LMFDB - Embedded newform 357.2.bj.a.26.11

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)

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")

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);

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			26.11
Character	$\chi$	$=$	357.26
Dual form			357.2.bj.a.206.11

$q$-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 $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{8}\right)$	$-1$

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	−0.747040	−	0.664779i	$-0.768526\pi$
$2$	−1.50134	+	0.402282i	−1.06161	+	0.284457i	−0.314566	+	0.949236i	$0.601859\pi$
$3$	−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	0.966829	−	0.255426i	$-0.0822157\pi$
$5$	1.05067	+	1.36926i	0.469872	+	0.612350i	−0.496956	+	0.867776i	$0.665549\pi$
$6$	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	−0.299753	−	0.954017i	$-0.596904\pi$
$11$	2.31944	−	3.02276i	0.699338	−	0.911395i	0.999091	+	0.0426214i	$0.0135709\pi$
$12$	−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	0.508157	−	0.861265i	$-0.330327\pi$
$19$	6.01033	−	1.61046i	1.37887	−	0.369466i	0.870709	+	0.491799i	$0.163660\pi$
$20$	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	0.837945	−	0.545755i	$-0.183757\pi$
$23$	7.22294	+	0.950918i	1.50609	+	0.198280i	0.668141	+	0.744035i	$0.267090\pi$
$24$	−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	0.478451	−	0.878114i	$-0.341198\pi$
$29$	1.05467	+	0.436859i	0.195847	+	0.0811227i	−0.282604	+	0.959237i	$0.591198\pi$
$30$	4.49425	+	1.17916i	0.820534	+	0.215284i
$31$	0.572819	−	0.0754130i	0.102881	−	0.0135446i	−0.0789098	−	0.996882i	$-0.525144\pi$
$31$	0.572819	−	0.0754130i	0.102881	−	0.0135446i	0.181791	+	0.983337i	$0.441811\pi$
$32$	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	−0.213092	−	0.977032i	$-0.568354\pi$
$37$	4.10888	−	3.15285i	0.675496	−	0.518326i	0.888588	+	0.458706i	$0.151687\pi$
$38$	−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	0.913636	−	0.406532i	$-0.133262\pi$
$41$	−0.127191	−	0.307067i	−0.0198639	−	0.0479558i	−0.933500	+	0.358577i	$0.883262\pi$
$42$	−7.12246	+	0.0579404i	−1.09902	+	0.00894039i
$43$	4.17249	+	4.17249i	0.636298	+	0.636298i	0.949640	−	0.313342i	$-0.101449\pi$
$43$	4.17249	+	4.17249i	0.636298	+	0.636298i	−0.313342	+	0.949640i	$0.601449\pi$
$44$	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	0.709708	−	0.704496i	$-0.248827\pi$
$47$	3.11556	+	1.79877i	0.454451	+	0.262377i	−0.255257	+	0.966873i	$0.582160\pi$
$48$	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	0.742199	+	0.670180i	$0.233783\pi$
$53$	−1.71559	+	6.40267i	−0.235654	+	0.879474i	−0.977853	+	0.209294i	$0.932884\pi$
$54$	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	−0.547610	−	0.836733i	$-0.684462\pi$
$59$	2.65000	−	9.88994i	0.345001	−	1.28756i	0.892611	−	0.450827i	$-0.148871\pi$
$60$	−1.24310	+	0.00647972i	−0.160483	+	0.000836529i
$61$	−0.507657	+	3.85604i	−0.0649988	+	0.493715i	0.927722	+	0.373273i	$0.121765\pi$
$61$	−0.507657	+	3.85604i	−0.0649988	+	0.493715i	−0.992720	+	0.120442i	$0.961569\pi$
$62$	−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	0.875230	−	0.483708i	$-0.160710\pi$
$67$	0.153162	+	0.265285i	0.0187118	+	0.0324097i	−0.856518	+	0.516117i	$0.827377\pi$
$68$	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	−0.924676	−	0.380754i	$-0.875664\pi$
$71$	−0.0134596	+	0.0324944i	−0.00159736	+	0.00385638i	0.923079	+	0.384611i	$0.125664\pi$
$72$	−0.0770056	−	7.38635i	−0.00907520	−	0.870489i
$73$	−1.30872	−	9.94070i	−0.153174	−	1.16347i	−0.879424	−	0.476040i	$-0.842072\pi$
$73$	−1.30872	−	9.94070i	−0.153174	−	1.16347i	0.726250	−	0.687431i	$-0.241262\pi$
$74$	−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	−0.908943	−	0.416920i	$-0.863109\pi$
$79$	0.683817	−	5.19411i	0.0769355	−	0.584383i	0.985878	−	0.167462i	$-0.0535573\pi$
$80$	−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	0.176897	−	0.984229i	$-0.443394\pi$
$83$	10.5784	−	10.5784i	1.16113	−	1.16113i	0.984229	−	0.176897i	$-0.0566059\pi$
$84$	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	0.971128	−	0.238558i	$-0.0766746\pi$
$89$	11.7934	+	6.80891i	1.25010	+	0.721743i	0.278967	+	0.960301i	$0.410008\pi$
$90$	−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	−0.269309	−	0.963054i	$-0.586795\pi$
$97$	−11.2348	−	4.65360i	−1.14072	−	0.472502i	−0.871412	+	0.490552i	$0.836795\pi$
$98$	−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	0.998350	+	0.0574172i	$0.0182865\pi$
$101$	5.51638	+	9.55464i	0.548900	+	0.950723i	−0.449450	+	0.893305i	$0.648380\pi$
$102$	6.38825	+	9.07736i	0.632531	+	0.898793i
$103$	−5.57225	−	3.21714i	−0.549050	−	0.316994i	0.199689	−	0.979859i	$-0.436007\pi$
$103$	−5.57225	−	3.21714i	−0.549050	−	0.316994i	−0.748739	+	0.662865i	$0.769340\pi$
$104$	−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	0.0905809	−	0.995889i	$-0.471128\pi$
$107$	11.1300	−	8.54037i	1.07598	−	0.825628i	0.985399	+	0.170261i	$0.0544610\pi$
$108$	0.315506	+	2.13764i	0.0303596	+	0.205695i
$109$	8.12405	−	10.5875i	0.778143	−	1.01410i	−0.221102	−	0.975251i	$-0.570965\pi$
$109$	8.12405	−	10.5875i	0.778143	−	1.01410i	0.999245	−	0.0388452i	$-0.0123679\pi$
$110$	−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	−0.966670	−	0.256026i	$-0.917587\pi$
$113$	−4.93418	−	11.9122i	−0.464169	−	1.12060i	0.502501	−	0.864577i	$-0.332413\pi$
$114$	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	0.941144	−	0.338007i	$-0.109753\pi$
$127$	6.79701	+	6.79701i	0.603137	+	0.603137i	−0.338007	+	0.941144i	$0.609753\pi$
$128$	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	0.837245	−	0.546828i	$-0.184165\pi$
$131$	1.05705	+	1.37758i	0.0923549	+	0.120359i	−0.744890	+	0.667187i	$0.767498\pi$
$132$	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	−0.632914	−	0.774222i	$-0.718141\pi$
$137$	−3.26415	+	1.88456i	−0.278875	+	0.161009i	0.354039	+	0.935231i	$0.384808\pi$
$138$	16.9339	−	9.89482i	1.44151	−	0.842303i
$139$	1.05586	−	2.54907i	0.0895569	−	0.216209i	−0.872755	−	0.488159i	$-0.837669\pi$
$139$	1.05586	−	2.54907i	0.0895569	−	0.216209i	0.962311	+	0.271950i	$0.0876685\pi$
$140$	−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	−0.738470	−	0.674286i	$-0.764451\pi$
$149$	2.62092	−	4.53956i	0.214714	−	0.371896i	0.953184	+	0.302391i	$0.0977847\pi$
$150$	−2.10852	−	5.01630i	−0.172160	−	0.409580i
$151$	−22.2797	−	5.96983i	−1.81310	−	0.485818i	−0.817203	−	0.576349i	$-0.804477\pi$
$151$	−22.2797	−	5.96983i	−1.81310	−	0.485818i	−0.995894	+	0.0905314i	$0.971143\pi$
$152$	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	0.997846	+	0.0655963i	$0.0208950\pi$
$157$	6.96329	+	12.0608i	0.555731	+	0.962555i	−0.442115	+	0.896958i	$0.645772\pi$
$158$	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	0.472297	−	0.881440i	$-0.343425\pi$
$163$	8.94168	+	1.17719i	0.700367	+	0.0922050i	0.228070	+	0.973645i	$0.426758\pi$
$164$	−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	0.236333	−	0.971672i	$-0.424054\pi$
$167$	−3.66532	−	1.51822i	−0.283631	−	0.117484i	−0.519964	+	0.854188i	$0.674054\pi$
$168$	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	−0.806822	−	0.590795i	$-0.798814\pi$
$173$	−5.85278	+	4.49100i	−0.444979	+	0.341444i	0.361843	+	0.932239i	$0.382148\pi$
$174$	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	0.421698	−	0.906736i	$-0.361434\pi$
$179$	4.46234	+	1.19568i	0.333531	+	0.0893694i	−0.0881669	+	0.996106i	$0.528101\pi$
$180$	1.98054	−	0.844663i	0.147621	−	0.0629575i
$181$	8.07877	+	19.5039i	0.600490	+	1.44971i	0.873078	+	0.487580i	$0.162120\pi$
$181$	8.07877	+	19.5039i	0.600490	+	1.44971i	−0.272588	+	0.962131i	$0.587880\pi$
$182$	−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	0.0992660	+	0.995061i	$0.468351\pi$
$191$	−11.2237	+	19.4399i	−0.812115	+	1.40662i	−0.911381	+	0.411564i	$0.864983\pi$
$192$	3.83689	+	9.12821i	0.276904	+	0.658771i
$193$	−2.02346	−	1.55266i	−0.145652	−	0.111763i	0.533365	−	0.845885i	$-0.320927\pi$
$193$	−2.02346	−	1.55266i	−0.145652	−	0.111763i	−0.679017	+	0.734122i	$0.737594\pi$
$194$	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	−0.120961	−	0.992657i	$-0.538597\pi$
$197$	6.95358	−	2.88027i	0.495422	−	0.205211i	0.616383	+	0.787447i	$0.288597\pi$
$198$	6.96954	+	16.3420i	0.495304	+	1.16137i
$199$	0.656612	+	4.98746i	0.0465460	+	0.353552i	0.998831	+	0.0483413i	$0.0153935\pi$
$199$	0.656612	+	4.98746i	0.0465460	+	0.353552i	−0.952285	+	0.305211i	$0.901273\pi$
$200$	−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	−0.953014	−	0.302925i	$-0.902037\pi$
$211$	−7.16606	−	17.3004i	−0.493332	−	1.19101i	0.459682	−	0.888083i	$-0.347963\pi$
$212$	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	0.825601	−	0.564255i	$-0.190836\pi$
$223$	3.90273	+	3.90273i	0.261346	+	0.261346i	−0.564255	+	0.825601i	$0.690836\pi$
$224$	−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	−0.937630	−	0.347636i	$-0.886984\pi$
$227$	−22.8423	−	17.5275i	−1.51610	−	1.16334i	−0.578467	−	0.815706i	$-0.696349\pi$
$228$	−1.69349	+	4.14949i	−0.112154	+	0.274807i
$229$	−4.36194	−	16.2790i	−0.288245	−	1.07574i	−0.946435	−	0.322893i	$-0.895344\pi$
$229$	−4.36194	−	16.2790i	−0.288245	−	1.07574i	0.658190	−	0.752852i	$-0.271322\pi$
$230$	−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	−0.861787	−	0.507270i	$-0.830655\pi$
$233$	−9.07998	+	6.96732i	−0.594850	+	0.456444i	0.266938	+	0.963714i	$0.413988\pi$
$234$	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	$-0.995721\pi$
$239$		−	0.415611i		−	0.0268836i	0.999910	−	0.0134418i	$-0.00427879\pi$
$240$	12.0244	−	7.02614i	0.776174	−	0.453535i
$241$	−3.26744	+	0.430167i	−0.210475	+	0.0277095i	−0.235026	−	0.971989i	$-0.575518\pi$
$241$	−3.26744	+	0.430167i	−0.210475	+	0.0277095i	0.0245515	+	0.999699i	$0.492184\pi$
$242$	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	$0.117509\pi$
$251$			11.4335i			0.721675i	−0.932629	+	0.360838i	$0.882491\pi$
$252$	−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	0.972760	+	0.231813i	$0.0744656\pi$
$257$	3.94739	+	14.7319i	0.246232	+	0.918948i	−0.726529	+	0.687136i	$0.758868\pi$
$258$	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	0.836407	−	0.548109i	$-0.184652\pi$
$263$	20.8668	+	5.59124i	1.28670	+	0.344771i	0.450295	+	0.892880i	$0.351319\pi$
$264$	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	0.995968	−	0.0897099i	$-0.0285940\pi$
$269$	0.175791	+	1.33526i	0.0107181	+	0.0814124i	−0.985250	+	0.171122i	$0.945261\pi$
$270$	11.9611	−	7.15745i	0.727932	−	0.435589i
$271$	−13.6213	−	7.86424i	−0.827433	−	0.477719i	0.0255401	−	0.999674i	$-0.491869\pi$
$271$	−13.6213	−	7.86424i	−0.827433	−	0.477719i	−0.852973	+	0.521955i	$0.825203\pi$
$272$	−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	−0.607293	−	0.794478i	$-0.707745\pi$
$277$	−16.4481	+	2.16543i	−0.988268	+	0.130108i	−0.380974	+	0.924586i	$0.624411\pi$
$278$	−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	−0.961569	−	0.274564i	$-0.911466\pi$
$281$	−11.5163	+	11.5163i	−0.687004	+	0.687004i	0.274564	+	0.961569i	$0.411466\pi$
$282$	9.59544	−	1.31418i	0.571400	−	0.0782584i
$283$	−4.48446	+	5.84426i	−0.266574	+	0.347405i	−0.907391	−	0.420288i	$-0.861929\pi$
$283$	−4.48446	+	5.84426i	−0.266574	+	0.347405i	0.640817	+	0.767694i	$0.278596\pi$
$284$	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	$-0.959497\pi$
$293$		−	4.34437i		−	0.253801i	0.991915	−	0.126900i	$-0.0405028\pi$
$294$	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	$0.0467726\pi$
$307$			5.13070i			0.292824i	−0.989224	+	0.146412i	$0.953227\pi$
$308$	−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	0.0601028	−	0.998192i	$-0.480857\pi$
$311$	6.63981	−	0.874147i	0.376509	−	0.0495683i	0.316406	+	0.948624i	$0.397524\pi$
$312$	9.05846	−	22.1956i	0.512834	−	1.25658i
$313$	0.102438	−	0.778094i	0.00579014	−	0.0439805i	−0.988306	−	0.152484i	$-0.951273\pi$
$313$	0.102438	−	0.778094i	0.00579014	−	0.0439805i	0.994096	+	0.108504i	$0.0346060\pi$
$314$	−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	0.196834	−	0.980437i	$-0.436934\pi$
$317$	2.37164	+	0.312232i	0.133205	+	0.0175367i	−0.0636290	+	0.997974i	$0.520267\pi$
$318$	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	0.0772623	−	0.997011i	$-0.475382\pi$
$331$	11.6925	−	3.13300i	0.642679	−	0.172205i	0.565417	+	0.824806i	$0.308715\pi$
$332$	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	0.240848	−	0.970563i	$-0.422575\pi$
$337$	−5.05088	−	2.09214i	−0.275139	−	0.113966i	−0.515987	+	0.856597i	$0.672575\pi$
$338$	−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	−0.211662	−	0.977343i	$-0.567888\pi$
$347$	−22.5488	−	17.3023i	−1.21048	−	0.928838i	−0.998823	+	0.0485053i	$0.984554\pi$
$348$	−0.709922	+	0.414823i	−0.0380558	+	0.0222368i
$349$	17.9561	−	17.9561i	0.961170	−	0.961170i	−0.0381037	−	0.999274i	$-0.512132\pi$
$349$	17.9561	−	17.9561i	0.961170	−	0.961170i	0.999274	+	0.0381037i	$0.0121317\pi$
$350$	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	−0.880346	−	0.474333i	$-0.842689\pi$
$353$	−17.0923	+	9.86827i	−0.909734	+	0.525235i	−0.0293884	+	0.999568i	$0.509356\pi$
$354$	−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	−0.576130	−	0.817358i	$-0.695438\pi$
$359$	−12.6264	+	3.38323i	−0.666395	+	0.178560i	−0.0902647	+	0.995918i	$0.528771\pi$
$360$	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	0.658321	−	0.752737i	$-0.271267\pi$
$367$	1.94674	+	1.49379i	0.101619	+	0.0779751i	−0.556702	+	0.830712i	$0.687934\pi$
$368$	−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	−0.378627	−	0.925549i	$-0.623604\pi$
$373$	11.8242	−	20.4802i	0.612236	−	1.06042i	0.990863	−	0.134874i	$-0.0430630\pi$
$374$	−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	−0.938194	−	0.346110i	$-0.887503\pi$
$379$	−0.585095	+	1.41254i	−0.0300543	+	0.0725575i	0.908140	+	0.418667i	$0.137503\pi$
$380$	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	−0.247991	−	0.968762i	$-0.579770\pi$
$383$	0.423186	−	0.113392i	0.0216238	−	0.00579407i	0.269615	+	0.962968i	$0.413104\pi$
$384$	−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	0.667696	+	0.744434i	$0.267281\pi$
$389$	−5.57695	+	20.8135i	−0.282763	+	1.05528i	−0.950459	+	0.310851i	$0.899386\pi$
$390$	−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	0.159900	−	0.987133i	$-0.448883\pi$
$397$	1.17284	+	0.154408i	0.0588633	+	0.00774950i	−0.101037	+	0.994883i	$0.532216\pi$
$398$	−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	0.757161	+	0.653228i	$0.226586\pi$
$401$	−2.86894	+	21.7918i	−0.143268	+	1.08823i	−0.900429	+	0.435002i	$0.856748\pi$
$402$	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	−0.623752	−	0.781622i	$-0.714393\pi$
$409$	−5.23236	+	3.02090i	−0.258723	+	0.149374i	0.365029	+	0.930996i	$0.381059\pi$
$410$	−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	0.485897	−	0.874016i	$-0.338493\pi$
$419$	29.6296	−	12.2730i	1.44750	−	0.599574i	0.961604	+	0.274442i	$0.0884932\pi$
$420$	2.62552	+	1.98091i	0.128112	+	0.0966584i
$421$			32.6093i			1.58928i	0.607081	+	0.794640i	$0.292340\pi$
$421$			32.6093i			1.58928i	−0.607081	+	0.794640i	$0.707660\pi$
$422$	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	−0.890472	−	0.455039i	$-0.849625\pi$
$431$	−4.57701	+	5.96488i	−0.220467	+	0.287318i	0.670005	+	0.742357i	$0.266292\pi$
$432$	−15.0352	−	18.9724i	−0.723381	−	0.912812i
$433$	−3.36078	+	3.36078i	−0.161509	+	0.161509i	−0.783235	−	0.621726i	$-0.786432\pi$
$433$	−3.36078	+	3.36078i	−0.161509	+	0.161509i	0.621726	+	0.783235i	$0.286432\pi$
$434$	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	0.780882	−	0.624678i	$-0.214770\pi$
$439$	−0.515797	−	0.672199i	−0.0246176	−	0.0320823i	−0.805500	+	0.592596i	$0.798103\pi$
$440$	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	0.969417	−	0.245418i	$-0.0789251\pi$
$443$	26.1324	+	15.0876i	1.24159	+	0.716831i	0.272171	+	0.962249i	$0.412258\pi$
$444$	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	0.434786	−	0.900534i	$-0.356824\pi$
$449$	29.2205	−	12.1035i	1.37900	−	0.571201i	0.944214	+	0.329333i	$0.106824\pi$
$450$	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	0.975328	+	0.220763i	$0.0708546\pi$
$457$	5.15307	+	19.2315i	0.241050	+	0.899612i	−0.734277	+	0.678850i	$0.762479\pi$
$458$	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	−0.876105	−	0.482120i	$-0.839867\pi$
$461$	−8.45921	+	8.45921i	−0.393984	+	0.393984i	0.482120	+	0.876105i	$0.339867\pi$
$462$	−16.3450	+	21.6638i	−0.760438	+	1.00789i
$463$		−	6.98382i		−	0.324566i	−0.986744	−	0.162283i	$-0.948114\pi$
$463$		−	6.98382i		−	0.324566i	0.986744	−	0.162283i	$-0.0518857\pi$
$464$	−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	−0.760665	−	0.649144i	$-0.775127\pi$
$467$	−23.6599	+	6.33965i	−1.09485	+	0.293364i	−0.334183	+	0.942508i	$0.608460\pi$
$468$	−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	−0.979303	−	0.202400i	$-0.935126\pi$
$479$	−1.87682	−	14.2559i	−0.0857540	−	0.651366i	0.893549	−	0.448966i	$-0.148208\pi$
$480$	−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	−0.0358676	−	0.999357i	$-0.511419\pi$
$487$	−22.2988	−	17.1105i	−1.01046	−	0.775349i	−0.974588	+	0.224007i	$0.928086\pi$
$488$	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	0.526992	−	0.849871i	$-0.323320\pi$
$491$	−7.15452	−	7.15452i	−0.322879	−	0.322879i	−0.849871	+	0.526992i	$0.823320\pi$
$492$	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	−0.886455	−	0.462814i	$-0.846840\pi$
$499$	2.00106	−	15.1996i	0.0895799	−	0.680427i	0.976035	−	0.217613i	$-0.0698270\pi$
$500$	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	0.849892	−	0.526956i	$-0.176667\pi$
$503$	−2.77400	−	6.69704i	−0.123687	−	0.298606i	−0.973579	+	0.228350i	$0.926667\pi$
$504$	−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	−0.945445	−	0.325782i	$-0.894372\pi$
$509$	−4.29983	+	7.44753i	−0.190587	+	0.330106i	0.754858	+	0.655888i	$0.227706\pi$
$510$	−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	0.181534	−	0.983385i	$-0.441894\pi$
$521$	−16.4653	−	12.6343i	−0.721358	−	0.553517i	−0.902892	+	0.429867i	$0.858560\pi$
$522$	−4.18902	+	3.28429i	−0.183348	+	0.143750i
$523$	13.3477	−	23.1188i	0.583652	−	1.01092i	−0.411390	−	0.911460i	$-0.634956\pi$
$523$	13.3477	−	23.1188i	0.583652	−	1.01092i	0.995042	−	0.0994558i	$-0.0317102\pi$
$524$	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	−0.998290	−	0.0584501i	$-0.981384\pi$
$541$	−27.9161	+	21.4208i	−1.20021	+	0.920952i	−0.201918	+	0.979402i	$0.564717\pi$
$542$	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	−0.305685	−	0.952133i	$-0.598885\pi$
$547$	−27.9510	−	11.5777i	−1.19510	−	0.495025i	−0.889411	+	0.457108i	$0.848885\pi$
$548$	−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	0.830742	−	0.556658i	$-0.187917\pi$
$557$	−1.57438	−	2.72691i	−0.0667088	−	0.115543i	−0.897451	+	0.441115i	$0.854583\pi$
$558$	−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	0.479029	−	0.877799i	$-0.340989\pi$
$563$	10.7956	+	2.89267i	0.454980	+	0.121911i	−0.0240487	+	0.999711i	$0.507656\pi$
$564$	−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	0.718293	+	0.695741i	$0.244924\pi$
$569$	10.5935	+	39.5356i	0.444103	+	1.65742i	−0.274189	+	0.961676i	$0.588409\pi$
$570$	28.9109	−	0.150700i	1.21095	−	0.00631213i
$571$	−5.37656	+	7.00687i	−0.225002	+	0.293228i	−0.892189	−	0.451662i	$-0.850831\pi$
$571$	−5.37656	+	7.00687i	−0.225002	+	0.293228i	0.667187	+	0.744890i	$0.267498\pi$
$572$	−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	0.00403355	−	0.999992i	$-0.498716\pi$
$577$	20.9478	−	12.0942i	0.872069	−	0.503489i	0.868035	+	0.496503i	$0.165383\pi$
$578$	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	0.876686	−	0.481064i	$-0.159749\pi$
$587$	9.58517	+	9.58517i	0.395622	+	0.395622i	−0.481064	+	0.876686i	$0.659749\pi$
$588$	−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	−0.852477	−	0.522764i	$-0.824901\pi$
$593$	−9.14627	−	34.1344i	−0.375592	−	1.40173i	0.476885	−	0.878966i	$-0.341766\pi$
$594$	−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	0.999074	−	0.0430162i	$-0.0136967\pi$
$599$	11.3142	+	19.5967i	0.462284	+	0.800699i	−0.536790	+	0.843716i	$0.680363\pi$
$600$	6.86602	+	5.21184i	0.280304	+	0.212773i
$601$	7.37834	+	17.8129i	0.300969	+	0.726603i	0.999934	+	0.0114477i	$0.00364401\pi$
$601$	7.37834	+	17.8129i	0.300969	+	0.726603i	−0.698966	+	0.715155i	$0.746356\pi$
$602$	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	0.182428	−	0.983219i	$-0.441604\pi$
$607$	29.0563	−	22.2957i	1.17936	−	0.904955i	0.996933	+	0.0782644i	$0.0249378\pi$
$608$		−	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	0.857263	−	0.514879i	$-0.172163\pi$
$613$	−0.427503	−	0.740458i	−0.0172667	−	0.0299068i	−0.874530	+	0.484972i	$0.838830\pi$
$614$	−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	0.733947	−	0.679207i	$-0.237676\pi$
$617$	19.1923	+	7.94973i	0.772654	+	0.320044i	0.0387072	+	0.999251i	$0.487676\pi$
$618$	−17.1617	+	2.35045i	−0.690344	+	0.0945488i
$619$	−17.3589	−	13.3199i	−0.697712	−	0.535373i	0.197893	−	0.980224i	$-0.436590\pi$
$619$	−17.3589	−	13.3199i	−0.697712	−	0.535373i	−0.895605	+	0.444850i	$0.853257\pi$
$620$	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	−0.0171534	+	0.999853i	$0.505460\pi$
$631$	−25.5469	+	25.5469i	−1.01701	+	1.01701i	−0.999853	+	0.0171534i	$0.994540\pi$
$632$	−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	−0.870390	−	0.492363i	$-0.836133\pi$
$641$	−3.97722	−	30.2100i	−0.157091	−	1.19322i	0.713299	−	0.700860i	$-0.247200\pi$
$642$	9.58480	−	36.5316i	0.378282	−	1.44179i
$643$	−0.545652	+	1.31732i	−0.0215184	+	0.0519501i	−0.934274	−	0.356557i	$-0.883951\pi$
$643$	−0.545652	+	1.31732i	−0.0215184	+	0.0519501i	0.912755	+	0.408507i	$0.133951\pi$
$644$	−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	0.981041	+	0.193801i	$0.0620815\pi$
$647$	16.7461	+	29.0051i	0.658357	+	1.14031i	−0.322684	+	0.946507i	$0.604585\pi$
$648$	−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	−0.986845	−	0.161669i	$-0.948312\pi$
$653$	0.209981	−	1.59497i	0.00821720	−	0.0624159i	0.995062	+	0.0992536i	$0.0316455\pi$
$654$	−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	0.800030	+	0.599960i	$0.204817\pi$
$661$	−4.95678	+	18.4990i	−0.192797	+	0.719527i	−0.992826	+	0.119566i	$0.961850\pi$
$662$	−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	0.869030	+	0.494759i	$0.164744\pi$
$673$	15.6790	+	37.8524i	0.604380	+	1.45910i	−0.264650	+	0.964345i	$0.585256\pi$
$674$	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	−0.219827	−	0.975539i	$-0.570549\pi$
$677$	17.3178	−	13.2884i	0.665577	−	0.510715i	0.885403	+	0.464824i	$0.153882\pi$
$678$	−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	−0.121142	−	0.992635i	$-0.538655\pi$
$683$	0.490217	−	0.0645383i	0.0187576	−	0.00246949i	0.139899	+	0.990166i	$0.455322\pi$
$684$	−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	0.396268	−	0.918135i	$-0.370305\pi$
$691$	14.2318	+	1.87365i	0.541404	+	0.0712771i	0.145135	+	0.989412i	$0.453638\pi$
$692$	−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	0.843796	−	0.536664i	$-0.180316\pi$
$709$	2.84984	+	3.71398i	0.107028	+	0.139481i	−0.736768	+	0.676145i	$0.763649\pi$
$710$	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	0.844522	−	0.535520i	$-0.179884\pi$
$719$	2.91393	+	3.79750i	0.108671	+	0.141623i	−0.735851	+	0.677143i	$0.763218\pi$
$720$	−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	−0.850396	−	0.526144i	$-0.823637\pi$
$733$	−35.8402	+	9.60335i	−1.32379	+	0.354708i	−0.473392	+	0.880852i	$0.656971\pi$
$734$	−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	0.735044	+	0.678020i	$0.237162\pi$
$739$	−6.53877	+	24.4030i	−0.240533	+	0.897680i	−0.975576	+	0.219660i	$0.929505\pi$
$740$	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	−0.0863342	−	0.996266i	$-0.527515\pi$
$743$	−23.2197	−	9.61792i	−0.851848	−	0.352847i	−0.765514	+	0.643419i	$0.777515\pi$
$744$	−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	−0.643151	−	0.765740i	$-0.722373\pi$
$751$	−1.91728	+	1.47118i	−0.0699625	+	0.0536841i	0.573188	+	0.819424i	$0.305706\pi$
$752$	−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	0.530025	−	0.847982i	$-0.322183\pi$
$757$	−8.74816	−	8.74816i	−0.317957	−	0.317957i	−0.847982	+	0.530025i	$0.822183\pi$
$758$	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	0.824257	−	0.566216i	$-0.191593\pi$
$761$	20.5801	+	11.8819i	0.746027	+	0.430719i	−0.0782293	+	0.996935i	$0.524927\pi$
$762$	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	−0.0633382	−	0.997992i	$-0.520175\pi$
$773$	13.6376	−	50.8962i	0.490510	−	1.83061i	0.553849	−	0.832617i	$-0.313159\pi$
$774$	−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	−0.795128	−	0.606442i	$-0.792596\pi$
$787$	−5.16331	−	39.2192i	−0.184052	−	1.39801i	0.611076	−	0.791572i	$-0.290737\pi$
$788$	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	−0.521773	−	0.853084i	$-0.674729\pi$
$797$	9.35332	−	9.35332i	0.331312	−	0.331312i	0.853084	+	0.521773i	$0.174729\pi$
$798$	−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	0.733770	−	0.679398i	$-0.237759\pi$
$809$	7.60662	+	5.83677i	0.267435	+	0.205210i	−0.466335	+	0.884608i	$0.654426\pi$
$810$	−14.2949	+	19.4563i	−0.502272	+	0.683626i
$811$	−15.7949	−	6.54245i	−0.554633	−	0.229736i	0.0877204	−	0.996145i	$-0.472042\pi$
$811$	−15.7949	−	6.54245i	−0.554633	−	0.229736i	−0.642353	+	0.766409i	$0.722042\pi$
$812$	−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	−0.837243	−	0.546831i	$-0.815834\pi$
$821$	−15.0641	+	11.5591i	−0.525739	+	0.403414i	0.311504	+	0.950245i	$0.399167\pi$
$822$	−3.83415	+	9.39466i	−0.133731	+	0.327676i
$823$	−2.14723	+	2.79832i	−0.0748477	+	0.0975435i	−0.829277	−	0.558838i	$-0.811247\pi$
$823$	−2.14723	+	2.79832i	−0.0748477	+	0.0975435i	0.754429	+	0.656382i	$0.227914\pi$
$824$	−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	0.786866	+	0.617124i	$0.211702\pi$
$827$	19.1767	+	46.2967i	0.666840	+	1.60989i	−0.120026	+	0.992771i	$0.538298\pi$
$828$	3.39035	−	8.43262i	0.117823	−	0.293054i
$829$	6.44839	+	11.1689i	0.223962	+	0.387914i	0.956008	−	0.293342i	$-0.0947675\pi$
$829$	6.44839	+	11.1689i	0.223962	+	0.387914i	−0.732046	+	0.681256i	$0.761434\pi$
$830$	−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	−0.784984	−	0.619516i	$-0.787329\pi$
$839$	−26.1265	+	10.8220i	−0.901988	+	0.373616i	−0.117004	+	0.993131i	$0.537329\pi$
$840$	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	−0.980013	−	0.198933i	$-0.936253\pi$
$853$	−4.27498	+	10.3207i	−0.146373	+	0.353375i	0.833641	+	0.552307i	$0.186253\pi$
$854$	−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	−0.833930	−	0.551870i	$-0.813914\pi$
$857$	−2.48915	+	3.24392i	−0.0850277	+	0.110810i	0.748902	+	0.662680i	$0.230581\pi$
$858$	0.300542	+	57.6572i	0.0102603	+	1.96839i
$859$	−7.65871	−	28.5827i	−0.261312	−	0.975229i	−0.964469	−	0.264195i	$-0.914894\pi$
$859$	−7.65871	−	28.5827i	−0.261312	−	0.975229i	0.703158	−	0.711034i	$-0.251773\pi$
$860$	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	−0.731423	−	0.681924i	$-0.761143\pi$
$863$	6.60546	−	11.4410i	0.224852	−	0.389456i	0.956275	+	0.292469i	$0.0944767\pi$
$864$	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	0.306895	−	0.951743i	$-0.400710\pi$
$877$	10.5724	+	1.39188i	0.357003	+	0.0470003i	0.0501082	+	0.998744i	$0.484043\pi$
$878$	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	−0.451954	−	0.892041i	$-0.649273\pi$
$881$	−41.6226	−	17.2407i	−1.40230	−	0.580852i	−0.950348	+	0.311189i	$0.899273\pi$
$882$	−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	−0.807404	−	0.589999i	$-0.799128\pi$
$887$	−13.2973	+	10.2034i	−0.446481	+	0.342597i	0.360924	+	0.932595i	$0.382462\pi$
$888$	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	0.926225	−	0.376971i	$-0.123034\pi$
$907$	24.1481	+	18.5295i	0.801824	+	0.615261i	−0.124401	+	0.992232i	$0.539701\pi$
$908$	−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	−0.768367	−	0.640010i	$-0.778930\pi$
$911$	−25.9309	+	10.7409i	−0.859129	+	0.355863i	−0.0907621	+	0.995873i	$0.528930\pi$
$912$	−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	−0.755214	−	0.655479i	$-0.772467\pi$
$919$	5.76149	−	9.97920i	0.190054	−	0.329183i	0.945268	+	0.326295i	$0.105800\pi$
$920$	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	−0.999442	−	0.0334015i	$-0.989366\pi$
$929$	−0.774491	+	5.88284i	−0.0254102	+	0.193010i	0.974032	+	0.226411i	$0.0726993\pi$
$930$	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	0.932792	−	0.360416i	$-0.117365\pi$
$937$	17.5207	+	17.5207i	0.572376	+	0.572376i	−0.360416	+	0.932792i	$0.617365\pi$
$938$	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	−0.986282	−	0.165067i	$-0.947216\pi$
$941$	−42.9765	−	32.9770i	−1.40099	−	1.07502i	−0.414712	−	0.909953i	$-0.636118\pi$
$942$	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	0.514590	−	0.857436i	$-0.327944\pi$
$947$	45.4214	−	34.8530i	1.47600	−	1.13257i	0.961406	−	0.275135i	$-0.0887226\pi$
$948$	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	$-0.985394\pi$
$953$		−	2.83206i		−	0.0917395i	0.998947	−	0.0458698i	$-0.0146059\pi$
$954$	−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	−0.415790	−	0.909461i	$-0.636495\pi$
$967$	15.3515	−	15.3515i	0.493670	−	0.493670i	0.909461	+	0.415790i	$0.136495\pi$
$968$	−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	−0.959112	−	0.283026i	$-0.908662\pi$
$971$	−8.41373	−	31.4005i	−0.270009	−	1.00769i	0.689103	−	0.724664i	$-0.258005\pi$
$972$	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	0.316484	−	0.948598i	$-0.397498\pi$
$977$	3.63417	+	0.973774i	0.116267	+	0.0311538i	−0.200216	+	0.979752i	$0.564164\pi$
$978$	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	0.950118	+	0.311889i	$0.100962\pi$
$983$	3.54592	+	26.9340i	0.113097	+	0.859060i	−0.837021	+	0.547171i	$0.815705\pi$
$984$	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	0.291721	−	0.956503i	$-0.405772\pi$
$991$	25.8472	−	3.40285i	0.821064	−	0.108095i	0.529342	+	0.848408i	$0.322439\pi$
$992$	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	−0.178735	−	0.983897i	$-0.557201\pi$
$997$	25.8253	−	33.6562i	0.817897	−	1.06590i	0.996632	−	0.0820065i	$-0.0261328\pi$
$998$	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.26.11	✓	352
3.2	odd	2	inner	357.2.bj.a.26.34	yes	352
7.3	odd	6	inner	357.2.bj.a.332.34	yes	352
17.2	even	8	inner	357.2.bj.a.257.11	yes	352
21.17	even	6	inner	357.2.bj.a.332.11	yes	352
51.2	odd	8	inner	357.2.bj.a.257.34	yes	352
119.87	odd	24	inner	357.2.bj.a.206.34	yes	352
357.206	even	24	inner	357.2.bj.a.206.11	yes	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bj.a.26.11	✓	352	1.1	even	1	trivial
357.2.bj.a.26.34	yes	352	3.2	odd	2	inner
357.2.bj.a.206.11	yes	352	357.206	even	24	inner
357.2.bj.a.206.34	yes	352	119.87	odd	24	inner
357.2.bj.a.257.11	yes	352	17.2	even	8	inner
357.2.bj.a.257.34	yes	352	51.2	odd	8	inner
357.2.bj.a.332.11	yes	352	21.17	even	6	inner
357.2.bj.a.332.34	yes	352	7.3	odd	6	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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