LMFDB - Embedded newform 896.2.bn.a.29.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(29,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 27, 0]))

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

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

chi := DirichletCharacter("896.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bn (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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$752$
Relative dimension:	$47$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			29.36
Character	$\chi$	$=$	896.29
Dual form			896.2.bn.a.309.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.929900 - 1.06550i) q^{2} +(-0.255588 + 2.59503i) q^{3} +(-0.270573 - 1.98161i) q^{4} +(-0.722686 + 0.386284i) q^{5} +(2.52733 + 2.68544i) q^{6} +(-0.195090 - 0.980785i) q^{7} +(-2.36301 - 1.55441i) q^{8} +(-3.72649 - 0.741245i) q^{9} +O(q^{10})$	\(q+(0.929900 - 1.06550i) q^{2} +(-0.255588 + 2.59503i) q^{3} +(-0.270573 - 1.98161i) q^{4} +(-0.722686 + 0.386284i) q^{5} +(2.52733 + 2.68544i) q^{6} +(-0.195090 - 0.980785i) q^{7} +(-2.36301 - 1.55441i) q^{8} +(-3.72649 - 0.741245i) q^{9} +(-0.260441 + 1.12923i) q^{10} +(-3.09531 + 3.77164i) q^{11} +(5.21150 - 0.195668i) q^{12} +(0.980249 - 1.83392i) q^{13} +(-1.22644 - 0.704164i) q^{14} +(-0.817707 - 1.97412i) q^{15} +(-3.85358 + 1.07234i) q^{16} +(-2.99065 + 7.22006i) q^{17} +(-4.25506 + 3.28128i) q^{18} +(0.449783 + 1.48273i) q^{19} +(0.961004 + 1.32757i) q^{20} +(2.59503 - 0.255588i) q^{21} +(1.14035 + 6.80529i) q^{22} +(1.54931 - 1.03522i) q^{23} +(4.63768 - 5.73479i) q^{24} +(-2.40479 + 3.59902i) q^{25} +(-1.04250 - 2.74981i) q^{26} +(0.605171 - 1.99498i) q^{27} +(-1.89075 + 0.651968i) q^{28} +(-5.24567 + 4.30501i) q^{29} +(-2.86381 - 0.964468i) q^{30} +(5.08207 - 5.08207i) q^{31} +(-2.44086 + 5.10315i) q^{32} +(-8.99639 - 8.99639i) q^{33} +(4.91196 + 9.90047i) q^{34} +(0.519851 + 0.633440i) q^{35} +(-0.460573 + 7.58502i) q^{36} +(-6.43458 - 1.95191i) q^{37} +(1.99810 + 0.899552i) q^{38} +(4.50853 + 3.01250i) q^{39} +(2.30816 + 0.210555i) q^{40} +(-5.43834 - 8.13905i) q^{41} +(2.14079 - 3.00267i) q^{42} +(0.567569 + 5.76262i) q^{43} +(8.31144 + 5.11319i) q^{44} +(2.97941 - 0.903795i) q^{45} +(0.337682 - 2.61343i) q^{46} +(-5.47609 - 2.26827i) q^{47} +(-1.79783 - 10.2742i) q^{48} +(-0.923880 + 0.382683i) q^{49} +(1.59854 + 5.90903i) q^{50} +(-17.9719 - 9.60618i) q^{51} +(-3.89934 - 1.44627i) q^{52} +(-6.20745 - 5.09433i) q^{53} +(-1.56290 - 2.49994i) q^{54} +(0.780011 - 3.92138i) q^{55} +(-1.06354 + 2.62086i) q^{56} +(-3.96270 + 0.788229i) q^{57} +(-0.290966 + 9.59247i) q^{58} +(4.89907 + 9.16551i) q^{59} +(-3.69069 + 2.15452i) q^{60} +(11.0401 + 1.08735i) q^{61} +(-0.689121 - 10.1407i) q^{62} +3.79949i q^{63} +(3.16764 + 7.34616i) q^{64} +1.70400i q^{65} +(-17.9514 + 1.21990i) q^{66} +(15.5409 + 1.53065i) q^{67} +(15.1166 + 3.97275i) q^{68} +(2.29043 + 4.28509i) q^{69} +(1.15834 + 0.0351356i) q^{70} +(-6.32256 + 1.25764i) q^{71} +(7.65354 + 7.54405i) q^{72} +(0.707719 - 3.55794i) q^{73} +(-8.06326 + 5.04095i) q^{74} +(-8.72493 - 7.16037i) q^{75} +(2.81651 - 1.29248i) q^{76} +(4.30303 + 2.30002i) q^{77} +(7.40229 - 2.00250i) q^{78} +(5.48061 - 2.27014i) q^{79} +(2.37070 - 2.26354i) q^{80} +(-5.50847 - 2.28168i) q^{81} +(-13.7293 - 1.77396i) q^{82} +(14.6240 - 4.43614i) q^{83} +(-1.20862 - 5.07319i) q^{84} +(-0.627694 - 6.37308i) q^{85} +(6.66784 + 4.75392i) q^{86} +(-9.83088 - 14.7130i) q^{87} +(13.1769 - 4.10107i) q^{88} +(-1.29525 - 0.865460i) q^{89} +(1.80756 - 4.01500i) q^{90} +(-1.98992 - 0.603635i) q^{91} +(-2.47060 - 2.79003i) q^{92} +(11.8892 + 14.4870i) q^{93} +(-7.50906 + 3.72550i) q^{94} +(-0.897808 - 0.897808i) q^{95} +(-12.6190 - 7.63842i) q^{96} +(0.303828 - 0.303828i) q^{97} +(-0.451367 + 1.34025i) q^{98} +(14.3303 - 11.7606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 752 q+O(q^{10}) $ 752 * q	$ 752 q + 112 q^{12} - 160 q^{32} + 112 q^{34} - 160 q^{45} - 384 q^{54} - 48 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} + 32 q^{74} - 512 q^{76} + 256 q^{85} + 160 q^{96}+O(q^{100}) $ 752 * q + 112 * q^12 - 160 * q^32 + 112 * q^34 - 160 * q^45 - 384 * q^54 - 48 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 + 32 * q^74 - 512 * q^76 + 256 * q^85 + 160 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{27}{32}\right)$

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 $

$2$	0.929900	−	1.06550i	0.657538	−	0.753421i
$2$	0.929900	−	1.06550i	0.657538	−	0.753421i
$3$	−0.255588	+	2.59503i	−0.147564	+	1.49824i	0.581361	+	0.813646i	$0.302521\pi$
$3$	−0.255588	+	2.59503i	−0.147564	+	1.49824i	−0.728925	+	0.684594i	$0.759979\pi$
$4$	−0.270573	−	1.98161i	−0.135287	−	0.990807i
$5$	−0.722686	+	0.386284i	−0.323195	+	0.172751i	−0.625013	−	0.780614i	$-0.714906\pi$
$5$	−0.722686	+	0.386284i	−0.323195	+	0.172751i	0.301818	+	0.953366i	$0.402406\pi$
$6$	2.52733	+	2.68544i	1.03178	+	1.09633i
$7$	−0.195090	−	0.980785i	−0.0737372	−	0.370702i
$7$	−0.195090	−	0.980785i	−0.0737372	−	0.370702i
$8$	−2.36301	−	1.55441i	−0.835451	−	0.549566i
$9$	−3.72649	−	0.741245i	−1.24216	−	0.247082i
$10$	−0.260441	+	1.12923i	−0.0823587	+	0.357093i
$11$	−3.09531	+	3.77164i	−0.933270	+	1.13719i	0.0570476	+	0.998371i	$0.481831\pi$
$11$	−3.09531	+	3.77164i	−0.933270	+	1.13719i	−0.990317	+	0.138821i	$0.955669\pi$
$12$	5.21150	−	0.195668i	1.50443	−	0.0564845i
$13$	0.980249	−	1.83392i	0.271872	−	0.508637i	−0.708521	−	0.705690i	$-0.750637\pi$
$13$	0.980249	−	1.83392i	0.271872	−	0.508637i	0.980393	+	0.197053i	$0.0631371\pi$
$14$	−1.22644	−	0.704164i	−0.327780	−	0.188196i
$15$	−0.817707	−	1.97412i	−0.211131	−	0.509716i
$16$	−3.85358	+	1.07234i	−0.963395	+	0.268086i
$17$	−2.99065	+	7.22006i	−0.725339	+	1.75112i	−0.0678043	+	0.997699i	$0.521599\pi$
$17$	−2.99065	+	7.22006i	−0.725339	+	1.75112i	−0.657535	+	0.753424i	$0.728401\pi$
$18$	−4.25506	+	3.28128i	−1.00293	+	0.773406i
$19$	0.449783	+	1.48273i	0.103187	+	0.340163i	0.993298	−	0.115582i	$-0.0368732\pi$
$19$	0.449783	+	1.48273i	0.103187	+	0.340163i	−0.890111	+	0.455744i	$0.849373\pi$
$20$	0.961004	+	1.32757i	0.214887	+	0.296853i
$21$	2.59503	−	0.255588i	0.566281	−	0.0557739i
$22$	1.14035	+	6.80529i	0.243124	+	1.45089i
$23$	1.54931	−	1.03522i	0.323054	−	0.215857i	−0.383459	−	0.923558i	$-0.625267\pi$
$23$	1.54931	−	1.03522i	0.323054	−	0.215857i	0.706513	+	0.707700i	$0.250267\pi$
$24$	4.63768	−	5.73479i	0.946663	−	1.17061i
$25$	−2.40479	+	3.59902i	−0.480958	+	0.719805i
$26$	−1.04250	−	2.74981i	−0.204452	−	0.539283i
$27$	0.605171	−	1.99498i	0.116465	−	0.383934i
$28$	−1.89075	+	0.651968i	−0.357318	+	0.123210i
$29$	−5.24567	+	4.30501i	−0.974096	+	0.799420i	−0.979680	−	0.200565i	$-0.935722\pi$
$29$	−5.24567	+	4.30501i	−0.974096	+	0.799420i	0.00558476	+	0.999984i	$0.498222\pi$
$30$	−2.86381	−	0.964468i	−0.522857	−	0.176087i
$31$	5.08207	−	5.08207i	0.912766	−	0.912766i	−0.0837229	−	0.996489i	$-0.526681\pi$
$31$	5.08207	−	5.08207i	0.912766	−	0.912766i	0.996489	+	0.0837229i	$0.0266811\pi$
$32$	−2.44086	+	5.10315i	−0.431488	+	0.902119i
$33$	−8.99639	−	8.99639i	−1.56607	−	1.56607i
$34$	4.91196	+	9.90047i	0.842395	+	1.69792i
$35$	0.519851	+	0.633440i	0.0878708	+	0.107071i
$36$	−0.460573	+	7.58502i	−0.0767621	+	1.26417i
$37$	−6.43458	−	1.95191i	−1.05784	−	0.320892i	−0.287005	−	0.957929i	$-0.592660\pi$
$37$	−6.43458	−	1.95191i	−1.05784	−	0.320892i	−0.770833	+	0.637038i	$0.780160\pi$
$38$	1.99810	+	0.899552i	0.324135	+	0.145927i
$39$	4.50853	+	3.01250i	0.721942	+	0.482386i
$40$	2.30816	+	0.210555i	0.364952	+	0.0332917i
$41$	−5.43834	−	8.13905i	−0.849326	−	1.27111i	−0.960773	−	0.277335i	$-0.910549\pi$
$41$	−5.43834	−	8.13905i	−0.849326	−	1.27111i	0.111447	−	0.993770i	$-0.464451\pi$
$42$	2.14079	−	3.00267i	0.330331	−	0.463322i
$43$	0.567569	+	5.76262i	0.0865534	+	0.878791i	0.936207	+	0.351450i	$0.114311\pi$
$43$	0.567569	+	5.76262i	0.0865534	+	0.878791i	−0.849653	+	0.527342i	$0.823189\pi$
$44$	8.31144	+	5.11319i	1.25300	+	0.770843i
$45$	2.97941	−	0.903795i	0.444145	−	0.134730i
$46$	0.337682	−	2.61343i	0.0497885	−	0.385330i
$47$	−5.47609	−	2.26827i	−0.798771	−	0.330862i	−0.0543066	−	0.998524i	$-0.517295\pi$
$47$	−5.47609	−	2.26827i	−0.798771	−	0.330862i	−0.744464	+	0.667663i	$0.767295\pi$
$48$	−1.79783	−	10.2742i	−0.259494	−	1.48296i
$49$	−0.923880	+	0.382683i	−0.131983	+	0.0546691i
$50$	1.59854	+	5.90903i	0.226068	+	0.835663i
$51$	−17.9719	−	9.60618i	−2.51657	−	1.34513i
$52$	−3.89934	−	1.44627i	−0.540742	−	0.200561i
$53$	−6.20745	−	5.09433i	−0.852659	−	0.699760i	0.102857	−	0.994696i	$-0.467201\pi$
$53$	−6.20745	−	5.09433i	−0.852659	−	0.699760i	−0.955517	+	0.294937i	$0.904701\pi$
$54$	−1.56290	−	2.49994i	−0.212684	−	0.340199i
$55$	0.780011	−	3.92138i	0.105177	−	0.528759i
$56$	−1.06354	+	2.62086i	−0.142121	+	0.350227i
$57$	−3.96270	+	0.788229i	−0.524872	+	0.104404i
$58$	−0.290966	+	9.59247i	−0.0382057	+	1.25955i
$59$	4.89907	+	9.16551i	0.637804	+	1.19325i	0.968383	+	0.249469i	$0.0802562\pi$
$59$	4.89907	+	9.16551i	0.637804	+	1.19325i	−0.330578	+	0.943779i	$0.607244\pi$
$60$	−3.69069	+	2.15452i	−0.476466	+	0.278148i
$61$	11.0401	+	1.08735i	1.41353	+	0.139221i	0.775772	−	0.631013i	$-0.217361\pi$
$61$	11.0401	+	1.08735i	1.41353	+	0.139221i	0.637761	+	0.770234i	$0.279861\pi$
$62$	−0.689121	−	10.1407i	−0.0875184	−	1.28788i
$63$			3.79949i			0.478691i
$64$	3.16764	+	7.34616i	0.395955	+	0.918270i
$65$			1.70400i			0.211355i
$66$	−17.9514	+	1.21990i	−2.20966	+	0.150159i
$67$	15.5409	+	1.53065i	1.89863	+	0.186998i	0.978728	−	0.205161i	$-0.0657719\pi$
$67$	15.5409	+	1.53065i	1.89863	+	0.186998i	0.919897	+	0.392160i	$0.128272\pi$
$68$	15.1166	+	3.97275i	1.83315	+	0.481767i
$69$	2.29043	+	4.28509i	0.275735	+	0.515864i
$70$	1.15834	+	0.0351356i	0.138448	+	0.00419951i
$71$	−6.32256	+	1.25764i	−0.750350	+	0.149254i	−0.555428	−	0.831565i	$-0.687445\pi$
$71$	−6.32256	+	1.25764i	−0.750350	+	0.149254i	−0.194922	+	0.980819i	$0.562445\pi$
$72$	7.65354	+	7.54405i	0.901978	+	0.889074i
$73$	0.707719	−	3.55794i	0.0828322	−	0.416426i	−0.917013	−	0.398856i	$-0.869407\pi$
$73$	0.707719	−	3.55794i	0.0828322	−	0.416426i	0.999846	−	0.0175693i	$-0.00559276\pi$
$74$	−8.06326	+	5.04095i	−0.937335	+	0.585999i
$75$	−8.72493	−	7.16037i	−1.00747	−	0.826808i
$76$	2.81651	−	1.29248i	0.323076	−	0.148258i
$77$	4.30303	+	2.30002i	0.490376	+	0.262112i
$78$	7.40229	−	2.00250i	0.838145	−	0.226739i
$79$	5.48061	−	2.27014i	0.616617	−	0.255411i	−0.0524378	−	0.998624i	$-0.516699\pi$
$79$	5.48061	−	2.27014i	0.616617	−	0.255411i	0.669055	+	0.743213i	$0.266699\pi$
$80$	2.37070	−	2.26354i	0.265052	−	0.253072i
$81$	−5.50847	−	2.28168i	−0.612052	−	0.253520i
$82$	−13.7293	−	1.77396i	−1.51614	−	0.195901i
$83$	14.6240	−	4.43614i	1.60519	−	0.486930i	0.644514	−	0.764592i	$-0.277060\pi$
$83$	14.6240	−	4.43614i	1.60519	−	0.486930i	0.960679	+	0.277662i	$0.0895596\pi$
$84$	−1.20862	−	5.07319i	−0.131871	−	0.553530i
$85$	−0.627694	−	6.37308i	−0.0680829	−	0.691258i
$86$	6.66784	+	4.75392i	0.719012	+	0.512628i
$87$	−9.83088	−	14.7130i	−1.05398	−	1.57739i
$88$	13.1769	−	4.10107i	1.40466	−	0.437175i
$89$	−1.29525	−	0.865460i	−0.137297	−	0.0917386i	0.485025	−	0.874500i	$-0.338810\pi$
$89$	−1.29525	−	0.865460i	−0.137297	−	0.0917386i	−0.622322	+	0.782762i	$0.713810\pi$
$90$	1.80756	−	4.01500i	0.190534	−	0.423218i
$91$	−1.98992	−	0.603635i	−0.208600	−	0.0632781i
$92$	−2.47060	−	2.79003i	−0.257578	−	0.290881i
$93$	11.8892	+	14.4870i	1.23285	+	1.50223i
$94$	−7.50906	+	3.72550i	−0.774500	+	0.384256i
$95$	−0.897808	−	0.897808i	−0.0921132	−	0.0921132i
$96$	−12.6190	−	7.63842i	−1.28792	−	0.779593i
$97$	0.303828	−	0.303828i	0.0308491	−	0.0308491i	−0.691514	−	0.722363i	$-0.743056\pi$
$97$	0.303828	−	0.303828i	0.0308491	−	0.0308491i	0.722363	+	0.691514i	$0.243056\pi$
$98$	−0.451367	+	1.34025i	−0.0455949	+	0.135386i
$99$	14.3303	−	11.7606i	1.44025	−	1.18198i
$100$	7.78254	+	3.79157i	0.778254	+	0.379157i
$101$	−5.15128	+	16.9815i	−0.512572	+	1.68972i	0.193097	+	0.981180i	$0.438147\pi$
$101$	−5.15128	+	16.9815i	−0.512572	+	1.68972i	−0.705668	+	0.708542i	$0.749353\pi$
$102$	−26.9474	+	10.2162i	−2.66819	+	1.01156i
$103$	−5.54810	+	8.30331i	−0.546670	+	0.818150i	−0.997213	−	0.0746049i	$-0.976230\pi$
$103$	−5.54810	+	8.30331i	−0.546670	+	0.818150i	0.450543	+	0.892755i	$0.351230\pi$
$104$	−5.16699	+	2.80986i	−0.506665	+	0.275530i
$105$	−1.77666	+	1.18713i	−0.173384	+	0.115852i
$106$	−11.2003	+	1.87682i	−1.08787	+	0.182293i
$107$	−1.35009	+	0.132972i	−0.130518	+	0.0128549i	−0.163065	−	0.986615i	$-0.552138\pi$
$107$	−1.35009	+	0.132972i	−0.130518	+	0.0128549i	0.0325470	+	0.999470i	$0.489638\pi$
$108$	−4.11702	−	0.659426i	−0.396161	−	0.0634533i
$109$	3.03111	+	9.99225i	0.290328	+	0.957084i	0.973857	+	0.227160i	$0.0729442\pi$
$109$	3.03111	+	9.99225i	0.290328	+	0.957084i	−0.683529	+	0.729923i	$0.739556\pi$
$110$	−3.45289	−	4.47759i	−0.329220	−	0.426921i
$111$	6.70985	−	16.1990i	0.636871	−	1.53754i
$112$	1.80353	+	3.57033i	0.170418	+	0.337365i
$113$	1.87981	+	4.53826i	0.176838	+	0.426924i	0.987300	−	0.158867i	$-0.0507840\pi$
$113$	1.87981	+	4.53826i	0.176838	+	0.426924i	−0.810462	+	0.585791i	$0.800784\pi$
$114$	−2.84505	+	4.95522i	−0.266464	+	0.464099i
$115$	−0.719778	+	1.34661i	−0.0671196	+	0.125572i
$116$	9.95019	+	9.23006i	0.923852	+	0.856990i
$117$	−5.01227	+	6.10747i	−0.463384	+	0.564636i
$118$	14.3215	+	3.30306i	1.31840	+	0.304071i
$119$	7.66478	+	1.52462i	0.702629	+	0.139762i
$120$	−1.13633	+	5.93592i	−0.103733	+	0.541873i
$121$	−2.49837	−	12.5601i	−0.227124	−	1.14183i
$122$	11.4247	−	10.7520i	1.03434	−	0.973443i
$123$	22.5110	−	12.0324i	2.02975	−	1.08492i
$124$	−11.4458	−	8.69562i	−1.02786	−	0.780890i
$125$	0.749263	−	7.60739i	0.0670161	−	0.680426i
$126$	4.04835	+	3.53315i	0.360656	+	0.314758i
$127$	−0.618458			−0.0548793			−0.0274396	−	0.999623i	$-0.508735\pi$
$127$	−0.618458			−0.0548793			−0.0274396	+	0.999623i	$0.508735\pi$
$128$	10.7729	+	3.45607i	0.952200	+	0.305477i
$129$	−15.0992			−1.32941
$130$	1.81561	+	1.58455i	0.159240	+	0.138974i
$131$	0.293880	−	2.98382i	0.0256765	−	0.260697i	−0.973773	−	0.227521i	$-0.926938\pi$
$131$	0.293880	−	2.98382i	0.0256765	−	0.260697i	0.999450	−	0.0331760i	$-0.0105622\pi$
$132$	−15.3932	+	20.2615i	−1.33980	+	1.76354i
$133$	1.36650	−	0.730407i	0.118490	−	0.0633343i
$134$	16.0824	−	15.1355i	1.38931	−	1.30751i
$135$	0.333280	+	1.67551i	0.0286842	+	0.144205i
$136$	18.2899	−	12.4124i	1.56834	−	1.06436i
$137$	−2.21305	−	0.440203i	−0.189074	−	0.0376091i	0.0996451	−	0.995023i	$-0.468229\pi$
$137$	−2.21305	−	0.440203i	−0.189074	−	0.0376091i	−0.288719	+	0.957414i	$0.593229\pi$
$138$	6.69563	+	1.54426i	0.569970	+	0.131456i
$139$	7.29708	−	8.89152i	0.618931	−	0.754169i	−0.365333	−	0.930877i	$-0.619045\pi$
$139$	7.29708	−	8.89152i	0.618931	−	0.754169i	0.984263	+	0.176708i	$0.0565448\pi$
$140$	1.11457	−	1.20153i	0.0941988	−	0.101548i
$141$	7.28585	−	13.6309i	0.613580	−	1.14793i
$142$	−4.53934	+	7.90615i	−0.380933	+	0.663469i
$143$	3.88271	+	9.37369i	0.324688	+	0.783867i
$144$	15.1552	−	1.13962i	1.26293	−	0.0949687i
$145$	2.12802	−	5.13749i	0.176722	−	0.426645i
$146$	−3.13287	−	4.06260i	−0.259278	−	0.336223i
$147$	−0.756942	−	2.49530i	−0.0624315	−	0.205809i
$148$	−2.12690	+	13.2790i	−0.174830	+	1.09152i
$149$	2.13810	−	0.210584i	0.175160	−	0.0172517i	−0.0100569	−	0.999949i	$-0.503201\pi$
$149$	2.13810	−	0.210584i	0.175160	−	0.0172517i	0.185217	+	0.982698i	$0.440701\pi$
$150$	−15.7427	+	2.63798i	−1.28538	+	0.215390i
$151$	4.48699	−	2.99811i	0.365146	−	0.243983i	−0.359438	−	0.933169i	$-0.617032\pi$
$151$	4.48699	−	2.99811i	0.365146	−	0.243983i	0.724585	+	0.689186i	$0.242032\pi$
$152$	1.24193	−	4.20286i	0.100734	−	0.340897i
$153$	16.4965	−	24.6887i	1.33366	−	1.99596i
$154$	6.45206	−	2.44609i	0.519922	−	0.197111i
$155$	−1.70962	+	5.63586i	−0.137320	+	0.452683i
$156$	4.74973	−	9.74926i	0.380283	−	0.780565i
$157$	2.81222	−	2.30793i	0.224440	−	0.184193i	−0.515453	−	0.856918i	$-0.672376\pi$
$157$	2.81222	−	2.30793i	0.224440	−	0.184193i	0.739893	+	0.672725i	$0.234876\pi$
$158$	2.67759	−	7.95059i	0.213017	−	0.632515i
$159$	14.8065	−	14.8065i	1.17423	−	1.17423i
$160$	−0.207286	−	4.63085i	−0.0163874	−	0.366100i
$161$	−1.31758	−	1.31758i	−0.103840	−	0.103840i
$162$	−7.55345	+	3.74753i	−0.593455	+	0.294434i
$163$	−2.07267	−	2.52556i	−0.162344	−	0.197817i	0.685485	−	0.728087i	$-0.259590\pi$
$163$	−2.07267	−	2.52556i	−0.162344	−	0.197817i	−0.847829	+	0.530270i	$0.822090\pi$
$164$	−14.6570	+	12.9789i	−1.14452	+	1.01348i
$165$	9.97673	+	3.02641i	0.776687	+	0.235606i
$166$	8.87216	−	19.7070i	0.688613	−	1.52956i
$167$	17.8700	+	11.9403i	1.38282	+	0.923971i	1.00000		0.000147671i	$4.70051e-5\pi$
$167$	17.8700	+	11.9403i	1.38282	+	0.923971i	0.382820	+	0.923823i	$0.374953\pi$
$168$	−6.52937	−	3.42977i	−0.503752	−	0.264613i
$169$	4.82005	+	7.21371i	0.370773	+	0.554901i
$170$	−7.37420	−	5.25752i	−0.565575	−	0.403233i
$171$	−0.577041	−	5.85879i	−0.0441274	−	0.448033i
$172$	11.2657	−	2.68391i	0.859003	−	0.204646i
$173$	10.4624	−	3.17372i	0.795438	−	0.241294i	0.133694	−	0.991023i	$-0.457316\pi$
$173$	10.4624	−	3.17372i	0.795438	−	0.241294i	0.661745	+	0.749729i	$0.269816\pi$
$174$	−24.8184	−	3.20679i	−1.88148	−	0.243106i
$175$	3.99902	+	1.65645i	0.302298	+	0.125216i
$176$	7.88352	−	17.8535i	0.594243	−	1.34576i
$177$	−25.0369	+	10.3706i	−1.88189	+	0.779504i
$178$	−2.12660	+	0.575298i	−0.159396	+	0.0431204i
$179$	1.57954	+	0.844281i	0.118060	+	0.0631046i	0.529370	−	0.848391i	$-0.322428\pi$
$179$	1.57954	+	0.844281i	0.118060	+	0.0631046i	−0.411309	+	0.911496i	$0.634928\pi$
$180$	−2.59712	−	5.65950i	−0.193578	−	0.421834i
$181$	−5.27281	−	4.32729i	−0.391925	−	0.321645i	0.417708	−	0.908582i	$-0.362834\pi$
$181$	−5.27281	−	4.32729i	−0.391925	−	0.321645i	−0.809633	+	0.586937i	$0.800334\pi$
$182$	−2.49359	+	1.55893i	−0.184838	+	0.115556i
$183$	−5.64341	+	28.3713i	−0.417173	+	2.09727i
$184$	−5.27018	+	0.0379691i	−0.388523	+	0.00279912i
$185$	5.40417	−	1.07496i	0.397322	−	0.0790323i
$186$	26.4916	+	0.803565i	1.94246	+	0.0589202i
$187$	−17.9745	−	33.6280i	−1.31443	−	2.45912i
$188$	−3.01316	+	11.4652i	−0.219757	+	0.836188i
$189$	−2.07471	−	0.204341i	−0.150913	−	0.0148636i
$190$	−1.79148	+	0.121741i	−0.129968	+	0.00883205i
$191$		−	25.4212i		−	1.83942i	−0.392604	−	0.919708i	$-0.628426\pi$
$191$		−	25.4212i		−	1.83942i	0.392604	−	0.919708i	$-0.371574\pi$
$192$	−19.8731	+	6.34253i	−1.43422	+	0.457733i
$193$			2.25890i			0.162599i	0.996690	+	0.0812997i	$0.0259071\pi$
$193$			2.25890i			0.162599i	−0.996690	+	0.0812997i	$0.974093\pi$
$194$	−0.0411987	−	0.606259i	−0.00295789	−	0.0435268i
$195$	−4.42193	−	0.435522i	−0.316661	−	0.0311884i
$196$	1.00831	+	1.72723i	0.0720220	+	0.123373i
$197$	2.45930	+	4.60102i	0.175218	+	0.327809i	0.954165	−	0.299280i	$-0.0967463\pi$
$197$	2.45930	+	4.60102i	0.175218	+	0.327809i	−0.778948	+	0.627089i	$0.784246\pi$
$198$	0.794873	−	26.2051i	0.0564892	−	1.86232i
$199$	−16.5098	+	3.28401i	−1.17035	+	0.232797i	−0.741737	−	0.670691i	$-0.765998\pi$
$199$	−16.5098	+	3.28401i	−1.17035	+	0.232797i	−0.428613	+	0.903488i	$0.640998\pi$
$200$	11.2769	−	4.76651i	0.797397	−	0.337043i
$201$	−7.94414	+	39.9379i	−0.560337	+	2.81700i
$202$	13.3036	+	21.2798i	0.936037	+	1.49724i
$203$	5.24567	+	4.30501i	0.368174	+	0.302152i
$204$	−14.1730	+	38.2125i	−0.992310	+	2.67541i
$205$	7.07419	+	3.78124i	0.494083	+	0.264093i
$206$	3.68799	+	13.6327i	0.256955	+	0.949838i
$207$	−6.54083	+	2.70930i	−0.454619	+	0.188310i
$208$	−1.81088	+	8.11831i	−0.125562	+	0.562904i
$209$	−6.98456	−	2.89310i	−0.483132	−	0.200120i
$210$	−0.387235	+	2.99694i	−0.0267218	+	0.206808i
$211$	−26.3220	+	7.98470i	−1.81208	+	0.549689i	−0.999452	−	0.0330904i	$-0.989465\pi$
$211$	−26.3220	+	7.98470i	−1.81208	+	0.549689i	−0.812630	+	0.582780i	$0.801965\pi$
$212$	−8.41541	+	13.6792i	−0.577973	+	0.939489i
$213$	−1.64763	−	16.7287i	−0.112894	−	1.14623i
$214$	−1.11377	+	1.56217i	−0.0761356	+	0.106788i
$215$	−2.63618	−	3.94532i	−0.179786	−	0.269069i
$216$	−4.53103	+	3.77348i	−0.308298	+	0.256753i
$217$	−5.97588	−	3.99295i	−0.405669	−	0.271059i
$218$	13.4654	+	6.06214i	0.911989	+	0.410580i
$219$	9.05207	+	2.74592i	0.611682	+	0.185552i
$220$	−7.98171	−	0.484660i	−0.538127	−	0.0326758i
$221$	10.3094	+	12.5621i	0.693487	+	0.845016i
$222$	−11.0205	−	22.2128i	−0.739650	−	1.49083i
$223$	0.934427	+	0.934427i	0.0625739	+	0.0625739i	0.737701	−	0.675127i	$-0.235911\pi$
$223$	0.934427	+	0.934427i	0.0625739	+	0.0625739i	−0.675127	+	0.737701i	$0.735911\pi$
$224$	5.48129	+	1.39839i	0.366234	+	0.0934338i
$225$	11.6292	−	11.6292i	0.775279	−	0.775279i
$226$	6.58355	+	2.21720i	0.437931	+	0.147486i
$227$	2.92422	−	2.39984i	0.194087	−	0.159283i	−0.532331	−	0.846536i	$-0.678684\pi$
$227$	2.92422	−	2.39984i	0.194087	−	0.159283i	0.726418	+	0.687253i	$0.241184\pi$
$228$	2.63416	+	7.63926i	0.174452	+	0.505922i
$229$	−3.58956	+	11.8332i	−0.237205	+	0.781959i	0.754822	+	0.655930i	$0.227723\pi$
$229$	−3.58956	+	11.8332i	−0.237205	+	0.781959i	−0.992027	+	0.126029i	$0.959777\pi$
$230$	0.765489	+	2.01913i	0.0504749	+	0.133138i
$231$	−7.06842	+	10.5786i	−0.465068	+	0.696023i
$232$	19.0873	−	2.01888i	1.25314	−	0.132546i
$233$	−23.6047	+	15.7721i	−1.54639	+	1.03327i	−0.568872	+	0.822426i	$0.692620\pi$
$233$	−23.6047	+	15.7721i	−1.54639	+	1.03327i	−0.977521	+	0.210840i	$0.932380\pi$
$234$	1.84659	+	11.0199i	0.120715	+	0.720393i
$235$	4.83370	−	0.476077i	0.315316	−	0.0310559i
$236$	16.8369	−	12.1880i	1.09599	−	0.793371i
$237$	4.49031	+	14.8026i	0.291677	+	0.961530i
$238$	8.75196	−	6.74907i	0.567305	−	0.437477i
$239$	3.28018	−	7.91905i	0.212177	−	0.512241i	−0.781580	−	0.623805i	$-0.785586\pi$
$239$	3.28018	−	7.91905i	0.212177	−	0.512241i	0.993757	+	0.111564i	$0.0355860\pi$
$240$	5.26803	+	6.73057i	0.340050	+	0.434456i
$241$	−6.27487	−	15.1489i	−0.404200	−	0.975825i	−0.986635	−	0.162947i	$-0.947900\pi$
$241$	−6.27487	−	15.1489i	−0.404200	−	0.975825i	0.582435	−	0.812877i	$-0.302100\pi$
$242$	−15.7060	−	9.01766i	−1.00962	−	0.579677i
$243$	10.2772	−	19.2272i	0.659280	−	1.23343i
$244$	−0.832433	−	22.1713i	−0.0532910	−	1.41937i
$245$	0.519851	−	0.633440i	0.0332120	−	0.0404690i
$246$	8.11250	−	35.1744i	0.517234	−	2.24264i
$247$	3.16011	+	0.628585i	0.201073	+	0.0399959i
$248$	−19.9086	+	4.10938i	−1.26420	+	0.260946i
$249$	7.77420	+	39.0835i	0.492670	+	2.47682i
$250$	−7.40893	−	7.87245i	−0.468582	−	0.497898i
$251$	−25.5051	+	13.6327i	−1.60987	+	0.860492i	−0.612311	+	0.790617i	$0.709760\pi$
$251$	−25.5051	+	13.6327i	−1.60987	+	0.860492i	−0.997556	+	0.0698742i	$0.977740\pi$
$252$	7.52913	−	1.02804i	0.474290	−	0.0647605i
$253$	−0.891126	+	9.04775i	−0.0560246	+	0.568827i
$254$	−0.575104	+	0.658966i	−0.0360852	+	0.0413472i
$255$	16.6988			1.04572
$256$	13.7002	−	8.26471i	0.856260	−	0.516545i
$257$	17.5097			1.09223			0.546113	−	0.837712i	$-0.316107\pi$
$257$	17.5097			1.09223			0.546113	+	0.837712i	$0.316107\pi$
$258$	−14.0408	+	16.0882i	−0.874140	+	1.00161i
$259$	−0.659078	+	6.69173i	−0.0409531	+	0.415804i
$260$	3.37667	−	0.461057i	0.209412	−	0.0285935i
$261$	22.7390	−	12.1542i	1.40751	−	0.752328i
$262$	−2.90597	−	3.08778i	−0.179532	−	0.190764i
$263$	−3.32529	−	16.7173i	−0.205046	−	1.03084i	−0.936960	−	0.349438i	$-0.886373\pi$
$263$	−3.32529	−	16.7173i	−0.205046	−	1.03084i	0.731914	−	0.681397i	$-0.238627\pi$
$264$	7.27452	+	35.2426i	0.447716	+	2.16903i
$265$	6.45390	+	1.28376i	0.396460	+	0.0788608i
$266$	0.492456	−	2.13520i	0.0301944	−	0.130918i
$267$	2.57694	−	3.14002i	0.157706	−	0.192166i
$268$	−1.17180	−	31.2102i	−0.0715793	−	1.90647i
$269$	3.07349	−	5.75010i	0.187394	−	0.350590i	−0.770627	−	0.637286i	$-0.780057\pi$
$269$	3.07349	−	5.75010i	0.187394	−	0.350590i	0.958022	+	0.286696i	$0.0925571\pi$
$270$	2.09517	+	1.20295i	0.127508	+	0.0732092i
$271$	12.4763	+	30.1206i	0.757884	+	1.82969i	0.507814	+	0.861466i	$0.330454\pi$
$271$	12.4763	+	30.1206i	0.757884	+	1.82969i	0.250070	+	0.968228i	$0.419546\pi$
$272$	3.78233	−	31.0301i	0.229337	−	1.88148i
$273$	2.07505	−	5.00961i	0.125588	−	0.303195i
$274$	−2.52695	+	1.94866i	−0.152659	+	0.117723i
$275$	−6.13066	−	20.2101i	−0.369693	−	1.21871i
$276$	7.87167	−	5.69817i	0.473819	−	0.342990i
$277$	−29.7609	+	2.93119i	−1.78816	+	0.176118i	−0.937125	−	0.348994i	$-0.886523\pi$
$277$	−29.7609	+	2.93119i	−1.78816	+	0.176118i	−0.851033	+	0.525112i	$0.824023\pi$
$278$	−2.68834	−	16.0433i	−0.161236	−	0.962210i
$279$	−22.7053	+	15.1712i	−1.35933	+	0.908276i
$280$	−0.243790	−	2.30488i	−0.0145692	−	0.137743i
$281$	1.70907	−	2.55780i	0.101955	−	0.152586i	−0.776985	−	0.629519i	$-0.783252\pi$
$281$	1.70907	−	2.55780i	0.101955	−	0.152586i	0.878939	+	0.476934i	$0.158252\pi$
$282$	−7.74856	−	20.4384i	−0.461420	−	1.21709i
$283$	−7.65900	+	25.2484i	−0.455281	+	1.50086i	0.366153	+	0.930555i	$0.380675\pi$
$283$	−7.65900	+	25.2484i	−0.455281	+	1.50086i	−0.821434	+	0.570304i	$0.806825\pi$
$284$	4.20286	+	12.1886i	0.249394	+	0.723259i
$285$	2.55931	−	2.10037i	0.151600	−	0.124415i
$286$	13.5982	+	4.57957i	0.804077	+	0.270796i
$287$	−6.92169	+	6.92169i	−0.408575	+	0.408575i
$288$	12.8785	−	17.2076i	0.758875	−	1.01397i
$289$	−31.1645	−	31.1645i	−1.83321	−	1.83321i
$290$	−3.49514	−	7.04474i	−0.205242	−	0.413682i
$291$	0.710788	+	0.866098i	0.0416671	+	0.0507716i
$292$	−7.24195	−	0.439741i	−0.423803	−	0.0257339i
$293$	8.44601	+	2.56207i	0.493421	+	0.149678i	0.527182	−	0.849752i	$-0.323248\pi$
$293$	8.44601	+	2.56207i	0.493421	+	0.149678i	−0.0337610	+	0.999430i	$0.510748\pi$
$294$	−3.36262	−	1.51386i	−0.196112	−	0.0882902i
$295$	−7.08098	−	4.73136i	−0.412270	−	0.275470i
$296$	12.1709	+	14.6143i	0.707420	+	0.849440i
$297$	5.65116	+	8.45756i	0.327914	+	0.490757i
$298$	1.76384	−	2.47396i	0.102177	−	0.143313i
$299$	−0.379790	−	3.85608i	−0.0219639	−	0.223003i
$300$	−11.8283	+	19.2268i	−0.682910	+	1.11006i
$301$	5.54117	−	1.68089i	0.319387	−	0.0968851i
$302$	0.977969	−	7.56882i	0.0562758	−	0.435537i
$303$	−42.7509	−	17.7080i	−2.45597	−	1.01730i
$304$	−3.32327	−	5.23152i	−0.190603	−	0.300048i
$305$	−8.39852	+	3.47878i	−0.480898	+	0.199194i
$306$	−10.9657	−	40.5349i	−0.626868	−	2.31723i
$307$	−8.52534	−	4.55689i	−0.486567	−	0.260075i	0.209823	−	0.977739i	$-0.432711\pi$
$307$	−8.52534	−	4.55689i	−0.486567	−	0.260075i	−0.696389	+	0.717664i	$0.745211\pi$
$308$	3.39346	−	9.14927i	0.193361	−	0.521328i
$309$	−20.1293	−	16.5197i	−1.14512	−	0.939773i
$310$	4.41522	+	7.06238i	0.250768	+	0.401116i
$311$	−2.50449	+	12.5909i	−0.142017	+	0.713966i	0.842503	+	0.538691i	$0.181081\pi$
$311$	−2.50449	+	12.5909i	−0.142017	+	0.713966i	−0.984520	+	0.175274i	$0.943919\pi$
$312$	−5.97105	−	14.1267i	−0.338044	−	0.799765i
$313$	19.3532	−	3.84959i	1.09391	−	0.217592i	0.385017	−	0.922910i	$-0.374196\pi$
$313$	19.3532	−	3.84959i	1.09391	−	0.217592i	0.708891	+	0.705318i	$0.249196\pi$
$314$	0.155988	−	5.14256i	0.00880291	−	0.290211i
$315$	−1.46768	−	2.74584i	−0.0826946	−	0.154711i
$316$	−5.98145	−	10.2462i	−0.336483	−	0.576395i
$317$	−6.28262	−	0.618784i	−0.352867	−	0.0347544i	−0.0799691	−	0.996797i	$-0.525482\pi$
$317$	−6.28262	−	0.618784i	−0.352867	−	0.0347544i	−0.272898	+	0.962043i	$0.587982\pi$
$318$	−2.00774	−	29.5448i	−0.112588	−	1.65679i
$319$		−	33.1101i		−	1.85381i
$320$	−5.12691	−	4.08536i	−0.286603	−	0.228379i
$321$		−	3.53751i		−	0.197445i
$322$	−2.62910	+	0.178662i	−0.146514	+	0.00995644i
$323$	−12.0506	−	1.18688i	−0.670512	−	0.0660397i
$324$	−3.03097	+	11.5330i	−0.168387	+	0.640723i
$325$	4.24302	+	7.93813i	0.235360	+	0.440328i
$326$	−4.61835	−	0.140087i	−0.255787	−	0.00775872i
$327$	−26.7049	+	5.31193i	−1.47678	+	0.293750i
$328$	0.199465	+	27.6860i	0.0110136	+	1.52871i
$329$	−1.15636	+	5.81339i	−0.0637519	+	0.320503i
$330$	12.5020	−	7.81593i	0.688212	−	0.430253i
$331$	7.80057	+	6.40176i	0.428758	+	0.351873i	0.823888	−	0.566753i	$-0.191800\pi$
$331$	7.80057	+	6.40176i	0.428758	+	0.351873i	−0.395130	+	0.918625i	$0.629300\pi$
$332$	−12.7476	−	27.7788i	−0.699614	−	1.52456i
$333$	22.5315	+	12.0434i	1.23472	+	0.659972i
$334$	29.3397	−	7.93711i	1.60540	−	0.434299i
$335$	−11.8225	+	4.89703i	−0.645931	+	0.267553i
$336$	−9.72607	+	3.76769i	−0.530601	+	0.205544i
$337$	−5.17454	−	2.14337i	−0.281875	−	0.116757i	0.237267	−	0.971445i	$-0.423748\pi$
$337$	−5.17454	−	2.14337i	−0.281875	−	0.116757i	−0.519142	+	0.854688i	$0.673748\pi$
$338$	12.1684	+	1.57228i	0.661871	+	0.0855205i
$339$	−12.2574	+	3.71824i	−0.665729	+	0.201947i
$340$	−12.4591	+	2.96823i	−0.675692	+	0.160975i
$341$	3.43718	+	34.8983i	0.186134	+	1.88985i
$342$	−6.77912	−	4.83325i	−0.366573	−	0.261352i
$343$	0.555570	+	0.831470i	0.0299980	+	0.0448951i
$344$	7.61628	−	14.4994i	0.410642	−	0.781753i
$345$	−3.31052	−	2.21202i	−0.178233	−	0.119091i
$346$	6.34735	−	14.0989i	0.341236	−	0.757960i
$347$	−6.73351	−	2.04259i	−0.361474	−	0.109652i	0.104323	−	0.994543i	$-0.466732\pi$
$347$	−6.73351	−	2.04259i	−0.361474	−	0.109652i	−0.465797	+	0.884892i	$0.654232\pi$
$348$	−26.4954	+	23.4619i	−1.42030	+	1.25769i
$349$	7.70764	+	9.39179i	0.412580	+	0.502731i	0.937290	−	0.348551i	$-0.113326\pi$
$349$	7.70764	+	9.39179i	0.412580	+	0.502731i	−0.524710	+	0.851281i	$0.675826\pi$
$350$	5.48363	−	2.72062i	0.293112	−	0.145423i
$351$	−3.06541	−	3.06541i	−0.163620	−	0.163620i
$352$	−11.6920	−	25.0019i	−0.623188	−	1.33261i
$353$	4.36156	−	4.36156i	0.232142	−	0.232142i	−0.581444	−	0.813586i	$-0.697512\pi$
$353$	4.36156	−	4.36156i	0.232142	−	0.232142i	0.813586	+	0.581444i	$0.197512\pi$
$354$	−12.2319	+	36.3204i	−0.650120	+	1.93041i
$355$	4.08342	−	3.35118i	0.216726	−	0.177862i
$356$	−1.36455	+	2.80086i	−0.0723208	+	0.148445i
$357$	−5.91546	+	19.5006i	−0.313079	+	1.03208i
$358$	2.36839	−	0.897899i	0.125173	−	0.0474555i
$359$	−9.77151	+	14.6241i	−0.515721	+	0.771830i	−0.994346	−	0.106189i	$-0.966135\pi$
$359$	−9.77151	+	14.6241i	−0.515721	+	0.771830i	0.478625	+	0.878019i	$0.341135\pi$
$360$	−8.44525	−	2.49554i	−0.445104	−	0.131527i
$361$	13.8017	−	9.22202i	0.726407	−	0.485369i
$362$	−9.51390	+	1.59423i	−0.500040	+	0.0837909i
$363$	33.2324	−	3.27311i	1.74425	−	0.171794i
$364$	−0.657753	+	4.10657i	−0.0344756	+	0.215243i
$365$	0.862917	+	2.84466i	0.0451671	+	0.148896i
$366$	24.9818	+	32.3955i	1.30582	+	1.69334i
$367$	5.84879	−	14.1202i	0.305304	−	0.737070i	−0.694541	−	0.719454i	$-0.744392\pi$
$367$	5.84879	−	14.1202i	0.305304	−	0.737070i	0.999845	−	0.0176161i	$-0.00560768\pi$
$368$	−4.86029	+	5.65068i	−0.253360	+	0.294562i
$369$	14.2329	+	34.3612i	0.740934	+	1.78877i
$370$	3.87997	−	6.75773i	0.201710	−	0.351318i
$371$	−3.78543	+	7.08203i	−0.196530	+	0.367681i
$372$	25.4908	−	27.4796i	1.32164	−	1.42475i
$373$	9.17473	−	11.1794i	0.475049	−	0.578849i	−0.479259	−	0.877674i	$-0.659094\pi$
$373$	9.17473	−	11.1794i	0.475049	−	0.578849i	0.954308	+	0.298824i	$0.0965945\pi$
$374$	−52.5450	−	12.1188i	−2.71704	−	0.626649i
$375$	19.5499	+	3.88872i	1.00955	+	0.200812i
$376$	9.41425	+	13.8720i	0.485503	+	0.715395i
$377$	2.75297	+	13.8401i	0.141785	+	0.712801i
$378$	−2.14700	+	2.02058i	−0.110430	+	0.103928i
$379$	10.0870	−	5.39161i	0.518134	−	0.276948i	−0.191532	−	0.981486i	$-0.561346\pi$
$379$	10.0870	−	5.39161i	0.518134	−	0.276948i	0.709666	+	0.704538i	$0.248846\pi$
$380$	−1.53619	+	2.02203i	−0.0788047	+	0.103728i
$381$	0.158070	−	1.60492i	0.00809819	−	0.0822223i
$382$	−27.0863	−	23.6392i	−1.38585	−	1.20949i
$383$	−20.9063			−1.06826			−0.534131	−	0.845401i	$-0.679361\pi$
$383$	−20.9063			−1.06826			−0.534131	+	0.845401i	$0.679361\pi$
$384$	−11.7220	+	27.0727i	−0.598188	+	1.38155i
$385$	−3.99820			−0.203767
$386$	2.40686	+	2.10055i	0.122506	+	0.106915i
$387$	2.15647	−	21.8950i	0.109620	−	1.11299i
$388$	−0.684278	−	0.519863i	−0.0347390	−	0.0263920i
$389$	5.38387	−	2.87774i	0.272973	−	0.145907i	−0.329231	−	0.944250i	$-0.606789\pi$
$389$	5.38387	−	2.87774i	0.272973	−	0.145907i	0.602204	+	0.798342i	$0.294289\pi$
$390$	−4.57600	+	4.30657i	−0.231715	+	0.218072i
$391$	2.84088	+	14.2821i	0.143670	+	0.722276i
$392$	2.77798	+	0.531799i	0.140309	+	0.0268599i
$393$	7.66798	+	1.52526i	0.386798	+	0.0769390i
$394$	7.18928	+	1.65811i	0.362191	+	0.0835344i
$395$	−3.08384	+	3.75767i	−0.155165	+	0.189069i
$396$	−27.1824	−	25.2151i	−1.36596	−	1.26710i
$397$	7.82708	−	14.6434i	0.392830	−	0.734933i	−0.605304	−	0.795994i	$-0.706948\pi$
$397$	7.82708	−	14.6434i	0.392830	−	0.734933i	0.998134	+	0.0610612i	$0.0194485\pi$
$398$	−11.8534	+	20.6450i	−0.594156	+	1.03484i
$399$	1.54617	+	3.73278i	0.0774052	+	0.186873i
$400$	5.40767	−	16.4479i	0.270384	−	0.822394i
$401$	−8.22977	+	19.8684i	−0.410975	+	0.992182i	0.573901	+	0.818924i	$0.305429\pi$
$401$	−8.22977	+	19.8684i	−0.410975	+	0.992182i	−0.984877	+	0.173257i	$0.944571\pi$
$402$	35.1665	+	45.6027i	1.75395	+	2.27446i
$403$	−4.33840	−	14.3018i	−0.216111	−	0.712423i
$404$	35.0446	+	5.61311i	1.74353	+	0.279263i
$405$	4.86227	−	0.478892i	0.241608	−	0.0237963i
$406$	9.46492	−	1.58602i	0.469736	−	0.0787130i
$407$	27.2789	−	18.2272i	1.35216	−	0.903487i
$408$	27.5359	+	50.6351i	1.36323	+	2.50681i
$409$	3.21643	−	4.81373i	0.159042	−	0.238024i	−0.743387	−	0.668861i	$-0.766782\pi$
$409$	3.21643	−	4.81373i	0.159042	−	0.238024i	0.902429	+	0.430838i	$0.141782\pi$
$410$	10.6072	−	4.02137i	0.523852	−	0.198601i
$411$	1.70797	−	5.63042i	0.0842479	−	0.277728i
$412$	17.9551	+	8.74753i	0.884585	+	0.430960i
$413$	8.03364	−	6.59304i	0.395309	−	0.324422i
$414$	−3.19556	+	9.48863i	−0.157053	+	0.466341i
$415$	−8.85496	+	8.85496i	−0.434673	+	0.434673i
$416$	6.96611	+	9.47871i	0.341542	+	0.464732i
$417$	21.2087	+	21.2087i	1.03859	+	1.03859i
$418$	−9.57753	+	4.75174i	−0.468452	+	0.232415i
$419$	18.6940	+	22.7787i	0.913262	+	1.11281i	0.993247	+	0.116016i	$0.0370125\pi$
$419$	18.6940	+	22.7787i	0.913262	+	1.11281i	−0.0799858	+	0.996796i	$0.525487\pi$
$420$	2.83314	+	3.19945i	0.138243	+	0.156117i
$421$	−28.2085	−	8.55696i	−1.37480	−	0.417041i	−0.485448	−	0.874266i	$-0.661343\pi$
$421$	−28.2085	−	8.55696i	−1.37480	−	0.417041i	−0.889351	+	0.457225i	$0.848843\pi$
$422$	−15.9692	+	35.4710i	−0.777366	+	1.72670i
$423$	18.7253	+	12.5118i	0.910453	+	0.608345i
$424$	6.74963	+	21.6869i	0.327791	+	1.05321i
$425$	−18.7933	−	28.1262i	−0.911609	−	1.36432i
$426$	−19.3565	−	13.8004i	−0.937824	−	0.668633i
$427$	−1.08735	−	11.0401i	−0.0526206	−	0.534265i
$428$	0.628798	+	2.63938i	0.0303941	+	0.127579i
$429$	−25.3173	+	7.67993i	−1.22233	+	0.370791i
$430$	−6.65512	−	0.859909i	−0.320938	−	0.0414685i
$431$	27.5715	+	11.4205i	1.32807	+	0.550106i	0.930105	−	0.367293i	$-0.119715\pi$
$431$	27.5715	+	11.4205i	1.32807	+	0.550106i	0.397968	+	0.917399i	$0.369715\pi$
$432$	−0.192773	+	8.33677i	−0.00927478	+	0.401103i
$433$	9.23868	−	3.82679i	0.443983	−	0.183904i	−0.149481	−	0.988765i	$-0.547760\pi$
$433$	9.23868	−	3.82679i	0.443983	−	0.183904i	0.593463	+	0.804861i	$0.297760\pi$
$434$	−9.81145	+	2.65424i	−0.470965	+	0.127408i
$435$	12.7880	+	6.83534i	0.613139	+	0.327729i
$436$	18.9806	−	8.71013i	0.909007	−	0.417139i
$437$	2.23180	+	1.83159i	0.106762	+	0.0876170i
$438$	11.3433	−	7.09154i	0.542003	−	0.338847i
$439$	−7.21555	+	36.2750i	−0.344379	+	1.73131i	0.288873	+	0.957367i	$0.406719\pi$
$439$	−7.21555	+	36.2750i	−0.344379	+	1.73131i	−0.633253	+	0.773945i	$0.718281\pi$
$440$	−7.93859	+	8.05381i	−0.378458	+	0.383950i
$441$	3.72649	−	0.741245i	0.177452	−	0.0352974i
$442$	22.9716	+	0.696792i	1.09265	+	0.0331430i
$443$	12.8364	+	24.0152i	0.609876	+	1.14100i	0.977483	+	0.211016i	$0.0676772\pi$
$443$	12.8364	+	24.0152i	0.609876	+	1.14100i	−0.367607	+	0.929981i	$0.619823\pi$
$444$	−33.9157	−	8.91331i	−1.60957	−	0.423007i
$445$	1.27037	+	0.125121i	0.0602215	+	0.00593130i
$446$	1.86455	−	0.126707i	0.0882892	−	0.00599975i
$447$			5.60225i			0.264977i
$448$	6.58703	−	4.53994i	0.311208	−	0.214492i
$449$			32.0367i			1.51190i	0.654627	+	0.755952i	$0.272826\pi$
$449$			32.0367i			1.51190i	−0.654627	+	0.755952i	$0.727174\pi$
$450$	−1.57690	−	23.2048i	−0.0743358	−	1.09389i
$451$	47.5309	+	4.68138i	2.23814	+	0.220438i
$452$	8.48446	−	4.95299i	0.399075	−	0.232969i
$453$	6.63336	+	12.4101i	0.311663	+	0.583080i
$454$	0.162200	−	5.34736i	0.00761244	−	0.250964i
$455$	1.67126	−	0.332434i	0.0783499	−	0.0155848i
$456$	10.5891	+	4.29705i	0.495881	+	0.201228i
$457$	0.976163	−	4.90750i	0.0456630	−	0.229563i	−0.951214	−	0.308531i	$-0.900163\pi$
$457$	0.976163	−	4.90750i	0.0456630	−	0.229563i	0.996877	+	0.0789681i	$0.0251625\pi$
$458$	9.27031	+	14.8283i	0.433173	+	0.692883i
$459$	12.5940	+	10.3357i	0.587839	+	0.482427i
$460$	2.86321	+	1.06197i	0.133498	+	0.0495144i
$461$	−16.9160	−	9.04179i	−0.787857	−	0.421118i	0.0278294	−	0.999613i	$-0.491140\pi$
$461$	−16.9160	−	9.04179i	−0.787857	−	0.421118i	−0.815686	+	0.578494i	$0.803640\pi$
$462$	4.69860	+	17.3685i	0.218599	+	0.808054i
$463$	−12.9588	+	5.36773i	−0.602249	+	0.249460i	−0.662910	−	0.748699i	$-0.730679\pi$
$463$	−12.9588	+	5.36773i	−0.602249	+	0.249460i	0.0606616	+	0.998158i	$0.480679\pi$
$464$	15.5982	−	22.2148i	0.724126	−	1.03130i
$465$	−14.1883	−	5.87697i	−0.657965	−	0.272538i
$466$	−5.14479	+	39.8172i	−0.238328	+	1.84450i
$467$	2.18678	−	0.663351i	0.101192	−	0.0306962i	−0.239283	−	0.970950i	$-0.576912\pi$
$467$	2.18678	−	0.663351i	0.101192	−	0.0306962i	0.340475	+	0.940254i	$0.389412\pi$
$468$	13.4588	+	8.27986i	0.622134	+	0.382737i
$469$	−1.53065	−	15.5409i	−0.0706787	−	0.717613i
$470$	3.98759	−	5.59300i	0.183934	−	0.257986i
$471$	5.27037	+	7.88767i	0.242846	+	0.363445i
$472$	2.67038	−	29.2733i	0.122914	−	1.34742i
$473$	−23.4913	−	15.6964i	−1.08013	−	0.721722i
$474$	19.9476	+	8.98048i	0.916226	+	0.412487i
$475$	−6.41803	−	1.94689i	−0.294479	−	0.0893294i
$476$	0.947323	−	15.6011i	0.0434205	−	0.715077i
$477$	19.3559	+	23.5852i	0.886244	+	1.07989i
$478$	−5.38750	−	10.8589i	−0.246418	−	0.496677i
$479$	−0.750153	−	0.750153i	−0.0342754	−	0.0342754i	0.689761	−	0.724037i	$-0.257715\pi$
$479$	−0.750153	−	0.750153i	−0.0342754	−	0.0342754i	−0.724037	+	0.689761i	$0.757715\pi$
$480$	12.0702	+	0.645674i	0.550925	+	0.0294709i
$481$	−9.88713	+	9.88713i	−0.450814	+	0.450814i
$482$	−21.9761	−	7.40107i	−1.00098	−	0.337110i
$483$	3.75591	−	3.08240i	0.170900	−	0.140254i
$484$	−24.2133	+	8.34922i	−1.10061	+	0.379510i
$485$	−0.102209	+	0.336937i	−0.00464105	+	0.0152995i
$486$	−10.9298	−	28.8297i	−0.495787	−	1.30774i
$487$	−5.71377	+	8.55127i	−0.258916	+	0.387495i	−0.938039	−	0.346529i	$-0.887360\pi$
$487$	−5.71377	+	8.55127i	−0.258916	+	0.387495i	0.679123	+	0.734024i	$0.262360\pi$
$488$	−24.3976	−	19.7301i	−1.10443	−	0.893142i
$489$	7.08364	−	4.73313i	0.320333	−	0.214040i
$490$	−0.191520	−	1.14294i	−0.00865199	−	0.0516326i
$491$	8.55430	−	0.842525i	0.386050	−	0.0380226i	0.0968693	−	0.995297i	$-0.469117\pi$
$491$	8.55430	−	0.842525i	0.386050	−	0.0380226i	0.289181	+	0.957275i	$0.406617\pi$
$492$	−29.9344	−	41.3525i	−1.34955	−	1.86432i
$493$	−15.3945	−	50.7488i	−0.693333	−	2.28561i
$494$	3.60834	−	2.78257i	0.162347	−	0.125194i
$495$	−5.81340	+	14.0348i	−0.261293	+	0.630817i
$496$	−14.1344	+	25.0339i	−0.634655	+	1.12405i
$497$	2.46694	+	5.95572i	0.110657	+	0.267151i
$498$	48.8726	+	28.0604i	2.19004	+	1.25742i
$499$	−8.25834	+	15.4503i	−0.369694	+	0.691649i	−0.996136	−	0.0878188i	$-0.972010\pi$
$499$	−8.25834	+	15.4503i	−0.369694	+	0.691649i	0.626442	+	0.779468i	$0.284510\pi$
$500$	−15.2776	+	0.573606i	−0.683237	+	0.0256525i
$501$	−35.5528	+	43.3213i	−1.58838	+	1.93545i
$502$	−9.19150	+	39.8527i	−0.410237	+	1.77871i
$503$	12.4733	+	2.48109i	0.556157	+	0.110627i	0.465163	−	0.885225i	$-0.345996\pi$
$503$	12.4733	+	2.48109i	0.556157	+	0.110627i	0.0909940	+	0.995851i	$0.470996\pi$
$504$	5.90596	−	8.97825i	0.263072	−	0.399923i
$505$	−2.83692	−	14.2622i	−0.126241	−	0.634657i
$506$	8.81171	+	9.36300i	0.391728	+	0.416236i
$507$	−19.9517	+	10.6644i	−0.886087	+	0.473624i
$508$	0.167338	+	1.22554i	0.00742442	+	0.0543747i
$509$	−1.39190	+	14.1322i	−0.0616950	+	0.626400i	0.913768	+	0.406237i	$0.133159\pi$
$509$	−1.39190	+	14.1322i	−0.0616950	+	0.626400i	−0.975463	+	0.220164i	$0.929341\pi$
$510$	15.5282	−	17.7925i	0.687599	−	0.787865i
$511$	−3.62765			−0.160478
$512$	3.93374	−	22.2829i	0.173849	−	0.984772i
$513$	3.23022			0.142618
$514$	16.2823	−	18.6566i	0.718180	−	0.822906i
$515$	0.802097	−	8.14383i	0.0353446	−	0.358860i
$516$	4.08544	+	29.9208i	0.179852	+	1.31719i
$517$	25.5053	−	13.6329i	1.12172	−	0.599573i
$518$	6.51715	+	6.92489i	0.286347	+	0.304262i
$519$	5.56184	+	27.9613i	0.244138	+	1.22736i
$520$	2.64871	−	4.02657i	0.116154	−	0.176577i
$521$	11.0254	+	2.19308i	0.483030	+	0.0960807i	0.430598	−	0.902544i	$-0.358303\pi$
$521$	11.0254	+	2.19308i	0.483030	+	0.0960807i	0.0524323	+	0.998624i	$0.483303\pi$
$522$	8.19465	−	35.5306i	0.358670	−	1.55513i
$523$	5.92619	−	7.22108i	0.259134	−	0.315756i	−0.627149	−	0.778899i	$-0.715778\pi$
$523$	5.92619	−	7.22108i	0.259134	−	0.315756i	0.886283	+	0.463143i	$0.153278\pi$
$524$	−5.99229	+	0.224983i	−0.261774	+	0.00982845i
$525$	−5.32063	+	9.95420i	−0.232211	+	0.434437i
$526$	−20.9045	−	12.0024i	−0.911478	−	0.523328i
$527$	21.4942	+	51.8915i	0.936301	+	2.26043i
$528$	44.3155	+	25.0211i	1.92859	+	1.08890i
$529$	−7.47303	+	18.0415i	−0.324914	+	0.784413i
$530$	7.36932	−	5.68285i	0.320103	−	0.246847i
$531$	−11.4624	−	37.7866i	−0.497427	−	1.63980i
$532$	−1.81712	−	2.51024i	−0.0787822	−	0.108833i
$533$	−20.2573	+	1.99517i	−0.877440	+	0.0864203i
$534$	−0.949381	−	5.66563i	−0.0410838	−	0.245176i
$535$	0.924327	−	0.617616i	0.0399622	−	0.0267019i
$536$	−34.3441	−	27.7738i	−1.48344	−	1.19965i
$537$	−2.59464	+	3.88316i	−0.111967	+	0.167571i
$538$	−3.26868	−	8.62181i	−0.140923	−	0.371713i
$539$	1.41635	−	4.66906i	0.0610063	−	0.201111i
$540$	3.23004	−	1.11378i	0.138999	−	0.0479295i
$541$	−28.5294	+	23.4135i	−1.22658	+	1.00662i	−0.227112	+	0.973869i	$0.572928\pi$
$541$	−28.5294	+	23.4135i	−1.22658	+	1.00662i	−0.999463	+	0.0327558i	$0.989572\pi$
$542$	43.6952	+	14.7156i	1.87687	+	0.632088i
$543$	12.5771	−	12.5771i	0.539735	−	0.539735i
$544$	−29.5453	−	32.8849i	−1.26675	−	1.40993i
$545$	−6.05039	−	6.05039i	−0.259170	−	0.259170i
$546$	−3.40814	−	6.86939i	−0.145855	−	0.293983i
$547$	3.90964	+	4.76391i	0.167164	+	0.203690i	0.849854	−	0.527018i	$-0.176690\pi$
$547$	3.90964	+	4.76391i	0.167164	+	0.203690i	−0.682690	+	0.730708i	$0.739190\pi$
$548$	−0.273520	+	4.50452i	−0.0116842	+	0.192423i
$549$	−40.3346	−	12.2354i	−1.72144	−	0.522193i
$550$	−27.2347	−	12.2611i	−1.16129	−	0.522817i
$551$	−8.74259	−	5.84161i	−0.372447	−	0.248861i
$552$	1.24846	−	13.6860i	0.0531382	−	0.582514i
$553$	−3.29574	−	4.93242i	−0.140149	−	0.209748i
$554$	−24.5515	+	34.4359i	−1.04309	+	1.46304i
$555$	1.40830	+	14.2987i	0.0597790	+	0.606947i
$556$	−19.5939	−	12.0542i	−0.830969	−	0.511211i
$557$	−29.8290	+	9.04854i	−1.26390	+	0.383399i	−0.849931	−	0.526893i	$-0.823357\pi$
$557$	−29.8290	+	9.04854i	−1.26390	+	0.383399i	−0.413966	+	0.910292i	$0.635857\pi$
$558$	−4.94877	+	38.3002i	−0.209498	+	1.62138i
$559$	11.1245	+	4.60793i	0.470517	+	0.194895i
$560$	−2.68255	−	1.88355i	−0.113358	−	0.0795947i
$561$	91.8596	−	38.0495i	3.87831	−	1.60645i
$562$	−1.13607	−	4.19951i	−0.0479223	−	0.177146i
$563$	16.0763	+	8.59295i	0.677535	+	0.362150i	0.773999	−	0.633187i	$-0.218253\pi$
$563$	16.0763	+	8.59295i	0.677535	+	0.362150i	−0.0964646	+	0.995336i	$0.530753\pi$
$564$	−28.9825	−	10.7496i	−1.22038	−	0.452640i
$565$	−3.11157	−	2.55360i	−0.130905	−	0.107431i
$566$	19.7800	+	31.6391i	0.831414	+	1.32989i
$567$	−1.16319	+	5.84776i	−0.0488495	+	0.245583i
$568$	16.8952	+	6.85602i	0.708905	+	0.287672i
$569$	17.4815	−	3.47729i	0.732862	−	0.145775i	0.185468	−	0.982650i	$-0.440620\pi$
$569$	17.4815	−	3.47729i	0.732862	−	0.145775i	0.547394	+	0.836875i	$0.315620\pi$
$570$	0.141959	−	4.68007i	0.00594602	−	0.196026i
$571$	−2.92904	−	5.47984i	−0.122576	−	0.229324i	0.813147	−	0.582058i	$-0.197752\pi$
$571$	−2.92904	−	5.47984i	−0.122576	−	0.229324i	−0.935724	+	0.352733i	$0.885252\pi$
$572$	17.5245	−	10.2303i	0.732735	−	0.427750i
$573$	65.9688	+	6.49736i	2.75589	+	0.271431i
$574$	0.938571	+	13.8115i	0.0391752	+	0.576482i
$575$			8.06548i			0.336354i
$576$	−6.35888	−	29.7234i	−0.264953	−	1.23847i
$577$		−	12.7793i		−	0.532010i	−0.963972	−	0.266005i	$-0.914296\pi$
$577$		−	12.7793i		−	0.532010i	0.963972	−	0.266005i	$-0.0857038\pi$
$578$	−62.1857	+	4.22587i	−2.58658	+	0.175773i
$579$	−5.86192	−	0.577348i	−0.243613	−	0.0239938i
$580$	−10.7563	−	2.82684i	−0.446631	−	0.117378i
$581$	−7.20391	−	13.4776i	−0.298868	−	0.559143i
$582$	1.58379	+	0.0480407i	0.0656501	+	0.00199135i
$583$	38.4279	−	7.64379i	1.59152	−	0.316574i
$584$	−7.20283	+	7.30737i	−0.298055	+	0.302381i
$585$	1.26308	−	6.34994i	0.0522220	−	0.262538i
$586$	10.5838	−	6.61674i	0.437214	−	0.273335i
$587$	19.0353	+	15.6219i	0.785672	+	0.644784i	0.939204	−	0.343359i	$-0.111565\pi$
$587$	19.0353	+	15.6219i	0.785672	+	0.644784i	−0.153532	+	0.988144i	$0.549065\pi$
$588$	−4.73992	+	2.17513i	−0.195471	+	0.0897007i
$589$	9.82118	+	5.24953i	0.404675	+	0.216303i
$590$	−11.6259	+	3.14508i	−0.478629	+	0.129481i
$591$	−12.5683	+	5.20598i	−0.516993	+	0.214145i
$592$	26.8893	+	0.621765i	1.10514	+	0.0255544i
$593$	−8.42572	−	3.49005i	−0.346003	−	0.143319i	0.202913	−	0.979197i	$-0.434959\pi$
$593$	−8.42572	−	3.49005i	−0.346003	−	0.143319i	−0.548916	+	0.835878i	$0.684959\pi$
$594$	14.2665	+	1.84338i	0.585363	+	0.0756348i
$595$	−6.12817	+	1.85896i	−0.251230	+	0.0762099i
$596$	−0.995809	−	4.17991i	−0.0407899	−	0.171216i
$597$	−4.30238	−	43.6828i	−0.176085	−	1.78782i
$598$	−4.46181	−	3.18110i	−0.182457	−	0.130085i
$599$	0.129051	+	0.193138i	0.00527288	+	0.00789142i	0.834097	−	0.551618i	$-0.185989\pi$
$599$	0.129051	+	0.193138i	0.00527288	+	0.00789142i	−0.828824	+	0.559510i	$0.810989\pi$
$600$	9.48699	+	30.4821i	0.387305	+	1.24443i
$601$	2.38649	+	1.59460i	0.0973468	+	0.0650451i	0.603291	−	0.797521i	$-0.293856\pi$
$601$	2.38649	+	1.59460i	0.0973468	+	0.0650451i	−0.505944	+	0.862566i	$0.668856\pi$
$602$	3.36174	−	7.46717i	0.137014	−	0.304339i
$603$	−56.7785	−	17.2236i	−2.31220	−	0.701398i
$604$	−7.15516	−	8.08027i	−0.291139	−	0.328782i
$605$	6.65731	+	8.11195i	0.270658	+	0.329798i
$606$	−58.6218	+	29.0843i	−2.38135	+	1.18147i
$607$	−15.2684	−	15.2684i	−0.619726	−	0.619726i	0.325735	−	0.945461i	$-0.394388\pi$
$607$	−15.2684	−	15.2684i	−0.619726	−	0.619726i	−0.945461	+	0.325735i	$0.894388\pi$
$608$	−8.66448	−	1.32384i	−0.351391	−	0.0536890i
$609$	−12.5123	+	12.5123i	−0.507026	+	0.507026i
$610$	−4.10315	+	12.1835i	−0.166132	+	0.493296i
$611$	−9.52776	+	7.81923i	−0.385452	+	0.316332i
$612$	−53.3869	−	26.0095i	−2.15804	−	1.05137i
$613$	9.56780	−	31.5408i	0.386440	−	1.27392i	−0.520934	−	0.853597i	$-0.674416\pi$
$613$	9.56780	−	31.5408i	0.386440	−	1.27392i	0.907374	−	0.420324i	$-0.138084\pi$
$614$	−12.7831	+	4.84629i	−0.515883	+	0.195580i
$615$	−11.6205	+	17.3913i	−0.468583	+	0.701285i
$616$	−6.59295	−	12.1236i	−0.265638	−	0.488475i
$617$	−23.7205	+	15.8495i	−0.954951	+	0.638078i	−0.932308	−	0.361666i	$-0.882208\pi$
$617$	−23.7205	+	15.8495i	−0.954951	+	0.638078i	−0.0226429	+	0.999744i	$0.507208\pi$
$618$	−36.3199	+	6.08608i	−1.46100	+	0.244818i
$619$	−5.89381	+	0.580489i	−0.236892	+	0.0233318i	−0.215767	−	0.976445i	$-0.569225\pi$
$619$	−5.89381	+	0.580489i	−0.236892	+	0.0233318i	−0.0211257	+	0.999777i	$0.506725\pi$
$620$	11.6307	+	1.86289i	0.467099	+	0.0748156i
$621$	−1.12764	−	3.71733i	−0.0452506	−	0.149171i
$622$	11.0867	+	14.3768i	0.444535	+	0.576458i
$623$	−0.596139	+	1.43921i	−0.0238838	+	0.0576606i
$624$	−20.6044	−	6.77423i	−0.824836	−	0.271186i
$625$	−5.88511	−	14.2079i	−0.235405	−	0.568317i
$626$	13.8948	−	24.2005i	0.555348	−	0.967248i
$627$	9.29284	−	17.3857i	0.371120	−	0.694317i
$628$	−5.33434	−	4.94827i	−0.212863	−	0.197457i
$629$	33.3364	−	40.6206i	1.32921	−	1.61965i
$630$	−4.29049	−	0.989544i	−0.170937	−	0.0394244i
$631$	−0.0517454	−	0.0102928i	−0.00205995	−	0.000409750i	0.194060	−	0.980990i	$-0.437834\pi$
$631$	−0.0517454	−	0.0102928i	−0.00205995	−	0.000409750i	−0.196120	+	0.980580i	$0.562834\pi$
$632$	−16.4795	−	3.15472i	−0.655518	−	0.125488i
$633$	−13.9929	−	70.3472i	−0.556169	−	2.79605i
$634$	−6.50152	+	6.11871i	−0.258208	+	0.243005i
$635$	0.446951	−	0.238900i	0.0177367	−	0.00948047i
$636$	−33.3469	−	25.3345i	−1.32229	−	1.00458i
$637$	−0.203822	+	2.06944i	−0.00807574	+	0.0819944i
$638$	−35.2787	−	30.7891i	−1.39670	−	1.21895i
$639$	24.4932			0.968934
$640$	−9.12046	+	1.66374i	−0.360518	+	0.0657652i
$641$	21.9819			0.868233			0.434116	−	0.900857i	$-0.357061\pi$
$641$	21.9819			0.868233			0.434116	+	0.900857i	$0.357061\pi$
$642$	−3.76921	−	3.28953i	−0.148759	−	0.129827i
$643$	0.478592	−	4.85923i	0.0188738	−	0.191629i	−0.981125	−	0.193376i	$-0.938056\pi$
$643$	0.478592	−	4.85923i	0.0188738	−	0.191629i	0.999998	+	0.00174714i	$0.000556131\pi$
$644$	−2.25443	+	2.96744i	−0.0888371	+	0.116933i
$645$	10.9120	−	5.83259i	0.429660	−	0.229658i
$646$	−12.4704	+	11.7362i	−0.490643	+	0.461754i
$647$	−4.31321	−	21.6840i	−0.169570	−	0.852484i	−0.968107	−	0.250538i	$-0.919392\pi$
$647$	−4.31321	−	21.6840i	−0.169570	−	0.852484i	0.798537	−	0.601946i	$-0.205608\pi$
$648$	9.46991	+	13.9540i	0.372013	+	0.548167i
$649$	−49.7331	−	9.89254i	−1.95220	−	0.388316i
$650$	12.4036	+	2.86074i	0.486511	+	0.112207i
$651$	11.8892	−	14.4870i	0.465974	−	0.567791i
$652$	−4.44387	+	4.79058i	−0.174035	+	0.187613i
$653$	1.43587	−	2.68632i	0.0561898	−	0.105124i	−0.852259	−	0.523121i	$-0.824768\pi$
$653$	1.43587	−	2.68632i	0.0561898	−	0.105124i	0.908448	+	0.417997i	$0.137268\pi$
$654$	−19.1730	+	33.3936i	−0.749724	+	1.30579i
$655$	0.940218	+	2.26989i	0.0367373	+	0.0886918i
$656$	29.6849	+	25.5327i	1.15900	+	0.996885i
$657$	−5.27461	+	12.7340i	−0.205782	+	0.496802i
$658$	5.11886	+	6.63797i	0.199554	+	0.258775i
$659$	9.34166	+	30.7953i	0.363899	+	1.19962i	0.927581	+	0.373623i	$0.121885\pi$
$659$	9.34166	+	30.7953i	0.363899	+	1.19962i	−0.563681	+	0.825992i	$0.690615\pi$
$660$	3.29774	−	20.5889i	0.128364	−	0.801421i
$661$	32.3210	−	3.18334i	1.25714	−	0.123818i	0.552579	−	0.833461i	$-0.313644\pi$
$661$	32.3210	−	3.18334i	1.25714	−	0.123818i	0.704561	+	0.709643i	$0.251144\pi$
$662$	14.0748	−	2.35850i	0.547033	−	0.0916655i
$663$	−35.2339	+	23.5425i	−1.36837	+	0.914316i
$664$	−41.4523	−	12.2490i	−1.60866	−	0.475353i
$665$	−0.705403	+	1.05571i	−0.0273544	+	0.0409387i
$666$	33.7842	−	12.8082i	1.30911	−	0.496307i
$667$	−3.67055	+	12.1002i	−0.142124	+	0.468521i
$668$	18.8260	−	38.6421i	0.728399	−	1.49511i
$669$	−2.66369	+	2.18604i	−0.102984	+	0.0845170i
$670$	−5.77594	+	17.1506i	−0.223144	+	0.662584i
$671$	−38.2734	+	38.2734i	−1.47753	+	1.47753i
$672$	−5.02981	+	13.8667i	−0.194029	+	0.534919i
$673$	−11.1898	−	11.1898i	−0.431334	−	0.431334i	0.457748	−	0.889082i	$-0.348656\pi$
$673$	−11.1898	−	11.1898i	−0.431334	−	0.431334i	−0.889082	+	0.457748i	$0.848656\pi$
$674$	−7.09556	+	3.52035i	−0.273311	+	0.135599i
$675$	5.72467	+	6.97553i	0.220343	+	0.268488i
$676$	12.9906	−	11.5033i	0.499639	−	0.442435i
$677$	−11.7628	−	3.56820i	−0.452080	−	0.137137i	0.0560299	−	0.998429i	$-0.482156\pi$
$677$	−11.7628	−	3.56820i	−0.452080	−	0.137137i	−0.508110	+	0.861292i	$0.669656\pi$
$678$	−7.43636	+	16.5178i	−0.285592	+	0.634362i
$679$	−0.357264	−	0.238716i	−0.0137106	−	0.00916110i
$680$	−8.42311	+	16.0354i	−0.323012	+	0.614928i
$681$	5.48027	+	8.20180i	0.210004	+	0.314294i
$682$	40.3803	+	28.7896i	1.54624	+	1.10241i
$683$	−3.09371	−	31.4109i	−0.118377	−	1.20191i	−0.852440	−	0.522825i	$-0.824878\pi$
$683$	−3.09371	−	31.4109i	−0.118377	−	1.20191i	0.734063	−	0.679081i	$-0.237622\pi$
$684$	−11.4537	+	2.72870i	−0.437944	+	0.104335i
$685$	1.76938	−	0.536737i	0.0676047	−	0.0205077i
$686$	1.40255	+	0.181224i	0.0535498	+	0.00691917i
$687$	−29.7900	−	12.3394i	−1.13656	−	0.470778i
$688$	−8.36667	−	21.5981i	−0.318976	−	0.823420i
$689$	−15.4274	+	6.39025i	−0.587738	+	0.243449i
$690$	−5.43536	+	1.47040i	−0.206921	+	0.0559771i
$691$	11.1386	+	5.95371i	0.423733	+	0.226490i	0.669458	−	0.742849i	$-0.266526\pi$
$691$	11.1386	+	5.95371i	0.423733	+	0.226490i	−0.245726	+	0.969339i	$0.579026\pi$
$692$	−9.11992	−	19.8736i	−0.346687	−	0.755482i
$693$	−14.3303	−	11.7606i	−0.544364	−	0.446748i
$694$	−8.43786	+	5.27514i	−0.320297	+	0.200242i
$695$	−1.83885	+	9.24453i	−0.0697516	+	0.350665i
$696$	0.360572	+	50.0481i	0.0136675	+	1.89707i
$697$	75.0286	−	14.9241i	2.84191	−	0.565291i
$698$	17.1743	+	0.520943i	0.650055	+	0.0197180i
$699$	−34.8960	−	65.2859i	−1.31989	−	2.46934i
$700$	2.20041	−	8.37270i	0.0831678	−	0.316458i
$701$	−34.3720	−	3.38535i	−1.29821	−	0.127863i	−0.574809	−	0.818288i	$-0.694924\pi$
$701$	−34.3720	−	3.38535i	−1.29821	−	0.127863i	−0.723404	+	0.690425i	$0.757424\pi$
$702$	−6.11672	+	0.415665i	−0.230861	+	0.0156883i
$703$		−	10.4187i		−	0.392949i
$704$	−37.5119	−	10.7914i	−1.41378	−	0.406716i
$705$			12.6653i			0.477001i
$706$	−0.591421	−	8.70305i	−0.0222584	−	0.327543i
$707$	17.6602	+	1.73937i	0.664179	+	0.0654159i
$708$	27.3249	+	46.8074i	1.02693	+	1.75913i
$709$	9.65501	+	18.0632i	0.362601	+	0.678379i	0.995386	−	0.0959481i	$-0.0305883\pi$
$709$	9.65501	+	18.0632i	0.362601	+	0.678379i	−0.632785	+	0.774328i	$0.718088\pi$
$710$	0.226499	−	7.46714i	0.00850035	−	0.280237i
$711$	−22.1062	+	4.39719i	−0.829046	+	0.164908i
$712$	1.71542	+	4.05844i	0.0642881	+	0.152097i
$713$	2.61266	−	13.1347i	0.0978449	−	0.491900i
$714$	15.2771	+	24.4365i	0.571732	+	0.914515i
$715$	−6.42688	−	5.27441i	−0.240352	−	0.197252i
$716$	1.24566	−	3.35848i	0.0465524	−	0.125512i
$717$	19.7118	+	10.5362i	0.736150	+	0.393480i
$718$	6.49543	+	24.0105i	0.242407	+	0.896063i
$719$	0.680494	−	0.281870i	0.0253781	−	0.0105120i	−0.369958	−	0.929048i	$-0.620628\pi$
$719$	0.680494	−	0.281870i	0.0253781	−	0.0105120i	0.395336	+	0.918536i	$0.370628\pi$
$720$	−10.5122	+	6.67780i	−0.391768	+	0.248867i
$721$	9.22615	+	3.82160i	0.343600	+	0.142324i
$722$	3.00818	−	23.2813i	0.111953	−	0.866439i
$723$	40.9155	−	12.4116i	1.52166	−	0.461592i
$724$	−7.14832	+	11.6195i	−0.265665	+	0.431836i
$725$	−2.87909	−	29.2319i	−0.106927	−	1.08565i
$726$	27.4153	−	38.4528i	1.01748	−	1.42712i
$727$	4.82426	+	7.22001i	0.178922	+	0.267775i	0.910080	−	0.414433i	$-0.136020\pi$
$727$	4.82426	+	7.22001i	0.178922	+	0.267775i	−0.731158	+	0.682208i	$0.761020\pi$
$728$	3.76390	+	4.51953i	0.139499	+	0.167505i
$729$	32.3960	+	21.6463i	1.19985	+	0.801715i
$730$	3.83340	+	1.72581i	0.141881	+	0.0638750i
$731$	−43.3039	−	13.1361i	−1.60165	−	0.485856i
$732$	57.7479	+	3.50653i	2.13443	+	0.129605i
$733$	−14.8059	−	18.0411i	−0.546869	−	0.666362i	0.424087	−	0.905622i	$-0.360595\pi$
$733$	−14.8059	−	18.0411i	−0.546869	−	0.666362i	−0.970956	+	0.239260i	$0.923095\pi$
$734$	−9.60629	−	19.3623i	−0.354575	−	0.714674i
$735$	1.51093	+	1.51093i	0.0557314	+	0.0557314i
$736$	1.50121	+	10.4332i	0.0553353	+	0.384573i
$737$	−53.8769	+	53.8769i	−1.98458	+	1.98458i
$738$	49.8470	+	16.7874i	1.83489	+	0.617952i
$739$	39.6496	−	32.5396i	1.45853	−	1.19699i	0.518886	−	0.854843i	$-0.326347\pi$
$739$	39.6496	−	32.5396i	1.45853	−	1.19699i	0.939647	−	0.342144i	$-0.111153\pi$
$740$	−3.59237	−	10.4181i	−0.132058	−	0.382978i
$741$	−2.43888	+	8.03992i	−0.0895946	+	0.295354i
$742$	4.02583	+	10.6189i	0.147793	+	0.389834i
$743$	16.2857	−	24.3733i	0.597466	−	0.894171i	−0.402307	−	0.915505i	$-0.631791\pi$
$743$	16.2857	−	24.3733i	0.597466	−	0.894171i	0.999772	+	0.0213342i	$0.00679141\pi$
$744$	−5.57557	−	52.7136i	−0.204410	−	1.93257i
$745$	−1.46383	+	0.978100i	−0.0536306	+	0.0358348i
$746$	−3.38009	−	20.1714i	−0.123754	−	0.738528i
$747$	−57.7844	+	5.69127i	−2.11422	+	0.208233i
$748$	−61.7742	+	44.7174i	−2.25869	+	1.63503i
$749$	0.393807	+	1.29821i	0.0143894	+	0.0474355i
$750$	22.3229	−	17.2143i	0.815116	−	0.628576i
$751$	−18.1745	+	43.8771i	−0.663197	+	1.60110i	0.129567	+	0.991571i	$0.458641\pi$
$751$	−18.1745	+	43.8771i	−0.663197	+	1.60110i	−0.792764	+	0.609529i	$0.791359\pi$
$752$	23.5349	+	2.86873i	0.858231	+	0.104612i
$753$	−28.8586	−	69.6708i	−1.05166	−	2.53894i
$754$	17.3066	+	9.93662i	0.630269	+	0.361870i
$755$	−2.08456	+	3.89995i	−0.0758651	+	0.141934i
$756$	0.156436	+	4.16656i	0.00568951	+	0.151536i
$757$	8.69988	−	10.6008i	0.316202	−	0.385294i	−0.590519	−	0.807024i	$-0.701077\pi$
$757$	8.69988	−	10.6008i	0.316202	−	0.385294i	0.906721	+	0.421730i	$0.138577\pi$
$758$	3.63514	−	15.7613i	0.132034	−	0.572477i
$759$	−23.2514	−	4.62499i	−0.843973	−	0.167877i
$760$	0.725972	+	3.51709i	0.0263338	+	0.127578i
$761$	−0.962825	−	4.84045i	−0.0349024	−	0.175466i	0.959402	−	0.282041i	$-0.0910115\pi$
$761$	−0.962825	−	4.84045i	−0.0349024	−	0.175466i	−0.994305	+	0.106575i	$0.966012\pi$
$762$	−1.56304	−	1.66083i	−0.0566231	−	0.0601657i
$763$	9.20891	−	4.92226i	0.333385	−	0.178198i
$764$	−50.3750	+	6.87830i	−1.82250	+	0.248848i
$765$	−2.38492	+	24.2145i	−0.0862269	+	0.875477i
$766$	−19.4408	+	22.2756i	−0.702424	+	0.804852i
$767$	21.6111			0.780332
$768$	17.9456	+	37.6647i	0.647555	+	1.35911i
$769$	−4.25130			−0.153306			−0.0766529	−	0.997058i	$-0.524423\pi$
$769$	−4.25130			−0.153306			−0.0766529	+	0.997058i	$0.524423\pi$
$770$	−3.71793	+	4.26008i	−0.133985	+	0.153523i
$771$	−4.47527	+	45.4382i	−0.161173	+	1.63642i
$772$	4.47627	−	0.611198i	0.161105	−	0.0219975i
$773$	−29.7225	+	15.8870i	−1.06904	+	0.571416i	−0.909470	−	0.415770i	$-0.863512\pi$
$773$	−29.7225	+	15.8870i	−1.06904	+	0.571416i	−0.159574	+	0.987186i	$0.551012\pi$
$774$	−21.3238	−	22.6579i	−0.766469	−	0.814422i
$775$	6.06917	+	30.5118i	0.218011	+	1.09602i
$776$	−1.19022	+	0.245677i	−0.0427265	+	0.00881929i
$777$	−17.1968	−	3.42065i	−0.616931	−	0.122715i
$778$	1.94024	−	8.41252i	0.0695608	−	0.301603i
$779$	9.62198	−	11.7244i	0.344743	−	0.420071i
$780$	0.333419	+	8.88040i	0.0119383	+	0.317969i
$781$	14.8269	−	27.7392i	0.530548	−	0.992586i
$782$	17.8593	+	10.2540i	0.638646	+	0.366681i
$783$	5.41388	+	13.0703i	0.193476	+	0.467093i
$784$	3.14988	−	2.46542i	0.112496	−	0.0880506i
$785$	−1.14084	+	2.75422i	−0.0407182	+	0.0983025i
$786$	8.75561	−	6.75188i	0.312302	−	0.240832i
$787$	1.50714	+	4.96839i	0.0537239	+	0.177104i	0.979696	−	0.200487i	$-0.0642525\pi$
$787$	1.50714	+	4.96839i	0.0537239	+	0.177104i	−0.925972	+	0.377591i	$0.876753\pi$
$788$	8.45202	−	6.11829i	0.301091	−	0.217955i
$789$	44.2319	−	4.35646i	1.57470	−	0.155094i
$790$	1.13613	+	6.78009i	0.0404217	+	0.241225i
$791$	4.08433	−	2.72906i	0.145222	−	0.0970343i
$792$	−52.1435	+	5.51527i	−1.85284	+	0.195976i
$793$	12.8161	−	19.1807i	0.455114	−	0.681126i
$794$	−8.32416	−	21.9567i	−0.295413	−	0.779213i
$795$	−4.98093	+	16.4199i	−0.176655	+	0.582355i
$796$	10.9747	+	31.8275i	0.388989	+	1.12810i
$797$	−20.7569	+	17.0347i	−0.735246	+	0.603401i	−0.925684	−	0.378298i	$-0.876509\pi$
$797$	−20.7569	+	17.0347i	−0.735246	+	0.603401i	0.190437	+	0.981699i	$0.439009\pi$
$798$	5.41505	+	1.82367i	0.191691	+	0.0645572i
$799$	32.7542	−	32.7542i	1.15876	−	1.15876i
$800$	−12.4966	−	21.0567i	−0.441822	−	0.744469i
$801$	4.18523	+	4.18523i	0.147878	+	0.147878i
$802$	13.5169	+	27.2444i	0.477299	+	0.962035i
$803$	11.2287	+	13.6822i	0.396251	+	0.482834i
$804$	81.2909	+	4.93610i	2.86691	+	0.174083i
$805$	1.46116	+	0.443237i	0.0514990	+	0.0156221i
$806$	−19.2728	−	8.67667i	−0.678856	−	0.305623i
$807$	14.1361	+	9.44545i	0.497615	+	0.332496i
$808$	38.5687	−	32.1203i	1.35684	−	1.12999i
$809$	−6.44352	−	9.64341i	−0.226542	−	0.339044i	0.700734	−	0.713423i	$-0.252856\pi$
$809$	−6.44352	−	9.64341i	−0.226542	−	0.339044i	−0.927276	+	0.374379i	$0.877856\pi$
$810$	4.01117	−	5.62607i	0.140938	−	0.197680i
$811$	1.39298	+	14.1432i	0.0489142	+	0.496634i	0.988164	+	0.153400i	$0.0490224\pi$
$811$	1.39298	+	14.1432i	0.0489142	+	0.496634i	−0.939250	+	0.343234i	$0.888478\pi$
$812$	7.11152	−	11.5597i	0.249565	−	0.405666i
$813$	−81.3525	+	24.6780i	−2.85316	+	0.865496i
$814$	5.94561	−	46.0150i	0.208393	−	1.61283i
$815$	2.47347	+	1.02455i	0.0866419	+	0.0358883i
$816$	79.5573	+	17.7462i	2.78506	+	0.621240i
$817$	−8.28915	+	3.43348i	−0.290001	+	0.120122i
$818$	−2.13806	−	7.90339i	−0.0747556	−	0.276335i
$819$	6.96796	+	3.72445i	0.243480	+	0.130143i
$820$	5.57886	−	15.0414i	0.194822	−	0.525269i
$821$	11.7306	+	9.62707i	0.409401	+	0.335987i	0.816447	−	0.577421i	$-0.195941\pi$
$821$	11.7306	+	9.62707i	0.409401	+	0.335987i	−0.407045	+	0.913408i	$0.633441\pi$
$822$	−4.41096	−	7.05556i	−0.153850	−	0.246091i
$823$	−2.36615	+	11.8954i	−0.0824788	+	0.414649i	0.917383	+	0.398006i	$0.130298\pi$
$823$	−2.36615	+	11.8954i	−0.0824788	+	0.414649i	−0.999862	+	0.0166427i	$0.994702\pi$
$824$	26.0169	−	10.9968i	0.906343	−	0.383093i
$825$	54.0127	−	10.7438i	1.88048	−	0.374051i
$826$	0.445609	−	14.6907i	0.0155047	−	0.511154i
$827$	−14.7501	−	27.5954i	−0.512910	−	0.959587i	−0.996444	−	0.0842611i	$-0.973147\pi$
$827$	−14.7501	−	27.5954i	−0.512910	−	0.959587i	0.483534	−	0.875326i	$-0.339353\pi$
$828$	7.13856	+	12.2283i	0.248082	+	0.424964i
$829$	44.8396	+	4.41631i	1.55734	+	0.153385i	0.839710	−	0.543036i	$-0.182725\pi$
$829$	44.8396	+	4.41631i	1.55734	+	0.153385i	0.717634	+	0.696421i	$0.245225\pi$
$830$	1.20072	+	17.6692i	0.0416776	+	0.613306i
$831$		−	77.9795i		−	2.70508i
$832$	16.5773	+	1.39187i	0.574716	+	0.0482545i
$833$		−	7.81494i		−	0.270772i
$834$	42.3198	−	2.87587i	1.46541	−	0.0995832i
$835$	−17.5267	−	1.72623i	−0.606538	−	0.0597388i
$836$	−3.84317	+	14.6235i	−0.132919	+	0.505764i
$837$	−7.06311	−	13.2141i	−0.244137	−	0.456748i
$838$	41.6542	+	1.26349i	1.43892	+	0.0436464i
$839$	6.02418	−	1.19828i	0.207978	−	0.0413693i	−0.0900018	−	0.995942i	$-0.528687\pi$
$839$	6.02418	−	1.19828i	0.207978	−	0.0413693i	0.297980	+	0.954572i	$0.403687\pi$
$840$	6.04355	−	0.0435408i	0.208522	−	0.00150230i
$841$	3.32631	−	16.7225i	0.114700	−	0.576637i
$842$	−35.3485	+	22.0990i	−1.21819	+	0.761582i
$843$	6.20076	+	5.08883i	0.213565	+	0.175269i
$844$	22.9446	+	49.9996i	0.789786	+	1.72106i
$845$	−6.26992	−	3.35134i	−0.215692	−	0.115290i
$846$	30.7439	−	8.31699i	1.05700	−	0.285944i
$847$	−11.8314	+	4.90072i	−0.406531	+	0.168391i
$848$	29.3838	+	12.9749i	1.00904	+	0.445559i
$849$	−63.5626	−	26.3285i	−2.18146	−	0.903592i
$850$	−47.4443	−	6.13028i	−1.62732	−	0.210267i
$851$	−11.9898	+	3.63707i	−0.411005	+	0.124677i
$852$	−32.7039	+	7.79128i	−1.12042	+	0.266925i
$853$	0.687317	+	6.97845i	0.0235333	+	0.238937i	0.999754	+	0.0221604i	$0.00705446\pi$
$853$	0.687317	+	6.97845i	0.0235333	+	0.238937i	−0.976221	+	0.216777i	$0.930446\pi$
$854$	−12.7743	−	9.10757i	−0.437127	−	0.311655i
$855$	2.68018	+	4.01117i	0.0916601	+	0.137179i
$856$	3.39697	+	1.78438i	0.116106	+	0.0609887i
$857$	−37.9226	−	25.3391i	−1.29541	−	0.865567i	−0.299343	−	0.954146i	$-0.596768\pi$
$857$	−37.9226	−	25.3391i	−1.29541	−	0.865567i	−0.996069	+	0.0885787i	$0.971768\pi$
$858$	−15.3596	+	34.1172i	−0.524369	+	1.16474i
$859$	−27.0913	−	8.21806i	−0.924344	−	0.280397i	−0.207988	−	0.978131i	$-0.566691\pi$
$859$	−27.0913	−	8.21806i	−0.924344	−	0.280397i	−0.716356	+	0.697735i	$0.754191\pi$
$860$	−7.10483	+	6.29139i	−0.242273	+	0.214535i
$861$	−16.1929	−	19.7311i	−0.551852	−	0.672433i
$862$	37.8073	−	18.7575i	1.28772	−	0.638883i
$863$	−11.9665	−	11.9665i	−0.407343	−	0.407343i	0.473468	−	0.880811i	$-0.343002\pi$
$863$	−11.9665	−	11.9665i	−0.407343	−	0.407343i	−0.880811	+	0.473468i	$0.843002\pi$
$864$	8.70355	+	7.95776i	0.296101	+	0.270728i
$865$	−6.33504	+	6.33504i	−0.215398	+	0.215398i
$866$	4.51361	−	13.4023i	0.153379	−	0.455429i
$867$	88.8381	−	72.9076i	3.01710	−	2.47607i
$868$	−6.29558	+	12.9223i	−0.213686	+	0.438610i
$869$	−8.40200	+	27.6977i	−0.285018	+	0.939580i
$870$	19.1746	−	7.26943i	0.650081	−	0.246457i
$871$	18.0411	−	27.0004i	0.611298	−	0.914872i
$872$	8.36945	−	28.3234i	0.283425	−	0.959150i
$873$	−1.35742	+	0.907002i	−0.0459418	+	0.0306974i
$874$	4.02691	−	0.674784i	0.136212	−	0.0228249i
$875$	−7.60739	+	0.749263i	−0.257177	+	0.0253297i
$876$	2.99210	−	18.6807i	0.101094	−	0.631162i
$877$	11.1147	+	36.6401i	0.375316	+	1.23725i	0.917752	+	0.397153i	$0.130002\pi$
$877$	11.1147	+	36.6401i	0.375316	+	1.23725i	−0.542437	+	0.840097i	$0.682498\pi$
$878$	31.9412	+	41.4203i	1.07796	+	1.39787i
$879$	−8.80734	+	21.2628i	−0.297064	+	0.717177i
$880$	1.19923	+	15.9478i	0.0404259	+	0.537600i
$881$	0.645409	+	1.55815i	0.0217444	+	0.0524955i	0.934379	−	0.356281i	$-0.115955\pi$
$881$	0.645409	+	1.55815i	0.0217444	+	0.0524955i	−0.912634	+	0.408777i	$0.865955\pi$
$882$	2.67547	−	4.65985i	0.0900876	−	0.156905i
$883$	−12.6431	+	23.6535i	−0.425473	+	0.796005i	−0.999743	−	0.0226615i	$-0.992786\pi$
$883$	−12.6431	+	23.6535i	−0.425473	+	0.796005i	0.574270	+	0.818666i	$0.305286\pi$
$884$	22.1037	−	23.8282i	0.743428	−	0.801431i
$885$	14.0878	−	17.1661i	0.473557	−	0.577031i
$886$	37.5247	+	8.65458i	1.26067	+	0.290756i
$887$	25.1992	+	5.01243i	0.846106	+	0.168301i	0.599061	−	0.800703i	$-0.295541\pi$
$887$	25.1992	+	5.01243i	0.846106	+	0.168301i	0.247045	+	0.969004i	$0.420541\pi$
$888$	−41.0353	+	27.8486i	−1.37705	+	0.934538i
$889$	0.120655	+	0.606574i	0.00404664	+	0.0203438i
$890$	1.31464	−	1.23723i	0.0440667	−	0.0414721i
$891$	25.6561	−	13.7135i	0.859511	−	0.459418i
$892$	1.59884	−	2.10450i	0.0535332	−	0.0704640i
$893$	0.900194	−	9.13982i	0.0301238	−	0.305853i
$894$	5.96919	+	5.20953i	0.199639	+	0.174233i
$895$	−1.46764			−0.0490579
$896$	1.28798	−	11.2402i	0.0430283	−	0.375507i
$897$	10.1037			0.337353
$898$	34.1350	+	29.7909i	1.13910	+	0.994135i
$899$	−4.78049	+	48.5372i	−0.159438	+	1.61880i
$900$	−26.1911	−	19.8980i	−0.873036	−	0.663267i
$901$	55.3457	−	29.5829i	1.84383	−	0.985549i
$902$	49.1870	−	46.2909i	1.63775	−	1.54132i
$903$	2.94571	+	14.8091i	0.0980272	+	0.492816i
$904$	2.61229	−	13.6460i	0.0868836	−	0.453858i
$905$	5.48215	+	1.09047i	0.182233	+	0.0362484i
$906$	19.3914	+	4.47236i	0.644235	+	0.148584i
$907$	−20.3605	+	24.8093i	−0.676059	+	0.823781i	−0.992164	−	0.124944i	$-0.960125\pi$
$907$	−20.3605	+	24.8093i	−0.676059	+	0.823781i	0.316104	+	0.948724i	$0.397625\pi$
$908$	−5.54678	−	5.14534i	−0.184076	−	0.170754i
$909$	31.7836	−	59.4630i	1.05420	−	1.97226i
$910$	1.19990	−	2.08985i	0.0397762	−	0.0692780i
$911$	−10.1718	−	24.5568i	−0.337006	−	0.813603i	−0.998000	−	0.0632126i	$-0.979865\pi$
$911$	−10.1718	−	24.5568i	−0.337006	−	0.813603i	0.660995	−	0.750391i	$-0.270135\pi$
$912$	14.4253	−	7.28687i	0.477670	−	0.241292i
$913$	−28.5342	+	68.8877i	−0.944345	+	2.27985i
$914$	−4.32120	−	5.60359i	−0.142933	−	0.185350i
$915$	−6.88097	−	22.6835i	−0.227478	−	0.749894i
$916$	24.4200	+	3.91137i	0.806860	+	0.129235i
$917$	−2.98382	+	0.293880i	−0.0985344	+	0.00970479i
$918$	22.7238	−	3.80780i	0.749998	−	0.125676i
$919$	25.4161	−	16.9825i	0.838401	−	0.560201i	−0.0605933	−	0.998163i	$-0.519299\pi$
$919$	25.4161	−	16.9825i	0.838401	−	0.560201i	0.898994	+	0.437961i	$0.144299\pi$
$920$	3.79402	−	2.06323i	0.125085	−	0.0680226i
$921$	14.0042	−	20.9588i	0.461455	−	0.690616i
$922$	−25.3642	+	9.61601i	−0.835326	+	0.316687i
$923$	−3.89129	+	12.8278i	−0.128083	+	0.422234i
$924$	22.8753	+	11.1446i	0.752542	+	0.366630i
$925$	22.4988	−	18.4643i	0.739755	−	0.607101i
$926$	−6.33112	+	18.7991i	−0.208054	+	0.617776i
$927$	26.8297	−	26.8297i	0.881203	−	0.881203i
$928$	−9.16515	−	37.2774i	−0.300861	−	1.22369i
$929$	34.5546	+	34.5546i	1.13370	+	1.13370i	0.989557	+	0.144143i	$0.0460427\pi$
$929$	34.5546	+	34.5546i	1.13370	+	1.13370i	0.144143	+	0.989557i	$0.453957\pi$
$930$	−19.4556	+	9.65257i	−0.637973	+	0.316520i
$931$	−0.982963	−	1.19774i	−0.0322153	−	0.0392545i
$932$	37.6410	+	42.5078i	1.23297	+	1.39239i
$933$	−32.0337	−	9.71731i	−1.04874	−	0.318130i
$934$	1.32668	−	2.94686i	0.0434104	−	0.0964241i
$935$	25.9799	+	17.3592i	0.849633	+	0.567707i
$936$	21.3375	−	6.64091i	0.697439	−	0.217065i
$937$	14.2317	+	21.2992i	0.464928	+	0.695814i	0.987648	−	0.156691i	$-0.0500826\pi$
$937$	14.2317	+	21.2992i	0.464928	+	0.695814i	−0.522720	+	0.852504i	$0.675083\pi$
$938$	−17.9822	−	12.8206i	−0.587139	−	0.418607i
$939$	5.04335	+	51.2060i	0.164584	+	1.67104i
$940$	−2.25127	−	9.44970i	−0.0734283	−	0.308215i
$941$	−32.5245	+	9.86620i	−1.06027	+	0.321629i	−0.771803	−	0.635861i	$-0.780645\pi$
$941$	−32.5245	+	9.86620i	−1.06027	+	0.321629i	−0.288465	+	0.957490i	$0.593145\pi$
$942$	13.3052	+	1.71917i	0.433507	+	0.0560136i
$943$	−16.8513	−	6.98006i	−0.548755	−	0.227302i
$944$	−28.7075	−	30.0666i	−0.934350	−	0.978583i
$945$	1.57830	−	0.653753i	0.0513420	−	0.0212666i
$946$	−38.5691	+	10.4339i	−1.25399	+	0.339235i
$947$	26.6451	+	14.2421i	0.865850	+	0.462806i	0.843616	−	0.536946i	$-0.180422\pi$
$947$	26.6451	+	14.2421i	0.865850	+	0.462806i	0.0222335	+	0.999753i	$0.492922\pi$
$948$	28.1180	−	12.9032i	0.913230	−	0.419077i
$949$	−5.83123	−	4.78557i	−0.189290	−	0.155346i
$950$	−8.04253	+	5.02799i	−0.260934	+	0.163130i
$951$	3.21152	−	16.1454i	0.104141	−	0.523551i
$952$	−15.7421	−	15.5169i	−0.510204	−	0.502905i
$953$	58.0716	−	11.5512i	1.88112	−	0.374179i	0.885265	−	0.465086i	$-0.153977\pi$
$953$	58.0716	−	11.5512i	1.88112	−	0.374179i	0.995859	+	0.0909071i	$0.0289766\pi$
$954$	43.1290	+	1.30822i	1.39635	+	0.0423552i
$955$	9.81981	+	18.3716i	0.317762	+	0.594490i
$956$	−16.5800	−	4.35736i	−0.536236	−	0.140927i
$957$	85.9216	+	8.46254i	2.77745	+	0.273555i
$958$	−1.49685	+	0.101720i	−0.0483611	+	0.00328641i
$959$			2.25641i			0.0728632i
$960$	11.9120	−	12.2603i	0.384458	−	0.395700i
$961$		−	20.6548i		−	0.666284i
$962$	1.34068	+	19.7288i	0.0432252	+	0.636080i
$963$	5.12966	+	0.505228i	0.165301	+	0.0162807i
$964$	−28.3214	+	16.5332i	−0.912171	+	0.532500i
$965$	−0.872578	−	1.63248i	−0.0280893	−	0.0525513i
$966$	0.208333	−	6.86824i	0.00670300	−	0.220982i
$967$	−42.5370	+	8.46113i	−1.36790	+	0.272092i	−0.823776	−	0.566915i	$-0.808137\pi$
$967$	−42.5370	+	8.46113i	−1.36790	+	0.272092i	−0.544121	+	0.839007i	$0.683137\pi$
$968$	−13.6199	+	33.5632i	−0.437760	+	1.07876i
$969$	6.15997	−	30.9682i	0.197887	−	0.994843i
$970$	0.263962	+	0.422220i	0.00847530	+	0.0135567i
$971$	−2.55496	−	2.09680i	−0.0819925	−	0.0672895i	0.592504	−	0.805567i	$-0.298139\pi$
$971$	−2.55496	−	2.09680i	−0.0819925	−	0.0672895i	−0.674497	+	0.738278i	$0.735639\pi$
$972$	−40.8816	−	15.1630i	−1.31128	−	0.486353i
$973$	−10.1443	−	5.42222i	−0.325210	−	0.173828i
$974$	3.79812	+	14.0398i	0.121700	+	0.449865i
$975$	−21.6841	+	8.98186i	−0.694448	+	0.287650i
$976$	−43.7097	+	7.64852i	−1.39911	+	0.244823i
$977$	−6.72887	−	2.78719i	−0.215276	−	0.0891701i	0.272439	−	0.962173i	$-0.412170\pi$
$977$	−6.72887	−	2.78719i	−0.215276	−	0.0891701i	−0.487715	+	0.873003i	$0.662170\pi$
$978$	1.54393	−	11.9489i	0.0493693	−	0.382085i
$979$	7.27341	−	2.20636i	0.232459	−	0.0705157i
$980$	−1.39589	−	0.858751i	−0.0445901	−	0.0274318i
$981$	−3.88871	−	39.4828i	−0.124157	−	1.26059i
$982$	7.05693	−	9.89805i	0.225196	−	0.315860i
$983$	−24.9990	−	37.4137i	−0.797345	−	1.19331i	−0.977761	−	0.209721i	$-0.932744\pi$
$983$	−24.9990	−	37.4137i	−0.797345	−	1.19331i	0.180416	−	0.983590i	$-0.442256\pi$
$984$	−71.8970	−	6.55860i	−2.29199	−	0.209081i
$985$	−3.55460	−	2.37511i	−0.113259	−	0.0756772i
$986$	−68.3881	−	30.7885i	−2.17792	−	0.980506i
$987$	−14.7904	−	4.48661i	−0.470782	−	0.142810i
$988$	0.390572	−	6.43220i	0.0124257	−	0.204635i
$989$	6.84490	+	8.34053i	0.217655	+	0.265213i
$990$	9.54817	+	19.2451i	0.303461	+	0.611650i
$991$	−3.97659	−	3.97659i	−0.126321	−	0.126321i	0.641120	−	0.767441i	$-0.278470\pi$
$991$	−3.97659	−	3.97659i	−0.126321	−	0.126321i	−0.767441	+	0.641120i	$0.778470\pi$
$992$	13.5299	+	38.3392i	0.429576	+	1.21727i
$993$	−18.6065	+	18.6065i	−0.590459	+	0.590459i
$994$	8.63982	+	2.90970i	0.274038	+	0.0922901i
$995$	10.6629	−	8.75078i	0.338035	−	0.277418i
$996$	75.3449	−	25.9804i	2.38740	−	0.823220i
$997$	3.20712	−	10.5725i	0.101571	−	0.334833i	−0.891396	−	0.453224i	$-0.850274\pi$
$997$	3.20712	−	10.5725i	0.101571	−	0.334833i	0.992967	+	0.118391i	$0.0377736\pi$
$998$	8.78280	+	23.1664i	0.278015	+	0.733321i
$999$	−7.78803	+	11.6556i	−0.246402	+	0.368767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bn.a.29.36	✓	752
128.53	even	32	inner	896.2.bn.a.309.36	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.bn.a.29.36	✓	752	1.1	even	1	trivial
896.2.bn.a.309.36	yes	752	128.53	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bn (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.929900 - 1.06550i) q^{2} +(-0.255588 + 2.59503i) q^{3} +(-0.270573 - 1.98161i) q^{4} +(-0.722686 + 0.386284i) q^{5} +(2.52733 + 2.68544i) q^{6} +(-0.195090 - 0.980785i) q^{7} +(-2.36301 - 1.55441i) q^{8} +(-3.72649 - 0.741245i) q^{9} +O(q^{10})\)	\(q+(0.929900 - 1.06550i) q^{2} +(-0.255588 + 2.59503i) q^{3} +(-0.270573 - 1.98161i) q^{4} +(-0.722686 + 0.386284i) q^{5} +(2.52733 + 2.68544i) q^{6} +(-0.195090 - 0.980785i) q^{7} +(-2.36301 - 1.55441i) q^{8} +(-3.72649 - 0.741245i) q^{9} +(-0.260441 + 1.12923i) q^{10} +(-3.09531 + 3.77164i) q^{11} +(5.21150 - 0.195668i) q^{12} +(0.980249 - 1.83392i) q^{13} +(-1.22644 - 0.704164i) q^{14} +(-0.817707 - 1.97412i) q^{15} +(-3.85358 + 1.07234i) q^{16} +(-2.99065 + 7.22006i) q^{17} +(-4.25506 + 3.28128i) q^{18} +(0.449783 + 1.48273i) q^{19} +(0.961004 + 1.32757i) q^{20} +(2.59503 - 0.255588i) q^{21} +(1.14035 + 6.80529i) q^{22} +(1.54931 - 1.03522i) q^{23} +(4.63768 - 5.73479i) q^{24} +(-2.40479 + 3.59902i) q^{25} +(-1.04250 - 2.74981i) q^{26} +(0.605171 - 1.99498i) q^{27} +(-1.89075 + 0.651968i) q^{28} +(-5.24567 + 4.30501i) q^{29} +(-2.86381 - 0.964468i) q^{30} +(5.08207 - 5.08207i) q^{31} +(-2.44086 + 5.10315i) q^{32} +(-8.99639 - 8.99639i) q^{33} +(4.91196 + 9.90047i) q^{34} +(0.519851 + 0.633440i) q^{35} +(-0.460573 + 7.58502i) q^{36} +(-6.43458 - 1.95191i) q^{37} +(1.99810 + 0.899552i) q^{38} +(4.50853 + 3.01250i) q^{39} +(2.30816 + 0.210555i) q^{40} +(-5.43834 - 8.13905i) q^{41} +(2.14079 - 3.00267i) q^{42} +(0.567569 + 5.76262i) q^{43} +(8.31144 + 5.11319i) q^{44} +(2.97941 - 0.903795i) q^{45} +(0.337682 - 2.61343i) q^{46} +(-5.47609 - 2.26827i) q^{47} +(-1.79783 - 10.2742i) q^{48} +(-0.923880 + 0.382683i) q^{49} +(1.59854 + 5.90903i) q^{50} +(-17.9719 - 9.60618i) q^{51} +(-3.89934 - 1.44627i) q^{52} +(-6.20745 - 5.09433i) q^{53} +(-1.56290 - 2.49994i) q^{54} +(0.780011 - 3.92138i) q^{55} +(-1.06354 + 2.62086i) q^{56} +(-3.96270 + 0.788229i) q^{57} +(-0.290966 + 9.59247i) q^{58} +(4.89907 + 9.16551i) q^{59} +(-3.69069 + 2.15452i) q^{60} +(11.0401 + 1.08735i) q^{61} +(-0.689121 - 10.1407i) q^{62} +3.79949i q^{63} +(3.16764 + 7.34616i) q^{64} +1.70400i q^{65} +(-17.9514 + 1.21990i) q^{66} +(15.5409 + 1.53065i) q^{67} +(15.1166 + 3.97275i) q^{68} +(2.29043 + 4.28509i) q^{69} +(1.15834 + 0.0351356i) q^{70} +(-6.32256 + 1.25764i) q^{71} +(7.65354 + 7.54405i) q^{72} +(0.707719 - 3.55794i) q^{73} +(-8.06326 + 5.04095i) q^{74} +(-8.72493 - 7.16037i) q^{75} +(2.81651 - 1.29248i) q^{76} +(4.30303 + 2.30002i) q^{77} +(7.40229 - 2.00250i) q^{78} +(5.48061 - 2.27014i) q^{79} +(2.37070 - 2.26354i) q^{80} +(-5.50847 - 2.28168i) q^{81} +(-13.7293 - 1.77396i) q^{82} +(14.6240 - 4.43614i) q^{83} +(-1.20862 - 5.07319i) q^{84} +(-0.627694 - 6.37308i) q^{85} +(6.66784 + 4.75392i) q^{86} +(-9.83088 - 14.7130i) q^{87} +(13.1769 - 4.10107i) q^{88} +(-1.29525 - 0.865460i) q^{89} +(1.80756 - 4.01500i) q^{90} +(-1.98992 - 0.603635i) q^{91} +(-2.47060 - 2.79003i) q^{92} +(11.8892 + 14.4870i) q^{93} +(-7.50906 + 3.72550i) q^{94} +(-0.897808 - 0.897808i) q^{95} +(-12.6190 - 7.63842i) q^{96} +(0.303828 - 0.303828i) q^{97} +(-0.451367 + 1.34025i) q^{98} +(14.3303 - 11.7606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 752 q+O(q^{10}) \) 752 * q	\( 752 q + 112 q^{12} - 160 q^{32} + 112 q^{34} - 160 q^{45} - 384 q^{54} - 48 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} + 32 q^{74} - 512 q^{76} + 256 q^{85} + 160 q^{96}+O(q^{100}) \) 752 * q + 112 * q^12 - 160 * q^32 + 112 * q^34 - 160 * q^45 - 384 * q^54 - 48 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 + 32 * q^74 - 512 * q^76 + 256 * q^85 + 160 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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