LMFDB - Embedded newform 3564.2.i.t.1189.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3564,2,Mod(1189,3564)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3564, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("3564.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3564 = 2^{2} \cdot 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3564.i (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:	$28.4586832804$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 18x^{9} + 152x^{8} - 204x^{7} + 162x^{6} - 408x^{5} + 2800x^{4} - 4422x^{3} + 3528x^{2} - 252x + 9 $ x^12 - 18x^9 + 152x^8 - 204x^7 + 162x^6 - 408x^5 + 2800x^4 - 4422x^3 + 3528x^2 - 252*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1189.2
Root			$1.81730 - 1.81730i$ of defining polynomial
Character	$\chi$	$=$	3564.1189
Dual form			3564.2.i.t.2377.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.665179 - 1.15212i) q^{5} +(2.41905 - 4.18992i) q^{7} +O(q^{10})$	$q+(-0.665179 - 1.15212i) q^{5} +(2.41905 - 4.18992i) q^{7} +(0.500000 - 0.866025i) q^{11} +(0.299154 + 0.518150i) q^{13} +7.47271 q^{17} +2.41487 q^{19} +(0.764279 + 1.32377i) q^{23} +(1.61507 - 2.79739i) q^{25} +(-1.43428 + 2.48425i) q^{29} +(2.98907 + 5.17722i) q^{31} -6.43641 q^{35} +9.73332 q^{37} +(3.01471 + 5.22163i) q^{41} +(1.64336 - 2.84638i) q^{43} +(-2.30866 + 3.99872i) q^{47} +(-8.20360 - 14.2091i) q^{49} -4.59097 q^{53} -1.33036 q^{55} +(4.74346 + 8.21592i) q^{59} +(4.73320 - 8.19815i) q^{61} +(0.397982 - 0.689325i) q^{65} +(1.25043 + 2.16581i) q^{67} +0.142348 q^{71} -11.6564 q^{73} +(-2.41905 - 4.18992i) q^{77} +(0.309059 - 0.535306i) q^{79} +(7.04948 - 12.2101i) q^{83} +(-4.97069 - 8.60949i) q^{85} -7.35318 q^{89} +2.89467 q^{91} +(-1.60632 - 2.78223i) q^{95} +(1.33724 - 2.31616i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{7}+O(q^{10}) $ 12 * q + 2 * q^7	$ 12 q + 2 q^{7} + 6 q^{11} + 6 q^{13} - 8 q^{17} + 4 q^{23} - 10 q^{25} - 4 q^{29} - 6 q^{31} - 28 q^{35} - 12 q^{37} + 22 q^{41} + 10 q^{43} + 20 q^{47} - 6 q^{49} - 8 q^{53} + 24 q^{59} + 10 q^{61} + 40 q^{65} + 6 q^{67} - 80 q^{71} - 16 q^{73} - 2 q^{77} + 14 q^{79} + 12 q^{83} - 6 q^{85} - 48 q^{89} + 20 q^{91} + 44 q^{95} - 20 q^{97}+O(q^{100}) $ 12 * q + 2 * q^7 + 6 * q^11 + 6 * q^13 - 8 * q^17 + 4 * q^23 - 10 * q^25 - 4 * q^29 - 6 * q^31 - 28 * q^35 - 12 * q^37 + 22 * q^41 + 10 * q^43 + 20 * q^47 - 6 * q^49 - 8 * q^53 + 24 * q^59 + 10 * q^61 + 40 * q^65 + 6 * q^67 - 80 * q^71 - 16 * q^73 - 2 * q^77 + 14 * q^79 + 12 * q^83 - 6 * q^85 - 48 * q^89 + 20 * q^91 + 44 * q^95 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3564\mathbb{Z}\right)^\times$.

$n$	$1541$	$1783$	$2917$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$5$	−0.665179	−	1.15212i	−0.297477	−	0.515246i	0.678081	−	0.734987i	$-0.262812\pi$
$5$	−0.665179	−	1.15212i	−0.297477	−	0.515246i	−0.975558	+	0.219742i	$0.929479\pi$
$6$		0			0
$7$	2.41905	−	4.18992i	0.914315	−	1.58364i	0.106414	−	0.994322i	$-0.466063\pi$
$7$	2.41905	−	4.18992i	0.914315	−	1.58364i	0.807901	−	0.589318i	$-0.200603\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	0.299154	+	0.518150i	0.0829704	+	0.143709i	0.904525	−	0.426422i	$-0.140226\pi$
$13$	0.299154	+	0.518150i	0.0829704	+	0.143709i	−0.821554	+	0.570130i	$0.806893\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	7.47271			1.81240			0.906199	−	0.422852i	$-0.138971\pi$
$17$	7.47271			1.81240			0.906199	+	0.422852i	$0.138971\pi$
$18$		0			0
$19$	2.41487			0.554009			0.277004	−	0.960869i	$-0.410658\pi$
$19$	2.41487			0.554009			0.277004	+	0.960869i	$0.410658\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.764279	+	1.32377i	0.159363	+	0.276025i	0.934639	−	0.355597i	$-0.115723\pi$
$23$	0.764279	+	1.32377i	0.159363	+	0.276025i	−0.775276	+	0.631623i	$0.782389\pi$
$24$		0			0
$25$	1.61507	−	2.79739i	0.323015	−	0.559478i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.43428	+	2.48425i	−0.266339	+	0.461313i	−0.967914	−	0.251283i	$-0.919148\pi$
$29$	−1.43428	+	2.48425i	−0.266339	+	0.461313i	0.701574	+	0.712596i	$0.252481\pi$
$30$		0			0
$31$	2.98907	+	5.17722i	0.536853	+	0.929857i	0.999071	+	0.0430905i	$0.0137204\pi$
$31$	2.98907	+	5.17722i	0.536853	+	0.929857i	−0.462218	+	0.886766i	$0.652946\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.43641			−1.08795
$36$		0			0
$37$	9.73332			1.60015			0.800074	−	0.599902i	$-0.204794\pi$
$37$	9.73332			1.60015			0.800074	+	0.599902i	$0.204794\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.01471	+	5.22163i	0.470819	+	0.815482i	0.999443	−	0.0333739i	$-0.0106252\pi$
$41$	3.01471	+	5.22163i	0.470819	+	0.815482i	−0.528624	+	0.848856i	$0.677292\pi$
$42$		0			0
$43$	1.64336	−	2.84638i	0.250610	−	0.434069i	−0.713084	−	0.701079i	$-0.752702\pi$
$43$	1.64336	−	2.84638i	0.250610	−	0.434069i	0.963694	+	0.267009i	$0.0860355\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.30866	+	3.99872i	−0.336753	+	0.583273i	−0.983820	−	0.179160i	$-0.942662\pi$
$47$	−2.30866	+	3.99872i	−0.336753	+	0.583273i	0.647067	+	0.762433i	$0.275995\pi$
$48$		0			0
$49$	−8.20360	−	14.2091i	−1.17194	−	2.02987i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.59097			−0.630618			−0.315309	−	0.948989i	$-0.602108\pi$
$53$	−4.59097			−0.630618			−0.315309	+	0.948989i	$0.602108\pi$
$54$		0			0
$55$	−1.33036			−0.179386
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.74346	+	8.21592i	0.617546	+	1.06962i	0.989932	+	0.141543i	$0.0452065\pi$
$59$	4.74346	+	8.21592i	0.617546	+	1.06962i	−0.372386	+	0.928078i	$0.621460\pi$
$60$		0			0
$61$	4.73320	−	8.19815i	0.606025	−	1.04967i	−0.385864	−	0.922556i	$-0.626097\pi$
$61$	4.73320	−	8.19815i	0.606025	−	1.04967i	0.991889	−	0.127110i	$-0.0405701\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.397982	−	0.689325i	0.0493636	−	0.0855002i
$66$		0			0
$67$	1.25043	+	2.16581i	0.152765	+	0.264596i	0.932243	−	0.361833i	$-0.117849\pi$
$67$	1.25043	+	2.16581i	0.152765	+	0.264596i	−0.779478	+	0.626429i	$0.784516\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.142348			0.0168937			0.00844683	−	0.999964i	$-0.497311\pi$
$71$	0.142348			0.0168937			0.00844683	+	0.999964i	$0.497311\pi$
$72$		0			0
$73$	−11.6564			−1.36428			−0.682139	−	0.731223i	$-0.738950\pi$
$73$	−11.6564			−1.36428			−0.682139	+	0.731223i	$0.738950\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.41905	−	4.18992i	−0.275676	−	0.477485i
$78$		0			0
$79$	0.309059	−	0.535306i	0.0347719	−	0.0602266i	−0.848116	−	0.529811i	$-0.822263\pi$
$79$	0.309059	−	0.535306i	0.0347719	−	0.0602266i	0.882888	+	0.469584i	$0.155596\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.04948	−	12.2101i	0.773781	−	1.34023i	−0.161697	−	0.986840i	$-0.551697\pi$
$83$	7.04948	−	12.2101i	0.773781	−	1.34023i	0.935477	−	0.353387i	$-0.114970\pi$
$84$		0			0
$85$	−4.97069	−	8.60949i	−0.539147	−	0.933830i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−7.35318			−0.779436			−0.389718	−	0.920934i	$-0.627427\pi$
$89$	−7.35318			−0.779436			−0.389718	+	0.920934i	$0.627427\pi$
$90$		0			0
$91$	2.89467			0.303444
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.60632	−	2.78223i	−0.164805	−	0.285451i
$96$		0			0
$97$	1.33724	−	2.31616i	0.135776	−	0.235170i	−0.790118	−	0.612955i	$-0.789981\pi$
$97$	1.33724	−	2.31616i	0.135776	−	0.235170i	0.925894	+	0.377785i	$0.123314\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.52028	−	9.56140i	0.549288	−	0.951395i	−0.449036	−	0.893514i	$-0.648232\pi$
$101$	5.52028	−	9.56140i	0.549288	−	0.951395i	0.998324	−	0.0578808i	$-0.0184343\pi$
$102$		0			0
$103$	2.17709	+	3.77084i	0.214515	+	0.371552i	0.953123	−	0.302584i	$-0.0978494\pi$
$103$	2.17709	+	3.77084i	0.214515	+	0.371552i	−0.738607	+	0.674136i	$0.764516\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−14.4796			−1.39979			−0.699897	−	0.714244i	$-0.746771\pi$
$107$	−14.4796			−1.39979			−0.699897	+	0.714244i	$0.746771\pi$
$108$		0			0
$109$	−3.98019			−0.381233			−0.190617	−	0.981665i	$-0.561049\pi$
$109$	−3.98019			−0.381233			−0.190617	+	0.981665i	$0.561049\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.48158	+	14.6905i	0.797880	+	1.38197i	0.920994	+	0.389576i	$0.127379\pi$
$113$	8.48158	+	14.6905i	0.797880	+	1.38197i	−0.123114	+	0.992393i	$0.539288\pi$
$114$		0			0
$115$	1.01677	−	1.76109i	0.0948138	−	0.164222i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	18.0769	−	31.3100i	1.65710	−	2.87019i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−10.9490			−0.979312
$126$		0			0
$127$	−7.48257			−0.663971			−0.331985	−	0.943285i	$-0.607718\pi$
$127$	−7.48257			−0.663971			−0.331985	+	0.943285i	$0.607718\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.72987	+	8.19238i	0.413251	+	0.715772i	0.995243	−	0.0974227i	$-0.0310599\pi$
$131$	4.72987	+	8.19238i	0.413251	+	0.715772i	−0.581992	+	0.813194i	$0.697727\pi$
$132$		0			0
$133$	5.84169	−	10.1181i	0.506539	−	0.877351i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.07989	+	13.9948i	−0.690311	+	1.19565i	0.281424	+	0.959583i	$0.409193\pi$
$137$	−8.07989	+	13.9948i	−0.690311	+	1.19565i	−0.971736	+	0.236071i	$0.924140\pi$
$138$		0			0
$139$	−10.7634	−	18.6427i	−0.912937	−	1.58125i	−0.809894	−	0.586576i	$-0.800475\pi$
$139$	−10.7634	−	18.6427i	−0.912937	−	1.58125i	−0.103043	−	0.994677i	$-0.532858\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.598308			0.0500330
$144$		0			0
$145$	3.81622			0.316920
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.09460	−	14.0203i	−0.663135	−	1.14858i	−0.979787	−	0.200042i	$-0.935892\pi$
$149$	−8.09460	−	14.0203i	−0.663135	−	1.14858i	0.316652	−	0.948542i	$-0.397441\pi$
$150$		0			0
$151$	−4.58143	+	7.93527i	−0.372832	+	0.645763i	−0.990000	−	0.141068i	$-0.954946\pi$
$151$	−4.58143	+	7.93527i	−0.372832	+	0.645763i	0.617168	+	0.786831i	$0.288280\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.97654	−	6.88756i	0.319403	−	0.553222i
$156$		0			0
$157$	−11.5000	−	19.9185i	−0.917798	−	1.58967i	−0.802753	−	0.596312i	$-0.796632\pi$
$157$	−11.5000	−	19.9185i	−0.917798	−	1.58967i	−0.115044	−	0.993360i	$-0.536701\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	7.39532			0.582833
$162$		0			0
$163$	−2.30655			−0.180663			−0.0903316	−	0.995912i	$-0.528793\pi$
$163$	−2.30655			−0.180663			−0.0903316	+	0.995912i	$0.528793\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.56951	+	14.8428i	0.663128	+	1.14857i	0.979789	+	0.200033i	$0.0641050\pi$
$167$	8.56951	+	14.8428i	0.663128	+	1.14857i	−0.316661	+	0.948539i	$0.602562\pi$
$168$		0			0
$169$	6.32101	−	10.9483i	0.486232	−	0.842178i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.54604	+	6.14192i	−0.269600	+	0.466961i	−0.968759	−	0.248006i	$-0.920225\pi$
$173$	−3.54604	+	6.14192i	−0.269600	+	0.466961i	0.699158	+	0.714967i	$0.253558\pi$
$174$		0			0
$175$	−7.81388	−	13.5340i	−0.590674	−	1.02308i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−17.7442			−1.32626			−0.663131	−	0.748503i	$-0.730773\pi$
$179$	−17.7442			−1.32626			−0.663131	+	0.748503i	$0.730773\pi$
$180$		0			0
$181$	11.1753			0.830656			0.415328	−	0.909672i	$-0.363667\pi$
$181$	11.1753			0.830656			0.415328	+	0.909672i	$0.363667\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.47440	−	11.2140i	−0.476007	−	0.824469i
$186$		0			0
$187$	3.73635	−	6.47155i	0.273229	−	0.473247i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−12.0795	+	20.9223i	−0.874042	+	1.51388i	−0.0162618	+	0.999868i	$0.505177\pi$
$191$	−12.0795	+	20.9223i	−0.874042	+	1.51388i	−0.857780	+	0.514017i	$0.828157\pi$
$192$		0			0
$193$	10.2172	+	17.6967i	0.735450	+	1.27384i	0.954526	+	0.298128i	$0.0963623\pi$
$193$	10.2172	+	17.6967i	0.735450	+	1.27384i	−0.219076	+	0.975708i	$0.570304\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.28776			0.0917491			0.0458745	−	0.998947i	$-0.485393\pi$
$197$	1.28776			0.0917491			0.0458745	+	0.998947i	$0.485393\pi$
$198$		0			0
$199$	14.0157			0.993547			0.496774	−	0.867880i	$-0.334518\pi$
$199$	14.0157			0.993547			0.496774	+	0.867880i	$0.334518\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	6.93920	+	12.0190i	0.487036	+	0.843571i
$204$		0			0
$205$	4.01065	−	6.94664i	0.280116	−	0.485175i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.20743	−	2.09134i	0.0835200	−	0.144661i
$210$		0			0
$211$	2.37400	+	4.11189i	0.163433	+	0.283074i	0.936098	−	0.351740i	$-0.114410\pi$
$211$	2.37400	+	4.11189i	0.163433	+	0.283074i	−0.772665	+	0.634814i	$0.781077\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.37251			−0.298203
$216$		0			0
$217$	28.9229			1.96341
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.23549	+	3.87198i	0.150375	+	0.260458i
$222$		0			0
$223$	−10.1674	+	17.6105i	−0.680861	+	1.17929i	0.293858	+	0.955849i	$0.405061\pi$
$223$	−10.1674	+	17.6105i	−0.680861	+	1.17929i	−0.974719	+	0.223436i	$0.928273\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	14.9589	−	25.9095i	0.992854	−	1.71967i	0.393083	−	0.919503i	$-0.371409\pi$
$227$	14.9589	−	25.9095i	0.992854	−	1.71967i	0.599772	−	0.800171i	$-0.295258\pi$
$228$		0			0
$229$	2.05997	+	3.56798i	0.136127	+	0.235779i	0.926027	−	0.377456i	$-0.123201\pi$
$229$	2.05997	+	3.56798i	0.136127	+	0.235779i	−0.789900	+	0.613235i	$0.789868\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	16.6559			1.09117			0.545583	−	0.838057i	$-0.316308\pi$
$233$	16.6559			1.09117			0.545583	+	0.838057i	$0.316308\pi$
$234$		0			0
$235$	6.14269			0.400705
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−8.63409	−	14.9547i	−0.558493	−	0.967339i	−0.997623	−	0.0689147i	$-0.978046\pi$
$239$	−8.63409	−	14.9547i	−0.558493	−	0.967339i	0.439129	−	0.898424i	$-0.355287\pi$
$240$		0			0
$241$	8.65375	−	14.9887i	0.557437	−	0.965509i	−0.440273	−	0.897864i	$-0.645118\pi$
$241$	8.65375	−	14.9887i	0.557437	−	0.965509i	0.997709	−	0.0676448i	$-0.0215485\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−10.9137	+	18.9031i	−0.697253	+	1.20768i
$246$		0			0
$247$	0.722417	+	1.25126i	0.0459663	+	0.0796160i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.50545			−0.410620			−0.205310	−	0.978697i	$-0.565820\pi$
$251$	−6.50545			−0.410620			−0.205310	+	0.978697i	$0.565820\pi$
$252$		0			0
$253$	1.52856			0.0960996
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.00358	+	1.73825i	0.0626017	+	0.108429i	0.895628	−	0.444805i	$-0.146727\pi$
$257$	1.00358	+	1.73825i	0.0626017	+	0.108429i	−0.833026	+	0.553234i	$0.813394\pi$
$258$		0			0
$259$	23.5454	−	40.7818i	1.46304	−	2.53406i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.95990	+	8.59080i	−0.305841	+	0.529731i	−0.977448	−	0.211176i	$-0.932271\pi$
$263$	−4.95990	+	8.59080i	−0.305841	+	0.529731i	0.671608	+	0.740907i	$0.265604\pi$
$264$		0			0
$265$	3.05382	+	5.28937i	0.187594	+	0.324923i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−16.2380			−0.990048			−0.495024	−	0.868879i	$-0.664841\pi$
$269$	−16.2380			−0.990048			−0.495024	+	0.868879i	$0.664841\pi$
$270$		0			0
$271$	−4.22363			−0.256567			−0.128284	−	0.991738i	$-0.540947\pi$
$271$	−4.22363			−0.256567			−0.128284	+	0.991738i	$0.540947\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.61507	−	2.79739i	−0.0973926	−	0.168689i
$276$		0			0
$277$	4.74664	−	8.22142i	0.285198	−	0.493977i	−0.687459	−	0.726223i	$-0.741274\pi$
$277$	4.74664	−	8.22142i	0.285198	−	0.493977i	0.972657	+	0.232246i	$0.0746073\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	12.4056	−	21.4871i	0.740056	−	1.28181i	−0.212414	−	0.977180i	$-0.568132\pi$
$281$	12.4056	−	21.4871i	0.740056	−	1.28181i	0.952469	−	0.304634i	$-0.0985343\pi$
$282$		0			0
$283$	−9.00231	−	15.5925i	−0.535132	−	0.926875i	−0.999157	−	0.0410531i	$-0.986929\pi$
$283$	−9.00231	−	15.5925i	−0.535132	−	0.926875i	0.464025	−	0.885822i	$-0.346405\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	29.1709			1.72191
$288$		0			0
$289$	38.8414			2.28479
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.35498	−	7.54305i	−0.254421	−	0.440670i	0.710317	−	0.703882i	$-0.248552\pi$
$293$	−4.35498	−	7.54305i	−0.254421	−	0.440670i	−0.964738	+	0.263212i	$0.915218\pi$
$294$		0			0
$295$	6.31051	−	10.9301i	0.367412	−	0.636376i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.457274	+	0.792022i	−0.0264448	+	0.0458038i
$300$		0			0
$301$	−7.95074	−	13.7711i	−0.458273	−	0.793752i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−12.5937			−0.721114
$306$		0			0
$307$	−15.4202			−0.880080			−0.440040	−	0.897978i	$-0.645036\pi$
$307$	−15.4202			−0.880080			−0.440040	+	0.897978i	$0.645036\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.53325	+	4.38772i	0.143648	+	0.248805i	0.928868	−	0.370412i	$-0.120784\pi$
$311$	2.53325	+	4.38772i	0.143648	+	0.248805i	−0.785220	+	0.619217i	$0.787450\pi$
$312$		0			0
$313$	−0.413716	+	0.716577i	−0.0233846	+	0.0405033i	−0.877481	−	0.479612i	$-0.840778\pi$
$313$	−0.413716	+	0.716577i	−0.0233846	+	0.0405033i	0.854096	+	0.520115i	$0.174111\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.57902	−	6.19905i	0.201018	−	0.348173i	−0.747839	−	0.663881i	$-0.768908\pi$
$317$	3.57902	−	6.19905i	0.201018	−	0.348173i	0.948857	+	0.315707i	$0.102242\pi$
$318$		0			0
$319$	1.43428	+	2.48425i	0.0803043	+	0.139091i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	18.0456			1.00408
$324$		0			0
$325$	1.93262			0.107203
$326$		0			0
$327$		0			0
$328$		0			0
$329$	11.1695	+	19.3462i	0.615796	+	1.06659i
$330$		0			0
$331$	0.212128	−	0.367417i	0.0116596	−	0.0201950i	−0.860137	−	0.510064i	$-0.829622\pi$
$331$	0.212128	−	0.367417i	0.0116596	−	0.0201950i	0.871796	+	0.489868i	$0.162955\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.66352	−	2.88131i	0.0908880	−	0.157423i
$336$		0			0
$337$	17.8431	+	30.9052i	0.971977	+	1.68351i	0.689569	+	0.724220i	$0.257800\pi$
$337$	17.8431	+	30.9052i	0.971977	+	1.68351i	0.282409	+	0.959294i	$0.408867\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	5.97814			0.323735
$342$		0			0
$343$	−45.5130			−2.45747
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.877257	−	1.51945i	−0.0470936	−	0.0815686i	0.841518	−	0.540230i	$-0.181663\pi$
$347$	−0.877257	−	1.51945i	−0.0470936	−	0.0815686i	−0.888611	+	0.458661i	$0.848329\pi$
$348$		0			0
$349$	2.47728	−	4.29077i	0.132606	−	0.229680i	−0.792075	−	0.610424i	$-0.790999\pi$
$349$	2.47728	−	4.29077i	0.132606	−	0.229680i	0.924680	+	0.380745i	$0.124332\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.17126	+	12.4210i	−0.381688	+	0.661103i	−0.991304	−	0.131594i	$-0.957990\pi$
$353$	−7.17126	+	12.4210i	−0.381688	+	0.661103i	0.609616	+	0.792697i	$0.291324\pi$
$354$		0			0
$355$	−0.0946873	−	0.164003i	−0.00502548	−	0.00870438i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−12.4052			−0.654719			−0.327360	−	0.944900i	$-0.606159\pi$
$359$	−12.4052			−0.654719			−0.327360	+	0.944900i	$0.606159\pi$
$360$		0			0
$361$	−13.1684			−0.693074
$362$		0			0
$363$		0			0
$364$		0			0
$365$	7.75359	+	13.4296i	0.405841	+	0.702938i
$366$		0			0
$367$	−6.91167	+	11.9714i	−0.360786	+	0.624900i	−0.988090	−	0.153874i	$-0.950825\pi$
$367$	−6.91167	+	11.9714i	−0.360786	+	0.624900i	0.627304	+	0.778774i	$0.284158\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−11.1058	+	19.2358i	−0.576583	+	0.998672i
$372$		0			0
$373$	13.0460	+	22.5964i	0.675497	+	1.17000i	0.976323	+	0.216316i	$0.0694043\pi$
$373$	13.0460	+	22.5964i	0.675497	+	1.17000i	−0.300826	+	0.953679i	$0.597262\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.71628			−0.0883931
$378$		0			0
$379$	11.0276			0.566451			0.283225	−	0.959053i	$-0.408596\pi$
$379$	11.0276			0.566451			0.283225	+	0.959053i	$0.408596\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−18.9756	−	32.8668i	−0.969610	−	1.67941i	−0.696685	−	0.717378i	$-0.745342\pi$
$383$	−18.9756	−	32.8668i	−0.969610	−	1.67941i	−0.272925	−	0.962035i	$-0.587991\pi$
$384$		0			0
$385$	−3.21820	+	5.57409i	−0.164015	+	0.284082i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.0487514	−	0.0844398i	0.00247179	−	0.00428127i	−0.864787	−	0.502139i	$-0.832547\pi$
$389$	0.0487514	−	0.0844398i	0.00247179	−	0.00428127i	0.867259	+	0.497858i	$0.165880\pi$
$390$		0			0
$391$	5.71123	+	9.89215i	0.288830	+	0.500267i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.822319			−0.0413753
$396$		0			0
$397$	−14.9953			−0.752594			−0.376297	−	0.926499i	$-0.622803\pi$
$397$	−14.9953			−0.752594			−0.376297	+	0.926499i	$0.622803\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.774675	−	1.34178i	−0.0386854	−	0.0670051i	0.846034	−	0.533128i	$-0.178984\pi$
$401$	−0.774675	−	1.34178i	−0.0386854	−	0.0670051i	−0.884720	+	0.466123i	$0.845650\pi$
$402$		0			0
$403$	−1.78838	+	3.09757i	−0.0890858	+	0.154301i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.86666	−	8.42930i	0.241231	−	0.417825i
$408$		0			0
$409$	−5.26896	−	9.12610i	−0.260533	−	0.451257i	0.705851	−	0.708361i	$-0.250565\pi$
$409$	−5.26896	−	9.12610i	−0.260533	−	0.451257i	−0.966384	+	0.257104i	$0.917232\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	45.8987			2.25853
$414$		0			0
$415$	−18.7567			−0.920728
$416$		0			0
$417$		0			0
$418$		0			0
$419$	16.9759	+	29.4031i	0.829328	+	1.43644i	0.898566	+	0.438838i	$0.144610\pi$
$419$	16.9759	+	29.4031i	0.829328	+	1.43644i	−0.0692388	+	0.997600i	$0.522057\pi$
$420$		0			0
$421$	−5.61751	+	9.72981i	−0.273781	+	0.474202i	−0.969827	−	0.243795i	$-0.921608\pi$
$421$	−5.61751	+	9.72981i	−0.273781	+	0.474202i	0.696046	+	0.717997i	$0.254941\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.0690	−	20.9041i	0.585431	−	1.01400i
$426$		0			0
$427$	−22.8997	−	39.6635i	−1.10819	−	1.91945i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−32.2229			−1.55212			−0.776061	−	0.630658i	$-0.782785\pi$
$431$	−32.2229			−1.55212			−0.776061	+	0.630658i	$0.782785\pi$
$432$		0			0
$433$	26.2169			1.25991			0.629953	−	0.776633i	$-0.283074\pi$
$433$	26.2169			1.25991			0.629953	+	0.776633i	$0.283074\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.84563	+	3.19673i	0.0882886	+	0.152920i
$438$		0			0
$439$	−14.1053	+	24.4310i	−0.673208	+	1.16603i	0.303782	+	0.952742i	$0.401751\pi$
$439$	−14.1053	+	24.4310i	−0.673208	+	1.16603i	−0.976989	+	0.213288i	$0.931583\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−11.0190	+	19.0854i	−0.523527	+	0.906776i	0.476098	+	0.879392i	$0.342051\pi$
$443$	−11.0190	+	19.0854i	−0.523527	+	0.906776i	−0.999625	+	0.0273836i	$0.991282\pi$
$444$		0			0
$445$	4.89118	+	8.47178i	0.231864	+	0.401601i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−14.6704			−0.692338			−0.346169	−	0.938172i	$-0.612518\pi$
$449$	−14.6704			−0.692338			−0.346169	+	0.938172i	$0.612518\pi$
$450$		0			0
$451$	6.02942			0.283914
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.92548	−	3.33502i	−0.0902677	−	0.156348i
$456$		0			0
$457$	−11.3679	+	19.6897i	−0.531767	+	0.921048i	0.467545	+	0.883969i	$0.345138\pi$
$457$	−11.3679	+	19.6897i	−0.531767	+	0.921048i	−0.999312	+	0.0370785i	$0.988195\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−8.11156	+	14.0496i	−0.377793	+	0.654357i	−0.990741	−	0.135767i	$-0.956650\pi$
$461$	−8.11156	+	14.0496i	−0.377793	+	0.654357i	0.612948	+	0.790123i	$0.289984\pi$
$462$		0			0
$463$	−8.39403	−	14.5389i	−0.390104	−	0.675680i	0.602359	−	0.798225i	$-0.294228\pi$
$463$	−8.39403	−	14.5389i	−0.390104	−	0.675680i	−0.992463	+	0.122546i	$0.960894\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−10.9741			−0.507822			−0.253911	−	0.967228i	$-0.581717\pi$
$467$	−10.9741			−0.507822			−0.253911	+	0.967228i	$0.581717\pi$
$468$		0			0
$469$	12.0994			0.558700
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.64336	−	2.84638i	−0.0755617	−	0.130877i
$474$		0			0
$475$	3.90019	−	6.75533i	0.178953	−	0.309956i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.95307	−	3.38282i	0.0892382	−	0.154565i	−0.817951	−	0.575288i	$-0.804890\pi$
$479$	1.95307	−	3.38282i	0.0892382	−	0.154565i	0.907189	+	0.420723i	$0.138223\pi$
$480$		0			0
$481$	2.91176	+	5.04332i	0.132765	+	0.229955i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.55801			−0.161561
$486$		0			0
$487$	−41.4163			−1.87675			−0.938376	−	0.345615i	$-0.887670\pi$
$487$	−41.4163			−1.87675			−0.938376	+	0.345615i	$0.887670\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.70955	+	16.8174i	0.438186	+	0.758960i	0.997550	−	0.0699620i	$-0.0222878\pi$
$491$	9.70955	+	16.8174i	0.438186	+	0.758960i	−0.559364	+	0.828922i	$0.688954\pi$
$492$		0			0
$493$	−10.7180	+	18.5641i	−0.482713	+	0.836083i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.344348	−	0.596428i	0.0154461	−	0.0267535i
$498$		0			0
$499$	−8.14534	−	14.1081i	−0.364635	−	0.631567i	0.624082	−	0.781359i	$-0.285473\pi$
$499$	−8.14534	−	14.1081i	−0.364635	−	0.631567i	−0.988718	+	0.149792i	$0.952140\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	8.89003			0.396387			0.198193	−	0.980163i	$-0.436493\pi$
$503$	8.89003			0.396387			0.198193	+	0.980163i	$0.436493\pi$
$504$		0			0
$505$	−14.6879			−0.653603
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.46378	+	9.46355i	0.242178	+	0.419464i	0.961334	−	0.275384i	$-0.0888049\pi$
$509$	5.46378	+	9.46355i	0.242178	+	0.419464i	−0.719156	+	0.694848i	$0.755472\pi$
$510$		0			0
$511$	−28.1974	+	48.8393i	−1.24738	+	2.16052i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2.89632	−	5.01657i	0.127627	−	0.221056i
$516$		0			0
$517$	2.30866	+	3.99872i	0.101535	+	0.175863i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	24.3814			1.06817			0.534084	−	0.845431i	$-0.320657\pi$
$521$	24.3814			1.06817			0.534084	+	0.845431i	$0.320657\pi$
$522$		0			0
$523$	−22.8100			−0.997412			−0.498706	−	0.866771i	$-0.666191\pi$
$523$	−22.8100			−0.997412			−0.498706	+	0.866771i	$0.666191\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	22.3365	+	38.6879i	0.972991	+	1.68527i
$528$		0			0
$529$	10.3318	−	17.8951i	0.449207	−	0.778049i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.80373	+	3.12414i	−0.0781280	+	0.135322i
$534$		0			0
$535$	9.63152	+	16.6823i	0.416407	+	0.721238i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−16.4072			−0.706709
$540$		0			0
$541$	−16.8424			−0.724112			−0.362056	−	0.932156i	$-0.617925\pi$
$541$	−16.8424			−0.724112			−0.362056	+	0.932156i	$0.617925\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.64754	+	4.58567i	0.113408	+	0.196429i
$546$		0			0
$547$	−16.2323	+	28.1151i	−0.694042	+	1.20212i	0.276460	+	0.961025i	$0.410839\pi$
$547$	−16.2323	+	28.1151i	−0.694042	+	1.20212i	−0.970503	+	0.241091i	$0.922495\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3.46360	+	5.99913i	−0.147554	+	0.255572i
$552$		0			0
$553$	−1.49526	−	2.58986i	−0.0635849	−	0.110132i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−22.7403			−0.963537			−0.481769	−	0.876298i	$-0.660005\pi$
$557$	−22.7403			−0.963537			−0.481769	+	0.876298i	$0.660005\pi$
$558$		0			0
$559$	1.96647			0.0831728
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.0171	−	20.8142i	−0.506460	−	0.877214i	−0.999972	−	0.00747504i	$-0.997621\pi$
$563$	−12.0171	−	20.8142i	−0.506460	−	0.877214i	0.493512	−	0.869739i	$-0.335713\pi$
$564$		0			0
$565$	11.2835	−	19.5437i	0.474702	−	0.822208i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.8496	−	32.6485i	0.790218	−	1.36870i	−0.135614	−	0.990762i	$-0.543301\pi$
$569$	18.8496	−	32.6485i	0.790218	−	1.36870i	0.925832	−	0.377936i	$-0.123366\pi$
$570$		0			0
$571$	15.7610	+	27.2989i	0.659578	+	1.14242i	0.980725	+	0.195393i	$0.0625982\pi$
$571$	15.7610	+	27.2989i	0.659578	+	1.14242i	−0.321147	+	0.947029i	$0.604068\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.93747			0.205907
$576$		0			0
$577$	27.3431			1.13831			0.569153	−	0.822232i	$-0.307271\pi$
$577$	27.3431			1.13831			0.569153	+	0.822232i	$0.307271\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−34.1061	−	59.0734i	−1.41496	−	2.45078i
$582$		0			0
$583$	−2.29548	+	3.97589i	−0.0950692	+	0.164665i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.16685	+	7.21720i	−0.171984	+	0.297886i	−0.939114	−	0.343607i	$-0.888351\pi$
$587$	−4.16685	+	7.21720i	−0.171984	+	0.297886i	0.767129	+	0.641493i	$0.221685\pi$
$588$		0			0
$589$	7.21822	+	12.5023i	0.297421	+	0.515149i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.73195			0.317513			0.158757	−	0.987318i	$-0.449252\pi$
$593$	7.73195			0.317513			0.158757	+	0.987318i	$0.449252\pi$
$594$		0			0
$595$	−48.0974			−1.97180
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−17.4097	−	30.1544i	−0.711340	−	1.23208i	−0.964354	−	0.264615i	$-0.914755\pi$
$599$	−17.4097	−	30.1544i	−0.711340	−	1.23208i	0.253014	−	0.967463i	$-0.418578\pi$
$600$		0			0
$601$	−12.9241	+	22.3853i	−0.527186	+	0.913114i	0.472312	+	0.881432i	$0.343420\pi$
$601$	−12.9241	+	22.3853i	−0.527186	+	0.913114i	−0.999498	+	0.0316820i	$0.989914\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.665179	+	1.15212i	−0.0270434	+	0.0468405i
$606$		0			0
$607$	5.64647	+	9.77997i	0.229183	+	0.396957i	0.957566	−	0.288213i	$-0.0930612\pi$
$607$	5.64647	+	9.77997i	0.229183	+	0.396957i	−0.728383	+	0.685170i	$0.759728\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.76258			−0.111762
$612$		0			0
$613$	12.9140			0.521590			0.260795	−	0.965394i	$-0.416015\pi$
$613$	12.9140			0.521590			0.260795	+	0.965394i	$0.416015\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−14.8911	−	25.7922i	−0.599494	−	1.03835i	−0.992896	−	0.118987i	$-0.962035\pi$
$617$	−14.8911	−	25.7922i	−0.599494	−	1.03835i	0.393402	−	0.919367i	$-0.371298\pi$
$618$		0			0
$619$	3.31714	−	5.74545i	0.133327	−	0.230929i	−0.791630	−	0.611001i	$-0.790767\pi$
$619$	3.31714	−	5.74545i	0.133327	−	0.230929i	0.924957	+	0.380072i	$0.124101\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−17.7877	+	30.8092i	−0.712650	+	1.23435i
$624$		0			0
$625$	−0.792287	−	1.37228i	−0.0316915	−	0.0548912i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	72.7342			2.90010
$630$		0			0
$631$	−9.68229			−0.385446			−0.192723	−	0.981253i	$-0.561732\pi$
$631$	−9.68229			−0.385446			−0.192723	+	0.981253i	$0.561732\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.97725	+	8.62085i	0.197516	+	0.342108i
$636$		0			0
$637$	4.90828	−	8.50139i	0.194473	−	0.336837i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	11.3286	−	19.6217i	0.447452	−	0.775009i	−0.550768	−	0.834658i	$-0.685665\pi$
$641$	11.3286	−	19.6217i	0.447452	−	0.775009i	0.998219	+	0.0596497i	$0.0189984\pi$
$642$		0			0
$643$	−7.53510	−	13.0512i	−0.297155	−	0.514688i	0.678329	−	0.734759i	$-0.262705\pi$
$643$	−7.53510	−	13.0512i	−0.297155	−	0.514688i	−0.975484	+	0.220070i	$0.929371\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.19177			0.164795			0.0823977	−	0.996600i	$-0.473742\pi$
$647$	4.19177			0.164795			0.0823977	+	0.996600i	$0.473742\pi$
$648$		0			0
$649$	9.48692			0.372394
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19.7483	−	34.2050i	−0.772809	−	1.33854i	−0.936018	−	0.351953i	$-0.885518\pi$
$653$	−19.7483	−	34.2050i	−0.772809	−	1.33854i	0.163209	−	0.986592i	$-0.447816\pi$
$654$		0			0
$655$	6.29243	−	10.8988i	0.245866	−	0.425852i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	20.9623	−	36.3078i	0.816575	−	1.41435i	−0.0916159	−	0.995794i	$-0.529203\pi$
$659$	20.9623	−	36.3078i	0.816575	−	1.41435i	0.908191	−	0.418556i	$-0.137463\pi$
$660$		0			0
$661$	19.9531	+	34.5599i	0.776087	+	1.34422i	0.934181	+	0.356799i	$0.116132\pi$
$661$	19.9531	+	34.5599i	0.776087	+	1.34422i	−0.158094	+	0.987424i	$0.550535\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−15.5431			−0.602735
$666$		0			0
$667$	−4.38477			−0.169779
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.73320	−	8.19815i	−0.182723	−	0.316486i
$672$		0			0
$673$	−12.4626	+	21.5859i	−0.480400	+	0.832077i	−0.999747	−	0.0224863i	$-0.992842\pi$
$673$	−12.4626	+	21.5859i	−0.480400	+	0.832077i	0.519347	+	0.854563i	$0.326175\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−24.3324	+	42.1449i	−0.935170	+	1.61976i	−0.160839	+	0.986981i	$0.551420\pi$
$677$	−24.3324	+	42.1449i	−0.935170	+	1.61976i	−0.774331	+	0.632781i	$0.781913\pi$
$678$		0			0
$679$	−6.46968	−	11.2058i	−0.248284	−	0.430040i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	36.3086			1.38931			0.694654	−	0.719344i	$-0.255557\pi$
$683$	36.3086			1.38931			0.694654	+	0.719344i	$0.255557\pi$
$684$		0			0
$685$	21.4983			0.821408
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.37341	−	2.37881i	−0.0523226	−	0.0906254i
$690$		0			0
$691$	−23.6896	+	41.0316i	−0.901196	+	1.56092i	−0.0752527	+	0.997164i	$0.523976\pi$
$691$	−23.6896	+	41.0316i	−0.901196	+	1.56092i	−0.825943	+	0.563753i	$0.809357\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−14.3191	+	24.8015i	−0.543156	+	0.940774i
$696$		0			0
$697$	22.5281	+	39.0197i	0.853311	+	1.47798i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−14.5991			−0.551401			−0.275701	−	0.961244i	$-0.588910\pi$
$701$	−14.5991			−0.551401			−0.275701	+	0.961244i	$0.588910\pi$
$702$		0			0
$703$	23.5047			0.886496
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−26.7076	−	46.2590i	−1.00444	−	1.73975i
$708$		0			0
$709$	20.1599	−	34.9180i	0.757121	−	1.31137i	−0.187193	−	0.982323i	$-0.559939\pi$
$709$	20.1599	−	34.9180i	0.757121	−	1.31137i	0.944313	−	0.329048i	$-0.106728\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.56897	+	7.91369i	−0.171109	+	0.296370i
$714$		0			0
$715$	−0.397982	−	0.689325i	−0.0148837	−	0.0257793i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−42.7901			−1.59580			−0.797900	−	0.602790i	$-0.794056\pi$
$719$	−42.7901			−1.59580			−0.797900	+	0.602790i	$0.794056\pi$
$720$		0			0
$721$	21.0660			0.784539
$722$		0			0
$723$		0			0
$724$		0			0
$725$	4.63294	+	8.02448i	0.172063	+	0.298022i
$726$		0			0
$727$	−4.26214	+	7.38224i	−0.158074	+	0.273792i	−0.934174	−	0.356818i	$-0.883862\pi$
$727$	−4.26214	+	7.38224i	−0.158074	+	0.273792i	0.776100	+	0.630610i	$0.217195\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	12.2803	−	21.2702i	0.454205	−	0.786706i
$732$		0			0
$733$	3.29471	+	5.70661i	0.121693	+	0.210779i	0.920435	−	0.390895i	$-0.127834\pi$
$733$	3.29471	+	5.70661i	0.121693	+	0.210779i	−0.798742	+	0.601673i	$0.794501\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.50086			0.0921205
$738$		0			0
$739$	11.1577			0.410444			0.205222	−	0.978715i	$-0.434208\pi$
$739$	11.1577			0.410444			0.205222	+	0.978715i	$0.434208\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	15.4893	+	26.8283i	0.568249	+	0.984236i	0.996739	+	0.0806899i	$0.0257123\pi$
$743$	15.4893	+	26.8283i	0.568249	+	0.984236i	−0.428490	+	0.903546i	$0.640954\pi$
$744$		0			0
$745$	−10.7687	+	18.6520i	−0.394535	+	0.683355i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−35.0268	+	60.6683i	−1.27985	+	2.21677i
$750$		0			0
$751$	13.2654	+	22.9763i	0.484061	+	0.838418i	0.999832	−	0.0183084i	$-0.00582808\pi$
$751$	13.2654	+	22.9763i	0.484061	+	0.838418i	−0.515772	+	0.856726i	$0.672495\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	12.1899			0.443636
$756$		0			0
$757$	27.8731			1.01306			0.506532	−	0.862221i	$-0.330927\pi$
$757$	27.8731			1.01306			0.506532	+	0.862221i	$0.330927\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.1092	+	22.7059i	0.475210	+	0.823088i	0.999597	−	0.0283925i	$-0.00903882\pi$
$761$	13.1092	+	22.7059i	0.475210	+	0.823088i	−0.524387	+	0.851480i	$0.675705\pi$
$762$		0			0
$763$	−9.62828	+	16.6767i	−0.348567	+	0.603736i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.83805	+	4.91565i	−0.102476	+	0.177494i
$768$		0			0
$769$	−0.144447	−	0.250190i	−0.00520889	−	0.00902207i	0.863409	−	0.504504i	$-0.168325\pi$
$769$	−0.144447	−	0.250190i	−0.00520889	−	0.00902207i	−0.868618	+	0.495482i	$0.834991\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.498896			0.0179440			0.00897202	−	0.999960i	$-0.497144\pi$
$773$	0.498896			0.0179440			0.00897202	+	0.999960i	$0.497144\pi$
$774$		0			0
$775$	19.3103			0.693645
$776$		0			0
$777$		0			0
$778$		0			0
$779$	7.28013	+	12.6096i	0.260838	+	0.451784i
$780$		0			0
$781$	0.0711742	−	0.123277i	0.00254681	−	0.00441121i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−15.2991	+	26.4988i	−0.546048	+	0.945782i
$786$		0			0
$787$	5.73662	+	9.93612i	0.204488	+	0.354184i	0.949970	−	0.312342i	$-0.101114\pi$
$787$	5.73662	+	9.93612i	0.204488	+	0.354184i	−0.745481	+	0.666527i	$0.767780\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	82.0695			2.91805
$792$		0			0
$793$	5.66383			0.201128
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−10.7986	−	18.7038i	−0.382507	−	0.662522i	0.608913	−	0.793237i	$-0.291606\pi$
$797$	−10.7986	−	18.7038i	−0.382507	−	0.662522i	−0.991420	+	0.130715i	$0.958273\pi$
$798$		0			0
$799$	−17.2519	+	29.8812i	−0.610330	+	1.05712i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.82819	+	10.0947i	−0.205673	+	0.356235i
$804$		0			0
$805$	−4.91921	−	8.52032i	−0.173379	−	0.300302i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	10.2898			0.361772			0.180886	−	0.983504i	$-0.442104\pi$
$809$	10.2898			0.361772			0.180886	+	0.983504i	$0.442104\pi$
$810$		0			0
$811$	24.7751			0.869971			0.434986	−	0.900437i	$-0.356753\pi$
$811$	24.7751			0.869971			0.434986	+	0.900437i	$0.356753\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.53427	+	2.65744i	0.0537432	+	0.0930860i
$816$		0			0
$817$	3.96850	−	6.87364i	0.138840	−	0.240478i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.76652	+	8.25585i	−0.166353	+	0.288131i	−0.937135	−	0.348968i	$-0.886532\pi$
$821$	−4.76652	+	8.25585i	−0.166353	+	0.288131i	0.770782	+	0.637099i	$0.219866\pi$
$822$		0			0
$823$	−11.4956	−	19.9109i	−0.400711	−	0.694051i	0.593101	−	0.805128i	$-0.297903\pi$
$823$	−11.4956	−	19.9109i	−0.400711	−	0.694051i	−0.993812	+	0.111077i	$0.964570\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−3.43382			−0.119406			−0.0597028	−	0.998216i	$-0.519015\pi$
$827$	−3.43382			−0.119406			−0.0597028	+	0.998216i	$0.519015\pi$
$828$		0			0
$829$	−40.9789			−1.42326			−0.711628	−	0.702556i	$-0.752042\pi$
$829$	−40.9789			−1.42326			−0.711628	+	0.702556i	$0.752042\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−61.3031	−	106.180i	−2.12403	−	3.67892i
$834$		0			0
$835$	11.4005	−	19.7463i	0.394531	−	0.683348i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11.1623	−	19.3337i	0.385367	−	0.667475i	−0.606453	−	0.795119i	$-0.707408\pi$
$839$	11.1623	−	19.3337i	0.385367	−	0.667475i	0.991820	+	0.127644i	$0.0407416\pi$
$840$		0			0
$841$	10.3857	+	17.9885i	0.358127	+	0.620294i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−16.8184			−0.578572
$846$		0			0
$847$	−4.83810			−0.166239
$848$		0			0
$849$		0			0
$850$		0			0
$851$	7.43897	+	12.8847i	0.255005	+	0.441681i
$852$		0			0
$853$	−13.1439	+	22.7658i	−0.450037	+	0.779487i	−0.998388	−	0.0567615i	$-0.981923\pi$
$853$	−13.1439	+	22.7658i	−0.450037	+	0.779487i	0.548351	+	0.836248i	$0.315256\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−23.9288	+	41.4459i	−0.817391	+	1.41576i	0.0902065	+	0.995923i	$0.471247\pi$
$857$	−23.9288	+	41.4459i	−0.817391	+	1.41576i	−0.907598	+	0.419840i	$0.862086\pi$
$858$		0			0
$859$	2.74322	+	4.75140i	0.0935975	+	0.162116i	0.909022	−	0.416747i	$-0.136830\pi$
$859$	2.74322	+	4.75140i	0.0935975	+	0.162116i	−0.815425	+	0.578863i	$0.803497\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	19.1189			0.650815			0.325407	−	0.945574i	$-0.394499\pi$
$863$	19.1189			0.650815			0.325407	+	0.945574i	$0.394499\pi$
$864$		0			0
$865$	9.43500			0.320800
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.309059	−	0.535306i	−0.0104841	−	0.0181590i
$870$		0			0
$871$	−0.748143	+	1.29582i	−0.0253499	+	0.0439073i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−26.4863	+	45.8756i	−0.895400	+	1.55088i
$876$		0			0
$877$	−2.02078	−	3.50009i	−0.0682368	−	0.118190i	0.829888	−	0.557929i	$-0.188404\pi$
$877$	−2.02078	−	3.50009i	−0.0682368	−	0.118190i	−0.898125	+	0.439740i	$0.855071\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−15.1415			−0.510129			−0.255065	−	0.966924i	$-0.582097\pi$
$881$	−15.1415			−0.510129			−0.255065	+	0.966924i	$0.582097\pi$
$882$		0			0
$883$	−35.1342			−1.18236			−0.591181	−	0.806539i	$-0.701338\pi$
$883$	−35.1342			−1.18236			−0.591181	+	0.806539i	$0.701338\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.70152	+	4.67917i	0.0907081	+	0.157111i	0.907809	−	0.419383i	$-0.137754\pi$
$887$	2.70152	+	4.67917i	0.0907081	+	0.157111i	−0.817101	+	0.576494i	$0.804420\pi$
$888$		0			0
$889$	−18.1007	+	31.3514i	−0.607078	+	1.05149i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−5.57511	+	9.65638i	−0.186564	+	0.323138i
$894$		0			0
$895$	11.8031	+	20.4435i	0.394533	+	0.683351i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−17.1487			−0.571940
$900$		0			0
$901$	−34.3070			−1.14293
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−7.43360	−	12.8754i	−0.247101	−	0.427992i
$906$		0			0
$907$	−16.6509	+	28.8401i	−0.552882	+	0.957620i	0.445182	+	0.895440i	$0.353139\pi$
$907$	−16.6509	+	28.8401i	−0.552882	+	0.957620i	−0.998065	+	0.0621806i	$0.980195\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	3.25397	−	5.63604i	0.107809	−	0.186730i	−0.807074	−	0.590451i	$-0.798950\pi$
$911$	3.25397	−	5.63604i	0.107809	−	0.186730i	0.914882	+	0.403721i	$0.132283\pi$
$912$		0			0
$913$	−7.04948	−	12.2101i	−0.233304	−	0.404094i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	45.7672			1.51137
$918$		0			0
$919$	−15.3385			−0.505971			−0.252985	−	0.967470i	$-0.581412\pi$
$919$	−15.3385			−0.505971			−0.252985	+	0.967470i	$0.581412\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.0425841	+	0.0737578i	0.00140167	+	0.00242777i
$924$		0			0
$925$	15.7200	−	27.2279i	0.516871	−	0.895247i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	5.70797	−	9.88650i	0.187273	−	0.324366i	−0.757067	−	0.653337i	$-0.773369\pi$
$929$	5.70797	−	9.88650i	0.187273	−	0.324366i	0.944340	+	0.328971i	$0.106702\pi$
$930$		0			0
$931$	−19.8106	−	34.3130i	−0.649267	−	1.12456i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−9.94138			−0.325118
$936$		0			0
$937$	16.1486			0.527552			0.263776	−	0.964584i	$-0.415032\pi$
$937$	16.1486			0.527552			0.263776	+	0.964584i	$0.415032\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	19.4028	+	33.6066i	0.632512	+	1.09554i	0.987036	+	0.160496i	$0.0513095\pi$
$941$	19.4028	+	33.6066i	0.632512	+	1.09554i	−0.354524	+	0.935047i	$0.615357\pi$
$942$		0			0
$943$	−4.60816	+	7.98157i	−0.150062	+	0.259916i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	30.3083	−	52.4956i	0.984889	−	1.70588i	0.342459	−	0.939533i	$-0.388740\pi$
$947$	30.3083	−	52.4956i	0.984889	−	1.70588i	0.642429	−	0.766345i	$-0.277927\pi$
$948$		0			0
$949$	−3.48705	−	6.03975i	−0.113195	−	0.196059i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	33.7474			1.09318			0.546592	−	0.837399i	$-0.315925\pi$
$953$	33.7474			1.09318			0.546592	+	0.837399i	$0.315925\pi$
$954$		0			0
$955$	32.1401			1.04003
$956$		0			0
$957$		0			0
$958$		0			0
$959$	39.0913	+	67.7081i	1.26232	+	2.18641i
$960$		0			0
$961$	−2.36909	+	4.10339i	−0.0764224	+	0.132367i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	13.5925	−	23.5430i	0.437559	−	0.757874i
$966$		0			0
$967$	22.2027	+	38.4562i	0.713991	+	1.23667i	0.963347	+	0.268257i	$0.0864476\pi$
$967$	22.2027	+	38.4562i	0.713991	+	1.23667i	−0.249356	+	0.968412i	$0.580219\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9.82990			−0.315456			−0.157728	−	0.987483i	$-0.550417\pi$
$971$	−9.82990			−0.315456			−0.157728	+	0.987483i	$0.550417\pi$
$972$		0			0
$973$	−104.148			−3.33885
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.36248	−	12.7522i	−0.235547	−	0.407979i	0.723885	−	0.689921i	$-0.242355\pi$
$977$	−7.36248	−	12.7522i	−0.235547	−	0.407979i	−0.959431	+	0.281942i	$0.909021\pi$
$978$		0			0
$979$	−3.67659	+	6.36804i	−0.117504	+	0.203523i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	23.8918	−	41.3818i	0.762030	−	1.31987i	−0.179773	−	0.983708i	$-0.557536\pi$
$983$	23.8918	−	41.3818i	0.762030	−	1.31987i	0.941803	−	0.336166i	$-0.109130\pi$
$984$		0			0
$985$	−0.856591	−	1.48366i	−0.0272933	−	0.0472733i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.02394			0.159752
$990$		0			0
$991$	39.1838			1.24471			0.622357	−	0.782733i	$-0.286175\pi$
$991$	39.1838			1.24471			0.622357	+	0.782733i	$0.286175\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−9.32296	−	16.1478i	−0.295558	−	0.511921i
$996$		0			0
$997$	12.2299	−	21.1828i	0.387324	−	0.670866i	−0.604764	−	0.796405i	$-0.706733\pi$
$997$	12.2299	−	21.1828i	0.387324	−	0.670866i	0.992089	+	0.125539i	$0.0400660\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3564.2.i.t.1189.2		12
3.2	odd	2		3564.2.i.s.1189.5		12
9.2	odd	6		3564.2.a.p.1.2	yes	6
9.4	even	3	inner	3564.2.i.t.2377.2		12
9.5	odd	6		3564.2.i.s.2377.5		12
9.7	even	3		3564.2.a.o.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3564.2.a.o.1.5	✓	6	9.7	even	3
3564.2.a.p.1.2	yes	6	9.2	odd	6
3564.2.i.s.1189.5		12	3.2	odd	2
3564.2.i.s.2377.5		12	9.5	odd	6
3564.2.i.t.1189.2		12	1.1	even	1	trivial
3564.2.i.t.2377.2		12	9.4	even	3	inner

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:	\( N \)	\(=\)	\( 3564 = 2^{2} \cdot 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3564.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.665179 - 1.15212i) q^{5} +(2.41905 - 4.18992i) q^{7} +O(q^{10})\)	\(q+(-0.665179 - 1.15212i) q^{5} +(2.41905 - 4.18992i) q^{7} +(0.500000 - 0.866025i) q^{11} +(0.299154 + 0.518150i) q^{13} +7.47271 q^{17} +2.41487 q^{19} +(0.764279 + 1.32377i) q^{23} +(1.61507 - 2.79739i) q^{25} +(-1.43428 + 2.48425i) q^{29} +(2.98907 + 5.17722i) q^{31} -6.43641 q^{35} +9.73332 q^{37} +(3.01471 + 5.22163i) q^{41} +(1.64336 - 2.84638i) q^{43} +(-2.30866 + 3.99872i) q^{47} +(-8.20360 - 14.2091i) q^{49} -4.59097 q^{53} -1.33036 q^{55} +(4.74346 + 8.21592i) q^{59} +(4.73320 - 8.19815i) q^{61} +(0.397982 - 0.689325i) q^{65} +(1.25043 + 2.16581i) q^{67} +0.142348 q^{71} -11.6564 q^{73} +(-2.41905 - 4.18992i) q^{77} +(0.309059 - 0.535306i) q^{79} +(7.04948 - 12.2101i) q^{83} +(-4.97069 - 8.60949i) q^{85} -7.35318 q^{89} +2.89467 q^{91} +(-1.60632 - 2.78223i) q^{95} +(1.33724 - 2.31616i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{7}+O(q^{10}) \) 12 * q + 2 * q^7	\( 12 q + 2 q^{7} + 6 q^{11} + 6 q^{13} - 8 q^{17} + 4 q^{23} - 10 q^{25} - 4 q^{29} - 6 q^{31} - 28 q^{35} - 12 q^{37} + 22 q^{41} + 10 q^{43} + 20 q^{47} - 6 q^{49} - 8 q^{53} + 24 q^{59} + 10 q^{61} + 40 q^{65} + 6 q^{67} - 80 q^{71} - 16 q^{73} - 2 q^{77} + 14 q^{79} + 12 q^{83} - 6 q^{85} - 48 q^{89} + 20 q^{91} + 44 q^{95} - 20 q^{97}+O(q^{100}) \) 12 * q + 2 * q^7 + 6 * q^11 + 6 * q^13 - 8 * q^17 + 4 * q^23 - 10 * q^25 - 4 * q^29 - 6 * q^31 - 28 * q^35 - 12 * q^37 + 22 * q^41 + 10 * q^43 + 20 * q^47 - 6 * q^49 - 8 * q^53 + 24 * q^59 + 10 * q^61 + 40 * q^65 + 6 * q^67 - 80 * q^71 - 16 * q^73 - 2 * q^77 + 14 * q^79 + 12 * q^83 - 6 * q^85 - 48 * q^89 + 20 * q^91 + 44 * q^95 - 20 * q^97

Introduction

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