LMFDB - Embedded newform 833.2.bc.f.80.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [833,2,Mod(31,833)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("833.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(833, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([8, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.bc (of order $48$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [160,16,0,16,0,0,0,-32,16,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$10$ over $\Q(\zeta_{48})$
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			80.8
Character	$\chi$	$=$	833.80
Dual form			833.2.bc.f.656.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.610037 - 0.795016i) q^{2} +(0.718354 - 0.0470834i) q^{3} +(0.257733 + 0.961873i) q^{4} +(-3.02536 + 1.02697i) q^{5} +(0.400790 - 0.599825i) q^{6} +(2.77356 + 1.14885i) q^{8} +(-2.46052 + 0.323934i) q^{9} +(-1.02912 + 3.03170i) q^{10} +(-1.77675 - 3.60290i) q^{11} +(0.230432 + 0.678830i) q^{12} +(-2.97778 + 2.97778i) q^{13} +(-2.12493 + 0.880173i) q^{15} +(0.880544 - 0.508383i) q^{16} +(-3.86202 + 1.44388i) q^{17} +(-1.24348 + 2.15376i) q^{18} +(-0.828402 - 0.635655i) q^{19} +(-1.76755 - 2.64533i) q^{20} +(-3.94825 - 0.785356i) q^{22} +(-0.184074 + 2.80843i) q^{23} +(2.04649 + 0.694690i) q^{24} +(4.13137 - 3.17011i) q^{25} +(0.550825 + 4.18393i) q^{26} +(-3.87046 + 0.769882i) q^{27} +(1.03153 - 5.18584i) q^{29} +(-0.596532 + 2.22629i) q^{30} +(-0.283985 - 4.33277i) q^{31} +(-0.650708 + 4.94262i) q^{32} +(-1.44598 - 2.50450i) q^{33} +(-1.20807 + 3.95119i) q^{34} +(-0.945740 - 2.28322i) q^{36} +(4.32467 + 2.13269i) q^{37} +(-1.01071 + 0.270820i) q^{38} +(-1.99889 + 2.27930i) q^{39} +(-9.57086 - 0.627307i) q^{40} +(0.667258 + 3.35453i) q^{41} +(-4.12022 + 9.94710i) q^{43} +(3.00761 - 2.63760i) q^{44} +(7.11129 - 3.50690i) q^{45} +(2.12045 + 1.85959i) q^{46} +(-12.6376 - 3.38625i) q^{47} +(0.608606 - 0.406658i) q^{48} -5.21839i q^{50} +(-2.70632 + 1.21905i) q^{51} +(-3.63171 - 2.09677i) q^{52} +(-2.75419 - 0.362596i) q^{53} +(-1.74906 + 3.54673i) q^{54} +(9.07540 + 9.07540i) q^{55} +(-0.625015 - 0.417621i) q^{57} +(-3.49356 - 3.98364i) q^{58} +(4.19605 + 5.46840i) q^{59} +(-1.39428 - 1.81706i) q^{60} +(5.26459 + 6.00311i) q^{61} +(-3.61786 - 2.41738i) q^{62} +(4.97043 + 4.97043i) q^{64} +(5.95076 - 12.0669i) q^{65} +(-2.87322 - 0.378266i) q^{66} +(-0.131030 - 0.0756499i) q^{67} +(-2.38420 - 3.34264i) q^{68} +2.02611i q^{69} +(2.01514 - 1.34647i) q^{71} +(-7.19655 - 1.92831i) q^{72} +(10.2545 + 8.99298i) q^{73} +(4.33374 - 2.13716i) q^{74} +(2.81853 - 2.47178i) q^{75} +(0.397913 - 0.960647i) q^{76} +(0.592681 + 2.97961i) q^{78} +(-7.04221 - 0.461571i) q^{79} +(-2.14187 + 2.44233i) q^{80} +(4.44745 - 1.19169i) q^{81} +(3.07396 + 1.51591i) q^{82} +(0.613584 + 1.48132i) q^{83} +(10.2012 - 8.33444i) q^{85} +(5.39461 + 9.34375i) q^{86} +(0.496835 - 3.77384i) q^{87} +(-0.788756 - 12.0341i) q^{88} +(0.344834 - 1.28694i) q^{89} +(1.55011 - 7.79293i) q^{90} +(-2.74879 + 0.546769i) q^{92} +(-0.408003 - 3.09909i) q^{93} +(-10.4016 + 7.98139i) q^{94} +(3.15902 + 1.07234i) q^{95} +(-0.234723 + 3.58119i) q^{96} +(7.22183 + 1.43651i) q^{97} +(5.53884 + 8.28946i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 128 q^{15} - 32 q^{18} - 96 q^{22} + 16 q^{23} - 32 q^{29} - 112 q^{30} - 16 q^{32} - 96 q^{36} - 48 q^{37} - 32 q^{43} + 16 q^{44} - 16 q^{46} + 48 q^{51}+ \cdots + 256 q^{99}+O(q^{100}) $ 160 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 128 * q^15 - 32 * q^18 - 96 * q^22 + 16 * q^23 - 32 * q^29 - 112 * q^30 - 16 * q^32 - 96 * q^36 - 48 * q^37 - 32 * q^43 + 16 * q^44 - 16 * q^46 + 48 * q^51 - 16 * q^53 - 32 * q^57 + 48 * q^58 - 48 * q^60 + 96 * q^64 + 32 * q^65 + 32 * q^71 + 80 * q^72 + 80 * q^74 + 224 * q^78 + 16 * q^79 + 64 * q^81 + 224 * q^85 - 48 * q^86 + 112 * q^88 + 512 * q^92 - 48 * q^93 + 48 * q^95 + 256 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{16}\right)$

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 $

$2$	0.610037	−	0.795016i	0.431361	−	0.562161i	−0.526211	−	0.850354i	$-0.676388\pi$
$2$	0.610037	−	0.795016i	0.431361	−	0.562161i	0.957572	+	0.288193i	$0.0930544\pi$
$3$	0.718354	−	0.0470834i	0.414742	−	0.0271836i	0.143396	−	0.989665i	$-0.454198\pi$
$3$	0.718354	−	0.0470834i	0.414742	−	0.0271836i	0.271346	+	0.962482i	$0.412531\pi$
$4$	0.257733	+	0.961873i	0.128867	+	0.480937i
$5$	−3.02536	+	1.02697i	−1.35298	+	0.459276i	−0.901413	−	0.432960i	$-0.857469\pi$
$5$	−3.02536	+	1.02697i	−1.35298	+	0.459276i	−0.451570	+	0.892236i	$0.649136\pi$
$6$	0.400790	−	0.599825i	0.163622	−	0.244878i
$7$		0			0
$7$		0			0
$8$	2.77356	+	1.14885i	0.980602	+	0.406179i
$9$	−2.46052	+	0.323934i	−0.820173	+	0.107978i
$10$	−1.02912	+	3.03170i	−0.325438	+	0.958708i
$11$	−1.77675	−	3.60290i	−0.535712	−	1.08632i	−0.981551	−	0.191203i	$-0.938761\pi$
$11$	−1.77675	−	3.60290i	−0.535712	−	1.08632i	0.445839	−	0.895113i	$-0.352905\pi$
$12$	0.230432	+	0.678830i	0.0665199	+	0.195961i
$13$	−2.97778	+	2.97778i	−0.825886	+	0.825886i	−0.986945	−	0.161058i	$-0.948509\pi$
$13$	−2.97778	+	2.97778i	−0.825886	+	0.825886i	0.161058	+	0.986945i	$0.448509\pi$
$14$		0			0
$15$	−2.12493	+	0.880173i	−0.548654	+	0.227260i
$16$	0.880544	−	0.508383i	0.220136	−	0.127096i
$17$	−3.86202	+	1.44388i	−0.936678	+	0.350192i
$17$	−3.86202	+	1.44388i	−0.936678	+	0.350192i
$18$	−1.24348	+	2.15376i	−0.293090	+	0.507647i
$19$	−0.828402	−	0.635655i	−0.190049	−	0.145829i	0.509355	−	0.860557i	$-0.329884\pi$
$19$	−0.828402	−	0.635655i	−0.190049	−	0.145829i	−0.699403	+	0.714727i	$0.746551\pi$
$20$	−1.76755	−	2.64533i	−0.395237	−	0.591513i
$21$		0			0
$22$	−3.94825	−	0.785356i	−0.841770	−	0.167438i
$23$	−0.184074	+	2.80843i	−0.0383821	+	0.585597i	0.934744	+	0.355323i	$0.115629\pi$
$23$	−0.184074	+	2.80843i	−0.0383821	+	0.585597i	−0.973126	+	0.230274i	$0.926038\pi$
$24$	2.04649	+	0.694690i	0.417738	+	0.141803i
$25$	4.13137	−	3.17011i	0.826274	−	0.634023i
$26$	0.550825	+	4.18393i	0.108026	+	0.820537i
$27$	−3.87046	+	0.769882i	−0.744870	+	0.148164i
$28$		0			0
$29$	1.03153	−	5.18584i	0.191550	−	0.962986i	−0.758686	−	0.651456i	$-0.774158\pi$
$29$	1.03153	−	5.18584i	0.191550	−	0.962986i	0.950236	−	0.311530i	$-0.100842\pi$
$30$	−0.596532	+	2.22629i	−0.108911	+	0.406463i
$31$	−0.283985	−	4.33277i	−0.0510052	−	0.778189i	−0.944376	−	0.328868i	$-0.893333\pi$
$31$	−0.283985	−	4.33277i	−0.0510052	−	0.778189i	0.893371	−	0.449321i	$-0.148334\pi$
$32$	−0.650708	+	4.94262i	−0.115030	+	0.873740i
$33$	−1.44598	−	2.50450i	−0.251712	−	0.435978i
$34$	−1.20807	+	3.95119i	−0.207182	+	0.677623i
$35$		0			0
$36$	−0.945740	−	2.28322i	−0.157623	−	0.380536i
$37$	4.32467	+	2.13269i	0.710972	+	0.350613i	0.761549	−	0.648108i	$-0.224439\pi$
$37$	4.32467	+	2.13269i	0.710972	+	0.350613i	−0.0505767	+	0.998720i	$0.516106\pi$
$38$	−1.01071	+	0.270820i	−0.163959	+	0.0439327i
$39$	−1.99889	+	2.27930i	−0.320079	+	0.364980i
$40$	−9.57086	−	0.627307i	−1.51329	−	0.0991860i
$41$	0.667258	+	3.35453i	0.104208	+	0.523890i	0.997263	+	0.0739411i	$0.0235577\pi$
$41$	0.667258	+	3.35453i	0.104208	+	0.523890i	−0.893054	+	0.449949i	$0.851442\pi$
$42$		0			0
$43$	−4.12022	+	9.94710i	−0.628328	+	1.51692i	0.213370	+	0.976971i	$0.431556\pi$
$43$	−4.12022	+	9.94710i	−0.628328	+	1.51692i	−0.841699	+	0.539948i	$0.818444\pi$
$44$	3.00761	−	2.63760i	0.453414	−	0.397633i
$45$	7.11129	−	3.50690i	1.06009	−	0.522778i
$46$	2.12045	+	1.85959i	0.312643	+	0.274181i
$47$	−12.6376	−	3.38625i	−1.84339	−	0.493935i	−0.844272	−	0.535915i	$-0.819967\pi$
$47$	−12.6376	−	3.38625i	−1.84339	−	0.493935i	−0.999118	+	0.0419802i	$0.986633\pi$
$48$	0.608606	−	0.406658i	0.0878447	−	0.0586960i
$49$		0			0
$50$		−	5.21839i		−	0.737992i
$51$	−2.70632	+	1.21905i	−0.378960	+	0.170701i
$52$	−3.63171	−	2.09677i	−0.503628	−	0.290770i
$53$	−2.75419	−	0.362596i	−0.378317	−	0.0498064i	−0.0610302	−	0.998136i	$-0.519439\pi$
$53$	−2.75419	−	0.362596i	−0.378317	−	0.0498064i	−0.317287	+	0.948329i	$0.602772\pi$
$54$	−1.74906	+	3.54673i	−0.238016	+	0.482649i
$55$	9.07540	+	9.07540i	1.22373	+	1.22373i
$56$		0			0
$57$	−0.625015	−	0.417621i	−0.0827852	−	0.0553153i
$58$	−3.49356	−	3.98364i	−0.458726	−	0.523077i
$59$	4.19605	+	5.46840i	0.546279	+	0.711925i	0.982153	−	0.188083i	$-0.0602273\pi$
$59$	4.19605	+	5.46840i	0.546279	+	0.711925i	−0.435874	+	0.900008i	$0.643561\pi$
$60$	−1.39428	−	1.81706i	−0.180001	−	0.234581i
$61$	5.26459	+	6.00311i	0.674061	+	0.768619i	0.983226	−	0.182389i	$-0.0583830\pi$
$61$	5.26459	+	6.00311i	0.674061	+	0.768619i	−0.309165	+	0.951008i	$0.600050\pi$
$62$	−3.61786	−	2.41738i	−0.459469	−	0.307008i
$63$		0			0
$64$	4.97043	+	4.97043i	0.621303	+	0.621303i
$65$	5.95076	−	12.0669i	0.738100	−	1.49672i
$66$	−2.87322	−	0.378266i	−0.353669	−	0.0465614i
$67$	−0.131030	−	0.0756499i	−0.0160078	−	0.00924211i	0.491975	−	0.870609i	$-0.336275\pi$
$67$	−0.131030	−	0.0756499i	−0.0160078	−	0.00924211i	−0.507983	+	0.861367i	$0.669609\pi$
$68$	−2.38420	−	3.34264i	−0.289127	−	0.405355i
$69$			2.02611i			0.243915i
$70$		0			0
$71$	2.01514	−	1.34647i	0.239153	−	0.159797i	−0.430219	−	0.902725i	$-0.641564\pi$
$71$	2.01514	−	1.34647i	0.239153	−	0.159797i	0.669371	+	0.742928i	$0.266564\pi$
$72$	−7.19655	−	1.92831i	−0.848122	−	0.227254i
$73$	10.2545	+	8.99298i	1.20020	+	1.05255i	0.997306	+	0.0733476i	$0.0233682\pi$
$73$	10.2545	+	8.99298i	1.20020	+	1.05255i	0.202895	+	0.979201i	$0.434965\pi$
$74$	4.33374	−	2.13716i	0.503787	−	0.248440i
$75$	2.81853	−	2.47178i	0.325455	−	0.285417i
$76$	0.397913	−	0.960647i	0.0456438	−	0.110194i
$77$		0			0
$78$	0.592681	+	2.97961i	0.0671079	+	0.337374i
$79$	−7.04221	−	0.461571i	−0.792311	−	0.0519308i	−0.336127	−	0.941817i	$-0.609117\pi$
$79$	−7.04221	−	0.461571i	−0.792311	−	0.0519308i	−0.456183	+	0.889886i	$0.650784\pi$
$80$	−2.14187	+	2.44233i	−0.239468	+	0.273061i
$81$	4.44745	−	1.19169i	0.494161	−	0.132410i
$82$	3.07396	+	1.51591i	0.339462	+	0.167404i
$83$	0.613584	+	1.48132i	0.0673496	+	0.162596i	0.953970	−	0.299901i	$-0.0969536\pi$
$83$	0.613584	+	1.48132i	0.0673496	+	0.162596i	−0.886621	+	0.462497i	$0.846954\pi$
$84$		0			0
$85$	10.2012	−	8.33444i	1.10647	−	0.903997i
$86$	5.39461	+	9.34375i	0.581716	+	1.00756i
$87$	0.496835	−	3.77384i	0.0532663	−	0.404598i
$88$	−0.788756	−	12.0341i	−0.0840817	−	1.28284i
$89$	0.344834	−	1.28694i	0.0365523	−	0.136415i	−0.945238	−	0.326381i	$-0.894171\pi$
$89$	0.344834	−	1.28694i	0.0365523	−	0.136415i	0.981791	+	0.189965i	$0.0608376\pi$
$90$	1.55011	−	7.79293i	0.163396	−	0.821447i
$91$		0			0
$92$	−2.74879	+	0.546769i	−0.286581	+	0.0570046i
$93$	−0.408003	−	3.09909i	−0.0423080	−	0.321361i
$94$	−10.4016	+	7.98139i	−1.07284	+	0.823218i
$95$	3.15902	+	1.07234i	0.324108	+	0.110020i
$96$	−0.234723	+	3.58119i	−0.0239564	+	0.365503i
$97$	7.22183	+	1.43651i	0.733266	+	0.145856i	0.547580	−	0.836753i	$-0.315549\pi$
$97$	7.22183	+	1.43651i	0.733266	+	0.145856i	0.185686	+	0.982609i	$0.440549\pi$
$98$		0			0
$99$	5.53884	+	8.28946i	0.556674	+	0.833122i
$100$	4.11404	+	3.15681i	0.411404	+	0.315681i
$101$	8.65672	−	14.9939i	0.861375	−	1.49195i	−0.00922616	−	0.999957i	$-0.502937\pi$
$101$	8.65672	−	14.9939i	0.861375	−	1.49195i	0.870602	−	0.491989i	$-0.163730\pi$
$102$	−0.681787	+	2.89523i	−0.0675070	+	0.286671i
$103$	5.21727	−	3.01219i	0.514073	−	0.296800i	−0.220434	−	0.975402i	$-0.570747\pi$
$103$	5.21727	−	3.01219i	0.514073	−	0.296800i	0.734506	+	0.678602i	$0.237414\pi$
$104$	−11.6801	+	4.83804i	−1.14532	+	0.474409i
$105$		0			0
$106$	−1.96843	+	1.96843i	−0.191191	+	0.191191i
$107$	2.92396	+	8.61371i	0.282670	+	0.832719i	0.991818	+	0.127659i	$0.0407464\pi$
$107$	2.92396	+	8.61371i	0.282670	+	0.832719i	−0.709148	+	0.705060i	$0.750920\pi$
$108$	−1.73807	−	3.52447i	−0.167246	−	0.339142i
$109$	−2.15010	+	6.33399i	−0.205942	+	0.606687i	−0.999999	−	0.00115670i	$-0.999632\pi$
$109$	−2.15010	+	6.33399i	−0.205942	+	0.606687i	0.794057	+	0.607843i	$0.207965\pi$
$110$	12.7514	−	1.67876i	1.21580	−	0.160063i
$111$	3.20706	+	1.32841i	0.304401	+	0.126087i
$112$		0			0
$113$	5.25777	−	7.86881i	0.494610	−	0.740236i	−0.497245	−	0.867610i	$-0.665655\pi$
$113$	5.25777	−	7.86881i	0.494610	−	0.740236i	0.991855	+	0.127374i	$0.0406550\pi$
$114$	−0.713298	+	0.242132i	−0.0668065	+	0.0226777i
$115$	−2.32728	−	8.68554i	−0.217020	−	0.809931i
$116$	5.25398	−	0.344364i	0.487820	−	0.0319734i
$117$	6.36227	−	8.29148i	0.588192	−	0.766547i
$118$	6.90721			0.635861
$119$		0			0
$120$	−6.90480			−0.630319
$121$	−3.12767	+	4.07606i	−0.284333	+	0.370551i
$122$	7.98416	−	0.523310i	0.722852	−	0.0473782i
$123$	0.637270	+	2.37832i	0.0574607	+	0.214446i
$124$	4.09439	−	1.38986i	0.367687	−	0.124813i
$125$	−0.368276	+	0.551164i	−0.0329396	+	0.0492976i
$126$		0			0
$127$	−14.6316	−	6.06062i	−1.29835	−	0.537793i	−0.376885	−	0.926260i	$-0.623005\pi$
$127$	−14.6316	−	6.06062i	−1.29835	−	0.537793i	−0.921463	+	0.388467i	$0.873005\pi$
$128$	−2.90152	+	0.381993i	−0.256461	+	0.0337637i
$129$	−2.49144	+	7.33953i	−0.219359	+	0.646210i
$130$	−5.96323	−	12.0922i	−0.523010	−	1.06056i
$131$	−2.01281	−	5.92954i	−0.175860	−	0.518066i	0.822882	−	0.568212i	$-0.192365\pi$
$131$	−2.01281	−	5.92954i	−0.175860	−	0.518066i	−0.998742	+	0.0501460i	$0.984031\pi$
$132$	2.03634	−	2.03634i	0.177240	−	0.177240i
$133$		0			0
$134$	−0.140076	+	0.0580213i	−0.0121007	+	0.00501228i
$135$	10.9189	−	6.30402i	0.939748	−	0.542564i
$136$	−12.3704	−	0.432187i	−1.06075	−	0.0370597i
$137$	−2.35120	+	4.07240i	−0.200876	+	0.347928i	−0.948811	−	0.315844i	$-0.897712\pi$
$137$	−2.35120	+	4.07240i	−0.200876	+	0.347928i	0.747935	+	0.663772i	$0.231046\pi$
$138$	1.61079	+	1.23600i	0.137120	+	0.105216i
$139$	−2.92538	−	4.37814i	−0.248127	−	0.371349i	0.686410	−	0.727215i	$-0.259186\pi$
$139$	−2.92538	−	4.37814i	−0.248127	−	0.371349i	−0.934537	+	0.355866i	$0.884186\pi$
$140$		0			0
$141$	−9.23774	−	1.83750i	−0.777958	−	0.154745i
$142$	0.158842	−	2.42346i	0.0133297	−	0.203373i
$143$	16.0194	+	5.43786i	1.33961	+	0.454736i
$144$	−2.00191	+	1.53612i	−0.166826	+	0.128010i
$145$	2.20497	+	16.7484i	0.183113	+	1.39088i
$146$	13.4052	−	2.66646i	1.10942	−	0.220678i
$147$		0			0
$148$	−0.936769	+	4.70945i	−0.0770019	+	0.387115i
$149$	−2.35169	+	8.77664i	−0.192658	+	0.719011i	0.800202	+	0.599730i	$0.204725\pi$
$149$	−2.35169	+	8.77664i	−0.192658	+	0.719011i	−0.992861	+	0.119280i	$0.961941\pi$
$150$	−0.245700	−	3.74865i	−0.0200613	−	0.306076i
$151$	−1.83133	+	13.9104i	−0.149032	+	1.13201i	0.739488	+	0.673170i	$0.235068\pi$
$151$	−1.83133	+	13.9104i	−0.149032	+	1.13201i	−0.888519	+	0.458839i	$0.848265\pi$
$152$	−1.56735	−	2.71474i	−0.127129	−	0.220194i
$153$	9.03486	−	4.80373i	0.730425	−	0.388358i
$154$		0			0
$155$	5.30879	+	12.8166i	0.426412	+	1.02945i
$156$	−2.70758	−	1.33523i	−0.216780	−	0.106904i
$157$	−10.1510	+	2.71996i	−0.810139	+	0.217076i	−0.640031	−	0.768349i	$-0.721078\pi$
$157$	−10.1510	+	2.71996i	−0.810139	+	0.217076i	−0.170108	+	0.985425i	$0.554412\pi$
$158$	−4.66297	+	5.31710i	−0.370966	+	0.423005i
$159$	−1.99556	−	0.130796i	−0.158258	−	0.0103728i
$160$	−3.10730	−	15.6215i	−0.245654	−	1.23499i
$161$		0			0
$162$	1.76570	−	4.26277i	0.138726	−	0.334915i
$163$	−4.18903	+	3.67368i	−0.328110	+	0.287745i	−0.807513	−	0.589850i	$-0.799187\pi$
$163$	−4.18903	+	3.67368i	−0.328110	+	0.287745i	0.479403	+	0.877595i	$0.340853\pi$
$164$	−3.05466	+	1.50639i	−0.238529	+	0.117629i
$165$	6.94665	+	6.09205i	0.540796	+	0.474265i
$166$	1.55198	+	0.415853i	0.120457	+	0.0322764i
$167$	−12.2208	+	8.16569i	−0.945675	+	0.631880i	−0.929828	−	0.367995i	$-0.880044\pi$
$167$	−12.2208	+	8.16569i	−0.945675	+	0.631880i	−0.0158470	+	0.999874i	$0.505044\pi$
$168$		0			0
$169$		−	4.73430i		−	0.364177i
$170$	−0.402908	−	13.1944i	−0.0309016	−	1.01197i
$171$	2.24421	+	1.29570i	0.171619	+	0.0990843i
$172$	−10.6298	−	1.39944i	−0.810512	−	0.106706i
$173$	3.61581	−	7.33213i	0.274905	−	0.557451i	−0.715010	−	0.699114i	$-0.753578\pi$
$173$	3.61581	−	7.33213i	0.274905	−	0.557451i	0.989915	+	0.141662i	$0.0452447\pi$
$174$	−2.69717	−	2.69717i	−0.204472	−	0.204472i
$175$		0			0
$176$	−3.39616	−	2.26924i	−0.255995	−	0.171051i
$177$	3.27172	+	3.73068i	0.245918	+	0.280415i
$178$	−0.812774	−	1.05923i	−0.0609200	−	0.0793925i
$179$	−9.31927	−	12.1451i	−0.696555	−	0.907768i	0.302413	−	0.953177i	$-0.402208\pi$
$179$	−9.31927	−	12.1451i	−0.696555	−	0.907768i	−0.998968	+	0.0454086i	$0.985541\pi$
$180$	5.20601	+	5.93631i	0.388033	+	0.442467i
$181$	−1.75360	−	1.17172i	−0.130344	−	0.0870931i	0.488689	−	0.872458i	$-0.337475\pi$
$181$	−1.75360	−	1.17172i	−0.130344	−	0.0870931i	−0.619033	+	0.785365i	$0.712475\pi$
$182$		0			0
$183$	4.06448	+	4.06448i	0.300455	+	0.300455i
$184$	−3.73699	+	7.57787i	−0.275495	+	0.558648i
$185$	−15.2739	−	2.01085i	−1.12296	−	0.147841i
$186$	−2.71273	−	1.56619i	−0.198907	−	0.114839i
$187$	12.0640	+	11.3491i	0.882208	+	0.829926i
$188$		−	13.0286i		−	0.950205i
$189$		0			0
$190$	2.77965	−	1.85730i	0.201657	−	0.134743i
$191$	−11.8212	−	3.16747i	−0.855350	−	0.229190i	−0.195608	−	0.980682i	$-0.562668\pi$
$191$	−11.8212	−	3.16747i	−0.855350	−	0.229190i	−0.659742	+	0.751492i	$0.729335\pi$
$192$	3.80455	+	3.33650i	0.274570	+	0.240791i
$193$	−24.5557	+	12.1095i	−1.76756	+	0.871664i	−0.808483	+	0.588519i	$0.799711\pi$
$193$	−24.5557	+	12.1095i	−1.76756	+	0.871664i	−0.959077	+	0.283145i	$0.908622\pi$
$194$	5.54764	−	4.86515i	0.398297	−	0.349297i
$195$	3.70660	−	8.94851i	0.265435	−	0.640816i
$196$		0			0
$197$	0.774375	+	3.89305i	0.0551720	+	0.277368i	0.998517	−	0.0544461i	$-0.0173393\pi$
$197$	0.774375	+	3.89305i	0.0551720	+	0.277368i	−0.943345	+	0.331814i	$0.892339\pi$
$198$	9.96915	+	0.653413i	0.708477	+	0.0464360i
$199$	5.32482	−	6.07179i	0.377466	−	0.430418i	−0.531647	−	0.846966i	$-0.678427\pi$
$199$	5.32482	−	6.07179i	0.377466	−	0.430418i	0.909114	+	0.416548i	$0.136760\pi$
$200$	15.1006	−	4.04619i	1.06777	−	0.286109i
$201$	−0.0976874	−	0.0481741i	−0.00689034	−	0.00339794i
$202$	−6.63945	−	16.0290i	−0.467150	−	1.12780i
$203$		0			0
$204$	−1.87008	−	2.28894i	−0.130932	−	0.160258i
$205$	−5.46370	−	9.46341i	−0.381602	−	0.660953i
$206$	0.787987	−	5.98536i	0.0549017	−	0.417020i
$207$	−0.456826	−	6.96981i	−0.0317516	−	0.484436i
$208$	−1.10821	+	4.13591i	−0.0768409	+	0.286774i
$209$	−0.818336	+	4.11406i	−0.0566055	+	0.284575i
$210$		0			0
$211$	10.7623	−	2.14076i	0.740911	−	0.147376i	0.189817	−	0.981820i	$-0.439211\pi$
$211$	10.7623	−	2.14076i	0.740911	−	0.147376i	0.551094	+	0.834443i	$0.314211\pi$
$212$	−0.361075	−	2.74264i	−0.0247987	−	0.188365i
$213$	1.38419	−	1.06212i	0.0948428	−	0.0727754i
$214$	8.63176	+	2.93009i	0.590055	+	0.200297i
$215$	2.24977	−	34.3249i	0.153433	−	2.34094i
$216$	−11.6194	−	2.31125i	−0.790603	−	0.157261i
$217$		0			0
$218$	3.72398	+	5.57334i	0.252220	+	0.377474i
$219$	7.78980	+	5.97732i	0.526386	+	0.403910i
$220$	−6.39035	+	11.0684i	−0.430838	+	0.746232i
$221$	7.20069	−	15.7998i	0.484371	−	1.06281i
$222$	3.01253	−	1.73929i	0.202188	−	0.116733i
$223$	3.08438	−	1.27759i	0.206545	−	0.0855538i	−0.277013	−	0.960866i	$-0.589344\pi$
$223$	3.08438	−	1.27759i	0.206545	−	0.0855538i	0.483558	+	0.875313i	$0.339344\pi$
$224$		0			0
$225$	−9.13841	+	9.13841i	−0.609228	+	0.609228i
$226$	−3.04840	−	8.98028i	−0.202776	−	0.597360i
$227$	−2.24461	−	4.55161i	−0.148980	−	0.302101i	0.809571	−	0.587021i	$-0.199700\pi$
$227$	−2.24461	−	4.55161i	−0.148980	−	0.302101i	−0.958551	+	0.284920i	$0.908033\pi$
$228$	0.240612	−	0.708820i	0.0159349	−	0.0469427i
$229$	−3.78656	+	0.498510i	−0.250223	+	0.0329424i	−0.254594	−	0.967048i	$-0.581942\pi$
$229$	−3.78656	+	0.498510i	−0.250223	+	0.0329424i	0.00437142	+	0.999990i	$0.498609\pi$
$230$	−8.32487	−	3.44828i	−0.548926	−	0.227373i
$231$		0			0
$232$	8.81874	−	13.1982i	0.578979	−	0.866503i
$233$	20.0838	−	6.81754i	1.31574	−	0.446632i	0.426668	−	0.904408i	$-0.359687\pi$
$233$	20.0838	−	6.81754i	1.31574	−	0.446632i	0.889067	+	0.457776i	$0.151354\pi$
$234$	−2.71063	−	10.1162i	−0.177200	−	0.661318i
$235$	41.7110	−	2.73388i	2.72093	−	0.178339i
$236$	−4.17845	+	5.44546i	−0.271994	+	0.354469i
$237$	−5.08053			−0.330016
$238$		0			0
$239$	−20.7489			−1.34214			−0.671068	−	0.741395i	$-0.734164\pi$
$239$	−20.7489			−1.34214			−0.671068	+	0.741395i	$0.734164\pi$
$240$	−1.42363	+	1.85531i	−0.0918947	+	0.119760i
$241$	−25.0886	+	1.64440i	−1.61610	+	0.105925i	−0.846425	−	0.532508i	$-0.821249\pi$
$241$	−25.0886	+	1.64440i	−1.61610	+	0.105925i	−0.769677	+	0.638433i	$0.779583\pi$
$242$	1.33254	+	4.97309i	0.0856586	+	0.319682i
$243$	14.3493	−	4.87093i	0.920508	−	0.312470i
$244$	−4.41737	+	6.61106i	−0.282793	+	0.423230i
$245$		0			0
$246$	2.27956	+	0.944226i	0.145340	+	0.0602016i
$247$	4.35964	−	0.573957i	0.277397	−	0.0365200i
$248$	4.19004	−	12.3435i	0.266068	−	0.783811i
$249$	0.510516	+	1.03522i	0.0323526	+	0.0656047i
$250$	0.213522	+	0.629016i	0.0135043	+	0.0397825i
$251$	9.91577	−	9.91577i	0.625878	−	0.625878i	−0.321150	−	0.947028i	$-0.604069\pi$
$251$	9.91577	−	9.91577i	0.625878	−	0.625878i	0.947028	+	0.321150i	$0.104069\pi$
$252$		0			0
$253$	10.4455	−	4.32668i	0.656705	−	0.272016i
$254$	−13.7441	+	7.93518i	−0.862383	+	0.497897i
$255$	6.93565	−	6.46738i	0.434327	−	0.405003i
$256$	−8.49559	+	14.7148i	−0.530975	+	0.919675i
$257$	15.4082	+	11.8231i	0.961134	+	0.737504i	0.964935	−	0.262489i	$-0.0845432\pi$
$257$	15.4082	+	11.8231i	0.961134	+	0.737504i	−0.00380084	+	0.999993i	$0.501210\pi$
$258$	4.31518	+	6.45812i	0.268651	+	0.402065i
$259$		0			0
$260$	13.1406	+	2.61382i	0.814944	+	0.162102i
$261$	−0.858226	+	13.0940i	−0.0531229	+	0.810499i
$262$	−5.94196	−	2.01702i	−0.367096	−	0.124612i
$263$	−3.68902	+	2.83068i	−0.227475	+	0.174548i	−0.716210	−	0.697884i	$-0.754125\pi$
$263$	−3.68902	+	2.83068i	−0.227475	+	0.174548i	0.488736	+	0.872432i	$0.337458\pi$
$264$	−1.13321	−	8.60760i	−0.0697444	−	0.529761i
$265$	8.70480	−	1.73149i	0.534732	−	0.106365i
$266$		0			0
$267$	0.187119	−	0.940712i	0.0114515	−	0.0575707i
$268$	0.0389950	−	0.145531i	0.00238200	−	0.00888974i
$269$	0.901311	+	13.7513i	0.0549539	+	0.838435i	0.933004	+	0.359866i	$0.117178\pi$
$269$	0.901311	+	13.7513i	0.0549539	+	0.838435i	−0.878050	+	0.478569i	$0.841156\pi$
$270$	1.64913	−	12.5264i	0.100363	−	0.762331i
$271$	11.6173	+	20.1218i	0.705703	+	1.22231i	0.966437	+	0.256903i	$0.0827020\pi$
$271$	11.6173	+	20.1218i	0.705703	+	1.22231i	−0.260734	+	0.965411i	$0.583965\pi$
$272$	−2.66664	+	3.23478i	−0.161689	+	0.196138i
$273$		0			0
$274$	1.80330	+	4.35355i	0.108941	+	0.263008i
$275$	−18.7620	−	9.25241i	−1.13139	−	0.557941i
$276$	−1.94886	+	0.522196i	−0.117308	+	0.0314325i
$277$	18.3125	−	20.8814i	1.10029	−	1.25464i	0.135737	−	0.990745i	$-0.456660\pi$
$277$	18.3125	−	20.8814i	1.10029	−	1.25464i	0.964552	−	0.263894i	$-0.0850070\pi$
$278$	−5.26528	−	0.345105i	−0.315790	−	0.0206980i
$279$	2.10228	+	10.5689i	0.125860	+	0.632742i
$280$		0			0
$281$	−1.24986	+	3.01742i	−0.0745603	+	0.180004i	−0.956765	−	0.290861i	$-0.906058\pi$
$281$	−1.24986	+	3.01742i	−0.0745603	+	0.180004i	0.882205	+	0.470865i	$0.156058\pi$
$282$	−7.09621	+	6.22321i	−0.422573	+	0.370586i
$283$	4.03898	−	1.99180i	0.240092	−	0.118400i	−0.318263	−	0.948003i	$-0.603099\pi$
$283$	4.03898	−	1.99180i	0.240092	−	0.118400i	0.558355	+	0.829602i	$0.311433\pi$
$284$	1.81450	+	1.59128i	0.107671	+	0.0944249i
$285$	2.31978	+	0.621583i	0.137412	+	0.0368194i
$286$	14.0956	−	9.41839i	0.833491	−	0.556921i
$287$		0			0
$288$		−	12.3722i		−	0.729039i
$289$	12.8304	−	11.1526i	0.754731	−	0.656034i
$290$	14.6603	+	8.46416i	0.860885	+	0.497032i
$291$	5.25547	+	0.691895i	0.308081	+	0.0405596i
$292$	−6.00717	+	12.1813i	−0.351543	+	0.712859i
$293$	−13.6324	−	13.6324i	−0.796413	−	0.796413i	0.186115	−	0.982528i	$-0.440410\pi$
$293$	−13.6324	−	13.6324i	−0.796413	−	0.796413i	−0.982528	+	0.186115i	$0.940410\pi$
$294$		0			0
$295$	−18.3105	−	12.2347i	−1.06608	−	0.712329i
$296$	9.54462	+	10.8835i	0.554770	+	0.632593i
$297$	9.65066	+	12.5770i	0.559988	+	0.729791i
$298$	5.54295	+	7.22371i	0.321094	+	0.418458i
$299$	−7.81473	−	8.91099i	−0.451938	−	0.515336i
$300$	3.10397	+	2.07400i	0.179208	+	0.119743i
$301$		0			0
$302$	9.94178	+	9.94178i	0.572085	+	0.572085i
$303$	5.51262	−	11.1785i	0.316692	−	0.642188i
$304$	−1.05260	−	0.138578i	−0.0603708	−	0.00794797i
$305$	−22.0923	−	12.7550i	−1.26500	−	0.730349i
$306$	1.69256	−	10.1133i	0.0967572	−	0.578139i
$307$			18.7741i			1.07149i	0.844379	+	0.535747i	$0.179970\pi$
$307$			18.7741i			1.07149i	−0.844379	+	0.535747i	$0.820030\pi$
$308$		0			0
$309$	3.60602	−	2.40946i	0.205139	−	0.137070i
$310$	13.4279	+	3.59800i	0.762655	+	0.204353i
$311$	−1.79127	−	1.57090i	−0.101574	−	0.0890777i	0.607053	−	0.794661i	$-0.292352\pi$
$311$	−1.79127	−	1.57090i	−0.101574	−	0.0890777i	−0.708627	+	0.705584i	$0.750685\pi$
$312$	−8.16262	+	4.02536i	−0.462117	+	0.227891i
$313$	−13.6862	+	12.0024i	−0.773588	+	0.678418i	−0.952191	−	0.305503i	$-0.901175\pi$
$313$	−13.6862	+	12.0024i	−0.773588	+	0.678418i	0.178603	+	0.983921i	$0.442842\pi$
$314$	−4.03009	+	9.72949i	−0.227431	+	0.549067i
$315$		0			0
$316$	−1.37104	−	6.89268i	−0.0771270	−	0.387743i
$317$	−15.4507	−	1.01269i	−0.867798	−	0.0568785i	−0.375002	−	0.927024i	$-0.622358\pi$
$317$	−15.4507	−	1.01269i	−0.867798	−	0.0568785i	−0.492795	+	0.870145i	$0.664025\pi$
$318$	−1.32135	+	1.50671i	−0.0740976	+	0.0844921i
$319$	−20.5168	+	5.49747i	−1.14872	+	0.307799i
$320$	−20.1418	−	9.93285i	−1.12596	−	0.555263i
$321$	2.50600	+	6.05002i	0.139871	+	0.337679i
$322$		0			0
$323$	4.11712	+	1.25880i	0.229083	+	0.0700417i
$324$	2.29251	+	3.97075i	0.127362	+	0.220597i
$325$	−2.86241	+	21.7422i	−0.158778	+	1.20604i
$326$	0.365170	+	5.57142i	0.0202249	+	0.308573i
$327$	−1.24631	+	4.65128i	−0.0689210	+	0.257217i
$328$	−2.00316	+	10.0706i	−0.110606	+	0.556055i
$329$		0			0
$330$	9.08099	−	1.80632i	0.499892	−	0.0994347i
$331$	0.522428	+	3.96824i	0.0287152	+	0.218114i	0.999786	−	0.0206772i	$-0.00658222\pi$
$331$	0.522428	+	3.96824i	0.0287152	+	0.218114i	−0.971071	+	0.238791i	$0.923249\pi$
$332$	−1.26670	+	0.971976i	−0.0695194	+	0.0533441i
$333$	−11.3318	−	3.84663i	−0.620979	−	0.210794i
$334$	−0.963300	+	14.6971i	−0.0527094	+	0.804190i
$335$	0.474102	+	0.0943048i	0.0259030	+	0.00515242i
$336$		0			0
$337$	13.6256	+	20.3921i	0.742232	+	1.11083i	0.989870	+	0.141976i	$0.0453456\pi$
$337$	13.6256	+	20.3921i	0.742232	+	1.11083i	−0.247638	+	0.968853i	$0.579654\pi$
$338$	−3.76384	−	2.88810i	−0.204726	−	0.157092i
$339$	3.40645	−	5.90015i	0.185013	−	0.320452i
$340$	10.6459	+	7.66419i	0.577353	+	0.415649i
$341$	−15.1060	+	8.72144i	−0.818035	+	0.472293i
$342$	2.39915	−	0.993760i	0.129731	−	0.0537364i
$343$		0			0
$344$	−22.8554	+	22.8554i	−1.23228	+	1.23228i
$345$	−2.08076	−	6.12971i	−0.112024	−	0.330013i
$346$	−3.62338	−	7.34749i	−0.194794	−	0.395004i
$347$	−6.13173	+	18.0635i	−0.329168	+	0.969699i	0.648802	+	0.760957i	$0.275270\pi$
$347$	−6.13173	+	18.0635i	−0.329168	+	0.969699i	−0.977971	+	0.208742i	$0.933063\pi$
$348$	3.75800	−	0.494750i	0.201450	−	0.0265214i
$349$	10.8607	+	4.49864i	0.581359	+	0.240807i	0.653928	−	0.756557i	$-0.273120\pi$
$349$	10.8607	+	4.49864i	0.581359	+	0.240807i	−0.0725692	+	0.997363i	$0.523120\pi$
$350$		0			0
$351$	9.23282	−	13.8179i	0.492812	−	0.737545i
$352$	18.9639	−	6.43738i	1.01078	−	0.343114i
$353$	1.52477	+	5.69053i	0.0811554	+	0.302876i	0.994558	−	0.104180i	$-0.0332219\pi$
$353$	1.52477	+	5.69053i	0.0811554	+	0.302876i	−0.913403	+	0.407056i	$0.866555\pi$
$354$	4.96182	−	0.325215i	0.263718	−	0.0172850i
$355$	−4.71373	+	6.14305i	−0.250179	+	0.326039i
$356$	1.32675			0.0703174
$357$		0			0
$358$	−15.3407			−0.810779
$359$	−7.67761	+	10.0057i	−0.405209	+	0.528079i	−0.950731	−	0.310018i	$-0.899665\pi$
$359$	−7.67761	+	10.0057i	−0.405209	+	0.528079i	0.545522	+	0.838097i	$0.316332\pi$
$360$	23.7525	−	1.55682i	1.25187	−	0.0820517i
$361$	−4.63537	−	17.2994i	−0.243967	−	0.910497i
$362$	−2.00129	+	0.679348i	−0.105186	+	0.0357057i
$363$	−2.05486	+	3.07531i	−0.107852	+	0.161412i
$364$		0			0
$365$	−40.2592	−	16.6759i	−2.10726	−	0.872856i
$366$	5.71081	−	0.751843i	0.298509	−	0.0392995i
$367$	−3.74544	+	11.0337i	−0.195510	+	0.575955i	−0.999834	−	0.0182369i	$-0.994195\pi$
$367$	−3.74544	+	11.0337i	−0.195510	+	0.575955i	0.804323	+	0.594192i	$0.202528\pi$
$368$	1.26567	+	2.56652i	0.0659776	+	0.133789i
$369$	−2.72844	−	8.03774i	−0.142037	−	0.418428i
$370$	−10.9163	+	10.9163i	−0.567512	+	0.567512i
$371$		0			0
$372$	2.87578	−	1.19119i	0.149102	−	0.0617601i
$373$	−23.1381	+	13.3588i	−1.19805	+	0.691692i	−0.960119	−	0.279591i	$-0.909801\pi$
$373$	−23.1381	+	13.3588i	−1.19805	+	0.691692i	−0.237926	+	0.971283i	$0.576468\pi$
$374$	16.3822	−	2.66773i	0.847103	−	0.137945i
$375$	−0.238602	+	0.413271i	−0.0123213	+	0.0213412i
$376$	−31.1610	−	23.9107i	−1.60701	−	1.23310i
$377$	12.3706	+	18.5139i	0.637119	+	0.953516i
$378$		0			0
$379$	8.26871	+	1.64475i	0.424735	+	0.0844851i	0.402830	−	0.915275i	$-0.368027\pi$
$379$	8.26871	+	1.64475i	0.424735	+	0.0844851i	0.0219055	+	0.999760i	$0.493027\pi$
$380$	−0.217273	+	3.31495i	−0.0111459	+	0.170053i
$381$	−10.7960	−	3.66476i	−0.553098	−	0.187751i
$382$	−9.72955	+	7.46574i	−0.497807	+	0.381981i
$383$	−2.43186	−	18.4718i	−0.124262	−	0.943867i	−0.934050	−	0.357143i	$-0.883751\pi$
$383$	−2.43186	−	18.4718i	−0.124262	−	0.943867i	0.809787	−	0.586724i	$-0.199583\pi$
$384$	−2.06633	+	0.411020i	−0.105447	+	0.0209748i
$385$		0			0
$386$	−5.35263	+	26.9095i	−0.272442	+	1.36966i
$387$	6.91569	−	25.8097i	0.351544	−	1.31198i
$388$	0.479563	+	7.31672i	0.0243461	+	0.371450i
$389$	−1.35731	+	10.3098i	−0.0688183	+	0.522727i	0.921965	+	0.387272i	$0.126583\pi$
$389$	−1.35731	+	10.3098i	−0.0688183	+	0.522727i	−0.990784	+	0.135454i	$0.956751\pi$
$390$	−4.85305	−	8.40573i	−0.245744	−	0.425641i
$391$	−3.34413	−	11.1120i	−0.169120	−	0.561957i
$392$		0			0
$393$	−1.72509	−	4.16474i	−0.0870193	−	0.210083i
$394$	3.56743	+	1.75926i	0.179725	+	0.0886304i
$395$	21.7793	−	5.83573i	1.09583	−	0.293628i
$396$	−6.54586	+	7.46413i	−0.328942	+	0.375087i
$397$	6.78502	+	0.444713i	0.340530	+	0.0223195i	0.234709	−	0.972066i	$-0.424586\pi$
$397$	6.78502	+	0.444713i	0.340530	+	0.0223195i	0.105821	+	0.994385i	$0.466253\pi$
$398$	−1.57883	−	7.93734i	−0.0791398	−	0.397863i
$399$		0			0
$400$	2.02623	−	4.89174i	0.101311	−	0.244587i
$401$	−6.23664	+	5.46939i	−0.311443	+	0.273128i	−0.800770	−	0.598972i	$-0.795576\pi$
$401$	−6.23664	+	5.46939i	−0.311443	+	0.273128i	0.489327	+	0.872101i	$0.337243\pi$
$402$	−0.0978921	+	0.0482751i	−0.00488242	+	0.00240774i
$403$	13.7477	+	12.0564i	0.684820	+	0.600571i
$404$	16.6533	+	4.46225i	0.828534	+	0.222005i
$405$	−12.2313	+	8.17270i	−0.607779	+	0.406105i
$406$		0			0
$407$		−	19.3707i		−	0.960167i
$408$	−8.90664	+	0.271975i	−0.440944	+	0.0134648i
$409$	−14.1840	−	8.18912i	−0.701352	−	0.404926i	0.106499	−	0.994313i	$-0.466036\pi$
$409$	−14.1840	−	8.18912i	−0.701352	−	0.404926i	−0.807851	+	0.589387i	$0.799369\pi$
$410$	−10.8566	−	1.42930i	−0.536170	−	0.0705882i
$411$	−1.49725	+	3.03612i	−0.0738539	+	0.149761i
$412$	4.24201	+	4.24201i	0.208989	+	0.208989i
$413$		0			0
$414$	−5.81979	−	3.88866i	−0.286027	−	0.191117i
$415$	−3.37759	−	3.85140i	−0.165799	−	0.189058i
$416$	−12.7803	−	16.6557i	−0.626608	−	0.816612i
$417$	−2.30759	−	3.00731i	−0.113003	−	0.147269i
$418$	2.77152	+	3.16032i	0.135560	+	0.154576i
$419$	−2.02600	−	1.35373i	−0.0989764	−	0.0661339i	0.505097	−	0.863063i	$-0.331457\pi$
$419$	−2.02600	−	1.35373i	−0.0989764	−	0.0661339i	−0.604074	+	0.796929i	$0.706457\pi$
$420$		0			0
$421$	15.3534	+	15.3534i	0.748278	+	0.748278i	0.974156	−	0.225878i	$-0.0725249\pi$
$421$	15.3534	+	15.3534i	0.748278	+	0.748278i	−0.225878	+	0.974156i	$0.572525\pi$
$422$	4.86349	−	9.86218i	0.236751	−	0.480084i
$423$	32.1921	+	4.23817i	1.56523	+	0.206067i
$424$	−7.22236	−	4.16983i	−0.350749	−	0.202505i
$425$	−11.3782	+	18.2082i	−0.551923	+	0.883230i
$426$		−	1.74838i		−	0.0847095i
$427$		0			0
$428$	−7.53170	+	5.03252i	−0.364058	+	0.243256i
$429$	11.7636	+	3.15206i	0.567954	+	0.152183i
$430$	−25.9164	−	22.7281i	−1.24980	−	1.09605i
$431$	−15.6040	+	7.69504i	−0.751618	+	0.370657i	−0.777397	−	0.629011i	$-0.783460\pi$
$431$	−15.6040	+	7.69504i	−0.751618	+	0.370657i	0.0257788	+	0.999668i	$0.491793\pi$
$432$	−3.01672	+	2.64559i	−0.145142	+	0.127286i
$433$	−3.86837	+	9.33908i	−0.185902	+	0.448808i	−0.989163	−	0.146819i	$-0.953096\pi$
$433$	−3.86837	+	9.33908i	−0.185902	+	0.448808i	0.803261	+	0.595627i	$0.203096\pi$
$434$		0			0
$435$	2.37252	+	11.9274i	0.113753	+	0.571877i
$436$	−6.64665	−	0.435645i	−0.318317	−	0.0208636i
$437$	1.93768	−	2.20950i	0.0926917	−	0.105695i
$438$	9.50413	−	2.54662i	0.454125	−	0.121682i
$439$	−13.1476	−	6.48366i	−0.627499	−	0.309448i	0.100593	−	0.994928i	$-0.467926\pi$
$439$	−13.1476	−	6.48366i	−0.627499	−	0.309448i	−0.728092	+	0.685480i	$0.759593\pi$
$440$	14.7449	+	35.5974i	0.702938	+	1.69704i
$441$		0			0
$442$	−8.16839	−	15.3631i	−0.388531	−	0.730749i
$443$	7.74365	+	13.4124i	0.367912	+	0.637242i	0.989239	−	0.146309i	$-0.0467395\pi$
$443$	7.74365	+	13.4124i	0.367912	+	0.637242i	−0.621327	+	0.783551i	$0.713406\pi$
$444$	−0.451194	+	3.42716i	−0.0214127	+	0.162646i
$445$	0.278401	+	4.24758i	0.0131975	+	0.201355i
$446$	0.865879	−	3.23151i	0.0410006	−	0.153016i
$447$	−1.27611	+	6.41546i	−0.0603581	+	0.303441i
$448$		0			0
$449$	20.9845	−	4.17408i	0.990321	−	0.196987i	0.326758	−	0.945108i	$-0.394044\pi$
$449$	20.9845	−	4.17408i	0.990321	−	0.196987i	0.663562	+	0.748121i	$0.269044\pi$
$450$	1.69041	+	12.8400i	0.0796868	+	0.605281i
$451$	10.9005	−	8.36424i	0.513284	−	0.393857i
$452$	8.92390	+	3.02926i	0.419745	+	0.142484i
$453$	−0.660599	+	10.0788i	−0.0310376	+	0.473543i
$454$	−4.98790	−	0.992155i	−0.234094	−	0.0465641i
$455$		0			0
$456$	−1.25373	−	1.87635i	−0.0587115	−	0.0878679i
$457$	11.2040	+	8.59710i	0.524099	+	0.402156i	0.836644	−	0.547748i	$-0.184515\pi$
$457$	11.2040	+	8.59710i	0.524099	+	0.402156i	−0.312544	+	0.949903i	$0.601181\pi$
$458$	−1.91362	+	3.31448i	−0.0894175	+	0.154876i
$459$	13.8362	−	8.56177i	0.645818	−	0.399629i
$460$	7.75457	−	4.47710i	0.361559	−	0.208746i
$461$	31.2776	−	12.9556i	1.45674	−	0.603402i	0.492950	−	0.870057i	$-0.335918\pi$
$461$	31.2776	−	12.9556i	1.45674	−	0.603402i	0.963792	+	0.266655i	$0.0859184\pi$
$462$		0			0
$463$	−1.64663	+	1.64663i	−0.0765253	+	0.0765253i	−0.744333	−	0.667808i	$-0.767233\pi$
$463$	−1.64663	+	1.64663i	−0.0765253	+	0.0765253i	0.667808	+	0.744333i	$0.267233\pi$
$464$	−1.72808	−	5.09077i	−0.0802243	−	0.236333i
$465$	4.41704	+	8.95687i	0.204835	+	0.415365i
$466$	6.83183	−	20.1259i	0.316478	−	0.932315i
$467$	−25.9052	+	3.41048i	−1.19875	+	0.157818i	−0.703347	−	0.710846i	$-0.748312\pi$
$467$	−25.9052	+	3.41048i	−1.19875	+	0.157818i	−0.495401	+	0.868665i	$0.664979\pi$
$468$	9.61512	+	3.98271i	0.444459	+	0.184101i
$469$		0			0
$470$	23.2718	−	34.8287i	1.07345	−	1.60653i
$471$	−7.16395	+	2.43183i	−0.330097	+	0.112053i
$472$	5.35565	+	19.9876i	0.246514	+	0.920003i
$473$	43.1591	−	2.82879i	1.98446	−	0.130068i
$474$	−3.09931	+	4.03910i	−0.142356	+	0.185522i
$475$	−5.43754			−0.249491
$476$		0			0
$477$	6.89420			0.315664
$478$	−12.6576	+	16.4957i	−0.578946	+	0.754497i
$479$	2.11560	−	0.138664i	0.0966644	−	0.00633572i	−0.0169942	−	0.999856i	$-0.505410\pi$
$479$	2.11560	−	0.138664i	0.0966644	−	0.00633572i	0.113659	+	0.993520i	$0.463743\pi$
$480$	−2.96765	−	11.0754i	−0.135454	−	0.505522i
$481$	−19.2286	+	6.52723i	−0.876748	+	0.297616i
$482$	−13.9977	+	20.9490i	−0.637577	+	0.954202i
$483$		0			0
$484$	−4.72675	−	1.95788i	−0.214852	−	0.0889948i
$485$	−23.3239	+	3.07065i	−1.05908	+	0.139431i
$486$	4.88114	−	14.3794i	0.221413	−	0.652262i
$487$	−17.9885	−	36.4771i	−0.815138	−	1.65294i	−0.755894	−	0.654694i	$-0.772798\pi$
$487$	−17.9885	−	36.4771i	−0.815138	−	1.65294i	−0.0592441	−	0.998244i	$-0.518869\pi$
$488$	7.70500	+	22.6982i	0.348789	+	1.02750i
$489$	−2.83623	+	2.83623i	−0.128259	+	0.128259i
$490$		0			0
$491$	13.1870	−	5.46223i	0.595121	−	0.246507i	−0.0647312	−	0.997903i	$-0.520619\pi$
$491$	13.1870	−	5.46223i	0.595121	−	0.246507i	0.659852	+	0.751396i	$0.270619\pi$
$492$	−2.12340	+	1.22595i	−0.0957302	+	0.0552699i
$493$	3.50394	+	21.5172i	0.157809	+	0.969087i
$494$	2.20323	−	3.81611i	0.0991282	−	0.171695i
$495$	−25.2700	−	19.3904i	−1.13580	−	0.871532i
$496$	−2.45277	−	3.67083i	−0.110133	−	0.164825i
$497$		0			0
$498$	1.13445	+	0.225657i	0.0508361	+	0.0101119i
$499$	−0.236321	+	3.60556i	−0.0105792	+	0.161407i	0.989300	+	0.145892i	$0.0466054\pi$
$499$	−0.236321	+	3.60556i	−0.0105792	+	0.161407i	−0.999880	+	0.0155147i	$0.995061\pi$
$500$	−0.625067	−	0.212182i	−0.0279539	−	0.00948905i
$501$	−8.39440	+	6.44125i	−0.375034	+	0.287774i
$502$	−1.83421	−	13.9322i	−0.0818647	−	0.621824i
$503$	−34.8179	+	6.92572i	−1.55245	+	0.308802i	−0.895477	−	0.445108i	$-0.853165\pi$
$503$	−34.8179	+	6.92572i	−1.55245	+	0.308802i	−0.656978	+	0.753910i	$0.728165\pi$
$504$		0			0
$505$	−10.7914	+	54.2521i	−0.480211	+	2.41419i
$506$	2.93238	−	10.9438i	0.130360	−	0.486511i
$507$	−0.222907	−	3.40090i	−0.00989964	−	0.151039i
$508$	2.05849	−	15.6358i	0.0913308	−	0.693726i
$509$	5.88751	+	10.1975i	0.260959	+	0.451994i	0.966497	−	0.256678i	$-0.0826279\pi$
$509$	5.88751	+	10.1975i	0.260959	+	0.451994i	−0.705538	+	0.708672i	$0.749295\pi$
$510$	−0.910669	−	9.45930i	−0.0403251	−	0.418865i
$511$		0			0
$512$	4.27598	+	10.3231i	0.188973	+	0.456222i
$513$	3.69568	+	1.82251i	0.163168	+	0.0804656i
$514$	18.7991	−	5.03720i	0.829193	−	0.222181i
$515$	−12.6907	+	14.4709i	−0.559218	+	0.637666i
$516$	−7.70182	−	0.504804i	−0.339054	−	0.0222228i
$517$	10.2537	+	51.5487i	0.450956	+	2.26711i
$518$		0			0
$519$	2.25221	−	5.43731i	0.0988609	−	0.238671i
$520$	30.3679	−	26.6319i	1.33172	−	1.16789i
$521$	−38.3681	+	18.9210i	−1.68094	+	0.828946i	−0.686094	+	0.727513i	$0.740676\pi$
$521$	−38.3681	+	18.9210i	−1.68094	+	0.828946i	−0.994842	+	0.101434i	$0.967657\pi$
$522$	9.88639	+	8.67013i	0.432716	+	0.379481i
$523$	17.4115	+	4.66539i	0.761350	+	0.204003i	0.618547	−	0.785748i	$-0.287722\pi$
$523$	17.4115	+	4.66539i	0.761350	+	0.204003i	0.142803	+	0.989751i	$0.454388\pi$
$524$	5.18470	−	3.46430i	0.226494	−	0.151339i
$525$		0			0
$526$			4.65965i			0.203171i
$527$	7.35275	+	16.3232i	0.320291	+	0.711051i
$528$	−2.54649	−	1.47022i	−0.110822	−	0.0639830i
$529$	14.9499	+	1.96819i	0.649994	+	0.0855733i
$530$	3.93369	−	7.97673i	0.170869	−	0.346487i
$531$	−12.0959	−	12.0959i	−0.524916	−	0.524916i
$532$		0			0
$533$	−11.9760	−	8.00210i	−0.518737	−	0.346609i
$534$	−0.633731	−	0.722632i	−0.0274242	−	0.0312714i
$535$	−17.6921	−	23.0568i	−0.764895	−	0.996831i
$536$	−0.276508	−	0.360353i	−0.0119433	−	0.0155649i
$537$	−7.26637	−	8.28570i	−0.313567	−	0.357555i
$538$	11.4824	+	7.67228i	0.495040	+	0.330775i
$539$		0			0
$540$	8.87783	+	8.87783i	0.382041	+	0.382041i
$541$	10.6507	−	21.5975i	0.457909	−	0.928548i	−0.538398	−	0.842690i	$-0.680970\pi$
$541$	10.6507	−	21.5975i	0.457909	−	0.928548i	0.996307	−	0.0858573i	$-0.0273629\pi$
$542$	23.0842	+	3.03909i	0.991550	+	0.130540i
$543$	−1.31487	−	0.759142i	−0.0564266	−	0.0325779i
$544$	−4.62349	−	20.0280i	−0.198231	−	0.858696i
$545$		−	21.3707i		−	0.915421i
$546$		0			0
$547$	5.98174	−	3.99687i	0.255761	−	0.170894i	−0.421080	−	0.907024i	$-0.638349\pi$
$547$	5.98174	−	3.99687i	0.255761	−	0.170894i	0.676840	+	0.736130i	$0.263349\pi$
$548$	−4.52311	−	1.21196i	−0.193218	−	0.0517725i
$549$	−14.8982	−	13.0654i	−0.635841	−	0.557617i
$550$	−18.8014	+	9.27180i	−0.801692	+	0.395351i
$551$	−4.15093	+	3.64027i	−0.176835	+	0.155081i
$552$	−2.32769	+	5.61954i	−0.0990731	+	0.239184i
$553$		0			0
$554$	−5.42973	−	27.2971i	−0.230687	−	1.15974i
$555$	−11.0668	−	0.725353i	−0.469758	−	0.0307895i
$556$	3.45725	−	3.94223i	0.146620	−	0.167188i
$557$	24.2512	−	6.49809i	1.02756	−	0.275333i	0.294609	−	0.955618i	$-0.404811\pi$
$557$	24.2512	−	6.49809i	1.02756	−	0.275333i	0.732948	+	0.680285i	$0.238144\pi$
$558$	9.68490	+	4.77606i	0.409994	+	0.202187i
$559$	−17.3511	−	41.8893i	−0.733875	−	1.77173i
$560$		0			0
$561$	9.20058	+	7.58463i	0.388449	+	0.320223i
$562$	1.63644	+	2.83440i	0.0690291	+	0.119562i
$563$	1.72571	−	13.1080i	0.0727299	−	0.552438i	−0.915825	−	0.401577i	$-0.868462\pi$
$563$	1.72571	−	13.1080i	0.0727299	−	0.552438i	0.988555	−	0.150861i	$-0.0482045\pi$
$564$	−0.613429	−	9.35912i	−0.0258300	−	0.394090i
$565$	−7.82561	+	29.2056i	−0.329226	+	1.22869i
$566$	0.880411	−	4.42612i	0.0370064	−	0.186044i
$567$		0			0
$568$	7.13600	−	1.41944i	0.299420	−	0.0595583i
$569$	−2.84720	−	21.6266i	−0.119361	−	0.906634i	−0.941421	−	0.337234i	$-0.890509\pi$
$569$	−2.84720	−	21.6266i	−0.119361	−	0.906634i	0.822060	−	0.569400i	$-0.192825\pi$
$570$	1.90932	−	1.46507i	0.0799727	−	0.0613652i
$571$	−14.0053	−	4.75417i	−0.586105	−	0.198956i	0.0126066	−	0.999921i	$-0.495987\pi$
$571$	−14.0053	−	4.75417i	−0.586105	−	0.198956i	−0.598712	+	0.800965i	$0.704320\pi$
$572$	−1.10180	+	16.8102i	−0.0460684	+	0.702868i
$573$	−8.64092	−	1.71879i	−0.360980	−	0.0718033i
$574$		0			0
$575$	8.14255	+	12.1862i	0.339568	+	0.508199i
$576$	−13.8399	−	10.6197i	−0.576663	−	0.442489i
$577$	−21.6933	+	37.5740i	−0.903105	+	1.56422i	−0.0796650	+	0.996822i	$0.525385\pi$
$577$	−21.6933	+	37.5740i	−0.903105	+	1.56422i	−0.823440	+	0.567403i	$0.807948\pi$
$578$	−1.03944	−	17.0039i	−0.0432349	−	0.707268i
$579$	−17.0695	+	9.85511i	−0.709386	+	0.409564i
$580$	−15.5415	+	6.43751i	−0.645327	+	0.267303i
$581$		0			0
$582$	3.75610	−	3.75610i	0.155695	−	0.155695i
$583$	3.58713	+	10.5673i	0.148564	+	0.437654i
$584$	18.1100	+	36.7235i	0.749397	+	1.51963i
$585$	−10.7331	+	31.6186i	−0.443758	+	1.30727i
$586$	−19.1542	+	2.52170i	−0.791255	+	0.104171i
$587$	−20.3730	−	8.43878i	−0.840884	−	0.348306i	−0.0796822	−	0.996820i	$-0.525391\pi$
$587$	−20.3730	−	8.43878i	−0.840884	−	0.348306i	−0.761202	+	0.648515i	$0.775391\pi$
$588$		0			0
$589$	−2.51890	+	3.76980i	−0.103789	+	0.155332i
$590$	−20.8968	+	7.09351i	−0.860308	+	0.292035i
$591$	0.739573	+	2.76013i	0.0304220	+	0.113536i
$592$	4.89229	−	0.320658i	0.201072	−	0.0131790i
$593$	14.7428	−	19.2132i	0.605414	−	0.788991i	−0.385612	−	0.922661i	$-0.626010\pi$
$593$	14.7428	−	19.2132i	0.605414	−	0.788991i	0.991026	+	0.133670i	$0.0426762\pi$
$594$	15.8862			0.651818
$595$		0			0
$596$	−9.04813			−0.370626
$597$	3.53922	−	4.61241i	0.144851	−	0.188773i
$598$	−11.8517	+	0.776799i	−0.484650	+	0.0317657i
$599$	6.97227	+	26.0209i	0.284879	+	1.06318i	0.948928	+	0.315494i	$0.102170\pi$
$599$	6.97227	+	26.0209i	0.284879	+	1.06318i	−0.664048	+	0.747690i	$0.731163\pi$
$600$	10.6571	−	3.61758i	0.435073	−	0.147687i
$601$	23.1053	−	34.5796i	0.942487	−	1.41053i	0.0308547	−	0.999524i	$-0.490177\pi$
$601$	23.1053	−	34.5796i	0.942487	−	1.41053i	0.911632	−	0.411007i	$-0.134823\pi$
$602$		0			0
$603$	0.346906	+	0.143693i	0.0141271	+	0.00585164i
$604$	−13.8520	+	1.82365i	−0.563630	+	0.0742033i
$605$	5.27633	−	15.5436i	0.214513	−	0.631936i
$606$	−5.52417	−	11.2019i	−0.224404	−	0.455047i
$607$	2.49019	+	7.33585i	0.101074	+	0.297753i	0.985690	−	0.168565i	$-0.0539135\pi$
$607$	2.49019	+	7.33585i	0.101074	+	0.297753i	−0.884617	+	0.466318i	$0.845580\pi$
$608$	3.68085	−	3.68085i	0.149278	−	0.149278i
$609$		0			0
$610$	−23.6175	+	9.78271i	−0.956246	+	0.396090i
$611$	47.7156	−	27.5486i	1.93037	−	1.11450i
$612$	6.94916	+	7.45231i	0.280903	+	0.301242i
$613$	−16.2538	+	28.1524i	−0.656484	+	1.13706i	0.325036	+	0.945702i	$0.394624\pi$
$613$	−16.2538	+	28.1524i	−0.656484	+	1.13706i	−0.981520	+	0.191362i	$0.938710\pi$
$614$	14.9257	+	11.4529i	0.602352	+	0.462201i
$615$	−4.37044	−	6.54083i	−0.176233	−	0.263752i
$616$		0			0
$617$	−9.52017	−	1.89368i	−0.383268	−	0.0762367i	−0.000303681	−	1.00000i	$-0.500097\pi$
$617$	−9.52017	−	1.89368i	−0.383268	−	0.0762367i	−0.382964	+	0.923763i	$0.625097\pi$
$618$	0.284243	−	4.33671i	0.0114339	−	0.174448i
$619$	−31.5611	−	10.7136i	−1.26855	−	0.430615i	−0.395599	−	0.918423i	$-0.629463\pi$
$619$	−31.5611	−	10.7136i	−1.26855	−	0.430615i	−0.872951	+	0.487809i	$0.837796\pi$
$620$	−10.9597	+	8.40964i	−0.440150	+	0.337739i
$621$	−1.44971	−	11.0116i	−0.0581747	−	0.441881i
$622$	−2.34163	+	0.465780i	−0.0938909	+	0.0186761i
$623$		0			0
$624$	−0.601357	+	3.02323i	−0.0240736	+	0.121026i
$625$	−6.19084	+	23.1045i	−0.247633	+	0.924181i
$626$	1.19307	+	18.2027i	0.0476845	+	0.727524i
$627$	−0.394151	+	2.99388i	−0.0157409	+	0.119564i
$628$	−5.23250	−	9.06296i	−0.208800	−	0.361652i
$629$	−19.7813	−	1.99221i	−0.788734	−	0.0794345i
$630$		0			0
$631$	−17.0014	−	41.0450i	−0.676815	−	1.63398i	−0.769782	−	0.638307i	$-0.779635\pi$
$631$	−17.0014	−	41.0450i	−0.676815	−	1.63398i	0.0929663	−	0.995669i	$-0.470365\pi$
$632$	−19.0017	−	9.37062i	−0.755849	−	0.372743i
$633$	7.63038	−	2.04455i	0.303280	−	0.0812637i
$634$	−10.2306	+	11.6658i	−0.406309	+	0.463307i
$635$	50.4900	+	3.30929i	2.00364	+	0.131325i
$636$	−0.388512	−	1.95318i	−0.0154055	−	0.0774487i
$637$		0			0
$638$	−8.14546	+	19.6649i	−0.322482	+	0.778540i
$639$	−4.52212	+	3.96579i	−0.178892	+	0.156884i
$640$	8.38586	−	4.13545i	0.331480	−	0.163468i
$641$	7.86047	+	6.89345i	0.310470	+	0.272275i	0.800373	−	0.599502i	$-0.204635\pi$
$641$	7.86047	+	6.89345i	0.310470	+	0.272275i	−0.489903	+	0.871777i	$0.662968\pi$
$642$	6.33862	+	1.69843i	0.250165	+	0.0670316i
$643$	21.4816	−	14.3536i	0.847153	−	0.566050i	−0.0544980	−	0.998514i	$-0.517356\pi$
$643$	21.4816	−	14.3536i	0.847153	−	0.566050i	0.901651	+	0.432464i	$0.142356\pi$
$644$		0			0
$645$		−	24.7634i		−	0.975057i
$646$	3.51236	−	2.50526i	0.138192	−	0.0985680i
$647$	10.4457	+	6.03082i	0.410662	+	0.237096i	0.691074	−	0.722784i	$-0.257138\pi$
$647$	10.4457	+	6.03082i	0.410662	+	0.237096i	−0.280412	+	0.959880i	$0.590471\pi$
$648$	13.7044	+	1.80421i	0.538358	+	0.0708762i
$649$	12.2468	−	24.8340i	0.480727	−	0.974818i
$650$	15.5392	+	15.5392i	0.609498	+	0.609498i
$651$		0			0
$652$	−4.61326	−	3.08248i	−0.180669	−	0.120719i
$653$	16.6249	+	18.9571i	0.650584	+	0.741849i	0.979263	−	0.202593i	$-0.0649367\pi$
$653$	16.6249	+	18.9571i	0.650584	+	0.741849i	−0.328679	+	0.944442i	$0.606603\pi$
$654$	2.93755	+	3.82829i	0.114867	+	0.149698i
$655$	12.1789	+	15.8719i	0.475870	+	0.620166i
$656$	2.29293	+	2.61459i	0.0895241	+	0.102083i
$657$	−28.1446	−	18.8056i	−1.09802	−	0.733677i
$658$		0			0
$659$	20.1037	+	20.1037i	0.783130	+	0.783130i	0.980358	−	0.197228i	$-0.0631938\pi$
$659$	20.1037	+	20.1037i	0.783130	+	0.783130i	−0.197228	+	0.980358i	$0.563194\pi$
$660$	−4.06940	+	8.25192i	−0.158401	+	0.321205i
$661$	−26.8556	−	3.53561i	−1.04456	−	0.137519i	−0.411334	−	0.911485i	$-0.634937\pi$
$661$	−26.8556	−	3.53561i	−1.04456	−	0.137519i	−0.633228	+	0.773965i	$0.718270\pi$
$662$	3.47351	+	2.00543i	0.135002	+	0.0779433i
$663$	4.42874	−	11.6889i	0.171998	−	0.453958i
$664$			4.81346i			0.186798i
$665$		0			0
$666$	−9.97095	+	6.66237i	−0.386366	+	0.258162i
$667$	14.3742	+	3.85155i	0.556570	+	0.149132i
$668$	−11.0041	−	9.65030i	−0.425760	−	0.373381i
$669$	2.15552	−	1.06298i	0.0833372	−	0.0410974i
$670$	0.364194	−	0.319389i	0.0140700	−	0.0123391i
$671$	12.2747	−	29.6338i	0.473861	−	1.14400i
$672$		0			0
$673$	−6.19645	−	31.1517i	−0.238856	−	1.20081i	−0.894963	−	0.446141i	$-0.852798\pi$
$673$	−6.19645	−	31.1517i	−0.238856	−	1.20081i	0.656107	−	0.754668i	$-0.272202\pi$
$674$	24.5242	+	1.60740i	0.944635	+	0.0619147i
$675$	−13.5497	+	15.4505i	−0.521528	+	0.594689i
$676$	4.55379	−	1.22019i	0.175146	−	0.0469302i
$677$	30.9549	+	15.2653i	1.18969	+	0.586692i	0.925857	−	0.377875i	$-0.123345\pi$
$677$	30.9549	+	15.2653i	1.18969	+	0.586692i	0.263837	+	0.964567i	$0.415012\pi$
$678$	−2.61265	−	6.30749i	−0.100338	−	0.242238i
$679$		0			0
$680$	37.8686	−	11.3965i	1.45220	−	0.437035i
$681$	−1.82673	−	3.16398i	−0.0700003	−	0.121244i
$682$	−2.28152	+	17.3299i	−0.0873641	+	0.663596i
$683$	−1.87161	−	28.5552i	−0.0716152	−	1.09264i	−0.870828	−	0.491588i	$-0.836417\pi$
$683$	−1.87161	−	28.5552i	−0.0716152	−	1.09264i	0.799213	−	0.601048i	$-0.205250\pi$
$684$	−0.667887	+	2.49259i	−0.0255373	+	0.0953065i
$685$	2.93099	−	14.7351i	0.111987	−	0.562998i
$686$		0			0
$687$	−2.69662	+	0.536390i	−0.102882	+	0.0204646i
$688$	1.42889	+	10.8535i	0.0544760	+	0.413786i
$689$	9.28110	−	7.12164i	0.353582	−	0.271313i
$690$	−6.14256	−	2.08512i	−0.233843	−	0.0793791i
$691$	−0.165204	+	2.52053i	−0.00628467	+	0.0958855i	−0.999849	−	0.0173848i	$-0.994466\pi$
$691$	−0.165204	+	2.52053i	−0.00628467	+	0.0958855i	0.993564	+	0.113270i	$0.0361326\pi$
$692$	7.98449	+	1.58821i	0.303525	+	0.0603748i
$693$		0			0
$694$	10.6202	+	15.8942i	0.403136	+	0.603336i
$695$	13.3465	+	10.2412i	0.506263	+	0.388470i
$696$	5.71356	−	9.89618i	0.216572	−	0.375114i
$697$	−7.42050	−	11.9918i	−0.281071	−	0.454223i
$698$	10.2019	−	5.89008i	0.386148	−	0.222943i
$699$	14.1063	−	5.84302i	0.533549	−	0.221003i
$700$		0			0
$701$	−27.0241	+	27.0241i	−1.02069	+	1.02069i	−0.0209056	+	0.999781i	$0.506655\pi$
$701$	−27.0241	+	27.0241i	−1.02069	+	1.02069i	−0.999781	+	0.0209056i	$0.993345\pi$
$702$	−5.35308	−	15.7697i	−0.202039	−	0.595188i
$703$	−2.22691	−	4.51573i	−0.0839896	−	0.170314i
$704$	9.07673	−	26.7392i	0.342092	−	1.00777i
$705$	29.8346	−	3.92779i	1.12363	−	0.147929i
$706$	5.45423	+	2.25922i	0.205273	+	0.0850267i
$707$		0			0
$708$	−2.74521	+	4.10850i	−0.103171	+	0.154407i
$709$	−6.16483	+	2.09268i	−0.231525	+	0.0785922i	−0.434791	−	0.900531i	$-0.643178\pi$
$709$	−6.16483	+	2.09268i	−0.231525	+	0.0785922i	0.203266	+	0.979124i	$0.434844\pi$
$710$	2.00827	+	7.49498i	0.0753692	+	0.281282i
$711$	17.4770	−	1.14550i	0.655439	−	0.0429598i
$712$	2.43491	−	3.17324i	0.0912522	−	0.118922i
$713$	12.2205			0.457663
$714$		0			0
$715$	−54.0490			−2.02132
$716$	9.28017	−	12.0942i	0.346816	−	0.451980i
$717$	−14.9051	+	0.976930i	−0.556640	+	0.0364841i
$718$	3.27103	+	12.2076i	0.122074	+	0.455585i
$719$	−23.1005	+	7.84157i	−0.861504	+	0.292441i	−0.717009	−	0.697064i	$-0.754489\pi$
$719$	−23.1005	+	7.84157i	−0.861504	+	0.292441i	−0.144496	+	0.989505i	$0.546156\pi$
$720$	4.47896	−	6.70324i	0.166921	−	0.249815i
$721$		0			0
$722$	−16.5811	−	6.86811i	−0.617084	−	0.255604i
$723$	−17.9451	+	2.36252i	−0.667385	+	0.0878630i
$724$	0.675083	−	1.98873i	0.0250893	−	0.0739106i
$725$	−12.1781	−	24.6947i	−0.452282	−	0.917138i
$726$	1.19138	+	3.50970i	0.0442163	+	0.130257i
$727$	−34.9002	+	34.9002i	−1.29438	+	1.29438i	−0.362325	+	0.932052i	$0.618017\pi$
$727$	−34.9002	+	34.9002i	−1.29438	+	1.29438i	−0.932052	+	0.362325i	$0.881983\pi$
$728$		0			0
$729$	−2.68303	+	1.11135i	−0.0993715	+	0.0411610i
$730$	−37.8172	+	21.8338i	−1.39968	+	0.808104i
$731$	1.55000	−	44.3650i	0.0573286	−	1.64090i
$732$	−2.86196	+	4.95707i	−0.105781	+	0.183218i
$733$	31.3722	+	24.0727i	1.15876	+	0.889146i	0.995246	−	0.0973948i	$-0.0310509\pi$
$733$	31.3722	+	24.0727i	1.15876	+	0.889146i	0.163512	+	0.986541i	$0.447718\pi$
$734$	6.48712	+	9.70866i	0.239444	+	0.358353i
$735$		0			0
$736$	−13.7612	−	2.73727i	−0.507245	−	0.100897i
$737$	−0.0397520	+	0.606498i	−0.00146428	+	0.0223406i
$738$	−8.05458	−	2.73416i	−0.296493	−	0.100646i
$739$	9.55548	−	7.33218i	0.351504	−	0.269719i	−0.417884	−	0.908500i	$-0.637228\pi$
$739$	9.55548	−	7.33218i	0.351504	−	0.269719i	0.769388	+	0.638782i	$0.220561\pi$
$740$	−2.00241	−	15.2098i	−0.0736101	−	0.559125i
$741$	3.10474	−	0.617571i	0.114055	−	0.0226870i
$742$		0			0
$743$	3.94527	−	19.8342i	0.144738	−	0.727647i	−0.838440	−	0.544995i	$-0.816532\pi$
$743$	3.94527	−	19.8342i	0.144738	−	0.727647i	0.983178	−	0.182652i	$-0.0584683\pi$
$744$	2.42876	−	9.06426i	0.0890427	−	0.332312i
$745$	−1.89864	−	28.9676i	−0.0695608	−	1.06129i
$746$	−3.49465	+	26.5445i	−0.127948	+	0.971864i
$747$	−1.98959	−	3.44606i	−0.0727951	−	0.126085i
$748$	−7.80707	+	14.5291i	−0.285455	+	0.531236i
$749$		0			0
$750$	0.183001	+	0.441803i	0.00668224	+	0.0161324i
$751$	12.6750	+	6.25060i	0.462516	+	0.228088i	0.658591	−	0.752501i	$-0.271153\pi$
$751$	12.6750	+	6.25060i	0.462516	+	0.228088i	−0.196075	+	0.980589i	$0.562820\pi$
$752$	−12.8495	+	3.44302i	−0.468574	+	0.125554i
$753$	6.65617	−	7.58990i	0.242564	−	0.276591i
$754$	22.2654	+	1.45935i	0.810858	+	0.0531464i
$755$	−8.74510	−	43.9646i	−0.318267	−	1.60004i
$756$		0			0
$757$	−12.0516	+	29.0951i	−0.438022	+	1.05748i	0.538609	+	0.842556i	$0.318950\pi$
$757$	−12.0516	+	29.0951i	−0.438022	+	1.05748i	−0.976631	+	0.214923i	$0.931050\pi$
$758$	6.35182	−	5.57040i	0.230709	−	0.202326i
$759$	7.29988	−	3.59990i	0.264969	−	0.130668i
$760$	7.52977	+	6.60343i	0.273134	+	0.239532i
$761$	−14.8898	−	3.98972i	−0.539756	−	0.144627i	−0.0213661	−	0.999772i	$-0.506802\pi$
$761$	−14.8898	−	3.98972i	−0.539756	−	0.144627i	−0.518389	+	0.855145i	$0.673468\pi$
$762$	−9.49953	+	6.34738i	−0.344132	+	0.229941i
$763$		0			0
$764$		−	12.1868i		−	0.440904i
$765$	−22.4004	+	23.8116i	−0.809889	+	0.860909i
$766$	−16.1689	−	9.33514i	−0.584207	−	0.337292i
$767$	−28.7786	−	3.78877i	−1.03913	−	0.136805i
$768$	−5.41002	+	10.9704i	−0.195217	+	0.395861i
$769$	−2.91916	−	2.91916i	−0.105267	−	0.105267i	0.652511	−	0.757779i	$-0.273715\pi$
$769$	−2.91916	−	2.91916i	−0.105267	−	0.105267i	−0.757779	+	0.652511i	$0.773715\pi$
$770$		0			0
$771$	11.6252	+	7.76770i	0.418671	+	0.279747i
$772$	−17.9767	−	20.4985i	−0.646995	−	0.737756i
$773$	−11.4019	−	14.8592i	−0.410096	−	0.534448i	0.541946	−	0.840413i	$-0.317688\pi$
$773$	−11.4019	−	14.8592i	−0.410096	−	0.534448i	−0.952043	+	0.305965i	$0.901021\pi$
$774$	−16.3003	−	21.2430i	−0.585902	−	0.763563i
$775$	−14.9086	−	17.0000i	−0.535534	−	0.610659i
$776$	18.3799	+	12.2810i	0.659799	+	0.440864i
$777$		0			0
$778$	7.36843	+	7.36843i	0.264171	+	0.264171i
$779$	1.57957	−	3.20305i	0.0565939	−	0.114761i
$780$	9.56265	+	1.25895i	0.342398	+	0.0450775i
$781$	−8.43161	−	4.86799i	−0.301707	−	0.174190i
$782$	−10.8742	−	4.12009i	−0.388862	−	0.147334i
$783$			20.8657i			0.745681i
$784$		0			0
$785$	27.9172	−	18.6536i	0.996406	−	0.665777i
$786$	−4.36340	−	1.16917i	−0.155637	−	0.0417029i
$787$	11.3321	+	9.93803i	0.403948	+	0.354252i	0.837083	−	0.547077i	$-0.184259\pi$
$787$	11.3321	+	9.93803i	0.403948	+	0.354252i	−0.433135	+	0.901329i	$0.642593\pi$
$788$	−3.54504	+	1.74822i	−0.126287	+	0.0622777i
$789$	−2.51674	+	2.20712i	−0.0895984	+	0.0785757i
$790$	8.64665	−	20.8749i	0.307634	−	0.742695i
$791$		0			0
$792$	5.83900	+	29.3546i	0.207480	+	1.04307i
$793$	−33.5527	−	2.19916i	−1.19149	−	0.0780944i
$794$	4.49267	−	5.12290i	0.159439	−	0.181805i
$795$	6.17160	−	1.65368i	0.218884	−	0.0586499i
$796$	7.21268	+	3.55690i	0.255647	+	0.126071i
$797$	2.08167	+	5.02558i	0.0737364	+	0.178015i	0.956450	−	0.291896i	$-0.0942860\pi$
$797$	2.08167	+	5.02558i	0.0737364	+	0.178015i	−0.882714	+	0.469911i	$0.844286\pi$
$798$		0			0
$799$	53.6962	−	5.16946i	1.89964	−	0.182882i
$800$	12.9803	+	22.4826i	0.458924	+	0.794880i
$801$	−0.431588	+	3.27824i	−0.0152494	+	0.115831i
$802$	0.543667	+	8.29476i	0.0191976	+	0.292898i
$803$	14.1810	−	52.9243i	0.500438	−	1.86766i
$804$	0.0211601	−	0.106379i	0.000746259	−	0.00375170i
$805$		0			0
$806$	17.9716	−	3.57477i	0.633023	−	0.125916i
$807$	1.29492	+	9.83590i	0.0455834	+	0.346240i
$808$	41.2356	−	31.6412i	1.45066	−	1.11313i
$809$	10.6953	+	3.63058i	0.376028	+	0.127644i	0.503054	−	0.864255i	$-0.332210\pi$
$809$	10.6953	+	3.63058i	0.376028	+	0.127644i	−0.127026	+	0.991899i	$0.540543\pi$
$810$	−0.964127	+	14.7097i	−0.0338760	+	0.516848i
$811$	42.8912	+	8.53159i	1.50611	+	0.299585i	0.878047	−	0.478575i	$-0.158846\pi$
$811$	42.8912	+	8.53159i	1.50611	+	0.299585i	0.628067	+	0.778159i	$0.283846\pi$
$812$		0			0
$813$	9.29276	+	13.9076i	0.325911	+	0.487761i
$814$	−15.4000	−	11.8168i	−0.539769	−	0.414179i
$815$	8.90056	−	15.4162i	0.311773	−	0.540007i
$816$	−1.76329	+	2.44927i	−0.0617274	+	0.0857417i
$817$	9.73613	−	5.62116i	0.340624	−	0.196659i
$818$	−15.1632	+	6.28082i	−0.530170	+	0.219604i
$819$		0			0
$820$	7.69442	−	7.69442i	0.268701	−	0.268701i
$821$	2.67537	+	7.88138i	0.0933710	+	0.275062i	0.983575	−	0.180500i	$-0.0577716\pi$
$821$	2.67537	+	7.88138i	0.0933710	+	0.275062i	−0.890204	+	0.455562i	$0.849438\pi$
$822$	1.50039	+	3.04249i	0.0523320	+	0.106119i
$823$	14.9964	−	44.1780i	0.522742	−	1.53995i	−0.289825	−	0.957080i	$-0.593597\pi$
$823$	14.9964	−	44.1780i	0.522742	−	1.53995i	0.812567	−	0.582868i	$-0.198070\pi$
$824$	17.9310	−	2.36066i	0.624655	−	0.0822373i
$825$	−13.9134	−	5.76312i	−0.484403	−	0.200646i
$826$		0			0
$827$	29.5342	−	44.2010i	1.02700	−	1.53702i	0.196116	−	0.980581i	$-0.437167\pi$
$827$	29.5342	−	44.2010i	1.02700	−	1.53702i	0.830888	−	0.556439i	$-0.187833\pi$
$828$	6.58634	−	2.23576i	0.228891	−	0.0776980i
$829$	13.0854	+	48.8353i	0.454474	+	1.69612i	0.689629	+	0.724163i	$0.257774\pi$
$829$	13.0854	+	48.8353i	0.454474	+	1.69612i	−0.235155	+	0.971958i	$0.575560\pi$
$830$	−5.12238	+	0.335739i	−0.177800	+	0.0116537i
$831$	12.1717	−	15.8624i	0.422230	−	0.550261i
$832$	−29.6016			−1.02625
$833$		0			0
$834$	−3.79858			−0.131534
$835$	28.5864	−	37.2546i	0.989275	−	1.28925i
$836$	−4.16811	+	0.273192i	−0.144157	+	0.00944856i
$837$	4.43488	+	16.5512i	0.153292	+	0.572093i
$838$	−2.31217	+	0.784876i	−0.0798726	+	0.0271131i
$839$	4.83475	−	7.23572i	0.166914	−	0.249805i	−0.738578	−	0.674168i	$-0.764502\pi$
$839$	4.83475	−	7.23572i	0.166914	−	0.249805i	0.905492	+	0.424364i	$0.139502\pi$
$840$		0			0
$841$	0.963620	+	0.399144i	0.0332283	+	0.0137636i
$842$	21.5723	−	2.84005i	0.743431	−	0.0978746i
$843$	−0.755770	+	2.22643i	−0.0260301	+	0.0766822i
$844$	4.83296	+	9.80027i	0.166357	+	0.337339i
$845$	4.86199	+	14.3230i	0.167258	+	0.492725i
$846$	23.0078	−	23.0078i	0.791024	−	0.791024i
$847$		0			0
$848$	−2.60953	+	1.08090i	−0.0896115	+	0.0371183i
$849$	2.80763	−	1.62099i	0.0963577	−	0.0556321i
$850$	7.53472	+	20.1535i	0.258439	+	0.691261i
$851$	−6.78557	+	11.7530i	−0.232606	+	0.402886i
$852$	1.37838	+	1.05767i	0.0472224	+	0.0362351i
$853$	−29.6753	−	44.4123i	−1.01606	−	1.52065i	−0.844557	−	0.535465i	$-0.820136\pi$
$853$	−29.6753	−	44.4123i	−1.01606	−	1.52065i	−0.171507	−	0.985183i	$-0.554864\pi$
$854$		0			0
$855$	−8.12019	−	1.61521i	−0.277705	−	0.0552389i
$856$	−1.78605	+	27.2499i	−0.0610459	+	0.931381i
$857$	20.1083	+	6.82585i	0.686887	+	0.233167i	0.642996	−	0.765870i	$-0.277691\pi$
$857$	20.1083	+	6.82585i	0.686887	+	0.233167i	0.0438912	+	0.999036i	$0.486025\pi$
$858$	9.68219	−	7.42941i	0.330545	−	0.253636i
$859$	3.47875	+	26.4237i	0.118693	+	0.901566i	0.942385	+	0.334529i	$0.108577\pi$
$859$	3.47875	+	26.4237i	0.118693	+	0.901566i	−0.823692	+	0.567037i	$0.808089\pi$
$860$	33.5961	−	6.68267i	1.14562	−	0.227877i
$861$		0			0
$862$	−3.40134	+	17.0997i	−0.115850	+	0.582417i
$863$	3.39936	−	12.6866i	0.115716	−	0.431856i	−0.883624	−	0.468197i	$-0.844904\pi$
$863$	3.39936	−	12.6866i	0.115716	−	0.431856i	0.999339	+	0.0363411i	$0.0115703\pi$
$864$	−1.28670	−	19.6312i	−0.0437743	−	0.667866i
$865$	−3.40923	+	25.8957i	−0.115917	+	0.880479i
$866$	5.06487	+	8.77261i	0.172111	+	0.298105i
$867$	8.69169	−	8.61560i	0.295185	−	0.292601i
$868$		0			0
$869$	10.8493	+	26.1925i	0.368037	+	0.888520i
$870$	10.9298	+	5.39000i	0.370556	+	0.182738i
$871$	0.615445	−	0.164908i	0.0208536	−	0.00558770i
$872$	−13.2402	+	15.0976i	−0.448371	+	0.511269i
$873$	−18.2348	−	1.19517i	−0.617154	−	0.0404504i
$874$	−0.574531	−	2.88836i	−0.0194338	−	0.0977003i
$875$		0			0
$876$	−3.74174	+	9.03335i	−0.126422	+	0.305209i
$877$	0.233081	−	0.204406i	0.00787058	−	0.00690231i	−0.655401	−	0.755281i	$-0.727501\pi$
$877$	0.233081	−	0.204406i	0.00787058	−	0.00690231i	0.663272	+	0.748378i	$0.269167\pi$
$878$	−13.1751	+	6.49724i	−0.444638	+	0.219271i
$879$	−10.4347	−	9.15103i	−0.351955	−	0.308656i
$880$	12.6051	+	3.37752i	0.424917	+	0.113856i
$881$	9.52056	−	6.36144i	0.320756	−	0.214322i	−0.384759	−	0.923017i	$-0.625716\pi$
$881$	9.52056	−	6.36144i	0.320756	−	0.214322i	0.705515	+	0.708695i	$0.250716\pi$
$882$		0			0
$883$		−	7.97351i		−	0.268330i	−0.990959	−	0.134165i	$-0.957165\pi$
$883$		−	7.97351i		−	0.268330i	0.990959	−	0.134165i	$-0.0428352\pi$
$884$	17.0532	+	2.85402i	0.573563	+	0.0959912i
$885$	−13.7294	−	7.92670i	−0.461510	−	0.266453i
$886$	15.3870	+	2.02573i	0.516936	+	0.0680559i
$887$	10.2398	−	20.7643i	0.343819	−	0.697196i	−0.654444	−	0.756111i	$-0.727097\pi$
$887$	10.2398	−	20.7643i	0.343819	−	0.697196i	0.998263	+	0.0589144i	$0.0187639\pi$
$888$	7.36885	+	7.36885i	0.247282	+	0.247282i
$889$		0			0
$890$	3.54673	+	2.36985i	0.118887	+	0.0794376i
$891$	−12.1956	−	13.9064i	−0.408567	−	0.465882i
$892$	2.02383	+	2.63750i	0.0677627	+	0.0883101i
$893$	8.31657	+	10.8384i	0.278303	+	0.362692i
$894$	4.32192	+	4.92820i	0.144546	+	0.164824i
$895$	40.6668	+	27.1727i	1.35934	+	0.908284i
$896$		0			0
$897$	−6.03330	−	6.03330i	−0.201446	−	0.201446i
$898$	9.48288	−	19.2294i	0.316448	−	0.641692i
$899$	−22.7620	−	2.99667i	−0.759155	−	0.0999447i
$900$	−11.1453	−	6.43472i	−0.371509	−	0.214491i
$901$	11.1603	−	2.57636i	0.371803	−	0.0858311i
$902$		−	13.7686i		−	0.458443i
$903$		0			0
$904$	23.6228	−	15.7843i	0.785684	−	0.524977i
$905$	6.50859	+	1.74397i	0.216353	+	0.0579716i
$906$	7.60981	+	6.67362i	0.252819	+	0.221716i
$907$	23.0597	−	11.3718i	0.765686	−	0.377594i	−0.0171259	−	0.999853i	$-0.505452\pi$
$907$	23.0597	−	11.3718i	0.765686	−	0.377594i	0.782811	+	0.622259i	$0.213785\pi$
$908$	3.79956	−	3.33213i	0.126093	−	0.110581i
$909$	−16.4430	+	39.6969i	−0.545380	+	1.31666i
$910$		0			0
$911$	7.50975	+	37.7541i	0.248809	+	1.25085i	0.879908	+	0.475145i	$0.157604\pi$
$911$	7.50975	+	37.7541i	0.248809	+	1.25085i	−0.631099	+	0.775703i	$0.717396\pi$
$912$	−0.762665	−	0.0499877i	−0.0252544	−	0.00165526i
$913$	4.24687	−	4.84263i	0.140551	−	0.160268i
$914$	13.6697	−	3.66278i	0.452152	−	0.121154i
$915$	−16.4706	−	8.12242i	−0.544502	−	0.268519i
$916$	−1.45542	−	3.51370i	−0.0480886	−	0.116096i
$917$		0			0
$918$	1.63384	−	16.2230i	0.0539247	−	0.535438i
$919$	−12.2096	−	21.1477i	−0.402758	−	0.697597i	0.591300	−	0.806452i	$-0.298615\pi$
$919$	−12.2096	−	21.1477i	−0.402758	−	0.697597i	−0.994058	+	0.108855i	$0.965282\pi$
$920$	3.52349	−	26.7636i	0.116166	−	0.882369i
$921$	0.883948	+	13.4864i	0.0291271	+	0.444393i
$922$	8.78058	−	32.7696i	0.289173	−	1.07921i
$923$	−1.99114	+	10.0101i	−0.0655391	+	0.329487i
$924$		0			0
$925$	24.6277	−	4.89876i	0.809754	−	0.161070i
$926$	0.304591	+	2.31360i	0.0100095	+	0.0760296i
$927$	−11.8614	+	9.10160i	−0.389581	+	0.298936i
$928$	24.9604	+	8.47292i	0.819366	+	0.278137i
$929$	−0.809590	+	12.3520i	−0.0265618	+	0.405255i	0.963788	+	0.266668i	$0.0859227\pi$
$929$	−0.809590	+	12.3520i	−0.0265618	+	0.405255i	−0.990350	+	0.138587i	$0.955744\pi$
$930$	9.81541	+	1.95241i	0.321860	+	0.0640219i
$931$		0			0
$932$	11.7339	+	17.5610i	0.384356	+	0.575229i
$933$	−1.36073	−	1.04412i	−0.0445483	−	0.0341831i
$934$	−13.0917	+	22.6755i	−0.428374	+	0.741966i
$935$	−48.1532	−	21.9456i	−1.57478	−	0.717699i
$936$	27.1718	−	15.6876i	0.888138	−	0.512767i
$937$	−16.2994	+	6.75144i	−0.532479	+	0.220560i	−0.632689	−	0.774406i	$-0.718049\pi$
$937$	−16.2994	+	6.75144i	−0.532479	+	0.220560i	0.100210	+	0.994966i	$0.468049\pi$
$938$		0			0
$939$	−9.26639	+	9.26639i	−0.302397	+	0.302397i
$940$	13.3800	+	39.4161i	0.436406	+	1.28561i
$941$	−11.7080	−	23.7416i	−0.381671	−	0.773953i	0.618256	−	0.785977i	$-0.287839\pi$
$941$	−11.7080	−	23.7416i	−0.381671	−	0.773953i	−0.999928	+	0.0120235i	$0.996173\pi$
$942$	−2.43693	+	7.17897i	−0.0793995	+	0.233903i
$943$	−9.54377	+	1.25646i	−0.310788	+	0.0409160i
$944$	6.47485	+	2.68197i	0.210738	+	0.0872907i
$945$		0			0
$946$	24.0797	−	36.0378i	0.782898	−	1.17169i
$947$	−8.76849	+	2.97650i	−0.284938	+	0.0967233i	−0.460249	−	0.887790i	$-0.652240\pi$
$947$	−8.76849	+	2.97650i	−0.284938	+	0.0967233i	0.175312	+	0.984513i	$0.443907\pi$
$948$	−1.30942	−	4.88683i	−0.0425280	−	0.158717i
$949$	−57.3147	+	3.75661i	−1.86052	+	0.121945i
$950$	−3.31710	+	4.32293i	−0.107621	+	0.140254i
$951$	−11.1467			−0.361458
$952$		0			0
$953$	−44.1963			−1.43166			−0.715829	−	0.698275i	$-0.753951\pi$
$953$	−44.1963			−1.43166			−0.715829	+	0.698275i	$0.753951\pi$
$954$	4.20572	−	5.48100i	0.136165	−	0.177454i
$955$	39.0162	−	2.55726i	1.26254	−	0.0827509i
$956$	−5.34769	−	19.9578i	−0.172957	−	0.645483i
$957$	−14.4795	+	4.91513i	−0.468056	+	0.158884i
$958$	1.18036	−	1.76653i	0.0381356	−	0.0570739i
$959$		0			0
$960$	−14.9366	−	6.18695i	−0.482078	−	0.199683i
$961$	12.0425	−	1.58543i	0.388468	−	0.0511428i
$962$	−6.54091	+	19.2689i	−0.210887	+	0.621254i
$963$	−9.98473	−	20.2470i	−0.321754	−	0.652452i
$964$	−8.04788	−	23.7083i	−0.259205	−	0.763592i
$965$	61.8538	−	61.8538i	1.99114	−	1.99114i
$966$		0			0
$967$	−47.6560	+	19.7398i	−1.53251	+	0.634788i	−0.980050	−	0.198749i	$-0.936312\pi$
$967$	−47.6560	+	19.7398i	−1.53251	+	0.634788i	−0.552464	+	0.833537i	$0.686312\pi$
$968$	−13.3575	+	7.71198i	−0.429328	+	0.247873i
$969$	3.01682	+	0.710418i	0.0969141	+	0.0228219i
$970$	−11.7872	+	20.4161i	−0.378465	+	0.655521i
$971$	29.5904	+	22.7055i	0.949603	+	0.728656i	0.962506	−	0.271261i	$-0.0874407\pi$
$971$	29.5904	+	22.7055i	0.949603	+	0.728656i	−0.0129032	+	0.999917i	$0.504107\pi$
$972$	8.38351	+	12.5468i	0.268901	+	0.402439i
$973$		0			0
$974$	−39.9736	−	7.95124i	−1.28084	−	0.254774i
$975$	−1.03253	+	15.7534i	−0.0330674	+	0.504511i
$976$	7.68758	+	2.60958i	0.246073	+	0.0835307i
$977$	−3.68293	+	2.82601i	−0.117827	+	0.0904121i	−0.665994	−	0.745957i	$-0.731993\pi$
$977$	−3.68293	+	2.82601i	−0.117827	+	0.0904121i	0.548167	+	0.836369i	$0.315326\pi$
$978$	0.524643	+	3.98506i	0.0167762	+	0.127428i
$979$	−5.24939	+	1.04417i	−0.167771	+	0.0333718i
$980$		0			0
$981$	3.23857	−	16.2814i	0.103400	−	0.519825i
$982$	3.70200	−	13.8160i	0.118135	−	0.440887i
$983$	0.938826	+	14.3237i	0.0299439	+	0.456856i	0.986333	+	0.164761i	$0.0526854\pi$
$983$	0.938826	+	14.3237i	0.0299439	+	0.456856i	−0.956390	+	0.292094i	$0.905648\pi$
$984$	−0.964822	+	7.32855i	−0.0307574	+	0.233626i
$985$	−6.34081	−	10.9826i	−0.202035	−	0.349935i
$986$	19.2441	+	10.3406i	0.612856	+	0.329313i
$987$		0			0
$988$	1.67570	+	4.04549i	0.0533110	+	0.128704i
$989$	−27.1773	−	13.4023i	−0.864187	−	0.426170i
$990$	−30.8313	+	8.26122i	−0.979883	+	0.262559i
$991$	9.75462	−	11.1230i	0.309866	−	0.353334i	−0.575856	−	0.817551i	$-0.695331\pi$
$991$	9.75462	−	11.1230i	0.309866	−	0.353334i	0.885721	+	0.464217i	$0.153664\pi$
$992$	21.6000	+	1.41574i	0.685802	+	0.0449498i
$993$	0.562126	+	2.82600i	0.0178385	+	0.0896804i
$994$		0			0
$995$	−9.87394	+	23.8378i	−0.313025	+	0.755709i
$996$	−0.864177	+	0.757863i	−0.0273825	+	0.0240138i
$997$	35.4937	−	17.5036i	1.12410	−	0.554343i	0.217382	−	0.976087i	$-0.430248\pi$
$997$	35.4937	−	17.5036i	1.12410	−	0.554343i	0.906715	+	0.421743i	$0.138582\pi$
$998$	2.72232	+	2.38741i	0.0861734	+	0.0755720i
$999$	−18.3804	−	4.92501i	−0.581530	−	0.155821i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.bc.f.80.8		160
7.2	even	3	inner	833.2.bc.f.607.3		160
7.3	odd	6		119.2.p.a.97.8	yes	80
7.4	even	3		119.2.p.a.97.7	yes	80
7.5	odd	6	inner	833.2.bc.f.607.4		160
7.6	odd	2	inner	833.2.bc.f.80.7		160
17.10	odd	16	inner	833.2.bc.f.129.4		160
119.10	even	48		119.2.p.a.27.7	✓	80
119.27	even	16	inner	833.2.bc.f.129.3		160
119.44	odd	48	inner	833.2.bc.f.656.7		160
119.61	even	48	inner	833.2.bc.f.656.8		160
119.95	odd	48		119.2.p.a.27.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.p.a.27.7	✓	80	119.10	even	48
119.2.p.a.27.8	yes	80	119.95	odd	48
119.2.p.a.97.7	yes	80	7.4	even	3
119.2.p.a.97.8	yes	80	7.3	odd	6
833.2.bc.f.80.7		160	7.6	odd	2	inner
833.2.bc.f.80.8		160	1.1	even	1	trivial
833.2.bc.f.129.3		160	119.27	even	16	inner
833.2.bc.f.129.4		160	17.10	odd	16	inner
833.2.bc.f.607.3		160	7.2	even	3	inner
833.2.bc.f.607.4		160	7.5	odd	6	inner
833.2.bc.f.656.7		160	119.44	odd	48	inner
833.2.bc.f.656.8		160	119.61	even	48	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.bc (of order \(48\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.610037 - 0.795016i) q^{2} +(0.718354 - 0.0470834i) q^{3} +(0.257733 + 0.961873i) q^{4} +(-3.02536 + 1.02697i) q^{5} +(0.400790 - 0.599825i) q^{6} +(2.77356 + 1.14885i) q^{8} +(-2.46052 + 0.323934i) q^{9} +(-1.02912 + 3.03170i) q^{10} +(-1.77675 - 3.60290i) q^{11} +(0.230432 + 0.678830i) q^{12} +(-2.97778 + 2.97778i) q^{13} +(-2.12493 + 0.880173i) q^{15} +(0.880544 - 0.508383i) q^{16} +(-3.86202 + 1.44388i) q^{17} +(-1.24348 + 2.15376i) q^{18} +(-0.828402 - 0.635655i) q^{19} +(-1.76755 - 2.64533i) q^{20} +(-3.94825 - 0.785356i) q^{22} +(-0.184074 + 2.80843i) q^{23} +(2.04649 + 0.694690i) q^{24} +(4.13137 - 3.17011i) q^{25} +(0.550825 + 4.18393i) q^{26} +(-3.87046 + 0.769882i) q^{27} +(1.03153 - 5.18584i) q^{29} +(-0.596532 + 2.22629i) q^{30} +(-0.283985 - 4.33277i) q^{31} +(-0.650708 + 4.94262i) q^{32} +(-1.44598 - 2.50450i) q^{33} +(-1.20807 + 3.95119i) q^{34} +(-0.945740 - 2.28322i) q^{36} +(4.32467 + 2.13269i) q^{37} +(-1.01071 + 0.270820i) q^{38} +(-1.99889 + 2.27930i) q^{39} +(-9.57086 - 0.627307i) q^{40} +(0.667258 + 3.35453i) q^{41} +(-4.12022 + 9.94710i) q^{43} +(3.00761 - 2.63760i) q^{44} +(7.11129 - 3.50690i) q^{45} +(2.12045 + 1.85959i) q^{46} +(-12.6376 - 3.38625i) q^{47} +(0.608606 - 0.406658i) q^{48} -5.21839i q^{50} +(-2.70632 + 1.21905i) q^{51} +(-3.63171 - 2.09677i) q^{52} +(-2.75419 - 0.362596i) q^{53} +(-1.74906 + 3.54673i) q^{54} +(9.07540 + 9.07540i) q^{55} +(-0.625015 - 0.417621i) q^{57} +(-3.49356 - 3.98364i) q^{58} +(4.19605 + 5.46840i) q^{59} +(-1.39428 - 1.81706i) q^{60} +(5.26459 + 6.00311i) q^{61} +(-3.61786 - 2.41738i) q^{62} +(4.97043 + 4.97043i) q^{64} +(5.95076 - 12.0669i) q^{65} +(-2.87322 - 0.378266i) q^{66} +(-0.131030 - 0.0756499i) q^{67} +(-2.38420 - 3.34264i) q^{68} +2.02611i q^{69} +(2.01514 - 1.34647i) q^{71} +(-7.19655 - 1.92831i) q^{72} +(10.2545 + 8.99298i) q^{73} +(4.33374 - 2.13716i) q^{74} +(2.81853 - 2.47178i) q^{75} +(0.397913 - 0.960647i) q^{76} +(0.592681 + 2.97961i) q^{78} +(-7.04221 - 0.461571i) q^{79} +(-2.14187 + 2.44233i) q^{80} +(4.44745 - 1.19169i) q^{81} +(3.07396 + 1.51591i) q^{82} +(0.613584 + 1.48132i) q^{83} +(10.2012 - 8.33444i) q^{85} +(5.39461 + 9.34375i) q^{86} +(0.496835 - 3.77384i) q^{87} +(-0.788756 - 12.0341i) q^{88} +(0.344834 - 1.28694i) q^{89} +(1.55011 - 7.79293i) q^{90} +(-2.74879 + 0.546769i) q^{92} +(-0.408003 - 3.09909i) q^{93} +(-10.4016 + 7.98139i) q^{94} +(3.15902 + 1.07234i) q^{95} +(-0.234723 + 3.58119i) q^{96} +(7.22183 + 1.43651i) q^{97} +(5.53884 + 8.28946i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 128 q^{15} - 32 q^{18} - 96 q^{22} + 16 q^{23} - 32 q^{29} - 112 q^{30} - 16 q^{32} - 96 q^{36} - 48 q^{37} - 32 q^{43} + 16 q^{44} - 16 q^{46} + 48 q^{51}+ \cdots + 256 q^{99}+O(q^{100}) \) 160 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 128 * q^15 - 32 * q^18 - 96 * q^22 + 16 * q^23 - 32 * q^29 - 112 * q^30 - 16 * q^32 - 96 * q^36 - 48 * q^37 - 32 * q^43 + 16 * q^44 - 16 * q^46 + 48 * q^51 - 16 * q^53 - 32 * q^57 + 48 * q^58 - 48 * q^60 + 96 * q^64 + 32 * q^65 + 32 * q^71 + 80 * q^72 + 80 * q^74 + 224 * q^78 + 16 * q^79 + 64 * q^81 + 224 * q^85 - 48 * q^86 + 112 * q^88 + 512 * q^92 - 48 * q^93 + 48 * q^95 + 256 * q^99

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