LMFDB - Embedded newform 867.2.e.f.616.4

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			616.4
Root			$1.81129 + 1.81129i$ of defining polynomial
Character	$\chi$	$=$	867.616
Dual form			867.2.e.f.829.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.56155i q^{2} +(0.707107 - 0.707107i) q^{3} -0.438447 q^{4} +(-0.397078 + 0.397078i) q^{5} +(1.10418 + 1.10418i) q^{6} +2.43845i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.56155i q^{2} +(0.707107 - 0.707107i) q^{3} -0.438447 q^{4} +(-0.397078 + 0.397078i) q^{5} +(1.10418 + 1.10418i) q^{6} +2.43845i q^{8} -1.00000i q^{9} +(-0.620058 - 0.620058i) q^{10} +(1.81129 + 1.81129i) q^{11} +(-0.310029 + 0.310029i) q^{12} -4.56155 q^{13} +0.561553i q^{15} -4.68466 q^{16} +1.56155 q^{18} +7.68466i q^{19} +(0.174098 - 0.174098i) q^{20} +(-2.82843 + 2.82843i) q^{22} +(4.63972 + 4.63972i) q^{23} +(1.72424 + 1.72424i) q^{24} +4.68466i q^{25} -7.12311i q^{26} +(-0.707107 - 0.707107i) q^{27} +(5.83095 - 5.83095i) q^{29} -0.876894 q^{30} +(3.62258 - 3.62258i) q^{31} -2.43845i q^{32} +2.56155 q^{33} +0.438447i q^{36} +(-2.20837 + 2.20837i) q^{37} -12.0000 q^{38} +(-3.22550 + 3.22550i) q^{39} +(-0.968253 - 0.968253i) q^{40} +(0.397078 + 0.397078i) q^{41} +7.68466i q^{43} +(-0.794156 - 0.794156i) q^{44} +(0.397078 + 0.397078i) q^{45} +(-7.24517 + 7.24517i) q^{46} +2.87689 q^{47} +(-3.31255 + 3.31255i) q^{48} -7.00000i q^{49} -7.31534 q^{50} +2.00000 q^{52} -4.24621i q^{53} +(1.10418 - 1.10418i) q^{54} -1.43845 q^{55} +(5.43387 + 5.43387i) q^{57} +(9.10534 + 9.10534i) q^{58} +1.12311i q^{59} -0.246211i q^{60} +(0.620058 + 0.620058i) q^{61} +(5.65685 + 5.65685i) q^{62} -5.56155 q^{64} +(1.81129 - 1.81129i) q^{65} +4.00000i q^{66} +4.00000 q^{67} +6.56155 q^{69} +(-7.24517 + 7.24517i) q^{71} +2.43845 q^{72} +(3.00252 - 3.00252i) q^{73} +(-3.44849 - 3.44849i) q^{74} +(3.31255 + 3.31255i) q^{75} -3.36932i q^{76} +(-5.03680 - 5.03680i) q^{78} +(-10.8677 - 10.8677i) q^{79} +(1.86017 - 1.86017i) q^{80} -1.00000 q^{81} +(-0.620058 + 0.620058i) q^{82} -9.12311i q^{83} -12.0000 q^{86} -8.24621i q^{87} +(-4.41674 + 4.41674i) q^{88} -7.12311 q^{89} +(-0.620058 + 0.620058i) q^{90} +(-2.03427 - 2.03427i) q^{92} -5.12311i q^{93} +4.49242i q^{94} +(-3.05141 - 3.05141i) q^{95} +(-1.72424 - 1.72424i) q^{96} +(-7.86522 + 7.86522i) q^{97} +10.9309 q^{98} +(1.81129 - 1.81129i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.790299	−	0.612721i	$-0.790075\pi$
$5$	−0.397078	+	0.397078i	−0.177579	+	0.177579i	0.612721	+	0.790299i	$0.290075\pi$
$6$	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	0.925318	−	0.379193i	$-0.123798\pi$
$11$	1.81129	+	1.81129i	0.546125	+	0.546125i	−0.379193	+	0.925318i	$0.623798\pi$
$12$	−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	0.999487	−	0.0320385i	$-0.0101999\pi$
$23$	4.63972	+	4.63972i	0.967448	+	0.967448i	−0.0320385	+	0.999487i	$0.510200\pi$
$24$	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	$-0.472422\pi$
$29$	5.83095	−	5.83095i	1.08278	−	1.08278i	0.996249	−	0.0865315i	$-0.0275783\pi$
$30$	−0.876894			−0.160098
$31$	3.62258	−	3.62258i	0.650635	−	0.650635i	−0.302511	−	0.953146i	$-0.597825\pi$
$31$	3.62258	−	3.62258i	0.650635	−	0.650635i	0.953146	+	0.302511i	$0.0978249\pi$
$32$		−	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	−0.864936	−	0.501882i	$-0.832641\pi$
$37$	−2.20837	+	2.20837i	−0.363054	+	0.363054i	0.501882	+	0.864936i	$0.332641\pi$
$38$	−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	0.737433	−	0.675420i	$-0.236038\pi$
$41$	0.397078	+	0.397078i	0.0620131	+	0.0620131i	−0.675420	+	0.737433i	$0.736038\pi$
$42$		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	0.745687	−	0.666297i	$-0.232122\pi$
$61$	0.620058	+	0.620058i	0.0793903	+	0.0793903i	−0.666297	+	0.745687i	$0.732122\pi$
$62$	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	−0.991319	−	0.131476i	$-0.958028\pi$
$71$	−7.24517	+	7.24517i	−0.859843	+	0.859843i	0.131476	+	0.991319i	$0.458028\pi$
$72$	2.43845			0.287374
$73$	3.00252	−	3.00252i	0.351419	−	0.351419i	−0.509218	−	0.860637i	$-0.670065\pi$
$73$	3.00252	−	3.00252i	0.351419	−	0.351419i	0.860637	+	0.509218i	$0.170065\pi$
$74$	−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	$-0.917577\pi$
$79$	−10.8677	−	10.8677i	−1.22272	−	1.22272i	−0.256055	−	0.966662i	$-0.582423\pi$
$80$	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	−0.982874	−	0.184281i	$-0.941004\pi$
$97$	−7.86522	+	7.86522i	−0.798592	+	0.798592i	0.184281	+	0.982874i	$0.441004\pi$
$98$	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	−0.393859	−	0.919171i	$-0.628860\pi$
$107$	5.43387	−	5.43387i	0.525312	−	0.525312i	0.919171	+	0.393859i	$0.128860\pi$
$108$	0.310029	+	0.310029i	0.0298326	+	0.0298326i
$109$	−10.6937	−	10.6937i	−1.02427	−	1.02427i	−0.999698	−	0.0245678i	$-0.992179\pi$
$109$	−10.6937	−	10.6937i	−1.02427	−	1.02427i	−0.0245678	−	0.999698i	$-0.507821\pi$
$110$		−	2.24621i		−	0.214168i
$111$			3.12311i			0.296432i
$112$		0			0
$113$	3.22550	+	3.22550i	0.303430	+	0.303430i	0.842354	−	0.538924i	$-0.181169\pi$
$113$	3.22550	+	3.22550i	0.303430	+	0.303430i	−0.538924	+	0.842354i	$0.681169\pi$
$114$	−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	$-0.448997\pi$
$131$	13.1250	−	13.1250i	1.14674	−	1.14674i	0.987190	−	0.159546i	$-0.0510031\pi$
$132$	−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	−0.378453	−	0.925621i	$-0.623544\pi$
$139$	6.45101	−	6.45101i	0.547168	−	0.547168i	0.925621	+	0.378453i	$0.123544\pi$
$140$		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	0.490542	−	0.871418i	$-0.336799\pi$
$163$	−4.86270	−	4.86270i	−0.380876	−	0.380876i	−0.871418	+	0.490542i	$0.836799\pi$
$164$	−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	−0.684662	−	0.728861i	$-0.740050\pi$
$167$	0.571175	−	0.571175i	0.0441989	−	0.0441989i	0.728861	+	0.684662i	$0.240050\pi$
$168$		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	$-0.496443\pi$
$173$	13.2991	−	13.2991i	1.01111	−	1.01111i	0.999938	−	0.0111741i	$-0.00355690\pi$
$174$	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	0.531626	−	0.846979i	$-0.321581\pi$
$181$	−4.24264	−	4.24264i	−0.315353	−	0.315353i	−0.846979	+	0.531626i	$0.821581\pi$
$182$		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	$0.0875940\pi$
$193$	17.1447	+	17.1447i	1.23410	+	1.23410i	0.271725	+	0.962375i	$0.412406\pi$
$194$	−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	$0.00130863\pi$
$197$	14.0933	+	14.0933i	1.00410	+	1.00410i	0.00411116	+	0.999992i	$0.498691\pi$
$198$	2.82843	+	2.82843i	0.201008	+	0.201008i
$199$	11.3137	−	11.3137i	0.802008	−	0.802008i	−0.181402	−	0.983409i	$-0.558063\pi$
$199$	11.3137	−	11.3137i	0.802008	−	0.802008i	0.983409	+	0.181402i	$0.0580634\pi$
$200$	−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	0.373985	−	0.927435i	$-0.377991\pi$
$211$	−8.03932	−	8.03932i	−0.553450	−	0.553450i	−0.927435	+	0.373985i	$0.877991\pi$
$212$			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	$-0.972703\pi$
$227$	−16.3016	−	16.3016i	−1.08198	−	1.08198i	−0.0856515	−	0.996325i	$-0.527297\pi$
$228$	−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	−0.693980	−	0.719994i	$-0.744145\pi$
$233$	0.397078	−	0.397078i	0.0260134	−	0.0260134i	0.719994	+	0.693980i	$0.244145\pi$
$234$	−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	−0.0263082	−	0.999654i	$-0.508375\pi$
$241$	15.1104	−	15.1104i	0.973346	−	0.973346i	0.999654	+	0.0263082i	$0.00837512\pi$
$242$	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	−0.994182	−	0.107711i	$-0.965648\pi$
$269$	−14.5392	+	14.5392i	−0.886471	+	0.886471i	0.107711	+	0.994182i	$0.465648\pi$
$270$			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	−0.568067	−	0.822982i	$-0.692309\pi$
$277$	4.24264	−	4.24264i	0.254916	−	0.254916i	0.822982	+	0.568067i	$0.192309\pi$
$278$	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	0.774364	−	0.632741i	$-0.218070\pi$
$283$	2.38247	+	2.38247i	0.141623	+	0.141623i	−0.632741	+	0.774364i	$0.718070\pi$
$284$	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	0.538346	−	0.842724i	$-0.319049\pi$
$313$	−5.38499	−	5.38499i	−0.304378	−	0.304378i	−0.842724	+	0.538346i	$0.819049\pi$
$314$			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	0.967550	−	0.252679i	$-0.0813116\pi$
$317$	12.7279	+	12.7279i	0.714871	+	0.714871i	−0.252679	+	0.967550i	$0.581312\pi$
$318$	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	$0.600482\pi$
$337$	−23.1497	+	23.1497i	−1.26105	+	1.26105i	−0.950587	+	0.310458i	$0.899518\pi$
$338$			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	0.997688	−	0.0679679i	$-0.0216515\pi$
$347$	17.3188	+	17.3188i	0.929720	+	0.929720i	−0.0679679	+	0.997688i	$0.521652\pi$
$348$			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	0.285037	−	0.958517i	$-0.407994\pi$
$367$	−12.9020	−	12.9020i	−0.673480	−	0.673480i	−0.958517	+	0.285037i	$0.907994\pi$
$368$	−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	−0.890616	−	0.454756i	$-0.849726\pi$
$379$	−8.48528	+	8.48528i	−0.435860	+	0.435860i	0.454756	+	0.890616i	$0.349726\pi$
$380$	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	0.605384	−	0.795934i	$-0.293020\pi$
$397$	−3.79668	−	3.79668i	−0.190550	−	0.190550i	−0.795934	+	0.605384i	$0.793020\pi$
$398$	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	0.589586	−	0.807706i	$-0.299291\pi$
$401$	−4.36786	−	4.36786i	−0.218120	−	0.218120i	−0.807706	+	0.589586i	$0.799291\pi$
$402$	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	$-0.958163\pi$
$419$	−22.9756	−	22.9756i	−1.12243	−	1.12243i	−0.131057	−	0.991375i	$-0.541837\pi$
$420$		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	0.985737	−	0.168294i	$-0.0538257\pi$
$431$	16.9706	+	16.9706i	0.817443	+	0.817443i	−0.168294	+	0.985737i	$0.553826\pi$
$432$	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	−0.603319	−	0.797500i	$-0.706155\pi$
$439$	4.06854	−	4.06854i	0.194181	−	0.194181i	0.797500	+	0.603319i	$0.206155\pi$
$440$		−	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	0.461859	−	0.886953i	$-0.347182\pi$
$449$	−9.00757	−	9.00757i	−0.425094	−	0.425094i	−0.886953	+	0.461859i	$0.847182\pi$
$450$			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	−0.0520010	−	0.998647i	$-0.516560\pi$
$479$	20.7184	−	20.7184i	0.946646	−	0.946646i	0.998647	+	0.0520010i	$0.0165599\pi$
$480$	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	0.815245	−	0.579117i	$-0.196602\pi$
$487$	5.21089	+	5.21089i	0.236128	+	0.236128i	−0.579117	+	0.815245i	$0.696602\pi$
$488$	−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	0.863772	−	0.503883i	$-0.168096\pi$
$499$	8.03932	+	8.03932i	0.359889	+	0.359889i	−0.503883	+	0.863772i	$0.668096\pi$
$500$	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	0.181381	−	0.983413i	$-0.441943\pi$
$503$	−17.9877	−	17.9877i	−0.802032	−	0.802032i	−0.983413	+	0.181381i	$0.941943\pi$
$504$		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	0.999669	−	0.0257398i	$-0.00819415\pi$
$521$	22.2303	+	22.2303i	0.973929	+	0.973929i	−0.0257398	+	0.999669i	$0.508194\pi$
$522$	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	$-0.419094\pi$
$541$	28.3606	−	28.3606i	1.21932	−	1.21932i	0.967871	−	0.251446i	$-0.0809062\pi$
$542$		−	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	−0.989700	−	0.143156i	$-0.954275\pi$
$547$	−19.7990	+	19.7990i	−0.846544	+	0.846544i	0.143156	+	0.989700i	$0.454275\pi$
$548$	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	0.927738	−	0.373233i	$-0.121751\pi$
$571$	13.2502	+	13.2502i	0.554504	+	0.554504i	−0.373233	+	0.927738i	$0.621751\pi$
$572$	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	$-0.997095\pi$
$601$	−24.7380	−	24.7380i	−1.00908	−	1.00908i	−0.00912658	−	0.999958i	$-0.502905\pi$
$602$		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	−0.451276	−	0.892384i	$-0.649031\pi$
$607$	10.8677	−	10.8677i	0.441108	−	0.441108i	0.892384	+	0.451276i	$0.149031\pi$
$608$	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	−0.981505	−	0.191437i	$-0.938685\pi$
$617$	−19.6249	+	19.6249i	−0.790068	+	0.790068i	0.191437	+	0.981505i	$0.438685\pi$
$618$	4.76493	+	4.76493i	0.191674	+	0.191674i
$619$	−13.6962	−	13.6962i	−0.550496	−	0.550496i	0.376088	−	0.926584i	$-0.377269\pi$
$619$	−13.6962	−	13.6962i	−0.550496	−	0.550496i	−0.926584	+	0.376088i	$0.877269\pi$
$620$		−	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	−0.708071	−	0.706141i	$-0.750435\pi$
$641$	−0.0488825	+	0.0488825i	−0.00193074	+	0.00193074i	0.706141	+	0.708071i	$0.250435\pi$
$642$	12.0000			0.473602
$643$	21.3873	−	21.3873i	0.843433	−	0.843433i	−0.145871	−	0.989304i	$-0.546598\pi$
$643$	21.3873	−	21.3873i	0.843433	−	0.843433i	0.989304	+	0.145871i	$0.0465984\pi$
$644$		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	0.648563	−	0.761161i	$-0.275370\pi$
$653$	−2.87731	−	2.87731i	−0.112598	−	0.112598i	−0.761161	+	0.648563i	$0.775370\pi$
$654$		−	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	$0.138587\pi$
$673$	34.4634	+	34.4634i	1.32847	+	1.32847i	0.421759	+	0.906708i	$0.361413\pi$
$674$	−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	−0.496270	−	0.868168i	$-0.665297\pi$
$677$	9.67651	−	9.67651i	0.371899	−	0.371899i	0.868168	+	0.496270i	$0.165297\pi$
$678$			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	−0.629696	−	0.776842i	$-0.716820\pi$
$683$	3.84556	−	3.84556i	0.147146	−	0.147146i	0.776842	+	0.629696i	$0.216820\pi$
$684$	−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	0.00510905	−	0.999987i	$-0.498374\pi$
$691$	−26.1522	−	26.1522i	−0.994878	−	0.994878i	−0.999987	+	0.00510905i	$0.998374\pi$
$692$	−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	−0.641382	−	0.767221i	$-0.721639\pi$
$709$	3.35072	−	3.35072i	0.125839	−	0.125839i	0.767221	+	0.641382i	$0.221639\pi$
$710$	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	−0.581372	−	0.813638i	$-0.697484\pi$
$719$	6.22803	−	6.22803i	0.232266	−	0.232266i	0.813638	+	0.581372i	$0.197484\pi$
$720$	−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	−0.762971	−	0.646432i	$-0.776260\pi$
$743$	−3.17662	+	3.17662i	−0.116539	+	0.116539i	0.646432	+	0.762971i	$0.276260\pi$
$744$	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	−0.698923	−	0.715197i	$-0.746337\pi$
$751$	0.445960	−	0.445960i	0.0162733	−	0.0162733i	0.715197	+	0.698923i	$0.246337\pi$
$752$	−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	−0.623991	−	0.781431i	$-0.714490\pi$
$787$	4.41674	−	4.41674i	0.157440	−	0.157440i	0.781431	+	0.623991i	$0.214490\pi$
$788$	−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	$0.132500\pi$
$809$	37.5148	+	37.5148i	1.31895	+	1.31895i	0.404344	+	0.914607i	$0.367500\pi$
$810$	0.620058	+	0.620058i	0.0217866	+	0.0217866i
$811$	−14.5881	+	14.5881i	−0.512257	+	0.512257i	−0.915218	−	0.402960i	$-0.867981\pi$
$811$	−14.5881	+	14.5881i	−0.512257	+	0.512257i	0.402960	+	0.915218i	$0.367981\pi$
$812$		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	−0.881288	−	0.472579i	$-0.843323\pi$
$821$	−11.7108	+	11.7108i	−0.408709	+	0.408709i	0.472579	+	0.881288i	$0.343323\pi$
$822$	−17.9388	−	17.9388i	−0.625688	−	0.625688i
$823$	25.8040	+	25.8040i	0.899472	+	0.899472i	0.995389	−	0.0959171i	$-0.0305784\pi$
$823$	25.8040	+	25.8040i	0.899472	+	0.899472i	−0.0959171	+	0.995389i	$0.530578\pi$
$824$			10.5227i			0.366577i
$825$			12.0000i			0.417786i
$826$		0			0
$827$	10.1988	+	10.1988i	0.354647	+	0.354647i	0.861835	−	0.507188i	$-0.169315\pi$
$827$	10.1988	+	10.1988i	0.354647	+	0.354647i	−0.507188	+	0.861835i	$0.669315\pi$
$828$	−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	0.559190	−	0.829040i	$-0.311112\pi$
$839$	−7.81634	−	7.81634i	−0.269850	−	0.269850i	−0.829040	+	0.559190i	$0.811112\pi$
$840$		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	−0.912090	−	0.409990i	$-0.865532\pi$
$853$	−14.6644	+	14.6644i	−0.502100	+	0.502100i	0.409990	+	0.912090i	$0.365532\pi$
$854$		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	0.630921	−	0.775847i	$-0.282677\pi$
$857$	−4.24264	−	4.24264i	−0.144926	−	0.144926i	−0.775847	+	0.630921i	$0.782677\pi$
$858$		−	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	0.173080	−	0.984908i	$-0.444628\pi$
$877$	−24.0416	−	24.0416i	−0.811828	−	0.811828i	−0.984908	+	0.173080i	$0.944628\pi$
$878$	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	−0.930974	−	0.365086i	$-0.881039\pi$
$881$	−16.7965	+	16.7965i	−0.565887	+	0.565887i	0.365086	+	0.930974i	$0.381039\pi$
$882$		−	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	−0.922252	−	0.386589i	$-0.873653\pi$
$887$	−15.9534	+	15.9534i	−0.535664	+	0.535664i	0.386589	+	0.922252i	$0.373653\pi$
$888$	−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	$-0.957675\pi$
$907$	−33.8434	−	33.8434i	−1.12375	−	1.12375i	−0.132578	−	0.991173i	$-0.542325\pi$
$908$	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	0.275011	−	0.961441i	$-0.411318\pi$
$911$	−20.7184	−	20.7184i	−0.686430	−	0.686430i	−0.961441	+	0.275011i	$0.911318\pi$
$912$	−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	0.231950	−	0.972728i	$-0.425489\pi$
$929$	−22.5785	−	22.5785i	−0.740778	−	0.740778i	−0.972728	+	0.231950i	$0.925489\pi$
$930$	−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	0.271038	−	0.962569i	$-0.412633\pi$
$941$	−21.2132	−	21.2132i	−0.691531	−	0.691531i	−0.962569	+	0.271038i	$0.912633\pi$
$942$	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	−0.555669	−	0.831404i	$-0.687538\pi$
$947$	8.48528	−	8.48528i	0.275735	−	0.275735i	0.831404	+	0.555669i	$0.187538\pi$
$948$	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	−0.730054	−	0.683389i	$-0.760505\pi$
$983$	−1.46310	+	1.46310i	−0.0466655	+	0.0466655i	0.683389	+	0.730054i	$0.260505\pi$
$984$			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	−0.778727	−	0.627363i	$-0.784134\pi$
$991$	−4.76493	+	4.76493i	−0.151363	+	0.151363i	0.627363	+	0.778727i	$0.284134\pi$
$992$	−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	0.810157	−	0.586214i	$-0.199382\pi$
$997$	7.07107	+	7.07107i	0.223943	+	0.223943i	−0.586214	+	0.810157i	$0.699382\pi$
$998$	−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.616.4		8
17.2	even	8		867.2.d.c.577.1		4
17.3	odd	16		867.2.h.j.733.4		16
17.4	even	4	inner	867.2.e.f.829.1		8
17.5	odd	16		867.2.h.j.712.2		16
17.6	odd	16		867.2.h.j.688.2		16
17.7	odd	16		867.2.h.j.757.3		16
17.8	even	8		51.2.a.b.1.2	✓	2
17.9	even	8		867.2.a.f.1.2		2
17.10	odd	16		867.2.h.j.757.4		16
17.11	odd	16		867.2.h.j.688.1		16
17.12	odd	16		867.2.h.j.712.1		16
17.13	even	4	inner	867.2.e.f.829.2		8
17.14	odd	16		867.2.h.j.733.3		16
17.15	even	8		867.2.d.c.577.2		4
17.16	even	2	inner	867.2.e.f.616.3		8
51.8	odd	8		153.2.a.e.1.1		2
51.26	odd	8		2601.2.a.t.1.1		2
68.59	odd	8		816.2.a.m.1.1		2
85.8	odd	8		1275.2.b.d.1174.2		4
85.42	odd	8		1275.2.b.d.1174.3		4
85.59	even	8		1275.2.a.n.1.1		2
119.76	odd	8		2499.2.a.o.1.2		2
136.59	odd	8		3264.2.a.bg.1.2		2
136.93	even	8		3264.2.a.bl.1.2		2
187.76	odd	8		6171.2.a.p.1.1		2
204.59	even	8		2448.2.a.v.1.2		2
221.25	even	8		8619.2.a.q.1.1		2
255.59	odd	8		3825.2.a.s.1.2		2
357.314	even	8		7497.2.a.v.1.1		2
408.59	even	8		9792.2.a.cz.1.1		2
408.365	odd	8		9792.2.a.cy.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.a.b.1.2	✓	2	17.8	even	8
153.2.a.e.1.1		2	51.8	odd	8
816.2.a.m.1.1		2	68.59	odd	8
867.2.a.f.1.2		2	17.9	even	8
867.2.d.c.577.1		4	17.2	even	8
867.2.d.c.577.2		4	17.15	even	8
867.2.e.f.616.3		8	17.16	even	2	inner
867.2.e.f.616.4		8	1.1	even	1	trivial
867.2.e.f.829.1		8	17.4	even	4	inner
867.2.e.f.829.2		8	17.13	even	4	inner
867.2.h.j.688.1		16	17.11	odd	16
867.2.h.j.688.2		16	17.6	odd	16
867.2.h.j.712.1		16	17.12	odd	16
867.2.h.j.712.2		16	17.5	odd	16
867.2.h.j.733.3		16	17.14	odd	16
867.2.h.j.733.4		16	17.3	odd	16
867.2.h.j.757.3		16	17.7	odd	16
867.2.h.j.757.4		16	17.10	odd	16
1275.2.a.n.1.1		2	85.59	even	8
1275.2.b.d.1174.2		4	85.8	odd	8
1275.2.b.d.1174.3		4	85.42	odd	8
2448.2.a.v.1.2		2	204.59	even	8
2499.2.a.o.1.2		2	119.76	odd	8
2601.2.a.t.1.1		2	51.26	odd	8
3264.2.a.bg.1.2		2	136.59	odd	8
3264.2.a.bl.1.2		2	136.93	even	8
3825.2.a.s.1.2		2	255.59	odd	8
6171.2.a.p.1.1		2	187.76	odd	8
7497.2.a.v.1.1		2	357.314	even	8
8619.2.a.q.1.1		2	221.25	even	8
9792.2.a.cy.1.1		2	408.365	odd	8
9792.2.a.cz.1.1		2	408.59	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more