LMFDB - Embedded newform 230.2.l.a.67.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] 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("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			67.4
Character	$\chi$	$=$	230.67
Dual form			230.2.l.a.103.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.212565 - 0.977147i) q^{2} +(0.628000 + 0.470115i) q^{3} +(-0.909632 + 0.415415i) q^{4} +(2.20366 + 0.379326i) q^{5} +(0.325880 - 0.713578i) q^{6} +(0.119361 + 1.66889i) q^{7} +(0.599278 + 0.800541i) q^{8} +(-0.671822 - 2.28802i) q^{9} +(-0.0977645 - 2.23393i) q^{10} +(2.43931 + 3.79564i) q^{11} +(-0.766541 - 0.166751i) q^{12} +(1.69134 + 0.120967i) q^{13} +(1.60538 - 0.471382i) q^{14} +(1.20557 + 1.27419i) q^{15} +(0.654861 - 0.755750i) q^{16} +(-1.34248 - 3.59932i) q^{17} +(-2.09292 + 1.14282i) q^{18} +(-1.30471 - 2.85692i) q^{19} +(-2.16210 + 0.570386i) q^{20} +(-0.709611 + 1.10418i) q^{21} +(3.19039 - 3.19039i) q^{22} +(2.54688 + 4.06367i) q^{23} +0.784469i q^{24} +(4.71222 + 1.67181i) q^{25} +(-0.241318 - 1.67840i) q^{26} +(1.47616 - 3.95773i) q^{27} +(-0.801857 - 1.46849i) q^{28} +(-8.84904 - 4.04122i) q^{29} +(0.988807 - 1.44887i) q^{30} +(1.11608 - 7.76254i) q^{31} +(-0.877679 - 0.479249i) q^{32} +(-0.252501 + 3.53042i) q^{33} +(-3.23170 + 2.07689i) q^{34} +(-0.370021 + 3.72294i) q^{35} +(1.56159 + 1.80217i) q^{36} +(-5.70496 + 10.4478i) q^{37} +(-2.51429 + 1.88217i) q^{38} +(1.00529 + 0.871092i) q^{39} +(1.01694 + 1.99144i) q^{40} +(-7.18190 - 2.10880i) q^{41} +(1.22978 + 0.458684i) q^{42} +(-3.02338 + 4.03876i) q^{43} +(-3.79564 - 2.43931i) q^{44} +(-0.612563 - 5.29684i) q^{45} +(3.42943 - 3.35247i) q^{46} +(2.25984 + 2.25984i) q^{47} +(0.766541 - 0.166751i) q^{48} +(4.15780 - 0.597802i) q^{49} +(0.631947 - 4.95990i) q^{50} +(0.849018 - 2.89149i) q^{51} +(-1.58875 + 0.592573i) q^{52} +(-4.53344 + 0.324238i) q^{53} +(-4.18106 - 0.601146i) q^{54} +(3.93563 + 9.28960i) q^{55} +(-1.26448 + 1.09568i) q^{56} +(0.523721 - 2.40751i) q^{57} +(-2.06787 + 9.50584i) q^{58} +(-5.22049 + 4.52358i) q^{59} +(-1.62594 - 0.658231i) q^{60} +(3.12421 + 0.449194i) q^{61} +(-7.82238 + 0.559468i) q^{62} +(3.73825 - 1.39430i) q^{63} +(-0.281733 + 0.959493i) q^{64} +(3.68125 + 0.908140i) q^{65} +(3.50341 - 0.503715i) q^{66} +(0.601491 - 0.130846i) q^{67} +(2.71637 + 2.71637i) q^{68} +(-0.310953 + 3.74931i) q^{69} +(3.71651 - 0.429803i) q^{70} +(-9.57147 - 6.15121i) q^{71} +(1.42904 - 1.90898i) q^{72} +(-3.89390 - 1.45235i) q^{73} +(11.4218 + 3.35373i) q^{74} +(2.17333 + 3.26518i) q^{75} +(2.37361 + 2.05675i) q^{76} +(-6.04335 + 4.52400i) q^{77} +(0.637494 - 1.16748i) q^{78} +(1.72151 + 1.98673i) q^{79} +(1.72976 - 1.41701i) q^{80} +(-3.23057 + 2.07616i) q^{81} +(-0.533981 + 7.46603i) q^{82} +(-3.89079 - 2.12453i) q^{83} +(0.186793 - 1.29918i) q^{84} +(-1.59305 - 8.44091i) q^{85} +(4.58913 + 2.09579i) q^{86} +(-3.65736 - 6.69795i) q^{87} +(-1.57674 + 4.22742i) q^{88} +(-1.31973 - 9.17890i) q^{89} +(-5.04558 + 1.72449i) q^{90} +2.83710i q^{91} +(-4.00483 - 2.63843i) q^{92} +(4.35019 - 4.35019i) q^{93} +(1.72783 - 2.68855i) q^{94} +(-1.79143 - 6.79058i) q^{95} +(-0.325880 - 0.713578i) q^{96} +(-1.16548 + 0.636402i) q^{97} +(-1.46795 - 3.93571i) q^{98} +(7.04571 - 8.13118i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{22}\right)$

Coefficient data

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

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

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

$2$	−0.212565	−	0.977147i	−0.150306	−	0.690947i
$2$	−0.212565	−	0.977147i	−0.150306	−	0.690947i
$3$	0.628000	+	0.470115i	0.362576	+	0.271421i	0.764997	−	0.644034i	$-0.222740\pi$
$3$	0.628000	+	0.470115i	0.362576	+	0.271421i	−0.402421	+	0.915455i	$0.631831\pi$
$4$	−0.909632	+	0.415415i	−0.454816	+	0.207708i
$5$	2.20366	+	0.379326i	0.985506	+	0.169640i
$5$	2.20366	+	0.379326i	0.985506	+	0.169640i
$6$	0.325880	−	0.713578i	0.133040	−	0.291317i
$7$	0.119361	+	1.66889i	0.0451143	+	0.630781i	0.968834	+	0.247711i	$0.0796785\pi$
$7$	0.119361	+	1.66889i	0.0451143	+	0.630781i	−0.923720	+	0.383070i	$0.874867\pi$
$8$	0.599278	+	0.800541i	0.211877	+	0.283034i
$9$	−0.671822	−	2.28802i	−0.223941	−	0.762672i
$10$	−0.0977645	−	2.23393i	−0.0309158	−	0.706431i
$11$	2.43931	+	3.79564i	0.735480	+	1.14443i	0.984407	+	0.175907i	$0.0562860\pi$
$11$	2.43931	+	3.79564i	0.735480	+	1.14443i	−0.248926	+	0.968522i	$0.580078\pi$
$12$	−0.766541	−	0.166751i	−0.221281	−	0.0481368i
$13$	1.69134	+	0.120967i	0.469094	+	0.0335503i	0.303886	−	0.952708i	$-0.401716\pi$
$13$	1.69134	+	0.120967i	0.469094	+	0.0335503i	0.165208	+	0.986259i	$0.447170\pi$
$14$	1.60538	−	0.471382i	0.429055	−	0.125982i
$15$	1.20557	+	1.27419i	0.311277	+	0.328994i
$16$	0.654861	−	0.755750i	0.163715	−	0.188937i
$17$	−1.34248	−	3.59932i	−0.325598	−	0.872963i	−0.991870	−	0.127254i	$-0.959384\pi$
$17$	−1.34248	−	3.59932i	−0.325598	−	0.872963i	0.666272	−	0.745709i	$-0.267889\pi$
$18$	−2.09292	+	1.14282i	−0.493306	+	0.269366i
$19$	−1.30471	−	2.85692i	−0.299321	−	0.655421i	0.698889	−	0.715230i	$-0.253678\pi$
$19$	−1.30471	−	2.85692i	−0.299321	−	0.655421i	−0.998210	+	0.0598088i	$0.980951\pi$
$20$	−2.16210	+	0.570386i	−0.483459	+	0.127542i
$21$	−0.709611	+	1.10418i	−0.154850	+	0.240951i
$22$	3.19039	−	3.19039i	0.680193	−	0.680193i
$23$	2.54688	+	4.06367i	0.531061	+	0.847334i
$23$	2.54688	+	4.06367i	0.531061	+	0.847334i
$24$			0.784469i			0.160129i
$25$	4.71222	+	1.67181i	0.942445	+	0.334362i
$26$	−0.241318	−	1.67840i	−0.0473263	−	0.329162i
$27$	1.47616	−	3.95773i	0.284087	−	0.761665i
$28$	−0.801857	−	1.46849i	−0.151537	−	0.277519i
$29$	−8.84904	−	4.04122i	−1.64323	−	0.750436i	−0.643341	−	0.765580i	$-0.722452\pi$
$29$	−8.84904	−	4.04122i	−1.64323	−	0.750436i	−0.999885	+	0.0151438i	$0.995179\pi$
$30$	0.988807	−	1.44887i	0.180531	−	0.264526i
$31$	1.11608	−	7.76254i	0.200455	−	1.39419i	−0.602484	−	0.798131i	$-0.705822\pi$
$31$	1.11608	−	7.76254i	0.200455	−	1.39419i	0.802938	−	0.596062i	$-0.203269\pi$
$32$	−0.877679	−	0.479249i	−0.155153	−	0.0847201i
$33$	−0.252501	+	3.53042i	−0.0439547	+	0.614567i
$34$	−3.23170	+	2.07689i	−0.554232	+	0.356183i
$35$	−0.370021	+	3.72294i	−0.0625450	+	0.629292i
$36$	1.56159	+	1.80217i	0.260264	+	0.300361i
$37$	−5.70496	+	10.4478i	−0.937889	+	1.71762i	−0.287921	+	0.957654i	$0.592964\pi$
$37$	−5.70496	+	10.4478i	−0.937889	+	1.71762i	−0.649968	+	0.759962i	$0.725218\pi$
$38$	−2.51429	+	1.88217i	−0.407872	+	0.305329i
$39$	1.00529	+	0.871092i	0.160976	+	0.139486i
$40$	1.01694	+	1.99144i	0.160792	+	0.314874i
$41$	−7.18190	−	2.10880i	−1.12162	−	0.329339i	−0.332214	−	0.943204i	$-0.607796\pi$
$41$	−7.18190	−	2.10880i	−1.12162	−	0.329339i	−0.789411	+	0.613865i	$0.789614\pi$
$42$	1.22978	+	0.458684i	0.189759	+	0.0707765i
$43$	−3.02338	+	4.03876i	−0.461061	+	0.615906i	−0.969470	−	0.245210i	$-0.921143\pi$
$43$	−3.02338	+	4.03876i	−0.461061	+	0.615906i	0.508409	+	0.861116i	$0.330234\pi$
$44$	−3.79564	−	2.43931i	−0.572215	−	0.367740i
$45$	−0.612563	−	5.29684i	−0.0913155	−	0.789607i
$46$	3.42943	−	3.35247i	0.505641	−	0.494294i
$47$	2.25984	+	2.25984i	0.329631	+	0.329631i	0.852446	−	0.522815i	$-0.175118\pi$
$47$	2.25984	+	2.25984i	0.329631	+	0.329631i	−0.522815	+	0.852446i	$0.675118\pi$
$48$	0.766541	−	0.166751i	0.110641	−	0.0240684i
$49$	4.15780	−	0.597802i	0.593972	−	0.0854003i
$50$	0.631947	−	4.95990i	0.0893709	−	0.701436i
$51$	0.849018	−	2.89149i	0.118886	−	0.404889i
$52$	−1.58875	+	0.592573i	−0.220320	+	0.0821751i
$53$	−4.53344	+	0.324238i	−0.622715	+	0.0445375i	−0.379132	−	0.925343i	$-0.623777\pi$
$53$	−4.53344	+	0.324238i	−0.622715	+	0.0445375i	−0.243583	+	0.969880i	$0.578323\pi$
$54$	−4.18106	−	0.601146i	−0.568971	−	0.0818056i
$55$	3.93563	+	9.28960i	0.530680	+	1.25261i
$56$	−1.26448	+	1.09568i	−0.168974	+	0.146417i
$57$	0.523721	−	2.40751i	0.0693685	−	0.318882i
$58$	−2.06787	+	9.50584i	−0.271524	+	1.24818i
$59$	−5.22049	+	4.52358i	−0.679650	+	0.588921i	−0.924749	−	0.380578i	$-0.875725\pi$
$59$	−5.22049	+	4.52358i	−0.679650	+	0.588921i	0.245098	+	0.969498i	$0.421180\pi$
$60$	−1.62594	−	0.658231i	−0.209908	−	0.0849772i
$61$	3.12421	+	0.449194i	0.400014	+	0.0575134i	0.339386	−	0.940647i	$-0.389781\pi$
$61$	3.12421	+	0.449194i	0.400014	+	0.0575134i	0.0606279	+	0.998160i	$0.480690\pi$
$62$	−7.82238	+	0.559468i	−0.993444	+	0.0710525i
$63$	3.73825	−	1.39430i	0.470976	−	0.175665i
$64$	−0.281733	+	0.959493i	−0.0352166	+	0.119937i
$65$	3.68125	+	0.908140i	0.456603	+	0.112641i
$66$	3.50341	−	0.503715i	0.431240	−	0.0620030i
$67$	0.601491	−	0.130846i	0.0734838	−	0.0159854i	−0.175673	−	0.984449i	$-0.556210\pi$
$67$	0.601491	−	0.130846i	0.0734838	−	0.0159854i	0.249157	+	0.968463i	$0.419847\pi$
$68$	2.71637	+	2.71637i	0.329408	+	0.329408i
$69$	−0.310953	+	3.74931i	−0.0374344	+	0.451364i
$70$	3.71651	−	0.429803i	0.444208	−	0.0513713i
$71$	−9.57147	−	6.15121i	−1.13592	−	0.730015i	−0.169137	−	0.985593i	$-0.554098\pi$
$71$	−9.57147	−	6.15121i	−1.13592	−	0.730015i	−0.966788	+	0.255578i	$0.917734\pi$
$72$	1.42904	−	1.90898i	0.168414	−	0.224975i
$73$	−3.89390	−	1.45235i	−0.455747	−	0.169985i	0.111098	−	0.993809i	$-0.464563\pi$
$73$	−3.89390	−	1.45235i	−0.455747	−	0.169985i	−0.566845	+	0.823825i	$0.691836\pi$
$74$	11.4218	+	3.35373i	1.32775	+	0.389863i
$75$	2.17333	+	3.26518i	0.250955	+	0.377031i
$76$	2.37361	+	2.05675i	0.272272	+	0.235925i
$77$	−6.04335	+	4.52400i	−0.688704	+	0.515557i
$78$	0.637494	−	1.16748i	0.0721820	−	0.132191i
$79$	1.72151	+	1.98673i	0.193685	+	0.223524i	0.844282	−	0.535898i	$-0.180027\pi$
$79$	1.72151	+	1.98673i	0.193685	+	0.223524i	−0.650598	+	0.759423i	$0.725482\pi$
$80$	1.72976	−	1.41701i	0.193394	−	0.158426i
$81$	−3.23057	+	2.07616i	−0.358952	+	0.230684i
$82$	−0.533981	+	7.46603i	−0.0589684	+	0.824485i
$83$	−3.89079	−	2.12453i	−0.427069	−	0.233197i	0.251314	−	0.967906i	$-0.419137\pi$
$83$	−3.89079	−	2.12453i	−0.427069	−	0.233197i	−0.678383	+	0.734708i	$0.737319\pi$
$84$	0.186793	−	1.29918i	0.0203808	−	0.141752i
$85$	−1.59305	−	8.44091i	−0.172790	−	0.915545i
$86$	4.58913	+	2.09579i	0.494859	+	0.225994i
$87$	−3.65736	−	6.69795i	−0.392110	−	0.718096i
$88$	−1.57674	+	4.22742i	−0.168082	+	0.450644i
$89$	−1.31973	−	9.17890i	−0.139891	−	0.972962i	−0.931968	−	0.362541i	$-0.881909\pi$
$89$	−1.31973	−	9.17890i	−0.139891	−	0.972962i	0.792077	−	0.610421i	$-0.209000\pi$
$90$	−5.04558	+	1.72449i	−0.531851	+	0.181777i
$91$			2.83710i			0.297409i
$92$	−4.00483	−	2.63843i	−0.417532	−	0.275076i
$93$	4.35019	−	4.35019i	0.451093	−	0.451093i
$94$	1.72783	−	2.68855i	0.178212	−	0.277303i
$95$	−1.79143	−	6.79058i	−0.183797	−	0.696699i
$96$	−0.325880	−	0.713578i	−0.0332600	−	0.0728292i
$97$	−1.16548	+	0.636402i	−0.118337	+	0.0646168i	−0.537327	−	0.843374i	$-0.680566\pi$
$97$	−1.16548	+	0.636402i	−0.118337	+	0.0646168i	0.418990	+	0.907991i	$0.362384\pi$
$98$	−1.46795	−	3.93571i	−0.148285	−	0.397567i
$99$	7.04571	−	8.13118i	0.708120	−	0.817214i
$100$	−4.98088	+	0.436798i	−0.498088	+	0.0436798i
$101$	8.36550	−	2.45633i	0.832399	−	0.244414i	0.162352	−	0.986733i	$-0.448092\pi$
$101$	8.36550	−	2.45633i	0.832399	−	0.244414i	0.670047	+	0.742319i	$0.266274\pi$
$102$	−3.00588	−	0.214985i	−0.297627	−	0.0212867i
$103$	10.4207	+	2.26689i	1.02678	+	0.223363i	0.694254	−	0.719730i	$-0.255734\pi$
$103$	10.4207	+	2.26689i	1.02678	+	0.223363i	0.332530	+	0.943093i	$0.392098\pi$
$104$	0.916744	+	1.42648i	0.0898942	+	0.139878i
$105$	−1.98258	+	2.16405i	−0.193480	+	0.211190i
$106$	1.28048	+	4.36091i	0.124371	+	0.423569i
$107$	−1.22468	−	1.63598i	−0.118394	−	0.158156i	0.737429	−	0.675425i	$-0.236040\pi$
$107$	−1.22468	−	1.63598i	−0.118394	−	0.158156i	−0.855823	+	0.517269i	$0.826949\pi$
$108$	0.301341	+	4.21330i	0.0289965	+	0.405425i
$109$	7.92219	−	17.3472i	0.758808	−	1.66156i	0.00894881	−	0.999960i	$-0.497151\pi$
$109$	7.92219	−	17.3472i	0.758808	−	1.66156i	0.749859	−	0.661598i	$-0.230121\pi$
$110$	8.24073	−	5.82033i	0.785722	−	0.554947i
$111$	−8.49440	+	3.87926i	−0.806253	+	0.368203i
$112$	1.33943	+	1.00268i	0.126564	+	0.0947446i
$113$	−2.14680	−	9.86869i	−0.201954	−	0.928368i	−0.960831	−	0.277134i	$-0.910615\pi$
$113$	−2.14680	−	9.86869i	−0.201954	−	0.928368i	0.758877	−	0.651234i	$-0.225748\pi$
$114$	−2.46381			−0.230757
$115$	4.07099	+	9.92104i	0.379622	+	0.925142i
$116$	9.72816			0.903237
$117$	−0.859506	−	3.95108i	−0.0794613	−	0.365278i
$118$	5.52990	+	4.13963i	0.509069	+	0.381084i
$119$	5.84663	−	2.67006i	0.535959	−	0.244764i
$120$	−0.297569	+	1.72870i	−0.0271642	+	0.157808i
$121$	−3.88711	+	8.51158i	−0.353373	+	0.773780i
$122$	−0.225171	−	3.14830i	−0.0203860	−	0.285033i
$123$	−3.51886	−	4.70064i	−0.317285	−	0.423843i
$124$	2.20945	+	7.52469i	0.198414	+	0.675737i
$125$	9.74997	+	5.47156i	0.872064	+	0.489392i
$126$	−2.15706	−	3.35644i	−0.192166	−	0.299016i
$127$	20.1526	+	4.38394i	1.78826	+	0.389012i	0.979870	−	0.199637i	$-0.0639764\pi$
$127$	20.1526	+	4.38394i	1.78826	+	0.389012i	0.808389	+	0.588649i	$0.200340\pi$
$128$	0.997452	+	0.0713392i	0.0881631	+	0.00630555i
$129$	−3.79736	+	1.11501i	−0.334339	+	0.0981708i
$130$	0.104879	−	3.79017i	0.00919850	−	0.332419i
$131$	−0.121623	+	0.140360i	−0.0106262	+	0.0122633i	−0.761038	−	0.648708i	$-0.775310\pi$
$131$	−0.121623	+	0.140360i	−0.0106262	+	0.0122633i	0.750412	+	0.660971i	$0.229855\pi$
$132$	−1.23691	−	3.31628i	−0.107659	−	0.288645i
$133$	4.61215	−	2.51842i	0.399924	−	0.218375i
$134$	−0.255712	−	0.559932i	−0.0220902	−	0.0483707i
$135$	4.75421	−	8.16154i	0.409178	−	0.702434i
$136$	2.07689	−	3.23170i	0.178092	−	0.277116i
$137$	3.24795	−	3.24795i	0.277491	−	0.277491i	−0.554616	−	0.832107i	$-0.687135\pi$
$137$	3.24795	−	3.24795i	0.277491	−	0.277491i	0.832107	+	0.554616i	$0.187135\pi$
$138$	3.72972	−	0.493126i	0.317495	−	0.0419777i
$139$			9.49865i			0.805665i	0.915274	+	0.402833i	$0.131974\pi$
$139$			9.49865i			0.805665i	−0.915274	+	0.402833i	$0.868026\pi$
$140$	−1.20998	−	3.54022i	−0.102262	−	0.299203i
$141$	0.356794	+	2.48156i	0.0300475	+	0.208985i
$142$	−3.97608	+	10.6603i	−0.333665	+	0.894590i
$143$	3.66656	+	6.71481i	0.306613	+	0.561521i
$144$	−2.16912	−	0.990602i	−0.180760	−	0.0825502i
$145$	−17.9673	−	12.2621i	−1.49211	−	1.01832i
$146$	−0.591451	+	4.11363i	−0.0489488	+	0.340447i
$147$	2.89214	+	1.57923i	0.238539	+	0.130252i
$148$	0.849218	−	11.8736i	0.0698053	−	0.976006i
$149$	−1.86660	+	1.19959i	−0.152918	+	0.0982742i	−0.614862	−	0.788635i	$-0.710788\pi$
$149$	−1.86660	+	1.19959i	−0.152918	+	0.0982742i	0.461944	+	0.886909i	$0.347152\pi$
$150$	2.72859	−	2.81773i	0.222788	−	0.230067i
$151$	−2.09332	−	2.41581i	−0.170352	−	0.196596i	0.664154	−	0.747596i	$-0.268792\pi$
$151$	−2.09332	−	2.41581i	−0.170352	−	0.196596i	−0.834505	+	0.551000i	$0.814247\pi$
$152$	1.50520	−	2.75656i	0.122087	−	0.223587i
$153$	−7.33339	+	5.48971i	−0.592870	+	0.443817i
$154$	5.70522	+	4.94360i	0.459739	+	0.398366i
$155$	5.40400	−	16.6826i	0.434060	−	1.33998i
$156$	−1.27631	−	0.374759i	−0.102187	−	0.0300047i
$157$	3.05572	+	1.13973i	0.243873	+	0.0909601i	0.468429	−	0.883501i	$-0.344820\pi$
$157$	3.05572	+	1.13973i	0.243873	+	0.0909601i	−0.224555	+	0.974461i	$0.572093\pi$
$158$	1.57539	−	2.10448i	0.125331	−	0.167423i
$159$	−2.99942	−	1.92761i	−0.237870	−	0.152870i
$160$	−1.75231	−	1.38903i	−0.138533	−	0.109812i
$161$	−6.47782	+	4.73550i	−0.510524	+	0.373210i
$162$	2.71542	+	2.71542i	0.213344	+	0.213344i
$163$	11.7107	−	2.54751i	0.917255	−	0.199537i	0.270930	−	0.962599i	$-0.412669\pi$
$163$	11.7107	−	2.54751i	0.917255	−	0.199537i	0.646325	+	0.763062i	$0.276305\pi$
$164$	7.40892	−	1.06524i	0.578539	−	0.0831814i
$165$	−1.89560	+	7.68406i	−0.147573	+	0.598203i
$166$	−1.24893	+	4.25347i	−0.0969359	+	0.330133i
$167$	−20.3025	+	7.57243i	−1.57105	+	0.585972i	−0.976011	−	0.217723i	$-0.930137\pi$
$167$	−20.3025	+	7.57243i	−1.57105	+	0.585972i	−0.595042	+	0.803695i	$0.702864\pi$
$168$	−1.30919	+	0.0936353i	−0.101006	+	0.00722412i
$169$	−10.0217	−	1.44090i	−0.770898	−	0.110838i
$170$	−7.90938	+	3.35088i	−0.606622	+	0.257001i
$171$	−5.66013	+	4.90453i	−0.432841	+	0.375059i
$172$	1.07240	−	4.92975i	0.0817698	−	0.375890i
$173$	−0.0584752	+	0.268806i	−0.00444579	+	0.0204370i	−0.979316	−	0.202335i	$-0.935147\pi$
$173$	−0.0584752	+	0.268806i	−0.00444579	+	0.0204370i	0.974871	+	0.222772i	$0.0715106\pi$
$174$	−5.76746	+	4.99753i	−0.437230	+	0.378862i
$175$	−2.22761	+	8.06373i	−0.168391	+	0.609561i
$176$	4.46597	+	0.642109i	0.336635	+	0.0484008i
$177$	−5.40507	+	0.386578i	−0.406270	+	0.0290570i
$178$	−8.68861	+	3.24068i	−0.651239	+	0.242899i
$179$	−5.44259	+	18.5358i	−0.406799	+	1.38543i	0.460508	+	0.887655i	$0.347667\pi$
$179$	−5.44259	+	18.5358i	−0.406799	+	1.38543i	−0.867307	+	0.497773i	$0.834151\pi$
$180$	2.75760	+	4.56371i	0.205539	+	0.340159i
$181$	9.05817	−	1.30237i	0.673288	−	0.0968043i	0.202813	−	0.979217i	$-0.434992\pi$
$181$	9.05817	−	1.30237i	0.673288	−	0.0968043i	0.470475	+	0.882413i	$0.344082\pi$
$182$	2.77227	−	0.603069i	0.205494	−	0.0447025i
$183$	1.75083	+	1.75083i	0.129425	+	0.129425i
$184$	−1.72685	+	4.47415i	−0.127305	+	0.329838i
$185$	−16.5349	+	20.8595i	−1.21567	+	1.53362i
$186$	−5.17547	−	3.32607i	−0.379484	−	0.243879i
$187$	10.3870	−	13.8754i	0.759574	−	1.01467i
$188$	−2.99439	−	1.11685i	−0.218388	−	0.0814546i
$189$	6.78121	+	1.99114i	0.493260	+	0.144834i
$190$	−6.25460	+	3.19393i	−0.453756	+	0.231712i
$191$	7.08566	+	6.13976i	0.512700	+	0.444257i	0.872387	−	0.488816i	$-0.162571\pi$
$191$	7.08566	+	6.13976i	0.512700	+	0.444257i	−0.359687	+	0.933073i	$0.617116\pi$
$192$	−0.628000	+	0.470115i	−0.0453220	+	0.0339276i
$193$	−3.47032	+	6.35541i	−0.249799	+	0.457473i	−0.972248	−	0.233951i	$-0.924834\pi$
$193$	−3.47032	+	6.35541i	−0.249799	+	0.457473i	0.722449	+	0.691424i	$0.243016\pi$
$194$	0.869599	+	1.00357i	0.0624336	+	0.0720522i
$195$	1.88490	+	2.30092i	0.134980	+	0.164773i
$196$	−3.53374	+	2.27099i	−0.252410	+	0.162214i
$197$	−0.822506	+	11.5001i	−0.0586011	+	0.819351i	0.880137	+	0.474720i	$0.157451\pi$
$197$	−0.822506	+	11.5001i	−0.0586011	+	0.819351i	−0.938738	+	0.344631i	$0.888004\pi$
$198$	−9.44303	−	5.15629i	−0.671087	−	0.366441i
$199$	−3.02058	+	21.0086i	−0.214123	+	1.48926i	0.545067	+	0.838393i	$0.316504\pi$
$199$	−3.02058	+	21.0086i	−0.214123	+	1.48926i	−0.759190	+	0.650869i	$0.774405\pi$
$200$	1.48558	+	4.77421i	0.105046	+	0.337587i
$201$	0.439249	+	0.200598i	0.0309822	+	0.0141491i
$202$	−4.17841	−	7.65219i	−0.293992	−	0.538407i
$203$	5.68812	−	15.2504i	0.399228	−	1.07037i
$204$	0.428874	+	2.98289i	0.0300272	+	0.208844i
$205$	−15.0265	−	7.37135i	−1.04950	−	0.514837i
$206$		−	10.6644i		−	0.743026i
$207$	7.58669	−	8.55736i	0.527312	−	0.594777i
$208$	1.19901	−	1.19901i	0.0831367	−	0.0831367i
$209$	7.66124	−	11.9211i	0.529939	−	0.824602i
$210$	2.53603	+	1.47727i	0.175002	+	0.101941i
$211$	−2.79578	−	6.12191i	−0.192470	−	0.421450i	0.788652	−	0.614839i	$-0.210779\pi$
$211$	−2.79578	−	6.12191i	−0.192470	−	0.421450i	−0.981122	+	0.193390i	$0.938052\pi$
$212$	3.98906	−	2.17819i	0.273970	−	0.149599i
$213$	−3.11911	−	8.36265i	−0.213718	−	0.572999i
$214$	−1.33827	+	1.54445i	−0.0914823	+	0.105576i
$215$	−8.19450	+	7.75321i	−0.558861	+	0.528764i
$216$	4.05295	−	1.19005i	0.275769	−	0.0809730i
$217$	13.0880	+	0.936075i	0.888474	+	0.0635449i
$218$	−18.6347	−	4.05373i	−1.26210	−	0.274554i
$219$	−1.76260	−	2.74265i	−0.119105	−	0.185331i
$220$	−7.43901	−	6.81520i	−0.501538	−	0.459481i
$221$	−1.83519	−	6.25007i	−0.123448	−	0.420426i
$222$	5.59622	+	7.47568i	0.375594	+	0.501735i
$223$	−1.12224	−	15.6910i	−0.0751510	−	1.05075i	−0.885451	−	0.464733i	$-0.846150\pi$
$223$	−1.12224	−	15.6910i	−0.0751510	−	1.05075i	0.810300	−	0.586015i	$-0.199304\pi$
$224$	0.695053	−	1.52195i	0.0464402	−	0.101690i
$225$	0.659348	−	11.9048i	0.0439566	−	0.793653i
$226$	−9.18682	+	4.19548i	−0.611098	+	0.279079i
$227$	9.63276	+	7.21100i	0.639349	+	0.478611i	0.869098	−	0.494639i	$-0.164700\pi$
$227$	9.63276	+	7.21100i	0.639349	+	0.478611i	−0.229749	+	0.973250i	$0.573791\pi$
$228$	0.523721	+	2.40751i	0.0346843	+	0.159441i
$229$	20.2031			1.33506			0.667529	−	0.744584i	$-0.267352\pi$
$229$	20.2031			1.33506			0.667529	+	0.744584i	$0.267352\pi$
$230$	8.82896	−	6.08683i	0.582164	−	0.401353i
$231$	−5.92202			−0.389640
$232$	−2.06787	−	9.50584i	−0.135762	−	0.624089i
$233$	−6.61089	−	4.94885i	−0.433094	−	0.324210i	0.360389	−	0.932802i	$-0.382644\pi$
$233$	−6.61089	−	4.94885i	−0.433094	−	0.324210i	−0.793483	+	0.608592i	$0.791735\pi$
$234$	−3.67809	+	1.67973i	−0.240444	+	0.109807i
$235$	4.12269	+	5.83712i	0.268935	+	0.380772i
$236$	2.86956	−	6.28347i	0.186793	−	0.409019i
$237$	0.147117	+	2.05697i	0.00955630	+	0.133615i
$238$	−3.85183	−	5.14545i	−0.249677	−	0.333530i
$239$	4.72365	+	16.0873i	0.305548	+	1.04060i	0.958947	+	0.283586i	$0.0915242\pi$
$239$	4.72365	+	16.0873i	0.305548	+	1.04060i	−0.653399	+	0.757014i	$0.726658\pi$
$240$	1.75245	−	0.0766932i	0.113120	−	0.00495052i
$241$	2.40237	+	3.73816i	0.154750	+	0.240796i	0.909969	−	0.414677i	$-0.136106\pi$
$241$	2.40237	+	3.73816i	0.154750	+	0.240796i	−0.755218	+	0.655473i	$0.772469\pi$
$242$	9.14332	+	1.98901i	0.587755	+	0.127858i
$243$	−15.6447	−	1.11893i	−1.00361	−	0.0717795i
$244$	−3.02848	+	0.889243i	−0.193879	+	0.0569280i
$245$	9.38915	+	0.259810i	0.599850	+	0.0165987i
$246$	−3.84523	+	4.43763i	−0.245163	+	0.282933i
$247$	−1.86112	−	4.98985i	−0.118420	−	0.317496i
$248$	6.88308	−	3.75845i	0.437076	−	0.238662i
$249$	−1.44464	−	3.16332i	−0.0915503	−	0.200467i
$250$	3.27402	−	10.6902i	0.207067	−	0.676109i
$251$	−8.24727	+	12.8330i	−0.520563	+	0.810012i	−0.997627	−	0.0688568i	$-0.978065\pi$
$251$	−8.24727	+	12.8330i	−0.520563	+	0.810012i	0.477063	+	0.878869i	$0.341701\pi$
$252$	−2.82122	+	2.82122i	−0.177720	+	0.177720i
$253$	−9.21162	+	19.5796i	−0.579130	+	1.23096i
$254$		−	20.6240i		−	1.29406i
$255$	2.96776	−	6.04980i	0.185848	−	0.378853i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−6.80711	+	18.2506i	−0.424616	+	1.13844i	0.531913	+	0.846799i	$0.321473\pi$
$257$	−6.80711	+	18.2506i	−0.424616	+	1.13844i	−0.956528	+	0.291639i	$0.905799\pi$
$258$	1.89671	+	3.47357i	0.118084	+	0.216255i
$259$	−18.1173	−	8.27387i	−1.12575	−	0.514113i
$260$	−3.72584	+	0.703175i	−0.231067	+	0.0436091i
$261$	−3.30140	+	22.9617i	−0.204351	+	1.42130i
$262$	0.163005	+	0.0890076i	0.0100705	+	0.00549890i
$263$	1.71863	−	24.0296i	0.105975	−	1.48173i	−0.614868	−	0.788630i	$-0.710791\pi$
$263$	1.71863	−	24.0296i	0.105975	−	1.48173i	0.720843	−	0.693098i	$-0.243755\pi$
$264$	−2.97757	+	1.91356i	−0.183256	+	0.117772i
$265$	−10.1131	−	1.00514i	−0.621245	−	0.0617452i
$266$	−3.44125	−	3.97141i	−0.210997	−	0.243503i
$267$	3.48635	−	6.38477i	0.213361	−	0.390742i
$268$	−0.492780	+	0.368890i	−0.0301013	+	0.0225336i
$269$	17.7119	+	15.3475i	1.07992	+	0.935752i	0.998144	−	0.0608994i	$-0.0193969\pi$
$269$	17.7119	+	15.3475i	1.07992	+	0.935752i	0.0817712	+	0.996651i	$0.473942\pi$
$270$	−8.98561	−	2.91071i	−0.546847	−	0.177140i
$271$	−0.266320	−	0.0781986i	−0.0161778	−	0.00475023i	0.273634	−	0.961834i	$-0.411774\pi$
$271$	−0.266320	−	0.0781986i	−0.0161778	−	0.00475023i	−0.289811	+	0.957084i	$0.593593\pi$
$272$	−3.59932	−	1.34248i	−0.218241	−	0.0813996i
$273$	−1.33376	+	1.78170i	−0.0807230	+	0.107833i
$274$	−3.86413	−	2.48332i	−0.233440	−	0.150023i
$275$	5.14900	+	21.9640i	0.310496	+	1.32448i
$276$	−1.27467	−	3.53967i	−0.0767259	−	0.213063i
$277$	−7.37648	−	7.37648i	−0.443210	−	0.443210i	0.449880	−	0.893089i	$-0.351467\pi$
$277$	−7.37648	−	7.37648i	−0.443210	−	0.443210i	−0.893089	+	0.449880i	$0.851467\pi$
$278$	9.28158	−	2.01908i	0.556672	−	0.121097i
$279$	−18.5106	+	2.66143i	−1.10820	+	0.159335i
$280$	−3.20211	+	1.93486i	−0.191363	+	0.115630i
$281$	3.55550	−	12.1089i	0.212104	−	0.722358i	−0.782867	−	0.622189i	$-0.786243\pi$
$281$	3.55550	−	12.1089i	0.212104	−	0.722358i	0.994970	−	0.100169i	$-0.0319384\pi$
$282$	2.34901	−	0.876134i	0.139881	−	0.0521730i
$283$	2.20061	−	0.157391i	0.130813	−	0.00935592i	−0.00577920	−	0.999983i	$-0.501840\pi$
$283$	2.20061	−	0.157391i	0.130813	−	0.00935592i	0.136592	+	0.990627i	$0.456385\pi$
$284$	11.2618	+	1.61921i	0.668266	+	0.0960822i
$285$	2.06733	−	5.10666i	0.122458	−	0.302492i
$286$	5.78197	−	5.01011i	0.341895	−	0.296254i
$287$	2.66211	−	12.2375i	0.157139	−	0.722358i
$288$	−0.506885	+	2.33011i	−0.0298685	+	0.137303i
$289$	1.69489	−	1.46863i	0.0996994	−	0.0863900i
$290$	−8.16269	+	20.1632i	−0.479329	+	1.18403i
$291$	−1.03110	−	0.148251i	−0.0604444	−	0.00869060i
$292$	4.14534	−	0.296481i	0.242588	−	0.0173502i
$293$	25.9638	−	9.68400i	1.51682	−	0.565745i	0.553208	−	0.833043i	$-0.313404\pi$
$293$	25.9638	−	9.68400i	1.51682	−	0.565745i	0.963614	+	0.267298i	$0.0861308\pi$
$294$	0.928368	−	3.16173i	0.0541435	−	0.184396i
$295$	−13.2201	+	7.98817i	−0.769704	+	0.465089i
$296$	−11.7828	+	1.69411i	−0.684861	+	0.0984681i
$297$	18.6229	−	4.05117i	1.08061	−	0.235073i
$298$	1.56895	+	1.56895i	0.0908868	+	0.0908868i
$299$	3.81607	+	7.18114i	0.220689	+	0.415296i
$300$	−3.33334	−	2.06728i	−0.192450	−	0.119354i
$301$	−7.10112	−	4.56361i	−0.409302	−	0.263042i
$302$	−1.91564	+	2.55900i	−0.110233	+	0.147254i
$303$	6.40829	+	2.39017i	0.368147	+	0.137312i
$304$	−3.01352	−	0.884848i	−0.172837	−	0.0507495i
$305$	6.71430	+	2.17496i	0.384460	+	0.124538i
$306$	6.92308	+	5.99888i	0.395766	+	0.342933i
$307$	−25.5592	+	19.1334i	−1.45874	+	1.09200i	−0.482355	+	0.875976i	$0.660218\pi$
$307$	−25.5592	+	19.1334i	−1.45874	+	1.09200i	−0.976388	+	0.216025i	$0.930691\pi$
$308$	3.61789	−	6.62567i	0.206148	−	0.377533i
$309$	5.47851	+	6.32254i	0.311662	+	0.359677i
$310$	−17.4501	−	1.73435i	−0.991098	−	0.0985047i
$311$	15.9063	−	10.2223i	0.901961	−	0.579655i	−0.00541011	−	0.999985i	$-0.501722\pi$
$311$	15.9063	−	10.2223i	0.901961	−	0.579655i	0.907371	+	0.420330i	$0.138086\pi$
$312$	−0.0948950	+	1.32681i	−0.00537237	+	0.0751155i
$313$	14.7793	+	8.07010i	0.835374	+	0.456149i	0.839186	−	0.543844i	$-0.183032\pi$
$313$	14.7793	+	8.07010i	0.835374	+	0.456149i	−0.00381211	+	0.999993i	$0.501213\pi$
$314$	0.464139	−	3.22816i	0.0261929	−	0.182175i
$315$	8.76673	−	1.65454i	0.493949	−	0.0932227i
$316$	−2.39125	−	1.09205i	−0.134519	−	0.0614326i
$317$	8.38984	+	15.3648i	0.471220	+	0.862976i	0.999900	+	0.0141542i	$0.00450559\pi$
$317$	8.38984	+	15.3648i	0.471220	+	0.862976i	−0.528679	+	0.848822i	$0.677313\pi$
$318$	−1.24599	+	3.34062i	−0.0698715	+	0.187333i
$319$	−6.24654	−	43.4456i	−0.349739	−	2.43249i
$320$	−0.984803	+	2.00753i	−0.0550521	+	0.112224i
$321$		−	1.60314i		−	0.0894784i
$322$	6.00424	+	5.32318i	0.334603	+	0.296649i
$323$	−8.53141	+	8.53141i	−0.474700	+	0.474700i
$324$	2.07616	−	3.23057i	0.115342	−	0.179476i
$325$	7.76775	+	3.39762i	0.430877	+	0.188466i
$326$	−4.97859	−	10.9016i	−0.275739	−	0.603783i
$327$	13.1303	−	7.16968i	0.726107	−	0.396484i
$328$	−2.61578	−	7.01317i	−0.144432	−	0.387237i
$329$	−3.50168	+	4.04115i	−0.193054	+	0.222796i
$330$	7.91140	+	0.218919i	0.435508	+	0.0120511i
$331$	−21.3950	+	6.28213i	−1.17597	+	0.345297i	−0.810621	−	0.585571i	$-0.800870\pi$
$331$	−21.3950	+	6.28213i	−1.17597	+	0.345297i	−0.365354	+	0.930869i	$0.619052\pi$
$332$	4.42175	+	0.316249i	0.242675	+	0.0173564i
$333$	27.7376	+	6.03393i	1.52001	+	0.330658i
$334$	11.7150	+	18.2289i	0.641015	+	0.997439i
$335$	1.37511	−	0.0601797i	0.0751305	−	0.00328797i
$336$	0.369784	+	1.25937i	0.0201734	+	0.0687042i
$337$	2.98176	+	3.98316i	0.162427	+	0.216976i	0.874369	−	0.485261i	$-0.161275\pi$
$337$	2.98176	+	3.98316i	0.162427	+	0.216976i	−0.711943	+	0.702237i	$0.752184\pi$
$338$	0.722290	+	10.0989i	0.0392874	+	0.549310i
$339$	3.29122	−	7.20677i	0.178755	−	0.391418i
$340$	4.95557	+	7.01634i	0.268753	+	0.380515i
$341$	32.1863	−	14.6990i	1.74299	−	0.795996i
$342$	5.99560	+	4.48825i	0.324205	+	0.242697i
$343$	3.98353	+	18.3120i	0.215090	+	0.988754i
$344$	−5.04504			−0.272010
$345$	−2.10744	+	8.14424i	−0.113461	+	0.438471i
$346$	0.275093			0.0147891
$347$	−1.26594	−	5.81944i	−0.0679593	−	0.312404i	0.930602	−	0.366034i	$-0.119285\pi$
$347$	−1.26594	−	5.81944i	−0.0679593	−	0.312404i	−0.998561	+	0.0536298i	$0.982921\pi$
$348$	6.10928	+	4.57335i	0.327492	+	0.245157i
$349$	10.9758	−	5.01247i	0.587520	−	0.268311i	−0.0993965	−	0.995048i	$-0.531691\pi$
$349$	10.9758	−	5.01247i	0.587520	−	0.268311i	0.686916	+	0.726737i	$0.258964\pi$
$350$	8.35296	+	0.462630i	0.446485	+	0.0247286i
$351$	2.97544	−	6.51531i	0.158817	−	0.347761i
$352$	−0.321875	−	4.50040i	−0.0171560	−	0.239872i
$353$	−20.2635	−	27.0688i	−1.07852	−	1.44073i	−0.888460	−	0.458955i	$-0.848224\pi$
$353$	−20.2635	−	27.0688i	−1.07852	−	1.44073i	−0.190056	−	0.981773i	$-0.560867\pi$
$354$	1.52667	+	5.19938i	0.0811418	+	0.276344i
$355$	−18.7589	−	17.1859i	−0.995622	−	0.912132i
$356$	5.01352	+	7.80119i	0.265716	+	0.413462i
$357$	4.92692	+	1.07178i	0.260760	+	0.0567249i
$358$	19.2691	+	1.37815i	1.01840	+	0.0728376i
$359$	−28.0862	+	8.24684i	−1.48233	+	0.435252i	−0.920085	−	0.391719i	$-0.871881\pi$
$359$	−28.0862	+	8.24684i	−1.48233	+	0.435252i	−0.562246	+	0.826970i	$0.690062\pi$
$360$	3.87325	−	3.66466i	0.204138	−	0.193145i
$361$	5.98265	−	6.90435i	0.314876	−	0.363387i
$362$	−3.19806	−	8.57432i	−0.168086	−	0.450656i
$363$	−6.44252	+	3.51788i	−0.338145	+	0.184641i
$364$	−1.17857	−	2.58072i	−0.0617741	−	0.135266i
$365$	−8.02991	−	4.67754i	−0.420305	−	0.244834i
$366$	1.33865	−	2.08298i	0.0699725	−	0.108879i
$367$	19.4435	−	19.4435i	1.01494	−	1.01494i	0.0150536	−	0.999887i	$-0.495208\pi$
$367$	19.4435	−	19.4435i	1.01494	−	1.01494i	0.999887	−	0.0150536i	$-0.00479189\pi$
$368$	4.73897	+	0.736337i	0.247036	+	0.0383842i
$369$			17.8490i			0.929184i
$370$	23.8975	+	11.7230i	1.24237	+	0.609452i
$371$	−1.08223	−	7.52710i	−0.0561868	−	0.390788i
$372$	−2.14994	+	5.76420i	−0.111469	+	0.298860i
$373$	−9.08869	−	16.6447i	−0.470595	−	0.861830i	−0.999910	−	0.0134046i	$-0.995733\pi$
$373$	−9.08869	−	16.6447i	−0.470595	−	0.861830i	0.529316	−	0.848425i	$-0.322449\pi$
$374$	−15.7663	−	7.20021i	−0.815253	−	0.372314i
$375$	3.55072	+	8.01975i	0.183358	+	0.414138i
$376$	−0.454823	+	3.16336i	−0.0234557	+	0.163138i
$377$	−14.4779	−	7.90553i	−0.745650	−	0.407156i
$378$	0.504189	−	7.04949i	0.0259327	−	0.362586i
$379$	11.1942	−	7.19405i	0.575005	−	0.369533i	−0.220586	−	0.975368i	$-0.570797\pi$
$379$	11.1942	−	7.19405i	0.575005	−	0.369533i	0.795591	+	0.605834i	$0.207161\pi$
$380$	4.45045	+	5.43274i	0.228303	+	0.278694i
$381$	10.5949	+	12.2272i	0.542793	+	0.626417i
$382$	4.49328	−	8.22883i	0.229896	−	0.421024i
$383$	−7.61880	+	5.70336i	−0.389303	+	0.291428i	−0.775944	−	0.630802i	$-0.782726\pi$
$383$	−7.61880	+	5.70336i	−0.389303	+	0.291428i	0.386641	+	0.922230i	$0.373635\pi$
$384$	0.592862	+	0.513718i	0.0302544	+	0.0262156i
$385$	−15.0336	+	7.67695i	−0.766181	+	0.391253i
$386$	6.94784	+	2.04007i	0.353636	+	0.103837i
$387$	11.2719	+	4.20421i	0.572984	+	0.213712i
$388$	0.795790	−	1.06305i	0.0404001	−	0.0539682i
$389$	18.0660	+	11.6103i	0.915984	+	0.588667i	0.911490	−	0.411323i	$-0.134933\pi$
$389$	18.0660	+	11.6103i	0.915984	+	0.588667i	0.00449402	+	0.999990i	$0.498570\pi$
$390$	1.84768	−	2.33092i	0.0935607	−	0.118031i
$391$	11.2073	−	14.6224i	0.566779	−	0.739487i
$392$	2.97024	+	2.97024i	0.150020	+	0.150020i
$393$	−0.142364	+	0.0309695i	−0.00718133	+	0.00156220i
$394$	11.4122	−	1.64082i	0.574936	−	0.0826633i
$395$	3.04000	+	5.03108i	0.152959	+	0.253141i
$396$	−3.03119	+	10.3233i	−0.152323	+	0.518764i
$397$	18.1098	−	6.75459i	0.908903	−	0.339003i	0.148847	−	0.988860i	$-0.452444\pi$
$397$	18.1098	−	6.75459i	0.908903	−	0.339003i	0.760057	+	0.649857i	$0.225171\pi$
$398$	21.1706	−	1.51415i	1.06119	−	0.0758975i
$399$	4.08037	+	0.586669i	0.204274	+	0.0293702i
$400$	4.34932	−	2.46646i	0.217466	−	0.123323i
$401$	−26.8260	+	23.2449i	−1.33963	+	1.16079i	−0.366527	+	0.930407i	$0.619453\pi$
$401$	−26.8260	+	23.2449i	−1.33963	+	1.16079i	−0.973099	+	0.230386i	$0.926001\pi$
$402$	0.102645	−	0.471851i	0.00511946	−	0.0235338i
$403$	2.82669	−	12.9941i	0.140808	−	0.647282i
$404$	−6.58913	+	5.70952i	−0.327822	+	0.284059i
$405$	−7.90661	+	3.34971i	−0.392883	+	0.166448i
$406$	−16.1110	−	2.31641i	−0.799576	−	0.114962i
$407$	−53.5725	+	3.83158i	−2.65549	+	0.189924i
$408$	2.82355	−	1.05313i	0.139787	−	0.0521378i
$409$	7.10271	−	24.1896i	0.351207	−	1.19610i	−0.574705	−	0.818360i	$-0.694883\pi$
$409$	7.10271	−	24.1896i	0.351207	−	1.19610i	0.925912	−	0.377739i	$-0.123298\pi$
$410$	−4.00877	+	16.2500i	−0.197979	+	0.802532i
$411$	3.56662	−	0.512803i	0.175928	−	0.0252947i
$412$	−10.4207	+	2.26689i	−0.513392	+	0.111682i
$413$	−8.17249	−	8.17249i	−0.402142	−	0.402142i
$414$	−9.97446	−	5.59432i	−0.490218	−	0.274946i
$415$	−7.76808	−	6.15761i	−0.381320	−	0.302265i
$416$	−1.42648	−	0.916744i	−0.0699390	−	0.0449471i
$417$	−4.46546	+	5.96515i	−0.218674	+	0.292115i
$418$	−13.2772	−	4.95214i	−0.649409	−	0.242217i
$419$	1.91896	+	0.563457i	0.0937472	+	0.0275267i	0.328270	−	0.944584i	$-0.393534\pi$
$419$	1.91896	+	0.563457i	0.0937472	+	0.0275267i	−0.234523	+	0.972111i	$0.575353\pi$
$420$	0.904440	−	2.79209i	0.0441321	−	0.136240i
$421$	7.26443	+	6.29466i	0.354046	+	0.306783i	0.813666	−	0.581333i	$-0.197469\pi$
$421$	7.26443	+	6.29466i	0.354046	+	0.306783i	−0.459619	+	0.888116i	$0.652014\pi$
$422$	−5.38772	+	4.03319i	−0.262270	+	0.196333i
$423$	3.65233	−	6.68875i	0.177582	−	0.325218i
$424$	−2.97635	−	3.43489i	−0.144544	−	0.166813i
$425$	−0.308678	−	19.2052i	−0.0149731	−	0.931587i
$426$	−7.50852	+	4.82544i	−0.363789	+	0.233793i
$427$	−0.376745	+	5.26758i	−0.0182320	+	0.254916i
$428$	1.79362	+	0.979391i	0.0866979	+	0.0473406i
$429$	−0.854130	+	5.94060i	−0.0412378	+	0.286815i
$430$	9.31789	+	6.35917i	0.449349	+	0.306666i
$431$	6.40337	+	2.92432i	0.308440	+	0.140860i	0.563621	−	0.826034i	$-0.309408\pi$
$431$	6.40337	+	2.92432i	0.308440	+	0.140860i	−0.255181	+	0.966893i	$0.582135\pi$
$432$	−2.02438	−	3.70737i	−0.0973978	−	0.178371i
$433$	−12.0683	+	32.3563i	−0.579964	+	1.55494i	0.232907	+	0.972499i	$0.425176\pi$
$433$	−12.0683	+	32.3563i	−0.579964	+	1.55494i	−0.812871	+	0.582444i	$0.802096\pi$
$434$	−1.86738	−	12.9879i	−0.0896371	−	0.623440i
$435$	−5.51886	−	16.1473i	−0.264609	−	0.774205i
$436$			19.0705i			0.913313i
$437$	8.28663	−	12.5781i	0.396403	−	0.601693i
$438$	−2.30531	+	2.30531i	−0.110152	+	0.110152i
$439$	−10.0531	+	15.6429i	−0.479809	+	0.746597i	−0.993798	−	0.111199i	$-0.964531\pi$
$439$	−10.0531	+	15.6429i	−0.479809	+	0.746597i	0.513989	+	0.857797i	$0.328167\pi$
$440$	−5.07817	+	8.71768i	−0.242092	+	0.415599i
$441$	−4.16108	−	9.11150i	−0.198147	−	0.433881i
$442$	−5.71714	+	3.12180i	−0.271937	+	0.148489i
$443$	5.81411	+	15.5882i	0.276237	+	0.740620i	0.998784	+	0.0492981i	$0.0156984\pi$
$443$	5.81411	+	15.5882i	0.276237	+	0.740620i	−0.722547	+	0.691322i	$0.757029\pi$
$444$	6.11527	−	7.05740i	0.290218	−	0.334929i
$445$	0.573565	−	20.7278i	0.0271896	−	0.982591i
$446$	−15.0939	+	4.43196i	−0.714716	+	0.209859i
$447$	−1.73617	−	0.124173i	−0.0821179	−	0.00587319i
$448$	−1.63492	−	0.355654i	−0.0772425	−	0.0168031i
$449$	12.0243	+	18.7101i	0.567460	+	0.882985i	0.999825	−	0.0187139i	$-0.00595717\pi$
$449$	12.0243	+	18.7101i	0.567460	+	0.882985i	−0.432365	+	0.901699i	$0.642321\pi$
$450$	−11.7729	+	1.88627i	−0.554979	+	0.0889195i
$451$	−9.51466	−	32.4040i	−0.448028	−	1.52584i
$452$	6.05240	+	8.08506i	0.284681	+	0.380289i
$453$	−0.178891	−	2.50123i	−0.00840505	−	0.117518i
$454$	4.99861	−	10.9454i	0.234596	−	0.513695i
$455$	−1.07619	+	6.25200i	−0.0504524	+	0.293098i
$456$	2.24116	−	1.02350i	0.104952	−	0.0479300i
$457$	−22.7364	−	17.0202i	−1.06356	−	0.796173i	−0.0838296	−	0.996480i	$-0.526715\pi$
$457$	−22.7364	−	17.0202i	−1.06356	−	0.796173i	−0.979733	+	0.200307i	$0.935806\pi$
$458$	−4.29448	−	19.7414i	−0.200668	−	0.922455i
$459$	−16.2268			−0.757404
$460$	−7.82445	−	7.33334i	−0.364817	−	0.341919i
$461$	32.3699			1.50761			0.753807	−	0.657095i	$-0.228215\pi$
$461$	32.3699			1.50761			0.753807	+	0.657095i	$0.228215\pi$
$462$	1.25882	+	5.78668i	0.0585654	+	0.269221i
$463$	10.9378	+	8.18793i	0.508323	+	0.380526i	0.822434	−	0.568861i	$-0.192616\pi$
$463$	10.9378	+	8.18793i	0.508323	+	0.380526i	−0.314111	+	0.949386i	$0.601707\pi$
$464$	−8.84904	+	4.04122i	−0.410807	+	0.187609i
$465$	11.2365	−	7.93619i	0.521078	−	0.368032i
$466$	−3.43051	+	7.51177i	−0.158915	+	0.347976i
$467$	−0.297165	−	4.15491i	−0.0137511	−	0.192266i	−0.999684	−	0.0251260i	$-0.992001\pi$
$467$	−0.297165	−	4.15491i	−0.0137511	−	0.192266i	0.985933	−	0.167140i	$-0.0534532\pi$
$468$	2.42317	+	3.23698i	0.112011	+	0.149630i
$469$	0.290163	+	0.988204i	0.0133985	+	0.0456310i
$470$	4.82738	−	5.26925i	0.222671	−	0.243052i
$471$	1.38319	+	2.15229i	0.0637341	+	0.0991722i
$472$	−6.74984	−	1.46834i	−0.310687	−	0.0675857i
$473$	−22.7047	−	1.62387i	−1.04396	−	0.0746656i
$474$	1.97869	−	0.580996i	0.0908842	−	0.0266860i
$475$	−1.37187	−	15.6437i	−0.0629456	−	0.717780i
$476$	−4.20909	+	4.85755i	−0.192923	+	0.222646i
$477$	3.78752	+	10.1547i	0.173419	+	0.464954i
$478$	14.7156	−	8.03530i	0.673074	−	0.367526i
$479$	−3.31968	−	7.26909i	−0.151680	−	0.332133i	0.818505	−	0.574500i	$-0.194803\pi$
$479$	−3.31968	−	7.26909i	−0.151680	−	0.332133i	−0.970185	+	0.242367i	$0.922076\pi$
$480$	−0.447450	−	1.69610i	−0.0204232	−	0.0774159i
$481$	−10.9129	+	16.9808i	−0.497584	+	0.774257i
$482$	3.14207	−	3.14207i	0.143117	−	0.143117i
$483$	−6.29430	−	0.0714242i	−0.286400	−	0.00324991i
$484$		−	9.35716i		−	0.425326i
$485$	−2.80973	+	0.960315i	−0.127583	+	0.0436057i
$486$	2.23216	+	15.5250i	0.101253	+	0.704230i
$487$	−4.26373	+	11.4315i	−0.193208	+	0.518011i	−0.997043	−	0.0768410i	$-0.975517\pi$
$487$	−4.26373	+	11.4315i	−0.193208	+	0.518011i	0.803835	+	0.594852i	$0.202789\pi$
$488$	1.51267	+	2.77025i	0.0684754	+	0.125403i
$489$	8.55196	+	3.90555i	0.386733	+	0.176615i
$490$	−1.74193	−	9.22980i	−0.0786925	−	0.416960i
$491$	5.67447	−	39.4668i	0.256085	−	1.78111i	−0.303994	−	0.952674i	$-0.598320\pi$
$491$	5.67447	−	39.4668i	0.256085	−	1.78111i	0.560079	−	0.828439i	$-0.310771\pi$
$492$	5.15358	+	2.81407i	0.232341	+	0.126868i
$493$	−2.66602	+	37.2758i	−0.120071	+	1.67882i
$494$	−4.48021	+	2.87925i	−0.201574	+	0.129544i
$495$	18.6107	−	15.2457i	0.836489	−	0.685245i
$496$	−5.13566	−	5.92686i	−0.230598	−	0.266124i
$497$	9.12323	−	16.7079i	0.409233	−	0.749454i
$498$	−2.78395	+	2.08404i	−0.124752	+	0.0933879i
$499$	−7.59110	−	6.57772i	−0.339824	−	0.294459i	0.468184	−	0.883631i	$-0.344909\pi$
$499$	−7.59110	−	6.57772i	−0.339824	−	0.294459i	−0.808008	+	0.589172i	$0.799454\pi$
$500$	−11.1419	−	0.926824i	−0.498279	−	0.0414488i
$501$	−16.3099	−	4.78901i	−0.728671	−	0.213957i
$502$	14.2928	+	5.33094i	0.637920	+	0.237932i
$503$	−24.4584	+	32.6726i	−1.09055	+	1.45680i	−0.213157	+	0.977018i	$0.568375\pi$
$503$	−24.4584	+	32.6726i	−1.09055	+	1.45680i	−0.877389	+	0.479780i	$0.840716\pi$
$504$	3.35644	+	2.15706i	0.149508	+	0.0960829i
$505$	19.3665	−	2.23967i	0.861796	−	0.0996640i
$506$	21.0902	+	4.83916i	0.937575	+	0.215127i
$507$	−5.61622	−	5.61622i	−0.249425	−	0.249425i
$508$	−20.1526	+	4.38394i	−0.894129	+	0.194506i
$509$	−20.9875	+	3.01754i	−0.930253	+	0.133750i	−0.590750	−	0.806855i	$-0.701168\pi$
$509$	−20.9875	+	3.01754i	−0.930253	+	0.133750i	−0.339503	+	0.940605i	$0.610259\pi$
$510$	−6.54239	−	1.61396i	−0.289702	−	0.0714674i
$511$	1.95903	−	6.67184i	0.0866624	−	0.295145i
$512$	−0.936950	+	0.349464i	−0.0414077	+	0.0154443i
$513$	−13.2329	+	0.946433i	−0.584245	+	0.0417860i
$514$	19.2804	+	2.77211i	0.850423	+	0.122272i
$515$	22.1038	+	8.94830i	0.974011	+	0.394309i
$516$	2.99101	−	2.59173i	0.131672	−	0.114094i
$517$	−3.06509	+	14.0900i	−0.134802	+	0.619677i
$518$	−4.23369	+	19.4620i	−0.186018	+	0.855109i
$519$	−0.163092	+	0.141320i	−0.00715896	+	0.00620327i
$520$	1.47909	+	3.49122i	0.0648624	+	0.153100i
$521$	−6.78921	−	0.976141i	−0.297441	−	0.0427655i	−0.00802106	−	0.999968i	$-0.502553\pi$
$521$	−6.78921	−	0.976141i	−0.297441	−	0.0427655i	−0.289420	+	0.957202i	$0.593462\pi$
$522$	23.1387	−	1.65492i	1.01276	−	0.0724337i
$523$	−10.4629	+	3.90244i	−0.457509	+	0.170642i	−0.567643	−	0.823275i	$-0.692145\pi$
$523$	−10.4629	+	3.90244i	−0.457509	+	0.170642i	0.110134	+	0.993917i	$0.464872\pi$
$524$	0.0523242	−	0.178200i	0.00228579	−	0.00778470i
$525$	−5.18981	+	4.01679i	−0.226502	+	0.175307i
$526$	−23.8458	+	3.42850i	−1.03972	+	0.149490i
$527$	−29.4382	+	6.40388i	−1.28235	+	0.278958i
$528$	2.50276	+	2.50276i	0.108919	+	0.108919i
$529$	−10.0268	+	20.6993i	−0.435949	+	0.899971i
$530$	1.16753	+	10.0957i	0.0507144	+	0.438528i
$531$	13.8573	+	8.90553i	0.601354	+	0.386467i
$532$	−3.14916	+	4.20679i	−0.136534	+	0.182388i
$533$	−11.8920	−	4.43547i	−0.515098	−	0.192122i
$534$	−6.97993	−	2.04949i	−0.302051	−	0.0886903i
$535$	−2.07821	−	4.06970i	−0.0898488	−	0.175948i
$536$	0.465208	+	0.403105i	0.0200939	+	0.0174115i
$537$	−12.1319	+	9.08182i	−0.523530	+	0.391909i
$538$	11.2318	−	20.5695i	0.484237	−	0.886814i
$539$	12.4112	+	14.3233i	0.534590	+	0.616949i
$540$	−0.934159	+	9.39897i	−0.0401998	+	0.404467i
$541$	−3.87412	+	2.48975i	−0.166561	+	0.107043i	−0.621266	−	0.783600i	$-0.713381\pi$
$541$	−3.87412	+	2.48975i	−0.166561	+	0.107043i	0.454704	+	0.890642i	$0.349745\pi$
$542$	−0.0198011	+	0.276856i	−0.000850531	+	0.0118920i
$543$	6.30079	+	3.44049i	0.270393	+	0.147646i
$544$	−0.546706	+	3.80243i	−0.0234398	+	0.163028i
$545$	24.0380	−	35.2222i	1.02968	−	1.50875i
$546$	2.02449	+	0.924555i	0.0866403	+	0.0395673i
$547$	4.67959	+	8.57003i	0.200085	+	0.366428i	0.958386	−	0.285477i	$-0.0921520\pi$
$547$	4.67959	+	8.57003i	0.200085	+	0.366428i	−0.758301	+	0.651905i	$0.773970\pi$
$548$	−1.60519	+	4.30369i	−0.0685704	+	0.183844i
$549$	−1.07115	−	7.45002i	−0.0457156	−	0.317959i
$550$	20.3675	−	9.70011i	0.868475	−	0.413614i
$551$			30.5536i			1.30163i
$552$	−3.18782	+	1.99795i	−0.135683	+	0.0850382i
$553$	−3.11015	+	3.11015i	−0.132257	+	0.132257i
$554$	−5.63992	+	8.77589i	−0.239617	+	0.372852i
$555$	−20.1903	+	5.32643i	−0.857029	+	0.226094i
$556$	−3.94588	−	8.64028i	−0.167343	−	0.366429i
$557$	−18.1382	+	9.90423i	−0.768542	+	0.419656i	−0.815144	−	0.579258i	$-0.803342\pi$
$557$	−18.1382	+	9.90423i	−0.768542	+	0.419656i	0.0466025	+	0.998914i	$0.485161\pi$
$558$	6.53532	+	17.5219i	0.276662	+	0.741760i
$559$	−5.60213	+	6.46520i	−0.236945	+	0.273449i
$560$	2.57130	+	2.71765i	0.108657	+	0.114842i
$561$	13.0461	−	3.83068i	0.550806	−	0.161731i
$562$	−12.5880	−	0.900310i	−0.530992	−	0.0379773i
$563$	24.3639	+	5.30005i	1.02682	+	0.223370i	0.694269	−	0.719716i	$-0.255728\pi$
$563$	24.3639	+	5.30005i	1.02682	+	0.223370i	0.332548	+	0.943086i	$0.392092\pi$
$564$	−1.35543	−	2.10909i	−0.0570738	−	0.0888086i
$565$	−0.987371	−	22.5616i	−0.0415390	−	0.949172i
$566$	−0.621568	−	2.11687i	−0.0261265	−	0.0889785i
$567$	−3.85049	−	5.14365i	−0.161705	−	0.216013i
$568$	−0.811671	−	11.3486i	−0.0340570	−	0.476179i
$569$	11.7064	−	25.6335i	0.490758	−	1.07461i	−0.488606	−	0.872505i	$-0.662494\pi$
$569$	11.7064	−	25.6335i	0.490758	−	1.07461i	0.979364	−	0.202106i	$-0.0647785\pi$
$570$	−5.42940	−	0.934587i	−0.227413	−	0.0391455i
$571$	19.0112	−	8.68214i	0.795595	−	0.363336i	0.0242118	−	0.999707i	$-0.492292\pi$
$571$	19.0112	−	8.68214i	0.795595	−	0.363336i	0.771383	+	0.636371i	$0.219565\pi$
$572$	−6.12466	−	4.58486i	−0.256085	−	0.191703i
$573$	1.56340	+	7.18684i	0.0653120	+	0.300235i
$574$	−12.5237			−0.522730
$575$	5.20778	+	23.4068i	0.217179	+	0.976132i
$576$	2.38461			0.0993587
$577$	−3.41363	−	15.6922i	−0.142111	−	0.653275i	−0.991992	−	0.126300i	$-0.959690\pi$
$577$	−3.41363	−	15.6922i	−0.142111	−	0.653275i	0.849881	−	0.526975i	$-0.176674\pi$
$578$	−1.79534	−	1.34398i	−0.0746764	−	0.0559020i
$579$	−5.16713	+	2.35975i	−0.214739	+	0.0980679i
$580$	21.4375	+	3.69014i	0.890145	+	0.153225i
$581$	3.08120	−	6.74688i	0.127830	−	0.279908i
$582$	0.0743146	+	1.03905i	0.00308044	+	0.0430702i
$583$	−12.2892	−	16.4164i	−0.508965	−	0.679897i
$584$	−1.17086	−	3.98759i	−0.0484506	−	0.165008i
$585$	−0.395310	−	9.03287i	−0.0163440	−	0.373463i
$586$	−14.9817	−	23.3120i	−0.618888	−	0.963009i
$587$	−26.2077	−	5.70114i	−1.08171	−	0.235311i	−0.363819	−	0.931469i	$-0.618527\pi$
$587$	−26.2077	−	5.70114i	−1.08171	−	0.235311i	−0.717888	+	0.696158i	$0.754891\pi$
$588$	−3.28681	−	0.235078i	−0.135546	−	0.00969443i
$589$	−23.6331	+	6.93930i	−0.973785	+	0.285929i
$590$	10.6157	+	11.2200i	0.437043	+	0.461919i
$591$	−5.92292	+	6.83541i	−0.243636	+	0.281171i
$592$	4.16000	+	11.1534i	0.170975	+	0.458402i
$593$	−2.99176	+	1.63363i	−0.122857	+	0.0670850i	−0.539502	−	0.841984i	$-0.681388\pi$
$593$	−2.99176	+	1.63363i	−0.122857	+	0.0670850i	0.416645	+	0.909069i	$0.363206\pi$
$594$	−7.91718	−	17.3362i	−0.324846	−	0.711313i
$595$	13.8968	−	3.66614i	0.569713	−	0.150297i
$596$	1.19959	−	1.86660i	0.0491371	−	0.0764589i
$597$	−11.7734	+	11.7734i	−0.481853	+	0.481853i
$598$	6.20587	−	5.25532i	0.253777	−	0.214906i
$599$		−	25.3198i		−	1.03454i	−0.855823	−	0.517269i	$-0.826949\pi$
$599$		−	25.3198i		−	1.03454i	0.855823	−	0.517269i	$-0.173051\pi$
$600$	−1.31148	+	3.69659i	−0.0535410	+	0.150913i
$601$	1.56139	+	10.8597i	0.0636906	+	0.442978i	0.996568	+	0.0827828i	$0.0263808\pi$
$601$	1.56139	+	10.8597i	0.0636906	+	0.442978i	−0.932877	+	0.360195i	$0.882710\pi$
$602$	−2.94987	+	7.90891i	−0.120228	+	0.322343i
$603$	−0.703473	−	1.28831i	−0.0286476	−	0.0524642i
$604$	2.90771	+	1.32791i	0.118313	+	0.0540318i
$605$	−11.7945	+	17.2821i	−0.479515	+	0.702618i
$606$	0.973366	−	6.76991i	0.0395403	−	0.275009i
$607$	4.60737	+	2.51582i	0.187008	+	0.102114i	0.570025	−	0.821627i	$-0.306933\pi$
$607$	4.60737	+	2.51582i	0.187008	+	0.102114i	−0.383018	+	0.923741i	$0.625115\pi$
$608$	−0.224058	+	3.13274i	−0.00908674	+	0.127049i
$609$	10.7416	−	6.90320i	0.435271	−	0.279732i
$610$	0.698030	−	7.02318i	0.0282624	−	0.284360i
$611$	3.54879	+	4.09552i	0.143569	+	0.165687i
$612$	4.39018	−	8.04001i	0.177463	−	0.324998i
$613$	−10.3772	+	7.76829i	−0.419132	+	0.313758i	−0.787945	−	0.615745i	$-0.788855\pi$
$613$	−10.3772	+	7.76829i	−0.419132	+	0.313758i	0.368813	+	0.929504i	$0.379764\pi$
$614$	24.1291	+	20.9080i	0.973773	+	0.843779i
$615$	−5.97129	−	11.6934i	−0.240785	−	0.471524i
$616$	−7.24329	−	2.12682i	−0.291841	−	0.0856921i
$617$	11.5521	+	4.30872i	0.465071	+	0.173463i	0.571066	−	0.820904i	$-0.306530\pi$
$617$	11.5521	+	4.30872i	0.465071	+	0.173463i	−0.105995	+	0.994367i	$0.533803\pi$
$618$	5.01351	−	6.69726i	0.201673	−	0.269403i
$619$	14.1064	+	9.06563i	0.566984	+	0.364378i	0.792510	−	0.609859i	$-0.208774\pi$
$619$	14.1064	+	9.06563i	0.566984	+	0.364378i	−0.225526	+	0.974237i	$0.572410\pi$
$620$	2.01456	+	17.4200i	0.0809068	+	0.699602i
$621$	19.8425	−	4.08124i	0.796252	−	0.163774i
$622$	−13.3698	−	13.3698i	−0.536082	−	0.536082i
$623$	15.1610	−	3.29808i	0.607415	−	0.132135i
$624$	1.31665	−	0.189306i	0.0527084	−	0.00757832i
$625$	19.4101	+	15.7559i	0.776404	+	0.630235i
$626$	4.74411	−	16.1570i	0.189613	−	0.645762i
$627$	10.4156	−	3.88480i	0.415957	−	0.155144i
$628$	−3.25304	+	0.232662i	−0.129811	+	0.00928424i
$629$	45.2639	+	6.50797i	1.80479	+	0.259490i
$630$	−3.48023	−	8.21469i	−0.138656	−	0.327281i
$631$	−16.3486	+	14.1661i	−0.650827	+	0.563944i	−0.916458	−	0.400130i	$-0.868965\pi$
$631$	−16.3486	+	14.1661i	−0.650827	+	0.563944i	0.265632	+	0.964075i	$0.414419\pi$
$632$	−0.558795	+	2.56874i	−0.0222277	+	0.102179i
$633$	1.12225	−	5.15889i	0.0446054	−	0.205048i
$634$	13.2303	−	11.4641i	0.525443	−	0.455299i
$635$	42.7466	+	17.3051i	1.69635	+	0.686733i
$636$	3.52913	+	0.507413i	0.139939	+	0.0201202i
$637$	7.10458	−	0.508130i	0.281494	−	0.0201328i
$638$	−41.1250	+	15.3388i	−1.62815	+	0.607270i
$639$	−7.64374	+	26.0322i	−0.302382	+	1.02982i
$640$	2.17098	+	0.535566i	0.0858157	+	0.0211701i
$641$	−6.94442	+	0.998456i	−0.274288	+	0.0394367i	−0.278086	−	0.960556i	$-0.589700\pi$
$641$	−6.94442	+	0.998456i	−0.274288	+	0.0394367i	0.00379821	+	0.999993i	$0.498791\pi$
$642$	−1.56650	+	0.340771i	−0.0618248	+	0.0134492i
$643$	−1.78726	−	1.78726i	−0.0704828	−	0.0704828i	0.670987	−	0.741469i	$-0.265871\pi$
$643$	−1.78726	−	1.78726i	−0.0704828	−	0.0704828i	−0.741469	+	0.670987i	$0.765871\pi$
$644$	3.92523	−	6.99855i	0.154676	−	0.275781i
$645$	−8.79104	+	1.01666i	−0.346147	+	0.0400308i
$646$	10.1499	+	6.52296i	0.399343	+	0.256642i
$647$	18.1426	−	24.2357i	0.713261	−	0.952805i	−0.286726	−	0.958013i	$-0.592567\pi$
$647$	18.1426	−	24.2357i	0.713261	−	0.952805i	0.999986	+	0.00520773i	$0.00165768\pi$
$648$	−3.59806	−	1.34201i	−0.141345	−	0.0527190i
$649$	−29.9043	−	8.78071i	−1.17385	−	0.344673i
$650$	1.66882	−	8.31245i	0.0654567	−	0.326041i
$651$	7.77922	+	6.74073i	0.304892	+	0.264190i
$652$	−9.59418	+	7.18211i	−0.375737	+	0.281273i
$653$	−2.30588	+	4.22291i	−0.0902361	+	0.165255i	−0.918899	−	0.394493i	$-0.870920\pi$
$653$	−2.30588	+	4.22291i	−0.0902361	+	0.165255i	0.828663	+	0.559748i	$0.189102\pi$
$654$	−9.79688	−	11.3062i	−0.383088	−	0.442107i
$655$	−0.321257	+	0.263171i	−0.0125526	+	0.0102829i
$656$	−6.29687	+	4.04675i	−0.245851	+	0.157999i
$657$	−0.706991	+	9.88502i	−0.0275823	+	0.385651i
$658$	4.69314	+	2.56265i	0.182958	+	0.0999024i
$659$	5.27064	−	36.6581i	0.205315	−	1.42800i	−0.582873	−	0.812564i	$-0.698071\pi$
$659$	5.27064	−	36.6581i	0.205315	−	1.42800i	0.788188	−	0.615435i	$-0.211020\pi$
$660$	−1.46777	−	7.77713i	−0.0571330	−	0.302724i
$661$	39.6324	+	18.0995i	1.54152	+	0.703989i	0.991372	−	0.131079i	$-0.0418440\pi$
$661$	39.6324	+	18.0995i	1.54152	+	0.703989i	0.550148	+	0.835067i	$0.314571\pi$
$662$	10.6864	+	19.5707i	0.415339	+	0.760636i
$663$	1.78575	−	4.78779i	0.0693530	−	0.185942i
$664$	−0.630887	−	4.38792i	−0.0244832	−	0.170284i
$665$	11.1189	−	3.80024i	0.431172	−	0.147367i
$666$		−	28.3863i		−	1.09995i
$667$	−6.11523	−	46.2521i	−0.236783	−	1.79089i
$668$	15.3221	−	15.3221i	0.592829	−	0.592829i
$669$	6.67181	−	10.3815i	0.257947	−	0.401373i
$670$	−0.351106	−	1.33090i	−0.0135644	−	0.0514170i
$671$	5.91595	+	12.9541i	0.228383	+	0.500088i
$672$	1.15199	−	0.629032i	0.0444388	−	0.0242654i
$673$	1.29137	+	3.46231i	0.0497788	+	0.133462i	0.959460	−	0.281846i	$-0.0909466\pi$
$673$	1.29137	+	3.46231i	0.0497788	+	0.133462i	−0.909681	+	0.415308i	$0.863674\pi$
$674$	3.25831	−	3.76029i	0.125506	−	0.144841i
$675$	13.5725	−	16.1819i	0.522408	−	0.622840i
$676$	9.71461	−	2.85247i	0.373639	−	0.109710i
$677$	−44.5462	−	3.18600i	−1.71205	−	0.122448i	−0.819406	−	0.573214i	$-0.805697\pi$
$677$	−44.5462	−	3.18600i	−1.71205	−	0.122448i	−0.892642	+	0.450766i	$0.851151\pi$
$678$	−7.74168	−	1.68410i	−0.297317	−	0.0646774i
$679$	−1.20120	−	1.86910i	−0.0460978	−	0.0717295i
$680$	5.80262	−	6.33375i	0.222520	−	0.242888i
$681$	2.65938	+	9.05701i	0.101908	+	0.347065i
$682$	−21.2048	−	28.3263i	−0.811973	−	1.08467i
$683$	1.56618	+	21.8981i	0.0599283	+	0.837907i	0.935165	+	0.354212i	$0.115251\pi$
$683$	1.56618	+	21.8981i	0.0599283	+	0.837907i	−0.875237	+	0.483695i	$0.839295\pi$
$684$	3.11122	−	6.81263i	0.118961	−	0.260487i
$685$	8.38941	−	5.92534i	0.320543	−	0.226396i
$686$	17.0467	−	7.78498i	0.650847	−	0.297232i
$687$	12.6875	+	9.49777i	0.484060	+	0.362363i
$688$	1.07240	+	4.92975i	0.0408849	+	0.187945i
$689$	−7.70681			−0.293606
$690$	8.40609	+	0.328099i	0.320014	+	0.0124905i
$691$	19.0780			0.725762			0.362881	−	0.931836i	$-0.381793\pi$
$691$	19.0780			0.725762			0.362881	+	0.931836i	$0.381793\pi$
$692$	−0.0584752	−	0.268806i	−0.00222290	−	0.0102185i
$693$	14.4110	+	10.7880i	0.547430	+	0.409801i
$694$	−5.41735	+	2.47402i	−0.205640	+	0.0939126i
$695$	−3.60308	+	20.9318i	−0.136673	+	0.793988i
$696$	3.17021	−	6.94180i	0.120167	−	0.263128i
$697$	2.05130	+	28.6810i	0.0776987	+	1.08637i
$698$	−7.23098	−	9.65946i	−0.273697	−	0.365616i
$699$	−1.82511	−	6.21576i	−0.0690320	−	0.235101i
$700$	−1.32349	−	8.26041i	−0.0500233	−	0.312214i
$701$	−6.32785	−	9.84632i	−0.238999	−	0.371890i	0.700946	−	0.713214i	$-0.252761\pi$
$701$	−6.32785	−	9.84632i	−0.238999	−	0.371890i	−0.939946	+	0.341324i	$0.889125\pi$
$702$	−6.99889	−	1.52251i	−0.264156	−	0.0574636i
$703$	37.2919	+	2.66717i	1.40649	+	0.100594i
$704$	−4.32913	+	1.27115i	−0.163160	+	0.0479081i
$705$	−0.155066	+	5.60385i	−0.00584013	+	0.211053i
$706$	−22.1429	+	25.5543i	−0.833359	+	0.961748i
$707$	5.09787	+	13.6679i	0.191725	+	0.514035i
$708$	4.75604	−	2.59699i	0.178743	−	0.0976009i
$709$	−13.8682	−	30.3671i	−0.520831	−	1.14046i	−0.969124	−	0.246574i	$-0.920695\pi$
$709$	−13.8682	−	30.3671i	−0.520831	−	1.14046i	0.448293	−	0.893887i	$-0.352032\pi$
$710$	−12.8056	+	21.9834i	−0.480587	+	0.825021i
$711$	3.38911	−	5.27356i	0.127102	−	0.197774i
$712$	6.55721	−	6.55721i	0.245742	−	0.245742i
$713$	34.3869	−	15.2348i	1.28780	−	0.570549i
$714$		−	5.04214i		−	0.188698i
$715$	5.53276	+	16.1880i	0.206913	+	0.605396i
$716$	−2.74928	−	19.1217i	−0.102745	−	0.714610i
$717$	−4.59641	+	12.3235i	−0.171656	+	0.460228i
$718$	14.0285	+	25.6913i	0.523540	+	0.958791i
$719$	20.4995	+	9.36179i	0.764501	+	0.349136i	0.759206	−	0.650850i	$-0.225587\pi$
$719$	20.4995	+	9.36179i	0.764501	+	0.349136i	0.00529470	+	0.999986i	$0.498315\pi$
$720$	−4.40423	−	3.00575i	−0.164136	−	0.112018i
$721$	−2.53936	+	17.6616i	−0.0945706	+	0.657753i
$722$	−8.01827	−	4.37831i	−0.298409	−	0.162944i
$723$	−0.248677	+	3.47695i	−0.00924838	+	0.129309i
$724$	−7.69858	+	4.94758i	−0.286115	+	0.183875i
$725$	−34.9425	−	33.8371i	−1.29773	−	1.25668i
$726$	4.80694	+	5.54751i	0.178402	+	0.205887i
$727$	14.1208	−	25.8602i	0.523710	−	0.959103i	−0.473230	−	0.880939i	$-0.656912\pi$
$727$	14.1208	−	25.8602i	0.523710	−	0.959103i	0.996940	−	0.0781647i	$-0.0249060\pi$
$728$	−2.27122	+	1.70021i	−0.0841769	+	0.0630140i
$729$	−0.592199	−	0.513143i	−0.0219333	−	0.0190053i
$730$	−2.86376	+	8.84069i	−0.105993	+	0.327209i
$731$	18.5956	+	5.46016i	0.687784	+	0.201951i
$732$	−2.31993	−	0.865290i	−0.0857472	−	0.0319821i
$733$	0.363562	−	0.485661i	0.0134285	−	0.0179383i	−0.793777	−	0.608209i	$-0.791888\pi$
$733$	0.363562	−	0.485661i	0.0134285	−	0.0179383i	0.807205	+	0.590271i	$0.200979\pi$
$734$	−23.1321	−	14.8661i	−0.853822	−	0.548718i
$735$	5.77424	+	4.57714i	0.212986	+	0.168830i
$736$	−0.287830	−	4.78719i	−0.0106096	−	0.176458i
$737$	1.96387	+	1.96387i	0.0723401	+	0.0723401i
$738$	17.4411	−	3.79409i	0.642017	−	0.139662i
$739$	−47.4485	+	6.82207i	−1.74542	+	0.250954i	−0.939861	−	0.341558i	$-0.889045\pi$
$739$	−47.4485	+	6.82207i	−1.74542	+	0.250954i	−0.805562	+	0.592512i	$0.798136\pi$
$740$	6.37536	−	25.8433i	0.234363	−	0.950018i
$741$	1.17702	−	4.00856i	0.0432389	−	0.147258i
$742$	−7.12504	+	2.65750i	−0.261568	+	0.0975600i
$743$	7.65113	−	0.547219i	0.280693	−	0.0200755i	0.0697168	−	0.997567i	$-0.477790\pi$
$743$	7.65113	−	0.547219i	0.280693	−	0.0200755i	0.210976	+	0.977491i	$0.432336\pi$
$744$	6.08947	+	0.875534i	0.223251	+	0.0320986i
$745$	−4.56838	+	1.93544i	−0.167373	+	0.0709090i
$746$	−14.3324	+	12.4191i	−0.524745	+	0.454694i
$747$	−2.24704	+	10.3295i	−0.0822150	+	0.377936i
$748$	−3.68430	+	16.9365i	−0.134711	+	0.619258i
$749$	2.58409	−	2.23913i	0.0944207	−	0.0818160i
$750$	7.08171	−	5.17429i	0.258588	−	0.188938i
$751$	−29.3300	−	4.21702i	−1.07027	−	0.153881i	−0.415411	−	0.909634i	$-0.636362\pi$
$751$	−29.3300	−	4.21702i	−1.07027	−	0.153881i	−0.654857	+	0.755752i	$0.727271\pi$
$752$	3.18775	−	0.227992i	0.116245	−	0.00831402i
$753$	−11.2123	+	4.18196i	−0.408598	+	0.152399i
$754$	−4.64737	+	15.8275i	−0.169247	+	0.576403i
$755$	−3.69657	−	6.11768i	−0.134532	−	0.222645i
$756$	−6.99556	+	1.00581i	−0.254426	+	0.0365809i
$757$	37.2775	−	8.10922i	1.35487	−	0.294735i	0.524247	−	0.851566i	$-0.324347\pi$
$757$	37.2775	−	8.10922i	1.35487	−	0.294735i	0.830625	+	0.556832i	$0.187983\pi$
$758$	−9.40913	−	9.40913i	−0.341755	−	0.341755i
$759$	−14.9896	+	7.96547i	−0.544086	+	0.289128i
$760$	4.36257	−	5.50356i	0.158247	−	0.199635i
$761$	−18.8519	−	12.1154i	−0.683379	−	0.439181i	0.152347	−	0.988327i	$-0.451317\pi$
$761$	−18.8519	−	12.1154i	−0.683379	−	0.439181i	−0.835727	+	0.549146i	$0.814953\pi$
$762$	9.69563	−	12.9518i	0.351236	−	0.469196i
$763$	29.8961	+	11.1507i	1.08231	+	0.403681i
$764$	−8.99589	−	2.64143i	−0.325460	−	0.0955637i
$765$	−18.2427	+	9.31570i	−0.659565	+	0.336810i
$766$	7.19252	+	6.23235i	0.259876	+	0.225184i
$767$	−9.37685	+	7.01942i	−0.338578	+	0.253457i
$768$	0.375956	−	0.688512i	0.0135661	−	0.0248445i
$769$	1.16713	+	1.34694i	0.0420879	+	0.0485720i	0.776403	−	0.630237i	$-0.217042\pi$
$769$	1.16713	+	1.34694i	0.0420879	+	0.0485720i	−0.734315	+	0.678809i	$0.762497\pi$
$770$	10.6971	+	13.0581i	0.385497	+	0.470583i
$771$	−12.8547	+	8.26122i	−0.462951	+	0.297521i
$772$	0.516578	−	7.22271i	0.0185921	−	0.259951i
$773$	13.8589	+	7.56752i	0.498469	+	0.272185i	0.708754	−	0.705455i	$-0.249257\pi$
$773$	13.8589	+	7.56752i	0.498469	+	0.272185i	−0.210285	+	0.977640i	$0.567439\pi$
$774$	1.71211	−	11.9080i	0.0615406	−	0.428024i
$775$	18.2367	−	34.7130i	0.655083	−	1.24693i
$776$	−1.20791	−	0.551636i	−0.0433616	−	0.0198026i
$777$	−7.48796	−	13.7132i	−0.268629	−	0.491958i
$778$	7.50479	−	20.1211i	0.269060	−	0.721377i
$779$	3.34564	+	23.2695i	0.119870	+	0.833715i
$780$	−2.67040	−	1.30998i	−0.0956157	−	0.0469048i
$781$		−	51.3346i		−	1.83690i
$782$	−16.6705	−	7.84299i	−0.596137	−	0.280465i
$783$	−29.0566	+	29.0566i	−1.03840	+	1.03840i
$784$	2.27099	−	3.53374i	0.0811069	−	0.126205i
$785$	6.30145	+	3.67068i	0.224908	+	0.131012i
$786$	0.0605234	+	0.132528i	0.00215880	+	0.00472711i
$787$	−5.81160	+	3.17337i	−0.207161	+	0.113118i	−0.579480	−	0.814986i	$-0.696744\pi$
$787$	−5.81160	+	3.17337i	−0.207161	+	0.113118i	0.372319	+	0.928105i	$0.378563\pi$
$788$	−4.02915	−	10.8026i	−0.143533	−	0.384826i
$789$	12.3760	−	14.2826i	0.440596	−	0.508475i
$790$	4.26990	−	4.03996i	0.151916	−	0.143735i
$791$	16.2135	−	4.76071i	0.576486	−	0.169271i
$792$	10.7317	+	0.767545i	0.381334	+	0.0272735i
$793$	5.22977	+	1.13767i	0.185715	+	0.0403997i
$794$	−10.4497	−	16.2601i	−0.370847	−	0.577050i
$795$	−5.87852	−	5.38556i	−0.208489	−	0.191006i
$796$	−5.97968	−	20.3649i	−0.211944	−	0.721815i
$797$	25.5617	+	34.1465i	0.905443	+	1.20953i	0.977246	+	0.212111i	$0.0680338\pi$
$797$	25.5617	+	34.1465i	0.905443	+	1.20953i	−0.0718031	+	0.997419i	$0.522875\pi$
$798$	−0.294084	−	4.11183i	−0.0104105	−	0.145557i
$799$	5.10009	−	11.1676i	0.180428	−	0.395083i
$800$	−3.33461	−	3.72564i	−0.117896	−	0.131721i
$801$	−20.1148	+	9.18614i	−0.710723	+	0.324576i
$802$	28.4159	+	21.2719i	1.00340	+	0.751137i
$803$	−3.98584	−	18.3226i	−0.140657	−	0.646590i
$804$	−0.482886			−0.0170301
$805$	−16.0712	+	7.97823i	−0.566435	+	0.281196i
$806$	−13.2980			−0.468402
$807$	3.90801	+	17.9648i	0.137569	+	0.632392i
$808$	6.97966	+	5.22490i	0.245543	+	0.183812i
$809$	20.3427	−	9.29021i	0.715212	−	0.326626i	−0.0243607	−	0.999703i	$-0.507755\pi$
$809$	20.3427	−	9.29021i	0.715212	−	0.326626i	0.739572	+	0.673077i	$0.235028\pi$
$810$	4.95383	+	7.01389i	0.174060	+	0.246443i
$811$	13.3790	−	29.2960i	0.469801	−	1.02872i	−0.515342	−	0.856985i	$-0.672335\pi$
$811$	13.3790	−	29.2960i	0.469801	−	1.02872i	0.985143	−	0.171736i	$-0.0549376\pi$
$812$	1.16117	+	16.2352i	0.0407489	+	0.569745i
$813$	−0.130487	−	0.174310i	−0.00457636	−	0.00611330i
$814$	15.1317	+	51.5337i	0.530365	+	1.80626i
$815$	26.7728	−	1.17167i	0.937810	−	0.0410418i
$816$	−1.62925	−	2.53517i	−0.0570353	−	0.0887486i
$817$	15.4830	+	3.36813i	0.541683	+	0.117836i
$818$	−25.1466	−	1.79852i	−0.879230	−	0.0628838i
$819$	6.49133	−	1.90603i	0.226825	−	0.0666020i
$820$	16.7308	+	0.462964i	0.584265	+	0.0161674i
$821$	9.12593	−	10.5319i	0.318497	−	0.367565i	−0.573814	−	0.818985i	$-0.694537\pi$
$821$	9.12593	−	10.5319i	0.318497	−	0.367565i	0.892312	+	0.451420i	$0.149082\pi$
$822$	−1.25922	−	3.37611i	−0.0439205	−	0.117755i
$823$	−14.4786	+	7.90592i	−0.504692	+	0.275583i	−0.711359	−	0.702828i	$-0.751920\pi$
$823$	−14.4786	+	7.90592i	−0.504692	+	0.275583i	0.206667	+	0.978411i	$0.433738\pi$
$824$	4.43017	+	9.70071i	0.154332	+	0.337940i
$825$	−7.09203	+	16.2140i	−0.246913	+	0.564499i
$826$	−6.24853	+	9.72291i	−0.217414	+	0.338303i
$827$	−17.6102	+	17.6102i	−0.612368	+	0.612368i	−0.943563	−	0.331194i	$-0.892548\pi$
$827$	−17.6102	+	17.6102i	−0.612368	+	0.612368i	0.331194	+	0.943563i	$0.392548\pi$
$828$	−3.34624	+	10.9357i	−0.116290	+	0.380041i
$829$		−	26.5027i		−	0.920477i	−0.887795	−	0.460238i	$-0.847764\pi$
$829$		−	26.5027i		−	0.920477i	0.887795	−	0.460238i	$-0.152236\pi$
$830$	−4.36567	+	8.89945i	−0.151535	+	0.308904i
$831$	−1.16464	−	8.10022i	−0.0404008	−	0.280993i
$832$	−0.592573	+	1.58875i	−0.0205438	+	0.0550800i
$833$	−7.73344	−	14.1627i	−0.267948	−	0.490710i
$834$	6.77803	+	3.09542i	0.234704	+	0.107186i
$835$	−47.6121	+	8.98580i	−1.64769	+	0.310967i
$836$	−2.01670	+	14.0264i	−0.0697489	+	0.485114i
$837$	−29.0745	−	15.8759i	−1.00496	−	0.548751i
$838$	0.142676	−	1.99487i	0.00492867	−	0.0689118i
$839$	−27.6812	+	17.7896i	−0.955661	+	0.614166i	−0.922794	−	0.385294i	$-0.874100\pi$
$839$	−27.6812	+	17.7896i	−0.955661	+	0.614166i	−0.0328669	+	0.999460i	$0.510464\pi$
$840$	−2.92053	−	0.290270i	−0.100768	−	0.0100153i
$841$	42.9831	+	49.6052i	1.48218	+	1.71052i
$842$	4.60664	−	8.43644i	0.158755	−	0.290739i
$843$	7.92544	−	5.93291i	0.272967	−	0.204340i
$844$	5.08627	+	4.40727i	0.175076	+	0.151705i
$845$	−21.5378	−	6.97673i	−0.740922	−	0.240007i
$846$	−7.31225	−	2.14707i	−0.251400	−	0.0738178i
$847$	−14.6689	−	5.47120i	−0.504028	−	0.187993i
$848$	−2.72373	+	3.63847i	−0.0935331	+	0.124946i
$849$	1.45598	+	0.935699i	0.0499690	+	0.0321131i
$850$	−18.7006	+	4.38397i	−0.641427	+	0.150369i
$851$	−56.9864	+	3.42632i	−1.95347	+	0.117453i
$852$	6.31121	+	6.31121i	0.216218	+	0.216218i
$853$	−27.2728	+	5.93283i	−0.933802	+	0.203136i	−0.653631	−	0.756814i	$-0.726755\pi$
$853$	−27.2728	+	5.93283i	−0.933802	+	0.203136i	−0.280172	+	0.959950i	$0.590391\pi$
$854$	5.22728	−	0.751570i	0.178874	−	0.0257182i
$855$	−14.3334	+	8.66089i	−0.490193	+	0.296196i
$856$	0.575747	−	1.96081i	0.0196786	−	0.0670193i
$857$	31.5700	−	11.7750i	1.07841	−	0.402226i	0.253411	−	0.967359i	$-0.418448\pi$
$857$	31.5700	−	11.7750i	1.07841	−	0.402226i	0.825000	+	0.565132i	$0.191175\pi$
$858$	5.98640	−	0.428156i	0.204372	−	0.0146170i
$859$	40.8861	+	5.87853i	1.39501	+	0.200573i	0.798483	−	0.602017i	$-0.205636\pi$
$859$	40.8861	+	5.87853i	1.39501	+	0.200573i	0.596531	+	0.802590i	$0.296545\pi$
$860$	4.23318	−	10.4567i	0.144350	−	0.356570i
$861$	7.42484	−	6.43366i	0.253038	−	0.219258i
$862$	1.49636	−	6.87865i	0.0509661	−	0.234288i
$863$	−1.82313	+	8.38081i	−0.0620602	+	0.285286i	−0.997709	−	0.0676451i	$-0.978451\pi$
$863$	−1.82313	+	8.38081i	−0.0620602	+	0.285286i	0.935649	+	0.352931i	$0.114815\pi$
$864$	−3.19233	+	2.76617i	−0.108605	+	0.0941070i
$865$	−0.230825	+	0.570176i	−0.00784827	+	0.0193866i
$866$	34.1821	+	4.91465i	1.16156	+	0.167007i
$867$	1.75481	−	0.125507i	0.0595966	−	0.00426243i
$868$	−12.2942	+	4.58548i	−0.417291	+	0.155641i
$869$	−3.34161	+	11.3805i	−0.113356	+	0.386056i
$870$	−14.6052	+	8.82510i	−0.495162	+	0.299199i
$871$	1.03315	−	0.148545i	0.0350071	−	0.00503326i
$872$	18.6347	−	4.05373i	0.631051	−	0.137277i
$873$	2.23909	+	2.23909i	0.0757819	+	0.0757819i
$874$	−14.0521	−	5.42358i	−0.475320	−	0.183455i
$875$	−7.96767	+	16.9247i	−0.269356	+	0.572160i
$876$	2.74265	+	1.76260i	0.0926657	+	0.0595526i
$877$	−8.53720	+	11.4044i	−0.288281	+	0.385098i	−0.921180	−	0.389136i	$-0.872774\pi$
$877$	−8.53720	+	11.4044i	−0.288281	+	0.385098i	0.632900	+	0.774234i	$0.281865\pi$
$878$	17.4224	+	6.49822i	0.587978	+	0.219304i
$879$	20.8579	+	6.12442i	0.703518	+	0.206571i
$880$	9.59790	+	3.10905i	0.323545	+	0.104806i
$881$	−17.0329	−	14.7591i	−0.573852	−	0.497245i	0.318904	−	0.947787i	$-0.396685\pi$
$881$	−17.0329	−	14.7591i	−0.573852	−	0.497245i	−0.892755	+	0.450542i	$0.851231\pi$
$882$	−8.01878	+	6.00278i	−0.270006	+	0.202124i
$883$	−11.9760	+	21.9325i	−0.403025	+	0.738086i	−0.997834	−	0.0657813i	$-0.979046\pi$
$883$	−11.9760	+	21.9325i	−0.403025	+	0.738086i	0.594809	+	0.803867i	$0.297228\pi$
$884$	4.26572	+	4.92290i	0.143472	+	0.165575i
$885$	−12.0576	−	1.19840i	−0.405311	−	0.0402836i
$886$	13.9961	−	8.99476i	0.470209	−	0.302185i
$887$	4.07578	−	56.9868i	0.136851	−	1.91343i	−0.213722	−	0.976894i	$-0.568559\pi$
$887$	4.07578	−	56.9868i	0.136851	−	1.91343i	0.350573	−	0.936535i	$-0.385987\pi$
$888$	−8.19601	−	4.47536i	−0.275040	−	0.150183i
$889$	−4.91087	+	34.1558i	−0.164705	+	1.14555i
$890$	−20.3760	+	3.84555i	−0.683005	+	0.128903i
$891$	−15.7607	−	7.19768i	−0.528004	−	0.241132i
$892$	7.53911	+	13.8068i	0.252428	+	0.462287i
$893$	3.50773	−	9.40459i	0.117382	−	0.314713i
$894$	0.247714	+	1.72289i	0.00828478	+	0.0576219i
$895$	−19.0247	+	38.7820i	−0.635926	+	1.29634i
$896$			1.67315i			0.0558961i
$897$	−0.979471	+	6.30375i	−0.0327036	+	0.210476i
$898$	15.7266	−	15.7266i	0.524803	−	0.524803i
$899$	−41.2464	+	64.1807i	−1.37565	+	2.14055i
$900$	4.34567	+	11.1029i	0.144856	+	0.370096i
$901$	7.25306	+	15.8820i	0.241635	+	0.529106i
$902$	−29.6410	+	16.1852i	−0.986936	+	0.538908i
$903$	−2.31408	−	6.20429i	−0.0770078	−	0.206466i
$904$	6.61376	−	7.63269i	0.219970	−	0.253859i
$905$	20.4551	+	0.566021i	0.679952	+	0.0188152i
$906$	−2.40604	+	0.706478i	−0.0799354	+	0.0234712i
$907$	31.2813	+	2.23728i	1.03868	+	0.0742878i	0.580246	−	0.814441i	$-0.302956\pi$
$907$	31.2813	+	2.23728i	1.03868	+	0.0742878i	0.458433	+	0.888729i	$0.348411\pi$
$908$	−11.7578	−	2.55776i	−0.390197	−	0.0848822i
$909$	−11.2403	−	17.4902i	−0.372816	−	0.580113i
$910$	6.33789	−	0.277368i	0.210099	−	0.00919465i
$911$	−0.944917	−	3.21809i	−0.0313065	−	0.106620i	0.942358	−	0.334607i	$-0.108604\pi$
$911$	−0.944917	−	3.21809i	−0.0313065	−	0.106620i	−0.973664	+	0.227987i	$0.926786\pi$
$912$	−1.47651	−	1.97238i	−0.0488920	−	0.0653121i
$913$	−1.42688	−	19.9504i	−0.0472229	−	0.660263i
$914$	−11.7983	+	25.8347i	−0.390253	+	0.854536i
$915$	3.19410	+	4.52237i	0.105594	+	0.149505i
$916$	−18.3774	+	8.39267i	−0.607206	+	0.277302i
$917$	−0.248762	−	0.186221i	−0.00821486	−	0.00614957i
$918$	3.44926	+	15.8560i	0.113843	+	0.523326i
$919$	−49.4619			−1.63160			−0.815798	−	0.578337i	$-0.803702\pi$
$919$	−49.4619			−1.63160			−0.815798	+	0.578337i	$0.803702\pi$
$920$	−5.50255	+	9.20446i	−0.181414	+	0.303462i
$921$	−25.0461			−0.825296
$922$	−6.88071	−	31.6301i	−0.226604	−	1.04168i
$923$	−15.4445	−	11.5616i	−0.508363	−	0.380556i
$924$	5.38686	−	2.46010i	0.177215	−	0.0809312i
$925$	−44.3498	+	39.6950i	−1.45821	+	1.30516i
$926$	5.67582	−	12.4283i	0.186519	−	0.408419i
$927$	−1.81419	−	25.3657i	−0.0595859	−	0.833119i
$928$	5.82987	+	7.78779i	0.191375	+	0.255647i
$929$	−14.5800	−	49.6549i	−0.478354	−	1.62912i	−0.746242	−	0.665674i	$-0.768144\pi$
$929$	−14.5800	−	49.6549i	−0.478354	−	1.62912i	0.267888	−	0.963450i	$-0.413674\pi$
$930$	−10.1433	−	9.29271i	−0.332612	−	0.304720i
$931$	−7.13260	−	11.0985i	−0.233761	−	0.363740i
$932$	8.06931	+	1.75537i	0.264319	+	0.0574991i
$933$	14.7948	+	1.05814i	0.484360	+	0.0346421i
$934$	−3.99679	+	1.17356i	−0.130779	+	0.0384001i
$935$	28.1527	−	26.6366i	0.920693	−	0.871112i
$936$	2.64792	−	3.05587i	0.0865501	−	0.0998841i
$937$	16.1461	+	43.2893i	0.527470	+	1.41420i	0.878457	+	0.477821i	$0.158573\pi$
$937$	16.1461	+	43.2893i	0.527470	+	1.41420i	−0.350988	+	0.936380i	$0.614154\pi$
$938$	0.903942	−	0.493590i	0.0295147	−	0.0161163i
$939$	5.48751	+	12.0160i	0.179078	+	0.392127i
$940$	−6.17496	−	3.59700i	−0.201405	−	0.117321i
$941$	7.54865	−	11.7459i	0.246079	−	0.382906i	−0.696139	−	0.717907i	$-0.745100\pi$
$941$	7.54865	−	11.7459i	0.246079	−	0.382906i	0.942218	+	0.335001i	$0.108737\pi$
$942$	1.80908	−	1.80908i	0.0589431	−	0.0589431i
$943$	−9.72197	−	34.5557i	−0.316591	−	1.12529i
$944$			6.90770i			0.224827i
$945$	14.1882	+	6.96009i	0.461542	+	0.226412i
$946$	3.23947	+	22.5310i	0.105324	+	0.732545i
$947$	15.7544	−	42.2392i	0.511950	−	1.37259i	−0.381892	−	0.924207i	$-0.624727\pi$
$947$	15.7544	−	42.2392i	0.511950	−	1.37259i	0.893841	−	0.448383i	$-0.148000\pi$
$948$	−0.988319	−	1.80997i	−0.0320991	−	0.0587851i
$949$	−6.41023	−	2.92745i	−0.208085	−	0.0950292i
$950$	−14.9945	+	4.66581i	−0.486487	+	0.151379i
$951$	−1.95442	+	13.5933i	−0.0633765	+	0.440793i
$952$	5.64125	+	3.08036i	0.182834	+	0.0998349i
$953$	3.88293	−	54.2904i	0.125780	−	1.75864i	−0.407969	−	0.912996i	$-0.633763\pi$
$953$	3.88293	−	54.2904i	0.125780	−	1.75864i	0.533749	−	0.845643i	$-0.320783\pi$
$954$	9.11757	−	5.85951i	0.295192	−	0.189709i
$955$	13.2854	+	16.2177i	0.429906	+	0.524793i
$956$	−10.9797	−	12.6712i	−0.355108	−	0.409817i
$957$	16.5016	−	30.2204i	0.533421	−	0.976888i
$958$	−6.39732	+	4.78897i	−0.206688	+	0.154725i
$959$	5.80815	+	5.03279i	0.187555	+	0.162517i
$960$	−1.56222	+	0.797756i	−0.0504206	+	0.0257475i
$961$	−29.2671	−	8.59360i	−0.944100	−	0.277213i
$962$	18.9124	+	7.05396i	0.609760	+	0.227429i
$963$	−2.92038	+	3.90118i	−0.0941081	+	0.125714i
$964$	−3.73816	−	2.40237i	−0.120398	−	0.0773751i
$965$	−10.0582	+	12.6888i	−0.323784	+	0.408466i
$966$	1.26816	+	6.16563i	0.0408023	+	0.198376i
$967$	30.1269	+	30.1269i	0.968814	+	0.968814i	0.999528	−	0.0307139i	$-0.00977808\pi$
$967$	30.1269	+	30.1269i	0.968814	+	0.968814i	−0.0307139	+	0.999528i	$0.509778\pi$
$968$	−9.14332	+	1.98901i	−0.293878	+	0.0639291i
$969$	−9.36846	+	1.34698i	−0.300958	+	0.0432713i
$970$	1.53562	+	2.54139i	0.0493058	+	0.0815991i
$971$	7.28019	−	24.7940i	0.233632	−	0.795679i	−0.756311	−	0.654213i	$-0.773000\pi$
$971$	7.28019	−	24.7940i	0.233632	−	0.795679i	0.989943	−	0.141466i	$-0.0451816\pi$
$972$	14.6958	−	5.48123i	0.471367	−	0.175811i
$973$	−15.8522	+	1.13377i	−0.508198	+	0.0363471i
$974$	12.0766	+	1.73635i	0.386959	+	0.0556363i
$975$	3.28087	+	5.78544i	0.105072	+	0.185282i
$976$	2.38540	−	2.06696i	0.0763548	−	0.0661618i
$977$	6.12814	−	28.1706i	0.196056	−	0.901257i	−0.769007	−	0.639240i	$-0.779249\pi$
$977$	6.12814	−	28.1706i	0.196056	−	0.901257i	0.965063	−	0.262017i	$-0.0843875\pi$
$978$	1.99845	−	9.18670i	0.0639032	−	0.293758i
$979$	31.6206	−	27.3994i	1.01060	−	0.875689i
$980$	−8.64860	+	3.66406i	−0.276269	+	0.117044i
$981$	−45.0129	−	6.47188i	−1.43715	−	0.206631i
$982$	−39.7711	+	2.84448i	−1.26915	+	0.0907711i
$983$	−14.7725	+	5.50986i	−0.471170	+	0.175737i	−0.573822	−	0.818980i	$-0.694540\pi$
$983$	−14.7725	+	5.50986i	−0.471170	+	0.175737i	0.102652	+	0.994717i	$0.467267\pi$
$984$	1.65429	−	5.63398i	0.0527367	−	0.179605i
$985$	−6.17482	+	25.0304i	−0.196746	+	0.797534i
$986$	36.9906	−	5.31845i	1.17802	−	0.169374i
$987$	−4.09886	+	0.891652i	−0.130468	+	0.0283816i
$988$	3.76579	+	3.76579i	0.119806	+	0.119806i
$989$	−24.1124	−	1.99979i	−0.766729	−	0.0635896i
$990$	−18.8533	−	14.9447i	−0.599197	−	0.474973i
$991$	10.2067	+	6.55944i	0.324226	+	0.208368i	0.692621	−	0.721302i	$-0.256456\pi$
$991$	10.2067	+	6.55944i	0.324226	+	0.208368i	−0.368394	+	0.929670i	$0.620092\pi$
$992$	−4.69975	+	6.27814i	−0.149217	+	0.199331i
$993$	−16.3894	−	6.11292i	−0.520101	−	0.193988i
$994$	−18.2654	−	5.36321i	−0.579343	−	0.170111i
$995$	−14.6254	+	45.1500i	−0.463658	+	1.43135i
$996$	2.62818	+	2.27733i	0.0832771	+	0.0721600i
$997$	−8.24816	+	6.17450i	−0.261222	+	0.195548i	−0.721859	−	0.692040i	$-0.756712\pi$
$997$	−8.24816	+	6.17450i	−0.261222	+	0.195548i	0.460637	+	0.887589i	$0.347621\pi$
$998$	−4.81380	+	8.81581i	−0.152378	+	0.279060i
$999$	32.9284	+	38.0013i	1.04181	+	1.20231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.67.4	yes	240
5.3	odd	4	inner	230.2.l.a.113.3	yes	240
23.11	odd	22	inner	230.2.l.a.57.3	✓	240
115.103	even	44	inner	230.2.l.a.103.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.3	✓	240	23.11	odd	22	inner
230.2.l.a.67.4	yes	240	1.1	even	1	trivial
230.2.l.a.103.4	yes	240	115.103	even	44	inner
230.2.l.a.113.3	yes	240	5.3	odd	4	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.212565 - 0.977147i) q^{2} +(0.628000 + 0.470115i) q^{3} +(-0.909632 + 0.415415i) q^{4} +(2.20366 + 0.379326i) q^{5} +(0.325880 - 0.713578i) q^{6} +(0.119361 + 1.66889i) q^{7} +(0.599278 + 0.800541i) q^{8} +(-0.671822 - 2.28802i) q^{9} +(-0.0977645 - 2.23393i) q^{10} +(2.43931 + 3.79564i) q^{11} +(-0.766541 - 0.166751i) q^{12} +(1.69134 + 0.120967i) q^{13} +(1.60538 - 0.471382i) q^{14} +(1.20557 + 1.27419i) q^{15} +(0.654861 - 0.755750i) q^{16} +(-1.34248 - 3.59932i) q^{17} +(-2.09292 + 1.14282i) q^{18} +(-1.30471 - 2.85692i) q^{19} +(-2.16210 + 0.570386i) q^{20} +(-0.709611 + 1.10418i) q^{21} +(3.19039 - 3.19039i) q^{22} +(2.54688 + 4.06367i) q^{23} +0.784469i q^{24} +(4.71222 + 1.67181i) q^{25} +(-0.241318 - 1.67840i) q^{26} +(1.47616 - 3.95773i) q^{27} +(-0.801857 - 1.46849i) q^{28} +(-8.84904 - 4.04122i) q^{29} +(0.988807 - 1.44887i) q^{30} +(1.11608 - 7.76254i) q^{31} +(-0.877679 - 0.479249i) q^{32} +(-0.252501 + 3.53042i) q^{33} +(-3.23170 + 2.07689i) q^{34} +(-0.370021 + 3.72294i) q^{35} +(1.56159 + 1.80217i) q^{36} +(-5.70496 + 10.4478i) q^{37} +(-2.51429 + 1.88217i) q^{38} +(1.00529 + 0.871092i) q^{39} +(1.01694 + 1.99144i) q^{40} +(-7.18190 - 2.10880i) q^{41} +(1.22978 + 0.458684i) q^{42} +(-3.02338 + 4.03876i) q^{43} +(-3.79564 - 2.43931i) q^{44} +(-0.612563 - 5.29684i) q^{45} +(3.42943 - 3.35247i) q^{46} +(2.25984 + 2.25984i) q^{47} +(0.766541 - 0.166751i) q^{48} +(4.15780 - 0.597802i) q^{49} +(0.631947 - 4.95990i) q^{50} +(0.849018 - 2.89149i) q^{51} +(-1.58875 + 0.592573i) q^{52} +(-4.53344 + 0.324238i) q^{53} +(-4.18106 - 0.601146i) q^{54} +(3.93563 + 9.28960i) q^{55} +(-1.26448 + 1.09568i) q^{56} +(0.523721 - 2.40751i) q^{57} +(-2.06787 + 9.50584i) q^{58} +(-5.22049 + 4.52358i) q^{59} +(-1.62594 - 0.658231i) q^{60} +(3.12421 + 0.449194i) q^{61} +(-7.82238 + 0.559468i) q^{62} +(3.73825 - 1.39430i) q^{63} +(-0.281733 + 0.959493i) q^{64} +(3.68125 + 0.908140i) q^{65} +(3.50341 - 0.503715i) q^{66} +(0.601491 - 0.130846i) q^{67} +(2.71637 + 2.71637i) q^{68} +(-0.310953 + 3.74931i) q^{69} +(3.71651 - 0.429803i) q^{70} +(-9.57147 - 6.15121i) q^{71} +(1.42904 - 1.90898i) q^{72} +(-3.89390 - 1.45235i) q^{73} +(11.4218 + 3.35373i) q^{74} +(2.17333 + 3.26518i) q^{75} +(2.37361 + 2.05675i) q^{76} +(-6.04335 + 4.52400i) q^{77} +(0.637494 - 1.16748i) q^{78} +(1.72151 + 1.98673i) q^{79} +(1.72976 - 1.41701i) q^{80} +(-3.23057 + 2.07616i) q^{81} +(-0.533981 + 7.46603i) q^{82} +(-3.89079 - 2.12453i) q^{83} +(0.186793 - 1.29918i) q^{84} +(-1.59305 - 8.44091i) q^{85} +(4.58913 + 2.09579i) q^{86} +(-3.65736 - 6.69795i) q^{87} +(-1.57674 + 4.22742i) q^{88} +(-1.31973 - 9.17890i) q^{89} +(-5.04558 + 1.72449i) q^{90} +2.83710i q^{91} +(-4.00483 - 2.63843i) q^{92} +(4.35019 - 4.35019i) q^{93} +(1.72783 - 2.68855i) q^{94} +(-1.79143 - 6.79058i) q^{95} +(-0.325880 - 0.713578i) q^{96} +(-1.16548 + 0.636402i) q^{97} +(-1.46795 - 3.93571i) q^{98} +(7.04571 - 8.13118i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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