LMFDB - Embedded newform 560.2.t.a.43.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(43,560)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("560.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.t (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.20
Character	$\chi$	$=$	560.43
Dual form			560.2.t.a.547.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.918365 + 1.07546i) q^{2} -1.03076i q^{3} +(-0.313212 - 1.97532i) q^{4} +(1.39292 - 1.74922i) q^{5} +(1.10853 + 0.946610i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.41202 + 1.47722i) q^{8} +1.93754 q^{9} +O(q^{10})$	\(q+(-0.918365 + 1.07546i) q^{2} -1.03076i q^{3} +(-0.313212 - 1.97532i) q^{4} +(1.39292 - 1.74922i) q^{5} +(1.10853 + 0.946610i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.41202 + 1.47722i) q^{8} +1.93754 q^{9} +(0.601999 + 3.10445i) q^{10} +(-1.92306 + 1.92306i) q^{11} +(-2.03608 + 0.322845i) q^{12} +3.00357 q^{13} +(-0.111080 - 1.40984i) q^{14} +(-1.80302 - 1.43576i) q^{15} +(-3.80380 + 1.23739i) q^{16} +(3.27336 - 3.27336i) q^{17} +(-1.77937 + 2.08374i) q^{18} +(-0.431743 + 0.431743i) q^{19} +(-3.89155 - 2.20359i) q^{20} +(0.728855 + 0.728855i) q^{21} +(-0.302096 - 3.83424i) q^{22} +(4.59827 + 4.59827i) q^{23} +(1.52265 - 2.48620i) q^{24} +(-1.11954 - 4.87305i) q^{25} +(-2.75837 + 3.23020i) q^{26} -5.08940i q^{27} +(1.61824 + 1.17529i) q^{28} +(-6.13612 - 6.13612i) q^{29} +(3.19993 - 0.620514i) q^{30} -9.03649i q^{31} +(2.16251 - 5.22719i) q^{32} +(1.98221 + 1.98221i) q^{33} +(0.514218 + 6.52650i) q^{34} +(0.251941 + 2.22183i) q^{35} +(-0.606862 - 3.82727i) q^{36} +1.43774 q^{37} +(-0.0678232 - 0.860819i) q^{38} -3.09594i q^{39} +(5.94373 - 2.16149i) q^{40} -5.37759i q^{41} +(-1.45321 + 0.114497i) q^{42} +4.94048 q^{43} +(4.40099 + 3.19634i) q^{44} +(2.69884 - 3.38919i) q^{45} +(-9.16813 + 0.722349i) q^{46} +(1.21319 + 1.21319i) q^{47} +(1.27545 + 3.92079i) q^{48} -1.00000i q^{49} +(6.26890 + 3.27122i) q^{50} +(-3.37404 - 3.37404i) q^{51} +(-0.940754 - 5.93301i) q^{52} +7.11286i q^{53} +(5.47343 + 4.67393i) q^{54} +(0.685183 + 6.04253i) q^{55} +(-2.75011 + 0.661000i) q^{56} +(0.445022 + 0.445022i) q^{57} +(12.2343 - 0.963932i) q^{58} +(4.68617 + 4.68617i) q^{59} +(-2.27137 + 4.01124i) q^{60} +(-9.51486 + 9.51486i) q^{61} +(9.71835 + 8.29880i) q^{62} +(-1.37005 + 1.37005i) q^{63} +(3.63564 + 7.12616i) q^{64} +(4.18373 - 5.25390i) q^{65} +(-3.95216 + 0.311388i) q^{66} -10.4358 q^{67} +(-7.49121 - 5.44069i) q^{68} +(4.73970 - 4.73970i) q^{69} +(-2.62085 - 1.76950i) q^{70} +11.9003 q^{71} +(4.67338 + 2.86218i) q^{72} +(5.87007 - 5.87007i) q^{73} +(-1.32037 + 1.54623i) q^{74} +(-5.02293 + 1.15397i) q^{75} +(0.988059 + 0.717605i) q^{76} -2.71962i q^{77} +(3.32955 + 2.84321i) q^{78} -13.4009 q^{79} +(-3.13392 + 8.37726i) q^{80} +0.566696 q^{81} +(5.78336 + 4.93859i) q^{82} -0.228442i q^{83} +(1.21144 - 1.66801i) q^{84} +(-1.16629 - 10.2854i) q^{85} +(-4.53716 + 5.31327i) q^{86} +(-6.32484 + 6.32484i) q^{87} +(-7.47923 + 1.79767i) q^{88} +7.38645 q^{89} +(1.16640 + 6.01500i) q^{90} +(-2.12384 + 2.12384i) q^{91} +(7.64283 - 10.5233i) q^{92} -9.31442 q^{93} +(-2.41889 + 0.190582i) q^{94} +(0.153829 + 1.35660i) q^{95} +(-5.38796 - 2.22902i) q^{96} +(-0.176238 + 0.176238i) q^{97} +(1.07546 + 0.918365i) q^{98} +(-3.72601 + 3.72601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) $ 144 * q + 8 * q^4 - 144 * q^9	$ 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) $ 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.918365	+	1.07546i	−0.649382	+	0.760462i
$2$	−0.918365	+	1.07546i	−0.649382	+	0.760462i
$3$		−	1.03076i		−	0.595107i	−0.954705	−	0.297554i	$-0.903829\pi$
$3$		−	1.03076i		−	0.595107i	0.954705	−	0.297554i	$-0.0961707\pi$
$4$	−0.313212	−	1.97532i	−0.156606	−	0.987661i
$5$	1.39292	−	1.74922i	0.622933	−	0.782275i
$5$	1.39292	−	1.74922i	0.622933	−	0.782275i
$6$	1.10853	+	0.946610i	0.452557	+	0.386452i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	2.41202	+	1.47722i	0.852776	+	0.522276i
$9$	1.93754			0.645847
$10$	0.601999	+	3.10445i	0.190369	+	0.981713i
$11$	−1.92306	+	1.92306i	−0.579824	+	0.579824i	−0.934855	−	0.355030i	$-0.884471\pi$
$11$	−1.92306	+	1.92306i	−0.579824	+	0.579824i	0.355030	+	0.934855i	$0.384471\pi$
$12$	−2.03608	+	0.322845i	−0.587764	+	0.0931975i
$13$	3.00357			0.833039			0.416520	−	0.909127i	$-0.363250\pi$
$13$	3.00357			0.833039			0.416520	+	0.909127i	$0.363250\pi$
$14$	−0.111080	−	1.40984i	−0.0296875	−	0.376797i
$15$	−1.80302	−	1.43576i	−0.465537	−	0.370712i
$16$	−3.80380	+	1.23739i	−0.950949	+	0.309348i
$17$	3.27336	−	3.27336i	0.793907	−	0.793907i	−0.188220	−	0.982127i	$-0.560272\pi$
$17$	3.27336	−	3.27336i	0.793907	−	0.793907i	0.982127	+	0.188220i	$0.0602717\pi$
$18$	−1.77937	+	2.08374i	−0.419402	+	0.491143i
$19$	−0.431743	+	0.431743i	−0.0990487	+	0.0990487i	−0.754895	−	0.655846i	$-0.772312\pi$
$19$	−0.431743	+	0.431743i	−0.0990487	+	0.0990487i	0.655846	+	0.754895i	$0.272312\pi$
$20$	−3.89155	−	2.20359i	−0.870178	−	0.492738i
$21$	0.728855	+	0.728855i	0.159049	+	0.159049i
$22$	−0.302096	−	3.83424i	−0.0644072	−	0.817462i
$23$	4.59827	+	4.59827i	0.958806	+	0.958806i	0.999184	−	0.0403784i	$-0.0128563\pi$
$23$	4.59827	+	4.59827i	0.958806	+	0.958806i	−0.0403784	+	0.999184i	$0.512856\pi$
$24$	1.52265	−	2.48620i	0.310810	−	0.507493i
$25$	−1.11954	−	4.87305i	−0.223908	−	0.974610i
$26$	−2.75837	+	3.23020i	−0.540961	+	0.633495i
$27$		−	5.08940i		−	0.979456i
$28$	1.61824	+	1.17529i	0.305818	+	0.222109i
$29$	−6.13612	−	6.13612i	−1.13945	−	1.13945i	−0.988549	−	0.150899i	$-0.951783\pi$
$29$	−6.13612	−	6.13612i	−1.13945	−	1.13945i	−0.150899	−	0.988549i	$-0.548217\pi$
$30$	3.19993	−	0.620514i	0.584224	−	0.113290i
$31$		−	9.03649i		−	1.62300i	−0.584351	−	0.811501i	$-0.698651\pi$
$31$		−	9.03649i		−	1.62300i	0.584351	−	0.811501i	$-0.301349\pi$
$32$	2.16251	−	5.22719i	0.382282	−	0.924046i
$33$	1.98221	+	1.98221i	0.345058	+	0.345058i
$34$	0.514218	+	6.52650i	0.0881876	+	1.11929i
$35$	0.251941	+	2.22183i	0.0425858	+	0.375558i
$36$	−0.606862	−	3.82727i	−0.101144	−	0.637878i
$37$	1.43774			0.236364			0.118182	−	0.992992i	$-0.462293\pi$
$37$	1.43774			0.236364			0.118182	+	0.992992i	$0.462293\pi$
$38$	−0.0678232	−	0.860819i	−0.0110024	−	0.139643i
$39$		−	3.09594i		−	0.495748i
$40$	5.94373	−	2.16149i	0.939786	−	0.341762i
$41$		−	5.37759i		−	0.839838i	−0.907561	−	0.419919i	$-0.862058\pi$
$41$		−	5.37759i		−	0.839838i	0.907561	−	0.419919i	$-0.137942\pi$
$42$	−1.45321	+	0.114497i	−0.224234	+	0.0176672i
$43$	4.94048			0.753416			0.376708	−	0.926332i	$-0.377056\pi$
$43$	4.94048			0.753416			0.376708	+	0.926332i	$0.377056\pi$
$44$	4.40099	+	3.19634i	0.663474	+	0.481866i
$45$	2.69884	−	3.38919i	0.402320	−	0.505230i
$46$	−9.16813	+	0.722349i	−1.35177	+	0.106505i
$47$	1.21319	+	1.21319i	0.176962	+	0.176962i	0.790030	−	0.613068i	$-0.210065\pi$
$47$	1.21319	+	1.21319i	0.176962	+	0.176962i	−0.613068	+	0.790030i	$0.710065\pi$
$48$	1.27545	+	3.92079i	0.184095	+	0.565917i
$49$		−	1.00000i		−	0.142857i
$50$	6.26890	+	3.27122i	0.886556	+	0.462621i
$51$	−3.37404	−	3.37404i	−0.472460	−	0.472460i
$52$	−0.940754	−	5.93301i	−0.130459	−	0.822761i
$53$			7.11286i			0.977026i	0.872557	+	0.488513i	$0.162460\pi$
$53$			7.11286i			0.977026i	−0.872557	+	0.488513i	$0.837540\pi$
$54$	5.47343	+	4.67393i	0.744839	+	0.636041i
$55$	0.685183	+	6.04253i	0.0923901	+	0.814774i
$56$	−2.75011	+	0.661000i	−0.367498	+	0.0883299i
$57$	0.445022	+	0.445022i	0.0589446	+	0.0589446i
$58$	12.2343	−	0.963932i	1.60645	−	0.126570i
$59$	4.68617	+	4.68617i	0.610088	+	0.610088i	0.942969	−	0.332881i	$-0.108021\pi$
$59$	4.68617	+	4.68617i	0.610088	+	0.610088i	−0.332881	+	0.942969i	$0.608021\pi$
$60$	−2.27137	+	4.01124i	−0.293232	+	0.517849i
$61$	−9.51486	+	9.51486i	−1.21825	+	1.21825i	−0.250010	+	0.968243i	$0.580434\pi$
$61$	−9.51486	+	9.51486i	−1.21825	+	1.21825i	−0.968243	+	0.250010i	$0.919566\pi$
$62$	9.71835	+	8.29880i	1.23423	+	1.05395i
$63$	−1.37005	+	1.37005i	−0.172610	+	0.172610i
$64$	3.63564	+	7.12616i	0.454455	+	0.890770i
$65$	4.18373	−	5.25390i	0.518928	−	0.651666i
$66$	−3.95216	+	0.311388i	−0.486478	+	0.0383292i
$67$	−10.4358			−1.27493			−0.637466	−	0.770478i	$-0.720017\pi$
$67$	−10.4358			−1.27493			−0.637466	+	0.770478i	$0.720017\pi$
$68$	−7.49121	−	5.44069i	−0.908442	−	0.659781i
$69$	4.73970	−	4.73970i	0.570592	−	0.570592i
$70$	−2.62085	−	1.76950i	−0.313252	−	0.211495i
$71$	11.9003			1.41231			0.706156	−	0.708057i	$-0.250428\pi$
$71$	11.9003			1.41231			0.706156	+	0.708057i	$0.250428\pi$
$72$	4.67338	+	2.86218i	0.550763	+	0.337311i
$73$	5.87007	−	5.87007i	0.687040	−	0.687040i	−0.274536	−	0.961577i	$-0.588524\pi$
$73$	5.87007	−	5.87007i	0.687040	−	0.687040i	0.961577	+	0.274536i	$0.0885244\pi$
$74$	−1.32037	+	1.54623i	−0.153490	+	0.179746i
$75$	−5.02293	+	1.15397i	−0.579998	+	0.133249i
$76$	0.988059	+	0.717605i	0.113338	+	0.0823149i
$77$		−	2.71962i		−	0.309929i
$78$	3.32955	+	2.84321i	0.376998	+	0.321930i
$79$	−13.4009			−1.50772			−0.753862	−	0.657033i	$-0.771811\pi$
$79$	−13.4009			−1.50772			−0.753862	+	0.657033i	$0.771811\pi$
$80$	−3.13392	+	8.37726i	−0.350383	+	0.936606i
$81$	0.566696			0.0629662
$82$	5.78336	+	4.93859i	0.638666	+	0.545376i
$83$		−	0.228442i		−	0.0250748i	−0.999921	−	0.0125374i	$-0.996009\pi$
$83$		−	0.228442i		−	0.0250748i	0.999921	−	0.0125374i	$-0.00399088\pi$
$84$	1.21144	−	1.66801i	0.132179	−	0.181995i
$85$	−1.16629	−	10.2854i	−0.126502	−	1.11561i
$86$	−4.53716	+	5.31327i	−0.489255	+	0.572945i
$87$	−6.32484	+	6.32484i	−0.678094	+	0.678094i
$88$	−7.47923	+	1.79767i	−0.797289	+	0.191632i
$89$	7.38645			0.782962			0.391481	−	0.920186i	$-0.371963\pi$
$89$	7.38645			0.782962			0.391481	+	0.920186i	$0.371963\pi$
$90$	1.16640	+	6.01500i	0.122949	+	0.634037i
$91$	−2.12384	+	2.12384i	−0.222639	+	0.222639i
$92$	7.64283	−	10.5233i	0.796821	−	1.09713i
$93$	−9.31442			−0.965860
$94$	−2.41889	+	0.190582i	−0.249489	+	0.0196570i
$95$	0.153829	+	1.35660i	0.0157826	+	0.139184i
$96$	−5.38796	−	2.22902i	−0.549906	−	0.227499i
$97$	−0.176238	+	0.176238i	−0.0178943	+	0.0178943i	−0.715997	−	0.698103i	$-0.754028\pi$
$97$	−0.176238	+	0.176238i	−0.0178943	+	0.0178943i	0.698103	+	0.715997i	$0.254028\pi$
$98$	1.07546	+	0.918365i	0.108637	+	0.0927689i
$99$	−3.72601	+	3.72601i	−0.374478	+	0.374478i
$100$	−9.27519	+	3.73775i	−0.927519	+	0.373775i
$101$	0.870913	+	0.870913i	0.0866591	+	0.0866591i	0.749108	−	0.662448i	$-0.230483\pi$
$101$	0.870913	+	0.870913i	0.0866591	+	0.0866591i	−0.662448	+	0.749108i	$0.730483\pi$
$102$	6.72723	−	0.530033i	0.666095	−	0.0524811i
$103$	6.28953	+	6.28953i	0.619726	+	0.619726i	0.945461	−	0.325735i	$-0.105612\pi$
$103$	6.28953	+	6.28953i	0.619726	+	0.619726i	−0.325735	+	0.945461i	$0.605612\pi$
$104$	7.24465	+	4.43693i	0.710396	+	0.435077i
$105$	2.29016	−	0.259690i	0.223497	−	0.0253431i
$106$	−7.64957	−	6.53220i	−0.742991	−	0.634463i
$107$		−	1.56313i		−	0.151114i	−0.997142	−	0.0755568i	$-0.975927\pi$
$107$		−	1.56313i		−	0.151114i	0.997142	−	0.0755568i	$-0.0240734\pi$
$108$	−10.0532	+	1.59406i	−0.967370	+	0.153389i
$109$	−9.10664	−	9.10664i	−0.872258	−	0.872258i	0.120460	−	0.992718i	$-0.461563\pi$
$109$	−9.10664	−	9.10664i	−0.872258	−	0.872258i	−0.992718	+	0.120460i	$0.961563\pi$
$110$	−7.12772	−	4.81236i	−0.679601	−	0.458840i
$111$		−	1.48196i		−	0.140662i
$112$	1.81472	−	3.56466i	0.171475	−	0.336828i
$113$	8.98397	+	8.98397i	0.845141	+	0.845141i	0.989522	−	0.144381i	$-0.0461192\pi$
$113$	8.98397	+	8.98397i	0.845141	+	0.845141i	−0.144381	+	0.989522i	$0.546119\pi$
$114$	−0.887294	+	0.0699091i	−0.0831027	+	0.00654759i
$115$	14.4484	−	1.63836i	1.34732	−	0.152778i
$116$	−10.1989	+	14.0427i	−0.946944	+	1.30383i
$117$	5.81954			0.538016
$118$	−9.34339	+	0.736158i	−0.860129	+	0.0677688i
$119$			4.62924i			0.424361i
$120$	−2.22797	−	6.12654i	−0.203385	−	0.559274i
$121$			3.60368i			0.327607i
$122$	−1.49470	−	18.9709i	−0.135324	−	1.71755i
$123$	−5.54298			−0.499794
$124$	−17.8500	+	2.83034i	−1.60298	+	0.254172i
$125$	−10.0835	−	4.82946i	−0.901893	−	0.431960i
$126$	−0.215223	−	2.73163i	−0.0191736	−	0.243353i
$127$	−7.94010	−	7.94010i	−0.704570	−	0.704570i	0.260818	−	0.965388i	$-0.416008\pi$
$127$	−7.94010	−	7.94010i	−0.704570	−	0.704570i	−0.965388	+	0.260818i	$0.916008\pi$
$128$	−11.0027	−	2.63444i	−0.972512	−	0.232854i
$129$		−	5.09243i		−	0.448364i
$130$	1.80815	+	9.32442i	0.158585	+	0.817805i
$131$	3.22262	+	3.22262i	0.281562	+	0.281562i	0.833732	−	0.552170i	$-0.186200\pi$
$131$	3.22262	+	3.22262i	0.281562	+	0.281562i	−0.552170	+	0.833732i	$0.686200\pi$
$132$	3.29464	−	4.53635i	0.286762	−	0.394838i
$133$		−	0.610577i		−	0.0529437i
$134$	9.58384	−	11.2232i	0.827918	−	0.969538i
$135$	−8.90248	−	7.08914i	−0.766204	−	0.610136i
$136$	12.7309	−	3.05993i	1.09166	−	0.262387i
$137$	12.2955	+	12.2955i	1.05047	+	1.05047i	0.998657	+	0.0518151i	$0.0165006\pi$
$137$	12.2955	+	12.2955i	1.05047	+	1.05047i	0.0518151	+	0.998657i	$0.483499\pi$
$138$	0.744566	+	9.45011i	0.0633817	+	0.804446i
$139$	−2.39212	−	2.39212i	−0.202897	−	0.202897i	0.598343	−	0.801240i	$-0.295826\pi$
$139$	−2.39212	−	2.39212i	−0.202897	−	0.202897i	−0.801240	+	0.598343i	$0.795826\pi$
$140$	4.30992	−	1.19357i	0.364255	−	0.100875i
$141$	1.25050	−	1.25050i	0.105311	−	0.105311i
$142$	−10.9289	+	12.7983i	−0.917130	+	1.07401i
$143$	−5.77604	+	5.77604i	−0.483017	+	0.483017i
$144$	−7.37002	+	2.39750i	−0.614168	+	0.199791i
$145$	−19.2806	+	2.18629i	−1.60116	+	0.181561i
$146$	0.922139	+	11.7039i	0.0763168	+	0.968620i
$147$	−1.03076			−0.0850153
$148$	−0.450319	−	2.84001i	−0.0370160	−	0.233447i
$149$	−7.29720	+	7.29720i	−0.597810	+	0.597810i	−0.939729	−	0.341920i	$-0.888923\pi$
$149$	−7.29720	+	7.29720i	−0.597810	+	0.597810i	0.341920	+	0.939729i	$0.388923\pi$
$150$	3.37183	−	6.46171i	0.275309	−	0.527596i
$151$	−18.6129			−1.51469			−0.757347	−	0.653013i	$-0.773505\pi$
$151$	−18.6129			−1.51469			−0.757347	+	0.653013i	$0.773505\pi$
$152$	−1.67915	+	0.403592i	−0.136197	+	0.0327356i
$153$	6.34228	−	6.34228i	0.512743	−	0.512743i
$154$	2.92483	+	2.49760i	0.235689	+	0.201262i
$155$	−15.8068	−	12.5871i	−1.26963	−	1.01102i
$156$	−6.11549	+	0.969688i	−0.489631	+	0.0776372i
$157$			5.42553i			0.433004i	0.976282	+	0.216502i	$0.0694648\pi$
$157$			5.42553i			0.433004i	−0.976282	+	0.216502i	$0.930535\pi$
$158$	12.3069	−	14.4121i	0.979088	−	1.14657i
$159$	7.33162			0.581435
$160$	−6.13130	−	11.0638i	−0.484722	−	0.874668i
$161$	−6.50294			−0.512503
$162$	−0.520434	+	0.609457i	−0.0408891	+	0.0478835i
$163$		−	13.1365i		−	1.02893i	−0.857511	−	0.514465i	$-0.827990\pi$
$163$		−	13.1365i		−	1.02893i	0.857511	−	0.514465i	$-0.172010\pi$
$164$	−10.6225	+	1.68433i	−0.829476	+	0.131524i
$165$	6.22837	−	0.706257i	0.484878	−	0.0549820i
$166$	0.245679	+	0.209793i	0.0190684	+	0.0162831i
$167$	−12.0845	+	12.0845i	−0.935128	+	0.935128i	−0.998020	−	0.0628922i	$-0.979968\pi$
$167$	−12.0845	+	12.0845i	−0.935128	+	0.935128i	0.0628922	+	0.998020i	$0.479968\pi$
$168$	0.681330	+	2.83469i	0.0525658	+	0.218701i
$169$	−3.97859			−0.306045
$170$	12.1326	+	8.19142i	0.930524	+	0.628254i
$171$	−0.836521	+	0.836521i	−0.0639703	+	0.0639703i
$172$	−1.54742	−	9.75904i	−0.117990	−	0.744120i
$173$	7.71760			0.586758			0.293379	−	0.955996i	$-0.405220\pi$
$173$	7.71760			0.586758			0.293379	+	0.955996i	$0.405220\pi$
$174$	−0.993579	−	12.6106i	−0.0753230	−	0.956007i
$175$	4.23740	+	2.65413i	0.320317	+	0.200634i
$176$	4.93535	−	9.69450i	0.372016	−	0.730751i
$177$	4.83030	−	4.83030i	0.363068	−	0.363068i
$178$	−6.78345	+	7.94380i	−0.508441	+	0.595413i
$179$	12.1397	−	12.1397i	0.907365	−	0.907365i	−0.0886942	−	0.996059i	$-0.528269\pi$
$179$	12.1397	−	12.1397i	0.907365	−	0.907365i	0.996059	+	0.0886942i	$0.0282694\pi$
$180$	−7.54005	−	4.26955i	−0.562002	−	0.318234i
$181$	9.74610	+	9.74610i	0.724422	+	0.724422i	0.969503	−	0.245080i	$-0.0788144\pi$
$181$	9.74610	+	9.74610i	0.724422	+	0.724422i	−0.245080	+	0.969503i	$0.578814\pi$
$182$	−0.333638	−	4.23456i	−0.0247309	−	0.313887i
$183$	9.80750	+	9.80750i	0.724991	+	0.724991i
$184$	4.29844	+	17.8838i	0.316886	+	1.31841i
$185$	2.00266	−	2.51493i	0.147239	−	0.184901i
$186$	8.55403	−	10.0172i	0.627212	−	0.734500i
$187$			12.5898i			0.920654i
$188$	2.01646	−	2.77643i	0.147065	−	0.202492i
$189$	3.59875	+	3.59875i	0.261771	+	0.261771i
$190$	−1.60023	−	1.08041i	−0.116093	−	0.0783815i
$191$			9.91809i			0.717647i	0.933405	+	0.358824i	$0.116822\pi$
$191$			9.91809i			0.717647i	−0.933405	+	0.358824i	$0.883178\pi$
$192$	7.34533	−	3.74746i	0.530103	−	0.270450i
$193$	14.4496	+	14.4496i	1.04011	+	1.04011i	0.999161	+	0.0409462i	$0.0130372\pi$
$193$	14.4496	+	14.4496i	1.04011	+	1.04011i	0.0409462	+	0.999161i	$0.486963\pi$
$194$	−0.0276855	−	0.351387i	−0.00198770	−	0.0252281i
$195$	−5.41549	−	4.31241i	−0.387811	−	0.308818i
$196$	−1.97532	+	0.313212i	−0.141094	+	0.0223723i
$197$	3.41855			0.243562			0.121781	−	0.992557i	$-0.461139\pi$
$197$	3.41855			0.243562			0.121781	+	0.992557i	$0.461139\pi$
$198$	−0.585324	−	7.42900i	−0.0415972	−	0.527956i
$199$			26.2912i			1.86374i	0.362796	+	0.931868i	$0.381822\pi$
$199$			26.2912i			1.86374i	−0.362796	+	0.931868i	$0.618178\pi$
$200$	4.49822	−	13.4077i	0.318072	−	0.948066i
$201$			10.7567i			0.758721i
$202$	−1.73644	+	0.136813i	−0.122176	+	0.00962613i
$203$	8.67778			0.609061
$204$	−5.60802	+	7.72161i	−0.392640	+	0.540621i
$205$	−9.40659	−	7.49056i	−0.656985	−	0.523163i
$206$	−12.5402	+	0.988032i	−0.873717	+	0.0688394i
$207$	8.90935	+	8.90935i	0.619242	+	0.619242i
$208$	−11.4250	+	3.71658i	−0.792178	+	0.257699i
$209$		−	1.66054i		−	0.114862i
$210$	−1.82392	+	2.70146i	−0.125862	+	0.186419i
$211$	−2.60327	−	2.60327i	−0.179216	−	0.179216i	0.611798	−	0.791014i	$-0.290447\pi$
$211$	−2.60327	−	2.60327i	−0.179216	−	0.179216i	−0.791014	+	0.611798i	$0.790447\pi$
$212$	14.0502	−	2.22783i	0.964971	−	0.153008i
$213$		−	12.2664i		−	0.840477i
$214$	1.68108	+	1.43552i	0.114916	+	0.0981304i
$215$	6.88170	−	8.64199i	0.469328	−	0.589379i
$216$	7.51817	−	12.2757i	0.511546	−	0.835257i
$217$	6.38977	+	6.38977i	0.433766	+	0.433766i
$218$	18.1570	−	1.43058i	1.22975	−	0.0968908i
$219$	−6.05061	−	6.05061i	−0.408863	−	0.408863i
$220$	11.7213	−	3.24605i	0.790252	−	0.218849i
$221$	9.83177	−	9.83177i	0.661356	−	0.661356i
$222$	1.59379	+	1.36098i	0.106968	+	0.0913432i
$223$	−16.1145	+	16.1145i	−1.07911	+	1.07911i	−0.0825166	+	0.996590i	$0.526296\pi$
$223$	−16.1145	+	16.1145i	−1.07911	+	1.07911i	−0.996590	+	0.0825166i	$0.973704\pi$
$224$	2.16706	+	5.22531i	0.144792	+	0.349131i
$225$	−2.16916	−	9.44174i	−0.144610	−	0.629450i
$226$	−17.9124	+	1.41131i	−1.19152	+	0.0938786i
$227$	−5.58873			−0.370937			−0.185469	−	0.982650i	$-0.559380\pi$
$227$	−5.58873			−0.370937			−0.185469	+	0.982650i	$0.559380\pi$
$228$	0.739675	−	1.01845i	0.0489862	−	0.0674484i
$229$	−18.0156	+	18.0156i	−1.19050	+	1.19050i	−0.213575	+	0.976927i	$0.568511\pi$
$229$	−18.0156	+	18.0156i	−1.19050	+	1.19050i	−0.976927	+	0.213575i	$0.931489\pi$
$230$	−11.5069	+	17.0433i	−0.758745	+	1.12380i
$231$	−2.80326			−0.184441
$232$	−5.73602	−	23.8648i	−0.376588	−	1.56680i
$233$	−0.970636	+	0.970636i	−0.0635885	+	0.0635885i	−0.738186	−	0.674597i	$-0.764317\pi$
$233$	−0.970636	+	0.970636i	−0.0635885	+	0.0635885i	0.674597	+	0.738186i	$0.264317\pi$
$234$	−5.34446	+	6.25866i	−0.349378	+	0.409141i
$235$	3.81202	−	0.432258i	0.248669	−	0.0281974i
$236$	7.78893	−	10.7245i	0.507016	−	0.698103i
$237$			13.8131i			0.897257i
$238$	−4.97854	−	4.25133i	−0.322711	−	0.275573i
$239$	10.5316			0.681234			0.340617	−	0.940202i	$-0.389364\pi$
$239$	10.5316			0.681234			0.340617	+	0.940202i	$0.389364\pi$
$240$	8.63491	+	3.23031i	0.557381	+	0.208515i
$241$	23.8821			1.53838			0.769189	−	0.639021i	$-0.220660\pi$
$241$	23.8821			1.53838			0.769189	+	0.639021i	$0.220660\pi$
$242$	−3.87560	−	3.30949i	−0.249133	−	0.212742i
$243$		−	15.8523i		−	1.01693i
$244$	21.7751	+	15.8148i	1.39401	+	1.01244i
$245$	−1.74922	−	1.39292i	−0.111754	−	0.0889905i
$246$	5.09048	−	5.96124i	0.324557	−	0.380074i
$247$	−1.29677	+	1.29677i	−0.0825114	+	0.0825114i
$248$	13.3489	−	21.7962i	0.847655	−	1.38406i
$249$	−0.235468			−0.0149222
$250$	14.4542	−	6.40913i	0.914162	−	0.405349i
$251$	−5.73078	+	5.73078i	−0.361723	+	0.361723i	−0.864447	−	0.502724i	$-0.832331\pi$
$251$	−5.73078	+	5.73078i	−0.361723	+	0.361723i	0.502724	+	0.864447i	$0.332331\pi$
$252$	3.13540	+	2.27717i	0.197512	+	0.143448i
$253$	−17.6855			−1.11188
$254$	15.8311	−	1.24732i	0.993334	−	0.0782639i
$255$	−10.6017	+	1.20216i	−0.663905	+	0.0752825i
$256$	12.9377	−	9.41356i	0.808608	−	0.588348i
$257$	−12.8802	+	12.8802i	−0.803444	+	0.803444i	−0.983632	−	0.180188i	$-0.942329\pi$
$257$	−12.8802	+	12.8802i	−0.803444	+	0.803444i	0.180188	+	0.983632i	$0.442329\pi$
$258$	5.47669	+	4.67671i	0.340964	+	0.291159i
$259$	−1.01664	+	1.01664i	−0.0631708	+	0.0631708i
$260$	−11.6885	−	6.61863i	−0.724892	−	0.410470i
$261$	−11.8890	−	11.8890i	−0.735910	−	0.735910i
$262$	−6.42533	+	0.506246i	−0.396958	+	0.0312760i
$263$	2.10457	+	2.10457i	0.129773	+	0.129773i	0.769010	−	0.639237i	$-0.220750\pi$
$263$	2.10457	+	2.10457i	0.129773	+	0.129773i	−0.639237	+	0.769010i	$0.720750\pi$
$264$	1.85296	+	7.70927i	0.114042	+	0.474472i
$265$	12.4419	+	9.90765i	0.764303	+	0.608622i
$266$	0.656649	+	0.560732i	0.0402617	+	0.0343807i
$267$		−	7.61363i		−	0.465946i
$268$	3.26861	+	20.6140i	0.199662	+	1.25920i
$269$	19.9367	+	19.9367i	1.21556	+	1.21556i	0.969170	+	0.246391i	$0.0792449\pi$
$269$	19.9367	+	19.9367i	1.21556	+	1.21556i	0.246391	+	0.969170i	$0.420755\pi$
$270$	15.7998	−	3.06382i	0.961544	−	0.186458i
$271$		−	8.19802i		−	0.497994i	−0.968504	−	0.248997i	$-0.919899\pi$
$271$		−	8.19802i		−	0.497994i	0.968504	−	0.248997i	$-0.0801009\pi$
$272$	−8.40078	+	16.5016i	−0.509372	+	1.00056i
$273$	2.18916	+	2.18916i	0.132494	+	0.132494i
$274$	−24.5149	+	1.93151i	−1.48100	+	0.116687i
$275$	11.5241	+	7.21823i	0.694930	+	0.435276i
$276$	−10.8470	−	7.87790i	−0.652910	−	0.474194i
$277$	−11.4636			−0.688780			−0.344390	−	0.938827i	$-0.611914\pi$
$277$	−11.4636			−0.688780			−0.344390	+	0.938827i	$0.611914\pi$
$278$	4.76947	−	0.375782i	0.286054	−	0.0225379i
$279$		−	17.5086i		−	1.04821i
$280$	−2.67445	+	5.73126i	−0.159829	+	0.342508i
$281$		−	13.0902i		−	0.780894i	−0.920625	−	0.390447i	$-0.872320\pi$
$281$		−	13.0902i		−	0.780894i	0.920625	−	0.390447i	$-0.127680\pi$
$282$	0.196444	+	2.49328i	0.0116980	+	0.148473i
$283$	1.03270			0.0613878			0.0306939	−	0.999529i	$-0.490228\pi$
$283$	1.03270			0.0613878			0.0306939	+	0.999529i	$0.490228\pi$
$284$	−3.72734	−	23.5070i	−0.221177	−	1.39489i
$285$	1.39832	−	0.158561i	0.0828294	−	0.00939232i
$286$	−0.907366	−	11.5164i	−0.0536537	−	0.680978i
$287$	3.80253	+	3.80253i	0.224456	+	0.224456i
$288$	4.18996	−	10.1279i	0.246896	−	0.596793i
$289$		−	4.42982i		−	0.260578i
$290$	15.3553	−	22.7432i	0.901695	−	1.33553i
$291$	0.181658	+	0.181658i	0.0106490	+	0.0106490i
$292$	−13.4339	−	9.75671i	−0.786158	−	0.570968i
$293$			5.34031i			0.311984i	0.987758	+	0.155992i	$0.0498575\pi$
$293$			5.34031i			0.311984i	−0.987758	+	0.155992i	$0.950143\pi$
$294$	0.946610	−	1.10853i	0.0552074	−	0.0646510i
$295$	14.7246	−	1.66968i	0.857300	−	0.0972123i
$296$	3.46786	+	2.12386i	0.201565	+	0.123447i
$297$	9.78722	+	9.78722i	0.567912	+	0.567912i
$298$	−1.14633	−	14.5493i	−0.0664050	−	0.842819i
$299$	13.8112	+	13.8112i	0.798723	+	0.798723i
$300$	3.85271	+	9.56046i	0.222436	+	0.551973i
$301$	−3.49345	+	3.49345i	−0.201359	+	0.201359i
$302$	17.0934	−	20.0173i	0.983615	−	1.15187i
$303$	0.897699	−	0.897699i	0.0515715	−	0.0515715i
$304$	1.10803	−	2.17650i	0.0635498	−	0.124831i
$305$	3.39013	+	29.8970i	0.194118	+	1.71190i
$306$	0.996318	+	12.6454i	0.0569557	+	0.722888i
$307$	−11.5897			−0.661459			−0.330729	−	0.943726i	$-0.607295\pi$
$307$	−11.5897			−0.661459			−0.330729	+	0.943726i	$0.607295\pi$
$308$	−5.37212	+	0.851818i	−0.306105	+	0.0485368i
$309$	6.48297	−	6.48297i	0.368803	−	0.368803i
$310$	28.0533	−	5.43996i	1.59332	−	0.308969i
$311$	13.2852			0.753336			0.376668	−	0.926348i	$-0.377070\pi$
$311$	13.2852			0.753336			0.376668	+	0.926348i	$0.377070\pi$
$312$	4.57339	−	7.46747i	0.258917	−	0.422762i
$313$	17.4843	−	17.4843i	0.988271	−	0.988271i	−0.0116614	−	0.999932i	$-0.503712\pi$
$313$	17.4843	−	17.4843i	0.988271	−	0.988271i	0.999932	+	0.0116614i	$0.00371202\pi$
$314$	−5.83492	−	4.98261i	−0.329283	−	0.281185i
$315$	0.488146	+	4.30489i	0.0275039	+	0.242553i
$316$	4.19734	+	26.4712i	0.236119	+	1.48912i
$317$		−	15.8635i		−	0.890984i	−0.895286	−	0.445492i	$-0.853029\pi$
$317$		−	15.8635i		−	0.890984i	0.895286	−	0.445492i	$-0.146971\pi$
$318$	−6.73310	+	7.88483i	−0.377574	+	0.442160i
$319$	23.6002			1.32136
$320$	17.5294	+	3.56664i	0.979922	+	0.199381i
$321$	−1.61121			−0.0899288
$322$	5.97207	−	6.99363i	0.332810	−	0.389740i
$323$			2.82650i			0.157271i
$324$	−0.177496	−	1.11941i	−0.00986090	−	0.0621893i
$325$	−3.36261	−	14.6365i	−0.186524	−	0.811889i
$326$	14.1277	+	12.0641i	0.782463	+	0.668169i
$327$	−9.38672	+	9.38672i	−0.519087	+	0.519087i
$328$	7.94388	−	12.9708i	0.438628	−	0.716194i
$329$	−1.71571			−0.0945903
$330$	−4.96037	+	7.34694i	−0.273059	+	0.404436i
$331$	16.7231	−	16.7231i	0.919184	−	0.919184i	−0.0777860	−	0.996970i	$-0.524785\pi$
$331$	16.7231	−	16.7231i	0.919184	−	0.919184i	0.996970	+	0.0777860i	$0.0247851\pi$
$332$	−0.451247	+	0.0715509i	−0.0247654	+	0.00392686i
$333$	2.78569			0.152655
$334$	−1.89838	−	24.0944i	−0.103874	−	1.31839i
$335$	−14.5362	+	18.2545i	−0.794198	+	0.997347i
$336$	−3.67429	−	1.87054i	−0.200449	−	0.102046i
$337$	−8.72617	+	8.72617i	−0.475345	+	0.475345i	−0.903639	−	0.428294i	$-0.859115\pi$
$337$	−8.72617	+	8.72617i	−0.475345	+	0.475345i	0.428294	+	0.903639i	$0.359115\pi$
$338$	3.65380	−	4.27880i	0.198740	−	0.232736i
$339$	9.26028	−	9.26028i	0.502949	−	0.502949i
$340$	−19.9516	+	5.52531i	−1.08203	+	0.299652i
$341$	17.3777	+	17.3777i	0.941056	+	0.941056i
$342$	−0.131410	−	1.66787i	−0.00710585	−	0.0901882i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	11.9165	+	7.29818i	0.642496	+	0.393491i
$345$	−1.68875	−	14.8928i	−0.0909190	−	0.801801i
$346$	−7.08757	+	8.29994i	−0.381030	+	0.446208i
$347$		−	0.743603i		−	0.0399187i	−0.999801	−	0.0199593i	$-0.993646\pi$
$347$		−	0.743603i		−	0.0399187i	0.999801	−	0.0199593i	$-0.00635368\pi$
$348$	14.4746	+	10.5126i	0.775921	+	0.563533i
$349$	−24.3070	−	24.3070i	−1.30113	−	1.30113i	−0.927634	−	0.373492i	$-0.878160\pi$
$349$	−24.3070	−	24.3070i	−1.30113	−	1.30113i	−0.373492	−	0.927634i	$-0.621840\pi$
$350$	−6.74589	+	2.11968i	−0.360583	+	0.113302i
$351$		−	15.2864i		−	0.815925i
$352$	5.89356	+	14.2108i	0.314128	+	0.757441i
$353$	−15.5529	−	15.5529i	−0.827800	−	0.827800i	0.159412	−	0.987212i	$-0.449040\pi$
$353$	−15.5529	−	15.5529i	−0.827800	−	0.827800i	−0.987212	+	0.159412i	$0.949040\pi$
$354$	0.758799	+	9.63075i	0.0403297	+	0.511869i
$355$	16.5762	−	20.8163i	0.879776	−	1.10482i
$356$	−2.31353	−	14.5906i	−0.122617	−	0.773301i
$357$	4.77161			0.252541
$358$	1.90705	+	24.2044i	0.100790	+	1.27924i
$359$		−	0.576020i		−	0.0304012i	−0.999884	−	0.0152006i	$-0.995161\pi$
$359$		−	0.576020i		−	0.0304012i	0.999884	−	0.0152006i	$-0.00483868\pi$
$360$	11.5162	−	4.18799i	0.606959	−	0.220726i
$361$			18.6272i			0.980379i
$362$	−19.4320	+	1.53103i	−1.02132	+	0.0804692i
$363$	3.71452			0.194962
$364$	4.86049	+	3.53006i	0.254759	+	0.185025i
$365$	−2.09150	−	18.4446i	−0.109474	−	0.965435i
$366$	−19.5544	+	1.54068i	−1.02213	+	0.0805324i
$367$	−5.15087	−	5.15087i	−0.268873	−	0.268873i	0.559773	−	0.828646i	$-0.310888\pi$
$367$	−5.15087	−	5.15087i	−0.268873	−	0.268873i	−0.828646	+	0.559773i	$0.810888\pi$
$368$	−23.1807	−	11.8010i	−1.20838	−	0.615171i
$369$		−	10.4193i		−	0.542407i
$370$	0.865521	+	4.46340i	0.0449963	+	0.232041i
$371$	−5.02955	−	5.02955i	−0.261121	−	0.261121i
$372$	2.91739	+	18.3990i	0.151260	+	0.953943i
$373$			19.5081i			1.01009i	0.863093	+	0.505046i	$0.168524\pi$
$373$			19.5081i			1.01009i	−0.863093	+	0.505046i	$0.831476\pi$
$374$	−13.5397	−	11.5620i	−0.700123	−	0.597856i
$375$	−4.97799	+	10.3936i	−0.257062	+	0.536723i
$376$	1.13409	+	4.71839i	0.0584860	+	0.243332i
$377$	−18.4302	−	18.4302i	−0.949206	−	0.949206i
$378$	−7.17526	+	0.565333i	−0.369056	+	0.0290776i
$379$	3.93724	+	3.93724i	0.202242	+	0.202242i	0.800960	−	0.598718i	$-0.204323\pi$
$379$	3.93724	+	3.93724i	0.202242	+	0.202242i	−0.598718	+	0.800960i	$0.704323\pi$
$380$	2.63154	−	0.728766i	0.134995	−	0.0373849i
$381$	−8.18431	+	8.18431i	−0.419295	+	0.419295i
$382$	−10.6665	−	9.10842i	−0.545744	−	0.466027i
$383$	−17.9135	+	17.9135i	−0.915338	+	0.915338i	−0.996686	−	0.0813475i	$-0.974078\pi$
$383$	−17.9135	+	17.9135i	−0.915338	+	0.915338i	0.0813475	+	0.996686i	$0.474078\pi$
$384$	−2.71546	+	11.3411i	−0.138573	+	0.578749i
$385$	−4.75721	−	3.78821i	−0.242450	−	0.193065i
$386$	−28.8100	+	2.26991i	−1.46639	+	0.115536i
$387$	9.57239			0.486592
$388$	0.403327	+	0.292927i	0.0204758	+	0.0148711i
$389$	−24.4320	+	24.4320i	−1.23875	+	1.23875i	−0.278243	+	0.960511i	$0.589752\pi$
$389$	−24.4320	+	24.4320i	−1.23875	+	1.23875i	−0.960511	+	0.278243i	$0.910248\pi$
$390$	9.61120	−	1.86376i	0.486682	−	0.0943750i
$391$	30.1036			1.52241
$392$	1.47722	−	2.41202i	0.0746109	−	0.121825i
$393$	3.32174	−	3.32174i	0.167559	−	0.167559i
$394$	−3.13948	+	3.67650i	−0.158165	+	0.185220i
$395$	−18.6665	+	23.4412i	−0.939211	+	1.17945i
$396$	8.52710	+	6.19304i	0.428503	+	0.311212i
$397$			31.3566i			1.57374i	0.617116	+	0.786872i	$0.288301\pi$
$397$			31.3566i			1.57374i	−0.617116	+	0.786872i	$0.711699\pi$
$398$	−28.2751	−	24.1450i	−1.41730	−	1.21028i
$399$	−0.629356			−0.0315072
$400$	10.2884	+	17.1508i	0.514418	+	0.857539i
$401$	−10.3232			−0.515517			−0.257759	−	0.966209i	$-0.582984\pi$
$401$	−10.3232			−0.515517			−0.257759	+	0.966209i	$0.582984\pi$
$402$	−11.5684	−	9.87860i	−0.576979	−	0.492700i
$403$		−	27.1417i		−	1.35202i
$404$	1.44755	−	1.99311i	0.0720185	−	0.0991612i
$405$	0.789363	−	0.991276i	0.0392238	−	0.0492569i
$406$	−7.96937	+	9.33257i	−0.395513	+	0.463168i
$407$	−2.76487	+	2.76487i	−0.137049	+	0.137049i
$408$	−3.15404	−	13.1224i	−0.156148	−	0.649657i
$409$	−2.81044			−0.138967			−0.0694837	−	0.997583i	$-0.522135\pi$
$409$	−2.81044			−0.138967			−0.0694837	+	0.997583i	$0.522135\pi$
$410$	16.6944	−	3.23731i	0.824480	−	0.159879i
$411$	12.6736	−	12.6736i	0.625143	−	0.625143i
$412$	10.4539	−	14.3938i	0.515026	−	0.709132i
$413$	−6.62725			−0.326106
$414$	−17.7636	+	1.39958i	−0.873035	+	0.0687857i
$415$	−0.399595	−	0.318202i	−0.0196154	−	0.0156199i
$416$	6.49525	−	15.7002i	0.318456	−	0.769767i
$417$	−2.46570	+	2.46570i	−0.120746	+	0.120746i
$418$	1.78583	+	1.52498i	0.0873480	+	0.0745891i
$419$	0.860576	−	0.860576i	0.0420419	−	0.0420419i	−0.685773	−	0.727815i	$-0.740536\pi$
$419$	0.860576	−	0.860576i	0.0420419	−	0.0420419i	0.727815	+	0.685773i	$0.240536\pi$
$420$	−1.23028	−	4.44247i	−0.0600314	−	0.216771i
$421$	−13.5924	−	13.5924i	−0.662454	−	0.662454i	0.293504	−	0.955958i	$-0.405179\pi$
$421$	−13.5924	−	13.5924i	−0.662454	−	0.662454i	−0.955958	+	0.293504i	$0.905179\pi$
$422$	5.19045	−	0.408951i	0.252667	−	0.0199074i
$423$	2.35061	+	2.35061i	0.114291	+	0.114291i
$424$	−10.5073	+	17.1563i	−0.510277	+	0.833185i
$425$	−19.6159	−	12.2866i	−0.951512	−	0.595988i
$426$	13.1919	+	11.2650i	0.639151	+	0.545790i
$427$		−	13.4561i		−	0.651184i
$428$	−3.08769	+	0.489592i	−0.149249	+	0.0236653i
$429$	5.95369	+	5.95369i	0.287447	+	0.287447i
$430$	2.97417	+	15.3375i	0.143427	+	0.739638i
$431$		−	23.8352i		−	1.14810i	−0.818819	−	0.574052i	$-0.805371\pi$
$431$		−	23.8352i		−	1.14810i	0.818819	−	0.574052i	$-0.194629\pi$
$432$	6.29758	+	19.3590i	0.302992	+	0.931412i
$433$	−10.8037	−	10.8037i	−0.519193	−	0.519193i	0.398134	−	0.917327i	$-0.369658\pi$
$433$	−10.8037	−	10.8037i	−0.519193	−	0.519193i	−0.917327	+	0.398134i	$0.869658\pi$
$434$	−12.7400	+	1.00378i	−0.611542	+	0.0481829i
$435$	2.25353	+	19.8735i	0.108049	+	0.952863i
$436$	−15.1362	+	20.8409i	−0.724894	+	0.998096i
$437$	−3.97054			−0.189937
$438$	12.0638	−	0.950500i	0.576433	−	0.0454166i
$439$		−	25.4145i		−	1.21297i	−0.795096	−	0.606483i	$-0.792580\pi$
$439$		−	25.4145i		−	1.21297i	0.795096	−	0.606483i	$-0.207420\pi$
$440$	−7.27347	+	15.5868i	−0.346749	+	0.743073i
$441$		−	1.93754i		−	0.0922639i
$442$	1.54449	+	19.6028i	0.0734637	+	0.932409i
$443$	−7.13613			−0.339048			−0.169524	−	0.985526i	$-0.554223\pi$
$443$	−7.13613			−0.339048			−0.169524	+	0.985526i	$0.554223\pi$
$444$	−2.92735	+	0.464169i	−0.138926	+	0.0220285i
$445$	10.2887	−	12.9205i	0.487733	−	0.612491i
$446$	−2.53145	−	32.1294i	−0.119868	−	1.52137i
$447$	7.52163	+	7.52163i	0.355761	+	0.355761i
$448$	−7.60974	−	2.46817i	−0.359526	−	0.116610i
$449$		−	14.1565i		−	0.668088i	−0.942557	−	0.334044i	$-0.891587\pi$
$449$		−	14.1565i		−	0.668088i	0.942557	−	0.334044i	$-0.108413\pi$
$450$	12.1463	+	6.33813i	0.572580	+	0.298782i
$451$	10.3414	+	10.3414i	0.486959	+	0.486959i
$452$	14.9323	−	20.5601i	0.702358	−	0.967067i
$453$			19.1853i			0.901405i
$454$	5.13249	−	6.01043i	0.240880	−	0.282084i
$455$	0.756721	+	6.67341i	0.0354757	+	0.312854i
$456$	0.416004	+	1.73079i	0.0194812	+	0.0810519i
$457$	−8.79607	−	8.79607i	−0.411463	−	0.411463i	0.470785	−	0.882248i	$-0.343971\pi$
$457$	−8.79607	−	8.79607i	−0.411463	−	0.411463i	−0.882248	+	0.470785i	$0.843971\pi$
$458$	−2.83009	−	35.9198i	−0.132242	−	1.67842i
$459$	−16.6595	−	16.6595i	−0.777597	−	0.777597i
$460$	−7.76171	−	28.0271i	−0.361891	−	1.30677i
$461$	13.7366	−	13.7366i	0.639776	−	0.639776i	−0.310724	−	0.950500i	$-0.600572\pi$
$461$	13.7366	−	13.7366i	0.639776	−	0.639776i	0.950500	+	0.310724i	$0.100572\pi$
$462$	2.57442	−	3.01479i	0.119773	−	0.140261i
$463$	−7.63941	+	7.63941i	−0.355033	+	0.355033i	−0.861978	−	0.506945i	$-0.830775\pi$
$463$	−7.63941	+	7.63941i	−0.355033	+	0.355033i	0.506945	+	0.861978i	$0.330775\pi$
$464$	30.9333	+	15.7478i	1.43604	+	0.731072i
$465$	−12.9743	+	16.2930i	−0.601667	+	0.755568i
$466$	−0.152479	−	1.93527i	−0.00706344	−	0.0896499i
$467$	−23.1820			−1.07274			−0.536368	−	0.843984i	$-0.680204\pi$
$467$	−23.1820			−1.07274			−0.536368	+	0.843984i	$0.680204\pi$
$468$	−1.82275	−	11.4955i	−0.0842567	−	0.531378i
$469$	7.37920	−	7.37920i	0.340740	−	0.340740i
$470$	−3.03595	+	4.49663i	−0.140038	+	0.207414i
$471$	5.59239			0.257684
$472$	4.38061	+	18.2256i	0.201634	+	0.838903i
$473$	−9.50084	+	9.50084i	−0.436849	+	0.436849i
$474$	−14.8554	−	12.6855i	−0.682330	−	0.582662i
$475$	2.58726	+	1.62055i	0.118712	+	0.0743561i
$476$	9.14423	−	1.44993i	0.419125	−	0.0664576i
$477$			13.7815i			0.631010i
$478$	−9.67187	+	11.3263i	−0.442381	+	0.518053i
$479$	17.3387			0.792226			0.396113	−	0.918202i	$-0.370359\pi$
$479$	17.3387			0.792226			0.396113	+	0.918202i	$0.370359\pi$
$480$	−11.4041	+	6.31987i	−0.520522	+	0.288461i
$481$	4.31836			0.196900
$482$	−21.9324	+	25.6841i	−0.998995	+	1.16988i
$483$			6.70294i			0.304994i
$484$	7.11843	−	1.12872i	0.323565	−	0.0513053i
$485$	0.0627933	+	0.553765i	0.00285130	+	0.0251452i
$486$	17.0485	+	14.5582i	0.773335	+	0.660374i
$487$	28.9586	−	28.9586i	1.31224	−	1.31224i	0.392481	−	0.919760i	$-0.371617\pi$
$487$	28.9586	−	28.9586i	1.31224	−	1.31224i	0.919760	−	0.392481i	$-0.128383\pi$
$488$	−37.0056	+	8.89445i	−1.67516	+	0.402633i
$489$	−13.5405			−0.612324
$490$	3.10445	−	0.601999i	0.140245	−	0.0271956i
$491$	−29.0399	+	29.0399i	−1.31055	+	1.31055i	−0.389549	+	0.921006i	$0.627369\pi$
$491$	−29.0399	+	29.0399i	−1.31055	+	1.31055i	−0.921006	+	0.389549i	$0.872631\pi$
$492$	1.73613	+	10.9492i	0.0782708	+	0.493627i
$493$	−40.1715			−1.80923
$494$	−0.203711	−	2.58553i	−0.00916541	−	0.116328i
$495$	1.32757	+	11.7076i	0.0596699	+	0.526220i
$496$	11.1817	+	34.3730i	0.502072	+	1.54339i
$497$	−8.41482	+	8.41482i	−0.377456	+	0.377456i
$498$	0.216246	−	0.253236i	0.00969020	−	0.0113478i
$499$	4.92186	−	4.92186i	0.220333	−	0.220333i	−0.588306	−	0.808639i	$-0.700205\pi$
$499$	4.92186	−	4.92186i	0.220333	−	0.220333i	0.808639	+	0.588306i	$0.200205\pi$
$500$	−6.38147	+	21.4307i	−0.285388	+	0.958412i
$501$	12.4562	+	12.4562i	0.556502	+	0.556502i
$502$	−0.900256	−	11.4261i	−0.0401804	−	0.509974i
$503$	−7.33668	−	7.33668i	−0.327126	−	0.327126i	0.524366	−	0.851493i	$-0.324302\pi$
$503$	−7.33668	−	7.33668i	−0.327126	−	0.327126i	−0.851493	+	0.524366i	$0.824302\pi$
$504$	−5.32844	+	1.28072i	−0.237348	+	0.0570476i
$505$	2.73653	−	0.310305i	0.121774	−	0.0138084i
$506$	16.2417	−	19.0200i	0.722034	−	0.845542i
$507$			4.10095i			0.182130i
$508$	−13.1973	+	18.1712i	−0.585536	+	0.806216i
$509$	−0.876354	−	0.876354i	−0.0388437	−	0.0388437i	0.687418	−	0.726262i	$-0.258744\pi$
$509$	−0.876354	−	0.876354i	−0.0388437	−	0.0388437i	−0.726262	+	0.687418i	$0.758744\pi$
$510$	8.44336	−	12.5057i	0.373878	−	0.553762i
$511$			8.30154i			0.367238i
$512$	−1.75768	+	22.5590i	−0.0776792	+	0.996978i
$513$	2.19731	+	2.19731i	0.0970138	+	0.0970138i
$514$	−2.02337	−	25.6808i	−0.0892469	−	1.13273i
$515$	19.7626	−	2.24095i	0.870844	−	0.0987480i
$516$	−10.0592	+	1.59501i	−0.442831	+	0.0702165i
$517$	−4.66608			−0.205214
$518$	−0.159705	−	2.02700i	−0.00701705	−	0.0890610i
$519$		−	7.95496i		−	0.349184i
$520$	17.8524	−	6.49219i	0.782879	−	0.284701i
$521$			8.21351i			0.359841i	0.983681	+	0.179920i	$0.0575840\pi$
$521$			8.21351i			0.359841i	−0.983681	+	0.179920i	$0.942416\pi$
$522$	23.7045	−	1.86766i	1.03752	−	0.0817452i
$523$	35.8513			1.56767			0.783833	−	0.620971i	$-0.213262\pi$
$523$	35.8513			1.56767			0.783833	+	0.620971i	$0.213262\pi$
$524$	5.35635	−	7.37508i	0.233993	−	0.322182i
$525$	2.73576	−	4.36773i	0.119399	−	0.190623i
$526$	−4.19613	+	0.330609i	−0.182960	+	0.0144153i
$527$	−29.5797	−	29.5797i	−1.28851	−	1.28851i
$528$	−9.99267	−	5.08714i	−0.434875	−	0.221389i
$529$			19.2882i			0.838618i
$530$	−22.0815	+	4.28194i	−0.959159	+	0.185995i
$531$	9.07966	+	9.07966i	0.394024	+	0.394024i
$532$	−1.20609	+	0.191240i	−0.0522905	+	0.00829132i
$533$		−	16.1519i		−	0.699619i
$534$	8.18812	+	6.99209i	0.354335	+	0.302577i
$535$	−2.73426	−	2.17732i	−0.118212	−	0.0941337i
$536$	−25.1712	−	15.4159i	−1.08723	−	0.665867i
$537$	−12.5131	−	12.5131i	−0.539979	−	0.539979i
$538$	−39.7502	+	3.13189i	−1.71375	+	0.135025i
$539$	1.92306	+	1.92306i	0.0828321	+	0.0828321i
$540$	−11.2150	+	19.8057i	−0.482615	+	0.852300i
$541$	7.44598	−	7.44598i	0.320128	−	0.320128i	−0.528688	−	0.848816i	$-0.677316\pi$
$541$	7.44598	−	7.44598i	0.320128	−	0.320128i	0.848816	+	0.528688i	$0.177316\pi$
$542$	8.81661	+	7.52877i	0.378706	+	0.323388i
$543$	10.0459	−	10.0459i	0.431109	−	0.431109i
$544$	−10.0318	−	24.1892i	−0.430110	−	1.03710i
$545$	−28.6143	+	3.24468i	−1.22570	+	0.138987i
$546$	−4.36480	+	0.343899i	−0.186796	+	0.0147175i
$547$	−21.2200			−0.907301			−0.453651	−	0.891180i	$-0.649879\pi$
$547$	−21.2200			−0.907301			−0.453651	+	0.891180i	$0.649879\pi$
$548$	20.4364	−	28.1386i	0.873000	−	1.20202i
$549$	−18.4355	+	18.4355i	−0.786806	+	0.786806i
$550$	−18.3462	+	5.76471i	−0.782286	+	0.245808i
$551$	5.29845			0.225722
$552$	18.4338	−	4.43065i	0.784595	−	0.188581i
$553$	9.47589	−	9.47589i	0.402956	−	0.402956i
$554$	10.5277	−	12.3286i	0.447281	−	0.523791i
$555$	−2.59228	−	2.06426i	−0.110036	−	0.0876229i
$556$	−3.97597	+	5.47446i	−0.168619	+	0.232169i
$557$			32.5436i			1.37892i	0.724325	+	0.689458i	$0.242151\pi$
$557$			32.5436i			1.37892i	−0.724325	+	0.689458i	$0.757849\pi$
$558$	18.8297	+	16.0793i	0.797126	+	0.680690i
$559$	14.8391			0.627626
$560$	−3.70760	−	8.13964i	−0.156675	−	0.343962i
$561$	12.9770			0.547888
$562$	14.0779	+	12.0216i	0.593841	+	0.507099i
$563$			24.4178i			1.02909i	0.857464	+	0.514544i	$0.172039\pi$
$563$			24.4178i			1.02909i	−0.857464	+	0.514544i	$0.827961\pi$
$564$	−2.86182	−	2.07848i	−0.120504	−	0.0875196i
$565$	28.2289	−	3.20097i	1.18760	−	0.134666i
$566$	−0.948397	+	1.11063i	−0.0398641	+	0.0466831i
$567$	−0.400715	+	0.400715i	−0.0168284	+	0.0168284i
$568$	28.7038	+	17.5794i	1.20439	+	0.737617i
$569$	−35.1121			−1.47198			−0.735988	−	0.676995i	$-0.763282\pi$
$569$	−35.1121			−1.47198			−0.735988	+	0.676995i	$0.763282\pi$
$570$	−1.11364	+	1.64945i	−0.0466454	+	0.0690879i
$571$	0.557667	−	0.557667i	0.0233376	−	0.0233376i	−0.695342	−	0.718679i	$-0.744747\pi$
$571$	0.557667	−	0.557667i	0.0233376	−	0.0233376i	0.718679	+	0.695342i	$0.244747\pi$
$572$	13.2187	+	9.60041i	0.552700	+	0.401413i
$573$	10.2231			0.427077
$574$	−7.58156	+	0.597345i	−0.316448	+	0.0249327i
$575$	17.2597	−	27.5556i	0.719778	−	1.14915i
$576$	7.04421	+	13.8072i	0.293509	+	0.575301i
$577$	19.2348	−	19.2348i	0.800753	−	0.800753i	−0.182460	−	0.983213i	$-0.558406\pi$
$577$	19.2348	−	19.2348i	0.800753	−	0.800753i	0.983213	+	0.182460i	$0.0584060\pi$
$578$	4.76408	+	4.06819i	0.198160	+	0.169215i
$579$	14.8940	−	14.8940i	0.618976	−	0.618976i
$580$	10.3575	+	37.4005i	0.430073	+	1.55297i
$581$	0.161533	+	0.161533i	0.00670152	+	0.00670152i
$582$	−0.362194	+	0.0285370i	−0.0150134	+	0.00118290i
$583$	−13.6784	−	13.6784i	−0.566503	−	0.566503i
$584$	22.8301	−	5.48732i	0.944717	−	0.227067i
$585$	8.10616	−	10.1796i	0.335148	−	0.420877i
$586$	−5.74327	−	4.90436i	−0.237252	−	0.202597i
$587$		−	1.27078i		−	0.0524507i	−0.999656	−	0.0262254i	$-0.991651\pi$
$587$		−	1.27078i		−	0.0524507i	0.999656	−	0.0262254i	$-0.00834875\pi$
$588$	0.322845	+	2.03608i	0.0133139	+	0.0839663i
$589$	3.90144	+	3.90144i	0.160756	+	0.160756i
$590$	−11.7269	+	17.3691i	−0.482789	+	0.715073i
$591$		−	3.52369i		−	0.144945i
$592$	−5.46888	+	1.77905i	−0.224770	+	0.0731185i
$593$	26.4410	+	26.4410i	1.08580	+	1.08580i	0.995956	+	0.0898465i	$0.0286377\pi$
$593$	26.4410	+	26.4410i	1.08580	+	1.08580i	0.0898465	+	0.995956i	$0.471362\pi$
$594$	−19.5140	+	1.53749i	−0.800668	+	0.0630840i
$595$	8.09755	+	6.44816i	0.331967	+	0.264349i
$596$	16.6999	+	12.1287i	0.684054	+	0.496813i
$597$	27.0999			1.10912
$598$	−27.5371	+	2.16962i	−1.12608	+	0.0887225i
$599$		−	25.9024i		−	1.05834i	−0.848515	−	0.529171i	$-0.822503\pi$
$599$		−	25.9024i		−	1.05834i	0.848515	−	0.529171i	$-0.177497\pi$
$600$	−13.8201	−	4.63657i	−0.564201	−	0.189287i
$601$			25.6209i			1.04510i	0.852609	+	0.522549i	$0.175019\pi$
$601$			25.6209i			1.04510i	−0.852609	+	0.522549i	$0.824981\pi$
$602$	−0.548791	−	6.96531i	−0.0223671	−	0.283885i
$603$	−20.2197			−0.823412
$604$	5.82978	+	36.7664i	0.237210	+	1.49600i
$605$	6.30363	+	5.01964i	0.256279	+	0.204078i
$606$	0.141021	+	1.78985i	0.00572858	+	0.0727077i
$607$	6.66943	+	6.66943i	0.270704	+	0.270704i	0.829384	−	0.558680i	$-0.188692\pi$
$607$	6.66943	+	6.66943i	0.270704	+	0.270704i	−0.558680	+	0.829384i	$0.688692\pi$
$608$	1.32315	+	3.19045i	0.0536610	+	0.129390i
$609$		−	8.94468i		−	0.362457i
$610$	−35.2663	−	23.8105i	−1.42789	−	0.964057i
$611$	3.64390	+	3.64390i	0.147416	+	0.147416i
$612$	−14.5145	−	10.5416i	−0.586715	−	0.426118i
$613$		−	43.6839i		−	1.76438i	−0.470896	−	0.882189i	$-0.656069\pi$
$613$		−	43.6839i		−	1.76438i	0.470896	−	0.882189i	$-0.343931\pi$
$614$	10.6436	−	12.4642i	0.429539	−	0.503015i
$615$	−7.72094	+	9.69590i	−0.311338	+	0.390976i
$616$	4.01747	−	6.55976i	0.161869	−	0.264300i
$617$	14.4015	+	14.4015i	0.579781	+	0.579781i	0.934843	−	0.355062i	$-0.115540\pi$
$617$	14.4015	+	14.4015i	0.579781	+	0.579781i	−0.355062	+	0.934843i	$0.615540\pi$
$618$	1.01842	+	12.9259i	0.0409668	+	0.519955i
$619$	−2.01084	−	2.01084i	−0.0808226	−	0.0808226i	0.665540	−	0.746362i	$-0.268201\pi$
$619$	−2.01084	−	2.01084i	−0.0808226	−	0.0808226i	−0.746362	+	0.665540i	$0.768201\pi$
$620$	−19.9127	+	35.1660i	−0.799715	+	1.41230i
$621$	23.4025	−	23.4025i	0.939108	−	0.939108i
$622$	−12.2007	+	14.2877i	−0.489203	+	0.572884i
$623$	−5.22301	+	5.22301i	−0.209255	+	0.209255i
$624$	3.83089	+	11.7763i	0.153358	+	0.471431i
$625$	−22.4933	+	10.9112i	−0.899730	+	0.436446i
$626$	2.74663	+	34.8605i	0.109778	+	1.39331i
$627$	−1.71161			−0.0683550
$628$	10.7172	−	1.69934i	0.427661	−	0.0678111i
$629$	4.70626	−	4.70626i	0.187651	−	0.187651i
$630$	−5.07802	−	3.42848i	−0.202313	−	0.136594i
$631$	9.65635			0.384413			0.192207	−	0.981354i	$-0.438436\pi$
$631$	9.65635			0.384413			0.192207	+	0.981354i	$0.438436\pi$
$632$	−32.3233	−	19.7961i	−1.28575	−	0.787448i
$633$	−2.68333	+	2.68333i	−0.106653	+	0.106653i
$634$	17.0605	+	14.5685i	0.677560	+	0.578589i
$635$	−24.9489	+	2.82904i	−0.990067	+	0.112267i
$636$	−2.29635	−	14.4823i	−0.0910563	−	0.574261i
$637$		−	3.00357i		−	0.119006i
$638$	−21.6736	+	25.3810i	−0.858067	+	1.00484i
$639$	23.0574			0.912138
$640$	−19.9341	+	15.5766i	−0.787966	+	0.615719i
$641$	15.9362			0.629442			0.314721	−	0.949184i	$-0.398089\pi$
$641$	15.9362			0.629442			0.314721	+	0.949184i	$0.398089\pi$
$642$	1.47968	−	1.73278i	0.0583981	−	0.0683875i
$643$			7.06535i			0.278630i	0.990248	+	0.139315i	$0.0444901\pi$
$643$			7.06535i			0.278630i	−0.990248	+	0.139315i	$0.955510\pi$
$644$	2.03680	+	12.8454i	0.0802612	+	0.506180i
$645$	−8.90778	−	7.09336i	−0.350744	−	0.279301i
$646$	−3.03978	−	2.59576i	−0.119599	−	0.102129i
$647$	14.5474	−	14.5474i	0.571918	−	0.571918i	−0.360746	−	0.932664i	$-0.617478\pi$
$647$	14.5474	−	14.5474i	0.571918	−	0.571918i	0.932664	+	0.360746i	$0.117478\pi$
$648$	1.36688	+	0.837135i	0.0536961	+	0.0328858i
$649$	−18.0236			−0.707487
$650$	18.8291	+	9.82533i	0.738536	+	0.385381i
$651$	6.58629	−	6.58629i	0.258137	−	0.258137i
$652$	−25.9488	+	4.11452i	−1.01624	+	0.161137i
$653$	19.5827			0.766332			0.383166	−	0.923680i	$-0.374834\pi$
$653$	19.5827			0.766332			0.383166	+	0.923680i	$0.374834\pi$
$654$	−1.47457	−	18.7154i	−0.0576604	−	0.731832i
$655$	10.1259	−	1.14821i	0.395653	−	0.0448645i
$656$	6.65418	+	20.4553i	0.259802	+	0.798644i
$657$	11.3735	−	11.3735i	0.443723	−	0.443723i
$658$	1.57565	−	1.84517i	0.0614252	−	0.0719324i
$659$	7.03436	−	7.03436i	0.274020	−	0.274020i	−0.556696	−	0.830716i	$-0.687931\pi$
$659$	7.03436	−	7.03436i	0.274020	−	0.274020i	0.830716	+	0.556696i	$0.187931\pi$
$660$	−3.34589	−	12.0818i	−0.130238	−	0.470285i
$661$	−18.4528	−	18.4528i	−0.717729	−	0.717729i	0.250410	−	0.968140i	$-0.419434\pi$
$661$	−18.4528	−	18.4528i	−0.717729	−	0.717729i	−0.968140	+	0.250410i	$0.919434\pi$
$662$	2.62705	+	33.3428i	0.102103	+	1.29591i
$663$	−10.1342	−	10.1342i	−0.393578	−	0.393578i
$664$	0.337459	−	0.551006i	0.0130960	−	0.0213832i
$665$	−1.06803	−	0.850486i	−0.0414166	−	0.0329804i
$666$	−2.55828	+	2.99589i	−0.0991313	+	0.116088i
$667$		−	56.4311i		−	2.18502i
$668$	27.6558	+	20.0858i	1.07004	+	0.777143i
$669$	16.6101	+	16.6101i	0.642184	+	0.642184i
$670$	−6.28233	−	32.3973i	−0.242707	−	1.25162i
$671$		−	36.5953i		−	1.41275i
$672$	5.38602	−	2.23371i	0.207770	−	0.0861671i
$673$	25.1493	+	25.1493i	0.969436	+	0.969436i	0.999547	−	0.0301107i	$-0.00958598\pi$
$673$	25.1493	+	25.1493i	0.969436	+	0.969436i	−0.0301107	+	0.999547i	$0.509586\pi$
$674$	−1.37081	−	17.3984i	−0.0528015	−	0.670162i
$675$	−24.8009	+	5.69779i	−0.954588	+	0.219308i
$676$	1.24614	+	7.85900i	0.0479286	+	0.302269i
$677$	−2.15006			−0.0826336			−0.0413168	−	0.999146i	$-0.513155\pi$
$677$	−2.15006			−0.0826336			−0.0413168	+	0.999146i	$0.513155\pi$
$678$	1.45471	+	18.4633i	0.0558679	+	0.709080i
$679$		−	0.249238i		−	0.00956488i
$680$	12.3806	−	26.5314i	0.474776	−	1.01743i
$681$			5.76062i			0.220747i
$682$	−34.6481	+	2.72989i	−1.32674	+	0.104533i
$683$	−5.19246			−0.198684			−0.0993420	−	0.995053i	$-0.531674\pi$
$683$	−5.19246			−0.198684			−0.0993420	+	0.995053i	$0.531674\pi$
$684$	1.91441	+	1.39039i	0.0731991	+	0.0531629i
$685$	38.6341	−	4.38085i	1.47613	−	0.167384i
$686$	−1.40984	+	0.111080i	−0.0538281	+	0.00424107i
$687$	18.5696	+	18.5696i	0.708476	+	0.708476i
$688$	−18.7926	+	6.11331i	−0.716461	+	0.233068i
$689$			21.3639i			0.813901i
$690$	17.5674	+	11.8608i	0.668781	+	0.451535i
$691$	−18.9431	−	18.9431i	−0.720631	−	0.720631i	0.248103	−	0.968734i	$-0.420193\pi$
$691$	−18.9431	−	18.9431i	−0.720631	−	0.720631i	−0.968734	+	0.248103i	$0.920193\pi$
$692$	−2.41725	−	15.2447i	−0.0918900	−	0.579518i
$693$		−	5.26937i		−	0.200167i
$694$	0.799712	+	0.682899i	0.0303567	+	0.0259225i
$695$	−7.51639	+	0.852310i	−0.285113	+	0.0323300i
$696$	−24.5988	+	5.91243i	−0.932415	+	0.224110i
$697$	−17.6028	−	17.6028i	−0.666754	−	0.666754i
$698$	48.4639	−	3.81843i	1.83438	−	0.144530i
$699$	1.00049	+	1.00049i	0.0378420	+	0.0378420i
$700$	3.91556	−	9.20154i	0.147994	−	0.347786i
$701$	−4.65276	+	4.65276i	−0.175732	+	0.175732i	−0.789492	−	0.613760i	$-0.789656\pi$
$701$	−4.65276	+	4.65276i	−0.175732	+	0.175732i	0.613760	+	0.789492i	$0.289656\pi$
$702$	16.4398	+	14.0384i	0.620480	+	0.529847i
$703$	−0.620736	+	0.620736i	−0.0234115	+	0.0234115i
$704$	−20.6956	−	6.71247i	−0.779994	−	0.252986i
$705$	−0.445553	−	3.92926i	−0.0167805	−	0.147985i
$706$	31.0098	−	2.44324i	1.16707	−	0.0919524i
$707$	−1.23166			−0.0463212
$708$	−11.0543	−	8.02849i	−0.415446	−	0.301729i
$709$	−36.8757	+	36.8757i	−1.38490	+	1.38490i	−0.549217	+	0.835679i	$0.685074\pi$
$709$	−36.8757	+	36.8757i	−1.38490	+	1.38490i	−0.835679	+	0.549217i	$0.814926\pi$
$710$	7.16400	+	36.9440i	0.268860	+	1.38648i
$711$	−25.9649			−0.973759
$712$	17.8162	+	10.9114i	0.667691	+	0.408922i
$713$	41.5523	−	41.5523i	1.55614	−	1.55614i
$714$	−4.38208	+	5.13166i	−0.163995	+	0.192048i
$715$	2.05799	+	18.1491i	0.0769646	+	0.678739i
$716$	−27.7822	−	20.1775i	−1.03827	−	0.754070i
$717$		−	10.8555i		−	0.405407i
$718$	0.619484	+	0.528996i	0.0231189	+	0.0197420i
$719$	0.437065			0.0162998			0.00814988	−	0.999967i	$-0.497406\pi$
$719$	0.437065			0.0162998			0.00814988	+	0.999967i	$0.497406\pi$
$720$	−6.07210	+	16.2313i	−0.226294	+	0.604905i
$721$	−8.89474			−0.331257
$722$	−20.0327	−	17.1066i	−0.745541	−	0.636640i
$723$		−	24.6166i		−	0.915500i
$724$	16.1991	−	22.3043i	0.602035	−	0.828933i
$725$	−23.0320	+	36.7712i	−0.855387	+	1.36565i
$726$	−3.41128	+	3.99480i	−0.126604	+	0.148261i
$727$	−1.89246	+	1.89246i	−0.0701874	+	0.0701874i	−0.741329	−	0.671142i	$-0.765804\pi$
$727$	−1.89246	+	1.89246i	−0.0701874	+	0.0701874i	0.671142	+	0.741329i	$0.265804\pi$
$728$	−8.26012	+	1.98536i	−0.306141	+	0.0735823i
$729$	−14.6398			−0.542215
$730$	21.7571	+	14.6896i	0.805267	+	0.543685i
$731$	16.1720	−	16.1720i	0.598143	−	0.598143i
$732$	16.3011	−	22.4448i	0.602508	−	0.829584i
$733$	6.84958			0.252995			0.126497	−	0.991967i	$-0.459626\pi$
$733$	6.84958			0.252995			0.126497	+	0.991967i	$0.459626\pi$
$734$	10.2699	−	0.809158i	0.379070	−	0.0298666i
$735$	−1.43576	+	1.80302i	−0.0529589	+	0.0665053i
$736$	33.9799	−	14.0922i	1.25251	−	0.519446i
$737$	20.0686	−	20.0686i	0.739237	−	0.739237i
$738$	11.2055	+	9.56872i	0.412480	+	0.352230i
$739$	14.4202	−	14.4202i	0.530455	−	0.530455i	−0.390253	−	0.920708i	$-0.627612\pi$
$739$	14.4202	−	14.4202i	0.530455	−	0.530455i	0.920708	+	0.390253i	$0.127612\pi$
$740$	−5.59506	−	3.16820i	−0.205678	−	0.116465i
$741$	1.33665	+	1.33665i	0.0491032	+	0.0491032i
$742$	10.0280	−	0.790099i	0.368140	−	0.0290055i
$743$	−0.103243	−	0.103243i	−0.00378761	−	0.00378761i	0.705210	−	0.708998i	$-0.250853\pi$
$743$	−0.103243	−	0.103243i	−0.00378761	−	0.00378761i	−0.708998	+	0.705210i	$0.750853\pi$
$744$	−22.4665	−	13.7594i	−0.823663	−	0.504446i
$745$	2.59998	+	22.9288i	0.0952559	+	0.840047i
$746$	−20.9801	−	17.9156i	−0.768137	−	0.655935i
$747$		−	0.442616i		−	0.0161945i
$748$	24.8688	−	3.94326i	0.909294	−	0.144180i
$749$	1.10530	+	1.10530i	0.0403868	+	0.0403868i
$750$	−6.60625	−	14.8987i	−0.241226	−	0.544024i
$751$			12.0723i			0.440525i	0.975441	+	0.220262i	$0.0706914\pi$
$751$			12.0723i			0.440525i	−0.975441	+	0.220262i	$0.929309\pi$
$752$	−6.11593	−	3.11354i	−0.223025	−	0.113539i
$753$	5.90703	+	5.90703i	0.215264	+	0.215264i
$754$	36.7466	−	2.89523i	1.33823	−	0.105438i
$755$	−25.9263	+	32.5580i	−0.943553	+	1.18491i
$756$	5.98152	−	8.23586i	0.217546	−	0.299535i
$757$	−6.47210			−0.235232			−0.117616	−	0.993059i	$-0.537525\pi$
$757$	−6.47210			−0.235232			−0.117616	+	0.993059i	$0.537525\pi$
$758$	−7.85015	+	0.618507i	−0.285130	+	0.0224652i
$759$			18.2294i			0.661687i
$760$	−1.63295	+	3.49938i	−0.0592335	+	0.126936i
$761$		−	24.1885i		−	0.876832i	−0.898772	−	0.438416i	$-0.855540\pi$
$761$		−	24.1885i		−	0.876832i	0.898772	−	0.438416i	$-0.144460\pi$
$762$	−1.28568	−	16.3180i	−0.0465754	−	0.591140i
$763$	12.8787			0.466241
$764$	19.5914	−	3.10647i	0.708793	−	0.112388i
$765$	−2.25974	−	19.9283i	−0.0817012	−	0.720511i
$766$	−2.81406	−	35.7164i	−0.101676	−	1.29048i
$767$	14.0752	+	14.0752i	0.508227	+	0.508227i
$768$	−9.70309	−	13.3356i	−0.350130	−	0.481209i
$769$		−	35.4315i		−	1.27769i	−0.769334	−	0.638847i	$-0.779412\pi$
$769$		−	35.4315i		−	1.27769i	0.769334	−	0.638847i	$-0.220588\pi$
$770$	8.44291	−	1.63721i	0.304261	−	0.0590009i
$771$	13.2763	+	13.2763i	0.478135	+	0.478135i
$772$	24.0169	−	33.0685i	0.864387	−	1.19016i
$773$		−	32.8433i		−	1.18129i	−0.806930	−	0.590646i	$-0.798873\pi$
$773$		−	32.8433i		−	1.18129i	0.806930	−	0.590646i	$-0.201127\pi$
$774$	−8.79095	+	10.2947i	−0.315984	+	0.370035i
$775$	−44.0353	+	10.1167i	−1.58179	+	0.363403i
$776$	−0.685431	+	0.164747i	−0.0246055	+	0.00591406i
$777$	1.04791	+	1.04791i	0.0375934	+	0.0375934i
$778$	−3.83807	−	48.7131i	−0.137601	−	1.74645i
$779$	2.32174	+	2.32174i	0.0831849	+	0.0831849i
$780$	−6.82220	+	12.0480i	−0.244274	+	0.431389i
$781$	−22.8851	+	22.8851i	−0.818893	+	0.818893i
$782$	−27.6461	+	32.3751i	−0.988623	+	1.15773i
$783$	−31.2292	+	31.2292i	−1.11604	+	1.11604i
$784$	1.23739	+	3.80380i	0.0441925	+	0.135850i
$785$	9.49044	+	7.55733i	0.338728	+	0.269733i
$786$	0.521816	+	6.62295i	0.0186126	+	0.236233i
$787$	29.1244			1.03817			0.519086	−	0.854722i	$-0.326272\pi$
$787$	29.1244			1.03817			0.519086	+	0.854722i	$0.326272\pi$
$788$	−1.07073	−	6.75274i	−0.0381433	−	0.240557i
$789$	2.16929	−	2.16929i	0.0772289	−	0.0772289i
$790$	−8.06736	−	41.6025i	−0.287024	−	1.48015i
$791$	−12.7053			−0.451747
$792$	−14.4913	+	3.48306i	−0.514927	+	0.123765i
$793$	−28.5785	+	28.5785i	−1.01485	+	1.01485i
$794$	−33.7227	−	28.7968i	−1.19677	−	1.02196i
$795$	10.2124	−	12.8246i	0.362195	−	0.454842i
$796$	51.9337	−	8.23474i	1.84074	−	0.291873i
$797$		−	16.0460i		−	0.568379i	−0.958768	−	0.284189i	$-0.908276\pi$
$797$		−	16.0460i		−	0.568379i	0.958768	−	0.284189i	$-0.0917244\pi$
$798$	0.577978	−	0.676845i	0.0204602	−	0.0239600i
$799$	7.94244			0.280983
$800$	−27.8934	−	4.68599i	−0.986180	−	0.165675i
$801$	14.3116			0.505674
$802$	9.48048	−	11.1022i	0.334768	−	0.392031i
$803$			22.5770i			0.796725i
$804$	21.2480	−	3.36914i	0.749360	−	0.118820i
$805$	−9.05808	+	11.3751i	−0.319255	+	0.400919i
$806$	29.1897	+	24.9260i	1.02816	+	0.877980i
$807$	20.5499	−	20.5499i	0.723390	−	0.723390i
$808$	0.814126	+	3.38719i	0.0286408	+	0.119161i
$809$	−27.9655			−0.983215			−0.491607	−	0.870817i	$-0.663590\pi$
$809$	−27.9655			−0.983215			−0.491607	+	0.870817i	$0.663590\pi$
$810$	0.341151	+	1.75928i	0.0119868	+	0.0618148i
$811$	31.0450	−	31.0450i	1.09014	−	1.09014i	0.0946256	−	0.995513i	$-0.469835\pi$
$811$	31.0450	−	31.0450i	1.09014	−	1.09014i	0.995513	−	0.0946256i	$-0.0301654\pi$
$812$	−2.71799	−	17.1414i	−0.0953827	−	0.601546i
$813$	−8.45015			−0.296360
$814$	−0.434337	−	5.51265i	−0.0152235	−	0.193218i
$815$	−22.9786	−	18.2981i	−0.804907	−	0.640955i
$816$	17.0092	+	8.65915i	0.595440	+	0.303131i
$817$	−2.13302	+	2.13302i	−0.0746249	+	0.0746249i
$818$	2.58101	−	3.02251i	0.0902429	−	0.105679i
$819$	−4.11503	+	4.11503i	−0.143791	+	0.143791i
$820$	−11.8500	+	20.9272i	−0.413820	+	0.730809i
$821$	7.89122	+	7.89122i	0.275405	+	0.275405i	0.831272	−	0.555866i	$-0.187613\pi$
$821$	7.89122	+	7.89122i	0.275405	+	0.275405i	−0.555866	+	0.831272i	$0.687613\pi$
$822$	1.99092	+	25.2689i	0.0694412	+	0.881355i
$823$	−22.8799	−	22.8799i	−0.797544	−	0.797544i	0.185164	−	0.982708i	$-0.440718\pi$
$823$	−22.8799	−	22.8799i	−0.797544	−	0.797544i	−0.982708	+	0.185164i	$0.940718\pi$
$824$	5.87942	+	24.4615i	0.204819	+	0.852155i
$825$	7.44023	−	11.8785i	0.259036	−	0.413558i
$826$	6.08623	−	7.12732i	0.211767	−	0.247991i
$827$			40.4958i			1.40818i	0.710112	+	0.704089i	$0.248644\pi$
$827$			40.4958i			1.40818i	−0.710112	+	0.704089i	$0.751356\pi$
$828$	14.8083	−	20.3893i	0.514624	−	0.708579i
$829$	1.92151	+	1.92151i	0.0667370	+	0.0667370i	0.739687	−	0.672951i	$-0.234973\pi$
$829$	1.92151	+	1.92151i	0.0667370	+	0.0667370i	−0.672951	+	0.739687i	$0.734973\pi$
$830$	0.709187	−	0.137522i	0.0246162	−	0.00477346i
$831$			11.8162i			0.409898i
$832$	10.9199	+	21.4039i	0.378579	+	0.742046i
$833$	−3.27336	−	3.27336i	−0.113415	−	0.113415i
$834$	−0.387340	−	4.91616i	−0.0134125	−	0.170233i
$835$	4.30569	+	37.9713i	0.149005	+	1.31405i
$836$	−3.28009	+	0.520100i	−0.113444	+	0.0179880i
$837$	−45.9903			−1.58966
$838$	0.135189	+	1.71584i	0.00467003	+	0.0592726i
$839$		−	23.5548i		−	0.813203i	−0.913606	−	0.406601i	$-0.866714\pi$
$839$		−	23.5548i		−	0.813203i	0.913606	−	0.406601i	$-0.133286\pi$
$840$	5.90753	+	2.75670i	0.203829	+	0.0951152i
$841$			46.3039i			1.59669i
$842$	27.1009	−	2.13525i	0.933957	−	0.0735857i
$843$	−13.4928			−0.464716
$844$	−4.32692	+	5.95767i	−0.148939	+	0.205071i
$845$	−5.54186	+	6.95943i	−0.190646	+	0.239412i
$846$	−4.68670	+	0.369261i	−0.161132	+	0.0126954i
$847$	−2.54819	−	2.54819i	−0.0875567	−	0.0875567i
$848$	−8.80138	−	27.0559i	−0.302241	−	0.929102i
$849$		−	1.06446i		−	0.0365323i
$850$	31.2283	−	9.81249i	1.07112	−	0.336566i
$851$	6.61114	+	6.61114i	0.226627	+	0.226627i
$852$	−24.2300	+	3.84197i	−0.830106	+	0.131624i
$853$		−	37.4423i		−	1.28200i	−0.767542	−	0.640999i	$-0.778520\pi$
$853$		−	37.4423i		−	1.28200i	0.767542	−	0.640999i	$-0.221480\pi$
$854$	14.4714	+	12.3576i	0.495201	+	0.422867i
$855$	0.298051	+	2.62847i	0.0101931	+	0.0898916i
$856$	2.30909	−	3.77030i	0.0789230	−	0.128866i
$857$	8.63350	+	8.63350i	0.294915	+	0.294915i	0.839018	−	0.544103i	$-0.183130\pi$
$857$	8.63350	+	8.63350i	0.294915	+	0.294915i	−0.544103	+	0.839018i	$0.683130\pi$
$858$	−11.8706	+	0.935273i	−0.405255	+	0.0319297i
$859$	−12.3211	−	12.3211i	−0.420391	−	0.420391i	0.464948	−	0.885338i	$-0.346073\pi$
$859$	−12.3211	−	12.3211i	−0.420391	−	0.420391i	−0.885338	+	0.464948i	$0.846073\pi$
$860$	−19.2261	−	10.8868i	−0.655606	−	0.371237i
$861$	3.91948	−	3.91948i	0.133576	−	0.133576i
$862$	25.6338	+	21.8894i	0.873089	+	0.745558i
$863$	−18.1212	+	18.1212i	−0.616851	+	0.616851i	−0.944722	−	0.327871i	$-0.893669\pi$
$863$	−18.1212	+	18.1212i	−0.616851	+	0.616851i	0.327871	+	0.944722i	$0.393669\pi$
$864$	−26.6033	−	11.0059i	−0.905062	−	0.374428i
$865$	10.7500	−	13.4998i	0.365511	−	0.459006i
$866$	21.5407	−	1.69717i	0.731982	−	0.0576722i
$867$	−4.56607			−0.155072
$868$	10.6205	−	14.6232i	0.360483	−	0.496344i
$869$	25.7708	−	25.7708i	0.874215	−	0.874215i
$870$	−23.4427	−	15.8276i	−0.794782	−	0.536605i
$871$	−31.3445			−1.06207
$872$	−8.51284	−	35.4179i	−0.288281	−	1.19940i
$873$	−0.341469	+	0.341469i	−0.0115570	+	0.0115570i
$874$	3.64641	−	4.27015i	0.123342	−	0.144440i
$875$	10.5450	−	3.71515i	0.356487	−	0.125595i
$876$	−10.0568	+	13.8470i	−0.339787	+	0.467848i
$877$			15.9401i			0.538259i	0.963104	+	0.269130i	$0.0867360\pi$
$877$			15.9401i			0.538259i	−0.963104	+	0.269130i	$0.913264\pi$
$878$	27.3322	+	23.3398i	0.922416	+	0.787679i
$879$	5.50456			0.185664
$880$	−10.0833	−	22.1367i	−0.339907	−	0.746228i
$881$	−24.6672			−0.831058			−0.415529	−	0.909580i	$-0.636404\pi$
$881$	−24.6672			−0.831058			−0.415529	+	0.909580i	$0.636404\pi$
$882$	2.08374	+	1.77937i	0.0701632	+	0.0599145i
$883$			18.8083i			0.632950i	0.948601	+	0.316475i	$0.102499\pi$
$883$			18.8083i			0.632950i	−0.948601	+	0.316475i	$0.897501\pi$
$884$	−22.5003	−	16.3415i	−0.756768	−	0.549623i
$885$	−1.72103	−	15.1775i	−0.0578517	−	0.510186i
$886$	6.55357	−	7.67459i	0.220171	−	0.257833i
$887$	18.5443	−	18.5443i	0.622657	−	0.622657i	−0.323553	−	0.946210i	$-0.604877\pi$
$887$	18.5443	−	18.5443i	0.622657	−	0.622657i	0.946210	+	0.323553i	$0.104877\pi$
$888$	2.18919	−	3.57452i	0.0734643	−	0.119953i
$889$	11.2290			0.376608
$890$	4.44664	+	22.9308i	0.149052	+	0.768644i
$891$	−1.08979	+	1.08979i	−0.0365094	+	0.0365094i
$892$	36.8786	+	26.7841i	1.23479	+	0.896797i
$893$	−1.04757			−0.0350557
$894$	−14.9968	+	1.18158i	−0.501567	+	0.0395181i
$895$	−4.32536	−	38.1447i	−0.144581	−	1.27504i
$896$	9.64292	−	5.91726i	0.322147	−	0.197682i
$897$	14.2360	−	14.2360i	0.475326	−	0.475326i
$898$	15.2247	+	13.0009i	0.508056	+	0.433844i
$899$	−55.4490	+	55.4490i	−1.84933	+	1.84933i
$900$	−17.9711	+	7.24205i	−0.599036	+	0.241402i
$901$	23.2830	+	23.2830i	0.775668	+	0.775668i
$902$	−20.6190	+	1.62455i	−0.686536	+	0.0540916i
$903$	3.60089	+	3.60089i	0.119830	+	0.119830i
$904$	8.39818	+	34.9408i	0.279319	+	1.16211i
$905$	30.6236	−	3.47252i	1.01796	−	0.115431i
$906$	−20.6330	−	17.6191i	−0.685485	−	0.585356i
$907$			16.1147i			0.535080i	0.963547	+	0.267540i	$0.0862108\pi$
$907$			16.1147i			0.535080i	−0.963547	+	0.267540i	$0.913789\pi$
$908$	1.75046	+	11.0395i	0.0580910	+	0.366360i
$909$	1.68743	+	1.68743i	0.0559686	+	0.0559686i
$910$	−7.87191	−	5.31481i	−0.260951	−	0.176184i
$911$		−	51.4805i		−	1.70563i	−0.522216	−	0.852813i	$-0.674895\pi$
$911$		−	51.4805i		−	1.70563i	0.522216	−	0.852813i	$-0.325105\pi$
$912$	−2.24344	−	1.14211i	−0.0742877	−	0.0378189i
$913$	0.439308	+	0.439308i	0.0145390	+	0.0145390i
$914$	17.5378	−	1.38179i	0.580099	−	0.0457055i
$915$	30.8166	−	3.49440i	1.01876	−	0.115521i
$916$	41.2292	+	29.9438i	1.36225	+	0.989373i
$917$	−4.55747			−0.150501
$918$	33.2160	−	2.61706i	1.09629	−	0.0863758i
$919$		−	18.8068i		−	0.620380i	−0.950675	−	0.310190i	$-0.899607\pi$
$919$		−	18.8068i		−	0.620380i	0.950675	−	0.310190i	$-0.100393\pi$
$920$	37.2700	+	17.3918i	1.22876	+	0.573389i
$921$			11.9461i			0.393639i
$922$	2.15790	+	27.3882i	0.0710666	+	0.901984i
$923$	35.7435			1.17651
$924$	0.878016	+	5.53735i	0.0288846	+	0.182165i
$925$	−1.60961	−	7.00620i	−0.0529237	−	0.230362i
$926$	−1.20009	−	15.2316i	−0.0394373	−	0.500542i
$927$	12.1862	+	12.1862i	0.400248	+	0.400248i
$928$	−45.3441	+	18.8052i	−1.48849	+	0.617312i
$929$		−	24.9791i		−	0.819538i	−0.912189	−	0.409769i	$-0.865609\pi$
$929$		−	24.9791i		−	0.819538i	0.912189	−	0.409769i	$-0.134391\pi$
$930$	−5.60727	−	28.9161i	−0.183870	−	0.948197i
$931$	0.431743	+	0.431743i	0.0141498	+	0.0141498i
$932$	2.22133	+	1.61330i	0.0727622	+	0.0528455i
$933$		−	13.6938i		−	0.448316i
$934$	21.2896	−	24.9313i	0.696615	−	0.815775i
$935$	22.0222	+	17.5365i	0.720204	+	0.573506i
$936$	14.0368	+	8.59674i	0.458808	+	0.280993i
$937$	13.1122	+	13.1122i	0.428357	+	0.428357i	0.888068	−	0.459712i	$-0.152047\pi$
$937$	13.1122	+	13.1122i	0.428357	+	0.428357i	−0.459712	+	0.888068i	$0.652047\pi$
$938$	1.15921	+	14.7128i	0.0378495	+	0.480390i
$939$	−18.0220	−	18.0220i	−0.588127	−	0.588127i
$940$	−2.04782	−	7.39458i	−0.0667926	−	0.241185i
$941$	5.11887	−	5.11887i	0.166870	−	0.166870i	−0.618732	−	0.785602i	$-0.712353\pi$
$941$	5.11887	−	5.11887i	0.166870	−	0.166870i	0.785602	+	0.618732i	$0.212353\pi$
$942$	−5.13586	+	6.01437i	−0.167335	+	0.195959i
$943$	24.7276	−	24.7276i	0.805242	−	0.805242i
$944$	−23.6239	−	12.0266i	−0.768891	−	0.391433i
$945$	11.3078	−	1.28223i	0.367842	−	0.0417109i
$946$	−1.49250	−	18.9430i	−0.0485254	−	0.615889i
$947$	−30.3645			−0.986715			−0.493357	−	0.869827i	$-0.664231\pi$
$947$	−30.3645			−0.986715			−0.493357	+	0.869827i	$0.664231\pi$
$948$	27.2853	−	4.32643i	0.886186	−	0.140516i
$949$	17.6312	−	17.6312i	0.572332	−	0.572332i
$950$	−4.11888	+	1.29423i	−0.133634	+	0.0419902i
$951$	−16.3514			−0.530231
$952$	−6.83840	+	11.1658i	−0.221634	+	0.361885i
$953$	−32.5543	+	32.5543i	−1.05454	+	1.05454i	−0.0561137	+	0.998424i	$0.517871\pi$
$953$	−32.5543	+	32.5543i	−1.05454	+	1.05454i	−0.998424	+	0.0561137i	$0.982129\pi$
$954$	−14.8214	−	12.6564i	−0.479859	−	0.409766i
$955$	17.3489	+	13.8151i	0.561398	+	0.447047i
$956$	−3.29863	−	20.8033i	−0.106685	−	0.672828i
$957$		−	24.3261i		−	0.786351i
$958$	−15.9233	+	18.6470i	−0.514457	+	0.602458i
$959$	−17.3884			−0.561501
$960$	3.67634	−	18.0685i	0.118653	−	0.583159i
$961$	−50.6582			−1.63414
$962$	−3.96583	+	4.64421i	−0.127863	+	0.149735i
$963$		−	3.02863i		−	0.0975963i
$964$	−7.48015	−	47.1748i	−0.240920	−	1.51940i
$965$	45.4028	−	5.14838i	1.46157	−	0.165732i
$966$	−7.20872	−	6.15575i	−0.231937	−	0.198058i
$967$	−30.8873	+	30.8873i	−0.993269	+	0.993269i	−0.999977	−	0.00670881i	$-0.997865\pi$
$967$	−30.8873	+	30.8873i	−0.993269	+	0.993269i	0.00670881	+	0.999977i	$0.497865\pi$
$968$	−5.32343	+	8.69214i	−0.171102	+	0.279376i
$969$	2.91344			0.0935931
$970$	−0.653217	−	0.441027i	−0.0209735	−	0.0141605i
$971$	−28.3930	+	28.3930i	−0.911176	+	0.911176i	−0.996365	−	0.0851889i	$-0.972851\pi$
$971$	−28.3930	+	28.3930i	−0.911176	+	0.911176i	0.0851889	+	0.996365i	$0.472851\pi$
$972$	−31.3135	+	4.96514i	−1.00438	+	0.159257i
$973$	3.38298			0.108453
$974$	4.54915	+	57.7383i	0.145764	+	1.85006i
$975$	−15.0867	+	3.46603i	−0.483161	+	0.111002i
$976$	24.4190	−	47.9662i	0.781633	−	1.53536i
$977$	13.4496	−	13.4496i	0.430290	−	0.430290i	−0.458437	−	0.888727i	$-0.651591\pi$
$977$	13.4496	−	13.4496i	0.430290	−	0.430290i	0.888727	+	0.458437i	$0.151591\pi$
$978$	12.4352	−	14.5623i	0.397632	−	0.465650i
$979$	−14.2046	+	14.2046i	−0.453980	+	0.453980i
$980$	−2.20359	+	3.89155i	−0.0703911	+	0.124311i
$981$	−17.6445	−	17.6445i	−0.563345	−	0.563345i
$982$	−4.56193	−	57.9005i	−0.145577	−	1.84768i
$983$	26.3066	+	26.3066i	0.839051	+	0.839051i	0.988734	−	0.149683i	$-0.0478254\pi$
$983$	26.3066	+	26.3066i	0.839051	+	0.839051i	−0.149683	+	0.988734i	$0.547825\pi$
$984$	−13.3698	−	8.18821i	−0.426212	−	0.261030i
$985$	4.76178	−	5.97980i	0.151723	−	0.190532i
$986$	36.8921	−	43.2027i	1.17488	−	1.37585i
$987$			1.76848i			0.0562914i
$988$	2.96770	+	2.15537i	0.0944151	+	0.0685715i
$989$	22.7177	+	22.7177i	0.722380	+	0.722380i
$990$	−13.8103	−	9.32415i	−0.438919	−	0.296341i
$991$		−	35.1807i		−	1.11755i	−0.829318	−	0.558777i	$-0.811271\pi$
$991$		−	35.1807i		−	1.11755i	0.829318	−	0.558777i	$-0.188729\pi$
$992$	−47.2355	−	19.5415i	−1.49973	−	0.620444i
$993$	−17.2374	−	17.2374i	−0.547013	−	0.547013i
$994$	−1.32190	−	16.7776i	−0.0419280	−	0.532154i
$995$	45.9892	+	36.6216i	1.45795	+	1.16098i
$996$	0.0737515	+	0.465125i	0.00233691	+	0.0147381i
$997$	23.0761			0.730828			0.365414	−	0.930845i	$-0.380927\pi$
$997$	23.0761			0.730828			0.365414	+	0.930845i	$0.380927\pi$
$998$	0.773183	+	9.81331i	0.0244747	+	0.310635i
$999$		−	7.31725i		−	0.231508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.t.a.43.20	✓	144
5.2	odd	4		560.2.bl.a.267.15	yes	144
16.3	odd	4		560.2.bl.a.323.15	yes	144
80.67	even	4	inner	560.2.t.a.547.20	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.t.a.43.20	✓	144	1.1	even	1	trivial
560.2.t.a.547.20	yes	144	80.67	even	4	inner
560.2.bl.a.267.15	yes	144	5.2	odd	4
560.2.bl.a.323.15	yes	144	16.3	odd	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.918365 + 1.07546i) q^{2} -1.03076i q^{3} +(-0.313212 - 1.97532i) q^{4} +(1.39292 - 1.74922i) q^{5} +(1.10853 + 0.946610i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.41202 + 1.47722i) q^{8} +1.93754 q^{9} +O(q^{10})\)	\(q+(-0.918365 + 1.07546i) q^{2} -1.03076i q^{3} +(-0.313212 - 1.97532i) q^{4} +(1.39292 - 1.74922i) q^{5} +(1.10853 + 0.946610i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.41202 + 1.47722i) q^{8} +1.93754 q^{9} +(0.601999 + 3.10445i) q^{10} +(-1.92306 + 1.92306i) q^{11} +(-2.03608 + 0.322845i) q^{12} +3.00357 q^{13} +(-0.111080 - 1.40984i) q^{14} +(-1.80302 - 1.43576i) q^{15} +(-3.80380 + 1.23739i) q^{16} +(3.27336 - 3.27336i) q^{17} +(-1.77937 + 2.08374i) q^{18} +(-0.431743 + 0.431743i) q^{19} +(-3.89155 - 2.20359i) q^{20} +(0.728855 + 0.728855i) q^{21} +(-0.302096 - 3.83424i) q^{22} +(4.59827 + 4.59827i) q^{23} +(1.52265 - 2.48620i) q^{24} +(-1.11954 - 4.87305i) q^{25} +(-2.75837 + 3.23020i) q^{26} -5.08940i q^{27} +(1.61824 + 1.17529i) q^{28} +(-6.13612 - 6.13612i) q^{29} +(3.19993 - 0.620514i) q^{30} -9.03649i q^{31} +(2.16251 - 5.22719i) q^{32} +(1.98221 + 1.98221i) q^{33} +(0.514218 + 6.52650i) q^{34} +(0.251941 + 2.22183i) q^{35} +(-0.606862 - 3.82727i) q^{36} +1.43774 q^{37} +(-0.0678232 - 0.860819i) q^{38} -3.09594i q^{39} +(5.94373 - 2.16149i) q^{40} -5.37759i q^{41} +(-1.45321 + 0.114497i) q^{42} +4.94048 q^{43} +(4.40099 + 3.19634i) q^{44} +(2.69884 - 3.38919i) q^{45} +(-9.16813 + 0.722349i) q^{46} +(1.21319 + 1.21319i) q^{47} +(1.27545 + 3.92079i) q^{48} -1.00000i q^{49} +(6.26890 + 3.27122i) q^{50} +(-3.37404 - 3.37404i) q^{51} +(-0.940754 - 5.93301i) q^{52} +7.11286i q^{53} +(5.47343 + 4.67393i) q^{54} +(0.685183 + 6.04253i) q^{55} +(-2.75011 + 0.661000i) q^{56} +(0.445022 + 0.445022i) q^{57} +(12.2343 - 0.963932i) q^{58} +(4.68617 + 4.68617i) q^{59} +(-2.27137 + 4.01124i) q^{60} +(-9.51486 + 9.51486i) q^{61} +(9.71835 + 8.29880i) q^{62} +(-1.37005 + 1.37005i) q^{63} +(3.63564 + 7.12616i) q^{64} +(4.18373 - 5.25390i) q^{65} +(-3.95216 + 0.311388i) q^{66} -10.4358 q^{67} +(-7.49121 - 5.44069i) q^{68} +(4.73970 - 4.73970i) q^{69} +(-2.62085 - 1.76950i) q^{70} +11.9003 q^{71} +(4.67338 + 2.86218i) q^{72} +(5.87007 - 5.87007i) q^{73} +(-1.32037 + 1.54623i) q^{74} +(-5.02293 + 1.15397i) q^{75} +(0.988059 + 0.717605i) q^{76} -2.71962i q^{77} +(3.32955 + 2.84321i) q^{78} -13.4009 q^{79} +(-3.13392 + 8.37726i) q^{80} +0.566696 q^{81} +(5.78336 + 4.93859i) q^{82} -0.228442i q^{83} +(1.21144 - 1.66801i) q^{84} +(-1.16629 - 10.2854i) q^{85} +(-4.53716 + 5.31327i) q^{86} +(-6.32484 + 6.32484i) q^{87} +(-7.47923 + 1.79767i) q^{88} +7.38645 q^{89} +(1.16640 + 6.01500i) q^{90} +(-2.12384 + 2.12384i) q^{91} +(7.64283 - 10.5233i) q^{92} -9.31442 q^{93} +(-2.41889 + 0.190582i) q^{94} +(0.153829 + 1.35660i) q^{95} +(-5.38796 - 2.22902i) q^{96} +(-0.176238 + 0.176238i) q^{97} +(1.07546 + 0.918365i) q^{98} +(-3.72601 + 3.72601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) \) 144 * q + 8 * q^4 - 144 * q^9	\( 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) \) 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

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