LMFDB - Embedded newform 880.2.bk.b.243.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(243,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.243"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bk (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [236] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$236$
Relative dimension:	$118$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			243.18
Character	$\chi$	$=$	880.243
Dual form			880.2.bk.b.507.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23734 + 0.684833i) q^{2} +0.322247 q^{3} +(1.06201 - 1.69474i) q^{4} +(-2.23514 + 0.0642867i) q^{5} +(-0.398728 + 0.220685i) q^{6} +(-3.32902 + 3.32902i) q^{7} +(-0.153447 + 2.82426i) q^{8} -2.89616 q^{9} +(2.72160 - 1.61024i) q^{10} +(0.707107 + 0.707107i) q^{11} +(0.342228 - 0.546124i) q^{12} -4.58312i q^{13} +(1.83930 - 6.39895i) q^{14} +(-0.720268 + 0.0207162i) q^{15} +(-1.74428 - 3.59965i) q^{16} +(1.19719 - 1.19719i) q^{17} +(3.58352 - 1.98338i) q^{18} +(-0.343132 - 0.343132i) q^{19} +(-2.26479 + 3.85626i) q^{20} +(-1.07277 + 1.07277i) q^{21} +(-1.35918 - 0.390679i) q^{22} +(3.33474 + 3.33474i) q^{23} +(-0.0494479 + 0.910109i) q^{24} +(4.99173 - 0.287380i) q^{25} +(3.13867 + 5.67087i) q^{26} -1.90002 q^{27} +(2.10638 + 9.17727i) q^{28} +(6.78356 - 6.78356i) q^{29} +(0.877027 - 0.518896i) q^{30} -0.588146i q^{31} +(4.62343 + 3.25944i) q^{32} +(0.227863 + 0.227863i) q^{33} +(-0.661452 + 2.30120i) q^{34} +(7.22683 - 7.65486i) q^{35} +(-3.07574 + 4.90823i) q^{36} +11.0588i q^{37} +(0.659559 + 0.189582i) q^{38} -1.47690i q^{39} +(0.161414 - 6.32250i) q^{40} -4.36269i q^{41} +(0.592708 - 2.06204i) q^{42} -10.6535i q^{43} +(1.94931 - 0.447409i) q^{44} +(6.47333 - 0.186184i) q^{45} +(-6.40994 - 1.84246i) q^{46} +(6.19042 + 6.19042i) q^{47} +(-0.562089 - 1.15998i) q^{48} -15.1648i q^{49} +(-5.97965 + 3.77409i) q^{50} +(0.385790 - 0.385790i) q^{51} +(-7.76720 - 4.86731i) q^{52} -5.50810 q^{53} +(2.35096 - 1.30119i) q^{54} +(-1.62594 - 1.53503i) q^{55} +(-8.89120 - 9.91286i) q^{56} +(-0.110573 - 0.110573i) q^{57} +(-3.74794 + 13.0392i) q^{58} +(6.92764 - 6.92764i) q^{59} +(-0.729821 + 1.24267i) q^{60} +(-5.91278 - 5.91278i) q^{61} +(0.402782 + 0.727734i) q^{62} +(9.64137 - 9.64137i) q^{63} +(-7.95291 - 0.866750i) q^{64} +(0.294634 + 10.2439i) q^{65} +(-0.437991 - 0.125895i) q^{66} -1.44289i q^{67} +(-0.757500 - 3.30035i) q^{68} +(1.07461 + 1.07461i) q^{69} +(-3.69973 + 14.4208i) q^{70} -3.21142 q^{71} +(0.444407 - 8.17951i) q^{72} +(-0.881978 + 0.881978i) q^{73} +(-7.57345 - 13.6835i) q^{74} +(1.60857 - 0.0926073i) q^{75} +(-0.945929 + 0.217111i) q^{76} -4.70795 q^{77} +(1.01143 + 1.82742i) q^{78} -10.2251 q^{79} +(4.13013 + 7.93360i) q^{80} +8.07620 q^{81} +(2.98772 + 5.39812i) q^{82} +14.8245 q^{83} +(0.678774 + 2.95735i) q^{84} +(-2.59893 + 2.75285i) q^{85} +(7.29588 + 13.1820i) q^{86} +(2.18598 - 2.18598i) q^{87} +(-2.10556 + 1.88855i) q^{88} +3.96258 q^{89} +(-7.88218 + 4.66352i) q^{90} +(15.2573 + 15.2573i) q^{91} +(9.19304 - 2.11000i) q^{92} -0.189528i q^{93} +(-11.8990 - 3.42023i) q^{94} +(0.789009 + 0.744891i) q^{95} +(1.48988 + 1.05034i) q^{96} +(3.66933 - 3.66933i) q^{97} +(10.3854 + 18.7640i) q^{98} +(-2.04789 - 2.04789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 236 q + 4 q^{3} + 4 q^{5} - 4 q^{7} + 12 q^{8} + 240 q^{9} - 8 q^{12} + 12 q^{14} - 4 q^{15} - 8 q^{16} + 8 q^{17} + 28 q^{18} + 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} + 12 q^{25} + 8 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) $ 236 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 + 12 * q^8 + 240 * q^9 - 8 * q^12 + 12 * q^14 - 4 * q^15 - 8 * q^16 + 8 * q^17 + 28 * q^18 + 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 + 12 * q^25 + 8 * q^26 + 4 * q^27 - 36 * q^28 + 8 * q^29 - 56 * q^30 - 40 * q^32 - 4 * q^33 - 44 * q^34 - 28 * q^35 - 32 * q^36 - 12 * q^38 - 40 * q^40 - 20 * q^42 - 40 * q^46 - 48 * q^47 - 40 * q^48 - 28 * q^51 - 4 * q^52 + 28 * q^53 - 24 * q^56 - 16 * q^57 - 76 * q^58 + 8 * q^59 - 4 * q^60 - 24 * q^61 + 12 * q^62 - 24 * q^63 - 32 * q^65 - 4 * q^66 + 36 * q^68 + 48 * q^69 + 28 * q^70 - 4 * q^71 + 20 * q^72 + 8 * q^73 - 68 * q^75 - 24 * q^76 + 12 * q^77 + 8 * q^78 + 40 * q^79 + 112 * q^80 + 244 * q^81 - 64 * q^82 + 24 * q^83 - 104 * q^84 + 8 * q^85 + 72 * q^86 - 140 * q^87 - 32 * q^88 + 36 * q^89 - 136 * q^90 + 12 * q^91 + 72 * q^92 - 16 * q^94 - 36 * q^95 + 72 * q^96 + 20 * q^97 + 136 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.23734	+	0.684833i	−0.874930	+	0.484250i
$2$	−1.23734	+	0.684833i	−0.874930	+	0.484250i
$3$	0.322247			0.186049			0.0930246	−	0.995664i	$-0.470346\pi$
$3$	0.322247			0.186049			0.0930246	+	0.995664i	$0.470346\pi$
$4$	1.06201	−	1.69474i	0.531004	−	0.847370i
$5$	−2.23514	+	0.0642867i	−0.999587	+	0.0287499i
$5$	−2.23514	+	0.0642867i	−0.999587	+	0.0287499i
$6$	−0.398728	+	0.220685i	−0.162780	+	0.0900944i
$7$	−3.32902	+	3.32902i	−1.25825	+	1.25825i	−0.306326	+	0.951927i	$0.599100\pi$
$7$	−3.32902	+	3.32902i	−1.25825	+	1.25825i	−0.951927	+	0.306326i	$0.900900\pi$
$8$	−0.153447	+	2.82426i	−0.0542518	+	0.998527i
$9$	−2.89616			−0.965386
$10$	2.72160	−	1.61024i	0.860646	−	0.509204i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$	0.342228	−	0.546124i	0.0987928	−	0.157652i
$13$		−	4.58312i		−	1.27113i	−0.772047	−	0.635565i	$-0.780767\pi$
$13$		−	4.58312i		−	1.27113i	0.772047	−	0.635565i	$-0.219233\pi$
$14$	1.83930	−	6.39895i	0.491573	−	1.71019i
$15$	−0.720268	+	0.0207162i	−0.185972	+	0.00534890i
$16$	−1.74428	−	3.59965i	−0.436071	−	0.899912i
$17$	1.19719	−	1.19719i	0.290361	−	0.290361i	−0.546862	−	0.837223i	$-0.684178\pi$
$17$	1.19719	−	1.19719i	0.290361	−	0.290361i	0.837223	+	0.546862i	$0.184178\pi$
$18$	3.58352	−	1.98338i	0.844644	−	0.467488i
$19$	−0.343132	−	0.343132i	−0.0787200	−	0.0787200i	0.666650	−	0.745370i	$-0.267727\pi$
$19$	−0.343132	−	0.343132i	−0.0787200	−	0.0787200i	−0.745370	+	0.666650i	$0.767727\pi$
$20$	−2.26479	+	3.85626i	−0.506422	+	0.862286i
$21$	−1.07277	+	1.07277i	−0.234097	+	0.234097i
$22$	−1.35918	−	0.390679i	−0.289778	−	0.0832931i
$23$	3.33474	+	3.33474i	0.695342	+	0.695342i	0.963402	−	0.268060i	$-0.0863827\pi$
$23$	3.33474	+	3.33474i	0.695342	+	0.695342i	−0.268060	+	0.963402i	$0.586383\pi$
$24$	−0.0494479	+	0.910109i	−0.0100935	+	0.185775i
$25$	4.99173	−	0.287380i	0.998347	−	0.0574760i
$26$	3.13867	+	5.67087i	0.615545	+	1.11215i
$27$	−1.90002			−0.365658
$28$	2.10638	+	9.17727i	0.398068	+	1.73434i
$29$	6.78356	−	6.78356i	1.25967	−	1.25967i	0.308427	−	0.951248i	$-0.400198\pi$
$29$	6.78356	−	6.78356i	1.25967	−	1.25967i	0.951248	−	0.308427i	$-0.0998025\pi$
$30$	0.877027	−	0.518896i	0.160122	−	0.0947370i
$31$		−	0.588146i		−	0.105634i	−0.998604	−	0.0528170i	$-0.983180\pi$
$31$		−	0.588146i		−	0.105634i	0.998604	−	0.0528170i	$-0.0168200\pi$
$32$	4.62343	+	3.25944i	0.817314	+	0.576193i
$33$	0.227863	+	0.227863i	0.0396658	+	0.0396658i
$34$	−0.661452	+	2.30120i	−0.113438	+	0.394653i
$35$	7.22683	−	7.65486i	1.22156	−	1.29391i
$36$	−3.07574	+	4.90823i	−0.512623	+	0.818039i
$37$			11.0588i			1.81806i	0.416732	+	0.909029i	$0.363175\pi$
$37$			11.0588i			1.81806i	−0.416732	+	0.909029i	$0.636825\pi$
$38$	0.659559	+	0.189582i	0.106995	+	0.0307543i
$39$		−	1.47690i		−	0.236493i
$40$	0.161414	−	6.32250i	0.0255218	−	0.999674i
$41$		−	4.36269i		−	0.681338i	−0.940183	−	0.340669i	$-0.889346\pi$
$41$		−	4.36269i		−	0.681338i	0.940183	−	0.340669i	$-0.110654\pi$
$42$	0.592708	−	2.06204i	0.0914568	−	0.318180i
$43$		−	10.6535i		−	1.62465i	−0.583208	−	0.812323i	$-0.698203\pi$
$43$		−	10.6535i		−	1.62465i	0.583208	−	0.812323i	$-0.301797\pi$
$44$	1.94931	−	0.447409i	0.293870	−	0.0674495i
$45$	6.47333	−	0.186184i	0.964987	−	0.0277547i
$46$	−6.40994	−	1.84246i	−0.945094	−	0.271656i
$47$	6.19042	+	6.19042i	0.902966	+	0.902966i	0.995692	−	0.0927261i	$-0.0295581\pi$
$47$	6.19042	+	6.19042i	0.902966	+	0.902966i	−0.0927261	+	0.995692i	$0.529558\pi$
$48$	−0.562089	−	1.15998i	−0.0811306	−	0.167428i
$49$		−	15.1648i		−	2.16640i
$50$	−5.97965	+	3.77409i	−0.845650	+	0.533737i
$51$	0.385790	−	0.385790i	0.0540214	−	0.0540214i
$52$	−7.76720	−	4.86731i	−1.07712	−	0.674974i
$53$	−5.50810			−0.756596			−0.378298	−	0.925684i	$-0.623490\pi$
$53$	−5.50810			−0.756596			−0.378298	+	0.925684i	$0.623490\pi$
$54$	2.35096	−	1.30119i	0.319925	−	0.177070i
$55$	−1.62594	−	1.53503i	−0.219242	−	0.206983i
$56$	−8.89120	−	9.91286i	−1.18814	−	1.32466i
$57$	−0.110573	−	0.110573i	−0.0146458	−	0.0146458i
$58$	−3.74794	+	13.0392i	−0.492129	+	1.71212i
$59$	6.92764	−	6.92764i	0.901902	−	0.901902i	−0.0936988	−	0.995601i	$-0.529869\pi$
$59$	6.92764	−	6.92764i	0.901902	−	0.901902i	0.995601	+	0.0936988i	$0.0298691\pi$
$60$	−0.729821	+	1.24267i	−0.0942195	+	0.160428i
$61$	−5.91278	−	5.91278i	−0.757054	−	0.757054i	0.218731	−	0.975785i	$-0.429808\pi$
$61$	−5.91278	−	5.91278i	−0.757054	−	0.757054i	−0.975785	+	0.218731i	$0.929808\pi$
$62$	0.402782	+	0.727734i	0.0511533	+	0.0924224i
$63$	9.64137	−	9.64137i	1.21470	−	1.21470i
$64$	−7.95291	−	0.866750i	−0.994113	−	0.108344i
$65$	0.294634	+	10.2439i	0.0365448	+	1.27060i
$66$	−0.437991	−	0.125895i	−0.0539130	−	0.0154966i
$67$		−	1.44289i		−	0.176277i	−0.996108	−	0.0881383i	$-0.971908\pi$
$67$		−	1.44289i		−	0.176277i	0.996108	−	0.0881383i	$-0.0280918\pi$
$68$	−0.757500	−	3.30035i	−0.0918604	−	0.400226i
$69$	1.07461	+	1.07461i	0.129368	+	0.129368i
$70$	−3.69973	+	14.4208i	−0.442202	+	1.72362i
$71$	−3.21142			−0.381125			−0.190563	−	0.981675i	$-0.561031\pi$
$71$	−3.21142			−0.381125			−0.190563	+	0.981675i	$0.561031\pi$
$72$	0.444407	−	8.17951i	0.0523739	−	0.963964i
$73$	−0.881978	+	0.881978i	−0.103228	+	0.103228i	−0.756834	−	0.653607i	$-0.773255\pi$
$73$	−0.881978	+	0.881978i	−0.103228	+	0.103228i	0.653607	+	0.756834i	$0.273255\pi$
$74$	−7.57345	−	13.6835i	−0.880395	−	1.59067i
$75$	1.60857	−	0.0926073i	0.185742	−	0.0106934i
$76$	−0.945929	+	0.217111i	−0.108505	+	0.0249043i
$77$	−4.70795			−0.536521
$78$	1.01143	+	1.82742i	0.114522	+	0.206914i
$79$	−10.2251			−1.15041			−0.575207	−	0.818008i	$-0.695079\pi$
$79$	−10.2251			−1.15041			−0.575207	+	0.818008i	$0.695079\pi$
$80$	4.13013	+	7.93360i	0.461763	+	0.887004i
$81$	8.07620			0.897355
$82$	2.98772	+	5.39812i	0.329938	+	0.596123i
$83$	14.8245			1.62720			0.813599	−	0.581427i	$-0.197505\pi$
$83$	14.8245			1.62720			0.813599	+	0.581427i	$0.197505\pi$
$84$	0.678774	+	2.95735i	0.0740603	+	0.322673i
$85$	−2.59893	+	2.75285i	−0.281893	+	0.298589i
$86$	7.29588	+	13.1820i	0.786735	+	1.42145i
$87$	2.18598	−	2.18598i	0.234362	−	0.234362i
$88$	−2.10556	+	1.88855i	−0.224453	+	0.201320i
$89$	3.96258			0.420033			0.210016	−	0.977698i	$-0.432648\pi$
$89$	3.96258			0.420033			0.210016	+	0.977698i	$0.432648\pi$
$90$	−7.88218	+	4.66352i	−0.830855	+	0.491578i
$91$	15.2573	+	15.2573i	1.59940	+	1.59940i
$92$	9.19304	−	2.11000i	0.958440	−	0.219983i
$93$		−	0.189528i		−	0.0196531i
$94$	−11.8990	−	3.42023i	−1.22729	−	0.352770i
$95$	0.789009	+	0.744891i	0.0809506	+	0.0764242i
$96$	1.48988	+	1.05034i	0.152061	+	0.107200i
$97$	3.66933	−	3.66933i	0.372564	−	0.372564i	−0.495846	−	0.868410i	$-0.665142\pi$
$97$	3.66933	−	3.66933i	0.372564	−	0.372564i	0.868410	+	0.495846i	$0.165142\pi$
$98$	10.3854	+	18.7640i	1.04908	+	1.89545i
$99$	−2.04789	−	2.04789i	−0.205821	−	0.205821i
$100$	4.81422	−	8.76489i	0.481422	−	0.876489i
$101$	4.06135	−	4.06135i	0.404119	−	0.404119i	−0.475563	−	0.879682i	$-0.657756\pi$
$101$	4.06135	−	4.06135i	0.404119	−	0.404119i	0.879682	+	0.475563i	$0.157756\pi$
$102$	−0.213151	+	0.741554i	−0.0211051	+	0.0734248i
$103$	0.764763	+	0.764763i	0.0753543	+	0.0753543i	0.743779	−	0.668425i	$-0.233031\pi$
$103$	0.764763	+	0.764763i	0.0753543	+	0.0753543i	−0.668425	+	0.743779i	$0.733031\pi$
$104$	12.9439	+	0.703267i	1.26926	+	0.0689610i
$105$	2.32882	−	2.46675i	0.227270	−	0.240730i
$106$	6.81538	−	3.77213i	0.661968	−	0.366382i
$107$	3.44777			0.333309			0.166654	−	0.986015i	$-0.446704\pi$
$107$	3.44777			0.333309			0.166654	+	0.986015i	$0.446704\pi$
$108$	−2.01783	+	3.22003i	−0.194166	+	0.309848i
$109$	−4.53672	+	4.53672i	−0.434539	+	0.434539i	−0.890169	−	0.455630i	$-0.849414\pi$
$109$	−4.53672	+	4.53672i	−0.434539	+	0.434539i	0.455630	+	0.890169i	$0.349414\pi$
$110$	3.06308	+	0.785847i	0.292053	+	0.0749276i
$111$			3.56367i			0.338248i
$112$	17.7901	+	6.17656i	1.68100	+	0.583630i
$113$	−8.61506	−	8.61506i	−0.810437	−	0.810437i	0.174263	−	0.984699i	$-0.444246\pi$
$113$	−8.61506	−	8.61506i	−0.810437	−	0.810437i	−0.984699	+	0.174263i	$0.944246\pi$
$114$	0.212541	+	0.0610922i	0.0199063	+	0.00572181i
$115$	−7.66801	−	7.23925i	−0.715045	−	0.675063i
$116$	−4.29217	−	18.7005i	−0.398518	−	1.73630i
$117$			13.2734i			1.22713i
$118$	−3.82755	+	13.3161i	−0.352354	+	1.22585i
$119$			7.97094i			0.730695i
$120$	0.0520151	−	2.03740i	0.00474831	−	0.185989i
$121$			1.00000i			0.0909091i
$122$	11.3654	+	3.26683i	1.02897	+	0.295765i
$123$		−	1.40586i		−	0.126762i
$124$	−0.996753	−	0.624615i	−0.0895111	−	0.0560921i
$125$	−11.1388	+	0.963238i	−0.996282	+	0.0861546i
$126$	−5.32690	+	18.5324i	−0.474558	+	1.65099i
$127$	−4.71482	−	4.71482i	−0.418373	−	0.418373i	0.466270	−	0.884643i	$-0.345598\pi$
$127$	−4.71482	−	4.71482i	−0.418373	−	0.418373i	−0.884643	+	0.466270i	$0.845598\pi$
$128$	10.4340	−	4.37395i	0.922245	−	0.386606i
$129$		−	3.43306i		−	0.302264i
$130$	−7.37995	−	12.4734i	−0.647265	−	1.09399i
$131$	−2.49439	+	2.49439i	−0.217936	+	0.217936i	−0.807628	−	0.589692i	$-0.799249\pi$
$131$	−2.49439	+	2.49439i	−0.217936	+	0.217936i	0.589692	+	0.807628i	$0.299249\pi$
$132$	0.628160	−	0.144176i	0.0546743	−	0.0125489i
$133$	2.28459			0.198099
$134$	0.988137	+	1.78534i	0.0853620	+	0.154230i
$135$	4.24681	−	0.122146i	0.365507	−	0.0105126i
$136$	3.19747	+	3.56488i	0.274181	+	0.305686i
$137$	−12.4747	−	12.4747i	−1.06579	−	1.06579i	−0.997678	−	0.0681078i	$-0.978304\pi$
$137$	−12.4747	−	12.4747i	−1.06579	−	1.06579i	−0.0681078	−	0.997678i	$-0.521696\pi$
$138$	−2.06558	−	0.593726i	−0.175834	−	0.0505413i
$139$	10.3288	−	10.3288i	0.876080	−	0.876080i	−0.117047	−	0.993126i	$-0.537343\pi$
$139$	10.3288	−	10.3288i	0.876080	−	0.876080i	0.993126	+	0.117047i	$0.0373427\pi$
$140$	−5.29804	−	20.3771i	−0.447766	−	1.72218i
$141$	1.99484	+	1.99484i	0.167996	+	0.167996i
$142$	3.97361	−	2.19929i	0.333458	−	0.184560i
$143$	3.24076	−	3.24076i	0.271006	−	0.271006i
$144$	5.05172	+	10.4252i	0.420976	+	0.868763i
$145$	−14.7261	+	15.5983i	−1.22294	+	1.29537i
$146$	0.487297	−	1.69531i	0.0403290	−	0.140305i
$147$		−	4.88680i		−	0.403057i
$148$	18.7418	+	11.7445i	1.54057	+	0.965395i
$149$	8.84414	+	8.84414i	0.724540	+	0.724540i	0.969526	−	0.244987i	$-0.0787836\pi$
$149$	8.84414	+	8.84414i	0.724540	+	0.724540i	−0.244987	+	0.969526i	$0.578784\pi$
$150$	−1.92692	+	1.21619i	−0.157333	+	0.0993014i
$151$	−7.67185			−0.624326			−0.312163	−	0.950029i	$-0.601053\pi$
$151$	−7.67185			−0.624326			−0.312163	+	0.950029i	$0.601053\pi$
$152$	1.02175	−	0.916443i	0.0828747	−	0.0743333i
$153$	−3.46725	+	3.46725i	−0.280310	+	0.280310i
$154$	5.82532	−	3.22416i	0.469418	−	0.259810i
$155$	0.0378099	+	1.31459i	0.00303697	+	0.105590i
$156$	−2.50295	−	1.56847i	−0.200397	−	0.125578i
$157$	10.9412			0.873201			0.436600	−	0.899656i	$-0.356182\pi$
$157$	10.9412			0.873201			0.436600	+	0.899656i	$0.356182\pi$
$158$	12.6519	−	7.00249i	1.00653	−	0.557088i
$159$	−1.77497			−0.140764
$160$	−10.5436	−	6.98809i	−0.833541	−	0.552457i
$161$	−22.2029			−1.74983
$162$	−9.99298	+	5.53085i	−0.785123	+	0.434544i
$163$	−1.49676			−0.117235			−0.0586177	−	0.998281i	$-0.518669\pi$
$163$	−1.49676			−0.117235			−0.0586177	+	0.998281i	$0.518669\pi$
$164$	−7.39363	−	4.63321i	−0.577345	−	0.361793i
$165$	−0.523955	−	0.494658i	−0.0407898	−	0.0385090i
$166$	−18.3429	+	10.1523i	−1.42368	+	0.787971i
$167$	4.65497	−	4.65497i	0.360213	−	0.360213i	−0.503678	−	0.863891i	$-0.668020\pi$
$167$	4.65497	−	4.65497i	0.360213	−	0.360213i	0.863891	+	0.503678i	$0.168020\pi$
$168$	−2.86516	−	3.19439i	−0.221052	−	0.246452i
$169$	−8.00502			−0.615771
$170$	1.33050	−	5.18604i	0.102045	−	0.397751i
$171$	0.993765	+	0.993765i	0.0759951	+	0.0759951i
$172$	−18.0549	−	11.3141i	−1.37668	−	0.862693i
$173$			14.2702i			1.08494i	0.840075	+	0.542471i	$0.182511\pi$
$173$			14.2702i			1.08494i	−0.840075	+	0.542471i	$0.817489\pi$
$174$	−1.20776	+	4.20182i	−0.0915602	+	0.318539i
$175$	−15.6609	+	17.5743i	−1.18385	+	1.32849i
$176$	1.31194	−	3.77873i	0.0988914	−	0.284833i
$177$	2.23241	−	2.23241i	0.167798	−	0.167798i
$178$	−4.90305	+	2.71371i	−0.367499	+	0.203401i
$179$	13.8345	+	13.8345i	1.03404	+	1.03404i	0.999400	+	0.0346380i	$0.0110278\pi$
$179$	13.8345	+	13.8345i	1.03404	+	1.03404i	0.0346380	+	0.999400i	$0.488972\pi$
$180$	6.55918	−	11.1683i	0.488893	−	0.832438i
$181$	−5.97832	+	5.97832i	−0.444365	+	0.444365i	−0.893476	−	0.449111i	$-0.851741\pi$
$181$	−5.97832	+	5.97832i	−0.444365	+	0.444365i	0.449111	+	0.893476i	$0.351741\pi$
$182$	−29.3272	−	8.42973i	−2.17388	−	0.624853i
$183$	−1.90537	−	1.90537i	−0.140849	−	0.140849i
$184$	−9.92989	+	8.90648i	−0.732041	+	0.656594i
$185$	−0.710935	−	24.7180i	−0.0522690	−	1.81731i
$186$	0.129795	+	0.234510i	0.00951703	+	0.0171951i
$187$	1.69308			0.123810
$188$	17.0654	−	3.91688i	1.24462	−	0.285668i
$189$	6.32520	−	6.32520i	0.460091	−	0.460091i
$190$	−1.48640	−	0.381342i	−0.107835	−	0.0276655i
$191$		−	16.8546i		−	1.21956i	−0.792572	−	0.609778i	$-0.791259\pi$
$191$		−	16.8546i		−	1.21956i	0.792572	−	0.609778i	$-0.208741\pi$
$192$	−2.56280	−	0.279307i	−0.184954	−	0.0201573i
$193$	−13.1945	−	13.1945i	−0.949758	−	0.949758i	0.0490393	−	0.998797i	$-0.484384\pi$
$193$	−13.1945	−	13.1945i	−0.949758	−	0.949758i	−0.998797	+	0.0490393i	$0.984384\pi$
$194$	−2.02732	+	7.05308i	−0.145553	+	0.506382i
$195$	0.0949448	+	3.30108i	0.00679914	+	0.236395i
$196$	−25.7004	−	16.1051i	−1.83574	−	1.15037i
$197$		−	14.7479i		−	1.05074i	−0.850873	−	0.525372i	$-0.823926\pi$
$197$		−	14.7479i		−	1.05074i	0.850873	−	0.525372i	$-0.176074\pi$
$198$	3.93640	+	1.13147i	0.279748	+	0.0804100i
$199$			5.22256i			0.370218i	0.982718	+	0.185109i	$0.0592638\pi$
$199$			5.22256i			0.370218i	−0.982718	+	0.185109i	$0.940736\pi$
$200$	0.0456689	+	14.1421i	0.00322928	+	0.999995i
$201$		−	0.464965i		−	0.0327961i
$202$	−2.24391	+	7.80660i	−0.157881	+	0.549271i
$203$			45.1652i			3.16998i
$204$	−0.244102	−	1.06353i	−0.0170905	−	0.0744617i
$205$	0.280463	+	9.75124i	0.0195884	+	0.681056i
$206$	−1.47000	−	0.422535i	−0.102420	−	0.0294394i
$207$	−9.65794	−	9.65794i	−0.671273	−	0.671273i
$208$	−16.4976	+	7.99426i	−1.14391	+	0.554302i
$209$		−	0.485263i		−	0.0335663i
$210$	−1.19223	+	4.64706i	−0.0822714	+	0.320678i
$211$	14.3738	−	14.3738i	0.989534	−	0.989534i	−0.0104116	−	0.999946i	$-0.503314\pi$
$211$	14.3738	−	14.3738i	0.989534	−	0.989534i	0.999946	+	0.0104116i	$0.00331418\pi$
$212$	−5.84964	+	9.33479i	−0.401755	+	0.641116i
$213$	−1.03487			−0.0709081
$214$	−4.26606	+	2.36115i	−0.291622	+	0.161405i
$215$	0.684880	+	23.8121i	0.0467084	+	1.62397i
$216$	0.291552	−	5.36615i	0.0198376	−	0.365120i
$217$	1.95795	+	1.95795i	0.132914	+	0.132914i
$218$	2.50656	−	8.72036i	0.169766	−	0.590617i
$219$	−0.284215	+	0.284215i	−0.0192054	+	0.0192054i
$220$	−4.32823	+	1.12534i	−0.291809	+	0.0758703i
$221$	−5.48686	−	5.48686i	−0.369086	−	0.369086i
$222$	−2.44052	−	4.40946i	−0.163797	−	0.295943i
$223$	4.82086	−	4.82086i	0.322829	−	0.322829i	−0.527023	−	0.849851i	$-0.676692\pi$
$223$	4.82086	−	4.82086i	0.322829	−	0.322829i	0.849851	+	0.527023i	$0.176692\pi$
$224$	−26.2422	+	4.54074i	−1.75338	+	0.303391i
$225$	−14.4568	+	0.832298i	−0.963790	+	0.0554865i
$226$	16.5596	+	4.75986i	1.10153	+	0.316621i
$227$			5.56975i			0.369677i	0.982769	+	0.184839i	$0.0591763\pi$
$227$			5.56975i			0.369677i	−0.982769	+	0.184839i	$0.940824\pi$
$228$	−0.304822	+	0.0699633i	−0.0201874	+	0.00463343i
$229$	−20.2746	−	20.2746i	−1.33978	−	1.33978i	−0.896264	−	0.443521i	$-0.853729\pi$
$229$	−20.2746	−	20.2746i	−1.33978	−	1.33978i	−0.443521	−	0.896264i	$-0.646271\pi$
$230$	14.4456	+	3.70608i	0.952514	+	0.244372i
$231$	−1.51712			−0.0998193
$232$	18.1176	+	20.1995i	1.18948	+	1.32616i
$233$	2.21441	−	2.21441i	0.145071	−	0.145071i	−0.630841	−	0.775912i	$-0.717290\pi$
$233$	2.21441	−	2.21441i	0.145071	−	0.145071i	0.775912	+	0.630841i	$0.217290\pi$
$234$	−9.09010	−	16.4237i	−0.594238	−	1.07365i
$235$	−14.2344	−	13.4385i	−0.928553	−	0.876632i
$236$	−4.38334	−	19.0977i	−0.285331	−	1.24316i
$237$	−3.29501			−0.214034
$238$	−5.45876	−	9.86274i	−0.353839	−	0.639306i
$239$	14.1934			0.918094			0.459047	−	0.888412i	$-0.348191\pi$
$239$	14.1934			0.918094			0.459047	+	0.888412i	$0.348191\pi$
$240$	1.33092	+	2.55658i	0.0859106	+	0.165026i
$241$	−17.7462			−1.14314			−0.571568	−	0.820555i	$-0.693665\pi$
$241$	−17.7462			−1.14314			−0.571568	+	0.820555i	$0.693665\pi$
$242$	−0.684833	−	1.23734i	−0.0440227	−	0.0795391i
$243$	8.30258			0.532611
$244$	−16.3000	+	3.74121i	−1.04350	+	0.239506i
$245$	0.974895	+	33.8955i	0.0622837	+	2.16550i
$246$	0.962782	+	1.73953i	0.0613847	+	0.110908i
$247$	−1.57262	+	1.57262i	−0.100063	+	0.100063i
$248$	1.66108	+	0.0902493i	0.105478	+	0.00573084i
$249$	4.77714			0.302739
$250$	13.1228	−	8.82005i	0.829956	−	0.557829i
$251$	19.6634	+	19.6634i	1.24114	+	1.24114i	0.959529	+	0.281611i	$0.0908688\pi$
$251$	19.6634	+	19.6634i	1.24114	+	1.24114i	0.281611	+	0.959529i	$0.409131\pi$
$252$	−6.10041	−	26.5788i	−0.384290	−	1.67431i
$253$			4.71604i			0.296495i
$254$	9.06269	+	2.60496i	0.568644	+	0.163450i
$255$	−0.837495	+	0.887098i	−0.0524460	+	0.0555522i
$256$	−9.91496	+	12.5576i	−0.619685	+	0.784851i
$257$	4.42450	−	4.42450i	0.275993	−	0.275993i	−0.555514	−	0.831507i	$-0.687479\pi$
$257$	4.42450	−	4.42450i	0.275993	−	0.275993i	0.831507	+	0.555514i	$0.187479\pi$
$258$	2.35107	+	4.24785i	0.146371	+	0.264460i
$259$	−36.8151	−	36.8151i	−2.28758	−	2.28758i
$260$	17.6737	+	10.3798i	1.09608	+	0.643728i
$261$	−19.6462	+	19.6462i	−1.21607	+	1.21607i
$262$	1.37816	−	4.79464i	0.0851431	−	0.296214i
$263$	−4.21964	−	4.21964i	−0.260194	−	0.260194i	0.564939	−	0.825133i	$-0.308900\pi$
$263$	−4.21964	−	4.21964i	−0.260194	−	0.260194i	−0.825133	+	0.564939i	$0.808900\pi$
$264$	−0.678509	+	0.608579i	−0.0417594	+	0.0374555i
$265$	12.3114	−	0.354098i	0.756283	−	0.0217520i
$266$	−2.82681	+	1.56456i	−0.173323	+	0.0959296i
$267$	1.27693			0.0781467
$268$	−2.44532	−	1.53236i	−0.149371	−	0.0936035i
$269$	12.0458	−	12.0458i	0.734445	−	0.734445i	−0.237052	−	0.971497i	$-0.576181\pi$
$269$	12.0458	−	12.0458i	0.734445	−	0.734445i	0.971497	+	0.237052i	$0.0761812\pi$
$270$	−5.17109	+	3.05949i	−0.314702	+	0.186195i
$271$		−	25.6087i		−	1.55562i	−0.628500	−	0.777810i	$-0.716331\pi$
$271$		−	25.6087i		−	1.55562i	0.628500	−	0.777810i	$-0.283669\pi$
$272$	−6.39770	−	2.22123i	−0.387917	−	0.134682i
$273$	4.91662	+	4.91662i	0.297568	+	0.297568i
$274$	23.9785	+	6.89232i	1.44859	+	0.416381i
$275$	3.73290	+	3.32648i	0.225102	+	0.200594i
$276$	2.96243	−	0.679940i	0.178317	−	0.0409276i
$277$			0.501410i			0.0301268i	0.999887	+	0.0150634i	$0.00479501\pi$
$277$			0.501410i			0.0301268i	−0.999887	+	0.0150634i	$0.995205\pi$
$278$	−5.70672	+	19.8538i	−0.342266	+	1.19075i
$279$			1.70336i			0.101978i
$280$	20.5104	+	21.5851i	1.22573	+	1.28996i
$281$			1.89558i			0.113081i	0.998400	+	0.0565403i	$0.0180069\pi$
$281$			1.89558i			0.113081i	−0.998400	+	0.0565403i	$0.981993\pi$
$282$	−3.83443	−	1.10216i	−0.228337	−	0.0656326i
$283$			18.6725i			1.10997i	0.831861	+	0.554984i	$0.187276\pi$
$283$			18.6725i			1.10997i	−0.831861	+	0.554984i	$0.812724\pi$
$284$	−3.41055	+	5.44252i	−0.202379	+	0.322954i
$285$	0.254256	+	0.240039i	0.0150608	+	0.0142187i
$286$	−1.79053	+	6.22929i	−0.105876	+	0.368346i
$287$	14.5235	+	14.5235i	0.857295	+	0.857295i
$288$	−13.3902	−	9.43985i	−0.789023	−	0.556248i
$289$			14.1335i			0.831381i
$290$	7.53895	−	29.3853i	0.442702	−	1.72557i
$291$	1.18243	−	1.18243i	0.0693153	−	0.0693153i
$292$	0.558056	+	2.43139i	0.0326578	+	0.142286i
$293$	−3.69134			−0.215651			−0.107825	−	0.994170i	$-0.534389\pi$
$293$	−3.69134			−0.215651			−0.107825	+	0.994170i	$0.534389\pi$
$294$	3.34665	+	6.04662i	0.195180	+	0.352646i
$295$	−15.0389	+	15.9296i	−0.875599	+	0.927459i
$296$	−31.2330	−	1.69694i	−1.81538	−	0.0986329i
$297$	−1.34351	−	1.34351i	−0.0779586	−	0.0779586i
$298$	−16.9999	−	4.88642i	−0.984780	−	0.283063i
$299$	15.2835	−	15.2835i	0.883869	−	0.883869i
$300$	1.55137	−	2.82446i	0.0895682	−	0.163070i
$301$	35.4658	+	35.4658i	2.04421	+	2.04421i
$302$	9.49266	−	5.25393i	0.546241	−	0.302330i
$303$	1.30876	−	1.30876i	0.0751860	−	0.0751860i
$304$	−0.636637	+	1.83368i	−0.0365136	+	0.105169i
$305$	13.5960	+	12.8358i	0.778506	+	0.734976i
$306$	1.91567	−	6.66464i	0.109511	−	0.380992i
$307$		−	12.5563i		−	0.716623i	−0.933602	−	0.358312i	$-0.883353\pi$
$307$		−	12.5563i		−	0.716623i	0.933602	−	0.358312i	$-0.116647\pi$
$308$	−4.99988	+	7.97875i	−0.284894	+	0.454631i
$309$	0.246442	+	0.246442i	0.0140196	+	0.0140196i
$310$	−0.947058	−	1.60070i	−0.0537893	−	0.0909135i
$311$	2.14722			0.121758			0.0608789	−	0.998145i	$-0.480610\pi$
$311$	2.14722			0.121758			0.0608789	+	0.998145i	$0.480610\pi$
$312$	4.17114	+	0.226626i	0.236144	+	0.0128301i
$313$	−16.6800	+	16.6800i	−0.942812	+	0.942812i	−0.998451	−	0.0556393i	$-0.982280\pi$
$313$	−16.6800	+	16.6800i	−0.942812	+	0.942812i	0.0556393	+	0.998451i	$0.482280\pi$
$314$	−13.5379	+	7.49288i	−0.763989	+	0.422848i
$315$	−20.9300	+	22.1697i	−1.17927	+	1.24912i
$316$	−10.8591	+	17.3289i	−0.610874	+	0.974826i
$317$	−20.2698			−1.13846			−0.569232	−	0.822177i	$-0.692759\pi$
$317$	−20.2698			−1.13846			−0.569232	+	0.822177i	$0.692759\pi$
$318$	2.19623	−	1.21556i	0.123159	−	0.0681650i
$319$	9.59340			0.537127
$320$	17.8316	+	1.42604i	0.996817	+	0.0797183i
$321$	1.11103			0.0620119
$322$	27.4724	−	15.2053i	1.53098	−	0.847356i
$323$	−0.821589			−0.0457144
$324$	8.57698	−	13.6870i	0.476499	−	0.760392i
$325$	−1.31710	−	22.8777i	−0.0730595	−	1.26903i
$326$	1.85200	−	1.02503i	0.102573	−	0.0567713i
$327$	−1.46194	+	1.46194i	−0.0808457	+	0.0808457i
$328$	12.3214	+	0.669443i	0.680335	+	0.0369638i
$329$	−41.2161			−2.27232
$330$	0.987067	+	0.253237i	0.0543362	+	0.0139402i
$331$	−4.47864	−	4.47864i	−0.246169	−	0.246169i	0.573228	−	0.819396i	$-0.305691\pi$
$331$	−4.47864	−	4.47864i	−0.246169	−	0.246169i	−0.819396	+	0.573228i	$0.805691\pi$
$332$	15.7437	−	25.1236i	0.864048	−	1.37884i
$333$		−	32.0281i		−	1.75513i
$334$	−2.57189	+	8.94765i	−0.140728	+	0.489594i
$335$	0.0927584	+	3.22506i	0.00506794	+	0.176204i
$336$	5.73279	+	1.99038i	0.312749	+	0.108584i
$337$	9.26132	−	9.26132i	0.504496	−	0.504496i	−0.408336	−	0.912832i	$-0.633891\pi$
$337$	9.26132	−	9.26132i	0.504496	−	0.504496i	0.912832	+	0.408336i	$0.133891\pi$
$338$	9.90491	−	5.48210i	0.538756	−	0.298187i
$339$	−2.77617	−	2.77617i	−0.150781	−	0.150781i
$340$	1.90529	+	7.32805i	0.103329	+	0.397419i
$341$	0.415882	−	0.415882i	0.0225213	−	0.0225213i
$342$	−1.91019	−	0.549059i	−0.103291	−	0.0296897i
$343$	27.1808	+	27.1808i	1.46762	+	1.46762i
$344$	30.0883	+	1.63475i	1.62225	+	0.0881399i
$345$	−2.47099	−	2.33282i	−0.133034	−	0.125595i
$346$	−9.77269	−	17.6570i	−0.525383	−	0.949247i
$347$	−30.4906			−1.63682			−0.818409	−	0.574636i	$-0.805144\pi$
$347$	−30.4906			−1.63682			−0.818409	+	0.574636i	$0.805144\pi$
$348$	−1.38314	−	6.02619i	−0.0741440	−	0.323038i
$349$	13.6528	−	13.6528i	0.730817	−	0.730817i	−0.239965	−	0.970782i	$-0.577136\pi$
$349$	13.6528	−	13.6528i	0.730817	−	0.730817i	0.970782	+	0.239965i	$0.0771360\pi$
$350$	7.34236	−	32.4704i	0.392466	−	1.73562i
$351$			8.70801i			0.464799i
$352$	0.964484	+	5.57403i	0.0514072	+	0.297097i
$353$	−8.28692	−	8.28692i	−0.441068	−	0.441068i	0.451303	−	0.892371i	$-0.350959\pi$
$353$	−8.28692	−	8.28692i	−0.441068	−	0.441068i	−0.892371	+	0.451303i	$0.850959\pi$
$354$	−1.23341	+	4.29107i	−0.0655553	+	0.228068i
$355$	7.17798	−	0.206452i	0.380968	−	0.0109573i
$356$	4.20829	−	6.71554i	0.223039	−	0.355923i
$357$			2.56861i			0.135945i
$358$	−26.5922	−	7.64361i	−1.40544	−	0.403977i
$359$		−	6.48935i		−	0.342495i	−0.985228	−	0.171247i	$-0.945220\pi$
$359$		−	6.48935i		−	0.342495i	0.985228	−	0.171247i	$-0.0547797\pi$
$360$	−0.467480	+	18.3109i	−0.0246384	+	0.965071i
$361$		−	18.7645i		−	0.987606i
$362$	3.30305	−	11.4914i	0.173604	−	0.603972i
$363$			0.322247i			0.0169136i
$364$	42.0606	−	9.65380i	2.20457	−	0.505997i
$365$	1.91465	−	2.02805i	0.100217	−	0.106153i
$366$	3.66245	+	1.05273i	0.191439	+	0.0550269i
$367$	13.7603	+	13.7603i	0.718284	+	0.718284i	0.968254	−	0.249970i	$-0.0804206\pi$
$367$	13.7603	+	13.7603i	0.718284	+	0.718284i	−0.249970	+	0.968254i	$0.580421\pi$
$368$	6.18717	−	17.8206i	0.322529	−	0.928965i
$369$			12.6350i			0.657754i
$370$	17.8074	+	30.0977i	0.925763	+	1.56470i
$371$	18.3366	−	18.3366i	0.951988	−	0.951988i
$372$	−0.321200	−	0.201280i	−0.0166535	−	0.0104359i
$373$	10.2637			0.531432			0.265716	−	0.964051i	$-0.414392\pi$
$373$	10.2637			0.531432			0.265716	+	0.964051i	$0.414392\pi$
$374$	−2.09491	+	1.15948i	−0.108325	+	0.0599552i
$375$	−3.58943	+	0.310400i	−0.185357	+	0.0160290i
$376$	−18.4333	+	16.5335i	−0.950623	+	0.852648i
$377$	−31.0899	−	31.0899i	−1.60121	−	1.60121i
$378$	−3.49470	+	12.1581i	−0.179748	+	0.625346i
$379$	−4.57466	+	4.57466i	−0.234985	+	0.234985i	−0.814770	−	0.579785i	$-0.803137\pi$
$379$	−4.57466	+	4.57466i	−0.234985	+	0.234985i	0.579785	+	0.814770i	$0.303137\pi$
$380$	2.10033	−	0.546085i	0.107745	−	0.0280136i
$381$	−1.51934	−	1.51934i	−0.0778379	−	0.0778379i
$382$	11.5426	+	20.8548i	0.590570	+	1.06703i
$383$	11.3307	−	11.3307i	0.578971	−	0.578971i	−0.355649	−	0.934620i	$-0.615740\pi$
$383$	11.3307	−	11.3307i	0.578971	−	0.578971i	0.934620	+	0.355649i	$0.115740\pi$
$384$	3.36232	−	1.40949i	0.171583	−	0.0719278i
$385$	10.5229	−	0.302659i	0.536299	−	0.0154249i
$386$	25.3620	+	7.28999i	1.29089	+	0.371051i
$387$			30.8543i			1.56841i
$388$	−2.32170	−	10.1154i	−0.117867	−	0.513533i
$389$	0.768766	+	0.768766i	0.0389780	+	0.0389780i	0.726327	−	0.687349i	$-0.241226\pi$
$389$	0.768766	+	0.768766i	0.0389780	+	0.0389780i	−0.687349	+	0.726327i	$0.741226\pi$
$390$	−2.37816	−	4.01952i	−0.120423	−	0.203536i
$391$	7.98463			0.403800
$392$	42.8293	+	2.32699i	2.16321	+	0.117531i
$393$	−0.803809	+	0.803809i	−0.0405468	+	0.0405468i
$394$	10.0998	+	18.2481i	0.508823	+	0.919326i
$395$	22.8546	−	0.657339i	1.14994	−	0.0330743i
$396$	−5.64552	+	1.29577i	−0.283698	+	0.0651148i
$397$	4.77834			0.239818			0.119909	−	0.992785i	$-0.461740\pi$
$397$	4.77834			0.239818			0.119909	+	0.992785i	$0.461740\pi$
$398$	−3.57658	−	6.46207i	−0.179278	−	0.323914i
$399$	0.736202			0.0368562
$400$	−9.74146	−	17.4672i	−0.487073	−	0.873361i
$401$	25.6804			1.28242			0.641209	−	0.767366i	$-0.278433\pi$
$401$	25.6804			1.28242			0.641209	+	0.767366i	$0.278433\pi$
$402$	0.318424	+	0.575319i	0.0158815	+	0.0286943i
$403$	−2.69554			−0.134275
$404$	−2.56975	−	11.1961i	−0.127850	−	0.557027i
$405$	−18.0515	+	0.519192i	−0.896984	+	0.0257989i
$406$	−30.9307	−	55.8846i	−1.53506	−	2.77351i
$407$	−7.81977	+	7.81977i	−0.387611	+	0.387611i
$408$	1.03037	+	1.14877i	0.0510111	+	0.0568726i
$409$	35.5727			1.75896			0.879479	−	0.475937i	$-0.157891\pi$
$409$	35.5727			1.75896			0.879479	+	0.475937i	$0.157891\pi$
$410$	−7.02500	−	11.8735i	−0.346940	−	0.586391i
$411$	−4.01993	−	4.01993i	−0.198289	−	0.198289i
$412$	2.10826	−	0.483890i	0.103866	−	0.0238395i
$413$			46.1245i			2.26964i
$414$	18.5642	+	5.33605i	0.912381	+	0.262252i
$415$	−33.1348	+	0.953017i	−1.62653	+	0.0467818i
$416$	14.9384	−	21.1897i	0.732416	−	1.03891i
$417$	3.32843	−	3.32843i	0.162994	−	0.162994i
$418$	0.332324	+	0.600433i	0.0162545	+	0.0293682i
$419$	−19.6192	−	19.6192i	−0.958459	−	0.958459i	0.0407117	−	0.999171i	$-0.487037\pi$
$419$	−19.6192	−	19.6192i	−0.958459	−	0.958459i	−0.999171	+	0.0407117i	$0.987037\pi$
$420$	−1.70728	−	6.56646i	−0.0833065	−	0.320410i
$421$	18.9240	−	18.9240i	0.922297	−	0.922297i	−0.0748944	−	0.997191i	$-0.523862\pi$
$421$	18.9240	−	18.9240i	0.922297	−	0.922297i	0.997191	+	0.0748944i	$0.0238620\pi$
$422$	−7.94159	+	27.6289i	−0.386591	+	1.34495i
$423$	−17.9284	−	17.9284i	−0.871710	−	0.871710i
$424$	0.845203	−	15.5563i	0.0410467	−	0.755481i
$425$	5.63200	−	6.32010i	0.273192	−	0.306570i
$426$	1.28048	−	0.708713i	0.0620396	−	0.0343372i
$427$	39.3676			1.90513
$428$	3.66156	−	5.84308i	0.176988	−	0.282436i
$429$	1.04432	−	1.04432i	0.0504204	−	0.0504204i
$430$	−17.1548	−	28.9946i	−0.827276	−	1.39824i
$431$			8.10870i			0.390582i	0.980745	+	0.195291i	$0.0625652\pi$
$431$			8.10870i			0.390582i	−0.980745	+	0.195291i	$0.937435\pi$
$432$	3.31417	+	6.83940i	0.159453	+	0.329061i
$433$	6.97287	+	6.97287i	0.335095	+	0.335095i	0.854518	−	0.519423i	$-0.173853\pi$
$433$	6.97287	+	6.97287i	0.335095	+	0.335095i	−0.519423	+	0.854518i	$0.673853\pi$
$434$	−3.76351	−	1.08178i	−0.180654	−	0.0519269i
$435$	−4.74545	+	5.02651i	−0.227527	+	0.241003i
$436$	2.87053	+	12.5066i	0.137474	+	0.598957i
$437$		−	2.28852i		−	0.109475i
$438$	0.157030	−	0.546309i	0.00750317	−	0.0261037i
$439$		−	12.5125i		−	0.597189i	−0.954380	−	0.298594i	$-0.903482\pi$
$439$		−	12.5125i		−	0.597189i	0.954380	−	0.298594i	$-0.0965177\pi$
$440$	4.58482	−	4.35654i	0.218573	−	0.207690i
$441$			43.9196i			2.09141i
$442$	10.5467	+	3.03151i	0.501655	+	0.144194i
$443$		−	21.0775i		−	1.00142i	−0.865615	−	0.500710i	$-0.833072\pi$
$443$		−	21.0775i		−	1.00142i	0.865615	−	0.500710i	$-0.166928\pi$
$444$	6.03949	+	3.78464i	0.286621	+	0.179611i
$445$	−8.85693	+	0.254741i	−0.419859	+	0.0120759i
$446$	−2.66354	+	9.26651i	−0.126122	+	0.438782i
$447$	2.84999	+	2.84999i	0.134800	+	0.134800i
$448$	29.3608	−	23.5900i	1.38717	−	1.11452i
$449$			35.7436i			1.68685i	0.537250	+	0.843423i	$0.319463\pi$
$449$			35.7436i			1.68685i	−0.537250	+	0.843423i	$0.680537\pi$
$450$	17.3180	−	10.9304i	0.816379	−	0.515262i
$451$	3.08489	−	3.08489i	0.145262	−	0.145262i
$452$	−23.7495	+	5.45103i	−1.11708	+	0.256395i
$453$	−2.47223			−0.116155
$454$	−3.81435	−	6.89166i	−0.179016	−	0.323442i
$455$	−35.0832	−	33.1215i	−1.64472	−	1.55276i
$456$	0.329255	−	0.295321i	0.0154188	−	0.0138297i
$457$	3.92154	+	3.92154i	0.183442	+	0.183442i	0.792854	−	0.609412i	$-0.208594\pi$
$457$	3.92154	+	3.92154i	0.183442	+	0.183442i	−0.609412	+	0.792854i	$0.708594\pi$
$458$	38.9713	+	11.2018i	1.82101	+	0.523426i
$459$	−2.27468	+	2.27468i	−0.106173	+	0.106173i
$460$	−20.4121	+	5.30714i	−0.951720	+	0.247447i
$461$	16.7480	+	16.7480i	0.780031	+	0.780031i	0.979836	−	0.199804i	$-0.0640307\pi$
$461$	16.7480	+	16.7480i	0.780031	+	0.780031i	−0.199804	+	0.979836i	$0.564031\pi$
$462$	1.87719	−	1.03897i	0.0873348	−	0.0483375i
$463$	−26.6090	+	26.6090i	−1.23662	+	1.23662i	−0.275251	+	0.961372i	$0.588761\pi$
$463$	−26.6090	+	26.6090i	−1.23662	+	1.23662i	−0.961372	+	0.275251i	$0.911239\pi$
$464$	−36.2509	−	12.5860i	−1.68290	−	0.584290i
$465$	0.0121841	+	0.423622i	0.000565025	+	0.0196450i
$466$	−1.22347	+	4.25647i	−0.0566762	+	0.197177i
$467$			23.0703i			1.06757i	0.845621	+	0.533784i	$0.179230\pi$
$467$			23.0703i			1.06757i	−0.845621	+	0.533784i	$0.820770\pi$
$468$	22.4950	+	14.0965i	1.03983	+	0.651611i
$469$	4.80340	+	4.80340i	0.221801	+	0.221801i
$470$	26.8159	+	6.87976i	1.23693	+	0.317340i
$471$	3.52576			0.162458
$472$	18.5024	+	20.6285i	0.851644	+	0.949503i
$473$	7.53317	−	7.53317i	0.346376	−	0.346376i
$474$	4.07703	−	2.25653i	0.187264	−	0.103646i
$475$	−1.81144	−	1.61422i	−0.0831144	−	0.0740653i
$476$	13.5087	+	8.46519i	0.619169	+	0.388002i
$477$	15.9523			0.730407
$478$	−17.5620	+	9.72011i	−0.803268	+	0.444587i
$479$	−9.40352			−0.429658			−0.214829	−	0.976652i	$-0.568919\pi$
$479$	−9.40352			−0.429658			−0.214829	+	0.976652i	$0.568919\pi$
$480$	−3.39763	−	2.25189i	−0.155080	−	0.102784i
$481$	50.6839			2.31099
$482$	21.9581	−	12.1532i	1.00016	−	0.553564i
$483$	−7.15480			−0.325555
$484$	1.69474	+	1.06201i	0.0770336	+	0.0482730i
$485$	−7.96560	+	8.43737i	−0.361699	+	0.383121i
$486$	−10.2731	+	5.68588i	−0.465997	+	0.257917i
$487$	8.82410	−	8.82410i	0.399858	−	0.399858i	−0.478325	−	0.878183i	$-0.658756\pi$
$487$	8.82410	−	8.82410i	0.399858	−	0.399858i	0.878183	+	0.478325i	$0.158756\pi$
$488$	17.6065	−	15.7919i	0.797010	−	0.714867i
$489$	−0.482327			−0.0218116
$490$	−24.4190	−	41.2725i	−1.10314	−	1.86450i
$491$	9.61111	+	9.61111i	0.433743	+	0.433743i	0.889900	−	0.456156i	$-0.150774\pi$
$491$	9.61111	+	9.61111i	0.433743	+	0.433743i	−0.456156	+	0.889900i	$0.650774\pi$
$492$	−2.38257	−	1.49304i	−0.107415	−	0.0673113i
$493$		−	16.2424i		−	0.731521i
$494$	0.868878	−	3.02284i	0.0390927	−	0.136004i
$495$	4.70899	+	4.44568i	0.211653	+	0.199819i
$496$	−2.11712	+	1.02589i	−0.0950614	+	0.0460639i
$497$	10.6909	−	10.6909i	0.479552	−	0.479552i
$498$	−5.91093	+	3.27154i	−0.264875	+	0.146601i
$499$	10.5920	+	10.5920i	0.474165	+	0.474165i	0.903260	−	0.429094i	$-0.141167\pi$
$499$	10.5920	+	10.5920i	0.474165	+	0.474165i	−0.429094	+	0.903260i	$0.641167\pi$
$500$	−10.1970	+	19.9003i	−0.456024	+	0.889967i
$501$	1.50005	−	1.50005i	0.0670173	−	0.0670173i
$502$	−37.7963	−	10.8641i	−1.68693	−	0.484888i
$503$	−26.8426	−	26.8426i	−1.19685	−	1.19685i	−0.975104	−	0.221747i	$-0.928824\pi$
$503$	−26.8426	−	26.8426i	−1.19685	−	1.19685i	−0.221747	−	0.975104i	$-0.571176\pi$
$504$	25.7503	+	28.7092i	1.14701	+	1.27881i
$505$	−8.81660	+	9.33879i	−0.392334	+	0.415570i
$506$	−3.22970	−	5.83533i	−0.143578	−	0.259412i
$507$	−2.57959			−0.114564
$508$	−12.9976	+	2.98322i	−0.576674	+	0.132359i
$509$	7.99722	−	7.99722i	0.354471	−	0.354471i	−0.507299	−	0.861770i	$-0.669356\pi$
$509$	7.99722	−	7.99722i	0.354471	−	0.354471i	0.861770	+	0.507299i	$0.169356\pi$
$510$	0.428750	−	1.67118i	0.0189854	−	0.0740012i
$511$		−	5.87225i		−	0.259773i
$512$	3.66828	−	22.3281i	0.162117	−	0.986772i
$513$	0.651957	+	0.651957i	0.0287846	+	0.0287846i
$514$	−2.44455	+	8.50464i	−0.107825	+	0.375124i
$515$	−1.75852	−	1.66019i	−0.0774896	−	0.0731567i
$516$	−5.81814	−	3.64593i	−0.256129	−	0.160503i
$517$			8.75458i			0.385026i
$518$	70.7648	+	20.3405i	3.10923	+	0.893709i
$519$			4.59852i			0.201852i
$520$	−28.9768	−	0.739780i	−1.27072	−	0.0324415i
$521$			17.8118i			0.780351i	0.920740	+	0.390176i	$0.127586\pi$
$521$			17.8118i			0.780351i	−0.920740	+	0.390176i	$0.872414\pi$
$522$	10.8546	−	37.7634i	0.475094	−	1.65286i
$523$		−	33.9568i		−	1.48483i	−0.669942	−	0.742414i	$-0.733681\pi$
$523$		−	33.9568i		−	1.48483i	0.669942	−	0.742414i	$-0.266319\pi$
$524$	1.57828	+	6.87640i	0.0689475	+	0.300397i
$525$	−5.04667	+	5.66326i	−0.220255	+	0.247165i
$526$	8.11087	+	2.33137i	0.353651	+	0.101653i
$527$	−0.704121	−	0.704121i	−0.0306720	−	0.0306720i
$528$	0.422769	−	1.21768i	0.0183987	−	0.0529929i
$529$		−	0.758999i		−	0.0329999i
$530$	−14.9908	+	8.86939i	−0.651161	+	0.385262i
$531$	−20.0635	+	20.0635i	−0.870683	+	0.870683i
$532$	2.42625	−	3.87179i	0.105191	−	0.167863i
$533$	−19.9948			−0.866069
$534$	−1.57999	+	0.874483i	−0.0683729	+	0.0378426i
$535$	−7.70627	+	0.221646i	−0.333171	+	0.00958260i
$536$	4.07509	+	0.221407i	0.176017	+	0.00956332i
$537$	4.45812	+	4.45812i	0.192382	+	0.192382i
$538$	−6.65535	+	23.1541i	−0.286933	+	0.998243i
$539$	10.7231	−	10.7231i	0.461878	−	0.461878i
$540$	4.30314	−	7.32696i	0.185178	−	0.315302i
$541$	−19.9583	−	19.9583i	−0.858075	−	0.858075i	0.133036	−	0.991111i	$-0.457527\pi$
$541$	−19.9583	−	19.9583i	−0.858075	−	0.858075i	−0.991111	+	0.133036i	$0.957527\pi$
$542$	17.5377	+	31.6866i	0.753309	+	1.36106i
$543$	−1.92649	+	1.92649i	−0.0826738	+	0.0826738i
$544$	9.43728	−	1.63295i	0.404620	−	0.0700121i
$545$	9.84858	−	10.4319i	0.421867	−	0.446853i
$546$	−9.45059	−	2.71645i	−0.404448	−	0.116253i
$547$		−	13.5464i		−	0.579203i	−0.957147	−	0.289601i	$-0.906477\pi$
$547$		−	13.5464i		−	0.579203i	0.957147	−	0.289601i	$-0.0935228\pi$
$548$	−34.3896	+	7.89315i	−1.46905	+	0.337178i
$549$	17.1243	+	17.1243i	0.730849	+	0.730849i
$550$	−6.89694	−	1.55957i	−0.294086	−	0.0665001i
$551$	−4.65532			−0.198323
$552$	−3.19987	+	2.87008i	−0.136196	+	0.122159i
$553$	34.0396	−	34.0396i	1.44751	−	1.44751i
$554$	−0.343382	−	0.620413i	−0.0145889	−	0.0263588i
$555$	−0.229096	−	7.96531i	−0.00972460	−	0.338109i
$556$	−6.53538	−	28.4740i	−0.277162	−	1.20756i
$557$	29.7472			1.26043			0.630214	−	0.776422i	$-0.282967\pi$
$557$	29.7472			1.26043			0.630214	+	0.776422i	$0.282967\pi$
$558$	−1.16652	−	2.10763i	−0.0493827	−	0.0892232i
$559$	−48.8264			−2.06514
$560$	−40.1604	−	12.6618i	−1.69709	−	0.535060i
$561$	0.545590			0.0230348
$562$	−1.29815	−	2.34547i	−0.0547593	−	0.0989375i
$563$	8.57691			0.361474			0.180737	−	0.983532i	$-0.442152\pi$
$563$	8.57691			0.361474			0.180737	+	0.983532i	$0.442152\pi$
$564$	5.49927	−	1.26220i	0.231561	−	0.0531483i
$565$	19.8097	+	18.7021i	0.833402	+	0.786802i
$566$	−12.7876	−	23.1042i	−0.537502	−	0.971143i
$567$	−26.8858	+	26.8858i	−1.12910	+	1.12910i
$568$	0.492783	−	9.06989i	0.0206767	−	0.380564i
$569$	−13.6295			−0.571380			−0.285690	−	0.958322i	$-0.592223\pi$
$569$	−13.6295			−0.571380			−0.285690	+	0.958322i	$0.592223\pi$
$570$	−0.478986	−	0.122886i	−0.0200625	−	0.00514714i
$571$	4.55985	+	4.55985i	0.190824	+	0.190824i	0.796052	−	0.605228i	$-0.206918\pi$
$571$	4.55985	+	4.55985i	0.190824	+	0.190824i	−0.605228	+	0.796052i	$0.706918\pi$
$572$	−2.05053	−	8.93395i	−0.0857370	−	0.373547i
$573$		−	5.43134i		−	0.226897i
$574$	−27.9167	−	8.02430i	−1.16522	−	0.334928i
$575$	17.6045	+	15.6878i	0.734158	+	0.654227i
$576$	23.0329	+	2.51024i	0.959703	+	0.104594i
$577$	−6.34252	+	6.34252i	−0.264043	+	0.264043i	−0.826694	−	0.562651i	$-0.809781\pi$
$577$	−6.34252	+	6.34252i	−0.264043	+	0.264043i	0.562651	+	0.826694i	$0.309781\pi$
$578$	−9.67907	−	17.4879i	−0.402596	−	0.727400i
$579$	−4.25187	−	4.25187i	−0.176702	−	0.176702i
$580$	10.7958	+	41.5225i	0.448272	+	1.72413i
$581$	−49.3510	+	49.3510i	−2.04743	+	2.04743i
$582$	−0.653297	+	2.27283i	−0.0270801	+	0.0942119i
$583$	−3.89481	−	3.89481i	−0.161307	−	0.161307i
$584$	−2.35560	−	2.62628i	−0.0974755	−	0.108676i
$585$	−0.853306	−	29.6681i	−0.0352799	−	1.22662i
$586$	4.56744	−	2.52796i	0.188679	−	0.104429i
$587$	−18.6432			−0.769487			−0.384743	−	0.923024i	$-0.625710\pi$
$587$	−18.6432			−0.769487			−0.384743	+	0.923024i	$0.625710\pi$
$588$	−8.28186	−	5.18982i	−0.341538	−	0.214025i
$589$	−0.201812	+	0.201812i	−0.00831551	+	0.00831551i
$590$	7.69907	−	30.0095i	0.316966	−	1.23547i
$591$		−	4.75246i		−	0.195490i
$592$	39.8079	−	19.2897i	1.63609	−	0.792802i
$593$	−31.0448	−	31.0448i	−1.27486	−	1.27486i	−0.943509	−	0.331346i	$-0.892497\pi$
$593$	−31.0448	−	31.0448i	−1.27486	−	1.27486i	−0.331346	−	0.943509i	$-0.607503\pi$
$594$	2.58246	+	0.742297i	0.105960	+	0.0304568i
$595$	−0.512426	−	17.8162i	−0.0210074	−	0.730393i
$596$	24.3810	−	5.59597i	0.998686	−	0.229220i
$597$			1.68295i			0.0688787i
$598$	−8.44421	+	29.3776i	−0.345310	+	1.20134i
$599$			6.98874i			0.285552i	0.989755	+	0.142776i	$0.0456029\pi$
$599$			6.98874i			0.285552i	−0.989755	+	0.142776i	$0.954397\pi$
$600$	0.0147167	+	4.55723i	0.000600805	+	0.186048i
$601$			30.1908i			1.23151i	0.787938	+	0.615754i	$0.211149\pi$
$601$			30.1908i			1.23151i	−0.787938	+	0.615754i	$0.788851\pi$
$602$	−68.1713	−	19.5950i	−2.77846	−	0.798633i
$603$			4.17883i			0.170175i
$604$	−8.14755	+	13.0018i	−0.331519	+	0.529035i
$605$	−0.0642867	−	2.23514i	−0.00261363	−	0.0908715i
$606$	−0.723093	+	2.51565i	−0.0293736	+	0.102191i
$607$	13.8432	+	13.8432i	0.561880	+	0.561880i	0.929841	−	0.367961i	$-0.119944\pi$
$607$	13.8432	+	13.8432i	0.561880	+	0.561880i	−0.367961	+	0.929841i	$0.619944\pi$
$608$	−0.468028	−	2.70487i	−0.0189810	−	0.109697i
$609$			14.5543i			0.589772i
$610$	−25.6132	−	6.57120i	−1.03705	−	0.266060i
$611$	28.3715	−	28.3715i	1.14779	−	1.14779i
$612$	2.19384	+	9.55832i	0.0886807	+	0.386372i
$613$	−7.03795			−0.284260			−0.142130	−	0.989848i	$-0.545395\pi$
$613$	−7.03795			−0.284260			−0.142130	+	0.989848i	$0.545395\pi$
$614$	8.59894	+	15.5363i	0.347025	+	0.626995i
$615$	0.0903783	+	3.14231i	0.00364441	+	0.126710i
$616$	0.722422	−	13.2965i	0.0291072	−	0.535731i
$617$	−21.4761	−	21.4761i	−0.864595	−	0.864595i	0.127273	−	0.991868i	$-0.459378\pi$
$617$	−21.4761	−	21.4761i	−0.864595	−	0.864595i	−0.991868	+	0.127273i	$0.959378\pi$
$618$	−0.473704	−	0.136160i	−0.0190552	−	0.00547717i
$619$	−22.3349	+	22.3349i	−0.897716	+	0.897716i	−0.995234	−	0.0975176i	$-0.968910\pi$
$619$	−22.3349	+	22.3349i	−0.897716	+	0.897716i	0.0975176	+	0.995234i	$0.468910\pi$
$620$	2.26804	+	1.33203i	0.0910867	+	0.0534954i
$621$	−6.33607	−	6.33607i	−0.254258	−	0.254258i
$622$	−2.65684	+	1.47049i	−0.106529	+	0.0589612i
$623$	−13.1915	+	13.1915i	−0.528507	+	0.528507i
$624$	−5.31631	+	2.57612i	−0.212823	+	0.103127i
$625$	24.8348	−	2.86905i	0.993393	−	0.114762i
$626$	9.21579	−	32.0619i	0.368337	−	1.28145i
$627$		−	0.156374i		−	0.00624499i
$628$	11.6196	−	18.5424i	0.463673	−	0.739924i
$629$	13.2395	+	13.2395i	0.527893	+	0.527893i
$630$	10.7150	−	41.7649i	0.426896	−	1.66396i
$631$	26.9088			1.07122			0.535612	−	0.844464i	$-0.320081\pi$
$631$	26.9088			1.07122			0.535612	+	0.844464i	$0.320081\pi$
$632$	1.56901	−	28.8784i	0.0624120	−	1.14872i
$633$	4.63191	−	4.63191i	0.184102	−	0.184102i
$634$	25.0805	−	13.8814i	0.996075	−	0.551301i
$635$	10.8414	+	10.2352i	0.430228	+	0.406172i
$636$	−1.88503	+	3.00811i	−0.0747462	+	0.119279i
$637$	−69.5021			−2.75377
$638$	−11.8703	+	6.56988i	−0.469948	+	0.260104i
$639$	9.30077			0.367933
$640$	−23.0403	+	10.4472i	−0.910749	+	0.412961i
$641$	18.4794			0.729893			0.364946	−	0.931029i	$-0.381087\pi$
$641$	18.4794			0.729893			0.364946	+	0.931029i	$0.381087\pi$
$642$	−1.37472	+	0.760873i	−0.0542560	+	0.0300293i
$643$	26.7004			1.05296			0.526480	−	0.850187i	$-0.323511\pi$
$643$	26.7004			1.05296			0.526480	+	0.850187i	$0.323511\pi$
$644$	−23.5796	+	37.6281i	−0.929166	+	1.48275i
$645$	0.220700	+	7.67338i	0.00869006	+	0.302139i
$646$	1.01658	−	0.562651i	0.0399969	−	0.0221372i
$647$	0.770414	−	0.770414i	0.0302881	−	0.0302881i	−0.691801	−	0.722089i	$-0.743182\pi$
$647$	0.770414	−	0.770414i	0.0302881	−	0.0302881i	0.722089	+	0.691801i	$0.243182\pi$
$648$	−1.23927	+	22.8093i	−0.0486831	+	0.896034i
$649$	9.79716			0.384572
$650$	17.2971	+	27.4055i	0.678449	+	1.07493i
$651$	0.630943	+	0.630943i	0.0247286	+	0.0247286i
$652$	−1.58957	+	2.53662i	−0.0622524	+	0.0993417i
$653$			28.7870i			1.12652i	0.826279	+	0.563261i	$0.190453\pi$
$653$			28.7870i			1.12652i	−0.826279	+	0.563261i	$0.809547\pi$
$654$	0.807730	−	2.81011i	0.0315848	−	0.109884i
$655$	5.41496	−	5.73568i	0.211580	−	0.224111i
$656$	−15.7042	+	7.60977i	−0.613145	+	0.297111i
$657$	2.55435	−	2.55435i	0.0996546	−	0.0996546i
$658$	50.9982	−	28.2262i	1.98812	−	1.10037i
$659$	−9.20191	−	9.20191i	−0.358455	−	0.358455i	0.504788	−	0.863243i	$-0.331571\pi$
$659$	−9.20191	−	9.20191i	−0.358455	−	0.358455i	−0.863243	+	0.504788i	$0.831571\pi$
$660$	−1.39476	+	0.362637i	−0.0542909	+	0.0141156i
$661$	15.3548	−	15.3548i	0.597234	−	0.597234i	−0.342342	−	0.939576i	$-0.611220\pi$
$661$	15.3548	−	15.3548i	0.597234	−	0.597234i	0.939576	+	0.342342i	$0.111220\pi$
$662$	8.60872	+	2.47447i	0.334587	+	0.0961730i
$663$	−1.76812	−	1.76812i	−0.0686682	−	0.0686682i
$664$	−2.27477	+	41.8682i	−0.0882784	+	1.62480i
$665$	−5.10639	+	0.146869i	−0.198017	+	0.00569533i
$666$	21.9339	+	39.6295i	0.849921	+	1.53561i
$667$	45.2428			1.75181
$668$	−2.94535	−	12.8326i	−0.113959	−	0.496507i
$669$	1.55351	−	1.55351i	0.0600620	−	0.0600620i
$670$	−2.32340	−	3.92696i	−0.0897608	−	0.151712i
$671$		−	8.36193i		−	0.322809i
$672$	−8.45647	+	1.46324i	−0.326216	+	0.0564457i
$673$	−8.98626	−	8.98626i	−0.346395	−	0.346395i	0.512370	−	0.858765i	$-0.328768\pi$
$673$	−8.98626	−	8.98626i	−0.346395	−	0.346395i	−0.858765	+	0.512370i	$0.828768\pi$
$674$	−5.11692	+	17.8018i	−0.197096	+	0.685701i
$675$	−9.48438	+	0.546027i	−0.365054	+	0.0210166i
$676$	−8.50139	+	13.5664i	−0.326976	+	0.521785i
$677$		−	47.1507i		−	1.81215i	−0.423118	−	0.906074i	$-0.639065\pi$
$677$		−	47.1507i		−	1.81215i	0.423118	−	0.906074i	$-0.360935\pi$
$678$	5.33628	+	1.53385i	0.204939	+	0.0589071i
$679$			24.4306i			0.937560i
$680$	−7.37598	−	7.76246i	−0.282856	−	0.297677i
$681$			1.79483i			0.0687782i
$682$	−0.229776	+	0.799395i	−0.00879859	+	0.0306104i
$683$		−	30.8596i		−	1.18081i	−0.807107	−	0.590406i	$-0.798968\pi$
$683$		−	30.8596i		−	1.18081i	0.807107	−	0.590406i	$-0.201032\pi$
$684$	2.73956	−	0.628787i	0.104750	−	0.0240423i
$685$	28.6847	+	27.0808i	1.09599	+	1.03470i
$686$	−52.2461	−	15.0175i	−1.99477	−	0.573371i
$687$	−6.53343	−	6.53343i	−0.249266	−	0.249266i
$688$	−38.3489	+	18.5827i	−1.46204	+	0.708460i
$689$			25.2443i			0.961731i
$690$	4.65504	+	1.19427i	0.177214	+	0.0454652i
$691$	−7.30096	+	7.30096i	−0.277742	+	0.277742i	−0.832207	−	0.554465i	$-0.812923\pi$
$691$	−7.30096	+	7.30096i	−0.277742	+	0.277742i	0.554465	+	0.832207i	$0.312923\pi$
$692$	24.1842	+	15.1550i	0.919346	+	0.576108i
$693$	13.6350			0.517949
$694$	37.7271	−	20.8809i	1.43210	−	0.792630i
$695$	−22.4224	+	23.7504i	−0.850530	+	0.900905i
$696$	5.83834	+	6.50921i	0.221302	+	0.246731i
$697$	−5.22297	−	5.22297i	−0.197834	−	0.197834i
$698$	−7.54322	+	26.2430i	−0.285515	+	0.993311i
$699$	0.713586	−	0.713586i	0.0269903	−	0.0269903i
$700$	13.1519	+	45.2052i	0.497093	+	1.70860i
$701$	−9.29422	−	9.29422i	−0.351038	−	0.351038i	0.509458	−	0.860496i	$-0.329846\pi$
$701$	−9.29422	−	9.29422i	−0.351038	−	0.351038i	−0.860496	+	0.509458i	$0.829846\pi$
$702$	−5.96354	−	10.7747i	−0.225079	−	0.406667i
$703$	3.79464	−	3.79464i	0.143118	−	0.143118i
$704$	−5.01067	−	6.23644i	−0.188847	−	0.235045i
$705$	−4.58700	−	4.33052i	−0.172756	−	0.163097i
$706$	15.9289	+	4.57856i	0.599491	+	0.172316i
$707$			27.0406i			1.01697i
$708$	−1.41252	−	6.15418i	−0.0530856	−	0.231288i
$709$	22.6155	+	22.6155i	0.849342	+	0.849342i	0.990051	−	0.140709i	$-0.0449381\pi$
$709$	22.6155	+	22.6155i	0.849342	+	0.849342i	−0.140709	+	0.990051i	$0.544938\pi$
$710$	−8.74020	+	5.17117i	−0.328014	+	0.194071i
$711$	29.6135			1.11059
$712$	−0.608047	+	11.1914i	−0.0227875	+	0.419414i
$713$	1.96131	−	1.96131i	0.0734518	−	0.0734518i
$714$	−1.75907	−	3.17824i	−0.0658315	−	0.118942i
$715$	−7.03522	+	7.45190i	−0.263102	+	0.278685i
$716$	38.1382	−	8.75352i	1.42529	−	0.327135i
$717$	4.57377			0.170811
$718$	4.44412	+	8.02951i	0.165853	+	0.299659i
$719$	20.3826			0.760144			0.380072	−	0.924957i	$-0.375899\pi$
$719$	20.3826			0.760144			0.380072	+	0.924957i	$0.375899\pi$
$720$	−11.9615	−	22.9770i	−0.445779	−	0.856301i
$721$	−5.09183			−0.189630
$722$	12.8506	+	23.2180i	0.478249	+	0.864086i
$723$	−5.71867			−0.212680
$724$	3.78268	+	16.4807i	0.140582	+	0.612501i
$725$	31.9123	−	35.8112i	1.18519	−	1.32999i
$726$	−0.220685	−	0.398728i	−0.00819040	−	0.0147982i
$727$	−32.9648	+	32.9648i	−1.22260	+	1.22260i	−0.255892	+	0.966705i	$0.582369\pi$
$727$	−32.9648	+	32.9648i	−1.22260	+	1.22260i	−0.966705	+	0.255892i	$0.917631\pi$
$728$	−45.4319	+	40.7495i	−1.68382	+	1.51028i
$729$	−21.5531			−0.798263
$730$	−0.980192	+	3.82059i	−0.0362785	+	0.141407i
$731$	−12.7543	−	12.7543i	−0.471734	−	0.471734i
$732$	−5.25263	+	1.20559i	−0.194143	+	0.0445599i
$733$		−	11.0676i		−	0.408790i	−0.978888	−	0.204395i	$-0.934477\pi$
$733$		−	11.0676i		−	0.408790i	0.978888	−	0.204395i	$-0.0655227\pi$
$734$	−26.4497	−	7.60265i	−0.976277	−	0.280619i
$735$	0.314157	+	10.9227i	0.0115878	+	0.402890i
$736$	4.54854	+	26.2873i	0.167661	+	0.968963i
$737$	1.02027	−	1.02027i	0.0375823	−	0.0375823i
$738$	−8.65290	−	15.6338i	−0.318517	−	0.575488i
$739$	3.07087	+	3.07087i	0.112964	+	0.112964i	0.761329	−	0.648365i	$-0.224547\pi$
$739$	3.07087	+	3.07087i	0.112964	+	0.112964i	−0.648365	+	0.761329i	$0.724547\pi$
$740$	−42.6457	−	25.0459i	−1.56769	−	0.920705i
$741$	−0.506771	+	0.506771i	−0.0186167	+	0.0186167i
$742$	−10.1310	+	35.2461i	−0.371922	+	1.29392i
$743$	−26.2416	−	26.2416i	−0.962712	−	0.962712i	0.0366175	−	0.999329i	$-0.488342\pi$
$743$	−26.2416	−	26.2416i	−0.962712	−	0.962712i	−0.999329	+	0.0366175i	$0.988342\pi$
$744$	0.535276	+	0.0290825i	0.0196242	+	0.00106622i
$745$	−20.3365	−	19.1994i	−0.745071	−	0.703410i
$746$	−12.6996	+	7.02889i	−0.464965	+	0.257346i
$747$	−42.9340			−1.57087
$748$	1.79806	−	2.86933i	0.0657437	−	0.104913i
$749$	−11.4777	+	11.4777i	−0.419387	+	0.419387i
$750$	4.22876	−	2.84223i	0.154413	−	0.103784i
$751$		−	30.1219i		−	1.09916i	−0.835439	−	0.549582i	$-0.814787\pi$
$751$		−	30.1219i		−	1.09916i	0.835439	−	0.549582i	$-0.185213\pi$
$752$	11.4855	−	33.0812i	0.418833	−	1.20635i
$753$	6.33645	+	6.33645i	0.230913	+	0.230913i
$754$	59.7600	+	17.1773i	2.17633	+	0.625560i
$755$	17.1477	−	0.493198i	0.624068	−	0.0179493i
$756$	−4.00216	−	17.4370i	−0.145557	−	0.634177i
$757$		−	24.0155i		−	0.872857i	−0.899739	−	0.436429i	$-0.856243\pi$
$757$		−	24.0155i		−	0.872857i	0.899739	−	0.436429i	$-0.143757\pi$
$758$	2.52752	−	8.79329i	0.0918037	−	0.319387i
$759$			1.51973i			0.0551626i
$760$	−2.22484	+	2.11407i	−0.0807034	+	0.0766853i
$761$			1.63523i			0.0592771i	0.999561	+	0.0296386i	$0.00943563\pi$
$761$			1.63523i			0.0592771i	−0.999561	+	0.0296386i	$0.990564\pi$
$762$	2.92042	+	0.839439i	0.105796	+	0.0304097i
$763$		−	30.2057i		−	1.09352i
$764$	−28.5642	−	17.8997i	−1.03341	−	0.647589i
$765$	7.52690	−	7.97269i	0.272136	−	0.288253i
$766$	−6.26025	+	21.7795i	−0.226192	+	0.786925i
$767$	−31.7502	−	31.7502i	−1.14643	−	1.14643i
$768$	−3.19506	+	4.04665i	−0.115292	+	0.146021i
$769$		−	35.4180i		−	1.27721i	−0.769536	−	0.638603i	$-0.779513\pi$
$769$		−	35.4180i		−	1.27721i	0.769536	−	0.638603i	$-0.220487\pi$
$770$	−12.8132	+	7.58095i	−0.461754	+	0.273199i
$771$	1.42578	−	1.42578i	0.0513482	−	0.0513482i
$772$	−36.3738	+	8.34856i	−1.30912	+	0.300471i
$773$	−5.81285			−0.209074			−0.104537	−	0.994521i	$-0.533336\pi$
$773$	−5.81285			−0.209074			−0.104537	+	0.994521i	$0.533336\pi$
$774$	−21.1300	−	38.1771i	−0.759503	−	1.37225i
$775$	−0.169021	−	2.93587i	−0.00607142	−	0.105459i
$776$	9.80011	+	10.9262i	0.351803	+	0.392228i
$777$	−11.8635	−	11.8635i	−0.425602	−	0.425602i
$778$	−1.47770	−	0.424747i	−0.0529781	−	0.0152279i
$779$	−1.49698	+	1.49698i	−0.0536349	+	0.0536349i
$780$	5.69529	+	3.34486i	0.203924	+	0.119765i
$781$	−2.27082	−	2.27082i	−0.0812562	−	0.0812562i
$782$	−9.87968	+	5.46814i	−0.353297	+	0.195540i
$783$	−12.8889	+	12.8889i	−0.460611	+	0.460611i
$784$	−54.5879	+	26.4517i	−1.94957	+	0.944703i
$785$	−24.4551	+	0.703372i	−0.872840	+	0.0251044i
$786$	0.444108	−	1.54506i	0.0158408	−	0.0551104i
$787$			51.8294i			1.84752i	0.382975	+	0.923759i	$0.374900\pi$
$787$			51.8294i			1.84752i	−0.382975	+	0.923759i	$0.625100\pi$
$788$	−24.9938	−	15.6624i	−0.890368	−	0.557948i
$789$	−1.35977	−	1.35977i	−0.0484089	−	0.0484089i
$790$	−27.8287	+	16.4649i	−0.990099	+	0.585796i
$791$	57.3595			2.03947
$792$	6.09803	−	5.46954i	0.216684	−	0.194352i
$793$	−27.0990	+	27.0990i	−0.962313	+	0.962313i
$794$	−5.91242	+	3.27236i	−0.209824	+	0.116132i
$795$	3.96731	−	0.114107i	0.140706	−	0.00404695i
$796$	8.85088	+	5.54640i	0.313711	+	0.196587i
$797$	20.1928			0.715267			0.357633	−	0.933862i	$-0.383584\pi$
$797$	20.1928			0.715267			0.357633	+	0.933862i	$0.383584\pi$
$798$	−0.910930	+	0.504176i	−0.0322466	+	0.0178476i
$799$	14.8222			0.524372
$800$	24.0156	+	14.9416i	0.849080	+	0.528264i
$801$	−11.4763			−0.405493
$802$	−31.7753	+	17.5868i	−1.12203	+	0.621012i
$803$	−1.24731			−0.0440165
$804$	−0.787995	−	0.493797i	−0.0277904	−	0.0174149i
$805$	49.6266	−	1.42735i	1.74911	−	0.0503075i
$806$	3.33530	−	1.84600i	0.117481	−	0.0650225i
$807$	3.88172	−	3.88172i	0.136643	−	0.136643i
$808$	10.8471	+	12.0935i	0.381600	+	0.425448i
$809$	−2.80919			−0.0987659			−0.0493830	−	0.998780i	$-0.515725\pi$
$809$	−2.80919			−0.0987659			−0.0493830	+	0.998780i	$0.515725\pi$
$810$	21.9802	−	13.0047i	0.772305	−	0.456937i
$811$	−7.94797	−	7.94797i	−0.279091	−	0.279091i	0.553655	−	0.832746i	$-0.313233\pi$
$811$	−7.94797	−	7.94797i	−0.279091	−	0.279091i	−0.832746	+	0.553655i	$0.813233\pi$
$812$	76.5433	+	47.9658i	2.68614	+	1.68327i
$813$		−	8.25233i		−	0.289422i
$814$	4.32045	−	15.0309i	0.151432	−	0.526834i
$815$	3.34548	−	0.0962219i	0.117187	−	0.00337051i
$816$	−2.06164	−	0.715783i	−0.0721717	−	0.0250574i
$817$	−3.65557	+	3.65557i	−0.127892	+	0.127892i
$818$	−44.0155	+	24.3614i	−1.53897	+	0.851776i
$819$	−44.1876	−	44.1876i	−1.54404	−	1.54404i
$820$	16.8237	+	9.88058i	0.587508	+	0.345045i
$821$	13.1035	−	13.1035i	0.457314	−	0.457314i	−0.440459	−	0.897773i	$-0.645184\pi$
$821$	13.1035	−	13.1035i	0.457314	−	0.457314i	0.897773	+	0.440459i	$0.145184\pi$
$822$	7.72699	+	2.22103i	0.269510	+	0.0774673i
$823$	−30.1843	−	30.1843i	−1.05216	−	1.05216i	−0.998563	−	0.0535968i	$-0.982931\pi$
$823$	−30.1843	−	30.1843i	−1.05216	−	1.05216i	−0.0535968	−	0.998563i	$-0.517069\pi$
$824$	−2.27724	+	2.04254i	−0.0793314	+	0.0711552i
$825$	1.20291	+	1.07195i	0.0418801	+	0.0373204i
$826$	−31.5876	−	57.0716i	−1.09907	−	1.98578i
$827$	5.09170			0.177056			0.0885278	−	0.996074i	$-0.471784\pi$
$827$	5.09170			0.177056			0.0885278	+	0.996074i	$0.471784\pi$
$828$	−26.6245	+	6.11089i	−0.925265	+	0.212368i
$829$	32.8027	−	32.8027i	1.13928	−	1.13928i	0.150706	−	0.988579i	$-0.451845\pi$
$829$	32.8027	−	32.8027i	1.13928	−	1.13928i	0.988579	−	0.150706i	$-0.0481546\pi$
$830$	40.3463	−	23.8710i	1.40044	−	0.828576i
$831$			0.161578i			0.00560507i
$832$	−3.97242	+	36.4492i	−0.137719	+	1.26365i
$833$	−18.1551	−	18.1551i	−0.629038	−	0.629038i
$834$	−1.83897	+	6.39781i	−0.0636784	+	0.221538i
$835$	−10.1053	+	10.7038i	−0.349708	+	0.370420i
$836$	−0.822393	−	0.515352i	−0.0284431	−	0.0178238i
$837$			1.11749i			0.0386260i
$838$	37.7114	+	10.8397i	1.30272	+	0.374450i
$839$			35.3276i			1.21964i	0.792538	+	0.609822i	$0.208759\pi$
$839$			35.3276i			1.21964i	−0.792538	+	0.609822i	$0.791241\pi$
$840$	6.60940	+	6.95572i	0.228046	+	0.239995i
$841$		−	63.0333i		−	2.17356i
$842$	−10.4556	+	36.3751i	−0.360322	+	1.25357i
$843$			0.610843i			0.0210385i
$844$	−9.09478	−	39.6250i	−0.313055	−	1.36395i
$845$	17.8924	−	0.514616i	0.615516	−	0.0177033i
$846$	34.4615	+	9.90553i	1.18481	+	0.340559i
$847$	−3.32902	−	3.32902i	−0.114387	−	0.114387i
$848$	9.60768	+	19.8272i	0.329929	+	0.680870i
$849$			6.01716i			0.206509i
$850$	−2.64047	+	11.6771i	−0.0905674	+	0.400520i
$851$	−36.8783	+	36.8783i	−1.26417	+	1.26417i
$852$	−1.09904	+	1.75383i	−0.0376524	+	0.0600853i
$853$	−1.25601			−0.0430050			−0.0215025	−	0.999769i	$-0.506845\pi$
$853$	−1.25601			−0.0430050			−0.0215025	+	0.999769i	$0.506845\pi$
$854$	−48.7109	+	26.9602i	−1.66685	+	0.922559i
$855$	−2.28509	−	2.15732i	−0.0781486	−	0.0737789i
$856$	−0.529051	+	9.73742i	−0.0180826	+	0.332818i
$857$	2.67405	+	2.67405i	0.0913438	+	0.0913438i	0.751302	−	0.659958i	$-0.229426\pi$
$857$	2.67405	+	2.67405i	0.0913438	+	0.0913438i	−0.659958	+	0.751302i	$0.729426\pi$
$858$	−0.576993	+	2.00737i	−0.0196982	+	0.0685304i
$859$	19.3059	−	19.3059i	0.658710	−	0.658710i	−0.296364	−	0.955075i	$-0.595774\pi$
$859$	19.3059	−	19.3059i	0.658710	−	0.658710i	0.955075	+	0.296364i	$0.0957743\pi$
$860$	41.0827	+	24.1280i	1.40091	+	0.822757i
$861$	4.68015	+	4.68015i	0.159499	+	0.159499i
$862$	−5.55311	−	10.0332i	−0.189140	−	0.341732i
$863$	5.14064	−	5.14064i	0.174990	−	0.174990i	−0.614178	−	0.789168i	$-0.710512\pi$
$863$	5.14064	−	5.14064i	0.174990	−	0.174990i	0.789168	+	0.614178i	$0.210512\pi$
$864$	−8.78459	−	6.19299i	−0.298858	−	0.210690i
$865$	−0.917383	−	31.8959i	−0.0311919	−	1.08449i
$866$	−13.4031	−	3.85254i	−0.455454	−	0.130915i
$867$			4.55447i			0.154678i
$868$	5.39757	−	1.23886i	0.183206	−	0.0420496i
$869$	−7.23024	−	7.23024i	−0.245269	−	0.245269i
$870$	2.42940	−	9.46932i	0.0823644	−	0.321040i
$871$	−6.61293			−0.224070
$872$	−12.1168	−	13.5090i	−0.410325	−	0.457474i
$873$	−10.6270	+	10.6270i	−0.359668	+	0.359668i
$874$	1.56725	+	2.83167i	0.0530131	+	0.0957825i
$875$	33.8746	−	40.2879i	1.14517	−	1.36198i
$876$	0.179832	+	0.783508i	0.00607595	+	0.0264723i
$877$	−59.0384			−1.99359			−0.996793	−	0.0800206i	$-0.974501\pi$
$877$	−59.0384			−1.99359			−0.996793	+	0.0800206i	$0.974501\pi$
$878$	8.56897	+	15.4822i	0.289189	+	0.522498i
$879$	−1.18952			−0.0401216
$880$	−2.68946	+	8.53035i	−0.0906617	+	0.287558i
$881$	−5.81576			−0.195938			−0.0979690	−	0.995189i	$-0.531235\pi$
$881$	−5.81576			−0.195938			−0.0979690	+	0.995189i	$0.531235\pi$
$882$	−30.0776	−	54.3434i	−1.01277	−	1.82984i
$883$	43.9447			1.47886			0.739428	−	0.673235i	$-0.235096\pi$
$883$	43.9447			1.47886			0.739428	+	0.673235i	$0.235096\pi$
$884$	−15.1259	+	3.47172i	−0.508739	+	0.116766i
$885$	−4.84624	+	5.13327i	−0.162905	+	0.172553i
$886$	14.4346	+	26.0799i	0.484938	+	0.876173i
$887$	−7.45975	+	7.45975i	−0.250474	+	0.250474i	−0.821165	−	0.570691i	$-0.806675\pi$
$887$	−7.45975	+	7.45975i	−0.250474	+	0.250474i	0.570691	+	0.821165i	$0.306675\pi$
$888$	−10.0647	−	0.546835i	−0.337750	−	0.0183506i
$889$	31.3915			1.05284
$890$	10.7846	−	6.38072i	0.361499	−	0.213882i
$891$	5.71073	+	5.71073i	0.191317	+	0.191317i
$892$	−3.05031	−	13.2899i	−0.102132	−	0.444978i
$893$		−	4.24827i		−	0.142163i
$894$	−5.47817	−	1.57463i	−0.183218	−	0.0526636i
$895$	−31.8114	−	30.0327i	−1.06334	−	1.00388i
$896$	−20.1741	+	49.2960i	−0.673968	+	1.64687i
$897$	4.92507	−	4.92507i	0.164443	−	0.164443i
$898$	−24.4784	−	44.2269i	−0.816855	−	1.47587i
$899$	−3.98972	−	3.98972i	−0.133065	−	0.133065i
$900$	−13.9427	+	25.3845i	−0.464758	+	0.846150i
$901$	−6.59424	+	6.59424i	−0.219686	+	0.219686i
$902$	−1.70441	+	5.92968i	−0.0567508	+	0.197437i
$903$	11.4287	+	11.4287i	0.380325	+	0.380325i
$904$	25.6531	−	23.0092i	0.853211	−	0.765275i
$905$	12.9781	−	13.7467i	0.431406	−	0.456957i
$906$	3.05898	−	1.69306i	0.101628	−	0.0562482i
$907$	19.6592			0.652773			0.326386	−	0.945236i	$-0.394169\pi$
$907$	19.6592			0.652773			0.326386	+	0.945236i	$0.394169\pi$
$908$	9.43927	+	5.91511i	0.313253	+	0.196300i
$909$	−11.7623	+	11.7623i	−0.390131	+	0.390131i
$910$	66.0924	+	16.9563i	2.19094	+	0.562096i
$911$			17.6580i			0.585034i	0.956260	+	0.292517i	$0.0944929\pi$
$911$			17.6580i			0.585034i	−0.956260	+	0.292517i	$0.905507\pi$
$912$	−0.205154	+	0.590896i	−0.00679333	+	0.0195665i
$913$	10.4825	+	10.4825i	0.346920	+	0.346920i
$914$	−7.53787	−	2.16667i	−0.249330	−	0.0716670i
$915$	4.38127	+	4.13629i	0.144840	+	0.136742i
$916$	−55.8920	+	12.8284i	−1.84672	+	0.423863i
$917$		−	16.6078i		−	0.548437i
$918$	1.25677	−	4.37232i	0.0414796	−	0.144308i
$919$			8.62046i			0.284363i	0.989841	+	0.142181i	$0.0454116\pi$
$919$			8.62046i			0.284363i	−0.989841	+	0.142181i	$0.954588\pi$
$920$	21.6222	−	20.5456i	0.712862	−	0.677369i
$921$		−	4.04621i		−	0.133327i
$922$	−32.1925	−	9.25333i	−1.06020	−	0.304742i
$923$			14.7183i			0.484460i
$924$	−1.61119	+	2.57112i	−0.0530044	+	0.0845838i
$925$	3.17808	+	55.2027i	0.104495	+	1.81505i
$926$	14.7016	−	51.1470i	0.483123	−	1.68079i
$927$	−2.21487	−	2.21487i	−0.0727460	−	0.0727460i
$928$	53.4739	−	9.25268i	1.75537	−	0.303734i
$929$			18.7119i			0.613918i	0.951723	+	0.306959i	$0.0993115\pi$
$929$			18.7119i			0.613918i	−0.951723	+	0.306959i	$0.900689\pi$
$930$	−0.305186	−	0.515819i	−0.0100075	−	0.0169144i
$931$	−5.20353	+	5.20353i	−0.170539	+	0.170539i
$932$	−1.40113	−	6.10457i	−0.0458955	−	0.199962i
$933$	0.691935			0.0226529
$934$	−15.7993	−	28.5458i	−0.516970	−	0.934047i
$935$	−3.78428	+	0.108843i	−0.123759	+	0.00355953i
$936$	−37.4877	−	2.03677i	−1.22532	−	0.0665740i
$937$	23.4142	+	23.4142i	0.764908	+	0.764908i	0.977205	−	0.212297i	$-0.0680945\pi$
$937$	23.4142	+	23.4142i	0.764908	+	0.764908i	−0.212297	+	0.977205i	$0.568094\pi$
$938$	−9.23296	−	2.65390i	−0.301467	−	0.0866529i
$939$	−5.37509	+	5.37509i	−0.175409	+	0.175409i
$940$	−37.8919	+	9.85187i	−1.23590	+	0.321332i
$941$	12.2360	+	12.2360i	0.398883	+	0.398883i	0.877839	−	0.478956i	$-0.158985\pi$
$941$	12.2360	+	12.2360i	0.398883	+	0.398883i	−0.478956	+	0.877839i	$0.658985\pi$
$942$	−4.36255	+	2.41456i	−0.142140	+	0.0786705i
$943$	14.5485	−	14.5485i	0.473763	−	0.473763i
$944$	−37.0208	−	12.8533i	−1.20493	−	0.418340i
$945$	−13.7311	+	14.5444i	−0.446673	+	0.473128i
$946$	−4.16211	+	14.4800i	−0.135322	+	0.470787i
$947$			28.5510i			0.927781i	0.885892	+	0.463891i	$0.153547\pi$
$947$			28.5510i			0.927781i	−0.885892	+	0.463891i	$0.846453\pi$
$948$	−3.49932	+	5.58418i	−0.113653	+	0.181366i
$949$	4.04222	+	4.04222i	0.131216	+	0.131216i
$950$	3.34683	+	0.756799i	0.108585	+	0.0245538i
$951$	−6.53186			−0.211810
$952$	−22.5120	−	1.22312i	−0.729619	−	0.0396415i
$953$	24.2478	−	24.2478i	0.785464	−	0.785464i	−0.195283	−	0.980747i	$-0.562562\pi$
$953$	24.2478	−	24.2478i	0.785464	−	0.785464i	0.980747	+	0.195283i	$0.0625625\pi$
$954$	−19.7384	+	10.9247i	−0.639054	+	0.353700i
$955$	1.08353	+	37.6725i	0.0350621	+	1.21905i
$956$	15.0735	−	24.0541i	0.487511	−	0.777965i
$957$	3.09144			0.0999321
$958$	11.6353	−	6.43984i	0.375920	−	0.208062i
$959$	83.0571			2.68206
$960$	5.74618	+	0.459538i	0.185457	+	0.0148315i
$961$	30.6541			0.988841
$962$	−62.7131	+	34.7100i	−2.02195	+	1.11910i
$963$	−9.98530			−0.321772
$964$	−18.8466	+	30.0753i	−0.607009	+	0.968659i
$965$	30.3397	+	28.6433i	0.976670	+	0.922060i
$966$	8.85290	−	4.89984i	0.284837	−	0.157650i
$967$	−7.92797	+	7.92797i	−0.254946	+	0.254946i	−0.822995	−	0.568049i	$-0.807699\pi$
$967$	−7.92797	+	7.92797i	−0.254946	+	0.254946i	0.568049	+	0.822995i	$0.307699\pi$
$968$	−2.82426	−	0.153447i	−0.0907752	−	0.00493198i
$969$	−0.264754			−0.00850513
$970$	4.07793	−	15.8950i	0.130935	−	0.510357i
$971$	−39.1809	−	39.1809i	−1.25737	−	1.25737i	−0.952342	−	0.305031i	$-0.901333\pi$
$971$	−39.1809	−	39.1809i	−1.25737	−	1.25737i	−0.305031	−	0.952342i	$-0.598667\pi$
$972$	8.81740	−	14.0707i	0.282818	−	0.451318i
$973$			68.7698i			2.20466i
$974$	−4.87535	+	16.9614i	−0.156216	+	0.543479i
$975$	−0.424431	−	7.37227i	−0.0135927	−	0.236102i
$976$	−10.9704	+	31.5975i	−0.351153	+	1.01141i
$977$	−13.4552	+	13.4552i	−0.430469	+	0.430469i	−0.888788	−	0.458319i	$-0.848452\pi$
$977$	−13.4552	+	13.4552i	−0.430469	+	0.430469i	0.458319	+	0.888788i	$0.348452\pi$
$978$	0.596801	−	0.330313i	0.0190836	−	0.0105623i
$979$	2.80197	+	2.80197i	0.0895512	+	0.0895512i
$980$	58.4794	+	34.3451i	1.86805	+	1.09711i
$981$	13.1391	−	13.1391i	0.419498	−	0.419498i
$982$	−18.4742	−	5.31018i	−0.589535	−	0.169455i
$983$	−2.82481	−	2.82481i	−0.0900974	−	0.0900974i	0.660622	−	0.750719i	$-0.270293\pi$
$983$	−2.82481	−	2.82481i	−0.0900974	−	0.0900974i	−0.750719	+	0.660622i	$0.770293\pi$
$984$	3.97053	+	0.215726i	0.126576	+	0.00687709i
$985$	0.948093	+	32.9636i	0.0302088	+	1.05031i
$986$	11.1233	+	20.0973i	0.354239	+	0.640029i
$987$	−13.2818			−0.422763
$988$	0.995046	+	4.33531i	0.0316566	+	0.137925i
$989$	35.5267	−	35.5267i	1.12968	−	1.12968i
$990$	−8.87115	−	2.27594i	−0.281944	−	0.0723340i
$991$			4.58708i			0.145713i	0.997342	+	0.0728567i	$0.0232116\pi$
$991$			4.58708i			0.145713i	−0.997342	+	0.0728567i	$0.976788\pi$
$992$	1.91702	−	2.71925i	0.0608656	−	0.0863362i
$993$	−1.44323	−	1.44323i	−0.0457995	−	0.0457995i
$994$	−5.90676	+	20.5497i	−0.187351	+	0.651797i
$995$	−0.335741	−	11.6732i	−0.0106437	−	0.370065i
$996$	5.07335	−	8.09600i	0.160755	−	0.256532i
$997$		−	18.2847i		−	0.579083i	−0.957165	−	0.289541i	$-0.906497\pi$
$997$		−	18.2847i		−	0.579083i	0.957165	−	0.289541i	$-0.0935028\pi$
$998$	−20.3597	−	5.85215i	−0.644476	−	0.185247i
$999$		−	21.0119i		−	0.664788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bk.b.243.18	yes	236
5.2	odd	4		880.2.s.b.67.41	✓	236
16.11	odd	4		880.2.s.b.683.41	yes	236
80.27	even	4	inner	880.2.bk.b.507.18	yes	236

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.s.b.67.41	✓	236	5.2	odd	4
880.2.s.b.683.41	yes	236	16.11	odd	4
880.2.bk.b.243.18	yes	236	1.1	even	1	trivial
880.2.bk.b.507.18	yes	236	80.27	even	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bk (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23734 + 0.684833i) q^{2} +0.322247 q^{3} +(1.06201 - 1.69474i) q^{4} +(-2.23514 + 0.0642867i) q^{5} +(-0.398728 + 0.220685i) q^{6} +(-3.32902 + 3.32902i) q^{7} +(-0.153447 + 2.82426i) q^{8} -2.89616 q^{9} +(2.72160 - 1.61024i) q^{10} +(0.707107 + 0.707107i) q^{11} +(0.342228 - 0.546124i) q^{12} -4.58312i q^{13} +(1.83930 - 6.39895i) q^{14} +(-0.720268 + 0.0207162i) q^{15} +(-1.74428 - 3.59965i) q^{16} +(1.19719 - 1.19719i) q^{17} +(3.58352 - 1.98338i) q^{18} +(-0.343132 - 0.343132i) q^{19} +(-2.26479 + 3.85626i) q^{20} +(-1.07277 + 1.07277i) q^{21} +(-1.35918 - 0.390679i) q^{22} +(3.33474 + 3.33474i) q^{23} +(-0.0494479 + 0.910109i) q^{24} +(4.99173 - 0.287380i) q^{25} +(3.13867 + 5.67087i) q^{26} -1.90002 q^{27} +(2.10638 + 9.17727i) q^{28} +(6.78356 - 6.78356i) q^{29} +(0.877027 - 0.518896i) q^{30} -0.588146i q^{31} +(4.62343 + 3.25944i) q^{32} +(0.227863 + 0.227863i) q^{33} +(-0.661452 + 2.30120i) q^{34} +(7.22683 - 7.65486i) q^{35} +(-3.07574 + 4.90823i) q^{36} +11.0588i q^{37} +(0.659559 + 0.189582i) q^{38} -1.47690i q^{39} +(0.161414 - 6.32250i) q^{40} -4.36269i q^{41} +(0.592708 - 2.06204i) q^{42} -10.6535i q^{43} +(1.94931 - 0.447409i) q^{44} +(6.47333 - 0.186184i) q^{45} +(-6.40994 - 1.84246i) q^{46} +(6.19042 + 6.19042i) q^{47} +(-0.562089 - 1.15998i) q^{48} -15.1648i q^{49} +(-5.97965 + 3.77409i) q^{50} +(0.385790 - 0.385790i) q^{51} +(-7.76720 - 4.86731i) q^{52} -5.50810 q^{53} +(2.35096 - 1.30119i) q^{54} +(-1.62594 - 1.53503i) q^{55} +(-8.89120 - 9.91286i) q^{56} +(-0.110573 - 0.110573i) q^{57} +(-3.74794 + 13.0392i) q^{58} +(6.92764 - 6.92764i) q^{59} +(-0.729821 + 1.24267i) q^{60} +(-5.91278 - 5.91278i) q^{61} +(0.402782 + 0.727734i) q^{62} +(9.64137 - 9.64137i) q^{63} +(-7.95291 - 0.866750i) q^{64} +(0.294634 + 10.2439i) q^{65} +(-0.437991 - 0.125895i) q^{66} -1.44289i q^{67} +(-0.757500 - 3.30035i) q^{68} +(1.07461 + 1.07461i) q^{69} +(-3.69973 + 14.4208i) q^{70} -3.21142 q^{71} +(0.444407 - 8.17951i) q^{72} +(-0.881978 + 0.881978i) q^{73} +(-7.57345 - 13.6835i) q^{74} +(1.60857 - 0.0926073i) q^{75} +(-0.945929 + 0.217111i) q^{76} -4.70795 q^{77} +(1.01143 + 1.82742i) q^{78} -10.2251 q^{79} +(4.13013 + 7.93360i) q^{80} +8.07620 q^{81} +(2.98772 + 5.39812i) q^{82} +14.8245 q^{83} +(0.678774 + 2.95735i) q^{84} +(-2.59893 + 2.75285i) q^{85} +(7.29588 + 13.1820i) q^{86} +(2.18598 - 2.18598i) q^{87} +(-2.10556 + 1.88855i) q^{88} +3.96258 q^{89} +(-7.88218 + 4.66352i) q^{90} +(15.2573 + 15.2573i) q^{91} +(9.19304 - 2.11000i) q^{92} -0.189528i q^{93} +(-11.8990 - 3.42023i) q^{94} +(0.789009 + 0.744891i) q^{95} +(1.48988 + 1.05034i) q^{96} +(3.66933 - 3.66933i) q^{97} +(10.3854 + 18.7640i) q^{98} +(-2.04789 - 2.04789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 236 q + 4 q^{3} + 4 q^{5} - 4 q^{7} + 12 q^{8} + 240 q^{9} - 8 q^{12} + 12 q^{14} - 4 q^{15} - 8 q^{16} + 8 q^{17} + 28 q^{18} + 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} + 12 q^{25} + 8 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) \) 236 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 + 12 * q^8 + 240 * q^9 - 8 * q^12 + 12 * q^14 - 4 * q^15 - 8 * q^16 + 8 * q^17 + 28 * q^18 + 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 + 12 * q^25 + 8 * q^26 + 4 * q^27 - 36 * q^28 + 8 * q^29 - 56 * q^30 - 40 * q^32 - 4 * q^33 - 44 * q^34 - 28 * q^35 - 32 * q^36 - 12 * q^38 - 40 * q^40 - 20 * q^42 - 40 * q^46 - 48 * q^47 - 40 * q^48 - 28 * q^51 - 4 * q^52 + 28 * q^53 - 24 * q^56 - 16 * q^57 - 76 * q^58 + 8 * q^59 - 4 * q^60 - 24 * q^61 + 12 * q^62 - 24 * q^63 - 32 * q^65 - 4 * q^66 + 36 * q^68 + 48 * q^69 + 28 * q^70 - 4 * q^71 + 20 * q^72 + 8 * q^73 - 68 * q^75 - 24 * q^76 + 12 * q^77 + 8 * q^78 + 40 * q^79 + 112 * q^80 + 244 * q^81 - 64 * q^82 + 24 * q^83 - 104 * q^84 + 8 * q^85 + 72 * q^86 - 140 * q^87 - 32 * q^88 + 36 * q^89 - 136 * q^90 + 12 * q^91 + 72 * q^92 - 16 * q^94 - 36 * q^95 + 72 * q^96 + 20 * q^97 + 136 * q^98 + 8 * q^99

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