LMFDB - Embedded newform 768.2.z.a.157.63

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(13,768)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 47, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("768.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.z (of order $64$, degree $32$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$2048$
Relative dimension:	$64$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			157.63
Character	$\chi$	$=$	768.157
Dual form			768.2.z.a.181.63

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40804 - 0.131964i) q^{2} +(0.740951 - 0.671559i) q^{3} +(1.96517 - 0.371622i) q^{4} +(-0.117521 - 0.469172i) q^{5} +(0.954670 - 1.04336i) q^{6} +(-3.34037 - 2.74137i) q^{7} +(2.71800 - 0.782592i) q^{8} +(0.0980171 - 0.995185i) q^{9} +O(q^{10})$	\(q+(1.40804 - 0.131964i) q^{2} +(0.740951 - 0.671559i) q^{3} +(1.96517 - 0.371622i) q^{4} +(-0.117521 - 0.469172i) q^{5} +(0.954670 - 1.04336i) q^{6} +(-3.34037 - 2.74137i) q^{7} +(2.71800 - 0.782592i) q^{8} +(0.0980171 - 0.995185i) q^{9} +(-0.227389 - 0.645106i) q^{10} +(-2.39451 + 1.13252i) q^{11} +(1.20653 - 1.59508i) q^{12} +(2.00347 - 1.20083i) q^{13} +(-5.06515 - 3.41916i) q^{14} +(-0.402154 - 0.268711i) q^{15} +(3.72379 - 1.46060i) q^{16} +(4.73629 - 3.16469i) q^{17} +(0.00668381 - 1.41420i) q^{18} +(1.12686 - 1.51940i) q^{19} +(-0.405304 - 0.878329i) q^{20} +(-4.31604 + 0.212034i) q^{21} +(-3.22212 + 1.91062i) q^{22} +(-2.37867 + 0.721560i) q^{23} +(1.48835 - 2.40516i) q^{24} +(4.20330 - 2.24671i) q^{25} +(2.66250 - 1.95521i) q^{26} +(-0.595699 - 0.803208i) q^{27} +(-7.58315 - 4.14591i) q^{28} +(-2.94951 + 1.05535i) q^{29} +(-0.601711 - 0.325287i) q^{30} +(2.57234 + 6.21018i) q^{31} +(5.05052 - 2.54800i) q^{32} +(-1.01366 + 2.44719i) q^{33} +(6.25128 - 5.08104i) q^{34} +(-0.893609 + 1.88938i) q^{35} +(-0.177212 - 1.99213i) q^{36} +(-0.0938209 + 0.632489i) q^{37} +(1.38616 - 2.28808i) q^{38} +(0.678042 - 2.23521i) q^{39} +(-0.686594 - 1.18324i) q^{40} +(-2.19866 - 1.17521i) q^{41} +(-6.04919 + 0.868115i) q^{42} +(-3.93600 + 4.34270i) q^{43} +(-4.28474 + 3.11544i) q^{44} +(-0.478432 + 0.0709686i) q^{45} +(-3.25404 + 1.32989i) q^{46} +(-2.44697 + 12.3018i) q^{47} +(1.77827 - 3.58298i) q^{48} +(2.27733 + 11.4489i) q^{49} +(5.62194 - 3.71815i) q^{50} +(1.38408 - 5.52558i) q^{51} +(3.49090 - 3.10437i) q^{52} +(6.37136 + 2.27971i) q^{53} +(-0.944765 - 1.05234i) q^{54} +(0.812751 + 0.990339i) q^{55} +(-11.2245 - 4.83691i) q^{56} +(-0.185415 - 1.88255i) q^{57} +(-4.01377 + 1.87521i) q^{58} +(11.7397 + 7.03653i) q^{59} +(-0.890160 - 0.378613i) q^{60} +(-9.96747 - 0.489671i) q^{61} +(4.44149 + 8.40475i) q^{62} +(-3.05558 + 3.05558i) q^{63} +(6.77510 - 4.25418i) q^{64} +(-0.798847 - 0.798847i) q^{65} +(-1.10434 + 3.57952i) q^{66} +(0.377461 - 7.68339i) q^{67} +(8.13155 - 7.97926i) q^{68} +(-1.27790 + 2.13205i) q^{69} +(-1.00891 + 2.77825i) q^{70} +(0.818103 - 0.0805761i) q^{71} +(-0.512412 - 2.78162i) q^{72} +(1.18323 - 0.971054i) q^{73} +(-0.0486381 + 0.902953i) q^{74} +(1.60564 - 4.48746i) q^{75} +(1.64983 - 3.40464i) q^{76} +(11.1032 + 2.78120i) q^{77} +(0.659746 - 3.23674i) q^{78} +(0.918380 - 0.182677i) q^{79} +(-1.12290 - 1.57545i) q^{80} +(-0.980785 - 0.195090i) q^{81} +(-3.25090 - 1.36460i) q^{82} +(1.80081 + 12.1401i) q^{83} +(-8.40297 + 2.02062i) q^{84} +(-2.04140 - 1.85022i) q^{85} +(-4.96897 + 6.63412i) q^{86} +(-1.47671 + 2.76273i) q^{87} +(-5.62198 + 4.95211i) q^{88} +(2.74057 + 0.831342i) q^{89} +(-0.664287 + 0.163063i) q^{90} +(-9.98425 - 1.48102i) q^{91} +(-4.40634 + 2.30195i) q^{92} +(6.07649 + 2.87396i) q^{93} +(-1.82205 + 17.6443i) q^{94} +(-0.845289 - 0.350130i) q^{95} +(2.03106 - 5.27966i) q^{96} +(-0.944653 + 0.391288i) q^{97} +(4.71741 + 15.8200i) q^{98} +(0.892361 + 2.49398i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2048 q+O(q^{10}) $ 2048 * q	$ 2048 q+O(q^{100}) $ 2048 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{27}{64}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.40804	−	0.131964i	0.995637	−	0.0933126i
$2$	1.40804	−	0.131964i	0.995637	−	0.0933126i
$3$	0.740951	−	0.671559i	0.427788	−	0.387725i
$3$	0.740951	−	0.671559i	0.427788	−	0.387725i
$4$	1.96517	−	0.371622i	0.982586	−	0.185811i
$5$	−0.117521	−	0.469172i	−0.0525572	−	0.209820i	0.938063	−	0.346465i	$-0.112618\pi$
$5$	−0.117521	−	0.469172i	−0.0525572	−	0.209820i	−0.990620	+	0.136645i	$0.956368\pi$
$6$	0.954670	−	1.04336i	0.389742	−	0.425951i
$7$	−3.34037	−	2.74137i	−1.26254	−	1.03614i	−0.997410	−	0.0719286i	$-0.977085\pi$
$7$	−3.34037	−	2.74137i	−1.26254	−	1.03614i	−0.265131	−	0.964212i	$-0.585415\pi$
$8$	2.71800	−	0.782592i	0.960960	−	0.276688i
$9$	0.0980171	−	0.995185i	0.0326724	−	0.331728i
$10$	−0.227389	−	0.645106i	−0.0719067	−	0.204000i
$11$	−2.39451	+	1.13252i	−0.721971	+	0.341467i	−0.752972	−	0.658053i	$-0.771380\pi$
$11$	−2.39451	+	1.13252i	−0.721971	+	0.341467i	0.0310013	+	0.999519i	$0.490130\pi$
$12$	1.20653	−	1.59508i	0.348295	−	0.460460i
$13$	2.00347	−	1.20083i	0.555662	−	0.333051i	−0.208554	−	0.978011i	$-0.566876\pi$
$13$	2.00347	−	1.20083i	0.555662	−	0.333051i	0.764217	+	0.644960i	$0.223126\pi$
$14$	−5.06515	−	3.41916i	−1.35372	−	0.913809i
$15$	−0.402154	−	0.268711i	−0.103836	−	0.0693808i
$16$	3.72379	−	1.46060i	0.930949	−	0.365150i
$17$	4.73629	−	3.16469i	1.14872	−	0.767550i	0.172644	−	0.984984i	$-0.444769\pi$
$17$	4.73629	−	3.16469i	1.14872	−	0.767550i	0.976075	+	0.217435i	$0.0697689\pi$
$18$	0.00668381	−	1.41420i	0.00157539	−	0.333330i
$19$	1.12686	−	1.51940i	0.258520	−	0.348574i	−0.654810	−	0.755793i	$-0.727252\pi$
$19$	1.12686	−	1.51940i	0.258520	−	0.348574i	0.913330	+	0.407219i	$0.133502\pi$
$20$	−0.405304	−	0.878329i	−0.0906288	−	0.196400i
$21$	−4.31604	+	0.212034i	−0.941838	+	0.0462695i
$22$	−3.22212	+	1.91062i	−0.686957	+	0.407346i
$23$	−2.37867	+	0.721560i	−0.495986	+	0.150456i	−0.528361	−	0.849020i	$-0.677193\pi$
$23$	−2.37867	+	0.721560i	−0.495986	+	0.150456i	0.0323745	+	0.999476i	$0.489693\pi$
$24$	1.48835	−	2.40516i	0.303809	−	0.490952i
$25$	4.20330	−	2.24671i	0.840659	−	0.449342i
$26$	2.66250	−	1.95521i	0.522160	−	0.383448i
$27$	−0.595699	−	0.803208i	−0.114642	−	0.154577i
$28$	−7.58315	−	4.14591i	−1.43308	−	0.783503i
$29$	−2.94951	+	1.05535i	−0.547710	+	0.195974i	−0.596180	−	0.802851i	$-0.703316\pi$
$29$	−2.94951	+	1.05535i	−0.547710	+	0.195974i	0.0484698	+	0.998825i	$0.484566\pi$
$30$	−0.601711	−	0.325287i	−0.109857	−	0.0593889i
$31$	2.57234	+	6.21018i	0.462006	+	1.11538i	0.967572	+	0.252594i	$0.0812837\pi$
$31$	2.57234	+	6.21018i	0.462006	+	1.11538i	−0.505566	+	0.862788i	$0.668716\pi$
$32$	5.05052	−	2.54800i	0.892814	−	0.450426i
$33$	−1.01366	+	2.44719i	−0.176456	+	0.426001i
$34$	6.25128	−	5.08104i	1.07208	−	0.871391i
$35$	−0.893609	+	1.88938i	−0.151047	+	0.319363i
$36$	−0.177212	−	1.99213i	−0.0295353	−	0.332022i
$37$	−0.0938209	+	0.632489i	−0.0154241	+	0.103981i	−0.995521	−	0.0945374i	$-0.969863\pi$
$37$	−0.0938209	+	0.632489i	−0.0154241	+	0.103981i	0.980097	+	0.198518i	$0.0636128\pi$
$38$	1.38616	−	2.28808i	0.224866	−	0.371176i
$39$	0.678042	−	2.23521i	0.108574	−	0.357919i
$40$	−0.686594	−	1.18324i	−0.108560	−	0.187087i
$41$	−2.19866	−	1.17521i	−0.343374	−	0.183537i	0.290691	−	0.956817i	$-0.406115\pi$
$41$	−2.19866	−	1.17521i	−0.343374	−	0.183537i	−0.634065	+	0.773280i	$0.718615\pi$
$42$	−6.04919	+	0.868115i	−0.933411	+	0.133953i
$43$	−3.93600	+	4.34270i	−0.600234	+	0.662256i	−0.962961	−	0.269639i	$-0.913096\pi$
$43$	−3.93600	+	4.34270i	−0.600234	+	0.662256i	0.362728	+	0.931895i	$0.381846\pi$
$44$	−4.28474	+	3.11544i	−0.645950	+	0.469670i
$45$	−0.478432	+	0.0709686i	−0.0713204	+	0.0105794i
$46$	−3.25404	+	1.32989i	−0.479783	+	0.196081i
$47$	−2.44697	+	12.3018i	−0.356928	+	1.79440i	0.217738	+	0.976007i	$0.430132\pi$
$47$	−2.44697	+	12.3018i	−0.356928	+	1.79440i	−0.574665	+	0.818388i	$0.694868\pi$
$48$	1.77827	−	3.58298i	0.256671	−	0.517159i
$49$	2.27733	+	11.4489i	0.325332	+	1.63556i
$50$	5.62194	−	3.71815i	0.795062	−	0.525825i
$51$	1.38408	−	5.52558i	0.193811	−	0.773736i
$52$	3.49090	−	3.10437i	0.484101	−	0.430499i
$53$	6.37136	+	2.27971i	0.875173	+	0.313142i	0.735882	−	0.677110i	$-0.236768\pi$
$53$	6.37136	+	2.27971i	0.875173	+	0.313142i	0.139291	+	0.990252i	$0.455518\pi$
$54$	−0.944765	−	1.05234i	−0.128566	−	0.143205i
$55$	0.812751	+	0.990339i	0.109591	+	0.133537i
$56$	−11.2245	−	4.83691i	−1.49994	−	0.646360i
$57$	−0.185415	−	1.88255i	−0.0245589	−	0.249350i
$58$	−4.01377	+	1.87521i	−0.527034	+	0.246227i
$59$	11.7397	+	7.03653i	1.52838	+	0.916078i	0.997648	+	0.0685412i	$0.0218345\pi$
$59$	11.7397	+	7.03653i	1.52838	+	0.916078i	0.530736	+	0.847537i	$0.321916\pi$
$60$	−0.890160	−	0.378613i	−0.114919	−	0.0488788i
$61$	−9.96747	−	0.489671i	−1.27620	−	0.0626959i	−0.600354	−	0.799735i	$-0.704973\pi$
$61$	−9.96747	−	0.489671i	−1.27620	−	0.0626959i	−0.675850	+	0.737039i	$0.736223\pi$
$62$	4.44149	+	8.40475i	0.564070	+	1.06740i
$63$	−3.05558	+	3.05558i	−0.384967	+	0.384967i
$64$	6.77510	−	4.25418i	0.846888	−	0.531772i
$65$	−0.798847	−	0.798847i	−0.0990848	−	0.0990848i
$66$	−1.10434	+	3.57952i	−0.135934	+	0.440608i
$67$	0.377461	−	7.68339i	0.0461142	−	0.938675i	−0.858597	−	0.512651i	$-0.828664\pi$
$67$	0.377461	−	7.68339i	0.0461142	−	0.938675i	0.904712	−	0.426025i	$-0.140086\pi$
$68$	8.13155	−	7.97926i	0.986096	−	0.967628i
$69$	−1.27790	+	2.13205i	−0.153842	+	0.256669i
$70$	−1.00891	+	2.77825i	−0.120588	+	0.332064i
$71$	0.818103	−	0.0805761i	0.0970909	−	0.00956262i	−0.0493550	−	0.998781i	$-0.515717\pi$
$71$	0.818103	−	0.0805761i	0.0970909	−	0.00956262i	0.146446	+	0.989219i	$0.453217\pi$
$72$	−0.512412	−	2.78162i	−0.0603884	−	0.327818i
$73$	1.18323	−	0.971054i	0.138487	−	0.113653i	−0.562600	−	0.826730i	$-0.690199\pi$
$73$	1.18323	−	0.971054i	0.138487	−	0.113653i	0.701086	+	0.713076i	$0.252699\pi$
$74$	−0.0486381	+	0.902953i	−0.00565406	+	0.104966i
$75$	1.60564	−	4.48746i	0.185403	−	0.518167i
$76$	1.64983	−	3.40464i	0.189249	−	0.390539i
$77$	11.1032	+	2.78120i	1.26533	+	0.316947i
$78$	0.659746	−	3.23674i	0.0747015	−	0.366489i
$79$	0.918380	−	0.182677i	0.103326	−	0.0205528i	−0.143157	−	0.989700i	$-0.545725\pi$
$79$	0.918380	−	0.182677i	0.103326	−	0.0205528i	0.246482	+	0.969147i	$0.420725\pi$
$80$	−1.12290	−	1.57545i	−0.125544	−	0.176140i
$81$	−0.980785	−	0.195090i	−0.108976	−	0.0216767i
$82$	−3.25090	−	1.36460i	−0.359002	−	0.150695i
$83$	1.80081	+	12.1401i	0.197664	+	1.33254i	0.829962	+	0.557819i	$0.188362\pi$
$83$	1.80081	+	12.1401i	0.197664	+	1.33254i	−0.632298	+	0.774725i	$0.717888\pi$
$84$	−8.40297	+	2.02062i	−0.916839	+	0.220468i
$85$	−2.04140	−	1.85022i	−0.221421	−	0.200684i
$86$	−4.96897	+	6.63412i	−0.535818	+	0.715376i
$87$	−1.47671	+	2.76273i	−0.158320	+	0.296196i
$88$	−5.62198	+	4.95211i	−0.599305	+	0.527896i
$89$	2.74057	+	0.831342i	0.290499	+	0.0881220i	0.432171	−	0.901792i	$-0.357748\pi$
$89$	2.74057	+	0.831342i	0.290499	+	0.0881220i	−0.141672	+	0.989914i	$0.545248\pi$
$90$	−0.664287	+	0.163063i	−0.0700220	+	0.0171883i
$91$	−9.98425	−	1.48102i	−1.04663	−	0.155254i
$92$	−4.40634	+	2.30195i	−0.459392	+	0.239995i
$93$	6.07649	+	2.87396i	0.630102	+	0.298016i
$94$	−1.82205	+	17.6443i	−0.187930	+	1.81987i
$95$	−0.845289	−	0.350130i	−0.0867248	−	0.0359226i
$96$	2.03106	−	5.27966i	0.207294	−	0.538853i
$97$	−0.944653	+	0.391288i	−0.0959149	+	0.0397293i	−0.430125	−	0.902769i	$-0.641531\pi$
$97$	−0.944653	+	0.391288i	−0.0959149	+	0.0397293i	0.334210	+	0.942499i	$0.391531\pi$
$98$	4.71741	+	15.8200i	0.476531	+	1.59806i
$99$	0.892361	+	2.49398i	0.0896856	+	0.250655i
$100$	7.42527	−	5.97720i	0.742527	−	0.597720i
$101$	−4.72187	+	3.50197i	−0.469843	+	0.348459i	−0.804572	−	0.593855i	$-0.797605\pi$
$101$	−4.72187	+	3.50197i	−0.469843	+	0.348459i	0.334729	+	0.942314i	$0.391355\pi$
$102$	1.21967	−	7.96290i	0.120766	−	0.788445i
$103$	−8.95280	−	16.7495i	−0.882146	−	1.65038i	−0.752276	−	0.658848i	$-0.771044\pi$
$103$	−8.95280	−	16.7495i	−0.882146	−	1.65038i	−0.129870	−	0.991531i	$-0.541456\pi$
$104$	4.50568	−	4.83177i	0.441818	−	0.473794i
$105$	0.606708	+	2.00005i	0.0592086	+	0.195185i
$106$	9.27198	+	2.36914i	0.900575	+	0.230111i
$107$	−0.244808	−	4.98317i	−0.0236665	−	0.481742i	−0.981149	−	0.193251i	$-0.938097\pi$
$107$	−0.244808	−	4.98317i	−0.0236665	−	0.481742i	0.957483	−	0.288490i	$-0.0931533\pi$
$108$	−1.46914	−	1.35707i	−0.141368	−	0.130584i
$109$	1.21230	+	0.899100i	0.116117	+	0.0861182i	0.652199	−	0.758047i	$-0.273846\pi$
$109$	1.21230	+	0.899100i	0.116117	+	0.0861182i	−0.536083	+	0.844166i	$0.680096\pi$
$110$	1.27508	+	1.28719i	0.121574	+	0.122728i
$111$	0.355237	+	0.531650i	0.0337176	+	0.0504620i
$112$	−16.4429	−	5.32935i	−1.55371	−	0.503576i
$113$	6.28627	−	9.40807i	0.591363	−	0.885037i	−0.408250	−	0.912870i	$-0.633861\pi$
$113$	6.28627	−	9.40807i	0.591363	−	0.885037i	0.999613	+	0.0278333i	$0.00886075\pi$
$114$	−0.509502	−	2.62625i	−0.0477192	−	0.245971i
$115$	0.618080	+	1.03120i	0.0576362	+	0.0961603i
$116$	−5.40410	+	3.17005i	−0.501758	+	0.294332i
$117$	−0.998676	−	2.11152i	−0.0923276	−	0.195210i
$118$	17.4586	+	8.35852i	1.60720	+	0.769464i
$119$	−24.4965	−	2.41270i	−2.24559	−	0.221172i
$120$	−1.30335	−	0.415635i	−0.118979	−	0.0379421i
$121$	−2.52726	+	3.07948i	−0.229751	+	0.279953i
$122$	−14.0993	+	0.625870i	−1.27649	+	0.0566636i
$123$	−2.41833	+	0.605759i	−0.218053	+	0.0546195i
$124$	7.36293	+	11.2481i	0.661211	+	1.01011i
$125$	−3.17212	−	3.49990i	−0.283723	−	0.313040i
$126$	−3.89917	+	4.70562i	−0.347365	+	0.419210i
$127$		−	11.5436i		−	1.02433i	−0.858887	−	0.512166i	$-0.828843\pi$
$127$		−	11.5436i		−	1.02433i	0.858887	−	0.512166i	$-0.171157\pi$
$128$	8.97824	−	6.88413i	0.793571	−	0.608477i
$129$			5.86098i			0.516031i
$130$	−1.23023	−	1.01939i	−0.107898	−	0.0894066i
$131$	4.40041	+	4.85510i	0.384465	+	0.424192i	0.902179	−	0.431362i	$-0.141967\pi$
$131$	4.40041	+	4.85510i	0.384465	+	0.424192i	−0.517714	+	0.855554i	$0.673217\pi$
$132$	−1.08258	+	5.18585i	−0.0942269	+	0.451370i
$133$	−7.92937	+	1.98620i	−0.687563	+	0.172226i
$134$	−0.482450	−	10.8684i	−0.0416773	−	0.938883i
$135$	−0.306835	+	0.373879i	−0.0264081	+	0.0321784i
$136$	10.3966	−	12.3082i	0.891501	−	1.05542i
$137$	19.3651	+	1.90730i	1.65447	+	0.162951i	0.881726	−	0.471762i	$-0.156382\pi$
$137$	19.3651	+	1.90730i	1.65447	+	0.162951i	0.772747	+	0.634714i	$0.218882\pi$
$138$	−1.51799	+	3.17066i	−0.129220	+	0.269905i
$139$	5.27766	+	11.1587i	0.447645	+	0.946467i	0.994048	+	0.108944i	$0.0347469\pi$
$139$	5.27766	+	11.1587i	0.447645	+	0.946467i	−0.546402	+	0.837523i	$0.684003\pi$
$140$	−1.05396	+	4.04503i	−0.0890759	+	0.341868i
$141$	6.44827	+	10.7583i	0.543042	+	0.906011i
$142$	1.14129	−	0.221415i	0.0957750	−	0.0185807i
$143$	−3.43735	+	5.14436i	−0.287446	+	0.430193i
$144$	−1.08857	−	3.84903i	−0.0907144	−	0.320752i
$145$	0.841772	+	1.25980i	0.0699053	+	0.104621i
$146$	1.53790	−	1.52343i	0.127277	−	0.126080i
$147$	9.37599	+	6.95371i	0.773319	+	0.573532i
$148$	0.0506728	+	1.27782i	0.00416528	+	0.105036i
$149$	0.0850020	+	1.73025i	0.00696363	+	0.141748i	0.999760	+	0.0219300i	$0.00698110\pi$
$149$	0.0850020	+	1.73025i	0.00696363	+	0.141748i	−0.992796	+	0.119818i	$0.961769\pi$
$150$	1.66863	−	6.53043i	0.136243	−	0.533207i
$151$	−1.00181	−	3.30252i	−0.0815260	−	0.268755i	0.906695	−	0.421786i	$-0.138597\pi$
$151$	−1.00181	−	3.30252i	−0.0815260	−	0.268755i	−0.988221	+	0.153031i	$0.951097\pi$
$152$	1.87375	−	5.01160i	0.151981	−	0.406495i
$153$	−2.68521	−	5.02368i	−0.217086	−	0.406140i
$154$	16.0008	+	2.45083i	1.28938	+	0.197494i
$155$	2.61134	−	1.93670i	0.209748	−	0.155560i
$156$	0.501817	−	4.64454i	0.0401775	−	0.371861i
$157$	−0.898624	−	2.51149i	−0.0717180	−	0.200438i	0.900336	−	0.435195i	$-0.143321\pi$
$157$	−0.898624	−	2.51149i	−0.0717180	−	0.200438i	−0.972054	+	0.234757i	$0.924571\pi$
$158$	1.26901	−	0.378410i	0.100957	−	0.0301047i
$159$	6.25182	−	2.58959i	0.495802	−	0.205368i
$160$	−1.78899	−	2.07012i	−0.141432	−	0.163657i
$161$	9.92369	+	4.11053i	0.782096	+	0.323955i
$162$	−1.40673	−	0.145267i	−0.110523	−	0.0114133i
$163$	17.6585	+	8.35183i	1.38312	+	0.654166i	0.966913	−	0.255105i	$-0.0821101\pi$
$163$	17.6585	+	8.35183i	1.38312	+	0.654166i	0.416204	+	0.909271i	$0.363360\pi$
$164$	−4.75749	−	1.49242i	−0.371497	−	0.116538i
$165$	1.26728	+	0.187983i	0.0986576	+	0.0146345i
$166$	4.13767	+	16.8561i	0.321145	+	1.30829i
$167$	−20.4442	−	6.20167i	−1.58202	−	0.479900i	−0.627640	−	0.778504i	$-0.715979\pi$
$167$	−20.4442	−	6.20167i	−1.58202	−	0.479900i	−0.954377	+	0.298604i	$0.903479\pi$
$168$	−11.5651	+	3.95401i	−0.892266	+	0.305058i
$169$	−3.55627	+	6.65332i	−0.273559	+	0.511793i
$170$	−3.11854	−	2.33579i	−0.239181	−	0.179147i
$171$	−1.40163	−	1.27036i	−0.107185	−	0.0971471i
$172$	−6.12106	+	9.99686i	−0.466727	+	0.762253i
$173$	1.55928	+	10.5118i	0.118550	+	0.799200i	0.964145	+	0.265375i	$0.0854959\pi$
$173$	1.55928	+	10.5118i	0.118550	+	0.799200i	−0.845595	+	0.533825i	$0.820754\pi$
$174$	−1.71469	+	4.08492i	−0.129991	+	0.309677i
$175$	−20.1996	−	4.01795i	−1.52695	−	0.303729i
$176$	−7.26249	+	7.71468i	−0.547431	+	0.581516i
$177$	13.4240	−	2.67020i	1.00901	−	0.200705i
$178$	3.96854	+	0.808909i	0.297455	+	0.0606303i
$179$	−15.1575	−	3.79675i	−1.13292	−	0.283782i	−0.369214	−	0.929344i	$-0.620373\pi$
$179$	−15.1575	−	3.79675i	−1.13292	−	0.283782i	−0.763708	+	0.645562i	$0.776623\pi$
$180$	−0.913827	+	0.317261i	−0.0681126	+	0.0236473i
$181$	3.84377	−	10.7426i	0.285705	−	0.798493i	−0.709853	−	0.704350i	$-0.751239\pi$
$181$	3.84377	−	10.7426i	0.285705	−	0.798493i	0.995559	−	0.0941435i	$-0.0300113\pi$
$182$	−14.2537	−	0.767784i	−1.05655	−	0.0569119i
$183$	−7.71425	+	6.33092i	−0.570254	+	0.467995i
$184$	−5.90054	+	3.82273i	−0.434993	+	0.281815i
$185$	0.307772	−	0.0303129i	0.0226279	−	0.00222865i
$186$	8.93521	+	3.24479i	0.655162	+	0.237919i
$187$	−7.75701	+	12.9418i	−0.567249	+	0.946397i
$188$	−0.237114	+	25.0844i	−0.0172933	+	1.82947i
$189$	−0.212034	+	4.31604i	−0.0154232	+	0.313946i
$190$	−1.23641	−	0.381451i	−0.0896984	−	0.0276733i
$191$	11.9342	+	11.9342i	0.863531	+	0.863531i	0.991746	−	0.128216i	$-0.0409250\pi$
$191$	11.9342	+	11.9342i	0.863531	+	0.863531i	−0.128216	+	0.991746i	$0.540925\pi$
$192$	2.16309	−	7.70202i	0.156107	−	0.555845i
$193$	−1.14705	+	1.14705i	−0.0825667	+	0.0825667i	−0.747184	−	0.664617i	$-0.768595\pi$
$193$	−1.14705	+	1.14705i	−0.0825667	+	0.0825667i	0.664617	+	0.747184i	$0.268595\pi$
$194$	−1.27848	+	0.675610i	−0.0917892	+	0.0485060i
$195$	−1.12838	−	0.0554337i	−0.0808050	−	0.00396969i
$196$	8.73000	+	21.6527i	0.623571	+	1.54662i
$197$	18.8085	+	11.2734i	1.34005	+	0.803197i	0.990994	−	0.133903i	$-0.0427512\pi$
$197$	18.8085	+	11.2734i	1.34005	+	0.803197i	0.349059	+	0.937101i	$0.386501\pi$
$198$	1.58560	+	3.39387i	0.112684	+	0.241192i
$199$	−1.00027	−	10.1559i	−0.0709071	−	0.719932i	−0.963256	−	0.268586i	$-0.913444\pi$
$199$	−1.00027	−	10.1559i	−0.0709071	−	0.719932i	0.892349	−	0.451347i	$-0.149056\pi$
$200$	9.66632	−	9.39603i	0.683512	−	0.664399i
$201$	−4.88017	−	5.94650i	−0.344221	−	0.419434i
$202$	−6.18646	+	5.55405i	−0.435277	+	0.390781i
$203$	12.7456	+	4.56044i	0.894563	+	0.320080i
$204$	0.666538	−	11.3731i	0.0466670	−	0.796273i
$205$	−0.292986	+	1.16966i	−0.0204630	+	0.0816929i
$206$	−14.8163	−	22.4026i	−1.03230	−	1.56086i
$207$	0.484936	+	2.43794i	0.0337054	+	0.169448i
$208$	5.70657	−	7.39792i	0.395679	−	0.512954i
$209$	−0.977534	+	4.91440i	−0.0676174	+	0.339936i
$210$	1.11820	+	2.73609i	0.0771635	+	0.188808i
$211$	−24.9515	+	3.70121i	−1.71773	+	0.254802i	−0.931660	−	0.363331i	$-0.881640\pi$
$211$	−24.9515	+	3.70121i	−1.71773	+	0.254802i	−0.786074	+	0.618132i	$0.787890\pi$
$212$	13.3680	+	2.11228i	0.918118	+	0.145072i
$213$	0.552063	−	0.609107i	0.0378267	−	0.0417353i
$214$	−1.00230	−	6.98422i	−0.0685158	−	0.477431i
$215$	2.50004	+	1.33630i	0.170501	+	0.0911348i
$216$	−2.24770	−	1.71693i	−0.152936	−	0.116822i
$217$	8.43184	−	27.7961i	0.572391	−	1.88692i
$218$	1.82561	+	1.10599i	0.123646	+	0.0749073i
$219$	0.224598	−	1.51411i	0.0151769	−	0.102314i
$220$	1.96523	+	1.64415i	0.132495	+	0.110849i
$221$	5.68875	−	12.0278i	0.382667	−	0.809080i
$222$	0.570348	+	0.701708i	0.0382792	+	0.0470955i
$223$	8.02164	−	19.3660i	0.537169	−	1.29684i	−0.389522	−	0.921017i	$-0.627360\pi$
$223$	8.02164	−	19.3660i	0.537169	−	1.29684i	0.926691	−	0.375824i	$-0.122640\pi$
$224$	−23.8556	−	5.33409i	−1.59392	−	0.356399i
$225$	−1.82389	−	4.40327i	−0.121593	−	0.293551i
$226$	7.60982	−	14.0765i	0.506197	−	0.936357i
$227$	−6.68823	+	2.39309i	−0.443913	+	0.158835i	−0.549352	−	0.835591i	$-0.685125\pi$
$227$	−6.68823	+	2.39309i	−0.443913	+	0.158835i	0.105439	+	0.994426i	$0.466375\pi$
$228$	−1.06397	−	3.63064i	−0.0704632	−	0.240445i
$229$	5.22930	+	7.05090i	0.345562	+	0.465937i	0.941461	−	0.337123i	$-0.109454\pi$
$229$	5.22930	+	7.05090i	0.345562	+	0.465937i	−0.595898	+	0.803060i	$0.703204\pi$
$230$	1.00636	+	1.37042i	0.0663577	+	0.0903625i
$231$	10.0947	−	5.39571i	0.664180	−	0.355011i
$232$	−7.19087	+	5.17671i	−0.472104	+	0.339868i
$233$	−5.70173	+	1.72960i	−0.373532	+	0.113310i	−0.471469	−	0.881883i	$-0.656276\pi$
$233$	−5.70173	+	1.72960i	−0.373532	+	0.113310i	0.0979361	+	0.995193i	$0.468776\pi$
$234$	−1.68482	−	2.84133i	−0.110140	−	0.185743i
$235$	6.05921	−	0.297670i	0.395259	−	0.0194178i
$236$	25.6855	+	9.46524i	1.67199	+	0.616135i
$237$	0.557796	−	0.752101i	0.0362328	−	0.0488542i
$238$	−34.8106	−	0.164523i	−2.25643	−	0.0106644i
$239$	−7.13102	+	4.76480i	−0.461268	+	0.308209i	−0.764403	−	0.644738i	$-0.776966\pi$
$239$	−7.13102	+	4.76480i	−0.461268	+	0.308209i	0.303136	+	0.952947i	$0.401966\pi$
$240$	−1.89002	−	0.413237i	−0.122000	−	0.0266743i
$241$	−18.7721	−	12.5431i	−1.20921	−	0.807971i	−0.223223	−	0.974767i	$-0.571658\pi$
$241$	−18.7721	−	12.5431i	−1.20921	−	0.807971i	−0.985991	+	0.166796i	$0.946658\pi$
$242$	−3.15212	+	4.66955i	−0.202626	+	0.300170i
$243$	−0.857729	+	0.514103i	−0.0550233	+	0.0329797i
$244$	−19.7698	+	2.74185i	−1.26563	+	0.175529i
$245$	5.10386	−	2.41395i	0.326074	−	0.154221i
$246$	−3.32517	+	1.17207i	−0.212005	+	0.0747283i
$247$	0.433090	−	4.39724i	0.0275569	−	0.279790i
$248$	11.8517	+	14.8662i	0.752582	+	0.944006i
$249$	9.48707	+	7.78584i	0.601219	+	0.493408i
$250$	−4.92835	−	4.50940i	−0.311696	−	0.285200i
$251$	−0.455928	−	1.82016i	−0.0287779	−	0.114888i	0.953940	−	0.299998i	$-0.0969859\pi$
$251$	−0.455928	−	1.82016i	−0.0287779	−	0.114888i	−0.982718	+	0.185110i	$0.940736\pi$
$252$	−4.86922	+	7.14027i	−0.306732	+	0.449795i
$253$	4.87855	−	4.42166i	0.306712	−	0.277987i
$254$	−1.52334	−	16.2539i	−0.0955830	−	1.01986i
$255$	−2.75510			−0.172531
$256$	11.7333	−	10.8780i	0.733330	−	0.679872i
$257$	6.39172			0.398705			0.199352	−	0.979928i	$-0.436116\pi$
$257$	6.39172			0.398705			0.199352	+	0.979928i	$0.436116\pi$
$258$	0.773439	+	8.25252i	0.0481522	+	0.513779i
$259$	2.04728	−	1.85555i	0.127212	−	0.115298i
$260$	−1.86674	−	1.27300i	−0.115770	−	0.0789483i
$261$	0.761167	+	3.03875i	0.0471151	+	0.188094i
$262$	6.83666	+	6.25550i	0.422370	+	0.386466i
$263$	13.1623	+	10.8020i	0.811622	+	0.666081i	0.945754	−	0.324883i	$-0.105325\pi$
$263$	13.1623	+	10.8020i	0.811622	+	0.666081i	−0.134132	+	0.990963i	$0.542825\pi$
$264$	−0.839981	+	7.44476i	−0.0516972	+	0.458193i
$265$	0.320804	−	3.25717i	0.0197068	−	0.200087i
$266$	−10.9028	+	3.84305i	−0.668493	+	0.235633i
$267$	2.58892	−	1.22447i	0.158439	−	0.0749362i
$268$	−2.11354	−	15.2394i	−0.129105	−	0.930897i
$269$	−14.2331	+	8.53098i	−0.867806	+	0.520143i	−0.877372	−	0.479811i	$-0.840705\pi$
$269$	−14.2331	+	8.53098i	−0.867806	+	0.520143i	0.00956554	+	0.999954i	$0.496955\pi$
$270$	−0.382698	+	0.566929i	−0.0232903	+	0.0345022i
$271$	−23.8199	−	15.9160i	−1.44696	−	0.966826i	−0.997285	−	0.0736330i	$-0.976541\pi$
$271$	−23.8199	−	15.9160i	−1.44696	−	0.966826i	−0.449673	−	0.893193i	$-0.648459\pi$
$272$	13.0146	−	18.7025i	0.789127	−	1.13400i
$273$	−8.39244	+	5.60765i	−0.507934	+	0.339390i
$274$	27.5186	+	0.130059i	1.66246	+	0.00785715i
$275$	−7.52038	+	10.1401i	−0.453496	+	0.611468i
$276$	−1.71898	+	4.66475i	−0.103471	+	0.280785i
$277$	−21.6989	+	1.06600i	−1.30376	+	0.0640496i	−0.689056	−	0.724708i	$-0.741975\pi$
$277$	−21.6989	+	1.06600i	−1.30376	+	0.0640496i	−0.614704	+	0.788758i	$0.710725\pi$
$278$	8.90372	+	15.0154i	0.534010	+	0.900566i
$279$	6.43241	−	1.95125i	0.385099	−	0.116818i
$280$	−0.950223	+	5.83467i	−0.0567867	+	0.348688i
$281$	−2.15750	+	1.15321i	−0.128706	+	0.0687947i	−0.534493	−	0.845173i	$-0.679497\pi$
$281$	−2.15750	+	1.15321i	−0.128706	+	0.0687947i	0.405787	+	0.913968i	$0.366997\pi$
$282$	10.4991	+	14.2972i	0.625215	+	0.851385i
$283$	−15.3127	−	20.6468i	−0.910245	−	1.22732i	−0.973352	−	0.229317i	$-0.926351\pi$
$283$	−15.3127	−	20.6468i	−0.910245	−	1.22732i	0.0631068	−	0.998007i	$-0.479899\pi$
$284$	1.57777	−	0.462371i	0.0936233	−	0.0274367i
$285$	−0.861451	+	0.308232i	−0.0510279	+	0.0182581i
$286$	−4.16107	+	7.69709i	−0.246049	+	0.455139i
$287$	4.12267	+	9.95300i	0.243353	+	0.587507i
$288$	−2.04069	−	5.27594i	−0.120249	−	0.310888i
$289$	5.91158	−	14.2718i	0.347740	−	0.839518i
$290$	1.35150	+	1.66277i	0.0793628	+	0.0976412i
$291$	−0.437169	+	0.924315i	−0.0256273	+	0.0541843i
$292$	1.96439	−	2.34800i	0.114957	−	0.137406i
$293$	−1.23893	+	8.35218i	−0.0723790	+	0.487940i	0.922429	+	0.386167i	$0.126201\pi$
$293$	−1.23893	+	8.35218i	−0.0723790	+	0.487940i	−0.994808	+	0.101772i	$0.967549\pi$
$294$	14.1194	+	8.55383i	0.823463	+	0.498870i
$295$	1.92167	−	6.33490i	0.111884	−	0.368832i
$296$	0.239975	+	1.79253i	0.0139483	+	0.104189i
$297$	2.33605	+	1.24865i	0.135551	+	0.0724538i
$298$	0.348018	+	2.42506i	0.0201601	+	0.140480i
$299$	−3.89911	+	4.30200i	−0.225491	+	0.248791i
$300$	1.48772	−	9.41532i	0.0858934	−	0.543594i
$301$	25.0526	−	3.71621i	1.44401	−	0.214199i
$302$	−1.84640	−	4.51789i	−0.106249	−	0.259975i
$303$	−1.14689	+	5.76580i	−0.0658871	+	0.331237i
$304$	1.97697	−	7.30382i	0.113387	−	0.418903i
$305$	0.941652	+	4.73400i	0.0539188	+	0.271068i
$306$	−4.44384	−	6.71920i	−0.254037	−	0.384111i
$307$	−7.82364	+	31.2337i	−0.446519	+	1.78260i	0.159549	+	0.987190i	$0.448996\pi$
$307$	−7.82364	+	31.2337i	−0.446519	+	1.78260i	−0.606068	+	0.795413i	$0.707254\pi$
$308$	22.8532	+	1.33935i	1.30218	+	0.0763166i
$309$	−17.8819	−	6.39824i	−1.01726	−	0.363983i
$310$	3.42130	−	3.07156i	0.194317	−	0.174453i
$311$	−16.8903	−	20.5809i	−0.957760	−	1.16703i	−0.985884	−	0.167430i	$-0.946453\pi$
$311$	−16.8903	−	20.5809i	−0.957760	−	1.16703i	0.0281235	−	0.999604i	$-0.491047\pi$
$312$	0.0936688	−	6.60593i	0.00530295	−	0.373987i
$313$	−1.15262	−	11.7028i	−0.0651500	−	0.661479i	−0.971193	−	0.238294i	$-0.923412\pi$
$313$	−1.15262	−	11.7028i	−0.0651500	−	0.661479i	0.906043	−	0.423185i	$-0.139088\pi$
$314$	−1.59673	−	3.41769i	−0.0901085	−	0.192872i
$315$	1.79269	+	1.07450i	0.101007	+	0.0605411i
$316$	1.73689	−	0.700282i	0.0977075	−	0.0393939i
$317$	8.45550	+	0.415392i	0.474908	+	0.0233307i	0.285115	−	0.958493i	$-0.407968\pi$
$317$	8.45550	+	0.415392i	0.474908	+	0.0233307i	0.189793	+	0.981824i	$0.439218\pi$
$318$	8.46110	−	4.47127i	0.474475	−	0.250736i
$319$	5.86741	−	5.86741i	0.328512	−	0.328512i
$320$	−2.79216	−	2.67873i	−0.156086	−	0.149746i
$321$	−3.52789	−	3.52789i	−0.196907	−	0.196907i
$322$	14.5154	+	4.47823i	0.808913	+	0.249562i
$323$	0.528726	−	10.7625i	0.0294191	−	0.598840i
$324$	−1.99991	−	0.0189045i	−0.111106	−	0.00105025i
$325$	5.72325	−	9.54866i	0.317469	−	0.529665i
$326$	25.9660	+	9.42946i	1.43812	+	0.522249i
$327$	1.50205	−	0.147939i	0.0830636	−	0.00818105i
$328$	−6.89569	−	1.47357i	−0.380751	−	0.0813644i
$329$	41.8975	−	34.3844i	2.30988	−	1.89567i
$330$	1.80919	+	0.0974532i	0.0995927	+	0.00536462i
$331$	10.7190	−	29.9577i	0.589171	−	1.64662i	−0.162213	−	0.986756i	$-0.551863\pi$
$331$	10.7190	−	29.9577i	0.589171	−	1.64662i	0.751383	−	0.659866i	$-0.229387\pi$
$332$	8.05041	+	23.1881i	0.441823	+	1.27261i
$333$	0.620248	+	0.155364i	0.0339894	+	0.00851389i
$334$	−29.6047	−	6.03432i	−1.61989	−	0.330183i
$335$	−3.64919	+	0.725869i	−0.199376	+	0.0396584i
$336$	−15.7624	+	7.09359i	−0.859907	+	0.386987i
$337$	−17.7744	−	3.53555i	−0.968235	−	0.192594i	−0.314450	−	0.949274i	$-0.601820\pi$
$337$	−17.7744	−	3.53555i	−0.968235	−	0.192594i	−0.653785	+	0.756680i	$0.726820\pi$
$338$	−4.12939	+	9.83745i	−0.224609	+	0.535087i
$339$	−1.66025	−	11.1925i	−0.0901726	−	0.607895i
$340$	−4.69928	−	2.87736i	−0.254854	−	0.156047i
$341$	−13.1926	−	11.9571i	−0.714421	−	0.647513i
$342$	−2.14120	−	1.60376i	−0.115783	−	0.0867215i
$343$	9.51939	−	17.8095i	0.513999	−	0.961624i
$344$	−7.29950	+	14.8838i	−0.393562	+	0.802479i
$345$	1.15048	+	0.348995i	0.0619398	+	0.0187892i
$346$	3.58272	+	14.5954i	0.192608	+	0.784651i
$347$	25.3806	+	3.76485i	1.36250	+	0.202108i	0.787636	−	0.616141i	$-0.211305\pi$
$347$	25.3806	+	3.76485i	1.36250	+	0.202108i	0.574864	+	0.818249i	$0.305055\pi$
$348$	−1.87530	+	5.97802i	−0.100527	+	0.320456i
$349$	17.7863	+	8.41229i	0.952079	+	0.450300i	0.839510	−	0.543344i	$-0.182842\pi$
$349$	17.7863	+	8.41229i	0.952079	+	0.450300i	0.112569	+	0.993644i	$0.464092\pi$
$350$	−28.9722	−	2.99183i	−1.54863	−	0.159920i
$351$	−2.15798	−	0.893866i	−0.115185	−	0.0477110i
$352$	−9.20784	+	11.8210i	−0.490779	+	0.630061i
$353$	−13.8968	+	5.75625i	−0.739653	+	0.306374i	−0.720512	−	0.693442i	$-0.756093\pi$
$353$	−13.8968	+	5.75625i	−0.739653	+	0.306374i	−0.0191411	+	0.999817i	$0.506093\pi$
$354$	18.5492	−	5.53125i	0.985881	−	0.293983i
$355$	−0.133949	−	0.374361i	−0.00710925	−	0.0198690i
$356$	5.69463	+	0.615274i	0.301815	+	0.0326095i
$357$	−19.7710	+	14.6632i	−1.04639	+	0.776058i
$358$	−21.8434	−	3.34574i	−1.15446	−	0.176828i
$359$	−6.31356	−	11.8118i	−0.333217	−	0.623405i	0.658393	−	0.752675i	$-0.271237\pi$
$359$	−6.31356	−	11.8118i	−0.333217	−	0.623405i	−0.991609	+	0.129270i	$0.958737\pi$
$360$	−1.24484	+	0.567310i	−0.0656088	+	0.0298998i
$361$	4.47666	+	14.7576i	0.235614	+	0.776714i
$362$	3.99456	−	15.6333i	0.209949	−	0.821669i
$363$	0.195473	+	3.97895i	0.0102597	+	0.208841i
$364$	−20.1711	+	0.799903i	−1.05726	+	0.0419263i
$365$	−0.594646	−	0.441020i	−0.0311252	−	0.0230840i
$366$	−10.0265	+	9.93222i	−0.524096	+	0.519165i
$367$	17.6606	+	26.4309i	0.921875	+	1.37968i	0.925115	+	0.379688i	$0.123969\pi$
$367$	17.6606	+	26.4309i	0.921875	+	1.37968i	−0.00324010	+	0.999995i	$0.501031\pi$
$368$	−7.80375	+	6.16122i	−0.406799	+	0.321176i
$369$	−1.38506	+	2.07289i	−0.0721033	+	0.107910i
$370$	0.429356	−	0.0832967i	0.0223212	−	0.00433039i
$371$	−15.0332	−	25.0813i	−0.780483	−	1.30216i
$372$	13.0094	+	3.38967i	0.674504	+	0.175746i
$373$	11.1358	+	23.5447i	0.576591	+	1.21910i	0.955863	+	0.293814i	$0.0949247\pi$
$373$	11.1358	+	23.5447i	0.576591	+	1.21910i	−0.379271	+	0.925286i	$0.623825\pi$
$374$	−9.21435	+	19.2462i	−0.476463	+	0.995200i
$375$	−4.70078	−	0.462986i	−0.242747	−	0.0239085i
$376$	2.97637	+	35.3512i	0.153495	+	1.82310i
$377$	−4.64195	+	5.65623i	−0.239073	+	0.291311i
$378$	0.271010	+	6.10516i	0.0139392	+	0.314015i
$379$	12.1118	−	3.03385i	0.622141	−	0.155838i	0.0809227	−	0.996720i	$-0.474213\pi$
$379$	12.1118	−	3.03385i	0.622141	−	0.155838i	0.541218	+	0.840882i	$0.317963\pi$
$380$	−1.79125	−	0.373938i	−0.0918893	−	0.0191826i
$381$	−7.75223	−	8.55326i	−0.397159	−	0.438197i
$382$	18.3788	+	15.2290i	0.940341	+	0.779185i
$383$		−	36.4136i		−	1.86065i	−0.366736	−	0.930325i	$-0.619525\pi$
$383$		−	36.4136i		−	1.86065i	0.366736	−	0.930325i	$-0.380475\pi$
$384$	2.02933	−	11.1302i	0.103559	−	0.567987i
$385$		−	5.53615i		−	0.282148i
$386$	−1.46373	+	1.76647i	−0.0745019	+	0.0899110i
$387$	3.93600	+	4.34270i	0.200078	+	0.220752i
$388$	−1.71099	+	1.12000i	−0.0868625	+	0.0568595i
$389$	−27.5512	+	6.90121i	−1.39690	+	0.349905i	−0.867065	−	0.498196i	$-0.833996\pi$
$389$	−27.5512	+	6.90121i	−1.39690	+	0.349905i	−0.529835	+	0.848101i	$0.677746\pi$
$390$	−1.59612	+	0.0708524i	−0.0808228	+	0.00358775i
$391$	−8.98254	+	10.9453i	−0.454266	+	0.553525i
$392$	15.1496	+	29.3359i	0.765170	+	1.48169i
$393$	6.52097	+	0.642260i	0.328940	+	0.0323977i
$394$	27.9709	+	13.3914i	1.40916	+	0.674649i
$395$	−0.193636	−	0.409409i	−0.00974290	−	0.0205996i
$396$	2.68046	+	4.56948i	0.134698	+	0.229625i
$397$	10.9374	+	18.2480i	0.548932	+	0.915839i	0.999731	+	0.0232126i	$0.00738945\pi$
$397$	10.9374	+	18.2480i	0.548932	+	0.915839i	−0.450798	+	0.892626i	$0.648861\pi$
$398$	−2.74863	−	14.1679i	−0.137777	−	0.710174i
$399$	−4.54142	+	6.79672i	−0.227355	+	0.340261i
$400$	12.3707	−	14.5056i	0.618533	−	0.725281i
$401$	12.5689	+	18.8108i	0.627663	+	0.939365i	0.999937	+	0.0112415i	$0.00357834\pi$
$401$	12.5689	+	18.8108i	0.627663	+	0.939365i	−0.372274	+	0.928123i	$0.621422\pi$
$402$	−7.65621	−	7.72893i	−0.381857	−	0.385484i
$403$	12.6110	+	9.35296i	0.628199	+	0.465904i
$404$	−7.97786	+	8.63673i	−0.396913	+	0.429693i
$405$	0.0237324	+	0.483084i	0.00117927	+	0.0240046i
$406$	18.5481	+	4.73933i	0.920528	+	0.235209i
$407$	−0.491650	−	1.62075i	−0.0243702	−	0.0803377i
$408$	−0.562321	−	16.1017i	−0.0278390	−	0.797154i
$409$	−18.1586	−	33.9724i	−0.897885	−	1.67982i	−0.717889	−	0.696157i	$-0.754892\pi$
$409$	−18.1586	−	33.9724i	−0.897885	−	1.67982i	−0.179996	−	0.983667i	$-0.557608\pi$
$410$	−0.258183	+	1.68560i	−0.0127507	+	0.0832459i
$411$	15.6295	−	11.5916i	0.770945	−	0.571772i
$412$	−23.8183	−	29.5886i	−1.17344	−	1.45773i
$413$	−19.9253	−	55.6876i	−0.980462	−	2.74021i
$414$	1.00453	+	3.36873i	0.0493700	+	0.165564i
$415$	5.48414	−	2.27160i	0.269206	−	0.111509i
$416$	7.05883	−	11.1697i	0.346088	−	0.547637i
$417$	11.4042	+	4.72377i	0.558466	+	0.231324i
$418$	−0.727887	+	7.04868i	−0.0356021	+	0.344762i
$419$	−20.3329	−	9.61676i	−0.993329	−	0.469810i	−0.139421	−	0.990233i	$-0.544524\pi$
$419$	−20.3329	−	9.61676i	−0.993329	−	0.469810i	−0.853908	+	0.520424i	$0.825774\pi$
$420$	1.93555	+	3.70497i	0.0944450	+	0.180784i
$421$	−29.0841	−	4.31422i	−1.41747	−	0.210262i	−0.606378	−	0.795177i	$-0.707378\pi$
$421$	−29.0841	−	4.31422i	−1.41747	−	0.210262i	−0.811095	+	0.584915i	$0.801128\pi$
$422$	−34.6444	+	8.50417i	−1.68646	+	0.413976i
$423$	12.0027	+	3.64097i	0.583590	+	0.177030i
$424$	19.1015	+	1.21009i	0.927649	+	0.0587670i
$425$	12.7979	−	23.9432i	0.620789	−	1.16141i
$426$	0.696948	−	0.930502i	0.0337672	−	0.0450829i
$427$	31.9527	+	28.9602i	1.54630	+	1.40148i
$428$	−2.33295	−	9.70181i	−0.112767	−	0.468955i
$429$	0.907832	+	6.12011i	0.0438305	+	0.295482i
$430$	3.69650	+	1.55165i	0.178261	+	0.0748272i
$431$	17.5064	+	3.48223i	0.843252	+	0.167733i	0.597770	−	0.801668i	$-0.296054\pi$
$431$	17.5064	+	3.48223i	0.843252	+	0.167733i	0.245482	+	0.969401i	$0.421054\pi$
$432$	−3.39143	−	2.12090i	−0.163170	−	0.102042i
$433$	−21.4302	+	4.26273i	−1.02987	+	0.204854i	−0.680974	−	0.732308i	$-0.738443\pi$
$433$	−21.4302	+	4.26273i	−1.02987	+	0.204854i	−0.348896	+	0.937162i	$0.613443\pi$
$434$	8.20432	−	40.2508i	0.393820	−	1.93210i
$435$	1.46974	+	0.368151i	0.0704687	+	0.0176515i
$436$	2.71649	+	1.31637i	0.130097	+	0.0630427i
$437$	−1.58409	+	4.42724i	−0.0757773	+	0.211783i
$438$	0.116435	−	2.16158i	0.00556346	−	0.103284i
$439$	11.4803	−	9.42160i	0.547923	−	0.449668i	−0.319254	−	0.947669i	$-0.603432\pi$
$439$	11.4803	−	9.42160i	0.547923	−	0.449668i	0.867177	+	0.498001i	$0.165932\pi$
$440$	2.98409	+	2.05570i	0.142261	+	0.0980014i
$441$	11.6170	−	1.14417i	0.553189	−	0.0544844i
$442$	6.42276	−	17.6864i	0.305499	−	0.841258i
$443$	5.13966	−	8.57501i	0.244193	−	0.407411i	−0.711092	−	0.703099i	$-0.751799\pi$
$443$	5.13966	−	8.57501i	0.244193	−	0.407411i	0.955284	+	0.295688i	$0.0955490\pi$
$444$	0.895674	+	0.912769i	0.0425068	+	0.0433181i
$445$	0.0679668	−	1.38350i	0.00322194	−	0.0655840i
$446$	8.73921	−	28.3267i	0.413814	−	1.34131i
$447$	1.22495	+	1.22495i	0.0579382	+	0.0579382i
$448$	−34.2936	−	4.36254i	−1.62022	−	0.206111i
$449$	12.5437	−	12.5437i	0.591972	−	0.591972i	−0.346192	−	0.938164i	$-0.612525\pi$
$449$	12.5437	−	12.5437i	0.591972	−	0.591972i	0.938164	+	0.346192i	$0.112525\pi$
$450$	−3.14920	−	5.95931i	−0.148455	−	0.280924i
$451$	6.59566	+	0.324024i	0.310578	+	0.0152577i
$452$	8.85735	−	20.8246i	0.416615	−	0.979506i
$453$	−2.96013	−	1.77423i	−0.139079	−	0.0833607i
$454$	−9.10151	+	4.25217i	−0.427155	+	0.199564i
$455$	0.478509	+	4.85838i	0.0224328	+	0.227764i
$456$	−1.97723	−	4.97169i	−0.0925923	−	0.232820i
$457$	8.36785	+	10.1963i	0.391432	+	0.476961i	0.931020	−	0.364968i	$-0.118920\pi$
$457$	8.36785	+	10.1963i	0.391432	+	0.476961i	−0.539588	+	0.841929i	$0.681420\pi$
$458$	8.29355	+	9.23789i	0.387532	+	0.431658i
$459$	−5.36331	−	1.91902i	−0.250338	−	0.0895723i
$460$	1.59785	+	1.79680i	0.0745002	+	0.0837762i
$461$	−0.924840	+	3.69217i	−0.0430741	+	0.171961i	−0.987750	−	0.156043i	$-0.950126\pi$
$461$	−0.924840	+	3.69217i	−0.0430741	+	0.171961i	0.944676	+	0.328004i	$0.106376\pi$
$462$	13.5017	−	8.92952i	0.628155	−	0.415439i
$463$	−1.31215	−	6.59663i	−0.0609809	−	0.306571i	0.938242	−	0.345979i	$-0.112453\pi$
$463$	−1.31215	−	6.59663i	−0.0609809	−	0.306571i	−0.999223	+	0.0394072i	$0.987453\pi$
$464$	−9.44192	+	8.23797i	−0.438330	+	0.382438i
$465$	0.634265	−	3.18867i	0.0294134	−	0.147871i
$466$	−7.80003	+	3.18777i	−0.361329	+	0.147671i
$467$	−26.4029	+	3.91649i	−1.22178	+	0.181234i	−0.726295	−	0.687383i	$-0.758759\pi$
$467$	−26.4029	+	3.91649i	−1.22178	+	0.181234i	−0.495484	+	0.868617i	$0.665009\pi$
$468$	−2.74726	−	3.77837i	−0.126992	−	0.174655i
$469$	−22.3239	+	24.6306i	−1.03082	+	1.13734i
$470$	8.49235	−	1.21873i	0.391723	−	0.0562158i
$471$	−2.35245	−	1.25741i	−0.108395	−	0.0579383i
$472$	37.4154	+	9.93790i	1.72218	+	0.457429i
$473$	4.50658	−	14.8562i	0.207213	−	0.683089i
$474$	0.686151	−	1.13260i	0.0315159	−	0.0520220i
$475$	1.32289	−	8.91821i	0.0606984	−	0.409195i
$476$	−49.0365	+	4.36209i	−2.24758	+	0.199936i
$477$	2.89323	−	6.11723i	0.132472	−	0.280089i
$478$	−9.41201	+	7.65008i	−0.430495	+	0.349907i
$479$	−4.13223	+	9.97609i	−0.188806	+	0.455819i	−0.989730	−	0.142947i	$-0.954342\pi$
$479$	−4.13223	+	9.97609i	−0.188806	+	0.455819i	0.800924	+	0.598766i	$0.204342\pi$
$480$	−2.71576	−	0.332441i	−0.123957	−	0.0151738i
$481$	0.571547	+	1.37984i	0.0260603	+	0.0629151i
$482$	−28.0871	−	15.1840i	−1.27933	−	0.691611i
$483$	10.1134	−	3.61864i	0.460177	−	0.164654i
$484$	−3.82210	+	6.99089i	−0.173732	+	0.317768i
$485$	0.294598	+	0.397220i	0.0133770	+	0.0180368i
$486$	−1.13988	+	0.837068i	−0.0517058	+	0.0379702i
$487$	11.9252	−	6.37414i	0.540381	−	0.288840i	−0.178538	−	0.983933i	$-0.557137\pi$
$487$	11.9252	−	6.37414i	0.540381	−	0.288840i	0.718920	+	0.695093i	$0.244637\pi$
$488$	−27.4749	+	6.46953i	−1.24373	+	0.292862i
$489$	18.6928	−	5.67040i	0.845318	−	0.256424i
$490$	6.86790	−	4.07247i	0.310260	−	0.183975i
$491$	26.7725	−	1.31525i	1.20823	−	0.0593564i	0.565039	−	0.825064i	$-0.308861\pi$
$491$	26.7725	−	1.31525i	1.20823	−	0.0593564i	0.643189	+	0.765708i	$0.277611\pi$
$492$	−4.52731	+	2.08912i	−0.204107	+	0.0941850i
$493$	−10.6299	+	14.3327i	−0.478745	+	0.645514i
$494$	0.0295325	−	6.24865i	0.00132873	−	0.281140i
$495$	1.06523	−	0.711767i	0.0478787	−	0.0319915i
$496$	18.6495	+	19.3683i	0.837386	+	0.869661i
$497$	−2.95366	−	1.97357i	−0.132490	−	0.0885267i
$498$	14.3857	+	9.71085i	0.644637	+	0.435153i
$499$	17.3636	−	10.4074i	0.777303	−	0.465898i	−0.0696458	−	0.997572i	$-0.522187\pi$
$499$	17.3636	−	10.4074i	0.777303	−	0.465898i	0.846949	+	0.531674i	$0.178437\pi$
$500$	−7.53440	−	5.69907i	−0.336949	−	0.254870i
$501$	−19.3129	+	9.13433i	−0.862837	+	0.408092i
$502$	−0.882162	−	2.50270i	−0.0393728	−	0.111701i
$503$	1.00737	−	10.2280i	0.0449166	−	0.456046i	−0.946251	−	0.323433i	$-0.895163\pi$
$503$	1.00737	−	10.2280i	0.0449166	−	0.456046i	0.991168	−	0.132613i	$-0.0423369\pi$
$504$	−5.91382	+	10.6964i	−0.263422	+	0.476454i
$505$	2.19795	+	1.80381i	0.0978074	+	0.0802684i
$506$	6.28571	−	6.86968i	0.279434	−	0.305394i
$507$	1.83307	+	7.31803i	0.0814095	+	0.325005i
$508$	−4.28987	−	22.6852i	−0.190332	−	1.00649i
$509$	−20.8812	+	18.9256i	−0.925541	+	0.838861i	−0.987241	−	0.159233i	$-0.949098\pi$
$509$	−20.8812	+	18.9256i	−0.925541	+	0.838861i	0.0617002	+	0.998095i	$0.480348\pi$
$510$	−3.87931	+	0.363575i	−0.171779	+	0.0160994i
$511$	−6.61446			−0.292606
$512$	15.0855	−	16.8650i	0.666690	−	0.745335i
$513$	−1.89166			−0.0835189
$514$	8.99982	−	0.843477i	0.396965	−	0.0372042i
$515$	−6.80625	+	6.16883i	−0.299919	+	0.271831i
$516$	2.17807	+	11.5178i	0.0958842	+	0.507045i
$517$	−8.07266	−	32.2279i	−0.355035	−	1.41738i
$518$	2.63780	−	2.88286i	0.115898	−	0.126666i
$519$	8.21467	+	6.74161i	0.360584	+	0.295924i
$520$	−2.79644	−	1.54610i	−0.122632	−	0.0678010i
$521$	0.997077	−	10.1235i	0.0436827	−	0.443518i	−0.948321	−	0.317312i	$-0.897220\pi$
$521$	0.997077	−	10.1235i	0.0436827	−	0.443518i	0.992004	−	0.126206i	$-0.0402802\pi$
$522$	1.47276	+	4.17824i	0.0644610	+	0.182877i
$523$	30.3039	−	14.3327i	1.32509	−	0.626723i	0.371673	−	0.928364i	$-0.378784\pi$
$523$	30.3039	−	14.3327i	1.32509	−	0.626723i	0.953422	+	0.301640i	$0.0975342\pi$
$524$	10.4518	+	7.90581i	0.456590	+	0.345367i
$525$	−17.6652	+	10.5881i	−0.770974	+	0.462104i
$526$	19.9586	+	13.4728i	0.870234	+	0.587440i
$527$	31.8367	+	21.2726i	1.38683	+	0.926648i
$528$	−0.200289	+	10.5934i	−0.00871647	+	0.461018i
$529$	−13.9864	+	9.34541i	−0.608104	+	0.406322i
$530$	0.0218757	−	4.62858i	0.000950219	−	0.201053i
$531$	8.15334	−	10.9935i	0.353825	−	0.477078i
$532$	−14.8444	+	6.84996i	−0.643588	+	0.296983i
$533$	−5.81619	+	0.285731i	−0.251927	+	0.0123764i
$534$	3.48373	−	2.06575i	0.150756	−	0.0893937i
$535$	−2.30919	+	0.700487i	−0.0998352	+	0.0302847i
$536$	−4.98702	−	21.1789i	−0.215406	−	0.914788i
$537$	−13.7807	+	7.36592i	−0.594680	+	0.317863i
$538$	−18.9150	+	13.8902i	−0.815484	+	0.598851i
$539$	−18.4191	−	24.8353i	−0.793368	−	1.06973i
$540$	−0.464041	+	0.848764i	−0.0199692	+	0.0365250i
$541$	11.4398	−	4.09322i	0.491834	−	0.175981i	−0.0792788	−	0.996852i	$-0.525262\pi$
$541$	11.4398	−	4.09322i	0.491834	−	0.175981i	0.571113	+	0.820871i	$0.306512\pi$
$542$	−35.6398	−	19.2670i	−1.53086	−	0.827589i
$543$	−4.36626	−	10.5411i	−0.187374	−	0.452361i
$544$	15.8571	−	28.0514i	0.679867	−	1.20269i
$545$	0.279362	−	0.674439i	0.0119665	−	0.0288898i
$546$	−11.0769	+	9.00331i	−0.474048	+	0.385306i
$547$	−8.49645	+	17.9642i	−0.363282	+	0.768095i	−0.999995	−	0.00300515i	$-0.999043\pi$
$547$	−8.49645	+	17.9642i	−0.363282	+	0.768095i	0.636713	+	0.771101i	$0.280293\pi$
$548$	38.7646	−	3.44834i	1.65594	−	0.147306i
$549$	−1.46430	+	9.87148i	−0.0624946	+	0.421305i
$550$	−9.25090	+	15.2701i	−0.394460	+	0.651117i
$551$	−1.72019	+	5.67071i	−0.0732826	+	0.241580i
$552$	−1.80482	+	6.79501i	−0.0768183	+	0.289215i
$553$	−3.56851	−	1.90741i	−0.151749	−	0.0811114i
$554$	−30.4123	+	4.36444i	−1.29209	+	0.185427i
$555$	0.207687	−	0.229147i	0.00881583	−	0.00972677i
$556$	14.5183	+	19.9674i	0.615714	+	0.846807i
$557$	14.4068	−	2.13705i	0.610436	−	0.0905496i	0.165647	−	0.986185i	$-0.447029\pi$
$557$	14.4068	−	2.13705i	0.610436	−	0.0905496i	0.444789	+	0.895635i	$0.353279\pi$
$558$	8.79962	−	3.59629i	0.372518	−	0.152243i
$559$	−2.67079	+	13.4269i	−0.112962	+	0.567899i
$560$	−0.567988	+	8.34086i	−0.0240019	+	0.352466i
$561$	2.94361	+	14.7985i	0.124279	+	0.624794i
$562$	−2.88568	+	1.90848i	−0.121725	+	0.0805044i
$563$	2.15694	−	8.61101i	0.0909044	−	0.362911i	−0.907456	−	0.420146i	$-0.861979\pi$
$563$	2.15694	−	8.61101i	0.0909044	−	0.362911i	0.998361	+	0.0572358i	$0.0182287\pi$
$564$	16.6700	+	18.7456i	0.701932	+	0.789330i
$565$	−5.15277	−	1.84369i	−0.216779	−	0.0775647i
$566$	−24.2856	−	27.0508i	−1.02080	−	1.13703i
$567$	2.74137	+	3.34037i	0.115127	+	0.140282i
$568$	2.16055	−	0.859247i	0.0906546	−	0.0360532i
$569$	−1.84374	−	18.7198i	−0.0772937	−	0.784776i	−0.953209	−	0.302311i	$-0.902242\pi$
$569$	−1.84374	−	18.7198i	−0.0772937	−	0.784776i	0.875916	−	0.482464i	$-0.160258\pi$
$570$	−1.17228	+	0.547684i	−0.0491016	+	0.0229400i
$571$	−0.553616	−	0.331825i	−0.0231681	−	0.0138864i	0.502472	−	0.864594i	$-0.332424\pi$
$571$	−0.553616	−	0.331825i	−0.0231681	−	0.0138864i	−0.525640	+	0.850707i	$0.676174\pi$
$572$	−4.84323	+	11.3869i	−0.202506	+	0.476112i
$573$	16.8572	+	0.828142i	0.704221	+	0.0345961i
$574$	7.11833	+	13.4702i	0.297113	+	0.562235i
$575$	−8.37710	+	8.37710i	−0.349349	+	0.349349i
$576$	−3.56961	−	7.15946i	−0.148734	−	0.298311i
$577$	23.2914	+	23.2914i	0.969635	+	0.969635i	0.999552	−	0.0299178i	$-0.00952456\pi$
$577$	23.2914	+	23.2914i	0.969635	+	0.969635i	−0.0299178	+	0.999552i	$0.509525\pi$
$578$	6.44039	−	20.8754i	0.267885	−	0.868304i
$579$	−0.0795965	+	1.62022i	−0.00330792	+	0.0673342i
$580$	2.12239	+	2.16290i	0.0881276	+	0.0898096i
$581$	27.2650	−	45.4890i	1.13114	−	1.88720i
$582$	−0.493576	+	1.35917i	−0.0204594	+	0.0563393i
$583$	−17.8381	+	1.75689i	−0.738777	+	0.0727632i
$584$	2.45609	−	3.56532i	0.101634	−	0.147534i
$585$	−0.873301	+	0.716700i	−0.0361066	+	0.0296319i
$586$	−0.642279	+	11.9237i	−0.0265323	+	0.492565i
$587$	−12.4392	+	34.7652i	−0.513421	+	1.43492i	0.353011	+	0.935619i	$0.385158\pi$
$587$	−12.4392	+	34.7652i	−0.513421	+	1.43492i	−0.866431	+	0.499296i	$0.833592\pi$
$588$	21.0096	+	10.1809i	0.866421	+	0.419853i
$589$	12.3344	+	3.08961i	0.508231	+	0.127305i
$590$	1.86982	−	9.17340i	0.0769791	−	0.377663i
$591$	21.5070	−	4.27800i	0.884679	−	0.175974i
$592$	0.574445	+	2.49229i	0.0236095	+	0.102433i
$593$	−42.5491	−	8.46354i	−1.74728	−	0.347556i	−0.784976	−	0.619526i	$-0.787325\pi$
$593$	−42.5491	−	8.46354i	−1.74728	−	0.347556i	−0.962306	+	0.271970i	$0.912325\pi$
$594$	3.45404	+	1.44987i	0.141721	+	0.0594890i
$595$	1.74690	+	11.7766i	0.0716158	+	0.482795i
$596$	0.810044	+	3.36866i	0.0331807	+	0.137986i
$597$	−7.56143	−	6.85328i	−0.309469	−	0.280486i
$598$	−4.92240	+	6.57195i	−0.201292	+	0.268747i
$599$	−9.26228	+	17.3285i	−0.378446	+	0.708024i	−0.996974	−	0.0777399i	$-0.975230\pi$
$599$	−9.26228	+	17.3285i	−0.378446	+	0.708024i	0.618527	+	0.785763i	$0.287730\pi$
$600$	0.852286	−	13.4535i	0.0347944	−	0.549237i
$601$	−5.47614	−	1.66117i	−0.223376	−	0.0677605i	0.176613	−	0.984280i	$-0.443486\pi$
$601$	−5.47614	−	1.66117i	−0.223376	−	0.0677605i	−0.399989	+	0.916520i	$0.630986\pi$
$602$	34.7848	−	8.53863i	1.41772	−	0.348009i
$603$	−7.60939	−	1.12875i	−0.309878	−	0.0459661i
$604$	−3.19601	−	6.11772i	−0.130044	−	0.248927i
$605$	1.74181	+	0.823816i	0.0708148	+	0.0334929i
$606$	−0.853991	+	8.26985i	−0.0346910	+	0.335940i
$607$	−15.5756	−	6.45162i	−0.632193	−	0.261863i	0.0434915	−	0.999054i	$-0.486152\pi$
$607$	−15.5756	−	6.45162i	−0.632193	−	0.261863i	−0.675685	+	0.737191i	$0.736152\pi$
$608$	1.81981	−	10.5450i	0.0738032	−	0.427655i
$609$	12.5064	−	5.18034i	0.506787	−	0.209918i
$610$	1.95060	+	6.54142i	0.0789777	+	0.264854i
$611$	9.86992	+	27.5846i	0.399294	+	1.11595i
$612$	−7.14381	−	8.87450i	−0.288771	−	0.358730i
$613$	−2.09882	+	1.55659i	−0.0847705	+	0.0628701i	−0.637255	−	0.770653i	$-0.719930\pi$
$613$	−2.09882	+	1.55659i	−0.0847705	+	0.0628701i	0.552484	+	0.833523i	$0.313680\pi$
$614$	−6.89430	+	45.0109i	−0.278231	+	1.81649i
$615$	0.568410	+	1.06342i	0.0229205	+	0.0428813i
$616$	32.3551	−	1.12994i	1.30362	−	0.0455264i
$617$	0.842757	+	2.77820i	0.0339281	+	0.111846i	0.972269	−	0.233866i	$-0.0751376\pi$
$617$	0.842757	+	2.77820i	0.0339281	+	0.111846i	−0.938341	+	0.345712i	$0.887638\pi$
$618$	−26.0228	−	6.64923i	−1.04679	−	0.267471i
$619$	0.276049	+	5.61912i	0.0110954	+	0.225851i	0.997939	+	0.0641726i	$0.0204408\pi$
$619$	0.276049	+	5.61912i	0.0110954	+	0.225851i	−0.986843	+	0.161679i	$0.948309\pi$
$620$	4.41201	−	4.77638i	0.177190	−	0.191824i
$621$	1.99653	+	1.48073i	0.0801181	+	0.0594196i
$622$	−26.4982	−	26.7499i	−1.06248	−	1.07257i
$623$	−6.87549	−	10.2899i	−0.275461	−	0.412256i
$624$	−0.739855	−	9.31379i	−0.0296179	−	0.372850i
$625$	11.9702	−	17.9146i	0.478806	−	0.716585i
$626$	−3.16728	−	16.3259i	−0.126590	−	0.652513i
$627$	2.57600	+	4.29780i	0.102876	+	0.171638i
$628$	−2.69927	−	4.60155i	−0.107713	−	0.183622i
$629$	1.55727	+	3.29257i	0.0620923	+	0.131283i
$630$	2.66598	+	1.27637i	0.106215	+	0.0508517i
$631$	2.06616	+	0.203499i	0.0822527	+	0.00810118i	0.139060	−	0.990284i	$-0.455592\pi$
$631$	2.06616	+	0.203499i	0.0822527	+	0.00810118i	−0.0568071	+	0.998385i	$0.518092\pi$
$632$	2.35320	−	1.21523i	0.0936052	−	0.0483394i
$633$	−16.0023	+	19.4988i	−0.636034	+	0.775009i
$634$	11.9605	−	0.530932i	0.475013	−	0.0210860i
$635$	−5.41594	+	1.35662i	−0.214925	+	0.0538360i
$636$	11.3235	−	7.41230i	0.449008	−	0.293917i
$637$	18.3108	+	20.2028i	0.725499	+	0.800464i
$638$	7.48728	−	9.03586i	0.296424	−	0.357733i
$639$		−	0.822061i		−	0.0325202i
$640$	−4.28498	−	3.40330i	−0.169379	−	0.134527i
$641$		−	20.8889i		−	0.825061i	−0.910944	−	0.412531i	$-0.864645\pi$
$641$		−	20.8889i		−	0.825061i	0.910944	−	0.412531i	$-0.135355\pi$
$642$	−5.43297	−	4.50186i	−0.214422	−	0.177674i
$643$	9.53522	+	10.5205i	0.376033	+	0.414888i	0.899336	−	0.437259i	$-0.144051\pi$
$643$	9.53522	+	10.5205i	0.376033	+	0.414888i	−0.523303	+	0.852146i	$0.675301\pi$
$644$	21.0293	+	4.39003i	0.828671	+	0.172991i
$645$	2.74981	−	0.688791i	0.108274	−	0.0271211i
$646$	−0.675789	−	15.2238i	−0.0265886	−	0.598972i
$647$	−29.6792	+	36.1642i	−1.16681	+	1.42176i	−0.279769	+	0.960067i	$0.590258\pi$
$647$	−29.6792	+	36.1642i	−1.16681	+	1.42176i	−0.887040	+	0.461693i	$0.847242\pi$
$648$	−2.81846	+	0.237298i	−0.110719	+	0.00932194i
$649$	−36.0799	−	3.55356i	−1.41626	−	0.139489i
$650$	6.79850	−	14.2002i	0.266659	−	0.556977i
$651$	−12.4191	−	26.2580i	−0.486743	−	1.02913i
$652$	37.8056	+	9.85050i	1.48058	+	0.385775i
$653$	−16.5054	−	27.5376i	−0.645905	−	1.07763i	−0.990319	−	0.138810i	$-0.955672\pi$
$653$	−16.5054	−	27.5376i	−0.645905	−	1.07763i	0.344414	−	0.938818i	$-0.388078\pi$
$654$	2.09543	−	0.406521i	0.0819378	−	0.0158962i
$655$	1.76073	−	2.63512i	0.0687976	−	0.102963i
$656$	−9.90389	−	1.16487i	−0.386682	−	0.0454805i
$657$	−0.850401	−	1.27272i	−0.0331773	−	0.0496533i
$658$	54.4560	−	53.9436i	2.12291	−	2.10294i
$659$	9.05286	+	6.71406i	0.352649	+	0.261543i	0.757493	−	0.652843i	$-0.226424\pi$
$659$	9.05286	+	6.71406i	0.352649	+	0.261543i	−0.404844	+	0.914386i	$0.632674\pi$
$660$	2.56028	−	0.101530i	0.0996588	−	0.00395205i
$661$	0.361574	+	7.36001i	0.0140636	+	0.286271i	0.995518	+	0.0945745i	$0.0301491\pi$
$661$	0.361574	+	7.36001i	0.0140636	+	0.286271i	−0.981454	+	0.191697i	$0.938601\pi$
$662$	11.1395	−	43.5962i	0.432949	−	1.69441i
$663$	−3.86232	−	12.7324i	−0.150000	−	0.494484i
$664$	14.3953	+	31.5874i	0.558646	+	1.22583i
$665$	1.86374	+	3.48681i	0.0722728	+	0.135213i
$666$	0.893838	+	0.136909i	0.0346355	+	0.00530511i
$667$	6.25440	−	4.63858i	0.242171	−	0.179606i
$668$	−42.4809	−	4.58984i	−1.64364	−	0.177586i
$669$	−7.06174	−	19.7362i	−0.273023	−	0.763047i
$670$	−5.04243	+	1.50362i	−0.194806	+	0.0580898i
$671$	24.4217	−	10.1158i	0.942790	−	0.390517i
$672$	−21.2580	+	12.0681i	−0.820045	+	0.465539i
$673$	−39.7078	−	16.4475i	−1.53062	−	0.634005i	−0.550938	−	0.834546i	$-0.685730\pi$
$673$	−39.7078	−	16.4475i	−1.53062	−	0.634005i	−0.979685	+	0.200541i	$0.935730\pi$
$674$	−25.4937	−	2.63263i	−0.981982	−	0.101405i
$675$	−4.30847	−	2.03776i	−0.165833	−	0.0784333i
$676$	−4.51616	+	14.3965i	−0.173699	+	0.553711i
$677$	13.2322	+	1.96281i	0.508554	+	0.0754369i	0.396077	−	0.918217i	$-0.370371\pi$
$677$	13.2322	+	1.96281i	0.508554	+	0.0754369i	0.112477	+	0.993654i	$0.464121\pi$
$678$	−3.81472	−	15.5405i	−0.146503	−	0.596828i
$679$	4.22816	+	1.28260i	0.162262	+	0.0492215i
$680$	−6.99649	−	3.43131i	−0.268303	−	0.131585i
$681$	−3.34855	+	6.26470i	−0.128317	+	0.240064i
$682$	−20.1537	−	15.0952i	−0.771725	−	0.578024i
$683$	−6.37532	−	5.77825i	−0.243945	−	0.221099i	0.540425	−	0.841392i	$-0.318264\pi$
$683$	−6.37532	−	5.77825i	−0.243945	−	0.221099i	−0.784370	+	0.620293i	$0.787014\pi$
$684$	−3.22654	−	1.97560i	−0.123370	−	0.0755391i
$685$	−1.38097	−	9.30971i	−0.0527640	−	0.355706i
$686$	11.0535	−	26.3328i	0.422024	−	1.00539i
$687$	8.60975	+	1.71259i	0.328483	+	0.0653393i
$688$	−8.31388	+	21.9203i	−0.316964	+	0.835702i
$689$	15.5024	−	3.08361i	0.590593	−	0.117476i
$690$	1.66598	+	0.339577i	0.0634228	+	0.0129275i
$691$	13.5542	+	3.39515i	0.515626	+	0.129158i	0.492054	−	0.870565i	$-0.336246\pi$
$691$	13.5542	+	3.39515i	0.515626	+	0.129158i	0.0235717	+	0.999722i	$0.492496\pi$
$692$	6.97069	+	20.0781i	0.264986	+	0.763255i
$693$	3.85611	−	10.7771i	0.146482	−	0.409389i
$694$	36.2338	+	1.95175i	1.37541	+	0.0740875i
$695$	4.61510	−	3.78751i	0.175061	−	0.143669i
$696$	−1.85162	+	8.66478i	−0.0701854	+	0.328438i
$697$	−14.1327	+	1.39195i	−0.535314	+	0.0527238i
$698$	26.1540	+	9.49772i	0.989944	+	0.359494i
$699$	−3.06317	+	5.11059i	−0.115860	+	0.193300i
$700$	−41.1889	−	0.389344i	−1.55679	−	0.0147158i
$701$	−1.09328	+	22.2542i	−0.0412926	+	0.840531i	0.885427	+	0.464778i	$0.153866\pi$
$701$	−1.09328	+	22.2542i	−0.0412926	+	0.840531i	−0.926720	+	0.375753i	$0.877384\pi$
$702$	−3.15649	−	0.973825i	−0.119134	−	0.0367547i
$703$	0.855279	+	0.855279i	0.0322575	+	0.0322575i
$704$	−11.4051	+	17.8596i	−0.429846	+	0.673108i
$705$	4.28967	−	4.28967i	0.161559	−	0.161559i
$706$	−18.8077	+	9.93893i	−0.707837	+	0.374057i
$707$	25.3730	+	1.24649i	0.954249	+	0.0468793i
$708$	25.3882	−	10.2361i	0.954147	−	0.384695i
$709$	29.1004	+	17.4421i	1.09289	+	0.655051i	0.942712	−	0.333608i	$-0.108266\pi$
$709$	29.1004	+	17.4421i	1.09289	+	0.655051i	0.150175	+	0.988659i	$0.452016\pi$
$710$	−0.238008	−	0.509441i	−0.00893227	−	0.0191190i
$711$	−0.0917805	−	0.931863i	−0.00344204	−	0.0349476i
$712$	8.09947	+	0.114847i	0.303541	+	0.00430406i
$713$	−10.5998	−	12.9159i	−0.396964	−	0.483702i
$714$	−25.9034	+	23.2555i	−0.969411	+	0.870314i
$715$	2.81755	+	1.00814i	0.105370	+	0.0377022i
$716$	−31.1980	−	1.82841i	−1.16592	−	0.0683309i
$717$	−2.08390	+	8.31939i	−0.0778246	+	0.310693i
$718$	−10.4485	−	15.7984i	−0.389934	−	0.589591i
$719$	6.90938	+	34.7358i	0.257676	+	1.29543i	0.865321	+	0.501217i	$0.167114\pi$
$719$	6.90938	+	34.7358i	0.257676	+	1.29543i	−0.607645	+	0.794209i	$0.707886\pi$
$720$	−1.67792	+	0.963071i	−0.0625325	+	0.0358915i
$721$	−16.0110	+	80.4925i	−0.596279	+	2.99770i
$722$	8.25079	+	20.1885i	0.307063	+	0.751339i
$723$	−22.3326	+	3.31273i	−0.830558	+	0.123202i
$724$	3.56148	−	22.5395i	0.132361	−	0.837675i
$725$	−10.0266	+	11.0626i	−0.372378	+	0.410856i
$726$	0.800313	+	5.57674i	0.0297024	+	0.206972i
$727$	−1.21295	−	0.648334i	−0.0449857	−	0.0240454i	0.448751	−	0.893657i	$-0.351869\pi$
$727$	−1.21295	−	0.648334i	−0.0449857	−	0.0240454i	−0.493736	+	0.869612i	$0.664369\pi$
$728$	−28.2963	+	3.78816i	−1.04873	+	0.140399i
$729$	−0.290285	+	0.956940i	−0.0107513	+	0.0354422i
$730$	−0.895486	−	0.542503i	−0.0331434	−	0.0200789i
$731$	−4.89872	+	33.0245i	−0.181186	+	1.22146i
$732$	−12.8071	+	15.3081i	−0.473365	+	0.565805i
$733$	−8.79079	+	18.5866i	−0.324695	+	0.686511i	−0.998633	−	0.0522781i	$-0.983352\pi$
$733$	−8.79079	+	18.5866i	−0.324695	+	0.686511i	0.673937	+	0.738789i	$0.264602\pi$
$734$	28.3548	+	34.8853i	1.04659	+	1.28764i
$735$	2.16060	−	5.21616i	0.0796951	−	0.192401i
$736$	−10.1750	+	9.70508i	−0.375054	+	0.357734i
$737$	7.79773	+	18.8254i	0.287233	+	0.693442i
$738$	−1.67668	+	3.10149i	−0.0617193	+	0.114168i
$739$	−15.1339	+	5.41499i	−0.556708	+	0.199193i	−0.600185	−	0.799861i	$-0.704907\pi$
$739$	−15.1339	+	5.41499i	−0.556708	+	0.199193i	0.0434769	+	0.999054i	$0.486157\pi$
$740$	0.593560	−	0.173945i	0.0218197	−	0.00639434i
$741$	−2.63211	−	3.54898i	−0.0966928	−	0.130375i
$742$	−24.4772	−	33.3317i	−0.898585	−	1.22365i
$743$	31.9527	−	17.0791i	1.17223	−	0.626570i	0.233883	−	0.972265i	$-0.424857\pi$
$743$	31.9527	−	17.0791i	1.17223	−	0.626570i	0.938347	+	0.345695i	$0.112357\pi$
$744$	18.7651	+	3.05604i	0.687960	+	0.112040i
$745$	0.801797	−	0.243223i	0.0293756	−	0.00891098i
$746$	18.7868	+	31.6825i	0.687833	+	1.15998i
$747$	12.2581	−	0.602202i	0.448501	−	0.0220334i
$748$	−10.4344	+	28.3155i	−0.381519	+	1.03532i
$749$	−12.8430	+	17.3168i	−0.469272	+	0.632741i
$750$	−6.67999	−	0.0315711i	−0.243919	−	0.00115281i
$751$	−10.1749	+	6.79867i	−0.371288	+	0.248087i	−0.727190	−	0.686437i	$-0.759174\pi$
$751$	−10.1749	+	6.79867i	−0.371288	+	0.248087i	0.355901	+	0.934524i	$0.384174\pi$
$752$	8.85595	+	49.3833i	0.322943	+	1.80082i
$753$	−1.56017	−	1.04247i	−0.0568557	−	0.0379898i
$754$	−5.78965	+	8.57679i	−0.210846	+	0.312348i
$755$	−1.43172	+	0.858137i	−0.0521055	+	0.0312308i
$756$	1.18725	+	8.56056i	0.0431800	+	0.311345i
$757$	−27.8567	+	13.1752i	−1.01247	+	0.478862i	−0.860461	−	0.509517i	$-0.829824\pi$
$757$	−27.8567	+	13.1752i	−1.01247	+	0.478862i	−0.152009	+	0.988379i	$0.548574\pi$
$758$	16.6536	−	5.87011i	0.604885	−	0.213212i
$759$	0.645362	−	6.55247i	0.0234251	−	0.237839i
$760$	−2.57151	−	0.290139i	−0.0932784	−	0.0105245i
$761$	−22.3999	−	18.3831i	−0.811996	−	0.666388i	0.133851	−	0.991002i	$-0.457266\pi$
$761$	−22.3999	−	18.3831i	−0.811996	−	0.666388i	−0.945847	+	0.324613i	$0.894766\pi$
$762$	−12.0442	−	11.0203i	−0.436315	−	0.399225i
$763$	−1.58475	−	6.32668i	−0.0573718	−	0.229041i
$764$	27.8878	+	19.0178i	1.00895	+	0.688039i
$765$	−2.04140	+	1.85022i	−0.0738069	+	0.0668947i
$766$	−4.80529	−	51.2720i	−0.173622	−	1.85253i
$767$	31.9699			1.15437
$768$	1.38860	−	15.9396i	0.0501068	−	0.575172i
$769$	24.4303			0.880978			0.440489	−	0.897758i	$-0.354805\pi$
$769$	24.4303			0.880978			0.440489	+	0.897758i	$0.354805\pi$
$770$	−0.730573	−	7.79514i	−0.0263280	−	0.280917i
$771$	4.73595	−	4.29242i	0.170561	−	0.154588i
$772$	−1.82789	+	2.68043i	−0.0657870	+	0.0964706i
$773$	4.03120	+	16.0935i	0.144992	+	0.578841i	0.998345	+	0.0575076i	$0.0183153\pi$
$773$	4.03120	+	16.0935i	0.144992	+	0.578841i	−0.853353	+	0.521334i	$0.825435\pi$
$774$	6.11513	+	5.59530i	0.219804	+	0.201119i
$775$	24.7648	+	20.3239i	0.889577	+	0.730057i
$776$	−2.26135	+	1.80280i	−0.0811778	+	0.0647167i
$777$	0.270826	−	2.74974i	0.00971584	−	0.0986465i
$778$	−37.8825	+	13.3530i	−1.35815	+	0.478727i
$779$	−4.26320	+	2.01635i	−0.152745	+	0.0722431i
$780$	−2.23806	+	0.310394i	−0.0801354	+	0.0111139i
$781$	−1.86770	+	1.11946i	−0.0668315	+	0.0400572i
$782$	−11.2034	+	16.5968i	−0.400633	+	0.593499i
$783$	2.60469	+	1.74040i	0.0930839	+	0.0621967i
$784$	25.2026	+	39.3070i	0.900092	+	1.40382i
$785$	−1.07271	+	0.716762i	−0.0382867	+	0.0255823i
$786$	9.26657	+	0.0437958i	0.330527	+	0.00156215i
$787$	−13.0739	+	17.6281i	−0.466035	+	0.628375i	−0.972225	−	0.234046i	$-0.924803\pi$
$787$	−13.0739	+	17.6281i	−0.466035	+	0.628375i	0.506191	+	0.862422i	$0.331053\pi$
$788$	41.1515	+	15.1645i	1.46596	+	0.540213i
$789$	17.0068	−	0.835491i	0.605458	−	0.0297443i
$790$	−0.326675	−	0.550913i	−0.0116226	−	0.0196006i
$791$	−46.7895	+	14.1934i	−1.66364	+	0.504661i
$792$	4.37721	+	6.08030i	0.155537	+	0.216054i
$793$	−20.5575	+	10.9882i	−0.730019	+	0.390203i
$794$	17.8084	+	24.2506i	0.631997	+	0.860620i
$795$	−1.94969	−	2.62885i	−0.0691482	−	0.0932356i
$796$	−5.73985	−	19.5863i	−0.203444	−	0.694220i
$797$	−0.154997	+	0.0554589i	−0.00549028	+	0.00196445i	−0.339634	−	0.940558i	$-0.610303\pi$
$797$	−0.154997	+	0.0554589i	−0.00549028	+	0.00196445i	0.334143	+	0.942522i	$0.391553\pi$
$798$	−5.49760	+	10.1694i	−0.194613	+	0.359992i
$799$	27.3417	+	66.0086i	0.967278	+	2.33522i
$800$	15.5042	−	22.0570i	0.548156	−	0.779833i
$801$	1.09596	−	2.64588i	0.0387239	−	0.0934877i
$802$	20.1800	+	24.8277i	0.712579	+	0.876697i
$803$	−1.73352	+	3.66523i	−0.0611747	+	0.129343i
$804$	−11.8002	−	9.87232i	−0.416162	−	0.348170i
$805$	0.762297	−	5.13899i	0.0268674	−	0.181126i
$806$	18.9911	+	11.5052i	0.668932	+	0.405252i
$807$	−4.81696	+	15.8794i	−0.169565	+	0.558981i
$808$	−10.0934	+	13.2137i	−0.355086	+	0.464855i
$809$	−21.5207	−	11.5031i	−0.756627	−	0.404426i	0.0475088	−	0.998871i	$-0.484872\pi$
$809$	−21.5207	−	11.5031i	−0.756627	−	0.404426i	−0.804136	+	0.594445i	$0.797372\pi$
$810$	0.0971659	+	0.677071i	0.00341406	+	0.0237899i
$811$	−13.7356	+	15.1550i	−0.482324	+	0.532162i	−0.932689	−	0.360682i	$-0.882544\pi$
$811$	−13.7356	+	15.1550i	−0.482324	+	0.532162i	0.450365	+	0.892845i	$0.351294\pi$
$812$	26.7420	+	4.22550i	0.938459	+	0.148286i
$813$	−28.3379	+	4.20353i	−0.993854	+	0.147424i
$814$	−0.906145	−	2.21721i	−0.0317604	−	0.0777132i
$815$	1.84320	−	9.26637i	0.0645643	−	0.324587i
$816$	−2.91662	−	22.5977i	−0.102102	−	0.791078i
$817$	2.16297	+	10.8740i	0.0756726	+	0.380432i
$818$	−30.0512	−	45.4383i	−1.05072	−	1.58871i
$819$	−2.45252	+	9.79101i	−0.0856980	+	0.342126i
$820$	−0.141094	+	2.40747i	−0.00492721	+	0.0840725i
$821$	−32.1876	−	11.5169i	−1.12336	−	0.401943i	−0.291298	−	0.956632i	$-0.594087\pi$
$821$	−32.1876	−	11.5169i	−1.12336	−	0.401943i	−0.832058	+	0.554689i	$0.812837\pi$
$822$	20.4773	−	18.3840i	0.714227	−	0.641216i
$823$	6.95794	+	8.47828i	0.242539	+	0.295534i	0.880025	−	0.474928i	$-0.157526\pi$
$823$	6.95794	+	8.47828i	0.242539	+	0.295534i	−0.637486	+	0.770462i	$0.720026\pi$
$824$	−37.4418	−	38.5189i	−1.30435	−	1.34187i
$825$	1.23741	+	12.5637i	0.0430812	+	0.437411i
$826$	−35.4045	−	75.7811i	−1.23188	−	2.63676i
$827$	−0.547081	−	0.327908i	−0.0190239	−	0.0114025i	0.504559	−	0.863377i	$-0.331655\pi$
$827$	−0.547081	−	0.327908i	−0.0190239	−	0.0114025i	−0.523583	+	0.851975i	$0.675405\pi$
$828$	1.85897	+	4.61075i	0.0646038	+	0.160235i
$829$	37.8096	+	1.85747i	1.31318	+	0.0645125i	0.693566	−	0.720393i	$-0.256038\pi$
$829$	37.8096	+	1.85747i	1.31318	+	0.0645125i	0.619616	+	0.784905i	$0.287288\pi$
$830$	7.42213	−	3.92223i	0.257626	−	0.136142i
$831$	−15.3619	+	15.3619i	−0.532900	+	0.532900i
$832$	8.46515	−	16.6589i	0.293476	−	0.577542i
$833$	47.0182	+	47.0182i	1.62909	+	1.62909i
$834$	16.6810	+	5.14633i	0.577615	+	0.178203i
$835$	−0.507021	+	10.3207i	−0.0175462	+	0.357161i
$836$	−0.0947241	+	10.0209i	−0.00327610	+	0.346580i
$837$	3.45572	−	5.76553i	0.119447	−	0.199286i
$838$	−29.8987	−	10.8576i	−1.03283	−	0.375070i
$839$	18.5716	−	1.82914i	0.641163	−	0.0631490i	0.227789	−	0.973711i	$-0.426850\pi$
$839$	18.5716	−	1.82914i	0.641163	−	0.0631490i	0.413374	+	0.910562i	$0.364350\pi$
$840$	3.21425	+	4.96133i	0.110902	+	0.171182i
$841$	−14.8315	+	12.1719i	−0.511430	+	0.419720i
$842$	−41.5210	−	2.23655i	−1.43091	−	0.0770767i
$843$	−0.824156	+	2.30336i	−0.0283855	+	0.0793320i
$844$	−47.6586	+	16.5460i	−1.64048	+	0.569538i
$845$	3.53949	+	0.886595i	0.121762	+	0.0304998i
$846$	17.3808	+	3.54272i	0.597563	+	0.121801i
$847$	16.8840	−	3.35844i	0.580141	−	0.115397i
$848$	27.0554	−	0.816850i	0.929085	−	0.0280508i
$849$	−25.2115	−	5.01488i	−0.865256	−	0.172110i
$850$	14.8604	−	35.4019i	0.509706	−	1.21427i
$851$	−0.233211	−	1.57218i	−0.00799435	−	0.0538936i
$852$	0.858540	−	1.40216i	0.0294131	−	0.0480372i
$853$	31.3273	+	28.3934i	1.07263	+	0.972173i	0.999683	−	0.0251633i	$-0.00801056\pi$
$853$	31.3273	+	28.3934i	1.07263	+	0.972173i	0.0729440	+	0.997336i	$0.476761\pi$
$854$	48.8125	+	36.5606i	1.67033	+	1.25108i
$855$	−0.431297	+	0.806900i	−0.0147500	+	0.0275954i
$856$	−4.56518	−	13.3527i	−0.156035	−	0.456386i
$857$	−2.73968	−	0.831074i	−0.0935858	−	0.0283889i	0.243145	−	0.969990i	$-0.421821\pi$
$857$	−2.73968	−	0.831074i	−0.0935858	−	0.0283889i	−0.336730	+	0.941601i	$0.609321\pi$
$858$	2.08590	+	8.49757i	0.0712115	+	0.290102i
$859$	−11.0800	−	1.64356i	−0.378045	−	0.0560777i	−0.0449959	−	0.998987i	$-0.514327\pi$
$859$	−11.0800	−	1.64356i	−0.378045	−	0.0560777i	−0.333049	+	0.942909i	$0.608077\pi$
$860$	5.40960	+	1.69699i	0.184466	+	0.0578667i
$861$	9.73872	+	4.60607i	0.331895	+	0.156974i
$862$	25.1093	+	2.59292i	0.855225	+	0.0883154i
$863$	−5.01416	−	2.07693i	−0.170684	−	0.0706996i	0.295705	−	0.955279i	$-0.404445\pi$
$863$	−5.01416	−	2.07693i	−0.170684	−	0.0706996i	−0.466389	+	0.884580i	$0.654445\pi$
$864$	−5.05516	−	2.53877i	−0.171980	−	0.0863708i
$865$	4.74861	−	1.96694i	0.161458	−	0.0668779i
$866$	−29.6121	+	8.83012i	−1.00626	+	0.300060i
$867$	−5.20417	−	14.5447i	−0.176743	−	0.493963i
$868$	6.24039	−	57.7575i	0.211812	−	1.96042i
$869$	−1.99218	+	1.47750i	−0.0675801	+	0.0501208i
$870$	2.11804	+	0.324420i	0.0718084	+	0.0109989i
$871$	−8.47023	−	15.8467i	−0.287003	−	0.536945i
$872$	3.99866	+	1.49503i	0.135412	+	0.0506280i
$873$	0.296812	+	0.978457i	0.0100456	+	0.0331157i
$874$	−1.64623	+	6.44278i	−0.0556846	+	0.217930i
$875$	1.00155	+	20.3869i	0.0338584	+	0.689204i
$876$	−0.121305	−	3.05896i	−0.00409853	−	0.103353i
$877$	38.0594	+	28.2267i	1.28517	+	0.953149i	0.999986	−	0.00532263i	$-0.00169425\pi$
$877$	38.0594	+	28.2267i	1.28517	+	0.953149i	0.285187	+	0.958472i	$0.407944\pi$
$878$	14.9214	−	14.7810i	0.503572	−	0.498835i
$879$	4.69100	+	7.02057i	0.158223	+	0.236798i
$880$	4.47301	+	2.50072i	0.150785	+	0.0842991i
$881$	−27.9508	+	41.8313i	−0.941685	+	1.40933i	−0.0294947	+	0.999565i	$0.509390\pi$
$881$	−27.9508	+	41.8313i	−0.941685	+	1.40933i	−0.912190	+	0.409766i	$0.865610\pi$
$882$	16.2062	−	3.14407i	0.545692	−	0.105866i
$883$	−7.65566	−	12.7727i	−0.257634	−	0.429836i	0.701550	−	0.712620i	$-0.252492\pi$
$883$	−7.65566	−	12.7727i	−0.257634	−	0.429836i	−0.959183	+	0.282785i	$0.908742\pi$
$884$	6.70955	−	25.7508i	0.225667	−	0.866094i
$885$	−2.83039	−	5.98437i	−0.0951427	−	0.201162i
$886$	6.10527	−	12.7522i	0.205111	−	0.428420i
$887$	−12.9096	−	1.27148i	−0.433460	−	0.0426921i	−0.121066	−	0.992645i	$-0.538631\pi$
$887$	−12.9096	−	1.27148i	−0.433460	−	0.0426921i	−0.312395	+	0.949952i	$0.601131\pi$
$888$	1.38160	+	1.16702i	0.0463635	+	0.0391627i
$889$	−31.6454	+	38.5600i	−1.06135	+	1.29326i
$890$	−0.0868715	−	1.95699i	−0.00291194	−	0.0655985i
$891$	2.56944	−	0.643611i	0.0860794	−	0.0215618i
$892$	8.56708	−	41.0384i	0.286847	−	1.37407i
$893$	15.9339	+	17.5803i	0.533206	+	0.588302i
$894$	1.88643	+	1.56313i	0.0630917	+	0.0522790i
$895$			7.55765i			0.252624i
$896$	−48.8626	−	1.61713i	−1.63238	−	0.0540244i
$897$			5.80605i			0.193859i
$898$	16.0067	−	19.3173i	0.534151	−	0.644628i
$899$	−14.1411	−	15.6023i	−0.471631	−	0.520365i
$900$	−5.22062	−	7.97538i	−0.174021	−	0.265846i
$901$	37.3912	−	9.36600i	1.24568	−	0.312027i
$902$	9.32974	−	0.414150i	0.310646	−	0.0137897i
$903$	16.0671	−	19.5779i	0.534681	−	0.651510i
$904$	9.72344	−	30.4908i	0.323397	−	1.01411i
$905$	−5.49186	−	0.540901i	−0.182556	−	0.0179802i
$906$	−4.40212	−	2.10757i	−0.146251	−	0.0700192i
$907$	16.1035	+	34.0480i	0.534708	+	1.13055i	0.972807	+	0.231619i	$0.0744021\pi$
$907$	16.1035	+	34.0480i	0.534708	+	1.13055i	−0.438098	+	0.898927i	$0.644348\pi$
$908$	−12.2542	+	7.18832i	−0.406670	+	0.238553i
$909$	3.02229	+	5.04238i	0.100243	+	0.167245i
$910$	1.31489	+	6.77767i	0.0435883	+	0.224677i
$911$	−17.5756	+	26.3038i	−0.582306	+	0.871483i	−0.999299	−	0.0374267i	$-0.988084\pi$
$911$	−17.5756	+	26.3038i	−0.582306	+	0.871483i	0.416993	+	0.908910i	$0.363084\pi$
$912$	−3.44011	−	6.73942i	−0.113913	−	0.223165i
$913$	−18.0609	−	27.0300i	−0.597727	−	0.894562i
$914$	13.1278	+	13.2525i	0.434230	+	0.438354i
$915$	3.87688	+	2.87529i	0.128166	+	0.0950542i
$916$	12.8967	+	11.9129i	0.426121	+	0.393613i
$917$	−1.38936	−	28.2810i	−0.0458806	−	0.933920i
$918$	−7.80501	−	1.99430i	−0.257604	−	0.0658218i
$919$	−15.5339	−	51.2083i	−0.512415	−	1.68921i	−0.706074	−	0.708138i	$-0.749536\pi$
$919$	−15.5339	−	51.2083i	−0.512415	−	1.68921i	0.193659	−	0.981069i	$-0.437964\pi$
$920$	2.48696	+	2.31911i	0.0819925	+	0.0764589i
$921$	15.1784	+	28.3967i	0.500144	+	0.935703i
$922$	−0.814981	+	5.32077i	−0.0268400	+	0.175230i
$923$	1.54228	−	1.14384i	0.0507649	−	0.0376498i
$924$	17.8326	−	14.3549i	0.586648	−	0.472241i
$925$	1.02666	+	2.86933i	0.0337564	+	0.0943429i
$926$	−2.71808	−	9.11518i	−0.0893218	−	0.299544i
$927$	−17.5464	+	7.26795i	−0.576299	+	0.238711i
$928$	−12.2075	+	12.8454i	−0.400731	+	0.421671i
$929$	−8.25666	−	3.42002i	−0.270892	−	0.112207i	0.243102	−	0.970001i	$-0.421835\pi$
$929$	−8.25666	−	3.42002i	−0.270892	−	0.112207i	−0.513995	+	0.857793i	$0.671835\pi$
$930$	0.472284	−	4.57348i	0.0154868	−	0.149970i
$931$	19.9616	+	9.44116i	0.654217	+	0.309421i
$932$	−10.5621	+	5.51785i	−0.345973	+	0.180743i
$933$	−26.3362	−	3.90660i	−0.862207	−	0.127896i
$934$	−36.6595	+	8.99882i	−1.19954	+	0.294450i
$935$	6.98354	+	2.11843i	0.228386	+	0.0692802i
$936$	−4.36687	−	4.95758i	−0.142736	−	0.162043i
$937$	−18.6854	+	34.9580i	−0.610426	+	1.14203i	0.366895	+	0.930263i	$0.380421\pi$
$937$	−18.6854	+	34.9580i	−0.610426	+	1.14203i	−0.977321	+	0.211765i	$0.932079\pi$
$938$	−28.1826	+	37.6269i	−0.920195	+	1.22856i
$939$	−8.71312	−	7.89712i	−0.284342	−	0.257713i
$940$	11.7968	−	2.83671i	0.384768	−	0.0925232i
$941$	4.38189	+	29.5403i	0.142846	+	0.962987i	0.935503	+	0.353319i	$0.114947\pi$
$941$	4.38189	+	29.5403i	0.142846	+	0.962987i	−0.792657	+	0.609668i	$0.791303\pi$
$942$	−3.47828	−	1.46005i	−0.113328	−	0.0475709i
$943$	6.07787	+	1.20896i	0.197923	+	0.0393693i
$944$	53.9940	+	9.05551i	1.75735	+	0.294732i
$945$	2.04988	−	0.407747i	0.0666827	−	0.0132640i
$946$	4.38498	−	21.5129i	0.142568	−	0.699444i
$947$	12.1185	+	3.03554i	0.393800	+	0.0986417i	0.434822	−	0.900517i	$-0.356811\pi$
$947$	12.1185	+	3.03554i	0.393800	+	0.0986417i	−0.0410221	+	0.999158i	$0.513061\pi$
$948$	0.816667	−	1.68530i	0.0265241	−	0.0547359i
$949$	1.20450	−	3.36634i	0.0390996	−	0.109276i
$950$	0.685805	−	12.7318i	0.0222505	−	0.413074i
$951$	6.54407	−	5.37058i	0.212206	−	0.174153i
$952$	−68.4699	+	12.6131i	−2.21912	+	0.408792i
$953$	−9.63480	+	0.948945i	−0.312102	+	0.0307393i	−0.252856	−	0.967504i	$-0.581370\pi$
$953$	−9.63480	+	0.948945i	−0.312102	+	0.0307393i	−0.0592463	+	0.998243i	$0.518870\pi$
$954$	3.26654	−	8.99512i	0.105758	−	0.291228i
$955$	4.19668	−	7.00173i	0.135801	−	0.226571i
$956$	−12.2430	+	12.0137i	−0.395966	+	0.388550i
$957$	0.407153	−	8.28778i	0.0131614	−	0.267906i
$958$	−4.50187	+	14.5921i	−0.145449	+	0.471448i
$959$	−59.4580	−	59.4580i	−1.92000	−	1.92000i
$960$	−3.86778	−	0.109708i	−0.124832	−	0.00354082i
$961$	−10.0291	+	10.0291i	−0.323520	+	0.323520i
$962$	0.986851	+	1.86744i	0.0318173	+	0.0602088i
$963$	−4.98317	−	0.244808i	−0.160581	−	0.00788882i
$964$	−41.5516	−	17.6732i	−1.33829	−	0.569216i
$965$	0.672968	+	0.403362i	0.0216636	+	0.0129847i
$966$	13.7626	−	6.42981i	0.442805	−	0.206876i
$967$	−4.50188	−	45.7084i	−0.144771	−	1.46988i	−0.743395	−	0.668853i	$-0.766786\pi$
$967$	−4.50188	−	45.7084i	−0.144771	−	1.46988i	0.598624	−	0.801030i	$-0.295714\pi$
$968$	−4.45914	+	10.3479i	−0.143322	+	0.332593i
$969$	−6.83587	−	8.32954i	−0.219600	−	0.267583i
$970$	0.467226	+	0.520426i	0.0150017	+	0.0167099i
$971$	9.82140	+	3.51415i	0.315184	+	0.112775i	0.489729	−	0.871875i	$-0.337096\pi$
$971$	9.82140	+	3.51415i	0.315184	+	0.112775i	−0.174545	+	0.984649i	$0.555846\pi$
$972$	−1.49453	+	1.32905i	−0.0479371	+	0.0426293i
$973$	12.9607	−	51.7421i	0.415502	−	1.65878i
$974$	15.9500	−	10.5488i	0.511071	−	0.338004i
$975$	−2.17184	−	10.9186i	−0.0695546	−	0.349675i
$976$	−37.8320	+	12.7351i	−1.21097	+	0.407640i
$977$	−8.22774	+	41.3636i	−0.263229	+	1.32334i	0.592356	+	0.805676i	$0.298198\pi$
$977$	−8.22774	+	41.3636i	−0.263229	+	1.32334i	−0.855585	+	0.517663i	$0.826802\pi$
$978$	25.5720	−	10.4509i	0.817702	−	0.334184i
$979$	−7.50381	+	1.11309i	−0.239823	+	0.0355744i
$980$	9.13289	−	6.64053i	0.291739	−	0.212124i
$981$	1.01360	−	1.11833i	0.0323616	−	0.0357056i
$982$	37.5233	−	5.38494i	1.19742	−	0.171840i
$983$	−5.24676	−	2.80445i	−0.167346	−	0.0894482i	0.385597	−	0.922667i	$-0.373995\pi$
$983$	−5.24676	−	2.80445i	−0.167346	−	0.0894482i	−0.552943	+	0.833219i	$0.686495\pi$
$984$	−6.09896	+	3.53902i	−0.194428	+	0.112820i
$985$	3.07876	−	10.1493i	0.0980974	−	0.323384i
$986$	−13.0759	+	21.5839i	−0.416422	+	0.687370i
$987$	7.95285	−	53.6138i	0.253142	−	1.70654i
$988$	−0.783014	−	8.80227i	−0.0249110	−	0.280038i
$989$	6.22890	−	13.1699i	0.198067	−	0.418778i
$990$	1.40597	−	1.14277i	0.0446846	−	0.0363196i
$991$	16.2015	−	39.1138i	0.514656	−	1.24249i	−0.426491	−	0.904492i	$-0.640250\pi$
$991$	16.2015	−	39.1138i	0.514656	−	1.24249i	0.941147	−	0.337998i	$-0.109750\pi$
$992$	28.8152	+	24.8103i	0.914883	+	0.787728i
$993$	−12.1761	−	29.3956i	−0.386396	−	0.932842i
$994$	−4.41931	−	2.38909i	−0.140172	−	0.0757775i
$995$	−4.64731	+	1.66283i	−0.147329	+	0.0527153i
$996$	21.5371	+	11.7749i	0.682430	+	0.373102i
$997$	−9.35715	−	12.6166i	−0.296344	−	0.399573i	0.629792	−	0.776764i	$-0.283140\pi$
$997$	−9.35715	−	12.6166i	−0.296344	−	0.399573i	−0.926136	+	0.377191i	$0.876890\pi$
$998$	23.0754	−	16.9454i	0.730438	−	0.536397i
$999$	0.563909	−	0.301416i	0.0178413	−	0.00953637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.157.63	✓	2048
256.181	even	64	inner	768.2.z.a.181.63	yes	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.157.63	✓	2048	1.1	even	1	trivial
768.2.z.a.181.63	yes	2048	256.181	even	64	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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.z (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40804 - 0.131964i) q^{2} +(0.740951 - 0.671559i) q^{3} +(1.96517 - 0.371622i) q^{4} +(-0.117521 - 0.469172i) q^{5} +(0.954670 - 1.04336i) q^{6} +(-3.34037 - 2.74137i) q^{7} +(2.71800 - 0.782592i) q^{8} +(0.0980171 - 0.995185i) q^{9} +O(q^{10})\)	\(q+(1.40804 - 0.131964i) q^{2} +(0.740951 - 0.671559i) q^{3} +(1.96517 - 0.371622i) q^{4} +(-0.117521 - 0.469172i) q^{5} +(0.954670 - 1.04336i) q^{6} +(-3.34037 - 2.74137i) q^{7} +(2.71800 - 0.782592i) q^{8} +(0.0980171 - 0.995185i) q^{9} +(-0.227389 - 0.645106i) q^{10} +(-2.39451 + 1.13252i) q^{11} +(1.20653 - 1.59508i) q^{12} +(2.00347 - 1.20083i) q^{13} +(-5.06515 - 3.41916i) q^{14} +(-0.402154 - 0.268711i) q^{15} +(3.72379 - 1.46060i) q^{16} +(4.73629 - 3.16469i) q^{17} +(0.00668381 - 1.41420i) q^{18} +(1.12686 - 1.51940i) q^{19} +(-0.405304 - 0.878329i) q^{20} +(-4.31604 + 0.212034i) q^{21} +(-3.22212 + 1.91062i) q^{22} +(-2.37867 + 0.721560i) q^{23} +(1.48835 - 2.40516i) q^{24} +(4.20330 - 2.24671i) q^{25} +(2.66250 - 1.95521i) q^{26} +(-0.595699 - 0.803208i) q^{27} +(-7.58315 - 4.14591i) q^{28} +(-2.94951 + 1.05535i) q^{29} +(-0.601711 - 0.325287i) q^{30} +(2.57234 + 6.21018i) q^{31} +(5.05052 - 2.54800i) q^{32} +(-1.01366 + 2.44719i) q^{33} +(6.25128 - 5.08104i) q^{34} +(-0.893609 + 1.88938i) q^{35} +(-0.177212 - 1.99213i) q^{36} +(-0.0938209 + 0.632489i) q^{37} +(1.38616 - 2.28808i) q^{38} +(0.678042 - 2.23521i) q^{39} +(-0.686594 - 1.18324i) q^{40} +(-2.19866 - 1.17521i) q^{41} +(-6.04919 + 0.868115i) q^{42} +(-3.93600 + 4.34270i) q^{43} +(-4.28474 + 3.11544i) q^{44} +(-0.478432 + 0.0709686i) q^{45} +(-3.25404 + 1.32989i) q^{46} +(-2.44697 + 12.3018i) q^{47} +(1.77827 - 3.58298i) q^{48} +(2.27733 + 11.4489i) q^{49} +(5.62194 - 3.71815i) q^{50} +(1.38408 - 5.52558i) q^{51} +(3.49090 - 3.10437i) q^{52} +(6.37136 + 2.27971i) q^{53} +(-0.944765 - 1.05234i) q^{54} +(0.812751 + 0.990339i) q^{55} +(-11.2245 - 4.83691i) q^{56} +(-0.185415 - 1.88255i) q^{57} +(-4.01377 + 1.87521i) q^{58} +(11.7397 + 7.03653i) q^{59} +(-0.890160 - 0.378613i) q^{60} +(-9.96747 - 0.489671i) q^{61} +(4.44149 + 8.40475i) q^{62} +(-3.05558 + 3.05558i) q^{63} +(6.77510 - 4.25418i) q^{64} +(-0.798847 - 0.798847i) q^{65} +(-1.10434 + 3.57952i) q^{66} +(0.377461 - 7.68339i) q^{67} +(8.13155 - 7.97926i) q^{68} +(-1.27790 + 2.13205i) q^{69} +(-1.00891 + 2.77825i) q^{70} +(0.818103 - 0.0805761i) q^{71} +(-0.512412 - 2.78162i) q^{72} +(1.18323 - 0.971054i) q^{73} +(-0.0486381 + 0.902953i) q^{74} +(1.60564 - 4.48746i) q^{75} +(1.64983 - 3.40464i) q^{76} +(11.1032 + 2.78120i) q^{77} +(0.659746 - 3.23674i) q^{78} +(0.918380 - 0.182677i) q^{79} +(-1.12290 - 1.57545i) q^{80} +(-0.980785 - 0.195090i) q^{81} +(-3.25090 - 1.36460i) q^{82} +(1.80081 + 12.1401i) q^{83} +(-8.40297 + 2.02062i) q^{84} +(-2.04140 - 1.85022i) q^{85} +(-4.96897 + 6.63412i) q^{86} +(-1.47671 + 2.76273i) q^{87} +(-5.62198 + 4.95211i) q^{88} +(2.74057 + 0.831342i) q^{89} +(-0.664287 + 0.163063i) q^{90} +(-9.98425 - 1.48102i) q^{91} +(-4.40634 + 2.30195i) q^{92} +(6.07649 + 2.87396i) q^{93} +(-1.82205 + 17.6443i) q^{94} +(-0.845289 - 0.350130i) q^{95} +(2.03106 - 5.27966i) q^{96} +(-0.944653 + 0.391288i) q^{97} +(4.71741 + 15.8200i) q^{98} +(0.892361 + 2.49398i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2048 q+O(q^{10}) \) 2048 * q	\( 2048 q+O(q^{100}) \) 2048 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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