LMFDB - Embedded newform 357.2.bj.a.206.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(26,357)] 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("357.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 20, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bj (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$352$
Relative dimension:	$44$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			206.11
Character	$\chi$	$=$	357.206
Dual form			357.2.bj.a.26.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50134 - 0.402282i) q^{2} +(-1.59673 - 0.671159i) q^{3} +(0.360133 + 0.207923i) q^{4} +(1.05067 - 1.36926i) q^{5} +(2.12724 + 1.64997i) q^{6} +(-2.10371 + 1.60449i) q^{7} +(1.74107 + 1.74107i) q^{8} +(2.09909 + 2.14332i) q^{9} +(-2.12823 + 1.63305i) q^{10} +(2.31944 + 3.02276i) q^{11} +(-0.435486 - 0.573704i) q^{12} -5.62118 q^{13} +(3.80384 - 1.56260i) q^{14} +(-2.59662 + 1.48117i) q^{15} +(-2.32938 - 4.03461i) q^{16} +(-0.191526 - 4.11865i) q^{17} +(-2.28922 - 4.06227i) q^{18} +(6.01033 + 1.61046i) q^{19} +(0.663080 - 0.274657i) q^{20} +(4.43593 - 1.15001i) q^{21} +(-2.26627 - 5.47125i) q^{22} +(7.22294 - 0.950918i) q^{23} +(-1.61149 - 3.94856i) q^{24} +(0.523135 + 1.95237i) q^{25} +(8.43930 + 2.26130i) q^{26} +(-1.91317 - 4.83113i) q^{27} +(-1.09123 + 0.140420i) q^{28} +(1.05467 - 0.436859i) q^{29} +(4.49425 - 1.17916i) q^{30} +(0.572819 + 0.0754130i) q^{31} +(0.599584 + 2.23768i) q^{32} +(-1.67477 - 6.38324i) q^{33} +(-1.36932 + 6.26054i) q^{34} +(-0.0133436 + 4.56631i) q^{35} +(0.310307 + 1.20833i) q^{36} +(4.10888 + 3.15285i) q^{37} +(-8.37568 - 4.83570i) q^{38} +(8.97551 + 3.77271i) q^{39} +(4.21326 - 0.554686i) q^{40} +(-0.127191 + 0.307067i) q^{41} +(-7.12246 - 0.0579404i) q^{42} +(4.17249 - 4.17249i) q^{43} +(0.206808 + 1.57086i) q^{44} +(5.14020 - 0.622277i) q^{45} +(-11.2266 - 1.47801i) q^{46} +(3.11556 - 1.79877i) q^{47} +(1.01153 + 8.00556i) q^{48} +(1.85122 - 6.75078i) q^{49} -3.14161i q^{50} +(-2.45846 + 6.70492i) q^{51} +(-2.02438 - 1.16877i) q^{52} +(-1.71559 - 6.40267i) q^{53} +(0.928841 + 8.02279i) q^{54} +6.57589 q^{55} +(-6.45625 - 0.869183i) q^{56} +(-8.51600 - 6.60537i) q^{57} +(-1.75916 + 0.231597i) q^{58} +(2.65000 + 9.88994i) q^{59} +(-1.24310 - 0.00647972i) q^{60} +(-0.507657 - 3.85604i) q^{61} +(-0.829657 - 0.343655i) q^{62} +(-7.85482 - 1.14096i) q^{63} +5.71681i q^{64} +(-5.90599 + 7.69684i) q^{65} +(-0.0534659 + 10.2571i) q^{66} +(0.153162 - 0.265285i) q^{67} +(0.787389 - 1.52309i) q^{68} +(-12.1713 - 3.32938i) q^{69} +(1.85698 - 6.85020i) q^{70} +(-0.0134596 - 0.0324944i) q^{71} +(-0.0770056 + 7.38635i) q^{72} +(-1.30872 + 9.94070i) q^{73} +(-4.90048 - 6.38643i) q^{74} +(0.475044 - 3.46851i) q^{75} +(1.82967 + 1.82967i) q^{76} +(-9.72943 - 2.63749i) q^{77} +(-11.9576 - 9.27480i) q^{78} +(0.683817 + 5.19411i) q^{79} +(-7.97181 - 1.04951i) q^{80} +(-0.187637 + 8.99804i) q^{81} +(0.314485 - 0.409844i) q^{82} +(10.5784 + 10.5784i) q^{83} +(1.83664 + 0.508175i) q^{84} +(-5.84072 - 4.06508i) q^{85} +(-7.94283 + 4.58579i) q^{86} +(-1.97723 - 0.0103064i) q^{87} +(-1.22452 + 9.30116i) q^{88} +(11.7934 - 6.80891i) q^{89} +(-7.96750 - 1.13356i) q^{90} +(11.8254 - 9.01914i) q^{91} +(2.79894 + 1.15936i) q^{92} +(-0.864022 - 0.504867i) q^{93} +(-5.40112 + 1.44722i) q^{94} +(8.51999 - 6.53762i) q^{95} +(0.544465 - 3.97539i) q^{96} +(-11.2348 + 4.65360i) q^{97} +(-5.49502 + 9.39048i) q^{98} +(-1.61001 + 11.3163i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 352 q - 12 q^{3} - 16 q^{7} - 4 q^{9} - 24 q^{10} - 12 q^{12} - 24 q^{15} + 112 q^{16} - 24 q^{18} - 24 q^{19} - 80 q^{22} - 60 q^{24} - 8 q^{25} - 72 q^{28} - 24 q^{31} + 24 q^{33} - 64 q^{36} - 40 q^{37}+ \cdots + 256 q^{99}+O(q^{100}) $ 352 * q - 12 * q^3 - 16 * q^7 - 4 * q^9 - 24 * q^10 - 12 * q^12 - 24 * q^15 + 112 * q^16 - 24 * q^18 - 24 * q^19 - 80 * q^22 - 60 * q^24 - 8 * q^25 - 72 * q^28 - 24 * q^31 + 24 * q^33 - 64 * q^36 - 40 * q^37 - 24 * q^39 - 24 * q^40 + 68 * q^42 - 48 * q^45 - 40 * q^46 + 48 * q^49 - 20 * q^51 - 240 * q^52 - 16 * q^57 - 8 * q^58 + 44 * q^60 - 24 * q^61 + 88 * q^63 - 12 * q^66 - 16 * q^67 + 64 * q^70 - 120 * q^73 - 156 * q^75 - 176 * q^78 - 24 * q^79 + 120 * q^82 - 104 * q^84 + 112 * q^85 + 132 * q^87 - 24 * q^88 - 96 * q^91 - 8 * q^93 - 120 * q^94 + 60 * q^96 + 256 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{8}\right)$	$-1$

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 $

$2$	−1.50134	−	0.402282i	−1.06161	−	0.284457i	−0.314566	−	0.949236i	$-0.601859\pi$
$2$	−1.50134	−	0.402282i	−1.06161	−	0.284457i	−0.747040	+	0.664779i	$0.768526\pi$
$3$	−1.59673	−	0.671159i	−0.921872	−	0.387494i
$3$	−1.59673	−	0.671159i	−0.921872	−	0.387494i
$4$	0.360133	+	0.207923i	0.180067	+	0.103962i
$5$	1.05067	−	1.36926i	0.469872	−	0.612350i	−0.496956	−	0.867776i	$-0.665549\pi$
$5$	1.05067	−	1.36926i	0.469872	−	0.612350i	0.966829	+	0.255426i	$0.0822157\pi$
$6$	2.12724	+	1.64997i	0.868440	+	0.673599i
$7$	−2.10371	+	1.60449i	−0.795129	+	0.606441i
$7$	−2.10371	+	1.60449i	−0.795129	+	0.606441i
$8$	1.74107	+	1.74107i	0.615562	+	0.615562i
$9$	2.09909	+	2.14332i	0.699697	+	0.714440i
$10$	−2.12823	+	1.63305i	−0.673006	+	0.516416i
$11$	2.31944	+	3.02276i	0.699338	+	0.911395i	0.999091	−	0.0426214i	$-0.0135709\pi$
$11$	2.31944	+	3.02276i	0.699338	+	0.911395i	−0.299753	+	0.954017i	$0.596904\pi$
$12$	−0.435486	−	0.573704i	−0.125714	−	0.165614i
$13$	−5.62118			−1.55904			−0.779518	−	0.626380i	$-0.784536\pi$
$13$	−5.62118			−1.55904			−0.779518	+	0.626380i	$0.784536\pi$
$14$	3.80384	−	1.56260i	1.01662	−	0.417621i
$15$	−2.59662	+	1.48117i	−0.670444	+	0.382435i
$16$	−2.32938	−	4.03461i	−0.582346	−	1.00865i
$17$	−0.191526	−	4.11865i	−0.0464519	−	0.998921i
$17$	−0.191526	−	4.11865i	−0.0464519	−	0.998921i
$18$	−2.28922	−	4.06227i	−0.539575	−	0.957487i
$19$	6.01033	+	1.61046i	1.37887	+	0.369466i	0.870709	−	0.491799i	$-0.163660\pi$
$19$	6.01033	+	1.61046i	1.37887	+	0.369466i	0.508157	+	0.861265i	$0.330327\pi$
$20$	0.663080	−	0.274657i	0.148269	−	0.0614151i
$21$	4.43593	−	1.15001i	0.967999	−	0.250953i
$22$	−2.26627	−	5.47125i	−0.483169	−	1.16647i
$23$	7.22294	−	0.950918i	1.50609	−	0.198280i	0.668141	−	0.744035i	$-0.267090\pi$
$23$	7.22294	−	0.950918i	1.50609	−	0.198280i	0.837945	+	0.545755i	$0.183757\pi$
$24$	−1.61149	−	3.94856i	−0.328943	−	0.805996i
$25$	0.523135	+	1.95237i	0.104627	+	0.390474i
$26$	8.43930	+	2.26130i	1.65508	+	0.443478i
$27$	−1.91317	−	4.83113i	−0.368190	−	0.929751i
$28$	−1.09123	+	0.140420i	−0.206223	+	0.0265369i
$29$	1.05467	−	0.436859i	0.195847	−	0.0811227i	−0.282604	−	0.959237i	$-0.591198\pi$
$29$	1.05467	−	0.436859i	0.195847	−	0.0811227i	0.478451	+	0.878114i	$0.341198\pi$
$30$	4.49425	−	1.17916i	0.820534	−	0.215284i
$31$	0.572819	+	0.0754130i	0.102881	+	0.0135446i	0.181791	−	0.983337i	$-0.441811\pi$
$31$	0.572819	+	0.0754130i	0.102881	+	0.0135446i	−0.0789098	+	0.996882i	$0.525144\pi$
$32$	0.599584	+	2.23768i	0.105993	+	0.395570i
$33$	−1.67477	−	6.38324i	−0.291540	−	1.11118i
$34$	−1.36932	+	6.26054i	−0.234836	+	1.07367i
$35$	−0.0133436	+	4.56631i	−0.00225549	+	0.771846i
$36$	0.310307	+	1.20833i	0.0517178	+	0.201388i
$37$	4.10888	+	3.15285i	0.675496	+	0.518326i	0.888588	−	0.458706i	$-0.151687\pi$
$37$	4.10888	+	3.15285i	0.675496	+	0.518326i	−0.213092	+	0.977032i	$0.568354\pi$
$38$	−8.37568	−	4.83570i	−1.35872	−	0.784454i
$39$	8.97551	+	3.77271i	1.43723	+	0.604117i
$40$	4.21326	−	0.554686i	0.666175	−	0.0877036i
$41$	−0.127191	+	0.307067i	−0.0198639	+	0.0479558i	−0.933500	−	0.358577i	$-0.883262\pi$
$41$	−0.127191	+	0.307067i	−0.0198639	+	0.0479558i	0.913636	+	0.406532i	$0.133262\pi$
$42$	−7.12246	−	0.0579404i	−1.09902	−	0.00894039i
$43$	4.17249	−	4.17249i	0.636298	−	0.636298i	−0.313342	−	0.949640i	$-0.601449\pi$
$43$	4.17249	−	4.17249i	0.636298	−	0.636298i	0.949640	+	0.313342i	$0.101449\pi$
$44$	0.206808	+	1.57086i	0.0311775	+	0.236816i
$45$	5.14020	−	0.622277i	0.766255	−	0.0927636i
$46$	−11.2266	−	1.47801i	−1.65527	−	0.217921i
$47$	3.11556	−	1.79877i	0.454451	−	0.262377i	−0.255257	−	0.966873i	$-0.582160\pi$
$47$	3.11556	−	1.79877i	0.454451	−	0.262377i	0.709708	+	0.704496i	$0.248827\pi$
$48$	1.01153	+	8.00556i	0.146002	+	1.15550i
$49$	1.85122	−	6.75078i	0.264460	−	0.964397i
$50$		−	3.14161i		−	0.444291i
$51$	−2.45846	+	6.70492i	−0.344253	+	0.938877i
$52$	−2.02438	−	1.16877i	−0.280731	−	0.162080i
$53$	−1.71559	−	6.40267i	−0.235654	−	0.879474i	−0.977853	−	0.209294i	$-0.932884\pi$
$53$	−1.71559	−	6.40267i	−0.235654	−	0.879474i	0.742199	−	0.670180i	$-0.233783\pi$
$54$	0.928841	+	8.02279i	0.126399	+	1.09176i
$55$	6.57589			0.886692
$56$	−6.45625	−	0.869183i	−0.862753	−	0.116149i
$57$	−8.51600	−	6.60537i	−1.12797	−	0.874902i
$58$	−1.75916	+	0.231597i	−0.230989	+	0.0304102i
$59$	2.65000	+	9.88994i	0.345001	+	1.28756i	0.892611	+	0.450827i	$0.148871\pi$
$59$	2.65000	+	9.88994i	0.345001	+	1.28756i	−0.547610	+	0.836733i	$0.684462\pi$
$60$	−1.24310	−	0.00647972i	−0.160483	−	0.000836529i
$61$	−0.507657	−	3.85604i	−0.0649988	−	0.493715i	−0.992720	−	0.120442i	$-0.961569\pi$
$61$	−0.507657	−	3.85604i	−0.0649988	−	0.493715i	0.927722	−	0.373273i	$-0.121765\pi$
$62$	−0.829657	−	0.343655i	−0.105367	−	0.0436442i
$63$	−7.85482	−	1.14096i	−0.989614	−	0.143747i
$64$			5.71681i			0.714602i
$65$	−5.90599	+	7.69684i	−0.732548	+	0.954675i
$66$	−0.0534659	+	10.2571i	−0.00658120	+	1.26257i
$67$	0.153162	−	0.265285i	0.0187118	−	0.0324097i	−0.856518	−	0.516117i	$-0.827377\pi$
$67$	0.153162	−	0.265285i	0.0187118	−	0.0324097i	0.875230	+	0.483708i	$0.160710\pi$
$68$	0.787389	−	1.52309i	0.0954849	−	0.184702i
$69$	−12.1713	−	3.32938i	−1.46525	−	0.400810i
$70$	1.85698	−	6.85020i	0.221951	−	0.818755i
$71$	−0.0134596	−	0.0324944i	−0.00159736	−	0.00385638i	0.923079	−	0.384611i	$-0.125664\pi$
$71$	−0.0134596	−	0.0324944i	−0.00159736	−	0.00385638i	−0.924676	+	0.380754i	$0.875664\pi$
$72$	−0.0770056	+	7.38635i	−0.00907520	+	0.870489i
$73$	−1.30872	+	9.94070i	−0.153174	+	1.16347i	0.726250	+	0.687431i	$0.241262\pi$
$73$	−1.30872	+	9.94070i	−0.153174	+	1.16347i	−0.879424	+	0.476040i	$0.842072\pi$
$74$	−4.90048	−	6.38643i	−0.569669	−	0.742407i
$75$	0.475044	−	3.46851i	0.0548533	−	0.400509i
$76$	1.82967	+	1.82967i	0.209878	+	0.209878i
$77$	−9.72943	−	2.63749i	−1.10877	−	0.300570i
$78$	−11.9576	−	9.27480i	−1.35393	−	1.05016i
$79$	0.683817	+	5.19411i	0.0769355	+	0.584383i	0.985878	+	0.167462i	$0.0535573\pi$
$79$	0.683817	+	5.19411i	0.0769355	+	0.584383i	−0.908943	+	0.416920i	$0.863109\pi$
$80$	−7.97181	−	1.04951i	−0.891276	−	0.117339i
$81$	−0.187637	+	8.99804i	−0.0208485	+	0.999783i
$82$	0.314485	−	0.409844i	0.0347290	−	0.0452597i
$83$	10.5784	+	10.5784i	1.16113	+	1.16113i	0.984229	+	0.176897i	$0.0566059\pi$
$83$	10.5784	+	10.5784i	1.16113	+	1.16113i	0.176897	+	0.984229i	$0.443394\pi$
$84$	1.83664	+	0.508175i	0.200394	+	0.0554464i
$85$	−5.84072	−	4.06508i	−0.633515	−	0.440920i
$86$	−7.94283	+	4.58579i	−0.856497	+	0.494499i
$87$	−1.97723	−	0.0103064i	−0.211981	−	0.00110496i
$88$	−1.22452	+	9.30116i	−0.130534	+	0.991507i
$89$	11.7934	−	6.80891i	1.25010	−	0.721743i	0.278967	−	0.960301i	$-0.410008\pi$
$89$	11.7934	−	6.80891i	1.25010	−	0.721743i	0.971128	+	0.238558i	$0.0766746\pi$
$90$	−7.96750	−	1.13356i	−0.839848	−	0.119488i
$91$	11.8254	−	9.01914i	1.23963	−	0.945463i
$92$	2.79894	+	1.15936i	0.291810	+	0.120871i
$93$	−0.864022	−	0.504867i	−0.0895949	−	0.0523522i
$94$	−5.40112	+	1.44722i	−0.557083	+	0.149270i
$95$	8.51999	−	6.53762i	0.874133	−	0.670746i
$96$	0.544465	−	3.97539i	0.0555692	−	0.405736i
$97$	−11.2348	+	4.65360i	−1.14072	+	0.472502i	−0.871412	−	0.490552i	$-0.836795\pi$
$97$	−11.2348	+	4.65360i	−1.14072	+	0.472502i	−0.269309	+	0.963054i	$0.586795\pi$
$98$	−5.49502	+	9.39048i	−0.555081	+	0.948582i
$99$	−1.61001	+	11.3163i	−0.161812	+	1.13734i
$100$	−0.217544	+	0.811885i	−0.0217544	+	0.0811885i
$101$	5.51638	−	9.55464i	0.548900	−	0.950723i	−0.449450	−	0.893305i	$-0.648380\pi$
$101$	5.51638	−	9.55464i	0.548900	−	0.950723i	0.998350	−	0.0574172i	$-0.0182865\pi$
$102$	6.38825	−	9.07736i	0.632531	−	0.898793i
$103$	−5.57225	+	3.21714i	−0.549050	+	0.316994i	−0.748739	−	0.662865i	$-0.769340\pi$
$103$	−5.57225	+	3.21714i	−0.549050	+	0.316994i	0.199689	+	0.979859i	$0.436007\pi$
$104$	−9.78689	−	9.78689i	−0.959684	−	0.959684i
$105$	3.08602	−	7.28220i	0.301165	−	0.710670i
$106$			10.3027i			1.00069i
$107$	11.1300	+	8.54037i	1.07598	+	0.825628i	0.985399	−	0.170261i	$-0.0544610\pi$
$107$	11.1300	+	8.54037i	1.07598	+	0.825628i	0.0905809	+	0.995889i	$0.471128\pi$
$108$	0.315506	−	2.13764i	0.0303596	−	0.205695i
$109$	8.12405	+	10.5875i	0.778143	+	1.01410i	0.999245	+	0.0388452i	$0.0123679\pi$
$109$	8.12405	+	10.5875i	0.778143	+	1.01410i	−0.221102	+	0.975251i	$0.570965\pi$
$110$	−9.87263	−	2.64536i	−0.941318	−	0.252225i
$111$	−4.44470	−	7.79197i	−0.421873	−	0.739581i
$112$	11.3738	+	4.75019i	1.07473	+	0.448850i
$113$	−4.93418	+	11.9122i	−0.464169	+	1.12060i	0.502501	+	0.864577i	$0.332413\pi$
$113$	−4.93418	+	11.9122i	−0.464169	+	1.12060i	−0.966670	+	0.256026i	$0.917587\pi$
$114$	10.1282	+	13.3427i	0.948590	+	1.24966i
$115$	6.28685	−	10.8891i	0.586252	−	1.01542i
$116$	0.470655	+	0.0619629i	0.0436992	+	0.00575311i
$117$	−11.7994	−	12.0480i	−1.09085	−	1.11384i
$118$		−	15.9142i		−	1.46502i
$119$	7.01126	+	8.35717i	0.642721	+	0.766100i
$120$	−7.09972	−	1.94208i	−0.648113	−	0.177287i
$121$	−0.910233	+	3.39704i	−0.0827485	+	0.308822i
$122$	−0.789051	+	5.99344i	−0.0714373	+	0.542620i
$123$	0.409181	−	0.404937i	0.0368946	−	0.0365119i
$124$	0.190611	+	0.146261i	0.0171174	+	0.0131346i
$125$	11.1956	+	4.63736i	1.00136	+	0.414778i
$126$	11.3338	+	4.87282i	1.00969	+	0.434105i
$127$	6.79701	−	6.79701i	0.603137	−	0.603137i	−0.338007	−	0.941144i	$-0.609753\pi$
$127$	6.79701	−	6.79701i	0.603137	−	0.603137i	0.941144	+	0.338007i	$0.109753\pi$
$128$	3.49894	−	13.0582i	0.309266	−	1.15420i
$129$	−9.46273	+	3.86193i	−0.833147	+	0.340024i
$130$	11.9632	−	9.17968i	1.04924	−	0.805111i
$131$	1.05705	−	1.37758i	0.0923549	−	0.120359i	−0.744890	−	0.667187i	$-0.767498\pi$
$131$	1.05705	−	1.37758i	0.0923549	−	0.120359i	0.837245	+	0.546828i	$0.184165\pi$
$132$	0.724082	−	2.64704i	0.0630233	−	0.230395i
$133$	−15.2280	+	6.25557i	−1.32043	+	0.542427i
$134$	−0.336668	+	0.336668i	−0.0290837	+	0.0290837i
$135$	−8.62515	−	2.45628i	−0.742335	−	0.211403i
$136$	6.83742	−	7.50434i	0.586304	−	0.643492i
$137$	−3.26415	−	1.88456i	−0.278875	−	0.161009i	0.354039	−	0.935231i	$-0.384808\pi$
$137$	−3.26415	−	1.88456i	−0.278875	−	0.161009i	−0.632914	+	0.774222i	$0.718141\pi$
$138$	16.9339	+	9.89482i	1.44151	+	0.842303i
$139$	1.05586	+	2.54907i	0.0895569	+	0.216209i	0.962311	−	0.271950i	$-0.0876685\pi$
$139$	1.05586	+	2.54907i	0.0895569	+	0.216209i	−0.872755	+	0.488159i	$0.837669\pi$
$140$	−0.954246	+	1.64170i	−0.0806485	+	0.138749i
$141$	−6.18196	+	0.781111i	−0.520615	+	0.0657814i
$142$	0.00713552	+	0.0541996i	0.000598799	+	0.00454833i
$143$	−13.0380	−	16.9915i	−1.09029	−	1.42090i
$144$	3.75787	−	13.4616i	0.313156	−	1.12180i
$145$	0.509936	−	1.90311i	0.0423479	−	0.158044i
$146$	5.96379	−	14.3979i	0.493567	−	1.19158i
$147$	−7.48674	+	9.53670i	−0.617496	+	0.786574i
$148$	0.824194	+	1.98978i	0.0677483	+	0.163559i
$149$	2.62092	+	4.53956i	0.214714	+	0.371896i	0.953184	−	0.302391i	$-0.0977847\pi$
$149$	2.62092	+	4.53956i	0.214714	+	0.371896i	−0.738470	+	0.674286i	$0.764451\pi$
$150$	−2.10852	+	5.01630i	−0.172160	+	0.409580i
$151$	−22.2797	+	5.96983i	−1.81310	+	0.485818i	−0.995894	−	0.0905314i	$-0.971143\pi$
$151$	−22.2797	+	5.96983i	−1.81310	+	0.485818i	−0.817203	+	0.576349i	$0.804477\pi$
$152$	7.66050	+	13.2684i	0.621348	+	1.07621i
$153$	8.42556	−	9.05593i	0.681166	−	0.732129i
$154$	13.5461	+	7.87374i	1.09158	+	0.634484i
$155$	0.705101	−	0.705101i	0.0566351	−	0.0566351i
$156$	2.44795	+	3.22490i	0.195993	+	0.258198i
$157$	6.96329	−	12.0608i	0.555731	−	0.962555i	−0.442115	−	0.896958i	$-0.645772\pi$
$157$	6.96329	−	12.0608i	0.555731	−	0.962555i	0.997846	−	0.0655963i	$-0.0208950\pi$
$158$	1.06286	−	8.07320i	0.0845564	−	0.642269i
$159$	−1.55788	+	11.3748i	−0.123548	+	0.902077i
$160$	3.69392	+	1.53007i	0.292030	+	0.120963i
$161$	−13.6692	+	13.5896i	−1.07729	+	1.07101i
$162$	3.90146	−	13.4336i	0.306528	−	1.05544i
$163$	8.94168	−	1.17719i	0.700367	−	0.0922050i	0.228070	−	0.973645i	$-0.426758\pi$
$163$	8.94168	−	1.17719i	0.700367	−	0.0922050i	0.472297	+	0.881440i	$0.343425\pi$
$164$	−0.109652	+	0.0841390i	−0.00856239	+	0.00657015i
$165$	−10.4999	−	4.41347i	−0.817417	−	0.343588i
$166$	−11.6262	−	20.1372i	−0.902369	−	1.56295i
$167$	−3.66532	+	1.51822i	−0.283631	+	0.117484i	−0.519964	−	0.854188i	$-0.674054\pi$
$167$	−3.66532	+	1.51822i	−0.283631	+	0.117484i	0.236333	+	0.971672i	$0.424054\pi$
$168$	9.72553	+	5.72102i	0.750341	+	0.441387i
$169$	18.5977			1.43059
$170$	7.13358	+	8.45268i	0.547121	+	0.648291i
$171$	9.16450	+	16.2626i	0.700827	+	1.24363i
$172$	2.37021	−	0.635095i	0.180727	−	0.0484256i
$173$	−5.85278	−	4.49100i	−0.444979	−	0.341444i	0.361843	−	0.932239i	$-0.382148\pi$
$173$	−5.85278	−	4.49100i	−0.444979	−	0.341444i	−0.806822	+	0.590795i	$0.798814\pi$
$174$	2.96434	+	0.810876i	0.224726	+	0.0614724i
$175$	−4.23308	−	3.26786i	−0.319991	−	0.247027i
$176$	6.79277	−	16.3992i	0.512024	−	1.23614i
$177$	2.40639	−	17.5701i	0.180875	−	1.32065i
$178$	−20.4449	+	5.47821i	−1.53241	+	0.410609i
$179$	4.46234	−	1.19568i	0.333531	−	0.0893694i	−0.0881669	−	0.996106i	$-0.528101\pi$
$179$	4.46234	−	1.19568i	0.333531	−	0.0893694i	0.421698	+	0.906736i	$0.361434\pi$
$180$	1.98054	+	0.844663i	0.147621	+	0.0629575i
$181$	8.07877	−	19.5039i	0.600490	−	1.44971i	−0.272588	−	0.962131i	$-0.587880\pi$
$181$	8.07877	−	19.5039i	0.600490	−	1.44971i	0.873078	−	0.487580i	$-0.162120\pi$
$182$	−21.3821	+	8.78364i	−1.58495	+	0.651087i
$183$	−1.77742	+	6.49777i	−0.131391	+	0.480329i
$184$	14.2313	+	10.9200i	1.04914	+	0.805036i
$185$	8.63413	−	2.31351i	0.634794	−	0.170092i
$186$	1.09409	+	1.10556i	0.0802226	+	0.0810633i
$187$	12.0055	−	10.1319i	0.877926	−	0.740919i
$188$	1.49602			0.109109
$189$	11.7763	+	7.09364i	0.856597	+	0.515986i
$190$	−15.4214	+	6.38774i	−1.11878	+	0.463415i
$191$	−11.2237	−	19.4399i	−0.812115	−	1.40662i	−0.911381	−	0.411564i	$-0.864983\pi$
$191$	−11.2237	−	19.4399i	−0.812115	−	1.40662i	0.0992660	−	0.995061i	$-0.468351\pi$
$192$	3.83689	−	9.12821i	0.276904	−	0.658771i
$193$	−2.02346	+	1.55266i	−0.145652	+	0.111763i	−0.679017	−	0.734122i	$-0.737594\pi$
$193$	−2.02346	+	1.55266i	−0.145652	+	0.111763i	0.533365	+	0.845885i	$0.320927\pi$
$194$	18.7393	−	2.46707i	1.34540	−	0.177126i
$195$	14.5961	−	8.32591i	1.04525	−	0.596231i
$196$	2.07033	−	2.04627i	0.147881	−	0.146162i
$197$	6.95358	+	2.88027i	0.495422	+	0.205211i	0.616383	−	0.787447i	$-0.288597\pi$
$197$	6.95358	+	2.88027i	0.495422	+	0.205211i	−0.120961	+	0.992657i	$0.538597\pi$
$198$	6.96954	−	16.3420i	0.495304	−	1.16137i
$199$	0.656612	−	4.98746i	0.0465460	−	0.353552i	−0.952285	−	0.305211i	$-0.901273\pi$
$199$	0.656612	−	4.98746i	0.0465460	−	0.353552i	0.998831	−	0.0483413i	$-0.0153935\pi$
$200$	−2.48840	+	4.31003i	−0.175956	+	0.304765i
$201$	−0.422607	+	0.320792i	−0.0298084	+	0.0226269i
$202$	−12.1256	+	12.1256i	−0.853155	+	0.853155i
$203$	−1.51779	+	2.61123i	−0.106528	+	0.183273i
$204$	−2.27948	+	1.90350i	−0.159596	+	0.133271i
$205$	0.286817	+	0.496782i	0.0200322	+	0.0346968i
$206$	9.66002	−	2.58840i	0.673046	−	0.180342i
$207$	17.1997	+	13.4850i	1.19546	+	0.937272i
$208$	13.0939	+	22.6793i	0.907898	+	1.57252i
$209$	9.07259	+	21.9032i	0.627564	+	1.51507i
$210$	−7.56266	+	9.69159i	−0.521873	+	0.668783i
$211$	−7.16606	+	17.3004i	−0.493332	+	1.19101i	0.459682	+	0.888083i	$0.347963\pi$
$211$	−7.16606	+	17.3004i	−0.493332	+	1.19101i	−0.953014	+	0.302925i	$0.902037\pi$
$212$	0.713421	−	2.66253i	0.0489980	−	0.182863i
$213$	−0.000317540		0.0609183i	−2.17575e−5		0.00417405i
$214$	−13.2743	−	17.2994i	−0.907412	−	1.18256i
$215$	−1.32931	−	10.0971i	−0.0906580	−	0.688616i
$216$	5.08037	−	11.7423i	0.345675	−	0.798963i
$217$	−1.32605	+	0.760435i	−0.0900178	+	0.0516217i
$218$	−7.93780	−	19.1635i	−0.537615	−	1.29792i
$219$	8.76146	−	14.9942i	0.592045	−	1.01322i
$220$	2.36820	+	1.36728i	0.159664	+	0.0921819i
$221$	1.07660	+	23.1517i	0.0724202	+	1.55735i
$222$	3.53843	+	13.4864i	0.237484	+	0.905148i
$223$	3.90273	−	3.90273i	0.261346	−	0.261346i	−0.564255	−	0.825601i	$-0.690836\pi$
$223$	3.90273	−	3.90273i	0.261346	−	0.261346i	0.825601	+	0.564255i	$0.190836\pi$
$224$	−4.85169	−	3.74541i	−0.324167	−	0.250251i
$225$	−3.08644	+	5.21944i	−0.205763	+	0.347963i
$226$	12.1999	−	15.8993i	0.811527	−	1.05760i
$227$	−22.8423	+	17.5275i	−1.51610	+	1.16334i	−0.578467	+	0.815706i	$0.696349\pi$
$227$	−22.8423	+	17.5275i	−1.51610	+	1.16334i	−0.937630	+	0.347636i	$0.886984\pi$
$228$	−1.69349	−	4.14949i	−0.112154	−	0.274807i
$229$	−4.36194	+	16.2790i	−0.288245	+	1.07574i	0.658190	+	0.752852i	$0.271322\pi$
$229$	−4.36194	+	16.2790i	−0.288245	+	1.07574i	−0.946435	+	0.322893i	$0.895344\pi$
$230$	−13.8192	+	13.8192i	−0.911210	+	0.911210i
$231$	13.7651	+	10.7414i	0.905676	+	0.706729i
$232$	2.59686	+	1.07566i	0.170492	+	0.0706202i
$233$	−9.07998	−	6.96732i	−0.594850	−	0.456444i	0.266938	−	0.963714i	$-0.413988\pi$
$233$	−9.07998	−	6.96732i	−0.594850	−	0.456444i	−0.861787	+	0.507270i	$0.830655\pi$
$234$	12.8682	+	22.8348i	0.841218	+	1.49276i
$235$	0.810439	−	6.15590i	0.0528672	−	0.401566i
$236$	−1.10199	+	4.11270i	−0.0717337	+	0.267714i
$237$	2.39420	−	8.75254i	0.155520	−	0.568538i
$238$	−7.16433	−	15.3674i	−0.464395	−	0.996123i
$239$			0.415611i			0.0268836i	0.999910	+	0.0134418i	$0.00427879\pi$
$239$			0.415611i			0.0268836i	−0.999910	+	0.0134418i	$0.995721\pi$
$240$	12.0244	+	7.02614i	0.776174	+	0.453535i
$241$	−3.26744	−	0.430167i	−0.210475	−	0.0277095i	0.0245515	−	0.999699i	$-0.492184\pi$
$241$	−3.26744	−	0.430167i	−0.210475	−	0.0277095i	−0.235026	+	0.971989i	$0.575518\pi$
$242$	2.73314	−	4.73393i	0.175693	−	0.304309i
$243$	6.33873	−	14.2415i	0.406629	−	0.913593i
$244$	0.618935	−	1.49424i	0.0396233	−	0.0956591i
$245$	−7.29852	−	9.62761i	−0.466286	−	0.615085i
$246$	−0.777217	+	0.443341i	−0.0495536	+	0.0282664i
$247$	−33.7852	−	9.05272i	−2.14970	−	0.576011i
$248$	0.866019	+	1.12862i	0.0549923	+	0.0716673i
$249$	−9.79102	−	23.9906i	−0.620481	−	1.52034i
$250$	−14.9428	−	11.4660i	−0.945068	−	0.725176i
$251$		−	11.4335i		−	0.721675i	−0.932629	−	0.360838i	$-0.882491\pi$
$251$		−	11.4335i		−	0.721675i	0.932629	−	0.360838i	$-0.117509\pi$
$252$	−2.59155	−	2.04410i	−0.163252	−	0.128766i
$253$	19.6276	+	19.6276i	1.23398	+	1.23398i
$254$	−12.9389	+	7.47029i	−0.811860	+	0.468728i
$255$	6.59773	+	10.4109i	0.413166	+	0.651955i
$256$	−4.78937	+	8.29544i	−0.299336	+	0.518465i
$257$	3.94739	−	14.7319i	0.246232	−	0.918948i	−0.726529	−	0.687136i	$-0.758868\pi$
$257$	3.94739	−	14.7319i	0.246232	−	0.918948i	0.972760	−	0.231813i	$-0.0744656\pi$
$258$	15.7603	−	1.99137i	0.981196	−	0.123977i
$259$	−13.7026	−	0.0400418i	−0.851440	−	0.00248808i
$260$	−3.72730	+	1.54390i	−0.231157	+	0.0957484i
$261$	3.15018	+	1.34349i	0.194991	+	0.0831599i
$262$	−2.14116	+	1.64297i	−0.132282	+	0.101503i
$263$	20.8668	−	5.59124i	1.28670	−	0.344771i	0.450295	−	0.892880i	$-0.351319\pi$
$263$	20.8668	−	5.59124i	1.28670	−	0.344771i	0.836407	+	0.548109i	$0.184652\pi$
$264$	8.19779	−	14.0296i	0.504539	−	0.863461i
$265$	−10.5694	−	4.37799i	−0.649273	−	0.268938i
$266$	25.3789	−	3.26577i	1.55608	−	0.200237i
$267$	−23.4007	+	2.95675i	−1.43210	+	0.180950i
$268$	0.110318	−	0.0636920i	0.00673873	−	0.00389061i
$269$	0.175791	−	1.33526i	0.0107181	−	0.0814124i	−0.985250	−	0.171122i	$-0.945261\pi$
$269$	0.175791	−	1.33526i	0.0107181	−	0.0814124i	0.995968	+	0.0897099i	$0.0285940\pi$
$270$	11.9611	+	7.15745i	0.727932	+	0.435589i
$271$	−13.6213	+	7.86424i	−0.827433	+	0.477719i	−0.852973	−	0.521955i	$-0.825203\pi$
$271$	−13.6213	+	7.86424i	−0.827433	+	0.477719i	0.0255401	+	0.999674i	$0.491869\pi$
$272$	−16.1710	+	10.3667i	−0.980512	+	0.628571i
$273$	−24.9352	+	6.46443i	−1.50915	+	0.391245i
$274$	4.14247	+	4.14247i	0.250256	+	0.250256i
$275$	−4.68815	+	6.10972i	−0.282706	+	0.368430i
$276$	−3.69103	−	3.72972i	−0.222174	−	0.224502i
$277$	−16.4481	−	2.16543i	−0.988268	−	0.130108i	−0.380974	−	0.924586i	$-0.624411\pi$
$277$	−16.4481	−	2.16543i	−0.988268	−	0.130108i	−0.607293	+	0.794478i	$0.707745\pi$
$278$	−0.559756	−	4.25177i	−0.0335719	−	0.255004i
$279$	1.04076	+	1.38603i	0.0623089	+	0.0829796i
$280$	−7.97350	+	7.92704i	−0.476508	+	0.473731i
$281$	−11.5163	−	11.5163i	−0.687004	−	0.687004i	0.274564	−	0.961569i	$-0.411466\pi$
$281$	−11.5163	−	11.5163i	−0.687004	−	0.687004i	−0.961569	+	0.274564i	$0.911466\pi$
$282$	9.59544	+	1.31418i	0.571400	+	0.0782584i
$283$	−4.48446	−	5.84426i	−0.266574	−	0.347405i	0.640817	−	0.767694i	$-0.278596\pi$
$283$	−4.48446	−	5.84426i	−0.266574	−	0.347405i	−0.907391	+	0.420288i	$0.861929\pi$
$284$	0.00190908	−	0.0145009i	0.000113283	−	0.000860469i
$285$	−17.9919	+	4.72054i	−1.06575	+	0.279621i
$286$	12.7391	+	30.7549i	0.753279	+	1.81858i
$287$	−0.225112	−	0.850058i	−0.0132879	−	0.0501773i
$288$	−3.53748	+	5.98219i	−0.208448	+	0.352504i
$289$	−16.9266	+	1.57766i	−0.995684	+	0.0928036i
$290$	−1.53117	+	2.65207i	−0.0899135	+	0.155735i
$291$	21.0622	+	0.109788i	1.23469	+	0.00643590i
$292$	−2.53821	+	3.30787i	−0.148538	+	0.193578i
$293$			4.34437i			0.253801i	0.991915	+	0.126900i	$0.0405028\pi$
$293$			4.34437i			0.253801i	−0.991915	+	0.126900i	$0.959497\pi$
$294$	15.0766	−	11.3060i	0.879284	−	0.659381i
$295$	16.3261	+	6.76250i	0.950544	+	0.393728i
$296$	1.66451	+	12.6432i	0.0967477	+	0.734872i
$297$	10.1658	−	16.9886i	0.589881	−	0.985777i
$298$	−2.10870	−	7.86977i	−0.122154	−	0.455883i
$299$	−40.6015	+	5.34528i	−2.34804	+	0.309126i
$300$	0.892263	−	1.15035i	0.0515148	−	0.0664157i
$301$	−2.08300	+	15.4724i	−0.120062	+	0.891816i
$302$	35.8509			2.06299
$303$	−15.2208	+	11.5538i	−0.874415	+	0.663749i
$304$	−7.50277	−	28.0007i	−0.430314	−	1.60595i
$305$	−5.81328	−	3.35630i	−0.332867	−	0.192181i
$306$	−16.2927	+	10.2066i	−0.931389	+	0.583470i
$307$		−	5.13070i		−	0.292824i	−0.989224	−	0.146412i	$-0.953227\pi$
$307$		−	5.13070i		−	0.292824i	0.989224	−	0.146412i	$-0.0467726\pi$
$308$	−2.95550	−	2.97282i	−0.168405	−	0.169392i
$309$	11.0566	−	1.39704i	0.628987	−	0.0794745i
$310$	−1.34224	+	0.774945i	−0.0762344	+	0.0440139i
$311$	6.63981	+	0.874147i	0.376509	+	0.0495683i	0.316406	−	0.948624i	$-0.397524\pi$
$311$	6.63981	+	0.874147i	0.376509	+	0.0495683i	0.0601028	+	0.998192i	$0.480857\pi$
$312$	9.05846	+	22.1956i	0.512834	+	1.25658i
$313$	0.102438	+	0.778094i	0.00579014	+	0.0439805i	0.994096	−	0.108504i	$-0.0346060\pi$
$313$	0.102438	+	0.778094i	0.00579014	+	0.0439805i	−0.988306	+	0.152484i	$0.951273\pi$
$314$	−15.3061	+	15.3061i	−0.863773	+	0.863773i
$315$	−9.81506	+	9.55649i	−0.553016	+	0.538447i
$316$	−0.833710	+	2.01275i	−0.0468999	+	0.113226i
$317$	2.37164	−	0.312232i	0.133205	−	0.0175367i	−0.0636290	−	0.997974i	$-0.520267\pi$
$317$	2.37164	−	0.312232i	0.133205	−	0.0175367i	0.196834	+	0.980437i	$0.436934\pi$
$318$	6.91476	−	16.4507i	0.387761	−	0.922507i
$319$	3.76677	+	2.17474i	0.210898	+	0.121762i
$320$	7.82778	+	6.00646i	0.437586	+	0.335772i
$321$	−12.0397	−	21.1067i	−0.671990	−	1.17806i
$322$	25.9890	−	14.9037i	1.44831	−	0.830549i
$323$	5.48181	−	25.0629i	0.305016	−	1.39454i
$324$	−1.93848	+	3.20148i	−0.107693	+	0.177860i
$325$	−2.94064	−	10.9746i	−0.163117	−	0.608762i
$326$	−13.8980	−	1.82971i	−0.769742	−	0.101338i
$327$	−5.86604	−	22.3579i	−0.324393	−	1.23639i
$328$	−0.756075	+	0.313176i	−0.0417473	+	0.0172923i
$329$	−3.66813	+	8.78297i	−0.202231	+	0.484221i
$330$	13.9885	+	10.8500i	0.770039	+	0.597275i
$331$	11.6925	+	3.13300i	0.642679	+	0.172205i	0.565417	−	0.824806i	$-0.308715\pi$
$331$	11.6925	+	3.13300i	0.642679	+	0.172205i	0.0772623	+	0.997011i	$0.475382\pi$
$332$	1.61014	+	6.00911i	0.0883677	+	0.329793i
$333$	1.86734	+	15.4248i	0.102329	+	0.845272i
$334$	6.11364	−	0.804875i	0.334523	−	0.0440408i
$335$	−0.202320	−	0.488445i	−0.0110539	−	0.0266866i
$336$	−14.9728	−	15.2184i	−0.816834	−	0.830233i
$337$	−5.05088	+	2.09214i	−0.275139	+	0.113966i	−0.515987	−	0.856597i	$-0.672575\pi$
$337$	−5.05088	+	2.09214i	−0.275139	+	0.113966i	0.240848	+	0.970563i	$0.422575\pi$
$338$	−27.9215	−	7.48153i	−1.51873	−	0.406942i
$339$	15.8735	−	15.7089i	0.862131	−	0.853190i
$340$	−1.25821	−	2.67839i	−0.0682362	−	0.145256i
$341$	1.10066	+	1.90641i	0.0596043	+	0.103238i
$342$	−7.21686	−	28.1023i	−0.390243	−	1.51960i
$343$	6.93713	+	17.1720i	0.374570	+	0.927199i
$344$	14.5292			0.783362
$345$	−17.3467	+	13.1675i	−0.933917	+	0.708916i
$346$	6.98036	+	9.09698i	0.375266	+	0.489056i
$347$	−22.5488	+	17.3023i	−1.21048	+	0.928838i	−0.998823	−	0.0485053i	$-0.984554\pi$
$347$	−22.5488	+	17.3023i	−1.21048	+	0.928838i	−0.211662	+	0.977343i	$0.567888\pi$
$348$	−0.709922	−	0.414823i	−0.0380558	−	0.0222368i
$349$	17.9561	+	17.9561i	0.961170	+	0.961170i	0.999274	−	0.0381037i	$-0.0121317\pi$
$349$	17.9561	+	17.9561i	0.961170	+	0.961170i	−0.0381037	+	0.999274i	$0.512132\pi$
$350$	5.04069	+	6.60905i	0.269436	+	0.353269i
$351$	10.7543	+	27.1566i	0.574022	+	1.44951i
$352$	−5.37326	+	7.00257i	−0.286396	+	0.373238i
$353$	−17.0923	−	9.86827i	−0.909734	−	0.525235i	−0.0293884	−	0.999568i	$-0.509356\pi$
$353$	−17.0923	−	9.86827i	−0.909734	−	0.525235i	−0.880346	+	0.474333i	$0.842689\pi$
$354$	−10.6810	+	25.4107i	−0.567686	+	1.35056i
$355$	−0.0586347	−	0.0157111i	−0.00311201	−	0.000833860i
$356$	5.66292			0.300134
$357$	−5.58610	−	18.0498i	−0.295648	−	0.955297i
$358$	−7.18049			−0.379501
$359$	−12.6264	−	3.38323i	−0.666395	−	0.178560i	−0.0902647	−	0.995918i	$-0.528771\pi$
$359$	−12.6264	−	3.38323i	−0.666395	−	0.178560i	−0.576130	+	0.817358i	$0.695438\pi$
$360$	10.0329	+	7.86603i	0.528779	+	0.414576i
$361$	17.0760	+	9.85886i	0.898739	+	0.518887i
$362$	−19.9750	+	26.0320i	−1.04986	+	1.36821i
$363$	3.73335	−	4.81324i	0.195950	−	0.252630i
$364$	6.13400	−	0.789327i	0.321509	−	0.0413720i
$365$	12.2363	+	12.2363i	0.640479	+	0.640479i
$366$	5.28245	−	9.04032i	0.276118	−	0.472545i
$367$	1.94674	−	1.49379i	0.101619	−	0.0779751i	−0.556702	−	0.830712i	$-0.687934\pi$
$367$	1.94674	−	1.49379i	0.101619	−	0.0779751i	0.658321	+	0.752737i	$0.271267\pi$
$368$	−20.6616	−	26.9267i	−1.07706	−	1.40365i
$369$	−0.925128	+	0.371950i	−0.0481602	+	0.0193629i
$370$	−13.8934			−0.722285
$371$	13.8821	+	10.7167i	0.720724	+	0.556385i
$372$	−0.206190	−	0.361470i	−0.0106904	−	0.0187413i
$373$	11.8242	+	20.4802i	0.612236	+	1.06042i	0.990863	+	0.134874i	$0.0430630\pi$
$373$	11.8242	+	20.4802i	0.612236	+	1.06042i	−0.378627	+	0.925549i	$0.623604\pi$
$374$	−22.1001	+	10.3819i	−1.14277	+	0.536833i
$375$	−14.7639	−	14.9186i	−0.762405	−	0.770395i
$376$	8.55620	+	2.29263i	0.441252	+	0.118233i
$377$	−5.92850	+	2.45566i	−0.305333	+	0.126473i
$378$	−14.8265	−	15.3873i	−0.762593	−	0.791439i
$379$	−0.585095	−	1.41254i	−0.0300543	−	0.0725575i	0.908140	−	0.418667i	$-0.137503\pi$
$379$	−0.585095	−	1.41254i	−0.0300543	−	0.0725575i	−0.938194	+	0.346110i	$0.887503\pi$
$380$	4.42766	−	0.582912i	0.227134	−	0.0299028i
$381$	−15.4149	+	6.29111i	−0.789727	+	0.322303i
$382$	9.03015	+	33.7010i	0.462023	+	1.72429i
$383$	0.423186	+	0.113392i	0.0216238	+	0.00579407i	0.269615	−	0.962968i	$-0.413104\pi$
$383$	0.423186	+	0.113392i	0.0216238	+	0.00579407i	−0.247991	+	0.968762i	$0.579770\pi$
$384$	−14.3510	+	18.5021i	−0.732347	+	0.944182i
$385$	−13.8338	+	10.5509i	−0.705035	+	0.537726i
$386$	3.66251	−	1.51706i	0.186417	−	0.0772163i
$387$	17.7014	+	0.184544i	0.899812	+	0.00938091i
$388$	−5.01362	−	0.660055i	−0.254528	−	0.0335092i
$389$	−5.57695	−	20.8135i	−0.282763	−	1.05528i	−0.950459	−	0.310851i	$-0.899386\pi$
$389$	−5.57695	−	20.8135i	−0.282763	−	1.05528i	0.667696	−	0.744434i	$-0.267281\pi$
$390$	−25.2630	+	6.62826i	−1.27924	+	0.335635i
$391$	−5.29988	−	29.5667i	−0.268027	−	1.49525i
$392$	14.9767	−	8.53049i	0.756438	−	0.430855i
$393$	−2.61240	+	1.49017i	−0.131778	+	0.0751689i
$394$	−9.28099	−	7.12156i	−0.467570	−	0.358779i
$395$	7.83053	+	4.52096i	0.393997	+	0.227474i
$396$	−2.93275	+	3.74064i	−0.147376	+	0.187974i
$397$	1.17284	−	0.154408i	0.0588633	−	0.00774950i	−0.101037	−	0.994883i	$-0.532216\pi$
$397$	1.17284	−	0.154408i	0.0588633	−	0.00774950i	0.159900	+	0.987133i	$0.448883\pi$
$398$	−2.99216	+	7.22372i	−0.149984	+	0.362093i
$399$	28.5135	+	0.231954i	1.42746	+	0.0116122i
$400$	6.65846	−	6.65846i	0.332923	−	0.332923i
$401$	−2.86894	−	21.7918i	−0.143268	−	1.08823i	−0.900429	−	0.435002i	$-0.856748\pi$
$401$	−2.86894	−	21.7918i	−0.143268	−	1.08823i	0.757161	−	0.653228i	$-0.226586\pi$
$402$	0.763526	−	0.311610i	0.0380812	−	0.0155417i
$403$	−3.21992	−	0.423910i	−0.160396	−	0.0211165i
$404$	3.97326	−	2.29396i	0.197677	−	0.114129i
$405$	12.1235	+	9.71087i	0.602420	+	0.482537i
$406$	3.32917	−	3.30977i	0.165224	−	0.164261i
$407$			19.7330i			0.978129i
$408$	−15.9541	+	7.39341i	−0.789846	+	0.366028i
$409$	−5.23236	−	3.02090i	−0.258723	−	0.149374i	0.365029	−	0.930996i	$-0.381059\pi$
$409$	−5.23236	−	3.02090i	−0.258723	−	0.149374i	−0.623752	+	0.781622i	$0.714393\pi$
$410$	−0.230763	−	0.861219i	−0.0113966	−	0.0425326i
$411$	3.94713	+	5.19990i	0.194697	+	0.256492i
$412$	−2.67567			−0.131821
$413$	−21.4432	−	16.5537i	−1.05515	−	0.814554i
$414$	−20.3978	−	27.1647i	−1.00250	−	1.33507i
$415$	25.5988	−	3.37015i	1.25660	−	0.165434i
$416$	−3.37037	−	12.5784i	−0.165246	−	0.616707i
$417$	0.0249099	−	4.77883i	0.00121984	−	0.234020i
$418$	−4.80976	−	36.5338i	−0.235253	−	1.78693i
$419$	29.6296	+	12.2730i	1.44750	+	0.599574i	0.961604	−	0.274442i	$-0.0884932\pi$
$419$	29.6296	+	12.2730i	1.44750	+	0.599574i	0.485897	+	0.874016i	$0.338493\pi$
$420$	2.62552	−	1.98091i	0.128112	−	0.0966584i
$421$		−	32.6093i		−	1.58928i	−0.607081	−	0.794640i	$-0.707660\pi$
$421$		−	32.6093i		−	1.58928i	0.607081	−	0.794640i	$-0.292340\pi$
$422$	17.7183	−	23.0910i	0.862514	−	1.12405i
$423$	10.3952	+	2.90186i	0.505430	+	0.141093i
$424$	8.16054	−	14.1345i	0.396311	−	0.686431i
$425$	7.94094	−	2.52854i	0.385192	−	0.122652i
$426$	0.0249831	−	0.0913312i	0.00121043	−	0.00442501i
$427$	7.25494	+	7.29747i	0.351091	+	0.353149i
$428$	2.23255	+	5.38986i	0.107915	+	0.260529i
$429$	9.41420	+	35.8814i	0.454522	+	1.73237i
$430$	−2.06614	+	15.6939i	−0.0996381	+	0.756827i
$431$	−4.57701	−	5.96488i	−0.220467	−	0.287318i	0.670005	−	0.742357i	$-0.266292\pi$
$431$	−4.57701	−	5.96488i	−0.220467	−	0.287318i	−0.890472	+	0.455039i	$0.849625\pi$
$432$	−15.0352	+	18.9724i	−0.723381	+	0.912812i
$433$	−3.36078	−	3.36078i	−0.161509	−	0.161509i	0.621726	−	0.783235i	$-0.286432\pi$
$433$	−3.36078	−	3.36078i	−0.161509	−	0.161509i	−0.783235	+	0.621726i	$0.786432\pi$
$434$	2.29675	−	0.608225i	0.110248	−	0.0291957i
$435$	−2.09152	+	2.69650i	−0.100281	+	0.129287i
$436$	0.724363	+	5.50208i	0.0346907	+	0.263502i
$437$	44.9437	+	5.91695i	2.14995	+	0.283046i
$438$	−19.1858	+	18.9869i	−0.916735	+	0.907227i
$439$	−0.515797	+	0.672199i	−0.0246176	+	0.0320823i	−0.805500	−	0.592596i	$-0.798103\pi$
$439$	−0.515797	+	0.672199i	−0.0246176	+	0.0320823i	0.780882	+	0.624678i	$0.214770\pi$
$440$	11.4491	+	11.4491i	0.545814	+	0.545814i
$441$	18.3549	−	10.2027i	0.874045	−	0.485845i
$442$	7.69718	−	35.1916i	0.366117	−	1.67390i
$443$	26.1324	−	15.0876i	1.24159	−	0.716831i	0.272171	−	0.962249i	$-0.412258\pi$
$443$	26.1324	−	15.0876i	1.24159	−	0.716831i	0.969417	+	0.245418i	$0.0789251\pi$
$444$	0.0194444	−	3.73031i	0.000922792	−	0.177032i
$445$	3.06777	−	23.3020i	0.145426	−	1.10462i
$446$	−7.42931	+	4.28931i	−0.351788	+	0.203105i
$447$	−1.13813	−	9.00751i	−0.0538316	−	0.426041i
$448$	−9.17257	−	12.0265i	−0.433363	−	0.568200i
$449$	29.2205	+	12.1035i	1.37900	+	0.571201i	0.944214	−	0.329333i	$-0.106824\pi$
$449$	29.2205	+	12.1035i	1.37900	+	0.571201i	0.434786	+	0.900534i	$0.356824\pi$
$450$	6.73348	−	6.59453i	0.317419	−	0.310869i
$451$	−1.22320	+	0.327756i	−0.0575983	+	0.0154334i
$452$	−4.25378	+	3.26404i	−0.200081	+	0.153528i
$453$	39.5814	+	5.42103i	1.85970	+	0.254702i
$454$	41.3450	−	17.1257i	1.94042	−	0.803747i
$455$	0.0750071	−	25.6680i	0.00351639	−	1.20334i
$456$	−3.32655	−	26.3274i	−0.155780	−	1.23289i
$457$	5.15307	−	19.2315i	0.241050	−	0.899612i	−0.734277	−	0.678850i	$-0.762479\pi$
$457$	5.15307	−	19.2315i	0.241050	−	0.899612i	0.975328	−	0.220763i	$-0.0708546\pi$
$458$	13.0975	−	22.6855i	0.612005	−	1.06002i
$459$	−19.5313	+	8.80498i	−0.911644	+	0.410981i
$460$	4.52821	−	2.61436i	0.211129	−	0.121895i
$461$	−8.45921	−	8.45921i	−0.393984	−	0.393984i	0.482120	−	0.876105i	$-0.339867\pi$
$461$	−8.45921	−	8.45921i	−0.393984	−	0.393984i	−0.876105	+	0.482120i	$0.839867\pi$
$462$	−16.3450	−	21.6638i	−0.760438	−	1.00789i
$463$			6.98382i			0.324566i	0.986744	+	0.162283i	$0.0518857\pi$
$463$			6.98382i			0.324566i	−0.986744	+	0.162283i	$0.948114\pi$
$464$	−4.21929	−	3.23757i	−0.195875	−	0.150300i
$465$	−1.59909	+	0.652621i	−0.0741560	+	0.0302646i
$466$	10.8293	+	14.1130i	0.501657	+	0.653773i
$467$	−23.6599	−	6.33965i	−1.09485	−	0.293364i	−0.334183	−	0.942508i	$-0.608460\pi$
$467$	−23.6599	−	6.33965i	−1.09485	−	0.293364i	−0.760665	+	0.649144i	$0.775127\pi$
$468$	−1.74429	−	6.79225i	−0.0806300	−	0.313972i
$469$	0.103438	+	0.803831i	0.00477631	+	0.0371175i
$470$	−3.69315	+	8.91606i	−0.170352	+	0.411267i
$471$	−19.2132	+	14.5843i	−0.885297	+	0.672010i
$472$	−12.6053	+	21.8330i	−0.580204	+	1.00494i
$473$	22.2902	+	2.93457i	1.02491	+	0.134932i
$474$	−7.11550	+	12.1774i	−0.326826	+	0.559325i
$475$			12.5769i			0.577067i
$476$	0.787341	+	4.46750i	0.0360877	+	0.204767i
$477$	10.1218	−	17.1168i	0.463445	−	0.783726i
$478$	0.167193	−	0.623972i	0.00764722	−	0.0285398i
$479$	−1.87682	+	14.2559i	−0.0857540	+	0.651366i	0.893549	+	0.448966i	$0.148208\pi$
$479$	−1.87682	+	14.2559i	−0.0857540	+	0.651366i	−0.979303	+	0.202400i	$0.935126\pi$
$480$	−4.87127	−	4.92232i	−0.222342	−	0.224672i
$481$	−23.0968	−	17.7228i	−1.05312	−	0.808089i
$482$	4.73249	+	1.96026i	0.215559	+	0.0892874i
$483$	30.9469	−	12.5247i	1.40813	−	0.569892i
$484$	−1.03413	+	1.03413i	−0.0470058	+	0.0470058i
$485$	−5.43205	+	20.2727i	−0.246657	+	0.920535i
$486$	−15.2457	+	18.8314i	−0.691558	+	0.854208i
$487$	−22.2988	+	17.1105i	−1.01046	+	0.775349i	−0.974588	−	0.224007i	$-0.928086\pi$
$487$	−22.2988	+	17.1105i	−1.01046	+	0.775349i	−0.0358676	+	0.999357i	$0.511419\pi$
$488$	5.82978	−	7.59751i	0.263902	−	0.343923i
$489$	−15.0675	−	4.12163i	−0.681377	−	0.186387i
$490$	7.08453	+	17.3904i	0.320047	+	0.785616i
$491$	−7.15452	+	7.15452i	−0.322879	+	0.322879i	−0.849871	−	0.526992i	$-0.823320\pi$
$491$	−7.15452	+	7.15452i	−0.322879	+	0.322879i	0.526992	+	0.849871i	$0.323320\pi$
$492$	0.231555	−	0.0607532i	0.0104393	−	0.00273897i
$493$	−2.00127	−	4.26015i	−0.0901326	−	0.191868i
$494$	47.0813	+	27.1824i	2.11829	+	1.22299i
$495$	13.8034	+	14.0942i	0.620416	+	0.633488i
$496$	−1.03005	−	2.48676i	−0.0462507	−	0.111659i
$497$	0.0804521	+	0.0467631i	0.00360877	+	0.00209761i
$498$	5.04866	+	39.9567i	0.226236	+	1.79050i
$499$	2.00106	+	15.1996i	0.0895799	+	0.680427i	0.976035	+	0.217613i	$0.0698270\pi$
$499$	2.00106	+	15.1996i	0.0895799	+	0.680427i	−0.886455	+	0.462814i	$0.846840\pi$
$500$	3.06769	+	3.99789i	0.137191	+	0.178791i
$501$	6.87149	+	0.0358181i	0.306996	+	0.00160023i
$502$	−4.59949	+	17.1655i	−0.205285	+	0.766135i
$503$	−2.77400	+	6.69704i	−0.123687	+	0.298606i	−0.973579	−	0.228350i	$-0.926667\pi$
$503$	−2.77400	+	6.69704i	−0.123687	+	0.298606i	0.849892	+	0.526956i	$0.176667\pi$
$504$	−11.6893	−	15.6623i	−0.520684	−	0.697655i
$505$	−7.28687	−	17.5921i	−0.324262	−	0.782837i
$506$	−21.5718	−	37.3635i	−0.958983	−	1.66101i
$507$	−29.6955	−	12.4820i	−1.31882	−	0.554346i
$508$	3.86109	−	1.03457i	0.171308	−	0.0459018i
$509$	−4.29983	−	7.44753i	−0.190587	−	0.330106i	0.754858	−	0.655888i	$-0.227706\pi$
$509$	−4.29983	−	7.44753i	−0.190587	−	0.330106i	−0.945445	+	0.325782i	$0.894372\pi$
$510$	−5.71731	−	18.2844i	−0.253167	−	0.809648i
$511$	−13.1966	−	23.0122i	−0.583783	−	1.01800i
$512$	−8.59100	+	8.59100i	−0.379672	+	0.379672i
$513$	−3.71845	−	32.1178i	−0.164173	−	1.41803i
$514$	−11.8527	+	20.5295i	−0.522802	+	0.905519i
$515$	−1.44949	+	11.0100i	−0.0638722	+	0.485157i
$516$	−4.21083	−	0.576711i	−0.185371	−	0.0253883i
$517$	12.6636	+	5.24543i	0.556944	+	0.230694i
$518$	20.5562	+	5.57244i	0.903186	+	0.244839i
$519$	6.33114	+	11.0991i	0.277906	+	0.487195i
$520$	−23.6835	+	3.11799i	−1.03859	+	0.136733i
$521$	−16.4653	+	12.6343i	−0.721358	+	0.553517i	−0.902892	−	0.429867i	$-0.858560\pi$
$521$	−16.4653	+	12.6343i	−0.721358	+	0.553517i	0.181534	+	0.983385i	$0.441894\pi$
$522$	−4.18902	−	3.28429i	−0.183348	−	0.143750i
$523$	13.3477	+	23.1188i	0.583652	+	1.01092i	0.995042	+	0.0994558i	$0.0317102\pi$
$523$	13.3477	+	23.1188i	0.583652	+	1.01092i	−0.411390	+	0.911460i	$0.634956\pi$
$524$	0.667109	−	0.276326i	0.0291428	−	0.0120713i
$525$	4.56584	+	8.05896i	0.199269	+	0.351722i
$526$	−33.5774			−1.46404
$527$	0.200890	−	2.37369i	0.00875092	−	0.103399i
$528$	−21.8527	+	21.6261i	−0.951016	+	0.941153i
$529$	29.0503	−	7.78400i	1.26306	−	0.338435i
$530$	14.1070	+	10.8247i	0.612771	+	0.470196i
$531$	−15.6347	+	26.4397i	−0.678489	+	1.14738i
$532$	−6.78479	−	0.913412i	−0.294158	−	0.0396014i
$533$	0.714965	−	1.72608i	0.0309686	−	0.0747648i
$534$	36.3218	+	4.97460i	1.57180	+	0.215272i
$535$	23.3879	−	6.26677i	1.01115	−	0.270936i
$536$	0.728548	−	0.195214i	0.0314685	−	0.00843195i
$537$	−7.92765	−	1.08576i	−0.342103	−	0.0468541i
$538$	−0.801074	+	1.93396i	−0.0345367	+	0.0833791i
$539$	24.6998	−	10.0623i	1.06389	−	0.433412i
$540$	−2.59549	−	2.67796i	−0.111692	−	0.115241i
$541$	−27.9161	−	21.4208i	−1.20021	−	0.920952i	−0.201918	−	0.979402i	$-0.564717\pi$
$541$	−27.9161	−	21.4208i	−1.20021	−	0.920952i	−0.998290	+	0.0584501i	$0.981384\pi$
$542$	23.6138	−	6.32729i	1.01430	−	0.271780i
$543$	−25.9898	+	25.7203i	−1.11533	+	1.10376i
$544$	9.10139	−	2.89806i	0.390219	−	0.124253i
$545$	23.0326			0.986609
$546$	40.0367	+	0.325693i	1.71341	+	0.0139384i
$547$	−27.9510	+	11.5777i	−1.19510	+	0.495025i	−0.889411	−	0.457108i	$-0.848885\pi$
$547$	−27.9510	+	11.5777i	−1.19510	+	0.495025i	−0.305685	+	0.952133i	$0.598885\pi$
$548$	−0.783687	−	1.35739i	−0.0334774	−	0.0579846i
$549$	7.19910	−	9.18225i	0.307250	−	0.391889i
$550$	9.49633	−	7.28679i	0.404925	−	0.310710i
$551$	7.04247	−	0.927159i	0.300019	−	0.0394983i
$552$	−15.3944	−	26.9878i	−0.655230	−	1.14868i
$553$	−9.77246	−	9.82974i	−0.415567	−	0.418003i
$554$	23.8230	+	9.86780i	1.01214	+	0.419243i
$555$	−15.3391	−	2.10083i	−0.651108	−	0.0891752i
$556$	−0.149760	+	1.13754i	−0.00635126	+	0.0482426i
$557$	−1.57438	+	2.72691i	−0.0667088	+	0.115543i	−0.897451	−	0.441115i	$-0.854583\pi$
$557$	−1.57438	+	2.72691i	−0.0667088	+	0.115543i	0.830742	+	0.556658i	$0.187917\pi$
$558$	−1.00496	−	2.49958i	−0.0425434	−	0.105816i
$559$	−23.4543	+	23.4543i	−0.992012	+	0.992012i
$560$	18.4543	−	10.5828i	0.779838	−	0.447206i
$561$	−25.9696	+	8.12037i	−1.09644	+	0.342842i
$562$	12.6570	+	21.9226i	0.533905	+	0.924751i
$563$	10.7956	−	2.89267i	0.454980	−	0.121911i	−0.0240487	−	0.999711i	$-0.507656\pi$
$563$	10.7956	−	2.89267i	0.454980	−	0.121911i	0.479029	+	0.877799i	$0.340989\pi$
$564$	−2.38874	−	1.00407i	−0.100584	−	0.0422789i
$565$	11.1266	+	19.2719i	0.468101	+	0.810774i
$566$	4.38165	+	10.5782i	0.184174	+	0.444636i
$567$	−14.0425	−	19.2304i	−0.589731	−	0.807599i
$568$	0.0331409	−	0.0800093i	0.00139056	−	0.00335712i
$569$	10.5935	−	39.5356i	0.444103	−	1.65742i	−0.274189	−	0.961676i	$-0.588409\pi$
$569$	10.5935	−	39.5356i	0.444103	−	1.65742i	0.718293	−	0.695741i	$-0.244924\pi$
$570$	28.9109	+	0.150700i	1.21095	+	0.00631213i
$571$	−5.37656	−	7.00687i	−0.225002	−	0.293228i	0.667187	−	0.744890i	$-0.267498\pi$
$571$	−5.37656	−	7.00687i	−0.225002	−	0.293228i	−0.892189	+	0.451662i	$0.850831\pi$
$572$	−1.16251	−	8.83010i	−0.0486068	−	0.369205i
$573$	4.87385	+	38.5732i	0.203608	+	1.61142i
$574$	−0.00399401	+	1.36678i	−0.000166707	+	0.0570484i
$575$	5.63511	+	13.6044i	0.235001	+	0.567341i
$576$	−12.2530	+	12.0001i	−0.510540	+	0.500005i
$577$	20.9478	+	12.0942i	0.872069	+	0.503489i	0.868035	−	0.496503i	$-0.165383\pi$
$577$	20.9478	+	12.0942i	0.872069	+	0.503489i	0.00403355	+	0.999992i	$0.498716\pi$
$578$	26.0473	+	4.44068i	1.08342	+	0.184708i
$579$	4.27300	−	1.12111i	0.177580	−	0.0465917i
$580$	0.579345	−	0.579345i	0.0240560	−	0.0240560i
$581$	−39.2267	−	5.28096i	−1.62740	−	0.219091i
$582$	−31.5774	−	8.63779i	−1.30892	−	0.358048i
$583$	15.3745	−	20.0364i	0.636746	−	0.829824i
$584$	−19.5861	+	15.0289i	−0.810477	+	0.621901i
$585$	−28.8940	+	3.49793i	−1.19462	+	0.144622i
$586$	1.74766	−	6.52236i	0.0721953	−	0.269436i
$587$	9.58517	−	9.58517i	0.395622	−	0.395622i	−0.481064	−	0.876686i	$-0.659749\pi$
$587$	9.58517	−	9.58517i	0.395622	−	0.395622i	0.876686	+	0.481064i	$0.159749\pi$
$588$	−4.67913	+	1.87782i	−0.192964	+	0.0774399i
$589$	3.32138	+	1.37576i	0.136855	+	0.0566873i
$590$	−21.7906	−	16.7205i	−0.897104	−	0.688372i
$591$	−9.16987	−	9.26597i	−0.377198	−	0.381151i
$592$	3.14938	−	23.9219i	0.129439	−	0.983185i
$593$	−9.14627	+	34.1344i	−0.375592	+	1.40173i	0.476885	+	0.878966i	$0.341766\pi$
$593$	−9.14627	+	34.1344i	−0.375592	+	1.40173i	−0.852477	+	0.522764i	$0.824901\pi$
$594$	−22.0965	+	21.4161i	−0.906632	+	0.878711i
$595$	18.8096	−	0.819609i	0.771118	−	0.0336007i
$596$			2.17980i			0.0892880i
$597$	−4.39581	+	7.52294i	−0.179909	+	0.307893i
$598$	63.1068	+	8.30817i	2.58063	+	0.339746i
$599$	11.3142	−	19.5967i	0.462284	−	0.800699i	−0.536790	−	0.843716i	$-0.680363\pi$
$599$	11.3142	−	19.5967i	0.462284	−	0.800699i	0.999074	+	0.0430162i	$0.0136967\pi$
$600$	6.86602	−	5.21184i	0.280304	−	0.212773i
$601$	7.37834	−	17.8129i	0.300969	−	0.726603i	−0.698966	−	0.715155i	$-0.746356\pi$
$601$	7.37834	−	17.8129i	0.300969	−	0.726603i	0.999934	−	0.0114477i	$-0.00364401\pi$
$602$	9.35157	−	22.3914i	0.381141	−	0.912605i
$603$	0.890092	−	0.228581i	0.0362474	−	0.00930856i
$604$	−9.26494	−	2.48253i	−0.376985	−	0.101013i
$605$	3.69506	+	4.81550i	0.150226	+	0.195778i
$606$	27.4995	−	11.2231i	1.11709	−	0.455907i
$607$	29.0563	+	22.2957i	1.17936	+	0.904955i	0.996933	−	0.0782644i	$-0.0249378\pi$
$607$	29.0563	+	22.2957i	1.17936	+	0.904955i	0.182428	+	0.983219i	$0.441604\pi$
$608$			14.4148i			0.584598i
$609$	4.17605	−	3.15076i	0.169222	−	0.127675i
$610$	7.37752	+	7.37752i	0.298707	+	0.298707i
$611$	−17.5131	+	10.1112i	−0.708505	+	0.409056i
$612$	4.91726	−	1.50947i	0.198769	−	0.0610169i
$613$	−0.427503	+	0.740458i	−0.0172667	+	0.0299068i	−0.874530	−	0.484972i	$-0.838830\pi$
$613$	−0.427503	+	0.740458i	−0.0172667	+	0.0299068i	0.857263	+	0.514879i	$0.172163\pi$
$614$	−2.06399	+	7.70291i	−0.0832958	+	0.310864i
$615$	−0.124550	−	0.985727i	−0.00502233	−	0.0397483i
$616$	−12.3476	−	21.5317i	−0.497498	−	0.867537i
$617$	19.1923	−	7.94973i	0.772654	−	0.320044i	0.0387072	−	0.999251i	$-0.487676\pi$
$617$	19.1923	−	7.94973i	0.772654	−	0.320044i	0.733947	+	0.679207i	$0.237676\pi$
$618$	−17.1617	−	2.35045i	−0.690344	−	0.0945488i
$619$	−17.3589	+	13.3199i	−0.697712	+	0.535373i	−0.895605	−	0.444850i	$-0.853257\pi$
$619$	−17.3589	+	13.3199i	−0.697712	+	0.535373i	0.197893	+	0.980224i	$0.436590\pi$
$620$	0.400537	−	0.107324i	0.0160860	−	0.00431022i
$621$	−18.4127	−	33.0756i	−0.738877	−	1.32728i
$622$	−9.61694	−	3.98347i	−0.385604	−	0.159722i
$623$	−13.8851	+	33.2464i	−0.556293	+	1.33199i
$624$	−5.68599	−	45.0008i	−0.227622	−	1.80147i
$625$	9.36034	−	5.40419i	0.374414	−	0.216168i
$626$	0.159219	−	1.20939i	0.00636369	−	0.0483370i
$627$	0.214041	−	41.0626i	0.00854798	−	1.63988i
$628$	5.01543	−	2.89566i	0.200137	−	0.115549i
$629$	12.1986	−	17.5269i	0.486389	−	0.698844i
$630$	18.5801	−	10.3991i	0.740250	−	0.414310i
$631$	−25.5469	−	25.5469i	−1.01701	−	1.01701i	−0.999853	−	0.0171534i	$-0.994540\pi$
$631$	−25.5469	−	25.5469i	−1.01701	−	1.01701i	−0.0171534	−	0.999853i	$-0.505460\pi$
$632$	−7.85275	+	10.2339i	−0.312366	+	0.407083i
$633$	23.0536	−	22.8145i	0.916298	−	0.906795i
$634$	−3.68624	−	0.485303i	−0.146399	−	0.0192738i
$635$	−2.16545	−	16.4482i	−0.0859333	−	0.652728i
$636$	−2.92612	+	3.77251i	−0.116028	+	0.149590i
$637$	−10.4060	+	37.9474i	−0.412302	+	1.50353i
$638$	−4.78033	−	4.78033i	−0.189255	−	0.189255i
$639$	0.0413929	−	0.0970570i	0.00163748	−	0.00383951i
$640$	−14.2038	−	18.5108i	−0.561456	−	0.731703i
$641$	−3.97722	+	30.2100i	−0.157091	+	1.19322i	0.713299	+	0.700860i	$0.247200\pi$
$641$	−3.97722	+	30.2100i	−0.157091	+	1.19322i	−0.870390	+	0.492363i	$0.836133\pi$
$642$	9.58480	+	36.5316i	0.378282	+	1.44179i
$643$	−0.545652	−	1.31732i	−0.0215184	−	0.0519501i	0.912755	−	0.408507i	$-0.133951\pi$
$643$	−0.545652	−	1.31732i	−0.0215184	−	0.0519501i	−0.934274	+	0.356557i	$0.883951\pi$
$644$	−7.74834	+	2.05191i	−0.305328	+	0.0808567i
$645$	−4.65421	+	17.0145i	−0.183259	+	0.669945i
$646$	−18.3124	+	35.4227i	−0.720493	+	1.39369i
$647$	16.7461	−	29.0051i	0.658357	−	1.14031i	−0.322684	−	0.946507i	$-0.604585\pi$
$647$	16.7461	−	29.0051i	0.658357	−	1.14031i	0.981041	−	0.193801i	$-0.0620815\pi$
$648$	−15.9929	+	15.3396i	−0.628262	+	0.602595i
$649$	−23.7484	+	30.9495i	−0.932205	+	1.21487i
$650$			17.6596i			0.692666i
$651$	2.62771	−	0.324221i	0.102988	−	0.0127072i
$652$	3.46496	+	1.43524i	0.135699	+	0.0562082i
$653$	0.209981	+	1.59497i	0.00821720	+	0.0624159i	0.995062	−	0.0992536i	$-0.0316455\pi$
$653$	0.209981	+	1.59497i	0.00821720	+	0.0624159i	−0.986845	+	0.161669i	$0.948312\pi$
$654$	−0.187269	+	35.9265i	−0.00732280	+	1.40484i
$655$	−0.775644	−	2.89474i	−0.0303069	−	0.113107i
$656$	1.53517	−	0.202109i	0.0599384	−	0.00789104i
$657$	−24.0532	+	18.0614i	−0.938405	+	0.704643i
$658$	9.04034	−	11.7106i	0.352429	−	0.456526i
$659$	−29.7391			−1.15847			−0.579236	−	0.815160i	$-0.696649\pi$
$659$	−29.7391			−1.15847			−0.579236	+	0.815160i	$0.696649\pi$
$660$	−2.86371	−	3.77261i	−0.111470	−	0.146849i
$661$	−4.95678	−	18.4990i	−0.192797	−	0.719527i	−0.992826	−	0.119566i	$-0.961850\pi$
$661$	−4.95678	−	18.4990i	−0.192797	−	0.719527i	0.800030	−	0.599960i	$-0.204817\pi$
$662$	−16.2941	−	9.40738i	−0.633287	−	0.365628i
$663$	13.8194	−	37.6896i	0.536703	−	1.46374i
$664$			36.8354i			1.42949i
$665$	−7.43407	+	27.4235i	−0.288281	+	1.06344i
$666$	3.40161	−	23.9090i	0.131810	−	0.926455i
$667$	7.20240	−	4.15831i	0.278878	−	0.161010i
$668$	−1.63568	−	0.215341i	−0.0632863	−	0.00833180i
$669$	−8.85095	+	3.61225i	−0.342198	+	0.139658i
$670$	0.107259	+	0.814710i	0.00414376	+	0.0314750i
$671$	10.4784	−	10.4784i	0.404514	−	0.404514i
$672$	5.23307	+	9.23666i	0.201870	+	0.356312i
$673$	15.6790	−	37.8524i	0.604380	−	1.45910i	−0.264650	−	0.964345i	$-0.585256\pi$
$673$	15.6790	−	37.8524i	0.604380	−	1.45910i	0.869030	−	0.494759i	$-0.164744\pi$
$674$	8.42471	−	1.10913i	0.324508	−	0.0427222i
$675$	8.43129	−	6.26255i	0.324520	−	0.241046i
$676$	6.69766	+	3.86690i	0.257602	+	0.148727i
$677$	17.3178	+	13.2884i	0.665577	+	0.510715i	0.885403	−	0.464824i	$-0.153882\pi$
$677$	17.3178	+	13.2884i	0.665577	+	0.510715i	−0.219827	+	0.975539i	$0.570549\pi$
$678$	−30.1509	+	17.1987i	−1.15794	+	0.660513i
$679$	16.1681	−	27.8160i	0.620475	−	1.06748i
$680$	−3.09151	−	17.2467i	−0.118554	−	0.661382i
$681$	48.2367	−	12.6559i	1.84844	−	0.484974i
$682$	−0.885556	−	3.30494i	−0.0339097	−	0.126553i
$683$	0.490217	+	0.0645383i	0.0187576	+	0.00246949i	0.139899	−	0.990166i	$-0.455322\pi$
$683$	0.490217	+	0.0645383i	0.0187576	+	0.00246949i	−0.121142	+	0.992635i	$0.538655\pi$
$684$	−0.0809242	+	7.76221i	−0.00309421	+	0.296796i
$685$	−6.00998	+	2.48941i	−0.229629	+	0.0951156i
$686$	−3.50699	−	28.5716i	−0.133898	−	1.09087i
$687$	17.8906	−	23.0656i	0.682570	−	0.880006i
$688$	−26.5537	−	7.11503i	−1.01235	−	0.271258i
$689$	9.64364	+	35.9906i	0.367394	+	1.37113i
$690$	31.3404	−	12.7906i	1.19311	−	0.486931i
$691$	14.2318	−	1.87365i	0.541404	−	0.0712771i	0.145135	−	0.989412i	$-0.453638\pi$
$691$	14.2318	−	1.87365i	0.541404	−	0.0712771i	0.396268	+	0.918135i	$0.370305\pi$
$692$	−1.17400	−	2.83429i	−0.0446288	−	0.107743i
$693$	−14.7700	−	26.3896i	−0.561065	−	1.00246i
$694$	40.8138	−	16.9056i	1.54927	−	0.641730i
$695$	4.59969	+	1.23248i	0.174476	+	0.0467507i
$696$	−3.42455	−	3.46044i	−0.129807	−	0.131168i
$697$	1.28906	+	0.465045i	0.0488267	+	0.0176149i
$698$	−19.7348	−	34.1817i	−0.746973	−	1.29380i
$699$	9.82210	+	17.2190i	0.371506	+	0.651284i
$700$	−0.845012	−	2.05702i	−0.0319384	−	0.0777481i
$701$	43.3704			1.63808			0.819038	−	0.573740i	$-0.194508\pi$
$701$	43.3704			1.63808			0.819038	+	0.573740i	$0.194508\pi$
$702$	−5.22118	−	45.0976i	−0.197061	−	1.70210i
$703$	19.6182	+	25.5669i	0.739914	+	0.964275i
$704$	−17.2805	+	13.2598i	−0.651285	+	0.499748i
$705$	−5.42564	+	9.28537i	−0.204341	+	0.349707i
$706$	21.6916	+	21.6916i	0.816373	+	0.816373i
$707$	3.72546	+	28.9512i	0.140110	+	1.08882i
$708$	4.51986	−	5.82725i	0.169867	−	0.219001i
$709$	2.84984	−	3.71398i	0.107028	−	0.139481i	−0.736768	−	0.676145i	$-0.763649\pi$
$709$	2.84984	−	3.71398i	0.107028	−	0.139481i	0.843796	+	0.536664i	$0.180316\pi$
$710$	0.0817102	+	0.0471754i	0.00306653	+	0.00177046i
$711$	−9.69724	+	12.3685i	−0.363675	+	0.463857i
$712$	32.3879	+	8.67832i	1.21379	+	0.325234i
$713$	4.20914			0.157634
$714$	1.12550	+	29.3460i	0.0421208	+	1.09825i
$715$	−36.9643			−1.38239
$716$	1.85565	+	0.497220i	0.0693489	+	0.0185820i
$717$	0.278941	−	0.663618i	0.0104172	−	0.0247833i
$718$	17.5955	+	10.1587i	0.656657	+	0.379121i
$719$	2.91393	−	3.79750i	0.108671	−	0.141623i	−0.735851	−	0.677143i	$-0.763218\pi$
$719$	2.91393	−	3.79750i	0.108671	−	0.141623i	0.844522	+	0.535520i	$0.179884\pi$
$720$	−14.4841	−	19.2892i	−0.539791	−	0.718864i
$721$	6.56054	−	15.7086i	0.244327	−	0.585017i
$722$	−21.6709	−	21.6709i	−0.806506	−	0.806506i
$723$	4.92851	+	2.87984i	0.183293	+	0.107102i
$724$	6.96474	−	5.34423i	0.258843	−	0.198617i
$725$	1.40464	+	1.83057i	0.0521672	+	0.0679856i
$726$	−7.54130	+	5.72444i	−0.279884	+	0.212454i
$727$	−39.5716			−1.46763			−0.733815	−	0.679349i	$-0.762262\pi$
$727$	−39.5716			−1.46763			−0.733815	+	0.679349i	$0.762262\pi$
$728$	36.2918	+	4.88584i	1.34506	+	0.181081i
$729$	−19.6795	+	18.4855i	−0.728872	+	0.684650i
$730$	−13.4484	−	23.2933i	−0.497748	−	0.862124i
$731$	−17.9842	−	16.3859i	−0.665168	−	0.606054i
$732$	−1.99115	+	1.97050i	−0.0735949	+	0.0728316i
$733$	−35.8402	−	9.60335i	−1.32379	−	0.354708i	−0.473392	−	0.880852i	$-0.656971\pi$
$733$	−35.8402	−	9.60335i	−1.32379	−	0.354708i	−0.850396	+	0.526144i	$0.823637\pi$
$734$	−3.52364	+	1.45954i	−0.130060	+	0.0538726i
$735$	5.19211	+	20.2712i	0.191514	+	0.747713i
$736$	6.45861	+	15.5925i	0.238067	+	0.574746i
$737$	1.15714	−	0.152341i	0.0426239	−	0.00561155i
$738$	1.53856	−	0.186259i	0.0566351	−	0.00685630i
$739$	−6.53877	−	24.4030i	−0.240533	−	0.897680i	−0.975576	−	0.219660i	$-0.929505\pi$
$739$	−6.53877	−	24.4030i	−0.240533	−	0.897680i	0.735044	−	0.678020i	$-0.237162\pi$
$740$	3.59047	+	0.962063i	0.131988	+	0.0353662i
$741$	47.8700	+	37.1300i	1.75855	+	1.36400i
$742$	−16.5306	−	21.6740i	−0.606858	−	0.795676i
$743$	−23.2197	+	9.61792i	−0.851848	+	0.352847i	−0.765514	−	0.643419i	$-0.777515\pi$
$743$	−23.2197	+	9.61792i	−0.851848	+	0.352847i	−0.0863342	+	0.996266i	$0.527515\pi$
$744$	−0.625316	−	2.38334i	−0.0229252	−	0.0873773i
$745$	8.96953	+	1.18086i	0.328618	+	0.0432634i
$746$	−9.51336	−	35.5043i	−0.348309	−	1.29991i
$747$	−0.467869	+	44.8778i	−0.0171184	+	1.64199i
$748$	6.43023	−	1.15263i	0.235112	−	0.0421444i
$749$	−37.1173	−	0.108464i	−1.35624	−	0.00396319i
$750$	16.1641	+	28.3372i	0.590230	+	1.03473i
$751$	−1.91728	−	1.47118i	−0.0699625	−	0.0536841i	0.573188	−	0.819424i	$-0.305706\pi$
$751$	−1.91728	−	1.47118i	−0.0699625	−	0.0536841i	−0.643151	+	0.765740i	$0.722373\pi$
$752$	−14.5146	−	8.38003i	−0.529295	−	0.305588i
$753$	−7.67369	+	18.2562i	−0.279645	+	0.665292i
$754$	9.88855	−	1.30185i	0.360120	−	0.0474107i
$755$	−15.2343	+	36.7789i	−0.554434	+	1.33852i
$756$	2.76609	+	5.00321i	0.100602	+	0.181965i
$757$	−8.74816	+	8.74816i	−0.317957	+	0.317957i	−0.847982	−	0.530025i	$-0.822183\pi$
$757$	−8.74816	+	8.74816i	−0.317957	+	0.317957i	0.530025	+	0.847982i	$0.322183\pi$
$758$	0.310184	+	2.35608i	0.0112664	+	0.0855766i
$759$	−18.1667	−	44.5132i	−0.659410	−	1.61573i
$760$	26.2164	+	3.45146i	0.950969	+	0.125197i
$761$	20.5801	−	11.8819i	0.746027	−	0.430719i	−0.0782293	−	0.996935i	$-0.524927\pi$
$761$	20.5801	−	11.8819i	0.746027	−	0.430719i	0.824257	+	0.566216i	$0.191593\pi$
$762$	25.6737	−	3.24396i	0.930060	−	0.117516i
$763$	−34.0782	−	9.23804i	−1.23371	−	0.334439i
$764$		−	9.33463i		−	0.337715i
$765$	−3.54743	−	21.0515i	−0.128257	−	0.761119i
$766$	−0.589729	−	0.340480i	−0.0213078	−	0.0123020i
$767$	−14.8961	−	55.5932i	−0.537869	−	2.00735i
$768$	13.2149	−	10.0311i	0.476851	−	0.361968i
$769$	−14.6714			−0.529065			−0.264533	−	0.964377i	$-0.585218\pi$
$769$	−14.6714			−0.529065			−0.264533	+	0.964377i	$0.585218\pi$
$770$	25.0136	−	10.2755i	0.901429	−	0.370302i
$771$	−16.1903	+	20.8735i	−0.583081	+	0.751740i
$772$	−1.05155	+	0.138439i	−0.0378461	+	0.00498253i
$773$	13.6376	+	50.8962i	0.490510	+	1.83061i	0.553849	+	0.832617i	$0.313159\pi$
$773$	13.6376	+	50.8962i	0.490510	+	1.83061i	−0.0633382	+	0.997992i	$0.520175\pi$
$774$	−26.5015	−	7.39802i	−0.952578	−	0.265916i
$775$	0.152428	+	1.15780i	0.00547537	+	0.0415895i
$776$	−27.6629	−	11.4583i	−0.993039	−	0.411330i
$777$	21.8525	+	9.26058i	0.783955	+	0.332222i
$778$			33.4916i			1.20073i
$779$	−1.25898	+	1.64074i	−0.0451077	+	0.0587855i
$780$	6.98768	+	0.0364237i	0.250199	+	0.00130418i
$781$	0.0670038	−	0.116054i	0.00239759	−	0.00415274i
$782$	−3.93723	+	46.5216i	−0.140795	+	1.66361i
$783$	−4.12829	−	4.25946i	−0.147533	−	0.152221i
$784$	−31.5489	+	8.25620i	−1.12675	+	0.294864i
$785$	−9.19818	−	22.2064i	−0.328297	−	0.792580i
$786$	4.52156	−	1.18632i	0.161279	−	0.0423147i
$787$	−5.16331	+	39.2192i	−0.184052	+	1.39801i	0.611076	+	0.791572i	$0.290737\pi$
$787$	−5.16331	+	39.2192i	−0.184052	+	1.39801i	−0.795128	+	0.606442i	$0.792596\pi$
$788$	1.90534	+	2.48309i	0.0678750	+	0.0884564i
$789$	−37.0712	−	5.07724i	−1.31977	−	0.180755i
$790$	−9.93756	−	9.93756i	−0.353563	−	0.353563i
$791$	−8.73286	−	32.9766i	−0.310505	−	1.17251i
$792$	−22.5057	+	16.8994i	−0.799706	+	0.600495i
$793$	2.85363	+	21.6755i	0.101336	+	0.769720i
$794$	−1.82295	−	0.239996i	−0.0646941	−	0.00851714i
$795$	13.9381	+	14.0842i	0.494335	+	0.499515i
$796$	1.27348	−	1.65963i	0.0451372	−	0.0588239i
$797$	9.35332	+	9.35332i	0.331312	+	0.331312i	0.853084	−	0.521773i	$-0.174729\pi$
$797$	9.35332	+	9.35332i	0.331312	+	0.331312i	−0.521773	+	0.853084i	$0.674729\pi$
$798$	−42.7150	−	11.8187i	−1.51210	−	0.418378i
$799$	−8.00521	−	12.4874i	−0.283204	−	0.441772i
$800$	−4.05511	+	2.34122i	−0.143370	+	0.0827746i
$801$	39.3490	+	10.9845i	1.39033	+	0.388117i
$802$	−4.45920	+	33.8710i	−0.157460	+	1.19603i
$803$	−33.0838	+	19.1009i	−1.16750	+	0.674058i
$804$	−0.218895	+	0.0276581i	−0.00771984	+	0.000975427i
$805$	4.24580	+	32.9948i	0.149645	+	1.16291i
$806$	4.66365	+	1.93175i	0.164270	+	0.0680430i
$807$	−1.17686	+	2.01407i	−0.0414276	+	0.0708986i
$808$	26.2397	−	7.03092i	0.923111	−	0.247347i
$809$	7.60662	−	5.83677i	0.267435	−	0.205210i	−0.466335	−	0.884608i	$-0.654426\pi$
$809$	7.60662	−	5.83677i	0.267435	−	0.205210i	0.733770	+	0.679398i	$0.237759\pi$
$810$	−14.2949	−	19.4563i	−0.502272	−	0.683626i
$811$	−15.7949	+	6.54245i	−0.554633	+	0.229736i	−0.642353	−	0.766409i	$-0.722042\pi$
$811$	−15.7949	+	6.54245i	−0.554633	+	0.229736i	0.0877204	+	0.996145i	$0.472042\pi$
$812$	−1.08954	+	0.624810i	−0.0382355	+	0.0219265i
$813$	27.0276	−	3.41503i	0.947900	−	0.119770i
$814$	7.93824	−	29.6259i	0.278235	−	1.03839i
$815$	7.78285	−	13.4803i	0.272621	−	0.472194i
$816$	32.7784	−	5.69941i	1.14747	−	0.199519i
$817$	31.7977	−	18.3584i	1.11246	−	0.642279i
$818$	6.64028	+	6.64028i	0.232172	+	0.232172i
$819$	44.1534	+	6.41354i	1.54284	+	0.224107i
$820$			0.238544i			0.00833031i
$821$	−15.0641	−	11.5591i	−0.525739	−	0.403414i	0.311504	−	0.950245i	$-0.399167\pi$
$821$	−15.0641	−	11.5591i	−0.525739	−	0.403414i	−0.837243	+	0.546831i	$0.815834\pi$
$822$	−3.83415	−	9.39466i	−0.133731	−	0.327676i
$823$	−2.14723	−	2.79832i	−0.0748477	−	0.0975435i	0.754429	−	0.656382i	$-0.227914\pi$
$823$	−2.14723	−	2.79832i	−0.0748477	−	0.0975435i	−0.829277	+	0.558838i	$0.811247\pi$
$824$	−15.3030	−	4.10042i	−0.533104	−	0.142845i
$825$	11.5863	−	6.60907i	0.403383	−	0.230098i
$826$	25.5342	+	33.4789i	0.888448	+	1.16488i
$827$	19.1767	−	46.2967i	0.666840	−	1.60989i	−0.120026	−	0.992771i	$-0.538298\pi$
$827$	19.1767	−	46.2967i	0.666840	−	1.60989i	0.786866	−	0.617124i	$-0.211702\pi$
$828$	3.39035	+	8.43262i	0.117823	+	0.293054i
$829$	6.44839	−	11.1689i	0.223962	−	0.387914i	−0.732046	−	0.681256i	$-0.761434\pi$
$829$	6.44839	−	11.1689i	0.223962	−	0.387914i	0.956008	+	0.293342i	$0.0947675\pi$
$830$	−39.7882	−	5.23822i	−1.38107	−	0.181821i
$831$	24.8098	+	14.4969i	0.860641	+	0.502891i
$832$		−	32.1353i		−	1.11409i
$833$	−28.1587	−	6.33158i	−0.975640	−	0.219376i
$834$	−1.95984	+	7.16461i	−0.0678636	+	0.248090i
$835$	−1.77219	+	6.61390i	−0.0613292	+	0.228884i
$836$	−1.28683	+	9.77446i	−0.0445060	+	0.338057i
$837$	−0.731571	−	2.91164i	−0.0252868	−	0.100641i
$838$	−39.5468	−	30.3453i	−1.36612	−	1.04826i
$839$	−26.1265	−	10.8220i	−0.901988	−	0.373616i	−0.117004	−	0.993131i	$-0.537329\pi$
$839$	−26.1265	−	10.8220i	−0.901988	−	0.373616i	−0.784984	+	0.619516i	$0.787329\pi$
$840$	18.0518	−	7.30585i	0.622847	−	0.252076i
$841$	−19.5846	+	19.5846i	−0.675331	+	0.675331i
$842$	−13.1181	+	48.9576i	−0.452081	+	1.68719i
$843$	10.6591	+	26.1177i	0.367120	+	0.899540i
$844$	−6.17789	+	4.74046i	−0.212652	+	0.163173i
$845$	19.5400	−	25.4650i	0.672196	−	0.876023i
$846$	−14.4393	−	8.53846i	−0.496433	−	0.293558i
$847$	−3.53565	−	8.60685i	−0.121486	−	0.295735i
$848$	−21.8360	+	21.8360i	−0.749851	+	0.749851i
$849$	3.23804	+	12.3415i	0.111129	+	0.423559i
$850$	−12.9392	+	0.601701i	−0.443811	+	0.0206382i
$851$	32.6763	+	18.8657i	1.12013	+	0.646707i
$852$	−0.0127807	+	0.0218727i	−0.000437859	+	0.000749346i
$853$	−4.27498	−	10.3207i	−0.146373	−	0.353375i	0.833641	−	0.552307i	$-0.186253\pi$
$853$	−4.27498	−	10.3207i	−0.146373	−	0.353375i	−0.980013	+	0.198933i	$0.936253\pi$
$854$	−7.95648	−	13.8745i	−0.272265	−	0.474776i
$855$	31.8965	+	4.53801i	1.09084	+	0.155197i
$856$	4.50878	+	34.2476i	0.154107	+	1.17056i
$857$	−2.48915	−	3.24392i	−0.0850277	−	0.110810i	0.748902	−	0.662680i	$-0.230581\pi$
$857$	−2.48915	−	3.24392i	−0.0850277	−	0.110810i	−0.833930	+	0.551870i	$0.813914\pi$
$858$	0.300542	−	57.6572i	0.0102603	−	1.96839i
$859$	−7.65871	+	28.5827i	−0.261312	+	0.975229i	0.703158	+	0.711034i	$0.251773\pi$
$859$	−7.65871	+	28.5827i	−0.261312	+	0.975229i	−0.964469	+	0.264195i	$0.914894\pi$
$860$	1.62069	−	3.91269i	0.0552651	−	0.133422i
$861$	−0.211081	+	1.50840i	−0.00719362	+	0.0514061i
$862$	4.47208	+	10.7965i	0.152320	+	0.367732i
$863$	6.60546	+	11.4410i	0.224852	+	0.389456i	0.956275	−	0.292469i	$-0.0944767\pi$
$863$	6.60546	+	11.4410i	0.224852	+	0.389456i	−0.731423	+	0.681924i	$0.761143\pi$
$864$	9.66340	−	7.17773i	0.328756	−	0.244191i
$865$	−12.2986	+	3.29541i	−0.418166	+	0.112047i
$866$	3.69368	+	6.39764i	0.125516	+	0.217401i
$867$	28.0861	+	8.84137i	0.953855	+	0.300269i
$868$	−0.635665	−	0.00185754i	−0.0215759	−	6.30490e-5i
$869$	−14.1145	+	14.1145i	−0.478800	+	0.478800i
$870$	4.22483	−	3.20697i	0.143235	−	0.108727i
$871$	−0.860954	+	1.49122i	−0.0291723	+	0.0505279i
$872$	−4.28899	+	32.5781i	−0.145244	+	1.10323i
$873$	−33.5570	−	14.3114i	−1.13573	−	0.484368i
$874$	−65.0954	−	26.9634i	−2.20188	−	0.912050i
$875$	−30.9929	+	8.20753i	−1.04775	+	0.277465i
$876$	6.27295	−	3.57822i	0.211943	−	0.120897i
$877$	10.5724	−	1.39188i	0.357003	−	0.0470003i	0.0501082	−	0.998744i	$-0.484043\pi$
$877$	10.5724	−	1.39188i	0.357003	−	0.0470003i	0.306895	+	0.951743i	$0.400710\pi$
$878$	1.04480	−	0.801703i	0.0352603	−	0.0270561i
$879$	2.91576	−	6.93678i	0.0983462	−	0.233972i
$880$	−15.3178	−	26.5311i	−0.516361	−	0.894364i
$881$	−41.6226	+	17.2407i	−1.40230	+	0.580852i	−0.950348	−	0.311189i	$-0.899273\pi$
$881$	−41.6226	+	17.2407i	−1.40230	+	0.580852i	−0.451954	+	0.892041i	$0.649273\pi$
$882$	−31.6614	+	7.93389i	−1.06609	+	0.267148i
$883$	11.0724			0.372615			0.186308	−	0.982491i	$-0.440348\pi$
$883$	11.0724			0.372615			0.186308	+	0.982491i	$0.440348\pi$
$884$	−4.42606	+	8.56156i	−0.148864	+	0.287956i
$885$	−21.5297	−	21.7553i	−0.723713	−	0.731297i
$886$	−45.3030	+	12.1389i	−1.52198	+	0.407815i
$887$	−13.2973	−	10.2034i	−0.446481	−	0.342597i	0.360924	−	0.932595i	$-0.382462\pi$
$887$	−13.2973	−	10.2034i	−0.446481	−	0.342597i	−0.807404	+	0.589999i	$0.799128\pi$
$888$	5.82783	−	21.3049i	0.195569	−	0.714947i
$889$	−3.39322	+	25.2047i	−0.113805	+	0.845338i
$890$	−13.9798	+	33.7501i	−0.468603	+	1.13131i
$891$	−27.6341	+	20.3033i	−0.925777	+	0.680185i
$892$	2.21697	−	0.594035i	0.0742297	−	0.0198898i
$893$	21.6224	−	5.79370i	0.723566	−	0.193879i
$894$	−1.91485	+	13.9812i	−0.0640421	+	0.467600i
$895$	3.05124	−	7.36635i	0.101992	−	0.246230i
$896$	13.5910	+	33.0848i	0.454045	+	1.10529i
$897$	68.4171	+	18.7151i	2.28438	+	0.624878i
$898$	−39.0008	−	29.9264i	−1.30147	−	0.998656i
$899$	0.637080	−	0.170705i	0.0212478	−	0.00569333i
$900$	−2.19677	+	1.23795i	−0.0732258	+	0.0412651i
$901$	−26.0418	+	8.29220i	−0.867578	+	0.276253i
$902$	1.96829			0.0655368
$903$	13.7104	−	23.3073i	0.456255	−	0.775617i
$904$	−29.3307	+	12.1492i	−0.975526	+	0.404076i
$905$	−18.2177	−	31.5540i	−0.605576	−	1.04889i
$906$	−57.2442	−	24.0617i	−1.90181	−	0.799396i
$907$	24.1481	−	18.5295i	0.801824	−	0.615261i	−0.124401	−	0.992232i	$-0.539701\pi$
$907$	24.1481	−	18.5295i	0.801824	−	0.615261i	0.926225	+	0.376971i	$0.123034\pi$
$908$	−11.8707	+	1.56280i	−0.393941	+	0.0518634i
$909$	32.0580	−	8.23271i	1.06330	−	0.273062i
$910$	−10.4384	+	38.5062i	−0.346030	+	1.27647i
$911$	−25.9309	−	10.7409i	−0.859129	−	0.355863i	−0.0907621	−	0.995873i	$-0.528930\pi$
$911$	−25.9309	−	10.7409i	−0.859129	−	0.355863i	−0.768367	+	0.640010i	$0.778930\pi$
$912$	−6.81305	+	49.7452i	−0.225603	+	1.64723i
$913$	−7.43991	+	56.5117i	−0.246225	+	1.87027i
$914$	−15.4730	+	26.8000i	−0.511801	+	0.886466i
$915$	7.02962	+	9.26074i	0.232392	+	0.306151i
$916$	−4.95566	+	4.95566i	−0.163739	+	0.163739i
$917$	−0.0134247	+	4.59405i	−0.000443323	+	0.151709i
$918$	32.8652	−	5.36215i	1.08471	−	0.176977i
$919$	5.76149	+	9.97920i	0.190054	+	0.329183i	0.945268	−	0.326295i	$-0.105800\pi$
$919$	5.76149	+	9.97920i	0.190054	+	0.329183i	−0.755214	+	0.655479i	$0.772467\pi$
$920$	29.9046	−	8.01293i	0.985927	−	0.264178i
$921$	−3.44351	+	8.19233i	−0.113468	+	0.269947i
$922$	9.29714	+	16.1031i	0.306185	+	0.530328i
$923$	0.0756590	+	0.182657i	0.00249035	+	0.00601223i
$924$	2.72389	+	6.73040i	0.0896095	+	0.221414i
$925$	−4.00603	+	9.67142i	−0.131718	+	0.317994i
$926$	2.80947	−	10.4851i	0.0923248	−	0.344561i
$927$	−18.5920	−	5.19004i	−0.610642	−	0.170463i
$928$	1.60991	+	2.09808i	0.0528480	+	0.0688729i
$929$	−0.774491	−	5.88284i	−0.0254102	−	0.193010i	0.974032	−	0.226411i	$-0.0726993\pi$
$929$	−0.774491	−	5.88284i	−0.0254102	−	0.193010i	−0.999442	+	0.0334015i	$0.989366\pi$
$930$	2.66331	−	0.336518i	0.0873335	−	0.0110349i
$931$	21.9983	−	37.5931i	0.720966	−	1.23206i
$932$	−1.82134	−	4.39710i	−0.0596600	−	0.144032i
$933$	−10.0153	−	5.85214i	−0.327886	−	0.191591i
$934$	32.9711	+	19.0359i	1.07885	+	0.622874i
$935$	−1.25945	−	27.0838i	−0.0411886	−	0.885735i
$936$	0.432863	−	41.5200i	0.0141486	−	1.35712i
$937$	17.5207	−	17.5207i	0.572376	−	0.572376i	−0.360416	−	0.932792i	$-0.617365\pi$
$937$	17.5207	−	17.5207i	0.572376	−	0.572376i	0.932792	+	0.360416i	$0.117365\pi$
$938$	0.168072	−	1.24843i	0.00548775	−	0.0407628i
$939$	0.358659	−	1.31116i	0.0117044	−	0.0427880i
$940$	1.57182	−	2.04844i	0.0512671	−	0.0668126i
$941$	−42.9765	+	32.9770i	−1.40099	+	1.07502i	−0.414712	+	0.909953i	$0.636118\pi$
$941$	−42.9765	+	32.9770i	−1.40099	+	1.07502i	−0.986282	+	0.165067i	$0.947216\pi$
$942$	34.7125	−	14.1669i	1.13099	−	0.461581i
$943$	−0.626699	+	2.33887i	−0.0204081	+	0.0761642i
$944$	33.7292	−	33.7292i	1.09779	−	1.09779i
$945$	22.0859	−	8.67166i	0.718455	−	0.282089i
$946$	−32.2847	−	13.3727i	−1.04967	−	0.434786i
$947$	45.4214	+	34.8530i	1.47600	+	1.13257i	0.961406	+	0.275135i	$0.0887226\pi$
$947$	45.4214	+	34.8530i	1.47600	+	1.13257i	0.514590	+	0.857436i	$0.327944\pi$
$948$	2.68209	−	2.65427i	0.0871102	−	0.0862067i
$949$	7.35654	−	55.8785i	0.238804	−	1.81389i
$950$	5.05945	−	18.8821i	0.164150	−	0.612617i
$951$	−3.99643	−	1.09320i	−0.129593	−	0.0354494i
$952$	−2.34332	+	26.7576i	−0.0759475	+	0.867217i
$953$			2.83206i			0.0917395i	0.998947	+	0.0458698i	$0.0146059\pi$
$953$			2.83206i			0.0917395i	−0.998947	+	0.0458698i	$0.985394\pi$
$954$	−22.0820	+	21.6263i	−0.714932	+	0.700178i
$955$	−38.4106	−	5.05685i	−1.24294	−	0.163636i
$956$	−0.0864151	+	0.149675i	−0.00279486	+	0.00484085i
$957$	−4.55491	−	6.00058i	−0.147239	−	0.193971i
$958$	8.55261	−	20.6478i	0.276322	−	0.667101i
$959$	9.89060	−	1.27273i	0.319384	−	0.0410986i
$960$	−8.46755	−	14.8444i	−0.273289	−	0.479100i
$961$	−29.6213	−	7.93699i	−0.955525	−	0.256032i
$962$	27.5465	+	35.8993i	0.888135	+	1.15744i
$963$	5.05819	+	41.7822i	0.162998	+	1.34641i
$964$	−1.08727	−	0.834295i	−0.0350187	−	0.0268708i
$965$			4.40196i			0.141704i
$966$	−51.5002	+	6.35437i	−1.65699	+	0.204449i
$967$	15.3515	+	15.3515i	0.493670	+	0.493670i	0.909461	−	0.415790i	$-0.136495\pi$
$967$	15.3515	+	15.3515i	0.493670	+	0.493670i	−0.415790	+	0.909461i	$0.636495\pi$
$968$	−7.49927	+	4.32971i	−0.241036	+	0.139162i
$969$	−25.5742	+	36.3396i	−0.821561	+	1.16740i
$970$	16.3107	−	28.2509i	0.523704	−	0.907083i
$971$	−8.41373	+	31.4005i	−0.270009	+	1.00769i	0.689103	+	0.724664i	$0.258005\pi$
$971$	−8.41373	+	31.4005i	−0.270009	+	1.00769i	−0.959112	+	0.283026i	$0.908662\pi$
$972$	5.24393	−	3.81088i	0.168199	−	0.122234i
$973$	−6.31119	−	3.66840i	−0.202327	−	0.117603i
$974$	40.3613	−	16.7182i	1.29326	−	0.535685i
$975$	−2.67031	+	19.4971i	−0.0855183	+	0.624408i
$976$	−14.3751	+	11.0304i	−0.460135	+	0.353074i
$977$	3.63417	−	0.973774i	0.116267	−	0.0311538i	−0.200216	−	0.979752i	$-0.564164\pi$
$977$	3.63417	−	0.973774i	0.116267	−	0.0311538i	0.316484	+	0.948598i	$0.397498\pi$
$978$	20.9634	+	12.2494i	0.670336	+	0.391691i
$979$	47.9357	+	19.8556i	1.53203	+	0.634589i
$980$	−0.626640	−	4.98476i	−0.0200173	−	0.159232i
$981$	−5.63921	+	39.6365i	−0.180046	+	1.26550i
$982$	13.6195	−	7.86322i	0.434615	−	0.250925i
$983$	3.54592	−	26.9340i	0.113097	−	0.859060i	−0.837021	−	0.547171i	$-0.815705\pi$
$983$	3.54592	−	26.9340i	0.113097	−	0.859060i	0.950118	−	0.311889i	$-0.100962\pi$
$984$	1.41744	+	0.00738848i	0.0451863	+	0.000235536i
$985$	11.2497	−	6.49503i	0.358446	−	0.206949i
$986$	1.29079	+	7.20101i	0.0411073	+	0.229327i
$987$	11.7518	−	11.5621i	0.374064	−	0.368027i
$988$	−10.2849	−	10.2849i	−0.327207	−	0.327207i
$989$	26.1699	−	34.1053i	0.832155	−	1.08448i
$990$	−15.0537	−	26.7130i	−0.478437	−	0.848996i
$991$	25.8472	+	3.40285i	0.821064	+	0.108095i	0.529342	−	0.848408i	$-0.322439\pi$
$991$	25.8472	+	3.40285i	0.821064	+	0.108095i	0.291721	+	0.956503i	$0.405772\pi$
$992$	0.174703	+	1.32700i	0.00554683	+	0.0421323i
$993$	−16.5670	−	12.8501i	−0.525739	−	0.407785i
$994$	−0.101974	−	0.102572i	−0.00323442	−	0.00325337i
$995$	−6.13923	−	6.13923i	−0.194627	−	0.194627i
$996$	1.46212	−	10.6756i	0.0463290	−	0.338269i
$997$	25.8253	+	33.6562i	0.817897	+	1.06590i	0.996632	+	0.0820065i	$0.0261328\pi$
$997$	25.8253	+	33.6562i	0.817897	+	1.06590i	−0.178735	+	0.983897i	$0.557201\pi$
$998$	3.11025	−	23.6247i	0.0984533	−	0.747827i
$999$	7.37084	−	25.8825i	0.233203	−	0.818885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bj.a.206.11	yes	352
3.2	odd	2	inner	357.2.bj.a.206.34	yes	352
7.5	odd	6	inner	357.2.bj.a.257.34	yes	352
17.9	even	8	inner	357.2.bj.a.332.11	yes	352
21.5	even	6	inner	357.2.bj.a.257.11	yes	352
51.26	odd	8	inner	357.2.bj.a.332.34	yes	352
119.26	odd	24	inner	357.2.bj.a.26.34	yes	352
357.26	even	24	inner	357.2.bj.a.26.11	✓	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bj.a.26.11	✓	352	357.26	even	24	inner
357.2.bj.a.26.34	yes	352	119.26	odd	24	inner
357.2.bj.a.206.11	yes	352	1.1	even	1	trivial
357.2.bj.a.206.34	yes	352	3.2	odd	2	inner
357.2.bj.a.257.11	yes	352	21.5	even	6	inner
357.2.bj.a.257.34	yes	352	7.5	odd	6	inner
357.2.bj.a.332.11	yes	352	17.9	even	8	inner
357.2.bj.a.332.34	yes	352	51.26	odd	8	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bj (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50134 - 0.402282i) q^{2} +(-1.59673 - 0.671159i) q^{3} +(0.360133 + 0.207923i) q^{4} +(1.05067 - 1.36926i) q^{5} +(2.12724 + 1.64997i) q^{6} +(-2.10371 + 1.60449i) q^{7} +(1.74107 + 1.74107i) q^{8} +(2.09909 + 2.14332i) q^{9} +(-2.12823 + 1.63305i) q^{10} +(2.31944 + 3.02276i) q^{11} +(-0.435486 - 0.573704i) q^{12} -5.62118 q^{13} +(3.80384 - 1.56260i) q^{14} +(-2.59662 + 1.48117i) q^{15} +(-2.32938 - 4.03461i) q^{16} +(-0.191526 - 4.11865i) q^{17} +(-2.28922 - 4.06227i) q^{18} +(6.01033 + 1.61046i) q^{19} +(0.663080 - 0.274657i) q^{20} +(4.43593 - 1.15001i) q^{21} +(-2.26627 - 5.47125i) q^{22} +(7.22294 - 0.950918i) q^{23} +(-1.61149 - 3.94856i) q^{24} +(0.523135 + 1.95237i) q^{25} +(8.43930 + 2.26130i) q^{26} +(-1.91317 - 4.83113i) q^{27} +(-1.09123 + 0.140420i) q^{28} +(1.05467 - 0.436859i) q^{29} +(4.49425 - 1.17916i) q^{30} +(0.572819 + 0.0754130i) q^{31} +(0.599584 + 2.23768i) q^{32} +(-1.67477 - 6.38324i) q^{33} +(-1.36932 + 6.26054i) q^{34} +(-0.0133436 + 4.56631i) q^{35} +(0.310307 + 1.20833i) q^{36} +(4.10888 + 3.15285i) q^{37} +(-8.37568 - 4.83570i) q^{38} +(8.97551 + 3.77271i) q^{39} +(4.21326 - 0.554686i) q^{40} +(-0.127191 + 0.307067i) q^{41} +(-7.12246 - 0.0579404i) q^{42} +(4.17249 - 4.17249i) q^{43} +(0.206808 + 1.57086i) q^{44} +(5.14020 - 0.622277i) q^{45} +(-11.2266 - 1.47801i) q^{46} +(3.11556 - 1.79877i) q^{47} +(1.01153 + 8.00556i) q^{48} +(1.85122 - 6.75078i) q^{49} -3.14161i q^{50} +(-2.45846 + 6.70492i) q^{51} +(-2.02438 - 1.16877i) q^{52} +(-1.71559 - 6.40267i) q^{53} +(0.928841 + 8.02279i) q^{54} +6.57589 q^{55} +(-6.45625 - 0.869183i) q^{56} +(-8.51600 - 6.60537i) q^{57} +(-1.75916 + 0.231597i) q^{58} +(2.65000 + 9.88994i) q^{59} +(-1.24310 - 0.00647972i) q^{60} +(-0.507657 - 3.85604i) q^{61} +(-0.829657 - 0.343655i) q^{62} +(-7.85482 - 1.14096i) q^{63} +5.71681i q^{64} +(-5.90599 + 7.69684i) q^{65} +(-0.0534659 + 10.2571i) q^{66} +(0.153162 - 0.265285i) q^{67} +(0.787389 - 1.52309i) q^{68} +(-12.1713 - 3.32938i) q^{69} +(1.85698 - 6.85020i) q^{70} +(-0.0134596 - 0.0324944i) q^{71} +(-0.0770056 + 7.38635i) q^{72} +(-1.30872 + 9.94070i) q^{73} +(-4.90048 - 6.38643i) q^{74} +(0.475044 - 3.46851i) q^{75} +(1.82967 + 1.82967i) q^{76} +(-9.72943 - 2.63749i) q^{77} +(-11.9576 - 9.27480i) q^{78} +(0.683817 + 5.19411i) q^{79} +(-7.97181 - 1.04951i) q^{80} +(-0.187637 + 8.99804i) q^{81} +(0.314485 - 0.409844i) q^{82} +(10.5784 + 10.5784i) q^{83} +(1.83664 + 0.508175i) q^{84} +(-5.84072 - 4.06508i) q^{85} +(-7.94283 + 4.58579i) q^{86} +(-1.97723 - 0.0103064i) q^{87} +(-1.22452 + 9.30116i) q^{88} +(11.7934 - 6.80891i) q^{89} +(-7.96750 - 1.13356i) q^{90} +(11.8254 - 9.01914i) q^{91} +(2.79894 + 1.15936i) q^{92} +(-0.864022 - 0.504867i) q^{93} +(-5.40112 + 1.44722i) q^{94} +(8.51999 - 6.53762i) q^{95} +(0.544465 - 3.97539i) q^{96} +(-11.2348 + 4.65360i) q^{97} +(-5.49502 + 9.39048i) q^{98} +(-1.61001 + 11.3163i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 352 q - 12 q^{3} - 16 q^{7} - 4 q^{9} - 24 q^{10} - 12 q^{12} - 24 q^{15} + 112 q^{16} - 24 q^{18} - 24 q^{19} - 80 q^{22} - 60 q^{24} - 8 q^{25} - 72 q^{28} - 24 q^{31} + 24 q^{33} - 64 q^{36} - 40 q^{37}+ \cdots + 256 q^{99}+O(q^{100}) \) 352 * q - 12 * q^3 - 16 * q^7 - 4 * q^9 - 24 * q^10 - 12 * q^12 - 24 * q^15 + 112 * q^16 - 24 * q^18 - 24 * q^19 - 80 * q^22 - 60 * q^24 - 8 * q^25 - 72 * q^28 - 24 * q^31 + 24 * q^33 - 64 * q^36 - 40 * q^37 - 24 * q^39 - 24 * q^40 + 68 * q^42 - 48 * q^45 - 40 * q^46 + 48 * q^49 - 20 * q^51 - 240 * q^52 - 16 * q^57 - 8 * q^58 + 44 * q^60 - 24 * q^61 + 88 * q^63 - 12 * q^66 - 16 * q^67 + 64 * q^70 - 120 * q^73 - 156 * q^75 - 176 * q^78 - 24 * q^79 + 120 * q^82 - 104 * q^84 + 112 * q^85 + 132 * q^87 - 24 * q^88 - 96 * q^91 - 8 * q^93 - 120 * q^94 + 60 * q^96 + 256 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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