LMFDB - Embedded newform 680.2.br.a.349.37

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(189,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 4, 4, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.189"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.br (of order $8$, degree $4$, 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:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$104$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			349.37
Character	$\chi$	$=$	680.349
Dual form			680.2.br.a.189.37

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.648820 + 1.25660i) q^{2} +(-1.86646 - 0.773113i) q^{3} +(-1.15807 - 1.63061i) q^{4} +(-1.01668 + 1.99157i) q^{5} +(2.18249 - 1.84377i) q^{6} +(-0.739929 + 0.306488i) q^{7} +(2.80039 - 0.397251i) q^{8} +(0.764647 + 0.764647i) q^{9} +(-1.84296 - 2.56973i) q^{10} +(-1.31559 - 3.17611i) q^{11} +(0.900840 + 3.93878i) q^{12} -2.51816i q^{13} +(0.0949480 - 1.12865i) q^{14} +(3.43730 - 2.93118i) q^{15} +(-1.31776 + 3.77670i) q^{16} +(-0.897680 + 4.02420i) q^{17} +(-1.45697 + 0.464734i) q^{18} +(-0.658797 - 0.658797i) q^{19} +(4.42486 - 0.648569i) q^{20} +1.61800 q^{21} +(4.84467 + 0.407560i) q^{22} +(-1.90342 - 4.59527i) q^{23} +(-5.53394 - 1.42357i) q^{24} +(-2.93273 - 4.04958i) q^{25} +(3.16431 + 1.63383i) q^{26} +(1.48331 + 3.58104i) q^{27} +(1.35665 + 0.851599i) q^{28} +(9.10861 + 3.77291i) q^{29} +(1.45312 + 6.22111i) q^{30} +(3.43384 + 1.42234i) q^{31} +(-3.89080 - 4.10630i) q^{32} +6.94518i q^{33} +(-4.47436 - 3.73900i) q^{34} +(0.141876 - 1.78522i) q^{35} +(0.361327 - 2.13235i) q^{36} +(-1.11757 - 0.462911i) q^{37} +(1.25528 - 0.400401i) q^{38} +(-1.94682 + 4.70005i) q^{39} +(-2.05594 + 5.98106i) q^{40} +(4.76899 + 11.5134i) q^{41} +(-1.04979 + 2.03317i) q^{42} +(2.63427 + 2.63427i) q^{43} +(-3.65546 + 5.82336i) q^{44} +(-2.30025 + 0.745450i) q^{45} +(7.00937 + 0.589667i) q^{46} +10.2098 q^{47} +(5.37937 - 6.03028i) q^{48} +(-4.49619 + 4.49619i) q^{49} +(6.99150 - 1.05781i) q^{50} +(4.78664 - 6.81699i) q^{51} +(-4.10614 + 2.91620i) q^{52} +(-3.65503 + 3.65503i) q^{53} +(-5.46232 - 0.459521i) q^{54} +(7.66299 + 0.608996i) q^{55} +(-1.95034 + 1.15223i) q^{56} +(0.720293 + 1.73894i) q^{57} +(-10.6509 + 8.99790i) q^{58} +(5.24423 - 5.24423i) q^{59} +(-8.76023 - 2.21039i) q^{60} +(8.77111 - 3.63311i) q^{61} +(-4.01525 + 3.39211i) q^{62} +(-0.800139 - 0.331429i) q^{63} +(7.68438 - 2.22492i) q^{64} +(5.01510 + 2.56016i) q^{65} +(-8.72729 - 4.50617i) q^{66} -5.11009 q^{67} +(7.60146 - 3.19653i) q^{68} +10.0484i q^{69} +(2.15125 + 1.33657i) q^{70} +(7.58430 + 3.14152i) q^{71} +(2.44507 + 1.83755i) q^{72} +(5.76929 + 2.38972i) q^{73} +(1.30679 - 1.10398i) q^{74} +(2.34303 + 9.82571i) q^{75} +(-0.311309 + 1.83717i) q^{76} +(1.94688 + 1.94688i) q^{77} +(-4.64292 - 5.49585i) q^{78} +(-11.6727 + 4.83500i) q^{79} +(-6.18184 - 6.46412i) q^{80} -11.0748i q^{81} +(-17.5618 - 1.47740i) q^{82} +(4.85020 - 4.85020i) q^{83} +(-1.87375 - 2.63832i) q^{84} +(-7.10183 - 5.87911i) q^{85} +(-5.01938 + 1.60105i) q^{86} +(-14.0840 - 14.0840i) q^{87} +(-4.94588 - 8.37174i) q^{88} +1.79163i q^{89} +(0.555718 - 3.37415i) q^{90} +(0.771788 + 1.86326i) q^{91} +(-5.28879 + 8.42536i) q^{92} +(-5.30949 - 5.30949i) q^{93} +(-6.62430 + 12.8296i) q^{94} +(1.98183 - 0.642257i) q^{95} +(4.08739 + 10.6723i) q^{96} +(-5.86683 - 2.43012i) q^{97} +(-2.73268 - 8.56711i) q^{98} +(1.42264 - 3.43457i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 16 q^{6} - 16 q^{9} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 16 q^{16} - 20 q^{20} + 24 q^{26} - 16 q^{31} - 40 q^{34} - 8 q^{36} + 32 q^{39} + 56 q^{40} - 32 q^{41} - 24 q^{44} + 32 q^{46} - 16 q^{49}+ \cdots - 160 q^{96}+O(q^{100}) $ 416 * q - 16 * q^6 - 16 * q^9 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 16 * q^16 - 20 * q^20 + 24 * q^26 - 16 * q^31 - 40 * q^34 - 8 * q^36 + 32 * q^39 + 56 * q^40 - 32 * q^41 - 24 * q^44 + 32 * q^46 - 16 * q^49 - 48 * q^50 - 64 * q^54 - 8 * q^56 - 40 * q^60 + 72 * q^65 - 112 * q^66 - 24 * q^70 + 48 * q^71 - 8 * q^74 - 40 * q^76 - 16 * q^79 - 56 * q^80 - 32 * q^84 + 96 * q^86 - 148 * q^90 + 40 * q^94 - 8 * q^95 - 160 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$	$-1$	$1$

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 $

$2$	−0.648820	+	1.25660i	−0.458785	+	0.888547i
$2$	−0.648820	+	1.25660i	−0.458785	+	0.888547i
$3$	−1.86646	−	0.773113i	−1.07760	−	0.446357i	−0.227934	−	0.973677i	$-0.573197\pi$
$3$	−1.86646	−	0.773113i	−1.07760	−	0.446357i	−0.849667	+	0.527320i	$0.823197\pi$
$4$	−1.15807	−	1.63061i	−0.579033	−	0.815304i
$5$	−1.01668	+	1.99157i	−0.454673	+	0.890659i
$5$	−1.01668	+	1.99157i	−0.454673	+	0.890659i
$6$	2.18249	−	1.84377i	0.890996	−	0.752718i
$7$	−0.739929	+	0.306488i	−0.279667	+	0.115842i	−0.518108	−	0.855315i	$-0.673364\pi$
$7$	−0.739929	+	0.306488i	−0.279667	+	0.115842i	0.238441	+	0.971157i	$0.423364\pi$
$8$	2.80039	−	0.397251i	0.990088	−	0.140450i
$9$	0.764647	+	0.764647i	0.254882	+	0.254882i
$10$	−1.84296	−	2.56973i	−0.582796	−	0.812619i
$11$	−1.31559	−	3.17611i	−0.396665	−	0.957634i	−0.988451	−	0.151539i	$-0.951577\pi$
$11$	−1.31559	−	3.17611i	−0.396665	−	0.957634i	0.591786	−	0.806095i	$-0.298423\pi$
$12$	0.900840	+	3.93878i	0.260050	+	1.13703i
$13$		−	2.51816i		−	0.698413i	−0.937046	−	0.349206i	$-0.886451\pi$
$13$		−	2.51816i		−	0.698413i	0.937046	−	0.349206i	$-0.113549\pi$
$14$	0.0949480	−	1.12865i	0.0253759	−	0.301644i
$15$	3.43730	−	2.93118i	0.887507	−	0.756828i
$16$	−1.31776	+	3.77670i	−0.329441	+	0.944176i
$17$	−0.897680	+	4.02420i	−0.217719	+	0.976011i
$17$	−0.897680	+	4.02420i	−0.217719	+	0.976011i
$18$	−1.45697	+	0.464734i	−0.343411	+	0.109539i
$19$	−0.658797	−	0.658797i	−0.151138	−	0.151138i	0.627488	−	0.778626i	$-0.284083\pi$
$19$	−0.658797	−	0.658797i	−0.151138	−	0.151138i	−0.778626	+	0.627488i	$0.784083\pi$
$20$	4.42486	−	0.648569i	0.989428	−	0.145024i
$21$	1.61800			0.353076
$22$	4.84467	+	0.407560i	1.03289	+	0.0868922i
$23$	−1.90342	−	4.59527i	−0.396891	−	0.958179i	−0.988399	−	0.151880i	$-0.951467\pi$
$23$	−1.90342	−	4.59527i	−0.396891	−	0.958179i	0.591508	−	0.806299i	$-0.298533\pi$
$24$	−5.53394	−	1.42357i	−1.12961	−	0.290584i
$25$	−2.93273	−	4.04958i	−0.586545	−	0.809916i
$26$	3.16431	+	1.63383i	0.620573	+	0.320421i
$27$	1.48331	+	3.58104i	0.285464	+	0.689171i
$28$	1.35665	+	0.851599i	0.256383	+	0.160937i
$29$	9.10861	+	3.77291i	1.69143	+	0.700611i	0.999766	−	0.0216126i	$-0.00688003\pi$
$29$	9.10861	+	3.77291i	1.69143	+	0.700611i	0.691659	+	0.722224i	$0.256880\pi$
$30$	1.45312	+	6.22111i	0.265303	+	1.13581i
$31$	3.43384	+	1.42234i	0.616736	+	0.255460i	0.669106	−	0.743167i	$-0.266677\pi$
$31$	3.43384	+	1.42234i	0.616736	+	0.255460i	−0.0523696	+	0.998628i	$0.516677\pi$
$32$	−3.89080	−	4.10630i	−0.687803	−	0.725898i
$33$			6.94518i			1.20900i
$34$	−4.47436	−	3.73900i	−0.767346	−	0.641233i
$35$	0.141876	−	1.78522i	0.0239814	−	0.301758i
$36$	0.361327	−	2.13235i	0.0602212	−	0.355392i
$37$	−1.11757	−	0.462911i	−0.183727	−	0.0761022i	0.288924	−	0.957352i	$-0.406703\pi$
$37$	−1.11757	−	0.462911i	−0.183727	−	0.0761022i	−0.472650	+	0.881250i	$0.656703\pi$
$38$	1.25528	−	0.400401i	0.203634	−	0.0649536i
$39$	−1.94682	+	4.70005i	−0.311741	+	0.752610i
$40$	−2.05594	+	5.98106i	−0.325073	+	0.945689i
$41$	4.76899	+	11.5134i	0.744791	+	1.79808i	0.585179	+	0.810904i	$0.301024\pi$
$41$	4.76899	+	11.5134i	0.744791	+	1.79808i	0.159612	+	0.987180i	$0.448976\pi$
$42$	−1.04979	+	2.03317i	−0.161986	+	0.313725i
$43$	2.63427	+	2.63427i	0.401722	+	0.401722i	0.878840	−	0.477117i	$-0.158318\pi$
$43$	2.63427	+	2.63427i	0.401722	+	0.401722i	−0.477117	+	0.878840i	$0.658318\pi$
$44$	−3.65546	+	5.82336i	−0.551081	+	0.877904i
$45$	−2.30025	+	0.745450i	−0.342901	+	0.111125i
$46$	7.00937	+	0.589667i	1.03348	+	0.0869416i
$47$	10.2098			1.48925			0.744625	−	0.667483i	$-0.232628\pi$
$47$	10.2098			1.48925			0.744625	+	0.667483i	$0.232628\pi$
$48$	5.37937	−	6.03028i	0.776445	−	0.870397i
$49$	−4.49619	+	4.49619i	−0.642313	+	0.642313i
$50$	6.99150	−	1.05781i	0.988747	−	0.149596i
$51$	4.78664	−	6.81699i	0.670264	−	0.954570i
$52$	−4.10614	+	2.91620i	−0.569419	+	0.404404i
$53$	−3.65503	+	3.65503i	−0.502057	+	0.502057i	−0.912077	−	0.410020i	$-0.865522\pi$
$53$	−3.65503	+	3.65503i	−0.502057	+	0.502057i	0.410020	+	0.912077i	$0.365522\pi$
$54$	−5.46232	−	0.459521i	−0.743328	−	0.0625328i
$55$	7.66299	+	0.608996i	1.03328	+	0.0821170i
$56$	−1.95034	+	1.15223i	−0.260625	+	0.153973i
$57$	0.720293	+	1.73894i	0.0954052	+	0.230328i
$58$	−10.6509	+	8.99790i	−1.39853	+	1.18148i
$59$	5.24423	−	5.24423i	0.682741	−	0.682741i	−0.277876	−	0.960617i	$-0.589631\pi$
$59$	5.24423	−	5.24423i	0.682741	−	0.682741i	0.960617	+	0.277876i	$0.0896305\pi$
$60$	−8.76023	−	2.21039i	−1.13094	−	0.285360i
$61$	8.77111	−	3.63311i	1.12303	−	0.465173i	0.257621	−	0.966246i	$-0.417061\pi$
$61$	8.77111	−	3.63311i	1.12303	−	0.465173i	0.865405	+	0.501074i	$0.167061\pi$
$62$	−4.01525	+	3.39211i	−0.509938	+	0.430798i
$63$	−0.800139	−	0.331429i	−0.100808	−	0.0417561i
$64$	7.68438	−	2.22492i	0.960548	−	0.278115i
$65$	5.01510	+	2.56016i	0.622047	+	0.317549i
$66$	−8.72729	−	4.50617i	−1.07426	−	0.554671i
$67$	−5.11009			−0.624297			−0.312149	−	0.950033i	$-0.601049\pi$
$67$	−5.11009			−0.624297			−0.312149	+	0.950033i	$0.601049\pi$
$68$	7.60146	−	3.19653i	0.921813	−	0.387636i
$69$			10.0484i			1.20969i
$70$	2.15125	+	1.33657i	0.257124	+	0.159750i
$71$	7.58430	+	3.14152i	0.900091	+	0.372830i	0.784255	−	0.620439i	$-0.213045\pi$
$71$	7.58430	+	3.14152i	0.900091	+	0.372830i	0.115836	+	0.993268i	$0.463045\pi$
$72$	2.44507	+	1.83755i	0.288154	+	0.216558i
$73$	5.76929	+	2.38972i	0.675245	+	0.279696i	0.693837	−	0.720132i	$-0.255919\pi$
$73$	5.76929	+	2.38972i	0.675245	+	0.279696i	−0.0185928	+	0.999827i	$0.505919\pi$
$74$	1.30679	−	1.10398i	0.151911	−	0.128336i
$75$	2.34303	+	9.82571i	0.270550	+	1.13458i
$76$	−0.311309	+	1.83717i	−0.0357096	+	0.210738i
$77$	1.94688	+	1.94688i	0.221868	+	0.221868i
$78$	−4.64292	−	5.49585i	−0.525708	−	0.622283i
$79$	−11.6727	+	4.83500i	−1.31328	+	0.543980i	−0.925841	−	0.377914i	$-0.876642\pi$
$79$	−11.6727	+	4.83500i	−1.31328	+	0.543980i	−0.387443	+	0.921894i	$0.626642\pi$
$80$	−6.18184	−	6.46412i	−0.691151	−	0.722711i
$81$		−	11.0748i		−	1.23053i
$82$	−17.5618	−	1.47740i	−1.93938	−	0.163151i
$83$	4.85020	−	4.85020i	0.532378	−	0.532378i	−0.388901	−	0.921279i	$-0.627145\pi$
$83$	4.85020	−	4.85020i	0.532378	−	0.532378i	0.921279	+	0.388901i	$0.127145\pi$
$84$	−1.87375	−	2.63832i	−0.204443	−	0.287864i
$85$	−7.10183	−	5.87911i	−0.770302	−	0.637679i
$86$	−5.01938	+	1.60105i	−0.541253	+	0.172645i
$87$	−14.0840	−	14.0840i	−1.50996	−	1.50996i
$88$	−4.94588	−	8.37174i	−0.527232	−	0.892430i
$89$			1.79163i			0.189913i	0.995481	+	0.0949564i	$0.0302712\pi$
$89$			1.79163i			0.189913i	−0.995481	+	0.0949564i	$0.969729\pi$
$90$	0.555718	−	3.37415i	0.0585779	−	0.355666i
$91$	0.771788	+	1.86326i	0.0809053	+	0.195323i
$92$	−5.28879	+	8.42536i	−0.551394	+	0.878404i
$93$	−5.30949	−	5.30949i	−0.550569	−	0.550569i
$94$	−6.62430	+	12.8296i	−0.683245	+	1.32327i
$95$	1.98183	−	0.642257i	0.203331	−	0.0658942i
$96$	4.08739	+	10.6723i	0.417167	+	1.08923i
$97$	−5.86683	−	2.43012i	−0.595686	−	0.246741i	0.0644085	−	0.997924i	$-0.479484\pi$
$97$	−5.86683	−	2.43012i	−0.595686	−	0.246741i	−0.660095	+	0.751182i	$0.729484\pi$
$98$	−2.73268	−	8.56711i	−0.276042	−	0.865408i
$99$	1.42264	−	3.43457i	0.142981	−	0.345187i
$100$	−3.20699	+	9.47181i	−0.320699	+	0.947181i
$101$		−	5.75052i		−	0.572198i	−0.958200	−	0.286099i	$-0.907641\pi$
$101$		−	5.75052i		−	0.572198i	0.958200	−	0.286099i	$-0.0923586\pi$
$102$	5.46054	+	10.4379i	0.540674	+	1.03350i
$103$		−	12.9489i		−	1.27589i	−0.770082	−	0.637945i	$-0.779785\pi$
$103$		−	12.9489i		−	1.27589i	0.770082	−	0.637945i	$-0.220215\pi$
$104$	−1.00034	−	7.05184i	−0.0980917	−	0.691490i
$105$	−1.64498	+	3.22236i	−0.160534	+	0.314470i
$106$	−2.22144	−	6.96435i	−0.215765	−	0.676438i
$107$	0.898334	−	2.16877i	0.0868452	−	0.209663i	−0.874490	−	0.485043i	$-0.838804\pi$
$107$	0.898334	−	2.16877i	0.0868452	−	0.209663i	0.961335	+	0.275380i	$0.0888038\pi$
$108$	4.12149	−	6.56578i	0.396591	−	0.631793i
$109$	−7.28774	+	3.01868i	−0.698039	+	0.289137i	−0.703345	−	0.710849i	$-0.748311\pi$
$109$	−7.28774	+	3.01868i	−0.698039	+	0.289137i	0.00530589	+	0.999986i	$0.498311\pi$
$110$	−5.73716	+	9.23416i	−0.547017	+	0.880442i
$111$	1.72801	+	1.72801i	0.164016	+	0.164016i
$112$	−0.182465	−	3.19837i	−0.0172413	−	0.302218i
$113$	2.50677	+	6.05188i	0.235817	+	0.569313i	0.996842	−	0.0794095i	$-0.0253035\pi$
$113$	2.50677	+	6.05188i	0.235817	+	0.569313i	−0.761025	+	0.648723i	$0.775303\pi$
$114$	−2.65249	−	0.223142i	−0.248428	−	0.0208991i
$115$	11.0870	+	0.881108i	1.03387	+	0.0821637i
$116$	−4.39624	−	19.2218i	−0.408180	−	1.78470i
$117$	1.92550	−	1.92550i	0.178013	−	0.178013i
$118$	3.18732	+	9.99244i	0.293416	+	0.919878i
$119$	−0.569152	−	3.25275i	−0.0521740	−	0.298179i
$120$	8.46137	−	9.57393i	0.772414	−	0.873976i
$121$	−0.578744	+	0.578744i	−0.0526131	+	0.0526131i
$122$	−1.12551	+	13.3790i	−0.101899	+	1.21128i
$123$		−	25.1762i		−	2.27006i
$124$	−1.65733	−	7.24641i	−0.148833	−	0.650747i
$125$	11.0467	−	1.72362i	0.988045	−	0.154165i
$126$	0.935618	−	0.790415i	0.0833515	−	0.0704157i
$127$	11.6008	−	11.6008i	1.02940	−	1.02940i	0.0298492	−	0.999554i	$-0.490497\pi$
$127$	11.6008	−	11.6008i	1.02940	−	1.02940i	0.999554	−	0.0298492i	$-0.00950269\pi$
$128$	−2.18996	+	11.0997i	−0.193567	+	0.981087i
$129$	−2.88017	−	6.95334i	−0.253585	−	0.612208i
$130$	−6.47099	+	4.64088i	−0.567543	+	0.407032i
$131$	7.95995	+	3.29712i	0.695464	+	0.288071i	0.702275	−	0.711906i	$-0.252168\pi$
$131$	7.95995	+	3.29712i	0.695464	+	0.288071i	−0.00681066	+	0.999977i	$0.502168\pi$
$132$	11.3249	−	8.04298i	0.985704	−	0.700052i
$133$	0.689376	+	0.285549i	0.0597765	+	0.0247602i
$134$	3.31553	−	6.42132i	0.286418	−	0.554718i
$135$	−8.63995	−	0.686637i	−0.743609	−	0.0590963i
$136$	−0.915236	+	11.6259i	−0.0784809	+	0.996916i
$137$		−	11.1253i		−	0.950503i	−0.879850	−	0.475251i	$-0.842357\pi$
$137$		−	11.1253i		−	0.950503i	0.879850	−	0.475251i	$-0.157643\pi$
$138$	−12.6268	−	6.51962i	−1.07487	−	0.554987i
$139$	−5.41665	+	13.0770i	−0.459435	+	1.10917i	0.509192	+	0.860653i	$0.329944\pi$
$139$	−5.41665	+	13.0770i	−0.459435	+	1.10917i	−0.968627	+	0.248520i	$0.920056\pi$
$140$	−3.07530	+	1.83606i	−0.259910	+	0.155176i
$141$	−19.0561	−	7.89331i	−1.60482	−	0.664737i
$142$	−8.86846	+	7.49212i	−0.744225	+	0.628725i
$143$	−7.99797	+	3.31287i	−0.668824	+	0.277036i
$144$	−3.89547	+	1.88022i	−0.324622	+	0.156685i
$145$	−16.7746	+	14.3046i	−1.39305	+	1.18793i
$146$	−6.74614	+	5.69917i	−0.558315	+	0.471667i
$147$	11.8680	−	4.91589i	0.978857	−	0.405456i
$148$	0.539390	+	2.35840i	0.0443376	+	0.193859i
$149$	20.6527			1.69194			0.845969	−	0.533232i	$-0.179023\pi$
$149$	20.6527			1.69194			0.845969	+	0.533232i	$0.179023\pi$
$150$	−13.8672	−	3.43087i	−1.13225	−	0.280129i
$151$	0.775751	−	0.775751i	0.0631297	−	0.0631297i	−0.674837	−	0.737967i	$-0.735786\pi$
$151$	0.775751	−	0.775751i	0.0631297	−	0.0631297i	0.737967	+	0.674837i	$0.235786\pi$
$152$	−2.10660	−	1.58318i	−0.170868	−	0.128413i
$153$	−3.76350	+	2.39068i	−0.304261	+	0.193275i
$154$	−3.70962	+	1.18327i	−0.298930	+	0.0953506i
$155$	−6.32381	+	5.39268i	−0.507941	+	0.433150i
$156$	9.91849	−	2.26846i	0.794114	−	0.181622i
$157$			4.01079i			0.320096i	0.987109	+	0.160048i	$0.0511649\pi$
$157$			4.01079i			0.320096i	−0.987109	+	0.160048i	$0.948835\pi$
$158$	1.49785	−	17.8049i	0.119162	−	1.41648i
$159$	9.64772	−	3.99621i	0.765114	−	0.316920i
$160$	12.1337	−	3.57403i	0.959252	−	0.282552i
$161$	2.81679	+	2.81679i	0.221994	+	0.221994i
$162$	13.9165	+	7.18552i	1.09338	+	0.564547i
$163$	6.54175	+	15.7932i	0.512389	+	1.23702i	0.942489	+	0.334236i	$0.108478\pi$
$163$	6.54175	+	15.7932i	0.512389	+	1.23702i	−0.430100	+	0.902781i	$0.641522\pi$
$164$	13.2510	−	21.1096i	1.03473	−	1.64838i
$165$	−13.8318	−	7.06102i	−1.07681	−	0.549700i
$166$	2.94783	+	9.24164i	0.228796	+	0.717290i
$167$	4.29888	−	10.3784i	0.332657	−	0.803105i	−0.665722	−	0.746199i	$-0.731877\pi$
$167$	4.29888	−	10.3784i	0.332657	−	0.803105i	0.998380	−	0.0569058i	$-0.0181235\pi$
$168$	4.53102	−	0.642751i	0.349576	−	0.0495893i
$169$	6.65886			0.512220
$170$	11.9955	−	5.10965i	0.920011	−	0.391892i
$171$		−	1.00749i		−	0.0770450i
$172$	1.24480	−	7.34612i	0.0949152	−	0.560136i
$173$	5.18252	+	2.14667i	0.394020	+	0.163208i	0.570891	−	0.821026i	$-0.306598\pi$
$173$	5.18252	+	2.14667i	0.394020	+	0.163208i	−0.176871	+	0.984234i	$0.556598\pi$
$174$	26.8358	−	8.55990i	2.03442	−	0.648924i
$175$	3.41116	+	2.09755i	0.257859	+	0.158560i
$176$	13.7289	−	0.783223i	1.03485	−	0.0590376i
$177$	−13.8425	+	5.73376i	−1.04047	+	0.430976i
$178$	−2.25136	−	1.16245i	−0.168747	−	0.0871291i
$179$	−12.2249	+	12.2249i	−0.913732	+	0.913732i	−0.996564	−	0.0828317i	$-0.973604\pi$
$179$	−12.2249	+	12.2249i	−0.913732	+	0.913732i	0.0828317	+	0.996564i	$0.473604\pi$
$180$	3.87938	+	2.88753i	0.289152	+	0.215223i
$181$	−4.22381	−	10.1972i	−0.313953	−	0.757950i	−0.999551	−	0.0299693i	$-0.990459\pi$
$181$	−4.22381	−	10.1972i	−0.313953	−	0.757950i	0.685598	−	0.727981i	$-0.259541\pi$
$182$	−2.84212	−	0.239095i	−0.210672	−	0.0177229i
$183$	−19.1797			−1.41781
$184$	−7.15580	−	12.1124i	−0.527533	−	0.892939i
$185$	2.05813	−	1.75508i	0.151317	−	0.129036i
$186$	10.1168	−	3.22698i	0.741799	−	0.236614i
$187$	13.9623	−	2.44306i	1.02102	−	0.178654i
$188$	−11.8236	−	16.6481i	−0.862325	−	1.21419i
$189$	−2.19509	−	2.19509i	−0.159670	−	0.159670i
$190$	−0.478790	+	2.90706i	−0.0347351	+	0.210901i
$191$			5.37161i			0.388676i	0.980935	+	0.194338i	$0.0622558\pi$
$191$			5.37161i			0.388676i	−0.980935	+	0.194338i	$0.937744\pi$
$192$	−16.0627	−	1.78818i	−1.15923	−	0.129051i
$193$	7.18708	+	17.3511i	0.517337	+	1.24896i	0.939533	+	0.342458i	$0.111259\pi$
$193$	7.18708	+	17.3511i	0.517337	+	1.24896i	−0.422196	+	0.906505i	$0.638741\pi$
$194$	6.86019	−	5.79553i	0.492533	−	0.416094i
$195$	−7.38119	−	8.65568i	−0.528578	−	0.619846i
$196$	12.5384	+	2.12464i	0.895600	+	0.151760i
$197$	−4.77474	−	11.5272i	−0.340186	−	0.821282i	−0.997696	−	0.0678366i	$-0.978390\pi$
$197$	−4.77474	−	11.5272i	−0.340186	−	0.821282i	0.657510	−	0.753446i	$-0.271610\pi$
$198$	3.39282	+	4.01610i	0.241117	+	0.285412i
$199$	6.72373	−	16.2325i	0.476632	−	1.15069i	−0.484546	−	0.874766i	$-0.661015\pi$
$199$	6.72373	−	16.2325i	0.476632	−	1.15069i	0.961179	−	0.275927i	$-0.0889848\pi$
$200$	−9.82149	−	10.1754i	−0.694484	−	0.719508i
$201$	9.53778	+	3.95068i	0.672743	+	0.278659i
$202$	7.22608	+	3.73105i	0.508425	+	0.262516i
$203$	−7.89607			−0.554196
$204$	−16.6591	+	0.0893974i	−1.16637	+	0.00625907i
$205$	−27.7782	−	2.20760i	−1.94012	−	0.154185i
$206$	16.2715	+	8.40148i	1.13369	+	0.585359i
$207$	2.05831	−	4.96920i	0.143062	−	0.345383i
$208$	9.51036	+	3.31834i	0.659425	+	0.230086i
$209$	−1.22571	+	2.95912i	−0.0847839	+	0.204686i
$210$	−2.98191	−	4.15781i	−0.205771	−	0.286916i
$211$	1.37308	−	0.568750i	0.0945269	−	0.0391543i	−0.334919	−	0.942247i	$-0.608709\pi$
$211$	1.37308	−	0.568750i	0.0945269	−	0.0391543i	0.429446	+	0.903093i	$0.358709\pi$
$212$	10.1927	+	1.72715i	0.700037	+	0.118621i
$213$	−11.7270	−	11.7270i	−0.803524	−	0.803524i
$214$	2.14241	+	2.53598i	0.146452	+	0.173356i
$215$	−7.92455	+	2.56813i	−0.540450	+	0.175145i
$216$	5.57643	+	9.43906i	0.379428	+	0.642247i
$217$	−2.97673			−0.202073
$218$	0.935167	−	11.1163i	0.0633375	−	0.752893i
$219$	−8.92063	−	8.92063i	−0.602800	−	0.602800i
$220$	−7.88122	−	13.2006i	−0.531352	−	0.889984i
$221$	10.1336	+	2.26050i	0.681659	+	0.152058i
$222$	−3.29258	+	1.05024i	−0.220983	+	0.0704878i
$223$	3.67807	+	3.67807i	0.246302	+	0.246302i	0.819451	−	0.573149i	$-0.194278\pi$
$223$	3.67807	+	3.67807i	0.246302	+	0.246302i	−0.573149	+	0.819451i	$0.694278\pi$
$224$	4.13745	+	1.84588i	0.276445	+	0.123333i
$225$	0.853999	−	5.33900i	0.0569333	−	0.355933i
$226$	−9.23122	−	0.776581i	−0.614051	−	0.0516574i
$227$	7.98332	−	3.30680i	0.529872	−	0.219480i	−0.101675	−	0.994818i	$-0.532420\pi$
$227$	7.98332	−	3.30680i	0.529872	−	0.219480i	0.631547	+	0.775338i	$0.282420\pi$
$228$	2.00138	−	3.18833i	0.132545	−	0.211152i
$229$	0.402482	−	0.402482i	0.0265968	−	0.0265968i	−0.693683	−	0.720280i	$-0.744013\pi$
$229$	0.402482	−	0.402482i	0.0265968	−	0.0265968i	0.720280	+	0.693683i	$0.244013\pi$
$230$	−8.30064	+	13.3602i	−0.547328	+	0.880944i
$231$	−2.12862	−	5.13894i	−0.140053	−	0.338117i
$232$	27.0065	+	6.94721i	1.77306	+	0.456107i
$233$	17.2651	+	7.15144i	1.13107	+	0.468506i	0.868146	−	0.496309i	$-0.165312\pi$
$233$	17.2651	+	7.15144i	1.13107	+	0.468506i	0.262928	+	0.964815i	$0.415312\pi$
$234$	1.17028	+	3.66889i	0.0765034	+	0.239843i
$235$	−10.3801	+	20.3335i	−0.677121	+	1.32641i
$236$	−14.6244	−	2.47812i	−0.951971	−	0.161312i
$237$	25.5247			1.65800
$238$	4.45667	+	1.39525i	0.288883	+	0.0904408i
$239$	−1.83542			−0.118723			−0.0593617	−	0.998237i	$-0.518907\pi$
$239$	−1.83542			−0.118723			−0.0593617	+	0.998237i	$0.518907\pi$
$240$	6.54066	+	16.8443i	0.422198	+	1.08729i
$241$	23.2271	+	9.62098i	1.49619	+	0.619742i	0.972653	−	0.232262i	$-0.0746126\pi$
$241$	23.2271	+	9.62098i	1.49619	+	0.619742i	0.523536	+	0.852004i	$0.324613\pi$
$242$	−0.351747	−	1.10275i	−0.0226111	−	0.0708873i
$243$	−4.11209	+	9.92746i	−0.263791	+	0.636847i
$244$	−16.0817	−	10.0949i	−1.02953	−	0.646257i
$245$	−4.38331	−	13.5257i	−0.280039	−	0.864123i
$246$	31.6363	+	16.3348i	2.01706	+	1.04147i
$247$	−1.65896	+	1.65896i	−0.105557	+	0.105557i
$248$	10.1811	+	2.61902i	0.646502	+	0.166308i
$249$	−12.8024	+	5.30295i	−0.811322	+	0.336061i
$250$	−5.00141	+	14.9995i	−0.316317	+	0.948654i
$251$	−3.79764			−0.239705			−0.119852	−	0.992792i	$-0.538242\pi$
$251$	−3.79764			−0.239705			−0.119852	+	0.992792i	$0.538242\pi$
$252$	0.386184	+	1.68853i	0.0243273	+	0.106367i
$253$	−12.0910	+	12.0910i	−0.760152	+	0.760152i
$254$	7.05069	+	22.1043i	0.442399	+	1.38695i
$255$	8.71007	+	16.4636i	0.545445	+	1.03099i
$256$	−12.5270	−	9.95361i	−0.782937	−	0.622101i
$257$	−11.2755	−	11.2755i	−0.703349	−	0.703349i	0.261779	−	0.965128i	$-0.415691\pi$
$257$	−11.2755	−	11.2755i	−0.703349	−	0.703349i	−0.965128	+	0.261779i	$0.915691\pi$
$258$	10.6063	+	0.892256i	0.660317	+	0.0555495i
$259$	0.968797			0.0601981
$260$	−1.63320	−	11.1425i	−0.101287	−	0.691029i
$261$	4.07992	+	9.84981i	0.252541	+	0.609688i
$262$	−9.30771	+	7.86320i	−0.575033	+	0.485790i
$263$	−9.56770	+	9.56770i	−0.589969	+	0.589969i	−0.937623	−	0.347654i	$-0.886979\pi$
$263$	−9.56770	+	9.56770i	−0.589969	+	0.589969i	0.347654	+	0.937623i	$0.386979\pi$
$264$	2.75898	+	19.4492i	0.169804	+	1.19702i
$265$	−3.56327	−	10.9953i	−0.218890	−	0.675433i
$266$	−0.806100	+	0.680997i	−0.0494252	+	0.0417546i
$267$	1.38514	−	3.34401i	0.0847689	−	0.204650i
$268$	5.91783	+	8.33256i	0.361489	+	0.508992i
$269$	2.96911	−	7.16806i	0.181030	−	0.437044i	−0.807150	−	0.590347i	$-0.798991\pi$
$269$	2.96911	−	7.16806i	0.181030	−	0.437044i	0.988179	+	0.153303i	$0.0489909\pi$
$270$	6.46860	−	10.4114i	0.393666	−	0.633619i
$271$	−21.9604			−1.33400			−0.666999	−	0.745059i	$-0.732421\pi$
$271$	−21.9604			−1.33400			−0.666999	+	0.745059i	$0.732421\pi$
$272$	−14.0153	−	8.69322i	−0.849801	−	0.527104i
$273$		−	4.07438i		−	0.246593i
$274$	13.9801	+	7.21834i	0.844567	+	0.436076i
$275$	−9.00366	+	14.6423i	−0.542941	+	0.882961i
$276$	16.3851	−	11.6368i	0.986265	−	0.700451i
$277$	−1.31819	+	3.18240i	−0.0792025	+	0.191212i	−0.958521	−	0.285023i	$-0.907999\pi$
$277$	−1.31819	+	3.18240i	−0.0792025	+	0.191212i	0.879318	+	0.476235i	$0.157999\pi$
$278$	−12.9180	−	15.2911i	−0.774772	−	0.917101i
$279$	1.53808	+	3.71326i	0.0920827	+	0.222307i
$280$	−0.311874	−	5.05568i	−0.0186380	−	0.302135i
$281$	−15.8250	−	15.8250i	−0.944041	−	0.944041i	0.0544739	−	0.998515i	$-0.482652\pi$
$281$	−15.8250	−	15.8250i	−0.944041	−	0.944041i	−0.998515	+	0.0544739i	$0.982652\pi$
$282$	22.2827	−	18.8245i	1.32692	−	1.12098i
$283$	−24.8341	+	10.2866i	−1.47624	+	0.611477i	−0.968271	−	0.249901i	$-0.919602\pi$
$283$	−24.8341	+	10.2866i	−1.47624	+	0.611477i	−0.507964	+	0.861378i	$0.669602\pi$
$284$	−3.66054	−	16.0051i	−0.217213	−	0.949729i
$285$	−4.19554	−	0.333429i	−0.248522	−	0.0197506i
$286$	1.02630	−	12.1997i	0.0606866	−	0.721381i
$287$	−7.05742	−	7.05742i	−0.416586	−	0.416586i
$288$	0.164779	−	6.11495i	0.00970970	−	0.360327i
$289$	−15.3883	−	7.22488i	−0.905197	−	0.424993i
$290$	−7.09147	−	30.3599i	−0.416425	−	1.78280i
$291$	9.07144	+	9.07144i	0.531777	+	0.531777i
$292$	−2.78453	−	12.1749i	−0.162952	−	0.712483i
$293$			27.1764i			1.58766i	0.608140	+	0.793830i	$0.291916\pi$
$293$			27.1764i			1.58766i	−0.608140	+	0.793830i	$0.708084\pi$
$294$	−1.52291	+	18.1028i	−0.0888179	+	1.05578i
$295$	5.11257	+	15.7760i	0.297665	+	0.918512i
$296$	−3.31352	−	0.852378i	−0.192594	−	0.0495435i
$297$	9.42235	−	9.42235i	0.546740	−	0.546740i
$298$	−13.3999	+	25.9521i	−0.776235	+	1.50337i
$299$	−11.5716	+	4.79313i	−0.669205	+	0.277194i
$300$	13.3085	−	15.1994i	0.768366	−	0.877537i
$301$	−2.75654	−	1.14180i	−0.158885	−	0.0658122i
$302$	0.471483	+	1.47813i	0.0271308	+	0.0850567i
$303$	−4.44580	+	10.7331i	−0.255404	+	0.616601i
$304$	3.35622	−	1.61994i	0.192492	−	0.0929100i
$305$	−1.68179	+	21.1620i	−0.0962993	+	1.21173i
$306$	−0.562291	−	6.28032i	−0.0321440	−	0.359022i
$307$	3.45261			0.197051			0.0985255	−	0.995135i	$-0.468587\pi$
$307$	3.45261			0.197051			0.0985255	+	0.995135i	$0.468587\pi$
$308$	0.919984	−	5.42923i	0.0524209	−	0.309359i
$309$	−10.0109	+	24.1685i	−0.569502	+	1.37490i
$310$	−2.67340	−	11.4454i	−0.151839	−	0.650052i
$311$	−5.20738	+	12.5717i	−0.295283	+	0.712877i	0.704711	+	0.709495i	$0.251077\pi$
$311$	−5.20738	+	12.5717i	−0.295283	+	0.712877i	−0.999994	+	0.00338247i	$0.998923\pi$
$312$	−3.58477	+	13.9354i	−0.202948	+	0.788934i
$313$	21.7726	−	9.01851i	1.23066	−	0.509756i	0.329877	−	0.944024i	$-0.392993\pi$
$313$	21.7726	−	9.01851i	1.23066	−	0.509756i	0.900784	+	0.434267i	$0.142993\pi$
$314$	−5.03994	−	2.60228i	−0.284420	−	0.146855i
$315$	1.47355	−	1.25658i	0.0830251	−	0.0708002i
$316$	21.4018	+	13.4344i	1.20394	+	0.755743i
$317$	4.81232	−	1.99333i	0.270287	−	0.111956i	−0.243424	−	0.969920i	$-0.578271\pi$
$317$	4.81232	−	1.99333i	0.270287	−	0.111956i	0.513710	+	0.857964i	$0.328271\pi$
$318$	−1.23800	+	14.7161i	−0.0694236	+	0.825238i
$319$		−	33.8936i		−	1.89767i
$320$	−3.38147	+	17.5660i	−0.189030	+	0.981971i
$321$	−3.35341	+	3.35341i	−0.187169	+	0.187169i
$322$	−5.36716	+	1.71198i	−0.299100	+	0.0954049i
$323$	3.24252	−	2.05974i	0.180418	−	0.114607i
$324$	−18.0586	+	12.8253i	−1.00325	+	0.712517i
$325$	−10.1975	+	7.38508i	−0.565656	+	0.409651i
$326$	−24.0901	−	2.02659i	−1.33423	−	0.112242i
$327$	15.9361			0.881266
$328$	17.9287	+	30.3474i	0.989948	+	1.67566i
$329$	−7.55451	+	3.12918i	−0.416494	+	0.172517i
$330$	17.8472	−	12.7997i	0.982457	−	0.704601i
$331$	−12.5846	+	12.5846i	−0.691713	+	0.691713i	−0.962609	−	0.270895i	$-0.912680\pi$
$331$	−12.5846	+	12.5846i	−0.691713	+	0.691713i	0.270895	+	0.962609i	$0.412680\pi$
$332$	−13.5256	−	2.29192i	−0.742315	−	0.125785i
$333$	−0.500580	−	1.20851i	−0.0274316	−	0.0662258i
$334$	10.2523	+	12.1357i	0.560979	+	0.664034i
$335$	5.19532	−	10.1771i	0.283851	−	0.556036i
$336$	−2.13214	+	6.11070i	−0.116318	+	0.333366i
$337$	−6.40806	+	15.4704i	−0.349069	+	0.842727i	0.647661	+	0.761928i	$0.275747\pi$
$337$	−6.40806	+	15.4704i	−0.349069	+	0.842727i	−0.996730	+	0.0807991i	$0.974253\pi$
$338$	−4.32040	+	8.36749i	−0.234999	+	0.455132i
$339$		−	13.2336i		−	0.718751i
$340$	−1.36213	+	18.3887i	−0.0738720	+	0.997268i
$341$		−	12.7775i		−	0.691939i
$342$	1.26601	+	0.653681i	0.0684581	+	0.0353470i
$343$	4.09425	−	9.88439i	0.221069	−	0.533707i
$344$	8.42345	+	6.33052i	0.454162	+	0.341319i
$345$	−20.0122	−	10.2160i	−1.07742	−	0.550013i
$346$	−6.06002	+	5.11954i	−0.325789	+	0.275228i
$347$	13.5431	+	32.6959i	0.727030	+	1.75521i	0.652248	+	0.758005i	$0.273826\pi$
$347$	13.5431	+	32.6959i	0.727030	+	1.75521i	0.0747814	+	0.997200i	$0.476174\pi$
$348$	−6.65526	+	39.2756i	−0.356759	+	2.10539i
$349$	−0.124066	+	0.124066i	−0.00664112	+	0.00664112i	−0.710420	−	0.703778i	$-0.751495\pi$
$349$	−0.124066	+	0.124066i	−0.00664112	+	0.00664112i	0.703778	+	0.710420i	$0.251495\pi$
$350$	−4.84900	+	2.92551i	−0.259190	+	0.156375i
$351$	9.01764	−	3.73523i	0.481326	−	0.199372i
$352$	−7.92337	+	17.7598i	−0.422317	+	0.946602i
$353$	9.49323			0.505274			0.252637	−	0.967561i	$-0.418702\pi$
$353$	9.49323			0.505274			0.252637	+	0.967561i	$0.418702\pi$
$354$	1.77628	−	21.1146i	0.0944082	−	1.12223i
$355$	−13.9674	+	11.9108i	−0.741311	+	0.632158i
$356$	2.92145	−	2.07483i	0.154837	−	0.109966i
$357$	−1.45244	+	6.51114i	−0.0768714	+	0.344606i
$358$	−7.43000	−	23.2935i	−0.392688	−	1.23110i
$359$	−9.22146	+	9.22146i	−0.486690	+	0.486690i	−0.907260	−	0.420570i	$-0.861830\pi$
$359$	−9.22146	+	9.22146i	−0.486690	+	0.486690i	0.420570	+	0.907260i	$0.361830\pi$
$360$	−6.14547	+	3.00133i	−0.323895	+	0.158184i
$361$		−	18.1320i		−	0.954314i
$362$	15.5542	+	1.30851i	0.817511	+	0.0687736i
$363$	1.52764	−	0.632768i	0.0801801	−	0.0332117i
$364$	2.14447	−	3.41626i	0.112401	−	0.179061i
$365$	−10.6248	+	9.06039i	−0.556129	+	0.474243i
$366$	12.4442	−	24.1012i	0.650468	−	1.25979i
$367$	4.74433	−	1.96516i	0.247652	−	0.102581i	−0.255405	−	0.966834i	$-0.582209\pi$
$367$	4.74433	−	1.96516i	0.247652	−	0.102581i	0.503057	+	0.864253i	$0.332209\pi$
$368$	19.8632	−	1.13318i	1.03544	−	0.0590712i
$369$	−5.15706	+	12.4502i	−0.268466	+	0.648134i
$370$	0.870077	+	3.72497i	0.0452332	+	0.193652i
$371$	1.58424	−	3.82469i	0.0822495	−	0.198568i
$372$	−2.50896	+	14.8064i	−0.130083	+	0.767678i
$373$	29.6618			1.53583			0.767914	−	0.640553i	$-0.221295\pi$
$373$	29.6618			1.53583			0.767914	+	0.640553i	$0.221295\pi$
$374$	−5.98906	+	19.1301i	−0.309687	+	0.989192i
$375$	−21.9507	−	5.32327i	−1.13353	−	0.274892i
$376$	28.5914	−	4.05585i	1.47449	−	0.209164i
$377$	9.50080	−	22.9369i	0.489316	−	1.18131i
$378$	4.18257	−	1.33413i	0.215128	−	0.0686200i
$379$	−33.7633	−	13.9852i	−1.73430	−	0.718372i	−0.999182	−	0.0404378i	$-0.987125\pi$
$379$	−33.7633	−	13.9852i	−1.73430	−	0.718372i	−0.735122	−	0.677935i	$-0.762875\pi$
$380$	−3.34236	−	2.48781i	−0.171459	−	0.127622i
$381$	−30.6211	+	12.6837i	−1.56877	+	0.649805i
$382$	−6.74994	−	3.48520i	−0.345357	−	0.178318i
$383$	8.40105	−	8.40105i	0.429274	−	0.429274i	−0.459107	−	0.888381i	$-0.651831\pi$
$383$	8.40105	−	8.40105i	0.429274	−	0.429274i	0.888381	+	0.459107i	$0.151831\pi$
$384$	12.6688	−	19.0241i	0.646502	−	0.970821i
$385$	−5.85672	+	1.89801i	−0.298486	+	0.0967313i
$386$	−26.4665	−	2.22651i	−1.34711	−	0.113326i
$387$			4.02857i			0.204784i
$388$	2.83161	+	12.3807i	0.143753	+	0.628537i
$389$	19.9631	+	19.9631i	1.01217	+	1.01217i	0.999925	+	0.0122458i	$0.00389805\pi$
$389$	19.9631	+	19.9631i	1.01217	+	1.01217i	0.0122458	+	0.999925i	$0.496102\pi$
$390$	15.6658	−	3.65920i	0.793266	−	0.185291i
$391$	20.2009	−	3.53467i	1.02160	−	0.178756i
$392$	−10.8050	+	14.3772i	−0.545733	+	0.726158i
$393$	−12.3079	−	12.3079i	−0.620850	−	0.620850i
$394$	17.5830	+	1.47918i	0.885820	+	0.0745201i
$395$	2.23816	−	28.1627i	0.112614	−	1.41702i
$396$	−7.24794	+	1.65768i	−0.364223	+	0.0833016i
$397$	24.6909	−	10.2273i	1.23920	−	0.513293i	0.335735	−	0.941956i	$-0.391015\pi$
$397$	24.6909	−	10.2273i	1.23920	−	0.513293i	0.903464	+	0.428663i	$0.141015\pi$
$398$	16.0352	+	18.9810i	0.803773	+	0.951431i
$399$	−1.06593	−	1.06593i	−0.0533633	−	0.0533633i
$400$	19.1587	−	5.73965i	0.957936	−	0.286983i
$401$	−1.51850	−	3.66598i	−0.0758303	−	0.183070i	0.881419	−	0.472336i	$-0.156589\pi$
$401$	−1.51850	−	3.66598i	−0.0758303	−	0.183070i	−0.957249	+	0.289265i	$0.906589\pi$
$402$	−11.1527	+	9.42186i	−0.556246	+	0.469919i
$403$	3.58169	−	8.64697i	0.178417	−	0.430736i
$404$	−9.37684	+	6.65948i	−0.466515	+	0.331322i
$405$	22.0562	+	11.2595i	1.09598	+	0.559487i
$406$	5.12313	−	9.92217i	0.254256	−	0.492429i
$407$			4.15852i			0.206130i
$408$	10.6964	−	20.9918i	0.529551	−	1.03925i
$409$	17.2403			0.852478			0.426239	−	0.904611i	$-0.359838\pi$
$409$	17.2403			0.852478			0.426239	+	0.904611i	$0.359838\pi$
$410$	20.7971	−	33.4737i	1.02710	−	1.65315i
$411$	−8.60115	+	20.7650i	−0.424263	+	1.02426i
$412$	−21.1145	+	14.9957i	−1.04024	+	0.738783i
$413$	−2.27306	+	5.48765i	−0.111850	+	0.270030i
$414$	4.90881	+	5.81058i	0.241255	+	0.285574i
$415$	4.72843	+	14.5906i	0.232109	+	0.716225i
$416$	−10.3403	+	9.79767i	−0.506976	+	0.480370i
$417$	20.2199	−	20.2199i	0.990174	−	0.990174i
$418$	−2.92315	−	3.46015i	−0.142976	−	0.169242i
$419$	−13.0025	−	31.3908i	−0.635214	−	1.53354i	−0.832986	−	0.553294i	$-0.813371\pi$
$419$	−13.0025	−	31.3908i	−0.635214	−	1.53354i	0.197772	−	0.980248i	$-0.436629\pi$
$420$	7.15940	−	1.04938i	0.349343	−	0.0512046i
$421$	2.90390			0.141527			0.0707637	−	0.997493i	$-0.477456\pi$
$421$	2.90390			0.141527			0.0707637	+	0.997493i	$0.477456\pi$
$422$	−0.176195	+	2.09443i	−0.00857702	+	0.101955i
$423$	7.80687	+	7.80687i	0.379583	+	0.379583i
$424$	−8.78355	+	11.6875i	−0.426567	+	0.567594i
$425$	18.9290	−	8.16665i	0.918190	−	0.396141i
$426$	22.3449	−	7.12742i	1.08261	−	0.345324i
$427$	−5.37649	+	5.37649i	−0.260187	+	0.260187i
$428$	−4.57675	+	1.04675i	−0.221225	+	0.0505965i
$429$	17.4891			0.844382
$430$	1.91449	−	11.6242i	0.0923251	−	0.560569i
$431$	−4.69595	+	1.94513i	−0.226196	+	0.0936935i	−0.492903	−	0.870084i	$-0.664064\pi$
$431$	−4.69595	+	1.94513i	−0.226196	+	0.0936935i	0.266707	+	0.963778i	$0.414064\pi$
$432$	−15.4792	+	0.883076i	−0.744742	+	0.0424870i
$433$	−13.2027	+	13.2027i	−0.634479	+	0.634479i	−0.949188	−	0.314709i	$-0.898093\pi$
$433$	−13.2027	+	13.2027i	−0.634479	+	0.634479i	0.314709	+	0.949188i	$0.398093\pi$
$434$	1.93136	−	3.74054i	0.0927082	−	0.179552i
$435$	42.3681	−	13.7304i	2.03139	−	0.658321i
$436$	13.3620	+	8.38762i	0.639923	+	0.401694i
$437$	−1.77338	+	4.28131i	−0.0848322	+	0.204803i
$438$	16.9975	−	5.42175i	0.812172	−	0.259061i
$439$	11.5575	+	4.78728i	0.551610	+	0.228484i	0.641038	−	0.767509i	$-0.278504\pi$
$439$	11.5575	+	4.78728i	0.551610	+	0.228484i	−0.0894281	+	0.995993i	$0.528504\pi$
$440$	21.7013	−	1.33871i	1.03457	−	0.0638204i
$441$	−6.87599			−0.327428
$442$	−9.41541	+	11.2672i	−0.447845	+	0.535924i
$443$	25.9778			1.23424			0.617122	−	0.786867i	$-0.288298\pi$
$443$	25.9778			1.23424			0.617122	+	0.786867i	$0.288298\pi$
$444$	0.816557	−	4.81886i	0.0387521	−	0.228693i
$445$	−3.56817	−	1.82152i	−0.169148	−	0.0863482i
$446$	−7.00826	+	2.23545i	−0.331851	+	0.105851i
$447$	−38.5475	−	15.9669i	−1.82323	−	0.755208i
$448$	−5.00398	+	4.00146i	−0.236416	+	0.189051i
$449$	6.21609	+	15.0070i	0.293356	+	0.708223i	1.00000		0.000653907i	$0.000208145\pi$
$449$	6.21609	+	15.0070i	0.293356	+	0.708223i	−0.706644	+	0.707569i	$0.749792\pi$
$450$	6.15487	+	4.53718i	0.290144	+	0.213885i
$451$	30.2937	−	30.2937i	1.42647	−	1.42647i
$452$	6.96524	−	11.0960i	0.327617	−	0.521914i
$453$	−2.04765	+	0.848164i	−0.0962070	+	0.0398502i
$454$	−1.02442	+	12.1773i	−0.0480786	+	0.571510i
$455$	−4.49548	−	0.357266i	−0.210751	−	0.0167489i
$456$	2.70790	+	4.58358i	0.126809	+	0.214646i
$457$	−14.3762	−	14.3762i	−0.672489	−	0.672489i	0.285800	−	0.958289i	$-0.407741\pi$
$457$	−14.3762	−	14.3762i	−0.672489	−	0.672489i	−0.958289	+	0.285800i	$0.907741\pi$
$458$	0.244619	+	0.766896i	0.0114303	+	0.0358347i
$459$	−15.7423	+	2.75453i	−0.734790	+	0.128570i
$460$	−11.4027	−	19.0989i	−0.531654	−	0.890491i
$461$	7.47698	+	7.47698i	0.348238	+	0.348238i	0.859453	−	0.511215i	$-0.170804\pi$
$461$	7.47698	+	7.47698i	0.348238	+	0.348238i	−0.511215	+	0.859453i	$0.670804\pi$
$462$	7.83866	+	0.659431i	0.364688	+	0.0306795i
$463$	25.7018			1.19446			0.597232	−	0.802068i	$-0.296267\pi$
$463$	25.7018			1.19446			0.597232	+	0.802068i	$0.296267\pi$
$464$	−26.2522	+	29.4287i	−1.21873	+	1.36619i
$465$	15.9723	−	5.17619i	0.740697	−	0.240040i
$466$	−20.1884	+	17.0553i	−0.935210	+	0.790070i
$467$	−15.1664	−	15.1664i	−0.701818	−	0.701818i	0.262982	−	0.964801i	$-0.415294\pi$
$467$	−15.1664	−	15.1664i	−0.701818	−	0.701818i	−0.964801	+	0.262982i	$0.915294\pi$
$468$	−5.36961	−	0.909881i	−0.248210	−	0.0420593i
$469$	3.78110	−	1.56618i	0.174595	−	0.0723197i
$470$	−18.8162	−	26.2363i	−0.867928	−	1.21019i
$471$	3.10079	−	7.48598i	0.142877	−	0.344936i
$472$	12.6026	−	16.7692i	0.580083	−	0.771864i
$473$	4.90112	−	11.8324i	0.225354	−	0.544052i
$474$	−16.5609	+	32.0742i	−0.760667	+	1.47322i
$475$	−0.735780	+	4.59992i	−0.0337599	+	0.211059i
$476$	−4.64484	+	4.69496i	−0.212896	+	0.215193i
$477$	−5.58961			−0.255931
$478$	1.19086	−	2.30638i	0.0544685	−	0.105491i
$479$	34.1920	+	14.1628i	1.56227	+	0.647114i	0.985482	−	0.169780i	$-0.0543058\pi$
$479$	34.1920	+	14.1628i	1.56227	+	0.647114i	0.576788	+	0.816894i	$0.304306\pi$
$480$	−25.4102	−	2.70993i	−1.15981	−	0.123691i
$481$	−1.16569	+	2.81422i	−0.0531507	+	0.128317i
$482$	−27.1599	+	22.9448i	−1.23710	+	1.04511i
$483$	−3.07973	−	7.43513i	−0.140133	−	0.338310i
$484$	1.61393	+	0.273480i	0.0733604	+	0.0124309i
$485$	10.8044	−	9.21357i	0.490605	−	0.418367i
$486$	−9.80680	−	11.6084i	−0.444846	−	0.526566i
$487$	8.38068	+	20.2327i	0.379765	+	0.916833i	0.992009	+	0.126165i	$0.0402668\pi$
$487$	8.38068	+	20.2327i	0.379765	+	0.916833i	−0.612245	+	0.790668i	$0.709733\pi$
$488$	23.1193	−	13.6585i	1.04656	−	0.618290i
$489$		−	34.5348i		−	1.56172i
$490$	19.8403	+	3.26767i	0.896292	+	0.147618i
$491$	10.3358	+	10.3358i	0.466448	+	0.466448i	0.900762	−	0.434314i	$-0.143009\pi$
$491$	10.3358	+	10.3358i	0.466448	+	0.466448i	−0.434314	+	0.900762i	$0.643009\pi$
$492$	−41.0525	+	29.1557i	−1.85079	+	1.31444i
$493$	−23.3595	+	33.2680i	−1.05206	+	1.49831i
$494$	−1.00827	−	3.16100i	−0.0453644	−	0.142220i
$495$	5.39382	+	6.32515i	0.242434	+	0.284294i
$496$	−9.89676	+	11.0943i	−0.444378	+	0.498148i
$497$	−6.57468			−0.294915
$498$	1.64282	−	19.5282i	0.0736163	−	0.875077i
$499$	−13.3726	−	32.2843i	−0.598640	−	1.44525i	−0.874967	−	0.484182i	$-0.839117\pi$
$499$	−13.3726	−	32.2843i	−0.598640	−	1.44525i	0.276327	−	0.961064i	$-0.410883\pi$
$500$	−15.6033	−	16.0167i	−0.697802	−	0.716290i
$501$	−16.0474	+	16.0474i	−0.716943	+	0.716943i
$502$	2.46398	−	4.77209i	0.109973	−	0.212989i
$503$	−32.3335	+	13.3930i	−1.44168	+	0.597163i	−0.960205	−	0.279298i	$-0.909898\pi$
$503$	−32.3335	+	13.3930i	−1.44168	+	0.597163i	−0.481474	+	0.876460i	$0.659898\pi$
$504$	−2.37236	−	0.610273i	−0.105673	−	0.0271837i
$505$	11.4526	+	5.84643i	0.509633	+	0.260163i
$506$	−7.34860	−	23.0383i	−0.326685	−	1.02418i
$507$	−12.4285	−	5.14805i	−0.551968	−	0.228633i
$508$	−32.3508	−	5.48185i	−1.43534	−	0.243218i
$509$		−	4.68831i		−	0.207806i	−0.994587	−	0.103903i	$-0.966867\pi$
$509$		−	4.68831i		−	0.207806i	0.994587	−	0.103903i	$-0.0331331\pi$
$510$	−26.3394	+	0.263100i	−1.16633	+	0.0116503i
$511$	−5.00129			−0.221244
$512$	20.6354	−	9.28327i	0.911966	−	0.410266i
$513$	1.38197	−	3.33638i	0.0610156	−	0.147305i
$514$	21.4846	−	6.85301i	0.947645	−	0.302273i
$515$	25.7886	+	13.1648i	1.13638	+	0.580112i
$516$	−8.00275	+	12.7489i	−0.352301	+	0.561237i
$517$	−13.4319	−	32.4274i	−0.590733	−	1.42616i
$518$	−0.628574	+	1.21739i	−0.0276180	+	0.0534889i
$519$	−8.01335	−	8.01335i	−0.351747	−	0.351747i
$520$	15.0613	+	5.17720i	0.660481	+	0.227035i
$521$	−31.4790	+	13.0390i	−1.37912	+	0.571250i	−0.944246	−	0.329241i	$-0.893207\pi$
$521$	−31.4790	+	13.0390i	−1.37912	+	0.571250i	−0.434874	+	0.900491i	$0.643207\pi$
$522$	−15.0244	−	1.26393i	−0.657598	−	0.0553208i
$523$			20.8969i			0.913758i	0.889529	+	0.456879i	$0.151033\pi$
$523$			20.8969i			0.913758i	−0.889529	+	0.456879i	$0.848967\pi$
$524$	−3.84184	−	16.7978i	−0.167832	−	0.733817i
$525$	−4.74514	−	6.55221i	−0.207095	−	0.285962i
$526$	−5.81502	−	18.2304i	−0.253547	−	0.794885i
$527$	−8.80628	+	12.5416i	−0.383608	+	0.546323i
$528$	−26.2299	−	9.15212i	−1.14151	−	0.398295i
$529$	−1.23000	+	1.23000i	−0.0534784	+	0.0534784i
$530$	16.1285	+	2.65635i	0.700578	+	0.115384i
$531$	8.01997			0.348037
$532$	−0.332725	−	1.45479i	−0.0144255	−	0.0630730i
$533$	28.9925	−	12.0091i	1.25580	−	0.520171i
$534$	3.30337	+	3.91022i	0.142951	+	0.169212i
$535$	3.40595	+	3.99404i	0.147252	+	0.172677i
$536$	−14.3103	+	2.02999i	−0.618109	+	0.0876822i
$537$	32.2685	−	13.3661i	1.39249	−	0.576788i
$538$	7.08094	+	8.38175i	0.305281	+	0.361363i
$539$	20.1955	+	8.36527i	0.869883	+	0.360317i
$540$	8.88600	+	14.8835i	0.382393	+	0.640486i
$541$	−8.31450	+	20.0730i	−0.357468	+	0.863005i	0.638186	+	0.769882i	$0.279685\pi$
$541$	−8.31450	+	20.0730i	−0.357468	+	0.863005i	−0.995655	+	0.0931229i	$0.970315\pi$
$542$	14.2483	−	27.5953i	0.612018	−	1.18532i
$543$			22.2981i			0.956903i
$544$	20.0172	−	11.9712i	0.858232	−	0.513261i
$545$	1.39737	−	17.5831i	0.0598567	−	0.753177i
$546$	5.11985	+	2.64354i	0.219109	+	0.113133i
$547$	−7.17008	−	2.96995i	−0.306571	−	0.126986i	0.224094	−	0.974567i	$-0.428058\pi$
$547$	−7.17008	−	2.96995i	−0.306571	−	0.126986i	−0.530665	+	0.847582i	$0.678058\pi$
$548$	−18.1411	+	12.8839i	−0.774949	+	0.550373i
$549$	9.48485	+	3.92875i	0.404804	+	0.167675i
$550$	−12.5576	−	20.8141i	−0.535460	−	0.887518i
$551$	−3.51514	−	8.48630i	−0.149750	−	0.361528i
$552$	3.99175	+	28.1396i	0.169900	+	1.19770i
$553$	7.15511	−	7.15511i	0.304266	−	0.304266i
$554$	−3.14372	−	3.72124i	−0.133564	−	0.158100i
$555$	−5.19829	+	1.68463i	−0.220655	+	0.0715085i
$556$	27.5962	−	6.31155i	1.17034	−	0.267669i
$557$		−	21.4735i		−	0.909863i	−0.890526	−	0.454932i	$-0.849664\pi$
$557$		−	21.4735i		−	0.909863i	0.890526	−	0.454932i	$-0.150336\pi$
$558$	−5.66401	−	0.476488i	−0.239777	−	0.0201713i
$559$	6.63352	−	6.63352i	0.280568	−	0.280568i
$560$	6.55530	+	2.88833i	0.277012	+	0.122054i
$561$	−27.9488	−	6.23455i	−1.18000	−	0.263223i
$562$	30.1532	−	9.61807i	1.27194	−	0.405714i
$563$	−9.94781	+	9.94781i	−0.419250	+	0.419250i	−0.884945	−	0.465695i	$-0.845804\pi$
$563$	−9.94781	+	9.94781i	−0.419250	+	0.419250i	0.465695	+	0.884945i	$0.345804\pi$
$564$	9.19738	+	40.2141i	0.387279	+	1.69332i
$565$	−14.6014	−	1.16040i	−0.614284	−	0.0488185i
$566$	3.18673	−	37.8806i	0.133948	−	1.59224i
$567$	3.39428	+	8.19453i	0.142547	+	0.344138i
$568$	22.4870	+	5.78461i	0.943533	+	0.242717i
$569$	25.7173	+	25.7173i	1.07813	+	1.07813i	0.996678	+	0.0814486i	$0.0259547\pi$
$569$	25.7173	+	25.7173i	1.07813	+	1.07813i	0.0814486	+	0.996678i	$0.474045\pi$
$570$	3.14113	−	5.05576i	0.131567	−	0.211762i
$571$	−16.0004	+	6.62758i	−0.669596	+	0.277356i	−0.691470	−	0.722405i	$-0.743037\pi$
$571$	−16.0004	+	6.62758i	−0.669596	+	0.277356i	0.0218742	+	0.999761i	$0.493037\pi$
$572$	14.6642	+	9.20503i	0.613140	+	0.384882i
$573$	4.15286	−	10.0259i	0.173488	−	0.418837i
$574$	13.4473	−	4.28933i	0.561280	−	0.179033i
$575$	−13.0267	+	21.1847i	−0.543250	+	0.883464i
$576$	7.57711	+	4.17456i	0.315713	+	0.173940i
$577$		−	13.3350i		−	0.555145i	−0.960705	−	0.277573i	$-0.910470\pi$
$577$		−	13.3350i		−	0.555145i	0.960705	−	0.277573i	$-0.0895299\pi$
$578$	19.0630	−	14.6493i	0.792917	−	0.609330i
$579$		−	37.9416i		−	1.57680i
$580$	42.7513	+	10.7870i	1.77515	+	0.447907i
$581$	−2.10227	+	5.07533i	−0.0872168	+	0.210560i
$582$	−17.2849	+	5.51341i	−0.716481	+	0.228538i
$583$	16.4173	+	6.80027i	0.679935	+	0.281638i
$584$	17.1056	+	4.40029i	0.707835	+	0.182085i
$585$	1.87716	+	5.79240i	0.0776111	+	0.239486i
$586$	−34.1497	−	17.6326i	−1.41071	−	0.728394i
$587$	−6.62698	−	6.62698i	−0.273525	−	0.273525i	0.556993	−	0.830517i	$-0.311955\pi$
$587$	−6.62698	−	6.62698i	−0.273525	−	0.273525i	−0.830517	+	0.556993i	$0.811955\pi$
$588$	−21.7598	−	13.6591i	−0.897361	−	0.563294i
$589$	−1.32517	−	3.19924i	−0.0546026	−	0.131822i
$590$	−23.1411	−	3.81132i	−0.952706	−	0.156910i
$591$			25.2065i			1.03686i
$592$	3.22097	−	3.61071i	0.132381	−	0.148399i
$593$	−13.0141	−	13.0141i	−0.534426	−	0.534426i	0.387460	−	0.921886i	$-0.373352\pi$
$593$	−13.0141	−	13.0141i	−0.534426	−	0.534426i	−0.921886	+	0.387460i	$0.873352\pi$
$594$	5.72668	+	17.9535i	0.234969	+	0.736641i
$595$	7.05673	+	2.17349i	0.289298	+	0.0891046i
$596$	−23.9172	−	33.6765i	−0.979689	−	1.37944i
$597$	−25.0991	+	25.0991i	−1.02724	+	1.02724i
$598$	1.48488	−	17.6507i	0.0607211	−	0.721792i
$599$		−	5.88190i		−	0.240328i	−0.992754	−	0.120164i	$-0.961658\pi$
$599$		−	5.88190i		−	0.240328i	0.992754	−	0.120164i	$-0.0383420\pi$
$600$	10.4647	+	26.5851i	0.427219	+	1.08533i
$601$	32.1759	−	13.3277i	1.31248	−	0.543648i	0.386874	−	0.922132i	$-0.373555\pi$
$601$	32.1759	−	13.3277i	1.31248	−	0.543648i	0.925608	+	0.378485i	$0.123555\pi$
$602$	3.22328	−	2.72304i	0.131371	−	0.110983i
$603$	−3.90741	−	3.90741i	−0.159122	−	0.159122i
$604$	−2.16332	−	0.366574i	−0.0880241	−	0.0149157i
$605$	−0.564214	−	1.74101i	−0.0229386	−	0.0707820i
$606$	−10.6027	−	12.5504i	−0.430703	−	0.509826i
$607$	−12.7745	−	5.29138i	−0.518502	−	0.214771i	0.108057	−	0.994145i	$-0.465537\pi$
$607$	−12.7745	−	5.29138i	−0.518502	−	0.214771i	−0.626559	+	0.779374i	$0.715537\pi$
$608$	−0.141969	+	5.26846i	−0.00575759	+	0.213664i
$609$	14.7377	+	6.10455i	0.597202	+	0.247369i
$610$	−25.5009	−	15.8437i	−1.03250	−	0.641491i
$611$		−	25.7099i		−	1.04011i
$612$	8.25665	+	3.36822i	0.333755	+	0.136152i
$613$	−9.54282			−0.385431			−0.192715	−	0.981255i	$-0.561729\pi$
$613$	−9.54282			−0.385431			−0.192715	+	0.981255i	$0.561729\pi$
$614$	−2.24012	+	4.33854i	−0.0904040	+	0.175089i
$615$	50.1402	+	25.5961i	2.02185	+	1.03213i
$616$	6.22544	+	4.67864i	0.250830	+	0.188508i
$617$	−4.68910	−	1.94229i	−0.188776	−	0.0781935i	0.286293	−	0.958142i	$-0.407577\pi$
$617$	−4.68910	−	1.94229i	−0.188776	−	0.0781935i	−0.475069	+	0.879949i	$0.657577\pi$
$618$	−23.8748	−	28.2607i	−0.960385	−	1.13681i
$619$	−12.3060	+	5.09733i	−0.494621	+	0.204879i	−0.616028	−	0.787724i	$-0.711259\pi$
$619$	−12.3060	+	5.09733i	−0.494621	+	0.204879i	0.121407	+	0.992603i	$0.461259\pi$
$620$	16.1167	+	4.06658i	0.647264	+	0.163318i
$621$	13.6325	−	13.6325i	0.547051	−	0.547051i
$622$	−12.4189	−	14.7003i	−0.497954	−	0.589430i
$623$	−0.549115	−	1.32568i	−0.0219998	−	0.0531123i
$624$	−15.1852	−	13.5461i	−0.607896	−	0.542279i
$625$	−7.79822	+	23.7526i	−0.311929	+	0.950105i
$626$	−2.79387	+	33.2108i	−0.111666	+	1.32737i
$627$	4.57546	−	4.57546i	0.182726	−	0.182726i
$628$	6.54003	−	4.64476i	0.260976	−	0.185346i
$629$	2.86606	−	4.08177i	0.114277	−	0.162751i
$630$	0.622945	+	2.66695i	0.0248187	+	0.106254i
$631$	−5.41599	+	5.41599i	−0.215607	+	0.215607i	−0.806644	−	0.591037i	$-0.798719\pi$
$631$	−5.41599	+	5.41599i	−0.215607	+	0.215607i	0.591037	+	0.806644i	$0.298719\pi$
$632$	−30.7675	+	18.1769i	−1.22386	+	0.723038i
$633$	−3.00251			−0.119339
$634$	−0.617519	+	7.34045i	−0.0245248	+	0.291526i
$635$	11.3095	+	34.8981i	0.448805	+	1.38489i
$636$	−17.6890	−	11.1038i	−0.701413	−	0.440293i
$637$	11.3221	+	11.3221i	0.448599	+	0.448599i
$638$	42.5905	+	21.9908i	1.68617	+	0.870624i
$639$	3.39716	+	8.20146i	0.134389	+	0.324445i
$640$	−19.8795	−	15.6463i	−0.785804	−	0.618475i
$641$	1.32058	−	3.18817i	0.0521599	−	0.125925i	−0.895652	−	0.444756i	$-0.853290\pi$
$641$	1.32058	−	3.18817i	0.0521599	−	0.125925i	0.947812	+	0.318831i	$0.103290\pi$
$642$	−2.03812	−	6.38964i	−0.0804383	−	0.252179i
$643$	−2.28217	−	0.945307i	−0.0900001	−	0.0372793i	0.337229	−	0.941423i	$-0.390510\pi$
$643$	−2.28217	−	0.945307i	−0.0900001	−	0.0372793i	−0.427229	+	0.904143i	$0.640510\pi$
$644$	1.33105	−	7.85512i	0.0524508	−	0.309535i
$645$	16.7763	+	1.33325i	0.660566	+	0.0524967i
$646$	0.484453	+	5.41093i	0.0190605	+	0.212890i
$647$			38.4771i			1.51269i	0.654172	+	0.756346i	$0.273017\pi$
$647$			38.4771i			1.51269i	−0.654172	+	0.756346i	$0.726983\pi$
$648$	−4.39946	−	31.0136i	−0.172827	−	1.21833i
$649$	−23.5555	−	9.75701i	−0.924635	−	0.382996i
$650$	−2.66373	−	17.6057i	−0.104480	−	0.690553i
$651$	5.55594	+	2.30135i	0.217755	+	0.0901969i
$652$	18.1767	−	28.9566i	0.711855	−	1.13403i
$653$	−15.6376	−	37.7525i	−0.611947	−	1.47737i	−0.860858	−	0.508845i	$-0.830073\pi$
$653$	−15.6376	−	37.7525i	−0.611947	−	1.47737i	0.248911	−	0.968526i	$-0.419927\pi$
$654$	−10.3396	+	20.0252i	−0.404311	+	0.783047i
$655$	−14.6592	+	12.5007i	−0.572781	+	0.488443i
$656$	−49.7669	+	2.83917i	−1.94307	+	0.110851i
$657$	2.58418	+	6.23876i	0.100818	+	0.243397i
$658$	0.969398	−	11.5232i	0.0377911	−	0.449223i
$659$	32.5515			1.26803			0.634014	−	0.773322i	$-0.281406\pi$
$659$	32.5515			1.26803			0.634014	+	0.773322i	$0.281406\pi$
$660$	4.50443	+	30.7314i	0.175335	+	1.19622i
$661$	−31.6703	−	31.6703i	−1.23183	−	1.23183i	−0.963260	−	0.268572i	$-0.913448\pi$
$661$	−31.6703	−	31.6703i	−1.23183	−	1.23183i	−0.268572	−	0.963260i	$-0.586552\pi$
$662$	−7.64864	−	23.9789i	−0.297273	−	0.931968i
$663$	−17.1663	−	12.0535i	−0.666684	−	0.468121i
$664$	11.6557	−	15.5092i	0.452329	−	0.601873i
$665$	−1.26957	+	1.08263i	−0.0492317	+	0.0419826i
$666$	1.84339	+	0.155076i	0.0714300	+	0.00600909i
$667$		−	49.0379i		−	1.89876i
$668$	−21.9015	+	5.00910i	−0.847394	+	0.193808i
$669$	−4.02141	−	9.70854i	−0.155477	−	0.375354i
$670$	9.41770	+	13.1315i	0.363838	+	0.507316i
$671$	−23.0784	−	23.0784i	−0.890930	−	0.890930i
$672$	−6.29530	−	6.64398i	−0.242847	−	0.256297i
$673$	−33.1545	+	13.7330i	−1.27801	+	0.529369i	−0.915390	−	0.402568i	$-0.868118\pi$
$673$	−33.1545	+	13.7330i	−1.27801	+	0.529369i	−0.362620	+	0.931937i	$0.618118\pi$
$674$	−15.2824	−	18.0898i	−0.588656	−	0.696795i
$675$	10.1515	−	16.5090i	0.390733	−	0.635432i
$676$	−7.71140	−	10.8580i	−0.296592	−	0.417615i
$677$	41.3616	+	17.1325i	1.58965	+	0.658456i	0.989905	−	0.141732i	$-0.0452670\pi$
$677$	41.3616	+	17.1325i	1.58965	+	0.658456i	0.599749	+	0.800188i	$0.295267\pi$
$678$	16.6293	+	8.58623i	0.638645	+	0.329752i
$679$	5.08584			0.195177
$680$	−22.2234	−	13.6426i	−0.852228	−	0.523170i
$681$	−17.4571			−0.668957
$682$	16.0561	+	8.29028i	0.614821	+	0.317451i
$683$	2.82950	+	1.17202i	0.108268	+	0.0448459i	0.436160	−	0.899869i	$-0.356338\pi$
$683$	2.82950	+	1.17202i	0.108268	+	0.0448459i	−0.327892	+	0.944715i	$0.606338\pi$
$684$	−1.64283	+	1.16674i	−0.0628151	+	0.0446116i
$685$	22.1569	+	11.3109i	0.846573	+	0.432168i
$686$	9.76425	+	11.5580i	0.372801	+	0.441286i
$687$	−1.06238	+	0.440053i	−0.0405324	+	0.0167891i
$688$	−13.4202	+	6.47751i	−0.511640	+	0.246953i
$689$	9.20396	+	9.20396i	0.350643	+	0.350643i
$690$	25.8217	−	18.5189i	0.983017	−	0.705002i
$691$	15.3642	+	37.0925i	0.584483	+	1.41107i	0.888711	+	0.458467i	$0.151601\pi$
$691$	15.3642	+	37.0925i	0.584483	+	1.41107i	−0.304229	+	0.952599i	$0.598399\pi$
$692$	−2.50133	−	10.9367i	−0.0950862	−	0.415749i
$693$			2.97736i			0.113100i
$694$	−49.8725	−	4.19555i	−1.89313	−	0.159261i
$695$	−20.5367	−	24.0827i	−0.779002	−	0.913510i
$696$	−45.0355	−	33.8457i	−1.70706	−	1.28292i
$697$	−50.6131	+	8.85605i	−1.91711	+	0.335447i
$698$	−0.0754046	−	0.236398i	−0.00285411	−	0.00894780i
$699$	−26.6957	−	26.6957i	−1.00973	−	1.00973i
$700$	−0.530060	−	7.99137i	−0.0200344	−	0.302045i
$701$	44.5817			1.68383			0.841914	−	0.539611i	$-0.181429\pi$
$701$	44.5817			1.68383			0.841914	+	0.539611i	$0.181429\pi$
$702$	−1.15715	+	13.7550i	−0.0436737	+	0.519149i
$703$	0.431285	+	1.04121i	0.0162662	+	0.0392701i
$704$	−17.1761	−	21.4794i	−0.647348	−	0.809535i
$705$	35.0941	−	29.9267i	1.32172	−	1.12711i
$706$	−6.15939	+	11.9292i	−0.231812	+	0.448959i
$707$	1.76247	+	4.25497i	0.0662844	+	0.160025i
$708$	25.3801	+	15.9317i	0.953842	+	0.598748i
$709$	29.7981	+	12.3428i	1.11909	+	0.463543i	0.864060	−	0.503389i	$-0.167914\pi$
$709$	29.7981	+	12.3428i	1.11909	+	0.463543i	0.255033	+	0.966932i	$0.417914\pi$
$710$	−5.90473	−	25.2793i	−0.221600	−	0.948714i
$711$	−12.6226	−	5.22844i	−0.473383	−	0.196082i
$712$	0.711729	+	5.01728i	0.0266732	+	0.188030i
$713$		−	18.4867i		−	0.692333i
$714$	−7.23950	−	6.04969i	−0.270931	−	0.226404i
$715$	1.53355	−	19.2967i	0.0573515	−	0.721654i
$716$	34.0913	+	5.77677i	1.27405	+	0.215888i
$717$	3.42573	+	1.41899i	0.127936	+	0.0529930i
$718$	−5.60459	−	17.5707i	−0.209161	−	0.655733i
$719$	−6.80153	+	16.4203i	−0.253654	+	0.612376i	−0.998494	−	0.0548683i	$-0.982526\pi$
$719$	−6.80153	+	16.4203i	−0.253654	+	0.612376i	0.744839	+	0.667244i	$0.232526\pi$
$720$	0.215845	−	9.66969i	0.00804407	−	0.360368i
$721$	3.96868	+	9.58124i	0.147801	+	0.356824i
$722$	22.7846	+	11.7644i	0.847954	+	0.437825i
$723$	−35.9143	−	35.9143i	−1.33567	−	1.33567i
$724$	−11.7361	+	18.6964i	−0.436170	+	0.694845i
$725$	−11.4344	−	47.9510i	−0.424661	−	1.78085i
$726$	−0.196027	+	2.33017i	−0.00727524	+	0.0864808i
$727$	10.0605			0.373123			0.186562	−	0.982443i	$-0.440266\pi$
$727$	10.0605			0.373123			0.186562	+	0.982443i	$0.440266\pi$
$728$	2.90149	+	4.91127i	0.107536	+	0.182024i
$729$	−8.14300	+	8.14300i	−0.301593	+	0.301593i
$730$	−4.49166	−	19.2297i	−0.166244	−	0.711722i
$731$	−12.9656	+	8.23609i	−0.479548	+	0.304623i
$732$	22.2114	+	31.2746i	0.820957	+	1.15594i
$733$	25.8836	−	25.8836i	0.956033	−	0.956033i	−0.0430403	−	0.999073i	$-0.513704\pi$
$733$	25.8836	−	25.8836i	0.956033	−	0.956033i	0.999073	+	0.0430403i	$0.0137044\pi$
$734$	−0.608794	+	7.23674i	−0.0224710	+	0.267113i
$735$	−2.27560	+	28.6339i	−0.0839368	+	1.05618i
$736$	−11.4637	+	25.6953i	−0.422557	+	0.947141i
$737$	6.72278	+	16.2302i	0.247637	+	0.597848i
$738$	−12.2989	−	14.5583i	−0.452730	−	0.535898i
$739$	−11.5914	+	11.5914i	−0.426398	+	0.426398i	−0.887399	−	0.461002i	$-0.847490\pi$
$739$	−11.5914	+	11.5914i	−0.426398	+	0.426398i	0.461002	+	0.887399i	$0.347490\pi$
$740$	−5.24531	−	1.32350i	−0.192821	−	0.0486527i
$741$	4.37894	−	1.81382i	0.160864	−	0.0666322i
$742$	3.77820	+	4.47228i	0.138702	+	0.164182i
$743$	40.3247	+	16.7031i	1.47937	+	0.612776i	0.968974	−	0.247163i	$-0.0794984\pi$
$743$	40.3247	+	16.7031i	1.47937	+	0.612776i	0.510397	+	0.859939i	$0.329498\pi$
$744$	−16.9779	−	12.7595i	−0.622438	−	0.467784i
$745$	−20.9972	+	41.1314i	−0.769278	+	1.50694i
$746$	−19.2451	+	37.2728i	−0.704614	+	1.36466i
$747$	7.41737			0.271388
$748$	−20.1529	−	19.9378i	−0.736864	−	0.728998i
$749$			1.88006i			0.0686961i
$750$	20.9313	−	24.1294i	0.764302	−	0.881079i
$751$	−13.9326	−	5.77108i	−0.508409	−	0.210590i	0.113708	−	0.993514i	$-0.463727\pi$
$751$	−13.9326	−	5.77108i	−0.508409	−	0.210590i	−0.622117	+	0.782924i	$0.713727\pi$
$752$	−13.4541	+	38.5593i	−0.490620	+	1.40611i
$753$	7.08813	+	2.93600i	0.258306	+	0.106994i
$754$	22.6582	+	26.8206i	0.825162	+	0.976749i
$755$	0.756275	+	2.33365i	0.0275237	+	0.0849303i
$756$	−1.03727	+	6.12140i	−0.0377252	+	0.222633i
$757$	−21.4211	−	21.4211i	−0.778562	−	0.778562i	0.201025	−	0.979586i	$-0.435573\pi$
$757$	−21.4211	−	21.4211i	−0.778562	−	0.778562i	−0.979586	+	0.201025i	$0.935573\pi$
$758$	39.4801	−	33.3529i	1.43398	−	1.21143i
$759$	31.9150	−	13.2196i	1.15844	−	0.479842i
$760$	5.29475	−	2.58585i	0.192061	−	0.0937988i
$761$			0.147141i			0.00533387i	0.999996	+	0.00266694i	$0.000848913\pi$
$761$			0.147141i			0.00533387i	−0.999996	+	0.00266694i	$0.999151\pi$
$762$	3.92932	−	46.7078i	0.142344	−	1.69204i
$763$	4.46722	−	4.46722i	0.161724	−	0.161724i
$764$	8.75898	−	6.22068i	0.316889	−	0.225056i
$765$	−0.934949	−	9.92584i	−0.0338032	−	0.358869i
$766$	5.10596	+	16.0075i	0.184486	+	0.578374i
$767$	−13.2058	−	13.2058i	−0.476835	−	0.476835i
$768$	15.6859	+	28.2628i	0.566015	+	1.01985i
$769$		−	25.9998i		−	0.937576i	−0.883311	−	0.468788i	$-0.844691\pi$
$769$		−	25.9998i		−	0.937576i	0.883311	−	0.468788i	$-0.155309\pi$
$770$	1.41493	−	8.59099i	0.0509904	−	0.309598i
$771$	12.3281	+	29.7626i	0.443985	+	1.07187i
$772$	19.9698	−	31.8131i	0.718729	−	1.14498i
$773$	−17.5516	−	17.5516i	−0.631289	−	0.631289i	0.317103	−	0.948391i	$-0.397290\pi$
$773$	−17.5516	−	17.5516i	−0.631289	−	0.631289i	−0.948391	+	0.317103i	$0.897290\pi$
$774$	−5.06229	−	2.61382i	−0.181960	−	0.0939517i
$775$	−4.31062	−	18.0770i	−0.154842	−	0.649344i
$776$	−17.3948	−	4.47468i	−0.624437	−	0.160632i
$777$	−1.80822	−	0.748989i	−0.0648695	−	0.0268698i
$778$	−38.0381	+	12.1331i	−1.36373	+	0.434993i
$779$	4.44317	−	10.7268i	0.159193	−	0.384326i
$780$	−5.56611	+	22.0597i	−0.199299	+	0.789864i
$781$		−	28.2215i		−	1.00985i
$782$	−8.66510	+	27.6778i	−0.309863	+	0.989755i
$783$			38.2147i			1.36568i
$784$	−11.0559	−	22.9057i	−0.394852	−	0.818060i
$785$	−7.98778	−	4.07769i	−0.285096	−	0.145539i
$786$	23.4516	−	7.48043i	0.836491	−	0.266818i
$787$	−5.58683	+	13.4878i	−0.199149	+	0.480788i	−0.991631	−	0.129108i	$-0.958789\pi$
$787$	−5.58683	+	13.4878i	−0.199149	+	0.480788i	0.792482	+	0.609896i	$0.208789\pi$
$788$	−13.2669	+	21.1350i	−0.472616	+	0.752905i
$789$	25.2546	−	10.4608i	0.899088	−	0.372415i
$790$	33.9370	+	21.0850i	1.20742	+	0.750170i
$791$	−3.70967	−	3.70967i	−0.131901	−	0.131901i
$792$	2.61957	−	10.1833i	0.0930825	−	0.361847i
$793$	−9.14877	−	22.0871i	−0.324882	−	0.784335i
$794$	−3.16835	+	37.6621i	−0.112440	+	1.33658i
$795$	−1.84988	+	23.2770i	−0.0656084	+	0.825550i
$796$	−34.2554	+	7.83457i	−1.21415	+	0.277689i
$797$	−14.6037	+	14.6037i	−0.517291	+	0.517291i	−0.916751	−	0.399460i	$-0.869198\pi$
$797$	−14.6037	+	14.6037i	−0.517291	+	0.517291i	0.399460	+	0.916751i	$0.369198\pi$
$798$	2.03104	−	0.647848i	0.0718981	−	0.0229336i
$799$	−9.16511	+	41.0862i	−0.324238	+	1.45352i
$800$	−5.21813	+	27.7988i	−0.184489	+	0.982835i
$801$	−1.36997	+	1.36997i	−0.0484054	+	0.0484054i
$802$	5.59189	+	0.470421i	0.197457	+	0.0166111i
$803$		−	21.4678i		−	0.757583i
$804$	−4.60337	−	20.1275i	−0.162349	−	0.709843i
$805$	−8.47362	+	2.74607i	−0.298656	+	0.0967864i
$806$	8.54187	+	10.1111i	0.300875	+	0.356147i
$807$	−11.0834	+	11.0834i	−0.390156	+	0.390156i
$808$	−2.28440	−	16.1037i	−0.0803649	−	0.566526i
$809$	2.45549	+	5.92808i	0.0863305	+	0.208420i	0.961149	−	0.276031i	$-0.0890193\pi$
$809$	2.45549	+	5.92808i	0.0863305	+	0.208420i	−0.874818	+	0.484451i	$0.839019\pi$
$810$	−28.4591	+	20.4103i	−0.999950	+	0.717146i
$811$	−11.3665	−	4.70816i	−0.399132	−	0.165326i	0.174083	−	0.984731i	$-0.444304\pi$
$811$	−11.3665	−	4.70816i	−0.399132	−	0.165326i	−0.573215	+	0.819405i	$0.694304\pi$
$812$	9.14417	+	12.8754i	0.320898	+	0.451838i
$813$	40.9881	+	16.9778i	1.43752	+	0.595439i
$814$	−5.22558	−	2.69813i	−0.183156	−	0.0945694i
$815$	−38.1041	−	3.02822i	−1.33473	−	0.106074i
$816$	19.4381	+	27.0609i	0.680470	+	0.947322i
$817$		−	3.47090i		−	0.121431i
$818$	−11.1858	+	21.6641i	−0.391104	+	0.757467i
$819$	−0.834591	+	2.01488i	−0.0291630	+	0.0704056i
$820$	28.5693	+	47.8519i	0.997683	+	1.67106i
$821$	0.756234	+	0.313242i	0.0263927	+	0.0109322i	0.395841	−	0.918319i	$-0.370453\pi$
$821$	0.756234	+	0.313242i	0.0263927	+	0.0109322i	−0.369448	+	0.929251i	$0.620453\pi$
$822$	−20.5126	−	24.2809i	−0.715460	−	0.846894i
$823$	0.0289680	−	0.0119989i	0.00100976	−	0.000418256i	−0.382178	−	0.924089i	$-0.624826\pi$
$823$	0.0289680	−	0.0119989i	0.00100976	−	0.000418256i	0.383188	+	0.923670i	$0.374826\pi$
$824$	−5.14395	−	36.2619i	−0.179198	−	1.26324i
$825$	28.1251	−	20.3683i	0.979190	−	0.709134i
$826$	−5.42095	−	6.41681i	−0.188619	−	0.223269i
$827$	−43.4870	+	18.0129i	−1.51219	+	0.626370i	−0.976009	−	0.217731i	$-0.930134\pi$
$827$	−43.4870	+	18.0129i	−1.51219	+	0.626370i	−0.536183	+	0.844102i	$0.680134\pi$
$828$	−10.4865	+	2.39837i	−0.364430	+	0.0833490i
$829$	23.2567			0.807738			0.403869	−	0.914817i	$-0.367665\pi$
$829$	23.2567			0.807738			0.403869	+	0.914817i	$0.367665\pi$
$830$	−21.4024	−	3.52495i	−0.742888	−	0.122353i
$831$	4.92071	−	4.92071i	0.170697	−	0.170697i
$832$	−5.60270	−	19.3505i	−0.194239	−	0.670859i
$833$	−14.0574	−	22.1297i	−0.487061	−	0.766748i
$834$	12.2892	+	38.5274i	0.425540	+	1.33409i
$835$	16.2988	+	19.1130i	0.564042	+	0.661434i
$836$	6.24461	−	1.42821i	0.215974	−	0.0493956i
$837$			14.4065i			0.497961i
$838$	47.8819	+	4.02809i	1.65405	+	0.139148i
$839$	−31.8256	+	13.1826i	−1.09874	+	0.455114i	−0.857047	−	0.515238i	$-0.827704\pi$
$839$	−31.8256	+	13.1826i	−1.09874	+	0.455114i	−0.241696	+	0.970352i	$0.577704\pi$
$840$	−3.32651	+	9.67734i	−0.114776	+	0.333900i
$841$	48.2258	+	48.2258i	1.66296	+	1.66296i
$842$	−1.88411	+	3.64903i	−0.0649306	+	0.125754i
$843$	17.3022	+	41.7713i	0.595920	+	1.43868i
$844$	−2.51753	−	1.58031i	−0.0866569	−	0.0543965i
$845$	−6.76992	+	13.2616i	−0.232892	+	0.456213i
$846$	−14.8753	+	4.74483i	−0.511425	+	0.163131i
$847$	0.250851	−	0.605607i	0.00861934	−	0.0208089i
$848$	−8.98750	−	18.6204i	−0.308632	−	0.639428i
$849$	54.3046			1.86373
$850$	−2.01931	+	29.0847i	−0.0692616	+	0.997599i
$851$			6.01663i			0.206248i
$852$	−5.54151	+	32.7029i	−0.189849	+	1.12038i
$853$	−27.8292	−	11.5273i	−0.952855	−	0.394686i	−0.148552	−	0.988905i	$-0.547461\pi$
$853$	−27.8292	−	11.5273i	−0.952855	−	0.394686i	−0.804303	+	0.594219i	$0.797461\pi$
$854$	−3.26770	−	10.2444i	−0.111818	−	0.350558i
$855$	2.00650	+	1.02430i	0.0686207	+	0.0350302i
$856$	1.65414	−	6.43027i	0.0565374	−	0.219782i
$857$	32.7884	−	13.5814i	1.12003	−	0.463932i	0.255650	−	0.966769i	$-0.417710\pi$
$857$	32.7884	−	13.5814i	1.12003	−	0.463932i	0.864381	+	0.502837i	$0.167710\pi$
$858$	−11.3473	+	21.9767i	−0.387389	+	0.750273i
$859$	−3.84458	+	3.84458i	−0.131175	+	0.131175i	−0.769646	−	0.638471i	$-0.779567\pi$
$859$	−3.84458	+	3.84458i	−0.131175	+	0.131175i	0.638471	+	0.769646i	$0.279567\pi$
$860$	13.3648	+	9.94776i	0.455735	+	0.339216i
$861$	7.71621	+	18.6286i	0.262968	+	0.634860i
$862$	0.602587	−	7.16295i	0.0205242	−	0.243971i
$863$	−35.1148			−1.19532			−0.597661	−	0.801749i	$-0.703903\pi$
$863$	−35.1148			−1.19532			−0.597661	+	0.801749i	$0.703903\pi$
$864$	8.93352	−	20.0240i	0.303925	−	0.681231i
$865$	−9.54422	+	8.13890i	−0.324513	+	0.276731i
$866$	−8.02427	−	25.1566i	−0.272676	−	0.854855i
$867$	23.1361	+	25.3819i	0.785742	+	0.862014i
$868$	3.44725	+	4.85388i	0.117007	+	0.164751i
$869$	30.7130	+	30.7130i	1.04187	+	1.04187i
$870$	−10.2357	+	62.1481i	−0.347024	+	2.10702i
$871$			12.8680i			0.436017i
$872$	−19.2094	+	11.3486i	−0.650511	+	0.384311i
$873$	−2.62787	−	6.34424i	−0.0889399	−	0.214720i
$874$	−4.22928	−	5.00622i	−0.143058	−	0.169338i
$875$	−7.64549	+	4.66103i	−0.258465	+	0.157572i
$876$	−4.21537	+	24.8767i	−0.142424	+	0.840507i
$877$	−5.50861	−	13.2990i	−0.186013	−	0.449074i	0.803173	−	0.595746i	$-0.203144\pi$
$877$	−5.50861	−	13.2990i	−0.186013	−	0.449074i	−0.989185	+	0.146672i	$0.953144\pi$
$878$	−13.5144	+	11.4170i	−0.456090	+	0.385307i
$879$	21.0104	−	50.7236i	0.708663	−	1.71086i
$880$	−12.3980	+	28.1383i	−0.417937	+	0.948543i
$881$	−10.2912	−	4.26275i	−0.346719	−	0.143616i	0.202527	−	0.979277i	$-0.435085\pi$
$881$	−10.2912	−	4.26275i	−0.346719	−	0.143616i	−0.549245	+	0.835661i	$0.685085\pi$
$882$	4.46128	−	8.64034i	0.150219	−	0.290935i
$883$	−21.7804			−0.732968			−0.366484	−	0.930424i	$-0.619439\pi$
$883$	−21.7804			−0.732968			−0.366484	+	0.930424i	$0.619439\pi$
$884$	−8.04937	−	19.1417i	−0.270730	−	0.643806i
$885$	2.65420	−	33.3978i	0.0892199	−	1.12265i
$886$	−16.8549	+	32.6436i	−0.566252	+	1.09668i
$887$	0.445547	−	1.07565i	0.0149600	−	0.0361167i	−0.916223	−	0.400669i	$-0.868778\pi$
$887$	0.445547	−	1.07565i	0.0149600	−	0.0361167i	0.931183	+	0.364552i	$0.118778\pi$
$888$	5.52556	+	4.15265i	0.185426	+	0.139354i
$889$	−5.02825	+	12.1393i	−0.168642	+	0.407138i
$890$	4.60401	−	3.30191i	0.154327	−	0.110680i
$891$	−35.1747	+	14.5698i	−1.17840	+	0.488107i
$892$	1.73804	−	10.2570i	0.0581940	−	0.343428i
$893$	−6.72617	−	6.72617i	−0.225083	−	0.225083i
$894$	45.0743	−	38.0790i	1.50751	−	1.27355i
$895$	−11.9180	−	36.7756i	−0.398374	−	1.22927i
$896$	−1.78153	−	8.88421i	−0.0595167	−	0.296801i
$897$	25.3036			0.844863
$898$	−22.8908	−	1.92570i	−0.763877	−	0.0642615i
$899$	25.9111	+	25.9111i	0.864184	+	0.864184i
$900$	−9.69480	+	4.79038i	−0.323160	+	0.159679i
$901$	−11.4275	−	17.9896i	−0.380706	−	0.599321i
$902$	18.4118	+	57.7221i	0.613045	+	1.92193i
$903$	4.26224	+	4.26224i	0.141838	+	0.141838i
$904$	9.42406	+	15.9518i	0.313440	+	0.530550i
$905$	24.6027	+	1.95523i	0.817821	+	0.0649941i
$906$	0.262755	−	3.12337i	0.00872946	−	0.103767i
$907$	30.4750	−	12.6232i	1.01191	−	0.419146i	0.185757	−	0.982596i	$-0.440526\pi$
$907$	30.4750	−	12.6232i	1.01191	−	0.419146i	0.826150	+	0.563450i	$0.190526\pi$
$908$	−14.6373	−	9.18817i	−0.485756	−	0.304920i
$909$	4.39711	−	4.39711i	0.145843	−	0.145843i
$910$	3.36569	−	5.41720i	0.111572	−	0.179578i
$911$	19.8214	+	47.8532i	0.656714	+	1.58545i	0.802849	+	0.596183i	$0.203317\pi$
$911$	19.8214	+	47.8532i	0.656714	+	1.58545i	−0.146135	+	0.989265i	$0.546683\pi$
$912$	−7.51664	+	0.428819i	−0.248901	+	0.0141996i
$913$	−21.7856	−	9.02391i	−0.720999	−	0.298648i
$914$	27.3926	−	8.73750i	0.906066	−	0.289011i
$915$	19.4996	−	38.1978i	0.644638	−	1.26278i
$916$	−1.12239	−	0.190190i	−0.0370849	−	0.00628404i
$917$	−6.90032			−0.227869
$918$	6.75262	−	21.5690i	0.222870	−	0.711882i
$919$	−9.92489			−0.327392			−0.163696	−	0.986511i	$-0.552342\pi$
$919$	−9.92489			−0.327392			−0.163696	+	0.986511i	$0.552342\pi$
$920$	31.3979	−	1.93687i	1.03516	−	0.0638567i
$921$	−6.44416	−	2.66926i	−0.212342	−	0.0879551i
$922$	−14.2467	+	4.54433i	−0.469192	+	0.149660i
$923$	7.91086	−	19.0985i	0.260389	−	0.628635i
$924$	−5.91452	+	9.42218i	−0.194573	+	0.309967i
$925$	1.40292	+	5.88327i	0.0461278	+	0.193441i
$926$	−16.6758	+	32.2968i	−0.548002	+	1.06134i
$927$	9.90131	−	9.90131i	0.325202	−	0.325202i
$928$	−19.9471	−	52.0823i	−0.654795	−	1.70968i
$929$	−20.7738	+	8.60481i	−0.681568	+	0.282315i	−0.696482	−	0.717574i	$-0.745252\pi$
$929$	−20.7738	+	8.60481i	−0.681568	+	0.282315i	0.0149143	+	0.999889i	$0.495252\pi$
$930$	−3.85875	+	23.4291i	−0.126533	+	0.768271i
$931$	5.92415			0.194156
$932$	−8.33294	−	36.4345i	−0.272955	−	1.19345i
$933$	19.4387	−	19.4387i	0.636395	−	0.636395i
$934$	28.8983	−	9.21779i	0.945582	−	0.301615i
$935$	−9.32963	+	30.2907i	−0.305112	+	0.990612i
$936$	4.62726	−	6.15708i	0.151247	−	0.201250i
$937$	21.1701	+	21.1701i	0.691596	+	0.691596i	0.962583	−	0.270987i	$-0.0873501\pi$
$937$	21.1701	+	21.1701i	0.691596	+	0.691596i	−0.270987	+	0.962583i	$0.587350\pi$
$938$	−0.485193	+	5.76749i	−0.0158421	+	0.188315i
$939$	−47.6100			−1.55369
$940$	45.1768	−	6.62175i	1.47351	−	0.215978i
$941$	−2.94935	−	7.12035i	−0.0961460	−	0.232117i	0.868488	−	0.495710i	$-0.165092\pi$
$941$	−2.94935	−	7.12035i	−0.0961460	−	0.232117i	−0.964634	+	0.263593i	$0.915092\pi$
$942$	7.39499	+	8.75349i	0.240942	+	0.285204i
$943$	43.8295	−	43.8295i	1.42729	−	1.42729i
$944$	12.8952	+	26.7166i	0.419705	+	0.869550i
$945$	6.60340	−	2.13998i	0.214808	−	0.0696137i
$946$	11.6885	+	13.8358i	0.380027	+	0.449840i
$947$	11.2256	−	27.1011i	0.364784	−	0.880666i	−0.629803	−	0.776755i	$-0.716864\pi$
$947$	11.2256	−	27.1011i	0.364784	−	0.880666i	0.994587	−	0.103911i	$-0.0331357\pi$
$948$	−29.5592	−	41.6207i	−0.960040	−	1.35178i
$949$	6.01770	−	14.5280i	0.195343	−	0.471599i
$950$	−5.30285	−	3.90910i	−0.172047	−	0.126828i
$951$	−10.5231			−0.341234
$952$	−2.88601	−	8.88287i	−0.0935360	−	0.287896i
$953$			42.6922i			1.38294i	0.722407	+	0.691468i	$0.243036\pi$
$953$			42.6922i			1.38294i	−0.722407	+	0.691468i	$0.756964\pi$
$954$	3.62665	−	7.02389i	0.117417	−	0.227407i
$955$	−10.6979	−	5.46120i	−0.346177	−	0.176720i
$956$	2.12554	+	2.99285i	0.0687448	+	0.0967956i
$957$	−26.2035	+	63.2609i	−0.847040	+	2.04494i
$958$	−39.9813	+	33.7764i	−1.29174	+	1.09127i
$959$	3.40979	+	8.23196i	0.110108	+	0.265824i
$960$	19.8919	−	30.1720i	0.642008	−	0.973798i
$961$	−12.1521	−	12.1521i	−0.392004	−	0.392004i
$962$	−2.78001	−	3.29071i	−0.0896312	−	0.106097i
$963$	2.34525	−	0.971435i	0.0755747	−	0.0313041i
$964$	−11.2105	−	49.0160i	−0.361065	−	1.57870i
$965$	−41.8630	−	3.32695i	−1.34762	−	0.107098i
$966$	11.3411	+	0.954079i	0.364895	+	0.0306970i
$967$	16.6642	+	16.6642i	0.535885	+	0.535885i	0.922318	−	0.386433i	$-0.126293\pi$
$967$	16.6642	+	16.6642i	0.535885	+	0.535885i	−0.386433	+	0.922318i	$0.626293\pi$
$968$	−1.39080	+	1.85062i	−0.0447021	+	0.0594810i
$969$	−7.64444	+	1.33759i	−0.245575	+	0.0429696i
$970$	4.56760	+	19.5548i	0.146657	+	0.627866i
$971$	26.5367	+	26.5367i	0.851603	+	0.851603i	0.990331	−	0.138728i	$-0.0443013\pi$
$971$	26.5367	+	26.5367i	0.851603	+	0.851603i	−0.138728	+	0.990331i	$0.544301\pi$
$972$	20.9499	−	4.79145i	0.671967	−	0.153686i
$973$		−	11.3362i		−	0.363421i
$974$	−30.8619	−	2.59628i	−0.988880	−	0.0831900i
$975$	24.7427	−	5.90014i	0.792402	−	0.188956i
$976$	2.16294	+	37.9135i	0.0692339	+	1.21358i
$977$	10.4866	−	10.4866i	0.335497	−	0.335497i	−0.519172	−	0.854670i	$-0.673760\pi$
$977$	10.4866	−	10.4866i	0.335497	−	0.335497i	0.854670	+	0.519172i	$0.173760\pi$
$978$	43.3963	+	22.4069i	1.38766	+	0.716493i
$979$	5.69043	−	2.35705i	0.181867	−	0.0753318i
$980$	−16.9789	+	22.8111i	−0.542371	+	0.728673i
$981$	−7.88077	−	3.26432i	−0.251614	−	0.104222i
$982$	−19.6940	+	6.28185i	−0.628460	+	0.200462i
$983$	5.28614	−	12.7619i	0.168602	−	0.407040i	−0.816883	−	0.576803i	$-0.804300\pi$
$983$	5.28614	−	12.7619i	0.168602	−	0.407040i	0.985485	+	0.169763i	$0.0543001\pi$
$984$	−10.0013	−	70.5031i	−0.318829	−	2.24756i
$985$	27.8117	+	2.21026i	0.886155	+	0.0704248i
$986$	−26.6483	−	50.9384i	−0.848654	−	1.62221i
$987$	16.5194			0.525818
$988$	4.62629	+	0.783926i	0.147182	+	0.0249400i
$989$	7.09104	−	17.1193i	0.225482	−	0.544362i
$990$	−11.4478	+	2.67397i	−0.363834	+	0.0849842i
$991$	11.0247	−	26.6160i	0.350211	−	0.845484i	−0.646382	−	0.763014i	$-0.723719\pi$
$991$	11.0247	−	26.6160i	0.350211	−	0.845484i	0.996593	−	0.0824706i	$-0.0262811\pi$
$992$	−7.51982	−	19.6344i	−0.238755	−	0.623393i
$993$	33.2180	−	13.7594i	1.05414	−	0.436640i
$994$	4.26578	−	8.26172i	0.135302	−	0.262046i
$995$	25.4924	+	29.8941i	0.808162	+	0.947705i
$996$	23.4731	+	14.7346i	0.743774	+	0.466884i
$997$	19.0207	−	7.87865i	0.602393	−	0.249519i	−0.0605792	−	0.998163i	$-0.519295\pi$
$997$	19.0207	−	7.87865i	0.602393	−	0.249519i	0.662972	+	0.748644i	$0.269295\pi$
$998$	49.2448	+	4.14274i	1.55882	+	0.131136i
$999$		−	4.68869i		−	0.148344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.br.a.349.37	yes	416
5.4	even	2	inner	680.2.br.a.349.68	yes	416
8.5	even	2	inner	680.2.br.a.349.89	yes	416
17.2	even	8	inner	680.2.br.a.189.16	✓	416
40.29	even	2	inner	680.2.br.a.349.16	yes	416
85.19	even	8	inner	680.2.br.a.189.89	yes	416
136.53	even	8	inner	680.2.br.a.189.68	yes	416
680.189	even	8	inner	680.2.br.a.189.37	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.br.a.189.16	✓	416	17.2	even	8	inner
680.2.br.a.189.37	yes	416	680.189	even	8	inner
680.2.br.a.189.68	yes	416	136.53	even	8	inner
680.2.br.a.189.89	yes	416	85.19	even	8	inner
680.2.br.a.349.16	yes	416	40.29	even	2	inner
680.2.br.a.349.37	yes	416	1.1	even	1	trivial
680.2.br.a.349.68	yes	416	5.4	even	2	inner
680.2.br.a.349.89	yes	416	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.br (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.648820 + 1.25660i) q^{2} +(-1.86646 - 0.773113i) q^{3} +(-1.15807 - 1.63061i) q^{4} +(-1.01668 + 1.99157i) q^{5} +(2.18249 - 1.84377i) q^{6} +(-0.739929 + 0.306488i) q^{7} +(2.80039 - 0.397251i) q^{8} +(0.764647 + 0.764647i) q^{9} +(-1.84296 - 2.56973i) q^{10} +(-1.31559 - 3.17611i) q^{11} +(0.900840 + 3.93878i) q^{12} -2.51816i q^{13} +(0.0949480 - 1.12865i) q^{14} +(3.43730 - 2.93118i) q^{15} +(-1.31776 + 3.77670i) q^{16} +(-0.897680 + 4.02420i) q^{17} +(-1.45697 + 0.464734i) q^{18} +(-0.658797 - 0.658797i) q^{19} +(4.42486 - 0.648569i) q^{20} +1.61800 q^{21} +(4.84467 + 0.407560i) q^{22} +(-1.90342 - 4.59527i) q^{23} +(-5.53394 - 1.42357i) q^{24} +(-2.93273 - 4.04958i) q^{25} +(3.16431 + 1.63383i) q^{26} +(1.48331 + 3.58104i) q^{27} +(1.35665 + 0.851599i) q^{28} +(9.10861 + 3.77291i) q^{29} +(1.45312 + 6.22111i) q^{30} +(3.43384 + 1.42234i) q^{31} +(-3.89080 - 4.10630i) q^{32} +6.94518i q^{33} +(-4.47436 - 3.73900i) q^{34} +(0.141876 - 1.78522i) q^{35} +(0.361327 - 2.13235i) q^{36} +(-1.11757 - 0.462911i) q^{37} +(1.25528 - 0.400401i) q^{38} +(-1.94682 + 4.70005i) q^{39} +(-2.05594 + 5.98106i) q^{40} +(4.76899 + 11.5134i) q^{41} +(-1.04979 + 2.03317i) q^{42} +(2.63427 + 2.63427i) q^{43} +(-3.65546 + 5.82336i) q^{44} +(-2.30025 + 0.745450i) q^{45} +(7.00937 + 0.589667i) q^{46} +10.2098 q^{47} +(5.37937 - 6.03028i) q^{48} +(-4.49619 + 4.49619i) q^{49} +(6.99150 - 1.05781i) q^{50} +(4.78664 - 6.81699i) q^{51} +(-4.10614 + 2.91620i) q^{52} +(-3.65503 + 3.65503i) q^{53} +(-5.46232 - 0.459521i) q^{54} +(7.66299 + 0.608996i) q^{55} +(-1.95034 + 1.15223i) q^{56} +(0.720293 + 1.73894i) q^{57} +(-10.6509 + 8.99790i) q^{58} +(5.24423 - 5.24423i) q^{59} +(-8.76023 - 2.21039i) q^{60} +(8.77111 - 3.63311i) q^{61} +(-4.01525 + 3.39211i) q^{62} +(-0.800139 - 0.331429i) q^{63} +(7.68438 - 2.22492i) q^{64} +(5.01510 + 2.56016i) q^{65} +(-8.72729 - 4.50617i) q^{66} -5.11009 q^{67} +(7.60146 - 3.19653i) q^{68} +10.0484i q^{69} +(2.15125 + 1.33657i) q^{70} +(7.58430 + 3.14152i) q^{71} +(2.44507 + 1.83755i) q^{72} +(5.76929 + 2.38972i) q^{73} +(1.30679 - 1.10398i) q^{74} +(2.34303 + 9.82571i) q^{75} +(-0.311309 + 1.83717i) q^{76} +(1.94688 + 1.94688i) q^{77} +(-4.64292 - 5.49585i) q^{78} +(-11.6727 + 4.83500i) q^{79} +(-6.18184 - 6.46412i) q^{80} -11.0748i q^{81} +(-17.5618 - 1.47740i) q^{82} +(4.85020 - 4.85020i) q^{83} +(-1.87375 - 2.63832i) q^{84} +(-7.10183 - 5.87911i) q^{85} +(-5.01938 + 1.60105i) q^{86} +(-14.0840 - 14.0840i) q^{87} +(-4.94588 - 8.37174i) q^{88} +1.79163i q^{89} +(0.555718 - 3.37415i) q^{90} +(0.771788 + 1.86326i) q^{91} +(-5.28879 + 8.42536i) q^{92} +(-5.30949 - 5.30949i) q^{93} +(-6.62430 + 12.8296i) q^{94} +(1.98183 - 0.642257i) q^{95} +(4.08739 + 10.6723i) q^{96} +(-5.86683 - 2.43012i) q^{97} +(-2.73268 - 8.56711i) q^{98} +(1.42264 - 3.43457i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 16 q^{6} - 16 q^{9} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 16 q^{16} - 20 q^{20} + 24 q^{26} - 16 q^{31} - 40 q^{34} - 8 q^{36} + 32 q^{39} + 56 q^{40} - 32 q^{41} - 24 q^{44} + 32 q^{46} - 16 q^{49}+ \cdots - 160 q^{96}+O(q^{100}) \) 416 * q - 16 * q^6 - 16 * q^9 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 16 * q^16 - 20 * q^20 + 24 * q^26 - 16 * q^31 - 40 * q^34 - 8 * q^36 + 32 * q^39 + 56 * q^40 - 32 * q^41 - 24 * q^44 + 32 * q^46 - 16 * q^49 - 48 * q^50 - 64 * q^54 - 8 * q^56 - 40 * q^60 + 72 * q^65 - 112 * q^66 - 24 * q^70 + 48 * q^71 - 8 * q^74 - 40 * q^76 - 16 * q^79 - 56 * q^80 - 32 * q^84 + 96 * q^86 - 148 * q^90 + 40 * q^94 - 8 * q^95 - 160 * q^96

Introduction

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