	+	0.428777i	$0.858945\pi$
$888$		0			0
$889$	−2.21051	−	21.3999i	−0.0741382	−	0.717730i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.62759	−	14.9434i	0.288711	−	0.500062i
$894$		0			0
$895$	−2.06381			−0.0689855
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−20.2340	+	35.0464i	−0.674842	+	1.16886i
$900$		0			0
$901$	−0.996076	−	1.72525i	−0.0331841	−	0.0574766i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	20.0980	+	34.8108i	0.668081	+	1.15715i
$906$		0			0
$907$	17.4176	−	30.1681i	0.578341	−	1.00172i	−0.417329	−	0.908755i	$-0.637034\pi$
$907$	17.4176	−	30.1681i	0.578341	−	1.00172i	0.995670	−	0.0929599i	$-0.0296328\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	58.3167			1.93212			0.966060	−	0.258319i	$-0.0831685\pi$
$911$	58.3167			1.93212			0.966060	+	0.258319i	$0.0831685\pi$
$912$		0			0
$913$	37.7795	−	65.4359i	1.25032	−	2.16561i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−26.8158	+	19.4096i	−0.885536	+	0.640962i
$918$		0			0
$919$	−0.113983	−	0.197424i	−0.00375995	−	0.00651242i	0.864139	−	0.503253i	$-0.167863\pi$
$919$	−0.113983	−	0.197424i	−0.00375995	−	0.00651242i	−0.867899	+	0.496740i	$0.834530\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	24.4402			0.804458
$924$		0			0
$925$	1.01352			0.0333244
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−12.4425	−	21.5511i	−0.408226	−	0.707069i	0.586465	−	0.809975i	$-0.300519\pi$
$929$	−12.4425	−	21.5511i	−0.408226	−	0.707069i	−0.994691	+	0.102906i	$0.967186\pi$
$930$		0			0
$931$	13.9361	+	15.5895i	0.456738	+	0.510924i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.18468	+	2.05192i	−0.0387432	+	0.0671051i
$936$		0			0
$937$	−44.3194			−1.44785			−0.723926	−	0.689878i	$-0.757664\pi$
$937$	−44.3194			−1.44785			−0.723926	+	0.689878i	$0.757664\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	30.1410	−	52.2057i	0.982568	−	1.70186i	0.330286	−	0.943881i	$-0.392855\pi$
$941$	30.1410	−	52.2057i	0.982568	−	1.70186i	0.652282	−	0.757977i	$-0.273812\pi$
$942$		0			0
$943$	0.720286	+	1.24757i	0.0234558	+	0.0406266i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.29884	−	12.6420i	−0.237180	−	0.410808i	0.722724	−	0.691137i	$-0.242890\pi$
$947$	−7.29884	−	12.6420i	−0.237180	−	0.410808i	−0.959904	+	0.280329i	$0.909557\pi$
$948$		0			0
$949$	6.51855	−	11.2905i	0.211601	−	0.366504i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−11.9601			−0.387427			−0.193713	−	0.981058i	$-0.562053\pi$
$953$	−11.9601			−0.387427			−0.193713	+	0.981058i	$0.562053\pi$
$954$		0			0
$955$	−1.69086	+	2.92865i	−0.0547148	+	0.0947688i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−39.1083	−	17.4961i	−1.26287	−	0.564978i
$960$		0			0
$961$	1.52659	+	2.64414i	0.0492450	+	0.0852948i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	14.9707			0.481924
$966$		0			0
$967$	−45.6499			−1.46800			−0.734001	−	0.679148i	$-0.762349\pi$
$967$	−45.6499			−1.46800			−0.734001	+	0.679148i	$0.762349\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.25397	−	2.17194i	−0.0402418	−	0.0697009i	0.845203	−	0.534445i	$-0.179479\pi$
$971$	−1.25397	−	2.17194i	−0.0402418	−	0.0697009i	−0.885445	+	0.464745i	$0.846146\pi$
$972$		0			0
$973$	1.67030	+	16.1701i	0.0535472	+	0.518390i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−28.8101	+	49.9005i	−0.921715	+	1.59646i	−0.124955	+	0.992162i	$0.539879\pi$
$977$	−28.8101	+	49.9005i	−0.921715	+	1.59646i	−0.796760	+	0.604296i	$0.793455\pi$
$978$		0			0
$979$	−8.42999			−0.269424
$980$		0			0
$981$		0			0
$982$		0			0
$983$	29.6868	−	51.4190i	0.946862	−	1.64001i	0.194881	−	0.980827i	$-0.437568\pi$
$983$	29.6868	−	51.4190i	0.946862	−	1.64001i	0.751980	−	0.659186i	$-0.229099\pi$
$984$		0			0
$985$	−13.7570	−	23.8278i	−0.438333	−	0.759215i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.88973	+	6.73721i	0.123686	+	0.214231i
$990$		0			0
$991$	−20.2341	+	35.0465i	−0.642758	+	1.11329i	0.342057	+	0.939679i	$0.388877\pi$
$991$	−20.2341	+	35.0465i	−0.642758	+	1.11329i	−0.984814	+	0.173610i	$0.944457\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−44.8380			−1.42146
$996$		0			0
$997$	7.07112	−	12.2475i	0.223945	−	0.387883i	−0.732058	−	0.681243i	$-0.761440\pi$
$997$	7.07112	−	12.2475i	0.223945	−	0.387883i	0.956002	+	0.293359i	$0.0947732\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.k.g.1621.2	yes	16
3.2	odd	2	inner	2268.2.k.g.1621.7	yes	16
7.2	even	3	inner	2268.2.k.g.1297.2	✓	16
9.2	odd	6		2268.2.l.n.109.2		16
9.4	even	3		2268.2.i.n.865.2		16
9.5	odd	6		2268.2.i.n.865.7		16
9.7	even	3		2268.2.l.n.109.7		16
21.2	odd	6	inner	2268.2.k.g.1297.7	yes	16
63.2	odd	6		2268.2.i.n.2053.7		16
63.16	even	3		2268.2.i.n.2053.2		16
63.23	odd	6		2268.2.l.n.541.2		16
63.58	even	3		2268.2.l.n.541.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.i.n.865.2		16	9.4	even	3
2268.2.i.n.865.7		16	9.5	odd	6
2268.2.i.n.2053.2		16	63.16	even	3
2268.2.i.n.2053.7		16	63.2	odd	6
2268.2.k.g.1297.2	✓	16	7.2	even	3	inner
2268.2.k.g.1297.7	yes	16	21.2	odd	6	inner
2268.2.k.g.1621.2	yes	16	1.1	even	1	trivial
2268.2.k.g.1621.7	yes	16	3.2	odd	2	inner
2268.2.l.n.109.2		16	9.2	odd	6
2268.2.l.n.109.7		16	9.7	even	3
2268.2.l.n.541.2		16	63.23	odd	6
2268.2.l.n.541.7		16	63.58	even	3

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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15101 - 1.99360i) q^{5} +(-0.271847 - 2.63175i) q^{7} +O(q^{10})\)	\(q+(-1.15101 - 1.99360i) q^{5} +(-0.271847 - 2.63175i) q^{7} +(2.23145 - 3.86499i) q^{11} -2.84296 q^{13} +(0.115312 - 0.199726i) q^{17} +(-1.49360 - 2.58700i) q^{19} +(-0.400294 - 0.693329i) q^{23} +(-0.149635 + 0.259175i) q^{25} +7.65502 q^{29} +(-2.64324 + 4.57822i) q^{31} +(-4.93376 + 3.57112i) q^{35} +(-1.69333 - 2.93293i) q^{37} -1.79939 q^{41} -9.71719 q^{43} +(2.88818 + 5.00247i) q^{47} +(-6.85220 + 1.43087i) q^{49} +(4.31905 - 7.48081i) q^{53} -10.2737 q^{55} +(-4.17793 + 7.23638i) q^{59} +(6.58675 + 11.4086i) q^{61} +(3.27227 + 5.66774i) q^{65} +(3.76545 - 6.52195i) q^{67} -8.59672 q^{71} +(-2.29287 + 3.97137i) q^{73} +(-10.7783 - 4.82194i) q^{77} +(-4.83657 - 8.37718i) q^{79} +16.9304 q^{83} -0.530900 q^{85} +(-0.944450 - 1.63584i) q^{89} +(0.772852 + 7.48196i) q^{91} +(-3.43829 + 5.95530i) q^{95} -15.4159 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{7}+O(q^{10}) \) 16 * q + 6 * q^7	\( 16 q + 6 q^{7} - 20 q^{13} + 8 q^{19} - 8 q^{31} - 4 q^{37} + 20 q^{43} + 10 q^{49} - 32 q^{55} + 28 q^{61} + 18 q^{67} - 20 q^{79} + 76 q^{85} - 2 q^{91} - 84 q^{97}+O(q^{100}) \) 16 * q + 6 * q^7 - 20 * q^13 + 8 * q^19 - 8 * q^31 - 4 * q^37 + 20 * q^43 + 10 * q^49 - 32 * q^55 + 28 * q^61 + 18 * q^67 - 20 * q^79 + 76 * q^85 - 2 * q^91 - 84 * q^97

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