LMFDB - Embedded newform 810.3.j.g.269.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(269,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("810.269");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.j (of order $6$, degree $2$, not 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:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.4
Character	$\chi$	$=$	810.269
Dual form			810.3.j.g.539.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-4.52502 + 2.12701i) q^{5} +(-1.70200 - 0.982651i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-4.52502 + 2.12701i) q^{5} +(-1.70200 - 0.982651i) q^{7} +2.82843 q^{8} +(0.594626 - 7.04602i) q^{10} +(3.30509 + 1.90819i) q^{11} +(-16.1249 + 9.30970i) q^{13} +(2.40699 - 1.38968i) q^{14} +(-2.00000 + 3.46410i) q^{16} +17.6477 q^{17} -26.0605 q^{19} +(8.20911 + 5.71055i) q^{20} +(-4.67410 + 2.69859i) q^{22} +(4.82055 + 8.34944i) q^{23} +(15.9516 - 19.2496i) q^{25} -26.3318i q^{26} +3.93060i q^{28} +(-5.20715 - 3.00635i) q^{29} +(-12.6666 - 21.9392i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-12.4788 + 21.6140i) q^{34} +(9.79170 + 0.826339i) q^{35} -39.9637i q^{37} +(18.4275 - 31.9174i) q^{38} +(-12.7987 + 6.01610i) q^{40} +(-30.7185 + 17.7353i) q^{41} +(52.8566 + 30.5168i) q^{43} -7.63278i q^{44} -13.6346 q^{46} +(35.4435 - 61.3899i) q^{47} +(-22.5688 - 39.0903i) q^{49} +(12.2963 + 33.1482i) q^{50} +(32.2497 + 18.6194i) q^{52} +83.3187 q^{53} +(-19.0144 - 1.60465i) q^{55} +(-4.81399 - 2.77936i) q^{56} +(7.36403 - 4.25162i) q^{58} +(32.3067 - 18.6523i) q^{59} +(2.37592 - 4.11521i) q^{61} +35.8265 q^{62} +8.00000 q^{64} +(53.1635 - 76.4244i) q^{65} +(8.03433 - 4.63862i) q^{67} +(-17.6477 - 30.5668i) q^{68} +(-7.93584 + 11.4080i) q^{70} +34.1966i q^{71} -22.9490i q^{73} +(48.9454 + 28.2586i) q^{74} +(26.0605 + 45.1381i) q^{76} +(-3.75018 - 6.49550i) q^{77} +(49.5443 - 85.8133i) q^{79} +(1.68186 - 19.9292i) q^{80} -50.1630i q^{82} +(18.9521 - 32.8260i) q^{83} +(-79.8563 + 37.5369i) q^{85} +(-74.7506 + 43.1573i) q^{86} +(9.34821 + 5.39719i) q^{88} -43.0816i q^{89} +36.5927 q^{91} +(9.64111 - 16.6989i) q^{92} +(50.1246 + 86.8184i) q^{94} +(117.924 - 55.4310i) q^{95} +(23.7789 + 13.7287i) q^{97} +63.8342 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 24 q^{7}+O(q^{10}) $ 24 * q - 24 * q^4 - 24 * q^7	$ 24 q - 24 q^{4} - 24 q^{7} - 12 q^{10} - 48 q^{13} - 48 q^{16} + 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{43} - 36 q^{49} + 96 q^{52} + 216 q^{55} - 396 q^{58} - 60 q^{61} + 192 q^{64} + 1032 q^{67} - 480 q^{70} - 240 q^{79} - 396 q^{85} - 240 q^{88} + 48 q^{91} - 48 q^{94} + 1440 q^{97}+O(q^{100}) $ 24 * q - 24 * q^4 - 24 * q^7 - 12 * q^10 - 48 * q^13 - 48 * q^16 + 120 * q^22 + 24 * q^25 + 60 * q^34 + 24 * q^43 - 36 * q^49 + 96 * q^52 + 216 * q^55 - 396 * q^58 - 60 * q^61 + 192 * q^64 + 1032 * q^67 - 480 * q^70 - 240 * q^79 - 396 * q^85 - 240 * q^88 + 48 * q^91 - 48 * q^94 + 1440 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	−4.52502	+	2.12701i	−0.905004	+	0.425402i
$5$	−4.52502	+	2.12701i	−0.905004	+	0.425402i
$6$		0			0
$7$	−1.70200	−	0.982651i	−0.243143	−	0.140379i	0.373477	−	0.927639i	$-0.378165\pi$
$7$	−1.70200	−	0.982651i	−0.243143	−	0.140379i	−0.616620	+	0.787261i	$0.711499\pi$
$8$	2.82843			0.353553
$9$		0			0
$10$	0.594626	−	7.04602i	0.0594626	−	0.704602i
$11$	3.30509	+	1.90819i	0.300463	+	0.173472i	0.642651	−	0.766159i	$-0.277835\pi$
$11$	3.30509	+	1.90819i	0.300463	+	0.173472i	−0.342188	+	0.939632i	$0.611168\pi$
$12$		0			0
$13$	−16.1249	+	9.30970i	−1.24037	+	0.716131i	−0.969170	−	0.246391i	$-0.920755\pi$
$13$	−16.1249	+	9.30970i	−1.24037	+	0.716131i	−0.271204	+	0.962522i	$0.587422\pi$
$14$	2.40699	−	1.38968i	0.171928	−	0.0992628i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	17.6477			1.03810			0.519051	−	0.854743i	$-0.326286\pi$
$17$	17.6477			1.03810			0.519051	+	0.854743i	$0.326286\pi$
$18$		0			0
$19$	−26.0605			−1.37160			−0.685802	−	0.727788i	$-0.740549\pi$
$19$	−26.0605			−1.37160			−0.685802	+	0.727788i	$0.740549\pi$
$20$	8.20911	+	5.71055i	0.410456	+	0.285528i
$21$		0			0
$22$	−4.67410	+	2.69859i	−0.212459	+	0.122663i
$23$	4.82055	+	8.34944i	0.209589	+	0.363019i	0.951585	−	0.307385i	$-0.0994540\pi$
$23$	4.82055	+	8.34944i	0.209589	+	0.363019i	−0.741996	+	0.670404i	$0.766121\pi$
$24$		0			0
$25$	15.9516	−	19.2496i	0.638066	−	0.769982i
$26$		−	26.3318i		−	1.01276i
$27$		0			0
$28$			3.93060i			0.140379i
$29$	−5.20715	−	3.00635i	−0.179557	−	0.103667i	0.407528	−	0.913193i	$-0.366391\pi$
$29$	−5.20715	−	3.00635i	−0.179557	−	0.103667i	−0.587085	+	0.809526i	$0.699724\pi$
$30$		0			0
$31$	−12.6666	−	21.9392i	−0.408600	−	0.707715i	0.586133	−	0.810215i	$-0.300649\pi$
$31$	−12.6666	−	21.9392i	−0.408600	−	0.707715i	−0.994733	+	0.102499i	$0.967316\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−12.4788	+	21.6140i	−0.367024	+	0.635705i
$35$	9.79170	+	0.826339i	0.279763	+	0.0236097i
$36$		0			0
$37$		−	39.9637i		−	1.08010i	−0.841633	−	0.540050i	$-0.818405\pi$
$37$		−	39.9637i		−	1.08010i	0.841633	−	0.540050i	$-0.181595\pi$
$38$	18.4275	−	31.9174i	0.484935	−	0.839933i
$39$		0			0
$40$	−12.7987	+	6.01610i	−0.319967	+	0.150402i
$41$	−30.7185	+	17.7353i	−0.749231	+	0.432568i	−0.825416	−	0.564525i	$-0.809059\pi$
$41$	−30.7185	+	17.7353i	−0.749231	+	0.432568i	0.0761853	+	0.997094i	$0.475726\pi$
$42$		0			0
$43$	52.8566	+	30.5168i	1.22922	+	0.709693i	0.966868	−	0.255278i	$-0.0821670\pi$
$43$	52.8566	+	30.5168i	1.22922	+	0.709693i	0.262356	+	0.964971i	$0.415500\pi$
$44$		−	7.63278i		−	0.173472i
$45$		0			0
$46$	−13.6346			−0.296404
$47$	35.4435	−	61.3899i	0.754116	−	1.30617i	−0.191696	−	0.981454i	$-0.561399\pi$
$47$	35.4435	−	61.3899i	0.754116	−	1.30617i	0.945813	−	0.324713i	$-0.105268\pi$
$48$		0			0
$49$	−22.5688	−	39.0903i	−0.460588	−	0.797761i
$50$	12.2963	+	33.1482i	0.245926	+	0.662964i
$51$		0			0
$52$	32.2497	+	18.6194i	0.620187	+	0.358065i
$53$	83.3187			1.57205			0.786025	−	0.618194i	$-0.212135\pi$
$53$	83.3187			1.57205			0.786025	+	0.618194i	$0.212135\pi$
$54$		0			0
$55$	−19.0144	−	1.60465i	−0.345716	−	0.0291755i
$56$	−4.81399	−	2.77936i	−0.0859641	−	0.0496314i
$57$		0			0
$58$	7.36403	−	4.25162i	0.126966	−	0.0733038i
$59$	32.3067	−	18.6523i	0.547571	−	0.316140i	−0.200571	−	0.979679i	$-0.564280\pi$
$59$	32.3067	−	18.6523i	0.547571	−	0.316140i	0.748142	+	0.663539i	$0.230946\pi$
$60$		0			0
$61$	2.37592	−	4.11521i	0.0389495	−	0.0674624i	−0.845894	−	0.533352i	$-0.820932\pi$
$61$	2.37592	−	4.11521i	0.0389495	−	0.0674624i	0.884843	+	0.465889i	$0.154266\pi$
$62$	35.8265			0.577847
$63$		0			0
$64$	8.00000			0.125000
$65$	53.1635	−	76.4244i	0.817901	−	1.17576i
$66$		0			0
$67$	8.03433	−	4.63862i	0.119915	−	0.0692332i	−0.438843	−	0.898564i	$-0.644611\pi$
$67$	8.03433	−	4.63862i	0.119915	−	0.0692332i	0.558758	+	0.829331i	$0.311278\pi$
$68$	−17.6477	−	30.5668i	−0.259525	−	0.449511i
$69$		0			0
$70$	−7.93584	+	11.4080i	−0.113369	+	0.162972i
$71$			34.1966i			0.481643i	0.970569	+	0.240821i	$0.0774168\pi$
$71$			34.1966i			0.481643i	−0.970569	+	0.240821i	$0.922583\pi$
$72$		0			0
$73$		−	22.9490i		−	0.314370i	−0.987569	−	0.157185i	$-0.949758\pi$
$73$		−	22.9490i		−	0.314370i	0.987569	−	0.157185i	$-0.0502419\pi$
$74$	48.9454	+	28.2586i	0.661424	+	0.381873i
$75$		0			0
$76$	26.0605	+	45.1381i	0.342901	+	0.593922i
$77$	−3.75018	−	6.49550i	−0.0487036	−	0.0843572i
$78$		0			0
$79$	49.5443	−	85.8133i	0.627144	−	1.08624i	−0.360979	−	0.932574i	$-0.617557\pi$
$79$	49.5443	−	85.8133i	0.627144	−	1.08624i	0.988122	−	0.153670i	$-0.0491094\pi$
$80$	1.68186	−	19.9292i	0.0210232	−	0.249114i
$81$		0			0
$82$		−	50.1630i		−	0.611744i
$83$	18.9521	−	32.8260i	0.228339	−	0.395494i	−0.728977	−	0.684538i	$-0.760004\pi$
$83$	18.9521	−	32.8260i	0.228339	−	0.395494i	0.957316	+	0.289044i	$0.0933374\pi$
$84$		0			0
$85$	−79.8563	+	37.5369i	−0.939486	+	0.441611i
$86$	−74.7506	+	43.1573i	−0.869193	+	0.501829i
$87$		0			0
$88$	9.34821	+	5.39719i	0.106230	+	0.0613317i
$89$		−	43.0816i		−	0.484063i	−0.970268	−	0.242031i	$-0.922186\pi$
$89$		−	43.0816i		−	0.484063i	0.970268	−	0.242031i	$-0.0778137\pi$
$90$		0			0
$91$	36.5927			0.402118
$92$	9.64111	−	16.6989i	0.104795	−	0.181510i
$93$		0			0
$94$	50.1246	+	86.8184i	0.533241	+	0.923600i
$95$	117.924	−	55.4310i	1.24131	−	0.583484i
$96$		0			0
$97$	23.7789	+	13.7287i	0.245143	+	0.141533i	0.617538	−	0.786541i	$-0.288130\pi$
$97$	23.7789	+	13.7287i	0.245143	+	0.141533i	−0.372395	+	0.928074i	$0.621463\pi$
$98$	63.8342			0.651369
$99$		0			0
$100$	−49.2928	−	8.37950i	−0.492928	−	0.0837950i
$101$	−155.639	−	89.8581i	−1.54098	−	0.889684i	−0.998777	−	0.0494344i	$-0.984258\pi$
$101$	−155.639	−	89.8581i	−1.54098	−	0.889684i	−0.542200	−	0.840249i	$-0.682409\pi$
$102$		0			0
$103$	−113.516	+	65.5383i	−1.10209	+	0.636294i	−0.936770	−	0.349945i	$-0.886200\pi$
$103$	−113.516	+	65.5383i	−1.10209	+	0.636294i	−0.165324	+	0.986239i	$0.552867\pi$
$104$	−45.6080	+	26.3318i	−0.438539	+	0.253190i
$105$		0			0
$106$	−58.9152	+	102.044i	−0.555804	+	0.962681i
$107$	208.077			1.94464			0.972320	−	0.233652i	$-0.0750675\pi$
$107$	208.077			1.94464			0.972320	+	0.233652i	$0.0750675\pi$
$108$		0			0
$109$	96.9352			0.889314			0.444657	−	0.895701i	$-0.353326\pi$
$109$	96.9352			0.889314			0.444657	+	0.895701i	$0.353326\pi$
$110$	15.4105	−	22.1531i	0.140095	−	0.201392i
$111$		0			0
$112$	6.80801	−	3.93060i	0.0607858	−	0.0350947i
$113$	−5.98564	−	10.3674i	−0.0529703	−	0.0917472i	0.838324	−	0.545172i	$-0.183536\pi$
$113$	−5.98564	−	10.3674i	−0.0529703	−	0.0917472i	−0.891295	+	0.453424i	$0.850202\pi$
$114$		0			0
$115$	−39.5725	−	27.5280i	−0.344108	−	0.239374i
$116$			12.0254i			0.103667i
$117$		0			0
$118$			52.7566i			0.447090i
$119$	−30.0365	−	17.3416i	−0.252407	−	0.145727i
$120$		0			0
$121$	−53.2176	−	92.1756i	−0.439815	−	0.761782i
$122$	3.36005	+	5.81978i	0.0275414	+	0.0477031i
$123$		0			0
$124$	−25.3332	+	43.8784i	−0.204300	+	0.353858i
$125$	−31.2375	+	121.034i	−0.249900	+	0.968272i
$126$		0			0
$127$		−	215.556i		−	1.69729i	−0.528964	−	0.848644i	$-0.677419\pi$
$127$		−	215.556i		−	1.69729i	0.528964	−	0.848644i	$-0.322581\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	56.0081	+	119.152i	0.430831	+	0.916554i
$131$	68.7409	−	39.6876i	0.524740	−	0.302959i	−0.214132	−	0.976805i	$-0.568692\pi$
$131$	68.7409	−	39.6876i	0.524740	−	0.302959i	0.738872	+	0.673846i	$0.235359\pi$
$132$		0			0
$133$	44.3550	+	25.6084i	0.333496	+	0.192544i
$134$			13.1200i			0.0979105i
$135$		0			0
$136$	49.9153			0.367024
$137$	−88.0331	+	152.478i	−0.642577	+	1.11298i	0.342278	+	0.939599i	$0.388801\pi$
$137$	−88.0331	+	152.478i	−0.642577	+	1.11298i	−0.984855	+	0.173378i	$0.944532\pi$
$138$		0			0
$139$	39.0272	+	67.5971i	0.280771	+	0.486310i	0.971575	−	0.236732i	$-0.0760764\pi$
$139$	39.0272	+	67.5971i	0.280771	+	0.486310i	−0.690804	+	0.723042i	$0.742743\pi$
$140$	−8.36044	−	17.7861i	−0.0597175	−	0.127043i
$141$		0			0
$142$	−41.8822	−	24.1807i	−0.294945	−	0.170286i
$143$	−71.0589			−0.496915
$144$		0			0
$145$	29.9570	+	2.52813i	0.206600	+	0.0174353i
$146$	28.1067	+	16.2274i	0.192512	+	0.111147i
$147$		0			0
$148$	−69.2192	+	39.9637i	−0.467697	+	0.270025i
$149$	95.9856	−	55.4173i	0.644199	−	0.371928i	−0.142031	−	0.989862i	$-0.545363\pi$
$149$	95.9856	−	55.4173i	0.644199	−	0.371928i	0.786230	+	0.617934i	$0.212030\pi$
$150$		0			0
$151$	6.31648	−	10.9405i	0.0418310	−	0.0724534i	−0.844352	−	0.535789i	$-0.820014\pi$
$151$	6.31648	−	10.9405i	0.0418310	−	0.0724534i	0.886183	+	0.463336i	$0.153348\pi$
$152$	−73.7102			−0.484935
$153$		0			0
$154$	10.6071			0.0688773
$155$	103.981	+	72.3333i	0.670848	+	0.466666i
$156$		0			0
$157$	178.526	−	103.072i	1.13711	−	0.656510i	0.191395	−	0.981513i	$-0.438699\pi$
$157$	178.526	−	103.072i	1.13711	−	0.656510i	0.945713	+	0.325003i	$0.105365\pi$
$158$	70.0663	+	121.358i	0.443457	+	0.768091i
$159$		0			0
$160$	23.2189	+	16.1519i	0.145118	+	0.100949i
$161$		−	18.9477i		−	0.117688i
$162$		0			0
$163$			235.021i			1.44185i	0.693015	+	0.720923i	$0.256282\pi$
$163$			235.021i			1.44185i	−0.693015	+	0.720923i	$0.743718\pi$
$164$	61.4369	+	35.4706i	0.374615	+	0.216284i
$165$		0			0
$166$	26.8023	+	46.4230i	0.161460	+	0.279656i
$167$	−63.0895	−	109.274i	−0.377781	−	0.654336i	0.612958	−	0.790116i	$-0.289979\pi$
$167$	−63.0895	−	109.274i	−0.377781	−	0.654336i	−0.990739	+	0.135779i	$0.956646\pi$
$168$		0			0
$169$	88.8409	−	153.877i	0.525686	−	0.910515i
$170$	10.4938	−	124.346i	0.0617282	−	0.731448i
$171$		0			0
$172$		−	122.067i		−	0.709693i
$173$	48.4962	−	83.9978i	0.280325	−	0.485537i	−0.691140	−	0.722721i	$-0.742891\pi$
$173$	48.4962	−	83.9978i	0.280325	−	0.485537i	0.971465	+	0.237184i	$0.0762245\pi$
$174$		0			0
$175$	−46.0653	+	17.0879i	−0.263230	+	0.0976450i
$176$	−13.2204	+	7.63278i	−0.0751157	+	0.0433681i
$177$		0			0
$178$	52.7639	+	30.4633i	0.296427	+	0.171142i
$179$			239.017i			1.33529i	0.744479	+	0.667645i	$0.232698\pi$
$179$			239.017i			1.33529i	−0.744479	+	0.667645i	$0.767302\pi$
$180$		0			0
$181$	271.084			1.49770			0.748851	−	0.662738i	$-0.230606\pi$
$181$	271.084			1.49770			0.748851	+	0.662738i	$0.230606\pi$
$182$	−25.8750	+	44.8168i	−0.142170	+	0.246246i
$183$		0			0
$184$	13.6346	+	23.6158i	0.0741010	+	0.128347i
$185$	85.0033	+	180.837i	0.459477	+	0.977496i
$186$		0			0
$187$	58.3273	+	33.6753i	0.311911	+	0.180082i
$188$	−141.774			−0.754116
$189$		0			0
$190$	−15.4962	+	183.623i	−0.0815592	+	0.966435i
$191$	−223.164	−	128.844i	−1.16840	−	0.674574i	−0.215094	−	0.976593i	$-0.569006\pi$
$191$	−223.164	−	128.844i	−1.16840	−	0.674574i	−0.953302	+	0.302020i	$0.902339\pi$
$192$		0			0
$193$	101.334	−	58.5050i	0.525045	−	0.303135i	−0.213952	−	0.976844i	$-0.568633\pi$
$193$	101.334	−	58.5050i	0.525045	−	0.303135i	0.738996	+	0.673710i	$0.235300\pi$
$194$	−33.6284	+	19.4154i	−0.173342	+	0.100079i
$195$		0			0
$196$	−45.1376	+	78.1806i	−0.230294	+	0.398881i
$197$	−127.741			−0.648430			−0.324215	−	0.945983i	$-0.605100\pi$
$197$	−127.741			−0.648430			−0.324215	+	0.945983i	$0.605100\pi$
$198$		0			0
$199$	−352.563			−1.77167			−0.885836	−	0.463998i	$-0.846414\pi$
$199$	−352.563			−1.77167			−0.885836	+	0.463998i	$0.846414\pi$
$200$	45.1180	−	54.4460i	0.225590	−	0.272230i
$201$		0			0
$202$	220.106	−	127.078i	1.08964	−	0.629101i
$203$	5.90839	+	10.2336i	0.0291054	+	0.0504120i
$204$		0			0
$205$	101.278	−	145.591i	0.494041	−	0.710201i
$206$		−	185.370i		−	0.899856i
$207$		0			0
$208$		−	74.4776i		−	0.358065i
$209$	−86.1323	−	49.7285i	−0.412116	−	0.237935i
$210$		0			0
$211$	−139.201	−	241.103i	−0.659720	−	1.14267i	−0.980688	−	0.195578i	$-0.937342\pi$
$211$	−139.201	−	241.103i	−0.659720	−	1.14267i	0.320968	−	0.947090i	$-0.395992\pi$
$212$	−83.3187	−	144.312i	−0.393013	−	0.680718i
$213$		0			0
$214$	−147.132	+	254.841i	−0.687534	+	1.19084i
$215$	−304.087	−	25.6624i	−1.41436	−	0.119360i
$216$		0			0
$217$			49.7874i			0.229435i
$218$	−68.5435	+	118.721i	−0.314420	+	0.544591i
$219$		0			0
$220$	16.2350	+	34.5385i	0.0737955	+	0.156993i
$221$	−284.567	+	164.295i	−1.28763	+	0.743416i
$222$		0			0
$223$	−310.388	−	179.203i	−1.39188	−	0.803600i	−0.398353	−	0.917232i	$-0.630418\pi$
$223$	−310.388	−	179.203i	−1.39188	−	0.803600i	−0.993523	+	0.113632i	$0.963751\pi$
$224$			11.1174i			0.0496314i
$225$		0			0
$226$	16.9300			0.0749113
$227$	−159.551	+	276.350i	−0.702868	+	1.21740i	0.264588	+	0.964362i	$0.414764\pi$
$227$	−159.551	+	276.350i	−0.702868	+	1.21740i	−0.967456	+	0.253041i	$0.918569\pi$
$228$		0			0
$229$	−12.4290	−	21.5276i	−0.0542750	−	0.0940071i	0.837611	−	0.546267i	$-0.183951\pi$
$229$	−12.4290	−	21.5276i	−0.0542750	−	0.0940071i	−0.891886	+	0.452259i	$0.850618\pi$
$230$	61.6968	−	29.0009i	0.268247	−	0.126091i
$231$		0			0
$232$	−14.7281	−	8.50325i	−0.0634830	−	0.0366519i
$233$	−223.302			−0.958376			−0.479188	−	0.877712i	$-0.659069\pi$
$233$	−223.302			−0.958376			−0.479188	+	0.877712i	$0.659069\pi$
$234$		0			0
$235$	−29.8054	+	353.179i	−0.126832	+	1.50289i
$236$	−64.6133	−	37.3045i	−0.273785	−	0.158070i
$237$		0			0
$238$	42.4780	−	24.5247i	0.178479	−	0.103045i
$239$	77.7097	−	44.8657i	0.325145	−	0.187723i	−0.328538	−	0.944491i	$-0.606556\pi$
$239$	77.7097	−	44.8657i	0.325145	−	0.187723i	0.653684	+	0.756768i	$0.273223\pi$
$240$		0			0
$241$	57.1228	−	98.9396i	0.237024	−	0.410538i	−0.722835	−	0.691021i	$-0.757161\pi$
$241$	57.1228	−	98.9396i	0.237024	−	0.410538i	0.959859	+	0.280483i	$0.0904946\pi$
$242$	150.522			0.621992
$243$		0			0
$244$	−9.50367			−0.0389495
$245$	185.270	+	128.880i	0.756203	+	0.526042i
$246$		0			0
$247$	420.222	−	242.615i	1.70130	−	0.982248i
$248$	−35.8265	−	62.0534i	−0.144462	−	0.250215i
$249$		0			0
$250$	−126.147	−	123.842i	−0.504590	−	0.495367i
$251$			285.710i			1.13829i	0.822238	+	0.569144i	$0.192725\pi$
$251$			285.710i			1.13829i	−0.822238	+	0.569144i	$0.807275\pi$
$252$		0			0
$253$			36.7942i			0.145432i
$254$	264.001	+	152.421i	1.03937	+	0.600082i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−128.509	−	222.584i	−0.500035	−	0.866085i	−1.00000		4.00144e-5i	$-0.999987\pi$
$257$	−128.509	−	222.584i	−0.500035	−	0.866085i	0.499965	−	0.866045i	$-0.333346\pi$
$258$		0			0
$259$	−39.2704	+	68.0183i	−0.151623	+	0.262619i
$260$	−185.534	−	15.6576i	−0.713594	−	0.0602214i
$261$		0			0
$262$			112.253i			0.428448i
$263$	−91.0191	+	157.650i	−0.346080	+	0.599428i	−0.985549	−	0.169388i	$-0.945821\pi$
$263$	−91.0191	+	157.650i	−0.346080	+	0.599428i	0.639469	+	0.768817i	$0.279154\pi$
$264$		0			0
$265$	−377.019	+	177.220i	−1.42271	+	0.668754i
$266$	−62.7274	+	36.2157i	−0.235817	+	0.136149i
$267$		0			0
$268$	−16.0687	−	9.27725i	−0.0599577	−	0.0346166i
$269$		−	377.258i		−	1.40244i	−0.712943	−	0.701222i	$-0.752638\pi$
$269$		−	377.258i		−	1.40244i	0.712943	−	0.701222i	$-0.247362\pi$
$270$		0			0
$271$	−282.266			−1.04157			−0.520787	−	0.853687i	$-0.674361\pi$
$271$	−282.266			−1.04157			−0.520787	+	0.853687i	$0.674361\pi$
$272$	−35.2954	+	61.1335i	−0.129763	+	0.224756i
$273$		0			0
$274$	−124.498	−	215.636i	−0.454371	−	0.786993i
$275$	89.4535	−	33.1827i	0.325285	−	0.120664i
$276$		0			0
$277$	−325.284	−	187.803i	−1.17431	−	0.677988i	−0.219619	−	0.975586i	$-0.570481\pi$
$277$	−325.284	−	187.803i	−1.17431	−	0.677988i	−0.954691	+	0.297597i	$0.903815\pi$
$278$	−110.386			−0.397071
$279$		0			0
$280$	27.6951	+	2.33724i	0.0989112	+	0.00834728i
$281$	366.787	+	211.764i	1.30529	+	0.753610i	0.981306	−	0.192453i	$-0.0616442\pi$
$281$	366.787	+	211.764i	1.30529	+	0.753610i	0.323984	+	0.946062i	$0.394977\pi$
$282$		0			0
$283$	−10.9325	+	6.31187i	−0.0386307	+	0.0223034i	−0.519191	−	0.854658i	$-0.673767\pi$
$283$	−10.9325	+	6.31187i	−0.0386307	+	0.0223034i	0.480560	+	0.876962i	$0.340433\pi$
$284$	59.2303	−	34.1966i	0.208557	−	0.120411i
$285$		0			0
$286$	50.2462	−	87.0290i	0.175686	−	0.304297i
$287$	69.7105			0.242894
$288$		0			0
$289$	22.4421			0.0776543
$290$	−24.2791	+	34.9021i	−0.0837211	+	0.120352i
$291$		0			0
$292$	−39.7489	+	22.9490i	−0.136126	+	0.0785925i
$293$	−8.01586	−	13.8839i	−0.0273579	−	0.0473853i	0.852022	−	0.523505i	$-0.175376\pi$
$293$	−8.01586	−	13.8839i	−0.0273579	−	0.0473853i	−0.879380	+	0.476120i	$0.842043\pi$
$294$		0			0
$295$	−106.515	+	153.119i	−0.361067	+	0.519046i
$296$		−	113.034i		−	0.381873i
$297$		0			0
$298$			156.744i			0.525986i
$299$	−155.462	−	89.7558i	−0.519938	−	0.300187i
$300$		0			0
$301$	−59.9747	−	103.879i	−0.199252	−	0.345114i
$302$	8.93286	+	15.4722i	0.0295790	+	0.0512323i
$303$		0			0
$304$	52.1210	−	90.2762i	0.171451	−	0.296961i
$305$	−1.99798	+	23.6750i	−0.00655074	+	0.0776230i
$306$		0			0
$307$		−	460.226i		−	1.49911i	−0.661943	−	0.749554i	$-0.730268\pi$
$307$		−	460.226i		−	1.49911i	0.661943	−	0.749554i	$-0.269732\pi$
$308$	−7.50036	+	12.9910i	−0.0243518	+	0.0421786i
$309$		0			0
$310$	−162.116	+	76.2035i	−0.522954	+	0.245818i
$311$	−127.789	+	73.7787i	−0.410896	+	0.237231i	−0.691174	−	0.722688i	$-0.742906\pi$
$311$	−127.789	+	73.7787i	−0.410896	+	0.237231i	0.280279	+	0.959919i	$0.409573\pi$
$312$		0			0
$313$	−180.912	−	104.449i	−0.577992	−	0.333704i	0.182343	−	0.983235i	$-0.441632\pi$
$313$	−180.912	−	104.449i	−0.577992	−	0.333704i	−0.760335	+	0.649531i	$0.774965\pi$
$314$			291.532i			0.928445i
$315$		0			0
$316$	−198.177			−0.627144
$317$	−247.350	+	428.423i	−0.780284	+	1.35149i	0.151492	+	0.988458i	$0.451592\pi$
$317$	−247.350	+	428.423i	−0.780284	+	1.35149i	−0.931776	+	0.363033i	$0.881741\pi$
$318$		0			0
$319$	−11.4734	−	19.8725i	−0.0359668	−	0.0622963i
$320$	−36.2002	+	17.0161i	−0.113126	+	0.0531753i
$321$		0			0
$322$	23.2061	+	13.3980i	0.0720686	+	0.0416088i
$323$	−459.908			−1.42386
$324$		0			0
$325$	−78.0106	+	458.901i	−0.240033	+	1.41200i
$326$	−287.841	−	166.185i	−0.882947	−	0.509769i
$327$		0			0
$328$	−86.8849	+	50.1630i	−0.264893	+	0.152936i
$329$	−120.650	+	69.6571i	−0.366716	+	0.211724i
$330$		0			0
$331$	−252.506	+	437.354i	−0.762859	+	1.32131i	0.178513	+	0.983938i	$0.442871\pi$
$331$	−252.506	+	437.354i	−0.762859	+	1.32131i	−0.941371	+	0.337372i	$0.890462\pi$
$332$	−75.8084			−0.228339
$333$		0			0
$334$	178.444			0.534263
$335$	−26.4891	+	38.0790i	−0.0790720	+	0.113669i
$336$		0			0
$337$	533.360	−	307.936i	1.58267	−	0.913756i	0.588204	−	0.808712i	$-0.299835\pi$
$337$	533.360	−	307.936i	1.58267	−	0.913756i	0.994468	−	0.105043i	$-0.0334982\pi$
$338$	125.640	+	217.615i	0.371716	+	0.643831i
$339$		0			0
$340$	144.872	+	100.778i	0.426095	+	0.296407i
$341$		−	96.6813i		−	0.283523i
$342$		0			0
$343$			185.009i			0.539384i
$344$	149.501	+	86.3145i	0.434596	+	0.250914i
$345$		0			0
$346$	68.5839	+	118.791i	0.198219	+	0.343326i
$347$	−129.356	−	224.051i	−0.372784	−	0.645681i	0.617209	−	0.786799i	$-0.288263\pi$
$347$	−129.356	−	224.051i	−0.372784	−	0.645681i	−0.989993	+	0.141119i	$0.954930\pi$
$348$		0			0
$349$	233.479	−	404.397i	0.668994	−	1.15873i	−0.309192	−	0.951000i	$-0.600059\pi$
$349$	233.479	−	404.397i	0.668994	−	1.15873i	0.978186	−	0.207732i	$-0.0666081\pi$
$350$	11.6448	−	68.5012i	0.0332709	−	0.195718i
$351$		0			0
$352$		−	21.5888i		−	0.0613317i
$353$	16.6680	−	28.8699i	0.0472182	−	0.0817843i	−0.841450	−	0.540334i	$-0.818298\pi$
$353$	16.6680	−	28.8699i	0.0472182	−	0.0817843i	0.888669	+	0.458550i	$0.151631\pi$
$354$		0			0
$355$	−72.7367	−	154.741i	−0.204892	−	0.435889i
$356$	−74.6195	+	43.0816i	−0.209605	+	0.121016i
$357$		0			0
$358$	−292.735	−	169.011i	−0.817695	−	0.472097i
$359$		−	618.698i		−	1.72339i	−0.507423	−	0.861697i	$-0.669402\pi$
$359$		−	618.698i		−	1.72339i	0.507423	−	0.861697i	$-0.330598\pi$
$360$		0			0
$361$	318.149			0.881299
$362$	−191.685	+	332.009i	−0.529518	+	0.917151i
$363$		0			0
$364$	−36.5927	−	63.3805i	−0.100529	−	0.174122i
$365$	48.8129	+	103.845i	0.133734	+	0.284506i
$366$		0			0
$367$	315.677	+	182.256i	0.860154	+	0.496610i	0.864064	−	0.503382i	$-0.167911\pi$
$367$	315.677	+	182.256i	0.860154	+	0.496610i	−0.00390987	+	0.999992i	$0.501245\pi$
$368$	−38.5644			−0.104795
$369$		0			0
$370$	−281.585	−	23.7635i	−0.761041	−	0.0642256i
$371$	−141.809	−	81.8732i	−0.382233	−	0.220683i
$372$		0			0
$373$	−433.179	+	250.096i	−1.16134	+	0.670499i	−0.951625	−	0.307263i	$-0.900587\pi$
$373$	−433.179	+	250.096i	−1.16134	+	0.670499i	−0.209714	+	0.977763i	$0.567253\pi$
$374$	−82.4873	+	47.6241i	−0.220554	+	0.127337i
$375$		0			0
$376$	100.249	−	173.637i	0.266620	−	0.461800i
$377$	111.953			0.296957
$378$		0			0
$379$	153.088			0.403927			0.201963	−	0.979393i	$-0.435268\pi$
$379$	153.088			0.403927			0.201963	+	0.979393i	$0.435268\pi$
$380$	−213.934	−	148.820i	−0.562983	−	0.391631i
$381$		0			0
$382$	315.601	−	182.212i	0.826181	−	0.476996i
$383$	311.776	+	540.011i	0.814036	+	1.40995i	0.910018	+	0.414568i	$0.136067\pi$
$383$	311.776	+	540.011i	0.814036	+	1.40995i	−0.0959828	+	0.995383i	$0.530599\pi$
$384$		0			0
$385$	30.7857	+	21.4156i	0.0799627	+	0.0556249i
$386$			165.477i			0.428697i
$387$		0			0
$388$		−	54.9150i		−	0.141533i
$389$	241.566	+	139.468i	0.620993	+	0.358531i	0.777256	−	0.629185i	$-0.216611\pi$
$389$	241.566	+	139.468i	0.620993	+	0.358531i	−0.156262	+	0.987716i	$0.549945\pi$
$390$		0			0
$391$	85.0718	+	147.349i	0.217575	+	0.376851i
$392$	−63.8342	−	110.564i	−0.162842	−	0.282051i
$393$		0			0
$394$	90.3263	−	156.450i	0.229254	−	0.397080i
$395$	−41.6632	+	493.689i	−0.105477	+	1.24984i
$396$		0			0
$397$		−	685.202i		−	1.72595i	−0.505246	−	0.862975i	$-0.668598\pi$
$397$		−	685.202i		−	1.72595i	0.505246	−	0.862975i	$-0.331402\pi$
$398$	249.300	−	431.800i	0.626381	−	1.08492i
$399$		0			0
$400$	34.7791	+	93.7572i	0.0869478	+	0.234393i
$401$	340.681	−	196.692i	0.849578	−	0.490504i	−0.0109302	−	0.999940i	$-0.503479\pi$
$401$	340.681	−	196.692i	0.849578	−	0.490504i	0.860509	+	0.509436i	$0.170146\pi$
$402$		0			0
$403$	408.494	+	235.844i	1.01363	+	0.585221i
$404$			359.432i			0.889684i
$405$		0			0
$406$	−16.7114			−0.0411612
$407$	76.2586	−	132.084i	0.187368	−	0.324530i
$408$		0			0
$409$	290.805	+	503.689i	0.711014	+	1.23151i	0.964477	+	0.264168i	$0.0850973\pi$
$409$	290.805	+	503.689i	0.711014	+	1.23151i	−0.253462	+	0.967345i	$0.581569\pi$
$410$	106.697	+	226.989i	0.260237	+	0.553631i
$411$		0			0
$412$	227.031	+	131.077i	0.551047	+	0.318147i
$413$	−73.3147			−0.177517
$414$		0			0
$415$	−15.9374	+	188.850i	−0.0384033	+	0.455060i
$416$	91.2160	+	52.6636i	0.219269	+	0.126595i
$417$		0			0
$418$	121.809	−	70.3267i	0.291410	−	0.168246i
$419$	162.461	−	93.7971i	0.387736	−	0.223860i	−0.293443	−	0.955977i	$-0.594801\pi$
$419$	162.461	−	93.7971i	0.387736	−	0.223860i	0.681179	+	0.732117i	$0.261468\pi$
$420$		0			0
$421$	−87.4522	+	151.472i	−0.207725	+	0.359790i	−0.950998	−	0.309199i	$-0.899939\pi$
$421$	−87.4522	+	151.472i	−0.207725	+	0.359790i	0.743273	+	0.668989i	$0.233273\pi$
$422$	393.720			0.932985
$423$		0			0
$424$	235.661			0.555804
$425$	281.510	−	339.711i	0.662377	−	0.799319i
$426$		0			0
$427$	−8.08763	+	4.66939i	−0.0189406	+	0.0109353i
$428$	−208.077	−	360.399i	−0.486160	−	0.842054i
$429$		0			0
$430$	246.452	−	354.283i	0.573144	−	0.823914i
$431$		−	1.74212i		−	0.00404203i	−0.999998	−	0.00202102i	$-0.999357\pi$
$431$		−	1.74212i		−	0.00404203i	0.999998	−	0.00202102i	$-0.000643310\pi$
$432$		0			0
$433$			180.676i			0.417266i	0.977994	+	0.208633i	$0.0669014\pi$
$433$			180.676i			0.417266i	−0.977994	+	0.208633i	$0.933099\pi$
$434$	−60.9768	−	35.2050i	−0.140500	−	0.0811175i
$435$		0			0
$436$	−96.9352	−	167.897i	−0.222328	−	0.385084i
$437$	−125.626	−	217.591i	−0.287474	−	0.497919i
$438$		0			0
$439$	−310.121	+	537.146i	−0.706427	+	1.22357i	0.259747	+	0.965677i	$0.416361\pi$
$439$	−310.121	+	537.146i	−0.706427	+	1.22357i	−0.966174	+	0.257891i	$0.916973\pi$
$440$	−53.7807	−	4.53865i	−0.122229	−	0.0103151i
$441$		0			0
$442$		−	464.696i		−	1.05135i
$443$	112.192	−	194.322i	0.253255	−	0.438650i	−0.711165	−	0.703025i	$-0.751832\pi$
$443$	112.192	−	194.322i	0.253255	−	0.438650i	0.964420	+	0.264375i	$0.0851656\pi$
$444$		0			0
$445$	91.6350	+	194.945i	0.205921	+	0.438079i
$446$	438.955	−	253.431i	0.984205	−	0.568231i
$447$		0			0
$448$	−13.6160	−	7.86121i	−0.0303929	−	0.0175473i
$449$		−	14.6582i		−	0.0326462i	−0.999867	−	0.0163231i	$-0.994804\pi$
$449$		−	14.6582i		−	0.0326462i	0.999867	−	0.0163231i	$-0.00519604\pi$
$450$		0			0
$451$	−135.370			−0.300154
$452$	−11.9713	+	20.7349i	−0.0264851	+	0.0458736i
$453$		0			0
$454$	−225.639	−	390.818i	−0.497002	−	0.860834i
$455$	−165.583	+	77.8332i	−0.363919	+	0.171062i
$456$		0			0
$457$	383.425	+	221.371i	0.839005	+	0.484400i	0.856926	−	0.515440i	$-0.172371\pi$
$457$	383.425	+	221.371i	0.839005	+	0.484400i	−0.0179210	+	0.999839i	$0.505705\pi$
$458$	35.1545			0.0767565
$459$		0			0
$460$	−8.10748	+	96.0696i	−0.0176250	+	0.208847i
$461$	454.601	+	262.464i	0.986120	+	0.569337i	0.904112	−	0.427295i	$-0.140533\pi$
$461$	454.601	+	262.464i	0.986120	+	0.569337i	0.0820078	+	0.996632i	$0.473867\pi$
$462$		0			0
$463$	2.48514	−	1.43480i	0.00536747	−	0.00309891i	−0.497314	−	0.867571i	$-0.665680\pi$
$463$	2.48514	−	1.43480i	0.00536747	−	0.00309891i	0.502681	+	0.864472i	$0.332347\pi$
$464$	20.8286	−	12.0254i	0.0448893	−	0.0259168i
$465$		0			0
$466$	157.898	−	273.487i	0.338837	−	0.586883i
$467$	692.793			1.48350			0.741748	−	0.670679i	$-0.233997\pi$
$467$	692.793			1.48350			0.741748	+	0.670679i	$0.233997\pi$
$468$		0			0
$469$	−18.2326			−0.0388755
$470$	−411.479	−	286.239i	−0.875487	−	0.609020i
$471$		0			0
$472$	91.3771	−	52.7566i	0.193595	−	0.111772i
$473$	116.464	+	201.722i	0.246224	+	0.426473i
$474$		0			0
$475$	−415.707	+	501.653i	−0.875174	+	1.05611i
$476$			69.3662i			0.145727i
$477$		0			0
$478$			126.899i			0.265480i
$479$	−767.464	−	443.096i	−1.60222	−	0.925043i	−0.991042	−	0.133551i	$-0.957362\pi$
$479$	−767.464	−	443.096i	−1.60222	−	0.925043i	−0.611179	−	0.791492i	$-0.709305\pi$
$480$		0			0
$481$	372.050	+	644.410i	0.773493	+	1.33973i
$482$	80.7839	+	139.922i	0.167601	+	0.290294i
$483$		0			0
$484$	−106.435	+	184.351i	−0.219907	+	0.380891i
$485$	−136.801	−	11.5449i	−0.282064	−	0.0238039i
$486$		0			0
$487$			151.898i			0.311905i	0.987765	+	0.155953i	$0.0498447\pi$
$487$			151.898i			0.311905i	−0.987765	+	0.155953i	$0.950155\pi$
$488$	6.72011	−	11.6396i	0.0137707	−	0.0238516i
$489$		0			0
$490$	−288.851	+	135.776i	−0.589492	+	0.277094i
$491$	8.54545	−	4.93372i	0.0174042	−	0.0100483i	−0.491273	−	0.871006i	$-0.663468\pi$
$491$	8.54545	−	4.93372i	0.0174042	−	0.0100483i	0.508677	+	0.860958i	$0.330135\pi$
$492$		0			0
$493$	−91.8944	−	53.0553i	−0.186398	−	0.107617i
$494$			686.219i			1.38911i
$495$		0			0
$496$	101.333			0.204300
$497$	33.6034	−	58.2027i	0.0676124	−	0.117108i
$498$		0			0
$499$	107.188	+	185.656i	0.214806	+	0.372055i	0.953213	−	0.302301i	$-0.0977547\pi$
$499$	107.188	+	185.656i	0.214806	+	0.372055i	−0.738406	+	0.674356i	$0.764421\pi$
$500$	240.874	−	66.9291i	0.481749	−	0.133858i
$501$		0			0
$502$	−349.922	−	202.028i	−0.697056	−	0.402446i
$503$	778.384			1.54748			0.773741	−	0.633502i	$-0.218383\pi$
$503$	778.384			1.54748			0.773741	+	0.633502i	$0.218383\pi$
$504$		0			0
$505$	895.398	+	75.5642i	1.77306	+	0.149632i
$506$	−45.0635	−	26.0174i	−0.0890584	−	0.0514179i
$507$		0			0
$508$	−373.353	+	215.556i	−0.734948	+	0.424322i
$509$	−388.299	+	224.184i	−0.762866	+	0.440441i	−0.830324	−	0.557281i	$-0.811844\pi$
$509$	−388.299	+	224.184i	−0.762866	+	0.440441i	0.0674580	+	0.997722i	$0.478511\pi$
$510$		0			0
$511$	−22.5509	+	39.0593i	−0.0441309	+	0.0764369i
$512$	22.6274			0.0441942
$513$		0			0
$514$	363.478			0.707156
$515$	374.260	−	538.011i	0.726719	−	1.04468i
$516$		0			0
$517$	234.288	−	135.266i	0.453168	−	0.261636i
$518$	−55.5367	−	96.1924i	−0.107214	−	0.185700i
$519$		0			0
$520$	150.369	−	216.161i	0.289172	−	0.415694i
$521$		−	603.440i		−	1.15823i	−0.815244	−	0.579117i	$-0.803397\pi$
$521$		−	603.440i		−	1.15823i	0.815244	−	0.579117i	$-0.196603\pi$
$522$		0			0
$523$		−	963.204i		−	1.84169i	−0.389928	−	0.920845i	$-0.627500\pi$
$523$		−	963.204i		−	1.84169i	0.389928	−	0.920845i	$-0.372500\pi$
$524$	−137.482	−	79.3752i	−0.262370	−	0.151479i
$525$		0			0
$526$	−128.720	−	222.950i	−0.244716	−	0.423860i
$527$	−223.536	−	387.177i	−0.424168	−	0.734680i
$528$		0			0
$529$	218.025	−	377.630i	0.412145	−	0.713855i
$530$	49.5435	−	587.065i	0.0934782	−	1.10767i
$531$		0			0
$532$		−	102.433i		−	0.192544i
$533$	330.221	−	571.959i	0.619551	−	1.07309i
$534$		0			0
$535$	−941.551	+	442.581i	−1.75991	+	0.827255i
$536$	22.7245	−	13.1200i	0.0423965	−	0.0244776i
$537$		0			0
$538$	462.044	+	266.761i	0.858818	+	0.495839i
$539$		−	172.263i		−	0.319597i
$540$		0			0
$541$	305.923			0.565477			0.282738	−	0.959197i	$-0.408757\pi$
$541$	305.923			0.565477			0.282738	+	0.959197i	$0.408757\pi$
$542$	199.593	−	345.704i	0.368252	−	0.637831i
$543$		0			0
$544$	−49.9153	−	86.4558i	−0.0917561	−	0.158926i
$545$	−438.634	+	206.182i	−0.804833	+	0.378316i
$546$		0			0
$547$	−432.376	−	249.632i	−0.790449	−	0.456366i	0.0496714	−	0.998766i	$-0.484183\pi$
$547$	−432.376	−	249.632i	−0.790449	−	0.456366i	−0.840121	+	0.542399i	$0.817516\pi$
$548$	352.132			0.642577
$549$		0			0
$550$	−22.6129	+	133.021i	−0.0411143	+	0.241857i
$551$	135.701	+	78.3470i	0.246281	+	0.142191i
$552$		0			0
$553$	−168.649	+	97.3696i	−0.304971	+	0.176075i
$554$	460.021	−	265.593i	0.830363	−	0.479410i
$555$		0			0
$556$	78.0544	−	135.194i	0.140386	−	0.243155i
$557$	842.880			1.51325			0.756625	−	0.653849i	$-0.226847\pi$
$557$	842.880			1.51325			0.756625	+	0.653849i	$0.226847\pi$
$558$		0			0
$559$	−1136.41			−2.03293
$560$	−22.4459	+	32.2668i	−0.0400820	+	0.0576193i
$561$		0			0
$562$	−518.715	+	299.480i	−0.922980	+	0.532883i
$563$	−313.512	−	543.018i	−0.556859	−	0.964509i	−0.997756	−	0.0669510i	$-0.978673\pi$
$563$	−313.512	−	543.018i	−0.556859	−	0.964509i	0.440897	−	0.897558i	$-0.354660\pi$
$564$		0			0
$565$	49.1368	+	34.1813i	0.0869678	+	0.0604979i
$566$		−	17.8527i		−	0.0315418i
$567$		0			0
$568$			96.7227i			0.170286i
$569$	−142.657	−	82.3630i	−0.250715	−	0.144750i	0.369377	−	0.929280i	$-0.379571\pi$
$569$	−142.657	−	82.3630i	−0.250715	−	0.144750i	−0.620092	+	0.784529i	$0.712905\pi$
$570$		0			0
$571$	377.206	+	653.339i	0.660605	+	1.14420i	0.980457	+	0.196734i	$0.0630336\pi$
$571$	377.206	+	653.339i	0.660605	+	1.14420i	−0.319852	+	0.947468i	$0.603633\pi$
$572$	71.0589	+	123.078i	0.124229	+	0.215171i
$573$		0			0
$574$	−49.2927	+	85.3775i	−0.0858759	+	0.148741i
$575$	237.619	+	40.3938i	0.413250	+	0.0702501i
$576$		0			0
$577$		−	924.607i		−	1.60244i	−0.598370	−	0.801220i	$-0.704185\pi$
$577$		−	924.607i		−	1.60244i	0.598370	−	0.801220i	$-0.295815\pi$
$578$	−15.8690	+	27.4859i	−0.0274550	+	0.0475534i
$579$		0			0
$580$	−25.5782	−	54.4152i	−0.0441003	−	0.0938193i
$581$	−64.5130	+	37.2466i	−0.111038	+	0.0641078i
$582$		0			0
$583$	275.376	+	158.988i	0.472343	+	0.272707i
$584$		−	64.9096i		−	0.111147i
$585$		0			0
$586$	22.6723			0.0386899
$587$	−49.9504	+	86.5166i	−0.0850944	+	0.147388i	−0.905431	−	0.424493i	$-0.860453\pi$
$587$	−49.9504	+	86.5166i	−0.0850944	+	0.147388i	0.820337	+	0.571880i	$0.193786\pi$
$588$		0			0
$589$	330.098	+	571.746i	0.560437	+	0.970706i
$590$	−112.214	−	238.725i	−0.190193	−	0.404618i
$591$		0			0
$592$	138.438	+	79.9275i	0.233849	+	0.135013i
$593$	519.869			0.876676			0.438338	−	0.898810i	$-0.355567\pi$
$593$	519.869			0.876676			0.438338	+	0.898810i	$0.355567\pi$
$594$		0			0
$595$	172.801	+	14.5830i	0.290422	+	0.0245092i
$596$	−191.971	−	110.835i	−0.322099	−	0.185964i
$597$		0			0
$598$	219.856	−	126.934i	0.367652	−	0.212264i
$599$	184.343	−	106.430i	0.307751	−	0.177680i	−0.338169	−	0.941086i	$-0.609807\pi$
$599$	184.343	−	106.430i	0.307751	−	0.177680i	0.645920	+	0.763405i	$0.276474\pi$
$600$		0			0
$601$	293.347	−	508.092i	0.488098	−	0.845411i	−0.511808	−	0.859100i	$-0.671024\pi$
$601$	293.347	−	508.092i	0.488098	−	0.845411i	0.999906	+	0.0136891i	$0.00435750\pi$
$602$	169.634			0.281784
$603$		0			0
$604$	−25.2659			−0.0418310
$605$	436.869	+	303.902i	0.722098	+	0.502317i
$606$		0			0
$607$	302.021	−	174.372i	0.497563	−	0.287268i	−0.230144	−	0.973157i	$-0.573920\pi$
$607$	302.021	−	174.372i	0.497563	−	0.287268i	0.727707	+	0.685889i	$0.240586\pi$
$608$	73.7102	+	127.670i	0.121234	+	0.209983i
$609$		0			0
$610$	−27.5831	−	19.1878i	−0.0452181	−	0.0314554i
$611$			1319.87i			2.16018i
$612$		0			0
$613$			513.615i			0.837871i	0.908016	+	0.418935i	$0.137597\pi$
$613$			513.615i			0.837871i	−0.908016	+	0.418935i	$0.862403\pi$
$614$	563.660	+	325.429i	0.918013	+	0.530015i
$615$		0			0
$616$	−10.6071	−	18.3721i	−0.0172193	−	0.0298248i
$617$	179.765	+	311.362i	0.291353	+	0.504639i	0.974130	−	0.225988i	$-0.0725611\pi$
$617$	179.765	+	311.362i	0.291353	+	0.504639i	−0.682777	+	0.730627i	$0.739228\pi$
$618$		0			0
$619$	−516.192	+	894.070i	−0.833912	+	1.44438i	0.0610007	+	0.998138i	$0.480571\pi$
$619$	−516.192	+	894.070i	−0.833912	+	1.44438i	−0.894913	+	0.446241i	$0.852763\pi$
$620$	21.3034	−	252.435i	0.0343603	−	0.407152i
$621$		0			0
$622$		−	208.678i		−	0.335495i
$623$	−42.3342	+	73.3249i	−0.0679521	+	0.117696i
$624$		0			0
$625$	−116.090	−	614.124i	−0.185745	−	0.982598i
$626$	255.848	−	147.714i	0.408702	−	0.235964i
$627$		0			0
$628$	−357.052	−	206.144i	−0.568554	−	0.328255i
$629$		−	705.269i		−	1.12125i
$630$		0			0
$631$	−1042.04			−1.65141			−0.825705	−	0.564102i	$-0.809222\pi$
$631$	−1042.04			−1.65141			−0.825705	+	0.564102i	$0.809222\pi$
$632$	140.133	−	242.717i	0.221729	−	0.384045i
$633$		0			0
$634$	−349.806	−	605.881i	−0.551744	−	0.955649i
$635$	458.490	+	975.394i	0.722031	+	1.53605i
$636$		0			0
$637$	727.838	+	420.217i	1.14260	+	0.659682i
$638$	32.4517			0.0508647
$639$		0			0
$640$	4.75701	−	56.3682i	0.00743283	−	0.0880753i
$641$	838.633	+	484.185i	1.30832	+	0.755359i	0.981816	−	0.189837i	$-0.0607960\pi$
$641$	838.633	+	484.185i	1.30832	+	0.755359i	0.326504	+	0.945196i	$0.394129\pi$
$642$		0			0
$643$	−750.259	+	433.162i	−1.16681	+	0.673658i	−0.952927	−	0.303201i	$-0.901945\pi$
$643$	−750.259	+	433.162i	−1.16681	+	0.673658i	−0.213883	+	0.976859i	$0.568611\pi$
$644$	−32.8184	+	18.9477i	−0.0509602	+	0.0294219i
$645$		0			0
$646$	325.204	−	563.270i	0.503412	−	0.871935i
$647$	−211.789			−0.327340			−0.163670	−	0.986515i	$-0.552333\pi$
$647$	−211.789			−0.327340			−0.163670	+	0.986515i	$0.552333\pi$
$648$		0			0
$649$	142.369			0.219366
$650$	−506.875	−	420.035i	−0.779808	−	0.646208i
$651$		0			0
$652$	407.068	−	235.021i	0.624338	−	0.360461i
$653$	129.849	+	224.905i	0.198850	+	0.344419i	0.948156	−	0.317806i	$-0.102946\pi$
$653$	129.849	+	224.905i	0.198850	+	0.344419i	−0.749306	+	0.662224i	$0.769613\pi$
$654$		0			0
$655$	−226.638	+	325.800i	−0.346012	+	0.497405i
$656$		−	141.882i		−	0.216284i
$657$		0			0
$658$		−	197.020i		−	0.299423i
$659$	−451.986	−	260.954i	−0.685866	−	0.395985i	0.116196	−	0.993226i	$-0.462930\pi$
$659$	−451.986	−	260.954i	−0.685866	−	0.395985i	−0.802061	+	0.597241i	$0.796263\pi$
$660$		0			0
$661$	−302.842	−	524.538i	−0.458158	−	0.793553i	0.540706	−	0.841212i	$-0.318157\pi$
$661$	−302.842	−	524.538i	−0.458158	−	0.793553i	−0.998864	+	0.0476590i	$0.984824\pi$
$662$	−357.098	−	618.511i	−0.539422	−	0.934307i
$663$		0			0
$664$	53.6046	−	92.8460i	0.0807299	−	0.139828i
$665$	−255.177	−	21.5348i	−0.383724	−	0.0323832i
$666$		0			0
$667$		−	57.9691i		−	0.0869102i
$668$	−126.179	+	218.548i	−0.188891	+	0.327168i
$669$		0			0
$670$	−27.9064	−	59.3683i	−0.0416514	−	0.0886094i
$671$	15.7052	−	9.06742i	0.0234057	−	0.0135133i
$672$		0			0
$673$	420.261	+	242.638i	0.624459	+	0.360531i	0.778603	−	0.627517i	$-0.215929\pi$
$673$	420.261	+	242.638i	0.624459	+	0.360531i	−0.154144	+	0.988048i	$0.549262\pi$
$674$			870.974i			1.29225i
$675$		0			0
$676$	−355.364			−0.525686
$677$	454.177	−	786.657i	0.670867	−	1.16198i	−0.306792	−	0.951777i	$-0.599256\pi$
$677$	454.177	−	786.657i	0.670867	−	1.16198i	0.977659	−	0.210198i	$-0.0674110\pi$
$678$		0			0
$679$	−26.9811	−	46.7327i	−0.0397366	−	0.0688258i
$680$	−225.868	+	106.170i	−0.332159	+	0.156133i
$681$		0			0
$682$	118.410	+	68.3640i	0.173622	+	0.100240i
$683$	−285.449			−0.417934			−0.208967	−	0.977923i	$-0.567010\pi$
$683$	−285.449			−0.417934			−0.208967	+	0.977923i	$0.567010\pi$
$684$		0			0
$685$	74.0295	−	877.213i	0.108072	−	1.28060i
$686$	−226.589	−	130.821i	−0.330304	−	0.190701i
$687$		0			0
$688$	−211.427	+	122.067i	−0.307306	+	0.177423i
$689$	−1343.50	+	775.672i	−1.94993	+	1.12579i
$690$		0			0
$691$	−194.223	+	336.404i	−0.281075	+	0.486837i	−0.971650	−	0.236424i	$-0.924024\pi$
$691$	−194.223	+	336.404i	−0.281075	+	0.486837i	0.690574	+	0.723261i	$0.257358\pi$
$692$	−193.985			−0.280325
$693$		0			0
$694$	365.874			0.527196
$695$	−320.379	−	222.867i	−0.460977	−	0.320672i
$696$		0			0
$697$	−542.111	+	312.988i	−0.777777	+	0.449050i
$698$	330.189	+	571.904i	0.473050	+	0.819347i
$699$		0			0
$700$	75.6624	+	62.6996i	0.108089	+	0.0895708i
$701$		−	519.499i		−	0.741083i	−0.928816	−	0.370542i	$-0.879172\pi$
$701$		−	519.499i		−	0.741083i	0.928816	−	0.370542i	$-0.120828\pi$
$702$		0			0
$703$			1041.47i			1.48147i
$704$	26.4407	+	15.2656i	0.0375578	+	0.0216840i
$705$		0			0
$706$	23.5721	+	40.8282i	0.0333883	+	0.0578303i
$707$	176.598	+	305.877i	0.249785	+	0.432641i
$708$		0			0
$709$	398.354	−	689.969i	0.561853	−	0.973157i	−0.435482	−	0.900197i	$-0.643422\pi$
$709$	398.354	−	689.969i	0.561853	−	0.973157i	0.997335	−	0.0729600i	$-0.0232445\pi$
$710$	240.950	+	20.3342i	0.339367	+	0.0286397i
$711$		0			0
$712$		−	121.853i		−	0.171142i
$713$	122.120	−	211.518i	0.171276	−	0.296659i
$714$		0			0
$715$	321.543	−	151.143i	0.449710	−	0.211389i
$716$	413.990	−	239.017i	0.578198	−	0.333823i
$717$		0			0
$718$	757.748	+	437.486i	1.05536	+	0.609312i
$719$		−	785.781i		−	1.09288i	−0.837498	−	0.546440i	$-0.815982\pi$
$719$		−	785.781i		−	1.09288i	0.837498	−	0.546440i	$-0.184018\pi$
$720$		0			0
$721$	257.605			0.357289
$722$	−224.965	+	389.651i	−0.311586	+	0.539683i
$723$		0			0
$724$	−271.084	−	469.531i	−0.374425	−	0.648524i
$725$	−140.934	+	52.2791i	−0.194391	+	0.0721092i
$726$		0			0
$727$	344.922	+	199.141i	0.474445	+	0.273921i	0.718099	−	0.695941i	$-0.245013\pi$
$727$	344.922	+	199.141i	0.474445	+	0.273921i	−0.243654	+	0.969862i	$0.578346\pi$
$728$	103.500			0.142170
$729$		0			0
$730$	−161.699	−	13.6461i	−0.221506	−	0.0186933i
$731$	932.799	+	538.552i	1.27606	+	0.736733i
$732$		0			0
$733$	445.371	−	257.135i	0.607600	−	0.350798i	−0.164425	−	0.986390i	$-0.552577\pi$
$733$	445.371	−	257.135i	0.607600	−	0.350798i	0.772026	+	0.635591i	$0.219244\pi$
$734$	−446.434	+	257.749i	−0.608221	+	0.351156i
$735$		0			0
$736$	27.2692	−	47.2316i	0.0370505	−	0.0641733i
$737$	35.4056			0.0480402
$738$		0			0
$739$	−105.919			−0.143328			−0.0716639	−	0.997429i	$-0.522831\pi$
$739$	−105.919			−0.143328			−0.0716639	+	0.997429i	$0.522831\pi$
$740$	228.215	−	328.067i	0.308399	−	0.443334i
$741$		0			0
$742$	200.548	−	115.786i	0.270280	−	0.156046i
$743$	−62.1326	−	107.617i	−0.0836239	−	0.144841i	0.821180	−	0.570669i	$-0.193316\pi$
$743$	−62.1326	−	107.617i	−0.0836239	−	0.144841i	−0.904804	+	0.425828i	$0.859983\pi$
$744$		0			0
$745$	−316.464	+	454.927i	−0.424783	+	0.610641i
$746$		−	707.379i		−	0.948229i
$747$		0			0
$748$		−	134.701i		−	0.180082i
$749$	−354.147	−	204.467i	−0.472826	−	0.272986i
$750$		0			0
$751$	−292.837	−	507.209i	−0.389930	−	0.675378i	0.602510	−	0.798111i	$-0.294167\pi$
$751$	−292.837	−	507.209i	−0.389930	−	0.675378i	−0.992440	+	0.122733i	$0.960834\pi$
$752$	141.774	+	245.559i	0.188529	+	0.326542i
$753$		0			0
$754$	−79.1626	+	137.114i	−0.104990	+	0.181848i
$755$	−5.31171	+	62.9411i	−0.00703538	+	0.0833657i
$756$		0			0
$757$			374.753i			0.495050i	0.968881	+	0.247525i	$0.0796173\pi$
$757$			374.753i			0.495050i	−0.968881	+	0.247525i	$0.920383\pi$
$758$	−108.250	+	187.494i	−0.142810	+	0.247354i
$759$		0			0
$760$	333.540	−	156.782i	0.438869	−	0.206293i
$761$	836.441	−	482.920i	1.09913	−	0.634585i	0.163141	−	0.986603i	$-0.447838\pi$
$761$	836.441	−	482.920i	1.09913	−	0.634585i	0.935993	+	0.352017i	$0.114504\pi$
$762$		0			0
$763$	−164.984	−	95.2535i	−0.216230	−	0.124841i
$764$			515.374i			0.674574i
$765$		0			0
$766$	−881.835			−1.15122
$767$	−347.294	+	601.531i	−0.452795	+	0.784264i
$768$		0			0
$769$	−139.177	−	241.061i	−0.180984	−	0.313473i	0.761232	−	0.648480i	$-0.224595\pi$
$769$	−139.177	−	241.061i	−0.180984	−	0.313473i	−0.942216	+	0.335006i	$0.891262\pi$
$770$	−47.9974	+	22.5615i	−0.0623343	+	0.0293006i
$771$		0			0
$772$	−202.667	−	117.010i	−0.262522	−	0.151567i
$773$	−621.766			−0.804354			−0.402177	−	0.915562i	$-0.631746\pi$
$773$	−621.766			−0.804354			−0.402177	+	0.915562i	$0.631746\pi$
$774$		0			0
$775$	−624.372	−	106.140i	−0.805642	−	0.136954i
$776$	67.2568	+	38.8308i	0.0866712	+	0.0500396i
$777$		0			0
$778$	−341.626	+	197.238i	−0.439109	+	0.253519i
$779$	800.538	−	462.191i	1.02765	−	0.593313i
$780$		0			0
$781$	−65.2539	+	113.023i	−0.0835517	+	0.144716i
$782$	−240.619			−0.307697
$783$		0			0
$784$	180.550			0.230294
$785$	−588.598	+	846.130i	−0.749807	+	1.07787i
$786$		0			0
$787$	360.109	−	207.909i	0.457571	−	0.264179i	−0.253451	−	0.967348i	$-0.581566\pi$
$787$	360.109	−	207.909i	0.457571	−	0.264179i	0.711022	+	0.703169i	$0.248232\pi$
$788$	127.741	+	221.253i	0.162107	+	0.280778i
$789$		0			0
$790$	−575.182	−	400.117i	−0.728079	−	0.506478i
$791$			23.5272i			0.0297436i
$792$		0			0
$793$			88.4763i			0.111572i
$794$	839.198	+	484.511i	1.05692	+	0.610216i
$795$		0			0
$796$	352.563	+	610.657i	0.442918	+	0.767157i
$797$	−47.3408	−	81.9968i	−0.0593988	−	0.102882i	0.834797	−	0.550558i	$-0.185585\pi$
$797$	−47.3408	−	81.9968i	−0.0593988	−	0.102882i	−0.894196	+	0.447676i	$0.852252\pi$
$798$		0			0
$799$	625.496	−	1083.39i	0.782849	−	1.35593i
$800$	−139.421	−	23.7008i	−0.174277	−	0.0296260i
$801$		0			0
$802$			556.330i			0.693678i
$803$	43.7912	−	75.8486i	0.0545345	−	0.0944565i
$804$		0			0
$805$	40.3020	+	85.7387i	0.0500646	+	0.106508i
$806$	−577.698	+	333.534i	−0.716747	+	0.413814i
$807$		0			0
$808$	−440.213	−	254.157i	−0.544818	−	0.314551i
$809$		−	1038.91i		−	1.28419i	−0.766624	−	0.642096i	$-0.778065\pi$
$809$		−	1038.91i		−	1.28419i	0.766624	−	0.642096i	$-0.221935\pi$
$810$		0			0
$811$	−414.046			−0.510537			−0.255269	−	0.966870i	$-0.582164\pi$
$811$	−414.046			−0.510537			−0.255269	+	0.966870i	$0.582164\pi$
$812$	11.8168	−	20.4673i	0.0145527	−	0.0252060i
$813$		0			0
$814$	107.846	+	186.795i	0.132489	+	0.229477i
$815$	−499.892	−	1063.47i	−0.613365	−	1.30488i
$816$		0			0
$817$	−1377.47	−	795.282i	−1.68601	−	0.973418i
$818$	−822.521			−1.00553
$819$		0			0
$820$	−353.450	−	29.8282i	−0.431036	−	0.0363759i
$821$	−312.574	−	180.465i	−0.380723	−	0.219811i	0.297410	−	0.954750i	$-0.403877\pi$
$821$	−312.574	−	180.465i	−0.380723	−	0.219811i	−0.678133	+	0.734939i	$0.737211\pi$
$822$		0			0
$823$	970.706	−	560.437i	1.17947	−	0.680969i	0.223580	−	0.974686i	$-0.428226\pi$
$823$	970.706	−	560.437i	1.17947	−	0.680969i	0.955892	+	0.293717i	$0.0948923\pi$
$824$	−321.071	+	185.370i	−0.389649	+	0.224964i
$825$		0			0
$826$	51.8413	−	89.7918i	0.0627619	−	0.108707i
$827$	−1158.15			−1.40042			−0.700212	−	0.713935i	$-0.746911\pi$
$827$	−1158.15			−1.40042			−0.700212	+	0.713935i	$0.746911\pi$
$828$		0			0
$829$	500.809			0.604112			0.302056	−	0.953290i	$-0.402327\pi$
$829$	500.809			0.604112			0.302056	+	0.953290i	$0.402327\pi$
$830$	−220.023	−	153.056i	−0.265088	−	0.184405i
$831$		0			0
$832$	−128.999	+	74.4776i	−0.155047	+	0.0895163i
$833$	−398.288	−	689.855i	−0.478137	−	0.828157i
$834$		0			0
$835$	517.909	+	360.276i	0.620250	+	0.431468i
$836$			198.914i			0.237935i
$837$		0			0
$838$			265.298i			0.316585i
$839$	379.506	+	219.108i	0.452332	+	0.261154i	0.708814	−	0.705395i	$-0.249230\pi$
$839$	379.506	+	219.108i	0.452332	+	0.261154i	−0.256483	+	0.966549i	$0.582564\pi$
$840$		0			0
$841$	−402.424	−	697.018i	−0.478506	−	0.828797i
$842$	−123.676	−	214.213i	−0.146884	−	0.254410i
$843$		0			0
$844$	−278.402	+	482.206i	−0.329860	+	0.571334i
$845$	−74.7088	+	885.262i	−0.0884128	+	1.04765i
$846$		0			0
$847$			209.177i			0.246963i
$848$	−166.637	+	288.624i	−0.196506	+	0.340359i
$849$		0			0
$850$	217.001	+	584.990i	0.255296	+	0.688223i
$851$	333.675	−	192.647i	0.392097	−	0.226378i
$852$		0			0
$853$	−468.681	−	270.593i	−0.549451	−	0.317225i	0.199450	−	0.979908i	$-0.436085\pi$
$853$	−468.681	−	270.593i	−0.549451	−	0.317225i	−0.748900	+	0.662683i	$0.769418\pi$
$854$		−	13.2070i		−	0.0154649i
$855$		0			0
$856$	588.529			0.687534
$857$	−162.748	+	281.888i	−0.189904	+	0.328924i	−0.945218	−	0.326439i	$-0.894151\pi$
$857$	−162.748	+	281.888i	−0.189904	+	0.328924i	0.755314	+	0.655363i	$0.227484\pi$
$858$		0			0
$859$	47.3782	+	82.0615i	0.0551551	+	0.0955314i	0.892285	−	0.451473i	$-0.149101\pi$
$859$	47.3782	+	82.0615i	0.0551551	+	0.0955314i	−0.837130	+	0.547005i	$0.815768\pi$
$860$	259.638	+	552.357i	0.301905	+	0.642275i
$861$		0			0
$862$	2.13365	+	1.23186i	0.00247523	+	0.00142907i
$863$	598.282			0.693259			0.346629	−	0.938002i	$-0.387326\pi$
$863$	598.282			0.693259			0.346629	+	0.938002i	$0.387326\pi$
$864$		0			0
$865$	−40.7818	+	483.244i	−0.0471466	+	0.558663i
$866$	−221.282	−	127.757i	−0.255522	−	0.147526i
$867$		0			0
$868$	86.2342	−	49.7874i	0.0993482	−	0.0573587i
$869$	327.497	−	189.081i	0.376867	−	0.217584i
$870$		0			0
$871$	−86.3684	+	149.594i	−0.0991600	+	0.171750i
$872$	274.174			0.314420
$873$		0			0
$874$	355.324			0.406549
$875$	172.100	−	175.304i	0.196686	−	0.200348i
$876$		0			0
$877$	−457.431	+	264.098i	−0.521586	+	0.301138i	−0.737583	−	0.675256i	$-0.764033\pi$
$877$	−457.431	+	264.098i	−0.521586	+	0.301138i	0.215997	+	0.976394i	$0.430700\pi$
$878$	−438.578	−	759.639i	−0.499519	−	0.865193i
$879$		0			0
$880$	43.5874	−	62.6584i	0.0495311	−	0.0712027i
$881$			240.234i			0.272684i	0.990662	+	0.136342i	$0.0435345\pi$
$881$			240.234i			0.272684i	−0.990662	+	0.136342i	$0.956465\pi$
$882$		0			0
$883$		−	195.733i		−	0.221668i	−0.993839	−	0.110834i	$-0.964648\pi$
$883$		−	195.733i		−	0.221668i	0.993839	−	0.110834i	$-0.0353522\pi$
$884$	569.134	+	328.590i	0.643817	+	0.371708i
$885$		0			0
$886$	158.663	+	274.813i	0.179078	+	0.310172i
$887$	388.301	+	672.556i	0.437768	+	0.758237i	0.997517	−	0.0704254i	$-0.0224357\pi$
$887$	388.301	+	672.556i	0.437768	+	0.758237i	−0.559749	+	0.828662i	$0.689102\pi$
$888$		0			0
$889$	−211.816	+	366.876i	−0.238263	+	0.412684i
$890$	−303.554	−	25.6174i	−0.341072	−	0.0287836i
$891$		0			0
$892$			716.811i			0.803600i
$893$	−923.674	+	1599.85i	−1.03435	+	1.79155i
$894$		0			0
$895$	−508.392	−	1081.56i	−0.568036	−	1.20844i
$896$	19.2560	−	11.1174i	0.0214910	−	0.0124078i
$897$		0			0
$898$	17.9525	+	10.3649i	0.0199917	+	0.0115422i
$899$			152.321i			0.169434i
$900$		0			0
$901$	1470.39			1.63195
$902$	95.7208	−	165.793i	0.106121	−	0.183806i
$903$		0			0
$904$	−16.9300	−	29.3235i	−0.0187278	−	0.0324375i
$905$	−1226.66	+	576.599i	−1.35543	+	0.637126i
$906$		0			0
$907$	−966.706	−	558.128i	−1.06583	−	0.615356i	−0.138790	−	0.990322i	$-0.544321\pi$
$907$	−966.706	−	558.128i	−1.06583	−	0.615356i	−0.927039	+	0.374966i	$0.877655\pi$
$908$	638.204			0.702868
$909$		0			0
$910$	21.7590	−	257.833i	0.0239110	−	0.283333i
$911$	208.954	+	120.640i	0.229368	+	0.132426i	0.610280	−	0.792185i	$-0.291057\pi$
$911$	208.954	+	120.640i	0.229368	+	0.132426i	−0.380912	+	0.924611i	$0.624390\pi$
$912$		0			0
$913$	125.277	−	72.3286i	0.137214	−	0.0792208i
$914$	−542.245	+	313.065i	−0.593266	+	0.342522i
$915$		0			0
$916$	−24.8580	+	43.0552i	−0.0271375	+	0.0470035i
$917$	−155.996			−0.170116
$918$		0			0
$919$	−80.4600			−0.0875517			−0.0437758	−	0.999041i	$-0.513939\pi$
$919$	−80.4600			−0.0875517			−0.0437758	+	0.999041i	$0.513939\pi$
$920$	−111.928	−	77.8610i	−0.121661	−	0.0846316i
$921$		0			0
$922$	−642.903	+	371.180i	−0.697292	+	0.402582i
$923$	−318.360	−	551.416i	−0.344919	−	0.597418i
$924$		0			0
$925$	−769.284	−	637.487i	−0.831658	−	0.689175i
$926$			4.05821i			0.00438252i
$927$		0			0
$928$			34.0130i			0.0366519i
$929$	−1079.36	−	623.169i	−1.16185	−	0.670795i	−0.210104	−	0.977679i	$-0.567380\pi$
$929$	−1079.36	−	623.169i	−1.16185	−	0.670795i	−0.951747	+	0.306884i	$0.900714\pi$
$930$		0			0
$931$	588.154	+	1018.71i	0.631744	+	1.09421i
$932$	223.302	+	386.770i	0.239594	+	0.414989i
$933$		0			0
$934$	−489.878	+	848.494i	−0.524495	+	0.908452i
$935$	−335.560	−	28.3185i	−0.358888	−	0.0302872i
$936$		0			0
$937$			937.917i			1.00098i	0.865743	+	0.500489i	$0.166846\pi$
$937$			937.917i			1.00098i	−0.865743	+	0.500489i	$0.833154\pi$
$938$	12.8924	−	22.3303i	0.0137446	−	0.0238063i
$939$		0			0
$940$	641.530	−	301.555i	0.682478	−	0.320803i
$941$	−197.137	+	113.817i	−0.209497	+	0.120953i	−0.601078	−	0.799191i	$-0.705262\pi$
$941$	−197.137	+	113.817i	−0.209497	+	0.120953i	0.391581	+	0.920144i	$0.371928\pi$
$942$		0			0
$943$	−296.160	−	170.988i	−0.314061	−	0.181323i
$944$			149.218i			0.158070i
$945$		0			0
$946$	−329.410			−0.348213
$947$	−135.712	+	235.059i	−0.143307	+	0.248215i	−0.928740	−	0.370732i	$-0.879107\pi$
$947$	−135.712	+	235.059i	−0.143307	+	0.248215i	0.785433	+	0.618946i	$0.212440\pi$
$948$		0			0
$949$	213.648	+	370.050i	0.225130	+	0.389937i
$950$	−320.447	−	863.858i	−0.337313	−	0.909324i
$951$		0			0
$952$	−84.9559	−	49.0493i	−0.0892394	−	0.0515224i
$953$	−1026.91			−1.07756			−0.538780	−	0.842447i	$-0.681114\pi$
$953$	−1026.91			−1.07756			−0.538780	+	0.842447i	$0.681114\pi$
$954$		0			0
$955$	1283.87	+	108.348i	1.34437	+	0.113454i
$956$	−155.419	−	89.7315i	−0.162573	−	0.0938614i
$957$		0			0
$958$	1085.36	−	626.632i	1.13294	−	0.654104i
$959$	299.665	−	173.012i	0.312476	−	0.180408i
$960$		0			0
$961$	159.615	−	276.461i	0.166093	−	0.287681i
$962$	−1052.32			−1.09388
$963$		0			0
$964$	−228.491			−0.237024
$965$	−334.096	+	480.274i	−0.346213	+	0.497693i
$966$		0			0
$967$	−571.327	+	329.856i	−0.590824	+	0.341113i	−0.765423	−	0.643527i	$-0.777470\pi$
$967$	−571.327	+	329.856i	−0.590824	+	0.341113i	0.174599	+	0.984640i	$0.444137\pi$
$968$	−150.522	−	260.712i	−0.155498	−	0.269330i
$969$		0			0
$970$	110.873	−	159.383i	0.114302	−	0.164312i
$971$			1463.21i			1.50691i	0.657499	+	0.753455i	$0.271614\pi$
$971$			1463.21i			1.50691i	−0.657499	+	0.753455i	$0.728386\pi$
$972$		0			0
$973$		−	153.401i		−	0.157657i
$974$	−186.036	−	107.408i	−0.191002	−	0.110275i
$975$		0			0
$976$	9.50367	+	16.4608i	0.00973736	+	0.0168656i
$977$	51.9006	+	89.8945i	0.0531225	+	0.0920108i	0.891364	−	0.453289i	$-0.149749\pi$
$977$	51.9006	+	89.8945i	0.0531225	+	0.0920108i	−0.838241	+	0.545299i	$0.816416\pi$
$978$		0			0
$979$	82.2080	−	142.388i	0.0839714	−	0.145443i
$980$	37.9575	−	449.777i	0.0387321	−	0.458956i
$981$		0			0
$982$			13.9547i			0.0142104i
$983$	−93.3792	+	161.738i	−0.0949941	+	0.164535i	−0.909606	−	0.415472i	$-0.863617\pi$
$983$	−93.3792	+	161.738i	−0.0949941	+	0.164535i	0.814612	+	0.580006i	$0.196950\pi$
$984$		0			0
$985$	578.029	−	271.706i	0.586832	−	0.275844i
$986$	129.958	−	75.0315i	0.131804	−	0.0760968i
$987$		0			0
$988$	−840.444	−	485.230i	−0.850652	−	0.491124i
$989$			588.431i			0.594976i
$990$		0			0
$991$	−1064.29			−1.07395			−0.536977	−	0.843597i	$-0.680434\pi$
$991$	−1064.29			−1.07395			−0.536977	+	0.843597i	$0.680434\pi$
$992$	−71.6531	+	124.107i	−0.0722309	+	0.125108i
$993$		0			0
$994$	47.5223	+	82.3111i	0.0478092	+	0.0828080i
$995$	1595.35	−	749.905i	1.60337	−	0.753674i
$996$		0			0
$997$	407.260	+	235.132i	0.408485	+	0.235839i	0.690139	−	0.723677i	$-0.257549\pi$
$997$	407.260	+	235.132i	0.408485	+	0.235839i	−0.281653	+	0.959516i	$0.590883\pi$
$998$	−303.174			−0.303782
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.j.g.269.4		24
3.2	odd	2	inner	810.3.j.g.269.8		24
5.4	even	2		810.3.j.h.269.8		24
9.2	odd	6		810.3.b.c.809.6	yes	24
9.4	even	3		810.3.j.h.539.4		24
9.5	odd	6		810.3.j.h.539.9		24
9.7	even	3		810.3.b.c.809.19	yes	24
15.14	odd	2		810.3.j.h.269.4		24
45.4	even	6	inner	810.3.j.g.539.9		24
45.14	odd	6	inner	810.3.j.g.539.4		24
45.29	odd	6		810.3.b.c.809.20	yes	24
45.34	even	6		810.3.b.c.809.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.3.b.c.809.5	✓	24	45.34	even	6
810.3.b.c.809.6	yes	24	9.2	odd	6
810.3.b.c.809.19	yes	24	9.7	even	3
810.3.b.c.809.20	yes	24	45.29	odd	6
810.3.j.g.269.4		24	1.1	even	1	trivial
810.3.j.g.269.8		24	3.2	odd	2	inner
810.3.j.g.539.4		24	45.14	odd	6	inner
810.3.j.g.539.9		24	45.4	even	6	inner
810.3.j.h.269.4		24	15.14	odd	2
810.3.j.h.269.8		24	5.4	even	2
810.3.j.h.539.4		24	9.4	even	3
810.3.j.h.539.9		24	9.5	odd	6

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-4.52502 + 2.12701i) q^{5} +(-1.70200 - 0.982651i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-4.52502 + 2.12701i) q^{5} +(-1.70200 - 0.982651i) q^{7} +2.82843 q^{8} +(0.594626 - 7.04602i) q^{10} +(3.30509 + 1.90819i) q^{11} +(-16.1249 + 9.30970i) q^{13} +(2.40699 - 1.38968i) q^{14} +(-2.00000 + 3.46410i) q^{16} +17.6477 q^{17} -26.0605 q^{19} +(8.20911 + 5.71055i) q^{20} +(-4.67410 + 2.69859i) q^{22} +(4.82055 + 8.34944i) q^{23} +(15.9516 - 19.2496i) q^{25} -26.3318i q^{26} +3.93060i q^{28} +(-5.20715 - 3.00635i) q^{29} +(-12.6666 - 21.9392i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-12.4788 + 21.6140i) q^{34} +(9.79170 + 0.826339i) q^{35} -39.9637i q^{37} +(18.4275 - 31.9174i) q^{38} +(-12.7987 + 6.01610i) q^{40} +(-30.7185 + 17.7353i) q^{41} +(52.8566 + 30.5168i) q^{43} -7.63278i q^{44} -13.6346 q^{46} +(35.4435 - 61.3899i) q^{47} +(-22.5688 - 39.0903i) q^{49} +(12.2963 + 33.1482i) q^{50} +(32.2497 + 18.6194i) q^{52} +83.3187 q^{53} +(-19.0144 - 1.60465i) q^{55} +(-4.81399 - 2.77936i) q^{56} +(7.36403 - 4.25162i) q^{58} +(32.3067 - 18.6523i) q^{59} +(2.37592 - 4.11521i) q^{61} +35.8265 q^{62} +8.00000 q^{64} +(53.1635 - 76.4244i) q^{65} +(8.03433 - 4.63862i) q^{67} +(-17.6477 - 30.5668i) q^{68} +(-7.93584 + 11.4080i) q^{70} +34.1966i q^{71} -22.9490i q^{73} +(48.9454 + 28.2586i) q^{74} +(26.0605 + 45.1381i) q^{76} +(-3.75018 - 6.49550i) q^{77} +(49.5443 - 85.8133i) q^{79} +(1.68186 - 19.9292i) q^{80} -50.1630i q^{82} +(18.9521 - 32.8260i) q^{83} +(-79.8563 + 37.5369i) q^{85} +(-74.7506 + 43.1573i) q^{86} +(9.34821 + 5.39719i) q^{88} -43.0816i q^{89} +36.5927 q^{91} +(9.64111 - 16.6989i) q^{92} +(50.1246 + 86.8184i) q^{94} +(117.924 - 55.4310i) q^{95} +(23.7789 + 13.7287i) q^{97} +63.8342 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 24 q^{7}+O(q^{10}) \) 24 * q - 24 * q^4 - 24 * q^7	\( 24 q - 24 q^{4} - 24 q^{7} - 12 q^{10} - 48 q^{13} - 48 q^{16} + 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{43} - 36 q^{49} + 96 q^{52} + 216 q^{55} - 396 q^{58} - 60 q^{61} + 192 q^{64} + 1032 q^{67} - 480 q^{70} - 240 q^{79} - 396 q^{85} - 240 q^{88} + 48 q^{91} - 48 q^{94} + 1440 q^{97}+O(q^{100}) \) 24 * q - 24 * q^4 - 24 * q^7 - 12 * q^10 - 48 * q^13 - 48 * q^16 + 120 * q^22 + 24 * q^25 + 60 * q^34 + 24 * q^43 - 36 * q^49 + 96 * q^52 + 216 * q^55 - 396 * q^58 - 60 * q^61 + 192 * q^64 + 1032 * q^67 - 480 * q^70 - 240 * q^79 - 396 * q^85 - 240 * q^88 + 48 * q^91 - 48 * q^94 + 1440 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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