LMFDB - Embedded newform 384.2.v.a.157.15

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			157.15
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.145323 + 1.40673i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.95776 - 0.408859i) q^{4} +(3.58870 - 1.91820i) q^{5} +(-1.38571 - 0.282506i) q^{6} +(-0.464401 - 2.33470i) q^{7} +(0.859660 - 2.69462i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(-0.145323 + 1.40673i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.95776 - 0.408859i) q^{4} +(3.58870 - 1.91820i) q^{5} +(-1.38571 - 0.282506i) q^{6} +(-0.464401 - 2.33470i) q^{7} +(0.859660 - 2.69462i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(2.17686 + 5.32708i) q^{10} +(2.45695 - 2.99380i) q^{11} +(0.598784 - 1.90826i) q^{12} +(0.816051 - 1.52672i) q^{13} +(3.35177 - 0.314000i) q^{14} +(1.55721 + 3.75943i) q^{15} +(3.66567 + 1.60090i) q^{16} +(0.917578 - 2.21523i) q^{17} +(0.416969 - 1.35135i) q^{18} +(-0.208613 - 0.687706i) q^{19} +(-7.81009 + 2.28811i) q^{20} +(2.36898 - 0.233324i) q^{21} +(3.85440 + 3.89132i) q^{22} +(-6.95064 + 4.64427i) q^{23} +(2.59738 + 1.11964i) q^{24} +(6.42141 - 9.61032i) q^{25} +(2.02909 + 1.36983i) q^{26} +(0.290285 - 0.956940i) q^{27} +(-0.0453765 + 4.76066i) q^{28} +(-5.23271 + 4.29437i) q^{29} +(-5.51479 + 1.64424i) q^{30} +(-5.24169 + 5.24169i) q^{31} +(-2.78473 + 4.92395i) q^{32} +(2.73856 + 2.73856i) q^{33} +(2.98288 + 1.61270i) q^{34} +(-6.14501 - 7.48772i) q^{35} +(1.84038 + 0.782943i) q^{36} +(8.27040 + 2.50880i) q^{37} +(0.997731 - 0.193523i) q^{38} +(1.43939 + 0.961767i) q^{39} +(-2.08376 - 11.3192i) q^{40} +(3.81647 + 5.71175i) q^{41} +(-0.0160432 + 3.36641i) q^{42} +(0.834759 + 8.47545i) q^{43} +(-6.03416 + 4.85660i) q^{44} +(-3.89396 + 1.18122i) q^{45} +(-5.52313 - 10.4526i) q^{46} +(2.77406 + 1.14905i) q^{47} +(-1.95249 + 3.49110i) q^{48} +(1.23201 - 0.510313i) q^{49} +(12.5859 + 10.4298i) q^{50} +(2.11462 + 1.13029i) q^{51} +(-2.22185 + 2.65531i) q^{52} +(-5.60232 - 4.59771i) q^{53} +(1.30397 + 0.547417i) q^{54} +(3.07454 - 15.4567i) q^{55} +(-6.69036 - 0.755665i) q^{56} +(0.704842 - 0.140202i) q^{57} +(-5.28058 - 7.98506i) q^{58} +(-0.745894 - 1.39547i) q^{59} +(-1.51157 - 7.99676i) q^{60} +(-0.755696 - 0.0744296i) q^{61} +(-6.61189 - 8.13536i) q^{62} +2.38044i q^{63} +(-6.52197 - 4.63292i) q^{64} -7.04430i q^{65} +(-4.25038 + 3.45443i) q^{66} +(1.26499 + 0.124590i) q^{67} +(-2.70211 + 3.96173i) q^{68} +(-3.94062 - 7.37239i) q^{69} +(11.4262 - 7.55622i) q^{70} +(0.459307 - 0.0913619i) q^{71} +(-1.36884 + 2.47513i) q^{72} +(-0.858965 + 4.31831i) q^{73} +(-4.73107 + 11.2696i) q^{74} +(8.93464 + 7.33247i) q^{75} +(0.127241 + 1.43166i) q^{76} +(-8.13062 - 4.34591i) q^{77} +(-1.56212 + 1.88506i) q^{78} +(14.1140 - 5.84620i) q^{79} +(16.2258 - 1.28635i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-8.58949 + 4.53868i) q^{82} +(-9.33541 + 2.83187i) q^{83} +(-4.73329 - 0.511784i) q^{84} +(-0.956340 - 9.70988i) q^{85} +(-12.0440 - 0.0573975i) q^{86} +(-3.76080 - 5.62843i) q^{87} +(-5.95501 - 9.19419i) q^{88} +(2.54044 + 1.69747i) q^{89} +(-1.09577 - 5.64940i) q^{90} +(-3.94342 - 1.19622i) q^{91} +(15.5066 - 6.25055i) q^{92} +(-4.70267 - 5.73022i) q^{93} +(-2.01954 + 3.73536i) q^{94} +(-2.06781 - 2.06781i) q^{95} +(-4.62729 - 3.25395i) q^{96} +(6.99279 - 6.99279i) q^{97} +(0.538833 + 1.80726i) q^{98} +(-2.99380 + 2.45695i) 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 $

$2$	−0.145323	+	1.40673i	−0.102759	+	0.994706i
$2$	−0.145323	+	1.40673i	−0.102759	+	0.994706i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$4$	−1.95776	−	0.408859i	−0.978881	−	0.204429i
$5$	3.58870	−	1.91820i	1.60491	−	0.857845i	0.606905	−	0.794774i	$-0.292411\pi$
$5$	3.58870	−	1.91820i	1.60491	−	0.857845i	0.998009	−	0.0630703i	$-0.0200892\pi$
$6$	−1.38571	−	0.282506i	−0.565713	−	0.115333i
$7$	−0.464401	−	2.33470i	−0.175527	−	0.882433i	−0.963702	−	0.266982i	$-0.913974\pi$
$7$	−0.464401	−	2.33470i	−0.175527	−	0.882433i	0.788175	−	0.615452i	$-0.211026\pi$
$8$	0.859660	−	2.69462i	0.303936	−	0.952693i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	2.17686	+	5.32708i	0.688384	+	1.68457i
$11$	2.45695	−	2.99380i	0.740797	−	0.902664i	−0.257172	−	0.966366i	$-0.582791\pi$
$11$	2.45695	−	2.99380i	0.740797	−	0.902664i	0.997969	+	0.0637020i	$0.0202907\pi$
$12$	0.598784	−	1.90826i	0.172854	−	0.550867i
$13$	0.816051	−	1.52672i	0.226332	−	0.423437i	−0.742965	−	0.669330i	$-0.766581\pi$
$13$	0.816051	−	1.52672i	0.226332	−	0.423437i	0.969297	+	0.245893i	$0.0790812\pi$
$14$	3.35177	−	0.314000i	0.895799	−	0.0839200i
$15$	1.55721	+	3.75943i	0.402069	+	0.970681i
$16$	3.66567	+	1.60090i	0.916417	+	0.400224i
$17$	0.917578	−	2.21523i	0.222545	−	0.537272i	−0.772689	−	0.634785i	$-0.781089\pi$
$17$	0.917578	−	2.21523i	0.222545	−	0.537272i	0.995234	+	0.0975130i	$0.0310888\pi$
$18$	0.416969	−	1.35135i	0.0982806	−	0.318515i
$19$	−0.208613	−	0.687706i	−0.0478592	−	0.157771i	0.929754	−	0.368182i	$-0.120020\pi$
$19$	−0.208613	−	0.687706i	−0.0478592	−	0.157771i	−0.977613	+	0.210411i	$0.932520\pi$
$20$	−7.81009	+	2.28811i	−1.74639	+	0.511636i
$21$	2.36898	−	0.233324i	0.516953	−	0.0509154i
$22$	3.85440	+	3.89132i	0.821762	+	0.829632i
$23$	−6.95064	+	4.64427i	−1.44931	+	0.968397i	−0.452239	+	0.891897i	$0.649375\pi$
$23$	−6.95064	+	4.64427i	−1.44931	+	0.968397i	−0.997070	+	0.0765003i	$0.975625\pi$
$24$	2.59738	+	1.11964i	0.530189	+	0.228546i
$25$	6.42141	−	9.61032i	1.28428	−	1.92206i
$26$	2.02909	+	1.36983i	0.397938	+	0.268646i
$27$	0.290285	−	0.956940i	0.0558653	−	0.184163i
$28$	−0.0453765	+	4.76066i	−0.00857536	+	0.899680i
$29$	−5.23271	+	4.29437i	−0.971689	+	0.797445i	−0.979277	−	0.202527i	$-0.935085\pi$
$29$	−5.23271	+	4.29437i	−0.971689	+	0.797445i	0.00758779	+	0.999971i	$0.497585\pi$
$30$	−5.51479	+	1.64424i	−1.00686	+	0.300195i
$31$	−5.24169	+	5.24169i	−0.941435	+	0.941435i	−0.998377	−	0.0569428i	$-0.981865\pi$
$31$	−5.24169	+	5.24169i	−0.941435	+	0.941435i	0.0569428	+	0.998377i	$0.481865\pi$
$32$	−2.78473	+	4.92395i	−0.492276	+	0.870439i
$33$	2.73856	+	2.73856i	0.476722	+	0.476722i
$34$	2.98288	+	1.61270i	0.511559	+	0.276576i
$35$	−6.14501	−	7.48772i	−1.03870	−	1.26565i
$36$	1.84038	+	0.782943i	0.306730	+	0.130491i
$37$	8.27040	+	2.50880i	1.35964	+	0.412444i	0.884121	−	0.467259i	$-0.154758\pi$
$37$	8.27040	+	2.50880i	1.35964	+	0.412444i	0.475524	+	0.879703i	$0.342258\pi$
$38$	0.997731	−	0.193523i	0.161853	−	0.0313935i
$39$	1.43939	+	0.961767i	0.230486	+	0.154006i
$40$	−2.08376	−	11.3192i	−0.329471	−	1.78972i
$41$	3.81647	+	5.71175i	0.596032	+	0.892025i	0.999739	−	0.0228635i	$-0.00727831\pi$
$41$	3.81647	+	5.71175i	0.596032	+	0.892025i	−0.403707	+	0.914889i	$0.632278\pi$
$42$	−0.0160432	+	3.36641i	−0.00247552	+	0.519448i
$43$	0.834759	+	8.47545i	0.127300	+	1.29249i	0.820457	+	0.571708i	$0.193719\pi$
$43$	0.834759	+	8.47545i	0.127300	+	1.29249i	−0.693158	+	0.720786i	$0.743781\pi$
$44$	−6.03416	+	4.85660i	−0.909683	+	0.732160i
$45$	−3.89396	+	1.18122i	−0.580478	+	0.176086i
$46$	−5.52313	−	10.4526i	−0.814342	−	1.54115i
$47$	2.77406	+	1.14905i	0.404638	+	0.167607i	0.575714	−	0.817651i	$-0.304724\pi$
$47$	2.77406	+	1.14905i	0.404638	+	0.167607i	−0.171075	+	0.985258i	$0.554724\pi$
$48$	−1.95249	+	3.49110i	−0.281817	+	0.503897i
$49$	1.23201	−	0.510313i	0.176001	−	0.0729019i
$50$	12.5859	+	10.4298i	1.77992	+	1.47499i
$51$	2.11462	+	1.13029i	0.296106	+	0.158272i
$52$	−2.22185	+	2.65531i	−0.308115	+	0.368226i
$53$	−5.60232	−	4.59771i	−0.769538	−	0.631544i	0.165452	−	0.986218i	$-0.447092\pi$
$53$	−5.60232	−	4.59771i	−0.769538	−	0.631544i	−0.934990	+	0.354674i	$0.884592\pi$
$54$	1.30397	+	0.547417i	0.177448	+	0.0744940i
$55$	3.07454	−	15.4567i	0.414570	−	2.08419i
$56$	−6.69036	−	0.755665i	−0.894036	−	0.100980i
$57$	0.704842	−	0.140202i	0.0933587	−	0.0185702i
$58$	−5.28058	−	7.98506i	−0.693374	−	1.04849i
$59$	−0.745894	−	1.39547i	−0.0971071	−	0.181675i	0.828677	−	0.559727i	$-0.189094\pi$
$59$	−0.745894	−	1.39547i	−0.0971071	−	0.181675i	−0.925784	+	0.378052i	$0.876594\pi$
$60$	−1.51157	−	7.99676i	−0.195142	−	1.03238i
$61$	−0.755696	−	0.0744296i	−0.0967570	−	0.00952973i	0.0495228	−	0.998773i	$-0.484230\pi$
$61$	−0.755696	−	0.0744296i	−0.0967570	−	0.00952973i	−0.146280	+	0.989243i	$0.546730\pi$
$62$	−6.61189	−	8.13536i	−0.839710	−	1.03319i
$63$			2.38044i			0.299907i
$64$	−6.52197	−	4.63292i	−0.815246	−	0.579115i
$65$		−	7.04430i		−	0.873738i
$66$	−4.25038	+	3.45443i	−0.523185	+	0.425211i
$67$	1.26499	+	0.124590i	0.154543	+	0.0152211i	0.174993	−	0.984570i	$-0.444010\pi$
$67$	1.26499	+	0.124590i	0.154543	+	0.0152211i	−0.0204499	+	0.999791i	$0.506510\pi$
$68$	−2.70211	+	3.96173i	−0.327680	+	0.480430i
$69$	−3.94062	−	7.37239i	−0.474395	−	0.887531i
$70$	11.4262	−	7.55622i	1.36569	−	0.903141i
$71$	0.459307	−	0.0913619i	0.0545097	−	0.0108427i	−0.167760	−	0.985828i	$-0.553653\pi$
$71$	0.459307	−	0.0913619i	0.0545097	−	0.0108427i	0.222270	+	0.974985i	$0.428653\pi$
$72$	−1.36884	+	2.47513i	−0.161319	+	0.291697i
$73$	−0.858965	+	4.31831i	−0.100534	+	0.505420i	0.897402	+	0.441213i	$0.145452\pi$
$73$	−0.858965	+	4.31831i	−0.100534	+	0.505420i	−0.997937	+	0.0642066i	$0.979548\pi$
$74$	−4.73107	+	11.2696i	−0.549976	+	1.31007i
$75$	8.93464	+	7.33247i	1.03168	+	0.846680i
$76$	0.127241	+	1.43166i	0.0145955	+	0.164223i
$77$	−8.13062	−	4.34591i	−0.926570	−	0.495262i
$78$	−1.56212	+	1.88506i	−0.176875	+	0.213441i
$79$	14.1140	−	5.84620i	1.58795	−	0.657749i	0.598300	−	0.801272i	$-0.295843\pi$
$79$	14.1140	−	5.84620i	1.58795	−	0.657749i	0.989647	+	0.143523i	$0.0458431\pi$
$80$	16.2258	−	1.28635i	1.81410	−	0.143818i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	−8.58949	+	4.53868i	−0.948550	+	0.501214i
$83$	−9.33541	+	2.83187i	−1.02469	+	0.310838i	−0.757521	−	0.652811i	$-0.773590\pi$
$83$	−9.33541	+	2.83187i	−1.02469	+	0.310838i	−0.267173	+	0.963648i	$0.586090\pi$
$84$	−4.73329	−	0.511784i	−0.516444	−	0.0558403i
$85$	−0.956340	−	9.70988i	−0.103730	−	1.05318i
$86$	−12.0440	−	0.0573975i	−1.29873	−	0.00618933i
$87$	−3.76080	−	5.62843i	−0.403200	−	0.603431i
$88$	−5.95501	−	9.19419i	−0.634806	−	0.980103i
$89$	2.54044	+	1.69747i	0.269286	+	0.179931i	0.682881	−	0.730530i	$-0.260727\pi$
$89$	2.54044	+	1.69747i	0.269286	+	0.179931i	−0.413594	+	0.910461i	$0.635727\pi$
$90$	−1.09577	−	5.64940i	−0.115505	−	0.595499i
$91$	−3.94342	−	1.19622i	−0.413383	−	0.125398i
$92$	15.5066	−	6.25055i	1.61667	−	0.651664i
$93$	−4.70267	−	5.73022i	−0.487644	−	0.594196i
$94$	−2.01954	+	3.73536i	−0.208300	+	0.385273i
$95$	−2.06781	−	2.06781i	−0.212153	−	0.212153i
$96$	−4.62729	−	3.25395i	−0.472271	−	0.332105i
$97$	6.99279	−	6.99279i	0.710010	−	0.710010i	−0.256527	−	0.966537i	$-0.582578\pi$
$97$	6.99279	−	6.99279i	0.710010	−	0.710010i	0.966537	+	0.256527i	$0.0825782\pi$
$98$	0.538833	+	1.80726i	0.0544304	+	0.182560i
$99$	−2.99380	+	2.45695i	−0.300888	+	0.246932i
$100$	−16.5009	+	16.1893i	−1.65009	+	1.61893i
$101$	−3.44088	+	11.3431i	−0.342381	+	1.12868i	0.601633	+	0.798773i	$0.294517\pi$
$101$	−3.44088	+	11.3431i	−0.342381	+	1.12868i	−0.944014	+	0.329906i	$0.892983\pi$
$102$	−1.89731	+	2.81044i	−0.187862	+	0.278275i
$103$	3.34569	−	5.00718i	0.329661	−	0.493372i	−0.629202	−	0.777242i	$-0.716618\pi$
$103$	3.34569	−	5.00718i	0.329661	−	0.493372i	0.958863	+	0.283870i	$0.0916183\pi$
$104$	−3.41242	−	3.51141i	−0.334615	−	0.344323i
$105$	8.05398	−	5.38150i	0.785988	−	0.525180i
$106$	7.28187	−	7.21279i	0.707277	−	0.700568i
$107$	18.0955	−	1.78225i	1.74936	−	0.172297i	0.827925	−	0.560838i	$-0.189521\pi$
$107$	18.0955	−	1.78225i	1.74936	−	0.172297i	0.921431	+	0.388542i	$0.127021\pi$
$108$	−0.959562	+	1.75478i	−0.0923339	+	0.168853i
$109$	5.59968	+	18.4597i	0.536352	+	1.76812i	0.634476	+	0.772942i	$0.281216\pi$
$109$	5.59968	+	18.4597i	0.536352	+	1.76812i	−0.0981238	+	0.995174i	$0.531284\pi$
$110$	21.2966	+	6.57125i	2.03055	+	0.626544i
$111$	−3.30736	+	7.98467i	−0.313920	+	0.757871i
$112$	2.03527	−	9.30169i	0.192315	−	0.878927i
$113$	−5.13713	−	12.4021i	−0.483260	−	1.16669i	−0.958052	−	0.286595i	$-0.907477\pi$
$113$	−5.13713	−	12.4021i	−0.483260	−	1.16669i	0.474792	−	0.880098i	$-0.342523\pi$
$114$	0.0947961	+	1.01190i	0.00887847	+	0.0947727i
$115$	−16.0351	+	29.9996i	−1.49528	+	2.79748i
$116$	12.0002	−	6.26792i	1.11419	−	0.581962i
$117$	−1.09822	+	1.33819i	−0.101531	+	0.123715i
$118$	2.07144	−	0.846476i	0.190692	−	0.0779244i
$119$	−5.59801	−	1.11351i	−0.513169	−	0.102076i
$120$	11.4689	−	0.964251i	1.04696	−	0.0880237i
$121$	−0.780244	−	3.92255i	−0.0709313	−	0.356596i
$122$	0.214522	−	1.05224i	0.0194219	−	0.0952655i
$123$	−6.05832	+	3.23824i	−0.546261	+	0.291982i
$124$	12.4051	−	8.11887i	1.11401	−	0.729096i
$125$	2.61575	−	26.5581i	0.233960	−	2.37543i
$126$	−3.34863	−	0.345932i	−0.298319	−	0.0308181i
$127$	−6.64223			−0.589403			−0.294701	−	0.955589i	$-0.595220\pi$
$127$	−6.64223			−0.589403			−0.294701	+	0.955589i	$0.595220\pi$
$128$	7.46504	−	8.50136i	0.659823	−	0.751421i
$129$	−8.51646			−0.749832
$130$	9.90941	+	1.02370i	0.869113	+	0.0897842i
$131$	−0.156907	+	1.59310i	−0.0137090	+	0.139190i	−0.999603	−	0.0281822i	$-0.991028\pi$
$131$	−0.156907	+	1.59310i	−0.0137090	+	0.139190i	0.985894	+	0.167372i	$0.0535281\pi$
$132$	−4.24176	−	6.48113i	−0.369198	−	0.564110i
$133$	−1.50871	+	0.806421i	−0.130821	+	0.0699255i
$134$	−0.359096	+	1.76138i	−0.0310211	+	0.152160i
$135$	−0.793858	−	3.99099i	−0.0683244	−	0.343490i
$136$	−5.18040	−	4.37687i	−0.444215	−	0.375313i
$137$	5.04237	+	1.00299i	0.430799	+	0.0856912i	0.405727	−	0.913994i	$-0.367018\pi$
$137$	5.04237	+	1.00299i	0.430799	+	0.0856912i	0.0250721	+	0.999686i	$0.492018\pi$
$138$	10.9436	−	4.47201i	0.931581	−	0.380683i
$139$	−9.77771	+	11.9142i	−0.829334	+	1.01055i	0.170349	+	0.985384i	$0.445510\pi$
$139$	−9.77771	+	11.9142i	−0.829334	+	1.01055i	−0.999683	+	0.0251630i	$0.991990\pi$
$140$	8.96905	+	17.1716i	0.758023	+	1.45127i
$141$	−1.41543	+	2.64808i	−0.119200	+	0.223008i
$142$	0.0617735	+	0.659397i	0.00518391	+	0.0553354i
$143$	−2.56571	−	6.19417i	−0.214555	−	0.517983i
$144$	−3.28291	−	2.28527i	−0.273576	−	0.190439i
$145$	−10.5411	+	25.4486i	−0.875394	+	2.11339i
$146$	−5.94985	−	1.83588i	−0.492413	−	0.151938i
$147$	0.387098	+	1.27609i	0.0319273	+	0.105250i
$148$	−15.1657	−	8.29306i	−1.24662	−	0.681685i
$149$	−21.1707	+	2.08513i	−1.73437	+	0.170820i	−0.915272	−	0.402837i	$-0.868024\pi$
$149$	−21.1707	+	2.08513i	−1.73437	+	0.170820i	−0.819096	+	0.573657i	$0.805524\pi$
$150$	−11.6132	+	11.5030i	−0.948213	+	0.939218i
$151$	1.51218	−	1.01041i	0.123060	−	0.0822259i	−0.492517	−	0.870303i	$-0.663923\pi$
$151$	1.51218	−	1.01041i	0.123060	−	0.0822259i	0.615577	+	0.788077i	$0.288923\pi$
$152$	−2.03244	−	0.0290596i	−0.164853	−	0.00235705i
$153$	−1.33212	+	1.99365i	−0.107695	+	0.161177i
$154$	7.29507	−	10.8060i	0.587853	−	0.870773i
$155$	−8.75623	+	28.8654i	−0.703317	+	2.31853i
$156$	−2.42475	−	2.47142i	−0.194135	−	0.197872i
$157$	−4.19016	+	3.43878i	−0.334411	+	0.274444i	−0.786580	−	0.617488i	$-0.788150\pi$
$157$	−4.19016	+	3.43878i	−0.334411	+	0.274444i	0.452169	+	0.891932i	$0.350650\pi$
$158$	6.17293	+	20.7041i	0.491092	+	1.64713i
$159$	5.12469	−	5.12469i	0.406415	−	0.406415i
$160$	−0.548443	+	23.0122i	−0.0433583	+	1.81928i
$161$	14.0709	+	14.0709i	1.10894	+	1.10894i
$162$	−0.672592	+	1.24403i	−0.0528438	+	0.0977405i
$163$	−6.53545	−	7.96347i	−0.511896	−	0.623747i	0.451357	−	0.892344i	$-0.350940\pi$
$163$	−6.53545	−	7.96347i	−0.511896	−	0.623747i	−0.963253	+	0.268596i	$0.913440\pi$
$164$	−5.13644	−	12.7426i	−0.401088	−	0.995033i
$165$	15.0810	+	4.57476i	1.17405	+	0.356144i
$166$	−2.62701	−	13.5439i	−0.203896	−	1.05121i
$167$	−8.68745	−	5.80477i	−0.672255	−	0.449187i	0.172022	−	0.985093i	$-0.444970\pi$
$167$	−8.68745	−	5.80477i	−0.672255	−	0.449187i	−0.844277	+	0.535906i	$0.819970\pi$
$168$	1.40780	−	6.58407i	0.108614	−	0.507972i
$169$	5.55746	+	8.31733i	0.427497	+	0.639795i
$170$	13.7981	+	0.0657574i	1.05827	+	0.00504336i
$171$	0.0704401	+	0.715191i	0.00538669	+	0.0546920i
$172$	1.83100	−	16.9342i	0.139613	−	1.29122i
$173$	−6.17933	+	1.87448i	−0.469806	+	0.142514i	−0.516306	−	0.856404i	$-0.672693\pi$
$173$	−6.17933	+	1.87448i	−0.469806	+	0.142514i	0.0465000	+	0.998918i	$0.485193\pi$
$174$	8.46419	−	4.47248i	0.641669	−	0.339058i
$175$	−25.4193	−	10.5290i	−1.92152	−	0.795919i
$176$	13.7991	−	7.04095i	1.04015	−	0.530732i
$177$	1.46186	−	0.605522i	0.109880	−	0.0455139i
$178$	−2.75706	+	3.32703i	−0.206650	+	0.249371i
$179$	−0.882040	−	0.471460i	−0.0659267	−	0.0352386i	0.438104	−	0.898924i	$-0.355650\pi$
$179$	−0.882040	−	0.471460i	−0.0659267	−	0.0352386i	−0.504031	+	0.863686i	$0.668150\pi$
$180$	8.10641	−	0.720469i	0.604216	−	0.0537006i
$181$	−4.31589	−	3.54196i	−0.320798	−	0.263272i	0.460187	−	0.887822i	$-0.347782\pi$
$181$	−4.31589	−	3.54196i	−0.320798	−	0.263272i	−0.780985	+	0.624550i	$0.785282\pi$
$182$	2.25583	−	5.37347i	0.167213	−	0.398308i
$183$	0.148142	−	0.744762i	0.0109510	−	0.0550544i
$184$	6.53936	+	22.7218i	0.482088	+	1.67508i
$185$	34.4923	−	6.86095i	2.53593	−	0.504427i
$186$	8.74426	−	5.78264i	0.641160	−	0.424004i
$187$	−4.37750	−	8.18973i	−0.320115	−	0.598893i
$188$	−4.96115	−	3.38377i	−0.361829	−	0.246787i
$189$	−2.36898	−	0.233324i	−0.172318	−	0.0169718i
$190$	3.20934	−	2.60834i	0.232830	−	0.189229i
$191$			17.4199i			1.26046i	0.776410	+	0.630229i	$0.217039\pi$
$191$			17.4199i			1.26046i	−0.776410	+	0.630229i	$0.782961\pi$
$192$	5.24987	−	6.03646i	0.378877	−	0.435644i
$193$			5.39374i			0.388250i	0.980977	+	0.194125i	$0.0621868\pi$
$193$			5.39374i			0.388250i	−0.980977	+	0.194125i	$0.937813\pi$
$194$	8.82074	+	10.8532i	0.633292	+	0.779211i
$195$	7.01038	+	0.690462i	0.502024	+	0.0494450i
$196$	−2.62062	+	0.495356i	−0.187187	+	0.0353826i
$197$	−12.4716	−	23.3327i	−0.888563	−	1.66239i	−0.739077	−	0.673621i	$-0.764738\pi$
$197$	−12.4716	−	23.3327i	−0.888563	−	1.66239i	−0.149487	−	0.988764i	$-0.547762\pi$
$198$	−3.02119	−	4.56851i	−0.214706	−	0.324670i
$199$	21.2643	−	4.22974i	1.50739	−	0.299838i	0.628856	−	0.777521i	$-0.283523\pi$
$199$	21.2643	−	4.22974i	1.50739	−	0.299838i	0.878532	+	0.477683i	$0.158523\pi$
$200$	−20.3759	−	25.5649i	−1.44080	−	1.80771i
$201$	−0.247981	+	1.24668i	−0.0174912	+	0.0879342i
$202$	−15.4566	−	6.48879i	−1.08752	−	0.456550i
$203$	12.4561	+	10.2225i	0.874249	+	0.717478i
$204$	−3.67780	−	3.07742i	−0.257498	−	0.215463i
$205$	24.6524	+	13.1770i	1.72180	+	0.920321i
$206$	6.55753	+	5.43413i	0.456885	+	0.378614i
$207$	7.72314	−	3.19903i	0.536795	−	0.222348i
$208$	5.43550	−	4.29005i	0.376884	−	0.297462i
$209$	−2.57140	−	1.06511i	−0.177868	−	0.0736752i
$210$	6.39987	+	12.1118i	0.441633	+	0.835794i
$211$	14.6983	−	4.45868i	1.01187	−	0.306948i	0.259541	−	0.965732i	$-0.416429\pi$
$211$	14.6983	−	4.45868i	1.01187	−	0.306948i	0.752332	+	0.658784i	$0.228929\pi$
$212$	9.08821	+	11.2918i	0.624181	+	0.775523i
$213$	0.0459020	+	0.466051i	0.00314515	+	0.0319333i
$214$	−0.122546	+	25.7144i	−0.00837710	+	1.75780i
$215$	19.2533	+	28.8146i	1.31306	+	1.96514i
$216$	−2.32905	−	1.60485i	−0.158471	−	0.109196i
$217$	14.6720	+	9.80352i	0.996000	+	0.665506i
$218$	−26.7815	+	5.19461i	−1.81387	+	0.351824i
$219$	−4.21332	−	1.27810i	−0.284710	−	0.0863658i
$220$	−12.3388	+	29.0036i	−0.831884	+	1.95542i
$221$	−2.63325	−	3.20863i	−0.177132	−	0.215836i
$222$	−10.7516	−	5.81290i	−0.721601	−	0.390137i
$223$	−10.8220	−	10.8220i	−0.724698	−	0.724698i	0.244861	−	0.969558i	$-0.421258\pi$
$223$	−10.8220	−	10.8220i	−0.724698	−	0.724698i	−0.969558	+	0.244861i	$0.921258\pi$
$224$	12.7892	+	4.21482i	0.854512	+	0.281615i
$225$	−8.17291	+	8.17291i	−0.544860	+	0.544860i
$226$	18.1929	−	5.42422i	1.21018	−	0.360814i
$227$	2.97786	−	2.44386i	0.197647	−	0.162205i	−0.530364	−	0.847770i	$-0.677945\pi$
$227$	2.97786	−	2.44386i	0.197647	−	0.162205i	0.728011	+	0.685565i	$0.240445\pi$
$228$	−1.43724	−	0.0136991i	−0.0951833	−	0.000907246i
$229$	−1.34856	+	4.44562i	−0.0891155	+	0.293775i	−0.990158	−	0.139957i	$-0.955303\pi$
$229$	−1.34856	+	4.44562i	−0.0891155	+	0.293775i	0.901042	+	0.433732i	$0.142803\pi$
$230$	−39.8710	−	26.9166i	−2.62901	−	1.77483i
$231$	5.12192	−	7.66550i	0.336998	−	0.504353i
$232$	7.07335	+	17.7919i	0.464388	+	1.16809i
$233$	−6.27986	+	4.19607i	−0.411407	+	0.274893i	−0.744003	−	0.668176i	$-0.767075\pi$
$233$	−6.27986	+	4.19607i	−0.411407	+	0.274893i	0.332596	+	0.943069i	$0.392075\pi$
$234$	−1.72287	−	1.73937i	−0.112627	−	0.113706i
$235$	12.1594	−	1.19759i	0.793191	−	0.0781225i
$236$	0.889733	+	3.03696i	0.0579167	+	0.197690i
$237$	4.43464	+	14.6190i	0.288061	+	0.949609i
$238$	2.37993	−	7.71306i	0.154268	−	0.499963i
$239$	−0.385680	+	0.931115i	−0.0249476	+	0.0602288i	−0.935862	−	0.352366i	$-0.885377\pi$
$239$	−0.385680	+	0.931115i	−0.0249476	+	0.0602288i	0.910915	+	0.412594i	$0.135377\pi$
$240$	−0.310257	+	16.2738i	−0.0200270	+	1.05047i
$241$	−1.46802	−	3.54411i	−0.0945634	−	0.228296i	0.869519	−	0.493899i	$-0.164429\pi$
$241$	−1.46802	−	3.54411i	−0.0945634	−	0.228296i	−0.964082	+	0.265603i	$0.914429\pi$
$242$	5.63135	−	0.527554i	0.361997	−	0.0339125i
$243$	−0.471397	+	0.881921i	−0.0302401	+	0.0565753i
$244$	1.44904	+	0.454689i	0.0927655	+	0.0291085i
$245$	3.44241	−	4.19459i	0.219928	−	0.267983i
$246$	−3.67491	−	8.99300i	−0.234304	−	0.573373i
$247$	−1.22018	−	0.242708i	−0.0776380	−	0.0154432i
$248$	9.61829	+	18.6304i	0.610762	+	1.18303i
$249$	−1.90320	−	9.56803i	−0.120610	−	0.606349i
$250$	36.9799	+	7.53915i	2.33882	+	0.476818i
$251$	10.4434	−	5.58213i	0.659183	−	0.352341i	−0.107649	−	0.994189i	$-0.534332\pi$
$251$	10.4434	−	5.58213i	0.659183	−	0.352341i	0.766832	+	0.641848i	$0.221832\pi$
$252$	0.973263	−	4.66033i	0.0613098	−	0.293573i
$253$	−3.17335	+	32.2195i	−0.199507	+	2.02562i
$254$	0.965268	−	9.34381i	0.0605663	−	0.586283i
$255$	9.75686			0.610998
$256$	10.8743	+	11.7367i	0.679641	+	0.733545i
$257$	−26.9794			−1.68293			−0.841465	−	0.540312i	$-0.818306\pi$
$257$	−26.9794			−1.68293			−0.841465	+	0.540312i	$0.818306\pi$
$258$	1.23763	−	11.9803i	0.0770518	−	0.745863i
$259$	2.01651	−	20.4740i	0.125300	−	1.27219i
$260$	−2.88013	+	13.7911i	−0.178618	+	0.855286i
$261$	5.96995	−	3.19100i	0.369531	−	0.197518i
$262$	−2.21826	−	0.452239i	−0.137044	−	0.0279394i
$263$	1.31512	+	6.61158i	0.0810941	+	0.407687i	0.999915	+	0.0130134i	$0.00414242\pi$
$263$	1.31512	+	6.61158i	0.0810941	+	0.407687i	−0.918821	+	0.394674i	$0.870858\pi$
$264$	9.73361	−	5.02515i	0.599062	−	0.309276i
$265$	−28.9244	−	5.75341i	−1.77681	−	0.353429i
$266$	−0.915164	−	2.23953i	−0.0561123	−	0.137314i
$267$	−1.93830	+	2.36183i	−0.118622	+	0.144542i
$268$	−2.42560	−	0.761119i	−0.148167	−	0.0464927i
$269$	−14.3316	+	26.8125i	−0.873810	+	1.63478i	−0.105763	+	0.994391i	$0.533728\pi$
$269$	−14.3316	+	26.8125i	−0.873810	+	1.63478i	−0.768047	+	0.640393i	$0.778772\pi$
$270$	5.72960	−	0.536759i	0.348693	−	0.0326661i
$271$	−3.78566	−	9.13939i	−0.229963	−	0.555179i	0.766210	−	0.642591i	$-0.222140\pi$
$271$	−3.78566	−	9.13939i	−0.229963	−	0.555179i	−0.996172	+	0.0874119i	$0.972140\pi$
$272$	6.90989	−	6.65135i	0.418974	−	0.403297i
$273$	1.57699	−	3.80718i	0.0954435	−	0.230421i
$274$	−2.14370	+	6.94748i	−0.129506	+	0.419713i
$275$	−12.9943	−	42.8364i	−0.783585	−	2.58313i
$276$	4.70054	+	16.0445i	0.282939	+	0.965768i
$277$	−9.91805	+	0.976842i	−0.595918	+	0.0586928i	−0.391480	−	0.920187i	$-0.628037\pi$
$277$	−9.91805	+	0.976842i	−0.595918	+	0.0586928i	−0.204438	+	0.978880i	$0.565537\pi$
$278$	−15.3391	−	15.4860i	−0.919976	−	0.928787i
$279$	6.16357	−	4.11837i	0.369003	−	0.246560i
$280$	−25.4592	+	10.1216i	−1.52148	+	0.604880i
$281$	11.2704	−	16.8674i	0.672336	−	1.00622i	−0.325814	−	0.945434i	$-0.605638\pi$
$281$	11.2704	−	16.8674i	0.672336	−	1.00622i	0.998151	−	0.0607885i	$-0.0193615\pi$
$282$	−3.51943	−	2.37594i	−0.209579	−	0.141485i
$283$	3.19988	−	10.5486i	0.190213	−	0.627048i	−0.809016	−	0.587787i	$-0.799999\pi$
$283$	3.19988	−	10.5486i	0.190213	−	0.627048i	0.999229	−	0.0392616i	$-0.0125006\pi$
$284$	−0.936569	−	0.00892696i	−0.0555751	−	0.000529718i
$285$	2.26053	−	1.85517i	0.133902	−	0.109891i
$286$	9.08637	−	2.70910i	0.537288	−	0.160192i
$287$	11.5628	−	11.5628i	0.682533	−	0.682533i
$288$	3.69184	−	4.28606i	0.217544	−	0.252559i
$289$	7.95553	+	7.95553i	0.467972	+	0.467972i
$290$	−34.2673	−	18.5268i	−2.01225	−	1.08793i
$291$	6.27370	+	7.64453i	0.367771	+	0.448130i
$292$	3.44723	−	8.10302i	0.201734	−	0.474194i
$293$	−29.4135	−	8.92249i	−1.71836	−	0.521257i	−0.731358	−	0.681994i	$-0.761113\pi$
$293$	−29.4135	−	8.92249i	−1.71836	−	0.521257i	−0.986997	+	0.160736i	$0.948613\pi$
$294$	−1.85137	+	0.359096i	−0.107974	+	0.0209429i
$295$	−5.35358	−	3.57715i	−0.311697	−	0.208269i
$296$	13.8700	−	20.1289i	0.806177	−	1.16997i
$297$	−2.15167	−	3.22020i	−0.124853	−	0.186855i
$298$	0.143372	−	30.0843i	0.00830532	−	1.74274i
$299$	1.41844	+	14.4017i	0.0820306	+	0.832871i
$300$	−14.4940	−	18.0082i	−0.836809	−	1.03971i
$301$	19.4000	−	5.88491i	1.11819	−	0.339201i
$302$	1.20162	+	2.27407i	0.0691452	+	0.130858i
$303$	−10.9512	−	4.53613i	−0.629129	−	0.260594i
$304$	0.336239	−	2.85487i	0.0192847	−	0.163738i
$305$	−2.85474	+	1.18247i	−0.163462	+	0.0677081i
$306$	−2.61094	−	2.16365i	−0.149257	−	0.123687i
$307$	−3.62799	−	1.93920i	−0.207060	−	0.110676i	0.364607	−	0.931161i	$-0.381203\pi$
$307$	−3.62799	−	1.93920i	−0.207060	−	0.110676i	−0.571667	+	0.820485i	$0.693703\pi$
$308$	14.1410	+	11.8325i	0.805756	+	0.674221i
$309$	4.65513	+	3.82037i	0.264821	+	0.217333i
$310$	−39.3333	−	16.5124i	−2.23398	−	0.937843i
$311$	5.68464	−	28.5786i	0.322346	−	1.62054i	−0.391456	−	0.920197i	$-0.628029\pi$
$311$	5.68464	−	28.5786i	0.322346	−	1.62054i	0.713803	−	0.700347i	$-0.246971\pi$
$312$	3.82898	−	3.05181i	0.216773	−	0.172775i
$313$	2.13035	−	0.423753i	0.120415	−	0.0239520i	−0.134515	−	0.990912i	$-0.542948\pi$
$313$	2.13035	−	0.423753i	0.120415	−	0.0239520i	0.254930	+	0.966960i	$0.417948\pi$
$314$	−4.22849	−	6.39415i	−0.238628	−	0.360843i
$315$	4.56615	+	8.54267i	0.257274	+	0.481325i
$316$	−30.0221	+	5.67485i	−1.68887	+	0.319235i
$317$	29.9923	+	2.95399i	1.68454	+	0.165912i	0.894476	−	0.447116i	$-0.147549\pi$
$317$	29.9923	+	2.95399i	1.68454	+	0.165912i	0.790061	+	0.613029i	$0.210049\pi$
$318$	6.46431	+	7.95378i	0.362501	+	0.446026i
$319$			26.2167i			1.46785i
$320$	−32.2922	−	4.11571i	−1.80519	−	0.230075i
$321$			18.1830i			1.01488i
$322$	−21.8387	+	17.7490i	−1.21702	+	0.989115i
$323$	−1.71485	−	0.168897i	−0.0954165	−	0.00939771i
$324$	−1.65227	−	1.12694i	−0.0917930	−	0.0626078i
$325$	−9.43211	−	17.6462i	−0.523200	−	0.978838i
$326$	12.1522	−	8.03632i	0.673047	−	0.445091i
$327$	−18.9197	+	3.76335i	−1.04626	+	0.208114i
$328$	18.6719	−	5.37377i	1.03098	−	0.296717i
$329$	1.39442	−	7.01022i	0.0768768	−	0.386486i
$330$	−8.62704	+	20.5500i	−0.474903	+	1.13124i
$331$	−10.8855	−	8.93347i	−0.598319	−	0.491028i	0.285800	−	0.958289i	$-0.407741\pi$
$331$	−10.8855	−	8.93347i	−0.598319	−	0.491028i	−0.884119	+	0.467261i	$0.845241\pi$
$332$	19.4343	−	1.72726i	1.06660	−	0.0947954i
$333$	−7.62204	−	4.07407i	−0.417685	−	0.223257i
$334$	9.42821	−	11.3773i	0.515889	−	0.622539i
$335$	4.77864	−	1.97938i	0.261085	−	0.108145i
$336$	9.05741	+	2.93720i	0.494122	+	0.160237i
$337$	1.27870	+	0.529654i	0.0696551	+	0.0288521i	0.417239	−	0.908797i	$-0.362998\pi$
$337$	1.27870	+	0.529654i	0.0696551	+	0.0288521i	−0.347584	+	0.937649i	$0.612998\pi$
$338$	−12.5078	+	6.60914i	−0.680337	+	0.359490i
$339$	12.8459	−	3.89677i	0.697695	−	0.211643i
$340$	−2.09768	+	19.4006i	−0.113763	+	1.05215i
$341$	2.81401	+	28.5711i	0.152387	+	1.54721i
$342$	−1.01631	−	0.00484342i	−0.0549560	−	0.000261902i
$343$	−11.0211	−	16.4942i	−0.595082	−	0.890603i
$344$	23.5557	+	5.03665i	1.27004	+	0.271558i
$345$	−28.2834	−	18.8984i	−1.52273	−	1.01745i
$346$	−1.73888	−	8.96504i	−0.0934830	−	0.481963i
$347$	−2.45708	−	0.745348i	−0.131903	−	0.0400124i	0.223643	−	0.974671i	$-0.428205\pi$
$347$	−2.45708	−	0.745348i	−0.131903	−	0.0400124i	−0.355546	+	0.934659i	$0.615705\pi$
$348$	5.06151	+	12.5568i	0.271326	+	0.673113i
$349$	−16.6507	−	20.2890i	−0.891293	−	1.08604i	−0.995803	−	0.0915198i	$-0.970828\pi$
$349$	−16.6507	−	20.2890i	−0.891293	−	1.08604i	0.104510	−	0.994524i	$-0.466672\pi$
$350$	18.5055	−	34.2279i	0.989159	−	1.82956i
$351$	−1.22410	−	1.22410i	−0.0653375	−	0.0653375i
$352$	7.89937	+	20.4348i	0.421038	+	1.08918i
$353$	−17.0056	+	17.0056i	−0.905114	+	0.905114i	−0.995873	−	0.0907586i	$-0.971071\pi$
$353$	−17.0056	+	17.0056i	−0.905114	+	0.905114i	0.0907586	+	0.995873i	$0.471071\pi$
$354$	0.639363	+	2.14444i	0.0339818	+	0.113975i
$355$	1.47306	−	1.20891i	0.0781821	−	0.0641624i
$356$	−4.27956	−	4.36193i	−0.226816	−	0.231182i
$357$	1.65685	−	5.46191i	0.0876900	−	0.289075i
$358$	0.791396	−	1.17228i	0.0418266	−	0.0619567i
$359$	−5.51925	+	8.26014i	−0.291295	+	0.435953i	−0.948036	−	0.318162i	$-0.896934\pi$
$359$	−5.51925	+	8.26014i	−0.291295	+	0.435953i	0.656742	+	0.754116i	$0.271934\pi$
$360$	−0.164543	+	11.5082i	−0.00867218	+	0.606536i
$361$	15.3685	−	10.2689i	0.808869	−	0.540469i
$362$	5.60977	−	5.55656i	0.294843	−	0.292046i
$363$	3.98014	−	0.392010i	0.208903	−	0.0205752i
$364$	7.23119	+	3.95422i	0.379017	+	0.207258i
$365$	5.20081	+	17.1448i	0.272223	+	0.897398i
$366$	1.02615	+	0.316627i	0.0536376	+	0.0165503i
$367$	1.23655	−	2.98529i	0.0645472	−	0.155831i	−0.888315	−	0.459236i	$-0.848123\pi$
$367$	1.23655	−	2.98529i	0.0645472	−	0.155831i	0.952862	+	0.303405i	$0.0981234\pi$
$368$	−32.9137	+	5.89709i	−1.71575	+	0.307407i
$369$	−2.62883	−	6.34655i	−0.136851	−	0.330388i
$370$	4.63897	+	49.5183i	0.241168	+	2.57434i
$371$	−8.13254	+	15.2149i	−0.422221	+	0.789919i
$372$	6.86386	+	13.1411i	0.355875	+	0.681336i
$373$	−0.770867	+	0.939304i	−0.0399140	+	0.0486353i	−0.792585	−	0.609762i	$-0.791265\pi$
$373$	−0.770867	+	0.939304i	−0.0399140	+	0.0486353i	0.752671	+	0.658397i	$0.228765\pi$
$374$	12.1569	−	4.96780i	0.628617	−	0.256879i
$375$	26.1739	+	5.20631i	1.35161	+	0.268853i
$376$	5.48102	−	6.48725i	0.282662	−	0.334554i
$377$	2.28617	+	11.4933i	0.117743	+	0.591937i
$378$	0.672489	−	3.29860i	0.0345891	−	0.169661i
$379$	8.71713	−	4.65940i	0.447769	−	0.239337i	−0.232070	−	0.972699i	$-0.574550\pi$
$379$	8.71713	−	4.65940i	0.447769	−	0.239337i	0.679839	+	0.733362i	$0.262050\pi$
$380$	3.20283	+	4.89372i	0.164302	+	0.251042i
$381$	0.651053	−	6.61025i	0.0333544	−	0.338653i
$382$	−24.5050	−	2.53150i	−1.25378	−	0.129523i
$383$	7.13004			0.364328			0.182164	−	0.983268i	$-0.441690\pi$
$383$	7.13004			0.364328			0.182164	+	0.983268i	$0.441690\pi$
$384$	7.72872	+	8.26238i	0.394405	+	0.421638i
$385$	−37.5147			−1.91192
$386$	−7.58753	−	0.783834i	−0.386195	−	0.0398961i
$387$	0.834759	−	8.47545i	0.0424332	−	0.430831i
$388$	−16.5493	+	10.8312i	−0.840163	+	0.549869i
$389$	5.10563	−	2.72902i	0.258866	−	0.138367i	−0.336859	−	0.941555i	$-0.609365\pi$
$389$	5.10563	−	2.72902i	0.258866	−	0.138367i	0.595725	+	0.803188i	$0.296865\pi$
$390$	−1.99006	+	9.76136i	−0.100771	+	0.494285i
$391$	3.91036	+	19.6587i	0.197756	+	0.994185i
$392$	−0.315995	−	3.75848i	−0.0159602	−	0.189832i
$393$	−1.57005	−	0.312303i	−0.0791986	−	0.0157536i
$394$	34.6351	−	14.1533i	1.74489	−	0.713035i
$395$	39.4366	−	48.0537i	1.98427	−	2.41784i
$396$	6.86569	−	3.58608i	0.345014	−	0.180207i
$397$	10.5716	−	19.7782i	0.530576	−	0.992637i	−0.463720	−	0.885982i	$-0.653486\pi$
$397$	10.5716	−	19.7782i	0.530576	−	0.992637i	0.994296	−	0.106656i	$-0.0340142\pi$
$398$	2.85990	+	30.5278i	0.143354	+	1.53022i
$399$	−0.654658	−	1.58048i	−0.0327739	−	0.0791232i
$400$	38.9239	−	24.9482i	1.94620	−	1.24741i
$401$	−0.435481	+	1.05134i	−0.0217469	+	0.0525017i	−0.934380	−	0.356278i	$-0.884046\pi$
$401$	−0.435481	+	1.05134i	−0.0217469	+	0.0525017i	0.912633	+	0.408780i	$0.134046\pi$
$402$	−1.71771	−	0.530012i	−0.0856714	−	0.0264346i
$403$	3.72513	+	12.2801i	0.185562	+	0.611715i
$404$	11.3742	−	20.8002i	0.565885	−	1.03485i
$405$	4.04959	−	0.398850i	0.201226	−	0.0198190i
$406$	−16.1904	+	16.0368i	−0.803516	+	0.795894i
$407$	27.8307	−	18.5959i	1.37952	−	0.921765i
$408$	4.86356	−	4.72644i	0.240782	−	0.233994i
$409$	−8.49058	+	12.7071i	−0.419832	+	0.628324i	−0.979750	−	0.200225i	$-0.935833\pi$
$409$	−8.49058	+	12.7071i	−0.419832	+	0.628324i	0.559918	+	0.828548i	$0.310833\pi$
$410$	−22.1190	+	32.7643i	−1.09238	+	1.61811i
$411$	−1.49240	+	4.91978i	−0.0736146	+	0.242675i
$412$	−8.59730	+	8.43495i	−0.423558	+	0.415560i
$413$	−2.91161	+	2.38949i	−0.143271	+	0.117579i
$414$	3.37781	+	11.3292i	0.166010	+	0.556802i
$415$	−28.0699	+	28.0699i	−1.37790	+	1.37790i
$416$	5.24503	+	8.26971i	0.257159	+	0.405456i
$417$	−10.8984	−	10.8984i	−0.533698	−	0.533698i
$418$	1.87200	−	3.46248i	0.0915627	−	0.169355i
$419$	2.24624	+	2.73705i	0.109736	+	0.133714i	0.824982	−	0.565159i	$-0.191185\pi$
$419$	2.24624	+	2.73705i	0.109736	+	0.133714i	−0.715246	+	0.698873i	$0.753685\pi$
$420$	−17.9680	+	7.24275i	−0.876751	+	0.353410i
$421$	6.00873	+	1.82273i	0.292848	+	0.0888344i	0.433290	−	0.901254i	$-0.357353\pi$
$421$	6.00873	+	1.82273i	0.292848	+	0.0888344i	−0.140443	+	0.990089i	$0.544853\pi$
$422$	4.13615	+	21.3245i	0.201345	+	1.03806i
$423$	−2.49659	−	1.66817i	−0.121388	−	0.0811091i
$424$	−17.2052	+	11.1437i	−0.835557	+	0.541185i
$425$	−15.3969	−	23.0431i	−0.746860	−	1.11775i
$426$	−0.662277	−	0.00315619i	−0.0320874	−	0.000152918i
$427$	0.177175	+	1.79889i	0.00857410	+	0.0870543i
$428$	−36.1554	−	3.90928i	−1.74763	−	0.188962i
$429$	6.41583	−	1.94622i	0.309759	−	0.0939644i
$430$	−43.3322	+	22.8967i	−2.08966	+	1.10418i
$431$	−22.1224	−	9.16341i	−1.06560	−	0.441386i	−0.220164	−	0.975463i	$-0.570659\pi$
$431$	−22.1224	−	9.16341i	−1.06560	−	0.441386i	−0.845436	+	0.534077i	$0.820659\pi$
$432$	2.59605	−	3.04311i	0.124903	−	0.146412i
$433$	28.0473	−	11.6176i	1.34786	−	0.558304i	0.412168	−	0.911108i	$-0.364772\pi$
$433$	28.0473	−	11.6176i	1.34786	−	0.558304i	0.935697	+	0.352804i	$0.114772\pi$
$434$	−15.9231	+	19.2148i	−0.764331	+	0.922341i
$435$	−24.2928	−	12.9848i	−1.16475	−	0.622572i
$436$	−3.41544	−	38.4292i	−0.163570	−	1.84042i
$437$	4.64389	+	3.81114i	0.222147	+	0.182312i
$438$	2.41022	−	5.74125i	0.115165	−	0.274328i
$439$	1.23520	−	6.20977i	0.0589529	−	0.296376i	−0.940049	−	0.341039i	$-0.889221\pi$
$439$	1.23520	−	6.20977i	0.0589529	−	0.296376i	0.999002	+	0.0446625i	$0.0142212\pi$
$440$	−39.0070	−	21.5723i	−1.85959	−	1.02842i
$441$	−1.30789	+	0.260155i	−0.0622805	+	0.0123884i
$442$	4.89634	−	3.23798i	0.232895	−	0.154015i
$443$	−6.45883	−	12.0836i	−0.306868	−	0.574110i	0.680463	−	0.732782i	$-0.261779\pi$
$443$	−6.45883	−	12.0836i	−0.306868	−	0.574110i	−0.987331	+	0.158673i	$0.949279\pi$
$444$	9.73962	−	14.2798i	0.462222	−	0.677691i
$445$	12.3730	+	1.21863i	0.586535	+	0.0577686i
$446$	16.7964	−	13.6510i	0.795330	−	0.646392i
$447$		−	21.2731i		−	1.00618i
$448$	−7.78766	+	17.3784i	−0.367933	+	0.821050i
$449$		−	16.3410i		−	0.771178i	−0.922671	−	0.385589i	$-0.873998\pi$
$449$		−	16.3410i		−	0.771178i	0.922671	−	0.385589i	$-0.126002\pi$
$450$	−10.3093	−	12.6848i	−0.485987	−	0.597965i
$451$	26.4767	+	2.60772i	1.24674	+	0.122793i
$452$	4.98656	+	26.3808i	0.234548	+	1.24085i
$453$	0.857324	+	1.60394i	0.0402806	+	0.0753597i
$454$	3.00510	+	4.54418i	0.141036	+	0.213269i
$455$	−16.4463	+	3.27138i	−0.771016	+	0.153365i
$456$	0.228134	−	2.01981i	0.0106834	−	0.0945862i
$457$	−5.31960	+	26.7435i	−0.248841	+	1.25101i	0.631017	+	0.775769i	$0.282638\pi$
$457$	−5.31960	+	26.7435i	−0.248841	+	1.25101i	−0.879858	+	0.475237i	$0.842362\pi$
$458$	−6.05779	−	2.54311i	−0.283062	−	0.118832i
$459$	−1.85348	−	1.52111i	−0.0865132	−	0.0709995i
$460$	43.6585	−	52.1760i	2.03559	−	2.43272i
$461$	2.23133	+	1.19267i	0.103923	+	0.0555482i	0.522539	−	0.852615i	$-0.324985\pi$
$461$	2.23133	+	1.19267i	0.103923	+	0.0555482i	−0.418616	+	0.908163i	$0.637485\pi$
$462$	10.0389	+	8.31912i	0.467053	+	0.387040i
$463$	−15.9263	+	6.59689i	−0.740158	+	0.306584i	−0.720719	−	0.693227i	$-0.756188\pi$
$463$	−15.9263	+	6.59689i	−0.740158	+	0.306584i	−0.0194394	+	0.999811i	$0.506188\pi$
$464$	−26.0562	+	7.36471i	−1.20963	+	0.341898i
$465$	−27.8682	−	11.5434i	−1.29236	−	0.535311i
$466$	−4.99011	−	9.44383i	−0.231163	−	0.437477i
$467$	7.76356	−	2.35505i	0.359255	−	0.108979i	−0.105497	−	0.994420i	$-0.533643\pi$
$467$	7.76356	−	2.35505i	0.359255	−	0.108979i	0.464752	+	0.885441i	$0.346143\pi$
$468$	2.69718	−	2.17083i	0.124677	−	0.100347i
$469$	−0.296579	−	3.01122i	−0.0136948	−	0.139045i
$470$	−0.0823459	+	17.2790i	−0.00379833	+	0.797019i
$471$	−3.01151	−	4.50704i	−0.138763	−	0.207674i
$472$	−4.40148	+	0.810272i	−0.202594	+	0.0372958i
$473$	27.4247	+	18.3246i	1.26099	+	0.842567i
$474$	−21.2095	+	4.11385i	−0.974183	+	0.188955i
$475$	−7.94867	−	2.41120i	−0.364710	−	0.110634i
$476$	10.5043	+	4.46879i	0.481464	+	0.204827i
$477$	4.59771	+	5.60232i	0.210515	+	0.256513i
$478$	−1.25378	−	0.677859i	−0.0573464	−	0.0310046i
$479$	19.1334	+	19.1334i	0.874229	+	0.874229i	0.992930	−	0.118701i	$-0.0378731\pi$
$479$	19.1334	+	19.1334i	0.874229	+	0.874229i	−0.118701	+	0.992930i	$0.537873\pi$
$480$	−22.8477	−	2.80140i	−1.04285	−	0.127866i
$481$	10.5793	−	10.5793i	0.482375	−	0.482375i
$482$	5.19893	−	1.55006i	0.236805	−	0.0706034i
$483$	−15.3823	+	12.6239i	−0.699918	+	0.574408i
$484$	−0.0762376	+	7.99843i	−0.00346534	+	0.363565i
$485$	11.6814	−	38.5086i	0.530427	−	1.74858i
$486$	−1.17212	−	0.791290i	−0.0531683	−	0.0358936i
$487$	2.71742	−	4.06691i	0.123138	−	0.184289i	−0.764779	−	0.644293i	$-0.777152\pi$
$487$	2.71742	−	4.06691i	0.123138	−	0.184289i	0.887917	+	0.460003i	$0.152152\pi$
$488$	−0.850202	+	1.97233i	−0.0384868	+	0.0892832i
$489$	8.56571	−	5.72343i	0.387355	−	0.258822i
$490$	5.40038	+	5.45210i	0.243964	+	0.246301i
$491$	−26.4613	+	2.60621i	−1.19418	+	0.117617i	−0.675507	−	0.737354i	$-0.736075\pi$
$491$	−26.4613	+	2.60621i	−1.19418	+	0.117617i	−0.518676	+	0.854971i	$0.673575\pi$
$492$	13.1847	−	3.86271i	0.594414	−	0.174144i
$493$	4.71160	+	15.5321i	0.212200	+	0.699528i
$494$	0.518744	−	1.68119i	0.0233394	−	0.0756401i
$495$	−6.03092	+	14.5599i	−0.271070	+	0.654420i
$496$	−27.6057	+	10.8229i	−1.23953	+	0.485962i
$497$	−0.426605	−	1.02992i	−0.0191358	−	0.0461980i
$498$	13.7362	−	1.28683i	0.615533	−	0.0576642i
$499$	−4.60535	+	8.61600i	−0.206164	+	0.385705i	−0.963659	−	0.267135i	$-0.913923\pi$
$499$	−4.60535	+	8.61600i	−0.206164	+	0.385705i	0.757495	+	0.652841i	$0.226423\pi$
$500$	−15.9795	+	50.9251i	−0.714627	+	2.27744i
$501$	6.62834	−	8.07665i	0.296132	−	0.360838i
$502$	6.33486	+	15.5023i	0.282739	+	0.691899i
$503$	−6.47063	−	1.28709i	−0.288511	−	0.0573885i	0.0487129	−	0.998813i	$-0.484488\pi$
$503$	−6.47063	−	1.28709i	−0.288511	−	0.0573885i	−0.337224	+	0.941424i	$0.609488\pi$
$504$	6.41438	+	2.04637i	0.285719	+	0.0911525i
$505$	9.40998	+	47.3072i	0.418739	+	2.10514i
$506$	−44.8629	−	9.14626i	−1.99440	−	0.406601i
$507$	−8.82201	+	4.71546i	−0.391799	+	0.209421i
$508$	13.0039	+	2.71574i	0.576956	+	0.120491i
$509$	−2.38311	+	24.1961i	−0.105629	+	1.07247i	0.785542	+	0.618808i	$0.212384\pi$
$509$	−2.38311	+	24.1961i	−0.105629	+	1.07247i	−0.891172	+	0.453666i	$0.850116\pi$
$510$	−1.41789	+	13.7252i	−0.0627854	+	0.607764i
$511$	10.4809			0.463646
$512$	−18.0906	+	13.5915i	−0.799501	+	0.600665i
$513$	−0.718651			−0.0317292
$514$	3.92072	−	37.9527i	0.172936	−	1.67402i
$515$	2.40191	−	24.3870i	0.105841	−	1.07462i
$516$	16.6732	+	3.48203i	0.733997	+	0.153288i
$517$	10.2558	−	5.48181i	0.451047	−	0.241090i
$518$	28.5083	+	5.81201i	1.25258	+	0.255365i
$519$	−1.25977	−	6.33331i	−0.0552979	−	0.278001i
$520$	−18.9817	−	6.05571i	−0.832404	−	0.265560i
$521$	32.2720	+	6.41931i	1.41386	+	0.281235i	0.842161	−	0.539226i	$-0.181283\pi$
$521$	32.2720	+	6.41931i	1.41386	+	0.281235i	0.571702	+	0.820461i	$0.306283\pi$
$522$	3.62130	+	8.86182i	0.158500	+	0.387871i
$523$	16.7638	−	20.4267i	0.733029	−	0.893198i	−0.264433	−	0.964404i	$-0.585185\pi$
$523$	16.7638	−	20.4267i	0.733029	−	0.893198i	0.997462	+	0.0712058i	$0.0226847\pi$
$524$	0.958540	−	3.05476i	0.0418740	−	0.133448i
$525$	12.9699	−	24.2649i	0.566051	−	1.05901i
$526$	−9.49180	+	0.889209i	−0.413862	+	0.0387713i
$527$	6.80188	+	16.4212i	0.296294	+	0.715318i
$528$	5.65450	+	14.4228i	0.246080	+	0.627672i
$529$	17.9404	−	43.3121i	0.780019	−	1.88313i
$530$	12.2969	−	39.8526i	0.534141	−	1.73109i
$531$	0.459319	+	1.51417i	0.0199328	+	0.0657095i
$532$	3.28340	−	0.961932i	0.142354	−	0.0417050i
$533$	11.8347	−	1.16562i	0.512618	−	0.0504884i
$534$	−3.04077	−	3.06989i	−0.131587	−	0.132847i
$535$	61.5205	−	41.1067i	2.65976	−	1.77720i
$536$	1.42318	−	3.30155i	0.0614721	−	0.142605i
$537$	0.555645	−	0.831581i	0.0239778	−	0.0358854i
$538$	−35.6351	−	24.0570i	−1.53634	−	1.03717i
$539$	1.49920	−	4.94218i	0.0645749	−	0.212875i
$540$	−0.0775678	+	8.13799i	−0.00333799	+	0.350203i
$541$	−33.3142	+	27.3402i	−1.43229	+	1.17545i	−0.477323	+	0.878728i	$0.658393\pi$
$541$	−33.3142	+	27.3402i	−1.43229	+	1.17545i	−0.954965	+	0.296720i	$0.904107\pi$
$542$	13.4068	−	3.99723i	0.575870	−	0.171696i
$543$	3.94794	−	3.94794i	0.169422	−	0.169422i
$544$	8.35246	+	10.6869i	0.358109	+	0.458198i
$545$	55.5049	+	55.5049i	2.37757	+	2.37757i
$546$	5.12649	+	2.77166i	0.219394	+	0.118616i
$547$	−15.7154	−	19.1493i	−0.671941	−	0.818763i	0.319737	−	0.947506i	$-0.396406\pi$
$547$	−15.7154	−	19.1493i	−0.671941	−	0.818763i	−0.991678	+	0.128744i	$0.958906\pi$
$548$	−9.46168	−	4.02523i	−0.404183	−	0.171950i
$549$	0.726655	+	0.220428i	0.0310129	+	0.00940766i
$550$	62.1475	−	12.0543i	2.64998	−	0.513998i
$551$	4.04488	+	2.70270i	0.172318	+	0.115139i
$552$	−23.2534	+	4.28074i	−0.989730	+	0.182200i
$553$	−20.2037	−	30.2369i	−0.859147	−	1.28580i
$554$	0.0671671	−	14.0939i	0.00285366	−	0.598794i
$555$	3.44707	+	34.9987i	0.146320	+	1.48561i
$556$	24.0136	−	19.3274i	1.01841	−	0.819665i
$557$	−20.1323	+	6.10706i	−0.853032	+	0.258764i	−0.686373	−	0.727250i	$-0.740798\pi$
$557$	−20.1323	+	6.10706i	−0.853032	+	0.258764i	−0.166659	+	0.986015i	$0.553298\pi$
$558$	4.89771	+	9.26895i	0.207337	+	0.392386i
$559$	13.6209	+	5.64195i	0.576102	+	0.238629i
$560$	−10.5385	−	37.2850i	−0.445333	−	1.57558i
$561$	8.57937	−	3.55369i	0.362221	−	0.150037i
$562$	22.0899	+	18.3056i	0.931807	+	0.772175i
$563$	19.3475	+	10.3415i	0.815401	+	0.435841i	0.825702	−	0.564106i	$-0.190779\pi$
$563$	19.3475	+	10.3415i	0.815401	+	0.435841i	−0.0103014	+	0.999947i	$0.503279\pi$
$564$	3.85376	−	4.60560i	0.162273	−	0.193931i
$565$	−42.2253	−	34.6534i	−1.77643	−	1.45788i
$566$	14.3740	+	6.03430i	0.604183	+	0.253641i
$567$	0.464401	−	2.33470i	0.0195030	−	0.0980481i
$568$	0.148663	−	1.31620i	0.00623774	−	0.0552265i
$569$	−18.9018	+	3.75980i	−0.792404	+	0.157619i	−0.574666	−	0.818388i	$-0.694868\pi$
$569$	−18.9018	+	3.75980i	−0.792404	+	0.157619i	−0.217738	+	0.976007i	$0.569868\pi$
$570$	2.28121	+	3.44955i	0.0955494	+	0.144486i
$571$	4.20667	+	7.87013i	0.176044	+	0.329355i	0.954432	−	0.298428i	$-0.0964624\pi$
$571$	4.20667	+	7.87013i	0.176044	+	0.329355i	−0.778388	+	0.627783i	$0.783962\pi$
$572$	2.49051	+	13.1757i	0.104133	+	0.550905i
$573$	−17.3360	−	1.70745i	−0.724221	−	0.0713295i
$574$	14.5854	+	17.9461i	0.608784	+	0.749056i
$575$			96.6206i			4.02936i
$576$	5.49281	+	5.81627i	0.228867	+	0.242345i
$577$			2.24149i			0.0933143i	0.998911	+	0.0466571i	$0.0148568\pi$
$577$			2.24149i			0.0933143i	−0.998911	+	0.0466571i	$0.985143\pi$
$578$	−12.3474	+	10.0351i	−0.513583	+	0.417407i
$579$	−5.36777	−	0.528679i	−0.223077	−	0.0219712i
$580$	31.0419	−	45.5124i	1.28895	−	1.88980i
$581$	10.9469	+	20.4803i	0.454155	+	0.849664i
$582$	−11.6655	+	7.71447i	−0.483550	+	0.319775i
$583$	−27.5292	+	5.47590i	−1.14014	+	0.226789i
$584$	10.8978	+	6.02686i	0.450954	+	0.249393i
$585$	−1.37428	+	6.90895i	−0.0568193	+	0.285650i
$586$	16.8260	−	40.0801i	0.695074	−	1.65570i
$587$	−8.77627	−	7.20250i	−0.362236	−	0.297279i	0.435616	−	0.900132i	$-0.356530\pi$
$587$	−8.77627	−	7.20250i	−0.362236	−	0.297279i	−0.797852	+	0.602853i	$0.794030\pi$
$588$	−0.236105	−	2.65655i	−0.00973680	−	0.109554i
$589$	4.69823	+	2.51125i	0.193587	+	0.103474i
$590$	5.81006	−	7.01118i	0.239197	−	0.288646i
$591$	24.4428	−	10.1245i	1.00544	−	0.416467i
$592$	26.3002	+	22.4365i	1.08093	+	0.922134i
$593$	22.8478	+	9.46389i	0.938248	+	0.388635i	0.798802	−	0.601594i	$-0.205468\pi$
$593$	22.8478	+	9.46389i	0.938248	+	0.388635i	0.139447	+	0.990230i	$0.455468\pi$
$594$	4.84263	−	2.55885i	0.198696	−	0.104991i
$595$	−22.2255	+	6.74204i	−0.911158	+	0.276397i
$596$	42.2996	+	4.57363i	1.73266	+	0.187343i
$597$	2.12510	+	21.5765i	0.0869746	+	0.883068i
$598$	−20.4654	−	0.0975312i	−0.836891	−	0.00398835i
$599$	15.4443	+	23.1141i	0.631038	+	0.944415i	0.999889	+	0.0149266i	$0.00475147\pi$
$599$	15.4443	+	23.1141i	0.631038	+	0.944415i	−0.368850	+	0.929489i	$0.620249\pi$
$600$	27.4390	−	17.7720i	1.12019	−	0.725540i
$601$	3.76267	+	2.51414i	0.153482	+	0.102554i	0.629940	−	0.776644i	$-0.283079\pi$
$601$	3.76267	+	2.51414i	0.153482	+	0.102554i	−0.476458	+	0.879197i	$0.658079\pi$
$602$	5.45921	+	28.1457i	0.222501	+	1.14713i
$603$	−1.21637	−	0.368983i	−0.0495346	−	0.0150261i
$604$	−3.37361	+	1.35987i	−0.137270	+	0.0553324i
$605$	−10.3243	−	12.5802i	−0.419742	−	0.511457i
$606$	7.97256	−	14.7461i	0.323863	−	0.599021i
$607$	1.82456	+	1.82456i	0.0740568	+	0.0740568i	0.743165	−	0.669108i	$-0.233324\pi$
$607$	1.82456	+	1.82456i	0.0740568	+	0.0740568i	−0.669108	+	0.743165i	$0.733324\pi$
$608$	3.96716	+	0.887875i	0.160890	+	0.0360081i
$609$	−11.3942	+	11.3942i	−0.461715	+	0.461715i
$610$	−1.24856	−	4.18767i	−0.0505525	−	0.169554i
$611$	4.01807	−	3.29754i	0.162554	−	0.133404i
$612$	3.42309	−	3.35845i	0.138370	−	0.135757i
$613$	3.16400	−	10.4303i	0.127793	−	0.421276i	−0.869574	−	0.493803i	$-0.835606\pi$
$613$	3.16400	−	10.4303i	0.127793	−	0.421276i	0.997366	+	0.0725269i	$0.0231063\pi$
$614$	3.25515	−	4.82178i	0.131367	−	0.194591i
$615$	−15.5299	+	23.2421i	−0.626226	+	0.937213i
$616$	−18.7001	+	18.1729i	−0.753450	+	0.732209i
$617$	−35.2805	+	23.5737i	−1.42034	+	0.949040i	−0.421225	+	0.906956i	$0.638400\pi$
$617$	−35.2805	+	23.5737i	−1.42034	+	0.949040i	−0.999114	+	0.0420837i	$0.986600\pi$
$618$	−6.05071	+	5.99332i	−0.243395	+	0.241087i
$619$	14.0294	−	1.38177i	0.563887	−	0.0555381i	0.187942	−	0.982180i	$-0.439818\pi$
$619$	14.0294	−	1.38177i	0.563887	−	0.0555381i	0.375945	+	0.926642i	$0.377318\pi$
$620$	28.9445	−	52.9316i	1.16244	−	2.12578i
$621$	2.42662	+	7.99951i	0.0973771	+	0.321009i
$622$	39.3762	+	12.1499i	1.57884	+	0.487165i
$623$	2.78330	−	6.71948i	0.111510	−	0.269210i
$624$	3.73662	+	5.82983i	0.149585	+	0.233380i
$625$	−19.4409	−	46.9346i	−0.777638	−	1.87738i
$626$	0.286517	+	3.05840i	0.0114515	+	0.122238i
$627$	1.31202	−	2.45462i	0.0523972	−	0.0980282i
$628$	9.60931	−	5.01912i	0.383453	−	0.200285i
$629$	13.1463	−	16.0188i	0.524177	−	0.638711i
$630$	−12.6808	+	5.18189i	−0.505214	+	0.206451i
$631$	12.5334	+	2.49304i	0.498945	+	0.0992463i	0.438146	−	0.898904i	$-0.355635\pi$
$631$	12.5334	+	2.49304i	0.498945	+	0.0992463i	0.0607988	+	0.998150i	$0.480635\pi$
$632$	−3.62007	−	43.0576i	−0.143999	−	1.71274i
$633$	2.99653	+	15.0646i	0.119101	+	0.598762i
$634$	−8.51402	+	41.7617i	−0.338135	+	1.65857i
$635$	−23.8370	+	12.7411i	−0.945941	+	0.505616i
$636$	−12.1282	+	7.93766i	−0.480915	+	0.314749i
$637$	0.226272	−	2.29737i	0.00896521	−	0.0910253i
$638$	−36.8797	−	3.80988i	−1.46008	−	0.150835i
$639$	−0.468306			−0.0185259
$640$	10.4825	−	44.8282i	0.414356	−	1.77199i
$641$	−8.27505			−0.326845			−0.163422	−	0.986556i	$-0.552253\pi$
$641$	−8.27505			−0.326845			−0.163422	+	0.986556i	$0.552253\pi$
$642$	−25.5786	−	2.64241i	−1.00951	−	0.104288i
$643$	−4.40186	+	44.6928i	−0.173592	+	1.76251i	0.375568	+	0.926795i	$0.377448\pi$
$643$	−4.40186	+	44.6928i	−0.173592	+	1.76251i	−0.549160	+	0.835717i	$0.685052\pi$
$644$	−21.7944	−	33.3004i	−0.858819	−	1.31222i
$645$	−30.5630	+	16.3363i	−1.20342	+	0.643239i
$646$	0.486799	−	2.38777i	0.0191528	−	0.0939457i
$647$	−8.90617	−	44.7743i	−0.350138	−	1.76026i	−0.607862	−	0.794043i	$-0.707973\pi$
$647$	−8.90617	−	44.7743i	−0.350138	−	1.76026i	0.257724	−	0.966218i	$-0.417027\pi$
$648$	1.82541	−	2.16053i	0.0717089	−	0.0848735i
$649$	−6.01037	−	1.19554i	−0.235928	−	0.0469290i
$650$	26.1942	−	10.7040i	1.02742	−	0.419846i
$651$	−11.1944	+	13.6404i	−0.438744	+	0.534611i
$652$	9.53893	+	18.2627i	0.373573	+	0.715221i
$653$	9.84531	−	18.4193i	0.385277	−	0.720802i	−0.612282	−	0.790640i	$-0.709748\pi$
$653$	9.84531	−	18.4193i	0.385277	−	0.720802i	0.997558	+	0.0698375i	$0.0222481\pi$
$654$	−2.54456	−	27.1617i	−0.0995000	−	1.06211i
$655$	2.49279	+	6.01814i	0.0974015	+	0.235148i
$656$	4.84599	+	27.0471i	0.189204	+	1.05601i
$657$	1.68492	−	4.06776i	0.0657350	−	0.158698i
$658$	9.65883	+	2.98031i	0.376540	+	0.116185i
$659$	−7.79075	−	25.6827i	−0.303485	−	1.00045i	−0.967529	−	0.252761i	$-0.918661\pi$
$659$	−7.79075	−	25.6827i	−0.303485	−	1.00045i	0.664044	−	0.747693i	$-0.268839\pi$
$660$	−27.6545	−	15.1223i	−1.07645	−	0.588634i
$661$	22.0230	−	2.16908i	0.856597	−	0.0843674i	0.339823	−	0.940489i	$-0.389633\pi$
$661$	22.0230	−	2.16908i	0.856597	−	0.0843674i	0.516774	+	0.856122i	$0.327133\pi$
$662$	14.1489	−	14.0146i	0.549911	−	0.544694i
$663$	3.45128	−	2.30607i	0.134037	−	0.0895605i
$664$	−0.394476	+	27.5898i	−0.0153086	+	1.07069i
$665$	−3.86742	+	5.78800i	−0.149972	+	0.224449i
$666$	6.83876	−	10.1301i	0.264996	−	0.392533i
$667$	16.4264	−	54.1507i	0.636034	−	2.09672i
$668$	14.6346	+	14.9163i	0.566231	+	0.577129i
$669$	11.8307	−	9.70919i	0.457400	−	0.375379i
$670$	2.09000	+	7.00989i	0.0807437	+	0.270816i
$671$	−2.07953	+	2.07953i	−0.0802794	+	0.0802794i
$672$	−5.44809	+	12.3145i	−0.210164	+	0.475041i
$673$	−19.5911	−	19.5911i	−0.755180	−	0.755180i	0.220261	−	0.975441i	$-0.429309\pi$
$673$	−19.5911	−	19.5911i	−0.755180	−	0.755180i	−0.975441	+	0.220261i	$0.929309\pi$
$674$	−0.930903	+	1.72181i	−0.0358570	+	0.0663216i
$675$	−7.33247	−	8.93464i	−0.282227	−	0.343894i
$676$	−7.47958	−	18.5556i	−0.287676	−	0.713676i
$677$	19.0033	+	5.76458i	0.730355	+	0.221551i	0.633495	−	0.773747i	$-0.281620\pi$
$677$	19.0033	+	5.76458i	0.730355	+	0.221551i	0.0968606	+	0.995298i	$0.469120\pi$
$678$	3.61489	+	18.6370i	0.138829	+	0.715750i
$679$	−19.5735	−	13.0786i	−0.751163	−	0.501911i
$680$	−26.9866	−	5.77023i	−1.03489	−	0.221278i
$681$	2.14021	+	3.20306i	0.0820132	+	0.122741i
$682$	−40.6007	−	0.193489i	−1.55468	−	0.00740909i
$683$	1.17636	+	11.9438i	0.0450123	+	0.457017i	0.991101	+	0.133110i	$0.0424965\pi$
$683$	1.17636	+	11.9438i	0.0450123	+	0.457017i	−0.946089	+	0.323907i	$0.895003\pi$
$684$	0.154507	−	1.42897i	0.00590772	−	0.0546382i
$685$	20.0195	−	6.07284i	0.764905	−	0.232031i
$686$	24.8045	−	13.1067i	0.947039	−	0.500415i
$687$	−4.29203	−	1.77782i	−0.163751	−	0.0678279i
$688$	−10.5084	+	32.4045i	−0.400628	+	1.23541i
$689$	−11.5912	+	4.80124i	−0.441590	+	0.182913i
$690$	30.6951	−	37.0407i	1.16854	−	1.41011i
$691$	7.34634	+	3.92670i	0.279468	+	0.149379i	0.605176	−	0.796092i	$-0.293103\pi$
$691$	7.34634	+	3.92670i	0.279468	+	0.149379i	−0.325708	+	0.945470i	$0.605603\pi$
$692$	12.8641	−	1.14331i	0.489018	−	0.0434622i
$693$	7.12655	+	5.84861i	0.270715	+	0.222170i
$694$	1.40557	−	3.34813i	0.0533547	−	0.127093i
$695$	−12.2355	+	61.5119i	−0.464118	+	2.33328i
$696$	−18.3995	+	5.29538i	−0.697431	+	0.200721i
$697$	16.1547	−	3.21338i	0.611904	−	0.121715i
$698$	30.9608	−	20.4746i	1.17188	−	0.774974i
$699$	−3.56033	−	6.66090i	−0.134664	−	0.251939i
$700$	45.4601	+	31.0062i	1.71823	+	1.17193i
$701$	−39.0375	−	3.84486i	−1.47443	−	0.145218i	−0.671371	−	0.741122i	$-0.734294\pi$
$701$	−39.0375	−	3.84486i	−1.47443	−	0.145218i	−0.803056	+	0.595903i	$0.796794\pi$
$702$	1.89986	−	1.54408i	0.0717056	−	0.0582776i
$703$		−	6.21097i		−	0.234251i
$704$	−29.8941	+	8.14262i	−1.12668	+	0.306887i
$705$			12.2182i			0.460165i
$706$	−21.4509	−	26.3935i	−0.807315	−	0.993331i
$707$	28.0806	+	2.76570i	1.05608	+	0.104015i
$708$	−3.10955	+	0.587775i	−0.116864	+	0.0220899i
$709$	−11.1339	−	20.8301i	−0.418143	−	0.782290i	0.581365	−	0.813643i	$-0.302519\pi$
$709$	−11.1339	−	20.8301i	−0.418143	−	0.782290i	−0.999508	+	0.0313521i	$0.990019\pi$
$710$	1.48654	+	2.24788i	0.0557889	+	0.0843615i
$711$	−14.9833	+	2.98037i	−0.561919	+	0.111773i
$712$	6.75796	−	5.38628i	0.253265	−	0.201860i
$713$	12.0893	−	60.7769i	0.452747	−	2.27611i
$714$	7.44265	+	3.12448i	0.278534	+	0.116931i
$715$	−21.0892	−	17.3075i	−0.788692	−	0.647263i
$716$	1.53406	+	1.28364i	0.0573306	+	0.0479718i
$717$	−0.888828	−	0.475088i	−0.0331939	−	0.0177425i
$718$	−10.8177	−	8.96446i	−0.403712	−	0.334551i
$719$	−16.7312	+	6.93029i	−0.623968	+	0.258456i	−0.672188	−	0.740381i	$-0.734645\pi$
$719$	−16.7312	+	6.93029i	−0.623968	+	0.258456i	0.0482197	+	0.998837i	$0.484645\pi$
$720$	−16.1650	−	1.90387i	−0.602434	−	0.0709531i
$721$	−13.2440	−	5.48584i	−0.493232	−	0.204303i
$722$	12.2122	+	23.1116i	0.454489	+	0.860125i
$723$	3.67094	−	1.11357i	0.136524	−	0.0414140i
$724$	7.00133	+	8.69891i	0.260203	+	0.323293i
$725$	7.66892	+	77.8639i	0.284817	+	2.89179i
$726$	−0.0269544	+	5.65594i	−0.00100037	+	0.209912i
$727$	−8.55852	−	12.8087i	−0.317418	−	0.475050i	0.638112	−	0.769944i	$-0.279716\pi$
$727$	−8.55852	−	12.8087i	−0.317418	−	0.475050i	−0.955530	+	0.294894i	$0.904716\pi$
$728$	−6.61337	+	9.59767i	−0.245108	+	0.355713i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	−24.8738	+	4.82459i	−0.920621	+	0.178566i
$731$	19.5410	+	5.92770i	0.722750	+	0.219244i
$732$	−0.594530	+	1.39750i	−0.0219745	+	0.0516530i
$733$	−17.8409	−	21.7392i	−0.658968	−	0.802954i	0.331093	−	0.943598i	$-0.392583\pi$
$733$	−17.8409	−	21.7392i	−0.658968	−	0.802954i	−0.990060	+	0.140644i	$0.955083\pi$
$734$	4.01979	+	2.17332i	0.148373	+	0.0802185i
$735$	3.83698	+	3.83698i	0.141529	+	0.141529i
$736$	−3.51248	−	47.1576i	−0.129472	−	1.73825i
$737$	3.48100	−	3.48100i	0.128224	−	0.128224i
$738$	9.30990	−	2.77575i	0.342702	−	0.102177i
$739$	−36.8609	+	30.2509i	−1.35595	+	1.11280i	−0.373221	+	0.927743i	$0.621747\pi$
$739$	−36.8609	+	30.2509i	−1.35595	+	1.11280i	−0.982728	+	0.185056i	$0.940753\pi$
$740$	−70.3329	−	0.670383i	−2.58549	−	0.0246438i
$741$	0.361138	−	1.19051i	0.0132667	−	0.0437346i
$742$	−20.2214	−	13.6513i	−0.742351	−	0.501157i
$743$	−16.0619	+	24.0383i	−0.589252	+	0.881878i	−0.999548	−	0.0300745i	$-0.990426\pi$
$743$	−16.0619	+	24.0383i	−0.589252	+	0.881878i	0.410296	+	0.911953i	$0.365426\pi$
$744$	−19.4835	+	7.74587i	−0.714299	+	0.283977i
$745$	−71.9754	+	48.0924i	−2.63697	+	1.76197i
$746$	−1.20932	−	1.22090i	−0.0442763	−	0.0447004i
$747$	9.70850	−	0.956204i	0.355215	−	0.0349857i
$748$	5.22167	+	17.8233i	0.190923	+	0.651686i
$749$	−12.5646	−	41.4198i	−0.459099	−	1.51345i
$750$	−11.1275	+	36.0629i	−0.406319	+	1.31683i
$751$	7.16052	−	17.2870i	0.261291	−	0.630812i	−0.737728	−	0.675098i	$-0.764101\pi$
$751$	7.16052	−	17.2870i	0.261291	−	0.630812i	0.999019	+	0.0442859i	$0.0141013\pi$
$752$	8.32927	+	8.65304i	0.303737	+	0.315544i
$753$	4.53161	+	10.9403i	0.165141	+	0.398686i
$754$	−16.5002	+	1.54577i	−0.600902	+	0.0562936i
$755$	3.48861	−	6.52672i	0.126963	−	0.237532i
$756$	4.54250	+	1.42537i	0.165209	+	0.0518402i
$757$	−24.4790	+	29.8277i	−0.889704	+	1.08411i	0.106258	+	0.994339i	$0.466113\pi$
$757$	−24.4790	+	29.8277i	−0.889704	+	1.08411i	−0.995963	+	0.0897691i	$0.971387\pi$
$758$	5.28771	+	12.9397i	0.192058	+	0.469992i
$759$	−31.7533	−	6.31613i	−1.15257	−	0.229261i
$760$	−7.34957	+	3.79435i	−0.266597	+	0.137635i
$761$	−1.99098	−	10.0093i	−0.0721730	−	0.362838i	0.927774	−	0.373143i	$-0.121720\pi$
$761$	−1.99098	−	10.0093i	−0.0721730	−	0.362838i	−0.999947	+	0.0103047i	$0.996720\pi$
$762$	9.20421	+	1.87647i	0.333433	+	0.0679775i
$763$	40.4973	−	21.6463i	1.46610	−	0.783647i
$764$	7.12227	−	34.1040i	0.257675	−	1.23384i
$765$	−0.956340	+	9.70988i	−0.0345765	+	0.351061i
$766$	−1.03616	+	10.0300i	−0.0374379	+	0.362399i
$767$	−2.73919			−0.0989063
$768$	−12.7461	+	9.67149i	−0.459934	+	0.348990i
$769$	16.7117			0.602641			0.301320	−	0.953523i	$-0.402573\pi$
$769$	16.7117			0.602641			0.301320	+	0.953523i	$0.402573\pi$
$770$	5.45173	−	52.7729i	0.196467	−	1.90180i
$771$	2.64445	−	26.8495i	0.0952374	−	0.966961i
$772$	2.20528	−	10.5597i	0.0793698	−	0.380051i
$773$	14.0336	−	7.50114i	0.504755	−	0.269797i	−0.199305	−	0.979937i	$-0.563868\pi$
$773$	14.0336	−	7.50114i	0.504755	−	0.269797i	0.704060	+	0.710140i	$0.251368\pi$
$774$	11.8013	+	2.40595i	0.424190	+	0.0864802i
$775$	16.7153	+	84.0333i	0.600430	+	3.01857i
$776$	−12.8315	−	24.8543i	−0.460624	−	0.892219i
$777$	20.1777	+	4.01360i	0.723872	+	0.143987i
$778$	3.09702	+	7.57882i	0.111034	+	0.271714i
$779$	3.13184	−	3.81616i	0.112210	−	0.136728i
$780$	−13.4424	−	4.21802i	−0.481314	−	0.151029i
$781$	0.854974	−	1.59954i	0.0305934	−	0.0572362i
$782$	−28.2227	+	2.64396i	−1.00924	+	0.0945477i
$783$	2.59048	+	6.25398i	0.0925763	+	0.223499i
$784$	5.33308	+	0.101674i	0.190467	+	0.00363123i
$785$	−8.44096	+	20.3783i	−0.301271	+	0.727332i
$786$	0.667488	−	2.16325i	0.0238085	−	0.0771605i
$787$	8.65912	+	28.5453i	0.308664	+	1.01753i	0.964822	+	0.262906i	$0.0846808\pi$
$787$	8.65912	+	28.5453i	0.308664	+	1.01753i	−0.656157	+	0.754624i	$0.727819\pi$
$788$	14.8766	+	50.7790i	0.529958	+	1.80893i
$789$	−6.70865	+	0.660744i	−0.238834	+	0.0235231i
$790$	61.8674	+	62.4599i	2.20114	+	2.22222i
$791$	−26.5695	+	17.7532i	−0.944704	+	0.631231i
$792$	4.04689	+	10.1793i	0.143800	+	0.361705i
$793$	−0.730321	+	1.09300i	−0.0259344	+	0.0388136i
$794$	26.2862	+	17.7456i	0.932861	+	0.629769i
$795$	8.56079	−	28.2212i	0.303620	−	1.00090i
$796$	−43.3599	−	0.413287i	−1.53685	−	0.0146486i
$797$	−6.31406	+	5.18181i	−0.223655	+	0.183549i	−0.739548	−	0.673104i	$-0.764961\pi$
$797$	−6.31406	+	5.18181i	−0.223655	+	0.183549i	0.515892	+	0.856654i	$0.327461\pi$
$798$	2.31845	−	0.691245i	0.0820722	−	0.0244698i
$799$	5.09083	−	5.09083i	0.180101	−	0.180101i
$800$	29.4388	+	58.3809i	1.04082	+	2.06408i
$801$	−2.16047	−	2.16047i	−0.0763364	−	0.0763364i
$802$	−1.41567	−	0.765388i	−0.0499890	−	0.0270268i
$803$	10.8177	+	13.1814i	0.381748	+	0.465162i
$804$	0.995205	−	2.33932i	0.0350982	−	0.0825014i
$805$	77.4867	+	23.5053i	2.73105	+	0.828454i
$806$	−17.8161	+	3.45566i	−0.627545	+	0.121720i
$807$	−25.2786	−	16.8906i	−0.889849	−	0.594578i
$808$	27.6073	+	19.0231i	0.971221	+	0.669229i
$809$	−6.55135	−	9.80479i	−0.230333	−	0.344718i	0.698242	−	0.715861i	$-0.253966\pi$
$809$	−6.55135	−	9.80479i	−0.230333	−	0.344718i	−0.928576	+	0.371143i	$0.878966\pi$
$810$	−0.0274247	+	5.75463i	−0.000963604	+	0.202197i
$811$	1.50989	+	15.3302i	0.0530194	+	0.538315i	0.984605	+	0.174793i	$0.0559257\pi$
$811$	1.50989	+	15.3302i	0.0530194	+	0.538315i	−0.931586	+	0.363522i	$0.881574\pi$
$812$	−20.2066	−	25.1060i	−0.709113	−	0.881048i
$813$	9.46645	−	2.87161i	0.332003	−	0.100712i
$814$	22.1149	+	41.8527i	0.775128	+	1.46694i
$815$	−38.7293	−	16.0422i	−1.35663	−	0.561934i
$816$	5.94203	+	7.52856i	0.208013	+	0.263552i
$817$	5.65448	−	2.34216i	0.197825	−	0.0819418i
$818$	−16.6415	−	13.7906i	−0.581856	−	0.482176i
$819$	3.63427	+	1.94256i	0.126992	+	0.0678785i
$820$	−42.8760	−	35.8768i	−1.49730	−	1.25287i
$821$	9.73571	+	7.98989i	0.339779	+	0.278849i	0.788772	−	0.614686i	$-0.210717\pi$
$821$	9.73571	+	7.98989i	0.339779	+	0.278849i	−0.448993	+	0.893535i	$0.648217\pi$
$822$	−6.70391	−	2.81435i	−0.233826	−	0.0981619i
$823$	−6.43819	+	32.3670i	−0.224421	+	1.12824i	0.690103	+	0.723711i	$0.257565\pi$
$823$	−6.43819	+	32.3670i	−0.224421	+	1.12824i	−0.914524	+	0.404531i	$0.867435\pi$
$824$	−10.6163	−	13.3198i	−0.369836	−	0.464019i
$825$	43.9038	−	8.73301i	1.52854	−	0.304045i
$826$	−2.93824	−	4.44309i	−0.102235	−	0.154595i
$827$	−8.52345	−	15.9463i	−0.296390	−	0.554506i	0.689012	−	0.724749i	$-0.258045\pi$
$827$	−8.52345	−	15.9463i	−0.296390	−	0.554506i	−0.985402	+	0.170244i	$0.945545\pi$
$828$	−16.4280	+	3.10526i	−0.570913	+	0.107915i
$829$	52.6928	+	5.18978i	1.83010	+	0.180249i	0.953583	−	0.301131i	$-0.0973640\pi$
$829$	52.6928	+	5.18978i	1.83010	+	0.180249i	0.876512	+	0.481379i	$0.159864\pi$
$830$	−35.4075	−	43.5658i	−1.22901	−	1.51219i
$831$		−	9.96604i		−	0.345718i
$832$	−12.3955	+	6.17655i	−0.429735	+	0.214133i
$833$		−	3.19742i		−	0.110784i
$834$	16.9149	−	13.7473i	0.585715	−	0.476030i
$835$	−42.3114	−	4.16730i	−1.46424	−	0.144216i
$836$	4.59872	+	3.13657i	0.159050	+	0.108481i
$837$	3.49440	+	6.53756i	0.120784	+	0.225971i
$838$	−4.17671	+	2.76209i	−0.144282	+	0.0954149i
$839$	42.9255	−	8.53841i	1.48195	−	0.294779i	0.613161	−	0.789958i	$-0.289898\pi$
$839$	42.9255	−	8.53841i	1.48195	−	0.294779i	0.868791	+	0.495179i	$0.164898\pi$
$840$	−7.57741	−	26.3287i	−0.261445	−	0.908426i
$841$	3.28197	−	16.4996i	0.113171	−	0.568951i
$842$	−3.43729	+	8.18776i	−0.118457	+	0.282169i
$843$	15.6814	+	12.8694i	0.540098	+	0.443247i
$844$	−30.5988	+	2.71951i	−1.05325	+	0.0936094i
$845$	35.8984	+	19.1881i	1.23494	+	0.660090i
$846$	2.70947	−	3.26960i	0.0931534	−	0.112411i
$847$	−8.79563	+	3.64327i	−0.302221	+	0.125184i
$848$	−13.1758	−	25.8224i	−0.452459	−	0.886746i
$849$	10.1841	+	4.21841i	0.349519	+	0.144776i
$850$	34.6529	−	18.3106i	1.18858	−	0.628047i
$851$	−69.1361	+	20.9722i	−2.36995	+	0.718918i
$852$	0.100684	−	0.931184i	0.00344937	−	0.0319018i
$853$	−2.06819	−	20.9987i	−0.0708136	−	0.718983i	−0.963393	−	0.268093i	$-0.913607\pi$
$853$	−2.06819	−	20.9987i	−0.0708136	−	0.718983i	0.892579	−	0.450890i	$-0.148893\pi$
$854$	−2.55629	−	0.0121825i	−0.0874745	−	0.000416875i
$855$	1.62467	+	2.43148i	0.0555624	+	0.0831550i
$856$	10.7535	−	50.2926i	0.367546	−	1.71897i
$857$	−7.72246	−	5.15999i	−0.263794	−	0.176262i	0.416638	−	0.909072i	$-0.363208\pi$
$857$	−7.72246	−	5.15999i	−0.263794	−	0.176262i	−0.680433	+	0.732811i	$0.738208\pi$
$858$	1.80544	+	9.30815i	0.0616365	+	0.317775i
$859$	−43.1920	−	13.1021i	−1.47369	−	0.447039i	−0.551632	−	0.834088i	$-0.685995\pi$
$859$	−43.1920	−	13.1021i	−1.47369	−	0.447039i	−0.922059	+	0.387048i	$0.873495\pi$
$860$	−25.9123	−	64.2840i	−0.883601	−	2.19207i
$861$	10.3738	+	12.6405i	0.353538	+	0.430788i
$862$	16.1053	−	29.7886i	0.548549	−	1.01460i
$863$	17.4194	+	17.4194i	0.592965	+	0.592965i	0.938431	−	0.345466i	$-0.112279\pi$
$863$	17.4194	+	17.4194i	0.592965	+	0.592965i	−0.345466	+	0.938431i	$0.612279\pi$
$864$	3.90356	+	4.09417i	0.132802	+	0.139286i
$865$	−18.5801	+	18.5801i	−0.631743	+	0.631743i
$866$	12.2668	+	41.1431i	0.416844	+	1.39810i
$867$	−8.69700	+	7.13744i	−0.295366	+	0.242400i
$868$	−24.7160	−	25.1917i	−0.838917	−	0.855063i
$869$	17.1749	−	56.6182i	0.582620	−	1.92064i
$870$	21.7963	−	32.2864i	0.738965	−	1.09461i
$871$	1.22251	−	1.82961i	0.0414231	−	0.0619941i
$872$	54.5557	+	0.780031i	1.84749	+	0.0264152i
$873$	−8.22265	+	5.49420i	−0.278295	+	0.185950i
$874$	−6.03610	+	5.97884i	−0.204174	+	0.202237i
$875$	−63.2200	+	6.22663i	−2.13723	+	0.210498i
$876$	7.72612	+	4.22486i	0.261041	+	0.142745i
$877$	−0.610560	−	2.01275i	−0.0206171	−	0.0679656i	0.946028	−	0.324084i	$-0.105056\pi$
$877$	−0.610560	−	2.01275i	−0.0206171	−	0.0679656i	−0.966645	+	0.256119i	$0.917556\pi$
$878$	8.55596	+	2.64001i	0.288750	+	0.0890961i
$879$	11.7626	−	28.3973i	0.396741	−	0.957818i
$880$	36.0149	−	51.7373i	1.21406	−	1.74406i
$881$	−16.4208	−	39.6433i	−0.553231	−	1.33562i	−0.915039	−	0.403365i	$-0.867840\pi$
$881$	−16.4208	−	39.6433i	−0.553231	−	1.33562i	0.361808	−	0.932253i	$-0.382160\pi$
$882$	−0.175902	−	1.87765i	−0.00592291	−	0.0632238i
$883$	−0.746712	+	1.39700i	−0.0251288	+	0.0470128i	−0.894172	−	0.447723i	$-0.852235\pi$
$883$	−0.746712	+	1.39700i	−0.0251288	+	0.0470128i	0.869044	+	0.494736i	$0.164735\pi$
$884$	3.84341	+	7.35836i	0.129268	+	0.247488i
$885$	4.08466	−	4.97718i	0.137304	−	0.167306i
$886$	17.9370	−	7.32978i	0.602604	−	0.246249i
$887$	−41.3828	−	8.23155i	−1.38950	−	0.276388i	−0.557045	−	0.830483i	$-0.688065\pi$
$887$	−41.3828	−	8.23155i	−1.38950	−	0.276388i	−0.832454	+	0.554094i	$0.813065\pi$
$888$	18.6725	+	15.7762i	0.626606	+	0.529414i
$889$	3.08466	+	15.5076i	0.103456	+	0.520109i
$890$	−3.51235	+	17.2283i	−0.117734	+	0.577494i
$891$	3.41560	−	1.82568i	0.114427	−	0.0611624i
$892$	16.7623	+	25.6117i	0.561243	+	0.857543i
$893$	0.211505	−	2.14745i	0.00707775	−	0.0718616i
$894$	29.9254	+	3.09146i	1.00086	+	0.103394i
$895$	−4.06973			−0.136036
$896$	−23.3149	−	13.4806i	−0.778896	−	0.450355i
$897$	−14.4714			−0.483185
$898$	22.9873	+	2.37471i	0.767096	+	0.0792452i
$899$	4.91846	−	49.9379i	0.164040	−	1.66552i
$900$	19.3422	−	12.6590i	0.644739	−	0.421968i
$901$	−15.3255	+	8.19167i	−0.510568	+	0.272904i
$902$	−7.51602	+	36.8665i	−0.250256	+	1.22752i
$903$	3.95505	+	19.8834i	0.131616	+	0.661677i
$904$	−37.8352	+	3.18100i	−1.25838	+	0.105798i
$905$	−22.2826	−	4.43229i	−0.740700	−	0.147334i
$906$	−2.38089	+	0.972932i	−0.0790999	+	0.0323235i
$907$	−18.9321	+	23.0689i	−0.628631	+	0.765990i	−0.985777	−	0.168059i	$-0.946250\pi$
$907$	−18.9321	+	23.0689i	−0.628631	+	0.765990i	0.357145	+	0.934049i	$0.383750\pi$
$908$	−6.82913	+	3.56698i	−0.226633	+	0.118374i
$909$	5.58769	−	10.4538i	0.185332	−	0.346732i
$910$	−2.21191	−	23.6109i	−0.0733241	−	0.782694i
$911$	−9.84720	−	23.7732i	−0.326252	−	0.787643i	−0.998864	−	0.0476474i	$-0.984828\pi$
$911$	−9.84720	−	23.7732i	−0.326252	−	0.787643i	0.672612	−	0.739995i	$-0.265172\pi$
$912$	2.80817	+	0.614447i	0.0929877	+	0.0203464i
$913$	−14.4586	+	34.9061i	−0.478509	+	1.15522i
$914$	−36.8477	−	11.3697i	−1.21881	−	0.376075i
$915$	−0.896963	−	2.95689i	−0.0296527	−	0.0977518i
$916$	4.45779	−	8.15209i	0.147290	−	0.269353i
$917$	3.79228	−	0.373507i	0.125232	−	0.0123343i
$918$	2.40915	−	2.38629i	0.0795136	−	0.0787594i
$919$	−13.6916	+	9.14844i	−0.451645	+	0.301779i	−0.760510	−	0.649327i	$-0.775051\pi$
$919$	−13.6916	+	9.14844i	−0.451645	+	0.301779i	0.308865	+	0.951106i	$0.400051\pi$
$920$	67.0528	+	68.9980i	2.21066	+	2.27480i
$921$	2.28547	−	3.42044i	0.0753087	−	0.112707i
$922$	−2.00202	+	2.96555i	−0.0659332	+	0.0976651i
$923$	0.235334	−	0.775792i	0.00774611	−	0.0255355i
$924$	−13.1616	+	12.9131i	−0.432985	+	0.424809i
$925$	77.2180	−	63.3712i	2.53891	−	2.08363i
$926$	−6.96557	−	23.3626i	−0.228903	−	0.767744i
$927$	−4.25826	+	4.25826i	−0.139859	+	0.139859i
$928$	−6.57358	−	37.7242i	−0.215788	−	1.23836i
$929$	−35.6539	−	35.6539i	−1.16977	−	1.16977i	−0.982264	−	0.187503i	$-0.939961\pi$
$929$	−35.6539	−	35.6539i	−1.16977	−	1.16977i	−0.187503	−	0.982264i	$-0.560039\pi$
$930$	20.2883	−	37.5254i	0.665278	−	1.23051i
$931$	−0.607958	−	0.740799i	−0.0199250	−	0.0242787i
$932$	14.0101	−	5.64733i	0.458915	−	0.184984i
$933$	27.8838	+	8.45846i	0.912874	+	0.276917i
$934$	2.18469	+	11.2635i	0.0714853	+	0.368552i
$935$	−31.4191	−	20.9936i	−1.02751	−	0.686563i
$936$	2.66181	+	4.10967i	0.0870039	+	0.134329i
$937$	−2.78040	−	4.16117i	−0.0908318	−	0.135939i	0.783271	−	0.621681i	$-0.213550\pi$
$937$	−2.78040	−	4.16117i	−0.0908318	−	0.135939i	−0.874103	+	0.485741i	$0.838550\pi$
$938$	4.27907	+	0.0203926i	0.139716	+	0.000665843i
$939$	0.212902	+	2.16163i	0.00694779	+	0.0705421i
$940$	−24.2948	−	2.62687i	−0.792410	−	0.0856789i
$941$	−29.1453	+	8.84112i	−0.950109	+	0.288212i	−0.727044	−	0.686591i	$-0.759106\pi$
$941$	−29.1453	+	8.84112i	−0.950109	+	0.288212i	−0.223065	+	0.974804i	$0.571606\pi$
$942$	6.77782	−	3.58140i	0.220833	−	0.116688i
$943$	−53.0538	−	21.9756i	−1.72767	−	0.715624i
$944$	−0.500197	−	6.30943i	−0.0162800	−	0.205354i
$945$	−8.94910	+	3.70684i	−0.291114	+	0.120583i
$946$	−29.7632	+	35.9161i	−0.967684	+	1.16773i
$947$	−14.3226	−	7.65560i	−0.465423	−	0.248774i	0.221978	−	0.975052i	$-0.428749\pi$
$947$	−14.3226	−	7.65560i	−0.465423	−	0.248774i	−0.687401	+	0.726278i	$0.741249\pi$
$948$	−2.70484	−	30.4338i	−0.0878492	−	0.988443i
$949$	5.89191	+	4.83536i	0.191259	+	0.156963i
$950$	4.54703	−	10.8312i	0.147525	−	0.351411i
$951$	−5.87952	+	29.5584i	−0.190657	+	0.958495i
$952$	−7.81289	+	14.1273i	−0.253217	+	0.457868i
$953$	19.8793	−	3.95423i	0.643952	−	0.128090i	0.137698	−	0.990474i	$-0.456030\pi$
$953$	19.8793	−	3.95423i	0.643952	−	0.128090i	0.506254	+	0.862384i	$0.331030\pi$
$954$	−8.54909	+	5.65358i	−0.276787	+	0.183041i
$955$	33.4148	+	62.5146i	1.08128	+	2.02293i
$956$	1.13576	−	1.66521i	0.0367333	−	0.0538568i
$957$	−26.0904	−	2.56968i	−0.843384	−	0.0830661i
$958$	−29.6960	+	24.1350i	−0.959435	+	0.779766i
$959$		−	12.2382i		−	0.395192i
$960$	7.26108	−	31.7333i	0.234350	−	1.02419i
$961$		−	23.9505i		−	0.772598i
$962$	13.3448	+	16.4196i	0.430253	+	0.529390i
$963$	−18.0955	−	1.78225i	−0.583119	−	0.0574322i
$964$	1.42499	+	7.53874i	0.0458959	+	0.242806i
$965$	10.3463	+	19.3565i	0.333058	+	0.623108i
$966$	−15.5230	−	23.4732i	−0.499444	−	0.755238i
$967$	26.4127	−	5.25381i	0.849375	−	0.168951i	0.248835	−	0.968546i	$-0.419952\pi$
$967$	26.4127	−	5.25381i	0.849375	−	0.168951i	0.600540	+	0.799595i	$0.294952\pi$
$968$	−11.2405	−	1.26960i	−0.361284	−	0.0408065i
$969$	0.336168	−	1.69003i	0.0107993	−	0.0542917i
$970$	52.4735	+	22.0288i	1.68482	+	0.707301i
$971$	36.5372	+	29.9853i	1.17253	+	0.962274i	0.999743	−	0.0226849i	$-0.00722145\pi$
$971$	36.5372	+	29.9853i	1.17253	+	0.962274i	0.172791	+	0.984958i	$0.444721\pi$
$972$	1.28346	−	1.53386i	0.0411671	−	0.0491985i
$973$	32.3568	+	17.2951i	1.03731	+	0.554454i
$974$	5.32613	+	4.41369i	0.170660	+	0.141424i
$975$	18.4858	−	7.65706i	0.592019	−	0.245222i
$976$	−2.65098	−	1.48263i	−0.0848557	−	0.0474577i
$977$	32.4891	+	13.4574i	1.03942	+	0.430541i	0.836103	−	0.548572i	$-0.184828\pi$
$977$	32.4891	+	13.4574i	1.03942	+	0.430541i	0.203316	+	0.979113i	$0.434828\pi$
$978$	6.80651	+	12.8814i	0.217648	+	0.411901i
$979$	11.3236	−	3.43498i	0.361904	−	0.109782i
$980$	−8.45442	+	6.80455i	−0.270067	+	0.217363i
$981$	−1.89078	−	19.1974i	−0.0603680	−	0.612927i
$982$	0.179202	−	37.6026i	0.00571856	−	1.19995i
$983$	−22.0422	−	32.9885i	−0.703037	−	1.05217i	−0.995395	−	0.0958605i	$-0.969440\pi$
$983$	−22.0422	−	32.9885i	−0.703037	−	1.05217i	0.292358	−	0.956309i	$-0.405560\pi$
$984$	3.51773	+	19.1087i	0.112141	+	0.609162i
$985$	−89.5135	−	59.8110i	−2.85214	−	1.90574i
$986$	−22.5341	+	4.37077i	−0.717631	+	0.139194i
$987$	6.83979	+	2.07483i	0.217713	+	0.0660425i
$988$	2.28958	+	0.974046i	0.0728414	+	0.0309885i
$989$	−45.1644	−	55.0329i	−1.43614	−	1.74995i
$990$	−19.6054	−	10.5997i	−0.623101	−	0.336882i
$991$	25.2456	+	25.2456i	0.801952	+	0.801952i	0.983400	−	0.181449i	$-0.0580786\pi$
$991$	25.2456	+	25.2456i	0.801952	+	0.801952i	−0.181449	+	0.983400i	$0.558079\pi$
$992$	−11.2131	−	40.4065i	−0.356017	−	1.28291i
$993$	9.95741	−	9.95741i	0.315989	−	0.315989i
$994$	1.51081	−	0.450447i	0.0479198	−	0.0142873i
$995$	68.1978	−	55.9685i	2.16201	−	1.77432i
$996$	−0.185961	+	19.5101i	−0.00589241	+	0.618200i
$997$	−3.19033	+	10.5171i	−0.101039	+	0.333080i	−0.992856	−	0.119315i	$-0.961930\pi$
$997$	−3.19033	+	10.5171i	−0.101039	+	0.333080i	0.891818	+	0.452395i	$0.149430\pi$
$998$	−11.4511	−	7.73057i	−0.362478	−	0.244707i
$999$	4.80154	−	7.18601i	0.151914	−	0.227355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.15	✓	512
128.53	even	32	inner	384.2.v.a.181.15	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.15	✓	512	1.1	even	1	trivial
384.2.v.a.181.15	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)

\(f(q)\)	\(=\)	\(q+(-0.145323 + 1.40673i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.95776 - 0.408859i) q^{4} +(3.58870 - 1.91820i) q^{5} +(-1.38571 - 0.282506i) q^{6} +(-0.464401 - 2.33470i) q^{7} +(0.859660 - 2.69462i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(-0.145323 + 1.40673i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.95776 - 0.408859i) q^{4} +(3.58870 - 1.91820i) q^{5} +(-1.38571 - 0.282506i) q^{6} +(-0.464401 - 2.33470i) q^{7} +(0.859660 - 2.69462i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(2.17686 + 5.32708i) q^{10} +(2.45695 - 2.99380i) q^{11} +(0.598784 - 1.90826i) q^{12} +(0.816051 - 1.52672i) q^{13} +(3.35177 - 0.314000i) q^{14} +(1.55721 + 3.75943i) q^{15} +(3.66567 + 1.60090i) q^{16} +(0.917578 - 2.21523i) q^{17} +(0.416969 - 1.35135i) q^{18} +(-0.208613 - 0.687706i) q^{19} +(-7.81009 + 2.28811i) q^{20} +(2.36898 - 0.233324i) q^{21} +(3.85440 + 3.89132i) q^{22} +(-6.95064 + 4.64427i) q^{23} +(2.59738 + 1.11964i) q^{24} +(6.42141 - 9.61032i) q^{25} +(2.02909 + 1.36983i) q^{26} +(0.290285 - 0.956940i) q^{27} +(-0.0453765 + 4.76066i) q^{28} +(-5.23271 + 4.29437i) q^{29} +(-5.51479 + 1.64424i) q^{30} +(-5.24169 + 5.24169i) q^{31} +(-2.78473 + 4.92395i) q^{32} +(2.73856 + 2.73856i) q^{33} +(2.98288 + 1.61270i) q^{34} +(-6.14501 - 7.48772i) q^{35} +(1.84038 + 0.782943i) q^{36} +(8.27040 + 2.50880i) q^{37} +(0.997731 - 0.193523i) q^{38} +(1.43939 + 0.961767i) q^{39} +(-2.08376 - 11.3192i) q^{40} +(3.81647 + 5.71175i) q^{41} +(-0.0160432 + 3.36641i) q^{42} +(0.834759 + 8.47545i) q^{43} +(-6.03416 + 4.85660i) q^{44} +(-3.89396 + 1.18122i) q^{45} +(-5.52313 - 10.4526i) q^{46} +(2.77406 + 1.14905i) q^{47} +(-1.95249 + 3.49110i) q^{48} +(1.23201 - 0.510313i) q^{49} +(12.5859 + 10.4298i) q^{50} +(2.11462 + 1.13029i) q^{51} +(-2.22185 + 2.65531i) q^{52} +(-5.60232 - 4.59771i) q^{53} +(1.30397 + 0.547417i) q^{54} +(3.07454 - 15.4567i) q^{55} +(-6.69036 - 0.755665i) q^{56} +(0.704842 - 0.140202i) q^{57} +(-5.28058 - 7.98506i) q^{58} +(-0.745894 - 1.39547i) q^{59} +(-1.51157 - 7.99676i) q^{60} +(-0.755696 - 0.0744296i) q^{61} +(-6.61189 - 8.13536i) q^{62} +2.38044i q^{63} +(-6.52197 - 4.63292i) q^{64} -7.04430i q^{65} +(-4.25038 + 3.45443i) q^{66} +(1.26499 + 0.124590i) q^{67} +(-2.70211 + 3.96173i) q^{68} +(-3.94062 - 7.37239i) q^{69} +(11.4262 - 7.55622i) q^{70} +(0.459307 - 0.0913619i) q^{71} +(-1.36884 + 2.47513i) q^{72} +(-0.858965 + 4.31831i) q^{73} +(-4.73107 + 11.2696i) q^{74} +(8.93464 + 7.33247i) q^{75} +(0.127241 + 1.43166i) q^{76} +(-8.13062 - 4.34591i) q^{77} +(-1.56212 + 1.88506i) q^{78} +(14.1140 - 5.84620i) q^{79} +(16.2258 - 1.28635i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-8.58949 + 4.53868i) q^{82} +(-9.33541 + 2.83187i) q^{83} +(-4.73329 - 0.511784i) q^{84} +(-0.956340 - 9.70988i) q^{85} +(-12.0440 - 0.0573975i) q^{86} +(-3.76080 - 5.62843i) q^{87} +(-5.95501 - 9.19419i) q^{88} +(2.54044 + 1.69747i) q^{89} +(-1.09577 - 5.64940i) q^{90} +(-3.94342 - 1.19622i) q^{91} +(15.5066 - 6.25055i) q^{92} +(-4.70267 - 5.73022i) q^{93} +(-2.01954 + 3.73536i) q^{94} +(-2.06781 - 2.06781i) q^{95} +(-4.62729 - 3.25395i) q^{96} +(6.99279 - 6.99279i) q^{97} +(0.538833 + 1.80726i) q^{98} +(-2.99380 + 2.45695i) 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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