LMFDB - Embedded newform 384.2.v.a.253.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			253.12
Character	$\chi$	$=$	384.253
Dual form			384.2.v.a.85.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.669779 - 1.24555i) q^{2} +(-0.634393 - 0.773010i) q^{3} +(-1.10279 + 1.66849i) q^{4} +(-2.98209 - 0.904607i) q^{5} +(-0.537921 + 1.30791i) q^{6} +(1.28096 - 0.254799i) q^{7} +(2.81681 + 0.256069i) q^{8} +(-0.195090 + 0.980785i) q^{9} +O(q^{10})$	\(q+(-0.669779 - 1.24555i) q^{2} +(-0.634393 - 0.773010i) q^{3} +(-1.10279 + 1.66849i) q^{4} +(-2.98209 - 0.904607i) q^{5} +(-0.537921 + 1.30791i) q^{6} +(1.28096 - 0.254799i) q^{7} +(2.81681 + 0.256069i) q^{8} +(-0.195090 + 0.980785i) q^{9} +(0.870606 + 4.32023i) q^{10} +(-4.61401 + 0.454440i) q^{11} +(1.98936 - 0.206006i) q^{12} +(0.573691 + 1.89121i) q^{13} +(-1.17533 - 1.42485i) q^{14} +(1.19255 + 2.87906i) q^{15} +(-1.56769 - 3.67999i) q^{16} +(-1.01284 + 2.44522i) q^{17} +(1.35229 - 0.413914i) q^{18} +(4.25442 + 2.27403i) q^{19} +(4.79796 - 3.97798i) q^{20} +(-1.00960 - 0.828555i) q^{21} +(3.65639 + 5.44261i) q^{22} +(4.72418 + 7.07024i) q^{23} +(-1.58902 - 2.33987i) q^{24} +(3.91720 + 2.61739i) q^{25} +(1.97135 - 1.98125i) q^{26} +(0.881921 - 0.471397i) q^{27} +(-0.987508 + 2.41826i) q^{28} +(0.221738 - 2.25134i) q^{29} +(2.78728 - 3.41371i) q^{30} +(-0.564249 + 0.564249i) q^{31} +(-3.53361 + 4.41742i) q^{32} +(3.27838 + 3.27838i) q^{33} +(3.72403 - 0.376208i) q^{34} +(-4.05044 - 0.398934i) q^{35} +(-1.42128 - 1.40711i) q^{36} +(-0.767807 - 1.43647i) q^{37} +(-0.0170933 - 6.82219i) q^{38} +(1.09798 - 1.64324i) q^{39} +(-8.16835 - 3.31173i) q^{40} +(-1.28052 + 0.855618i) q^{41} +(-0.355801 + 1.81245i) q^{42} +(-5.67657 + 6.91691i) q^{43} +(4.33007 - 8.19957i) q^{44} +(1.46900 - 2.74831i) q^{45} +(5.64219 - 10.6197i) q^{46} +(-0.668810 - 0.277030i) q^{47} +(-1.85014 + 3.54641i) q^{48} +(-4.89121 + 2.02601i) q^{49} +(0.636435 - 6.63215i) q^{50} +(2.53272 - 0.768293i) q^{51} +(-3.78811 - 1.12841i) q^{52} +(-0.988824 - 10.0397i) q^{53} +(-1.17784 - 0.782746i) q^{54} +(14.1705 + 2.81868i) q^{55} +(3.67348 - 0.389707i) q^{56} +(-0.941123 - 4.73134i) q^{57} +(-2.95267 + 1.23171i) q^{58} +(-3.27822 + 10.8068i) q^{59} +(-6.11881 - 1.18526i) q^{60} +(-4.64458 + 3.81171i) q^{61} +(1.08072 + 0.324879i) q^{62} +1.30606i q^{63} +(7.86886 + 1.44260i) q^{64} -6.15871i q^{65} +(1.88760 - 6.27918i) q^{66} +(-5.87783 + 4.82381i) q^{67} +(-2.96286 - 4.38649i) q^{68} +(2.46838 - 8.13716i) q^{69} +(2.21601 + 5.31223i) q^{70} +(2.72547 + 13.7019i) q^{71} +(-0.800681 + 2.71273i) q^{72} +(-11.0320 - 2.19440i) q^{73} +(-1.27493 + 1.91846i) q^{74} +(-0.461776 - 4.68849i) q^{75} +(-8.48594 + 4.59065i) q^{76} +(-5.79458 + 1.75777i) q^{77} +(-2.78214 - 0.266980i) q^{78} +(8.36408 - 3.46452i) q^{79} +(1.34606 + 12.3922i) q^{80} +(-0.923880 - 0.382683i) q^{81} +(1.92338 + 1.02188i) q^{82} +(-2.67324 + 5.00129i) q^{83} +(2.49581 - 0.770774i) q^{84} +(5.23236 - 6.37565i) q^{85} +(12.4174 + 2.43765i) q^{86} +(-1.88098 + 1.25683i) q^{87} +(-13.1132 + 0.0985687i) q^{88} +(6.59157 - 9.86499i) q^{89} +(-4.40707 + 0.0110421i) q^{90} +(1.21675 + 2.27639i) q^{91} +(-17.0064 + 0.0852213i) q^{92} +(0.794126 + 0.0782146i) q^{93} +(0.102899 + 1.01859i) q^{94} +(-10.6300 - 10.6300i) q^{95} +(5.65641 - 0.0708656i) q^{96} +(-9.66618 + 9.66618i) q^{97} +(5.79952 + 4.73528i) q^{98} +(0.454440 - 4.61401i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{3}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.669779	−	1.24555i	−0.473605	−	0.880737i
$2$	−0.669779	−	1.24555i	−0.473605	−	0.880737i
$3$	−0.634393	−	0.773010i	−0.366267	−	0.446298i
$3$	−0.634393	−	0.773010i	−0.366267	−	0.446298i
$4$	−1.10279	+	1.66849i	−0.551397	+	0.834243i
$5$	−2.98209	−	0.904607i	−1.33363	−	0.404553i	−0.458610	−	0.888637i	$-0.651653\pi$
$5$	−2.98209	−	0.904607i	−1.33363	−	0.404553i	−0.875021	+	0.484085i	$0.839153\pi$
$6$	−0.537921	+	1.30791i	−0.219605	+	0.533954i
$7$	1.28096	−	0.254799i	0.484158	−	0.0963051i	0.0530248	−	0.998593i	$-0.483114\pi$
$7$	1.28096	−	0.254799i	0.484158	−	0.0963051i	0.431134	+	0.902288i	$0.358114\pi$
$8$	2.81681	+	0.256069i	0.995893	+	0.0905340i
$9$	−0.195090	+	0.980785i	−0.0650301	+	0.326928i
$10$	0.870606	+	4.32023i	0.275310	+	1.36618i
$11$	−4.61401	+	0.454440i	−1.39118	+	0.137019i	−0.765687	−	0.643214i	$-0.777601\pi$
$11$	−4.61401	+	0.454440i	−1.39118	+	0.137019i	−0.625490	+	0.780233i	$0.715101\pi$
$12$	1.98936	−	0.206006i	0.574279	−	0.0594687i
$13$	0.573691	+	1.89121i	0.159113	+	0.524526i	0.999857	−	0.0169071i	$-0.00538196\pi$
$13$	0.573691	+	1.89121i	0.159113	+	0.524526i	−0.840744	+	0.541433i	$0.817882\pi$
$14$	−1.17533	−	1.42485i	−0.314119	−	0.380806i
$15$	1.19255	+	2.87906i	0.307914	+	0.743371i
$16$	−1.56769	−	3.67999i	−0.391923	−	0.919998i
$17$	−1.01284	+	2.44522i	−0.245651	+	0.593053i	−0.997826	−	0.0659103i	$-0.979005\pi$
$17$	−1.01284	+	2.44522i	−0.245651	+	0.593053i	0.752175	+	0.658964i	$0.229005\pi$
$18$	1.35229	−	0.413914i	0.318737	−	0.0975605i
$19$	4.25442	+	2.27403i	0.976031	+	0.521699i	0.880663	−	0.473743i	$-0.157097\pi$
$19$	4.25442	+	2.27403i	0.976031	+	0.521699i	0.0953675	+	0.995442i	$0.469597\pi$
$20$	4.79796	−	3.97798i	1.07286	−	0.889504i
$21$	−1.00960	−	0.828555i	−0.220312	−	0.180805i
$22$	3.65639	+	5.44261i	0.779546	+	1.16037i
$23$	4.72418	+	7.07024i	0.985060	+	1.47425i	0.877226	+	0.480078i	$0.159392\pi$
$23$	4.72418	+	7.07024i	0.985060	+	1.47425i	0.107835	+	0.994169i	$0.465608\pi$
$24$	−1.58902	−	2.33987i	−0.324358	−	0.477625i
$25$	3.91720	+	2.61739i	0.783441	+	0.523478i
$26$	1.97135	−	1.98125i	0.386613	−	0.388555i
$27$	0.881921	−	0.471397i	0.169726	−	0.0907203i
$28$	−0.987508	+	2.41826i	−0.186621	+	0.457008i
$29$	0.221738	−	2.25134i	0.0411756	−	0.418063i	−0.952396	−	0.304862i	$-0.901390\pi$
$29$	0.221738	−	2.25134i	0.0411756	−	0.418063i	0.993572	−	0.113201i	$-0.0361104\pi$
$30$	2.78728	−	3.41371i	0.508885	−	0.623256i
$31$	−0.564249	+	0.564249i	−0.101342	+	0.101342i	−0.755960	−	0.654618i	$-0.772830\pi$
$31$	−0.564249	+	0.564249i	−0.101342	+	0.101342i	0.654618	+	0.755960i	$0.272830\pi$
$32$	−3.53361	+	4.41742i	−0.624660	+	0.780897i
$33$	3.27838	+	3.27838i	0.570693	+	0.570693i
$34$	3.72403	−	0.376208i	0.638666	−	0.0645192i
$35$	−4.05044	−	0.398934i	−0.684649	−	0.0674321i
$36$	−1.42128	−	1.40711i	−0.236880	−	0.234518i
$37$	−0.767807	−	1.43647i	−0.126227	−	0.236154i	0.810868	−	0.585229i	$-0.198996\pi$
$37$	−0.767807	−	1.43647i	−0.126227	−	0.236154i	−0.937094	+	0.349076i	$0.886496\pi$
$38$	−0.0170933	−	6.82219i	−0.00277291	−	1.10671i
$39$	1.09798	−	1.64324i	0.175817	−	0.263128i
$40$	−8.16835	−	3.31173i	−1.29153	−	0.523630i
$41$	−1.28052	+	0.855618i	−0.199984	+	0.133625i	−0.651530	−	0.758623i	$-0.725873\pi$
$41$	−1.28052	+	0.855618i	−0.199984	+	0.133625i	0.451546	+	0.892248i	$0.350873\pi$
$42$	−0.355801	+	1.81245i	−0.0549012	+	0.279667i
$43$	−5.67657	+	6.91691i	−0.865668	+	1.05482i	0.132307	+	0.991209i	$0.457762\pi$
$43$	−5.67657	+	6.91691i	−0.865668	+	1.05482i	−0.997975	+	0.0636108i	$0.979738\pi$
$44$	4.33007	−	8.19957i	0.652783	−	1.23613i
$45$	1.46900	−	2.74831i	0.218986	−	0.409694i
$46$	5.64219	−	10.6197i	0.831895	−	1.56579i
$47$	−0.668810	−	0.277030i	−0.0975559	−	0.0404090i	0.333372	−	0.942795i	$-0.391814\pi$
$47$	−0.668810	−	0.277030i	−0.0975559	−	0.0404090i	−0.430928	+	0.902386i	$0.641814\pi$
$48$	−1.85014	+	3.54641i	−0.267044	+	0.511880i
$49$	−4.89121	+	2.02601i	−0.698745	+	0.289430i
$50$	0.636435	−	6.63215i	0.0900055	−	0.937927i
$51$	2.53272	−	0.768293i	0.354652	−	0.107583i
$52$	−3.78811	−	1.12841i	−0.525317	−	0.156483i
$53$	−0.988824	−	10.0397i	−0.135825	−	1.37906i	−0.785507	−	0.618853i	$-0.787598\pi$
$53$	−0.988824	−	10.0397i	−0.135825	−	1.37906i	0.649682	−	0.760207i	$-0.274902\pi$
$54$	−1.17784	−	0.782746i	−0.160284	−	0.106518i
$55$	14.1705	+	2.81868i	1.91075	+	0.380071i
$56$	3.67348	−	0.389707i	0.490889	−	0.0520768i
$57$	−0.941123	−	4.73134i	−0.124655	−	0.626682i
$58$	−2.95267	+	1.23171i	−0.387705	+	0.161732i
$59$	−3.27822	+	10.8068i	−0.426788	+	1.40693i	0.435352	+	0.900260i	$0.356624\pi$
$59$	−3.27822	+	10.8068i	−0.426788	+	1.40693i	−0.862140	+	0.506670i	$0.830876\pi$
$60$	−6.11881	−	1.18526i	−0.789935	−	0.153017i
$61$	−4.64458	+	3.81171i	−0.594678	+	0.488040i	−0.882924	−	0.469517i	$-0.844428\pi$
$61$	−4.64458	+	3.81171i	−0.594678	+	0.488040i	0.288245	+	0.957557i	$0.406928\pi$
$62$	1.08072	+	0.324879i	0.137252	+	0.0412597i
$63$			1.30606i			0.164548i
$64$	7.86886	+	1.44260i	0.983607	+	0.180324i
$65$		−	6.15871i		−	0.763894i
$66$	1.88760	−	6.27918i	0.232348	−	0.772914i
$67$	−5.87783	+	4.82381i	−0.718091	+	0.589322i	−0.920855	−	0.389906i	$-0.872508\pi$
$67$	−5.87783	+	4.82381i	−0.718091	+	0.589322i	0.202764	+	0.979228i	$0.435008\pi$
$68$	−2.96286	−	4.38649i	−0.359300	−	0.531940i
$69$	2.46838	−	8.13716i	0.297158	−	0.979599i
$70$	2.21601	+	5.31223i	0.264863	+	0.634933i
$71$	2.72547	+	13.7019i	0.323454	+	1.62611i	0.710250	+	0.703949i	$0.248582\pi$
$71$	2.72547	+	13.7019i	0.323454	+	1.62611i	−0.386796	+	0.922165i	$0.626418\pi$
$72$	−0.800681	+	2.71273i	−0.0943612	+	0.319698i
$73$	−11.0320	−	2.19440i	−1.29120	−	0.256835i	−0.498733	−	0.866756i	$-0.666201\pi$
$73$	−11.0320	−	2.19440i	−1.29120	−	0.256835i	−0.792462	+	0.609921i	$0.791201\pi$
$74$	−1.27493	+	1.91846i	−0.148208	+	0.223016i
$75$	−0.461776	−	4.68849i	−0.0533213	−	0.541381i
$76$	−8.48594	+	4.59065i	−0.973404	+	0.526584i
$77$	−5.79458	+	1.75777i	−0.660354	+	0.200316i
$78$	−2.78214	−	0.266980i	−0.315015	−	0.0302295i
$79$	8.36408	−	3.46452i	0.941033	−	0.389789i	0.141179	−	0.989984i	$-0.454911\pi$
$79$	8.36408	−	3.46452i	0.941033	−	0.389789i	0.799853	+	0.600195i	$0.204911\pi$
$80$	1.34606	+	12.3922i	0.150494	+	1.38549i
$81$	−0.923880	−	0.382683i	−0.102653	−	0.0425204i
$82$	1.92338	+	1.02188i	0.212402	+	0.112848i
$83$	−2.67324	+	5.00129i	−0.293427	+	0.548963i	−0.984833	−	0.173503i	$-0.944491\pi$
$83$	−2.67324	+	5.00129i	−0.293427	+	0.548963i	0.691407	+	0.722466i	$0.256991\pi$
$84$	2.49581	−	0.770774i	0.272315	−	0.0840983i
$85$	5.23236	−	6.37565i	0.567529	−	0.691536i
$86$	12.4174	+	2.43765i	1.33900	+	0.262858i
$87$	−1.88098	+	1.25683i	−0.201662	+	0.134746i
$88$	−13.1132	+	0.0985687i	−1.39787	+	0.0105075i
$89$	6.59157	−	9.86499i	0.698705	−	1.04569i	−0.297158	−	0.954828i	$-0.596039\pi$
$89$	6.59157	−	9.86499i	0.698705	−	1.04569i	0.995864	−	0.0908584i	$-0.0289611\pi$
$90$	−4.40707	+	0.0110421i	−0.464546	+	0.00116394i
$91$	1.21675	+	2.27639i	0.127551	+	0.238630i
$92$	−17.0064	+	0.0852213i	−1.77304	+	0.00888493i
$93$	0.794126	+	0.0782146i	0.0823471	+	0.00811048i
$94$	0.102899	+	1.01859i	0.0106133	+	0.105059i
$95$	−10.6300	−	10.6300i	−1.09061	−	1.09061i
$96$	5.65641	−	0.0708656i	0.577305	−	0.00723269i
$97$	−9.66618	+	9.66618i	−0.981452	+	0.981452i	−0.999831	−	0.0183790i	$-0.994149\pi$
$97$	−9.66618	+	9.66618i	−0.981452	+	0.981452i	0.0183790	+	0.999831i	$0.494149\pi$
$98$	5.79952	+	4.73528i	0.585840	+	0.478335i
$99$	0.454440	−	4.61401i	0.0456730	−	0.463725i
$100$	−8.68695	+	3.64936i	−0.868695	+	0.364936i
$101$	4.10838	−	2.19598i	0.408799	−	0.218508i	−0.254162	−	0.967162i	$-0.581800\pi$
$101$	4.10838	−	2.19598i	0.408799	−	0.218508i	0.662961	+	0.748654i	$0.269300\pi$
$102$	−2.65331	−	2.64005i	−0.262717	−	0.261404i
$103$	−12.1054	−	8.08854i	−1.19278	−	0.796987i	−0.209269	−	0.977858i	$-0.567108\pi$
$103$	−12.1054	−	8.08854i	−1.19278	−	0.796987i	−0.983507	+	0.180871i	$0.942108\pi$
$104$	1.13170	+	5.47407i	0.110972	+	0.536777i
$105$	2.26119	+	3.38411i	0.220670	+	0.330256i
$106$	−11.8427	+	7.95601i	−1.15026	+	0.772756i
$107$	3.50407	+	2.87571i	0.338751	+	0.278006i	0.788353	−	0.615223i	$-0.210934\pi$
$107$	3.50407	+	2.87571i	0.338751	+	0.278006i	−0.449602	+	0.893229i	$0.648434\pi$
$108$	−0.186058	+	1.99133i	−0.0179034	+	0.191616i
$109$	−3.62622	−	1.93825i	−0.347329	−	0.185651i	0.288503	−	0.957479i	$-0.406843\pi$
$109$	−3.62622	−	1.93825i	−0.347329	−	0.185651i	−0.635831	+	0.771828i	$0.719343\pi$
$110$	−5.98027	−	19.5380i	−0.570197	−	1.86287i
$111$	−0.623312	+	1.50481i	−0.0591621	+	0.142830i
$112$	−2.94582	−	4.31449i	−0.278353	−	0.407681i
$113$	−6.57400	−	15.8710i	−0.618430	−	1.49302i	−0.853527	−	0.521049i	$-0.825541\pi$
$113$	−6.57400	−	15.8710i	−0.618430	−	1.49302i	0.235097	−	0.971972i	$-0.424459\pi$
$114$	−5.26278	+	4.34117i	−0.492905	+	0.406588i
$115$	−7.69215	−	25.3576i	−0.717297	−	2.36461i
$116$	3.51180	+	2.85273i	0.326062	+	0.264869i
$117$	−1.96679	+	0.193712i	−0.181830	+	0.0179087i
$118$	15.6561	−	3.15500i	1.44127	−	0.290441i
$119$	−0.674375	+	3.39031i	−0.0618198	+	0.310789i
$120$	2.62194	+	8.41516i	0.239350	+	0.768195i
$121$	10.2939	−	2.04759i	0.935812	−	0.186145i
$122$	7.85852	+	3.23206i	0.711477	+	0.292617i
$123$	1.47376	+	0.447059i	0.132884	+	0.0403100i
$124$	−0.319192	−	1.56369i	−0.0286643	−	0.140424i
$125$	0.570982	+	0.695744i	0.0510702	+	0.0622292i
$126$	1.62676	−	0.874770i	0.144923	−	0.0779307i
$127$	9.18145			0.814722			0.407361	−	0.913267i	$-0.366449\pi$
$127$	9.18145			0.814722			0.407361	+	0.913267i	$0.366449\pi$
$128$	−3.47357	−	10.7673i	−0.307023	−	0.951702i
$129$	8.94802			0.787829
$130$	−7.67099	+	4.12497i	−0.672790	+	0.361784i
$131$	−8.80307	−	10.7266i	−0.769127	−	0.937185i	0.230226	−	0.973137i	$-0.426053\pi$
$131$	−8.80307	−	10.7266i	−0.769127	−	0.937185i	−0.999353	+	0.0359526i	$0.988553\pi$
$132$	−9.08532	+	1.85456i	−0.790775	+	0.161419i
$133$	6.02917	+	1.82893i	0.522796	+	0.158588i
$134$	9.94514	+	4.09025i	0.859129	+	0.353344i
$135$	−3.05640	+	0.607955i	−0.263053	+	0.0523245i
$136$	−3.47914	+	6.62837i	−0.298333	+	0.568378i
$137$	−4.41684	+	22.2050i	−0.377356	+	1.89710i	0.0607078	+	0.998156i	$0.480664\pi$
$137$	−4.41684	+	22.2050i	−0.377356	+	1.89710i	−0.438064	+	0.898944i	$0.644336\pi$
$138$	−11.7885	+	2.37560i	−1.00350	+	0.202225i
$139$	3.28750	−	0.323791i	0.278842	−	0.0274636i	0.0423706	−	0.999102i	$-0.486509\pi$
$139$	3.28750	−	0.323791i	0.278842	−	0.0274636i	0.236472	+	0.971638i	$0.424009\pi$
$140$	5.13241	−	6.31816i	0.433768	−	0.533982i
$141$	0.210141	+	0.692743i	0.0176971	+	0.0583395i
$142$	15.2409	−	12.5719i	1.27899	−	1.05501i
$143$	−3.50645	−	8.46533i	−0.293224	−	0.707906i
$144$	3.91512	−	0.819640i	0.326260	−	0.0683033i
$145$	−2.69782	+	6.51311i	−0.224042	+	0.540884i
$146$	4.65575	+	15.2106i	0.385313	+	1.25884i
$147$	4.66908	+	2.49567i	0.385099	+	0.205840i
$148$	3.24346	+	0.303050i	0.266610	+	0.0249105i
$149$	10.4854	+	8.60515i	0.858997	+	0.704961i	0.956957	−	0.290229i	$-0.0937316\pi$
$149$	10.4854	+	8.60515i	0.858997	+	0.704961i	−0.0979597	+	0.995190i	$0.531232\pi$
$150$	−5.53047	+	3.71542i	−0.451561	+	0.303363i
$151$	6.85659	+	10.2616i	0.557982	+	0.835079i	0.998020	−	0.0629004i	$-0.0200351\pi$
$151$	6.85659	+	10.2616i	0.557982	+	0.835079i	−0.440038	+	0.897979i	$0.645035\pi$
$152$	11.4016	+	7.49495i	0.924791	+	0.607921i
$153$	−2.20064	−	1.47042i	−0.177911	−	0.118877i
$154$	6.07048	+	6.04013i	0.489173	+	0.486728i
$155$	2.19307	−	1.17222i	0.176151	−	0.0941548i
$156$	1.53088	+	3.64411i	0.122568	+	0.291762i
$157$	−0.966653	+	9.81459i	−0.0771473	+	0.783290i	0.876307	+	0.481753i	$0.160000\pi$
$157$	−0.966653	+	9.81459i	−0.0771473	+	0.783290i	−0.953454	+	0.301537i	$0.902500\pi$
$158$	−9.91731	−	8.09743i	−0.788979	−	0.644197i
$159$	−7.13349	+	7.13349i	−0.565723	+	0.565723i
$160$	14.5336	−	9.97662i	1.14898	−	0.788721i
$161$	7.85300	+	7.85300i	0.618903	+	0.618903i
$162$	0.142143	+	1.40705i	0.0111678	+	0.110548i
$163$	13.5042	+	1.33005i	1.05773	+	0.104177i	0.611896	−	0.790938i	$-0.290407\pi$
$163$	13.5042	+	1.33005i	1.05773	+	0.104177i	0.445835	+	0.895115i	$0.352907\pi$
$164$	−0.0154348	−	3.08011i	−0.00120526	−	0.240516i
$165$	−6.81079	−	12.7421i	−0.530219	−	0.991970i
$166$	8.01984	−	0.0200941i	0.622460	−	0.00155961i
$167$	7.83504	−	11.7260i	0.606294	−	0.907383i	−0.393636	−	0.919266i	$-0.628783\pi$
$167$	7.83504	−	11.7260i	0.606294	−	0.907383i	0.999929	+	0.0118840i	$0.00378287\pi$
$168$	−2.63168	−	2.59241i	−0.203038	−	0.200009i
$169$	7.56157	−	5.05248i	0.581659	−	0.388652i
$170$	−11.4457	−	2.24690i	−0.877846	−	0.172329i
$171$	−3.06034	+	3.72903i	−0.234030	+	0.285166i
$172$	−5.28070	−	17.0992i	−0.402650	−	1.30380i
$173$	5.80164	−	10.8541i	0.441091	−	0.825223i	−0.558901	−	0.829234i	$-0.688777\pi$
$173$	5.80164	−	10.8541i	0.441091	−	0.825223i	0.999992	+	0.00401137i	$0.00127686\pi$
$174$	2.82528	+	1.50106i	0.214184	+	0.113795i
$175$	5.68470	+	2.35468i	0.429723	+	0.177997i
$176$	8.90569	+	16.2671i	0.671292	+	1.22618i
$177$	10.4335	−	4.32169i	0.784228	−	0.324838i
$178$	−16.7022	−	1.60278i	−1.25189	−	0.120134i
$179$	−16.2733	+	4.93645i	−1.21632	+	0.368968i	−0.832284	−	0.554349i	$-0.812967\pi$
$179$	−16.2733	+	4.93645i	−1.21632	+	0.368968i	−0.384039	+	0.923317i	$0.625467\pi$
$180$	2.96551	+	5.48183i	0.221036	+	0.408591i
$181$	−1.76848	−	17.9557i	−0.131450	−	1.33464i	−0.804019	−	0.594603i	$-0.797309\pi$
$181$	−1.76848	−	17.9557i	−0.131450	−	1.33464i	0.672569	−	0.740035i	$-0.265191\pi$
$182$	2.02040	−	3.04020i	0.149762	−	0.225355i
$183$	5.89299	+	1.17219i	0.435622	+	0.0866506i
$184$	11.4967	+	21.1253i	0.847546	+	1.55737i
$185$	0.990233	+	4.97824i	0.0728034	+	0.366007i
$186$	−0.434469	−	1.04151i	−0.0318568	−	0.0763673i
$187$	3.56206	−	11.7426i	0.260484	−	0.858701i
$188$	1.19978	−	0.810393i	0.0875029	−	0.0591040i
$189$	1.00960	−	0.828555i	0.0734374	−	0.0602685i
$190$	−6.12043	+	20.3599i	−0.444023	+	1.47706i
$191$			12.7566i			0.923038i	0.887130	+	0.461519i	$0.152695\pi$
$191$			12.7566i			0.923038i	−0.887130	+	0.461519i	$0.847305\pi$
$192$	−3.87681	−	6.99788i	−0.279785	−	0.505029i
$193$		−	4.44879i		−	0.320231i	−0.987098	−	0.160115i	$-0.948813\pi$
$193$		−	4.44879i		−	0.320231i	0.987098	−	0.160115i	$-0.0511866\pi$
$194$	18.5139	+	5.56552i	1.32922	+	0.399581i
$195$	−4.76075	+	3.90704i	−0.340924	+	0.279789i
$196$	2.01363	−	10.3952i	0.143831	−	0.742514i
$197$	−5.96994	+	19.6803i	−0.425341	+	1.40216i	0.438653	+	0.898657i	$0.355456\pi$
$197$	−5.96994	+	19.6803i	−0.425341	+	1.40216i	−0.863993	+	0.503503i	$0.832044\pi$
$198$	−6.05136	+	2.52434i	−0.430051	+	0.179397i
$199$	−3.60152	−	18.1061i	−0.255305	−	1.28350i	−0.869336	−	0.494222i	$-0.835453\pi$
$199$	−3.60152	−	18.1061i	−0.255305	−	1.28350i	0.614031	−	0.789282i	$-0.289547\pi$
$200$	10.3638	+	8.37577i	0.732831	+	0.592256i
$201$	7.45771	+	1.48343i	0.526026	+	0.104633i
$202$	−5.48691	−	3.64638i	−0.386057	−	0.256558i
$203$	−0.289602	−	2.94038i	−0.0203261	−	0.206374i
$204$	−1.51118	+	5.07308i	−0.105804	+	0.355187i
$205$	4.59263	−	1.39316i	0.320764	−	0.0973026i
$206$	−1.96678	+	20.4954i	−0.137032	+	1.42798i
$207$	−7.85603	+	3.25407i	−0.546032	+	0.226174i
$208$	6.06025	−	5.07601i	0.420203	−	0.351958i
$209$	−20.6633	−	8.55904i	−1.42931	−	0.592041i
$210$	2.70059	−	5.08304i	0.186358	−	0.350763i
$211$	7.49992	−	14.0314i	0.516316	−	0.965959i	−0.479755	−	0.877402i	$-0.659275\pi$
$211$	7.49992	−	14.0314i	0.516316	−	0.965959i	0.996071	−	0.0885565i	$-0.0282254\pi$
$212$	17.8416	+	9.42188i	1.22536	+	0.647097i
$213$	8.86268	−	10.7992i	0.607261	−	0.739949i
$214$	1.23490	−	6.29059i	0.0844159	−	0.430016i
$215$	23.1851	−	15.4918i	1.58121	−	1.05653i
$216$	2.60492	−	1.10200i	0.177242	−	0.0749818i
$217$	−0.579012	+	0.866552i	−0.0393059	+	0.0588254i
$218$	0.0145694	+	5.81484i	0.000986762	+	0.393831i
$219$	5.30232	+	9.91994i	0.358298	+	0.670328i
$220$	−20.3301	+	20.5348i	−1.37065	+	1.38446i
$221$	−5.20547	−	0.512695i	−0.350158	−	0.0344876i
$222$	2.29179	−	0.231521i	0.153815	−	0.0155387i
$223$	−11.1109	−	11.1109i	−0.744040	−	0.744040i	0.229313	−	0.973353i	$-0.426352\pi$
$223$	−11.1109	−	11.1109i	−0.744040	−	0.744040i	−0.973353	+	0.229313i	$0.926352\pi$
$224$	−3.40087	+	6.55891i	−0.227230	+	0.438236i
$225$	−3.33131	+	3.33131i	−0.222087	+	0.222087i
$226$	−15.3651	+	18.8183i	−1.02207	+	1.25178i
$227$	−1.73063	+	17.5714i	−0.114866	+	1.16626i	0.749012	+	0.662556i	$0.230528\pi$
$227$	−1.73063	+	17.5714i	−0.114866	+	1.16626i	−0.863878	+	0.503700i	$0.831972\pi$
$228$	8.93204	+	3.64744i	0.591539	+	0.241558i
$229$	10.5789	−	5.65453i	0.699072	−	0.373662i	−0.0832563	−	0.996528i	$-0.526532\pi$
$229$	10.5789	−	5.65453i	0.699072	−	0.373662i	0.782328	+	0.622866i	$0.214032\pi$
$230$	−26.4322	+	26.5650i	−1.74289	+	1.75164i
$231$	5.03482	+	3.36416i	0.331267	+	0.221345i
$232$	1.20109	−	6.28482i	0.0788555	−	0.412618i
$233$	11.4747	+	17.1731i	0.751732	+	1.12505i	0.988164	+	0.153399i	$0.0490219\pi$
$233$	11.4747	+	17.1731i	0.751732	+	1.12505i	−0.236432	+	0.971648i	$0.575978\pi$
$234$	1.55859	+	2.31999i	0.101888	+	0.151662i
$235$	1.74385	+	1.43114i	0.113756	+	0.0933572i
$236$	−14.4159	−	17.3874i	−0.938393	−	1.13182i
$237$	−7.98422	−	4.26766i	−0.518631	−	0.277214i
$238$	4.67448	−	1.43079i	0.303002	−	0.0927443i
$239$	−0.119482	+	0.288455i	−0.00772864	+	0.0186586i	−0.927697	−	0.373335i	$-0.878214\pi$
$239$	−0.119482	+	0.288455i	−0.00772864	+	0.0186586i	0.919968	+	0.391993i	$0.128214\pi$
$240$	8.72538	−	8.90205i	0.563221	−	0.574625i
$241$	2.05387	+	4.95848i	0.132301	+	0.319404i	0.976122	−	0.217221i	$-0.0696992\pi$
$241$	2.05387	+	4.95848i	0.132301	+	0.319404i	−0.843821	+	0.536624i	$0.819699\pi$
$242$	−9.44503	−	11.4502i	−0.607150	−	0.736045i
$243$	0.290285	+	0.956940i	0.0186218	+	0.0613878i
$244$	−1.23777	−	11.9530i	−0.0792402	−	0.765210i
$245$	16.4188	−	1.61711i	1.04896	−	0.103313i
$246$	−0.430256	−	2.13507i	−0.0274321	−	0.136127i
$247$	−1.85994	+	9.35057i	−0.118345	+	0.594963i
$248$	−1.73387	+	1.44490i	−0.110101	+	0.0917511i
$249$	5.56194	−	1.10634i	0.352473	−	0.0701113i
$250$	0.484153	−	1.17718i	0.0306205	−	0.0744515i
$251$	13.9088	+	4.21918i	0.877913	+	0.266312i	0.696900	−	0.717169i	$-0.254562\pi$
$251$	13.9088	+	4.21918i	0.877913	+	0.266312i	0.181013	+	0.983481i	$0.442062\pi$
$252$	−2.17914	−	1.44031i	−0.137273	−	0.0907312i
$253$	−25.0104	−	30.4753i	−1.57239	−	1.91597i
$254$	−6.14954	−	11.4360i	−0.385856	−	0.717556i
$255$	−8.24781			−0.516498
$256$	−11.0847	+	11.5382i	−0.692792	+	0.721137i
$257$	−27.9795			−1.74531			−0.872657	−	0.488334i	$-0.837605\pi$
$257$	−27.9795			−1.74531			−0.872657	+	0.488334i	$0.837605\pi$
$258$	−5.99319	−	11.1452i	−0.373120	−	0.693871i
$259$	−1.34954	−	1.64442i	−0.0838565	−	0.102179i
$260$	10.2757	+	6.79179i	0.637273	+	0.421209i
$261$	2.16482	+	0.656691i	0.133999	+	0.0406482i
$262$	−7.46438	+	18.1491i	−0.461151	+	1.12125i
$263$	25.8451	−	5.14092i	1.59368	−	0.317003i	0.683096	−	0.730328i	$-0.260633\pi$
$263$	25.8451	−	5.14092i	1.59368	−	0.317003i	0.910583	+	0.413326i	$0.135633\pi$
$264$	8.39510	+	10.0741i	0.516683	+	0.620017i
$265$	−6.13322	+	30.8338i	−0.376761	+	1.89411i
$266$	−1.76019	−	8.73462i	−0.107924	−	0.535554i
$267$	−11.8074	+	1.16293i	−0.722600	+	0.0711699i
$268$	−1.56643	−	15.1267i	−0.0956849	−	0.924013i
$269$	4.61335	+	15.2082i	0.281281	+	0.927258i	0.977768	+	0.209689i	$0.0672452\pi$
$269$	4.61335	+	15.2082i	0.281281	+	0.927258i	−0.696487	+	0.717569i	$0.745255\pi$
$270$	2.80435	+	3.39970i	0.170667	+	0.206899i
$271$	0.219261	+	0.529343i	0.0133192	+	0.0321553i	0.930399	−	0.366548i	$-0.119460\pi$
$271$	0.219261	+	0.529343i	0.0133192	+	0.0321553i	−0.917080	+	0.398703i	$0.869460\pi$
$272$	10.5862	−	0.106101i	0.641884	−	0.00643329i
$273$	0.987770	−	2.38469i	0.0597826	−	0.144328i
$274$	30.6157	−	9.37101i	1.84956	−	0.566124i
$275$	−19.2635	−	10.2965i	−1.16163	−	0.620904i
$276$	10.8546	+	13.0921i	0.653371	+	0.788049i
$277$	13.3701	+	10.9726i	0.803333	+	0.659279i	0.943693	−	0.330822i	$-0.107326\pi$
$277$	13.3701	+	10.9726i	0.803333	+	0.659279i	−0.140360	+	0.990101i	$0.544826\pi$
$278$	−2.60520	−	3.87788i	−0.156249	−	0.232580i
$279$	−0.443328	−	0.663487i	−0.0265413	−	0.0397219i
$280$	−11.3072	−	2.16091i	−0.675733	−	0.129139i
$281$	−11.3432	−	7.57932i	−0.676681	−	0.452144i	0.169153	−	0.985590i	$-0.445897\pi$
$281$	−11.3432	−	7.57932i	−0.676681	−	0.452144i	−0.845834	+	0.533446i	$0.820897\pi$
$282$	0.722098	−	0.725726i	0.0430003	−	0.0432164i
$283$	2.72693	−	1.45758i	0.162099	−	0.0866439i	−0.388352	−	0.921511i	$-0.626956\pi$
$283$	2.72693	−	1.45758i	0.162099	−	0.0866439i	0.550452	+	0.834867i	$0.314456\pi$
$284$	−25.8670	−	10.5629i	−1.53493	−	0.626795i
$285$	−1.47349	+	14.9606i	−0.0872823	+	0.886192i
$286$	−8.19545	+	10.0374i	−0.484607	+	0.593522i
$287$	−1.42229	+	1.42229i	−0.0839552	+	0.0839552i
$288$	−3.64317	−	4.32751i	−0.214676	−	0.255001i
$289$	7.06756	+	7.06756i	0.415739	+	0.415739i
$290$	9.91935	−	1.00207i	0.582484	−	0.0588437i
$291$	13.6042	+	1.33990i	0.797494	+	0.0785463i
$292$	15.8273	−	15.9867i	0.926223	−	0.935553i
$293$	−11.9320	−	22.3233i	−0.697077	−	1.30414i	−0.942332	−	0.334680i	$-0.891372\pi$
$293$	−11.9320	−	22.3233i	−0.697077	−	1.30414i	0.245255	−	0.969459i	$-0.421128\pi$
$294$	−0.0187594	−	7.48712i	−0.00109407	−	0.436658i
$295$	19.5519	−	29.2615i	1.13836	−	1.70367i
$296$	−1.79493	−	4.24287i	−0.104328	−	0.246612i
$297$	−3.85497	+	2.57581i	−0.223688	+	0.149464i
$298$	3.69525	−	18.8236i	0.214060	−	1.09042i
$299$	−10.6611	+	12.9905i	−0.616545	+	0.751262i
$300$	8.33193	+	4.39997i	0.481044	+	0.254033i
$301$	−5.50904	+	10.3067i	−0.317536	+	0.594068i
$302$	8.18897	−	15.4132i	0.471222	−	0.886933i
$303$	−4.30384	−	1.78271i	−0.247249	−	0.102414i
$304$	1.69880	−	19.2212i	0.0974330	−	1.10241i
$305$	17.2987	−	7.16535i	0.990519	−	0.410287i
$306$	−0.357542	+	3.72587i	−0.0204393	+	0.212994i
$307$	2.20165	−	0.667862i	0.125655	−	0.0381169i	−0.226831	−	0.973934i	$-0.572837\pi$
$307$	2.20165	−	0.667862i	0.125655	−	0.0381169i	0.352486	+	0.935817i	$0.385337\pi$
$308$	3.45742	−	11.6066i	0.197005	−	0.661350i
$309$	1.42703	+	14.4889i	0.0811809	+	0.824243i
$310$	−2.92893	−	1.94645i	−0.166352	−	0.110551i
$311$	−25.3452	−	5.04148i	−1.43720	−	0.285876i	−0.585824	−	0.810438i	$-0.699229\pi$
$311$	−25.3452	−	5.04148i	−1.43720	−	0.285876i	−0.851372	+	0.524563i	$0.824229\pi$
$312$	3.51357	−	4.34753i	0.198917	−	0.246131i
$313$	2.90155	+	14.5871i	0.164005	+	0.824510i	0.971938	+	0.235236i	$0.0755863\pi$
$313$	2.90155	+	14.5871i	0.164005	+	0.824510i	−0.807933	+	0.589274i	$0.799414\pi$
$314$	12.8720	−	5.36959i	0.726410	−	0.303023i
$315$	1.18147	−	3.89478i	0.0665683	−	0.219446i
$316$	−3.44336	+	17.7760i	−0.193704	+	0.999978i
$317$	0.209816	−	0.172191i	0.0117844	−	0.00967123i	−0.628483	−	0.777824i	$-0.716324\pi$
$317$	0.209816	−	0.172191i	0.0117844	−	0.00967123i	0.640267	+	0.768152i	$0.278824\pi$
$318$	13.6630	+	4.10727i	0.766182	+	0.230324i
$319$			10.4885i			0.587241i
$320$	−22.1607	−	11.4202i	−1.23882	−	0.638407i
$321$		−	4.53301i		−	0.253008i
$322$	4.52154	−	15.0411i	0.251975	−	0.838206i
$323$	−9.86958	+	8.09976i	−0.549158	+	0.450682i
$324$	1.65735	−	1.11946i	0.0920750	−	0.0621922i
$325$	−2.70276	+	8.90981i	−0.149922	+	0.494227i
$326$	−7.38819	−	17.7110i	−0.409194	−	0.980922i
$327$	0.802158	+	4.03272i	0.0443594	+	0.223010i
$328$	−3.82609	+	2.08221i	−0.211260	+	0.114971i
$329$	−0.927307	−	0.184453i	−0.0511241	−	0.0101692i
$330$	−11.3092	+	17.0176i	−0.622551	+	0.936786i
$331$	2.35076	+	23.8677i	0.129210	+	1.31189i	0.813023	+	0.582231i	$0.197820\pi$
$331$	2.35076	+	23.8677i	0.129210	+	1.31189i	−0.683814	+	0.729657i	$0.739680\pi$
$332$	−5.39655	−	9.97566i	−0.296174	−	0.547485i
$333$	1.55866	−	0.472813i	0.0854138	−	0.0259100i
$334$	−19.8530	−	1.90514i	−1.08631	−	0.104245i
$335$	21.8919	−	9.06791i	1.19608	−	0.495433i
$336$	−1.46634	+	5.01423i	−0.0799952	+	0.273549i
$337$	−19.1783	−	7.94392i	−1.04471	−	0.432733i	−0.206709	−	0.978402i	$-0.566275\pi$
$337$	−19.1783	−	7.94392i	−1.04471	−	0.432733i	−0.838001	+	0.545669i	$0.816275\pi$
$338$	−11.3577	−	6.03428i	−0.617777	−	0.328221i
$339$	−8.09797	+	15.1502i	−0.439822	+	0.822848i
$340$	4.86747	+	15.7611i	0.263976	+	0.854768i
$341$	2.34703	−	2.85987i	0.127099	−	0.154871i
$342$	6.69444	+	1.31418i	0.361994	+	0.0710627i
$343$	−13.3509	+	8.92077i	−0.720879	+	0.481676i
$344$	−17.7610	+	18.0301i	−0.957610	+	0.972115i
$345$	−14.7219	+	22.0328i	−0.792598	+	1.18621i
$346$	−17.4052	+	0.0436095i	−0.935708	+	0.00234446i
$347$	−11.0726	−	20.7155i	−0.594410	−	1.11206i	−0.981759	−	0.190130i	$-0.939109\pi$
$347$	−11.0726	−	20.7155i	−0.594410	−	1.11206i	0.387348	−	0.921933i	$-0.373391\pi$
$348$	−0.0226724	−	4.52441i	−0.00121537	−	0.242534i
$349$	−18.4427	−	1.81645i	−0.987216	−	0.0972323i	−0.408497	−	0.912760i	$-0.633947\pi$
$349$	−18.4427	−	1.81645i	−0.987216	−	0.0972323i	−0.578719	+	0.815527i	$0.696447\pi$
$350$	−0.874617	−	8.65770i	−0.0467502	−	0.462773i
$351$	1.39746	+	1.39746i	0.0745908	+	0.0745908i
$352$	14.2967	−	21.9878i	0.762014	−	1.17196i
$353$	−4.03513	+	4.03513i	−0.214769	+	0.214769i	−0.806290	−	0.591521i	$-0.798528\pi$
$353$	−4.03513	+	4.03513i	−0.214769	+	0.214769i	0.591521	+	0.806290i	$0.298528\pi$
$354$	−12.3710	−	10.1009i	−0.657511	−	0.536854i
$355$	4.26721	−	43.3258i	0.226480	−	2.29949i
$356$	9.19045	+	21.8770i	0.487093	+	1.15948i
$357$	3.04856	−	1.62949i	0.161347	−	0.0862418i
$358$	17.0481	+	16.9629i	0.901021	+	0.896517i
$359$	8.96302	+	5.98890i	0.473050	+	0.316082i	0.769143	−	0.639077i	$-0.220684\pi$
$359$	8.96302	+	5.98890i	0.473050	+	0.316082i	−0.296092	+	0.955159i	$0.595684\pi$
$360$	4.84166	−	7.36531i	0.255178	−	0.388186i
$361$	2.37301	+	3.55147i	0.124896	+	0.186919i
$362$	−21.1803	+	14.2291i	−1.11321	+	0.747864i
$363$	−8.11321	−	6.65834i	−0.425833	−	0.349472i
$364$	−5.13995	−	0.480247i	−0.269407	−	0.0251718i
$365$	30.9133	+	16.5235i	1.61808	+	0.864879i
$366$	−2.48698	−	8.12512i	−0.129996	−	0.424707i
$367$	−9.24905	+	22.3292i	−0.482796	+	1.16557i	0.475479	+	0.879727i	$0.342275\pi$
$367$	−9.24905	+	22.3292i	−0.482796	+	1.16557i	−0.958275	+	0.285847i	$0.907725\pi$
$368$	18.6124	−	28.4689i	0.970236	−	1.48405i
$369$	−0.589360	−	1.42284i	−0.0306809	−	0.0740702i
$370$	5.53741	−	4.56770i	0.287876	−	0.237463i
$371$	−3.82476	−	12.6085i	−0.198571	−	0.654603i
$372$	−1.00626	+	1.23873i	−0.0521720	+	0.0642254i
$373$	−18.7364	+	1.84538i	−0.970135	+	0.0955500i	−0.570653	−	0.821191i	$-0.693310\pi$
$373$	−18.7364	+	1.84538i	−0.970135	+	0.0955500i	−0.399482	+	0.916741i	$0.630810\pi$
$374$	−17.0117	+	3.42818i	−0.879656	+	0.177267i
$375$	0.175590	−	0.882750i	0.00906743	−	0.0455850i
$376$	−1.81297	−	0.951603i	−0.0934969	−	0.0490752i
$377$	4.38495	−	0.872221i	0.225837	−	0.0449217i
$378$	−1.70821	−	0.702556i	−0.0878610	−	0.0361356i
$379$	−6.11174	−	1.85398i	−0.313939	−	0.0952323i	0.129383	−	0.991595i	$-0.458700\pi$
$379$	−6.11174	−	1.85398i	−0.313939	−	0.0952323i	−0.443322	+	0.896362i	$0.646200\pi$
$380$	29.4586	−	6.01329i	1.51119	−	0.308475i
$381$	−5.82465	−	7.09736i	−0.298406	−	0.363609i
$382$	15.8890	−	8.54412i	0.812954	−	0.437155i
$383$	−19.8577			−1.01468			−0.507340	−	0.861746i	$-0.669371\pi$
$383$	−19.8577			−1.01468			−0.507340	+	0.861746i	$0.669371\pi$
$384$	−6.11961	+	9.51579i	−0.312290	+	0.485601i
$385$	18.8701			0.961707
$386$	−5.54119	+	2.97970i	−0.282039	+	0.151663i
$387$	−5.67657	−	6.91691i	−0.288556	−	0.351607i
$388$	−5.46809	−	26.7877i	−0.277600	−	1.35994i
$389$	−8.89293	−	2.69764i	−0.450890	−	0.136776i	0.0566692	−	0.998393i	$-0.481952\pi$
$389$	−8.89293	−	2.69764i	−0.450890	−	0.136776i	−0.507559	+	0.861617i	$0.669452\pi$
$390$	8.05507	+	3.31290i	0.407884	+	0.167755i
$391$	−22.0732	+	4.39063i	−1.11629	+	0.222043i
$392$	−14.2964	+	4.45439i	−0.722079	+	0.224981i
$393$	−2.70714	+	13.6097i	−0.136557	+	0.686520i
$394$	28.5113	−	5.74555i	1.43638	−	0.289457i
$395$	−28.0765	+	2.76529i	−1.41268	+	0.139137i
$396$	7.19726	+	5.84653i	0.361676	+	0.293799i
$397$	−3.63333	−	11.9775i	−0.182352	−	0.601133i	−0.999688	−	0.0249724i	$-0.992050\pi$
$397$	−3.63333	−	11.9775i	−0.182352	−	0.601133i	0.817336	−	0.576161i	$-0.195450\pi$
$398$	−20.1398	+	16.6129i	−1.00952	+	0.832730i
$399$	−2.41109	−	5.82088i	−0.120705	−	0.291408i
$400$	3.49100	−	18.5185i	0.174550	−	0.925927i
$401$	8.54054	−	20.6187i	0.426494	−	1.02965i	−0.553897	−	0.832585i	$-0.686860\pi$
$401$	8.54054	−	20.6187i	0.426494	−	1.02965i	0.980391	−	0.197063i	$-0.0631402\pi$
$402$	−3.14732	−	10.2825i	−0.156974	−	0.512846i
$403$	−1.39082	−	0.743406i	−0.0692815	−	0.0370317i
$404$	−0.866741	+	9.27649i	−0.0431220	+	0.461523i
$405$	2.40891	+	1.97694i	0.119700	+	0.0982352i
$406$	−3.46842	+	2.33012i	−0.172135	+	0.115642i
$407$	4.19546	+	6.27895i	0.207961	+	0.311236i
$408$	7.33094	−	1.51559i	0.362936	−	0.0750327i
$409$	24.0594	+	16.0760i	1.18966	+	0.794907i	0.983018	−	0.183508i	$-0.0587455\pi$
$409$	24.0594	+	16.0760i	1.18966	+	0.794907i	0.206645	+	0.978416i	$0.433745\pi$
$410$	−4.81130	−	4.78725i	−0.237613	−	0.236425i
$411$	19.9667	−	10.6724i	0.984884	−	0.526432i
$412$	26.8453	−	11.2776i	1.32257	−	0.555609i
$413$	−1.44570	+	14.6784i	−0.0711383	+	0.722279i
$414$	9.31492	+	7.60558i	0.457803	+	0.373794i
$415$	12.4961	−	12.4961i	0.613407	−	0.613407i
$416$	−10.3814	−	4.14855i	−0.508992	−	0.203399i
$417$	−2.33586	−	2.33586i	−0.114388	−	0.114388i
$418$	3.17915	+	31.4699i	0.155497	+	1.53924i
$419$	18.9400	+	1.86543i	0.925282	+	0.0911323i	0.549423	−	0.835545i	$-0.314848\pi$
$419$	18.9400	+	1.86543i	0.925282	+	0.0911323i	0.375859	+	0.926677i	$0.377348\pi$
$420$	−8.13998	+	0.0407905i	−0.397190	+	0.00199037i
$421$	−1.49449	−	2.79599i	−0.0728368	−	0.136268i	0.842867	−	0.538122i	$-0.180866\pi$
$421$	−1.49449	−	2.79599i	−0.0728368	−	0.136268i	−0.915704	+	0.401854i	$0.868366\pi$
$422$	−22.5001	+	0.0563750i	−1.09529	+	0.00274429i
$423$	0.402185	−	0.601913i	0.0195549	−	0.0292660i
$424$	−0.214477	−	28.5332i	−0.0104159	−	1.38569i
$425$	−10.3676	+	6.92742i	−0.502903	+	0.336029i
$426$	−19.3870	−	3.80584i	−0.939303	−	0.184394i
$427$	−4.97832	+	6.06610i	−0.240918	+	0.293559i
$428$	−8.66235	+	2.67517i	−0.418711	+	0.129309i
$429$	−4.31932	+	8.08087i	−0.208539	+	0.390148i
$430$	−34.8247	−	18.5022i	−1.67940	−	0.892254i
$431$	25.0807	+	10.3888i	1.20809	+	0.500409i	0.893606	−	0.448853i	$-0.148167\pi$
$431$	25.0807	+	10.3888i	1.20809	+	0.500409i	0.314488	+	0.949261i	$0.398167\pi$
$432$	−3.11732	−	2.50646i	−0.149982	−	0.120592i
$433$	−12.3193	+	5.10282i	−0.592028	+	0.245226i	−0.658523	−	0.752561i	$-0.728818\pi$
$433$	−12.3193	+	5.10282i	−0.592028	+	0.245226i	0.0664951	+	0.997787i	$0.478818\pi$
$434$	1.46714	+	0.140790i	0.0704252	+	0.00675816i
$435$	6.74618	−	2.04643i	0.323455	−	0.0981189i
$436$	7.23292	−	3.91280i	0.346394	−	0.187389i
$437$	4.02069	+	40.8227i	0.192336	+	1.95282i
$438$	8.80441	−	13.2485i	0.420691	−	0.633037i
$439$	−1.91213	−	0.380346i	−0.0912609	−	0.0181529i	0.149249	−	0.988800i	$-0.452315\pi$
$439$	−1.91213	−	0.380346i	−0.0912609	−	0.0181529i	−0.240510	+	0.970647i	$0.577315\pi$
$440$	39.1938	+	11.5683i	1.86849	+	0.551498i
$441$	−1.03285	−	5.19248i	−0.0491833	−	0.247261i
$442$	2.84793	+	6.82708i	0.135462	+	0.324731i
$443$	−1.63473	+	5.38899i	−0.0776685	+	0.256039i	−0.987173	−	0.159656i	$-0.948962\pi$
$443$	−1.63473	+	5.38899i	−0.0776685	+	0.256039i	0.909504	+	0.415695i	$0.136462\pi$
$444$	−1.82337	−	2.69948i	−0.0865331	−	0.128112i
$445$	−28.5806	+	23.4555i	−1.35485	+	1.11190i
$446$	−6.39734	+	21.2810i	−0.302923	+	1.00768i
$447$		−	13.5644i		−	0.641573i
$448$	10.4473	−	0.157069i	0.493588	−	0.00742080i
$449$		−	28.0313i		−	1.32288i	−0.749998	−	0.661440i	$-0.769946\pi$
$449$		−	28.0313i		−	1.32288i	0.749998	−	0.661440i	$-0.230054\pi$
$450$	6.38055	+	1.91807i	0.300782	+	0.0904189i
$451$	5.51952	−	4.52975i	0.259904	−	0.213298i
$452$	33.7304	+	6.53385i	1.58654	+	0.307326i
$453$	3.58256	−	11.8101i	0.168323	−	0.554888i
$454$	23.0452	−	9.61337i	1.08157	−	0.451178i
$455$	−1.56924	−	7.88908i	−0.0735669	−	0.369846i
$456$	−1.43942	−	13.5683i	−0.0674068	−	0.635394i
$457$	24.1870	+	4.81109i	1.13142	+	0.225053i	0.725077	−	0.688668i	$-0.241804\pi$
$457$	24.1870	+	4.81109i	1.13142	+	0.225053i	0.406342	+	0.913721i	$0.366804\pi$
$458$	−14.1285	−	9.38925i	−0.660182	−	0.438731i
$459$	0.259421	+	2.63394i	0.0121087	+	0.122942i
$460$	50.7917	+	15.1300i	2.36818	+	0.705439i
$461$	27.6319	−	8.38204i	1.28694	−	0.390390i	0.428614	−	0.903488i	$-0.359002\pi$
$461$	27.6319	−	8.38204i	1.28694	−	0.390390i	0.858331	+	0.513097i	$0.171502\pi$
$462$	0.818016	−	8.52436i	0.0380576	−	0.396589i
$463$	−15.8815	+	6.57834i	−0.738077	+	0.305722i	−0.719866	−	0.694113i	$-0.755797\pi$
$463$	−15.8815	+	6.57834i	−0.738077	+	0.305722i	−0.0182107	+	0.999834i	$0.505797\pi$
$464$	−8.63252	+	2.71342i	−0.400755	+	0.125967i
$465$	−2.29740	−	0.951616i	−0.106540	−	0.0441301i
$466$	13.7045	−	25.7945i	0.634847	−	1.19491i
$467$	2.85110	−	5.33403i	0.131933	−	0.246829i	−0.807277	−	0.590173i	$-0.799060\pi$
$467$	2.85110	−	5.33403i	0.131933	−	0.246829i	0.939210	+	0.343344i	$0.111560\pi$
$468$	1.84576	−	3.49518i	0.0853201	−	0.161565i
$469$	−6.30017	+	7.67678i	−0.290915	+	0.354481i
$470$	0.614564	−	3.13060i	0.0283477	−	0.144404i
$471$	8.20002	−	5.47908i	0.377837	−	0.252463i
$472$	−12.0014	+	29.6014i	−0.552410	+	1.36251i
$473$	23.0484	−	34.4944i	1.05977	−	1.58605i
$474$	0.0320789	+	12.8031i	0.00147343	+	0.588068i
$475$	10.7134	+	20.0433i	0.491564	+	0.919651i
$476$	−4.91299	−	4.86400i	−0.225187	−	0.222941i
$477$	10.0397	+	0.988824i	0.459686	+	0.0452752i
$478$	0.439311	−	0.0443800i	0.0200936	−	0.00202990i
$479$	−26.8634	−	26.8634i	−1.22742	−	1.22742i	−0.964936	−	0.262484i	$-0.915458\pi$
$479$	−26.8634	−	26.8634i	−1.22742	−	1.22742i	−0.262484	−	0.964936i	$-0.584542\pi$
$480$	−16.9320	−	4.90550i	−0.772838	−	0.223905i
$481$	2.27617	−	2.27617i	0.103784	−	0.103784i
$482$	4.80040	−	5.87928i	0.218652	−	0.267794i
$483$	1.08856	−	11.0523i	0.0495312	−	0.502899i
$484$	−7.93570	+	19.4334i	−0.360714	+	0.883334i
$485$	37.5695	−	20.0813i	1.70594	−	0.911846i
$486$	0.997491	−	1.00250i	0.0452471	−	0.0454744i
$487$	−22.8109	−	15.2418i	−1.03366	−	0.690671i	−0.0816284	−	0.996663i	$-0.526012\pi$
$487$	−22.8109	−	15.2418i	−1.03366	−	0.690671i	−0.952034	+	0.305992i	$0.901012\pi$
$488$	−14.0590	+	9.54754i	−0.636420	+	0.432197i
$489$	−7.53884	−	11.2827i	−0.340918	−	0.510220i
$490$	−13.0111	−	19.3673i	−0.587783	−	0.874927i
$491$	11.2668	+	9.24641i	0.508463	+	0.417285i	0.853333	−	0.521366i	$-0.174577\pi$
$491$	11.2668	+	9.24641i	0.508463	+	0.417285i	−0.344871	+	0.938650i	$0.612077\pi$
$492$	−2.37116	+	1.96593i	−0.106900	+	0.0886309i
$493$	5.28044	+	2.82245i	0.237819	+	0.127117i
$494$	12.8924	−	3.94616i	0.580055	−	0.177546i
$495$	−5.52905	+	13.3483i	−0.248512	+	0.599962i
$496$	2.96100	+	1.19186i	0.132953	+	0.0535162i
$497$	6.98246	+	16.8572i	0.313206	+	0.756147i
$498$	−5.10327	−	6.18667i	−0.228683	−	0.277231i
$499$	−6.55769	−	21.6178i	−0.293562	−	0.967745i	−0.972373	−	0.233432i	$-0.925004\pi$
$499$	−6.55769	−	21.6178i	−0.293562	−	0.967745i	0.678811	−	0.734313i	$-0.262496\pi$
$500$	−1.79051	+	0.185414i	−0.0800742	+	0.00829198i
$501$	−14.0348	+	1.38231i	−0.627028	+	0.0617569i
$502$	−4.06059	−	20.1500i	−0.181233	−	0.899338i
$503$	0.763754	−	3.83965i	0.0340541	−	0.171202i	−0.960016	−	0.279947i	$-0.909683\pi$
$503$	0.763754	−	3.83965i	0.0340541	−	0.171202i	0.994070	+	0.108745i	$0.0346832\pi$
$504$	−0.334441	+	3.67892i	−0.0148972	+	0.163872i
$505$	−14.2381	+	2.83213i	−0.633586	+	0.126028i
$506$	−21.2071	+	51.5635i	−0.942770	+	2.29228i
$507$	−8.70263	−	2.63991i	−0.386497	−	0.117243i
$508$	−10.1252	+	15.3191i	−0.449235	+	0.679676i
$509$	17.3957	+	21.1967i	0.771052	+	0.939529i	0.999420	−	0.0340454i	$-0.0108391\pi$
$509$	17.3957	+	21.1967i	0.771052	+	0.939529i	−0.228368	+	0.973575i	$0.573339\pi$
$510$	5.52421	+	10.2731i	0.244616	+	0.454899i
$511$	−14.6907			−0.649878
$512$	21.7957	+	6.07849i	0.963242	+	0.268634i
$513$	4.82403			0.212986
$514$	18.7401	+	34.8499i	0.826589	+	1.53716i
$515$	28.7823	+	35.0713i	1.26830	+	1.54543i
$516$	−9.86782	+	14.9297i	−0.434407	+	0.657241i
$517$	3.21179	+	0.974285i	0.141254	+	0.0428490i
$518$	−1.14432	+	2.78232i	−0.0502784	+	0.122248i
$519$	−12.0709	+	2.40104i	−0.529852	+	0.105394i
$520$	1.57705	−	17.3479i	0.0691584	−	0.760757i
$521$	4.40081	−	22.1244i	0.192803	−	0.969287i	−0.756277	−	0.654252i	$-0.772984\pi$
$521$	4.40081	−	22.1244i	0.192803	−	0.969287i	0.949080	−	0.315035i	$-0.102016\pi$
$522$	−0.632008	−	3.13623i	−0.0276623	−	0.137269i
$523$	−1.57777	+	0.155397i	−0.0689913	+	0.00679505i	−0.132454	−	0.991189i	$-0.542286\pi$
$523$	−1.57777	+	0.155397i	−0.0689913	+	0.00679505i	0.0634626	+	0.997984i	$0.479786\pi$
$524$	27.6051	−	2.85861i	1.20593	−	0.124879i
$525$	−1.78614	−	5.88813i	−0.0779537	−	0.256979i
$526$	−23.7138	−	28.7482i	−1.03397	−	1.25348i
$527$	−0.808218	−	1.95121i	−0.0352065	−	0.0849961i
$528$	6.92492	−	17.2039i	0.301369	−	0.748705i
$529$	−18.8687	+	45.5530i	−0.820377	+	1.98057i
$530$	42.5130	−	13.0126i	1.84665	−	0.565230i
$531$	−9.95964	−	5.32354i	−0.432212	−	0.231022i
$532$	−9.70048	+	8.04266i	−0.420569	+	0.348694i
$533$	−2.35277	−	1.93087i	−0.101910	−	0.0836353i
$534$	9.35682	+	13.9278i	0.404909	+	0.602715i
$535$	−7.84805	−	11.7454i	−0.339301	−	0.507800i
$536$	−17.7920	+	12.0826i	−0.768496	+	0.521890i
$537$	14.1396	+	9.44778i	0.610169	+	0.407702i
$538$	15.8526	−	15.9323i	0.683455	−	0.686888i
$539$	21.6474	−	11.5708i	0.932420	−	0.498389i
$540$	2.35621	−	5.77001i	0.101395	−	0.248302i
$541$	−2.65908	+	26.9980i	−0.114323	+	1.16074i	0.751273	+	0.659992i	$0.229440\pi$
$541$	−2.65908	+	26.9980i	−0.114323	+	1.16074i	−0.865595	+	0.500745i	$0.833060\pi$
$542$	0.512468	−	0.627644i	0.0220124	−	0.0269596i
$543$	−12.7580	+	12.7580i	−0.547500	+	0.547500i
$544$	−7.22258	−	13.1146i	−0.309666	−	0.562284i
$545$	9.06035	+	9.06035i	0.388103	+	0.388103i
$546$	−3.63184	+	0.366895i	−0.155428	+	0.0157017i
$547$	33.0554	+	3.25567i	1.41335	+	0.139202i	0.775688	−	0.631117i	$-0.217403\pi$
$547$	33.0554	+	3.25567i	1.41335	+	0.139202i	0.637659	+	0.770319i	$0.279903\pi$
$548$	−32.1778	−	31.8569i	−1.37457	−	1.36086i
$549$	−2.83236	−	5.29897i	−0.120882	−	0.226154i
$550$	0.0773965	+	30.8900i	0.00330020	+	1.31715i
$551$	6.06299	−	9.07390i	0.258292	−	0.386561i
$552$	9.03663	−	22.2888i	0.384625	−	0.948673i
$553$	9.83132	−	6.56908i	0.418070	−	0.279346i
$554$	4.71188	−	24.0024i	0.200189	−	1.01976i
$555$	3.22003	−	3.92362i	0.136683	−	0.166548i
$556$	−3.08520	+	5.84223i	−0.130841	+	0.247766i
$557$	−18.3561	+	34.3418i	−0.777772	+	1.45511i	0.109561	+	0.993980i	$0.465056\pi$
$557$	−18.3561	+	34.3418i	−0.777772	+	1.45511i	−0.887333	+	0.461129i	$0.847444\pi$
$558$	−0.529475	+	0.996576i	−0.0224145	+	0.0421884i
$559$	−16.3379	−	6.76738i	−0.691019	−	0.286230i
$560$	4.88178	+	15.5310i	0.206293	+	0.656304i
$561$	−11.3369	+	4.69588i	−0.478643	+	0.198260i
$562$	−1.84296	+	19.2051i	−0.0777405	+	0.810116i
$563$	−9.55502	+	2.89848i	−0.402696	+	0.122156i	−0.485134	−	0.874440i	$-0.661229\pi$
$563$	−9.55502	+	2.89848i	−0.402696	+	0.122156i	0.0824383	+	0.996596i	$0.473729\pi$
$564$	−1.38757	−	0.413334i	−0.0584274	−	0.0174045i
$565$	5.24720	+	53.2757i	0.220751	+	2.24133i
$566$	−3.64193	−	2.42028i	−0.153082	−	0.101732i
$567$	−1.28096	−	0.254799i	−0.0537954	−	0.0107006i
$568$	4.16852	+	39.2935i	0.174907	+	1.64872i
$569$	−5.26810	−	26.4845i	−0.220850	−	1.11029i	−0.918976	−	0.394314i	$-0.870982\pi$
$569$	−5.26810	−	26.4845i	−0.220850	−	1.11029i	0.698126	−	0.715975i	$-0.254018\pi$
$570$	19.6212	−	8.18500i	0.821840	−	0.342832i
$571$	−2.40099	+	7.91499i	−0.100478	+	0.331232i	−0.992739	−	0.120288i	$-0.961618\pi$
$571$	−2.40099	+	7.91499i	−0.100478	+	0.331232i	0.892261	+	0.451520i	$0.149118\pi$
$572$	17.9912	+	3.48504i	0.752249	+	0.145717i
$573$	9.86102	−	8.09273i	0.411950	−	0.338078i
$574$	2.72416	+	0.818916i	0.113704	+	0.0341809i
$575$			40.0606i			1.67064i
$576$	−2.95001	+	7.43622i	−0.122917	+	0.309843i
$577$		−	17.5111i		−	0.728997i	−0.931204	−	0.364499i	$-0.881240\pi$
$577$		−	17.5111i		−	0.728997i	0.931204	−	0.364499i	$-0.118760\pi$
$578$	4.06930	−	13.5367i	0.169261	−	0.563053i
$579$	−3.43896	+	2.82228i	−0.142918	+	0.117290i
$580$	−7.89190	−	11.6839i	−0.327693	−	0.485147i
$581$	−2.15000	+	7.08761i	−0.0891971	+	0.294043i
$582$	−7.44290	−	17.8422i	−0.308518	−	0.739582i
$583$	9.12489	+	45.8739i	0.377914	+	1.89990i
$584$	−30.5131	−	9.00615i	−1.26264	−	0.372677i
$585$	6.04037	+	1.20150i	0.249739	+	0.0496761i
$586$	−19.8129	+	29.8136i	−0.818465	+	1.23159i
$587$	4.12112	+	41.8424i	0.170097	+	1.72702i	0.579762	+	0.814786i	$0.303146\pi$
$587$	4.12112	+	41.8424i	0.170097	+	1.72702i	−0.409665	+	0.912236i	$0.634354\pi$
$588$	−9.31303	+	5.03808i	−0.384063	+	0.207767i
$589$	−3.68367	+	1.11743i	−0.151783	+	0.0460429i
$590$	−49.5421	−	4.75417i	−2.03962	−	0.195726i
$591$	19.0003	−	7.87020i	0.781569	−	0.323737i
$592$	−4.08250	+	5.07746i	−0.167790	+	0.208682i
$593$	−21.5415	−	8.92279i	−0.884604	−	0.366415i	−0.106323	−	0.994332i	$-0.533908\pi$
$593$	−21.5415	−	8.92279i	−0.884604	−	0.366415i	−0.778281	+	0.627917i	$0.783908\pi$
$594$	5.79028	+	3.07634i	0.237578	+	0.126224i
$595$	5.07795	−	9.50017i	0.208175	−	0.389469i
$596$	−25.9208	+	8.00505i	−1.06176	+	0.327900i
$597$	−11.7114	+	14.2704i	−0.479315	+	0.584047i
$598$	23.3209	+	4.57810i	0.953663	+	0.187213i
$599$	1.70672	−	1.14040i	0.0697348	−	0.0465953i	−0.520214	−	0.854036i	$-0.674148\pi$
$599$	1.70672	−	1.14040i	0.0697348	−	0.0465953i	0.589949	+	0.807441i	$0.299148\pi$
$600$	−0.100160	−	13.3249i	−0.00408901	−	0.543985i
$601$	25.7674	−	38.5636i	1.05107	−	1.57304i	0.255856	−	0.966715i	$-0.417643\pi$
$601$	25.7674	−	38.5636i	1.05107	−	1.57304i	0.795216	−	0.606326i	$-0.207357\pi$
$602$	16.5274	−	0.0414101i	0.673605	−	0.00168775i
$603$	−3.58441	−	6.70596i	−0.145969	−	0.273088i
$604$	−24.6828	+	0.123689i	−1.00433	+	0.00503282i
$605$	−32.5497	−	3.20587i	−1.32333	−	0.130337i
$606$	0.662166	+	6.55468i	0.0268986	+	0.266266i
$607$	−5.82004	−	5.82004i	−0.236228	−	0.236228i	0.579058	−	0.815286i	$-0.303420\pi$
$607$	−5.82004	−	5.82004i	−0.236228	−	0.236228i	−0.815286	+	0.579058i	$0.803420\pi$
$608$	−25.0788	+	10.7580i	−1.01708	+	0.436295i
$609$	−2.08922	+	2.08922i	−0.0846596	+	0.0846596i
$610$	−20.5111	−	16.7472i	−0.830470	−	0.678074i
$611$	0.140231	−	1.42379i	0.00567313	−	0.0576002i
$612$	4.88023	−	2.05017i	0.197272	−	0.0828732i
$613$	−2.56847	+	1.37288i	−0.103740	+	0.0554500i	−0.522451	−	0.852670i	$-0.674982\pi$
$613$	−2.56847	+	1.37288i	−0.103740	+	0.0554500i	0.418711	+	0.908120i	$0.362482\pi$
$614$	−2.30647	−	2.29494i	−0.0930816	−	0.0926163i
$615$	−3.99046	−	2.66634i	−0.160911	−	0.107517i
$616$	−16.7724	+	3.46749i	−0.675778	+	0.139709i
$617$	−3.95824	−	5.92392i	−0.159353	−	0.238488i	0.743198	−	0.669071i	$-0.233308\pi$
$617$	−3.95824	−	5.92392i	−0.159353	−	0.238488i	−0.902551	+	0.430583i	$0.858308\pi$
$618$	17.0908	−	11.4818i	0.687494	−	0.461865i
$619$	9.02508	+	7.40669i	0.362749	+	0.297700i	0.798058	−	0.602581i	$-0.205861\pi$
$619$	9.02508	+	7.40669i	0.362749	+	0.297700i	−0.435309	+	0.900281i	$0.643361\pi$
$620$	−0.462669	+	4.95182i	−0.0185812	+	0.198870i
$621$	7.49925	+	4.00843i	0.300934	+	0.160853i
$622$	10.6963	+	34.9454i	0.428881	+	1.40118i
$623$	5.92997	−	14.3162i	0.237579	−	0.573567i
$624$	−7.76839	−	1.46445i	−0.310984	−	0.0586249i
$625$	−10.0878	−	24.3541i	−0.403512	−	0.974164i
$626$	16.2255	−	13.3841i	0.648503	−	0.534938i
$627$	6.49246	+	21.4028i	0.259284	+	0.854745i
$628$	−15.3095	−	12.4363i	−0.610915	−	0.496263i
$629$	4.29015	−	0.422543i	0.171059	−	0.0168479i
$630$	−5.64248	+	1.13706i	−0.224802	+	0.0453016i
$631$	−7.49085	+	37.6590i	−0.298206	+	1.49918i	0.483394	+	0.875403i	$0.339404\pi$
$631$	−7.49085	+	37.6590i	−0.298206	+	1.49918i	−0.781600	+	0.623780i	$0.785596\pi$
$632$	24.4472	−	7.61711i	0.972457	−	0.302992i
$633$	−15.6043	+	3.10389i	−0.620215	+	0.123368i
$634$	−0.355003	−	0.146006i	−0.0140990	−	0.00579864i
$635$	−27.3799	−	8.30561i	−1.08654	−	0.329598i
$636$	−4.03537	−	19.7689i	−0.160013	−	0.783888i
$637$	−6.63764	−	8.08799i	−0.262993	−	0.320458i
$638$	13.0639	−	7.02495i	0.517205	−	0.278120i
$639$	−13.9703			−0.552657
$640$	0.618328	+	35.2512i	0.0244416	+	1.39343i
$641$	−3.87653			−0.153114			−0.0765568	−	0.997065i	$-0.524393\pi$
$641$	−3.87653			−0.153114			−0.0765568	+	0.997065i	$0.524393\pi$
$642$	−5.64610	+	3.03612i	−0.222834	+	0.119826i
$643$	−5.31682	−	6.47856i	−0.209675	−	0.255490i	0.657545	−	0.753416i	$-0.271595\pi$
$643$	−5.31682	−	6.47856i	−0.209675	−	0.255490i	−0.867219	+	0.497926i	$0.834095\pi$
$644$	−21.7629	+	4.44238i	−0.857576	+	0.175054i
$645$	−26.6838	−	8.09445i	−1.05067	−	0.318719i
$646$	16.6991	+	6.86802i	0.657017	+	0.270219i
$647$	40.8052	−	8.11666i	1.60422	−	0.319099i	0.689841	−	0.723961i	$-0.257680\pi$
$647$	40.8052	−	8.11666i	1.60422	−	0.319099i	0.914378	+	0.404862i	$0.132680\pi$
$648$	−2.50440	−	1.31452i	−0.0983822	−	0.0516394i
$649$	10.2147	−	51.3526i	0.400961	−	2.01577i
$650$	12.9079	−	2.60117i	0.506288	−	0.102026i
$651$	1.03718	−	0.102153i	0.0406501	−	0.00400369i
$652$	−17.1115	+	21.0648i	−0.670139	+	0.824962i
$653$	6.39646	+	21.0863i	0.250313	+	0.825171i	0.988584	+	0.150668i	$0.0481423\pi$
$653$	6.39646	+	21.0863i	0.250313	+	0.825171i	−0.738272	+	0.674504i	$0.764358\pi$
$654$	4.48569	−	3.70016i	0.175404	−	0.144688i
$655$	16.5482	+	39.9509i	0.646592	+	1.56101i
$656$	5.15614	+	3.37097i	0.201313	+	0.131614i
$657$	4.30446	−	10.3919i	0.167933	−	0.405426i
$658$	0.391345	+	1.27855i	0.0152562	+	0.0498431i
$659$	32.1305	+	17.1741i	1.25163	+	0.669009i	0.957961	−	0.286898i	$-0.0926242\pi$
$659$	32.1305	+	17.1741i	1.25163	+	0.669009i	0.293667	+	0.955908i	$0.405124\pi$
$660$	28.7709	+	2.68818i	1.11991	+	0.104637i
$661$	19.1801	+	15.7407i	0.746019	+	0.612242i	0.928658	−	0.370938i	$-0.120964\pi$
$661$	19.1801	+	15.7407i	0.746019	+	0.612242i	−0.182638	+	0.983180i	$0.558464\pi$
$662$	28.1540	−	18.9141i	1.09423	−	0.735116i
$663$	2.90600	+	4.34914i	0.112860	+	0.168906i
$664$	−8.81070	+	13.4032i	−0.341921	+	0.520143i
$665$	−16.3251	−	10.9081i	−0.633060	−	0.422997i
$666$	−1.63287	−	1.62471i	−0.0632723	−	0.0629561i
$667$	16.9650	−	9.06800i	0.656889	−	0.351114i
$668$	10.9242	+	26.0040i	0.422669	+	1.00612i
$669$	−1.54016	+	15.6375i	−0.0595460	+	0.604581i
$670$	−25.9572	−	21.1939i	−1.00282	−	0.818793i
$671$	19.6980	−	19.6980i	0.760431	−	0.760431i
$672$	7.22759	−	1.53203i	0.278811	−	0.0590992i
$673$	−2.97514	−	2.97514i	−0.114683	−	0.114683i	0.647436	−	0.762120i	$-0.275841\pi$
$673$	−2.97514	−	2.97514i	−0.114683	−	0.114683i	−0.762120	+	0.647436i	$0.775841\pi$
$674$	2.95067	+	29.2082i	0.113656	+	1.12506i
$675$	4.68849	+	0.461776i	0.180460	+	0.0177738i
$676$	0.0911435	+	18.1882i	0.00350552	+	0.699547i
$677$	−21.5576	−	40.3315i	−0.828527	−	1.55006i	−0.835108	−	0.550087i	$-0.814595\pi$
$677$	−21.5576	−	40.3315i	−0.828527	−	1.55006i	0.00658058	−	0.999978i	$-0.497905\pi$
$678$	24.2942	−	0.0608704i	0.933015	−	0.00233771i
$679$	−9.91908	+	14.8450i	−0.380659	+	0.569697i
$680$	16.3712	−	16.6192i	0.627806	−	0.637315i
$681$	14.6808	−	9.80940i	0.562570	−	0.375897i
$682$	−5.13410	−	1.00787i	−0.196595	−	0.0385934i
$683$	27.8469	−	33.9316i	1.06553	−	1.29836i	0.113109	−	0.993583i	$-0.463919\pi$
$683$	27.8469	−	33.9316i	1.06553	−	1.29836i	0.952425	−	0.304774i	$-0.0985808\pi$
$684$	−2.84692	−	9.21848i	−0.108855	−	0.352477i
$685$	33.2582	−	62.2217i	1.27073	−	2.37737i
$686$	20.0534	+	10.6543i	0.765642	+	0.406781i
$687$	−11.0822	−	4.59039i	−0.422811	−	0.175134i
$688$	34.3533	+	10.0461i	1.30971	+	0.383004i
$689$	18.4199	−	7.62976i	0.701741	−	0.290671i
$690$	37.3034	+	3.57971i	1.42012	+	0.136277i
$691$	17.4684	−	5.29899i	0.664530	−	0.201583i	0.0600403	−	0.998196i	$-0.480877\pi$
$691$	17.4684	−	5.29899i	0.664530	−	0.201583i	0.604490	+	0.796613i	$0.293377\pi$
$692$	11.7119	+	21.6498i	0.445221	+	0.823002i
$693$	−0.593526	−	6.02617i	−0.0225462	−	0.228915i
$694$	−18.3859	+	27.6663i	−0.697920	+	1.05020i
$695$	−10.0965	−	2.00833i	−0.382983	−	0.0761801i
$696$	−5.62019	+	3.05859i	−0.213033	+	0.115936i
$697$	−0.795206	−	3.99777i	−0.0301206	−	0.151426i
$698$	10.0901	+	24.1880i	0.381914	+	0.915528i
$699$	5.99551	−	19.7646i	0.226771	−	0.747564i
$700$	−10.1978	+	6.88812i	−0.385441	+	0.260346i
$701$	18.0596	−	14.8211i	0.682100	−	0.559785i	−0.228261	−	0.973600i	$-0.573304\pi$
$701$	18.0596	−	14.8211i	0.682100	−	0.559785i	0.910361	+	0.413815i	$0.135804\pi$
$702$	0.804618	−	2.67659i	0.0303683	−	0.101021i
$703$		−	7.85735i		−	0.296345i
$704$	−36.9626	−	3.08022i	−1.39308	−	0.116090i
$705$		−	2.25592i		−	0.0849628i
$706$	7.72861	+	2.32332i	0.290870	+	0.0874392i
$707$	4.70315	−	3.85978i	0.176880	−	0.145162i
$708$	−4.29529	+	22.1740i	−0.161427	+	0.833352i
$709$	1.66181	−	5.47824i	0.0624105	−	0.205740i	−0.920190	−	0.391472i	$-0.871966\pi$
$709$	1.66181	−	5.47824i	0.0624105	−	0.205740i	0.982600	+	0.185733i	$0.0594658\pi$
$710$	−56.8225	+	23.7036i	−2.13251	+	0.889581i
$711$	1.76620	+	8.87926i	0.0662375	+	0.332998i
$712$	21.0933	−	26.0999i	0.790506	−	0.978136i
$713$	−6.65499	−	1.32376i	−0.249231	−	0.0495752i
$714$	−4.07148	−	2.70574i	−0.152371	−	0.101260i
$715$	2.79877	+	28.4163i	0.104668	+	1.06271i
$716$	9.70969	−	32.5957i	0.362868	−	1.21816i
$717$	0.298777	−	0.0906330i	0.0111580	−	0.00338475i
$718$	1.45624	−	15.1751i	0.0543464	−	0.566331i
$719$	0.817078	−	0.338445i	0.0304719	−	0.0126219i	−0.367395	−	0.930065i	$-0.619750\pi$
$719$	0.817078	−	0.338445i	0.0304719	−	0.0126219i	0.397867	+	0.917443i	$0.369750\pi$
$720$	−12.4167	−	1.09741i	−0.462743	−	0.0408980i
$721$	−17.5675	−	7.27668i	−0.654246	−	0.270998i
$722$	2.83414	−	5.33441i	0.105476	−	0.198526i
$723$	2.52999	−	4.73329i	0.0940915	−	0.176033i
$724$	31.9091	+	16.8508i	1.18589	+	0.626253i
$725$	6.76122	−	8.23858i	0.251106	−	0.305973i
$726$	−2.85925	+	14.5650i	−0.106117	+	0.540559i
$727$	−14.0634	+	9.39686i	−0.521583	+	0.348510i	−0.788327	−	0.615257i	$-0.789052\pi$
$727$	−14.0634	+	9.39686i	−0.521583	+	0.348510i	0.266744	+	0.963767i	$0.414052\pi$
$728$	2.84446	+	6.72373i	0.105423	+	0.249198i
$729$	0.555570	−	0.831470i	0.0205767	−	0.0307952i
$730$	−0.124203	−	49.5712i	−0.00459696	−	1.83471i
$731$	−11.1639	−	20.8862i	−0.412912	−	0.772505i
$732$	−8.45453	+	8.53969i	−0.312488	+	0.315636i
$733$	−0.357380	−	0.0351989i	−0.0132001	−	0.00130010i	0.0914149	−	0.995813i	$-0.470861\pi$
$733$	−0.357380	−	0.0351989i	−0.0132001	−	0.00130010i	−0.104615	+	0.994513i	$0.533361\pi$
$734$	34.0069	−	3.43545i	1.25522	−	0.126805i
$735$	−11.6660	−	11.6660i	−0.430307	−	0.430307i
$736$	−47.9256	−	4.11476i	−1.76656	−	0.151672i
$737$	24.9282	−	24.9282i	0.918243	−	0.918243i
$738$	−1.37748	+	1.68707i	−0.0507057	+	0.0621018i
$739$	−1.93463	+	19.6426i	−0.0711664	+	0.722565i	0.891707	+	0.452613i	$0.149508\pi$
$739$	−1.93463	+	19.6426i	−0.0711664	+	0.722565i	−0.962874	+	0.269952i	$0.912992\pi$
$740$	−9.39814	−	3.83778i	−0.345483	−	0.141079i
$741$	8.40803	−	4.49418i	0.308877	−	0.165098i
$742$	−13.1428	+	13.2089i	−0.482488	+	0.484912i
$743$	−4.35601	−	2.91059i	−0.159806	−	0.106779i	0.473096	−	0.881011i	$-0.343136\pi$
$743$	−4.35601	−	2.91059i	−0.159806	−	0.106779i	−0.632902	+	0.774232i	$0.718136\pi$
$744$	2.21688	+	0.423667i	0.0812746	+	0.0155324i
$745$	−23.4841	−	35.1465i	−0.860392	−	1.28767i
$746$	14.8478	+	22.1012i	0.543615	+	0.809181i
$747$	−4.38367	−	3.59758i	−0.160390	−	0.131629i
$748$	15.6641	+	18.8929i	0.572735	+	0.690792i
$749$	5.22131	+	2.79085i	0.190783	+	0.101975i
$750$	−1.21712	+	0.372541i	−0.0444428	+	0.0136033i
$751$	7.98760	−	19.2838i	0.291472	−	0.703675i	−0.708526	−	0.705684i	$-0.750640\pi$
$751$	7.98760	−	19.2838i	0.291472	−	0.703675i	0.999998	+	0.00200966i	$0.000639696\pi$
$752$	0.0290203	+	2.89551i	0.00105826	+	0.105588i
$753$	−5.56216	−	13.4282i	−0.202696	−	0.489352i
$754$	−4.02334	−	4.87749i	−0.146521	−	0.177628i
$755$	−11.1643	−	36.8036i	−0.406309	−	1.33942i
$756$	0.269055	+	2.59822i	0.00978545	+	0.0944965i
$757$	−10.5319	+	1.03730i	−0.382788	+	0.0377013i	−0.287581	−	0.957756i	$-0.592851\pi$
$757$	−10.5319	+	1.03730i	−0.382788	+	0.0377013i	−0.0952066	+	0.995458i	$0.530351\pi$
$758$	1.78429	+	8.85423i	0.0648083	+	0.321600i
$759$	−7.69127	+	38.6666i	−0.279176	+	1.40351i
$760$	−27.2206	−	32.6646i	−0.987394	−	1.18487i
$761$	−28.3683	+	5.64280i	−1.02835	+	0.204551i	−0.680307	−	0.732928i	$-0.738153\pi$
$761$	−28.3683	+	5.64280i	−1.02835	+	0.204551i	−0.348042	+	0.937479i	$0.613153\pi$
$762$	−4.93889	+	12.0086i	−0.178917	+	0.435024i
$763$	−5.13892	−	1.55887i	−0.186041	−	0.0564350i
$764$	−21.2843	−	14.0679i	−0.770038	−	0.508960i
$765$	5.23236	+	6.37565i	0.189176	+	0.230512i
$766$	13.3002	+	24.7338i	0.480558	+	0.893667i
$767$	−22.3186			−0.805879
$768$	15.9512	+	1.24882i	0.575589	+	0.0450627i
$769$	35.2249			1.27024			0.635121	−	0.772412i	$-0.280950\pi$
$769$	35.2249			1.27024			0.635121	+	0.772412i	$0.280950\pi$
$770$	−12.6388	−	23.5036i	−0.455469	−	0.847012i
$771$	17.7500	+	21.6285i	0.639251	+	0.778930i
$772$	7.42274	+	4.90609i	0.267150	+	0.176574i
$773$	−5.94641	−	1.80382i	−0.213877	−	0.0648790i	0.181528	−	0.983386i	$-0.441896\pi$
$773$	−5.94641	−	1.80382i	−0.213877	−	0.0648790i	−0.395405	+	0.918507i	$0.629396\pi$
$774$	−4.81333	+	11.7033i	−0.173011	+	0.420665i
$775$	−3.68714	+	0.733418i	−0.132446	+	0.0263451i
$776$	−29.7030	+	24.7526i	−1.06628	+	0.888567i
$777$	−0.415015	+	2.08642i	−0.0148886	+	0.0748500i
$778$	2.59625	+	12.8834i	0.0930799	+	0.461893i
$779$	−7.39359	+	0.728205i	−0.264903	+	0.0260906i
$780$	−1.26873	−	12.2519i	−0.0454278	−	0.438689i
$781$	−18.8021	−	61.9821i	−0.672790	−	2.21789i
$782$	20.2529	+	24.5525i	0.724242	+	0.877996i
$783$	−0.865719	−	2.09003i	−0.0309383	−	0.0746916i
$784$	15.1236	+	14.8235i	0.540129	+	0.529410i
$785$	11.7610	−	28.3936i	0.419768	−	1.01341i
$786$	18.7648	−	5.74362i	0.669318	−	0.204868i
$787$	−10.1488	−	5.42464i	−0.361765	−	0.193367i	0.280493	−	0.959856i	$-0.409502\pi$
$787$	−10.1488	−	5.42464i	−0.361765	−	0.193367i	−0.642258	+	0.766489i	$0.722002\pi$
$788$	−26.2526	−	31.6640i	−0.935211	−	1.12798i
$789$	−20.3700	−	16.7172i	−0.725190	−	0.595148i
$790$	22.2493	+	33.1185i	0.791596	+	1.17830i
$791$	−12.4650	−	18.6551i	−0.443203	−	0.663301i
$792$	2.46158	−	12.8804i	0.0874683	−	0.457686i
$793$	−9.87329	−	6.59712i	−0.350611	−	0.234271i
$794$	−12.4850	+	12.5478i	−0.443078	+	0.445304i
$795$	27.7257	−	14.8197i	0.983330	−	0.525601i
$796$	34.1814	+	13.9582i	1.21153	+	0.494734i
$797$	−0.864621	+	8.77864i	−0.0306264	+	0.310955i	0.967651	+	0.252291i	$0.0811841\pi$
$797$	−0.864621	+	8.77864i	−0.0306264	+	0.310955i	−0.998278	+	0.0586642i	$0.981316\pi$
$798$	−5.63530	+	6.90183i	−0.199488	+	0.244322i
$799$	1.35480	−	1.35480i	0.0479294	−	0.0479294i
$800$	−25.4040	+	8.05510i	−0.898166	+	0.284791i
$801$	8.38948	+	8.38948i	0.296428	+	0.296428i
$802$	−31.4019	+	3.17228i	−1.10884	+	0.112017i
$803$	51.8989	+	5.11159i	1.83147	+	0.180384i
$804$	−10.6994	+	10.8072i	−0.377339	+	0.381139i
$805$	−16.3145	−	30.5222i	−0.575010	−	1.07577i
$806$	0.00558800	+	2.23025i	0.000196829	+	0.0785572i
$807$	8.82939	−	13.2141i	0.310809	−	0.465159i
$808$	12.1349	−	5.13362i	0.426903	−	0.180600i
$809$	−23.1961	+	15.4991i	−0.815531	+	0.544921i	−0.891939	−	0.452156i	$-0.850655\pi$
$809$	−23.1961	+	15.4991i	−0.815531	+	0.544921i	0.0764075	+	0.997077i	$0.475655\pi$
$810$	0.848946	−	4.32454i	0.0298289	−	0.151949i
$811$	0.413481	−	0.503828i	0.0145193	−	0.0176918i	−0.765700	−	0.643198i	$-0.777607\pi$
$811$	0.413481	−	0.503828i	0.0145193	−	0.0176918i	0.780219	+	0.625506i	$0.215107\pi$
$812$	5.22535	+	2.75943i	0.183374	+	0.0968372i
$813$	0.270090	−	0.505303i	0.00947247	−	0.0177218i
$814$	5.01072	−	9.43116i	0.175626	−	0.330562i
$815$	−39.0676	−	16.1823i	−1.36848	−	0.566842i
$816$	−6.79785	−	8.11595i	−0.237972	−	0.284115i
$817$	−39.8798	+	16.5187i	−1.39522	+	0.577918i
$818$	3.90898	−	40.7346i	0.136674	−	1.42425i
$819$	−2.47002	+	0.749274i	−0.0863096	+	0.0261817i
$820$	−2.74026	+	9.19912i	−0.0956940	+	0.321247i
$821$	0.827769	+	8.40448i	0.0288893	+	0.293318i	0.998764	+	0.0497123i	$0.0158304\pi$
$821$	0.827769	+	8.40448i	0.0288893	+	0.293318i	−0.969874	+	0.243606i	$0.921670\pi$
$822$	−26.6663	−	17.7214i	−0.930094	−	0.618104i
$823$	11.7968	+	2.34654i	0.411212	+	0.0817951i	0.396361	−	0.918095i	$-0.370273\pi$
$823$	11.7968	+	2.34654i	0.411212	+	0.0817951i	0.0148505	+	0.999890i	$0.495273\pi$
$824$	−32.0273	−	25.8837i	−1.11572	−	0.901701i
$825$	4.26128	+	21.4229i	0.148359	+	0.745850i
$826$	19.2510	−	8.03061i	0.669830	−	0.279421i
$827$	−5.00784	+	16.5086i	−0.174140	+	0.574061i	0.825809	+	0.563949i	$0.190719\pi$
$827$	−5.00784	+	16.5086i	−0.174140	+	0.574061i	−0.999949	+	0.0101118i	$0.996781\pi$
$828$	3.23420	−	16.6963i	0.112396	−	0.580235i
$829$	28.6288	−	23.4951i	0.994320	−	0.816017i	0.0113782	−	0.999935i	$-0.496378\pi$
$829$	28.6288	−	23.4951i	0.994320	−	0.816017i	0.982942	+	0.183918i	$0.0588781\pi$
$830$	−23.9341	−	7.19488i	−0.830764	−	0.249738i
$831$		−	17.2962i		−	0.599998i
$832$	1.78605	+	15.7092i	0.0619201	+	0.544619i
$833$		−	14.0121i		−	0.485492i
$834$	−1.34492	+	4.47395i	−0.0465709	+	0.154920i
$835$	−33.9722	+	27.8803i	−1.17566	+	0.964836i
$836$	37.0680	−	25.0377i	1.28202	−	0.865945i
$837$	−0.231638	+	0.763609i	−0.00800658	+	0.0263942i
$838$	−10.3621	−	24.8402i	−0.357954	−	0.858091i
$839$	−7.33682	−	36.8847i	−0.253295	−	1.27340i	−0.872672	−	0.488306i	$-0.837615\pi$
$839$	−7.33682	−	36.8847i	−0.253295	−	1.27340i	0.619377	−	0.785094i	$-0.287385\pi$
$840$	5.50279	+	10.1114i	0.189864	+	0.348878i
$841$	23.4234	+	4.65921i	0.807704	+	0.160662i
$842$	−2.48157	+	3.73415i	−0.0855206	+	0.128687i
$843$	1.33719	+	13.5767i	0.0460553	+	0.467607i
$844$	15.1403	+	27.9872i	0.521150	+	0.963359i
$845$	−27.1198	+	8.22670i	−0.932949	+	0.283007i
$846$	−1.01909	−	0.0977939i	−0.0350370	−	0.00336222i
$847$	12.6644	−	5.24577i	0.435155	−	0.180247i
$848$	−35.3958	+	19.3780i	−1.21550	+	0.665445i
$849$	−2.85667	−	1.18327i	−0.0980407	−	0.0406098i
$850$	15.5725	+	8.27356i	0.534131	+	0.283781i
$851$	6.52890	−	12.2147i	0.223808	−	0.418715i
$852$	8.24462	+	26.6966i	0.282456	+	0.914609i
$853$	4.06983	−	4.95910i	0.139348	−	0.169796i	−0.698660	−	0.715454i	$-0.746220\pi$
$853$	4.06983	−	4.95910i	0.139348	−	0.169796i	0.838008	+	0.545657i	$0.183720\pi$
$854$	10.8900	+	2.13781i	0.372648	+	0.0731542i
$855$	12.4995	−	8.35190i	0.427474	−	0.285629i
$856$	9.13392	+	8.99763i	0.312191	+	0.307533i
$857$	−0.859437	+	1.28624i	−0.0293578	+	0.0439371i	−0.845858	−	0.533408i	$-0.820911\pi$
$857$	−0.859437	+	1.28624i	−0.0293578	+	0.0439371i	0.816500	+	0.577345i	$0.195911\pi$
$858$	12.9581	−	0.0324672i	0.442383	−	0.00110841i
$859$	21.5260	+	40.2723i	0.734457	+	1.37407i	0.920190	+	0.391472i	$0.128034\pi$
$859$	21.5260	+	40.2723i	0.734457	+	1.37407i	−0.185733	+	0.982600i	$0.559466\pi$
$860$	0.279462	+	55.7683i	0.00952959	+	1.90168i
$861$	2.00174	+	0.197154i	0.0682191	+	0.00671899i
$862$	−3.85878	−	38.1974i	−0.131430	−	1.30101i
$863$	11.6518	+	11.6518i	0.396631	+	0.396631i	0.877043	−	0.480412i	$-0.159513\pi$
$863$	11.6518	+	11.6518i	0.396631	+	0.396631i	−0.480412	+	0.877043i	$0.659513\pi$
$864$	−1.03401	+	5.56155i	−0.0351776	+	0.189208i
$865$	−27.1197	+	27.1197i	−0.922099	+	0.922099i
$866$	14.6070	+	11.9265i	0.496367	+	0.405281i
$867$	0.979685	−	9.94691i	0.0332719	−	0.337815i
$868$	−0.807301	−	1.92170i	−0.0274016	−	0.0652268i
$869$	−37.0175	+	19.7863i	−1.25573	+	0.671204i
$870$	−7.06738	−	7.03205i	−0.239607	−	0.238409i
$871$	−12.4949	−	8.34880i	−0.423372	−	0.282888i
$872$	−9.71805	−	6.38826i	−0.329095	−	0.216334i
$873$	−7.59467	−	11.3662i	−0.257041	−	0.384689i
$874$	48.1538	−	32.3502i	1.62883	−	1.09426i
$875$	0.908682	+	0.745736i	0.0307191	+	0.0252105i
$876$	−22.3987	−	2.09280i	−0.756780	−	0.0707091i
$877$	50.7122	+	27.1062i	1.71243	+	0.915313i	0.969199	+	0.246278i	$0.0792075\pi$
$877$	50.7122	+	27.1062i	1.71243	+	0.915313i	0.743231	+	0.669035i	$0.233293\pi$
$878$	0.806962	+	2.63640i	0.0272337	+	0.0889742i
$879$	−9.68651	+	23.3853i	−0.326718	+	0.788767i
$880$	−11.8422	−	56.5661i	−0.399202	−	1.90684i
$881$	10.9140	+	26.3487i	0.367702	+	0.887711i	0.994126	+	0.108229i	$0.0345179\pi$
$881$	10.9140	+	26.3487i	0.367702	+	0.887711i	−0.626424	+	0.779483i	$0.715482\pi$
$882$	−5.77572	+	4.76428i	−0.194479	+	0.160422i
$883$	0.466975	+	1.53941i	0.0157150	+	0.0518053i	0.964447	−	0.264276i	$-0.0851329\pi$
$883$	0.466975	+	1.53941i	0.0157150	+	0.0518053i	−0.948732	+	0.316081i	$0.897633\pi$
$884$	6.59599	−	8.11987i	0.221847	−	0.273101i
$885$	−35.0230	+	3.44947i	−1.17729	+	0.115953i
$886$	7.80717	−	1.57329i	0.262287	−	0.0528557i
$887$	−7.50772	+	37.7439i	−0.252085	+	1.26732i	0.622568	+	0.782566i	$0.286089\pi$
$887$	−7.50772	+	37.7439i	−0.252085	+	1.26732i	−0.874653	+	0.484750i	$0.838911\pi$
$888$	−2.14109	+	4.07915i	−0.0718501	+	0.136887i
$889$	11.7611	−	2.33943i	0.394455	−	0.0784619i
$890$	48.3577	+	19.8886i	1.62095	+	0.666668i
$891$	4.43670	+	1.34586i	0.148635	+	0.0450879i
$892$	30.7914	−	6.28535i	1.03097	−	0.210449i
$893$	−2.21542	−	2.69950i	−0.0741362	−	0.0903353i
$894$	−16.8951	+	9.08512i	−0.565057	+	0.303852i
$895$	52.9940			1.77139
$896$	−7.19301	−	12.9074i	−0.240301	−	0.431207i
$897$	16.8051			0.561107
$898$	−34.9144	+	18.7748i	−1.16511	+	0.626523i
$899$	1.14520	+	1.39543i	0.0381946	+	0.0465402i
$900$	−1.88450	−	9.23198i	−0.0628166	−	0.307733i
$901$	25.5508	+	7.75076i	0.851221	+	0.258215i
$902$	−9.33889	−	3.84091i	−0.310951	−	0.127888i
$903$	11.4621	−	2.27995i	0.381434	−	0.0758720i
$904$	−14.4536	−	46.3891i	−0.480721	−	1.54288i
$905$	−10.9691	+	55.1454i	−0.364625	+	1.83309i
$906$	−17.1096	+	3.44790i	−0.568429	+	0.114549i
$907$	−19.6262	+	1.93301i	−0.651678	+	0.0641847i	−0.418454	−	0.908238i	$-0.637428\pi$
$907$	−19.6262	+	1.93301i	−0.651678	+	0.0641847i	−0.233225	+	0.972423i	$0.574928\pi$
$908$	−27.4092	−	22.2652i	−0.909605	−	0.738896i
$909$	1.35228	+	4.45785i	0.0448521	+	0.147858i
$910$	−8.77521	+	7.23850i	−0.290895	+	0.239954i
$911$	4.09841	+	9.89443i	0.135786	+	0.327817i	0.977117	−	0.212704i	$-0.0682271\pi$
$911$	4.09841	+	9.89443i	0.135786	+	0.327817i	−0.841330	+	0.540521i	$0.818227\pi$
$912$	−15.9359	+	10.8806i	−0.527691	+	0.360293i
$913$	10.0616	−	24.2908i	0.332990	−	0.803909i
$914$	−10.2075	−	33.3485i	−0.337633	−	1.10307i
$915$	−16.5131	−	8.82641i	−0.545905	−	0.291792i
$916$	−2.23181	+	23.8865i	−0.0737412	+	0.789232i
$917$	−14.0095	−	11.4973i	−0.462635	−	0.379675i
$918$	3.10696	−	2.08728i	0.102545	−	0.0688905i
$919$	−26.0960	−	39.0555i	−0.860829	−	1.28832i	−0.956151	−	0.292874i	$-0.905388\pi$
$919$	−26.0960	−	39.0555i	−0.860829	−	1.28832i	0.0953224	−	0.995446i	$-0.469612\pi$
$920$	−15.1740	−	73.3974i	−0.500274	−	2.41984i
$921$	−1.91297	−	1.27821i	−0.0630346	−	0.0421184i
$922$	−28.9475	−	28.8028i	−0.953335	−	0.948570i
$923$	−24.3495	+	13.0151i	−0.801474	+	0.428397i
$924$	−11.1654	+	4.69055i	−0.367315	+	0.154308i
$925$	0.752137	−	7.63658i	0.0247301	−	0.251089i
$926$	18.8308	+	15.3752i	0.618817	+	0.505261i
$927$	10.2948	−	10.2948i	0.338124	−	0.338124i
$928$	9.16158	+	8.93486i	0.300744	+	0.293301i
$929$	−0.350441	−	0.350441i	−0.0114976	−	0.0114976i	0.701335	−	0.712832i	$-0.252588\pi$
$929$	−0.350441	−	0.350441i	−0.0114976	−	0.0114976i	−0.712832	+	0.701335i	$0.752588\pi$
$930$	0.353466	+	3.49890i	0.0115906	+	0.114734i
$931$	−25.4165	−	2.50331i	−0.832992	−	0.0820425i
$932$	−41.3073	+	0.206996i	−1.35307	+	0.00678039i
$933$	12.1817	+	22.7904i	0.398812	+	0.746124i
$934$	−8.55340	+	0.0214310i	−0.279876	+	0.000701243i
$935$	−21.2448	+	31.7951i	−0.694779	+	1.03981i
$936$	−5.58967	+	0.0420163i	−0.182704	+	0.00137335i
$937$	−19.4268	+	12.9806i	−0.634645	+	0.424057i	−0.830842	−	0.556508i	$-0.812141\pi$
$937$	−19.4268	+	12.9806i	−0.634645	+	0.424057i	0.196197	+	0.980565i	$0.437141\pi$
$938$	13.7815	+	2.70544i	0.449983	+	0.0883358i
$939$	9.43524	−	11.4969i	0.307907	−	0.375186i
$940$	−4.31094	+	1.33134i	−0.140607	+	0.0434234i
$941$	2.88305	−	5.39380i	0.0939846	−	0.175833i	−0.830536	−	0.556965i	$-0.811966\pi$
$941$	2.88305	−	5.39380i	0.0939846	−	0.175833i	0.924521	+	0.381132i	$0.124466\pi$
$942$	−12.3167	−	6.54377i	−0.401299	−	0.213208i
$943$	−12.0989	−	5.01151i	−0.393993	−	0.163197i
$944$	44.9083	−	4.87799i	1.46164	−	0.158765i
$945$	−3.76023	+	1.55754i	−0.122320	+	0.0506667i
$946$	−58.4018	−	5.60436i	−1.89881	−	0.182214i
$947$	−17.9929	+	5.45809i	−0.584691	+	0.177364i	−0.568752	−	0.822509i	$-0.692574\pi$
$947$	−17.9929	+	5.45809i	−0.584691	+	0.177364i	−0.0159388	+	0.999873i	$0.505074\pi$
$948$	15.9255	−	8.61523i	0.517235	−	0.279810i
$949$	−2.17889	−	22.1226i	−0.0707298	−	0.718131i
$950$	17.7894	−	26.7687i	0.577164	−	0.868490i
$951$	−0.266211	−	0.0529527i	−0.00863250	−	0.00171711i
$952$	−2.76774	+	9.37718i	−0.0897029	+	0.303916i
$953$	1.75602	+	8.82812i	0.0568831	+	0.285971i	0.998748	−	0.0500206i	$-0.0159287\pi$
$953$	1.75602	+	8.82812i	0.0568831	+	0.285971i	−0.941865	+	0.335991i	$0.890929\pi$
$954$	−5.49275	−	13.1673i	−0.177834	−	0.426306i
$955$	11.5397	−	38.0415i	0.373418	−	1.23099i
$956$	−0.349519	−	0.517460i	−0.0113042	−	0.0167358i
$957$	8.10769	−	6.65381i	0.262084	−	0.215087i
$958$	−15.4672	+	51.4523i	−0.499723	+	1.66235i
$959$			29.5692i			0.954838i
$960$	5.23066	+	24.3753i	0.168819	+	0.786710i
$961$			30.3632i			0.979460i
$962$	−4.35961	−	1.31055i	−0.140560	−	0.0422540i
$963$	−3.50407	+	2.87571i	−0.112917	+	0.0926686i
$964$	−10.5381	−	2.04132i	−0.339411	−	0.0657466i
$965$	−4.02440	+	13.2667i	−0.129550	+	0.427070i
$966$	−14.4953	+	6.04676i	−0.466380	+	0.194551i
$967$	−0.546300	−	2.74643i	−0.0175678	−	0.0883193i	0.971007	−	0.239052i	$-0.0768367\pi$
$967$	−0.546300	−	2.74643i	−0.0175678	−	0.0883193i	−0.988575	+	0.150733i	$0.951837\pi$
$968$	29.5204	−	3.13172i	0.948821	−	0.100657i
$969$	12.5224	+	2.49086i	0.402277	+	0.0800179i
$970$	−50.1756	−	33.3447i	−1.61104	−	1.07063i
$971$	−1.35207	−	13.7278i	−0.0433899	−	0.440545i	−0.992196	−	0.124687i	$-0.960207\pi$
$971$	−1.35207	−	13.7278i	−0.0433899	−	0.440545i	0.948806	−	0.315859i	$-0.102293\pi$
$972$	−1.91677	−	0.570971i	−0.0614803	−	0.0183139i
$973$	4.12867	−	1.25242i	0.132359	−	0.0401506i
$974$	−3.70614	+	38.6208i	−0.118752	+	1.23749i
$975$	8.60199	−	3.56306i	0.275484	−	0.114109i
$976$	21.3084	+	11.1164i	0.682064	+	0.355828i
$977$	36.9795	+	15.3174i	1.18308	+	0.490047i	0.885495	−	0.464649i	$-0.153819\pi$
$977$	36.9795	+	15.3174i	1.18308	+	0.490047i	0.297583	+	0.954696i	$0.403819\pi$
$978$	−9.00378	+	16.9469i	−0.287909	+	0.541902i
$979$	−25.9305	+	48.5126i	−0.828744	+	1.55047i
$980$	−15.4084	+	29.1779i	−0.492203	+	0.932052i
$981$	2.60845	−	3.17841i	0.0832814	−	0.101479i
$982$	3.97062	−	20.2264i	0.126708	−	0.645450i
$983$	12.7223	−	8.50077i	0.405778	−	0.271132i	−0.335887	−	0.941902i	$-0.609036\pi$
$983$	12.7223	−	8.50077i	0.405778	−	0.271132i	0.741666	+	0.670770i	$0.234036\pi$
$984$	4.03682	+	1.63667i	0.128689	+	0.0521750i
$985$	35.6058	−	53.2879i	1.13450	−	1.69789i
$986$	−0.0212157	−	8.46747i	−0.000675644	−	0.269659i
$987$	0.445694	+	0.833834i	0.0141866	+	0.0265412i
$988$	−13.5502	−	13.4150i	−0.431088	−	0.426789i
$989$	−75.7214	−	7.45791i	−2.40780	−	0.237148i
$990$	20.3292	−	2.05370i	0.646105	−	0.0652708i
$991$	−6.74092	−	6.74092i	−0.214132	−	0.214132i	0.591888	−	0.806020i	$-0.298383\pi$
$991$	−6.74092	−	6.74092i	−0.214132	−	0.214132i	−0.806020	+	0.591888i	$0.798383\pi$
$992$	−0.498690	−	4.48636i	−0.0158334	−	0.142442i
$993$	16.9587	−	16.9587i	0.538167	−	0.538167i
$994$	16.3197	−	19.9876i	0.517631	−	0.633967i
$995$	−5.63881	+	57.2518i	−0.178762	+	1.81501i
$996$	−4.28776	+	10.5001i	−0.135863	+	0.332708i
$997$	−15.7752	+	8.43205i	−0.499607	+	0.267046i	−0.701895	−	0.712281i	$-0.747662\pi$
$997$	−15.7752	+	8.43205i	−0.499607	+	0.267046i	0.202288	+	0.979326i	$0.435162\pi$
$998$	−22.5339	+	22.6471i	−0.713297	+	0.716880i
$999$	−1.35429	−	0.904908i	−0.0428479	−	0.0286300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.253.12	yes	512
128.85	even	32	inner	384.2.v.a.85.12	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.85.12	✓	512	128.85	even	32	inner
384.2.v.a.253.12	yes	512	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.669779 - 1.24555i) q^{2} +(-0.634393 - 0.773010i) q^{3} +(-1.10279 + 1.66849i) q^{4} +(-2.98209 - 0.904607i) q^{5} +(-0.537921 + 1.30791i) q^{6} +(1.28096 - 0.254799i) q^{7} +(2.81681 + 0.256069i) q^{8} +(-0.195090 + 0.980785i) q^{9} +O(q^{10})\)	\(q+(-0.669779 - 1.24555i) q^{2} +(-0.634393 - 0.773010i) q^{3} +(-1.10279 + 1.66849i) q^{4} +(-2.98209 - 0.904607i) q^{5} +(-0.537921 + 1.30791i) q^{6} +(1.28096 - 0.254799i) q^{7} +(2.81681 + 0.256069i) q^{8} +(-0.195090 + 0.980785i) q^{9} +(0.870606 + 4.32023i) q^{10} +(-4.61401 + 0.454440i) q^{11} +(1.98936 - 0.206006i) q^{12} +(0.573691 + 1.89121i) q^{13} +(-1.17533 - 1.42485i) q^{14} +(1.19255 + 2.87906i) q^{15} +(-1.56769 - 3.67999i) q^{16} +(-1.01284 + 2.44522i) q^{17} +(1.35229 - 0.413914i) q^{18} +(4.25442 + 2.27403i) q^{19} +(4.79796 - 3.97798i) q^{20} +(-1.00960 - 0.828555i) q^{21} +(3.65639 + 5.44261i) q^{22} +(4.72418 + 7.07024i) q^{23} +(-1.58902 - 2.33987i) q^{24} +(3.91720 + 2.61739i) q^{25} +(1.97135 - 1.98125i) q^{26} +(0.881921 - 0.471397i) q^{27} +(-0.987508 + 2.41826i) q^{28} +(0.221738 - 2.25134i) q^{29} +(2.78728 - 3.41371i) q^{30} +(-0.564249 + 0.564249i) q^{31} +(-3.53361 + 4.41742i) q^{32} +(3.27838 + 3.27838i) q^{33} +(3.72403 - 0.376208i) q^{34} +(-4.05044 - 0.398934i) q^{35} +(-1.42128 - 1.40711i) q^{36} +(-0.767807 - 1.43647i) q^{37} +(-0.0170933 - 6.82219i) q^{38} +(1.09798 - 1.64324i) q^{39} +(-8.16835 - 3.31173i) q^{40} +(-1.28052 + 0.855618i) q^{41} +(-0.355801 + 1.81245i) q^{42} +(-5.67657 + 6.91691i) q^{43} +(4.33007 - 8.19957i) q^{44} +(1.46900 - 2.74831i) q^{45} +(5.64219 - 10.6197i) q^{46} +(-0.668810 - 0.277030i) q^{47} +(-1.85014 + 3.54641i) q^{48} +(-4.89121 + 2.02601i) q^{49} +(0.636435 - 6.63215i) q^{50} +(2.53272 - 0.768293i) q^{51} +(-3.78811 - 1.12841i) q^{52} +(-0.988824 - 10.0397i) q^{53} +(-1.17784 - 0.782746i) q^{54} +(14.1705 + 2.81868i) q^{55} +(3.67348 - 0.389707i) q^{56} +(-0.941123 - 4.73134i) q^{57} +(-2.95267 + 1.23171i) q^{58} +(-3.27822 + 10.8068i) q^{59} +(-6.11881 - 1.18526i) q^{60} +(-4.64458 + 3.81171i) q^{61} +(1.08072 + 0.324879i) q^{62} +1.30606i q^{63} +(7.86886 + 1.44260i) q^{64} -6.15871i q^{65} +(1.88760 - 6.27918i) q^{66} +(-5.87783 + 4.82381i) q^{67} +(-2.96286 - 4.38649i) q^{68} +(2.46838 - 8.13716i) q^{69} +(2.21601 + 5.31223i) q^{70} +(2.72547 + 13.7019i) q^{71} +(-0.800681 + 2.71273i) q^{72} +(-11.0320 - 2.19440i) q^{73} +(-1.27493 + 1.91846i) q^{74} +(-0.461776 - 4.68849i) q^{75} +(-8.48594 + 4.59065i) q^{76} +(-5.79458 + 1.75777i) q^{77} +(-2.78214 - 0.266980i) q^{78} +(8.36408 - 3.46452i) q^{79} +(1.34606 + 12.3922i) q^{80} +(-0.923880 - 0.382683i) q^{81} +(1.92338 + 1.02188i) q^{82} +(-2.67324 + 5.00129i) q^{83} +(2.49581 - 0.770774i) q^{84} +(5.23236 - 6.37565i) q^{85} +(12.4174 + 2.43765i) q^{86} +(-1.88098 + 1.25683i) q^{87} +(-13.1132 + 0.0985687i) q^{88} +(6.59157 - 9.86499i) q^{89} +(-4.40707 + 0.0110421i) q^{90} +(1.21675 + 2.27639i) q^{91} +(-17.0064 + 0.0852213i) q^{92} +(0.794126 + 0.0782146i) q^{93} +(0.102899 + 1.01859i) q^{94} +(-10.6300 - 10.6300i) q^{95} +(5.65641 - 0.0708656i) q^{96} +(-9.66618 + 9.66618i) q^{97} +(5.79952 + 4.73528i) q^{98} +(0.454440 - 4.61401i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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