LMFDB - Embedded newform 384.2.v.a.157.3

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			157.3
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37250 - 0.340965i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.76749 + 0.935945i) q^{4} +(2.97786 - 1.59170i) q^{5} +(-0.473851 + 1.33247i) q^{6} +(-0.855624 - 4.30151i) q^{7} +(-2.10674 - 1.88723i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(-1.37250 - 0.340965i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.76749 + 0.935945i) q^{4} +(2.97786 - 1.59170i) q^{5} +(-0.473851 + 1.33247i) q^{6} +(-0.855624 - 4.30151i) q^{7} +(-2.10674 - 1.88723i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-4.62982 + 1.16926i) q^{10} +(-2.53974 + 3.09468i) q^{11} +(1.10468 - 1.66724i) q^{12} +(2.25873 - 4.22579i) q^{13} +(-0.292324 + 6.19554i) q^{14} +(-1.29216 - 3.11954i) q^{15} +(2.24802 + 3.30854i) q^{16} +(0.483363 - 1.16694i) q^{17} +(1.27960 + 0.602174i) q^{18} +(1.78597 + 5.88754i) q^{19} +(6.75308 - 0.0261947i) q^{20} +(-4.36466 + 0.429882i) q^{21} +(4.54096 - 3.38147i) q^{22} +(-6.40796 + 4.28166i) q^{23} +(-2.08464 + 1.91162i) q^{24} +(3.55631 - 5.32240i) q^{25} +(-4.54095 + 5.02973i) q^{26} +(-0.290285 + 0.956940i) q^{27} +(2.51367 - 8.40368i) q^{28} +(0.780911 - 0.640877i) q^{29} +(0.709825 + 4.72213i) q^{30} +(4.72181 - 4.72181i) q^{31} +(-1.95730 - 5.30745i) q^{32} +(2.83084 + 2.83084i) q^{33} +(-1.06130 + 1.43681i) q^{34} +(-9.39465 - 11.4474i) q^{35} +(-1.55093 - 1.26278i) q^{36} +(-4.90301 - 1.48731i) q^{37} +(-0.443787 - 8.68957i) q^{38} +(-3.98405 - 2.66206i) q^{39} +(-9.27750 - 2.26661i) q^{40} +(1.78809 + 2.67607i) q^{41} +(6.13705 + 0.898185i) q^{42} +(-0.524113 - 5.32141i) q^{43} +(-7.38540 + 3.09275i) q^{44} +(-3.23117 + 0.980165i) q^{45} +(10.2548 - 3.69167i) q^{46} +(5.85917 + 2.42695i) q^{47} +(3.51295 - 1.91290i) q^{48} +(-11.3037 + 4.68216i) q^{49} +(-6.69577 + 6.09239i) q^{50} +(-1.11395 - 0.595416i) q^{51} +(7.94739 - 5.35498i) q^{52} +(-2.39350 - 1.96430i) q^{53} +(0.724697 - 1.21442i) q^{54} +(-2.63719 + 13.2580i) q^{55} +(-6.31536 + 10.6769i) q^{56} +(6.03424 - 1.20029i) q^{57} +(-1.29031 + 0.613337i) q^{58} +(-3.18871 - 5.96565i) q^{59} +(0.635849 - 6.72313i) q^{60} +(13.2874 + 1.30869i) q^{61} +(-8.09064 + 4.87070i) q^{62} +4.38578i q^{63} +(0.876727 + 7.95181i) q^{64} -16.1791i q^{65} +(-2.92010 - 4.85053i) q^{66} +(2.13624 + 0.210401i) q^{67} +(1.94653 - 1.61015i) q^{68} +(3.63295 + 6.79678i) q^{69} +(8.99095 + 18.9148i) q^{70} +(0.601606 - 0.119667i) q^{71} +(1.69808 + 2.26197i) q^{72} +(-0.184671 + 0.928403i) q^{73} +(6.22224 + 3.71308i) q^{74} +(-4.94819 - 4.06087i) q^{75} +(-2.35374 + 12.0777i) q^{76} +(15.4849 + 8.27683i) q^{77} +(4.56042 + 5.01208i) q^{78} +(11.2310 - 4.65202i) q^{79} +(11.9605 + 6.27421i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-1.54170 - 4.28257i) q^{82} +(9.92276 - 3.01004i) q^{83} +(-8.11683 - 3.32527i) q^{84} +(-0.418034 - 4.24437i) q^{85} +(-1.09507 + 7.48231i) q^{86} +(-0.561248 - 0.839967i) q^{87} +(11.1910 - 1.72662i) q^{88} +(6.17591 + 4.12661i) q^{89} +(4.76897 - 0.243557i) q^{90} +(-20.1099 - 6.10028i) q^{91} +(-15.3334 + 1.57028i) q^{92} +(-4.23626 - 5.16190i) q^{93} +(-7.21418 - 5.32874i) q^{94} +(14.6896 + 14.6896i) q^{95} +(-5.47374 + 1.42765i) q^{96} +(-4.74084 + 4.74084i) q^{97} +(17.1108 - 2.57207i) q^{98} +(3.09468 - 2.53974i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{27}{32}\right)$	$1$

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 $

$2$	−1.37250	−	0.340965i	−0.970501	−	0.241098i
$2$	−1.37250	−	0.340965i	−0.970501	−	0.241098i
$3$	0.0980171	−	0.995185i	0.0565902	−	0.574570i
$3$	0.0980171	−	0.995185i	0.0565902	−	0.574570i
$4$	1.76749	+	0.935945i	0.883743	+	0.467972i
$5$	2.97786	−	1.59170i	1.33174	−	0.711831i	0.356777	−	0.934190i	$-0.383876\pi$
$5$	2.97786	−	1.59170i	1.33174	−	0.711831i	0.974965	+	0.222359i	$0.0713757\pi$
$6$	−0.473851	+	1.33247i	−0.193449	+	0.543977i
$7$	−0.855624	−	4.30151i	−0.323395	−	1.62582i	−0.710440	−	0.703757i	$-0.751504\pi$
$7$	−0.855624	−	4.30151i	−0.323395	−	1.62582i	0.387045	−	0.922061i	$-0.373496\pi$
$8$	−2.10674	−	1.88723i	−0.744846	−	0.667236i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	−4.62982	+	1.16926i	−1.46408	+	0.369751i
$11$	−2.53974	+	3.09468i	−0.765760	+	0.933081i	−0.999228	−	0.0392831i	$-0.987493\pi$
$11$	−2.53974	+	3.09468i	−0.765760	+	0.933081i	0.233468	+	0.972364i	$0.424993\pi$
$12$	1.10468	−	1.66724i	0.318894	−	0.481290i
$13$	2.25873	−	4.22579i	0.626460	−	1.17202i	−0.345841	−	0.938293i	$-0.612406\pi$
$13$	2.25873	−	4.22579i	0.626460	−	1.17202i	0.972301	−	0.233731i	$-0.0750936\pi$
$14$	−0.292324	+	6.19554i	−0.0781267	+	1.65583i
$15$	−1.29216	−	3.11954i	−0.333633	−	0.805462i
$16$	2.24802	+	3.30854i	0.562004	+	0.827135i
$17$	0.483363	−	1.16694i	0.117233	−	0.283025i	−0.854361	−	0.519680i	$-0.826051\pi$
$17$	0.483363	−	1.16694i	0.117233	−	0.283025i	0.971594	+	0.236655i	$0.0760511\pi$
$18$	1.27960	+	0.602174i	0.301606	+	0.141934i
$19$	1.78597	+	5.88754i	0.409729	+	1.35069i	0.882833	+	0.469688i	$0.155633\pi$
$19$	1.78597	+	5.88754i	0.409729	+	1.35069i	−0.473104	+	0.881007i	$0.656867\pi$
$20$	6.75308	−	0.0261947i	1.51003	−	0.00585732i
$21$	−4.36466	+	0.429882i	−0.952448	+	0.0938079i
$22$	4.54096	−	3.38147i	0.968135	−	0.720933i
$23$	−6.40796	+	4.28166i	−1.33615	+	0.892788i	−0.998818	−	0.0485971i	$-0.984525\pi$
$23$	−6.40796	+	4.28166i	−1.33615	+	0.892788i	−0.337333	+	0.941385i	$0.609525\pi$
$24$	−2.08464	+	1.91162i	−0.425525	+	0.390207i
$25$	3.55631	−	5.32240i	0.711262	−	1.06448i
$26$	−4.54095	+	5.02973i	−0.890553	+	0.986412i
$27$	−0.290285	+	0.956940i	−0.0558653	+	0.184163i
$28$	2.51367	−	8.40368i	0.475039	−	1.58815i
$29$	0.780911	−	0.640877i	0.145011	−	0.119008i	−0.559091	−	0.829106i	$-0.688850\pi$
$29$	0.780911	−	0.640877i	0.145011	−	0.119008i	0.704102	+	0.710099i	$0.251350\pi$
$30$	0.709825	+	4.72213i	0.129596	+	0.862139i
$31$	4.72181	−	4.72181i	0.848063	−	0.848063i	−0.141828	−	0.989891i	$-0.545298\pi$
$31$	4.72181	−	4.72181i	0.848063	−	0.848063i	0.989891	+	0.141828i	$0.0452981\pi$
$32$	−1.95730	−	5.30745i	−0.346004	−	0.938233i
$33$	2.83084	+	2.83084i	0.492786	+	0.492786i
$34$	−1.06130	+	1.43681i	−0.182011	+	0.246411i
$35$	−9.39465	−	11.4474i	−1.58799	−	1.93497i
$36$	−1.55093	−	1.26278i	−0.258488	−	0.210463i
$37$	−4.90301	−	1.48731i	−0.806050	−	0.244513i	−0.139741	−	0.990188i	$-0.544627\pi$
$37$	−4.90301	−	1.48731i	−0.806050	−	0.244513i	−0.666309	+	0.745676i	$0.732127\pi$
$38$	−0.443787	−	8.68957i	−0.0719917	−	1.40963i
$39$	−3.98405	−	2.66206i	−0.637959	−	0.426270i
$40$	−9.27750	−	2.26661i	−1.46690	−	0.358382i
$41$	1.78809	+	2.67607i	0.279253	+	0.417932i	0.944409	−	0.328773i	$-0.106635\pi$
$41$	1.78809	+	2.67607i	0.279253	+	0.417932i	−0.665156	+	0.746704i	$0.731635\pi$
$42$	6.13705	+	0.898185i	0.946968	+	0.138593i
$43$	−0.524113	−	5.32141i	−0.0799265	−	0.811507i	−0.948675	−	0.316253i	$-0.897575\pi$
$43$	−0.524113	−	5.32141i	−0.0799265	−	0.811507i	0.868748	−	0.495254i	$-0.164925\pi$
$44$	−7.38540	+	3.09275i	−1.11339	+	0.466250i
$45$	−3.23117	+	0.980165i	−0.481675	+	0.146114i
$46$	10.2548	−	3.69167i	1.51199	−	0.544307i
$47$	5.85917	+	2.42695i	0.854647	+	0.354007i	0.766612	−	0.642111i	$-0.221941\pi$
$47$	5.85917	+	2.42695i	0.854647	+	0.354007i	0.0880355	+	0.996117i	$0.471941\pi$
$48$	3.51295	−	1.91290i	0.507051	−	0.276103i
$49$	−11.3037	+	4.68216i	−1.61482	+	0.668881i
$50$	−6.69577	+	6.09239i	−0.946925	+	0.861594i
$51$	−1.11395	−	0.595416i	−0.155984	−	0.0833750i
$52$	7.94739	−	5.35498i	1.10210	−	0.742602i
$53$	−2.39350	−	1.96430i	−0.328773	−	0.269817i	0.455496	−	0.890238i	$-0.349462\pi$
$53$	−2.39350	−	1.96430i	−0.328773	−	0.269817i	−0.784269	+	0.620421i	$0.786962\pi$
$54$	0.724697	−	1.21442i	0.0986188	−	0.165262i
$55$	−2.63719	+	13.2580i	−0.355599	+	1.78771i
$56$	−6.31536	+	10.6769i	−0.843925	+	1.42677i
$57$	6.03424	−	1.20029i	0.799255	−	0.158982i
$58$	−1.29031	+	0.613337i	−0.169426	+	0.0805351i
$59$	−3.18871	−	5.96565i	−0.415134	−	0.776661i	0.584256	−	0.811569i	$-0.301386\pi$
$59$	−3.18871	−	5.96565i	−0.415134	−	0.776661i	−0.999391	+	0.0349079i	$0.988886\pi$
$60$	0.635849	−	6.72313i	0.0820877	−	0.867952i
$61$	13.2874	+	1.30869i	1.70127	+	0.167561i	0.901511	−	0.432757i	$-0.142459\pi$
$61$	13.2874	+	1.30869i	1.70127	+	0.167561i	0.799761	+	0.600318i	$0.204959\pi$
$62$	−8.09064	+	4.87070i	−1.02751	+	0.618579i
$63$			4.38578i			0.552557i
$64$	0.876727	+	7.95181i	0.109591	+	0.993977i
$65$		−	16.1791i		−	2.00677i
$66$	−2.92010	−	4.85053i	−0.359439	−	0.597059i
$67$	2.13624	+	0.210401i	0.260983	+	0.0257045i	0.227662	−	0.973740i	$-0.426892\pi$
$67$	2.13624	+	0.210401i	0.260983	+	0.0257045i	0.0333204	+	0.999445i	$0.489392\pi$
$68$	1.94653	−	1.61015i	0.236052	−	0.195260i
$69$	3.63295	+	6.79678i	0.437356	+	0.818236i
$70$	8.99095	+	18.9148i	1.07462	+	2.26075i
$71$	0.601606	−	0.119667i	0.0713975	−	0.0142019i	−0.159262	−	0.987236i	$-0.550912\pi$
$71$	0.601606	−	0.119667i	0.0713975	−	0.0142019i	0.230660	+	0.973034i	$0.425912\pi$
$72$	1.69808	+	2.26197i	0.200121	+	0.266576i
$73$	−0.184671	+	0.928403i	−0.0216141	+	0.108661i	−0.990086	−	0.140460i	$-0.955142\pi$
$73$	−0.184671	+	0.928403i	−0.0216141	+	0.108661i	0.968472	+	0.249121i	$0.0801418\pi$
$74$	6.22224	+	3.71308i	0.723320	+	0.431637i
$75$	−4.94819	−	4.06087i	−0.571367	−	0.468909i
$76$	−2.35374	+	12.0777i	−0.269993	+	1.38541i
$77$	15.4849	+	8.27683i	1.76466	+	0.943233i
$78$	4.56042	+	5.01208i	0.516366	+	0.567506i
$79$	11.2310	−	4.65202i	1.26358	−	0.523393i	0.352575	−	0.935784i	$-0.385306\pi$
$79$	11.2310	−	4.65202i	1.26358	−	0.523393i	0.911007	+	0.412391i	$0.135306\pi$
$80$	11.9605	+	6.27421i	1.33722	+	0.701478i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	−1.54170	−	4.28257i	−0.170253	−	0.472931i
$83$	9.92276	−	3.01004i	1.08916	−	0.330394i	0.305888	−	0.952068i	$-0.401047\pi$
$83$	9.92276	−	3.01004i	1.08916	−	0.330394i	0.783277	+	0.621673i	$0.213547\pi$
$84$	−8.11683	−	3.32527i	−0.885619	−	0.362817i
$85$	−0.418034	−	4.24437i	−0.0453421	−	0.460366i
$86$	−1.09507	+	7.48231i	−0.118084	+	0.806839i
$87$	−0.561248	−	0.839967i	−0.0601721	−	0.0900539i
$88$	11.1910	−	1.72662i	1.19296	−	0.184059i
$89$	6.17591	+	4.12661i	0.654645	+	0.437420i	0.838032	−	0.545621i	$-0.183706\pi$
$89$	6.17591	+	4.12661i	0.654645	+	0.437420i	−0.183387	+	0.983041i	$0.558706\pi$
$90$	4.76897	−	0.243557i	0.502693	−	0.0256731i
$91$	−20.1099	−	6.10028i	−2.10809	−	0.639483i
$92$	−15.3334	+	1.57028i	−1.59862	+	0.163713i
$93$	−4.23626	−	5.16190i	−0.439280	−	0.535264i
$94$	−7.21418	−	5.32874i	−0.744085	−	0.549618i
$95$	14.6896	+	14.6896i	1.50712	+	1.50712i
$96$	−5.47374	+	1.42765i	−0.558661	+	0.145709i
$97$	−4.74084	+	4.74084i	−0.481360	+	0.481360i	−0.905566	−	0.424206i	$-0.860553\pi$
$97$	−4.74084	+	4.74084i	−0.481360	+	0.481360i	0.424206	+	0.905566i	$0.360553\pi$
$98$	17.1108	−	2.57207i	1.72845	−	0.259818i
$99$	3.09468	−	2.53974i	0.311027	−	0.255253i
$100$	11.2672	−	6.07875i	1.12672	−	0.607875i
$101$	−0.319769	+	1.05414i	−0.0318182	+	0.104891i	−0.971411	−	0.237403i	$-0.923704\pi$
$101$	−0.319769	+	1.05414i	−0.0318182	+	0.104891i	0.939593	+	0.342294i	$0.111204\pi$
$102$	1.32587	+	1.19702i	0.131281	+	0.118523i
$103$	−6.75902	+	10.1156i	−0.665986	+	0.996718i	0.332574	+	0.943077i	$0.392083\pi$
$103$	−6.75902	+	10.1156i	−0.665986	+	0.996718i	−0.998560	+	0.0536412i	$0.982917\pi$
$104$	−12.7336	+	4.63991i	−1.24863	+	0.454981i
$105$	−12.3131	+	8.22737i	−1.20164	+	0.802909i
$106$	2.61531	+	3.51209i	0.254022	+	0.341124i
$107$	3.44738	−	0.339538i	0.333271	−	0.0328244i	0.0700023	−	0.997547i	$-0.477699\pi$
$107$	3.44738	−	0.339538i	0.333271	−	0.0328244i	0.263269	+	0.964722i	$0.415199\pi$
$108$	−1.40872	+	1.41969i	−0.135554	+	0.136610i
$109$	−0.540057	−	1.78033i	−0.0517281	−	0.170525i	0.927270	−	0.374393i	$-0.122149\pi$
$109$	−0.540057	−	1.78033i	−0.0517281	−	0.170525i	−0.978998	+	0.203868i	$0.934649\pi$
$110$	8.14006	−	17.2974i	0.776124	−	1.64924i
$111$	−1.96073	+	4.73362i	−0.186104	+	0.449295i
$112$	12.3083	−	12.5007i	1.16302	−	1.18121i
$113$	7.26628	+	17.5424i	0.683554	+	1.65025i	0.757380	+	0.652975i	$0.226479\pi$
$113$	7.26628	+	17.5424i	0.683554	+	1.65025i	−0.0738256	+	0.997271i	$0.523521\pi$
$114$	−8.69123	−	0.410077i	−0.814008	−	0.0384073i
$115$	−12.2669	+	22.9498i	−1.14389	+	2.14008i
$116$	1.98007	−	0.401852i	0.183845	−	0.0373110i
$117$	−3.03974	+	3.70394i	−0.281024	+	0.342429i
$118$	2.34241	+	9.27506i	0.215636	+	0.853838i
$119$	−5.43319	−	1.08073i	−0.498060	−	0.0990703i
$120$	−3.16505	+	9.01066i	−0.288928	+	0.822557i
$121$	−0.980782	−	4.93073i	−0.0891620	−	0.448248i
$122$	−17.7906	−	6.32669i	−1.61069	−	0.572792i
$123$	2.83845	−	1.51718i	0.255934	−	0.136800i
$124$	12.7651	−	3.92639i	1.14634	−	0.352600i
$125$	0.463740	−	4.70843i	0.0414782	−	0.421135i
$126$	1.49540	−	6.01946i	0.133221	−	0.536257i
$127$	−16.7484			−1.48618			−0.743088	−	0.669193i	$-0.766640\pi$
$127$	−16.7484			−1.48618			−0.743088	+	0.669193i	$0.766640\pi$
$128$	1.50798	−	11.2128i	0.133288	−	0.991077i
$129$	−5.34716			−0.470791
$130$	−5.51649	+	22.2057i	−0.483828	+	1.94757i
$131$	1.36011	−	13.8094i	0.118833	−	1.20653i	−0.732077	−	0.681221i	$-0.761449\pi$
$131$	1.36011	−	13.8094i	0.118833	−	1.20653i	0.850911	−	0.525311i	$-0.176051\pi$
$132$	2.35396	+	7.65298i	0.204886	+	0.666107i
$133$	23.7972	−	12.7199i	2.06348	−	1.10295i
$134$	−2.86023	−	1.01715i	−0.247087	−	0.0878688i
$135$	0.658735	+	3.31169i	0.0566949	+	0.285024i
$136$	−3.22061	+	1.54623i	−0.276165	+	0.132588i
$137$	−0.887171	−	0.176469i	−0.0757962	−	0.0150768i	0.157047	−	0.987591i	$-0.449803\pi$
$137$	−0.887171	−	0.176469i	−0.0757962	−	0.0150768i	−0.232843	+	0.972514i	$0.574803\pi$
$138$	−2.66875	−	10.5673i	−0.227179	−	0.899545i
$139$	1.81983	−	2.21747i	0.154356	−	0.188083i	−0.690091	−	0.723723i	$-0.742429\pi$
$139$	1.81983	−	2.21747i	0.154356	−	0.188083i	0.844447	+	0.535640i	$0.179929\pi$
$140$	−5.89077	−	29.0260i	−0.497861	−	2.45315i
$141$	2.98956	−	5.59307i	0.251766	−	0.471022i
$142$	−0.866504	−	0.0408842i	−0.0727154	−	0.00343092i
$143$	7.34089	+	17.7225i	0.613876	+	1.48203i
$144$	−1.55936	−	3.68353i	−0.129946	−	0.306961i
$145$	1.30536	−	3.15142i	0.108404	−	0.261711i
$146$	0.570012	−	1.21126i	0.0471746	−	0.100245i
$147$	3.55166	+	11.7082i	0.292936	+	0.965680i
$148$	−7.27396	−	7.21775i	−0.597916	−	0.593295i
$149$	−9.25334	+	0.911375i	−0.758064	+	0.0746627i	−0.469661	−	0.882847i	$-0.655624\pi$
$149$	−9.25334	+	0.911375i	−0.758064	+	0.0746627i	−0.288402	+	0.957509i	$0.593124\pi$
$150$	5.40675	+	7.26069i	0.441459	+	0.592832i
$151$	7.21921	−	4.82372i	0.587491	−	0.392549i	−0.225999	−	0.974128i	$-0.572565\pi$
$151$	7.21921	−	4.82372i	0.587491	−	0.392549i	0.813490	+	0.581578i	$0.197565\pi$
$152$	7.34857	−	15.7741i	0.596048	−	1.27944i
$153$	−0.701735	+	1.05022i	−0.0567319	+	0.0849053i
$154$	−18.4308	−	16.6397i	−1.48520	−	1.34087i
$155$	6.54520	−	21.5766i	0.525723	−	1.73308i
$156$	−4.55022	−	8.43400i	−0.364309	−	0.675260i
$157$	−1.70159	+	1.39645i	−0.135801	+	0.111449i	−0.699842	−	0.714298i	$-0.746746\pi$
$157$	−1.70159	+	1.39645i	−0.135801	+	0.111449i	0.564041	+	0.825747i	$0.309246\pi$
$158$	−17.0006	+	2.55551i	−1.35250	+	0.203305i
$159$	−2.18944	+	2.18944i	−0.173634	+	0.173634i
$160$	−14.2764	−	12.6894i	−1.12865	−	1.00319i
$161$	23.9004	+	23.9004i	1.88362	+	1.88362i
$162$	−1.13754	−	0.840241i	−0.0893735	−	0.0660156i
$163$	3.99788	+	4.87143i	0.313138	+	0.381560i	0.905667	−	0.423989i	$-0.139370\pi$
$163$	3.99788	+	4.87143i	0.313138	+	0.381560i	−0.592529	+	0.805549i	$0.701870\pi$
$164$	0.655776	+	6.40347i	0.0512075	+	0.500027i
$165$	12.9357	+	3.92401i	1.00704	+	0.305484i
$166$	−14.6453	+	0.747951i	−1.13669	+	0.0580522i
$167$	15.3503	+	10.2567i	1.18784	+	0.793689i	0.982729	−	0.185050i	$-0.0592448\pi$
$167$	15.3503	+	10.2567i	1.18784	+	0.793689i	0.205110	+	0.978739i	$0.434245\pi$
$168$	10.0065	+	7.33147i	0.772019	+	0.565635i
$169$	−5.53304	−	8.28078i	−0.425619	−	0.636983i
$170$	−0.873430	+	5.96791i	−0.0669890	+	0.457718i
$171$	−0.603047	−	6.12284i	−0.0461161	−	0.468225i
$172$	4.05418	−	9.89606i	0.309128	−	0.754567i
$173$	2.61421	−	0.793013i	0.198755	−	0.0602917i	−0.189338	−	0.981912i	$-0.560634\pi$
$173$	2.61421	−	0.793013i	0.198755	−	0.0602917i	0.388093	+	0.921620i	$0.373134\pi$
$174$	0.483911	+	1.34422i	0.0366852	+	0.101905i
$175$	−25.9372	−	10.7435i	−1.96067	−	0.812135i
$176$	−15.9482	−	1.44593i	−1.20214	−	0.108991i
$177$	−6.24947	+	2.58861i	−0.469739	+	0.194572i
$178$	−7.06938	−	7.76952i	−0.529872	−	0.582350i
$179$	−13.3470	−	7.13409i	−0.997598	−	0.533227i	−0.110042	−	0.993927i	$-0.535099\pi$
$179$	−13.3470	−	7.13409i	−0.997598	−	0.533227i	−0.887556	+	0.460700i	$0.847599\pi$
$180$	−6.62843	−	1.29177i	−0.494054	−	0.0962828i
$181$	15.7698	+	12.9420i	1.17216	+	0.961969i	0.999734	−	0.0230536i	$-0.00733885\pi$
$181$	15.7698	+	12.9420i	1.17216	+	0.961969i	0.172428	+	0.985022i	$0.444839\pi$
$182$	25.5208	+	15.2294i	1.89173	+	1.12888i
$183$	2.60478	−	13.0951i	0.192551	−	0.968018i
$184$	21.5804	+	3.07293i	1.59093	+	0.226540i
$185$	−16.9679	+	3.37512i	−1.24750	+	0.248144i
$186$	4.05422	+	8.52909i	0.297270	+	0.625383i
$187$	2.38370	+	4.45958i	0.174313	+	0.326117i
$188$	8.08451	+	9.77345i	0.589623	+	0.712802i
$189$	4.36466	+	0.429882i	0.317483	+	0.0312693i
$190$	−15.1527	−	25.1700i	−1.09930	−	1.82602i
$191$		−	10.2935i		−	0.744813i	−0.928070	−	0.372407i	$-0.878533\pi$
$191$		−	10.2935i		−	0.744813i	0.928070	−	0.372407i	$-0.121467\pi$
$192$	7.99946	−	0.0930917i	0.577311	−	0.00671832i
$193$			15.7970i			1.13709i	0.822651	+	0.568547i	$0.192494\pi$
$193$			15.7970i			1.13709i	−0.822651	+	0.568547i	$0.807506\pi$
$194$	8.12324	−	4.89032i	0.583215	−	0.351105i
$195$	−16.1012	−	1.58583i	−1.15303	−	0.113563i
$196$	−24.3615	−	2.30402i	−1.74010	−	0.164573i
$197$	1.70010	+	3.18066i	0.121127	+	0.226613i	0.935176	−	0.354184i	$-0.115241\pi$
$197$	1.70010	+	3.18066i	0.121127	+	0.226613i	−0.814049	+	0.580796i	$0.802741\pi$
$198$	−5.11340	+	2.43060i	−0.363393	+	0.172735i
$199$	−18.3139	+	3.64286i	−1.29824	+	0.258235i	−0.795368	−	0.606127i	$-0.792722\pi$
$199$	−18.3139	+	3.64286i	−1.29824	+	0.258235i	−0.502869	+	0.864362i	$0.667722\pi$
$200$	−17.5368	+	4.50134i	−1.24004	+	0.318293i
$201$	0.418775	−	2.10533i	0.0295381	−	0.148498i
$202$	0.798305	−	1.33777i	0.0561685	−	0.0941250i
$203$	−3.42490	−	2.81075i	−0.240381	−	0.197276i
$204$	−1.41161	−	2.09498i	−0.0988322	−	0.146678i
$205$	9.58420	+	5.12286i	0.669390	+	0.357796i
$206$	12.7258	−	11.5790i	0.886647	−	0.806748i
$207$	7.12014	−	2.94926i	0.494884	−	0.204988i
$208$	19.0589	−	2.02654i	1.32149	−	0.140515i
$209$	−22.7559	−	9.42582i	−1.57406	−	0.651998i
$210$	19.7050	−	7.09369i	1.35977	−	0.489511i
$211$	2.97206	−	0.901564i	0.204605	−	0.0620662i	−0.186319	−	0.982489i	$-0.559656\pi$
$211$	2.97206	−	0.901564i	0.204605	−	0.0620662i	0.390924	+	0.920423i	$0.372156\pi$
$212$	−2.39201	−	5.71205i	−0.164284	−	0.392305i
$213$	−0.0601230	−	0.610439i	−0.00411956	−	0.0418266i
$214$	−4.84729	−	0.709422i	−0.331354	−	0.0484951i
$215$	−10.0308	−	15.0122i	−0.684097	−	1.02382i
$216$	2.41752	−	1.46819i	0.164491	−	0.0998979i
$217$	−24.3510	−	16.2708i	−1.65306	−	1.10454i
$218$	0.134196	+	2.62764i	0.00908893	+	0.177966i
$219$	0.905832	+	0.274781i	0.0612104	+	0.0185680i
$220$	−17.0700	+	20.9652i	−1.15086	+	1.41347i
$221$	−3.83947	−	4.67841i	−0.258271	−	0.314704i
$222$	4.30509	−	5.82833i	0.288939	−	0.391172i
$223$	17.1567	+	17.1567i	1.14890	+	1.14890i	0.986769	+	0.162131i	$0.0518368\pi$
$223$	17.1567	+	17.1567i	1.14890	+	1.14890i	0.162131	+	0.986769i	$0.448163\pi$
$224$	−21.1553	+	12.9605i	−1.41350	+	0.865960i
$225$	−4.52633	+	4.52633i	−0.301755	+	0.301755i
$226$	−3.99161	−	26.5543i	−0.265518	−	1.76637i
$227$	7.94248	−	6.51823i	0.527161	−	0.432630i	−0.332794	−	0.942999i	$-0.607991\pi$
$227$	7.94248	−	6.51823i	0.527161	−	0.432630i	0.859955	+	0.510370i	$0.170491\pi$
$228$	11.7888	+	3.52623i	0.780735	+	0.233530i
$229$	0.306548	−	1.01055i	0.0202573	−	0.0667793i	−0.946229	−	0.323498i	$-0.895141\pi$
$229$	0.306548	−	1.01055i	0.0202573	−	0.0667793i	0.966486	+	0.256718i	$0.0826412\pi$
$230$	24.6613	−	27.3159i	1.62612	−	1.80115i
$231$	9.75476	−	14.5990i	0.641816	−	0.960546i
$232$	−2.85466	−	0.123595i	−0.187418	−	0.00811444i
$233$	−1.12444	+	0.751324i	−0.0736643	+	0.0492209i	−0.591857	−	0.806043i	$-0.701605\pi$
$233$	−1.12444	+	0.751324i	−0.0736643	+	0.0492209i	0.518193	+	0.855264i	$0.326605\pi$
$234$	5.43495	−	4.04719i	0.355294	−	0.264573i
$235$	21.3108	−	2.09893i	1.39016	−	0.136919i
$236$	−0.0524767	−	13.5287i	−0.00341594	−	0.880640i
$237$	−3.52879	−	11.6329i	−0.229219	−	0.755635i
$238$	7.08854	+	3.33582i	0.459482	+	0.216229i
$239$	−0.154385	+	0.372718i	−0.00998633	+	0.0241091i	−0.928794	−	0.370596i	$-0.879153\pi$
$239$	−0.154385	+	0.372718i	−0.00998633	+	0.0241091i	0.918808	+	0.394705i	$0.129153\pi$
$240$	7.41633	−	11.2879i	0.478722	−	0.728632i
$241$	−2.39595	−	5.78433i	−0.154336	−	0.372601i	0.827733	−	0.561123i	$-0.189630\pi$
$241$	−2.39595	−	5.78433i	−0.154336	−	0.372601i	−0.982069	+	0.188522i	$0.939630\pi$
$242$	−0.335084	+	7.10181i	−0.0215400	+	0.456522i
$243$	0.471397	−	0.881921i	0.0302401	−	0.0565753i
$244$	22.2604	+	14.7493i	1.42507	+	0.944229i
$245$	−26.2084	+	31.9350i	−1.67439	+	2.04025i
$246$	−4.41306	+	1.11451i	−0.281367	+	0.0710589i
$247$	28.9135	+	5.75126i	1.83972	+	0.365944i
$248$	−18.8588	+	1.03650i	−1.19753	+	0.0658177i
$249$	−2.02294	−	10.1700i	−0.128199	−	0.644499i
$250$	−2.24189	+	6.30418i	−0.141790	+	0.398711i
$251$	0.492423	−	0.263206i	0.0310815	−	0.0166134i	−0.455783	−	0.890091i	$-0.650641\pi$
$251$	0.492423	−	0.263206i	0.0310815	−	0.0166134i	0.486864	+	0.873478i	$0.338141\pi$
$252$	−4.10485	+	7.75181i	−0.258581	+	0.488318i
$253$	3.02417	−	30.7049i	0.190128	−	1.93040i
$254$	22.9870	+	5.71060i	1.44234	+	0.358315i
$255$	−4.26490			−0.267079
$256$	−5.89285	+	14.8753i	−0.368303	+	0.929706i
$257$	−8.38637			−0.523127			−0.261564	−	0.965186i	$-0.584238\pi$
$257$	−8.38637			−0.523127			−0.261564	+	0.965186i	$0.584238\pi$
$258$	7.33895	+	1.82319i	0.456903	+	0.113507i
$259$	−2.20256	+	22.3629i	−0.136860	+	1.38956i
$260$	15.1427	−	28.5963i	0.939111	−	1.77347i
$261$	−0.890934	+	0.476214i	−0.0551475	+	0.0294769i
$262$	−6.57525	+	18.4896i	−0.406220	+	1.14229i
$263$	−1.50467	−	7.56451i	−0.0927822	−	0.466448i	−0.999043	−	0.0437295i	$-0.986076\pi$
$263$	−1.50467	−	7.56451i	−0.0927822	−	0.466448i	0.906261	−	0.422718i	$-0.138924\pi$
$264$	−0.621406	−	11.3063i	−0.0382449	−	0.695855i
$265$	−10.2541	−	2.03967i	−0.629904	−	0.125296i
$266$	−36.9986	+	9.34395i	−2.26853	+	0.572915i
$267$	4.71209	−	5.74169i	0.288375	−	0.351386i
$268$	3.57884	+	2.37128i	0.218613	+	0.144849i
$269$	13.9223	−	26.0468i	0.848859	−	1.58810i	0.0406758	−	0.999172i	$-0.487049\pi$
$269$	13.9223	−	26.0468i	0.848859	−	1.58810i	0.808183	−	0.588931i	$-0.200451\pi$
$270$	0.225057	−	4.76988i	0.0136965	−	0.290286i
$271$	11.2414	+	27.1390i	0.682864	+	1.64858i	0.758685	+	0.651458i	$0.225842\pi$
$271$	11.2414	+	27.1390i	0.682864	+	1.64858i	−0.0758207	+	0.997121i	$0.524158\pi$
$272$	4.94748	−	1.02408i	0.299985	−	0.0620939i
$273$	−8.04202	+	19.4152i	−0.486725	+	1.17506i
$274$	1.15747	+	0.544697i	0.0699252	+	0.0329064i
$275$	7.43901	+	24.5231i	0.448589	+	1.47880i
$276$	0.0597877	+	15.4135i	0.00359880	+	0.927781i
$277$	−28.8138	+	2.83791i	−1.73126	+	0.170514i	−0.913987	−	0.405744i	$-0.867013\pi$
$277$	−28.8138	+	2.83791i	−1.73126	+	0.170514i	−0.817268	+	0.576258i	$0.804513\pi$
$278$	−3.25378	+	2.42297i	−0.195149	+	0.145320i
$279$	−5.55227	+	3.70991i	−0.332405	+	0.222106i
$280$	−1.81179	+	41.8466i	−0.108275	+	2.50081i
$281$	−4.00400	+	5.99241i	−0.238859	+	0.357477i	−0.931460	−	0.363843i	$-0.881464\pi$
$281$	−4.00400	+	5.99241i	−0.238859	+	0.357477i	0.692602	+	0.721320i	$0.256464\pi$
$282$	−6.01019	+	6.65713i	−0.357902	+	0.396426i
$283$	−0.400118	+	1.31901i	−0.0237845	+	0.0784071i	−0.968029	−	0.250837i	$-0.919294\pi$
$283$	−0.400118	+	1.31901i	−0.0237845	+	0.0784071i	0.944245	+	0.329245i	$0.106794\pi$
$284$	1.17533	+	0.351561i	0.0697432	+	0.0208613i
$285$	16.0587	−	13.1790i	0.951233	−	0.780657i
$286$	−4.03260	−	26.8270i	−0.238453	−	1.58631i
$287$	9.98121	−	9.98121i	0.589172	−	0.589172i
$288$	0.884255	+	5.58732i	0.0521052	+	0.329236i
$289$	10.8927	+	10.8927i	0.640747	+	0.640747i
$290$	−2.86612	+	3.88023i	−0.168305	+	0.227855i
$291$	4.25333	+	5.18270i	0.249335	+	0.303815i
$292$	−1.19534	+	1.46810i	−0.0699518	+	0.0859139i
$293$	−0.704442	−	0.213690i	−0.0411539	−	0.0124839i	0.269641	−	0.962961i	$-0.413095\pi$
$293$	−0.704442	−	0.213690i	−0.0411539	−	0.0124839i	−0.310795	+	0.950477i	$0.600595\pi$
$294$	−0.882535	−	17.2805i	−0.0514705	−	1.00782i
$295$	−18.9911	−	12.6894i	−1.10570	−	0.738807i
$296$	7.52248	+	12.3865i	0.437235	+	0.719950i
$297$	−2.22418	−	3.32872i	−0.129060	−	0.193152i
$298$	13.0109	+	1.90421i	0.753702	+	0.110308i
$299$	3.61954	+	36.7498i	0.209324	+	2.12530i
$300$	−4.94510	−	11.8088i	−0.285506	−	0.681779i
$301$	−22.4417	+	6.80760i	−1.29352	+	0.392384i
$302$	−11.5531	+	4.15904i	−0.664804	+	0.239326i
$303$	1.01772	+	0.421553i	0.0584664	+	0.0242176i
$304$	−15.4643	+	19.1442i	−0.886937	+	1.09800i
$305$	41.6510	−	17.2524i	2.38493	−	0.987870i
$306$	1.32122	−	1.20216i	0.0755289	−	0.0687227i
$307$	−4.16641	−	2.22699i	−0.237790	−	0.127101i	0.348199	−	0.937421i	$-0.386794\pi$
$307$	−4.16641	−	2.22699i	−0.237790	−	0.127101i	−0.585988	+	0.810320i	$0.699294\pi$
$308$	19.6226	+	29.1222i	1.11810	+	1.65939i
$309$	9.40438	+	7.71797i	0.534996	+	0.439060i
$310$	−16.3401	+	27.3822i	−0.928057	+	1.55520i
$311$	2.67355	−	13.4408i	0.151603	−	0.762160i	−0.827923	−	0.560842i	$-0.810478\pi$
$311$	2.67355	−	13.4408i	0.151603	−	0.762160i	0.979526	−	0.201318i	$-0.0645224\pi$
$312$	3.36945	+	13.1271i	0.190758	+	0.743175i
$313$	−1.37776	+	0.274054i	−0.0778757	+	0.0154904i	−0.233874	−	0.972267i	$-0.575140\pi$
$313$	−1.37776	+	0.274054i	−0.0778757	+	0.0154904i	0.155999	+	0.987757i	$0.450140\pi$
$314$	2.81156	−	1.33645i	0.158665	−	0.0754201i
$315$	6.98086	+	13.0603i	0.393327	+	0.735863i
$316$	24.2046	+	2.28918i	1.36162	+	0.128777i
$317$	−29.6144	−	2.91676i	−1.66331	−	0.163822i	−0.777822	−	0.628484i	$-0.783676\pi$
$317$	−29.6144	−	2.91676i	−1.66331	−	0.163822i	−0.885488	+	0.464662i	$0.846176\pi$
$318$	3.75152	−	2.25848i	0.210375	−	0.126649i
$319$			4.04433i			0.226439i
$320$	15.2677	+	22.2839i	0.853490	+	1.24571i
$321$		−	3.46406i		−	0.193345i
$322$	−24.6540	−	40.9524i	−1.37391	−	2.28219i
$323$	7.73369	+	0.761702i	0.430314	+	0.0423822i
$324$	1.27477	+	1.54109i	0.0708208	+	0.0856160i
$325$	−14.4586	−	27.0501i	−0.802018	−	1.50047i
$326$	−3.82609	−	8.04916i	−0.211907	−	0.445801i
$327$	−1.82469	+	0.362954i	−0.100906	+	0.0200714i
$328$	1.28331	−	9.01233i	0.0708588	−	0.497623i
$329$	5.42629	−	27.2798i	0.299161	−	1.50399i
$330$	−16.4163	−	9.79630i	−0.903685	−	0.539269i
$331$	21.0460	+	17.2720i	1.15679	+	0.949355i	0.999272	−	0.0381605i	$-0.0121498\pi$
$331$	21.0460	+	17.2720i	1.15679	+	0.949355i	0.157521	+	0.987516i	$0.449650\pi$
$332$	20.3556	+	3.96696i	1.11716	+	0.217715i
$333$	4.51864	+	2.41526i	0.247620	+	0.132356i
$334$	−17.5710	−	19.3112i	−0.961441	−	1.05666i
$335$	6.69631	−	2.77370i	0.365859	−	0.151544i
$336$	−11.2341	−	13.4743i	−0.612871	−	0.735082i
$337$	−16.6306	−	6.88862i	−0.905927	−	0.375247i	−0.119431	−	0.992843i	$-0.538107\pi$
$337$	−16.6306	−	6.88862i	−0.905927	−	0.375247i	−0.786496	+	0.617595i	$0.788107\pi$
$338$	4.77062	+	13.2519i	0.259487	+	0.720808i
$339$	18.1701	−	5.51184i	0.986864	−	0.299362i
$340$	3.23362	−	7.89312i	0.175368	−	0.428064i
$341$	2.62033	+	26.6047i	0.141899	+	1.44072i
$342$	−1.25999	+	8.60918i	−0.0681326	+	0.465531i
$343$	12.7559	+	19.0905i	0.688752	+	1.03079i
$344$	−8.93855	+	12.2000i	−0.481934	+	0.657778i
$345$	21.6369	+	14.4573i	1.16489	+	0.778355i
$346$	−3.85838	+	0.197052i	−0.207428	+	0.0105936i
$347$	−33.2146	−	10.0755i	−1.78305	−	0.540883i	−0.786043	−	0.618172i	$-0.787874\pi$
$347$	−33.2146	−	10.0755i	−1.78305	−	0.540883i	−0.997009	+	0.0772888i	$0.975374\pi$
$348$	−0.205836	−	2.00993i	−0.0110339	−	0.107743i
$349$	−6.06091	−	7.38524i	−0.324433	−	0.395323i	0.585095	−	0.810965i	$-0.301057\pi$
$349$	−6.06091	−	7.38524i	−0.324433	−	0.395323i	−0.909529	+	0.415642i	$0.863557\pi$
$350$	31.9355	+	23.5891i	1.70703	+	1.26089i
$351$	3.38816	+	3.38816i	0.180846	+	0.180846i
$352$	21.3959	+	7.42232i	1.14040	+	0.395611i
$353$	−6.56981	+	6.56981i	−0.349676	+	0.349676i	−0.859989	−	0.510313i	$-0.829530\pi$
$353$	−6.56981	+	6.56981i	−0.349676	+	0.349676i	0.510313	+	0.859989i	$0.329530\pi$
$354$	9.45999	−	1.42201i	0.502793	−	0.0755792i
$355$	1.60103	−	1.31393i	0.0849738	−	0.0697362i
$356$	7.05356	+	13.0740i	0.373838	+	0.692923i
$357$	−1.60807	+	5.30110i	−0.0851081	+	0.280564i
$358$	15.8862	+	14.3423i	0.839609	+	0.758017i
$359$	−11.6791	+	17.4790i	−0.616398	+	0.922504i	−1.00000		0.000994428i	$-0.999683\pi$
$359$	−11.6791	+	17.4790i	−0.616398	+	0.922504i	0.383602	+	0.923499i	$0.374683\pi$
$360$	8.65704	+	4.03301i	0.456266	+	0.212558i
$361$	−15.6755	+	10.4740i	−0.825027	+	0.551266i
$362$	−17.2313	−	23.1397i	−0.905655	−	1.21620i
$363$	−5.00312	+	0.492764i	−0.262596	+	0.0258634i
$364$	−29.8345	−	29.6039i	−1.56375	−	1.55167i
$365$	0.927816	+	3.05860i	0.0485641	+	0.160094i
$366$	−8.04001	+	17.0848i	−0.420258	+	0.893038i
$367$	6.67092	−	16.1050i	0.348219	−	0.840676i	−0.648611	−	0.761120i	$-0.724650\pi$
$367$	6.67092	−	16.1050i	0.348219	−	0.840676i	0.996830	−	0.0795556i	$-0.0253501\pi$
$368$	−28.5712	−	11.5757i	−1.48938	−	0.603427i
$369$	−1.23166	−	2.97349i	−0.0641177	−	0.154794i
$370$	24.4391	+	1.15311i	1.27053	+	0.0599472i
$371$	−6.40150	+	11.9764i	−0.332349	+	0.621782i
$372$	−2.65628	−	13.0885i	−0.137722	−	0.678606i
$373$	13.5992	−	16.5707i	0.704142	−	0.857999i	−0.290972	−	0.956732i	$-0.593979\pi$
$373$	13.5992	−	16.5707i	0.704142	−	0.857999i	0.995114	+	0.0987321i	$0.0314787\pi$
$374$	−1.75105	−	6.93352i	−0.0905448	−	0.358524i
$375$	−4.64030	−	0.923014i	−0.239624	−	0.0476642i
$376$	−7.76355	−	16.1705i	−0.400375	−	0.833932i
$377$	−0.944344	−	4.74754i	−0.0486362	−	0.244511i
$378$	−5.84390	−	2.07821i	−0.300578	−	0.106891i
$379$	−0.527170	+	0.281778i	−0.0270789	+	0.0144740i	−0.484881	−	0.874580i	$-0.661137\pi$
$379$	−0.527170	+	0.281778i	−0.0270789	+	0.0144740i	0.457802	+	0.889054i	$0.348637\pi$
$380$	12.2150	+	39.7122i	0.626616	+	2.03719i
$381$	−1.64163	+	16.6677i	−0.0841031	+	0.853913i
$382$	−3.50973	+	14.1278i	−0.179573	+	0.722842i
$383$	29.6835			1.51675			0.758377	−	0.651816i	$-0.225993\pi$
$383$	29.6835			1.51675			0.758377	+	0.651816i	$0.225993\pi$
$384$	−11.0110	−	2.59976i	−0.561901	−	0.132669i
$385$	59.2861			3.02150
$386$	5.38623	−	21.6813i	0.274152	−	1.10355i
$387$	−0.524113	+	5.32141i	−0.0266422	+	0.270502i
$388$	−12.8165	+	3.94221i	−0.650661	+	0.200135i
$389$	−10.2905	+	5.50041i	−0.521751	+	0.278882i	−0.711177	−	0.703013i	$-0.751837\pi$
$389$	−10.2905	+	5.50041i	−0.521751	+	0.278882i	0.189426	+	0.981895i	$0.439337\pi$
$390$	21.5581	+	7.66647i	1.09163	+	0.388207i
$391$	1.89908	+	9.54732i	0.0960406	+	0.482829i
$392$	32.6504	+	11.4686i	1.64909	+	0.579254i
$393$	−13.6096	−	2.70711i	−0.686513	−	0.136556i
$394$	−1.24888	−	4.94512i	−0.0629179	−	0.249131i
$395$	26.0397	−	31.7294i	1.31020	−	1.59648i
$396$	7.84686	−	1.59250i	0.394320	−	0.0800263i
$397$	−11.0626	+	20.6967i	−0.555216	+	1.03874i	0.435162	+	0.900352i	$0.356691\pi$
$397$	−11.0626	+	20.6967i	−0.555216	+	1.03874i	−0.990379	+	0.138385i	$0.955809\pi$
$398$	26.3778	+	1.24458i	1.32220	+	0.0623852i
$399$	−10.3261	−	24.9294i	−0.516951	−	1.24803i
$400$	25.6040	−	0.198635i	1.28020	−	0.00993176i
$401$	10.2654	−	24.7828i	0.512629	−	1.23759i	−0.429720	−	0.902962i	$-0.641388\pi$
$401$	10.2654	−	24.7828i	0.512629	−	1.23759i	0.942349	−	0.334633i	$-0.108612\pi$
$402$	−1.29261	+	2.74676i	−0.0644695	+	0.136996i
$403$	−9.28809	−	30.6187i	−0.462673	−	1.52523i
$404$	−1.55180	+	1.56389i	−0.0772050	+	0.0778062i
$405$	3.36031	−	0.330961i	0.166975	−	0.0164456i
$406$	3.74230	+	5.02551i	0.185727	+	0.249412i
$407$	17.0551	−	11.3959i	0.845391	−	0.564872i
$408$	1.22311	+	3.35666i	0.0605529	+	0.166179i
$409$	−10.2694	+	15.3693i	−0.507789	+	0.759961i	−0.993460	−	0.114181i	$-0.963575\pi$
$409$	−10.2694	+	15.3693i	−0.507789	+	0.759961i	0.485671	+	0.874142i	$0.338575\pi$
$410$	−11.4076	−	10.2990i	−0.563379	−	0.508630i
$411$	−0.262578	+	0.865602i	−0.0129520	+	0.0426970i
$412$	−21.4141	+	11.5531i	−1.05500	+	0.569180i
$413$	−22.9330	+	18.8206i	−1.12846	+	0.926101i
$414$	−10.7780	+	1.62013i	−0.529708	+	0.0796250i
$415$	24.7576	−	24.7576i	1.21530	−	1.21530i
$416$	−26.8492	−	3.71698i	−1.31639	−	0.182240i
$417$	−2.02841	−	2.02841i	−0.0993319	−	0.0993319i
$418$	28.0185	+	20.6959i	1.37043	+	1.01227i
$419$	−18.0036	−	21.9374i	−0.879531	−	1.07171i	−0.996904	−	0.0786240i	$-0.974947\pi$
$419$	−18.0036	−	21.9374i	−0.879531	−	1.07171i	0.117373	−	0.993088i	$-0.462553\pi$
$420$	−29.4637	+	3.01736i	−1.43768	+	0.147232i
$421$	−34.3877	−	10.4314i	−1.67596	−	0.508396i	−0.697804	−	0.716289i	$-0.745839\pi$
$421$	−34.3877	−	10.4314i	−1.67596	−	0.508396i	−0.978152	+	0.207893i	$0.933339\pi$
$422$	−4.38654	+	0.224026i	−0.213533	+	0.0109054i
$423$	−5.27311	−	3.52338i	−0.256387	−	0.171313i
$424$	1.33541	+	8.65535i	0.0648534	+	0.420341i
$425$	−4.49194	−	6.72266i	−0.217891	−	0.326097i
$426$	−0.125620	+	0.858324i	−0.00608629	+	0.0415859i
$427$	−5.73963	−	58.2755i	−0.277760	−	2.82015i
$428$	6.41099	+	2.62643i	0.309887	+	0.126953i
$429$	18.3567	−	5.56843i	0.886268	−	0.268847i
$430$	8.64864	+	24.0243i	0.417075	+	1.15856i
$431$	−0.413419	−	0.171244i	−0.0199137	−	0.00824852i	0.372704	−	0.927950i	$-0.378431\pi$
$431$	−0.413419	−	0.171244i	−0.0199137	−	0.00824852i	−0.392618	+	0.919702i	$0.628431\pi$
$432$	−3.81864	+	1.19080i	−0.183724	+	0.0572923i
$433$	30.4916	−	12.6300i	1.46533	−	0.606960i	0.499542	−	0.866290i	$-0.333502\pi$
$433$	30.4916	−	12.6300i	1.46533	−	0.606960i	0.965789	+	0.259330i	$0.0835016\pi$
$434$	27.8739	+	30.6345i	1.33799	+	1.47050i
$435$	−3.00830	−	1.60797i	−0.144237	−	0.0770962i
$436$	0.711747	−	3.65217i	0.0340865	−	0.174907i
$437$	−36.6528	−	30.0802i	−1.75334	−	1.43893i
$438$	−1.14956	−	0.685992i	−0.0549281	−	0.0327780i
$439$	4.13234	−	20.7747i	0.197226	−	0.991521i	−0.747650	−	0.664093i	$-0.768818\pi$
$439$	4.13234	−	20.7747i	0.197226	−	0.991521i	0.944876	−	0.327428i	$-0.106182\pi$
$440$	30.5769	−	22.9543i	1.45769	−	1.09430i
$441$	12.0000	−	2.38695i	0.571428	−	0.113664i
$442$	3.67448	+	7.73021i	0.174777	+	0.367689i
$443$	2.62814	+	4.91690i	0.124866	+	0.233609i	0.936585	−	0.350440i	$-0.113968\pi$
$443$	2.62814	+	4.91690i	0.124866	+	0.233609i	−0.811719	+	0.584048i	$0.801468\pi$
$444$	−7.89597	+	6.53147i	−0.374726	+	0.309970i
$445$	24.9594	+	2.45828i	1.18319	+	0.116534i
$446$	−17.6977	−	29.3974i	−0.838011	−	1.39201i
$447$			9.29812i			0.439786i
$448$	33.4547	−	10.5750i	1.58058	−	0.499622i
$449$			19.6541i			0.927534i	0.885957	+	0.463767i	$0.153503\pi$
$449$			19.6541i			0.927534i	−0.885957	+	0.463767i	$0.846497\pi$
$450$	7.75568	−	4.66904i	0.365606	−	0.220101i
$451$	−12.8229	−	1.26294i	−0.603806	−	0.0594697i
$452$	−3.57562	+	37.8067i	−0.168183	+	1.77828i
$453$	−4.09289	−	7.65726i	−0.192301	−	0.359769i
$454$	−13.1235	+	6.23813i	−0.615916	+	0.292770i
$455$	−69.5944	+	13.8432i	−3.26264	+	0.648979i
$456$	−14.9778	−	8.85931i	−0.701400	−	0.414875i
$457$	−1.17569	+	5.91061i	−0.0549966	+	0.276487i	−0.998492	−	0.0548993i	$-0.982516\pi$
$457$	−1.17569	+	5.91061i	−0.0549966	+	0.276487i	0.943495	+	0.331386i	$0.107516\pi$
$458$	−0.765299	+	1.28246i	−0.0357601	+	0.0599254i
$459$	0.976381	+	0.801295i	0.0455736	+	0.0374013i
$460$	−43.1613	+	29.0823i	−2.01241	+	1.35597i
$461$	21.2884	+	11.3789i	0.991501	+	0.529968i	0.885620	−	0.464410i	$-0.153734\pi$
$461$	21.2884	+	11.3789i	0.991501	+	0.529968i	0.105881	+	0.994379i	$0.466234\pi$
$462$	−18.3661	+	16.7111i	−0.854469	+	0.777469i
$463$	−24.9805	+	10.3473i	−1.16094	+	0.480878i	−0.878188	−	0.478315i	$-0.841248\pi$
$463$	−24.9805	+	10.3473i	−1.16094	+	0.480878i	−0.282753	+	0.959193i	$0.591248\pi$
$464$	3.87586	+	1.14297i	0.179932	+	0.0530611i
$465$	−20.8312	−	8.62857i	−0.966024	−	0.400140i
$466$	1.79946	−	0.647796i	0.0833583	−	0.0300086i
$467$	−24.2546	+	7.35755i	−1.12237	+	0.340467i	−0.796314	−	0.604884i	$-0.793220\pi$
$467$	−24.2546	+	7.35755i	−1.12237	+	0.340467i	−0.326055	+	0.945351i	$0.605720\pi$
$468$	−8.83939	+	3.70163i	−0.408601	+	0.171108i
$469$	−0.922772	−	9.36906i	−0.0426097	−	0.432623i
$470$	−29.9646	−	4.38545i	−1.38216	−	0.202286i
$471$	1.22295	+	1.83027i	0.0563504	+	0.0843343i
$472$	−4.54077	+	18.5859i	−0.209006	+	0.855485i
$473$	17.7992	+	11.8930i	0.818407	+	0.546842i
$474$	0.876853	+	17.1692i	0.0402752	+	0.788609i
$475$	37.6873	+	11.4323i	1.72921	+	0.524550i
$476$	−8.59159	−	6.99534i	−0.393795	−	0.320631i
$477$	1.96430	+	2.39350i	0.0899389	+	0.109591i
$478$	0.338976	−	0.458914i	0.0155044	−	0.0209902i
$479$	−10.6293	−	10.6293i	−0.485667	−	0.485667i	0.421269	−	0.906936i	$-0.361585\pi$
$479$	−10.6293	−	10.6293i	−0.485667	−	0.485667i	−0.906936	+	0.421269i	$0.861585\pi$
$480$	−14.0277	+	12.9639i	−0.640272	+	0.591719i
$481$	−17.3597	+	17.3597i	−0.791533	+	0.791533i
$482$	1.31617	+	8.75589i	0.0599501	+	0.398820i
$483$	26.1280	−	21.4427i	1.18886	−	0.975676i
$484$	2.88137	−	9.63295i	0.130971	−	0.437861i
$485$	−6.57158	+	21.6636i	−0.298400	+	0.983693i
$486$	−0.947694	+	1.04970i	−0.0429883	+	0.0476155i
$487$	−9.71915	+	14.5457i	−0.440417	+	0.659130i	−0.983575	−	0.180500i	$-0.942228\pi$
$487$	−9.71915	+	14.5457i	−0.440417	+	0.659130i	0.543158	+	0.839630i	$0.317228\pi$
$488$	−25.5232	−	27.8334i	−1.15538	−	1.25996i
$489$	5.23984	−	3.50115i	0.236954	−	0.158327i
$490$	46.8596	−	34.8945i	2.11690	−	1.57637i
$491$	−8.99366	+	0.885798i	−0.405878	+	0.0399755i	−0.298897	−	0.954285i	$-0.596619\pi$
$491$	−8.99366	+	0.885798i	−0.405878	+	0.0399755i	−0.106982	+	0.994261i	$0.534119\pi$
$492$	6.43692	−	0.0249683i	0.290199	−	0.00112566i
$493$	−0.370403	−	1.22105i	−0.0166821	−	0.0549935i
$494$	−37.7227	−	17.7521i	−1.69723	−	0.798704i
$495$	5.17303	−	12.4888i	0.232511	−	0.561330i
$496$	26.2370	+	5.00759i	1.17808	+	0.224848i
$497$	−1.02950	−	2.48543i	−0.0461793	−	0.111487i
$498$	−0.691137	+	14.6480i	−0.0309706	+	0.656395i
$499$	−7.16763	+	13.4097i	−0.320867	+	0.600300i	−0.989707	−	0.143106i	$-0.954291\pi$
$499$	−7.16763	+	13.4097i	−0.320867	+	0.600300i	0.668840	+	0.743406i	$0.266791\pi$
$500$	5.22648	−	7.88805i	0.233735	−	0.352764i
$501$	11.7119	−	14.2710i	0.523250	−	0.637582i
$502$	−0.765592	+	0.193350i	−0.0341700	+	0.00862961i
$503$	−2.33202	−	0.463867i	−0.103980	−	0.0206828i	0.142826	−	0.989748i	$-0.454381\pi$
$503$	−2.33202	−	0.463867i	−0.103980	−	0.0206828i	−0.246806	+	0.969065i	$0.579381\pi$
$504$	8.27698	−	9.23971i	0.368686	−	0.411570i
$505$	0.725643	+	3.64805i	0.0322907	+	0.162336i
$506$	−14.6199	+	41.1112i	−0.649936	+	1.82762i
$507$	−8.78324	+	4.69474i	−0.390077	+	0.208501i
$508$	−29.6025	−	15.6755i	−1.31340	−	0.695490i
$509$	−1.42326	+	14.4506i	−0.0630848	+	0.640511i	0.910704	+	0.413059i	$0.135540\pi$
$509$	−1.42326	+	14.4506i	−0.0630848	+	0.640511i	−0.973789	+	0.227452i	$0.926960\pi$
$510$	5.85356	+	1.45418i	0.259200	+	0.0643922i
$511$	4.15154			0.183653
$512$	13.1599	−	18.4070i	0.581589	−	0.813483i
$513$	−6.15246			−0.271638
$514$	11.5102	+	2.85945i	0.507695	+	0.126125i
$515$	−4.02645	+	40.8812i	−0.177426	+	1.80144i
$516$	−9.45103	−	5.00464i	−0.416058	−	0.220317i
$517$	−22.3914	+	11.9684i	−0.984772	+	0.526371i
$518$	10.6480	−	29.9420i	0.467845	−	1.31558i
$519$	−0.532957	−	2.67935i	−0.0233942	−	0.117611i
$520$	−30.5336	+	34.0851i	−1.33899	+	1.49473i
$521$	−11.7058	−	2.32844i	−0.512842	−	0.102011i	−0.0681163	−	0.997677i	$-0.521699\pi$
$521$	−11.7058	−	2.32844i	−0.512842	−	0.102011i	−0.444726	+	0.895667i	$0.646699\pi$
$522$	1.38518	−	0.349825i	0.0606275	−	0.0153114i
$523$	9.60590	−	11.7048i	0.420037	−	0.511816i	−0.519403	−	0.854529i	$-0.673846\pi$
$523$	9.60590	−	11.7048i	0.420037	−	0.511816i	0.939440	+	0.342713i	$0.111346\pi$
$524$	15.3288	−	23.1349i	0.669641	−	1.01065i
$525$	−13.2341	+	24.7593i	−0.577583	+	1.08058i
$526$	−0.514072	+	10.8953i	−0.0224146	+	0.475057i
$527$	−3.22773	−	7.79244i	−0.140602	−	0.339444i
$528$	−3.00217	+	15.7297i	−0.130653	+	0.684548i
$529$	13.9276	−	33.6242i	0.605548	−	1.46192i
$530$	13.3782	+	6.29572i	0.581114	+	0.273468i
$531$	1.96359	+	6.47310i	0.0852128	+	0.280909i
$532$	53.9663	−	0.209331i	2.33974	−	0.00907567i
$533$	15.3473	−	1.51158i	0.664767	−	0.0654739i
$534$	−8.42503	+	6.27379i	−0.364587	+	0.271494i
$535$	9.72540	−	6.49830i	0.420466	−	0.280946i
$536$	−4.10342	−	4.47483i	−0.177241	−	0.193283i
$537$	−8.40797	+	12.5834i	−0.362831	+	0.543015i
$538$	−27.9894	+	31.0021i	−1.20671	+	1.33660i
$539$	14.2188	−	46.8730i	0.612445	−	2.01896i
$540$	−1.93525	+	6.46990i	−0.0832798	+	0.278420i
$541$	9.71713	−	7.97464i	0.417772	−	0.342857i	−0.401906	−	0.915681i	$-0.631652\pi$
$541$	9.71713	−	7.97464i	0.417772	−	0.342857i	0.819678	+	0.572824i	$0.194152\pi$
$542$	−6.17526	−	41.0811i	−0.265250	−	1.76458i
$543$	14.4254	−	14.4254i	0.619051	−	0.619051i
$544$	−7.13957	−	0.281374i	−0.306107	−	0.0120638i
$545$	−4.44197	−	4.44197i	−0.190273	−	0.190273i
$546$	17.6575	−	23.9052i	0.755672	−	1.02305i
$547$	2.51798	+	3.06817i	0.107661	+	0.131185i	0.824053	−	0.566513i	$-0.191708\pi$
$547$	2.51798	+	3.06817i	0.107661	+	0.131185i	−0.716392	+	0.697698i	$0.754208\pi$
$548$	−1.40290	−	1.14225i	−0.0599288	−	0.0487945i
$549$	−12.7767	−	3.87578i	−0.545298	−	0.165414i
$550$	−1.84849	−	36.1943i	−0.0788198	−	1.54333i
$551$	5.16787	+	3.45306i	0.220158	+	0.147105i
$552$	5.17339	−	21.1753i	0.220194	−	0.901280i
$553$	−29.6202	−	44.3297i	−1.25958	−	1.88509i
$554$	40.5145	+	5.92947i	1.72129	+	0.251919i
$555$	1.69572	+	17.2170i	0.0719795	+	0.730820i
$556$	5.29195	−	2.21608i	0.224428	−	0.0939829i
$557$	3.41013	−	1.03445i	0.144492	−	0.0438311i	−0.217210	−	0.976125i	$-0.569696\pi$
$557$	3.41013	−	1.03445i	0.144492	−	0.0438311i	0.361702	+	0.932294i	$0.382196\pi$
$558$	8.88541	−	3.19870i	0.376149	−	0.135412i
$559$	−23.6710	−	9.80485i	−1.00118	−	0.414701i
$560$	16.7549	−	56.8165i	0.708024	−	2.40094i
$561$	4.67175	−	1.93510i	0.197242	−	0.0817002i
$562$	7.53867	−	6.85933i	0.318000	−	0.289344i
$563$	31.3170	+	16.7393i	1.31985	+	0.705476i	0.972642	−	0.232310i	$-0.0746285\pi$
$563$	31.3170	+	16.7393i	1.31985	+	0.705476i	0.347212	+	0.937787i	$0.387129\pi$
$564$	10.5188	−	7.08761i	0.442922	−	0.298442i
$565$	49.5602	+	40.6730i	2.08501	+	1.71113i
$566$	0.998896	−	1.67391i	0.0419867	−	0.0703597i
$567$	0.855624	−	4.30151i	0.0359328	−	0.180646i
$568$	−1.49327	−	0.883262i	−0.0626562	−	0.0370609i
$569$	25.1870	−	5.01001i	1.05589	−	0.210030i	0.363533	−	0.931581i	$-0.381570\pi$
$569$	25.1870	−	5.01001i	1.05589	−	0.210030i	0.692361	+	0.721551i	$0.256570\pi$
$570$	−26.5340	+	12.6127i	−1.11139	+	0.528287i
$571$	−0.200972	−	0.375993i	−0.00841043	−	0.0157348i	0.877681	−	0.479245i	$-0.159090\pi$
$571$	−0.200972	−	0.375993i	−0.00841043	−	0.0157348i	−0.886091	+	0.463511i	$0.846590\pi$
$572$	−3.61233	+	38.1949i	−0.151039	+	1.59701i
$573$	−10.2440	−	1.00894i	−0.427947	−	0.0421491i
$574$	−17.1024	+	10.2959i	−0.713840	+	0.429744i
$575$			49.3326i			2.05731i
$576$	0.691441	−	7.97006i	0.0288100	−	0.332086i
$577$			4.18486i			0.174218i	0.996199	+	0.0871090i	$0.0277628\pi$
$577$			4.18486i			0.174218i	−0.996199	+	0.0871090i	$0.972237\pi$
$578$	−11.2362	−	18.6642i	−0.467362	−	0.776329i
$579$	15.7210	+	1.54838i	0.653341	+	0.0643484i
$580$	5.25676	−	4.34835i	0.218275	−	0.180555i
$581$	−21.4379	−	40.1074i	−0.889392	−	1.66394i
$582$	−4.07056	−	8.56346i	−0.168730	−	0.354967i
$583$	12.1577	−	2.41832i	0.503522	−	0.100157i
$584$	2.14116	−	1.60739i	0.0886020	−	0.0665143i
$585$	−3.15638	+	15.8682i	−0.130500	+	0.656069i
$586$	0.893982	+	0.533478i	0.0369301	+	0.0220378i
$587$	−28.0485	−	23.0188i	−1.15769	−	0.950088i	−0.158381	−	0.987378i	$-0.550627\pi$
$587$	−28.0485	−	23.0188i	−1.15769	−	0.950088i	−0.999304	+	0.0372904i	$0.988127\pi$
$588$	−4.68076	+	24.0183i	−0.193031	+	0.990499i
$589$	36.2329	+	19.3669i	1.49295	+	0.797998i
$590$	21.7385	+	23.8915i	0.894960	+	0.983596i
$591$	3.33198	−	1.38015i	0.137060	−	0.0567719i
$592$	−6.10121	−	19.5653i	−0.250758	−	0.804129i
$593$	−13.9434	−	5.77554i	−0.572586	−	0.237173i	0.0775528	−	0.996988i	$-0.475289\pi$
$593$	−13.9434	−	5.77554i	−0.572586	−	0.237173i	−0.650139	+	0.759815i	$0.725289\pi$
$594$	1.91770	+	5.32701i	0.0786841	+	0.218570i
$595$	−17.8995	+	5.42976i	−0.733808	+	0.222598i
$596$	−17.2082	−	7.04978i	−0.704874	−	0.288770i
$597$	1.83024	+	18.5828i	0.0749069	+	0.760542i
$598$	7.56259	−	51.6731i	0.309257	−	2.11307i
$599$	21.3398	+	31.9373i	0.871921	+	1.30492i	0.951360	+	0.308082i	$0.0996870\pi$
$599$	21.3398	+	31.9373i	0.871921	+	1.30492i	−0.0794393	+	0.996840i	$0.525313\pi$
$600$	2.76076	+	17.8936i	0.112707	+	0.730502i
$601$	12.0324	+	8.03981i	0.490813	+	0.327951i	0.776227	−	0.630454i	$-0.217131\pi$
$601$	12.0324	+	8.03981i	0.490813	+	0.327951i	−0.285414	+	0.958404i	$0.592131\pi$
$602$	33.1222	−	1.69159i	1.34996	−	0.0689441i
$603$	−2.05414	−	0.623117i	−0.0836511	−	0.0253753i
$604$	17.2746	−	1.76908i	0.702893	−	0.0719829i
$605$	−10.7689	−	13.1219i	−0.437817	−	0.533482i
$606$	−1.25308	−	0.925585i	−0.0509028	−	0.0375993i
$607$	4.57537	+	4.57537i	0.185709	+	0.185709i	0.793838	−	0.608129i	$-0.208080\pi$
$607$	4.57537	+	4.57537i	0.185709	+	0.185709i	−0.608129	+	0.793838i	$0.708080\pi$
$608$	27.7521	−	21.0026i	1.12550	−	0.851767i
$609$	−3.13291	+	3.13291i	−0.126952	+	0.126952i
$610$	−63.0483	+	9.47733i	−2.55275	+	0.383726i
$611$	23.4901	−	19.2778i	0.950307	−	0.779896i
$612$	−2.22325	+	1.19947i	−0.0898698	+	0.0484855i
$613$	2.66986	−	8.80134i	0.107834	−	0.355483i	−0.886371	−	0.462975i	$-0.846782\pi$
$613$	2.66986	−	8.80134i	0.107834	−	0.355483i	0.994206	+	0.107492i	$0.0342820\pi$
$614$	4.95905	+	4.47714i	0.200131	+	0.180683i
$615$	6.03761	−	9.03593i	0.243460	−	0.364364i
$616$	−17.0023	−	46.6606i	−0.685044	−	1.88001i
$617$	6.26133	−	4.18368i	0.252071	−	0.168429i	−0.423115	−	0.906076i	$-0.639063\pi$
$617$	6.26133	−	4.18368i	0.252071	−	0.168429i	0.675186	+	0.737647i	$0.264063\pi$
$618$	−10.2759	−	13.7994i	−0.413358	−	0.555095i
$619$	1.06588	−	0.104980i	0.0428411	−	0.00421948i	−0.0765739	−	0.997064i	$-0.524398\pi$
$619$	1.06588	−	0.104980i	0.0428411	−	0.00421948i	0.119415	+	0.992844i	$0.461898\pi$
$620$	31.7631	−	32.0105i	1.27564	−	1.28557i
$621$	−2.23716	−	7.37494i	−0.0897742	−	0.295946i
$622$	−8.25228	+	17.5359i	−0.330886	+	0.703125i
$623$	12.4664	−	30.0966i	0.499456	−	1.20579i
$624$	−0.148687	−	19.1657i	−0.00595225	−	0.767243i
$625$	6.13469	+	14.8104i	0.245387	+	0.592418i
$626$	1.98441	+	0.0936304i	0.0793132	+	0.00374222i
$627$	−11.6109	+	21.7225i	−0.463695	+	0.867512i
$628$	−4.31453	+	0.875625i	−0.172169	+	0.0349413i
$629$	−4.10554	+	5.00262i	−0.163699	+	0.199467i
$630$	−5.12810	−	20.3054i	−0.204309	−	0.808986i
$631$	−38.8194	−	7.72166i	−1.54538	−	0.307395i	−0.652533	−	0.757761i	$-0.726294\pi$
$631$	−38.8194	−	7.72166i	−1.54538	−	0.307395i	−0.892844	+	0.450366i	$0.851294\pi$
$632$	−32.4402	−	11.3948i	−1.29040	−	0.453261i
$633$	−0.605910	−	3.04612i	−0.0240828	−	0.121072i
$634$	39.6511	+	14.1007i	1.57475	+	0.560011i
$635$	−49.8744	+	26.6584i	−1.97920	+	1.05791i
$636$	−5.91900	+	1.82061i	−0.234704	+	0.0721919i
$637$	−5.74629	+	58.3430i	−0.227676	+	2.31164i
$638$	1.37897	−	5.55082i	0.0545941	−	0.219759i
$639$	−0.613393			−0.0242654
$640$	−13.3568	−	35.7903i	−0.527974	−	1.41474i
$641$	−38.1977			−1.50872			−0.754360	−	0.656461i	$-0.772052\pi$
$641$	−38.1977			−1.50872			−0.754360	+	0.656461i	$0.772052\pi$
$642$	−1.18112	+	4.75441i	−0.0466152	+	0.187642i
$643$	−1.67192	+	16.9753i	−0.0659342	+	0.669442i	0.904239	+	0.427028i	$0.140439\pi$
$643$	−1.67192	+	16.9753i	−0.0659342	+	0.669442i	−0.970173	+	0.242414i	$0.922061\pi$
$644$	19.8742	+	64.6131i	0.783153	+	2.54611i
$645$	−15.9231	+	8.51108i	−0.626972	+	0.335123i
$646$	−10.3547	−	3.68235i	−0.407402	−	0.144880i
$647$	7.43997	+	37.4033i	0.292496	+	1.47047i	0.795375	+	0.606118i	$0.207274\pi$
$647$	7.43997	+	37.4033i	0.292496	+	1.47047i	−0.502879	+	0.864357i	$0.667726\pi$
$648$	−1.22416	−	2.54979i	−0.0480897	−	0.100165i
$649$	26.5603	+	5.28316i	1.04258	+	0.207382i
$650$	10.6212	+	42.0560i	0.416598	+	1.64957i
$651$	−18.5793	+	22.6390i	−0.728180	+	0.887290i
$652$	2.50681	+	12.3520i	0.0981742	+	0.483741i
$653$	−1.80146	+	3.37029i	−0.0704964	+	0.131890i	−0.914701	−	0.404132i	$-0.867574\pi$
$653$	−1.80146	+	3.37029i	−0.0704964	+	0.131890i	0.844204	+	0.536022i	$0.180074\pi$
$654$	2.62814	+	0.124003i	0.102768	+	0.00484890i
$655$	−17.9302	−	43.2874i	−0.700592	−	1.69138i
$656$	−4.83422	+	11.9318i	−0.188745	+	0.465859i
$657$	0.362245	−	0.874537i	0.0141325	−	0.0341189i
$658$	−16.7490	+	35.5912i	−0.652945	+	1.38749i
$659$	−6.71740	−	22.1443i	−0.261673	−	0.862620i	−0.985065	−	0.172183i	$-0.944918\pi$
$659$	−6.71740	−	22.1443i	−0.261673	−	0.862620i	0.723392	−	0.690437i	$-0.242582\pi$
$660$	19.1910	+	19.0427i	0.747011	+	0.741238i
$661$	2.45098	−	0.241400i	0.0953321	−	0.00938939i	−0.0502386	−	0.998737i	$-0.515998\pi$
$661$	2.45098	−	0.241400i	0.0953321	−	0.00938939i	0.145571	+	0.989348i	$0.453498\pi$
$662$	−22.9964	−	30.8817i	−0.893780	−	1.20025i
$663$	−5.03221	+	3.36242i	−0.195435	+	0.130585i
$664$	−26.5853	−	12.3852i	−1.03171	−	0.480637i
$665$	50.6186	−	75.7561i	1.96290	−	2.93769i
$666$	−5.37829	−	4.85563i	−0.208405	−	0.188152i
$667$	−2.26003	+	7.45031i	−0.0875085	+	0.288477i
$668$	17.5317	+	32.4956i	0.678320	+	1.25729i
$669$	18.7558	−	15.3925i	0.725140	−	0.595107i
$670$	−10.1364	+	1.52369i	−0.391603	+	0.0588653i
$671$	−37.7964	+	37.7964i	−1.45911	+	1.45911i
$672$	10.8245	+	22.3238i	0.417565	+	0.861160i
$673$	9.65918	+	9.65918i	0.372334	+	0.372334i	0.868327	−	0.495993i	$-0.165196\pi$
$673$	9.65918	+	9.65918i	0.372334	+	0.372334i	−0.495993	+	0.868327i	$0.665196\pi$
$674$	20.4766	+	15.1250i	0.788731	+	0.582595i
$675$	4.06087	+	4.94819i	0.156303	+	0.190456i
$676$	−2.02922	−	19.8148i	−0.0780470	−	0.762107i
$677$	36.9816	+	11.2183i	1.42132	+	0.431153i	0.905062	−	0.425280i	$-0.139825\pi$
$677$	36.9816	+	11.2183i	1.42132	+	0.431153i	0.516258	+	0.856433i	$0.327325\pi$
$678$	−26.8177	+	1.36961i	−1.02993	+	0.0525996i
$679$	24.4492	+	16.3364i	0.938273	+	0.626934i
$680$	−7.12941	+	9.73071i	−0.273400	+	0.373156i
$681$	−5.70834	−	8.54313i	−0.218744	−	0.327374i
$682$	5.47486	−	37.4082i	0.209643	−	1.43244i
$683$	2.68559	+	27.2673i	0.102761	+	1.04335i	0.898875	+	0.438206i	$0.144386\pi$
$683$	2.68559	+	27.2673i	0.102761	+	1.04335i	−0.796113	+	0.605148i	$0.793114\pi$
$684$	4.66476	−	11.3864i	0.178362	−	0.435372i
$685$	−2.92276	+	0.886610i	−0.111673	+	0.0338756i
$686$	−10.9982	−	30.5509i	−0.419912	−	1.16644i
$687$	−0.975641	−	0.404124i	−0.0372230	−	0.0154183i
$688$	16.4279	−	13.6967i	0.626307	−	0.522180i
$689$	−13.7070	+	5.67762i	−0.522195	+	0.216300i
$690$	−24.7671	−	27.2200i	−0.942867	−	1.03625i
$691$	11.8437	+	6.33059i	0.450556	+	0.240827i	0.681036	−	0.732250i	$-0.261530\pi$
$691$	11.8437	+	6.33059i	0.450556	+	0.240827i	−0.230480	+	0.973077i	$0.574030\pi$
$692$	5.36280	+	1.04512i	0.203863	+	0.0397295i
$693$	−13.5726	−	11.1387i	−0.515580	−	0.423126i
$694$	42.1514	+	25.1536i	1.60005	+	0.954818i
$695$	1.88965	−	9.49994i	0.0716787	−	0.360353i
$696$	−0.402806	+	2.82880i	−0.0152683	+	0.107225i
$697$	3.98712	−	0.793087i	0.151023	−	0.0300403i
$698$	5.80047	+	12.2028i	0.219551	+	0.461882i
$699$	0.637492	+	1.19266i	0.0241122	+	0.0451107i
$700$	−35.7883	−	43.2649i	−1.35267	−	1.63526i
$701$	−25.8076	−	2.54182i	−0.974738	−	0.0960033i	−0.401910	−	0.915679i	$-0.631654\pi$
$701$	−25.8076	−	2.54182i	−0.974738	−	0.0960033i	−0.572828	+	0.819676i	$0.694154\pi$
$702$	−3.49499	−	5.80547i	−0.131910	−	0.219113i
$703$		−	31.5230i		−	1.18891i
$704$	−26.8350	−	17.4823i	−1.01138	−	0.658891i
$705$		−	21.4139i		−	0.806494i
$706$	11.2571	−	6.77696i	0.423667	−	0.255054i
$707$	4.80798	+	0.473545i	0.180823	+	0.0178095i
$708$	−13.4687	−	1.27382i	−0.506183	−	0.0478729i
$709$	−18.8691	−	35.3016i	−0.708645	−	1.32578i	−0.936011	−	0.351971i	$-0.885511\pi$
$709$	−18.8691	−	35.3016i	−0.708645	−	1.32578i	0.227366	−	0.973809i	$-0.426989\pi$
$710$	−2.64541	+	1.25747i	−0.0992804	+	0.0471920i
$711$	−11.9227	+	2.37158i	−0.447137	+	0.0889411i
$712$	−5.22319	−	20.3491i	−0.195747	−	0.762614i
$713$	−10.0400	+	50.4744i	−0.376000	+	1.89028i
$714$	4.01456	−	6.72744i	0.150241	−	0.251768i
$715$	50.0691	+	41.0906i	1.87248	+	1.53670i
$716$	−16.9134	−	25.1014i	−0.632085	−	0.938084i
$717$	0.355791	+	0.190174i	0.0132873	+	0.00710219i
$718$	21.9892	−	20.0076i	0.820628	−	0.746678i
$719$	−27.1882	+	11.2617i	−1.01395	+	0.419992i	−0.826894	−	0.562358i	$-0.809894\pi$
$719$	−27.1882	+	11.2617i	−1.01395	+	0.419992i	−0.187055	+	0.982349i	$0.559894\pi$
$720$	−10.5066	−	8.48703i	−0.391559	−	0.316293i
$721$	49.2955	+	20.4189i	1.83586	+	0.760438i
$722$	25.0859	−	9.03078i	0.933599	−	0.336091i
$723$	−5.99132	+	1.81745i	−0.222819	+	0.0675915i
$724$	15.7600	+	37.6344i	0.585716	+	1.39867i
$725$	−0.633839	−	6.43547i	−0.0235402	−	0.239007i
$726$	7.03477	+	1.02957i	0.261085	+	0.0382109i
$727$	6.56790	+	9.82956i	0.243590	+	0.364558i	0.933039	−	0.359776i	$-0.117147\pi$
$727$	6.56790	+	9.82956i	0.243590	+	0.364558i	−0.689448	+	0.724335i	$0.742147\pi$
$728$	30.8538	+	50.8038i	1.14352	+	1.88291i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	−0.230549	−	4.51427i	−0.00853299	−	0.167080i
$731$	−6.46312	−	1.96056i	−0.239047	−	0.0725141i
$732$	16.8602	−	20.7075i	0.623171	−	0.765371i
$733$	−26.3998	−	32.1682i	−0.975099	−	1.18816i	−0.982133	−	0.188186i	$-0.939739\pi$
$733$	−26.3998	−	32.1682i	−0.975099	−	1.18816i	0.00703464	−	0.999975i	$-0.497761\pi$
$734$	−14.6470	+	19.8295i	−0.540632	+	0.731921i
$735$	29.2124	+	29.2124i	1.07752	+	1.07752i
$736$	35.2670	+	25.6294i	1.29996	+	0.944713i
$737$	−6.07660	+	6.07660i	−0.223835	+	0.223835i
$738$	0.676592	+	4.50105i	0.0249057	+	0.165686i
$739$	−28.8409	+	23.6692i	−1.06093	+	0.870684i	−0.991912	−	0.126931i	$-0.959487\pi$
$739$	−28.8409	+	23.6692i	−1.06093	+	0.870684i	−0.0690200	+	0.997615i	$0.521987\pi$
$740$	−33.1494	−	9.91550i	−1.21860	−	0.364501i
$741$	8.55759	−	28.2106i	0.314371	−	1.03634i
$742$	12.8695	−	14.2548i	0.472456	−	0.523311i
$743$	−3.45051	+	5.16405i	−0.126587	+	0.189451i	−0.889350	−	0.457228i	$-0.848842\pi$
$743$	−3.45051	+	5.16405i	−0.126587	+	0.189451i	0.762763	+	0.646678i	$0.223842\pi$
$744$	−0.816978	+	18.8696i	−0.0299519	+	0.691792i
$745$	−26.1046	+	17.4425i	−0.956397	+	0.639044i
$746$	−24.3149	+	18.1064i	−0.890233	+	0.662922i
$747$	−10.3193	+	1.01636i	−0.377564	+	0.0371869i
$748$	0.0392286	+	10.1133i	0.00143434	+	0.369778i
$749$	−4.41019	−	14.5384i	−0.161145	−	0.531223i
$750$	6.05408	+	2.84901i	0.221064	+	0.104031i
$751$	9.72457	−	23.4772i	0.354854	−	0.856695i	−0.641152	−	0.767414i	$-0.721543\pi$
$751$	9.72457	−	23.4772i	0.354854	−	0.856695i	0.996007	−	0.0892806i	$-0.0284568\pi$
$752$	5.14185	+	24.8411i	0.187504	+	0.905861i
$753$	−0.213672	−	0.515851i	−0.00778665	−	0.0187986i
$754$	−0.322635	+	6.83796i	−0.0117497	+	0.249024i
$755$	13.8199	−	25.8552i	0.502958	−	0.940968i
$756$	7.31214	+	4.84489i	0.265940	+	0.176207i
$757$	−17.4222	+	21.2290i	−0.633222	+	0.771583i	−0.986469	−	0.163947i	$-0.947577\pi$
$757$	−17.4222	+	21.2290i	−0.633222	+	0.771583i	0.353247	+	0.935530i	$0.385077\pi$
$758$	0.819614	−	0.206993i	0.0297697	−	0.00751832i
$759$	−30.2606	−	6.01921i	−1.09839	−	0.218484i
$760$	−3.22455	−	58.6697i	−0.116967	−	2.12817i
$761$	−0.418119	−	2.10203i	−0.0151568	−	0.0761983i	0.972467	−	0.233042i	$-0.0748680\pi$
$761$	−0.418119	−	2.10203i	−0.0151568	−	0.0761983i	−0.987623	+	0.156844i	$0.949868\pi$
$762$	7.93623	−	22.3166i	0.287499	−	0.808446i
$763$	−7.19603	+	3.84636i	−0.260514	+	0.139247i
$764$	9.63417	−	18.1937i	0.348552	−	0.658224i
$765$	−0.418034	+	4.24437i	−0.0151140	+	0.153455i
$766$	−40.7404	−	10.1210i	−1.47201	−	0.365687i
$767$	−32.4120			−1.17033
$768$	14.2261	+	7.32251i	0.513339	+	0.264228i
$769$	−26.5869			−0.958747			−0.479373	−	0.877611i	$-0.659136\pi$
$769$	−26.5869			−0.958747			−0.479373	+	0.877611i	$0.659136\pi$
$770$	−81.3699	−	20.2145i	−2.93237	−	0.728478i
$771$	−0.822008	+	8.34598i	−0.0296039	+	0.300573i
$772$	−14.7851	+	27.9210i	−0.532129	+	1.00490i
$773$	20.3037	−	10.8525i	0.730272	−	0.390339i	−0.0639606	−	0.997952i	$-0.520373\pi$
$773$	20.3037	−	10.8525i	0.730272	−	0.390339i	0.794233	+	0.607614i	$0.207873\pi$
$774$	2.53375	−	7.12490i	0.0910739	−	0.256099i
$775$	−8.33912	−	41.9236i	−0.299550	−	1.50594i
$776$	18.9348	−	1.04068i	0.679720	−	0.0373581i
$777$	22.0394	+	4.38390i	0.790658	+	0.157272i
$778$	15.9992	−	4.04057i	0.573597	−	0.144862i
$779$	−12.5620	+	15.3068i	−0.450080	+	0.548424i
$780$	−26.9743	−	17.8727i	−0.965836	−	0.639946i
$781$	−1.15759	+	2.16570i	−0.0414219	+	0.0774949i
$782$	0.648820	−	13.7512i	0.0232018	−	0.491741i
$783$	0.386594	+	0.933321i	0.0138158	+	0.0333542i
$784$	−40.9021	−	26.8733i	−1.46079	−	0.959761i
$785$	−2.84435	+	6.86687i	−0.101519	+	0.245089i
$786$	17.7561	+	8.35589i	0.633337	+	0.298045i
$787$	9.77022	+	32.2081i	0.348271	+	1.14809i	0.939775	+	0.341793i	$0.111034\pi$
$787$	9.77022	+	32.2081i	0.348271	+	1.14809i	−0.591505	+	0.806302i	$0.701466\pi$
$788$	0.0279786	+	7.21297i	0.000996697	+	0.256952i
$789$	−7.67557	+	0.755977i	−0.273257	+	0.0269135i
$790$	−46.5579	+	34.6699i	−1.65646	+	1.23350i
$791$	69.2414	−	46.2656i	2.46194	−	1.64502i
$792$	−11.3128	−	0.489798i	−0.401982	−	0.0174042i
$793$	35.5429	−	53.1937i	1.26216	−	1.88896i
$794$	22.2402	−	24.6341i	0.789276	−	0.874233i
$795$	−3.03492	+	10.0048i	−0.107638	+	0.354834i
$796$	−35.7791	−	10.7021i	−1.26816	−	0.379325i
$797$	17.9596	−	14.7391i	0.636162	−	0.522084i	−0.260116	−	0.965577i	$-0.583761\pi$
$797$	17.9596	−	14.7391i	0.636162	−	0.522084i	0.896278	+	0.443493i	$0.146261\pi$
$798$	5.67247	+	37.7363i	0.200803	+	1.33585i
$799$	5.66421	−	5.66421i	0.200385	−	0.200385i
$800$	−35.2091	−	8.45743i	−1.24483	−	0.299015i
$801$	−5.25218	−	5.25218i	−0.185577	−	0.185577i
$802$	−22.5392	+	30.5142i	−0.795888	+	1.07749i
$803$	−2.40410	−	2.92940i	−0.0848387	−	0.103376i
$804$	2.71065	−	3.32918i	0.0955972	−	0.117411i
$805$	109.215	+	33.1299i	3.84931	+	1.16767i
$806$	2.30796	+	45.1910i	0.0812943	+	1.59178i
$807$	−24.5568	−	16.4083i	−0.864440	−	0.577600i
$808$	2.66307	−	1.61732i	0.0936864	−	0.0568970i
$809$	9.25318	+	13.8484i	0.325324	+	0.486883i	0.957696	−	0.287783i	$-0.0929182\pi$
$809$	9.25318	+	13.8484i	0.325324	+	0.486883i	−0.632371	+	0.774666i	$0.717918\pi$
$810$	−4.72485	−	0.691503i	−0.166014	−	0.0242969i
$811$	−0.446166	−	4.53000i	−0.0156670	−	0.159070i	0.984168	−	0.177239i	$-0.0567164\pi$
$811$	−0.446166	−	4.53000i	−0.0156670	−	0.159070i	−0.999835	+	0.0181686i	$0.994216\pi$
$812$	−3.42277	−	8.17347i	−0.120116	−	0.286833i
$813$	28.1102	−	8.52714i	0.985868	−	0.299060i
$814$	−27.2937	+	9.82558i	−0.956642	+	0.344386i
$815$	19.6590	+	8.14303i	0.688625	+	0.285238i
$816$	−0.534209	−	5.02404i	−0.0187011	−	0.175876i
$817$	30.3940	−	12.5896i	1.06335	−	0.440454i
$818$	19.3351	−	17.5927i	0.676035	−	0.615115i
$819$	18.5334	+	9.90631i	0.647610	+	0.346155i
$820$	12.1452	+	18.0249i	0.424130	+	0.629456i
$821$	29.6771	+	24.3554i	1.03574	+	0.850009i	0.988854	−	0.148891i	$-0.0475704\pi$
$821$	29.6771	+	24.3554i	1.03574	+	0.850009i	0.0468855	+	0.998900i	$0.485070\pi$
$822$	0.655526	−	1.09851i	0.0228641	−	0.0383148i
$823$	5.14160	−	25.8486i	0.179225	−	0.901024i	−0.781581	−	0.623803i	$-0.785587\pi$
$823$	5.14160	−	25.8486i	0.179225	−	0.901024i	0.960806	−	0.277221i	$-0.0894134\pi$
$824$	33.3299	−	8.55511i	1.16110	−	0.298031i
$825$	25.1342	−	4.99951i	0.875061	−	0.174060i
$826$	37.8925	−	18.0119i	1.31845	−	0.626712i
$827$	−5.85798	−	10.9595i	−0.203702	−	0.381099i	0.759239	−	0.650812i	$-0.225571\pi$
$827$	−5.85798	−	10.9595i	−0.203702	−	0.381099i	−0.962941	+	0.269713i	$0.913071\pi$
$828$	15.3451	+	1.45128i	0.533279	+	0.0504356i
$829$	−47.5867	−	4.68688i	−1.65275	−	0.162782i	−0.771761	−	0.635912i	$-0.780624\pi$
$829$	−47.5867	−	4.68688i	−1.65275	−	0.162782i	−0.880992	+	0.473130i	$0.843124\pi$
$830$	−42.4211	+	25.5382i	−1.47246	+	0.886443i
$831$			28.9532i			1.00438i
$832$	35.5830	+	14.2562i	1.23362	+	0.494243i
$833$			15.4540i			0.535450i
$834$	2.09237	+	3.47561i	0.0724529	+	0.120350i
$835$	62.0366	+	6.11008i	2.14687	+	0.211448i
$836$	−31.3988	−	37.9583i	−1.08595	−	1.31282i
$837$	3.14782	+	5.88916i	0.108805	+	0.203559i
$838$	17.2299	+	36.2475i	0.595198	+	1.25215i
$839$	−6.63471	+	1.31973i	−0.229056	+	0.0455620i	−0.308284	−	0.951295i	$-0.599755\pi$
$839$	−6.63471	+	1.31973i	−0.229056	+	0.0455620i	0.0792278	+	0.996857i	$0.474755\pi$
$840$	41.4675	+	5.90476i	1.43077	+	0.203733i
$841$	−5.45852	+	27.4418i	−0.188225	+	0.946270i
$842$	43.6403	+	26.0421i	1.50394	+	0.897469i
$843$	5.57110	+	4.57208i	0.191879	+	0.157471i
$844$	6.09689	+	1.18818i	0.209863	+	0.0408988i
$845$	−29.6572	−	15.8521i	−1.02024	−	0.545329i
$846$	6.03597	+	6.63377i	0.207521	+	0.228074i
$847$	−20.3704	+	8.43769i	−0.699935	+	0.289923i
$848$	1.11832	−	12.3348i	0.0384033	−	0.423577i
$849$	1.27344	+	0.527477i	0.0437044	+	0.0181029i
$850$	3.87298	+	10.7584i	0.132842	+	0.369011i
$851$	37.7865	−	11.4624i	1.29530	−	0.392926i
$852$	0.465070	−	1.13521i	0.0159331	−	0.0388918i
$853$	−0.872230	−	8.85590i	−0.0298646	−	0.303220i	−0.998501	−	0.0547371i	$-0.982568\pi$
$853$	−0.872230	−	8.85590i	−0.0298646	−	0.303220i	0.968636	−	0.248483i	$-0.0799321\pi$
$854$	−11.9923	+	81.9398i	−0.410366	+	2.80392i
$855$	−11.5415	−	17.2731i	−0.394712	−	0.590728i
$856$	−7.90354	−	5.79069i	−0.270137	−	0.197922i
$857$	−4.23321	−	2.82854i	−0.144604	−	0.0966210i	0.481164	−	0.876631i	$-0.340214\pi$
$857$	−4.23321	−	2.82854i	−0.144604	−	0.0966210i	−0.625768	+	0.780010i	$0.715214\pi$
$858$	−27.0931	+	1.38368i	−0.924942	+	0.0472379i
$859$	23.2323	+	7.04745i	0.792677	+	0.240456i	0.660555	−	0.750777i	$-0.270321\pi$
$859$	23.2323	+	7.04745i	0.792677	+	0.240456i	0.132122	+	0.991233i	$0.457821\pi$
$860$	−3.67877	−	35.9222i	−0.125445	−	1.22494i
$861$	−8.95482	−	10.9115i	−0.305179	−	0.371862i
$862$	0.509027	+	0.375992i	0.0173375	+	0.0128063i
$863$	−17.8777	−	17.8777i	−0.608565	−	0.608565i	0.334006	−	0.942571i	$-0.391599\pi$
$863$	−17.8777	−	17.8777i	−0.608565	−	0.608565i	−0.942571	+	0.334006i	$0.891599\pi$
$864$	5.64708	−	0.332345i	0.192118	−	0.0113066i
$865$	6.52253	−	6.52253i	0.221773	−	0.221773i
$866$	−46.1559	+	6.93810i	−1.56844	+	0.235766i
$867$	11.9079	−	9.77258i	0.404414	−	0.331894i
$868$	−27.8115	−	51.5497i	−0.943984	−	1.74971i
$869$	−14.1272	+	46.5712i	−0.479233	+	1.57982i
$870$	3.58061	+	3.23265i	0.121394	+	0.109597i
$871$	5.71430	−	8.55205i	0.193622	−	0.289775i
$872$	−2.22213	+	4.76991i	−0.0752509	+	0.161530i
$873$	5.57464	−	3.72486i	0.188673	−	0.126067i
$874$	40.0496	+	53.7823i	1.35470	+	1.81921i
$875$	−20.6501	+	2.03386i	−0.698102	+	0.0687571i
$876$	1.34387	+	1.33348i	0.0454050	+	0.0450541i
$877$	13.8371	+	45.6147i	0.467245	+	1.54030i	0.801605	+	0.597854i	$0.203980\pi$
$877$	13.8371	+	45.6147i	0.467245	+	1.54030i	−0.334360	+	0.942445i	$0.608520\pi$
$878$	−12.7550	+	27.1042i	−0.430462	+	0.914721i
$879$	−0.281708	+	0.680104i	−0.00950179	+	0.0229393i
$880$	−49.7932	+	21.0791i	−1.67853	+	0.710575i
$881$	9.22126	+	22.2621i	0.310672	+	0.750029i	0.999681	+	0.0252754i	$0.00804627\pi$
$881$	9.22126	+	22.2621i	0.310672	+	0.750029i	−0.689008	+	0.724753i	$0.741954\pi$
$882$	−17.2838	−	0.815499i	−0.581976	−	0.0274593i
$883$	−17.7077	+	33.1287i	−0.595910	+	1.11487i	0.385457	+	0.922726i	$0.374044\pi$
$883$	−17.7077	+	33.1287i	−0.595910	+	1.11487i	−0.981367	+	0.192144i	$0.938456\pi$
$884$	−2.40748	−	11.8625i	−0.0809723	−	0.398981i
$885$	−14.4898	+	17.6558i	−0.487068	+	0.593494i
$886$	−1.93062	−	7.64452i	−0.0648603	−	0.256823i
$887$	−50.6359	−	10.0721i	−1.70019	−	0.338188i	−0.752793	−	0.658258i	$-0.771294\pi$
$887$	−50.6359	−	10.0721i	−1.70019	−	0.338188i	−0.947394	+	0.320070i	$0.896294\pi$
$888$	13.0642	−	6.27217i	0.438405	−	0.210480i
$889$	14.3303	+	72.0433i	0.480623	+	2.41625i
$890$	−33.4184	−	11.8842i	−1.12019	−	0.398361i
$891$	−3.53070	+	1.88720i	−0.118283	+	0.0632235i
$892$	14.2665	+	46.3821i	0.477679	+	1.55299i
$893$	−3.82447	+	38.8305i	−0.127981	+	1.29941i
$894$	3.17033	−	12.7616i	0.106032	−	0.426812i
$895$	−51.1008			−1.70811
$896$	−49.5221	+	3.10730i	−1.65442	+	0.103808i
$897$	36.9277			1.23298
$898$	6.70135	−	26.9752i	0.223627	−	0.900172i
$899$	0.661214	−	6.71342i	0.0220527	−	0.223905i
$900$	−12.2366	+	3.76383i	−0.407887	+	0.125461i
$901$	−3.44915	+	1.84361i	−0.114908	+	0.0614195i
$902$	17.1687	+	6.10553i	0.571656	+	0.203292i
$903$	4.57515	+	23.0009i	0.152252	+	0.765420i
$904$	17.7983	−	50.6704i	0.591962	−	1.68527i
$905$	67.5602	+	13.4385i	2.24578	+	0.446713i
$906$	3.00662	+	11.9051i	0.0998882	+	0.395520i
$907$	−16.5932	+	20.2188i	−0.550967	+	0.671356i	−0.971807	−	0.235780i	$-0.924236\pi$
$907$	−16.5932	+	20.2188i	−0.550967	+	0.671356i	0.420839	+	0.907135i	$0.361736\pi$
$908$	20.1389	−	4.08715i	0.668334	−	0.135637i
$909$	0.519276	−	0.971498i	0.0172233	−	0.0322226i
$910$	100.238	+	4.72952i	3.32286	+	0.156782i
$911$	9.31846	+	22.4968i	0.308734	+	0.745351i	0.999747	+	0.0225079i	$0.00716508\pi$
$911$	9.31846	+	22.4968i	0.308734	+	0.745351i	−0.691012	+	0.722843i	$0.742835\pi$
$912$	17.5363	+	17.2663i	0.580684	+	0.571743i
$913$	−15.8861	+	38.3525i	−0.525754	+	1.26928i
$914$	3.62894	−	7.71141i	0.120035	−	0.255071i
$915$	−13.0868	−	43.1415i	−0.432637	−	1.42621i
$916$	1.48764	−	1.49923i	0.0491531	−	0.0495359i
$917$	−60.5650	+	5.96513i	−2.00003	+	0.196986i
$918$	−1.06687	−	1.43269i	−0.0352118	−	0.0472857i
$919$	−34.5894	+	23.1119i	−1.14100	+	0.762391i	−0.974663	−	0.223678i	$-0.928194\pi$
$919$	−34.5894	+	23.1119i	−1.14100	+	0.762391i	−0.166336	+	0.986069i	$0.553194\pi$
$920$	69.1547	−	25.1988i	2.27996	−	0.830779i
$921$	−2.62465	+	3.92807i	−0.0864852	+	0.129434i
$922$	−25.3385	−	22.8761i	−0.834478	−	0.753384i
$923$	0.853181	−	2.81256i	0.0280828	−	0.0925765i
$924$	30.9053	−	16.6737i	1.01671	−	0.548523i
$925$	−25.3527	+	20.8064i	−0.833591	+	0.684111i
$926$	37.8136	−	5.68410i	1.24263	−	0.186791i
$927$	8.60260	−	8.60260i	0.282546	−	0.282546i
$928$	−4.92989	−	2.89026i	−0.161832	−	0.0948773i
$929$	5.93788	+	5.93788i	0.194816	+	0.194816i	0.797773	−	0.602958i	$-0.206011\pi$
$929$	5.93788	+	5.93788i	0.194816	+	0.194816i	−0.602958	+	0.797773i	$0.706011\pi$
$930$	25.6487	+	18.9454i	0.841054	+	0.621243i
$931$	−47.7545	−	58.1890i	−1.56509	−	1.90707i
$932$	−2.69062	+	0.275545i	−0.0881343	+	0.00902579i
$933$	−13.1141	−	3.97811i	−0.429335	−	0.130237i
$934$	35.7980	−	1.82825i	1.17135	−	0.0598220i
$935$	14.1967	+	9.48590i	0.464280	+	0.310222i
$936$	13.3941	−	2.06655i	0.437801	−	0.0675473i
$937$	−20.7635	−	31.0747i	−0.678313	−	1.01517i	−0.997716	−	0.0675477i	$-0.978483\pi$
$937$	−20.7635	−	31.0747i	−0.678313	−	1.01517i	0.319403	−	0.947619i	$-0.396517\pi$
$938$	−1.92802	+	13.1736i	−0.0629520	+	0.430134i
$939$	0.137690	+	1.39799i	0.00449334	+	0.0456217i
$940$	39.6310	+	16.2359i	1.29262	+	0.529556i
$941$	0.0510400	−	0.0154828i	0.00166386	−	0.000504725i	−0.289453	−	0.957192i	$-0.593473\pi$
$941$	0.0510400	−	0.0154828i	0.00166386	−	0.000504725i	0.291116	+	0.956688i	$0.405973\pi$
$942$	−1.05443	−	2.92902i	−0.0343552	−	0.0954325i
$943$	−22.9161	−	9.49214i	−0.746249	−	0.309107i
$944$	12.5693	−	23.9608i	0.409096	−	0.779858i
$945$	13.6816	−	5.66711i	0.445063	−	0.184351i
$946$	−20.3742	−	22.3920i	−0.662422	−	0.728027i
$947$	3.29776	+	1.76269i	0.107163	+	0.0572797i	0.524107	−	0.851652i	$-0.324399\pi$
$947$	3.29776	+	1.76269i	0.107163	+	0.0572797i	−0.416944	+	0.908932i	$0.636899\pi$
$948$	4.65063	−	23.8637i	0.151045	−	0.775056i
$949$	3.50612	+	2.87740i	0.113813	+	0.0934042i
$950$	−47.8276	−	28.5408i	−1.55173	−	0.925986i
$951$	−5.80544	+	29.1859i	−0.188254	+	0.946418i
$952$	9.40675	+	12.5305i	0.304875	+	0.406116i
$953$	−22.1003	+	4.39602i	−0.715898	+	0.142401i	−0.539582	−	0.841933i	$-0.681418\pi$
$953$	−22.1003	+	4.39602i	−0.715898	+	0.142401i	−0.176316	+	0.984334i	$0.556418\pi$
$954$	−1.87989	−	3.95482i	−0.0608636	−	0.128042i
$955$	−16.3842	−	30.6527i	−0.530181	−	0.991899i
$956$	−0.621717	+	0.514278i	−0.0201078	+	0.0166330i
$957$	4.02485	+	0.396414i	0.130105	+	0.0128142i
$958$	10.9645	+	18.2129i	0.354246	+	0.588433i
$959$			3.96717i			0.128107i
$960$	23.6731	−	13.0100i	0.764047	−	0.419895i
$961$		−	13.5911i		−	0.438421i
$962$	29.7451	−	17.9070i	0.959020	−	0.577346i
$963$	−3.44738	−	0.339538i	−0.111090	−	0.0109415i
$964$	1.17901	−	12.4662i	0.0379732	−	0.401509i
$965$	25.1442	+	47.0414i	0.809419	+	1.51432i
$966$	−43.1717	+	20.5213i	−1.38903	+	0.660261i
$967$	48.6112	−	9.66936i	1.56323	−	0.310946i	0.663765	−	0.747941i	$-0.268957\pi$
$967$	48.6112	−	9.66936i	1.56323	−	0.310946i	0.899464	+	0.436995i	$0.143957\pi$
$968$	−7.23916	+	12.2387i	−0.232675	+	0.393368i
$969$	1.51607	−	7.62179i	0.0487031	−	0.244847i
$970$	16.4060	−	27.4925i	0.526764	−	0.882731i
$971$	45.2240	+	37.1143i	1.45131	+	1.19106i	0.944288	+	0.329120i	$0.106752\pi$
$971$	45.2240	+	37.1143i	1.45131	+	1.19106i	0.507018	+	0.861936i	$0.330748\pi$
$972$	1.65862	−	1.11758i	0.0532002	−	0.0358465i
$973$	−11.0955	−	5.93069i	−0.355707	−	0.190129i
$974$	18.2991	−	16.6501i	0.586340	−	0.533502i
$975$	−28.3370	+	11.7376i	−0.907512	+	0.375904i
$976$	25.5403	+	46.9037i	0.817526	+	1.50135i
$977$	−27.8651	−	11.5421i	−0.891484	−	0.369265i	−0.110545	−	0.993871i	$-0.535259\pi$
$977$	−27.8651	−	11.5421i	−0.891484	−	0.369265i	−0.780940	+	0.624606i	$0.785259\pi$
$978$	−8.38542	+	3.01871i	−0.268136	+	0.0965277i
$979$	−28.4558	+	8.63196i	−0.909450	+	0.275879i
$980$	−76.2124	+	31.9151i	−2.43452	+	1.01949i
$981$	0.182355	+	1.85148i	0.00582215	+	0.0591133i
$982$	12.6458	+	1.85077i	0.403543	+	0.0590603i
$983$	6.86656	+	10.2765i	0.219009	+	0.327770i	0.924663	−	0.380786i	$-0.124347\pi$
$983$	6.86656	+	10.2765i	0.219009	+	0.327770i	−0.705654	+	0.708557i	$0.749347\pi$
$984$	−8.84315	−	2.16049i	−0.281909	−	0.0688740i
$985$	10.1253	+	6.76553i	0.322620	+	0.215568i
$986$	0.0920397	+	1.80219i	0.00293114	+	0.0573933i
$987$	−26.6166	−	8.07405i	−0.847215	−	0.257000i
$988$	45.7214	+	37.2268i	1.45459	+	1.18434i
$989$	26.1430	+	31.8553i	0.831298	+	1.01294i
$990$	−11.3582	+	15.3770i	−0.360987	+	0.488713i
$991$	31.6083	+	31.6083i	1.00407	+	1.00407i	0.999992	+	0.00407783i	$0.00129802\pi$
$991$	31.6083	+	31.6083i	1.00407	+	1.00407i	0.00407783	+	0.999992i	$0.498702\pi$
$992$	−34.3028	−	15.8188i	−1.08911	−	0.502247i
$993$	19.2517	−	19.2517i	0.610934	−	0.610934i
$994$	0.565538	+	3.76226i	0.0179378	+	0.119332i
$995$	−48.7379	+	39.9982i	−1.54510	+	1.26803i
$996$	5.94305	−	19.8687i	0.188313	−	0.629565i
$997$	17.3309	−	57.1323i	0.548875	−	1.80940i	−0.0374206	−	0.999300i	$-0.511914\pi$
$997$	17.3309	−	57.1323i	0.548875	−	1.80940i	0.586295	−	0.810097i	$-0.300586\pi$
$998$	14.4098	−	15.9608i	0.456133	−	0.505231i
$999$	2.84654	−	4.26014i	0.0900605	−	0.134785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.3	✓	512
128.53	even	32	inner	384.2.v.a.181.3	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.3	✓	512	1.1	even	1	trivial
384.2.v.a.181.3	yes	512	128.53	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)

\(f(q)\)	\(=\)	\(q+(-1.37250 - 0.340965i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.76749 + 0.935945i) q^{4} +(2.97786 - 1.59170i) q^{5} +(-0.473851 + 1.33247i) q^{6} +(-0.855624 - 4.30151i) q^{7} +(-2.10674 - 1.88723i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(-1.37250 - 0.340965i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.76749 + 0.935945i) q^{4} +(2.97786 - 1.59170i) q^{5} +(-0.473851 + 1.33247i) q^{6} +(-0.855624 - 4.30151i) q^{7} +(-2.10674 - 1.88723i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-4.62982 + 1.16926i) q^{10} +(-2.53974 + 3.09468i) q^{11} +(1.10468 - 1.66724i) q^{12} +(2.25873 - 4.22579i) q^{13} +(-0.292324 + 6.19554i) q^{14} +(-1.29216 - 3.11954i) q^{15} +(2.24802 + 3.30854i) q^{16} +(0.483363 - 1.16694i) q^{17} +(1.27960 + 0.602174i) q^{18} +(1.78597 + 5.88754i) q^{19} +(6.75308 - 0.0261947i) q^{20} +(-4.36466 + 0.429882i) q^{21} +(4.54096 - 3.38147i) q^{22} +(-6.40796 + 4.28166i) q^{23} +(-2.08464 + 1.91162i) q^{24} +(3.55631 - 5.32240i) q^{25} +(-4.54095 + 5.02973i) q^{26} +(-0.290285 + 0.956940i) q^{27} +(2.51367 - 8.40368i) q^{28} +(0.780911 - 0.640877i) q^{29} +(0.709825 + 4.72213i) q^{30} +(4.72181 - 4.72181i) q^{31} +(-1.95730 - 5.30745i) q^{32} +(2.83084 + 2.83084i) q^{33} +(-1.06130 + 1.43681i) q^{34} +(-9.39465 - 11.4474i) q^{35} +(-1.55093 - 1.26278i) q^{36} +(-4.90301 - 1.48731i) q^{37} +(-0.443787 - 8.68957i) q^{38} +(-3.98405 - 2.66206i) q^{39} +(-9.27750 - 2.26661i) q^{40} +(1.78809 + 2.67607i) q^{41} +(6.13705 + 0.898185i) q^{42} +(-0.524113 - 5.32141i) q^{43} +(-7.38540 + 3.09275i) q^{44} +(-3.23117 + 0.980165i) q^{45} +(10.2548 - 3.69167i) q^{46} +(5.85917 + 2.42695i) q^{47} +(3.51295 - 1.91290i) q^{48} +(-11.3037 + 4.68216i) q^{49} +(-6.69577 + 6.09239i) q^{50} +(-1.11395 - 0.595416i) q^{51} +(7.94739 - 5.35498i) q^{52} +(-2.39350 - 1.96430i) q^{53} +(0.724697 - 1.21442i) q^{54} +(-2.63719 + 13.2580i) q^{55} +(-6.31536 + 10.6769i) q^{56} +(6.03424 - 1.20029i) q^{57} +(-1.29031 + 0.613337i) q^{58} +(-3.18871 - 5.96565i) q^{59} +(0.635849 - 6.72313i) q^{60} +(13.2874 + 1.30869i) q^{61} +(-8.09064 + 4.87070i) q^{62} +4.38578i q^{63} +(0.876727 + 7.95181i) q^{64} -16.1791i q^{65} +(-2.92010 - 4.85053i) q^{66} +(2.13624 + 0.210401i) q^{67} +(1.94653 - 1.61015i) q^{68} +(3.63295 + 6.79678i) q^{69} +(8.99095 + 18.9148i) q^{70} +(0.601606 - 0.119667i) q^{71} +(1.69808 + 2.26197i) q^{72} +(-0.184671 + 0.928403i) q^{73} +(6.22224 + 3.71308i) q^{74} +(-4.94819 - 4.06087i) q^{75} +(-2.35374 + 12.0777i) q^{76} +(15.4849 + 8.27683i) q^{77} +(4.56042 + 5.01208i) q^{78} +(11.2310 - 4.65202i) q^{79} +(11.9605 + 6.27421i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-1.54170 - 4.28257i) q^{82} +(9.92276 - 3.01004i) q^{83} +(-8.11683 - 3.32527i) q^{84} +(-0.418034 - 4.24437i) q^{85} +(-1.09507 + 7.48231i) q^{86} +(-0.561248 - 0.839967i) q^{87} +(11.1910 - 1.72662i) q^{88} +(6.17591 + 4.12661i) q^{89} +(4.76897 - 0.243557i) q^{90} +(-20.1099 - 6.10028i) q^{91} +(-15.3334 + 1.57028i) q^{92} +(-4.23626 - 5.16190i) q^{93} +(-7.21418 - 5.32874i) q^{94} +(14.6896 + 14.6896i) q^{95} +(-5.47374 + 1.42765i) q^{96} +(-4.74084 + 4.74084i) q^{97} +(17.1108 - 2.57207i) q^{98} +(3.09468 - 2.53974i) 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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