LMFDB - Embedded newform 867.2.i.e.653.2

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			653.2
Character	$\chi$	$=$	867.653
Dual form			867.2.i.e.158.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06586 - 0.855706i) q^{2} +(1.46637 - 0.921821i) q^{3} +(2.12132 + 2.12132i) q^{4} +(2.77408 - 0.551799i) q^{5} +(-3.81812 + 0.649569i) q^{6} +(0.616930 - 3.10152i) q^{7} +(-0.855706 - 2.06586i) q^{8} +(1.30049 - 2.70347i) q^{9} +O(q^{10})$	\(q+(-2.06586 - 0.855706i) q^{2} +(1.46637 - 0.921821i) q^{3} +(2.12132 + 2.12132i) q^{4} +(2.77408 - 0.551799i) q^{5} +(-3.81812 + 0.649569i) q^{6} +(0.616930 - 3.10152i) q^{7} +(-0.855706 - 2.06586i) q^{8} +(1.30049 - 2.70347i) q^{9} +(-6.20303 - 1.23386i) q^{10} +(0.785695 + 1.17588i) q^{11} +(5.06612 + 1.15517i) q^{12} +(2.82843 - 2.82843i) q^{13} +(-3.92847 + 5.87938i) q^{14} +(3.55917 - 3.36635i) q^{15} -1.00000i q^{16} +(-5.00000 + 4.47214i) q^{18} +(7.05525 + 4.71417i) q^{20} +(-1.95440 - 5.11667i) q^{21} +(-0.616930 - 3.10152i) q^{22} +(-5.87938 + 3.92847i) q^{23} +(-3.15913 - 2.24051i) q^{24} +(2.77164 - 1.14805i) q^{25} +(-8.26343 + 3.42282i) q^{26} +(-0.585110 - 5.16310i) q^{27} +(7.88801 - 5.27060i) q^{28} +(-0.551799 - 2.77408i) q^{29} +(-10.2333 + 3.90879i) q^{30} +(2.62934 + 1.75687i) q^{31} +(-2.56712 + 6.19757i) q^{32} +(2.23607 + 1.00000i) q^{33} -8.94427i q^{35} +(8.49367 - 2.97616i) q^{36} +(-3.51373 + 5.25868i) q^{37} +(1.54022 - 6.75483i) q^{39} +(-3.51373 - 5.25868i) q^{40} +(5.54816 + 1.10360i) q^{41} +(-0.340867 + 12.2427i) q^{42} +(1.53073 + 3.69552i) q^{43} +(-0.827698 + 4.16112i) q^{44} +(2.11590 - 8.21724i) q^{45} +(15.5076 - 3.08465i) q^{46} +(6.32456 + 6.32456i) q^{47} +(-0.921821 - 1.46637i) q^{48} +(-2.77164 - 1.14805i) q^{49} -6.70820 q^{50} +12.0000 q^{52} +(-3.20935 + 11.1669i) 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} +(14.6912 + 0.409040i) q^{60} +(6.20303 + 1.23386i) q^{61} +(-3.92847 - 5.87938i) q^{62} +(-7.58253 - 5.70134i) q^{63} +(9.19239 - 9.19239i) q^{64} +(6.28556 - 9.40700i) q^{65} +(-3.76369 - 3.97927i) q^{66} +8.00000i q^{67} +(-5.00000 + 11.1803i) q^{69} +(-7.65367 + 18.4776i) q^{70} +(-10.5829 - 7.07125i) q^{71} +(-6.69781 - 0.373256i) q^{72} +(11.7588 - 7.85695i) q^{74} +(3.00595 - 4.23842i) q^{75} +(4.13171 - 1.71141i) q^{77} +(-8.96202 + 12.6365i) q^{78} +(-2.62934 + 1.75687i) q^{79} +(-0.551799 - 2.77408i) q^{80} +(-5.61745 - 7.03166i) q^{81} +(-10.5174 - 7.02747i) q^{82} +(-3.42282 + 8.26343i) q^{83} +(6.70820 - 15.0000i) q^{84} -8.94427i q^{86} +(-3.36635 - 3.55917i) q^{87} +(1.75687 - 2.62934i) q^{88} +(-9.48683 + 9.48683i) q^{89} +(-11.4027 + 15.1651i) q^{90} +(-7.02747 - 10.5174i) q^{91} +(-20.8056 - 4.13849i) q^{92} +(5.47510 + 0.152440i) q^{93} +(-7.65367 - 18.4776i) q^{94} +(1.94871 + 11.4544i) q^{96} +(-12.4061 + 2.46772i) q^{97} +(4.74342 + 4.74342i) q^{98} +(4.20073 - 0.594884i) 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 $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{11}{16}\right)$

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	$-0.665215\pi$
$2$	−2.06586	−	0.855706i	−1.46078	−	0.605076i	−0.964736	+	0.263221i	$0.915215\pi$
$3$	1.46637	−	0.921821i	0.846610	−	0.532214i
$3$	1.46637	−	0.921821i	0.846610	−	0.532214i
$4$	2.12132	+	2.12132i	1.06066	+	1.06066i
$5$	2.77408	−	0.551799i	1.24061	−	0.246772i	0.469187	−	0.883099i	$-0.344547\pi$
$5$	2.77408	−	0.551799i	1.24061	−	0.246772i	0.771419	+	0.636327i	$0.219547\pi$
$6$	−3.81812	+	0.649569i	−1.55874	+	0.265185i
$7$	0.616930	−	3.10152i	0.233178	−	1.17226i	−0.669789	−	0.742552i	$-0.733615\pi$
$7$	0.616930	−	3.10152i	0.233178	−	1.17226i	0.902966	−	0.429711i	$-0.141385\pi$
$8$	−0.855706	−	2.06586i	−0.302538	−	0.730391i
$9$	1.30049	−	2.70347i	0.433497	−	0.901155i
$10$	−6.20303	−	1.23386i	−1.96157	−	0.390181i
$11$	0.785695	+	1.17588i	0.236896	+	0.354540i	0.930801	−	0.365527i	$-0.119111\pi$
$11$	0.785695	+	1.17588i	0.236896	+	0.354540i	−0.693905	+	0.720067i	$0.744111\pi$
$12$	5.06612	+	1.15517i	1.46246	+	0.333467i
$13$	2.82843	−	2.82843i	0.784465	−	0.784465i	−0.196116	−	0.980581i	$-0.562833\pi$
$13$	2.82843	−	2.82843i	0.784465	−	0.784465i	0.980581	+	0.196116i	$0.0628330\pi$
$14$	−3.92847	+	5.87938i	−1.04993	+	1.57133i
$15$	3.55917	−	3.36635i	0.918974	−	0.869187i
$16$		−	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	$-0.875000\pi$
$19$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$20$	7.05525	+	4.71417i	1.57760	+	1.05412i
$21$	−1.95440	−	5.11667i	−0.426484	−	1.11655i
$22$	−0.616930	−	3.10152i	−0.131530	−	0.661245i
$23$	−5.87938	+	3.92847i	−1.22594	+	0.819144i	−0.988346	−	0.152222i	$-0.951357\pi$
$23$	−5.87938	+	3.92847i	−1.22594	+	0.819144i	−0.237589	+	0.971366i	$0.576357\pi$
$24$	−3.15913	−	2.24051i	−0.644856	−	0.457341i
$25$	2.77164	−	1.14805i	0.554328	−	0.229610i
$26$	−8.26343	+	3.42282i	−1.62059	+	0.671271i
$27$	−0.585110	−	5.16310i	−0.112604	−	0.993640i
$28$	7.88801	−	5.27060i	1.49069	−	0.996050i
$29$	−0.551799	−	2.77408i	−0.102466	−	0.515134i	−0.997594	−	0.0693239i	$-0.977916\pi$
$29$	−0.551799	−	2.77408i	−0.102466	−	0.515134i	0.895128	−	0.445810i	$-0.147084\pi$
$30$	−10.2333	+	3.90879i	−1.86834	+	0.713644i
$31$	2.62934	+	1.75687i	0.472243	+	0.315543i	0.768819	−	0.639467i	$-0.220845\pi$
$31$	2.62934	+	1.75687i	0.472243	+	0.315543i	−0.296576	+	0.955009i	$0.595845\pi$
$32$	−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
$36$	8.49367	−	2.97616i	1.41561	−	0.496026i
$37$	−3.51373	+	5.25868i	−0.577654	+	0.864521i	−0.999104	−	0.0423311i	$-0.986522\pi$
$37$	−3.51373	+	5.25868i	−0.577654	+	0.864521i	0.421449	+	0.906852i	$0.361522\pi$
$38$		0			0
$39$	1.54022	−	6.75483i	0.246633	−	1.08164i
$40$	−3.51373	−	5.25868i	−0.555570	−	0.831470i
$41$	5.54816	+	1.10360i	0.866477	+	0.172353i	0.608264	−	0.793735i	$-0.291866\pi$
$41$	5.54816	+	1.10360i	0.866477	+	0.172353i	0.258213	+	0.966088i	$0.416866\pi$
$42$	−0.340867	+	12.2427i	−0.0525969	+	1.88909i
$43$	1.53073	+	3.69552i	0.233435	+	0.563561i	0.996577	−	0.0826692i	$-0.0263445\pi$
$43$	1.53073	+	3.69552i	0.233435	+	0.563561i	−0.763142	+	0.646230i	$0.776344\pi$
$44$	−0.827698	+	4.16112i	−0.124780	+	0.627312i
$45$	2.11590	−	8.21724i	0.315419	−	1.22495i
$46$	15.5076	−	3.08465i	2.28647	−	0.454807i
$47$	6.32456	+	6.32456i	0.922531	+	0.922531i	0.997208	−	0.0746766i	$-0.0237924\pi$
$47$	6.32456	+	6.32456i	0.922531	+	0.922531i	−0.0746766	+	0.997208i	$0.523792\pi$
$48$	−0.921821	−	1.46637i	−0.133053	−	0.211652i
$49$	−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	$-0.375000\pi$
$53$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$54$	−3.20935	+	11.1669i	−0.436737	+	1.51963i
$55$	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	−0.973948	−	0.226771i	$-0.927183\pi$
$59$	−3.42282	−	8.26343i	−0.445614	−	1.07581i	0.528334	−	0.849036i	$-0.322817\pi$
$60$	14.6912	+	0.409040i	1.89663	+	0.0528069i
$61$	6.20303	+	1.23386i	0.794217	+	0.157980i	0.575492	−	0.817807i	$-0.304810\pi$
$61$	6.20303	+	1.23386i	0.794217	+	0.157980i	0.218724	+	0.975787i	$0.429810\pi$
$62$	−3.92847	−	5.87938i	−0.498917	−	0.746682i
$63$	−7.58253	−	5.70134i	−0.955309	−	0.718301i
$64$	9.19239	−	9.19239i	1.14905	−	1.14905i
$65$	6.28556	−	9.40700i	0.779628	−	1.16680i
$66$	−3.76369	−	3.97927i	−0.463278	−	0.489815i
$67$			8.00000i			0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$			8.00000i			0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$		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	$-0.584991\pi$
$71$	−10.5829	−	7.07125i	−1.25596	−	0.839204i	−0.992111	+	0.125361i	$0.959991\pi$
$72$	−6.69781	−	0.373256i	−0.789345	−	0.0439887i
$73$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$73$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$74$	11.7588	−	7.85695i	1.36693	−	0.913352i
$75$	3.00595	−	4.23842i	0.347098	−	0.489411i
$76$		0			0
$77$	4.13171	−	1.71141i	0.470853	−	0.195034i
$78$	−8.96202	+	12.6365i	−1.01475	+	1.43081i
$79$	−2.62934	+	1.75687i	−0.295824	+	0.197663i	−0.694621	−	0.719376i	$-0.744428\pi$
$79$	−2.62934	+	1.75687i	−0.295824	+	0.197663i	0.398797	+	0.917039i	$0.369428\pi$
$80$	−0.551799	−	2.77408i	−0.0616930	−	0.310152i
$81$	−5.61745	−	7.03166i	−0.624161	−	0.781296i
$82$	−10.5174	−	7.02747i	−1.16145	−	0.776054i
$83$	−3.42282	+	8.26343i	−0.375704	+	0.907029i	0.617057	+	0.786919i	$0.288325\pi$
$83$	−3.42282	+	8.26343i	−0.375704	+	0.907029i	−0.992761	+	0.120111i	$0.961675\pi$
$84$	6.70820	−	15.0000i	0.731925	−	1.63663i
$85$		0			0
$86$		−	8.94427i		−	0.964486i
$87$	−3.36635	−	3.55917i	−0.360910	−	0.381583i
$88$	1.75687	−	2.62934i	0.187283	−	0.280288i
$89$	−9.48683	+	9.48683i	−1.00560	+	1.00560i	−0.00561807	+	0.999984i	$0.501788\pi$
$89$	−9.48683	+	9.48683i	−1.00560	+	1.00560i	−0.999984	+	0.00561807i	$0.998212\pi$
$90$	−11.4027	+	15.1651i	−1.20195	+	1.59854i
$91$	−7.02747	−	10.5174i	−0.736679	−	1.10252i
$92$	−20.8056	−	4.13849i	−2.16913	−	0.431467i
$93$	5.47510	+	0.152440i	0.567742	+	0.0158073i
$94$	−7.65367	−	18.4776i	−0.789416	−	1.90582i
$95$		0			0
$96$	1.94871	+	11.4544i	0.198889	+	1.16906i
$97$	−12.4061	+	2.46772i	−1.25964	+	0.250559i	−0.779373	−	0.626561i	$-0.784462\pi$
$97$	−12.4061	+	2.46772i	−1.25964	+	0.250559i	−0.480272	+	0.877120i	$0.659462\pi$
$98$	4.74342	+	4.74342i	0.479157	+	0.479157i
$99$	4.20073	−	0.594884i	0.422189	−	0.0597881i
$100$	8.31492	+	3.44415i	0.831492	+	0.344415i
$101$	4.47214			0.444994			0.222497	−	0.974933i	$-0.428579\pi$
$101$	4.47214			0.444994			0.222497	+	0.974933i	$0.428579\pi$
$102$		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
$105$	−8.24502	−	13.1156i	−0.804632	−	1.27995i
$106$		0			0
$107$	−4.16112	+	0.827698i	−0.402271	+	0.0800166i	−0.392079	−	0.919931i	$-0.628244\pi$
$107$	−4.16112	+	0.827698i	−0.402271	+	0.0800166i	−0.0101914	+	0.999948i	$0.503244\pi$
$108$	9.71139	−	12.1938i	0.934479	−	1.17335i
$109$	3.70158	−	18.6091i	0.354547	−	1.78243i	−0.232211	−	0.972665i	$-0.574596\pi$
$109$	3.70158	−	18.6091i	0.354547	−	1.78243i	0.586758	−	0.809762i	$-0.300404\pi$
$110$	−3.42282	−	8.26343i	−0.326354	−	0.787887i
$111$	−0.304881	+	10.9502i	−0.0289380	+	1.03935i
$112$	−3.10152	−	0.616930i	−0.293066	−	0.0582944i
$113$	−3.14278	−	4.70350i	−0.295648	−	0.442468i	0.653673	−	0.756777i	$-0.273227\pi$
$113$	−3.14278	−	4.70350i	−0.295648	−	0.442468i	−0.949321	+	0.314309i	$0.898227\pi$
$114$		0			0
$115$	−14.1421	+	14.1421i	−1.31876	+	1.31876i
$116$	4.71417	−	7.05525i	0.437700	−	0.655064i
$117$	−3.96821	−	11.3249i	−0.366861	−	1.04699i
$118$			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
$123$	9.15298	−	3.49613i	0.825297	−	0.315235i
$124$	1.85079	+	9.30455i	0.166206	+	0.835573i
$125$	−4.70350	+	3.14278i	−0.420694	+	0.281099i
$126$	10.7857	+	18.2666i	0.960871	+	1.62732i
$127$	−11.0866	+	4.59220i	−0.983773	+	0.407492i	−0.815822	−	0.578303i	$-0.803715\pi$
$127$	−11.0866	+	4.59220i	−0.983773	+	0.407492i	−0.167951	+	0.985795i	$0.553715\pi$
$128$	−14.4610	+	5.98994i	−1.27818	+	0.529441i
$129$	5.65123	+	4.00794i	0.497563	+	0.352879i
$130$	−21.0347	+	14.0549i	−1.84487	+	1.23270i
$131$	−0.275899	−	1.38704i	−0.0241054	−	0.121186i	0.966859	−	0.255311i	$-0.0821778\pi$
$131$	−0.275899	−	1.38704i	−0.0241054	−	0.121186i	−0.990964	+	0.134125i	$0.957178\pi$
$132$	2.62210	+	6.86474i	0.228224	+	0.597499i
$133$		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	$0.938814\pi$
$138$	19.8964	−	18.8185i	1.69369	−	1.60193i
$139$	1.75687	−	2.62934i	0.149016	−	0.223018i	−0.749451	−	0.662060i	$-0.769682\pi$
$139$	1.75687	−	2.62934i	0.149016	−	0.223018i	0.898466	+	0.439043i	$0.144682\pi$
$140$	18.9737	−	18.9737i	1.60357	−	1.60357i
$141$	15.1043	+	3.44404i	1.27201	+	0.290040i
$142$	15.8118	+	23.6640i	1.32690	+	1.98584i
$143$	5.54816	+	1.10360i	0.463960	+	0.0922875i
$144$	−2.70347	−	1.30049i	−0.225289	−	0.108374i
$145$	−3.06147	−	7.39104i	−0.254241	−	0.613792i
$146$		0			0
$147$	−5.12255	+	0.871488i	−0.422501	+	0.0718791i
$148$	−18.6091	+	3.70158i	−1.52966	+	0.304268i
$149$	−12.6491	−	12.6491i	−1.03626	−	1.03626i	−0.999318	−	0.0369380i	$-0.988240\pi$
$149$	−12.6491	−	12.6491i	−1.03626	−	1.03626i	−0.0369380	−	0.999318i	$-0.511760\pi$
$150$	−9.83672	+	6.18377i	−0.803165	+	0.504902i
$151$	18.4776	+	7.65367i	1.50369	+	0.622847i	0.974243	−	0.225500i	$-0.0724014\pi$
$151$	18.4776	+	7.65367i	1.50369	+	0.622847i	0.529442	+	0.848346i	$0.322401\pi$
$152$		0			0
$153$		0			0
$154$	−10.0000			−0.805823
$155$	8.26343	+	3.42282i	0.663735	+	0.274928i
$156$	17.5965	−	11.0619i	1.40884	−	0.885657i
$157$	−1.41421	−	1.41421i	−0.112867	−	0.112867i	0.648418	−	0.761285i	$-0.275431\pi$
$157$	−1.41421	−	1.41421i	−0.112867	−	0.112867i	−0.761285	+	0.648418i	$0.775431\pi$
$158$	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
$162$	5.58781	+	19.3333i	0.439020	+	1.51897i
$163$	9.30455	+	1.85079i	0.728788	+	0.144965i	0.545520	−	0.838098i	$-0.316332\pi$
$163$	9.30455	+	1.85079i	0.728788	+	0.144965i	0.183268	+	0.983063i	$0.441332\pi$
$164$	9.42834	+	14.1105i	0.736230	+	1.10185i
$165$	6.75483	+	1.54022i	0.525863	+	0.119906i
$166$	14.1421	−	14.1421i	1.09764	−	1.09764i
$167$	5.49986	−	8.23113i	0.425592	−	0.636944i	−0.555265	−	0.831674i	$-0.687383\pi$
$167$	5.49986	−	8.23113i	0.425592	−	0.636944i	0.980857	+	0.194730i	$0.0623830\pi$
$168$	−8.89793	+	8.41587i	−0.686490	+	0.649298i
$169$		−	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	$-0.131830\pi$
$173$	11.7588	+	7.85695i	0.894002	+	0.597353i	−0.0214548	+	0.999770i	$0.506830\pi$
$174$	3.90879	+	10.2333i	0.296325	+	0.775788i
$175$	−1.85079	−	9.30455i	−0.139907	−	0.703358i
$176$	1.17588	−	0.785695i	0.0886350	−	0.0592240i
$177$	−12.6365	−	8.96202i	−0.949820	−	0.673627i
$178$	27.7164	−	11.4805i	2.07743	−	0.860500i
$179$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$179$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$180$	21.9199	−	12.9429i	1.63381	−	0.964707i
$181$	15.7760	−	10.5412i	1.17262	−	0.783522i	0.192380	−	0.981320i	$-0.438379\pi$
$181$	15.7760	−	10.5412i	1.17262	−	0.783522i	0.980243	+	0.197799i	$0.0633793\pi$
$182$	5.51799	+	27.7408i	0.409020	+	2.05628i
$183$	10.2333	−	3.90879i	0.756471	−	0.288946i
$184$	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
$189$	−16.3744	−	1.37055i	−1.19106	−	0.0996925i
$190$		0			0
$191$	−6.32456	+	6.32456i	−0.457629	+	0.457629i	−0.897876	−	0.440248i	$-0.854891\pi$
$191$	−6.32456	+	6.32456i	−0.457629	+	0.457629i	0.440248	+	0.897876i	$0.354891\pi$
$192$	5.00572	−	21.9532i	0.361256	−	1.58434i
$193$	7.02747	+	10.5174i	0.505848	+	0.757055i	0.993234	−	0.116131i	$-0.0370494\pi$
$193$	7.02747	+	10.5174i	0.505848	+	0.757055i	−0.487386	+	0.873187i	$0.662049\pi$
$194$	27.7408	+	5.51799i	1.99167	+	0.396168i
$195$	0.545387	−	19.5883i	0.0390560	−	1.40275i
$196$	−3.44415	−	8.31492i	−0.246011	−	0.593923i
$197$	4.96619	−	24.9667i	0.353826	−	1.77880i	−0.236491	−	0.971634i	$-0.575997\pi$
$197$	4.96619	−	24.9667i	0.353826	−	1.77880i	0.590317	−	0.807171i	$-0.299003\pi$
$198$	−9.18715	−	2.36564i	−0.652902	−	0.168119i
$199$	−9.30455	+	1.85079i	−0.659582	+	0.131199i	−0.513522	−	0.858077i	$-0.671659\pi$
$199$	−9.30455	+	1.85079i	−0.659582	+	0.131199i	−0.146060	+	0.989276i	$0.546659\pi$
$200$	−4.74342	−	4.74342i	−0.335410	−	0.335410i
$201$	7.37457	+	11.7310i	0.520162	+	0.827439i
$202$	−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
$207$	2.97442	+	21.0036i	0.206736	+	1.45985i
$208$	−2.82843	−	2.82843i	−0.196116	−	0.196116i
$209$		0			0
$210$	5.80992	+	34.1503i	0.400922	+	2.35660i
$211$	−4.31851	+	21.7106i	−0.297298	+	1.49462i	0.486542	+	0.873657i	$0.338258\pi$
$211$	−4.31851	+	21.7106i	−0.297298	+	1.49462i	−0.783840	+	0.620963i	$0.786742\pi$
$212$		0			0
$213$	−22.0369	−	0.613560i	−1.50994	−	0.0420405i
$214$	9.30455	+	1.85079i	0.636046	+	0.126517i
$215$	6.28556	+	9.40700i	0.428672	+	0.641552i
$216$	−10.1656	+	5.62685i	−0.691678	+	0.382859i
$217$	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	0.575109	+	0.818077i	$0.304960\pi$
$223$	−6.12293	+	14.7821i	−0.410022	+	0.989881i	−0.985131	+	0.171804i	$0.945040\pi$
$224$	17.6381	+	11.7854i	1.17850	+	0.787447i
$225$	0.500776	−	8.98606i	0.0333851	−	0.599070i
$226$	2.46772	+	12.4061i	0.164150	+	0.825239i
$227$	−5.87938	+	3.92847i	−0.390228	+	0.260742i	−0.735171	−	0.677882i	$-0.762898\pi$
$227$	−5.87938	+	3.92847i	−0.390228	+	0.260742i	0.344943	+	0.938624i	$0.387898\pi$
$228$		0			0
$229$	−18.4776	+	7.65367i	−1.22103	+	0.505769i	−0.897738	−	0.440529i	$-0.854791\pi$
$229$	−18.4776	+	7.65367i	−1.22103	+	0.505769i	−0.323295	+	0.946298i	$0.604791\pi$
$230$	41.3171	−	17.1141i	2.72437	−	1.12847i
$231$	4.48101	−	6.31827i	0.294829	−	0.415712i
$232$	−5.25868	+	3.51373i	−0.345249	+	0.230688i
$233$	1.10360	+	5.54816i	0.0722991	+	0.363472i	0.999950	−	0.00997588i	$-0.00317547\pi$
$233$	1.10360	+	5.54816i	0.0722991	+	0.363472i	−0.927651	+	0.373448i	$0.878175\pi$
$234$	−1.49302	+	26.7912i	−0.0976021	+	1.75140i
$235$	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	$-0.0934153\pi$
$240$	−3.36635	−	3.55917i	−0.217297	−	0.229744i
$241$	14.0549	−	21.0347i	0.905358	−	1.35496i	−0.0293579	−	0.999569i	$-0.509346\pi$
$241$	14.0549	−	21.0347i	0.905358	−	1.35496i	0.934716	−	0.355395i	$-0.115654\pi$
$242$	−14.2302	+	14.2302i	−0.914755	+	0.914755i
$243$	−14.7192	−	5.13274i	−0.944237	−	0.329266i
$244$	10.5412	+	15.7760i	0.674831	+	1.00996i
$245$	−8.32224	−	1.65540i	−0.531688	−	0.105759i
$246$	−21.9004	−	0.609761i	−1.39632	−	0.0388769i
$247$		0			0
$248$	1.37950	−	6.93520i	0.0875981	−	0.440386i
$249$	2.59827	+	15.2725i	0.164659	+	0.967855i
$250$	12.4061	−	2.46772i	0.784628	−	0.156072i
$251$	12.6491	+	12.6491i	0.798405	+	0.798405i	0.982844	−	0.184439i	$-0.0590469\pi$
$251$	12.6491	+	12.6491i	0.798405	+	0.798405i	−0.184439	+	0.982844i	$0.559047\pi$
$252$	−3.99060	−	28.1793i	−0.251384	−	1.77513i
$253$	−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	$-0.129335\pi$
$257$	20.6586	+	8.55706i	1.28865	+	0.533775i	0.370065	+	0.929006i	$0.379335\pi$
$258$	−8.24502	−	13.1156i	−0.513313	−	0.816543i
$259$	14.1421	+	14.1421i	0.878750	+	0.878750i
$260$	33.2890	−	6.62159i	2.06449	−	0.410653i
$261$	−8.21724	−	2.11590i	−0.508634	−	0.130971i
$262$	−0.616930	+	3.10152i	−0.0381140	+	0.191612i
$263$	6.84565	+	16.5269i	0.422121	+	1.01909i	0.981721	+	0.190327i	$0.0609548\pi$
$263$	6.84565	+	16.5269i	0.422121	+	1.01909i	−0.559600	+	0.828763i	$0.689045\pi$
$264$	0.152440	−	5.47510i	0.00938205	−	0.336969i
$265$		0			0
$266$		0			0
$267$	−5.16606	+	22.6564i	−0.316157	+	1.38655i
$268$	−16.9706	+	16.9706i	−1.03664	+	1.03664i
$269$	−14.1425	+	21.1658i	−0.862284	+	1.29050i	0.0932573	+	0.995642i	$0.470272\pi$
$269$	−14.1425	+	21.1658i	−0.862284	+	1.29050i	−0.955541	+	0.294857i	$0.904728\pi$
$270$	−2.74109	+	32.7488i	−0.166817	+	1.99303i
$271$		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
$276$	−34.3237	+	13.1105i	−2.06604	+	0.789158i
$277$	1.23386	+	6.20303i	0.0741354	+	0.372704i	0.999987	−	0.00518447i	$-0.00165027\pi$
$277$	1.23386	+	6.20303i	0.0741354	+	0.372704i	−0.925851	+	0.377888i	$0.876650\pi$
$278$	−5.87938	+	3.92847i	−0.352622	+	0.235614i
$279$	8.16906	−	4.82353i	0.489069	−	0.288777i
$280$	−18.4776	+	7.65367i	−1.10425	+	0.457394i
$281$	16.5269	−	6.84565i	0.985910	−	0.408377i	0.169298	−	0.985565i	$-0.445850\pi$
$281$	16.5269	−	6.84565i	0.985910	−	0.408377i	0.816612	+	0.577188i	$0.195850\pi$
$282$	−28.2562	−	20.0397i	−1.68263	−	1.19335i
$283$	−2.62934	+	1.75687i	−0.156298	+	0.104435i	−0.631260	−	0.775571i	$-0.717462\pi$
$283$	−2.62934	+	1.75687i	−0.156298	+	0.104435i	0.474962	+	0.880006i	$0.342462\pi$
$284$	−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
$291$	−15.9171	+	15.0548i	−0.933077	+	0.882526i
$292$		0			0
$293$	12.6491	−	12.6491i	0.738969	−	0.738969i	−0.233410	−	0.972379i	$-0.574988\pi$
$293$	12.6491	−	12.6491i	0.738969	−	0.738969i	0.972379	+	0.233410i	$0.0749883\pi$
$294$	11.3282	+	2.58303i	0.660674	+	0.150645i
$295$	−14.0549	−	21.0347i	−0.818310	−	1.22469i
$296$	13.8704	+	2.75899i	0.806201	+	0.160363i
$297$	5.61145	−	4.74464i	0.325609	−	0.275312i
$298$	15.3073	+	36.9552i	0.886730	+	2.14076i
$299$	−5.51799	+	27.7408i	−0.319113	+	1.60429i
$300$	15.3676	−	2.61446i	0.887252	−	0.150946i
$301$	12.4061	−	2.46772i	0.715073	−	0.142237i
$302$	−31.6228	−	31.6228i	−1.81969	−	1.81969i
$303$	6.55781	−	4.12251i	0.376736	−	0.236832i
$304$		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
$309$	5.86549	−	3.68729i	0.333676	−	0.209762i
$310$	−14.1421	−	14.1421i	−0.803219	−	0.803219i
$311$	1.38704	−	0.275899i	0.0786518	−	0.0156448i	−0.155608	−	0.987819i	$-0.549734\pi$
$311$	1.38704	−	0.275899i	0.0786518	−	0.0156448i	0.234259	+	0.972174i	$0.424734\pi$
$312$	−15.2725	+	2.59827i	−0.864635	+	0.147098i
$313$	4.93544	−	24.8121i	0.278967	−	1.40246i	−0.546237	−	0.837630i	$-0.683940\pi$
$313$	4.93544	−	24.8121i	0.278967	−	1.40246i	0.825205	−	0.564834i	$-0.191060\pi$
$314$	1.71141	+	4.13171i	0.0965806	+	0.233166i
$315$	−24.1805	−	11.6319i	−1.36242	−	0.655386i
$316$	−9.30455	−	1.85079i	−0.523422	−	0.104115i
$317$	−7.85695	−	11.7588i	−0.441290	−	0.660438i	0.542439	−	0.840095i	$-0.317501\pi$
$317$	−7.85695	−	11.7588i	−0.441290	−	0.660438i	−0.983729	+	0.179658i	$0.942501\pi$
$318$		0			0
$319$	2.82843	−	2.82843i	0.158362	−	0.158362i
$320$	20.4281	−	30.5728i	1.14196	−	1.70907i
$321$	−5.33876	+	5.04952i	−0.297980	+	0.281837i
$322$		−	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
$327$	−11.7264	−	30.7000i	−0.648470	−	1.69772i
$328$	−2.46772	−	12.4061i	−0.136257	−	0.685010i
$329$	23.5175	−	15.7139i	1.29656	−	0.866335i
$330$	−12.6365	−	8.96202i	−0.695619	−	0.493343i
$331$	25.8686	−	10.7151i	1.42187	−	0.588957i	0.466539	−	0.884501i	$-0.345501\pi$
$331$	25.8686	−	10.7151i	1.42187	−	0.588957i	0.955329	+	0.295543i	$0.0955007\pi$
$332$	−24.7903	+	10.2685i	−1.36054	+	0.563556i
$333$	9.64707	+	16.3381i	0.528656	+	0.895323i
$334$	−18.4054	+	12.2981i	−1.00710	+	0.672921i
$335$	4.41439	+	22.1926i	0.241184	+	1.21251i
$336$	−5.11667	+	1.95440i	−0.279137	+	0.106621i
$337$	−21.0347	−	14.0549i	−1.14583	−	0.765621i	−0.170282	−	0.985395i	$-0.554468\pi$
$337$	−21.0347	−	14.0549i	−1.14583	−	0.765621i	−0.975551	+	0.219774i	$0.929468\pi$
$338$	−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
$345$	−7.70110	+	33.7741i	−0.414613	+	1.81834i
$346$	−17.5687	−	26.2934i	−0.944498	−	1.41354i
$347$	−34.6760	−	6.89748i	−1.86151	−	0.370276i	−0.869238	−	0.494395i	$-0.835390\pi$
$347$	−34.6760	−	6.89748i	−1.86151	−	0.370276i	−0.992267	+	0.124118i	$0.960390\pi$
$348$	0.409040	−	14.6912i	0.0219269	−	0.787533i
$349$	5.35757	+	12.9343i	0.286784	+	0.692358i	0.999963	−	0.00862428i	$-0.00274523\pi$
$349$	5.35757	+	12.9343i	0.286784	+	0.692358i	−0.713179	+	0.700982i	$0.752745\pi$
$350$	−4.13849	+	20.8056i	−0.221212	+	1.11211i
$351$	−16.2584	−	12.9485i	−0.867809	−	0.691141i
$352$	−9.30455	+	1.85079i	−0.495934	+	0.0986474i
$353$	12.6491	+	12.6491i	0.673244	+	0.673244i	0.958463	−	0.285218i	$-0.0920661\pi$
$353$	12.6491	+	12.6491i	0.673244	+	0.673244i	−0.285218	+	0.958463i	$0.592066\pi$
$354$	18.4364	+	29.3274i	0.979885	+	1.55874i
$355$	−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	$-0.124557\pi$
$359$	24.7903	+	10.2685i	1.30838	+	0.541949i	0.383970	+	0.923346i	$0.374557\pi$
$360$	−18.7862	+	2.66040i	−0.990121	+	0.140215i
$361$	13.4350	+	13.4350i	0.707107	+	0.707107i
$362$	−41.6112	+	8.27698i	−2.18704	+	0.435028i
$363$	−2.61446	−	15.3676i	−0.137224	−	0.806592i
$364$	7.40316	−	37.2182i	0.388031	−	1.95076i
$365$		0			0
$366$	−24.4854	−	0.681734i	−1.27987	−	0.0356348i
$367$	−15.5076	−	3.08465i	−0.809489	−	0.161017i	−0.227041	−	0.973885i	$-0.572905\pi$
$367$	−15.5076	−	3.08465i	−0.809489	−	0.161017i	−0.582448	+	0.812868i	$0.697905\pi$
$368$	3.92847	+	5.87938i	0.204786	+	0.306484i
$369$	10.1989	−	13.5640i	0.530932	−	0.706116i
$370$	28.2843	−	28.2843i	1.47043	−	1.47043i
$371$		0			0
$372$	11.2911	+	11.9378i	0.585415	+	0.618947i
$373$			4.00000i			0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$			4.00000i			0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$		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
$378$	32.6544	+	16.8430i	1.67956	+	0.866313i
$379$	−1.85079	−	9.30455i	−0.0950687	−	0.477942i	−0.998761	−	0.0497604i	$-0.984154\pi$
$379$	−1.85079	−	9.30455i	−0.0950687	−	0.477942i	0.903693	−	0.428182i	$-0.140846\pi$
$380$		0			0
$381$	−12.0238	+	16.9537i	−0.615999	+	0.868564i
$382$	18.4776	−	7.65367i	0.945396	−	0.391596i
$383$	33.0537	−	13.6913i	1.68897	−	0.699593i	0.689276	−	0.724499i	$-0.257929\pi$
$383$	33.0537	−	13.6913i	1.68897	−	0.699593i	0.999690	+	0.0249059i	$0.00792860\pi$
$384$	−15.6835	+	22.1139i	−0.800347	+	1.12850i
$385$	10.5174	−	7.02747i	0.536014	−	0.358153i
$386$	−5.51799	−	27.7408i	−0.280858	−	1.41197i
$387$	11.9814	+	0.667701i	0.609049	+	0.0339412i
$388$	−31.5521	−	21.0824i	−1.60181	−	1.07030i
$389$	1.71141	−	4.13171i	0.0867720	−	0.209486i	−0.874537	−	0.484959i	$-0.838834\pi$
$389$	1.71141	−	4.13171i	0.0867720	−	0.209486i	0.961309	+	0.275473i	$0.0888344\pi$
$390$	−17.8885	+	40.0000i	−0.905822	+	2.02548i
$391$		0			0
$392$			6.70820i			0.338815i
$393$	−1.68317	−	1.77959i	−0.0849049	−	0.0897682i
$394$	−31.6236	+	47.3281i	−1.59317	+	2.38435i
$395$	−6.32456	+	6.32456i	−0.318223	+	0.318223i
$396$	10.1730	+	7.64915i	0.511214	+	0.384384i
$397$	10.5412	+	15.7760i	0.529048	+	0.791776i	0.995697	−	0.0926663i	$-0.0295390\pi$
$397$	10.5412	+	15.7760i	0.529048	+	0.791776i	−0.466649	+	0.884442i	$0.654539\pi$
$398$	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	$-0.982611\pi$
$401$	−1.10360	+	5.54816i	−0.0551110	+	0.277062i	0.943397	+	0.331665i	$0.107611\pi$
$402$	−5.19655	−	30.5450i	−0.259180	−	1.52345i
$403$	12.4061	−	2.46772i	0.617990	−	0.122926i
$404$	9.48683	+	9.48683i	0.471988	+	0.471988i
$405$	−19.4633	−	16.4067i	−0.967140	−	0.815255i
$406$	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
$411$	4.12251	+	6.55781i	0.203348	+	0.323473i
$412$	8.48528	+	8.48528i	0.418040	+	0.418040i
$413$	−27.7408	+	5.51799i	−1.36504	+	0.271522i
$414$	11.8282	−	45.9358i	0.581325	−	2.25762i
$415$	−4.93544	+	24.8121i	−0.242271	+	1.21798i
$416$	10.2685	+	24.7903i	0.503453	+	1.21544i
$417$	0.152440	−	5.47510i	0.00746503	−	0.268117i
$418$		0			0
$419$	5.49986	+	8.23113i	0.268686	+	0.402117i	0.941137	−	0.338024i	$-0.109759\pi$
$419$	5.49986	+	8.23113i	0.268686	+	0.402117i	−0.672451	+	0.740141i	$0.734759\pi$
$420$	10.3321	−	45.3128i	0.504155	−	2.21104i
$421$	−14.1421	+	14.1421i	−0.689246	+	0.689246i	−0.962065	−	0.272820i	$-0.912044\pi$
$421$	−14.1421	+	14.1421i	−0.689246	+	0.689246i	0.272820	+	0.962065i	$0.412044\pi$
$422$	27.4993	−	41.1556i	1.33865	−	2.00343i
$423$	25.3232	−	8.87319i	1.23126	−	0.431429i
$424$		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
$429$	9.15298	−	3.49613i	0.441910	−	0.168795i
$430$	−4.93544	−	24.8121i	−0.238008	−	1.19655i
$431$	10.5829	−	7.07125i	0.509759	−	0.340610i	−0.273944	−	0.961746i	$-0.588328\pi$
$431$	10.5829	−	7.07125i	0.509759	−	0.340610i	0.783703	+	0.621135i	$0.213328\pi$
$432$	−5.16310	+	0.585110i	−0.248410	+	0.0281511i
$433$	−33.2597	+	13.7766i	−1.59836	+	0.662061i	−0.991182	−	0.132507i	$-0.957697\pi$
$433$	−33.2597	+	13.7766i	−1.59836	+	0.662061i	−0.607175	+	0.794568i	$0.707697\pi$
$434$	−20.6586	+	8.55706i	−0.991643	+	0.410752i
$435$	−11.3025	−	8.01588i	−0.541912	−	0.384332i
$436$	47.3281	−	31.6236i	2.26660	−	1.51450i
$437$		0			0
$438$		0			0
$439$	18.4054	+	12.2981i	0.878440	+	0.586955i	0.910950	−	0.412516i	$-0.135350\pi$
$439$	18.4054	+	12.2981i	0.878440	+	0.586955i	−0.0325100	+	0.999471i	$0.510350\pi$
$440$	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	$0.860290\pi$
$444$	−23.8756	+	22.5821i	−1.13309	+	1.07170i
$445$	−21.0824	+	31.5521i	−0.999402	+	1.49571i
$446$	25.2982	−	25.2982i	1.19791	−	1.19791i
$447$	−30.2085	−	6.88807i	−1.42881	−	0.325795i
$448$	−22.8393	−	34.1814i	−1.07905	−	1.61492i
$449$	−16.6445	−	3.31079i	−0.785501	−	0.156246i	−0.213985	−	0.976837i	$-0.568645\pi$
$449$	−16.6445	−	3.31079i	−0.785501	−	0.156246i	−0.571516	+	0.820591i	$0.693645\pi$
$450$	−8.72396	+	18.1354i	−0.411251	+	0.854911i
$451$	3.06147	+	7.39104i	0.144159	+	0.348030i
$452$	3.31079	−	16.6445i	0.155727	−	0.782890i
$453$	34.1503	−	5.80992i	1.60452	−	0.272974i
$454$	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	0.894244	−	0.447580i	$-0.147714\pi$
$457$	25.8686	+	10.7151i	1.21008	+	0.501233i	0.315839	+	0.948813i	$0.397714\pi$
$458$	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	$-0.688466\pi$
$461$	−33.0537	−	13.6913i	−1.53947	−	0.637667i	−0.981373	+	0.192112i	$0.938466\pi$
$462$	−14.6637	+	9.21821i	−0.682218	+	0.428870i
$463$	−2.82843	−	2.82843i	−0.131448	−	0.131448i	0.638322	−	0.769770i	$-0.279629\pi$
$463$	−2.82843	−	2.82843i	−0.131448	−	0.131448i	−0.769770	+	0.638322i	$0.779629\pi$
$464$	−2.77408	+	0.551799i	−0.128783	+	0.0256166i
$465$	15.2725	−	2.59827i	0.708245	−	0.120492i
$466$	2.46772	−	12.4061i	0.114315	−	0.574700i
$467$	−6.84565	−	16.5269i	−0.316779	−	0.764772i	−0.999421	−	0.0340192i	$-0.989169\pi$
$467$	−6.84565	−	16.5269i	−0.316779	−	0.764772i	0.682642	−	0.730753i	$-0.260831\pi$
$468$	15.6059	−	32.4416i	0.721382	−	1.49961i
$469$	24.8121	+	4.93544i	1.14572	+	0.227897i
$470$	−31.4278	−	47.0350i	−1.44966	−	2.16956i
$471$	−3.37741	−	0.770110i	−0.155623	−	0.0354848i
$472$	−14.1421	+	14.1421i	−0.650945	+	0.650945i
$473$	−3.14278	+	4.70350i	−0.144505	+	0.216267i
$474$	8.89793	−	8.41587i	0.408695	−	0.386554i
$475$		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	$-0.239883\pi$
$479$	8.23113	+	5.49986i	0.376090	+	0.251295i	−0.353131	+	0.935574i	$0.614883\pi$
$480$	11.7264	+	30.7000i	0.535233	+	1.40126i
$481$	4.93544	+	24.8121i	0.225037	+	1.13134i
$482$	−47.0350	+	31.4278i	−2.14239	+	1.43150i
$483$	31.5913	+	22.4051i	1.43746	+	1.01947i
$484$	24.9447	−	10.3325i	1.13385	−	0.469657i
$485$	−33.0537	+	13.6913i	−1.50089	+	0.621690i
$486$	26.0157	+	23.1988i	1.18009	+	1.05232i
$487$	−23.6640	+	15.8118i	−1.07232	+	0.716501i	−0.960795	−	0.277260i	$-0.910574\pi$
$487$	−23.6640	+	15.8118i	−1.07232	+	0.716501i	−0.111525	+	0.993762i	$0.535574\pi$
$488$	−2.75899	−	13.8704i	−0.124894	−	0.627883i
$489$	15.3500	−	5.86319i	0.694152	−	0.265142i
$490$	15.7760	+	10.5412i	0.712688	+	0.476203i
$491$	−6.84565	+	16.5269i	−0.308940	+	0.745847i	0.690800	+	0.723046i	$0.257258\pi$
$491$	−6.84565	+	16.5269i	−0.308940	+	0.745847i	−0.999740	+	0.0228010i	$0.992742\pi$
$492$	26.8328	+	12.0000i	1.20972	+	0.541002i
$493$		0			0
$494$		0			0
$495$	11.3249	−	3.96821i	0.509016	−	0.178358i
$496$	1.75687	−	2.62934i	0.0788857	−	0.118061i
$497$	−28.4605	+	28.4605i	−1.27663	+	1.27663i
$498$	7.70110	−	33.7741i	0.345095	−	1.51346i
$499$	−1.75687	−	2.62934i	−0.0786482	−	0.117705i	0.790060	−	0.613029i	$-0.210049\pi$
$499$	−1.75687	−	2.62934i	−0.0786482	−	0.117705i	−0.868708	+	0.495324i	$0.835049\pi$
$500$	−16.6445	−	3.31079i	−0.744364	−	0.148063i
$501$	0.477214	−	17.1398i	0.0213203	−	0.765749i
$502$	−15.3073	−	36.9552i	−0.683200	−	1.64939i
$503$	−2.48309	+	12.4834i	−0.110716	+	0.556605i	0.885114	+	0.465374i	$0.154080\pi$
$503$	−2.48309	+	12.4834i	−0.110716	+	0.556605i	−0.995830	+	0.0912312i	$0.970920\pi$
$504$	−5.28974	+	20.5431i	−0.235624	+	0.915062i
$505$	12.4061	−	2.46772i	0.552062	−	0.109812i
$506$	15.8114	+	15.8114i	0.702902	+	0.702902i
$507$	−2.76546	−	4.39911i	−0.122819	−	0.195372i
$508$	−33.2597	−	13.7766i	−1.47566	−	0.611238i
$509$	−17.8885			−0.792896			−0.396448	−	0.918057i	$-0.629757\pi$
$509$	−17.8885			−0.792896			−0.396448	+	0.918057i	$0.629757\pi$
$510$		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
$516$	3.48595	+	20.4902i	0.153460	+	0.902031i
$517$	−2.46772	+	12.4061i	−0.108530	+	0.545618i
$518$	−17.1141	−	41.3171i	−0.751951	−	1.81537i
$519$	24.4854	+	0.681734i	1.07479	+	0.0299248i
$520$	−24.8121	−	4.93544i	−1.08808	−	0.216433i
$521$	−18.8567	−	28.2210i	−0.826126	−	1.23639i	−0.969102	−	0.246659i	$-0.920667\pi$
$521$	−18.8567	−	28.2210i	−0.826126	−	1.23639i	0.142976	−	0.989726i	$-0.454333\pi$
$522$	15.1651	+	11.4027i	0.663756	+	0.499082i
$523$	−16.9706	+	16.9706i	−0.742071	+	0.742071i	−0.972976	−	0.230905i	$-0.925831\pi$
$523$	−16.9706	+	16.9706i	−0.742071	+	0.742071i	0.230905	+	0.972976i	$0.425831\pi$
$524$	2.35708	−	3.52763i	0.102970	−	0.154105i
$525$	−11.2911	−	11.9378i	−0.492783	−	0.521009i
$526$		−	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
$531$	−26.7912	−	1.49302i	−1.16264	−	0.0647918i
$532$		0			0
$533$	18.8140	−	12.5711i	0.814925	−	0.544516i
$534$	30.0595	−	42.3842i	1.30080	−	1.83415i
$535$	−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
$540$	20.2117	−	39.1853i	0.869771	−	1.68627i
$541$	5.25868	+	3.51373i	0.226088	+	0.151067i	0.663456	−	0.748216i	$-0.269089\pi$
$541$	5.25868	+	3.51373i	0.226088	+	0.151067i	−0.437368	+	0.899283i	$0.644089\pi$
$542$		0			0
$543$	13.4164	−	30.0000i	0.575753	−	1.28742i
$544$		0			0
$545$		−	53.6656i		−	2.29878i
$546$	33.6635	+	35.5917i	1.44066	+	1.52318i
$547$	−1.75687	+	2.62934i	−0.0751182	+	0.112422i	−0.867126	−	0.498088i	$-0.834036\pi$
$547$	−1.75687	+	2.62934i	−0.0751182	+	0.112422i	0.792008	+	0.610510i	$0.209036\pi$
$548$	−9.48683	+	9.48683i	−0.405257	+	0.405257i
$549$	11.4027	−	15.1651i	0.486654	−	0.647229i
$550$	−5.27060	−	7.88801i	−0.224739	−	0.336346i
$551$		0			0
$552$	27.3755	+	0.762201i	1.16518	+	0.0324414i
$553$	3.82683	+	9.23880i	0.162734	+	0.392874i
$554$	2.75899	−	13.8704i	0.117218	−	0.589297i
$555$	5.19655	+	30.5450i	0.220581	+	1.29656i
$556$	9.30455	−	1.85079i	0.394601	−	0.0784909i
$557$	9.48683	+	9.48683i	0.401970	+	0.401970i	0.878927	−	0.476957i	$-0.158260\pi$
$557$	9.48683	+	9.48683i	0.401970	+	0.401970i	−0.476957	+	0.878927i	$0.658260\pi$
$558$	−21.0036	+	2.97442i	−0.889155	+	0.125917i
$559$	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	$-0.435355\pi$
$563$	−8.26343	−	3.42282i	−0.348262	−	0.144255i	−0.549956	+	0.835194i	$0.685355\pi$
$564$	24.7351	+	39.3469i	1.04153	+	1.65680i
$565$	−11.3137	−	11.3137i	−0.475971	−	0.475971i
$566$	6.93520	−	1.37950i	0.291508	−	0.0579846i
$567$	−25.2744	+	13.0846i	−1.06142	+	0.549500i
$568$	−5.55237	+	27.9136i	−0.232972	+	1.17123i
$569$	−6.84565	−	16.5269i	−0.286985	−	0.692842i	0.712981	−	0.701184i	$-0.247345\pi$
$569$	−6.84565	−	16.5269i	−0.286985	−	0.692842i	−0.999965	+	0.00834171i	$0.997345\pi$
$570$		0			0
$571$	−34.1167	−	6.78623i	−1.42774	−	0.283995i	−0.580090	−	0.814553i	$-0.696982\pi$
$571$	−34.1167	−	6.78623i	−1.42774	−	0.283995i	−0.847649	+	0.530558i	$0.821982\pi$
$572$	9.42834	+	14.1105i	0.394219	+	0.589990i
$573$	−3.44404	+	15.1043i	−0.143877	+	0.630989i
$574$	−28.2843	+	28.2843i	−1.18056	+	1.18056i
$575$	−11.7854	+	17.6381i	−0.491486	+	0.735561i
$576$	−12.8967	−	36.8059i	−0.537362	−	1.53358i
$577$			12.0000i			0.499567i	0.968302	+	0.249783i	$0.0803594\pi$
$577$			12.0000i			0.499567i	−0.968302	+	0.249783i	$0.919641\pi$
$578$		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
$582$	45.7649	−	17.4806i	1.89702	−	0.724596i
$583$		0			0
$584$		0			0
$585$	−17.2572	−	29.2265i	−0.713497	−	1.20837i
$586$	−36.9552	+	15.3073i	−1.52660	+	0.632340i
$587$	−16.5269	+	6.84565i	−0.682136	+	0.282550i	−0.696720	−	0.717343i	$-0.745358\pi$
$587$	−16.5269	+	6.84565i	−0.682136	+	0.282550i	0.0145832	+	0.999894i	$0.495358\pi$
$588$	−12.7153	−	9.01786i	−0.524369	−	0.371890i
$589$		0			0
$590$	11.0360	+	55.4816i	0.454344	+	2.28414i
$591$	−15.7326	−	41.1884i	−0.647152	−	1.69427i
$592$	5.25868	+	3.51373i	0.216130	+	0.144414i
$593$	−6.84565	+	16.5269i	−0.281117	+	0.678677i	−0.999862	−	0.0165969i	$-0.994717\pi$
$593$	−6.84565	+	16.5269i	−0.281117	+	0.678677i	0.718745	+	0.695274i	$0.244717\pi$
$594$	−15.6525	+	5.00000i	−0.642229	+	0.205152i
$595$		0			0
$596$		−	53.6656i		−	2.19823i
$597$	−11.9378	+	11.2911i	−0.488583	+	0.462113i
$598$	35.1373	−	52.5868i	1.43687	−	2.15043i
$599$	12.6491	−	12.6491i	0.516829	−	0.516829i	−0.399782	−	0.916610i	$-0.630914\pi$
$599$	12.6491	−	12.6491i	0.516829	−	0.516829i	0.916610	+	0.399782i	$0.130914\pi$
$600$	−11.3282	−	2.58303i	−0.462472	−	0.105452i
$601$	7.02747	+	10.5174i	0.286656	+	0.429012i	0.946652	−	0.322258i	$-0.104442\pi$
$601$	7.02747	+	10.5174i	0.286656	+	0.429012i	−0.659995	+	0.751270i	$0.729442\pi$
$602$	−27.7408	−	5.51799i	−1.13063	−	0.224896i
$603$	21.6277	+	10.4039i	0.880749	+	0.423681i
$604$	22.9610	+	55.4328i	0.934270	+	2.25553i
$605$	4.96619	−	24.9667i	0.201904	−	1.01504i
$606$	−17.0752	+	2.90496i	−0.693631	+	0.118006i
$607$	21.7106	−	4.31851i	0.881206	−	0.175283i	0.266307	−	0.963888i	$-0.414197\pi$
$607$	21.7106	−	4.31851i	0.881206	−	0.175283i	0.614900	+	0.788605i	$0.289197\pi$
$608$		0			0
$609$	−13.1156	+	8.24502i	−0.531472	+	0.334105i
$610$	−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
$615$	23.4619	−	14.7491i	0.946077	−	0.594743i
$616$	−7.07107	−	7.07107i	−0.284901	−	0.284901i
$617$	38.8371	−	7.72518i	1.56352	−	0.311004i	0.663951	−	0.747776i	$-0.268878\pi$
$617$	38.8371	−	7.72518i	1.56352	−	0.311004i	0.899572	+	0.436772i	$0.143878\pi$
$618$	−15.2725	+	2.59827i	−0.614350	+	0.104518i
$619$	0.616930	−	3.10152i	0.0247965	−	0.124660i	−0.966404	−	0.257026i	$-0.917257\pi$
$619$	0.616930	−	3.10152i	0.0247965	−	0.124660i	0.991201	+	0.132366i	$0.0422573\pi$
$620$	10.2685	+	24.7903i	0.412392	+	0.995602i
$621$	23.7232	+	28.0573i	0.951980	+	1.12590i
$622$	−3.10152	−	0.616930i	−0.124359	−	0.0247366i
$623$	23.5708	+	35.2763i	0.944346	+	1.41331i
$624$	−6.75483	−	1.54022i	−0.270410	−	0.0616582i
$625$	−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	$-0.875000\pi$
$631$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$632$	5.87938	+	3.92847i	0.233869	+	0.156266i
$633$	13.6808	+	35.8167i	0.543762	+	1.42359i
$634$	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
$639$	−32.8798	+	19.4143i	−1.30071	+	0.768020i
$640$	−36.8107	+	24.5961i	−1.45507	+	0.972248i
$641$	−4.41439	−	22.1926i	−0.174358	−	0.876556i	−0.964591	−	0.263750i	$-0.915041\pi$
$641$	−4.41439	−	22.1926i	−0.174358	−	0.876556i	0.790233	−	0.612806i	$-0.209959\pi$
$642$	15.3500	−	5.86319i	0.605817	−	0.231401i
$643$	−18.4054	−	12.2981i	−0.725837	−	0.484989i	0.136936	−	0.990580i	$-0.456274\pi$
$643$	−18.4054	−	12.2981i	−0.725837	−	0.484989i	−0.862773	+	0.505591i	$0.831274\pi$
$644$	−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	$0.823147\pi$
$648$	−9.71953	+	17.6219i	−0.381819	+	0.692253i
$649$	7.02747	−	10.5174i	0.275852	−	0.412842i
$650$	−18.9737	+	18.9737i	−0.744208	+	0.744208i
$651$	3.85055	−	16.8871i	0.150915	−	0.661857i
$652$	15.8118	+	23.6640i	0.619238	+	0.926755i
$653$	36.0630	+	7.17338i	1.41126	+	0.280716i	0.841126	−	0.540839i	$-0.181893\pi$
$653$	36.0630	+	7.17338i	1.41126	+	0.280716i	0.570129	+	0.821555i	$0.306893\pi$
$654$	−2.04520	+	73.4562i	−0.0799737	+	2.87237i
$655$	−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	$-0.194263\pi$
$659$	6.32456	+	6.32456i	0.246370	+	0.246370i	−0.573109	+	0.819479i	$0.694263\pi$
$660$	11.0619	+	17.5965i	0.430582	+	0.684941i
$661$	35.1074	+	14.5420i	1.36552	+	0.565617i	0.940570	−	0.339600i	$-0.110292\pi$
$661$	35.1074	+	14.5420i	1.36552	+	0.565617i	0.424950	+	0.905217i	$0.360292\pi$
$662$	−62.6099			−2.43340
$663$		0			0
$664$	20.0000			0.776151
$665$		0			0
$666$	−5.94884	−	42.0073i	−0.230513	−	1.62775i
$667$	14.1421	+	14.1421i	0.547586	+	0.547586i
$668$	29.1278	−	5.79389i	1.12699	−	0.224172i
$669$	4.64793	+	27.3203i	0.179700	+	1.05626i
$670$	9.87088	−	49.6242i	0.381345	−	1.91715i
$671$	3.42282	+	8.26343i	0.132137	+	0.319006i
$672$	36.7281	+	1.02260i	1.41682	+	0.0394477i
$673$	−24.8121	−	4.93544i	−0.956437	−	0.190247i	−0.307890	−	0.951422i	$-0.599623\pi$
$673$	−24.8121	−	4.93544i	−0.956437	−	0.190247i	−0.648547	+	0.761175i	$0.724623\pi$
$674$	31.4278	+	47.0350i	1.21055	+	1.81172i
$675$	−7.54922	−	13.6385i	−0.290569	−	0.524947i
$676$	6.36396	−	6.36396i	0.244768	−	0.244768i
$677$	7.85695	−	11.7588i	0.301967	−	0.451926i	−0.649193	−	0.760624i	$-0.724893\pi$
$677$	7.85695	−	11.7588i	0.301967	−	0.451926i	0.951160	+	0.308698i	$0.0998932\pi$
$678$	15.0548	+	15.9171i	0.578175	+	0.611292i
$679$			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	$-0.355695\pi$
$683$	−5.87938	−	3.92847i	−0.224968	−	0.150319i	−0.662947	+	0.748666i	$0.730695\pi$
$684$		0			0
$685$	2.46772	+	12.4061i	0.0942867	+	0.474011i
$686$	−23.5175	+	15.7139i	−0.897903	+	0.599959i
$687$	−20.0397	+	28.2562i	−0.764562	+	1.07804i
$688$	3.69552	−	1.53073i	0.140890	−	0.0583587i
$689$		0			0
$690$	44.8101	−	63.1827i	1.70589	−	2.40532i
$691$	−34.1814	+	22.8393i	−1.30032	+	0.868847i	−0.996476	−	0.0838745i	$-0.973271\pi$
$691$	−34.1814	+	22.8393i	−1.30032	+	0.868847i	−0.303845	+	0.952721i	$0.598271\pi$
$692$	8.27698	+	41.6112i	0.314644	+	1.58182i
$693$	0.746512	−	13.3956i	0.0283577	−	0.508858i
$694$	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
$699$	6.73270	+	7.11834i	0.254654	+	0.269240i
$700$	15.8118	−	23.6640i	0.597630	−	0.894417i
$701$	9.48683	−	9.48683i	0.358313	−	0.358313i	−0.504878	−	0.863191i	$-0.668463\pi$
$701$	9.48683	−	9.48683i	0.358313	−	0.358313i	0.863191	+	0.504878i	$0.168463\pi$
$702$	22.5074	+	40.6622i	0.849488	+	1.53470i
$703$		0			0
$704$	18.0315	+	3.58669i	0.679588	+	0.135179i
$705$	43.8008	+	1.21952i	1.64963	+	0.0459299i
$706$	−15.3073	−	36.9552i	−0.576099	−	1.39083i
$707$	2.75899	−	13.8704i	0.103763	−	0.521650i
$708$	−7.79482	−	45.8175i	−0.292947	−	1.72193i
$709$	6.20303	−	1.23386i	0.232960	−	0.0463386i	−0.0772298	−	0.997013i	$-0.524608\pi$
$709$	6.20303	−	1.23386i	0.232960	−	0.0463386i	0.310189	+	0.950675i	$0.399608\pi$
$710$	56.9210	+	56.9210i	2.13621	+	2.13621i
$711$	1.33020	+	9.39311i	0.0498864	+	0.352269i
$712$	27.7164	+	11.4805i	1.03872	+	0.430250i
$713$	−22.3607			−0.837414
$714$		0			0
$715$	16.0000			0.598366
$716$		0			0
$717$	−8.24502	−	13.1156i	−0.307916	−	0.489812i
$718$	−42.4264	−	42.4264i	−1.58334	−	1.58334i
$719$	−4.16112	+	0.827698i	−0.155184	+	0.0308679i	−0.272071	−	0.962277i	$-0.587708\pi$
$719$	−4.16112	+	0.827698i	−0.155184	+	0.0308679i	0.116887	+	0.993145i	$0.462708\pi$
$720$	−8.21724	−	2.11590i	−0.306238	−	0.0788548i
$721$	2.46772	−	12.4061i	0.0919027	−	0.462026i
$722$	−16.2584	−	39.2513i	−0.605076	−	1.46078i
$723$	1.21952	−	43.8008i	0.0453545	−	1.62897i
$724$	55.8273	+	11.1047i	2.07480	+	0.412704i
$725$	−4.71417	−	7.05525i	−0.175080	−	0.262026i
$726$	−7.74908	+	33.9846i	−0.287595	+	1.26129i
$727$	5.65685	−	5.65685i	0.209801	−	0.209801i	−0.594382	−	0.804183i	$-0.702603\pi$
$727$	5.65685	−	5.65685i	0.209801	−	0.209801i	0.804183	+	0.594382i	$0.202603\pi$
$728$	−15.7139	+	23.5175i	−0.582396	+	0.871617i
$729$	−26.3153	+	6.04197i	−0.974640	+	0.223777i
$730$		0			0
$731$		0			0
$732$	30.0000	+	13.4164i	1.10883	+	0.495885i
$733$	−13.0112	+	31.4119i	−0.480581	+	1.16023i	0.478752	+	0.877950i	$0.341089\pi$
$733$	−13.0112	+	31.4119i	−0.480581	+	1.16023i	−0.959333	+	0.282275i	$0.908911\pi$
$734$	29.3969	+	19.6424i	1.08506	+	0.725013i
$735$	−13.7295	+	5.24419i	−0.506419	+	0.193435i
$736$	−9.25395	−	46.5227i	−0.341105	−	1.71485i
$737$	−9.40700	+	6.28556i	−0.346511	+	0.231532i
$738$	−32.6762	+	19.2941i	−1.20283	+	0.710227i
$739$	22.1731	−	9.18440i	0.815651	−	0.337854i	0.0644448	−	0.997921i	$-0.479472\pi$
$739$	22.1731	−	9.18440i	0.815651	−	0.337854i	0.751206	+	0.660068i	$0.229472\pi$
$740$	−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	$-0.103903\pi$
$743$	−1.37950	−	6.93520i	−0.0506088	−	0.254428i	−0.997804	+	0.0662284i	$0.978903\pi$
$744$	−4.37016	−	11.4412i	−0.160218	−	0.419456i
$745$	−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
$750$	15.9171	−	15.0548i	0.581210	−	0.549722i
$751$	−19.3255	+	28.9227i	−0.705199	+	1.05540i	0.289952	+	0.957041i	$0.406361\pi$
$751$	−19.3255	+	28.9227i	−0.705199	+	1.05540i	−0.995151	+	0.0983636i	$0.968639\pi$
$752$	6.32456	−	6.32456i	0.230633	−	0.230633i
$753$	30.2085	+	6.88807i	1.10086	+	0.251015i
$754$	14.0549	+	21.0347i	0.511851	+	0.766039i
$755$	55.4816	+	11.0360i	2.01918	+	0.401640i
$756$	−31.8280	−	37.6428i	−1.15757	−	1.36905i
$757$	−4.59220	−	11.0866i	−0.166906	−	0.402948i	0.818191	−	0.574947i	$-0.194977\pi$
$757$	−4.59220	−	11.0866i	−0.166906	−	0.402948i	−0.985097	+	0.171999i	$0.944977\pi$
$758$	−4.13849	+	20.8056i	−0.150317	+	0.755693i
$759$	−17.0752	+	2.90496i	−0.619789	+	0.105443i
$760$		0			0
$761$	−3.16228	−	3.16228i	−0.114632	−	0.114632i	0.647464	−	0.762096i	$-0.275830\pi$
$761$	−3.16228	−	3.16228i	−0.114632	−	0.114632i	−0.762096	+	0.647464i	$0.775830\pi$
$762$	39.3469	−	24.7351i	1.42539	−	0.896057i
$763$	−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
$768$	13.1973	−	8.29639i	0.476218	−	0.299370i
$769$	−14.1421	−	14.1421i	−0.509978	−	0.509978i	0.404541	−	0.914520i	$-0.367431\pi$
$769$	−14.1421	−	14.1421i	−0.509978	−	0.509978i	−0.914520	+	0.404541i	$0.867431\pi$
$770$	−27.7408	+	5.51799i	−0.999709	+	0.198854i
$771$	38.1812	−	6.49569i	1.37506	−	0.233936i
$772$	−7.40316	+	37.2182i	−0.266445	+	1.33951i
$773$	−15.4027	−	37.1854i	−0.553997	−	1.33747i	−0.914453	−	0.404691i	$-0.867379\pi$
$773$	−15.4027	−	37.1854i	−0.553997	−	1.33747i	0.360456	−	0.932776i	$-0.382621\pi$
$774$	−24.1805	−	11.6319i	−0.869151	−	0.418101i
$775$	9.30455	+	1.85079i	0.334229	+	0.0664823i
$776$	15.7139	+	23.5175i	0.564096	+	0.844229i
$777$	33.7741	+	7.70110i	1.21164	+	0.276275i
$778$	−7.07107	+	7.07107i	−0.253510	+	0.253510i
$779$		0			0
$780$	42.7101	−	40.3962i	1.52927	−	1.44642i
$781$		−	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
$786$	1.95440	+	5.11667i	0.0697110	+	0.182506i
$787$	−6.78623	−	34.1167i	−0.241903	−	1.21613i	−0.890495	−	0.454992i	$-0.849642\pi$
$787$	−6.78623	−	34.1167i	−0.241903	−	1.21613i	0.648593	−	0.761136i	$-0.275358\pi$
$788$	63.4973	−	42.4275i	2.26200	−	1.51142i
$789$	25.2731	+	17.9240i	0.899745	+	0.638113i
$790$	18.4776	−	7.65367i	0.657403	−	0.272305i
$791$	−16.5269	+	6.84565i	−0.587627	+	0.243403i
$792$	−4.82353	−	8.16906i	−0.171397	−	0.290275i
$793$	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	$-0.772384\pi$
$797$	6.84565	−	16.5269i	0.242485	−	0.585411i	0.997528	+	0.0702638i	$0.0223841\pi$
$798$		0			0
$799$		0			0
$800$			20.1246i			0.711512i
$801$	13.3098	+	37.9849i	0.470278	+	1.34213i
$802$	7.02747	−	10.5174i	0.248149	−	0.371381i
$803$		0			0
$804$	−9.24132	+	40.5290i	−0.325916	+	1.42935i
$805$	35.1373	+	52.5868i	1.23843	+	1.85344i
$806$	−27.7408	−	5.51799i	−0.977128	−	0.194363i
$807$	−1.22712	+	44.0737i	−0.0431967	+	1.55147i
$808$	−3.82683	−	9.23880i	−0.134628	−	0.325020i
$809$	−3.31079	+	16.6445i	−0.116401	+	0.585189i	0.877923	+	0.478801i	$0.158928\pi$
$809$	−3.31079	+	16.6445i	−0.116401	+	0.585189i	−0.994325	+	0.106388i	$0.966072\pi$
$810$	26.1691	+	50.5488i	0.919489	+	1.77610i
$811$	−46.5227	+	9.25395i	−1.63363	+	0.324950i	−0.924808	−	0.380434i	$-0.875775\pi$
$811$	−46.5227	+	9.25395i	−1.63363	+	0.324950i	−0.708826	+	0.705384i	$0.750775\pi$
$812$	−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
$819$	−37.5725	+	5.32080i	−1.31289	+	0.185924i
$820$	33.9411	+	33.9411i	1.18528	+	1.18528i
$821$	19.4186	−	3.86259i	0.677712	−	0.134805i	0.155779	−	0.987792i	$-0.450211\pi$
$821$	19.4186	−	3.86259i	0.677712	−	0.134805i	0.521933	+	0.852987i	$0.325211\pi$
$822$	−2.90496	−	17.0752i	−0.101322	−	0.595565i
$823$	−6.78623	+	34.1167i	−0.236553	+	1.18923i	0.661705	+	0.749764i	$0.269833\pi$
$823$	−6.78623	+	34.1167i	−0.236553	+	1.18923i	−0.898258	+	0.439468i	$0.855167\pi$
$824$	−3.42282	−	8.26343i	−0.119240	−	0.287870i
$825$	7.34562	+	0.204520i	0.255742	+	0.00712048i
$826$	62.0303	+	12.3386i	2.15831	+	0.429315i
$827$	−21.2138	−	31.7486i	−0.737675	−	1.10401i	−0.990636	−	0.136532i	$-0.956404\pi$
$827$	−21.2138	−	31.7486i	−0.737675	−	1.10401i	0.252961	−	0.967477i	$-0.418596\pi$
$828$	−38.2457	+	50.8651i	−1.32913	+	1.76769i
$829$	21.2132	−	21.2132i	0.736765	−	0.736765i	−0.235185	−	0.971951i	$-0.575570\pi$
$829$	21.2132	−	21.2132i	0.736765	−	0.736765i	0.971951	+	0.235185i	$0.0755698\pi$
$830$	31.4278	−	47.0350i	1.09087	−	1.63261i
$831$	7.52738	+	7.95855i	0.261122	+	0.276079i
$832$		−	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
$837$	7.53244	−	14.6035i	0.260359	−	0.504771i
$838$	−4.31851	−	21.7106i	−0.149180	−	0.749980i
$839$	8.23113	−	5.49986i	0.284170	−	0.189876i	−0.405313	−	0.914178i	$-0.632838\pi$
$839$	8.23113	−	5.49986i	0.284170	−	0.189876i	0.689483	+	0.724301i	$0.257838\pi$
$840$	−20.0397	+	28.2562i	−0.691435	+	0.974930i
$841$	19.4015	−	8.03635i	0.669016	−	0.277116i
$842$	41.3171	−	17.1141i	1.42388	−	0.589792i
$843$	17.9240	−	25.2731i	0.617337	−	0.870451i
$844$	−55.2161	+	36.8942i	−1.90062	+	1.26995i
$845$	−1.65540	−	8.32224i	−0.0569474	−	0.286294i
$846$	−59.9070	−	3.33851i	−2.05965	−	0.114780i
$847$	−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
$852$	−45.4457	−	48.0488i	−1.55694	−	1.64613i
$853$	−3.51373	+	5.25868i	−0.120308	+	0.180054i	−0.886735	−	0.462277i	$-0.847032\pi$
$853$	−3.51373	+	5.25868i	−0.120308	+	0.180054i	0.766427	+	0.642331i	$0.222032\pi$
$854$	−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	$-0.375602\pi$
$857$	11.0963	+	2.20720i	0.379043	+	0.0753963i	−0.00189186	+	0.999998i	$0.500602\pi$
$858$	−21.9004	−	0.609761i	−0.747668	−	0.0208169i
$859$	7.65367	+	18.4776i	0.261140	+	0.630447i	0.999010	−	0.0444959i	$-0.0141681\pi$
$859$	7.65367	+	18.4776i	0.261140	+	0.630447i	−0.737870	+	0.674943i	$0.764168\pi$
$860$	−6.62159	+	33.2890i	−0.225794	+	1.13514i
$861$	−5.19655	−	30.5450i	−0.177098	−	1.04097i
$862$	−27.9136	+	5.55237i	−0.950742	+	0.189114i
$863$	−12.6491	−	12.6491i	−0.430581	−	0.430581i	0.458245	−	0.888826i	$-0.348478\pi$
$863$	−12.6491	−	12.6491i	−0.430581	−	0.430581i	−0.888826	+	0.458245i	$0.848478\pi$
$864$	33.5008	+	9.62804i	1.13972	+	0.327553i
$865$	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
$870$	16.4900	+	26.2313i	0.559065	+	0.889323i
$871$	22.6274	+	22.6274i	0.766701	+	0.766701i
$872$	−41.6112	+	8.27698i	−1.40913	+	0.280294i
$873$	−9.46257	+	36.7486i	−0.320260	+	1.24375i
$874$		0			0
$875$	6.84565	+	16.5269i	0.231425	+	0.558710i
$876$		0			0
$877$	31.0152	+	6.16930i	1.04731	+	0.208322i	0.688610	−	0.725132i	$-0.258221\pi$
$877$	31.0152	+	6.16930i	1.04731	+	0.208322i	0.358697	+	0.933454i	$0.383221\pi$
$878$	−27.4993	−	41.1556i	−0.928057	−	1.38894i
$879$	6.88807	−	30.2085i	0.232329	−	1.01891i
$880$	2.82843	−	2.82843i	0.0953463	−	0.0953463i
$881$	−3.14278	+	4.70350i	−0.105883	+	0.158465i	−0.880627	−	0.473810i	$-0.842879\pi$
$881$	−3.14278	+	4.70350i	−0.105883	+	0.158465i	0.774744	+	0.632275i	$0.217879\pi$
$882$	18.9924	−	6.65489i	0.639508	−	0.224082i
$883$		−	16.0000i		−	0.538443i	−0.963078	−	0.269221i	$-0.913234\pi$
$883$		−	16.0000i		−	0.538443i	0.963078	−	0.269221i	$-0.0867663\pi$
$884$		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	$-0.624720\pi$
$887$	−41.1556	−	27.4993i	−1.38187	−	0.923337i	−1.00000		0.000878410i	$0.999720\pi$
$888$	22.8825	−	8.74032i	0.767885	−	0.293306i
$889$	7.40316	+	37.2182i	0.248294	+	1.24826i
$890$	70.5525	−	47.1417i	2.36493	−	1.58019i
$891$	3.85476	−	12.1302i	0.129139	−	0.406376i
$892$	−44.3462	+	18.3688i	−1.48482	+	0.615033i
$893$		0			0
$894$	56.5123	+	40.0794i	1.89005	+	1.34046i
$895$		0			0
$896$	9.65648	+	48.5464i	0.322600	+	1.62182i
$897$	17.4806	+	45.7649i	0.583662	+	1.52805i
$898$	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
$903$	15.9171	−	15.0548i	0.529688	−	0.500991i
$904$	−7.02747	+	10.5174i	−0.233730	+	0.349802i
$905$	37.9473	−	37.9473i	1.26141	−	1.26141i
$906$	−75.5213	−	17.2202i	−2.50903	−	0.572102i
$907$	−12.2981	−	18.4054i	−0.408351	−	0.611140i	0.569109	−	0.822262i	$-0.307288\pi$
$907$	−12.2981	−	18.4054i	−0.408351	−	0.611140i	−0.977460	+	0.211122i	$0.932288\pi$
$908$	−20.8056	−	4.13849i	−0.690458	−	0.137341i
$909$	5.81597	−	12.0903i	0.192904	−	0.401009i
$910$	30.6147	+	73.9104i	1.01487	+	2.45010i
$911$	3.03489	−	15.2574i	0.100550	−	0.505501i	−0.897383	−	0.441252i	$-0.854535\pi$
$911$	3.03489	−	15.2574i	0.100550	−	0.505501i	0.997934	−	0.0642497i	$-0.0204654\pi$
$912$		0			0
$913$	−12.4061	+	2.46772i	−0.410581	+	0.0816696i
$914$	−44.2719	−	44.2719i	−1.46438	−	1.46438i
$915$	26.2313	−	16.4900i	0.867178	−	0.545144i
$916$	−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
$921$	−17.5965	+	11.0619i	−0.579823	+	0.364501i
$922$	56.5685	+	56.5685i	1.86299	+	1.86299i
$923$	−49.9334	+	9.93238i	−1.64358	+	0.326928i
$924$	22.9087	−	3.89741i	0.753642	−	0.128215i
$925$	−3.70158	+	18.6091i	−0.121707	+	0.611863i
$926$	3.42282	+	8.26343i	0.112481	+	0.271553i
$927$	5.20196	−	10.8139i	0.170855	−	0.355174i
$928$	18.6091	+	3.70158i	0.610873	+	0.121510i
$929$	21.9995	+	32.9245i	0.721779	+	1.08022i	0.993047	+	0.117715i	$0.0375568\pi$
$929$	21.9995	+	32.9245i	0.721779	+	1.08022i	−0.271269	+	0.962504i	$0.587443\pi$
$930$	−33.7741	−	7.70110i	−1.10750	−	0.252529i
$931$		0			0
$932$	−9.42834	+	14.1105i	−0.308836	+	0.462205i
$933$	1.77959	−	1.68317i	0.0582610	−	0.0551046i
$934$			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	−0.935888	−	0.352297i	$-0.885401\pi$
$937$	−0.765367	+	1.84776i	−0.0250034	+	0.0603637i	0.910885	+	0.412661i	$0.135401\pi$
$938$	−47.0350	−	31.4278i	−1.53575	−	1.02615i
$939$	−15.6352	−	40.9334i	−0.510234	−	1.33581i
$940$	14.8063	+	74.4364i	0.482929	+	2.42785i
$941$	30.5728	−	20.4281i	0.996644	−	0.665936i	0.0535853	−	0.998563i	$-0.482935\pi$
$941$	30.5728	−	20.4281i	0.996644	−	0.665936i	0.943058	+	0.332627i	$0.107935\pi$
$942$	6.31827	+	4.48101i	0.205860	+	0.145999i
$943$	−36.9552	+	15.3073i	−1.20343	+	0.498475i
$944$	−8.26343	+	3.42282i	−0.268952	+	0.111403i
$945$	−46.1802	+	5.23338i	−1.50224	+	0.170242i
$946$	10.5174	−	7.02747i	0.341949	−	0.228483i
$947$	−9.65648	−	48.5464i	−0.313793	−	1.57755i	−0.739801	−	0.672826i	$-0.765080\pi$
$947$	−9.65648	−	48.5464i	−0.313793	−	1.57755i	0.426007	−	0.904720i	$-0.359920\pi$
$948$	−15.3500	+	5.86319i	−0.498545	+	0.190427i
$949$		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
$957$	1.54022	−	6.75483i	0.0497882	−	0.218353i
$958$	−12.2981	−	18.4054i	−0.397333	−	0.594650i
$959$	13.8704	+	2.75899i	0.447899	+	0.0890926i
$960$	1.77251	−	63.6621i	0.0572074	−	2.05468i
$961$	−8.03635	−	19.4015i	−0.259237	−	0.625854i
$962$	11.0360	−	55.4816i	0.355814	−	1.78880i
$963$	−3.17384	+	12.3259i	−0.102276	+	0.397195i
$964$	74.4364	−	14.8063i	2.39743	−	0.476879i
$965$	25.2982	+	25.2982i	0.814379	+	0.814379i
$966$	−46.0911	−	73.3186i	−1.48296	−	2.35899i
$967$	−29.5641	−	12.2459i	−0.950719	−	0.393801i	−0.147218	−	0.989104i	$-0.547032\pi$
$967$	−29.5641	−	12.2459i	−0.950719	−	0.393801i	−0.803501	+	0.595303i	$0.797032\pi$
$968$	−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	$-0.516681\pi$
$971$	−24.7903	−	10.2685i	−0.795558	−	0.329531i	−0.743176	+	0.669096i	$0.766681\pi$
$972$	−20.3359	−	42.1123i	−0.652276	−	1.35075i
$973$	−7.07107	−	7.07107i	−0.226688	−	0.226688i
$974$	62.4168	−	12.4155i	1.99996	−	0.397817i
$975$	−3.48595	−	20.4902i	−0.111640	−	0.656211i
$976$	1.23386	−	6.20303i	0.0394949	−	0.198554i
$977$	−6.84565	−	16.5269i	−0.219012	−	0.528741i	0.775741	−	0.631052i	$-0.217376\pi$
$977$	−6.84565	−	16.5269i	−0.219012	−	0.528741i	−0.994753	+	0.102311i	$0.967376\pi$
$978$	−36.7281	−	1.02260i	−1.17444	−	0.0326992i
$979$	−18.6091	−	3.70158i	−0.594749	−	0.118303i
$980$	−14.1425	−	21.1658i	−0.451766	−	0.676115i
$981$	−45.4952	−	34.2080i	−1.45255	−	1.09218i
$982$	28.2843	−	28.2843i	0.902587	−	0.902587i
$983$	19.6424	−	29.3969i	0.626494	−	0.937615i	−0.373456	−	0.927648i	$-0.621827\pi$
$983$	19.6424	−	29.3969i	0.626494	−	0.937615i	0.999950	−	0.00996724i	$-0.00317272\pi$
$984$	−15.0548	−	15.9171i	−0.479928	−	0.507419i
$985$		−	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
$990$	−26.7912	−	1.49302i	−0.851482	−	0.0474514i
$991$	−6.78623	−	34.1167i	−0.215572	−	1.08375i	−0.925288	−	0.379265i	$-0.876177\pi$
$991$	−6.78623	−	34.1167i	−0.215572	−	1.08375i	0.709717	−	0.704487i	$-0.248823\pi$
$992$	−17.6381	+	11.7854i	−0.560011	+	0.374188i
$993$	28.0556	−	39.5586i	0.890317	−	1.25535i
$994$	83.1492	−	34.4415i	2.63733	−	1.09242i
$995$	−24.7903	+	10.2685i	−0.785905	+	0.325533i
$996$	−26.8861	+	37.9096i	−0.851918	+	1.20121i
$997$	−5.25868	+	3.51373i	−0.166544	+	0.111281i	−0.636049	−	0.771649i	$-0.719432\pi$
$997$	−5.25868	+	3.51373i	−0.166544	+	0.111281i	0.469505	+	0.882930i	$0.344432\pi$
$998$	1.37950	+	6.93520i	0.0436672	+	0.219530i
$999$	29.2070	+	15.0649i	0.924069	+	0.476632i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-2.06586 - 0.855706i) q^{2} +(1.46637 - 0.921821i) q^{3} +(2.12132 + 2.12132i) q^{4} +(2.77408 - 0.551799i) q^{5} +(-3.81812 + 0.649569i) q^{6} +(0.616930 - 3.10152i) q^{7} +(-0.855706 - 2.06586i) q^{8} +(1.30049 - 2.70347i) q^{9} +O(q^{10})\)	\(q+(-2.06586 - 0.855706i) q^{2} +(1.46637 - 0.921821i) q^{3} +(2.12132 + 2.12132i) q^{4} +(2.77408 - 0.551799i) q^{5} +(-3.81812 + 0.649569i) q^{6} +(0.616930 - 3.10152i) q^{7} +(-0.855706 - 2.06586i) q^{8} +(1.30049 - 2.70347i) q^{9} +(-6.20303 - 1.23386i) q^{10} +(0.785695 + 1.17588i) q^{11} +(5.06612 + 1.15517i) q^{12} +(2.82843 - 2.82843i) q^{13} +(-3.92847 + 5.87938i) q^{14} +(3.55917 - 3.36635i) q^{15} -1.00000i q^{16} +(-5.00000 + 4.47214i) q^{18} +(7.05525 + 4.71417i) q^{20} +(-1.95440 - 5.11667i) q^{21} +(-0.616930 - 3.10152i) q^{22} +(-5.87938 + 3.92847i) q^{23} +(-3.15913 - 2.24051i) q^{24} +(2.77164 - 1.14805i) q^{25} +(-8.26343 + 3.42282i) q^{26} +(-0.585110 - 5.16310i) q^{27} +(7.88801 - 5.27060i) q^{28} +(-0.551799 - 2.77408i) q^{29} +(-10.2333 + 3.90879i) q^{30} +(2.62934 + 1.75687i) q^{31} +(-2.56712 + 6.19757i) q^{32} +(2.23607 + 1.00000i) q^{33} -8.94427i q^{35} +(8.49367 - 2.97616i) q^{36} +(-3.51373 + 5.25868i) q^{37} +(1.54022 - 6.75483i) q^{39} +(-3.51373 - 5.25868i) q^{40} +(5.54816 + 1.10360i) q^{41} +(-0.340867 + 12.2427i) q^{42} +(1.53073 + 3.69552i) q^{43} +(-0.827698 + 4.16112i) q^{44} +(2.11590 - 8.21724i) q^{45} +(15.5076 - 3.08465i) q^{46} +(6.32456 + 6.32456i) q^{47} +(-0.921821 - 1.46637i) q^{48} +(-2.77164 - 1.14805i) q^{49} -6.70820 q^{50} +12.0000 q^{52} +(-3.20935 + 11.1669i) 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} +(14.6912 + 0.409040i) q^{60} +(6.20303 + 1.23386i) q^{61} +(-3.92847 - 5.87938i) q^{62} +(-7.58253 - 5.70134i) q^{63} +(9.19239 - 9.19239i) q^{64} +(6.28556 - 9.40700i) q^{65} +(-3.76369 - 3.97927i) q^{66} +8.00000i q^{67} +(-5.00000 + 11.1803i) q^{69} +(-7.65367 + 18.4776i) q^{70} +(-10.5829 - 7.07125i) q^{71} +(-6.69781 - 0.373256i) q^{72} +(11.7588 - 7.85695i) q^{74} +(3.00595 - 4.23842i) q^{75} +(4.13171 - 1.71141i) q^{77} +(-8.96202 + 12.6365i) q^{78} +(-2.62934 + 1.75687i) q^{79} +(-0.551799 - 2.77408i) q^{80} +(-5.61745 - 7.03166i) q^{81} +(-10.5174 - 7.02747i) q^{82} +(-3.42282 + 8.26343i) q^{83} +(6.70820 - 15.0000i) q^{84} -8.94427i q^{86} +(-3.36635 - 3.55917i) q^{87} +(1.75687 - 2.62934i) q^{88} +(-9.48683 + 9.48683i) q^{89} +(-11.4027 + 15.1651i) q^{90} +(-7.02747 - 10.5174i) q^{91} +(-20.8056 - 4.13849i) q^{92} +(5.47510 + 0.152440i) q^{93} +(-7.65367 - 18.4776i) q^{94} +(1.94871 + 11.4544i) q^{96} +(-12.4061 + 2.46772i) q^{97} +(4.74342 + 4.74342i) q^{98} +(4.20073 - 0.594884i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more