LMFDB - Embedded newform 384.2.v.a.13.15

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			13.15
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.229611 - 1.39545i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-1.89456 + 0.640821i) q^{4} +(-0.159671 - 1.62116i) q^{5} +(1.26871 - 0.624802i) q^{6} +(-2.66520 + 3.98875i) q^{7} +(1.32924 + 2.49662i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(-0.229611 - 1.39545i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-1.89456 + 0.640821i) q^{4} +(-0.159671 - 1.62116i) q^{5} +(1.26871 - 0.624802i) q^{6} +(-2.66520 + 3.98875i) q^{7} +(1.32924 + 2.49662i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(-2.22559 + 0.595050i) q^{10} +(3.99771 - 2.13682i) q^{11} +(-1.16319 - 1.62696i) q^{12} +(6.81274 + 0.670996i) q^{13} +(6.17805 + 2.80329i) q^{14} +(1.50501 - 0.623395i) q^{15} +(3.17870 - 2.42815i) q^{16} +(3.66004 + 1.51604i) q^{17} +(0.966185 + 1.03271i) q^{18} +(-3.65067 + 2.99603i) q^{19} +(1.34138 + 2.96907i) q^{20} +(-4.59066 - 1.39256i) q^{21} +(-3.89974 - 5.08796i) q^{22} +(-1.17853 + 5.92485i) q^{23} +(-2.00326 + 1.99674i) q^{24} +(2.30125 - 0.457746i) q^{25} +(-0.627939 - 9.66090i) q^{26} +(-0.773010 - 0.634393i) q^{27} +(2.49329 - 9.26483i) q^{28} +(-0.852848 + 1.59557i) q^{29} +(-1.21548 - 1.95702i) q^{30} +(-1.81765 + 1.81765i) q^{31} +(-4.11822 - 3.87818i) q^{32} +(3.20528 + 3.20528i) q^{33} +(1.27517 - 5.45550i) q^{34} +(6.89197 + 3.68384i) q^{35} +(1.21925 - 1.58538i) q^{36} +(-0.545096 + 0.664201i) q^{37} +(5.01904 + 4.40641i) q^{38} +(1.33553 + 6.71416i) q^{39} +(3.83519 - 2.55356i) q^{40} +(-2.41635 - 0.480641i) q^{41} +(-0.889183 + 6.72578i) q^{42} +(0.604548 - 1.99293i) q^{43} +(-6.20457 + 6.61014i) q^{44} +(1.03343 + 1.25924i) q^{45} +(8.53844 + 0.284162i) q^{46} +(1.28072 - 3.09193i) q^{47} +(3.24632 + 2.33697i) q^{48} +(-6.12806 - 14.7944i) q^{49} +(-1.16715 - 3.10617i) q^{50} +(-0.388305 + 3.94253i) q^{51} +(-13.3371 + 3.09451i) q^{52} +(1.15519 + 2.16120i) q^{53} +(-0.707772 + 1.22436i) q^{54} +(-4.10245 - 6.13975i) q^{55} +(-13.5011 - 1.35196i) q^{56} +(-3.92676 - 2.62378i) q^{57} +(2.42235 + 0.823746i) q^{58} +(7.51336 - 0.740001i) q^{59} +(-2.45184 + 2.14550i) q^{60} +(-11.9569 + 3.62709i) q^{61} +(2.95379 + 2.11909i) q^{62} -4.79723i q^{63} +(-4.46622 + 6.63724i) q^{64} -11.1517i q^{65} +(3.73684 - 5.20877i) q^{66} +(8.08187 - 2.45161i) q^{67} +(-7.90567 - 0.526791i) q^{68} +(-6.01184 + 0.592115i) q^{69} +(3.55813 - 10.4632i) q^{70} +(0.265968 + 0.177714i) q^{71} +(-2.49227 - 1.33737i) q^{72} +(-1.60314 - 2.39927i) q^{73} +(1.05202 + 0.608146i) q^{74} +(1.10605 + 2.06928i) q^{75} +(4.99649 - 8.01558i) q^{76} +(-2.13144 + 21.6409i) q^{77} +(9.06262 - 3.40531i) q^{78} +(-0.479447 - 1.15749i) q^{79} +(-4.44397 - 4.76549i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-0.115891 + 3.48225i) q^{82} +(-0.187886 - 0.228940i) q^{83} +(9.58965 - 0.303504i) q^{84} +(1.87335 - 6.17560i) q^{85} +(-2.91984 - 0.386018i) q^{86} +(-1.77443 - 0.352956i) q^{87} +(10.6488 + 7.14040i) q^{88} +(-2.91955 - 14.6776i) q^{89} +(1.51992 - 1.73124i) q^{90} +(-20.8337 + 25.3860i) q^{91} +(-1.56399 - 11.9802i) q^{92} +(-2.26702 - 1.21175i) q^{93} +(-4.60870 - 1.07724i) q^{94} +(5.43997 + 5.43997i) q^{95} +(2.51573 - 5.06666i) q^{96} +(-8.38535 + 8.38535i) q^{97} +(-19.2378 + 11.9484i) q^{98} +(-2.13682 + 3.99771i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

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 $

$2$	−0.229611	−	1.39545i	−0.162360	−	0.986732i
$2$	−0.229611	−	1.39545i	−0.162360	−	0.986732i
$3$	0.290285	+	0.956940i	0.167596	+	0.552490i
$3$	0.290285	+	0.956940i	0.167596	+	0.552490i
$4$	−1.89456	+	0.640821i	−0.947279	+	0.320411i
$5$	−0.159671	−	1.62116i	−0.0714070	−	0.725007i	−0.962517	−	0.271220i	$-0.912573\pi$
$5$	−0.159671	−	1.62116i	−0.0714070	−	0.725007i	0.891110	−	0.453787i	$-0.149927\pi$
$6$	1.26871	−	0.624802i	0.517948	−	0.255074i
$7$	−2.66520	+	3.98875i	−1.00735	+	1.50761i	−0.152785	+	0.988259i	$0.548824\pi$
$7$	−2.66520	+	3.98875i	−1.00735	+	1.50761i	−0.854564	+	0.519346i	$0.826176\pi$
$8$	1.32924	+	2.49662i	0.469959	+	0.882688i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	−2.22559	+	0.595050i	−0.703794	+	0.188171i
$11$	3.99771	−	2.13682i	1.20535	−	0.644275i	0.258522	−	0.966005i	$-0.416764\pi$
$11$	3.99771	−	2.13682i	1.20535	−	0.644275i	0.946831	+	0.321730i	$0.104264\pi$
$12$	−1.16319	−	1.62696i	−0.335784	−	0.469662i
$13$	6.81274	+	0.670996i	1.88951	+	0.186101i	0.975562	−	0.219724i	$-0.0705156\pi$
$13$	6.81274	+	0.670996i	1.88951	+	0.186101i	0.913951	+	0.405824i	$0.133016\pi$
$14$	6.17805	+	2.80329i	1.65115	+	0.749210i
$15$	1.50501	−	0.623395i	0.388591	−	0.160960i
$16$	3.17870	−	2.42815i	0.794674	−	0.607036i
$17$	3.66004	+	1.51604i	0.887691	+	0.367694i	0.779475	−	0.626434i	$-0.215486\pi$
$17$	3.66004	+	1.51604i	0.887691	+	0.367694i	0.108216	+	0.994127i	$0.465486\pi$
$18$	0.966185	+	1.03271i	0.227732	+	0.243412i
$19$	−3.65067	+	2.99603i	−0.837522	+	0.687337i	−0.952003	−	0.306089i	$-0.900980\pi$
$19$	−3.65067	+	2.99603i	−0.837522	+	0.687337i	0.114481	+	0.993425i	$0.463480\pi$
$20$	1.34138	+	2.96907i	0.299942	+	0.663904i
$21$	−4.59066	−	1.39256i	−1.00176	−	0.303882i
$22$	−3.89974	−	5.08796i	−0.831427	−	1.08476i
$23$	−1.17853	+	5.92485i	−0.245740	+	1.23542i	0.638954	+	0.769245i	$0.279367\pi$
$23$	−1.17853	+	5.92485i	−0.245740	+	1.23542i	−0.884694	+	0.466173i	$0.845633\pi$
$24$	−2.00326	+	1.99674i	−0.408913	+	0.407583i
$25$	2.30125	−	0.457746i	0.460249	−	0.0915492i
$26$	−0.627939	−	9.66090i	−0.123149	−	1.89466i
$27$	−0.773010	−	0.634393i	−0.148766	−	0.122089i
$28$	2.49329	−	9.26483i	0.471188	−	1.75089i
$29$	−0.852848	+	1.59557i	−0.158370	+	0.296289i	−0.948575	−	0.316554i	$-0.897474\pi$
$29$	−0.852848	+	1.59557i	−0.158370	+	0.296289i	0.790205	+	0.612843i	$0.209974\pi$
$30$	−1.21548	−	1.95702i	−0.221916	−	0.357302i
$31$	−1.81765	+	1.81765i	−0.326460	+	0.326460i	−0.851239	−	0.524779i	$-0.824148\pi$
$31$	−1.81765	+	1.81765i	−0.326460	+	0.326460i	0.524779	+	0.851239i	$0.324148\pi$
$32$	−4.11822	−	3.87818i	−0.728005	−	0.685572i
$33$	3.20528	+	3.20528i	0.557968	+	0.557968i
$34$	1.27517	−	5.45550i	0.218690	−	0.935611i
$35$	6.89197	+	3.68384i	1.16496	+	0.622682i
$36$	1.21925	−	1.58538i	0.203208	−	0.264231i
$37$	−0.545096	+	0.664201i	−0.0896132	+	0.109194i	−0.815887	−	0.578212i	$-0.803751\pi$
$37$	−0.545096	+	0.664201i	−0.0896132	+	0.109194i	0.726273	+	0.687406i	$0.241251\pi$
$38$	5.01904	+	4.40641i	0.814197	+	0.714814i
$39$	1.33553	+	6.71416i	0.213856	+	1.07513i
$40$	3.83519	−	2.55356i	0.606397	−	0.403754i
$41$	−2.41635	−	0.480641i	−0.377370	−	0.0750636i	0.00276103	−	0.999996i	$-0.499121\pi$
$41$	−2.41635	−	0.480641i	−0.377370	−	0.0750636i	−0.380131	+	0.924933i	$0.624121\pi$
$42$	−0.889183	+	6.72578i	−0.137204	+	1.03781i
$43$	0.604548	−	1.99293i	0.0921926	−	0.303918i	−0.898702	−	0.438561i	$-0.855488\pi$
$43$	0.604548	−	1.99293i	0.0921926	−	0.303918i	0.990894	+	0.134642i	$0.0429885\pi$
$44$	−6.20457	+	6.61014i	−0.935374	+	0.996516i
$45$	1.03343	+	1.25924i	0.154055	+	0.187717i
$46$	8.53844	+	0.284162i	1.25892	+	0.0418975i
$47$	1.28072	−	3.09193i	0.186812	−	0.451004i	−0.802530	−	0.596611i	$-0.796513\pi$
$47$	1.28072	−	3.09193i	0.186812	−	0.451004i	0.989343	+	0.145607i	$0.0465134\pi$
$48$	3.24632	+	2.33697i	0.468565	+	0.337312i
$49$	−6.12806	−	14.7944i	−0.875437	−	2.11349i
$50$	−1.16715	−	3.10617i	−0.165060	−	0.439278i
$51$	−0.388305	+	3.94253i	−0.0543736	+	0.552064i
$52$	−13.3371	+	3.09451i	−1.84952	+	0.429131i
$53$	1.15519	+	2.16120i	0.158677	+	0.296864i	0.948679	−	0.316240i	$-0.102421\pi$
$53$	1.15519	+	2.16120i	0.158677	+	0.296864i	−0.790002	+	0.613104i	$0.789921\pi$
$54$	−0.707772	+	1.22436i	−0.0963156	+	0.166614i
$55$	−4.10245	−	6.13975i	−0.553175	−	0.827884i
$56$	−13.5011	−	1.35196i	−1.80416	−	0.180663i
$57$	−3.92676	−	2.62378i	−0.520112	−	0.347528i
$58$	2.42235	+	0.823746i	0.318071	+	0.108163i
$59$	7.51336	−	0.740001i	0.978156	−	0.0963400i	0.403714	−	0.914885i	$-0.367719\pi$
$59$	7.51336	−	0.740001i	0.978156	−	0.0963400i	0.574442	+	0.818545i	$0.305219\pi$
$60$	−2.45184	+	2.14550i	−0.316531	+	0.276983i
$61$	−11.9569	+	3.62709i	−1.53093	+	0.464401i	−0.939670	−	0.342082i	$-0.888868\pi$
$61$	−11.9569	+	3.62709i	−1.53093	+	0.464401i	−0.591256	+	0.806484i	$0.701368\pi$
$62$	2.95379	+	2.11909i	0.375132	+	0.269124i
$63$		−	4.79723i		−	0.604394i
$64$	−4.46622	+	6.63724i	−0.558277	+	0.829655i
$65$		−	11.1517i		−	1.38320i
$66$	3.73684	−	5.20877i	0.459973	−	0.641156i
$67$	8.08187	−	2.45161i	0.987357	−	0.299512i	0.245005	−	0.969522i	$-0.421210\pi$
$67$	8.08187	−	2.45161i	0.987357	−	0.299512i	0.742352	+	0.670010i	$0.233710\pi$
$68$	−7.90567	−	0.526791i	−0.958704	−	0.0638828i
$69$	−6.01184	+	0.592115i	−0.723741	+	0.0712822i
$70$	3.55813	−	10.4632i	0.425278	−	1.25060i
$71$	0.265968	+	0.177714i	0.0315646	+	0.0210908i	0.571252	−	0.820774i	$-0.306458\pi$
$71$	0.265968	+	0.177714i	0.0315646	+	0.0210908i	−0.539688	+	0.841865i	$0.681458\pi$
$72$	−2.49227	−	1.33737i	−0.293717	−	0.157611i
$73$	−1.60314	−	2.39927i	−0.187633	−	0.280813i	0.725712	−	0.687998i	$-0.241510\pi$
$73$	−1.60314	−	2.39927i	−0.187633	−	0.280813i	−0.913346	+	0.407185i	$0.866510\pi$
$74$	1.05202	+	0.608146i	0.122295	+	0.0706955i
$75$	1.10605	+	2.06928i	0.127716	+	0.238940i
$76$	4.99649	−	8.01558i	0.573137	−	0.919450i
$77$	−2.13144	+	21.6409i	−0.242900	+	2.46621i
$78$	9.06262	−	3.40531i	1.02614	−	0.385575i
$79$	−0.479447	−	1.15749i	−0.0539421	−	0.130228i	0.894611	−	0.446846i	$-0.147453\pi$
$79$	−0.479447	−	1.15749i	−0.0539421	−	0.130228i	−0.948553	+	0.316618i	$0.897453\pi$
$80$	−4.44397	−	4.76549i	−0.496851	−	0.532798i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	−0.115891	+	3.48225i	−0.0127980	+	0.384550i
$83$	−0.187886	−	0.228940i	−0.0206232	−	0.0251294i	0.762597	−	0.646874i	$-0.223924\pi$
$83$	−0.187886	−	0.228940i	−0.0206232	−	0.0251294i	−0.783220	+	0.621745i	$0.786424\pi$
$84$	9.58965	−	0.303504i	1.04632	−	0.0331150i
$85$	1.87335	−	6.17560i	0.203193	−	0.669838i
$86$	−2.91984	−	0.386018i	−0.314854	−	0.0416253i
$87$	−1.77443	−	0.352956i	−0.190239	−	0.0378409i
$88$	10.6488	+	7.14040i	1.13516	+	0.761169i
$89$	−2.91955	−	14.6776i	−0.309471	−	1.55582i	−0.752061	−	0.659093i	$-0.770940\pi$
$89$	−2.91955	−	14.6776i	−0.309471	−	1.55582i	0.442590	−	0.896724i	$-0.354060\pi$
$90$	1.51992	−	1.73124i	0.160214	−	0.182489i
$91$	−20.8337	+	25.3860i	−2.18397	+	2.66117i
$92$	−1.56399	−	11.9802i	−0.163057	−	1.24902i
$93$	−2.26702	−	1.21175i	−0.235079	−	0.125652i
$94$	−4.60870	−	1.07724i	−0.475351	−	0.111109i
$95$	5.43997	+	5.43997i	0.558129	+	0.558129i
$96$	2.51573	−	5.06666i	0.256761	−	0.517114i
$97$	−8.38535	+	8.38535i	−0.851403	+	0.851403i	−0.990306	−	0.138903i	$-0.955642\pi$
$97$	−8.38535	+	8.38535i	−0.851403	+	0.851403i	0.138903	+	0.990306i	$0.455642\pi$
$98$	−19.2378	+	11.9484i	−1.94331	+	1.20697i
$99$	−2.13682	+	3.99771i	−0.214758	+	0.401785i
$100$	−4.06651	+	2.34191i	−0.406651	+	0.234191i
$101$	11.5966	+	9.51705i	1.15390	+	0.946982i	0.999160	−	0.0409729i	$-0.0130457\pi$
$101$	11.5966	+	9.51705i	1.15390	+	0.946982i	0.154741	+	0.987955i	$0.450546\pi$
$102$	5.59075	−	0.363388i	0.553567	−	0.0359807i
$103$	12.4944	−	2.48529i	1.23111	−	0.244883i	0.463672	−	0.886007i	$-0.346532\pi$
$103$	12.4944	−	2.48529i	1.23111	−	0.244883i	0.767437	+	0.641124i	$0.221532\pi$
$104$	7.38057	+	17.9007i	0.723725	+	1.75531i
$105$	−1.52458	+	7.66457i	−0.148784	+	0.747985i
$106$	2.75061	−	2.10824i	0.267162	−	0.204770i
$107$	−12.8461	−	3.89684i	−1.24188	−	0.376721i	−0.400068	−	0.916486i	$-0.631013\pi$
$107$	−12.8461	−	3.89684i	−1.24188	−	0.376721i	−0.841816	+	0.539764i	$0.818513\pi$
$108$	1.87105	+	0.706533i	0.180041	+	0.0679862i
$109$	−0.986792	+	0.809840i	−0.0945176	+	0.0775686i	−0.680465	−	0.732780i	$-0.738222\pi$
$109$	−0.986792	+	0.809840i	−0.0945176	+	0.0775686i	0.585948	+	0.810349i	$0.300722\pi$
$110$	−7.62575	+	7.13452i	−0.727086	+	0.680250i
$111$	−0.793834	−	0.328817i	−0.0753474	−	0.0312099i
$112$	1.21341	+	19.1505i	0.114656	+	1.80955i
$113$	10.9051	−	4.51705i	1.02587	−	0.424929i	0.194649	−	0.980873i	$-0.437643\pi$
$113$	10.9051	−	4.51705i	1.02587	−	0.424929i	0.831219	+	0.555945i	$0.187643\pi$
$114$	−2.75972	+	6.08204i	−0.258471	+	0.569635i
$115$	9.79334	+	0.964560i	0.913234	+	0.0899457i
$116$	0.593297	−	3.56941i	0.0550862	−	0.331412i
$117$	−6.03737	+	3.22704i	−0.558155	+	0.298340i
$118$	−2.75779	−	10.3146i	−0.253875	−	0.949536i
$119$	−15.8018	+	10.5584i	−1.44855	+	0.967891i
$120$	3.55690	+	2.92879i	0.324699	+	0.267361i
$121$	5.30439	−	7.93858i	0.482217	−	0.721689i
$122$	7.80686	+	15.8525i	0.706800	+	1.43521i
$123$	−0.241484	−	2.45182i	−0.0217738	−	0.221073i
$124$	2.27886	−	4.60843i	0.204647	−	0.413850i
$125$	−3.47391	−	11.4519i	−0.310716	−	1.02429i
$126$	−6.69429	+	1.10150i	−0.596374	+	0.0981291i
$127$	−18.3589			−1.62909			−0.814546	−	0.580100i	$-0.803014\pi$
$127$	−18.3589			−1.62909			−0.814546	+	0.580100i	$0.803014\pi$
$128$	10.2874	+	4.70840i	0.909288	+	0.416167i
$129$	2.08260			0.183363
$130$	−15.5616	+	2.56056i	−1.36485	+	0.224576i
$131$	0.636955	+	2.09976i	0.0556510	+	0.183457i	0.980359	−	0.197220i	$-0.0631912\pi$
$131$	0.636955	+	2.09976i	0.0556510	+	0.183457i	−0.924708	+	0.380676i	$0.875691\pi$
$132$	−8.12660	−	4.01858i	−0.707330	−	0.349772i
$133$	−2.22065	−	22.5466i	−0.192555	−	1.95504i
$134$	−5.27678	−	10.7149i	−0.455844	−	0.925628i
$135$	−0.905029	+	1.35447i	−0.0778925	+	0.116574i
$136$	1.08012	+	11.1529i	0.0926195	+	0.956355i
$137$	9.57096	−	6.39511i	0.817702	−	0.546371i	−0.0749132	−	0.997190i	$-0.523868\pi$
$137$	9.57096	−	6.39511i	0.817702	−	0.546371i	0.892615	+	0.450819i	$0.148868\pi$
$138$	2.20665	+	8.25326i	0.187843	+	0.702564i
$139$	8.32464	−	4.44961i	0.706086	−	0.377411i	−0.0789350	−	0.996880i	$-0.525152\pi$
$139$	8.32464	−	4.44961i	0.706086	−	0.377411i	0.785021	+	0.619469i	$0.212652\pi$
$140$	−15.4179	−	2.56272i	−1.30305	−	0.216589i
$141$	3.33057	+	0.328032i	0.280484	+	0.0276253i
$142$	0.186922	−	0.411950i	0.0156861	−	0.0345701i
$143$	28.6691	−	11.8751i	2.39743	−	0.993049i
$144$	−1.29398	+	3.78492i	−0.107832	+	0.315410i
$145$	2.72285	+	1.12784i	0.226120	+	0.0936621i
$146$	−2.97996	+	2.78800i	−0.246623	+	0.230737i
$147$	12.3785	−	10.1588i	1.02096	−	0.837882i
$148$	0.607081	−	1.60768i	0.0499018	−	0.132150i
$149$	−8.54505	−	2.59211i	−0.700038	−	0.212354i	−0.0798493	−	0.996807i	$-0.525444\pi$
$149$	−8.54505	−	2.59211i	−0.700038	−	0.212354i	−0.620188	+	0.784453i	$0.712944\pi$
$150$	2.63361	−	2.01857i	0.215033	−	0.164815i
$151$	−1.04701	+	5.26365i	−0.0852041	+	0.428350i	0.914513	+	0.404557i	$0.132574\pi$
$151$	−1.04701	+	5.26365i	−0.0852041	+	0.428350i	−0.999717	+	0.0237930i	$0.992426\pi$
$152$	−12.3326	−	5.13189i	−1.00031	−	0.416251i
$153$	−3.88548	+	0.772870i	−0.314123	+	0.0624829i
$154$	30.6882	−	1.99467i	2.47292	−	0.160735i
$155$	3.23694	+	2.65649i	0.259997	+	0.213374i
$156$	−6.83282	−	11.8645i	−0.547063	−	0.949923i
$157$	3.75258	−	7.02059i	0.299489	−	0.560304i	−0.686497	−	0.727132i	$-0.740853\pi$
$157$	3.75258	−	7.02059i	0.299489	−	0.560304i	0.985986	+	0.166828i	$0.0533526\pi$
$158$	−1.50513	+	0.934817i	−0.119742	+	0.0743700i
$159$	−1.73281	+	1.73281i	−0.137421	+	0.137421i
$160$	−5.62961	+	7.29554i	−0.445060	+	0.576763i
$161$	−20.4917	−	20.4917i	−1.61498	−	1.61498i
$162$	−1.37710	−	0.321882i	−0.108195	−	0.0252895i
$163$	−0.432499	−	0.231176i	−0.0338759	−	0.0181071i	0.454372	−	0.890812i	$-0.349864\pi$
$163$	−0.432499	−	0.231176i	−0.0338759	−	0.0181071i	−0.488248	+	0.872705i	$0.662364\pi$
$164$	4.88591	−	0.637844i	0.381526	−	0.0498072i
$165$	4.68450	−	5.70808i	0.364688	−	0.444373i
$166$	−0.276333	+	0.314753i	−0.0214476	+	0.0244296i
$167$	−2.94345	−	14.7977i	−0.227771	−	1.14508i	−0.910213	−	0.414141i	$-0.864082\pi$
$167$	−2.94345	−	14.7977i	−0.227771	−	1.14508i	0.682442	−	0.730940i	$-0.260918\pi$
$168$	−2.62541	−	13.3122i	−0.202555	−	1.02706i
$169$	33.2129	+	6.60646i	2.55484	+	0.508190i
$170$	−9.04788	−	1.19618i	−0.693941	−	0.0917425i
$171$	1.37092	−	4.51932i	0.104837	−	0.345601i
$172$	0.131759	+	4.16312i	0.0100465	+	0.317435i
$173$	−0.904465	−	1.10209i	−0.0687652	−	0.0837906i	0.737492	−	0.675356i	$-0.236010\pi$
$173$	−0.904465	−	1.10209i	−0.0687652	−	0.0837906i	−0.806257	+	0.591566i	$0.798510\pi$
$174$	−0.0851036	+	2.55717i	−0.00645168	+	0.193859i
$175$	−4.30744	+	10.3991i	−0.325612	+	0.786096i
$176$	7.51899	−	16.4993i	0.566765	−	1.24368i
$177$	2.88915	+	6.97503i	0.217162	+	0.524275i
$178$	−19.8114	+	7.44421i	−1.48493	+	0.557967i
$179$	0.408240	−	4.14493i	0.0305133	−	0.309807i	−0.967799	−	0.251726i	$-0.919002\pi$
$179$	0.408240	−	4.14493i	0.0305133	−	0.309807i	0.998312	−	0.0580808i	$-0.0184981\pi$
$180$	−2.76485	−	1.72346i	−0.206079	−	0.128459i
$181$	−0.715809	−	1.33918i	−0.0532057	−	0.0995408i	0.853913	−	0.520416i	$-0.174223\pi$
$181$	−0.715809	−	1.33918i	−0.0532057	−	0.0995408i	−0.907119	+	0.420875i	$0.861723\pi$
$182$	40.2085	+	23.2435i	2.98045	+	1.72292i
$183$	−6.94182	−	10.3892i	−0.513154	−	0.767989i
$184$	−16.3587	+	4.93325i	−1.20598	+	0.363684i
$185$	1.16382	+	0.777637i	0.0855654	+	0.0571730i
$186$	−1.17040	+	3.44174i	−0.0858179	+	0.252361i
$187$	17.8713	−	1.76017i	1.30688	−	0.128716i
$188$	−0.445022	+	6.67855i	−0.0324566	+	0.487083i
$189$	4.59066	−	1.39256i	0.333921	−	0.101294i
$190$	6.34212	−	8.84027i	0.460106	−	0.641341i
$191$		−	15.3004i		−	1.10710i	−0.832816	−	0.553549i	$-0.813273\pi$
$191$		−	15.3004i		−	1.10710i	0.832816	−	0.553549i	$-0.186727\pi$
$192$	−7.64791	−	2.34721i	−0.551941	−	0.169396i
$193$			6.82274i			0.491112i	0.969382	+	0.245556i	$0.0789705\pi$
$193$			6.82274i			0.491112i	−0.969382	+	0.245556i	$0.921030\pi$
$194$	13.6267	+	9.77596i	0.978340	+	0.701873i
$195$	10.6715	−	3.23717i	0.764203	−	0.231819i
$196$	21.0905	+	24.1019i	1.50647	+	1.72157i
$197$	−15.8012	+	1.55628i	−1.12579	+	0.110880i	−0.643725	−	0.765257i	$-0.722612\pi$
$197$	−15.8012	+	1.55628i	−1.12579	+	0.110880i	−0.482062	+	0.876137i	$0.660112\pi$
$198$	6.06923	+	2.06390i	0.431322	+	0.146675i
$199$	−11.5779	−	7.73607i	−0.820732	−	0.548396i	0.0728252	−	0.997345i	$-0.476798\pi$
$199$	−11.5779	−	7.73607i	−0.820732	−	0.548396i	−0.893557	+	0.448949i	$0.851798\pi$
$200$	4.20174	+	5.13688i	0.297108	+	0.363232i
$201$	4.69209	+	7.02220i	0.330954	+	0.495308i
$202$	10.6179	−	18.3676i	0.747070	−	1.29234i
$203$	−4.09130	−	7.65429i	−0.287153	−	0.537226i
$204$	−1.79079	−	7.71818i	−0.125380	−	0.540380i
$205$	−0.393379	+	3.99404i	−0.0274748	+	0.278956i
$206$	−6.33695	−	16.8646i	−0.441516	−	1.17502i
$207$	−2.31176	−	5.58109i	−0.160679	−	0.387913i
$208$	23.2849	−	14.4094i	1.61452	−	0.999114i
$209$	−8.19235	+	19.7781i	−0.566677	+	1.36808i
$210$	11.0456	+	0.367601i	0.762217	+	0.0253669i
$211$	15.3079	+	18.6527i	1.05384	+	1.28411i	0.957399	+	0.288770i	$0.0932462\pi$
$211$	15.3079	+	18.6527i	1.05384	+	1.28411i	0.0964418	+	0.995339i	$0.469254\pi$
$212$	−3.57351	−	3.35426i	−0.245430	−	0.230371i
$213$	−0.0928555	+	0.306103i	−0.00636235	+	0.0209739i
$214$	−2.48822	+	18.8209i	−0.170091	+	1.28657i
$215$	−3.32739	−	0.661859i	−0.226926	−	0.0451384i
$216$	0.556318	−	2.77318i	0.0378527	−	0.188691i
$217$	−2.40576	−	12.0946i	−0.163313	−	0.821032i
$218$	1.35667	+	1.19107i	0.0918852	+	0.0806695i
$219$	1.83059	−	2.23058i	0.123700	−	0.150729i
$220$	11.7068	+	9.00318i	0.789273	+	0.606994i
$221$	23.9177	+	12.7843i	1.60888	+	0.859962i
$222$	−0.276574	+	1.18326i	−0.0185624	+	0.0794149i
$223$	−18.6402	−	18.6402i	−1.24824	−	1.24824i	−0.956497	−	0.291744i	$-0.905765\pi$
$223$	−18.6402	−	18.6402i	−1.24824	−	1.24824i	−0.291744	−	0.956497i	$-0.594235\pi$
$224$	26.4449	−	6.09042i	1.76693	−	0.406933i
$225$	−1.65911	+	1.65911i	−0.110607	+	0.110607i
$226$	−8.80725	−	14.1804i	−0.585850	−	0.943265i
$227$	5.62182	−	10.5177i	0.373133	−	0.698083i	−0.623344	−	0.781948i	$-0.714226\pi$
$227$	5.62182	−	10.5177i	0.373133	−	0.698083i	0.996477	+	0.0838647i	$0.0267264\pi$
$228$	9.12084	+	2.45454i	0.604042	+	0.162556i
$229$	16.0525	+	13.1739i	1.06078	+	0.870559i	0.991894	−	0.127066i	$-0.0405559\pi$
$229$	16.0525	+	13.1739i	1.06078	+	0.870559i	0.0688850	+	0.997625i	$0.478056\pi$
$230$	−0.902665	−	13.8876i	−0.0595200	−	0.915720i
$231$	−21.3278	+	4.24236i	−1.40326	+	0.279127i
$232$	−5.11716	−	0.00833852i	−0.335958	−	0.000547451i
$233$	0.890203	−	4.47535i	0.0583191	−	0.293190i	−0.940608	−	0.339494i	$-0.889744\pi$
$233$	0.890203	−	4.47535i	0.0583191	−	0.293190i	0.998927	+	0.0463038i	$0.0147442\pi$
$234$	5.88942	+	7.68388i	0.385003	+	0.502311i
$235$	−5.21702	−	1.58257i	−0.340321	−	0.103235i
$236$	−13.7603	+	6.21670i	−0.895718	+	0.404672i
$237$	0.968471	−	0.794804i	0.0629090	−	0.0516281i
$238$	18.3621	+	19.6263i	1.19024	+	1.27219i
$239$	12.9555	+	5.36632i	0.838019	+	0.347119i	0.760072	−	0.649839i	$-0.225164\pi$
$239$	12.9555	+	5.36632i	0.838019	+	0.347119i	0.0779466	+	0.996958i	$0.475164\pi$
$240$	3.27027	−	5.63596i	0.211095	−	0.363800i
$241$	−13.1501	+	5.44696i	−0.847074	+	0.350869i	−0.763639	−	0.645644i	$-0.776589\pi$
$241$	−13.1501	+	5.44696i	−0.847074	+	0.350869i	−0.0834349	+	0.996513i	$0.526589\pi$
$242$	−12.2958	−	5.57922i	−0.790406	−	0.358646i
$243$	0.995185	+	0.0980171i	0.0638411	+	0.00628780i
$244$	20.3288	−	14.5340i	1.30141	−	0.930443i
$245$	−23.0058	+	12.2968i	−1.46978	+	0.785616i
$246$	−3.36595	+	0.899944i	−0.214605	+	0.0573783i
$247$	−26.8814	+	17.9616i	−1.71042	+	1.14287i
$248$	−6.95409	−	2.12188i	−0.441585	−	0.134740i
$249$	0.164541	−	0.246254i	0.0104274	−	0.0156057i
$250$	−15.1829	+	7.47715i	−0.960254	+	0.472896i
$251$	−0.151544	−	1.53865i	−0.00956539	−	0.0971190i	0.989217	−	0.146460i	$-0.0467879\pi$
$251$	−0.151544	−	1.53865i	−0.00956539	−	0.0971190i	−0.998782	+	0.0493409i	$0.984288\pi$
$252$	3.07416	+	9.08862i	0.193654	+	0.572529i
$253$	7.94894	+	26.2041i	0.499745	+	1.64744i
$254$	4.21541	+	25.6189i	0.264498	+	1.60748i
$255$	6.45349			0.404133
$256$	4.20822	−	15.4367i	0.263014	−	0.964792i
$257$	−0.597096			−0.0372458			−0.0186229	−	0.999827i	$-0.505928\pi$
$257$	−0.597096			−0.0372458			−0.0186229	+	0.999827i	$0.505928\pi$
$258$	−0.478189	−	2.90617i	−0.0297707	−	0.180930i
$259$	−1.19654	−	3.94448i	−0.0743496	−	0.245098i
$260$	7.14625	+	21.1276i	0.443192	+	1.31028i
$261$	−0.177332	−	1.80048i	−0.0109766	−	0.111447i
$262$	2.78386	−	1.37097i	0.171987	−	0.0846986i
$263$	10.3191	−	15.4437i	0.636306	−	0.952299i	−0.363480	−	0.931602i	$-0.618411\pi$
$263$	10.3191	−	15.4437i	0.636306	−	0.952299i	0.999786	−	0.0206970i	$-0.00658853\pi$
$264$	−3.74176	+	12.2630i	−0.230290	+	0.754734i
$265$	3.31922	−	2.21783i	0.203898	−	0.136240i
$266$	−30.9528	+	8.27576i	−1.89784	+	0.507419i
$267$	13.1980	−	7.05450i	0.807707	−	0.431728i
$268$	−13.7405	+	9.82374i	−0.839336	+	0.600081i
$269$	−20.8719	−	2.05571i	−1.27258	−	0.125339i	−0.560927	−	0.827865i	$-0.689555\pi$
$269$	−20.8719	−	2.05571i	−1.27258	−	0.125339i	−0.711657	+	0.702527i	$0.752055\pi$
$270$	2.09790	+	0.951920i	0.127674	+	0.0579320i
$271$	−9.42446	+	3.90374i	−0.572495	+	0.237135i	−0.650100	−	0.759849i	$-0.725273\pi$
$271$	−9.42446	+	3.90374i	−0.572495	+	0.237135i	0.0776046	+	0.996984i	$0.475273\pi$
$272$	15.3153	−	4.06809i	0.928628	−	0.246664i
$273$	−30.3406	−	12.5675i	−1.83629	−	0.760618i
$274$	−11.1217	−	11.8874i	−0.671884	−	0.718144i
$275$	8.22158	−	6.74728i	0.495780	−	0.406876i
$276$	11.0103	−	4.97431i	0.662744	−	0.299418i
$277$	−8.58630	−	2.60463i	−0.515901	−	0.156497i	0.0215891	−	0.999767i	$-0.493127\pi$
$277$	−8.58630	−	2.60463i	−0.515901	−	0.156497i	−0.537490	+	0.843270i	$0.680627\pi$
$278$	−8.12063	−	10.5949i	−0.487043	−	0.635441i
$279$	0.501489	−	2.52116i	0.0300234	−	0.150938i
$280$	−0.0360179	+	22.1034i	−0.00215248	+	1.32093i
$281$	19.0300	−	3.78530i	1.13524	−	0.225812i	0.408519	−	0.912750i	$-0.366045\pi$
$281$	19.0300	−	3.78530i	1.13524	−	0.225812i	0.726716	+	0.686938i	$0.241045\pi$
$282$	−0.306983	−	4.72296i	−0.0182805	−	0.281248i
$283$	−18.4339	−	15.1283i	−1.09578	−	0.899284i	−0.100367	−	0.994950i	$-0.532002\pi$
$283$	−18.4339	−	15.1283i	−1.09578	−	0.899284i	−0.995413	+	0.0956663i	$0.969502\pi$
$284$	−0.617775	−	0.166252i	−0.0366582	−	0.00986523i
$285$	−3.62658	+	6.78486i	−0.214820	+	0.401901i
$286$	−23.1539	−	37.2796i	−1.36912	−	2.20439i
$287$	8.35720	−	8.35720i	0.493310	−	0.493310i
$288$	5.57877	+	0.936631i	0.328732	+	0.0551915i
$289$	−0.923275	−	0.923275i	−0.0543103	−	0.0543103i
$290$	0.948649	−	4.05856i	0.0557066	−	0.238327i
$291$	−10.4584	−	5.59014i	−0.613083	−	0.327700i
$292$	4.57474	+	3.51823i	0.267717	+	0.205889i
$293$	17.4578	−	21.2724i	1.01990	−	1.24275i	0.0501223	−	0.998743i	$-0.484039\pi$
$293$	17.4578	−	21.2724i	1.01990	−	1.24275i	0.969774	−	0.244004i	$-0.0784611\pi$
$294$	−17.0183	−	14.9410i	−0.992528	−	0.871378i
$295$	−2.39933	−	12.0622i	−0.139694	−	0.702291i
$296$	−2.38282	−	0.478011i	−0.138499	−	0.0277838i
$297$	−4.44585	−	0.884335i	−0.257975	−	0.0513143i
$298$	−1.65512	+	12.5194i	−0.0958787	+	0.725227i
$299$	−12.0045	+	39.5737i	−0.694241	+	2.28861i
$300$	−3.42152	−	3.21158i	−0.197541	−	0.185421i
$301$	6.33804	+	7.72293i	0.365319	+	0.445142i
$302$	7.58557	+	0.252450i	0.436500	+	0.0145269i
$303$	−5.74095	+	13.8599i	−0.329809	+	0.796229i
$304$	−4.32959	+	18.3878i	−0.248319	+	1.05462i
$305$	7.78928	+	18.8050i	0.446013	+	1.07677i
$306$	1.97065	+	5.24453i	0.112655	+	0.299810i
$307$	−1.73227	+	17.5881i	−0.0988661	+	1.00380i	0.809920	+	0.586541i	$0.199511\pi$
$307$	−1.73227	+	17.5881i	−0.0988661	+	1.00380i	−0.908786	+	0.417263i	$0.862989\pi$
$308$	−9.82980	−	42.3658i	−0.560105	−	2.41401i
$309$	6.00521	+	11.2349i	0.341624	+	0.639134i
$310$	2.96376	−	5.12694i	0.168330	−	0.291191i
$311$	15.9755	+	23.9090i	0.905885	+	1.35575i	0.934425	+	0.356160i	$0.115914\pi$
$311$	15.9755	+	23.9090i	0.905885	+	1.35575i	−0.0285395	+	0.999593i	$0.509086\pi$
$312$	−14.9875	+	12.2591i	−0.848498	+	0.694033i
$313$	9.17356	+	6.12957i	0.518520	+	0.346464i	0.787132	−	0.616784i	$-0.211565\pi$
$313$	9.17356	+	6.12957i	0.518520	+	0.346464i	−0.268612	+	0.963248i	$0.586565\pi$
$314$	−10.6585	−	3.62453i	−0.601494	−	0.204544i
$315$	−7.77710	+	0.765977i	−0.438190	+	0.0431579i
$316$	1.65008	+	1.88569i	0.0928245	+	0.106078i
$317$	26.2393	−	7.95959i	1.47374	−	0.447055i	0.551667	−	0.834064i	$-0.313992\pi$
$317$	26.2393	−	7.95959i	1.47374	−	0.447055i	0.922076	+	0.387009i	$0.126492\pi$
$318$	2.81592	+	2.02018i	0.157909	+	0.113286i
$319$			8.20098i			0.459167i
$320$	11.4732	+	6.18070i	0.641370	+	0.345512i
$321$		−	13.4242i		−	0.749265i
$322$	−23.8901	+	33.3003i	−1.33134	+	1.85575i
$323$	−17.9037	+	5.43104i	−0.996190	+	0.302191i
$324$	−0.132974	+	1.99557i	−0.00738746	+	0.110865i
$325$	15.9849	−	1.57438i	0.886684	−	0.0873308i
$326$	−0.223287	+	0.656611i	−0.0123667	+	0.0363663i
$327$	−1.06142	−	0.709217i	−0.0586966	−	0.0392198i
$328$	−2.01194	−	6.67159i	−0.111091	−	0.368377i
$329$	8.91956	+	13.3491i	0.491751	+	0.735958i
$330$	−9.04095	−	5.22634i	−0.497688	−	0.287701i
$331$	−6.63929	−	12.4212i	−0.364929	−	0.682733i	0.630711	−	0.776018i	$-0.282763\pi$
$331$	−6.63929	−	12.4212i	−0.364929	−	0.682733i	−0.995639	+	0.0932846i	$0.970263\pi$
$332$	0.502671	+	0.313339i	0.0275877	+	0.0171967i
$333$	0.0842202	−	0.855102i	0.00461524	−	0.0468593i
$334$	−19.9736	+	7.50515i	−1.09291	+	0.410663i
$335$	−5.26490	−	12.7106i	−0.287652	−	0.694454i
$336$	−17.9737	+	6.72026i	−0.980543	+	0.366620i
$337$	−4.83897	+	11.6823i	−0.263596	+	0.636376i	−0.999156	−	0.0410834i	$-0.986919\pi$
$337$	−4.83897	+	11.6823i	−0.263596	+	0.636376i	0.735560	+	0.677459i	$0.236919\pi$
$338$	1.59293	−	47.8639i	0.0866439	−	2.60345i
$339$	7.48814	+	9.12433i	0.406700	+	0.495565i
$340$	0.408290	+	12.9005i	0.0221426	+	0.699629i
$341$	−3.38245	+	11.1504i	−0.183170	+	0.603830i
$342$	−6.62125	−	0.875364i	−0.358036	−	0.0473342i
$343$	42.4084	+	8.43556i	2.28984	+	0.455477i
$344$	5.77917	−	1.13976i	0.311592	−	0.0614518i
$345$	1.91983	+	9.65164i	0.103360	+	0.519627i
$346$	−1.33024	+	1.51519i	−0.0715142	+	0.0814570i
$347$	7.65700	−	9.33008i	0.411049	−	0.500865i	−0.525795	−	0.850611i	$-0.676232\pi$
$347$	7.65700	−	9.33008i	0.411049	−	0.500865i	0.936845	+	0.349746i	$0.113732\pi$
$348$	3.58794	−	0.468397i	0.192334	−	0.0251087i
$349$	−2.41604	−	1.29140i	−0.129328	−	0.0691271i	0.405464	−	0.914111i	$-0.367110\pi$
$349$	−2.41604	−	1.29140i	−0.129328	−	0.0691271i	−0.534792	+	0.844984i	$0.679610\pi$
$350$	15.5004	+	3.62307i	0.828532	+	0.193661i
$351$	−4.84064	−	4.84064i	−0.258374	−	0.258374i
$352$	−24.7504	−	6.70395i	−1.31920	−	0.357321i
$353$	−5.99949	+	5.99949i	−0.319320	+	0.319320i	−0.848506	−	0.529186i	$-0.822498\pi$
$353$	−5.99949	+	5.99949i	−0.319320	+	0.319320i	0.529186	+	0.848506i	$0.322498\pi$
$354$	9.06992	−	5.63321i	0.482061	−	0.299402i
$355$	0.245637	−	0.459554i	0.0130370	−	0.0243906i
$356$	14.9369	+	25.9366i	0.791656	+	1.37463i
$357$	−14.6908	−	12.0565i	−0.777521	−	0.638095i
$358$	−5.87778	+	0.382044i	−0.310650	+	0.0201916i
$359$	−20.0222	+	3.98267i	−1.05673	+	0.210197i	−0.692728	−	0.721199i	$-0.743591\pi$
$359$	−20.0222	+	3.98267i	−1.05673	+	0.210197i	−0.364006	+	0.931397i	$0.618591\pi$
$360$	−1.77016	+	4.25393i	−0.0932957	+	0.224202i
$361$	0.644506	−	3.24015i	0.0339214	−	0.170534i
$362$	−1.70441	+	1.30637i	−0.0895816	+	0.0686611i
$363$	9.13653	+	2.77154i	0.479544	+	0.145468i
$364$	23.2028	−	61.4458i	1.21616	−	3.22064i
$365$	−3.63364	+	2.98205i	−0.190193	+	0.156088i
$366$	−12.9036	+	12.0724i	−0.674484	+	0.631036i
$367$	0.791209	+	0.327729i	0.0413008	+	0.0171073i	0.403238	−	0.915095i	$-0.367885\pi$
$367$	0.791209	+	0.327729i	0.0413008	+	0.0171073i	−0.361937	+	0.932202i	$0.617885\pi$
$368$	10.6402	+	21.6949i	0.554660	+	1.13093i
$369$	2.27615	−	0.942812i	0.118492	−	0.0490808i
$370$	0.817928	−	1.80260i	0.0425220	−	0.0937127i
$371$	−11.6993	−	1.15228i	−0.607397	−	0.0598234i
$372$	5.07151	+	0.842971i	0.262946	+	0.0437060i
$373$	24.5720	−	13.1340i	1.27229	−	0.680054i	0.309654	−	0.950849i	$-0.399787\pi$
$373$	24.5720	−	13.1340i	1.27229	−	0.680054i	0.962637	+	0.270795i	$0.0872867\pi$
$374$	−6.55967	−	24.5343i	−0.339192	−	1.26864i
$375$	9.95039	−	6.64864i	0.513836	−	0.343334i
$376$	9.42176	−	0.912463i	0.485890	−	0.0470567i
$377$	−6.88085	+	10.2979i	−0.354382	+	0.530369i
$378$	−2.99732	−	6.08629i	−0.154165	−	0.313045i
$379$	−2.15822	−	21.9127i	−0.110860	−	1.12558i	−0.876198	−	0.481952i	$-0.839928\pi$
$379$	−2.15822	−	21.9127i	−0.110860	−	1.12558i	0.765338	−	0.643629i	$-0.222572\pi$
$380$	−13.7924	−	6.82028i	−0.707534	−	0.349873i
$381$	−5.32931	−	17.5684i	−0.273029	−	0.900056i
$382$	−21.3509	+	3.51314i	−1.09241	+	0.179748i
$383$	−9.20089			−0.470143			−0.235072	−	0.971978i	$-0.575533\pi$
$383$	−9.20089			−0.470143			−0.235072	+	0.971978i	$0.575533\pi$
$384$	−1.51937	+	11.2112i	−0.0775352	+	0.572120i
$385$	35.4238			1.80536
$386$	9.52079	−	1.56658i	0.484596	−	0.0797367i
$387$	0.604548	+	1.99293i	0.0307309	+	0.101306i
$388$	10.5130	−	21.2600i	0.533717	−	1.07931i
$389$	1.21153	+	12.3009i	0.0614272	+	0.623681i	0.975779	+	0.218760i	$0.0702011\pi$
$389$	1.21153	+	12.3009i	0.0614272	+	0.623681i	−0.914352	+	0.404921i	$0.867299\pi$
$390$	−6.96761	−	14.1483i	−0.352818	−	0.716426i
$391$	−13.2958	+	19.8985i	−0.672396	+	1.00631i
$392$	28.7904	−	34.9649i	1.45413	−	1.76599i
$393$	−1.82445	+	1.21906i	−0.0920312	+	0.0614933i
$394$	5.79984	+	21.6924i	0.292192	+	1.09285i
$395$	−1.79993	+	0.962081i	−0.0905641	+	0.0484075i
$396$	1.48651	−	8.94320i	0.0747000	−	0.449413i
$397$	−10.9149	−	1.07502i	−0.547803	−	0.0539539i	−0.179670	−	0.983727i	$-0.557503\pi$
$397$	−10.9149	−	1.07502i	−0.547803	−	0.0539539i	−0.368133	+	0.929773i	$0.620003\pi$
$398$	−8.13690	+	17.9326i	−0.407866	+	0.898880i
$399$	20.9312	−	8.66997i	1.04787	−	0.434041i
$400$	6.20349	−	7.04279i	0.310174	−	0.352140i
$401$	−33.3398	−	13.8098i	−1.66491	−	0.689628i	−0.666474	−	0.745528i	$-0.732197\pi$
$401$	−33.3398	−	13.8098i	−1.66491	−	0.689628i	−0.998436	+	0.0558999i	$0.982197\pi$
$402$	8.72177	−	8.15994i	0.435002	−	0.406981i
$403$	−13.6028	+	11.1635i	−0.677605	+	0.556096i
$404$	−28.0691	−	10.5993i	−1.39649	−	0.527334i
$405$	−1.55886	−	0.472876i	−0.0774606	−	0.0234974i
$406$	−9.74177	+	7.46672i	−0.483476	+	0.370567i
$407$	−0.759856	+	3.82005i	−0.0376647	+	0.189353i
$408$	−10.3591	+	4.27113i	−0.512854	+	0.211453i
$409$	−33.1458	+	6.59310i	−1.63895	+	0.326008i	−0.926667	−	0.375883i	$-0.877340\pi$
$409$	−33.1458	+	6.59310i	−1.63895	+	0.326008i	−0.712285	+	0.701890i	$0.752340\pi$
$410$	5.66381	−	0.368136i	0.279716	−	0.0181809i
$411$	8.89804	+	7.30243i	0.438908	+	0.360203i
$412$	−22.0787	+	12.7152i	−1.08774	+	0.626433i
$413$	−17.0729	+	31.9412i	−0.840103	+	1.57172i
$414$	−7.25732	+	4.50743i	−0.356678	+	0.221528i
$415$	−0.341150	+	0.341150i	−0.0167464	+	0.0167464i
$416$	−25.4541	−	29.1843i	−1.24799	−	1.43088i
$417$	6.67453	+	6.67453i	0.326853	+	0.326853i
$418$	29.4804	+	6.89074i	1.44193	+	0.337037i
$419$	−24.8930	−	13.3056i	−1.21610	−	0.650020i	−0.266608	−	0.963805i	$-0.585903\pi$
$419$	−24.8930	−	13.3056i	−1.21610	−	0.650020i	−0.949494	+	0.313785i	$0.898403\pi$
$420$	−2.02322	−	15.4979i	−0.0987229	−	0.756222i
$421$	12.0089	−	14.6328i	0.585276	−	0.713161i	−0.393216	−	0.919446i	$-0.628638\pi$
$421$	12.0089	−	14.6328i	0.585276	−	0.713161i	0.978492	+	0.206285i	$0.0661375\pi$
$422$	22.5141	−	25.6443i	1.09597	−	1.24834i
$423$	0.652905	+	3.28238i	0.0317453	+	0.159595i
$424$	−3.86018	+	5.75683i	−0.187467	+	0.279576i
$425$	9.11662	+	1.81341i	0.442221	+	0.0879632i
$426$	0.448472	+	0.0592904i	0.0217286	+	0.00287263i
$427$	17.4000	−	57.3600i	0.842044	−	2.77585i
$428$	26.8349	−	0.849303i	1.29712	−	0.0410526i
$429$	19.6860	+	23.9875i	0.950449	+	1.15813i
$430$	−0.159585	+	4.79518i	−0.00769588	+	0.231244i
$431$	2.66732	−	6.43948i	0.128480	−	0.310179i	−0.846529	−	0.532342i	$-0.821312\pi$
$431$	2.66732	−	6.43948i	0.128480	−	0.310179i	0.975009	+	0.222164i	$0.0713119\pi$
$432$	−3.99756	−	0.139562i	−0.192333	−	0.00671469i
$433$	13.5526	+	32.7189i	0.651297	+	1.57237i	0.810898	+	0.585188i	$0.198979\pi$
$433$	13.5526	+	32.7189i	0.651297	+	1.57237i	−0.159601	+	0.987182i	$0.551021\pi$
$434$	−16.3249	+	6.13415i	−0.783623	+	0.294449i
$435$	−0.288875	+	2.93300i	−0.0138505	+	0.140627i
$436$	1.35057	−	2.16664i	0.0646807	−	0.103763i
$437$	−13.4486	−	25.1606i	−0.643335	−	1.20360i
$438$	−3.53299	−	2.04233i	−0.168813	−	0.0975863i
$439$	−3.39594	−	5.08238i	−0.162079	−	0.242569i	0.741537	−	0.670912i	$-0.234097\pi$
$439$	−3.39594	−	5.08238i	−0.162079	−	0.242569i	−0.903616	+	0.428344i	$0.859097\pi$
$440$	9.87547	−	18.4035i	0.470794	−	0.877352i
$441$	13.3146	+	8.89656i	0.634031	+	0.423646i
$442$	12.3480	−	36.3113i	0.587335	−	1.72715i
$443$	−38.7782	+	3.81932i	−1.84241	+	0.181461i	−0.958289	−	0.285802i	$-0.907740\pi$
$443$	−38.7782	+	3.81932i	−1.84241	+	0.181461i	−0.884118	+	0.467264i	$0.845240\pi$
$444$	1.71468	+	0.114257i	0.0813750	+	0.00542239i
$445$	−23.3286	+	7.07664i	−1.10588	+	0.335465i
$446$	−21.7315	+	30.2915i	−1.02901	+	1.43434i
$447$		−	8.92955i		−	0.422353i
$448$	−14.5709	−	35.5042i	−0.688411	−	1.67741i
$449$		−	7.70267i		−	0.363511i	−0.983344	−	0.181756i	$-0.941822\pi$
$449$		−	7.70267i		−	0.363511i	0.983344	−	0.181756i	$-0.0581780\pi$
$450$	2.69615	+	1.93425i	0.127098	+	0.0911814i
$451$	−10.6869	+	3.24183i	−0.503226	+	0.152652i
$452$	−17.7658	+	15.5461i	−0.835632	+	0.731225i
$453$	−5.34093	+	0.526036i	−0.250939	+	0.0247153i
$454$	−15.9677	−	5.42999i	−0.749402	−	0.254842i
$455$	44.4814	+	29.7215i	2.08532	+	1.39337i
$456$	1.33095	−	13.2913i	0.0623273	−	0.622420i
$457$	−7.03703	−	10.5317i	−0.329178	−	0.492650i	0.629555	−	0.776956i	$-0.283237\pi$
$457$	−7.03703	−	10.5317i	−0.329178	−	0.492650i	−0.958734	+	0.284305i	$0.908237\pi$
$458$	14.6977	−	25.4253i	0.686781	−	1.18805i
$459$	−1.86749	−	3.49382i	−0.0871668	−	0.163078i
$460$	−19.1722	+	4.44837i	−0.893907	+	0.207406i
$461$	−2.95102	+	29.9622i	−0.137443	+	1.39548i	0.640892	+	0.767631i	$0.278565\pi$
$461$	−2.95102	+	29.9622i	−0.137443	+	1.39548i	−0.778335	+	0.627849i	$0.783935\pi$
$462$	10.8171	+	28.7877i	0.503256	+	1.33933i
$463$	−2.27140	−	5.48364i	−0.105561	−	0.254846i	0.862270	−	0.506449i	$-0.169042\pi$
$463$	−2.27140	−	5.48364i	−0.105561	−	0.254846i	−0.967831	+	0.251603i	$0.919042\pi$
$464$	1.16332	+	7.14266i	0.0540058	+	0.331590i
$465$	−1.60247	+	3.86869i	−0.0743126	+	0.179406i
$466$	−6.44953	−	0.214643i	−0.298769	−	0.00994313i
$467$	18.3590	+	22.3705i	0.849554	+	1.03518i	0.998923	+	0.0464031i	$0.0147759\pi$
$467$	18.3590	+	22.3705i	0.849554	+	1.03518i	−0.149369	+	0.988782i	$0.547724\pi$
$468$	9.37019	−	9.98269i	0.433137	−	0.461450i
$469$	−11.7609	+	38.7706i	−0.543069	+	1.79026i
$470$	−1.01051	+	7.64347i	−0.0466111	+	0.352567i
$471$	7.80760	+	1.55303i	0.359755	+	0.0715598i
$472$	11.8346	+	17.7744i	0.544732	+	0.818131i
$473$	−1.84172	−	9.25894i	−0.0846823	−	0.425727i
$474$	−1.33148	−	1.16896i	−0.0611569	−	0.0536920i
$475$	−7.02968	+	8.56569i	−0.322544	+	0.393021i
$476$	23.1714	−	30.1297i	1.06206	−	1.38099i
$477$	−2.16120	−	1.15519i	−0.0989547	−	0.0528924i
$478$	4.51372	−	19.3108i	0.206453	−	0.883257i
$479$	−22.0116	−	22.0116i	−1.00574	−	1.00574i	−0.999983	−	0.00575333i	$-0.998169\pi$
$479$	−22.0116	−	22.0116i	−1.00574	−	1.00574i	−0.00575333	−	0.999983i	$-0.501831\pi$
$480$	−8.61559	−	3.26942i	−0.393246	−	0.149228i
$481$	−4.15927	+	4.15927i	−0.189646	+	0.189646i
$482$	10.6204	+	17.0996i	0.483744	+	0.778867i
$483$	13.6609	−	25.5578i	0.621594	−	1.16292i
$484$	−4.96226	+	18.4393i	−0.225557	+	0.838148i
$485$	14.9329	+	12.2551i	0.678069	+	0.556477i
$486$	−0.0917275	−	1.41124i	−0.00416084	−	0.0640149i
$487$	3.55644	−	0.707420i	0.161158	−	0.0320563i	−0.113852	−	0.993498i	$-0.536319\pi$
$487$	3.55644	−	0.707420i	0.161158	−	0.0320563i	0.275010	+	0.961441i	$0.411319\pi$
$488$	−24.9491	−	25.0306i	−1.12939	−	1.13308i
$489$	0.0956734	−	0.480982i	0.00432650	−	0.0217508i
$490$	22.4420	+	29.2799i	1.01383	+	1.32273i
$491$	6.34241	+	1.92395i	0.286229	+	0.0868267i	0.430135	−	0.902765i	$-0.358466\pi$
$491$	6.34241	+	1.92395i	0.286229	+	0.0868267i	−0.143905	+	0.989591i	$0.545966\pi$
$492$	2.02868	+	4.49037i	0.0914602	+	0.202442i
$493$	−5.54040	+	4.54689i	−0.249527	+	0.204782i
$494$	31.2367	+	33.3875i	1.40541	+	1.50217i
$495$	6.82213	+	2.82582i	0.306632	+	0.127011i
$496$	−1.36424	+	10.1913i	−0.0612562	+	0.457602i
$497$	−1.41772	+	0.587237i	−0.0635932	+	0.0263412i
$498$	−0.381415	−	0.173067i	−0.0170916	−	0.00775530i
$499$	10.4654	+	1.03076i	0.468498	+	0.0461430i	0.329512	−	0.944151i	$-0.393116\pi$
$499$	10.4654	+	1.03076i	0.468498	+	0.0461430i	0.138986	+	0.990294i	$0.455616\pi$
$500$	13.9202	+	19.4702i	0.622528	+	0.870733i
$501$	13.3061	−	7.11225i	0.594472	−	0.317752i
$502$	−2.11232	+	0.564764i	−0.0942774	+	0.0252067i
$503$	20.9585	−	14.0040i	0.934493	−	0.624408i	0.00769601	−	0.999970i	$-0.497550\pi$
$503$	20.9585	−	14.0040i	0.934493	−	0.624408i	0.926797	+	0.375562i	$0.122550\pi$
$504$	11.9768	−	6.37669i	0.533491	−	0.284040i
$505$	13.5771	−	20.3195i	0.604172	−	0.904208i
$506$	34.7414	−	17.1091i	1.54444	−	0.760592i
$507$	3.31921	+	33.7006i	0.147412	+	1.49669i
$508$	34.7820	−	11.7648i	1.54320	−	0.521978i
$509$	6.50072	+	21.4300i	0.288139	+	0.949869i	0.974836	+	0.222924i	$0.0715602\pi$
$509$	6.50072	+	21.4300i	0.288139	+	0.949869i	−0.686696	+	0.726944i	$0.740940\pi$
$510$	−1.48179	−	9.00551i	−0.0656148	−	0.398771i
$511$	13.8428			0.612368
$512$	−22.5073	−	2.32793i	−0.994694	−	0.102881i
$513$	4.72267			0.208511
$514$	0.137100	+	0.833217i	0.00604722	+	0.0367516i
$515$	−6.02405	−	19.8586i	−0.265452	−	0.875077i
$516$	−3.94561	+	1.33458i	−0.173696	+	0.0587514i
$517$	−1.48695	−	15.0973i	−0.0653962	−	0.663978i
$518$	−5.22958	+	2.57541i	−0.229775	+	0.113157i
$519$	0.792086	−	1.18544i	0.0347687	−	0.0520350i
$520$	27.8416	−	14.8234i	1.22093	−	0.650047i
$521$	−14.9880	+	10.0146i	−0.656634	+	0.438749i	−0.838742	−	0.544530i	$-0.816708\pi$
$521$	−14.9880	+	10.0146i	−0.656634	+	0.438749i	0.182107	+	0.983279i	$0.441708\pi$
$522$	−2.47176	+	0.660868i	−0.108186	+	0.0289254i
$523$	−7.87185	+	4.20759i	−0.344212	+	0.183985i	−0.634440	−	0.772973i	$-0.718769\pi$
$523$	−7.87185	+	4.20759i	−0.344212	+	0.183985i	0.290227	+	0.956958i	$0.406269\pi$
$524$	−2.55232	−	3.56994i	−0.111499	−	0.155954i
$525$	−11.2017	−	1.10327i	−0.488881	−	0.0481506i
$526$	−23.9203	−	10.8538i	−1.04297	−	0.473248i
$527$	−9.40831	+	3.89705i	−0.409833	+	0.169758i
$528$	17.9715	+	2.40573i	0.782109	+	0.104696i
$529$	−12.4657	−	5.16348i	−0.541989	−	0.224499i
$530$	−3.85700	−	4.12256i	−0.167537	−	0.179073i
$531$	−5.83601	+	4.78949i	−0.253261	+	0.207846i
$532$	18.6555	+	41.2929i	0.808819	+	1.79027i
$533$	−16.1394	−	4.89584i	−0.699076	−	0.212063i
$534$	−12.8746	−	16.7974i	−0.557139	−	0.726895i
$535$	−4.26626	+	21.4479i	−0.184446	+	0.927275i
$536$	16.8635	+	16.9186i	0.728393	+	0.730771i
$537$	4.08496	−	0.812548i	0.176279	−	0.0350641i
$538$	1.92379	+	29.5977i	0.0829406	+	1.27605i
$539$	−56.1112	−	46.0493i	−2.41688	−	1.98348i
$540$	0.846655	−	3.14609i	0.0364342	−	0.135386i
$541$	19.3845	−	36.2658i	0.833403	−	1.55919i	0.00436741	−	0.999990i	$-0.498610\pi$
$541$	19.3845	−	36.2658i	0.833403	−	1.55919i	0.829035	−	0.559196i	$-0.188890\pi$
$542$	7.61143	+	12.2550i	0.326939	+	0.526398i
$543$	1.07373	−	1.07373i	0.0460782	−	0.0460782i
$544$	−9.19338	−	20.4377i	−0.394163	−	0.876259i
$545$	1.47045	+	1.47045i	0.0629870	+	0.0629870i
$546$	−10.5707	+	45.2243i	−0.452386	+	1.93542i
$547$	34.8961	+	18.6523i	1.49205	+	0.797517i	0.997434	−	0.0715954i	$-0.0228090\pi$
$547$	34.8961	+	18.6523i	1.49205	+	0.797517i	0.494615	+	0.869112i	$0.335309\pi$
$548$	−14.0346	+	18.2492i	−0.599529	+	0.779566i
$549$	7.92671	−	9.65872i	0.338304	−	0.412224i
$550$	−11.3033	−	9.92355i	−0.481972	−	0.423142i
$551$	−1.66690	−	8.38005i	−0.0710121	−	0.357002i
$552$	−9.46949	−	14.2222i	−0.403048	−	0.605338i
$553$	5.89475	+	1.17254i	0.250670	+	0.0498614i
$554$	−1.66311	+	12.5798i	−0.0706590	+	0.534465i
$555$	−0.406314	+	1.33944i	−0.0172471	+	0.0568560i
$556$	−12.9201	+	13.7646i	−0.547934	+	0.583751i
$557$	7.89816	+	9.62393i	0.334656	+	0.407779i	0.912965	−	0.408039i	$-0.133787\pi$
$557$	7.89816	+	9.62393i	0.334656	+	0.407779i	−0.578309	+	0.815818i	$0.696287\pi$
$558$	−3.63329	−	0.120917i	−0.153809	−	0.00511884i
$559$	5.45587	−	13.1716i	0.230759	−	0.557101i
$560$	30.8524	−	5.02491i	1.30375	−	0.212341i
$561$	6.87213	+	16.5908i	0.290142	+	0.700464i
$562$	−9.65170	−	25.6863i	−0.407132	−	1.08351i
$563$	−2.73601	+	27.7792i	−0.115309	+	1.17075i	0.747160	+	0.664644i	$0.231417\pi$
$563$	−2.73601	+	27.7792i	−0.115309	+	1.17075i	−0.862469	+	0.506110i	$0.831083\pi$
$564$	−6.52016	+	1.51282i	−0.274548	+	0.0637013i
$565$	−9.06412	−	16.9578i	−0.381330	−	0.713419i
$566$	−16.8782	+	29.1972i	−0.709442	+	1.22725i
$567$	2.66520	+	3.98875i	0.111928	+	0.167512i
$568$	−0.0901480	+	0.900247i	−0.00378253	+	0.0377735i
$569$	−7.34811	−	4.90985i	−0.308049	−	0.205832i	0.391930	−	0.919995i	$-0.371807\pi$
$569$	−7.34811	−	4.90985i	−0.308049	−	0.205832i	−0.699979	+	0.714163i	$0.746807\pi$
$570$	10.3006	+	3.50284i	0.431446	+	0.146718i
$571$	6.82086	−	0.671796i	0.285444	−	0.0281138i	0.0457181	−	0.998954i	$-0.485442\pi$
$571$	6.82086	−	0.671796i	0.285444	−	0.0281138i	0.239726	+	0.970841i	$0.422942\pi$
$572$	−46.7055	+	40.8699i	−1.95285	+	1.70886i
$573$	14.6416	−	4.44148i	0.611661	−	0.185545i
$574$	−13.5810	−	9.74314i	−0.566858	−	0.406671i
$575$			14.1740i			0.591097i
$576$	0.0260723	−	7.99996i	0.00108634	−	0.333332i
$577$		−	5.13038i		−	0.213581i	−0.994282	−	0.106790i	$-0.965943\pi$
$577$		−	5.13038i		−	0.213581i	0.994282	−	0.106790i	$-0.0340573\pi$
$578$	−1.07639	+	1.50038i	−0.0447719	+	0.0624075i
$579$	−6.52896	+	1.98054i	−0.271334	+	0.0823084i
$580$	−5.88134	−	0.391901i	−0.244209	−	0.0162728i
$581$	1.41394	−	0.139261i	0.0586600	−	0.00577751i
$582$	−5.39939	+	15.8777i	−0.223812	+	0.658154i
$583$	9.23620	+	6.17143i	0.382524	+	0.255595i
$584$	3.85910	−	7.19165i	0.159691	−	0.297593i
$585$	6.19556	+	9.27231i	0.256155	+	0.383363i
$586$	−33.6931	−	19.4771i	−1.39185	−	0.804592i
$587$	4.18093	+	7.82196i	0.172565	+	0.322847i	0.953305	−	0.302010i	$-0.0976575\pi$
$587$	4.18093	+	7.82196i	0.172565	+	0.322847i	−0.780740	+	0.624856i	$0.785157\pi$
$588$	−16.9418	+	27.1788i	−0.698670	+	1.12084i
$589$	1.18991	−	12.0814i	0.0490295	−	0.497805i
$590$	−16.2813	+	6.11777i	−0.670292	+	0.251864i
$591$	−6.07611	−	14.6690i	−0.249938	−	0.603403i
$592$	−0.119917	+	3.43487i	−0.00492857	+	0.141172i
$593$	7.00234	−	16.9051i	0.287551	−	0.694211i	−0.712420	−	0.701753i	$-0.752401\pi$
$593$	7.00234	−	16.9051i	0.287551	−	0.694211i	0.999972	+	0.00754264i	$0.00240092\pi$
$594$	−0.213228	+	6.40701i	−0.00874884	+	0.262883i
$595$	19.6401	+	23.9315i	0.805165	+	0.981096i
$596$	17.8502	−	0.564942i	0.731171	−	0.0231409i
$597$	4.04209	−	13.3250i	0.165432	−	0.545355i
$598$	57.9795	+	7.66518i	2.37096	+	0.313453i
$599$	−6.36540	−	1.26616i	−0.260083	−	0.0517338i	0.0633262	−	0.997993i	$-0.479829\pi$
$599$	−6.36540	−	1.26616i	−0.260083	−	0.0517338i	−0.323410	+	0.946259i	$0.604829\pi$
$600$	−3.69599	+	5.51197i	−0.150888	+	0.225025i
$601$	1.14323	+	5.74739i	0.0466332	+	0.234441i	0.997072	−	0.0764715i	$-0.0243654\pi$
$601$	1.14323	+	5.74739i	0.0466332	+	0.234441i	−0.950439	+	0.310912i	$0.899365\pi$
$602$	9.32167	−	10.6177i	0.379923	−	0.432745i
$603$	−5.35779	+	6.52848i	−0.218186	+	0.265860i
$604$	−1.38945	−	10.6432i	−0.0565358	−	0.433067i
$605$	−13.7167	−	7.33173i	−0.557663	−	0.298077i
$606$	20.6589	+	4.82882i	0.839212	+	0.196157i
$607$	23.3150	+	23.3150i	0.946326	+	0.946326i	0.998631	−	0.0523052i	$-0.0166569\pi$
$607$	23.3150	+	23.3150i	0.946326	+	0.946326i	−0.0523052	+	0.998631i	$0.516657\pi$
$608$	26.6534	+	1.81967i	1.08094	+	0.0737973i
$609$	6.13706	−	6.13706i	0.248686	−	0.248686i
$610$	24.4529	−	15.1874i	0.990069	−	0.614919i
$611$	10.7999	−	20.2052i	0.436916	−	0.817413i
$612$	6.86600	−	3.95415i	0.277541	−	0.159837i
$613$	9.29854	+	7.63112i	0.375565	+	0.308218i	0.803173	−	0.595746i	$-0.203144\pi$
$613$	9.29854	+	7.63112i	0.375565	+	0.308218i	−0.427608	+	0.903964i	$0.640644\pi$
$614$	24.9410	−	1.62112i	1.00654	−	0.0654229i
$615$	−3.93625	+	0.782969i	−0.158725	+	0.0315724i
$616$	−56.8623	+	23.4446i	−2.29105	+	0.944611i
$617$	1.27090	−	6.38924i	0.0511645	−	0.257221i	−0.946734	−	0.322016i	$-0.895639\pi$
$617$	1.27090	−	6.38924i	0.0511645	−	0.257221i	0.997899	+	0.0647951i	$0.0206394\pi$
$618$	14.2989	−	10.9596i	0.575188	−	0.440861i
$619$	1.64257	+	0.498268i	0.0660204	+	0.0200271i	0.323122	−	0.946357i	$-0.395268\pi$
$619$	1.64257	+	0.498268i	0.0660204	+	0.0200271i	−0.257102	+	0.966384i	$0.582768\pi$
$620$	−7.83490	−	2.95857i	−0.314657	−	0.118819i
$621$	4.66970	−	3.83232i	0.187389	−	0.153786i
$622$	29.6956	−	27.7827i	1.19069	−	1.11399i
$623$	66.3262	+	27.4732i	2.65730	+	1.10069i
$624$	20.5482	+	18.0994i	0.822587	+	0.724557i
$625$	−7.17216	+	2.97081i	−0.286886	+	0.118832i
$626$	6.44716	−	14.2087i	0.257680	−	0.567892i
$627$	−21.3046	−	2.09832i	−0.850822	−	0.0837987i
$628$	−2.61054	+	15.7056i	−0.104172	+	0.626723i
$629$	−3.00203	+	1.60462i	−0.119699	+	0.0639803i
$630$	2.85459	+	10.6767i	0.113730	+	0.425369i
$631$	28.5484	−	19.0754i	1.13649	−	0.759381i	0.162669	−	0.986681i	$-0.447990\pi$
$631$	28.5484	−	19.0754i	1.13649	−	0.759381i	0.973825	+	0.227300i	$0.0729898\pi$
$632$	2.25251	−	2.73558i	0.0895999	−	0.108816i
$633$	−13.4059	+	20.0634i	−0.532837	+	0.797447i
$634$	−17.1320	−	34.7879i	−0.680400	−	1.38161i
$635$	2.93138	+	29.7628i	0.116328	+	1.18110i
$636$	2.17249	−	4.39333i	0.0861447	−	0.174207i
$637$	−31.8218	−	104.903i	−1.26083	−	4.15639i
$638$	11.4441	−	1.88304i	0.453075	−	0.0745501i
$639$	−0.319877			−0.0126541
$640$	5.99049	−	17.4294i	0.236795	−	0.688957i
$641$	2.52462			0.0997165			0.0498582	−	0.998756i	$-0.484123\pi$
$641$	2.52462			0.0997165			0.0498582	+	0.998756i	$0.484123\pi$
$642$	−18.7328	+	3.08234i	−0.739324	+	0.121650i
$643$	1.12342	+	3.70341i	0.0443033	+	0.146048i	0.976302	−	0.216414i	$-0.0694361\pi$
$643$	1.12342	+	3.70341i	0.0443033	+	0.146048i	−0.931998	+	0.362462i	$0.881936\pi$
$644$	51.9543	+	25.6912i	2.04729	+	1.01238i
$645$	−0.332531	−	3.37624i	−0.0130934	−	0.132939i
$646$	11.6896	+	23.7367i	0.459922	+	0.933909i
$647$	−11.4755	+	17.1743i	−0.451148	+	0.675190i	−0.985423	−	0.170120i	$-0.945584\pi$
$647$	−11.4755	+	17.1743i	−0.451148	+	0.675190i	0.534276	+	0.845310i	$0.320584\pi$
$648$	2.81526	−	0.272647i	0.110594	−	0.0107106i
$649$	28.4550	−	19.0130i	1.11696	−	0.746325i
$650$	−5.86728	−	21.9447i	−0.230134	−	0.860740i
$651$	10.8754	−	5.81303i	0.426241	−	0.227831i
$652$	0.967536	+	0.160821i	0.0378917	+	0.00629823i
$653$	21.0012	+	2.06844i	0.821841	+	0.0809443i	0.500192	−	0.865915i	$-0.333263\pi$
$653$	21.0012	+	2.06844i	0.821841	+	0.0809443i	0.321649	+	0.946859i	$0.395763\pi$
$654$	−0.745963	+	1.64400i	−0.0291695	+	0.0642855i
$655$	3.30235	−	1.36788i	0.129034	−	0.0534475i
$656$	−8.84790	+	4.33943i	−0.345453	+	0.169426i
$657$	2.66593	+	1.10426i	0.104008	+	0.0430814i
$658$	16.5799	−	15.5119i	0.646353	−	0.604717i
$659$	2.35478	−	1.93251i	0.0917290	−	0.0752801i	−0.587411	−	0.809289i	$-0.699853\pi$
$659$	2.35478	−	1.93251i	0.0917290	−	0.0752801i	0.679140	+	0.734009i	$0.262353\pi$
$660$	−5.21720	+	13.8162i	−0.203079	+	0.537795i
$661$	0.328397	+	0.0996183i	0.0127732	+	0.00387470i	0.296665	−	0.954982i	$-0.404126\pi$
$661$	0.328397	+	0.0996183i	0.0127732	+	0.00387470i	−0.283892	+	0.958856i	$0.591626\pi$
$662$	−15.8088	+	12.1169i	−0.614425	+	0.470935i
$663$	−5.29084	+	26.5988i	−0.205479	+	1.03301i
$664$	0.321829	−	0.773398i	0.0124894	−	0.0300137i
$665$	−36.1972	+	7.20008i	−1.40367	+	0.279207i
$666$	−1.21259	+	0.0788159i	−0.0469869	+	0.00305405i
$667$	−8.44839	−	6.93342i	−0.327123	−	0.268463i
$668$	15.0592	+	26.1489i	0.582658	+	1.01173i
$669$	12.4266	−	23.2485i	0.480440	−	0.898840i
$670$	−16.5281	+	10.2654i	−0.638536	+	0.396587i
$671$	−40.0498	+	40.0498i	−1.54611	+	1.54611i
$672$	13.5047	+	23.5383i	0.520956	+	0.908009i
$673$	17.8017	+	17.8017i	0.686206	+	0.686206i	0.961391	−	0.275185i	$-0.0887391\pi$
$673$	17.8017	+	17.8017i	0.686206	+	0.686206i	−0.275185	+	0.961391i	$0.588739\pi$
$674$	17.4132	+	4.07015i	0.670730	+	0.156776i
$675$	−2.06928	−	1.10605i	−0.0796465	−	0.0425720i
$676$	−67.1574	+	8.76723i	−2.58298	+	0.337201i
$677$	10.1232	−	12.3352i	0.389067	−	0.474080i	−0.541236	−	0.840871i	$-0.682043\pi$
$677$	10.1232	−	12.3352i	0.389067	−	0.474080i	0.930304	+	0.366791i	$0.119543\pi$
$678$	11.0132	−	12.5444i	0.422958	−	0.481764i
$679$	−11.0984	−	55.7956i	−0.425919	−	2.14124i
$680$	17.9083	−	3.53185i	0.686751	−	0.135440i
$681$	11.6967	+	2.32662i	0.448219	+	0.0891564i
$682$	16.3365	+	2.15977i	0.625557	+	0.0827019i
$683$	1.80442	−	5.94837i	0.0690442	−	0.227608i	−0.915627	−	0.402029i	$-0.868305\pi$
$683$	1.80442	−	5.94837i	0.0690442	−	0.227608i	0.984671	+	0.174420i	$0.0558052\pi$
$684$	0.298787	+	9.44062i	0.0114244	+	0.360971i
$685$	−11.8957	−	14.4950i	−0.454513	−	0.553825i
$686$	2.03395	−	61.1157i	0.0776567	−	2.33341i
$687$	−7.94689	+	19.1855i	−0.303193	+	0.731972i
$688$	−2.91744	−	7.80284i	−0.111226	−	0.297480i
$689$	6.41983	+	15.4988i	0.244576	+	0.590459i
$690$	13.0276	−	4.89515i	0.495951	−	0.186355i
$691$	0.310713	−	3.15472i	0.0118201	−	0.120011i	−0.987464	−	0.157844i	$-0.949546\pi$
$691$	0.310713	−	3.15472i	0.0118201	−	0.120011i	0.999284	+	0.0378332i	$0.0120456\pi$
$692$	2.41981	+	1.50838i	0.0919872	+	0.0573400i
$693$	−10.2508	−	19.1779i	−0.389396	−	0.728508i
$694$	−14.7778	−	8.54267i	−0.560957	−	0.324275i
$695$	−8.54275	−	12.7851i	−0.324045	−	0.484968i
$696$	−1.47745	−	4.89924i	−0.0560028	−	0.185705i
$697$	−8.11527	−	5.42245i	−0.307388	−	0.205390i
$698$	−1.24733	+	3.66798i	−0.0472123	+	0.138835i
$699$	4.54106	−	0.447255i	0.171759	−	0.0169167i
$700$	1.49674	−	22.4619i	0.0565715	−	0.848981i
$701$	−34.9106	+	10.5900i	−1.31856	+	0.399980i	−0.869681	−	0.493615i	$-0.835675\pi$
$701$	−34.9106	+	10.5900i	−1.31856	+	0.399980i	−0.448875	+	0.893594i	$0.648175\pi$
$702$	−5.64340	+	7.86633i	−0.212997	+	0.296896i
$703$		−	4.05791i		−	0.153047i
$704$	−3.67205	+	36.0772i	−0.138396	+	1.35971i
$705$		−	5.45177i		−	0.205326i
$706$	9.74953	+	6.99443i	0.366928	+	0.263239i
$707$	−68.8682	+	20.8910i	−2.59006	+	0.785685i
$708$	−9.94341	−	11.3632i	−0.373696	−	0.427054i
$709$	2.21102	−	0.217767i	0.0830367	−	0.00817840i	−0.0564134	−	0.998407i	$-0.517966\pi$
$709$	2.21102	−	0.217767i	0.0830367	−	0.00817840i	0.139450	+	0.990229i	$0.455466\pi$
$710$	−0.697685	−	0.237255i	−0.0261837	−	0.00890402i
$711$	1.04171	+	0.696050i	0.0390673	+	0.0261039i
$712$	32.7635	−	26.7991i	1.22786	−	1.00434i
$713$	−8.62717	−	12.9115i	−0.323090	−	0.483538i
$714$	−13.4510	+	23.2686i	−0.503391	+	0.870806i
$715$	−23.8292	−	44.5813i	−0.891161	−	1.66724i
$716$	1.88272	+	8.11442i	0.0703607	+	0.303250i
$717$	−1.37448	+	13.9554i	−0.0513310	+	0.521172i
$718$	10.1549	+	27.0256i	0.378979	+	1.00859i
$719$	−12.6031	−	30.4267i	−0.470018	−	1.13472i	−0.964155	−	0.265339i	$-0.914516\pi$
$719$	−12.6031	−	30.4267i	−0.470018	−	1.13472i	0.494138	−	0.869384i	$-0.335484\pi$
$720$	6.34259	+	1.49342i	0.236374	+	0.0556565i
$721$	−23.3868	+	56.4608i	−0.870971	+	2.10271i
$722$	−4.66945	−	0.155401i	−0.173779	−	0.00578343i
$723$	−9.02969	−	11.0027i	−0.335818	−	0.409195i
$724$	2.21432	+	2.07846i	0.0822945	+	0.0772452i
$725$	−1.23225	+	4.06218i	−0.0457645	+	0.150865i
$726$	1.76969	−	13.3859i	0.0656794	−	0.496799i
$727$	−11.1356	−	2.21502i	−0.412998	−	0.0821504i	−0.0157817	−	0.999875i	$-0.505024\pi$
$727$	−11.1356	−	2.21502i	−0.412998	−	0.0821504i	−0.397216	+	0.917725i	$0.630024\pi$
$728$	−91.0722	−	18.2697i	−3.37536	−	0.677120i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	4.99562	+	4.38584i	0.184896	+	0.162327i
$731$	5.23402	−	6.37768i	0.193587	−	0.235887i
$732$	19.8093	+	15.2344i	0.732172	+	0.563080i
$733$	−9.74581	−	5.20925i	−0.359970	−	0.192408i	0.281491	−	0.959564i	$-0.409171\pi$
$733$	−9.74581	−	5.20925i	−0.359970	−	0.192408i	−0.641460	+	0.767156i	$0.721671\pi$
$734$	0.275660	−	1.17934i	0.0101748	−	0.0435303i
$735$	−18.4456	−	18.4456i	−0.680374	−	0.680374i
$736$	27.8311	−	19.8293i	1.02587	−	0.730918i
$737$	27.0703	−	27.0703i	0.997147	−	0.997147i
$738$	−1.83828	−	2.95977i	−0.0676679	−	0.108951i
$739$	17.2350	−	32.2445i	0.634001	−	1.18613i	−0.335731	−	0.941958i	$-0.608983\pi$
$739$	17.2350	−	32.2445i	0.634001	−	1.18613i	0.969731	−	0.244174i	$-0.0785168\pi$
$740$	−2.70324	−	0.727480i	−0.0993732	−	0.0267427i
$741$	−24.9914	−	20.5099i	−0.918083	−	0.753451i
$742$	1.07834	+	16.5904i	0.0395871	+	0.609051i
$743$	42.0652	−	8.36728i	1.54322	−	0.306966i	0.651181	−	0.758922i	$-0.274274\pi$
$743$	42.0652	−	8.36728i	1.54322	−	0.306966i	0.892040	+	0.451957i	$0.149274\pi$
$744$	0.0118476	−	7.27060i	0.000434354	−	0.266553i
$745$	−2.83785	+	14.2668i	−0.103971	+	0.522696i
$746$	−23.9699	−	31.2733i	−0.877599	−	1.14500i
$747$	0.283414	+	0.0859727i	0.0103696	+	0.00314558i
$748$	−32.7302	+	14.7870i	−1.19674	+	0.540667i
$749$	49.7810	−	40.8542i	1.81896	−	1.49278i
$750$	−11.5626	−	12.3587i	−0.422205	−	0.451275i
$751$	5.30290	+	2.19653i	0.193506	+	0.0801526i	0.477332	−	0.878723i	$-0.341604\pi$
$751$	5.30290	+	2.19653i	0.193506	+	0.0801526i	−0.283826	+	0.958876i	$0.591604\pi$
$752$	−3.43664	−	12.9381i	−0.125321	−	0.471803i
$753$	1.42841	−	0.591667i	0.0520541	−	0.0215615i
$754$	15.9501	+	7.23736i	0.580870	+	0.263569i
$755$	8.70043	+	0.856917i	0.316641	+	0.0311864i
$756$	−7.80489	+	5.58008i	−0.283861	+	0.202946i
$757$	9.61029	−	5.13681i	0.349292	−	0.186700i	−0.287415	−	0.957806i	$-0.592796\pi$
$757$	9.61029	−	5.13681i	0.349292	−	0.186700i	0.636707	+	0.771106i	$0.280296\pi$
$758$	−30.0825	+	8.04308i	−1.09265	+	0.292138i
$759$	−22.7683	+	15.2133i	−0.826438	+	0.552208i
$760$	−6.35048	+	20.8126i	−0.230356	+	0.754951i
$761$	7.61171	−	11.3917i	0.275924	−	0.412950i	−0.667463	−	0.744643i	$-0.732620\pi$
$761$	7.61171	−	11.3917i	0.275924	−	0.412950i	0.943387	+	0.331693i	$0.107620\pi$
$762$	−23.2921	+	11.4707i	−0.843785	+	0.415539i
$763$	−0.600251	−	6.09445i	−0.0217305	−	0.220634i
$764$	9.80483	+	28.9875i	0.354726	+	1.04873i
$765$	1.87335	+	6.17560i	0.0677310	+	0.223279i
$766$	2.11263	+	12.8394i	0.0763323	+	0.463905i
$767$	51.6831			1.86617
$768$	15.9936	−	0.454012i	0.577118	−	0.0163827i
$769$	−29.4575			−1.06226			−0.531132	−	0.847289i	$-0.678233\pi$
$769$	−29.4575			−1.06226			−0.531132	+	0.847289i	$0.678233\pi$
$770$	−8.13369	−	49.4321i	−0.293118	−	1.78141i
$771$	−0.173328	−	0.571385i	−0.00624225	−	0.0205779i
$772$	−4.37216	−	12.9261i	−0.157357	−	0.465220i
$773$	2.71402	+	27.5559i	0.0976166	+	0.991118i	0.911834	+	0.410558i	$0.134666\pi$
$773$	2.71402	+	27.5559i	0.0976166	+	0.991118i	−0.814218	+	0.580560i	$0.802834\pi$
$774$	2.64222	−	1.30121i	0.0949725	−	0.0467711i
$775$	−3.35084	+	5.01489i	−0.120366	+	0.180140i
$776$	−32.0812	−	9.78884i	−1.15165	−	0.351399i
$777$	3.42729	−	2.29004i	0.122953	−	0.0821548i
$778$	16.8871	−	4.51506i	0.605433	−	0.161873i
$779$	10.2613	−	5.48479i	0.367650	−	0.196513i
$780$	−18.1434	+	12.9715i	−0.649637	+	0.464456i
$781$	1.44301	+	0.142124i	0.0516348	+	0.00508559i
$782$	30.8202	+	13.9847i	1.10213	+	0.500090i
$783$	1.67148	−	0.692348i	0.0597337	−	0.0247425i
$784$	−55.4023	−	32.1472i	−1.97865	−	1.14812i
$785$	−11.9807	−	4.96257i	−0.427610	−	0.177122i
$786$	2.12004	+	2.26601i	0.0756195	+	0.0808260i
$787$	6.78283	−	5.56653i	0.241782	−	0.198425i	−0.505696	−	0.862711i	$-0.668764\pi$
$787$	6.78283	−	5.56653i	0.241782	−	0.198425i	0.747478	+	0.664286i	$0.231264\pi$
$788$	28.9390	−	13.0742i	1.03091	−	0.465749i
$789$	17.7742	+	5.39174i	0.632778	+	0.191951i
$790$	1.75582	+	2.29080i	0.0624692	+	0.0815031i
$791$	−11.0469	+	55.5366i	−0.392783	+	1.97466i
$792$	−12.8211	−	0.0208923i	−0.455578	−	0.000742374i
$793$	−83.8931	+	16.6874i	−2.97913	+	0.592586i
$794$	1.00604	+	15.4780i	0.0357030	+	0.549294i
$795$	3.08585	+	2.53249i	0.109444	+	0.0898182i
$796$	26.8923	+	7.23710i	0.953174	+	0.256512i
$797$	19.8274	−	37.0945i	0.702324	−	1.31396i	−0.237196	−	0.971462i	$-0.576228\pi$
$797$	19.8274	−	37.0945i	0.702324	−	1.31396i	0.939520	−	0.342494i	$-0.111272\pi$
$798$	−16.9045	−	27.2177i	−0.598414	−	0.963495i
$799$	9.37498	−	9.37498i	0.331663	−	0.331663i
$800$	−11.2523	−	7.03955i	−0.397827	−	0.248886i
$801$	10.5819	+	10.5819i	0.373894	+	0.373894i
$802$	−11.6157	+	49.6949i	−0.410164	+	1.75479i
$803$	−11.5357	−	6.16595i	−0.407086	−	0.217592i
$804$	−13.3894	−	10.2972i	−0.472208	−	0.363153i
$805$	−29.9486	+	36.4924i	−1.05555	+	1.28619i
$806$	18.7015	+	16.4188i	0.658733	+	0.578327i
$807$	−4.09161	−	20.5699i	−0.144032	−	0.724096i
$808$	−8.34579	+	41.6027i	−0.293604	+	1.46358i
$809$	24.2060	+	4.81488i	0.851039	+	0.169282i	0.601293	−	0.799029i	$-0.294653\pi$
$809$	24.2060	+	4.81488i	0.851039	+	0.169282i	0.249747	+	0.968311i	$0.419653\pi$
$810$	−0.301942	+	2.28389i	−0.0106092	+	0.0802479i
$811$	−14.7329	+	48.5678i	−0.517341	+	1.70544i	0.175610	+	0.984460i	$0.443810\pi$
$811$	−14.7329	+	48.5678i	−0.517341	+	1.70544i	−0.692951	+	0.720985i	$0.743690\pi$
$812$	12.6562	+	11.8797i	0.444147	+	0.416896i
$813$	−6.47142	−	7.88545i	−0.226963	−	0.276555i
$814$	5.50516	+	0.183214i	0.192956	+	0.00642164i
$815$	−0.305716	+	0.738064i	−0.0107088	+	0.0258533i
$816$	8.33872	+	13.4750i	0.291914	+	0.471718i
$817$	3.76386	+	9.08677i	0.131681	+	0.317906i
$818$	16.8110	+	44.7394i	0.587782	+	1.56428i
$819$	3.21892	−	32.6822i	0.112478	−	1.14201i
$820$	−1.81419	−	7.81903i	−0.0633542	−	0.273052i
$821$	−7.56595	−	14.1549i	−0.264054	−	0.494010i	0.714598	−	0.699535i	$-0.246610\pi$
$821$	−7.56595	−	14.1549i	−0.264054	−	0.494010i	−0.978652	+	0.205526i	$0.934110\pi$
$822$	8.14709	−	14.0935i	0.284162	−	0.491567i
$823$	−7.01610	−	10.5003i	−0.244566	−	0.366019i	0.688796	−	0.724955i	$-0.258140\pi$
$823$	−7.01610	−	10.5003i	−0.244566	−	0.366019i	−0.933362	+	0.358936i	$0.883140\pi$
$824$	22.8129	+	27.8902i	0.794726	+	0.971601i
$825$	8.84334	+	5.90893i	0.307886	+	0.205723i
$826$	48.4924	+	16.4903i	1.68727	+	0.573772i
$827$	30.2576	−	2.98012i	1.05216	−	0.103629i	0.442878	−	0.896582i	$-0.353957\pi$
$827$	30.2576	−	2.98012i	1.05216	−	0.103629i	0.609283	+	0.792953i	$0.291457\pi$
$828$	7.95625	+	9.09227i	0.276499	+	0.315978i
$829$	−7.41190	+	2.24838i	−0.257426	+	0.0780893i	−0.416360	−	0.909200i	$-0.636694\pi$
$829$	−7.41190	+	2.24838i	−0.257426	+	0.0780893i	0.158934	+	0.987289i	$0.449194\pi$
$830$	0.554389	+	0.397725i	0.0192431	+	0.0138052i
$831$		−	8.97266i		−	0.311258i
$832$	−34.8807	+	42.2209i	−1.20927	+	1.46375i
$833$		−	63.4387i		−	2.19802i
$834$	7.78142	−	10.8465i	0.269448	−	0.375584i
$835$	−23.5195	+	7.13457i	−0.813927	+	0.246902i
$836$	2.84666	−	42.7205i	0.0984540	−	1.47752i
$837$	2.55817	−	0.251958i	0.0884233	−	0.00870893i
$838$	−12.8516	+	37.7920i	−0.443950	+	1.30550i
$839$	−31.5970	−	21.1124i	−1.09085	−	0.728882i	−0.126090	−	0.992019i	$-0.540243\pi$
$839$	−31.5970	−	21.1124i	−1.09085	−	0.728882i	−0.964759	+	0.263137i	$0.915243\pi$
$840$	−21.1620	+	6.38180i	−0.730160	+	0.220193i
$841$	14.2931	+	21.3911i	0.492864	+	0.737623i
$842$	−23.1767	−	13.3979i	−0.798723	−	0.461722i
$843$	9.14643	+	17.1118i	0.315020	+	0.589361i
$844$	−40.9548	−	25.5291i	−1.40972	−	0.878747i
$845$	5.40703	−	54.8985i	0.186008	−	1.88857i
$846$	4.43047	−	1.66477i	0.152323	−	0.0572358i
$847$	17.5278	+	42.3158i	0.602261	+	1.45399i
$848$	8.91970	+	4.06485i	0.306304	+	0.139587i
$849$	9.12581	−	22.0316i	0.313197	−	0.756124i
$850$	0.437243	−	13.1382i	0.0149973	−	0.450635i
$851$	−3.29289	−	4.01239i	−0.112879	−	0.137543i
$852$	−0.0202375	−	0.639434i	−0.000693327	−	0.0219067i
$853$	−3.27809	+	10.8064i	−0.112240	+	0.370005i	−0.995007	−	0.0998059i	$-0.968178\pi$
$853$	−3.27809	+	10.8064i	−0.112240	+	0.370005i	0.882767	+	0.469811i	$0.155678\pi$
$854$	−84.0383	−	11.1103i	−2.87573	−	0.380186i
$855$	−7.54545	−	1.50088i	−0.258049	−	0.0513291i
$856$	−7.34676	−	37.2518i	−0.251107	−	1.27324i
$857$	0.424810	+	2.13567i	0.0145112	+	0.0729530i	0.987362	−	0.158479i	$-0.0506590\pi$
$857$	0.424810	+	2.13567i	0.0145112	+	0.0729530i	−0.972851	+	0.231432i	$0.925659\pi$
$858$	28.9532	−	32.9786i	0.988445	−	1.12587i
$859$	−34.2001	+	41.6730i	−1.16689	+	1.42186i	−0.279931	+	0.960020i	$0.590311\pi$
$859$	−34.2001	+	41.6730i	−1.16689	+	1.42186i	−0.886962	+	0.461843i	$0.847189\pi$
$860$	6.72807	−	0.878332i	0.229425	−	0.0299509i
$861$	10.4233	+	5.57137i	0.355225	+	0.189872i
$862$	−9.59841	−	2.24353i	−0.326923	−	0.0764151i
$863$	18.1218	+	18.1218i	0.616874	+	0.616874i	0.944728	−	0.327855i	$-0.106326\pi$
$863$	18.1218	+	18.1218i	0.616874	+	0.616874i	−0.327855	+	0.944728i	$0.606326\pi$
$864$	0.723133	+	5.61044i	0.0246015	+	0.190871i
$865$	−1.64226	+	1.64226i	−0.0558385	+	0.0558385i
$866$	42.5457	−	26.4246i	1.44576	−	0.897944i
$867$	0.615506	−	1.15153i	0.0209037	−	0.0391081i
$868$	12.3083	+	21.3722i	0.417771	+	0.725419i
$869$	−4.39003	−	3.60281i	−0.148922	−	0.122217i
$870$	4.15918	−	0.270338i	0.141009	−	0.00916533i
$871$	56.7047	−	11.2793i	1.92136	−	0.382183i
$872$	−3.33355	−	1.38717i	−0.112888	−	0.0469755i
$873$	2.31351	−	11.6308i	0.0783005	−	0.393643i
$874$	−32.0224	+	24.5440i	−1.08317	+	0.830214i
$875$	54.9375	+	16.6651i	1.85723	+	0.563384i
$876$	−2.03876	+	5.39905i	−0.0688832	+	0.182417i
$877$	−0.471450	+	0.386909i	−0.0159197	+	0.0130650i	−0.642320	−	0.766437i	$-0.722028\pi$
$877$	−0.471450	+	0.386909i	−0.0159197	+	0.0130650i	0.626400	+	0.779502i	$0.284528\pi$
$878$	−6.31246	+	5.90583i	−0.213035	+	0.199312i
$879$	25.4242	+	10.5310i	0.857536	+	0.355203i
$880$	−27.9487	−	9.55506i	−0.942149	−	0.322101i
$881$	14.5507	−	6.02708i	0.490224	−	0.203058i	−0.123857	−	0.992300i	$-0.539527\pi$
$881$	14.5507	−	6.02708i	0.490224	−	0.203058i	0.614082	+	0.789242i	$0.289527\pi$
$882$	9.35751	−	20.6227i	0.315084	−	0.694401i
$883$	−18.8726	−	1.85879i	−0.635115	−	0.0625534i	−0.224664	−	0.974436i	$-0.572129\pi$
$883$	−18.8726	−	1.85879i	−0.635115	−	0.0625534i	−0.410451	+	0.911883i	$0.634629\pi$
$884$	−53.5058	−	8.89356i	−1.79959	−	0.299123i
$885$	10.8464	−	5.79750i	0.364596	−	0.194881i
$886$	14.2336	+	53.2360i	0.478186	+	1.78850i
$887$	−32.9859	+	22.0404i	−1.10756	+	0.740046i	−0.968195	−	0.250196i	$-0.919505\pi$
$887$	−32.9859	+	22.0404i	−1.10756	+	0.740046i	−0.139362	+	0.990242i	$0.544505\pi$
$888$	−0.234269	−	2.41898i	−0.00786156	−	0.0811756i
$889$	48.9301	−	73.2291i	1.64106	−	2.45603i
$890$	15.2316	+	30.9290i	0.510564	+	1.03674i
$891$	−0.444307	−	4.51112i	−0.0148848	−	0.151128i
$892$	47.2600	+	23.3699i	1.58238	+	0.782482i
$893$	4.58803	+	15.1247i	0.153533	+	0.506129i
$894$	−12.4607	+	2.05032i	−0.416749	+	0.0685731i
$895$	−6.78480			−0.226791
$896$	−46.1986	+	28.4851i	−1.54339	+	0.951621i
$897$	−41.3544			−1.38078
$898$	−10.7487	+	1.76862i	−0.358688	+	0.0590195i
$899$	−1.35000	−	4.45036i	−0.0450251	−	0.148428i
$900$	2.08008	−	4.20646i	0.0693360	−	0.140215i
$901$	0.951565	+	9.66141i	0.0317012	+	0.321868i
$902$	6.97764	+	14.1687i	0.232330	+	0.471765i
$903$	−5.55054	+	8.30698i	−0.184711	+	0.276439i
$904$	25.7729	+	21.2217i	0.857195	+	0.705823i
$905$	−2.05675	+	1.37427i	−0.0683685	+	0.0456824i
$906$	1.96039	+	7.33222i	0.0651297	+	0.243597i
$907$	3.28667	−	1.75676i	0.109132	−	0.0583323i	−0.415928	−	0.909398i	$-0.636543\pi$
$907$	3.28667	−	1.75676i	0.109132	−	0.0583323i	0.525060	+	0.851065i	$0.324043\pi$
$908$	−3.91090	+	23.5289i	−0.129788	+	0.780835i
$909$	−14.9296	−	1.47044i	−0.495183	−	0.0487713i
$910$	31.2614	−	68.8959i	1.03631	−	2.28388i
$911$	−33.5877	+	13.9125i	−1.11281	+	0.460942i	−0.861905	−	0.507070i	$-0.830729\pi$
$911$	−33.5877	+	13.9125i	−1.11281	+	0.460942i	−0.250906	+	0.968011i	$0.580729\pi$
$912$	−18.8529	+	1.19455i	−0.624281	+	0.0395555i
$913$	−1.24032	−	0.513756i	−0.0410485	−	0.0170029i
$914$	−13.0806	+	12.2380i	−0.432668	+	0.404797i
$915$	−15.7341	+	12.9127i	−0.520155	+	0.426880i
$916$	−38.8545	−	14.6720i	−1.28379	−	0.484777i
$917$	−10.0730	−	3.05562i	−0.332641	−	0.100905i
$918$	−4.44665	+	3.40820i	−0.146761	+	0.112487i
$919$	3.51773	−	17.6848i	0.116039	−	0.583368i	−0.878389	−	0.477947i	$-0.841381\pi$
$919$	3.51773	−	17.6848i	0.116039	−	0.583368i	0.994428	−	0.105421i	$-0.0336189\pi$
$920$	10.6096	+	25.7324i	0.349788	+	0.848372i
$921$	−17.3336	+	3.44787i	−0.571161	+	0.113611i
$922$	42.4884	−	2.76166i	1.39928	−	0.0909504i
$923$	1.69273	+	1.38918i	0.0557168	+	0.0457256i
$924$	37.6881	−	21.7047i	1.23985	−	0.714031i
$925$	−0.950364	+	1.77801i	−0.0312478	+	0.0584605i
$926$	−7.13060	+	4.42872i	−0.234326	+	0.145537i
$927$	−9.00796	+	9.00796i	−0.295860	+	0.295860i
$928$	9.70011	−	3.26339i	0.318422	−	0.107126i
$929$	−24.5278	−	24.5278i	−0.804732	−	0.804732i	0.179099	−	0.983831i	$-0.442682\pi$
$929$	−24.5278	−	24.5278i	−0.804732	−	0.804732i	−0.983831	+	0.179099i	$0.942682\pi$
$930$	5.76651	+	1.34786i	0.189091	+	0.0441982i
$931$	66.6961	+	35.6498i	2.18588	+	1.16838i
$932$	1.18136	+	9.04927i	0.0386967	+	0.296419i
$933$	−18.2420	+	22.2280i	−0.597217	+	0.727711i
$934$	27.0015	−	30.7556i	0.883516	−	1.00635i
$935$	−5.70704	−	28.6912i	−0.186640	−	0.938304i
$936$	−16.0818	−	10.7835i	−0.525651	−	0.352469i
$937$	−34.3780	−	6.83821i	−1.12308	−	0.223395i	−0.401591	−	0.915819i	$-0.631543\pi$
$937$	−34.3780	−	6.83821i	−1.12308	−	0.223395i	−0.721490	+	0.692425i	$0.756543\pi$
$938$	56.8028	+	7.50962i	1.85468	+	0.245198i
$939$	−3.20269	+	10.5579i	−0.104516	+	0.344543i
$940$	10.8981	−	0.344915i	0.355457	−	0.0112499i
$941$	20.3049	+	24.7416i	0.661922	+	0.806554i	0.990440	−	0.137943i	$-0.0440492\pi$
$941$	20.3049	+	24.7416i	0.661922	+	0.806554i	−0.328518	+	0.944498i	$0.606549\pi$
$942$	0.374461	−	11.2517i	0.0122006	−	0.366600i
$943$	5.69546	−	13.7501i	0.185470	−	0.447764i
$944$	22.0859	−	20.5958i	0.718834	−	0.670335i
$945$	−2.99057	−	7.21987i	−0.0972831	−	0.234862i
$946$	−12.4975	+	4.69598i	−0.406329	+	0.152679i
$947$	2.75180	−	27.9395i	0.0894214	−	0.907911i	−0.840906	−	0.541181i	$-0.817977\pi$
$947$	2.75180	−	27.9395i	0.0894214	−	0.907911i	0.930327	−	0.366730i	$-0.119523\pi$
$948$	−1.32550	+	2.12642i	−0.0430502	+	0.0690629i
$949$	−9.31187	−	17.4213i	−0.302276	−	0.565519i
$950$	13.5671	+	7.84278i	0.440174	+	0.254453i
$951$	15.2337	+	22.7989i	0.493987	+	0.739303i
$952$	−47.3649	−	25.4164i	−1.53511	−	0.823750i
$953$	−11.5976	−	7.74924i	−0.375682	−	0.251023i	0.353366	−	0.935485i	$-0.385037\pi$
$953$	−11.5976	−	7.74924i	−0.375682	−	0.251023i	−0.729048	+	0.684463i	$0.760037\pi$
$954$	−1.11577	+	3.28109i	−0.0361244	+	0.106229i
$955$	−24.8045	+	2.44303i	−0.802654	+	0.0790546i
$956$	−27.9837	−	1.86468i	−0.905058	−	0.0603081i
$957$	−7.84785	+	2.38062i	−0.253685	+	0.0769545i
$958$	−25.6620	+	35.7702i	−0.829101	+	1.15568i
$959$			55.2204i			1.78316i
$960$	−2.58407	+	12.7733i	−0.0834006	+	0.412257i
$961$			24.3923i			0.786848i
$962$	6.75907	+	4.84904i	0.217921	+	0.156339i
$963$	12.8461	−	3.89684i	0.413961	−	0.125574i
$964$	21.4231	−	18.7464i	0.689993	−	0.603782i
$965$	11.0608	−	1.08939i	0.356060	−	0.0350688i
$966$	−38.8013	−	13.1948i	−1.24841	−	0.424535i
$967$	−10.3529	−	6.91758i	−0.332927	−	0.222454i	0.377859	−	0.925863i	$-0.376660\pi$
$967$	−10.3529	−	6.91758i	−0.332927	−	0.222454i	−0.710786	+	0.703409i	$0.751660\pi$
$968$	26.8705	+	2.69073i	0.863649	+	0.0864832i
$969$	−10.3944	−	15.5563i	−0.333915	−	0.499739i
$970$	13.6727	−	23.6521i	0.439003	−	0.759422i
$971$	−15.7591	−	29.4832i	−0.505734	−	0.946162i	−0.997165	−	0.0752452i	$-0.976026\pi$
$971$	−15.7591	−	29.4832i	−0.505734	−	0.946162i	0.491431	−	0.870916i	$-0.336474\pi$
$972$	−1.94825	+	0.452036i	−0.0624900	+	0.0144991i
$973$	−4.43841	+	45.0640i	−0.142289	+	1.44468i
$974$	−1.80377	−	4.80040i	−0.0577964	−	0.153815i
$975$	6.14676	+	14.8396i	0.196854	+	0.475248i
$976$	−29.2003	+	40.5626i	−0.934679	+	1.29838i
$977$	15.6133	−	37.6939i	0.499514	−	1.20593i	−0.450232	−	0.892912i	$-0.648659\pi$
$977$	15.6133	−	37.6939i	0.499514	−	1.20593i	0.949746	−	0.313022i	$-0.101341\pi$
$978$	−0.693154	−	0.0230684i	−0.0221646	−	0.000737647i
$979$	−43.0348	−	52.4380i	−1.37540	−	1.67593i
$980$	35.7057	−	38.0396i	1.14058	−	1.21513i
$981$	0.370565	−	1.22159i	0.0118312	−	0.0390023i
$982$	1.22849	−	9.29228i	0.0392026	−	0.296529i
$983$	−27.9150	−	5.55265i	−0.890351	−	0.177102i	−0.271340	−	0.962484i	$-0.587467\pi$
$983$	−27.9150	−	5.55265i	−0.890351	−	0.177102i	−0.619012	+	0.785382i	$0.712467\pi$
$984$	5.80028	−	3.86197i	0.184906	−	0.123115i
$985$	5.04598	+	25.3678i	0.160778	+	0.808286i
$986$	7.61709	+	6.68733i	0.242578	+	0.212968i
$987$	−10.1851	+	12.4105i	−0.324194	+	0.395031i
$988$	39.4182	−	51.2554i	1.25406	−	1.63065i
$989$	11.0953	+	5.93057i	0.352811	+	0.188581i
$990$	2.37685	−	10.1688i	0.0755413	−	0.323185i
$991$	−17.6381	−	17.6381i	−0.560293	−	0.560293i	0.369098	−	0.929391i	$-0.379667\pi$
$991$	−17.6381	−	17.6381i	−0.560293	−	0.560293i	−0.929391	+	0.369098i	$0.879667\pi$
$992$	14.5347	−	0.436303i	0.461476	−	0.0138526i
$993$	9.95910	−	9.95910i	0.316043	−	0.316043i
$994$	1.14498	+	1.84351i	0.0363166	+	0.0584727i
$995$	−10.6928	+	20.0048i	−0.338985	+	0.634196i
$996$	−0.153929	+	0.571983i	−0.00487742	+	0.0181240i
$997$	43.2092	+	35.4609i	1.36845	+	1.12306i	0.979420	+	0.201832i	$0.0646895\pi$
$997$	43.2092	+	35.4609i	1.36845	+	1.12306i	0.389029	+	0.921225i	$0.372810\pi$
$998$	−0.964614	−	14.8407i	−0.0305343	−	0.469773i
$999$	0.842730	−	0.167629i	0.0266628	−	0.00530356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.15	✓	512
128.69	even	32	inner	384.2.v.a.325.15	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.15	✓	512	1.1	even	1	trivial
384.2.v.a.325.15	yes	512	128.69	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.229611 - 1.39545i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-1.89456 + 0.640821i) q^{4} +(-0.159671 - 1.62116i) q^{5} +(1.26871 - 0.624802i) q^{6} +(-2.66520 + 3.98875i) q^{7} +(1.32924 + 2.49662i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(-0.229611 - 1.39545i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-1.89456 + 0.640821i) q^{4} +(-0.159671 - 1.62116i) q^{5} +(1.26871 - 0.624802i) q^{6} +(-2.66520 + 3.98875i) q^{7} +(1.32924 + 2.49662i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(-2.22559 + 0.595050i) q^{10} +(3.99771 - 2.13682i) q^{11} +(-1.16319 - 1.62696i) q^{12} +(6.81274 + 0.670996i) q^{13} +(6.17805 + 2.80329i) q^{14} +(1.50501 - 0.623395i) q^{15} +(3.17870 - 2.42815i) q^{16} +(3.66004 + 1.51604i) q^{17} +(0.966185 + 1.03271i) q^{18} +(-3.65067 + 2.99603i) q^{19} +(1.34138 + 2.96907i) q^{20} +(-4.59066 - 1.39256i) q^{21} +(-3.89974 - 5.08796i) q^{22} +(-1.17853 + 5.92485i) q^{23} +(-2.00326 + 1.99674i) q^{24} +(2.30125 - 0.457746i) q^{25} +(-0.627939 - 9.66090i) q^{26} +(-0.773010 - 0.634393i) q^{27} +(2.49329 - 9.26483i) q^{28} +(-0.852848 + 1.59557i) q^{29} +(-1.21548 - 1.95702i) q^{30} +(-1.81765 + 1.81765i) q^{31} +(-4.11822 - 3.87818i) q^{32} +(3.20528 + 3.20528i) q^{33} +(1.27517 - 5.45550i) q^{34} +(6.89197 + 3.68384i) q^{35} +(1.21925 - 1.58538i) q^{36} +(-0.545096 + 0.664201i) q^{37} +(5.01904 + 4.40641i) q^{38} +(1.33553 + 6.71416i) q^{39} +(3.83519 - 2.55356i) q^{40} +(-2.41635 - 0.480641i) q^{41} +(-0.889183 + 6.72578i) q^{42} +(0.604548 - 1.99293i) q^{43} +(-6.20457 + 6.61014i) q^{44} +(1.03343 + 1.25924i) q^{45} +(8.53844 + 0.284162i) q^{46} +(1.28072 - 3.09193i) q^{47} +(3.24632 + 2.33697i) q^{48} +(-6.12806 - 14.7944i) q^{49} +(-1.16715 - 3.10617i) q^{50} +(-0.388305 + 3.94253i) q^{51} +(-13.3371 + 3.09451i) q^{52} +(1.15519 + 2.16120i) q^{53} +(-0.707772 + 1.22436i) q^{54} +(-4.10245 - 6.13975i) q^{55} +(-13.5011 - 1.35196i) q^{56} +(-3.92676 - 2.62378i) q^{57} +(2.42235 + 0.823746i) q^{58} +(7.51336 - 0.740001i) q^{59} +(-2.45184 + 2.14550i) q^{60} +(-11.9569 + 3.62709i) q^{61} +(2.95379 + 2.11909i) q^{62} -4.79723i q^{63} +(-4.46622 + 6.63724i) q^{64} -11.1517i q^{65} +(3.73684 - 5.20877i) q^{66} +(8.08187 - 2.45161i) q^{67} +(-7.90567 - 0.526791i) q^{68} +(-6.01184 + 0.592115i) q^{69} +(3.55813 - 10.4632i) q^{70} +(0.265968 + 0.177714i) q^{71} +(-2.49227 - 1.33737i) q^{72} +(-1.60314 - 2.39927i) q^{73} +(1.05202 + 0.608146i) q^{74} +(1.10605 + 2.06928i) q^{75} +(4.99649 - 8.01558i) q^{76} +(-2.13144 + 21.6409i) q^{77} +(9.06262 - 3.40531i) q^{78} +(-0.479447 - 1.15749i) q^{79} +(-4.44397 - 4.76549i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-0.115891 + 3.48225i) q^{82} +(-0.187886 - 0.228940i) q^{83} +(9.58965 - 0.303504i) q^{84} +(1.87335 - 6.17560i) q^{85} +(-2.91984 - 0.386018i) q^{86} +(-1.77443 - 0.352956i) q^{87} +(10.6488 + 7.14040i) q^{88} +(-2.91955 - 14.6776i) q^{89} +(1.51992 - 1.73124i) q^{90} +(-20.8337 + 25.3860i) q^{91} +(-1.56399 - 11.9802i) q^{92} +(-2.26702 - 1.21175i) q^{93} +(-4.60870 - 1.07724i) q^{94} +(5.43997 + 5.43997i) q^{95} +(2.51573 - 5.06666i) q^{96} +(-8.38535 + 8.38535i) q^{97} +(-19.2378 + 11.9484i) q^{98} +(-2.13682 + 3.99771i) 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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