LMFDB - Embedded newform 867.2.i.e.158.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(65,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 9]))

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

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

chi := DirichletCharacter("867.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.i (of order $16$, degree $8$, 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:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			158.4
Character	$\chi$	$=$	867.158
Dual form			867.2.i.e.653.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.06586 - 0.855706i) q^{2} +(0.290496 + 1.70752i) q^{3} +(2.12132 - 2.12132i) q^{4} +(-2.77408 - 0.551799i) q^{5} +(2.06126 + 3.27891i) q^{6} +(0.616930 + 3.10152i) q^{7} +(0.855706 - 2.06586i) q^{8} +(-2.83122 + 0.992053i) q^{9} +O(q^{10})$	\(q+(2.06586 - 0.855706i) q^{2} +(0.290496 + 1.70752i) q^{3} +(2.12132 - 2.12132i) q^{4} +(-2.77408 - 0.551799i) q^{5} +(2.06126 + 3.27891i) q^{6} +(0.616930 + 3.10152i) q^{7} +(0.855706 - 2.06586i) q^{8} +(-2.83122 + 0.992053i) q^{9} +(-6.20303 + 1.23386i) q^{10} +(-0.785695 + 1.17588i) q^{11} +(4.23842 + 3.00595i) q^{12} +(2.82843 + 2.82843i) q^{13} +(3.92847 + 5.87938i) q^{14} +(0.136347 - 4.89708i) q^{15} +1.00000i q^{16} +(-5.00000 + 4.47214i) q^{18} +(-7.05525 + 4.71417i) q^{20} +(-5.11667 + 1.95440i) q^{21} +(-0.616930 + 3.10152i) q^{22} +(5.87938 + 3.92847i) q^{23} +(3.77606 + 0.861009i) q^{24} +(2.77164 + 1.14805i) q^{25} +(8.26343 + 3.42282i) q^{26} +(-2.51641 - 4.54617i) q^{27} +(7.88801 + 5.27060i) q^{28} +(0.551799 - 2.77408i) q^{29} +(-3.90879 - 10.2333i) q^{30} +(2.62934 - 1.75687i) q^{31} +(2.56712 + 6.19757i) q^{32} +(-2.23607 - 1.00000i) q^{33} -8.94427i q^{35} +(-3.90147 + 8.11040i) q^{36} +(-3.51373 - 5.25868i) q^{37} +(-4.00794 + 5.65123i) q^{39} +(-3.51373 + 5.25868i) q^{40} +(-5.54816 + 1.10360i) q^{41} +(-8.89793 + 8.41587i) q^{42} +(1.53073 - 3.69552i) q^{43} +(0.827698 + 4.16112i) q^{44} +(8.40146 - 1.18977i) q^{45} +(15.5076 + 3.08465i) q^{46} +(-6.32456 + 6.32456i) q^{47} +(-1.70752 + 0.290496i) q^{48} +(-2.77164 + 1.14805i) q^{49} +6.70820 q^{50} +12.0000 q^{52} +(-9.08872 - 7.23844i) q^{54} +(2.82843 - 2.82843i) q^{55} +(6.93520 + 1.37950i) q^{56} +(-1.23386 - 6.20303i) q^{58} +(3.42282 - 8.26343i) q^{59} +(-10.0990 - 10.6775i) q^{60} +(6.20303 - 1.23386i) q^{61} +(3.92847 - 5.87938i) q^{62} +(-4.82353 - 8.16906i) q^{63} +(9.19239 + 9.19239i) q^{64} +(-6.28556 - 9.40700i) q^{65} +(-5.47510 - 0.152440i) q^{66} -8.00000i q^{67} +(-5.00000 + 11.1803i) q^{69} +(-7.65367 - 18.4776i) q^{70} +(10.5829 - 7.07125i) q^{71} +(-0.373256 + 6.69781i) q^{72} +(-11.7588 - 7.85695i) q^{74} +(-1.15517 + 5.06612i) q^{75} +(-4.13171 - 1.71141i) q^{77} +(-3.44404 + 15.1043i) q^{78} +(-2.62934 - 1.75687i) q^{79} +(0.551799 - 2.77408i) q^{80} +(7.03166 - 5.61745i) q^{81} +(-10.5174 + 7.02747i) q^{82} +(3.42282 + 8.26343i) q^{83} +(-6.70820 + 15.0000i) q^{84} -8.94427i q^{86} +(4.89708 + 0.136347i) q^{87} +(1.75687 + 2.62934i) q^{88} +(9.48683 + 9.48683i) q^{89} +(16.3381 - 9.64707i) q^{90} +(-7.02747 + 10.5174i) q^{91} +(20.8056 - 4.13849i) q^{92} +(3.76369 + 3.97927i) q^{93} +(-7.65367 + 18.4776i) q^{94} +(-9.83672 + 6.18377i) q^{96} +(-12.4061 - 2.46772i) q^{97} +(-4.74342 + 4.74342i) q^{98} +(1.05795 - 4.10862i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 160 q^{18} + 384 q^{52} - 160 q^{69}+O(q^{100}) $ 32 * q - 160 * q^18 + 384 * q^52 - 160 * q^69

Display 100 coefficients 10 coefficients

Character values

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

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{5}{16}\right)$

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 $

$2$	2.06586	−	0.855706i	1.46078	−	0.605076i	0.496046	−	0.868296i	$-0.334785\pi$
$2$	2.06586	−	0.855706i	1.46078	−	0.605076i	0.964736	+	0.263221i	$0.0847847\pi$
$3$	0.290496	+	1.70752i	0.167718	+	0.985835i
$3$	0.290496	+	1.70752i	0.167718	+	0.985835i
$4$	2.12132	−	2.12132i	1.06066	−	1.06066i
$5$	−2.77408	−	0.551799i	−1.24061	−	0.246772i	−0.469187	−	0.883099i	$-0.655453\pi$
$5$	−2.77408	−	0.551799i	−1.24061	−	0.246772i	−0.771419	+	0.636327i	$0.780453\pi$
$6$	2.06126	+	3.27891i	0.841504	+	1.33861i
$7$	0.616930	+	3.10152i	0.233178	+	1.17226i	0.902966	+	0.429711i	$0.141385\pi$
$7$	0.616930	+	3.10152i	0.233178	+	1.17226i	−0.669789	+	0.742552i	$0.733615\pi$
$8$	0.855706	−	2.06586i	0.302538	−	0.730391i
$9$	−2.83122	+	0.992053i	−0.943741	+	0.330684i
$10$	−6.20303	+	1.23386i	−1.96157	+	0.390181i
$11$	−0.785695	+	1.17588i	−0.236896	+	0.354540i	−0.930801	−	0.365527i	$-0.880889\pi$
$11$	−0.785695	+	1.17588i	−0.236896	+	0.354540i	0.693905	+	0.720067i	$0.255889\pi$
$12$	4.23842	+	3.00595i	1.22353	+	0.867744i
$13$	2.82843	+	2.82843i	0.784465	+	0.784465i	0.980581	−	0.196116i	$-0.0628330\pi$
$13$	2.82843	+	2.82843i	0.784465	+	0.784465i	−0.196116	+	0.980581i	$0.562833\pi$
$14$	3.92847	+	5.87938i	1.04993	+	1.57133i
$15$	0.136347	−	4.89708i	0.0352046	−	1.26442i
$16$			1.00000i			0.250000i
$17$		0			0
$17$		0			0
$18$	−5.00000	+	4.47214i	−1.17851	+	1.05409i
$19$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$19$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$20$	−7.05525	+	4.71417i	−1.57760	+	1.05412i
$21$	−5.11667	+	1.95440i	−1.11655	+	0.426484i
$22$	−0.616930	+	3.10152i	−0.131530	+	0.661245i
$23$	5.87938	+	3.92847i	1.22594	+	0.819144i	0.988346	−	0.152222i	$-0.0486429\pi$
$23$	5.87938	+	3.92847i	1.22594	+	0.819144i	0.237589	+	0.971366i	$0.423643\pi$
$24$	3.77606	+	0.861009i	0.770786	+	0.175753i
$25$	2.77164	+	1.14805i	0.554328	+	0.229610i
$26$	8.26343	+	3.42282i	1.62059	+	0.671271i
$27$	−2.51641	−	4.54617i	−0.484282	−	0.874912i
$28$	7.88801	+	5.27060i	1.49069	+	0.996050i
$29$	0.551799	−	2.77408i	0.102466	−	0.515134i	−0.895128	−	0.445810i	$-0.852916\pi$
$29$	0.551799	−	2.77408i	0.102466	−	0.515134i	0.997594	−	0.0693239i	$-0.0220842\pi$
$30$	−3.90879	−	10.2333i	−0.713644	−	1.86834i
$31$	2.62934	−	1.75687i	0.472243	−	0.315543i	−0.296576	−	0.955009i	$-0.595845\pi$
$31$	2.62934	−	1.75687i	0.472243	−	0.315543i	0.768819	+	0.639467i	$0.220845\pi$
$32$	2.56712	+	6.19757i	0.453807	+	1.09559i
$33$	−2.23607	−	1.00000i	−0.389249	−	0.174078i
$34$		0			0
$35$		−	8.94427i		−	1.51186i
$36$	−3.90147	+	8.11040i	−0.650245	+	1.35173i
$37$	−3.51373	−	5.25868i	−0.577654	−	0.864521i	0.421449	−	0.906852i	$-0.361522\pi$
$37$	−3.51373	−	5.25868i	−0.577654	−	0.864521i	−0.999104	+	0.0423311i	$0.986522\pi$
$38$		0			0
$39$	−4.00794	+	5.65123i	−0.641784	+	0.904921i
$40$	−3.51373	+	5.25868i	−0.555570	+	0.831470i
$41$	−5.54816	+	1.10360i	−0.866477	+	0.172353i	−0.608264	−	0.793735i	$-0.708134\pi$
$41$	−5.54816	+	1.10360i	−0.866477	+	0.172353i	−0.258213	+	0.966088i	$0.583134\pi$
$42$	−8.89793	+	8.41587i	−1.37298	+	1.29860i
$43$	1.53073	−	3.69552i	0.233435	−	0.563561i	−0.763142	−	0.646230i	$-0.776344\pi$
$43$	1.53073	−	3.69552i	0.233435	−	0.563561i	0.996577	+	0.0826692i	$0.0263445\pi$
$44$	0.827698	+	4.16112i	0.124780	+	0.627312i
$45$	8.40146	−	1.18977i	1.25242	−	0.177360i
$46$	15.5076	+	3.08465i	2.28647	+	0.454807i
$47$	−6.32456	+	6.32456i	−0.922531	+	0.922531i	−0.997208	−	0.0746766i	$-0.976208\pi$
$47$	−6.32456	+	6.32456i	−0.922531	+	0.922531i	0.0746766	+	0.997208i	$0.476208\pi$
$48$	−1.70752	+	0.290496i	−0.246459	+	0.0419295i
$49$	−2.77164	+	1.14805i	−0.395948	+	0.164007i
$50$	6.70820			0.948683
$51$		0			0
$52$	12.0000			1.66410
$53$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$53$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$54$	−9.08872	−	7.23844i	−1.23682	−	0.985028i
$55$	2.82843	−	2.82843i	0.381385	−	0.381385i
$56$	6.93520	+	1.37950i	0.926755	+	0.184343i
$57$		0			0
$58$	−1.23386	−	6.20303i	−0.162014	−	0.814498i
$59$	3.42282	−	8.26343i	0.445614	−	1.07581i	−0.528334	−	0.849036i	$-0.677183\pi$
$59$	3.42282	−	8.26343i	0.445614	−	1.07581i	0.973948	−	0.226771i	$-0.0728167\pi$
$60$	−10.0990	−	10.6775i	−1.30378	−	1.37846i
$61$	6.20303	−	1.23386i	0.794217	−	0.157980i	0.218724	−	0.975787i	$-0.429810\pi$
$61$	6.20303	−	1.23386i	0.794217	−	0.157980i	0.575492	+	0.817807i	$0.304810\pi$
$62$	3.92847	−	5.87938i	0.498917	−	0.746682i
$63$	−4.82353	−	8.16906i	−0.607708	−	1.02920i
$64$	9.19239	+	9.19239i	1.14905	+	1.14905i
$65$	−6.28556	−	9.40700i	−0.779628	−	1.16680i
$66$	−5.47510	−	0.152440i	−0.673939	−	0.0187641i
$67$		−	8.00000i		−	0.977356i	−0.872464	−	0.488678i	$-0.837479\pi$
$67$		−	8.00000i		−	0.977356i	0.872464	−	0.488678i	$-0.162521\pi$
$68$		0			0
$69$	−5.00000	+	11.1803i	−0.601929	+	1.34595i
$70$	−7.65367	−	18.4776i	−0.914788	−	2.20849i
$71$	10.5829	−	7.07125i	1.25596	−	0.839204i	0.263846	−	0.964565i	$-0.415009\pi$
$71$	10.5829	−	7.07125i	1.25596	−	0.839204i	0.992111	+	0.125361i	$0.0400090\pi$
$72$	−0.373256	+	6.69781i	−0.0439887	+	0.789345i
$73$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$73$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$74$	−11.7588	−	7.85695i	−1.36693	−	0.913352i
$75$	−1.15517	+	5.06612i	−0.133387	+	0.584985i
$76$		0			0
$77$	−4.13171	−	1.71141i	−0.470853	−	0.195034i
$78$	−3.44404	+	15.1043i	−0.389960	+	1.71022i
$79$	−2.62934	−	1.75687i	−0.295824	−	0.197663i	0.398797	−	0.917039i	$-0.369428\pi$
$79$	−2.62934	−	1.75687i	−0.295824	−	0.197663i	−0.694621	+	0.719376i	$0.744428\pi$
$80$	0.551799	−	2.77408i	0.0616930	−	0.310152i
$81$	7.03166	−	5.61745i	0.781296	−	0.624161i
$82$	−10.5174	+	7.02747i	−1.16145	+	0.776054i
$83$	3.42282	+	8.26343i	0.375704	+	0.907029i	0.992761	+	0.120111i	$0.0383249\pi$
$83$	3.42282	+	8.26343i	0.375704	+	0.907029i	−0.617057	+	0.786919i	$0.711675\pi$
$84$	−6.70820	+	15.0000i	−0.731925	+	1.63663i
$85$		0			0
$86$		−	8.94427i		−	0.964486i
$87$	4.89708	+	0.136347i	0.525022	+	0.0146179i
$88$	1.75687	+	2.62934i	0.187283	+	0.280288i
$89$	9.48683	+	9.48683i	1.00560	+	1.00560i	0.999984	+	0.00561807i	$0.00178830\pi$
$89$	9.48683	+	9.48683i	1.00560	+	1.00560i	0.00561807	+	0.999984i	$0.498212\pi$
$90$	16.3381	−	9.64707i	1.72219	−	1.01689i
$91$	−7.02747	+	10.5174i	−0.736679	+	1.10252i
$92$	20.8056	−	4.13849i	2.16913	−	0.431467i
$93$	3.76369	+	3.97927i	0.390277	+	0.412632i
$94$	−7.65367	+	18.4776i	−0.789416	+	1.90582i
$95$		0			0
$96$	−9.83672	+	6.18377i	−1.00396	+	0.631128i
$97$	−12.4061	−	2.46772i	−1.25964	−	0.250559i	−0.480272	−	0.877120i	$-0.659462\pi$
$97$	−12.4061	−	2.46772i	−1.25964	−	0.250559i	−0.779373	+	0.626561i	$0.784462\pi$
$98$	−4.74342	+	4.74342i	−0.479157	+	0.479157i
$99$	1.05795	−	4.10862i	0.106328	−	0.412932i
$100$	8.31492	−	3.44415i	0.831492	−	0.344415i
$101$	−4.47214			−0.444994			−0.222497	−	0.974933i	$-0.571421\pi$
$101$	−4.47214			−0.444994			−0.222497	+	0.974933i	$0.571421\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$	8.26343	−	3.42282i	0.810296	−	0.335636i
$105$	15.2725	−	2.59827i	1.49044	−	0.253566i
$106$		0			0
$107$	4.16112	+	0.827698i	0.402271	+	0.0800166i	0.392079	−	0.919931i	$-0.371756\pi$
$107$	4.16112	+	0.827698i	0.402271	+	0.0800166i	0.0101914	+	0.999948i	$0.496756\pi$
$108$	−14.9820	−	4.30579i	−1.44164	−	0.414325i
$109$	3.70158	+	18.6091i	0.354547	+	1.78243i	0.586758	+	0.809762i	$0.300404\pi$
$109$	3.70158	+	18.6091i	0.354547	+	1.78243i	−0.232211	+	0.972665i	$0.574596\pi$
$110$	3.42282	−	8.26343i	0.326354	−	0.787887i
$111$	7.95855	−	7.52738i	0.755392	−	0.714468i
$112$	−3.10152	+	0.616930i	−0.293066	+	0.0582944i
$113$	3.14278	−	4.70350i	0.295648	−	0.442468i	−0.653673	−	0.756777i	$-0.726773\pi$
$113$	3.14278	−	4.70350i	0.295648	−	0.442468i	0.949321	+	0.314309i	$0.101773\pi$
$114$		0			0
$115$	−14.1421	−	14.1421i	−1.31876	−	1.31876i
$116$	−4.71417	−	7.05525i	−0.437700	−	0.655064i
$117$	−10.8139	−	5.20196i	−0.999742	−	0.480922i
$118$		−	20.0000i		−	1.84115i
$119$		0			0
$120$	−10.0000	−	4.47214i	−0.912871	−	0.408248i
$121$	3.44415	+	8.31492i	0.313105	+	0.755901i
$122$	11.7588	−	7.85695i	1.06459	−	0.711335i
$123$	−3.49613	−	9.15298i	−0.315235	−	0.825297i
$124$	1.85079	−	9.30455i	0.166206	−	0.835573i
$125$	4.70350	+	3.14278i	0.420694	+	0.281099i
$126$	−16.9550	−	12.7486i	−1.51048	−	1.13573i
$127$	−11.0866	−	4.59220i	−0.983773	−	0.407492i	−0.167951	−	0.985795i	$-0.553715\pi$
$127$	−11.0866	−	4.59220i	−0.983773	−	0.407492i	−0.815822	+	0.578303i	$0.803715\pi$
$128$	14.4610	+	5.98994i	1.27818	+	0.529441i
$129$	6.75483	+	1.54022i	0.594730	+	0.135609i
$130$	−21.0347	−	14.0549i	−1.84487	−	1.23270i
$131$	0.275899	−	1.38704i	0.0241054	−	0.121186i	−0.966859	−	0.255311i	$-0.917822\pi$
$131$	0.275899	−	1.38704i	0.0241054	−	0.121186i	0.990964	+	0.134125i	$0.0428222\pi$
$132$	−6.86474	+	2.62210i	−0.597499	+	0.228224i
$133$		0			0
$134$	−6.84565	−	16.5269i	−0.591374	−	1.42770i
$135$	4.47214	+	14.0000i	0.384900	+	1.20493i
$136$		0			0
$137$			4.47214i			0.382080i	0.981582	+	0.191040i	$0.0611861\pi$
$137$			4.47214i			0.382080i	−0.981582	+	0.191040i	$0.938814\pi$
$138$	−0.762201	+	27.3755i	−0.0648829	+	2.33036i
$139$	1.75687	+	2.62934i	0.149016	+	0.223018i	0.898466	−	0.439043i	$-0.144682\pi$
$139$	1.75687	+	2.62934i	0.149016	+	0.223018i	−0.749451	+	0.662060i	$0.769682\pi$
$140$	−18.9737	−	18.9737i	−1.60357	−	1.60357i
$141$	−12.6365	−	8.96202i	−1.06419	−	0.754739i
$142$	15.8118	−	23.6640i	1.32690	−	1.98584i
$143$	−5.54816	+	1.10360i	−0.463960	+	0.0922875i
$144$	−0.992053	−	2.83122i	−0.0826711	−	0.235935i
$145$	−3.06147	+	7.39104i	−0.254241	+	0.613792i
$146$		0			0
$147$	−2.76546	−	4.39911i	−0.228092	−	0.362833i
$148$	−18.6091	−	3.70158i	−1.52966	−	0.304268i
$149$	12.6491	−	12.6491i	1.03626	−	1.03626i	0.0369380	−	0.999318i	$-0.488240\pi$
$149$	12.6491	−	12.6491i	1.03626	−	1.03626i	0.999318	−	0.0369380i	$-0.0117604\pi$
$150$	1.94871	+	11.4544i	0.159111	+	0.935245i
$151$	18.4776	−	7.65367i	1.50369	−	0.622847i	0.529442	−	0.848346i	$-0.322401\pi$
$151$	18.4776	−	7.65367i	1.50369	−	0.622847i	0.974243	+	0.225500i	$0.0724014\pi$
$152$		0			0
$153$		0			0
$154$	−10.0000			−0.805823
$155$	−8.26343	+	3.42282i	−0.663735	+	0.274928i
$156$	3.48595	+	20.4902i	0.279099	+	1.64053i
$157$	−1.41421	+	1.41421i	−0.112867	+	0.112867i	−0.761285	−	0.648418i	$-0.775431\pi$
$157$	−1.41421	+	1.41421i	−0.112867	+	0.112867i	0.648418	+	0.761285i	$0.275431\pi$
$158$	−6.93520	−	1.37950i	−0.551735	−	0.109747i
$159$		0			0
$160$	−3.70158	−	18.6091i	−0.292635	−	1.47118i
$161$	−8.55706	+	20.6586i	−0.674391	+	1.62812i
$162$	9.71953	−	17.6219i	0.763638	−	1.38451i
$163$	9.30455	−	1.85079i	0.728788	−	0.144965i	0.183268	−	0.983063i	$-0.441332\pi$
$163$	9.30455	−	1.85079i	0.728788	−	0.144965i	0.545520	+	0.838098i	$0.316332\pi$
$164$	−9.42834	+	14.1105i	−0.736230	+	1.10185i
$165$	5.65123	+	4.00794i	0.439948	+	0.312018i
$166$	14.1421	+	14.1421i	1.09764	+	1.09764i
$167$	−5.49986	−	8.23113i	−0.425592	−	0.636944i	0.555265	−	0.831674i	$-0.312617\pi$
$167$	−5.49986	−	8.23113i	−0.425592	−	0.636944i	−0.980857	+	0.194730i	$0.937617\pi$
$168$	−0.340867	+	12.2427i	−0.0262984	+	0.944545i
$169$			3.00000i			0.230769i
$170$		0			0
$171$		0			0
$172$	−4.59220	−	11.0866i	−0.350152	−	0.845342i
$173$	−11.7588	+	7.85695i	−0.894002	+	0.597353i	−0.915456	−	0.402417i	$-0.868170\pi$
$173$	−11.7588	+	7.85695i	−0.894002	+	0.597353i	0.0214548	+	0.999770i	$0.493170\pi$
$174$	10.2333	−	3.90879i	0.775788	−	0.296325i
$175$	−1.85079	+	9.30455i	−0.139907	+	0.703358i
$176$	−1.17588	−	0.785695i	−0.0886350	−	0.0592240i
$177$	15.1043	+	3.44404i	1.13531	+	0.258870i
$178$	27.7164	+	11.4805i	2.07743	+	0.860500i
$179$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$179$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$180$	15.2983	−	20.3461i	1.14027	−	1.51651i
$181$	15.7760	+	10.5412i	1.17262	+	0.783522i	0.980243	−	0.197799i	$-0.0633793\pi$
$181$	15.7760	+	10.5412i	1.17262	+	0.783522i	0.192380	+	0.981320i	$0.438379\pi$
$182$	−5.51799	+	27.7408i	−0.409020	+	2.05628i
$183$	3.90879	+	10.2333i	0.288946	+	0.756471i
$184$	13.1467	−	8.78434i	0.969187	−	0.647590i
$185$	6.84565	+	16.5269i	0.503302	+	1.21508i
$186$	11.1803	+	5.00000i	0.819782	+	0.366618i
$187$		0			0
$188$			26.8328i			1.95698i
$189$	12.5476	−	10.6093i	0.912703	−	0.771716i
$190$		0			0
$191$	6.32456	+	6.32456i	0.457629	+	0.457629i	0.897876	−	0.440248i	$-0.145109\pi$
$191$	6.32456	+	6.32456i	0.457629	+	0.457629i	−0.440248	+	0.897876i	$0.645109\pi$
$192$	−13.0258	+	18.3665i	−0.940056	+	1.32549i
$193$	7.02747	−	10.5174i	0.505848	−	0.757055i	−0.487386	−	0.873187i	$-0.662049\pi$
$193$	7.02747	−	10.5174i	0.505848	−	0.757055i	0.993234	+	0.116131i	$0.0370494\pi$
$194$	−27.7408	+	5.51799i	−1.99167	+	0.396168i
$195$	14.2367	−	13.4654i	1.01951	−	0.964277i
$196$	−3.44415	+	8.31492i	−0.246011	+	0.593923i
$197$	−4.96619	−	24.9667i	−0.353826	−	1.77880i	−0.590317	−	0.807171i	$-0.700997\pi$
$197$	−4.96619	−	24.9667i	−0.353826	−	1.77880i	0.236491	−	0.971634i	$-0.424003\pi$
$198$	−1.33020	−	9.39311i	−0.0945333	−	0.667539i
$199$	−9.30455	−	1.85079i	−0.659582	−	0.131199i	−0.146060	−	0.989276i	$-0.546659\pi$
$199$	−9.30455	−	1.85079i	−0.659582	−	0.131199i	−0.513522	+	0.858077i	$0.671659\pi$
$200$	4.74342	−	4.74342i	0.335410	−	0.335410i
$201$	13.6601	−	2.32397i	0.963511	−	0.163920i
$202$	−9.23880	+	3.82683i	−0.650039	+	0.269255i
$203$	8.94427			0.627765
$204$		0			0
$205$	16.0000			1.11749
$206$	8.26343	−	3.42282i	0.575740	−	0.238479i
$207$	−20.5431	−	5.28974i	−1.42784	−	0.367662i
$208$	−2.82843	+	2.82843i	−0.196116	+	0.196116i
$209$		0			0
$210$	29.3274	−	18.4364i	2.02378	−	1.27223i
$211$	−4.31851	−	21.7106i	−0.297298	−	1.49462i	−0.783840	−	0.620963i	$-0.786742\pi$
$211$	−4.31851	−	21.7106i	−0.297298	−	1.49462i	0.486542	−	0.873657i	$-0.338258\pi$
$212$		0			0
$213$	15.1486	+	16.0163i	1.03796	+	1.09742i
$214$	9.30455	−	1.85079i	0.636046	−	0.126517i
$215$	−6.28556	+	9.40700i	−0.428672	+	0.641552i
$216$	−11.5451	+	1.30835i	−0.785541	+	0.0890216i
$217$	7.07107	+	7.07107i	0.480015	+	0.480015i
$218$	23.5708	+	35.2763i	1.59642	+	2.38921i
$219$		0			0
$220$		−	12.0000i		−	0.809040i
$221$		0			0
$222$	10.0000	−	22.3607i	0.671156	−	1.50075i
$223$	−6.12293	−	14.7821i	−0.410022	−	0.989881i	−0.985131	−	0.171804i	$-0.945040\pi$
$223$	−6.12293	−	14.7821i	−0.410022	−	0.989881i	0.575109	−	0.818077i	$-0.304960\pi$
$224$	−17.6381	+	11.7854i	−1.17850	+	0.787447i
$225$	−8.98606	−	0.500776i	−0.599070	−	0.0333851i
$226$	2.46772	−	12.4061i	0.164150	−	0.825239i
$227$	5.87938	+	3.92847i	0.390228	+	0.260742i	0.735171	−	0.677882i	$-0.237102\pi$
$227$	5.87938	+	3.92847i	0.390228	+	0.260742i	−0.344943	+	0.938624i	$0.612102\pi$
$228$		0			0
$229$	−18.4776	−	7.65367i	−1.22103	−	0.505769i	−0.323295	−	0.946298i	$-0.604791\pi$
$229$	−18.4776	−	7.65367i	−1.22103	−	0.505769i	−0.897738	+	0.440529i	$0.854791\pi$
$230$	−41.3171	−	17.1141i	−2.72437	−	1.12847i
$231$	1.72202	−	7.55213i	0.113300	−	0.496894i
$232$	−5.25868	−	3.51373i	−0.345249	−	0.230688i
$233$	−1.10360	+	5.54816i	−0.0722991	+	0.363472i	−0.999950	−	0.00997588i	$-0.996825\pi$
$233$	−1.10360	+	5.54816i	−0.0722991	+	0.363472i	0.927651	+	0.373448i	$0.121825\pi$
$234$	−26.7912	−	1.49302i	−1.75140	−	0.0976021i
$235$	21.0347	−	14.0549i	1.37215	−	0.916843i
$236$	−10.2685	−	24.7903i	−0.668421	−	1.61371i
$237$	2.23607	−	5.00000i	0.145248	−	0.324785i
$238$		0			0
$239$		−	8.94427i		−	0.578557i	−0.957245	−	0.289278i	$-0.906585\pi$
$239$		−	8.94427i		−	0.578557i	0.957245	−	0.289278i	$-0.0934153\pi$
$240$	4.89708	+	0.136347i	0.316105	+	0.00880114i
$241$	14.0549	+	21.0347i	0.905358	+	1.35496i	0.934716	+	0.355395i	$0.115654\pi$
$241$	14.0549	+	21.0347i	0.905358	+	1.35496i	−0.0293579	+	0.999569i	$0.509346\pi$
$242$	14.2302	+	14.2302i	0.914755	+	0.914755i
$243$	11.6346	+	10.3748i	0.746357	+	0.665546i
$244$	10.5412	−	15.7760i	0.674831	−	1.00996i
$245$	8.32224	−	1.65540i	0.531688	−	0.105759i
$246$	−15.0548	−	15.9171i	−0.959857	−	1.01484i
$247$		0			0
$248$	−1.37950	−	6.93520i	−0.0875981	−	0.440386i
$249$	−13.1156	+	8.24502i	−0.831169	+	0.522507i
$250$	12.4061	+	2.46772i	0.784628	+	0.156072i
$251$	−12.6491	+	12.6491i	−0.798405	+	0.798405i	−0.982844	−	0.184439i	$-0.940953\pi$
$251$	−12.6491	+	12.6491i	−0.798405	+	0.798405i	0.184439	+	0.982844i	$0.440953\pi$
$252$	−27.5615	−	7.09693i	−1.73621	−	0.447065i
$253$	−9.23880	+	3.82683i	−0.580838	+	0.240591i
$254$	−26.8328			−1.68364
$255$		0			0
$256$	9.00000			0.562500
$257$	−20.6586	+	8.55706i	−1.28865	+	0.533775i	−0.918582	−	0.395231i	$-0.870665\pi$
$257$	−20.6586	+	8.55706i	−1.28865	+	0.533775i	−0.370065	+	0.929006i	$0.620665\pi$
$258$	15.2725	−	2.59827i	0.950824	−	0.161761i
$259$	14.1421	−	14.1421i	0.878750	−	0.878750i
$260$	−33.2890	−	6.62159i	−2.06449	−	0.410653i
$261$	1.18977	+	8.40146i	0.0736448	+	0.520037i
$262$	−0.616930	−	3.10152i	−0.0381140	−	0.191612i
$263$	−6.84565	+	16.5269i	−0.422121	+	1.01909i	0.559600	+	0.828763i	$0.310955\pi$
$263$	−6.84565	+	16.5269i	−0.422121	+	1.01909i	−0.981721	+	0.190327i	$0.939045\pi$
$264$	−3.97927	+	3.76369i	−0.244907	+	0.231639i
$265$		0			0
$266$		0			0
$267$	−13.4430	+	18.9548i	−0.822700	+	1.16002i
$268$	−16.9706	−	16.9706i	−1.03664	−	1.03664i
$269$	14.1425	+	21.1658i	0.862284	+	1.29050i	0.955541	+	0.294857i	$0.0952721\pi$
$269$	14.1425	+	21.1658i	0.862284	+	1.29050i	−0.0932573	+	0.995642i	$0.529728\pi$
$270$	21.2187	+	25.0952i	1.29133	+	1.52724i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$	−20.0000	−	8.94427i	−1.21046	−	0.541332i
$274$	3.82683	+	9.23880i	0.231188	+	0.558136i
$275$	−3.52763	+	2.35708i	−0.212724	+	0.142138i
$276$	13.1105	+	34.3237i	0.789158	+	2.06604i
$277$	1.23386	−	6.20303i	0.0741354	−	0.372704i	−0.925851	−	0.377888i	$-0.876650\pi$
$277$	1.23386	−	6.20303i	0.0741354	−	0.372704i	0.999987	+	0.00518447i	$0.00165027\pi$
$278$	5.87938	+	3.92847i	0.352622	+	0.235614i
$279$	−5.70134	+	7.58253i	−0.341330	+	0.453954i
$280$	−18.4776	−	7.65367i	−1.10425	−	0.457394i
$281$	−16.5269	−	6.84565i	−0.985910	−	0.408377i	−0.169298	−	0.985565i	$-0.554150\pi$
$281$	−16.5269	−	6.84565i	−0.985910	−	0.408377i	−0.816612	+	0.577188i	$0.804150\pi$
$282$	−33.7741	−	7.70110i	−2.01122	−	0.458594i
$283$	−2.62934	−	1.75687i	−0.156298	−	0.104435i	0.474962	−	0.880006i	$-0.342462\pi$
$283$	−2.62934	−	1.75687i	−0.156298	−	0.104435i	−0.631260	+	0.775571i	$0.717462\pi$
$284$	7.44928	−	37.4501i	0.442034	−	2.22225i
$285$		0			0
$286$	−10.5174	+	7.02747i	−0.621904	+	0.415543i
$287$	−6.84565	−	16.5269i	−0.404086	−	0.975550i
$288$	−13.4164	−	15.0000i	−0.790569	−	0.883883i
$289$		0			0
$290$			17.8885i			1.05045i
$291$	0.609761	−	21.9004i	0.0357448	−	1.28383i
$292$		0			0
$293$	−12.6491	−	12.6491i	−0.738969	−	0.738969i	0.233410	−	0.972379i	$-0.425012\pi$
$293$	−12.6491	−	12.6491i	−0.738969	−	0.738969i	−0.972379	+	0.233410i	$0.925012\pi$
$294$	−9.47740	−	6.72152i	−0.552733	−	0.392007i
$295$	−14.0549	+	21.0347i	−0.818310	+	1.22469i
$296$	−13.8704	+	2.75899i	−0.806201	+	0.160363i
$297$	7.32286	+	0.612927i	0.424916	+	0.0355656i
$298$	15.3073	−	36.9552i	0.886730	−	2.14076i
$299$	5.51799	+	27.7408i	0.319113	+	1.60429i
$300$	8.29639	+	13.1973i	0.478992	+	0.761949i
$301$	12.4061	+	2.46772i	0.715073	+	0.142237i
$302$	31.6228	−	31.6228i	1.81969	−	1.81969i
$303$	−1.29914	−	7.63625i	−0.0746335	−	0.438691i
$304$		0			0
$305$	−17.8885			−1.02430
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$	−12.3951	+	5.13424i	−0.706279	+	0.292550i
$309$	1.16198	+	6.83007i	0.0661029	+	0.388549i
$310$	−14.1421	+	14.1421i	−0.803219	+	0.803219i
$311$	−1.38704	−	0.275899i	−0.0786518	−	0.0156448i	0.155608	−	0.987819i	$-0.450266\pi$
$311$	−1.38704	−	0.275899i	−0.0786518	−	0.0156448i	−0.234259	+	0.972174i	$0.575266\pi$
$312$	8.24502	+	13.1156i	0.466782	+	0.742526i
$313$	4.93544	+	24.8121i	0.278967	+	1.40246i	0.825205	+	0.564834i	$0.191060\pi$
$313$	4.93544	+	24.8121i	0.278967	+	1.40246i	−0.546237	+	0.837630i	$0.683940\pi$
$314$	−1.71141	+	4.13171i	−0.0965806	+	0.233166i
$315$	8.87319	+	25.3232i	0.499948	+	1.42680i
$316$	−9.30455	+	1.85079i	−0.523422	+	0.104115i
$317$	7.85695	−	11.7588i	0.441290	−	0.660438i	−0.542439	−	0.840095i	$-0.682499\pi$
$317$	7.85695	−	11.7588i	0.441290	−	0.660438i	0.983729	+	0.179658i	$0.0574990\pi$
$318$		0			0
$319$	2.82843	+	2.82843i	0.158362	+	0.158362i
$320$	−20.4281	−	30.5728i	−1.14196	−	1.70907i
$321$	−0.204520	+	7.34562i	−0.0114152	+	0.409993i
$322$			50.0000i			2.78639i
$323$		0			0
$324$	3.00000	−	26.8328i	0.166667	−	1.49071i
$325$	4.59220	+	11.0866i	0.254729	+	0.614971i
$326$	17.6381	−	11.7854i	0.976886	−	0.652734i
$327$	−30.7000	+	11.7264i	−1.69772	+	0.648470i
$328$	−2.46772	+	12.4061i	−0.136257	+	0.685010i
$329$	−23.5175	−	15.7139i	−1.29656	−	0.866335i
$330$	15.1043	+	3.44404i	0.831462	+	0.189588i
$331$	25.8686	+	10.7151i	1.42187	+	0.588957i	0.955329	−	0.295543i	$-0.0955007\pi$
$331$	25.8686	+	10.7151i	1.42187	+	0.588957i	0.466539	+	0.884501i	$0.345501\pi$
$332$	24.7903	+	10.2685i	1.36054	+	0.563556i
$333$	15.1651	+	11.4027i	0.831040	+	0.624863i
$334$	−18.4054	−	12.2981i	−1.00710	−	0.672921i
$335$	−4.41439	+	22.1926i	−0.241184	+	1.21251i
$336$	−1.95440	−	5.11667i	−0.106621	−	0.279137i
$337$	−21.0347	+	14.0549i	−1.14583	+	0.765621i	−0.975551	−	0.219774i	$-0.929468\pi$
$337$	−21.0347	+	14.0549i	−1.14583	+	0.765621i	−0.170282	+	0.985395i	$0.554468\pi$
$338$	2.56712	+	6.19757i	0.139633	+	0.337103i
$339$	8.94427	+	4.00000i	0.485786	+	0.217250i
$340$		0			0
$341$			4.47214i			0.242180i
$342$		0			0
$343$	7.02747	+	10.5174i	0.379448	+	0.567884i
$344$	−6.32456	−	6.32456i	−0.340997	−	0.340997i
$345$	20.0397	−	28.2562i	1.07890	−	1.52126i
$346$	−17.5687	+	26.2934i	−0.944498	+	1.41354i
$347$	34.6760	−	6.89748i	1.86151	−	0.370276i	0.869238	−	0.494395i	$-0.164610\pi$
$347$	34.6760	−	6.89748i	1.86151	−	0.370276i	0.992267	+	0.124118i	$0.0396102\pi$
$348$	10.6775	−	10.0990i	0.572375	−	0.541366i
$349$	5.35757	−	12.9343i	0.286784	−	0.692358i	−0.713179	−	0.700982i	$-0.752745\pi$
$349$	5.35757	−	12.9343i	0.286784	−	0.692358i	0.999963	+	0.00862428i	$0.00274523\pi$
$350$	4.13849	+	20.8056i	0.221212	+	1.11211i
$351$	5.74105	−	19.9760i	0.306435	−	1.06624i
$352$	−9.30455	−	1.85079i	−0.495934	−	0.0986474i
$353$	−12.6491	+	12.6491i	−0.673244	+	0.673244i	−0.958463	−	0.285218i	$-0.907934\pi$
$353$	−12.6491	+	12.6491i	−0.673244	+	0.673244i	0.285218	+	0.958463i	$0.407934\pi$
$354$	34.1503	−	5.80992i	1.81507	−	0.308794i
$355$	−33.2597	+	13.7766i	−1.76524	+	0.731186i
$356$	40.2492			2.13320
$357$		0			0
$358$		0			0
$359$	−24.7903	+	10.2685i	−1.30838	+	0.541949i	−0.924412	−	0.381396i	$-0.875443\pi$
$359$	−24.7903	+	10.2685i	−1.30838	+	0.541949i	−0.383970	+	0.923346i	$0.625443\pi$
$360$	4.73129	−	18.3743i	0.249361	−	0.968411i
$361$	13.4350	−	13.4350i	0.707107	−	0.707107i
$362$	41.6112	+	8.27698i	2.18704	+	0.435028i
$363$	−13.1973	+	8.29639i	−0.692681	+	0.435448i
$364$	7.40316	+	37.2182i	0.388031	+	1.95076i
$365$		0			0
$366$	16.8317	+	17.7959i	0.879809	+	0.930204i
$367$	−15.5076	+	3.08465i	−0.809489	+	0.161017i	−0.582448	−	0.812868i	$-0.697905\pi$
$367$	−15.5076	+	3.08465i	−0.809489	+	0.161017i	−0.227041	+	0.973885i	$0.572905\pi$
$368$	−3.92847	+	5.87938i	−0.204786	+	0.306484i
$369$	14.6133	−	8.62860i	0.760736	−	0.449187i
$370$	28.2843	+	28.2843i	1.47043	+	1.47043i
$371$		0			0
$372$	16.4253	+	0.457321i	0.851613	+	0.0237110i
$373$		−	4.00000i		−	0.207112i	−0.994624	−	0.103556i	$-0.966978\pi$
$373$		−	4.00000i		−	0.207112i	0.994624	−	0.103556i	$-0.0330221\pi$
$374$		0			0
$375$	−4.00000	+	8.94427i	−0.206559	+	0.461880i
$376$	7.65367	+	18.4776i	0.394708	+	0.952909i
$377$	9.40700	−	6.28556i	0.484485	−	0.323723i
$378$	16.8430	−	32.6544i	0.866313	−	1.67956i
$379$	−1.85079	+	9.30455i	−0.0950687	+	0.477942i	0.903693	+	0.428182i	$0.140846\pi$
$379$	−1.85079	+	9.30455i	−0.0950687	+	0.477942i	−0.998761	+	0.0497604i	$0.984154\pi$
$380$		0			0
$381$	4.62066	−	20.2645i	0.236724	−	1.03818i
$382$	18.4776	+	7.65367i	0.945396	+	0.391596i
$383$	−33.0537	−	13.6913i	−1.68897	−	0.699593i	−0.689276	−	0.724499i	$-0.742071\pi$
$383$	−33.0537	−	13.6913i	−1.68897	−	0.699593i	−0.999690	+	0.0249059i	$0.992071\pi$
$384$	−6.02706	+	26.4325i	−0.307567	+	1.34888i
$385$	10.5174	+	7.02747i	0.536014	+	0.358153i
$386$	5.51799	−	27.7408i	0.280858	−	1.41197i
$387$	−0.667701	+	11.9814i	−0.0339412	+	0.609049i
$388$	−31.5521	+	21.0824i	−1.60181	+	1.07030i
$389$	−1.71141	−	4.13171i	−0.0867720	−	0.209486i	0.874537	−	0.484959i	$-0.161166\pi$
$389$	−1.71141	−	4.13171i	−0.0867720	−	0.209486i	−0.961309	+	0.275473i	$0.911166\pi$
$390$	17.8885	−	40.0000i	0.905822	−	2.02548i
$391$		0			0
$392$			6.70820i			0.338815i
$393$	2.44854	+	0.0681734i	0.123513	+	0.00343889i
$394$	−31.6236	−	47.3281i	−1.59317	−	2.38435i
$395$	6.32456	+	6.32456i	0.318223	+	0.318223i
$396$	−6.47145	−	10.9599i	−0.325203	−	0.550758i
$397$	10.5412	−	15.7760i	0.529048	−	0.791776i	−0.466649	−	0.884442i	$-0.654539\pi$
$397$	10.5412	−	15.7760i	0.529048	−	0.791776i	0.995697	+	0.0926663i	$0.0295390\pi$
$398$	−20.8056	+	4.13849i	−1.04289	+	0.207444i
$399$		0			0
$400$	−1.14805	+	2.77164i	−0.0574025	+	0.138582i
$401$	1.10360	+	5.54816i	0.0551110	+	0.277062i	0.998508	−	0.0546036i	$-0.0173895\pi$
$401$	1.10360	+	5.54816i	0.0551110	+	0.277062i	−0.943397	+	0.331665i	$0.892389\pi$
$402$	26.2313	−	16.4900i	1.30830	−	0.822449i
$403$	12.4061	+	2.46772i	0.617990	+	0.122926i
$404$	−9.48683	+	9.48683i	−0.471988	+	0.471988i
$405$	−22.6061	+	11.7032i	−1.12331	+	0.581536i
$406$	18.4776	−	7.65367i	0.917027	−	0.379845i
$407$	8.94427			0.443351
$408$		0			0
$409$	14.0000			0.692255			0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000			0.692255			0.346128	+	0.938187i	$0.387496\pi$
$410$	33.0537	−	13.6913i	1.63241	−	0.676165i
$411$	−7.63625	+	1.29914i	−0.376668	+	0.0640817i
$412$	8.48528	−	8.48528i	0.418040	−	0.418040i
$413$	27.7408	+	5.51799i	1.36504	+	0.271522i
$414$	−46.9656	+	6.65100i	−2.30823	+	0.326879i
$415$	−4.93544	−	24.8121i	−0.242271	−	1.21798i
$416$	−10.2685	+	24.7903i	−0.503453	+	1.21544i
$417$	−3.97927	+	3.76369i	−0.194866	+	0.184309i
$418$		0			0
$419$	−5.49986	+	8.23113i	−0.268686	+	0.402117i	−0.941137	−	0.338024i	$-0.890241\pi$
$419$	−5.49986	+	8.23113i	−0.268686	+	0.402117i	0.672451	+	0.740141i	$0.265241\pi$
$420$	26.8861	−	37.9096i	1.31191	−	1.84980i
$421$	−14.1421	−	14.1421i	−0.689246	−	0.689246i	0.272820	−	0.962065i	$-0.412044\pi$
$421$	−14.1421	−	14.1421i	−0.689246	−	0.689246i	−0.962065	+	0.272820i	$0.912044\pi$
$422$	−27.4993	−	41.1556i	−1.33865	−	2.00343i
$423$	11.6319	−	24.1805i	0.565564	−	1.17570i
$424$		0			0
$425$		0			0
$426$	45.0000	+	20.1246i	2.18026	+	0.975041i
$427$	7.65367	+	18.4776i	0.370387	+	0.894193i
$428$	10.5829	−	7.07125i	0.511543	−	0.341802i
$429$	−3.49613	−	9.15298i	−0.168795	−	0.441910i
$430$	−4.93544	+	24.8121i	−0.238008	+	1.19655i
$431$	−10.5829	−	7.07125i	−0.509759	−	0.340610i	0.273944	−	0.961746i	$-0.411672\pi$
$431$	−10.5829	−	7.07125i	−0.509759	−	0.340610i	−0.783703	+	0.621135i	$0.786672\pi$
$432$	4.54617	−	2.51641i	0.218728	−	0.121071i
$433$	−33.2597	−	13.7766i	−1.59836	−	0.662061i	−0.607175	−	0.794568i	$-0.707697\pi$
$433$	−33.2597	−	13.7766i	−1.59836	−	0.662061i	−0.991182	+	0.132507i	$0.957697\pi$
$434$	20.6586	+	8.55706i	0.991643	+	0.410752i
$435$	−13.5097	−	3.08044i	−0.647739	−	0.147696i
$436$	47.3281	+	31.6236i	2.26660	+	1.51450i
$437$		0			0
$438$		0			0
$439$	18.4054	−	12.2981i	0.878440	−	0.586955i	−0.0325100	−	0.999471i	$-0.510350\pi$
$439$	18.4054	−	12.2981i	0.878440	−	0.586955i	0.910950	+	0.412516i	$0.135350\pi$
$440$	−3.42282	−	8.26343i	−0.163177	−	0.393944i
$441$	6.70820	−	6.00000i	0.319438	−	0.285714i
$442$		0			0
$443$			17.8885i			0.849910i	0.905214	+	0.424955i	$0.139710\pi$
$443$			17.8885i			0.849910i	−0.905214	+	0.424955i	$0.860290\pi$
$444$	0.914642	−	32.8506i	0.0434070	−	1.55902i
$445$	−21.0824	−	31.5521i	−0.999402	−	1.49571i
$446$	−25.2982	−	25.2982i	−1.19791	−	1.19791i
$447$	25.2731	+	17.9240i	1.19538	+	0.847778i
$448$	−22.8393	+	34.1814i	−1.07905	+	1.61492i
$449$	16.6445	−	3.31079i	0.785501	−	0.156246i	0.213985	−	0.976837i	$-0.431355\pi$
$449$	16.6445	−	3.31079i	0.785501	−	0.156246i	0.571516	+	0.820591i	$0.306355\pi$
$450$	−18.9924	+	6.65489i	−0.895312	+	0.313715i
$451$	3.06147	−	7.39104i	0.144159	−	0.348030i
$452$	−3.31079	−	16.6445i	−0.155727	−	0.782890i
$453$	18.4364	+	29.3274i	0.866219	+	1.37792i
$454$	15.5076	+	3.08465i	0.727807	+	0.144770i
$455$	25.2982	−	25.2982i	1.18600	−	1.18600i
$456$		0			0
$457$	25.8686	−	10.7151i	1.21008	−	0.501233i	0.315839	−	0.948813i	$-0.397714\pi$
$457$	25.8686	−	10.7151i	1.21008	−	0.501233i	0.894244	+	0.447580i	$0.147714\pi$
$458$	−44.7214			−2.08969
$459$		0			0
$460$	−60.0000			−2.79751
$461$	33.0537	−	13.6913i	1.53947	−	0.637667i	0.558092	−	0.829779i	$-0.311534\pi$
$461$	33.0537	−	13.6913i	1.53947	−	0.637667i	0.981373	+	0.192112i	$0.0615336\pi$
$462$	−2.90496	−	17.0752i	−0.135151	−	0.794409i
$463$	−2.82843	+	2.82843i	−0.131448	+	0.131448i	−0.769770	−	0.638322i	$-0.779629\pi$
$463$	−2.82843	+	2.82843i	−0.131448	+	0.131448i	0.638322	+	0.769770i	$0.279629\pi$
$464$	2.77408	+	0.551799i	0.128783	+	0.0256166i
$465$	−8.24502	−	13.1156i	−0.382354	−	0.608223i
$466$	2.46772	+	12.4061i	0.114315	+	0.574700i
$467$	6.84565	−	16.5269i	0.316779	−	0.764772i	−0.682642	−	0.730753i	$-0.739169\pi$
$467$	6.84565	−	16.5269i	0.316779	−	0.764772i	0.999421	−	0.0340192i	$-0.0108307\pi$
$468$	−33.9747	+	11.9046i	−1.57048	+	0.550292i
$469$	24.8121	−	4.93544i	1.14572	−	0.227897i
$470$	31.4278	−	47.0350i	1.44966	−	2.16956i
$471$	−2.82562	−	2.00397i	−0.130198	−	0.0923380i
$472$	−14.1421	−	14.1421i	−0.650945	−	0.650945i
$473$	3.14278	+	4.70350i	0.144505	+	0.216267i
$474$	0.340867	−	12.2427i	0.0156565	−	0.562326i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−7.65367	−	18.4776i	−0.350071	−	0.845145i
$479$	−8.23113	+	5.49986i	−0.376090	+	0.251295i	−0.729220	−	0.684279i	$-0.760117\pi$
$479$	−8.23113	+	5.49986i	−0.376090	+	0.251295i	0.353131	+	0.935574i	$0.385117\pi$
$480$	30.7000	−	11.7264i	1.40126	−	0.535233i
$481$	4.93544	−	24.8121i	0.225037	−	1.13134i
$482$	47.0350	+	31.4278i	2.14239	+	1.43150i
$483$	−37.7606	−	8.61009i	−1.71817	−	0.391773i
$484$	24.9447	+	10.3325i	1.13385	+	0.469657i
$485$	33.0537	+	13.6913i	1.50089	+	0.621690i
$486$	32.9131	+	11.4772i	1.49297	+	0.520615i
$487$	−23.6640	−	15.8118i	−1.07232	−	0.716501i	−0.111525	−	0.993762i	$-0.535574\pi$
$487$	−23.6640	−	15.8118i	−1.07232	−	0.716501i	−0.960795	+	0.277260i	$0.910574\pi$
$488$	2.75899	−	13.8704i	0.124894	−	0.627883i
$489$	5.86319	+	15.3500i	0.265142	+	0.694152i
$490$	15.7760	−	10.5412i	0.712688	−	0.476203i
$491$	6.84565	+	16.5269i	0.308940	+	0.745847i	0.999740	+	0.0228010i	$0.00725842\pi$
$491$	6.84565	+	16.5269i	0.308940	+	0.745847i	−0.690800	+	0.723046i	$0.742742\pi$
$492$	−26.8328	−	12.0000i	−1.20972	−	0.541002i
$493$		0			0
$494$		0			0
$495$	−5.20196	+	10.8139i	−0.233811	+	0.486047i
$496$	1.75687	+	2.62934i	0.0788857	+	0.118061i
$497$	28.4605	+	28.4605i	1.27663	+	1.27663i
$498$	−20.0397	+	28.2562i	−0.898000	+	1.26619i
$499$	−1.75687	+	2.62934i	−0.0786482	+	0.117705i	−0.868708	−	0.495324i	$-0.835049\pi$
$499$	−1.75687	+	2.62934i	−0.0786482	+	0.117705i	0.790060	+	0.613029i	$0.210049\pi$
$500$	16.6445	−	3.31079i	0.744364	−	0.148063i
$501$	12.4571	−	11.7822i	0.556542	−	0.526391i
$502$	−15.3073	+	36.9552i	−0.683200	+	1.64939i
$503$	2.48309	+	12.4834i	0.110716	+	0.556605i	0.995830	+	0.0912312i	$0.0290802\pi$
$503$	2.48309	+	12.4834i	0.110716	+	0.556605i	−0.885114	+	0.465374i	$0.845920\pi$
$504$	−21.0036	+	2.97442i	−0.935576	+	0.132491i
$505$	12.4061	+	2.46772i	0.552062	+	0.109812i
$506$	−15.8114	+	15.8114i	−0.702902	+	0.702902i
$507$	−5.12255	+	0.871488i	−0.227500	+	0.0387041i
$508$	−33.2597	+	13.7766i	−1.47566	+	0.611238i
$509$	17.8885			0.792896			0.396448	−	0.918057i	$-0.370243\pi$
$509$	17.8885			0.792896			0.396448	+	0.918057i	$0.370243\pi$
$510$		0			0
$511$		0			0
$512$	−10.3293	+	4.27853i	−0.456494	+	0.189086i
$513$		0			0
$514$	−35.3553	+	35.3553i	−1.55946	+	1.55946i
$515$	−11.0963	−	2.20720i	−0.488962	−	0.0972606i
$516$	17.5965	−	11.0619i	0.774641	−	0.486971i
$517$	−2.46772	−	12.4061i	−0.108530	−	0.545618i
$518$	17.1141	−	41.3171i	0.751951	−	1.81537i
$519$	−16.8317	−	17.7959i	−0.738831	−	0.781151i
$520$	−24.8121	+	4.93544i	−1.08808	+	0.216433i
$521$	18.8567	−	28.2210i	0.826126	−	1.23639i	−0.142976	−	0.989726i	$-0.545667\pi$
$521$	18.8567	−	28.2210i	0.826126	−	1.23639i	0.969102	−	0.246659i	$-0.0793327\pi$
$522$	9.64707	+	16.3381i	0.422241	+	0.715100i
$523$	−16.9706	−	16.9706i	−0.742071	−	0.742071i	0.230905	−	0.972976i	$-0.425831\pi$
$523$	−16.9706	−	16.9706i	−0.742071	−	0.742071i	−0.972976	+	0.230905i	$0.925831\pi$
$524$	−2.35708	−	3.52763i	−0.102970	−	0.154105i
$525$	−16.4253	−	0.457321i	−0.716859	−	0.0199591i
$526$			40.0000i			1.74408i
$527$		0			0
$528$	1.00000	−	2.23607i	0.0435194	−	0.0973124i
$529$	10.3325	+	24.9447i	0.449237	+	1.08455i
$530$		0			0
$531$	−1.49302	+	26.7912i	−0.0647918	+	1.16264i
$532$		0			0
$533$	−18.8140	−	12.5711i	−0.814925	−	0.544516i
$534$	−11.5517	+	50.6612i	−0.499889	+	2.19233i
$535$	−11.0866	−	4.59220i	−0.479314	−	0.198538i
$536$	−16.5269	−	6.84565i	−0.713852	−	0.295687i
$537$		0			0
$538$	47.3281	+	31.6236i	2.04046	+	1.36339i
$539$	0.827698	−	4.16112i	0.0356515	−	0.179232i
$540$	39.1853	+	20.2117i	1.68627	+	0.869771i
$541$	5.25868	−	3.51373i	0.226088	−	0.151067i	−0.437368	−	0.899283i	$-0.644089\pi$
$541$	5.25868	−	3.51373i	0.226088	−	0.151067i	0.663456	+	0.748216i	$0.269089\pi$
$542$		0			0
$543$	−13.4164	+	30.0000i	−0.575753	+	1.28742i
$544$		0			0
$545$		−	53.6656i		−	2.29878i
$546$	−48.9708	−	1.36347i	−2.09576	−	0.0583510i
$547$	−1.75687	−	2.62934i	−0.0751182	−	0.112422i	0.792008	−	0.610510i	$-0.209036\pi$
$547$	−1.75687	−	2.62934i	−0.0751182	−	0.112422i	−0.867126	+	0.498088i	$0.834036\pi$
$548$	9.48683	+	9.48683i	0.405257	+	0.405257i
$549$	−16.3381	+	9.64707i	−0.697294	+	0.411727i
$550$	−5.27060	+	7.88801i	−0.224739	+	0.336346i
$551$		0			0
$552$	18.8185	+	19.8964i	0.800967	+	0.846846i
$553$	3.82683	−	9.23880i	0.162734	−	0.392874i
$554$	−2.75899	−	13.8704i	−0.117218	−	0.589297i
$555$	−26.2313	+	16.4900i	−1.11345	+	0.699963i
$556$	9.30455	+	1.85079i	0.394601	+	0.0784909i
$557$	−9.48683	+	9.48683i	−0.401970	+	0.401970i	−0.878927	−	0.476957i	$-0.841740\pi$
$557$	−9.48683	+	9.48683i	−0.401970	+	0.401970i	0.476957	+	0.878927i	$0.341740\pi$
$558$	−5.28974	+	20.5431i	−0.223933	+	0.869658i
$559$	14.7821	−	6.12293i	0.625215	−	0.258973i
$560$	8.94427			0.377964
$561$		0			0
$562$	−40.0000			−1.68730
$563$	8.26343	−	3.42282i	0.348262	−	0.144255i	−0.201694	−	0.979449i	$-0.564645\pi$
$563$	8.26343	−	3.42282i	0.348262	−	0.144255i	0.549956	+	0.835194i	$0.314645\pi$
$564$	−45.8175	+	7.79482i	−1.92926	+	0.328221i
$565$	−11.3137	+	11.3137i	−0.475971	+	0.475971i
$566$	−6.93520	−	1.37950i	−0.291508	−	0.0579846i
$567$	21.7606	+	18.3432i	0.913861	+	0.770344i
$568$	−5.55237	−	27.9136i	−0.232972	−	1.17123i
$569$	6.84565	−	16.5269i	0.286985	−	0.692842i	−0.712981	−	0.701184i	$-0.752655\pi$
$569$	6.84565	−	16.5269i	0.286985	−	0.692842i	0.999965	+	0.00834171i	$0.00265528\pi$
$570$		0			0
$571$	−34.1167	+	6.78623i	−1.42774	+	0.283995i	−0.847649	−	0.530558i	$-0.821982\pi$
$571$	−34.1167	+	6.78623i	−1.42774	+	0.283995i	−0.580090	+	0.814553i	$0.696982\pi$
$572$	−9.42834	+	14.1105i	−0.394219	+	0.589990i
$573$	−8.96202	+	12.6365i	−0.374394	+	0.527899i
$574$	−28.2843	−	28.2843i	−1.18056	−	1.18056i
$575$	11.7854	+	17.6381i	0.491486	+	0.735561i
$576$	−35.1450	−	16.9064i	−1.46438	−	0.704432i
$577$		−	12.0000i		−	0.499567i	−0.968302	−	0.249783i	$-0.919641\pi$
$577$		−	12.0000i		−	0.499567i	0.968302	−	0.249783i	$-0.0803594\pi$
$578$		0			0
$579$	20.0000	+	8.94427i	0.831172	+	0.371711i
$580$	9.18440	+	22.1731i	0.381362	+	0.920688i
$581$	−23.5175	+	15.7139i	−0.975671	+	0.651922i
$582$	−17.4806	−	45.7649i	−0.724596	−	1.89702i
$583$		0			0
$584$		0			0
$585$	27.1281	+	20.3977i	1.12161	+	0.843342i
$586$	−36.9552	−	15.3073i	−1.52660	−	0.632340i
$587$	16.5269	+	6.84565i	0.682136	+	0.282550i	0.696720	−	0.717343i	$-0.254642\pi$
$587$	16.5269	+	6.84565i	0.682136	+	0.282550i	−0.0145832	+	0.999894i	$0.504642\pi$
$588$	−15.1984	−	3.46550i	−0.626770	−	0.142915i
$589$		0			0
$590$	−11.0360	+	55.4816i	−0.454344	+	2.28414i
$591$	41.1884	−	15.7326i	1.69427	−	0.647152i
$592$	5.25868	−	3.51373i	0.216130	−	0.144414i
$593$	6.84565	+	16.5269i	0.281117	+	0.678677i	0.999862	−	0.0165969i	$-0.00528319\pi$
$593$	6.84565	+	16.5269i	0.281117	+	0.678677i	−0.718745	+	0.695274i	$0.755283\pi$
$594$	15.6525	−	5.00000i	0.642229	−	0.205152i
$595$		0			0
$596$		−	53.6656i		−	2.19823i
$597$	0.457321	−	16.4253i	0.0187169	−	0.672243i
$598$	35.1373	+	52.5868i	1.43687	+	2.15043i
$599$	−12.6491	−	12.6491i	−0.516829	−	0.516829i	0.399782	−	0.916610i	$-0.369086\pi$
$599$	−12.6491	−	12.6491i	−0.516829	−	0.516829i	−0.916610	+	0.399782i	$0.869086\pi$
$600$	9.47740	+	6.72152i	0.386913	+	0.274405i
$601$	7.02747	−	10.5174i	0.286656	−	0.429012i	−0.659995	−	0.751270i	$-0.729442\pi$
$601$	7.02747	−	10.5174i	0.286656	−	0.429012i	0.946652	+	0.322258i	$0.104442\pi$
$602$	27.7408	−	5.51799i	1.13063	−	0.224896i
$603$	7.93642	+	22.6498i	0.323196	+	0.922371i
$604$	22.9610	−	55.4328i	0.934270	−	2.25553i
$605$	−4.96619	−	24.9667i	−0.201904	−	1.01504i
$606$	−9.21821	−	14.6637i	−0.374464	−	0.595673i
$607$	21.7106	+	4.31851i	0.881206	+	0.175283i	0.614900	−	0.788605i	$-0.289197\pi$
$607$	21.7106	+	4.31851i	0.881206	+	0.175283i	0.266307	+	0.963888i	$0.414197\pi$
$608$		0			0
$609$	2.59827	+	15.2725i	0.105287	+	0.618873i
$610$	−36.9552	+	15.3073i	−1.49627	+	0.619776i
$611$	−35.7771			−1.44739
$612$		0			0
$613$	6.00000			0.242338			0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000			0.242338			0.121169	+	0.992632i	$0.461336\pi$
$614$	−24.7903	+	10.2685i	−1.00045	+	0.414402i
$615$	4.64793	+	27.3203i	0.187423	+	1.10166i
$616$	−7.07107	+	7.07107i	−0.284901	+	0.284901i
$617$	−38.8371	−	7.72518i	−1.56352	−	0.311004i	−0.663951	−	0.747776i	$-0.731122\pi$
$617$	−38.8371	−	7.72518i	−1.56352	−	0.311004i	−0.899572	+	0.436772i	$0.856122\pi$
$618$	8.24502	+	13.1156i	0.331663	+	0.527588i
$619$	0.616930	+	3.10152i	0.0247965	+	0.124660i	0.991201	−	0.132366i	$-0.0422573\pi$
$619$	0.616930	+	3.10152i	0.0247965	+	0.124660i	−0.966404	+	0.257026i	$0.917257\pi$
$620$	−10.2685	+	24.7903i	−0.412392	+	0.995602i
$621$	3.06463	−	36.6143i	0.122979	−	1.46928i
$622$	−3.10152	+	0.616930i	−0.124359	+	0.0247366i
$623$	−23.5708	+	35.2763i	−0.944346	+	1.41331i
$624$	−5.65123	−	4.00794i	−0.226230	−	0.160446i
$625$	−21.9203	−	21.9203i	−0.876812	−	0.876812i
$626$	31.4278	+	47.0350i	1.25611	+	1.87990i
$627$		0			0
$628$			6.00000i			0.239426i
$629$		0			0
$630$	40.0000	+	44.7214i	1.59364	+	1.78174i
$631$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$631$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$632$	−5.87938	+	3.92847i	−0.233869	+	0.156266i
$633$	35.8167	−	13.6808i	1.42359	−	0.543762i
$634$	6.16930	−	31.0152i	0.245014	−	1.23177i
$635$	28.2210	+	18.8567i	1.11992	+	0.748304i
$636$		0			0
$637$	−11.0866	−	4.59220i	−0.439265	−	0.181950i
$638$	8.26343	+	3.42282i	0.327152	+	0.135511i
$639$	−22.9474	+	30.5191i	−0.907787	+	1.20732i
$640$	−36.8107	−	24.5961i	−1.45507	−	0.972248i
$641$	4.41439	−	22.1926i	0.174358	−	0.876556i	−0.790233	−	0.612806i	$-0.790041\pi$
$641$	4.41439	−	22.1926i	0.174358	−	0.876556i	0.964591	−	0.263750i	$-0.0849594\pi$
$642$	5.86319	+	15.3500i	0.231401	+	0.605817i
$643$	−18.4054	+	12.2981i	−0.725837	+	0.484989i	−0.862773	−	0.505591i	$-0.831274\pi$
$643$	−18.4054	+	12.2981i	−0.725837	+	0.484989i	0.136936	+	0.990580i	$0.456274\pi$
$644$	25.6712	+	61.9757i	1.01159	+	2.44219i
$645$	−17.8885	−	8.00000i	−0.704361	−	0.315000i
$646$		0			0
$647$			26.8328i			1.05491i	0.849584	+	0.527453i	$0.176853\pi$
$647$			26.8328i			1.05491i	−0.849584	+	0.527453i	$0.823147\pi$
$648$	−5.58781	−	19.3333i	−0.219510	−	0.759484i
$649$	7.02747	+	10.5174i	0.275852	+	0.412842i
$650$	18.9737	+	18.9737i	0.744208	+	0.744208i
$651$	−10.0198	+	14.1281i	−0.392709	+	0.553723i
$652$	15.8118	−	23.6640i	0.619238	−	0.926755i
$653$	−36.0630	+	7.17338i	−1.41126	+	0.280716i	−0.841126	−	0.540839i	$-0.818107\pi$
$653$	−36.0630	+	7.17338i	−1.41126	+	0.280716i	−0.570129	+	0.821555i	$0.693107\pi$
$654$	−53.3876	+	50.4952i	−2.08762	+	1.97452i
$655$	−1.53073	+	3.69552i	−0.0598107	+	0.144396i
$656$	−1.10360	−	5.54816i	−0.0430882	−	0.216619i
$657$		0			0
$658$	−62.0303	−	12.3386i	−2.41819	−	0.481009i
$659$	−6.32456	+	6.32456i	−0.246370	+	0.246370i	−0.819479	−	0.573109i	$-0.805737\pi$
$659$	−6.32456	+	6.32456i	−0.246370	+	0.246370i	0.573109	+	0.819479i	$0.305737\pi$
$660$	20.4902	−	3.48595i	0.797580	−	0.135690i
$661$	35.1074	−	14.5420i	1.36552	−	0.565617i	0.424950	−	0.905217i	$-0.360292\pi$
$661$	35.1074	−	14.5420i	1.36552	−	0.565617i	0.940570	+	0.339600i	$0.110292\pi$
$662$	62.6099			2.43340
$663$		0			0
$664$	20.0000			0.776151
$665$		0			0
$666$	41.0862	+	10.5795i	1.59206	+	0.409946i
$667$	14.1421	−	14.1421i	0.547586	−	0.547586i
$668$	−29.1278	−	5.79389i	−1.12699	−	0.224172i
$669$	23.4619	−	14.7491i	0.907091	−	0.570235i
$670$	9.87088	+	49.6242i	0.381345	+	1.91715i
$671$	−3.42282	+	8.26343i	−0.132137	+	0.319006i
$672$	−25.2476	−	26.6938i	−0.973948	−	1.02974i
$673$	−24.8121	+	4.93544i	−0.956437	+	0.190247i	−0.648547	−	0.761175i	$-0.724623\pi$
$673$	−24.8121	+	4.93544i	−0.956437	+	0.190247i	−0.307890	+	0.951422i	$0.599623\pi$
$674$	−31.4278	+	47.0350i	−1.21055	+	1.81172i
$675$	−1.75533	−	15.4893i	−0.0675627	−	0.596184i
$676$	6.36396	+	6.36396i	0.244768	+	0.244768i
$677$	−7.85695	−	11.7588i	−0.301967	−	0.451926i	0.649193	−	0.760624i	$-0.275107\pi$
$677$	−7.85695	−	11.7588i	−0.301967	−	0.451926i	−0.951160	+	0.308698i	$0.900107\pi$
$678$	21.9004	+	0.609761i	0.841080	+	0.0234177i
$679$		−	40.0000i		−	1.53506i
$680$		0			0
$681$	−5.00000	+	11.1803i	−0.191600	+	0.428432i
$682$	3.82683	+	9.23880i	0.146537	+	0.353772i
$683$	5.87938	−	3.92847i	0.224968	−	0.150319i	−0.437979	−	0.898985i	$-0.644305\pi$
$683$	5.87938	−	3.92847i	0.224968	−	0.150319i	0.662947	+	0.748666i	$0.269305\pi$
$684$		0			0
$685$	2.46772	−	12.4061i	0.0942867	−	0.474011i
$686$	23.5175	+	15.7139i	0.897903	+	0.599959i
$687$	7.70110	−	33.7741i	0.293815	−	1.28856i
$688$	3.69552	+	1.53073i	0.140890	+	0.0583587i
$689$		0			0
$690$	17.2202	−	75.5213i	0.655561	−	2.87505i
$691$	−34.1814	−	22.8393i	−1.30032	−	0.868847i	−0.303845	−	0.952721i	$-0.598271\pi$
$691$	−34.1814	−	22.8393i	−1.30032	−	0.868847i	−0.996476	+	0.0838745i	$0.973271\pi$
$692$	−8.27698	+	41.6112i	−0.314644	+	1.58182i
$693$	13.3956	+	0.746512i	0.508858	+	0.0283577i
$694$	65.7334	−	43.9217i	2.49521	−	1.66724i
$695$	−3.42282	−	8.26343i	−0.129835	−	0.313450i
$696$	4.47214	−	10.0000i	0.169516	−	0.379049i
$697$		0			0
$698$		−	31.3050i		−	1.18491i
$699$	−9.79416	−	0.272693i	−0.370449	−	0.0103142i
$700$	15.8118	+	23.6640i	0.597630	+	0.894417i
$701$	−9.48683	−	9.48683i	−0.358313	−	0.358313i	0.504878	−	0.863191i	$-0.331537\pi$
$701$	−9.48683	−	9.48683i	−0.358313	−	0.358313i	−0.863191	+	0.504878i	$0.831537\pi$
$702$	−5.23338	−	46.1802i	−0.197521	−	1.74296i
$703$		0			0
$704$	−18.0315	+	3.58669i	−0.679588	+	0.135179i
$705$	30.1095	+	31.8342i	1.13399	+	1.19895i
$706$	−15.3073	+	36.9552i	−0.576099	+	1.39083i
$707$	−2.75899	−	13.8704i	−0.103763	−	0.521650i
$708$	39.3469	−	24.7351i	1.47875	−	0.929601i
$709$	6.20303	+	1.23386i	0.232960	+	0.0463386i	0.310189	−	0.950675i	$-0.399608\pi$
$709$	6.20303	+	1.23386i	0.232960	+	0.0463386i	−0.0772298	+	0.997013i	$0.524608\pi$
$710$	−56.9210	+	56.9210i	−2.13621	+	2.13621i
$711$	9.18715	+	2.36564i	0.344545	+	0.0887186i
$712$	27.7164	−	11.4805i	1.03872	−	0.430250i
$713$	22.3607			0.837414
$714$		0			0
$715$	16.0000			0.598366
$716$		0			0
$717$	15.2725	−	2.59827i	0.570362	−	0.0970343i
$718$	−42.4264	+	42.4264i	−1.58334	+	1.58334i
$719$	4.16112	+	0.827698i	0.155184	+	0.0308679i	0.272071	−	0.962277i	$-0.412292\pi$
$719$	4.16112	+	0.827698i	0.155184	+	0.0308679i	−0.116887	+	0.993145i	$0.537292\pi$
$720$	1.18977	+	8.40146i	0.0443400	+	0.313104i
$721$	2.46772	+	12.4061i	0.0919027	+	0.462026i
$722$	16.2584	−	39.2513i	0.605076	−	1.46078i
$723$	−31.8342	+	30.1095i	−1.18393	+	1.11979i
$724$	55.8273	−	11.1047i	2.07480	−	0.412704i
$725$	4.71417	−	7.05525i	0.175080	−	0.262026i
$726$	−20.1646	+	28.4322i	−0.748377	+	1.05522i
$727$	5.65685	+	5.65685i	0.209801	+	0.209801i	0.804183	−	0.594382i	$-0.202603\pi$
$727$	5.65685	+	5.65685i	0.209801	+	0.209801i	−0.594382	+	0.804183i	$0.702603\pi$
$728$	15.7139	+	23.5175i	0.582396	+	0.871617i
$729$	−14.3354	+	22.8800i	−0.530941	+	0.847409i
$730$		0			0
$731$		0			0
$732$	30.0000	+	13.4164i	1.10883	+	0.495885i
$733$	−13.0112	−	31.4119i	−0.480581	−	1.16023i	−0.959333	−	0.282275i	$-0.908911\pi$
$733$	−13.0112	−	31.4119i	−0.480581	−	1.16023i	0.478752	−	0.877950i	$-0.341089\pi$
$734$	−29.3969	+	19.6424i	−1.08506	+	0.725013i
$735$	5.24419	+	13.7295i	0.193435	+	0.506419i
$736$	−9.25395	+	46.5227i	−0.341105	+	1.71485i
$737$	9.40700	+	6.28556i	0.346511	+	0.231532i
$738$	22.8054	−	30.3301i	0.839477	−	1.11647i
$739$	22.1731	+	9.18440i	0.815651	+	0.337854i	0.751206	−	0.660068i	$-0.229472\pi$
$739$	22.1731	+	9.18440i	0.815651	+	0.337854i	0.0644448	+	0.997921i	$0.479472\pi$
$740$	49.5806	+	20.5369i	1.82262	+	0.754953i
$741$		0			0
$742$		0			0
$743$	1.37950	−	6.93520i	0.0506088	−	0.254428i	−0.947196	−	0.320656i	$-0.896097\pi$
$743$	1.37950	−	6.93520i	0.0506088	−	0.254428i	0.997804	+	0.0662284i	$0.0210966\pi$
$744$	11.4412	−	4.37016i	0.419456	−	0.160218i
$745$	−42.0694	+	28.1099i	−1.54130	+	1.02987i
$746$	−3.42282	−	8.26343i	−0.125319	−	0.302546i
$747$	−17.8885	−	20.0000i	−0.654508	−	0.731762i
$748$		0			0
$749$			13.4164i			0.490225i
$750$	−0.609761	+	21.9004i	−0.0222653	+	0.799690i
$751$	−19.3255	−	28.9227i	−0.705199	−	1.05540i	−0.995151	−	0.0983636i	$-0.968639\pi$
$751$	−19.3255	−	28.9227i	−0.705199	−	1.05540i	0.289952	−	0.957041i	$-0.406361\pi$
$752$	−6.32456	−	6.32456i	−0.230633	−	0.230633i
$753$	−25.2731	−	17.9240i	−0.921002	−	0.653189i
$754$	14.0549	−	21.0347i	0.511851	−	0.766039i
$755$	−55.4816	+	11.0360i	−2.01918	+	0.401640i
$756$	4.11164	−	49.1233i	0.149539	−	1.78660i
$757$	−4.59220	+	11.0866i	−0.166906	+	0.402948i	−0.985097	−	0.171999i	$-0.944977\pi$
$757$	−4.59220	+	11.0866i	−0.166906	+	0.402948i	0.818191	+	0.574947i	$0.194977\pi$
$758$	4.13849	+	20.8056i	0.150317	+	0.755693i
$759$	−9.21821	−	14.6637i	−0.334600	−	0.532259i
$760$		0			0
$761$	3.16228	−	3.16228i	0.114632	−	0.114632i	−0.647464	−	0.762096i	$-0.724170\pi$
$761$	3.16228	−	3.16228i	0.114632	−	0.114632i	0.762096	+	0.647464i	$0.224170\pi$
$762$	−7.79482	−	45.8175i	−0.282377	−	1.65979i
$763$	−55.4328	+	22.9610i	−2.00680	+	0.831244i
$764$	26.8328			0.970777
$765$		0			0
$766$	−80.0000			−2.89052
$767$	33.0537	−	13.6913i	1.19350	−	0.494364i
$768$	2.61446	+	15.3676i	0.0943413	+	0.554532i
$769$	−14.1421	+	14.1421i	−0.509978	+	0.509978i	−0.914520	−	0.404541i	$-0.867431\pi$
$769$	−14.1421	+	14.1421i	−0.509978	+	0.509978i	0.404541	+	0.914520i	$0.367431\pi$
$770$	27.7408	+	5.51799i	0.999709	+	0.198854i
$771$	−20.6126	−	32.7891i	−0.742343	−	1.18087i
$772$	−7.40316	−	37.2182i	−0.266445	−	1.33951i
$773$	15.4027	−	37.1854i	0.553997	−	1.33747i	−0.360456	−	0.932776i	$-0.617379\pi$
$773$	15.4027	−	37.1854i	0.553997	−	1.33747i	0.914453	−	0.404691i	$-0.132621\pi$
$774$	8.87319	+	25.3232i	0.318940	+	0.910225i
$775$	9.30455	−	1.85079i	0.334229	−	0.0664823i
$776$	−15.7139	+	23.5175i	−0.564096	+	0.844229i
$777$	28.2562	+	20.0397i	1.01368	+	0.718920i
$778$	−7.07107	−	7.07107i	−0.253510	−	0.253510i
$779$		0			0
$780$	1.63616	−	58.7650i	0.0585840	−	2.10412i
$781$			18.0000i			0.644091i
$782$		0			0
$783$	−14.0000	+	4.47214i	−0.500319	+	0.159821i
$784$	−1.14805	−	2.77164i	−0.0410018	−	0.0989871i
$785$	4.70350	−	3.14278i	0.167875	−	0.112171i
$786$	5.11667	−	1.95440i	0.182506	−	0.0697110i
$787$	−6.78623	+	34.1167i	−0.241903	+	1.21613i	0.648593	+	0.761136i	$0.275358\pi$
$787$	−6.78623	+	34.1167i	−0.241903	+	1.21613i	−0.890495	+	0.454992i	$0.849642\pi$
$788$	−63.4973	−	42.4275i	−2.26200	−	1.51142i
$789$	−30.2085	−	6.88807i	−1.07545	−	0.245222i
$790$	18.4776	+	7.65367i	0.657403	+	0.272305i
$791$	16.5269	+	6.84565i	0.587627	+	0.243403i
$792$	−7.58253	−	5.70134i	−0.269433	−	0.202588i
$793$	21.0347	+	14.0549i	0.746964	+	0.499106i
$794$	8.27698	−	41.6112i	0.293739	−	1.47673i
$795$		0			0
$796$	−23.6640	+	15.8118i	−0.838750	+	0.560435i
$797$	−6.84565	−	16.5269i	−0.242485	−	0.585411i	0.755043	−	0.655675i	$-0.227616\pi$
$797$	−6.84565	−	16.5269i	−0.242485	−	0.585411i	−0.997528	+	0.0702638i	$0.977616\pi$
$798$		0			0
$799$		0			0
$800$			20.1246i			0.711512i
$801$	−36.2708	−	17.4479i	−1.28157	−	0.616492i
$802$	7.02747	+	10.5174i	0.248149	+	0.371381i
$803$		0			0
$804$	24.0476	−	33.9074i	0.848095	−	1.19582i
$805$	35.1373	−	52.5868i	1.23843	−	1.85344i
$806$	27.7408	−	5.51799i	0.977128	−	0.194363i
$807$	−32.0325	+	30.2971i	−1.12760	+	1.06651i
$808$	−3.82683	+	9.23880i	−0.134628	+	0.325020i
$809$	3.31079	+	16.6445i	0.116401	+	0.585189i	0.994325	+	0.106388i	$0.0339285\pi$
$809$	3.31079	+	16.6445i	0.116401	+	0.585189i	−0.877923	+	0.478801i	$0.841072\pi$
$810$	−36.6865	+	43.5213i	−1.28903	+	1.52918i
$811$	−46.5227	−	9.25395i	−1.63363	−	0.324950i	−0.708826	−	0.705384i	$-0.750775\pi$
$811$	−46.5227	−	9.25395i	−1.63363	−	0.324950i	−0.924808	+	0.380434i	$0.875775\pi$
$812$	18.9737	−	18.9737i	0.665845	−	0.665845i
$813$		0			0
$814$	18.4776	−	7.65367i	0.647639	−	0.268261i
$815$	−26.8328			−0.939913
$816$		0			0
$817$		0			0
$818$	28.9220	−	11.9799i	1.01123	−	0.418867i
$819$	9.46257	−	36.7486i	0.330649	−	1.28410i
$820$	33.9411	−	33.9411i	1.18528	−	1.18528i
$821$	−19.4186	−	3.86259i	−0.677712	−	0.134805i	−0.155779	−	0.987792i	$-0.549789\pi$
$821$	−19.4186	−	3.86259i	−0.677712	−	0.134805i	−0.521933	+	0.852987i	$0.674789\pi$
$822$	−14.6637	+	9.21821i	−0.511456	+	0.321522i
$823$	−6.78623	−	34.1167i	−0.236553	−	1.18923i	−0.898258	−	0.439468i	$-0.855167\pi$
$823$	−6.78623	−	34.1167i	−0.236553	−	1.18923i	0.661705	−	0.749764i	$-0.269833\pi$
$824$	3.42282	−	8.26343i	0.119240	−	0.287870i
$825$	−5.04952	−	5.33876i	−0.175802	−	0.185872i
$826$	62.0303	−	12.3386i	2.15831	−	0.429315i
$827$	21.2138	−	31.7486i	0.737675	−	1.10401i	−0.252961	−	0.967477i	$-0.581404\pi$
$827$	21.2138	−	31.7486i	0.737675	−	1.10401i	0.990636	−	0.136532i	$-0.0435956\pi$
$828$	−54.7997	+	32.3572i	−1.90442	+	1.12449i
$829$	21.2132	+	21.2132i	0.736765	+	0.736765i	0.971951	−	0.235185i	$-0.0755698\pi$
$829$	21.2132	+	21.2132i	0.736765	+	0.736765i	−0.235185	+	0.971951i	$0.575570\pi$
$830$	−31.4278	−	47.0350i	−1.09087	−	1.63261i
$831$	10.9502	+	0.304881i	0.379858	+	0.0105762i
$832$			52.0000i			1.80278i
$833$		0			0
$834$	−5.00000	+	11.1803i	−0.173136	+	0.387144i
$835$	10.7151	+	25.8686i	0.370813	+	0.895221i
$836$		0			0
$837$	−14.6035	−	7.53244i	−0.504771	−	0.260359i
$838$	−4.31851	+	21.7106i	−0.149180	+	0.749980i
$839$	−8.23113	−	5.49986i	−0.284170	−	0.189876i	0.405313	−	0.914178i	$-0.367162\pi$
$839$	−8.23113	−	5.49986i	−0.284170	−	0.189876i	−0.689483	+	0.724301i	$0.742162\pi$
$840$	7.70110	−	33.7741i	0.265713	−	1.16532i
$841$	19.4015	+	8.03635i	0.669016	+	0.277116i
$842$	−41.3171	−	17.1141i	−1.42388	−	0.589792i
$843$	6.88807	−	30.2085i	0.237238	−	1.04044i
$844$	−55.2161	−	36.8942i	−1.90062	−	1.26995i
$845$	1.65540	−	8.32224i	0.0569474	−	0.286294i
$846$	3.33851	−	59.9070i	0.114780	−	2.05965i
$847$	−23.6640	+	15.8118i	−0.813106	+	0.543300i
$848$		0			0
$849$	2.23607	−	5.00000i	0.0767417	−	0.171600i
$850$		0			0
$851$		−	44.7214i		−	1.53303i
$852$	66.1106	+	1.84068i	2.26491	+	0.0630607i
$853$	−3.51373	−	5.25868i	−0.120308	−	0.180054i	0.766427	−	0.642331i	$-0.222032\pi$
$853$	−3.51373	−	5.25868i	−0.120308	−	0.180054i	−0.886735	+	0.462277i	$0.847032\pi$
$854$	31.6228	+	31.6228i	1.08211	+	1.08211i
$855$		0			0
$856$	5.27060	−	7.88801i	0.180145	−	0.269607i
$857$	−11.0963	+	2.20720i	−0.379043	+	0.0753963i	−0.380935	−	0.924602i	$-0.624398\pi$
$857$	−11.0963	+	2.20720i	−0.379043	+	0.0753963i	0.00189186	+	0.999998i	$0.499398\pi$
$858$	−15.0548	−	15.9171i	−0.513961	−	0.543401i
$859$	7.65367	−	18.4776i	0.261140	−	0.630447i	−0.737870	−	0.674943i	$-0.764168\pi$
$859$	7.65367	−	18.4776i	0.261140	−	0.630447i	0.999010	+	0.0444959i	$0.0141681\pi$
$860$	6.62159	+	33.2890i	0.225794	+	1.13514i
$861$	26.2313	−	16.4900i	0.893959	−	0.561979i
$862$	−27.9136	−	5.55237i	−0.950742	−	0.189114i
$863$	12.6491	−	12.6491i	0.430581	−	0.430581i	−0.458245	−	0.888826i	$-0.651522\pi$
$863$	12.6491	−	12.6491i	0.430581	−	0.430581i	0.888826	+	0.458245i	$0.151522\pi$
$864$	21.7153	−	27.2662i	0.738771	−	0.927614i
$865$	36.9552	−	15.3073i	1.25651	−	0.520465i
$866$	−80.4984			−2.73545
$867$		0			0
$868$	30.0000			1.01827
$869$	4.13171	−	1.71141i	0.140159	−	0.0580557i
$870$	−30.5450	+	5.19655i	−1.03557	+	0.176179i
$871$	22.6274	−	22.6274i	0.766701	−	0.766701i
$872$	41.6112	+	8.27698i	1.40913	+	0.280294i
$873$	37.5725	−	5.32080i	1.27163	−	0.180082i
$874$		0			0
$875$	−6.84565	+	16.5269i	−0.231425	+	0.558710i
$876$		0			0
$877$	31.0152	−	6.16930i	1.04731	−	0.208322i	0.358697	−	0.933454i	$-0.383221\pi$
$877$	31.0152	−	6.16930i	1.04731	−	0.208322i	0.688610	+	0.725132i	$0.258221\pi$
$878$	27.4993	−	41.1556i	0.928057	−	1.38894i
$879$	17.9240	−	25.2731i	0.604563	−	0.852440i
$880$	2.82843	+	2.82843i	0.0953463	+	0.0953463i
$881$	3.14278	+	4.70350i	0.105883	+	0.158465i	0.880627	−	0.473810i	$-0.157121\pi$
$881$	3.14278	+	4.70350i	0.105883	+	0.158465i	−0.774744	+	0.632275i	$0.782121\pi$
$882$	8.72396	−	18.1354i	0.293751	−	0.610651i
$883$			16.0000i			0.538443i	0.963078	+	0.269221i	$0.0867663\pi$
$883$			16.0000i			0.538443i	−0.963078	+	0.269221i	$0.913234\pi$
$884$		0			0
$885$	−40.0000	−	17.8885i	−1.34459	−	0.601317i
$886$	15.3073	+	36.9552i	0.514260	+	1.24153i
$887$	41.1556	−	27.4993i	1.38187	−	0.923337i	0.381872	−	0.924215i	$-0.375280\pi$
$887$	41.1556	−	27.4993i	1.38187	−	0.923337i	1.00000		0.000878410i	$0.000279607\pi$
$888$	−8.74032	−	22.8825i	−0.293306	−	0.767885i
$889$	7.40316	−	37.2182i	0.248294	−	1.24826i
$890$	−70.5525	−	47.1417i	−2.36493	−	1.58019i
$891$	1.08068	+	12.6820i	0.0362041	+	0.424862i
$892$	−44.3462	−	18.3688i	−1.48482	−	0.615033i
$893$		0			0
$894$	67.5483	+	15.4022i	2.25915	+	0.515127i
$895$		0			0
$896$	−9.65648	+	48.5464i	−0.322600	+	1.62182i
$897$	−45.7649	+	17.4806i	−1.52805	+	0.583662i
$898$	31.5521	−	21.0824i	1.05291	−	0.703529i
$899$	−3.42282	−	8.26343i	−0.114158	−	0.275601i
$900$	−20.1246	+	18.0000i	−0.670820	+	0.600000i
$901$		0			0
$902$		−	17.8885i		−	0.595623i
$903$	−0.609761	+	21.9004i	−0.0202916	+	0.728800i
$904$	−7.02747	−	10.5174i	−0.233730	−	0.349802i
$905$	−37.9473	−	37.9473i	−1.26141	−	1.26141i
$906$	63.1827	+	44.8101i	2.09910	+	1.48872i
$907$	−12.2981	+	18.4054i	−0.408351	+	0.611140i	−0.977460	−	0.211122i	$-0.932288\pi$
$907$	−12.2981	+	18.4054i	−0.408351	+	0.611140i	0.569109	+	0.822262i	$0.307288\pi$
$908$	20.8056	−	4.13849i	0.690458	−	0.137341i
$909$	12.6616	−	4.43660i	0.419959	−	0.147153i
$910$	30.6147	−	73.9104i	1.01487	−	2.45010i
$911$	−3.03489	−	15.2574i	−0.100550	−	0.505501i	−0.997934	−	0.0642497i	$-0.979535\pi$
$911$	−3.03489	−	15.2574i	−0.100550	−	0.505501i	0.897383	−	0.441252i	$-0.145465\pi$
$912$		0			0
$913$	−12.4061	−	2.46772i	−0.410581	−	0.0816696i
$914$	44.2719	−	44.2719i	1.46438	−	1.46438i
$915$	−5.19655	−	30.5450i	−0.171793	−	1.00979i
$916$	−55.4328	+	22.9610i	−1.83155	+	0.758653i
$917$	4.47214			0.147683
$918$		0			0
$919$	−24.0000			−0.791687			−0.395843	−	0.918318i	$-0.629548\pi$
$919$	−24.0000			−0.791687			−0.395843	+	0.918318i	$0.629548\pi$
$920$	−41.3171	+	17.1141i	−1.36219	+	0.564236i
$921$	−3.48595	−	20.4902i	−0.114866	−	0.675175i
$922$	56.5685	−	56.5685i	1.86299	−	1.86299i
$923$	49.9334	+	9.93238i	1.64358	+	0.326928i
$924$	−12.3675	−	19.6734i	−0.406862	−	0.647209i
$925$	−3.70158	−	18.6091i	−0.121707	−	0.611863i
$926$	−3.42282	+	8.26343i	−0.112481	+	0.271553i
$927$	−11.3249	+	3.96821i	−0.371958	+	0.130333i
$928$	18.6091	−	3.70158i	0.610873	−	0.121510i
$929$	−21.9995	+	32.9245i	−0.721779	+	1.08022i	0.271269	+	0.962504i	$0.412557\pi$
$929$	−21.9995	+	32.9245i	−0.721779	+	1.08022i	−0.993047	+	0.117715i	$0.962443\pi$
$930$	−28.2562	−	20.0397i	−0.926556	−	0.657128i
$931$		0			0
$932$	9.42834	+	14.1105i	0.308836	+	0.462205i
$933$	0.0681734	−	2.44854i	0.00223190	−	0.0801616i
$934$		−	40.0000i		−	1.30884i
$935$		0			0
$936$	−20.0000	+	17.8885i	−0.653720	+	0.584705i
$937$	−0.765367	−	1.84776i	−0.0250034	−	0.0603637i	0.910885	−	0.412661i	$-0.135401\pi$
$937$	−0.765367	−	1.84776i	−0.0250034	−	0.0603637i	−0.935888	+	0.352297i	$0.885401\pi$
$938$	47.0350	−	31.4278i	1.53575	−	1.02615i
$939$	−40.9334	+	15.6352i	−1.33581	+	0.510234i
$940$	14.8063	−	74.4364i	0.482929	−	2.42785i
$941$	−30.5728	−	20.4281i	−0.996644	−	0.665936i	−0.0535853	−	0.998563i	$-0.517065\pi$
$941$	−30.5728	−	20.4281i	−0.996644	−	0.665936i	−0.943058	+	0.332627i	$0.892065\pi$
$942$	−7.55213	−	1.72202i	−0.246062	−	0.0561064i
$943$	−36.9552	−	15.3073i	−1.20343	−	0.498475i
$944$	8.26343	+	3.42282i	0.268952	+	0.111403i
$945$	−40.6622	+	22.5074i	−1.32274	+	0.732166i
$946$	10.5174	+	7.02747i	0.341949	+	0.228483i
$947$	9.65648	−	48.5464i	0.313793	−	1.57755i	−0.426007	−	0.904720i	$-0.640080\pi$
$947$	9.65648	−	48.5464i	0.313793	−	1.57755i	0.739801	−	0.672826i	$-0.234920\pi$
$948$	−5.86319	−	15.3500i	−0.190427	−	0.498545i
$949$		0			0
$950$		0			0
$951$	22.3607	+	10.0000i	0.725095	+	0.324272i
$952$		0			0
$953$			13.4164i			0.434600i	0.976105	+	0.217300i	$0.0697250\pi$
$953$			13.4164i			0.434600i	−0.976105	+	0.217300i	$0.930275\pi$
$954$		0			0
$955$	−14.0549	−	21.0347i	−0.454807	−	0.680667i
$956$	−18.9737	−	18.9737i	−0.613652	−	0.613652i
$957$	−4.00794	+	5.65123i	−0.129558	+	0.182678i
$958$	−12.2981	+	18.4054i	−0.397333	+	0.594650i
$959$	−13.8704	+	2.75899i	−0.447899	+	0.0890926i
$960$	46.2692	−	43.7625i	1.49333	−	1.41243i
$961$	−8.03635	+	19.4015i	−0.259237	+	0.625854i
$962$	−11.0360	−	55.4816i	−0.355814	−	1.78880i
$963$	−12.6022	+	1.78465i	−0.406100	+	0.0575096i
$964$	74.4364	+	14.8063i	2.39743	+	0.476879i
$965$	−25.2982	+	25.2982i	−0.814379	+	0.814379i
$966$	−85.3758	+	14.5248i	−2.74692	+	0.467328i
$967$	−29.5641	+	12.2459i	−0.950719	+	0.393801i	−0.803501	−	0.595303i	$-0.797032\pi$
$967$	−29.5641	+	12.2459i	−0.950719	+	0.393801i	−0.147218	+	0.989104i	$0.547032\pi$
$968$	20.1246			0.646830
$969$		0			0
$970$	80.0000			2.56865
$971$	24.7903	−	10.2685i	0.795558	−	0.329531i	0.0523823	−	0.998627i	$-0.483319\pi$
$971$	24.7903	−	10.2685i	0.795558	−	0.329531i	0.743176	+	0.669096i	$0.233319\pi$
$972$	46.6890	−	2.67227i	1.49755	−	0.0857132i
$973$	−7.07107	+	7.07107i	−0.226688	+	0.226688i
$974$	−62.4168	−	12.4155i	−1.99996	−	0.397817i
$975$	−17.5965	+	11.0619i	−0.563538	+	0.354263i
$976$	1.23386	+	6.20303i	0.0394949	+	0.198554i
$977$	6.84565	−	16.5269i	0.219012	−	0.528741i	−0.775741	−	0.631052i	$-0.782624\pi$
$977$	6.84565	−	16.5269i	0.219012	−	0.528741i	0.994753	+	0.102311i	$0.0326236\pi$
$978$	25.2476	+	26.6938i	0.807330	+	0.853573i
$979$	−18.6091	+	3.70158i	−0.594749	+	0.118303i
$980$	14.1425	−	21.1658i	0.451766	−	0.676115i
$981$	−28.9412	−	49.0144i	−0.924022	−	1.56491i
$982$	28.2843	+	28.2843i	0.902587	+	0.902587i
$983$	−19.6424	−	29.3969i	−0.626494	−	0.937615i	−0.999950	−	0.00996724i	$-0.996827\pi$
$983$	−19.6424	−	29.3969i	−0.626494	−	0.937615i	0.373456	−	0.927648i	$-0.378173\pi$
$984$	−21.9004	−	0.609761i	−0.698160	−	0.0194385i
$985$			72.0000i			2.29411i
$986$		0			0
$987$	20.0000	−	44.7214i	0.636607	−	1.42350i
$988$		0			0
$989$	23.5175	−	15.7139i	0.747813	−	0.499673i
$990$	−1.49302	+	26.7912i	−0.0474514	+	0.851482i
$991$	−6.78623	+	34.1167i	−0.215572	+	1.08375i	0.709717	+	0.704487i	$0.248823\pi$
$991$	−6.78623	+	34.1167i	−0.215572	+	1.08375i	−0.925288	+	0.379265i	$0.876177\pi$
$992$	17.6381	+	11.7854i	0.560011	+	0.374188i
$993$	−10.7815	+	47.2838i	−0.342142	+	1.50051i
$994$	83.1492	+	34.4415i	2.63733	+	1.09242i
$995$	24.7903	+	10.2685i	0.785905	+	0.325533i
$996$	−10.3321	+	45.3128i	−0.327385	+	1.43579i
$997$	−5.25868	−	3.51373i	−0.166544	−	0.111281i	0.469505	−	0.882930i	$-0.344432\pi$
$997$	−5.25868	−	3.51373i	−0.166544	−	0.111281i	−0.636049	+	0.771649i	$0.719432\pi$
$998$	−1.37950	+	6.93520i	−0.0436672	+	0.219530i
$999$	−15.0649	+	29.2070i	−0.476632	+	0.924069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.i.e.158.4	yes	32
3.2	odd	2	inner	867.2.i.e.158.2	yes	32
17.2	even	8	inner	867.2.i.e.224.4	yes	32
17.3	odd	16	inner	867.2.i.e.827.3	yes	32
17.4	even	4	inner	867.2.i.e.131.2	yes	32
17.5	odd	16	inner	867.2.i.e.329.1	yes	32
17.6	odd	16	inner	867.2.i.e.503.4	yes	32
17.7	odd	16	inner	867.2.i.e.653.2	yes	32
17.8	even	8	inner	867.2.i.e.65.2	yes	32
17.9	even	8	inner	867.2.i.e.65.1	✓	32
17.10	odd	16	inner	867.2.i.e.653.1	yes	32
17.11	odd	16	inner	867.2.i.e.503.3	yes	32
17.12	odd	16	inner	867.2.i.e.329.2	yes	32
17.13	even	4	inner	867.2.i.e.131.1	yes	32
17.14	odd	16	inner	867.2.i.e.827.4	yes	32
17.15	even	8	inner	867.2.i.e.224.3	yes	32
17.16	even	2	inner	867.2.i.e.158.3	yes	32
51.2	odd	8	inner	867.2.i.e.224.2	yes	32
51.5	even	16	inner	867.2.i.e.329.3	yes	32
51.8	odd	8	inner	867.2.i.e.65.3	yes	32
51.11	even	16	inner	867.2.i.e.503.1	yes	32
51.14	even	16	inner	867.2.i.e.827.1	yes	32
51.20	even	16	inner	867.2.i.e.827.2	yes	32
51.23	even	16	inner	867.2.i.e.503.2	yes	32
51.26	odd	8	inner	867.2.i.e.65.4	yes	32
51.29	even	16	inner	867.2.i.e.329.4	yes	32
51.32	odd	8	inner	867.2.i.e.224.1	yes	32
51.38	odd	4	inner	867.2.i.e.131.4	yes	32
51.41	even	16	inner	867.2.i.e.653.4	yes	32
51.44	even	16	inner	867.2.i.e.653.3	yes	32
51.47	odd	4	inner	867.2.i.e.131.3	yes	32
51.50	odd	2	inner	867.2.i.e.158.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.i.e.65.1	✓	32	17.9	even	8	inner
867.2.i.e.65.2	yes	32	17.8	even	8	inner
867.2.i.e.65.3	yes	32	51.8	odd	8	inner
867.2.i.e.65.4	yes	32	51.26	odd	8	inner
867.2.i.e.131.1	yes	32	17.13	even	4	inner
867.2.i.e.131.2	yes	32	17.4	even	4	inner
867.2.i.e.131.3	yes	32	51.47	odd	4	inner
867.2.i.e.131.4	yes	32	51.38	odd	4	inner
867.2.i.e.158.1	yes	32	51.50	odd	2	inner
867.2.i.e.158.2	yes	32	3.2	odd	2	inner
867.2.i.e.158.3	yes	32	17.16	even	2	inner
867.2.i.e.158.4	yes	32	1.1	even	1	trivial
867.2.i.e.224.1	yes	32	51.32	odd	8	inner
867.2.i.e.224.2	yes	32	51.2	odd	8	inner
867.2.i.e.224.3	yes	32	17.15	even	8	inner
867.2.i.e.224.4	yes	32	17.2	even	8	inner
867.2.i.e.329.1	yes	32	17.5	odd	16	inner
867.2.i.e.329.2	yes	32	17.12	odd	16	inner
867.2.i.e.329.3	yes	32	51.5	even	16	inner
867.2.i.e.329.4	yes	32	51.29	even	16	inner
867.2.i.e.503.1	yes	32	51.11	even	16	inner
867.2.i.e.503.2	yes	32	51.23	even	16	inner
867.2.i.e.503.3	yes	32	17.11	odd	16	inner
867.2.i.e.503.4	yes	32	17.6	odd	16	inner
867.2.i.e.653.1	yes	32	17.10	odd	16	inner
867.2.i.e.653.2	yes	32	17.7	odd	16	inner
867.2.i.e.653.3	yes	32	51.44	even	16	inner
867.2.i.e.653.4	yes	32	51.41	even	16	inner
867.2.i.e.827.1	yes	32	51.14	even	16	inner
867.2.i.e.827.2	yes	32	51.20	even	16	inner
867.2.i.e.827.3	yes	32	17.3	odd	16	inner
867.2.i.e.827.4	yes	32	17.14	odd	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.06586 - 0.855706i) q^{2} +(0.290496 + 1.70752i) q^{3} +(2.12132 - 2.12132i) q^{4} +(-2.77408 - 0.551799i) q^{5} +(2.06126 + 3.27891i) q^{6} +(0.616930 + 3.10152i) q^{7} +(0.855706 - 2.06586i) q^{8} +(-2.83122 + 0.992053i) q^{9} +O(q^{10})\)	\(q+(2.06586 - 0.855706i) q^{2} +(0.290496 + 1.70752i) q^{3} +(2.12132 - 2.12132i) q^{4} +(-2.77408 - 0.551799i) q^{5} +(2.06126 + 3.27891i) q^{6} +(0.616930 + 3.10152i) q^{7} +(0.855706 - 2.06586i) q^{8} +(-2.83122 + 0.992053i) q^{9} +(-6.20303 + 1.23386i) q^{10} +(-0.785695 + 1.17588i) q^{11} +(4.23842 + 3.00595i) q^{12} +(2.82843 + 2.82843i) q^{13} +(3.92847 + 5.87938i) q^{14} +(0.136347 - 4.89708i) q^{15} +1.00000i q^{16} +(-5.00000 + 4.47214i) q^{18} +(-7.05525 + 4.71417i) q^{20} +(-5.11667 + 1.95440i) q^{21} +(-0.616930 + 3.10152i) q^{22} +(5.87938 + 3.92847i) q^{23} +(3.77606 + 0.861009i) q^{24} +(2.77164 + 1.14805i) q^{25} +(8.26343 + 3.42282i) q^{26} +(-2.51641 - 4.54617i) q^{27} +(7.88801 + 5.27060i) q^{28} +(0.551799 - 2.77408i) q^{29} +(-3.90879 - 10.2333i) q^{30} +(2.62934 - 1.75687i) q^{31} +(2.56712 + 6.19757i) q^{32} +(-2.23607 - 1.00000i) q^{33} -8.94427i q^{35} +(-3.90147 + 8.11040i) q^{36} +(-3.51373 - 5.25868i) q^{37} +(-4.00794 + 5.65123i) q^{39} +(-3.51373 + 5.25868i) q^{40} +(-5.54816 + 1.10360i) q^{41} +(-8.89793 + 8.41587i) q^{42} +(1.53073 - 3.69552i) q^{43} +(0.827698 + 4.16112i) q^{44} +(8.40146 - 1.18977i) q^{45} +(15.5076 + 3.08465i) q^{46} +(-6.32456 + 6.32456i) q^{47} +(-1.70752 + 0.290496i) q^{48} +(-2.77164 + 1.14805i) q^{49} +6.70820 q^{50} +12.0000 q^{52} +(-9.08872 - 7.23844i) q^{54} +(2.82843 - 2.82843i) q^{55} +(6.93520 + 1.37950i) q^{56} +(-1.23386 - 6.20303i) q^{58} +(3.42282 - 8.26343i) q^{59} +(-10.0990 - 10.6775i) q^{60} +(6.20303 - 1.23386i) q^{61} +(3.92847 - 5.87938i) q^{62} +(-4.82353 - 8.16906i) q^{63} +(9.19239 + 9.19239i) q^{64} +(-6.28556 - 9.40700i) q^{65} +(-5.47510 - 0.152440i) q^{66} -8.00000i q^{67} +(-5.00000 + 11.1803i) q^{69} +(-7.65367 - 18.4776i) q^{70} +(10.5829 - 7.07125i) q^{71} +(-0.373256 + 6.69781i) q^{72} +(-11.7588 - 7.85695i) q^{74} +(-1.15517 + 5.06612i) q^{75} +(-4.13171 - 1.71141i) q^{77} +(-3.44404 + 15.1043i) q^{78} +(-2.62934 - 1.75687i) q^{79} +(0.551799 - 2.77408i) q^{80} +(7.03166 - 5.61745i) q^{81} +(-10.5174 + 7.02747i) q^{82} +(3.42282 + 8.26343i) q^{83} +(-6.70820 + 15.0000i) q^{84} -8.94427i q^{86} +(4.89708 + 0.136347i) q^{87} +(1.75687 + 2.62934i) q^{88} +(9.48683 + 9.48683i) q^{89} +(16.3381 - 9.64707i) q^{90} +(-7.02747 + 10.5174i) q^{91} +(20.8056 - 4.13849i) q^{92} +(3.76369 + 3.97927i) q^{93} +(-7.65367 + 18.4776i) q^{94} +(-9.83672 + 6.18377i) q^{96} +(-12.4061 - 2.46772i) q^{97} +(-4.74342 + 4.74342i) q^{98} +(1.05795 - 4.10862i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 160 q^{18} + 384 q^{52} - 160 q^{69}+O(q^{100}) \) 32 * q - 160 * q^18 + 384 * q^52 - 160 * q^69

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