LMFDB - Embedded newform 384.2.v.a.13.13

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			13.13
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.542361 - 1.30608i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-1.41169 + 1.41673i) q^{4} +(0.155407 + 1.57788i) q^{5} +(1.09240 - 0.898142i) q^{6} +(0.0321569 - 0.0481261i) q^{7} +(2.61601 + 1.07540i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(-0.542361 - 1.30608i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-1.41169 + 1.41673i) q^{4} +(0.155407 + 1.57788i) q^{5} +(1.09240 - 0.898142i) q^{6} +(0.0321569 - 0.0481261i) q^{7} +(2.61601 + 1.07540i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(1.97655 - 1.05875i) q^{10} +(-4.37401 + 2.33796i) q^{11} +(-1.76552 - 0.939647i) q^{12} +(-4.81489 - 0.474226i) q^{13} +(-0.0802972 - 0.0158977i) q^{14} +(-1.46482 + 0.606749i) q^{15} +(-0.0142664 - 3.99997i) q^{16} +(0.601152 + 0.249005i) q^{17} +(1.17658 + 0.784646i) q^{18} +(-1.22364 + 1.00422i) q^{19} +(-2.45482 - 2.00730i) q^{20} +(0.0553885 + 0.0168019i) q^{21} +(5.42586 + 4.44479i) q^{22} +(-1.04724 + 5.26485i) q^{23} +(-0.269704 + 2.81554i) q^{24} +(2.43838 - 0.485024i) q^{25} +(1.99203 + 6.54584i) q^{26} +(-0.773010 - 0.634393i) q^{27} +(0.0227864 + 0.113497i) q^{28} +(-3.92836 + 7.34945i) q^{29} +(1.58692 + 1.58410i) q^{30} +(-0.512601 + 0.512601i) q^{31} +(-5.21655 + 2.18806i) q^{32} +(-3.50700 - 3.50700i) q^{33} +(-0.000820501 - 0.920203i) q^{34} +(0.0809345 + 0.0432604i) q^{35} +(0.386682 - 1.96226i) q^{36} +(6.25335 - 7.61973i) q^{37} +(1.97525 + 1.05353i) q^{38} +(-0.943884 - 4.74523i) q^{39} +(-1.29030 + 4.29487i) q^{40} +(10.1759 + 2.02412i) q^{41} +(-0.00809591 - 0.0814545i) q^{42} +(0.0283767 - 0.0935456i) q^{43} +(2.86248 - 9.49728i) q^{44} +(-1.00584 - 1.22562i) q^{45} +(7.44430 - 1.48766i) q^{46} +(-2.08609 + 5.03627i) q^{47} +(3.82360 - 1.17478i) q^{48} +(2.67750 + 6.46406i) q^{49} +(-1.95596 - 2.92166i) q^{50} +(-0.0637780 + 0.647549i) q^{51} +(7.46899 - 6.15196i) q^{52} +(-3.80411 - 7.11700i) q^{53} +(-0.409318 + 1.35368i) q^{54} +(-4.36877 - 6.53832i) q^{55} +(0.135878 - 0.0913171i) q^{56} +(-1.31618 - 0.879445i) q^{57} +(11.7296 + 1.14470i) q^{58} +(-6.36002 + 0.626407i) q^{59} +(1.20827 - 2.93180i) q^{60} +(4.53892 - 1.37687i) q^{61} +(0.947512 + 0.391483i) q^{62} +0.0578808i q^{63} +(5.68704 + 5.62651i) q^{64} -7.67101i q^{65} +(-2.67836 + 6.48248i) q^{66} +(-3.87274 + 1.17478i) q^{67} +(-1.20141 + 0.500154i) q^{68} +(-5.34214 + 0.526155i) q^{69} +(0.0126058 - 0.129170i) q^{70} +(1.73828 + 1.16148i) q^{71} +(-2.77259 + 0.559217i) q^{72} +(5.28352 + 7.90735i) q^{73} +(-13.3435 - 4.03473i) q^{74} +(1.17196 + 2.19259i) q^{75} +(0.304695 - 3.15122i) q^{76} +(-0.0281376 + 0.285686i) q^{77} +(-5.68572 + 3.80641i) q^{78} +(-3.36565 - 8.12539i) q^{79} +(6.30925 - 0.644136i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-2.87537 - 14.3884i) q^{82} +(8.89528 + 10.8389i) q^{83} +(-0.101995 + 0.0547516i) q^{84} +(-0.299476 + 0.987241i) q^{85} +(-0.137568 + 0.0136732i) q^{86} +(-8.17333 - 1.62578i) q^{87} +(-13.9567 + 1.41232i) q^{88} +(-2.14254 - 10.7713i) q^{89} +(-1.05523 + 1.97843i) q^{90} +(-0.177655 + 0.216473i) q^{91} +(-5.98050 - 8.91599i) q^{92} +(-0.639328 - 0.341728i) q^{93} +(7.70919 - 0.00687391i) q^{94} +(-1.77470 - 1.77470i) q^{95} +(-3.60813 - 4.35676i) q^{96} +(10.4308 - 10.4308i) q^{97} +(6.99041 - 7.00289i) q^{98} +(2.33796 - 4.37401i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

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 $

$2$	−0.542361	−	1.30608i	−0.383507	−	0.923538i
$2$	−0.542361	−	1.30608i	−0.383507	−	0.923538i
$3$	0.290285	+	0.956940i	0.167596	+	0.552490i
$3$	0.290285	+	0.956940i	0.167596	+	0.552490i
$4$	−1.41169	+	1.41673i	−0.705845	+	0.708367i
$5$	0.155407	+	1.57788i	0.0695003	+	0.705648i	0.965292	+	0.261174i	$0.0841095\pi$
$5$	0.155407	+	1.57788i	0.0695003	+	0.705648i	−0.895792	+	0.444474i	$0.853390\pi$
$6$	1.09240	−	0.898142i	0.445971	−	0.366665i
$7$	0.0321569	−	0.0481261i	0.0121542	−	0.0181900i	−0.825343	−	0.564632i	$-0.809018\pi$
$7$	0.0321569	−	0.0481261i	0.0121542	−	0.0181900i	0.837497	+	0.546442i	$0.184018\pi$
$8$	2.61601	+	1.07540i	0.924900	+	0.380211i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	1.97655	−	1.05875i	0.625039	−	0.334807i
$11$	−4.37401	+	2.33796i	−1.31881	+	0.704921i	−0.972435	−	0.233173i	$-0.925089\pi$
$11$	−4.37401	+	2.33796i	−1.31881	+	0.704921i	−0.346380	+	0.938094i	$0.612589\pi$
$12$	−1.76552	−	0.939647i	−0.509662	−	0.271253i
$13$	−4.81489	−	0.474226i	−1.33541	−	0.131527i	−0.595025	−	0.803708i	$-0.702858\pi$
$13$	−4.81489	−	0.474226i	−1.33541	−	0.131527i	−0.740387	+	0.672181i	$0.765358\pi$
$14$	−0.0802972	−	0.0158977i	−0.0214603	−	0.00424884i
$15$	−1.46482	+	0.606749i	−0.378215	+	0.156662i
$16$	−0.0142664	−	3.99997i	−0.00356660	−	0.999994i
$17$	0.601152	+	0.249005i	0.145801	+	0.0603927i	0.454391	−	0.890803i	$-0.349857\pi$
$17$	0.601152	+	0.249005i	0.145801	+	0.0603927i	−0.308590	+	0.951195i	$0.599857\pi$
$18$	1.17658	+	0.784646i	0.277322	+	0.184943i
$19$	−1.22364	+	1.00422i	−0.280723	+	0.230383i	−0.764209	−	0.644969i	$-0.776870\pi$
$19$	−1.22364	+	1.00422i	−0.280723	+	0.230383i	0.483486	+	0.875352i	$0.339370\pi$
$20$	−2.45482	−	2.00730i	−0.548914	−	0.448846i
$21$	0.0553885	+	0.0168019i	0.0120868	+	0.00366648i
$22$	5.42586	+	4.44479i	1.15680	+	0.947633i
$23$	−1.04724	+	5.26485i	−0.218365	+	1.09780i	0.703621	+	0.710575i	$0.251565\pi$
$23$	−1.04724	+	5.26485i	−0.218365	+	1.09780i	−0.921987	+	0.387222i	$0.873435\pi$
$24$	−0.269704	+	2.81554i	−0.0550531	+	0.574719i
$25$	2.43838	−	0.485024i	0.487676	−	0.0970049i
$26$	1.99203	+	6.54584i	0.390670	+	1.28374i
$27$	−0.773010	−	0.634393i	−0.148766	−	0.122089i
$28$	0.0227864	+	0.113497i	0.00430623	+	0.0214489i
$29$	−3.92836	+	7.34945i	−0.729479	+	1.36476i	0.193959	+	0.981010i	$0.437867\pi$
$29$	−3.92836	+	7.34945i	−0.729479	+	1.36476i	−0.923438	+	0.383749i	$0.874633\pi$
$30$	1.58692	+	1.58410i	0.289732	+	0.289215i
$31$	−0.512601	+	0.512601i	−0.0920658	+	0.0920658i	−0.751640	−	0.659574i	$-0.770737\pi$
$31$	−0.512601	+	0.512601i	−0.0920658	+	0.0920658i	0.659574	+	0.751640i	$0.270737\pi$
$32$	−5.21655	+	2.18806i	−0.922164	+	0.386799i
$33$	−3.50700	−	3.50700i	−0.610490	−	0.610490i
$34$	−0.000820501	−	0.920203i	−0.000140715	−	0.157814i
$35$	0.0809345	+	0.0432604i	0.0136804	+	0.00731235i
$36$	0.386682	−	1.96226i	0.0644470	−	0.327044i
$37$	6.25335	−	7.61973i	1.02804	−	1.25268i	0.0609814	−	0.998139i	$-0.480577\pi$
$37$	6.25335	−	7.61973i	1.02804	−	1.25268i	0.967063	−	0.254537i	$-0.0819230\pi$
$38$	1.97525	+	1.05353i	0.320427	+	0.170905i
$39$	−0.943884	−	4.74523i	−0.151142	−	0.759844i
$40$	−1.29030	+	4.29487i	−0.204014	+	0.679079i
$41$	10.1759	+	2.02412i	1.58921	+	0.316114i	0.908967	−	0.416869i	$-0.136872\pi$
$41$	10.1759	+	2.02412i	1.58921	+	0.316114i	0.680247	+	0.732983i	$0.261872\pi$
$42$	−0.00809591	−	0.0814545i	−0.00124923	−	0.0125687i
$43$	0.0283767	−	0.0935456i	0.00432741	−	0.0142656i	−0.954750	−	0.297409i	$-0.903877\pi$
$43$	0.0283767	−	0.0935456i	0.00432741	−	0.0142656i	0.959077	+	0.283144i	$0.0913774\pi$
$44$	2.86248	−	9.49728i	0.431536	−	1.43177i
$45$	−1.00584	−	1.22562i	−0.149941	−	0.182704i
$46$	7.44430	−	1.48766i	1.09760	−	0.219344i
$47$	−2.08609	+	5.03627i	−0.304288	+	0.734616i	0.695582	+	0.718447i	$0.255147\pi$
$47$	−2.08609	+	5.03627i	−0.304288	+	0.734616i	−0.999869	+	0.0161684i	$0.994853\pi$
$48$	3.82360	−	1.17478i	0.551888	−	0.169565i
$49$	2.67750	+	6.46406i	0.382500	+	0.923437i
$50$	−1.95596	−	2.92166i	−0.276615	−	0.413186i
$51$	−0.0637780	+	0.647549i	−0.00893071	+	0.0906750i
$52$	7.46899	−	6.15196i	1.03576	−	0.853124i
$53$	−3.80411	−	7.11700i	−0.522535	−	0.977595i	−0.995340	−	0.0964276i	$-0.969258\pi$
$53$	−3.80411	−	7.11700i	−0.522535	−	0.977595i	0.472805	−	0.881167i	$-0.343242\pi$
$54$	−0.409318	+	1.35368i	−0.0557011	+	0.184213i
$55$	−4.36877	−	6.53832i	−0.589084	−	0.881627i
$56$	0.135878	−	0.0913171i	0.0181574	−	0.0122028i
$57$	−1.31618	−	0.879445i	−0.174333	−	0.116485i
$58$	11.7296	+	1.14470i	1.54017	+	0.150307i
$59$	−6.36002	+	0.626407i	−0.828004	+	0.0815513i	−0.503135	−	0.864208i	$-0.667820\pi$
$59$	−6.36002	+	0.626407i	−0.828004	+	0.0815513i	−0.324869	+	0.945759i	$0.605320\pi$
$60$	1.20827	−	2.93180i	0.155987	−	0.378494i
$61$	4.53892	−	1.37687i	0.581149	−	0.176290i	0.0139960	−	0.999902i	$-0.495545\pi$
$61$	4.53892	−	1.37687i	0.581149	−	0.176290i	0.567153	+	0.823612i	$0.308045\pi$
$62$	0.947512	+	0.391483i	0.120334	+	0.0497184i
$63$			0.0578808i			0.00729230i
$64$	5.68704	+	5.62651i	0.710880	+	0.703314i
$65$		−	7.67101i		−	0.951472i
$66$	−2.67836	+	6.48248i	−0.329683	+	0.797938i
$67$	−3.87274	+	1.17478i	−0.473131	+	0.143523i	−0.517840	−	0.855477i	$-0.673264\pi$
$67$	−3.87274	+	1.17478i	−0.473131	+	0.143523i	0.0447094	+	0.999000i	$0.485764\pi$
$68$	−1.20141	+	0.500154i	−0.145693	+	0.0606526i
$69$	−5.34214	+	0.526155i	−0.643119	+	0.0633416i
$70$	0.0126058	−	0.129170i	0.00150668	−	0.0154387i
$71$	1.73828	+	1.16148i	0.206296	+	0.137843i	0.654427	−	0.756125i	$-0.272910\pi$
$71$	1.73828	+	1.16148i	0.206296	+	0.137843i	−0.448131	+	0.893968i	$0.647910\pi$
$72$	−2.77259	+	0.559217i	−0.326753	+	0.0659044i
$73$	5.28352	+	7.90735i	0.618390	+	0.925486i	0.999999	+	0.00116213i	$0.000369919\pi$
$73$	5.28352	+	7.90735i	0.618390	+	0.925486i	−0.381610	+	0.924324i	$0.624630\pi$
$74$	−13.3435	−	4.03473i	−1.55116	−	0.469028i
$75$	1.17196	+	2.19259i	0.135327	+	0.253179i
$76$	0.304695	−	3.15122i	0.0349509	−	0.361470i
$77$	−0.0281376	+	0.285686i	−0.00320658	+	0.0325569i
$78$	−5.68572	+	3.80641i	−0.643781	+	0.430992i
$79$	−3.36565	−	8.12539i	−0.378665	−	0.914178i	−0.992217	−	0.124524i	$-0.960260\pi$
$79$	−3.36565	−	8.12539i	−0.378665	−	0.914178i	0.613552	−	0.789655i	$-0.289740\pi$
$80$	6.30925	−	0.644136i	0.705396	−	0.0720166i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	−2.87537	−	14.3884i	−0.317531	−	1.58893i
$83$	8.89528	+	10.8389i	0.976384	+	1.18973i	0.981834	+	0.189742i	$0.0607652\pi$
$83$	8.89528	+	10.8389i	0.976384	+	1.18973i	−0.00545011	+	0.999985i	$0.501735\pi$
$84$	−0.101995	+	0.0547516i	−0.0111286	+	0.00597389i
$85$	−0.299476	+	0.987241i	−0.0324828	+	0.107081i
$86$	−0.137568	+	0.0136732i	−0.0148344	+	0.00147442i
$87$	−8.17333	−	1.62578i	−0.876273	−	0.174301i
$88$	−13.9567	+	1.41232i	−1.48779	+	0.150554i
$89$	−2.14254	−	10.7713i	−0.227109	−	1.14175i	−0.911075	−	0.412240i	$-0.864747\pi$
$89$	−2.14254	−	10.7713i	−0.227109	−	1.14175i	0.683967	−	0.729513i	$-0.260253\pi$
$90$	−1.05523	+	1.97843i	−0.111231	+	0.208545i
$91$	−0.177655	+	0.216473i	−0.0186233	+	0.0226925i
$92$	−5.98050	−	8.91599i	−0.623510	−	0.929557i
$93$	−0.639328	−	0.341728i	−0.0662953	−	0.0354356i
$94$	7.70919	−	0.00687391i	0.795142	−	0.000708990i
$95$	−1.77470	−	1.77470i	−0.182080	−	0.182080i
$96$	−3.60813	−	4.35676i	−0.368253	−	0.444660i
$97$	10.4308	−	10.4308i	1.05909	−	1.05909i	0.0609440	−	0.998141i	$-0.480589\pi$
$97$	10.4308	−	10.4308i	1.05909	−	1.05909i	0.998141	−	0.0609440i	$-0.0194111\pi$
$98$	6.99041	−	7.00289i	0.706138	−	0.707398i
$99$	2.33796	−	4.37401i	0.234974	−	0.439605i
$100$	−2.75509	+	4.13924i	−0.275509	+	0.413924i
$101$	−4.84371	−	3.97513i	−0.481967	−	0.395540i	0.361795	−	0.932258i	$-0.382164\pi$
$101$	−4.84371	−	3.97513i	−0.481967	−	0.395540i	−0.843762	+	0.536718i	$0.819664\pi$
$102$	0.880341	−	0.267906i	0.0871668	−	0.0265267i
$103$	−14.2918	+	2.84281i	−1.40821	+	0.280110i	−0.839916	−	0.542716i	$-0.817396\pi$
$103$	−14.2918	+	2.84281i	−1.40821	+	0.280110i	−0.568293	+	0.822826i	$0.692396\pi$
$104$	−12.0858	−	6.41851i	−1.18511	−	0.629387i
$105$	−0.0179036	+	0.0900074i	−0.00174721	+	0.00878382i
$106$	−7.23216	+	8.82846i	−0.702450	+	0.857496i
$107$	9.91454	+	3.00754i	0.958475	+	0.290750i	0.730497	−	0.682916i	$-0.239289\pi$
$107$	9.91454	+	3.00754i	0.958475	+	0.290750i	0.227978	+	0.973666i	$0.426789\pi$
$108$	1.99002	−	0.199583i	0.191489	−	0.0192049i
$109$	−6.57417	+	5.39528i	−0.629691	+	0.516774i	−0.894234	−	0.447600i	$-0.852279\pi$
$109$	−6.57417	+	5.39528i	−0.629691	+	0.516774i	0.264543	+	0.964374i	$0.414779\pi$
$110$	−6.17012	+	9.25209i	−0.588298	+	0.882152i
$111$	9.10688	+	3.77219i	0.864387	+	0.358041i
$112$	−0.192962	−	0.127940i	−0.0182332	−	0.0120892i
$113$	8.96291	−	3.71256i	0.843159	−	0.349248i	0.0810608	−	0.996709i	$-0.474169\pi$
$113$	8.96291	−	3.71256i	0.843159	−	0.349248i	0.762098	+	0.647461i	$0.224169\pi$
$114$	−0.434779	+	2.19602i	−0.0407208	+	0.205676i
$115$	−8.47003	−	0.834225i	−0.789834	−	0.0777919i
$116$	−4.86658	−	15.9406i	−0.451851	−	1.48005i
$117$	4.26690	−	2.28071i	0.394475	−	0.210852i
$118$	4.26756	+	7.96695i	0.392861	+	0.733417i
$119$	0.0313148	−	0.0209239i	0.00287063	−	0.00191809i
$120$	−4.48449	+	0.0119958i	−0.409376	+	0.00109506i
$121$	7.55468	−	11.3064i	0.686789	−	1.02785i
$122$	−4.26003	−	5.18143i	−0.385685	−	0.469105i
$123$	1.01696	+	10.3253i	0.0916959	+	0.931004i
$124$	−0.00258553	−	1.44985i	−0.000232187	−	0.130200i
$125$	3.44550	+	11.3583i	0.308175	+	1.01592i
$126$	0.0755970	−	0.0313923i	0.00673471	−	0.00279665i
$127$	−2.23986			−0.198756			−0.0993779	−	0.995050i	$-0.531685\pi$
$127$	−2.23986			−0.198756			−0.0993779	+	0.995050i	$0.531685\pi$
$128$	4.26424	−	10.4793i	0.376910	−	0.926250i
$129$	0.0977548			0.00860683
$130$	−10.0190	+	4.16046i	−0.878720	+	0.364896i
$131$	0.725608	+	2.39201i	0.0633966	+	0.208991i	0.982916	−	0.184053i	$-0.0589220\pi$
$131$	0.725608	+	2.39201i	0.0633966	+	0.208991i	−0.919520	+	0.393044i	$0.871422\pi$
$132$	9.91927	−	0.0176891i	0.863362	−	0.00153964i
$133$	0.00898062	+	0.0911818i	0.000778718	+	0.00790646i
$134$	3.63479	+	4.42095i	0.313998	+	0.381912i
$135$	0.880863	−	1.31830i	0.0758126	−	0.113462i
$136$	1.30484	+	1.29788i	0.111889	+	0.111292i
$137$	0.845783	−	0.565134i	0.0722601	−	0.0482827i	−0.518915	−	0.854826i	$-0.673664\pi$
$137$	0.845783	−	0.565134i	0.0722601	−	0.0482827i	0.591176	+	0.806543i	$0.298664\pi$
$138$	3.58457	+	6.69190i	0.305139	+	0.569652i
$139$	6.65943	−	3.55954i	0.564845	−	0.301916i	−0.164149	−	0.986435i	$-0.552488\pi$
$139$	6.65943	−	3.55954i	0.564845	−	0.301916i	0.728995	+	0.684519i	$0.239988\pi$
$140$	−0.175543	+	0.0535924i	−0.0148361	+	0.00452938i
$141$	−5.42497	−	0.534313i	−0.456865	−	0.0449973i
$142$	0.574213	−	2.90028i	0.0481869	−	0.243386i
$143$	22.1691	−	9.18276i	1.85388	−	0.767901i
$144$	2.23413	+	3.31793i	0.186177	+	0.276494i
$145$	−12.2070	−	5.05631i	−1.01374	−	0.419904i
$146$	7.46206	−	11.1893i	0.617564	−	0.926037i
$147$	−5.40848	+	4.43863i	−0.446084	+	0.366092i
$148$	1.96734	+	19.6160i	0.161714	+	1.61243i
$149$	−13.7007	−	4.15606i	−1.12240	−	0.340478i	−0.326077	−	0.945343i	$-0.605727\pi$
$149$	−13.7007	−	4.15606i	−1.12240	−	0.340478i	−0.796327	+	0.604866i	$0.793227\pi$
$150$	2.22807	−	2.71985i	0.181921	−	0.222075i
$151$	−0.0820805	+	0.412646i	−0.00667961	+	0.0335807i	−0.983981	−	0.178271i	$-0.942950\pi$
$151$	−0.0820805	+	0.412646i	−0.00667961	+	0.0335807i	0.977302	+	0.211852i	$0.0679495\pi$
$152$	−4.28100	+	1.31114i	−0.347235	+	0.106348i
$153$	−0.638180	+	0.126942i	−0.0515938	+	0.0102626i
$154$	0.388389	−	0.118195i	0.0312973	−	0.00952442i
$155$	−0.888483	−	0.729159i	−0.0713646	−	0.0585675i
$156$	8.05519	+	5.36155i	0.644932	+	0.429268i
$157$	0.140075	−	0.262063i	0.0111792	−	0.0209149i	−0.876270	−	0.481821i	$-0.839976\pi$
$157$	0.140075	−	0.262063i	0.0111792	−	0.0209149i	0.887449	+	0.460906i	$0.152476\pi$
$158$	−8.78702	+	8.80270i	−0.699057	+	0.700305i
$159$	5.70627	−	5.70627i	0.452536	−	0.452536i
$160$	−4.26318	−	7.89103i	−0.337034	−	0.623841i
$161$	0.219701	+	0.219701i	0.0173148	+	0.0173148i
$162$	−1.41421	+	0.00126099i	−0.111111	+	9.90724e-5i
$163$	15.8098	+	8.45053i	1.23832	+	0.661897i	0.954851	−	0.297084i	$-0.0960142\pi$
$163$	15.8098	+	8.45053i	1.23832	+	0.661897i	0.283471	+	0.958981i	$0.408514\pi$
$164$	−17.2329	+	11.5592i	−1.34566	+	0.902619i
$165$	4.98860	−	6.07862i	0.388362	−	0.473220i
$166$	9.33206	−	17.4966i	0.724308	−	1.35800i
$167$	0.0606693	+	0.305005i	0.00469473	+	0.0236020i	0.983062	−	0.183275i	$-0.0586699\pi$
$167$	0.0606693	+	0.305005i	0.00469473	+	0.0236020i	−0.978367	+	0.206877i	$0.933670\pi$
$168$	0.126828	+	0.103519i	0.00978501	+	0.00798664i
$169$	10.2081	+	2.03052i	0.785239	+	0.156194i
$170$	1.45184	−	0.144301i	0.111351	−	0.0110674i
$171$	0.459509	−	1.51480i	0.0351395	−	0.115839i
$172$	0.0924700	+	0.172260i	0.00705077	+	0.0131347i
$173$	12.0609	+	14.6962i	0.916971	+	1.11733i	0.992749	+	0.120208i	$0.0383561\pi$
$173$	12.0609	+	14.6962i	0.916971	+	1.11733i	−0.0757777	+	0.997125i	$0.524144\pi$
$174$	2.30950	+	11.5568i	0.175083	+	0.876117i
$175$	0.0550684	−	0.132947i	0.00416278	−	0.0100498i
$176$	9.41418	+	17.4626i	0.709620	+	1.31629i
$177$	−2.44565	−	5.90432i	−0.183826	−	0.443796i
$178$	−12.9061	+	8.64025i	−0.967355	+	0.647614i
$179$	−0.966878	+	9.81687i	−0.0722678	+	0.733748i	0.888959	+	0.457987i	$0.151430\pi$
$179$	−0.966878	+	9.81687i	−0.0722678	+	0.733748i	−0.961226	+	0.275760i	$0.911070\pi$
$180$	3.15630	+	0.305186i	0.235257	+	0.0227473i
$181$	−0.357480	−	0.668799i	−0.0265713	−	0.0497114i	0.868285	−	0.496065i	$-0.165222\pi$
$181$	−0.357480	−	0.668799i	−0.0265713	−	0.0497114i	−0.894857	+	0.446354i	$0.852722\pi$
$182$	0.379084	+	0.114625i	0.0280995	+	0.00849655i
$183$	2.63516	+	3.94379i	0.194796	+	0.291534i
$184$	−8.40141	+	12.6467i	−0.619360	+	0.932327i
$185$	12.9948	+	8.68286i	0.955398	+	0.638376i
$186$	−0.0995775	+	1.02035i	−0.00730138	+	0.0748160i
$187$	−3.21161	+	0.316316i	−0.234856	+	0.0231313i
$188$	−4.19014	−	10.0651i	−0.305597	−	0.734072i
$189$	−0.0553885	+	0.0168019i	−0.00402892	+	0.00122216i
$190$	−1.35537	+	3.28042i	−0.0983288	+	0.237987i
$191$			0.860718i			0.0622794i	0.999515	+	0.0311397i	$0.00991367\pi$
$191$			0.860718i			0.0622794i	−0.999515	+	0.0311397i	$0.990086\pi$
$192$	−3.73337	+	7.07544i	−0.269433	+	0.510626i
$193$			11.5965i			0.834734i	0.908738	+	0.417367i	$0.137047\pi$
$193$			11.5965i			0.834734i	−0.908738	+	0.417367i	$0.862953\pi$
$194$	−19.2807	−	7.96618i	−1.38427	−	0.571939i
$195$	7.34070	−	2.22678i	0.525678	−	0.159463i
$196$	−12.9377	−	5.33194i	−0.924118	−	0.380853i
$197$	9.92983	−	0.978003i	0.707471	−	0.0696798i	0.262119	−	0.965035i	$-0.415579\pi$
$197$	9.92983	−	0.978003i	0.707471	−	0.0696798i	0.445352	+	0.895356i	$0.353079\pi$
$198$	−6.98083	−	0.681267i	−0.496106	−	0.0484156i
$199$	−11.2466	−	7.51473i	−0.797249	−	0.532705i	0.0889353	−	0.996037i	$-0.471654\pi$
$199$	−11.2466	−	7.51473i	−0.797249	−	0.532705i	−0.886185	+	0.463332i	$0.846654\pi$
$200$	6.90043	+	1.35340i	0.487934	+	0.0957000i
$201$	−2.24840	−	3.36496i	−0.158590	−	0.237346i
$202$	−2.56480	+	8.48223i	−0.180459	+	0.596807i
$203$	0.227377	+	0.425392i	0.0159587	+	0.0298567i
$204$	−0.827370	−	1.00449i	−0.0579275	−	0.0703287i
$205$	−1.61240	+	16.3709i	−0.112615	+	1.14340i
$206$	11.4642	+	17.1244i	0.798751	+	1.19311i
$207$	−2.05424	−	4.95938i	−0.142780	−	0.344701i
$208$	−1.82820	+	19.2662i	−0.126763	+	1.33587i
$209$	3.00441	−	7.25329i	0.207820	−	0.501721i
$210$	0.127267	−	0.0254330i	0.00878226	−	0.00175504i
$211$	12.8631	+	15.6737i	0.885533	+	1.07903i	0.996365	+	0.0851862i	$0.0271485\pi$
$211$	12.8631	+	15.6737i	0.885533	+	1.07903i	−0.110832	+	0.993839i	$0.535352\pi$
$212$	15.4531	+	4.65757i	1.06132	+	0.319884i
$213$	−0.606873	+	2.00059i	−0.0415823	+	0.137078i
$214$	−1.44917	−	14.5804i	−0.0990631	−	0.996693i
$215$	0.152013	+	0.0302373i	0.0103672	+	0.00206217i
$216$	−1.33998	−	2.49087i	−0.0911740	−	0.169483i
$217$	0.00818586	+	0.0411531i	0.000555693	+	0.00279366i
$218$	10.6122	+	5.66020i	0.718751	+	0.383357i
$219$	−6.03314	+	7.35140i	−0.407682	+	0.496762i
$220$	15.4304	+	3.04070i	1.04032	+	0.205004i
$221$	−2.77640	−	1.48402i	−0.186761	−	0.0998257i
$222$	−0.0124298	−	13.9402i	−0.000834234	−	0.935605i
$223$	−13.1006	−	13.1006i	−0.877284	−	0.877284i	0.115969	−	0.993253i	$-0.463003\pi$
$223$	−13.1006	−	13.1006i	−0.877284	−	0.877284i	−0.993253	+	0.115969i	$0.963003\pi$
$224$	−0.0624448	+	0.321414i	−0.00417227	+	0.0214753i
$225$	−1.75798	+	1.75798i	−0.117198	+	0.117198i
$226$	−9.71003	−	9.69272i	−0.645901	−	0.644750i
$227$	7.20050	−	13.4712i	0.477914	−	0.894114i	−0.521257	−	0.853400i	$-0.674537\pi$
$227$	7.20050	−	13.4712i	0.477914	−	0.894114i	0.999171	−	0.0407145i	$-0.0129634\pi$
$228$	3.10398	−	0.623176i	0.205566	−	0.0412709i
$229$	21.8004	+	17.8911i	1.44061	+	1.18228i	0.950543	+	0.310593i	$0.100528\pi$
$229$	21.8004	+	17.8911i	1.44061	+	1.18228i	0.490067	+	0.871685i	$0.336972\pi$
$230$	3.50425	+	11.5150i	0.231063	+	0.759276i
$231$	−0.281552	+	0.0560042i	−0.0185248	+	0.00368481i
$232$	−18.1802	+	15.0017i	−1.19359	+	0.984909i
$233$	−3.30150	+	16.5977i	−0.216288	+	1.08735i	0.708162	+	0.706050i	$0.249525\pi$
$233$	−3.30150	+	16.5977i	−0.216288	+	1.08735i	−0.924450	+	0.381304i	$0.875475\pi$
$234$	−5.29299	−	4.33595i	−0.346013	−	0.283450i
$235$	−8.27081	−	2.50892i	−0.539528	−	0.163664i
$236$	8.09092	−	9.89474i	0.526674	−	0.644093i
$237$	6.79852	−	5.57940i	0.441611	−	0.362421i
$238$	−0.0443122	−	0.0295514i	−0.00287233	−	0.00191553i
$239$	21.7836	+	9.02307i	1.40907	+	0.583654i	0.952088	−	0.305824i	$-0.0989320\pi$
$239$	21.7836	+	9.02307i	1.40907	+	0.583654i	0.456977	+	0.889478i	$0.348932\pi$
$240$	2.44788	+	5.85059i	0.158010	+	0.377654i
$241$	−17.9566	+	7.43787i	−1.15669	+	0.479116i	−0.876771	−	0.480909i	$-0.840307\pi$
$241$	−17.9566	+	7.43787i	−1.15669	+	0.479116i	−0.279917	+	0.960024i	$0.590307\pi$
$242$	−18.8644	−	3.73488i	−1.21265	−	0.240087i
$243$	0.995185	+	0.0980171i	0.0638411	+	0.00628780i
$244$	−4.45689	+	8.37415i	−0.285323	+	0.536100i
$245$	−9.78339	+	5.22933i	−0.625038	+	0.334090i
$246$	12.9342	−	6.92828i	0.824651	−	0.441731i
$247$	6.36794	−	4.25492i	0.405182	−	0.270734i
$248$	−1.89222	+	0.789720i	−0.120156	+	0.0501472i
$249$	−7.79005	+	11.6586i	−0.493674	+	0.738836i
$250$	12.9661	−	10.6604i	0.820050	−	0.674222i
$251$	−2.18957	−	22.2311i	−0.138204	−	1.40321i	−0.774894	−	0.632091i	$-0.782197\pi$
$251$	−2.18957	−	22.2311i	−0.138204	−	1.40321i	0.636689	−	0.771120i	$-0.280303\pi$
$252$	−0.0820017	−	0.0817097i	−0.00516562	−	0.00514723i
$253$	−7.72834	−	25.4769i	−0.485877	−	1.60172i
$254$	1.21482	+	2.92544i	0.0762243	+	0.183559i
$255$	−1.03166			−0.0646053
$256$	−15.9996	+	0.114130i	−0.999975	+	0.00713315i
$257$	7.91143			0.493501			0.246751	−	0.969079i	$-0.420637\pi$
$257$	7.91143			0.493501			0.246751	+	0.969079i	$0.420637\pi$
$258$	−0.0530184	−	0.127676i	−0.00330078	−	0.00794874i
$259$	−0.165620	−	0.545976i	−0.0102911	−	0.0339253i
$260$	10.8678	+	10.8291i	0.673991	+	0.671591i
$261$	−0.816821	−	8.29333i	−0.0505600	−	0.513344i
$262$	2.73061	−	2.24503i	0.168698	−	0.138699i
$263$	−5.40841	+	8.09426i	−0.333497	+	0.499114i	−0.959884	−	0.280399i	$-0.909533\pi$
$263$	−5.40841	+	8.09426i	−0.333497	+	0.499114i	0.626386	+	0.779513i	$0.284533\pi$
$264$	−5.40293	−	12.9458i	−0.332527	−	0.796757i
$265$	10.6386	−	7.10846i	0.653522	−	0.436669i
$266$	0.114220	−	0.0611828i	0.00700327	−	0.00375136i
$267$	9.68552	−	5.17702i	0.592744	−	0.316829i
$268$	3.80275	−	7.14507i	0.232290	−	0.436455i
$269$	−28.1085	−	2.76844i	−1.71380	−	0.168795i	−0.807058	−	0.590472i	$-0.798942\pi$
$269$	−28.1085	−	2.76844i	−1.71380	−	0.168795i	−0.906746	+	0.421677i	$0.861442\pi$
$270$	−2.19956	−	0.435481i	−0.133861	−	0.0265025i
$271$	−1.78172	+	0.738013i	−0.108232	+	0.0448311i	−0.436142	−	0.899878i	$-0.643656\pi$
$271$	−1.78172	+	0.738013i	−0.108232	+	0.0448311i	0.327910	+	0.944709i	$0.393656\pi$
$272$	0.987439	−	2.40815i	0.0598723	−	0.146015i
$273$	−0.258722	−	0.107166i	−0.0156586	−	0.00648599i
$274$	−1.19683	−	0.798154i	−0.0723032	−	0.0482182i
$275$	−9.53155	+	7.82234i	−0.574774	+	0.471705i
$276$	6.79603	−	8.31116i	0.409073	−	0.500273i
$277$	11.3870	+	3.45421i	0.684178	+	0.207543i	0.613192	−	0.789934i	$-0.289885\pi$
$277$	11.3870	+	3.45421i	0.684178	+	0.207543i	0.0709862	+	0.997477i	$0.477385\pi$
$278$	−8.26085	−	6.76719i	−0.495453	−	0.405869i
$279$	0.141426	−	0.710998i	0.00846696	−	0.0425663i
$280$	0.165204	+	0.200207i	0.00987280	+	0.0119646i
$281$	−20.8527	+	4.14786i	−1.24397	+	0.247440i	−0.772826	−	0.634618i	$-0.781158\pi$
$281$	−20.8527	+	4.14786i	−1.24397	+	0.247440i	−0.471141	+	0.882058i	$0.656158\pi$
$282$	2.24444	+	7.37524i	0.133654	+	0.439189i
$283$	−13.6660	−	11.2154i	−0.812357	−	0.666684i	0.133579	−	0.991038i	$-0.457353\pi$
$283$	−13.6660	−	11.2154i	−0.812357	−	0.666684i	−0.945936	+	0.324354i	$0.894853\pi$
$284$	−4.09942	+	0.823029i	−0.243256	+	0.0488378i
$285$	1.18311	−	2.21345i	0.0700815	−	0.131113i
$286$	−24.0171	−	23.9743i	−1.42016	−	1.41763i
$287$	0.424639	−	0.424639i	0.0250657	−	0.0250657i
$288$	3.12178	−	4.71747i	0.183953	−	0.277979i
$289$	−11.7214	−	11.7214i	−0.689496	−	0.689496i
$290$	0.0166611	+	18.6857i	0.000978376	+	1.09726i
$291$	13.0095	+	6.95374i	0.762632	+	0.407635i
$292$	−18.6613	−	3.67738i	−1.09207	−	0.215202i
$293$	0.0715920	−	0.0872351i	0.00418245	−	0.00509633i	−0.770915	−	0.636938i	$-0.780201\pi$
$293$	0.0715920	−	0.0872351i	0.00418245	−	0.00509633i	0.775097	+	0.631842i	$0.217701\pi$
$294$	8.73055	+	4.65657i	0.509176	+	0.271577i
$295$	−1.97679	−	9.93798i	−0.115093	−	0.578611i
$296$	24.5531	−	13.2085i	1.42712	−	0.767726i
$297$	4.86434	+	0.967578i	0.282258	+	0.0561446i
$298$	2.00257	+	20.1483i	0.116006	+	1.16716i
$299$	7.53909	−	24.8531i	0.435997	−	1.43729i
$300$	−4.76077	−	1.43490i	−0.274863	−	0.0828438i
$301$	−0.00358948	−	0.00437379i	−0.000206894	−	0.000252101i
$302$	0.583466	−	0.116600i	0.0335747	−	0.00670955i
$303$	2.39791	−	5.78906i	0.137756	−	0.332573i
$304$	4.03430	+	4.88022i	0.231383	+	0.279900i
$305$	2.87791	+	6.94788i	0.164788	+	0.397835i
$306$	0.511920	+	0.764665i	0.0292645	+	0.0437130i
$307$	−2.22788	+	22.6200i	−0.127152	+	1.29099i	0.693872	+	0.720098i	$0.255903\pi$
$307$	−2.22788	+	22.6200i	−0.127152	+	1.29099i	−0.821024	+	0.570894i	$0.806597\pi$
$308$	−0.365019	−	0.443163i	−0.0207989	−	0.0252516i
$309$	−6.86908	−	12.8511i	−0.390768	−	0.731076i
$310$	−0.470462	+	1.55590i	−0.0267204	+	0.0883690i
$311$	−12.2148	−	18.2807i	−0.692636	−	1.03660i	−0.996476	−	0.0838795i	$-0.973269\pi$
$311$	−12.2148	−	18.2807i	−0.692636	−	1.03660i	0.303840	−	0.952723i	$-0.401731\pi$
$312$	2.63380	−	13.4286i	0.149109	−	0.760246i
$313$	12.0890	+	8.07758i	0.683308	+	0.456572i	0.848156	−	0.529747i	$-0.177713\pi$
$313$	12.0890	+	8.07758i	0.683308	+	0.456572i	−0.164848	+	0.986319i	$0.552713\pi$
$314$	−0.418246	−	0.0408171i	−0.0236030	−	0.00230344i
$315$	−0.0913288	+	0.00899510i	−0.00514580	+	0.000506817i
$316$	16.2628	+	6.70230i	0.914852	+	0.377034i
$317$	−28.9337	+	8.77694i	−1.62508	+	0.492962i	−0.965876	−	0.259004i	$-0.916606\pi$
$317$	−28.9337	+	8.77694i	−1.62508	+	0.492962i	−0.659202	+	0.751966i	$0.729106\pi$
$318$	−10.5477	−	4.35798i	−0.591485	−	0.244384i
$319$		−	41.3309i		−	2.31409i
$320$	−7.99413	+	9.84785i	−0.446886	+	0.550511i
$321$			10.3607i			0.578276i
$322$	0.167790	−	0.406104i	0.00935055	−	0.0226313i
$323$	−0.985652	+	0.298994i	−0.0548431	+	0.0166365i
$324$	0.768661	+	1.84639i	0.0427034	+	0.102577i
$325$	−11.9706	+	1.17900i	−0.664007	+	0.0653990i
$326$	2.46243	−	25.2321i	0.136382	−	1.39748i
$327$	−7.07134	−	4.72492i	−0.391046	−	0.261289i
$328$	24.4436	+	16.2383i	1.34967	+	0.896610i
$329$	0.175294	+	0.262346i	0.00966428	+	0.0144636i
$330$	−10.6448	−	3.21870i	−0.585976	−	0.177184i
$331$	−11.2453	−	21.0384i	−0.618095	−	1.15637i	−0.974994	−	0.222231i	$-0.928666\pi$
$331$	−11.2453	−	21.0384i	−0.618095	−	1.15637i	0.356899	−	0.934143i	$-0.383834\pi$
$332$	−27.9132	−	2.69896i	−1.53194	−	0.148125i
$333$	−0.966176	+	9.80975i	−0.0529461	+	0.537571i
$334$	0.365457	−	0.244662i	0.0199969	−	0.0133873i
$335$	−2.45552	−	5.92814i	−0.134159	−	0.323889i
$336$	0.0664170	−	0.221792i	0.00362335	−	0.0120998i
$337$	−12.8508	+	31.0245i	−0.700025	+	1.69001i	0.0235110	+	0.999724i	$0.492516\pi$
$337$	−12.8508	+	31.0245i	−0.700025	+	1.69001i	−0.723536	+	0.690287i	$0.757484\pi$
$338$	−2.88446	−	14.4339i	−0.156894	−	0.785100i
$339$	6.15449	+	7.49927i	0.334266	+	0.407304i
$340$	−0.975890	−	1.81796i	−0.0529251	−	0.0985925i
$341$	1.04368	−	3.44056i	0.0565186	−	0.186317i
$342$	−2.22767	+	0.221412i	−0.120458	+	0.0119726i
$343$	0.794571	+	0.158050i	0.0429028	+	0.00853390i
$344$	0.174833	−	0.214200i	0.00942634	−	0.0115489i
$345$	−1.66042	−	8.34748i	−0.0893938	−	0.449413i
$346$	12.6531	−	23.7231i	0.680234	−	1.27536i
$347$	−16.6379	+	20.2733i	−0.893169	+	1.08833i	0.102442	+	0.994739i	$0.467334\pi$
$347$	−16.6379	+	20.2733i	−0.893169	+	1.08833i	−0.995611	+	0.0935905i	$0.970166\pi$
$348$	13.8415	−	9.28434i	0.741982	−	0.497693i
$349$	16.4725	+	8.80473i	0.881753	+	0.471307i	0.849144	−	0.528162i	$-0.177118\pi$
$349$	16.4725	+	8.80473i	0.881753	+	0.471307i	0.0326088	+	0.999468i	$0.489618\pi$
$350$	−0.203506		0.000181457i	−0.0108779		9.69926e-6i
$351$	3.42112	+	3.42112i	0.182606	+	0.182606i
$352$	17.7017	−	21.7667i	0.943502	−	1.16017i
$353$	4.91497	−	4.91497i	0.261598	−	0.261598i	−0.564105	−	0.825703i	$-0.690779\pi$
$353$	4.91497	−	4.91497i	0.261598	−	0.261598i	0.825703	+	0.564105i	$0.190779\pi$
$354$	−6.38509	+	6.39649i	−0.339364	+	0.339969i
$355$	−1.56253	+	2.92330i	−0.0829307	+	0.155153i
$356$	18.2846	+	12.1703i	0.969083	+	0.645024i
$357$	0.0291131	+	0.0238925i	0.00154083	+	0.00126453i
$358$	13.3460	−	4.06147i	0.705359	−	0.214655i
$359$	29.5254	−	5.87297i	1.55829	−	0.309963i	0.660652	−	0.750693i	$-0.270280\pi$
$359$	29.5254	−	5.87297i	1.55829	−	0.309963i	0.897640	+	0.440729i	$0.145280\pi$
$360$	−1.31326	−	4.28791i	−0.0692147	−	0.225992i
$361$	−3.21787	+	16.1773i	−0.169361	+	0.851437i
$362$	−0.679621	+	0.829628i	−0.0357201	+	0.0436043i
$363$	13.0125	+	3.94731i	0.682981	+	0.207180i
$364$	−0.0558910	−	0.557281i	−0.00292949	−	0.0292095i
$365$	−11.6557	+	9.56561i	−0.610089	+	0.500687i
$366$	3.72170	−	5.58069i	0.194536	−	0.291707i
$367$	19.5474	+	8.09681i	1.02037	+	0.422650i	0.829227	−	0.558913i	$-0.188781\pi$
$367$	19.5474	+	8.09681i	1.02037	+	0.422650i	0.191141	+	0.981563i	$0.438781\pi$
$368$	21.0742	+	4.11384i	1.09857	+	0.214449i
$369$	−9.58552	+	3.97045i	−0.499002	+	0.206694i
$370$	4.29263	−	21.6815i	0.223163	−	1.12717i
$371$	−0.464842	−	0.0457829i	−0.0241334	−	0.00237693i
$372$	1.38667	−	0.423344i	0.0718955	−	0.0219494i
$373$	−9.63101	+	5.14788i	−0.498675	+	0.266547i	−0.701502	−	0.712667i	$-0.747487\pi$
$373$	−9.63101	+	5.14788i	−0.498675	+	0.266547i	0.202827	+	0.979214i	$0.434987\pi$
$374$	2.15499	+	4.02306i	0.111432	+	0.208028i
$375$	−9.86903	+	6.59428i	−0.509635	+	0.340527i
$376$	−10.8732	+	10.9316i	−0.560744	+	0.563752i
$377$	22.3999	−	33.5239i	1.15366	−	1.72657i
$378$	0.0519852	+	0.0632291i	0.00267383	+	0.00325215i
$379$	−0.997057	−	10.1233i	−0.0512154	−	0.519999i	−0.986229	−	0.165386i	$-0.947113\pi$
$379$	−0.997057	−	10.1233i	−0.0512154	−	0.519999i	0.935013	−	0.354612i	$-0.115387\pi$
$380$	5.01959	−	0.00895146i	0.257500	−	0.000459200i
$381$	−0.650198	−	2.14342i	−0.0333107	−	0.109811i
$382$	1.12417	−	0.466820i	0.0575174	−	0.0238846i
$383$	11.6928			0.597473			0.298737	−	0.954336i	$-0.403435\pi$
$383$	11.6928			0.597473			0.298737	+	0.954336i	$0.403435\pi$
$384$	11.2659	+	1.03864i	0.574912	+	0.0530029i
$385$	−0.455150			−0.0231966
$386$	15.1459	−	6.28948i	0.770908	−	0.320126i
$387$	0.0283767	+	0.0935456i	0.00144247	+	0.00475519i
$388$	0.0526122	+	29.5027i	0.00267098	+	1.49777i
$389$	0.294453	+	2.98963i	0.0149294	+	0.151580i	0.999759	−	0.0219423i	$-0.00698500\pi$
$389$	0.294453	+	2.98963i	0.0149294	+	0.151580i	−0.984830	+	0.173523i	$0.944485\pi$
$390$	−6.88966	−	8.37982i	−0.348871	−	0.424329i
$391$	−1.94053	+	2.90420i	−0.0981367	+	0.146872i
$392$	0.0529360	+	19.7894i	0.00267367	+	0.999518i
$393$	−2.07838	+	1.38873i	−0.104840	+	0.0700520i
$394$	−6.66290	−	12.4387i	−0.335672	−	0.626654i
$395$	12.2978	−	6.57332i	0.618771	−	0.330740i
$396$	2.89634	+	9.48701i	0.145547	+	0.476740i
$397$	−7.43477	−	0.732261i	−0.373141	−	0.0367511i	−0.0902910	−	0.995915i	$-0.528780\pi$
$397$	−7.43477	−	0.732261i	−0.373141	−	0.0367511i	−0.282850	+	0.959164i	$0.591280\pi$
$398$	−3.71513	+	18.7646i	−0.186222	+	0.940586i
$399$	−0.0846486	+	0.0350626i	−0.00423773	+	0.00175532i
$400$	−1.97487	−	9.74655i	−0.0987436	−	0.487327i
$401$	−24.6232	−	10.1993i	−1.22962	−	0.509327i	−0.329167	−	0.944272i	$-0.606768\pi$
$401$	−24.6232	−	10.1993i	−1.22962	−	0.509327i	−0.900457	+	0.434945i	$0.856768\pi$
$402$	−3.17547	+	4.76161i	−0.158378	+	0.237487i
$403$	2.71121	−	2.22503i	0.135055	−	0.110837i
$404$	12.4695	−	1.25060i	0.620381	−	0.0622195i
$405$	1.51724	+	0.460250i	0.0753923	+	0.0228700i
$406$	0.432276	−	0.527688i	0.0214535	−	0.0261887i
$407$	−9.53763	+	47.9489i	−0.472763	+	2.37674i
$408$	−0.863217	+	1.62541i	−0.0427356	+	0.0804697i
$409$	−12.4430	+	2.47506i	−0.615266	+	0.122384i	−0.492878	−	0.870098i	$-0.664055\pi$
$409$	−12.4430	+	2.47506i	−0.615266	+	0.122384i	−0.122388	+	0.992482i	$0.539055\pi$
$410$	22.2563	−	6.77304i	1.09916	−	0.334496i
$411$	0.786318	+	0.645314i	0.0387862	+	0.0318310i
$412$	16.1480	−	24.2608i	0.795556	−	1.19524i
$413$	−0.174372	+	0.326226i	−0.00858027	+	0.0160526i
$414$	−5.36320	+	5.37278i	−0.263587	+	0.264058i
$415$	−15.7201	+	15.7201i	−0.771670	+	0.771670i
$416$	26.1548	−	8.06147i	1.28234	−	0.395246i
$417$	5.33940	+	5.33940i	0.261471	+	0.261471i
$418$	−11.1029	+	0.00989988i	−0.543059	+	0.000484219i
$419$	−24.1513	−	12.9091i	−1.17987	−	0.630652i	−0.239527	−	0.970890i	$-0.576992\pi$
$419$	−24.1513	−	12.9091i	−1.17987	−	0.630652i	−0.940339	+	0.340238i	$0.889492\pi$
$420$	−0.102242	−	0.152427i	−0.00498891	−	0.00743768i
$421$	4.76599	−	5.80738i	0.232280	−	0.283034i	−0.643806	−	0.765189i	$-0.722646\pi$
$421$	4.76599	−	5.80738i	0.232280	−	0.283034i	0.876086	+	0.482155i	$0.160146\pi$
$422$	13.4947	−	25.3011i	0.656913	−	1.23164i
$423$	−1.06348	−	5.34648i	−0.0517082	−	0.259955i
$424$	−2.29800	−	22.7091i	−0.111601	−	1.10285i
$425$	1.58661	+	0.315597i	0.0769620	+	0.0153087i
$426$	2.94208	−	0.292418i	0.142544	−	0.0141677i
$427$	0.0796941	−	0.262716i	0.00385667	−	0.0127137i
$428$	−18.2571	+	9.80054i	−0.882492	+	0.473727i
$429$	15.2227	+	18.5489i	0.734959	+	0.895551i
$430$	−0.0429537	−	0.214941i	−0.00207141	−	0.0103654i
$431$	−5.12399	+	12.3704i	−0.246814	+	0.595862i	−0.997930	−	0.0643085i	$-0.979516\pi$
$431$	−5.12399	+	12.3704i	−0.246814	+	0.595862i	0.751116	+	0.660170i	$0.229516\pi$
$432$	−2.52653	+	3.10107i	−0.121558	+	0.149200i
$433$	−5.52846	−	13.3469i	−0.265681	−	0.641410i	0.733590	−	0.679592i	$-0.237843\pi$
$433$	−5.52846	−	13.3469i	−0.265681	−	0.641410i	−0.999271	+	0.0381821i	$0.987843\pi$
$434$	0.0493096	−	0.0330112i	0.00236694	−	0.00158459i
$435$	1.29508	−	13.1492i	0.0620943	−	0.630454i
$436$	1.63701	−	16.9303i	0.0783985	−	0.810814i
$437$	−4.00560	−	7.49396i	−0.191614	−	0.358485i
$438$	12.8737	+	3.89265i	0.615127	+	0.185998i
$439$	2.83784	+	4.24712i	0.135443	+	0.202704i	0.892991	−	0.450075i	$-0.148603\pi$
$439$	2.83784	+	4.24712i	0.135443	+	0.202704i	−0.757548	+	0.652779i	$0.773603\pi$
$440$	−4.39745	−	21.8025i	−0.209640	−	1.03939i
$441$	−5.81750	−	3.88713i	−0.277024	−	0.185101i
$442$	−0.432433	+	4.43107i	−0.0205688	+	0.210765i
$443$	37.0647	−	3.65056i	1.76100	−	0.173443i	0.834819	−	0.550525i	$-0.185572\pi$
$443$	37.0647	−	3.65056i	1.76100	−	0.173443i	0.926180	+	0.377082i	$0.123072\pi$
$444$	−18.2003	+	7.57685i	−0.863747	+	0.359582i
$445$	16.6628	−	5.05460i	0.789892	−	0.239611i
$446$	−10.0052	+	24.2158i	−0.473760	+	1.14665i
$447$		−	14.3172i		−	0.677179i
$448$	0.453659	−	0.0927643i	0.0214334	−	0.00438270i
$449$		−	39.4355i		−	1.86108i	−0.366195	−	0.930538i	$-0.619340\pi$
$449$		−	39.4355i		−	1.86108i	0.366195	−	0.930538i	$-0.380660\pi$
$450$	3.24951	+	1.34260i	0.153184	+	0.0632907i
$451$	−49.2420	+	14.9374i	−2.31871	+	0.703374i
$452$	−7.39314	+	17.9390i	−0.347744	+	0.843781i
$453$	−0.418705	+	0.0412388i	−0.0196725	+	0.00193757i
$454$	−21.4997	−	2.09818i	−1.00903	−	0.0984726i
$455$	−0.369176	−	0.246676i	−0.0173072	−	0.0115643i
$456$	−2.49739	−	3.71606i	−0.116951	−	0.174020i
$457$	8.51655	+	12.7459i	0.398387	+	0.596229i	0.975383	−	0.220519i	$-0.0707750\pi$
$457$	8.51655	+	12.7459i	0.398387	+	0.596229i	−0.576996	+	0.816747i	$0.695775\pi$
$458$	11.5435	−	38.1765i	0.539395	−	1.78387i
$459$	−0.306729	−	0.573851i	−0.0143169	−	0.0267850i
$460$	13.1389	−	10.8221i	0.612606	−	0.504583i
$461$	0.609193	−	6.18524i	0.0283730	−	0.288075i	−0.970519	−	0.241023i	$-0.922517\pi$
$461$	0.609193	−	6.18524i	0.0283730	−	0.288075i	0.998892	−	0.0470526i	$-0.0149829\pi$
$462$	0.225849	+	0.337355i	0.0105074	+	0.0156952i
$463$	10.6529	+	25.7184i	0.495083	+	1.19524i	0.952102	+	0.305779i	$0.0989170\pi$
$463$	10.6529	+	25.7184i	0.495083	+	1.19524i	−0.457019	+	0.889457i	$0.651083\pi$
$464$	29.4537	+	15.6085i	1.36735	+	0.724606i
$465$	0.439849	−	1.06189i	0.0203975	−	0.0492439i
$466$	23.4686	−	4.68995i	1.08716	−	0.217258i
$467$	−4.96675	−	6.05200i	−0.229834	−	0.280053i	0.645305	−	0.763925i	$-0.276730\pi$
$467$	−4.96675	−	6.05200i	−0.229834	−	0.280053i	−0.875139	+	0.483872i	$0.839230\pi$
$468$	−2.79239	+	9.26472i	−0.129078	+	0.428262i
$469$	−0.0679974	+	0.224158i	−0.00313983	+	0.0103506i
$470$	1.20891	+	12.1631i	0.0557629	+	0.561041i
$471$	0.291440	+	0.0579710i	0.0134288	+	0.00267116i
$472$	−17.3115	−	5.20086i	−0.796827	−	0.239389i
$473$	0.0945855	+	0.475513i	0.00434904	+	0.0218641i
$474$	−10.9744	−	5.85336i	−0.504071	−	0.268854i
$475$	−2.49664	+	3.04216i	−0.114554	+	0.139584i
$476$	−0.0145632	+	0.0739028i	−0.000667504	+	0.00338733i
$477$	7.11700	+	3.80411i	0.325865	+	0.174178i
$478$	−0.0297321	−	33.3449i	−0.00135991	−	1.52516i
$479$	13.8867	+	13.8867i	0.634499	+	0.634499i	0.949193	−	0.314694i	$-0.101902\pi$
$479$	13.8867	+	13.8867i	0.634499	+	0.634499i	−0.314694	+	0.949193i	$0.601902\pi$
$480$	6.31371	−	6.37026i	0.288180	−	0.290761i
$481$	−33.7227	+	33.7227i	−1.53762	+	1.53762i
$482$	19.4534	+	19.4188i	0.886079	+	0.884500i
$483$	−0.146465	+	0.274016i	−0.00666438	+	0.0124682i
$484$	5.35326	+	26.6640i	0.243330	+	1.21200i
$485$	18.0795	+	14.8375i	0.820948	+	0.673735i
$486$	−0.411731	−	1.35295i	−0.0186765	−	0.0613711i
$487$	39.5977	−	7.87647i	1.79434	−	0.356917i	0.818350	−	0.574720i	$-0.194889\pi$
$487$	39.5977	−	7.87647i	1.79434	−	0.356917i	0.975993	+	0.217802i	$0.0698889\pi$
$488$	13.3545	+	1.27925i	0.604532	+	0.0579088i
$489$	−3.49730	+	17.5821i	−0.158154	+	0.795091i
$490$	12.1361	+	9.94171i	0.548251	+	0.449120i
$491$	−33.4614	−	10.1504i	−1.51009	−	0.458081i	−0.576705	−	0.816953i	$-0.695662\pi$
$491$	−33.4614	−	10.1504i	−1.51009	−	0.458081i	−0.933387	+	0.358871i	$0.883162\pi$
$492$	−16.0639	−	13.1354i	−0.724215	−	0.592190i
$493$	−4.19160	+	3.43995i	−0.188780	+	0.154928i
$494$	−9.01099	−	6.00934i	−0.405424	−	0.270373i
$495$	7.26499	+	3.00926i	0.326537	+	0.135256i
$496$	2.05770	+	2.04308i	0.0923936	+	0.0917368i
$497$	0.111795	−	0.0463071i	0.00501471	−	0.00207716i
$498$	19.4521	+	3.85124i	0.871670	+	0.172578i
$499$	18.0885	+	1.78156i	0.809754	+	0.0797538i	0.494416	−	0.869226i	$-0.335382\pi$
$499$	18.0885	+	1.78156i	0.809754	+	0.0797538i	0.315338	+	0.948979i	$0.397882\pi$
$500$	−20.9556	−	11.1530i	−0.937165	−	0.498778i
$501$	−0.274260	+	0.146595i	−0.0122531	+	0.00654939i
$502$	−27.8480	+	14.9170i	−1.24292	+	0.665779i
$503$	−26.4166	+	17.6510i	−1.17786	+	0.787020i	−0.981113	−	0.193434i	$-0.938037\pi$
$503$	−26.4166	+	17.6510i	−1.17786	+	0.787020i	−0.196746	+	0.980454i	$0.563037\pi$
$504$	−0.0622449	+	0.151417i	−0.00277261	+	0.00674465i
$505$	5.51952	−	8.26054i	0.245615	−	0.367589i
$506$	−29.0834	+	23.9115i	−1.29291	+	1.06300i
$507$	1.02017	+	10.3580i	0.0453074	+	0.460014i
$508$	3.16199	−	3.17329i	0.140291	−	0.140792i
$509$	−4.62941	−	15.2611i	−0.205195	−	0.676438i	−0.997775	−	0.0666698i	$-0.978763\pi$
$509$	−4.62941	−	15.2611i	−0.205195	−	0.676438i	0.792580	−	0.609768i	$-0.208737\pi$
$510$	0.559534	+	1.34744i	0.0247766	+	0.0596655i
$511$	0.550452			0.0243506
$512$	8.82662	+	20.8348i	0.390085	+	0.920779i
$513$	1.58296			0.0698893
$514$	−4.29085	−	10.3330i	−0.189261	−	0.455767i
$515$	−6.70665	−	22.1089i	−0.295530	−	0.974232i
$516$	−0.137999	+	0.138493i	−0.00607509	+	0.00609679i
$517$	−2.65000	−	26.9059i	−0.116547	−	1.18332i
$518$	−0.623263	+	0.512429i	−0.0273846	+	0.0225148i
$519$	−10.5623	+	15.8076i	−0.463634	+	0.693878i
$520$	8.24939	−	20.0675i	0.361760	−	0.880016i
$521$	−9.95033	+	6.64860i	−0.435932	+	0.291280i	−0.754107	−	0.656752i	$-0.771930\pi$
$521$	−9.95033	+	6.64860i	−0.435932	+	0.291280i	0.318175	+	0.948032i	$0.396930\pi$
$522$	−10.3887	+	5.56481i	−0.454703	+	0.243565i
$523$	27.1091	−	14.4901i	1.18540	−	0.633608i	0.243628	−	0.969869i	$-0.421662\pi$
$523$	27.1091	−	14.4901i	1.18540	−	0.633608i	0.941769	+	0.336261i	$0.109162\pi$
$524$	−4.41317	−	2.34878i	−0.192790	−	0.102607i
$525$	0.143208	+	0.0141047i	0.00625009	+	0.000615580i
$526$	13.5051	+	2.67381i	0.588849	+	0.116584i
$527$	−0.435791	+	0.180511i	−0.0189834	+	0.00786317i
$528$	−13.9779	+	14.0779i	−0.608309	+	0.612663i
$529$	−5.37267	−	2.22543i	−0.233594	−	0.0967580i
$530$	−15.0542	−	10.0395i	−0.653911	−	0.436086i
$531$	4.94015	−	4.05428i	0.214384	−	0.175941i
$532$	−0.141858	−	0.115997i	−0.00615033	−	0.00502912i
$533$	−48.0362	−	14.5716i	−2.08068	−	0.631167i
$534$	−12.0147	−	9.84226i	−0.519925	−	0.425916i
$535$	−3.20474	+	16.1113i	−0.138553	+	0.696553i
$536$	−11.3945	−	1.09149i	−0.492167	−	0.0471453i
$537$	−9.67483	+	1.92444i	−0.417500	+	0.0830459i
$538$	11.6291	+	38.2134i	0.501367	+	1.64750i
$539$	−26.8241	−	22.0140i	−1.15540	−	0.948210i
$540$	0.624181	+	3.10898i	0.0268605	+	0.133789i
$541$	0.361717	−	0.676726i	0.0155514	−	0.0290947i	−0.874026	−	0.485880i	$-0.838499\pi$
$541$	0.361717	−	0.676726i	0.0155514	−	0.0290947i	0.889577	+	0.456785i	$0.150999\pi$
$542$	1.93024	+	1.92680i	0.0829109	+	0.0827631i
$543$	0.536229	−	0.536229i	0.0230118	−	0.0230118i
$544$	−3.68078	+	0.0164100i	−0.157812	+	0.000703572i
$545$	−9.53476	−	9.53476i	−0.408424	−	0.408424i
$546$	0.000353125		0.396034i	1.51123e−5		0.0169487i
$547$	33.0907	+	17.6874i	1.41486	+	0.756257i	0.988914	−	0.148492i	$-0.0474420\pi$
$547$	33.0907	+	17.6874i	1.41486	+	0.756257i	0.425944	+	0.904749i	$0.359942\pi$
$548$	−0.393339	+	1.99604i	−0.0168026	+	0.0852667i
$549$	−3.00903	+	3.66651i	−0.128422	+	0.156483i
$550$	15.3861	+	8.20643i	0.656067	+	0.349924i
$551$	−2.57354	−	12.9380i	−0.109636	−	0.551179i
$552$	−14.5409	−	4.36850i	−0.618903	−	0.185936i
$553$	−0.499272	−	0.0993115i	−0.0212312	−	0.00422315i
$554$	−1.66439	−	16.7457i	−0.0707131	−	0.711458i
$555$	−4.53678	+	14.9558i	−0.192576	+	0.634837i
$556$	−4.35813	+	14.4596i	−0.184826	+	0.613223i
$557$	5.22503	+	6.36672i	0.221392	+	0.269767i	0.871847	−	0.489778i	$-0.162922\pi$
$557$	5.22503	+	6.36672i	0.221392	+	0.269767i	−0.650456	+	0.759544i	$0.725422\pi$
$558$	−1.00532	+	0.200903i	−0.0425587	+	0.00850492i
$559$	−0.180993	+	0.436955i	−0.00765518	+	0.0184812i
$560$	0.171886	−	0.324353i	0.00726351	−	0.0137064i
$561$	−1.23498	−	2.98150i	−0.0521408	−	0.125879i
$562$	16.7271	+	24.9856i	0.705591	+	1.05396i
$563$	1.76513	−	17.9217i	0.0743914	−	0.755308i	−0.883549	−	0.468340i	$-0.844852\pi$
$563$	1.76513	−	17.9217i	0.0743914	−	0.755308i	0.957940	−	0.286969i	$-0.0926476\pi$
$564$	8.41535	−	6.93145i	0.354350	−	0.291867i
$565$	7.25086	+	13.5654i	0.305046	+	0.570701i
$566$	−7.23628	+	23.9316i	−0.304163	+	1.00592i
$567$	−0.0321569	−	0.0481261i	−0.00135046	−	0.00202111i
$568$	3.29831	+	4.90780i	0.138394	+	0.205927i
$569$	11.3073	+	7.55530i	0.474027	+	0.316735i	0.769534	−	0.638606i	$-0.220489\pi$
$569$	11.3073	+	7.55530i	0.474027	+	0.316735i	−0.295507	+	0.955341i	$0.595489\pi$
$570$	−3.53261	−	0.344752i	−0.147965	−	0.0144401i
$571$	16.6783	−	1.64267i	0.697966	−	0.0687437i	0.257190	−	0.966361i	$-0.417203\pi$
$571$	16.6783	−	1.64267i	0.697966	−	0.0687437i	0.440776	+	0.897617i	$0.354703\pi$
$572$	−18.2864	+	44.3710i	−0.764594	+	1.85524i
$573$	−0.823656	+	0.249853i	−0.0344087	+	0.0104378i
$574$	−0.784920	−	0.324305i	−0.0327619	−	0.0135362i
$575$			13.3456i			0.556552i
$576$	−7.85452	−	1.51872i	−0.327272	−	0.0632801i
$577$		−	20.9813i		−	0.873463i	−0.899592	−	0.436732i	$-0.856136\pi$
$577$		−	20.9813i		−	0.873463i	0.899592	−	0.436732i	$-0.143864\pi$
$578$	−8.95188	+	21.6664i	−0.372349	+	0.901203i
$579$	−11.0971	+	3.36628i	−0.461182	+	0.139898i
$580$	24.3960	−	10.1562i	1.01299	−	0.421711i
$581$	0.807680	−	0.0795496i	0.0335082	−	0.00330027i
$582$	2.02628	−	20.7629i	0.0839919	−	0.860651i
$583$	33.2785	+	22.2360i	1.37825	+	0.920920i
$584$	5.31821	+	26.3676i	0.220069	+	1.09110i
$585$	4.26178	+	6.37821i	0.176203	+	0.263707i
$586$	−0.152765	−	0.0461920i	−0.00631065	−	0.00190817i
$587$	−3.77091	−	7.05487i	−0.155642	−	0.291186i	0.792000	−	0.610522i	$-0.209040\pi$
$587$	−3.77091	−	7.05487i	−0.155642	−	0.291186i	−0.947642	+	0.319336i	$0.896540\pi$
$588$	1.34675	−	13.9283i	0.0555389	−	0.574395i
$589$	0.112478	−	1.14200i	0.00463456	−	0.0470554i
$590$	−11.9077	+	7.97181i	−0.490231	+	0.328194i
$591$	3.81837	+	9.21836i	0.157067	+	0.379193i
$592$	−30.5679	−	24.9045i	−1.25633	−	1.02357i
$593$	−0.716631	+	1.73010i	−0.0294285	+	0.0710467i	−0.937911	−	0.346877i	$-0.887242\pi$
$593$	−0.716631	+	1.73010i	−0.0294285	+	0.0710467i	0.908482	+	0.417924i	$0.137242\pi$
$594$	−1.37450	−	6.87800i	−0.0563962	−	0.282208i
$595$	0.0378819	+	0.0461592i	0.00155301	+	0.00189234i
$596$	25.2291	−	13.5432i	1.03343	−	0.554749i
$597$	3.92643	−	12.9437i	0.160698	−	0.529751i
$598$	−36.5490	+	3.63267i	−1.49460	+	0.148551i
$599$	−28.0457	−	5.57863i	−1.14592	−	0.227937i	−0.414618	−	0.909995i	$-0.636085\pi$
$599$	−28.0457	−	5.57863i	−1.14592	−	0.227937i	−0.731298	+	0.682059i	$0.761085\pi$
$600$	0.707964	+	6.99617i	0.0289025	+	0.285618i
$601$	−2.42907	−	12.2117i	−0.0990837	−	0.498127i	−0.998176	−	0.0603685i	$-0.980772\pi$
$601$	−2.42907	−	12.2117i	−0.0990837	−	0.498127i	0.899092	−	0.437759i	$-0.144228\pi$
$602$	−0.00376573	+	0.00706032i	−0.000153480	+	0.000287757i
$603$	2.56739	−	3.12838i	0.104552	−	0.127397i
$604$	−0.468738	−	0.698815i	−0.0190727	−	0.0284344i
$605$	19.0141	+	10.1633i	0.773034	+	0.413195i
$606$	−8.86151	+	0.00790138i	−0.359974	+	0.000320972i
$607$	−30.3203	−	30.3203i	−1.23066	−	1.23066i	−0.963709	−	0.266955i	$-0.913983\pi$
$607$	−30.3203	−	30.3203i	−1.23066	−	1.23066i	−0.266955	−	0.963709i	$-0.586017\pi$
$608$	4.18590	−	7.91596i	0.169761	−	0.321035i
$609$	−0.341071	+	0.341071i	−0.0138209	+	0.0138209i
$610$	7.51362	−	7.52704i	0.304218	−	0.304761i
$611$	12.4326	−	23.2598i	0.502971	−	0.940992i
$612$	0.721069	−	1.08333i	0.0291475	−	0.0437911i
$613$	31.4219	+	25.7873i	1.26912	+	1.04154i	0.996849	+	0.0793195i	$0.0252747\pi$
$613$	31.4219	+	25.7873i	1.26912	+	1.04154i	0.272271	+	0.962221i	$0.412225\pi$
$614$	30.7519	−	9.35842i	1.24104	−	0.377675i
$615$	−16.1341	+	3.20926i	−0.650588	+	0.129410i
$616$	−0.380834	+	0.717099i	−0.0153443	+	0.0288927i
$617$	−4.54570	+	22.8528i	−0.183003	+	0.920018i	0.774715	+	0.632310i	$0.217893\pi$
$617$	−4.54570	+	22.8528i	−0.183003	+	0.920018i	−0.957718	+	0.287708i	$0.907107\pi$
$618$	−13.0591	+	15.9415i	−0.525314	+	0.641262i
$619$	33.5992	+	10.1922i	1.35047	+	0.409659i	0.880927	−	0.473253i	$-0.156920\pi$
$619$	33.5992	+	10.1922i	1.35047	+	0.409659i	0.469538	+	0.882912i	$0.344420\pi$
$620$	2.28729	−	0.229397i	0.0918596	−	0.00921281i
$621$	4.14951	−	3.40542i	0.166514	−	0.136655i
$622$	−17.2512	+	25.8682i	−0.691711	+	1.03722i
$623$	−0.587277	−	0.243258i	−0.0235288	−	0.00974594i
$624$	−18.9673	+	3.84321i	−0.759301	+	0.153852i
$625$	−5.90200	+	2.44469i	−0.236080	+	0.0977876i
$626$	3.99339	−	20.1701i	0.159608	−	0.806159i
$627$	7.81311	+	0.769524i	0.312025	+	0.0307318i
$628$	0.173530	+	0.568400i	0.00692460	+	0.0226816i
$629$	5.65657	−	3.02350i	0.225542	−	0.120555i
$630$	0.0612815	+	0.114404i	0.00244151	+	0.00455797i
$631$	−29.0322	+	19.3987i	−1.15575	+	0.772250i	−0.977334	−	0.211704i	$-0.932099\pi$
$631$	−29.0322	+	19.3987i	−1.15575	+	0.772250i	−0.178420	+	0.983954i	$0.557099\pi$
$632$	−0.0665411	−	24.8755i	−0.00264686	−	0.989496i
$633$	−11.2649	+	16.8591i	−0.447739	+	0.670088i
$634$	27.1559	+	33.0294i	1.07850	+	1.31177i
$635$	−0.348091	−	3.53423i	−0.0138136	−	0.140252i
$636$	0.0287821	+	16.1397i	0.00114128	+	0.639982i
$637$	−9.82647	−	32.3935i	−0.389339	−	1.28348i
$638$	−53.9815	+	22.4163i	−2.13715	+	0.887469i
$639$	−2.09061			−0.0827034
$640$	17.1978	+	5.09989i	0.679802	+	0.201591i
$641$	1.42891			0.0564385			0.0282193	−	0.999602i	$-0.491016\pi$
$641$	1.42891			0.0564385			0.0282193	+	0.999602i	$0.491016\pi$
$642$	13.5319	−	5.61922i	0.534060	−	0.221773i
$643$	−7.70311	−	25.3937i	−0.303781	−	1.00143i	−0.967377	−	0.253341i	$-0.918471\pi$
$643$	−7.70311	−	25.3937i	−0.303781	−	1.00143i	0.663596	−	0.748091i	$-0.269029\pi$
$644$	−0.621407	+	0.00110816i	−0.0244868	+	4.36675e-5i
$645$	0.0151918	+	0.154245i	0.000598177	+	0.00607340i
$646$	0.925089	+	1.12518i	0.0363971	+	0.0442695i
$647$	12.2031	−	18.2633i	0.479754	−	0.718003i	−0.510096	−	0.860118i	$-0.670390\pi$
$647$	12.2031	−	18.2633i	0.479754	−	0.718003i	0.989850	+	0.142114i	$0.0453901\pi$
$648$	1.99464	−	2.00534i	0.0783570	−	0.0787773i
$649$	26.3543	−	17.6094i	1.03450	−	0.691229i
$650$	8.03223	+	14.9951i	0.315050	+	0.588155i
$651$	−0.0370048	+	0.0197795i	−0.00145033	+	0.000775220i
$652$	−34.2907	+	10.4688i	−1.34293	+	0.409990i
$653$	23.5561	+	2.32008i	0.921822	+	0.0907916i	0.547782	−	0.836621i	$-0.315472\pi$
$653$	23.5561	+	2.32008i	0.921822	+	0.0907916i	0.374040	+	0.927413i	$0.377972\pi$
$654$	−2.33590	+	11.7983i	−0.0913410	+	0.461352i
$655$	−3.66153	+	1.51666i	−0.143068	+	0.0592606i
$656$	7.95125	−	40.7324i	0.310444	−	1.59033i
$657$	−8.78618	−	3.63936i	−0.342782	−	0.141985i
$658$	0.247572	−	0.371234i	0.00965138	−	0.0144722i
$659$	6.84491	−	5.61747i	0.266640	−	0.218826i	−0.491567	−	0.870840i	$-0.663576\pi$
$659$	6.84491	−	5.61747i	0.266640	−	0.218826i	0.758207	+	0.652014i	$0.226076\pi$
$660$	1.56944	+	15.6486i	0.0610903	+	0.609122i
$661$	21.4317	+	6.50123i	0.833596	+	0.252869i	0.678102	−	0.734968i	$-0.262803\pi$
$661$	21.4317	+	6.50123i	0.833596	+	0.252869i	0.155494	+	0.987837i	$0.450303\pi$
$662$	−21.3788	+	26.0976i	−0.830912	+	1.01431i
$663$	0.614169	−	3.08764i	0.0238523	−	0.119914i
$664$	11.6140	+	37.9207i	0.450710	+	1.47161i
$665$	−0.142478	+	0.0283406i	−0.00552506	+	0.00109900i
$666$	13.3363	−	4.05852i	0.516772	−	0.157264i
$667$	−34.5798	−	28.3789i	−1.33893	−	1.09884i
$668$	−0.517757	−	0.344620i	−0.0200326	−	0.0133338i
$669$	8.73361	−	16.3394i	0.337661	−	0.631719i
$670$	−6.41085	+	6.42229i	−0.247673	+	0.248115i
$671$	−16.6342	+	16.6342i	−0.642158	+	0.642158i
$672$	−0.325700	+	0.0335455i	−0.0125642	+	0.00129405i
$673$	3.98289	+	3.98289i	0.153529	+	0.153529i	0.779692	−	0.626163i	$-0.215376\pi$
$673$	3.98289	+	3.98289i	0.153529	+	0.153529i	−0.626163	+	0.779692i	$0.715376\pi$
$674$	47.4902	−	0.0423447i	1.82925	−	0.00163106i
$675$	−2.19259	−	1.17196i	−0.0843929	−	0.0451089i
$676$	−17.2874	+	11.5957i	−0.664899	+	0.445989i
$677$	24.1865	−	29.4713i	0.929563	−	1.13268i	−0.0613430	−	0.998117i	$-0.519538\pi$
$677$	24.1865	−	29.4713i	0.929563	−	1.13268i	0.990906	−	0.134559i	$-0.0429616\pi$
$678$	6.45669	−	12.1056i	0.247968	−	0.464911i
$679$	−0.166572	−	0.837414i	−0.00639245	−	0.0321370i
$680$	−1.84511	+	2.26058i	−0.0707568	+	0.0866892i
$681$	14.9813	+	2.97997i	0.574086	+	0.114193i
$682$	−5.05970	+	0.502893i	−0.193746	+	0.0192568i
$683$	−13.5637	+	44.7134i	−0.518999	+	1.71091i	0.169371	+	0.985552i	$0.445826\pi$
$683$	−13.5637	+	44.7134i	−0.518999	+	1.71091i	−0.688371	+	0.725359i	$0.741674\pi$
$684$	1.49738	+	2.78942i	0.0572538	+	0.106656i
$685$	1.02315	+	1.24672i	0.0390927	+	0.0476346i
$686$	−0.224518	−	1.12349i	−0.00857215	−	0.0428952i
$687$	−10.7924	+	26.0552i	−0.411756	+	0.994067i
$688$	−0.374585	−	0.112172i	−0.0142809	−	0.00427650i
$689$	14.9413	+	36.0716i	0.569220	+	1.37422i
$690$	−10.0019	+	6.69598i	−0.380767	+	0.254912i
$691$	−2.76183	+	28.0413i	−0.105065	+	1.06674i	0.787651	+	0.616122i	$0.211297\pi$
$691$	−2.76183	+	28.0413i	−0.105065	+	1.06674i	−0.892716	+	0.450620i	$0.851203\pi$
$692$	−37.8468	−	3.65945i	−1.43872	−	0.139111i
$693$	−0.135323	−	0.253172i	−0.00514050	−	0.00961719i
$694$	35.5023	+	10.7350i	1.34765	+	0.407493i
$695$	6.65144	+	9.95458i	0.252303	+	0.377599i
$696$	−19.6332	−	13.0426i	−0.744193	−	0.494380i
$697$	5.61327	+	3.75067i	0.212618	+	0.142067i
$698$	2.56565	−	26.2897i	0.0971112	−	0.995081i
$699$	−16.8414	+	1.65873i	−0.637001	+	0.0627391i
$700$	0.110611	+	0.265697i	0.00418069	+	0.0100424i
$701$	26.0527	−	7.90300i	0.983997	−	0.298492i	0.243019	−	0.970022i	$-0.421862\pi$
$701$	26.0527	−	7.90300i	0.983997	−	0.298492i	0.740978	+	0.671530i	$0.234362\pi$
$702$	2.61277	−	6.32373i	0.0986128	−	0.238674i
$703$			15.6036i			0.588500i
$704$	−38.0297	−	11.3144i	−1.43330	−	0.426427i
$705$		−	8.64297i		−	0.325513i
$706$	−9.08504	−	3.75366i	−0.341920	−	0.141271i
$707$	−0.347066	+	0.105281i	−0.0130528	+	0.00395951i
$708$	11.8173	+	4.87023i	0.444123	+	0.183035i
$709$	36.3493	−	3.58009i	1.36513	−	0.134453i	0.611233	−	0.791451i	$-0.290674\pi$
$709$	36.3493	−	3.58009i	1.36513	−	0.134453i	0.753893	+	0.656998i	$0.228174\pi$
$710$	4.66552	+	0.455313i	0.175094	+	0.0170876i
$711$	7.31266	+	4.88616i	0.274246	+	0.183245i
$712$	5.97850	−	30.4819i	0.224054	−	1.14236i
$713$	−2.16195	−	3.23558i	−0.0809655	−	0.121173i
$714$	0.0154157	−	0.0509825i	0.000576919	−	0.00190797i
$715$	17.9345	+	33.5531i	0.670713	+	1.25482i
$716$	−12.5430	−	15.2282i	−0.468752	−	0.569104i
$717$	−2.31109	+	23.4649i	−0.0863092	+	0.876312i
$718$	−23.6840	−	35.3773i	−0.883879	−	1.32027i
$719$	−12.8962	−	31.1342i	−0.480948	−	1.16111i	−0.959159	−	0.282866i	$-0.908715\pi$
$719$	−12.8962	−	31.1342i	−0.480948	−	1.16111i	0.478212	−	0.878245i	$-0.341285\pi$
$720$	−4.88809	+	4.04081i	−0.182168	+	0.150592i
$721$	−0.322765	+	0.779223i	−0.0120204	+	0.0290198i
$722$	22.8741	−	4.57115i	0.851286	−	0.170121i
$723$	−12.3301	−	15.0243i	−0.458563	−	0.558760i
$724$	1.45216	+	0.437682i	0.0539691	+	0.0162663i
$725$	−6.01419	+	19.8261i	−0.223361	+	0.736323i
$726$	−1.90199	−	19.1363i	−0.0705894	−	0.710213i
$727$	50.7513	+	10.0951i	1.88226	+	0.374405i	0.996044	−	0.0888617i	$-0.0283229\pi$
$727$	50.7513	+	10.0951i	1.88226	+	0.374405i	0.886219	+	0.463267i	$0.153323\pi$
$728$	−0.697541	+	0.375246i	−0.0258526	+	0.0139075i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	18.8151	+	10.0353i	0.696377	+	0.371423i
$731$	0.0403521	−	0.0491691i	0.00149248	−	0.00181859i
$732$	−9.30733	−	1.83409i	−0.344009	−	0.0677901i
$733$	−9.27157	−	4.95576i	−0.342453	−	0.183045i	0.291200	−	0.956662i	$-0.405945\pi$
$733$	−9.27157	−	4.95576i	−0.342453	−	0.183045i	−0.633653	+	0.773617i	$0.718445\pi$
$734$	−0.0266799	−	29.9219i	−0.000984774	−	1.10444i
$735$	−7.84413	−	7.84413i	−0.289335	−	0.289335i
$736$	−6.05682	−	29.7558i	−0.223257	−	1.09681i
$737$	14.1928	−	14.1928i	0.522800	−	0.522800i
$738$	10.3845	+	10.3660i	0.382260	+	0.381579i
$739$	8.13762	−	15.2244i	0.299347	−	0.560039i	−0.686612	−	0.727024i	$-0.740903\pi$
$739$	8.13762	−	15.2244i	0.299347	−	0.560039i	0.985959	+	0.166985i	$0.0534030\pi$
$740$	−30.6459	+	6.15269i	−1.12657	+	0.226177i
$741$	5.92022	+	4.85860i	0.217485	+	0.178485i
$742$	0.192316	+	0.631952i	0.00706014	+	0.0231997i
$743$	13.0444	−	2.59468i	0.478551	−	0.0951897i	0.0500798	−	0.998745i	$-0.484052\pi$
$743$	13.0444	−	2.59468i	0.478551	−	0.0951897i	0.428471	+	0.903556i	$0.359052\pi$
$744$	−1.30500	−	1.58150i	−0.0478435	−	0.0579805i
$745$	4.42856	−	22.2639i	0.162250	−	0.815686i
$746$	11.9470	+	9.78686i	0.437412	+	0.358322i
$747$	−13.4179	−	4.07029i	−0.490937	−	0.148924i
$748$	4.08566	−	4.99654i	0.149387	−	0.182692i
$749$	0.463562	−	0.380435i	0.0169382	−	0.0139008i
$750$	13.9652	+	9.31327i	0.509938	+	0.340072i
$751$	−15.3312	−	6.35038i	−0.559442	−	0.231729i	0.0850008	−	0.996381i	$-0.472911\pi$
$751$	−15.3312	−	6.35038i	−0.559442	−	0.231729i	−0.644443	+	0.764652i	$0.722911\pi$
$752$	20.1747	+	8.27246i	0.735696	+	0.301666i
$753$	20.6382	−	8.54862i	0.752098	−	0.311529i
$754$	−55.9337	−	11.0741i	−2.03699	−	0.403294i
$755$	−0.663861	−	0.0653846i	−0.0241604	−	0.00237959i
$756$	0.0543875	−	0.102190i	0.00197805	−	0.00371661i
$757$	25.7350	−	13.7556i	0.935353	−	0.499957i	0.0680194	−	0.997684i	$-0.478332\pi$
$757$	25.7350	−	13.7556i	0.935353	−	0.499957i	0.867333	+	0.497727i	$0.165832\pi$
$758$	−12.6811	+	6.79271i	−0.460597	+	0.246722i
$759$	22.1365	−	14.7911i	0.803503	−	0.536884i
$760$	−2.73412	−	6.55113i	−0.0991770	−	0.237635i
$761$	10.1988	−	15.2636i	0.369708	−	0.553307i	−0.599241	−	0.800569i	$-0.704531\pi$
$761$	10.1988	−	15.2636i	0.369708	−	0.553307i	0.968949	+	0.247262i	$0.0795308\pi$
$762$	−2.44683	+	2.01172i	−0.0886394	+	0.0728768i
$763$	0.0482494	+	0.489884i	0.00174675	+	0.0177350i
$764$	−1.21941	−	1.21507i	−0.0441166	−	0.0439596i
$765$	−0.299476	−	0.987241i	−0.0108276	−	0.0356938i
$766$	−6.34171	−	15.2717i	−0.229135	−	0.551789i
$767$	30.9199			1.11645
$768$	−4.75365	−	15.2775i	−0.171533	−	0.551280i
$769$	52.2399			1.88382			0.941910	−	0.335866i	$-0.109029\pi$
$769$	52.2399			1.88382			0.941910	+	0.335866i	$0.109029\pi$
$770$	0.246856	+	0.594462i	0.00889606	+	0.0214229i
$771$	2.29657	+	7.57076i	0.0827088	+	0.272654i
$772$	−16.4291	−	16.3706i	−0.591297	−	0.589192i
$773$	−0.451217	−	4.58128i	−0.0162291	−	0.164777i	0.983654	−	0.180069i	$-0.0576322\pi$
$773$	−0.451217	−	4.58128i	−0.0162291	−	0.164777i	−0.999883	+	0.0152921i	$0.995132\pi$
$774$	0.106788	−	0.0877977i	0.00383840	−	0.00315582i
$775$	−1.00129	+	1.49854i	−0.0359675	+	0.0538291i
$776$	38.5043	−	16.0698i	1.38222	−	0.576872i
$777$	0.474390	−	0.316977i	0.0170186	−	0.0113715i
$778$	3.74500	−	2.00604i	0.134265	−	0.0719200i
$779$	−14.4844	+	7.74206i	−0.518957	+	0.277388i
$780$	−7.20804	+	13.5433i	−0.258089	+	0.484929i
$781$	−10.3188	−	1.01631i	−0.369235	−	0.0363664i
$782$	4.84559	+	0.959357i	0.173278	+	0.0343065i
$783$	7.69911	−	3.18907i	0.275144	−	0.113968i
$784$	25.8179	−	10.8022i	0.922067	−	0.385791i
$785$	0.435271	+	0.180295i	0.0155355	+	0.00643501i
$786$	2.94102	+	1.96133i	0.104903	+	0.0699585i
$787$	3.15071	−	2.58572i	0.112311	−	0.0921709i	−0.576562	−	0.817054i	$-0.695606\pi$
$787$	3.15071	−	2.58572i	0.112311	−	0.0921709i	0.688872	+	0.724883i	$0.258106\pi$
$788$	−12.6323	+	15.4486i	−0.450006	+	0.550332i
$789$	−9.31571	−	2.82589i	−0.331648	−	0.100604i
$790$	−15.2551	−	12.4968i	−0.542754	−	0.444617i
$791$	0.109548	−	0.550734i	0.00389507	−	0.0195819i
$792$	10.8199	−	8.92824i	0.384470	−	0.317251i
$793$	−22.5074	+	4.47699i	−0.799260	+	0.158983i
$794$	3.07594	+	10.1076i	0.109161	+	0.358704i
$795$	9.89058	+	8.11699i	0.350783	+	0.287880i
$796$	26.5230	−	5.32495i	0.940085	−	0.188738i
$797$	6.04046	−	11.3009i	0.213964	−	0.400299i	−0.751927	−	0.659246i	$-0.770876\pi$
$797$	6.04046	−	11.3009i	0.213964	−	0.400299i	0.965891	+	0.258947i	$0.0833756\pi$
$798$	0.0917046	+	0.0915412i	0.00324631	+	0.00324052i
$799$	−2.50812	+	2.50812i	−0.0887308	+	0.0887308i
$800$	−11.6587	+	7.86549i	−0.412196	+	0.278087i
$801$	7.76566	+	7.76566i	0.274386	+	0.274386i
$802$	0.0336077	+	37.6915i	0.00118673	+	1.33093i
$803$	−41.5973	−	22.2342i	−1.46794	−	0.784628i
$804$	7.94129	+	1.56490i	0.280068	+	0.0551899i
$805$	−0.312518	+	0.380804i	−0.0110148	+	0.0134216i
$806$	−4.37652	−	2.33428i	−0.154156	−	0.0822216i
$807$	−5.51022	−	27.7018i	−0.193969	−	0.975148i
$808$	−8.39635	−	15.6079i	−0.295383	−	0.549084i
$809$	−2.72654	−	0.542343i	−0.0958602	−	0.0190678i	0.146927	−	0.989147i	$-0.453062\pi$
$809$	−2.72654	−	0.542343i	−0.0958602	−	0.0190678i	−0.242787	+	0.970080i	$0.578062\pi$
$810$	−0.221769	−	2.23126i	−0.00779216	−	0.0783984i
$811$	13.8640	−	45.7033i	0.486829	−	1.60486i	−0.277968	−	0.960590i	$-0.589661\pi$
$811$	13.8640	−	45.7033i	0.486829	−	1.60486i	0.764798	−	0.644271i	$-0.222839\pi$
$812$	−0.923653	−	0.278389i	−0.0324139	−	0.00976955i
$813$	−1.22344	−	1.49077i	−0.0429079	−	0.0522835i
$814$	67.7979	−	13.5487i	2.37632	−	0.474882i
$815$	−10.8769	+	26.2593i	−0.381003	+	0.919821i
$816$	2.59109	+	0.245872i	0.0907063	+	0.00860725i
$817$	0.0592172	+	0.142963i	0.00207175	+	0.00500164i
$818$	9.98122	+	14.9092i	0.348985	+	0.521286i
$819$	0.0274486	−	0.278690i	0.000959131	−	0.00973822i
$820$	−20.9170	−	25.3950i	−0.730455	−	0.886832i
$821$	−9.94454	−	18.6049i	−0.347067	−	0.649316i	0.646456	−	0.762951i	$-0.276250\pi$
$821$	−9.94454	−	18.6049i	−0.347067	−	0.649316i	−0.993523	+	0.113635i	$0.963750\pi$
$822$	0.416364	−	1.37699i	0.0145224	−	0.0480279i
$823$	11.7709	+	17.6164i	0.410307	+	0.614068i	0.977858	−	0.209270i	$-0.0671088\pi$
$823$	11.7709	+	17.6164i	0.410307	+	0.614068i	−0.567550	+	0.823339i	$0.692109\pi$
$824$	−40.4446	−	7.93252i	−1.40895	−	0.276342i
$825$	−10.2524	−	6.85042i	−0.356942	−	0.238501i
$826$	0.520650	+	0.0508109i	0.0181157	+	0.00176794i
$827$	−22.1705	+	2.18361i	−0.770945	+	0.0759314i	−0.475838	−	0.879533i	$-0.657855\pi$
$827$	−22.1705	+	2.18361i	−0.770945	+	0.0759314i	−0.295107	+	0.955464i	$0.595355\pi$
$828$	9.92607	+	4.09079i	0.344955	+	0.142165i
$829$	−38.8204	+	11.7761i	−1.34829	+	0.408999i	−0.880167	−	0.474664i	$-0.842570\pi$
$829$	−38.8204	+	11.7761i	−1.34829	+	0.408999i	−0.468123	+	0.883663i	$0.655070\pi$
$830$	29.0577	+	12.0057i	1.00861	+	0.416725i
$831$			11.8994i			0.412785i
$832$	−24.7142	−	29.7880i	−0.856812	−	1.03271i
$833$			4.55260i			0.157738i
$834$	4.07780	−	9.86956i	0.141203	−	0.341755i
$835$	−0.471832	+	0.143129i	−0.0163284	+	0.00495318i
$836$	6.03469	+	14.4959i	0.208714	+	0.501349i
$837$	0.721436	−	0.0710552i	0.0249365	−	0.00245603i
$838$	−3.76164	+	38.5449i	−0.129944	+	1.33151i
$839$	17.3870	+	11.6176i	0.600267	+	0.401086i	0.818246	−	0.574868i	$-0.194947\pi$
$839$	17.3870	+	11.6176i	0.600267	+	0.401086i	−0.217979	+	0.975953i	$0.569947\pi$
$840$	−0.143630	+	0.216207i	−0.00495570	+	0.00745985i
$841$	−22.4708	−	33.6300i	−0.774856	−	1.15965i
$842$	−10.1698	−	3.07507i	−0.350474	−	0.105974i
$843$	−10.0225	−	18.7507i	−0.345192	−	0.645809i
$844$	−40.3642	−	3.90286i	−1.38939	−	0.134342i
$845$	−1.61749	+	16.4227i	−0.0556435	+	0.564958i
$846$	−6.40613	+	4.28871i	−0.220247	+	0.147449i
$847$	−0.301197	−	0.727155i	−0.0103493	−	0.0249853i
$848$	−28.4135	+	15.3179i	−0.975725	+	0.526019i
$849$	6.76541	−	16.3332i	0.232188	−	0.560552i
$850$	−0.448322	−	2.24341i	−0.0153773	−	0.0769483i
$851$	33.5679	+	40.9026i	1.15069	+	1.40212i
$852$	−1.97759	−	3.68399i	−0.0677511	−	0.126211i
$853$	−6.85882	+	22.6105i	−0.234841	+	0.774168i	0.757737	+	0.652560i	$0.226305\pi$
$853$	−6.85882	+	22.6105i	−0.234841	+	0.774168i	−0.992578	+	0.121608i	$0.961195\pi$
$854$	−0.386352	+	0.0384002i	−0.0132207	+	0.00131403i
$855$	2.46157	+	0.489638i	0.0841841	+	0.0167453i
$856$	22.7022	+	18.5298i	0.775947	+	0.633337i
$857$	−4.49861	−	22.6160i	−0.153669	−	0.772548i	−0.978351	−	0.206951i	$-0.933646\pi$
$857$	−4.49861	−	22.6160i	−0.153669	−	0.772548i	0.824682	−	0.565597i	$-0.191354\pi$
$858$	15.9702	−	29.9423i	0.545213	−	1.02221i
$859$	−12.5266	+	15.2637i	−0.427401	+	0.520789i	−0.941533	−	0.336922i	$-0.890614\pi$
$859$	−12.5266	+	15.2637i	−0.427401	+	0.520789i	0.514132	+	0.857711i	$0.328114\pi$
$860$	−0.257434	+	0.172677i	−0.00877842	+	0.00588822i
$861$	0.529621	+	0.283088i	0.0180494	+	0.00964762i
$862$	18.9358	−	0.0168841i	0.644956	−	0.000575076i
$863$	10.4914	+	10.4914i	0.357133	+	0.357133i	0.862755	−	0.505622i	$-0.168737\pi$
$863$	10.4914	+	10.4914i	0.357133	+	0.357133i	−0.505622	+	0.862755i	$0.668737\pi$
$864$	5.42054	+	1.61795i	0.184410	+	0.0550437i
$865$	−21.3145	+	21.3145i	−0.724714	+	0.724714i
$866$	−14.4337	+	14.4594i	−0.490476	+	0.491352i
$867$	7.81416	−	14.6193i	0.265383	−	0.496496i
$868$	−0.0698589	−	0.0464982i	−0.00237117	−	0.00157825i
$869$	33.7182	+	27.6718i	1.14381	+	0.938703i
$870$	−17.8763	+	5.44011i	−0.606062	+	0.184437i
$871$	19.2040	−	3.81990i	0.650701	−	0.129433i
$872$	−23.0002	+	7.04427i	−0.778884	+	0.238549i
$873$	−2.87785	+	14.4679i	−0.0974003	+	0.489664i
$874$	−7.61522	+	9.29607i	−0.257589	+	0.314444i
$875$	0.657427	+	0.199428i	0.0222251	+	0.00674191i
$876$	−1.89806	−	18.9252i	−0.0641294	−	0.639425i
$877$	37.9395	−	31.1362i	1.28113	−	1.05139i	0.285461	−	0.958390i	$-0.407853\pi$
$877$	37.9395	−	31.1362i	1.28113	−	1.05139i	0.995666	−	0.0930037i	$-0.0296468\pi$
$878$	4.00795	−	6.00991i	0.135262	−	0.202825i
$879$	0.104261	+	0.0431863i	0.00351663	+	0.00145664i
$880$	−26.0908	+	17.5682i	−0.879520	+	0.592225i
$881$	−39.6863	+	16.4386i	−1.33707	+	0.553831i	−0.932663	−	0.360750i	$-0.882521\pi$
$881$	−39.6863	+	16.4386i	−1.33707	+	0.553831i	−0.404403	+	0.914581i	$0.632521\pi$
$882$	−1.92172	+	9.70635i	−0.0647076	+	0.326830i
$883$	−55.7217	−	5.48811i	−1.87519	−	0.184690i	−0.904732	−	0.425980i	$-0.859929\pi$
$883$	−55.7217	−	5.48811i	−1.87519	−	0.184690i	−0.970453	+	0.241291i	$0.922429\pi$
$884$	6.02187	−	1.83845i	0.202537	−	0.0618337i
$885$	8.93622	−	4.77651i	0.300388	−	0.160561i
$886$	−24.8704	−	46.4296i	−0.835537	−	1.55983i
$887$	−21.1927	+	14.1605i	−0.711582	+	0.475464i	−0.857928	−	0.513770i	$-0.828249\pi$
$887$	−21.1927	+	14.1605i	−0.711582	+	0.475464i	0.146346	+	0.989233i	$0.453249\pi$
$888$	19.7671	+	19.6616i	0.663340	+	0.659801i
$889$	−0.0720270	+	0.107796i	−0.00241571	+	0.00361536i
$890$	−15.6390	−	19.0215i	−0.524219	−	0.637603i
$891$	0.486130	+	4.93576i	0.0162860	+	0.165354i
$892$	37.0541	−	0.0660788i	1.24066	−	0.00221248i
$893$	−2.50488	−	8.25749i	−0.0838227	−	0.276326i
$894$	−18.6994	+	7.76508i	−0.625401	+	0.259703i
$895$	−15.6401			−0.522790
$896$	−0.367205	−	0.542204i	−0.0122674	−	0.0181138i
$897$	25.9714			0.867159
$898$	−51.5059	+	21.3883i	−1.71877	+	0.713736i
$899$	−1.75365	−	5.78101i	−0.0584875	−	0.192808i
$900$	−0.00886712	−	4.97230i	−0.000295571	−	0.165743i
$901$	−0.514681	−	5.22564i	−0.0171465	−	0.174091i
$902$	46.2164	+	56.2125i	1.53884	+	1.87167i
$903$	0.00314349	−	0.00470456i	0.000104609	−	0.000156558i
$904$	27.4395	−	0.0733997i	0.912626	−	0.00244124i
$905$	0.999727	−	0.667996i	0.0332320	−	0.0222049i
$906$	0.280950	+	0.524495i	0.00933394	+	0.0174252i
$907$	30.4136	−	16.2564i	1.00987	−	0.539785i	0.118446	−	0.992961i	$-0.462209\pi$
$907$	30.4136	−	16.2564i	1.00987	−	0.539785i	0.891422	+	0.453175i	$0.149709\pi$
$908$	8.92021	+	29.2183i	0.296028	+	0.969644i
$909$	6.23586	+	0.614179i	0.206830	+	0.0203710i
$910$	−0.121951	+	0.615961i	−0.00404265	+	0.0204189i
$911$	43.3878	−	17.9718i	1.43750	−	0.595433i	0.478311	−	0.878191i	$-0.341249\pi$
$911$	43.3878	−	17.9718i	1.43750	−	0.595433i	0.959191	+	0.282758i	$0.0912493\pi$
$912$	−3.49898	+	5.27724i	−0.115863	+	0.174747i
$913$	−64.2491	−	26.6128i	−2.12633	−	0.880756i
$914$	12.0281	−	18.0362i	0.397855	−	0.596584i
$915$	−5.81330	+	4.77085i	−0.192182	+	0.157719i
$916$	−56.1223	+	5.62864i	−1.85433	+	0.185975i
$917$	0.138451	+	0.0419988i	0.00457207	+	0.00138692i
$918$	−0.583137	+	0.711847i	−0.0192464	+	0.0234945i
$919$	2.11604	−	10.6380i	0.0698016	−	0.350917i	−0.930062	−	0.367401i	$-0.880248\pi$
$919$	2.11604	−	10.6380i	0.0698016	−	0.350917i	0.999864	+	0.0164849i	$0.00524753\pi$
$920$	−21.2606	−	11.2910i	−0.700941	−	0.372253i
$921$	−22.2927	+	4.43430i	−0.734570	+	0.146115i
$922$	−8.40882	+	2.55898i	−0.276930	+	0.0842755i
$923$	−7.81884	−	6.41675i	−0.257360	−	0.211210i
$924$	0.318121	−	0.477945i	0.0104654	−	0.0157232i
$925$	11.5523	−	21.6128i	0.379837	−	0.710626i
$926$	27.8126	−	27.8622i	0.913978	−	0.915609i
$927$	10.3038	−	10.3038i	0.338421	−	0.338421i
$928$	4.41144	−	46.9343i	0.144813	−	1.54069i
$929$	10.4063	+	10.4063i	0.341421	+	0.341421i	0.856901	−	0.515481i	$-0.172387\pi$
$929$	10.4063	+	10.4063i	0.341421	+	0.341421i	−0.515481	+	0.856901i	$0.672387\pi$
$930$	−1.62547	+	0.00144935i	−0.0533012	+	4.75261e-5i
$931$	−9.76764	−	5.22091i	−0.320121	−	0.171108i
$932$	−18.8539	−	28.1082i	−0.617579	−	0.920714i
$933$	13.9478	−	16.9954i	0.456629	−	0.556404i
$934$	−5.21063	+	9.76934i	−0.170497	+	0.319663i
$935$	−0.998216	−	5.01837i	−0.0326452	−	0.164118i
$936$	13.6149	−	1.37774i	0.445018	−	0.0450327i
$937$	−24.8835	−	4.94964i	−0.812910	−	0.161698i	−0.228906	−	0.973449i	$-0.573515\pi$
$937$	−24.8835	−	4.94964i	−0.812910	−	0.161698i	−0.584004	+	0.811751i	$0.698515\pi$
$938$	0.329647	−	0.0327642i	0.0107633	−	0.00106979i
$939$	−4.22052	+	13.9132i	−0.137732	+	0.454040i
$940$	15.2303	−	8.17571i	0.496757	−	0.266662i
$941$	9.77269	+	11.9081i	0.318580	+	0.388191i	0.907536	−	0.419974i	$-0.137961\pi$
$941$	9.77269	+	11.9081i	0.318580	+	0.388191i	−0.588956	+	0.808165i	$0.700461\pi$
$942$	−0.0823509	−	0.412085i	−0.00268314	−	0.0134265i
$943$	−21.3134	+	51.4550i	−0.694058	+	1.67561i
$944$	2.59635	+	25.4310i	0.0845039	+	0.827708i
$945$	−0.0351191	−	0.0847851i	−0.00114243	−	0.00275806i
$946$	0.569759	−	0.381436i	0.0185245	−	0.0124016i
$947$	4.70622	−	47.7830i	0.152931	−	1.55274i	−0.546144	−	0.837691i	$-0.683905\pi$
$947$	4.70622	−	47.7830i	0.152931	−	1.55274i	0.699076	−	0.715048i	$-0.253595\pi$
$948$	−1.69287	+	17.5081i	−0.0549820	+	0.568636i
$949$	−21.6897	−	40.5787i	−0.704079	−	1.31724i
$950$	5.32739	+	1.61086i	0.172843	+	0.0522632i
$951$	−16.7980	−	25.1400i	−0.544713	−	0.815221i
$952$	0.104421	−	0.0210613i	0.00338432	−	0.000682599i
$953$	−11.0199	−	7.36324i	−0.356969	−	0.238519i	0.364135	−	0.931346i	$-0.381365\pi$
$953$	−11.0199	−	7.36324i	−0.356969	−	0.238519i	−0.721103	+	0.692827i	$0.756365\pi$
$954$	1.10850	−	11.3586i	0.0358889	−	0.367747i
$955$	−1.35811	+	0.133762i	−0.0439473	+	0.00432843i
$956$	−43.5350	+	18.1238i	−1.40802	+	0.586166i
$957$	39.5513	−	11.9977i	1.27851	−	0.387832i
$958$	10.6055	−	25.6687i	0.342649	−	0.829319i
$959$		−	0.0588772i		−	0.00190125i
$960$	−11.7444	−	4.79123i	−0.379048	−	0.154636i
$961$			30.4745i			0.983048i
$962$	62.3344	+	25.7547i	2.00974	+	0.830364i
$963$	−9.91454	+	3.00754i	−0.319492	+	0.0969167i
$964$	14.8117	−	35.9397i	0.477052	−	1.15754i
$965$	−18.2978	+	1.80218i	−0.589028	+	0.0580142i
$966$	0.437324	+	0.0426790i	0.0140707	+	0.00137317i
$967$	−37.5541	−	25.0928i	−1.20766	−	0.806931i	−0.221894	−	0.975071i	$-0.571224\pi$
$967$	−37.5541	−	25.0928i	−1.20766	−	0.806931i	−0.985763	+	0.168140i	$0.946224\pi$
$968$	31.9220	−	21.4533i	1.02601	−	0.689536i
$969$	−0.572239	−	0.856416i	−0.0183830	−	0.0275121i
$970$	9.57330	−	31.6605i	0.307380	−	1.01656i
$971$	−0.733058	−	1.37146i	−0.0235250	−	0.0440121i	0.869884	−	0.493256i	$-0.164193\pi$
$971$	−0.733058	−	1.37146i	−0.0235250	−	0.0440121i	−0.893409	+	0.449244i	$0.851693\pi$
$972$	−1.54376	+	1.27154i	−0.0495160	+	0.0407847i
$973$	0.0428394	−	0.434956i	0.00137337	−	0.0139441i
$974$	−31.7635	−	47.4459i	−1.01777	−	1.52026i
$975$	−4.60310	−	11.1129i	−0.147417	−	0.355897i
$976$	−5.57218	−	18.1359i	−0.178361	−	0.580517i
$977$	2.68749	−	6.48818i	0.0859805	−	0.207575i	−0.875041	−	0.484049i	$-0.839166\pi$
$977$	2.68749	−	6.48818i	0.0859805	−	0.207575i	0.961022	+	0.276473i	$0.0891658\pi$
$978$	24.8605	−	4.96810i	0.794950	−	0.158862i
$979$	34.5543	+	42.1046i	1.10436	+	1.34567i
$980$	6.40254	−	21.2426i	0.204522	−	0.678571i
$981$	2.46876	−	8.13842i	0.0788215	−	0.259840i
$982$	4.89092	+	49.2084i	0.156075	+	1.57030i
$983$	27.5421	+	5.47847i	0.878457	+	0.174736i	0.613662	−	0.789569i	$-0.289696\pi$
$983$	27.5421	+	5.47847i	0.878457	+	0.174736i	0.264795	+	0.964305i	$0.414696\pi$
$984$	−8.44348	+	28.1048i	−0.269168	+	0.895949i
$985$	3.08634	+	15.5161i	0.0983389	+	0.494383i
$986$	6.76621	+	3.60886i	0.215480	+	0.114930i
$987$	−0.200164	+	0.243901i	−0.00637130	+	0.00776346i
$988$	−2.96146	+	15.0283i	−0.0942167	+	0.478114i
$989$	0.462786	+	0.247364i	0.0147157	+	0.00786572i
$990$	−0.00991585	−	11.1208i	−0.000315146	−	0.353441i
$991$	−12.5462	−	12.5462i	−0.398543	−	0.398543i	0.479176	−	0.877719i	$-0.340936\pi$
$991$	−12.5462	−	12.5462i	−0.398543	−	0.398543i	−0.877719	+	0.479176i	$0.840936\pi$
$992$	1.55240	−	3.79561i	0.0492889	−	0.120511i
$993$	16.8682	−	16.8682i	0.535295	−	0.535295i
$994$	−0.121114	−	0.120898i	−0.00384151	−	0.00383467i
$995$	10.1095	−	18.9136i	0.320493	−	0.599601i
$996$	−5.52004	−	27.4948i	−0.174909	−	0.871205i
$997$	−34.7268	−	28.4995i	−1.09981	−	0.902589i	−0.104047	−	0.994572i	$-0.533179\pi$
$997$	−34.7268	−	28.4995i	−1.09981	−	0.902589i	−0.995761	+	0.0919836i	$0.970679\pi$
$998$	−7.48364	−	24.5913i	−0.236891	−	0.778424i
$999$	−9.66781	+	1.92305i	−0.305876	+	0.0608425i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.13	✓	512
128.69	even	32	inner	384.2.v.a.325.13	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.13	✓	512	1.1	even	1	trivial
384.2.v.a.325.13	yes	512	128.69	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.542361 - 1.30608i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-1.41169 + 1.41673i) q^{4} +(0.155407 + 1.57788i) q^{5} +(1.09240 - 0.898142i) q^{6} +(0.0321569 - 0.0481261i) q^{7} +(2.61601 + 1.07540i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(-0.542361 - 1.30608i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-1.41169 + 1.41673i) q^{4} +(0.155407 + 1.57788i) q^{5} +(1.09240 - 0.898142i) q^{6} +(0.0321569 - 0.0481261i) q^{7} +(2.61601 + 1.07540i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(1.97655 - 1.05875i) q^{10} +(-4.37401 + 2.33796i) q^{11} +(-1.76552 - 0.939647i) q^{12} +(-4.81489 - 0.474226i) q^{13} +(-0.0802972 - 0.0158977i) q^{14} +(-1.46482 + 0.606749i) q^{15} +(-0.0142664 - 3.99997i) q^{16} +(0.601152 + 0.249005i) q^{17} +(1.17658 + 0.784646i) q^{18} +(-1.22364 + 1.00422i) q^{19} +(-2.45482 - 2.00730i) q^{20} +(0.0553885 + 0.0168019i) q^{21} +(5.42586 + 4.44479i) q^{22} +(-1.04724 + 5.26485i) q^{23} +(-0.269704 + 2.81554i) q^{24} +(2.43838 - 0.485024i) q^{25} +(1.99203 + 6.54584i) q^{26} +(-0.773010 - 0.634393i) q^{27} +(0.0227864 + 0.113497i) q^{28} +(-3.92836 + 7.34945i) q^{29} +(1.58692 + 1.58410i) q^{30} +(-0.512601 + 0.512601i) q^{31} +(-5.21655 + 2.18806i) q^{32} +(-3.50700 - 3.50700i) q^{33} +(-0.000820501 - 0.920203i) q^{34} +(0.0809345 + 0.0432604i) q^{35} +(0.386682 - 1.96226i) q^{36} +(6.25335 - 7.61973i) q^{37} +(1.97525 + 1.05353i) q^{38} +(-0.943884 - 4.74523i) q^{39} +(-1.29030 + 4.29487i) q^{40} +(10.1759 + 2.02412i) q^{41} +(-0.00809591 - 0.0814545i) q^{42} +(0.0283767 - 0.0935456i) q^{43} +(2.86248 - 9.49728i) q^{44} +(-1.00584 - 1.22562i) q^{45} +(7.44430 - 1.48766i) q^{46} +(-2.08609 + 5.03627i) q^{47} +(3.82360 - 1.17478i) q^{48} +(2.67750 + 6.46406i) q^{49} +(-1.95596 - 2.92166i) q^{50} +(-0.0637780 + 0.647549i) q^{51} +(7.46899 - 6.15196i) q^{52} +(-3.80411 - 7.11700i) q^{53} +(-0.409318 + 1.35368i) q^{54} +(-4.36877 - 6.53832i) q^{55} +(0.135878 - 0.0913171i) q^{56} +(-1.31618 - 0.879445i) q^{57} +(11.7296 + 1.14470i) q^{58} +(-6.36002 + 0.626407i) q^{59} +(1.20827 - 2.93180i) q^{60} +(4.53892 - 1.37687i) q^{61} +(0.947512 + 0.391483i) q^{62} +0.0578808i q^{63} +(5.68704 + 5.62651i) q^{64} -7.67101i q^{65} +(-2.67836 + 6.48248i) q^{66} +(-3.87274 + 1.17478i) q^{67} +(-1.20141 + 0.500154i) q^{68} +(-5.34214 + 0.526155i) q^{69} +(0.0126058 - 0.129170i) q^{70} +(1.73828 + 1.16148i) q^{71} +(-2.77259 + 0.559217i) q^{72} +(5.28352 + 7.90735i) q^{73} +(-13.3435 - 4.03473i) q^{74} +(1.17196 + 2.19259i) q^{75} +(0.304695 - 3.15122i) q^{76} +(-0.0281376 + 0.285686i) q^{77} +(-5.68572 + 3.80641i) q^{78} +(-3.36565 - 8.12539i) q^{79} +(6.30925 - 0.644136i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-2.87537 - 14.3884i) q^{82} +(8.89528 + 10.8389i) q^{83} +(-0.101995 + 0.0547516i) q^{84} +(-0.299476 + 0.987241i) q^{85} +(-0.137568 + 0.0136732i) q^{86} +(-8.17333 - 1.62578i) q^{87} +(-13.9567 + 1.41232i) q^{88} +(-2.14254 - 10.7713i) q^{89} +(-1.05523 + 1.97843i) q^{90} +(-0.177655 + 0.216473i) q^{91} +(-5.98050 - 8.91599i) q^{92} +(-0.639328 - 0.341728i) q^{93} +(7.70919 - 0.00687391i) q^{94} +(-1.77470 - 1.77470i) q^{95} +(-3.60813 - 4.35676i) q^{96} +(10.4308 - 10.4308i) q^{97} +(6.99041 - 7.00289i) q^{98} +(2.33796 - 4.37401i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more