LMFDB - Embedded newform 867.2.i.i.65.4

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:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			65.4
Character	$\chi$	$=$	867.65
Dual form			867.2.i.i.827.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.556851 + 1.34436i) q^{2} +(0.339031 + 1.69855i) q^{3} +(-0.0830021 + 0.0830021i) q^{4} +(1.69526 + 2.53714i) q^{5} +(-2.09466 + 1.40162i) q^{6} +(1.79329 + 1.19824i) q^{7} +(2.53091 + 1.04834i) q^{8} +(-2.77012 + 1.15172i) q^{9} +(-2.46681 + 3.69185i) q^{10} +(-0.321478 - 1.61618i) q^{11} +(-0.169123 - 0.112843i) q^{12} +(-3.12551 - 3.12551i) q^{13} +(-0.612265 + 3.07806i) q^{14} +(-3.73470 + 3.73965i) q^{15} +4.22099i q^{16} +(-3.09087 - 3.08269i) q^{18} +(0.797694 - 0.330416i) q^{19} +(-0.351298 - 0.0698774i) q^{20} +(-1.42728 + 3.45222i) q^{21} +(1.99371 - 1.33215i) q^{22} +(0.751858 - 0.149554i) q^{23} +(-0.922593 + 4.65429i) q^{24} +(-1.64974 + 3.98282i) q^{25} +(2.46136 - 5.94226i) q^{26} +(-2.89540 - 4.31470i) q^{27} +(-0.248303 + 0.0493905i) q^{28} +(6.64464 - 4.43981i) q^{29} +(-7.10709 - 2.93834i) q^{30} +(2.83296 + 0.563512i) q^{31} +(-0.612694 + 0.253786i) q^{32} +(2.63616 - 1.09398i) q^{33} +6.58114i q^{35} +(0.134330 - 0.325520i) q^{36} +(-0.464638 + 2.33589i) q^{37} +(0.888394 + 0.888394i) q^{38} +(4.24918 - 6.36847i) q^{39} +(1.63078 + 8.19848i) q^{40} +(1.71091 - 2.56055i) q^{41} +(-5.43581 + 0.00359897i) q^{42} +(-10.5751 - 4.38037i) q^{43} +(0.160829 + 0.107463i) q^{44} +(-7.61814 - 5.07570i) q^{45} +(0.619727 + 0.927487i) q^{46} +(2.21238 - 2.21238i) q^{47} +(-7.16954 + 1.43105i) q^{48} +(-0.898671 - 2.16958i) q^{49} -6.27299 q^{50} +0.518848 q^{52} +(-2.43710 - 5.88369i) q^{53} +(4.18819 - 6.29511i) q^{54} +(3.55548 - 3.55548i) q^{55} +(3.28250 + 4.91261i) q^{56} +(0.831669 + 1.24290i) q^{57} +(9.66877 + 6.46046i) q^{58} +(-5.62864 - 2.33146i) q^{59} +(-0.000410749 - 0.620386i) q^{60} +(-3.24818 + 4.86125i) q^{61} +(0.819979 + 4.12231i) q^{62} +(-6.34765 - 1.25389i) q^{63} +(5.28702 + 5.28702i) q^{64} +(2.63129 - 13.2284i) q^{65} +(2.93865 + 2.93476i) q^{66} +7.19481i q^{67} +(0.508927 + 1.22636i) q^{69} +(-8.84742 + 3.66472i) q^{70} +(2.13271 + 0.424222i) q^{71} +(-8.21831 + 0.0108825i) q^{72} +(-10.4594 + 6.98874i) q^{73} +(-3.39901 + 0.676105i) q^{74} +(-7.32431 - 1.45186i) q^{75} +(-0.0387851 + 0.0936354i) q^{76} +(1.36006 - 3.28348i) q^{77} +(10.9277 + 2.16613i) q^{78} +(-5.84360 + 1.16236i) q^{79} +(-10.7092 + 7.15567i) q^{80} +(6.34708 - 6.38079i) q^{81} +(4.39502 + 0.874225i) q^{82} +(11.9985 - 4.96993i) q^{83} +(-0.168074 - 0.405009i) q^{84} -16.6560i q^{86} +(9.79395 + 9.78099i) q^{87} +(0.880669 - 4.42742i) q^{88} +(-3.42023 - 3.42023i) q^{89} +(2.58139 - 13.0679i) q^{90} +(-1.85984 - 9.35006i) q^{91} +(-0.0499925 + 0.0748190i) q^{92} +(0.00331239 + 5.00297i) q^{93} +(4.20619 + 1.74226i) q^{94} +(2.19061 + 1.46372i) q^{95} +(-0.638789 - 0.954647i) q^{96} +(-1.97085 - 2.94959i) q^{97} +(2.41627 - 2.41627i) q^{98} +(2.75191 + 4.10675i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{3} + 16 q^{4} - 16 q^{6} - 24 q^{9} + 32 q^{10} + 40 q^{12} + 16 q^{13} - 16 q^{15} + 16 q^{18} - 32 q^{19} - 16 q^{21} - 32 q^{22} + 16 q^{24} - 16 q^{27} + 32 q^{28} + 8 q^{30} + 24 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) $ 32 * q + 8 * q^3 + 16 * q^4 - 16 * q^6 - 24 * q^9 + 32 * q^10 + 40 * q^12 + 16 * q^13 - 16 * q^15 + 16 * q^18 - 32 * q^19 - 16 * q^21 - 32 * q^22 + 16 * q^24 - 16 * q^27 + 32 * q^28 + 8 * q^30 + 24 * q^36 - 96 * q^37 + 48 * q^39 + 80 * q^40 + 24 * q^42 + 32 * q^43 - 40 * q^45 - 64 * q^46 + 48 * q^48 + 64 * q^49 - 96 * q^52 + 48 * q^54 + 48 * q^55 - 8 * q^57 - 48 * q^60 - 64 * q^61 - 16 * q^64 - 120 * q^66 + 80 * q^69 - 64 * q^72 - 144 * q^73 + 8 * q^75 - 32 * q^76 - 40 * q^78 + 64 * q^79 - 48 * q^81 - 32 * q^82 + 56 * q^87 + 32 * q^88 + 24 * q^90 + 48 * q^91 + 56 * q^93 + 48 * q^94 - 72 * q^96 - 32 * q^97 - 16 * q^99

Character values

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

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{9}{16}\right)$

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 $

$2$	0.556851	+	1.34436i	0.393753	+	0.950605i	0.989115	+	0.147147i	$0.0470089\pi$
$2$	0.556851	+	1.34436i	0.393753	+	0.950605i	−0.595361	+	0.803458i	$0.702991\pi$
$3$	0.339031	+	1.69855i	0.195740	+	0.980656i
$3$	0.339031	+	1.69855i	0.195740	+	0.980656i
$4$	−0.0830021	+	0.0830021i	−0.0415010	+	0.0415010i
$5$	1.69526	+	2.53714i	0.758144	+	1.13464i	0.986928	+	0.161165i	$0.0515251\pi$
$5$	1.69526	+	2.53714i	0.758144	+	1.13464i	−0.228784	+	0.973477i	$0.573475\pi$
$6$	−2.09466	+	1.40162i	−0.855143	+	0.572208i
$7$	1.79329	+	1.19824i	0.677800	+	0.452891i	0.846227	−	0.532823i	$-0.178869\pi$
$7$	1.79329	+	1.19824i	0.677800	+	0.452891i	−0.168427	+	0.985714i	$0.553869\pi$
$8$	2.53091	+	1.04834i	0.894813	+	0.370644i
$9$	−2.77012	+	1.15172i	−0.923372	+	0.383906i
$10$	−2.46681	+	3.69185i	−0.780075	+	1.16746i
$11$	−0.321478	−	1.61618i	−0.0969292	−	0.487296i	−0.998504	−	0.0546734i	$-0.982588\pi$
$11$	−0.321478	−	1.61618i	−0.0969292	−	0.487296i	0.901575	−	0.432623i	$-0.142412\pi$
$12$	−0.169123	−	0.112843i	−0.0488216	−	0.0325748i
$13$	−3.12551	−	3.12551i	−0.866861	−	0.866861i	0.125262	−	0.992124i	$-0.460023\pi$
$13$	−3.12551	−	3.12551i	−0.866861	−	0.866861i	−0.992124	+	0.125262i	$0.960023\pi$
$14$	−0.612265	+	3.07806i	−0.163635	+	0.822647i
$15$	−3.73470	+	3.73965i	−0.964295	+	0.965572i
$16$			4.22099i			1.05525i
$17$		0			0
$17$		0			0
$18$	−3.09087	−	3.08269i	−0.728524	−	0.726597i
$19$	0.797694	−	0.330416i	0.183004	−	0.0758025i	−0.289300	−	0.957238i	$-0.593423\pi$
$19$	0.797694	−	0.330416i	0.183004	−	0.0758025i	0.472304	+	0.881436i	$0.343423\pi$
$20$	−0.351298	−	0.0698774i	−0.0785525	−	0.0156251i
$21$	−1.42728	+	3.45222i	−0.311458	+	0.753337i
$22$	1.99371	−	1.33215i	0.425060	−	0.284016i
$23$	0.751858	−	0.149554i	0.156773	−	0.0311841i	−0.116080	−	0.993240i	$-0.537033\pi$
$23$	0.751858	−	0.149554i	0.156773	−	0.0311841i	0.272853	+	0.962056i	$0.412033\pi$
$24$	−0.922593	+	4.65429i	−0.188323	+	0.950053i
$25$	−1.64974	+	3.98282i	−0.329947	+	0.796563i
$26$	2.46136	−	5.94226i	0.482713	−	1.16537i
$27$	−2.89540	−	4.31470i	−0.557221	−	0.830364i
$28$	−0.248303	+	0.0493905i	−0.0469248	+	0.00933393i
$29$	6.64464	−	4.43981i	1.23388	−	0.824451i	0.244477	−	0.969655i	$-0.421384\pi$
$29$	6.64464	−	4.43981i	1.23388	−	0.824451i	0.989402	+	0.145204i	$0.0463837\pi$
$30$	−7.10709	−	2.93834i	−1.29757	−	0.536466i
$31$	2.83296	+	0.563512i	0.508815	+	0.101210i	0.442820	−	0.896610i	$-0.353978\pi$
$31$	2.83296	+	0.563512i	0.508815	+	0.101210i	0.0659948	+	0.997820i	$0.478978\pi$
$32$	−0.612694	+	0.253786i	−0.108310	+	0.0448635i
$33$	2.63616	−	1.09398i	0.458897	−	0.190437i
$34$		0			0
$35$			6.58114i			1.11242i
$36$	0.134330	−	0.325520i	0.0223884	−	0.0542534i
$37$	−0.464638	+	2.33589i	−0.0763860	+	0.384018i	0.923614	+	0.383324i	$0.125221\pi$
$37$	−0.464638	+	2.33589i	−0.0763860	+	0.384018i	−1.00000		0.000693887i	$0.999779\pi$
$38$	0.888394	+	0.888394i	0.144117	+	0.144117i
$39$	4.24918	−	6.36847i	0.680414	−	1.01977i
$40$	1.63078	+	8.19848i	0.257849	+	1.29629i
$41$	1.71091	−	2.56055i	0.267199	−	0.399891i	−0.673471	−	0.739213i	$-0.735198\pi$
$41$	1.71091	−	2.56055i	0.267199	−	0.399891i	0.940670	+	0.339322i	$0.110198\pi$
$42$	−5.43581	+	0.00359897i	−0.838764	+	0.000555333i
$43$	−10.5751	−	4.38037i	−1.61269	−	0.668000i	−0.619557	−	0.784952i	$-0.712688\pi$
$43$	−10.5751	−	4.38037i	−1.61269	−	0.668000i	−0.993138	+	0.116952i	$0.962688\pi$
$44$	0.160829	+	0.107463i	0.0242459	+	0.0162006i
$45$	−7.61814	−	5.07570i	−1.13564	−	0.756640i
$46$	0.619727	+	0.927487i	0.0913738	+	0.136751i
$47$	2.21238	−	2.21238i	0.322708	−	0.322708i	−0.527097	−	0.849805i	$-0.676719\pi$
$47$	2.21238	−	2.21238i	0.322708	−	0.322708i	0.849805	+	0.527097i	$0.176719\pi$
$48$	−7.16954	+	1.43105i	−1.03483	+	0.206554i
$49$	−0.898671	−	2.16958i	−0.128382	−	0.309940i
$50$	−6.27299			−0.887135
$51$		0			0
$52$	0.518848			0.0719513
$53$	−2.43710	−	5.88369i	−0.334762	−	0.808187i	−0.998201	−	0.0599567i	$-0.980904\pi$
$53$	−2.43710	−	5.88369i	−0.334762	−	0.808187i	0.663439	−	0.748230i	$-0.269096\pi$
$54$	4.18819	−	6.29511i	0.569941	−	0.856655i
$55$	3.55548	−	3.55548i	0.479420	−	0.479420i
$56$	3.28250	+	4.91261i	0.438642	+	0.656475i
$57$	0.831669	+	1.24290i	0.110157	+	0.164626i
$58$	9.66877	+	6.46046i	1.26957	+	0.848301i
$59$	−5.62864	−	2.33146i	−0.732786	−	0.303530i	−0.0150898	−	0.999886i	$-0.504803\pi$
$59$	−5.62864	−	2.33146i	−0.732786	−	0.303530i	−0.717696	+	0.696356i	$0.754803\pi$
$60$	−0.000410749	−	0.620386i	−5.30274e−5	−	0.0800915i
$61$	−3.24818	+	4.86125i	−0.415887	+	0.622419i	−0.978976	−	0.203978i	$-0.934613\pi$
$61$	−3.24818	+	4.86125i	−0.415887	+	0.622419i	0.563089	+	0.826397i	$0.309613\pi$
$62$	0.819979	+	4.12231i	0.104137	+	0.523534i
$63$	−6.34765	−	1.25389i	−0.799729	−	0.157975i
$64$	5.28702	+	5.28702i	0.660877	+	0.660877i
$65$	2.63129	−	13.2284i	0.326372	−	1.64078i
$66$	2.93865	+	2.93476i	0.361723	+	0.361244i
$67$			7.19481i			0.878985i	0.898246	+	0.439493i	$0.144842\pi$
$67$			7.19481i			0.878985i	−0.898246	+	0.439493i	$0.855158\pi$
$68$		0			0
$69$	0.508927	+	1.22636i	0.0612676	+	0.147637i
$70$	−8.84742	+	3.66472i	−1.05747	+	0.438018i
$71$	2.13271	+	0.424222i	0.253106	+	0.0503459i	0.320012	−	0.947413i	$-0.396313\pi$
$71$	2.13271	+	0.424222i	0.253106	+	0.0503459i	−0.0669064	+	0.997759i	$0.521313\pi$
$72$	−8.21831	+	0.0108825i	−0.968537	+	0.00128251i
$73$	−10.4594	+	6.98874i	−1.22418	+	0.817970i	−0.988107	−	0.153765i	$-0.950860\pi$
$73$	−10.4594	+	6.98874i	−1.22418	+	0.817970i	−0.236072	+	0.971736i	$0.575860\pi$
$74$	−3.39901	+	0.676105i	−0.395127	+	0.0785956i
$75$	−7.32431	−	1.45186i	−0.845738	−	0.167646i
$76$	−0.0387851	+	0.0936354i	−0.00444895	+	0.0107407i
$77$	1.36006	−	3.28348i	0.154994	−	0.374187i
$78$	10.9277	+	2.16613i	1.23732	+	0.245266i
$79$	−5.84360	+	1.16236i	−0.657456	+	0.130776i	−0.512534	−	0.858667i	$-0.671293\pi$
$79$	−5.84360	+	1.16236i	−0.657456	+	0.130776i	−0.144922	+	0.989443i	$0.546293\pi$
$80$	−10.7092	+	7.15567i	−1.19733	+	0.800028i
$81$	6.34708	−	6.38079i	0.705232	−	0.708977i
$82$	4.39502	+	0.874225i	0.485349	+	0.0965420i
$83$	11.9985	−	4.96993i	1.31700	−	0.545521i	0.390084	−	0.920779i	$-0.372446\pi$
$83$	11.9985	−	4.96993i	1.31700	−	0.545521i	0.926920	+	0.375258i	$0.122446\pi$
$84$	−0.168074	−	0.405009i	−0.0183384	−	0.0441901i
$85$		0			0
$86$		−	16.6560i		−	1.79606i
$87$	9.79395	+	9.78099i	1.05002	+	1.04863i
$88$	0.880669	−	4.42742i	0.0938796	−	0.471965i
$89$	−3.42023	−	3.42023i	−0.362544	−	0.362544i	0.502205	−	0.864749i	$-0.332522\pi$
$89$	−3.42023	−	3.42023i	−0.362544	−	0.362544i	−0.864749	+	0.502205i	$0.832522\pi$
$90$	2.58139	−	13.0679i	0.272102	−	1.37748i
$91$	−1.85984	−	9.35006i	−0.194964	−	0.980152i
$92$	−0.0499925	+	0.0748190i	−0.00521208	+	0.00780042i
$93$	0.00331239	+	5.00297i	0.000343479	+	0.518783i
$94$	4.20619	+	1.74226i	0.433836	+	0.179701i
$95$	2.19061	+	1.46372i	0.224752	+	0.150174i
$96$	−0.638789	−	0.954647i	−0.0651962	−	0.0974333i
$97$	−1.97085	−	2.94959i	−0.200110	−	0.299486i	0.717820	−	0.696229i	$-0.245140\pi$
$97$	−1.97085	−	2.94959i	−0.200110	−	0.299486i	−0.917929	+	0.396744i	$0.870140\pi$
$98$	2.41627	−	2.41627i	0.244080	−	0.244080i
$99$	2.75191	+	4.10675i	0.276578	+	0.412744i
$100$	−0.193650	−	0.467514i	−0.0193650	−	0.0467514i
$101$	−3.73948			−0.372092			−0.186046	−	0.982541i	$-0.559567\pi$
$101$	−3.73948			−0.372092			−0.186046	+	0.982541i	$0.559567\pi$
$102$		0			0
$103$	9.33404			0.919710			0.459855	−	0.887994i	$-0.347901\pi$
$103$	9.33404			0.919710			0.459855	+	0.887994i	$0.347901\pi$
$104$	−4.63380	−	11.1870i	−0.454382	−	1.09698i
$105$	−11.1784	+	2.23121i	−1.09090	+	0.217744i
$106$	6.55268	−	6.55268i	0.636453	−	0.636453i
$107$	−1.05001	−	1.57145i	−0.101508	−	0.151918i	0.777239	−	0.629206i	$-0.216620\pi$
$107$	−1.05001	−	1.57145i	−0.101508	−	0.151918i	−0.878747	+	0.477288i	$0.841620\pi$
$108$	0.598453	+	0.117805i	0.0575862	+	0.0113357i
$109$	−3.49469	−	2.33508i	−0.334730	−	0.223660i	0.376834	−	0.926281i	$-0.377013\pi$
$109$	−3.49469	−	2.33508i	−0.334730	−	0.223660i	−0.711564	+	0.702621i	$0.752013\pi$
$110$	6.75970	+	2.79996i	0.644513	+	0.266966i
$111$	−4.12515	+	0.00273120i	−0.391542	+	0.000259234i
$112$	−5.05774	+	7.56945i	−0.477912	+	0.715246i
$113$	3.21617	+	16.1688i	0.302552	+	1.52103i	0.770595	+	0.637325i	$0.219959\pi$
$113$	3.21617	+	16.1688i	0.302552	+	1.52103i	−0.468043	+	0.883705i	$0.655041\pi$
$114$	−1.20778	+	1.81017i	−0.113119	+	0.169538i
$115$	1.65403	+	1.65403i	0.154239	+	0.154239i
$116$	−0.183006	+	0.920032i	−0.0169917	+	0.0854228i
$117$	12.2577	+	5.05832i	1.13323	+	0.467642i
$118$		−	8.86518i		−	0.816106i
$119$		0			0
$120$	−13.3726	+	5.54949i	−1.22075	+	0.506597i
$121$	7.65399	−	3.17039i	0.695817	−	0.288217i
$122$	−8.34401	−	1.65973i	−0.755431	−	0.150265i
$123$	4.92927	+	2.03795i	0.444457	+	0.183756i
$124$	−0.281914	+	0.188369i	−0.0253167	+	0.0169161i
$125$	2.06210	−	0.410177i	0.184440	−	0.0366873i
$126$	−1.84902	−	9.23175i	−0.164724	−	0.822430i
$127$	4.71179	−	11.3753i	0.418104	−	1.00939i	−0.564792	−	0.825233i	$-0.691044\pi$
$127$	4.71179	−	11.3753i	0.418104	−	1.00939i	0.982896	−	0.184159i	$-0.0589563\pi$
$128$	−4.67113	+	11.2771i	−0.412874	+	0.996766i
$129$	3.85495	−	19.4474i	0.339410	−	1.71225i
$130$	19.2490	−	3.82886i	1.68825	−	0.335813i
$131$	2.93217	−	1.95921i	0.256185	−	0.171177i	−0.420846	−	0.907132i	$-0.638267\pi$
$131$	2.93217	−	1.95921i	0.256185	−	0.171177i	0.677030	+	0.735955i	$0.263267\pi$
$132$	−0.128004	+	0.309609i	−0.0111413	+	0.0269480i
$133$	1.82641	+	0.363296i	0.158370	+	0.0315018i
$134$	−9.67240	+	4.00644i	−0.835568	+	0.346103i
$135$	6.03852	−	14.6606i	0.519713	−	1.26178i
$136$		0			0
$137$			14.6484i			1.25150i	0.780025	+	0.625748i	$0.215206\pi$
$137$			14.6484i			1.25150i	−0.780025	+	0.625748i	$0.784794\pi$
$138$	−1.36527	+	1.36708i	−0.116220	+	0.116374i
$139$	−0.984156	+	4.94769i	−0.0834750	+	0.419657i	0.916340	+	0.400402i	$0.131130\pi$
$139$	−0.984156	+	4.94769i	−0.0834750	+	0.419657i	−0.999815	+	0.0192553i	$0.993870\pi$
$140$	−0.546249	−	0.546249i	−0.0461664	−	0.0461664i
$141$	4.50789	+	3.00776i	0.379633	+	0.253299i
$142$	0.617296	+	3.10335i	0.0518023	+	0.260428i
$143$	−4.04660	+	6.05617i	−0.338394	+	0.506442i
$144$	−4.86139	−	11.6926i	−0.405116	−	0.974385i
$145$	22.5288	+	9.33173i	1.87091	+	0.774958i
$146$	−15.2197	−	10.1695i	−1.25959	−	0.841632i
$147$	3.38046	−	2.26199i	0.278816	−	0.186566i
$148$	−0.155318	−	0.232450i	−0.0127671	−	0.0191073i
$149$	−4.44785	+	4.44785i	−0.364382	+	0.364382i	−0.865423	−	0.501041i	$-0.832950\pi$
$149$	−4.44785	+	4.44785i	−0.364382	+	0.364382i	0.501041	+	0.865423i	$0.332950\pi$
$150$	−2.12674	−	10.6550i	−0.173647	−	0.869974i
$151$	−5.82179	−	14.0551i	−0.473771	−	1.14378i	−0.962484	−	0.271339i	$-0.912533\pi$
$151$	−5.82179	−	14.0551i	−0.473771	−	1.14378i	0.488713	−	0.872445i	$-0.337467\pi$
$152$	2.36528			0.191850
$153$		0			0
$154$	5.17153			0.416734
$155$	3.37291	+	8.14291i	0.270918	+	0.654055i
$156$	0.175906	+	0.881287i	0.0140837	+	0.0705594i
$157$	−1.74527	+	1.74527i	−0.139287	+	0.139287i	−0.773312	−	0.634025i	$-0.781402\pi$
$157$	−1.74527	+	1.74527i	−0.139287	+	0.139287i	0.634025	+	0.773312i	$0.281402\pi$
$158$	−4.81665	−	7.20863i	−0.383192	−	0.573488i
$159$	9.16747	−	6.13429i	0.727027	−	0.486481i
$160$	−1.68257	−	1.12425i	−0.133018	−	0.0888801i
$161$	1.52750	+	0.632711i	0.120384	+	0.0498646i
$162$	12.1125	+	4.97960i	0.951644	+	0.391235i
$163$	−0.617171	+	0.923662i	−0.0483406	+	0.0723468i	−0.854853	−	0.518871i	$-0.826353\pi$
$163$	−0.617171	+	0.923662i	−0.0483406	+	0.0723468i	0.806512	+	0.591218i	$0.201353\pi$
$164$	0.0705224	+	0.354540i	0.00550688	+	0.0276849i
$165$	7.24455	+	4.83372i	0.563988	+	0.376305i
$166$	13.3627	+	13.3627i	1.03715	+	1.03715i
$167$	−3.87453	+	19.4786i	−0.299820	+	1.50730i	0.477747	+	0.878497i	$0.341453\pi$
$167$	−3.87453	+	19.4786i	−0.299820	+	1.50730i	−0.777567	+	0.628800i	$0.783547\pi$
$168$	−7.23142	+	7.24100i	−0.557916	+	0.558655i
$169$			6.53766i			0.502897i
$170$		0			0
$171$	−1.82916	+	1.83401i	−0.139879	+	0.140250i
$172$	1.24134	−	0.514179i	0.0946511	−	0.0392058i
$173$	11.4127	+	2.27012i	0.867689	+	0.172594i	0.608811	−	0.793316i	$-0.291647\pi$
$173$	11.4127	+	2.27012i	0.867689	+	0.172594i	0.258879	+	0.965910i	$0.416647\pi$
$174$	−7.69538	+	18.6131i	−0.583385	+	1.41106i
$175$	−7.73082	+	5.16557i	−0.584395	+	0.390480i
$176$	6.82187	−	1.35695i	0.514217	−	0.102284i
$177$	2.05181	−	10.3509i	0.154223	−	0.778024i
$178$	2.69345	−	6.50257i	0.201883	−	0.487389i
$179$	−0.324004	+	0.782216i	−0.0242172	+	0.0584656i	−0.935526	−	0.353259i	$-0.885073\pi$
$179$	−0.324004	+	0.782216i	−0.0242172	+	0.0584656i	0.911308	+	0.411725i	$0.135073\pi$
$180$	1.05361	−	0.211028i	0.0785318	−	0.0157291i
$181$	−1.40629	+	0.279729i	−0.104529	+	0.0207921i	−0.247078	−	0.968996i	$-0.579470\pi$
$181$	−1.40629	+	0.279729i	−0.104529	+	0.0207921i	0.142549	+	0.989788i	$0.454470\pi$
$182$	11.5342	−	7.70689i	0.854970	−	0.571272i
$183$	−9.35828	−	3.86907i	−0.691784	−	0.286010i
$184$	2.05967	+	0.409694i	0.151841	+	0.0302030i
$185$	−6.71416	+	2.78110i	−0.493635	+	0.204470i
$186$	−6.72393	+	2.79036i	−0.493023	+	0.204599i
$187$		0			0
$188$			0.367264i			0.0267855i
$189$	−0.0222598	−	11.2069i	−0.00161916	−	0.815181i
$190$	−0.747918	+	3.76004i	−0.0542596	+	0.272782i
$191$	−0.509849	−	0.509849i	−0.0368914	−	0.0368914i	0.688420	−	0.725312i	$-0.258304\pi$
$191$	−0.509849	−	0.509849i	−0.0368914	−	0.0368914i	−0.725312	+	0.688420i	$0.758304\pi$
$192$	−7.18778	+	10.7727i	−0.518733	+	0.777453i
$193$	−2.26724	−	11.3982i	−0.163200	−	0.820460i	−0.972471	−	0.233025i	$-0.925138\pi$
$193$	−2.26724	−	11.3982i	−0.163200	−	0.820460i	0.809271	−	0.587435i	$-0.199862\pi$
$194$	2.86783	−	4.29202i	0.205898	−	0.308149i
$195$	23.3612	−	0.0154671i	1.67293	−	0.00110762i
$196$	0.254671	+	0.105488i	0.0181908	+	0.00753488i
$197$	19.3433	+	12.9248i	1.37815	+	0.920852i	0.999988	−	0.00488610i	$-0.00155530\pi$
$197$	19.3433	+	12.9248i	1.37815	+	0.920852i	0.378165	+	0.925738i	$0.376555\pi$
$198$	−3.98853	+	5.98641i	−0.283453	+	0.425435i
$199$	13.3975	+	20.0507i	0.949720	+	1.42136i	0.906459	+	0.422293i	$0.138775\pi$
$199$	13.3975	+	20.0507i	0.949720	+	1.42136i	0.0432612	+	0.999064i	$0.486225\pi$
$200$	−8.35068	+	8.35068i	−0.590482	+	0.590482i
$201$	−12.2207	+	2.43926i	−0.861982	+	0.172052i
$202$	−2.08233	−	5.02720i	−0.146512	−	0.353712i
$203$	17.2357			1.20971
$204$		0			0
$205$	9.39691			0.656309
$206$	5.19767	+	12.5483i	0.362139	+	0.874281i
$207$	−1.91049	+	1.28021i	−0.132788	+	0.0889808i
$208$	13.1927	−	13.1927i	0.914753	−	0.914753i
$209$	−0.790451	−	1.18299i	−0.0546767	−	0.0818294i
$210$	−9.22424	−	13.7853i	−0.636533	−	0.951275i
$211$	−12.9792	−	8.67243i	−0.893525	−	0.597035i	0.0217944	−	0.999762i	$-0.493062\pi$
$211$	−12.9792	−	8.67243i	−0.893525	−	0.597035i	−0.915320	+	0.402728i	$0.868062\pi$
$212$	0.690643	+	0.286074i	0.0474336	+	0.0196476i
$213$	0.00249363	+	3.76633i	0.000170861	+	0.258065i
$214$	1.52789	−	2.28665i	0.104444	−	0.156312i
$215$	−6.81403	−	34.2564i	−0.464713	−	2.33627i
$216$	−2.80475	−	13.9555i	−0.190839	−	0.949551i
$217$	4.40510	+	4.40510i	0.299038	+	0.299038i
$218$	1.19316	−	5.99840i	0.0808107	−	0.406263i
$219$	−15.4168	−	15.3964i	−1.04177	−	1.04039i
$220$			0.590224i			0.0397929i
$221$		0			0
$222$	−2.30077	−	5.54415i	−0.154417	−	0.372099i
$223$	−2.24695	+	0.930718i	−0.150467	+	0.0623255i	−0.456646	−	0.889648i	$-0.650949\pi$
$223$	−2.24695	+	0.930718i	−0.150467	+	0.0623255i	0.306179	+	0.951974i	$0.400949\pi$
$224$	−1.40283	−	0.279041i	−0.0937307	−	0.0186442i
$225$	−0.0171254	−	12.9329i	−0.00114169	−	0.862193i
$226$	−19.9457	+	13.3273i	−1.32677	+	0.886518i
$227$	−1.37743	+	0.273987i	−0.0914231	+	0.0181852i	−0.240590	−	0.970627i	$-0.577341\pi$
$227$	−1.37743	+	0.273987i	−0.0914231	+	0.0181852i	0.149167	+	0.988812i	$0.452341\pi$
$228$	−0.172193	−	0.0341329i	−0.0114038	−	0.00226051i
$229$	−4.16234	+	10.0488i	−0.275055	+	0.664043i	−0.999685	−	0.0250960i	$-0.992011\pi$
$229$	−4.16234	+	10.0488i	−0.275055	+	0.664043i	0.724630	+	0.689139i	$0.242011\pi$
$230$	−1.30256	+	3.14466i	−0.0858884	+	0.207353i
$231$	6.03825	+	1.19693i	0.397287	+	0.0787520i
$232$	21.4714	−	4.27093i	1.40967	−	0.280400i
$233$	−11.9201	+	7.96478i	−0.780914	+	0.521790i	−0.880959	−	0.473193i	$-0.843101\pi$
$233$	−11.9201	+	7.96478i	−0.780914	+	0.521790i	0.100045	+	0.994983i	$0.468101\pi$
$234$	0.0255506	+	19.2955i	0.00167030	+	1.26139i
$235$	9.36366	+	1.86255i	0.610818	+	0.121499i
$236$	0.660704	−	0.273673i	0.0430082	−	0.0178146i
$237$	−3.95549	−	9.53155i	−0.256937	−	0.619140i
$238$		0			0
$239$		−	23.7093i		−	1.53362i	−0.641872	−	0.766812i	$-0.721842\pi$
$239$		−	23.7093i		−	1.53362i	0.641872	−	0.766812i	$-0.278158\pi$
$240$	−15.7850	−	15.7641i	−1.01892	−	1.01757i
$241$	0.549058	−	2.76030i	0.0353679	−	0.177807i	−0.959064	−	0.283191i	$-0.908607\pi$
$241$	0.549058	−	2.76030i	0.0353679	−	0.177807i	0.994432	+	0.105384i	$0.0336071\pi$
$242$	8.52427	+	8.52427i	0.547961	+	0.547961i
$243$	12.9899	+	8.61753i	0.833304	+	0.552815i
$244$	−0.133888	−	0.673099i	−0.00857128	−	0.0430908i
$245$	3.98105	−	5.95806i	0.254340	−	0.380646i
$246$	0.00513881	+	7.76154i	0.000327638	+	0.494858i
$247$	−3.52592	−	1.46048i	−0.224349	−	0.0929284i
$248$	6.57923	+	4.39610i	0.417782	+	0.279153i
$249$	12.5095	+	18.6950i	0.792758	+	1.18475i
$250$	1.69971	+	2.54379i	0.107499	+	0.160883i
$251$	−10.7058	+	10.7058i	−0.675745	+	0.675745i	−0.959034	−	0.283289i	$-0.908574\pi$
$251$	−10.7058	+	10.7058i	−0.675745	+	0.675745i	0.283289	+	0.959034i	$0.408574\pi$
$252$	0.630944	−	0.422793i	0.0397457	−	0.0266334i
$253$	−0.483411	−	1.16706i	−0.0303918	−	0.0733723i
$254$	17.9162			1.12416
$255$		0			0
$256$	−2.80767			−0.175479
$257$	7.61319	+	18.3799i	0.474898	+	1.14650i	0.961973	+	0.273145i	$0.0880637\pi$
$257$	7.61319	+	18.3799i	0.474898	+	1.14650i	−0.487075	+	0.873360i	$0.661936\pi$
$258$	28.2910	−	5.64690i	1.76132	−	0.351561i
$259$	−3.63218	+	3.63218i	−0.225693	+	0.225693i
$260$	0.879583	+	1.31639i	0.0545494	+	0.0816389i
$261$	−13.2930	+	19.9515i	−0.822817	+	1.23497i
$262$	4.26667	+	2.85090i	0.263596	+	0.176129i
$263$	0.121128	+	0.0501727i	0.00746905	+	0.00309378i	0.386415	−	0.922325i	$-0.373713\pi$
$263$	0.121128	+	0.0501727i	0.00746905	+	0.00309378i	−0.378946	+	0.925419i	$0.623713\pi$
$264$	7.81875	−	0.00517669i	0.481211	−	0.000318603i
$265$	10.7962	−	16.1577i	0.663205	−	0.992557i
$266$	0.528640	+	2.65765i	0.0324130	+	0.162951i
$267$	4.64985	−	6.96898i	0.284566	−	0.426495i
$268$	−0.597184	−	0.597184i	−0.0364788	−	0.0364788i
$269$	1.15992	−	5.83131i	0.0707216	−	0.355541i	−0.929179	−	0.369630i	$-0.879485\pi$
$269$	1.15992	−	5.83131i	0.0707216	−	0.355541i	0.999901	+	0.0140883i	$0.00448458\pi$
$270$	23.0716	−	0.0458262i	1.40409	−	0.00278890i
$271$		−	6.87483i		−	0.417616i	−0.977957	−	0.208808i	$-0.933042\pi$
$271$		−	6.87483i		−	0.417616i	0.977957	−	0.208808i	$-0.0669584\pi$
$272$		0			0
$273$	15.2510	−	6.32899i	0.923030	−	0.383048i
$274$	−19.6927	+	8.15697i	−1.18968	+	0.492781i
$275$	6.96730	+	1.38588i	0.420144	+	0.0835718i
$276$	−0.144033	−	0.0595485i	−0.00866974	−	0.00358440i
$277$	6.89904	−	4.60979i	0.414523	−	0.276975i	−0.330771	−	0.943711i	$-0.607309\pi$
$277$	6.89904	−	4.60979i	0.414523	−	0.276975i	0.745294	+	0.666736i	$0.232309\pi$
$278$	−7.19949	+	1.43207i	−0.431797	+	0.0858897i
$279$	−8.49665	+	1.70179i	−0.508681	+	0.101883i
$280$	−6.89927	+	16.6563i	−0.412310	+	0.995404i
$281$	−5.07041	+	12.2411i	−0.302475	+	0.730240i	0.697432	+	0.716651i	$0.254326\pi$
$281$	−5.07041	+	12.2411i	−0.302475	+	0.730240i	−0.999908	+	0.0135893i	$0.995674\pi$
$282$	−1.53328	+	7.73509i	−0.0913056	+	0.460618i
$283$	−13.7634	+	2.73771i	−0.818149	+	0.162740i	−0.586385	−	0.810032i	$-0.699450\pi$
$283$	−13.7634	+	2.73771i	−0.818149	+	0.162740i	−0.231763	+	0.972772i	$0.574450\pi$
$284$	−0.212231	+	0.141808i	−0.0125936	+	0.00841475i
$285$	−1.74351	+	4.21709i	−0.103276	+	0.249799i
$286$	−10.3950	−	2.06770i	−0.614670	−	0.122266i
$287$	6.13631	−	2.54174i	0.362215	−	0.150034i
$288$	1.40494	−	1.40867i	0.0827870	−	0.0830066i
$289$		0			0
$290$			35.4832i			2.08364i
$291$	4.34183	−	4.34759i	0.254523	−	0.254860i
$292$	0.288071	−	1.44823i	0.0168581	−	0.0847513i
$293$	18.6721	+	18.6721i	1.09083	+	1.09083i	0.995440	+	0.0953949i	$0.0304114\pi$
$293$	18.6721	+	18.6721i	1.09083	+	1.09083i	0.0953949	+	0.995440i	$0.469589\pi$
$294$	4.92334	+	3.28496i	0.287135	+	0.191583i
$295$	−3.62678	−	18.2331i	−0.211159	−	1.06157i
$296$	−3.62476	+	5.42484i	−0.210685	+	0.315312i
$297$	−6.04252	+	6.06657i	−0.350622	+	0.352018i
$298$	−8.45629	−	3.50271i	−0.489860	−	0.202907i
$299$	−2.81737	−	1.88251i	−0.162933	−	0.108868i
$300$	0.728440	−	0.487426i	0.0420565	−	0.0281415i
$301$	−13.7156	−	20.5268i	−0.790552	−	1.18315i
$302$	15.6531	−	15.6531i	0.900738	−	0.900738i
$303$	−1.26780	−	6.35167i	−0.0728331	−	0.364894i
$304$	1.39468	+	3.36705i	0.0799904	+	0.193114i
$305$	−17.8402			−1.02152
$306$		0			0
$307$	−24.4315			−1.39438			−0.697189	−	0.716887i	$-0.745566\pi$
$307$	−24.4315			−1.39438			−0.697189	+	0.716887i	$0.745566\pi$
$308$	0.159648	+	0.385424i	0.00909677	+	0.0219616i
$309$	3.16453	+	15.8543i	0.180024	+	0.901919i
$310$	−9.06879	+	9.06879i	−0.515073	+	0.515073i
$311$	−12.9649	−	19.4033i	−0.735169	−	1.10026i	−0.991042	−	0.133548i	$-0.957363\pi$
$311$	−12.9649	−	19.4033i	−0.735169	−	1.10026i	0.255873	−	0.966710i	$-0.417637\pi$
$312$	17.4306	−	11.6635i	0.986814	−	0.660314i
$313$	−1.34251	−	0.897040i	−0.0758834	−	0.0507037i	0.517050	−	0.855955i	$-0.327030\pi$
$313$	−1.34251	−	0.897040i	−0.0758834	−	0.0507037i	−0.592933	+	0.805252i	$0.702030\pi$
$314$	−3.31812	−	1.37441i	−0.187252	−	0.0775624i
$315$	−7.57963	−	18.2305i	−0.427064	−	1.02717i
$316$	0.388552	−	0.581510i	0.0218578	−	0.0327125i
$317$	−4.75728	−	23.9165i	−0.267195	−	1.34328i	−0.848327	−	0.529472i	$-0.822390\pi$
$317$	−4.75728	−	23.9165i	−0.267195	−	1.34328i	0.581132	−	0.813809i	$-0.302610\pi$
$318$	13.3516	+	8.90847i	0.748720	+	0.499562i
$319$	−9.31162	−	9.31162i	−0.521351	−	0.521351i
$320$	−4.45101	+	22.3768i	−0.248819	+	1.25090i
$321$	2.31319	−	2.31626i	0.129110	−	0.129281i
$322$			2.40583i			0.134072i
$323$		0			0
$324$	0.00279782	+	1.05644i	0.000155435	+	0.0586911i
$325$	17.6046	−	7.29207i	0.976529	−	0.404491i
$326$	−1.58540	−	0.315357i	−0.0878074	−	0.0174660i
$327$	2.78143	−	6.72755i	0.153813	−	0.372034i
$328$	7.01448	−	4.68693i	0.387310	−	0.258792i
$329$	6.61839	−	1.31648i	0.364883	−	0.0725798i
$330$	−2.46411	+	12.4309i	−0.135645	+	0.684301i
$331$	11.6584	−	28.1459i	0.640804	−	1.54704i	−0.184793	−	0.982777i	$-0.559161\pi$
$331$	11.6584	−	28.1459i	0.640804	−	1.54704i	0.825597	−	0.564260i	$-0.190839\pi$
$332$	−0.583384	+	1.40841i	−0.0320173	+	0.0772967i
$333$	−1.40319	−	7.00582i	−0.0768944	−	0.383917i
$334$	−28.3437	+	5.63791i	−1.55090	+	0.308493i
$335$	−18.2542	+	12.1971i	−0.997334	+	0.666397i
$336$	−14.5718	−	6.02453i	−0.794956	−	0.328665i
$337$	−16.8950	−	3.36062i	−0.920329	−	0.183065i	−0.287880	−	0.957667i	$-0.592950\pi$
$337$	−16.8950	−	3.36062i	−0.920329	−	0.183065i	−0.632449	+	0.774602i	$0.717950\pi$
$338$	−8.78896	+	3.64051i	−0.478057	+	0.198018i
$339$	−26.3730	+	10.9445i	−1.43239	+	0.594425i
$340$		0			0
$341$		−	4.75973i		−	0.257754i
$342$	−3.48413	−	1.43777i	−0.188400	−	0.0777459i
$343$	3.93346	−	19.7748i	0.212387	−	1.06774i
$344$	−22.1727	−	22.1727i	−1.19547	−	1.19547i
$345$	−2.24868	+	3.37022i	−0.121065	+	0.181447i
$346$	3.30331	+	16.6068i	0.177587	+	0.892789i
$347$	11.2418	−	16.8245i	0.603491	−	0.903188i	−0.396398	−	0.918079i	$-0.629740\pi$
$347$	11.2418	−	16.8245i	0.603491	−	0.903188i	0.999889	+	0.0148907i	$0.00474004\pi$
$348$	−1.62476	+	0.00107573i	−0.0870963	+	5.76652e-5i
$349$	7.02410	+	2.90948i	0.375992	+	0.155741i	0.562673	−	0.826680i	$-0.309773\pi$
$349$	7.02410	+	2.90948i	0.375992	+	0.155741i	−0.186681	+	0.982421i	$0.559773\pi$
$350$	−11.2493	−	7.51653i	−0.601300	−	0.401776i
$351$	−4.43603	+	22.5353i	−0.236778	+	1.20284i
$352$	0.607131	+	0.908636i	0.0323602	+	0.0484304i
$353$	8.44344	−	8.44344i	0.449399	−	0.449399i	−0.445756	−	0.895155i	$-0.647065\pi$
$353$	8.44344	−	8.44344i	0.449399	−	0.449399i	0.895155	+	0.445756i	$0.147065\pi$
$354$	15.0579	−	3.00557i	0.800319	−	0.159744i
$355$	2.53919	+	6.13014i	0.134766	+	0.325354i
$356$	0.567772			0.0300919
$357$		0			0
$358$	−1.23200			−0.0651133
$359$	−8.80076	−	21.2469i	−0.464487	−	1.12137i	−0.966536	−	0.256531i	$-0.917420\pi$
$359$	−8.80076	−	21.2469i	−0.464487	−	1.12137i	0.502049	−	0.864839i	$-0.332580\pi$
$360$	−13.9598	−	20.8325i	−0.735746	−	1.09797i
$361$	−12.9079	+	12.9079i	−0.679363	+	0.679363i
$362$	−1.15915	−	1.73479i	−0.0609236	−	0.0911786i
$363$	7.97999	+	11.9258i	0.418841	+	0.625942i
$364$	0.930445	+	0.621703i	0.0487685	+	0.0325861i
$365$	−35.4628	−	14.6892i	−1.85621	−	0.768866i
$366$	−0.00975609	−	14.7354i	−0.000509959	−	0.770231i
$367$	−9.11720	+	13.6449i	−0.475914	+	0.712256i	−0.989299	−	0.145903i	$-0.953391\pi$
$367$	−9.11720	+	13.6449i	−0.475914	+	0.712256i	0.513385	+	0.858159i	$0.328391\pi$
$368$	0.631265	+	3.17358i	0.0329070	+	0.165434i
$369$	−1.79037	+	9.06352i	−0.0932031	+	0.471828i
$370$	−7.47758	−	7.47758i	−0.388741	−	0.388741i
$371$	2.67963	−	13.4714i	0.139119	−	0.699400i
$372$	−0.415531	−	0.414982i	−0.0215443	−	0.0215158i
$373$			1.61824i			0.0837894i	0.999122	+	0.0418947i	$0.0133394\pi$
$373$			1.61824i			0.0837894i	−0.999122	+	0.0418947i	$0.986661\pi$
$374$		0			0
$375$	1.39582	+	3.36351i	0.0720798	+	0.173691i
$376$	7.91865	−	3.28001i	0.408373	−	0.169154i
$377$	−34.6446	−	6.89124i	−1.78429	−	0.354917i
$378$	15.0537	−	6.27050i	0.774278	−	0.322520i
$379$	12.9123	−	8.62771i	0.663260	−	0.443176i	−0.177838	−	0.984060i	$-0.556910\pi$
$379$	12.9123	−	8.62771i	0.663260	−	0.443176i	0.841097	+	0.540884i	$0.181910\pi$
$380$	−0.303317	+	0.0603334i	−0.0155598	+	0.00309504i
$381$	20.9189	+	4.14663i	1.07171	+	0.212438i
$382$	0.401510	−	0.969330i	0.0205430	−	0.0495952i
$383$	8.47433	−	20.4588i	0.433018	−	1.04540i	−0.545291	−	0.838247i	$-0.683581\pi$
$383$	8.47433	−	20.4588i	0.433018	−	1.04540i	0.978309	−	0.207151i	$-0.0664191\pi$
$384$	−20.7384	−	4.11084i	−1.05830	−	0.209781i
$385$	10.6363	−	2.11569i	0.542076	−	0.107826i
$386$	14.0607	−	9.39509i	0.715673	−	0.478197i
$387$	34.3393	−	0.0454712i	1.74557	−	0.00231143i
$388$	0.408407	+	0.0812372i	0.0207337	+	0.00412419i
$389$	−14.0162	+	5.80572i	−0.710652	+	0.294362i	−0.708574	−	0.705636i	$-0.750661\pi$
$389$	−14.0162	+	5.80572i	−0.710652	+	0.294362i	−0.00207747	+	0.999998i	$0.500661\pi$
$390$	13.0295	+	31.3972i	0.659774	+	1.58986i
$391$		0			0
$392$		−	6.43314i		−	0.324922i
$393$	4.32191	+	4.31619i	0.218011	+	0.217723i
$394$	−6.60419	+	33.2015i	−0.332714	+	1.67267i
$395$	−12.8555	−	12.8555i	−0.646831	−	0.646831i
$396$	−0.569283	−	0.112454i	−0.0286076	−	0.00565103i
$397$	7.34266	+	36.9140i	0.368517	+	1.85266i	0.506518	+	0.862230i	$0.330932\pi$
$397$	7.34266	+	36.9140i	0.368517	+	1.85266i	−0.138000	+	0.990432i	$0.544068\pi$
$398$	−19.4949	+	29.1762i	−0.977193	+	1.46247i
$399$	0.00213550	+	3.22541i	0.000106909	+	0.161473i
$400$	−16.8114	−	6.96352i	−0.840571	−	0.348176i
$401$	−2.93829	−	1.96330i	−0.146731	−	0.0980426i	0.480038	−	0.877248i	$-0.340623\pi$
$401$	−2.93829	−	1.96330i	−0.146731	−	0.0980426i	−0.626769	+	0.779205i	$0.715623\pi$
$402$	−10.0844	−	15.0707i	−0.502962	−	0.751658i
$403$	−7.09320	−	10.6157i	−0.353338	−	0.528807i
$404$	0.310384	−	0.310384i	0.0154422	−	0.0154422i
$405$	26.9489	+	5.28632i	1.33910	+	0.262679i
$406$	9.59773	+	23.1710i	0.476327	+	1.14996i
$407$	3.92459			0.194535
$408$		0			0
$409$	12.2079			0.603641			0.301820	−	0.953365i	$-0.402406\pi$
$409$	12.2079			0.603641			0.301820	+	0.953365i	$0.402406\pi$
$410$	5.23268	+	12.6328i	0.258424	+	0.623890i
$411$	−24.8810	+	4.96626i	−1.22729	+	0.244967i
$412$	−0.774744	+	0.774744i	−0.0381689	+	0.0381689i
$413$	−7.30014	−	10.9254i	−0.359216	−	0.537605i
$414$	−2.78492	−	1.85550i	−0.136871	−	0.0911926i
$415$	32.9499	+	22.0164i	1.61745	+	1.08074i
$416$	2.70819	+	1.12177i	0.132780	+	0.0549993i
$417$	−8.73753	+	0.00578500i	−0.427879	+	0.000283293i
$418$	1.15020	−	1.72140i	0.0562583	−	0.0841965i
$419$	6.12442	+	30.7895i	0.299198	+	1.50417i	0.779130	+	0.626862i	$0.215661\pi$
$419$	6.12442	+	30.7895i	0.299198	+	1.50417i	−0.479933	+	0.877305i	$0.659339\pi$
$420$	0.742633	−	1.11302i	0.0362368	−	0.0543100i
$421$	−10.7245	−	10.7245i	−0.522682	−	0.522682i	0.395699	−	0.918380i	$-0.370502\pi$
$421$	−10.7245	−	10.7245i	−0.522682	−	0.522682i	−0.918380	+	0.395699i	$0.870502\pi$
$422$	4.43136	−	22.2780i	0.215715	−	1.08447i
$423$	−3.58050	+	8.67658i	−0.174090	+	0.421870i
$424$		−	17.4460i		−	0.847253i
$425$		0			0
$426$	−5.06191	+	2.10064i	−0.245250	+	0.101776i
$427$	−11.6499	+	4.82553i	−0.563776	+	0.233524i
$428$	0.217586	+	0.0432806i	0.0105174	+	0.00209205i
$429$	−11.6586	−	4.82011i	−0.562883	−	0.232717i
$430$	42.2585	−	28.2362i	2.03789	−	1.36167i
$431$	−11.2336	+	2.23450i	−0.541102	+	0.107632i	−0.458072	−	0.888915i	$-0.651460\pi$
$431$	−11.2336	+	2.23450i	−0.541102	+	0.107632i	−0.0830303	+	0.996547i	$0.526460\pi$
$432$	18.2123	−	12.2215i	0.876239	−	0.588005i
$433$	−10.2528	+	24.7526i	−0.492720	+	1.18953i	0.460610	+	0.887603i	$0.347631\pi$
$433$	−10.2528	+	24.7526i	−0.492720	+	1.18953i	−0.953330	+	0.301930i	$0.902369\pi$
$434$	−3.46905	+	8.37502i	−0.166520	+	0.402014i
$435$	−8.21241	+	41.4299i	−0.393755	+	1.98641i
$436$	0.483882	−	0.0962502i	0.0231738	−	0.00460955i
$437$	0.550338	−	0.367724i	0.0263262	−	0.0175906i
$438$	12.1134	−	29.2991i	0.578799	−	1.39997i
$439$	8.36252	+	1.66341i	0.399121	+	0.0793902i	0.390570	−	0.920573i	$-0.372278\pi$
$439$	8.36252	+	1.66341i	0.399121	+	0.0793902i	0.00855138	+	0.999963i	$0.497278\pi$
$440$	12.7259	−	5.27126i	0.606685	−	0.251297i
$441$	4.98817	+	4.97498i	0.237532	+	0.236904i
$442$		0			0
$443$		−	18.8773i		−	0.896886i	−0.893811	−	0.448443i	$-0.851979\pi$
$443$		−	18.8773i		−	0.896886i	0.893811	−	0.448443i	$-0.148021\pi$
$444$	0.342169	−	0.342622i	0.0162386	−	0.0162601i
$445$	2.87941	−	14.4758i	0.136497	−	0.686217i
$446$	−2.50244	−	2.50244i	−0.118494	−	0.118494i
$447$	−9.06283	−	6.04691i	−0.428657	−	0.286009i
$448$	3.14605	+	15.8163i	0.148637	+	0.747248i
$449$	−15.1475	+	22.6698i	−0.714853	+	1.06985i	0.279123	+	0.960255i	$0.409956\pi$
$449$	−15.1475	+	22.6698i	−0.714853	+	1.06985i	−0.993976	+	0.109598i	$0.965044\pi$
$450$	17.3769	−	7.22473i	0.819156	−	0.340577i
$451$	−4.68833	−	1.94197i	−0.220765	−	0.0914438i
$452$	−1.60899	−	1.07509i	−0.0756805	−	0.0505681i
$453$	21.8994	−	14.6537i	1.02892	−	0.688490i
$454$	−1.13536	−	1.69919i	−0.0532851	−	0.0797468i
$455$	20.5695	−	20.5695i	0.964311	−	0.964311i
$456$	0.801903	+	4.01754i	0.0375526	+	0.188138i
$457$	4.03405	+	9.73907i	0.188705	+	0.455574i	0.989711	−	0.143082i	$-0.0457014\pi$
$457$	4.03405	+	9.73907i	0.188705	+	0.455574i	−0.801006	+	0.598657i	$0.795701\pi$
$458$	−15.8270			−0.739546
$459$		0			0
$460$	−0.274576			−0.0128022
$461$	−3.78349	−	9.13414i	−0.176215	−	0.425419i	0.810952	−	0.585112i	$-0.198950\pi$
$461$	−3.78349	−	9.13414i	−0.176215	−	0.425419i	−0.987167	+	0.159693i	$0.948950\pi$
$462$	1.75331	+	8.78408i	0.0815713	+	0.408672i
$463$	16.2123	−	16.2123i	0.753448	−	0.753448i	−0.221673	−	0.975121i	$-0.571152\pi$
$463$	16.2123	−	16.2123i	0.753448	−	0.753448i	0.975121	+	0.221673i	$0.0711518\pi$
$464$	18.7404	+	28.0469i	0.870000	+	1.30205i
$465$	−12.6876	+	8.48974i	−0.588373	+	0.393702i
$466$	−17.3453	−	11.5897i	−0.803504	−	0.536884i
$467$	23.8791	+	9.89105i	1.10499	+	0.457703i	0.859211	−	0.511621i	$-0.170955\pi$
$467$	23.8791	+	9.89105i	1.10499	+	0.457703i	0.245783	+	0.969325i	$0.420955\pi$
$468$	−1.43727	+	0.597567i	−0.0664378	+	0.0276226i
$469$	−8.62109	+	12.9024i	−0.398085	+	0.595776i
$470$	2.71024	+	13.6253i	0.125014	+	0.628487i
$471$	−3.55611	−	2.37271i	−0.163857	−	0.109329i
$472$	−11.8014	−	11.8014i	−0.543205	−	0.543205i
$473$	−3.67978	+	18.4995i	−0.169196	+	0.850608i
$474$	10.6112	−	10.6253i	0.487388	−	0.488034i
$475$			3.72217i			0.170785i
$476$		0			0
$477$	13.5274	+	13.4916i	0.619378	+	0.617740i
$478$	31.8737	−	13.2025i	1.45787	−	0.603870i
$479$	8.49821	+	1.69040i	0.388293	+	0.0772363i	0.385376	−	0.922759i	$-0.374072\pi$
$479$	8.49821	+	1.69040i	0.388293	+	0.0772363i	0.00291662	+	0.999996i	$0.499072\pi$
$480$	1.33916	−	3.23907i	0.0611238	−	0.147843i
$481$	8.75309	−	5.84863i	0.399107	−	0.266675i
$482$	4.01658	−	0.798947i	0.182950	−	0.0363910i
$483$	−0.556819	+	2.80904i	−0.0253361	+	0.127816i
$484$	−0.372148	+	0.898446i	−0.0169158	+	0.0408384i
$485$	4.14240	−	10.0006i	0.188097	−	0.454106i
$486$	−4.35159	+	22.2618i	−0.197392	+	1.00982i
$487$	−38.0711	+	7.57282i	−1.72517	+	0.343157i	−0.955433	−	0.295207i	$-0.904611\pi$
$487$	−38.0711	+	7.57282i	−1.72517	+	0.343157i	−0.769735	+	0.638364i	$0.779611\pi$
$488$	−13.3171	+	8.89820i	−0.602836	+	0.402802i
$489$	−1.77812	−	0.735143i	−0.0804094	−	0.0332443i
$490$	10.2266	+	2.03420i	0.461992	+	0.0918958i
$491$	11.7073	−	4.84934i	0.528345	−	0.218848i	−0.102533	−	0.994730i	$-0.532695\pi$
$491$	11.7073	−	4.84934i	0.528345	−	0.218848i	0.630878	+	0.775882i	$0.282695\pi$
$492$	−0.578293	+	0.239986i	−0.0260715	+	0.0108194i
$493$		0			0
$494$		−	5.55337i		−	0.249858i
$495$	−5.75417	+	13.9440i	−0.258631	+	0.626736i
$496$	−2.37857	+	11.9579i	−0.106801	+	0.536926i
$497$	3.31625	+	3.31625i	0.148754	+	0.148754i
$498$	−18.1668	+	27.2276i	−0.814076	+	1.22010i
$499$	−7.24100	−	36.4030i	−0.324152	−	1.62962i	−0.707991	−	0.706221i	$-0.750398\pi$
$499$	−7.24100	−	36.4030i	−0.324152	−	1.62962i	0.383839	−	0.923400i	$-0.374602\pi$
$500$	−0.137113	+	0.205204i	−0.00613187	+	0.00917700i
$501$	−34.3988	+	0.0227750i	−1.53683	+	0.00101751i
$502$	−20.3540	−	8.43090i	−0.908444	−	0.376290i
$503$	−26.5648	−	17.7500i	−1.18446	−	0.791433i	−0.202275	−	0.979329i	$-0.564833\pi$
$503$	−26.5648	−	17.7500i	−1.18446	−	0.791433i	−0.982189	+	0.187895i	$0.939833\pi$
$504$	−14.7509	−	9.82797i	−0.657055	−	0.437773i
$505$	−6.33939	−	9.48756i	−0.282099	−	0.422191i
$506$	1.29976	−	1.29976i	0.0577812	−	0.0577812i
$507$	−11.1045	+	2.21647i	−0.493169	+	0.0984369i
$508$	0.553083	+	1.33526i	0.0245391	+	0.0592426i
$509$	2.30289			0.102074			0.0510369	−	0.998697i	$-0.483747\pi$
$509$	2.30289			0.102074			0.0510369	+	0.998697i	$0.483747\pi$
$510$		0			0
$511$	−27.1309			−1.20020
$512$	7.77882	+	18.7797i	0.343778	+	0.829954i
$513$	−3.73529	−	2.48512i	−0.164917	−	0.109721i
$514$	−20.4697	+	20.4697i	−0.902880	+	0.902880i
$515$	15.8236	+	23.6817i	0.697272	+	1.04354i
$516$	1.29421	+	1.93415i	0.0569744	+	0.0851461i
$517$	−4.28683	−	2.86437i	−0.188534	−	0.125975i
$518$	−6.90554	−	2.86037i	−0.303412	−	0.125677i
$519$	0.0133441	+	20.1546i	0.000585740	+	0.884688i
$520$	20.5274	−	30.7215i	0.900187	−	1.34723i
$521$	0.537016	+	2.69976i	0.0235271	+	0.118279i	0.990764	−	0.135596i	$-0.0432949\pi$
$521$	0.537016	+	2.69976i	0.0235271	+	0.118279i	−0.967237	+	0.253875i	$0.918295\pi$
$522$	−34.2243	−	6.76053i	−1.49795	−	0.295900i
$523$	−29.8001	−	29.8001i	−1.30307	−	1.30307i	−0.926313	−	0.376755i	$-0.877040\pi$
$523$	−29.8001	−	29.8001i	−1.30307	−	1.30307i	−0.376755	−	0.926313i	$-0.622960\pi$
$524$	−0.0807574	+	0.405995i	−0.00352790	+	0.0177360i
$525$	−11.3949	−	11.3799i	−0.497316	−	0.496658i
$526$			0.190778i			0.00831830i
$527$		0			0
$528$	4.61767	+	11.1272i	0.200958	+	0.484249i
$529$	−20.7063	+	8.57683i	−0.900274	+	0.372906i
$530$	27.7336	+	5.51655i	1.20467	+	0.239624i
$531$	18.2772	−	0.0242021i	0.793161	−	0.00105028i
$532$	−0.181750	+	0.121442i	−0.00787987	+	0.00526516i
$533$	−13.3505	+	2.65558i	−0.578275	+	0.115026i
$534$	11.9581	+	2.37038i	0.517477	+	0.102576i
$535$	2.20694	−	5.32803i	0.0954144	−	0.230351i
$536$	−7.54259	+	18.2094i	−0.325790	+	0.786527i
$537$	−1.43848	−	0.285141i	−0.0620749	−	0.0123047i
$538$	8.48527	−	1.68783i	0.365826	−	0.0727674i
$539$	−3.21753	+	2.14988i	−0.138589	+	0.0926021i
$540$	0.715648	+	1.71807i	0.0307966	+	0.0739339i
$541$	−14.3553	−	2.85545i	−0.617184	−	0.122765i	−0.123410	−	0.992356i	$-0.539383\pi$
$541$	−14.3553	−	2.85545i	−0.617184	−	0.122765i	−0.493774	+	0.869590i	$0.664383\pi$
$542$	9.24223	−	3.82826i	0.396988	−	0.164438i
$543$	−0.951908	−	2.29381i	−0.0408503	−	0.0984369i
$544$		0			0
$545$		−	12.8251i		−	0.549365i
$546$	17.0009	+	16.9784i	0.727573	+	0.726610i
$547$	5.35079	−	26.9003i	0.228783	−	1.15017i	−0.680099	−	0.733120i	$-0.738063\pi$
$547$	5.35079	−	26.9003i	0.228783	−	1.15017i	0.908883	−	0.417052i	$-0.136937\pi$
$548$	−1.21585	−	1.21585i	−0.0519384	−	0.0519384i
$549$	3.39905	−	17.2072i	0.145068	−	0.734386i
$550$	2.01663	+	10.1383i	0.0859893	+	0.432297i
$551$	3.83341	−	5.73710i	0.163309	−	0.244409i
$552$	0.00240823	+	3.63734i	0.000102501	+	0.154816i
$553$	−11.8721	−	4.91757i	−0.504851	−	0.209116i
$554$	10.0389	+	6.70781i	0.426514	+	0.284987i
$555$	−7.00013	−	10.4614i	−0.297139	−	0.444063i
$556$	−0.328981	−	0.492355i	−0.0139519	−	0.0208805i
$557$	−31.0707	+	31.0707i	−1.31651	+	1.31651i	−0.399984	+	0.916522i	$0.630984\pi$
$557$	−31.0707	+	31.0707i	−1.31651	+	1.31651i	−0.916522	+	0.399984i	$0.869016\pi$
$558$	−7.01918	−	10.4749i	−0.297146	−	0.443438i
$559$	19.3619	+	46.7436i	0.818919	+	1.97705i
$560$	−27.7789			−1.17387
$561$		0			0
$562$	−19.2798			−0.813270
$563$	−14.0437	−	33.9044i	−0.591870	−	1.42890i	−0.881695	−	0.471821i	$-0.843597\pi$
$563$	−14.0437	−	33.9044i	−0.591870	−	1.42890i	0.289825	−	0.957080i	$-0.406403\pi$
$564$	−0.623814	+	0.124514i	−0.0262673	+	0.00524298i
$565$	−35.5701	+	35.5701i	−1.49645	+	1.49645i
$566$	−11.3446	−	16.9784i	−0.476850	−	0.713657i
$567$	19.0279	−	3.83729i	0.799095	−	0.161151i
$568$	4.95297	+	3.30947i	0.207822	+	0.138862i
$569$	22.8578	+	9.46803i	0.958251	+	0.396920i	0.806326	−	0.591472i	$-0.201453\pi$
$569$	22.8578	+	9.46803i	0.958251	+	0.396920i	0.151925	+	0.988392i	$0.451453\pi$
$570$	−6.64016	+	0.00439636i	−0.278126	+	0.000184143i
$571$	1.09497	−	1.63874i	0.0458232	−	0.0685792i	−0.807851	−	0.589387i	$-0.799369\pi$
$571$	1.09497	−	1.63874i	0.0458232	−	0.0685792i	0.853674	+	0.520808i	$0.174369\pi$
$572$	−0.166798	−	0.838551i	−0.00697418	−	0.0350616i
$573$	0.693147	−	1.03886i	0.0289566	−	0.0433989i
$574$	6.83402	+	6.83402i	0.285247	+	0.285247i
$575$	−0.644722	+	3.24124i	−0.0268868	+	0.135169i
$576$	−20.7348	−	8.55649i	−0.863951	−	0.356520i
$577$			26.8179i			1.11645i	0.829691	+	0.558223i	$0.188517\pi$
$577$			26.8179i			1.11645i	−0.829691	+	0.558223i	$0.811483\pi$
$578$		0			0
$579$	18.5917	−	7.71536i	0.772644	−	0.320639i
$580$	−2.64449	+	1.09538i	−0.109806	+	0.0454833i
$581$	27.4719	+	5.46450i	1.13973	+	0.226706i
$582$	8.26247	+	3.41602i	0.342490	+	0.141599i
$583$	−8.72562	+	5.83027i	−0.361378	+	0.241465i
$584$	−33.7984	+	6.72291i	−1.39859	+	0.278196i
$585$	7.94643	+	39.6748i	0.328544	+	1.64035i
$586$	−14.7044	+	35.4995i	−0.607433	+	1.46647i
$587$	17.1080	−	41.3023i	0.706122	−	1.70473i	−0.00334911	−	0.999994i	$-0.501066\pi$
$587$	17.1080	−	41.3023i	0.706122	−	1.70473i	0.709471	−	0.704735i	$-0.248934\pi$
$588$	−0.0928353	+	0.468335i	−0.00382846	+	0.0193138i
$589$	2.44603	−	0.486546i	0.100787	−	0.0200478i
$590$	22.4922	−	15.0288i	0.925988	−	0.618726i
$591$	−15.3953	+	37.2374i	−0.633280	+	1.53174i
$592$	−9.85977	−	1.96123i	−0.405234	−	0.0806061i
$593$	−20.3889	+	8.44534i	−0.837270	+	0.346809i	−0.759777	−	0.650184i	$-0.774692\pi$
$593$	−20.3889	+	8.44534i	−0.837270	+	0.346809i	−0.0774935	+	0.996993i	$0.524692\pi$
$594$	−11.5204	−	4.74513i	−0.472689	−	0.194695i
$595$		0			0
$596$		−	0.738361i		−	0.0302444i
$597$	−29.5149	+	29.5540i	−1.20796	+	1.20956i
$598$	0.961908	−	4.83584i	0.0393353	−	0.197752i
$599$	16.9345	+	16.9345i	0.691926	+	0.691926i	0.962655	−	0.270729i	$-0.0872649\pi$
$599$	16.9345	+	16.9345i	0.691926	+	0.691926i	−0.270729	+	0.962655i	$0.587265\pi$
$600$	−17.0151	−	11.3529i	−0.694641	−	0.463479i
$601$	0.514619	+	2.58716i	0.0209917	+	0.105533i	0.989861	−	0.142041i	$-0.0453666\pi$
$601$	0.514619	+	2.58716i	0.0209917	+	0.105533i	−0.968869	+	0.247574i	$0.920367\pi$
$602$	19.9578	−	29.8690i	0.813421	−	1.21737i
$603$	−8.28640	−	19.9304i	−0.337448	−	0.811630i
$604$	1.64982	+	0.683377i	0.0671302	+	0.0278062i
$605$	21.0192	+	14.0446i	0.854553	+	0.570994i
$606$	7.83295	−	5.24131i	0.318192	−	0.212914i
$607$	20.1517	+	30.1592i	0.817934	+	1.22412i	0.971747	+	0.236025i	$0.0758447\pi$
$607$	20.1517	+	30.1592i	0.817934	+	1.22412i	−0.153813	+	0.988100i	$0.549155\pi$
$608$	−0.404887	+	0.404887i	−0.0164203	+	0.0164203i
$609$	5.84344	+	29.2756i	0.236788	+	1.18631i
$610$	−9.93432	−	23.9836i	−0.402229	−	0.971066i
$611$	−13.8296			−0.559487
$612$		0			0
$613$	−25.0887			−1.01333			−0.506663	−	0.862144i	$-0.669121\pi$
$613$	−25.0887			−1.01333			−0.506663	+	0.862144i	$0.669121\pi$
$614$	−13.6047	−	32.8447i	−0.549041	−	1.32550i
$615$	3.18584	+	15.9611i	0.128466	+	0.643613i
$616$	6.88440	−	6.88440i	0.277380	−	0.277380i
$617$	5.48342	+	8.20652i	0.220754	+	0.330382i	0.925272	−	0.379304i	$-0.123837\pi$
$617$	5.48342	+	8.20652i	0.220754	+	0.330382i	−0.704518	+	0.709686i	$0.748837\pi$
$618$	−19.5517	+	13.0827i	−0.786484	+	0.526265i
$619$	−26.8643	−	17.9502i	−1.07977	−	0.721478i	−0.117361	−	0.993089i	$-0.537443\pi$
$619$	−26.8643	−	17.9502i	−1.07977	−	0.721478i	−0.962407	+	0.271611i	$0.912443\pi$
$620$	−0.955837	−	0.395921i	−0.0383873	−	0.0159006i
$621$	−2.82221	−	2.81102i	−0.113251	−	0.112802i
$622$	18.8655	−	28.2341i	0.756436	−	1.13209i
$623$	−2.03521	−	10.2317i	−0.0815391	−	0.409925i
$624$	26.8812	+	17.9357i	1.07611	+	0.718004i
$625$	19.7780	+	19.7780i	0.791122	+	0.791122i
$626$	0.458362	−	2.30434i	0.0183198	−	0.0920999i
$627$	1.74138	−	1.74369i	0.0695441	−	0.0696362i
$628$		−	0.289721i		−	0.0115611i
$629$		0			0
$630$	20.2876	−	20.3414i	0.808279	−	0.810422i
$631$	3.56930	−	1.47845i	0.142092	−	0.0588563i	−0.310504	−	0.950572i	$-0.600498\pi$
$631$	3.56930	−	1.47845i	0.142092	−	0.0588563i	0.452596	+	0.891716i	$0.350498\pi$
$632$	−16.0082	−	3.18423i	−0.636772	−	0.126662i
$633$	10.3302	−	24.9860i	0.410587	−	0.993104i
$634$	29.5032	−	19.7134i	1.17172	−	0.782919i
$635$	36.8483	−	7.32959i	1.46228	−	0.290866i
$636$	−0.251760	+	1.27008i	−0.00998293	+	0.0503618i
$637$	−3.97225	+	9.58987i	−0.157386	+	0.379964i
$638$	7.33297	−	17.7033i	0.290315	−	0.700882i
$639$	−6.39644	+	1.28114i	−0.253039	+	0.0506810i
$640$	−36.5304	+	7.26634i	−1.44399	+	0.287227i
$641$	31.1140	−	20.7897i	1.22893	−	0.821145i	0.240181	−	0.970728i	$-0.422793\pi$
$641$	31.1140	−	20.7897i	1.22893	−	0.821145i	0.988749	+	0.149583i	$0.0477932\pi$
$642$	4.40198	+	1.81995i	0.173732	+	0.0718276i
$643$	−41.6621	−	8.28711i	−1.64299	−	0.326812i	−0.714920	−	0.699206i	$-0.753537\pi$
$643$	−41.6621	−	8.28711i	−1.64299	−	0.326812i	−0.928075	+	0.372395i	$0.878537\pi$
$644$	−0.179302	+	0.0742693i	−0.00706549	+	0.00292662i
$645$	55.8760	−	23.1879i	2.20011	−	0.913024i
$646$		0			0
$647$			48.3331i			1.90017i	0.311989	+	0.950086i	$0.399005\pi$
$647$			48.3331i			1.90017i	−0.311989	+	0.950086i	$0.600995\pi$
$648$	22.7531	−	9.49533i	0.893828	−	0.373012i
$649$	−1.95857	+	9.84639i	−0.0768806	+	0.386505i
$650$	19.6063	+	19.6063i	0.769023	+	0.769023i
$651$	−5.98880	+	8.97574i	−0.234720	+	0.351787i
$652$	−0.0254394	−	0.127892i	−0.000996282	−	0.00500865i
$653$	−3.59464	+	5.37976i	−0.140669	+	0.210526i	−0.895114	−	0.445837i	$-0.852906\pi$
$653$	−3.59464	+	5.37976i	−0.140669	+	0.210526i	0.754445	+	0.656363i	$0.227906\pi$
$654$	10.5931	−	0.00701353i	0.414222	−	0.000274251i
$655$	9.94158	+	4.11794i	0.388450	+	0.160901i
$656$	10.8081	+	7.22172i	0.421984	+	0.281961i
$657$	20.9247	−	31.4059i	0.816349	−	1.22526i
$658$	5.45528	+	8.16440i	0.212669	+	0.318281i
$659$	−17.7005	+	17.7005i	−0.689515	+	0.689515i	−0.962125	−	0.272610i	$-0.912113\pi$
$659$	−17.7005	+	17.7005i	−0.689515	+	0.689515i	0.272610	+	0.962125i	$0.412113\pi$
$660$	−1.00252	+	0.200104i	−0.0390231	+	0.00778904i
$661$	−9.53615	−	23.0223i	−0.370913	−	0.895464i	−0.993596	−	0.112990i	$-0.963957\pi$
$661$	−9.53615	−	23.0223i	−0.370913	−	0.895464i	0.622683	−	0.782474i	$-0.286043\pi$
$662$	44.3302			1.72294
$663$		0			0
$664$	35.5773			1.38067
$665$	2.17451	+	5.24974i	0.0843240	+	0.203576i
$666$	8.63697	−	5.78760i	0.334676	−	0.224265i
$667$	4.33184	−	4.33184i	0.167729	−	0.167729i
$668$	−1.29517	−	1.93835i	−0.0501115	−	0.0749972i
$669$	−2.34265	−	3.50101i	−0.0905723	−	0.135357i
$670$	−26.5621	−	17.7482i	−1.02618	−	0.685674i
$671$	8.90086	+	3.68686i	0.343614	+	0.142329i
$672$	−0.00164024	−	2.47738i	−6.32736e−5	−	0.0955670i
$673$	10.4352	−	15.6174i	0.402248	−	0.602006i	−0.573949	−	0.818891i	$-0.694589\pi$
$673$	10.4352	−	15.6174i	0.402248	−	0.602006i	0.976197	+	0.216884i	$0.0695894\pi$
$674$	−4.89012	−	24.5843i	−0.188360	−	0.946952i
$675$	21.9613	−	4.41374i	0.845291	−	0.169885i
$676$	−0.542640	−	0.542640i	−0.0208708	−	0.0208708i
$677$	1.93347	−	9.72023i	0.0743095	−	0.373579i	−0.925679	−	0.378309i	$-0.876506\pi$
$677$	1.93347	−	9.72023i	0.0743095	−	0.373579i	0.999989	+	0.00473017i	$0.00150567\pi$
$678$	−29.3992	−	29.3603i	−1.12907	−	1.12758i
$679$		−	7.65102i		−	0.293619i
$680$		0			0
$681$	−0.932371	−	2.24673i	−0.0357285	−	0.0860950i
$682$	6.39878	−	2.65046i	0.245022	−	0.101491i
$683$	2.34194	+	0.465840i	0.0896118	+	0.0178249i	0.239693	−	0.970849i	$-0.422953\pi$
$683$	2.34194	+	0.465840i	0.0896118	+	0.0178249i	−0.150081	+	0.988674i	$0.547953\pi$
$684$	−0.000402615	−	0.304050i	−1.53944e−5	−	0.0116257i
$685$	−37.1650	+	24.8328i	−1.42000	+	0.948814i
$686$	28.7748	−	5.72366i	1.09863	−	0.218530i
$687$	−18.4795	−	3.66308i	−0.705037	−	0.139755i
$688$	18.4895	−	44.6375i	0.704905	−	1.70179i
$689$	−10.7724	+	26.0068i	−0.410394	+	0.990779i
$690$	−5.78297	−	1.14632i	−0.220154	−	0.0436398i
$691$	31.9778	−	6.36078i	1.21649	−	0.241975i	0.455203	−	0.890388i	$-0.349567\pi$
$691$	31.9778	−	6.36078i	1.21649	−	0.241975i	0.761290	+	0.648412i	$0.224567\pi$
$692$	−1.13570	+	0.758850i	−0.0431728	+	0.0288472i
$693$	0.0141184	+	10.6620i	0.000536313	+	0.405017i
$694$	28.8782	+	5.74423i	1.09620	+	0.218048i
$695$	−14.2214	+	5.89068i	−0.539447	+	0.223446i
$696$	14.5338	+	35.0222i	0.550904	+	1.32751i
$697$		0			0
$698$			11.0631i			0.418743i
$699$	−17.5698	−	17.5466i	−0.664552	−	0.663673i
$700$	0.212921	−	1.07043i	0.00804766	−	0.0404583i
$701$	−31.7150	−	31.7150i	−1.19786	−	1.19786i	−0.974807	−	0.223051i	$-0.928398\pi$
$701$	−31.7150	−	31.7150i	−1.19786	−	1.19786i	−0.223051	−	0.974807i	$-0.571602\pi$
$702$	−32.7657	+	6.58518i	−1.23666	+	0.248542i
$703$	0.401176	+	2.01685i	0.0151307	+	0.0760669i
$704$	6.84510	−	10.2444i	0.257985	−	0.386101i
$705$	0.0109483	+	16.5361i	0.000412337	+	0.622784i
$706$	16.0527	+	6.64926i	0.604153	+	0.250248i
$707$	−6.70596	−	4.48078i	−0.252204	−	0.168517i
$708$	0.688845	+	1.02945i	0.0258884	+	0.0386892i
$709$	−21.9367	−	32.8306i	−0.823849	−	1.23298i	−0.969852	−	0.243693i	$-0.921641\pi$
$709$	−21.9367	−	32.8306i	−0.823849	−	1.23298i	0.146003	−	0.989284i	$-0.453359\pi$
$710$	−6.82716	+	6.82716i	−0.256219	+	0.256219i
$711$	14.8487	−	9.95007i	0.556871	−	0.373157i
$712$	−5.07074	−	12.2419i	−0.190034	−	0.458783i
$713$	2.21426			0.0829248
$714$		0			0
$715$	−22.2254			−0.831182
$716$	−0.0380325	−	0.0918186i	−0.00142134	−	0.00343142i
$717$	40.2713	−	8.03817i	1.50396	−	0.300191i
$718$	23.6628	−	23.6628i	0.883086	−	0.883086i
$719$	24.4159	+	36.5410i	0.910560	+	1.36275i	0.931799	+	0.362975i	$0.118239\pi$
$719$	24.4159	+	36.5410i	0.910560	+	1.36275i	−0.0212393	+	0.999774i	$0.506761\pi$
$720$	21.4245	−	32.1561i	0.798442	−	1.19839i
$721$	16.7386	+	11.1844i	0.623379	+	0.416529i
$722$	−24.5406	−	10.1650i	−0.913307	−	0.378304i
$723$	4.87465	−	0.00322743i	0.181290	−	0.000120030i
$724$	0.0935070	−	0.139943i	0.00347516	−	0.00520094i
$725$	6.72103	+	33.7889i	0.249613	+	1.25489i
$726$	−11.5889	+	17.3689i	−0.430103	+	0.644619i
$727$	0.0802760	+	0.0802760i	0.00297727	+	0.00297727i	0.708594	−	0.705617i	$-0.249330\pi$
$727$	0.0802760	+	0.0802760i	0.00297727	+	0.00297727i	−0.705617	+	0.708594i	$0.749330\pi$
$728$	5.09492	−	25.6139i	0.188830	−	0.949315i
$729$	−10.2333	+	24.9856i	−0.379010	+	0.925392i
$730$		−	55.8544i		−	2.06726i
$731$		0			0
$732$	1.09790	−	0.455616i	0.0405795	−	0.0168400i
$733$	7.54651	−	3.12587i	0.278737	−	0.115457i	−0.238936	−	0.971035i	$-0.576799\pi$
$733$	7.54651	−	3.12587i	0.278737	−	0.115457i	0.517673	+	0.855579i	$0.326799\pi$
$734$	−23.4205	−	4.65863i	−0.864467	−	0.171953i
$735$	11.4697	+	4.74203i	0.423068	+	0.174912i
$736$	−0.422704	+	0.282442i	−0.0155811	+	0.0104109i
$737$	11.6281	−	2.31297i	0.428326	−	0.0851993i
$738$	−13.1816	+	2.64013i	−0.485221	+	0.0971846i
$739$	−4.49550	+	10.8531i	−0.165370	+	0.399237i	−0.984741	−	0.174025i	$-0.944323\pi$
$739$	−4.49550	+	10.8531i	−0.165370	+	0.399237i	0.819372	+	0.573263i	$0.194323\pi$
$740$	0.326452	−	0.788126i	0.0120006	−	0.0289721i
$741$	1.28530	−	6.48409i	0.0472168	−	0.238199i
$742$	19.6025	−	3.89919i	0.719632	−	0.143144i
$743$	34.1272	−	22.8030i	1.25200	−	0.836563i	0.260354	−	0.965513i	$-0.416161\pi$
$743$	34.1272	−	22.8030i	1.25200	−	0.836563i	0.991651	+	0.128951i	$0.0411609\pi$
$744$	−5.23642	+	12.6655i	−0.191976	+	0.464341i
$745$	−18.8251	−	3.74454i	−0.689697	−	0.137189i
$746$	−2.17550	+	0.901121i	−0.0796507	+	0.0329924i
$747$	−27.5132	+	27.5862i	−1.00666	+	1.00933i
$748$		0			0
$749$		−	4.07622i		−	0.148942i
$750$	−3.74449	+	3.74945i	−0.136730	+	0.136911i
$751$	−0.329510	+	1.65656i	−0.0120240	+	0.0604487i	−0.986331	−	0.164773i	$-0.947311\pi$
$751$	−0.329510	+	1.65656i	−0.0120240	+	0.0604487i	0.974307	+	0.225222i	$0.0723107\pi$
$752$	9.33841	+	9.33841i	0.340537	+	0.340537i
$753$	−21.8139	−	14.5547i	−0.794944	−	0.530403i
$754$	−10.0276	−	50.4121i	−0.365184	−	1.83590i
$755$	25.7901	−	38.5977i	0.938599	−	1.40471i
$756$	0.932042	+	0.928347i	0.0338980	+	0.0337637i
$757$	50.2881	+	20.8300i	1.82775	+	0.757080i	0.970038	+	0.242954i	$0.0781164\pi$
$757$	50.2881	+	20.8300i	1.82775	+	0.757080i	0.857715	+	0.514126i	$0.171884\pi$
$758$	18.7890	+	12.5544i	0.682446	+	0.455996i
$759$	1.81841	−	1.21677i	0.0660041	−	0.0441658i
$760$	4.00977	+	6.00104i	0.145450	+	0.217681i
$761$	24.1395	−	24.1395i	0.875055	−	0.875055i	−0.117963	−	0.993018i	$-0.537636\pi$
$761$	24.1395	−	24.1395i	0.875055	−	0.875055i	0.993018	+	0.117963i	$0.0376365\pi$
$762$	6.07415	+	30.4315i	0.220043	+	1.10242i
$763$	−3.46901	−	8.37493i	−0.125587	−	0.303193i
$764$	0.0846370			0.00306206
$765$		0			0
$766$	32.2229			1.16426
$767$	10.3054	+	24.8794i	0.372106	+	0.898343i
$768$	−0.951887	−	4.76895i	−0.0343483	−	0.172085i
$769$	−31.3211	+	31.3211i	−1.12947	+	1.12947i	−0.139204	+	0.990264i	$0.544454\pi$
$769$	−31.3211	+	31.3211i	−1.12947	+	1.12947i	−0.990264	+	0.139204i	$0.955546\pi$
$770$	8.76709	+	13.1209i	0.315944	+	0.472843i
$771$	−28.6379	+	19.1627i	−1.03137	+	0.690128i
$772$	1.13426	+	0.757888i	0.0408229	+	0.0272770i
$773$	12.8222	+	5.31114i	0.461184	+	0.191028i	0.601164	−	0.799126i	$-0.294704\pi$
$773$	12.8222	+	5.31114i	0.461184	+	0.191028i	−0.139980	+	0.990154i	$0.544704\pi$
$774$	19.1830	+	46.1390i	0.689520	+	1.65843i
$775$	−6.91801	+	10.3535i	−0.248502	+	0.371910i
$776$	−1.89589	−	9.53128i	−0.0680584	−	0.342153i
$777$	−7.40085	−	4.93801i	−0.265504	−	0.177150i
$778$	−15.6099	−	15.6099i	−0.559643	−	0.559643i
$779$	0.518733	−	2.60785i	0.0185856	−	0.0934359i
$780$	−1.93774	+	1.94031i	−0.0693822	+	0.0694742i
$781$		−	3.58322i		−	0.128218i
$782$		0			0
$783$	−38.3954	−	15.8146i	−1.37214	−	0.565168i
$784$	9.15778	−	3.79328i	0.327064	−	0.135474i
$785$	−7.38666	−	1.46930i	−0.263641	−	0.0524415i
$786$	−3.39584	+	8.21367i	−0.121126	+	0.292972i
$787$	19.9038	−	13.2993i	0.709495	−	0.474070i	−0.147719	−	0.989029i	$-0.547193\pi$
$787$	19.9038	−	13.2993i	0.709495	−	0.474070i	0.857214	+	0.514960i	$0.172193\pi$
$788$	−2.67832	+	0.532750i	−0.0954111	+	0.0189784i
$789$	−0.0441546	+	0.222751i	−0.00157195	+	0.00793015i
$790$	10.1238	−	24.4410i	0.360189	−	0.869572i
$791$	−13.6065	+	32.8490i	−0.483792	+	1.16798i
$792$	2.65959	+	13.2788i	0.0945045	+	0.471840i
$793$	25.3461	−	5.04166i	0.900067	−	0.179034i
$794$	−45.5369	+	30.4268i	−1.61604	+	1.07981i
$795$	31.1048	+	12.8599i	1.10317	+	0.456094i
$796$	−2.77627	−	0.552234i	−0.0984022	−	0.0195734i
$797$	43.2651	−	17.9210i	1.53253	−	0.634795i	0.552476	−	0.833529i	$-0.313683\pi$
$797$	43.2651	−	17.9210i	1.53253	−	0.634795i	0.980053	+	0.198734i	$0.0636830\pi$
$798$	−4.33492	+	1.79895i	−0.153455	+	0.0636820i
$799$		0			0
$800$		−	2.85893i		−	0.101078i
$801$	13.4136	+	5.53529i	0.473945	+	0.195580i
$802$	1.00319	−	5.04338i	0.0354239	−	0.178088i
$803$	14.6575	+	14.6575i	0.517252	+	0.517252i
$804$	0.811880	−	1.21681i	0.0286328	−	0.0429135i
$805$	0.984236	+	4.94809i	0.0346897	+	0.174397i
$806$	10.3215	−	15.4472i	0.363559	−	0.544104i
$807$	10.2980	−	0.00681816i	0.362507	−	0.000240011i
$808$	−9.46429	−	3.92024i	−0.332952	−	0.137913i
$809$	−9.74138	−	6.50898i	−0.342489	−	0.228844i	0.372415	−	0.928066i	$-0.378530\pi$
$809$	−9.74138	−	6.50898i	−0.342489	−	0.228844i	−0.714904	+	0.699223i	$0.753530\pi$
$810$	7.89983	+	39.1727i	0.277572	+	1.37639i
$811$	10.4602	+	15.6548i	0.367308	+	0.549716i	0.968380	−	0.249479i	$-0.0802594\pi$
$811$	10.4602	+	15.6548i	0.367308	+	0.549716i	−0.601072	+	0.799195i	$0.705259\pi$
$812$	−1.43060	+	1.43060i	−0.0502042	+	0.0502042i
$813$	11.6772	−	2.33078i	0.409538	−	0.0817440i
$814$	2.18541	+	5.27605i	0.0765987	+	0.184926i
$815$	−3.38972			−0.118737
$816$		0			0
$817$	−9.88307			−0.345765
$818$	6.79797	+	16.4118i	0.237686	+	0.573824i
$819$	15.9206	+	23.7587i	0.556311	+	0.830197i
$820$	−0.779963	+	0.779963i	−0.0272375	+	0.0272375i
$821$	−16.8304	−	25.1885i	−0.587386	−	0.879086i	0.412100	−	0.911139i	$-0.364795\pi$
$821$	−16.8304	−	25.1885i	−0.587386	−	0.879086i	−0.999486	+	0.0320530i	$0.989795\pi$
$822$	−20.5314	−	30.6834i	−0.716116	−	1.07021i
$823$	−19.0816	−	12.7499i	−0.665142	−	0.444434i	0.176622	−	0.984279i	$-0.443483\pi$
$823$	−19.0816	−	12.7499i	−0.665142	−	0.444434i	−0.841765	+	0.539845i	$0.818483\pi$
$824$	23.6236	+	9.78523i	0.822968	+	0.340884i
$825$	0.00814639	+	12.3041i	0.000283621	+	0.428375i
$826$	10.6226	−	15.8978i	0.369607	−	0.553156i
$827$	3.41591	+	17.1729i	0.118783	+	0.597161i	0.993623	+	0.112750i	$0.0359660\pi$
$827$	3.41591	+	17.1729i	0.118783	+	0.597161i	−0.874841	+	0.484411i	$0.839034\pi$
$828$	0.0523144	−	0.264835i	0.00181805	−	0.00920364i
$829$	31.1358	+	31.1358i	1.08139	+	1.08139i	0.996380	+	0.0850121i	$0.0270929\pi$
$829$	31.1358	+	31.1358i	1.08139	+	1.08139i	0.0850121	+	0.996380i	$0.472907\pi$
$830$	−11.2498	+	56.5564i	−0.390485	+	1.96310i
$831$	10.1689	+	10.1555i	0.352756	+	0.352289i
$832$		−	33.0493i		−	1.14578i
$833$		0			0
$834$	−4.87328	−	11.7432i	−0.168748	−	0.406632i
$835$	−55.9881	+	23.1910i	−1.93755	+	0.802559i
$836$	0.163800	+	0.0325818i	0.00566514	+	0.00112687i
$837$	−5.77119	−	13.8550i	−0.199481	−	0.478898i
$838$	−37.9818	+	25.3786i	−1.31206	+	0.876690i
$839$	−19.3977	+	3.85845i	−0.669684	+	0.133209i	−0.518211	−	0.855253i	$-0.673402\pi$
$839$	−19.3977	+	3.85845i	−0.669684	+	0.133209i	−0.151473	+	0.988461i	$0.548402\pi$
$840$	−30.6306	−	6.07172i	−1.05685	−	0.209494i
$841$	13.3415	−	32.2093i	0.460053	−	1.11067i
$842$	8.44564	−	20.3896i	0.291056	−	0.702671i
$843$	−22.5110	−	4.46223i	−0.775321	−	0.153687i
$844$	1.79713	−	0.357471i	0.0618598	−	0.0123047i
$845$	−16.5869	+	11.0830i	−0.570608	+	0.381268i
$846$	−13.6582	+	0.0180859i	−0.469580	+	0.000621805i
$847$	17.5247	+	3.48588i	0.602156	+	0.119776i
$848$	24.8350	−	10.2870i	0.852837	−	0.353257i
$849$	−9.31634	−	22.4496i	−0.319736	−	0.770468i
$850$		0			0
$851$			1.82575i			0.0625858i
$852$	−0.312820	−	0.312406i	−0.0107170	−	0.0107029i
$853$	−1.20474	+	6.05663i	−0.0412495	+	0.207375i	−0.995914	−	0.0903095i	$-0.971214\pi$
$853$	−1.20474	+	6.05663i	−0.0412495	+	0.207375i	0.954664	+	0.297685i	$0.0962144\pi$
$854$	−12.9745	−	12.9745i	−0.443977	−	0.443977i
$855$	−7.75403	−	1.53170i	−0.265182	−	0.0523831i
$856$	−1.01007	−	5.07796i	−0.0345235	−	0.173561i
$857$	−14.4466	+	21.6208i	−0.493486	+	0.738554i	−0.991710	−	0.128494i	$-0.958986\pi$
$857$	−14.4466	+	21.6208i	−0.493486	+	0.738554i	0.498224	+	0.867048i	$0.333986\pi$
$858$	−0.0121542	−	18.3574i	−0.000414937	−	0.626712i
$859$	3.03380	+	1.25664i	0.103512	+	0.0428761i	0.433838	−	0.900991i	$-0.357159\pi$
$859$	3.03380	+	1.25664i	0.103512	+	0.0428761i	−0.330326	+	0.943867i	$0.607159\pi$
$860$	3.40893	+	2.27778i	0.116244	+	0.0776715i
$861$	6.39766	+	9.56107i	0.218032	+	0.325840i
$862$	−9.25940	−	13.8577i	−0.315376	−	0.471994i
$863$	10.3922	−	10.3922i	0.353754	−	0.353754i	−0.507750	−	0.861504i	$-0.669523\pi$
$863$	10.3922	−	10.3922i	0.353754	−	0.353754i	0.861504	+	0.507750i	$0.169523\pi$
$864$	2.86901	+	1.90878i	0.0976056	+	0.0649379i
$865$	13.5878	+	32.8040i	0.462000	+	1.11537i
$866$	−38.9856			−1.32479
$867$		0			0
$868$	−0.731265			−0.0248208
$869$	3.75718	+	9.07062i	0.127453	+	0.307700i
$870$	−60.2698	+	12.0299i	−2.04334	+	0.407851i
$871$	22.4875	−	22.4875i	0.761958	−	0.761958i
$872$	−6.39680	−	9.57349i	−0.216623	−	0.324199i
$873$	8.85659	+	5.90084i	0.299750	+	0.199713i
$874$	0.800809	+	0.535083i	0.0270878	+	0.0180995i
$875$	4.18943	+	1.73532i	0.141629	+	0.0586644i
$876$	2.55755	−	0.00169332i	0.0864117	−	5.72119e-5i
$877$	7.40929	−	11.0888i	0.250194	−	0.374442i	−0.685020	−	0.728524i	$-0.740207\pi$
$877$	7.40929	−	11.0888i	0.250194	−	0.374442i	0.935214	+	0.354082i	$0.115207\pi$
$878$	2.42046	+	12.1685i	0.0816867	+	0.410667i
$879$	−25.3850	+	38.0458i	−0.856214	+	1.28325i
$880$	15.0076	+	15.0076i	0.505907	+	0.505907i
$881$	3.84700	−	19.3402i	0.129609	−	0.651587i	−0.860289	−	0.509806i	$-0.829717\pi$
$881$	3.84700	−	19.3402i	0.129609	−	0.651587i	0.989898	−	0.141781i	$-0.0452828\pi$
$882$	−3.91048	+	9.47622i	−0.131673	+	0.319081i
$883$		−	44.5932i		−	1.50068i	−0.661051	−	0.750341i	$-0.729889\pi$
$883$		−	44.5932i		−	1.50068i	0.661051	−	0.750341i	$-0.270111\pi$
$884$		0			0
$885$	29.7401	−	12.3418i	0.999702	−	0.414866i
$886$	25.3778	−	10.5118i	0.852584	−	0.353152i
$887$	−16.3954	−	3.26124i	−0.550502	−	0.109502i	−0.0880011	−	0.996120i	$-0.528048\pi$
$887$	−16.3954	−	3.26124i	−0.550502	−	0.109502i	−0.462501	+	0.886619i	$0.653048\pi$
$888$	−10.4432	−	4.31764i	−0.350452	−	0.144890i
$889$	22.0799	−	14.7533i	0.740536	−	0.494810i
$890$	21.0640	−	4.18990i	0.706068	−	0.140446i
$891$	−12.3529	−	8.20674i	−0.413839	−	0.274936i
$892$	0.109250	−	0.263753i	0.00365797	−	0.00883111i
$893$	1.03380	−	2.49580i	0.0345947	−	0.0835189i
$894$	3.08257	−	15.5509i	0.103097	−	0.520101i
$895$	−2.53386	+	0.504016i	−0.0846976	+	0.0168474i
$896$	−21.8894	+	14.6260i	−0.731272	+	0.488620i
$897$	2.24235	−	5.42367i	0.0748699	−	0.181091i
$898$	−38.9112	−	7.73992i	−1.29848	−	0.258284i
$899$	21.3259	−	8.83348i	0.711259	−	0.294613i
$900$	1.07488	+	1.07204i	0.0358293	+	0.0357345i
$901$		0			0
$902$		−	7.38418i		−	0.245866i
$903$	30.2157	−	30.2557i	1.00552	−	1.00685i
$904$	−8.81050	+	44.2934i	−0.293033	+	1.47318i
$905$	−3.09374	−	3.09374i	−0.102839	−	0.102839i
$906$	31.8945	+	21.2807i	1.05962	+	0.707004i
$907$	1.79747	+	9.03651i	0.0596841	+	0.300052i	0.999085	−	0.0427682i	$-0.0136177\pi$
$907$	1.79747	+	9.03651i	0.0596841	+	0.300052i	−0.939401	+	0.342821i	$0.888618\pi$
$908$	0.0915878	−	0.137071i	0.00303945	−	0.00454886i
$909$	10.3588	−	4.30683i	0.343579	−	0.142848i
$910$	39.1068	+	16.1986i	1.29638	+	0.536978i
$911$	1.66735	+	1.11409i	0.0552417	+	0.0369113i	0.582884	−	0.812555i	$-0.301924\pi$
$911$	1.66735	+	1.11409i	0.0552417	+	0.0369113i	−0.527643	+	0.849466i	$0.676924\pi$
$912$	−5.24626	+	3.51046i	−0.173721	+	0.116243i
$913$	−11.8895	−	17.7940i	−0.393486	−	0.588894i
$914$	−10.8464	+	10.8464i	−0.358768	+	0.358768i
$915$	−6.04837	−	30.3023i	−0.199953	−	1.00176i
$916$	−0.488587	−	1.17955i	−0.0161434	−	0.0389735i
$917$	7.60583			0.251167
$918$		0			0
$919$	4.18774			0.138141			0.0690703	−	0.997612i	$-0.477997\pi$
$919$	4.18774			0.138141			0.0690703	+	0.997612i	$0.477997\pi$
$920$	2.45223	+	5.92020i	0.0808475	+	0.195183i
$921$	−8.28303	−	41.4980i	−0.272935	−	1.36741i
$922$	10.1727	−	10.1727i	0.335021	−	0.335021i
$923$	−5.33990	−	7.99172i	−0.175765	−	0.263051i
$924$	−0.600534	+	0.401840i	−0.0197561	+	0.0132196i
$925$	−8.53690	−	5.70418i	−0.280692	−	0.187552i
$926$	30.8229	+	12.7673i	1.01290	+	0.419558i
$927$	−25.8564	+	10.7502i	−0.849234	+	0.353083i
$928$	−2.94437	+	4.40656i	−0.0966536	+	0.144652i
$929$	4.77057	+	23.9833i	0.156517	+	0.786866i	0.976674	+	0.214727i	$0.0688863\pi$
$929$	4.77057	+	23.9833i	0.156517	+	0.786866i	−0.820157	+	0.572139i	$0.806114\pi$
$930$	−18.4784	−	12.3292i	−0.605929	−	0.404289i
$931$	−1.43373	−	1.43373i	−0.0469885	−	0.0469885i
$932$	0.328303	−	1.65049i	0.0107539	−	0.0540636i
$933$	28.5619	−	28.5997i	0.935073	−	0.936312i
$934$			37.6099i			1.23063i
$935$		0			0
$936$	25.7205	+	25.6524i	0.840699	+	0.838476i
$937$	46.7545	−	19.3663i	1.52740	−	0.632671i	0.548345	−	0.836252i	$-0.315258\pi$
$937$	46.7545	−	19.3663i	1.52740	−	0.632671i	0.979058	+	0.203582i	$0.0652582\pi$
$938$	−22.1461	−	4.40513i	−0.723095	−	0.143832i
$939$	1.06851	−	2.58445i	0.0348695	−	0.0843403i
$940$	−0.931798	+	0.622608i	−0.0303919	+	0.0203072i
$941$	3.53463	−	0.703081i	0.115226	−	0.0229198i	−0.137141	−	0.990552i	$-0.543791\pi$
$941$	3.53463	−	0.703081i	0.115226	−	0.0229198i	0.252366	+	0.967632i	$0.418791\pi$
$942$	1.20955	−	6.10194i	0.0394093	−	0.198812i
$943$	0.903419	−	2.18105i	0.0294194	−	0.0710246i
$944$	9.84105	−	23.7584i	0.320299	−	0.773270i
$945$	28.3957	−	19.0551i	0.923711	−	0.619861i
$946$	−26.9191	+	5.35453i	−0.875214	+	0.174091i
$947$	−22.2883	+	14.8925i	−0.724271	+	0.483943i	−0.862244	−	0.506493i	$-0.830941\pi$
$947$	−22.2883	+	14.8925i	−0.724271	+	0.483943i	0.137972	+	0.990436i	$0.455941\pi$
$948$	1.11945	+	0.462824i	0.0363581	+	0.0150318i
$949$	54.5344	+	10.8476i	1.77026	+	0.352127i
$950$	−5.00393	+	2.07269i	−0.162349	+	0.0672471i
$951$	39.0103	−	16.1889i	1.26500	−	0.524960i
$952$		0			0
$953$			24.2594i			0.785838i	0.919573	+	0.392919i	$0.128535\pi$
$953$			24.2594i			0.785838i	−0.919573	+	0.392919i	$0.871465\pi$
$954$	−10.6048	+	25.6985i	−0.343344	+	0.832021i
$955$	0.429230	−	2.15788i	0.0138895	−	0.0698275i
$956$	1.96792	+	1.96792i	0.0636470	+	0.0636470i
$957$	12.6593	−	18.9731i	0.409217	−	0.613315i
$958$	2.45974	+	12.3659i	0.0794705	+	0.399525i
$959$	−17.5522	+	26.2688i	−0.566792	+	0.848264i
$960$	−39.5170	+	0.0261636i	−1.27541	+	0.000844428i
$961$	−20.9321	−	8.67037i	−0.675230	−	0.279689i
$962$	12.7368	+	8.51048i	0.410652	+	0.274389i
$963$	4.71851	+	3.14378i	0.152052	+	0.101307i
$964$	0.183538	+	0.274684i	0.00591135	+	0.00884697i
$965$	25.0752	−	25.0752i	0.807200	−	0.807200i
$966$	−4.08642	+	0.815652i	−0.131478	+	0.0262432i
$967$	−5.07976	−	12.2636i	−0.163354	−	0.394372i	0.820914	−	0.571051i	$-0.193464\pi$
$967$	−5.07976	−	12.2636i	−0.163354	−	0.394372i	−0.984268	+	0.176680i	$0.943464\pi$
$968$	22.6952			0.729452
$969$		0			0
$970$	15.7512			0.505739
$971$	−5.91933	−	14.2905i	−0.189960	−	0.458605i	0.799991	−	0.600012i	$-0.204837\pi$
$971$	−5.91933	−	14.2905i	−0.189960	−	0.458605i	−0.989952	+	0.141407i	$0.954837\pi$
$972$	−1.79346	+	0.362918i	−0.0575254	+	0.0116406i
$973$	−7.69338	+	7.69338i	−0.246638	+	0.246638i
$974$	−31.3806	−	46.9643i	−1.00550	−	1.50483i
$975$	18.3544	+	27.4300i	0.587812	+	0.878464i
$976$	−20.5193	−	13.7105i	−0.656805	−	0.438863i
$977$	−18.6618	−	7.72995i	−0.597042	−	0.247303i	0.0636347	−	0.997973i	$-0.479731\pi$
$977$	−18.6618	−	7.72995i	−0.597042	−	0.247303i	−0.660677	+	0.750670i	$0.729731\pi$
$978$	−0.00185371	−	2.79980i	−5.92750e−5	−	0.0895277i
$979$	−4.42817	+	6.62723i	−0.141525	+	0.211807i
$980$	0.164096	+	0.824966i	0.00524185	+	0.0263526i
$981$	12.3700	+	2.44353i	0.394945	+	0.0780159i
$982$	13.0385	+	13.0385i	0.416075	+	0.416075i
$983$	5.08915	−	25.5849i	0.162319	−	0.816031i	−0.810728	−	0.585423i	$-0.800929\pi$
$983$	5.08915	−	25.5849i	0.162319	−	0.816031i	0.973047	−	0.230608i	$-0.0740714\pi$
$984$	10.3391	+	10.3254i	0.329598	+	0.329162i
$985$			70.9874i			2.26185i
$986$		0			0
$987$	4.47994	+	10.7953i	0.142598	+	0.343618i
$988$	0.413882	−	0.171435i	0.0131673	−	0.00545409i
$989$	−8.60611	−	1.71186i	−0.273658	−	0.0544340i
$990$	−21.9499	+	0.0290655i	−0.697615	+	0.000923762i
$991$	−30.0243	+	20.0616i	−0.953754	+	0.637278i	−0.931990	−	0.362485i	$-0.881928\pi$
$991$	−30.0243	+	20.0616i	−0.953754	+	0.637278i	−0.0217647	+	0.999763i	$0.506928\pi$
$992$	−1.87875	+	0.373707i	−0.0596504	+	0.0118652i
$993$	51.7596	+	10.2600i	1.64254	+	0.325592i
$994$	−2.61157	+	6.30488i	−0.0828339	+	0.199979i
$995$	−28.1592	+	67.9824i	−0.892707	+	2.15519i
$996$	−2.59004	−	0.513408i	−0.0820685	−	0.0162680i
$997$	14.4897	−	2.88218i	0.458894	−	0.0912797i	0.0397704	−	0.999209i	$-0.487337\pi$
$997$	14.4897	−	2.88218i	0.458894	−	0.0912797i	0.419124	+	0.907929i	$0.362337\pi$
$998$	44.9065	−	30.0056i	1.42149	−	0.949809i
$999$	11.4240	−	4.75858i	0.361439	−	0.150555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.i.i.65.4		32
3.2	odd	2	inner	867.2.i.i.65.1		32
17.2	even	8		867.2.i.d.158.1		32
17.3	odd	16		867.2.i.c.653.4		32
17.4	even	4		867.2.i.f.224.1		32
17.5	odd	16		51.2.i.a.44.1	yes	32
17.6	odd	16		867.2.i.b.827.1		32
17.7	odd	16		867.2.i.f.329.4		32
17.8	even	8		867.2.i.h.131.4		32
17.9	even	8		51.2.i.a.29.4	yes	32
17.10	odd	16		867.2.i.g.329.4		32
17.11	odd	16	inner	867.2.i.i.827.1		32
17.12	odd	16		867.2.i.h.503.1		32
17.13	even	4		867.2.i.g.224.1		32
17.14	odd	16		867.2.i.d.653.4		32
17.15	even	8		867.2.i.c.158.1		32
17.16	even	2		867.2.i.b.65.4		32
51.2	odd	8		867.2.i.d.158.4		32
51.5	even	16		51.2.i.a.44.4	yes	32
51.8	odd	8		867.2.i.h.131.1		32
51.11	even	16	inner	867.2.i.i.827.4		32
51.14	even	16		867.2.i.d.653.1		32
51.20	even	16		867.2.i.c.653.1		32
51.23	even	16		867.2.i.b.827.4		32
51.26	odd	8		51.2.i.a.29.1	✓	32
51.29	even	16		867.2.i.h.503.4		32
51.32	odd	8		867.2.i.c.158.4		32
51.38	odd	4		867.2.i.f.224.4		32
51.41	even	16		867.2.i.f.329.1		32
51.44	even	16		867.2.i.g.329.1		32
51.47	odd	4		867.2.i.g.224.4		32
51.50	odd	2		867.2.i.b.65.1		32
68.39	even	16		816.2.cj.c.401.4		32
68.43	odd	8		816.2.cj.c.641.3		32
204.107	odd	16		816.2.cj.c.401.3		32
204.179	even	8		816.2.cj.c.641.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.1	✓	32	51.26	odd	8
51.2.i.a.29.4	yes	32	17.9	even	8
51.2.i.a.44.1	yes	32	17.5	odd	16
51.2.i.a.44.4	yes	32	51.5	even	16
816.2.cj.c.401.3		32	204.107	odd	16
816.2.cj.c.401.4		32	68.39	even	16
816.2.cj.c.641.3		32	68.43	odd	8
816.2.cj.c.641.4		32	204.179	even	8
867.2.i.b.65.1		32	51.50	odd	2
867.2.i.b.65.4		32	17.16	even	2
867.2.i.b.827.1		32	17.6	odd	16
867.2.i.b.827.4		32	51.23	even	16
867.2.i.c.158.1		32	17.15	even	8
867.2.i.c.158.4		32	51.32	odd	8
867.2.i.c.653.1		32	51.20	even	16
867.2.i.c.653.4		32	17.3	odd	16
867.2.i.d.158.1		32	17.2	even	8
867.2.i.d.158.4		32	51.2	odd	8
867.2.i.d.653.1		32	51.14	even	16
867.2.i.d.653.4		32	17.14	odd	16
867.2.i.f.224.1		32	17.4	even	4
867.2.i.f.224.4		32	51.38	odd	4
867.2.i.f.329.1		32	51.41	even	16
867.2.i.f.329.4		32	17.7	odd	16
867.2.i.g.224.1		32	17.13	even	4
867.2.i.g.224.4		32	51.47	odd	4
867.2.i.g.329.1		32	51.44	even	16
867.2.i.g.329.4		32	17.10	odd	16
867.2.i.h.131.1		32	51.8	odd	8
867.2.i.h.131.4		32	17.8	even	8
867.2.i.h.503.1		32	17.12	odd	16
867.2.i.h.503.4		32	51.29	even	16
867.2.i.i.65.1		32	3.2	odd	2	inner
867.2.i.i.65.4		32	1.1	even	1	trivial
867.2.i.i.827.1		32	17.11	odd	16	inner
867.2.i.i.827.4		32	51.11	even	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.556851 + 1.34436i) q^{2} +(0.339031 + 1.69855i) q^{3} +(-0.0830021 + 0.0830021i) q^{4} +(1.69526 + 2.53714i) q^{5} +(-2.09466 + 1.40162i) q^{6} +(1.79329 + 1.19824i) q^{7} +(2.53091 + 1.04834i) q^{8} +(-2.77012 + 1.15172i) q^{9} +(-2.46681 + 3.69185i) q^{10} +(-0.321478 - 1.61618i) q^{11} +(-0.169123 - 0.112843i) q^{12} +(-3.12551 - 3.12551i) q^{13} +(-0.612265 + 3.07806i) q^{14} +(-3.73470 + 3.73965i) q^{15} +4.22099i q^{16} +(-3.09087 - 3.08269i) q^{18} +(0.797694 - 0.330416i) q^{19} +(-0.351298 - 0.0698774i) q^{20} +(-1.42728 + 3.45222i) q^{21} +(1.99371 - 1.33215i) q^{22} +(0.751858 - 0.149554i) q^{23} +(-0.922593 + 4.65429i) q^{24} +(-1.64974 + 3.98282i) q^{25} +(2.46136 - 5.94226i) q^{26} +(-2.89540 - 4.31470i) q^{27} +(-0.248303 + 0.0493905i) q^{28} +(6.64464 - 4.43981i) q^{29} +(-7.10709 - 2.93834i) q^{30} +(2.83296 + 0.563512i) q^{31} +(-0.612694 + 0.253786i) q^{32} +(2.63616 - 1.09398i) q^{33} +6.58114i q^{35} +(0.134330 - 0.325520i) q^{36} +(-0.464638 + 2.33589i) q^{37} +(0.888394 + 0.888394i) q^{38} +(4.24918 - 6.36847i) q^{39} +(1.63078 + 8.19848i) q^{40} +(1.71091 - 2.56055i) q^{41} +(-5.43581 + 0.00359897i) q^{42} +(-10.5751 - 4.38037i) q^{43} +(0.160829 + 0.107463i) q^{44} +(-7.61814 - 5.07570i) q^{45} +(0.619727 + 0.927487i) q^{46} +(2.21238 - 2.21238i) q^{47} +(-7.16954 + 1.43105i) q^{48} +(-0.898671 - 2.16958i) q^{49} -6.27299 q^{50} +0.518848 q^{52} +(-2.43710 - 5.88369i) q^{53} +(4.18819 - 6.29511i) q^{54} +(3.55548 - 3.55548i) q^{55} +(3.28250 + 4.91261i) q^{56} +(0.831669 + 1.24290i) q^{57} +(9.66877 + 6.46046i) q^{58} +(-5.62864 - 2.33146i) q^{59} +(-0.000410749 - 0.620386i) q^{60} +(-3.24818 + 4.86125i) q^{61} +(0.819979 + 4.12231i) q^{62} +(-6.34765 - 1.25389i) q^{63} +(5.28702 + 5.28702i) q^{64} +(2.63129 - 13.2284i) q^{65} +(2.93865 + 2.93476i) q^{66} +7.19481i q^{67} +(0.508927 + 1.22636i) q^{69} +(-8.84742 + 3.66472i) q^{70} +(2.13271 + 0.424222i) q^{71} +(-8.21831 + 0.0108825i) q^{72} +(-10.4594 + 6.98874i) q^{73} +(-3.39901 + 0.676105i) q^{74} +(-7.32431 - 1.45186i) q^{75} +(-0.0387851 + 0.0936354i) q^{76} +(1.36006 - 3.28348i) q^{77} +(10.9277 + 2.16613i) q^{78} +(-5.84360 + 1.16236i) q^{79} +(-10.7092 + 7.15567i) q^{80} +(6.34708 - 6.38079i) q^{81} +(4.39502 + 0.874225i) q^{82} +(11.9985 - 4.96993i) q^{83} +(-0.168074 - 0.405009i) q^{84} -16.6560i q^{86} +(9.79395 + 9.78099i) q^{87} +(0.880669 - 4.42742i) q^{88} +(-3.42023 - 3.42023i) q^{89} +(2.58139 - 13.0679i) q^{90} +(-1.85984 - 9.35006i) q^{91} +(-0.0499925 + 0.0748190i) q^{92} +(0.00331239 + 5.00297i) q^{93} +(4.20619 + 1.74226i) q^{94} +(2.19061 + 1.46372i) q^{95} +(-0.638789 - 0.954647i) q^{96} +(-1.97085 - 2.94959i) q^{97} +(2.41627 - 2.41627i) q^{98} +(2.75191 + 4.10675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{3} + 16 q^{4} - 16 q^{6} - 24 q^{9} + 32 q^{10} + 40 q^{12} + 16 q^{13} - 16 q^{15} + 16 q^{18} - 32 q^{19} - 16 q^{21} - 32 q^{22} + 16 q^{24} - 16 q^{27} + 32 q^{28} + 8 q^{30} + 24 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) \) 32 * q + 8 * q^3 + 16 * q^4 - 16 * q^6 - 24 * q^9 + 32 * q^10 + 40 * q^12 + 16 * q^13 - 16 * q^15 + 16 * q^18 - 32 * q^19 - 16 * q^21 - 32 * q^22 + 16 * q^24 - 16 * q^27 + 32 * q^28 + 8 * q^30 + 24 * q^36 - 96 * q^37 + 48 * q^39 + 80 * q^40 + 24 * q^42 + 32 * q^43 - 40 * q^45 - 64 * q^46 + 48 * q^48 + 64 * q^49 - 96 * q^52 + 48 * q^54 + 48 * q^55 - 8 * q^57 - 48 * q^60 - 64 * q^61 - 16 * q^64 - 120 * q^66 + 80 * q^69 - 64 * q^72 - 144 * q^73 + 8 * q^75 - 32 * q^76 - 40 * q^78 + 64 * q^79 - 48 * q^81 - 32 * q^82 + 56 * q^87 + 32 * q^88 + 24 * q^90 + 48 * q^91 + 56 * q^93 + 48 * q^94 - 72 * q^96 - 32 * q^97 - 16 * q^99

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