LMFDB - Embedded newform 867.2.i.e.827.4

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			827.4
Character	$\chi$	$=$	867.827
Dual form			867.2.i.e.65.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.855706 - 2.06586i) q^{2} +(0.385055 - 1.68871i) q^{3} +(-2.12132 - 2.12132i) q^{4} +(-1.57139 + 2.35175i) q^{5} +(-3.15913 - 2.24051i) q^{6} +(-2.62934 + 1.75687i) q^{7} +(-2.06586 + 0.855706i) q^{8} +(-2.70347 - 1.30049i) q^{9} +O(q^{10})$	\(q+(0.855706 - 2.06586i) q^{2} +(0.385055 - 1.68871i) q^{3} +(-2.12132 - 2.12132i) q^{4} +(-1.57139 + 2.35175i) q^{5} +(-3.15913 - 2.24051i) q^{6} +(-2.62934 + 1.75687i) q^{7} +(-2.06586 + 0.855706i) q^{8} +(-2.70347 - 1.30049i) q^{9} +(3.51373 + 5.25868i) q^{10} +(-0.275899 + 1.38704i) q^{11} +(-4.39911 + 2.76546i) q^{12} +(-2.82843 + 2.82843i) q^{13} +(1.37950 + 6.93520i) q^{14} +(3.36635 + 3.55917i) q^{15} -1.00000i q^{16} +(-5.00000 + 4.47214i) q^{18} +(8.32224 - 1.65540i) q^{20} +(1.95440 + 5.11667i) q^{21} +(2.62934 + 1.75687i) q^{22} +(-6.93520 - 1.37950i) q^{23} +(0.649569 + 3.81812i) q^{24} +(-1.14805 - 2.77164i) q^{25} +(3.42282 + 8.26343i) q^{26} +(-3.23713 + 4.06460i) q^{27} +(9.30455 + 1.85079i) q^{28} +(2.35175 + 1.57139i) q^{29} +(10.2333 - 3.90879i) q^{30} +(3.10152 - 0.616930i) q^{31} +(-6.19757 - 2.56712i) q^{32} +(2.23607 + 1.00000i) q^{33} -8.94427i q^{35} +(2.97616 + 8.49367i) q^{36} +(1.23386 + 6.20303i) q^{37} +(3.68729 + 5.86549i) q^{39} +(1.23386 - 6.20303i) q^{40} +(-3.14278 - 4.70350i) q^{41} +(12.2427 + 0.340867i) q^{42} +(3.69552 - 1.53073i) q^{43} +(3.52763 - 2.35708i) q^{44} +(7.30663 - 4.31430i) q^{45} +(-8.78434 + 13.1467i) q^{46} +(-6.32456 - 6.32456i) q^{47} +(-1.68871 - 0.385055i) q^{48} +(1.14805 - 2.77164i) q^{49} -6.70820 q^{50} +12.0000 q^{52} +(5.62685 + 10.1656i) q^{54} +(-2.82843 - 2.82843i) q^{55} +(3.92847 - 5.87938i) q^{56} +(5.25868 - 3.51373i) q^{58} +(-8.26343 + 3.42282i) q^{59} +(0.409040 - 14.6912i) q^{60} +(-3.51373 - 5.25868i) q^{61} +(1.37950 - 6.93520i) q^{62} +(9.39311 - 1.33020i) q^{63} +(-9.19239 + 9.19239i) q^{64} +(-2.20720 - 11.0963i) q^{65} +(3.97927 - 3.76369i) q^{66} +8.00000i q^{67} +(-5.00000 + 11.1803i) q^{69} +(-18.4776 - 7.65367i) q^{70} +(-12.4834 + 2.48309i) q^{71} +(6.69781 + 0.373256i) q^{72} +(13.8704 + 2.75899i) q^{74} +(-5.12255 + 0.871488i) q^{75} +(-1.71141 - 4.13171i) q^{77} +(15.2725 - 2.59827i) q^{78} +(-3.10152 - 0.616930i) q^{79} +(2.35175 + 1.57139i) q^{80} +(5.61745 + 7.03166i) q^{81} +(-12.4061 + 2.46772i) q^{82} +(-8.26343 - 3.42282i) q^{83} +(6.70820 - 15.0000i) q^{84} -8.94427i q^{86} +(3.55917 - 3.36635i) q^{87} +(-0.616930 - 3.10152i) q^{88} +(9.48683 - 9.48683i) q^{89} +(-2.66040 - 18.7862i) q^{90} +(2.46772 - 12.4061i) q^{91} +(11.7854 + 17.6381i) q^{92} +(0.152440 - 5.47510i) q^{93} +(-18.4776 + 7.65367i) q^{94} +(-6.72152 + 9.47740i) q^{96} +(7.02747 - 10.5174i) q^{97} +(-4.74342 - 4.74342i) q^{98} +(2.54972 - 3.39101i) 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 $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{7}{16}\right)$

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 $

$2$	0.855706	−	2.06586i	0.605076	−	1.46078i	−0.263221	−	0.964736i	$-0.584785\pi$
$2$	0.855706	−	2.06586i	0.605076	−	1.46078i	0.868296	−	0.496046i	$-0.165215\pi$
$3$	0.385055	−	1.68871i	0.222312	−	0.974976i
$3$	0.385055	−	1.68871i	0.222312	−	0.974976i
$4$	−2.12132	−	2.12132i	−1.06066	−	1.06066i
$5$	−1.57139	+	2.35175i	−0.702747	+	1.05174i	0.292680	+	0.956210i	$0.405453\pi$
$5$	−1.57139	+	2.35175i	−0.702747	+	1.05174i	−0.995427	+	0.0955247i	$0.969547\pi$
$6$	−3.15913	−	2.24051i	−1.28971	−	0.914683i
$7$	−2.62934	+	1.75687i	−0.993796	+	0.664033i	−0.942345	−	0.334642i	$-0.891385\pi$
$7$	−2.62934	+	1.75687i	−0.993796	+	0.664033i	−0.0514510	+	0.998676i	$0.516385\pi$
$8$	−2.06586	+	0.855706i	−0.730391	+	0.302538i
$9$	−2.70347	−	1.30049i	−0.901155	−	0.433497i
$10$	3.51373	+	5.25868i	1.11114	+	1.66294i
$11$	−0.275899	+	1.38704i	−0.0831868	+	0.418208i	0.916642	+	0.399709i	$0.130889\pi$
$11$	−0.275899	+	1.38704i	−0.0831868	+	0.418208i	−0.999829	+	0.0184992i	$0.994111\pi$
$12$	−4.39911	+	2.76546i	−1.26991	+	0.798321i
$13$	−2.82843	+	2.82843i	−0.784465	+	0.784465i	−0.980581	−	0.196116i	$-0.937167\pi$
$13$	−2.82843	+	2.82843i	−0.784465	+	0.784465i	0.196116	+	0.980581i	$0.437167\pi$
$14$	1.37950	+	6.93520i	0.368686	+	1.85351i
$15$	3.36635	+	3.55917i	0.869187	+	0.918974i
$16$		−	1.00000i		−	0.250000i
$17$		0			0
$17$		0			0
$18$	−5.00000	+	4.47214i	−1.17851	+	1.05409i
$19$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$19$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$20$	8.32224	−	1.65540i	1.86091	−	0.370158i
$21$	1.95440	+	5.11667i	0.426484	+	1.11655i
$22$	2.62934	+	1.75687i	0.560577	+	0.374565i
$23$	−6.93520	−	1.37950i	−1.44609	−	0.287645i	−0.591229	−	0.806504i	$-0.701357\pi$
$23$	−6.93520	−	1.37950i	−1.44609	−	0.287645i	−0.854860	+	0.518859i	$0.826357\pi$
$24$	0.649569	+	3.81812i	0.132593	+	0.779371i
$25$	−1.14805	−	2.77164i	−0.229610	−	0.554328i
$26$	3.42282	+	8.26343i	0.671271	+	1.62059i
$27$	−3.23713	+	4.06460i	−0.622986	+	0.782233i
$28$	9.30455	+	1.85079i	1.75839	+	0.349766i
$29$	2.35175	+	1.57139i	0.436709	+	0.291800i	0.754425	−	0.656386i	$-0.227916\pi$
$29$	2.35175	+	1.57139i	0.436709	+	0.291800i	−0.317716	+	0.948186i	$0.602916\pi$
$30$	10.2333	−	3.90879i	1.86834	−	0.713644i
$31$	3.10152	−	0.616930i	0.557049	−	0.110804i	0.0914659	−	0.995808i	$-0.470845\pi$
$31$	3.10152	−	0.616930i	0.557049	−	0.110804i	0.465583	+	0.885004i	$0.345845\pi$
$32$	−6.19757	−	2.56712i	−1.09559	−	0.453807i
$33$	2.23607	+	1.00000i	0.389249	+	0.174078i
$34$		0			0
$35$		−	8.94427i		−	1.51186i
$36$	2.97616	+	8.49367i	0.496026	+	1.41561i
$37$	1.23386	+	6.20303i	0.202845	+	1.01977i	0.939251	+	0.343232i	$0.111522\pi$
$37$	1.23386	+	6.20303i	0.202845	+	1.01977i	−0.736406	+	0.676540i	$0.763478\pi$
$38$		0			0
$39$	3.68729	+	5.86549i	0.590438	+	0.939229i
$40$	1.23386	−	6.20303i	0.195090	−	0.980785i
$41$	−3.14278	−	4.70350i	−0.490820	−	0.734564i	0.500543	−	0.865712i	$-0.333134\pi$
$41$	−3.14278	−	4.70350i	−0.490820	−	0.734564i	−0.991363	+	0.131148i	$0.958134\pi$
$42$	12.2427	+	0.340867i	1.88909	+	0.0525969i
$43$	3.69552	−	1.53073i	0.563561	−	0.233435i	−0.0826692	−	0.996577i	$-0.526344\pi$
$43$	3.69552	−	1.53073i	0.563561	−	0.233435i	0.646230	+	0.763142i	$0.276344\pi$
$44$	3.52763	−	2.35708i	0.531810	−	0.355344i
$45$	7.30663	−	4.31430i	1.08921	−	0.643138i
$46$	−8.78434	+	13.1467i	−1.29518	+	1.93837i
$47$	−6.32456	−	6.32456i	−0.922531	−	0.922531i	0.0746766	−	0.997208i	$-0.476208\pi$
$47$	−6.32456	−	6.32456i	−0.922531	−	0.922531i	−0.997208	+	0.0746766i	$0.976208\pi$
$48$	−1.68871	−	0.385055i	−0.243744	−	0.0555779i
$49$	1.14805	−	2.77164i	0.164007	−	0.395948i
$50$	−6.70820			−0.948683
$51$		0			0
$52$	12.0000			1.66410
$53$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$53$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$54$	5.62685	+	10.1656i	0.765718	+	1.38336i
$55$	−2.82843	−	2.82843i	−0.381385	−	0.381385i
$56$	3.92847	−	5.87938i	0.524965	−	0.785665i
$57$		0			0
$58$	5.25868	−	3.51373i	0.690498	−	0.461376i
$59$	−8.26343	+	3.42282i	−1.07581	+	0.445614i	−0.849036	−	0.528334i	$-0.822817\pi$
$59$	−8.26343	+	3.42282i	−1.07581	+	0.445614i	−0.226771	+	0.973948i	$0.572817\pi$
$60$	0.409040	−	14.6912i	0.0528069	−	1.89663i
$61$	−3.51373	−	5.25868i	−0.449888	−	0.673304i	0.535324	−	0.844647i	$-0.320190\pi$
$61$	−3.51373	−	5.25868i	−0.449888	−	0.673304i	−0.985212	+	0.171342i	$0.945190\pi$
$62$	1.37950	−	6.93520i	0.175196	−	0.880771i
$63$	9.39311	−	1.33020i	1.18342	−	0.167590i
$64$	−9.19239	+	9.19239i	−1.14905	+	1.14905i
$65$	−2.20720	−	11.0963i	−0.273769	−	1.37633i
$66$	3.97927	−	3.76369i	0.489815	−	0.463278i
$67$			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
$70$	−18.4776	−	7.65367i	−2.20849	−	0.914788i
$71$	−12.4834	+	2.48309i	−1.48150	+	0.294689i	−0.868617	−	0.495483i	$-0.834991\pi$
$71$	−12.4834	+	2.48309i	−1.48150	+	0.294689i	−0.612885	+	0.790172i	$0.709991\pi$
$72$	6.69781	+	0.373256i	0.789345	+	0.0439887i
$73$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$73$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$74$	13.8704	+	2.75899i	1.61240	+	0.320727i
$75$	−5.12255	+	0.871488i	−0.591501	+	0.100631i
$76$		0			0
$77$	−1.71141	−	4.13171i	−0.195034	−	0.470853i
$78$	15.2725	−	2.59827i	1.72927	−	0.294197i
$79$	−3.10152	−	0.616930i	−0.348948	−	0.0694100i	0.0175048	−	0.999847i	$-0.494428\pi$
$79$	−3.10152	−	0.616930i	−0.348948	−	0.0694100i	−0.366453	+	0.930437i	$0.619428\pi$
$80$	2.35175	+	1.57139i	0.262934	+	0.175687i
$81$	5.61745	+	7.03166i	0.624161	+	0.781296i
$82$	−12.4061	+	2.46772i	−1.37002	+	0.272514i
$83$	−8.26343	−	3.42282i	−0.907029	−	0.375704i	−0.120111	−	0.992761i	$-0.538325\pi$
$83$	−8.26343	−	3.42282i	−0.907029	−	0.375704i	−0.786919	+	0.617057i	$0.788325\pi$
$84$	6.70820	−	15.0000i	0.731925	−	1.63663i
$85$		0			0
$86$		−	8.94427i		−	0.964486i
$87$	3.55917	−	3.36635i	0.381583	−	0.360910i
$88$	−0.616930	−	3.10152i	−0.0657649	−	0.330623i
$89$	9.48683	−	9.48683i	1.00560	−	1.00560i	0.00561807	−	0.999984i	$-0.498212\pi$
$89$	9.48683	−	9.48683i	1.00560	−	1.00560i	0.999984	−	0.00561807i	$-0.00178830\pi$
$90$	−2.66040	−	18.7862i	−0.280431	−	1.98024i
$91$	2.46772	−	12.4061i	0.258687	−	1.30051i
$92$	11.7854	+	17.6381i	1.22872	+	1.83890i
$93$	0.152440	−	5.47510i	0.0158073	−	0.567742i
$94$	−18.4776	+	7.65367i	−1.90582	+	0.789416i
$95$		0			0
$96$	−6.72152	+	9.47740i	−0.686012	+	0.967284i
$97$	7.02747	−	10.5174i	0.713531	−	1.06788i	−0.280614	−	0.959821i	$-0.590538\pi$
$97$	7.02747	−	10.5174i	0.713531	−	1.06788i	0.994145	−	0.108054i	$-0.0344621\pi$
$98$	−4.74342	−	4.74342i	−0.479157	−	0.479157i
$99$	2.54972	−	3.39101i	0.256256	−	0.340809i
$100$	−3.44415	+	8.31492i	−0.344415	+	0.831492i
$101$	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	$0.436859\pi$
$104$	3.42282	−	8.26343i	0.335636	−	0.810296i
$105$	−15.1043	−	3.44404i	−1.47402	−	0.336104i
$106$		0			0
$107$	2.35708	−	3.52763i	0.227868	−	0.341029i	−0.699864	−	0.714276i	$-0.746756\pi$
$107$	2.35708	−	3.52763i	0.227868	−	0.341029i	0.927732	+	0.373248i	$0.121756\pi$
$108$	15.4893	−	1.75533i	1.49046	−	0.168907i
$109$	−15.7760	+	10.5412i	−1.51107	+	1.00966i	−0.523580	+	0.851976i	$0.675404\pi$
$109$	−15.7760	+	10.5412i	−1.51107	+	1.00966i	−0.987489	+	0.157688i	$0.949596\pi$
$110$	−8.26343	+	3.42282i	−0.787887	+	0.326354i
$111$	10.9502	+	0.304881i	1.03935	+	0.0289380i
$112$	1.75687	+	2.62934i	0.166008	+	0.248449i
$113$	1.10360	−	5.54816i	0.103818	−	0.521927i	−0.893521	−	0.449021i	$-0.851773\pi$
$113$	1.10360	−	5.54816i	0.103818	−	0.521927i	0.997339	−	0.0729058i	$-0.0232272\pi$
$114$		0			0
$115$	14.1421	−	14.1421i	1.31876	−	1.31876i
$116$	−1.65540	−	8.32224i	−0.153700	−	0.772700i
$117$	11.3249	−	3.96821i	1.04699	−	0.366861i
$118$			20.0000i			1.84115i
$119$		0			0
$120$	−10.0000	−	4.47214i	−0.912871	−	0.408248i
$121$	8.31492	+	3.44415i	0.755901	+	0.313105i
$122$	−13.8704	+	2.75899i	−1.25577	+	0.249788i
$123$	−9.15298	+	3.49613i	−0.825297	+	0.315235i
$124$	−7.88801	−	5.27060i	−0.708365	−	0.473314i
$125$	−5.54816	−	1.10360i	−0.496242	−	0.0987088i
$126$	5.28974	−	20.5431i	0.471247	−	1.83012i
$127$	4.59220	+	11.0866i	0.407492	+	0.983773i	0.985795	+	0.167951i	$0.0537150\pi$
$127$	4.59220	+	11.0866i	0.407492	+	0.983773i	−0.578303	+	0.815822i	$0.696285\pi$
$128$	5.98994	+	14.4610i	0.529441	+	1.27818i
$129$	−1.16198	−	6.83007i	−0.102307	−	0.601354i
$130$	−24.8121	−	4.93544i	−2.17617	−	0.432867i
$131$	1.17588	+	0.785695i	0.102737	+	0.0686465i	0.605877	−	0.795558i	$-0.292822\pi$
$131$	1.17588	+	0.785695i	0.102737	+	0.0686465i	−0.503141	+	0.864205i	$0.667822\pi$
$132$	−2.62210	−	6.86474i	−0.228224	−	0.597499i
$133$		0			0
$134$	16.5269	+	6.84565i	1.42770	+	0.591374i
$135$	−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	$0.938814\pi$
$138$	18.8185	+	19.8964i	1.60193	+	1.69369i
$139$	−0.616930	−	3.10152i	−0.0523273	−	0.263067i	0.945762	−	0.324862i	$-0.105318\pi$
$139$	−0.616930	−	3.10152i	−0.0523273	−	0.263067i	−0.998089	+	0.0617944i	$0.980318\pi$
$140$	−18.9737	+	18.9737i	−1.60357	+	1.60357i
$141$	−13.1156	+	8.24502i	−1.10453	+	0.694356i
$142$	−5.55237	+	27.9136i	−0.465944	+	2.34246i
$143$	−3.14278	−	4.70350i	−0.262812	−	0.393327i
$144$	−1.30049	+	2.70347i	−0.108374	+	0.225289i
$145$	−7.39104	+	3.06147i	−0.613792	+	0.254241i
$146$		0			0
$147$	−4.23842	−	3.00595i	−0.349579	−	0.247927i
$148$	10.5412	−	15.7760i	0.866482	−	1.29678i
$149$	12.6491	+	12.6491i	1.03626	+	1.03626i	0.999318	+	0.0369380i	$0.0117604\pi$
$149$	12.6491	+	12.6491i	1.03626	+	1.03626i	0.0369380	+	0.999318i	$0.488240\pi$
$150$	−2.58303	+	11.3282i	−0.210903	+	0.924943i
$151$	−7.65367	+	18.4776i	−0.622847	+	1.50369i	0.225500	+	0.974243i	$0.427599\pi$
$151$	−7.65367	+	18.4776i	−0.622847	+	1.50369i	−0.848346	+	0.529442i	$0.822401\pi$
$152$		0			0
$153$		0			0
$154$	−10.0000			−0.805823
$155$	−3.42282	+	8.26343i	−0.274928	+	0.663735i
$156$	4.62066	−	20.2645i	0.369949	−	1.62246i
$157$	1.41421	+	1.41421i	0.112867	+	0.112867i	0.761285	−	0.648418i	$-0.224569\pi$
$157$	1.41421	+	1.41421i	0.112867	+	0.112867i	−0.648418	+	0.761285i	$0.724569\pi$
$158$	−3.92847	+	5.87938i	−0.312533	+	0.467738i
$159$		0			0
$160$	15.7760	−	10.5412i	1.24720	−	0.833355i
$161$	20.6586	−	8.55706i	1.62812	−	0.674391i
$162$	19.3333	−	5.58781i	1.51897	−	0.439020i
$163$	−5.27060	−	7.88801i	−0.412825	−	0.617837i	0.565540	−	0.824721i	$-0.308668\pi$
$163$	−5.27060	−	7.88801i	−0.412825	−	0.617837i	−0.978365	+	0.206884i	$0.933668\pi$
$164$	−3.31079	+	16.6445i	−0.258529	+	1.29972i
$165$	−5.86549	+	3.68729i	−0.456627	+	0.287055i
$166$	−14.1421	+	14.1421i	−1.09764	+	1.09764i
$167$	−1.93130	−	9.70928i	−0.149448	−	0.751327i	−0.980714	−	0.195451i	$-0.937383\pi$
$167$	−1.93130	−	9.70928i	−0.149448	−	0.751327i	0.831265	−	0.555876i	$-0.187617\pi$
$168$	−8.41587	−	8.89793i	−0.649298	−	0.686490i
$169$		−	3.00000i		−	0.230769i
$170$		0			0
$171$		0			0
$172$	−11.0866	−	4.59220i	−0.845342	−	0.350152i
$173$	13.8704	−	2.75899i	1.05455	−	0.209762i	0.362774	−	0.931877i	$-0.381830\pi$
$173$	13.8704	−	2.75899i	1.05455	−	0.209762i	0.691773	+	0.722115i	$0.256830\pi$
$174$	−3.90879	−	10.2333i	−0.296325	−	0.775788i
$175$	7.88801	+	5.27060i	0.596278	+	0.398420i
$176$	1.38704	+	0.275899i	0.104552	+	0.0207967i
$177$	2.59827	+	15.2725i	0.195298	+	1.14795i
$178$	−11.4805	−	27.7164i	−0.860500	−	2.07743i
$179$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$179$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$180$	−24.6517	−	6.34769i	−1.83743	−	0.473129i
$181$	18.6091	+	3.70158i	1.38320	+	0.275136i	0.829932	−	0.557865i	$-0.188379\pi$
$181$	18.6091	+	3.70158i	1.38320	+	0.275136i	0.553271	+	0.833001i	$0.313379\pi$
$182$	−23.5175	−	15.7139i	−1.74323	−	1.16479i
$183$	−10.2333	+	3.90879i	−0.756471	+	0.288946i
$184$	15.5076	−	3.08465i	1.14323	−	0.227403i
$185$	−16.5269	−	6.84565i	−1.21508	−	0.503302i
$186$	−11.1803	−	5.00000i	−0.819782	−	0.366618i
$187$		0			0
$188$			26.8328i			1.95698i
$189$	1.37055	−	16.3744i	0.0996925	−	1.19106i
$190$		0			0
$191$	6.32456	−	6.32456i	0.457629	−	0.457629i	−0.440248	−	0.897876i	$-0.645109\pi$
$191$	6.32456	−	6.32456i	0.457629	−	0.457629i	0.897876	+	0.440248i	$0.145109\pi$
$192$	11.9837	+	19.0628i	0.864847	+	1.37574i
$193$	−2.46772	+	12.4061i	−0.177630	+	0.893008i	0.784440	+	0.620205i	$0.212951\pi$
$193$	−2.46772	+	12.4061i	−0.177630	+	0.893008i	−0.962070	+	0.272803i	$0.912049\pi$
$194$	−15.7139	−	23.5175i	−1.12819	−	1.68846i
$195$	−19.5883	−	0.545387i	−1.40275	−	0.0390560i
$196$	−8.31492	+	3.44415i	−0.593923	+	0.246011i
$197$	−21.1658	+	14.1425i	−1.50800	+	1.00761i	−0.519824	+	0.854273i	$0.674003\pi$
$197$	−21.1658	+	14.1425i	−1.50800	+	1.00761i	−0.988174	+	0.153339i	$0.950997\pi$
$198$	−4.82353	−	8.16906i	−0.342794	−	0.580550i
$199$	5.27060	−	7.88801i	0.373623	−	0.559166i	−0.596243	−	0.802804i	$-0.703341\pi$
$199$	5.27060	−	7.88801i	0.373623	−	0.559166i	0.969866	+	0.243637i	$0.0783407\pi$
$200$	4.74342	+	4.74342i	0.335410	+	0.335410i
$201$	13.5097	+	3.08044i	0.952898	+	0.217278i
$202$	3.82683	−	9.23880i	0.269255	−	0.650039i
$203$	−8.94427			−0.627765
$204$		0			0
$205$	16.0000			1.11749
$206$	3.42282	−	8.26343i	0.238479	−	0.575740i
$207$	16.9550	+	12.7486i	1.17846	+	0.886088i
$208$	2.82843	+	2.82843i	0.196116	+	0.196116i
$209$		0			0
$210$	−20.0397	+	28.2562i	−1.38287	+	1.94986i
$211$	18.4054	−	12.2981i	1.26708	−	0.846634i	0.273732	−	0.961806i	$-0.411742\pi$
$211$	18.4054	−	12.2981i	1.26708	−	0.846634i	0.993346	+	0.115172i	$0.0367419\pi$
$212$		0			0
$213$	−0.613560	+	22.0369i	−0.0420405	+	1.50994i
$214$	−5.27060	−	7.88801i	−0.360291	−	0.539213i
$215$	−2.20720	+	11.0963i	−0.150529	+	0.756763i
$216$	3.20935	−	11.1669i	0.218368	−	0.759813i
$217$	−7.07107	+	7.07107i	−0.480015	+	0.480015i
$218$	8.27698	+	41.6112i	0.560588	+	2.81827i
$219$		0			0
$220$			12.0000i			0.809040i
$221$		0			0
$222$	10.0000	−	22.3607i	0.671156	−	1.50075i
$223$	−14.7821	−	6.12293i	−0.989881	−	0.410022i	−0.171804	−	0.985131i	$-0.554960\pi$
$223$	−14.7821	−	6.12293i	−0.989881	−	0.410022i	−0.818077	+	0.575109i	$0.804960\pi$
$224$	20.8056	−	4.13849i	1.39013	−	0.276515i
$225$	−0.500776	+	8.98606i	−0.0333851	+	0.599070i
$226$	−10.5174	−	7.02747i	−0.699604	−	0.467460i
$227$	−6.93520	−	1.37950i	−0.460305	−	0.0915604i	−0.0405098	−	0.999179i	$-0.512898\pi$
$227$	−6.93520	−	1.37950i	−0.460305	−	0.0915604i	−0.419796	+	0.907619i	$0.637898\pi$
$228$		0			0
$229$	7.65367	+	18.4776i	0.505769	+	1.22103i	0.946298	+	0.323295i	$0.104791\pi$
$229$	7.65367	+	18.4776i	0.505769	+	1.22103i	−0.440529	+	0.897738i	$0.645209\pi$
$230$	−17.1141	−	41.3171i	−1.12847	−	2.72437i
$231$	−7.63625	+	1.29914i	−0.502428	+	0.0854769i
$232$	−6.20303	−	1.23386i	−0.407249	−	0.0810068i
$233$	−4.70350	−	3.14278i	−0.308137	−	0.205890i	0.391881	−	0.920016i	$-0.371825\pi$
$233$	−4.70350	−	3.14278i	−0.308137	−	0.205890i	−0.700018	+	0.714126i	$0.746825\pi$
$234$	1.49302	−	26.7912i	0.0976021	−	1.75140i
$235$	24.8121	−	4.93544i	1.61856	−	0.321952i
$236$	24.7903	+	10.2685i	1.61371	+	0.668421i
$237$	−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	$-0.0934153\pi$
$240$	3.55917	−	3.36635i	0.229744	−	0.217297i
$241$	−4.93544	−	24.8121i	−0.317920	−	1.59829i	−0.727561	−	0.686043i	$-0.759346\pi$
$241$	−4.93544	−	24.8121i	−0.317920	−	1.59829i	0.409642	−	0.912247i	$-0.365654\pi$
$242$	14.2302	−	14.2302i	0.914755	−	0.914755i
$243$	14.0374	−	6.77865i	0.900503	−	0.434851i
$244$	−3.70158	+	18.6091i	−0.236969	+	1.19133i
$245$	4.71417	+	7.05525i	0.301177	+	0.450744i
$246$	−0.609761	+	21.9004i	−0.0388769	+	1.39632i
$247$		0			0
$248$	−5.87938	+	3.92847i	−0.373341	+	0.249458i
$249$	−8.96202	+	12.6365i	−0.567945	+	0.800808i
$250$	−7.02747	+	10.5174i	−0.444456	+	0.665176i
$251$	−12.6491	−	12.6491i	−0.798405	−	0.798405i	0.184439	−	0.982844i	$-0.440953\pi$
$251$	−12.6491	−	12.6491i	−0.798405	−	0.798405i	−0.982844	+	0.184439i	$0.940953\pi$
$252$	−22.7476	−	17.1040i	−1.43296	−	1.07745i
$253$	3.82683	−	9.23880i	0.240591	−	0.580838i
$254$	26.8328			1.68364
$255$		0			0
$256$	9.00000			0.562500
$257$	−8.55706	+	20.6586i	−0.533775	+	1.28865i	0.395231	+	0.918582i	$0.370665\pi$
$257$	−8.55706	+	20.6586i	−0.533775	+	1.28865i	−0.929006	+	0.370065i	$0.879335\pi$
$258$	−15.1043	−	3.44404i	−0.940350	−	0.214416i
$259$	−14.1421	−	14.1421i	−0.878750	−	0.878750i
$260$	−18.8567	+	28.2210i	−1.16944	+	1.75019i
$261$	−4.31430	−	7.30663i	−0.267048	−	0.452269i
$262$	2.62934	−	1.75687i	0.162441	−	0.108540i
$263$	16.5269	−	6.84565i	1.01909	−	0.422121i	0.190327	−	0.981721i	$-0.439045\pi$
$263$	16.5269	−	6.84565i	1.01909	−	0.422121i	0.828763	+	0.559600i	$0.189045\pi$
$264$	−5.47510	−	0.152440i	−0.336969	−	0.00938205i
$265$		0			0
$266$		0			0
$267$	−12.3675	−	19.6734i	−0.756881	−	1.20399i
$268$	16.9706	−	16.9706i	1.03664	−	1.03664i
$269$	4.96619	+	24.9667i	0.302794	+	1.52225i	0.769968	+	0.638082i	$0.220272\pi$
$269$	4.96619	+	24.9667i	0.302794	+	1.52225i	−0.467174	+	0.884165i	$0.654728\pi$
$270$	−32.7488	−	2.74109i	−1.99303	−	0.166817i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$	−20.0000	−	8.94427i	−1.21046	−	0.541332i
$274$	9.23880	+	3.82683i	0.558136	+	0.231188i
$275$	4.16112	−	0.827698i	0.250925	−	0.0499121i
$276$	34.3237	−	13.1105i	2.06604	−	0.789158i
$277$	−5.25868	−	3.51373i	−0.315963	−	0.211120i	0.387468	−	0.921883i	$-0.373350\pi$
$277$	−5.25868	−	3.51373i	−0.315963	−	0.211120i	−0.703431	+	0.710763i	$0.748350\pi$
$278$	−6.93520	−	1.37950i	−0.415946	−	0.0827367i
$279$	−9.18715	−	2.36564i	−0.550020	−	0.141627i
$280$	7.65367	+	18.4776i	0.457394	+	1.10425i
$281$	−6.84565	−	16.5269i	−0.408377	−	0.985910i	−0.985565	−	0.169298i	$-0.945850\pi$
$281$	−6.84565	−	16.5269i	−0.408377	−	0.985910i	0.577188	−	0.816612i	$-0.304150\pi$
$282$	5.80992	+	34.1503i	0.345976	+	2.03362i
$283$	−3.10152	−	0.616930i	−0.184366	−	0.0366727i	0.102044	−	0.994780i	$-0.467462\pi$
$283$	−3.10152	−	0.616930i	−0.184366	−	0.0366727i	−0.286410	+	0.958107i	$0.592462\pi$
$284$	31.7486	+	21.2138i	1.88394	+	1.25881i
$285$		0			0
$286$	−12.4061	+	2.46772i	−0.733586	+	0.145919i
$287$	16.5269	+	6.84565i	0.975550	+	0.404086i
$288$	13.4164	+	15.0000i	0.790569	+	0.883883i
$289$		0			0
$290$			17.8885i			1.05045i
$291$	−15.0548	−	15.9171i	−0.882526	−	0.933077i
$292$		0			0
$293$	−12.6491	+	12.6491i	−0.738969	+	0.738969i	−0.972379	−	0.233410i	$-0.925012\pi$
$293$	−12.6491	+	12.6491i	−0.738969	+	0.738969i	0.233410	+	0.972379i	$0.425012\pi$
$294$	−9.83672	+	6.18377i	−0.573689	+	0.360645i
$295$	4.93544	−	24.8121i	0.287352	−	1.44462i
$296$	−7.85695	−	11.7588i	−0.456676	−	0.683464i
$297$	−4.74464	−	5.61145i	−0.275312	−	0.325609i
$298$	36.9552	−	15.3073i	2.14076	−	0.886730i
$299$	23.5175	−	15.7139i	1.36005	−	0.908758i
$300$	12.7153	+	9.01786i	0.734117	+	0.520647i
$301$	−7.02747	+	10.5174i	−0.405057	+	0.606210i
$302$	31.6228	+	31.6228i	1.81969	+	1.81969i
$303$	1.72202	−	7.55213i	0.0989274	−	0.433858i
$304$		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	$0.611253\pi$
$308$	−5.13424	+	12.3951i	−0.292550	+	0.706279i
$309$	1.54022	−	6.75483i	0.0876201	−	0.384269i
$310$	14.1421	+	14.1421i	0.803219	+	0.803219i
$311$	−0.785695	+	1.17588i	−0.0445527	+	0.0666778i	−0.853077	−	0.521785i	$-0.825266\pi$
$311$	−0.785695	+	1.17588i	−0.0445527	+	0.0666778i	0.808525	+	0.588462i	$0.200266\pi$
$312$	−12.6365	−	8.96202i	−0.715403	−	0.507375i
$313$	−21.0347	+	14.0549i	−1.18895	+	0.794432i	−0.982906	−	0.184110i	$-0.941060\pi$
$313$	−21.0347	+	14.0549i	−1.18895	+	0.794432i	−0.206046	+	0.978542i	$0.566060\pi$
$314$	4.13171	−	1.71141i	0.233166	−	0.0965806i
$315$	−11.6319	+	24.1805i	−0.655386	+	1.36242i
$316$	5.27060	+	7.88801i	0.296495	+	0.443735i
$317$	2.75899	−	13.8704i	0.154961	−	0.779039i	−0.822639	−	0.568564i	$-0.807499\pi$
$317$	2.75899	−	13.8704i	0.154961	−	0.779039i	0.977599	−	0.210475i	$-0.0675010\pi$
$318$		0			0
$319$	−2.82843	+	2.82843i	−0.158362	+	0.158362i
$320$	−7.17338	−	36.0630i	−0.401004	−	2.01598i
$321$	−5.04952	−	5.33876i	−0.281837	−	0.297980i
$322$		−	50.0000i		−	2.78639i
$323$		0			0
$324$	3.00000	−	26.8328i	0.166667	−	1.49071i
$325$	11.0866	+	4.59220i	0.614971	+	0.254729i
$326$	−20.8056	+	4.13849i	−1.15232	+	0.229210i
$327$	11.7264	+	30.7000i	0.648470	+	1.69772i
$328$	10.5174	+	7.02747i	0.580724	+	0.388027i
$329$	27.7408	+	5.51799i	1.52940	+	0.304217i
$330$	2.59827	+	15.2725i	0.143030	+	0.840723i
$331$	−10.7151	−	25.8686i	−0.588957	−	1.42187i	−0.884501	−	0.466539i	$-0.845501\pi$
$331$	−10.7151	−	25.8686i	−0.588957	−	1.42187i	0.295543	−	0.955329i	$-0.404499\pi$
$332$	10.2685	+	24.7903i	0.563556	+	1.36054i
$333$	4.73129	−	18.3743i	0.259273	−	1.00691i
$334$	−21.7106	−	4.31851i	−1.18795	−	0.236298i
$335$	−18.8140	−	12.5711i	−1.02792	−	0.686834i
$336$	5.11667	−	1.95440i	0.279137	−	0.106621i
$337$	−24.8121	+	4.93544i	−1.35160	+	0.268850i	−0.817188	−	0.576372i	$-0.804468\pi$
$337$	−24.8121	+	4.93544i	−1.35160	+	0.268850i	−0.534415	+	0.845222i	$0.679468\pi$
$338$	−6.19757	−	2.56712i	−0.337103	−	0.139633i
$339$	−8.94427	−	4.00000i	−0.485786	−	0.217250i
$340$		0			0
$341$			4.47214i			0.242180i
$342$		0			0
$343$	−2.46772	−	12.4061i	−0.133244	−	0.669864i
$344$	−6.32456	+	6.32456i	−0.340997	+	0.340997i
$345$	−18.4364	−	29.3274i	−0.992584	−	1.57894i
$346$	6.16930	−	31.0152i	0.331663	−	1.66738i
$347$	19.6424	+	29.3969i	1.05446	+	1.57811i	0.789404	+	0.613874i	$0.210390\pi$
$347$	19.6424	+	29.3969i	1.05446	+	1.57811i	0.265054	+	0.964234i	$0.414610\pi$
$348$	−14.6912	−	0.409040i	−0.787533	−	0.0219269i
$349$	12.9343	−	5.35757i	0.692358	−	0.286784i	−0.00862428	−	0.999963i	$-0.502745\pi$
$349$	12.9343	−	5.35757i	0.692358	−	0.286784i	0.700982	+	0.713179i	$0.252745\pi$
$350$	17.6381	−	11.7854i	0.942798	−	0.629957i
$351$	−2.34044	−	20.6524i	−0.124923	−	1.10234i
$352$	5.27060	−	7.88801i	0.280924	−	0.420433i
$353$	−12.6491	−	12.6491i	−0.673244	−	0.673244i	0.285218	−	0.958463i	$-0.407934\pi$
$353$	−12.6491	−	12.6491i	−0.673244	−	0.673244i	−0.958463	+	0.285218i	$0.907934\pi$
$354$	33.7741	+	7.70110i	1.79508	+	0.409309i
$355$	13.7766	−	33.2597i	0.731186	−	1.76524i
$356$	−40.2492			−2.13320
$357$		0			0
$358$		0			0
$359$	−10.2685	+	24.7903i	−0.541949	+	1.30838i	0.381396	+	0.924412i	$0.375443\pi$
$359$	−10.2685	+	24.7903i	−0.541949	+	1.30838i	−0.923346	+	0.383970i	$0.874557\pi$
$360$	−11.4027	+	15.1651i	−0.600974	+	0.799269i
$361$	−13.4350	−	13.4350i	−0.707107	−	0.707107i
$362$	23.5708	−	35.2763i	1.23886	−	1.85408i
$363$	9.01786	−	12.7153i	0.473315	−	0.667379i
$364$	−31.5521	+	21.0824i	−1.65378	+	1.10502i
$365$		0			0
$366$	−0.681734	+	24.4854i	−0.0356348	+	1.27987i
$367$	8.78434	+	13.1467i	0.458539	+	0.686252i	0.986637	−	0.162931i	$-0.0520949\pi$
$367$	8.78434	+	13.1467i	0.458539	+	0.686252i	−0.528099	+	0.849183i	$0.677095\pi$
$368$	−1.37950	+	6.93520i	−0.0719112	+	0.361522i
$369$	2.37954	+	16.8029i	0.123874	+	0.874725i
$370$	−28.2843	+	28.2843i	−1.47043	+	1.47043i
$371$		0			0
$372$	−11.9378	+	11.2911i	−0.618947	+	0.585415i
$373$			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
$376$	18.4776	+	7.65367i	0.952909	+	0.394708i
$377$	−11.0963	+	2.20720i	−0.571489	+	0.113676i
$378$	−32.6544	−	16.8430i	−1.67956	−	0.866313i
$379$	7.88801	+	5.27060i	0.405180	+	0.270733i	0.741417	−	0.671045i	$-0.234154\pi$
$379$	7.88801	+	5.27060i	0.405180	+	0.270733i	−0.336237	+	0.941778i	$0.609154\pi$
$380$		0			0
$381$	20.4902	−	3.48595i	1.04974	−	0.178591i
$382$	−7.65367	−	18.4776i	−0.391596	−	0.945396i
$383$	−13.6913	−	33.0537i	−0.699593	−	1.68897i	−0.724499	−	0.689276i	$-0.757929\pi$
$383$	−13.6913	−	33.0537i	−0.699593	−	1.68897i	0.0249059	−	0.999690i	$-0.492071\pi$
$384$	26.7269	−	4.54698i	1.36390	−	0.232037i
$385$	12.4061	+	2.46772i	0.632271	+	0.125767i
$386$	23.5175	+	15.7139i	1.19701	+	0.799816i
$387$	−11.9814	−	0.667701i	−0.609049	−	0.0339412i
$388$	−37.2182	+	7.40316i	−1.88947	+	0.375838i
$389$	4.13171	+	1.71141i	0.209486	+	0.0867720i	0.484959	−	0.874537i	$-0.338834\pi$
$389$	4.13171	+	1.71141i	0.209486	+	0.0867720i	−0.275473	+	0.961309i	$0.588834\pi$
$390$	−17.8885	+	40.0000i	−0.905822	+	2.02548i
$391$		0			0
$392$			6.70820i			0.338815i
$393$	1.77959	−	1.68317i	0.0897682	−	0.0849049i
$394$	11.1047	+	55.8273i	0.559449	+	2.81254i
$395$	6.32456	−	6.32456i	0.318223	−	0.318223i
$396$	−12.6022	+	1.78465i	−0.633284	+	0.0896821i
$397$	−3.70158	+	18.6091i	−0.185777	+	0.933964i	0.769589	+	0.638539i	$0.220461\pi$
$397$	−3.70158	+	18.6091i	−0.185777	+	0.933964i	−0.955366	+	0.295424i	$0.904539\pi$
$398$	−11.7854	−	17.6381i	−0.590750	−	0.884120i
$399$		0			0
$400$	−2.77164	+	1.14805i	−0.138582	+	0.0574025i
$401$	4.70350	−	3.14278i	0.234882	−	0.156943i	−0.432560	−	0.901605i	$-0.642389\pi$
$401$	4.70350	−	3.14278i	0.234882	−	0.156943i	0.667441	+	0.744662i	$0.267389\pi$
$402$	17.9240	−	25.2731i	0.893970	−	1.26051i
$403$	−7.02747	+	10.5174i	−0.350063	+	0.523907i
$404$	−9.48683	−	9.48683i	−0.471988	−	0.471988i
$405$	−25.3639	+	2.16136i	−1.26034	+	0.107399i
$406$	−7.65367	+	18.4776i	−0.379845	+	0.917027i
$407$	−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	$0.387496\pi$
$410$	13.6913	−	33.0537i	0.676165	−	1.63241i
$411$	7.55213	+	1.72202i	0.372519	+	0.0849409i
$412$	−8.48528	−	8.48528i	−0.418040	−	0.418040i
$413$	15.7139	−	23.5175i	0.773230	−	1.15722i
$414$	40.8453	−	24.1177i	2.00744	−	1.18532i
$415$	21.0347	−	14.0549i	1.03255	−	0.689930i
$416$	24.7903	−	10.2685i	1.21544	−	0.503453i
$417$	−5.47510	−	0.152440i	−0.268117	−	0.00746503i
$418$		0			0
$419$	−1.93130	+	9.70928i	−0.0943500	+	0.474329i	0.904504	+	0.426465i	$0.140241\pi$
$419$	−1.93130	+	9.70928i	−0.0943500	+	0.474329i	−0.998854	+	0.0478640i	$0.984759\pi$
$420$	24.7351	+	39.3469i	1.20695	+	1.91993i
$421$	14.1421	−	14.1421i	0.689246	−	0.689246i	−0.272820	−	0.962065i	$-0.587956\pi$
$421$	14.1421	−	14.1421i	0.689246	−	0.689246i	0.962065	+	0.272820i	$0.0879562\pi$
$422$	−9.65648	−	48.5464i	−0.470070	−	2.36320i
$423$	8.87319	+	25.3232i	0.431429	+	1.23126i
$424$		0			0
$425$		0			0
$426$	45.0000	+	20.1246i	2.18026	+	0.975041i
$427$	18.4776	+	7.65367i	0.894193	+	0.370387i
$428$	−12.4834	+	2.48309i	−0.603406	+	0.120025i
$429$	−9.15298	+	3.49613i	−0.441910	+	0.168795i
$430$	21.0347	+	14.0549i	1.01438	+	0.677789i
$431$	12.4834	+	2.48309i	0.601302	+	0.119606i	0.486349	−	0.873764i	$-0.338328\pi$
$431$	12.4834	+	2.48309i	0.601302	+	0.119606i	0.114953	+	0.993371i	$0.463328\pi$
$432$	4.06460	+	3.23713i	0.195558	+	0.155747i
$433$	13.7766	+	33.2597i	0.662061	+	1.59836i	0.794568	+	0.607175i	$0.207697\pi$
$433$	13.7766	+	33.2597i	0.662061	+	1.59836i	−0.132507	+	0.991182i	$0.542303\pi$
$434$	8.55706	+	20.6586i	0.410752	+	0.991643i
$435$	2.32397	+	13.6601i	0.111426	+	0.654953i
$436$	55.8273	+	11.1047i	2.67364	+	0.531820i
$437$		0			0
$438$		0			0
$439$	21.7106	−	4.31851i	1.03619	−	0.206111i	0.352446	−	0.935832i	$-0.385350\pi$
$439$	21.7106	−	4.31851i	1.03619	−	0.206111i	0.683745	+	0.729721i	$0.260350\pi$
$440$	8.26343	+	3.42282i	0.393944	+	0.163177i
$441$	−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	$0.860290\pi$
$444$	−22.5821	−	23.8756i	−1.07170	−	1.13309i
$445$	7.40316	+	37.2182i	0.350943	+	1.76431i
$446$	−25.2982	+	25.2982i	−1.19791	+	1.19791i
$447$	26.2313	−	16.4900i	1.24070	−	0.779952i
$448$	8.02009	−	40.3197i	0.378913	−	1.90493i
$449$	9.42834	+	14.1105i	0.444951	+	0.665916i	0.984368	−	0.176123i	$-0.0563555\pi$
$449$	9.42834	+	14.1105i	0.444951	+	0.665916i	−0.539417	+	0.842039i	$0.681355\pi$
$450$	18.1354	+	8.72396i	0.854911	+	0.411251i
$451$	7.39104	−	3.06147i	0.348030	−	0.144159i
$452$	−14.1105	+	9.42834i	−0.663702	+	0.443472i
$453$	28.2562	+	20.0397i	1.32759	+	0.941547i
$454$	−8.78434	+	13.1467i	−0.412269	+	0.617005i
$455$	25.2982	+	25.2982i	1.18600	+	1.18600i
$456$		0			0
$457$	−10.7151	+	25.8686i	−0.501233	+	1.21008i	0.447580	+	0.894244i	$0.352286\pi$
$457$	−10.7151	+	25.8686i	−0.501233	+	1.21008i	−0.948813	+	0.315839i	$0.897714\pi$
$458$	44.7214			2.08969
$459$		0			0
$460$	−60.0000			−2.79751
$461$	13.6913	−	33.0537i	0.637667	−	1.53947i	−0.192112	−	0.981373i	$-0.561534\pi$
$461$	13.6913	−	33.0537i	0.637667	−	1.53947i	0.829779	−	0.558092i	$-0.188466\pi$
$462$	−3.85055	+	16.8871i	−0.179144	+	0.785658i
$463$	2.82843	+	2.82843i	0.131448	+	0.131448i	0.769770	−	0.638322i	$-0.220371\pi$
$463$	2.82843	+	2.82843i	0.131448	+	0.131448i	−0.638322	+	0.769770i	$0.720371\pi$
$464$	1.57139	−	2.35175i	0.0729499	−	0.109177i
$465$	12.6365	+	8.96202i	0.586005	+	0.415604i
$466$	−10.5174	+	7.02747i	−0.487207	+	0.325541i
$467$	−16.5269	+	6.84565i	−0.764772	+	0.316779i	−0.730753	−	0.682642i	$-0.760831\pi$
$467$	−16.5269	+	6.84565i	−0.764772	+	0.316779i	−0.0340192	+	0.999421i	$0.510831\pi$
$468$	−32.4416	−	15.6059i	−1.49961	−	0.721382i
$469$	−14.0549	−	21.0347i	−0.648997	−	0.971292i
$470$	11.0360	−	55.4816i	0.509052	−	2.55918i
$471$	2.93274	−	1.84364i	0.135134	−	0.0849506i
$472$	14.1421	−	14.1421i	0.650945	−	0.650945i
$473$	1.10360	+	5.54816i	0.0507435	+	0.255105i
$474$	8.41587	+	8.89793i	0.386554	+	0.408695i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−18.4776	−	7.65367i	−0.845145	−	0.350071i
$479$	9.70928	−	1.93130i	0.443628	−	0.0882432i	0.0317786	−	0.999495i	$-0.489883\pi$
$479$	9.70928	−	1.93130i	0.443628	−	0.0882432i	0.411850	+	0.911252i	$0.364883\pi$
$480$	−11.7264	−	30.7000i	−0.535233	−	1.40126i
$481$	−21.0347	−	14.0549i	−0.959100	−	0.640850i
$482$	−55.4816	−	11.0360i	−2.52712	−	0.502675i
$483$	−6.49569	−	38.1812i	−0.295564	−	1.73731i
$484$	−10.3325	−	24.9447i	−0.469657	−	1.13385i
$485$	13.6913	+	33.0537i	0.621690	+	1.50089i
$486$	−1.99179	−	34.7999i	−0.0903496	−	1.57856i
$487$	−27.9136	−	5.55237i	−1.26489	−	0.251602i	−0.483332	−	0.875437i	$-0.660574\pi$
$487$	−27.9136	−	5.55237i	−1.26489	−	0.251602i	−0.781556	+	0.623835i	$0.785574\pi$
$488$	11.7588	+	7.85695i	0.532294	+	0.355667i
$489$	−15.3500	+	5.86319i	−0.694152	+	0.265142i
$490$	18.6091	−	3.70158i	0.840673	−	0.167220i
$491$	−16.5269	−	6.84565i	−0.745847	−	0.308940i	−0.0228010	−	0.999740i	$-0.507258\pi$
$491$	−16.5269	−	6.84565i	−0.745847	−	0.308940i	−0.723046	+	0.690800i	$0.757258\pi$
$492$	26.8328	+	12.0000i	1.20972	+	0.541002i
$493$		0			0
$494$		0			0
$495$	3.96821	+	11.3249i	0.178358	+	0.509016i
$496$	−0.616930	−	3.10152i	−0.0277010	−	0.139262i
$497$	28.4605	−	28.4605i	1.27663	−	1.27663i
$498$	18.4364	+	29.3274i	0.826156	+	1.31419i
$499$	0.616930	−	3.10152i	0.0276176	−	0.138843i	−0.964517	−	0.264022i	$-0.914951\pi$
$499$	0.616930	−	3.10152i	0.0276176	−	0.138843i	0.992134	+	0.125180i	$0.0399507\pi$
$500$	9.42834	+	14.1105i	0.421648	+	0.631041i
$501$	−17.1398	−	0.477214i	−0.765749	−	0.0213203i
$502$	−36.9552	+	15.3073i	−1.64939	+	0.683200i
$503$	10.5829	−	7.07125i	0.471867	−	0.315292i	−0.296801	−	0.954939i	$-0.595920\pi$
$503$	10.5829	−	7.07125i	0.471867	−	0.315292i	0.768668	+	0.639648i	$0.220920\pi$
$504$	−18.2666	+	10.7857i	−0.813658	+	0.480435i
$505$	−7.02747	+	10.5174i	−0.312718	+	0.468016i
$506$	−15.8114	−	15.8114i	−0.702902	−	0.702902i
$507$	−5.06612	−	1.15517i	−0.224994	−	0.0513027i
$508$	13.7766	−	33.2597i	0.611238	−	1.47566i
$509$	−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
$512$	−4.27853	+	10.3293i	−0.189086	+	0.456494i
$513$		0			0
$514$	35.3553	+	35.3553i	1.55946	+	1.55946i
$515$	−6.28556	+	9.40700i	−0.276975	+	0.414522i
$516$	−12.0238	+	16.9537i	−0.529319	+	0.746345i
$517$	10.5174	−	7.02747i	0.462553	−	0.309068i
$518$	−41.3171	+	17.1141i	−1.81537	+	0.751951i
$519$	0.681734	−	24.4854i	0.0299248	−	1.07479i
$520$	14.0549	+	21.0347i	0.616350	+	0.922433i
$521$	6.62159	−	33.2890i	0.290097	−	1.45842i	−0.510845	−	0.859673i	$-0.670667\pi$
$521$	6.62159	−	33.2890i	0.290097	−	1.45842i	0.800942	−	0.598743i	$-0.204333\pi$
$522$	−18.7862	+	2.66040i	−0.822251	+	0.116443i
$523$	16.9706	−	16.9706i	0.742071	−	0.742071i	−0.230905	−	0.972976i	$-0.574169\pi$
$523$	16.9706	−	16.9706i	0.742071	−	0.742071i	0.972976	+	0.230905i	$0.0741688\pi$
$524$	−0.827698	−	4.16112i	−0.0361582	−	0.181779i
$525$	11.9378	−	11.2911i	0.521009	−	0.492783i
$526$		−	40.0000i		−	1.74408i
$527$		0			0
$528$	1.00000	−	2.23607i	0.0435194	−	0.0973124i
$529$	24.9447	+	10.3325i	1.08455	+	0.449237i
$530$		0			0
$531$	26.7912	+	1.49302i	1.16264	+	0.0647918i
$532$		0			0
$533$	22.1926	+	4.41439i	0.961270	+	0.191208i
$534$	−51.2255	+	8.71488i	−2.21674	+	0.377130i
$535$	4.59220	+	11.0866i	0.198538	+	0.479314i
$536$	−6.84565	−	16.5269i	−0.295687	−	0.713852i
$537$		0			0
$538$	55.8273	+	11.1047i	2.40688	+	0.478759i
$539$	3.52763	+	2.35708i	0.151946	+	0.101527i
$540$	−20.2117	+	39.1853i	−0.869771	+	1.68627i
$541$	6.20303	−	1.23386i	0.266689	−	0.0530478i	−0.0599343	−	0.998202i	$-0.519089\pi$
$541$	6.20303	−	1.23386i	0.266689	−	0.0530478i	0.326623	+	0.945155i	$0.394089\pi$
$542$		0			0
$543$	13.4164	−	30.0000i	0.575753	−	1.28742i
$544$		0			0
$545$		−	53.6656i		−	2.29878i
$546$	−35.5917	+	33.6635i	−1.52318	+	1.44066i
$547$	0.616930	+	3.10152i	0.0263780	+	0.132611i	0.991730	−	0.128338i	$-0.0409644\pi$
$547$	0.616930	+	3.10152i	0.0263780	+	0.132611i	−0.965352	+	0.260950i	$0.915964\pi$
$548$	9.48683	−	9.48683i	0.405257	−	0.405257i
$549$	2.66040	+	18.7862i	0.113543	+	0.801777i
$550$	1.85079	−	9.30455i	0.0789179	−	0.396747i
$551$		0			0
$552$	0.762201	−	27.3755i	0.0324414	−	1.16518i
$553$	9.23880	−	3.82683i	0.392874	−	0.162734i
$554$	−11.7588	+	7.85695i	−0.499582	+	0.333810i
$555$	−17.9240	+	25.2731i	−0.760834	+	1.07278i
$556$	−5.27060	+	7.88801i	−0.223523	+	0.334526i
$557$	−9.48683	−	9.48683i	−0.401970	−	0.401970i	0.476957	−	0.878927i	$-0.341740\pi$
$557$	−9.48683	−	9.48683i	−0.401970	−	0.401970i	−0.878927	+	0.476957i	$0.841740\pi$
$558$	−12.7486	+	16.9550i	−0.539691	+	0.717764i
$559$	−6.12293	+	14.7821i	−0.258973	+	0.625215i
$560$	−8.94427			−0.377964
$561$		0			0
$562$	−40.0000			−1.68730
$563$	3.42282	−	8.26343i	0.144255	−	0.348262i	−0.835194	−	0.549956i	$-0.814645\pi$
$563$	3.42282	−	8.26343i	0.144255	−	0.348262i	0.979449	+	0.201694i	$0.0646446\pi$
$564$	45.3128	+	10.3321i	1.90801	+	0.435060i
$565$	11.3137	+	11.3137i	0.475971	+	0.475971i
$566$	−3.92847	+	5.87938i	−0.165126	+	0.247129i
$567$	−27.1239	−	8.61950i	−1.13910	−	0.361985i
$568$	23.6640	−	15.8118i	0.992921	−	0.663449i
$569$	−16.5269	+	6.84565i	−0.692842	+	0.286985i	−0.701184	−	0.712981i	$-0.747345\pi$
$569$	−16.5269	+	6.84565i	−0.692842	+	0.286985i	0.00834171	+	0.999965i	$0.497345\pi$
$570$		0			0
$571$	19.3255	+	28.9227i	0.808749	+	1.21038i	0.974539	+	0.224217i	$0.0719824\pi$
$571$	19.3255	+	28.9227i	0.808749	+	1.21038i	−0.165791	+	0.986161i	$0.553018\pi$
$572$	−3.31079	+	16.6445i	−0.138431	+	0.695941i
$573$	−8.24502	−	13.1156i	−0.344441	−	0.547913i
$574$	28.2843	−	28.2843i	1.18056	−	1.18056i
$575$	4.13849	+	20.8056i	0.172587	+	0.867653i
$576$	36.8059	−	12.8967i	1.53358	−	0.537362i
$577$			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
$580$	22.1731	+	9.18440i	0.920688	+	0.381362i
$581$	27.7408	−	5.51799i	1.15088	−	0.228925i
$582$	−45.7649	+	17.4806i	−1.89702	+	0.724596i
$583$		0			0
$584$		0			0
$585$	−8.46358	+	32.8689i	−0.349926	+	1.35896i
$586$	15.3073	+	36.9552i	0.632340	+	1.52660i
$587$	6.84565	+	16.5269i	0.282550	+	0.682136i	0.999894	−	0.0145832i	$-0.00464214\pi$
$587$	6.84565	+	16.5269i	0.282550	+	0.682136i	−0.717343	+	0.696720i	$0.754642\pi$
$588$	2.61446	+	15.3676i	0.107819	+	0.633751i
$589$		0			0
$590$	−47.0350	−	31.4278i	−1.93640	−	1.29386i
$591$	15.7326	+	41.1884i	0.647152	+	1.69427i
$592$	6.20303	−	1.23386i	0.254943	−	0.0507113i
$593$	−16.5269	−	6.84565i	−0.678677	−	0.281117i	0.0165969	−	0.999862i	$-0.494717\pi$
$593$	−16.5269	−	6.84565i	−0.678677	−	0.281117i	−0.695274	+	0.718745i	$0.744717\pi$
$594$	−15.6525	+	5.00000i	−0.642229	+	0.205152i
$595$		0			0
$596$		−	53.6656i		−	2.19823i
$597$	−11.2911	−	11.9378i	−0.462113	−	0.488583i
$598$	−12.3386	−	62.0303i	−0.504563	−	2.53661i
$599$	−12.6491	+	12.6491i	−0.516829	+	0.516829i	−0.916610	−	0.399782i	$-0.869086\pi$
$599$	−12.6491	+	12.6491i	−0.516829	+	0.516829i	0.399782	+	0.916610i	$0.369086\pi$
$600$	9.83672	−	6.18377i	0.401582	−	0.252451i
$601$	−2.46772	+	12.4061i	−0.100660	+	0.506054i	0.897255	+	0.441513i	$0.145558\pi$
$601$	−2.46772	+	12.4061i	−0.100660	+	0.506054i	−0.997915	+	0.0645405i	$0.979442\pi$
$602$	15.7139	+	23.5175i	0.640451	+	0.958502i
$603$	10.4039	−	21.6277i	0.423681	−	0.880749i
$604$	55.4328	−	22.9610i	2.25553	−	0.934270i
$605$	−21.1658	+	14.1425i	−0.860511	+	0.574975i
$606$	−14.1281	−	10.0198i	−0.573914	−	0.407029i
$607$	−12.2981	+	18.4054i	−0.499163	+	0.747051i	−0.992428	−	0.122829i	$-0.960803\pi$
$607$	−12.2981	+	18.4054i	−0.499163	+	0.747051i	0.493265	+	0.869879i	$0.335803\pi$
$608$		0			0
$609$	−3.44404	+	15.1043i	−0.139559	+	0.612055i
$610$	15.3073	−	36.9552i	0.619776	−	1.49627i
$611$	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	$0.461336\pi$
$614$	−10.2685	+	24.7903i	−0.414402	+	1.00045i
$615$	6.16088	−	27.0193i	0.248431	−	1.08952i
$616$	7.07107	+	7.07107i	0.284901	+	0.284901i
$617$	−21.9995	+	32.9245i	−0.885665	+	1.32549i	0.0592732	+	0.998242i	$0.481122\pi$
$617$	−21.9995	+	32.9245i	−0.885665	+	1.32549i	−0.944938	+	0.327249i	$0.893878\pi$
$618$	−12.6365	−	8.96202i	−0.508316	−	0.360505i
$619$	−2.62934	+	1.75687i	−0.105682	+	0.0706145i	−0.607288	−	0.794482i	$-0.707743\pi$
$619$	−2.62934	+	1.75687i	−0.105682	+	0.0706145i	0.501606	+	0.865096i	$0.332743\pi$
$620$	24.7903	−	10.2685i	0.995602	−	0.412392i
$621$	28.0573	−	23.7232i	1.12590	−	0.951980i
$622$	1.75687	+	2.62934i	0.0704440	+	0.105427i
$623$	−8.27698	+	41.6112i	−0.331610	+	1.66712i
$624$	5.86549	−	3.68729i	0.234807	−	0.147610i
$625$	21.9203	−	21.9203i	0.876812	−	0.876812i
$626$	11.0360	+	55.4816i	0.441086	+	2.21749i
$627$		0			0
$628$		−	6.00000i		−	0.239426i
$629$		0			0
$630$	40.0000	+	44.7214i	1.59364	+	1.78174i
$631$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$631$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$632$	6.93520	−	1.37950i	0.275867	−	0.0548734i
$633$	−13.6808	−	35.8167i	−0.543762	−	1.42359i
$634$	−26.2934	−	17.5687i	−1.04424	−	0.697741i
$635$	−33.2890	−	6.62159i	−1.32103	−	0.262770i
$636$		0			0
$637$	4.59220	+	11.0866i	0.181950	+	0.439265i
$638$	3.42282	+	8.26343i	0.135511	+	0.327152i
$639$	36.9776	+	9.52153i	1.46281	+	0.376666i
$640$	−43.4212	−	8.63702i	−1.71637	−	0.341408i
$641$	18.8140	+	12.5711i	0.743109	+	0.496529i	0.868568	−	0.495569i	$-0.165041\pi$
$641$	18.8140	+	12.5711i	0.743109	+	0.496529i	−0.125460	+	0.992099i	$0.540041\pi$
$642$	−15.3500	+	5.86319i	−0.605817	+	0.231401i
$643$	−21.7106	+	4.31851i	−0.856183	+	0.170305i	−0.603617	−	0.797274i	$-0.706274\pi$
$643$	−21.7106	+	4.31851i	−0.856183	+	0.170305i	−0.252566	+	0.967580i	$0.581274\pi$
$644$	−61.9757	−	25.6712i	−2.44219	−	1.01159i
$645$	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	$0.823147\pi$
$648$	−17.6219	−	9.71953i	−0.692253	−	0.381819i
$649$	−2.46772	−	12.4061i	−0.0968664	−	0.486981i
$650$	18.9737	−	18.9737i	0.744208	−	0.744208i
$651$	9.21821	+	14.6637i	0.361290	+	0.574716i
$652$	−5.55237	+	27.9136i	−0.217448	+	1.09318i
$653$	−20.4281	−	30.5728i	−0.799412	−	1.19640i	−0.977197	−	0.212335i	$-0.931893\pi$
$653$	−20.4281	−	30.5728i	−0.799412	−	1.19640i	0.177785	−	0.984069i	$-0.443107\pi$
$654$	73.4562	+	2.04520i	2.87237	+	0.0799737i
$655$	−3.69552	+	1.53073i	−0.144396	+	0.0598107i
$656$	−4.70350	+	3.14278i	−0.183641	+	0.122705i
$657$		0			0
$658$	35.1373	−	52.5868i	1.36980	−	2.05005i
$659$	−6.32456	−	6.32456i	−0.246370	−	0.246370i	0.573109	−	0.819479i	$-0.305737\pi$
$659$	−6.32456	−	6.32456i	−0.246370	−	0.246370i	−0.819479	+	0.573109i	$0.805737\pi$
$660$	20.2645	+	4.62066i	0.788794	+	0.179859i
$661$	−14.5420	+	35.1074i	−0.565617	+	1.36552i	0.339600	+	0.940570i	$0.389708\pi$
$661$	−14.5420	+	35.1074i	−0.565617	+	1.36552i	−0.905217	+	0.424950i	$0.860292\pi$
$662$	−62.6099			−2.43340
$663$		0			0
$664$	20.0000			0.776151
$665$		0			0
$666$	−33.9101	−	25.4972i	−1.31399	−	0.987995i
$667$	−14.1421	−	14.1421i	−0.547586	−	0.547586i
$668$	−16.4996	+	24.6934i	−0.638388	+	0.955416i
$669$	−16.0318	+	22.6049i	−0.619824	+	0.873957i
$670$	−42.0694	+	28.1099i	−1.62528	+	1.08598i
$671$	8.26343	−	3.42282i	0.319006	−	0.132137i
$672$	1.02260	−	36.7281i	0.0394477	−	1.41682i
$673$	14.0549	+	21.0347i	0.541778	+	0.810828i	0.996824	−	0.0796399i	$-0.0253771\pi$
$673$	14.0549	+	21.0347i	0.541778	+	0.810828i	−0.455046	+	0.890468i	$0.650377\pi$
$674$	−11.0360	+	55.4816i	−0.425090	+	2.13707i
$675$	14.9820	+	4.30579i	0.576657	+	0.165730i
$676$	−6.36396	+	6.36396i	−0.244768	+	0.244768i
$677$	−2.75899	−	13.8704i	−0.106037	−	0.533083i	−0.996891	−	0.0787934i	$-0.974893\pi$
$677$	−2.75899	−	13.8704i	−0.106037	−	0.533083i	0.890854	−	0.454289i	$-0.150107\pi$
$678$	−15.9171	+	15.0548i	−0.611292	+	0.578175i
$679$			40.0000i			1.53506i
$680$		0			0
$681$	−5.00000	+	11.1803i	−0.191600	+	0.428432i
$682$	9.23880	+	3.82683i	0.353772	+	0.146537i
$683$	−6.93520	+	1.37950i	−0.265368	+	0.0527850i	−0.325981	−	0.945376i	$-0.605695\pi$
$683$	−6.93520	+	1.37950i	−0.265368	+	0.0527850i	0.0606128	+	0.998161i	$0.480695\pi$
$684$		0			0
$685$	−10.5174	−	7.02747i	−0.401847	−	0.268506i
$686$	−27.7408	−	5.51799i	−1.05915	−	0.210678i
$687$	34.1503	−	5.80992i	1.30292	−	0.221662i
$688$	−1.53073	−	3.69552i	−0.0583587	−	0.140890i
$689$		0			0
$690$	−76.3625	+	12.9914i	−2.90707	+	0.494573i
$691$	−40.3197	−	8.02009i	−1.53383	−	0.305098i	−0.645307	−	0.763923i	$-0.723271\pi$
$691$	−40.3197	−	8.02009i	−1.53383	−	0.305098i	−0.888527	+	0.458825i	$0.848271\pi$
$692$	−35.2763	−	23.5708i	−1.34100	−	0.896029i
$693$	−0.746512	+	13.3956i	−0.0283577	+	0.508858i
$694$	77.5379	−	15.4232i	2.94330	−	0.585458i
$695$	8.26343	+	3.42282i	0.313450	+	0.129835i
$696$	−4.47214	+	10.0000i	−0.169516	+	0.379049i
$697$		0			0
$698$		−	31.3050i		−	1.18491i
$699$	−7.11834	+	6.73270i	−0.269240	+	0.254654i
$700$	−5.55237	−	27.9136i	−0.209860	−	1.05504i
$701$	−9.48683	+	9.48683i	−0.358313	+	0.358313i	−0.863191	−	0.504878i	$-0.831537\pi$
$701$	−9.48683	+	9.48683i	−0.358313	+	0.358313i	0.504878	+	0.863191i	$0.331537\pi$
$702$	−44.6677	−	12.8374i	−1.68587	−	0.484516i
$703$		0			0
$704$	−10.2140	−	15.2864i	−0.384956	−	0.576127i
$705$	1.21952	−	43.8008i	0.0459299	−	1.64963i
$706$	−36.9552	+	15.3073i	−1.39083	+	0.576099i
$707$	−11.7588	+	7.85695i	−0.442234	+	0.295491i
$708$	26.8861	−	37.9096i	1.01044	−	1.42473i
$709$	−3.51373	+	5.25868i	−0.131961	+	0.197494i	−0.891566	−	0.452891i	$-0.850392\pi$
$709$	−3.51373	+	5.25868i	−0.131961	+	0.197494i	0.759605	+	0.650385i	$0.225392\pi$
$710$	−56.9210	−	56.9210i	−2.13621	−	2.13621i
$711$	7.58253	+	5.70134i	0.284367	+	0.213817i
$712$	−11.4805	+	27.7164i	−0.430250	+	1.03872i
$713$	−22.3607			−0.837414
$714$		0			0
$715$	16.0000			0.598366
$716$		0			0
$717$	−15.1043	−	3.44404i	−0.564079	−	0.128620i
$718$	42.4264	+	42.4264i	1.58334	+	1.58334i
$719$	2.35708	−	3.52763i	0.0879044	−	0.131558i	−0.784911	−	0.619608i	$-0.787292\pi$
$719$	2.35708	−	3.52763i	0.0879044	−	0.131558i	0.872816	+	0.488050i	$0.162292\pi$
$720$	−4.31430	−	7.30663i	−0.160784	−	0.272302i
$721$	−10.5174	+	7.02747i	−0.391687	+	0.261717i
$722$	−39.2513	+	16.2584i	−1.46078	+	0.605076i
$723$	−43.8008	−	1.21952i	−1.62897	−	0.0453545i
$724$	−31.6236	−	47.3281i	−1.17528	−	1.75893i
$725$	1.65540	−	8.32224i	0.0614799	−	0.309080i
$726$	−18.5513	−	29.5102i	−0.688503	−	1.09522i
$727$	−5.65685	+	5.65685i	−0.209801	+	0.209801i	−0.804183	−	0.594382i	$-0.797397\pi$
$727$	−5.65685	+	5.65685i	−0.209801	+	0.209801i	0.594382	+	0.804183i	$0.297397\pi$
$728$	5.51799	+	27.7408i	0.204510	+	1.02814i
$729$	−6.04197	−	26.3153i	−0.223777	−	0.974640i
$730$		0			0
$731$		0			0
$732$	30.0000	+	13.4164i	1.10883	+	0.495885i
$733$	−31.4119	−	13.0112i	−1.16023	−	0.480581i	−0.282275	−	0.959333i	$-0.591089\pi$
$733$	−31.4119	−	13.0112i	−1.16023	−	0.480581i	−0.877950	+	0.478752i	$0.841089\pi$
$734$	34.6760	−	6.89748i	1.27991	−	0.254591i
$735$	13.7295	−	5.24419i	0.506419	−	0.193435i
$736$	39.4401	+	26.3530i	1.45378	+	0.971385i
$737$	−11.0963	−	2.20720i	−0.408738	−	0.0813031i
$738$	36.7486	+	9.46257i	1.35273	+	0.348322i
$739$	−9.18440	−	22.1731i	−0.337854	−	0.815651i	−0.997921	−	0.0644448i	$-0.979472\pi$
$739$	−9.18440	−	22.1731i	−0.337854	−	0.815651i	0.660068	−	0.751206i	$-0.270528\pi$
$740$	20.5369	+	49.5806i	0.754953	+	1.82262i
$741$		0			0
$742$		0			0
$743$	5.87938	+	3.92847i	0.215693	+	0.144122i	0.658724	−	0.752385i	$-0.271097\pi$
$743$	5.87938	+	3.92847i	0.215693	+	0.144122i	−0.443030	+	0.896507i	$0.646097\pi$
$744$	4.37016	+	11.4412i	0.160218	+	0.419456i
$745$	−49.6242	+	9.87088i	−1.81809	+	0.361641i
$746$	8.26343	+	3.42282i	0.302546	+	0.125319i
$747$	17.8885	+	20.0000i	0.654508	+	0.731762i
$748$		0			0
$749$			13.4164i			0.490225i
$750$	15.0548	+	15.9171i	0.549722	+	0.581210i
$751$	6.78623	+	34.1167i	0.247633	+	1.24493i	0.881757	+	0.471704i	$0.156361\pi$
$751$	6.78623	+	34.1167i	0.247633	+	1.24493i	−0.634124	+	0.773231i	$0.718639\pi$
$752$	−6.32456	+	6.32456i	−0.230633	+	0.230633i
$753$	−26.2313	+	16.4900i	−0.955920	+	0.600931i
$754$	−4.93544	+	24.8121i	−0.179738	+	0.903604i
$755$	−31.4278	−	47.0350i	−1.14377	−	1.71178i
$756$	−37.6428	+	31.8280i	−1.36905	+	1.15757i
$757$	−11.0866	+	4.59220i	−0.402948	+	0.166906i	−0.574947	−	0.818191i	$-0.694977\pi$
$757$	−11.0866	+	4.59220i	−0.402948	+	0.166906i	0.171999	+	0.985097i	$0.444977\pi$
$758$	17.6381	−	11.7854i	0.640646	−	0.428066i
$759$	−14.1281	−	10.0198i	−0.512817	−	0.363697i
$760$		0			0
$761$	3.16228	+	3.16228i	0.114632	+	0.114632i	0.762096	−	0.647464i	$-0.224170\pi$
$761$	3.16228	+	3.16228i	0.114632	+	0.114632i	−0.647464	+	0.762096i	$0.724170\pi$
$762$	10.3321	−	45.3128i	0.374293	−	1.64151i
$763$	22.9610	−	55.4328i	0.831244	−	2.00680i
$764$	−26.8328			−0.970777
$765$		0			0
$766$	−80.0000			−2.89052
$767$	13.6913	−	33.0537i	0.494364	−	1.19350i
$768$	3.46550	−	15.1984i	0.125050	−	0.548424i
$769$	14.1421	+	14.1421i	0.509978	+	0.509978i	0.914520	−	0.404541i	$-0.132569\pi$
$769$	14.1421	+	14.1421i	0.509978	+	0.509978i	−0.404541	+	0.914520i	$0.632569\pi$
$770$	15.7139	−	23.5175i	0.566290	−	0.847512i
$771$	31.5913	+	22.4051i	1.13773	+	0.806899i
$772$	31.5521	−	21.0824i	1.13558	−	0.758772i
$773$	−37.1854	+	15.4027i	−1.33747	+	0.553997i	−0.932776	−	0.360456i	$-0.882621\pi$
$773$	−37.1854	+	15.4027i	−1.33747	+	0.553997i	−0.404691	+	0.914453i	$0.632621\pi$
$774$	−11.6319	+	24.1805i	−0.418101	+	0.869151i
$775$	−5.27060	−	7.88801i	−0.189326	−	0.283346i
$776$	−5.51799	+	27.7408i	−0.198084	+	0.995837i
$777$	−29.3274	+	18.4364i	−1.05212	+	0.661403i
$778$	7.07107	−	7.07107i	0.253510	−	0.253510i
$779$		0			0
$780$	40.3962	+	42.7101i	1.44642	+	1.52927i
$781$		−	18.0000i		−	0.644091i
$782$		0			0
$783$	−14.0000	+	4.47214i	−0.500319	+	0.159821i
$784$	−2.77164	−	1.14805i	−0.0989871	−	0.0410018i
$785$	−5.54816	+	1.10360i	−0.198022	+	0.0393891i
$786$	−1.95440	−	5.11667i	−0.0697110	−	0.182506i
$787$	28.9227	+	19.3255i	1.03098	+	0.688881i	0.951403	−	0.307947i	$-0.0996421\pi$
$787$	28.9227	+	19.3255i	1.03098	+	0.688881i	0.0795801	+	0.996828i	$0.474642\pi$
$788$	74.9002	+	14.8986i	2.66821	+	0.530739i
$789$	−5.19655	−	30.5450i	−0.185002	−	1.08743i
$790$	−7.65367	−	18.4776i	−0.272305	−	0.657403i
$791$	6.84565	+	16.5269i	0.243403	+	0.587627i
$792$	−2.36564	+	9.18715i	−0.0840595	+	0.326451i
$793$	24.8121	+	4.93544i	0.881104	+	0.175263i
$794$	35.2763	+	23.5708i	1.25191	+	0.836498i
$795$		0			0
$796$	−27.9136	+	5.55237i	−0.989373	+	0.196798i
$797$	16.5269	+	6.84565i	0.585411	+	0.242485i	0.655675	−	0.755043i	$-0.272384\pi$
$797$	16.5269	+	6.84565i	0.585411	+	0.242485i	−0.0702638	+	0.997528i	$0.522384\pi$
$798$		0			0
$799$		0			0
$800$			20.1246i			0.711512i
$801$	−37.9849	+	13.3098i	−1.34213	+	0.470278i
$802$	−2.46772	−	12.4061i	−0.0871382	−	0.438073i
$803$		0			0
$804$	−22.1237	−	35.1929i	−0.780243	−	1.24116i
$805$	−12.3386	+	62.0303i	−0.434878	+	2.18628i
$806$	15.7139	+	23.5175i	0.553498	+	0.828369i
$807$	44.0737	+	1.22712i	1.55147	+	0.0431967i
$808$	−9.23880	+	3.82683i	−0.325020	+	0.134628i
$809$	14.1105	−	9.42834i	0.496099	−	0.331483i	−0.282222	−	0.959349i	$-0.591072\pi$
$809$	14.1105	−	9.42834i	0.496099	−	0.331483i	0.778321	+	0.627866i	$0.216072\pi$
$810$	−17.2390	+	54.2477i	−0.605717	+	1.90607i
$811$	26.3530	−	39.4401i	0.925379	−	1.38493i	0.00243400	−	0.999997i	$-0.499225\pi$
$811$	26.3530	−	39.4401i	0.925379	−	1.38493i	0.922945	−	0.384931i	$-0.125775\pi$
$812$	18.9737	+	18.9737i	0.665845	+	0.665845i
$813$		0			0
$814$	−7.65367	+	18.4776i	−0.268261	+	0.647639i
$815$	26.8328			0.939913
$816$		0			0
$817$		0			0
$818$	11.9799	−	28.9220i	0.418867	−	1.01123i
$819$	−22.8054	+	30.3301i	−0.796884	+	1.05982i
$820$	−33.9411	−	33.9411i	−1.18528	−	1.18528i
$821$	−10.9997	+	16.4623i	−0.383893	+	0.574537i	−0.972215	−	0.234090i	$-0.924789\pi$
$821$	−10.9997	+	16.4623i	−0.383893	+	0.574537i	0.588322	+	0.808627i	$0.299789\pi$
$822$	10.0198	−	14.1281i	0.349482	−	0.492773i
$823$	28.9227	−	19.3255i	1.00818	−	0.673646i	0.0622671	−	0.998060i	$-0.480167\pi$
$823$	28.9227	−	19.3255i	1.00818	−	0.673646i	0.945915	+	0.324414i	$0.105167\pi$
$824$	−8.26343	+	3.42282i	−0.287870	+	0.119240i
$825$	0.204520	−	7.34562i	0.00712048	−	0.255742i
$826$	−35.1373	−	52.5868i	−1.22258	−	1.82973i
$827$	7.44928	−	37.4501i	0.259037	−	1.30227i	−0.603943	−	0.797028i	$-0.706404\pi$
$827$	7.44928	−	37.4501i	0.259037	−	1.30227i	0.862980	−	0.505239i	$-0.168596\pi$
$828$	−8.92326	−	63.0109i	−0.310105	−	2.18978i
$829$	−21.2132	+	21.2132i	−0.736765	+	0.736765i	−0.971951	−	0.235185i	$-0.924430\pi$
$829$	−21.2132	+	21.2132i	−0.736765	+	0.736765i	0.235185	+	0.971951i	$0.424430\pi$
$830$	−11.0360	−	55.4816i	−0.383064	−	1.92579i
$831$	−7.95855	+	7.52738i	−0.276079	+	0.261122i
$832$		−	52.0000i		−	1.80278i
$833$		0			0
$834$	−5.00000	+	11.1803i	−0.173136	+	0.387144i
$835$	25.8686	+	10.7151i	0.895221	+	0.370813i
$836$		0			0
$837$	−7.53244	+	14.6035i	−0.260359	+	0.504771i
$838$	18.4054	+	12.2981i	0.635803	+	0.424830i
$839$	9.70928	+	1.93130i	0.335202	+	0.0666757i	0.359822	−	0.933021i	$-0.382838\pi$
$839$	9.70928	+	1.93130i	0.335202	+	0.0666757i	−0.0246200	+	0.999697i	$0.507838\pi$
$840$	34.1503	−	5.80992i	1.17830	−	0.200461i
$841$	−8.03635	−	19.4015i	−0.277116	−	0.669016i
$842$	−17.1141	−	41.3171i	−0.589792	−	1.42388i
$843$	−30.5450	+	5.19655i	−1.05203	+	0.178979i
$844$	−65.1318	−	12.9555i	−2.24193	−	0.445948i
$845$	7.05525	+	4.71417i	0.242708	+	0.162172i
$846$	59.9070	+	3.33851i	2.05965	+	0.114780i
$847$	−27.9136	+	5.55237i	−0.959124	+	0.190782i
$848$		0			0
$849$	−2.23607	+	5.00000i	−0.0767417	+	0.171600i
$850$		0			0
$851$		−	44.7214i		−	1.53303i
$852$	48.0488	−	45.4457i	1.64613	−	1.55694i
$853$	1.23386	+	6.20303i	0.0422465	+	0.212388i	0.996143	−	0.0877495i	$-0.0279675\pi$
$853$	1.23386	+	6.20303i	0.0422465	+	0.212388i	−0.953896	+	0.300137i	$0.902968\pi$
$854$	31.6228	−	31.6228i	1.08211	−	1.08211i
$855$		0			0
$856$	−1.85079	+	9.30455i	−0.0632587	+	0.318023i
$857$	−6.28556	−	9.40700i	−0.214711	−	0.321337i	0.708443	−	0.705768i	$-0.249398\pi$
$857$	−6.28556	−	9.40700i	−0.214711	−	0.321337i	−0.923154	+	0.384431i	$0.874398\pi$
$858$	−0.609761	+	21.9004i	−0.0208169	+	0.747668i
$859$	18.4776	−	7.65367i	0.630447	−	0.261140i	−0.0444959	−	0.999010i	$-0.514168\pi$
$859$	18.4776	−	7.65367i	0.630447	−	0.261140i	0.674943	+	0.737870i	$0.264168\pi$
$860$	28.2210	−	18.8567i	0.962329	−	0.643007i
$861$	17.9240	−	25.2731i	0.610850	−	0.861304i
$862$	15.8118	−	23.6640i	0.538552	−	0.806000i
$863$	12.6491	+	12.6491i	0.430581	+	0.430581i	0.888826	−	0.458245i	$-0.151522\pi$
$863$	12.6491	+	12.6491i	0.430581	+	0.430581i	−0.458245	+	0.888826i	$0.651522\pi$
$864$	30.4967	−	16.8806i	1.03752	−	0.574288i
$865$	−15.3073	+	36.9552i	−0.520465	+	1.25651i
$866$	80.4984			2.73545
$867$		0			0
$868$	30.0000			1.01827
$869$	1.71141	−	4.13171i	0.0580557	−	0.140159i
$870$	30.2085	+	6.88807i	1.02416	+	0.233528i
$871$	−22.6274	−	22.6274i	−0.766701	−	0.766701i
$872$	23.5708	−	35.2763i	0.798210	−	1.19461i
$873$	−32.6762	+	19.2941i	−1.10592	+	0.653008i
$874$		0			0
$875$	16.5269	−	6.84565i	0.558710	−	0.231425i
$876$		0			0
$877$	−17.5687	−	26.2934i	−0.593252	−	0.887864i	0.406415	−	0.913689i	$-0.366779\pi$
$877$	−17.5687	−	26.2934i	−0.593252	−	0.887864i	−0.999666	+	0.0258245i	$0.991779\pi$
$878$	9.65648	−	48.5464i	0.325890	−	1.63836i
$879$	16.4900	+	26.2313i	0.556195	+	0.884758i
$880$	−2.82843	+	2.82843i	−0.0953463	+	0.0953463i
$881$	1.10360	+	5.54816i	0.0371811	+	0.186922i	0.994913	−	0.100741i	$-0.0321215\pi$
$881$	1.10360	+	5.54816i	0.0371811	+	0.186922i	−0.957731	+	0.287664i	$0.907121\pi$
$882$	6.65489	+	18.9924i	0.224082	+	0.639508i
$883$		−	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
$886$	36.9552	+	15.3073i	1.24153	+	0.514260i
$887$	−48.5464	+	9.65648i	−1.63003	+	0.324233i	−0.923543	−	0.383495i	$-0.874720\pi$
$887$	−48.5464	+	9.65648i	−1.63003	+	0.324233i	−0.706485	+	0.707728i	$0.749720\pi$
$888$	−22.8825	+	8.74032i	−0.767885	+	0.293306i
$889$	−31.5521	−	21.0824i	−1.05822	−	0.707081i
$890$	83.2224	+	16.5540i	2.78962	+	0.554890i
$891$	−11.3030	+	5.85159i	−0.378666	+	0.196036i
$892$	18.3688	+	44.3462i	0.615033	+	1.48482i
$893$		0			0
$894$	−11.6198	−	68.3007i	−0.388625	−	2.28432i
$895$		0			0
$896$	−41.1556	−	27.4993i	−1.37491	−	0.918688i
$897$	−17.4806	−	45.7649i	−0.583662	−	1.52805i
$898$	37.2182	−	7.40316i	1.24199	−	0.247047i
$899$	8.26343	+	3.42282i	0.275601	+	0.114158i
$900$	20.1246	−	18.0000i	0.670820	−	0.600000i
$901$		0			0
$902$		−	17.8885i		−	0.595623i
$903$	15.0548	+	15.9171i	0.500991	+	0.529688i
$904$	2.46772	+	12.4061i	0.0820751	+	0.412619i
$905$	−37.9473	+	37.9473i	−1.26141	+	1.26141i
$906$	65.5781	−	41.2251i	2.17869	−	1.36961i
$907$	4.31851	−	21.7106i	0.143394	−	0.720889i	−0.840454	−	0.541883i	$-0.817712\pi$
$907$	4.31851	−	21.7106i	0.143394	−	0.720889i	0.983848	−	0.179006i	$-0.0572883\pi$
$908$	11.7854	+	17.6381i	0.391113	+	0.585342i
$909$	−12.0903	−	5.81597i	−0.401009	−	0.192904i
$910$	73.9104	−	30.6147i	2.45010	−	1.01487i
$911$	−12.9346	+	8.64264i	−0.428543	+	0.286344i	−0.751077	−	0.660214i	$-0.770465\pi$
$911$	−12.9346	+	8.64264i	−0.428543	+	0.286344i	0.322534	+	0.946558i	$0.395465\pi$
$912$		0			0
$913$	7.02747	−	10.5174i	0.232575	−	0.348074i
$914$	44.2719	+	44.2719i	1.46438	+	1.46438i
$915$	6.88807	−	30.2085i	0.227713	−	0.998663i
$916$	22.9610	−	55.4328i	0.758653	−	1.83155i
$917$	−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	$0.629548\pi$
$920$	−17.1141	+	41.3171i	−0.564236	+	1.36219i
$921$	−4.62066	+	20.2645i	−0.152256	+	0.667738i
$922$	−56.5685	−	56.5685i	−1.86299	−	1.86299i
$923$	28.2850	−	42.3315i	0.931013	−	1.39336i
$924$	18.9548	+	13.4430i	0.623567	+	0.442243i
$925$	15.7760	−	10.5412i	0.518713	−	0.346593i
$926$	8.26343	−	3.42282i	0.271553	−	0.112481i
$927$	−10.8139	−	5.20196i	−0.355174	−	0.170855i
$928$	−10.5412	−	15.7760i	−0.346032	−	0.517873i
$929$	−7.72518	+	38.8371i	−0.253455	+	1.27420i	0.618954	+	0.785427i	$0.287557\pi$
$929$	−7.72518	+	38.8371i	−0.253455	+	1.27420i	−0.872409	+	0.488777i	$0.837443\pi$
$930$	29.3274	−	18.4364i	0.961684	−	0.604554i
$931$		0			0
$932$	3.31079	+	16.6445i	0.108449	+	0.545208i
$933$	1.68317	+	1.77959i	0.0551046	+	0.0582610i
$934$			40.0000i			1.30884i
$935$		0			0
$936$	−20.0000	+	17.8885i	−0.653720	+	0.584705i
$937$	−1.84776	−	0.765367i	−0.0603637	−	0.0250034i	0.352297	−	0.935888i	$-0.385401\pi$
$937$	−1.84776	−	0.765367i	−0.0603637	−	0.0250034i	−0.412661	+	0.910885i	$0.635401\pi$
$938$	−55.4816	+	11.0360i	−1.81154	+	0.360337i
$939$	15.6352	+	40.9334i	0.510234	+	1.33581i
$940$	−63.1041	−	42.1648i	−2.05823	−	1.37526i
$941$	36.0630	+	7.17338i	1.17562	+	0.233846i	0.743981	−	0.668200i	$-0.232935\pi$
$941$	36.0630	+	7.17338i	1.17562	+	0.233846i	0.431640	+	0.902046i	$0.357935\pi$
$942$	−1.29914	−	7.63625i	−0.0423282	−	0.248802i
$943$	15.3073	+	36.9552i	0.498475	+	1.20343i
$944$	3.42282	+	8.26343i	0.111403	+	0.268952i
$945$	36.3549	+	28.9538i	1.18262	+	0.941867i
$946$	12.4061	+	2.46772i	0.403356	+	0.0802325i
$947$	41.1556	+	27.4993i	1.33738	+	0.893608i	0.998878	−	0.0473581i	$-0.0150802\pi$
$947$	41.1556	+	27.4993i	1.33738	+	0.893608i	0.338501	+	0.940966i	$0.390080\pi$
$948$	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
$955$	4.93544	+	24.8121i	0.159707	+	0.802901i
$956$	−18.9737	+	18.9737i	−0.613652	+	0.613652i
$957$	3.68729	+	5.86549i	0.119193	+	0.189604i
$958$	4.31851	−	21.7106i	0.139525	−	0.701438i
$959$	−7.85695	−	11.7588i	−0.253714	−	0.379710i
$960$	−63.6621	−	1.77251i	−2.05468	−	0.0572074i
$961$	−19.4015	+	8.03635i	−0.625854	+	0.259237i
$962$	−47.0350	+	31.4278i	−1.51647	+	1.01327i
$963$	−10.9599	+	6.47145i	−0.353179	+	0.208540i
$964$	−42.1648	+	63.1041i	−1.35804	+	2.03245i
$965$	−25.2982	−	25.2982i	−0.814379	−	0.814379i
$966$	−84.4354	−	19.2528i	−2.71666	−	0.619447i
$967$	12.2459	−	29.5641i	0.393801	−	0.950719i	−0.595303	−	0.803501i	$-0.702968\pi$
$967$	12.2459	−	29.5641i	0.393801	−	0.950719i	0.989104	−	0.147218i	$-0.0470318\pi$
$968$	−20.1246			−0.646830
$969$		0			0
$970$	80.0000			2.56865
$971$	10.2685	−	24.7903i	0.329531	−	0.795558i	−0.669096	−	0.743176i	$-0.733319\pi$
$971$	10.2685	−	24.7903i	0.329531	−	0.795558i	0.998627	−	0.0523823i	$-0.0166815\pi$
$972$	−44.1576	−	15.3982i	−1.41636	−	0.493899i
$973$	7.07107	+	7.07107i	0.226688	+	0.226688i
$974$	−35.3563	+	52.9144i	−1.13289	+	1.69549i
$975$	12.0238	−	16.9537i	0.385070	−	0.542953i
$976$	−5.25868	+	3.51373i	−0.168326	+	0.112472i
$977$	−16.5269	+	6.84565i	−0.528741	+	0.219012i	−0.631052	−	0.775741i	$-0.717376\pi$
$977$	−16.5269	+	6.84565i	−0.528741	+	0.219012i	0.102311	+	0.994753i	$0.467376\pi$
$978$	−1.02260	+	36.7281i	−0.0326992	+	1.17444i
$979$	10.5412	+	15.7760i	0.336898	+	0.504204i
$980$	4.96619	−	24.9667i	0.158639	−	0.797533i
$981$	56.3587	−	7.98120i	1.79939	−	0.254820i
$982$	−28.2843	+	28.2843i	−0.902587	+	0.902587i
$983$	−6.89748	−	34.6760i	−0.219996	−	1.10599i	−0.920019	−	0.391873i	$-0.871827\pi$
$983$	−6.89748	−	34.6760i	−0.219996	−	1.10599i	0.700024	−	0.714120i	$-0.253173\pi$
$984$	15.9171	−	15.0548i	0.507419	−	0.479928i
$985$		−	72.0000i		−	2.29411i
$986$		0			0
$987$	20.0000	−	44.7214i	0.636607	−	1.42350i
$988$		0			0
$989$	−27.7408	+	5.51799i	−0.882106	+	0.175462i
$990$	26.7912	+	1.49302i	0.851482	+	0.0474514i
$991$	28.9227	+	19.3255i	0.918760	+	0.613896i	0.922458	−	0.386097i	$-0.126177\pi$
$991$	28.9227	+	19.3255i	0.918760	+	0.613896i	−0.00369779	+	0.999993i	$0.501177\pi$
$992$	−20.8056	−	4.13849i	−0.660578	−	0.131397i
$993$	−47.8105	+	8.13388i	−1.51722	+	0.258121i
$994$	−34.4415	−	83.1492i	−1.09242	−	2.63733i
$995$	10.2685	+	24.7903i	0.325533	+	0.785905i
$996$	45.8175	−	7.79482i	1.45178	−	0.246988i
$997$	−6.20303	−	1.23386i	−0.196452	−	0.0390767i	0.0958835	−	0.995393i	$-0.469432\pi$
$997$	−6.20303	−	1.23386i	−0.196452	−	0.0390767i	−0.292335	+	0.956316i	$0.594432\pi$
$998$	−5.87938	−	3.92847i	−0.186108	−	0.124354i
$999$	−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.827.4	yes	32
3.2	odd	2	inner	867.2.i.e.827.1	yes	32
17.2	even	8	inner	867.2.i.e.503.3	yes	32
17.3	odd	16	inner	867.2.i.e.65.2	yes	32
17.4	even	4	inner	867.2.i.e.329.1	yes	32
17.5	odd	16	inner	867.2.i.e.224.4	yes	32
17.6	odd	16	inner	867.2.i.e.158.3	yes	32
17.7	odd	16	inner	867.2.i.e.131.1	yes	32
17.8	even	8	inner	867.2.i.e.653.1	yes	32
17.9	even	8	inner	867.2.i.e.653.2	yes	32
17.10	odd	16	inner	867.2.i.e.131.2	yes	32
17.11	odd	16	inner	867.2.i.e.158.4	yes	32
17.12	odd	16	inner	867.2.i.e.224.3	yes	32
17.13	even	4	inner	867.2.i.e.329.2	yes	32
17.14	odd	16	inner	867.2.i.e.65.1	✓	32
17.15	even	8	inner	867.2.i.e.503.4	yes	32
17.16	even	2	inner	867.2.i.e.827.3	yes	32
51.2	odd	8	inner	867.2.i.e.503.1	yes	32
51.5	even	16	inner	867.2.i.e.224.2	yes	32
51.8	odd	8	inner	867.2.i.e.653.3	yes	32
51.11	even	16	inner	867.2.i.e.158.2	yes	32
51.14	even	16	inner	867.2.i.e.65.4	yes	32
51.20	even	16	inner	867.2.i.e.65.3	yes	32
51.23	even	16	inner	867.2.i.e.158.1	yes	32
51.26	odd	8	inner	867.2.i.e.653.4	yes	32
51.29	even	16	inner	867.2.i.e.224.1	yes	32
51.32	odd	8	inner	867.2.i.e.503.2	yes	32
51.38	odd	4	inner	867.2.i.e.329.3	yes	32
51.41	even	16	inner	867.2.i.e.131.3	yes	32
51.44	even	16	inner	867.2.i.e.131.4	yes	32
51.47	odd	4	inner	867.2.i.e.329.4	yes	32
51.50	odd	2	inner	867.2.i.e.827.2	yes	32

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

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)

\(f(q)\)	\(=\)	\(q+(0.855706 - 2.06586i) q^{2} +(0.385055 - 1.68871i) q^{3} +(-2.12132 - 2.12132i) q^{4} +(-1.57139 + 2.35175i) q^{5} +(-3.15913 - 2.24051i) q^{6} +(-2.62934 + 1.75687i) q^{7} +(-2.06586 + 0.855706i) q^{8} +(-2.70347 - 1.30049i) q^{9} +O(q^{10})\)	\(q+(0.855706 - 2.06586i) q^{2} +(0.385055 - 1.68871i) q^{3} +(-2.12132 - 2.12132i) q^{4} +(-1.57139 + 2.35175i) q^{5} +(-3.15913 - 2.24051i) q^{6} +(-2.62934 + 1.75687i) q^{7} +(-2.06586 + 0.855706i) q^{8} +(-2.70347 - 1.30049i) q^{9} +(3.51373 + 5.25868i) q^{10} +(-0.275899 + 1.38704i) q^{11} +(-4.39911 + 2.76546i) q^{12} +(-2.82843 + 2.82843i) q^{13} +(1.37950 + 6.93520i) q^{14} +(3.36635 + 3.55917i) q^{15} -1.00000i q^{16} +(-5.00000 + 4.47214i) q^{18} +(8.32224 - 1.65540i) q^{20} +(1.95440 + 5.11667i) q^{21} +(2.62934 + 1.75687i) q^{22} +(-6.93520 - 1.37950i) q^{23} +(0.649569 + 3.81812i) q^{24} +(-1.14805 - 2.77164i) q^{25} +(3.42282 + 8.26343i) q^{26} +(-3.23713 + 4.06460i) q^{27} +(9.30455 + 1.85079i) q^{28} +(2.35175 + 1.57139i) q^{29} +(10.2333 - 3.90879i) q^{30} +(3.10152 - 0.616930i) q^{31} +(-6.19757 - 2.56712i) q^{32} +(2.23607 + 1.00000i) q^{33} -8.94427i q^{35} +(2.97616 + 8.49367i) q^{36} +(1.23386 + 6.20303i) q^{37} +(3.68729 + 5.86549i) q^{39} +(1.23386 - 6.20303i) q^{40} +(-3.14278 - 4.70350i) q^{41} +(12.2427 + 0.340867i) q^{42} +(3.69552 - 1.53073i) q^{43} +(3.52763 - 2.35708i) q^{44} +(7.30663 - 4.31430i) q^{45} +(-8.78434 + 13.1467i) q^{46} +(-6.32456 - 6.32456i) q^{47} +(-1.68871 - 0.385055i) q^{48} +(1.14805 - 2.77164i) q^{49} -6.70820 q^{50} +12.0000 q^{52} +(5.62685 + 10.1656i) q^{54} +(-2.82843 - 2.82843i) q^{55} +(3.92847 - 5.87938i) q^{56} +(5.25868 - 3.51373i) q^{58} +(-8.26343 + 3.42282i) q^{59} +(0.409040 - 14.6912i) q^{60} +(-3.51373 - 5.25868i) q^{61} +(1.37950 - 6.93520i) q^{62} +(9.39311 - 1.33020i) q^{63} +(-9.19239 + 9.19239i) q^{64} +(-2.20720 - 11.0963i) q^{65} +(3.97927 - 3.76369i) q^{66} +8.00000i q^{67} +(-5.00000 + 11.1803i) q^{69} +(-18.4776 - 7.65367i) q^{70} +(-12.4834 + 2.48309i) q^{71} +(6.69781 + 0.373256i) q^{72} +(13.8704 + 2.75899i) q^{74} +(-5.12255 + 0.871488i) q^{75} +(-1.71141 - 4.13171i) q^{77} +(15.2725 - 2.59827i) q^{78} +(-3.10152 - 0.616930i) q^{79} +(2.35175 + 1.57139i) q^{80} +(5.61745 + 7.03166i) q^{81} +(-12.4061 + 2.46772i) q^{82} +(-8.26343 - 3.42282i) q^{83} +(6.70820 - 15.0000i) q^{84} -8.94427i q^{86} +(3.55917 - 3.36635i) q^{87} +(-0.616930 - 3.10152i) q^{88} +(9.48683 - 9.48683i) q^{89} +(-2.66040 - 18.7862i) q^{90} +(2.46772 - 12.4061i) q^{91} +(11.7854 + 17.6381i) q^{92} +(0.152440 - 5.47510i) q^{93} +(-18.4776 + 7.65367i) q^{94} +(-6.72152 + 9.47740i) q^{96} +(7.02747 - 10.5174i) q^{97} +(-4.74342 - 4.74342i) q^{98} +(2.54972 - 3.39101i) 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

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