LMFDB - Embedded newform 867.2.i.b.827.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(65,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.65"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [32,0,-8,16,0,16,0,0,-24,-32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			827.1
Character	$\chi$	$=$	867.827
Dual form			867.2.i.b.65.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.556851 + 1.34436i) q^{2} +(0.963229 + 1.43951i) q^{3} +(-0.0830021 - 0.0830021i) q^{4} +(1.69526 - 2.53714i) q^{5} +(-2.47159 + 0.493332i) q^{6} +(-1.79329 + 1.19824i) q^{7} +(-2.53091 + 1.04834i) q^{8} +(-1.14438 + 2.77316i) q^{9} +(2.46681 + 3.69185i) q^{10} +(-0.321478 + 1.61618i) q^{11} +(0.0395323 - 0.199432i) q^{12} +(-3.12551 + 3.12551i) q^{13} +(-0.612265 - 3.07806i) q^{14} +(5.28516 - 0.00349923i) q^{15} -4.22099i q^{16} +(-3.09087 - 3.08269i) q^{18} +(0.797694 + 0.330416i) q^{19} +(-0.351298 + 0.0698774i) q^{20} +(-3.45222 - 1.42728i) q^{21} +(-1.99371 - 1.33215i) q^{22} +(0.751858 + 0.149554i) q^{23} +(-3.94694 - 2.63348i) q^{24} +(-1.64974 - 3.98282i) q^{25} +(-2.46136 - 5.94226i) q^{26} +(-5.09429 + 1.02384i) q^{27} +(0.248303 + 0.0493905i) q^{28} +(6.64464 + 4.43981i) q^{29} +(-2.93834 + 7.10709i) q^{30} +(-2.83296 + 0.563512i) q^{31} +(0.612694 + 0.253786i) q^{32} +(-2.63616 + 1.09398i) q^{33} +6.58114i q^{35} +(0.325163 - 0.135192i) q^{36} +(0.464638 + 2.33589i) q^{37} +(-0.888394 + 0.888394i) q^{38} +(-7.50979 - 1.48862i) q^{39} +(-1.63078 + 8.19848i) q^{40} +(1.71091 + 2.56055i) q^{41} +(3.84115 - 3.84624i) q^{42} +(-10.5751 + 4.38037i) q^{43} +(0.160829 - 0.107463i) q^{44} +(5.09586 + 7.60467i) q^{45} +(-0.619727 + 0.927487i) q^{46} +(-2.21238 - 2.21238i) q^{47} +(6.07615 - 4.06578i) q^{48} +(-0.898671 + 2.16958i) q^{49} +6.27299 q^{50} +0.518848 q^{52} +(2.43710 - 5.88369i) q^{53} +(1.46035 - 7.41867i) q^{54} +(3.55548 + 3.55548i) q^{55} +(3.28250 - 4.91261i) q^{56} +(0.292725 + 1.46655i) q^{57} +(-9.66877 + 6.46046i) q^{58} +(5.62864 - 2.33146i) q^{59} +(-0.438969 - 0.438389i) q^{60} +(3.24818 + 4.86125i) q^{61} +(0.819979 - 4.12231i) q^{62} +(-1.27070 - 6.34431i) q^{63} +(5.28702 - 5.28702i) q^{64} +(2.63129 + 13.2284i) q^{65} +(-0.00274973 - 4.15313i) q^{66} -7.19481i q^{67} +(0.508927 + 1.22636i) q^{69} +(-8.84742 - 3.66472i) q^{70} +(2.13271 - 0.424222i) q^{71} +(-0.0108825 - 8.21831i) q^{72} +(10.4594 + 6.98874i) q^{73} +(-3.39901 - 0.676105i) q^{74} +(4.14423 - 6.21118i) q^{75} +(-0.0387851 - 0.0936354i) q^{76} +(-1.36006 - 3.28348i) q^{77} +(6.18308 - 9.26691i) q^{78} +(5.84360 + 1.16236i) q^{79} +(-10.7092 - 7.15567i) q^{80} +(-6.38079 - 6.34708i) q^{81} +(-4.39502 + 0.874225i) q^{82} +(-11.9985 - 4.96993i) q^{83} +(0.168074 + 0.405009i) q^{84} -16.6560i q^{86} +(0.00916431 + 13.8416i) q^{87} +(-0.880669 - 4.42742i) q^{88} +(3.42023 - 3.42023i) q^{89} +(-13.0610 + 2.61599i) q^{90} +(1.85984 - 9.35006i) q^{91} +(-0.0499925 - 0.0748190i) q^{92} +(-3.53997 - 3.53529i) q^{93} +(4.20619 - 1.74226i) q^{94} +(2.19061 - 1.46372i) q^{95} +(0.224837 + 1.12643i) q^{96} +(1.97085 - 2.94959i) q^{97} +(-2.41627 - 2.41627i) q^{98} +(-4.11402 - 2.74103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 16 q^{4} + 16 q^{6} - 24 q^{9} - 32 q^{10} - 40 q^{12} + 16 q^{13} - 16 q^{15} + 16 q^{18} - 32 q^{19} - 16 q^{21} + 32 q^{22} - 16 q^{24} + 16 q^{27} - 32 q^{28} + 8 q^{30} + 24 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 16 * q^4 + 16 * q^6 - 24 * q^9 - 32 * q^10 - 40 * q^12 + 16 * q^13 - 16 * q^15 + 16 * q^18 - 32 * q^19 - 16 * q^21 + 32 * q^22 - 16 * q^24 + 16 * q^27 - 32 * q^28 + 8 * q^30 + 24 * q^36 + 96 * q^37 - 48 * q^39 - 80 * q^40 + 24 * q^42 + 32 * q^43 + 40 * q^45 + 64 * q^46 - 48 * q^48 + 64 * q^49 - 96 * q^52 - 48 * q^54 + 48 * q^55 + 8 * q^57 - 48 * q^60 + 64 * q^61 - 16 * q^64 - 120 * q^66 + 80 * q^69 - 64 * q^72 + 144 * q^73 - 8 * q^75 - 32 * q^76 + 40 * q^78 - 64 * q^79 - 48 * q^81 + 32 * q^82 + 56 * q^87 - 32 * q^88 - 24 * q^90 - 48 * q^91 + 56 * q^93 + 48 * q^94 + 72 * q^96 + 32 * q^97 + 16 * q^99

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.556851	+	1.34436i	−0.393753	+	0.950605i	0.595361	+	0.803458i	$0.297009\pi$
$2$	−0.556851	+	1.34436i	−0.393753	+	0.950605i	−0.989115	+	0.147147i	$0.952991\pi$
$3$	0.963229	+	1.43951i	0.556121	+	0.831102i
$3$	0.963229	+	1.43951i	0.556121	+	0.831102i
$4$	−0.0830021	−	0.0830021i	−0.0415010	−	0.0415010i
$5$	1.69526	−	2.53714i	0.758144	−	1.13464i	−0.228784	−	0.973477i	$-0.573475\pi$
$5$	1.69526	−	2.53714i	0.758144	−	1.13464i	0.986928	−	0.161165i	$-0.0515251\pi$
$6$	−2.47159	+	0.493332i	−1.00902	+	0.201402i
$7$	−1.79329	+	1.19824i	−0.677800	+	0.452891i	−0.846227	−	0.532823i	$-0.821131\pi$
$7$	−1.79329	+	1.19824i	−0.677800	+	0.452891i	0.168427	+	0.985714i	$0.446131\pi$
$8$	−2.53091	+	1.04834i	−0.894813	+	0.370644i
$9$	−1.14438	+	2.77316i	−0.381460	+	0.924385i
$10$	2.46681	+	3.69185i	0.780075	+	1.16746i
$11$	−0.321478	+	1.61618i	−0.0969292	+	0.487296i	0.901575	+	0.432623i	$0.142412\pi$
$11$	−0.321478	+	1.61618i	−0.0969292	+	0.487296i	−0.998504	+	0.0546734i	$0.982588\pi$
$12$	0.0395323	−	0.199432i	0.0114120	−	0.0575711i
$13$	−3.12551	+	3.12551i	−0.866861	+	0.866861i	−0.992124	−	0.125262i	$-0.960023\pi$
$13$	−3.12551	+	3.12551i	−0.866861	+	0.866861i	0.125262	+	0.992124i	$0.460023\pi$
$14$	−0.612265	−	3.07806i	−0.163635	−	0.822647i
$15$	5.28516	−	0.00349923i	1.36462	−	0.000903497i
$16$		−	4.22099i		−	1.05525i
$17$		0			0
$17$		0			0
$18$	−3.09087	−	3.08269i	−0.728524	−	0.726597i
$19$	0.797694	+	0.330416i	0.183004	+	0.0758025i	0.472304	−	0.881436i	$-0.343423\pi$
$19$	0.797694	+	0.330416i	0.183004	+	0.0758025i	−0.289300	+	0.957238i	$0.593423\pi$
$20$	−0.351298	+	0.0698774i	−0.0785525	+	0.0156251i
$21$	−3.45222	−	1.42728i	−0.753337	−	0.311458i
$22$	−1.99371	−	1.33215i	−0.425060	−	0.284016i
$23$	0.751858	+	0.149554i	0.156773	+	0.0311841i	0.272853	−	0.962056i	$-0.412033\pi$
$23$	0.751858	+	0.149554i	0.156773	+	0.0311841i	−0.116080	+	0.993240i	$0.537033\pi$
$24$	−3.94694	−	2.63348i	−0.805666	−	0.537558i
$25$	−1.64974	−	3.98282i	−0.329947	−	0.796563i
$26$	−2.46136	−	5.94226i	−0.482713	−	1.16537i
$27$	−5.09429	+	1.02384i	−0.980396	+	0.197038i
$28$	0.248303	+	0.0493905i	0.0469248	+	0.00933393i
$29$	6.64464	+	4.43981i	1.23388	+	0.824451i	0.989402	−	0.145204i	$-0.0463837\pi$
$29$	6.64464	+	4.43981i	1.23388	+	0.824451i	0.244477	+	0.969655i	$0.421384\pi$
$30$	−2.93834	+	7.10709i	−0.536466	+	1.29757i
$31$	−2.83296	+	0.563512i	−0.508815	+	0.101210i	−0.442820	−	0.896610i	$-0.646022\pi$
$31$	−2.83296	+	0.563512i	−0.508815	+	0.101210i	−0.0659948	+	0.997820i	$0.521022\pi$
$32$	0.612694	+	0.253786i	0.108310	+	0.0448635i
$33$	−2.63616	+	1.09398i	−0.458897	+	0.190437i
$34$		0			0
$35$			6.58114i			1.11242i
$36$	0.325163	−	0.135192i	0.0541939	−	0.0225320i
$37$	0.464638	+	2.33589i	0.0763860	+	0.384018i	1.00000		0.000693887i	$0.000220871\pi$
$37$	0.464638	+	2.33589i	0.0763860	+	0.384018i	−0.923614	+	0.383324i	$0.874779\pi$
$38$	−0.888394	+	0.888394i	−0.144117	+	0.144117i
$39$	−7.50979	−	1.48862i	−1.20253	−	0.238370i
$40$	−1.63078	+	8.19848i	−0.257849	+	1.29629i
$41$	1.71091	+	2.56055i	0.267199	+	0.399891i	0.940670	−	0.339322i	$-0.110198\pi$
$41$	1.71091	+	2.56055i	0.267199	+	0.399891i	−0.673471	+	0.739213i	$0.735198\pi$
$42$	3.84115	−	3.84624i	0.592703	−	0.593488i
$43$	−10.5751	+	4.38037i	−1.61269	+	0.668000i	−0.993138	−	0.116952i	$-0.962688\pi$
$43$	−10.5751	+	4.38037i	−1.61269	+	0.668000i	−0.619557	+	0.784952i	$0.712688\pi$
$44$	0.160829	−	0.107463i	0.0242459	−	0.0162006i
$45$	5.09586	+	7.60467i	0.759645	+	1.13364i
$46$	−0.619727	+	0.927487i	−0.0913738	+	0.136751i
$47$	−2.21238	−	2.21238i	−0.322708	−	0.322708i	0.527097	−	0.849805i	$-0.323281\pi$
$47$	−2.21238	−	2.21238i	−0.322708	−	0.322708i	−0.849805	+	0.527097i	$0.823281\pi$
$48$	6.07615	−	4.06578i	0.877017	−	0.586844i
$49$	−0.898671	+	2.16958i	−0.128382	+	0.309940i
$50$	6.27299			0.887135
$51$		0			0
$52$	0.518848			0.0719513
$53$	2.43710	−	5.88369i	0.334762	−	0.808187i	−0.663439	−	0.748230i	$-0.730904\pi$
$53$	2.43710	−	5.88369i	0.334762	−	0.808187i	0.998201	−	0.0599567i	$-0.0190963\pi$
$54$	1.46035	−	7.41867i	0.198729	−	1.00955i
$55$	3.55548	+	3.55548i	0.479420	+	0.479420i
$56$	3.28250	−	4.91261i	0.438642	−	0.656475i
$57$	0.292725	+	1.46655i	0.0387724	+	0.194250i
$58$	−9.66877	+	6.46046i	−1.26957	+	0.848301i
$59$	5.62864	−	2.33146i	0.732786	−	0.303530i	0.0150898	−	0.999886i	$-0.495197\pi$
$59$	5.62864	−	2.33146i	0.732786	−	0.303530i	0.717696	+	0.696356i	$0.245197\pi$
$60$	−0.438969	−	0.438389i	−0.0566707	−	0.0565957i
$61$	3.24818	+	4.86125i	0.415887	+	0.622419i	0.978976	−	0.203978i	$-0.0653870\pi$
$61$	3.24818	+	4.86125i	0.415887	+	0.622419i	−0.563089	+	0.826397i	$0.690387\pi$
$62$	0.819979	−	4.12231i	0.104137	−	0.523534i
$63$	−1.27070	−	6.34431i	−0.160093	−	0.799308i
$64$	5.28702	−	5.28702i	0.660877	−	0.660877i
$65$	2.63129	+	13.2284i	0.326372	+	1.64078i
$66$	−0.00274973	−	4.15313i	−0.000338468	−	0.511215i
$67$		−	7.19481i		−	0.878985i	−0.898246	−	0.439493i	$-0.855158\pi$
$67$		−	7.19481i		−	0.878985i	0.898246	−	0.439493i	$-0.144842\pi$
$68$		0			0
$69$	0.508927	+	1.22636i	0.0612676	+	0.147637i
$70$	−8.84742	−	3.66472i	−1.05747	−	0.438018i
$71$	2.13271	−	0.424222i	0.253106	−	0.0503459i	−0.0669064	−	0.997759i	$-0.521313\pi$
$71$	2.13271	−	0.424222i	0.253106	−	0.0503459i	0.320012	+	0.947413i	$0.396313\pi$
$72$	−0.0108825	−	8.21831i	−0.00128251	−	0.968537i
$73$	10.4594	+	6.98874i	1.22418	+	0.817970i	0.988107	−	0.153765i	$-0.0491400\pi$
$73$	10.4594	+	6.98874i	1.22418	+	0.817970i	0.236072	+	0.971736i	$0.424140\pi$
$74$	−3.39901	−	0.676105i	−0.395127	−	0.0785956i
$75$	4.14423	−	6.21118i	0.478535	−	0.717205i
$76$	−0.0387851	−	0.0936354i	−0.00444895	−	0.0107407i
$77$	−1.36006	−	3.28348i	−0.154994	−	0.374187i
$78$	6.18308	−	9.26691i	0.700096	−	1.04927i
$79$	5.84360	+	1.16236i	0.657456	+	0.130776i	0.512534	−	0.858667i	$-0.328707\pi$
$79$	5.84360	+	1.16236i	0.657456	+	0.130776i	0.144922	+	0.989443i	$0.453707\pi$
$80$	−10.7092	−	7.15567i	−1.19733	−	0.800028i
$81$	−6.38079	−	6.34708i	−0.708977	−	0.705232i
$82$	−4.39502	+	0.874225i	−0.485349	+	0.0965420i
$83$	−11.9985	−	4.96993i	−1.31700	−	0.545521i	−0.390084	−	0.920779i	$-0.627554\pi$
$83$	−11.9985	−	4.96993i	−1.31700	−	0.545521i	−0.926920	+	0.375258i	$0.877554\pi$
$84$	0.168074	+	0.405009i	0.0183384	+	0.0441901i
$85$		0			0
$86$		−	16.6560i		−	1.79606i
$87$	0.00916431	+	13.8416i	0.000982518	+	1.48397i
$88$	−0.880669	−	4.42742i	−0.0938796	−	0.471965i
$89$	3.42023	−	3.42023i	0.362544	−	0.362544i	−0.502205	−	0.864749i	$-0.667478\pi$
$89$	3.42023	−	3.42023i	0.362544	−	0.362544i	0.864749	+	0.502205i	$0.167478\pi$
$90$	−13.0610	+	2.61599i	−1.37675	+	0.275749i
$91$	1.85984	−	9.35006i	0.194964	−	0.980152i
$92$	−0.0499925	−	0.0748190i	−0.00521208	−	0.00780042i
$93$	−3.53997	−	3.53529i	−0.367078	−	0.366592i
$94$	4.20619	−	1.74226i	0.433836	−	0.179701i
$95$	2.19061	−	1.46372i	0.224752	−	0.150174i
$96$	0.224837	+	1.12643i	0.0229473	+	0.114966i
$97$	1.97085	−	2.94959i	0.200110	−	0.299486i	−0.717820	−	0.696229i	$-0.754860\pi$
$97$	1.97085	−	2.94959i	0.200110	−	0.299486i	0.917929	+	0.396744i	$0.129860\pi$
$98$	−2.41627	−	2.41627i	−0.244080	−	0.244080i
$99$	−4.11402	−	2.74103i	−0.413475	−	0.275484i
$100$	−0.193650	+	0.467514i	−0.0193650	+	0.0467514i
$101$	3.73948			0.372092			0.186046	−	0.982541i	$-0.440433\pi$
$101$	3.73948			0.372092			0.186046	+	0.982541i	$0.440433\pi$
$102$		0			0
$103$	9.33404			0.919710			0.459855	−	0.887994i	$-0.347901\pi$
$103$	9.33404			0.919710			0.459855	+	0.887994i	$0.347901\pi$
$104$	4.63380	−	11.1870i	0.454382	−	1.09698i
$105$	−9.47363	+	6.33915i	−0.924531	+	0.618638i
$106$	6.55268	+	6.55268i	0.636453	+	0.636453i
$107$	−1.05001	+	1.57145i	−0.101508	+	0.151918i	−0.878747	−	0.477288i	$-0.841620\pi$
$107$	−1.05001	+	1.57145i	−0.101508	+	0.151918i	0.777239	+	0.629206i	$0.216620\pi$
$108$	0.507817	+	0.337855i	0.0488647	+	0.0325102i
$109$	3.49469	−	2.33508i	0.334730	−	0.223660i	−0.376834	−	0.926281i	$-0.622987\pi$
$109$	3.49469	−	2.33508i	0.334730	−	0.223660i	0.711564	+	0.702621i	$0.247987\pi$
$110$	−6.75970	+	2.79996i	−0.644513	+	0.266966i
$111$	−2.91499	+	2.91885i	−0.276678	+	0.277045i
$112$	5.05774	+	7.56945i	0.477912	+	0.715246i
$113$	3.21617	−	16.1688i	0.302552	−	1.52103i	−0.468043	−	0.883705i	$-0.655041\pi$
$113$	3.21617	−	16.1688i	0.302552	−	1.52103i	0.770595	−	0.637325i	$-0.219959\pi$
$114$	−2.13458	−	0.423125i	−0.199922	−	0.0396293i
$115$	1.65403	−	1.65403i	0.154239	−	0.154239i
$116$	−0.183006	−	0.920032i	−0.0169917	−	0.0854228i
$117$	−5.09076	−	12.2443i	−0.470641	−	1.13199i
$118$			8.86518i			0.816106i
$119$		0			0
$120$	−13.3726	+	5.54949i	−1.22075	+	0.506597i
$121$	7.65399	+	3.17039i	0.695817	+	0.288217i
$122$	−8.34401	+	1.65973i	−0.755431	+	0.150265i
$123$	−2.03795	+	4.92927i	−0.183756	+	0.444457i
$124$	0.281914	+	0.188369i	0.0253167	+	0.0169161i
$125$	2.06210	+	0.410177i	0.184440	+	0.0366873i
$126$	9.23662	+	1.82457i	0.822863	+	0.162545i
$127$	4.71179	+	11.3753i	0.418104	+	1.00939i	0.982896	+	0.184159i	$0.0589563\pi$
$127$	4.71179	+	11.3753i	0.418104	+	1.00939i	−0.564792	+	0.825233i	$0.691044\pi$
$128$	4.67113	+	11.2771i	0.412874	+	0.996766i
$129$	−16.4919	−	11.0037i	−1.45203	−	0.968824i
$130$	−19.2490	−	3.82886i	−1.68825	−	0.335813i
$131$	2.93217	+	1.95921i	0.256185	+	0.171177i	0.677030	−	0.735955i	$-0.263267\pi$
$131$	2.93217	+	1.95921i	0.256185	+	0.171177i	−0.420846	+	0.907132i	$0.638267\pi$
$132$	0.309609	+	0.128004i	0.0269480	+	0.0111413i
$133$	−1.82641	+	0.363296i	−0.158370	+	0.0315018i
$134$	9.67240	+	4.00644i	0.835568	+	0.346103i
$135$	−6.03852	+	14.6606i	−0.519713	+	1.26178i
$136$		0			0
$137$			14.6484i			1.25150i	0.780025	+	0.625748i	$0.215206\pi$
$137$			14.6484i			1.25150i	−0.780025	+	0.625748i	$0.784794\pi$
$138$	−1.93207	+	0.00127919i	−0.164468	+	0.000108892i
$139$	0.984156	+	4.94769i	0.0834750	+	0.419657i	0.999815	+	0.0192553i	$0.00612953\pi$
$139$	0.984156	+	4.94769i	0.0834750	+	0.419657i	−0.916340	+	0.400402i	$0.868870\pi$
$140$	0.546249	−	0.546249i	0.0461664	−	0.0461664i
$141$	1.05371	−	5.31577i	0.0887387	−	0.447668i
$142$	−0.617296	+	3.10335i	−0.0518023	+	0.260428i
$143$	−4.04660	−	6.05617i	−0.338394	−	0.506442i
$144$	11.7055	+	4.83041i	0.975455	+	0.402534i
$145$	22.5288	−	9.33173i	1.87091	−	0.774958i
$146$	−15.2197	+	10.1695i	−1.25959	+	0.841632i
$147$	−3.98876	+	0.796160i	−0.328988	+	0.0656662i
$148$	0.155318	−	0.232450i	0.0127671	−	0.0191073i
$149$	4.44785	+	4.44785i	0.364382	+	0.364382i	0.865423	−	0.501041i	$-0.167050\pi$
$149$	4.44785	+	4.44785i	0.364382	+	0.364382i	−0.501041	+	0.865423i	$0.667050\pi$
$150$	6.04233	+	9.03004i	0.493354	+	0.737299i
$151$	−5.82179	+	14.0551i	−0.473771	+	1.14378i	0.488713	+	0.872445i	$0.337467\pi$
$151$	−5.82179	+	14.0551i	−0.473771	+	1.14378i	−0.962484	+	0.271339i	$0.912533\pi$
$152$	−2.36528			−0.191850
$153$		0			0
$154$	5.17153			0.416734
$155$	−3.37291	+	8.14291i	−0.270918	+	0.654055i
$156$	0.499770	+	0.746887i	0.0400136	+	0.0597988i
$157$	−1.74527	−	1.74527i	−0.139287	−	0.139287i	0.634025	−	0.773312i	$-0.281402\pi$
$157$	−1.74527	−	1.74527i	−0.139287	−	0.139287i	−0.773312	+	0.634025i	$0.781402\pi$
$158$	−4.81665	+	7.20863i	−0.383192	+	0.573488i
$159$	10.8171	−	2.15911i	0.857854	−	0.171228i
$160$	1.68257	−	1.12425i	0.133018	−	0.0888801i
$161$	−1.52750	+	0.632711i	−0.120384	+	0.0498646i
$162$	12.0859	−	5.04369i	0.949559	−	0.396270i
$163$	0.617171	+	0.923662i	0.0483406	+	0.0723468i	0.854853	−	0.518871i	$-0.173647\pi$
$163$	0.617171	+	0.923662i	0.0483406	+	0.0723468i	−0.806512	+	0.591218i	$0.798647\pi$
$164$	0.0705224	−	0.354540i	0.00550688	−	0.0276849i
$165$	−1.69341	+	8.54288i	−0.131831	+	0.665062i
$166$	13.3627	−	13.3627i	1.03715	−	1.03715i
$167$	−3.87453	−	19.4786i	−0.299820	−	1.50730i	−0.777567	−	0.628800i	$-0.783547\pi$
$167$	−3.87453	−	19.4786i	−0.299820	−	1.50730i	0.477747	−	0.878497i	$-0.341453\pi$
$168$	10.2335	−	0.00677549i	0.789535	−	0.000522740i
$169$		−	6.53766i		−	0.502897i
$170$		0			0
$171$	−1.82916	+	1.83401i	−0.139879	+	0.140250i
$172$	1.24134	+	0.514179i	0.0946511	+	0.0392058i
$173$	11.4127	−	2.27012i	0.867689	−	0.172594i	0.258879	−	0.965910i	$-0.416647\pi$
$173$	11.4127	−	2.27012i	0.867689	−	0.172594i	0.608811	+	0.793316i	$0.291647\pi$
$174$	−18.6131	−	7.69538i	−1.41106	−	0.583385i
$175$	7.73082	+	5.16557i	0.584395	+	0.390480i
$176$	6.82187	+	1.35695i	0.514217	+	0.102284i
$177$	8.77783	+	5.85675i	0.659782	+	0.440221i
$178$	2.69345	+	6.50257i	0.201883	+	0.487389i
$179$	0.324004	+	0.782216i	0.0242172	+	0.0584656i	0.935526	−	0.353259i	$-0.114927\pi$
$179$	0.324004	+	0.782216i	0.0242172	+	0.0584656i	−0.911308	+	0.411725i	$0.864927\pi$
$180$	0.208237	−	1.05417i	0.0155210	−	0.0785732i
$181$	1.40629	+	0.279729i	0.104529	+	0.0207921i	0.247078	−	0.968996i	$-0.420530\pi$
$181$	1.40629	+	0.279729i	0.104529	+	0.0207921i	−0.142549	+	0.989788i	$0.545530\pi$
$182$	11.5342	+	7.70689i	0.854970	+	0.571272i
$183$	−3.86907	+	9.35828i	−0.286010	+	0.691784i
$184$	−2.05967	+	0.409694i	−0.151841	+	0.0302030i
$185$	6.71416	+	2.78110i	0.493635	+	0.204470i
$186$	6.72393	−	2.79036i	0.493023	−	0.204599i
$187$		0			0
$188$			0.367264i			0.0267855i
$189$	7.90873	−	7.94021i	0.575275	−	0.577565i
$190$	0.747918	+	3.76004i	0.0542596	+	0.272782i
$191$	0.509849	−	0.509849i	0.0368914	−	0.0368914i	−0.688420	−	0.725312i	$-0.741696\pi$
$191$	0.509849	−	0.509849i	0.0368914	−	0.0368914i	0.725312	+	0.688420i	$0.241696\pi$
$192$	12.7033	+	2.51811i	0.916784	+	0.181729i
$193$	2.26724	−	11.3982i	0.163200	−	0.820460i	−0.809271	−	0.587435i	$-0.800138\pi$
$193$	2.26724	−	11.3982i	0.163200	−	0.820460i	0.972471	−	0.233025i	$-0.0748623\pi$
$194$	2.86783	+	4.29202i	0.205898	+	0.308149i
$195$	−16.5079	+	16.5298i	−1.18215	+	1.18372i
$196$	0.254671	−	0.105488i	0.0181908	−	0.00753488i
$197$	19.3433	−	12.9248i	1.37815	−	0.920852i	0.378165	−	0.925738i	$-0.376555\pi$
$197$	19.3433	−	12.9248i	1.37815	−	0.920852i	0.999988	+	0.00488610i	$0.00155530\pi$
$198$	5.97582	−	4.00437i	0.424683	−	0.284578i
$199$	−13.3975	+	20.0507i	−0.949720	+	1.42136i	−0.0432612	+	0.999064i	$0.513775\pi$
$199$	−13.3975	+	20.0507i	−0.949720	+	1.42136i	−0.906459	+	0.422293i	$0.861225\pi$
$200$	8.35068	+	8.35068i	0.590482	+	0.590482i
$201$	10.3570	−	6.93025i	0.730526	−	0.488822i
$202$	−2.08233	+	5.02720i	−0.146512	+	0.353712i
$203$	−17.2357			−1.20971
$204$		0			0
$205$	9.39691			0.656309
$206$	−5.19767	+	12.5483i	−0.362139	+	0.874281i
$207$	−1.27515	+	1.91387i	−0.0886288	+	0.133023i
$208$	13.1927	+	13.1927i	0.914753	+	0.914753i
$209$	−0.790451	+	1.18299i	−0.0546767	+	0.0818294i
$210$	−3.24669	−	16.2659i	−0.224043	−	1.12245i
$211$	12.9792	−	8.67243i	0.893525	−	0.597035i	−0.0217944	−	0.999762i	$-0.506938\pi$
$211$	12.9792	−	8.67243i	0.893525	−	0.597035i	0.915320	+	0.402728i	$0.131938\pi$
$212$	−0.690643	+	0.286074i	−0.0474336	+	0.0196476i
$213$	2.66496	+	2.66143i	0.182600	+	0.182358i
$214$	−1.52789	−	2.28665i	−0.104444	−	0.156312i
$215$	−6.81403	+	34.2564i	−0.464713	+	2.33627i
$216$	11.8199	−	7.93178i	0.804240	−	0.539689i
$217$	4.40510	−	4.40510i	0.299038	−	0.299038i
$218$	1.19316	+	5.99840i	0.0808107	+	0.406263i
$219$	0.0144256	+	21.7882i	0.000974794	+	1.47231i
$220$		−	0.590224i		−	0.0397929i
$221$		0			0
$222$	−2.30077	−	5.54415i	−0.154417	−	0.372099i
$223$	−2.24695	−	0.930718i	−0.150467	−	0.0623255i	0.306179	−	0.951974i	$-0.400949\pi$
$223$	−2.24695	−	0.930718i	−0.150467	−	0.0623255i	−0.456646	+	0.889648i	$0.650949\pi$
$224$	−1.40283	+	0.279041i	−0.0937307	+	0.0186442i
$225$	12.9329	−	0.0171254i	0.862193	−	0.00114169i
$226$	19.9457	+	13.3273i	1.32677	+	0.886518i
$227$	−1.37743	−	0.273987i	−0.0914231	−	0.0181852i	0.149167	−	0.988812i	$-0.452341\pi$
$227$	−1.37743	−	0.273987i	−0.0914231	−	0.0181852i	−0.240590	+	0.970627i	$0.577341\pi$
$228$	0.0974302	−	0.146024i	0.00645247	−	0.00967066i
$229$	−4.16234	−	10.0488i	−0.275055	−	0.664043i	0.724630	−	0.689139i	$-0.242011\pi$
$229$	−4.16234	−	10.0488i	−0.275055	−	0.664043i	−0.999685	+	0.0250960i	$0.992011\pi$
$230$	1.30256	+	3.14466i	0.0858884	+	0.207353i
$231$	3.41655	−	5.12057i	0.224793	−	0.336909i
$232$	−21.4714	−	4.27093i	−1.40967	−	0.280400i
$233$	−11.9201	−	7.96478i	−0.780914	−	0.521790i	0.100045	−	0.994983i	$-0.468101\pi$
$233$	−11.9201	−	7.96478i	−0.780914	−	0.521790i	−0.880959	+	0.473193i	$0.843101\pi$
$234$	19.2955	−	0.0255506i	1.26139	−	0.00167030i
$235$	−9.36366	+	1.86255i	−0.610818	+	0.121499i
$236$	−0.660704	−	0.273673i	−0.0430082	−	0.0178146i
$237$	3.95549	+	9.53155i	0.256937	+	0.619140i
$238$		0			0
$239$		−	23.7093i		−	1.53362i	−0.641872	−	0.766812i	$-0.721842\pi$
$239$		−	23.7093i		−	1.53362i	0.641872	−	0.766812i	$-0.278158\pi$
$240$	−0.0147702	−	22.3086i	−0.000953412	−	1.44001i
$241$	−0.549058	−	2.76030i	−0.0353679	−	0.177807i	0.959064	−	0.283191i	$-0.0913929\pi$
$241$	−0.549058	−	2.76030i	−0.0353679	−	0.177807i	−0.994432	+	0.105384i	$0.966393\pi$
$242$	−8.52427	+	8.52427i	−0.547961	+	0.547961i
$243$	2.99053	−	15.2989i	0.191842	−	0.981426i
$244$	0.133888	−	0.673099i	0.00857128	−	0.0430908i
$245$	3.98105	+	5.95806i	0.254340	+	0.380646i
$246$	−5.49187	−	5.48460i	−0.350149	−	0.349686i
$247$	−3.52592	+	1.46048i	−0.224349	+	0.0929284i
$248$	6.57923	−	4.39610i	0.417782	−	0.279153i
$249$	−4.40302	−	22.0591i	−0.279030	−	1.39794i
$250$	−1.69971	+	2.54379i	−0.107499	+	0.160883i
$251$	10.7058	+	10.7058i	0.675745	+	0.675745i	0.959034	−	0.283289i	$-0.0914257\pi$
$251$	10.7058	+	10.7058i	0.675745	+	0.675745i	−0.283289	+	0.959034i	$0.591426\pi$
$252$	−0.421120	+	0.632061i	−0.0265281	+	0.0398161i
$253$	−0.483411	+	1.16706i	−0.0303918	+	0.0733723i
$254$	−17.9162			−1.12416
$255$		0			0
$256$	−2.80767			−0.175479
$257$	−7.61319	+	18.3799i	−0.474898	+	1.14650i	0.487075	+	0.873360i	$0.338064\pi$
$257$	−7.61319	+	18.3799i	−0.474898	+	1.14650i	−0.961973	+	0.273145i	$0.911936\pi$
$258$	23.9765	−	16.0435i	1.49271	−	0.998827i
$259$	−3.63218	−	3.63218i	−0.225693	−	0.225693i
$260$	0.879583	−	1.31639i	0.0545494	−	0.0816389i
$261$	−19.9163	+	13.3458i	−1.23279	+	0.826085i
$262$	−4.26667	+	2.85090i	−0.263596	+	0.176129i
$263$	−0.121128	+	0.0501727i	−0.00746905	+	0.00309378i	−0.386415	−	0.922325i	$-0.626287\pi$
$263$	−0.121128	+	0.0501727i	−0.00746905	+	0.00309378i	0.378946	+	0.925419i	$0.376287\pi$
$264$	5.52503	−	5.53235i	0.340042	−	0.340493i
$265$	−10.7962	−	16.1577i	−0.663205	−	0.992557i
$266$	0.528640	−	2.65765i	0.0324130	−	0.162951i
$267$	8.21792	+	1.62899i	0.502929	+	0.0996926i
$268$	−0.597184	+	0.597184i	−0.0364788	+	0.0364788i
$269$	1.15992	+	5.83131i	0.0707216	+	0.355541i	0.999901	−	0.0140883i	$-0.00448458\pi$
$269$	1.15992	+	5.83131i	0.0707216	+	0.355541i	−0.929179	+	0.369630i	$0.879485\pi$
$270$	−16.3465	−	16.2817i	−0.994817	−	0.990873i
$271$			6.87483i			0.417616i	0.977957	+	0.208808i	$0.0669584\pi$
$271$			6.87483i			0.417616i	−0.977957	+	0.208808i	$0.933042\pi$
$272$		0			0
$273$	15.2510	−	6.32899i	0.923030	−	0.383048i
$274$	−19.6927	−	8.15697i	−1.18968	−	0.492781i
$275$	6.96730	−	1.38588i	0.420144	−	0.0835718i
$276$	0.0595485	−	0.144033i	0.00358440	−	0.00866974i
$277$	−6.89904	−	4.60979i	−0.414523	−	0.276975i	0.330771	−	0.943711i	$-0.392691\pi$
$277$	−6.89904	−	4.60979i	−0.414523	−	0.276975i	−0.745294	+	0.666736i	$0.767691\pi$
$278$	−7.19949	−	1.43207i	−0.431797	−	0.0858897i
$279$	1.67928	−	8.50112i	0.100536	−	0.508949i
$280$	−6.89927	−	16.6563i	−0.412310	−	0.995404i
$281$	5.07041	+	12.2411i	0.302475	+	0.730240i	0.999908	+	0.0135893i	$0.00432576\pi$
$281$	5.07041	+	12.2411i	0.302475	+	0.730240i	−0.697432	+	0.716651i	$0.745674\pi$
$282$	6.55953	+	4.37666i	0.390614	+	0.260626i
$283$	13.7634	+	2.73771i	0.818149	+	0.162740i	0.586385	−	0.810032i	$-0.300550\pi$
$283$	13.7634	+	2.73771i	0.818149	+	0.162740i	0.231763	+	0.972772i	$0.425550\pi$
$284$	−0.212231	−	0.141808i	−0.0125936	−	0.00841475i
$285$	4.21709	+	1.74351i	0.249799	+	0.103276i
$286$	10.3950	−	2.06770i	0.614670	−	0.122266i
$287$	−6.13631	−	2.54174i	−0.362215	−	0.150034i
$288$	−1.40494	+	1.40867i	−0.0827870	+	0.0830066i
$289$		0			0
$290$			35.4832i			2.08364i
$291$	6.14435	−	0.00406809i	0.360188	−	0.000238475i
$292$	−0.288071	−	1.44823i	−0.0168581	−	0.0847513i
$293$	−18.6721	+	18.6721i	−1.09083	+	1.09083i	−0.0953949	+	0.995440i	$0.530411\pi$
$293$	−18.6721	+	18.6721i	−1.09083	+	1.09083i	−0.995440	+	0.0953949i	$0.969589\pi$
$294$	1.15082	−	5.80567i	0.0671174	−	0.338594i
$295$	3.62678	−	18.2331i	0.211159	−	1.06157i
$296$	−3.62476	−	5.42484i	−0.210685	−	0.315312i
$297$	−0.0170072	−	8.56241i	−0.000986857	−	0.496842i
$298$	−8.45629	+	3.50271i	−0.489860	+	0.202907i
$299$	−2.81737	+	1.88251i	−0.162933	+	0.108868i
$300$	−0.859520	+	0.171561i	−0.0496244	+	0.00990507i
$301$	13.7156	−	20.5268i	0.790552	−	1.18315i
$302$	−15.6531	−	15.6531i	−0.900738	−	0.900738i
$303$	3.60197	+	5.38301i	0.206928	+	0.309246i
$304$	1.39468	−	3.36705i	0.0799904	−	0.193114i
$305$	17.8402			1.02152
$306$		0			0
$307$	−24.4315			−1.39438			−0.697189	−	0.716887i	$-0.745566\pi$
$307$	−24.4315			−1.39438			−0.697189	+	0.716887i	$0.745566\pi$
$308$	−0.159648	+	0.385424i	−0.00909677	+	0.0219616i
$309$	8.99082	+	13.4364i	0.511470	+	0.764372i
$310$	−9.06879	−	9.06879i	−0.515073	−	0.515073i
$311$	−12.9649	+	19.4033i	−0.735169	+	1.10026i	0.255873	+	0.966710i	$0.417637\pi$
$311$	−12.9649	+	19.4033i	−0.735169	+	1.10026i	−0.991042	+	0.133548i	$0.957363\pi$
$312$	20.5672	−	4.10523i	1.16439	−	0.232413i
$313$	1.34251	−	0.897040i	0.0758834	−	0.0507037i	−0.517050	−	0.855955i	$-0.672970\pi$
$313$	1.34251	−	0.897040i	0.0758834	−	0.0507037i	0.592933	+	0.805252i	$0.297970\pi$
$314$	3.31812	−	1.37441i	0.187252	−	0.0775624i
$315$	−18.2505	−	7.53133i	−1.02830	−	0.424342i
$316$	−0.388552	−	0.581510i	−0.0218578	−	0.0327125i
$317$	−4.75728	+	23.9165i	−0.267195	+	1.34328i	0.581132	+	0.813809i	$0.302610\pi$
$317$	−4.75728	+	23.9165i	−0.267195	+	1.34328i	−0.848327	+	0.529472i	$0.822390\pi$
$318$	−3.12092	+	15.7444i	−0.175012	+	0.882902i
$319$	−9.31162	+	9.31162i	−0.521351	+	0.521351i
$320$	−4.45101	−	22.3768i	−0.248819	−	1.25090i
$321$	−3.27351	+	0.00216735i	−0.182710	+	0.000120970i
$322$		−	2.40583i		−	0.134072i
$323$		0			0
$324$	0.00279782	+	1.05644i	0.000155435	+	0.0586911i
$325$	17.6046	+	7.29207i	0.976529	+	0.404491i
$326$	−1.58540	+	0.315357i	−0.0878074	+	0.0174660i
$327$	6.72755	+	2.78143i	0.372034	+	0.153813i
$328$	−7.01448	−	4.68693i	−0.387310	−	0.258792i
$329$	6.61839	+	1.31648i	0.364883	+	0.0725798i
$330$	−10.5417	−	7.03366i	−0.580302	−	0.387190i
$331$	11.6584	+	28.1459i	0.640804	+	1.54704i	0.825597	+	0.564260i	$0.190839\pi$
$331$	11.6584	+	28.1459i	0.640804	+	1.54704i	−0.184793	+	0.982777i	$0.559161\pi$
$332$	0.583384	+	1.40841i	0.0320173	+	0.0772967i
$333$	−7.00952	−	1.38463i	−0.384119	−	0.0758774i
$334$	28.3437	+	5.63791i	1.55090	+	0.308493i
$335$	−18.2542	−	12.1971i	−0.997334	−	0.666397i
$336$	−6.02453	+	14.5718i	−0.328665	+	0.794956i
$337$	16.8950	−	3.36062i	0.920329	−	0.183065i	0.287880	−	0.957667i	$-0.407050\pi$
$337$	16.8950	−	3.36062i	0.920329	−	0.183065i	0.632449	+	0.774602i	$0.282050\pi$
$338$	8.78896	+	3.64051i	0.478057	+	0.198018i
$339$	26.3730	−	10.9445i	1.43239	−	0.594425i
$340$		0			0
$341$		−	4.75973i		−	0.257754i
$342$	−1.44700	−	3.48031i	−0.0782446	−	0.188194i
$343$	−3.93346	−	19.7748i	−0.212387	−	1.06774i
$344$	22.1727	−	22.1727i	1.19547	−	1.19547i
$345$	3.97421	+	0.787785i	0.213964	+	0.0424129i
$346$	−3.30331	+	16.6068i	−0.177587	+	0.892789i
$347$	11.2418	+	16.8245i	0.603491	+	0.903188i	0.999889	−	0.0148907i	$-0.00474004\pi$
$347$	11.2418	+	16.8245i	0.603491	+	0.903188i	−0.396398	+	0.918079i	$0.629740\pi$
$348$	1.14812	−	1.14964i	0.0615456	−	0.0616272i
$349$	7.02410	−	2.90948i	0.375992	−	0.155741i	−0.186681	−	0.982421i	$-0.559773\pi$
$349$	7.02410	−	2.90948i	0.375992	−	0.155741i	0.562673	+	0.826680i	$0.309773\pi$
$350$	−11.2493	+	7.51653i	−0.601300	+	0.401776i
$351$	12.7222	−	19.1223i	0.679063	−	1.02067i
$352$	−0.607131	+	0.908636i	−0.0323602	+	0.0484304i
$353$	−8.44344	−	8.44344i	−0.449399	−	0.449399i	0.445756	−	0.895155i	$-0.352935\pi$
$353$	−8.44344	−	8.44344i	−0.449399	−	0.449399i	−0.895155	+	0.445756i	$0.852935\pi$
$354$	−12.7615	+	8.53920i	−0.678267	+	0.453853i
$355$	2.53919	−	6.13014i	0.134766	−	0.325354i
$356$	−0.567772			−0.0300919
$357$		0			0
$358$	−1.23200			−0.0651133
$359$	8.80076	−	21.2469i	0.464487	−	1.12137i	−0.502049	−	0.864839i	$-0.667420\pi$
$359$	8.80076	−	21.2469i	0.464487	−	1.12137i	0.966536	−	0.256531i	$-0.0825795\pi$
$360$	−20.8694	−	13.9046i	−1.09992	−	0.732835i
$361$	−12.9079	−	12.9079i	−0.679363	−	0.679363i
$362$	−1.15915	+	1.73479i	−0.0609236	+	0.0911786i
$363$	2.80874	+	14.0718i	0.147421	+	0.738578i
$364$	−0.930445	+	0.621703i	−0.0487685	+	0.0325861i
$365$	35.4628	−	14.6892i	1.85621	−	0.768866i
$366$	−10.4264	−	10.4126i	−0.544996	−	0.544275i
$367$	9.11720	+	13.6449i	0.475914	+	0.712256i	0.989299	−	0.145903i	$-0.0466086\pi$
$367$	9.11720	+	13.6449i	0.475914	+	0.712256i	−0.513385	+	0.858159i	$0.671609\pi$
$368$	0.631265	−	3.17358i	0.0329070	−	0.165434i
$369$	−9.05875	+	1.81437i	−0.471579	+	0.0944523i
$370$	−7.47758	+	7.47758i	−0.388741	+	0.388741i
$371$	2.67963	+	13.4714i	0.139119	+	0.699400i
$372$	0.000388817		0.587261i	2.01592e−5		0.0304481i
$373$		−	1.61824i		−	0.0837894i	−0.999122	−	0.0418947i	$-0.986661\pi$
$373$		−	1.61824i		−	0.0837894i	0.999122	−	0.0418947i	$-0.0133394\pi$
$374$		0			0
$375$	1.39582	+	3.36351i	0.0720798	+	0.173691i
$376$	7.91865	+	3.28001i	0.408373	+	0.169154i
$377$	−34.6446	+	6.89124i	−1.78429	+	0.354917i
$378$	6.27050	+	15.0537i	0.322520	+	0.774278i
$379$	−12.9123	−	8.62771i	−0.663260	−	0.443176i	0.177838	−	0.984060i	$-0.443090\pi$
$379$	−12.9123	−	8.62771i	−0.663260	−	0.443176i	−0.841097	+	0.540884i	$0.818090\pi$
$380$	−0.303317	−	0.0603334i	−0.0155598	−	0.00309504i
$381$	−11.8363	+	17.7397i	−0.606391	+	0.908831i
$382$	0.401510	+	0.969330i	0.0205430	+	0.0495952i
$383$	−8.47433	−	20.4588i	−0.433018	−	1.04540i	−0.978309	−	0.207151i	$-0.933581\pi$
$383$	−8.47433	−	20.4588i	−0.433018	−	1.04540i	0.545291	−	0.838247i	$-0.316419\pi$
$384$	−11.7342	+	17.5866i	−0.598806	+	0.897462i
$385$	−10.6363	−	2.11569i	−0.542076	−	0.107826i
$386$	14.0607	+	9.39509i	0.715673	+	0.478197i
$387$	−0.0454712	−	34.3393i	−0.00231143	−	1.74557i
$388$	−0.408407	+	0.0812372i	−0.0207337	+	0.00412419i
$389$	14.0162	+	5.80572i	0.710652	+	0.294362i	0.708574	−	0.705636i	$-0.249339\pi$
$389$	14.0162	+	5.80572i	0.710652	+	0.294362i	0.00207747	+	0.999998i	$0.499339\pi$
$390$	−13.0295	−	31.3972i	−0.659774	−	1.58986i
$391$		0			0
$392$		−	6.43314i		−	0.324922i
$393$	0.00404406	+	6.10806i	0.000203996	+	0.308111i
$394$	6.60419	+	33.2015i	0.332714	+	1.67267i
$395$	12.8555	−	12.8555i	0.646831	−	0.646831i
$396$	0.113961	+	0.568983i	0.00572677	+	0.0285925i
$397$	−7.34266	+	36.9140i	−0.368517	+	1.85266i	0.138000	+	0.990432i	$0.455932\pi$
$397$	−7.34266	+	36.9140i	−0.368517	+	1.85266i	−0.506518	+	0.862230i	$0.669068\pi$
$398$	−19.4949	−	29.1762i	−0.977193	−	1.46247i
$399$	−2.28222	−	2.27920i	−0.114254	−	0.114103i
$400$	−16.8114	+	6.96352i	−0.840571	+	0.348176i
$401$	−2.93829	+	1.96330i	−0.146731	+	0.0980426i	−0.626769	−	0.779205i	$-0.715623\pi$
$401$	−2.93829	+	1.96330i	−0.146731	+	0.0980426i	0.480038	+	0.877248i	$0.340623\pi$
$402$	3.54943	+	17.7826i	0.177029	+	0.886917i
$403$	7.09320	−	10.6157i	0.353338	−	0.528807i
$404$	−0.310384	−	0.310384i	−0.0154422	−	0.0154422i
$405$	−26.9205	+	5.42898i	−1.33769	+	0.269768i
$406$	9.59773	−	23.1710i	0.476327	−	1.14996i
$407$	−3.92459			−0.194535
$408$		0			0
$409$	12.2079			0.603641			0.301820	−	0.953365i	$-0.402406\pi$
$409$	12.2079			0.603641			0.301820	+	0.953365i	$0.402406\pi$
$410$	−5.23268	+	12.6328i	−0.258424	+	0.623890i
$411$	−21.0865	+	14.1098i	−1.04012	+	0.695983i
$412$	−0.774744	−	0.774744i	−0.0381689	−	0.0381689i
$413$	−7.30014	+	10.9254i	−0.359216	+	0.537605i
$414$	−1.86286	−	2.78000i	−0.0915548	−	0.136629i
$415$	−32.9499	+	22.0164i	−1.61745	+	1.08074i
$416$	−2.70819	+	1.12177i	−0.132780	+	0.0549993i
$417$	−6.17428	+	6.18246i	−0.302356	+	0.302756i
$418$	−1.15020	−	1.72140i	−0.0562583	−	0.0841965i
$419$	6.12442	−	30.7895i	0.299198	−	1.50417i	−0.479933	−	0.877305i	$-0.659339\pi$
$419$	6.12442	−	30.7895i	0.299198	−	1.50417i	0.779130	−	0.626862i	$-0.215661\pi$
$420$	1.31249	+	0.260168i	0.0640431	+	0.0126949i
$421$	−10.7245	+	10.7245i	−0.522682	+	0.522682i	−0.918380	−	0.395699i	$-0.870502\pi$
$421$	−10.7245	+	10.7245i	−0.522682	+	0.522682i	0.395699	+	0.918380i	$0.370502\pi$
$422$	4.43136	+	22.2780i	0.215715	+	1.08447i
$423$	8.66707	−	3.60347i	0.421407	−	0.175207i
$424$			17.4460i			0.847253i
$425$		0			0
$426$	−5.06191	+	2.10064i	−0.245250	+	0.101776i
$427$	−11.6499	−	4.82553i	−0.563776	−	0.233524i
$428$	0.217586	−	0.0432806i	0.0105174	−	0.00209205i
$429$	4.82011	−	11.6586i	0.232717	−	0.562883i
$430$	−42.2585	−	28.2362i	−2.03789	−	1.36167i
$431$	−11.2336	−	2.23450i	−0.541102	−	0.107632i	−0.0830303	−	0.996547i	$-0.526460\pi$
$431$	−11.2336	−	2.23450i	−0.541102	−	0.107632i	−0.458072	+	0.888915i	$0.651460\pi$
$432$	4.32161	+	21.5029i	0.207924	+	1.03456i
$433$	−10.2528	−	24.7526i	−0.492720	−	1.18953i	−0.953330	−	0.301930i	$-0.902369\pi$
$433$	−10.2528	−	24.7526i	−0.492720	−	1.18953i	0.460610	−	0.887603i	$-0.347631\pi$
$434$	3.46905	+	8.37502i	0.166520	+	0.402014i
$435$	35.1335	+	23.4418i	1.68452	+	1.12395i
$436$	−0.483882	−	0.0962502i	−0.0231738	−	0.00460955i
$437$	0.550338	+	0.367724i	0.0263262	+	0.0175906i
$438$	−29.2991	−	12.1134i	−1.39997	−	0.578799i
$439$	−8.36252	+	1.66341i	−0.399121	+	0.0793902i	−0.390570	−	0.920573i	$-0.627722\pi$
$439$	−8.36252	+	1.66341i	−0.399121	+	0.0793902i	−0.00855138	+	0.999963i	$0.502722\pi$
$440$	−12.7259	−	5.27126i	−0.606685	−	0.251297i
$441$	−4.98817	−	4.97498i	−0.237532	−	0.236904i
$442$		0			0
$443$		−	18.8773i		−	0.896886i	−0.893811	−	0.448443i	$-0.851979\pi$
$443$		−	18.8773i		−	0.896886i	0.893811	−	0.448443i	$-0.148021\pi$
$444$	0.484221		0.000320596i	0.0229801		1.52148e-5i
$445$	−2.87941	−	14.4758i	−0.136497	−	0.686217i
$446$	2.50244	−	2.50244i	0.118494	−	0.118494i
$447$	−2.11843	+	10.6870i	−0.100198	+	0.505479i
$448$	−3.14605	+	15.8163i	−0.148637	+	0.747248i
$449$	−15.1475	−	22.6698i	−0.714853	−	1.06985i	−0.993976	−	0.109598i	$-0.965044\pi$
$449$	−15.1475	−	22.6698i	−0.714853	−	1.06985i	0.279123	−	0.960255i	$-0.409956\pi$
$450$	−7.17868	+	17.3960i	−0.338406	+	0.820055i
$451$	−4.68833	+	1.94197i	−0.220765	+	0.0914438i
$452$	−1.60899	+	1.07509i	−0.0756805	+	0.0505681i
$453$	−25.8401	+	5.15770i	−1.21407	+	0.242330i
$454$	1.13536	−	1.69919i	0.0532851	−	0.0797468i
$455$	−20.5695	−	20.5695i	−0.964311	−	0.964311i
$456$	−2.27831	−	3.40485i	−0.106691	−	0.159446i
$457$	4.03405	−	9.73907i	0.188705	−	0.455574i	−0.801006	−	0.598657i	$-0.795701\pi$
$457$	4.03405	−	9.73907i	0.188705	−	0.455574i	0.989711	+	0.143082i	$0.0457014\pi$
$458$	15.8270			0.739546
$459$		0			0
$460$	−0.274576			−0.0128022
$461$	3.78349	−	9.13414i	0.176215	−	0.425419i	−0.810952	−	0.585112i	$-0.801050\pi$
$461$	3.78349	−	9.13414i	0.176215	−	0.425419i	0.987167	+	0.159693i	$0.0510504\pi$
$462$	4.98137	+	7.44447i	0.231754	+	0.346348i
$463$	16.2123	+	16.2123i	0.753448	+	0.753448i	0.975121	−	0.221673i	$-0.0711518\pi$
$463$	16.2123	+	16.2123i	0.753448	+	0.753448i	−0.221673	+	0.975121i	$0.571152\pi$
$464$	18.7404	−	28.0469i	0.870000	−	1.30205i
$465$	−14.9707	+	2.98816i	−0.694249	+	0.138573i
$466$	17.3453	−	11.5897i	0.803504	−	0.536884i
$467$	−23.8791	+	9.89105i	−1.10499	+	0.457703i	−0.859211	−	0.511621i	$-0.829045\pi$
$467$	−23.8791	+	9.89105i	−1.10499	+	0.457703i	−0.245783	+	0.969325i	$0.579045\pi$
$468$	−0.593759	+	1.43885i	−0.0274465	+	0.0665107i
$469$	8.62109	+	12.9024i	0.398085	+	0.595776i
$470$	2.71024	−	13.6253i	0.125014	−	0.628487i
$471$	0.831237	−	4.19342i	0.0383014	−	0.193223i
$472$	−11.8014	+	11.8014i	−0.543205	+	0.543205i
$473$	−3.67978	−	18.4995i	−0.169196	−	0.850608i
$474$	−15.0164	+	0.00994217i	−0.689728	+	0.000456659i
$475$		−	3.72217i		−	0.170785i
$476$		0			0
$477$	13.5274	+	13.4916i	0.619378	+	0.617740i
$478$	31.8737	+	13.2025i	1.45787	+	0.603870i
$479$	8.49821	−	1.69040i	0.388293	−	0.0772363i	0.00291662	−	0.999996i	$-0.499072\pi$
$479$	8.49821	−	1.69040i	0.388293	−	0.0772363i	0.385376	+	0.922759i	$0.374072\pi$
$480$	3.23907	+	1.33916i	0.147843	+	0.0611238i
$481$	−8.75309	−	5.84863i	−0.399107	−	0.266675i
$482$	4.01658	+	0.798947i	0.182950	+	0.0363910i
$483$	−2.38213	−	1.58941i	−0.108391	−	0.0723205i
$484$	−0.372148	−	0.898446i	−0.0169158	−	0.0408384i
$485$	−4.14240	−	10.0006i	−0.188097	−	0.454106i
$486$	18.9019	+	12.5396i	0.857409	+	0.568806i
$487$	38.0711	+	7.57282i	1.72517	+	0.343157i	0.955433	−	0.295207i	$-0.0953885\pi$
$487$	38.0711	+	7.57282i	1.72517	+	0.343157i	0.769735	+	0.638364i	$0.220389\pi$
$488$	−13.3171	−	8.89820i	−0.602836	−	0.402802i
$489$	−0.735143	+	1.77812i	−0.0332443	+	0.0804094i
$490$	−10.2266	+	2.03420i	−0.461992	+	0.0918958i
$491$	−11.7073	−	4.84934i	−0.528345	−	0.218848i	0.102533	−	0.994730i	$-0.467305\pi$
$491$	−11.7073	−	4.84934i	−0.528345	−	0.218848i	−0.630878	+	0.775882i	$0.717305\pi$
$492$	0.578293	−	0.239986i	0.0260715	−	0.0108194i
$493$		0			0
$494$		−	5.55337i		−	0.249858i
$495$	−13.9287	+	5.79108i	−0.626049	+	0.260290i
$496$	2.37857	+	11.9579i	0.106801	+	0.536926i
$497$	−3.31625	+	3.31625i	−0.148754	+	0.148754i
$498$	32.1072	+	6.36442i	1.43876	+	0.285196i
$499$	7.24100	−	36.4030i	0.324152	−	1.62962i	−0.383839	−	0.923400i	$-0.625398\pi$
$499$	7.24100	−	36.4030i	0.324152	−	1.62962i	0.707991	−	0.706221i	$-0.249602\pi$
$500$	−0.137113	−	0.205204i	−0.00613187	−	0.00917700i
$501$	24.3075	−	24.3397i	1.08598	−	1.08742i
$502$	−20.3540	+	8.43090i	−0.908444	+	0.376290i
$503$	−26.5648	+	17.7500i	−1.18446	+	0.791433i	−0.982189	−	0.187895i	$-0.939833\pi$
$503$	−26.5648	+	17.7500i	−1.18446	+	0.791433i	−0.202275	+	0.979329i	$0.564833\pi$
$504$	9.86701	+	14.7248i	0.439511	+	0.655893i
$505$	6.33939	−	9.48756i	0.282099	−	0.422191i
$506$	−1.29976	−	1.29976i	−0.0577812	−	0.0577812i
$507$	9.41104	−	6.29727i	0.417959	−	0.279672i
$508$	0.553083	−	1.33526i	0.0245391	−	0.0592426i
$509$	−2.30289			−0.102074			−0.0510369	−	0.998697i	$-0.516253\pi$
$509$	−2.30289			−0.102074			−0.0510369	+	0.998697i	$0.516253\pi$
$510$		0			0
$511$	−27.1309			−1.20020
$512$	−7.77882	+	18.7797i	−0.343778	+	0.829954i
$513$	−4.40197	−	0.866521i	−0.194352	−	0.0382578i
$514$	−20.4697	−	20.4697i	−0.902880	−	0.902880i
$515$	15.8236	−	23.6817i	0.697272	−	1.04354i
$516$	0.455527	+	2.28219i	0.0200535	+	0.100468i
$517$	4.28683	−	2.86437i	0.188534	−	0.125975i
$518$	6.90554	−	2.86037i	0.303412	−	0.125677i
$519$	14.2609	+	14.2420i	0.625983	+	0.625155i
$520$	−20.5274	−	30.7215i	−0.900187	−	1.34723i
$521$	0.537016	−	2.69976i	0.0235271	−	0.118279i	−0.967237	−	0.253875i	$-0.918295\pi$
$521$	0.537016	−	2.69976i	0.0235271	−	0.118279i	0.990764	+	0.135596i	$0.0432949\pi$
$522$	−6.85114	−	34.2062i	−0.299866	−	1.49717i
$523$	−29.8001	+	29.8001i	−1.30307	+	1.30307i	−0.376755	+	0.926313i	$0.622960\pi$
$523$	−29.8001	+	29.8001i	−1.30307	+	1.30307i	−0.926313	+	0.376755i	$0.877040\pi$
$524$	−0.0807574	−	0.405995i	−0.00352790	−	0.0177360i
$525$	0.0106624	+	16.1042i	0.000465344	+	0.702846i
$526$		−	0.190778i		−	0.00831830i
$527$		0			0
$528$	4.61767	+	11.1272i	0.200958	+	0.484249i
$529$	−20.7063	−	8.57683i	−0.900274	−	0.372906i
$530$	27.7336	−	5.51655i	1.20467	−	0.239624i
$531$	0.0242021	+	18.2772i	0.00105028	+	0.793161i
$532$	0.181750	+	0.121442i	0.00787987	+	0.00526516i
$533$	−13.3505	−	2.65558i	−0.578275	−	0.115026i
$534$	−6.76611	+	10.1407i	−0.292798	+	0.438832i
$535$	2.20694	+	5.32803i	0.0954144	+	0.230351i
$536$	7.54259	+	18.2094i	0.325790	+	0.786527i
$537$	−0.813917	+	1.21986i	−0.0351231	+	0.0526409i
$538$	−8.48527	−	1.68783i	−0.365826	−	0.0727674i
$539$	−3.21753	−	2.14988i	−0.138589	−	0.0926021i
$540$	1.71807	−	0.715648i	0.0739339	−	0.0307966i
$541$	14.3553	−	2.85545i	0.617184	−	0.122765i	0.123410	−	0.992356i	$-0.460617\pi$
$541$	14.3553	−	2.85545i	0.617184	−	0.122765i	0.493774	+	0.869590i	$0.335617\pi$
$542$	−9.24223	−	3.82826i	−0.396988	−	0.164438i
$543$	0.951908	+	2.29381i	0.0408503	+	0.0984369i
$544$		0			0
$545$		−	12.8251i		−	0.549365i
$546$	0.0159080	+	24.0271i	0.000680798	+	1.02826i
$547$	−5.35079	−	26.9003i	−0.228783	−	1.15017i	−0.908883	−	0.417052i	$-0.863063\pi$
$547$	−5.35079	−	26.9003i	−0.228783	−	1.15017i	0.680099	−	0.733120i	$-0.261937\pi$
$548$	1.21585	−	1.21585i	0.0519384	−	0.0519384i
$549$	−17.1981	+	3.44460i	−0.733999	+	0.147012i
$550$	−2.01663	+	10.1383i	−0.0859893	+	0.432297i
$551$	3.83341	+	5.73710i	0.163309	+	0.244409i
$552$	−2.57369	−	2.57029i	−0.109544	−	0.109399i
$553$	−11.8721	+	4.91757i	−0.504851	+	0.209116i
$554$	10.0389	−	6.70781i	0.426514	−	0.284987i
$555$	2.46386	+	12.3439i	0.104585	+	0.523971i
$556$	0.328981	−	0.492355i	0.0139519	−	0.0208805i
$557$	31.0707	+	31.0707i	1.31651	+	1.31651i	0.916522	+	0.399984i	$0.130984\pi$
$557$	31.0707	+	31.0707i	1.31651	+	1.31651i	0.399984	+	0.916522i	$0.369016\pi$
$558$	10.4934	+	6.99141i	0.444223	+	0.295970i
$559$	19.3619	−	46.7436i	0.818919	−	1.97705i
$560$	27.7789			1.17387
$561$		0			0
$562$	−19.2798			−0.813270
$563$	14.0437	−	33.9044i	0.591870	−	1.42890i	−0.289825	−	0.957080i	$-0.593597\pi$
$563$	14.0437	−	33.9044i	0.591870	−	1.42890i	0.881695	−	0.471821i	$-0.156403\pi$
$564$	−0.528680	+	0.353759i	−0.0222614	+	0.0148959i
$565$	−35.5701	−	35.5701i	−1.49645	−	1.49645i
$566$	−11.3446	+	16.9784i	−0.476850	+	0.713657i
$567$	19.0479	+	3.73645i	0.799938	+	0.156916i
$568$	−4.95297	+	3.30947i	−0.207822	+	0.138862i
$569$	−22.8578	+	9.46803i	−0.958251	+	0.396920i	−0.806326	−	0.591472i	$-0.798547\pi$
$569$	−22.8578	+	9.46803i	−0.958251	+	0.396920i	−0.151925	+	0.988392i	$0.548547\pi$
$570$	−4.69219	+	4.69841i	−0.196534	+	0.196795i
$571$	−1.09497	−	1.63874i	−0.0458232	−	0.0685792i	0.807851	−	0.589387i	$-0.200631\pi$
$571$	−1.09497	−	1.63874i	−0.0458232	−	0.0685792i	−0.853674	+	0.520808i	$0.825631\pi$
$572$	−0.166798	+	0.838551i	−0.00697418	+	0.0350616i
$573$	1.22503	+	0.242831i	0.0511765	+	0.0101444i
$574$	6.83402	−	6.83402i	0.285247	−	0.285247i
$575$	−0.644722	−	3.24124i	−0.0268868	−	0.135169i
$576$	8.61137	+	20.7121i	0.358807	+	0.863003i
$577$		−	26.8179i		−	1.11645i	−0.829691	−	0.558223i	$-0.811483\pi$
$577$		−	26.8179i		−	1.11645i	0.829691	−	0.558223i	$-0.188517\pi$
$578$		0			0
$579$	18.5917	−	7.71536i	0.772644	−	0.320639i
$580$	−2.64449	−	1.09538i	−0.109806	−	0.0454833i
$581$	27.4719	−	5.46450i	1.13973	−	0.226706i
$582$	−3.41602	+	8.26247i	−0.141599	+	0.342490i
$583$	8.72562	+	5.83027i	0.361378	+	0.241465i
$584$	−33.7984	−	6.72291i	−1.39859	−	0.278196i
$585$	−39.6957	−	7.84133i	−1.64121	−	0.324199i
$586$	−14.7044	−	35.4995i	−0.607433	−	1.46647i
$587$	−17.1080	−	41.3023i	−0.706122	−	1.70473i	−0.709471	−	0.704735i	$-0.751066\pi$
$587$	−17.1080	−	41.3023i	−0.706122	−	1.70473i	0.00334911	−	0.999994i	$-0.498934\pi$
$588$	0.397158	+	0.264993i	0.0163785	+	0.0109281i
$589$	−2.44603	−	0.486546i	−0.100787	−	0.0200478i
$590$	22.4922	+	15.0288i	0.925988	+	0.618726i
$591$	37.2374	+	15.3953i	1.53174	+	0.633280i
$592$	9.85977	−	1.96123i	0.405234	−	0.0806061i
$593$	20.3889	+	8.44534i	0.837270	+	0.346809i	0.759777	−	0.650184i	$-0.225308\pi$
$593$	20.3889	+	8.44534i	0.837270	+	0.346809i	0.0774935	+	0.996993i	$0.475308\pi$
$594$	11.5204	+	4.74513i	0.472689	+	0.194695i
$595$		0			0
$596$		−	0.738361i		−	0.0302444i
$597$	−41.7680	+	0.0276540i	−1.70945	+	0.00113180i
$598$	−0.961908	−	4.83584i	−0.0393353	−	0.197752i
$599$	−16.9345	+	16.9345i	−0.691926	+	0.691926i	−0.962655	−	0.270729i	$-0.912735\pi$
$599$	−16.9345	+	16.9345i	−0.691926	+	0.691926i	0.270729	+	0.962655i	$0.412735\pi$
$600$	−3.97727	+	20.0645i	−0.162371	+	0.819130i
$601$	−0.514619	+	2.58716i	−0.0209917	+	0.105533i	−0.989861	−	0.142041i	$-0.954633\pi$
$601$	−0.514619	+	2.58716i	−0.0209917	+	0.105533i	0.968869	+	0.247574i	$0.0796334\pi$
$602$	19.9578	+	29.8690i	0.813421	+	1.21737i
$603$	19.9523	+	8.23359i	0.812521	+	0.335298i
$604$	1.64982	−	0.683377i	0.0671302	−	0.0278062i
$605$	21.0192	−	14.0446i	0.854553	−	0.570994i
$606$	−9.24246	+	1.84480i	−0.375449	+	0.0749400i
$607$	−20.1517	+	30.1592i	−0.817934	+	1.22412i	0.153813	+	0.988100i	$0.450845\pi$
$607$	−20.1517	+	30.1592i	−0.817934	+	1.22412i	−0.971747	+	0.236025i	$0.924155\pi$
$608$	0.404887	+	0.404887i	0.0164203	+	0.0164203i
$609$	−16.6019	−	24.8110i	−0.672744	−	1.00539i
$610$	−9.93432	+	23.9836i	−0.402229	+	0.971066i
$611$	13.8296			0.559487
$612$		0			0
$613$	−25.0887			−1.01333			−0.506663	−	0.862144i	$-0.669121\pi$
$613$	−25.0887			−1.01333			−0.506663	+	0.862144i	$0.669121\pi$
$614$	13.6047	−	32.8447i	0.549041	−	1.32550i
$615$	9.05138	+	13.5269i	0.364987	+	0.545459i
$616$	6.88440	+	6.88440i	0.277380	+	0.277380i
$617$	5.48342	−	8.20652i	0.220754	−	0.330382i	−0.704518	−	0.709686i	$-0.748837\pi$
$617$	5.48342	−	8.20652i	0.220754	−	0.330382i	0.925272	+	0.379304i	$0.123837\pi$
$618$	−23.0699	+	4.60478i	−0.928009	+	0.185231i
$619$	26.8643	−	17.9502i	1.07977	−	0.721478i	0.117361	−	0.993089i	$-0.462557\pi$
$619$	26.8643	−	17.9502i	1.07977	−	0.721478i	0.962407	+	0.271611i	$0.0875565\pi$
$620$	0.955837	−	0.395921i	0.0383873	−	0.0159006i
$621$	−3.98330	+	0.00791187i	−0.159844	+	0.000317492i
$622$	−18.8655	−	28.2341i	−0.756436	−	1.13209i
$623$	−2.03521	+	10.2317i	−0.0815391	+	0.409925i
$624$	−6.28346	+	31.6987i	−0.251540	+	1.26897i
$625$	19.7780	−	19.7780i	0.791122	−	0.791122i
$626$	0.458362	+	2.30434i	0.0183198	+	0.0920999i
$627$	−2.46432	+	0.00163159i	−0.0984154	+	6.51594e-5i
$628$			0.289721i			0.0115611i
$629$		0			0
$630$	20.2876	−	20.3414i	0.808279	−	0.810422i
$631$	3.56930	+	1.47845i	0.142092	+	0.0588563i	0.452596	−	0.891716i	$-0.350498\pi$
$631$	3.56930	+	1.47845i	0.142092	+	0.0588563i	−0.310504	+	0.950572i	$0.600498\pi$
$632$	−16.0082	+	3.18423i	−0.636772	+	0.126662i
$633$	24.9860	+	10.3302i	0.993104	+	0.410587i
$634$	−29.5032	−	19.7134i	−1.17172	−	0.782919i
$635$	36.8483	+	7.32959i	1.46228	+	0.290866i
$636$	−1.07705	−	0.718633i	−0.0427080	−	0.0284957i
$637$	−3.97225	−	9.58987i	−0.157386	−	0.379964i
$638$	−7.33297	−	17.7033i	−0.290315	−	0.700882i
$639$	−1.26419	+	6.39981i	−0.0500107	+	0.253173i
$640$	36.5304	+	7.26634i	1.44399	+	0.287227i
$641$	31.1140	+	20.7897i	1.22893	+	0.821145i	0.988749	−	0.149583i	$-0.0477932\pi$
$641$	31.1140	+	20.7897i	1.22893	+	0.821145i	0.240181	+	0.970728i	$0.422793\pi$
$642$	1.81995	−	4.40198i	0.0718276	−	0.173732i
$643$	41.6621	−	8.28711i	1.64299	−	0.326812i	0.714920	−	0.699206i	$-0.246463\pi$
$643$	41.6621	−	8.28711i	1.64299	−	0.326812i	0.928075	+	0.372395i	$0.121463\pi$
$644$	0.179302	+	0.0742693i	0.00706549	+	0.00292662i
$645$	−55.8760	+	23.1879i	−2.20011	+	0.913024i
$646$		0			0
$647$			48.3331i			1.90017i	0.311989	+	0.950086i	$0.399005\pi$
$647$			48.3331i			1.90017i	−0.311989	+	0.950086i	$0.600995\pi$
$648$	22.8031	+	9.37469i	0.895791	+	0.368272i
$649$	1.95857	+	9.84639i	0.0768806	+	0.386505i
$650$	−19.6063	+	19.6063i	−0.769023	+	0.769023i
$651$	10.5843	+	2.09807i	0.414832	+	0.0822297i
$652$	0.0254394	−	0.127892i	0.000996282	−	0.00500865i
$653$	−3.59464	−	5.37976i	−0.140669	−	0.210526i	0.754445	−	0.656363i	$-0.227906\pi$
$653$	−3.59464	−	5.37976i	−0.140669	−	0.210526i	−0.895114	+	0.445837i	$0.852906\pi$
$654$	−7.48548	+	7.49540i	−0.292705	+	0.293093i
$655$	9.94158	−	4.11794i	0.388450	−	0.160901i
$656$	10.8081	−	7.22172i	0.421984	−	0.281961i
$657$	−31.3504	+	21.0078i	−1.22309	+	0.819591i
$658$	−5.45528	+	8.16440i	−0.212669	+	0.318281i
$659$	17.7005	+	17.7005i	0.689515	+	0.689515i	0.962125	−	0.272610i	$-0.0878869\pi$
$659$	17.7005	+	17.7005i	0.689515	+	0.689515i	−0.272610	+	0.962125i	$0.587887\pi$
$660$	0.849633	−	0.568521i	0.0330719	−	0.0221296i
$661$	−9.53615	+	23.0223i	−0.370913	+	0.895464i	0.622683	+	0.782474i	$0.286043\pi$
$661$	−9.53615	+	23.0223i	−0.370913	+	0.895464i	−0.993596	+	0.112990i	$0.963957\pi$
$662$	−44.3302			−1.72294
$663$		0			0
$664$	35.5773			1.38067
$665$	−2.17451	+	5.24974i	−0.0843240	+	0.203576i
$666$	5.76470	−	8.65227i	0.223378	−	0.335268i
$667$	4.33184	+	4.33184i	0.167729	+	0.167729i
$668$	−1.29517	+	1.93835i	−0.0501115	+	0.0749972i
$669$	−0.824552	−	4.13101i	−0.0318790	−	0.159714i
$670$	26.5621	−	17.7482i	1.02618	−	0.685674i
$671$	−8.90086	+	3.68686i	−0.343614	+	0.142329i
$672$	−1.75293	−	1.75061i	−0.0676208	−	0.0675313i
$673$	−10.4352	−	15.6174i	−0.402248	−	0.602006i	0.573949	−	0.818891i	$-0.305411\pi$
$673$	−10.4352	−	15.6174i	−0.402248	−	0.602006i	−0.976197	+	0.216884i	$0.930411\pi$
$674$	−4.89012	+	24.5843i	−0.188360	+	0.946952i
$675$	12.4820	+	18.6005i	0.480432	+	0.715935i
$676$	−0.542640	+	0.542640i	−0.0208708	+	0.0208708i
$677$	1.93347	+	9.72023i	0.0743095	+	0.373579i	0.999989	−	0.00473017i	$-0.00150567\pi$
$677$	1.93347	+	9.72023i	0.0743095	+	0.373579i	−0.925679	+	0.378309i	$0.876506\pi$
$678$	0.0275092	+	41.5493i	0.00105648	+	1.59569i
$679$			7.65102i			0.293619i
$680$		0			0
$681$	−0.932371	−	2.24673i	−0.0357285	−	0.0860950i
$682$	6.39878	+	2.65046i	0.245022	+	0.101491i
$683$	2.34194	−	0.465840i	0.0896118	−	0.0178249i	−0.150081	−	0.988674i	$-0.547953\pi$
$683$	2.34194	−	0.465840i	0.0896118	−	0.0178249i	0.239693	+	0.970849i	$0.422953\pi$
$684$	0.304050		0.000402615i	0.0116257		1.53944e-5i
$685$	37.1650	+	24.8328i	1.42000	+	0.948814i
$686$	28.7748	+	5.72366i	1.09863	+	0.218530i
$687$	10.4560	−	15.6710i	0.398923	−	0.597887i
$688$	18.4895	+	44.6375i	0.704905	+	1.70179i
$689$	10.7724	+	26.0068i	0.410394	+	0.990779i
$690$	−3.27211	+	4.90409i	−0.124567	+	0.186695i
$691$	−31.9778	−	6.36078i	−1.21649	−	0.241975i	−0.455203	−	0.890388i	$-0.650433\pi$
$691$	−31.9778	−	6.36078i	−1.21649	−	0.241975i	−0.761290	+	0.648412i	$0.775433\pi$
$692$	−1.13570	−	0.758850i	−0.0431728	−	0.0288472i
$693$	10.6620	−	0.0141184i	0.405017	−	0.000536313i
$694$	−28.8782	+	5.74423i	−1.09620	+	0.218048i
$695$	14.2214	+	5.89068i	0.539447	+	0.223446i
$696$	−14.5338	−	35.0222i	−0.550904	−	1.32751i
$697$		0			0
$698$			11.0631i			0.418743i
$699$	−0.0164403	−	24.8311i	−0.000621829	−	0.939197i
$700$	−0.212921	−	1.07043i	−0.00804766	−	0.0404583i
$701$	31.7150	−	31.7150i	1.19786	−	1.19786i	0.223051	−	0.974807i	$-0.428398\pi$
$701$	31.7150	−	31.7150i	1.19786	−	1.19786i	0.974807	−	0.223051i	$-0.0716016\pi$
$702$	18.6228	+	27.7515i	0.702872	+	1.04741i
$703$	−0.401176	+	2.01685i	−0.0151307	+	0.0760669i
$704$	6.84510	+	10.2444i	0.257985	+	0.386101i
$705$	−11.7005	−	11.6850i	−0.440667	−	0.440083i
$706$	16.0527	−	6.64926i	0.604153	−	0.250248i
$707$	−6.70596	+	4.48078i	−0.252204	+	0.168517i
$708$	−0.242455	−	1.21470i	−0.00911202	−	0.0456512i
$709$	21.9367	−	32.8306i	0.823849	−	1.23298i	−0.146003	−	0.989284i	$-0.546641\pi$
$709$	21.9367	−	32.8306i	0.823849	−	1.23298i	0.969852	−	0.243693i	$-0.0783591\pi$
$710$	6.82716	+	6.82716i	0.256219	+	0.256219i
$711$	−9.91071	+	14.8750i	−0.371681	+	0.557857i
$712$	−5.07074	+	12.2419i	−0.190034	+	0.458783i
$713$	−2.21426			−0.0829248
$714$		0			0
$715$	−22.2254			−0.831182
$716$	0.0380325	−	0.0918186i	0.00142134	−	0.00343142i
$717$	34.1297	−	22.8374i	1.27460	−	0.852880i
$718$	23.6628	+	23.6628i	0.883086	+	0.883086i
$719$	24.4159	−	36.5410i	0.910560	−	1.36275i	−0.0212393	−	0.999774i	$-0.506761\pi$
$719$	24.4159	−	36.5410i	0.910560	−	1.36275i	0.931799	−	0.362975i	$-0.118239\pi$
$720$	32.0992	−	21.5095i	1.19627	−	0.801613i
$721$	−16.7386	+	11.1844i	−0.623379	+	0.416529i
$722$	24.5406	−	10.1650i	0.913307	−	0.378304i
$723$	3.44461	−	3.44918i	0.128107	−	0.128276i
$724$	−0.0935070	−	0.139943i	−0.00347516	−	0.00520094i
$725$	6.72103	−	33.7889i	0.249613	−	1.25489i
$726$	−20.4816	−	4.05995i	−0.760144	−	0.150679i
$727$	0.0802760	−	0.0802760i	0.00297727	−	0.00297727i	−0.705617	−	0.708594i	$-0.749330\pi$
$727$	0.0802760	−	0.0802760i	0.00297727	−	0.00297727i	0.708594	+	0.705617i	$0.249330\pi$
$728$	5.09492	+	25.6139i	0.188830	+	0.949315i
$729$	24.9035	−	10.4315i	0.922352	−	0.386351i
$730$			55.8544i			2.06726i
$731$		0			0
$732$	1.09790	−	0.455616i	0.0405795	−	0.0168400i
$733$	7.54651	+	3.12587i	0.278737	+	0.115457i	0.517673	−	0.855579i	$-0.326799\pi$
$733$	7.54651	+	3.12587i	0.278737	+	0.115457i	−0.238936	+	0.971035i	$0.576799\pi$
$734$	−23.4205	+	4.65863i	−0.864467	+	0.171953i
$735$	−4.74203	+	11.4697i	−0.174912	+	0.423068i
$736$	0.422704	+	0.282442i	0.0155811	+	0.0104109i
$737$	11.6281	+	2.31297i	0.428326	+	0.0851993i
$738$	2.60521	−	13.1885i	0.0958992	−	0.485477i
$739$	−4.49550	−	10.8531i	−0.165370	−	0.399237i	0.819372	−	0.573263i	$-0.194323\pi$
$739$	−4.49550	−	10.8531i	−0.165370	−	0.399237i	−0.984741	+	0.174025i	$0.944323\pi$
$740$	−0.326452	−	0.788126i	−0.0120006	−	0.0289721i
$741$	−5.49865	−	3.66882i	−0.201998	−	0.134777i
$742$	−19.6025	−	3.89919i	−0.719632	−	0.143144i
$743$	34.1272	+	22.8030i	1.25200	+	0.836563i	0.991651	−	0.128951i	$-0.0411609\pi$
$743$	34.1272	+	22.8030i	1.25200	+	0.836563i	0.260354	+	0.965513i	$0.416161\pi$
$744$	12.6655	+	5.23642i	0.464341	+	0.191976i
$745$	18.8251	−	3.74454i	0.689697	−	0.137189i
$746$	2.17550	+	0.901121i	0.0796507	+	0.0329924i
$747$	27.5132	−	27.5862i	1.00666	−	1.00933i
$748$		0			0
$749$		−	4.07622i		−	0.148942i
$750$	−5.29902	+	0.00350841i	−0.193493	+	0.000128109i
$751$	0.329510	+	1.65656i	0.0120240	+	0.0604487i	0.986331	−	0.164773i	$-0.0526893\pi$
$751$	0.329510	+	1.65656i	0.0120240	+	0.0604487i	−0.974307	+	0.225222i	$0.927689\pi$
$752$	−9.33841	+	9.33841i	−0.340537	+	0.340537i
$753$	−5.09898	+	25.7233i	−0.185817	+	0.937409i
$754$	10.0276	−	50.4121i	0.365184	−	1.83590i
$755$	25.7901	+	38.5977i	0.938599	+	1.40471i
$756$	−1.31549	+	0.00261291i	−0.0478441	+	9.50307e-5i
$757$	50.2881	−	20.8300i	1.82775	−	0.757080i	0.857715	−	0.514126i	$-0.171884\pi$
$757$	50.2881	−	20.8300i	1.82775	−	0.757080i	0.970038	−	0.242954i	$-0.0781164\pi$
$758$	18.7890	−	12.5544i	0.682446	−	0.455996i
$759$	−2.14563	+	0.428269i	−0.0778814	+	0.0155452i
$760$	−4.00977	+	6.00104i	−0.145450	+	0.217681i
$761$	−24.1395	−	24.1395i	−0.875055	−	0.875055i	0.117963	−	0.993018i	$-0.462364\pi$
$761$	−24.1395	−	24.1395i	−0.875055	−	0.875055i	−0.993018	+	0.117963i	$0.962364\pi$
$762$	−17.2574	−	25.7906i	−0.625170	−	0.934294i
$763$	−3.46901	+	8.37493i	−0.125587	+	0.303193i
$764$	−0.0846370			−0.00306206
$765$		0			0
$766$	32.2229			1.16426
$767$	−10.3054	+	24.8794i	−0.372106	+	0.898343i
$768$	−2.70443	−	4.04167i	−0.0975877	−	0.145841i
$769$	−31.3211	−	31.3211i	−1.12947	−	1.12947i	−0.990264	−	0.139204i	$-0.955546\pi$
$769$	−31.3211	−	31.3211i	−1.12947	−	1.12947i	−0.139204	−	0.990264i	$-0.544454\pi$
$770$	8.76709	−	13.1209i	0.315944	−	0.472843i
$771$	−33.7913	+	6.74476i	−1.21696	+	0.242907i
$772$	−1.13426	+	0.757888i	−0.0408229	+	0.0272770i
$773$	−12.8222	+	5.31114i	−0.461184	+	0.191028i	−0.601164	−	0.799126i	$-0.705296\pi$
$773$	−12.8222	+	5.31114i	−0.461184	+	0.191028i	0.139980	+	0.990154i	$0.455296\pi$
$774$	46.1897	+	19.0608i	1.66025	+	0.685125i
$775$	6.91801	+	10.3535i	0.248502	+	0.371910i
$776$	−1.89589	+	9.53128i	−0.0680584	+	0.342153i
$777$	1.72994	−	8.72719i	0.0620613	−	0.313086i
$778$	−15.6099	+	15.6099i	−0.559643	+	0.559643i
$779$	0.518733	+	2.60785i	0.0185856	+	0.0934359i
$780$	2.74219	−	0.00181557i	0.0981863	−	6.50078e-5i
$781$			3.58322i			0.128218i
$782$		0			0
$783$	−38.3954	−	15.8146i	−1.37214	−	0.565168i
$784$	9.15778	+	3.79328i	0.327064	+	0.135474i
$785$	−7.38666	+	1.46930i	−0.263641	+	0.0524415i
$786$	−8.21367	−	3.39584i	−0.292972	−	0.121126i
$787$	−19.9038	−	13.2993i	−0.709495	−	0.474070i	0.147719	−	0.989029i	$-0.452807\pi$
$787$	−19.9038	−	13.2993i	−0.709495	−	0.474070i	−0.857214	+	0.514960i	$0.827807\pi$
$788$	−2.67832	−	0.532750i	−0.0954111	−	0.0189784i
$789$	−0.188898	−	0.126037i	−0.00672494	−	0.00448702i
$790$	10.1238	+	24.4410i	0.360189	+	0.869572i
$791$	13.6065	+	32.8490i	0.483792	+	1.16798i
$792$	13.2858	+	2.62442i	0.472089	+	0.0932546i
$793$	−25.3461	−	5.04166i	−0.900067	−	0.179034i
$794$	−45.5369	−	30.4268i	−1.61604	−	1.07981i
$795$	12.8599	−	31.1048i	0.456094	−	1.10317i
$796$	2.77627	−	0.552234i	0.0984022	−	0.0195734i
$797$	−43.2651	−	17.9210i	−1.53253	−	0.634795i	−0.552476	−	0.833529i	$-0.686317\pi$
$797$	−43.2651	−	17.9210i	−1.53253	−	0.634795i	−0.980053	+	0.198734i	$0.936317\pi$
$798$	4.33492	−	1.79895i	0.153455	−	0.0636820i
$799$		0			0
$800$		−	2.85893i		−	0.101078i
$801$	5.57079	+	13.3989i	0.196834	+	0.473426i
$802$	−1.00319	−	5.04338i	−0.0354239	−	0.178088i
$803$	−14.6575	+	14.6575i	−0.517252	+	0.517252i
$804$	−1.43488	−	0.284427i	−0.0506042	−	0.0100310i
$805$	−0.984236	+	4.94809i	−0.0346897	+	0.174397i
$806$	10.3215	+	15.4472i	0.363559	+	0.544104i
$807$	−7.27696	+	7.28661i	−0.256161	+	0.256501i
$808$	−9.46429	+	3.92024i	−0.332952	+	0.137913i
$809$	−9.74138	+	6.50898i	−0.342489	+	0.228844i	−0.714904	−	0.699223i	$-0.753530\pi$
$809$	−9.74138	+	6.50898i	−0.342489	+	0.228844i	0.372415	+	0.928066i	$0.378530\pi$
$810$	7.69224	−	39.2140i	0.270278	−	1.37784i
$811$	−10.4602	+	15.6548i	−0.367308	+	0.549716i	−0.968380	−	0.249479i	$-0.919741\pi$
$811$	−10.4602	+	15.6548i	−0.367308	+	0.549716i	0.601072	+	0.799195i	$0.294741\pi$
$812$	1.43060	+	1.43060i	0.0502042	+	0.0502042i
$813$	−9.89638	+	6.62203i	−0.347081	+	0.232245i
$814$	2.18541	−	5.27605i	0.0765987	−	0.184926i
$815$	3.38972			0.118737
$816$		0			0
$817$	−9.88307			−0.345765
$818$	−6.79797	+	16.4118i	−0.237686	+	0.573824i
$819$	23.8008	+	15.8576i	0.831667	+	0.554111i
$820$	−0.779963	−	0.779963i	−0.0272375	−	0.0272375i
$821$	−16.8304	+	25.1885i	−0.587386	+	0.879086i	−0.999486	−	0.0320530i	$-0.989795\pi$
$821$	−16.8304	+	25.1885i	−0.587386	+	0.879086i	0.412100	+	0.911139i	$0.364795\pi$
$822$	−7.22651	−	36.2048i	−0.252054	−	1.26279i
$823$	19.0816	−	12.7499i	0.665142	−	0.444434i	−0.176622	−	0.984279i	$-0.556517\pi$
$823$	19.0816	−	12.7499i	0.665142	−	0.444434i	0.841765	+	0.539845i	$0.181517\pi$
$824$	−23.6236	+	9.78523i	−0.822968	+	0.340884i
$825$	8.70609	+	8.69457i	0.303107	+	0.302706i
$826$	−10.6226	−	15.8978i	−0.369607	−	0.553156i
$827$	3.41591	−	17.1729i	0.118783	−	0.597161i	−0.874841	−	0.484411i	$-0.839034\pi$
$827$	3.41591	−	17.1729i	0.118783	−	0.597161i	0.993623	−	0.112750i	$-0.0359660\pi$
$828$	0.264695	−	0.0530156i	0.00919880	−	0.00184242i
$829$	31.1358	−	31.1358i	1.08139	−	1.08139i	0.0850121	−	0.996380i	$-0.472907\pi$
$829$	31.1358	−	31.1358i	1.08139	−	1.08139i	0.996380	−	0.0850121i	$-0.0270929\pi$
$830$	−11.2498	−	56.5564i	−0.390485	−	1.96310i
$831$	−0.00951518	−	14.3715i	−0.000330078	−	0.498542i
$832$			33.0493i			1.14578i
$833$		0			0
$834$	−4.87328	−	11.7432i	−0.168748	−	0.406632i
$835$	−55.9881	−	23.1910i	−1.93755	−	0.802559i
$836$	0.163800	−	0.0325818i	0.00566514	−	0.00112687i
$837$	13.8550	−	5.77119i	0.478898	−	0.199481i
$838$	37.9818	+	25.3786i	1.31206	+	0.876690i
$839$	−19.3977	−	3.85845i	−0.669684	−	0.133209i	−0.151473	−	0.988461i	$-0.548402\pi$
$839$	−19.3977	−	3.85845i	−0.669684	−	0.133209i	−0.518211	+	0.855253i	$0.673402\pi$
$840$	17.3313	−	25.9754i	0.597988	−	0.896236i
$841$	13.3415	+	32.2093i	0.460053	+	1.11067i
$842$	−8.44564	−	20.3896i	−0.291056	−	0.702671i
$843$	−12.7372	+	19.0898i	−0.438691	+	0.657489i
$844$	−1.79713	−	0.357471i	−0.0618598	−	0.0123047i
$845$	−16.5869	−	11.0830i	−0.570608	−	0.381268i
$846$	0.0180859	+	13.6582i	0.000621805	+	0.469580i
$847$	−17.5247	+	3.48588i	−0.602156	+	0.119776i
$848$	−24.8350	−	10.2870i	−0.852837	−	0.353257i
$849$	9.31634	+	22.4496i	0.319736	+	0.770468i
$850$		0			0
$851$			1.82575i			0.0625858i
$852$	−0.000292709	−	0.442102i	−1.00281e−5	−	0.0151462i
$853$	1.20474	+	6.05663i	0.0412495	+	0.207375i	0.995914	−	0.0903095i	$-0.0287856\pi$
$853$	1.20474	+	6.05663i	0.0412495	+	0.207375i	−0.954664	+	0.297685i	$0.903786\pi$
$854$	12.9745	−	12.9745i	0.443977	−	0.443977i
$855$	1.55223	+	7.74995i	0.0530852	+	0.265043i
$856$	1.01007	−	5.07796i	0.0345235	−	0.173561i
$857$	−14.4466	−	21.6208i	−0.493486	−	0.738554i	0.498224	−	0.867048i	$-0.333986\pi$
$857$	−14.4466	−	21.6208i	−0.493486	−	0.738554i	−0.991710	+	0.128494i	$0.958986\pi$
$858$	12.9893	+	12.9721i	0.443446	+	0.442859i
$859$	3.03380	−	1.25664i	0.103512	−	0.0428761i	−0.330326	−	0.943867i	$-0.607159\pi$
$859$	3.03380	−	1.25664i	0.103512	−	0.0428761i	0.433838	+	0.900991i	$0.357159\pi$
$860$	3.40893	−	2.27778i	0.116244	−	0.0776715i
$861$	−2.25181	−	11.2816i	−0.0767414	−	0.384474i
$862$	9.25940	−	13.8577i	0.315376	−	0.471994i
$863$	−10.3922	−	10.3922i	−0.353754	−	0.353754i	0.507750	−	0.861504i	$-0.330477\pi$
$863$	−10.3922	−	10.3922i	−0.353754	−	0.353754i	−0.861504	+	0.507750i	$0.830477\pi$
$864$	−3.38107	−	0.665559i	−0.115026	−	0.0226428i
$865$	13.5878	−	32.8040i	0.462000	−	1.11537i
$866$	38.9856			1.32479
$867$		0			0
$868$	−0.731265			−0.0248208
$869$	−3.75718	+	9.07062i	−0.127453	+	0.307700i
$870$	−51.0784	+	34.1784i	−1.73172	+	1.15876i
$871$	22.4875	+	22.4875i	0.761958	+	0.761958i
$872$	−6.39680	+	9.57349i	−0.216623	+	0.324199i
$873$	5.92427	+	8.84093i	0.200506	+	0.299220i
$874$	−0.800809	+	0.535083i	−0.0270878	+	0.0180995i
$875$	−4.18943	+	1.73532i	−0.141629	+	0.0586644i
$876$	1.80726	−	1.80966i	0.0610618	−	0.0611427i
$877$	−7.40929	−	11.0888i	−0.250194	−	0.374442i	0.685020	−	0.728524i	$-0.259793\pi$
$877$	−7.40929	−	11.0888i	−0.250194	−	0.374442i	−0.935214	+	0.354082i	$0.884793\pi$
$878$	2.42046	−	12.1685i	0.0816867	−	0.410667i
$879$	−44.8641	−	8.89316i	−1.51323	−	0.299959i
$880$	15.0076	−	15.0076i	0.505907	−	0.505907i
$881$	3.84700	+	19.3402i	0.129609	+	0.651587i	0.989898	+	0.141781i	$0.0452828\pi$
$881$	3.84700	+	19.3402i	0.129609	+	0.651587i	−0.860289	+	0.509806i	$0.829717\pi$
$882$	9.46583	−	3.93557i	0.318731	−	0.132517i
$883$			44.5932i			1.50068i	0.661051	+	0.750341i	$0.270111\pi$
$883$			44.5932i			1.50068i	−0.661051	+	0.750341i	$0.729889\pi$
$884$		0			0
$885$	29.7401	−	12.3418i	0.999702	−	0.414866i
$886$	25.3778	+	10.5118i	0.852584	+	0.353152i
$887$	−16.3954	+	3.26124i	−0.550502	+	0.109502i	−0.462501	−	0.886619i	$-0.653048\pi$
$887$	−16.3954	+	3.26124i	−0.550502	+	0.109502i	−0.0880011	+	0.996120i	$0.528048\pi$
$888$	4.31764	−	10.4432i	0.144890	−	0.350452i
$889$	−22.0799	−	14.7533i	−0.740536	−	0.494810i
$890$	21.0640	+	4.18990i	0.706068	+	0.140446i
$891$	12.3093	−	8.27205i	0.412377	−	0.277124i
$892$	0.109250	+	0.263753i	0.00365797	+	0.00883111i
$893$	−1.03380	−	2.49580i	−0.0345947	−	0.0835189i
$894$	−13.1875	−	8.79900i	−0.441057	−	0.294283i
$895$	2.53386	+	0.504016i	0.0846976	+	0.0168474i
$896$	−21.8894	−	14.6260i	−0.731272	−	0.488620i
$897$	−5.42367	−	2.24235i	−0.181091	−	0.0748699i
$898$	38.9112	−	7.73992i	1.29848	−	0.258284i
$899$	−21.3259	−	8.83348i	−0.711259	−	0.294613i
$900$	−1.07488	−	1.07204i	−0.0358293	−	0.0357345i
$901$		0			0
$902$		−	7.38418i		−	0.245866i
$903$	42.7598	−	0.0283106i	1.42296	−	0.000942119i
$904$	8.81050	+	44.2934i	0.293033	+	1.47318i
$905$	3.09374	−	3.09374i	0.102839	−	0.102839i
$906$	7.45530	−	37.6104i	0.247686	−	1.24952i
$907$	−1.79747	+	9.03651i	−0.0596841	+	0.300052i	−0.999085	−	0.0427682i	$-0.986382\pi$
$907$	−1.79747	+	9.03651i	−0.0596841	+	0.300052i	0.939401	+	0.342821i	$0.111382\pi$
$908$	0.0915878	+	0.137071i	0.00303945	+	0.00454886i
$909$	−4.27938	+	10.3702i	−0.141938	+	0.343956i
$910$	39.1068	−	16.1986i	1.29638	−	0.536978i
$911$	1.66735	−	1.11409i	0.0552417	−	0.0369113i	−0.527643	−	0.849466i	$-0.676924\pi$
$911$	1.66735	−	1.11409i	0.0552417	−	0.0369113i	0.582884	+	0.812555i	$0.301924\pi$
$912$	6.19031	−	1.23559i	0.204982	−	0.0409145i
$913$	11.8895	−	17.7940i	0.393486	−	0.588894i
$914$	10.8464	+	10.8464i	0.358768	+	0.358768i
$915$	17.1842	+	25.6811i	0.568091	+	0.848991i
$916$	−0.488587	+	1.17955i	−0.0161434	+	0.0389735i
$917$	−7.60583			−0.251167
$918$		0			0
$919$	4.18774			0.138141			0.0690703	−	0.997612i	$-0.477997\pi$
$919$	4.18774			0.138141			0.0690703	+	0.997612i	$0.477997\pi$
$920$	−2.45223	+	5.92020i	−0.0808475	+	0.195183i
$921$	−23.5331	−	35.1694i	−0.775443	−	1.15887i
$922$	10.1727	+	10.1727i	0.335021	+	0.335021i
$923$	−5.33990	+	7.99172i	−0.175765	+	0.263051i
$924$	−0.708599	+	0.141437i	−0.0233112	+	0.00465293i
$925$	8.53690	−	5.70418i	0.280692	−	0.187552i
$926$	−30.8229	+	12.7673i	−1.01290	+	0.419558i
$927$	−10.6817	+	25.8847i	−0.350832	+	0.850166i
$928$	2.94437	+	4.40656i	0.0966536	+	0.144652i
$929$	4.77057	−	23.9833i	0.156517	−	0.786866i	−0.820157	−	0.572139i	$-0.806114\pi$
$929$	4.77057	−	23.9833i	0.156517	−	0.786866i	0.976674	−	0.214727i	$-0.0688863\pi$
$930$	4.31929	−	21.7899i	0.141635	−	0.714520i
$931$	−1.43373	+	1.43373i	−0.0469885	+	0.0469885i
$932$	0.328303	+	1.65049i	0.0107539	+	0.0540636i
$933$	−40.4193	+	0.0267611i	−1.32327	+	0.000876118i
$934$		−	37.6099i		−	1.23063i
$935$		0			0
$936$	25.7205	+	25.6524i	0.840699	+	0.838476i
$937$	46.7545	+	19.3663i	1.52740	+	0.632671i	0.979058	−	0.203582i	$-0.0652582\pi$
$937$	46.7545	+	19.3663i	1.52740	+	0.632671i	0.548345	+	0.836252i	$0.315258\pi$
$938$	−22.1461	+	4.40513i	−0.723095	+	0.143832i
$939$	2.58445	+	1.06851i	0.0843403	+	0.0348695i
$940$	0.931798	+	0.622608i	0.0303919	+	0.0203072i
$941$	3.53463	+	0.703081i	0.115226	+	0.0229198i	0.252366	−	0.967632i	$-0.418791\pi$
$941$	3.53463	+	0.703081i	0.115226	+	0.0229198i	−0.137141	+	0.990552i	$0.543791\pi$
$942$	5.17458	+	3.45259i	0.168597	+	0.112492i
$943$	0.903419	+	2.18105i	0.0294194	+	0.0710246i
$944$	−9.84105	−	23.7584i	−0.320299	−	0.773270i
$945$	−6.73804	−	33.5262i	−0.219188	−	1.09061i
$946$	26.9191	+	5.35453i	0.875214	+	0.174091i
$947$	−22.2883	−	14.8925i	−0.724271	−	0.483943i	0.137972	−	0.990436i	$-0.455941\pi$
$947$	−22.2883	−	14.8925i	−0.724271	−	0.483943i	−0.862244	+	0.506493i	$0.830941\pi$
$948$	0.462824	−	1.11945i	0.0150318	−	0.0363581i
$949$	−54.5344	+	10.8476i	−1.77026	+	0.352127i
$950$	5.00393	+	2.07269i	0.162349	+	0.0672471i
$951$	−39.0103	+	16.1889i	−1.26500	+	0.524960i
$952$		0			0
$953$			24.2594i			0.785838i	0.919573	+	0.392919i	$0.128535\pi$
$953$			24.2594i			0.785838i	−0.919573	+	0.392919i	$0.871465\pi$
$954$	−25.6704	+	10.6729i	−0.831109	+	0.345547i
$955$	−0.429230	−	2.15788i	−0.0138895	−	0.0698275i
$956$	−1.96792	+	1.96792i	−0.0636470	+	0.0636470i
$957$	−22.3734	−	4.43495i	−0.723229	−	0.143362i
$958$	−2.45974	+	12.3659i	−0.0794705	+	0.399525i
$959$	−17.5522	−	26.2688i	−0.566792	−	0.848264i
$960$	27.9242	−	27.9612i	0.901250	−	0.902445i
$961$	−20.9321	+	8.67037i	−0.675230	+	0.279689i
$962$	12.7368	−	8.51048i	0.410652	−	0.274389i
$963$	−3.15626	−	4.71017i	−0.101709	−	0.151783i
$964$	−0.183538	+	0.274684i	−0.00591135	+	0.00884697i
$965$	−25.0752	−	25.0752i	−0.807200	−	0.807200i
$966$	3.46322	−	2.31737i	0.111427	−	0.0745601i
$967$	−5.07976	+	12.2636i	−0.163354	+	0.394372i	−0.984268	−	0.176680i	$-0.943464\pi$
$967$	−5.07976	+	12.2636i	−0.163354	+	0.394372i	0.820914	+	0.571051i	$0.193464\pi$
$968$	−22.6952			−0.729452
$969$		0			0
$970$	15.7512			0.505739
$971$	5.91933	−	14.2905i	0.189960	−	0.458605i	−0.799991	−	0.600012i	$-0.795163\pi$
$971$	5.91933	−	14.2905i	0.189960	−	0.458605i	0.989952	+	0.141407i	$0.0451626\pi$
$972$	−1.51806	+	1.02162i	−0.0486918	+	0.0327685i
$973$	−7.69338	−	7.69338i	−0.246638	−	0.246638i
$974$	−31.3806	+	46.9643i	−1.00550	+	1.50483i
$975$	6.46027	+	32.3660i	0.206894	+	1.03654i
$976$	20.5193	−	13.7105i	0.656805	−	0.438863i
$977$	18.6618	−	7.72995i	0.597042	−	0.247303i	−0.0636347	−	0.997973i	$-0.520269\pi$
$977$	18.6618	−	7.72995i	0.597042	−	0.247303i	0.660677	+	0.750670i	$0.270269\pi$
$978$	−1.98107	−	1.97845i	−0.0633475	−	0.0632637i
$979$	4.42817	+	6.62723i	0.141525	+	0.211807i
$980$	0.164096	−	0.824966i	0.00524185	−	0.0263526i
$981$	2.47628	+	12.3635i	0.0790616	+	0.394737i
$982$	13.0385	−	13.0385i	0.416075	−	0.416075i
$983$	5.08915	+	25.5849i	0.162319	+	0.816031i	0.973047	+	0.230608i	$0.0740714\pi$
$983$	5.08915	+	25.5849i	0.162319	+	0.816031i	−0.810728	+	0.585423i	$0.800929\pi$
$984$	−0.00967440	−	14.6120i	−0.000308409	−	0.465814i
$985$		−	70.9874i		−	2.26185i
$986$		0			0
$987$	4.47994	+	10.7953i	0.142598	+	0.343618i
$988$	0.413882	+	0.171435i	0.0131673	+	0.00545409i
$989$	−8.60611	+	1.71186i	−0.273658	+	0.0544340i
$990$	−0.0290655	−	21.9499i	−0.000923762	−	0.697615i
$991$	30.0243	+	20.0616i	0.953754	+	0.637278i	0.931990	−	0.362485i	$-0.118072\pi$
$991$	30.0243	+	20.0616i	0.953754	+	0.637278i	0.0217647	+	0.999763i	$0.493072\pi$
$992$	−1.87875	−	0.373707i	−0.0596504	−	0.0118652i
$993$	−29.2866	+	43.8933i	−0.929381	+	1.39291i
$994$	−2.61157	−	6.30488i	−0.0828339	−	0.199979i
$995$	28.1592	+	67.9824i	0.892707	+	2.15519i
$996$	−1.46549	+	2.19641i	−0.0464359	+	0.0695960i
$997$	−14.4897	−	2.88218i	−0.458894	−	0.0912797i	−0.0397704	−	0.999209i	$-0.512663\pi$
$997$	−14.4897	−	2.88218i	−0.458894	−	0.0912797i	−0.419124	+	0.907929i	$0.637663\pi$
$998$	44.9065	+	30.0056i	1.42149	+	0.949809i
$999$	−4.75858	−	11.4240i	−0.150555	−	0.361439i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.1	✓	32	51.44	even	16
51.2.i.a.29.4	yes	32	17.10	odd	16
51.2.i.a.44.1	yes	32	17.15	even	8
51.2.i.a.44.4	yes	32	51.32	odd	8
816.2.cj.c.401.3		32	204.83	even	8
816.2.cj.c.401.4		32	68.15	odd	8
816.2.cj.c.641.3		32	68.27	even	16
816.2.cj.c.641.4		32	204.95	odd	16
867.2.i.b.65.1		32	51.14	even	16	inner
867.2.i.b.65.4		32	17.14	odd	16	inner
867.2.i.b.827.1		32	1.1	even	1	trivial
867.2.i.b.827.4		32	3.2	odd	2	inner
867.2.i.c.158.1		32	17.11	odd	16
867.2.i.c.158.4		32	51.11	even	16
867.2.i.c.653.1		32	51.26	odd	8
867.2.i.c.653.4		32	17.9	even	8
867.2.i.d.158.1		32	17.6	odd	16
867.2.i.d.158.4		32	51.23	even	16
867.2.i.d.653.1		32	51.8	odd	8
867.2.i.d.653.4		32	17.8	even	8
867.2.i.f.224.1		32	17.12	odd	16
867.2.i.f.224.4		32	51.29	even	16
867.2.i.f.329.1		32	51.38	odd	4
867.2.i.f.329.4		32	17.4	even	4
867.2.i.g.224.1		32	17.5	odd	16
867.2.i.g.224.4		32	51.5	even	16
867.2.i.g.329.1		32	51.47	odd	4
867.2.i.g.329.4		32	17.13	even	4
867.2.i.h.131.1		32	51.41	even	16
867.2.i.h.131.4		32	17.7	odd	16
867.2.i.h.503.1		32	17.2	even	8
867.2.i.h.503.4		32	51.2	odd	8
867.2.i.i.65.1		32	51.20	even	16
867.2.i.i.65.4		32	17.3	odd	16
867.2.i.i.827.1		32	17.16	even	2
867.2.i.i.827.4		32	51.50	odd	2

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

\(f(q)\)	\(=\)	\(q+(-0.556851 + 1.34436i) q^{2} +(0.963229 + 1.43951i) q^{3} +(-0.0830021 - 0.0830021i) q^{4} +(1.69526 - 2.53714i) q^{5} +(-2.47159 + 0.493332i) q^{6} +(-1.79329 + 1.19824i) q^{7} +(-2.53091 + 1.04834i) q^{8} +(-1.14438 + 2.77316i) q^{9} +(2.46681 + 3.69185i) q^{10} +(-0.321478 + 1.61618i) q^{11} +(0.0395323 - 0.199432i) q^{12} +(-3.12551 + 3.12551i) q^{13} +(-0.612265 - 3.07806i) q^{14} +(5.28516 - 0.00349923i) q^{15} -4.22099i q^{16} +(-3.09087 - 3.08269i) q^{18} +(0.797694 + 0.330416i) q^{19} +(-0.351298 + 0.0698774i) q^{20} +(-3.45222 - 1.42728i) q^{21} +(-1.99371 - 1.33215i) q^{22} +(0.751858 + 0.149554i) q^{23} +(-3.94694 - 2.63348i) q^{24} +(-1.64974 - 3.98282i) q^{25} +(-2.46136 - 5.94226i) q^{26} +(-5.09429 + 1.02384i) q^{27} +(0.248303 + 0.0493905i) q^{28} +(6.64464 + 4.43981i) q^{29} +(-2.93834 + 7.10709i) q^{30} +(-2.83296 + 0.563512i) q^{31} +(0.612694 + 0.253786i) q^{32} +(-2.63616 + 1.09398i) q^{33} +6.58114i q^{35} +(0.325163 - 0.135192i) q^{36} +(0.464638 + 2.33589i) q^{37} +(-0.888394 + 0.888394i) q^{38} +(-7.50979 - 1.48862i) q^{39} +(-1.63078 + 8.19848i) q^{40} +(1.71091 + 2.56055i) q^{41} +(3.84115 - 3.84624i) q^{42} +(-10.5751 + 4.38037i) q^{43} +(0.160829 - 0.107463i) q^{44} +(5.09586 + 7.60467i) q^{45} +(-0.619727 + 0.927487i) q^{46} +(-2.21238 - 2.21238i) q^{47} +(6.07615 - 4.06578i) q^{48} +(-0.898671 + 2.16958i) q^{49} +6.27299 q^{50} +0.518848 q^{52} +(2.43710 - 5.88369i) q^{53} +(1.46035 - 7.41867i) q^{54} +(3.55548 + 3.55548i) q^{55} +(3.28250 - 4.91261i) q^{56} +(0.292725 + 1.46655i) q^{57} +(-9.66877 + 6.46046i) q^{58} +(5.62864 - 2.33146i) q^{59} +(-0.438969 - 0.438389i) q^{60} +(3.24818 + 4.86125i) q^{61} +(0.819979 - 4.12231i) q^{62} +(-1.27070 - 6.34431i) q^{63} +(5.28702 - 5.28702i) q^{64} +(2.63129 + 13.2284i) q^{65} +(-0.00274973 - 4.15313i) q^{66} -7.19481i q^{67} +(0.508927 + 1.22636i) q^{69} +(-8.84742 - 3.66472i) q^{70} +(2.13271 - 0.424222i) q^{71} +(-0.0108825 - 8.21831i) q^{72} +(10.4594 + 6.98874i) q^{73} +(-3.39901 - 0.676105i) q^{74} +(4.14423 - 6.21118i) q^{75} +(-0.0387851 - 0.0936354i) q^{76} +(-1.36006 - 3.28348i) q^{77} +(6.18308 - 9.26691i) q^{78} +(5.84360 + 1.16236i) q^{79} +(-10.7092 - 7.15567i) q^{80} +(-6.38079 - 6.34708i) q^{81} +(-4.39502 + 0.874225i) q^{82} +(-11.9985 - 4.96993i) q^{83} +(0.168074 + 0.405009i) q^{84} -16.6560i q^{86} +(0.00916431 + 13.8416i) q^{87} +(-0.880669 - 4.42742i) q^{88} +(3.42023 - 3.42023i) q^{89} +(-13.0610 + 2.61599i) q^{90} +(1.85984 - 9.35006i) q^{91} +(-0.0499925 - 0.0748190i) q^{92} +(-3.53997 - 3.53529i) q^{93} +(4.20619 - 1.74226i) q^{94} +(2.19061 - 1.46372i) q^{95} +(0.224837 + 1.12643i) q^{96} +(1.97085 - 2.94959i) q^{97} +(-2.41627 - 2.41627i) q^{98} +(-4.11402 - 2.74103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 16 q^{4} + 16 q^{6} - 24 q^{9} - 32 q^{10} - 40 q^{12} + 16 q^{13} - 16 q^{15} + 16 q^{18} - 32 q^{19} - 16 q^{21} + 32 q^{22} - 16 q^{24} + 16 q^{27} - 32 q^{28} + 8 q^{30} + 24 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 16 * q^4 + 16 * q^6 - 24 * q^9 - 32 * q^10 - 40 * q^12 + 16 * q^13 - 16 * q^15 + 16 * q^18 - 32 * q^19 - 16 * q^21 + 32 * q^22 - 16 * q^24 + 16 * q^27 - 32 * q^28 + 8 * q^30 + 24 * q^36 + 96 * q^37 - 48 * q^39 - 80 * q^40 + 24 * q^42 + 32 * q^43 + 40 * q^45 + 64 * q^46 - 48 * q^48 + 64 * q^49 - 96 * q^52 - 48 * q^54 + 48 * q^55 + 8 * q^57 - 48 * q^60 + 64 * q^61 - 16 * q^64 - 120 * q^66 + 80 * q^69 - 64 * q^72 + 144 * q^73 - 8 * q^75 - 32 * q^76 + 40 * q^78 - 64 * q^79 - 48 * q^81 + 32 * q^82 + 56 * q^87 - 32 * q^88 - 24 * q^90 - 48 * q^91 + 56 * q^93 + 48 * q^94 + 72 * q^96 + 32 * q^97 + 16 * q^99

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