LMFDB - Embedded newform 261.2.o.b.154.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(64,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("261.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.o (of order $14$, degree $6$, 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 87)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			154.1
Character	$\chi$	$=$	261.154
Dual form			261.2.o.b.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00695 - 2.09096i) q^{2} +(-2.11117 + 2.64732i) q^{4} +(-1.71239 + 0.824646i) q^{5} +(-2.13259 - 2.67418i) q^{7} +(3.13608 + 0.715791i) q^{8} +(3.44860 + 2.75017i) q^{10} +(-0.806696 + 0.184123i) q^{11} +(1.20608 + 5.28419i) q^{13} +(-3.44418 + 7.15191i) q^{14} +(-0.154263 - 0.675869i) q^{16} +6.71892i q^{17} +(-3.45146 - 2.75245i) q^{19} +(1.43205 - 6.27423i) q^{20} +(1.19730 + 1.50136i) q^{22} +(0.139227 + 0.0670480i) q^{23} +(-0.865194 + 1.08492i) q^{25} +(9.83456 - 7.84280i) q^{26} +11.5817 q^{28} +(-5.06676 - 1.82425i) q^{29} +(-2.48781 - 5.16599i) q^{31} +(3.77201 - 3.00808i) q^{32} +(14.0490 - 6.76563i) q^{34} +(5.85708 + 2.82062i) q^{35} +(-9.49071 - 2.16619i) q^{37} +(-2.27980 + 9.98844i) q^{38} +(-5.96049 + 1.36044i) q^{40} -5.43514i q^{41} +(-1.93772 + 4.02372i) q^{43} +(1.21564 - 2.52430i) q^{44} -0.358631i q^{46} +(1.18672 - 0.270862i) q^{47} +(-1.04566 + 4.58133i) q^{49} +(3.13973 + 0.716622i) q^{50} +(-16.5352 - 7.96294i) q^{52} +(0.419909 - 0.202218i) q^{53} +(1.22955 - 0.980530i) q^{55} +(-4.77382 - 9.91293i) q^{56} +(1.28756 + 12.4313i) q^{58} -11.5925 q^{59} +(8.77189 - 6.99535i) q^{61} +(-8.29676 + 10.4038i) q^{62} +(-11.3372 - 5.45970i) q^{64} +(-6.42288 - 8.05404i) q^{65} +(-2.88159 + 12.6251i) q^{67} +(-17.7871 - 14.1848i) q^{68} -15.0871i q^{70} +(-0.750585 - 3.28853i) q^{71} +(-0.425383 + 0.883317i) q^{73} +(5.02727 + 22.0259i) q^{74} +(14.5732 - 3.32625i) q^{76} +(2.21273 + 1.76459i) q^{77} +(4.74548 + 1.08313i) q^{79} +(0.821511 + 1.03014i) q^{80} +(-11.3647 + 5.47293i) q^{82} +(4.81847 - 6.04218i) q^{83} +(-5.54073 - 11.5054i) q^{85} +10.3646 q^{86} -2.66166 q^{88} +(-2.02075 - 4.19613i) q^{89} +(11.5588 - 14.4943i) q^{91} +(-0.471429 + 0.227028i) q^{92} +(-1.76133 - 2.20864i) q^{94} +(8.18006 + 1.86705i) q^{95} +(7.82946 + 6.24379i) q^{97} +(10.6323 - 2.42675i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} + 4 q^{5} + 8 q^{7} + 28 q^{11} - 10 q^{13} - 22 q^{16} + 20 q^{20} + 4 q^{22} - 18 q^{23} - 18 q^{25} - 28 q^{26} + 8 q^{28} - 28 q^{29} + 28 q^{31} + 14 q^{32} + 34 q^{34} - 28 q^{37} + 4 q^{38}+ \cdots + 42 q^{98}+O(q^{100}) $ 24 * q - 2 * q^4 + 4 * q^5 + 8 * q^7 + 28 * q^11 - 10 * q^13 - 22 * q^16 + 20 * q^20 + 4 * q^22 - 18 * q^23 - 18 * q^25 - 28 * q^26 + 8 * q^28 - 28 * q^29 + 28 * q^31 + 14 * q^32 + 34 * q^34 - 28 * q^37 + 4 * q^38 - 14 * q^43 - 14 * q^44 + 20 * q^49 - 42 * q^50 - 68 * q^52 - 6 * q^53 - 14 * q^55 + 50 * q^58 - 28 * q^59 + 8 * q^62 - 20 * q^64 - 18 * q^65 + 8 * q^67 - 14 * q^68 + 42 * q^71 - 84 * q^73 - 10 * q^74 - 14 * q^76 + 70 * q^77 - 14 * q^79 - 36 * q^80 - 50 * q^82 + 32 * q^83 + 14 * q^85 + 128 * q^86 - 20 * q^88 + 14 * q^89 + 34 * q^91 + 58 * q^92 - 44 * q^94 + 56 * q^97 + 42 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{5}{14}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00695	−	2.09096i	−0.712022	−	1.47853i	−0.871018	−	0.491251i	$-0.836540\pi$
$2$	−1.00695	−	2.09096i	−0.712022	−	1.47853i	0.158996	−	0.987279i	$-0.449174\pi$
$3$		0			0
$3$		0			0
$4$	−2.11117	+	2.64732i	−1.05558	+	1.32366i
$5$	−1.71239	+	0.824646i	−0.765806	+	0.368793i	−0.775654	−	0.631159i	$-0.782580\pi$
$5$	−1.71239	+	0.824646i	−0.765806	+	0.368793i	0.00984749	+	0.999952i	$0.496865\pi$
$6$		0			0
$7$	−2.13259	−	2.67418i	−0.806042	−	1.01074i	−0.999560	−	0.0296476i	$-0.990561\pi$
$7$	−2.13259	−	2.67418i	−0.806042	−	1.01074i	0.193519	−	0.981097i	$-0.438010\pi$
$8$	3.13608	+	0.715791i	1.10877	+	0.253070i
$9$		0			0
$10$	3.44860	+	2.75017i	1.09054	+	0.869679i
$11$	−0.806696	+	0.184123i	−0.243228	+	0.0555152i	−0.342397	−	0.939555i	$-0.611239\pi$
$11$	−0.806696	+	0.184123i	−0.243228	+	0.0555152i	0.0991689	+	0.995071i	$0.468382\pi$
$12$		0			0
$13$	1.20608	+	5.28419i	0.334507	+	1.46557i	0.810301	+	0.586015i	$0.199304\pi$
$13$	1.20608	+	5.28419i	0.334507	+	1.46557i	−0.475793	+	0.879557i	$0.657839\pi$
$14$	−3.44418	+	7.15191i	−0.920496	+	1.91143i
$15$		0			0
$16$	−0.154263	−	0.675869i	−0.0385657	−	0.168967i
$17$			6.71892i			1.62958i	0.579758	+	0.814788i	$0.303147\pi$
$17$			6.71892i			1.62958i	−0.579758	+	0.814788i	$0.696853\pi$
$18$		0			0
$19$	−3.45146	−	2.75245i	−0.791819	−	0.631455i	0.141729	−	0.989905i	$-0.454734\pi$
$19$	−3.45146	−	2.75245i	−0.791819	−	0.631455i	−0.933549	+	0.358451i	$0.883305\pi$
$20$	1.43205	−	6.27423i	0.320217	−	1.40296i
$21$		0			0
$22$	1.19730	+	1.50136i	0.255265	+	0.320092i
$23$	0.139227	+	0.0670480i	0.0290308	+	0.0139805i	0.448343	−	0.893862i	$-0.352014\pi$
$23$	0.139227	+	0.0670480i	0.0290308	+	0.0139805i	−0.419312	+	0.907842i	$0.637729\pi$
$24$		0			0
$25$	−0.865194	+	1.08492i	−0.173039	+	0.216984i
$26$	9.83456	−	7.84280i	1.92871	−	1.53810i
$27$		0			0
$28$	11.5817			2.18873
$29$	−5.06676	−	1.82425i	−0.940875	−	0.338755i
$29$	−5.06676	−	1.82425i	−0.940875	−	0.338755i
$30$		0			0
$31$	−2.48781	−	5.16599i	−0.446824	−	0.927840i	−0.995761	−	0.0919761i	$-0.970682\pi$
$31$	−2.48781	−	5.16599i	−0.446824	−	0.927840i	0.548937	−	0.835864i	$-0.315033\pi$
$32$	3.77201	−	3.00808i	0.666804	−	0.531758i
$33$		0			0
$34$	14.0490	−	6.76563i	2.40938	−	1.16030i
$35$	5.85708	+	2.82062i	0.990027	+	0.476772i
$36$		0			0
$37$	−9.49071	−	2.16619i	−1.56026	−	0.356120i	−0.646677	−	0.762764i	$-0.723842\pi$
$37$	−9.49071	−	2.16619i	−1.56026	−	0.356120i	−0.913587	+	0.406644i	$0.866699\pi$
$38$	−2.27980	+	9.98844i	−0.369832	+	1.62034i
$39$		0			0
$40$	−5.96049	+	1.36044i	−0.942436	+	0.215105i
$41$		−	5.43514i		−	0.848827i	−0.905469	−	0.424413i	$-0.860480\pi$
$41$		−	5.43514i		−	0.848827i	0.905469	−	0.424413i	$-0.139520\pi$
$42$		0			0
$43$	−1.93772	+	4.02372i	−0.295500	+	0.613612i	−0.994872	−	0.101146i	$-0.967749\pi$
$43$	−1.93772	+	4.02372i	−0.295500	+	0.613612i	0.699372	+	0.714758i	$0.253463\pi$
$44$	1.21564	−	2.52430i	0.183264	−	0.380553i
$45$		0			0
$46$		−	0.358631i		−	0.0528772i
$47$	1.18672	−	0.270862i	0.173101	−	0.0395092i	−0.135092	−	0.990833i	$-0.543133\pi$
$47$	1.18672	−	0.270862i	0.173101	−	0.0395092i	0.308193	+	0.951324i	$0.400276\pi$
$48$		0			0
$49$	−1.04566	+	4.58133i	−0.149380	+	0.654476i
$50$	3.13973	+	0.716622i	0.444024	+	0.101346i
$51$		0			0
$52$	−16.5352	−	7.96294i	−2.29302	−	1.10426i
$53$	0.419909	−	0.202218i	0.0576790	−	0.0277767i	−0.404822	−	0.914396i	$-0.632666\pi$
$53$	0.419909	−	0.202218i	0.0576790	−	0.0277767i	0.462501	+	0.886619i	$0.346952\pi$
$54$		0			0
$55$	1.22955	−	0.980530i	0.165792	−	0.132215i
$56$	−4.77382	−	9.91293i	−0.637928	−	1.32467i
$57$		0			0
$58$	1.28756	+	12.4313i	0.169064	+	1.63231i
$59$	−11.5925			−1.50921			−0.754605	−	0.656179i	$-0.772172\pi$
$59$	−11.5925			−1.50921			−0.754605	+	0.656179i	$0.772172\pi$
$60$		0			0
$61$	8.77189	−	6.99535i	1.12312	−	0.895662i	0.127757	−	0.991805i	$-0.459222\pi$
$61$	8.77189	−	6.99535i	1.12312	−	0.895662i	0.995368	+	0.0961432i	$0.0306507\pi$
$62$	−8.29676	+	10.4038i	−1.05369	+	1.32129i
$63$		0			0
$64$	−11.3372	−	5.45970i	−1.41715	−	0.682463i
$65$	−6.42288	−	8.05404i	−0.796660	−	0.998980i
$66$		0			0
$67$	−2.88159	+	12.6251i	−0.352042	+	1.54240i	0.420415	+	0.907332i	$0.361885\pi$
$67$	−2.88159	+	12.6251i	−0.352042	+	1.54240i	−0.772457	+	0.635067i	$0.780973\pi$
$68$	−17.7871	−	14.1848i	−2.15701	−	1.72016i
$69$		0			0
$70$		−	15.0871i		−	1.80326i
$71$	−0.750585	−	3.28853i	−0.0890780	−	0.390276i	0.910660	−	0.413156i	$-0.135574\pi$
$71$	−0.750585	−	3.28853i	−0.0890780	−	0.390276i	−0.999738	+	0.0228799i	$0.992716\pi$
$72$		0			0
$73$	−0.425383	+	0.883317i	−0.0497873	+	0.103384i	−0.924378	−	0.381477i	$-0.875416\pi$
$73$	−0.425383	+	0.883317i	−0.0497873	+	0.103384i	0.874591	+	0.484861i	$0.161130\pi$
$74$	5.02727	+	22.0259i	0.584409	+	2.56046i
$75$		0			0
$76$	14.5732	−	3.32625i	1.67167	−	0.381547i
$77$	2.21273	+	1.76459i	0.252164	+	0.201094i
$78$		0			0
$79$	4.74548	+	1.08313i	0.533909	+	0.121861i	0.480971	−	0.876737i	$-0.340284\pi$
$79$	4.74548	+	1.08313i	0.533909	+	0.121861i	0.0529379	+	0.998598i	$0.483141\pi$
$80$	0.821511	+	1.03014i	0.0918477	+	0.115173i
$81$		0			0
$82$	−11.3647	+	5.47293i	−1.25502	+	0.604384i
$83$	4.81847	−	6.04218i	0.528896	−	0.663215i	−0.443575	−	0.896237i	$-0.646290\pi$
$83$	4.81847	−	6.04218i	0.528896	−	0.663215i	0.972471	+	0.233022i	$0.0748615\pi$
$84$		0			0
$85$	−5.54073	−	11.5054i	−0.600976	−	1.24794i
$86$	10.3646			1.11765
$87$		0			0
$88$	−2.66166			−0.283734
$89$	−2.02075	−	4.19613i	−0.214199	−	0.444789i	0.765990	−	0.642852i	$-0.222249\pi$
$89$	−2.02075	−	4.19613i	−0.214199	−	0.444789i	−0.980189	+	0.198063i	$0.936535\pi$
$90$		0			0
$91$	11.5588	−	14.4943i	1.21169	−	1.51941i
$92$	−0.471429	+	0.227028i	−0.0491498	+	0.0236693i
$93$		0			0
$94$	−1.76133	−	2.20864i	−0.181668	−	0.227804i
$95$	8.18006	+	1.86705i	0.839256	+	0.191555i
$96$		0			0
$97$	7.82946	+	6.24379i	0.794961	+	0.633960i	0.934382	−	0.356273i	$-0.115953\pi$
$97$	7.82946	+	6.24379i	0.794961	+	0.633960i	−0.139421	+	0.990233i	$0.544524\pi$
$98$	10.6323	−	2.42675i	1.07402	−	0.245139i
$99$		0			0
$100$	−1.04556	−	4.58089i	−0.104556	−	0.458089i
$101$	−6.58733	+	13.6787i	−0.655463	+	1.36108i	0.262698	+	0.964878i	$0.415388\pi$
$101$	−6.58733	+	13.6787i	−0.655463	+	1.36108i	−0.918162	+	0.396206i	$0.870327\pi$
$102$		0			0
$103$	−0.0464759	−	0.203624i	−0.00457941	−	0.0200637i	0.972587	−	0.232541i	$-0.0747040\pi$
$103$	−0.0464759	−	0.203624i	−0.00457941	−	0.0200637i	−0.977166	+	0.212477i	$0.931847\pi$
$104$			17.4350i			1.70964i
$105$		0			0
$106$	−0.845657	−	0.674389i	−0.0821375	−	0.0655025i
$107$	−0.572801	+	2.50960i	−0.0553747	+	0.242613i	−0.995039	−	0.0994854i	$-0.968280\pi$
$107$	−0.572801	+	2.50960i	−0.0553747	+	0.242613i	0.939664	+	0.342098i	$0.111137\pi$
$108$		0			0
$109$	0.718366	+	0.900802i	0.0688070	+	0.0862812i	0.815044	−	0.579399i	$-0.196713\pi$
$109$	0.718366	+	0.900802i	0.0688070	+	0.0862812i	−0.746237	+	0.665681i	$0.768141\pi$
$110$	−3.28834	−	1.58358i	−0.313531	−	0.150988i
$111$		0			0
$112$	−1.47841	+	1.85387i	−0.139697	+	0.175175i
$113$	−3.40029	+	2.71164i	−0.319872	+	0.255089i	−0.770241	−	0.637753i	$-0.779864\pi$
$113$	−3.40029	+	2.71164i	−0.319872	+	0.255089i	0.450369	+	0.892843i	$0.351293\pi$
$114$		0			0
$115$	−0.293702			−0.0273878
$116$	15.5262	−	9.56206i	1.44157	−	0.887815i
$117$		0			0
$118$	11.6731	+	24.2393i	1.07459	+	2.23141i
$119$	17.9676	−	14.3287i	1.64709	−	1.31351i
$120$		0			0
$121$	−9.29380	+	4.47566i	−0.844891	+	0.406878i
$122$	−23.4598	−	11.2977i	−2.12395	−	1.02284i
$123$		0			0
$124$	18.9282	+	4.32025i	1.69981	+	0.387970i
$125$	2.70151	−	11.8361i	0.241631	−	1.05865i
$126$		0			0
$127$	0.379767	−	0.0866794i	0.0336989	−	0.00769155i	−0.205638	−	0.978628i	$-0.565927\pi$
$127$	0.379767	−	0.0866794i	0.0336989	−	0.00769155i	0.239337	+	0.970937i	$0.423070\pi$
$128$			19.5541i			1.72835i
$129$		0			0
$130$	−10.3731	+	21.5400i	−0.909782	+	1.88918i
$131$	0.329927	−	0.685100i	0.0288258	−	0.0598575i	−0.886059	−	0.463573i	$-0.846567\pi$
$131$	0.329927	−	0.685100i	0.0288258	−	0.0598575i	0.914885	+	0.403716i	$0.132281\pi$
$132$		0			0
$133$			15.0997i			1.30931i
$134$	29.3001	−	6.68756i	2.53114	−	0.577717i
$135$		0			0
$136$	−4.80934	+	21.0711i	−0.412397	+	1.80683i
$137$	14.5588	+	3.32295i	1.24384	+	0.283899i	0.793285	−	0.608850i	$-0.208369\pi$
$137$	14.5588	+	3.32295i	1.24384	+	0.283899i	0.450555	+	0.892749i	$0.351226\pi$
$138$		0			0
$139$	−3.29720	−	1.58785i	−0.279665	−	0.134679i	0.288794	−	0.957391i	$-0.406746\pi$
$139$	−3.29720	−	1.58785i	−0.279665	−	0.134679i	−0.568459	+	0.822712i	$0.692460\pi$
$140$	−19.8324	+	9.55077i	−1.67614	+	0.807187i
$141$		0			0
$142$	−6.12036	+	4.88083i	−0.513609	+	0.409590i
$143$	−1.94588	−	4.04067i	−0.162723	−	0.337898i
$144$		0			0
$145$	10.1807	−	1.05445i	0.845458	−	0.0875671i
$146$	2.27532			0.188307
$147$		0			0
$148$	25.7711	−	20.5518i	2.11837	−	1.68935i
$149$	−9.67852	+	12.1365i	−0.792896	+	0.994260i	0.206978	+	0.978346i	$0.433637\pi$
$149$	−9.67852	+	12.1365i	−0.792896	+	0.994260i	−0.999873	+	0.0159140i	$0.994934\pi$
$150$		0			0
$151$	5.93334	+	2.85734i	0.482848	+	0.232527i	0.659441	−	0.751757i	$-0.270793\pi$
$151$	5.93334	+	2.85734i	0.482848	+	0.232527i	−0.176593	+	0.984284i	$0.556507\pi$
$152$	−8.85390	−	11.1024i	−0.718146	−	0.900526i
$153$		0			0
$154$	1.46157	−	6.40357i	0.117777	−	0.516015i
$155$	8.52023	+	6.79466i	0.684361	+	0.545760i
$156$		0			0
$157$		−	10.0667i		−	0.803407i	−0.915770	−	0.401704i	$-0.868418\pi$
$157$		−	10.0667i		−	0.803407i	0.915770	−	0.401704i	$-0.131582\pi$
$158$	−2.51370	−	11.0133i	−0.199980	−	0.876168i
$159$		0			0
$160$	−3.97857	+	8.26159i	−0.314534	+	0.653136i
$161$	−0.117614	−	0.515302i	−0.00926931	−	0.0406115i
$162$		0			0
$163$	1.44138	−	0.328985i	0.112897	−	0.0257681i	−0.165699	−	0.986176i	$-0.552988\pi$
$163$	1.44138	−	0.328985i	0.112897	−	0.0257681i	0.278596	+	0.960408i	$0.410131\pi$
$164$	14.3886	+	11.4745i	1.12356	+	0.896009i
$165$		0			0
$166$	−17.4859	−	3.99104i	−1.35717	−	0.309765i
$167$	7.77867	+	9.75414i	0.601931	+	0.754798i	0.985678	−	0.168640i	$-0.0539377\pi$
$167$	7.77867	+	9.75414i	0.601931	+	0.754798i	−0.383746	+	0.923439i	$0.625366\pi$
$168$		0			0
$169$	−14.7555	+	7.10586i	−1.13504	+	0.546605i
$170$	−18.4781	+	23.1708i	−1.41721	+	1.77712i
$171$		0			0
$172$	−6.56123	−	13.6245i	−0.500289	−	1.03886i
$173$	2.64519			0.201110			0.100555	−	0.994931i	$-0.467938\pi$
$173$	2.64519			0.201110			0.100555	+	0.994931i	$0.467938\pi$
$174$		0			0
$175$	4.74636			0.358791
$176$	0.248886	+	0.516817i	0.0187605	+	0.0389566i
$177$		0			0
$178$	−6.73914	+	8.45061i	−0.505120	+	0.633400i
$179$	−5.72859	+	2.75874i	−0.428175	+	0.206198i	−0.635544	−	0.772065i	$-0.719224\pi$
$179$	−5.72859	+	2.75874i	−0.428175	+	0.206198i	0.207369	+	0.978263i	$0.433510\pi$
$180$		0			0
$181$	−10.7455	−	13.4744i	−0.798705	−	1.00154i	−0.999759	−	0.0219643i	$-0.993008\pi$
$181$	−10.7455	−	13.4744i	−0.798705	−	1.00154i	0.201054	−	0.979580i	$-0.435563\pi$
$182$	−41.9461	−	9.57391i	−3.10925	−	0.709666i
$183$		0			0
$184$	0.388634	+	0.309925i	0.0286505	+	0.0228480i
$185$	18.0382	−	4.11710i	1.32619	−	0.302695i
$186$		0			0
$187$	−1.23711	−	5.42012i	−0.0904663	−	0.396359i
$188$	−1.78831	+	3.71347i	−0.130426	+	0.270833i
$189$		0			0
$190$	−4.33301	−	18.9842i	−0.314350	−	1.37726i
$191$		−	16.4482i		−	1.19015i	−0.803671	−	0.595074i	$-0.797123\pi$
$191$		−	16.4482i		−	1.19015i	0.803671	−	0.595074i	$-0.202877\pi$
$192$		0			0
$193$	−9.77612	−	7.79620i	−0.703701	−	0.561183i	0.204933	−	0.978776i	$-0.434302\pi$
$193$	−9.77612	−	7.79620i	−0.703701	−	0.561183i	−0.908634	+	0.417593i	$0.862874\pi$
$194$	5.17160	−	22.6583i	0.371299	−	1.62677i
$195$		0			0
$196$	−9.92070	−	12.4402i	−0.708621	−	0.888583i
$197$	−12.7451	−	6.13771i	−0.908050	−	0.437294i	−0.0792604	−	0.996854i	$-0.525256\pi$
$197$	−12.7451	−	6.13771i	−0.908050	−	0.437294i	−0.828790	+	0.559560i	$0.810970\pi$
$198$		0			0
$199$	8.05509	−	10.1008i	0.571010	−	0.716024i	−0.409540	−	0.912292i	$-0.634311\pi$
$199$	8.05509	−	10.1008i	0.571010	−	0.716024i	0.980550	+	0.196268i	$0.0628822\pi$
$200$	−3.48989	+	2.78310i	−0.246773	+	0.196795i
$201$		0			0
$202$	35.2347			2.47911
$203$	5.92694	+	17.4398i	0.415989	+	1.22403i
$204$		0			0
$205$	4.48207	+	9.30711i	0.313041	+	0.650037i
$206$	−0.378970	+	0.302219i	−0.0264041	+	0.0210566i
$207$		0			0
$208$	3.38537	−	1.63031i	0.234733	−	0.113041i
$209$	3.29107	+	1.58490i	0.227648	+	0.109629i
$210$		0			0
$211$	13.4042	+	3.05943i	0.922787	+	0.210620i	0.657417	−	0.753527i	$-0.271649\pi$
$211$	13.4042	+	3.05943i	0.922787	+	0.210620i	0.265369	+	0.964147i	$0.414506\pi$
$212$	−0.351164	+	1.53855i	−0.0241181	+	0.105668i
$213$		0			0
$214$	5.82426	−	1.32935i	0.398138	−	0.0908724i
$215$		−	8.48813i		−	0.578886i
$216$		0			0
$217$	−8.50931	+	17.6698i	−0.577650	+	1.19950i
$218$	1.16018	−	2.40914i	0.0785772	−	0.163167i
$219$		0			0
$220$			5.32507i			0.359016i
$221$	−35.5041	+	8.10357i	−2.38826	+	0.545105i
$222$		0			0
$223$	3.00379	−	13.1605i	0.201149	−	0.881291i	−0.769090	−	0.639141i	$-0.779290\pi$
$223$	3.00379	−	13.1605i	0.201149	−	0.881291i	0.970239	−	0.242150i	$-0.0778527\pi$
$224$	−16.0883	−	3.67204i	−1.07494	−	0.245349i
$225$		0			0
$226$	9.09384	+	4.37936i	0.604913	+	0.291311i
$227$	−24.2997	+	11.7021i	−1.61283	+	0.776698i	−0.999910	−	0.0134459i	$-0.995720\pi$
$227$	−24.2997	+	11.7021i	−1.61283	+	0.776698i	−0.612921	+	0.790144i	$0.710006\pi$
$228$		0			0
$229$	8.53536	−	6.80672i	0.564032	−	0.449801i	−0.299499	−	0.954097i	$-0.596819\pi$
$229$	8.53536	−	6.80672i	0.564032	−	0.449801i	0.863531	+	0.504296i	$0.168248\pi$
$230$	0.295744	+	0.614118i	0.0195008	+	0.0404937i
$231$		0			0
$232$	−14.5840	−	9.34775i	−0.957488	−	0.613710i
$233$	5.48306			0.359207			0.179604	−	0.983739i	$-0.442518\pi$
$233$	5.48306			0.359207			0.179604	+	0.983739i	$0.442518\pi$
$234$		0			0
$235$	−1.80877	+	1.44245i	−0.117991	+	0.0940949i
$236$	24.4737	−	30.6890i	1.59310	−	1.99768i
$237$		0			0
$238$	−48.0531	−	23.1412i	−3.11482	−	1.50002i
$239$	0.474367	+	0.594838i	0.0306843	+	0.0384769i	0.796937	−	0.604063i	$-0.206452\pi$
$239$	0.474367	+	0.594838i	0.0306843	+	0.0384769i	−0.766253	+	0.642539i	$0.777881\pi$
$240$		0			0
$241$	−5.57063	+	24.4065i	−0.358836	+	1.57216i	0.397263	+	0.917705i	$0.369960\pi$
$241$	−5.57063	+	24.4065i	−0.358836	+	1.57216i	−0.756098	+	0.654458i	$0.772897\pi$
$242$	18.7168	+	14.9262i	1.20316	+	0.959490i
$243$		0			0
$244$			37.9904i			2.43208i
$245$	−1.98739	−	8.70734i	−0.126970	−	0.556292i
$246$		0			0
$247$	10.3817	−	21.5579i	0.660573	−	1.37169i
$248$	−4.10422	−	17.9817i	−0.260618	−	1.14184i
$249$		0			0
$250$	−27.4691	+	6.26964i	−1.73730	+	0.396527i
$251$	8.20753	+	6.54528i	0.518054	+	0.413135i	0.847304	−	0.531108i	$-0.178224\pi$
$251$	8.20753	+	6.54528i	0.518054	+	0.413135i	−0.329249	+	0.944243i	$0.606796\pi$
$252$		0			0
$253$	−0.124659	−	0.0284525i	−0.00783722	−	0.00178879i
$254$	−0.563650	−	0.706795i	−0.0353666	−	0.0443483i
$255$		0			0
$256$	18.2123	−	8.77060i	1.13827	−	0.548162i
$257$	0.169465	−	0.212503i	0.0105710	−	0.0132556i	−0.776518	−	0.630095i	$-0.783016\pi$
$257$	0.169465	−	0.212503i	0.0105710	−	0.0132556i	0.787089	+	0.616840i	$0.211587\pi$
$258$		0			0
$259$	14.4470	+	29.9995i	0.897691	+	1.86408i
$260$	34.8814			2.16325
$261$		0			0
$262$	−1.76474			−0.109026
$263$	−3.18585	−	6.61549i	−0.196448	−	0.407929i	0.779354	−	0.626584i	$-0.215547\pi$
$263$	−3.18585	−	6.61549i	−0.196448	−	0.407929i	−0.975802	+	0.218655i	$0.929833\pi$
$264$		0			0
$265$	−0.552293	+	0.692553i	−0.0339271	+	0.0425432i
$266$	31.5727	−	15.2046i	1.93585	−	0.932255i
$267$		0			0
$268$	−27.3391	−	34.2822i	−1.67000	−	2.09412i
$269$	29.2703	+	6.68076i	1.78464	+	0.407333i	0.981962	−	0.189077i	$-0.0605495\pi$
$269$	29.2703	+	6.68076i	1.78464	+	0.407333i	0.802680	+	0.596410i	$0.203407\pi$
$270$		0			0
$271$	−0.137209	−	0.109421i	−0.00833488	−	0.00664684i	0.619314	−	0.785144i	$-0.287411\pi$
$271$	−0.137209	−	0.109421i	−0.00833488	−	0.00664684i	−0.627648	+	0.778497i	$0.715982\pi$
$272$	4.54111	−	1.03648i	0.275345	−	0.0628457i
$273$		0			0
$274$	−7.71185	−	33.7878i	−0.465890	−	2.04120i
$275$	0.498190	−	1.03450i	0.0300420	−	0.0623828i
$276$		0			0
$277$	−0.652185	−	2.85741i	−0.0391860	−	0.171685i	0.951548	−	0.307499i	$-0.0994922\pi$
$277$	−0.652185	−	2.85741i	−0.0391860	−	0.171685i	−0.990734	+	0.135814i	$0.956635\pi$
$278$			8.49318i			0.509387i
$279$		0			0
$280$	16.3493	+	13.0381i	0.977059	+	0.779178i
$281$	−2.26831	+	9.93812i	−0.135316	+	0.592858i	0.861112	+	0.508415i	$0.169768\pi$
$281$	−2.26831	+	9.93812i	−0.135316	+	0.592858i	−0.996428	+	0.0844434i	$0.973089\pi$
$282$		0			0
$283$	11.9907	+	15.0359i	0.712773	+	0.893789i	0.997905	−	0.0646996i	$-0.0206089\pi$
$283$	11.9907	+	15.0359i	0.712773	+	0.893789i	−0.285132	+	0.958488i	$0.592038\pi$
$284$	10.2904	+	4.95560i	0.610623	+	0.294061i
$285$		0			0
$286$	−6.48946	+	8.13752i	−0.383730	+	0.481182i
$287$	−14.5345	+	11.5909i	−0.857947	+	0.684190i
$288$		0			0
$289$	−28.1439			−1.65552
$290$	−12.4562	−	20.2256i	−0.731456	−	1.18769i
$291$		0			0
$292$	−1.44037	−	2.99096i	−0.0842912	−	0.175033i
$293$	−8.69694	+	6.93558i	−0.508081	+	0.405181i	−0.843699	−	0.536817i	$-0.819626\pi$
$293$	−8.69694	+	6.93558i	−0.508081	+	0.405181i	0.335618	+	0.941998i	$0.391055\pi$
$294$		0			0
$295$	19.8509	−	9.55968i	1.15576	−	0.556586i
$296$	−28.2131	−	13.5867i	−1.63986	−	0.789713i
$297$		0			0
$298$	35.1227	+	8.01652i	2.03460	+	0.464385i
$299$	−0.186376	+	0.816566i	−0.0107784	+	0.0472232i
$300$		0			0
$301$	14.8925	−	3.39912i	0.858390	−	0.195922i
$302$		−	15.2836i		−	0.879470i
$303$		0			0
$304$	−1.32786	+	2.75733i	−0.0761581	+	0.158144i
$305$	−9.25225	+	19.2125i	−0.529782	+	1.10010i
$306$		0			0
$307$		−	3.09566i		−	0.176678i	−0.996090	−	0.0883392i	$-0.971844\pi$
$307$		−	3.09566i		−	0.176678i	0.996090	−	0.0883392i	$-0.0281559\pi$
$308$	−9.34288	+	2.13245i	−0.532360	+	0.121508i
$309$		0			0
$310$	5.62787	−	24.6573i	0.319642	−	1.40044i
$311$	14.2761	+	3.25843i	0.809523	+	0.184768i	0.607199	−	0.794550i	$-0.292293\pi$
$311$	14.2761	+	3.25843i	0.809523	+	0.184768i	0.202325	+	0.979318i	$0.435150\pi$
$312$		0			0
$313$	6.02573	+	2.90184i	0.340594	+	0.164022i	0.596360	−	0.802717i	$-0.296613\pi$
$313$	6.02573	+	2.90184i	0.340594	+	0.164022i	−0.255765	+	0.966739i	$0.582327\pi$
$314$	−21.0490	+	10.1366i	−1.18786	+	0.572044i
$315$		0			0
$316$	−12.8859	+	10.2762i	−0.724889	+	0.578080i
$317$	2.41609	+	5.01705i	0.135701	+	0.281786i	0.957735	−	0.287653i	$-0.0928749\pi$
$317$	2.41609	+	5.01705i	0.135701	+	0.281786i	−0.822034	+	0.569439i	$0.807161\pi$
$318$		0			0
$319$	4.42323	+	0.538708i	0.247653	+	0.0301619i
$320$	23.9161			1.33695
$321$		0			0
$322$	−0.959043	+	0.764811i	−0.0534454	+	0.0426213i
$323$	18.4935	−	23.1901i	1.02900	−	1.29033i
$324$		0			0
$325$	−6.77641	−	3.26335i	−0.375888	−	0.181018i
$326$	−2.13929	−	2.68259i	−0.118484	−	0.148575i
$327$		0			0
$328$	3.89043	−	17.0451i	0.214813	−	0.941157i
$329$	−3.25512	−	2.59587i	−0.179461	−	0.143115i
$330$		0			0
$331$			34.6315i			1.90352i	0.306847	+	0.951759i	$0.400726\pi$
$331$			34.6315i			1.90352i	−0.306847	+	0.951759i	$0.599274\pi$
$332$	5.82297	+	25.5121i	0.319577	+	1.40016i
$333$		0			0
$334$	12.5627	−	26.0868i	0.687403	−	1.42741i
$335$	−5.47680	−	23.9954i	−0.299229	−	1.31101i
$336$		0			0
$337$	8.60703	−	1.96450i	0.468855	−	0.107013i	0.0184351	−	0.999830i	$-0.494132\pi$
$337$	8.60703	−	1.96450i	0.468855	−	0.107013i	0.450419	+	0.892817i	$0.351274\pi$
$338$	29.7161	+	23.6978i	1.61634	+	1.28899i
$339$		0			0
$340$	42.1560	+	9.62184i	2.28623	+	0.521818i
$341$	2.95809	+	3.70932i	0.160189	+	0.200871i
$342$		0			0
$343$	−7.09048	+	3.41460i	−0.382850	+	0.184371i
$344$	−8.95700	+	11.2317i	−0.482929	+	0.605574i
$345$		0			0
$346$	−2.66358	−	5.53098i	−0.143195	−	0.297347i
$347$	−16.3136			−0.875759			−0.437880	−	0.899034i	$-0.644270\pi$
$347$	−16.3136			−0.875759			−0.437880	+	0.899034i	$0.644270\pi$
$348$		0			0
$349$	−9.44632			−0.505650			−0.252825	−	0.967512i	$-0.581360\pi$
$349$	−9.44632			−0.505650			−0.252825	+	0.967512i	$0.581360\pi$
$350$	−4.77936	−	9.92444i	−0.255468	−	0.530484i
$351$		0			0
$352$	−2.48901	+	3.12112i	−0.132665	+	0.166356i
$353$	13.4827	−	6.49294i	0.717613	−	0.345584i	−0.0391859	−	0.999232i	$-0.512476\pi$
$353$	13.4827	−	6.49294i	0.717613	−	0.345584i	0.756799	+	0.653648i	$0.226762\pi$
$354$		0			0
$355$	3.99717	+	5.01229i	0.212148	+	0.266025i
$356$	15.3747	+	3.50917i	0.814856	+	0.185986i
$357$		0			0
$358$	11.5368	+	9.20031i	0.609740	+	0.486252i
$359$	−15.0352	+	3.43168i	−0.793527	+	0.181117i	−0.600024	−	0.799982i	$-0.704842\pi$
$359$	−15.0352	+	3.43168i	−0.793527	+	0.181117i	−0.193503	+	0.981100i	$0.561985\pi$
$360$		0			0
$361$	0.108713	+	0.476304i	0.00572175	+	0.0250686i
$362$	−17.3542	+	36.0364i	−0.912118	+	1.89403i
$363$		0			0
$364$	13.9684	+	61.1997i	0.732145	+	3.20774i
$365$		−	1.86338i		−	0.0975336i
$366$		0			0
$367$	−26.0706	−	20.7906i	−1.36088	−	1.08526i	−0.987506	−	0.157580i	$-0.949631\pi$
$367$	−26.0706	−	20.7906i	−1.36088	−	1.08526i	−0.373370	−	0.927683i	$-0.621798\pi$
$368$	0.0238382	−	0.104442i	0.00124265	−	0.00544441i
$369$		0			0
$370$	−26.7723	−	33.5714i	−1.39182	−	1.74529i
$371$	−1.43626	−	0.691666i	−0.0745668	−	0.0359095i
$372$		0			0
$373$	−2.02994	+	2.54547i	−0.105106	+	0.131799i	−0.831602	−	0.555371i	$-0.812576\pi$
$373$	−2.02994	+	2.54547i	−0.105106	+	0.131799i	0.726496	+	0.687171i	$0.241148\pi$
$374$	−10.0875	+	8.04454i	−0.521614	+	0.415973i
$375$		0			0
$376$	3.91554			0.201929
$377$	3.52876	−	28.9740i	0.181741	−	1.49224i
$378$		0			0
$379$	−11.2522	−	23.3653i	−0.577984	−	1.20020i	−0.961024	−	0.276465i	$-0.910837\pi$
$379$	−11.2522	−	23.3653i	−0.577984	−	1.20020i	0.383040	−	0.923732i	$-0.374877\pi$
$380$	−22.2122	+	17.7136i	−1.13946	+	0.908689i
$381$		0			0
$382$	−34.3924	+	16.5625i	−1.75967	+	0.847412i
$383$	−26.6637	−	12.8406i	−1.36245	−	0.656123i	−0.397272	−	0.917701i	$-0.630043\pi$
$383$	−26.6637	−	12.8406i	−1.36245	−	0.656123i	−0.965182	+	0.261578i	$0.915757\pi$
$384$		0			0
$385$	−5.24422	−	1.19696i	−0.267270	−	0.0610027i
$386$	−6.45743	+	28.2918i	−0.328675	+	1.44002i
$387$		0			0
$388$	−33.0586	+	7.54542i	−1.67830	+	0.383061i
$389$			11.6584i			0.591103i	0.955327	+	0.295551i	$0.0955033\pi$
$389$			11.6584i			0.591103i	−0.955327	+	0.295551i	$0.904497\pi$
$390$		0			0
$391$	−0.450490	+	0.935452i	−0.0227823	+	0.0473078i
$392$	−6.55855	+	13.6190i	−0.331257	+	0.687862i
$393$		0			0
$394$			32.8298i			1.65394i
$395$	−9.01934	+	2.05861i	−0.453812	+	0.103580i
$396$		0			0
$397$	−4.79777	+	21.0204i	−0.240793	+	1.05498i	0.699504	+	0.714628i	$0.253404\pi$
$397$	−4.79777	+	21.0204i	−0.240793	+	1.05498i	−0.940297	+	0.340354i	$0.889453\pi$
$398$	−29.2314	−	6.67187i	−1.46524	−	0.334430i
$399$		0			0
$400$	0.866730	+	0.417395i	0.0433365	+	0.0208697i
$401$	18.0240	−	8.67991i	0.900077	−	0.433454i	0.0741601	−	0.997246i	$-0.476372\pi$
$401$	18.0240	−	8.67991i	0.900077	−	0.433454i	0.825917	+	0.563792i	$0.190658\pi$
$402$		0			0
$403$	24.2976	−	19.3767i	1.21035	−	0.965222i
$404$	−22.3050	−	46.3169i	−1.10972	−	2.30435i
$405$		0			0
$406$	30.4977	−	29.9540i	1.51358	−	1.48659i
$407$	8.05497			0.399270
$408$		0			0
$409$	−22.2527	+	17.7460i	−1.10033	+	0.877482i	−0.993160	−	0.116759i	$-0.962749\pi$
$409$	−22.2527	+	17.7460i	−1.10033	+	0.877482i	−0.107167	+	0.994241i	$0.534178\pi$
$410$	14.9475	−	18.7436i	0.738207	−	0.925682i
$411$		0			0
$412$	0.637178	+	0.306849i	0.0313915	+	0.0151173i
$413$	24.7219	+	31.0003i	1.21649	+	1.52543i
$414$		0			0
$415$	−3.26848	+	14.3201i	−0.160443	+	0.702947i
$416$	20.4446	+	16.3040i	1.00238	+	0.799372i
$417$		0			0
$418$		−	8.47740i		−	0.414643i
$419$	−2.46307	−	10.7914i	−0.120329	−	0.527196i	−0.998781	−	0.0493649i	$-0.984280\pi$
$419$	−2.46307	−	10.7914i	−0.120329	−	0.527196i	0.878452	−	0.477831i	$-0.158577\pi$
$420$		0			0
$421$	−11.6154	+	24.1196i	−0.566099	+	1.17552i	0.399802	+	0.916602i	$0.369079\pi$
$421$	−11.6154	+	24.1196i	−0.566099	+	1.17552i	−0.965900	+	0.258914i	$0.916635\pi$
$422$	−7.10029	−	31.1084i	−0.345637	−	1.51433i
$423$		0			0
$424$	1.46162	−	0.333605i	0.0709824	−	0.0162013i
$425$	−7.28948	−	5.81316i	−0.353592	−	0.281980i
$426$		0			0
$427$	−37.4136	−	8.53941i	−1.81057	−	0.413251i
$428$	−5.43445	−	6.81459i	−0.262684	−	0.329396i
$429$		0			0
$430$	−17.7483	+	8.54714i	−0.855900	+	0.412180i
$431$	−20.6592	+	25.9059i	−0.995120	+	1.24784i	−0.0264091	+	0.999651i	$0.508407\pi$
$431$	−20.6592	+	25.9059i	−0.995120	+	1.24784i	−0.968711	+	0.248190i	$0.920164\pi$
$432$		0			0
$433$	−2.30859	−	4.79384i	−0.110944	−	0.230377i	0.838103	−	0.545512i	$-0.183665\pi$
$433$	−2.30859	−	4.79384i	−0.110944	−	0.230377i	−0.949047	+	0.315135i	$0.897950\pi$
$434$	45.5152			2.18480
$435$		0			0
$436$	−3.90131			−0.186839
$437$	−0.295989	−	0.614628i	−0.0141591	−	0.0294016i
$438$		0			0
$439$	19.4239	−	24.3568i	0.927053	−	1.16249i	−0.0593651	−	0.998236i	$-0.518908\pi$
$439$	19.4239	−	24.3568i	0.927053	−	1.16249i	0.986418	−	0.164252i	$-0.0525210\pi$
$440$	4.55781	−	2.19493i	0.217285	−	0.104639i
$441$		0			0
$442$	52.6951	+	66.0776i	2.50645	+	3.14299i
$443$	12.5788	+	2.87103i	0.597636	+	0.136407i	0.510629	−	0.859801i	$-0.329413\pi$
$443$	12.5788	+	2.87103i	0.597636	+	0.136407i	0.0870071	+	0.996208i	$0.472270\pi$
$444$		0			0
$445$	6.92065	+	5.51903i	0.328070	+	0.261627i
$446$	−30.5427	+	6.97117i	−1.44624	+	0.330094i
$447$		0			0
$448$	9.57731	+	41.9609i	0.452485	+	1.98247i
$449$	14.6872	−	30.4983i	0.693132	−	1.43930i	−0.195509	−	0.980702i	$-0.562636\pi$
$449$	14.6872	−	30.4983i	0.693132	−	1.43930i	0.888642	−	0.458602i	$-0.151650\pi$
$450$		0			0
$451$	1.00074	+	4.38451i	0.0471228	+	0.206458i
$452$		−	14.7264i		−	0.692671i
$453$		0			0
$454$	48.9373	+	39.0262i	2.29674	+	1.83159i
$455$	−7.84058	+	34.3518i	−0.367572	+	1.61044i
$456$		0			0
$457$	4.76027	+	5.96919i	0.222676	+	0.279227i	0.880603	−	0.473855i	$-0.157138\pi$
$457$	4.76027	+	5.96919i	0.222676	+	0.279227i	−0.657927	+	0.753082i	$0.728566\pi$
$458$	−22.8273	−	10.9930i	−1.06665	−	0.513670i
$459$		0			0
$460$	0.620054	−	0.777523i	0.0289102	−	0.0362522i
$461$	13.2633	−	10.5771i	0.617731	−	0.492624i	−0.263908	−	0.964548i	$-0.585012\pi$
$461$	13.2633	−	10.5771i	0.617731	−	0.492624i	0.881639	+	0.471924i	$0.156440\pi$
$462$		0			0
$463$	−9.31660			−0.432979			−0.216490	−	0.976285i	$-0.569461\pi$
$463$	−9.31660			−0.432979			−0.216490	+	0.976285i	$0.569461\pi$
$464$	−0.451342	+	3.70588i	−0.0209530	+	0.172041i
$465$		0			0
$466$	−5.52118	−	11.4648i	−0.255764	−	0.531099i
$467$	19.8211	−	15.8068i	0.917212	−	0.731452i	−0.0463531	−	0.998925i	$-0.514760\pi$
$467$	19.8211	−	15.8068i	0.917212	−	0.731452i	0.963565	+	0.267473i	$0.0861885\pi$
$468$		0			0
$469$	39.9069	−	19.2182i	1.84273	−	0.887413i
$470$	4.83744	+	2.32959i	0.223135	+	0.107456i
$471$		0			0
$472$	−36.3550	−	8.29778i	−1.67337	−	0.381936i
$473$	0.822293	−	3.60270i	0.0378091	−	0.165652i
$474$		0			0
$475$	5.97236	−	1.36315i	0.274031	−	0.0625458i
$476$			77.8162i			3.56670i
$477$		0			0
$478$	0.766115	−	1.59086i	0.0350413	−	0.0727640i
$479$	9.99005	−	20.7446i	0.456457	−	0.947843i	−0.538024	−	0.842929i	$-0.680829\pi$
$479$	9.99005	−	20.7446i	0.456457	−	0.947843i	0.994481	−	0.104914i	$-0.0334566\pi$
$480$		0			0
$481$		−	52.7634i		−	2.40580i
$482$	56.6424	−	12.9282i	2.57999	−	0.588866i
$483$		0			0
$484$	7.77228	−	34.0526i	0.353285	−	1.54784i
$485$	−18.5560	−	4.23530i	−0.842586	−	0.192315i
$486$		0			0
$487$	−1.38231	−	0.665685i	−0.0626384	−	0.0301651i	0.402302	−	0.915507i	$-0.368210\pi$
$487$	−1.38231	−	0.665685i	−0.0626384	−	0.0301651i	−0.464941	+	0.885342i	$0.653924\pi$
$488$	32.5166	−	15.6592i	1.47196	−	0.708857i
$489$		0			0
$490$	−16.2055	+	12.9234i	−0.732089	+	0.583821i
$491$	8.74266	+	18.1543i	0.394551	+	0.819293i	0.999731	+	0.0232042i	$0.00738680\pi$
$491$	8.74266	+	18.1543i	0.394551	+	0.819293i	−0.605180	+	0.796089i	$0.706899\pi$
$492$		0			0
$493$	12.2570	−	34.0432i	0.552027	−	1.53323i
$494$	−55.5305			−2.49843
$495$		0			0
$496$	−3.10776	+	2.47835i	−0.139542	+	0.111281i
$497$	−7.19342	+	9.02026i	−0.322669	+	0.404614i
$498$		0			0
$499$	31.2688	+	15.0583i	1.39978	+	0.674100i	0.973117	−	0.230309i	$-0.0739738\pi$
$499$	31.2688	+	15.0583i	1.39978	+	0.674100i	0.426666	+	0.904409i	$0.359688\pi$
$500$	25.6306	+	32.1398i	1.14624	+	1.43734i
$501$		0			0
$502$	5.42132	−	23.7524i	0.241966	−	1.06012i
$503$	−22.5450	−	17.9790i	−1.00523	−	0.801646i	−0.0250384	−	0.999686i	$-0.507971\pi$
$503$	−22.5450	−	17.9790i	−1.00523	−	0.801646i	−0.980194	+	0.198041i	$0.936542\pi$
$504$		0			0
$505$		−	28.8556i		−	1.28406i
$506$	0.0660322	+	0.289306i	0.00293549	+	0.0128612i
$507$		0			0
$508$	−0.572285	+	1.18836i	−0.0253910	+	0.0527250i
$509$	−0.690039	−	3.02326i	−0.0305854	−	0.134004i	0.957330	−	0.288997i	$-0.0933216\pi$
$509$	−0.690039	−	3.02326i	−0.0305854	−	0.134004i	−0.987916	+	0.154993i	$0.950464\pi$
$510$		0			0
$511$	3.26931	−	0.746199i	0.144626	−	0.0330099i
$512$	−6.10192	−	4.86612i	−0.269669	−	0.215054i
$513$		0			0
$514$	−0.614978	−	0.140365i	−0.0271255	−	0.00619122i
$515$	0.247503	+	0.310359i	0.0109063	+	0.0136760i
$516$		0			0
$517$	−0.907452	+	0.437006i	−0.0399097	+	0.0192195i
$518$	48.1802	−	60.4160i	2.11691	−	2.65453i
$519$		0			0
$520$	−14.3777	−	29.8556i	−0.630503	−	1.30925i
$521$	−33.4475			−1.46536			−0.732680	−	0.680573i	$-0.761731\pi$
$521$	−33.4475			−1.46536			−0.732680	+	0.680573i	$0.761731\pi$
$522$		0			0
$523$	−23.5081			−1.02794			−0.513969	−	0.857809i	$-0.671825\pi$
$523$	−23.5081			−1.02794			−0.513969	+	0.857809i	$0.671825\pi$
$524$	1.11715	+	2.31979i	0.0488029	+	0.101340i
$525$		0			0
$526$	−10.6247	+	13.3230i	−0.463259	+	0.580909i
$527$	34.7099	−	16.7154i	1.51199	−	0.728134i
$528$		0			0
$529$	−14.3254	−	17.9635i	−0.622842	−	0.781020i
$530$	2.00423	+	0.457453i	0.0870582	+	0.0198705i
$531$		0			0
$532$	−39.9737	−	31.8779i	−1.73308	−	1.38208i
$533$	28.7204	−	6.55523i	1.24402	−	0.283939i
$534$		0			0
$535$	−1.08867	−	4.76979i	−0.0470675	−	0.206216i
$536$	−18.0738	+	37.5307i	−0.780671	+	1.62108i
$537$		0			0
$538$	−15.5046	−	67.9302i	−0.668452	−	2.92868i
$539$		−	3.88827i		−	0.167480i
$540$		0			0
$541$	25.6227	+	20.4334i	1.10161	+	0.878501i	0.993294	−	0.115616i	$-0.0368841\pi$
$541$	25.6227	+	20.4334i	1.10161	+	0.878501i	0.108312	+	0.994117i	$0.465456\pi$
$542$	−0.0906310	+	0.397081i	−0.00389294	+	0.0170561i
$543$		0			0
$544$	20.2110	+	25.3438i	0.866541	+	1.08661i
$545$	−1.97297	−	0.950132i	−0.0845127	−	0.0406992i
$546$		0			0
$547$	−17.5465	+	22.0026i	−0.750235	+	0.940765i	−0.999618	−	0.0276401i	$-0.991201\pi$
$547$	−17.5465	+	22.0026i	−0.750235	+	0.940765i	0.249383	+	0.968405i	$0.419772\pi$
$548$	−39.5330	+	31.5265i	−1.68876	+	1.34675i
$549$		0			0
$550$	−2.66475			−0.113625
$551$	12.4666	+	20.2423i	0.531094	+	0.862353i
$552$		0			0
$553$	−7.22368	−	15.0001i	−0.307182	−	0.637870i
$554$	−5.31800	+	4.24097i	−0.225940	+	0.180181i
$555$		0			0
$556$	11.1645	−	5.37653i	0.473480	−	0.228016i
$557$	11.9640	+	5.76157i	0.506932	+	0.244125i	0.669826	−	0.742518i	$-0.266369\pi$
$557$	11.9640	+	5.76157i	0.506932	+	0.244125i	−0.162894	+	0.986644i	$0.552083\pi$
$558$		0			0
$559$	−23.5992	−	5.38636i	−0.998139	−	0.227819i
$560$	1.00284	−	4.39373i	0.0423778	−	0.185669i
$561$		0			0
$562$	23.0643	−	5.26426i	0.972907	−	0.222060i
$563$			12.5201i			0.527658i	0.964569	+	0.263829i	$0.0849855\pi$
$563$			12.5201i			0.527658i	−0.964569	+	0.263829i	$0.915014\pi$
$564$		0			0
$565$	3.58649	−	7.44743i	0.150885	−	0.313316i
$566$	19.3653	−	40.2124i	0.813983	−	1.69025i
$567$		0			0
$568$		−	10.8504i		−	0.455271i
$569$	−12.6153	+	2.87936i	−0.528860	+	0.120709i	−0.478610	−	0.878028i	$-0.658859\pi$
$569$	−12.6153	+	2.87936i	−0.528860	+	0.120709i	−0.0502506	+	0.998737i	$0.516002\pi$
$570$		0			0
$571$	−4.56081	+	19.9822i	−0.190864	+	0.836229i	0.785286	+	0.619133i	$0.212516\pi$
$571$	−4.56081	+	19.9822i	−0.190864	+	0.836229i	−0.976150	+	0.217096i	$0.930341\pi$
$572$	14.8051	+	3.37916i	0.619030	+	0.141290i
$573$		0			0
$574$	38.8717	+	18.7196i	1.62247	+	0.781342i
$575$	−0.193200	+	0.0930400i	−0.00805698	+	0.00388004i
$576$		0			0
$577$	1.84202	−	1.46896i	0.0766841	−	0.0611536i	−0.584398	−	0.811468i	$-0.698669\pi$
$577$	1.84202	−	1.46896i	0.0766841	−	0.0611536i	0.661082	+	0.750314i	$0.270098\pi$
$578$	28.3395	+	58.8476i	1.17877	+	2.44774i
$579$		0			0
$580$	−18.7016	+	29.1776i	−0.776544	+	1.21153i
$581$	−26.4337			−1.09665
$582$		0			0
$583$	−0.301506	+	0.240443i	−0.0124871	+	0.00995814i
$584$	−1.96631	+	2.46567i	−0.0813663	+	0.102030i
$585$		0			0
$586$	23.2594	+	11.2011i	0.960837	+	0.462715i
$587$	−5.07686	−	6.36618i	−0.209544	−	0.262760i	0.665942	−	0.746004i	$-0.268030\pi$
$587$	−5.07686	−	6.36618i	−0.209544	−	0.262760i	−0.875486	+	0.483244i	$0.839459\pi$
$588$		0			0
$589$	−5.63255	+	24.6778i	−0.232085	+	1.01683i
$590$	−39.9778	−	31.8812i	−1.64586	−	1.31253i
$591$		0			0
$592$			6.74864i			0.277367i
$593$	7.80289	+	34.1867i	0.320426	+	1.40388i	0.836797	+	0.547514i	$0.184426\pi$
$593$	7.80289	+	34.1867i	0.320426	+	1.40388i	−0.516370	+	0.856365i	$0.672717\pi$
$594$		0			0
$595$	−18.9515	+	39.3532i	−0.776936	+	1.61333i
$596$	−11.6962	−	51.2444i	−0.479095	−	2.09905i
$597$		0			0
$598$	1.89508	−	0.432539i	0.0774954	−	0.0176878i
$599$	−20.1222	−	16.0469i	−0.822171	−	0.655659i	0.119261	−	0.992863i	$-0.461948\pi$
$599$	−20.1222	−	16.0469i	−0.822171	−	0.655659i	−0.941432	+	0.337204i	$0.890519\pi$
$600$		0			0
$601$	0.871592	+	0.198935i	0.0355530	+	0.00811473i	0.240260	−	0.970708i	$-0.422767\pi$
$601$	0.871592	+	0.198935i	0.0355530	+	0.00811473i	−0.204707	+	0.978823i	$0.565624\pi$
$602$	−22.1034	−	27.7168i	−0.900869	−	1.12965i
$603$		0			0
$604$	−20.0906	+	9.67512i	−0.817475	+	0.393675i
$605$	12.2238	−	15.3282i	0.496969	−	0.623180i
$606$		0			0
$607$	−1.84678	−	3.83488i	−0.0749585	−	0.155653i	0.860122	−	0.510088i	$-0.170387\pi$
$607$	−1.84678	−	3.83488i	−0.0749585	−	0.155653i	−0.935080	+	0.354436i	$0.884673\pi$
$608$	−21.2985			−0.863769
$609$		0			0
$610$	49.4891			2.00375
$611$	2.86257	+	5.94419i	0.115807	+	0.240476i
$612$		0			0
$613$	8.60900	−	10.7953i	0.347714	−	0.436020i	−0.576964	−	0.816770i	$-0.695763\pi$
$613$	8.60900	−	10.7953i	0.347714	−	0.436020i	0.924678	+	0.380750i	$0.124334\pi$
$614$	−6.47288	+	3.11718i	−0.261224	+	0.125799i
$615$		0			0
$616$	5.67622	+	7.11775i	0.228701	+	0.286782i
$617$	−4.99156	−	1.13929i	−0.200953	−	0.0458662i	0.120860	−	0.992670i	$-0.461435\pi$
$617$	−4.99156	−	1.13929i	−0.200953	−	0.0458662i	−0.321812	+	0.946803i	$0.604292\pi$
$618$		0			0
$619$	−31.5229	−	25.1387i	−1.26701	−	1.01041i	−0.998894	−	0.0470219i	$-0.985027\pi$
$619$	−31.5229	−	25.1387i	−1.26701	−	1.01041i	−0.268118	−	0.963386i	$-0.586402\pi$
$620$	−35.9753	+	8.21113i	−1.44480	+	0.329767i
$621$		0			0
$622$	−7.56212	−	33.1318i	−0.303213	−	1.32846i
$623$	−6.91178	+	14.3525i	−0.276915	+	0.575019i
$624$		0			0
$625$	3.59062	+	15.7315i	0.143625	+	0.629261i
$626$		−	15.5216i		−	0.620366i
$627$		0			0
$628$	26.6497	+	21.2524i	1.06344	+	0.848064i
$629$	14.5545	−	63.7673i	0.580325	−	2.54257i
$630$		0			0
$631$	1.53439	+	1.92407i	0.0610832	+	0.0765959i	0.811434	−	0.584443i	$-0.198687\pi$
$631$	1.53439	+	1.92407i	0.0610832	+	0.0765959i	−0.750351	+	0.661039i	$0.770116\pi$
$632$	14.1069	+	6.79355i	0.561144	+	0.270233i
$633$		0			0
$634$	8.05756	−	10.1039i	0.320007	−	0.401276i
$635$	−0.578832	+	0.461603i	−0.0229702	+	0.0183182i
$636$		0			0
$637$	−25.4698			−1.00915
$638$	−3.32756	−	9.79123i	−0.131739	−	0.387638i
$639$		0			0
$640$	−16.1252	−	33.4843i	−0.637404	−	1.32358i
$641$	−13.3801	+	10.6703i	−0.528482	+	0.421450i	−0.851041	−	0.525099i	$-0.824028\pi$
$641$	−13.3801	+	10.6703i	−0.528482	+	0.421450i	0.322559	+	0.946549i	$0.395457\pi$
$642$		0			0
$643$	−36.0341	+	17.3531i	−1.42105	+	0.684340i	−0.977309	−	0.211816i	$-0.932062\pi$
$643$	−36.0341	+	17.3531i	−1.42105	+	0.684340i	−0.443738	+	0.896157i	$0.646348\pi$
$644$	1.61248	+	0.776527i	0.0635404	+	0.0305995i
$645$		0			0
$646$	−67.1115	−	15.3178i	−2.64047	−	0.602669i
$647$	−1.67703	+	7.34755i	−0.0659308	+	0.288862i	−0.997136	−	0.0756346i	$-0.975902\pi$
$647$	−1.67703	+	7.34755i	−0.0659308	+	0.288862i	0.931205	+	0.364496i	$0.118759\pi$
$648$		0			0
$649$	9.35160	−	2.13444i	0.367082	−	0.0837841i
$650$			17.4552i			0.684650i
$651$		0			0
$652$	−2.17206	+	4.51033i	−0.0850645	+	0.176638i
$653$	−17.3043	+	35.9328i	−0.677170	+	1.40616i	0.224820	+	0.974400i	$0.427821\pi$
$653$	−17.3043	+	35.9328i	−0.677170	+	1.40616i	−0.901990	+	0.431757i	$0.857894\pi$
$654$		0			0
$655$			1.44524i			0.0564700i
$656$	−3.67344	+	0.838440i	−0.143424	+	0.0327356i
$657$		0			0
$658$	−2.15011	+	9.42023i	−0.0838199	+	0.367239i
$659$	−8.75482	−	1.99823i	−0.341039	−	0.0778400i	0.0485712	−	0.998820i	$-0.484533\pi$
$659$	−8.75482	−	1.99823i	−0.341039	−	0.0778400i	−0.389610	+	0.920980i	$0.627390\pi$
$660$		0			0
$661$	−22.0949	−	10.6403i	−0.859390	−	0.413860i	−0.0483357	−	0.998831i	$-0.515392\pi$
$661$	−22.0949	−	10.6403i	−0.859390	−	0.413860i	−0.811054	+	0.584971i	$0.801106\pi$
$662$	72.4129	−	34.8722i	2.81441	−	1.35535i
$663$		0			0
$664$	19.4361	−	15.4998i	0.754266	−	0.601507i
$665$	−12.4519	−	25.8566i	−0.482863	−	1.00267i
$666$		0			0
$667$	−0.583116	−	0.593701i	−0.0225783	−	0.0229882i
$668$	−42.2444			−1.63449
$669$		0			0
$670$	−44.6585	+	35.6140i	−1.72531	+	1.37589i
$671$	−5.78824	+	7.25822i	−0.223453	+	0.280201i
$672$		0			0
$673$	19.2378	+	9.26446i	0.741564	+	0.357119i	0.766221	−	0.642577i	$-0.222135\pi$
$673$	19.2378	+	9.26446i	0.741564	+	0.357119i	−0.0246564	+	0.999696i	$0.507849\pi$
$674$	−12.7745	−	16.0188i	−0.492057	−	0.617020i
$675$		0			0
$676$	12.3398	−	54.0642i	0.474608	−	2.07939i
$677$	6.90970	+	5.51030i	0.265561	+	0.211778i	0.747213	−	0.664585i	$-0.231392\pi$
$677$	6.90970	+	5.51030i	0.265561	+	0.211778i	−0.481652	+	0.876363i	$0.659963\pi$
$678$		0			0
$679$		−	34.2528i		−	1.31450i
$680$	−9.14070	−	40.0480i	−0.350530	−	1.53577i
$681$		0			0
$682$	4.77738	−	9.92034i	0.182935	−	0.379869i
$683$	7.09180	+	31.0712i	0.271360	+	1.18891i	0.908409	+	0.418083i	$0.137298\pi$
$683$	7.09180	+	31.0712i	0.271360	+	1.18891i	−0.637049	+	0.770823i	$0.719845\pi$
$684$		0			0
$685$	−27.6706	+	6.31564i	−1.05724	+	0.241308i
$686$	14.2795	+	11.3876i	0.545196	+	0.434779i
$687$		0			0
$688$	3.01843	+	0.688936i	0.115076	+	0.0262654i
$689$	1.57500	+	1.97499i	0.0600028	+	0.0752412i
$690$		0			0
$691$	6.23726	−	3.00371i	0.237277	−	0.114266i	−0.311467	−	0.950257i	$-0.600820\pi$
$691$	6.23726	−	3.00371i	0.237277	−	0.114266i	0.548744	+	0.835990i	$0.315106\pi$
$692$	−5.58445	+	7.00267i	−0.212289	+	0.266202i
$693$		0			0
$694$	16.4270	+	34.1110i	0.623560	+	1.29484i
$695$	6.95551			0.263838
$696$		0			0
$697$	36.5183			1.38323
$698$	9.51199	+	19.7518i	0.360034	+	0.747618i
$699$		0			0
$700$	−10.0204	+	12.5652i	−0.378735	+	0.474918i
$701$	−40.3171	+	19.4157i	−1.52276	+	0.733321i	−0.993359	−	0.115052i	$-0.963296\pi$
$701$	−40.3171	+	19.4157i	−1.52276	+	0.733321i	−0.529398	+	0.848374i	$0.677582\pi$
$702$		0			0
$703$	26.7945	+	33.5992i	1.01057	+	1.26722i
$704$	10.1509	+	2.31688i	0.382577	+	0.0873208i
$705$		0			0
$706$	−27.1529	−	21.6537i	−1.02191	−	0.814949i
$707$	50.6274	−	11.5554i	1.90404	−	0.434584i
$708$		0			0
$709$	1.40825	+	6.16993i	0.0528878	+	0.231717i	0.994463	−	0.105086i	$-0.0335117\pi$
$709$	1.40825	+	6.16993i	0.0528878	+	0.231717i	−0.941575	+	0.336802i	$0.890655\pi$
$710$	6.45552	−	13.4050i	0.242272	−	0.503082i
$711$		0			0
$712$	−3.33369	−	14.6059i	−0.124935	−	0.547378i
$713$		−	0.886046i		−	0.0331827i
$714$		0			0
$715$	6.66424	+	5.31456i	0.249229	+	0.198753i
$716$	4.79074	−	20.9896i	0.179038	−	0.784418i
$717$		0			0
$718$	22.3152	+	27.9824i	0.832797	+	1.04429i
$719$	41.6772	+	20.0707i	1.55430	+	0.748511i	0.996667	−	0.0815773i	$-0.0259958\pi$
$719$	41.6772	+	20.0707i	1.55430	+	0.748511i	0.557632	+	0.830088i	$0.311710\pi$
$720$		0			0
$721$	−0.445413	+	0.558531i	−0.0165881	+	0.0208008i
$722$	0.886461	−	0.706929i	0.0329907	−	0.0263092i
$723$		0			0
$724$	58.3566			2.16881
$725$	6.36290	−	3.91870i	0.236312	−	0.145537i
$726$		0			0
$727$	−9.14331	−	18.9863i	−0.339107	−	0.704162i	0.659774	−	0.751464i	$-0.270652\pi$
$727$	−9.14331	−	18.9863i	−0.339107	−	0.704162i	−0.998881	+	0.0473020i	$0.984938\pi$
$728$	46.6242	−	37.1816i	1.72801	−	1.37804i
$729$		0			0
$730$	−3.89624	+	1.87633i	−0.144206	+	0.0694461i
$731$	−27.0351	−	13.0194i	−0.999928	−	0.481540i
$732$		0			0
$733$	30.5332	+	6.96900i	1.12777	+	0.257406i	0.745409	−	0.666607i	$-0.232254\pi$
$733$	30.5332	+	6.96900i	1.12777	+	0.257406i	0.382360	+	0.924013i	$0.375111\pi$
$734$	−17.2205	+	75.4477i	−0.635619	+	2.78483i
$735$		0			0
$736$	0.726850	−	0.165899i	0.0267920	−	0.00611511i
$737$		−	10.7152i		−	0.394698i
$738$		0			0
$739$	20.2629	−	42.0764i	0.745383	−	1.54780i	−0.0886328	−	0.996064i	$-0.528250\pi$
$739$	20.2629	−	42.0764i	0.745383	−	1.54780i	0.834016	−	0.551740i	$-0.186036\pi$
$740$	−27.1824	+	56.4448i	−0.999245	+	2.07495i
$741$		0			0
$742$			3.69963i			0.135818i
$743$	7.43840	−	1.69777i	0.272889	−	0.0622850i	−0.0838866	−	0.996475i	$-0.526733\pi$
$743$	7.43840	−	1.69777i	0.272889	−	0.0622850i	0.356775	+	0.934190i	$0.383876\pi$
$744$		0			0
$745$	6.56515	−	28.7638i	0.240529	−	1.05382i
$746$	7.36652	+	1.68136i	0.269707	+	0.0615590i
$747$		0			0
$748$	16.9606	+	8.16778i	0.620140	+	0.298643i
$749$	7.93267	−	3.82017i	0.289854	−	0.139586i
$750$		0			0
$751$	−41.1510	+	32.8168i	−1.50162	+	1.19750i	−0.576923	+	0.816799i	$0.695747\pi$
$751$	−41.1510	+	32.8168i	−1.50162	+	1.19750i	−0.924697	+	0.380703i	$0.875682\pi$
$752$	−0.366134	−	0.760285i	−0.0133515	−	0.0277247i
$753$		0			0
$754$	−64.1366	+	21.7969i	−2.33572	+	0.793796i
$755$	−12.5165			−0.455522
$756$		0			0
$757$	13.7753	−	10.9854i	0.500671	−	0.399272i	−0.340329	−	0.940306i	$-0.610539\pi$
$757$	13.7753	−	10.9854i	0.500671	−	0.399272i	0.841000	+	0.541034i	$0.181967\pi$
$758$	−37.5255	+	47.0555i	−1.36299	+	1.70913i
$759$		0			0
$760$	24.3169	+	11.7104i	0.882068	+	0.424782i
$761$	0.853678	+	1.07048i	0.0309458	+	0.0388048i	0.797064	−	0.603895i	$-0.206386\pi$
$761$	0.853678	+	1.07048i	0.0309458	+	0.0388048i	−0.766118	+	0.642700i	$0.777814\pi$
$762$		0			0
$763$	0.876929	−	3.84208i	0.0317469	−	0.139092i
$764$	43.5436	+	34.7249i	1.57535	+	1.25630i
$765$		0			0
$766$			68.6826i			2.48160i
$767$	−13.9815	−	61.2568i	−0.504842	−	2.21186i
$768$		0			0
$769$	−6.94776	+	14.4272i	−0.250543	+	0.520257i	−0.987871	−	0.155278i	$-0.950373\pi$
$769$	−6.94776	+	14.4272i	−0.250543	+	0.520257i	0.737328	+	0.675535i	$0.236087\pi$
$770$	2.77789	+	12.1707i	0.100108	+	0.438602i
$771$		0			0
$772$	41.2781	−	9.42146i	1.48563	−	0.339086i
$773$	−26.5907	−	21.2053i	−0.956399	−	0.762703i	0.0150656	−	0.999887i	$-0.495204\pi$
$773$	−26.5907	−	21.2053i	−0.956399	−	0.762703i	−0.971465	+	0.237184i	$0.923776\pi$
$774$		0			0
$775$	7.75712	+	1.77051i	0.278644	+	0.0635987i
$776$	20.0846	+	25.1853i	0.720995	+	0.904099i
$777$		0			0
$778$	24.3771	−	11.7394i	0.873963	−	0.420878i
$779$	−14.9600	+	18.7592i	−0.535996	+	0.672118i
$780$		0			0
$781$	1.21099	+	2.51464i	0.0433325	+	0.0899809i
$782$	2.40961			0.0861675
$783$		0			0
$784$	3.25768			0.116346
$785$	8.30143	+	17.2381i	0.296291	+	0.615254i
$786$		0			0
$787$	−31.1762	+	39.0937i	−1.11131	+	1.39354i	−0.201014	+	0.979588i	$0.564424\pi$
$787$	−31.1762	+	39.0937i	−1.11131	+	1.39354i	−0.910298	+	0.413953i	$0.864148\pi$
$788$	43.1556	−	20.7826i	1.53735	−	0.740350i
$789$		0			0
$790$	13.3865	+	16.7861i	0.476270	+	0.597224i
$791$	14.5028	+	3.31017i	0.515660	+	0.117696i
$792$		0			0
$793$	47.5444	+	37.9154i	1.68835	+	1.34641i
$794$	48.7838	−	11.1346i	1.73127	−	0.395152i
$795$		0			0
$796$	9.73433	+	42.6489i	0.345024	+	1.51165i
$797$	−9.48100	+	19.6875i	−0.335834	+	0.697367i	−0.998679	−	0.0513901i	$-0.983635\pi$
$797$	−9.48100	+	19.6875i	−0.335834	+	0.697367i	0.662844	+	0.748757i	$0.269349\pi$
$798$		0			0
$799$	1.81990	+	7.97349i	0.0643833	+	0.282082i
$800$			6.69490i			0.236700i
$801$		0			0
$802$	−36.2986	−	28.9472i	−1.28175	−	1.02216i
$803$	0.180516	−	0.790891i	0.00637026	−	0.0279099i
$804$		0			0
$805$	0.626344	+	0.785411i	0.0220757	+	0.0276821i
$806$	−64.9823	−	31.2938i	−2.28891	−	1.10228i
$807$		0			0
$808$	−30.4495	+	38.1825i	−1.07121	+	1.34325i
$809$	−3.61100	+	2.87968i	−0.126956	+	0.101244i	−0.684909	−	0.728628i	$-0.740158\pi$
$809$	−3.61100	+	2.87968i	−0.126956	+	0.101244i	0.557953	+	0.829872i	$0.311587\pi$
$810$		0			0
$811$	−5.86604			−0.205985			−0.102992	−	0.994682i	$-0.532842\pi$
$811$	−5.86604			−0.205985			−0.102992	+	0.994682i	$0.532842\pi$
$812$	−58.6816	−	21.1279i	−2.05932	−	0.741443i
$813$		0			0
$814$	−8.11096	−	16.8426i	−0.284289	−	0.590332i
$815$	−2.19691	+	1.75198i	−0.0769544	+	0.0613691i
$816$		0			0
$817$	17.7631	−	8.55424i	0.621451	−	0.299275i
$818$	59.5135	+	28.6602i	2.08084	+	1.00208i
$819$		0			0
$820$	−34.1013	−	7.78341i	−1.19087	−	0.271808i
$821$	2.65143	−	11.6167i	0.0925354	−	0.405424i	−0.907353	−	0.420370i	$-0.861900\pi$
$821$	2.65143	−	11.6167i	0.0925354	−	0.405424i	0.999888	+	0.0149456i	$0.00475750\pi$
$822$		0			0
$823$	9.13650	−	2.08535i	0.318478	−	0.0726906i	−0.0602935	−	0.998181i	$-0.519204\pi$
$823$	9.13650	−	2.08535i	0.318478	−	0.0726906i	0.378772	+	0.925490i	$0.376347\pi$
$824$		−	0.671850i		−	0.0234050i
$825$		0			0
$826$	39.9265	−	82.9083i	1.38922	−	2.88475i
$827$	−16.9637	+	35.2256i	−0.589887	+	1.22491i	0.365845	+	0.930676i	$0.380780\pi$
$827$	−16.9637	+	35.2256i	−0.589887	+	1.22491i	−0.955732	+	0.294238i	$0.904934\pi$
$828$		0			0
$829$			6.57154i			0.228239i	0.993467	+	0.114119i	$0.0364047\pi$
$829$			6.57154i			0.228239i	−0.993467	+	0.114119i	$0.963595\pi$
$830$	33.2340	−	7.58544i	1.15357	−	0.263294i
$831$		0			0
$832$	15.1765	−	66.4928i	0.526152	−	2.30522i
$833$	−30.7816	−	7.02569i	−1.06652	−	0.243426i
$834$		0			0
$835$	−21.3639	−	10.2883i	−0.739327	−	0.356041i
$836$	−11.1437	+	5.36654i	−0.385414	+	0.185606i
$837$		0			0
$838$	−20.0842	+	16.0166i	−0.693798	+	0.553285i
$839$	−8.06762	−	16.7526i	−0.278525	−	0.578363i	0.714036	−	0.700109i	$-0.246865\pi$
$839$	−8.06762	−	16.7526i	−0.278525	−	0.578363i	−0.992561	+	0.121745i	$0.961151\pi$
$840$		0			0
$841$	22.3442	+	18.4861i	0.770490	+	0.637452i
$842$	62.1291			2.14111
$843$		0			0
$844$	−36.3979	+	29.0264i	−1.25287	+	0.999130i
$845$	19.4074	−	24.3361i	0.667634	−	0.837187i
$846$		0			0
$847$	31.7885	+	15.3085i	1.09227	+	0.526008i
$848$	−0.201449	−	0.252609i	−0.00691779	−	0.00867463i
$849$		0			0
$850$	−4.81492	+	21.0956i	−0.165151	+	0.723572i
$851$	−1.17612	−	0.937925i	−0.0403169	−	0.0321517i
$852$		0			0
$853$		−	15.0581i		−	0.515578i	−0.966201	−	0.257789i	$-0.917006\pi$
$853$		−	15.0581i		−	0.515578i	0.966201	−	0.257789i	$-0.0829939\pi$
$854$	19.8181	+	86.8290i	0.678163	+	2.97123i
$855$		0			0
$856$	−3.59270	+	7.46032i	−0.122796	+	0.254989i
$857$	1.46838	+	6.43339i	0.0501589	+	0.219760i	0.993795	−	0.111223i	$-0.0354767\pi$
$857$	1.46838	+	6.43339i	0.0501589	+	0.219760i	−0.943637	+	0.330983i	$0.892620\pi$
$858$		0			0
$859$	−10.3600	+	2.36460i	−0.353479	+	0.0806792i	−0.395573	−	0.918434i	$-0.629454\pi$
$859$	−10.3600	+	2.36460i	−0.353479	+	0.0806792i	0.0420946	+	0.999114i	$0.486597\pi$
$860$	22.4708	+	17.9199i	0.766249	+	0.611063i
$861$		0			0
$862$	74.9709	+	17.1116i	2.55352	+	0.582824i
$863$	25.7393	+	32.2760i	0.876175	+	1.09869i	0.994398	+	0.105701i	$0.0337088\pi$
$863$	25.7393	+	32.2760i	0.876175	+	1.09869i	−0.118223	+	0.992987i	$0.537720\pi$
$864$		0			0
$865$	−4.52961	+	2.18135i	−0.154011	+	0.0741680i
$866$	−7.69907	+	9.65433i	−0.261625	+	0.328067i
$867$		0			0
$868$	−28.8130	−	59.8308i	−0.977977	−	2.03079i
$869$	−4.02759			−0.136627
$870$		0			0
$871$	−70.1888			−2.37826
$872$	1.60807	+	3.33919i	0.0544561	+	0.113079i
$873$		0			0
$874$	−0.987113	+	1.23780i	−0.0333896	+	0.0418692i
$875$	−37.4130	+	18.0172i	−1.26479	+	0.609092i
$876$		0			0
$877$	15.2676	+	19.1450i	0.515550	+	0.646479i	0.969657	−	0.244468i	$-0.0786132\pi$
$877$	15.2676	+	19.1450i	0.515550	+	0.646479i	−0.454107	+	0.890947i	$0.650042\pi$
$878$	−70.4880	−	16.0884i	−2.37886	−	0.542958i
$879$		0			0
$880$	−0.852383	−	0.679752i	−0.0287338	−	0.0229144i
$881$	−12.0649	+	2.75373i	−0.406476	+	0.0927755i	−0.420870	−	0.907121i	$-0.638275\pi$
$881$	−12.0649	+	2.75373i	−0.406476	+	0.0927755i	0.0143941	+	0.999896i	$0.495418\pi$
$882$		0			0
$883$	6.42165	+	28.1351i	0.216106	+	0.946822i	0.960324	+	0.278885i	$0.0899650\pi$
$883$	6.42165	+	28.1351i	0.216106	+	0.946822i	−0.744218	+	0.667936i	$0.767178\pi$
$884$	53.5023	−	111.099i	1.79948	−	3.73666i
$885$		0			0
$886$	−6.66304	−	29.1927i	−0.223849	−	0.980747i
$887$			46.9153i			1.57526i	0.616147	+	0.787631i	$0.288693\pi$
$887$			46.9153i			1.57526i	−0.616147	+	0.787631i	$0.711307\pi$
$888$		0			0
$889$	−1.04168	−	0.830714i	−0.0349369	−	0.0278613i
$890$	4.57130	−	20.0282i	0.153230	−	0.671346i
$891$		0			0
$892$	28.4985	+	35.7360i	0.954201	+	1.19653i
$893$	−4.84146	−	2.33152i	−0.162013	−	0.0780215i
$894$		0			0
$895$	7.53462	−	9.44812i	0.251855	−	0.315816i
$896$	52.2911	−	41.7007i	1.74692	−	1.39312i
$897$		0			0
$898$	−78.5600			−2.62158
$899$	3.18108	+	30.7133i	0.106095	+	1.02434i
$900$		0			0
$901$	1.35868	+	2.82134i	0.0452643	+	0.0939924i
$902$	8.16013	−	6.50748i	0.271703	−	0.216676i
$903$		0			0
$904$	−12.6045	+	6.07003i	−0.419221	+	0.201886i
$905$	29.5121	+	14.2123i	0.981016	+	0.472432i
$906$		0			0
$907$	20.6912	+	4.72262i	0.687039	+	0.156812i	0.551769	−	0.833997i	$-0.313953\pi$
$907$	20.6912	+	4.72262i	0.687039	+	0.156812i	0.135270	+	0.990809i	$0.456810\pi$
$908$	20.3215	−	89.0345i	0.674394	−	2.95471i
$909$		0			0
$910$	79.7233	−	18.1963i	2.64280	−	0.603202i
$911$		−	46.1944i		−	1.53049i	−0.643739	−	0.765245i	$-0.722618\pi$
$911$		−	46.1944i		−	1.53049i	0.643739	−	0.765245i	$-0.277382\pi$
$912$		0			0
$913$	−2.77454	+	5.76139i	−0.0918239	+	0.190674i
$914$	7.68796	−	15.9642i	0.254295	−	0.528049i
$915$		0			0
$916$			36.9660i			1.22139i
$917$	−2.53568	+	0.578752i	−0.0837354	+	0.0191121i
$918$		0			0
$919$	11.0939	−	48.6055i	0.365954	−	1.60335i	−0.371824	−	0.928303i	$-0.621267\pi$
$919$	11.0939	−	48.6055i	0.365954	−	1.60335i	0.737777	−	0.675044i	$-0.235876\pi$
$920$	−0.921074	−	0.210229i	−0.0303669	−	0.00693105i
$921$		0			0
$922$	−35.4717	−	17.0823i	−1.16820	−	0.562575i
$923$	16.4719	−	7.93247i	0.542180	−	0.261100i
$924$		0			0
$925$	10.5614	−	8.42247i	0.347258	−	0.276929i
$926$	9.38137	+	19.4806i	0.308291	+	0.640173i
$927$		0			0
$928$	−24.5994	+	8.36013i	−0.807514	+	0.274435i
$929$	−16.6870			−0.547484			−0.273742	−	0.961803i	$-0.588261\pi$
$929$	−16.6870			−0.547484			−0.273742	+	0.961803i	$0.588261\pi$
$930$		0			0
$931$	16.2189	−	12.9342i	0.531554	−	0.423900i
$932$	−11.5757	+	14.5154i	−0.379174	+	0.475469i
$933$		0			0
$934$	−53.0103	−	25.5284i	−1.73455	−	0.835315i
$935$	6.58810	+	8.26122i	0.215454	+	0.270171i
$936$		0			0
$937$	5.03903	−	22.0775i	0.164618	−	0.721239i	−0.823471	−	0.567358i	$-0.807966\pi$
$937$	5.03903	−	22.0775i	0.164618	−	0.721239i	0.988089	−	0.153881i	$-0.0491772\pi$
$938$	−80.3687	−	64.0919i	−2.62413	−	2.09268i
$939$		0			0
$940$		−	7.83366i		−	0.255506i
$941$	−0.897147	−	3.93066i	−0.0292461	−	0.128136i	0.958197	−	0.286108i	$-0.0923615\pi$
$941$	−0.897147	−	3.93066i	−0.0292461	−	0.128136i	−0.987444	+	0.157972i	$0.949504\pi$
$942$		0			0
$943$	0.364416	−	0.756717i	0.0118670	−	0.0246421i
$944$	1.78828	+	7.83499i	0.0582037	+	0.255007i
$945$		0			0
$946$	−8.36110	+	1.90837i	−0.271843	+	0.0620463i
$947$	−22.0167	−	17.5577i	−0.715446	−	0.570549i	0.196676	−	0.980469i	$-0.436985\pi$
$947$	−22.0167	−	17.5577i	−0.715446	−	0.570549i	−0.912122	+	0.409919i	$0.865557\pi$
$948$		0			0
$949$	−5.18066	−	1.18245i	−0.168171	−	0.0383840i
$950$	−8.86418	−	11.1153i	−0.287592	−	0.360629i
$951$		0			0
$952$	66.6042	−	32.0749i	2.15865	−	1.03955i
$953$	−20.2660	+	25.4128i	−0.656482	+	0.823202i	−0.992955	−	0.118491i	$-0.962194\pi$
$953$	−20.2660	+	25.4128i	−0.656482	+	0.823202i	0.336473	+	0.941693i	$0.390766\pi$
$954$		0			0
$955$	13.5639	+	28.1658i	0.438918	+	0.911423i
$956$	−2.57620			−0.0833202
$957$		0			0
$958$	−53.4355			−1.72642
$959$	−22.1617	−	46.0192i	−0.715639	−	1.48604i
$960$		0			0
$961$	−1.17010	+	1.46726i	−0.0377451	+	0.0473309i
$962$	−110.326	+	53.1302i	−3.55705	+	1.71299i
$963$		0			0
$964$	−52.8514	−	66.2736i	−1.70223	−	2.13453i
$965$	23.1697	+	5.28833i	0.745859	+	0.170237i
$966$		0			0
$967$	1.03303	+	0.823813i	0.0332200	+	0.0264920i	0.639959	−	0.768409i	$-0.278951\pi$
$967$	1.03303	+	0.823813i	0.0332200	+	0.0264920i	−0.606739	+	0.794901i	$0.707523\pi$
$968$	−32.3498	+	7.38363i	−1.03976	+	0.237319i
$969$		0			0
$970$	9.82922	+	43.0646i	0.315597	+	1.38272i
$971$	17.1222	−	35.5546i	0.549478	−	1.14100i	−0.422594	−	0.906319i	$-0.638880\pi$
$971$	17.1222	−	35.5546i	0.549478	−	1.14100i	0.972072	−	0.234684i	$-0.0754054\pi$
$972$		0			0
$973$	2.78537	+	12.2035i	0.0892949	+	0.391227i
$974$			3.56066i			0.114091i
$975$		0			0
$976$	−6.08111	−	4.84952i	−0.194652	−	0.155229i
$977$	4.16227	−	18.2361i	0.133163	−	0.583424i	−0.863681	−	0.504038i	$-0.831847\pi$
$977$	4.16227	−	18.2361i	0.133163	−	0.583424i	0.996844	−	0.0793858i	$-0.0252959\pi$
$978$		0			0
$979$	2.40274	+	3.01294i	0.0767918	+	0.0962939i
$980$	27.2469	+	13.1214i	0.870370	+	0.419148i
$981$		0			0
$982$	29.1565	−	36.5610i	0.930420	−	1.16671i
$983$	6.29633	−	5.02115i	0.200822	−	0.160150i	−0.517916	−	0.855432i	$-0.673292\pi$
$983$	6.29633	−	5.02115i	0.200822	−	0.160150i	0.718737	+	0.695282i	$0.244720\pi$
$984$		0			0
$985$	26.8861			0.856662
$986$	−83.5250	+	8.65098i	−2.65998	+	0.275503i
$987$		0			0
$988$	35.1531	+	72.9961i	1.11837	+	2.32231i
$989$	−0.539565	+	0.430289i	−0.0171572	+	0.0136824i
$990$		0			0
$991$	−54.5016	+	26.2466i	−1.73130	+	0.833751i	−0.745359	+	0.666663i	$0.767722\pi$
$991$	−54.5016	+	26.2466i	−1.73130	+	0.833751i	−0.985942	+	0.167087i	$0.946564\pi$
$992$	−24.9238	−	12.0027i	−0.791330	−	0.381085i
$993$		0			0
$994$	26.1044	+	5.95816i	0.827981	+	0.188981i
$995$	−5.46394	+	23.9391i	−0.173219	+	0.758921i
$996$		0			0
$997$	2.89082	−	0.659811i	0.0915532	−	0.0208964i	−0.176499	−	0.984301i	$-0.556477\pi$
$997$	2.89082	−	0.659811i	0.0915532	−	0.0208964i	0.268052	+	0.963404i	$0.413620\pi$
$998$		−	80.5446i		−	2.54960i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.o.b.154.1		24
3.2	odd	2		87.2.i.a.67.4	yes	24
29.10	odd	28		7569.2.a.bn.1.2		12
29.13	even	14	inner	261.2.o.b.100.1		24
29.19	odd	28		7569.2.a.bt.1.11		12
87.68	even	28		2523.2.a.v.1.11		12
87.71	odd	14		87.2.i.a.13.4	✓	24
87.77	even	28		2523.2.a.s.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.i.a.13.4	✓	24	87.71	odd	14
87.2.i.a.67.4	yes	24	3.2	odd	2
261.2.o.b.100.1		24	29.13	even	14	inner
261.2.o.b.154.1		24	1.1	even	1	trivial
2523.2.a.s.1.2		12	87.77	even	28
2523.2.a.v.1.11		12	87.68	even	28
7569.2.a.bn.1.2		12	29.10	odd	28
7569.2.a.bt.1.11		12	29.19	odd	28

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.o (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00695 - 2.09096i) q^{2} +(-2.11117 + 2.64732i) q^{4} +(-1.71239 + 0.824646i) q^{5} +(-2.13259 - 2.67418i) q^{7} +(3.13608 + 0.715791i) q^{8} +(3.44860 + 2.75017i) q^{10} +(-0.806696 + 0.184123i) q^{11} +(1.20608 + 5.28419i) q^{13} +(-3.44418 + 7.15191i) q^{14} +(-0.154263 - 0.675869i) q^{16} +6.71892i q^{17} +(-3.45146 - 2.75245i) q^{19} +(1.43205 - 6.27423i) q^{20} +(1.19730 + 1.50136i) q^{22} +(0.139227 + 0.0670480i) q^{23} +(-0.865194 + 1.08492i) q^{25} +(9.83456 - 7.84280i) q^{26} +11.5817 q^{28} +(-5.06676 - 1.82425i) q^{29} +(-2.48781 - 5.16599i) q^{31} +(3.77201 - 3.00808i) q^{32} +(14.0490 - 6.76563i) q^{34} +(5.85708 + 2.82062i) q^{35} +(-9.49071 - 2.16619i) q^{37} +(-2.27980 + 9.98844i) q^{38} +(-5.96049 + 1.36044i) q^{40} -5.43514i q^{41} +(-1.93772 + 4.02372i) q^{43} +(1.21564 - 2.52430i) q^{44} -0.358631i q^{46} +(1.18672 - 0.270862i) q^{47} +(-1.04566 + 4.58133i) q^{49} +(3.13973 + 0.716622i) q^{50} +(-16.5352 - 7.96294i) q^{52} +(0.419909 - 0.202218i) q^{53} +(1.22955 - 0.980530i) q^{55} +(-4.77382 - 9.91293i) q^{56} +(1.28756 + 12.4313i) q^{58} -11.5925 q^{59} +(8.77189 - 6.99535i) q^{61} +(-8.29676 + 10.4038i) q^{62} +(-11.3372 - 5.45970i) q^{64} +(-6.42288 - 8.05404i) q^{65} +(-2.88159 + 12.6251i) q^{67} +(-17.7871 - 14.1848i) q^{68} -15.0871i q^{70} +(-0.750585 - 3.28853i) q^{71} +(-0.425383 + 0.883317i) q^{73} +(5.02727 + 22.0259i) q^{74} +(14.5732 - 3.32625i) q^{76} +(2.21273 + 1.76459i) q^{77} +(4.74548 + 1.08313i) q^{79} +(0.821511 + 1.03014i) q^{80} +(-11.3647 + 5.47293i) q^{82} +(4.81847 - 6.04218i) q^{83} +(-5.54073 - 11.5054i) q^{85} +10.3646 q^{86} -2.66166 q^{88} +(-2.02075 - 4.19613i) q^{89} +(11.5588 - 14.4943i) q^{91} +(-0.471429 + 0.227028i) q^{92} +(-1.76133 - 2.20864i) q^{94} +(8.18006 + 1.86705i) q^{95} +(7.82946 + 6.24379i) q^{97} +(10.6323 - 2.42675i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} + 4 q^{5} + 8 q^{7} + 28 q^{11} - 10 q^{13} - 22 q^{16} + 20 q^{20} + 4 q^{22} - 18 q^{23} - 18 q^{25} - 28 q^{26} + 8 q^{28} - 28 q^{29} + 28 q^{31} + 14 q^{32} + 34 q^{34} - 28 q^{37} + 4 q^{38}+ \cdots + 42 q^{98}+O(q^{100}) \) 24 * q - 2 * q^4 + 4 * q^5 + 8 * q^7 + 28 * q^11 - 10 * q^13 - 22 * q^16 + 20 * q^20 + 4 * q^22 - 18 * q^23 - 18 * q^25 - 28 * q^26 + 8 * q^28 - 28 * q^29 + 28 * q^31 + 14 * q^32 + 34 * q^34 - 28 * q^37 + 4 * q^38 - 14 * q^43 - 14 * q^44 + 20 * q^49 - 42 * q^50 - 68 * q^52 - 6 * q^53 - 14 * q^55 + 50 * q^58 - 28 * q^59 + 8 * q^62 - 20 * q^64 - 18 * q^65 + 8 * q^67 - 14 * q^68 + 42 * q^71 - 84 * q^73 - 10 * q^74 - 14 * q^76 + 70 * q^77 - 14 * q^79 - 36 * q^80 - 50 * q^82 + 32 * q^83 + 14 * q^85 + 128 * q^86 - 20 * q^88 + 14 * q^89 + 34 * q^91 + 58 * q^92 - 44 * q^94 + 56 * q^97 + 42 * q^98

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