LMFDB - Embedded newform 840.2.dc.e.53.147

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(53,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 6, 6, 9, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.53"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.dc (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [704,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$704$
Relative dimension:	$176$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			53.147
Character	$\chi$	$=$	840.53
Dual form			840.2.dc.e.317.147

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.15997 + 0.808999i) q^{2} +(-1.62994 - 0.585913i) q^{3} +(0.691042 + 1.87682i) q^{4} +(-1.18933 - 1.89354i) q^{5} +(-1.41667 - 1.99826i) q^{6} +(-0.390444 + 2.61678i) q^{7} +(-0.716761 + 2.73610i) q^{8} +(2.31341 + 1.91001i) q^{9} +(0.152283 - 3.15861i) q^{10} +(1.80988 - 3.13480i) q^{11} +(-0.0267027 - 3.46400i) q^{12} +(-3.53835 + 3.53835i) q^{13} +(-2.56988 + 2.71951i) q^{14} +(0.829095 + 3.78320i) q^{15} +(-3.04492 + 2.59393i) q^{16} +(-0.454220 + 0.121708i) q^{17} +(1.13829 + 4.08709i) q^{18} +(-1.11463 - 1.93060i) q^{19} +(2.73195 - 3.54068i) q^{20} +(2.16961 - 4.03643i) q^{21} +(4.63544 - 2.17207i) q^{22} +(-5.95804 - 1.59645i) q^{23} +(2.77140 - 4.03972i) q^{24} +(-2.17097 + 4.50410i) q^{25} +(-6.96688 + 1.24184i) q^{26} +(-2.65162 - 4.46866i) q^{27} +(-5.18105 + 1.07551i) q^{28} +5.01369i q^{29} +(-2.09888 + 5.05912i) q^{30} +(-3.14658 + 5.45004i) q^{31} +(-5.63049 + 0.545528i) q^{32} +(-4.78671 + 4.04910i) q^{33} +(-0.625341 - 0.226286i) q^{34} +(5.41935 - 2.37291i) q^{35} +(-1.98608 + 5.66176i) q^{36} +(-2.03682 + 7.60153i) q^{37} +(0.268917 - 3.14116i) q^{38} +(7.84046 - 3.69413i) q^{39} +(6.03338 - 1.89692i) q^{40} +3.45830i q^{41} +(5.78214 - 2.92692i) q^{42} +(-8.67614 + 8.67614i) q^{43} +(7.13415 + 1.23054i) q^{44} +(0.865252 - 6.65217i) q^{45} +(-5.61960 - 6.67188i) q^{46} +(1.02243 - 3.81577i) q^{47} +(6.48286 - 2.44389i) q^{48} +(-6.69511 - 2.04341i) q^{49} +(-6.16206 + 3.46829i) q^{50} +(0.811661 + 0.0677568i) q^{51} +(-9.08599 - 4.19570i) q^{52} +(1.80177 - 0.482783i) q^{53} +(0.539343 - 7.32865i) q^{54} +(-8.08840 + 0.301252i) q^{55} +(-6.87993 - 2.94390i) q^{56} +(0.685619 + 3.79983i) q^{57} +(-4.05607 + 5.81572i) q^{58} +(-9.17243 - 5.29571i) q^{59} +(-6.52745 + 4.17041i) q^{60} +(6.15442 - 3.55326i) q^{61} +(-8.05900 + 3.77628i) q^{62} +(-5.90133 + 5.30795i) q^{63} +(-6.97251 - 3.92226i) q^{64} +(10.9083 + 2.49172i) q^{65} +(-8.82813 + 0.824379i) q^{66} +(13.6095 - 3.64664i) q^{67} +(-0.542309 - 0.768384i) q^{68} +(8.77587 + 6.09302i) q^{69} +(8.20594 + 1.63175i) q^{70} -1.40104i q^{71} +(-6.88414 + 4.96071i) q^{72} +(7.71519 - 2.06728i) q^{73} +(-8.51227 + 7.16973i) q^{74} +(6.17756 - 6.06941i) q^{75} +(2.85313 - 3.42609i) q^{76} +(7.49643 + 5.96001i) q^{77} +(12.0832 + 2.05786i) q^{78} +(13.2759 - 7.66486i) q^{79} +(8.53313 + 2.68063i) q^{80} +(1.70374 + 8.83727i) q^{81} +(-2.79776 + 4.01151i) q^{82} +(-2.69687 - 2.69687i) q^{83} +(9.07496 + 1.28262i) q^{84} +(0.770677 + 0.715331i) q^{85} +(-17.0830 + 3.04504i) q^{86} +(2.93759 - 8.17202i) q^{87} +(7.27987 + 7.19890i) q^{88} +(3.58068 + 6.20191i) q^{89} +(6.38526 - 7.01630i) q^{90} +(-7.87756 - 10.6406i) q^{91} +(-1.12100 - 12.2854i) q^{92} +(8.32199 - 7.03961i) q^{93} +(4.27294 - 3.59902i) q^{94} +(-2.32999 + 4.40672i) q^{95} +(9.49699 + 2.40980i) q^{96} +(4.12334 - 4.12334i) q^{97} +(-6.11298 - 7.78662i) q^{98} +(10.1745 - 3.79520i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 704 q - 16 q^{6} - 24 q^{7} + 12 q^{10} + 10 q^{12} + 32 q^{15} - 72 q^{16} + 6 q^{18} + 64 q^{22} - 8 q^{25} + 24 q^{28} + 8 q^{30} - 16 q^{31} + 44 q^{33} - 240 q^{36} + 16 q^{40} - 78 q^{42} - 8 q^{46}+ \cdots - 80 q^{97}+O(q^{100}) $ 704 * q - 16 * q^6 - 24 * q^7 + 12 * q^10 + 10 * q^12 + 32 * q^15 - 72 * q^16 + 6 * q^18 + 64 * q^22 - 8 * q^25 + 24 * q^28 + 8 * q^30 - 16 * q^31 + 44 * q^33 - 240 * q^36 + 16 * q^40 - 78 * q^42 - 8 * q^46 - 20 * q^48 - 60 * q^52 + 272 * q^55 + 8 * q^57 - 20 * q^58 - 14 * q^60 + 12 * q^63 - 84 * q^66 + 112 * q^70 - 38 * q^72 + 104 * q^73 - 64 * q^76 - 16 * q^78 - 168 * q^81 - 72 * q^82 - 64 * q^87 + 52 * q^88 - 44 * q^90 + 40 * q^96 - 80 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	1.15997	+	0.808999i	0.820220	+	0.572048i
$2$	1.15997	+	0.808999i	0.820220	+	0.572048i
$3$	−1.62994	−	0.585913i	−0.941047	−	0.338277i
$3$	−1.62994	−	0.585913i	−0.941047	−	0.338277i
$4$	0.691042	+	1.87682i	0.345521	+	0.938411i
$5$	−1.18933	−	1.89354i	−0.531886	−	0.846816i
$5$	−1.18933	−	1.89354i	−0.531886	−	0.846816i
$6$	−1.41667	−	1.99826i	−0.578354	−	0.815786i
$7$	−0.390444	+	2.61678i	−0.147574	+	0.989051i
$7$	−0.390444	+	2.61678i	−0.147574	+	0.989051i
$8$	−0.716761	+	2.73610i	−0.253413	+	0.967358i
$9$	2.31341	+	1.91001i	0.771137	+	0.636669i
$10$	0.152283	−	3.15861i	0.0481560	−	0.998840i
$11$	1.80988	−	3.13480i	0.545698	−	0.945176i	−0.452865	−	0.891579i	$-0.649598\pi$
$11$	1.80988	−	3.13480i	0.545698	−	0.945176i	0.998563	−	0.0535972i	$-0.0170687\pi$
$12$	−0.0267027	−	3.46400i	−0.00770841	−	0.999970i
$13$	−3.53835	+	3.53835i	−0.981361	+	0.981361i	−0.999829	−	0.0184688i	$-0.994121\pi$
$13$	−3.53835	+	3.53835i	−0.981361	+	0.981361i	0.0184688	+	0.999829i	$0.494121\pi$
$14$	−2.56988	+	2.71951i	−0.686828	+	0.726820i
$15$	0.829095	+	3.78320i	0.214071	+	0.976818i
$16$	−3.04492	+	2.59393i	−0.761230	+	0.648482i
$17$	−0.454220	+	0.121708i	−0.110164	+	0.0295185i	−0.313480	−	0.949595i	$-0.601495\pi$
$17$	−0.454220	+	0.121708i	−0.110164	+	0.0295185i	0.203316	+	0.979113i	$0.434828\pi$
$18$	1.13829	+	4.08709i	0.268296	+	0.963336i
$19$	−1.11463	−	1.93060i	−0.255714	−	0.442909i	0.709375	−	0.704831i	$-0.248977\pi$
$19$	−1.11463	−	1.93060i	−0.255714	−	0.442909i	−0.965089	+	0.261922i	$0.915644\pi$
$20$	2.73195	−	3.54068i	0.610883	−	0.791721i
$21$	2.16961	−	4.03643i	0.473447	−	0.880822i
$22$	4.63544	−	2.17207i	0.988279	−	0.463087i
$23$	−5.95804	−	1.59645i	−1.24234	−	0.332883i	−0.422965	−	0.906146i	$-0.639011\pi$
$23$	−5.95804	−	1.59645i	−1.24234	−	0.332883i	−0.819372	+	0.573263i	$0.805677\pi$
$24$	2.77140	−	4.03972i	0.565709	−	0.824605i
$25$	−2.17097	+	4.50410i	−0.434194	+	0.900819i
$26$	−6.96688	+	1.24184i	−1.36632	+	0.243546i
$27$	−2.65162	−	4.46866i	−0.510305	−	0.859993i
$28$	−5.18105	+	1.07551i	−0.979126	+	0.203253i
$29$			5.01369i			0.931020i	0.885043	+	0.465510i	$0.154129\pi$
$29$			5.01369i			0.931020i	−0.885043	+	0.465510i	$0.845871\pi$
$30$	−2.09888	+	5.05912i	−0.383202	+	0.923665i
$31$	−3.14658	+	5.45004i	−0.565142	+	0.978855i	0.431894	+	0.901924i	$0.357845\pi$
$31$	−3.14658	+	5.45004i	−0.565142	+	0.978855i	−0.997036	+	0.0769310i	$0.975488\pi$
$32$	−5.63049	+	0.545528i	−0.995339	+	0.0964367i
$33$	−4.78671	+	4.04910i	−0.833259	+	0.704858i
$34$	−0.625341	−	0.226286i	−0.107245	−	0.0388078i
$35$	5.41935	−	2.37291i	0.916037	−	0.401095i
$36$	−1.98608	+	5.66176i	−0.331013	+	0.943626i
$37$	−2.03682	+	7.60153i	−0.334852	+	1.24968i	0.569178	+	0.822214i	$0.307261\pi$
$37$	−2.03682	+	7.60153i	−0.334852	+	1.24968i	−0.904030	+	0.427469i	$0.859405\pi$
$38$	0.268917	−	3.14116i	0.0436241	−	0.509564i
$39$	7.84046	−	3.69413i	1.25548	−	0.591534i
$40$	6.03338	−	1.89692i	0.953961	−	0.299930i
$41$			3.45830i			0.540096i	0.962847	+	0.270048i	$0.0870395\pi$
$41$			3.45830i			0.540096i	−0.962847	+	0.270048i	$0.912960\pi$
$42$	5.78214	−	2.92692i	0.892204	−	0.451633i
$43$	−8.67614	+	8.67614i	−1.32310	+	1.32310i	−0.411844	+	0.911254i	$0.635115\pi$
$43$	−8.67614	+	8.67614i	−1.32310	+	1.32310i	−0.911254	+	0.411844i	$0.864885\pi$
$44$	7.13415	+	1.23054i	1.07551	+	0.185511i
$45$	0.865252	−	6.65217i	0.128984	−	0.991647i
$46$	−5.61960	−	6.67188i	−0.828564	−	0.983714i
$47$	1.02243	−	3.81577i	0.149137	−	0.556587i	−0.850399	−	0.526138i	$-0.823640\pi$
$47$	1.02243	−	3.81577i	0.149137	−	0.556587i	0.999536	−	0.0304492i	$-0.00969379\pi$
$48$	6.48286	−	2.44389i	0.935720	−	0.352744i
$49$	−6.69511	−	2.04341i	−0.956444	−	0.291916i
$50$	−6.16206	+	3.46829i	−0.871447	+	0.490490i
$51$	0.811661	+	0.0677568i	0.113655	+	0.00948785i
$52$	−9.08599	−	4.19570i	−1.26000	−	0.581839i
$53$	1.80177	−	0.482783i	0.247492	−	0.0663154i	−0.132940	−	0.991124i	$-0.542442\pi$
$53$	1.80177	−	0.482783i	0.247492	−	0.0663154i	0.380433	+	0.924809i	$0.375775\pi$
$54$	0.539343	−	7.32865i	0.0733953	−	0.997303i
$55$	−8.08840	+	0.301252i	−1.09064	+	0.0406209i
$56$	−6.87993	−	2.94390i	−0.919369	−	0.393395i
$57$	0.685619	+	3.79983i	0.0908125	+	0.503300i
$58$	−4.05607	+	5.81572i	−0.532588	+	0.763641i
$59$	−9.17243	−	5.29571i	−1.19415	−	0.689442i	−0.234904	−	0.972019i	$-0.575478\pi$
$59$	−9.17243	−	5.29571i	−1.19415	−	0.689442i	−0.959245	+	0.282576i	$0.908811\pi$
$60$	−6.52745	+	4.17041i	−0.842691	+	0.538398i
$61$	6.15442	−	3.55326i	0.787993	−	0.454948i	−0.0512626	−	0.998685i	$-0.516325\pi$
$61$	6.15442	−	3.55326i	0.787993	−	0.454948i	0.839255	+	0.543737i	$0.182991\pi$
$62$	−8.05900	+	3.77628i	−1.02349	+	0.479588i
$63$	−5.90133	+	5.30795i	−0.743498	+	0.668738i
$64$	−6.97251	−	3.92226i	−0.871563	−	0.490283i
$65$	10.9083	+	2.49172i	1.35300	+	0.309059i
$66$	−8.82813	+	0.824379i	−1.08667	+	0.101474i
$67$	13.6095	−	3.64664i	1.66266	−	0.445508i	0.699543	−	0.714591i	$-0.253387\pi$
$67$	13.6095	−	3.64664i	1.66266	−	0.445508i	0.963117	+	0.269082i	$0.0867204\pi$
$68$	−0.542309	−	0.768384i	−0.0657646	−	0.0931803i
$69$	8.77587	+	6.09302i	1.05649	+	0.733513i
$70$	8.20594	+	1.63175i	0.980797	+	0.195031i
$71$		−	1.40104i		−	0.166272i	−0.996538	−	0.0831362i	$-0.973506\pi$
$71$		−	1.40104i		−	0.166272i	0.996538	−	0.0831362i	$-0.0264937\pi$
$72$	−6.88414	+	4.96071i	−0.811303	+	0.584625i
$73$	7.71519	−	2.06728i	0.902995	−	0.241957i	0.222693	−	0.974889i	$-0.428515\pi$
$73$	7.71519	−	2.06728i	0.902995	−	0.241957i	0.680302	+	0.732932i	$0.261849\pi$
$74$	−8.51227	+	7.16973i	−0.989532	+	0.833464i
$75$	6.17756	−	6.06941i	0.713323	−	0.700835i
$76$	2.85313	−	3.42609i	0.327276	−	0.392999i
$77$	7.49643	+	5.96001i	0.854297	+	0.679206i
$78$	12.0832	+	2.05786i	1.36815	+	0.233006i
$79$	13.2759	−	7.66486i	1.49366	−	0.862364i	0.493685	−	0.869641i	$-0.335649\pi$
$79$	13.2759	−	7.66486i	1.49366	−	0.862364i	0.999974	+	0.00727636i	$0.00231616\pi$
$80$	8.53313	+	2.68063i	0.954032	+	0.299703i
$81$	1.70374	+	8.83727i	0.189305	+	0.981918i
$82$	−2.79776	+	4.01151i	−0.308961	+	0.442997i
$83$	−2.69687	−	2.69687i	−0.296020	−	0.296020i	0.543433	−	0.839453i	$-0.317124\pi$
$83$	−2.69687	−	2.69687i	−0.296020	−	0.296020i	−0.839453	+	0.543433i	$0.817124\pi$
$84$	9.07496	+	1.28262i	0.990159	+	0.139945i
$85$	0.770677	+	0.715331i	0.0835917	+	0.0775885i
$86$	−17.0830	+	3.04504i	−1.84211	+	0.328355i
$87$	2.93759	−	8.17202i	0.314943	−	0.876133i
$88$	7.27987	+	7.19890i	0.776037	+	0.767406i
$89$	3.58068	+	6.20191i	0.379551	+	0.657401i	0.990997	−	0.133885i	$-0.0427452\pi$
$89$	3.58068	+	6.20191i	0.379551	+	0.657401i	−0.611446	+	0.791286i	$0.709412\pi$
$90$	6.38526	−	7.01630i	0.673065	−	0.739583i
$91$	−7.87756	−	10.6406i	−0.825793	−	1.11544i
$92$	−1.12100	−	12.2854i	−0.116872	−	1.28084i
$93$	8.32199	−	7.03961i	0.862950	−	0.729974i
$94$	4.27294	−	3.59902i	0.440720	−	0.371210i
$95$	−2.32999	+	4.40672i	−0.239052	+	0.452120i
$96$	9.49699	+	2.40980i	0.969283	+	0.245949i
$97$	4.12334	−	4.12334i	0.418662	−	0.418662i	−0.466080	−	0.884742i	$-0.654334\pi$
$97$	4.12334	−	4.12334i	0.418662	−	0.418662i	0.884742	+	0.466080i	$0.154334\pi$
$98$	−6.11298	−	7.78662i	−0.617504	−	0.786568i
$99$	10.1745	−	3.79520i	1.02257	−	0.381432i
$100$	−9.95362	−	0.962002i	−0.995362	−	0.0962002i
$101$	−4.16986	+	7.22242i	−0.414917	+	0.718657i	−0.995420	−	0.0956010i	$-0.969523\pi$
$101$	−4.16986	+	7.22242i	−0.414917	+	0.718657i	0.580503	+	0.814258i	$0.302856\pi$
$102$	0.886684	+	0.735228i	0.0877948	+	0.0727985i
$103$	−2.44576	+	9.12771i	−0.240988	+	0.899380i	0.734369	+	0.678750i	$0.237478\pi$
$103$	−2.44576	+	9.12771i	−0.240988	+	0.899380i	−0.975358	+	0.220630i	$0.929189\pi$
$104$	−7.14513	−	12.2174i	−0.700637	−	1.19802i
$105$	−10.2235	+	0.692435i	−0.997714	+	0.0675747i
$106$	2.48057	+	0.897619i	0.240934	+	0.0871845i
$107$	−0.476188	−	0.127594i	−0.0460348	−	0.0123350i	0.235728	−	0.971819i	$-0.424253\pi$
$107$	−0.476188	−	0.127594i	−0.0460348	−	0.0123350i	−0.281763	+	0.959484i	$0.590919\pi$
$108$	6.55449	−	8.06466i	0.630706	−	0.776022i
$109$	8.86257	−	15.3504i	0.848880	−	1.47030i	−0.0333278	−	0.999444i	$-0.510611\pi$
$109$	8.86257	−	15.3504i	0.848880	−	1.47030i	0.882208	−	0.470860i	$-0.156056\pi$
$110$	−9.62598	−	6.19406i	−0.917801	−	0.590581i
$111$	7.77374	−	11.1966i	0.737850	−	1.06274i
$112$	−5.59887	−	8.98068i	−0.529044	−	0.848595i
$113$	−0.307737	+	0.307737i	−0.0289494	+	0.0289494i	−0.721433	−	0.692484i	$-0.756516\pi$
$113$	−0.307737	+	0.307737i	−0.0289494	+	0.0289494i	0.692484	+	0.721433i	$0.256516\pi$
$114$	−2.27877	+	4.96234i	−0.213426	+	0.464766i
$115$	4.06316	+	13.1805i	0.378891	+	1.22909i
$116$	−9.40981	+	3.46467i	−0.873679	+	0.321687i
$117$	−14.9439	+	1.42738i	−1.38157	+	0.131962i
$118$	−6.35549	−	13.5633i	−0.585070	−	1.24861i
$119$	−0.141136	−	1.23611i	−0.0129379	−	0.113314i
$120$	−10.9455	−	0.443163i	−0.999181	−	0.0404551i
$121$	−1.05130	−	1.82090i	−0.0955723	−	0.165536i
$122$	10.0135	+	0.857262i	0.906580	+	0.0776129i
$123$	2.02626	−	5.63682i	0.182702	−	0.508255i
$124$	−12.4032	−	2.13937i	−1.11384	−	0.192121i
$125$	11.1107	−	1.24606i	0.993770	−	0.111451i
$126$	−11.1395	+	1.38287i	−0.992382	+	0.123196i
$127$	−6.14976	+	6.14976i	−0.545703	+	0.545703i	−0.925195	−	0.379492i	$-0.876099\pi$
$127$	−6.14976	+	6.14976i	−0.545703	+	0.545703i	0.379492	+	0.925195i	$0.376099\pi$
$128$	−4.91476	−	10.1904i	−0.434408	−	0.900716i
$129$	19.2251	−	9.05812i	1.69267	−	0.797523i
$130$	10.6374	+	11.7151i	0.932964	+	1.02748i
$131$	−1.51545	−	2.62483i	−0.132405	−	0.229333i	0.792198	−	0.610264i	$-0.208937\pi$
$131$	−1.51545	−	2.62483i	−0.132405	−	0.229333i	−0.924603	+	0.380931i	$0.875603\pi$
$132$	−10.9073	−	6.18570i	−0.949355	−	0.538396i
$133$	5.48715	−	2.16296i	0.475797	−	0.187552i
$134$	18.7366	+	6.78005i	1.61860	+	0.585707i
$135$	−5.30790	+	10.3357i	−0.456831	+	0.889553i
$136$	−0.00743787	−	1.33003i	−0.000637793	−	0.114049i
$137$	13.0607	−	3.49961i	1.11585	−	0.298992i	0.346649	−	0.937995i	$-0.387319\pi$
$137$	13.0607	−	3.49961i	1.11585	−	0.298992i	0.769204	+	0.639003i	$0.220653\pi$
$138$	5.25047	+	14.1674i	0.446949	+	1.20601i
$139$	−11.0070			−0.933598			−0.466799	−	0.884363i	$-0.654593\pi$
$139$	−11.0070			−0.933598			−0.466799	+	0.884363i	$0.654593\pi$
$140$	8.19852	+	8.53137i	0.692902	+	0.721032i
$141$	−3.90221	+	5.62042i	−0.328626	+	0.473325i
$142$	1.13344	−	1.62516i	0.0951159	−	0.136380i
$143$	4.68803	+	17.4960i	0.392033	+	1.46309i
$144$	−11.9986	+	0.184996i	−0.999881	+	0.0154164i
$145$	9.49362	−	5.96296i	0.788402	−	0.495197i
$146$	10.6218	+	3.84361i	0.879065	+	0.318099i
$147$	9.71536	+	7.25339i	0.801310	+	0.598250i
$148$	−15.6742	+	1.43022i	−1.28842	+	0.117563i
$149$	−16.5508	+	9.55563i	−1.35590	+	0.782828i	−0.989068	−	0.147460i	$-0.952890\pi$
$149$	−16.5508	+	9.55563i	−1.35590	+	0.782828i	−0.366830	+	0.930288i	$0.619557\pi$
$150$	12.0759	−	2.04267i	0.985994	−	0.166783i
$151$	−3.15829	+	5.47031i	−0.257018	+	0.445168i	−0.965442	−	0.260619i	$-0.916073\pi$
$151$	−3.15829	+	5.47031i	−0.257018	+	0.445168i	0.708424	+	0.705787i	$0.249407\pi$
$152$	6.08123	−	1.66597i	0.493253	−	0.135128i
$153$	−1.28326	−	0.586002i	−0.103745	−	0.0473755i
$154$	3.87396	+	12.9780i	0.312172	+	1.04580i
$155$	14.0622	−	0.523746i	1.12950	−	0.0420683i
$156$	12.3513	+	12.1623i	0.988896	+	0.973767i
$157$	1.82391	−	0.488715i	0.145564	−	0.0390037i	−0.185301	−	0.982682i	$-0.559326\pi$
$157$	1.82391	−	0.488715i	0.145564	−	0.0390037i	0.330865	+	0.943678i	$0.392659\pi$
$158$	21.6005	+	1.84923i	1.71844	+	0.147117i
$159$	−3.21965	−	0.268774i	−0.255335	−	0.0213152i
$160$	7.72951	+	10.0127i	0.611071	+	0.791575i
$161$	6.50385	−	14.9676i	0.512575	−	1.17961i
$162$	−5.17305	+	11.6293i	−0.406433	+	0.913681i
$163$	2.47344	+	0.662756i	0.193735	+	0.0519110i	0.354382	−	0.935101i	$-0.384691\pi$
$163$	2.47344	+	0.662756i	0.193735	+	0.0519110i	−0.160647	+	0.987012i	$0.551358\pi$
$164$	−6.49061	+	2.38983i	−0.506832	+	0.186614i
$165$	13.3601	+	4.24808i	1.04008	+	0.330712i
$166$	−0.946512	−	5.31003i	−0.0734636	−	0.412139i
$167$	−1.70262	−	1.70262i	−0.131753	−	0.131753i	0.638155	−	0.769908i	$-0.279698\pi$
$167$	−1.70262	−	1.70262i	−0.131753	−	0.131753i	−0.769908	+	0.638155i	$0.779698\pi$
$168$	9.48901	+	8.82943i	0.732093	+	0.681205i
$169$		−	12.0398i		−	0.926137i
$170$	0.315258	+	1.45324i	0.0241791	+	0.111458i
$171$	1.10885	−	6.59522i	0.0847962	−	0.504349i
$172$	−22.2791	−	10.2880i	−1.69877	−	0.784452i
$173$	−4.90870	+	18.3195i	−0.373202	+	1.39281i	0.482753	+	0.875756i	$0.339637\pi$
$173$	−4.90870	+	18.3195i	−0.373202	+	1.39281i	−0.855955	+	0.517051i	$0.827030\pi$
$174$	10.0187	−	7.10276i	0.759513	−	0.538459i
$175$	−10.9386	−	7.43955i	−0.826881	−	0.562377i
$176$	2.62050	+	14.2399i	0.197528	+	1.07337i
$177$	11.8477	+	14.0059i	0.890527	+	1.05275i
$178$	−0.863877	+	10.0908i	−0.0647503	+	0.756335i
$179$	−8.26123	−	4.76962i	−0.617473	−	0.356498i	0.158411	−	0.987373i	$-0.449363\pi$
$179$	−8.26123	−	4.76962i	−0.617473	−	0.356498i	−0.775885	+	0.630875i	$0.782696\pi$
$180$	13.0829	−	2.97301i	0.975139	−	0.221595i
$181$			14.7638i			1.09739i	0.836024	+	0.548693i	$0.184875\pi$
$181$			14.7638i			1.09739i	−0.836024	+	0.548693i	$0.815125\pi$
$182$	−0.529462	−	18.7157i	−0.0392463	−	1.38730i
$183$	−12.1132	+	2.18564i	−0.895436	+	0.161567i
$184$	8.63855	−	15.1575i	0.636842	−	1.11743i
$185$	16.8162	−	5.18395i	1.23635	−	0.381132i
$186$	15.3483	−	1.43323i	1.12539	−	0.105090i
$187$	−0.440552	+	1.64416i	−0.0322163	+	0.120233i
$188$	7.86806	−	0.717934i	0.573838	−	0.0523607i
$189$	12.7288	−	5.19397i	0.925885	−	0.377806i
$190$	−6.26774	+	3.22669i	−0.454710	+	0.234088i
$191$	7.08955	−	4.09316i	0.512982	−	0.296170i	−0.221077	−	0.975256i	$-0.570957\pi$
$191$	7.08955	−	4.09316i	0.512982	−	0.296170i	0.734059	+	0.679086i	$0.237624\pi$
$192$	9.06666	+	10.4783i	0.654330	+	0.756209i
$193$	−0.000137696	0	3.68955e-5i	−9.91158e−6	0	2.65580e-6i	−0.258824	−	0.965924i	$-0.583335\pi$
$193$	−0.000137696	0	3.68955e-5i	−9.91158e−6	0	2.65580e-6i	0.258814	+	0.965927i	$0.416668\pi$
$194$	8.11871	−	1.44716i	0.582890	−	0.103900i
$195$	−16.3199	−	10.4526i	−1.16869	−	0.748530i
$196$	−0.791479	−	13.9776i	−0.0565342	−	0.998401i
$197$	−3.78639	+	3.78639i	−0.269769	+	0.269769i	−0.829007	−	0.559238i	$-0.811094\pi$
$197$	−3.78639	+	3.78639i	−0.269769	+	0.269769i	0.559238	+	0.829007i	$0.311094\pi$
$198$	14.8723	+	3.82883i	1.05693	+	0.272103i
$199$	1.24696	+	0.719935i	0.0883949	+	0.0510348i	0.543546	−	0.839379i	$-0.317081\pi$
$199$	1.24696	+	0.719935i	0.0883949	+	0.0510348i	−0.455151	+	0.890414i	$0.650415\pi$
$200$	−10.7676	−	9.16836i	−0.761384	−	0.648301i
$201$	−24.3192	−	2.03015i	−1.71535	−	0.143196i
$202$	−10.6798	+	5.00434i	−0.751430	+	0.352104i
$203$	−13.1198	−	1.95757i	−0.920826	−	0.137394i
$204$	0.433724	+	1.57017i	0.0303668	+	0.109934i
$205$	6.54842	−	4.11307i	0.457362	−	0.287270i
$206$	−10.2213	+	8.60921i	−0.712152	+	0.599832i
$207$	−10.7342	−	15.0731i	−0.746076	−	1.04766i
$208$	1.59578	−	19.9522i	0.110647	−	1.38344i
$209$	−8.06937			−0.558170
$210$	−12.4191	−	7.46762i	−0.857001	−	0.515315i
$211$		−	7.47348i		−	0.514496i	−0.966345	−	0.257248i	$-0.917184\pi$
$211$		−	7.47348i		−	0.514496i	0.966345	−	0.257248i	$-0.0828157\pi$
$212$	2.15120	+	3.04798i	0.147745	+	0.209336i
$213$	−0.820886	+	2.28361i	−0.0562462	+	0.156470i
$214$	−0.449138	−	0.533240i	−0.0307024	−	0.0364515i
$215$	26.7474	+	6.10977i	1.82416	+	0.416683i
$216$	14.1273	−	4.05215i	0.961240	−	0.275714i
$217$	−13.0330	−	10.3618i	−0.884738	−	0.703408i
$218$	22.6988	−	10.6362i	1.53735	−	0.720372i
$219$	−13.7865	−	1.15089i	−0.931609	−	0.0777700i
$220$	−6.15482	−	14.9723i	−0.414958	−	1.00943i
$221$	1.17654	−	2.03783i	0.0791428	−	0.137079i
$222$	18.0753	−	6.69877i	1.21314	−	0.449592i
$223$	−1.16189	−	1.16189i	−0.0778058	−	0.0778058i	0.667133	−	0.744939i	$-0.267521\pi$
$223$	−1.16189	−	1.16189i	−0.0778058	−	0.0778058i	−0.744939	+	0.667133i	$0.767521\pi$
$224$	0.770859	−	14.9468i	0.0515052	−	0.998673i
$225$	−13.6252	+	6.27326i	−0.908347	+	0.418218i
$226$	−0.605923	+	0.108006i	−0.0403054	+	0.00718442i
$227$	6.21857	+	23.2080i	0.412741	+	1.54037i	0.789318	+	0.613985i	$0.210434\pi$
$227$	6.21857	+	23.2080i	0.412741	+	1.54037i	−0.376577	+	0.926385i	$0.622899\pi$
$228$	−6.65782	+	3.91263i	−0.440925	+	0.259120i
$229$	10.2919	+	17.8262i	0.680111	+	1.17799i	0.974947	+	0.222438i	$0.0714016\pi$
$229$	10.2919	+	17.8262i	0.680111	+	1.17799i	−0.294836	+	0.955548i	$0.595265\pi$
$230$	−5.94987	+	18.5760i	−0.392323	+	1.22487i
$231$	−8.72668	−	14.1067i	−0.574173	−	0.928154i
$232$	−13.7180	−	3.59362i	−0.900630	−	0.235933i
$233$	−13.6763	−	3.66454i	−0.895962	−	0.240072i	−0.218681	−	0.975796i	$-0.570175\pi$
$233$	−13.6763	−	3.66454i	−0.895962	−	0.240072i	−0.677281	+	0.735724i	$0.736842\pi$
$234$	−18.4892	−	10.4339i	−1.20868	−	0.682085i
$235$	−8.44132	+	2.60221i	−0.550651	+	0.169749i
$236$	3.60056	−	20.8746i	0.234377	−	1.35882i
$237$	−26.1299	+	4.71473i	−1.69732	+	0.306254i
$238$	0.836302	−	1.54803i	0.0542094	−	0.100344i
$239$	15.8251			1.02364			0.511820	−	0.859093i	$-0.328972\pi$
$239$	15.8251			1.02364			0.511820	+	0.859093i	$0.328972\pi$
$240$	−12.3379	−	9.36894i	−0.796406	−	0.604762i
$241$	9.15358	−	15.8545i	0.589634	−	1.02128i	−0.404647	−	0.914473i	$-0.632605\pi$
$241$	9.15358	−	15.8545i	0.589634	−	1.02128i	0.994280	−	0.106802i	$-0.0340612\pi$
$242$	0.253636	−	2.96268i	0.0163044	−	0.190448i
$243$	2.40087	−	15.4025i	0.154016	−	0.988068i
$244$	10.9218	+	9.09530i	0.699196	+	0.582267i
$245$	4.09344	+	15.1077i	0.261520	+	0.965198i
$246$	6.91058	−	4.89928i	0.440603	−	0.312367i
$247$	10.7751	+	2.88717i	0.685601	+	0.183706i
$248$	−12.6565	−	12.5157i	−0.803689	−	0.794750i
$249$	2.81560	+	5.97586i	0.178432	+	0.378705i
$250$	13.8961	+	7.54314i	0.878865	+	0.477070i
$251$	9.77314			0.616875			0.308438	−	0.951245i	$-0.400194\pi$
$251$	9.77314			0.616875			0.308438	+	0.951245i	$0.400194\pi$
$252$	−14.0401	−	7.40773i	−0.884446	−	0.466643i
$253$	−15.7879	+	15.7879i	−0.992574	+	0.992574i
$254$	−12.1087	+	2.15836i	−0.759764	+	0.135428i
$255$	−0.837036	−	1.61750i	−0.0524172	−	0.101292i
$256$	2.54309	−	15.7966i	0.158943	−	0.987288i
$257$	−0.921736	+	3.43996i	−0.0574963	+	0.214579i	−0.988697	−	0.149928i	$-0.952096\pi$
$257$	−0.921736	+	3.43996i	−0.0574963	+	0.214579i	0.931201	+	0.364507i	$0.118762\pi$
$258$	29.6284	+	5.04593i	1.84458	+	0.314146i
$259$	−19.0963	−	8.29789i	−1.18659	−	0.515606i
$260$	2.86156	+	22.1948i	0.177467	+	1.37646i
$261$	−9.57619	+	11.5987i	−0.592751	+	0.717944i
$262$	0.365618	−	4.27071i	0.0225880	−	0.263845i
$263$	−7.06174	−	26.3548i	−0.435446	−	1.62511i	−0.739997	−	0.672610i	$-0.765173\pi$
$263$	−7.06174	−	26.3548i	−0.435446	−	1.62511i	0.304552	−	0.952496i	$-0.401493\pi$
$264$	−7.64783	−	15.9992i	−0.470691	−	0.984680i
$265$	−3.05708	−	2.83753i	−0.187795	−	0.174308i
$266$	8.11474	+	1.93014i	0.497547	+	0.118345i
$267$	−2.20251	−	12.2067i	−0.134791	−	0.747039i
$268$	16.2488	+	23.0225i	0.992554	+	1.40633i
$269$	16.8628	+	9.73576i	1.02815	+	0.593600i	0.916453	−	0.400143i	$-0.131040\pi$
$269$	16.8628	+	9.73576i	1.02815	+	0.593600i	0.111692	+	0.993743i	$0.464373\pi$
$270$	−14.5185	+	7.69495i	−0.883570	+	0.468299i
$271$	9.60297	+	16.6328i	0.583339	+	1.01037i	0.995080	+	0.0990721i	$0.0315875\pi$
$271$	9.60297	+	16.6328i	0.583339	+	1.01037i	−0.411741	+	0.911301i	$0.635079\pi$
$272$	1.06736	−	1.54880i	0.0647183	−	0.0939099i
$273$	6.60548	+	21.9591i	0.399782	+	1.32903i
$274$	17.9812	+	6.50668i	1.08628	+	0.393083i
$275$	10.1902	+	14.9574i	0.614495	+	0.901965i
$276$	−5.37101	+	20.6813i	−0.323297	+	1.24487i
$277$	−11.5679	+	3.09960i	−0.695045	+	0.186237i	−0.589010	−	0.808126i	$-0.700482\pi$
$277$	−11.5679	+	3.09960i	−0.695045	+	0.186237i	−0.106035	+	0.994362i	$0.533816\pi$
$278$	−12.7677	−	8.90462i	−0.765756	−	0.534063i
$279$	−17.6889	+	6.59819i	−1.05901	+	0.395023i
$280$	2.60815	+	16.5287i	0.155866	+	0.987778i
$281$		−	4.95569i		−	0.295632i	−0.989015	−	0.147816i	$-0.952776\pi$
$281$		−	4.95569i		−	0.295632i	0.989015	−	0.147816i	$-0.0472243\pi$
$282$	−9.07335	+	3.36261i	−0.540310	+	0.200241i
$283$	0.837251	+	3.12466i	0.0497694	+	0.185742i	0.986336	−	0.164749i	$-0.0526814\pi$
$283$	0.837251	+	3.12466i	0.0497694	+	0.185742i	−0.936566	+	0.350491i	$0.886015\pi$
$284$	2.62950	−	0.968176i	0.156032	−	0.0574506i
$285$	6.37970	−	5.81752i	0.377901	−	0.344600i
$286$	−8.71625	+	24.0873i	−0.515403	+	1.42431i
$287$	−9.04962	−	1.35027i	−0.534182	−	0.0797040i
$288$	−14.0676	−	9.49224i	−0.828941	−	0.559336i
$289$	−14.5309	+	8.38944i	−0.854761	+	0.493496i
$290$	15.8363	+	0.763498i	0.929940	+	0.0448342i
$291$	−9.13672	+	4.30488i	−0.535604	+	0.252357i
$292$	9.21144	+	13.0515i	0.539059	+	0.763779i
$293$	−8.73789	−	8.73789i	−0.510473	−	0.510473i	0.404198	−	0.914671i	$-0.367551\pi$
$293$	−8.73789	−	8.73789i	−0.510473	−	0.510473i	−0.914671	+	0.404198i	$0.867551\pi$
$294$	5.40151	+	16.2734i	0.315022	+	0.949084i
$295$	0.881467	+	23.6667i	0.0513210	+	1.37793i
$296$	−19.3386	−	11.0214i	−1.12404	−	0.640608i
$297$	−18.8074	+	0.224591i	−1.09132	+	0.0130321i
$298$	−26.9289	−	2.30540i	−1.55995	−	0.133548i
$299$	26.7304	−	15.4328i	1.54586	−	0.892502i
$300$	15.6602	+	7.39996i	0.904140	+	0.427237i
$301$	−19.3160	−	26.0911i	−1.11336	−	1.50387i
$302$	−8.08898	+	3.79033i	−0.465469	+	0.218109i
$303$	11.0283	−	9.32893i	0.633562	−	0.535933i
$304$	8.40179	+	2.98725i	0.481876	+	0.171330i
$305$	−14.0479	−	7.42762i	−0.804380	−	0.425304i
$306$	−1.01446	−	1.71790i	−0.0579929	−	0.0982057i
$307$	−3.26352	−	3.26352i	−0.186259	−	0.186259i	0.607818	−	0.794077i	$-0.292045\pi$
$307$	−3.26352	−	3.26352i	−0.186259	−	0.186259i	−0.794077	+	0.607818i	$0.792045\pi$
$308$	−6.00553	+	18.1881i	−0.342197	+	1.03636i
$309$	9.33449	−	13.4446i	0.531021	−	0.764838i
$310$	16.7354	+	10.7688i	0.950505	+	0.611625i
$311$	20.5422	+	11.8600i	1.16484	+	0.672522i	0.952460	−	0.304665i	$-0.0985445\pi$
$311$	20.5422	+	11.8600i	1.16484	+	0.672522i	0.212382	+	0.977187i	$0.431878\pi$
$312$	4.48778	+	24.1001i	0.254070	+	1.36440i
$313$	−0.622980	+	2.32499i	−0.0352129	+	0.131416i	−0.981295	−	0.192511i	$-0.938337\pi$
$313$	−0.622980	+	2.32499i	−0.0352129	+	0.131416i	0.946082	+	0.323928i	$0.105003\pi$
$314$	2.51104	+	0.908647i	0.141706	+	0.0512779i
$315$	17.0694	+	4.86147i	0.961754	+	0.273913i
$316$	23.5598	+	19.6198i	1.32534	+	1.10370i
$317$	−3.19701	−	0.856636i	−0.179562	−	0.0481135i	0.167918	−	0.985801i	$-0.446296\pi$
$317$	−3.19701	−	0.856636i	−0.179562	−	0.0481135i	−0.347480	+	0.937688i	$0.612962\pi$
$318$	−3.51725	−	2.91646i	−0.197237	−	0.163547i
$319$	15.7169	+	9.07416i	0.879978	+	0.508055i
$320$	0.865686	+	17.8676i	0.0483933	+	0.998828i
$321$	0.701399	+	0.486976i	0.0391483	+	0.0271803i
$322$	19.6530	−	12.1003i	1.09522	−	0.674322i
$323$	0.741256	+	0.741256i	0.0412446	+	0.0412446i
$324$	−15.4086	+	9.30455i	−0.856034	+	0.516919i
$325$	−8.25541	−	23.6187i	−0.457928	−	1.31013i
$326$	2.33293	+	2.76978i	0.129209	+	0.153404i
$327$	−23.4395	+	19.8276i	−1.29621	+	1.09647i
$328$	−9.46226	−	2.47878i	−0.522466	−	0.136867i
$329$	9.58584	+	4.16533i	0.528484	+	0.229642i
$330$	12.0606	+	15.7359i	0.663914	+	0.866235i
$331$	13.9873	−	8.07560i	0.768814	−	0.443875i	−0.0636375	−	0.997973i	$-0.520270\pi$
$331$	13.9873	−	8.07560i	0.768814	−	0.443875i	0.832451	+	0.554098i	$0.186937\pi$
$332$	3.19789	−	6.92519i	0.175507	−	0.380069i
$333$	−19.2310	+	13.6951i	−1.05385	+	0.750488i
$334$	−0.597564	−	3.35240i	−0.0326973	−	0.183435i
$335$	−23.0912	−	21.4329i	−1.26161	−	1.17101i
$336$	3.86393	+	17.9184i	0.210795	+	0.977530i
$337$	−0.560049	+	0.560049i	−0.0305078	+	0.0305078i	−0.722196	−	0.691688i	$-0.756867\pi$
$337$	−0.560049	+	0.560049i	−0.0305078	+	0.0305078i	0.691688	+	0.722196i	$0.256867\pi$
$338$	9.74017	−	13.9657i	0.529795	−	0.759636i
$339$	0.681900	−	0.321286i	0.0370357	−	0.0174498i
$340$	−0.809978	+	1.94075i	−0.0439272	+	0.105252i
$341$	11.3898	+	19.7278i	0.616794	+	1.06832i
$342$	6.62176	−	6.75316i	0.358064	−	0.365169i
$343$	7.96123	−	16.7218i	0.429866	−	0.902893i
$344$	−17.5201	−	29.9575i	−0.944619	−	1.61520i
$345$	1.09992	−	23.8641i	0.0592175	−	1.28480i
$346$	−20.5144	+	17.2789i	−1.10286	+	0.928919i
$347$	−0.241294	−	0.900520i	−0.0129533	−	0.0483424i	0.959147	−	0.282909i	$-0.0912995\pi$
$347$	−0.241294	−	0.900520i	−0.0129533	−	0.0483424i	−0.972100	+	0.234567i	$0.924633\pi$
$348$	17.3674	−	0.133879i	0.930992	−	0.00717668i
$349$	−24.9120			−1.33351			−0.666754	−	0.745278i	$-0.732317\pi$
$349$	−24.9120			−1.33351			−0.666754	+	0.745278i	$0.732317\pi$
$350$	−6.66982	−	17.4789i	−0.356517	−	0.934289i
$351$	25.1940	+	6.42929i	1.34476	+	0.343170i
$352$	−8.48036	+	18.6378i	−0.452005	+	0.993396i
$353$	0.287477	+	1.07288i	0.0153009	+	0.0571036i	0.973154	−	0.230154i	$-0.0739230\pi$
$353$	0.287477	+	1.07288i	0.0153009	+	0.0571036i	−0.957853	+	0.287258i	$0.907256\pi$
$354$	2.41214	+	25.8312i	0.128204	+	1.37291i
$355$	−2.65292	+	1.66630i	−0.140802	+	0.0884381i
$356$	−9.16549	+	11.0061i	−0.485770	+	0.583321i
$357$	−0.494213	+	2.09749i	−0.0261565	+	0.111011i
$358$	−5.72413	−	12.2159i	−0.302530	−	0.645632i
$359$	−7.84472	−	13.5874i	−0.414028	−	0.717118i	0.581298	−	0.813691i	$-0.302545\pi$
$359$	−7.84472	−	13.5874i	−0.414028	−	0.717118i	−0.995326	+	0.0965730i	$0.969212\pi$
$360$	17.5808	+	7.13543i	0.926591	+	0.376070i
$361$	7.01520	−	12.1507i	0.369221	−	0.639509i
$362$	−11.9439	+	17.1255i	−0.627758	+	0.900098i
$363$	0.646661	+	3.58392i	0.0339409	+	0.188107i
$364$	14.5268	−	22.1379i	0.761411	−	1.16034i
$365$	−13.0904	−	12.1503i	−0.685183	−	0.635977i
$366$	−15.8191	−	7.26433i	−0.826879	−	0.379712i
$367$	−3.73211	−	13.9284i	−0.194814	−	0.727057i	−0.992315	−	0.123739i	$-0.960511\pi$
$367$	−3.73211	−	13.9284i	−0.194814	−	0.727057i	0.797500	−	0.603318i	$-0.206155\pi$
$368$	22.2828	−	10.5936i	1.16157	−	0.552232i
$369$	−6.60538	+	8.00047i	−0.343862	+	0.416488i
$370$	23.7001	+	7.59111i	1.23211	+	0.394643i
$371$	0.559849	+	4.90335i	0.0290659	+	0.254569i
$372$	18.9629	+	10.7542i	0.983183	+	0.557580i
$373$	7.28565	+	1.95218i	0.377237	+	0.101080i	0.442455	−	0.896791i	$-0.354108\pi$
$373$	7.28565	+	1.95218i	0.377237	+	0.101080i	−0.0652182	+	0.997871i	$0.520774\pi$
$374$	−1.84115	+	1.55077i	−0.0952036	+	0.0801882i
$375$	−18.8398	−	4.47889i	−0.972885	−	0.231289i
$376$	9.70749	+	5.53247i	0.500626	+	0.285316i
$377$	−17.7402	−	17.7402i	−0.913666	−	0.913666i
$378$	18.9669	+	4.27277i	0.975552	+	0.219768i
$379$	34.6937			1.78209			0.891047	−	0.453910i	$-0.149971\pi$
$379$	34.6937			1.78209			0.891047	+	0.453910i	$0.149971\pi$
$380$	−9.88075	−	1.32775i	−0.506872	−	0.0681120i
$381$	13.6270	−	6.42051i	0.698130	−	0.328933i
$382$	11.5350	+	0.987518i	0.590182	+	0.0505258i
$383$	−6.55796	−	1.75720i	−0.335096	−	0.0897888i	0.0873475	−	0.996178i	$-0.472161\pi$
$383$	−6.55796	−	1.75720i	−0.335096	−	0.0897888i	−0.422444	+	0.906389i	$0.638828\pi$
$384$	2.04006	+	19.4894i	0.104106	+	0.994566i
$385$	2.36975	−	21.2832i	0.120774	−	1.08469i
$386$	−0.000189571	0	6.85983e-5i	−9.64892e−6	0	3.49156e-6i
$387$	−36.6430	+	3.49999i	−1.86267	+	0.177915i
$388$	10.5882	+	4.88938i	0.537533	+	0.248220i
$389$	−13.1303	−	7.58077i	−0.665732	−	0.384360i	0.128726	−	0.991680i	$-0.458911\pi$
$389$	−13.1303	−	7.58077i	−0.665732	−	0.384360i	−0.794457	+	0.607320i	$0.792245\pi$
$390$	−10.4743	−	25.3275i	−0.530389	−	1.28251i
$391$	2.90056			0.146688
$392$	10.3898	−	16.8539i	0.524763	−	0.851248i
$393$	0.932166	+	5.16624i	0.0470215	+	0.260602i
$394$	−7.45528	+	1.32890i	−0.375591	+	0.0669490i
$395$	−30.3032	−	16.0224i	−1.52472	−	0.806174i
$396$	14.1539	+	16.4730i	0.711260	+	0.827801i
$397$	−4.50622	+	16.8175i	−0.226161	+	0.844044i	0.755775	+	0.654831i	$0.227260\pi$
$397$	−4.50622	+	16.8175i	−0.226161	+	0.844044i	−0.981936	+	0.189213i	$0.939406\pi$
$398$	0.864009	+	1.84389i	0.0433089	+	0.0924260i
$399$	−10.2110	+	0.310496i	−0.511191	+	0.0155442i
$400$	−5.07286	−	19.3460i	−0.253643	−	0.967298i
$401$	−31.6286	+	18.2608i	−1.57946	+	0.911901i	−0.584524	+	0.811377i	$0.698719\pi$
$401$	−31.6286	+	18.2608i	−1.57946	+	0.911901i	−0.994935	+	0.100524i	$0.967948\pi$
$402$	−26.5671	−	22.0291i	−1.32505	−	1.09871i
$403$	−8.15043	−	30.4178i	−0.406002	−	1.51522i
$404$	−16.4367	−	2.83510i	−0.817758	−	0.141051i
$405$	14.7074	−	13.7366i	0.730815	−	0.682575i
$406$	−13.6348	−	12.8846i	−0.676684	−	0.639451i
$407$	20.1428	+	20.1428i	0.998444	+	0.998444i
$408$	−0.767157	+	2.17222i	−0.0379799	+	0.107541i
$409$	−25.0552	−	14.4656i	−1.23890	−	0.715279i	−0.270031	−	0.962852i	$-0.587034\pi$
$409$	−25.0552	−	14.4656i	−1.23890	−	0.715279i	−0.968869	+	0.247572i	$0.920367\pi$
$410$	10.9234	+	0.526639i	0.539469	+	0.0260088i
$411$	−23.3387	−	1.94830i	−1.15121	−	0.0961023i
$412$	−18.8212	+	1.71737i	−0.927254	+	0.0846088i
$413$	17.4390	−	21.9346i	0.858119	−	1.07933i
$414$	−0.257105	−	26.1683i	−0.0126360	−	1.28610i
$415$	−1.89914	+	8.31409i	−0.0932253	+	0.408123i
$416$	17.9923	−	21.8529i	0.882147	−	1.07143i
$417$	17.9407	+	6.44912i	0.878559	+	0.315815i
$418$	−9.36019	−	6.52811i	−0.457822	−	0.319300i
$419$			38.2984i			1.87100i	0.353327	+	0.935500i	$0.385050\pi$
$419$			38.2984i			1.87100i	−0.353327	+	0.935500i	$0.614950\pi$
$420$	−8.36447	−	18.7092i	−0.408144	−	0.912917i
$421$		−	7.79263i		−	0.379790i	−0.981804	−	0.189895i	$-0.939185\pi$
$421$		−	7.79263i		−	0.379790i	0.981804	−	0.189895i	$-0.0608147\pi$
$422$	6.04604	−	8.66898i	0.294316	−	0.421999i
$423$	9.65345	−	6.87459i	0.469367	−	0.334254i
$424$	0.0295041	+	5.27587i	0.00143285	+	0.256219i
$425$	0.437913	−	2.31007i	0.0212419	−	0.112055i
$426$	−2.79963	+	1.98481i	−0.135643	+	0.0961644i
$427$	6.89515	+	17.4921i	0.333680	+	0.846504i
$428$	−0.0895943	−	0.981893i	−0.00433071	−	0.0474616i
$429$	2.60991	−	31.2641i	0.126007	−	1.50945i
$430$	26.0833	+	28.7258i	1.25785	+	1.38528i
$431$	−27.1326	−	15.6650i	−1.30693	−	0.754558i	−0.325350	−	0.945594i	$-0.605482\pi$
$431$	−27.1326	−	15.6650i	−1.30693	−	0.754558i	−0.981583	+	0.191036i	$0.938815\pi$
$432$	19.6654	+	6.72859i	0.946150	+	0.323729i
$433$	3.67103	+	3.67103i	0.176418	+	0.176418i	0.789792	−	0.613374i	$-0.210188\pi$
$433$	3.67103	+	3.67103i	0.176418	+	0.176418i	−0.613374	+	0.789792i	$0.710188\pi$
$434$	−6.73511	−	22.5631i	−0.323296	−	1.08306i
$435$	−18.9678	+	4.15683i	−0.909437	+	0.199305i
$436$	34.9344	+	6.02568i	1.67306	+	0.288578i
$437$	3.55891	+	13.2820i	0.170246	+	0.635365i
$438$	−15.0609	−	12.4883i	−0.719636	−	0.596714i
$439$	−20.2878	+	11.7132i	−0.968284	+	0.559039i	−0.898713	−	0.438538i	$-0.855496\pi$
$439$	−20.2878	+	11.7132i	−0.968284	+	0.559039i	−0.0695713	+	0.997577i	$0.522163\pi$
$440$	4.97319	−	22.3466i	0.237088	−	1.06533i
$441$	−11.5856	−	17.5150i	−0.551695	−	0.834046i
$442$	3.01335	−	1.41199i	0.143330	−	0.0671617i
$443$	4.11963	−	15.3747i	0.195730	−	0.730473i	−0.796347	−	0.604840i	$-0.793237\pi$
$443$	4.11963	−	15.3747i	0.195730	−	0.730473i	0.992077	−	0.125633i	$-0.0400962\pi$
$444$	26.3861	+	6.85257i	1.25223	+	0.325209i
$445$	7.48493	−	14.1563i	0.354820	−	0.671072i
$446$	−0.407785	−	2.28772i	−0.0193092	−	0.108327i
$447$	32.5757	−	5.87776i	1.54078	−	0.278008i
$448$	12.9861	−	16.7141i	0.613535	−	0.789668i
$449$	37.1684			1.75409			0.877043	−	0.480413i	$-0.159513\pi$
$449$	37.1684			1.75409			0.877043	+	0.480413i	$0.159513\pi$
$450$	−20.8798	−	3.74600i	−0.984285	−	0.176588i
$451$	10.8411	+	6.25909i	0.510486	+	0.294729i
$452$	−0.790226	−	0.364908i	−0.0371691	−	0.0171638i
$453$	8.35295	−	7.06580i	0.392456	−	0.331980i
$454$	−11.5619	+	31.9513i	−0.542628	+	1.49955i
$455$	−10.7793	+	27.5717i	−0.505343	+	1.29258i
$456$	−10.8882	−	0.847650i	−0.509885	−	0.0396948i
$457$	30.4541	+	8.16015i	1.42458	+	0.381716i	0.887107	−	0.461564i	$-0.152712\pi$
$457$	30.4541	+	8.16015i	1.42458	+	0.381716i	0.537475	+	0.843280i	$0.319378\pi$
$458$	−2.48304	+	29.0039i	−0.116025	+	1.35526i
$459$	1.74829	+	1.70703i	0.0816032	+	0.0796772i
$460$	−21.9296	+	16.7341i	−1.02247	+	0.780231i
$461$	−2.80296			−0.130547			−0.0652735	−	0.997867i	$-0.520792\pi$
$461$	−2.80296			−0.130547			−0.0652735	+	0.997867i	$0.520792\pi$
$462$	1.28967	−	23.4232i	0.0600008	−	1.08975i
$463$	−0.544403	−	0.544403i	−0.0253005	−	0.0253005i	0.694343	−	0.719644i	$-0.255695\pi$
$463$	−0.544403	−	0.544403i	−0.0253005	−	0.0253005i	−0.719644	+	0.694343i	$0.755695\pi$
$464$	−13.0052	−	15.2663i	−0.603749	−	0.708721i
$465$	−23.2274	−	7.38554i	−1.07714	−	0.342496i
$466$	−12.8994	−	15.3148i	−0.597553	−	0.709446i
$467$	11.2295	+	3.00893i	0.519638	+	0.139236i	0.509099	−	0.860708i	$-0.329979\pi$
$467$	11.2295	+	3.00893i	0.519638	+	0.139236i	0.0105386	+	0.999944i	$0.496645\pi$
$468$	−13.0058	−	27.0607i	−0.601194	−	1.25088i
$469$	4.22875	+	37.0368i	0.195265	+	1.71020i
$470$	−11.8968	−	3.81054i	−0.548760	−	0.175767i
$471$	−3.25921	−	0.272076i	−0.150176	−	0.0125366i
$472$	21.0640	−	21.3010i	0.969551	−	0.980456i
$473$	11.4952	+	42.9006i	0.528550	+	1.97257i
$474$	−34.1240	−	15.6701i	−1.56737	−	0.719754i
$475$	11.1154	−	0.829138i	0.510011	−	0.0380435i
$476$	2.22244	−	1.11909i	0.101865	−	0.0512936i
$477$	5.09036	+	2.32452i	0.233072	+	0.106433i
$478$	18.3566	+	12.8025i	0.839609	+	0.585571i
$479$	1.81573	−	3.14493i	0.0829626	−	0.143695i	−0.821559	−	0.570124i	$-0.806895\pi$
$479$	1.81573	−	3.14493i	0.0829626	−	0.143695i	0.904521	+	0.426429i	$0.140228\pi$
$480$	−6.73205	−	20.8490i	−0.307275	−	0.951621i
$481$	−19.6899	−	34.1038i	−0.897780	−	1.55500i
$482$	23.4441	−	10.9854i	1.06785	−	0.500371i
$483$	−19.3706	+	20.5856i	−0.881392	+	0.936675i
$484$	2.69101	−	3.23141i	0.122319	−	0.146882i
$485$	−12.7117	−	2.90367i	−0.577210	−	0.131849i
$486$	15.2455	−	15.9240i	0.691550	−	0.722329i
$487$	7.19360	+	26.8469i	0.325973	+	1.21655i	0.913330	+	0.407220i	$0.133502\pi$
$487$	7.19360	+	26.8469i	0.325973	+	1.21655i	−0.587357	+	0.809328i	$0.699832\pi$
$488$	5.31082	+	19.3860i	0.240410	+	0.877561i
$489$	−3.64324	−	2.52947i	−0.164753	−	0.114387i
$490$	−7.47389	+	20.8360i	−0.337636	+	0.941277i
$491$	−7.63283			−0.344465			−0.172232	−	0.985056i	$-0.555098\pi$
$491$	−7.63283			−0.344465			−0.172232	+	0.985056i	$0.555098\pi$
$492$	11.9795	−	0.0923460i	0.540080	−	0.00416328i
$493$	−0.610206	−	2.27732i	−0.0274823	−	0.102565i
$494$	10.1630	+	12.0660i	0.457255	+	0.542877i
$495$	−19.2872	−	14.7520i	−0.866895	−	0.663052i
$496$	−4.55590	−	24.7569i	−0.204566	−	1.11162i
$497$	3.66621	+	0.547026i	0.164452	+	0.0245375i
$498$	−1.56846	+	9.20961i	−0.0702844	+	0.412693i
$499$	10.5848	+	18.3334i	0.473842	+	0.820718i	0.999552	−	0.0299463i	$-0.00953362\pi$
$499$	10.5848	+	18.3334i	0.473842	+	0.820718i	−0.525710	+	0.850664i	$0.676200\pi$
$500$	10.0166	+	19.9917i	0.447956	+	0.894056i
$501$	1.77758	+	3.77276i	0.0794165	+	0.168554i
$502$	11.3365	+	7.90646i	0.505973	+	0.352883i
$503$	−10.7237	+	10.7237i	−0.478145	+	0.478145i	−0.904538	−	0.426393i	$-0.859784\pi$
$503$	−10.7237	+	10.7237i	−0.478145	+	0.478145i	0.426393	+	0.904538i	$0.359784\pi$
$504$	−10.2932	−	19.9512i	−0.458497	−	0.888696i
$505$	18.6353	−	0.694071i	0.829259	−	0.0308858i
$506$	−31.0857	+	5.54102i	−1.38193	+	0.246328i
$507$	−7.05427	+	19.6241i	−0.313291	+	0.871538i
$508$	−15.7917	−	7.29226i	−0.700645	−	0.323542i
$509$	−4.04529	+	2.33555i	−0.179304	+	0.103521i	−0.586966	−	0.809612i	$-0.699678\pi$
$509$	−4.04529	+	2.33555i	−0.179304	+	0.103521i	0.407662	+	0.913133i	$0.366344\pi$
$510$	0.337619	−	2.55340i	0.0149500	−	0.113067i
$511$	2.39727	+	20.9961i	0.106049	+	0.928815i
$512$	15.7293	−	16.2662i	0.695145	−	0.718870i
$513$	−5.67159	+	10.1001i	−0.250407	+	0.445931i
$514$	−3.85211	+	3.24456i	−0.169909	+	0.143111i
$515$	20.1925	−	6.22475i	0.889787	−	0.274295i
$516$	30.2858	+	29.8225i	1.33326	+	1.31286i
$517$	−10.1112	−	10.1112i	−0.444689	−	0.444689i
$518$	−15.4381	−	25.0741i	−0.678309	−	1.10169i
$519$	18.7345	−	26.9837i	0.822355	−	1.18445i
$520$	−14.6362	+	28.0602i	−0.641840	+	1.23052i
$521$	−7.71541	−	4.45449i	−0.338018	−	0.195155i	0.321377	−	0.946951i	$-0.395854\pi$
$521$	−7.71541	−	4.45449i	−0.338018	−	0.195155i	−0.659395	+	0.751796i	$0.729188\pi$
$522$	−20.4914	+	5.70701i	−0.896885	+	0.249789i
$523$	−33.3999	−	8.94949i	−1.46048	−	0.391334i	−0.560823	−	0.827936i	$-0.689515\pi$
$523$	−33.3999	−	8.94949i	−1.46048	−	0.391334i	−0.899655	+	0.436602i	$0.856182\pi$
$524$	3.87911	−	4.65810i	0.169459	−	0.203490i
$525$	13.4703	+	18.5351i	0.587894	+	0.808938i
$526$	13.1296	−	36.2836i	0.572478	−	1.58204i
$527$	0.765926	−	2.85848i	0.0333643	−	0.124517i
$528$	4.07208	−	24.7456i	0.177214	−	1.07691i
$529$	13.0310	+	7.52344i	0.566565	+	0.327106i
$530$	−1.25055	−	5.76461i	−0.0543202	−	0.250399i
$531$	−11.1048	−	29.7706i	−0.481906	−	1.29193i
$532$	7.85134	+	8.80371i	0.340399	+	0.381689i
$533$	−12.2367	−	12.2367i	−0.530029	−	0.530029i
$534$	7.32038	−	15.9412i	0.316784	−	0.689843i
$535$	0.324742	+	1.05343i	0.0140398	+	0.0455438i
$536$	0.222856	+	39.8506i	0.00962590	+	1.72129i
$537$	10.6707	+	12.6146i	0.460476	+	0.544359i
$538$	11.6841	+	24.9352i	0.503737	+	1.07503i
$539$	−18.5230	+	17.2895i	−0.797842	+	0.744710i
$540$	−23.0662	−	2.81960i	−0.992611	−	0.121336i
$541$	−2.78130	+	1.60579i	−0.119577	+	0.0690381i	−0.558596	−	0.829440i	$-0.688660\pi$
$541$	−2.78130	+	1.60579i	−0.119577	+	0.0690381i	0.439018	+	0.898478i	$0.355326\pi$
$542$	−2.31682	+	27.0623i	−0.0995160	+	1.16243i
$543$	8.65032	−	24.0642i	0.371221	−	1.03269i
$544$	2.49108	−	0.933064i	0.106804	−	0.0400048i
$545$	−39.6072	+	1.47517i	−1.69658	+	0.0631893i
$546$	−10.1028	+	30.8157i	−0.432359	+	1.31879i
$547$	21.7476	+	21.7476i	0.929861	+	0.929861i	0.997697	−	0.0678354i	$-0.0216093\pi$
$547$	21.7476	+	21.7476i	0.929861	+	0.929861i	−0.0678354	+	0.997697i	$0.521609\pi$
$548$	15.5937	+	22.0943i	0.666128	+	0.943821i
$549$	21.0245	+	3.53484i	0.897302	+	0.150863i
$550$	−0.280183	+	25.5940i	−0.0119471	+	1.09133i
$551$	9.67942	−	5.58842i	0.412357	−	0.238075i
$552$	−22.9613	+	19.6444i	−0.977298	+	0.836122i
$553$	14.8738	+	37.7329i	0.632497	+	1.60457i
$554$	−15.9259	−	5.76296i	−0.676627	−	0.244845i
$555$	−30.4468	−	1.40332i	−1.29240	−	0.0595677i
$556$	−7.60627	−	20.6581i	−0.322578	−	0.876099i
$557$	−10.6868	−	39.8838i	−0.452816	−	1.68993i	−0.694431	−	0.719559i	$-0.744344\pi$
$557$	−10.6868	−	39.8838i	−0.452816	−	1.68993i	0.241616	−	0.970372i	$-0.422323\pi$
$558$	−25.8565	−	6.65666i	−1.09459	−	0.281799i
$559$		−	61.3984i		−	2.59687i
$560$	−10.3463	+	21.2827i	−0.437212	+	0.899358i
$561$	1.68141	−	2.42176i	0.0709891	−	0.102247i
$562$	4.00915	−	5.74844i	0.169116	−	0.242483i
$563$	1.16389	−	0.311864i	0.0490523	−	0.0131435i	−0.234209	−	0.972186i	$-0.575250\pi$
$563$	1.16389	−	0.311864i	0.0490523	−	0.0131435i	0.283262	+	0.959043i	$0.408583\pi$
$564$	−13.2451	−	3.43981i	−0.557720	−	0.144842i
$565$	0.948713	+	0.216709i	0.0399127	+	0.00911703i
$566$	−1.55667	+	4.30184i	−0.0654315	+	0.180820i
$567$	−23.7904	+	1.00788i	−0.999104	+	0.0423269i
$568$	3.83338	+	1.00421i	0.160845	+	0.0421357i
$569$	8.59199	+	14.8818i	0.360195	+	0.623876i	0.987993	−	0.154501i	$-0.0493769\pi$
$569$	8.59199	+	14.8818i	0.360195	+	0.623876i	−0.627798	+	0.778376i	$0.716044\pi$
$570$	12.1066	−	1.58695i	0.507090	−	0.0664702i
$571$	1.43609	+	0.829130i	0.0600987	+	0.0346980i	0.529748	−	0.848155i	$-0.322286\pi$
$571$	1.43609	+	0.829130i	0.0600987	+	0.0346980i	−0.469650	+	0.882853i	$0.655620\pi$
$572$	−29.5972	+	20.8890i	−1.23752	+	0.873414i
$573$	−13.9538	+	2.51774i	−0.582928	+	0.105180i
$574$	−9.40489	−	8.88740i	−0.392552	−	0.370953i
$575$	20.1253	−	23.3697i	0.839283	−	0.974586i
$576$	−8.63873	−	22.3913i	−0.359947	−	0.932973i
$577$	1.59166	+	5.94014i	0.0662615	+	0.247291i	0.991110	−	0.133044i	$-0.0424752\pi$
$577$	1.59166	+	5.94014i	0.0662615	+	0.247291i	−0.924849	+	0.380335i	$0.875809\pi$
$578$	−23.6424	−	2.02404i	−0.983395	−	0.0841891i
$579$	0.000246054	0	2.05404e-5i	1.02257e−5	0	8.53630e-7i
$580$	17.7519	+	13.6972i	0.737108	+	0.568744i
$581$	8.11009	−	6.00414i	0.336463	−	0.249094i
$582$	−14.0809	−	2.39808i	−0.583673	−	0.0994036i
$583$	1.74756	−	6.52197i	0.0723763	−	0.270112i
$584$	0.126337	+	22.5913i	0.00522785	+	0.934834i
$585$	20.4761	+	26.5992i	0.846583	+	1.09974i
$586$	−3.06671	−	17.2046i	−0.126685	−	0.710715i
$587$	−15.6511	+	15.6511i	−0.645991	+	0.645991i	−0.952022	−	0.306031i	$-0.900999\pi$
$587$	−15.6511	+	15.6511i	−0.645991	+	0.645991i	0.306031	+	0.952022i	$0.400999\pi$
$588$	−6.89960	+	23.2464i	−0.284535	+	0.958666i
$589$	14.0291			0.578059
$590$	−18.1239	+	28.1657i	−0.746148	+	1.15956i
$591$	8.39009	−	3.95310i	0.345122	−	0.162609i
$592$	−13.5158	−	28.4294i	−0.555497	−	1.16844i
$593$	18.0838	+	4.84554i	0.742613	+	0.198983i	0.610239	−	0.792217i	$-0.291073\pi$
$593$	18.0838	+	4.84554i	0.742613	+	0.198983i	0.132374	+	0.991200i	$0.457740\pi$
$594$	−21.9977	−	14.9547i	−0.902576	−	0.613598i
$595$	−2.17277	+	1.73740i	−0.0890749	+	0.0712264i
$596$	−29.3715	−	24.4596i	−1.20311	−	1.00191i
$597$	−1.61066	−	1.90406i	−0.0659198	−	0.0779281i
$598$	43.4915	+	3.72333i	1.77850	+	0.152258i
$599$	−14.2081	+	24.6092i	−0.580528	+	1.00550i	0.414888	+	0.909872i	$0.363821\pi$
$599$	−14.2081	+	24.6092i	−0.580528	+	1.00550i	−0.995417	+	0.0956325i	$0.969513\pi$
$600$	12.1787	+	21.2528i	0.497193	+	0.867640i
$601$	−10.4635			−0.426816			−0.213408	−	0.976963i	$-0.568456\pi$
$601$	−10.4635			−0.426816			−0.213408	+	0.976963i	$0.568456\pi$
$602$	−1.29826	−	45.8914i	−0.0529130	−	1.87040i
$603$	38.4494	+	17.5580i	1.56578	+	0.715016i
$604$	−12.4493	−	2.14733i	−0.506555	−	0.0873734i
$605$	−2.19760	+	4.15632i	−0.0893450	+	0.168979i
$606$	20.3396	−	1.89933i	0.826239	−	0.0771550i
$607$	0.450119	+	0.120609i	0.0182698	+	0.00489537i	0.267942	−	0.963435i	$-0.413656\pi$
$607$	0.450119	+	0.120609i	0.0182698	+	0.00489537i	−0.249673	+	0.968330i	$0.580323\pi$
$608$	7.32911	+	10.2621i	0.297235	+	0.416185i
$609$	20.2375	+	10.8778i	0.820063	+	0.440789i
$610$	−10.2861	−	19.9805i	−0.416474	−	0.808987i
$611$	9.88379	+	17.1192i	0.399855	+	0.692570i
$612$	0.213036	−	2.81340i	0.00861147	−	0.113725i
$613$	3.28492	+	12.2595i	0.132677	+	0.495156i	0.999997	−	0.00259495i	$-0.000825999\pi$
$613$	3.28492	+	12.2595i	0.132677	+	0.495156i	−0.867320	+	0.497751i	$0.834159\pi$
$614$	−1.14539	−	6.42576i	−0.0462241	−	0.259322i
$615$	−13.0834	+	2.86726i	−0.527575	+	0.115619i
$616$	−21.6803	+	16.2391i	−0.873526	+	0.654291i
$617$	−1.74047	−	1.74047i	−0.0700688	−	0.0700688i	0.671204	−	0.741273i	$-0.265777\pi$
$617$	−1.74047	−	1.74047i	−0.0700688	−	0.0700688i	−0.741273	+	0.671204i	$0.765777\pi$
$618$	21.7044	−	8.04371i	0.873078	−	0.323565i
$619$	−6.22239	+	10.7775i	−0.250099	+	0.433184i	−0.963553	−	0.267518i	$-0.913797\pi$
$619$	−6.22239	+	10.7775i	−0.250099	+	0.433184i	0.713454	+	0.700702i	$0.247130\pi$
$620$	10.7005	+	26.0303i	0.429744	+	1.04540i
$621$	8.66449	+	30.8576i	0.347694	+	1.23827i
$622$	14.2335	+	30.3759i	0.570711	+	1.21796i
$623$	−17.6271	+	6.94835i	−0.706215	+	0.278380i
$624$	−14.2913	+	31.5859i	−0.572109	+	1.26445i
$625$	−15.5738	−	19.5565i	−0.622951	−	0.782261i
$626$	−2.60355	+	2.19292i	−0.104059	+	0.0876469i
$627$	13.1526	+	4.72795i	0.525264	+	0.188816i
$628$	2.17763	+	3.08543i	0.0868968	+	0.123122i
$629$		−	3.70066i		−	0.147555i
$630$	15.8671	+	19.4483i	0.632159	+	0.774839i
$631$	−42.2270			−1.68103			−0.840515	−	0.541788i	$-0.817748\pi$
$631$	−42.2270			−1.68103			−0.840515	+	0.541788i	$0.817748\pi$
$632$	11.4562	+	41.8182i	0.455702	+	1.66344i
$633$	−4.37881	+	12.1813i	−0.174042	+	0.484164i
$634$	−3.01541	−	3.58005i	−0.119757	−	0.142182i
$635$	18.9589	+	4.33068i	0.752361	+	0.171858i
$636$	−1.72047	−	6.22844i	−0.0682212	−	0.246974i
$637$	30.9199	−	16.4593i	1.22509	−	0.652141i
$638$	10.8901	+	23.2407i	0.431143	+	0.920107i
$639$	2.67599	−	3.24117i	0.105861	−	0.128219i
$640$	−13.4507	+	21.4261i	−0.531685	+	0.846942i
$641$	2.24285	+	1.29491i	0.0885874	+	0.0511460i	0.543639	−	0.839319i	$-0.317046\pi$
$641$	2.24285	+	1.29491i	0.0885874	+	0.0511460i	−0.455052	+	0.890465i	$0.650379\pi$
$642$	0.419636	+	1.13231i	0.0165617	+	0.0446885i
$643$	−4.31064	+	4.31064i	−0.169995	+	0.169995i	−0.786977	−	0.616982i	$-0.788355\pi$
$643$	−4.31064	+	4.31064i	−0.169995	+	0.169995i	0.616982	+	0.786977i	$0.288355\pi$
$644$	32.5859	+	1.86334i	1.28406	+	0.0734259i
$645$	−40.0169	−	25.6302i	−1.57566	−	1.00919i
$646$	0.260156	+	1.45951i	0.0102357	+	0.0574235i
$647$	−11.6272	+	3.11550i	−0.457112	+	0.122483i	−0.480025	−	0.877255i	$-0.659373\pi$
$647$	−11.6272	+	3.11550i	−0.457112	+	0.122483i	0.0229132	+	0.999737i	$0.492706\pi$
$648$	−25.4008	−	1.67259i	−0.997839	−	0.0657055i
$649$	−33.2019	+	19.1691i	−1.30329	+	0.752454i
$650$	9.53150	−	34.0755i	0.373856	−	1.33655i
$651$	15.1719	+	24.5254i	0.594632	+	0.961226i
$652$	0.465375	+	5.10019i	0.0182255	+	0.199739i
$653$	5.91629	−	22.0799i	0.231522	−	0.864053i	−0.748164	−	0.663514i	$-0.769064\pi$
$653$	5.91629	−	22.0799i	0.231522	−	0.864053i	0.979686	−	0.200538i	$-0.0642691\pi$
$654$	−43.2295	+	4.03681i	−1.69041	+	0.157852i
$655$	−3.16785	+	5.99136i	−0.123778	+	0.234102i
$656$	−8.97058	−	10.5303i	−0.350242	−	0.411137i
$657$	21.7969	+	9.95360i	0.850379	+	0.388327i
$658$	7.74950	+	12.5866i	0.302107	+	0.490676i
$659$			45.6738i			1.77920i	0.456740	+	0.889600i	$0.349017\pi$
$659$			45.6738i			1.77920i	−0.456740	+	0.889600i	$0.650983\pi$
$660$	1.25952	+	28.0102i	0.0490268	+	1.09029i
$661$	18.7808	+	10.8431i	0.730490	+	0.421748i	0.818601	−	0.574362i	$-0.194750\pi$
$661$	18.7808	+	10.8431i	0.730490	+	0.421748i	−0.0881117	+	0.996111i	$0.528083\pi$
$662$	22.7580	+	1.94833i	0.884514	+	0.0757238i
$663$	−3.11168	+	2.63219i	−0.120848	+	0.102226i
$664$	9.31191	−	5.44589i	0.361372	−	0.211342i
$665$	−10.6217	−	7.81765i	−0.411892	−	0.303156i
$666$	−33.3866	+	0.328026i	−1.29371	+	0.0127108i
$667$	8.00412	−	29.8718i	0.309921	−	1.15664i
$668$	2.01893	−	4.37210i	0.0781149	−	0.169162i
$669$	1.21304	+	2.57457i	0.0468989	+	0.0995388i
$670$	−9.44584	−	43.5423i	−0.364925	−	1.68218i
$671$		−	25.7238i		−	0.993056i
$672$	−10.0140	+	23.9107i	−0.386297	+	0.922374i
$673$	1.91550	+	1.91550i	0.0738372	+	0.0738372i	0.743061	−	0.669224i	$-0.233373\pi$
$673$	1.91550	+	1.91550i	0.0738372	+	0.0738372i	−0.669224	+	0.743061i	$0.733373\pi$
$674$	−1.10272	+	0.196559i	−0.0424750	+	0.00757116i
$675$	25.8839	−	2.24186i	0.996270	−	0.0862892i
$676$	22.5965	−	8.32000i	0.869098	−	0.320000i
$677$	31.6060	+	8.46881i	1.21472	+	0.325483i	0.808612	−	0.588342i	$-0.200219\pi$
$677$	31.6060	+	8.46881i	1.21472	+	0.325483i	0.406107	+	0.913825i	$0.366886\pi$
$678$	1.05090	+	0.178976i	0.0403596	+	0.00687352i
$679$	9.17996	+	12.3998i	0.352294	+	0.475862i
$680$	−2.50961	+	1.59593i	−0.0962391	+	0.0612011i
$681$	3.46199	−	41.4712i	0.132664	−	1.58918i
$682$	−2.74792	+	32.0979i	−0.105223	+	1.22909i
$683$	−38.6903	+	10.3670i	−1.48044	+	0.396684i	−0.906498	−	0.422210i	$-0.861255\pi$
$683$	−38.6903	+	10.3670i	−1.48044	+	0.396684i	−0.573946	+	0.818893i	$0.694588\pi$
$684$	13.1443	−	2.47645i	0.502585	−	0.0946894i
$685$	−22.1602	−	20.5688i	−0.846698	−	0.785893i
$686$	22.7627	−	12.9561i	0.869083	−	0.494666i
$687$	−6.33067	−	35.0858i	−0.241530	−	1.33861i
$688$	3.91290	−	48.9234i	0.149178	−	1.86519i
$689$	−4.66704	+	8.08355i	−0.177800	+	0.307959i
$690$	20.5819	−	26.7917i	0.783538	−	1.01994i
$691$	23.2404	−	13.4179i	0.884107	−	0.510439i	0.0120967	−	0.999927i	$-0.496149\pi$
$691$	23.2404	−	13.4179i	0.884107	−	0.510439i	0.872010	+	0.489487i	$0.162816\pi$
$692$	−37.7746	+	3.44680i	−1.43597	+	0.131028i
$693$	5.95865	+	28.1062i	0.226350	+	1.06767i
$694$	0.448627	−	1.23978i	0.0170296	−	0.0470613i
$695$	13.0910	+	20.8421i	0.496568	+	0.790586i
$696$	20.2539	+	13.8949i	0.767724	+	0.526686i
$697$	−0.420902	−	1.57083i	−0.0159428	−	0.0594993i
$698$	−28.8971	−	20.1538i	−1.09377	−	0.762831i
$699$	20.1444	+	13.9861i	0.761931	+	0.529003i
$700$	6.40368	−	25.6709i	0.242036	−	0.970267i
$701$	−11.0406			−0.416997			−0.208499	−	0.978023i	$-0.566858\pi$
$701$	−11.0406			−0.416997			−0.208499	+	0.978023i	$0.566858\pi$
$702$	24.0229	+	27.8397i	0.906687	+	1.05074i
$703$	16.9458	−	4.54061i	0.639123	−	0.171252i
$704$	−24.9149	+	14.7586i	−0.939014	+	0.556235i
$705$	15.2835	+	0.704431i	0.575610	+	0.0265304i
$706$	−0.534494	+	1.47707i	−0.0201160	+	0.0555904i
$707$	−17.2714	−	13.7316i	−0.649558	−	0.516429i
$708$	−18.0994	+	31.9147i	−0.680217	+	1.19943i
$709$	−19.1991	−	33.2537i	−0.721036	−	1.24887i	−0.960585	−	0.277986i	$-0.910333\pi$
$709$	−19.1991	−	33.2537i	−0.721036	−	1.24887i	0.239549	−	0.970884i	$-0.423000\pi$
$710$	−4.42533	−	0.213353i	−0.166080	−	0.00800701i
$711$	45.3526	+	7.62514i	1.70086	+	0.285965i
$712$	−19.5356	+	5.35180i	−0.732126	+	0.200567i
$713$	27.4482	−	27.4482i	1.02794	−	1.02794i
$714$	−2.27013	+	2.03319i	−0.0849576	+	0.0760904i
$715$	27.5536	−	29.6855i	1.03045	−	1.11017i
$716$	3.24288	−	18.8009i	0.121192	−	0.702622i
$717$	−25.7939	−	9.27212i	−0.963292	−	0.346274i
$718$	1.89262	−	22.1073i	0.0706321	−	0.825039i
$719$	−10.4454	−	18.0920i	−0.389549	−	0.674718i	0.602840	−	0.797862i	$-0.294036\pi$
$719$	−10.4454	−	18.0920i	−0.389549	−	0.674718i	−0.992389	+	0.123144i	$0.960702\pi$
$720$	14.6206	+	22.4997i	0.544878	+	0.838515i
$721$	−22.9303	−	9.96389i	−0.853969	−	0.371074i
$722$	17.9673	−	8.41909i	0.668673	−	0.313326i
$723$	−24.2091	+	20.4786i	−0.900347	+	0.761608i
$724$	−27.7091	+	10.2024i	−1.02980	+	0.379170i
$725$	−22.5822	−	10.8846i	−0.838681	−	0.404243i
$726$	−2.14928	+	4.68038i	−0.0797674	+	0.173705i
$727$	−11.9596	+	11.9596i	−0.443558	+	0.443558i	−0.893206	−	0.449648i	$-0.851549\pi$
$727$	−11.9596	+	11.9596i	−0.443558	+	0.443558i	0.449648	+	0.893206i	$0.351549\pi$
$728$	34.7601	−	13.9270i	1.28830	−	0.516170i
$729$	−12.9378	+	23.6984i	−0.479177	+	0.877718i
$730$	−5.35484	−	24.6841i	−0.198191	−	0.913599i
$731$	2.88492	−	4.99682i	0.106703	−	0.184814i
$732$	−12.4728	−	21.2240i	−0.461009	−	0.784463i
$733$	−5.07379	−	1.35952i	−0.187405	−	0.0502149i	0.163896	−	0.986478i	$-0.447594\pi$
$733$	−5.07379	−	1.35952i	−0.187405	−	0.0502149i	−0.351301	+	0.936263i	$0.614260\pi$
$734$	6.93895	−	19.1758i	0.256121	−	0.707790i
$735$	2.17976	−	27.0231i	0.0804017	−	0.996763i
$736$	34.4176	+	5.73852i	1.26865	+	0.211525i
$737$	13.1999	−	49.2628i	0.486226	−	1.81462i
$738$	−14.1344	+	3.93653i	−0.520294	+	0.144906i
$739$	−6.23773	+	10.8041i	−0.229459	+	0.397434i	−0.957648	−	0.287942i	$-0.907029\pi$
$739$	−6.23773	+	10.8041i	−0.229459	+	0.397434i	0.728189	+	0.685376i	$0.240362\pi$
$740$	21.3501	+	27.9788i	0.784845	+	1.02852i
$741$	−15.8711	−	11.0192i	−0.583039	−	0.404799i
$742$	−3.31740	+	6.14063i	−0.121785	+	0.225430i
$743$	−31.5243	+	31.5243i	−1.15651	+	1.15651i	−0.171294	+	0.985220i	$0.554795\pi$
$743$	−31.5243	+	31.5243i	−1.15651	+	1.15651i	−0.985220	+	0.171294i	$0.945205\pi$
$744$	13.2962	+	27.8155i	0.487463	+	1.01977i
$745$	37.7784	+	19.9748i	1.38409	+	0.731820i
$746$	6.87179	+	8.15855i	0.251594	+	0.298706i
$747$	−1.08793	−	11.3900i	−0.0398052	−	0.416738i
$748$	−3.39024	+	0.309348i	−0.123959	+	0.0113109i
$749$	0.519811	−	1.19626i	0.0189935	−	0.0437105i
$750$	−18.2302	−	20.4368i	−0.665671	−	0.746245i
$751$	23.5929	+	40.8641i	0.860916	+	1.49115i	0.871045	+	0.491202i	$0.163442\pi$
$751$	23.5929	+	40.8641i	0.860916	+	1.49115i	−0.0101290	+	0.999949i	$0.503224\pi$
$752$	6.78460	+	14.2708i	0.247409	+	0.520404i
$753$	−15.9296	−	5.72621i	−0.580508	−	0.208675i
$754$	−6.22623	−	34.9298i	−0.226746	−	1.27207i
$755$	14.1145	−	0.525695i	0.513679	−	0.0191320i
$756$	18.5443	+	20.3005i	0.674450	+	0.738321i
$757$	5.56781	+	5.56781i	0.202366	+	0.202366i	0.801013	−	0.598647i	$-0.204295\pi$
$757$	5.56781	+	5.56781i	0.202366	+	0.202366i	−0.598647	+	0.801013i	$0.704295\pi$
$758$	40.2435	+	28.0671i	1.46171	+	1.01944i
$759$	34.9836	−	16.4830i	1.26982	−	0.598293i
$760$	−10.3872	−	9.53365i	−0.376783	−	0.345822i
$761$	−21.1998	+	12.2397i	−0.768494	+	0.443690i	−0.832337	−	0.554270i	$-0.812998\pi$
$761$	−21.1998	+	12.2397i	−0.768494	+	0.443690i	0.0638434	+	0.997960i	$0.479664\pi$
$762$	21.0010	+	3.57662i	0.760786	+	0.129567i
$763$	36.7084	+	29.1849i	1.32893	+	1.05656i
$764$	12.5813	+	10.4773i	0.455176	+	0.379055i
$765$	0.416606	+	3.12685i	0.0150624	+	0.113052i
$766$	−6.18544	−	7.34368i	−0.223489	−	0.265338i
$767$	51.1933	−	13.7172i	1.84848	−	0.495299i
$768$	−13.4005	+	24.2575i	−0.483550	+	0.875317i
$769$		−	21.9585i		−	0.791844i	−0.918284	−	0.395922i	$-0.870425\pi$
$769$		−	21.9585i		−	0.791844i	0.918284	−	0.395922i	$-0.129575\pi$
$770$	19.9669	−	22.7707i	0.719558	−	0.820598i
$771$	3.51789	−	5.06688i	0.126694	−	0.182479i
$772$	−0.000164400	0	0.000232935i	−5.91689e−6	0	8.38350e-6i
$773$	19.4954	−	5.22378i	0.701201	−	0.187886i	0.109432	−	0.993994i	$-0.465097\pi$
$773$	19.4954	−	5.22378i	0.701201	−	0.187886i	0.591768	+	0.806108i	$0.298430\pi$
$774$	−45.3361	−	25.5842i	−1.62957	−	0.919606i
$775$	−17.7164	−	26.0044i	−0.636391	−	0.934104i
$776$	8.32643	+	14.2373i	0.298901	+	0.511091i
$777$	26.2640	+	24.7138i	0.942214	+	0.886604i
$778$	−9.09785	−	19.4158i	−0.326174	−	0.696091i
$779$	6.67658	−	3.85473i	0.239213	−	0.138110i
$780$	8.34002	−	37.8528i	0.298621	−	1.35535i
$781$	−4.39196	−	2.53570i	−0.157157	−	0.0907345i
$782$	3.36455	+	2.34655i	0.120316	+	0.0839124i
$783$	22.4045	−	13.2944i	0.800671	−	0.475104i
$784$	25.6865	−	11.1446i	0.917376	−	0.398021i
$785$	−3.09464	−	2.87239i	−0.110452	−	0.102520i
$786$	−3.09820	+	6.74678i	−0.110509	+	0.240650i
$787$	12.6040	−	3.37722i	0.449283	−	0.120385i	−0.0270808	−	0.999633i	$-0.508621\pi$
$787$	12.6040	−	3.37722i	0.449283	−	0.120385i	0.476364	+	0.879248i	$0.341954\pi$
$788$	−9.72295	−	4.48983i	−0.346366	−	0.159944i
$789$	−3.93140	+	47.0943i	−0.139961	+	1.67660i
$790$	−22.1886	−	43.1007i	−0.789435	−	1.53345i
$791$	−0.685127	−	0.925434i	−0.0243603	−	0.0329047i
$792$	3.09138	+	30.5586i	0.109848	+	1.08585i
$793$	−9.20382	+	34.3491i	−0.326837	+	1.21977i
$794$	−18.8324	+	15.8621i	−0.668336	+	0.562927i
$795$	3.32031	+	6.41619i	0.117759	+	0.227559i
$796$	−0.489485	+	2.83783i	−0.0173493	+	0.100584i
$797$	29.5625	−	29.5625i	1.04716	−	1.04716i	0.0483256	−	0.998832i	$-0.484611\pi$
$797$	29.5625	−	29.5625i	1.04716	−	1.04716i	0.998832	−	0.0483256i	$-0.0153885\pi$
$798$	−12.0956	−	7.90055i	−0.428181	−	0.279677i
$799$			1.85764i			0.0657184i
$800$	9.76650	−	26.5446i	0.345298	−	0.938493i
$801$	−3.56212	+	21.1867i	−0.125861	+	0.748595i
$802$	−51.4611	−	4.40562i	−1.81715	−	0.155568i
$803$	7.48303	−	27.9271i	0.264071	−	0.985525i
$804$	−12.9954	−	47.0458i	−0.458312	−	1.65918i
$805$	−36.0769	+	5.48616i	−1.27154	+	0.193362i
$806$	15.1537	−	41.8773i	0.533768	−	1.47507i
$807$	−21.7811	−	25.7489i	−0.766731	−	0.906403i
$808$	−16.7725	−	16.5859i	−0.590053	−	0.583491i
$809$	−10.3820	+	17.9821i	−0.365010	+	0.632216i	−0.988778	−	0.149394i	$-0.952268\pi$
$809$	−10.3820	+	17.9821i	−0.365010	+	0.632216i	0.623768	+	0.781610i	$0.285601\pi$
$810$	28.1729	−	4.03570i	0.989895	−	0.141800i
$811$			35.2287i			1.23705i	0.785766	+	0.618524i	$0.212269\pi$
$811$			35.2287i			1.23705i	−0.785766	+	0.618524i	$0.787731\pi$
$812$	−5.39230	−	25.9762i	−0.189233	−	0.911586i
$813$	−5.90688	−	32.7370i	−0.207163	−	1.14814i
$814$	7.06948	+	39.6605i	0.247785	+	1.39010i
$815$	−1.68679	−	5.47178i	−0.0590857	−	0.191668i
$816$	−2.64720	+	1.89907i	−0.0926705	+	0.0664809i
$817$	26.4208	+	7.07943i	0.924347	+	0.247678i
$818$	−17.3605	−	37.0493i	−0.606996	−	1.29540i
$819$	2.09960	−	39.6623i	0.0733661	−	1.38591i
$820$	12.2447	+	9.44791i	0.427605	+	0.329935i
$821$	7.22244	+	12.5096i	0.252065	+	0.436589i	0.964094	−	0.265560i	$-0.0855570\pi$
$821$	7.22244	+	12.5096i	0.252065	+	0.436589i	−0.712029	+	0.702150i	$0.752224\pi$
$822$	−25.4959	−	21.1409i	−0.889272	−	0.737374i
$823$	21.4032	−	5.73497i	0.746069	−	0.199909i	0.134295	−	0.990941i	$-0.457123\pi$
$823$	21.4032	−	5.73497i	0.746069	−	0.199909i	0.611774	+	0.791033i	$0.290456\pi$
$824$	−23.2213	−	13.2342i	−0.808953	−	0.461037i
$825$	−7.84575	−	30.3503i	−0.273154	−	1.05666i
$826$	37.9737	−	11.3352i	1.32128	−	0.394403i
$827$	−19.3461	+	19.3461i	−0.672731	+	0.672731i	−0.958345	−	0.285614i	$-0.907803\pi$
$827$	−19.3461	+	19.3461i	−0.672731	+	0.672731i	0.285614	+	0.958345i	$0.407803\pi$
$828$	20.8719	−	30.5623i	0.725347	−	1.06211i
$829$	−3.88539	+	6.72970i	−0.134945	+	0.233732i	−0.925577	−	0.378560i	$-0.876419\pi$
$829$	−3.88539	+	6.72970i	−0.134945	+	0.233732i	0.790631	+	0.612293i	$0.209753\pi$
$830$	−8.92903	+	8.10766i	−0.309931	+	0.281421i
$831$	20.6710	+	1.72560i	0.717070	+	0.0598604i
$832$	38.5495	−	10.7928i	1.33646	−	0.374174i
$833$	3.28975	+	0.113311i	0.113983	+	0.00392601i
$834$	15.5933	+	21.9948i	0.539950	+	0.761616i
$835$	−1.19899	+	5.24896i	−0.0414928	+	0.181648i
$836$	−5.57627	−	15.1448i	−0.192859	−	0.523793i
$837$	32.6979	−	0.390465i	1.13020	−	0.0134964i
$838$	−30.9834	+	44.4248i	−1.07030	+	1.53463i
$839$	50.1273			1.73059			0.865294	−	0.501265i	$-0.167132\pi$
$839$	50.1273			1.73059			0.865294	+	0.501265i	$0.167132\pi$
$840$	5.43326	−	28.4689i	0.187465	−	0.982271i
$841$	3.86286			0.133202
$842$	6.30423	−	9.03919i	0.217258	−	0.311511i
$843$	−2.90361	+	8.07748i	−0.100005	+	0.278203i
$844$	14.0264	−	5.16449i	0.482808	−	0.177769i
$845$	−22.7978	+	14.3193i	−0.784268	+	0.492600i
$846$	16.7592	−	0.164661i	0.576194	−	0.00566115i
$847$	5.17536	−	2.04005i	0.177828	−	0.0700971i
$848$	−4.23395	+	6.14370i	−0.145394	+	0.210976i
$849$	0.466112	−	5.58357i	0.0159969	−	0.191628i
$850$	2.37681	−	2.32533i	0.0815239	−	0.0797583i
$851$	24.2709	−	42.0385i	0.831997	−	1.44106i
$852$	−4.85319	+	0.0374115i	−0.166268	+	0.00128170i
$853$	28.3031	−	28.3031i	0.969081	−	0.969081i	−0.0304551	−	0.999536i	$-0.509696\pi$
$853$	28.3031	−	28.3031i	0.969081	−	0.969081i	0.999536	+	0.0304551i	$0.00969565\pi$
$854$	−6.15298	+	25.8684i	−0.210551	+	0.885200i
$855$	−13.8071	+	5.74426i	−0.472192	+	0.196449i
$856$	0.690423	−	1.21144i	0.0235982	−	0.0414063i
$857$	29.7773	−	7.97881i	1.01717	−	0.272551i	0.288550	−	0.957465i	$-0.406827\pi$
$857$	29.7773	−	7.97881i	1.01717	−	0.272551i	0.728624	+	0.684914i	$0.240160\pi$
$858$	28.3201	−	34.1539i	0.966831	−	1.16600i
$859$	−9.29758	−	16.1039i	−0.317229	−	0.549457i	0.662680	−	0.748903i	$-0.269419\pi$
$859$	−9.29758	−	16.1039i	−0.317229	−	0.549457i	−0.979909	+	0.199446i	$0.936086\pi$
$860$	7.01665	+	54.4223i	0.239266	+	1.85578i
$861$	13.9592	+	7.50316i	0.475728	+	0.255707i
$862$	−18.7999	−	40.1212i	−0.640328	−	1.36653i
$863$	5.85955	+	1.57006i	0.199461	+	0.0534455i	0.357166	−	0.934041i	$-0.383743\pi$
$863$	5.85955	+	1.57006i	0.199461	+	0.0534455i	−0.157705	+	0.987486i	$0.550410\pi$
$864$	17.3677	+	23.7142i	0.590862	+	0.806773i
$865$	40.5268	−	12.4932i	1.37795	−	0.424782i
$866$	1.28841	+	7.22812i	0.0437820	+	0.245622i
$867$	28.6000	−	5.16042i	0.971308	−	0.175257i
$868$	10.4410	−	31.6211i	0.354390	−	1.07329i
$869$		−	55.4898i		−	1.88236i
$870$	−25.3649	−	10.5232i	−0.859950	−	0.356768i
$871$	−35.2519	+	61.0581i	−1.19446	+	2.06887i
$872$	35.6480	+	35.2515i	1.20719	+	1.19377i
$873$	17.4146	−	1.66337i	0.589395	−	0.0562967i
$874$	−6.61693	+	18.2858i	−0.223821	+	0.618528i
$875$	−1.07742	+	29.5608i	−0.0364234	+	0.999336i
$876$	−7.36707	−	26.6702i	−0.248910	−	0.901103i
$877$	9.97344	−	37.2214i	0.336779	−	1.25688i	−0.565148	−	0.824989i	$-0.691181\pi$
$877$	9.97344	−	37.2214i	0.336779	−	1.25688i	0.901927	−	0.431888i	$-0.142152\pi$
$878$	−33.0091	−	2.82593i	−1.11400	−	0.0953705i
$879$	9.12259	+	19.3619i	0.307697	+	0.653060i
$880$	23.8471	−	21.8980i	0.803886	−	0.738181i
$881$			48.9415i			1.64888i	0.565948	+	0.824441i	$0.308510\pi$
$881$			48.9415i			1.64888i	−0.565948	+	0.824441i	$0.691490\pi$
$882$	0.730671	−	29.6895i	0.0246030	−	0.999697i
$883$	−0.347333	+	0.347333i	−0.0116887	+	0.0116887i	−0.712927	−	0.701238i	$-0.752631\pi$
$883$	−0.347333	+	0.347333i	−0.0116887	+	0.0116887i	0.701238	+	0.712927i	$0.252631\pi$
$884$	4.63768	+	0.799933i	0.155982	+	0.0269047i
$885$	12.4299	−	39.0918i	0.417826	−	1.31406i
$886$	17.2167	−	14.5013i	0.578407	−	0.487182i
$887$	−3.82344	+	14.2693i	−0.128379	+	0.479115i	−0.999938	−	0.0111753i	$-0.996443\pi$
$887$	−3.82344	+	14.2693i	−0.128379	+	0.479115i	0.871559	+	0.490291i	$0.163109\pi$
$888$	25.0632	+	29.2950i	0.841067	+	0.983078i
$889$	−13.6914	−	18.4937i	−0.459196	−	0.620259i
$890$	20.1347	−	10.3655i	0.674916	−	0.347453i
$891$	30.7866	+	10.6535i	1.03139	+	0.356904i
$892$	1.37774	−	2.98357i	0.0461303	−	0.0998973i
$893$	−8.50635	+	2.27927i	−0.284654	+	0.0762728i
$894$	42.5417	+	19.5357i	1.42281	+	0.653370i
$895$	0.793901	+	21.3156i	0.0265372	+	0.712503i
$896$	28.5851	−	8.88208i	0.954962	−	0.296729i
$897$	−52.6112	+	9.49286i	−1.75664	+	0.316957i
$898$	43.1141	+	30.0692i	1.43874	+	1.00342i
$899$	−27.3248	−	15.7760i	−0.911334	−	0.526159i
$900$	−21.1894	−	21.2370i	−0.706313	−	0.707900i
$901$	−0.759642	+	0.438579i	−0.0253073	+	0.0146112i
$902$	7.51167	+	16.0307i	0.250111	+	0.533765i
$903$	16.1968	+	53.8445i	0.538997	+	1.79183i
$904$	−0.621425	−	1.06257i	−0.0206683	−	0.0353407i
$905$	27.9559	−	17.5591i	0.929284	−	0.583685i
$906$	15.4054	−	1.43857i	0.511809	−	0.0477932i
$907$	39.6700	−	10.6295i	1.31722	−	0.352948i	0.469285	−	0.883047i	$-0.344512\pi$
$907$	39.6700	−	10.6295i	1.31722	−	0.352948i	0.847936	+	0.530099i	$0.177845\pi$
$908$	−39.2600	+	27.7089i	−1.30289	+	0.919551i
$909$	−23.4415	+	8.74395i	−0.777505	+	0.290019i
$910$	−34.8091	+	23.2618i	−1.15391	+	0.771120i
$911$			13.1205i			0.434702i	0.976094	+	0.217351i	$0.0697416\pi$
$911$			13.1205i			0.434702i	−0.976094	+	0.217351i	$0.930258\pi$
$912$	−11.9441	−	9.79175i	−0.395510	−	0.324237i
$913$	−13.3351	+	3.57313i	−0.441328	+	0.118253i
$914$	28.7242	+	34.1028i	0.950110	+	1.12802i
$915$	18.5453	+	20.3374i	0.613088	+	0.672334i
$916$	−26.3444	+	31.6348i	−0.870443	+	1.04524i
$917$	7.46031	−	2.94075i	0.246361	−	0.0971121i
$918$	0.646973	+	3.39446i	0.0213533	+	0.112034i
$919$	1.81166	−	1.04596i	0.0597613	−	0.0345032i	−0.469822	−	0.882761i	$-0.655682\pi$
$919$	1.81166	−	1.04596i	0.0597613	−	0.0345032i	0.529583	+	0.848258i	$0.322348\pi$
$920$	−38.9755	+	1.66995i	−1.28498	+	0.0550566i
$921$	3.40720	+	7.23148i	0.112271	+	0.238286i
$922$	−3.25134	−	2.26759i	−0.107077	−	0.0746792i
$923$	4.95735	+	4.95735i	0.163173	+	0.163173i
$924$	20.4453	−	26.1268i	0.672601	−	0.859507i
$925$	−29.8161	−	25.6767i	−0.980349	−	0.844246i
$926$	−0.191067	−	1.07191i	−0.00627887	−	0.0352251i
$927$	−23.0920	+	16.4447i	−0.758442	+	0.540116i
$928$	−2.73511	−	28.2296i	−0.0897845	−	0.926680i
$929$	−7.40326	−	12.8228i	−0.242893	−	0.420703i	0.718644	−	0.695378i	$-0.244763\pi$
$929$	−7.40326	−	12.8228i	−0.242893	−	0.420703i	−0.961537	+	0.274675i	$0.911430\pi$
$930$	−20.9681	−	27.3579i	−0.687571	−	0.897101i
$931$	3.51757	+	15.2032i	0.115284	+	0.498265i
$932$	−2.57318	−	28.2003i	−0.0842873	−	0.923731i
$933$	−26.5336	−	31.3671i	−0.868671	−	1.02691i
$934$	10.5916	+	12.5749i	0.346567	+	0.411462i
$935$	3.63724	−	1.12126i	0.118951	−	0.0366690i
$936$	6.80575	−	41.9112i	0.222453	−	1.36991i
$937$	12.6740	−	12.6740i	0.414042	−	0.414042i	−0.469102	−	0.883144i	$-0.655422\pi$
$937$	12.6740	−	12.6740i	0.414042	−	0.414042i	0.883144	+	0.469102i	$0.155422\pi$
$938$	−25.0575	+	46.3825i	−0.818157	+	1.51444i
$939$	2.37767	−	3.42459i	0.0775922	−	0.111757i
$940$	−10.7172	−	14.0446i	−0.349556	−	0.458085i
$941$	21.7770	−	37.7188i	0.709909	−	1.22960i	−0.254982	−	0.966946i	$-0.582070\pi$
$941$	21.7770	−	37.7188i	0.709909	−	1.22960i	0.964891	−	0.262652i	$-0.0845971\pi$
$942$	−3.56046	−	2.95229i	−0.116006	−	0.0961909i
$943$	5.52101	−	20.6047i	0.179789	−	0.670981i
$944$	41.6660	−	7.66760i	1.35611	−	0.249559i
$945$	−24.9738	−	17.9251i	−0.812397	−	0.583104i
$946$	−21.3725	+	59.0629i	−0.694881	+	1.92030i
$947$	−41.3479	−	11.0791i	−1.34363	−	0.360024i	−0.485849	−	0.874043i	$-0.661489\pi$
$947$	−41.3479	−	11.0791i	−1.34363	−	0.360024i	−0.857779	+	0.514019i	$0.828156\pi$
$948$	−26.9056	−	45.7831i	−0.873852	−	1.48697i
$949$	−19.9843	+	34.6138i	−0.648717	+	1.12361i
$950$	13.5643	+	8.03059i	0.440084	+	0.260547i
$951$	4.70902	+	3.26944i	0.152701	+	0.106019i
$952$	3.48329	+	0.499837i	0.112894	+	0.0161998i
$953$	−13.3541	+	13.3541i	−0.432582	+	0.432582i	−0.889506	−	0.456924i	$-0.848951\pi$
$953$	−13.3541	+	13.3541i	−0.432582	+	0.432582i	0.456924	+	0.889506i	$0.348951\pi$
$954$	4.02411	+	6.81446i	0.130285	+	0.220626i
$955$	−16.1824	−	8.55621i	−0.523650	−	0.276872i
$956$	10.9358	+	29.7009i	0.353689	+	0.960594i
$957$	−20.3010	−	23.9991i	−0.656237	−	0.775780i
$958$	4.65042	−	2.17909i	0.150248	−	0.0704032i
$959$	4.05825	+	35.5435i	0.131048	+	1.14776i
$960$	9.05784	−	29.6303i	0.292340	−	0.956314i
$961$	−4.30193	−	7.45116i	−0.138772	−	0.240360i
$962$	4.75039	−	55.4883i	0.153159	−	1.78902i
$963$	−0.857913	−	1.20470i	−0.0276458	−	0.0388209i
$964$	36.0815	+	6.22353i	1.16211	+	0.200447i
$965$	0.000233630	0	0.000216852i	7.52081e−6	0	6.98070e-6i
$966$	−39.1229	+	8.20777i	−1.25876	+	0.264081i
$967$	−28.8723	+	28.8723i	−0.928470	+	0.928470i	−0.997607	−	0.0691376i	$-0.977975\pi$
$967$	−28.8723	+	28.8723i	−0.928470	+	0.928470i	0.0691376	+	0.997607i	$0.477975\pi$
$968$	5.73569	−	1.57130i	0.184352	−	0.0505036i
$969$	−0.773891	−	1.64251i	−0.0248610	−	0.0527651i
$970$	−12.3961	−	13.6519i	−0.398015	−	0.438337i
$971$	−26.3180	−	45.5842i	−0.844586	−	1.46287i	−0.885980	−	0.463723i	$-0.846513\pi$
$971$	−26.3180	−	45.5842i	−0.844586	−	1.46287i	0.0413946	−	0.999143i	$-0.486820\pi$
$972$	30.5668	−	6.13775i	0.980430	−	0.196868i
$973$	4.29760	−	28.8028i	0.137775	−	0.923376i
$974$	−13.3748	+	36.9611i	−0.428555	+	1.18431i
$975$	−0.382673	+	43.3340i	−0.0122553	+	1.38780i
$976$	−9.52284	+	26.7835i	−0.304819	+	0.857319i
$977$	−22.5132	+	6.03240i	−0.720262	+	0.192994i	−0.600288	−	0.799784i	$-0.704948\pi$
$977$	−22.5132	+	6.03240i	−0.720262	+	0.192994i	−0.119973	+	0.992777i	$0.538281\pi$
$978$	−2.17969	−	5.88148i	−0.0696989	−	0.188069i
$979$	25.9223			0.828480
$980$	−25.5258	+	18.1227i	−0.815392	+	0.578910i
$981$	49.8222	−	18.5843i	1.59070	−	0.593350i
$982$	−8.85382	−	6.17495i	−0.282537	−	0.197051i
$983$	−3.64182	−	13.5914i	−0.116156	−	0.433500i	0.883215	−	0.468969i	$-0.155374\pi$
$983$	−3.64182	−	13.5914i	−0.116156	−	0.433500i	−0.999371	+	0.0354687i	$0.988708\pi$
$984$	13.9706	+	9.58432i	0.445366	+	0.305537i
$985$	11.6730	+	2.66639i	0.371932	+	0.0849583i
$986$	1.13453	−	3.13527i	0.0361308	−	0.0998472i
$987$	−13.1838	−	12.4057i	−0.419646	−	0.394878i
$988$	2.02732	+	22.2180i	0.0644977	+	0.706850i
$989$	65.5438	−	37.8417i	2.08417	−	1.20330i
$990$	−10.4382	−	32.7151i	−0.331746	−	1.03975i
$991$	10.5743	−	18.3152i	0.335903	−	0.581801i	−0.647755	−	0.761849i	$-0.724292\pi$
$991$	10.5743	−	18.3152i	0.335903	−	0.581801i	0.983658	+	0.180048i	$0.0576252\pi$
$992$	14.7436	−	32.4029i	0.468111	−	1.02879i
$993$	−27.5301	+	4.96737i	−0.873642	+	0.157635i
$994$	3.81014	+	3.60049i	0.120850	+	0.114201i
$995$	−0.119833	−	3.21742i	−0.00379895	−	0.101999i
$996$	−9.26993	+	9.41396i	−0.293729	+	0.298293i
$997$	24.0627	−	6.44759i	0.762074	−	0.204197i	0.143207	−	0.989693i	$-0.454259\pi$
$997$	24.0627	−	6.44759i	0.762074	−	0.204197i	0.618867	+	0.785496i	$0.287592\pi$
$998$	−2.55370	+	29.8293i	−0.0808361	+	0.944229i
$999$	39.3695	−	11.0545i	1.24560	−	0.349750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dc.e.53.147	yes	704
3.2	odd	2	inner	840.2.dc.e.53.30	yes	704
5.2	odd	4	inner	840.2.dc.e.557.59	yes	704
7.2	even	3	inner	840.2.dc.e.653.92	yes	704
8.5	even	2	inner	840.2.dc.e.53.4	✓	704
15.2	even	4	inner	840.2.dc.e.557.118	yes	704
21.2	odd	6	inner	840.2.dc.e.653.85	yes	704
24.5	odd	2	inner	840.2.dc.e.53.173	yes	704
35.2	odd	12	inner	840.2.dc.e.317.173	yes	704
40.37	odd	4	inner	840.2.dc.e.557.85	yes	704
56.37	even	6	inner	840.2.dc.e.653.118	yes	704
105.2	even	12	inner	840.2.dc.e.317.4	yes	704
120.77	even	4	inner	840.2.dc.e.557.92	yes	704
168.149	odd	6	inner	840.2.dc.e.653.59	yes	704
280.37	odd	12	inner	840.2.dc.e.317.30	yes	704
840.317	even	12	inner	840.2.dc.e.317.147	yes	704

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dc.e.53.4	✓	704	8.5	even	2	inner
840.2.dc.e.53.30	yes	704	3.2	odd	2	inner
840.2.dc.e.53.147	yes	704	1.1	even	1	trivial
840.2.dc.e.53.173	yes	704	24.5	odd	2	inner
840.2.dc.e.317.4	yes	704	105.2	even	12	inner
840.2.dc.e.317.30	yes	704	280.37	odd	12	inner
840.2.dc.e.317.147	yes	704	840.317	even	12	inner
840.2.dc.e.317.173	yes	704	35.2	odd	12	inner
840.2.dc.e.557.59	yes	704	5.2	odd	4	inner
840.2.dc.e.557.85	yes	704	40.37	odd	4	inner
840.2.dc.e.557.92	yes	704	120.77	even	4	inner
840.2.dc.e.557.118	yes	704	15.2	even	4	inner
840.2.dc.e.653.59	yes	704	168.149	odd	6	inner
840.2.dc.e.653.85	yes	704	21.2	odd	6	inner
840.2.dc.e.653.92	yes	704	7.2	even	3	inner
840.2.dc.e.653.118	yes	704	56.37	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.dc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15997 + 0.808999i) q^{2} +(-1.62994 - 0.585913i) q^{3} +(0.691042 + 1.87682i) q^{4} +(-1.18933 - 1.89354i) q^{5} +(-1.41667 - 1.99826i) q^{6} +(-0.390444 + 2.61678i) q^{7} +(-0.716761 + 2.73610i) q^{8} +(2.31341 + 1.91001i) q^{9} +(0.152283 - 3.15861i) q^{10} +(1.80988 - 3.13480i) q^{11} +(-0.0267027 - 3.46400i) q^{12} +(-3.53835 + 3.53835i) q^{13} +(-2.56988 + 2.71951i) q^{14} +(0.829095 + 3.78320i) q^{15} +(-3.04492 + 2.59393i) q^{16} +(-0.454220 + 0.121708i) q^{17} +(1.13829 + 4.08709i) q^{18} +(-1.11463 - 1.93060i) q^{19} +(2.73195 - 3.54068i) q^{20} +(2.16961 - 4.03643i) q^{21} +(4.63544 - 2.17207i) q^{22} +(-5.95804 - 1.59645i) q^{23} +(2.77140 - 4.03972i) q^{24} +(-2.17097 + 4.50410i) q^{25} +(-6.96688 + 1.24184i) q^{26} +(-2.65162 - 4.46866i) q^{27} +(-5.18105 + 1.07551i) q^{28} +5.01369i q^{29} +(-2.09888 + 5.05912i) q^{30} +(-3.14658 + 5.45004i) q^{31} +(-5.63049 + 0.545528i) q^{32} +(-4.78671 + 4.04910i) q^{33} +(-0.625341 - 0.226286i) q^{34} +(5.41935 - 2.37291i) q^{35} +(-1.98608 + 5.66176i) q^{36} +(-2.03682 + 7.60153i) q^{37} +(0.268917 - 3.14116i) q^{38} +(7.84046 - 3.69413i) q^{39} +(6.03338 - 1.89692i) q^{40} +3.45830i q^{41} +(5.78214 - 2.92692i) q^{42} +(-8.67614 + 8.67614i) q^{43} +(7.13415 + 1.23054i) q^{44} +(0.865252 - 6.65217i) q^{45} +(-5.61960 - 6.67188i) q^{46} +(1.02243 - 3.81577i) q^{47} +(6.48286 - 2.44389i) q^{48} +(-6.69511 - 2.04341i) q^{49} +(-6.16206 + 3.46829i) q^{50} +(0.811661 + 0.0677568i) q^{51} +(-9.08599 - 4.19570i) q^{52} +(1.80177 - 0.482783i) q^{53} +(0.539343 - 7.32865i) q^{54} +(-8.08840 + 0.301252i) q^{55} +(-6.87993 - 2.94390i) q^{56} +(0.685619 + 3.79983i) q^{57} +(-4.05607 + 5.81572i) q^{58} +(-9.17243 - 5.29571i) q^{59} +(-6.52745 + 4.17041i) q^{60} +(6.15442 - 3.55326i) q^{61} +(-8.05900 + 3.77628i) q^{62} +(-5.90133 + 5.30795i) q^{63} +(-6.97251 - 3.92226i) q^{64} +(10.9083 + 2.49172i) q^{65} +(-8.82813 + 0.824379i) q^{66} +(13.6095 - 3.64664i) q^{67} +(-0.542309 - 0.768384i) q^{68} +(8.77587 + 6.09302i) q^{69} +(8.20594 + 1.63175i) q^{70} -1.40104i q^{71} +(-6.88414 + 4.96071i) q^{72} +(7.71519 - 2.06728i) q^{73} +(-8.51227 + 7.16973i) q^{74} +(6.17756 - 6.06941i) q^{75} +(2.85313 - 3.42609i) q^{76} +(7.49643 + 5.96001i) q^{77} +(12.0832 + 2.05786i) q^{78} +(13.2759 - 7.66486i) q^{79} +(8.53313 + 2.68063i) q^{80} +(1.70374 + 8.83727i) q^{81} +(-2.79776 + 4.01151i) q^{82} +(-2.69687 - 2.69687i) q^{83} +(9.07496 + 1.28262i) q^{84} +(0.770677 + 0.715331i) q^{85} +(-17.0830 + 3.04504i) q^{86} +(2.93759 - 8.17202i) q^{87} +(7.27987 + 7.19890i) q^{88} +(3.58068 + 6.20191i) q^{89} +(6.38526 - 7.01630i) q^{90} +(-7.87756 - 10.6406i) q^{91} +(-1.12100 - 12.2854i) q^{92} +(8.32199 - 7.03961i) q^{93} +(4.27294 - 3.59902i) q^{94} +(-2.32999 + 4.40672i) q^{95} +(9.49699 + 2.40980i) q^{96} +(4.12334 - 4.12334i) q^{97} +(-6.11298 - 7.78662i) q^{98} +(10.1745 - 3.79520i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 704 q - 16 q^{6} - 24 q^{7} + 12 q^{10} + 10 q^{12} + 32 q^{15} - 72 q^{16} + 6 q^{18} + 64 q^{22} - 8 q^{25} + 24 q^{28} + 8 q^{30} - 16 q^{31} + 44 q^{33} - 240 q^{36} + 16 q^{40} - 78 q^{42} - 8 q^{46}+ \cdots - 80 q^{97}+O(q^{100}) \) 704 * q - 16 * q^6 - 24 * q^7 + 12 * q^10 + 10 * q^12 + 32 * q^15 - 72 * q^16 + 6 * q^18 + 64 * q^22 - 8 * q^25 + 24 * q^28 + 8 * q^30 - 16 * q^31 + 44 * q^33 - 240 * q^36 + 16 * q^40 - 78 * q^42 - 8 * q^46 - 20 * q^48 - 60 * q^52 + 272 * q^55 + 8 * q^57 - 20 * q^58 - 14 * q^60 + 12 * q^63 - 84 * q^66 + 112 * q^70 - 38 * q^72 + 104 * q^73 - 64 * q^76 - 16 * q^78 - 168 * q^81 - 72 * q^82 - 64 * q^87 + 52 * q^88 - 44 * q^90 + 40 * q^96 - 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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