LMFDB - Embedded newform 833.2.bc.f.656.7

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			656.7
Character	$\chi$	$=$	833.656
Dual form			833.2.bc.f.80.7

$q$-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 $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{16}\right)$

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	0.957572	−	0.288193i	$-0.0930544\pi$
$2$	0.610037	+	0.795016i	0.431361	+	0.562161i	−0.526211	+	0.850354i	$0.676388\pi$
$3$	−0.718354	−	0.0470834i	−0.414742	−	0.0271836i	−0.143396	−	0.989665i	$-0.545802\pi$
$3$	−0.718354	−	0.0470834i	−0.414742	−	0.0271836i	−0.271346	+	0.962482i	$0.587469\pi$
$4$	0.257733	−	0.961873i	0.128867	−	0.480937i
$5$	3.02536	+	1.02697i	1.35298	+	0.459276i	0.901413	−	0.432960i	$-0.142531\pi$
$5$	3.02536	+	1.02697i	1.35298	+	0.459276i	0.451570	+	0.892236i	$0.350864\pi$
$6$	−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	0.445839	+	0.895113i	$0.352905\pi$
$11$	−1.77675	+	3.60290i	−0.535712	+	1.08632i	−0.981551	+	0.191203i	$0.938761\pi$
$12$	−0.230432	+	0.678830i	−0.0665199	+	0.195961i
$13$	2.97778	+	2.97778i	0.825886	+	0.825886i	0.986945	−	0.161058i	$-0.0514908\pi$
$13$	2.97778	+	2.97778i	0.825886	+	0.825886i	−0.161058	+	0.986945i	$0.551491\pi$
$14$		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	$-0.670116\pi$
$19$	0.828402	−	0.635655i	0.190049	−	0.145829i	0.699403	+	0.714727i	$0.253449\pi$
$20$	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	−0.973126	−	0.230274i	$-0.926038\pi$
$23$	−0.184074	−	2.80843i	−0.0383821	−	0.585597i	0.934744	−	0.355323i	$-0.115629\pi$
$24$	−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	0.950236	+	0.311530i	$0.100842\pi$
$29$	1.03153	+	5.18584i	0.191550	+	0.962986i	−0.758686	+	0.651456i	$0.774158\pi$
$30$	−0.596532	−	2.22629i	−0.108911	−	0.406463i
$31$	0.283985	−	4.33277i	0.0510052	−	0.778189i	−0.893371	−	0.449321i	$-0.851666\pi$
$31$	0.283985	−	4.33277i	0.0510052	−	0.778189i	0.944376	−	0.328868i	$-0.106667\pi$
$32$	−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	−0.0505767	−	0.998720i	$-0.516106\pi$
$37$	4.32467	−	2.13269i	0.710972	−	0.350613i	0.761549	+	0.648108i	$0.224439\pi$
$38$	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	0.893054	+	0.449949i	$0.148558\pi$
$41$	−0.667258	+	3.35453i	−0.104208	+	0.523890i	−0.997263	+	0.0739411i	$0.976442\pi$
$42$		0			0
$43$	−4.12022	−	9.94710i	−0.628328	−	1.51692i	−0.841699	−	0.539948i	$-0.818444\pi$
$43$	−4.12022	−	9.94710i	−0.628328	−	1.51692i	0.213370	−	0.976971i	$-0.431556\pi$
$44$	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	$-0.180033\pi$
$47$	12.6376	−	3.38625i	1.84339	−	0.493935i	0.999118	+	0.0419802i	$0.0133666\pi$
$48$	−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	−0.317287	−	0.948329i	$-0.602772\pi$
$53$	−2.75419	+	0.362596i	−0.378317	+	0.0498064i	−0.0610302	+	0.998136i	$0.519439\pi$
$54$	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	$-0.939773\pi$
$59$	−4.19605	+	5.46840i	−0.546279	+	0.711925i	0.435874	+	0.900008i	$0.356439\pi$
$60$	−1.39428	+	1.81706i	−0.180001	+	0.234581i
$61$	−5.26459	+	6.00311i	−0.674061	+	0.768619i	−0.983226	−	0.182389i	$-0.941617\pi$
$61$	−5.26459	+	6.00311i	−0.674061	+	0.768619i	0.309165	+	0.951008i	$0.399950\pi$
$62$	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	−0.507983	−	0.861367i	$-0.669609\pi$
$67$	−0.131030	+	0.0756499i	−0.0160078	+	0.00924211i	0.491975	+	0.870609i	$0.336275\pi$
$68$	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	0.669371	−	0.742928i	$-0.266564\pi$
$71$	2.01514	+	1.34647i	0.239153	+	0.159797i	−0.430219	+	0.902725i	$0.641564\pi$
$72$	−7.19655	+	1.92831i	−0.848122	+	0.227254i
$73$	−10.2545	+	8.99298i	−1.20020	+	1.05255i	−0.202895	+	0.979201i	$0.565035\pi$
$73$	−10.2545	+	8.99298i	−1.20020	+	1.05255i	−0.997306	+	0.0733476i	$0.976632\pi$
$74$	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	−0.456183	−	0.889886i	$-0.650784\pi$
$79$	−7.04221	+	0.461571i	−0.792311	+	0.0519308i	−0.336127	+	0.941817i	$0.609117\pi$
$80$	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	$-0.903046\pi$
$83$	−0.613584	+	1.48132i	−0.0673496	+	0.162596i	0.886621	+	0.462497i	$0.153046\pi$
$84$		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	$-0.105829\pi$
$89$	−0.344834	−	1.28694i	−0.0365523	−	0.136415i	−0.981791	+	0.189965i	$0.939162\pi$
$90$	−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	$-0.684451\pi$
$97$	−7.22183	+	1.43651i	−0.733266	+	0.145856i	−0.185686	+	0.982609i	$0.559451\pi$
$98$		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	−0.870602	−	0.491989i	$-0.836270\pi$
$101$	−8.65672	−	14.9939i	−0.861375	−	1.49195i	0.00922616	−	0.999957i	$-0.497063\pi$
$102$	−0.681787	−	2.89523i	−0.0675070	−	0.286671i
$103$	−5.21727	−	3.01219i	−0.514073	−	0.296800i	0.220434	−	0.975402i	$-0.429253\pi$
$103$	−5.21727	−	3.01219i	−0.514073	−	0.296800i	−0.734506	+	0.678602i	$0.762586\pi$
$104$	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	−0.709148	−	0.705060i	$-0.750920\pi$
$107$	2.92396	−	8.61371i	0.282670	−	0.832719i	0.991818	−	0.127659i	$-0.0407464\pi$
$108$	1.73807	−	3.52447i	0.167246	−	0.339142i
$109$	−2.15010	−	6.33399i	−0.205942	−	0.606687i	0.794057	−	0.607843i	$-0.207965\pi$
$109$	−2.15010	−	6.33399i	−0.205942	−	0.606687i	−0.999999	+	0.00115670i	$0.999632\pi$
$110$	−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	0.991855	−	0.127374i	$-0.0406550\pi$
$113$	5.25777	+	7.86881i	0.494610	+	0.740236i	−0.497245	+	0.867610i	$0.665655\pi$
$114$	−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	−0.921463	−	0.388467i	$-0.873005\pi$
$127$	−14.6316	+	6.06062i	−1.29835	+	0.537793i	−0.376885	+	0.926260i	$0.623005\pi$
$128$	−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	$-0.807635\pi$
$131$	2.01281	−	5.92954i	0.175860	−	0.518066i	0.998742	+	0.0501460i	$0.0159687\pi$
$132$	−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	0.747935	−	0.663772i	$-0.231046\pi$
$137$	−2.35120	−	4.07240i	−0.200876	−	0.347928i	−0.948811	+	0.315844i	$0.897712\pi$
$138$	−1.61079	+	1.23600i	−0.137120	+	0.105216i
$139$	2.92538	−	4.37814i	0.248127	−	0.371349i	−0.686410	−	0.727215i	$-0.740814\pi$
$139$	2.92538	−	4.37814i	0.248127	−	0.371349i	0.934537	+	0.355866i	$0.115814\pi$
$140$		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	−0.992861	−	0.119280i	$-0.961941\pi$
$149$	−2.35169	−	8.77664i	−0.192658	−	0.719011i	0.800202	−	0.599730i	$-0.204725\pi$
$150$	0.245700	−	3.74865i	0.0200613	−	0.306076i
$151$	−1.83133	−	13.9104i	−0.149032	−	1.13201i	−0.888519	−	0.458839i	$-0.848265\pi$
$151$	−1.83133	−	13.9104i	−0.149032	−	1.13201i	0.739488	−	0.673170i	$-0.235068\pi$
$152$	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	$-0.278922\pi$
$157$	10.1510	+	2.71996i	0.810139	+	0.217076i	0.170108	+	0.985425i	$0.445588\pi$
$158$	−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	0.479403	−	0.877595i	$-0.340853\pi$
$163$	−4.18903	−	3.67368i	−0.328110	−	0.287745i	−0.807513	+	0.589850i	$0.799187\pi$
$164$	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	$-0.119956\pi$
$167$	12.2208	+	8.16569i	0.945675	+	0.631880i	0.0158470	+	0.999874i	$0.494956\pi$
$168$		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	$-0.246422\pi$
$173$	−3.61581	−	7.33213i	−0.274905	−	0.557451i	−0.989915	+	0.141662i	$0.954755\pi$
$174$	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	−0.998968	−	0.0454086i	$-0.985541\pi$
$179$	−9.31927	+	12.1451i	−0.696555	+	0.907768i	0.302413	+	0.953177i	$0.402208\pi$
$180$	−5.20601	+	5.93631i	−0.388033	+	0.442467i
$181$	1.75360	−	1.17172i	0.130344	−	0.0870931i	−0.488689	−	0.872458i	$-0.662525\pi$
$181$	1.75360	−	1.17172i	0.130344	−	0.0870931i	0.619033	+	0.785365i	$0.287525\pi$
$182$		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	−0.659742	−	0.751492i	$-0.729335\pi$
$191$	−11.8212	+	3.16747i	−0.855350	+	0.229190i	−0.195608	+	0.980682i	$0.562668\pi$
$192$	−3.80455	+	3.33650i	−0.274570	+	0.240791i
$193$	−24.5557	−	12.1095i	−1.76756	−	0.871664i	−0.959077	−	0.283145i	$-0.908622\pi$
$193$	−24.5557	−	12.1095i	−1.76756	−	0.871664i	−0.808483	−	0.588519i	$-0.799711\pi$
$194$	−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	−0.943345	−	0.331814i	$-0.892339\pi$
$197$	0.774375	−	3.89305i	0.0551720	−	0.277368i	0.998517	+	0.0544461i	$0.0173393\pi$
$198$	9.96915	−	0.653413i	0.708477	−	0.0464360i
$199$	−5.32482	−	6.07179i	−0.377466	−	0.430418i	0.531647	−	0.846966i	$-0.321573\pi$
$199$	−5.32482	−	6.07179i	−0.377466	−	0.430418i	−0.909114	+	0.416548i	$0.863240\pi$
$200$	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	0.551094	−	0.834443i	$-0.314211\pi$
$211$	10.7623	+	2.14076i	0.740911	+	0.147376i	0.189817	+	0.981820i	$0.439211\pi$
$212$	−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	$-0.410656\pi$
$223$	−3.08438	−	1.27759i	−0.206545	−	0.0855538i	−0.483558	+	0.875313i	$0.660656\pi$
$224$		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	$-0.800300\pi$
$227$	2.24461	−	4.55161i	0.148980	−	0.302101i	0.958551	+	0.284920i	$0.0919671\pi$
$228$	0.240612	+	0.708820i	0.0159349	+	0.0469427i
$229$	3.78656	+	0.498510i	0.250223	+	0.0329424i	0.254594	−	0.967048i	$-0.418058\pi$
$229$	3.78656	+	0.498510i	0.250223	+	0.0329424i	−0.00437142	+	0.999990i	$0.501391\pi$
$230$	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	0.889067	−	0.457776i	$-0.151354\pi$
$233$	20.0838	+	6.81754i	1.31574	+	0.446632i	0.426668	+	0.904408i	$0.359687\pi$
$234$	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	$-0.178751\pi$
$241$	25.0886	+	1.64440i	1.61610	+	0.105925i	0.769677	+	0.638433i	$0.220417\pi$
$242$	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	$-0.395931\pi$
$251$	−9.91577	−	9.91577i	−0.625878	−	0.625878i	−0.947028	+	0.321150i	$0.895931\pi$
$252$		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	$-0.915457\pi$
$257$	−15.4082	+	11.8231i	−0.961134	+	0.737504i	0.00380084	+	0.999993i	$0.498790\pi$
$258$	−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	0.488736	−	0.872432i	$-0.337458\pi$
$263$	−3.68902	−	2.83068i	−0.227475	−	0.174548i	−0.716210	+	0.697884i	$0.754125\pi$
$264$	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	0.878050	+	0.478569i	$0.158844\pi$
$269$	−0.901311	+	13.7513i	−0.0549539	+	0.838435i	−0.933004	+	0.359866i	$0.882822\pi$
$270$	1.64913	+	12.5264i	0.100363	+	0.762331i
$271$	−11.6173	+	20.1218i	−0.705703	+	1.22231i	0.260734	+	0.965411i	$0.416035\pi$
$271$	−11.6173	+	20.1218i	−0.705703	+	1.22231i	−0.966437	+	0.256903i	$0.917298\pi$
$272$	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	0.964552	+	0.263894i	$0.0850070\pi$
$277$	18.3125	+	20.8814i	1.10029	+	1.25464i	0.135737	+	0.990745i	$0.456660\pi$
$278$	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	0.882205	−	0.470865i	$-0.156058\pi$
$281$	−1.24986	−	3.01742i	−0.0745603	−	0.180004i	−0.956765	+	0.290861i	$0.906058\pi$
$282$	−7.09621	−	6.22321i	−0.422573	−	0.370586i
$283$	−4.03898	−	1.99180i	−0.240092	−	0.118400i	0.318263	−	0.948003i	$-0.396901\pi$
$283$	−4.03898	−	1.99180i	−0.240092	−	0.118400i	−0.558355	+	0.829602i	$0.688567\pi$
$284$	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	$-0.559590\pi$
$293$	13.6324	−	13.6324i	0.796413	−	0.796413i	0.982528	+	0.186115i	$0.0595896\pi$
$294$		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	$-0.707648\pi$
$311$	1.79127	−	1.57090i	0.101574	−	0.0890777i	0.708627	+	0.705584i	$0.249315\pi$
$312$	−8.16262	−	4.02536i	−0.462117	−	0.227891i
$313$	13.6862	+	12.0024i	0.773588	+	0.678418i	0.952191	−	0.305503i	$-0.0988246\pi$
$313$	13.6862	+	12.0024i	0.773588	+	0.678418i	−0.178603	+	0.983921i	$0.557158\pi$
$314$	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	−0.492795	−	0.870145i	$-0.664025\pi$
$317$	−15.4507	+	1.01269i	−0.867798	+	0.0568785i	−0.375002	+	0.927024i	$0.622358\pi$
$318$	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	−0.971071	−	0.238791i	$-0.923249\pi$
$331$	0.522428	−	3.96824i	0.0287152	−	0.218114i	0.999786	+	0.0206772i	$0.00658222\pi$
$332$	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	−0.247638	−	0.968853i	$-0.579654\pi$
$337$	13.6256	−	20.3921i	0.742232	−	1.11083i	0.989870	−	0.141976i	$-0.0453456\pi$
$338$	−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	−0.977971	−	0.208742i	$-0.933063\pi$
$347$	−6.13173	−	18.0635i	−0.329168	−	0.969699i	0.648802	−	0.760957i	$-0.275270\pi$
$348$	−3.75800	−	0.494750i	−0.201450	−	0.0265214i
$349$	−10.8607	+	4.49864i	−0.581359	+	0.240807i	−0.653928	−	0.756557i	$-0.726880\pi$
$349$	−10.8607	+	4.49864i	−0.581359	+	0.240807i	0.0725692	+	0.997363i	$0.476880\pi$
$350$		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	$-0.966778\pi$
$353$	−1.52477	+	5.69053i	−0.0811554	+	0.302876i	0.913403	+	0.407056i	$0.133445\pi$
$354$	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	0.545522	−	0.838097i	$-0.316332\pi$
$359$	−7.67761	−	10.0057i	−0.405209	−	0.528079i	−0.950731	+	0.310018i	$0.899665\pi$
$360$	−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	$-0.00580530\pi$
$367$	3.74544	+	11.0337i	0.195510	+	0.575955i	−0.804323	+	0.594192i	$0.797472\pi$
$368$	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	−0.237926	−	0.971283i	$-0.576468\pi$
$373$	−23.1381	−	13.3588i	−1.19805	−	0.691692i	−0.960119	+	0.279591i	$0.909801\pi$
$374$	−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	0.0219055	−	0.999760i	$-0.493027\pi$
$379$	8.26871	−	1.64475i	0.424735	−	0.0844851i	0.402830	+	0.915275i	$0.368027\pi$
$380$	−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	−0.809787	−	0.586724i	$-0.800417\pi$
$383$	2.43186	−	18.4718i	0.124262	−	0.943867i	0.934050	−	0.357143i	$-0.116249\pi$
$384$	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	−0.990784	−	0.135454i	$-0.956751\pi$
$389$	−1.35731	−	10.3098i	−0.0688183	−	0.522727i	0.921965	−	0.387272i	$-0.126583\pi$
$390$	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	$-0.575414\pi$
$397$	−6.78502	+	0.444713i	−0.340530	+	0.0223195i	−0.105821	+	0.994385i	$0.533747\pi$
$398$	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	0.489327	−	0.872101i	$-0.337243\pi$
$401$	−6.23664	−	5.46939i	−0.311443	−	0.273128i	−0.800770	+	0.598972i	$0.795576\pi$
$402$	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	$-0.533964\pi$
$409$	14.1840	−	8.18912i	0.701352	−	0.404926i	0.807851	+	0.589387i	$0.200631\pi$
$410$	−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	$-0.668543\pi$
$419$	2.02600	−	1.35373i	0.0989764	−	0.0661339i	0.604074	+	0.796929i	$0.293543\pi$
$420$		0			0
$421$	15.3534	−	15.3534i	0.748278	−	0.748278i	−0.225878	−	0.974156i	$-0.572525\pi$
$421$	15.3534	−	15.3534i	0.748278	−	0.748278i	0.974156	+	0.225878i	$0.0725249\pi$
$422$	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	0.0257788	−	0.999668i	$-0.491793\pi$
$431$	−15.6040	−	7.69504i	−0.751618	−	0.370657i	−0.777397	+	0.629011i	$0.783460\pi$
$432$	3.01672	+	2.64559i	0.145142	+	0.127286i
$433$	3.86837	+	9.33908i	0.185902	+	0.448808i	0.989163	−	0.146819i	$-0.0469036\pi$
$433$	3.86837	+	9.33908i	0.185902	+	0.448808i	−0.803261	+	0.595627i	$0.796904\pi$
$434$		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	$-0.532074\pi$
$439$	13.1476	−	6.48366i	0.627499	−	0.309448i	0.728092	+	0.685480i	$0.240407\pi$
$440$	−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	−0.621327	−	0.783551i	$-0.713406\pi$
$443$	7.74365	−	13.4124i	0.367912	−	0.637242i	0.989239	+	0.146309i	$0.0467395\pi$
$444$	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	0.663562	−	0.748121i	$-0.269044\pi$
$449$	20.9845	+	4.17408i	0.990321	+	0.196987i	0.326758	+	0.945108i	$0.394044\pi$
$450$	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	−0.312544	−	0.949903i	$-0.601181\pi$
$457$	11.2040	−	8.59710i	0.524099	−	0.402156i	0.836644	+	0.547748i	$0.184515\pi$
$458$	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	$-0.664082\pi$
$461$	−31.2776	−	12.9556i	−1.45674	−	0.603402i	−0.963792	+	0.266655i	$0.914082\pi$
$462$		0			0
$463$	−1.64663	−	1.64663i	−0.0765253	−	0.0765253i	0.667808	−	0.744333i	$-0.267233\pi$
$463$	−1.64663	−	1.64663i	−0.0765253	−	0.0765253i	−0.744333	+	0.667808i	$0.767233\pi$
$464$	−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	$-0.251688\pi$
$467$	25.9052	+	3.41048i	1.19875	+	0.157818i	0.495401	+	0.868665i	$0.335021\pi$
$468$	−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	$-0.494590\pi$
$479$	−2.11560	−	0.138664i	−0.0966644	−	0.00633572i	−0.113659	+	0.993520i	$0.536257\pi$
$480$	−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	−0.0592441	+	0.998244i	$0.518869\pi$
$487$	−17.9885	+	36.4771i	−0.815138	+	1.65294i	−0.755894	+	0.654694i	$0.772798\pi$
$488$	−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	0.659852	−	0.751396i	$-0.270619\pi$
$491$	13.1870	+	5.46223i	0.595121	+	0.246507i	−0.0647312	+	0.997903i	$0.520619\pi$
$492$	−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	−0.999880	−	0.0155147i	$-0.995061\pi$
$499$	−0.236321	−	3.60556i	−0.0105792	−	0.161407i	0.989300	−	0.145892i	$-0.0466054\pi$
$500$	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	$-0.146835\pi$
$503$	34.8179	+	6.92572i	1.55245	+	0.308802i	0.656978	+	0.753910i	$0.271835\pi$
$504$		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	$-0.917372\pi$
$509$	−5.88751	+	10.1975i	−0.260959	+	0.451994i	0.705538	+	0.708672i	$0.250705\pi$
$510$	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	0.994842	+	0.101434i	$0.0323430\pi$
$521$	38.3681	+	18.9210i	1.68094	+	0.828946i	0.686094	+	0.727513i	$0.259324\pi$
$522$	9.88639	−	8.67013i	0.432716	−	0.379481i
$523$	−17.4115	+	4.66539i	−0.761350	+	0.204003i	−0.618547	−	0.785748i	$-0.712278\pi$
$523$	−17.4115	+	4.66539i	−0.761350	+	0.204003i	−0.142803	+	0.989751i	$0.545612\pi$
$524$	−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	0.996307	+	0.0858573i	$0.0273629\pi$
$541$	10.6507	+	21.5975i	0.457909	+	0.928548i	−0.538398	+	0.842690i	$0.680970\pi$
$542$	−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	0.676840	−	0.736130i	$-0.263349\pi$
$547$	5.98174	+	3.99687i	0.255761	+	0.170894i	−0.421080	+	0.907024i	$0.638349\pi$
$548$	−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	0.732948	−	0.680285i	$-0.238144\pi$
$557$	24.2512	+	6.49809i	1.02756	+	0.275333i	0.294609	+	0.955618i	$0.404811\pi$
$558$	−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	−0.988555	−	0.150861i	$-0.951795\pi$
$563$	−1.72571	−	13.1080i	−0.0727299	−	0.552438i	0.915825	−	0.401577i	$-0.131538\pi$
$564$	−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	0.822060	+	0.569400i	$0.192825\pi$
$569$	−2.84720	+	21.6266i	−0.119361	+	0.906634i	−0.941421	+	0.337234i	$0.890509\pi$
$570$	−1.90932	−	1.46507i	−0.0799727	−	0.0613652i
$571$	−14.0053	+	4.75417i	−0.586105	+	0.198956i	−0.598712	−	0.800965i	$-0.704320\pi$
$571$	−14.0053	+	4.75417i	−0.586105	+	0.198956i	0.0126066	+	0.999921i	$0.495987\pi$
$572$	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	0.823440	+	0.567403i	$0.192052\pi$
$577$	21.6933	+	37.5740i	0.903105	+	1.56422i	0.0796650	+	0.996822i	$0.474615\pi$
$578$	−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	$-0.474609\pi$
$587$	20.3730	−	8.43878i	0.840884	−	0.348306i	0.761202	+	0.648515i	$0.224609\pi$
$588$		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	$-0.373990\pi$
$593$	−14.7428	−	19.2132i	−0.605414	−	0.788991i	−0.991026	+	0.133670i	$0.957324\pi$
$594$	−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	−0.664048	−	0.747690i	$-0.731163\pi$
$599$	6.97227	−	26.0209i	0.284879	−	1.06318i	0.948928	−	0.315494i	$-0.102170\pi$
$600$	−10.6571	−	3.61758i	−0.435073	−	0.147687i
$601$	−23.1053	−	34.5796i	−0.942487	−	1.41053i	−0.911632	−	0.411007i	$-0.865177\pi$
$601$	−23.1053	−	34.5796i	−0.942487	−	1.41053i	−0.0308547	−	0.999524i	$-0.509823\pi$
$602$		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	$-0.946087\pi$
$607$	−2.49019	+	7.33585i	−0.101074	+	0.297753i	0.884617	+	0.466318i	$0.154420\pi$
$608$	−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	−0.981520	−	0.191362i	$-0.938710\pi$
$613$	−16.2538	−	28.1524i	−0.656484	−	1.13706i	0.325036	−	0.945702i	$-0.394624\pi$
$614$	−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	−0.382964	−	0.923763i	$-0.625097\pi$
$617$	−9.52017	+	1.89368i	−0.383268	+	0.0762367i	−0.000303681		1.00000i	$0.500097\pi$
$618$	0.284243	+	4.33671i	0.0114339	+	0.174448i
$619$	31.5611	−	10.7136i	1.26855	−	0.430615i	0.395599	−	0.918423i	$-0.370537\pi$
$619$	31.5611	−	10.7136i	1.26855	−	0.430615i	0.872951	+	0.487809i	$0.162204\pi$
$620$	−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	0.0929663	+	0.995669i	$0.470365\pi$
$631$	−17.0014	+	41.0450i	−0.676815	+	1.63398i	−0.769782	+	0.638307i	$0.779635\pi$
$632$	−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	−0.489903	−	0.871777i	$-0.662968\pi$
$641$	7.86047	−	6.89345i	0.310470	−	0.272275i	0.800373	+	0.599502i	$0.204635\pi$
$642$	−6.33862	+	1.69843i	−0.250165	+	0.0670316i
$643$	−21.4816	−	14.3536i	−0.847153	−	0.566050i	0.0544980	−	0.998514i	$-0.482644\pi$
$643$	−21.4816	−	14.3536i	−0.847153	−	0.566050i	−0.901651	+	0.432464i	$0.857644\pi$
$644$		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	$-0.742862\pi$
$647$	−10.4457	+	6.03082i	−0.410662	+	0.237096i	0.280412	+	0.959880i	$0.409529\pi$
$648$	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	−0.328679	−	0.944442i	$-0.606603\pi$
$653$	16.6249	−	18.9571i	0.650584	−	0.741849i	0.979263	+	0.202593i	$0.0649367\pi$
$654$	−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	−0.197228	−	0.980358i	$-0.563194\pi$
$659$	20.1037	−	20.1037i	0.783130	−	0.783130i	0.980358	+	0.197228i	$0.0631938\pi$
$660$	−4.06940	−	8.25192i	−0.158401	−	0.321205i
$661$	26.8556	−	3.53561i	1.04456	−	0.137519i	0.411334	−	0.911485i	$-0.365063\pi$
$661$	26.8556	−	3.53561i	1.04456	−	0.137519i	0.633228	+	0.773965i	$0.281730\pi$
$662$	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	0.656107	+	0.754668i	$0.272202\pi$
$673$	−6.19645	+	31.1517i	−0.238856	+	1.20081i	−0.894963	+	0.446141i	$0.852798\pi$
$674$	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	$-0.876655\pi$
$677$	−30.9549	+	15.2653i	−1.18969	+	0.586692i	−0.263837	+	0.964567i	$0.584988\pi$
$678$	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	0.799213	+	0.601048i	$0.205250\pi$
$683$	−1.87161	+	28.5552i	−0.0716152	+	1.09264i	−0.870828	+	0.491588i	$0.836417\pi$
$684$	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	$-0.00553405\pi$
$691$	0.165204	+	2.52053i	0.00628467	+	0.0958855i	−0.993564	+	0.113270i	$0.963867\pi$
$692$	−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	−0.999781	−	0.0209056i	$-0.993345\pi$
$701$	−27.0241	−	27.0241i	−1.02069	−	1.02069i	−0.0209056	−	0.999781i	$-0.506655\pi$
$702$	−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	0.203266	−	0.979124i	$-0.434844\pi$
$709$	−6.16483	−	2.09268i	−0.231525	−	0.0785922i	−0.434791	+	0.900531i	$0.643178\pi$
$710$	−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	$-0.245511\pi$
$719$	23.1005	+	7.84157i	0.861504	+	0.292441i	0.144496	+	0.989505i	$0.453844\pi$
$720$	−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	0.932052	+	0.362325i	$0.118017\pi$
$727$	34.9002	+	34.9002i	1.29438	+	1.29438i	0.362325	+	0.932052i	$0.381983\pi$
$728$		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	$-0.968949\pi$
$733$	−31.3722	+	24.0727i	−1.15876	+	0.889146i	−0.163512	+	0.986541i	$0.552282\pi$
$734$	−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	0.769388	−	0.638782i	$-0.220561\pi$
$739$	9.55548	+	7.33218i	0.351504	+	0.269719i	−0.417884	+	0.908500i	$0.637228\pi$
$740$	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	0.983178	+	0.182652i	$0.0584683\pi$
$743$	3.94527	+	19.8342i	0.144738	+	0.727647i	−0.838440	+	0.544995i	$0.816532\pi$
$744$	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	−0.196075	−	0.980589i	$-0.562820\pi$
$751$	12.6750	−	6.25060i	0.462516	−	0.228088i	0.658591	+	0.752501i	$0.271153\pi$
$752$	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	−0.976631	−	0.214923i	$-0.931050\pi$
$757$	−12.0516	−	29.0951i	−0.438022	−	1.05748i	0.538609	−	0.842556i	$-0.318950\pi$
$758$	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	$-0.493198\pi$
$761$	14.8898	−	3.98972i	0.539756	−	0.144627i	0.518389	+	0.855145i	$0.326532\pi$
$762$	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	$-0.726285\pi$
$769$	2.91916	−	2.91916i	0.105267	−	0.105267i	0.757779	+	0.652511i	$0.226285\pi$
$770$		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	$-0.682312\pi$
$773$	11.4019	−	14.8592i	0.410096	−	0.534448i	0.952043	+	0.305965i	$0.0989791\pi$
$774$	−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	$-0.815741\pi$
$787$	−11.3321	+	9.93803i	−0.403948	+	0.354252i	0.433135	+	0.901329i	$0.357407\pi$
$788$	−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	$-0.905714\pi$
$797$	−2.08167	+	5.02558i	−0.0737364	+	0.178015i	0.882714	+	0.469911i	$0.155714\pi$
$798$		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	−0.127026	−	0.991899i	$-0.540543\pi$
$809$	10.6953	−	3.63058i	0.376028	−	0.127644i	0.503054	+	0.864255i	$0.332210\pi$
$810$	0.964127	+	14.7097i	0.0338760	+	0.516848i
$811$	−42.8912	+	8.53159i	−1.50611	+	0.299585i	−0.878047	−	0.478575i	$-0.841154\pi$
$811$	−42.8912	+	8.53159i	−1.50611	+	0.299585i	−0.628067	+	0.778159i	$0.716154\pi$
$812$		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	−0.890204	−	0.455562i	$-0.849438\pi$
$821$	2.67537	−	7.88138i	0.0933710	−	0.275062i	0.983575	+	0.180500i	$0.0577716\pi$
$822$	−1.50039	+	3.04249i	−0.0523320	+	0.106119i
$823$	14.9964	+	44.1780i	0.522742	+	1.53995i	0.812567	+	0.582868i	$0.198070\pi$
$823$	14.9964	+	44.1780i	0.522742	+	1.53995i	−0.289825	+	0.957080i	$0.593597\pi$
$824$	−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	0.830888	+	0.556439i	$0.187833\pi$
$827$	29.5342	+	44.2010i	1.02700	+	1.53702i	0.196116	+	0.980581i	$0.437167\pi$
$828$	6.58634	+	2.23576i	0.228891	+	0.0776980i
$829$	−13.0854	+	48.8353i	−0.454474	+	1.69612i	0.235155	+	0.971958i	$0.424440\pi$
$829$	−13.0854	+	48.8353i	−0.454474	+	1.69612i	−0.689629	+	0.724163i	$0.742226\pi$
$830$	−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	$-0.235498\pi$
$839$	−4.83475	−	7.23572i	−0.166914	−	0.249805i	−0.905492	+	0.424364i	$0.860498\pi$
$840$		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	0.171507	−	0.985183i	$-0.445136\pi$
$853$	29.6753	−	44.4123i	1.01606	−	1.52065i	0.844557	−	0.535465i	$-0.179864\pi$
$854$		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	$-0.722309\pi$
$857$	−20.1083	+	6.82585i	−0.686887	+	0.233167i	−0.0438912	+	0.999036i	$0.513975\pi$
$858$	9.68219	+	7.42941i	0.330545	+	0.253636i
$859$	−3.47875	+	26.4237i	−0.118693	+	0.901566i	0.823692	+	0.567037i	$0.191911\pi$
$859$	−3.47875	+	26.4237i	−0.118693	+	0.901566i	−0.942385	+	0.334529i	$0.891423\pi$
$860$	−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	0.999339	−	0.0363411i	$-0.0115703\pi$
$863$	3.39936	+	12.6866i	0.115716	+	0.431856i	−0.883624	+	0.468197i	$0.844904\pi$
$864$	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	0.663272	−	0.748378i	$-0.269167\pi$
$877$	0.233081	+	0.204406i	0.00787058	+	0.00690231i	−0.655401	+	0.755281i	$0.727501\pi$
$878$	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	$-0.374284\pi$
$881$	−9.52056	−	6.36144i	−0.320756	−	0.214322i	−0.705515	+	0.708695i	$0.749284\pi$
$882$		0			0
$883$			7.97351i			0.268330i	0.990959	+	0.134165i	$0.0428352\pi$
$883$			7.97351i			0.268330i	−0.990959	+	0.134165i	$0.957165\pi$
$884$	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	$-0.272903\pi$
$887$	−10.2398	−	20.7643i	−0.343819	−	0.697196i	−0.998263	+	0.0589144i	$0.981236\pi$
$888$	−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	0.782811	−	0.622259i	$-0.213785\pi$
$907$	23.0597	+	11.3718i	0.765686	+	0.377594i	−0.0171259	+	0.999853i	$0.505452\pi$
$908$	−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	−0.631099	−	0.775703i	$-0.717396\pi$
$911$	7.50975	−	37.7541i	0.248809	−	1.25085i	0.879908	−	0.475145i	$-0.157604\pi$
$912$	−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	−0.994058	−	0.108855i	$-0.965282\pi$
$919$	−12.2096	+	21.1477i	−0.402758	+	0.697597i	0.591300	+	0.806452i	$0.298615\pi$
$920$	−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	0.990350	+	0.138587i	$0.0442560\pi$
$929$	0.809590	+	12.3520i	0.0265618	+	0.405255i	−0.963788	+	0.266668i	$0.914077\pi$
$930$	−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	$-0.281951\pi$
$937$	16.2994	+	6.75144i	0.532479	+	0.220560i	−0.100210	+	0.994966i	$0.531951\pi$
$938$		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	$-0.712161\pi$
$941$	11.7080	−	23.7416i	0.381671	−	0.773953i	0.999928	+	0.0120235i	$0.00382730\pi$
$942$	−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	0.175312	−	0.984513i	$-0.443907\pi$
$947$	−8.76849	−	2.97650i	−0.284938	−	0.0967233i	−0.460249	+	0.887790i	$0.652240\pi$
$948$	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	−0.552464	−	0.833537i	$-0.686312\pi$
$967$	−47.6560	−	19.7398i	−1.53251	−	0.634788i	−0.980050	+	0.198749i	$0.936312\pi$
$968$	−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	$-0.912559\pi$
$971$	−29.5904	+	22.7055i	−0.949603	+	0.728656i	0.0129032	+	0.999917i	$0.495893\pi$
$972$	−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	0.548167	−	0.836369i	$-0.315326\pi$
$977$	−3.68293	−	2.82601i	−0.117827	−	0.0904121i	−0.665994	+	0.745957i	$0.731993\pi$
$978$	−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	0.956390	+	0.292094i	$0.0943521\pi$
$983$	−0.938826	+	14.3237i	−0.0299439	+	0.456856i	−0.986333	+	0.164761i	$0.947315\pi$
$984$	−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	0.885721	−	0.464217i	$-0.153664\pi$
$991$	9.75462	+	11.1230i	0.309866	+	0.353334i	−0.575856	+	0.817551i	$0.695331\pi$
$992$	−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	$-0.569752\pi$
$997$	−35.4937	−	17.5036i	−1.12410	−	0.554343i	−0.906715	+	0.421743i	$0.861418\pi$
$998$	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.656.7		160
7.2	even	3		119.2.p.a.27.8	yes	80
7.3	odd	6	inner	833.2.bc.f.129.3		160
7.4	even	3	inner	833.2.bc.f.129.4		160
7.5	odd	6		119.2.p.a.27.7	✓	80
7.6	odd	2	inner	833.2.bc.f.656.8		160
17.12	odd	16	inner	833.2.bc.f.607.3		160
119.12	even	48		119.2.p.a.97.8	yes	80
119.46	odd	48	inner	833.2.bc.f.80.8		160
119.80	even	48	inner	833.2.bc.f.80.7		160
119.97	even	16	inner	833.2.bc.f.607.4		160
119.114	odd	48		119.2.p.a.97.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.p.a.27.7	✓	80	7.5	odd	6
119.2.p.a.27.8	yes	80	7.2	even	3
119.2.p.a.97.7	yes	80	119.114	odd	48
119.2.p.a.97.8	yes	80	119.12	even	48
833.2.bc.f.80.7		160	119.80	even	48	inner
833.2.bc.f.80.8		160	119.46	odd	48	inner
833.2.bc.f.129.3		160	7.3	odd	6	inner
833.2.bc.f.129.4		160	7.4	even	3	inner
833.2.bc.f.607.3		160	17.12	odd	16	inner
833.2.bc.f.607.4		160	119.97	even	16	inner
833.2.bc.f.656.7		160	1.1	even	1	trivial
833.2.bc.f.656.8		160	7.6	odd	2	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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