LMFDB - Embedded newform 1323.2.s.d.656.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(656,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("1323.656");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.s (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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			656.16
Character	$\chi$	$=$	1323.656
Dual form			1323.2.s.d.962.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.575298 - 0.332148i) q^{2} +(-0.779355 + 1.34988i) q^{4} -0.0283039 q^{5} +2.36404i q^{8} +O(q^{10})$	\(q+(0.575298 - 0.332148i) q^{2} +(-0.779355 + 1.34988i) q^{4} -0.0283039 q^{5} +2.36404i q^{8} +(-0.0162832 + 0.00940110i) q^{10} -1.02228i q^{11} +(4.87844 - 2.81657i) q^{13} +(-0.773498 - 1.33974i) q^{16} +(2.83940 + 4.91798i) q^{17} +(-1.81237 - 1.04637i) q^{19} +(0.0220588 - 0.0382070i) q^{20} +(-0.339550 - 0.588118i) q^{22} +7.26133i q^{23} -4.99920 q^{25} +(1.87104 - 3.24073i) q^{26} +(3.52577 + 2.03560i) q^{29} +(2.87364 + 1.65910i) q^{31} +(-4.98462 - 2.87787i) q^{32} +(3.26700 + 1.88620i) q^{34} +(1.23632 - 2.14137i) q^{37} -1.39020 q^{38} -0.0669116i q^{40} +(3.52867 + 6.11183i) q^{41} +(-1.15994 + 2.00908i) q^{43} +(1.37996 + 0.796722i) q^{44} +(2.41184 + 4.17742i) q^{46} +(5.43997 + 9.42231i) q^{47} +(-2.87603 + 1.66048i) q^{50} +8.78043i q^{52} +(-10.0454 + 5.79973i) q^{53} +0.0289346i q^{55} +2.70449 q^{58} +(-3.01111 + 5.21540i) q^{59} +(2.05220 - 1.18484i) q^{61} +2.20427 q^{62} -0.729528 q^{64} +(-0.138079 + 0.0797200i) q^{65} +(-6.38995 + 11.0677i) q^{67} -8.85160 q^{68} -7.93415i q^{71} +(9.43889 - 5.44955i) q^{73} -1.64257i q^{74} +(2.82496 - 1.63099i) q^{76} +(7.80018 + 13.5103i) q^{79} +(0.0218930 + 0.0379198i) q^{80} +(4.06007 + 2.34408i) q^{82} +(3.07406 - 5.32442i) q^{83} +(-0.0803661 - 0.139198i) q^{85} +1.54109i q^{86} +2.41672 q^{88} +(6.02582 - 10.4370i) q^{89} +(-9.80194 - 5.65915i) q^{92} +(6.25921 + 3.61376i) q^{94} +(0.0512971 + 0.0296164i) q^{95} +(-6.77565 - 3.91192i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.575298	−	0.332148i	0.406797	−	0.234864i	−0.282616	−	0.959233i	$-0.591202\pi$
$2$	0.575298	−	0.332148i	0.406797	−	0.234864i	0.689413	+	0.724369i	$0.257869\pi$
$3$		0			0
$3$		0			0
$4$	−0.779355	+	1.34988i	−0.389677	+	0.674941i
$5$	−0.0283039			−0.0126579			−0.00632895	−	0.999980i	$-0.502015\pi$
$5$	−0.0283039			−0.0126579			−0.00632895	+	0.999980i	$0.502015\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			2.36404i			0.835814i
$9$		0			0
$10$	−0.0162832	+	0.00940110i	−0.00514919	+	0.00297289i
$11$		−	1.02228i		−	0.308230i	−0.988053	−	0.154115i	$-0.950747\pi$
$11$		−	1.02228i		−	0.308230i	0.988053	−	0.154115i	$-0.0492526\pi$
$12$		0			0
$13$	4.87844	−	2.81657i	1.35304	−	0.781176i	0.364363	−	0.931257i	$-0.381287\pi$
$13$	4.87844	−	2.81657i	1.35304	−	0.781176i	0.988674	+	0.150081i	$0.0479534\pi$
$14$		0			0
$15$		0			0
$16$	−0.773498	−	1.33974i	−0.193375	−	0.334935i
$17$	2.83940	+	4.91798i	0.688656	+	1.19279i	0.972273	+	0.233849i	$0.0751321\pi$
$17$	2.83940	+	4.91798i	0.688656	+	1.19279i	−0.283617	+	0.958938i	$0.591535\pi$
$18$		0			0
$19$	−1.81237	−	1.04637i	−0.415786	−	0.240054i	0.277487	−	0.960729i	$-0.410498\pi$
$19$	−1.81237	−	1.04637i	−0.415786	−	0.240054i	−0.693273	+	0.720675i	$0.743832\pi$
$20$	0.0220588	−	0.0382070i	0.00493250	−	0.00854334i
$21$		0			0
$22$	−0.339550	−	0.588118i	−0.0723923	−	0.125387i
$23$			7.26133i			1.51409i	0.653362	+	0.757046i	$0.273358\pi$
$23$			7.26133i			1.51409i	−0.653362	+	0.757046i	$0.726642\pi$
$24$		0			0
$25$	−4.99920			−0.999840
$26$	1.87104	−	3.24073i	0.366941	−	0.635560i
$27$		0			0
$28$		0			0
$29$	3.52577	+	2.03560i	0.654718	+	0.378002i	0.790262	−	0.612770i	$-0.209945\pi$
$29$	3.52577	+	2.03560i	0.654718	+	0.378002i	−0.135543	+	0.990771i	$0.543278\pi$
$30$		0			0
$31$	2.87364	+	1.65910i	0.516122	+	0.297983i	0.735346	−	0.677691i	$-0.237019\pi$
$31$	2.87364	+	1.65910i	0.516122	+	0.297983i	−0.219225	+	0.975674i	$0.570353\pi$
$32$	−4.98462	−	2.87787i	−0.881165	−	0.508741i
$33$		0			0
$34$	3.26700	+	1.88620i	0.560286	+	0.323481i
$35$		0			0
$36$		0			0
$37$	1.23632	−	2.14137i	0.203250	−	0.352040i	−0.746324	−	0.665583i	$-0.768183\pi$
$37$	1.23632	−	2.14137i	0.203250	−	0.352040i	0.949574	+	0.313543i	$0.101516\pi$
$38$	−1.39020			−0.225520
$39$		0			0
$40$		−	0.0669116i		−	0.0105796i
$41$	3.52867	+	6.11183i	0.551085	+	0.954508i	0.998197	+	0.0600295i	$0.0191195\pi$
$41$	3.52867	+	6.11183i	0.551085	+	0.954508i	−0.447111	+	0.894478i	$0.647547\pi$
$42$		0			0
$43$	−1.15994	+	2.00908i	−0.176890	+	0.306382i	−0.940814	−	0.338924i	$-0.889937\pi$
$43$	−1.15994	+	2.00908i	−0.176890	+	0.306382i	0.763924	+	0.645306i	$0.223270\pi$
$44$	1.37996	+	0.796722i	0.208037	+	0.120110i
$45$		0			0
$46$	2.41184	+	4.17742i	0.355606	+	0.615928i
$47$	5.43997	+	9.42231i	0.793502	+	1.37439i	0.923786	+	0.382908i	$0.125078\pi$
$47$	5.43997	+	9.42231i	0.793502	+	1.37439i	−0.130285	+	0.991477i	$0.541589\pi$
$48$		0			0
$49$		0			0
$50$	−2.87603	+	1.66048i	−0.406732	+	0.234827i
$51$		0			0
$52$			8.78043i			1.21763i
$53$	−10.0454	+	5.79973i	−1.37985	+	0.796655i	−0.992141	−	0.125128i	$-0.960066\pi$
$53$	−10.0454	+	5.79973i	−1.37985	+	0.796655i	−0.387706	+	0.921783i	$0.626732\pi$
$54$		0			0
$55$			0.0289346i			0.00390155i
$56$		0			0
$57$		0			0
$58$	2.70449			0.355117
$59$	−3.01111	+	5.21540i	−0.392013	+	0.678987i	−0.992715	−	0.120486i	$-0.961555\pi$
$59$	−3.01111	+	5.21540i	−0.392013	+	0.678987i	0.600702	+	0.799473i	$0.294888\pi$
$60$		0			0
$61$	2.05220	−	1.18484i	0.262757	−	0.151703i	−0.362834	−	0.931854i	$-0.618191\pi$
$61$	2.05220	−	1.18484i	0.262757	−	0.151703i	0.625592	+	0.780151i	$0.284858\pi$
$62$	2.20427			0.279942
$63$		0			0
$64$	−0.729528			−0.0911909
$65$	−0.138079	+	0.0797200i	−0.0171266	+	0.00988805i
$66$		0			0
$67$	−6.38995	+	11.0677i	−0.780656	+	1.35214i	0.150903	+	0.988549i	$0.451782\pi$
$67$	−6.38995	+	11.0677i	−0.780656	+	1.35214i	−0.931560	+	0.363588i	$0.881552\pi$
$68$	−8.85160			−1.07341
$69$		0			0
$70$		0			0
$71$		−	7.93415i		−	0.941610i	−0.882237	−	0.470805i	$-0.843964\pi$
$71$		−	7.93415i		−	0.941610i	0.882237	−	0.470805i	$-0.156036\pi$
$72$		0			0
$73$	9.43889	−	5.44955i	1.10474	−	0.637821i	0.167277	−	0.985910i	$-0.446503\pi$
$73$	9.43889	−	5.44955i	1.10474	−	0.637821i	0.937462	+	0.348089i	$0.113169\pi$
$74$		−	1.64257i		−	0.190945i
$75$		0			0
$76$	2.82496	−	1.63099i	0.324045	−	0.187087i
$77$		0			0
$78$		0			0
$79$	7.80018	+	13.5103i	0.877588	+	1.52003i	0.853980	+	0.520306i	$0.174182\pi$
$79$	7.80018	+	13.5103i	0.877588	+	1.52003i	0.0236086	+	0.999721i	$0.492484\pi$
$80$	0.0218930	+	0.0379198i	0.00244772	+	0.00423957i
$81$		0			0
$82$	4.06007	+	2.34408i	0.448360	+	0.258861i
$83$	3.07406	−	5.32442i	0.337421	−	0.584431i	−0.646526	−	0.762892i	$-0.723779\pi$
$83$	3.07406	−	5.32442i	0.337421	−	0.584431i	0.983947	+	0.178461i	$0.0571119\pi$
$84$		0			0
$85$	−0.0803661	−	0.139198i	−0.00871693	−	0.0150982i
$86$			1.54109i			0.166180i
$87$		0			0
$88$	2.41672			0.257623
$89$	6.02582	−	10.4370i	0.638736	−	1.10632i	−0.346975	−	0.937874i	$-0.612791\pi$
$89$	6.02582	−	10.4370i	0.638736	−	1.10632i	0.985711	−	0.168448i	$-0.0538756\pi$
$90$		0			0
$91$		0			0
$92$	−9.80194	−	5.65915i	−1.02192	−	0.590007i
$93$		0			0
$94$	6.25921	+	3.61376i	0.645588	+	0.372730i
$95$	0.0512971	+	0.0296164i	0.00526297	+	0.00303858i
$96$		0			0
$97$	−6.77565	−	3.91192i	−0.687963	−	0.397196i	0.114885	−	0.993379i	$-0.463350\pi$
$97$	−6.77565	−	3.91192i	−0.687963	−	0.397196i	−0.802848	+	0.596183i	$0.796683\pi$
$98$		0			0
$99$		0			0
$100$	3.89615	−	6.74833i	0.389615	−	0.674833i
$101$	0.453847			0.0451595			0.0225797	−	0.999745i	$-0.492812\pi$
$101$	0.453847			0.0451595			0.0225797	+	0.999745i	$0.492812\pi$
$102$		0			0
$103$		−	5.29218i		−	0.521454i	−0.965413	−	0.260727i	$-0.916038\pi$
$103$		−	5.29218i		−	0.521454i	0.965413	−	0.260727i	$-0.0839622\pi$
$104$	6.65848	+	11.5328i	0.652918	+	1.13089i
$105$		0			0
$106$	−3.85274	+	6.67315i	−0.374212	+	0.648153i
$107$	−7.85273	−	4.53377i	−0.759152	−	0.438296i	0.0698394	−	0.997558i	$-0.477751\pi$
$107$	−7.85273	−	4.53377i	−0.759152	−	0.438296i	−0.828991	+	0.559262i	$0.811085\pi$
$108$		0			0
$109$	−2.36514	−	4.09654i	−0.226539	−	0.392377i	0.730241	−	0.683190i	$-0.239408\pi$
$109$	−2.36514	−	4.09654i	−0.226539	−	0.392377i	−0.956780	+	0.290812i	$0.906074\pi$
$110$	0.00961059	+	0.0166460i	0.000916334	+	0.00158714i
$111$		0			0
$112$		0			0
$113$	8.21108	−	4.74067i	0.772433	−	0.445965i	−0.0613086	−	0.998119i	$-0.519527\pi$
$113$	8.21108	−	4.74067i	0.772433	−	0.445965i	0.833742	+	0.552154i	$0.186194\pi$
$114$		0			0
$115$		−	0.205524i		−	0.0191652i
$116$	−5.49565	+	3.17291i	−0.510258	+	0.294598i
$117$		0			0
$118$			4.00054i			0.368280i
$119$		0			0
$120$		0			0
$121$	9.95494			0.904994
$122$	0.787084	−	1.36327i	0.0712593	−	0.123425i
$123$		0			0
$124$	−4.47918	+	2.58606i	−0.402242	+	0.232235i
$125$	0.283017			0.0253138
$126$		0			0
$127$	4.37297			0.388039			0.194019	−	0.980998i	$-0.437848\pi$
$127$	4.37297			0.388039			0.194019	+	0.980998i	$0.437848\pi$
$128$	9.54954	−	5.51343i	0.844068	−	0.487323i
$129$		0			0
$130$	−0.0529577	+	0.0917255i	−0.00464470	+	0.00804486i
$131$	−2.54463			−0.222325			−0.111162	−	0.993802i	$-0.535457\pi$
$131$	−2.54463			−0.222325			−0.111162	+	0.993802i	$0.535457\pi$
$132$		0			0
$133$		0			0
$134$			8.48964i			0.733393i
$135$		0			0
$136$	−11.6263	+	6.71245i	−0.996948	+	0.575588i
$137$		−	11.3453i		−	0.969298i	−0.874709	−	0.484649i	$-0.838947\pi$
$137$		−	11.3453i		−	0.969298i	0.874709	−	0.484649i	$-0.161053\pi$
$138$		0			0
$139$	−3.04891	+	1.76029i	−0.258605	+	0.149306i	−0.623698	−	0.781665i	$-0.714371\pi$
$139$	−3.04891	+	1.76029i	−0.258605	+	0.149306i	0.365093	+	0.930971i	$0.381037\pi$
$140$		0			0
$141$		0			0
$142$	−2.63531	−	4.56450i	−0.221151	−	0.383044i
$143$	−2.87933	−	4.98715i	−0.240782	−	0.417047i
$144$		0			0
$145$	−0.0997930	−	0.0576155i	−0.00828736	−	0.00478471i
$146$	3.62012	−	6.27022i	0.299603	−	0.518927i
$147$		0			0
$148$	1.92707	+	3.33778i	0.158404	+	0.274364i
$149$			15.9125i			1.30360i	0.758391	+	0.651800i	$0.225986\pi$
$149$			15.9125i			1.30360i	−0.758391	+	0.651800i	$0.774014\pi$
$150$		0			0
$151$	3.46016			0.281584			0.140792	−	0.990039i	$-0.455035\pi$
$151$	3.46016			0.281584			0.140792	+	0.990039i	$0.455035\pi$
$152$	2.47366	−	4.28451i	0.200640	−	0.347520i
$153$		0			0
$154$		0			0
$155$	−0.0813354	−	0.0469590i	−0.00653302	−	0.00377184i
$156$		0			0
$157$	−14.1585	−	8.17442i	−1.12997	−	0.652390i	−0.186045	−	0.982541i	$-0.559567\pi$
$157$	−14.1585	−	8.17442i	−1.12997	−	0.652390i	−0.943928	+	0.330151i	$0.892900\pi$
$158$	8.97485	+	5.18163i	0.714001	+	0.412228i
$159$		0			0
$160$	0.141084	+	0.0814550i	0.0111537	+	0.00643959i
$161$		0			0
$162$		0			0
$163$	−5.17782	+	8.96824i	−0.405558	+	0.702447i	−0.994386	−	0.105811i	$-0.966256\pi$
$163$	−5.17782	+	8.96824i	−0.405558	+	0.702447i	0.588828	+	0.808258i	$0.299589\pi$
$164$	−11.0003			−0.858982
$165$		0			0
$166$		−	4.08417i		−	0.316993i
$167$	−2.94297	−	5.09738i	−0.227734	−	0.394447i	0.729402	−	0.684085i	$-0.239798\pi$
$167$	−2.94297	−	5.09738i	−0.227734	−	0.394447i	−0.957136	+	0.289638i	$0.906465\pi$
$168$		0			0
$169$	9.36614	−	16.2226i	0.720473	−	1.24790i
$170$	−0.0924689	−	0.0533870i	−0.00709204	−	0.00409459i
$171$		0			0
$172$	−1.80802	−	3.13157i	−0.137860	−	0.238780i
$173$	2.43276	+	4.21366i	0.184959	+	0.320359i	0.943563	−	0.331194i	$-0.107451\pi$
$173$	2.43276	+	4.21366i	0.184959	+	0.320359i	−0.758604	+	0.651552i	$0.774118\pi$
$174$		0			0
$175$		0			0
$176$	−1.36959	+	0.790735i	−0.103237	+	0.0596039i
$177$		0			0
$178$		−	8.00586i		−	0.600065i
$179$	−0.175495	+	0.101322i	−0.0131171	+	0.00757319i	−0.506544	−	0.862214i	$-0.669077\pi$
$179$	−0.175495	+	0.101322i	−0.0131171	+	0.00757319i	0.493427	+	0.869787i	$0.335744\pi$
$180$		0			0
$181$		−	6.26273i		−	0.465505i	−0.972536	−	0.232753i	$-0.925227\pi$
$181$		−	6.26273i		−	0.465505i	0.972536	−	0.232753i	$-0.0747732\pi$
$182$		0			0
$183$		0			0
$184$	−17.1661			−1.26550
$185$	−0.0349928	+	0.0606093i	−0.00257272	+	0.00445608i
$186$		0			0
$187$	5.02758	−	2.90267i	0.367653	−	0.212264i
$188$	−16.9587			−1.23684
$189$		0			0
$190$	0.0393482			0.00285462
$191$	11.9541	−	6.90168i	0.864965	−	0.499388i	−0.000706698	−	1.00000i	$-0.500225\pi$
$191$	11.9541	−	6.90168i	0.864965	−	0.499388i	0.865672	+	0.500612i	$0.166892\pi$
$192$		0			0
$193$	10.5387	−	18.2536i	0.758593	−	1.31392i	−0.184976	−	0.982743i	$-0.559221\pi$
$193$	10.5387	−	18.2536i	0.758593	−	1.31392i	0.943568	−	0.331178i	$-0.107446\pi$
$194$	−5.19736			−0.373148
$195$		0			0
$196$		0			0
$197$			15.1679i			1.08067i	0.841451	+	0.540334i	$0.181702\pi$
$197$			15.1679i			1.08067i	−0.841451	+	0.540334i	$0.818298\pi$
$198$		0			0
$199$	8.38940	−	4.84362i	0.594709	−	0.343355i	−0.172249	−	0.985054i	$-0.555103\pi$
$199$	8.38940	−	4.84362i	0.594709	−	0.343355i	0.766957	+	0.641698i	$0.221770\pi$
$200$		−	11.8183i		−	0.835680i
$201$		0			0
$202$	0.261097	−	0.150745i	0.0183707	−	0.0106064i
$203$		0			0
$204$		0			0
$205$	−0.0998751	−	0.172989i	−0.00697558	−	0.0120821i
$206$	−1.75779	−	3.04458i	−0.122471	−	0.212126i
$207$		0			0
$208$	−7.54694	−	4.35723i	−0.523286	−	0.302119i
$209$	−1.06969	+	1.85275i	−0.0739919	+	0.128158i
$210$		0			0
$211$	−7.05942	−	12.2273i	−0.485991	−	0.841761i	0.513880	−	0.857862i	$-0.328208\pi$
$211$	−7.05942	−	12.2273i	−0.485991	−	0.841761i	−0.999870	+	0.0161017i	$0.994874\pi$
$212$		−	18.0802i		−	1.24175i
$213$		0			0
$214$	−6.02354			−0.411761
$215$	0.0328309	−	0.0568649i	0.00223905	−	0.00387815i
$216$		0			0
$217$		0			0
$218$	−2.72132	−	1.57115i	−0.184311	−	0.106412i
$219$		0			0
$220$	−0.0390584	−	0.0225504i	−0.00263331	−	0.00152034i
$221$	27.7037	+	15.9947i	1.86355	+	1.07592i
$222$		0			0
$223$	2.58777	+	1.49405i	0.173290	+	0.100049i	0.584136	−	0.811656i	$-0.301433\pi$
$223$	2.58777	+	1.49405i	0.173290	+	0.100049i	−0.410846	+	0.911705i	$0.634767\pi$
$224$		0			0
$225$		0			0
$226$	3.14921	−	5.45459i	0.209482	−	0.362834i
$227$	28.7733			1.90975			0.954876	−	0.297005i	$-0.0959877\pi$
$227$	28.7733			1.90975			0.954876	+	0.297005i	$0.0959877\pi$
$228$		0			0
$229$			8.86119i			0.585564i	0.956179	+	0.292782i	$0.0945810\pi$
$229$			8.86119i			0.585564i	−0.956179	+	0.292782i	$0.905419\pi$
$230$	−0.0682645	−	0.118238i	−0.00450122	−	0.00779635i
$231$		0			0
$232$	−4.81224	+	8.33505i	−0.315939	+	0.547223i
$233$	−11.1789	−	6.45412i	−0.732351	−	0.422823i	0.0869305	−	0.996214i	$-0.472294\pi$
$233$	−11.1789	−	6.45412i	−0.732351	−	0.422823i	−0.819282	+	0.573391i	$0.805628\pi$
$234$		0			0
$235$	−0.153973	−	0.266688i	−0.0100441	−	0.0173968i
$236$	−4.69345	−	8.12929i	−0.305518	−	0.529172i
$237$		0			0
$238$		0			0
$239$	4.85712	−	2.80426i	0.314181	−	0.181392i	−0.334615	−	0.942355i	$-0.608606\pi$
$239$	4.85712	−	2.80426i	0.314181	−	0.181392i	0.648796	+	0.760963i	$0.275273\pi$
$240$		0			0
$241$		−	10.9868i		−	0.707719i	−0.935299	−	0.353860i	$-0.884869\pi$
$241$		−	10.9868i		−	0.707719i	0.935299	−	0.353860i	$-0.115131\pi$
$242$	5.72705	−	3.30652i	0.368149	−	0.212551i
$243$		0			0
$244$			3.69364i			0.236461i
$245$		0			0
$246$		0			0
$247$	−11.7887			−0.750098
$248$	−3.92218	+	6.79341i	−0.249058	+	0.431382i
$249$		0			0
$250$	0.162819	−	0.0940035i	0.0102976	−	0.00594530i
$251$	−24.2241			−1.52901			−0.764505	−	0.644618i	$-0.777016\pi$
$251$	−24.2241			−1.52901			−0.764505	+	0.644618i	$0.777016\pi$
$252$		0			0
$253$	7.42314			0.466689
$254$	2.51576	−	1.45248i	0.157853	−	0.0911365i
$255$		0			0
$256$	4.39208	−	7.60731i	0.274505	−	0.475457i
$257$	−17.7228			−1.10552			−0.552760	−	0.833340i	$-0.686425\pi$
$257$	−17.7228			−1.10552			−0.552760	+	0.833340i	$0.686425\pi$
$258$		0			0
$259$		0			0
$260$		−	0.248521i		−	0.0154126i
$261$		0			0
$262$	−1.46392	+	0.845193i	−0.0904411	+	0.0522162i
$263$			2.89866i			0.178739i	0.995999	+	0.0893695i	$0.0284852\pi$
$263$			2.89866i			0.178739i	−0.995999	+	0.0893695i	$0.971515\pi$
$264$		0			0
$265$	0.284325	−	0.164155i	0.0174660	−	0.0100840i
$266$		0			0
$267$		0			0
$268$	−9.96008	−	17.2514i	−0.608408	−	1.05379i
$269$	−10.9469	−	18.9606i	−0.667444	−	1.15605i	−0.978616	−	0.205694i	$-0.934055\pi$
$269$	−10.9469	−	18.9606i	−0.667444	−	1.15605i	0.311172	−	0.950354i	$-0.399278\pi$
$270$		0			0
$271$	7.77992	+	4.49174i	0.472596	+	0.272854i	0.717326	−	0.696738i	$-0.245366\pi$
$271$	7.77992	+	4.49174i	0.472596	+	0.272854i	−0.244730	+	0.969591i	$0.578699\pi$
$272$	4.39254	−	7.60811i	0.266337	−	0.461309i
$273$		0			0
$274$	−3.76834	−	6.52695i	−0.227654	−	0.394308i
$275$			5.11060i			0.308181i
$276$		0			0
$277$	15.9018			0.955448			0.477724	−	0.878510i	$-0.341462\pi$
$277$	15.9018			0.955448			0.477724	+	0.878510i	$0.341462\pi$
$278$	−1.16936	+	2.02538i	−0.0701333	+	0.121474i
$279$		0			0
$280$		0			0
$281$	4.50324	+	2.59995i	0.268641	+	0.155100i	0.628270	−	0.777996i	$-0.283763\pi$
$281$	4.50324	+	2.59995i	0.268641	+	0.155100i	−0.359629	+	0.933095i	$0.617097\pi$
$282$		0			0
$283$	−16.2587	−	9.38694i	−0.966476	−	0.557995i	−0.0683162	−	0.997664i	$-0.521763\pi$
$283$	−16.2587	−	9.38694i	−0.966476	−	0.557995i	−0.898160	+	0.439668i	$0.855096\pi$
$284$	10.7102	+	6.18352i	0.635531	+	0.366924i
$285$		0			0
$286$	−3.31295	−	1.91273i	−0.195899	−	0.113102i
$287$		0			0
$288$		0			0
$289$	−7.62438	+	13.2058i	−0.448493	+	0.776813i
$290$	−0.0765476			−0.00449503
$291$		0			0
$292$			16.9885i			0.994178i
$293$	−11.4201	−	19.7802i	−0.667169	−	1.15557i	−0.978692	−	0.205332i	$-0.934173\pi$
$293$	−11.4201	−	19.7802i	−0.667169	−	1.15557i	0.311523	−	0.950238i	$-0.399161\pi$
$294$		0			0
$295$	0.0852263	−	0.147616i	0.00496206	−	0.00859455i
$296$	5.06229	+	2.92272i	0.294240	+	0.169879i
$297$		0			0
$298$	5.28530	+	9.15440i	0.306169	+	0.530300i
$299$	20.4520	+	35.4240i	1.18277	+	2.04862i
$300$		0			0
$301$		0			0
$302$	1.99062	−	1.14929i	0.114548	−	0.0661341i
$303$		0			0
$304$			3.23746i			0.185681i
$305$	−0.0580853	+	0.0335356i	−0.00332596	+	0.00192024i
$306$		0			0
$307$			18.6325i			1.06341i	0.846928	+	0.531707i	$0.178449\pi$
$307$			18.6325i			1.06341i	−0.846928	+	0.531707i	$0.821551\pi$
$308$		0			0
$309$		0			0
$310$	−0.0623894			−0.00354348
$311$	10.2747	−	17.7964i	0.582628	−	1.00914i	−0.412539	−	0.910940i	$-0.635358\pi$
$311$	10.2747	−	17.7964i	0.582628	−	1.00914i	0.995167	−	0.0982007i	$-0.0313087\pi$
$312$		0			0
$313$	0.624466	−	0.360536i	0.0352969	−	0.0203787i	−0.482248	−	0.876035i	$-0.660179\pi$
$313$	0.624466	−	0.360536i	0.0352969	−	0.0203787i	0.517545	+	0.855656i	$0.326846\pi$
$314$	−10.8605			−0.612893
$315$		0			0
$316$	−24.3164			−1.36791
$317$	−18.9915	+	10.9647i	−1.06667	+	0.615841i	−0.927269	−	0.374396i	$-0.877850\pi$
$317$	−18.9915	+	10.9647i	−1.06667	+	0.615841i	−0.139398	+	0.990236i	$0.544517\pi$
$318$		0			0
$319$	2.08096	−	3.60433i	0.116512	−	0.201804i
$320$	0.0206485			0.00115429
$321$		0			0
$322$		0			0
$323$		−	11.8843i		−	0.661258i
$324$		0			0
$325$	−24.3883	+	14.0806i	−1.35282	+	0.781051i
$326$			6.87921i			0.381004i
$327$		0			0
$328$	−14.4486	+	8.34191i	−0.797791	+	0.460605i
$329$		0			0
$330$		0			0
$331$	−10.8338	−	18.7647i	−0.595480	−	1.03140i	−0.993479	−	0.114016i	$-0.963629\pi$
$331$	−10.8338	−	18.7647i	−0.595480	−	1.03140i	0.397999	−	0.917386i	$-0.369705\pi$
$332$	4.79156	+	8.29923i	0.262971	+	0.455479i
$333$		0			0
$334$	−3.38617	−	1.95501i	−0.185283	−	0.106973i
$335$	0.180861	−	0.313260i	0.00988147	−	0.0171152i
$336$		0			0
$337$	12.6455	+	21.9026i	0.688844	+	1.19311i	0.972212	+	0.234101i	$0.0752147\pi$
$337$	12.6455	+	21.9026i	0.688844	+	1.19311i	−0.283369	+	0.959011i	$0.591452\pi$
$338$		−	12.4438i		−	0.676853i
$339$		0			0
$340$	0.250535			0.0135872
$341$	1.69607	−	2.93768i	0.0918474	−	0.159084i
$342$		0			0
$343$		0			0
$344$	−4.74955	−	2.74215i	−0.256078	−	0.147847i
$345$		0			0
$346$	2.79912	+	1.61607i	0.150482	+	0.0868806i
$347$	−4.92420	−	2.84299i	−0.264345	−	0.152620i	0.361970	−	0.932190i	$-0.382104\pi$
$347$	−4.92420	−	2.84299i	−0.264345	−	0.152620i	−0.626315	+	0.779570i	$0.715438\pi$
$348$		0			0
$349$	−9.68412	−	5.59113i	−0.518379	−	0.299286i	0.217892	−	0.975973i	$-0.430082\pi$
$349$	−9.68412	−	5.59113i	−0.518379	−	0.299286i	−0.736271	+	0.676687i	$0.763415\pi$
$350$		0			0
$351$		0			0
$352$	−2.94200	+	5.09570i	−0.156809	+	0.271601i
$353$	14.0422			0.747391			0.373696	−	0.927551i	$-0.378090\pi$
$353$	14.0422			0.747391			0.373696	+	0.927551i	$0.378090\pi$
$354$		0			0
$355$			0.224567i			0.0119188i
$356$	9.39250	+	16.2683i	0.497802	+	0.862218i
$357$		0			0
$358$	−0.0673081	+	0.116581i	−0.00355734	+	0.00616150i
$359$	−23.5052	−	13.5707i	−1.24056	−	0.716235i	−0.271348	−	0.962481i	$-0.587469\pi$
$359$	−23.5052	−	13.5707i	−1.24056	−	0.716235i	−0.969207	+	0.246246i	$0.920803\pi$
$360$		0			0
$361$	−7.31022	−	12.6617i	−0.384748	−	0.666403i
$362$	−2.08016	−	3.60294i	−0.109331	−	0.189366i
$363$		0			0
$364$		0			0
$365$	−0.267158	+	0.154244i	−0.0139837	+	0.00807347i
$366$		0			0
$367$		−	6.88076i		−	0.359173i	−0.983742	−	0.179586i	$-0.942524\pi$
$367$		−	6.88076i		−	0.359173i	0.983742	−	0.179586i	$-0.0574759\pi$
$368$	9.72828	−	5.61662i	0.507122	−	0.292787i
$369$		0			0
$370$			0.0464912i			0.00241696i
$371$		0			0
$372$		0			0
$373$	−0.247851			−0.0128332			−0.00641662	−	0.999979i	$-0.502042\pi$
$373$	−0.247851			−0.0128332			−0.00641662	+	0.999979i	$0.502042\pi$
$374$	1.92824	−	3.33980i	0.0997067	−	0.172697i
$375$		0			0
$376$	−22.2747	+	12.8603i	−1.14873	+	0.663220i
$377$	22.9337			1.18114
$378$		0			0
$379$	−8.91863			−0.458119			−0.229060	−	0.973412i	$-0.573565\pi$
$379$	−8.91863			−0.458119			−0.229060	+	0.973412i	$0.573565\pi$
$380$	−0.0799573	+	0.0461634i	−0.00410172	+	0.00236813i
$381$		0			0
$382$	4.58476	−	7.94104i	0.234577	−	0.406299i
$383$	0.327089			0.0167135			0.00835675	−	0.999965i	$-0.497340\pi$
$383$	0.327089			0.0167135			0.00835675	+	0.999965i	$0.497340\pi$
$384$		0			0
$385$		0			0
$386$		−	14.0017i		−	0.712665i
$387$		0			0
$388$	10.5613	−	6.09755i	0.536167	−	0.309556i
$389$		−	6.60890i		−	0.335085i	−0.985865	−	0.167542i	$-0.946417\pi$
$389$		−	6.60890i		−	0.335085i	0.985865	−	0.167542i	$-0.0535831\pi$
$390$		0			0
$391$	−35.7111	+	20.6178i	−1.80599	+	1.04269i
$392$		0			0
$393$		0			0
$394$	5.03799	+	8.72606i	0.253810	+	0.439613i
$395$	−0.220776	−	0.382394i	−0.0111084	−	0.0192404i
$396$		0			0
$397$	6.50435	+	3.75529i	0.326444	+	0.188472i	0.654261	−	0.756269i	$-0.272980\pi$
$397$	6.50435	+	3.75529i	0.326444	+	0.188472i	−0.327817	+	0.944741i	$0.606313\pi$
$398$	3.21760	−	5.57305i	0.161284	−	0.279352i
$399$		0			0
$400$	3.86687	+	6.69762i	0.193344	+	0.334881i
$401$			6.33464i			0.316337i	0.987412	+	0.158168i	$0.0505589\pi$
$401$			6.33464i			0.316337i	−0.987412	+	0.158168i	$0.949441\pi$
$402$		0			0
$403$	18.6919			0.931109
$404$	−0.353708	+	0.612640i	−0.0175976	+	0.0304800i
$405$		0			0
$406$		0			0
$407$	−2.18909	−	1.26387i	−0.108509	−	0.0626479i
$408$		0			0
$409$	29.0045	+	16.7457i	1.43418	+	0.828024i	0.997436	−	0.0715625i	$-0.0227986\pi$
$409$	29.0045	+	16.7457i	1.43418	+	0.828024i	0.436743	+	0.899586i	$0.356132\pi$
$410$	−0.114916	−	0.0663467i	−0.00567529	−	0.00327663i
$411$		0			0
$412$	7.14382	+	4.12448i	0.351951	+	0.203199i
$413$		0			0
$414$		0			0
$415$	−0.0870078	+	0.150702i	−0.00427105	+	0.00739767i
$416$	−32.4229			−1.58966
$417$		0			0
$418$			1.42118i			0.0695122i
$419$	−0.896459	−	1.55271i	−0.0437949	−	0.0758550i	0.843297	−	0.537448i	$-0.180611\pi$
$419$	−0.896459	−	1.55271i	−0.0437949	−	0.0758550i	−0.887092	+	0.461593i	$0.847278\pi$
$420$		0			0
$421$	1.90262	−	3.29543i	0.0927278	−	0.160609i	−0.815930	−	0.578150i	$-0.803775\pi$
$421$	1.90262	−	3.29543i	0.0927278	−	0.160609i	0.908658	+	0.417541i	$0.137108\pi$
$422$	−8.12254	−	4.68955i	−0.395399	−	0.228284i
$423$		0			0
$424$	−13.7108	−	23.7478i	−0.665855	−	1.15330i
$425$	−14.1947	−	24.5860i	−0.688545	−	1.19260i
$426$		0			0
$427$		0			0
$428$	12.2401	−	7.06684i	0.591649	−	0.341589i
$429$		0			0
$430$		−	0.0436190i		−	0.00210349i
$431$	−1.15145	+	0.664787i	−0.0554632	+	0.0320217i	−0.527475	−	0.849570i	$-0.676861\pi$
$431$	−1.15145	+	0.664787i	−0.0554632	+	0.0320217i	0.472012	+	0.881592i	$0.343528\pi$
$432$		0			0
$433$		−	37.4292i		−	1.79873i	−0.437194	−	0.899367i	$-0.644028\pi$
$433$		−	37.4292i		−	1.79873i	0.437194	−	0.899367i	$-0.355972\pi$
$434$		0			0
$435$		0			0
$436$	7.37313			0.353109
$437$	7.59804	−	13.1602i	0.363464	−	0.629537i
$438$		0			0
$439$	20.5584	−	11.8694i	0.981201	−	0.566496i	0.0785682	−	0.996909i	$-0.474965\pi$
$439$	20.5584	−	11.8694i	0.981201	−	0.566496i	0.902632	+	0.430412i	$0.141632\pi$
$440$	−0.0684026			−0.00326097
$441$		0			0
$442$	21.2505			1.01078
$443$	9.74317	−	5.62522i	0.462912	−	0.267262i	−0.250356	−	0.968154i	$-0.580548\pi$
$443$	9.74317	−	5.62522i	0.462912	−	0.267262i	0.713268	+	0.700891i	$0.247214\pi$
$444$		0			0
$445$	−0.170554	+	0.295409i	−0.00808505	+	0.0140037i
$446$	1.98498			0.0939916
$447$		0			0
$448$		0			0
$449$			14.3953i			0.679357i	0.940542	+	0.339679i	$0.110318\pi$
$449$			14.3953i			0.679357i	−0.940542	+	0.339679i	$0.889682\pi$
$450$		0			0
$451$	6.24803	−	3.60730i	0.294208	−	0.169861i
$452$			14.7787i			0.695129i
$453$		0			0
$454$	16.5532	−	9.55701i	0.776881	−	0.448533i
$455$		0			0
$456$		0			0
$457$	10.3135	+	17.8635i	0.482444	+	0.835617i	0.999797	−	0.0201547i	$-0.00641589\pi$
$457$	10.3135	+	17.8635i	0.482444	+	0.835617i	−0.517353	+	0.855772i	$0.673083\pi$
$458$	2.94323	+	5.09782i	0.137528	+	0.238206i
$459$		0			0
$460$	0.277433	+	0.160176i	0.0129354	+	0.00746825i
$461$	0.832511	−	1.44195i	0.0387739	−	0.0671584i	−0.845987	−	0.533203i	$-0.820988\pi$
$461$	0.832511	−	1.44195i	0.0387739	−	0.0671584i	0.884761	+	0.466045i	$0.154321\pi$
$462$		0			0
$463$	0.604175	+	1.04646i	0.0280784	+	0.0486332i	0.879723	−	0.475486i	$-0.157728\pi$
$463$	0.604175	+	1.04646i	0.0280784	+	0.0486332i	−0.851645	+	0.524119i	$0.824395\pi$
$464$		−	6.29814i		−	0.292384i
$465$		0			0
$466$	−8.57490			−0.397224
$467$	−4.61994	+	8.00197i	−0.213785	+	0.370287i	−0.952896	−	0.303297i	$-0.901913\pi$
$467$	−4.61994	+	8.00197i	−0.213785	+	0.370287i	0.739111	+	0.673584i	$0.235246\pi$
$468$		0			0
$469$		0			0
$470$	−0.177160	−	0.102283i	−0.00817179	−	0.00471798i
$471$		0			0
$472$	−12.3294	−	7.11839i	−0.567507	−	0.327650i
$473$	2.05385	+	1.18579i	0.0944361	+	0.0545227i
$474$		0			0
$475$	9.06039	+	5.23102i	0.415719	+	0.240016i
$476$		0			0
$477$		0			0
$478$	1.86286	−	3.22657i	0.0852052	−	0.147580i
$479$	−17.5448			−0.801643			−0.400822	−	0.916156i	$-0.631275\pi$
$479$	−17.5448			−0.801643			−0.400822	+	0.916156i	$0.631275\pi$
$480$		0			0
$481$		−	13.9288i		−	0.635097i
$482$	−3.64923	−	6.32066i	−0.166218	−	0.287898i
$483$		0			0
$484$	−7.75843	+	13.4380i	−0.352656	+	0.610818i
$485$	0.191777	+	0.110723i	0.00870817	+	0.00502766i
$486$		0			0
$487$	21.5949	+	37.4034i	0.978558	+	1.69491i	0.667657	+	0.744469i	$0.267297\pi$
$487$	21.5949	+	37.4034i	0.978558	+	1.69491i	0.310900	+	0.950442i	$0.399369\pi$
$488$	2.80100	+	4.85148i	0.126796	+	0.219616i
$489$		0			0
$490$		0			0
$491$	−23.0046	+	13.2817i	−1.03818	+	0.599396i	−0.919319	−	0.393514i	$-0.871259\pi$
$491$	−23.0046	+	13.2817i	−1.03818	+	0.599396i	−0.118866	+	0.992910i	$0.537926\pi$
$492$		0			0
$493$			23.1196i			1.04125i
$494$	−6.78202	+	3.91560i	−0.305138	+	0.176171i
$495$		0			0
$496$		−	5.13324i		−	0.230489i
$497$		0			0
$498$		0			0
$499$	5.31518			0.237940			0.118970	−	0.992898i	$-0.462041\pi$
$499$	5.31518			0.237940			0.118970	+	0.992898i	$0.462041\pi$
$500$	−0.220570	+	0.382039i	−0.00986421	+	0.0170853i
$501$		0			0
$502$	−13.9361	+	8.04598i	−0.621996	+	0.359110i
$503$	35.5334			1.58436			0.792178	−	0.610290i	$-0.208947\pi$
$503$	35.5334			1.58436			0.792178	+	0.610290i	$0.208947\pi$
$504$		0			0
$505$	−0.0128457			−0.000571624
$506$	4.27051	−	2.46558i	0.189847	−	0.109608i
$507$		0			0
$508$	−3.40810	+	5.90300i	−0.151210	+	0.261903i
$509$	13.6331			0.604276			0.302138	−	0.953264i	$-0.402300\pi$
$509$	13.6331			0.604276			0.302138	+	0.953264i	$0.402300\pi$
$510$		0			0
$511$		0			0
$512$			16.2184i			0.716760i
$513$		0			0
$514$	−10.1959	+	5.88661i	−0.449722	+	0.259647i
$515$			0.149789i			0.00660051i
$516$		0			0
$517$	9.63227	−	5.56120i	0.423627	−	0.244581i
$518$		0			0
$519$		0			0
$520$	−0.188461	−	0.326424i	−0.00826457	−	0.0143147i
$521$	−5.11259	−	8.85526i	−0.223987	−	0.387956i	0.732028	−	0.681274i	$-0.238574\pi$
$521$	−5.11259	−	8.85526i	−0.223987	−	0.387956i	−0.956015	+	0.293318i	$0.905241\pi$
$522$		0			0
$523$	−4.48150	−	2.58740i	−0.195962	−	0.113139i	0.398808	−	0.917034i	$-0.369424\pi$
$523$	−4.48150	−	2.58740i	−0.195962	−	0.113139i	−0.594771	+	0.803895i	$0.702757\pi$
$524$	1.98317	−	3.43495i	0.0866350	−	0.150056i
$525$		0			0
$526$	0.962785	+	1.66759i	0.0419794	+	0.0727105i
$527$			18.8434i			0.820831i
$528$		0			0
$529$	−29.7269			−1.29247
$530$	0.109048	−	0.188876i	0.00473673	−	0.00820426i
$531$		0			0
$532$		0			0
$533$	34.4288	+	19.8775i	1.49128	+	0.860990i
$534$		0			0
$535$	0.222263	+	0.128324i	0.00960927	+	0.00554791i
$536$	−26.1645	−	15.1061i	−1.13013	−	0.652484i
$537$		0			0
$538$	−12.5955	−	7.27199i	−0.543029	−	0.313518i
$539$		0			0
$540$		0			0
$541$	12.7197	−	22.0312i	0.546864	−	0.947196i	−0.451623	−	0.892209i	$-0.649155\pi$
$541$	12.7197	−	22.0312i	0.546864	−	0.947196i	0.998487	−	0.0549871i	$-0.0175118\pi$
$542$	5.96769			0.256334
$543$		0			0
$544$		−	32.6857i		−	1.40139i
$545$	0.0669427	+	0.115948i	0.00286751	+	0.00496667i
$546$		0			0
$547$	14.7771	−	25.5947i	0.631824	−	1.09435i	−0.355355	−	0.934732i	$-0.615640\pi$
$547$	14.7771	−	25.5947i	0.631824	−	1.09435i	0.987179	−	0.159620i	$-0.0510267\pi$
$548$	15.3149	+	8.84205i	0.654219	+	0.377714i
$549$		0			0
$550$	1.69748	+	2.94012i	0.0723807	+	0.125367i
$551$	−4.25999	−	7.37852i	−0.181482	−	0.314336i
$552$		0			0
$553$		0			0
$554$	9.14828	−	5.28176i	0.388673	−	0.224401i
$555$		0			0
$556$		−	5.48757i		−	0.232725i
$557$	16.9788	−	9.80269i	0.719413	−	0.415353i	−0.0951237	−	0.995465i	$-0.530325\pi$
$557$	16.9788	−	9.80269i	0.719413	−	0.415353i	0.814537	+	0.580112i	$0.196991\pi$
$558$		0			0
$559$			13.0683i			0.552728i
$560$		0			0
$561$		0			0
$562$	3.45427			0.145710
$563$	−7.23796	+	12.5365i	−0.305044	+	0.528351i	−0.977271	−	0.211994i	$-0.932004\pi$
$563$	−7.23796	+	12.5365i	−0.305044	+	0.528351i	0.672227	+	0.740345i	$0.265338\pi$
$564$		0			0
$565$	−0.232406	+	0.134180i	−0.00977738	+	0.00564497i
$566$	−12.4714			−0.524213
$567$		0			0
$568$	18.7566			0.787011
$569$	6.70970	−	3.87385i	0.281285	−	0.162400i	−0.352720	−	0.935729i	$-0.614743\pi$
$569$	6.70970	−	3.87385i	0.281285	−	0.162400i	0.634005	+	0.773329i	$0.281410\pi$
$570$		0			0
$571$	−8.06856	+	13.9752i	−0.337659	+	0.584842i	−0.983992	−	0.178213i	$-0.942968\pi$
$571$	−8.06856	+	13.9752i	−0.337659	+	0.584842i	0.646333	+	0.763055i	$0.276302\pi$
$572$	8.97609			0.375309
$573$		0			0
$574$		0			0
$575$		−	36.3008i		−	1.51385i
$576$		0			0
$577$	10.5403	−	6.08542i	0.438797	−	0.253339i	−0.264290	−	0.964443i	$-0.585138\pi$
$577$	10.5403	−	6.08542i	0.438797	−	0.253339i	0.703087	+	0.711104i	$0.251804\pi$
$578$			10.1297i			0.421340i
$579$		0			0
$580$	0.155548	−	0.0898059i	0.00645879	−	0.00372899i
$581$		0			0
$582$		0			0
$583$	5.92897	+	10.2693i	0.245553	+	0.425310i
$584$	12.8829	+	22.3139i	0.533100	+	0.923356i
$585$		0			0
$586$	−13.1399	−	7.58633i	−0.542805	−	0.313388i
$587$	−16.8761	+	29.2302i	−0.696550	+	1.20646i	0.273106	+	0.961984i	$0.411949\pi$
$587$	−16.8761	+	29.2302i	−0.696550	+	1.20646i	−0.969655	+	0.244476i	$0.921384\pi$
$588$		0			0
$589$	−3.47207	−	6.01380i	−0.143064	−	0.247794i
$590$		−	0.113231i		−	0.00466165i
$591$		0			0
$592$	−3.82518			−0.157214
$593$	9.15123	−	15.8504i	0.375796	−	0.650897i	−0.614650	−	0.788800i	$-0.710703\pi$
$593$	9.15123	−	15.8504i	0.375796	−	0.650897i	0.990446	+	0.137903i	$0.0440361\pi$
$594$		0			0
$595$		0			0
$596$	−21.4799	−	12.4015i	−0.879853	−	0.507983i
$597$		0			0
$598$	23.5320	+	13.5862i	0.962296	+	0.555582i
$599$	−34.1905	−	19.7399i	−1.39699	−	0.806551i	−0.402911	−	0.915239i	$-0.632002\pi$
$599$	−34.1905	−	19.7399i	−1.39699	−	0.806551i	−0.994076	+	0.108689i	$0.965335\pi$
$600$		0			0
$601$	34.4865	+	19.9108i	1.40673	+	0.812177i	0.995072	−	0.0991600i	$-0.0316155\pi$
$601$	34.4865	+	19.9108i	1.40673	+	0.812177i	0.411661	+	0.911337i	$0.364949\pi$
$602$		0			0
$603$		0			0
$604$	−2.69670	+	4.67082i	−0.109727	+	0.190053i
$605$	−0.281764			−0.0114553
$606$		0			0
$607$			24.9536i			1.01283i	0.862289	+	0.506417i	$0.169030\pi$
$607$			24.9536i			1.01283i	−0.862289	+	0.506417i	$0.830970\pi$
$608$	6.02264	+	10.4315i	0.244250	+	0.423054i
$609$		0			0
$610$	−0.0222776	+	0.0385859i	−0.000901992	+	0.00156230i
$611$	53.0772	+	30.6441i	2.14727	+	1.23973i
$612$		0			0
$613$	−14.0285	−	24.2980i	−0.566605	−	0.981388i	−0.996898	−	0.0786994i	$-0.974923\pi$
$613$	−14.0285	−	24.2980i	−0.566605	−	0.981388i	0.430294	−	0.902689i	$-0.358410\pi$
$614$	6.18876	+	10.7192i	0.249758	+	0.432594i
$615$		0			0
$616$		0			0
$617$	−29.8093	+	17.2104i	−1.20008	+	0.692865i	−0.960573	−	0.278030i	$-0.910319\pi$
$617$	−29.8093	+	17.2104i	−1.20008	+	0.692865i	−0.239506	+	0.970895i	$0.576985\pi$
$618$		0			0
$619$		−	19.9635i		−	0.802399i	−0.915991	−	0.401200i	$-0.868593\pi$
$619$		−	19.9635i		−	0.802399i	0.915991	−	0.401200i	$-0.131407\pi$
$620$	0.126778	−	0.0731955i	0.00509154	−	0.00293960i
$621$		0			0
$622$		−	13.6510i		−	0.547354i
$623$		0			0
$624$		0			0
$625$	24.9880			0.999519
$626$	0.239503	−	0.414831i	0.00957245	−	0.0165800i
$627$		0			0
$628$	22.0690	−	12.7416i	0.880650	−	0.508443i
$629$	14.0417			0.559878
$630$		0			0
$631$	−46.8447			−1.86486			−0.932429	−	0.361354i	$-0.882314\pi$
$631$	−46.8447			−1.86486			−0.932429	+	0.361354i	$0.882314\pi$
$632$	−31.9389	+	18.4399i	−1.27046	+	0.733501i
$633$		0			0
$634$	−7.28384	+	12.6160i	−0.289278	+	0.501044i
$635$	−0.123772			−0.00491176
$636$		0			0
$637$		0			0
$638$		−	2.76475i		−	0.109458i
$639$		0			0
$640$	−0.270290	+	0.156052i	−0.0106841	+	0.00616849i
$641$		−	3.85994i		−	0.152459i	−0.997090	−	0.0762293i	$-0.975712\pi$
$641$		−	3.85994i		−	0.152459i	0.997090	−	0.0762293i	$-0.0242881\pi$
$642$		0			0
$643$	31.0233	−	17.9113i	1.22344	−	0.706352i	0.257789	−	0.966201i	$-0.417006\pi$
$643$	31.0233	−	17.9113i	1.22344	−	0.706352i	0.965649	+	0.259849i	$0.0836727\pi$
$644$		0			0
$645$		0			0
$646$	−3.94734	−	6.83699i	−0.155306	−	0.268998i
$647$	21.8246	+	37.8013i	0.858013	+	1.48612i	0.873821	+	0.486248i	$0.161635\pi$
$647$	21.8246	+	37.8013i	0.858013	+	1.48612i	−0.0158075	+	0.999875i	$0.505032\pi$
$648$		0			0
$649$	5.33162	+	3.07821i	0.209284	+	0.120830i
$650$	−9.35369	+	16.2011i	−0.366882	+	0.635458i
$651$		0			0
$652$	−8.07072	−	13.9789i	−0.316074	−	0.547456i
$653$		−	7.45002i		−	0.291542i	−0.989318	−	0.145771i	$-0.953434\pi$
$653$		−	7.45002i		−	0.291542i	0.989318	−	0.145771i	$-0.0465663\pi$
$654$		0			0
$655$	0.0720229			0.00281417
$656$	5.45884	−	9.45498i	0.213132	−	0.369155i
$657$		0			0
$658$		0			0
$659$	7.52607	+	4.34518i	0.293174	+	0.169264i	0.639372	−	0.768897i	$-0.279194\pi$
$659$	7.52607	+	4.34518i	0.293174	+	0.169264i	−0.346198	+	0.938161i	$0.612528\pi$
$660$		0			0
$661$	−24.9853	−	14.4253i	−0.971815	−	0.561077i	−0.0720256	−	0.997403i	$-0.522946\pi$
$661$	−24.9853	−	14.4253i	−0.971815	−	0.561077i	−0.899789	+	0.436325i	$0.856280\pi$
$662$	−12.4653	−	7.19686i	−0.484479	−	0.279714i
$663$		0			0
$664$	12.5871	+	7.26719i	0.488476	+	0.282022i
$665$		0			0
$666$		0			0
$667$	−14.7812	+	25.6017i	−0.572329	+	0.991303i
$668$	9.17449			0.354972
$669$		0			0
$670$		−	0.240290i		−	0.00928322i
$671$	−1.21124	−	2.09793i	−0.0467594	−	0.0809897i
$672$		0			0
$673$	−3.60695	+	6.24742i	−0.139038	+	0.240820i	−0.927133	−	0.374733i	$-0.877734\pi$
$673$	−3.60695	+	6.24742i	−0.139038	+	0.240820i	0.788095	+	0.615554i	$0.211068\pi$
$674$	14.5498	+	8.40036i	0.560439	+	0.323570i
$675$		0			0
$676$	14.5991	+	25.2864i	0.561504	+	0.972553i
$677$	−18.1911	−	31.5079i	−0.699140	−	1.21095i	−0.968765	−	0.247980i	$-0.920233\pi$
$677$	−18.1911	−	31.5079i	−0.699140	−	1.21095i	0.269626	−	0.962965i	$-0.413100\pi$
$678$		0			0
$679$		0			0
$680$	0.329070	−	0.189989i	0.0126193	−	0.00728573i
$681$		0			0
$682$		−	2.25339i		−	0.0862867i
$683$	−20.5530	+	11.8663i	−0.786438	+	0.454050i	−0.838707	−	0.544583i	$-0.816688\pi$
$683$	−20.5530	+	11.8663i	−0.786438	+	0.454050i	0.0522688	+	0.998633i	$0.483355\pi$
$684$		0			0
$685$			0.321118i			0.0122693i
$686$		0			0
$687$		0			0
$688$	3.58886			0.136824
$689$	−32.6707	+	56.5874i	−1.24466	+	2.15581i
$690$		0			0
$691$	2.86127	−	1.65195i	0.108848	−	0.0628433i	−0.444588	−	0.895735i	$-0.646650\pi$
$691$	2.86127	−	1.65195i	0.108848	−	0.0628433i	0.553436	+	0.832892i	$0.313316\pi$
$692$	−7.58393			−0.288298
$693$		0			0
$694$	−3.77718			−0.143380
$695$	0.0862962	−	0.0498231i	0.00327340	−	0.00188990i
$696$		0			0
$697$	−20.0386	+	34.7079i	−0.759016	+	1.31465i
$698$	−7.42834			−0.281167
$699$		0			0
$700$		0			0
$701$			0.873603i			0.0329955i	0.999864	+	0.0164978i	$0.00525164\pi$
$701$			0.873603i			0.0329955i	−0.999864	+	0.0164978i	$0.994748\pi$
$702$		0			0
$703$	−4.48135	+	2.58731i	−0.169017	+	0.0975821i
$704$			0.745784i			0.0281078i
$705$		0			0
$706$	8.07845	−	4.66410i	0.304037	−	0.175536i
$707$		0			0
$708$		0			0
$709$	−8.07767	−	13.9909i	−0.303363	−	0.525441i	0.673532	−	0.739158i	$-0.264776\pi$
$709$	−8.07767	−	13.9909i	−0.303363	−	0.525441i	−0.976896	+	0.213717i	$0.931443\pi$
$710$	0.0745897	+	0.129193i	0.00279930	+	0.00484853i
$711$		0			0
$712$	24.6735	+	14.2453i	0.924680	+	0.533864i
$713$	−12.0473	+	20.8665i	−0.451174	+	0.781456i
$714$		0			0
$715$	0.0814965	+	0.141156i	0.00304779	+	0.00527894i
$716$		−	0.315864i		−	0.0118044i
$717$		0			0
$718$	−18.0300			−0.672872
$719$	−22.5953	+	39.1361i	−0.842661	+	1.45953i	0.0449767	+	0.998988i	$0.485679\pi$
$719$	−22.5953	+	39.1361i	−0.842661	+	1.45953i	−0.887637	+	0.460543i	$0.847655\pi$
$720$		0			0
$721$		0			0
$722$	−8.41110	−	4.85615i	−0.313029	−	0.180727i
$723$		0			0
$724$	8.45395	+	4.88089i	0.314189	+	0.181397i
$725$	−17.6260	−	10.1764i	−0.654613	−	0.377941i
$726$		0			0
$727$	−7.15775	−	4.13253i	−0.265466	−	0.153267i	0.361359	−	0.932427i	$-0.382313\pi$
$727$	−7.15775	−	4.13253i	−0.265466	−	0.153267i	−0.626826	+	0.779160i	$0.715646\pi$
$728$		0			0
$729$		0			0
$730$	−0.102463	+	0.177472i	−0.00379234	+	0.00656853i
$731$	−13.1742			−0.487264
$732$		0			0
$733$		−	12.2166i		−	0.451230i	−0.974217	−	0.225615i	$-0.927561\pi$
$733$		−	12.2166i		−	0.451230i	0.974217	−	0.225615i	$-0.0724392\pi$
$734$	−2.28543	−	3.95849i	−0.0843569	−	0.146110i
$735$		0			0
$736$	20.8972	−	36.1949i	0.770280	−	1.33416i
$737$	11.3143	+	6.53234i	0.416769	+	0.240622i
$738$		0			0
$739$	10.3536	+	17.9330i	0.380863	+	0.659674i	0.991186	−	0.132478i	$-0.0422935\pi$
$739$	10.3536	+	17.9330i	0.380863	+	0.659674i	−0.610323	+	0.792153i	$0.708960\pi$
$740$	−0.0545436	−	0.0944723i	−0.00200506	−	0.00347287i
$741$		0			0
$742$		0			0
$743$	−10.2862	+	5.93873i	−0.377363	+	0.217871i	−0.676670	−	0.736286i	$-0.736578\pi$
$743$	−10.2862	+	5.93873i	−0.377363	+	0.217871i	0.299307	+	0.954157i	$0.403244\pi$
$744$		0			0
$745$		−	0.450385i		−	0.0165008i
$746$	−0.142588	+	0.0823233i	−0.00522053	+	0.00301407i
$747$		0			0
$748$			9.04885i			0.330859i
$749$		0			0
$750$		0			0
$751$	23.7108			0.865221			0.432610	−	0.901581i	$-0.357593\pi$
$751$	23.7108			0.865221			0.432610	+	0.901581i	$0.357593\pi$
$752$	8.41562	−	14.5763i	0.306886	−	0.531542i
$753$		0			0
$754$	13.1937	−	7.61738i	0.480486	−	0.277409i
$755$	−0.0979362			−0.00356426
$756$		0			0
$757$	44.2494			1.60827			0.804136	−	0.594446i	$-0.202628\pi$
$757$	44.2494			1.60827			0.804136	+	0.594446i	$0.202628\pi$
$758$	−5.13087	+	2.96231i	−0.186362	+	0.107596i
$759$		0			0
$760$	−0.0700143	+	0.121268i	−0.00253969	+	0.00439887i
$761$	48.7535			1.76731			0.883656	−	0.468137i	$-0.155075\pi$
$761$	48.7535			1.76731			0.883656	+	0.468137i	$0.155075\pi$
$762$		0			0
$763$		0			0
$764$			21.5154i			0.778401i
$765$		0			0
$766$	0.188174	−	0.108642i	0.00679900	−	0.00392540i
$767$			33.9240i			1.22493i
$768$		0			0
$769$	23.3870	−	13.5025i	0.843357	−	0.486912i	−0.0150472	−	0.999887i	$-0.504790\pi$
$769$	23.3870	−	13.5025i	0.843357	−	0.486912i	0.858404	+	0.512975i	$0.171457\pi$
$770$		0			0
$771$		0			0
$772$	16.4268	+	28.4520i	0.591213	+	1.02401i
$773$	−13.3567	−	23.1345i	−0.480408	−	0.832092i	0.519339	−	0.854568i	$-0.326178\pi$
$773$	−13.3567	−	23.1345i	−0.480408	−	0.832092i	−0.999747	+	0.0224765i	$0.992845\pi$
$774$		0			0
$775$	−14.3659	−	8.29417i	−0.516039	−	0.297935i
$776$	9.24794	−	16.0179i	0.331982	−	0.575009i
$777$		0			0
$778$	−2.19514	−	3.80209i	−0.0786994	−	0.136311i
$779$		−	14.7692i		−	0.529161i
$780$		0			0
$781$	−8.11095			−0.290233
$782$	−13.6963	+	23.7228i	−0.489780	+	0.848324i
$783$		0			0
$784$		0			0
$785$	0.400742	+	0.231368i	0.0143031	+	0.00825789i
$786$		0			0
$787$	41.0093	+	23.6767i	1.46182	+	0.843983i	0.999096	−	0.0425177i	$-0.0135379\pi$
$787$	41.0093	+	23.6767i	1.46182	+	0.843983i	0.462726	+	0.886501i	$0.346871\pi$
$788$	−20.4749	−	11.8212i	−0.729388	−	0.421112i
$789$		0			0
$790$	−0.254023	−	0.146660i	−0.00903775	−	0.00521795i
$791$		0			0
$792$		0			0
$793$	6.67436	−	11.5603i	0.237014	−	0.410520i
$794$	4.98925			0.177062
$795$		0			0
$796$			15.0996i			0.535191i
$797$	4.42781	+	7.66919i	0.156841	+	0.271657i	0.933728	−	0.357984i	$-0.116536\pi$
$797$	4.42781	+	7.66919i	0.156841	+	0.271657i	−0.776887	+	0.629640i	$0.783202\pi$
$798$		0			0
$799$	−30.8925	+	53.5074i	−1.09290	+	1.89296i
$800$	24.9191	+	14.3871i	0.881023	+	0.508659i
$801$		0			0
$802$	2.10404	+	3.64430i	0.0742962	+	0.128685i
$803$	−5.57098	−	9.64922i	−0.196596	−	0.340514i
$804$		0			0
$805$		0			0
$806$	10.7534	−	6.20848i	0.378772	−	0.218684i
$807$		0			0
$808$			1.07291i			0.0377449i
$809$	−6.40871	+	3.70007i	−0.225318	+	0.130087i	−0.608410	−	0.793623i	$-0.708192\pi$
$809$	−6.40871	+	3.70007i	−0.225318	+	0.130087i	0.383092	+	0.923710i	$0.374859\pi$
$810$		0			0
$811$			25.0843i			0.880829i	0.897794	+	0.440415i	$0.145169\pi$
$811$			25.0843i			0.880829i	−0.897794	+	0.440415i	$0.854831\pi$
$812$		0			0
$813$		0			0
$814$	−1.67917			−0.0588550
$815$	0.146553	−	0.253836i	0.00513351	−	0.00889150i
$816$		0			0
$817$	4.20449	−	2.42746i	0.147096	−	0.0849262i
$818$	22.2483			0.777893
$819$		0			0
$820$	0.311353			0.0108729
$821$	18.3781	−	10.6106i	0.641401	−	0.370313i	−0.143753	−	0.989614i	$-0.545917\pi$
$821$	18.3781	−	10.6106i	0.641401	−	0.370313i	0.785154	+	0.619300i	$0.212584\pi$
$822$		0			0
$823$	−8.47690	+	14.6824i	−0.295486	+	0.511797i	−0.975098	−	0.221775i	$-0.928815\pi$
$823$	−8.47690	+	14.6824i	−0.295486	+	0.511797i	0.679612	+	0.733572i	$0.262148\pi$
$824$	12.5109			0.435838
$825$		0			0
$826$		0			0
$827$		−	25.3052i		−	0.879949i	−0.898010	−	0.439975i	$-0.854987\pi$
$827$		−	25.3052i		−	0.879949i	0.898010	−	0.439975i	$-0.145013\pi$
$828$		0			0
$829$	35.9640	−	20.7638i	1.24908	−	0.721158i	0.278156	−	0.960536i	$-0.410277\pi$
$829$	35.9640	−	20.7638i	1.24908	−	0.721158i	0.970927	+	0.239378i	$0.0769434\pi$
$830$			0.115598i			0.00401247i
$831$		0			0
$832$	−3.55896	+	2.05477i	−0.123385	+	0.0712362i
$833$		0			0
$834$		0			0
$835$	0.0832977	+	0.144276i	0.00288264	+	0.00499287i
$836$	−1.66733	−	2.88791i	−0.0576659	−	0.0998803i
$837$		0			0
$838$	−1.03146	−	0.595515i	−0.0356312	−	0.0205717i
$839$	−6.61780	+	11.4624i	−0.228472	+	0.395725i	−0.957355	−	0.288913i	$-0.906706\pi$
$839$	−6.61780	+	11.4624i	−0.228472	+	0.395725i	0.728884	+	0.684638i	$0.240040\pi$
$840$		0			0
$841$	−6.21265	−	10.7606i	−0.214229	−	0.371056i
$842$		−	2.52780i		−	0.0871138i
$843$		0			0
$844$	22.0072			0.757519
$845$	−0.265099	+	0.459164i	−0.00911967	+	0.0157957i
$846$		0			0
$847$		0			0
$848$	15.5403	+	8.97217i	0.533654	+	0.308106i
$849$		0			0
$850$	−16.3324	−	9.42951i	−0.560196	−	0.323429i
$851$	15.5492	+	8.97735i	0.533020	+	0.307739i
$852$		0			0
$853$	−15.3814	−	8.88048i	−0.526651	−	0.304062i	0.213001	−	0.977052i	$-0.431676\pi$
$853$	−15.3814	−	8.88048i	−0.526651	−	0.304062i	−0.739651	+	0.672990i	$0.765010\pi$
$854$		0			0
$855$		0			0
$856$	10.7180	−	18.5642i	0.366334	−	0.634510i
$857$	18.3431			0.626590			0.313295	−	0.949656i	$-0.398567\pi$
$857$	18.3431			0.626590			0.313295	+	0.949656i	$0.398567\pi$
$858$		0			0
$859$		−	3.10760i		−	0.106030i	−0.998594	−	0.0530150i	$-0.983117\pi$
$859$		−	3.10760i		−	0.106030i	0.998594	−	0.0530150i	$-0.0168831\pi$
$860$	0.0511739	+	0.0886358i	0.00174502	+	0.00302246i
$861$		0			0
$862$	−0.441616	+	0.764902i	−0.0150415	+	0.0260527i
$863$	−35.8587	−	20.7030i	−1.22064	−	0.704739i	−0.255589	−	0.966786i	$-0.582269\pi$
$863$	−35.8587	−	20.7030i	−1.22064	−	0.704739i	−0.965055	+	0.262047i	$0.915603\pi$
$864$		0			0
$865$	−0.0688566	−	0.119263i	−0.00234119	−	0.00405507i
$866$	−12.4321	−	21.5330i	−0.422458	−	0.731720i
$867$		0			0
$868$		0			0
$869$	13.8114	−	7.97399i	0.468518	−	0.270499i
$870$		0			0
$871$			71.9910i			2.43932i
$872$	9.68438	−	5.59128i	0.327954	−	0.189345i
$873$		0			0
$874$		−	10.0947i		−	0.341459i
$875$		0			0
$876$		0			0
$877$	−22.7957			−0.769756			−0.384878	−	0.922967i	$-0.625756\pi$
$877$	−22.7957			−0.769756			−0.384878	+	0.922967i	$0.625756\pi$
$878$	7.88482	−	13.6569i	0.266100	−	0.460898i
$879$		0			0
$880$	0.0387648	−	0.0223809i	0.00130676	−	0.000754460i
$881$	43.4050			1.46235			0.731175	−	0.682190i	$-0.238972\pi$
$881$	43.4050			1.46235			0.731175	+	0.682190i	$0.238972\pi$
$882$		0			0
$883$	−29.9309			−1.00725			−0.503627	−	0.863921i	$-0.668001\pi$
$883$	−29.9309			−1.00725			−0.503627	+	0.863921i	$0.668001\pi$
$884$	−43.1820	+	24.9312i	−1.45237	+	0.838526i
$885$		0			0
$886$	3.73682	−	6.47236i	0.125541	−	0.217443i
$887$	38.9575			1.30807			0.654033	−	0.756466i	$-0.273076\pi$
$887$	38.9575			1.30807			0.654033	+	0.756466i	$0.273076\pi$
$888$		0			0
$889$		0			0
$890$			0.226597i			0.00759556i
$891$		0			0
$892$	−4.03358	+	2.32879i	−0.135054	+	0.0779736i
$893$		−	22.7689i		−	0.761933i
$894$		0			0
$895$	0.00496721	−	0.00286782i	0.000166035	−	9.58606e-5i
$896$		0			0
$897$		0			0
$898$	4.78138	+	8.28160i	0.159557	+	0.276361i
$899$	6.75453	+	11.6992i	0.225276	+	0.390190i
$900$		0			0
$901$	−57.0460	−	32.9355i	−1.90048	−	1.09724i
$902$	2.39632	−	4.15054i	0.0797886	−	0.138198i
$903$		0			0
$904$	11.2071	+	19.4113i	0.372743	+	0.645611i
$905$			0.177260i			0.00589232i
$906$		0			0
$907$	−28.1053			−0.933220			−0.466610	−	0.884463i	$-0.654525\pi$
$907$	−28.1053			−0.933220			−0.466610	+	0.884463i	$0.654525\pi$
$908$	−22.4246	+	38.8406i	−0.744187	+	1.28897i
$909$		0			0
$910$		0			0
$911$	−32.3883	−	18.6994i	−1.07307	−	0.619538i	−0.144052	−	0.989570i	$-0.546013\pi$
$911$	−32.3883	−	18.6994i	−1.07307	−	0.619538i	−0.929019	+	0.370032i	$0.879347\pi$
$912$		0			0
$913$	−5.44307	−	3.14256i	−0.180139	−	0.104003i
$914$	11.8666	+	6.85121i	0.392513	+	0.226618i
$915$		0			0
$916$	−11.9616	−	6.90601i	−0.395221	−	0.228181i
$917$		0			0
$918$		0			0
$919$	12.9115	−	22.3634i	0.425911	−	0.737699i	−0.570594	−	0.821232i	$-0.693287\pi$
$919$	12.9115	−	22.3634i	0.425911	−	0.737699i	0.996505	+	0.0835328i	$0.0266203\pi$
$920$	0.485867			0.0160186
$921$		0			0
$922$		−	1.10607i		−	0.0364264i
$923$	−22.3471	−	38.7063i	−0.735563	−	1.27403i
$924$		0			0
$925$	−6.18063	+	10.7052i	−0.203218	+	0.351983i
$926$	0.695162	+	0.401352i	0.0228444	+	0.0131892i
$927$		0			0
$928$	−11.7164	−	20.2934i	−0.384610	−	0.666164i
$929$	−7.97094	−	13.8061i	−0.261518	−	0.452963i	0.705127	−	0.709081i	$-0.250890\pi$
$929$	−7.97094	−	13.8061i	−0.261518	−	0.452963i	−0.966646	+	0.256118i	$0.917556\pi$
$930$		0			0
$931$		0			0
$932$	17.4246	−	10.0601i	0.570762	−	0.329529i
$933$		0			0
$934$			6.13802i			0.200842i
$935$	−0.142300	+	0.0821570i	−0.00465371	+	0.00268682i
$936$		0			0
$937$		−	15.0698i		−	0.492308i	−0.969231	−	0.246154i	$-0.920833\pi$
$937$		−	15.0698i		−	0.492308i	0.969231	−	0.246154i	$-0.0791668\pi$
$938$		0			0
$939$		0			0
$940$	0.479997			0.0156558
$941$	−5.76861	+	9.99152i	−0.188051	+	0.325714i	−0.944600	−	0.328222i	$-0.893550\pi$
$941$	−5.76861	+	9.99152i	−0.188051	+	0.325714i	0.756549	+	0.653937i	$0.226884\pi$
$942$		0			0
$943$	−44.3800	+	25.6228i	−1.44521	+	0.834393i
$944$	9.31636			0.303222
$945$		0			0
$946$	1.57543			0.0512218
$947$	−24.5364	+	14.1661i	−0.797325	+	0.460336i	−0.842535	−	0.538642i	$-0.818938\pi$
$947$	−24.5364	+	14.1661i	−0.797325	+	0.460336i	0.0452102	+	0.998977i	$0.485604\pi$
$948$		0			0
$949$	30.6981	−	53.1706i	0.996501	−	1.72599i
$950$	6.94989			0.225484
$951$		0			0
$952$		0			0
$953$			29.8498i			0.966931i	0.875364	+	0.483465i	$0.160622\pi$
$953$			29.8498i			0.966931i	−0.875364	+	0.483465i	$0.839378\pi$
$954$		0			0
$955$	−0.338347	+	0.195345i	−0.0109486	+	0.00632120i
$956$			8.74205i			0.282738i
$957$		0			0
$958$	−10.0935	+	5.82748i	−0.326106	+	0.188277i
$959$		0			0
$960$		0			0
$961$	−9.99478	−	17.3115i	−0.322412	−	0.558434i
$962$	−4.62642	−	8.01319i	−0.149162	−	0.258356i
$963$		0			0
$964$	14.8308	+	8.56258i	0.477669	+	0.275782i
$965$	−0.298287	+	0.516648i	−0.00960219	+	0.0166315i
$966$		0			0
$967$	8.17864	+	14.1658i	0.263007	+	0.455542i	0.967040	−	0.254626i	$-0.0819523\pi$
$967$	8.17864	+	14.1658i	0.263007	+	0.455542i	−0.704032	+	0.710168i	$0.748619\pi$
$968$			23.5339i			0.756407i
$969$		0			0
$970$	0.147106			0.00472327
$971$	10.7315	−	18.5875i	0.344390	−	0.596500i	−0.640853	−	0.767663i	$-0.721419\pi$
$971$	10.7315	−	18.5875i	0.344390	−	0.596500i	0.985243	+	0.171163i	$0.0547526\pi$
$972$		0			0
$973$		0			0
$974$	24.8470	+	14.3454i	0.796148	+	0.459657i
$975$		0			0
$976$	−3.17475	−	1.83294i	−0.101621	−	0.0586710i
$977$	−18.6219	−	10.7513i	−0.595766	−	0.343966i	0.171608	−	0.985165i	$-0.445104\pi$
$977$	−18.6219	−	10.7513i	−0.595766	−	0.343966i	−0.767374	+	0.641199i	$0.778437\pi$
$978$		0			0
$979$	−10.6696	−	6.16010i	−0.341002	−	0.196878i
$980$		0			0
$981$		0			0
$982$	−8.82301	+	15.2819i	−0.281554	+	0.487665i
$983$	−25.4194			−0.810752			−0.405376	−	0.914150i	$-0.632859\pi$
$983$	−25.4194			−0.810752			−0.405376	+	0.914150i	$0.632859\pi$
$984$		0			0
$985$		−	0.429311i		−	0.0136790i
$986$	7.67912	+	13.3006i	0.244553	+	0.423578i
$987$		0			0
$988$	9.18759	−	15.9134i	0.292296	−	0.506272i
$989$	−14.5886	−	8.42273i	−0.463890	−	0.267827i
$990$		0			0
$991$	−11.8768	−	20.5713i	−0.377280	−	0.653468i	0.613385	−	0.789784i	$-0.289807\pi$
$991$	−11.8768	−	20.5713i	−0.377280	−	0.653468i	−0.990665	+	0.136315i	$0.956474\pi$
$992$	−9.54935	−	16.5400i	−0.303192	−	0.525144i
$993$		0			0
$994$		0			0
$995$	−0.237453	+	0.137093i	−0.00752776	+	0.00434615i
$996$		0			0
$997$		−	12.1666i		−	0.385320i	−0.981266	−	0.192660i	$-0.938289\pi$
$997$		−	12.1666i		−	0.385320i	0.981266	−	0.192660i	$-0.0617114\pi$
$998$	3.05781	−	1.76543i	0.0967934	−	0.0558837i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.d.656.16		48
3.2	odd	2		441.2.s.d.362.9		48
7.2	even	3		1323.2.o.e.440.10		48
7.3	odd	6		1323.2.i.d.521.9		48
7.4	even	3		1323.2.i.d.521.10		48
7.5	odd	6		1323.2.o.e.440.9		48
7.6	odd	2	inner	1323.2.s.d.656.15		48
9.4	even	3		441.2.i.d.68.16		48
9.5	odd	6		1323.2.i.d.1097.9		48
21.2	odd	6		441.2.o.e.146.16	yes	48
21.5	even	6		441.2.o.e.146.15	✓	48
21.11	odd	6		441.2.i.d.227.9		48
21.17	even	6		441.2.i.d.227.10		48
21.20	even	2		441.2.s.d.362.10		48
63.4	even	3		441.2.s.d.374.10		48
63.5	even	6		1323.2.o.e.881.10		48
63.13	odd	6		441.2.i.d.68.15		48
63.23	odd	6		1323.2.o.e.881.9		48
63.31	odd	6		441.2.s.d.374.9		48
63.32	odd	6	inner	1323.2.s.d.962.15		48
63.40	odd	6		441.2.o.e.293.16	yes	48
63.41	even	6		1323.2.i.d.1097.10		48
63.58	even	3		441.2.o.e.293.15	yes	48
63.59	even	6	inner	1323.2.s.d.962.16		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.15		48	63.13	odd	6
441.2.i.d.68.16		48	9.4	even	3
441.2.i.d.227.9		48	21.11	odd	6
441.2.i.d.227.10		48	21.17	even	6
441.2.o.e.146.15	✓	48	21.5	even	6
441.2.o.e.146.16	yes	48	21.2	odd	6
441.2.o.e.293.15	yes	48	63.58	even	3
441.2.o.e.293.16	yes	48	63.40	odd	6
441.2.s.d.362.9		48	3.2	odd	2
441.2.s.d.362.10		48	21.20	even	2
441.2.s.d.374.9		48	63.31	odd	6
441.2.s.d.374.10		48	63.4	even	3
1323.2.i.d.521.9		48	7.3	odd	6
1323.2.i.d.521.10		48	7.4	even	3
1323.2.i.d.1097.9		48	9.5	odd	6
1323.2.i.d.1097.10		48	63.41	even	6
1323.2.o.e.440.9		48	7.5	odd	6
1323.2.o.e.440.10		48	7.2	even	3
1323.2.o.e.881.9		48	63.23	odd	6
1323.2.o.e.881.10		48	63.5	even	6
1323.2.s.d.656.15		48	7.6	odd	2	inner
1323.2.s.d.656.16		48	1.1	even	1	trivial
1323.2.s.d.962.15		48	63.32	odd	6	inner
1323.2.s.d.962.16		48	63.59	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.575298 - 0.332148i) q^{2} +(-0.779355 + 1.34988i) q^{4} -0.0283039 q^{5} +2.36404i q^{8} +O(q^{10})\)	\(q+(0.575298 - 0.332148i) q^{2} +(-0.779355 + 1.34988i) q^{4} -0.0283039 q^{5} +2.36404i q^{8} +(-0.0162832 + 0.00940110i) q^{10} -1.02228i q^{11} +(4.87844 - 2.81657i) q^{13} +(-0.773498 - 1.33974i) q^{16} +(2.83940 + 4.91798i) q^{17} +(-1.81237 - 1.04637i) q^{19} +(0.0220588 - 0.0382070i) q^{20} +(-0.339550 - 0.588118i) q^{22} +7.26133i q^{23} -4.99920 q^{25} +(1.87104 - 3.24073i) q^{26} +(3.52577 + 2.03560i) q^{29} +(2.87364 + 1.65910i) q^{31} +(-4.98462 - 2.87787i) q^{32} +(3.26700 + 1.88620i) q^{34} +(1.23632 - 2.14137i) q^{37} -1.39020 q^{38} -0.0669116i q^{40} +(3.52867 + 6.11183i) q^{41} +(-1.15994 + 2.00908i) q^{43} +(1.37996 + 0.796722i) q^{44} +(2.41184 + 4.17742i) q^{46} +(5.43997 + 9.42231i) q^{47} +(-2.87603 + 1.66048i) q^{50} +8.78043i q^{52} +(-10.0454 + 5.79973i) q^{53} +0.0289346i q^{55} +2.70449 q^{58} +(-3.01111 + 5.21540i) q^{59} +(2.05220 - 1.18484i) q^{61} +2.20427 q^{62} -0.729528 q^{64} +(-0.138079 + 0.0797200i) q^{65} +(-6.38995 + 11.0677i) q^{67} -8.85160 q^{68} -7.93415i q^{71} +(9.43889 - 5.44955i) q^{73} -1.64257i q^{74} +(2.82496 - 1.63099i) q^{76} +(7.80018 + 13.5103i) q^{79} +(0.0218930 + 0.0379198i) q^{80} +(4.06007 + 2.34408i) q^{82} +(3.07406 - 5.32442i) q^{83} +(-0.0803661 - 0.139198i) q^{85} +1.54109i q^{86} +2.41672 q^{88} +(6.02582 - 10.4370i) q^{89} +(-9.80194 - 5.65915i) q^{92} +(6.25921 + 3.61376i) q^{94} +(0.0512971 + 0.0296164i) q^{95} +(-6.77565 - 3.91192i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 120 * q^32 - 96 * q^44 - 48 * q^50 - 48 * q^53 - 48 * q^64 + 120 * q^65 - 24 * q^79 - 24 * q^85 + 144 * q^92 + 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more