LMFDB - Embedded newform 867.2.e.f.616.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(616,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("867.616");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.e (of order $4$, 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:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.5473632256.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 49x^{4} + 256 $ x^8 + 49*x^4 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			616.3
Root			$-1.81129 - 1.81129i$ of defining polynomial
Character	$\chi$	$=$	867.616
Dual form			867.2.e.f.829.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.56155i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.438447 q^{4} +(0.397078 - 0.397078i) q^{5} +(-1.10418 - 1.10418i) q^{6} +2.43845i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.56155i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.438447 q^{4} +(0.397078 - 0.397078i) q^{5} +(-1.10418 - 1.10418i) q^{6} +2.43845i q^{8} -1.00000i q^{9} +(0.620058 + 0.620058i) q^{10} +(-1.81129 - 1.81129i) q^{11} +(0.310029 - 0.310029i) q^{12} -4.56155 q^{13} +0.561553i q^{15} -4.68466 q^{16} +1.56155 q^{18} +7.68466i q^{19} +(-0.174098 + 0.174098i) q^{20} +(2.82843 - 2.82843i) q^{22} +(-4.63972 - 4.63972i) q^{23} +(-1.72424 - 1.72424i) q^{24} +4.68466i q^{25} -7.12311i q^{26} +(0.707107 + 0.707107i) q^{27} +(-5.83095 + 5.83095i) q^{29} -0.876894 q^{30} +(-3.62258 + 3.62258i) q^{31} -2.43845i q^{32} +2.56155 q^{33} +0.438447i q^{36} +(2.20837 - 2.20837i) q^{37} -12.0000 q^{38} +(3.22550 - 3.22550i) q^{39} +(0.968253 + 0.968253i) q^{40} +(-0.397078 - 0.397078i) q^{41} +7.68466i q^{43} +(0.794156 + 0.794156i) q^{44} +(-0.397078 - 0.397078i) q^{45} +(7.24517 - 7.24517i) q^{46} +2.87689 q^{47} +(3.31255 - 3.31255i) q^{48} -7.00000i q^{49} -7.31534 q^{50} +2.00000 q^{52} -4.24621i q^{53} +(-1.10418 + 1.10418i) q^{54} -1.43845 q^{55} +(-5.43387 - 5.43387i) q^{57} +(-9.10534 - 9.10534i) q^{58} +1.12311i q^{59} -0.246211i q^{60} +(-0.620058 - 0.620058i) q^{61} +(-5.65685 - 5.65685i) q^{62} -5.56155 q^{64} +(-1.81129 + 1.81129i) q^{65} +4.00000i q^{66} +4.00000 q^{67} +6.56155 q^{69} +(7.24517 - 7.24517i) q^{71} +2.43845 q^{72} +(-3.00252 + 3.00252i) q^{73} +(3.44849 + 3.44849i) q^{74} +(-3.31255 - 3.31255i) q^{75} -3.36932i q^{76} +(5.03680 + 5.03680i) q^{78} +(10.8677 + 10.8677i) q^{79} +(-1.86017 + 1.86017i) q^{80} -1.00000 q^{81} +(0.620058 - 0.620058i) q^{82} -9.12311i q^{83} -12.0000 q^{86} -8.24621i q^{87} +(4.41674 - 4.41674i) q^{88} -7.12311 q^{89} +(0.620058 - 0.620058i) q^{90} +(2.03427 + 2.03427i) q^{92} -5.12311i q^{93} +4.49242i q^{94} +(3.05141 + 3.05141i) q^{95} +(1.72424 + 1.72424i) q^{96} +(7.86522 - 7.86522i) q^{97} +10.9309 q^{98} +(-1.81129 + 1.81129i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 20 q^{4}+O(q^{10}) $ 8 * q - 20 * q^4	$ 8 q - 20 q^{4} - 20 q^{13} + 12 q^{16} - 4 q^{18} - 40 q^{30} + 4 q^{33} - 96 q^{38} + 56 q^{47} - 108 q^{50} + 16 q^{52} - 28 q^{55} - 28 q^{64} + 32 q^{67} + 36 q^{69} + 36 q^{72} - 8 q^{81} - 96 q^{86} - 24 q^{89} - 28 q^{98}+O(q^{100}) $ 8 * q - 20 * q^4 - 20 * q^13 + 12 * q^16 - 4 * q^18 - 40 * q^30 + 4 * q^33 - 96 * q^38 + 56 * q^47 - 108 * q^50 + 16 * q^52 - 28 * q^55 - 28 * q^64 + 32 * q^67 + 36 * q^69 + 36 * q^72 - 8 * q^81 - 96 * q^86 - 24 * q^89 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$			1.56155i			1.10418i	0.833783	+	0.552092i	$0.186170\pi$
$2$			1.56155i			1.10418i	−0.833783	+	0.552092i	$0.813830\pi$
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−0.438447			−0.219224
$5$	0.397078	−	0.397078i	0.177579	−	0.177579i	−0.612721	−	0.790299i	$-0.709925\pi$
$5$	0.397078	−	0.397078i	0.177579	−	0.177579i	0.790299	+	0.612721i	$0.209925\pi$
$6$	−1.10418	−	1.10418i	−0.450781	−	0.450781i
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$			2.43845i			0.862121i
$9$		−	1.00000i		−	0.333333i
$10$	0.620058	+	0.620058i	0.196080	+	0.196080i
$11$	−1.81129	−	1.81129i	−0.546125	−	0.546125i	0.379193	−	0.925318i	$-0.376202\pi$
$11$	−1.81129	−	1.81129i	−0.546125	−	0.546125i	−0.925318	+	0.379193i	$0.876202\pi$
$12$	0.310029	−	0.310029i	0.0894977	−	0.0894977i
$13$	−4.56155			−1.26515			−0.632574	−	0.774500i	$-0.718001\pi$
$13$	−4.56155			−1.26515			−0.632574	+	0.774500i	$0.718001\pi$
$14$		0			0
$15$			0.561553i			0.144992i
$16$	−4.68466			−1.17116
$17$		0			0
$17$		0			0
$18$	1.56155			0.368062
$19$			7.68466i			1.76298i	0.472201	+	0.881491i	$0.343460\pi$
$19$			7.68466i			1.76298i	−0.472201	+	0.881491i	$0.656540\pi$
$20$	−0.174098	+	0.174098i	−0.0389294	+	0.0389294i
$21$		0			0
$22$	2.82843	−	2.82843i	0.603023	−	0.603023i
$23$	−4.63972	−	4.63972i	−0.967448	−	0.967448i	0.0320385	−	0.999487i	$-0.489800\pi$
$23$	−4.63972	−	4.63972i	−0.967448	−	0.967448i	−0.999487	+	0.0320385i	$0.989800\pi$
$24$	−1.72424	−	1.72424i	−0.351960	−	0.351960i
$25$			4.68466i			0.936932i
$26$		−	7.12311i		−	1.39696i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	−5.83095	+	5.83095i	−1.08278	+	1.08278i	−0.0865315	+	0.996249i	$0.527578\pi$
$29$	−5.83095	+	5.83095i	−1.08278	+	1.08278i	−0.996249	+	0.0865315i	$0.972422\pi$
$30$	−0.876894			−0.160098
$31$	−3.62258	+	3.62258i	−0.650635	+	0.650635i	−0.953146	−	0.302511i	$-0.902175\pi$
$31$	−3.62258	+	3.62258i	−0.650635	+	0.650635i	0.302511	+	0.953146i	$0.402175\pi$
$32$		−	2.43845i		−	0.431061i
$33$	2.56155			0.445909
$34$		0			0
$35$		0			0
$36$			0.438447i			0.0730745i
$37$	2.20837	−	2.20837i	0.363054	−	0.363054i	−0.501882	−	0.864936i	$-0.667359\pi$
$37$	2.20837	−	2.20837i	0.363054	−	0.363054i	0.864936	+	0.501882i	$0.167359\pi$
$38$	−12.0000			−1.94666
$39$	3.22550	−	3.22550i	0.516494	−	0.516494i
$40$	0.968253	+	0.968253i	0.153094	+	0.153094i
$41$	−0.397078	−	0.397078i	−0.0620131	−	0.0620131i	0.675420	−	0.737433i	$-0.263962\pi$
$41$	−0.397078	−	0.397078i	−0.0620131	−	0.0620131i	−0.737433	+	0.675420i	$0.763962\pi$
$42$		0			0
$43$			7.68466i			1.17190i	0.810347	+	0.585950i	$0.199278\pi$
$43$			7.68466i			1.17190i	−0.810347	+	0.585950i	$0.800722\pi$
$44$	0.794156	+	0.794156i	0.119723	+	0.119723i
$45$	−0.397078	−	0.397078i	−0.0591929	−	0.0591929i
$46$	7.24517	−	7.24517i	1.06824	−	1.06824i
$47$	2.87689			0.419638			0.209819	−	0.977740i	$-0.432712\pi$
$47$	2.87689			0.419638			0.209819	+	0.977740i	$0.432712\pi$
$48$	3.31255	−	3.31255i	0.478126	−	0.478126i
$49$		−	7.00000i		−	1.00000i
$50$	−7.31534			−1.03455
$51$		0			0
$52$	2.00000			0.277350
$53$		−	4.24621i		−	0.583262i	−0.956531	−	0.291631i	$-0.905802\pi$
$53$		−	4.24621i		−	0.583262i	0.956531	−	0.291631i	$-0.0941979\pi$
$54$	−1.10418	+	1.10418i	−0.150260	+	0.150260i
$55$	−1.43845			−0.193960
$56$		0			0
$57$	−5.43387	−	5.43387i	−0.719734	−	0.719734i
$58$	−9.10534	−	9.10534i	−1.19559	−	1.19559i
$59$			1.12311i			0.146216i	0.997324	+	0.0731079i	$0.0232918\pi$
$59$			1.12311i			0.146216i	−0.997324	+	0.0731079i	$0.976708\pi$
$60$		−	0.246211i		−	0.0317857i
$61$	−0.620058	−	0.620058i	−0.0793903	−	0.0793903i	0.666297	−	0.745687i	$-0.267878\pi$
$61$	−0.620058	−	0.620058i	−0.0793903	−	0.0793903i	−0.745687	+	0.666297i	$0.767878\pi$
$62$	−5.65685	−	5.65685i	−0.718421	−	0.718421i
$63$		0			0
$64$	−5.56155			−0.695194
$65$	−1.81129	+	1.81129i	−0.224663	+	0.224663i
$66$			4.00000i			0.492366i
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$		0			0
$69$	6.56155			0.789918
$70$		0			0
$71$	7.24517	−	7.24517i	0.859843	−	0.859843i	−0.131476	−	0.991319i	$-0.541972\pi$
$71$	7.24517	−	7.24517i	0.859843	−	0.859843i	0.991319	+	0.131476i	$0.0419717\pi$
$72$	2.43845			0.287374
$73$	−3.00252	+	3.00252i	−0.351419	+	0.351419i	−0.860637	−	0.509218i	$-0.829935\pi$
$73$	−3.00252	+	3.00252i	−0.351419	+	0.351419i	0.509218	+	0.860637i	$0.329935\pi$
$74$	3.44849	+	3.44849i	0.400878	+	0.400878i
$75$	−3.31255	−	3.31255i	−0.382501	−	0.382501i
$76$		−	3.36932i		−	0.386487i
$77$		0			0
$78$	5.03680	+	5.03680i	0.570305	+	0.570305i
$79$	10.8677	+	10.8677i	1.22272	+	1.22272i	0.966662	+	0.256055i	$0.0824228\pi$
$79$	10.8677	+	10.8677i	1.22272	+	1.22272i	0.256055	+	0.966662i	$0.417577\pi$
$80$	−1.86017	+	1.86017i	−0.207974	+	0.207974i
$81$	−1.00000			−0.111111
$82$	0.620058	−	0.620058i	0.0684739	−	0.0684739i
$83$		−	9.12311i		−	1.00139i	−0.865624	−	0.500695i	$-0.833078\pi$
$83$		−	9.12311i		−	1.00139i	0.865624	−	0.500695i	$-0.166922\pi$
$84$		0			0
$85$		0			0
$86$	−12.0000			−1.29399
$87$		−	8.24621i		−	0.884087i
$88$	4.41674	−	4.41674i	0.470826	−	0.470826i
$89$	−7.12311			−0.755048			−0.377524	−	0.926000i	$-0.623224\pi$
$89$	−7.12311			−0.755048			−0.377524	+	0.926000i	$0.623224\pi$
$90$	0.620058	−	0.620058i	0.0653598	−	0.0653598i
$91$		0			0
$92$	2.03427	+	2.03427i	0.212087	+	0.212087i
$93$		−	5.12311i		−	0.531241i
$94$			4.49242i			0.463358i
$95$	3.05141	+	3.05141i	0.313068	+	0.313068i
$96$	1.72424	+	1.72424i	0.175980	+	0.175980i
$97$	7.86522	−	7.86522i	0.798592	−	0.798592i	−0.184281	−	0.982874i	$-0.558996\pi$
$97$	7.86522	−	7.86522i	0.798592	−	0.798592i	0.982874	+	0.184281i	$0.0589957\pi$
$98$	10.9309			1.10418
$99$	−1.81129	+	1.81129i	−0.182042	+	0.182042i
$100$		−	2.05398i		−	0.205398i
$101$	19.1231			1.90282			0.951410	−	0.307927i	$-0.0996352\pi$
$101$	19.1231			1.90282			0.951410	+	0.307927i	$0.0996352\pi$
$102$		0			0
$103$	4.31534			0.425203			0.212602	−	0.977139i	$-0.431806\pi$
$103$	4.31534			0.425203			0.212602	+	0.977139i	$0.431806\pi$
$104$		−	11.1231i		−	1.09071i
$105$		0			0
$106$	6.63068			0.644029
$107$	−5.43387	+	5.43387i	−0.525312	+	0.525312i	−0.919171	−	0.393859i	$-0.871140\pi$
$107$	−5.43387	+	5.43387i	−0.525312	+	0.525312i	0.393859	+	0.919171i	$0.371140\pi$
$108$	−0.310029	−	0.310029i	−0.0298326	−	0.0298326i
$109$	10.6937	+	10.6937i	1.02427	+	1.02427i	0.999698	+	0.0245678i	$0.00782096\pi$
$109$	10.6937	+	10.6937i	1.02427	+	1.02427i	0.0245678	+	0.999698i	$0.492179\pi$
$110$		−	2.24621i		−	0.214168i
$111$			3.12311i			0.296432i
$112$		0			0
$113$	−3.22550	−	3.22550i	−0.303430	−	0.303430i	0.538924	−	0.842354i	$-0.318831\pi$
$113$	−3.22550	−	3.22550i	−0.303430	−	0.303430i	−0.842354	+	0.538924i	$0.818831\pi$
$114$	8.48528	−	8.48528i	0.794719	−	0.794719i
$115$	−3.68466			−0.343596
$116$	2.55656	−	2.55656i	0.237371	−	0.237371i
$117$			4.56155i			0.421716i
$118$	−1.75379			−0.161449
$119$		0			0
$120$	−1.36932			−0.125001
$121$		−	4.43845i		−	0.403495i
$122$	0.968253	−	0.968253i	0.0876615	−	0.0876615i
$123$	0.561553			0.0506335
$124$	1.58831	−	1.58831i	0.142635	−	0.142635i
$125$	3.84556	+	3.84556i	0.343958	+	0.343958i
$126$		0			0
$127$			0.807764i			0.0716775i	0.999358	+	0.0358387i	$0.0114103\pi$
$127$			0.807764i			0.0716775i	−0.999358	+	0.0358387i	$0.988590\pi$
$128$		−	13.5616i		−	1.19868i
$129$	−5.43387	−	5.43387i	−0.478426	−	0.478426i
$130$	−2.82843	−	2.82843i	−0.248069	−	0.248069i
$131$	−13.1250	+	13.1250i	−1.14674	+	1.14674i	−0.159546	+	0.987190i	$0.551003\pi$
$131$	−13.1250	+	13.1250i	−1.14674	+	1.14674i	−0.987190	+	0.159546i	$0.948997\pi$
$132$	−1.12311			−0.0977538
$133$		0			0
$134$			6.24621i			0.539590i
$135$	0.561553			0.0483308
$136$		0			0
$137$	−16.2462			−1.38801			−0.694004	−	0.719971i	$-0.744155\pi$
$137$	−16.2462			−1.38801			−0.694004	+	0.719971i	$0.744155\pi$
$138$			10.2462i			0.872215i
$139$	−6.45101	+	6.45101i	−0.547168	+	0.547168i	−0.925621	−	0.378453i	$-0.876456\pi$
$139$	−6.45101	+	6.45101i	−0.547168	+	0.547168i	0.378453	+	0.925621i	$0.376456\pi$
$140$		0			0
$141$	−2.03427	+	2.03427i	−0.171317	+	0.171317i
$142$	11.3137	+	11.3137i	0.949425	+	0.949425i
$143$	8.26230	+	8.26230i	0.690928	+	0.690928i
$144$			4.68466i			0.390388i
$145$			4.63068i			0.384557i
$146$	−4.68860	−	4.68860i	−0.388031	−	0.388031i
$147$	4.94975	+	4.94975i	0.408248	+	0.408248i
$148$	−0.968253	+	0.968253i	−0.0795899	+	0.0795899i
$149$	4.24621			0.347863			0.173932	−	0.984758i	$-0.444353\pi$
$149$	4.24621			0.347863			0.173932	+	0.984758i	$0.444353\pi$
$150$	5.17273	−	5.17273i	0.422351	−	0.422351i
$151$			8.00000i			0.651031i	0.945537	+	0.325515i	$0.105538\pi$
$151$			8.00000i			0.651031i	−0.945537	+	0.325515i	$0.894462\pi$
$152$	−18.7386			−1.51990
$153$		0			0
$154$		0			0
$155$			2.87689i			0.231078i
$156$	−1.41421	+	1.41421i	−0.113228	+	0.113228i
$157$	5.68466			0.453685			0.226843	−	0.973931i	$-0.427160\pi$
$157$	5.68466			0.453685			0.226843	+	0.973931i	$0.427160\pi$
$158$	−16.9706	+	16.9706i	−1.35011	+	1.35011i
$159$	3.00252	+	3.00252i	0.238116	+	0.238116i
$160$	−0.968253	−	0.968253i	−0.0765471	−	0.0765471i
$161$		0			0
$162$		−	1.56155i		−	0.122687i
$163$	4.86270	+	4.86270i	0.380876	+	0.380876i	0.871418	−	0.490542i	$-0.163201\pi$
$163$	4.86270	+	4.86270i	0.380876	+	0.380876i	−0.490542	+	0.871418i	$0.663201\pi$
$164$	0.174098	+	0.174098i	0.0135947	+	0.0135947i
$165$	1.01714	−	1.01714i	0.0791839	−	0.0791839i
$166$	14.2462			1.10572
$167$	−0.571175	+	0.571175i	−0.0441989	+	0.0441989i	−0.728861	−	0.684662i	$-0.759950\pi$
$167$	−0.571175	+	0.571175i	−0.0441989	+	0.0441989i	0.684662	+	0.728861i	$0.259950\pi$
$168$		0			0
$169$	7.80776			0.600597
$170$		0			0
$171$	7.68466			0.587661
$172$		−	3.36932i		−	0.256908i
$173$	−13.2991	+	13.2991i	−1.01111	+	1.01111i	−0.0111741	+	0.999938i	$0.503557\pi$
$173$	−13.2991	+	13.2991i	−1.01111	+	1.01111i	−0.999938	+	0.0111741i	$0.996443\pi$
$174$	12.8769			0.976195
$175$		0			0
$176$	8.48528	+	8.48528i	0.639602	+	0.639602i
$177$	−0.794156	−	0.794156i	−0.0596924	−	0.0596924i
$178$		−	11.1231i		−	0.833712i
$179$			9.12311i			0.681893i	0.940083	+	0.340946i	$0.110747\pi$
$179$			9.12311i			0.681893i	−0.940083	+	0.340946i	$0.889253\pi$
$180$	0.174098	+	0.174098i	0.0129765	+	0.0129765i
$181$	4.24264	+	4.24264i	0.315353	+	0.315353i	0.846979	−	0.531626i	$-0.178419\pi$
$181$	4.24264	+	4.24264i	0.315353	+	0.315353i	−0.531626	+	0.846979i	$0.678419\pi$
$182$		0			0
$183$	0.876894			0.0648219
$184$	11.3137	−	11.3137i	0.834058	−	0.834058i
$185$		−	1.75379i		−	0.128941i
$186$	8.00000			0.586588
$187$		0			0
$188$	−1.26137			−0.0919946
$189$		0			0
$190$	−4.76493	+	4.76493i	−0.345685	+	0.345685i
$191$	13.1231			0.949555			0.474777	−	0.880106i	$-0.342529\pi$
$191$	13.1231			0.949555			0.474777	+	0.880106i	$0.342529\pi$
$192$	3.93261	−	3.93261i	0.283812	−	0.283812i
$193$	−17.1447	−	17.1447i	−1.23410	−	1.23410i	−0.962375	−	0.271725i	$-0.912406\pi$
$193$	−17.1447	−	17.1447i	−1.23410	−	1.23410i	−0.271725	−	0.962375i	$-0.587594\pi$
$194$	12.2820	+	12.2820i	0.881793	+	0.881793i
$195$		−	2.56155i		−	0.183437i
$196$			3.06913i			0.219224i
$197$	−14.0933	−	14.0933i	−1.00410	−	1.00410i	−0.999992	−	0.00411116i	$-0.998691\pi$
$197$	−14.0933	−	14.0933i	−1.00410	−	1.00410i	−0.00411116	−	0.999992i	$-0.501309\pi$
$198$	−2.82843	−	2.82843i	−0.201008	−	0.201008i
$199$	−11.3137	+	11.3137i	−0.802008	+	0.802008i	−0.983409	−	0.181402i	$-0.941937\pi$
$199$	−11.3137	+	11.3137i	−0.802008	+	0.802008i	0.181402	+	0.983409i	$0.441937\pi$
$200$	−11.4233			−0.807749
$201$	−2.82843	+	2.82843i	−0.199502	+	0.199502i
$202$			29.8617i			2.10106i
$203$		0			0
$204$		0			0
$205$	−0.315342			−0.0220244
$206$			6.73863i			0.469503i
$207$	−4.63972	+	4.63972i	−0.322483	+	0.322483i
$208$	21.3693			1.48170
$209$	13.9192	−	13.9192i	0.962808	−	0.962808i
$210$		0			0
$211$	8.03932	+	8.03932i	0.553450	+	0.553450i	0.927435	−	0.373985i	$-0.122009\pi$
$211$	8.03932	+	8.03932i	0.553450	+	0.553450i	−0.373985	+	0.927435i	$0.622009\pi$
$212$			1.86174i			0.127865i
$213$			10.2462i			0.702059i
$214$	−8.48528	−	8.48528i	−0.580042	−	0.580042i
$215$	3.05141	+	3.05141i	0.208104	+	0.208104i
$216$	−1.72424	+	1.72424i	−0.117320	+	0.117320i
$217$		0			0
$218$	−16.6987	+	16.6987i	−1.13098	+	1.13098i
$219$		−	4.24621i		−	0.286932i
$220$	0.630683			0.0425206
$221$		0			0
$222$	−4.87689			−0.327316
$223$			13.9309i			0.932880i	0.884553	+	0.466440i	$0.154464\pi$
$223$			13.9309i			0.932880i	−0.884553	+	0.466440i	$0.845536\pi$
$224$		0			0
$225$	4.68466			0.312311
$226$	5.03680	−	5.03680i	0.335043	−	0.335043i
$227$	16.3016	+	16.3016i	1.08198	+	1.08198i	0.996325	+	0.0856515i	$0.0272972\pi$
$227$	16.3016	+	16.3016i	1.08198	+	1.08198i	0.0856515	+	0.996325i	$0.472703\pi$
$228$	2.38247	+	2.38247i	0.157783	+	0.157783i
$229$		−	6.00000i		−	0.396491i	−0.980152	−	0.198246i	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$		−	5.75379i		−	0.379394i
$231$		0			0
$232$	−14.2185	−	14.2185i	−0.933488	−	0.933488i
$233$	−0.397078	+	0.397078i	−0.0260134	+	0.0260134i	−0.719994	−	0.693980i	$-0.755855\pi$
$233$	−0.397078	+	0.397078i	−0.0260134	+	0.0260134i	0.693980	+	0.719994i	$0.255855\pi$
$234$	−7.12311			−0.465652
$235$	1.14235	−	1.14235i	0.0745188	−	0.0745188i
$236$		−	0.492423i		−	0.0320540i
$237$	−15.3693			−0.998344
$238$		0			0
$239$	10.2462			0.662772			0.331386	−	0.943495i	$-0.392484\pi$
$239$	10.2462			0.662772			0.331386	+	0.943495i	$0.392484\pi$
$240$		−	2.63068i		−	0.169810i
$241$	−15.1104	+	15.1104i	−0.973346	+	0.973346i	−0.999654	−	0.0263082i	$-0.991625\pi$
$241$	−15.1104	+	15.1104i	−0.973346	+	0.973346i	0.0263082	+	0.999654i	$0.491625\pi$
$242$	6.93087			0.445533
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	0.271863	+	0.271863i	0.0174042	+	0.0174042i
$245$	−2.77954	−	2.77954i	−0.177579	−	0.177579i
$246$			0.876894i			0.0559087i
$247$		−	35.0540i		−	2.23043i
$248$	−8.83348	−	8.83348i	−0.560926	−	0.560926i
$249$	6.45101	+	6.45101i	0.408816	+	0.408816i
$250$	−6.00505	+	6.00505i	−0.379793	+	0.379793i
$251$	24.4924			1.54595			0.772974	−	0.634438i	$-0.218768\pi$
$251$	24.4924			1.54595			0.772974	+	0.634438i	$0.218768\pi$
$252$		0			0
$253$			16.8078i			1.05670i
$254$	−1.26137			−0.0791452
$255$		0			0
$256$	10.0540			0.628373
$257$			9.36932i			0.584442i	0.956351	+	0.292221i	$0.0943943\pi$
$257$			9.36932i			0.584442i	−0.956351	+	0.292221i	$0.905606\pi$
$258$	8.48528	−	8.48528i	0.528271	−	0.528271i
$259$		0			0
$260$	0.794156	−	0.794156i	0.0492514	−	0.0492514i
$261$	5.83095	+	5.83095i	0.360927	+	0.360927i
$262$	−20.4954	−	20.4954i	−1.26621	−	1.26621i
$263$		−	12.4924i		−	0.770316i	−0.922851	−	0.385158i	$-0.874147\pi$
$263$		−	12.4924i		−	0.770316i	0.922851	−	0.385158i	$-0.125853\pi$
$264$			6.24621i			0.384428i
$265$	−1.68608	−	1.68608i	−0.103575	−	0.103575i
$266$		0			0
$267$	5.03680	−	5.03680i	0.308247	−	0.308247i
$268$	−1.75379			−0.107130
$269$	14.5392	−	14.5392i	0.886471	−	0.886471i	−0.107711	−	0.994182i	$-0.534352\pi$
$269$	14.5392	−	14.5392i	0.886471	−	0.886471i	0.994182	+	0.107711i	$0.0343520\pi$
$270$			0.876894i			0.0533661i
$271$	−0.807764			−0.0490682			−0.0245341	−	0.999699i	$-0.507810\pi$
$271$	−0.807764			−0.0490682			−0.0245341	+	0.999699i	$0.507810\pi$
$272$		0			0
$273$		0			0
$274$		−	25.3693i		−	1.53262i
$275$	8.48528	−	8.48528i	0.511682	−	0.511682i
$276$	−2.87689			−0.173169
$277$	−4.24264	+	4.24264i	−0.254916	+	0.254916i	−0.822982	−	0.568067i	$-0.807691\pi$
$277$	−4.24264	+	4.24264i	−0.254916	+	0.254916i	0.568067	+	0.822982i	$0.307691\pi$
$278$	−10.0736	−	10.0736i	−0.604174	−	0.604174i
$279$	3.62258	+	3.62258i	0.216878	+	0.216878i
$280$		0			0
$281$			19.1231i			1.14079i	0.821371	+	0.570394i	$0.193210\pi$
$281$			19.1231i			1.14079i	−0.821371	+	0.570394i	$0.806790\pi$
$282$	−3.17662	−	3.17662i	−0.189165	−	0.189165i
$283$	−2.38247	−	2.38247i	−0.141623	−	0.141623i	0.632741	−	0.774364i	$-0.281930\pi$
$283$	−2.38247	−	2.38247i	−0.141623	−	0.141623i	−0.774364	+	0.632741i	$0.781930\pi$
$284$	−3.17662	+	3.17662i	−0.188498	+	0.188498i
$285$	−4.31534			−0.255619
$286$	−12.9020	+	12.9020i	−0.762912	+	0.762912i
$287$		0			0
$288$	−2.43845			−0.143687
$289$		0			0
$290$	−7.23106			−0.424622
$291$			11.1231i			0.652048i
$292$	1.31645	−	1.31645i	0.0770393	−	0.0770393i
$293$	7.12311			0.416136			0.208068	−	0.978114i	$-0.433282\pi$
$293$	7.12311			0.416136			0.208068	+	0.978114i	$0.433282\pi$
$294$	−7.72929	+	7.72929i	−0.450781	+	0.450781i
$295$	0.445960	+	0.445960i	0.0259648	+	0.0259648i
$296$	5.38499	+	5.38499i	0.312996	+	0.312996i
$297$		−	2.56155i		−	0.148636i
$298$			6.63068i			0.384105i
$299$	21.1643	+	21.1643i	1.22396	+	1.22396i
$300$	1.45238	+	1.45238i	0.0838532	+	0.0838532i
$301$		0			0
$302$	−12.4924			−0.718858
$303$	−13.5221	+	13.5221i	−0.776823	+	0.776823i
$304$		−	36.0000i		−	2.06474i
$305$	−0.492423			−0.0281960
$306$		0			0
$307$	−0.492423			−0.0281040			−0.0140520	−	0.999901i	$-0.504473\pi$
$307$	−0.492423			−0.0281040			−0.0140520	+	0.999901i	$0.504473\pi$
$308$		0			0
$309$	−3.05141	+	3.05141i	−0.173588	+	0.173588i
$310$	−4.49242			−0.255152
$311$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$311$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$312$	7.86522	+	7.86522i	0.445281	+	0.445281i
$313$	5.38499	+	5.38499i	0.304378	+	0.304378i	0.842724	−	0.538346i	$-0.180951\pi$
$313$	5.38499	+	5.38499i	0.304378	+	0.304378i	−0.538346	+	0.842724i	$0.680951\pi$
$314$			8.87689i			0.500952i
$315$		0			0
$316$	−4.76493	−	4.76493i	−0.268048	−	0.268048i
$317$	−12.7279	−	12.7279i	−0.714871	−	0.714871i	0.252679	−	0.967550i	$-0.418688\pi$
$317$	−12.7279	−	12.7279i	−0.714871	−	0.714871i	−0.967550	+	0.252679i	$0.918688\pi$
$318$	−4.68860	+	4.68860i	−0.262924	+	0.262924i
$319$	21.1231			1.18267
$320$	−2.20837	+	2.20837i	−0.123452	+	0.123452i
$321$		−	7.68466i		−	0.428916i
$322$		0			0
$323$		0			0
$324$	0.438447			0.0243582
$325$		−	21.3693i		−	1.18536i
$326$	−7.59336	+	7.59336i	−0.420557	+	0.420557i
$327$	−15.1231			−0.836310
$328$	0.968253	−	0.968253i	0.0534628	−	0.0534628i
$329$		0			0
$330$	1.58831	+	1.58831i	0.0874337	+	0.0874337i
$331$			6.06913i			0.333590i	0.985992	+	0.166795i	$0.0533417\pi$
$331$			6.06913i			0.333590i	−0.985992	+	0.166795i	$0.946658\pi$
$332$			4.00000i			0.219529i
$333$	−2.20837	−	2.20837i	−0.121018	−	0.121018i
$334$	−0.891921	−	0.891921i	−0.0488037	−	0.0488037i
$335$	1.58831	−	1.58831i	0.0867787	−	0.0867787i
$336$		0			0
$337$	23.1497	−	23.1497i	1.26105	−	1.26105i	0.310458	−	0.950587i	$-0.399518\pi$
$337$	23.1497	−	23.1497i	1.26105	−	1.26105i	0.950587	−	0.310458i	$-0.100482\pi$
$338$			12.1922i			0.663170i
$339$	4.56155			0.247750
$340$		0			0
$341$	13.1231			0.710656
$342$			12.0000i			0.648886i
$343$		0			0
$344$	−18.7386			−1.01032
$345$	2.60545	−	2.60545i	0.140273	−	0.140273i
$346$	−20.7672	−	20.7672i	−1.11645	−	1.11645i
$347$	−17.3188	−	17.3188i	−0.929720	−	0.929720i	0.0679679	−	0.997688i	$-0.478348\pi$
$347$	−17.3188	−	17.3188i	−0.929720	−	0.929720i	−0.997688	+	0.0679679i	$0.978348\pi$
$348$			3.61553i			0.193813i
$349$		−	7.43845i		−	0.398171i	−0.979982	−	0.199085i	$-0.936203\pi$
$349$		−	7.43845i		−	0.398171i	0.979982	−	0.199085i	$-0.0637971\pi$
$350$		0			0
$351$	−3.22550	−	3.22550i	−0.172165	−	0.172165i
$352$	−4.41674	+	4.41674i	−0.235413	+	0.235413i
$353$	−22.4924			−1.19715			−0.598575	−	0.801066i	$-0.704266\pi$
$353$	−22.4924			−1.19715			−0.598575	+	0.801066i	$0.704266\pi$
$354$	1.24012	−	1.24012i	0.0659114	−	0.0659114i
$355$		−	5.75379i		−	0.305379i
$356$	3.12311			0.165524
$357$		0			0
$358$	−14.2462			−0.752936
$359$		−	2.24621i		−	0.118550i	−0.998242	−	0.0592752i	$-0.981121\pi$
$359$		−	2.24621i		−	0.118550i	0.998242	−	0.0592752i	$-0.0188790\pi$
$360$	0.968253	−	0.968253i	0.0510314	−	0.0510314i
$361$	−40.0540			−2.10810
$362$	−6.62511	+	6.62511i	−0.348208	+	0.348208i
$363$	3.13846	+	3.13846i	0.164726	+	0.164726i
$364$		0			0
$365$			2.38447i			0.124809i
$366$			1.36932i			0.0715753i
$367$	12.9020	+	12.9020i	0.673480	+	0.673480i	0.958517	−	0.285037i	$-0.0920058\pi$
$367$	12.9020	+	12.9020i	0.673480	+	0.673480i	−0.285037	+	0.958517i	$0.592006\pi$
$368$	21.7355	+	21.7355i	1.13304	+	1.13304i
$369$	−0.397078	+	0.397078i	−0.0206710	+	0.0206710i
$370$	2.73863			0.142375
$371$		0			0
$372$			2.24621i			0.116461i
$373$	16.2462			0.841197			0.420598	−	0.907247i	$-0.361820\pi$
$373$	16.2462			0.841197			0.420598	+	0.907247i	$0.361820\pi$
$374$		0			0
$375$	−5.43845			−0.280840
$376$			7.01515i			0.361779i
$377$	26.5982	−	26.5982i	1.36988	−	1.36988i
$378$		0			0
$379$	8.48528	−	8.48528i	0.435860	−	0.435860i	−0.454756	−	0.890616i	$-0.650274\pi$
$379$	8.48528	−	8.48528i	0.435860	−	0.435860i	0.890616	+	0.454756i	$0.150274\pi$
$380$	−1.33788	−	1.33788i	−0.0686318	−	0.0686318i
$381$	−0.571175	−	0.571175i	−0.0292622	−	0.0292622i
$382$			20.4924i			1.04848i
$383$			10.2462i			0.523557i	0.965128	+	0.261778i	$0.0843090\pi$
$383$			10.2462i			0.523557i	−0.965128	+	0.261778i	$0.915691\pi$
$384$	9.58947	+	9.58947i	0.489360	+	0.489360i
$385$		0			0
$386$	26.7723	−	26.7723i	1.36267	−	1.36267i
$387$	7.68466			0.390633
$388$	−3.44849	+	3.44849i	−0.175070	+	0.175070i
$389$		−	21.8617i		−	1.10843i	−0.832372	−	0.554217i	$-0.813018\pi$
$389$		−	21.8617i		−	1.10843i	0.832372	−	0.554217i	$-0.186982\pi$
$390$	4.00000			0.202548
$391$		0			0
$392$	17.0691			0.862121
$393$		−	18.5616i		−	0.936306i
$394$	22.0074	−	22.0074i	1.10871	−	1.10871i
$395$	8.63068			0.434257
$396$	0.794156	−	0.794156i	0.0399078	−	0.0399078i
$397$	3.79668	+	3.79668i	0.190550	+	0.190550i	0.795934	−	0.605384i	$-0.206980\pi$
$397$	3.79668	+	3.79668i	0.190550	+	0.190550i	−0.605384	+	0.795934i	$0.706980\pi$
$398$	−17.6670	−	17.6670i	−0.885564	−	0.885564i
$399$		0			0
$400$		−	21.9460i		−	1.09730i
$401$	4.36786	+	4.36786i	0.218120	+	0.218120i	0.807706	−	0.589586i	$-0.200709\pi$
$401$	4.36786	+	4.36786i	0.218120	+	0.218120i	−0.589586	+	0.807706i	$0.700709\pi$
$402$	−4.41674	−	4.41674i	−0.220287	−	0.220287i
$403$	16.5246	−	16.5246i	0.823149	−	0.823149i
$404$	−8.38447			−0.417143
$405$	−0.397078	+	0.397078i	−0.0197310	+	0.0197310i
$406$		0			0
$407$	−8.00000			−0.396545
$408$		0			0
$409$	−2.31534			−0.114486			−0.0572431	−	0.998360i	$-0.518231\pi$
$409$	−2.31534			−0.114486			−0.0572431	+	0.998360i	$0.518231\pi$
$410$		−	0.492423i		−	0.0243190i
$411$	11.4878	−	11.4878i	0.566652	−	0.566652i
$412$	−1.89205			−0.0932146
$413$		0			0
$414$	−7.24517	−	7.24517i	−0.356080	−	0.356080i
$415$	−3.62258	−	3.62258i	−0.177826	−	0.177826i
$416$			11.1231i			0.545355i
$417$		−	9.12311i		−	0.446760i
$418$	21.7355	+	21.7355i	1.06312	+	1.06312i
$419$	22.9756	+	22.9756i	1.12243	+	1.12243i	0.991375	+	0.131057i	$0.0418372\pi$
$419$	22.9756	+	22.9756i	1.12243	+	1.12243i	0.131057	+	0.991375i	$0.458163\pi$
$420$		0			0
$421$	−28.5616			−1.39200			−0.696002	−	0.718039i	$-0.745040\pi$
$421$	−28.5616			−1.39200			−0.696002	+	0.718039i	$0.745040\pi$
$422$	−12.5538	+	12.5538i	−0.611111	+	0.611111i
$423$		−	2.87689i		−	0.139879i
$424$	10.3542			0.502843
$425$		0			0
$426$	−16.0000			−0.775203
$427$		0			0
$428$	2.38247	−	2.38247i	0.115161	−	0.115161i
$429$	−11.6847			−0.564141
$430$	−4.76493	+	4.76493i	−0.229786	+	0.229786i
$431$	−16.9706	−	16.9706i	−0.817443	−	0.817443i	0.168294	−	0.985737i	$-0.446174\pi$
$431$	−16.9706	−	16.9706i	−0.817443	−	0.817443i	−0.985737	+	0.168294i	$0.946174\pi$
$432$	−3.31255	−	3.31255i	−0.159375	−	0.159375i
$433$		−	14.3153i		−	0.687951i	−0.938979	−	0.343976i	$-0.888226\pi$
$433$		−	14.3153i		−	0.687951i	0.938979	−	0.343976i	$-0.111774\pi$
$434$		0			0
$435$	−3.27439	−	3.27439i	−0.156995	−	0.156995i
$436$	−4.68860	−	4.68860i	−0.224543	−	0.224543i
$437$	35.6547	−	35.6547i	1.70559	−	1.70559i
$438$	6.63068			0.316826
$439$	−4.06854	+	4.06854i	−0.194181	+	0.194181i	−0.797500	−	0.603319i	$-0.793845\pi$
$439$	−4.06854	+	4.06854i	−0.194181	+	0.194181i	0.603319	+	0.797500i	$0.293845\pi$
$440$		−	3.50758i		−	0.167217i
$441$	−7.00000			−0.333333
$442$		0			0
$443$	−22.8769			−1.08691			−0.543457	−	0.839437i	$-0.682885\pi$
$443$	−22.8769			−1.08691			−0.543457	+	0.839437i	$0.682885\pi$
$444$		−	1.36932i		−	0.0649849i
$445$	−2.82843	+	2.82843i	−0.134080	+	0.134080i
$446$	−21.7538			−1.03007
$447$	−3.00252	+	3.00252i	−0.142015	+	0.142015i
$448$		0			0
$449$	9.00757	+	9.00757i	0.425094	+	0.425094i	0.886953	−	0.461859i	$-0.152818\pi$
$449$	9.00757	+	9.00757i	0.425094	+	0.425094i	−0.461859	+	0.886953i	$0.652818\pi$
$450$			7.31534i			0.344849i
$451$			1.43845i			0.0677338i
$452$	1.41421	+	1.41421i	0.0665190	+	0.0665190i
$453$	−5.65685	−	5.65685i	−0.265782	−	0.265782i
$454$	−25.4558	+	25.4558i	−1.19470	+	1.19470i
$455$		0			0
$456$	13.2502	−	13.2502i	0.620498	−	0.620498i
$457$		−	6.80776i		−	0.318454i	−0.987242	−	0.159227i	$-0.949100\pi$
$457$		−	6.80776i		−	0.318454i	0.987242	−	0.159227i	$-0.0509001\pi$
$458$	9.36932			0.437799
$459$		0			0
$460$	1.61553			0.0753244
$461$			8.24621i			0.384064i	0.981389	+	0.192032i	$0.0615078\pi$
$461$			8.24621i			0.384064i	−0.981389	+	0.192032i	$0.938492\pi$
$462$		0			0
$463$	−24.9848			−1.16114			−0.580572	−	0.814209i	$-0.697171\pi$
$463$	−24.9848			−1.16114			−0.580572	+	0.814209i	$0.697171\pi$
$464$	27.3160	−	27.3160i	1.26811	−	1.26811i
$465$	−2.03427	−	2.03427i	−0.0943371	−	0.0943371i
$466$	−0.620058	−	0.620058i	−0.0287236	−	0.0287236i
$467$			3.36932i			0.155913i	0.996957	+	0.0779567i	$0.0248396\pi$
$467$			3.36932i			0.155913i	−0.996957	+	0.0779567i	$0.975160\pi$
$468$		−	2.00000i		−	0.0924500i
$469$		0			0
$470$	1.78384	+	1.78384i	0.0822825	+	0.0822825i
$471$	−4.01966	+	4.01966i	−0.185216	+	0.185216i
$472$	−2.73863			−0.126056
$473$	13.9192	−	13.9192i	0.640003	−	0.640003i
$474$		−	24.0000i		−	1.10236i
$475$	−36.0000			−1.65179
$476$		0			0
$477$	−4.24621			−0.194421
$478$			16.0000i			0.731823i
$479$	−20.7184	+	20.7184i	−0.946646	+	0.946646i	−0.998647	−	0.0520010i	$-0.983440\pi$
$479$	−20.7184	+	20.7184i	−0.946646	+	0.946646i	0.0520010	+	0.998647i	$0.483440\pi$
$480$	1.36932			0.0625005
$481$	−10.0736	+	10.0736i	−0.459316	+	0.459316i
$482$	−23.5957	−	23.5957i	−1.07475	−	1.07475i
$483$		0			0
$484$			1.94602i			0.0884557i
$485$		−	6.24621i		−	0.283626i
$486$	1.10418	+	1.10418i	0.0500868	+	0.0500868i
$487$	−5.21089	−	5.21089i	−0.236128	−	0.236128i	0.579117	−	0.815245i	$-0.303398\pi$
$487$	−5.21089	−	5.21089i	−0.236128	−	0.236128i	−0.815245	+	0.579117i	$0.803398\pi$
$488$	1.51198	−	1.51198i	0.0684441	−	0.0684441i
$489$	−6.87689			−0.310984
$490$	4.34041	−	4.34041i	0.196080	−	0.196080i
$491$			3.36932i			0.152055i	0.997106	+	0.0760276i	$0.0242237\pi$
$491$			3.36932i			0.152055i	−0.997106	+	0.0760276i	$0.975776\pi$
$492$	−0.246211			−0.0111001
$493$		0			0
$494$	54.7386			2.46281
$495$			1.43845i			0.0646534i
$496$	16.9706	−	16.9706i	0.762001	−	0.762001i
$497$		0			0
$498$	−10.0736	+	10.0736i	−0.451408	+	0.451408i
$499$	−8.03932	−	8.03932i	−0.359889	−	0.359889i	0.503883	−	0.863772i	$-0.331904\pi$
$499$	−8.03932	−	8.03932i	−0.359889	−	0.359889i	−0.863772	+	0.503883i	$0.831904\pi$
$500$	−1.68608	−	1.68608i	−0.0754036	−	0.0754036i
$501$		−	0.807764i		−	0.0360882i
$502$			38.2462i			1.70701i
$503$	17.9877	+	17.9877i	0.802032	+	0.802032i	0.983413	−	0.181381i	$-0.0580567\pi$
$503$	17.9877	+	17.9877i	0.802032	+	0.802032i	−0.181381	+	0.983413i	$0.558057\pi$
$504$		0			0
$505$	7.59336	−	7.59336i	0.337900	−	0.337900i
$506$	−26.2462			−1.16679
$507$	−5.52092	+	5.52092i	−0.245193	+	0.245193i
$508$		−	0.354162i		−	0.0157134i
$509$	16.8769			0.748055			0.374028	−	0.927418i	$-0.377977\pi$
$509$	16.8769			0.748055			0.374028	+	0.927418i	$0.377977\pi$
$510$		0			0
$511$		0			0
$512$		−	11.4233i		−	0.504843i
$513$	−5.43387	+	5.43387i	−0.239911	+	0.239911i
$514$	−14.6307			−0.645332
$515$	1.71353	−	1.71353i	0.0755070	−	0.0755070i
$516$	2.38247	+	2.38247i	0.104882	+	0.104882i
$517$	−5.21089	−	5.21089i	−0.229175	−	0.229175i
$518$		0			0
$519$		−	18.8078i		−	0.825569i
$520$	−4.41674	−	4.41674i	−0.193687	−	0.193687i
$521$	−22.2303	−	22.2303i	−0.973929	−	0.973929i	0.0257398	−	0.999669i	$-0.491806\pi$
$521$	−22.2303	−	22.2303i	−0.973929	−	0.973929i	−0.999669	+	0.0257398i	$0.991806\pi$
$522$	−9.10534	+	9.10534i	−0.398530	+	0.398530i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	5.75462	−	5.75462i	0.251392	−	0.251392i
$525$		0			0
$526$	19.5076			0.850571
$527$		0			0
$528$	−12.0000			−0.522233
$529$			20.0540i			0.871912i
$530$	2.63290	−	2.63290i	0.114366	−	0.114366i
$531$	1.12311			0.0487386
$532$		0			0
$533$	1.81129	+	1.81129i	0.0784557	+	0.0784557i
$534$	7.86522	+	7.86522i	0.340362	+	0.340362i
$535$			4.31534i			0.186568i
$536$			9.75379i			0.421300i
$537$	−6.45101	−	6.45101i	−0.278382	−	0.278382i
$538$	22.7037	+	22.7037i	0.978828	+	0.978828i
$539$	−12.6790	+	12.6790i	−0.546125	+	0.546125i
$540$	−0.246211			−0.0105952
$541$	−28.3606	+	28.3606i	−1.21932	+	1.21932i	−0.251446	+	0.967871i	$0.580906\pi$
$541$	−28.3606	+	28.3606i	−1.21932	+	1.21932i	−0.967871	+	0.251446i	$0.919094\pi$
$542$		−	1.26137i		−	0.0541803i
$543$	−6.00000			−0.257485
$544$		0			0
$545$	8.49242			0.363775
$546$		0			0
$547$	19.7990	−	19.7990i	0.846544	−	0.846544i	−0.143156	−	0.989700i	$-0.545725\pi$
$547$	19.7990	−	19.7990i	0.846544	−	0.846544i	0.989700	+	0.143156i	$0.0457252\pi$
$548$	7.12311			0.304284
$549$	−0.620058	+	0.620058i	−0.0264634	+	0.0264634i
$550$	13.2502	+	13.2502i	0.564991	+	0.564991i
$551$	−44.8089	−	44.8089i	−1.90892	−	1.90892i
$552$			16.0000i			0.681005i
$553$		0			0
$554$	−6.62511	−	6.62511i	−0.281474	−	0.281474i
$555$	1.24012	+	1.24012i	0.0526400	+	0.0526400i
$556$	2.82843	−	2.82843i	0.119952	−	0.119952i
$557$	6.49242			0.275093			0.137546	−	0.990495i	$-0.456078\pi$
$557$	6.49242			0.275093			0.137546	+	0.990495i	$0.456078\pi$
$558$	−5.65685	+	5.65685i	−0.239474	+	0.239474i
$559$		−	35.0540i		−	1.48263i
$560$		0			0
$561$		0			0
$562$	−29.8617			−1.25964
$563$			22.8769i			0.964146i	0.876131	+	0.482073i	$0.160116\pi$
$563$			22.8769i			0.964146i	−0.876131	+	0.482073i	$0.839884\pi$
$564$	0.891921	−	0.891921i	0.0375566	−	0.0375566i
$565$	−2.56155			−0.107765
$566$	3.72035	−	3.72035i	0.156378	−	0.156378i
$567$		0			0
$568$	17.6670	+	17.6670i	0.741289	+	0.741289i
$569$		−	12.8769i		−	0.539827i	−0.962885	−	0.269914i	$-0.913005\pi$
$569$		−	12.8769i		−	0.539827i	0.962885	−	0.269914i	$-0.0869952\pi$
$570$		−	6.73863i		−	0.282250i
$571$	−13.2502	−	13.2502i	−0.554504	−	0.554504i	0.373233	−	0.927738i	$-0.378249\pi$
$571$	−13.2502	−	13.2502i	−0.554504	−	0.554504i	−0.927738	+	0.373233i	$0.878249\pi$
$572$	−3.62258	−	3.62258i	−0.151468	−	0.151468i
$573$	−9.27944	+	9.27944i	−0.387654	+	0.387654i
$574$		0			0
$575$	21.7355	−	21.7355i	0.906433	−	0.906433i
$576$			5.56155i			0.231731i
$577$	−41.0540			−1.70910			−0.854550	−	0.519370i	$-0.826167\pi$
$577$	−41.0540			−1.70910			−0.854550	+	0.519370i	$0.826167\pi$
$578$		0			0
$579$	24.2462			1.00764
$580$		−	2.03031i		−	0.0843040i
$581$		0			0
$582$	−17.3693			−0.719981
$583$	−7.69113	+	7.69113i	−0.318534	+	0.318534i
$584$	−7.32150	−	7.32150i	−0.302966	−	0.302966i
$585$	1.81129	+	1.81129i	0.0748877	+	0.0748877i
$586$			11.1231i			0.459491i
$587$		−	36.9848i		−	1.52653i	−0.646087	−	0.763264i	$-0.723596\pi$
$587$		−	36.9848i		−	1.52653i	0.646087	−	0.763264i	$-0.276404\pi$
$588$	−2.17020	−	2.17020i	−0.0894977	−	0.0894977i
$589$	−27.8383	−	27.8383i	−1.14706	−	1.14706i
$590$	−0.696391	+	0.696391i	−0.0286699	+	0.0286699i
$591$	19.9309			0.819846
$592$	−10.3455	+	10.3455i	−0.425196	+	0.425196i
$593$			44.2462i			1.81697i	0.417913	+	0.908487i	$0.362762\pi$
$593$			44.2462i			1.81697i	−0.417913	+	0.908487i	$0.637238\pi$
$594$	4.00000			0.164122
$595$		0			0
$596$	−1.86174			−0.0762598
$597$		−	16.0000i		−	0.654836i
$598$	−33.0492	+	33.0492i	−1.35148	+	1.35148i
$599$	41.6155			1.70036			0.850182	−	0.526489i	$-0.176492\pi$
$599$	41.6155			1.70036			0.850182	+	0.526489i	$0.176492\pi$
$600$	8.07749	−	8.07749i	0.329762	−	0.329762i
$601$	24.7380	+	24.7380i	1.00908	+	1.00908i	0.999958	+	0.00912658i	$0.00290512\pi$
$601$	24.7380	+	24.7380i	1.00908	+	1.00908i	0.00912658	+	0.999958i	$0.497095\pi$
$602$		0			0
$603$		−	4.00000i		−	0.162893i
$604$		−	3.50758i		−	0.142721i
$605$	−1.76241	−	1.76241i	−0.0716521	−	0.0716521i
$606$	−21.1154	−	21.1154i	−0.857756	−	0.857756i
$607$	−10.8677	+	10.8677i	−0.441108	+	0.441108i	−0.892384	−	0.451276i	$-0.850969\pi$
$607$	−10.8677	+	10.8677i	−0.441108	+	0.441108i	0.451276	+	0.892384i	$0.350969\pi$
$608$	18.7386			0.759952
$609$		0			0
$610$		−	0.768944i		−	0.0311336i
$611$	−13.1231			−0.530904
$612$		0			0
$613$	2.31534			0.0935158			0.0467579	−	0.998906i	$-0.485111\pi$
$613$	2.31534			0.0935158			0.0467579	+	0.998906i	$0.485111\pi$
$614$		−	0.768944i		−	0.0310320i
$615$	0.222980	−	0.222980i	0.00899143	−	0.00899143i
$616$		0			0
$617$	19.6249	−	19.6249i	0.790068	−	0.790068i	−0.191437	−	0.981505i	$-0.561315\pi$
$617$	19.6249	−	19.6249i	0.790068	−	0.790068i	0.981505	+	0.191437i	$0.0613146\pi$
$618$	−4.76493	−	4.76493i	−0.191674	−	0.191674i
$619$	13.6962	+	13.6962i	0.550496	+	0.550496i	0.926584	−	0.376088i	$-0.122731\pi$
$619$	13.6962	+	13.6962i	0.550496	+	0.550496i	−0.376088	+	0.926584i	$0.622731\pi$
$620$		−	1.26137i		−	0.0506577i
$621$		−	6.56155i		−	0.263306i
$622$		0			0
$623$		0			0
$624$	−15.1104	+	15.1104i	−0.604900	+	0.604900i
$625$	−20.3693			−0.814773
$626$	−8.40895	+	8.40895i	−0.336089	+	0.336089i
$627$			19.6847i			0.786130i
$628$	−2.49242			−0.0994585
$629$		0			0
$630$		0			0
$631$			11.6847i			0.465159i	0.972577	+	0.232579i	$0.0747166\pi$
$631$			11.6847i			0.465159i	−0.972577	+	0.232579i	$0.925283\pi$
$632$	−26.5004	+	26.5004i	−1.05413	+	1.05413i
$633$	−11.3693			−0.451890
$634$	19.8753	−	19.8753i	0.789350	−	0.789350i
$635$	0.320745	+	0.320745i	0.0127284	+	0.0127284i
$636$	−1.31645	−	1.31645i	−0.0522006	−	0.0522006i
$637$			31.9309i			1.26515i
$638$			32.9848i			1.30588i
$639$	−7.24517	−	7.24517i	−0.286614	−	0.286614i
$640$	−5.38499	−	5.38499i	−0.212860	−	0.212860i
$641$	0.0488825	−	0.0488825i	0.00193074	−	0.00193074i	−0.706141	−	0.708071i	$-0.749565\pi$
$641$	0.0488825	−	0.0488825i	0.00193074	−	0.00193074i	0.708071	+	0.706141i	$0.249565\pi$
$642$	12.0000			0.473602
$643$	−21.3873	+	21.3873i	−0.843433	+	0.843433i	−0.989304	−	0.145871i	$-0.953402\pi$
$643$	−21.3873	+	21.3873i	−0.843433	+	0.843433i	0.145871	+	0.989304i	$0.453402\pi$
$644$		0			0
$645$	−4.31534			−0.169916
$646$		0			0
$647$	15.3693			0.604230			0.302115	−	0.953271i	$-0.402307\pi$
$647$	15.3693			0.604230			0.302115	+	0.953271i	$0.402307\pi$
$648$		−	2.43845i		−	0.0957913i
$649$	2.03427	−	2.03427i	0.0798521	−	0.0798521i
$650$	33.3693			1.30885
$651$		0			0
$652$	−2.13204	−	2.13204i	−0.0834970	−	0.0834970i
$653$	2.87731	+	2.87731i	0.112598	+	0.112598i	0.761161	−	0.648563i	$-0.224630\pi$
$653$	2.87731	+	2.87731i	0.112598	+	0.112598i	−0.648563	+	0.761161i	$0.724630\pi$
$654$		−	23.6155i		−	0.923440i
$655$			10.4233i			0.407272i
$656$	1.86017	+	1.86017i	0.0726276	+	0.0726276i
$657$	3.00252	+	3.00252i	0.117140	+	0.117140i
$658$		0			0
$659$	−47.8617			−1.86443			−0.932214	−	0.361907i	$-0.882126\pi$
$659$	−47.8617			−1.86443			−0.932214	+	0.361907i	$0.882126\pi$
$660$	−0.445960	+	0.445960i	−0.0173590	+	0.0173590i
$661$			25.6847i			0.999017i	0.866309	+	0.499509i	$0.166486\pi$
$661$			25.6847i			0.999017i	−0.866309	+	0.499509i	$0.833514\pi$
$662$	−9.47727			−0.368344
$663$		0			0
$664$	22.2462			0.863320
$665$		0			0
$666$	3.44849	−	3.44849i	0.133626	−	0.133626i
$667$	54.1080			2.09507
$668$	0.250430	−	0.250430i	0.00968944	−	0.00968944i
$669$	−9.85061	−	9.85061i	−0.380847	−	0.380847i
$670$	2.48023	+	2.48023i	0.0958197	+	0.0958197i
$671$			2.24621i			0.0867140i
$672$		0			0
$673$	−34.4634	−	34.4634i	−1.32847	−	1.32847i	−0.906708	−	0.421759i	$-0.861413\pi$
$673$	−34.4634	−	34.4634i	−1.32847	−	1.32847i	−0.421759	−	0.906708i	$-0.638587\pi$
$674$	36.1495	+	36.1495i	1.39243	+	1.39243i
$675$	−3.31255	+	3.31255i	−0.127500	+	0.127500i
$676$	−3.42329			−0.131665
$677$	−9.67651	+	9.67651i	−0.371899	+	0.371899i	−0.868168	−	0.496270i	$-0.834703\pi$
$677$	−9.67651	+	9.67651i	−0.371899	+	0.371899i	0.496270	+	0.868168i	$0.334703\pi$
$678$			7.12311i			0.273561i
$679$		0			0
$680$		0			0
$681$	−23.0540			−0.883430
$682$			20.4924i			0.784695i
$683$	−3.84556	+	3.84556i	−0.147146	+	0.147146i	−0.776842	−	0.629696i	$-0.783180\pi$
$683$	−3.84556	+	3.84556i	−0.147146	+	0.147146i	0.629696	+	0.776842i	$0.283180\pi$
$684$	−3.36932			−0.128829
$685$	−6.45101	+	6.45101i	−0.246480	+	0.246480i
$686$		0			0
$687$	4.24264	+	4.24264i	0.161867	+	0.161867i
$688$		−	36.0000i		−	1.37249i
$689$			19.3693i			0.737912i
$690$	4.06854	+	4.06854i	0.154887	+	0.154887i
$691$	26.1522	+	26.1522i	0.994878	+	0.994878i	0.999987	−	0.00510905i	$-0.00162627\pi$
$691$	26.1522	+	26.1522i	0.994878	+	0.994878i	−0.00510905	+	0.999987i	$0.501626\pi$
$692$	5.83095	−	5.83095i	0.221660	−	0.221660i
$693$		0			0
$694$	27.0442	−	27.0442i	1.02658	−	1.02658i
$695$			5.12311i			0.194330i
$696$	20.1080			0.762190
$697$		0			0
$698$	11.6155			0.439654
$699$		−	0.561553i		−	0.0212399i
$700$		0			0
$701$	9.36932			0.353874			0.176937	−	0.984222i	$-0.443381\pi$
$701$	9.36932			0.353874			0.176937	+	0.984222i	$0.443381\pi$
$702$	5.03680	−	5.03680i	0.190102	−	0.190102i
$703$	16.9706	+	16.9706i	0.640057	+	0.640057i
$704$	10.0736	+	10.0736i	0.379663	+	0.379663i
$705$			1.61553i			0.0608443i
$706$		−	35.1231i		−	1.32188i
$707$		0			0
$708$	0.348195	+	0.348195i	0.0130860	+	0.0130860i
$709$	−3.35072	+	3.35072i	−0.125839	+	0.125839i	−0.767221	−	0.641382i	$-0.778361\pi$
$709$	−3.35072	+	3.35072i	−0.125839	+	0.125839i	0.641382	+	0.767221i	$0.278361\pi$
$710$	8.98485			0.337195
$711$	10.8677	−	10.8677i	0.407572	−	0.407572i
$712$		−	17.3693i		−	0.650943i
$713$	33.6155			1.25891
$714$		0			0
$715$	6.56155			0.245388
$716$		−	4.00000i		−	0.149487i
$717$	−7.24517	+	7.24517i	−0.270576	+	0.270576i
$718$	3.50758			0.130902
$719$	−6.22803	+	6.22803i	−0.232266	+	0.232266i	−0.813638	−	0.581372i	$-0.802516\pi$
$719$	−6.22803	+	6.22803i	−0.232266	+	0.232266i	0.581372	+	0.813638i	$0.302516\pi$
$720$	1.86017	+	1.86017i	0.0693246	+	0.0693246i
$721$		0			0
$722$		−	62.5464i		−	2.32774i
$723$		−	21.3693i		−	0.794733i
$724$	−1.86017	−	1.86017i	−0.0691328	−	0.0691328i
$725$	−27.3160	−	27.3160i	−1.01449	−	1.01449i
$726$	−4.90086	+	4.90086i	−0.181888	+	0.181888i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$	−3.72348			−0.137812
$731$		0			0
$732$	−0.384472			−0.0142105
$733$		−	28.2462i		−	1.04330i	−0.853160	−	0.521649i	$-0.825317\pi$
$733$		−	28.2462i		−	1.04330i	0.853160	−	0.521649i	$-0.174683\pi$
$734$	−20.1472	+	20.1472i	−0.743646	+	0.743646i
$735$	3.93087			0.144992
$736$	−11.3137	+	11.3137i	−0.417029	+	0.417029i
$737$	−7.24517	−	7.24517i	−0.266879	−	0.266879i
$738$	−0.620058	−	0.620058i	−0.0228246	−	0.0228246i
$739$			8.31534i			0.305885i	0.988235	+	0.152942i	$0.0488749\pi$
$739$			8.31534i			0.305885i	−0.988235	+	0.152942i	$0.951125\pi$
$740$			0.768944i			0.0282669i
$741$	24.7869	+	24.7869i	0.910570	+	0.910570i
$742$		0			0
$743$	3.17662	−	3.17662i	0.116539	−	0.116539i	−0.646432	−	0.762971i	$-0.723740\pi$
$743$	3.17662	−	3.17662i	0.116539	−	0.116539i	0.762971	+	0.646432i	$0.223740\pi$
$744$	12.4924			0.457994
$745$	1.68608	−	1.68608i	0.0617731	−	0.0617731i
$746$			25.3693i			0.928837i
$747$	−9.12311			−0.333797
$748$		0			0
$749$		0			0
$750$		−	8.49242i		−	0.310099i
$751$	−0.445960	+	0.445960i	−0.0162733	+	0.0162733i	−0.715197	−	0.698923i	$-0.753663\pi$
$751$	−0.445960	+	0.445960i	−0.0162733	+	0.0162733i	0.698923	+	0.715197i	$0.253663\pi$
$752$	−13.4773			−0.491465
$753$	−17.3188	+	17.3188i	−0.631131	+	0.631131i
$754$	41.5345	+	41.5345i	1.51260	+	1.51260i
$755$	3.17662	+	3.17662i	0.115609	+	0.115609i
$756$		0			0
$757$			21.0540i			0.765220i	0.923910	+	0.382610i	$0.124975\pi$
$757$			21.0540i			0.765220i	−0.923910	+	0.382610i	$0.875025\pi$
$758$	13.2502	+	13.2502i	0.481269	+	0.481269i
$759$	−11.8849	−	11.8849i	−0.431394	−	0.431394i
$760$	−7.44070	+	7.44070i	−0.269902	+	0.269902i
$761$	32.2462			1.16892			0.584462	−	0.811421i	$-0.301306\pi$
$761$	32.2462			1.16892			0.584462	+	0.811421i	$0.301306\pi$
$762$	0.891921	−	0.891921i	0.0323109	−	0.0323109i
$763$		0			0
$764$	−5.75379			−0.208165
$765$		0			0
$766$	−16.0000			−0.578103
$767$		−	5.12311i		−	0.184985i
$768$	−7.10923	+	7.10923i	−0.256532	+	0.256532i
$769$	29.5464			1.06547			0.532735	−	0.846282i	$-0.321164\pi$
$769$	29.5464			1.06547			0.532735	+	0.846282i	$0.321164\pi$
$770$		0			0
$771$	−6.62511	−	6.62511i	−0.238597	−	0.238597i
$772$	7.51703	+	7.51703i	0.270544	+	0.270544i
$773$			33.3693i			1.20021i	0.799921	+	0.600105i	$0.204875\pi$
$773$			33.3693i			1.20021i	−0.799921	+	0.600105i	$0.795125\pi$
$774$			12.0000i			0.431331i
$775$	−16.9706	−	16.9706i	−0.609601	−	0.609601i
$776$	19.1789	+	19.1789i	0.688484	+	0.688484i
$777$		0			0
$778$	34.1383			1.22392
$779$	3.05141	−	3.05141i	0.109328	−	0.109328i
$780$			1.12311i			0.0402136i
$781$	−26.2462			−0.939163
$782$		0			0
$783$	−8.24621			−0.294696
$784$			32.7926i			1.17116i
$785$	2.25725	−	2.25725i	0.0805648	−	0.0805648i
$786$	28.9848			1.03386
$787$	−4.41674	+	4.41674i	−0.157440	+	0.157440i	−0.781431	−	0.623991i	$-0.785510\pi$
$787$	−4.41674	+	4.41674i	−0.157440	+	0.157440i	0.623991	+	0.781431i	$0.285510\pi$
$788$	6.17915	+	6.17915i	0.220123	+	0.220123i
$789$	8.83348	+	8.83348i	0.314480	+	0.314480i
$790$			13.4773i			0.479500i
$791$		0			0
$792$	−4.41674	−	4.41674i	−0.156942	−	0.156942i
$793$	2.82843	+	2.82843i	0.100440	+	0.100440i
$794$	−5.92872	+	5.92872i	−0.210402	+	0.210402i
$795$	2.38447			0.0845685
$796$	4.96046	−	4.96046i	0.175819	−	0.175819i
$797$			31.6155i			1.11988i	0.828533	+	0.559940i	$0.189176\pi$
$797$			31.6155i			1.11988i	−0.828533	+	0.559940i	$0.810824\pi$
$798$		0			0
$799$		0			0
$800$	11.4233			0.403874
$801$			7.12311i			0.251683i
$802$	−6.82064	+	6.82064i	−0.240845	+	0.240845i
$803$	10.8769			0.383837
$804$	1.24012	−	1.24012i	0.0437355	−	0.0437355i
$805$		0			0
$806$	25.8040	+	25.8040i	0.908909	+	0.908909i
$807$			20.5616i			0.723801i
$808$			46.6307i			1.64046i
$809$	−37.5148	−	37.5148i	−1.31895	−	1.31895i	−0.914607	−	0.404344i	$-0.867500\pi$
$809$	−37.5148	−	37.5148i	−1.31895	−	1.31895i	−0.404344	−	0.914607i	$-0.632500\pi$
$810$	−0.620058	−	0.620058i	−0.0217866	−	0.0217866i
$811$	14.5881	−	14.5881i	0.512257	−	0.512257i	−0.402960	−	0.915218i	$-0.632019\pi$
$811$	14.5881	−	14.5881i	0.512257	−	0.512257i	0.915218	+	0.402960i	$0.132019\pi$
$812$		0			0
$813$	0.571175	−	0.571175i	0.0200320	−	0.0200320i
$814$		−	12.4924i		−	0.437859i
$815$	3.86174			0.135271
$816$		0			0
$817$	−59.0540			−2.06604
$818$		−	3.61553i		−	0.126414i
$819$		0			0
$820$	0.138261			0.00482827
$821$	11.7108	−	11.7108i	0.408709	−	0.408709i	−0.472579	−	0.881288i	$-0.656677\pi$
$821$	11.7108	−	11.7108i	0.408709	−	0.408709i	0.881288	+	0.472579i	$0.156677\pi$
$822$	17.9388	+	17.9388i	0.625688	+	0.625688i
$823$	−25.8040	−	25.8040i	−0.899472	−	0.899472i	0.0959171	−	0.995389i	$-0.469422\pi$
$823$	−25.8040	−	25.8040i	−0.899472	−	0.899472i	−0.995389	+	0.0959171i	$0.969422\pi$
$824$			10.5227i			0.366577i
$825$			12.0000i			0.417786i
$826$		0			0
$827$	−10.1988	−	10.1988i	−0.354647	−	0.354647i	0.507188	−	0.861835i	$-0.330685\pi$
$827$	−10.1988	−	10.1988i	−0.354647	−	0.354647i	−0.861835	+	0.507188i	$0.830685\pi$
$828$	2.03427	−	2.03427i	0.0706958	−	0.0706958i
$829$	−50.4924			−1.75367			−0.876837	−	0.480787i	$-0.840351\pi$
$829$	−50.4924			−1.75367			−0.876837	+	0.480787i	$0.840351\pi$
$830$	5.65685	−	5.65685i	0.196352	−	0.196352i
$831$		−	6.00000i		−	0.208138i
$832$	25.3693			0.879523
$833$		0			0
$834$	14.2462			0.493306
$835$			0.453602i			0.0156976i
$836$	−6.10281	+	6.10281i	−0.211070	+	0.211070i
$837$	−5.12311			−0.177080
$838$	−35.8776	+	35.8776i	−1.23937	+	1.23937i
$839$	7.81634	+	7.81634i	0.269850	+	0.269850i	0.829040	−	0.559190i	$-0.188888\pi$
$839$	7.81634	+	7.81634i	0.269850	+	0.269850i	−0.559190	+	0.829040i	$0.688888\pi$
$840$		0			0
$841$		−	39.0000i		−	1.34483i
$842$		−	44.6004i		−	1.53703i
$843$	−13.5221	−	13.5221i	−0.465725	−	0.465725i
$844$	−3.52482	−	3.52482i	−0.121329	−	0.121329i
$845$	3.10029	−	3.10029i	0.106653	−	0.106653i
$846$	4.49242			0.154453
$847$		0			0
$848$			19.8920i			0.683096i
$849$	3.36932			0.115635
$850$		0			0
$851$	−20.4924			−0.702471
$852$		−	4.49242i		−	0.153908i
$853$	14.6644	−	14.6644i	0.502100	−	0.502100i	−0.409990	−	0.912090i	$-0.634468\pi$
$853$	14.6644	−	14.6644i	0.502100	−	0.502100i	0.912090	+	0.409990i	$0.134468\pi$
$854$		0			0
$855$	3.05141	−	3.05141i	0.104356	−	0.104356i
$856$	−13.2502	−	13.2502i	−0.452883	−	0.452883i
$857$	4.24264	+	4.24264i	0.144926	+	0.144926i	0.775847	−	0.630921i	$-0.217323\pi$
$857$	4.24264	+	4.24264i	0.144926	+	0.144926i	−0.630921	+	0.775847i	$0.717323\pi$
$858$		−	18.2462i		−	0.622915i
$859$		−	12.0000i		−	0.409435i	−0.978821	−	0.204717i	$-0.934372\pi$
$859$		−	12.0000i		−	0.409435i	0.978821	−	0.204717i	$-0.0656275\pi$
$860$	−1.33788	−	1.33788i	−0.0456214	−	0.0456214i
$861$		0			0
$862$	26.5004	−	26.5004i	0.902608	−	0.902608i
$863$	26.2462			0.893431			0.446716	−	0.894676i	$-0.352594\pi$
$863$	26.2462			0.893431			0.446716	+	0.894676i	$0.352594\pi$
$864$	1.72424	−	1.72424i	0.0586599	−	0.0586599i
$865$			10.5616i			0.359104i
$866$	22.3542			0.759625
$867$		0			0
$868$		0			0
$869$		−	39.3693i		−	1.33551i
$870$	5.11313	−	5.11313i	0.173351	−	0.173351i
$871$	−18.2462			−0.618249
$872$	−26.0759	+	26.0759i	−0.883041	+	0.883041i
$873$	−7.86522	−	7.86522i	−0.266197	−	0.266197i
$874$	55.6766	+	55.6766i	1.88329	+	1.88329i
$875$		0			0
$876$			1.86174i			0.0629023i
$877$	24.0416	+	24.0416i	0.811828	+	0.811828i	0.984908	−	0.173080i	$-0.0553718\pi$
$877$	24.0416	+	24.0416i	0.811828	+	0.811828i	−0.173080	+	0.984908i	$0.555372\pi$
$878$	−6.35324	−	6.35324i	−0.214412	−	0.214412i
$879$	−5.03680	+	5.03680i	−0.169887	+	0.169887i
$880$	6.73863			0.227159
$881$	16.7965	−	16.7965i	0.565887	−	0.565887i	−0.365086	−	0.930974i	$-0.618961\pi$
$881$	16.7965	−	16.7965i	0.565887	−	0.565887i	0.930974	+	0.365086i	$0.118961\pi$
$882$		−	10.9309i		−	0.368062i
$883$	38.4233			1.29305			0.646523	−	0.762894i	$-0.276222\pi$
$883$	38.4233			1.29305			0.646523	+	0.762894i	$0.276222\pi$
$884$		0			0
$885$	−0.630683			−0.0212002
$886$		−	35.7235i		−	1.20015i
$887$	15.9534	−	15.9534i	0.535664	−	0.535664i	−0.386589	−	0.922252i	$-0.626347\pi$
$887$	15.9534	−	15.9534i	0.535664	−	0.535664i	0.922252	+	0.386589i	$0.126347\pi$
$888$	−7.61553			−0.255560
$889$		0			0
$890$	−4.41674	−	4.41674i	−0.148049	−	0.148049i
$891$	1.81129	+	1.81129i	0.0606805	+	0.0606805i
$892$		−	6.10795i		−	0.204509i
$893$			22.1080i			0.739814i
$894$	−4.68860	−	4.68860i	−0.156810	−	0.156810i
$895$	3.62258	+	3.62258i	0.121090	+	0.121090i
$896$		0			0
$897$	−29.9309			−0.999363
$898$	−14.0658	+	14.0658i	−0.469382	+	0.469382i
$899$		−	42.2462i		−	1.40899i
$900$	−2.05398			−0.0684658
$901$		0			0
$902$	−2.24621			−0.0747907
$903$		0			0
$904$	7.86522	−	7.86522i	0.261593	−	0.261593i
$905$	3.36932			0.112000
$906$	8.83348	−	8.83348i	0.293473	−	0.293473i
$907$	33.8434	+	33.8434i	1.12375	+	1.12375i	0.991173	+	0.132578i	$0.0423254\pi$
$907$	33.8434	+	33.8434i	1.12375	+	1.12375i	0.132578	+	0.991173i	$0.457675\pi$
$908$	−7.14740	−	7.14740i	−0.237195	−	0.237195i
$909$		−	19.1231i		−	0.634273i
$910$		0			0
$911$	20.7184	+	20.7184i	0.686430	+	0.686430i	0.961441	−	0.275011i	$-0.0886815\pi$
$911$	20.7184	+	20.7184i	0.686430	+	0.686430i	−0.275011	+	0.961441i	$0.588682\pi$
$912$	25.4558	+	25.4558i	0.842927	+	0.842927i
$913$	−16.5246	+	16.5246i	−0.546885	+	0.546885i
$914$	10.6307			0.351632
$915$	0.348195	−	0.348195i	0.0115110	−	0.0115110i
$916$			2.63068i			0.0869202i
$917$		0			0
$918$		0			0
$919$	−4.31534			−0.142350			−0.0711750	−	0.997464i	$-0.522675\pi$
$919$	−4.31534			−0.142350			−0.0711750	+	0.997464i	$0.522675\pi$
$920$		−	8.98485i		−	0.296222i
$921$	0.348195	−	0.348195i	0.0114734	−	0.0114734i
$922$	−12.8769			−0.424078
$923$	−33.0492	+	33.0492i	−1.08783	+	1.08783i
$924$		0			0
$925$	10.3455	+	10.3455i	0.340156	+	0.340156i
$926$		−	39.0152i		−	1.28212i
$927$		−	4.31534i		−	0.141734i
$928$	14.2185	+	14.2185i	0.466744	+	0.466744i
$929$	22.5785	+	22.5785i	0.740778	+	0.740778i	0.972728	−	0.231950i	$-0.0745106\pi$
$929$	22.5785	+	22.5785i	0.740778	+	0.740778i	−0.231950	+	0.972728i	$0.574511\pi$
$930$	3.17662	−	3.17662i	0.104166	−	0.104166i
$931$	53.7926			1.76298
$932$	0.174098	−	0.174098i	0.00570276	−	0.00570276i
$933$		0			0
$934$	−5.26137			−0.172157
$935$		0			0
$936$	−11.1231			−0.363570
$937$		−	22.0000i		−	0.718709i	−0.933201	−	0.359354i	$-0.882997\pi$
$937$		−	22.0000i		−	0.718709i	0.933201	−	0.359354i	$-0.117003\pi$
$938$		0			0
$939$	−7.61553			−0.248523
$940$	−0.500861	+	0.500861i	−0.0163363	+	0.0163363i
$941$	21.2132	+	21.2132i	0.691531	+	0.691531i	0.962569	−	0.271038i	$-0.0873669\pi$
$941$	21.2132	+	21.2132i	0.691531	+	0.691531i	−0.271038	+	0.962569i	$0.587367\pi$
$942$	−6.27691	−	6.27691i	−0.204513	−	0.204513i
$943$			3.68466i			0.119989i
$944$		−	5.26137i		−	0.171243i
$945$		0			0
$946$	21.7355	+	21.7355i	0.706682	+	0.706682i
$947$	−8.48528	+	8.48528i	−0.275735	+	0.275735i	−0.831404	−	0.555669i	$-0.812462\pi$
$947$	−8.48528	+	8.48528i	−0.275735	+	0.275735i	0.555669	+	0.831404i	$0.312462\pi$
$948$	6.73863			0.218861
$949$	13.6962	−	13.6962i	0.444597	−	0.444597i
$950$		−	56.2159i		−	1.82388i
$951$	18.0000			0.583690
$952$		0			0
$953$	−54.3542			−1.76070			−0.880352	−	0.474321i	$-0.842694\pi$
$953$	−54.3542			−1.76070			−0.880352	+	0.474321i	$0.842694\pi$
$954$		−	6.63068i		−	0.214676i
$955$	5.21089	−	5.21089i	0.168621	−	0.168621i
$956$	−4.49242			−0.145295
$957$	−14.9363	+	14.9363i	−0.482822	+	0.482822i
$958$	−32.3528	−	32.3528i	−1.04527	−	1.04527i
$959$		0			0
$960$		−	3.12311i		−	0.100798i
$961$			4.75379i			0.153348i
$962$	−15.7304	−	15.7304i	−0.507170	−	0.507170i
$963$	5.43387	+	5.43387i	0.175104	+	0.175104i
$964$	6.62511	−	6.62511i	0.213380	−	0.213380i
$965$	−13.6155			−0.438299
$966$		0			0
$967$			46.5616i			1.49732i	0.662955	+	0.748659i	$0.269302\pi$
$967$			46.5616i			1.49732i	−0.662955	+	0.748659i	$0.730698\pi$
$968$	10.8229			0.347862
$969$		0			0
$970$	9.75379			0.313175
$971$		−	2.38447i		−	0.0765213i	−0.999268	−	0.0382607i	$-0.987818\pi$
$971$		−	2.38447i		−	0.0765213i	0.999268	−	0.0382607i	$-0.0121817\pi$
$972$	−0.310029	+	0.310029i	−0.00994418	+	0.00994418i
$973$		0			0
$974$	8.13709	−	8.13709i	0.260729	−	0.260729i
$975$	15.1104	+	15.1104i	0.483920	+	0.483920i
$976$	2.90476	+	2.90476i	0.0929791	+	0.0929791i
$977$			8.24621i			0.263820i	0.991262	+	0.131910i	$0.0421109\pi$
$977$			8.24621i			0.263820i	−0.991262	+	0.131910i	$0.957889\pi$
$978$		−	10.7386i		−	0.343384i
$979$	12.9020	+	12.9020i	0.412350	+	0.412350i
$980$	1.21868	+	1.21868i	0.0389294	+	0.0389294i
$981$	10.6937	−	10.6937i	0.341422	−	0.341422i
$982$	−5.26137			−0.167897
$983$	1.46310	−	1.46310i	0.0466655	−	0.0466655i	−0.683389	−	0.730054i	$-0.739495\pi$
$983$	1.46310	−	1.46310i	0.0466655	−	0.0466655i	0.730054	+	0.683389i	$0.239495\pi$
$984$			1.36932i			0.0436522i
$985$	−11.1922			−0.356614
$986$		0			0
$987$		0			0
$988$			15.3693i			0.488963i
$989$	35.6547	−	35.6547i	1.13375	−	1.13375i
$990$	−2.24621			−0.0713893
$991$	4.76493	−	4.76493i	0.151363	−	0.151363i	−0.627363	−	0.778727i	$-0.715866\pi$
$991$	4.76493	−	4.76493i	0.151363	−	0.151363i	0.778727	+	0.627363i	$0.215866\pi$
$992$	8.83348	+	8.83348i	0.280463	+	0.280463i
$993$	−4.29152	−	4.29152i	−0.136187	−	0.136187i
$994$		0			0
$995$			8.98485i			0.284839i
$996$	−2.82843	−	2.82843i	−0.0896221	−	0.0896221i
$997$	−7.07107	−	7.07107i	−0.223943	−	0.223943i	0.586214	−	0.810157i	$-0.300618\pi$
$997$	−7.07107	−	7.07107i	−0.223943	−	0.223943i	−0.810157	+	0.586214i	$0.800618\pi$
$998$	12.5538	−	12.5538i	0.397384	−	0.397384i
$999$	3.12311			0.0988107

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.e.f.616.3		8
17.2	even	8		867.2.d.c.577.2		4
17.3	odd	16		867.2.h.j.733.3		16
17.4	even	4	inner	867.2.e.f.829.2		8
17.5	odd	16		867.2.h.j.712.1		16
17.6	odd	16		867.2.h.j.688.1		16
17.7	odd	16		867.2.h.j.757.4		16
17.8	even	8		867.2.a.f.1.2		2
17.9	even	8		51.2.a.b.1.2	✓	2
17.10	odd	16		867.2.h.j.757.3		16
17.11	odd	16		867.2.h.j.688.2		16
17.12	odd	16		867.2.h.j.712.2		16
17.13	even	4	inner	867.2.e.f.829.1		8
17.14	odd	16		867.2.h.j.733.4		16
17.15	even	8		867.2.d.c.577.1		4
17.16	even	2	inner	867.2.e.f.616.4		8
51.8	odd	8		2601.2.a.t.1.1		2
51.26	odd	8		153.2.a.e.1.1		2
68.43	odd	8		816.2.a.m.1.1		2
85.9	even	8		1275.2.a.n.1.1		2
85.43	odd	8		1275.2.b.d.1174.2		4
85.77	odd	8		1275.2.b.d.1174.3		4
119.111	odd	8		2499.2.a.o.1.2		2
136.43	odd	8		3264.2.a.bg.1.2		2
136.77	even	8		3264.2.a.bl.1.2		2
187.43	odd	8		6171.2.a.p.1.1		2
204.179	even	8		2448.2.a.v.1.2		2
221.77	even	8		8619.2.a.q.1.1		2
255.179	odd	8		3825.2.a.s.1.2		2
357.230	even	8		7497.2.a.v.1.1		2
408.77	odd	8		9792.2.a.cy.1.1		2
408.179	even	8		9792.2.a.cz.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.a.b.1.2	✓	2	17.9	even	8
153.2.a.e.1.1		2	51.26	odd	8
816.2.a.m.1.1		2	68.43	odd	8
867.2.a.f.1.2		2	17.8	even	8
867.2.d.c.577.1		4	17.15	even	8
867.2.d.c.577.2		4	17.2	even	8
867.2.e.f.616.3		8	1.1	even	1	trivial
867.2.e.f.616.4		8	17.16	even	2	inner
867.2.e.f.829.1		8	17.13	even	4	inner
867.2.e.f.829.2		8	17.4	even	4	inner
867.2.h.j.688.1		16	17.6	odd	16
867.2.h.j.688.2		16	17.11	odd	16
867.2.h.j.712.1		16	17.5	odd	16
867.2.h.j.712.2		16	17.12	odd	16
867.2.h.j.733.3		16	17.3	odd	16
867.2.h.j.733.4		16	17.14	odd	16
867.2.h.j.757.3		16	17.10	odd	16
867.2.h.j.757.4		16	17.7	odd	16
1275.2.a.n.1.1		2	85.9	even	8
1275.2.b.d.1174.2		4	85.43	odd	8
1275.2.b.d.1174.3		4	85.77	odd	8
2448.2.a.v.1.2		2	204.179	even	8
2499.2.a.o.1.2		2	119.111	odd	8
2601.2.a.t.1.1		2	51.8	odd	8
3264.2.a.bg.1.2		2	136.43	odd	8
3264.2.a.bl.1.2		2	136.77	even	8
3825.2.a.s.1.2		2	255.179	odd	8
6171.2.a.p.1.1		2	187.43	odd	8
7497.2.a.v.1.1		2	357.230	even	8
8619.2.a.q.1.1		2	221.77	even	8
9792.2.a.cy.1.1		2	408.77	odd	8
9792.2.a.cz.1.1		2	408.179	even	8

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.56155i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.438447 q^{4} +(0.397078 - 0.397078i) q^{5} +(-1.10418 - 1.10418i) q^{6} +2.43845i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.56155i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.438447 q^{4} +(0.397078 - 0.397078i) q^{5} +(-1.10418 - 1.10418i) q^{6} +2.43845i q^{8} -1.00000i q^{9} +(0.620058 + 0.620058i) q^{10} +(-1.81129 - 1.81129i) q^{11} +(0.310029 - 0.310029i) q^{12} -4.56155 q^{13} +0.561553i q^{15} -4.68466 q^{16} +1.56155 q^{18} +7.68466i q^{19} +(-0.174098 + 0.174098i) q^{20} +(2.82843 - 2.82843i) q^{22} +(-4.63972 - 4.63972i) q^{23} +(-1.72424 - 1.72424i) q^{24} +4.68466i q^{25} -7.12311i q^{26} +(0.707107 + 0.707107i) q^{27} +(-5.83095 + 5.83095i) q^{29} -0.876894 q^{30} +(-3.62258 + 3.62258i) q^{31} -2.43845i q^{32} +2.56155 q^{33} +0.438447i q^{36} +(2.20837 - 2.20837i) q^{37} -12.0000 q^{38} +(3.22550 - 3.22550i) q^{39} +(0.968253 + 0.968253i) q^{40} +(-0.397078 - 0.397078i) q^{41} +7.68466i q^{43} +(0.794156 + 0.794156i) q^{44} +(-0.397078 - 0.397078i) q^{45} +(7.24517 - 7.24517i) q^{46} +2.87689 q^{47} +(3.31255 - 3.31255i) q^{48} -7.00000i q^{49} -7.31534 q^{50} +2.00000 q^{52} -4.24621i q^{53} +(-1.10418 + 1.10418i) q^{54} -1.43845 q^{55} +(-5.43387 - 5.43387i) q^{57} +(-9.10534 - 9.10534i) q^{58} +1.12311i q^{59} -0.246211i q^{60} +(-0.620058 - 0.620058i) q^{61} +(-5.65685 - 5.65685i) q^{62} -5.56155 q^{64} +(-1.81129 + 1.81129i) q^{65} +4.00000i q^{66} +4.00000 q^{67} +6.56155 q^{69} +(7.24517 - 7.24517i) q^{71} +2.43845 q^{72} +(-3.00252 + 3.00252i) q^{73} +(3.44849 + 3.44849i) q^{74} +(-3.31255 - 3.31255i) q^{75} -3.36932i q^{76} +(5.03680 + 5.03680i) q^{78} +(10.8677 + 10.8677i) q^{79} +(-1.86017 + 1.86017i) q^{80} -1.00000 q^{81} +(0.620058 - 0.620058i) q^{82} -9.12311i q^{83} -12.0000 q^{86} -8.24621i q^{87} +(4.41674 - 4.41674i) q^{88} -7.12311 q^{89} +(0.620058 - 0.620058i) q^{90} +(2.03427 + 2.03427i) q^{92} -5.12311i q^{93} +4.49242i q^{94} +(3.05141 + 3.05141i) q^{95} +(1.72424 + 1.72424i) q^{96} +(7.86522 - 7.86522i) q^{97} +10.9309 q^{98} +(-1.81129 + 1.81129i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 20 q^{4}+O(q^{10}) \) 8 * q - 20 * q^4	\( 8 q - 20 q^{4} - 20 q^{13} + 12 q^{16} - 4 q^{18} - 40 q^{30} + 4 q^{33} - 96 q^{38} + 56 q^{47} - 108 q^{50} + 16 q^{52} - 28 q^{55} - 28 q^{64} + 32 q^{67} + 36 q^{69} + 36 q^{72} - 8 q^{81} - 96 q^{86} - 24 q^{89} - 28 q^{98}+O(q^{100}) \) 8 * q - 20 * q^4 - 20 * q^13 + 12 * q^16 - 4 * q^18 - 40 * q^30 + 4 * q^33 - 96 * q^38 + 56 * q^47 - 108 * q^50 + 16 * q^52 - 28 * q^55 - 28 * q^64 + 32 * q^67 + 36 * q^69 + 36 * q^72 - 8 * q^81 - 96 * q^86 - 24 * q^89 - 28 * q^98

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