LMFDB - Embedded newform 2646.2.f.q.883.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(883,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("2646.883");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.f (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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			883.2
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	2646.883
Dual form			2646.2.f.q.1765.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.258819 - 0.448288i) q^{5} +1.00000 q^{8} +0.517638 q^{10} +(-0.732051 + 1.26795i) q^{11} +(-1.22474 - 2.12132i) q^{13} +(-0.500000 + 0.866025i) q^{16} -3.48477 q^{17} -0.517638 q^{19} +(-0.258819 + 0.448288i) q^{20} +(-0.732051 - 1.26795i) q^{22} +(3.96410 + 6.86603i) q^{23} +(2.36603 - 4.09808i) q^{25} +2.44949 q^{26} +(1.36603 - 2.36603i) q^{29} +(3.67423 + 6.36396i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.74238 - 3.01790i) q^{34} -8.00000 q^{37} +(0.258819 - 0.448288i) q^{38} +(-0.258819 - 0.448288i) q^{40} +(-2.82843 - 4.89898i) q^{41} +(6.09808 - 10.5622i) q^{43} +1.46410 q^{44} -7.92820 q^{46} +(2.31079 - 4.00240i) q^{47} +(2.36603 + 4.09808i) q^{50} +(-1.22474 + 2.12132i) q^{52} -6.73205 q^{53} +0.757875 q^{55} +(1.36603 + 2.36603i) q^{58} +(-7.39924 - 12.8159i) q^{59} +(2.19067 - 3.79435i) q^{61} -7.34847 q^{62} +1.00000 q^{64} +(-0.633975 + 1.09808i) q^{65} +(1.90192 + 3.29423i) q^{67} +(1.74238 + 3.01790i) q^{68} +0.803848 q^{71} -4.62158 q^{73} +(4.00000 - 6.92820i) q^{74} +(0.258819 + 0.448288i) q^{76} +(-7.06218 + 12.2321i) q^{79} +0.517638 q^{80} +5.65685 q^{82} +(4.94975 - 8.57321i) q^{83} +(0.901924 + 1.56218i) q^{85} +(6.09808 + 10.5622i) q^{86} +(-0.732051 + 1.26795i) q^{88} -16.1112 q^{89} +(3.96410 - 6.86603i) q^{92} +(2.31079 + 4.00240i) q^{94} +(0.133975 + 0.232051i) q^{95} +(-0.517638 + 0.896575i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 8 q^{11} - 4 q^{16} + 8 q^{22} + 4 q^{23} + 12 q^{25} + 4 q^{29} - 4 q^{32} - 64 q^{37} + 28 q^{43} - 16 q^{44} - 8 q^{46} + 12 q^{50} - 40 q^{53} + 4 q^{58} + 8 q^{64}+ \cdots + 8 q^{95}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 + 8 * q^11 - 4 * q^16 + 8 * q^22 + 4 * q^23 + 12 * q^25 + 4 * q^29 - 4 * q^32 - 64 * q^37 + 28 * q^43 - 16 * q^44 - 8 * q^46 + 12 * q^50 - 40 * q^53 + 4 * q^58 + 8 * q^64 - 12 * q^65 + 36 * q^67 + 48 * q^71 + 32 * q^74 - 8 * q^79 + 28 * q^85 + 28 * q^86 + 8 * q^88 + 4 * q^92 + 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.258819	−	0.448288i	−0.115747	−	0.200480i	0.802331	−	0.596880i	$-0.203593\pi$
$5$	−0.258819	−	0.448288i	−0.115747	−	0.200480i	−0.918078	+	0.396399i	$0.870260\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	0.517638			0.163692
$11$	−0.732051	+	1.26795i	−0.220722	+	0.382301i	−0.955027	−	0.296518i	$-0.904175\pi$
$11$	−0.732051	+	1.26795i	−0.220722	+	0.382301i	0.734306	+	0.678819i	$0.237508\pi$
$12$		0			0
$13$	−1.22474	−	2.12132i	−0.339683	−	0.588348i	0.644690	−	0.764444i	$-0.276986\pi$
$13$	−1.22474	−	2.12132i	−0.339683	−	0.588348i	−0.984373	+	0.176096i	$0.943653\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.48477			−0.845180			−0.422590	−	0.906321i	$-0.638879\pi$
$17$	−3.48477			−0.845180			−0.422590	+	0.906321i	$0.638879\pi$
$18$		0			0
$19$	−0.517638			−0.118754			−0.0593772	−	0.998236i	$-0.518911\pi$
$19$	−0.517638			−0.118754			−0.0593772	+	0.998236i	$0.518911\pi$
$20$	−0.258819	+	0.448288i	−0.0578737	+	0.100240i
$21$		0			0
$22$	−0.732051	−	1.26795i	−0.156074	−	0.270328i
$23$	3.96410	+	6.86603i	0.826572	+	1.43167i	0.900712	+	0.434417i	$0.143046\pi$
$23$	3.96410	+	6.86603i	0.826572	+	1.43167i	−0.0741394	+	0.997248i	$0.523621\pi$
$24$		0			0
$25$	2.36603	−	4.09808i	0.473205	−	0.819615i
$26$	2.44949			0.480384
$27$		0			0
$28$		0			0
$29$	1.36603	−	2.36603i	0.253665	−	0.439360i	−0.710867	−	0.703326i	$-0.751697\pi$
$29$	1.36603	−	2.36603i	0.253665	−	0.439360i	0.964532	+	0.263966i	$0.0850307\pi$
$30$		0			0
$31$	3.67423	+	6.36396i	0.659912	+	1.14300i	0.980638	+	0.195829i	$0.0627398\pi$
$31$	3.67423	+	6.36396i	0.659912	+	1.14300i	−0.320726	+	0.947172i	$0.603927\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	1.74238	−	3.01790i	0.298816	−	0.517565i
$35$		0			0
$36$		0			0
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$	0.258819	−	0.448288i	0.0419860	−	0.0727219i
$39$		0			0
$40$	−0.258819	−	0.448288i	−0.0409229	−	0.0708805i
$41$	−2.82843	−	4.89898i	−0.441726	−	0.765092i	0.556092	−	0.831121i	$-0.312300\pi$
$41$	−2.82843	−	4.89898i	−0.441726	−	0.765092i	−0.997818	+	0.0660290i	$0.978967\pi$
$42$		0			0
$43$	6.09808	−	10.5622i	0.929948	−	1.61072i	0.146544	−	0.989204i	$-0.453185\pi$
$43$	6.09808	−	10.5622i	0.929948	−	1.61072i	0.783404	−	0.621513i	$-0.213482\pi$
$44$	1.46410			0.220722
$45$		0			0
$46$	−7.92820			−1.16895
$47$	2.31079	−	4.00240i	0.337063	−	0.583811i	−0.646816	−	0.762646i	$-0.723900\pi$
$47$	2.31079	−	4.00240i	0.337063	−	0.583811i	0.983879	+	0.178836i	$0.0572331\pi$
$48$		0			0
$49$		0			0
$50$	2.36603	+	4.09808i	0.334607	+	0.579555i
$51$		0			0
$52$	−1.22474	+	2.12132i	−0.169842	+	0.294174i
$53$	−6.73205			−0.924718			−0.462359	−	0.886693i	$-0.652997\pi$
$53$	−6.73205			−0.924718			−0.462359	+	0.886693i	$0.652997\pi$
$54$		0			0
$55$	0.757875			0.102192
$56$		0			0
$57$		0			0
$58$	1.36603	+	2.36603i	0.179368	+	0.310674i
$59$	−7.39924	−	12.8159i	−0.963299	−	1.66848i	−0.714118	−	0.700025i	$-0.753172\pi$
$59$	−7.39924	−	12.8159i	−0.963299	−	1.66848i	−0.249180	−	0.968457i	$-0.580161\pi$
$60$		0			0
$61$	2.19067	−	3.79435i	0.280487	−	0.485817i	−0.691018	−	0.722838i	$-0.742837\pi$
$61$	2.19067	−	3.79435i	0.280487	−	0.485817i	0.971505	+	0.237020i	$0.0761708\pi$
$62$	−7.34847			−0.933257
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.633975	+	1.09808i	−0.0786349	+	0.136200i
$66$		0			0
$67$	1.90192	+	3.29423i	0.232357	+	0.402454i	0.958501	−	0.285088i	$-0.0920229\pi$
$67$	1.90192	+	3.29423i	0.232357	+	0.402454i	−0.726144	+	0.687542i	$0.758690\pi$
$68$	1.74238	+	3.01790i	0.211295	+	0.365974i
$69$		0			0
$70$		0			0
$71$	0.803848			0.0953992			0.0476996	−	0.998862i	$-0.484811\pi$
$71$	0.803848			0.0953992			0.0476996	+	0.998862i	$0.484811\pi$
$72$		0			0
$73$	−4.62158			−0.540915			−0.270457	−	0.962732i	$-0.587175\pi$
$73$	−4.62158			−0.540915			−0.270457	+	0.962732i	$0.587175\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$		0			0
$76$	0.258819	+	0.448288i	0.0296886	+	0.0514221i
$77$		0			0
$78$		0			0
$79$	−7.06218	+	12.2321i	−0.794557	+	1.37621i	0.128563	+	0.991701i	$0.458964\pi$
$79$	−7.06218	+	12.2321i	−0.794557	+	1.37621i	−0.923120	+	0.384512i	$0.874370\pi$
$80$	0.517638			0.0578737
$81$		0			0
$82$	5.65685			0.624695
$83$	4.94975	−	8.57321i	0.543305	−	0.941033i	−0.455406	−	0.890284i	$-0.650506\pi$
$83$	4.94975	−	8.57321i	0.543305	−	0.941033i	0.998711	−	0.0507487i	$-0.0161607\pi$
$84$		0			0
$85$	0.901924	+	1.56218i	0.0978274	+	0.169442i
$86$	6.09808	+	10.5622i	0.657572	+	1.13895i
$87$		0			0
$88$	−0.732051	+	1.26795i	−0.0780369	+	0.135164i
$89$	−16.1112			−1.70778			−0.853889	−	0.520455i	$-0.825763\pi$
$89$	−16.1112			−1.70778			−0.853889	+	0.520455i	$0.825763\pi$
$90$		0			0
$91$		0			0
$92$	3.96410	−	6.86603i	0.413286	−	0.715833i
$93$		0			0
$94$	2.31079	+	4.00240i	0.238340	+	0.412816i
$95$	0.133975	+	0.232051i	0.0137455	+	0.0238079i
$96$		0			0
$97$	−0.517638	+	0.896575i	−0.0525582	+	0.0910334i	−0.891108	−	0.453792i	$-0.850071\pi$
$97$	−0.517638	+	0.896575i	−0.0525582	+	0.0910334i	0.838549	+	0.544826i	$0.183404\pi$
$98$		0			0
$99$		0			0
$100$	−4.73205			−0.473205
$101$	−2.89778	+	5.01910i	−0.288340	+	0.499419i	−0.973414	−	0.229055i	$-0.926437\pi$
$101$	−2.89778	+	5.01910i	−0.288340	+	0.499419i	0.685074	+	0.728474i	$0.259770\pi$
$102$		0			0
$103$	−5.60609	−	9.71003i	−0.552384	−	0.956757i	−0.998102	−	0.0615838i	$-0.980385\pi$
$103$	−5.60609	−	9.71003i	−0.552384	−	0.956757i	0.445718	−	0.895174i	$-0.352948\pi$
$104$	−1.22474	−	2.12132i	−0.120096	−	0.208013i
$105$		0			0
$106$	3.36603	−	5.83013i	0.326937	−	0.566272i
$107$	−3.07180			−0.296962			−0.148481	−	0.988915i	$-0.547438\pi$
$107$	−3.07180			−0.296962			−0.148481	+	0.988915i	$0.547438\pi$
$108$		0			0
$109$	10.5885			1.01419			0.507095	−	0.861890i	$-0.330719\pi$
$109$	10.5885			1.01419			0.507095	+	0.861890i	$0.330719\pi$
$110$	−0.378937	+	0.656339i	−0.0361303	+	0.0625794i
$111$		0			0
$112$		0			0
$113$	−7.33013	−	12.6962i	−0.689560	−	1.19435i	−0.971980	−	0.235063i	$-0.924470\pi$
$113$	−7.33013	−	12.6962i	−0.689560	−	1.19435i	0.282420	−	0.959291i	$-0.408863\pi$
$114$		0			0
$115$	2.05197	−	3.55412i	0.191347	−	0.331423i
$116$	−2.73205			−0.253665
$117$		0			0
$118$	14.7985			1.36231
$119$		0			0
$120$		0			0
$121$	4.42820	+	7.66987i	0.402564	+	0.697261i
$122$	2.19067	+	3.79435i	0.198334	+	0.343525i
$123$		0			0
$124$	3.67423	−	6.36396i	0.329956	−	0.571501i
$125$	−5.03768			−0.450584
$126$		0			0
$127$	−5.92820			−0.526043			−0.263021	−	0.964790i	$-0.584719\pi$
$127$	−5.92820			−0.526043			−0.263021	+	0.964790i	$0.584719\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.633975	−	1.09808i	−0.0556033	−	0.0963077i
$131$	−6.24384	−	10.8147i	−0.545527	−	0.944881i	−0.998574	−	0.0533937i	$-0.982996\pi$
$131$	−6.24384	−	10.8147i	−0.545527	−	0.944881i	0.453046	−	0.891487i	$-0.350337\pi$
$132$		0			0
$133$		0			0
$134$	−3.80385			−0.328602
$135$		0			0
$136$	−3.48477			−0.298816
$137$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$137$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$138$		0			0
$139$	−10.1075	−	17.5068i	−0.857311	−	1.48491i	−0.874485	−	0.485053i	$-0.838800\pi$
$139$	−10.1075	−	17.5068i	−0.857311	−	1.48491i	0.0171736	−	0.999853i	$-0.494533\pi$
$140$		0			0
$141$		0			0
$142$	−0.401924	+	0.696152i	−0.0337287	+	0.0584198i
$143$	3.58630			0.299902
$144$		0			0
$145$	−1.41421			−0.117444
$146$	2.31079	−	4.00240i	0.191242	−	0.331241i
$147$		0			0
$148$	4.00000	+	6.92820i	0.328798	+	0.569495i
$149$	−1.19615	−	2.07180i	−0.0979926	−	0.169728i	0.812861	−	0.582458i	$-0.197909\pi$
$149$	−1.19615	−	2.07180i	−0.0979926	−	0.169728i	−0.910854	+	0.412729i	$0.864575\pi$
$150$		0			0
$151$	8.69615	−	15.0622i	0.707683	−	1.22574i	−0.258032	−	0.966136i	$-0.583074\pi$
$151$	8.69615	−	15.0622i	0.707683	−	1.22574i	0.965715	−	0.259606i	$-0.0835928\pi$
$152$	−0.517638			−0.0419860
$153$		0			0
$154$		0			0
$155$	1.90192	−	3.29423i	0.152766	−	0.264599i
$156$		0			0
$157$	−8.64256	−	14.9694i	−0.689752	−	1.19469i	−0.971918	−	0.235320i	$-0.924386\pi$
$157$	−8.64256	−	14.9694i	−0.689752	−	1.19469i	0.282166	−	0.959366i	$-0.408947\pi$
$158$	−7.06218	−	12.2321i	−0.561837	−	0.973130i
$159$		0			0
$160$	−0.258819	+	0.448288i	−0.0204614	+	0.0354403i
$161$		0			0
$162$		0			0
$163$	−7.07180			−0.553906			−0.276953	−	0.960883i	$-0.589325\pi$
$163$	−7.07180			−0.553906			−0.276953	+	0.960883i	$0.589325\pi$
$164$	−2.82843	+	4.89898i	−0.220863	+	0.382546i
$165$		0			0
$166$	4.94975	+	8.57321i	0.384175	+	0.665410i
$167$	−6.64136	−	11.5032i	−0.513924	−	0.890143i	−0.999870	−	0.0161534i	$-0.994858\pi$
$167$	−6.64136	−	11.5032i	−0.513924	−	0.890143i	0.485945	−	0.873989i	$-0.338475\pi$
$168$		0			0
$169$	3.50000	−	6.06218i	0.269231	−	0.466321i
$170$	−1.80385			−0.138349
$171$		0			0
$172$	−12.1962			−0.929948
$173$	9.71003	−	16.8183i	0.738240	−	1.27867i	−0.215048	−	0.976604i	$-0.568991\pi$
$173$	9.71003	−	16.8183i	0.738240	−	1.27867i	0.953287	−	0.302065i	$-0.0976760\pi$
$174$		0			0
$175$		0			0
$176$	−0.732051	−	1.26795i	−0.0551804	−	0.0955753i
$177$		0			0
$178$	8.05558	−	13.9527i	0.603791	−	1.04580i
$179$	8.19615			0.612609			0.306305	−	0.951934i	$-0.400907\pi$
$179$	8.19615			0.612609			0.306305	+	0.951934i	$0.400907\pi$
$180$		0			0
$181$	20.9730			1.55891			0.779454	−	0.626459i	$-0.215497\pi$
$181$	20.9730			1.55891			0.779454	+	0.626459i	$0.215497\pi$
$182$		0			0
$183$		0			0
$184$	3.96410	+	6.86603i	0.292237	+	0.506170i
$185$	2.07055	+	3.58630i	0.152230	+	0.263670i
$186$		0			0
$187$	2.55103	−	4.41851i	0.186549	−	0.323113i
$188$	−4.62158			−0.337063
$189$		0			0
$190$	−0.267949			−0.0194391
$191$	−3.59808	+	6.23205i	−0.260348	+	0.450935i	−0.966334	−	0.257290i	$-0.917171\pi$
$191$	−3.59808	+	6.23205i	−0.260348	+	0.450935i	0.705987	+	0.708225i	$0.250504\pi$
$192$		0			0
$193$	11.8660	+	20.5526i	0.854135	+	1.47941i	0.877445	+	0.479677i	$0.159246\pi$
$193$	11.8660	+	20.5526i	0.854135	+	1.47941i	−0.0233098	+	0.999728i	$0.507420\pi$
$194$	−0.517638	−	0.896575i	−0.0371642	−	0.0643704i
$195$		0			0
$196$		0			0
$197$	−9.66025			−0.688265			−0.344132	−	0.938921i	$-0.611827\pi$
$197$	−9.66025			−0.688265			−0.344132	+	0.938921i	$0.611827\pi$
$198$		0			0
$199$	−11.5911			−0.821672			−0.410836	−	0.911709i	$-0.634763\pi$
$199$	−11.5911			−0.821672			−0.410836	+	0.911709i	$0.634763\pi$
$200$	2.36603	−	4.09808i	0.167303	−	0.289778i
$201$		0			0
$202$	−2.89778	−	5.01910i	−0.203887	−	0.353142i
$203$		0			0
$204$		0			0
$205$	−1.46410	+	2.53590i	−0.102257	+	0.177115i
$206$	11.2122			0.781189
$207$		0			0
$208$	2.44949			0.169842
$209$	0.378937	−	0.656339i	0.0262116	−	0.0453999i
$210$		0			0
$211$	−0.633975	−	1.09808i	−0.0436446	−	0.0755947i	0.843378	−	0.537321i	$-0.180564\pi$
$211$	−0.633975	−	1.09808i	−0.0436446	−	0.0755947i	−0.887022	+	0.461726i	$0.847230\pi$
$212$	3.36603	+	5.83013i	0.231180	+	0.400415i
$213$		0			0
$214$	1.53590	−	2.66025i	0.104992	−	0.181851i
$215$	−6.31319			−0.430556
$216$		0			0
$217$		0			0
$218$	−5.29423	+	9.16987i	−0.358570	+	0.621062i
$219$		0			0
$220$	−0.378937	−	0.656339i	−0.0255480	−	0.0442504i
$221$	4.26795	+	7.39230i	0.287093	+	0.497260i
$222$		0			0
$223$	1.88108	−	3.25813i	0.125967	−	0.218181i	−0.796144	−	0.605108i	$-0.793130\pi$
$223$	1.88108	−	3.25813i	0.125967	−	0.218181i	0.922110	+	0.386927i	$0.126463\pi$
$224$		0			0
$225$		0			0
$226$	14.6603			0.975186
$227$	−1.67303	+	2.89778i	−0.111043	+	0.192332i	−0.916191	−	0.400742i	$-0.868752\pi$
$227$	−1.67303	+	2.89778i	−0.111043	+	0.192332i	0.805148	+	0.593074i	$0.202086\pi$
$228$		0			0
$229$	6.90018	+	11.9515i	0.455977	+	0.789775i	0.998744	−	0.0501083i	$-0.0159567\pi$
$229$	6.90018	+	11.9515i	0.455977	+	0.789775i	−0.542767	+	0.839883i	$0.682623\pi$
$230$	2.05197	+	3.55412i	0.135303	+	0.234351i
$231$		0			0
$232$	1.36603	−	2.36603i	0.0896840	−	0.155337i
$233$	−1.39230			−0.0912129			−0.0456065	−	0.998959i	$-0.514522\pi$
$233$	−1.39230			−0.0912129			−0.0456065	+	0.998959i	$0.514522\pi$
$234$		0			0
$235$	−2.39230			−0.156057
$236$	−7.39924	+	12.8159i	−0.481649	+	0.834241i
$237$		0			0
$238$		0			0
$239$	−6.23205	−	10.7942i	−0.403118	−	0.698221i	0.590983	−	0.806684i	$-0.298740\pi$
$239$	−6.23205	−	10.7942i	−0.403118	−	0.698221i	−0.994100	+	0.108464i	$0.965407\pi$
$240$		0			0
$241$	6.36396	−	11.0227i	0.409939	−	0.710035i	−0.584944	−	0.811074i	$-0.698883\pi$
$241$	6.36396	−	11.0227i	0.409939	−	0.710035i	0.994882	+	0.101039i	$0.0322167\pi$
$242$	−8.85641			−0.569311
$243$		0			0
$244$	−4.38134			−0.280487
$245$		0			0
$246$		0			0
$247$	0.633975	+	1.09808i	0.0403388	+	0.0698689i
$248$	3.67423	+	6.36396i	0.233314	+	0.404112i
$249$		0			0
$250$	2.51884	−	4.36276i	0.159305	−	0.275925i
$251$	−0.517638			−0.0326730			−0.0163365	−	0.999867i	$-0.505200\pi$
$251$	−0.517638			−0.0326730			−0.0163365	+	0.999867i	$0.505200\pi$
$252$		0			0
$253$	−11.6077			−0.729770
$254$	2.96410	−	5.13397i	0.185984	−	0.322134i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.88108	−	3.25813i	−0.117339	−	0.203237i	0.801373	−	0.598164i	$-0.204103\pi$
$257$	−1.88108	−	3.25813i	−0.117339	−	0.203237i	−0.918712	+	0.394928i	$0.870770\pi$
$258$		0			0
$259$		0			0
$260$	1.26795			0.0786349
$261$		0			0
$262$	12.4877			0.771492
$263$	1.33013	−	2.30385i	0.0820191	−	0.142061i	−0.822098	−	0.569346i	$-0.807196\pi$
$263$	1.33013	−	2.30385i	0.0820191	−	0.142061i	0.904117	+	0.427285i	$0.140530\pi$
$264$		0			0
$265$	1.74238	+	3.01790i	0.107034	+	0.185388i
$266$		0			0
$267$		0			0
$268$	1.90192	−	3.29423i	0.116178	−	0.201227i
$269$	26.9072			1.64056			0.820281	−	0.571961i	$-0.193817\pi$
$269$	26.9072			1.64056			0.820281	+	0.571961i	$0.193817\pi$
$270$		0			0
$271$	−14.7985			−0.898943			−0.449472	−	0.893295i	$-0.648388\pi$
$271$	−14.7985			−0.898943			−0.449472	+	0.893295i	$0.648388\pi$
$272$	1.74238	−	3.01790i	0.105647	−	0.182987i
$273$		0			0
$274$		0			0
$275$	3.46410	+	6.00000i	0.208893	+	0.361814i
$276$		0			0
$277$	8.09808	−	14.0263i	0.486566	−	0.842757i	−0.513315	−	0.858201i	$-0.671583\pi$
$277$	8.09808	−	14.0263i	0.486566	−	0.842757i	0.999881	+	0.0154431i	$0.00491589\pi$
$278$	20.2151			1.21242
$279$		0			0
$280$		0			0
$281$	−8.69615	+	15.0622i	−0.518769	+	0.898534i	0.480993	+	0.876724i	$0.340276\pi$
$281$	−8.69615	+	15.0622i	−0.518769	+	0.898534i	−0.999762	+	0.0218099i	$0.993057\pi$
$282$		0			0
$283$	4.88040	+	8.45310i	0.290109	+	0.502484i	0.973835	−	0.227255i	$-0.0729749\pi$
$283$	4.88040	+	8.45310i	0.290109	+	0.502484i	−0.683726	+	0.729739i	$0.739642\pi$
$284$	−0.401924	−	0.696152i	−0.0238498	−	0.0413090i
$285$		0			0
$286$	−1.79315	+	3.10583i	−0.106031	+	0.183651i
$287$		0			0
$288$		0			0
$289$	−4.85641			−0.285671
$290$	0.707107	−	1.22474i	0.0415227	−	0.0719195i
$291$		0			0
$292$	2.31079	+	4.00240i	0.135229	+	0.234223i
$293$	1.48356	+	2.56961i	0.0866707	+	0.150118i	0.906102	−	0.423059i	$-0.139044\pi$
$293$	1.48356	+	2.56961i	0.0866707	+	0.150118i	−0.819431	+	0.573178i	$0.805711\pi$
$294$		0			0
$295$	−3.83013	+	6.63397i	−0.222999	+	0.386245i
$296$	−8.00000			−0.464991
$297$		0			0
$298$	2.39230			0.138582
$299$	9.71003	−	16.8183i	0.561545	−	0.972625i
$300$		0			0
$301$		0			0
$302$	8.69615	+	15.0622i	0.500407	+	0.866731i
$303$		0			0
$304$	0.258819	−	0.448288i	0.0148443	−	0.0257111i
$305$	−2.26795			−0.129862
$306$		0			0
$307$	11.9329			0.681046			0.340523	−	0.940236i	$-0.389396\pi$
$307$	11.9329			0.681046			0.340523	+	0.940236i	$0.389396\pi$
$308$		0			0
$309$		0			0
$310$	1.90192	+	3.29423i	0.108022	+	0.187100i
$311$	−9.09085	−	15.7458i	−0.515495	−	0.892863i	−0.999838	−	0.0179854i	$-0.994275\pi$
$311$	−9.09085	−	15.7458i	−0.515495	−	0.892863i	0.484343	−	0.874878i	$-0.339059\pi$
$312$		0			0
$313$	−3.34607	+	5.79555i	−0.189131	+	0.327584i	−0.944961	−	0.327184i	$-0.893900\pi$
$313$	−3.34607	+	5.79555i	−0.189131	+	0.327584i	0.755830	+	0.654768i	$0.227234\pi$
$314$	17.2851			0.975456
$315$		0			0
$316$	14.1244			0.794557
$317$	16.2942	−	28.2224i	0.915175	−	1.58513i	0.108530	−	0.994093i	$-0.465386\pi$
$317$	16.2942	−	28.2224i	0.915175	−	1.58513i	0.806645	−	0.591037i	$-0.201281\pi$
$318$		0			0
$319$	2.00000	+	3.46410i	0.111979	+	0.193952i
$320$	−0.258819	−	0.448288i	−0.0144684	−	0.0250600i
$321$		0			0
$322$		0			0
$323$	1.80385			0.100369
$324$		0			0
$325$	−11.5911			−0.642959
$326$	3.53590	−	6.12436i	0.195835	−	0.339197i
$327$		0			0
$328$	−2.82843	−	4.89898i	−0.156174	−	0.270501i
$329$		0			0
$330$		0			0
$331$	6.02628	−	10.4378i	0.331234	−	0.573715i	−0.651520	−	0.758632i	$-0.725868\pi$
$331$	6.02628	−	10.4378i	0.331234	−	0.573715i	0.982754	+	0.184917i	$0.0592016\pi$
$332$	−9.89949			−0.543305
$333$		0			0
$334$	13.2827			0.726798
$335$	0.984508	−	1.70522i	0.0537894	−	0.0931660i
$336$		0			0
$337$	10.6603	+	18.4641i	0.580701	+	1.00580i	0.995396	+	0.0958434i	$0.0305548\pi$
$337$	10.6603	+	18.4641i	0.580701	+	1.00580i	−0.414695	+	0.909960i	$0.636112\pi$
$338$	3.50000	+	6.06218i	0.190375	+	0.329739i
$339$		0			0
$340$	0.901924	−	1.56218i	0.0489137	−	0.0847210i
$341$	−10.7589			−0.582627
$342$		0			0
$343$		0			0
$344$	6.09808	−	10.5622i	0.328786	−	0.569474i
$345$		0			0
$346$	9.71003	+	16.8183i	0.522014	+	0.904155i
$347$	10.8564	+	18.8038i	0.582802	+	1.00944i	0.995145	+	0.0984148i	$0.0313772\pi$
$347$	10.8564	+	18.8038i	0.582802	+	1.00944i	−0.412343	+	0.911029i	$0.635289\pi$
$348$		0			0
$349$	−17.2987	+	29.9623i	−0.925980	+	1.60384i	−0.136002	+	0.990709i	$0.543425\pi$
$349$	−17.2987	+	29.9623i	−0.925980	+	1.60384i	−0.789978	+	0.613136i	$0.789908\pi$
$350$		0			0
$351$		0			0
$352$	1.46410			0.0780369
$353$	−0.0507680	+	0.0879327i	−0.00270211	+	0.00468019i	−0.867373	−	0.497658i	$-0.834193\pi$
$353$	−0.0507680	+	0.0879327i	−0.00270211	+	0.00468019i	0.864671	+	0.502338i	$0.167527\pi$
$354$		0			0
$355$	−0.208051	−	0.360355i	−0.0110422	−	0.0191257i
$356$	8.05558	+	13.9527i	0.426945	+	0.739490i
$357$		0			0
$358$	−4.09808	+	7.09808i	−0.216590	+	0.375145i
$359$	13.9282			0.735102			0.367551	−	0.930003i	$-0.380196\pi$
$359$	13.9282			0.735102			0.367551	+	0.930003i	$0.380196\pi$
$360$		0			0
$361$	−18.7321			−0.985897
$362$	−10.4865	+	18.1631i	−0.551157	+	0.954632i
$363$		0			0
$364$		0			0
$365$	1.19615	+	2.07180i	0.0626095	+	0.108443i
$366$		0			0
$367$	−0.138701	+	0.240237i	−0.00724012	+	0.0125403i	−0.869623	−	0.493717i	$-0.835638\pi$
$367$	−0.138701	+	0.240237i	−0.00724012	+	0.0125403i	0.862383	+	0.506257i	$0.168971\pi$
$368$	−7.92820			−0.413286
$369$		0			0
$370$	−4.14110			−0.215286
$371$		0			0
$372$		0			0
$373$	−9.56218	−	16.5622i	−0.495111	−	0.857557i	0.504873	−	0.863193i	$-0.331539\pi$
$373$	−9.56218	−	16.5622i	−0.495111	−	0.857557i	−0.999984	+	0.00563639i	$0.998206\pi$
$374$	2.55103	+	4.41851i	0.131910	+	0.228476i
$375$		0			0
$376$	2.31079	−	4.00240i	0.119170	−	0.206408i
$377$	−6.69213			−0.344662
$378$		0			0
$379$	−27.5167			−1.41344			−0.706718	−	0.707495i	$-0.749825\pi$
$379$	−27.5167			−1.41344			−0.706718	+	0.707495i	$0.749825\pi$
$380$	0.133975	−	0.232051i	0.00687275	−	0.0119040i
$381$		0			0
$382$	−3.59808	−	6.23205i	−0.184094	−	0.318859i
$383$	17.1093	+	29.6341i	0.874243	+	1.51423i	0.857567	+	0.514372i	$0.171975\pi$
$383$	17.1093	+	29.6341i	0.874243	+	1.51423i	0.0166751	+	0.999861i	$0.494692\pi$
$384$		0			0
$385$		0			0
$386$	−23.7321			−1.20793
$387$		0			0
$388$	1.03528			0.0525582
$389$	−2.43782	+	4.22243i	−0.123602	+	0.214086i	−0.921186	−	0.389123i	$-0.872778\pi$
$389$	−2.43782	+	4.22243i	−0.123602	+	0.214086i	0.797583	+	0.603209i	$0.206111\pi$
$390$		0			0
$391$	−13.8140	−	23.9265i	−0.698602	−	1.21001i
$392$		0			0
$393$		0			0
$394$	4.83013	−	8.36603i	0.243338	−	0.421474i
$395$	7.31130			0.367872
$396$		0			0
$397$	−26.3896			−1.32446			−0.662228	−	0.749303i	$-0.730389\pi$
$397$	−26.3896			−1.32446			−0.662228	+	0.749303i	$0.730389\pi$
$398$	5.79555	−	10.0382i	0.290505	−	0.503169i
$399$		0			0
$400$	2.36603	+	4.09808i	0.118301	+	0.204904i
$401$	−12.5263	−	21.6962i	−0.625533	−	1.08345i	−0.988438	−	0.151628i	$-0.951548\pi$
$401$	−12.5263	−	21.6962i	−0.625533	−	1.08345i	0.362905	−	0.931826i	$-0.381785\pi$
$402$		0			0
$403$	9.00000	−	15.5885i	0.448322	−	0.776516i
$404$	5.79555			0.288340
$405$		0			0
$406$		0			0
$407$	5.85641	−	10.1436i	0.290291	−	0.502799i
$408$		0			0
$409$	8.90138	+	15.4176i	0.440145	+	0.762354i	0.997700	−	0.0677865i	$-0.0215937\pi$
$409$	8.90138	+	15.4176i	0.440145	+	0.762354i	−0.557555	+	0.830140i	$0.688260\pi$
$410$	−1.46410	−	2.53590i	−0.0723068	−	0.125239i
$411$		0			0
$412$	−5.60609	+	9.71003i	−0.276192	+	0.478379i
$413$		0			0
$414$		0			0
$415$	−5.12436			−0.251545
$416$	−1.22474	+	2.12132i	−0.0600481	+	0.104006i
$417$		0			0
$418$	0.378937	+	0.656339i	0.0185344	+	0.0321026i
$419$	11.3323	+	19.6281i	0.553619	+	0.958896i	0.998010	+	0.0630626i	$0.0200868\pi$
$419$	11.3323	+	19.6281i	0.553619	+	0.958896i	−0.444391	+	0.895833i	$0.646580\pi$
$420$		0			0
$421$	−14.0263	+	24.2942i	−0.683599	+	1.18403i	0.290276	+	0.956943i	$0.406253\pi$
$421$	−14.0263	+	24.2942i	−0.683599	+	1.18403i	−0.973875	+	0.227085i	$0.927080\pi$
$422$	1.26795			0.0617228
$423$		0			0
$424$	−6.73205			−0.326937
$425$	−8.24504	+	14.2808i	−0.399943	+	0.692722i
$426$		0			0
$427$		0			0
$428$	1.53590	+	2.66025i	0.0742405	+	0.128588i
$429$		0			0
$430$	3.15660	−	5.46739i	0.152225	−	0.263661i
$431$	26.7846			1.29017			0.645085	−	0.764111i	$-0.276822\pi$
$431$	26.7846			1.29017			0.645085	+	0.764111i	$0.276822\pi$
$432$		0			0
$433$	20.2523			0.973261			0.486631	−	0.873608i	$-0.338226\pi$
$433$	20.2523			0.973261			0.486631	+	0.873608i	$0.338226\pi$
$434$		0			0
$435$		0			0
$436$	−5.29423	−	9.16987i	−0.253548	−	0.439157i
$437$	−2.05197	−	3.55412i	−0.0981590	−	0.170016i
$438$		0			0
$439$	9.14162	−	15.8338i	0.436306	−	0.755704i	−0.561095	−	0.827751i	$-0.689620\pi$
$439$	9.14162	−	15.8338i	0.436306	−	0.755704i	0.997401	+	0.0720474i	$0.0229533\pi$
$440$	0.757875			0.0361303
$441$		0			0
$442$	−8.53590			−0.406011
$443$	−18.4904	+	32.0263i	−0.878505	+	1.52161i	−0.0255224	+	0.999674i	$0.508125\pi$
$443$	−18.4904	+	32.0263i	−0.878505	+	1.52161i	−0.852982	+	0.521940i	$0.825208\pi$
$444$		0			0
$445$	4.16987	+	7.22243i	0.197671	+	0.342376i
$446$	1.88108	+	3.25813i	0.0890719	+	0.154277i
$447$		0			0
$448$		0			0
$449$	23.7846			1.12247			0.561233	−	0.827658i	$-0.310327\pi$
$449$	23.7846			1.12247			0.561233	+	0.827658i	$0.310327\pi$
$450$		0			0
$451$	8.28221			0.389994
$452$	−7.33013	+	12.6962i	−0.344780	+	0.597177i
$453$		0			0
$454$	−1.67303	−	2.89778i	−0.0785193	−	0.135999i
$455$		0			0
$456$		0			0
$457$	11.1340	−	19.2846i	0.520825	−	0.902096i	−0.478881	−	0.877880i	$-0.658958\pi$
$457$	11.1340	−	19.2846i	0.520825	−	0.902096i	0.999707	−	0.0242164i	$-0.00770906\pi$
$458$	−13.8004			−0.644849
$459$		0			0
$460$	−4.10394			−0.191347
$461$	−19.4894	+	33.7566i	−0.907712	+	1.57220i	−0.0904771	+	0.995899i	$0.528839\pi$
$461$	−19.4894	+	33.7566i	−0.907712	+	1.57220i	−0.817235	+	0.576305i	$0.804494\pi$
$462$		0			0
$463$	−3.33013	−	5.76795i	−0.154764	−	0.268059i	0.778209	−	0.628005i	$-0.216128\pi$
$463$	−3.33013	−	5.76795i	−0.154764	−	0.268059i	−0.932973	+	0.359946i	$0.882795\pi$
$464$	1.36603	+	2.36603i	0.0634161	+	0.109840i
$465$		0			0
$466$	0.696152	−	1.20577i	0.0322486	−	0.0558563i
$467$	24.5964			1.13819			0.569094	−	0.822273i	$-0.307294\pi$
$467$	24.5964			1.13819			0.569094	+	0.822273i	$0.307294\pi$
$468$		0			0
$469$		0			0
$470$	1.19615	−	2.07180i	0.0551744	−	0.0955649i
$471$		0			0
$472$	−7.39924	−	12.8159i	−0.340577	−	0.589898i
$473$	8.92820	+	15.4641i	0.410519	+	0.711040i
$474$		0			0
$475$	−1.22474	+	2.12132i	−0.0561951	+	0.0973329i
$476$		0			0
$477$		0			0
$478$	12.4641			0.570095
$479$	6.64136	−	11.5032i	0.303452	−	0.525594i	−0.673464	−	0.739220i	$-0.735194\pi$
$479$	6.64136	−	11.5032i	0.303452	−	0.525594i	0.976915	+	0.213627i	$0.0685276\pi$
$480$		0			0
$481$	9.79796	+	16.9706i	0.446748	+	0.773791i
$482$	6.36396	+	11.0227i	0.289870	+	0.502070i
$483$		0			0
$484$	4.42820	−	7.66987i	0.201282	−	0.348631i
$485$	0.535898			0.0243339
$486$		0			0
$487$	−32.3205			−1.46458			−0.732291	−	0.680992i	$-0.761549\pi$
$487$	−32.3205			−1.46458			−0.732291	+	0.680992i	$0.761549\pi$
$488$	2.19067	−	3.79435i	0.0991670	−	0.171762i
$489$		0			0
$490$		0			0
$491$	−2.53590	−	4.39230i	−0.114443	−	0.198222i	0.803114	−	0.595826i	$-0.203175\pi$
$491$	−2.53590	−	4.39230i	−0.114443	−	0.198222i	−0.917557	+	0.397604i	$0.869842\pi$
$492$		0			0
$493$	−4.76028	+	8.24504i	−0.214392	+	0.371338i
$494$	−1.26795			−0.0570477
$495$		0			0
$496$	−7.34847			−0.329956
$497$		0			0
$498$		0			0
$499$	−3.66025	−	6.33975i	−0.163855	−	0.283806i	0.772393	−	0.635145i	$-0.219060\pi$
$499$	−3.66025	−	6.33975i	−0.163855	−	0.283806i	−0.936248	+	0.351339i	$0.885726\pi$
$500$	2.51884	+	4.36276i	0.112646	+	0.195109i
$501$		0			0
$502$	0.258819	−	0.448288i	0.0115517	−	0.0200081i
$503$	28.9406			1.29040			0.645199	−	0.764015i	$-0.276774\pi$
$503$	28.9406			1.29040			0.645199	+	0.764015i	$0.276774\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$	5.80385	−	10.0526i	0.258012	−	0.446891i
$507$		0			0
$508$	2.96410	+	5.13397i	0.131511	+	0.227783i
$509$	3.81294	+	6.60420i	0.169005	+	0.292726i	0.938070	−	0.346445i	$-0.112611\pi$
$509$	3.81294	+	6.60420i	0.169005	+	0.292726i	−0.769065	+	0.639171i	$0.779278\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	3.76217			0.165942
$515$	−2.90192	+	5.02628i	−0.127874	+	0.221484i
$516$		0			0
$517$	3.38323	+	5.85993i	0.148794	+	0.257719i
$518$		0			0
$519$		0			0
$520$	−0.633975	+	1.09808i	−0.0278016	+	0.0481538i
$521$	−32.5269			−1.42503			−0.712515	−	0.701657i	$-0.752444\pi$
$521$	−32.5269			−1.42503			−0.712515	+	0.701657i	$0.752444\pi$
$522$		0			0
$523$	−39.2562			−1.71655			−0.858277	−	0.513187i	$-0.828465\pi$
$523$	−39.2562			−1.71655			−0.858277	+	0.513187i	$0.828465\pi$
$524$	−6.24384	+	10.8147i	−0.272764	+	0.472440i
$525$		0			0
$526$	1.33013	+	2.30385i	0.0579963	+	0.100453i
$527$	−12.8038	−	22.1769i	−0.557744	−	0.966042i
$528$		0			0
$529$	−19.9282	+	34.5167i	−0.866444	+	1.50072i
$530$	−3.48477			−0.151369
$531$		0			0
$532$		0			0
$533$	−6.92820	+	12.0000i	−0.300094	+	0.519778i
$534$		0			0
$535$	0.795040	+	1.37705i	0.0343726	+	0.0595350i
$536$	1.90192	+	3.29423i	0.0821506	+	0.142289i
$537$		0			0
$538$	−13.4536	+	23.3023i	−0.580026	+	1.00464i
$539$		0			0
$540$		0			0
$541$	20.7321			0.891340			0.445670	−	0.895197i	$-0.352965\pi$
$541$	20.7321			0.891340			0.445670	+	0.895197i	$0.352965\pi$
$542$	7.39924	−	12.8159i	0.317824	−	0.550488i
$543$		0			0
$544$	1.74238	+	3.01790i	0.0747041	+	0.129391i
$545$	−2.74049	−	4.74668i	−0.117390	−	0.203325i
$546$		0			0
$547$	5.73205	−	9.92820i	0.245085	−	0.424499i	−0.717071	−	0.697000i	$-0.754518\pi$
$547$	5.73205	−	9.92820i	0.245085	−	0.424499i	0.962155	+	0.272501i	$0.0878509\pi$
$548$		0			0
$549$		0			0
$550$	−6.92820			−0.295420
$551$	−0.707107	+	1.22474i	−0.0301238	+	0.0521759i
$552$		0			0
$553$		0			0
$554$	8.09808	+	14.0263i	0.344054	+	0.595920i
$555$		0			0
$556$	−10.1075	+	17.5068i	−0.428655	+	0.742453i
$557$	−2.87564			−0.121845			−0.0609225	−	0.998143i	$-0.519404\pi$
$557$	−2.87564			−0.121845			−0.0609225	+	0.998143i	$0.519404\pi$
$558$		0			0
$559$	−29.8744			−1.26355
$560$		0			0
$561$		0			0
$562$	−8.69615	−	15.0622i	−0.366825	−	0.635360i
$563$	0.637756	+	1.10463i	0.0268782	+	0.0465545i	0.879152	−	0.476542i	$-0.158110\pi$
$563$	0.637756	+	1.10463i	0.0268782	+	0.0465545i	−0.852273	+	0.523097i	$0.824777\pi$
$564$		0			0
$565$	−3.79435	+	6.57201i	−0.159630	+	0.276487i
$566$	−9.76079			−0.410277
$567$		0			0
$568$	0.803848			0.0337287
$569$	13.4641	−	23.3205i	0.564445	−	0.977647i	−0.432657	−	0.901559i	$-0.642424\pi$
$569$	13.4641	−	23.3205i	0.564445	−	0.977647i	0.997101	−	0.0760878i	$-0.0242429\pi$
$570$		0			0
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$	−1.79315	−	3.10583i	−0.0749754	−	0.129861i
$573$		0			0
$574$		0			0
$575$	37.5167			1.56455
$576$		0			0
$577$	−26.2880			−1.09439			−0.547193	−	0.837007i	$-0.684304\pi$
$577$	−26.2880			−1.09439			−0.547193	+	0.837007i	$0.684304\pi$
$578$	2.42820	−	4.20577i	0.101000	−	0.174937i
$579$		0			0
$580$	0.707107	+	1.22474i	0.0293610	+	0.0508548i
$581$		0			0
$582$		0			0
$583$	4.92820	−	8.53590i	0.204105	−	0.353521i
$584$	−4.62158			−0.191242
$585$		0			0
$586$	−2.96713			−0.122571
$587$	−1.76097	+	3.05008i	−0.0726828	+	0.125890i	−0.900076	−	0.435732i	$-0.856489\pi$
$587$	−1.76097	+	3.05008i	−0.0726828	+	0.125890i	0.827393	+	0.561623i	$0.189823\pi$
$588$		0			0
$589$	−1.90192	−	3.29423i	−0.0783674	−	0.135736i
$590$	−3.83013	−	6.63397i	−0.157684	−	0.273116i
$591$		0			0
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	−6.79367			−0.278982			−0.139491	−	0.990223i	$-0.544547\pi$
$593$	−6.79367			−0.278982			−0.139491	+	0.990223i	$0.544547\pi$
$594$		0			0
$595$		0			0
$596$	−1.19615	+	2.07180i	−0.0489963	+	0.0848641i
$597$		0			0
$598$	9.71003	+	16.8183i	0.397073	+	0.687750i
$599$	−6.19615	−	10.7321i	−0.253168	−	0.438500i	0.711228	−	0.702961i	$-0.248139\pi$
$599$	−6.19615	−	10.7321i	−0.253168	−	0.438500i	−0.964396	+	0.264461i	$0.914806\pi$
$600$		0			0
$601$	−20.9730	+	36.3262i	−0.855505	+	1.48178i	0.0206704	+	0.999786i	$0.493420\pi$
$601$	−20.9730	+	36.3262i	−0.855505	+	1.48178i	−0.876176	+	0.481992i	$0.839913\pi$
$602$		0			0
$603$		0			0
$604$	−17.3923			−0.707683
$605$	2.29221	−	3.97022i	0.0931915	−	0.161412i
$606$		0			0
$607$	−10.6945	−	18.5235i	−0.434078	−	0.751845i	0.563142	−	0.826360i	$-0.309592\pi$
$607$	−10.6945	−	18.5235i	−0.434078	−	0.751845i	−0.997220	+	0.0745153i	$0.976259\pi$
$608$	0.258819	+	0.448288i	0.0104965	+	0.0181805i
$609$		0			0
$610$	1.13397	−	1.96410i	0.0459133	−	0.0795241i
$611$	−11.3205			−0.457979
$612$		0			0
$613$	20.4449			0.825760			0.412880	−	0.910785i	$-0.364523\pi$
$613$	20.4449			0.825760			0.412880	+	0.910785i	$0.364523\pi$
$614$	−5.96644	+	10.3342i	−0.240786	+	0.417054i
$615$		0			0
$616$		0			0
$617$	21.1962	+	36.7128i	0.853325	+	1.47800i	0.878190	+	0.478311i	$0.158751\pi$
$617$	21.1962	+	36.7128i	0.853325	+	1.47800i	−0.0248653	+	0.999691i	$0.507916\pi$
$618$		0			0
$619$	−3.74358	+	6.48408i	−0.150467	+	0.260617i	−0.931399	−	0.363999i	$-0.881411\pi$
$619$	−3.74358	+	6.48408i	−0.150467	+	0.260617i	0.780932	+	0.624616i	$0.214745\pi$
$620$	−3.80385			−0.152766
$621$		0			0
$622$	18.1817			0.729020
$623$		0			0
$624$		0			0
$625$	−10.5263	−	18.2321i	−0.421051	−	0.729282i
$626$	−3.34607	−	5.79555i	−0.133736	−	0.231637i
$627$		0			0
$628$	−8.64256	+	14.9694i	−0.344876	+	0.597343i
$629$	27.8781			1.11157
$630$		0			0
$631$	−3.87564			−0.154287			−0.0771435	−	0.997020i	$-0.524580\pi$
$631$	−3.87564			−0.154287			−0.0771435	+	0.997020i	$0.524580\pi$
$632$	−7.06218	+	12.2321i	−0.280918	+	0.486565i
$633$		0			0
$634$	16.2942	+	28.2224i	0.647126	+	1.12086i
$635$	1.53433	+	2.65754i	0.0608881	+	0.105461i
$636$		0			0
$637$		0			0
$638$	−4.00000			−0.158362
$639$		0			0
$640$	0.517638			0.0204614
$641$	−1.52628	+	2.64359i	−0.0602844	+	0.104416i	−0.894593	−	0.446883i	$-0.852534\pi$
$641$	−1.52628	+	2.64359i	−0.0602844	+	0.104416i	0.834308	+	0.551298i	$0.185867\pi$
$642$		0			0
$643$	−0.845807	−	1.46498i	−0.0333554	−	0.0577732i	0.848866	−	0.528608i	$-0.177286\pi$
$643$	−0.845807	−	1.46498i	−0.0333554	−	0.0577732i	−0.882221	+	0.470835i	$0.843953\pi$
$644$		0			0
$645$		0			0
$646$	−0.901924	+	1.56218i	−0.0354857	+	0.0614631i
$647$	−15.8338			−0.622489			−0.311244	−	0.950330i	$-0.600746\pi$
$647$	−15.8338			−0.622489			−0.311244	+	0.950330i	$0.600746\pi$
$648$		0			0
$649$	21.6665			0.850483
$650$	5.79555	−	10.0382i	0.227320	−	0.393730i
$651$		0			0
$652$	3.53590	+	6.12436i	0.138476	+	0.239848i
$653$	−20.6603	−	35.7846i	−0.808498	−	1.40036i	−0.913904	−	0.405931i	$-0.866947\pi$
$653$	−20.6603	−	35.7846i	−0.808498	−	1.40036i	0.105406	−	0.994429i	$-0.466386\pi$
$654$		0			0
$655$	−3.23205	+	5.59808i	−0.126287	+	0.218735i
$656$	5.65685			0.220863
$657$		0			0
$658$		0			0
$659$	−19.5622	+	33.8827i	−0.762034	+	1.31988i	0.179766	+	0.983709i	$0.442466\pi$
$659$	−19.5622	+	33.8827i	−0.762034	+	1.31988i	−0.941800	+	0.336173i	$0.890867\pi$
$660$		0			0
$661$	10.7267	+	18.5792i	0.417221	+	0.722648i	0.995659	−	0.0930785i	$-0.0296708\pi$
$661$	10.7267	+	18.5792i	0.417221	+	0.722648i	−0.578438	+	0.815727i	$0.696337\pi$
$662$	6.02628	+	10.4378i	0.234218	+	0.405677i
$663$		0			0
$664$	4.94975	−	8.57321i	0.192087	−	0.332705i
$665$		0			0
$666$		0			0
$667$	21.6603			0.838688
$668$	−6.64136	+	11.5032i	−0.256962	+	0.445071i
$669$		0			0
$670$	0.984508	+	1.70522i	0.0380349	+	0.0658783i
$671$	3.20736	+	5.55532i	0.123819	+	0.214461i
$672$		0			0
$673$	20.0885	−	34.7942i	0.774353	−	1.34122i	−0.160804	−	0.986986i	$-0.551409\pi$
$673$	20.0885	−	34.7942i	0.774353	−	1.34122i	0.935157	−	0.354233i	$-0.115258\pi$
$674$	−21.3205			−0.821235
$675$		0			0
$676$	−7.00000			−0.269231
$677$	−0.568406	+	0.984508i	−0.0218456	+	0.0378377i	−0.876742	−	0.480962i	$-0.840288\pi$
$677$	−0.568406	+	0.984508i	−0.0218456	+	0.0378377i	0.854896	+	0.518800i	$0.173621\pi$
$678$		0			0
$679$		0			0
$680$	0.901924	+	1.56218i	0.0345872	+	0.0599068i
$681$		0			0
$682$	5.37945	−	9.31749i	0.205990	−	0.356785i
$683$	13.6077			0.520684			0.260342	−	0.965516i	$-0.416165\pi$
$683$	13.6077			0.520684			0.260342	+	0.965516i	$0.416165\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$	6.09808	+	10.5622i	0.232487	+	0.402679i
$689$	8.24504	+	14.2808i	0.314111	+	0.544057i
$690$		0			0
$691$	−18.4913	+	32.0279i	−0.703442	+	1.21840i	0.263809	+	0.964575i	$0.415021\pi$
$691$	−18.4913	+	32.0279i	−0.703442	+	1.21840i	−0.967251	+	0.253822i	$0.918312\pi$
$692$	−19.4201			−0.738240
$693$		0			0
$694$	−21.7128			−0.824207
$695$	−5.23205	+	9.06218i	−0.198463	+	0.343748i
$696$		0			0
$697$	9.85641	+	17.0718i	0.373338	+	0.646640i
$698$	−17.2987	−	29.9623i	−0.654767	−	1.13409i
$699$		0			0
$700$		0			0
$701$	−20.5359			−0.775630			−0.387815	−	0.921737i	$-0.626770\pi$
$701$	−20.5359			−0.775630			−0.387815	+	0.921737i	$0.626770\pi$
$702$		0			0
$703$	4.14110			0.156185
$704$	−0.732051	+	1.26795i	−0.0275902	+	0.0477876i
$705$		0			0
$706$	−0.0507680	−	0.0879327i	−0.00191068	−	0.00330939i
$707$		0			0
$708$		0			0
$709$	11.2679	−	19.5167i	0.423177	−	0.732964i	−0.573072	−	0.819505i	$-0.694248\pi$
$709$	11.2679	−	19.5167i	0.423177	−	0.732964i	0.996248	+	0.0865418i	$0.0275816\pi$
$710$	0.416102			0.0156160
$711$		0			0
$712$	−16.1112			−0.603791
$713$	−29.1301	+	50.4548i	−1.09093	+	1.88955i
$714$		0			0
$715$	−0.928203	−	1.60770i	−0.0347128	−	0.0601244i
$716$	−4.09808	−	7.09808i	−0.153152	−	0.265268i
$717$		0			0
$718$	−6.96410	+	12.0622i	−0.259898	+	0.450156i
$719$	−34.0155			−1.26856			−0.634281	−	0.773102i	$-0.718704\pi$
$719$	−34.0155			−1.26856			−0.634281	+	0.773102i	$0.718704\pi$
$720$		0			0
$721$		0			0
$722$	9.36603	−	16.2224i	0.348567	−	0.603736i
$723$		0			0
$724$	−10.4865	−	18.1631i	−0.389727	−	0.675027i
$725$	−6.46410	−	11.1962i	−0.240071	−	0.415815i
$726$		0			0
$727$	−14.8864	+	25.7840i	−0.552106	+	0.956276i	0.446016	+	0.895025i	$0.352842\pi$
$727$	−14.8864	+	25.7840i	−0.552106	+	0.956276i	−0.998122	+	0.0612512i	$0.980491\pi$
$728$		0			0
$729$		0			0
$730$	−2.39230			−0.0885432
$731$	−21.2504	+	36.8067i	−0.785973	+	1.36135i
$732$		0			0
$733$	15.0573	+	26.0800i	0.556154	+	0.963287i	0.997813	+	0.0661037i	$0.0210568\pi$
$733$	15.0573	+	26.0800i	0.556154	+	0.963287i	−0.441659	+	0.897183i	$0.645610\pi$
$734$	−0.138701	−	0.240237i	−0.00511954	−	0.00886730i
$735$		0			0
$736$	3.96410	−	6.86603i	0.146119	−	0.253085i
$737$	−5.56922			−0.205145
$738$		0			0
$739$	−16.1436			−0.593852			−0.296926	−	0.954901i	$-0.595961\pi$
$739$	−16.1436			−0.593852			−0.296926	+	0.954901i	$0.595961\pi$
$740$	2.07055	−	3.58630i	0.0761150	−	0.131835i
$741$		0			0
$742$		0			0
$743$	−14.1244	−	24.4641i	−0.518172	−	0.897501i	−0.999777	−	0.0211123i	$-0.993279\pi$
$743$	−14.1244	−	24.4641i	−0.518172	−	0.897501i	0.481605	−	0.876389i	$-0.340054\pi$
$744$		0			0
$745$	−0.619174	+	1.07244i	−0.0226848	+	0.0392912i
$746$	19.1244			0.700192
$747$		0			0
$748$	−5.10205			−0.186549
$749$		0			0
$750$		0			0
$751$	25.0885	+	43.4545i	0.915491	+	1.58568i	0.806181	+	0.591669i	$0.201531\pi$
$751$	25.0885	+	43.4545i	0.915491	+	1.58568i	0.109310	+	0.994008i	$0.465136\pi$
$752$	2.31079	+	4.00240i	0.0842658	+	0.145953i
$753$		0			0
$754$	3.34607	−	5.79555i	0.121857	−	0.211062i
$755$	−9.00292			−0.327650
$756$		0			0
$757$	20.2487			0.735952			0.367976	−	0.929835i	$-0.380051\pi$
$757$	20.2487			0.735952			0.367976	+	0.929835i	$0.380051\pi$
$758$	13.7583	−	23.8301i	0.499725	−	0.865549i
$759$		0			0
$760$	0.133975	+	0.232051i	0.00485977	+	0.00841737i
$761$	19.8869	+	34.4452i	0.720900	+	1.24864i	0.960639	+	0.277799i	$0.0896048\pi$
$761$	19.8869	+	34.4452i	0.720900	+	1.24864i	−0.239739	+	0.970837i	$0.577062\pi$
$762$		0			0
$763$		0			0
$764$	7.19615			0.260348
$765$		0			0
$766$	−34.2185			−1.23637
$767$	−18.1244	+	31.3923i	−0.654433	+	1.13351i
$768$		0			0
$769$	14.9372	+	25.8719i	0.538648	+	0.932966i	0.998977	+	0.0452178i	$0.0143982\pi$
$769$	14.9372	+	25.8719i	0.538648	+	0.932966i	−0.460329	+	0.887748i	$0.652268\pi$
$770$		0			0
$771$		0			0
$772$	11.8660	−	20.5526i	0.427068	−	0.739703i
$773$	13.5230			0.486387			0.243194	−	0.969978i	$-0.421805\pi$
$773$	13.5230			0.486387			0.243194	+	0.969978i	$0.421805\pi$
$774$		0			0
$775$	34.7733			1.24909
$776$	−0.517638	+	0.896575i	−0.0185821	+	0.0321852i
$777$		0			0
$778$	−2.43782	−	4.22243i	−0.0874002	−	0.151382i
$779$	1.46410	+	2.53590i	0.0524569	+	0.0908580i
$780$		0			0
$781$	−0.588457	+	1.01924i	−0.0210567	+	0.0364712i
$782$	27.6279			0.987973
$783$		0			0
$784$		0			0
$785$	−4.47372	+	7.74871i	−0.159674	+	0.276563i
$786$		0			0
$787$	−18.0938	−	31.3393i	−0.644973	−	1.11713i	−0.984308	−	0.176461i	$-0.943535\pi$
$787$	−18.0938	−	31.3393i	−0.644973	−	1.11713i	0.339334	−	0.940666i	$-0.389798\pi$
$788$	4.83013	+	8.36603i	0.172066	+	0.298027i
$789$		0			0
$790$	−3.65565	+	6.33178i	−0.130062	+	0.225274i
$791$		0			0
$792$		0			0
$793$	−10.7321			−0.381106
$794$	13.1948	−	22.8541i	0.468266	−	0.811060i
$795$		0			0
$796$	5.79555	+	10.0382i	0.205418	+	0.355794i
$797$	−12.2796	−	21.2690i	−0.434967	−	0.753385i	0.562326	−	0.826916i	$-0.309907\pi$
$797$	−12.2796	−	21.2690i	−0.434967	−	0.753385i	−0.997293	+	0.0735308i	$0.976573\pi$
$798$		0			0
$799$	−8.05256	+	13.9474i	−0.284879	+	0.493425i
$800$	−4.73205			−0.167303
$801$		0			0
$802$	25.0526			0.884637
$803$	3.38323	−	5.85993i	0.119392	−	0.206792i
$804$		0			0
$805$		0			0
$806$	9.00000	+	15.5885i	0.317011	+	0.549080i
$807$		0			0
$808$	−2.89778	+	5.01910i	−0.101943	+	0.176571i
$809$	−33.3205			−1.17149			−0.585743	−	0.810497i	$-0.699197\pi$
$809$	−33.3205			−1.17149			−0.585743	+	0.810497i	$0.699197\pi$
$810$		0			0
$811$	−7.82894			−0.274911			−0.137456	−	0.990508i	$-0.543892\pi$
$811$	−7.82894			−0.274911			−0.137456	+	0.990508i	$0.543892\pi$
$812$		0			0
$813$		0			0
$814$	5.85641	+	10.1436i	0.205267	+	0.355533i
$815$	1.83032	+	3.17020i	0.0641132	+	0.111047i
$816$		0			0
$817$	−3.15660	+	5.46739i	−0.110435	+	0.191280i
$818$	−17.8028			−0.622459
$819$		0			0
$820$	2.92820			0.102257
$821$	−3.33975	+	5.78461i	−0.116558	+	0.201884i	−0.918401	−	0.395650i	$-0.870519\pi$
$821$	−3.33975	+	5.78461i	−0.116558	+	0.201884i	0.801844	+	0.597534i	$0.203853\pi$
$822$		0			0
$823$	3.66025	+	6.33975i	0.127588	+	0.220990i	0.922742	−	0.385419i	$-0.125943\pi$
$823$	3.66025	+	6.33975i	0.127588	+	0.220990i	−0.795153	+	0.606408i	$0.792610\pi$
$824$	−5.60609	−	9.71003i	−0.195297	−	0.338265i
$825$		0			0
$826$		0			0
$827$	52.7321			1.83367			0.916837	−	0.399263i	$-0.130734\pi$
$827$	52.7321			1.83367			0.916837	+	0.399263i	$0.130734\pi$
$828$		0			0
$829$	1.89469			0.0658052			0.0329026	−	0.999459i	$-0.489525\pi$
$829$	1.89469			0.0658052			0.0329026	+	0.999459i	$0.489525\pi$
$830$	2.56218	−	4.43782i	0.0889345	−	0.154039i
$831$		0			0
$832$	−1.22474	−	2.12132i	−0.0424604	−	0.0735436i
$833$		0			0
$834$		0			0
$835$	−3.43782	+	5.95448i	−0.118971	+	0.206063i
$836$	−0.757875			−0.0262116
$837$		0			0
$838$	−22.6646			−0.782935
$839$	22.4751	−	38.9280i	0.775927	−	1.34395i	−0.158345	−	0.987384i	$-0.550616\pi$
$839$	22.4751	−	38.9280i	0.775927	−	1.34395i	0.934272	−	0.356561i	$-0.116051\pi$
$840$		0			0
$841$	10.7679	+	18.6506i	0.371309	+	0.643125i
$842$	−14.0263	−	24.2942i	−0.483378	−	0.837234i
$843$		0			0
$844$	−0.633975	+	1.09808i	−0.0218223	+	0.0377973i
$845$	−3.62347			−0.124651
$846$		0			0
$847$		0			0
$848$	3.36603	−	5.83013i	0.115590	−	0.200207i
$849$		0			0
$850$	−8.24504	−	14.2808i	−0.282803	−	0.489829i
$851$	−31.7128	−	54.9282i	−1.08710	−	1.88291i
$852$		0			0
$853$	11.7992	−	20.4367i	0.403996	−	0.699741i	−0.590208	−	0.807251i	$-0.700954\pi$
$853$	11.7992	−	20.4367i	0.403996	−	0.699741i	0.994204	+	0.107510i	$0.0342878\pi$
$854$		0			0
$855$		0			0
$856$	−3.07180			−0.104992
$857$	−2.72689	+	4.72311i	−0.0931488	+	0.161339i	−0.908835	−	0.417157i	$-0.863027\pi$
$857$	−2.72689	+	4.72311i	−0.0931488	+	0.161339i	0.815686	+	0.578495i	$0.196360\pi$
$858$		0			0
$859$	4.84821	+	8.39735i	0.165419	+	0.286514i	0.936804	−	0.349855i	$-0.113769\pi$
$859$	4.84821	+	8.39735i	0.165419	+	0.286514i	−0.771385	+	0.636369i	$0.780436\pi$
$860$	3.15660	+	5.46739i	0.107639	+	0.186436i
$861$		0			0
$862$	−13.3923	+	23.1962i	−0.456144	+	0.790064i
$863$	−21.1962			−0.721525			−0.360763	−	0.932658i	$-0.617484\pi$
$863$	−21.1962			−0.721525			−0.360763	+	0.932658i	$0.617484\pi$
$864$		0			0
$865$	−10.0526			−0.341797
$866$	−10.1261	+	17.5390i	−0.344100	+	0.595998i
$867$		0			0
$868$		0			0
$869$	−10.3397	−	17.9090i	−0.350752	−	0.607520i
$870$		0			0
$871$	4.65874	−	8.06918i	0.157855	−	0.273414i
$872$	10.5885			0.358570
$873$		0			0
$874$	4.10394			0.138818
$875$		0			0
$876$		0			0
$877$	−12.0263	−	20.8301i	−0.406099	−	0.703383i	0.588350	−	0.808606i	$-0.299778\pi$
$877$	−12.0263	−	20.8301i	−0.406099	−	0.703383i	−0.994449	+	0.105223i	$0.966444\pi$
$878$	9.14162	+	15.8338i	0.308515	+	0.534363i
$879$		0			0
$880$	−0.378937	+	0.656339i	−0.0127740	+	0.0221252i
$881$	0.480473			0.0161876			0.00809378	−	0.999967i	$-0.497424\pi$
$881$	0.480473			0.0161876			0.00809378	+	0.999967i	$0.497424\pi$
$882$		0			0
$883$	38.2487			1.28717			0.643586	−	0.765374i	$-0.277446\pi$
$883$	38.2487			1.28717			0.643586	+	0.765374i	$0.277446\pi$
$884$	4.26795	−	7.39230i	0.143547	−	0.248630i
$885$		0			0
$886$	−18.4904	−	32.0263i	−0.621197	−	1.07594i
$887$	−13.4858	−	23.3581i	−0.452809	−	0.784288i	0.545751	−	0.837948i	$-0.316245\pi$
$887$	−13.4858	−	23.3581i	−0.452809	−	0.784288i	−0.998559	+	0.0536600i	$0.982911\pi$
$888$		0			0
$889$		0			0
$890$	−8.33975			−0.279549
$891$		0			0
$892$	−3.76217			−0.125967
$893$	−1.19615	+	2.07180i	−0.0400277	+	0.0693300i
$894$		0			0
$895$	−2.12132	−	3.67423i	−0.0709079	−	0.122816i
$896$		0			0
$897$		0			0
$898$	−11.8923	+	20.5981i	−0.396851	+	0.687367i
$899$	20.0764			0.669585
$900$		0			0
$901$	23.4596			0.781553
$902$	−4.14110	+	7.17260i	−0.137884	+	0.238822i
$903$		0			0
$904$	−7.33013	−	12.6962i	−0.243796	−	0.422268i
$905$	−5.42820	−	9.40192i	−0.180440	−	0.312531i
$906$		0			0
$907$	2.56218	−	4.43782i	0.0850757	−	0.147355i	−0.820348	−	0.571865i	$-0.806220\pi$
$907$	2.56218	−	4.43782i	0.0850757	−	0.147355i	0.905423	+	0.424510i	$0.139553\pi$
$908$	3.34607			0.111043
$909$		0			0
$910$		0			0
$911$	13.8923	−	24.0622i	0.460273	−	0.797216i	−0.538702	−	0.842497i	$-0.681085\pi$
$911$	13.8923	−	24.0622i	0.460273	−	0.797216i	0.998974	+	0.0452811i	$0.0144183\pi$
$912$		0			0
$913$	7.24693	+	12.5521i	0.239838	+	0.415412i
$914$	11.1340	+	19.2846i	0.368279	+	0.637878i
$915$		0			0
$916$	6.90018	−	11.9515i	0.227988	−	0.394888i
$917$		0			0
$918$		0			0
$919$	16.3731			0.540098			0.270049	−	0.962847i	$-0.412960\pi$
$919$	16.3731			0.540098			0.270049	+	0.962847i	$0.412960\pi$
$920$	2.05197	−	3.55412i	0.0676514	−	0.117176i
$921$		0			0
$922$	−19.4894	−	33.7566i	−0.641849	−	1.11172i
$923$	−0.984508	−	1.70522i	−0.0324055	−	0.0561279i
$924$		0			0
$925$	−18.9282	+	32.7846i	−0.622355	+	1.07795i
$926$	6.66025			0.218870
$927$		0			0
$928$	−2.73205			−0.0896840
$929$	−2.01978	+	3.49837i	−0.0662670	+	0.114778i	−0.897255	−	0.441512i	$-0.854442\pi$
$929$	−2.01978	+	3.49837i	−0.0662670	+	0.114778i	0.830988	+	0.556290i	$0.187776\pi$
$930$		0			0
$931$		0			0
$932$	0.696152	+	1.20577i	0.0228032	+	0.0394964i
$933$		0			0
$934$	−12.2982	+	21.3011i	−0.402410	+	0.696994i
$935$	−2.64102			−0.0863705
$936$		0			0
$937$	−31.7690			−1.03785			−0.518925	−	0.854820i	$-0.673667\pi$
$937$	−31.7690			−1.03785			−0.518925	+	0.854820i	$0.673667\pi$
$938$		0			0
$939$		0			0
$940$	1.19615	+	2.07180i	0.0390142	+	0.0675746i
$941$	29.1994	+	50.5749i	0.951874	+	1.64869i	0.741364	+	0.671103i	$0.234179\pi$
$941$	29.1994	+	50.5749i	0.951874	+	1.64869i	0.210510	+	0.977592i	$0.432488\pi$
$942$		0			0
$943$	22.4243	−	38.8401i	0.730237	−	1.26481i
$944$	14.7985			0.481649
$945$		0			0
$946$	−17.8564			−0.580562
$947$	−17.8301	+	30.8827i	−0.579401	+	1.00355i	0.416147	+	0.909297i	$0.363380\pi$
$947$	−17.8301	+	30.8827i	−0.579401	+	1.00355i	−0.995548	+	0.0942550i	$0.969953\pi$
$948$		0			0
$949$	5.66025	+	9.80385i	0.183740	+	0.318246i
$950$	−1.22474	−	2.12132i	−0.0397360	−	0.0688247i
$951$		0			0
$952$		0			0
$953$	−23.7128			−0.768133			−0.384067	−	0.923305i	$-0.625477\pi$
$953$	−23.7128			−0.768133			−0.384067	+	0.923305i	$0.625477\pi$
$954$		0			0
$955$	3.72500			0.120538
$956$	−6.23205	+	10.7942i	−0.201559	+	0.349110i
$957$		0			0
$958$	6.64136	+	11.5032i	0.214573	+	0.371651i
$959$		0			0
$960$		0			0
$961$	−11.5000	+	19.9186i	−0.370968	+	0.642535i
$962$	−19.5959			−0.631798
$963$		0			0
$964$	−12.7279			−0.409939
$965$	6.14231	−	10.6388i	0.197728	−	0.342475i
$966$		0			0
$967$	0.232051	+	0.401924i	0.00746225	+	0.0129250i	0.869732	−	0.493524i	$-0.164291\pi$
$967$	0.232051	+	0.401924i	0.00746225	+	0.0129250i	−0.862270	+	0.506449i	$0.830958\pi$
$968$	4.42820	+	7.66987i	0.142328	+	0.246519i
$969$		0			0
$970$	−0.267949	+	0.464102i	−0.00860333	+	0.0149014i
$971$	28.5988			0.917780			0.458890	−	0.888493i	$-0.348247\pi$
$971$	28.5988			0.917780			0.458890	+	0.888493i	$0.348247\pi$
$972$		0			0
$973$		0			0
$974$	16.1603	−	27.9904i	0.517808	−	0.896870i
$975$		0			0
$976$	2.19067	+	3.79435i	0.0701217	+	0.121454i
$977$	−8.07180	−	13.9808i	−0.258240	−	0.447284i	0.707531	−	0.706683i	$-0.249809\pi$
$977$	−8.07180	−	13.9808i	−0.258240	−	0.447284i	−0.965770	+	0.259398i	$0.916476\pi$
$978$		0			0
$979$	11.7942	−	20.4281i	0.376944	−	0.652886i
$980$		0			0
$981$		0			0
$982$	5.07180			0.161848
$983$	11.8177	−	20.4689i	0.376927	−	0.652858i	−0.613686	−	0.789550i	$-0.710314\pi$
$983$	11.8177	−	20.4689i	0.376927	−	0.652858i	0.990614	+	0.136693i	$0.0436473\pi$
$984$		0			0
$985$	2.50026	+	4.33057i	0.0796648	+	0.137984i
$986$	−4.76028	−	8.24504i	−0.151598	−	0.262576i
$987$		0			0
$988$	0.633975	−	1.09808i	0.0201694	−	0.0349345i
$989$	96.6936			3.07468
$990$		0			0
$991$	14.6795			0.466309			0.233155	−	0.972440i	$-0.425095\pi$
$991$	14.6795			0.466309			0.233155	+	0.972440i	$0.425095\pi$
$992$	3.67423	−	6.36396i	0.116657	−	0.202056i
$993$		0			0
$994$		0			0
$995$	3.00000	+	5.19615i	0.0951064	+	0.164729i
$996$		0			0
$997$	21.9389	−	37.9993i	0.694812	−	1.20345i	−0.275432	−	0.961320i	$-0.588821\pi$
$997$	21.9389	−	37.9993i	0.694812	−	1.20345i	0.970244	−	0.242129i	$-0.0778456\pi$
$998$	7.32051			0.231727
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.f.q.883.2		8
3.2	odd	2		882.2.f.s.295.3	yes	8
7.2	even	3		2646.2.e.t.2125.2		8
7.3	odd	6		2646.2.h.q.667.2		8
7.4	even	3		2646.2.h.q.667.3		8
7.5	odd	6		2646.2.e.t.2125.3		8
7.6	odd	2	inner	2646.2.f.q.883.3		8
9.2	odd	6		7938.2.a.cj.1.2		4
9.4	even	3	inner	2646.2.f.q.1765.2		8
9.5	odd	6		882.2.f.s.589.4	yes	8
9.7	even	3		7938.2.a.co.1.3		4
21.2	odd	6		882.2.e.q.655.3		8
21.5	even	6		882.2.e.q.655.2		8
21.11	odd	6		882.2.h.t.79.1		8
21.17	even	6		882.2.h.t.79.4		8
21.20	even	2		882.2.f.s.295.2	✓	8
63.4	even	3		2646.2.e.t.1549.2		8
63.5	even	6		882.2.h.t.67.4		8
63.13	odd	6	inner	2646.2.f.q.1765.3		8
63.20	even	6		7938.2.a.cj.1.3		4
63.23	odd	6		882.2.h.t.67.1		8
63.31	odd	6		2646.2.e.t.1549.3		8
63.32	odd	6		882.2.e.q.373.3		8
63.34	odd	6		7938.2.a.co.1.2		4
63.40	odd	6		2646.2.h.q.361.2		8
63.41	even	6		882.2.f.s.589.1	yes	8
63.58	even	3		2646.2.h.q.361.3		8
63.59	even	6		882.2.e.q.373.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.q.373.2		8	63.59	even	6
882.2.e.q.373.3		8	63.32	odd	6
882.2.e.q.655.2		8	21.5	even	6
882.2.e.q.655.3		8	21.2	odd	6
882.2.f.s.295.2	✓	8	21.20	even	2
882.2.f.s.295.3	yes	8	3.2	odd	2
882.2.f.s.589.1	yes	8	63.41	even	6
882.2.f.s.589.4	yes	8	9.5	odd	6
882.2.h.t.67.1		8	63.23	odd	6
882.2.h.t.67.4		8	63.5	even	6
882.2.h.t.79.1		8	21.11	odd	6
882.2.h.t.79.4		8	21.17	even	6
2646.2.e.t.1549.2		8	63.4	even	3
2646.2.e.t.1549.3		8	63.31	odd	6
2646.2.e.t.2125.2		8	7.2	even	3
2646.2.e.t.2125.3		8	7.5	odd	6
2646.2.f.q.883.2		8	1.1	even	1	trivial
2646.2.f.q.883.3		8	7.6	odd	2	inner
2646.2.f.q.1765.2		8	9.4	even	3	inner
2646.2.f.q.1765.3		8	63.13	odd	6	inner
2646.2.h.q.361.2		8	63.40	odd	6
2646.2.h.q.361.3		8	63.58	even	3
2646.2.h.q.667.2		8	7.3	odd	6
2646.2.h.q.667.3		8	7.4	even	3
7938.2.a.cj.1.2		4	9.2	odd	6
7938.2.a.cj.1.3		4	63.20	even	6
7938.2.a.co.1.2		4	63.34	odd	6
7938.2.a.co.1.3		4	9.7	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.258819 - 0.448288i) q^{5} +1.00000 q^{8} +0.517638 q^{10} +(-0.732051 + 1.26795i) q^{11} +(-1.22474 - 2.12132i) q^{13} +(-0.500000 + 0.866025i) q^{16} -3.48477 q^{17} -0.517638 q^{19} +(-0.258819 + 0.448288i) q^{20} +(-0.732051 - 1.26795i) q^{22} +(3.96410 + 6.86603i) q^{23} +(2.36603 - 4.09808i) q^{25} +2.44949 q^{26} +(1.36603 - 2.36603i) q^{29} +(3.67423 + 6.36396i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.74238 - 3.01790i) q^{34} -8.00000 q^{37} +(0.258819 - 0.448288i) q^{38} +(-0.258819 - 0.448288i) q^{40} +(-2.82843 - 4.89898i) q^{41} +(6.09808 - 10.5622i) q^{43} +1.46410 q^{44} -7.92820 q^{46} +(2.31079 - 4.00240i) q^{47} +(2.36603 + 4.09808i) q^{50} +(-1.22474 + 2.12132i) q^{52} -6.73205 q^{53} +0.757875 q^{55} +(1.36603 + 2.36603i) q^{58} +(-7.39924 - 12.8159i) q^{59} +(2.19067 - 3.79435i) q^{61} -7.34847 q^{62} +1.00000 q^{64} +(-0.633975 + 1.09808i) q^{65} +(1.90192 + 3.29423i) q^{67} +(1.74238 + 3.01790i) q^{68} +0.803848 q^{71} -4.62158 q^{73} +(4.00000 - 6.92820i) q^{74} +(0.258819 + 0.448288i) q^{76} +(-7.06218 + 12.2321i) q^{79} +0.517638 q^{80} +5.65685 q^{82} +(4.94975 - 8.57321i) q^{83} +(0.901924 + 1.56218i) q^{85} +(6.09808 + 10.5622i) q^{86} +(-0.732051 + 1.26795i) q^{88} -16.1112 q^{89} +(3.96410 - 6.86603i) q^{92} +(2.31079 + 4.00240i) q^{94} +(0.133975 + 0.232051i) q^{95} +(-0.517638 + 0.896575i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 8 q^{11} - 4 q^{16} + 8 q^{22} + 4 q^{23} + 12 q^{25} + 4 q^{29} - 4 q^{32} - 64 q^{37} + 28 q^{43} - 16 q^{44} - 8 q^{46} + 12 q^{50} - 40 q^{53} + 4 q^{58} + 8 q^{64}+ \cdots + 8 q^{95}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 + 8 * q^11 - 4 * q^16 + 8 * q^22 + 4 * q^23 + 12 * q^25 + 4 * q^29 - 4 * q^32 - 64 * q^37 + 28 * q^43 - 16 * q^44 - 8 * q^46 + 12 * q^50 - 40 * q^53 + 4 * q^58 + 8 * q^64 - 12 * q^65 + 36 * q^67 + 48 * q^71 + 32 * q^74 - 8 * q^79 + 28 * q^85 + 28 * q^86 + 8 * q^88 + 4 * q^92 + 8 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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