LMFDB - Embedded newform 384.2.v.a.229.22

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			229.22
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.22

$q$-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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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	0.801361	+	0.598181i	$0.204110\pi$
$5$	2.75419	+	3.35599i	1.23171	+	1.50084i	0.430350	+	0.902662i	$0.358390\pi$
$6$	0.188576	−	1.40158i	0.0769858	−	0.572194i
$7$	−1.44146	+	0.963152i	−0.544820	+	0.364037i	−0.797317	−	0.603560i	$-0.793748\pi$
$7$	−1.44146	+	0.963152i	−0.544820	+	0.364037i	0.252497	+	0.967598i	$0.418748\pi$
$8$	−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	0.446849	−	0.894609i	$-0.352546\pi$
$11$	4.36272	−	1.32342i	1.31541	−	0.399025i	0.868560	+	0.495585i	$0.165046\pi$
$12$	−1.45193	−	1.37546i	−0.419137	−	0.397061i
$13$	−0.620604	−	0.509317i	−0.172125	−	0.141259i	0.544387	−	0.838834i	$-0.316762\pi$
$13$	−0.620604	−	0.509317i	−0.172125	−	0.141259i	−0.716512	+	0.697575i	$0.754262\pi$
$14$	−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	−0.0845544	−	0.996419i	$-0.526947\pi$
$17$	2.30989	−	0.956789i	0.560231	−	0.232055i	0.644786	+	0.764364i	$0.276947\pi$
$18$	−0.494393	−	1.32498i	−0.116530	−	0.312301i
$19$	−0.650927	−	6.60897i	−0.149333	−	1.51620i	−0.719395	−	0.694601i	$-0.755581\pi$
$19$	−0.650927	−	6.60897i	−0.149333	−	1.51620i	0.570062	−	0.821602i	$-0.306919\pi$
$20$	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	−0.950269	−	0.311431i	$-0.899192\pi$
$23$	−8.19619	+	1.63032i	−1.70902	+	0.339946i	−0.758755	+	0.651377i	$0.774192\pi$
$24$	−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	0.753368	+	0.657599i	$0.228428\pi$
$29$	−1.28370	+	4.23179i	−0.238377	+	0.785824i	−0.991745	+	0.128225i	$0.959072\pi$
$30$	5.22307	−	3.22737i	0.953599	−	0.589234i
$31$	0.608999	+	0.608999i	0.109379	+	0.109379i	0.759678	−	0.650299i	$-0.225356\pi$
$31$	0.608999	+	0.608999i	0.109379	+	0.109379i	−0.650299	+	0.759678i	$0.725356\pi$
$32$	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	−0.375377	−	0.926872i	$-0.622487\pi$
$37$	−5.62269	−	0.553787i	−0.924365	−	0.0910420i	−0.548988	+	0.835830i	$0.684987\pi$
$38$	−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	−0.996847	−	0.0793486i	$-0.974716\pi$
$41$	−0.680305	−	3.42013i	−0.106246	−	0.534134i	0.890601	−	0.454785i	$-0.150284\pi$
$42$	1.07811	+	2.20195i	0.166357	+	0.339769i
$43$	1.97830	+	1.05742i	0.301688	+	0.161256i	0.615294	−	0.788298i	$-0.289037\pi$
$43$	1.97830	+	1.05742i	0.301688	+	0.161256i	−0.313606	+	0.949553i	$0.601537\pi$
$44$	−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	0.711473	−	0.702714i	$-0.248028\pi$
$47$	−1.97791	−	4.77510i	−0.288508	−	0.696520i	−0.999981	+	0.00619362i	$0.998028\pi$
$48$	−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	−0.776298	−	0.630366i	$-0.782905\pi$
$53$	−3.50204	−	11.5447i	−0.481042	−	1.58578i	0.295255	−	0.955418i	$-0.404595\pi$
$54$	−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	−0.651528	−	0.758625i	$-0.725872\pi$
$59$	−0.265665	+	0.218026i	−0.0345866	+	0.0283845i	0.616941	+	0.787009i	$0.288372\pi$
$60$	0.617127	−	8.66095i	0.0796707	−	1.11812i
$61$	5.70688	+	10.6768i	0.730691	+	1.36703i	0.922656	+	0.385624i	$0.126014\pi$
$61$	5.70688	+	10.6768i	0.730691	+	1.36703i	−0.191965	+	0.981402i	$0.561486\pi$
$62$	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	0.977916	−	0.208997i	$-0.0670199\pi$
$67$	2.13507	+	3.99444i	0.260840	+	0.487998i	−0.717076	+	0.696995i	$0.754520\pi$
$68$	−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	0.714191	−	0.699951i	$-0.246795\pi$
$71$	−1.73400	−	2.59512i	−0.205788	−	0.307984i	−0.919979	+	0.391967i	$0.871795\pi$
$72$	−2.20162	+	1.77563i	−0.259464	+	0.209260i
$73$	−3.87613	−	2.58994i	−0.453666	−	0.303130i	0.307663	−	0.951495i	$-0.400453\pi$
$73$	−3.87613	−	2.58994i	−0.453666	−	0.303130i	−0.761329	+	0.648365i	$0.775453\pi$
$74$	−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	−0.974583	−	0.224027i	$-0.928080\pi$
$79$	−1.12913	+	2.72597i	−0.127038	+	0.306696i	0.847545	+	0.530723i	$0.178080\pi$
$80$	−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	−0.302378	−	0.953188i	$-0.597781\pi$
$83$	−3.76251	+	0.370574i	−0.412989	+	0.0406758i	−0.110610	+	0.993864i	$0.535281\pi$
$84$	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	0.638705	−	0.769452i	$-0.279470\pi$
$89$	8.81450	+	1.75331i	0.934335	+	0.185851i	0.295630	+	0.955303i	$0.404470\pi$
$90$	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	0.729190	−	0.684311i	$-0.239897\pi$
$97$	0.442002	+	0.442002i	0.0448785	+	0.0448785i	−0.684311	+	0.729190i	$0.739897\pi$
$98$	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	0.778195	+	0.628023i	$0.216136\pi$
$101$	−1.08105	+	10.9761i	−0.107568	+	1.09216i	−0.885763	+	0.464137i	$0.846364\pi$
$102$	−0.905430	−	3.41794i	−0.0896510	−	0.338426i
$103$	2.76886	−	13.9200i	0.272824	−	1.37158i	−0.564754	−	0.825259i	$-0.691029\pi$
$103$	2.76886	−	13.9200i	0.272824	−	1.37158i	0.837578	−	0.546318i	$-0.183971\pi$
$104$	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	−0.978979	−	0.203959i	$-0.934619\pi$
$107$	−2.74637	+	5.13810i	−0.265502	+	0.496719i	0.713478	+	0.700678i	$0.247119\pi$
$108$	−1.95030	+	0.443074i	−0.187668	+	0.0426349i
$109$	0.294037	+	2.98541i	0.0281637	+	0.285951i	0.998943	+	0.0459749i	$0.0146394\pi$
$109$	0.294037	+	2.98541i	0.0281637	+	0.285951i	−0.970779	+	0.239976i	$0.922861\pi$
$110$	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	−0.0904835	−	0.995898i	$-0.528841\pi$
$113$	−9.12780	−	3.78086i	−0.858671	−	0.355673i	−0.768188	+	0.640225i	$0.778841\pi$
$114$	−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	0.0818366	−	0.996646i	$-0.473921\pi$
$131$	10.9417	−	5.84848i	0.955983	−	0.510984i	0.874147	+	0.485662i	$0.161421\pi$
$132$	−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	−0.738498	−	0.674255i	$-0.764465\pi$
$137$	1.95520	−	2.92616i	0.167044	−	0.249999i	0.905542	+	0.424257i	$0.139465\pi$
$138$	0.739432	+	11.7951i	0.0629447	+	1.00406i
$139$	−14.1093	+	4.28001i	−1.19674	+	0.363026i	−0.824903	−	0.565274i	$-0.808771\pi$
$139$	−14.1093	+	4.28001i	−1.19674	+	0.363026i	−0.371833	+	0.928300i	$0.621271\pi$
$140$	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	−0.493404	−	0.869800i	$-0.664248\pi$
$149$	6.15124	−	11.5082i	0.503929	−	0.942785i	0.997333	−	0.0729846i	$-0.0232524\pi$
$150$	18.5270	+	6.34785i	1.51273	+	0.518300i
$151$	9.35580	−	1.86099i	0.761365	−	0.151445i	0.200887	−	0.979614i	$-0.435618\pi$
$151$	9.35580	−	1.86099i	0.761365	−	0.151445i	0.560478	+	0.828170i	$0.310618\pi$
$152$	−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	−0.957287	−	0.289139i	$-0.906631\pi$
$157$	−0.00870494	+	0.0286963i	−0.000694730	+	0.00229022i	0.956592	+	0.291430i	$0.0941309\pi$
$158$	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	−0.519390	−	0.854537i	$-0.673841\pi$
$163$	−18.2060	−	5.52273i	−1.42600	−	0.432573i	−0.906613	+	0.421964i	$0.861341\pi$
$164$	−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	0.0300140	−	0.999549i	$-0.490445\pi$
$167$	−4.19692	−	0.834820i	−0.324768	−	0.0646003i	−0.354782	+	0.934949i	$0.615445\pi$
$168$	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	0.202664	−	0.979248i	$-0.435040\pi$
$173$	7.79281	−	0.767524i	0.592476	−	0.0583538i	0.389812	+	0.920895i	$0.372540\pi$
$174$	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	−0.831619	−	0.555346i	$-0.812586\pi$
$179$	−1.66841	+	2.03296i	−0.124703	+	0.151951i	0.706916	+	0.707297i	$0.250086\pi$
$180$	−3.53848	−	7.92918i	−0.263743	−	0.591007i
$181$	3.57769	+	11.7941i	0.265928	+	0.876646i	0.983615	+	0.180281i	$0.0577007\pi$
$181$	3.57769	+	11.7941i	0.265928	+	0.876646i	−0.717687	+	0.696365i	$0.754799\pi$
$182$	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	$0.0287442\pi$
$191$			2.49262i			0.180360i	−0.995925	+	0.0901799i	$0.971256\pi$
$192$	7.94695	+	0.919773i	0.573522	+	0.0663789i
$193$			14.4797i			1.04227i	0.853473	+	0.521137i	$0.174492\pi$
$193$			14.4797i			1.04227i	−0.853473	+	0.521137i	$0.825508\pi$
$194$	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	0.540532	−	0.841323i	$-0.318223\pi$
$197$	20.6485	−	16.9458i	1.47114	−	1.20734i	0.930610	−	0.366012i	$-0.119277\pi$
$198$	−3.91040	−	5.12623i	−0.277900	−	0.364305i
$199$	0.873650	+	1.30751i	0.0619314	+	0.0926870i	0.861143	−	0.508363i	$-0.169749\pi$
$199$	0.873650	+	1.30751i	0.0619314	+	0.0926870i	−0.799211	+	0.601050i	$0.794749\pi$
$200$	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	0.00414326	−	0.999991i	$-0.498681\pi$
$211$	2.95304	−	0.290849i	0.203296	−	0.0200229i	0.199152	+	0.979969i	$0.436181\pi$
$212$	−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	−0.930399	−	0.366548i	$-0.880540\pi$
$223$	−8.42010	+	8.42010i	−0.563852	+	0.563852i	0.366548	+	0.930399i	$0.380540\pi$
$224$	−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	0.365725	+	0.930723i	$0.380821\pi$
$227$	−6.86199	+	22.6210i	−0.455446	+	1.50141i	−0.821171	+	0.570682i	$0.806679\pi$
$228$	−8.14527	+	10.4911i	−0.539434	+	0.694791i
$229$	1.74546	−	17.7219i	0.115343	−	1.17110i	−0.747018	−	0.664804i	$-0.768515\pi$
$229$	1.74546	−	17.7219i	0.115343	−	1.17110i	0.862361	−	0.506294i	$-0.168985\pi$
$230$	−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	0.135163	−	0.990823i	$-0.456844\pi$
$233$	9.75711	−	1.94081i	0.639209	−	0.127147i	0.504046	+	0.863677i	$0.331844\pi$
$234$	−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	0.507310	−	0.861764i	$-0.330640\pi$
$239$	22.8090	−	9.44780i	1.47539	−	0.611127i	0.968081	+	0.250637i	$0.0806399\pi$
$240$	−16.8241	+	4.30363i	−1.08599	+	0.277798i
$241$	24.7625	+	10.2570i	1.59509	+	0.660710i	0.990711	−	0.135984i	$-0.0434197\pi$
$241$	24.7625	+	10.2570i	1.59509	+	0.660710i	0.604383	+	0.796694i	$0.293420\pi$
$242$	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	0.646394	−	0.763004i	$-0.276276\pi$
$251$	−3.61307	−	4.40254i	−0.228055	−	0.277886i	−0.874448	+	0.485119i	$0.838776\pi$
$252$	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	−0.923581	−	0.383403i	$-0.874752\pi$
$263$	−14.9653	+	9.99952i	−0.922803	+	0.616597i	0.000778714		1.00000i	$0.499752\pi$
$264$	−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	−0.996938	−	0.0781930i	$-0.975085\pi$
$269$	−20.7987	−	17.0691i	−1.26812	−	1.04072i	−0.271184	−	0.962528i	$-0.587415\pi$
$270$	0.218325	−	6.13586i	0.0132869	−	0.373416i
$271$	−16.1450	−	6.68746i	−0.980736	−	0.406234i	−0.166038	−	0.986119i	$-0.553097\pi$
$271$	−16.1450	−	6.68746i	−0.980736	−	0.406234i	−0.814698	+	0.579885i	$0.803097\pi$
$272$	−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	−0.831830	−	0.555030i	$-0.812707\pi$
$277$	1.52787	−	2.85844i	0.0918007	−	0.171747i	0.923631	+	0.383283i	$0.125207\pi$
$278$	−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	−0.780001	−	0.625778i	$-0.784782\pi$
$281$	3.01904	−	15.1777i	0.180101	−	0.905428i	0.960102	−	0.279650i	$-0.0902183\pi$
$282$	−7.06569	+	1.87174i	−0.420756	+	0.111461i
$283$	−1.05100	+	10.6709i	−0.0624753	+	0.634322i	0.912055	+	0.410067i	$0.134495\pi$
$283$	−1.05100	+	10.6709i	−0.0624753	+	0.634322i	−0.974531	+	0.224255i	$0.928005\pi$
$284$	−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	−0.434816	−	0.900519i	$-0.643186\pi$
$293$	−17.7499	−	1.74821i	−1.03696	−	0.102132i	−0.602143	+	0.798388i	$0.705686\pi$
$294$	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	−0.790710	−	0.612191i	$-0.790288\pi$
$307$	−0.631155	+	0.769064i	−0.0360219	+	0.0438928i	0.754688	+	0.656084i	$0.227788\pi$
$308$	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	0.822889	−	0.568202i	$-0.192361\pi$
$311$	10.8076	+	7.22143i	0.612845	+	0.409490i	−0.210044	+	0.977692i	$0.567361\pi$
$312$	1.99345	+	1.08747i	0.112857	+	0.0615660i
$313$	1.91076	+	2.85965i	0.108002	+	0.161637i	0.881534	−	0.472121i	$-0.156512\pi$
$313$	1.91076	+	2.85965i	0.108002	+	0.161637i	−0.773531	+	0.633758i	$0.781512\pi$
$314$	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	0.881823	−	0.471580i	$-0.156316\pi$
$317$	−0.00349352	−	0.00653592i	−0.000196216	−	0.000367094i	−0.882019	+	0.471213i	$0.843816\pi$
$318$	−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	0.997441	+	0.0714987i	$0.0227782\pi$
$331$	3.78098	+	12.4642i	0.207822	+	0.685096i	−0.789619	+	0.613597i	$0.789722\pi$
$332$	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	0.970543	−	0.240928i	$-0.0774518\pi$
$337$	2.09099	+	5.04810i	0.113903	+	0.274987i	−0.856639	+	0.515916i	$0.827452\pi$
$338$	−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	0.0727566	−	0.997350i	$-0.476820\pi$
$347$	−0.939929	−	0.0925749i	−0.0504580	−	0.00496968i	−0.123215	+	0.992380i	$0.539320\pi$
$348$	7.68450	−	4.37860i	0.411932	−	0.234718i
$349$	5.26868	+	1.59824i	0.282026	+	0.0855516i	0.428129	−	0.903718i	$-0.359173\pi$
$349$	5.26868	+	1.59824i	0.282026	+	0.0855516i	−0.146103	+	0.989269i	$0.546673\pi$
$350$	−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	0.992409	+	0.122983i	$0.0392459\pi$
$353$	20.9563	+	20.9563i	1.11539	+	1.11539i	0.122983	+	0.992409i	$0.460754\pi$
$354$	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	−0.744637	−	0.667470i	$-0.767377\pi$
$359$	3.76573	−	18.9316i	0.198748	−	0.999172i	0.943384	−	0.331702i	$-0.107623\pi$
$360$	−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	−0.834166	−	0.551514i	$-0.814050\pi$
$367$	−19.8092	+	8.20523i	−1.03403	+	0.428310i	−0.199865	+	0.979823i	$0.564050\pi$
$368$	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	−0.128972	−	0.991648i	$-0.541168\pi$
$373$	6.07828	−	1.84383i	0.314721	−	0.0954697i	0.443694	+	0.896179i	$0.353668\pi$
$374$	−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	0.985417	+	0.170158i	$0.0544278\pi$
$379$	18.6904	+	22.7743i	0.960060	+	1.16984i	−0.0253570	+	0.999678i	$0.508072\pi$
$380$	−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	0.855433	−	0.517914i	$-0.173291\pi$
$389$	3.56167	+	4.33991i	0.180584	+	0.220042i	−0.674849	+	0.737956i	$0.735791\pi$
$390$	−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	0.455383	−	0.890296i	$-0.349502\pi$
$397$	−6.55459	−	5.37921i	−0.328965	−	0.269975i	−0.784348	+	0.620321i	$0.787002\pi$
$398$	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	0.378642	−	0.925543i	$-0.376391\pi$
$401$	26.0493	−	10.7900i	1.30084	−	0.538826i	0.922198	+	0.386718i	$0.126391\pi$
$402$	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	−0.998174	−	0.0604048i	$-0.980761\pi$
$409$	−1.06914	+	5.37493i	−0.0528655	+	0.265773i	0.945308	+	0.326178i	$0.105761\pi$
$410$	−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	−0.111906	−	0.993719i	$-0.535695\pi$
$419$	−15.4961	−	4.70068i	−0.757032	−	0.229643i	−0.645127	+	0.764076i	$0.723195\pi$
$420$	7.45225	+	13.0788i	0.363632	+	0.638179i
$421$	20.6771	+	2.03652i	1.00774	+	0.0992537i	0.588395	−	0.808573i	$-0.299760\pi$
$421$	20.6771	+	2.03652i	1.00774	+	0.0992537i	0.419344	+	0.907827i	$0.362260\pi$
$422$	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	0.884330	−	0.466863i	$-0.154616\pi$
$431$	−1.47623	−	3.56394i	−0.0711076	−	0.171669i	−0.955437	+	0.295194i	$0.904616\pi$
$432$	2.07352	+	3.42060i	0.0997624	+	0.164574i
$433$	9.72632	−	23.4814i	0.467417	−	1.12844i	−0.497870	−	0.867252i	$-0.665884\pi$
$433$	9.72632	−	23.4814i	0.467417	−	1.12844i	0.965287	−	0.261193i	$-0.0841158\pi$
$434$	−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	0.992082	−	0.125594i	$-0.0400838\pi$
$439$	26.3099	+	17.5797i	1.25570	+	0.839033i	0.263619	+	0.964627i	$0.415084\pi$
$440$	−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	−0.432282	−	0.901738i	$-0.642291\pi$
$443$	7.74121	−	6.35304i	0.367796	−	0.301842i	0.800078	+	0.599896i	$0.204791\pi$
$444$	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	$0.00374286\pi$
$449$			0.498307i			0.0235166i	−0.999931	+	0.0117583i	$0.996257\pi$
$450$	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	0.902565	−	0.430554i	$-0.141682\pi$
$457$	18.1748	+	12.1440i	0.850181	+	0.568073i	−0.0523838	+	0.998627i	$0.516682\pi$
$458$	−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	−0.867289	−	0.497805i	$-0.834140\pi$
$461$	−4.50567	+	5.49017i	−0.209850	+	0.255703i	0.657439	+	0.753508i	$0.271640\pi$
$462$	7.61761	+	8.17971i	0.354403	+	0.380554i
$463$	1.80401	−	4.35527i	0.0838395	−	0.202406i	−0.876400	−	0.481584i	$-0.840062\pi$
$463$	1.80401	−	4.35527i	0.0838395	−	0.202406i	0.960240	+	0.279177i	$0.0900617\pi$
$464$	−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	−0.852764	−	0.522297i	$-0.825075\pi$
$467$	−34.3007	+	3.37832i	−1.58725	+	0.156330i	−0.734483	+	0.678627i	$0.762575\pi$
$468$	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	−0.983790	−	0.179322i	$-0.942610\pi$
$479$	−17.6066	+	17.6066i	−0.804468	+	0.804468i	0.179322	+	0.983790i	$0.442610\pi$
$480$	−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	0.903730	+	0.428103i	$0.140818\pi$
$487$	−2.09725	+	10.5436i	−0.0950356	+	0.477776i	−0.998766	+	0.0496731i	$0.984182\pi$
$488$	−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	−0.954760	−	0.297378i	$-0.903888\pi$
$491$	−3.92345	+	7.34025i	−0.177063	+	0.331261i	0.777697	+	0.628639i	$0.216388\pi$
$492$	−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	0.820605	−	0.571495i	$-0.193636\pi$
$499$	9.38618	+	7.70304i	0.420183	+	0.344836i	−0.400422	+	0.916331i	$0.631136\pi$
$500$	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	−0.740960	−	0.671550i	$-0.765629\pi$
$503$	3.65626	−	5.47197i	0.163024	−	0.243983i	0.903984	+	0.427566i	$0.140629\pi$
$504$	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	0.0531616	−	0.998586i	$-0.483070\pi$
$509$	20.5980	−	11.0099i	0.912990	−	0.488004i	0.859829	+	0.510582i	$0.170570\pi$
$510$	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	−0.462093	−	0.886832i	$-0.652901\pi$
$521$	12.1903	−	18.2441i	0.534068	−	0.799290i	0.996161	+	0.0875421i	$0.0279012\pi$
$522$	6.24169	−	0.391291i	0.273192	−	0.0171263i
$523$	−6.06993	+	1.84129i	−0.265419	+	0.0805141i	−0.420189	−	0.907436i	$-0.638036\pi$
$523$	−6.06993	+	1.84129i	−0.265419	+	0.0805141i	0.154770	+	0.987951i	$0.450536\pi$
$524$	−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	0.777243	+	0.629200i	$0.216617\pi$
$541$	−5.08394	+	16.7595i	−0.218576	+	0.720548i	−0.995819	+	0.0913476i	$0.970883\pi$
$542$	−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	0.195211	−	0.980761i	$-0.437461\pi$
$547$	−4.38196	−	1.32925i	−0.187359	−	0.0568348i	−0.382570	+	0.923927i	$0.624961\pi$
$548$	−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	0.0827974	−	0.996566i	$-0.473615\pi$
$557$	8.45912	−	0.833151i	0.358424	−	0.0353017i	0.275627	+	0.961265i	$0.411115\pi$
$558$	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	−0.621391	−	0.783501i	$-0.713432\pi$
$563$	6.36570	−	7.75662i	0.268282	−	0.326903i	0.889673	+	0.456598i	$0.150932\pi$
$564$	−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	−0.965579	−	0.260110i	$-0.916241\pi$
$569$	−19.9507	−	29.8584i	−0.836378	−	1.25173i	0.129201	−	0.991618i	$-0.458759\pi$
$570$	−24.7294	−	32.4184i	−1.03580	−	1.35786i
$571$	−13.3223	+	10.9333i	−0.557520	+	0.457545i	−0.870468	−	0.492226i	$-0.836184\pi$
$571$	−13.3223	+	10.9333i	−0.557520	+	0.457545i	0.312948	+	0.949770i	$0.398684\pi$
$572$	−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	$0.120710\pi$
$577$			17.7849i			0.740396i	−0.928953	+	0.370198i	$0.879290\pi$
$578$	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	−0.957421	−	0.288695i	$-0.906779\pi$
$587$	−7.79526	−	25.6975i	−0.321745	−	1.06065i	0.635676	−	0.771956i	$-0.280721\pi$
$588$	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	−0.981255	−	0.192715i	$-0.938271\pi$
$593$	−10.3171	−	24.9077i	−0.423673	−	1.02284i	0.557582	−	0.830122i	$-0.311729\pi$
$594$	−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	−0.998541	−	0.0540044i	$-0.982802\pi$
$599$	−2.36609	−	11.8952i	−0.0966760	−	0.486023i	0.901865	−	0.432019i	$-0.142198\pi$
$600$	0.333941	−	39.1672i	0.0136331	−	1.59900i
$601$	−0.715017	−	0.142226i	−0.0291661	−	0.00580151i	0.180486	−	0.983578i	$-0.442233\pi$
$601$	−0.715017	−	0.142226i	−0.0291661	−	0.00580151i	−0.209652	+	0.977776i	$0.567233\pi$
$602$	−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	−0.813189	−	0.582000i	$-0.802270\pi$
$607$	−5.69587	+	5.69587i	−0.231188	+	0.231188i	0.582000	+	0.813189i	$0.302270\pi$
$608$	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	−0.656280	−	0.754517i	$-0.727871\pi$
$613$	3.33226	−	33.8330i	0.134589	−	1.36650i	0.790869	−	0.611986i	$-0.209629\pi$
$614$	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	−0.327165	−	0.944967i	$-0.606093\pi$
$617$	−6.65210	+	1.32318i	−0.267803	+	0.0532694i	0.0593619	+	0.998237i	$0.481093\pi$
$618$	−18.9879	−	6.50576i	−0.763805	−	0.261700i
$619$	−12.2408	+	22.9010i	−0.492000	+	0.920468i	0.506310	+	0.862352i	$0.331009\pi$
$619$	−12.2408	+	22.9010i	−0.492000	+	0.920468i	−0.998310	+	0.0581160i	$0.981491\pi$
$620$	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	−0.873098	−	0.487544i	$-0.837893\pi$
$631$	−2.22424	+	3.32881i	−0.0885457	+	0.132518i	0.784553	+	0.620062i	$0.212893\pi$
$632$	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	−0.396326	−	0.918110i	$-0.629715\pi$
$643$	3.72420	−	1.99063i	0.146868	−	0.0785027i	0.543194	+	0.839607i	$0.317215\pi$
$644$	−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	−0.656099	−	0.754675i	$-0.727795\pi$
$647$	−5.34029	+	3.56827i	−0.209948	+	0.140283i	0.446151	+	0.894958i	$0.352795\pi$
$648$	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	0.498067	−	0.867138i	$-0.334043\pi$
$653$	−6.52239	−	5.35279i	−0.255241	−	0.209471i	−0.753308	+	0.657667i	$0.771543\pi$
$654$	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	−0.846443	−	0.532479i	$-0.821260\pi$
$659$	−3.08426	−	31.3150i	−0.120146	−	1.21986i	0.726297	−	0.687381i	$-0.241240\pi$
$660$	−8.76968	−	38.6020i	−0.341359	−	1.50258i
$661$	2.55162	−	4.77375i	0.0992466	−	0.185677i	−0.827398	−	0.561616i	$-0.810180\pi$
$661$	2.55162	−	4.77375i	0.0992466	−	0.185677i	0.926644	+	0.375939i	$0.122680\pi$
$662$	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	−0.946206	−	0.323564i	$-0.895119\pi$
$673$	−16.1527	+	16.1527i	−0.622642	+	0.622642i	0.323564	+	0.946206i	$0.395119\pi$
$674$	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	0.612242	−	0.790670i	$-0.290268\pi$
$677$	27.5405	+	2.71251i	1.05847	+	0.104250i	0.446226	+	0.894920i	$0.352768\pi$
$678$	−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	0.968848	−	0.247656i	$-0.0796602\pi$
$683$	34.0057	+	18.1764i	1.30119	+	0.695502i	0.332345	+	0.943158i	$0.392160\pi$
$684$	−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	−0.978284	−	0.207270i	$-0.933542\pi$
$691$	−15.3553	+	18.7105i	−0.584143	+	0.711781i	0.394141	+	0.919050i	$0.371042\pi$
$692$	−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	−0.984828	−	0.173531i	$-0.944482\pi$
$701$	−15.4085	−	28.8274i	−0.581973	−	1.08879i	0.402856	−	0.915263i	$-0.368018\pi$
$702$	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	−0.934908	−	0.354891i	$-0.884518\pi$
$709$	−20.4823	+	16.8094i	−0.769228	+	0.631289i	0.165680	+	0.986180i	$0.447018\pi$
$710$	−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	0.682863	+	0.730546i	$0.260734\pi$
$719$	−8.48851	+	20.4931i	−0.316568	+	0.764263i	−0.999431	+	0.0337168i	$0.989266\pi$
$720$	−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	−0.999822	−	0.0188816i	$-0.993989\pi$
$727$	−2.24689	−	11.2959i	−0.0833326	−	0.418941i	0.916489	−	0.400060i	$-0.131011\pi$
$728$	−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	0.665661	−	0.746254i	$-0.268150\pi$
$733$	21.7821	+	6.60754i	0.804541	+	0.244055i	0.138880	+	0.990309i	$0.455650\pi$
$734$	−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	−0.999750	−	0.0223728i	$-0.992878\pi$
$739$	−4.24238	+	13.9853i	−0.156059	+	0.514456i	0.843691	+	0.536829i	$0.180378\pi$
$740$	−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	0.705818	+	0.708393i	$0.250580\pi$
$743$	−5.92489	+	29.7864i	−0.217363	+	1.09276i	−0.923181	+	0.384365i	$0.874420\pi$
$744$	−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	−0.538332	−	0.842733i	$-0.680945\pi$
$751$	−8.85402	+	3.66745i	−0.323088	+	0.133827i	0.215244	+	0.976560i	$0.430945\pi$
$752$	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	−0.937167	−	0.348880i	$-0.886562\pi$
$757$	−41.8913	+	12.7076i	−1.52257	+	0.461865i	−0.585399	+	0.810745i	$0.699062\pi$
$758$	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	−0.519573	+	0.854426i	$0.673909\pi$
$761$	−41.5943	+	27.7924i	−1.50779	+	1.00747i	−0.988219	+	0.153048i	$0.951091\pi$
$762$	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

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

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