LMFDB - Embedded newform 264.2.z.b.139.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [264,2,Mod(19,264)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(264, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("264.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 264 = 2^{3} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	264.z (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.10805061336$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.5
Character	$\chi$	$=$	264.139
Dual form			264.2.z.b.19.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0536155 + 1.41320i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-1.99425 - 0.151538i) q^{4} +(-2.61989 - 3.60596i) q^{5} +(-1.32746 - 0.487693i) q^{6} +(0.177135 + 0.545166i) q^{7} +(0.321076 - 2.81014i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(5.23640 - 3.50908i) q^{10} +(2.97258 - 1.47097i) q^{11} +(0.760379 - 1.84982i) q^{12} +(-2.23991 - 1.62739i) q^{13} +(-0.779925 + 0.221098i) q^{14} +(4.23906 - 1.37736i) q^{15} +(3.95407 + 0.604411i) q^{16} +(-1.09530 - 1.50755i) q^{17} +(0.874032 - 1.11179i) q^{18} +(-5.35403 - 1.73963i) q^{19} +(4.67827 + 7.58821i) q^{20} -0.573222 q^{21} +(1.91940 + 4.27971i) q^{22} -5.60437i q^{23} +(2.57339 + 1.17374i) q^{24} +(-4.59408 + 14.1391i) q^{25} +(2.41992 - 3.07818i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.270639 - 1.11404i) q^{28} +(-1.02359 - 3.15029i) q^{29} +(1.71919 + 6.06448i) q^{30} +(-2.94026 + 4.04692i) q^{31} +(-1.06615 + 5.55548i) q^{32} +(0.480399 + 3.28165i) q^{33} +(2.18919 - 1.46704i) q^{34} +(1.50178 - 2.06702i) q^{35} +(1.52431 + 1.29479i) q^{36} +(3.22436 - 1.04766i) q^{37} +(2.74550 - 7.47303i) q^{38} +(2.23991 - 1.62739i) q^{39} +(-10.9745 + 6.20447i) q^{40} +(-5.06064 - 1.64430i) q^{41} +(0.0307335 - 0.810075i) q^{42} -6.43027i q^{43} +(-6.15098 + 2.48303i) q^{44} +4.45722i q^{45} +(7.92008 + 0.300481i) q^{46} +(2.73390 + 0.888298i) q^{47} +(-1.79670 + 3.57377i) q^{48} +(5.39729 - 3.92136i) q^{49} +(-19.7351 - 7.25042i) q^{50} +(1.77223 - 0.575833i) q^{51} +(4.22033 + 3.58486i) q^{52} +(-2.24188 + 3.08569i) q^{53} +(0.787280 + 1.17481i) q^{54} +(-13.0921 - 6.86524i) q^{55} +(1.58887 - 0.322736i) q^{56} +(3.30898 - 4.55441i) q^{57} +(4.50686 - 1.27763i) q^{58} +(-0.678959 - 2.08962i) q^{59} +(-8.66248 + 2.10441i) q^{60} +(-7.90608 + 5.74410i) q^{61} +(-5.56145 - 4.37214i) q^{62} +(0.177135 - 0.545166i) q^{63} +(-7.79382 - 1.80454i) q^{64} +12.3406i q^{65} +(-4.66337 + 0.502951i) q^{66} +8.82089 q^{67} +(1.95585 + 3.17241i) q^{68} +(5.33007 + 1.73185i) q^{69} +(2.84058 + 2.23313i) q^{70} +(0.234212 + 0.322365i) q^{71} +(-1.91152 + 2.08473i) q^{72} +(6.92610 - 2.25043i) q^{73} +(1.30767 + 4.61283i) q^{74} +(-12.0275 - 8.73847i) q^{75} +(10.4137 + 4.28060i) q^{76} +(1.32847 + 1.35999i) q^{77} +(2.17973 + 3.25269i) q^{78} +(10.4106 + 7.56373i) q^{79} +(-8.17973 - 15.8417i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.59505 - 7.06353i) q^{82} +(4.25392 + 5.85502i) q^{83} +(1.14315 + 0.0868651i) q^{84} +(-2.56661 + 7.89921i) q^{85} +(9.08724 + 0.344762i) q^{86} +3.31241 q^{87} +(-3.17922 - 8.82568i) q^{88} -14.6815 q^{89} +(-6.29892 - 0.238976i) q^{90} +(0.490431 - 1.50939i) q^{91} +(-0.849277 + 11.1765i) q^{92} +(-2.94026 - 4.04692i) q^{93} +(-1.40192 + 3.81591i) q^{94} +(7.75391 + 23.8641i) q^{95} +(-4.95411 - 2.73071i) q^{96} +(4.28190 + 3.11098i) q^{97} +(5.25228 + 7.83768i) q^{98} +(-3.26948 - 0.557199i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{3} + 4 q^{4} - 12 q^{9} + 4 q^{11} + 6 q^{12} - 16 q^{14} + 20 q^{16} - 5 q^{18} + 25 q^{20} + 3 q^{22} + 20 q^{24} - 4 q^{25} + 4 q^{26} + 12 q^{27} - 25 q^{28} - 10 q^{30} - 4 q^{33} + 4 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) $ 48 * q + 12 * q^3 + 4 * q^4 - 12 * q^9 + 4 * q^11 + 6 * q^12 - 16 * q^14 + 20 * q^16 - 5 * q^18 + 25 * q^20 + 3 * q^22 + 20 * q^24 - 4 * q^25 + 4 * q^26 + 12 * q^27 - 25 * q^28 - 10 * q^30 - 4 * q^33 + 4 * q^36 + 26 * q^38 - 65 * q^40 - 60 * q^41 - 4 * q^42 - 43 * q^44 - 5 * q^46 + 5 * q^48 - 12 * q^49 - 80 * q^50 - 15 * q^52 - 14 * q^56 + 73 * q^58 - 8 * q^59 - 25 * q^60 - 45 * q^62 - 38 * q^64 - 13 * q^66 + 8 * q^67 - 55 * q^68 - 40 * q^70 + 20 * q^72 + 60 * q^74 - 36 * q^75 + 46 * q^78 - 12 * q^81 - 35 * q^82 - 100 * q^83 + 45 * q^84 + 81 * q^86 - 18 * q^88 + 96 * q^89 + 10 * q^90 - 20 * q^91 + 59 * q^92 + 35 * q^94 - 40 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/264\mathbb{Z}\right)^\times$.

$n$	$89$	$133$	$145$	$199$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−0.0536155	+	1.41320i	−0.0379118	+	0.999281i
$2$	−0.0536155	+	1.41320i	−0.0379118	+	0.999281i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	−1.99425	−	0.151538i	−0.997125	−	0.0757692i
$5$	−2.61989	−	3.60596i	−1.17165	−	1.61264i	−0.651854	−	0.758344i	$-0.726009\pi$
$5$	−2.61989	−	3.60596i	−1.17165	−	1.61264i	−0.519794	−	0.854292i	$-0.673991\pi$
$6$	−1.32746	−	0.487693i	−0.541934	−	0.199100i
$7$	0.177135	+	0.545166i	0.0669509	+	0.206054i	0.978935	−	0.204172i	$-0.0654501\pi$
$7$	0.177135	+	0.545166i	0.0669509	+	0.206054i	−0.911984	+	0.410225i	$0.865450\pi$
$8$	0.321076	−	2.81014i	0.113518	−	0.993536i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	5.23640	−	3.50908i	1.65590	−	1.10967i
$11$	2.97258	−	1.47097i	0.896267	−	0.443515i
$11$	2.97258	−	1.47097i	0.896267	−	0.443515i
$12$	0.760379	−	1.84982i	0.219502	−	0.533996i
$13$	−2.23991	−	1.62739i	−0.621239	−	0.451357i	0.232115	−	0.972688i	$-0.425435\pi$
$13$	−2.23991	−	1.62739i	−0.621239	−	0.451357i	−0.853354	+	0.521332i	$0.825435\pi$
$14$	−0.779925	+	0.221098i	−0.208444	+	0.0590908i
$15$	4.23906	−	1.37736i	1.09452	−	0.355632i
$16$	3.95407	+	0.604411i	0.988518	+	0.151103i
$17$	−1.09530	−	1.50755i	−0.265649	−	0.365634i	0.655266	−	0.755398i	$-0.272557\pi$
$17$	−1.09530	−	1.50755i	−0.265649	−	0.365634i	−0.920915	+	0.389764i	$0.872557\pi$
$18$	0.874032	−	1.11179i	0.206011	−	0.262050i
$19$	−5.35403	−	1.73963i	−1.22830	−	0.399099i	−0.378202	−	0.925723i	$-0.623457\pi$
$19$	−5.35403	−	1.73963i	−1.22830	−	0.399099i	−0.850098	+	0.526624i	$0.823457\pi$
$20$	4.67827	+	7.58821i	1.04609	+	1.69677i
$21$	−0.573222			−0.125087
$22$	1.91940	+	4.27971i	0.409217	+	0.912437i
$23$		−	5.60437i		−	1.16859i	−0.811541	−	0.584296i	$-0.801371\pi$
$23$		−	5.60437i		−	1.16859i	0.811541	−	0.584296i	$-0.198629\pi$
$24$	2.57339	+	1.17374i	0.525291	+	0.239589i
$25$	−4.59408	+	14.1391i	−0.918817	+	2.82783i
$26$	2.41992	−	3.07818i	0.474584	−	0.603681i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−0.270639	−	1.11404i	−0.0511459	−	0.210534i
$29$	−1.02359	−	3.15029i	−0.190076	−	0.584994i	0.809923	−	0.586536i	$-0.199509\pi$
$29$	−1.02359	−	3.15029i	−0.190076	−	0.584994i	−0.999999	+	0.00154281i	$0.999509\pi$
$30$	1.71919	+	6.06448i	0.313881	+	1.10722i
$31$	−2.94026	+	4.04692i	−0.528086	+	0.726848i	−0.986837	−	0.161717i	$-0.948297\pi$
$31$	−2.94026	+	4.04692i	−0.528086	+	0.726848i	0.458751	+	0.888565i	$0.348297\pi$
$32$	−1.06615	+	5.55548i	−0.188471	+	0.982079i
$33$	0.480399	+	3.28165i	0.0836267	+	0.571262i
$34$	2.18919	−	1.46704i	0.375443	−	0.251596i
$35$	1.50178	−	2.06702i	0.253846	−	0.349390i
$36$	1.52431	+	1.29479i	0.254052	+	0.215798i
$37$	3.22436	−	1.04766i	0.530082	−	0.172234i	−0.0317338	−	0.999496i	$-0.510103\pi$
$37$	3.22436	−	1.04766i	0.530082	−	0.172234i	0.561816	+	0.827262i	$0.310103\pi$
$38$	2.74550	−	7.47303i	0.445379	−	1.21229i
$39$	2.23991	−	1.62739i	0.358673	−	0.260591i
$40$	−10.9745	+	6.20447i	−1.73521	+	0.981012i
$41$	−5.06064	−	1.64430i	−0.790340	−	0.256797i	−0.114091	−	0.993470i	$-0.536396\pi$
$41$	−5.06064	−	1.64430i	−0.790340	−	0.256797i	−0.676249	+	0.736673i	$0.736396\pi$
$42$	0.0307335	−	0.810075i	0.00474229	−	0.124997i
$43$		−	6.43027i		−	0.980608i	−0.871552	−	0.490304i	$-0.836886\pi$
$43$		−	6.43027i		−	0.980608i	0.871552	−	0.490304i	$-0.163114\pi$
$44$	−6.15098	+	2.48303i	−0.927295	+	0.374330i
$45$			4.45722i			0.664442i
$46$	7.92008	+	0.300481i	1.16775	+	0.0443035i
$47$	2.73390	+	0.888298i	0.398780	+	0.129572i	0.501540	−	0.865135i	$-0.332767\pi$
$47$	2.73390	+	0.888298i	0.398780	+	0.129572i	−0.102759	+	0.994706i	$0.532767\pi$
$48$	−1.79670	+	3.57377i	−0.259332	+	0.515830i
$49$	5.39729	−	3.92136i	0.771041	−	0.560194i
$50$	−19.7351	−	7.25042i	−2.79096	−	1.02536i
$51$	1.77223	−	0.575833i	0.248162	−	0.0806327i
$52$	4.22033	+	3.58486i	0.585254	+	0.497130i
$53$	−2.24188	+	3.08569i	−0.307946	+	0.423852i	−0.934739	−	0.355334i	$-0.884367\pi$
$53$	−2.24188	+	3.08569i	−0.307946	+	0.423852i	0.626793	+	0.779186i	$0.284367\pi$
$54$	0.787280	+	1.17481i	0.107135	+	0.159872i
$55$	−13.0921	−	6.86524i	−1.76534	−	0.925709i
$56$	1.58887	−	0.322736i	0.212322	−	0.0431274i
$57$	3.30898	−	4.55441i	0.438285	−	0.603247i
$58$	4.50686	−	1.27763i	0.591779	−	0.167761i
$59$	−0.678959	−	2.08962i	−0.0883929	−	0.272045i	0.897083	−	0.441863i	$-0.145682\pi$
$59$	−0.678959	−	2.08962i	−0.0883929	−	0.272045i	−0.985476	+	0.169817i	$0.945682\pi$
$60$	−8.66248	+	2.10441i	−1.11832	+	0.271678i
$61$	−7.90608	+	5.74410i	−1.01227	+	0.735457i	−0.964684	−	0.263410i	$-0.915153\pi$
$61$	−7.90608	+	5.74410i	−1.01227	+	0.735457i	−0.0475859	+	0.998867i	$0.515153\pi$
$62$	−5.56145	−	4.37214i	−0.706305	−	0.555263i
$63$	0.177135	−	0.545166i	0.0223170	−	0.0686845i
$64$	−7.79382	−	1.80454i	−0.974228	−	0.225568i
$65$			12.3406i			1.53066i
$66$	−4.66337	+	0.502951i	−0.574021	+	0.0619090i
$67$	8.82089			1.07764			0.538822	−	0.842420i	$-0.318870\pi$
$67$	8.82089			1.07764			0.538822	+	0.842420i	$0.318870\pi$
$68$	1.95585	+	3.17241i	0.237181	+	0.384711i
$69$	5.33007	+	1.73185i	0.641665	+	0.208490i
$70$	2.84058	+	2.23313i	0.339515	+	0.266910i
$71$	0.234212	+	0.322365i	0.0277958	+	0.0382576i	0.822689	−	0.568492i	$-0.192473\pi$
$71$	0.234212	+	0.322365i	0.0277958	+	0.0382576i	−0.794893	+	0.606750i	$0.792473\pi$
$72$	−1.91152	+	2.08473i	−0.225274	+	0.245688i
$73$	6.92610	−	2.25043i	0.810638	−	0.263392i	0.125770	−	0.992059i	$-0.459860\pi$
$73$	6.92610	−	2.25043i	0.810638	−	0.263392i	0.684868	+	0.728667i	$0.259860\pi$
$74$	1.30767	+	4.61283i	0.152014	+	0.536231i
$75$	−12.0275	−	8.73847i	−1.38881	−	1.00903i
$76$	10.4137	+	4.28060i	1.19453	+	0.491019i
$77$	1.32847	+	1.35999i	0.151394	+	0.154985i
$78$	2.17973	+	3.25269i	0.246806	+	0.368294i
$79$	10.4106	+	7.56373i	1.17128	+	0.850986i	0.991162	−	0.132658i	$-0.0423513\pi$
$79$	10.4106	+	7.56373i	1.17128	+	0.850986i	0.180120	+	0.983645i	$0.442351\pi$
$80$	−8.17973	−	15.8417i	−0.914522	−	1.77116i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	2.59505	−	7.06353i	0.286576	−	0.780036i
$83$	4.25392	+	5.85502i	0.466928	+	0.642671i	0.975927	−	0.218096i	$-0.0699844\pi$
$83$	4.25392	+	5.85502i	0.466928	+	0.642671i	−0.508999	+	0.860767i	$0.669984\pi$
$84$	1.14315	+	0.0868651i	0.124728	+	0.00947776i
$85$	−2.56661	+	7.89921i	−0.278388	+	0.856790i
$86$	9.08724	+	0.344762i	0.979903	+	0.0371767i
$87$	3.31241			0.355127
$88$	−3.17922	−	8.82568i	−0.338906	−	0.940820i
$89$	−14.6815			−1.55623			−0.778116	−	0.628121i	$-0.783824\pi$
$89$	−14.6815			−1.55623			−0.778116	+	0.628121i	$0.783824\pi$
$90$	−6.29892	−	0.238976i	−0.663965	−	0.0251902i
$91$	0.490431	−	1.50939i	0.0514111	−	0.158227i
$92$	−0.849277	+	11.1765i	−0.0885433	+	1.16523i
$93$	−2.94026	−	4.04692i	−0.304891	−	0.419646i
$94$	−1.40192	+	3.81591i	−0.144597	+	0.393581i
$95$	7.75391	+	23.8641i	0.795535	+	2.44840i
$96$	−4.95411	−	2.73071i	−0.505627	−	0.278702i
$97$	4.28190	+	3.11098i	0.434761	+	0.315872i	0.783550	−	0.621329i	$-0.213407\pi$
$97$	4.28190	+	3.11098i	0.434761	+	0.315872i	−0.348789	+	0.937201i	$0.613407\pi$
$98$	5.25228	+	7.83768i	0.530560	+	0.791725i
$99$	−3.26948	−	0.557199i	−0.328596	−	0.0560006i
$100$	11.3044	−	27.5008i	1.13044	−	2.75008i
$101$	−3.71865	−	2.70176i	−0.370020	−	0.268835i	0.387199	−	0.921996i	$-0.373443\pi$
$101$	−3.71865	−	2.70176i	−0.370020	−	0.268835i	−0.757219	+	0.653161i	$0.773443\pi$
$102$	0.718746	+	2.53538i	0.0711664	+	0.251040i
$103$	3.93207	−	1.27761i	0.387438	−	0.125886i	−0.108820	−	0.994062i	$-0.534707\pi$
$103$	3.93207	−	1.27761i	0.387438	−	0.125886i	0.496258	+	0.868175i	$0.334707\pi$
$104$	−5.29238	+	5.77195i	−0.518961	+	0.565987i
$105$	1.50178	+	2.06702i	0.146558	+	0.201720i
$106$	−4.24048	−	3.33366i	−0.411872	−	0.323794i
$107$	0.186062	+	0.0604551i	0.0179873	+	0.00584441i	0.317997	−	0.948092i	$-0.396990\pi$
$107$	0.186062	+	0.0604551i	0.0179873	+	0.00584441i	−0.300010	+	0.953936i	$0.596990\pi$
$108$	−1.70245	+	1.04959i	−0.163819	+	0.100997i
$109$	−17.0415			−1.63228			−0.816138	−	0.577857i	$-0.803889\pi$
$109$	−17.0415			−1.63228			−0.816138	+	0.577857i	$0.803889\pi$
$110$	10.4039	−	18.1336i	0.991971	−	1.72897i
$111$			3.39030i			0.321793i
$112$	0.370901	+	2.26269i	0.0350469	+	0.213804i
$113$	4.60491	−	14.1725i	0.433194	−	1.33323i	−0.461732	−	0.887019i	$-0.652772\pi$
$113$	4.60491	−	14.1725i	0.433194	−	1.33323i	0.894926	−	0.446214i	$-0.147228\pi$
$114$	6.25887	+	4.92042i	0.586197	+	0.460840i
$115$	−20.2092	+	14.6828i	−1.88451	+	1.36918i
$116$	1.56391	+	6.43758i	0.145205	+	0.597714i
$117$	0.855569	+	2.63317i	0.0790974	+	0.243437i
$118$	2.98945	−	0.847466i	0.275201	−	0.0780156i
$119$	0.627849	−	0.864160i	0.0575548	−	0.0792174i
$120$	−2.50950	−	12.3546i	−0.229085	−	1.12782i
$121$	6.67248	−	8.74517i	0.606590	−	0.795015i
$122$	−7.69366	−	11.4808i	−0.696551	−	1.03942i
$123$	3.12765	−	4.30484i	0.282011	−	0.388154i
$124$	6.47688	−	7.62501i	0.581641	−	0.684746i
$125$	41.8259	−	13.5900i	3.74102	−	1.21553i
$126$	0.760930	+	0.279556i	0.0677891	+	0.0249049i
$127$	12.4721	−	9.06148i	1.10672	−	0.804076i	0.124572	−	0.992211i	$-0.460244\pi$
$127$	12.4721	−	9.06148i	1.10672	−	0.804076i	0.982143	+	0.188134i	$0.0602441\pi$
$128$	2.96804	−	10.9175i	0.262340	−	0.964975i
$129$	6.11555	+	1.98706i	0.538445	+	0.174951i
$130$	−17.4397	−	0.661647i	−1.52956	−	0.0580303i
$131$			4.61457i			0.403177i	0.979470	+	0.201589i	$0.0646104\pi$
$131$			4.61457i			0.403177i	−0.979470	+	0.201589i	$0.935390\pi$
$132$	−0.460740	−	6.61723i	−0.0401023	−	0.575956i
$133$		−	3.22699i		−	0.279816i
$134$	−0.472936	+	12.4657i	−0.0408554	+	1.07687i
$135$	−4.23906	−	1.37736i	−0.364841	−	0.118544i
$136$	−4.58810	+	2.59391i	−0.393427	+	0.222426i
$137$	9.34533	−	6.78978i	0.798425	−	0.580090i	−0.112026	−	0.993705i	$-0.535734\pi$
$137$	9.34533	−	6.78978i	0.798425	−	0.580090i	0.910452	+	0.413615i	$0.135734\pi$
$138$	−2.73321	+	7.43959i	−0.232667	+	0.633300i
$139$	10.3520	−	3.36357i	0.878045	−	0.285294i	0.164900	−	0.986310i	$-0.447270\pi$
$139$	10.3520	−	3.36357i	0.878045	−	0.285294i	0.713146	+	0.701016i	$0.247270\pi$
$140$	−3.30815	+	3.89457i	−0.279590	+	0.329152i
$141$	−1.68964	+	2.32559i	−0.142294	+	0.195850i
$142$	−0.468122	+	0.313703i	−0.0392839	+	0.0263254i
$143$	−9.05216	−	1.54271i	−0.756980	−	0.129007i
$144$	−2.84365	−	2.81312i	−0.236971	−	0.234427i
$145$	−8.67813	+	11.9444i	−0.720679	+	0.991930i
$146$	2.80895	+	9.90860i	0.232470	+	0.820041i
$147$	2.06158	+	6.34489i	0.170036	+	0.523318i
$148$	−6.58895	+	1.60068i	−0.541609	+	0.131575i
$149$	−13.9438	+	10.1308i	−1.14232	+	0.829944i	−0.987441	−	0.157990i	$-0.949499\pi$
$149$	−13.9438	+	10.1308i	−1.14232	+	0.829944i	−0.154879	+	0.987934i	$0.549499\pi$
$150$	12.9940	−	16.5287i	1.06096	−	1.34956i
$151$	2.49222	−	7.67027i	0.202814	−	0.624198i	−0.796982	−	0.604003i	$-0.793571\pi$
$151$	2.49222	−	7.67027i	0.202814	−	0.624198i	0.999796	−	0.0201947i	$-0.00642860\pi$
$152$	−6.60767	+	14.4871i	−0.535953	+	1.17506i
$153$			1.86343i			0.150650i
$154$	−1.99316	+	1.80448i	−0.160614	+	0.145409i
$155$	22.2962			1.79087
$156$	−4.71355	+	2.90599i	−0.377386	+	0.232665i
$157$	2.72919	+	0.886768i	0.217813	+	0.0707718i	0.415891	−	0.909415i	$-0.363470\pi$
$157$	2.72919	+	0.886768i	0.217813	+	0.0707718i	−0.198078	+	0.980186i	$0.563470\pi$
$158$	−11.2472	+	14.3067i	−0.894780	+	1.13818i
$159$	−2.24188	−	3.08569i	−0.177793	−	0.244711i
$160$	22.8260	−	10.7102i	1.80456	−	0.846717i
$161$	3.05531	−	0.992732i	0.240792	−	0.0782382i
$162$	−1.36060	+	0.385711i	−0.106899	+	0.0303043i
$163$	9.73312	+	7.07153i	0.762357	+	0.553885i	0.899632	−	0.436648i	$-0.143835\pi$
$163$	9.73312	+	7.07153i	0.762357	+	0.553885i	−0.137275	+	0.990533i	$0.543835\pi$
$164$	9.84302	+	4.04603i	0.768610	+	0.315942i
$165$	10.5749	−	10.3298i	0.823256	−	0.804177i
$166$	−8.50236	+	5.69770i	−0.659911	+	0.442228i
$167$	1.10300	+	0.801375i	0.0853525	+	0.0620122i	0.629643	−	0.776884i	$-0.283201\pi$
$167$	1.10300	+	0.801375i	0.0853525	+	0.0620122i	−0.544291	+	0.838897i	$0.683201\pi$
$168$	−0.184048	+	1.61084i	−0.0141996	+	0.124279i
$169$	−1.64842	−	5.07332i	−0.126802	−	0.390256i
$170$	−11.0255	−	4.05064i	−0.845620	−	0.310670i
$171$	3.30898	+	4.55441i	0.253044	+	0.348285i
$172$	−0.974433	+	12.8236i	−0.0742998	+	0.977789i
$173$	2.78777	−	8.57988i	0.211950	−	0.652316i	−0.787406	−	0.616435i	$-0.788576\pi$
$173$	2.78777	−	8.57988i	0.211950	−	0.652316i	0.999356	−	0.0358809i	$-0.0114237\pi$
$174$	−0.177596	+	4.68108i	−0.0134635	+	0.354872i
$175$	−8.52196			−0.644199
$176$	12.6429	−	4.01967i	0.952993	−	0.302994i
$177$	2.19716			0.165148
$178$	0.787153	−	20.7478i	0.0589996	−	1.55511i
$179$	4.49299	−	13.8280i	0.335822	−	1.03355i	−0.630494	−	0.776194i	$-0.717148\pi$
$179$	4.49299	−	13.8280i	0.335822	−	1.03355i	0.966316	−	0.257359i	$-0.0828522\pi$
$180$	0.675439	−	8.88881i	0.0503443	−	0.662532i
$181$	3.38939	+	4.66509i	0.251931	+	0.346753i	0.916186	−	0.400752i	$-0.131251\pi$
$181$	3.38939	+	4.66509i	0.251931	+	0.346753i	−0.664255	+	0.747506i	$0.731251\pi$
$182$	2.10677	+	0.774002i	0.156164	+	0.0573729i
$183$	−3.01985	−	9.29416i	−0.223234	−	0.687044i
$184$	−15.7491	−	1.79943i	−1.16104	−	0.132656i
$185$	−12.2253	−	8.88219i	−0.898821	−	0.653032i
$186$	5.87674	−	3.93819i	0.430903	−	0.288762i
$187$	−5.47343	−	2.87016i	−0.400257	−	0.209887i
$188$	−5.31747	−	2.18578i	−0.387816	−	0.159414i
$189$	0.463746	+	0.336931i	0.0337326	+	0.0245082i
$190$	−34.1404	+	9.67832i	−2.47680	+	0.702139i
$191$	−2.24504	+	0.729459i	−0.162446	+	0.0527818i	−0.389111	−	0.921191i	$-0.627218\pi$
$191$	−2.24504	+	0.729459i	−0.162446	+	0.0527818i	0.226665	+	0.973973i	$0.427218\pi$
$192$	4.12464	−	6.85473i	0.297670	−	0.494697i
$193$	−9.93231	−	13.6707i	−0.714943	−	0.984035i	−0.999677	−	0.0254284i	$-0.991905\pi$
$193$	−9.93231	−	13.6707i	−0.714943	−	0.984035i	0.284733	−	0.958607i	$-0.408095\pi$
$194$	−4.62600	+	5.88437i	−0.332128	+	0.422473i
$195$	−11.7366	−	3.81346i	−0.840476	−	0.273087i
$196$	−11.3578	+	7.00228i	−0.811270	+	0.500163i
$197$	14.0467			1.00078			0.500391	−	0.865799i	$-0.333190\pi$
$197$	14.0467			1.00078			0.500391	+	0.865799i	$0.333190\pi$
$198$	0.962726	−	4.59055i	0.0684180	−	0.326236i
$199$		−	1.05909i		−	0.0750771i	−0.999295	−	0.0375386i	$-0.988048\pi$
$199$		−	1.05909i		−	0.0750771i	0.999295	−	0.0375386i	$-0.0119517\pi$
$200$	38.2580	+	17.4498i	2.70525	+	1.23389i
$201$	−2.72580	+	8.38916i	−0.192263	+	0.591726i
$202$	4.01750	−	5.11033i	0.282670	−	0.359562i
$203$	1.53612	−	1.11605i	0.107814	−	0.0783316i
$204$	−3.62153	+	0.879794i	−0.253558	+	0.0615979i
$205$	7.32901	+	22.5564i	0.511880	+	1.57541i
$206$	1.59469	+	5.62528i	0.111107	+	0.391932i
$207$	−3.29417	+	4.53403i	−0.228960	+	0.315137i
$208$	−7.87315	−	7.78864i	−0.545905	−	0.540045i
$209$	−18.4743	+	2.70444i	−1.27789	+	0.187070i
$210$	−3.00162	+	2.01148i	−0.207131	+	0.138805i
$211$	−8.15913	+	11.2301i	−0.561698	+	0.773110i	−0.991541	−	0.129793i	$-0.958569\pi$
$211$	−8.15913	+	11.2301i	−0.561698	+	0.773110i	0.429844	+	0.902903i	$0.358569\pi$
$212$	4.93848	−	5.81390i	0.339176	−	0.399300i
$213$	−0.378962	+	0.123132i	−0.0259661	+	0.00843689i
$214$	−0.0954107	+	0.259700i	−0.00652214	+	0.0177528i
$215$	−23.1873	+	16.8466i	−1.58136	+	1.14893i
$216$	−1.39201	−	2.46218i	−0.0947140	−	0.167530i
$217$	−2.72707	−	0.886078i	−0.185125	−	0.0601509i
$218$	0.913686	−	24.0829i	0.0618826	−	1.63110i
$219$			7.28253i			0.492108i
$220$	25.0686	+	15.6750i	1.69012	+	1.05681i
$221$			5.15925i			0.347049i
$222$	−4.79116	−	0.181772i	−0.321561	−	0.0121998i
$223$	−23.1044	−	7.50707i	−1.54718	−	0.502711i	−0.593837	−	0.804585i	$-0.702388\pi$
$223$	−23.1044	−	7.50707i	−1.54718	−	0.502711i	−0.953348	+	0.301875i	$0.902388\pi$
$224$	−3.21751	+	0.402841i	−0.214979	+	0.0269160i
$225$	12.0275	−	8.73847i	0.801831	−	0.582565i
$226$	19.7816	+	7.26751i	1.31585	+	0.483428i
$227$	−23.7521	+	7.71753i	−1.57648	+	0.512230i	−0.961147	−	0.276036i	$-0.910979\pi$
$227$	−23.7521	+	7.71753i	−1.57648	+	0.512230i	−0.615335	+	0.788266i	$0.710979\pi$
$228$	−7.28910	+	8.58121i	−0.482732	+	0.568304i
$229$	8.32560	−	11.4592i	0.550171	−	0.757245i	−0.439864	−	0.898064i	$-0.644973\pi$
$229$	8.32560	−	11.4592i	0.550171	−	0.757245i	0.990035	+	0.140819i	$0.0449735\pi$
$230$	−19.6662	−	29.3467i	−1.29675	−	1.93507i
$231$	−1.70395	+	0.843193i	−0.112112	+	0.0554780i
$232$	−9.18141	+	1.86495i	−0.602789	+	0.122440i
$233$	−6.37850	+	8.77926i	−0.417870	+	0.575148i	−0.965116	−	0.261824i	$-0.915676\pi$
$233$	−6.37850	+	8.77926i	−0.417870	+	0.575148i	0.547246	+	0.836972i	$0.315676\pi$
$234$	−3.76706	+	1.06791i	−0.246261	+	0.0698114i
$235$	−3.95934	−	12.1856i	−0.258279	−	0.794900i
$236$	1.03736	+	4.27011i	0.0675261	+	0.277961i
$237$	−10.4106	+	7.56373i	−0.676240	+	0.491317i
$238$	1.18757	+	0.933607i	0.0769785	+	0.0605167i
$239$	3.23205	−	9.94724i	0.209064	−	0.643433i	−0.790458	−	0.612516i	$-0.790157\pi$
$239$	3.23205	−	9.94724i	0.209064	−	0.643433i	0.999522	−	0.0309168i	$-0.00984268\pi$
$240$	17.5941	−	2.88403i	1.13569	−	0.186163i
$241$			0.436300i			0.0281045i	0.999901	+	0.0140523i	$0.00447312\pi$
$241$			0.436300i			0.0281045i	−0.999901	+	0.0140523i	$0.995527\pi$
$242$	12.0009	+	9.89841i	0.771447	+	0.636294i
$243$	−1.00000			−0.0641500
$244$	16.6372	−	10.2571i	1.06509	−	0.656644i
$245$	−28.2806	−	9.18891i	−1.80678	−	0.587058i
$246$	5.91590	+	4.65079i	0.377184	+	0.296524i
$247$	9.16150	+	12.6097i	0.582932	+	0.802337i
$248$	10.4284	+	9.56192i	0.662203	+	0.607183i
$249$	−6.88298	+	2.23642i	−0.436191	+	0.141727i
$250$	16.9629	+	59.8368i	1.07283	+	3.78441i
$251$	14.0260	+	10.1905i	0.885316	+	0.643220i	0.934652	−	0.355563i	$-0.115711\pi$
$251$	14.0260	+	10.1905i	0.885316	+	0.643220i	−0.0493367	+	0.998782i	$0.515711\pi$
$252$	−0.435866	+	1.06036i	−0.0274570	+	0.0667961i
$253$	−8.24387	−	16.6594i	−0.518288	−	1.04737i
$254$	12.1370	+	18.1113i	0.761540	+	1.13640i
$255$	−6.71947	−	4.88198i	−0.420790	−	0.305722i
$256$	15.2694	+	4.77977i	0.954336	+	0.298736i
$257$	−5.21439	−	16.0482i	−0.325265	−	1.00106i	−0.971321	−	0.237772i	$-0.923583\pi$
$257$	−5.21439	−	16.0482i	−0.325265	−	1.00106i	0.646056	−	0.763290i	$-0.276417\pi$
$258$	−3.13600	+	8.53594i	−0.195239	+	0.531425i
$259$	1.14230	+	1.57224i	0.0709789	+	0.0976941i
$260$	1.87008	−	24.6103i	0.115977	−	1.52626i
$261$	−1.02359	+	3.15029i	−0.0633586	+	0.194998i
$262$	−6.52130	−	0.247412i	−0.402887	−	0.0152852i
$263$	−2.69577			−0.166228			−0.0831142	−	0.996540i	$-0.526487\pi$
$263$	−2.69577			−0.166228			−0.0831142	+	0.996540i	$0.526487\pi$
$264$	9.37615	−	0.296331i	0.577062	−	0.0182379i
$265$	17.0003			1.04432
$266$	4.56037	+	0.173017i	0.279614	+	0.0106083i
$267$	4.53682	−	13.9629i	0.277649	−	0.854515i
$268$	−17.5911	−	1.33670i	−1.07455	−	0.0816521i
$269$	11.3170	+	15.5766i	0.690012	+	0.949720i	0.999999	−	0.00102058i	$-0.000324862\pi$
$269$	11.3170	+	15.5766i	0.690012	+	0.949720i	−0.309987	+	0.950741i	$0.600325\pi$
$270$	2.17375	−	5.91678i	0.132290	−	0.360084i
$271$	−0.994437	−	3.06056i	−0.0604078	−	0.185916i	0.916299	−	0.400495i	$-0.131162\pi$
$271$	−0.994437	−	3.06056i	−0.0604078	−	0.185916i	−0.976707	+	0.214579i	$0.931162\pi$
$272$	−3.41971	−	6.62297i	−0.207350	−	0.401576i
$273$	1.28397	+	0.932855i	0.0777091	+	0.0564590i
$274$	9.09424	+	13.5708i	0.549403	+	0.819844i
$275$	7.14198	+	48.7875i	0.430678	+	2.94200i
$276$	−10.3671	−	4.26144i	−0.624024	−	0.256509i
$277$	11.6890	+	8.49253i	0.702322	+	0.510266i	0.880687	−	0.473698i	$-0.157081\pi$
$277$	11.6890	+	8.49253i	0.702322	+	0.510266i	−0.178366	+	0.983964i	$0.557081\pi$
$278$	4.19836	+	14.8098i	0.251801	+	0.888230i
$279$	4.75744	−	1.54579i	0.284820	−	0.0925438i
$280$	−5.32643	−	4.88388i	−0.318315	−	0.291867i
$281$	−3.71462	−	5.11274i	−0.221596	−	0.305001i	0.683716	−	0.729748i	$-0.260363\pi$
$281$	−3.71462	−	5.11274i	−0.221596	−	0.305001i	−0.905312	+	0.424748i	$0.860363\pi$
$282$	−3.19593	−	2.51249i	−0.190315	−	0.149616i
$283$	−7.03675	−	2.28638i	−0.418292	−	0.135911i	0.0923066	−	0.995731i	$-0.470576\pi$
$283$	−7.03675	−	2.28638i	−0.418292	−	0.135911i	−0.510598	+	0.859819i	$0.670576\pi$
$284$	−0.418226	−	0.678368i	−0.0248172	−	0.0402537i
$285$	−25.0922			−1.48633
$286$	2.66548	−	12.7098i	0.157613	−	0.751544i
$287$		−	3.05016i		−	0.180045i
$288$	4.12796	−	3.86781i	0.243242	−	0.227913i
$289$	4.18026	−	12.8655i	0.245898	−	0.756796i
$290$	−16.4145	−	12.9043i	−0.963895	−	0.757767i
$291$	−4.28190	+	3.11098i	−0.251009	+	0.182369i
$292$	−14.1534	+	3.43834i	−0.828265	+	0.201214i
$293$	−5.37478	−	16.5419i	−0.313998	−	0.966387i	−0.976165	−	0.217031i	$-0.930363\pi$
$293$	−5.37478	−	16.5419i	−0.313998	−	0.966387i	0.662167	−	0.749357i	$-0.269637\pi$
$294$	−9.07712	+	2.57324i	−0.529388	+	0.150074i
$295$	−5.75630	+	7.92287i	−0.335145	+	0.461287i
$296$	−1.90881	−	9.39731i	−0.110947	−	0.546207i
$297$	1.54025	−	2.93728i	0.0893746	−	0.170438i
$298$	−13.5691	−	20.2485i	−0.786039	−	1.17296i
$299$	−9.12049	+	12.5533i	−0.527452	+	0.725975i
$300$	22.6616	+	19.2493i	1.30837	+	1.11136i
$301$	3.50557	−	1.13903i	0.202058	−	0.0656525i
$302$	10.7060	+	3.93325i	0.616060	+	0.226333i
$303$	3.71865	−	2.70176i	0.213631	−	0.155212i
$304$	−20.1188	−	10.1147i	−1.15389	−	0.580116i
$305$	41.4261	+	13.4601i	2.37205	+	0.770725i
$306$	−2.63340	−	0.0999088i	−0.150541	−	0.00571141i
$307$		−	2.57600i		−	0.147020i	−0.997294	−	0.0735101i	$-0.976580\pi$
$307$		−	2.57600i		−	0.147020i	0.997294	−	0.0735101i	$-0.0234201\pi$
$308$	−2.44322	−	2.91348i	−0.139215	−	0.166011i
$309$			4.13442i			0.235199i
$310$	−1.19542	+	31.5089i	−0.0678953	+	1.78959i
$311$	20.6332	+	6.70413i	1.17000	+	0.380156i	0.828643	−	0.559777i	$-0.189113\pi$
$311$	20.6332	+	6.70413i	1.17000	+	0.380156i	0.341358	+	0.939934i	$0.389113\pi$
$312$	−3.85402	−	6.81698i	−0.218191	−	0.385936i
$313$	8.99181	−	6.53293i	0.508247	−	0.369263i	−0.303911	−	0.952700i	$-0.598293\pi$
$313$	8.99181	−	6.53293i	0.508247	−	0.369263i	0.812158	+	0.583437i	$0.198293\pi$
$314$	−1.39950	+	3.80934i	−0.0789786	+	0.214973i
$315$	−2.42992	+	0.789530i	−0.136911	+	0.0444850i
$316$	−19.6151	−	16.6616i	−1.10344	−	0.937287i
$317$	0.994212	−	1.36842i	0.0558405	−	0.0768579i	−0.780184	−	0.625551i	$-0.784874\pi$
$317$	0.994212	−	1.36842i	0.0558405	−	0.0768579i	0.836024	+	0.548693i	$0.184874\pi$
$318$	4.48088	−	3.00278i	0.251275	−	0.168388i
$319$	−7.67669	−	7.85881i	−0.429812	−	0.440009i
$320$	13.9118	+	32.8319i	0.777694	+	1.83536i
$321$	−0.114992	+	0.158273i	−0.00641825	+	0.00883396i
$322$	1.23911	+	4.37099i	0.0690531	+	0.243586i
$323$	3.24169	+	9.97689i	0.180372	+	0.555129i
$324$	−0.472136	−	1.94347i	−0.0262298	−	0.107971i
$325$	33.3002	−	24.1940i	1.84716	−	1.34204i
$326$	−10.5153	+	13.3757i	−0.582389	+	0.740810i
$327$	5.26610	−	16.2074i	0.291216	−	0.896271i
$328$	−6.24558	+	13.6932i	−0.344854	+	0.756080i
$329$			1.64778i			0.0908450i
$330$	14.0311	+	15.4983i	0.772388	+	0.853152i
$331$	−17.9457			−0.986382			−0.493191	−	0.869921i	$-0.664170\pi$
$331$	−17.9457			−0.986382			−0.493191	+	0.869921i	$0.664170\pi$
$332$	−7.59612	−	12.3210i	−0.416891	−	0.676203i
$333$	−3.22436	−	1.04766i	−0.176694	−	0.0574114i
$334$	−1.19164	+	1.51579i	−0.0652035	+	0.0829402i
$335$	−23.1097	−	31.8078i	−1.26262	−	1.73785i
$336$	−2.26656	−	0.346462i	−0.123651	−	0.0189010i
$337$	−10.0662	+	3.27069i	−0.548339	+	0.178166i	−0.570067	−	0.821598i	$-0.693083\pi$
$337$	−10.0662	+	3.27069i	−0.548339	+	0.178166i	0.0217288	+	0.999764i	$0.493083\pi$
$338$	7.25799	−	2.05754i	0.394782	−	0.111915i
$339$	12.0558	+	8.75907i	0.654782	+	0.475727i
$340$	6.31550	−	15.3641i	0.342506	−	0.833234i
$341$	−2.78726	+	16.3548i	−0.150938	+	0.885664i
$342$	−6.61370	+	4.43205i	−0.357628	+	0.239658i
$343$	6.34007	+	4.60633i	0.342331	+	0.248718i
$344$	−18.0700	−	2.06461i	−0.974269	−	0.111316i
$345$	−7.71921	−	23.7573i	−0.415588	−	1.27905i
$346$	11.9756	+	4.39968i	0.643811	+	0.236528i
$347$	−15.9760	−	21.9891i	−0.857639	−	1.18044i	−0.982127	−	0.188218i	$-0.939729\pi$
$347$	−15.9760	−	21.9891i	−0.857639	−	1.18044i	0.124488	−	0.992221i	$-0.460271\pi$
$348$	−6.60577	−	0.501957i	−0.354107	−	0.0269077i
$349$	11.3104	−	34.8099i	0.605433	−	1.86333i	0.111646	−	0.993748i	$-0.464388\pi$
$349$	11.3104	−	34.8099i	0.605433	−	1.86333i	0.493787	−	0.869583i	$-0.335612\pi$
$350$	0.456909	−	12.0432i	0.0244228	−	0.643736i
$351$	−2.76868			−0.147781
$352$	5.00273	+	18.0824i	0.266646	+	0.963794i
$353$	−18.9076			−1.00635			−0.503174	−	0.864185i	$-0.667835\pi$
$353$	−18.9076			−1.00635			−0.503174	+	0.864185i	$0.667835\pi$
$354$	−0.117802	+	3.10501i	−0.00626108	+	0.165030i
$355$	0.548827	−	1.68912i	0.0291287	−	0.0896490i
$356$	29.2785	+	2.22480i	1.55176	+	0.117914i
$357$	0.627849	+	0.864160i	0.0332293	+	0.0457362i
$358$	19.3008	+	7.09087i	1.02008	+	0.374764i
$359$	5.58150	+	17.1781i	0.294581	+	0.906626i	0.983362	+	0.181657i	$0.0581459\pi$
$359$	5.58150	+	17.1781i	0.294581	+	0.906626i	−0.688782	+	0.724969i	$0.741854\pi$
$360$	12.5254	+	1.43111i	0.660148	+	0.0754259i
$361$	10.2680	+	7.46017i	0.540424	+	0.392641i
$362$	−6.77441	+	4.53975i	−0.356055	+	0.238604i
$363$	6.25524	+	9.04832i	0.328315	+	0.474913i
$364$	−1.20677	+	2.93579i	−0.0632521	+	0.153877i
$365$	−26.2605	−	19.0794i	−1.37454	−	0.998661i
$366$	13.2964	−	3.76934i	0.695013	−	0.197026i
$367$	19.2687	−	6.26078i	1.00582	−	0.326810i	0.240630	−	0.970617i	$-0.422646\pi$
$367$	19.2687	−	6.26078i	1.00582	−	0.326810i	0.765188	+	0.643807i	$0.222646\pi$
$368$	3.38734	−	22.1601i	0.176577	−	1.15517i
$369$	3.12765	+	4.30484i	0.162819	+	0.224101i
$370$	13.2078	−	16.8005i	0.686638	−	0.873417i
$371$	−2.07933	−	0.675615i	−0.107953	−	0.0350762i
$372$	5.25035	+	8.51614i	0.272218	+	0.441541i
$373$	−11.3572			−0.588054			−0.294027	−	0.955797i	$-0.594996\pi$
$373$	−11.3572			−0.588054			−0.294027	+	0.955797i	$0.594996\pi$
$374$	4.34956	−	7.58114i	0.224910	−	0.392012i
$375$			43.9783i			2.27103i
$376$	3.37404	−	7.39744i	0.174003	−	0.381494i
$377$	−2.83399	+	8.72214i	−0.145958	+	0.449213i
$378$	−0.501014	+	0.637300i	−0.0257694	+	0.0327792i
$379$	5.98473	−	4.34816i	0.307415	−	0.223350i	−0.423371	−	0.905956i	$-0.639153\pi$
$379$	5.98473	−	4.34816i	0.307415	−	0.223350i	0.730787	+	0.682606i	$0.239153\pi$
$380$	−11.8469	−	48.7660i	−0.607734	−	2.50164i
$381$	4.76390	+	14.6618i	0.244062	+	0.751146i
$382$	−0.910500	−	3.21180i	−0.0465852	−	0.164330i
$383$	7.48969	−	10.3087i	0.382705	−	0.526748i	−0.573594	−	0.819140i	$-0.694451\pi$
$383$	7.48969	−	10.3087i	0.382705	−	0.526748i	0.956299	+	0.292392i	$0.0944511\pi$
$384$	9.46594	+	6.19645i	0.483057	+	0.316211i
$385$	1.42363	−	8.35345i	0.0725548	−	0.425731i
$386$	19.8519	−	13.3034i	1.01043	−	0.677123i
$387$	−3.77962	+	5.20220i	−0.192129	+	0.264443i
$388$	−8.06774	−	6.85295i	−0.409578	−	0.347906i
$389$	−9.66740	+	3.14113i	−0.490157	+	0.159262i	−0.543659	−	0.839306i	$-0.682962\pi$
$389$	−9.66740	+	3.14113i	−0.490157	+	0.159262i	0.0535024	+	0.998568i	$0.482962\pi$
$390$	6.01843	−	16.3817i	0.304755	−	0.829519i
$391$	−8.44886	+	6.13846i	−0.427277	+	0.310435i
$392$	−9.28665	−	16.4262i	−0.469046	−	0.829649i
$393$	−4.38872	−	1.42598i	−0.221382	−	0.0719313i
$394$	−0.753118	+	19.8507i	−0.0379415	+	1.00006i
$395$		−	57.3563i		−	2.88591i
$396$	6.43574	+	1.60665i	0.323408	+	0.0807370i
$397$			4.03410i			0.202466i	0.994863	+	0.101233i	$0.0322787\pi$
$397$			4.03410i			0.202466i	−0.994863	+	0.101233i	$0.967721\pi$
$398$	1.49671	+	0.0567838i	0.0750231	+	0.00284631i
$399$	3.06905	+	0.997195i	0.153645	+	0.0499222i
$400$	−26.7112	+	53.1305i	−1.33556	+	2.65652i
$401$	−4.47108	+	3.24843i	−0.223275	+	0.162219i	−0.693800	−	0.720168i	$-0.744065\pi$
$401$	−4.47108	+	3.24843i	−0.223275	+	0.162219i	0.470525	+	0.882387i	$0.344065\pi$
$402$	−11.7094	−	4.30189i	−0.584011	−	0.214559i
$403$	13.1718	−	4.27979i	0.656136	−	0.213191i
$404$	7.00651	+	5.95150i	0.348587	+	0.296098i
$405$	2.61989	−	3.60596i	0.130183	−	0.179182i
$406$	1.49484	+	2.23067i	0.0741879	+	0.110706i
$407$	8.04361	−	7.85720i	0.398707	−	0.389467i
$408$	−1.04915	−	5.16511i	−0.0519407	−	0.255711i
$409$	−17.7257	+	24.3974i	−0.876481	+	1.20637i	0.100902	+	0.994896i	$0.467827\pi$
$409$	−17.7257	+	24.3974i	−0.876481	+	1.20637i	−0.977383	+	0.211476i	$0.932173\pi$
$410$	−32.2696	+	9.14797i	−1.59368	+	0.451786i
$411$	3.56960	+	10.9861i	0.176075	+	0.541904i
$412$	−8.03513	+	1.95201i	−0.395863	+	0.0961685i
$413$	1.01892	−	0.740291i	0.0501379	−	0.0364273i
$414$	−6.23086	−	4.89840i	−0.306230	−	0.240743i
$415$	9.96819	−	30.6789i	0.489319	−	1.50597i
$416$	11.4290	−	10.7087i	0.560353	−	0.525038i
$417$			10.8847i			0.533028i
$418$	−2.83140	−	26.2528i	−0.138488	−	1.28406i
$419$	0.189936			0.00927899			0.00463950	−	0.999989i	$-0.498523\pi$
$419$	0.189936			0.00927899			0.00463950	+	0.999989i	$0.498523\pi$
$420$	−2.68168	−	4.34973i	−0.130853	−	0.212245i
$421$	−2.89694	−	0.941273i	−0.141188	−	0.0458748i	0.237570	−	0.971370i	$-0.423649\pi$
$421$	−2.89694	−	0.941273i	−0.141188	−	0.0458748i	−0.378759	+	0.925495i	$0.623649\pi$
$422$	−15.4329	−	12.1326i	−0.751260	−	0.590604i
$423$	−1.68964	−	2.32559i	−0.0821533	−	0.113074i
$424$	7.95141	+	7.29075i	0.386155	+	0.354070i
$425$	26.3473	−	8.56077i	1.27803	−	0.415258i
$426$	−0.153692	−	0.542150i	−0.00744640	−	0.0262673i
$427$	−4.53194	−	3.29265i	−0.219316	−	0.159342i
$428$	−0.361892	−	0.148758i	−0.0174927	−	0.00719049i
$429$	4.26447	−	8.13239i	0.205891	−	0.392636i
$430$	−22.5643	−	33.6715i	−1.08815	−	1.62378i
$431$	−23.6615	−	17.1911i	−1.13973	−	0.828064i	−0.152650	−	0.988280i	$-0.548781\pi$
$431$	−23.6615	−	17.1911i	−1.13973	−	0.828064i	−0.987082	+	0.160216i	$0.948781\pi$
$432$	3.55418	−	1.83517i	0.171000	−	0.0882945i
$433$	−2.49299	−	7.67265i	−0.119806	−	0.368724i	0.873113	−	0.487517i	$-0.162097\pi$
$433$	−2.49299	−	7.67265i	−0.119806	−	0.368724i	−0.992919	+	0.118793i	$0.962097\pi$
$434$	1.39842	−	3.80638i	0.0671261	−	0.182712i
$435$	−8.67813	−	11.9444i	−0.416084	−	0.572691i
$436$	33.9849	+	2.58244i	1.62758	+	0.123676i
$437$	−9.74954	+	30.0060i	−0.466384	+	1.43538i
$438$	−10.2916	−	0.390456i	−0.491754	−	0.0186567i
$439$	28.4746			1.35902			0.679508	−	0.733668i	$-0.262193\pi$
$439$	28.4746			1.35902			0.679508	+	0.733668i	$0.262193\pi$
$440$	−23.4959	+	34.5864i	−1.12012	+	1.64884i
$441$	−6.67142			−0.317687
$442$	−7.29104	−	0.276616i	−0.346799	−	0.0131573i
$443$	−3.31218	+	10.1938i	−0.157366	+	0.484324i	−0.998393	−	0.0566698i	$-0.981952\pi$
$443$	−3.31218	+	10.1938i	−0.157366	+	0.484324i	0.841027	+	0.540994i	$0.181952\pi$
$444$	0.513760	−	6.76110i	0.0243820	−	0.320868i
$445$	38.4637	+	52.9408i	1.82336	+	2.50963i
$446$	11.8477	−	32.2486i	0.561006	−	1.52701i
$447$	−5.32605	−	16.3919i	−0.251914	−	0.775310i
$448$	−0.396786	−	4.56858i	−0.0187464	−	0.215845i
$449$	−4.50011	−	3.26952i	−0.212373	−	0.154298i	0.476514	−	0.879167i	$-0.341900\pi$
$449$	−4.50011	−	3.26952i	−0.212373	−	0.154298i	−0.688887	+	0.724869i	$0.741900\pi$
$450$	11.7043	+	17.4657i	0.551747	+	0.823341i
$451$	−17.4619	+	2.55624i	−0.822249	+	0.120369i
$452$	−11.3310	+	27.5656i	−0.532967	+	1.29658i
$453$	6.52472	+	4.74049i	0.306558	+	0.222728i
$454$	−9.63290	−	33.9802i	−0.452095	−	1.59477i
$455$	−6.72768	+	2.18596i	−0.315399	+	0.102479i
$456$	−11.7361	−	10.7610i	−0.549594	−	0.503931i
$457$	13.7721	+	18.9556i	0.644230	+	0.886707i	0.998832	−	0.0483105i	$-0.0153837\pi$
$457$	13.7721	+	18.9556i	0.644230	+	0.886707i	−0.354602	+	0.935017i	$0.615384\pi$
$458$	15.7477	+	12.3801i	0.735843	+	0.578484i
$459$	−1.77223	−	0.575833i	−0.0827206	−	0.0268776i
$460$	42.5271	−	26.2187i	1.98284	−	1.22246i
$461$	−0.109438			−0.00509703			−0.00254851	−	0.999997i	$-0.500811\pi$
$461$	−0.109438			−0.00509703			−0.00254851	+	0.999997i	$0.500811\pi$
$462$	−1.10024	−	2.45322i	−0.0511878	−	0.114134i
$463$			33.7787i			1.56983i	0.619604	+	0.784915i	$0.287293\pi$
$463$			33.7787i			1.56983i	−0.619604	+	0.784915i	$0.712707\pi$
$464$	−2.14328	−	13.0751i	−0.0994994	−	0.606998i
$465$	−6.88990	+	21.2049i	−0.319512	+	0.983355i
$466$	−12.0648	−	9.48478i	−0.558892	−	0.439374i
$467$	−3.75120	+	2.72540i	−0.173585	+	0.126117i	−0.671185	−	0.741290i	$-0.734215\pi$
$467$	−3.75120	+	2.72540i	−0.173585	+	0.126117i	0.497601	+	0.867406i	$0.334215\pi$
$468$	−1.30719	−	5.38086i	−0.0604250	−	0.248730i
$469$	1.56249	+	4.80885i	0.0721491	+	0.222052i
$470$	17.4329	−	4.94199i	0.804120	−	0.227957i
$471$	−1.68673	+	2.32159i	−0.0777205	+	0.106973i
$472$	−6.09013	+	1.23704i	−0.280321	+	0.0569396i
$473$	−9.45875	−	19.1145i	−0.434914	−	0.878886i
$474$	−10.1309	−	15.1177i	−0.465326	−	0.694381i
$475$	49.1938	−	67.7094i	2.25717	−	3.10672i
$476$	−1.38304	+	1.62821i	−0.0633916	+	0.0746288i
$477$	3.62744	−	1.17863i	0.166089	−	0.0539656i
$478$	13.8841	+	5.10085i	0.635045	+	0.233308i
$479$	−26.9587	+	19.5867i	−1.23178	+	0.894938i	−0.997022	−	0.0771172i	$-0.975428\pi$
$479$	−26.9587	+	19.5867i	−1.23178	+	0.894938i	−0.234754	+	0.972055i	$0.575428\pi$
$480$	3.13238	+	25.0185i	0.142973	+	1.14193i
$481$	−8.92724	−	2.90063i	−0.407047	−	0.132258i
$482$	−0.616577	−	0.0233924i	−0.0280843	−	0.00106549i
$483$			3.21255i			0.146176i
$484$	−14.6318	+	16.4289i	−0.665083	+	0.746769i
$485$		−	23.5908i		−	1.07120i
$486$	0.0536155	−	1.41320i	0.00243205	−	0.0641039i
$487$	21.8323	+	7.09376i	0.989318	+	0.321449i	0.758589	−	0.651569i	$-0.225889\pi$
$487$	21.8323	+	7.09376i	0.989318	+	0.321449i	0.230729	+	0.973018i	$0.425889\pi$
$488$	13.6033	+	24.0615i	0.615793	+	1.08921i
$489$	−9.73312	+	7.07153i	−0.440147	+	0.319785i
$490$	14.5020	−	39.4733i	0.655134	−	1.78322i
$491$	36.8578	−	11.9758i	1.66337	−	0.540462i	0.681796	−	0.731543i	$-0.261199\pi$
$491$	36.8578	−	11.9758i	1.66337	−	0.540462i	0.981574	+	0.191081i	$0.0611993\pi$
$492$	−6.88967	+	8.11097i	−0.310610	+	0.365671i
$493$	−3.62808	+	4.99362i	−0.163400	+	0.224901i
$494$	−18.3112	+	12.2709i	−0.823860	+	0.552095i
$495$	6.55644	+	13.2494i	0.294690	+	0.595518i
$496$	−14.0720	+	14.2247i	−0.631852	+	0.638707i
$497$	−0.134255	+	0.184786i	−0.00602217	+	0.00828881i
$498$	−2.79146	−	9.84692i	−0.125088	−	0.441251i
$499$	9.13091	+	28.1021i	0.408756	+	1.25802i	0.917718	+	0.397232i	$0.130029\pi$
$499$	9.13091	+	28.1021i	0.408756	+	1.25802i	−0.508963	+	0.860789i	$0.669971\pi$
$500$	−85.4707	+	20.7637i	−3.82237	+	0.928583i
$501$	−1.10300	+	0.801375i	−0.0492783	+	0.0358028i
$502$	−15.1532	+	19.2752i	−0.676321	+	0.860294i
$503$	6.70934	−	20.6492i	0.299155	−	0.920704i	−0.682639	−	0.730756i	$-0.739168\pi$
$503$	6.70934	−	20.6492i	0.299155	−	0.920704i	0.981794	−	0.189948i	$-0.0608321\pi$
$504$	−1.47512	−	0.672816i	−0.0657072	−	0.0299696i
$505$			20.4876i			0.911687i
$506$	23.9851	−	10.7570i	1.06627	−	0.478207i
$507$	5.33441			0.236909
$508$	−26.2456	+	16.1809i	−1.16446	+	0.717910i
$509$	3.31891	+	1.07838i	0.147108	+	0.0477983i	0.381645	−	0.924309i	$-0.375358\pi$
$509$	3.31891	+	1.07838i	0.147108	+	0.0477983i	−0.234537	+	0.972107i	$0.575358\pi$
$510$	7.25947	−	9.23419i	0.321455	−	0.408897i
$511$	2.45371	+	3.37725i	0.108546	+	0.149401i
$512$	−7.57343	+	21.3224i	−0.334701	+	0.942324i
$513$	−5.35403	+	1.73963i	−0.236386	+	0.0768066i
$514$	22.9589	−	6.50852i	1.01267	−	0.287079i
$515$	−14.9086	−	10.8317i	−0.656950	−	0.477302i
$516$	−11.8948	−	4.88945i	−0.523641	−	0.215246i
$517$	9.43340	−	1.38095i	0.414881	−	0.0607342i
$518$	−2.28313	+	1.53000i	−0.100315	+	0.0672241i
$519$	7.29848	+	5.30265i	0.320368	+	0.232761i
$520$	34.6789	+	3.96228i	1.52077	+	0.173757i
$521$	1.61127	+	4.95897i	0.0705908	+	0.217256i	0.980128	−	0.198367i	$-0.0635637\pi$
$521$	1.61127	+	4.95897i	0.0705908	+	0.217256i	−0.909537	+	0.415623i	$0.863564\pi$
$522$	−4.39710	−	1.61544i	−0.192456	−	0.0707058i
$523$	20.5226	+	28.2469i	0.897391	+	1.23515i	0.971293	+	0.237887i	$0.0764548\pi$
$523$	20.5226	+	28.2469i	0.897391	+	1.23515i	−0.0739020	+	0.997266i	$0.523545\pi$
$524$	0.699285	−	9.20262i	0.0305484	−	0.402018i
$525$	2.63343	−	8.10486i	0.114932	−	0.353725i
$526$	0.144535	−	3.80966i	0.00630203	−	0.166109i
$527$	9.32139			0.406046
$528$	−0.0839327	+	13.2662i	−0.00365270	+	0.577339i
$529$	−8.40896			−0.365607
$530$	−0.911481	+	24.0248i	−0.0395922	+	1.04357i
$531$	−0.678959	+	2.08962i	−0.0294643	+	0.0906818i
$532$	−0.489013	+	6.43543i	−0.0212014	+	0.279011i
$533$	8.65946	+	11.9187i	0.375083	+	0.516257i
$534$	19.4891	+	7.16005i	0.843375	+	0.309846i
$535$	−0.269461	−	0.829317i	−0.0116498	−	0.0358545i
$536$	2.83218	−	24.7880i	0.122331	−	1.07068i
$537$	11.7628	+	8.54617i	0.507602	+	0.368794i
$538$	−22.6195	+	15.1581i	−0.975197	+	0.653510i
$539$	10.2757	−	19.5958i	0.442605	−	0.844052i
$540$	8.24503	+	3.38917i	0.354810	+	0.145847i
$541$	−31.6067	−	22.9636i	−1.35888	−	0.987282i	−0.998515	−	0.0544693i	$-0.982653\pi$
$541$	−31.6067	−	22.9636i	−1.35888	−	0.987282i	−0.360362	−	0.932813i	$-0.617347\pi$
$542$	4.37850	−	1.24124i	0.188072	−	0.0533159i
$543$	−5.48414	+	1.78191i	−0.235347	+	0.0764689i
$544$	9.54291	−	4.47763i	0.409149	−	0.191977i
$545$	44.6467	+	61.4509i	1.91245	+	2.63227i
$546$	−1.38715	+	1.76448i	−0.0593645	+	0.0755128i
$547$	−27.9643	−	9.08616i	−1.19567	−	0.388496i	−0.357503	−	0.933912i	$-0.616372\pi$
$547$	−27.9643	−	9.08616i	−1.19567	−	0.388496i	−0.838166	+	0.545416i	$0.816372\pi$
$548$	−19.6658	+	12.1243i	−0.840083	+	0.517926i
$549$	9.77245			0.417078
$550$	−69.3293	+	7.47726i	−2.95621	+	0.318831i
$551$			18.6474i			0.794407i
$552$	6.57810	−	14.4222i	0.279982	−	0.613850i
$553$	−2.27941	+	7.01530i	−0.0969304	+	0.298321i
$554$	−12.6283	+	16.0635i	−0.536526	+	0.682471i
$555$	12.2253	−	8.88219i	0.518935	−	0.377028i
$556$	−21.1542	+	5.13908i	−0.897138	+	0.217945i
$557$	8.85736	+	27.2602i	0.375298	+	1.15505i	0.943277	+	0.332006i	$0.107726\pi$
$557$	8.85736	+	27.2602i	0.375298	+	1.15505i	−0.567979	+	0.823043i	$0.692274\pi$
$558$	1.92943	+	6.80608i	0.0816792	+	0.288124i
$559$	−10.4646	+	14.4032i	−0.442604	+	0.609192i
$560$	7.18746	−	7.26544i	0.303726	−	0.307021i
$561$	4.42107	−	4.31861i	0.186658	−	0.182332i
$562$	7.42447	−	4.97537i	0.313182	−	0.209873i
$563$	1.86925	−	2.57280i	0.0787795	−	0.108431i	−0.767809	−	0.640679i	$-0.778653\pi$
$563$	1.86925	−	2.57280i	0.0787795	−	0.108431i	0.846588	+	0.532249i	$0.178653\pi$
$564$	3.72199	−	4.38177i	0.156724	−	0.184506i
$565$	−63.1697	+	20.5251i	−2.65757	+	0.863497i
$566$	3.60838	−	9.82173i	0.151672	−	0.412838i
$567$	−0.463746	+	0.336931i	−0.0194755	+	0.0141498i
$568$	0.981091	−	0.554665i	0.0411657	−	0.0232732i
$569$	4.77065	+	1.55008i	0.199996	+	0.0649827i	0.407302	−	0.913293i	$-0.366470\pi$
$569$	4.77065	+	1.55008i	0.199996	+	0.0649827i	−0.207306	+	0.978276i	$0.566470\pi$
$570$	1.34533	−	35.4602i	0.0563496	−	1.48526i
$571$			28.7933i			1.20496i	0.798134	+	0.602480i	$0.205821\pi$
$571$			28.7933i			1.20496i	−0.798134	+	0.602480i	$0.794179\pi$
$572$	17.8185	+	4.44829i	0.745029	+	0.185992i
$573$		−	2.36058i		−	0.0986145i
$574$	4.31047	+	0.163536i	0.179916	+	0.00682584i
$575$	79.2410	+	25.7470i	3.30458	+	1.07372i
$576$	5.24465	+	6.04100i	0.218527	+	0.251708i
$577$	18.8736	−	13.7125i	0.785718	−	0.570857i	−0.120972	−	0.992656i	$-0.538601\pi$
$577$	18.8736	−	13.7125i	0.785718	−	0.570857i	0.906690	+	0.421799i	$0.138601\pi$
$578$	17.9574	+	6.59733i	0.746929	+	0.274413i
$579$	16.0708	−	5.22173i	0.667880	−	0.217007i
$580$	19.1164	−	22.5051i	0.793765	−	0.934473i
$581$	−2.43844	+	3.35622i	−0.101163	+	0.139240i
$582$	−4.16685	−	6.21796i	−0.172722	−	0.257743i
$583$	−2.12522	+	12.4702i	−0.0880177	+	0.516463i
$584$	−4.10021	−	20.1859i	−0.169668	−	0.835298i
$585$	7.25363	−	9.98376i	0.299901	−	0.412778i
$586$	23.6651	−	6.70873i	0.977597	−	0.277135i
$587$	−4.73849	−	14.5836i	−0.195579	−	0.601929i	−0.999969	−	0.00782832i	$-0.997508\pi$
$587$	−4.73849	−	14.5836i	−0.195579	−	0.601929i	0.804391	−	0.594100i	$-0.202492\pi$
$588$	−3.14981	−	12.9657i	−0.129896	−	0.534697i
$589$	22.7824	−	16.5524i	0.938732	−	0.682029i
$590$	−10.8879	−	8.55957i	−0.448249	−	0.352392i
$591$	−4.34065	+	13.3592i	−0.178551	+	0.549522i
$592$	13.3826	−	2.19368i	0.550021	−	0.0901597i
$593$		−	9.39308i		−	0.385728i	−0.981226	−	0.192864i	$-0.938222\pi$
$593$		−	9.39308i		−	0.385728i	0.981226	−	0.192864i	$-0.0617775\pi$
$594$	4.06837	+	2.33417i	0.166927	+	0.0957720i
$595$	−4.76102			−0.195183
$596$	29.3426	−	18.0902i	1.20192	−	0.741005i
$597$	1.00726	+	0.327278i	0.0412243	+	0.0133946i
$598$	−17.2513	−	13.5621i	−0.705456	−	0.554596i
$599$	4.49421	+	6.18575i	0.183628	+	0.252743i	0.890900	−	0.454199i	$-0.150074\pi$
$599$	4.49421	+	6.18575i	0.183628	+	0.252743i	−0.707272	+	0.706942i	$0.750074\pi$
$600$	−28.4181	+	30.9932i	−1.16016	+	1.26529i
$601$	−7.60599	+	2.47134i	−0.310255	+	0.100808i	−0.460006	−	0.887916i	$-0.652153\pi$
$601$	−7.60599	+	2.47134i	−0.310255	+	0.100808i	0.149751	+	0.988724i	$0.452153\pi$
$602$	1.42172	+	5.01513i	0.0579449	+	0.204401i
$603$	−7.13625	−	5.18479i	−0.290611	−	0.211141i
$604$	−6.13246	+	14.9188i	−0.249526	+	0.607036i
$605$	−49.0159	−	1.14940i	−1.99278	−	0.0467296i
$606$	3.61874	+	5.40004i	0.147001	+	0.219362i
$607$	17.1141	+	12.4341i	0.694640	+	0.504685i	0.878182	−	0.478327i	$-0.158756\pi$
$607$	17.1141	+	12.4341i	0.694640	+	0.504685i	−0.183542	+	0.983012i	$0.558756\pi$
$608$	15.3727	−	27.8895i	0.623445	−	1.13107i
$609$	0.586744	+	1.80581i	0.0237761	+	0.0731752i
$610$	−21.2429	+	57.8215i	−0.860100	+	2.34112i
$611$	−4.67808	−	6.43883i	−0.189255	−	0.260487i
$612$	0.282382	−	3.71615i	0.0114146	−	0.150217i
$613$	−12.0863	+	37.1978i	−0.488161	+	1.50241i	0.339188	+	0.940718i	$0.389848\pi$
$613$	−12.0863	+	37.1978i	−0.488161	+	1.50241i	−0.827350	+	0.561687i	$0.810152\pi$
$614$	3.64040	+	0.138114i	0.146915	+	0.00557381i
$615$	−23.7172			−0.956369
$616$	4.24831	−	3.29654i	0.171169	−	0.132821i
$617$	29.8433			1.20145			0.600723	−	0.799457i	$-0.294879\pi$
$617$	29.8433			1.20145			0.600723	+	0.799457i	$0.294879\pi$
$618$	−5.84275	−	0.221669i	−0.235030	−	0.00891683i
$619$	9.48424	−	29.1895i	0.381204	−	1.17322i	−0.557993	−	0.829846i	$-0.688428\pi$
$619$	9.48424	−	29.1895i	0.381204	−	1.17322i	0.939197	−	0.343379i	$-0.111572\pi$
$620$	−44.4642	−	3.37873i	−1.78572	−	0.135693i
$621$	−3.29417	−	4.53403i	−0.132190	−	0.181944i
$622$	−10.5805	+	28.7993i	−0.424240	+	1.15475i
$623$	−2.60060	−	8.00384i	−0.104191	−	0.320667i
$624$	9.84038	−	5.08099i	0.393930	−	0.203402i
$625$	−98.4469	−	71.5258i	−3.93787	−	2.86103i
$626$	8.75022	+	13.0575i	0.349729	+	0.521881i
$627$	3.13679	−	18.4058i	0.125271	−	0.735056i
$628$	−5.30831	−	2.18201i	−0.211825	−	0.0870718i
$629$	−5.11104	−	3.71339i	−0.203791	−	0.148062i
$630$	−0.985480	−	3.47629i	−0.0392625	−	0.138499i
$631$	−10.4935	+	3.40954i	−0.417739	+	0.135732i	−0.510342	−	0.859971i	$-0.670481\pi$
$631$	−10.4935	+	3.40954i	−0.417739	+	0.135732i	0.0926029	+	0.995703i	$0.470481\pi$
$632$	24.5978	−	26.8267i	0.978447	−	1.06711i
$633$	−8.15913	−	11.2301i	−0.324296	−	0.446356i
$634$	1.88054	+	1.47839i	0.0746856	+	0.0587142i
$635$	−65.3507	−	21.2337i	−2.59336	−	0.842635i
$636$	4.00328	+	6.49336i	0.158740	+	0.257479i
$637$	−18.4710			−0.731849
$638$	11.5176	−	10.4273i	0.455988	−	0.412821i
$639$		−	0.398465i		−	0.0157630i
$640$	−47.1439	+	17.8998i	−1.86352	+	0.707553i
$641$	−14.2288	+	43.7918i	−0.562005	+	1.72967i	0.114683	+	0.993402i	$0.463415\pi$
$641$	−14.2288	+	43.7918i	−0.562005	+	1.72967i	−0.676688	+	0.736270i	$0.736585\pi$
$642$	−0.217506	−	0.170993i	−0.00858428	−	0.00674855i
$643$	−12.2251	+	8.88202i	−0.482109	+	0.350273i	−0.802142	−	0.597134i	$-0.796306\pi$
$643$	−12.2251	+	8.88202i	−0.482109	+	0.350273i	0.320033	+	0.947407i	$0.396306\pi$
$644$	−6.24350	+	1.51676i	−0.246028	+	0.0597687i
$645$	−8.85677	−	27.2583i	−0.348735	−	1.07330i
$646$	−14.2731	+	4.04623i	−0.561568	+	0.159197i
$647$	18.2327	−	25.0952i	0.716801	−	0.986592i	−0.282823	−	0.959172i	$-0.591271\pi$
$647$	18.2327	−	25.0952i	0.716801	−	0.986592i	0.999624	−	0.0274202i	$-0.00872922\pi$
$648$	2.77182	−	0.563021i	0.108888	−	0.0221175i
$649$	−5.09203	−	5.21284i	−0.199880	−	0.204622i
$650$	32.4055	+	48.3569i	1.27105	+	1.89672i
$651$	1.68542	−	2.31978i	0.0660569	−	0.0909195i
$652$	−18.3387	−	15.5773i	−0.718198	−	0.610056i
$653$	30.5916	−	9.93981i	1.19714	−	0.388975i	0.358433	−	0.933556i	$-0.383311\pi$
$653$	30.5916	−	9.93981i	1.19714	−	0.388975i	0.838708	+	0.544581i	$0.183311\pi$
$654$	22.6219	+	8.31100i	0.884586	+	0.324986i
$655$	16.6400	−	12.0897i	0.650178	−	0.472382i
$656$	−19.0163	−	9.56040i	−0.742462	−	0.373271i
$657$	−6.92610	−	2.25043i	−0.270213	−	0.0877974i
$658$	−2.32864	−	0.0883464i	−0.0907797	−	0.00344410i
$659$			26.3804i			1.02764i	0.857899	+	0.513818i	$0.171769\pi$
$659$			26.3804i			1.02764i	−0.857899	+	0.513818i	$0.828231\pi$
$660$	−22.6544	+	18.9978i	−0.881821	+	0.739488i
$661$		−	15.5089i		−	0.603226i	−0.953430	−	0.301613i	$-0.902475\pi$
$661$		−	15.5089i		−	0.603226i	0.953430	−	0.301613i	$-0.0975251\pi$
$662$	0.962164	−	25.3607i	0.0373956	−	0.985673i
$663$	−4.90674	−	1.59430i	−0.190562	−	0.0619173i
$664$	17.8193	−	10.0742i	0.691522	−	0.390955i
$665$	−11.6364	+	8.45434i	−0.451241	+	0.327845i
$666$	1.65343	−	4.50049i	0.0640689	−	0.174391i
$667$	−17.6554	+	5.73658i	−0.683619	+	0.222121i
$668$	−2.07821	−	1.76529i	−0.0804085	−	0.0683011i
$669$	14.2793	−	19.6538i	0.552070	−	0.759859i
$670$	46.1897	−	30.9532i	1.78446	−	1.19583i
$671$	−15.0521	+	28.7044i	−0.581078	+	1.10812i
$672$	0.611141	−	3.18452i	0.0235753	−	0.122846i
$673$	−2.52149	+	3.47053i	−0.0971962	+	0.133779i	−0.854845	−	0.518883i	$-0.826348\pi$
$673$	−2.52149	+	3.47053i	−0.0971962	+	0.133779i	0.757649	+	0.652662i	$0.226348\pi$
$674$	−4.08243	−	14.4008i	−0.157249	−	0.554699i
$675$	4.59408	+	14.1391i	0.176826	+	0.544216i
$676$	2.51857	+	10.3673i	0.0968679	+	0.398742i
$677$	3.49953	−	2.54256i	0.134498	−	0.0977183i	−0.518502	−	0.855076i	$-0.673510\pi$
$677$	3.49953	−	2.54256i	0.134498	−	0.0977183i	0.653000	+	0.757358i	$0.273510\pi$
$678$	−13.0247	+	16.5676i	−0.500209	+	0.636276i
$679$	−0.937527	+	2.88541i	−0.0359790	+	0.110732i
$680$	21.3738	+	9.74879i	0.819650	+	0.373849i
$681$		−	24.9744i		−	0.957023i
$682$	−22.9632	−	4.81582i	−0.879305	−	0.184407i
$683$	−38.9009			−1.48850			−0.744251	−	0.667900i	$-0.767194\pi$
$683$	−38.9009			−1.48850			−0.744251	+	0.667900i	$0.767194\pi$
$684$	−5.90876	−	9.58408i	−0.225927	−	0.366456i
$685$	−48.9674	−	15.9105i	−1.87095	−	0.607908i
$686$	−6.84958	+	8.71279i	−0.261518	+	0.332656i
$687$	8.32560	+	11.4592i	0.317641	+	0.437196i
$688$	3.88653	−	25.4258i	0.148173	−	0.969348i
$689$	10.0432	−	3.26324i	0.382617	−	0.124320i
$690$	33.9876	−	9.63500i	1.29389	−	0.366798i
$691$	32.0241	+	23.2669i	1.21826	+	0.885114i	0.995954	−	0.0898638i	$-0.0286432\pi$
$691$	32.0241	+	23.2669i	1.21826	+	0.885114i	0.222301	+	0.974978i	$0.428643\pi$
$692$	−6.85969	+	16.6880i	−0.260766	+	0.634381i
$693$	−0.275375	−	1.88111i	−0.0104606	−	0.0714576i
$694$	31.9315	−	21.3983i	1.21210	−	0.812270i
$695$	−39.2500	−	28.5168i	−1.48884	−	1.08170i
$696$	1.06354	−	9.30834i	0.0403132	−	0.352832i
$697$	3.06405	+	9.43017i	0.116059	+	0.357193i
$698$	48.5868	+	17.8502i	1.83904	+	0.675640i
$699$	−6.37850	−	8.77926i	−0.241257	−	0.332062i
$700$	16.9949	+	1.29140i	0.642348	+	0.0488105i
$701$	−4.94989	+	15.2342i	−0.186955	+	0.575387i	−0.999977	−	0.00684587i	$-0.997821\pi$
$701$	−4.94989	+	15.2342i	−0.186955	+	0.575387i	0.813022	+	0.582233i	$0.197821\pi$
$702$	0.148444	−	3.91269i	0.00560266	−	0.147675i
$703$	−19.0859			−0.719838
$704$	−25.8222	+	6.10034i	−0.973211	+	0.229915i
$705$	12.8127			0.482553
$706$	1.01374	−	26.7201i	0.0381525	−	1.00563i
$707$	0.814204	−	2.50586i	0.0306213	−	0.0942426i
$708$	−4.38168	−	0.332954i	−0.164674	−	0.0125132i
$709$	−12.1663	−	16.7455i	−0.456915	−	0.628889i	0.516950	−	0.856015i	$-0.327067\pi$
$709$	−12.1663	−	16.7455i	−0.456915	−	0.628889i	−0.973865	+	0.227126i	$0.927067\pi$
$710$	2.35763	+	0.866164i	0.0884803	+	0.0325066i
$711$	−3.97649	−	12.2384i	−0.149130	−	0.458975i
$712$	−4.71387	+	41.2570i	−0.176660	+	1.54617i
$713$	22.6804	+	16.4783i	0.849389	+	0.617117i
$714$	−1.25489	+	0.840942i	−0.0469631	+	0.0314715i
$715$	18.1527	+	36.6835i	0.678872	+	1.37188i
$716$	−11.0556	+	26.8956i	−0.413168	+	1.00514i
$717$	8.46162	+	6.14773i	0.316005	+	0.229591i
$718$	−24.5753	+	6.96675i	−0.917142	+	0.259997i
$719$	5.19193	−	1.68696i	0.193626	−	0.0629130i	−0.210599	−	0.977573i	$-0.567541\pi$
$719$	5.19193	−	1.68696i	0.193626	−	0.0629130i	0.404225	+	0.914660i	$0.367541\pi$
$720$	−2.69399	+	17.6242i	−0.100399	+	0.656813i
$721$	1.39302	+	1.91732i	0.0518786	+	0.0714048i
$722$	−11.0932	+	14.1108i	−0.412847	+	0.525149i
$723$	−0.414946	−	0.134824i	−0.0154320	−	0.00501416i
$724$	−6.05235	−	9.81698i	−0.224934	−	0.364845i
$725$	49.2448			1.82891
$726$	−13.1224	+	8.35475i	−0.487019	+	0.310074i
$727$		−	30.2575i		−	1.12219i	−0.827751	−	0.561095i	$-0.810380\pi$
$727$		−	30.2575i		−	1.12219i	0.827751	−	0.561095i	$-0.189620\pi$
$728$	−4.08414	−	1.86281i	−0.151368	−	0.0690404i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	28.3709	−	36.0883i	1.05005	−	1.33569i
$731$	−9.69395	+	7.04307i	−0.358544	+	0.260497i
$732$	4.61393	+	18.9925i	0.170536	+	0.701983i
$733$	4.53372	+	13.9534i	0.167457	+	0.515379i	0.999209	−	0.0397680i	$-0.0126619\pi$
$733$	4.53372	+	13.9534i	0.167457	+	0.515379i	−0.831752	+	0.555147i	$0.812662\pi$
$734$	7.81461	+	27.5661i	0.288443	+	1.01748i
$735$	17.4783	−	24.0569i	0.644699	−	0.887351i
$736$	31.1349	+	5.97511i	1.14765	+	0.220245i
$737$	26.2208	−	12.9753i	0.965856	−	0.477950i
$738$	−6.25128	+	4.18918i	−0.230113	+	0.154206i
$739$	21.4098	−	29.4681i	0.787572	−	1.08400i	−0.206834	−	0.978376i	$-0.566316\pi$
$739$	21.4098	−	29.4681i	0.787572	−	1.08400i	0.994406	−	0.105624i	$-0.0336841\pi$
$740$	23.0343	+	19.5659i	0.846758	+	0.719258i
$741$	−14.8236	+	4.81648i	−0.544559	+	0.176938i
$742$	1.06626	−	2.90228i	0.0391437	−	0.106546i
$743$	35.1101	−	25.5089i	1.28806	−	0.935833i	0.288299	−	0.957541i	$-0.406910\pi$
$743$	35.1101	−	25.5089i	1.28806	−	0.935833i	0.999764	+	0.0217080i	$0.00691040\pi$
$744$	−12.3165	+	6.96318i	−0.451544	+	0.255283i
$745$	73.0622	+	23.7394i	2.67679	+	0.869743i
$746$	0.608922	−	16.0500i	0.0222942	−	0.587631i
$747$		−	7.23720i		−	0.264795i
$748$	10.4804	+	6.55325i	0.383203	+	0.239611i
$749$			0.112143i			0.00409763i
$750$	−62.1500	−	2.35792i	−2.26940	−	0.0860990i
$751$	−14.3158	−	4.65150i	−0.522393	−	0.169736i	0.0359383	−	0.999354i	$-0.488558\pi$
$751$	−14.3158	−	4.65150i	−0.522393	−	0.169736i	−0.558331	+	0.829618i	$0.688558\pi$
$752$	10.2731	+	5.16479i	0.374623	+	0.188341i
$753$	−14.0260	+	10.1905i	−0.511137	+	0.371363i
$754$	−12.1742	−	4.47263i	−0.443356	−	0.162884i
$755$	−34.1881	+	11.1084i	−1.24423	+	0.404275i
$756$	−0.873768	−	0.742201i	−0.0317786	−	0.0269936i
$757$	16.9793	−	23.3700i	0.617122	−	0.849396i	−0.380017	−	0.924979i	$-0.624082\pi$
$757$	16.9793	−	23.3700i	0.617122	−	0.849396i	0.997139	+	0.0755835i	$0.0240819\pi$
$758$	5.82394	+	8.69073i	0.211535	+	0.315662i
$759$	18.3916	−	2.69233i	0.667572	−	0.0977255i
$760$	69.5511	−	14.1274i	2.52288	−	0.512455i
$761$	−15.4935	+	21.3250i	−0.561639	+	0.773029i	−0.991534	−	0.129850i	$-0.958551\pi$
$761$	−15.4935	+	21.3250i	−0.561639	+	0.773029i	0.429895	+	0.902879i	$0.358551\pi$
$762$	−20.9754	+	5.94623i	−0.759858	+	0.215409i
$763$	−3.01864	−	9.29043i	−0.109282	−	0.336336i
$764$	4.58772	−	1.11451i	0.165978	−	0.0403217i
$765$	6.71947	−	4.88198i	0.242943	−	0.176508i
$766$	14.1666	+	11.1371i	0.511861	+	0.402400i
$767$	−1.87982	+	5.78549i	−0.0678764	+	0.208902i
$768$	−9.26433	+	13.0450i	−0.334298	+	0.470721i
$769$			6.43239i			0.231958i	0.993252	+	0.115979i	$0.0370005\pi$
$769$			6.43239i			0.231958i	−0.993252	+	0.115979i	$0.962999\pi$
$770$	11.7287	+	2.45974i	0.422674	+	0.0886429i
$771$	16.8741			0.607706
$772$	17.7359	+	28.7678i	0.638329	+	1.03538i
$773$	31.4408	+	10.2157i	1.13085	+	0.367434i	0.813898	−	0.581008i	$-0.197342\pi$
$773$	31.4408	+	10.2157i	1.13085	+	0.367434i	0.316949	+	0.948443i	$0.397342\pi$
$774$	−7.14909	−	5.62027i	−0.256969	−	0.202016i
$775$	−43.7122	−	60.1646i	−1.57019	−	2.16118i
$776$	10.1171	−	11.0339i	0.363183	−	0.396093i
$777$	−1.84828	+	0.600541i	−0.0663065	+	0.0215443i
$778$	−3.92071	−	13.8304i	−0.140564	−	0.495842i
$779$	24.2344	+	17.6073i	0.868287	+	0.630847i
$780$	22.8279	+	9.38354i	0.817369	+	0.335985i
$781$	1.17040	+	0.613737i	0.0418803	+	0.0219612i
$782$	−8.22186	−	12.2690i	−0.294013	−	0.438739i
$783$	−2.67979	−	1.94698i	−0.0957680	−	0.0695795i
$784$	23.7114	−	12.2432i	0.846835	−	0.437256i
$785$	−3.95251	−	12.1646i	−0.141071	−	0.434173i
$786$	2.25050	−	6.12567i	0.0802725	−	0.218495i
$787$	−0.490039	−	0.674481i	−0.0174680	−	0.0240427i	0.800194	−	0.599742i	$-0.204730\pi$
$787$	−0.490039	−	0.674481i	−0.0174680	−	0.0240427i	−0.817662	+	0.575699i	$0.804730\pi$
$788$	−28.0125	−	2.12861i	−0.997906	−	0.0758285i
$789$	0.833039	−	2.56383i	0.0296570	−	0.0912748i
$790$	81.0557	+	3.07518i	2.88383	+	0.109410i
$791$	8.54205			0.303720
$792$	−2.61556	+	9.00882i	−0.0929400	+	0.320114i
$793$	27.0568			0.960815
$794$	−5.70098	−	0.216290i	−0.202320	−	0.00767585i
$795$	−5.25340	+	16.1683i	−0.186319	+	0.573430i
$796$	−0.160493	+	2.11210i	−0.00568853	+	0.0748613i
$797$	−1.07205	−	1.47555i	−0.0379741	−	0.0522668i	0.789608	−	0.613612i	$-0.210284\pi$
$797$	−1.07205	−	1.47555i	−0.0379741	−	0.0522668i	−0.827582	+	0.561345i	$0.810284\pi$
$798$	−1.57378	+	4.28371i	−0.0557112	+	0.151642i
$799$	−1.65528	−	5.09444i	−0.0585597	−	0.180228i
$800$	−73.6517	−	40.5968i	−2.60398	−	1.43531i
$801$	11.8775	+	8.62954i	0.419673	+	0.304910i
$802$	−4.35095	−	6.49268i	−0.153637	−	0.229265i
$803$	17.2781	−	16.8777i	0.609730	−	0.595600i
$804$	6.70722	−	16.3170i	0.236545	−	0.575457i
$805$	−11.5843	−	8.41651i	−0.408294	−	0.296643i
$806$	5.34197	+	18.8439i	0.188163	+	0.663746i
$807$	−18.3114	+	5.94972i	−0.644590	+	0.209440i
$808$	−8.78630	+	9.58248i	−0.309101	+	0.337110i
$809$	−24.9075	−	34.2822i	−0.875700	−	1.20530i	−0.977593	−	0.210502i	$-0.932490\pi$
$809$	−24.9075	−	34.2822i	−0.875700	−	1.20530i	0.101894	−	0.994795i	$-0.467510\pi$
$810$	4.95547	+	3.89575i	0.174117	+	0.136883i
$811$	−3.53638	−	1.14904i	−0.124179	−	0.0403482i	0.246268	−	0.969202i	$-0.420796\pi$
$811$	−3.53638	−	1.14904i	−0.124179	−	0.0403482i	−0.370447	+	0.928854i	$0.620796\pi$
$812$	−3.23253	+	1.99291i	−0.113439	+	0.0699375i
$813$	3.21807			0.112863
$814$	10.6725	+	11.7885i	0.374071	+	0.413186i
$815$		−	53.6239i		−	1.87836i
$816$	7.35557	−	1.20573i	0.257496	−	0.0422089i
$817$	−11.1863	+	34.4279i	−0.391359	+	1.20448i
$818$	−33.5279	−	26.3580i	−1.17228	−	0.921587i
$819$	−1.28397	+	0.932855i	−0.0448654	+	0.0325966i
$820$	−11.1977	−	46.0937i	−0.391042	−	1.60966i
$821$	−5.88119	−	18.1004i	−0.205255	−	0.631710i	−0.999703	−	0.0243776i	$-0.992240\pi$
$821$	−5.88119	−	18.1004i	−0.205255	−	0.631710i	0.794448	−	0.607332i	$-0.207760\pi$
$822$	−15.7169	+	4.45552i	−0.548190	+	0.155404i
$823$	−20.8515	+	28.6996i	−0.726837	+	1.00040i	0.272432	+	0.962175i	$0.412172\pi$
$823$	−20.8515	+	28.6996i	−0.726837	+	1.00040i	−0.999269	+	0.0382300i	$0.987828\pi$
$824$	−2.32776	−	11.4599i	−0.0810915	−	0.399224i
$825$	−48.6067	−	8.28374i	−1.69227	−	0.288403i
$826$	0.991547	+	1.47963i	0.0345003	+	0.0514829i
$827$	−5.57376	+	7.67162i	−0.193819	+	0.266768i	−0.894855	−	0.446357i	$-0.852721\pi$
$827$	−5.57376	+	7.67162i	−0.193819	+	0.266768i	0.701036	+	0.713126i	$0.252721\pi$
$828$	7.25647	−	8.54280i	0.252180	−	0.296883i
$829$	21.5904	−	7.01515i	0.749866	−	0.243646i	0.0909427	−	0.995856i	$-0.471012\pi$
$829$	21.5904	−	7.01515i	0.749866	−	0.243646i	0.658924	+	0.752210i	$0.271012\pi$
$830$	42.8209	+	15.7319i	1.48634	+	0.546062i
$831$	−11.6890	+	8.49253i	−0.405486	+	0.294602i
$832$	14.5208	+	16.7256i	0.503417	+	0.579855i
$833$	−11.8233	−	3.84162i	−0.409653	−	0.133104i
$834$	−15.3823	−	0.583590i	−0.532645	−	0.0202081i
$835$		−	6.07688i		−	0.210299i
$836$	37.2521	−	2.59377i	1.28839	−	0.0897073i
$837$			5.00227i			0.172904i
$838$	−0.0101835	+	0.268417i	−0.000351784	+	0.00927232i
$839$	−13.4282	−	4.36309i	−0.463594	−	0.150631i	0.0679014	−	0.997692i	$-0.478370\pi$
$839$	−13.4282	−	4.36309i	−0.463594	−	0.150631i	−0.531495	+	0.847061i	$0.678370\pi$
$840$	6.29080	−	3.55654i	0.217053	−	0.122712i
$841$	14.5849	−	10.5966i	0.502928	−	0.365399i
$842$	1.48553	−	4.04348i	0.0511946	−	0.139348i
$843$	6.01039	−	1.95289i	0.207009	−	0.0672612i
$844$	17.9731	−	21.1592i	0.618661	−	0.728329i
$845$	−13.9755	+	19.2357i	−0.480773	+	0.661728i
$846$	3.37711	−	2.26311i	0.116108	−	0.0778073i
$847$	5.94950	+	2.08854i	0.204427	+	0.0717630i
$848$	−10.7296	+	10.8460i	−0.368456	+	0.372453i
$849$	4.34895	−	5.98582i	0.149256	−	0.205433i
$850$	10.6854	+	37.6930i	0.366507	+	1.29286i
$851$	−5.87147	−	18.0705i	−0.201271	−	0.619450i
$852$	0.774405	−	0.188129i	0.0265307	−	0.00644521i
$853$	19.1248	−	13.8950i	0.654822	−	0.475756i	−0.210088	−	0.977682i	$-0.567375\pi$
$853$	19.1248	−	13.8950i	0.654822	−	0.475756i	0.864910	+	0.501926i	$0.167375\pi$
$854$	4.89614	−	6.22798i	0.167542	−	0.213117i
$855$	7.75391	−	23.8641i	0.265178	−	0.816135i
$856$	0.229627	−	0.503449i	0.00784850	−	0.0172075i
$857$		−	9.83122i		−	0.335828i	−0.985802	−	0.167914i	$-0.946297\pi$
$857$		−	9.83122i		−	0.335828i	0.985802	−	0.167914i	$-0.0537031\pi$
$858$	11.2640	+	6.46256i	0.384548	+	0.220628i
$859$	32.0250			1.09268			0.546340	−	0.837564i	$-0.316021\pi$
$859$	32.0250			1.09268			0.546340	+	0.837564i	$0.316021\pi$
$860$	48.7943	−	30.0825i	1.66387	−	1.02581i
$861$	2.90087	+	0.942550i	0.0988614	+	0.0321220i
$862$	25.5630	−	32.5166i	0.870678	−	1.10752i
$863$	23.7712	+	32.7182i	0.809180	+	1.11374i	0.991449	+	0.130492i	$0.0416558\pi$
$863$	23.7712	+	32.7182i	0.809180	+	1.11374i	−0.182269	+	0.983249i	$0.558344\pi$
$864$	2.40289	+	5.12114i	0.0817481	+	0.174225i
$865$	−38.2424	+	12.4257i	−1.30028	+	0.422486i
$866$	10.9766	−	3.11172i	0.373001	−	0.105741i
$867$	10.9441	+	7.95133i	0.371680	+	0.270041i
$868$	5.30418	+	2.18032i	0.180036	+	0.0740048i
$869$	42.0723	+	7.17014i	1.42721	+	0.243230i
$870$	17.3451	−	11.6235i	0.588054	−	0.394074i
$871$	−19.7580	−	14.3550i	−0.669474	−	0.486401i
$872$	−5.47161	+	47.8890i	−0.185292	+	1.62172i
$873$	−1.63554	−	5.03367i	−0.0553546	−	0.170364i
$874$	−41.8816	−	15.3868i	−1.41667	−	0.520466i
$875$	14.8177	+	20.3948i	0.500929	+	0.689469i
$876$	1.10358	−	14.5232i	0.0372866	−	0.490693i
$877$	9.70220	−	29.8603i	0.327620	−	1.00831i	−0.642624	−	0.766182i	$-0.722154\pi$
$877$	9.70220	−	29.8603i	0.327620	−	1.00831i	0.970244	−	0.242129i	$-0.0778457\pi$
$878$	−1.52668	+	40.2402i	−0.0515228	+	1.35804i
$879$	17.3932			0.586657
$880$	−47.6177	−	35.0587i	−1.60519	−	1.18183i
$881$	−26.9234			−0.907072			−0.453536	−	0.891238i	$-0.649838\pi$
$881$	−26.9234			−0.907072			−0.453536	+	0.891238i	$0.649838\pi$
$882$	0.357691	−	9.42803i	0.0120441	−	0.317458i
$883$	−1.14008	+	3.50881i	−0.0383668	+	0.118081i	−0.968406	−	0.249380i	$-0.919773\pi$
$883$	−1.14008	+	3.50881i	−0.0383668	+	0.118081i	0.930039	+	0.367461i	$0.119773\pi$
$884$	0.781825	−	10.2888i	0.0262956	−	0.346051i
$885$	−5.75630	−	7.92287i	−0.193496	−	0.266324i
$886$	−14.2283	−	5.22731i	−0.478010	−	0.175615i
$887$	−16.0444	−	49.3797i	−0.538719	−	1.65801i	−0.735473	−	0.677554i	$-0.763040\pi$
$887$	−16.0444	−	49.3797i	−0.538719	−	1.65801i	0.196754	−	0.980453i	$-0.436960\pi$
$888$	9.52723	+	1.08854i	0.319713	+	0.0365291i
$889$	7.14925	+	5.19424i	0.239778	+	0.174209i
$890$	−76.8780	+	51.5184i	−2.57696	+	1.72690i
$891$	2.31756	+	2.37254i	0.0776410	+	0.0794830i
$892$	44.9383	+	18.4722i	1.50465	+	0.618495i
$893$	−13.0921	−	9.51196i	−0.438110	−	0.318305i
$894$	23.4505	−	6.64790i	0.784303	−	0.222339i
$895$	−61.6343	+	20.0262i	−2.06021	+	0.669402i
$896$	6.47757	−	0.315790i	0.216400	−	0.0105498i
$897$	−9.12049	−	12.5533i	−0.304524	−	0.419142i
$898$	4.86175	−	6.18424i	0.162239	−	0.206371i
$899$	15.7586	+	5.12027i	0.525578	+	0.170771i
$900$	−25.3100	+	15.6041i	−0.843667	+	0.520136i
$901$	7.10736			0.236780
$902$	−2.67624	−	24.8142i	−0.0891091	−	0.826221i
$903$			3.68597i			0.122662i
$904$	−38.3482	−	17.4909i	−1.27544	−	0.581739i
$905$	7.94234	−	24.4440i	0.264012	−	0.812546i
$906$	−7.04907	+	8.96655i	−0.234190	+	0.297894i
$907$	−35.3774	+	25.7032i	−1.17469	+	0.853461i	−0.991563	−	0.129629i	$-0.958621\pi$
$907$	−35.3774	+	25.7032i	−1.17469	+	0.853461i	−0.183126	+	0.983090i	$0.558621\pi$
$908$	48.5371	−	11.7913i	1.61076	−	0.391309i
$909$	1.42040	+	4.37154i	0.0471117	+	0.144995i
$910$	−2.72848	−	9.62474i	−0.0904482	−	0.319057i
$911$	−4.95722	+	6.82303i	−0.164240	+	0.226057i	−0.883202	−	0.468992i	$-0.844617\pi$
$911$	−4.95722	+	6.82303i	−0.164240	+	0.226057i	0.718962	+	0.695049i	$0.244617\pi$
$912$	15.8367	−	16.0085i	0.524404	−	0.530094i
$913$	21.2577	+	11.1471i	0.703526	+	0.368916i
$914$	−27.5264	+	18.4463i	−0.910493	+	0.610150i
$915$	−25.6027	+	35.2391i	−0.846399	+	1.16497i
$916$	−18.3398	+	21.5909i	−0.605965	+	0.713383i
$917$	−2.51571	+	0.817404i	−0.0830761	+	0.0269931i
$918$	0.908784	−	2.47364i	0.0299943	−	0.0816422i
$919$	−17.5993	+	12.7866i	−0.580546	+	0.421791i	−0.838921	−	0.544253i	$-0.816813\pi$
$919$	−17.5993	+	12.7866i	−0.580546	+	0.421791i	0.258375	+	0.966045i	$0.416813\pi$
$920$	34.7721	+	61.5049i	1.14640	+	2.02776i
$921$	2.44992	+	0.796029i	0.0807277	+	0.0262300i
$922$	0.00586756	−	0.154657i	0.000193238	−	0.00509336i
$923$		−	1.10322i		−	0.0363130i
$924$	3.52588	−	1.42332i	0.115993	−	0.0468240i
$925$			50.4028i			1.65723i
$926$	−47.7360	−	1.81106i	−1.56870	−	0.0595151i
$927$	−3.93207	−	1.27761i	−0.129146	−	0.0419621i
$928$	18.5926	−	2.32785i	0.610334	−	0.0764154i
$929$	30.9158	−	22.4617i	1.01432	−	0.736943i	0.0492058	−	0.998789i	$-0.484331\pi$
$929$	30.9158	−	22.4617i	1.01432	−	0.736943i	0.965110	+	0.261845i	$0.0843310\pi$
$930$	−29.5973	−	10.8737i	−0.970535	−	0.356563i
$931$	−35.7190	+	11.6058i	−1.17064	+	0.380365i
$932$	14.0507	−	16.5414i	0.460247	−	0.541833i
$933$	−12.7520	+	17.5516i	−0.417482	+	0.574615i
$934$	−3.65041	−	5.44730i	−0.119445	−	0.178241i
$935$	3.99006	+	27.2565i	0.130489	+	0.891382i
$936$	7.67429	−	1.55882i	0.250842	−	0.0509518i
$937$	1.48734	−	2.04715i	0.0485893	−	0.0668774i	−0.784031	−	0.620722i	$-0.786840\pi$
$937$	1.48734	−	2.04715i	0.0485893	−	0.0668774i	0.832620	+	0.553844i	$0.186840\pi$
$938$	−6.87963	+	1.95028i	−0.224628	+	0.0636788i
$939$	3.43457	+	10.5705i	0.112083	+	0.344955i
$940$	6.04932	+	24.9011i	0.197307	+	0.812184i
$941$	−31.3754	+	22.7955i	−1.02281	+	0.743113i	−0.966856	−	0.255321i	$-0.917819\pi$
$941$	−31.3754	+	22.7955i	−1.02281	+	0.743113i	−0.0559508	+	0.998434i	$0.517819\pi$
$942$	−3.19043	−	2.50816i	−0.103950	−	0.0817202i
$943$	−9.21528	+	28.3617i	−0.300091	+	0.923585i
$944$	−1.42166	−	8.67288i	−0.0462712	−	0.282278i
$945$		−	2.55497i		−	0.0831133i
$946$	27.5197	−	12.3422i	0.894743	−	0.401281i
$947$	−18.5601			−0.603122			−0.301561	−	0.953447i	$-0.597508\pi$
$947$	−18.5601			−0.603122			−0.301561	+	0.953447i	$0.597508\pi$
$948$	21.9075	−	13.5064i	0.711523	−	0.438667i
$949$	−19.1761	−	6.23071i	−0.622484	−	0.202257i
$950$	93.0492	+	73.1508i	3.01891	+	2.37332i
$951$	0.994212	+	1.36842i	0.0322395	+	0.0443739i
$952$	−2.22683	−	2.04181i	−0.0721719	−	0.0661754i
$953$	−18.0360	+	5.86025i	−0.584243	+	0.189832i	−0.586200	−	0.810166i	$-0.699377\pi$
$953$	−18.0360	+	5.86025i	−0.584243	+	0.189832i	0.00195755	+	0.999998i	$0.499377\pi$
$954$	1.47115	+	5.18948i	0.0476301	+	0.168016i
$955$	8.51215	+	6.18444i	0.275447	+	0.200124i
$956$	−7.95291	+	19.3475i	−0.257216	+	0.625743i
$957$	9.84640	−	4.87246i	0.318289	−	0.157504i
$958$	−26.2344	−	39.1481i	−0.847595	−	1.26482i
$959$	5.35695	+	3.89205i	0.172985	+	0.125681i
$960$	−35.5240	+	3.08530i	−1.14653	+	0.0995775i
$961$	1.84709	+	5.68476i	0.0595836	+	0.183379i
$962$	4.57781	−	12.4604i	0.147594	−	0.401740i
$963$	−0.114992	−	0.158273i	−0.00370558	−	0.00510029i
$964$	0.0661161	−	0.870091i	0.00212946	−	0.0280237i
$965$	−23.2744	+	71.6311i	−0.749228	+	2.30589i
$966$	−4.53996	−	0.172242i	−0.146071	−	0.00554180i
$967$	−12.9244			−0.415620			−0.207810	−	0.978169i	$-0.566634\pi$
$967$	−12.9244			−0.415620			−0.207810	+	0.978169i	$0.566634\pi$
$968$	−22.4328	−	21.5585i	−0.721018	−	0.692917i
$969$	−10.4903			−0.336998
$970$	33.3384	+	1.26483i	1.07043	+	0.0406112i
$971$	7.04662	−	21.6873i	0.226137	−	0.695977i	−0.772037	−	0.635577i	$-0.780762\pi$
$971$	7.04662	−	21.6873i	0.226137	−	0.695977i	0.998174	−	0.0604003i	$-0.0192377\pi$
$972$	1.99425	+	0.151538i	0.0639656	+	0.00486060i
$973$	3.66741	+	5.04776i	0.117572	+	0.161824i
$974$	−11.1954	+	30.4731i	−0.358725	+	0.976420i
$975$	12.7196	+	39.1468i	0.407352	+	1.25370i
$976$	−34.7330	+	17.9341i	−1.11178	+	0.574056i
$977$	23.3651	+	16.9758i	0.747516	+	0.543102i	0.895056	−	0.445954i	$-0.147135\pi$
$977$	23.3651	+	16.9758i	0.747516	+	0.543102i	−0.147540	+	0.989056i	$0.547135\pi$
$978$	−9.47161	−	14.1340i	−0.302869	−	0.451954i
$979$	−43.6418	+	21.5960i	−1.39480	+	0.690211i
$980$	55.0061	+	22.6106i	1.75710	+	0.722269i
$981$	13.7868	+	10.0167i	0.440180	+	0.319809i
$982$	14.9481	+	52.7294i	0.477012	+	1.68266i
$983$	−14.5318	+	4.72167i	−0.463492	+	0.150598i	−0.531449	−	0.847091i	$-0.678352\pi$
$983$	−14.5318	+	4.72167i	−0.463492	+	0.150598i	0.0679563	+	0.997688i	$0.478352\pi$
$984$	−11.0930	−	10.1713i	−0.353632	−	0.324250i
$985$	−36.8006	−	50.6517i	−1.17257	−	1.61390i
$986$	−6.86244	−	5.39492i	−0.218545	−	0.171809i
$987$	−1.56713	−	0.509192i	−0.0498823	−	0.0162078i
$988$	−16.3595	−	26.5353i	−0.520464	−	0.844199i
$989$	−36.0376			−1.14593
$990$	−19.0756	+	8.55516i	−0.606262	+	0.271901i
$991$			9.18481i			0.291765i	0.989302	+	0.145882i	$0.0466021\pi$
$991$			9.18481i			0.291765i	−0.989302	+	0.145882i	$0.953398\pi$
$992$	−19.3478	−	20.6492i	−0.614294	−	0.655612i
$993$	5.54551	−	17.0673i	0.175982	−	0.541615i
$994$	−0.253942	−	0.199636i	−0.00805454	−	0.00633209i
$995$	−3.81905	+	2.77470i	−0.121072	+	0.0879640i
$996$	14.0653	−	3.41694i	0.445676	−	0.108270i
$997$	−7.53832	−	23.2006i	−0.238741	−	0.734769i	−0.996603	−	0.0823544i	$-0.973756\pi$
$997$	−7.53832	−	23.2006i	−0.238741	−	0.734769i	0.757862	−	0.652415i	$-0.226244\pi$
$998$	−40.2033	+	11.3971i	−1.27261	+	0.360768i
$999$	1.99277	−	2.74281i	0.0630484	−	0.0867786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	264.2.z.b.139.5	yes	48
3.2	odd	2		792.2.bp.d.667.8		48
4.3	odd	2		1056.2.bp.a.271.1		48
8.3	odd	2	inner	264.2.z.b.139.2	yes	48
8.5	even	2		1056.2.bp.a.271.12		48
11.8	odd	10	inner	264.2.z.b.19.2	✓	48
24.11	even	2		792.2.bp.d.667.11		48
33.8	even	10		792.2.bp.d.19.11		48
44.19	even	10		1056.2.bp.a.943.12		48
88.19	even	10	inner	264.2.z.b.19.5	yes	48
88.85	odd	10		1056.2.bp.a.943.1		48
264.107	odd	10		792.2.bp.d.19.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.z.b.19.2	✓	48	11.8	odd	10	inner
264.2.z.b.19.5	yes	48	88.19	even	10	inner
264.2.z.b.139.2	yes	48	8.3	odd	2	inner
264.2.z.b.139.5	yes	48	1.1	even	1	trivial
792.2.bp.d.19.8		48	264.107	odd	10
792.2.bp.d.19.11		48	33.8	even	10
792.2.bp.d.667.8		48	3.2	odd	2
792.2.bp.d.667.11		48	24.11	even	2
1056.2.bp.a.271.1		48	4.3	odd	2
1056.2.bp.a.271.12		48	8.5	even	2
1056.2.bp.a.943.1		48	88.85	odd	10
1056.2.bp.a.943.12		48	44.19	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	264.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0536155 + 1.41320i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-1.99425 - 0.151538i) q^{4} +(-2.61989 - 3.60596i) q^{5} +(-1.32746 - 0.487693i) q^{6} +(0.177135 + 0.545166i) q^{7} +(0.321076 - 2.81014i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(5.23640 - 3.50908i) q^{10} +(2.97258 - 1.47097i) q^{11} +(0.760379 - 1.84982i) q^{12} +(-2.23991 - 1.62739i) q^{13} +(-0.779925 + 0.221098i) q^{14} +(4.23906 - 1.37736i) q^{15} +(3.95407 + 0.604411i) q^{16} +(-1.09530 - 1.50755i) q^{17} +(0.874032 - 1.11179i) q^{18} +(-5.35403 - 1.73963i) q^{19} +(4.67827 + 7.58821i) q^{20} -0.573222 q^{21} +(1.91940 + 4.27971i) q^{22} -5.60437i q^{23} +(2.57339 + 1.17374i) q^{24} +(-4.59408 + 14.1391i) q^{25} +(2.41992 - 3.07818i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.270639 - 1.11404i) q^{28} +(-1.02359 - 3.15029i) q^{29} +(1.71919 + 6.06448i) q^{30} +(-2.94026 + 4.04692i) q^{31} +(-1.06615 + 5.55548i) q^{32} +(0.480399 + 3.28165i) q^{33} +(2.18919 - 1.46704i) q^{34} +(1.50178 - 2.06702i) q^{35} +(1.52431 + 1.29479i) q^{36} +(3.22436 - 1.04766i) q^{37} +(2.74550 - 7.47303i) q^{38} +(2.23991 - 1.62739i) q^{39} +(-10.9745 + 6.20447i) q^{40} +(-5.06064 - 1.64430i) q^{41} +(0.0307335 - 0.810075i) q^{42} -6.43027i q^{43} +(-6.15098 + 2.48303i) q^{44} +4.45722i q^{45} +(7.92008 + 0.300481i) q^{46} +(2.73390 + 0.888298i) q^{47} +(-1.79670 + 3.57377i) q^{48} +(5.39729 - 3.92136i) q^{49} +(-19.7351 - 7.25042i) q^{50} +(1.77223 - 0.575833i) q^{51} +(4.22033 + 3.58486i) q^{52} +(-2.24188 + 3.08569i) q^{53} +(0.787280 + 1.17481i) q^{54} +(-13.0921 - 6.86524i) q^{55} +(1.58887 - 0.322736i) q^{56} +(3.30898 - 4.55441i) q^{57} +(4.50686 - 1.27763i) q^{58} +(-0.678959 - 2.08962i) q^{59} +(-8.66248 + 2.10441i) q^{60} +(-7.90608 + 5.74410i) q^{61} +(-5.56145 - 4.37214i) q^{62} +(0.177135 - 0.545166i) q^{63} +(-7.79382 - 1.80454i) q^{64} +12.3406i q^{65} +(-4.66337 + 0.502951i) q^{66} +8.82089 q^{67} +(1.95585 + 3.17241i) q^{68} +(5.33007 + 1.73185i) q^{69} +(2.84058 + 2.23313i) q^{70} +(0.234212 + 0.322365i) q^{71} +(-1.91152 + 2.08473i) q^{72} +(6.92610 - 2.25043i) q^{73} +(1.30767 + 4.61283i) q^{74} +(-12.0275 - 8.73847i) q^{75} +(10.4137 + 4.28060i) q^{76} +(1.32847 + 1.35999i) q^{77} +(2.17973 + 3.25269i) q^{78} +(10.4106 + 7.56373i) q^{79} +(-8.17973 - 15.8417i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.59505 - 7.06353i) q^{82} +(4.25392 + 5.85502i) q^{83} +(1.14315 + 0.0868651i) q^{84} +(-2.56661 + 7.89921i) q^{85} +(9.08724 + 0.344762i) q^{86} +3.31241 q^{87} +(-3.17922 - 8.82568i) q^{88} -14.6815 q^{89} +(-6.29892 - 0.238976i) q^{90} +(0.490431 - 1.50939i) q^{91} +(-0.849277 + 11.1765i) q^{92} +(-2.94026 - 4.04692i) q^{93} +(-1.40192 + 3.81591i) q^{94} +(7.75391 + 23.8641i) q^{95} +(-4.95411 - 2.73071i) q^{96} +(4.28190 + 3.11098i) q^{97} +(5.25228 + 7.83768i) q^{98} +(-3.26948 - 0.557199i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{3} + 4 q^{4} - 12 q^{9} + 4 q^{11} + 6 q^{12} - 16 q^{14} + 20 q^{16} - 5 q^{18} + 25 q^{20} + 3 q^{22} + 20 q^{24} - 4 q^{25} + 4 q^{26} + 12 q^{27} - 25 q^{28} - 10 q^{30} - 4 q^{33} + 4 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) \) 48 * q + 12 * q^3 + 4 * q^4 - 12 * q^9 + 4 * q^11 + 6 * q^12 - 16 * q^14 + 20 * q^16 - 5 * q^18 + 25 * q^20 + 3 * q^22 + 20 * q^24 - 4 * q^25 + 4 * q^26 + 12 * q^27 - 25 * q^28 - 10 * q^30 - 4 * q^33 + 4 * q^36 + 26 * q^38 - 65 * q^40 - 60 * q^41 - 4 * q^42 - 43 * q^44 - 5 * q^46 + 5 * q^48 - 12 * q^49 - 80 * q^50 - 15 * q^52 - 14 * q^56 + 73 * q^58 - 8 * q^59 - 25 * q^60 - 45 * q^62 - 38 * q^64 - 13 * q^66 + 8 * q^67 - 55 * q^68 - 40 * q^70 + 20 * q^72 + 60 * q^74 - 36 * q^75 + 46 * q^78 - 12 * q^81 - 35 * q^82 - 100 * q^83 + 45 * q^84 + 81 * q^86 - 18 * q^88 + 96 * q^89 + 10 * q^90 - 20 * q^91 + 59 * q^92 + 35 * q^94 - 40 * q^97 - 16 * q^99

Introduction

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