LMFDB - Embedded newform 384.2.v.a.109.22

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			109.22
Character	$\chi$	$=$	384.109
Dual form			384.2.v.a.229.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.827011 + 1.14719i) q^{2} +(0.881921 + 0.471397i) q^{3} +(-0.632104 + 1.89748i) q^{4} +(2.75419 - 3.35599i) q^{5} +(0.188576 + 1.40158i) q^{6} +(-1.44146 - 0.963152i) q^{7} +(-2.69954 + 0.844095i) q^{8} +(0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(0.827011 + 1.14719i) q^{2} +(0.881921 + 0.471397i) q^{3} +(-0.632104 + 1.89748i) q^{4} +(2.75419 - 3.35599i) q^{5} +(0.188576 + 1.40158i) q^{6} +(-1.44146 - 0.963152i) q^{7} +(-2.69954 + 0.844095i) q^{8} +(0.555570 + 0.831470i) q^{9} +(6.12771 + 0.384145i) q^{10} +(4.36272 + 1.32342i) q^{11} +(-1.45193 + 1.37546i) q^{12} +(-0.620604 + 0.509317i) q^{13} +(-0.0871816 - 2.45017i) q^{14} +(4.01098 - 1.66140i) q^{15} +(-3.20089 - 2.39881i) q^{16} +(2.30989 + 0.956789i) q^{17} +(-0.494393 + 1.32498i) q^{18} +(-0.650927 + 6.60897i) q^{19} +(4.62700 + 7.34736i) q^{20} +(-0.817227 - 1.52892i) q^{21} +(2.08980 + 6.09936i) q^{22} +(-8.19619 - 1.63032i) q^{23} +(-2.77868 - 0.528128i) q^{24} +(-2.70165 - 13.5821i) q^{25} +(-1.09753 - 0.290742i) q^{26} +(0.0980171 + 0.995185i) q^{27} +(2.73872 - 2.12633i) q^{28} +(-1.28370 - 4.23179i) q^{29} +(5.22307 + 3.22737i) q^{30} +(0.608999 - 0.608999i) q^{31} +(0.104732 - 5.65588i) q^{32} +(3.22372 + 3.22372i) q^{33} +(0.812686 + 3.44117i) q^{34} +(-7.20238 + 2.18482i) q^{35} +(-1.92888 + 0.528610i) q^{36} +(-5.62269 + 0.553787i) q^{37} +(-8.12009 + 4.71896i) q^{38} +(-0.787414 + 0.156626i) q^{39} +(-4.60226 + 11.3844i) q^{40} +(-0.680305 + 3.42013i) q^{41} +(1.07811 - 2.20195i) q^{42} +(1.97830 - 1.05742i) q^{43} +(-5.26885 + 7.44165i) q^{44} +(4.32055 + 0.425537i) q^{45} +(-4.90805 - 10.7509i) q^{46} +(-1.97791 + 4.77510i) q^{47} +(-1.69214 - 3.62445i) q^{48} +(-1.52864 - 3.69047i) q^{49} +(13.3470 - 14.3319i) q^{50} +(1.58612 + 1.93269i) q^{51} +(-0.574134 - 1.49953i) q^{52} +(-3.50204 + 11.5447i) q^{53} +(-1.06061 + 0.935474i) q^{54} +(16.4571 - 10.9963i) q^{55} +(4.70426 + 1.38334i) q^{56} +(-3.68952 + 5.52175i) q^{57} +(3.79305 - 4.97239i) q^{58} +(-0.265665 - 0.218026i) q^{59} +(0.617127 + 8.66095i) q^{60} +(5.70688 - 10.6768i) q^{61} +(1.20229 + 0.194990i) q^{62} -1.73363i q^{63} +(6.57501 - 4.55733i) q^{64} +3.48550i q^{65} +(-1.03218 + 6.36428i) q^{66} +(2.13507 - 3.99444i) q^{67} +(-3.27558 + 3.77819i) q^{68} +(-6.45986 - 5.30147i) q^{69} +(-8.46286 - 6.45565i) q^{70} +(-1.73400 + 2.59512i) q^{71} +(-2.20162 - 1.77563i) q^{72} +(-3.87613 + 2.58994i) q^{73} +(-5.28533 - 5.99233i) q^{74} +(4.01992 - 13.2519i) q^{75} +(-12.1290 - 5.41268i) q^{76} +(-5.01403 - 6.10961i) q^{77} +(-0.830882 - 0.773784i) q^{78} +(-1.12913 - 2.72597i) q^{79} +(-16.8662 + 4.13536i) q^{80} +(-0.382683 + 0.923880i) q^{81} +(-4.48617 + 2.04804i) q^{82} +(-3.76251 - 0.370574i) q^{83} +(3.41768 - 0.584235i) q^{84} +(9.57285 - 5.11680i) q^{85} +(2.84915 + 1.39499i) q^{86} +(0.862730 - 4.33724i) q^{87} +(-12.8944 + 0.109938i) q^{88} +(8.81450 - 1.75331i) q^{89} +(3.08497 + 5.30843i) q^{90} +(1.38513 - 0.136423i) q^{91} +(8.27436 - 14.5216i) q^{92} +(0.824169 - 0.250009i) q^{93} +(-7.11372 + 1.68002i) q^{94} +(20.3869 + 20.3869i) q^{95} +(2.75853 - 4.93867i) q^{96} +(0.442002 - 0.442002i) q^{97} +(2.96948 - 4.80571i) q^{98} +(1.32342 + 4.36272i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{23}{32}\right)$	$1$

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 $

$2$	0.827011	+	1.14719i	0.584785	+	0.811188i
$2$	0.827011	+	1.14719i	0.584785	+	0.811188i
$3$	0.881921	+	0.471397i	0.509177	+	0.272161i
$3$	0.881921	+	0.471397i	0.509177	+	0.272161i
$4$	−0.632104	+	1.89748i	−0.316052	+	0.948742i
$5$	2.75419	−	3.35599i	1.23171	−	1.50084i	0.430350	−	0.902662i	$-0.358390\pi$
$5$	2.75419	−	3.35599i	1.23171	−	1.50084i	0.801361	−	0.598181i	$-0.204110\pi$
$6$	0.188576	+	1.40158i	0.0769858	+	0.572194i
$7$	−1.44146	−	0.963152i	−0.544820	−	0.364037i	0.252497	−	0.967598i	$-0.418748\pi$
$7$	−1.44146	−	0.963152i	−0.544820	−	0.364037i	−0.797317	+	0.603560i	$0.793748\pi$
$8$	−2.69954	+	0.844095i	−0.954431	+	0.298433i
$9$	0.555570	+	0.831470i	0.185190	+	0.277157i
$10$	6.12771	+	0.384145i	1.93775	+	0.121477i
$11$	4.36272	+	1.32342i	1.31541	+	0.399025i	0.868560	−	0.495585i	$-0.165046\pi$
$11$	4.36272	+	1.32342i	1.31541	+	0.399025i	0.446849	+	0.894609i	$0.352546\pi$
$12$	−1.45193	+	1.37546i	−0.419137	+	0.397061i
$13$	−0.620604	+	0.509317i	−0.172125	+	0.141259i	−0.716512	−	0.697575i	$-0.754262\pi$
$13$	−0.620604	+	0.509317i	−0.172125	+	0.141259i	0.544387	+	0.838834i	$0.316762\pi$
$14$	−0.0871816	−	2.45017i	−0.0233003	−	0.654835i
$15$	4.01098	−	1.66140i	1.03563	−	0.428972i
$16$	−3.20089	−	2.39881i	−0.800222	−	0.599704i
$17$	2.30989	+	0.956789i	0.560231	+	0.232055i	0.644786	−	0.764364i	$-0.276947\pi$
$17$	2.30989	+	0.956789i	0.560231	+	0.232055i	−0.0845544	+	0.996419i	$0.526947\pi$
$18$	−0.494393	+	1.32498i	−0.116530	+	0.312301i
$19$	−0.650927	+	6.60897i	−0.149333	+	1.51620i	0.570062	+	0.821602i	$0.306919\pi$
$19$	−0.650927	+	6.60897i	−0.149333	+	1.51620i	−0.719395	+	0.694601i	$0.755581\pi$
$20$	4.62700	+	7.34736i	1.03463	+	1.64292i
$21$	−0.817227	−	1.52892i	−0.178333	−	0.333638i
$22$	2.08980	+	6.09936i	0.445548	+	1.30039i
$23$	−8.19619	−	1.63032i	−1.70902	−	0.339946i	−0.758755	−	0.651377i	$-0.774192\pi$
$23$	−8.19619	−	1.63032i	−1.70902	−	0.339946i	−0.950269	+	0.311431i	$0.899192\pi$
$24$	−2.77868	−	0.528128i	−0.567196	−	0.107804i
$25$	−2.70165	−	13.5821i	−0.540330	−	2.71642i
$26$	−1.09753	−	0.290742i	−0.215244	−	0.0570192i
$27$	0.0980171	+	0.995185i	0.0188634	+	0.191523i
$28$	2.73872	−	2.12633i	0.517569	−	0.401839i
$29$	−1.28370	−	4.23179i	−0.238377	−	0.785824i	−0.991745	−	0.128225i	$-0.959072\pi$
$29$	−1.28370	−	4.23179i	−0.238377	−	0.785824i	0.753368	−	0.657599i	$-0.228428\pi$
$30$	5.22307	+	3.22737i	0.953599	+	0.589234i
$31$	0.608999	−	0.608999i	0.109379	−	0.109379i	−0.650299	−	0.759678i	$-0.725356\pi$
$31$	0.608999	−	0.608999i	0.109379	−	0.109379i	0.759678	+	0.650299i	$0.225356\pi$
$32$	0.104732	−	5.65588i	0.0185141	−	0.999829i
$33$	3.22372	+	3.22372i	0.561177	+	0.561177i
$34$	0.812686	+	3.44117i	0.139374	+	0.590155i
$35$	−7.20238	+	2.18482i	−1.21742	+	0.369301i
$36$	−1.92888	+	0.528610i	−0.321480	+	0.0881017i
$37$	−5.62269	+	0.553787i	−0.924365	+	0.0910420i	−0.548988	−	0.835830i	$-0.684987\pi$
$37$	−5.62269	+	0.553787i	−0.924365	+	0.0910420i	−0.375377	+	0.926872i	$0.622487\pi$
$38$	−8.12009	+	4.71896i	−1.31725	+	0.765516i
$39$	−0.787414	+	0.156626i	−0.126087	+	0.0250803i
$40$	−4.60226	+	11.3844i	−0.727681	+	1.80003i
$41$	−0.680305	+	3.42013i	−0.106246	+	0.534134i	0.890601	+	0.454785i	$0.150284\pi$
$41$	−0.680305	+	3.42013i	−0.106246	+	0.534134i	−0.996847	+	0.0793486i	$0.974716\pi$
$42$	1.07811	−	2.20195i	0.166357	−	0.339769i
$43$	1.97830	−	1.05742i	0.301688	−	0.161256i	−0.313606	−	0.949553i	$-0.601537\pi$
$43$	1.97830	−	1.05742i	0.301688	−	0.161256i	0.615294	+	0.788298i	$0.289037\pi$
$44$	−5.26885	+	7.44165i	−0.794309	+	1.12187i
$45$	4.32055	+	0.425537i	0.644069	+	0.0634353i
$46$	−4.90805	−	10.7509i	−0.723652	−	1.58513i
$47$	−1.97791	+	4.77510i	−0.288508	+	0.696520i	−0.999981	−	0.00619362i	$-0.998028\pi$
$47$	−1.97791	+	4.77510i	−0.288508	+	0.696520i	0.711473	+	0.702714i	$0.248028\pi$
$48$	−1.69214	−	3.62445i	−0.244239	−	0.523145i
$49$	−1.52864	−	3.69047i	−0.218377	−	0.527210i
$50$	13.3470	−	14.3319i	1.88755	−	2.02684i
$51$	1.58612	+	1.93269i	0.222101	+	0.270630i
$52$	−0.574134	−	1.49953i	−0.0796180	−	0.207947i
$53$	−3.50204	+	11.5447i	−0.481042	+	1.58578i	0.295255	+	0.955418i	$0.404595\pi$
$53$	−3.50204	+	11.5447i	−0.481042	+	1.58578i	−0.776298	+	0.630366i	$0.782905\pi$
$54$	−1.06061	+	0.935474i	−0.144330	+	0.127302i
$55$	16.4571	−	10.9963i	2.21908	−	1.48274i
$56$	4.70426	+	1.38334i	0.628634	+	0.184856i
$57$	−3.68952	+	5.52175i	−0.488688	+	0.731374i
$58$	3.79305	−	4.97239i	0.498051	−	0.652907i
$59$	−0.265665	−	0.218026i	−0.0345866	−	0.0283845i	0.616941	−	0.787009i	$-0.288372\pi$
$59$	−0.265665	−	0.218026i	−0.0345866	−	0.0283845i	−0.651528	+	0.758625i	$0.725872\pi$
$60$	0.617127	+	8.66095i	0.0796707	+	1.11812i
$61$	5.70688	−	10.6768i	0.730691	−	1.36703i	−0.191965	−	0.981402i	$-0.561486\pi$
$61$	5.70688	−	10.6768i	0.730691	−	1.36703i	0.922656	−	0.385624i	$-0.126014\pi$
$62$	1.20229	+	0.194990i	0.152691	+	0.0247638i
$63$		−	1.73363i		−	0.218417i
$64$	6.57501	−	4.55733i	0.821876	−	0.569667i
$65$			3.48550i			0.432322i
$66$	−1.03218	+	6.36428i	−0.127052	+	0.783389i
$67$	2.13507	−	3.99444i	0.260840	−	0.487998i	−0.717076	−	0.696995i	$-0.754520\pi$
$67$	2.13507	−	3.99444i	0.260840	−	0.487998i	0.977916	+	0.208997i	$0.0670199\pi$
$68$	−3.27558	+	3.77819i	−0.397223	+	0.458173i
$69$	−6.45986	−	5.30147i	−0.777676	−	0.638222i
$70$	−8.46286	−	6.45565i	−1.01150	−	0.771598i
$71$	−1.73400	+	2.59512i	−0.205788	+	0.307984i	−0.919979	−	0.391967i	$-0.871795\pi$
$71$	−1.73400	+	2.59512i	−0.205788	+	0.307984i	0.714191	+	0.699951i	$0.246795\pi$
$72$	−2.20162	−	1.77563i	−0.259464	−	0.209260i
$73$	−3.87613	+	2.58994i	−0.453666	+	0.303130i	−0.761329	−	0.648365i	$-0.775453\pi$
$73$	−3.87613	+	2.58994i	−0.453666	+	0.303130i	0.307663	+	0.951495i	$0.400453\pi$
$74$	−5.28533	−	5.99233i	−0.614407	−	0.696594i
$75$	4.01992	−	13.2519i	0.464181	−	1.53020i
$76$	−12.1290	−	5.41268i	−1.39129	−	0.620877i
$77$	−5.01403	−	6.10961i	−0.571401	−	0.696254i
$78$	−0.830882	−	0.773784i	−0.0940788	−	0.0876138i
$79$	−1.12913	−	2.72597i	−0.127038	−	0.306696i	0.847545	−	0.530723i	$-0.178080\pi$
$79$	−1.12913	−	2.72597i	−0.127038	−	0.306696i	−0.974583	+	0.224027i	$0.928080\pi$
$80$	−16.8662	+	4.13536i	−1.88570	+	0.462347i
$81$	−0.382683	+	0.923880i	−0.0425204	+	0.102653i
$82$	−4.48617	+	2.04804i	−0.495414	+	0.226168i
$83$	−3.76251	−	0.370574i	−0.412989	−	0.0406758i	−0.110610	−	0.993864i	$-0.535281\pi$
$83$	−3.76251	−	0.370574i	−0.412989	−	0.0406758i	−0.302378	+	0.953188i	$0.597781\pi$
$84$	3.41768	−	0.584235i	0.372899	−	0.0637453i
$85$	9.57285	−	5.11680i	1.03832	−	0.554994i
$86$	2.84915	+	1.39499i	0.307231	+	0.150426i
$87$	0.862730	−	4.33724i	0.0924944	−	0.465001i
$88$	−12.8944	+	0.109938i	−1.37455	+	0.0117195i
$89$	8.81450	−	1.75331i	0.934335	−	0.185851i	0.295630	−	0.955303i	$-0.404470\pi$
$89$	8.81450	−	1.75331i	0.934335	−	0.185851i	0.638705	+	0.769452i	$0.279470\pi$
$90$	3.08497	+	5.30843i	0.325184	+	0.559557i
$91$	1.38513	−	0.136423i	0.145201	−	0.0143010i
$92$	8.27436	−	14.5216i	0.862661	−	1.51398i
$93$	0.824169	−	0.250009i	0.0854624	−	0.0259247i
$94$	−7.11372	+	1.68002i	−0.733724	+	0.173280i
$95$	20.3869	+	20.3869i	2.09165	+	2.09165i
$96$	2.75853	−	4.93867i	0.281541	−	0.504051i
$97$	0.442002	−	0.442002i	0.0448785	−	0.0448785i	−0.684311	−	0.729190i	$-0.739897\pi$
$97$	0.442002	−	0.442002i	0.0448785	−	0.0448785i	0.729190	+	0.684311i	$0.239897\pi$
$98$	2.96948	−	4.80571i	0.299962	−	0.485450i
$99$	1.32342	+	4.36272i	0.133008	+	0.438469i
$100$	27.4796	+	3.45897i	2.74796	+	0.345897i
$101$	−1.08105	−	10.9761i	−0.107568	−	1.09216i	−0.885763	−	0.464137i	$-0.846364\pi$
$101$	−1.08105	−	10.9761i	−0.107568	−	1.09216i	0.778195	−	0.628023i	$-0.216136\pi$
$102$	−0.905430	+	3.41794i	−0.0896510	+	0.338426i
$103$	2.76886	+	13.9200i	0.272824	+	1.37158i	0.837578	+	0.546318i	$0.183971\pi$
$103$	2.76886	+	13.9200i	0.272824	+	1.37158i	−0.564754	+	0.825259i	$0.691029\pi$
$104$	1.24543	−	1.89877i	0.122125	−	0.186190i
$105$	−7.38184	−	1.46834i	−0.720394	−	0.143295i
$106$	−16.1402	+	5.53007i	−1.56768	+	0.537128i
$107$	−2.74637	−	5.13810i	−0.265502	−	0.496719i	0.713478	−	0.700678i	$-0.247119\pi$
$107$	−2.74637	−	5.13810i	−0.265502	−	0.496719i	−0.978979	+	0.203959i	$0.934619\pi$
$108$	−1.95030	−	0.443074i	−0.187668	−	0.0426349i
$109$	0.294037	−	2.98541i	0.0281637	−	0.285951i	−0.970779	−	0.239976i	$-0.922861\pi$
$109$	0.294037	−	2.98541i	0.0281637	−	0.285951i	0.998943	−	0.0459749i	$-0.0146394\pi$
$110$	26.2251	+	9.78543i	2.50046	+	0.933004i
$111$	−5.21982	−	2.16212i	−0.495444	−	0.205220i
$112$	2.30353	+	6.54074i	0.217663	+	0.618041i
$113$	−9.12780	+	3.78086i	−0.858671	+	0.355673i	−0.768188	−	0.640225i	$-0.778841\pi$
$113$	−9.12780	+	3.78086i	−0.858671	+	0.355673i	−0.0904835	+	0.995898i	$0.528841\pi$
$114$	−9.38578	+	0.333964i	−0.879059	+	0.0312786i
$115$	−28.0452	+	23.0161i	−2.61523	+	2.14626i
$116$	8.84118	+	0.239133i	0.820883	+	0.0222029i
$117$	−0.768271	−	0.233052i	−0.0710267	−	0.0215457i
$118$	0.0304095	−	0.485079i	0.00279942	−	0.0446551i
$119$	−2.40808	−	3.60395i	−0.220748	−	0.330373i
$120$	−9.42541	+	7.87067i	−0.860418	+	0.718490i
$121$	8.13570	+	5.43610i	0.739609	+	0.494191i
$122$	16.9680	−	2.28296i	1.53621	−	0.206689i
$123$	−2.21221	+	2.69559i	−0.199468	+	0.243053i
$124$	0.770615	+	1.54052i	0.0692033	+	0.138342i
$125$	−33.8782	−	18.1083i	−3.03016	−	1.61965i
$126$	1.98881	−	1.43373i	0.177177	−	0.127727i
$127$	20.9525			1.85924			0.929618	−	0.368526i	$-0.120137\pi$
$127$	20.9525			1.85924			0.929618	+	0.368526i	$0.120137\pi$
$128$	10.6657	+	3.77383i	0.942728	+	0.333563i
$129$	2.24317			0.197500
$130$	−3.99854	+	2.88254i	−0.350695	+	0.252816i
$131$	10.9417	+	5.84848i	0.955983	+	0.510984i	0.874147	−	0.485662i	$-0.161421\pi$
$131$	10.9417	+	5.84848i	0.955983	+	0.510984i	0.0818366	+	0.996646i	$0.473921\pi$
$132$	−8.15468	+	4.07923i	−0.709774	+	0.355051i
$133$	7.30373	−	8.89962i	0.633314	−	0.771695i
$134$	6.34812	−	0.854106i	0.548394	−	0.0737835i
$135$	3.60979	+	2.41198i	0.310681	+	0.207590i
$136$	−7.04326	−	0.633118i	−0.603955	−	0.0542894i
$137$	1.95520	+	2.92616i	0.167044	+	0.249999i	0.905542	−	0.424257i	$-0.139465\pi$
$137$	1.95520	+	2.92616i	0.167044	+	0.249999i	−0.738498	+	0.674255i	$0.764465\pi$
$138$	0.739432	−	11.7951i	0.0629447	−	1.00406i
$139$	−14.1093	−	4.28001i	−1.19674	−	0.363026i	−0.371833	−	0.928300i	$-0.621271\pi$
$139$	−14.1093	−	4.28001i	−1.19674	−	0.363026i	−0.824903	+	0.565274i	$0.808771\pi$
$140$	0.406997	−	15.0474i	0.0343975	−	1.27174i
$141$	−3.99533	+	3.27888i	−0.336467	+	0.276132i
$142$	−4.41114	+	0.156957i	−0.370174	+	0.0131715i
$143$	−3.38156	+	1.40069i	−0.282780	+	0.117131i
$144$	0.216223	−	3.99415i	0.0180186	−	0.332846i
$145$	−17.7374	−	7.34707i	−1.47301	−	0.610141i
$146$	−6.17677	−	2.30475i	−0.511193	−	0.190743i
$147$	0.391533	−	3.97530i	0.0322931	−	0.327877i
$148$	2.50333	−	11.0190i	0.205772	−	0.905758i
$149$	6.15124	+	11.5082i	0.503929	+	0.942785i	0.997333	+	0.0729846i	$0.0232524\pi$
$149$	6.15124	+	11.5082i	0.503929	+	0.942785i	−0.493404	+	0.869800i	$0.664248\pi$
$150$	18.5270	−	6.34785i	1.51273	−	0.518300i
$151$	9.35580	+	1.86099i	0.761365	+	0.151445i	0.560478	−	0.828170i	$-0.310618\pi$
$151$	9.35580	+	1.86099i	0.761365	+	0.151445i	0.200887	+	0.979614i	$0.435618\pi$
$152$	−3.82140	−	18.3906i	−0.309957	−	1.49168i
$153$	0.487767	+	2.45217i	0.0394336	+	0.198246i
$154$	2.86224	−	10.8048i	0.230646	−	0.870673i
$155$	−0.366496	−	3.72109i	−0.0294376	−	0.298885i
$156$	0.200532	−	1.59311i	0.0160554	−	0.127551i
$157$	−0.00870494	−	0.0286963i	−0.000694730	−	0.00229022i	0.956592	−	0.291430i	$-0.0941309\pi$
$157$	−0.00870494	−	0.0286963i	−0.000694730	−	0.00229022i	−0.957287	+	0.289139i	$0.906631\pi$
$158$	2.19341	−	3.54974i	0.174498	−	0.282402i
$159$	−8.53065	+	8.53065i	−0.676525	+	0.676525i
$160$	−18.6926	−	15.9289i	−1.47778	−	1.25929i
$161$	10.2442	+	10.2442i	0.807358	+	0.807358i
$162$	−1.37635	+	0.325047i	−0.108136	+	0.0255381i
$163$	−18.2060	+	5.52273i	−1.42600	+	0.432573i	−0.906613	−	0.421964i	$-0.861341\pi$
$163$	−18.2060	+	5.52273i	−1.42600	+	0.432573i	−0.519390	+	0.854537i	$0.673841\pi$
$164$	−6.05961	−	3.45274i	−0.473176	−	0.269614i
$165$	19.6975	−	1.94003i	1.53345	−	0.151031i
$166$	−2.68651	−	4.62279i	−0.208514	−	0.358798i
$167$	−4.19692	+	0.834820i	−0.324768	+	0.0646003i	−0.354782	−	0.934949i	$-0.615445\pi$
$167$	−4.19692	+	0.834820i	−0.324768	+	0.0646003i	0.0300140	+	0.999549i	$0.490445\pi$
$168$	3.49669	+	3.43757i	0.269776	+	0.265214i
$169$	−2.41043	+	12.1180i	−0.185418	+	0.932157i
$170$	13.7868	+	6.75026i	1.05740	+	0.517721i
$171$	−5.85680	+	3.13052i	−0.447880	+	0.239397i
$172$	0.755952	+	4.42220i	0.0576408	+	0.337189i
$173$	7.79281	+	0.767524i	0.592476	+	0.0583538i	0.389812	−	0.920895i	$-0.372540\pi$
$173$	7.79281	+	0.767524i	0.592476	+	0.0583538i	0.202664	+	0.979248i	$0.435040\pi$
$174$	5.68914	−	2.59723i	0.431292	−	0.196895i
$175$	−9.18733	+	22.1802i	−0.694497	+	1.67666i
$176$	−10.7899	−	14.7015i	−0.813322	−	1.10816i
$177$	−0.131519	−	0.317515i	−0.00988558	−	0.0238659i
$178$	9.30108	+	8.66192i	0.697145	+	0.649238i
$179$	−1.66841	−	2.03296i	−0.124703	−	0.151951i	0.706916	−	0.707297i	$-0.250086\pi$
$179$	−1.66841	−	2.03296i	−0.124703	−	0.151951i	−0.831619	+	0.555346i	$0.812586\pi$
$180$	−3.53848	+	7.92918i	−0.263743	+	0.591007i
$181$	3.57769	−	11.7941i	0.265928	−	0.876646i	−0.717687	−	0.696365i	$-0.754799\pi$
$181$	3.57769	−	11.7941i	0.265928	−	0.876646i	0.983615	−	0.180281i	$-0.0577007\pi$
$182$	1.30202	+	1.47618i	0.0965120	+	0.109422i
$183$	10.0660	−	6.72591i	0.744102	−	0.497193i
$184$	23.5021	−	2.51725i	1.73260	−	0.185574i
$185$	−13.6275	+	20.3949i	−1.00191	+	1.49946i
$186$	0.968406	+	0.738721i	0.0710070	+	0.0541657i
$187$	8.81118	+	7.23114i	0.644337	+	0.528794i
$188$	−7.81043	−	6.77142i	−0.569634	−	0.493856i
$189$	0.817227	−	1.52892i	0.0594445	−	0.111213i
$190$	−6.52750	+	40.2478i	−0.473555	+	2.91989i
$191$		−	2.49262i		−	0.180360i	−0.995925	−	0.0901799i	$-0.971256\pi$
$191$		−	2.49262i		−	0.180360i	0.995925	−	0.0901799i	$-0.0287442\pi$
$192$	7.94695	−	0.919773i	0.573522	−	0.0663789i
$193$		−	14.4797i		−	1.04227i	−0.853473	−	0.521137i	$-0.825508\pi$
$193$		−	14.4797i		−	1.04227i	0.853473	−	0.521137i	$-0.174492\pi$
$194$	0.872602	+	0.141521i	0.0626491	+	0.0101606i
$195$	−1.64305	+	3.07393i	−0.117661	+	0.220129i
$196$	7.96886	−	0.567813i	0.569205	−	0.0405581i
$197$	20.6485	+	16.9458i	1.47114	+	1.20734i	0.930610	+	0.366012i	$0.119277\pi$
$197$	20.6485	+	16.9458i	1.47114	+	1.20734i	0.540532	+	0.841323i	$0.318223\pi$
$198$	−3.91040	+	5.12623i	−0.277900	+	0.364305i
$199$	0.873650	−	1.30751i	0.0619314	−	0.0926870i	−0.799211	−	0.601050i	$-0.794749\pi$
$199$	0.873650	−	1.30751i	0.0619314	−	0.0926870i	0.861143	+	0.508363i	$0.169749\pi$
$200$	18.7578	+	34.3850i	1.32638	+	2.43139i
$201$	3.76593	−	2.51631i	0.265628	−	0.177487i
$202$	11.6976	−	10.3175i	0.823043	−	0.725938i
$203$	−2.22546	+	7.33635i	−0.156196	+	0.514911i
$204$	−4.66983	+	1.78797i	−0.326954	+	0.125183i
$205$	9.60421	+	11.7028i	0.670787	+	0.817357i
$206$	−13.6790	+	14.6884i	−0.953063	+	1.02339i
$207$	−3.19799	−	7.72064i	−0.222276	−	0.536622i
$208$	3.20824	−	0.141552i	0.222452	−	0.00981485i
$209$	−11.5862	+	27.9716i	−0.801436	+	1.93484i
$210$	−4.42040	−	9.68274i	−0.305037	−	0.668172i
$211$	2.95304	+	0.290849i	0.203296	+	0.0200229i	0.199152	−	0.979969i	$-0.436181\pi$
$211$	2.95304	+	0.290849i	0.203296	+	0.0200229i	0.00414326	+	0.999991i	$0.498681\pi$
$212$	−19.6922	−	13.9425i	−1.35247	−	0.957576i
$213$	−2.75258	+	1.47129i	−0.188604	+	0.100811i
$214$	3.62311	−	7.39988i	0.247671	−	0.505846i
$215$	1.89991	−	9.55150i	0.129573	−	0.651407i
$216$	−1.10463	−	2.60380i	−0.0751607	−	0.177166i
$217$	−1.46441	+	0.291288i	−0.0994103	+	0.0197739i
$218$	3.66802	−	2.13165i	0.248429	−	0.144374i
$219$	−4.63933	+	0.456934i	−0.313497	+	0.0308767i
$220$	10.4627	+	38.1779i	0.705393	+	2.57395i
$221$	−1.92084	+	0.582680i	−0.129210	+	0.0391953i
$222$	−1.83648	−	7.77625i	−0.123257	−	0.521908i
$223$	−8.42010	−	8.42010i	−0.563852	−	0.563852i	0.366548	−	0.930399i	$-0.380540\pi$
$223$	−8.42010	−	8.42010i	−0.563852	−	0.563852i	−0.930399	+	0.366548i	$0.880540\pi$
$224$	−5.59844	+	8.05185i	−0.374062	+	0.537987i
$225$	9.79217	−	9.79217i	0.652811	−	0.652811i
$226$	−11.8862	−	7.34454i	−0.790656	−	0.488551i
$227$	−6.86199	−	22.6210i	−0.455446	−	1.50141i	−0.821171	−	0.570682i	$-0.806679\pi$
$227$	−6.86199	−	22.6210i	−0.455446	−	1.50141i	0.365725	−	0.930723i	$-0.380821\pi$
$228$	−8.14527	−	10.4911i	−0.539434	−	0.694791i
$229$	1.74546	+	17.7219i	0.115343	+	1.17110i	0.862361	+	0.506294i	$0.168985\pi$
$229$	1.74546	+	17.7219i	0.115343	+	1.17110i	−0.747018	+	0.664804i	$0.768515\pi$
$230$	−49.5976	−	13.1387i	−3.27037	−	0.866339i
$231$	−1.54193	−	7.75179i	−0.101451	−	0.510030i
$232$	7.03743	+	10.3403i	0.462030	+	0.678875i
$233$	9.75711	+	1.94081i	0.639209	+	0.127147i	0.504046	−	0.863677i	$-0.331844\pi$
$233$	9.75711	+	1.94081i	0.639209	+	0.127147i	0.135163	+	0.990823i	$0.456844\pi$
$234$	−0.368013	−	1.07409i	−0.0240577	−	0.0702156i
$235$	10.5776	+	19.7894i	0.690009	+	1.29092i
$236$	0.581628	−	0.366280i	0.0378608	−	0.0238428i
$237$	0.289206	−	2.93636i	0.0187860	−	0.190737i
$238$	2.14291	−	5.74304i	0.138905	−	0.372266i
$239$	22.8090	+	9.44780i	1.47539	+	0.611127i	0.968081	−	0.250637i	$-0.0806399\pi$
$239$	22.8090	+	9.44780i	1.47539	+	0.611127i	0.507310	+	0.861764i	$0.330640\pi$
$240$	−16.8241	−	4.30363i	−1.08599	−	0.277798i
$241$	24.7625	−	10.2570i	1.59509	−	0.660710i	0.604383	−	0.796694i	$-0.293420\pi$
$241$	24.7625	−	10.2570i	1.59509	−	0.660710i	0.990711	+	0.135984i	$0.0434197\pi$
$242$	0.492059	+	13.8289i	0.0316308	+	0.888958i
$243$	−0.773010	+	0.634393i	−0.0495886	+	0.0406963i
$244$	16.6517	+	17.5776i	1.06602	+	1.12529i
$245$	−16.5953	−	5.03414i	−1.06024	−	0.321619i
$246$	−4.92188	−	0.308552i	−0.313808	−	0.0196726i
$247$	−2.96209	−	4.43309i	−0.188473	−	0.282070i
$248$	−1.12996	+	2.15807i	−0.0717527	+	0.137038i
$249$	−3.14355	−	2.10045i	−0.199214	−	0.133111i
$250$	−7.24397	−	53.8406i	−0.458149	−	3.40518i
$251$	−3.61307	+	4.40254i	−0.228055	+	0.277886i	−0.874448	−	0.485119i	$-0.838776\pi$
$251$	−3.61307	+	4.40254i	−0.228055	+	0.277886i	0.646394	+	0.763004i	$0.276276\pi$
$252$	3.28953	+	1.09583i	0.207221	+	0.0690310i
$253$	−33.6001	−	17.9596i	−2.11242	−	1.12911i
$254$	17.3280	+	24.0366i	1.08725	+	1.50819i
$255$	10.8545			0.679738
$256$	4.49138	+	15.3567i	0.280711	+	0.959792i
$257$	28.7389			1.79268			0.896340	−	0.443366i	$-0.146216\pi$
$257$	28.7389			1.79268			0.896340	+	0.443366i	$0.146216\pi$
$258$	1.85513	+	2.57335i	0.115495	+	0.160210i
$259$	8.63826	+	4.61725i	0.536755	+	0.286902i
$260$	−6.61367	−	2.20320i	−0.410162	−	0.136636i
$261$	2.80542	−	3.41841i	0.173651	−	0.211594i
$262$	2.33960	+	17.3890i	0.144541	+	1.07430i
$263$	−14.9653	−	9.99952i	−0.922803	−	0.616597i	0.000778714	−	1.00000i	$-0.499752\pi$
$263$	−14.9653	−	9.99952i	−0.922803	−	0.616597i	−0.923581	+	0.383403i	$0.874752\pi$
$264$	−11.4237	−	5.98142i	−0.703079	−	0.368131i
$265$	29.0985	+	43.5491i	1.78751	+	2.67520i
$266$	16.2499	+	1.01870i	0.996343	+	0.0624606i
$267$	8.60020	+	2.60884i	0.526324	+	0.159659i
$268$	6.22979	+	6.57616i	0.380545	+	0.401703i
$269$	−20.7987	+	17.0691i	−1.26812	+	1.04072i	−0.271184	+	0.962528i	$0.587415\pi$
$269$	−20.7987	+	17.0691i	−1.26812	+	1.04072i	−0.996938	+	0.0781930i	$0.975085\pi$
$270$	0.218325	+	6.13586i	0.0132869	+	0.373416i
$271$	−16.1450	+	6.68746i	−0.980736	+	0.406234i	−0.814698	−	0.579885i	$-0.803097\pi$
$271$	−16.1450	+	6.68746i	−0.980736	+	0.406234i	−0.166038	+	0.986119i	$0.553097\pi$
$272$	−5.09855	−	8.60358i	−0.309145	−	0.521668i
$273$	1.28588	+	0.532629i	0.0778250	+	0.0322362i
$274$	−1.73990	+	4.66295i	−0.105111	+	0.281699i
$275$	6.18825	−	62.8304i	0.373166	−	3.78881i
$276$	14.1428	−	8.90640i	0.851294	−	0.536103i
$277$	1.52787	+	2.85844i	0.0918007	+	0.171747i	0.923631	−	0.383283i	$-0.125207\pi$
$277$	1.52787	+	2.85844i	0.0918007	+	0.171747i	−0.831830	+	0.555030i	$0.812707\pi$
$278$	−6.75856	−	19.7257i	−0.405352	−	1.18307i
$279$	0.844706	+	0.168022i	0.0505712	+	0.0100592i
$280$	17.5989	−	11.9775i	1.05174	−	0.715792i
$281$	3.01904	+	15.1777i	0.180101	+	0.905428i	0.960102	+	0.279650i	$0.0902183\pi$
$281$	3.01904	+	15.1777i	0.180101	+	0.905428i	−0.780001	+	0.625778i	$0.784782\pi$
$282$	−7.06569	−	1.87174i	−0.420756	−	0.111461i
$283$	−1.05100	−	10.6709i	−0.0624753	−	0.634322i	−0.974531	−	0.224255i	$-0.928005\pi$
$283$	−1.05100	−	10.6709i	−0.0624753	−	0.634322i	0.912055	−	0.410067i	$-0.134495\pi$
$284$	−3.82812	−	4.93062i	−0.227157	−	0.292579i
$285$	8.36931	+	27.5899i	0.495755	+	1.63429i
$286$	−4.40345	−	2.72092i	−0.260381	−	0.160891i
$287$	4.27473	−	4.27473i	0.252330	−	0.252330i
$288$	4.76088	−	3.05516i	0.280538	−	0.180027i
$289$	−7.60066	−	7.60066i	−0.447098	−	0.447098i
$290$	−6.24052	−	26.4243i	−0.366456	−	1.55169i
$291$	0.598169	−	0.181452i	0.0350653	−	0.0106369i
$292$	−2.46426	−	8.99200i	−0.144210	−	0.526217i
$293$	−17.7499	+	1.74821i	−1.03696	+	0.102132i	−0.602143	−	0.798388i	$-0.705686\pi$
$293$	−17.7499	+	1.74821i	−1.03696	+	0.102132i	−0.434816	+	0.900519i	$0.643186\pi$
$294$	4.88424	−	2.83845i	0.284855	−	0.165542i
$295$	−1.46338	+	0.291085i	−0.0852015	+	0.0169476i
$296$	14.7112	−	6.24106i	0.855072	−	0.362754i
$297$	−0.889422	+	4.47143i	−0.0516095	+	0.259458i
$298$	−8.11493	+	16.5740i	−0.470085	+	0.960108i
$299$	5.91694	−	3.16267i	0.342186	−	0.182902i
$300$	22.6043	+	16.0043i	1.30506	+	0.924010i
$301$	−3.87010	−	0.381171i	−0.223069	−	0.0219704i
$302$	5.60245	+	12.2720i	0.322385	+	0.706173i
$303$	4.22069	−	10.1896i	0.242472	−	0.585379i
$304$	17.9372	−	19.5931i	1.02877	−	1.12374i
$305$	−20.1135	−	48.5582i	−1.15169	−	2.78043i
$306$	−2.40972	+	2.58753i	−0.137755	+	0.147919i
$307$	−0.631155	−	0.769064i	−0.0360219	−	0.0438928i	0.754688	−	0.656084i	$-0.227788\pi$
$307$	−0.631155	−	0.769064i	−0.0360219	−	0.0438928i	−0.790710	+	0.612191i	$0.790288\pi$
$308$	14.7623	−	5.65212i	0.841158	−	0.322060i
$309$	−4.11992	+	13.5816i	−0.234374	+	0.772628i
$310$	3.96572	−	3.49783i	0.225237	−	0.198663i
$311$	10.8076	−	7.22143i	0.612845	−	0.409490i	−0.210044	−	0.977692i	$-0.567361\pi$
$311$	10.8076	−	7.22143i	0.612845	−	0.409490i	0.822889	+	0.568202i	$0.192361\pi$
$312$	1.99345	−	1.08747i	0.112857	−	0.0615660i
$313$	1.91076	−	2.85965i	0.108002	−	0.161637i	−0.773531	−	0.633758i	$-0.781512\pi$
$313$	1.91076	−	2.85965i	0.108002	−	0.161637i	0.881534	+	0.472121i	$0.156512\pi$
$314$	0.0257212	−	0.0337185i	0.00145153	−	0.00190284i
$315$	−5.81804	−	4.77474i	−0.327809	−	0.269026i
$316$	5.88622	−	0.419416i	0.331125	−	0.0235940i
$317$	−0.00349352	+	0.00653592i	−0.000196216	+	0.000367094i	−0.882019	−	0.471213i	$-0.843816\pi$
$317$	−0.00349352	+	0.00653592i	−0.000196216	+	0.000367094i	0.881823	+	0.471580i	$0.156316\pi$
$318$	−16.8413	−	2.73136i	−0.944411	−	0.153167i
$319$		−	20.1610i		−	1.12880i
$320$	2.81445	−	34.6174i	0.157332	−	1.93517i
$321$		−	5.82603i		−	0.325177i
$322$	−3.28001	+	20.2242i	−0.182788	+	1.12705i
$323$	−7.82696	+	14.6432i	−0.435504	+	0.814770i
$324$	−1.51115	−	1.31012i	−0.0839528	−	0.0727846i
$325$	8.59426	+	7.05313i	0.476724	+	0.391237i
$326$	−21.3922	−	16.3184i	−1.18480	−	0.903794i
$327$	1.66663	−	2.49429i	0.0921649	−	0.137935i
$328$	−1.05040	−	9.80700i	−0.0579988	−	0.541501i
$329$	7.45023	−	4.97808i	0.410744	−	0.274451i
$330$	18.5156	+	20.9924i	1.01925	+	1.15559i
$331$	3.78098	−	12.4642i	0.207822	−	0.685096i	−0.789619	−	0.613597i	$-0.789722\pi$
$331$	3.78098	−	12.4642i	0.207822	−	0.685096i	0.997441	−	0.0714987i	$-0.0227782\pi$
$332$	3.08145	−	6.90505i	0.169117	−	0.378964i
$333$	−3.58426	−	4.36743i	−0.196416	−	0.239334i
$334$	−4.42860	−	4.12428i	−0.242322	−	0.225670i
$335$	−7.52489	−	18.1667i	−0.411129	−	0.992553i
$336$	−1.05175	+	6.85429i	−0.0573778	+	0.373932i
$337$	2.09099	−	5.04810i	0.113903	−	0.274987i	−0.856639	−	0.515916i	$-0.827452\pi$
$337$	2.09099	−	5.04810i	0.113903	−	0.274987i	0.970543	+	0.240928i	$0.0774518\pi$
$338$	−15.8952	+	7.25653i	−0.864584	+	0.394703i
$339$	−9.83228	−	0.968396i	−0.534016	−	0.0525960i
$340$	3.65800	+	21.3987i	0.198383	+	1.16051i
$341$	3.46285	−	1.85093i	0.187524	−	0.100234i
$342$	−8.43495	−	4.12990i	−0.456110	−	0.223319i
$343$	−3.71851	+	18.6942i	−0.200780	+	1.00939i
$344$	−4.44793	+	4.52443i	−0.239816	+	0.243941i
$345$	−35.5834	+	7.07797i	−1.91574	+	0.381065i
$346$	5.56424	+	9.57460i	0.299135	+	0.514734i
$347$	−0.939929	+	0.0925749i	−0.0504580	+	0.00496968i	−0.123215	−	0.992380i	$-0.539320\pi$
$347$	−0.939929	+	0.0925749i	−0.0504580	+	0.00496968i	0.0727566	+	0.997350i	$0.476820\pi$
$348$	7.68450	+	4.37860i	0.411932	+	0.234718i
$349$	5.26868	−	1.59824i	0.282026	−	0.0855516i	−0.146103	−	0.989269i	$-0.546673\pi$
$349$	5.26868	−	1.59824i	0.282026	−	0.0855516i	0.428129	+	0.903718i	$0.359173\pi$
$350$	−33.0430	+	7.80362i	−1.76622	+	0.417121i
$351$	−0.567694	−	0.567694i	−0.0303013	−	0.0303013i
$352$	7.94200	−	24.5364i	0.423310	−	1.30780i
$353$	20.9563	−	20.9563i	1.11539	−	1.11539i	0.122983	−	0.992409i	$-0.460754\pi$
$353$	20.9563	−	20.9563i	1.11539	−	1.11539i	0.992409	−	0.122983i	$-0.0392459\pi$
$354$	0.255483	−	0.413466i	0.0135788	−	0.0219755i
$355$	3.93341	+	12.9667i	0.208764	+	0.688202i
$356$	−2.24480	+	17.8336i	−0.118974	+	0.945181i
$357$	−0.424849	−	4.31356i	−0.0224854	−	0.228298i
$358$	0.952406	−	3.59527i	0.0503362	−	0.190016i
$359$	3.76573	+	18.9316i	0.198748	+	0.999172i	0.943384	+	0.331702i	$0.107623\pi$
$359$	3.76573	+	18.9316i	0.198748	+	0.999172i	−0.744637	+	0.667470i	$0.767377\pi$
$360$	−12.0227	+	2.49820i	−0.633651	+	0.131667i
$361$	−24.6199	−	4.89720i	−1.29578	−	0.257748i
$362$	16.4889	−	5.64953i	0.866636	−	0.296933i
$363$	4.61249	+	8.62935i	0.242093	+	0.452924i
$364$	−0.616683	+	2.71449i	−0.0323230	+	0.142278i
$365$	−1.98376	+	20.1414i	−0.103835	+	1.05425i
$366$	16.0406	+	5.98528i	0.838458	+	0.312856i
$367$	−19.8092	−	8.20523i	−1.03403	−	0.428310i	−0.199865	−	0.979823i	$-0.564050\pi$
$367$	−19.8092	−	8.20523i	−1.03403	−	0.428310i	−0.834166	+	0.551514i	$0.814050\pi$
$368$	22.3242	+	24.8796i	1.16373	+	1.29694i
$369$	−3.22169	+	1.33447i	−0.167714	+	0.0694696i
$370$	−34.6670	+	1.23352i	−1.80225	+	0.0641274i
$371$	16.1673	−	13.2682i	0.839366	−	0.688850i
$372$	−0.0465728	+	1.72188i	−0.00241469	+	0.0892753i
$373$	6.07828	+	1.84383i	0.314721	+	0.0954697i	0.443694	−	0.896179i	$-0.353668\pi$
$373$	6.07828	+	1.84383i	0.314721	+	0.0954697i	−0.128972	+	0.991648i	$0.541168\pi$
$374$	−1.00858	+	16.0884i	−0.0521523	+	0.831909i
$375$	−21.3417	−	31.9402i	−1.10208	−	1.64938i
$376$	1.30881	−	14.5601i	0.0674965	−	0.750880i
$377$	2.95199	+	1.97246i	0.152035	+	0.101587i
$378$	2.42983	−	0.326920i	0.124977	−	0.0168150i
$379$	18.6904	−	22.7743i	0.960060	−	1.16984i	−0.0253570	−	0.999678i	$-0.508072\pi$
$379$	18.6904	−	22.7743i	0.960060	−	1.16984i	0.985417	−	0.170158i	$-0.0544278\pi$
$380$	−51.5704	+	25.7971i	−2.64550	+	1.32336i
$381$	18.4785	+	9.87695i	0.946681	+	0.506011i
$382$	2.85952	−	2.06143i	0.146306	−	0.105472i
$383$	−2.34463			−0.119805			−0.0599026	−	0.998204i	$-0.519079\pi$
$383$	−2.34463			−0.119805			−0.0599026	+	0.998204i	$0.519079\pi$
$384$	7.62738	+	8.35602i	0.389233	+	0.426417i
$385$	−34.3133			−1.74877
$386$	16.6110	−	11.9749i	0.845479	−	0.609506i
$387$	1.97830	+	1.05742i	0.100563	+	0.0537519i
$388$	0.559300	+	1.11808i	0.0283941	+	0.0567620i
$389$	3.56167	−	4.33991i	0.180584	−	0.220042i	−0.674849	−	0.737956i	$-0.735791\pi$
$389$	3.56167	−	4.33991i	0.180584	−	0.220042i	0.855433	+	0.517914i	$0.173291\pi$
$390$	−4.88522	+	0.657280i	−0.247373	+	0.0332827i
$391$	−17.3724	−	11.6079i	−0.878562	−	0.587036i
$392$	7.24173	+	8.67224i	0.365763	+	0.438014i
$393$	6.89279	+	10.3158i	0.347695	+	0.520363i
$394$	−2.36354	+	37.7021i	−0.119073	+	1.89941i
$395$	−12.2582	−	3.71848i	−0.616776	−	0.187097i
$396$	−9.11472	−	0.246532i	−0.458032	−	0.0123887i
$397$	−6.55459	+	5.37921i	−0.328965	+	0.269975i	−0.784348	−	0.620321i	$-0.787002\pi$
$397$	−6.55459	+	5.37921i	−0.328965	+	0.269975i	0.455383	+	0.890296i	$0.349502\pi$
$398$	2.22249	−	0.0790802i	0.111403	−	0.00396393i
$399$	10.6366	−	4.40581i	0.532495	−	0.220566i
$400$	−23.9333	+	49.9556i	−1.19667	+	2.49778i
$401$	26.0493	+	10.7900i	1.30084	+	0.538826i	0.922198	−	0.386718i	$-0.126391\pi$
$401$	26.0493	+	10.7900i	1.30084	+	0.538826i	0.378642	+	0.925543i	$0.376391\pi$
$402$	6.00116	+	2.23923i	0.299311	+	0.111683i
$403$	−0.0677740	+	0.688121i	−0.00337606	+	0.0342777i
$404$	21.5103	+	4.88675i	1.07018	+	0.243125i
$405$	2.04655	+	3.82882i	0.101694	+	0.190256i
$406$	−10.2567	+	3.51422i	−0.509031	+	0.174408i
$407$	−25.2631	−	5.02514i	−1.25225	−	0.249087i
$408$	−5.91315	−	3.87853i	−0.292745	−	0.192016i
$409$	−1.06914	−	5.37493i	−0.0528655	−	0.265773i	0.945308	−	0.326178i	$-0.105761\pi$
$409$	−1.06914	−	5.37493i	−0.0528655	−	0.265773i	−0.998174	+	0.0604048i	$0.980761\pi$
$410$	−5.48254	+	20.6962i	−0.270763	+	1.02211i
$411$	0.344948	+	3.50231i	0.0170150	+	0.172756i
$412$	−28.1631	−	3.54502i	−1.38750	−	0.174651i
$413$	0.172953	+	0.570151i	0.00851048	+	0.0280553i
$414$	6.21229	−	10.0538i	0.305317	−	0.494116i
$415$	−11.6063	+	11.6063i	−0.569730	+	0.569730i
$416$	2.81564	+	3.56341i	0.138048	+	0.174710i
$417$	−10.4257	−	10.4257i	−0.510550	−	0.510550i
$418$	−41.6708	+	9.84122i	−2.03819	+	0.481350i
$419$	−15.4961	+	4.70068i	−0.757032	+	0.229643i	−0.645127	−	0.764076i	$-0.723195\pi$
$419$	−15.4961	+	4.70068i	−0.757032	+	0.229643i	−0.111906	+	0.993719i	$0.535695\pi$
$420$	7.45225	−	13.0788i	0.363632	−	0.638179i
$421$	20.6771	−	2.03652i	1.00774	−	0.0992537i	0.419344	−	0.907827i	$-0.362260\pi$
$421$	20.6771	−	2.03652i	1.00774	−	0.0992537i	0.588395	+	0.808573i	$0.299760\pi$
$422$	2.10854	+	3.62824i	0.102642	+	0.176620i
$423$	−5.06922	+	1.00833i	−0.246474	+	0.0490267i
$424$	−0.290920	−	34.1214i	−0.0141283	−	1.65708i
$425$	6.75470	−	33.9582i	0.327651	−	1.64721i
$426$	−3.96426	−	1.94097i	−0.192069	−	0.0940404i
$427$	−18.5096	+	9.89360i	−0.895744	+	0.478785i
$428$	11.4855	−	1.96338i	0.555170	−	0.0949036i
$429$	−3.64255	−	0.358760i	−0.175864	−	0.0173211i
$430$	12.5287	−	5.71963i	0.604186	−	0.275825i
$431$	−1.47623	+	3.56394i	−0.0711076	+	0.171669i	−0.955437	−	0.295194i	$-0.904616\pi$
$431$	−1.47623	+	3.56394i	−0.0711076	+	0.171669i	0.884330	+	0.466863i	$0.154616\pi$
$432$	2.07352	−	3.42060i	0.0997624	−	0.164574i
$433$	9.72632	+	23.4814i	0.467417	+	1.12844i	0.965287	+	0.261193i	$0.0841158\pi$
$433$	9.72632	+	23.4814i	0.467417	+	1.12844i	−0.497870	+	0.867252i	$0.665884\pi$
$434$	−1.54524	−	1.43906i	−0.0741741	−	0.0690770i
$435$	−12.1796	−	14.8409i	−0.583967	−	0.711566i
$436$	5.47891	+	2.44502i	0.262392	+	0.117095i
$437$	16.1099	−	53.1072i	0.770640	−	2.54046i
$438$	−4.36097	−	4.94432i	−0.208375	−	0.236249i
$439$	26.3099	−	17.5797i	1.25570	−	0.839033i	0.263619	−	0.964627i	$-0.415084\pi$
$439$	26.3099	−	17.5797i	1.25570	−	0.839033i	0.992082	+	0.125594i	$0.0400838\pi$
$440$	−35.1447	+	43.5763i	−1.67546	+	2.07742i
$441$	2.21924	−	3.32133i	0.105678	−	0.158159i
$442$	−2.25700	−	1.72169i	−0.107355	−	0.0818924i
$443$	7.74121	+	6.35304i	0.367796	+	0.301842i	0.800078	−	0.599896i	$-0.204791\pi$
$443$	7.74121	+	6.35304i	0.367796	+	0.301842i	−0.432282	+	0.901738i	$0.642291\pi$
$444$	7.40206	−	8.53785i	0.351286	−	0.405188i
$445$	18.3927	−	34.4103i	0.871897	−	1.63120i
$446$	2.69596	−	16.6230i	0.127657	−	0.787122i
$447$			13.0490i			0.617195i
$448$	−13.8670	+	0.236479i	−0.655154	+	0.0111726i
$449$		−	0.498307i		−	0.0235166i	−0.999931	−	0.0117583i	$-0.996257\pi$
$449$		−	0.498307i		−	0.0235166i	0.999931	−	0.0117583i	$-0.00374286\pi$
$450$	19.3317	+	3.13527i	0.911307	+	0.147798i
$451$	−7.49423	+	14.0207i	−0.352889	+	0.660210i
$452$	−1.40440	−	19.7097i	−0.0660573	−	0.927068i
$453$	7.37382	+	6.05154i	0.346452	+	0.284326i
$454$	20.2757	−	26.5798i	0.951584	−	1.24745i
$455$	3.35706	−	5.02420i	0.157381	−	0.235538i
$456$	5.29910	−	18.0205i	0.248153	−	0.843886i
$457$	18.1748	−	12.1440i	0.850181	−	0.568073i	−0.0523838	−	0.998627i	$-0.516682\pi$
$457$	18.1748	−	12.1440i	0.850181	−	0.568073i	0.902565	+	0.430554i	$0.141682\pi$
$458$	−18.8870	+	16.6586i	−0.882529	+	0.778406i
$459$	−0.725772	+	2.39255i	−0.0338762	+	0.111675i
$460$	−25.9452	−	67.7639i	−1.20970	−	3.15951i
$461$	−4.50567	−	5.49017i	−0.209850	−	0.255703i	0.657439	−	0.753508i	$-0.271640\pi$
$461$	−4.50567	−	5.49017i	−0.209850	−	0.255703i	−0.867289	+	0.497805i	$0.834140\pi$
$462$	7.61761	−	8.17971i	0.354403	−	0.380554i
$463$	1.80401	+	4.35527i	0.0838395	+	0.202406i	0.960240	−	0.279177i	$-0.0900617\pi$
$463$	1.80401	+	4.35527i	0.0838395	+	0.202406i	−0.876400	+	0.481584i	$0.840062\pi$
$464$	−6.04230	+	16.6248i	−0.280507	+	0.771789i
$465$	1.43089	−	3.45448i	0.0663560	−	0.160197i
$466$	5.84276	+	12.7984i	0.270660	+	0.592872i
$467$	−34.3007	−	3.37832i	−1.58725	−	0.156330i	−0.734483	−	0.678627i	$-0.762575\pi$
$467$	−34.3007	−	3.37832i	−1.58725	−	0.156330i	−0.852764	+	0.522297i	$0.825075\pi$
$468$	0.927840	−	1.31047i	0.0428894	−	0.0605764i
$469$	−6.92487	+	3.70142i	−0.319761	+	0.170916i
$470$	−13.9544	+	28.5006i	−0.643669	+	1.31464i
$471$	0.00585029	−	0.0294114i	0.000269567	−	0.00135521i
$472$	0.901207	+	0.364322i	0.0414814	+	0.0167693i
$473$	10.0302	−	1.99513i	0.461188	−	0.0917360i
$474$	3.60775	−	2.09663i	0.165709	−	0.0963014i
$475$	91.5225	−	9.01418i	4.19934	−	0.413599i
$476$	8.36059	−	2.29122i	0.383207	−	0.105018i
$477$	−11.5447	+	3.50204i	−0.528595	+	0.160347i
$478$	8.02485	+	33.9798i	0.367048	+	1.55420i
$479$	−17.6066	−	17.6066i	−0.804468	−	0.804468i	0.179322	−	0.983790i	$-0.442610\pi$
$479$	−17.6066	−	17.6066i	−0.804468	−	0.804468i	−0.983790	+	0.179322i	$0.942610\pi$
$480$	−8.97662	−	22.8596i	−0.409725	−	1.04339i
$481$	3.20741	−	3.20741i	0.146245	−	0.146245i
$482$	32.2456	+	19.9248i	1.46875	+	0.907548i
$483$	4.20550	+	13.8637i	0.191357	+	0.630820i
$484$	−15.4575	+	12.0012i	−0.702615	+	0.545508i
$485$	−0.265997	−	2.70071i	−0.0120783	−	0.122633i
$486$	−1.36706	−	0.362142i	−0.0620111	−	0.0164271i
$487$	−2.09725	−	10.5436i	−0.0950356	−	0.477776i	−0.998766	−	0.0496731i	$-0.984182\pi$
$487$	−2.09725	−	10.5436i	−0.0950356	−	0.477776i	0.903730	−	0.428103i	$-0.140818\pi$
$488$	−6.39368	+	33.6396i	−0.289428	+	1.52279i
$489$	−18.6596	−	3.71163i	−0.843818	−	0.167846i
$490$	−7.94940	−	23.2013i	−0.359117	−	1.04813i
$491$	−3.92345	−	7.34025i	−0.177063	−	0.331261i	0.777697	−	0.628639i	$-0.216388\pi$
$491$	−3.92345	−	7.34025i	−0.177063	−	0.331261i	−0.954760	+	0.297378i	$0.903888\pi$
$492$	−3.71649	−	5.90153i	−0.167552	−	0.266061i
$493$	1.08372	−	11.0032i	0.0488083	−	0.495559i
$494$	2.63592	−	7.06431i	0.118596	−	0.317838i
$495$	18.2862	+	7.57438i	0.821902	+	0.340443i
$496$	−3.41021	+	0.488463i	−0.153123	+	0.0219326i
$497$	4.99898	−	2.07065i	0.224235	−	0.0928812i
$498$	−0.190126	−	5.34335i	−0.00851977	−	0.239441i
$499$	9.38618	−	7.70304i	0.420183	−	0.344836i	−0.400422	−	0.916331i	$-0.631136\pi$
$499$	9.38618	−	7.70304i	0.420183	−	0.344836i	0.820605	+	0.571495i	$0.193636\pi$
$500$	55.7747	−	52.8370i	2.49432	−	2.36294i
$501$	−4.09489	−	1.24217i	−0.182946	−	0.0554961i
$502$	−8.03861	−	0.503939i	−0.358781	−	0.0224919i
$503$	3.65626	+	5.47197i	0.163024	+	0.243983i	0.903984	−	0.427566i	$-0.140629\pi$
$503$	3.65626	+	5.47197i	0.163024	+	0.243983i	−0.740960	+	0.671550i	$0.765629\pi$
$504$	1.46335	+	4.67999i	0.0651827	+	0.208463i
$505$	−39.8130	−	26.6022i	−1.77165	−	1.18378i
$506$	−7.18450	−	53.3985i	−0.319390	−	2.37385i
$507$	−7.83821	+	9.55089i	−0.348107	+	0.424170i
$508$	−13.2442	+	39.7571i	−0.587615	+	1.76393i
$509$	20.5980	+	11.0099i	0.912990	+	0.488004i	0.859829	−	0.510582i	$-0.170570\pi$
$509$	20.5980	+	11.0099i	0.912990	+	0.488004i	0.0531616	+	0.998586i	$0.483070\pi$
$510$	8.97683	+	12.4523i	0.397501	+	0.551395i
$511$	8.08179			0.357517
$512$	−13.9027	+	17.8526i	−0.614416	+	0.788982i
$513$	−6.64095			−0.293205
$514$	23.7674	+	32.9690i	1.04833	+	1.45420i
$515$	54.3413	+	29.0460i	2.39456	+	1.27992i
$516$	−1.41792	+	4.25638i	−0.0624204	+	0.187377i
$517$	−14.9485	+	18.2148i	−0.657435	+	0.801086i
$518$	1.84707	+	13.7283i	0.0811555	+	0.603185i
$519$	6.51083	+	4.35040i	0.285794	+	0.190961i
$520$	−2.94209	−	9.40923i	−0.129019	−	0.412622i
$521$	12.1903	+	18.2441i	0.534068	+	0.799290i	0.996161	−	0.0875421i	$-0.0279012\pi$
$521$	12.1903	+	18.2441i	0.534068	+	0.799290i	−0.462093	+	0.886832i	$0.652901\pi$
$522$	6.24169	+	0.391291i	0.273192	+	0.0171263i
$523$	−6.06993	−	1.84129i	−0.265419	−	0.0805141i	0.154770	−	0.987951i	$-0.450536\pi$
$523$	−6.06993	−	1.84129i	−0.265419	−	0.0805141i	−0.420189	+	0.907436i	$0.638036\pi$
$524$	−18.0137	+	17.0649i	−0.786932	+	0.745484i
$525$	−18.5582	+	15.2303i	−0.809945	+	0.664704i
$526$	−0.905127	−	25.4379i	−0.0394654	−	1.10914i
$527$	1.98941	−	0.824039i	0.0866599	−	0.0358957i
$528$	−2.58566	−	18.0519i	−0.112526	−	0.785607i
$529$	43.2703	+	17.9232i	1.88132	+	0.779268i
$530$	−25.8943	+	69.3972i	−1.12478	+	3.01442i
$531$	0.0336861	−	0.342021i	0.00146185	−	0.0148424i
$532$	12.2702	+	19.4842i	0.531979	+	0.844747i
$533$	−1.31973	−	2.46904i	−0.0571637	−	0.106946i
$534$	4.11962	+	12.0236i	0.178273	+	0.520313i
$535$	−24.8074	−	4.93450i	−1.07252	−	0.213337i
$536$	−2.39202	+	12.5853i	−0.103319	+	0.543604i
$537$	−0.513073	−	2.57939i	−0.0221407	−	0.111309i
$538$	−36.7823	−	9.74384i	−1.58580	−	0.420087i
$539$	−1.78501	−	18.1235i	−0.0768858	−	0.780634i
$540$	−6.85846	+	5.32489i	−0.295141	+	0.229147i
$541$	−5.08394	−	16.7595i	−0.218576	−	0.720548i	−0.995819	−	0.0913476i	$-0.970883\pi$
$541$	−5.08394	−	16.7595i	−0.218576	−	0.720548i	0.777243	−	0.629200i	$-0.216617\pi$
$542$	−21.0239	−	12.9908i	−0.903053	−	0.558002i
$543$	8.71493	−	8.71493i	0.373993	−	0.373993i
$544$	5.65341	−	12.9643i	0.242388	−	0.555839i
$545$	−9.20917	−	9.20917i	−0.394478	−	0.394478i
$546$	0.452409	+	1.91564i	0.0193613	+	0.0819820i
$547$	−4.38196	+	1.32925i	−0.187359	+	0.0568348i	−0.382570	−	0.923927i	$-0.624961\pi$
$547$	−4.38196	+	1.32925i	−0.187359	+	0.0568348i	0.195211	+	0.980761i	$0.437461\pi$
$548$	−6.78823	+	1.86032i	−0.289979	+	0.0794688i
$549$	12.0480	−	1.18663i	0.514197	−	0.0506440i
$550$	77.1963	−	44.8623i	3.29166	−	1.91294i
$551$	28.8034	−	5.72935i	1.22707	−	0.244078i
$552$	21.9136	+	8.85879i	0.932705	+	0.377055i
$553$	−0.997924	+	5.01690i	−0.0424360	+	0.213340i
$554$	−2.01562	+	4.11672i	−0.0856354	+	0.174903i
$555$	−21.6324	+	11.5628i	−0.918246	+	0.490813i
$556$	17.0398	−	24.0668i	0.722649	−	1.02066i
$557$	8.45912	+	0.833151i	0.358424	+	0.0353017i	0.275627	−	0.961265i	$-0.411115\pi$
$557$	8.45912	+	0.833151i	0.358424	+	0.0353017i	0.0827974	+	0.996566i	$0.473615\pi$
$558$	0.505827	+	1.10800i	0.0214134	+	0.0469053i
$559$	−0.689178	+	1.66382i	−0.0291491	+	0.0703722i
$560$	28.2950	+	10.2838i	1.19568	+	0.434570i
$561$	4.36202	+	10.5309i	0.184165	+	0.444613i
$562$	−14.9150	+	16.0156i	−0.629152	+	0.675576i
$563$	6.36570	+	7.75662i	0.268282	+	0.326903i	0.889673	−	0.456598i	$-0.150932\pi$
$563$	6.36570	+	7.75662i	0.268282	+	0.326903i	−0.621391	+	0.783501i	$0.713432\pi$
$564$	−3.69616	−	9.65367i	−0.155636	−	0.406493i
$565$	−12.4512	+	41.0460i	−0.523824	+	1.72682i
$566$	11.3724	−	10.0307i	0.478020	−	0.421621i
$567$	1.44146	−	0.963152i	0.0605356	−	0.0404486i
$568$	2.49048	−	8.46927i	0.104498	−	0.355363i
$569$	−19.9507	+	29.8584i	−0.836378	+	1.25173i	0.129201	+	0.991618i	$0.458759\pi$
$569$	−19.9507	+	29.8584i	−0.836378	+	1.25173i	−0.965579	+	0.260110i	$0.916241\pi$
$570$	−24.7294	+	32.4184i	−1.03580	+	1.35786i
$571$	−13.3223	−	10.9333i	−0.557520	−	0.457545i	0.312948	−	0.949770i	$-0.398684\pi$
$571$	−13.3223	−	10.9333i	−0.557520	−	0.457545i	−0.870468	+	0.492226i	$0.836184\pi$
$572$	−0.520284	−	7.30183i	−0.0217542	−	0.305305i
$573$	1.17501	−	2.19830i	0.0490869	−	0.0918351i
$574$	8.43920	+	1.36869i	0.352245	+	0.0571281i
$575$			115.726i			4.82612i
$576$	7.44216	+	2.93500i	0.310090	+	0.122292i
$577$		−	17.7849i		−	0.740396i	−0.928953	−	0.370198i	$-0.879290\pi$
$577$		−	17.7849i		−	0.740396i	0.928953	−	0.370198i	$-0.120710\pi$
$578$	2.43359	−	15.0053i	0.101224	−	0.624136i
$579$	6.82569	−	12.7700i	0.283666	−	0.530702i
$580$	25.1528	−	29.0123i	1.04441	−	1.20467i
$581$	5.06658	+	4.15803i	0.210197	+	0.172504i
$582$	0.702853	+	0.536152i	0.0291342	+	0.0222242i
$583$	−30.5568	+	45.7315i	−1.26553	+	1.89401i
$584$	8.27759	−	10.2635i	0.342529	−	0.424705i
$585$	−2.89808	+	1.93644i	−0.119821	+	0.0800618i
$586$	−16.6849	−	18.9168i	−0.689246	−	0.781444i
$587$	−7.79526	+	25.6975i	−0.321745	+	1.06065i	0.635676	+	0.771956i	$0.280721\pi$
$587$	−7.79526	+	25.6975i	−0.321745	+	1.06065i	−0.957421	+	0.288695i	$0.906779\pi$
$588$	7.29558	+	3.25573i	0.300865	+	0.134264i
$589$	3.62845	+	4.42127i	0.149507	+	0.182175i
$590$	−1.54417	−	1.43805i	−0.0635723	−	0.0592037i
$591$	10.2221	+	24.6784i	0.420483	+	1.01514i
$592$	19.3260	+	11.7152i	0.794295	+	0.481491i
$593$	−10.3171	+	24.9077i	−0.423673	+	1.02284i	0.557582	+	0.830122i	$0.311729\pi$
$593$	−10.3171	+	24.9077i	−0.423673	+	1.02284i	−0.981255	+	0.192715i	$0.938271\pi$
$594$	−5.86515	+	2.67758i	−0.240650	+	0.109863i
$595$	−18.7271	−	1.84446i	−0.767737	−	0.0756155i
$596$	−25.7248	+	4.39752i	−1.05373	+	0.180129i
$597$	1.38685	−	0.741285i	0.0567599	−	0.0303388i
$598$	8.52157	+	4.17231i	0.348473	+	0.170618i
$599$	−2.36609	+	11.8952i	−0.0966760	+	0.486023i	0.901865	+	0.432019i	$0.142198\pi$
$599$	−2.36609	+	11.8952i	−0.0966760	+	0.486023i	−0.998541	+	0.0540044i	$0.982802\pi$
$600$	0.333941	+	39.1672i	0.0136331	+	1.59900i
$601$	−0.715017	+	0.142226i	−0.0291661	+	0.00580151i	−0.209652	−	0.977776i	$-0.567233\pi$
$601$	−0.715017	+	0.142226i	−0.0291661	+	0.00580151i	0.180486	+	0.983578i	$0.442233\pi$
$602$	−2.76334	−	4.75498i	−0.112625	−	0.193799i
$603$	4.50743	−	0.443943i	0.183557	−	0.0180788i
$604$	−9.44503	+	16.5761i	−0.384313	+	0.674474i
$605$	40.6507	−	12.3313i	1.65269	−	0.501337i
$606$	15.1800	−	3.58500i	0.616647	−	0.145631i
$607$	−5.69587	−	5.69587i	−0.231188	−	0.231188i	0.582000	−	0.813189i	$-0.302270\pi$
$607$	−5.69587	−	5.69587i	−0.231188	−	0.231188i	−0.813189	+	0.582000i	$0.802270\pi$
$608$	37.3114	+	4.37374i	1.51318	+	0.177379i
$609$	−5.42101	+	5.42101i	−0.219670	+	0.219670i
$610$	39.0715	−	63.2322i	1.58196	−	2.56020i
$611$	−1.20454	−	3.97083i	−0.0487304	−	0.160643i
$612$	−4.96127	−	0.624497i	−0.200547	−	0.0252438i
$613$	3.33226	+	33.8330i	0.134589	+	1.36650i	0.790869	+	0.611986i	$0.209629\pi$
$613$	3.33226	+	33.8330i	0.134589	+	1.36650i	−0.656280	+	0.754517i	$0.727871\pi$
$614$	0.360293	−	1.36008i	0.0145402	−	0.0548884i
$615$	2.95351	+	14.8483i	0.119097	+	0.598742i
$616$	18.6926	+	12.2608i	0.753148	+	0.494002i
$617$	−6.65210	−	1.32318i	−0.267803	−	0.0532694i	0.0593619	−	0.998237i	$-0.481093\pi$
$617$	−6.65210	−	1.32318i	−0.267803	−	0.0532694i	−0.327165	+	0.944967i	$0.606093\pi$
$618$	−18.9879	+	6.50576i	−0.763805	+	0.261700i
$619$	−12.2408	−	22.9010i	−0.492000	−	0.920468i	−0.998310	−	0.0581160i	$-0.981491\pi$
$619$	−12.2408	−	22.9010i	−0.492000	−	0.920468i	0.506310	−	0.862352i	$-0.331009\pi$
$620$	7.29238	+	1.65670i	0.292869	+	0.0665346i
$621$	0.819106	−	8.31652i	0.0328696	−	0.333731i
$622$	17.2224	+	6.42624i	0.690556	+	0.257669i
$623$	−14.3944	−	5.96237i	−0.576701	−	0.238877i
$624$	2.89614	+	1.38752i	0.115939	+	0.0555451i
$625$	−90.1078	+	37.3239i	−3.60431	+	1.49295i
$626$	4.86079	−	0.172956i	0.194276	−	0.00691271i
$627$	−23.4039	+	19.2071i	−0.934661	+	0.767056i
$628$	0.0599533	+	0.00162159i	0.00239240	+	6.47086e-5i
$629$	−13.5177	−	4.10054i	−0.538985	−	0.163499i
$630$	0.665965	−	10.6232i	0.0265327	−	0.423237i
$631$	−2.22424	−	3.32881i	−0.0885457	−	0.132518i	0.784553	−	0.620062i	$-0.212893\pi$
$631$	−2.22424	−	3.32881i	−0.0885457	−	0.132518i	−0.873098	+	0.487544i	$0.837893\pi$
$632$	5.34912	+	6.40576i	0.212777	+	0.254808i
$633$	2.46724	+	1.64856i	0.0980641	+	0.0655243i
$634$	−0.0103871	+	0.00139754i	−0.000412526	+	5.55032e-5i
$635$	57.7072	−	70.3164i	2.29004	−	2.79042i
$636$	−10.7945	−	21.5790i	−0.428030	−	0.855664i
$637$	2.82830	+	1.51176i	0.112061	+	0.0598980i
$638$	23.1285	−	16.6733i	0.915667	−	0.660104i
$639$	−3.12112			−0.123470
$640$	42.0404	−	25.4003i	1.66179	−	1.00403i
$641$	46.0442			1.81864			0.909319	−	0.416100i	$-0.136603\pi$
$641$	46.0442			1.81864			0.909319	+	0.416100i	$0.136603\pi$
$642$	6.68358	−	4.81819i	0.263780	−	0.190159i
$643$	3.72420	+	1.99063i	0.146868	+	0.0785027i	0.543194	−	0.839607i	$-0.317215\pi$
$643$	3.72420	+	1.99063i	0.146868	+	0.0785027i	−0.396326	+	0.918110i	$0.629715\pi$
$644$	−25.9137	+	12.9628i	−1.02114	+	0.510807i
$645$	6.17812	−	7.52806i	0.243263	−	0.296417i
$646$	−23.2716	+	3.13107i	−0.915608	+	0.123190i
$647$	−5.34029	−	3.56827i	−0.209948	−	0.140283i	0.446151	−	0.894958i	$-0.352795\pi$
$647$	−5.34029	−	3.56827i	−0.209948	−	0.140283i	−0.656099	+	0.754675i	$0.727795\pi$
$648$	0.253226	−	2.81707i	0.00994766	−	0.110665i
$649$	−0.870483	−	1.30277i	−0.0341694	−	0.0511382i
$650$	−0.983747	+	15.6923i	−0.0385857	+	0.615502i
$651$	−1.42880	−	0.433423i	−0.0559992	−	0.0169872i
$652$	1.02880	−	38.0365i	0.0402908	−	1.48962i
$653$	−6.52239	+	5.35279i	−0.255241	+	0.209471i	−0.753308	−	0.657667i	$-0.771543\pi$
$653$	−6.52239	+	5.35279i	−0.255241	+	0.209471i	0.498067	+	0.867138i	$0.334043\pi$
$654$	4.23975	−	0.150858i	0.165788	−	0.00589903i
$655$	49.7630	−	20.6125i	1.94440	−	0.805397i
$656$	10.3818	−	9.31552i	0.405342	−	0.363710i
$657$	−4.30692	−	1.78398i	−0.168029	−	0.0695999i
$658$	11.8722	+	4.42992i	0.462828	+	0.172696i
$659$	−3.08426	+	31.3150i	−0.120146	+	1.21986i	0.726297	+	0.687381i	$0.241240\pi$
$659$	−3.08426	+	31.3150i	−0.120146	+	1.21986i	−0.846443	+	0.532479i	$0.821260\pi$
$660$	−8.76968	+	38.6020i	−0.341359	+	1.50258i
$661$	2.55162	+	4.77375i	0.0992466	+	0.185677i	0.926644	−	0.375939i	$-0.122680\pi$
$661$	2.55162	+	4.77375i	0.0992466	+	0.185677i	−0.827398	+	0.561616i	$0.810180\pi$
$662$	17.4258	−	5.97054i	0.677273	−	0.232052i
$663$	−1.96870	−	0.391599i	−0.0764580	−	0.0152084i
$664$	10.4698	−	2.17553i	0.406308	−	0.0844271i
$665$	−9.75118	−	49.0225i	−0.378134	−	1.90101i
$666$	2.04606	−	7.72375i	0.0792834	−	0.299289i
$667$	3.62226	+	36.7774i	0.140254	+	1.42403i
$668$	1.06884	−	8.49129i	0.0413545	−	0.328538i
$669$	−3.45666	−	11.3951i	−0.133642	−	0.440559i
$670$	14.6175	−	23.6566i	0.564725	−	0.913933i
$671$	39.0273	−	39.0273i	1.50663	−	1.50663i
$672$	−8.73300	+	4.46201i	−0.336883	+	0.172126i
$673$	−16.1527	−	16.1527i	−0.622642	−	0.622642i	0.323564	−	0.946206i	$-0.395119\pi$
$673$	−16.1527	−	16.1527i	−0.622642	−	0.622642i	−0.946206	+	0.323564i	$0.895119\pi$
$674$	7.52041	−	1.77606i	0.289675	−	0.0684114i
$675$	13.2519	−	4.01992i	0.510066	−	0.154727i
$676$	−21.4701	−	12.2336i	−0.825775	−	0.470524i
$677$	27.5405	−	2.71251i	1.05847	−	0.104250i	0.446226	−	0.894920i	$-0.352768\pi$
$677$	27.5405	−	2.71251i	1.05847	−	0.104250i	0.612242	+	0.790670i	$0.290268\pi$
$678$	−7.02048	−	12.0804i	−0.269620	−	0.463945i
$679$	−1.06284	+	0.211412i	−0.0407881	+	0.00811326i
$680$	−21.5232	+	21.8934i	−0.825377	+	0.839573i
$681$	4.61171	−	23.1846i	0.176721	−	0.888437i
$682$	4.98719	+	2.44182i	0.190969	+	0.0935019i
$683$	34.0057	−	18.1764i	1.30119	−	0.695502i	0.332345	−	0.943158i	$-0.392160\pi$
$683$	34.0057	−	18.1764i	1.30119	−	0.695502i	0.968848	+	0.247656i	$0.0796602\pi$
$684$	−2.23801	−	13.0920i	−0.0855725	−	0.500585i
$685$	15.2051	+	1.49757i	0.580958	+	0.0572194i
$686$	−24.5211	+	11.1945i	−0.936220	+	0.427407i
$687$	−6.81470	+	16.4521i	−0.259997	+	0.627688i
$688$	−8.86888	−	1.36088i	−0.338123	−	0.0518831i
$689$	−3.70652	−	8.94833i	−0.141207	−	0.340904i
$690$	−37.5477	−	34.9674i	−1.42941	−	1.33119i
$691$	−15.3553	−	18.7105i	−0.584143	−	0.711781i	0.394141	−	0.919050i	$-0.371042\pi$
$691$	−15.3553	−	18.7105i	−0.584143	−	0.711781i	−0.978284	+	0.207270i	$0.933542\pi$
$692$	−6.38223	+	14.3016i	−0.242616	+	0.543664i
$693$	2.29431	−	7.56333i	0.0871536	−	0.287307i
$694$	−0.883533	−	1.00172i	−0.0335385	−	0.0380248i
$695$	−53.2234	+	35.5627i	−2.01888	+	1.34897i
$696$	1.33207	+	12.4368i	0.0504919	+	0.471414i
$697$	−4.84377	+	7.24921i	−0.183471	+	0.274584i
$698$	6.19074	+	4.72243i	0.234323	+	0.178747i
$699$	7.69011	+	6.31111i	0.290867	+	0.238708i
$700$	−36.2792	−	31.4530i	−1.37122	−	1.18881i
$701$	−15.4085	+	28.8274i	−0.581973	+	1.08879i	0.402856	+	0.915263i	$0.368018\pi$
$701$	−15.4085	+	28.8274i	−0.581973	+	1.08879i	−0.984828	+	0.173531i	$0.944482\pi$
$702$	0.181765	−	1.12074i	0.00686029	−	0.0422998i
$703$		−	37.5207i		−	1.41512i
$704$	34.7161	−	11.1809i	1.30841	−	0.421396i
$705$			22.4389i			0.845099i
$706$	41.3720	+	6.70982i	1.55706	+	0.252528i
$707$	−9.01334	+	16.8628i	−0.338982	+	0.634190i
$708$	0.685613	−	0.0488527i	0.0257669	−	0.00183600i
$709$	−20.4823	−	16.8094i	−0.769228	−	0.631289i	0.165680	−	0.986180i	$-0.447018\pi$
$709$	−20.4823	−	16.8094i	−0.769228	−	0.631289i	−0.934908	+	0.354891i	$0.884518\pi$
$710$	−11.6224	+	15.2360i	−0.436179	+	0.571797i
$711$	1.63925	−	2.45331i	0.0614766	−	0.0920063i
$712$	−22.3151	+	12.1734i	−0.836294	+	0.456218i
$713$	−5.98434	+	3.99861i	−0.224115	+	0.149749i
$714$	4.59713	−	4.05475i	0.172043	−	0.151745i
$715$	−4.61276	+	15.2062i	−0.172507	+	0.568681i
$716$	4.91212	−	1.88073i	0.183574	−	0.0702863i
$717$	15.6621	+	19.0843i	0.584911	+	0.712716i
$718$	−18.6039	+	19.9767i	−0.694292	+	0.745523i
$719$	−8.48851	−	20.4931i	−0.316568	−	0.764263i	−0.999431	−	0.0337168i	$-0.989266\pi$
$719$	−8.48851	−	20.4931i	−0.316568	−	0.764263i	0.682863	−	0.730546i	$-0.260734\pi$
$720$	−12.8088	−	11.7263i	−0.477356	−	0.437013i
$721$	9.41587	−	22.7319i	0.350665	−	0.846581i
$722$	−14.7429	−	32.2938i	−0.548674	−	1.20185i
$723$	26.6737	+	2.62713i	0.992005	+	0.0977040i
$724$	20.1176	+	14.2437i	0.747664	+	0.529363i
$725$	−54.0086	+	28.8682i	−2.00583	+	1.07214i
$726$	−6.08496	+	12.4280i	−0.225834	+	0.461246i
$727$	−2.24689	+	11.2959i	−0.0833326	+	0.418941i	0.916489	+	0.400060i	$0.131011\pi$
$727$	−2.24689	+	11.2959i	−0.0833326	+	0.418941i	−0.999822	+	0.0188816i	$0.993989\pi$
$728$	−3.62404	+	1.53746i	−0.134316	+	0.0569819i
$729$	−0.980785	+	0.195090i	−0.0363254	+	0.00722557i
$730$	−24.7467	+	14.3814i	−0.915916	+	0.532281i
$731$	5.58139	−	0.549719i	0.206435	−	0.0203321i
$732$	6.39952	+	23.3516i	0.236533	+	0.863100i
$733$	21.7821	−	6.60754i	0.804541	−	0.244055i	0.138880	−	0.990309i	$-0.455650\pi$
$733$	21.7821	−	6.60754i	0.804541	−	0.244055i	0.665661	+	0.746254i	$0.268150\pi$
$734$	−6.96944	−	29.5108i	−0.257247	−	1.08926i
$735$	−12.2627	−	12.2627i	−0.452317	−	0.452317i
$736$	−10.0793	+	46.1860i	−0.371529	+	1.70244i
$737$	14.6010	−	14.6010i	0.537835	−	0.537835i
$738$	−4.19526	−	2.59228i	−0.154430	−	0.0954231i
$739$	−4.24238	−	13.9853i	−0.156059	−	0.514456i	0.843691	−	0.536829i	$-0.180378\pi$
$739$	−4.24238	−	13.9853i	−0.156059	−	0.514456i	−0.999750	+	0.0223728i	$0.992878\pi$
$740$	−30.0851	−	38.7496i	−1.10595	−	1.42446i
$741$	−0.522591	−	5.30595i	−0.0191979	−	0.194919i
$742$	28.5918	+	7.57411i	1.04964	+	0.278054i
$743$	−5.92489	−	29.7864i	−0.217363	−	1.09276i	−0.923181	−	0.384365i	$-0.874420\pi$
$743$	−5.92489	−	29.7864i	−0.217363	−	1.09276i	0.705818	−	0.708393i	$-0.250580\pi$
$744$	−2.01384	+	1.37059i	−0.0738311	+	0.0502481i
$745$	55.5629	+	11.0521i	2.03567	+	0.404919i
$746$	2.91158	+	8.49782i	0.106601	+	0.311127i
$747$	−1.78221	−	3.33429i	−0.0652078	−	0.121995i
$748$	−19.2906	+	12.1482i	−0.705333	+	0.444183i
$749$	−0.989989	+	10.0515i	−0.0361734	+	0.367275i
$750$	18.9917	−	50.8980i	0.693478	−	1.85853i
$751$	−8.85402	−	3.66745i	−0.323088	−	0.133827i	0.215244	−	0.976560i	$-0.430945\pi$
$751$	−8.85402	−	3.66745i	−0.323088	−	0.133827i	−0.538332	+	0.842733i	$0.680945\pi$
$752$	17.7857	−	10.5399i	0.648576	−	0.384351i
$753$	−5.26178	+	2.17950i	−0.191750	+	0.0794255i
$754$	0.178541	+	5.01775i	0.00650207	+	0.182736i
$755$	32.0131	−	26.2725i	1.16508	−	0.956153i
$756$	2.38453	+	2.51711i	0.0867247	+	0.0915465i
$757$	−41.8913	−	12.7076i	−1.52257	−	0.461865i	−0.585399	−	0.810745i	$-0.699062\pi$
$757$	−41.8913	−	12.7076i	−1.52257	−	0.461865i	−0.937167	+	0.348880i	$0.886562\pi$
$758$	41.5837	+	2.60687i	1.51039	+	0.0946859i
$759$	−21.1665	−	31.6779i	−0.768295	−	1.14984i
$760$	−72.2436	−	37.8267i	−2.62055	−	1.37212i
$761$	−41.5943	−	27.7924i	−1.50779	−	1.00747i	−0.988219	−	0.153048i	$-0.951091\pi$
$761$	−41.5943	−	27.7924i	−1.50779	−	1.00747i	−0.519573	−	0.854426i	$-0.673909\pi$
$762$	3.95114	+	29.3667i	0.143135	+	1.06384i
$763$	−3.29925	+	4.02014i	−0.119441	+	0.145539i
$764$	4.72971	+	1.57560i	0.171115	+	0.0570031i
$765$	9.57285	+	5.11680i	0.346107	+	0.184998i
$766$	−1.93904	−	2.68975i	−0.0700603	−	0.0971845i
$767$	0.275917			0.00996278
$768$	−3.27805	+	15.6606i	−0.118286	+	0.565103i
$769$	−40.9030			−1.47500			−0.737500	−	0.675348i	$-0.763994\pi$
$769$	−40.9030			−1.47500			−0.737500	+	0.675348i	$0.763994\pi$
$770$	−28.3775	−	39.3640i	−1.02266	−	1.41858i
$771$	25.3454	+	13.5474i	0.912793	+	0.487898i
$772$	27.4750	+	9.15269i	0.988848	+	0.329413i
$773$	−22.8407	+	27.8314i	−0.821522	+	1.00103i	0.178333	+	0.983970i	$0.442930\pi$
$773$	−22.8407	+	27.8314i	−0.821522	+	1.00103i	−0.999855	+	0.0170568i	$0.994570\pi$
$774$	0.423008	+	3.14399i	0.0152047	+	0.113009i
$775$	−9.91680	−	6.62620i	−0.356222	−	0.238020i
$776$	−0.820108	+	1.56629i	−0.0294402	+	0.0562266i
$777$	5.44171	+	8.14410i	0.195220	+	0.292168i
$778$	7.92426	+	0.496771i	0.284099	+	0.0178101i
$779$	−22.1607	−	6.72237i	−0.793989	−	0.240854i
$780$	−4.79416	−	5.06071i	−0.171658	−	0.181202i
$781$	−10.9994	+	9.02695i	−0.393588	+	0.323010i
$782$	−1.05071	−	29.5294i	−0.0375734	−	1.05597i
$783$	4.08559	−	1.69231i	0.146007	−	0.0604781i
$784$	−3.95974	+	15.4797i	−0.141419	+	0.552847i
$785$	−0.120280	−	0.0498215i	−0.00429297	−	0.00177820i
$786$	−6.13379	+	16.4386i	−0.218785	+	0.586347i
$787$	−3.18515	+	32.3394i	−0.113538	+	1.15278i	0.754507	+	0.656292i	$0.227876\pi$
$787$	−3.18515	+	32.3394i	−0.113538	+	1.15278i	−0.868046	+	0.496484i	$0.834624\pi$
$788$	−45.2063	+	28.4686i	−1.61041	+	1.01415i
$789$	−8.48451	−	15.8734i	−0.302057	−	0.565108i
$790$	−5.87184	−	17.1377i	−0.208911	−	0.609733i
$791$	16.7989	+	3.34151i	0.597300	+	0.118810i
$792$	−7.25516	−	10.6602i	−0.257801	−	0.378795i
$793$	1.89617	+	9.53269i	0.0673349	+	0.338516i
$794$	−11.5917	−	3.07071i	−0.411375	−	0.108975i
$795$	5.13375	+	52.1238i	0.182075	+	1.84864i
$796$	1.92874	+	2.48422i	0.0683624	+	0.0880509i
$797$	−5.66671	−	18.6806i	−0.200725	−	0.661702i	−0.998289	−	0.0584681i	$-0.981378\pi$
$797$	−5.66671	−	18.6806i	−0.200725	−	0.661702i	0.797564	−	0.603234i	$-0.206122\pi$
$798$	13.8509	+	8.55854i	0.490316	+	0.302969i
$799$	−9.13753	+	9.13753i	−0.323262	+	0.323262i
$800$	−77.1019	+	13.8578i	−2.72596	+	0.489946i
$801$	6.35490	+	6.35490i	0.224539	+	0.224539i
$802$	9.16489	+	38.8070i	0.323623	+	1.37032i
$803$	−20.3380	+	6.16947i	−0.717713	+	0.217716i
$804$	2.39420	+	8.73636i	0.0844371	+	0.308108i
$805$	62.5940	−	6.16497i	2.20615	−	0.217287i
$806$	−0.845457	+	0.491334i	−0.0297800	+	0.0173065i
$807$	−26.3892	+	5.24913i	−0.928943	+	0.184778i
$808$	12.1832	+	28.7178i	0.428603	+	1.01029i
$809$	−4.86834	+	24.4748i	−0.171162	+	0.860488i	0.795799	+	0.605561i	$0.207051\pi$
$809$	−4.86834	+	24.4748i	−0.171162	+	0.860488i	−0.966960	+	0.254927i	$0.917949\pi$
$810$	−2.69988	+	5.51426i	−0.0948640	+	0.193751i
$811$	17.4887	−	9.34791i	0.614111	−	0.328249i	−0.134847	−	0.990866i	$-0.543054\pi$
$811$	17.4887	−	9.34791i	0.614111	−	0.328249i	0.748958	+	0.662617i	$0.230554\pi$
$812$	−12.5139	−	8.86010i	−0.439151	−	0.310929i
$813$	−17.3910	−	1.71287i	−0.609930	−	0.0600729i
$814$	−15.1281	−	33.1375i	−0.530238	−	1.16147i
$815$	−31.6085	+	76.3097i	−1.10720	+	2.67301i
$816$	−0.440821	−	9.99112i	−0.0154318	−	0.349759i
$817$	5.70076	+	13.7628i	0.199444	+	0.481501i
$818$	5.28189	−	5.67164i	0.184677	−	0.198304i
$819$	0.882966	+	1.07590i	0.0308533	+	0.0375949i
$820$	−28.2767	+	10.8265i	−0.987464	+	0.378077i
$821$	3.63400	−	11.9797i	0.126828	−	0.418094i	−0.870414	−	0.492321i	$-0.836149\pi$
$821$	3.63400	−	11.9797i	0.126828	−	0.418094i	0.997241	+	0.0742263i	$0.0236487\pi$
$822$	−3.73256	+	3.29218i	−0.130188	+	0.114828i
$823$	4.10985	−	2.74611i	0.143260	−	0.0957235i	−0.481875	−	0.876240i	$-0.660044\pi$
$823$	4.10985	−	2.74611i	0.143260	−	0.0957235i	0.625135	+	0.780517i	$0.285044\pi$
$824$	−19.2244	−	35.2403i	−0.669715	−	1.22766i
$825$	35.0756	−	52.4943i	1.22117	−	1.82762i
$826$	−0.511039	+	0.669932i	−0.0177813	+	0.0233099i
$827$	−27.4314	−	22.5124i	−0.953884	−	0.782833i	0.0223053	−	0.999751i	$-0.492899\pi$
$827$	−27.4314	−	22.5124i	−0.953884	−	0.782833i	−0.976190	+	0.216918i	$0.930399\pi$
$828$	16.6713	−	1.18789i	0.579366	−	0.0412821i
$829$	3.91916	−	7.33223i	0.136118	−	0.254659i	−0.804622	−	0.593787i	$-0.797632\pi$
$829$	3.91916	−	7.33223i	0.136118	−	0.254659i	0.940740	+	0.339128i	$0.110132\pi$
$830$	−22.9132	−	3.71612i	−0.795329	−	0.128988i
$831$			3.24115i			0.112434i
$832$	−1.75935	+	6.17706i	−0.0609945	+	0.214151i
$833$		−	9.98717i		−	0.346035i
$834$	3.33812	−	20.5825i	0.115590	−	0.712714i
$835$	−8.75747	+	16.3841i	−0.303065	+	0.566995i
$836$	−45.7520	−	39.6657i	−1.58237	−	1.37187i
$837$	0.665759	+	0.546374i	0.0230120	+	0.0188855i
$838$	−18.2080	−	13.8895i	−0.628985	−	0.479804i
$839$	−9.97370	+	14.9267i	−0.344330	+	0.515327i	−0.962704	−	0.270558i	$-0.912792\pi$
$839$	−9.97370	+	14.9267i	−0.344330	+	0.515327i	0.618373	+	0.785884i	$0.287792\pi$
$840$	21.1670	−	2.26714i	0.730330	−	0.0782238i
$841$	7.85246	−	5.24685i	0.270775	−	0.180926i
$842$	19.4365	+	22.0364i	0.669825	+	0.759424i
$843$	−4.49218	+	14.8087i	−0.154719	+	0.510040i
$844$	−2.41851	+	5.41950i	−0.0832485	+	0.186547i
$845$	34.0292	+	41.4647i	1.17064	+	1.42643i
$846$	−5.34905	−	4.98147i	−0.183904	−	0.171267i
$847$	−6.49148	−	15.6718i	−0.223050	−	0.538490i
$848$	38.9032	−	28.5525i	1.33594	−	0.980497i
$849$	4.10335	−	9.90637i	0.140827	−	0.339986i
$850$	44.5428	−	20.3348i	1.52780	−	0.697479i
$851$	46.9875	+	4.62786i	1.61071	+	0.158641i
$852$	−1.05182	−	6.15298i	−0.0360348	−	0.210798i
$853$	−16.3444	+	8.73627i	−0.559622	+	0.299124i	−0.726853	−	0.686794i	$-0.759018\pi$
$853$	−16.3444	+	8.73627i	−0.559622	+	0.299124i	0.167230	+	0.985918i	$0.446518\pi$
$854$	−26.6575	−	13.0520i	−0.912202	−	0.446630i
$855$	−5.62472	+	28.2774i	−0.192361	+	0.967066i
$856$	11.7510	+	11.5523i	0.401640	+	0.394849i
$857$	−19.6672	+	3.91206i	−0.671820	+	0.133633i	−0.519201	−	0.854652i	$-0.673771\pi$
$857$	−19.6672	+	3.91206i	−0.671820	+	0.133633i	−0.152618	+	0.988285i	$0.548771\pi$
$858$	−2.60086	−	4.47540i	−0.0887920	−	0.152788i
$859$	−20.3161	+	2.00096i	−0.693175	+	0.0682718i	−0.438468	−	0.898747i	$-0.644479\pi$
$859$	−20.3161	+	2.00096i	−0.693175	+	0.0682718i	−0.254707	+	0.967018i	$0.581979\pi$
$860$	16.9229	+	9.64259i	0.577065	+	0.328810i
$861$	5.78507	−	1.75488i	0.197155	−	0.0598063i
$862$	−5.30939	+	1.25390i	−0.180838	+	0.0427078i
$863$	12.4769	+	12.4769i	0.424720	+	0.424720i	0.886825	−	0.462105i	$-0.152906\pi$
$863$	12.4769	+	12.4769i	0.424720	+	0.424720i	−0.462105	+	0.886825i	$0.652906\pi$
$864$	5.63892	−	0.450146i	0.191840	−	0.0153143i
$865$	24.0387	−	24.0387i	0.817339	−	0.817339i
$866$	−18.8939	+	30.5774i	−0.642042	+	1.03906i
$867$	−3.12026	−	10.2861i	−0.105969	−	0.349335i
$868$	0.372942	−	2.96281i	0.0126585	−	0.100564i
$869$	−1.31850	−	13.3870i	−0.0447270	−	0.454121i
$870$	6.95269	−	26.2459i	0.235718	−	0.889820i
$871$	0.709399	+	3.56639i	0.0240371	+	0.120843i
$872$	1.72621	+	8.30743i	0.0584567	+	0.281325i
$873$	0.613074	+	0.121948i	0.0207494	+	0.00412731i
$874$	74.2473	−	25.4391i	2.51145	−	0.860490i
$875$	31.3930	+	58.7322i	1.06128	+	1.98551i
$876$	2.06551	−	9.09188i	0.0697872	−	0.307186i
$877$	3.38078	−	34.3256i	0.114161	−	1.15909i	−0.751942	−	0.659229i	$-0.770883\pi$
$877$	3.38078	−	34.3256i	0.114161	−	1.15909i	0.866103	−	0.499865i	$-0.166617\pi$
$878$	41.9258	+	15.6439i	1.41493	+	0.527956i
$879$	−16.4781	−	6.82545i	−0.555792	−	0.230217i
$880$	−79.0554	−	4.27965i	−2.66496	−	0.144267i
$881$	42.4785	−	17.5952i	1.43114	−	0.592797i	0.473505	−	0.880791i	$-0.342988\pi$
$881$	42.4785	−	17.5952i	1.43114	−	0.592797i	0.957632	+	0.287994i	$0.0929884\pi$
$882$	5.64555	−	0.200879i	0.190096	−	0.00676396i
$883$	−12.3159	+	10.1074i	−0.414462	+	0.340140i	−0.818403	−	0.574645i	$-0.805140\pi$
$883$	−12.3159	+	10.1074i	−0.414462	+	0.340140i	0.403941	+	0.914785i	$0.367640\pi$
$884$	0.108544	−	4.01307i	0.00365073	−	0.134974i
$885$	−1.42781	−	0.433120i	−0.0479951	−	0.0145592i
$886$	−0.886102	+	14.1347i	−0.0297692	+	0.474864i
$887$	−4.76506	−	7.13141i	−0.159995	−	0.239449i	0.742807	−	0.669505i	$-0.233494\pi$
$887$	−4.76506	−	7.13141i	−0.159995	−	0.239449i	−0.902802	+	0.430056i	$0.858494\pi$
$888$	15.9161	+	1.43070i	0.534111	+	0.0480112i
$889$	−30.2022	−	20.1805i	−1.01295	−	0.676831i
$890$	54.6862	−	7.35775i	1.83309	−	0.246632i
$891$	−2.89222	+	3.52418i	−0.0968929	+	0.118064i
$892$	21.2994	−	10.6546i	0.713156	−	0.356743i
$893$	−30.2710	−	16.1802i	−1.01298	−	0.541450i
$894$	−14.9697	+	10.7916i	−0.500661	+	0.360926i
$895$	−11.4177			−0.381652
$896$	−11.7395	−	15.7126i	−0.392188	−	0.524920i
$897$	6.70915			0.224012
$898$	0.571655	−	0.412106i	0.0190764	−	0.0137521i
$899$	−3.35893	−	1.79538i	−0.112027	−	0.0598794i
$900$	12.3908	+	24.7701i	0.413027	+	0.825671i
$901$	−19.1352	+	23.3163i	−0.637485	+	0.776777i
$902$	−22.2823	+	2.99796i	−0.741919	+	0.0998213i
$903$	−3.23344	−	2.16052i	−0.107602	−	0.0718974i
$904$	21.4494	−	17.9113i	0.713398	−	0.595721i
$905$	−29.7271	−	44.4898i	−0.988163	−	1.47889i
$906$	−0.844049	+	13.4639i	−0.0280416	+	0.447308i
$907$	−41.8447	−	12.6935i	−1.38943	−	0.421479i	−0.495081	−	0.868847i	$-0.664862\pi$
$907$	−41.8447	−	12.6935i	−1.38943	−	0.421479i	−0.894350	+	0.447368i	$0.852362\pi$
$908$	47.2604	+	1.27828i	1.56839	+	0.0424213i
$909$	8.52567	−	6.99684i	0.282779	−	0.232071i
$910$	8.54005	−	0.303871i	0.283100	−	0.0100732i
$911$	−54.8876	+	22.7352i	−1.81851	+	0.753250i	−0.841430	+	0.540367i	$0.818285\pi$
$911$	−54.8876	+	22.7352i	−1.81851	+	0.753250i	−0.977078	+	0.212883i	$0.931715\pi$
$912$	25.0554	−	8.82404i	0.829667	−	0.292193i
$913$	−15.9243	−	6.59607i	−0.527018	−	0.218298i
$914$	28.9623	+	10.8068i	0.957987	+	0.357456i
$915$	5.15168	−	52.3059i	0.170309	−	1.72918i
$916$	−34.7304	−	7.89012i	−1.14752	−	0.260697i
$917$	−10.1391	−	18.9689i	−0.334822	−	0.626408i
$918$	−3.34494	+	1.14607i	−0.110399	+	0.0378258i
$919$	53.0095	+	10.5442i	1.74862	+	0.347822i	0.962714	−	0.270522i	$-0.0871964\pi$
$919$	53.0095	+	10.5442i	1.74862	+	0.347822i	0.785907	+	0.618345i	$0.212196\pi$
$920$	56.2813	−	85.8056i	1.85554	−	2.82893i
$921$	−0.194094	−	0.975778i	−0.00639563	−	0.0321530i
$922$	2.57205	−	9.70931i	0.0847059	−	0.319759i
$923$	−0.245608	−	2.49370i	−0.00808427	−	0.0820810i
$924$	15.6836	+	1.97416i	0.515951	+	0.0649450i
$925$	22.7122	+	74.8720i	0.746771	+	2.46177i
$926$	−3.50440	+	5.67141i	−0.115162	+	0.186374i
$927$	−10.0357	+	10.0357i	−0.329617	+	0.329617i
$928$	−24.0690	+	6.81725i	−0.790102	+	0.223787i
$929$	−38.5310	−	38.5310i	−1.26416	−	1.26416i	−0.949057	−	0.315105i	$-0.897960\pi$
$929$	−38.5310	−	38.5310i	−1.26416	−	1.26416i	−0.315105	−	0.949057i	$-0.602040\pi$
$930$	5.14631	−	1.21538i	0.168754	−	0.0398540i
$931$	25.3852	−	7.70053i	0.831968	−	0.252375i
$932$	−9.85016	+	17.2872i	−0.322653	+	0.566260i
$933$	12.9356	−	1.27405i	0.423494	−	0.0417105i
$934$	−24.4915	−	42.1434i	−0.801385	−	1.37897i
$935$	48.5353	−	9.65427i	1.58727	−	0.315728i
$936$	2.27069	−	0.0193600i	0.0742200	−	0.000632802i
$937$	10.4560	−	52.5660i	0.341583	−	1.71726i	−0.303232	−	0.952917i	$-0.598066\pi$
$937$	10.4560	−	52.5660i	0.341583	−	1.71726i	0.644815	−	0.764339i	$-0.276934\pi$
$938$	−9.97318	−	4.88304i	−0.325636	−	0.159437i
$939$	3.03317	−	1.62126i	0.0989836	−	0.0529078i
$940$	−44.2362	+	7.56196i	−1.44283	+	0.246644i
$941$	−31.4143	−	3.09404i	−1.02408	−	0.100863i	−0.427990	−	0.903783i	$-0.640778\pi$
$941$	−31.4143	−	3.09404i	−1.02408	−	0.100863i	−0.596086	+	0.802921i	$0.703278\pi$
$942$	0.0385788	−	0.0176122i	0.00125697	−	0.000573835i
$943$	11.1518	−	26.9229i	0.363153	−	0.876730i
$944$	0.327361	+	1.33516i	0.0106547	+	0.0434557i
$945$	−2.88025	−	6.95355i	−0.0936946	−	0.226199i
$946$	10.5839	+	9.85656i	0.344111	+	0.320464i
$947$	18.0913	+	22.0443i	0.587888	+	0.716343i	0.978968	−	0.204013i	$-0.0653986\pi$
$947$	18.0913	+	22.0443i	0.587888	+	0.716343i	−0.391080	+	0.920357i	$0.627899\pi$
$948$	5.38889	+	2.40485i	0.175023	+	0.0781059i
$949$	1.08644	−	3.58151i	0.0352673	−	0.116261i
$950$	86.0311	+	97.5391i	2.79122	+	3.16459i
$951$	−0.00616202	+	0.00411733i	−0.000199817	+	0.000133514i
$952$	9.54278	+	7.69635i	0.309283	+	0.249440i
$953$	5.14851	−	7.70530i	0.166777	−	0.249599i	−0.738662	−	0.674076i	$-0.764542\pi$
$953$	5.14851	−	7.70530i	0.166777	−	0.249599i	0.905439	+	0.424477i	$0.139542\pi$
$954$	−13.5651	−	10.3478i	−0.439187	−	0.335021i
$955$	−8.36521	−	6.86515i	−0.270692	−	0.222151i
$956$	−32.3447	+	37.3077i	−1.04610	+	1.20662i
$957$	9.50381	−	17.7804i	0.307215	−	0.574758i
$958$	5.63733	−	34.7591i	0.182134	−	1.12302i
$959$		−	6.10109i		−	0.197014i
$960$	18.8007	−	29.2031i	0.606788	−	0.942526i
$961$			30.2582i			0.976072i
$962$	6.33209	+	1.02696i	0.204155	+	0.0331104i
$963$	2.74637	−	5.13810i	0.0885006	−	0.165573i
$964$	3.80995	+	53.4700i	0.122710	+	1.72215i
$965$	−48.5938	−	39.8799i	−1.56429	−	1.28378i
$966$	−12.4263	+	16.2900i	−0.399811	+	0.524121i
$967$	−3.58961	+	5.37223i	−0.115434	+	0.172759i	−0.884688	−	0.466184i	$-0.845628\pi$
$967$	−3.58961	+	5.37223i	−0.115434	+	0.172759i	0.769253	+	0.638944i	$0.220628\pi$
$968$	−26.5512	−	7.80765i	−0.853388	−	0.250947i
$969$	−13.8055	+	9.22456i	−0.443498	+	0.296336i
$970$	2.87825	−	2.53867i	0.0924151	−	0.0815116i
$971$	−14.7603	+	48.6583i	−0.473682	+	1.56152i	0.316466	+	0.948604i	$0.397504\pi$
$971$	−14.7603	+	48.6583i	−0.473682	+	1.56152i	−0.790148	+	0.612916i	$0.789996\pi$
$972$	−0.715128	−	1.86778i	−0.0229377	−	0.0599090i
$973$	16.2157	+	19.7589i	0.519851	+	0.633440i
$974$	10.3611	−	11.1256i	0.331991	−	0.356488i
$975$	4.25464	+	10.2716i	0.136258	+	0.328955i
$976$	−43.8788	+	20.4856i	−1.40453	+	0.655727i
$977$	3.85685	−	9.31126i	0.123392	−	0.297894i	−0.850098	−	0.526624i	$-0.823458\pi$
$977$	3.85685	−	9.31126i	0.123392	−	0.297894i	0.973490	+	0.228731i	$0.0734575\pi$
$978$	−11.1738	−	24.4758i	−0.357298	−	0.782649i
$979$	40.7755	+	4.01604i	1.30319	+	0.128353i
$980$	20.0422	−	28.3073i	0.640224	−	0.904243i
$981$	2.64564	−	1.41412i	0.0844687	−	0.0451495i
$982$	5.17595	−	10.5714i	0.165171	−	0.337348i
$983$	0.992280	−	4.98853i	0.0316488	−	0.159109i	−0.961729	−	0.274002i	$-0.911652\pi$
$983$	0.992280	−	4.98853i	0.0316488	−	0.159109i	0.993378	+	0.114893i	$0.0366524\pi$
$984$	3.69662	−	9.14416i	0.117844	−	0.291505i
$985$	113.740	−	22.6242i	3.62404	−	0.720867i
$986$	13.5191	−	7.85654i	0.430534	−	0.250203i
$987$	8.91716	−	0.878264i	0.283836	−	0.0279555i
$988$	10.2841	−	2.81835i	0.327180	−	0.0896637i
$989$	−17.9385	+	5.44158i	−0.570410	+	0.173032i
$990$	6.43359	+	27.2419i	0.204473	+	0.865803i
$991$	35.4276	+	35.4276i	1.12540	+	1.12540i	0.990917	+	0.134479i	$0.0429359\pi$
$991$	35.4276	+	35.4276i	1.12540	+	1.12540i	0.134479	+	0.990917i	$0.457064\pi$
$992$	−3.38065	−	3.50821i	−0.107336	−	0.111386i
$993$	9.21013	−	9.21013i	0.292275	−	0.292275i
$994$	6.50965	+	4.02235i	0.206473	+	0.127581i
$995$	−1.98179	−	6.53309i	−0.0628270	−	0.207113i
$996$	5.97262	−	4.63712i	0.189250	−	0.146933i
$997$	2.14506	+	21.7792i	0.0679348	+	0.689753i	0.967484	+	0.252933i	$0.0813953\pi$
$997$	2.14506	+	21.7792i	0.0679348	+	0.689753i	−0.899549	+	0.436820i	$0.856105\pi$
$998$	16.5994	+	4.39726i	0.525444	+	0.139193i
$999$	−1.10224	−	5.54134i	−0.0348733	−	0.175320i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.109.22	✓	512
128.101	even	32	inner	384.2.v.a.229.22	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.109.22	✓	512	1.1	even	1	trivial
384.2.v.a.229.22	yes	512	128.101	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)

\(f(q)\)	\(=\)	\(q+(0.827011 + 1.14719i) q^{2} +(0.881921 + 0.471397i) q^{3} +(-0.632104 + 1.89748i) q^{4} +(2.75419 - 3.35599i) q^{5} +(0.188576 + 1.40158i) q^{6} +(-1.44146 - 0.963152i) q^{7} +(-2.69954 + 0.844095i) q^{8} +(0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(0.827011 + 1.14719i) q^{2} +(0.881921 + 0.471397i) q^{3} +(-0.632104 + 1.89748i) q^{4} +(2.75419 - 3.35599i) q^{5} +(0.188576 + 1.40158i) q^{6} +(-1.44146 - 0.963152i) q^{7} +(-2.69954 + 0.844095i) q^{8} +(0.555570 + 0.831470i) q^{9} +(6.12771 + 0.384145i) q^{10} +(4.36272 + 1.32342i) q^{11} +(-1.45193 + 1.37546i) q^{12} +(-0.620604 + 0.509317i) q^{13} +(-0.0871816 - 2.45017i) q^{14} +(4.01098 - 1.66140i) q^{15} +(-3.20089 - 2.39881i) q^{16} +(2.30989 + 0.956789i) q^{17} +(-0.494393 + 1.32498i) q^{18} +(-0.650927 + 6.60897i) q^{19} +(4.62700 + 7.34736i) q^{20} +(-0.817227 - 1.52892i) q^{21} +(2.08980 + 6.09936i) q^{22} +(-8.19619 - 1.63032i) q^{23} +(-2.77868 - 0.528128i) q^{24} +(-2.70165 - 13.5821i) q^{25} +(-1.09753 - 0.290742i) q^{26} +(0.0980171 + 0.995185i) q^{27} +(2.73872 - 2.12633i) q^{28} +(-1.28370 - 4.23179i) q^{29} +(5.22307 + 3.22737i) q^{30} +(0.608999 - 0.608999i) q^{31} +(0.104732 - 5.65588i) q^{32} +(3.22372 + 3.22372i) q^{33} +(0.812686 + 3.44117i) q^{34} +(-7.20238 + 2.18482i) q^{35} +(-1.92888 + 0.528610i) q^{36} +(-5.62269 + 0.553787i) q^{37} +(-8.12009 + 4.71896i) q^{38} +(-0.787414 + 0.156626i) q^{39} +(-4.60226 + 11.3844i) q^{40} +(-0.680305 + 3.42013i) q^{41} +(1.07811 - 2.20195i) q^{42} +(1.97830 - 1.05742i) q^{43} +(-5.26885 + 7.44165i) q^{44} +(4.32055 + 0.425537i) q^{45} +(-4.90805 - 10.7509i) q^{46} +(-1.97791 + 4.77510i) q^{47} +(-1.69214 - 3.62445i) q^{48} +(-1.52864 - 3.69047i) q^{49} +(13.3470 - 14.3319i) q^{50} +(1.58612 + 1.93269i) q^{51} +(-0.574134 - 1.49953i) q^{52} +(-3.50204 + 11.5447i) q^{53} +(-1.06061 + 0.935474i) q^{54} +(16.4571 - 10.9963i) q^{55} +(4.70426 + 1.38334i) q^{56} +(-3.68952 + 5.52175i) q^{57} +(3.79305 - 4.97239i) q^{58} +(-0.265665 - 0.218026i) q^{59} +(0.617127 + 8.66095i) q^{60} +(5.70688 - 10.6768i) q^{61} +(1.20229 + 0.194990i) q^{62} -1.73363i q^{63} +(6.57501 - 4.55733i) q^{64} +3.48550i q^{65} +(-1.03218 + 6.36428i) q^{66} +(2.13507 - 3.99444i) q^{67} +(-3.27558 + 3.77819i) q^{68} +(-6.45986 - 5.30147i) q^{69} +(-8.46286 - 6.45565i) q^{70} +(-1.73400 + 2.59512i) q^{71} +(-2.20162 - 1.77563i) q^{72} +(-3.87613 + 2.58994i) q^{73} +(-5.28533 - 5.99233i) q^{74} +(4.01992 - 13.2519i) q^{75} +(-12.1290 - 5.41268i) q^{76} +(-5.01403 - 6.10961i) q^{77} +(-0.830882 - 0.773784i) q^{78} +(-1.12913 - 2.72597i) q^{79} +(-16.8662 + 4.13536i) q^{80} +(-0.382683 + 0.923880i) q^{81} +(-4.48617 + 2.04804i) q^{82} +(-3.76251 - 0.370574i) q^{83} +(3.41768 - 0.584235i) q^{84} +(9.57285 - 5.11680i) q^{85} +(2.84915 + 1.39499i) q^{86} +(0.862730 - 4.33724i) q^{87} +(-12.8944 + 0.109938i) q^{88} +(8.81450 - 1.75331i) q^{89} +(3.08497 + 5.30843i) q^{90} +(1.38513 - 0.136423i) q^{91} +(8.27436 - 14.5216i) q^{92} +(0.824169 - 0.250009i) q^{93} +(-7.11372 + 1.68002i) q^{94} +(20.3869 + 20.3869i) q^{95} +(2.75853 - 4.93867i) q^{96} +(0.442002 - 0.442002i) q^{97} +(2.96948 - 4.80571i) q^{98} +(1.32342 + 4.36272i) 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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