LMFDB - Embedded newform 966.2.bf.a.11.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(11,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 44, 27]))

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

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

chi := DirichletCharacter("966.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.bf (of order $66$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$64$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.16
Character	$\chi$	$=$	966.11
Dual form			966.2.bf.a.527.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.458227 + 0.888835i) q^{2} +(-0.118210 - 1.72801i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(0.829499 + 0.790926i) q^{5} +(1.59009 + 0.686752i) q^{6} +(2.21783 - 1.44264i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.97205 + 0.408537i) q^{9} +O(q^{10})$	\(q+(-0.458227 + 0.888835i) q^{2} +(-0.118210 - 1.72801i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(0.829499 + 0.790926i) q^{5} +(1.59009 + 0.686752i) q^{6} +(2.21783 - 1.44264i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.97205 + 0.408537i) q^{9} +(-1.08310 + 0.374865i) q^{10} +(-4.60895 + 2.37608i) q^{11} +(-1.33903 + 1.09864i) q^{12} +(-4.57275 + 5.27724i) q^{13} +(0.266002 + 2.63235i) q^{14} +(1.26867 - 1.52688i) q^{15} +(-0.327068 + 0.945001i) q^{16} +(-4.36579 - 0.416883i) q^{17} +(0.998751 - 2.82887i) q^{18} +(-0.149687 - 1.56760i) q^{19} +(0.163112 - 1.13447i) q^{20} +(-2.75507 - 3.66191i) q^{21} -5.18538i q^{22} +(1.89681 + 4.40478i) q^{23} +(-0.362929 - 1.69360i) q^{24} +(-0.175404 - 3.68219i) q^{25} +(-2.59524 - 6.48259i) q^{26} +(1.05728 + 5.08745i) q^{27} +(-2.46161 - 0.969779i) q^{28} +(-4.34390 + 1.98379i) q^{29} +(0.775805 + 1.82730i) q^{30} +(4.30663 + 1.72411i) q^{31} +(-0.690079 - 0.723734i) q^{32} +(4.65072 + 7.68345i) q^{33} +(2.37106 - 3.68945i) q^{34} +(2.98071 + 0.557471i) q^{35} +(2.05674 + 2.18399i) q^{36} +(-1.37919 + 0.334588i) q^{37} +(1.46193 + 0.585267i) q^{38} +(9.65968 + 7.27795i) q^{39} +(0.933616 + 0.664825i) q^{40} +(3.09276 + 10.5330i) q^{41} +(4.51728 - 0.770824i) q^{42} +(-8.13417 - 1.16952i) q^{43} +(4.60895 + 2.37608i) q^{44} +(-2.78844 - 2.01179i) q^{45} +(-4.78430 - 0.332441i) q^{46} +(2.17853 - 1.25777i) q^{47} +(1.67164 + 0.453469i) q^{48} +(2.83757 - 6.39908i) q^{49} +(3.35324 + 1.53137i) q^{50} +(-0.204298 + 7.59343i) q^{51} +(6.95117 + 0.663756i) q^{52} +(5.30939 - 1.02330i) q^{53} +(-5.00638 - 1.39145i) q^{54} +(-5.70242 - 1.67438i) q^{55} +(1.98995 - 1.74359i) q^{56} +(-2.69113 + 0.443967i) q^{57} +(0.227225 - 4.77004i) q^{58} +(-7.76772 + 2.68843i) q^{59} +(-1.97966 - 0.147754i) q^{60} +(-5.66701 - 7.20619i) q^{61} +(-3.50587 + 3.03785i) q^{62} +(-6.00214 + 5.19368i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-7.96700 + 0.760756i) q^{65} +(-8.96040 + 0.612964i) q^{66} +(3.59172 - 0.171095i) q^{67} +(2.19283 + 3.79809i) q^{68} +(7.38730 - 3.79839i) q^{69} +(-1.86134 + 2.39392i) q^{70} +(4.96204 + 7.72108i) q^{71} +(-2.88366 + 0.827346i) q^{72} +(-7.50739 - 10.5426i) q^{73} +(0.334588 - 1.37919i) q^{74} +(-6.34214 + 0.738373i) q^{75} +(-1.19010 + 1.03123i) q^{76} +(-6.79405 + 11.9188i) q^{77} +(-10.8952 + 5.25091i) q^{78} +(-1.41813 + 7.35796i) q^{79} +(-1.01873 + 0.525191i) q^{80} +(8.66620 - 2.42839i) q^{81} +(-10.7793 - 2.07753i) q^{82} +(-12.3510 - 3.62659i) q^{83} +(-1.38480 + 4.36833i) q^{84} +(-3.29170 - 3.79882i) q^{85} +(4.76680 - 6.69404i) q^{86} +(3.94151 + 7.27180i) q^{87} +(-4.22389 + 3.00782i) q^{88} +(0.275498 - 0.110293i) q^{89} +(3.06589 - 1.55661i) q^{90} +(-2.52843 + 18.3009i) q^{91} +(2.48778 - 4.10012i) q^{92} +(2.47020 - 7.64572i) q^{93} +(0.119695 + 2.51270i) q^{94} +(1.11569 - 1.41871i) q^{95} +(-1.16905 + 1.27802i) q^{96} +(2.02296 + 6.88956i) q^{97} +(4.38748 + 5.45436i) q^{98} +(12.7273 - 8.94476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9	$ 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9} + 64 q^{16} + 44 q^{18} - 132 q^{21} - 4 q^{24} + 72 q^{25} + 108 q^{27} + 44 q^{30} + 8 q^{36} + 44 q^{37} - 4 q^{39} - 88 q^{43} - 12 q^{46} + 60 q^{49} - 48 q^{54} + 96 q^{55} + 44 q^{58} - 176 q^{61} - 110 q^{63} + 128 q^{64} + 56 q^{69} - 120 q^{70} + 44 q^{72} + 40 q^{73} - 268 q^{75} + 16 q^{78} + 88 q^{79} + 8 q^{81} - 56 q^{82} - 22 q^{84} + 64 q^{85} - 42 q^{87} - 32 q^{93} + 8 q^{94} + 4 q^{96} + 132 q^{99}+O(q^{100}) $ 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9 + 64 * q^16 + 44 * q^18 - 132 * q^21 - 4 * q^24 + 72 * q^25 + 108 * q^27 + 44 * q^30 + 8 * q^36 + 44 * q^37 - 4 * q^39 - 88 * q^43 - 12 * q^46 + 60 * q^49 - 48 * q^54 + 96 * q^55 + 44 * q^58 - 176 * q^61 - 110 * q^63 + 128 * q^64 + 56 * q^69 - 120 * q^70 + 44 * q^72 + 40 * q^73 - 268 * q^75 + 16 * q^78 + 88 * q^79 + 8 * q^81 - 56 * q^82 - 22 * q^84 + 64 * q^85 - 42 * q^87 - 32 * q^93 + 8 * q^94 + 4 * q^96 + 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.458227	+	0.888835i	−0.324015	+	0.628502i
$2$	−0.458227	+	0.888835i	−0.324015	+	0.628502i
$3$	−0.118210	−	1.72801i	−0.0682486	−	0.997668i
$3$	−0.118210	−	1.72801i	−0.0682486	−	0.997668i
$4$	−0.580057	−	0.814576i	−0.290028	−	0.407288i
$5$	0.829499	+	0.790926i	0.370963	+	0.353713i	0.852513	−	0.522706i	$-0.175077\pi$
$5$	0.829499	+	0.790926i	0.370963	+	0.353713i	−0.481550	+	0.876419i	$0.659926\pi$
$6$	1.59009	+	0.686752i	0.649150	+	0.280365i
$7$	2.21783	−	1.44264i	0.838262	−	0.545268i
$7$	2.21783	−	1.44264i	0.838262	−	0.545268i
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	−2.97205	+	0.408537i	−0.990684	+	0.136179i
$10$	−1.08310	+	0.374865i	−0.342507	+	0.118543i
$11$	−4.60895	+	2.37608i	−1.38965	+	0.716415i	−0.980586	−	0.196090i	$-0.937175\pi$
$11$	−4.60895	+	2.37608i	−1.38965	+	0.716415i	−0.409065	+	0.912505i	$0.634145\pi$
$12$	−1.33903	+	1.09864i	−0.386544	+	0.317149i
$13$	−4.57275	+	5.27724i	−1.26825	+	1.46364i	−0.445459	+	0.895302i	$0.646960\pi$
$13$	−4.57275	+	5.27724i	−1.26825	+	1.46364i	−0.822794	+	0.568340i	$0.807586\pi$
$14$	0.266002	+	2.63235i	0.0710920	+	0.703524i
$15$	1.26867	−	1.52688i	0.327570	−	0.394239i
$16$	−0.327068	+	0.945001i	−0.0817670	+	0.236250i
$17$	−4.36579	−	0.416883i	−1.05886	−	0.101109i	−0.448933	−	0.893566i	$-0.648196\pi$
$17$	−4.36579	−	0.416883i	−1.05886	−	0.101109i	−0.609928	+	0.792457i	$0.708802\pi$
$18$	0.998751	−	2.82887i	0.235408	−	0.666771i
$19$	−0.149687	−	1.56760i	−0.0343406	−	0.359631i	−0.996267	−	0.0863232i	$-0.972488\pi$
$19$	−0.149687	−	1.56760i	−0.0343406	−	0.359631i	0.961927	−	0.273308i	$-0.0881178\pi$
$20$	0.163112	−	1.13447i	0.0364730	−	0.253676i
$21$	−2.75507	−	3.66191i	−0.601206	−	0.799094i
$22$		−	5.18538i		−	1.10553i
$23$	1.89681	+	4.40478i	0.395511	+	0.918461i
$23$	1.89681	+	4.40478i	0.395511	+	0.918461i
$24$	−0.362929	−	1.69360i	−0.0740825	−	0.345705i
$25$	−0.175404	−	3.68219i	−0.0350809	−	0.736439i
$26$	−2.59524	−	6.48259i	−0.508968	−	1.27134i
$27$	1.05728	+	5.08745i	0.203474	+	0.979080i
$28$	−2.46161	−	0.969779i	−0.465201	−	0.183271i
$29$	−4.34390	+	1.98379i	−0.806642	+	0.368381i	−0.775669	−	0.631139i	$-0.782588\pi$
$29$	−4.34390	+	1.98379i	−0.806642	+	0.368381i	−0.0309721	+	0.999520i	$0.509860\pi$
$30$	0.775805	+	1.82730i	0.141642	+	0.333618i
$31$	4.30663	+	1.72411i	0.773493	+	0.309660i	0.724623	−	0.689145i	$-0.242014\pi$
$31$	4.30663	+	1.72411i	0.773493	+	0.309660i	0.0488700	+	0.998805i	$0.484438\pi$
$32$	−0.690079	−	0.723734i	−0.121990	−	0.127939i
$33$	4.65072	+	7.68345i	0.809586	+	1.33752i
$34$	2.37106	−	3.68945i	0.406634	−	0.632735i
$35$	2.98071	+	0.557471i	0.503832	+	0.0942297i
$36$	2.05674	+	2.18399i	0.342791	+	0.363998i
$37$	−1.37919	+	0.334588i	−0.226737	+	0.0550059i	−0.347518	−	0.937673i	$-0.612975\pi$
$37$	−1.37919	+	0.334588i	−0.226737	+	0.0550059i	0.120781	+	0.992679i	$0.461460\pi$
$38$	1.46193	+	0.585267i	0.237156	+	0.0949428i
$39$	9.65968	+	7.27795i	1.54679	+	1.16540i
$40$	0.933616	+	0.664825i	0.147618	+	0.105118i
$41$	3.09276	+	10.5330i	0.483007	+	1.64497i	0.735612	+	0.677403i	$0.236894\pi$
$41$	3.09276	+	10.5330i	0.483007	+	1.64497i	−0.252605	+	0.967569i	$0.581287\pi$
$42$	4.51728	−	0.770824i	0.697032	−	0.118941i
$43$	−8.13417	−	1.16952i	−1.24045	−	0.178350i	−0.509313	−	0.860581i	$-0.670101\pi$
$43$	−8.13417	−	1.16952i	−1.24045	−	0.178350i	−0.731136	+	0.682231i	$0.761010\pi$
$44$	4.60895	+	2.37608i	0.694826	+	0.358207i
$45$	−2.78844	−	2.01179i	−0.415676	−	0.299900i
$46$	−4.78430	−	0.332441i	−0.705406	−	0.0490157i
$47$	2.17853	−	1.25777i	0.317771	−	0.183465i	−0.332627	−	0.943058i	$-0.607935\pi$
$47$	2.17853	−	1.25777i	0.317771	−	0.183465i	0.650399	+	0.759593i	$0.274602\pi$
$48$	1.67164	+	0.453469i	0.241280	+	0.0654526i
$49$	2.83757	−	6.39908i	0.405367	−	0.914154i
$50$	3.35324	+	1.53137i	0.474220	+	0.216569i
$51$	−0.204298	+	7.59343i	−0.0286074	+	1.06329i
$52$	6.95117	+	0.663756i	0.963953	+	0.0920464i
$53$	5.30939	−	1.02330i	0.729301	−	0.140561i	0.188933	−	0.981990i	$-0.439497\pi$
$53$	5.30939	−	1.02330i	0.729301	−	0.140561i	0.540368	+	0.841429i	$0.318285\pi$
$54$	−5.00638	−	1.39145i	−0.681282	−	0.189353i
$55$	−5.70242	−	1.67438i	−0.768915	−	0.225774i
$56$	1.98995	−	1.74359i	0.265918	−	0.232997i
$57$	−2.69113	+	0.443967i	−0.356449	+	0.0588049i
$58$	0.227225	−	4.77004i	0.0298361	−	0.626336i
$59$	−7.76772	+	2.68843i	−1.01127	+	0.350004i	−0.781946	−	0.623346i	$-0.785773\pi$
$59$	−7.76772	+	2.68843i	−1.01127	+	0.350004i	−0.229324	+	0.973350i	$0.573652\pi$
$60$	−1.97966	−	0.147754i	−0.255573	−	0.0190750i
$61$	−5.66701	−	7.20619i	−0.725586	−	0.922658i	0.273646	−	0.961830i	$-0.411770\pi$
$61$	−5.66701	−	7.20619i	−0.725586	−	0.922658i	−0.999232	+	0.0391726i	$0.987528\pi$
$62$	−3.50587	+	3.03785i	−0.445245	+	0.385807i
$63$	−6.00214	+	5.19368i	−0.756199	+	0.654342i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	−7.96700	+	0.760756i	−0.988184	+	0.0943601i
$66$	−8.96040	+	0.612964i	−1.10295	+	0.0754507i
$67$	3.59172	−	0.171095i	0.438799	−	0.0209026i	0.172979	−	0.984925i	$-0.444661\pi$
$67$	3.59172	−	0.171095i	0.438799	−	0.0209026i	0.265819	+	0.964023i	$0.414358\pi$
$68$	2.19283	+	3.79809i	0.265919	+	0.460586i
$69$	7.38730	−	3.79839i	0.889326	−	0.457273i
$70$	−1.86134	+	2.39392i	−0.222473	+	0.286128i
$71$	4.96204	+	7.72108i	0.588885	+	0.916324i	0.999989	+	0.00473485i	$0.00150716\pi$
$71$	4.96204	+	7.72108i	0.588885	+	0.916324i	−0.411103	+	0.911589i	$0.634856\pi$
$72$	−2.88366	+	0.827346i	−0.339843	+	0.0975036i
$73$	−7.50739	−	10.5426i	−0.878673	−	1.23392i	−0.971213	−	0.238215i	$-0.923438\pi$
$73$	−7.50739	−	10.5426i	−0.878673	−	1.23392i	0.0925396	−	0.995709i	$-0.470502\pi$
$74$	0.334588	−	1.37919i	0.0388950	−	0.160328i
$75$	−6.34214	+	0.738373i	−0.732327	+	0.0852600i
$76$	−1.19010	+	1.03123i	−0.136514	+	0.118290i
$77$	−6.79405	+	11.9188i	−0.774254	+	1.35828i
$78$	−10.8952	+	5.25091i	−1.23364	+	0.594549i
$79$	−1.41813	+	7.35796i	−0.159552	+	0.827835i	0.810649	+	0.585533i	$0.199115\pi$
$79$	−1.41813	+	7.35796i	−0.159552	+	0.827835i	−0.970201	+	0.242302i	$0.922098\pi$
$80$	−1.01873	+	0.525191i	−0.113897	+	0.0587181i
$81$	8.66620	−	2.42839i	0.962911	−	0.269821i
$82$	−10.7793	−	2.07753i	−1.19037	−	0.229425i
$83$	−12.3510	−	3.62659i	−1.35570	−	0.398070i	−0.478457	−	0.878111i	$-0.658804\pi$
$83$	−12.3510	−	3.62659i	−1.35570	−	0.398070i	−0.877246	+	0.480041i	$0.840622\pi$
$84$	−1.38480	+	4.36833i	−0.151094	+	0.476624i
$85$	−3.29170	−	3.79882i	−0.357035	−	0.412040i
$86$	4.76680	−	6.69404i	0.514017	−	0.721837i
$87$	3.94151	+	7.27180i	0.422574	+	0.779619i
$88$	−4.22389	+	3.00782i	−0.450268	+	0.320634i
$89$	0.275498	−	0.110293i	0.0292027	−	0.0116910i	−0.357015	−	0.934099i	$-0.616206\pi$
$89$	0.275498	−	0.110293i	0.0292027	−	0.0116910i	0.386218	+	0.922408i	$0.373781\pi$
$90$	3.06589	−	1.55661i	0.323173	−	0.164081i
$91$	−2.52843	+	18.3009i	−0.265052	+	1.91845i
$92$	2.48778	−	4.10012i	0.259369	−	0.427467i
$93$	2.47020	−	7.64572i	0.256148	−	0.792824i
$94$	0.119695	+	2.51270i	0.0123456	+	0.259165i
$95$	1.11569	−	1.41871i	0.114467	−	0.145557i
$96$	−1.16905	+	1.27802i	−0.119315	+	0.130437i
$97$	2.02296	+	6.88956i	0.205400	+	0.699529i	0.996172	+	0.0874174i	$0.0278614\pi$
$97$	2.02296	+	6.88956i	0.205400	+	0.699529i	−0.790772	+	0.612111i	$0.790320\pi$
$98$	4.38748	+	5.45436i	0.443202	+	0.550973i
$99$	12.7273	−	8.94476i	1.27914	−	0.898982i
$100$	−2.89768	+	2.27876i	−0.289768	+	0.227876i
$101$	−1.21681	−	1.27615i	−0.121077	−	0.126982i	0.660405	−	0.750909i	$-0.270385\pi$
$101$	−1.21681	−	1.27615i	−0.121077	−	0.126982i	−0.781482	+	0.623928i	$0.785536\pi$
$102$	−6.65569	−	3.66110i	−0.659012	−	0.362503i
$103$	2.14434	+	0.102148i	0.211288	+	0.0100649i	0.152959	−	0.988233i	$-0.451120\pi$
$103$	2.14434	+	0.102148i	0.211288	+	0.0100649i	0.0583291	+	0.998297i	$0.481423\pi$
$104$	−3.77518	+	5.87429i	−0.370187	+	0.576022i
$105$	0.610966	−	5.21661i	0.0596242	−	0.509089i
$106$	−1.52336	+	5.18808i	−0.147962	+	0.503911i
$107$	4.38761	−	3.45046i	0.424166	−	0.333568i	−0.383151	−	0.923686i	$-0.625161\pi$
$107$	4.38761	−	3.45046i	0.424166	−	0.333568i	0.807317	+	0.590118i	$0.200919\pi$
$108$	3.53083	−	3.81225i	0.339754	−	0.366834i
$109$	−1.06072	+	11.1083i	−0.101598	+	1.06399i	0.790597	+	0.612336i	$0.209770\pi$
$109$	−1.06072	+	11.1083i	−0.101598	+	1.06399i	−0.892196	+	0.451649i	$0.850836\pi$
$110$	4.10125	−	4.30127i	0.391039	−	0.410110i
$111$	0.741206	+	2.34370i	0.0703521	+	0.222455i
$112$	0.637916	+	2.56770i	0.0602774	+	0.242624i
$113$	−2.93899	+	1.88878i	−0.276477	+	0.177681i	−0.671530	−	0.740977i	$-0.734363\pi$
$113$	−2.93899	+	1.88878i	−0.276477	+	0.177681i	0.395053	+	0.918658i	$0.370726\pi$
$114$	0.838534	−	2.59541i	0.0785359	−	0.243082i
$115$	−1.91046	+	5.15400i	−0.178151	+	0.480613i
$116$	4.13566	+	2.38772i	0.383986	+	0.221694i
$117$	11.4345	−	17.5524i	1.05712	−	1.62272i
$118$	1.16980	−	8.13613i	0.107689	−	0.748992i
$119$	−10.2840	+	5.37370i	−0.942734	+	0.492607i
$120$	1.03846	−	1.69189i	0.0947983	−	0.154448i
$121$	9.21605	−	12.9421i	0.837823	−	1.17656i
$122$	9.00189	−	1.73497i	0.814993	−	0.157077i
$123$	17.8355	−	6.58942i	1.60817	−	0.594148i
$124$	−1.09367	−	4.50816i	−0.0982143	−	0.404845i
$125$	6.51965	−	7.52407i	0.583135	−	0.672974i
$126$	−1.86598	−	7.71480i	−0.166235	−	0.687289i
$127$	13.2531	+	8.51723i	1.17602	+	0.755782i	0.974650	−	0.223734i	$-0.0718245\pi$
$127$	13.2531	+	8.51723i	1.17602	+	0.755782i	0.201369	+	0.979515i	$0.435461\pi$
$128$	−0.189251	+	0.981929i	−0.0167276	+	0.0867911i
$129$	−1.05940	+	14.1942i	−0.0932749	+	1.24973i
$130$	2.97450	−	7.42995i	0.260881	−	0.651649i
$131$	−10.5332	−	3.64557i	−0.920287	−	0.318515i	−0.174468	−	0.984663i	$-0.555821\pi$
$131$	−10.5332	−	3.64557i	−0.920287	−	0.318515i	−0.745819	+	0.666148i	$0.767942\pi$
$132$	3.56107	−	8.24520i	0.309951	−	0.717653i
$133$	−2.59346	−	3.26072i	−0.224882	−	0.282740i
$134$	−1.49375	+	3.27085i	−0.129040	+	0.282558i
$135$	−3.14678	+	5.05627i	−0.270832	+	0.435174i
$136$	−4.38069	+	0.208678i	−0.375641	+	0.0178940i
$137$	−8.75985	+	15.1725i	−0.748405	+	1.29628i	0.200182	+	0.979759i	$0.435847\pi$
$137$	−8.75985	+	15.1725i	−0.748405	+	1.29628i	−0.948587	+	0.316516i	$0.897487\pi$
$138$	−0.00890983	+	8.30662i	−0.000758455	+	0.707106i
$139$	−14.6905			−1.24603			−0.623017	−	0.782208i	$-0.714093\pi$
$139$	−14.6905			−1.24603			−0.623017	+	0.782208i	$0.714093\pi$
$140$	−1.27488	−	2.75138i	−0.107747	−	0.232534i
$141$	−2.43097	−	3.61584i	−0.204725	−	0.304509i
$142$	−9.13651	+	0.872431i	−0.766719	+	0.0732127i
$143$	8.53646	−	35.1878i	0.713854	−	2.94255i
$144$	0.585996	−	2.94221i	0.0488330	−	0.245184i
$145$	−5.17229	−	1.79015i	−0.429535	−	0.148664i
$146$	12.8108	−	1.84191i	1.06023	−	0.152438i
$147$	−11.3931	−	4.14691i	−0.939688	−	0.342032i
$148$	1.07256	+	0.929375i	0.0881635	+	0.0763941i
$149$	0.314100	−	6.59378i	0.0257321	−	0.540183i	−0.948792	−	0.315901i	$-0.897693\pi$
$149$	0.314100	−	6.59378i	0.0257321	−	0.540183i	0.974524	−	0.224282i	$-0.0720037\pi$
$150$	2.24984	−	5.97546i	0.183699	−	0.487894i
$151$	3.73327	+	10.7866i	0.303809	+	0.877799i	0.988800	+	0.149247i	$0.0476851\pi$
$151$	3.73327	+	10.7866i	0.303809	+	0.877799i	−0.684991	+	0.728552i	$0.740194\pi$
$152$	−0.371256	−	1.53034i	−0.0301128	−	0.124127i
$153$	13.1457	−	0.544590i	1.06277	−	0.0440275i
$154$	−7.48065	−	11.5003i	−0.602808	−	0.926722i
$155$	2.20870	+	4.83637i	0.177407	+	0.388467i
$156$	0.325281	−	12.0902i	0.0260433	−	0.967988i
$157$	17.2933	−	12.3145i	1.38016	−	0.982806i	0.381875	−	0.924214i	$-0.375278\pi$
$157$	17.2933	−	12.3145i	1.38016	−	0.982806i	0.998282	−	0.0585917i	$-0.0186610\pi$
$158$	−5.89019	−	4.63209i	−0.468598	−	0.368510i
$159$	−2.39590	−	9.05373i	−0.190007	−	0.718007i
$160$		−	1.14614i		−	0.0906102i
$161$	10.5613	+	7.03266i	0.832349	+	0.554252i
$162$	−1.81265	+	8.81557i	−0.142415	+	0.692617i
$163$	5.66232	+	2.91913i	0.443507	+	0.228644i	0.665490	−	0.746407i	$-0.268223\pi$
$163$	5.66232	+	2.91913i	0.443507	+	0.228644i	−0.221983	+	0.975051i	$0.571253\pi$
$164$	6.78592	−	8.62900i	0.529891	−	0.673812i
$165$	−2.21927	+	10.0518i	−0.172770	+	0.782530i
$166$	8.88302	−	9.31624i	0.689456	−	0.723081i
$167$	2.75502	−	1.25818i	0.213190	−	0.0973606i	−0.305958	−	0.952045i	$-0.598977\pi$
$167$	2.75502	−	1.25818i	0.213190	−	0.0973606i	0.519148	+	0.854684i	$0.326249\pi$
$168$	−3.24817	−	3.23255i	−0.250602	−	0.249396i
$169$	−5.08908	−	35.3953i	−0.391468	−	2.72272i
$170$	4.88487	−	1.18506i	0.374653	−	0.0908897i
$171$	1.08530	+	4.59782i	0.0829949	+	0.351604i
$172$	3.76562	+	7.30429i	0.287126	+	0.556947i
$173$	9.88504	+	0.470882i	0.751546	+	0.0358005i	0.419859	−	0.907589i	$-0.362079\pi$
$173$	9.88504	+	0.470882i	0.751546	+	0.0358005i	0.331686	+	0.943390i	$0.392382\pi$
$174$	−8.26954	+	0.171219i	−0.626912	+	0.0129801i
$175$	−5.70110	−	7.91344i	−0.430963	−	0.598200i
$176$	−0.737957	−	5.13260i	−0.0556256	−	0.386884i
$177$	5.56387	+	13.1049i	0.418206	+	0.985026i
$178$	−0.0282083	+	0.295411i	−0.00211430	+	0.0221420i
$179$	−23.2926	−	5.65073i	−1.74097	−	0.422355i	−0.765671	−	0.643233i	$-0.777593\pi$
$179$	−23.2926	−	5.65073i	−1.74097	−	0.422355i	−0.975302	+	0.220877i	$0.929108\pi$
$180$	−0.0213053	+	3.43835i	−0.00158800	+	0.256279i
$181$	−7.95882	−	1.14431i	−0.591574	−	0.0850556i	−0.159975	−	0.987121i	$-0.551141\pi$
$181$	−7.95882	−	1.14431i	−0.591574	−	0.0850556i	−0.431599	+	0.902065i	$0.642051\pi$
$182$	−15.1079	−	10.6333i	−1.11987	−	0.788193i
$183$	−11.7825	+	10.6445i	−0.870986	+	0.786864i
$184$	2.50437	+	4.09001i	0.184624	+	0.301519i
$185$	−1.40867	−	0.813296i	−0.103567	−	0.0597947i
$186$	5.66387	+	5.69907i	0.415295	+	0.417876i
$187$	21.1123	−	8.45208i	1.54388	−	0.618077i
$188$	−2.28822	−	1.04500i	−0.166886	−	0.0762142i
$189$	9.68425	+	9.75783i	0.704425	+	0.709778i
$190$	0.749763	+	1.64175i	0.0543935	+	0.119105i
$191$	1.43024	−	4.13240i	0.103488	−	0.299010i	−0.881355	−	0.472454i	$-0.843368\pi$
$191$	1.43024	−	4.13240i	0.103488	−	0.299010i	0.984844	+	0.173444i	$0.0554895\pi$
$192$	−0.600259	−	1.62471i	−0.0433200	−	0.117253i
$193$	−14.2838	+	13.6196i	−1.02817	+	0.980360i	−0.999815	−	0.0192380i	$-0.993876\pi$
$193$	−14.2838	+	13.6196i	−1.02817	+	0.980360i	−0.0283569	+	0.999598i	$0.509027\pi$
$194$	−7.05066	−	1.35890i	−0.506208	−	0.0975635i
$195$	2.25637	+	13.6771i	0.161582	+	0.979440i
$196$	−6.85849	+	1.40042i	−0.489892	+	0.100030i
$197$	−1.95843	−	1.69699i	−0.139532	−	0.120905i	0.582298	−	0.812975i	$-0.302154\pi$
$197$	−1.95843	−	1.69699i	−0.139532	−	0.120905i	−0.721831	+	0.692070i	$0.756699\pi$
$198$	2.11842	+	15.4112i	0.150549	+	1.09523i
$199$	−1.72698	+	4.31379i	−0.122422	+	0.305797i	−0.976902	−	0.213689i	$-0.931452\pi$
$199$	−1.72698	+	4.31379i	−0.122422	+	0.305797i	0.854479	+	0.519485i	$0.173876\pi$
$200$	−0.697650	−	3.61975i	−0.0493313	−	0.255955i
$201$	−0.720231	−	6.18631i	−0.0508012	−	0.436349i
$202$	1.69186	−	0.496776i	0.119039	−	0.0349530i
$203$	−6.77214	+	10.6664i	−0.475311	+	0.748635i
$204$	6.30393	−	4.23820i	0.441363	−	0.296734i
$205$	−5.76535	+	11.1832i	−0.402670	+	0.781070i
$206$	−1.07339	+	1.85916i	−0.0747864	+	0.129534i
$207$	−7.43692	−	12.3163i	−0.516902	−	0.856045i
$208$	−3.49139	−	6.04727i	−0.242085	−	0.419303i
$209$	4.41463	+	6.86930i	0.305367	+	0.475160i
$210$	4.35674	+	2.93344i	0.300644	+	0.202426i
$211$	5.71725	−	12.5190i	0.393592	−	0.861845i	−0.604289	−	0.796766i	$-0.706543\pi$
$211$	5.71725	−	12.5190i	0.393592	−	0.861845i	0.997880	−	0.0650797i	$-0.0207302\pi$
$212$	−3.91330	−	3.73133i	−0.268767	−	0.256269i
$213$	12.7556	−	9.48717i	0.873996	−	0.650050i
$214$	1.05637	+	5.48096i	0.0722118	+	0.374670i
$215$	−5.82229	−	7.40364i	−0.397077	−	0.504924i
$216$	1.77054	+	4.88520i	0.120470	+	0.332396i
$217$	12.0387	−	2.38913i	0.817238	−	0.162185i
$218$	−9.38743	−	6.03294i	−0.635797	−	0.408602i
$219$	−17.3304	+	14.2191i	−1.17108	+	0.960838i
$220$	1.94382	+	5.61629i	0.131052	+	0.378650i
$221$	22.1637	−	21.1330i	1.49089	−	1.42156i
$222$	−2.42281	−	0.415138i	−0.162608	−	0.0278622i
$223$	5.40119	+	6.23330i	0.361690	+	0.417413i	0.907205	−	0.420688i	$-0.138211\pi$
$223$	5.40119	+	6.23330i	0.361690	+	0.417413i	−0.545515	+	0.838101i	$0.683666\pi$
$224$	−2.57457	−	0.609584i	−0.172021	−	0.0407295i
$225$	2.02562	+	10.8720i	0.135041	+	0.724801i
$226$	−0.332086	−	3.47777i	−0.0220901	−	0.231338i
$227$	9.29087	+	7.30642i	0.616657	+	0.484944i	0.876948	−	0.480586i	$-0.159576\pi$
$227$	9.29087	+	7.30642i	0.616657	+	0.484944i	−0.260291	+	0.965530i	$0.583818\pi$
$228$	1.92265	+	1.93460i	0.127331	+	0.128122i
$229$	10.9384	−	6.31531i	0.722832	−	0.417327i	−0.0929621	−	0.995670i	$-0.529634\pi$
$229$	10.9384	−	6.31531i	0.722832	−	0.417327i	0.815794	+	0.578342i	$0.196300\pi$
$230$	−3.70563	−	4.05978i	−0.244342	−	0.267694i
$231$	21.3990	+	10.3313i	1.40795	+	0.679748i
$232$	−4.01736	+	2.58180i	−0.263753	+	0.169504i
$233$	−2.62798	−	6.56438i	−0.172165	−	0.430047i	0.817041	−	0.576580i	$-0.195613\pi$
$233$	−2.62798	−	6.56438i	−0.172165	−	0.430047i	−0.989206	+	0.146533i	$0.953189\pi$
$234$	10.3616	+	18.2064i	0.677357	+	1.19019i
$235$	2.80189	+	0.679732i	0.182775	+	0.0443408i
$236$	6.69565	+	4.76795i	0.435850	+	0.310367i
$237$	12.8823	+	1.58076i	0.836794	+	0.102681i
$238$	−0.0639296	−	11.6032i	−0.00414394	−	0.752122i
$239$	−0.667429	+	2.27306i	−0.0431724	+	0.147032i	−0.978259	−	0.207388i	$-0.933504\pi$
$239$	−0.667429	+	2.27306i	−0.0431724	+	0.147032i	0.935086	+	0.354420i	$0.115322\pi$
$240$	1.02796	+	1.69829i	0.0663545	+	0.109624i
$241$	−5.60739	−	10.8768i	−0.361204	−	0.700638i	0.636286	−	0.771454i	$-0.280470\pi$
$241$	−5.60739	−	10.8768i	−0.361204	−	0.700638i	−0.997489	+	0.0708159i	$0.977440\pi$
$242$	7.28039	+	14.1220i	0.468001	+	0.907796i
$243$	−5.22071	−	14.6882i	−0.334909	−	0.942251i
$244$	−2.58280	+	8.79621i	−0.165347	+	0.563119i
$245$	7.41495	−	3.06373i	0.473724	−	0.195734i
$246$	−2.31578	+	18.8723i	−0.147649	+	1.20325i
$247$	8.95706	+	6.37829i	0.569924	+	0.405841i
$248$	4.50816	+	1.09367i	0.286269	+	0.0694480i
$249$	−4.80678	+	21.7714i	−0.304617	+	1.37971i
$250$	3.70019	+	9.24262i	0.234020	+	0.584555i
$251$	20.2131	−	12.9902i	1.27584	−	0.819933i	0.285472	−	0.958387i	$-0.407850\pi$
$251$	20.2131	−	12.9902i	1.27584	−	0.819933i	0.990369	+	0.138454i	$0.0442134\pi$
$252$	7.71223	+	1.87657i	0.485825	+	0.118213i
$253$	−19.2084	−	15.7945i	−1.20762	−	0.992990i
$254$	−13.6433	+	7.87698i	−0.856058	+	0.494245i
$255$	−6.17530	+	6.13715i	−0.386712	+	0.384324i
$256$	−0.786053	−	0.618159i	−0.0491283	−	0.0386349i
$257$	−1.18851	−	12.4467i	−0.0741374	−	0.776402i	−0.953728	−	0.300670i	$-0.902790\pi$
$257$	−1.18851	−	12.4467i	−0.0741374	−	0.776402i	0.879591	−	0.475731i	$-0.157816\pi$
$258$	−12.1309	−	7.44579i	−0.755234	−	0.463555i
$259$	−2.57612	+	2.73174i	−0.160072	+	0.169742i
$260$	5.24100	+	6.04844i	0.325033	+	0.375108i
$261$	12.0998	−	7.67058i	0.748961	−	0.474797i
$262$	8.06689	−	7.69176i	0.498374	−	0.475199i
$263$	4.51934	+	13.0578i	0.278675	+	0.805177i	0.994293	+	0.106686i	$0.0340238\pi$
$263$	4.51934	+	13.0578i	0.278675	+	0.805177i	−0.715618	+	0.698492i	$0.753855\pi$
$264$	5.69685	+	6.94338i	0.350617	+	0.427335i
$265$	5.21349	+	3.35051i	0.320262	+	0.205820i
$266$	4.08664	−	0.811012i	0.250568	−	0.0497263i
$267$	−0.223154	−	0.463026i	−0.0136568	−	0.0283367i
$268$	−2.22277	−	2.82649i	−0.135777	−	0.172655i
$269$	0.733427	+	3.80538i	0.0447179	+	0.232018i	0.997411	−	0.0719167i	$-0.0229116\pi$
$269$	0.733427	+	3.80538i	0.0447179	+	0.232018i	−0.952693	+	0.303935i	$0.901699\pi$
$270$	−3.05225	−	5.11389i	−0.185754	−	0.311221i
$271$	6.47615	+	6.17500i	0.393398	+	0.375104i	0.860802	−	0.508939i	$-0.169962\pi$
$271$	6.47615	+	6.17500i	0.393398	+	0.375104i	−0.467404	+	0.884044i	$0.654811\pi$
$272$	1.82187	−	3.98933i	0.110467	−	0.241889i
$273$	31.9230	+	2.20582i	1.93207	+	0.133502i
$274$	−9.47187	−	14.7385i	−0.572217	−	0.890386i
$275$	9.55761	+	16.5543i	0.576346	+	0.998260i
$276$	−7.37913	−	3.81423i	−0.444172	−	0.229590i
$277$	8.84122	−	15.3134i	0.531217	−	0.920095i	−0.468119	−	0.883665i	$-0.655068\pi$
$277$	8.84122	−	15.3134i	0.531217	−	0.920095i	0.999336	−	0.0364297i	$-0.0115985\pi$
$278$	6.73159	−	13.0575i	0.403734	−	0.783134i
$279$	−13.5039	−	3.36474i	−0.808457	−	0.201442i
$280$	3.02971	+	0.127597i	0.181060	+	0.00762536i
$281$	−12.7292	+	3.73764i	−0.759363	+	0.222969i	−0.638418	−	0.769690i	$-0.720411\pi$
$281$	−12.7292	+	3.73764i	−0.759363	+	0.222969i	−0.120945	+	0.992659i	$0.538592\pi$
$282$	4.32783	−	0.503860i	0.257718	−	0.0300044i
$283$	−1.77272	−	9.19773i	−0.105377	−	0.546749i	−0.995795	−	0.0916053i	$-0.970800\pi$
$283$	−1.77272	−	9.19773i	−0.105377	−	0.546749i	0.890418	−	0.455143i	$-0.150412\pi$
$284$	3.41114	−	8.52062i	0.202414	−	0.505606i
$285$	−2.58343	−	1.76021i	−0.153029	−	0.104266i
$286$	27.3645	+	23.7115i	1.61810	+	1.40209i
$287$	22.0545	+	18.8986i	1.30184	+	1.11555i
$288$	2.34662	+	1.86905i	0.138276	+	0.110135i
$289$	2.19358	+	0.422778i	0.129034	+	0.0248693i
$290$	3.96123	−	3.77702i	0.232611	−	0.221794i
$291$	11.6661	−	4.31011i	0.683879	−	0.252663i
$292$	−4.23308	+	12.2307i	−0.247722	+	0.715746i
$293$	−6.98320	−	15.2911i	−0.407963	−	0.893315i	−0.996400	−	0.0847718i	$-0.972984\pi$
$293$	−6.98320	−	15.2911i	−0.407963	−	0.893315i	0.588437	−	0.808543i	$-0.299743\pi$
$294$	8.90655	−	8.22638i	0.519441	−	0.479772i
$295$	−8.56967	−	3.91363i	−0.498945	−	0.227861i
$296$	−1.31753	+	0.527461i	−0.0765801	+	0.0306581i
$297$	−16.9612	−	20.9356i	−0.984186	−	1.21481i
$298$	5.71685	+	3.30063i	0.331168	+	0.191200i
$299$	−31.9187	−	10.1321i	−1.84591	−	0.585954i
$300$	4.28026	+	4.73786i	0.247121	+	0.273540i
$301$	−19.7274	+	9.14091i	−1.13707	+	0.526873i
$302$	−11.2982	−	1.62443i	−0.650137	−	0.0934756i
$303$	−2.06137	+	2.25351i	−0.118422	+	0.129461i
$304$	1.53034	+	0.371256i	0.0877709	+	0.0212930i
$305$	0.998781	−	10.4597i	0.0571900	−	0.598921i
$306$	−5.53965	+	11.9339i	−0.316681	+	0.682215i
$307$	−0.614161	−	4.27158i	−0.0350520	−	0.243792i	0.964761	−	0.263128i	$-0.0847540\pi$
$307$	−0.614161	−	4.27158i	−0.0350520	−	0.243792i	−0.999813	+	0.0193355i	$0.993845\pi$
$308$	13.6497	−	1.37932i	0.777765	−	0.0785941i
$309$	−0.0769704	−	3.71752i	−0.00437870	−	0.211483i
$310$	−5.31083	−	0.252986i	−0.301635	−	0.0143686i
$311$	−0.988065	−	1.91658i	−0.0560280	−	0.108679i	0.859159	−	0.511709i	$-0.170987\pi$
$311$	−0.988065	−	1.91658i	−0.0560280	−	0.108679i	−0.915187	+	0.403030i	$0.867957\pi$
$312$	10.5971	+	5.82915i	0.599943	+	0.330011i
$313$	2.69658	−	0.654184i	0.152420	−	0.0369767i	−0.158823	−	0.987307i	$-0.550770\pi$
$313$	2.69658	−	0.654184i	0.152420	−	0.0369767i	0.311243	+	0.950330i	$0.399255\pi$
$314$	3.02132	+	21.0138i	0.170503	+	1.18587i
$315$	−9.08658	−	0.439101i	−0.511971	−	0.0247406i
$316$	6.81621	−	3.11286i	0.383442	−	0.175112i
$317$	−16.4088	+	17.2090i	−0.921608	+	0.966554i	−0.999538	−	0.0304047i	$-0.990320\pi$
$317$	−16.4088	+	17.2090i	−0.921608	+	0.966554i	0.0779302	+	0.996959i	$0.475169\pi$
$318$	9.14514	+	2.01910i	0.512834	+	0.113225i
$319$	15.3072	−	19.4646i	0.857037	−	1.08981i
$320$	1.01873	+	0.525191i	0.0569486	+	0.0293591i
$321$	−6.48109	−	7.17397i	−0.361739	−	0.400412i
$322$	−11.0904	+	6.16473i	−0.618042	+	0.343547i
$323$			6.90620i			0.384271i
$324$	−7.00499	−	5.65067i	−0.389166	−	0.313926i
$325$	20.2339	+	15.9121i	1.12237	+	0.882645i
$326$	−5.18925	+	3.69525i	−0.287406	+	0.204661i
$327$	19.3207	+	0.519816i	1.06844	+	0.0287459i
$328$	4.56027	+	9.98561i	0.251799	+	0.551363i
$329$	3.01710	−	5.93237i	0.166338	−	0.327062i
$330$	−7.91745	−	6.57856i	−0.435842	−	0.362138i
$331$	7.59379	+	31.3020i	0.417392	+	1.72051i	0.660775	+	0.750584i	$0.270228\pi$
$331$	7.59379	+	31.3020i	0.417392	+	1.72051i	−0.243382	+	0.969930i	$0.578257\pi$
$332$	4.21017	+	12.1645i	0.231063	+	0.667613i
$333$	3.96233	−	1.55786i	0.217134	−	0.0853703i
$334$	−0.144112	+	3.02529i	−0.00788548	+	0.165537i
$335$	3.11465	+	2.69886i	0.170172	+	0.147455i
$336$	4.36160	−	1.40585i	0.237945	−	0.0766956i
$337$	−3.84005	+	0.552116i	−0.209181	+	0.0300757i	−0.246108	−	0.969242i	$-0.579152\pi$
$337$	−3.84005	+	0.552116i	−0.209181	+	0.0300757i	0.0369277	+	0.999318i	$0.488243\pi$
$338$	33.7926	+	11.6957i	1.83807	+	0.636163i
$339$	3.61125	+	4.85534i	0.196136	+	0.263706i
$340$	−1.18506	+	4.88487i	−0.0642687	+	0.264919i
$341$	−23.9457	+	2.28653i	−1.29673	+	0.123823i
$342$	−4.58402	−	1.14219i	−0.247876	−	0.0617627i
$343$	−2.93834	−	18.2857i	−0.158655	−	0.987334i
$344$	−8.21782			−0.443075
$345$	9.13200	+	2.69204i	0.491651	+	0.144935i
$346$	−4.94812	+	8.57040i	−0.266013	+	0.460748i
$347$	−20.1807	+	0.961326i	−1.08336	+	0.0516067i	−0.581657	−	0.813434i	$-0.697595\pi$
$347$	−20.1807	+	0.961326i	−1.08336	+	0.0516067i	−0.501701	+	0.865041i	$0.667292\pi$
$348$	3.63714	−	7.42872i	0.194971	−	0.398221i
$349$	−10.3675	+	22.7017i	−0.554962	+	1.21520i	0.399464	+	0.916749i	$0.369196\pi$
$349$	−10.3675	+	22.7017i	−0.554962	+	1.21520i	−0.954426	+	0.298448i	$0.903531\pi$
$350$	9.64615	−	1.44120i	0.515608	−	0.0770351i
$351$	−31.6824	−	17.6841i	−1.69108	−	0.943908i
$352$	4.90019	+	1.69597i	0.261181	+	0.0903956i
$353$	4.95071	−	12.3663i	0.263500	−	0.658191i	−0.736330	−	0.676622i	$-0.763443\pi$
$353$	4.95071	−	12.3663i	0.263500	−	0.658191i	0.999830	+	0.0184314i	$0.00586724\pi$
$354$	−14.1976	−	1.05966i	−0.754595	−	0.0563200i
$355$	−1.99080	+	10.3292i	−0.105660	+	0.548219i
$356$	−0.249646	−	0.160438i	−0.0132312	−	0.00850319i
$357$	10.5015	+	17.1357i	0.555798	+	0.906916i
$358$	15.6959	−	18.1140i	0.829552	−	0.957354i
$359$	−0.475317	−	1.95928i	−0.0250863	−	0.103407i	0.957892	−	0.287128i	$-0.0927007\pi$
$359$	−0.475317	−	1.95928i	−0.0250863	−	0.103407i	−0.982978	+	0.183722i	$0.941186\pi$
$360$	−3.04636	−	1.59448i	−0.160557	−	0.0840364i
$361$	16.2217	−	3.12648i	0.853773	−	0.164551i
$362$	4.66404	−	6.54973i	0.245137	−	0.344246i
$363$	−23.4536	−	14.3956i	−1.23099	−	0.755571i
$364$	16.3741	−	8.55595i	0.858235	−	0.448454i
$365$	2.11108	−	14.6829i	0.110499	−	0.768538i
$366$	−4.06217	−	15.3503i	−0.212333	−	0.802372i
$367$	16.5960	+	9.58171i	0.866304	+	0.500161i	0.866118	−	0.499839i	$-0.166607\pi$
$367$	16.5960	+	9.58171i	0.866304	+	0.500161i	0.000185929		1.00000i	$0.499941\pi$
$368$	−4.78291	+	0.351819i	−0.249326	+	0.0183399i
$369$	−13.4949	−	30.0410i	−0.702518	−	1.56387i
$370$	1.36838	−	0.879402i	0.0711385	−	0.0457179i
$371$	10.2991	−	9.92906i	0.534702	−	0.515491i
$372$	−7.66087	+	2.42278i	−0.397198	+	0.125615i
$373$	−20.0525	+	21.0304i	−1.03828	+	1.08891i	−0.0423192	+	0.999104i	$0.513475\pi$
$373$	−20.0525	+	21.0304i	−1.03828	+	1.08891i	−0.995959	+	0.0898106i	$0.971374\pi$
$374$	−2.16170	+	22.6383i	−0.111779	+	1.17060i
$375$	−13.7724	−	10.3766i	−0.711203	−	0.535846i
$376$	1.97736	−	1.55501i	0.101974	−	0.0801935i
$377$	9.39463	−	31.9952i	0.483848	−	1.64783i
$378$	−13.1107	+	4.13641i	−0.674341	+	0.212754i
$379$	−4.63751	+	7.21611i	−0.238213	+	0.370667i	−0.939691	−	0.342024i	$-0.888887\pi$
$379$	−4.63751	+	7.21611i	−0.238213	+	0.370667i	0.701478	+	0.712691i	$0.252524\pi$
$380$	−1.80281	−	0.0858784i	−0.0924822	−	0.00440547i
$381$	13.1512	−	23.9083i	0.673758	−	1.22486i
$382$	3.01765	+	3.16482i	0.154396	+	0.161926i
$383$	−26.4105	+	20.7694i	−1.34951	+	1.06127i	−0.357664	+	0.933850i	$0.616427\pi$
$383$	−26.4105	+	20.7694i	−1.34951	+	1.06127i	−0.991849	+	0.127418i	$0.959331\pi$
$384$	1.71916	+	0.210955i	0.0877303	+	0.0107652i
$385$	−15.0626	+	4.51306i	−0.767659	+	0.230007i
$386$	−5.56035	−	18.9368i	−0.283015	−	0.963859i
$387$	24.6530	+	0.152759i	1.25318	+	0.00776518i
$388$	4.43864	−	5.64419i	0.225338	−	0.286540i
$389$	0.414413	+	8.69959i	0.0210116	+	0.441087i	0.984722	+	0.174136i	$0.0557132\pi$
$389$	0.414413	+	8.69959i	0.0210116	+	0.441087i	−0.963710	+	0.266951i	$0.913984\pi$
$390$	−13.1907	−	4.26168i	−0.667935	−	0.215799i
$391$	−6.44479	−	20.0211i	−0.325927	−	1.01251i
$392$	1.89800	−	6.73777i	0.0958635	−	0.340309i
$393$	−5.05446	+	18.6324i	−0.254964	+	0.939880i
$394$	2.40575	−	0.963116i	0.121200	−	0.0485211i
$395$	−6.99593	+	4.98178i	−0.352004	+	0.250661i
$396$	−14.6688	−	5.17891i	−0.737133	−	0.260250i
$397$	−14.8462	+	20.8485i	−0.745107	+	1.04636i	0.251801	+	0.967779i	$0.418977\pi$
$397$	−14.8462	+	20.8485i	−0.745107	+	1.04636i	−0.996908	+	0.0785773i	$0.974962\pi$
$398$	−3.04290	−	3.51170i	−0.152527	−	0.176025i
$399$	−5.32799	+	4.86698i	−0.266733	+	0.243654i
$400$	3.53704	+	1.03857i	0.176852	+	0.0519285i
$401$	6.61658	+	1.27524i	0.330416	+	0.0636825i	0.351762	−	0.936090i	$-0.385583\pi$
$401$	6.61658	+	1.27524i	0.330416	+	0.0636825i	−0.0213452	+	0.999772i	$0.506795\pi$
$402$	5.82864	+	2.19457i	0.290706	+	0.109455i
$403$	−28.7917	+	14.8432i	−1.43422	+	0.739390i
$404$	−0.333704	+	1.73142i	−0.0166024	+	0.0861415i
$405$	9.10927	+	4.83997i	0.452643	+	0.240500i
$406$	−6.37751	−	10.9069i	−0.316510	−	0.541303i
$407$	5.56161	−	4.81916i	0.275679	−	0.238877i
$408$	0.878439	+	7.54521i	0.0434892	+	0.373544i
$409$	7.71968	−	31.8210i	0.381714	−	1.57345i	−0.379656	−	0.925128i	$-0.623958\pi$
$409$	7.71968	−	31.8210i	0.381714	−	1.57345i	0.761370	−	0.648318i	$-0.224527\pi$
$410$	−7.29821	−	10.2489i	−0.360433	−	0.506157i
$411$	27.2538	+	13.3436i	1.34433	+	0.658191i
$412$	−1.16063	−	1.80598i	−0.0571803	−	0.0889743i
$413$	−13.3491	+	17.1685i	−0.656864	+	0.844808i
$414$	14.3550	−	0.966529i	0.705509	−	0.0475023i
$415$	−7.37681	−	12.7770i	−0.362113	−	0.627199i
$416$	6.97488	−	0.332254i	0.341971	−	0.0162901i
$417$	1.73657	+	25.3854i	0.0850401	+	1.24313i
$418$	−8.12858	+	0.776186i	−0.397582	+	0.0379645i
$419$	−6.60973	+	1.94079i	−0.322906	+	0.0948139i	−0.439169	−	0.898405i	$-0.644727\pi$
$419$	−6.60973	+	1.94079i	−0.322906	+	0.0948139i	0.116262	+	0.993219i	$0.462909\pi$
$420$	−4.60372	+	2.52825i	−0.224638	+	0.123366i
$421$	18.3120	−	15.8674i	0.892473	−	0.773332i	−0.0822823	−	0.996609i	$-0.526221\pi$
$421$	18.3120	−	15.8674i	0.892473	−	0.773332i	0.974755	+	0.223277i	$0.0716755\pi$
$422$	8.50756	+	10.8182i	0.414142	+	0.526624i
$423$	−5.96086	+	4.62818i	−0.289827	+	0.225030i
$424$	5.10972	−	1.76849i	0.248150	−	0.0858855i
$425$	−0.769263	+	16.1488i	−0.0373147	+	0.783333i
$426$	2.58760	+	15.6849i	0.125370	+	0.759934i
$427$	−22.9644	−	7.80665i	−1.11133	−	0.377790i
$428$	−5.35572	−	1.57258i	−0.258879	−	0.0760136i
$429$	−61.8140	−	10.5916i	−2.98441	−	0.511365i
$430$	9.24854	−	1.78251i	0.446004	−	0.0859603i
$431$	−2.32777	−	0.222275i	−0.112125	−	0.0107066i	0.0388429	−	0.999245i	$-0.487633\pi$
$431$	−2.32777	−	0.222275i	−0.112125	−	0.0107066i	−0.150967	+	0.988539i	$0.548239\pi$
$432$	−5.15345	−	0.664809i	−0.247945	−	0.0319856i
$433$	−6.98695	−	3.19083i	−0.335771	−	0.153342i	0.240393	−	0.970676i	$-0.422724\pi$
$433$	−6.98695	−	3.19083i	−0.335771	−	0.153342i	−0.576164	+	0.817334i	$0.695451\pi$
$434$	−3.39289	+	11.7952i	−0.162864	+	0.566185i
$435$	−2.48198	+	9.14939i	−0.119002	+	0.438680i
$436$	9.66386	−	5.57943i	0.462815	−	0.267206i
$437$	6.62099	−	3.63277i	0.316725	−	0.173779i
$438$	−4.69720	−	21.9194i	−0.224441	−	1.04735i
$439$	−22.3775	−	11.5364i	−1.06802	−	0.550603i	−0.167704	−	0.985837i	$-0.553635\pi$
$439$	−22.3775	−	11.5364i	−1.06802	−	0.550603i	−0.900317	+	0.435234i	$0.856665\pi$
$440$	−5.88267	−	0.845800i	−0.280445	−	0.0403219i
$441$	−5.81914	+	20.1777i	−0.277102	+	0.960841i
$442$	8.62780	+	29.3836i	0.410383	+	1.39763i
$443$	6.78616	+	4.83240i	0.322420	+	0.229594i	0.729794	−	0.683667i	$-0.239616\pi$
$443$	6.78616	+	4.83240i	0.322420	+	0.229594i	−0.407374	+	0.913261i	$0.633555\pi$
$444$	1.47918	−	1.96325i	0.0701990	−	0.0931717i
$445$	0.315758	+	0.126411i	0.0149684	+	0.00599244i
$446$	−8.01535	+	1.94450i	−0.379538	+	0.0920748i
$447$	−11.4313	+	0.236681i	−0.540680	+	0.0111946i
$448$	1.72156	−	2.00904i	0.0813359	−	0.0949183i
$449$	15.6219	−	24.3082i	0.737244	−	1.14717i	−0.246768	−	0.969075i	$-0.579369\pi$
$449$	15.6219	−	24.3082i	0.737244	−	1.14717i	0.984012	−	0.178100i	$-0.0569950\pi$
$450$	−10.5916	−	3.18140i	−0.499294	−	0.149973i
$451$	−39.2815	−	41.1973i	−1.84969	−	1.93990i
$452$	3.24333	+	1.29843i	0.152554	+	0.0610732i
$453$	18.1980	−	7.72622i	0.855018	−	0.363009i
$454$	−10.7515	+	4.91006i	−0.504594	+	0.230440i
$455$	−16.5720	+	13.1808i	−0.776906	+	0.617923i
$456$	−2.60056	+	0.822436i	−0.121782	+	0.0385141i
$457$	14.1074	+	35.2385i	0.659915	+	1.64839i	0.757242	+	0.653135i	$0.226546\pi$
$457$	14.1074	+	35.2385i	0.659915	+	1.64839i	−0.0973271	+	0.995252i	$0.531029\pi$
$458$	0.600989	+	12.6163i	0.0280824	+	0.589521i
$459$	−2.49501	−	22.6515i	−0.116457	−	1.05728i
$460$	5.30650	−	1.43340i	0.247417	−	0.0668325i
$461$		−	7.85415i		−	0.365804i	−0.983131	−	0.182902i	$-0.941451\pi$
$461$		−	7.85415i		−	0.365804i	0.983131	−	0.182902i	$-0.0585492\pi$
$462$	−18.9884	+	14.2861i	−0.883420	+	0.664650i
$463$	−1.58219	+	11.0044i	−0.0735305	+	0.511416i	0.919456	+	0.393192i	$0.128629\pi$
$463$	−1.58219	+	11.0044i	−0.0735305	+	0.511416i	−0.992987	+	0.118224i	$0.962280\pi$
$464$	−0.453935	−	4.75382i	−0.0210734	−	0.220691i
$465$	8.09622	−	4.38837i	0.375453	−	0.203506i
$466$	7.03887	+	0.672130i	0.326069	+	0.0311358i
$467$	−3.00874	+	8.69319i	−0.139228	+	0.402273i	−0.992962	−	0.118437i	$-0.962212\pi$
$467$	−3.00874	+	8.69319i	−0.139228	+	0.402273i	0.853734	+	0.520710i	$0.174333\pi$
$468$	−20.9304	+	0.867089i	−0.967508	+	0.0400812i
$469$	7.71901	−	5.56103i	0.356431	−	0.256785i
$470$	−1.88807	+	2.17895i	−0.0870903	+	0.100508i
$471$	−23.3239	−	28.4274i	−1.07471	−	1.30986i
$472$	−7.30605	+	3.76653i	−0.336288	+	0.173369i
$473$	40.2689	−	13.9372i	1.85156	−	0.640833i
$474$	−7.30804	+	10.7259i	−0.335669	+	0.492656i
$475$	−5.74593	+	0.826141i	−0.263642	+	0.0379059i
$476$	10.3426	+	5.26006i	0.474052	+	0.241094i
$477$	−15.3617	+	5.21039i	−0.703365	+	0.238567i
$478$	−1.71454	−	1.63481i	−0.0784212	−	0.0747744i
$479$	−22.3714	−	31.4163i	−1.02218	−	1.43545i	−0.896325	−	0.443398i	$-0.853773\pi$
$479$	−22.3714	−	31.4163i	−1.02218	−	1.43545i	−0.125853	−	0.992049i	$-0.540167\pi$
$480$	−1.98054	+	0.135485i	−0.0903989	+	0.00618402i
$481$	4.54099	−	8.80830i	0.207051	−	0.401624i
$482$	12.2372			0.557387
$483$	10.9041	−	19.0814i	0.496153	−	0.868235i
$484$	−15.8882			−0.722190
$485$	−3.77109	+	7.31489i	−0.171236	+	0.332152i
$486$	15.4477	+	2.09018i	0.700721	+	0.0948127i
$487$	17.3406	+	24.3515i	0.785777	+	1.10347i	0.992157	+	0.124998i	$0.0398925\pi$
$487$	17.3406	+	24.3515i	0.785777	+	1.10347i	−0.206379	+	0.978472i	$0.566168\pi$
$488$	−6.63487	−	6.32634i	−0.300347	−	0.286380i
$489$	4.37495	−	10.1296i	0.197842	−	0.458077i
$490$	−0.674580	+	7.99455i	−0.0304744	+	0.361157i
$491$	2.33146	−	0.335214i	0.105217	−	0.0151280i	−0.0895050	−	0.995986i	$-0.528528\pi$
$491$	2.33146	−	0.335214i	0.105217	−	0.0151280i	0.194722	+	0.980858i	$0.437619\pi$
$492$	−15.7132	−	10.7061i	−0.708405	−	0.482669i
$493$	19.7916	−	6.84993i	0.891368	−	0.308505i
$494$	−9.77361	+	5.03865i	−0.439736	+	0.226699i
$495$	17.6319	+	2.64670i	0.792497	+	0.118960i
$496$	−3.03785	+	3.50587i	−0.136403	+	0.157418i
$497$	22.1437	+	9.96562i	0.993282	+	0.447019i
$498$	−17.1486	−	14.2487i	−0.768449	−	0.638499i
$499$	−11.8947	+	34.3674i	−0.532478	+	1.53850i	0.282655	+	0.959222i	$0.408785\pi$
$499$	−11.8947	+	34.3674i	−0.532478	+	1.53850i	−0.815133	+	0.579274i	$0.803336\pi$
$500$	−9.91069	−	0.946357i	−0.443220	−	0.0423224i
$501$	−2.49981	−	4.61198i	−0.111683	−	0.206048i
$502$	2.28395	+	23.9186i	0.101938	+	1.06754i
$503$	2.98908	−	20.7895i	0.133276	−	0.926958i	−0.807967	−	0.589228i	$-0.799432\pi$
$503$	2.98908	−	20.7895i	0.133276	−	0.926958i	0.941243	−	0.337730i	$-0.109659\pi$
$504$	−5.20191	+	5.99501i	−0.231712	+	0.267039i
$505$		−	2.02097i		−	0.0899320i
$506$	22.8405	−	9.83566i	1.01538	−	0.437249i
$507$	−60.5620	+	12.9781i	−2.68965	+	0.576376i
$508$	−0.749603	−	15.7361i	−0.0332583	−	0.698177i
$509$	8.15868	+	20.3794i	0.361627	+	0.903301i	0.991911	+	0.126936i	$0.0405143\pi$
$509$	8.15868	+	20.3794i	0.361627	+	0.903301i	−0.630284	+	0.776365i	$0.717061\pi$
$510$	−2.62523	−	8.30103i	−0.116247	−	0.367576i
$511$	−31.8594	−	12.5514i	−1.40938	−	0.555239i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	7.81680	−	2.41892i	0.345120	−	0.106798i
$514$	11.6076	+	4.64700i	0.511991	+	0.204970i
$515$	1.69794	+	1.78075i	0.0748201	+	0.0784691i
$516$	12.1768	−	7.37048i	0.536052	−	0.324467i
$517$	−7.05217	+	10.9734i	−0.310154	+	0.482609i
$518$	−1.24762	−	3.54150i	−0.0548172	−	0.155605i
$519$	−0.354820	−	17.1371i	−0.0155749	−	0.752237i
$520$	−7.77764	+	1.88683i	−0.341072	+	0.0827431i
$521$	17.4539	+	6.98749i	0.764669	+	0.306127i	0.721015	−	0.692919i	$-0.243676\pi$
$521$	17.4539	+	6.98749i	0.764669	+	0.306127i	0.0436542	+	0.999047i	$0.486100\pi$
$522$	1.27341	+	14.2696i	0.0557357	+	0.624565i
$523$	25.6184	+	18.2428i	1.12022	+	0.797702i	0.981278	−	0.192599i	$-0.0616915\pi$
$523$	25.6184	+	18.2428i	1.12022	+	0.797702i	0.138939	+	0.990301i	$0.455631\pi$
$524$	3.14025	+	10.6947i	0.137182	+	0.467200i
$525$	−13.0006	+	10.7870i	−0.567393	+	0.470784i
$526$	−13.6771	−	1.96647i	−0.596350	−	0.0857422i
$527$	−18.0831	−	9.32249i	−0.787712	−	0.406094i
$528$	−8.78197	+	1.88192i	−0.382186	+	0.0819002i
$529$	−15.8043	+	16.7100i	−0.687141	+	0.726524i
$530$	−5.36701	+	3.09864i	−0.233128	+	0.134596i
$531$	21.9877	−	11.1636i	0.954187	−	0.484457i
$532$	−1.15175	+	4.00397i	−0.0499347	+	0.173594i
$533$	−69.7273	−	31.8434i	−3.02023	−	1.37929i
$534$	0.513809	+	0.0138238i	0.0222347	+	0.000598215i
$535$	6.36857	+	0.608125i	0.275337	+	0.0262915i
$536$	3.53081	−	0.680509i	0.152508	−	0.0293935i
$537$	−7.01111	+	40.9179i	−0.302552	+	1.76574i
$538$	−3.71843	−	1.09183i	−0.160313	−	0.0470722i
$539$	2.12652	+	36.2353i	0.0915957	+	1.56077i
$540$	5.94403	−	0.369631i	0.255790	−	0.0159064i
$541$	0.733907	−	15.4066i	0.0315531	−	0.662382i	−0.926587	−	0.376081i	$-0.877271\pi$
$541$	0.733907	−	15.4066i	0.0315531	−	0.662382i	0.958140	−	0.286301i	$-0.0924256\pi$
$542$	−8.45610	+	2.92668i	−0.363220	+	0.125712i
$543$	−1.03656	+	13.8882i	−0.0444831	+	0.596000i
$544$	2.71103	+	3.44736i	0.116234	+	0.147804i
$545$	−9.66573	+	8.37540i	−0.414034	+	0.358763i
$546$	−16.5886	+	27.3636i	−0.709926	+	1.17105i
$547$	−0.177084	+	0.0519966i	−0.00757158	+	0.00222322i	−0.285516	−	0.958374i	$-0.592165\pi$
$547$	−0.177084	+	0.0519966i	−0.00757158	+	0.00222322i	0.277945	+	0.960597i	$0.410347\pi$
$548$	17.4404	−	1.66535i	0.745016	−	0.0711404i
$549$	19.7866	+	19.1020i	0.844473	+	0.815253i
$550$	−19.0936	+	0.909539i	−0.814153	+	0.0387829i
$551$	3.76001	+	6.51253i	0.160182	+	0.277443i
$552$	6.77154	−	4.81105i	0.288216	−	0.204772i
$553$	7.46972	+	18.3646i	0.317645	+	0.780941i
$554$	9.55984	+	14.8754i	0.406159	+	0.631995i
$555$	−1.23887	+	2.53034i	−0.0525870	+	0.107407i
$556$	8.52134	+	11.9666i	0.361385	+	0.507495i
$557$	−1.08261	+	4.46260i	−0.0458718	+	0.189086i	−0.990138	−	0.140097i	$-0.955258\pi$
$557$	−1.08261	+	4.46260i	−0.0458718	+	0.189086i	0.944266	+	0.329184i	$0.106774\pi$
$558$	9.17854	−	10.4609i	0.388559	−	0.442846i
$559$	43.3674	−	37.5780i	1.83424	−	1.58938i
$560$	−1.50171	+	2.63445i	−0.0634587	+	0.111326i
$561$	−17.1010	−	35.4832i	−0.722004	−	1.49810i
$562$	2.51073	−	13.0269i	0.105909	−	0.549506i
$563$	36.7433	−	18.9425i	1.54855	−	0.798331i	0.549244	−	0.835662i	$-0.314916\pi$
$563$	36.7433	−	18.9425i	1.54855	−	0.798331i	0.999303	+	0.0373305i	$0.0118854\pi$
$564$	−1.53528	+	4.07761i	−0.0646468	+	0.171698i
$565$	−3.93177	−	0.757787i	−0.165411	−	0.0318803i
$566$	8.98758	+	2.63899i	0.377776	+	0.110925i
$567$	15.7169	−	17.8880i	0.660047	−	0.751224i
$568$	6.01035	+	6.93632i	0.252189	+	0.291041i
$569$	21.4482	−	30.1198i	0.899154	−	1.26269i	−0.0651462	−	0.997876i	$-0.520751\pi$
$569$	21.4482	−	30.1198i	0.899154	−	1.26269i	0.964301	−	0.264810i	$-0.0853092\pi$
$570$	2.74834	−	1.48967i	0.115115	−	0.0623955i
$571$	6.21526	−	4.42587i	0.260101	−	0.185217i	−0.442566	−	0.896736i	$-0.645932\pi$
$571$	6.21526	−	4.42587i	0.260101	−	0.185217i	0.702667	+	0.711519i	$0.251992\pi$
$572$	−33.6147	+	13.4573i	−1.40550	+	0.562678i
$573$	−7.30990	−	1.98298i	−0.305376	−	0.0828400i
$574$	−26.9037	+	10.9430i	−1.12294	+	0.456752i
$575$	15.8866	−	7.75702i	0.662515	−	0.323490i
$576$	−2.73657	+	1.22931i	−0.114024	+	0.0512213i
$577$	1.26344	+	26.5228i	0.0525976	+	1.10416i	0.858732	+	0.512426i	$0.171253\pi$
$577$	1.26344	+	26.5228i	0.0525976	+	1.10416i	−0.806134	+	0.591733i	$0.798444\pi$
$578$	−1.38094	+	1.75600i	−0.0574394	+	0.0730401i
$579$	25.2233	+	23.0726i	1.04825	+	0.958866i
$580$	1.54201	+	5.25161i	0.0640286	+	0.218061i
$581$	−32.6244	+	9.77496i	−1.35349	+	0.405534i
$582$	−1.51474	+	12.3443i	−0.0627881	+	0.511686i
$583$	−22.0393	+	17.3319i	−0.912774	+	0.717813i
$584$	−8.93135	−	9.36693i	−0.369582	−	0.387606i
$585$	23.3675	−	5.51582i	0.966129	−	0.228051i
$586$	16.7911	+	0.799861i	0.693636	+	0.0330420i
$587$	6.95230	−	10.8180i	0.286952	−	0.446506i	−0.667613	−	0.744508i	$-0.732684\pi$
$587$	6.95230	−	10.8180i	0.286952	−	0.446506i	0.954565	+	0.298002i	$0.0963203\pi$
$588$	3.23068	+	11.6860i	0.133231	+	0.481923i
$589$	2.05807	−	7.00913i	0.0848012	−	0.288806i
$590$	7.40543	−	5.82369i	0.304877	−	0.239758i
$591$	−2.70091	+	3.58479i	−0.111101	+	0.147459i
$592$	0.134903	−	1.41277i	0.00554448	−	0.0580644i
$593$	−17.7194	+	18.5836i	−0.727650	+	0.763137i	−0.978802	−	0.204811i	$-0.934342\pi$
$593$	−17.7194	+	18.5836i	−0.727650	+	0.763137i	0.251152	+	0.967948i	$0.419191\pi$
$594$	26.3804	−	5.48242i	1.08240	−	0.224946i
$595$	−12.7808	−	3.67641i	−0.523961	−	0.150718i
$596$	−5.55333	+	3.56891i	−0.227473	+	0.146188i
$597$	7.65843	+	2.47431i	0.313439	+	0.101267i
$598$	23.6318	−	23.7277i	0.966375	−	0.970297i
$599$	−3.74489	−	2.16211i	−0.153012	−	0.0883415i	0.421539	−	0.906810i	$-0.361490\pi$
$599$	−3.74489	−	2.16211i	−0.153012	−	0.0883415i	−0.574551	+	0.818469i	$0.694823\pi$
$600$	−6.17250	+	1.63344i	−0.251991	+	0.0666848i
$601$	3.56742	−	24.8120i	0.145518	−	1.01210i	−0.777923	−	0.628360i	$-0.783726\pi$
$601$	3.56742	−	24.8120i	0.145518	−	1.01210i	0.923441	−	0.383741i	$-0.125364\pi$
$602$	0.914869	−	21.7230i	0.0372873	−	0.885365i
$603$	−10.6049	+	1.97585i	−0.431864	+	0.0804630i
$604$	6.62098	−	9.29786i	0.269404	−	0.378325i
$605$	17.8810	−	3.44628i	0.726965	−	0.140111i
$606$	−1.05843	−	2.86483i	−0.0429958	−	0.116376i
$607$	−7.30401	−	30.1075i	−0.296461	−	1.22203i	−0.903929	−	0.427683i	$-0.859330\pi$
$607$	−7.30401	−	30.1075i	−0.296461	−	1.22203i	0.607468	−	0.794344i	$-0.292185\pi$
$608$	−1.03123	+	1.19010i	−0.0418218	+	0.0482649i
$609$	19.2322	+	10.4415i	0.779329	+	0.423109i
$610$	8.83929	+	5.68067i	0.357892	+	0.230003i
$611$	−3.32430	+	17.2481i	−0.134487	+	0.697784i
$612$	−8.06885	−	10.3923i	−0.326164	−	0.420082i
$613$	5.51230	−	13.7691i	0.222640	−	0.556127i	−0.774427	−	0.632663i	$-0.781962\pi$
$613$	5.51230	−	13.7691i	0.222640	−	0.556127i	0.997067	+	0.0765359i	$0.0243860\pi$
$614$	4.07816	+	1.41146i	0.164581	+	0.0569621i
$615$	20.0063	+	8.64063i	0.806730	+	0.348424i
$616$	−5.02867	+	12.7644i	−0.202611	+	0.514292i
$617$	−5.49321	+	12.0285i	−0.221148	+	0.484247i	−0.987390	−	0.158305i	$-0.949397\pi$
$617$	−5.49321	+	12.0285i	−0.221148	+	0.484247i	0.766242	+	0.642552i	$0.222124\pi$
$618$	3.33954	+	1.63505i	0.134336	+	0.0657715i
$619$	−20.8055	+	0.991088i	−0.836243	+	0.0398352i	−0.461334	−	0.887226i	$-0.652629\pi$
$619$	−20.8055	+	0.991088i	−0.836243	+	0.0398352i	−0.374909	+	0.927062i	$0.622326\pi$
$620$	2.65842	−	4.60452i	0.106765	−	0.184922i
$621$	−20.4037	+	14.3070i	−0.818771	+	0.574121i
$622$	2.15628			0.0864590
$623$	0.451895	−	0.642055i	0.0181048	−	0.0257234i
$624$	−10.0370	+	6.74802i	−0.401803	+	0.270137i
$625$	−6.98936	+	0.667403i	−0.279574	+	0.0266961i
$626$	−0.654184	+	2.69658i	−0.0261465	+	0.107777i
$627$	11.3484	−	8.44056i	0.453211	−	0.337084i
$628$	−20.0622	−	6.94360i	−0.800570	−	0.277080i
$629$	6.16074	−	0.885781i	0.245645	−	0.0353184i
$630$	4.55400	−	7.87527i	0.181436	−	0.313758i
$631$	34.2137	+	29.6464i	1.36203	+	1.18020i	0.964955	+	0.262416i	$0.0845194\pi$
$631$	34.2137	+	29.6464i	1.36203	+	1.18020i	0.397073	+	0.917787i	$0.370026\pi$
$632$	−0.356549	+	7.48488i	−0.0141828	+	0.297733i
$633$	−22.3089	−	8.39960i	−0.886698	−	0.333854i
$634$	−7.77705	−	22.4703i	−0.308866	−	0.892410i
$635$	4.25691	+	17.5472i	0.168930	+	0.696340i
$636$	−5.98519	+	7.20332i	−0.237328	+	0.285630i
$637$	20.7940	+	44.2359i	0.823887	+	1.75269i
$638$	10.2867	+	22.5248i	0.407255	+	0.891764i
$639$	−17.9018	−	20.9203i	−0.708183	−	0.827594i
$640$	−0.933616	+	0.664825i	−0.0369044	+	0.0262795i
$641$	−15.8301	−	12.4489i	−0.625251	−	0.491703i	0.254541	−	0.967062i	$-0.418076\pi$
$641$	−15.8301	−	12.4489i	−0.625251	−	0.491703i	−0.879792	+	0.475359i	$0.842318\pi$
$642$	9.34629	−	2.47332i	0.368868	−	0.0976142i
$643$			12.6062i			0.497141i	0.968614	+	0.248570i	$0.0799607\pi$
$643$			12.6062i			0.497141i	−0.968614	+	0.248570i	$0.920039\pi$
$644$	−0.397533	−	12.6823i	−0.0156650	−	0.499755i
$645$	−12.1053	+	10.9362i	−0.476647	+	0.430611i
$646$	−6.13848	−	3.16461i	−0.241515	−	0.124510i
$647$	−21.9395	+	27.8983i	−0.862530	+	1.09680i	0.131886	+	0.991265i	$0.457897\pi$
$647$	−21.9395	+	27.8983i	−0.862530	+	1.09680i	−0.994416	+	0.105531i	$0.966346\pi$
$648$	8.23239	−	3.63700i	0.323399	−	0.142875i
$649$	29.4131	−	30.8476i	1.15457	−	1.21087i
$650$	−23.4149	+	10.6932i	−0.918410	+	0.419424i
$651$	−5.55153	−	20.5205i	−0.217582	−	0.804263i
$652$	−0.906615	−	6.30565i	−0.0355058	−	0.246948i
$653$	18.2278	−	4.42202i	0.713309	−	0.173047i	0.137347	−	0.990523i	$-0.456143\pi$
$653$	18.2278	−	4.42202i	0.713309	−	0.173047i	0.575962	+	0.817476i	$0.304627\pi$
$654$	−9.31530	+	16.9348i	−0.364257	+	0.662201i
$655$	−5.85388	−	11.3549i	−0.228730	−	0.443675i
$656$	−10.9652	−	0.522337i	−0.428119	−	0.0203938i
$657$	26.6194	+	28.2663i	1.03852	+	1.10277i
$658$	3.89039	+	5.40007i	0.151663	+	0.210517i
$659$	3.60467	+	25.0711i	0.140418	+	0.976629i	0.931194	+	0.364524i	$0.118768\pi$
$659$	3.60467	+	25.0711i	0.140418	+	0.976629i	−0.790776	+	0.612106i	$0.790323\pi$
$660$	9.47525	−	4.02284i	0.368823	−	0.156589i
$661$	1.59027	−	16.6540i	0.0618542	−	0.647767i	−0.910383	−	0.413767i	$-0.864213\pi$
$661$	1.59027	−	16.6540i	0.0618542	−	0.647767i	0.972237	−	0.233999i	$-0.0751813\pi$
$662$	−31.3020	−	7.59379i	−1.21659	−	0.295141i
$663$	−39.1381	−	35.8010i	−1.52000	−	1.39039i
$664$	−12.7414	−	1.83194i	−0.494464	−	0.0710932i
$665$	0.427714	−	4.75600i	0.0165860	−	0.184430i
$666$	−0.430963	+	4.23572i	−0.0166995	+	0.164131i
$667$	−16.9777	−	15.3711i	−0.657379	−	0.595170i
$668$	−2.62295	−	1.51436i	−0.101485	−	0.0585924i
$669$	10.1327	−	10.0702i	0.391755	−	0.389335i
$670$	−3.82606	+	1.53172i	−0.147814	+	0.0591757i
$671$	43.2414	+	19.7477i	1.66932	+	0.762352i
$672$	−0.749029	+	4.52095i	−0.0288944	+	0.174399i
$673$	15.5514	+	34.0528i	0.599461	+	1.31264i	0.929553	+	0.368688i	$0.120193\pi$
$673$	15.5514	+	34.0528i	0.599461	+	1.31264i	−0.330092	+	0.943949i	$0.607080\pi$
$674$	1.26887	−	3.66617i	0.0488751	−	0.141215i
$675$	18.5475	−	4.78548i	0.713894	−	0.184193i
$676$	−25.8802	+	24.6767i	−0.995393	+	0.949105i
$677$	4.79341	+	0.923853i	0.184226	+	0.0355066i	0.280529	−	0.959845i	$-0.409490\pi$
$677$	4.79341	+	0.923853i	0.184226	+	0.0355066i	−0.0963039	+	0.995352i	$0.530702\pi$
$678$	−5.97037	+	0.984956i	−0.229291	+	0.0378270i
$679$	14.4258	+	12.3615i	0.553610	+	0.474390i
$680$	−3.79882	−	3.29170i	−0.145678	−	0.126231i
$681$	11.5273	−	16.9184i	0.441727	−	0.648315i
$682$	8.94019	−	22.3315i	0.342338	−	0.855118i
$683$	6.90785	+	35.8413i	0.264322	+	1.37143i	0.834997	+	0.550255i	$0.185469\pi$
$683$	6.90785	+	35.8413i	0.264322	+	1.37143i	−0.570675	+	0.821176i	$0.693319\pi$
$684$	3.11574	−	3.55106i	0.119133	−	0.135778i
$685$	−19.2666	+	5.65719i	−0.736140	+	0.216150i
$686$	17.5994	+	5.76729i	0.671948	+	0.220196i
$687$	−12.2060	−	18.1552i	−0.465686	−	0.692665i
$688$	3.76562	−	7.30429i	0.143563	−	0.278473i
$689$	−18.8783	+	32.6982i	−0.719207	+	1.24570i
$690$	−6.57731	+	6.88328i	−0.250394	+	0.262042i
$691$	8.71359	+	15.0924i	0.331481	+	0.574141i	0.982802	−	0.184660i	$-0.0591185\pi$
$691$	8.71359	+	15.0924i	0.331481	+	0.574141i	−0.651322	+	0.758802i	$0.725785\pi$
$692$	−5.35032	−	8.32525i	−0.203389	−	0.316479i
$693$	15.3230	−	38.1990i	0.582073	−	1.45106i
$694$	8.39288	−	18.3778i	0.318589	−	0.697613i
$695$	−12.1858	−	11.6191i	−0.462233	−	0.440738i
$696$	4.93628	+	6.63685i	0.187109	+	0.251569i
$697$	−9.11133	−	47.2741i	−0.345116	−	1.79063i
$698$	−15.4274	−	19.6176i	−0.583937	−	0.742536i
$699$	−11.0327	+	5.31716i	−0.417294	+	0.201113i
$700$	−3.13913	+	9.23423i	−0.118648	+	0.349021i
$701$	−41.9441	−	26.9558i	−1.58421	−	1.01811i	−0.974193	−	0.225718i	$-0.927527\pi$
$701$	−41.9441	−	26.9558i	−1.58421	−	1.01811i	−0.610014	−	0.792390i	$-0.708836\pi$
$702$	30.2360	−	20.0571i	1.14118	−	0.757006i
$703$	0.730945	+	2.11193i	0.0275681	+	0.0796529i
$704$	−3.75284	+	3.57832i	−0.141440	+	0.134863i
$705$	0.843374	−	4.92206i	0.0317633	−	0.185375i
$706$	8.72304	+	10.0669i	0.328296	+	0.378874i
$707$	−4.53971	−	1.07487i	−0.170733	−	0.0404247i
$708$	7.44759	−	12.1338i	0.279897	−	0.456016i
$709$	1.64729	+	17.2512i	0.0618652	+	0.647881i	0.972223	+	0.234058i	$0.0752007\pi$
$709$	1.64729	+	17.2512i	0.0618652	+	0.647881i	−0.910357	+	0.413823i	$0.864193\pi$
$710$	−8.26875	−	6.50262i	−0.310321	−	0.244039i
$711$	1.20876	−	22.4476i	0.0453321	−	0.841850i
$712$	0.256997	−	0.148377i	0.00963138	−	0.00556068i
$713$	0.574488	+	22.2401i	0.0215148	+	0.832898i
$714$	−20.0429	+	1.48208i	−0.750085	+	0.0554655i
$715$	34.9119	−	22.4365i	1.30563	−	0.839078i
$716$	8.90810	+	22.2514i	0.332911	+	0.831572i
$717$	4.00677	+	0.884628i	0.149635	+	0.0330370i
$718$	1.95928	+	0.475317i	0.0731197	+	0.0177387i
$719$	20.9715	+	14.9337i	0.782105	+	0.556934i	0.899896	−	0.436104i	$-0.143642\pi$
$719$	20.9715	+	14.9337i	0.782105	+	0.556934i	−0.117792	+	0.993038i	$0.537581\pi$
$720$	2.81315	−	1.97708i	0.104840	−	0.0736815i
$721$	4.90316	−	2.86697i	0.182603	−	0.106772i
$722$	−4.65429	+	15.8511i	−0.173215	+	0.589915i
$723$	−18.1324	+	10.9754i	−0.674352	+	0.408179i
$724$	3.68444	+	7.14682i	0.136931	+	0.265610i
$725$	8.06664	+	15.6471i	0.299588	+	0.581119i
$726$	23.5423	−	14.2500i	0.873738	−	0.528866i
$727$	−8.56950	+	29.1850i	−0.317825	+	1.08241i	0.633377	+	0.773844i	$0.281668\pi$
$727$	−8.56950	+	29.1850i	−0.317825	+	1.08241i	−0.951202	+	0.308569i	$0.900150\pi$
$728$	0.101788	+	18.4744i	0.00377251	+	0.684708i
$729$	−24.7643	+	10.7577i	−0.917196	+	0.398435i
$730$	12.0833	+	8.60450i	0.447224	+	0.318467i
$731$	35.0246	+	8.49687i	1.29543	+	0.314268i
$732$	15.5053	+	3.42331i	0.573091	+	0.126529i
$733$	9.06841	+	22.6518i	0.334949	+	0.836663i	0.996248	+	0.0865405i	$0.0275812\pi$
$733$	9.06841	+	22.6518i	0.334949	+	0.836663i	−0.661299	+	0.750122i	$0.729995\pi$
$734$	−16.1213	+	10.3605i	−0.595048	+	0.382414i
$735$	−6.17068	−	12.4510i	−0.227609	−	0.459261i
$736$	1.87895	−	4.41243i	0.0692589	−	0.162644i
$737$	−16.1475	+	9.32279i	−0.594802	+	0.343409i
$738$	32.8853	+	1.77081i	1.21052	+	0.0651844i
$739$	6.40877	+	5.03991i	0.235750	+	0.185396i	0.729044	−	0.684467i	$-0.239965\pi$
$739$	6.40877	+	5.03991i	0.235750	+	0.185396i	−0.493294	+	0.869863i	$0.664207\pi$
$740$	0.154617	+	1.61923i	0.00568385	+	0.0595240i
$741$	9.96295	−	16.2319i	0.365998	−	0.596293i
$742$	4.10599	+	13.7039i	0.150736	+	0.503088i
$743$	26.4162	+	30.4859i	0.969115	+	1.11842i	0.992930	+	0.118702i	$0.0378733\pi$
$743$	26.4162	+	30.4859i	0.969115	+	1.11842i	−0.0238148	+	0.999716i	$0.507581\pi$
$744$	1.35696	−	7.91944i	0.0497486	−	0.290341i
$745$	5.47573	−	5.22110i	0.200615	−	0.191286i
$746$	−9.50402	−	27.4601i	−0.347967	−	1.00538i
$747$	38.1895	+	5.73257i	1.39728	+	0.209744i
$748$	−19.1312	−	12.2949i	−0.699505	−	0.449545i
$749$	4.75322	−	13.9823i	0.173679	−	0.510902i
$750$	15.5340	−	7.48654i	0.567220	−	0.273370i
$751$	1.74223	+	2.21542i	0.0635748	+	0.0808419i	0.816801	−	0.576920i	$-0.195746\pi$
$751$	1.74223	+	2.21542i	0.0635748	+	0.0808419i	−0.753226	+	0.657762i	$0.771503\pi$
$752$	0.476071	+	2.47009i	0.0173605	+	0.0900749i
$753$	−24.8366	−	33.3929i	−0.905095	−	1.21691i
$754$	24.1336	+	23.0113i	0.878893	+	0.838023i
$755$	−5.43464	+	11.9002i	−0.197787	+	0.433092i
$756$	2.33108	−	13.5487i	0.0847806	−	0.492760i
$757$	17.0712	+	26.5634i	0.620465	+	0.965462i	0.999201	+	0.0399574i	$0.0127222\pi$
$757$	17.0712	+	26.5634i	0.620465	+	0.965462i	−0.378737	+	0.925504i	$0.623641\pi$
$758$	−4.28890	−	7.42860i	−0.155780	−	0.269819i
$759$	−25.0224	+	35.0594i	−0.908256	+	1.27258i
$760$	0.902427	−	1.56305i	0.0327345	−	0.0566977i
$761$	10.3003	−	19.9797i	0.373385	−	0.724265i	−0.625027	−	0.780603i	$-0.714912\pi$
$761$	10.3003	−	19.9797i	0.373385	−	0.724265i	0.998412	+	0.0563380i	$0.0179424\pi$
$762$	15.2243	+	22.6447i	0.551518	+	0.820331i
$763$	13.6729	+	26.1667i	0.494991	+	0.947297i
$764$	−4.19577	+	1.23199i	−0.151798	+	0.0445718i
$765$	11.3351	+	9.94552i	0.409820	+	0.359581i
$766$	−6.35863	−	32.9917i	−0.229747	−	1.19204i
$767$	21.3323	−	53.2856i	0.770266	−	1.92403i
$768$	−0.975267	+	1.43138i	−0.0351919	+	0.0516505i
$769$	−25.7095	−	22.2774i	−0.927107	−	0.803343i	0.0536528	−	0.998560i	$-0.482914\pi$
$769$	−25.7095	−	22.2774i	−0.927107	−	0.803343i	−0.980760	+	0.195217i	$0.937459\pi$
$770$	2.89070	−	15.4561i	0.104174	−	0.557000i
$771$	−21.3675	+	3.52508i	−0.769531	+	0.126953i
$772$	19.3796	+	3.73512i	0.697488	+	0.134430i
$773$	−8.80180	+	8.39250i	−0.316579	+	0.301857i	−0.831661	−	0.555283i	$-0.812610\pi$
$773$	−8.80180	+	8.39250i	−0.316579	+	0.301857i	0.515082	+	0.857141i	$0.327761\pi$
$774$	−11.4324	+	21.8424i	−0.410930	+	0.785110i
$775$	5.59312	−	16.1603i	0.200911	−	0.580494i
$776$	2.98285	+	6.53154i	0.107078	+	0.234468i
$777$	5.02500	+	4.12865i	0.180271	+	0.148115i
$778$	−7.92240	−	3.61804i	−0.284032	−	0.129713i
$779$	16.0485	−	6.42484i	0.574996	−	0.230194i
$780$	9.83224	−	9.77151i	0.352051	−	0.349876i
$781$	−41.2157	−	23.7959i	−1.47481	−	0.851484i
$782$	20.7487	+	3.44586i	0.741971	+	0.123224i
$783$	−14.6852	−	20.0019i	−0.524805	−	0.714811i
$784$	5.11906	+	4.77444i	0.182824	+	0.170516i
$785$	24.0847	+	3.46285i	0.859618	+	0.123594i
$786$	−14.2450	−	13.0304i	−0.508104	−	0.464780i
$787$	19.5780	+	4.74957i	0.697880	+	0.169304i	0.568977	−	0.822353i	$-0.307339\pi$
$787$	19.5780	+	4.74957i	0.697880	+	0.169304i	0.128903	+	0.991657i	$0.458854\pi$
$788$	−0.246326	+	2.57964i	−0.00877499	+	0.0918958i
$789$	22.0298	−	9.35304i	0.784281	−	0.332977i
$790$	−1.22226	−	8.50102i	−0.0434861	−	0.302453i
$791$	−3.79337	+	8.42890i	−0.134877	+	0.299697i
$792$	11.3248	−	10.6650i	0.402410	−	0.378964i
$793$	63.9426	+	3.04596i	2.27067	+	0.108165i
$794$	−11.7280	−	22.7491i	−0.416211	−	0.807336i
$795$	5.17343	−	9.40504i	0.183483	−	0.333562i
$796$	4.51566	−	1.09549i	0.160053	−	0.0388285i
$797$	−3.43937	−	23.9213i	−0.121829	−	0.847336i	−0.955482	−	0.295049i	$-0.904664\pi$
$797$	−3.43937	−	23.9213i	−0.121829	−	0.847336i	0.833654	−	0.552288i	$-0.186245\pi$
$798$	−1.88452	−	6.96589i	−0.0667113	−	0.246590i
$799$	−10.0354	+	4.58299i	−0.355025	+	0.162135i
$800$	−2.54389	+	2.66795i	−0.0899399	+	0.0943263i
$801$	−0.773735	+	0.440346i	−0.0273386	+	0.0155589i
$802$	−4.16537	+	5.29670i	−0.147084	+	0.187033i
$803$	59.6513	+	30.7524i	2.10505	+	1.08523i
$804$	−4.62145	+	4.17510i	−0.162986	+	0.147244i
$805$	3.19830	+	14.1868i	0.112725	+	0.500019i
$806$		−	32.3926i		−	1.14098i
$807$	6.48905	−	1.71721i	0.228425	−	0.0604485i
$808$	−1.38604	−	1.08999i	−0.0487606	−	0.0383458i
$809$	−3.40102	+	2.42186i	−0.119574	+	0.0851480i	−0.638279	−	0.769805i	$-0.720353\pi$
$809$	−3.40102	+	2.42186i	−0.119574	+	0.0851480i	0.518706	+	0.854953i	$0.326414\pi$
$810$	−8.47605	+	5.87884i	−0.297818	+	0.206561i
$811$	12.2813	+	26.8924i	0.431256	+	0.944320i	0.993121	+	0.117091i	$0.0373568\pi$
$811$	12.2813	+	26.8924i	0.431256	+	0.944320i	−0.561865	+	0.827229i	$0.689916\pi$
$812$	12.6168	−	0.670704i	0.442764	−	0.0235371i
$813$	9.90492	−	11.9208i	0.347381	−	0.418081i
$814$	1.73497	+	7.15162i	0.0608105	+	0.250664i
$815$	2.38807	+	6.89988i	0.0836506	+	0.241692i
$816$	−7.10897	−	2.67663i	−0.248864	−	0.0937007i
$817$	−0.615749	+	12.9262i	−0.0215423	+	0.452229i
$818$	24.7462	+	21.4427i	0.865232	+	0.749728i
$819$	0.0380590	−	55.4241i	0.00132989	−	1.93668i
$820$	12.4538	−	1.79059i	0.434906	−	0.0625300i
$821$	−17.0547	−	5.90269i	−0.595213	−	0.206005i	0.0128186	−	0.999918i	$-0.495920\pi$
$821$	−17.0547	−	5.90269i	−0.595213	−	0.206005i	−0.608032	+	0.793912i	$0.708041\pi$
$822$	−24.3487	+	18.1097i	−0.849257	+	0.631650i
$823$	−5.15377	+	21.2441i	−0.179649	+	0.740524i	0.808687	+	0.588239i	$0.200178\pi$
$823$	−5.15377	+	21.2441i	−0.179649	+	0.740524i	−0.988337	+	0.152285i	$0.951337\pi$
$824$	2.13705	−	0.204064i	0.0744478	−	0.00710890i
$825$	27.4762	−	18.4726i	0.956598	−	0.643132i
$826$	−9.14311	−	19.7322i	−0.318130	−	0.686571i
$827$	34.9313			1.21468			0.607340	−	0.794442i	$-0.292237\pi$
$827$	34.9313			1.21468			0.607340	+	0.794442i	$0.292237\pi$
$828$	−5.71875	+	13.2021i	−0.198740	+	0.458805i
$829$	−19.9641	+	34.5789i	−0.693383	+	1.20097i	0.277340	+	0.960772i	$0.410547\pi$
$829$	−19.9641	+	34.5789i	−0.693383	+	1.20097i	−0.970723	+	0.240203i	$0.922786\pi$
$830$	14.7369	−	0.702005i	0.511526	−	0.0243670i
$831$	−27.5069	−	13.4675i	−0.954205	−	0.467183i
$832$	−2.90075	+	6.35176i	−0.100566	+	0.220208i
$833$	−15.0559	+	26.7541i	−0.521656	+	0.926976i
$834$	−23.3592	−	10.0887i	−0.808863	−	0.349345i
$835$	3.28041	+	1.13536i	0.113523	+	0.0392908i
$836$	3.03483	−	7.58064i	0.104962	−	0.262182i
$837$	−4.21802	+	23.7326i	−0.145796	+	0.820320i
$838$	1.30371	−	6.76429i	0.0450359	−	0.233668i
$839$	−27.2270	−	17.4977i	−0.939980	−	0.604088i	−0.0215907	−	0.999767i	$-0.506873\pi$
$839$	−27.2270	−	17.4977i	−0.939980	−	0.604088i	−0.918389	+	0.395679i	$0.870509\pi$
$840$	−0.137653	−	5.25046i	−0.00474949	−	0.181158i
$841$	−4.05694	+	4.68196i	−0.139895	+	0.161447i
$842$	5.71250	+	23.5472i	0.196866	+	0.811492i
$843$	7.96341	+	21.5544i	0.274274	+	0.742375i
$844$	−13.5140	+	2.60462i	−0.465172	+	0.0896545i
$845$	23.7737	−	33.3855i	0.817839	−	1.14849i
$846$	−1.38227	−	7.41898i	−0.0475234	−	0.255070i
$847$	1.76879	−	41.9990i	0.0607764	−	1.44310i
$848$	−0.769511	+	5.35207i	−0.0264251	+	0.183791i
$849$	−15.6842	+	4.15054i	−0.538282	+	0.142446i
$850$	−14.0011	−	8.08357i	−0.480235	−	0.277264i
$851$	−4.08984	−	5.44038i	−0.140198	−	0.186494i
$852$	−15.1270	−	4.88727i	−0.518241	−	0.167435i
$853$	−22.3383	+	14.3559i	−0.764848	+	0.491538i	−0.863974	−	0.503537i	$-0.832032\pi$
$853$	−22.3383	+	14.3559i	−0.764848	+	0.491538i	0.0991257	+	0.995075i	$0.468395\pi$
$854$	17.4617	−	16.8344i	0.597528	−	0.576061i
$855$	−2.73628	+	4.67228i	−0.0935789	+	0.159789i
$856$	3.85190	−	4.03976i	0.131655	−	0.138076i
$857$	−3.25260	+	34.0628i	−0.111107	+	1.16356i	0.752218	+	0.658914i	$0.228984\pi$
$857$	−3.25260	+	34.0628i	−0.111107	+	1.16356i	−0.863325	+	0.504649i	$0.831622\pi$
$858$	37.7389	−	50.0891i	1.28839	−	1.71001i
$859$	28.2735	−	22.2345i	0.964680	−	0.758633i	−0.00575767	−	0.999983i	$-0.501833\pi$
$859$	28.2735	−	22.2345i	0.964680	−	0.758633i	0.970438	+	0.241350i	$0.0775903\pi$
$860$	−2.65357	+	9.03723i	−0.0904860	+	0.308167i
$861$	30.0500	−	40.3445i	1.02410	−	1.37494i
$862$	1.26421	−	1.96715i	0.0430592	−	0.0670014i
$863$	−27.0753	−	1.28975i	−0.921653	−	0.0439037i	−0.418611	−	0.908166i	$-0.637483\pi$
$863$	−27.0753	−	1.28975i	−0.921653	−	0.0439037i	−0.503042	+	0.864262i	$0.667786\pi$
$864$	2.95235	−	4.27593i	0.100441	−	0.145470i
$865$	7.82720	+	8.20893i	0.266133	+	0.279112i
$866$	6.03773	−	4.74812i	0.205170	−	0.161348i
$867$	0.471262	−	3.84051i	0.0160049	−	0.130431i
$868$	−8.92924	−	8.42058i	−0.303078	−	0.285813i
$869$	−10.9470	−	37.2820i	−0.371351	−	1.26471i
$870$	−6.99500	−	6.39857i	−0.237153	−	0.216932i
$871$	−15.5211	+	19.7367i	−0.525914	+	0.668754i
$872$	0.530960	+	11.1462i	0.0179806	+	0.377459i
$873$	−8.82697	−	19.6497i	−0.298748	−	0.665041i
$874$	0.195015	+	7.54960i	0.00659650	+	0.255369i
$875$	3.60494	−	26.0927i	0.121869	−	0.882093i
$876$	21.6351	+	5.86902i	0.730984	+	0.198296i
$877$	12.8925	−	5.16137i	0.435348	−	0.174287i	−0.143628	−	0.989632i	$-0.545877\pi$
$877$	12.8925	−	5.16137i	0.435348	−	0.174287i	0.578976	+	0.815345i	$0.303452\pi$
$878$	20.5079	−	14.6036i	0.692110	−	0.492849i
$879$	−25.5977	+	13.8746i	−0.863389	+	0.467979i
$880$	3.44737	−	4.84116i	0.116211	−	0.163195i
$881$	8.26403	+	9.53720i	0.278422	+	0.321316i	0.877687	−	0.479235i	$-0.159086\pi$
$881$	8.26403	+	9.53720i	0.278422	+	0.321316i	−0.599265	+	0.800551i	$0.704540\pi$
$882$	−15.2681	−	14.4182i	−0.514105	−	0.485486i
$883$	43.8939	+	12.8884i	1.47715	+	0.433729i	0.918415	−	0.395619i	$-0.129470\pi$
$883$	43.8939	+	12.8884i	1.47715	+	0.433729i	0.558732	+	0.829348i	$0.311288\pi$
$884$	−30.0707	−	5.79564i	−1.01139	−	0.194929i
$885$	−5.74979	+	15.2711i	−0.193277	+	0.513333i
$886$	−7.40481	+	3.81744i	−0.248769	+	0.128249i
$887$	5.41381	−	28.0895i	0.181778	−	0.943154i	−0.770389	−	0.637575i	$-0.779938\pi$
$887$	5.41381	−	28.0895i	0.181778	−	0.943154i	0.952167	−	0.305579i	$-0.0988501\pi$
$888$	1.06721	+	2.21436i	0.0358131	+	0.0743092i
$889$	41.6804	−	0.229645i	1.39792	−	0.00770205i
$890$	−0.257047	+	0.222733i	−0.00861624	+	0.00746601i
$891$	−34.1720	+	31.7839i	−1.14481	+	1.06480i
$892$	1.94450	−	8.01535i	0.0651067	−	0.268374i
$893$	−2.29778	−	3.22678i	−0.0768923	−	0.107980i
$894$	5.02773	−	10.2690i	0.168153	−	0.343445i
$895$	−14.8519	−	23.1100i	−0.496444	−	0.772482i
$896$	0.996844	+	2.45078i	0.0333022	+	0.0818747i
$897$	−13.7353	+	56.3536i	−0.458607	+	1.88159i
$898$	14.4476	+	25.0240i	0.482123	+	0.835061i
$899$	−22.1278	+	1.05408i	−0.738005	+	0.0351555i
$900$	7.68110	−	7.95641i	0.256037	−	0.265214i
$901$	−23.6063	+	2.25413i	−0.786440	+	0.0750959i
$902$	54.6174	−	16.0371i	1.81856	−	0.533978i
$903$	18.1276	+	33.0087i	0.603248	+	1.09846i
$904$	−2.64028	+	2.28781i	−0.0878143	+	0.0760915i
$905$	−5.69677	−	7.24403i	−0.189367	−	0.240800i
$906$	−1.47148	+	19.7154i	−0.0488867	+	0.655001i
$907$	−32.2999	+	11.1791i	−1.07250	+	0.371196i	−0.805558	−	0.592517i	$-0.798134\pi$
$907$	−32.2999	+	11.1791i	−1.07250	+	0.371196i	−0.266941	+	0.963713i	$0.586013\pi$
$908$	0.562401	−	11.8063i	0.0186639	−	0.391804i
$909$	4.13777	+	3.29568i	0.137241	+	0.109311i
$910$	−4.12181	−	20.7695i	−0.136637	−	0.688503i
$911$	−46.7930	−	13.7397i	−1.55032	−	0.455216i	−0.609125	−	0.793074i	$-0.708479\pi$
$911$	−46.7930	−	13.7397i	−1.55032	−	0.455216i	−0.941197	+	0.337858i	$0.890298\pi$
$912$	0.460633	−	2.68833i	0.0152531	−	0.0890194i
$913$	65.5424	−	12.6323i	2.16914	−	0.418067i
$914$	−37.7856	−	3.60809i	−1.24984	−	0.119345i
$915$	−18.1926	−	0.489463i	−0.601428	−	0.0161812i
$916$	−11.4892	−	5.24695i	−0.379614	−	0.173364i
$917$	−28.6201	+	7.11034i	−0.945118	+	0.234804i
$918$	21.2768	+	8.16188i	0.702238	+	0.269382i
$919$	41.8542	−	24.1645i	1.38064	−	0.797115i	0.388407	−	0.921488i	$-0.373025\pi$
$919$	41.8542	−	24.1645i	1.38064	−	0.797115i	0.992236	+	0.124373i	$0.0396920\pi$
$920$	−1.15752	+	5.37342i	−0.0381624	+	0.177157i
$921$	−7.30875	+	1.56622i	−0.240831	+	0.0516088i
$922$	6.98105	+	3.59898i	0.229909	+	0.118526i
$923$	−63.4361	−	9.12074i	−2.08803	−	0.300213i
$924$	−3.99702	−	23.4238i	−0.131492	−	0.770587i
$925$	1.47393	+	5.01975i	0.0484626	+	0.165048i
$926$	−9.05606	−	6.44879i	−0.297601	−	0.211921i
$927$	−6.41483	+	0.572455i	−0.210691	+	0.0188019i
$928$	4.43337	+	1.77485i	0.145533	+	0.0582624i
$929$	−55.3208	+	13.4207i	−1.81502	+	0.440318i	−0.991842	−	0.127472i	$-0.959314\pi$
$929$	−55.3208	+	13.4207i	−1.81502	+	0.440318i	−0.823174	+	0.567790i	$0.807799\pi$
$930$	0.190630	+	9.20708i	0.00625101	+	0.301912i
$931$	−10.4559	−	3.49030i	−0.342679	−	0.114390i
$932$	−3.82281	+	5.94841i	−0.125220	+	0.194846i
$933$	−3.19507	+	1.93395i	−0.104602	+	0.0633146i
$934$	−6.34813	−	6.65773i	−0.207717	−	0.217847i
$935$	24.1976	+	9.68725i	0.791346	+	0.316807i
$936$	8.82017	−	19.0010i	0.288296	−	0.621067i
$937$	13.2730	−	6.06158i	0.433610	−	0.198023i	−0.186638	−	0.982429i	$-0.559759\pi$
$937$	13.2730	−	6.06158i	0.433610	−	0.198023i	0.620248	+	0.784406i	$0.287032\pi$
$938$	1.40579	+	9.40914i	0.0459005	+	0.307219i
$939$	−1.44920	−	4.58240i	−0.0472929	−	0.149541i
$940$	−1.07156	−	2.67664i	−0.0349506	−	0.0873024i
$941$	0.839504	+	17.6233i	0.0273670	+	0.574505i	0.970356	+	0.241680i	$0.0776986\pi$
$941$	0.839504	+	17.6233i	0.0273670	+	0.574505i	−0.942989	+	0.332824i	$0.891998\pi$
$942$	35.9549	−	7.70492i	1.17147	−	0.251040i
$943$	−40.5291	+	33.6019i	−1.31981	+	1.09423i
$944$		−	8.21980i		−	0.267532i
$945$	0.315353	+	15.7536i	0.0102584	+	0.512466i
$946$	−6.06439	+	42.1788i	−0.197170	+	1.37135i
$947$	1.74115	+	18.2341i	0.0565797	+	0.592530i	0.978654	+	0.205516i	$0.0658873\pi$
$947$	1.74115	+	18.2341i	0.0565797	+	0.592530i	−0.922074	+	0.387014i	$0.873507\pi$
$948$	−6.18480	−	11.4105i	−0.200873	−	0.370597i
$949$	89.9655	+	8.59066i	2.92040	+	0.278865i
$950$	1.89864	−	5.48575i	0.0615999	−	0.177981i
$951$	31.6771	+	26.3203i	1.02720	+	0.853493i
$952$	−9.41458	+	6.78257i	−0.305128	+	0.219825i
$953$	2.09476	−	2.41749i	0.0678561	−	0.0783101i	−0.720807	−	0.693136i	$-0.756228\pi$
$953$	2.09476	−	2.41749i	0.0678561	−	0.0783101i	0.788663	+	0.614826i	$0.210774\pi$
$954$	2.40798	−	16.0416i	0.0779611	−	0.519366i
$955$	4.45480	−	2.29661i	0.144154	−	0.0743165i
$956$	2.23872	−	0.774830i	0.0724055	−	0.0250598i
$957$	−35.4446	−	24.1501i	−1.14576	−	0.780660i
$958$	38.1751	−	5.48875i	1.23338	−	0.177334i
$959$	2.46062	+	46.2874i	0.0794574	+	1.49470i
$960$	0.787112	−	1.82246i	0.0254039	−	0.0588196i
$961$	−6.86127	−	6.54221i	−0.221331	−	0.211039i
$962$	5.74832	+	8.07239i	0.185333	+	0.260264i
$963$	−11.6306	+	12.0474i	−0.374790	+	0.388223i
$964$	−5.60739	+	10.8768i	−0.180602	+	0.350319i
$965$	−22.6205			−0.728180
$966$	11.9637	+	18.4355i	0.384926	+	0.593154i
$967$	−21.0789			−0.677853			−0.338926	−	0.940813i	$-0.610064\pi$
$967$	−21.0789			−0.677853			−0.338926	+	0.940813i	$0.610064\pi$
$968$	7.28039	−	14.1220i	0.234001	−	0.453898i
$969$	11.9340	−	0.816382i	0.383375	−	0.0262260i
$970$	−4.77372	−	6.70375i	−0.153275	−	0.215245i
$971$	−19.2616	−	18.3659i	−0.618134	−	0.589389i	0.314924	−	0.949117i	$-0.398021\pi$
$971$	−19.2616	−	18.3659i	−0.618134	−	0.589389i	−0.933057	+	0.359728i	$0.882870\pi$
$972$	−8.93637	+	12.7727i	−0.286634	+	0.409684i
$973$	−32.5811	+	21.1932i	−1.04450	+	0.679422i
$974$	−29.5904	+	4.25445i	−0.948136	+	0.136321i
$975$	25.1045	−	36.8454i	0.803986	−	1.18000i
$976$	8.66335	−	2.99841i	0.277307	−	0.0959769i
$977$	42.4168	−	21.8674i	1.35703	−	0.699599i	0.382523	−	0.923946i	$-0.375055\pi$
$977$	42.4168	−	21.8674i	1.35703	−	0.699599i	0.974509	+	0.224347i	$0.0720249\pi$
$978$	6.99885	+	8.53027i	0.223799	+	0.272768i
$979$	−1.00769	+	1.16294i	−0.0322060	+	0.0371677i
$980$	−6.79673	−	4.26291i	−0.217114	−	0.136174i
$981$	−1.38566	−	33.4479i	−0.0442406	−	1.06791i
$982$	−0.770388	+	2.22589i	−0.0245841	+	0.0710310i
$983$	−14.8917	−	1.42199i	−0.474972	−	0.0453543i	−0.145175	−	0.989406i	$-0.546374\pi$
$983$	−14.8917	−	1.42199i	−0.474972	−	0.0453543i	−0.329797	+	0.944052i	$0.606980\pi$
$984$	16.7162	−	9.06061i	0.532892	−	0.288842i
$985$	−0.282323	−	2.95662i	−0.00899556	−	0.0942058i
$986$	−2.98056	+	20.7303i	−0.0949205	+	0.660186i
$987$	−10.6079	−	4.51231i	−0.337652	−	0.143629i
$988$		−	10.9960i		−	0.349829i
$989$	−10.2775	−	38.0476i	−0.326805	−	1.20984i
$990$	−10.4319	+	14.4591i	−0.331548	+	0.459541i
$991$	0.750962	+	15.7646i	0.0238551	+	0.500780i	0.978903	+	0.204327i	$0.0655007\pi$
$991$	0.750962	+	15.7646i	0.0238551	+	0.500780i	−0.955048	+	0.296453i	$0.904196\pi$
$992$	−1.72411	−	4.30663i	−0.0547407	−	0.136736i
$993$	53.1926	−	16.8224i	1.68802	−	0.533842i
$994$	−19.0046	+	15.1156i	−0.602791	+	0.479438i
$995$	−4.84442	+	2.21237i	−0.153578	+	0.0701369i
$996$	20.5227	−	8.71319i	0.650287	−	0.276088i
$997$	−41.9136	−	16.7797i	−1.32742	−	0.531417i	−0.403839	−	0.914830i	$-0.632325\pi$
$997$	−41.9136	−	16.7797i	−1.32742	−	0.531417i	−0.923577	+	0.383413i	$0.874749\pi$
$998$	−25.0965	−	26.3204i	−0.794416	−	0.833159i
$999$	−3.16039	−	6.66280i	−0.0999904	−	0.210802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.bf.a.11.16	✓	1280
3.2	odd	2	inner	966.2.bf.a.11.35	yes	1280
7.2	even	3	inner	966.2.bf.a.149.59	yes	1280
21.2	odd	6	inner	966.2.bf.a.149.20	yes	1280
23.21	odd	22	inner	966.2.bf.a.389.20	yes	1280
69.44	even	22	inner	966.2.bf.a.389.59	yes	1280
161.44	odd	66	inner	966.2.bf.a.527.35	yes	1280
483.44	even	66	inner	966.2.bf.a.527.16	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.bf.a.11.16	✓	1280	1.1	even	1	trivial
966.2.bf.a.11.35	yes	1280	3.2	odd	2	inner
966.2.bf.a.149.20	yes	1280	21.2	odd	6	inner
966.2.bf.a.149.59	yes	1280	7.2	even	3	inner
966.2.bf.a.389.20	yes	1280	23.21	odd	22	inner
966.2.bf.a.389.59	yes	1280	69.44	even	22	inner
966.2.bf.a.527.16	yes	1280	483.44	even	66	inner
966.2.bf.a.527.35	yes	1280	161.44	odd	66	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.bf (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.458227 + 0.888835i) q^{2} +(-0.118210 - 1.72801i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(0.829499 + 0.790926i) q^{5} +(1.59009 + 0.686752i) q^{6} +(2.21783 - 1.44264i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.97205 + 0.408537i) q^{9} +O(q^{10})\)	\(q+(-0.458227 + 0.888835i) q^{2} +(-0.118210 - 1.72801i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(0.829499 + 0.790926i) q^{5} +(1.59009 + 0.686752i) q^{6} +(2.21783 - 1.44264i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.97205 + 0.408537i) q^{9} +(-1.08310 + 0.374865i) q^{10} +(-4.60895 + 2.37608i) q^{11} +(-1.33903 + 1.09864i) q^{12} +(-4.57275 + 5.27724i) q^{13} +(0.266002 + 2.63235i) q^{14} +(1.26867 - 1.52688i) q^{15} +(-0.327068 + 0.945001i) q^{16} +(-4.36579 - 0.416883i) q^{17} +(0.998751 - 2.82887i) q^{18} +(-0.149687 - 1.56760i) q^{19} +(0.163112 - 1.13447i) q^{20} +(-2.75507 - 3.66191i) q^{21} -5.18538i q^{22} +(1.89681 + 4.40478i) q^{23} +(-0.362929 - 1.69360i) q^{24} +(-0.175404 - 3.68219i) q^{25} +(-2.59524 - 6.48259i) q^{26} +(1.05728 + 5.08745i) q^{27} +(-2.46161 - 0.969779i) q^{28} +(-4.34390 + 1.98379i) q^{29} +(0.775805 + 1.82730i) q^{30} +(4.30663 + 1.72411i) q^{31} +(-0.690079 - 0.723734i) q^{32} +(4.65072 + 7.68345i) q^{33} +(2.37106 - 3.68945i) q^{34} +(2.98071 + 0.557471i) q^{35} +(2.05674 + 2.18399i) q^{36} +(-1.37919 + 0.334588i) q^{37} +(1.46193 + 0.585267i) q^{38} +(9.65968 + 7.27795i) q^{39} +(0.933616 + 0.664825i) q^{40} +(3.09276 + 10.5330i) q^{41} +(4.51728 - 0.770824i) q^{42} +(-8.13417 - 1.16952i) q^{43} +(4.60895 + 2.37608i) q^{44} +(-2.78844 - 2.01179i) q^{45} +(-4.78430 - 0.332441i) q^{46} +(2.17853 - 1.25777i) q^{47} +(1.67164 + 0.453469i) q^{48} +(2.83757 - 6.39908i) q^{49} +(3.35324 + 1.53137i) q^{50} +(-0.204298 + 7.59343i) q^{51} +(6.95117 + 0.663756i) q^{52} +(5.30939 - 1.02330i) q^{53} +(-5.00638 - 1.39145i) q^{54} +(-5.70242 - 1.67438i) q^{55} +(1.98995 - 1.74359i) q^{56} +(-2.69113 + 0.443967i) q^{57} +(0.227225 - 4.77004i) q^{58} +(-7.76772 + 2.68843i) q^{59} +(-1.97966 - 0.147754i) q^{60} +(-5.66701 - 7.20619i) q^{61} +(-3.50587 + 3.03785i) q^{62} +(-6.00214 + 5.19368i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-7.96700 + 0.760756i) q^{65} +(-8.96040 + 0.612964i) q^{66} +(3.59172 - 0.171095i) q^{67} +(2.19283 + 3.79809i) q^{68} +(7.38730 - 3.79839i) q^{69} +(-1.86134 + 2.39392i) q^{70} +(4.96204 + 7.72108i) q^{71} +(-2.88366 + 0.827346i) q^{72} +(-7.50739 - 10.5426i) q^{73} +(0.334588 - 1.37919i) q^{74} +(-6.34214 + 0.738373i) q^{75} +(-1.19010 + 1.03123i) q^{76} +(-6.79405 + 11.9188i) q^{77} +(-10.8952 + 5.25091i) q^{78} +(-1.41813 + 7.35796i) q^{79} +(-1.01873 + 0.525191i) q^{80} +(8.66620 - 2.42839i) q^{81} +(-10.7793 - 2.07753i) q^{82} +(-12.3510 - 3.62659i) q^{83} +(-1.38480 + 4.36833i) q^{84} +(-3.29170 - 3.79882i) q^{85} +(4.76680 - 6.69404i) q^{86} +(3.94151 + 7.27180i) q^{87} +(-4.22389 + 3.00782i) q^{88} +(0.275498 - 0.110293i) q^{89} +(3.06589 - 1.55661i) q^{90} +(-2.52843 + 18.3009i) q^{91} +(2.48778 - 4.10012i) q^{92} +(2.47020 - 7.64572i) q^{93} +(0.119695 + 2.51270i) q^{94} +(1.11569 - 1.41871i) q^{95} +(-1.16905 + 1.27802i) q^{96} +(2.02296 + 6.88956i) q^{97} +(4.38748 + 5.45436i) q^{98} +(12.7273 - 8.94476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9	\( 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9} + 64 q^{16} + 44 q^{18} - 132 q^{21} - 4 q^{24} + 72 q^{25} + 108 q^{27} + 44 q^{30} + 8 q^{36} + 44 q^{37} - 4 q^{39} - 88 q^{43} - 12 q^{46} + 60 q^{49} - 48 q^{54} + 96 q^{55} + 44 q^{58} - 176 q^{61} - 110 q^{63} + 128 q^{64} + 56 q^{69} - 120 q^{70} + 44 q^{72} + 40 q^{73} - 268 q^{75} + 16 q^{78} + 88 q^{79} + 8 q^{81} - 56 q^{82} - 22 q^{84} + 64 q^{85} - 42 q^{87} - 32 q^{93} + 8 q^{94} + 4 q^{96} + 132 q^{99}+O(q^{100}) \) 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9 + 64 * q^16 + 44 * q^18 - 132 * q^21 - 4 * q^24 + 72 * q^25 + 108 * q^27 + 44 * q^30 + 8 * q^36 + 44 * q^37 - 4 * q^39 - 88 * q^43 - 12 * q^46 + 60 * q^49 - 48 * q^54 + 96 * q^55 + 44 * q^58 - 176 * q^61 - 110 * q^63 + 128 * q^64 + 56 * q^69 - 120 * q^70 + 44 * q^72 + 40 * q^73 - 268 * q^75 + 16 * q^78 + 88 * q^79 + 8 * q^81 - 56 * q^82 - 22 * q^84 + 64 * q^85 - 42 * q^87 - 32 * q^93 + 8 * q^94 + 4 * q^96 + 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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