LMFDB - Embedded newform 1323.2.i.d.521.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(521,1323)]

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, 1]))

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

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

chi := DirichletCharacter("1323.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.i (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			521.9
Character	$\chi$	$=$	1323.521
Dual form			1323.2.i.d.1097.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.664297i q^{2} +1.55871 q^{4} +(-0.0141520 + 0.0245119i) q^{5} +2.36404i q^{8} +O(q^{10})$	\(q+0.664297i q^{2} +1.55871 q^{4} +(-0.0141520 + 0.0245119i) q^{5} +2.36404i q^{8} +(-0.0162832 - 0.00940110i) q^{10} +(-0.885324 + 0.511142i) q^{11} +(-4.87844 + 2.81657i) q^{13} +1.54700 q^{16} +(-2.83940 + 4.91798i) q^{17} +(-1.81237 + 1.04637i) q^{19} +(-0.0220588 + 0.0382070i) q^{20} +(-0.339550 - 0.588118i) q^{22} +(-6.28849 - 3.63066i) q^{23} +(2.49960 + 4.32943i) q^{25} +(-1.87104 - 3.24073i) q^{26} +(3.52577 + 2.03560i) q^{29} +3.31820i q^{31} +5.75574i q^{32} +(-3.26700 - 1.88620i) q^{34} +(1.23632 + 2.14137i) q^{37} +(-0.695101 - 1.20395i) q^{38} +(-0.0579471 - 0.0334558i) q^{40} +(-3.52867 - 6.11183i) q^{41} +(-1.15994 + 2.00908i) q^{43} +(-1.37996 + 0.796722i) q^{44} +(2.41184 - 4.17742i) q^{46} +10.8799 q^{47} +(-2.87603 + 1.66048i) q^{50} +(-7.60408 + 4.39022i) q^{52} +(10.0454 + 5.79973i) q^{53} -0.0289346i q^{55} +(-1.35224 + 2.34215i) q^{58} -6.02222 q^{59} -2.36968i q^{61} -2.20427 q^{62} -0.729528 q^{64} -0.159440i q^{65} +12.7799 q^{67} +(-4.42580 + 7.66571i) q^{68} -7.93415i q^{71} +(9.43889 + 5.44955i) q^{73} +(-1.42251 + 0.821285i) q^{74} +(-2.82496 + 1.63099i) q^{76} -15.6004 q^{79} +(-0.0218930 + 0.0379198i) q^{80} +(4.06007 - 2.34408i) q^{82} +(-3.07406 + 5.32442i) q^{83} +(-0.0803661 - 0.139198i) q^{85} +(-1.33463 - 0.770546i) q^{86} +(-1.20836 - 2.09294i) q^{88} +(-6.02582 - 10.4370i) q^{89} +(-9.80194 - 5.65915i) q^{92} +7.22751i q^{94} -0.0592328i q^{95} +(6.77565 + 3.91192i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4}+O(q^{10}) $ 48 * q - 48 * q^4	$ 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) $ 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$			0.664297i			0.469729i	0.972028	+	0.234864i	$0.0754646\pi$
$2$			0.664297i			0.469729i	−0.972028	+	0.234864i	$0.924535\pi$
$3$		0			0
$3$		0			0
$4$	1.55871			0.779355
$5$	−0.0141520	+	0.0245119i	−0.00632895	+	0.0109621i	−0.869173	−	0.494509i	$-0.835348\pi$
$5$	−0.0141520	+	0.0245119i	−0.00632895	+	0.0109621i	0.862844	+	0.505471i	$0.168681\pi$
$6$		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
$11$	−0.885324	+	0.511142i	−0.266935	+	0.154115i	−0.627494	−	0.778621i	$-0.715919\pi$
$11$	−0.885324	+	0.511142i	−0.266935	+	0.154115i	0.360559	+	0.932736i	$0.382586\pi$
$12$		0			0
$13$	−4.87844	+	2.81657i	−1.35304	+	0.781176i	−0.988674	−	0.150081i	$-0.952047\pi$
$13$	−4.87844	+	2.81657i	−1.35304	+	0.781176i	−0.364363	+	0.931257i	$0.618713\pi$
$14$		0			0
$15$		0			0
$16$	1.54700			0.386749
$17$	−2.83940	+	4.91798i	−0.688656	+	1.19279i	0.283617	+	0.958938i	$0.408465\pi$
$17$	−2.83940	+	4.91798i	−0.688656	+	1.19279i	−0.972273	+	0.233849i	$0.924868\pi$
$18$		0			0
$19$	−1.81237	+	1.04637i	−0.415786	+	0.240054i	−0.693273	−	0.720675i	$-0.743832\pi$
$19$	−1.81237	+	1.04637i	−0.415786	+	0.240054i	0.277487	+	0.960729i	$0.410498\pi$
$20$	−0.0220588	+	0.0382070i	−0.00493250	+	0.00854334i
$21$		0			0
$22$	−0.339550	−	0.588118i	−0.0723923	−	0.125387i
$23$	−6.28849	−	3.63066i	−1.31124	−	0.757046i	−0.328940	−	0.944351i	$-0.606691\pi$
$23$	−6.28849	−	3.63066i	−1.31124	−	0.757046i	−0.982302	+	0.187305i	$0.940025\pi$
$24$		0			0
$25$	2.49960	+	4.32943i	0.499920	+	0.865887i
$26$	−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
$31$			3.31820i			0.595966i	0.954571	+	0.297983i	$0.0963139\pi$
$31$			3.31820i			0.595966i	−0.954571	+	0.297983i	$0.903686\pi$
$32$			5.75574i			1.01748i
$33$		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	0.949574	−	0.313543i	$-0.101516\pi$
$37$	1.23632	+	2.14137i	0.203250	+	0.352040i	−0.746324	+	0.665583i	$0.768183\pi$
$38$	−0.695101	−	1.20395i	−0.112760	−	0.195306i
$39$		0			0
$40$	−0.0579471	−	0.0334558i	−0.00916224	−	0.00528982i
$41$	−3.52867	−	6.11183i	−0.551085	−	0.954508i	−0.998197	−	0.0600295i	$-0.980881\pi$
$41$	−3.52867	−	6.11183i	−0.551085	−	0.954508i	0.447111	−	0.894478i	$-0.352453\pi$
$42$		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
$47$	10.8799			1.58700			0.793502	−	0.608568i	$-0.208256\pi$
$47$	10.8799			1.58700			0.793502	+	0.608568i	$0.208256\pi$
$48$		0			0
$49$		0			0
$50$	−2.87603	+	1.66048i	−0.406732	+	0.234827i
$51$		0			0
$52$	−7.60408	+	4.39022i	−1.05450	+	0.608814i
$53$	10.0454	+	5.79973i	1.37985	+	0.796655i	0.992141	−	0.125128i	$-0.0399342\pi$
$53$	10.0454	+	5.79973i	1.37985	+	0.796655i	0.387706	+	0.921783i	$0.373268\pi$
$54$		0			0
$55$		−	0.0289346i		−	0.00390155i
$56$		0			0
$57$		0			0
$58$	−1.35224	+	2.34215i	−0.177558	+	0.307540i
$59$	−6.02222			−0.784027			−0.392013	−	0.919960i	$-0.628221\pi$
$59$	−6.02222			−0.784027			−0.392013	+	0.919960i	$0.628221\pi$
$60$		0			0
$61$		−	2.36968i		−	0.303406i	−0.988426	−	0.151703i	$-0.951524\pi$
$61$		−	2.36968i		−	0.303406i	0.988426	−	0.151703i	$-0.0484757\pi$
$62$	−2.20427			−0.279942
$63$		0			0
$64$	−0.729528			−0.0911909
$65$		−	0.159440i		−	0.0197761i
$66$		0			0
$67$	12.7799			1.56131			0.780656	−	0.624960i	$-0.214885\pi$
$67$	12.7799			1.56131			0.780656	+	0.624960i	$0.214885\pi$
$68$	−4.42580	+	7.66571i	−0.536707	+	0.929604i
$69$		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	0.937462	−	0.348089i	$-0.113169\pi$
$73$	9.43889	+	5.44955i	1.10474	+	0.637821i	0.167277	+	0.985910i	$0.446503\pi$
$74$	−1.42251	+	0.821285i	−0.165363	+	0.0954725i
$75$		0			0
$76$	−2.82496	+	1.63099i	−0.324045	+	0.187087i
$77$		0			0
$78$		0			0
$79$	−15.6004			−1.75518			−0.877588	−	0.479415i	$-0.840849\pi$
$79$	−15.6004			−1.75518			−0.877588	+	0.479415i	$0.840849\pi$
$80$	−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	−0.983947	−	0.178461i	$-0.942888\pi$
$83$	−3.07406	+	5.32442i	−0.337421	+	0.584431i	0.646526	+	0.762892i	$0.276221\pi$
$84$		0			0
$85$	−0.0803661	−	0.139198i	−0.00871693	−	0.0150982i
$86$	−1.33463	−	0.770546i	−0.143916	−	0.0830902i
$87$		0			0
$88$	−1.20836	−	2.09294i	−0.128812	−	0.223108i
$89$	−6.02582	−	10.4370i	−0.638736	−	1.10632i	−0.985711	−	0.168448i	$-0.946124\pi$
$89$	−6.02582	−	10.4370i	−0.638736	−	1.10632i	0.346975	−	0.937874i	$-0.387209\pi$
$90$		0			0
$91$		0			0
$92$	−9.80194	−	5.65915i	−1.02192	−	0.590007i
$93$		0			0
$94$			7.22751i			0.745461i
$95$		−	0.0592328i		−	0.00607716i
$96$		0			0
$97$	6.77565	+	3.91192i	0.687963	+	0.397196i	0.802848	−	0.596183i	$-0.203317\pi$
$97$	6.77565	+	3.91192i	0.687963	+	0.397196i	−0.114885	+	0.993379i	$0.536650\pi$
$98$		0			0
$99$		0			0
$100$	3.89615	+	6.74833i	0.389615	+	0.674833i
$101$	0.226924	+	0.393043i	0.0225797	+	0.0391093i	0.877094	−	0.480318i	$-0.159479\pi$
$101$	0.226924	+	0.393043i	0.0225797	+	0.0391093i	−0.854515	+	0.519427i	$0.826145\pi$
$102$		0			0
$103$	−4.58316	−	2.64609i	−0.451592	−	0.260727i	0.256910	−	0.966435i	$-0.417296\pi$
$103$	−4.58316	−	2.64609i	−0.451592	−	0.260727i	−0.708502	+	0.705708i	$0.750629\pi$
$104$	−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	$-0.522249\pi$
$107$	7.85273	−	4.53377i	0.759152	−	0.438296i	0.828991	+	0.559262i	$0.188915\pi$
$108$		0			0
$109$	−2.36514	+	4.09654i	−0.226539	+	0.392377i	−0.956780	−	0.290812i	$-0.906074\pi$
$109$	−2.36514	+	4.09654i	−0.226539	+	0.392377i	0.730241	+	0.683190i	$0.239408\pi$
$110$	0.0192212			0.00183267
$111$		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
$115$	0.177989	−	0.102762i	0.0165976	−	0.00958261i
$116$	5.49565	+	3.17291i	0.510258	+	0.294598i
$117$		0			0
$118$		−	4.00054i		−	0.368280i
$119$		0			0
$120$		0			0
$121$	−4.97747	+	8.62123i	−0.452497	+	0.783748i
$122$	1.57417			0.142519
$123$		0			0
$124$			5.17211i			0.464469i
$125$	−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	$0.437848\pi$
$128$			11.0269i			0.974646i
$129$		0			0
$130$	0.105915			0.00928940
$131$	−1.27231	+	2.20371i	−0.111162	+	0.192539i	−0.916239	−	0.400632i	$-0.868791\pi$
$131$	−1.27231	+	2.20371i	−0.111162	+	0.192539i	0.805077	+	0.593171i	$0.202124\pi$
$132$		0			0
$133$		0			0
$134$			8.48964i			0.733393i
$135$		0			0
$136$	−11.6263	−	6.71245i	−0.996948	−	0.575588i
$137$	−9.82536	+	5.67267i	−0.839437	+	0.484649i	−0.857073	−	0.515195i	$-0.827719\pi$
$137$	−9.82536	+	5.67267i	−0.839437	+	0.484649i	0.0176357	+	0.999844i	$0.494386\pi$
$138$		0			0
$139$	3.04891	−	1.76029i	0.258605	−	0.149306i	−0.365093	−	0.930971i	$-0.618963\pi$
$139$	3.04891	−	1.76029i	0.258605	−	0.149306i	0.623698	+	0.781665i	$0.285629\pi$
$140$		0			0
$141$		0			0
$142$	5.27063			0.442301
$143$	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
$149$	−13.7806	−	7.95623i	−1.12895	−	0.651800i	−0.185279	−	0.982686i	$-0.559319\pi$
$149$	−13.7806	−	7.95623i	−1.12895	−	0.651800i	−0.943671	+	0.330886i	$0.892652\pi$
$150$		0			0
$151$	−1.73008	−	2.99659i	−0.140792	−	0.243859i	0.787003	−	0.616949i	$-0.211632\pi$
$151$	−1.73008	−	2.99659i	−0.140792	−	0.243859i	−0.927795	+	0.373090i	$0.878298\pi$
$152$	−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
$157$		−	16.3488i		−	1.30478i	−0.757883	−	0.652390i	$-0.773766\pi$
$157$		−	16.3488i		−	1.30478i	0.757883	−	0.652390i	$-0.226234\pi$
$158$		−	10.3633i		−	0.824457i
$159$		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	0.588828	−	0.808258i	$-0.299589\pi$
$163$	−5.17782	−	8.96824i	−0.405558	−	0.702447i	−0.994386	+	0.105811i	$0.966256\pi$
$164$	−5.50017	−	9.52657i	−0.429491	−	0.743900i
$165$		0			0
$166$	−3.53699	−	2.04208i	−0.274524	−	0.158497i
$167$	2.94297	+	5.09738i	0.227734	+	0.394447i	0.957136	−	0.289638i	$-0.0935349\pi$
$167$	2.94297	+	5.09738i	0.227734	+	0.394447i	−0.729402	+	0.684085i	$0.760202\pi$
$168$		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
$173$	4.86551			0.369918			0.184959	−	0.982746i	$-0.440785\pi$
$173$	4.86551			0.369918			0.184959	+	0.982746i	$0.440785\pi$
$174$		0			0
$175$		0			0
$176$	−1.36959	+	0.790735i	−0.103237	+	0.0596039i
$177$		0			0
$178$	6.93328	−	4.00293i	0.519671	−	0.300032i
$179$	0.175495	+	0.101322i	0.0131171	+	0.00757319i	0.506544	−	0.862214i	$-0.330923\pi$
$179$	0.175495	+	0.101322i	0.0131171	+	0.00757319i	−0.493427	+	0.869787i	$0.664256\pi$
$180$		0			0
$181$			6.26273i			0.465505i	0.972536	+	0.232753i	$0.0747732\pi$
$181$			6.26273i			0.465505i	−0.972536	+	0.232753i	$0.925227\pi$
$182$		0			0
$183$		0			0
$184$	8.58303	−	14.8662i	0.632749	−	1.09595i
$185$	−0.0699856			−0.00514544
$186$		0			0
$187$		−	5.80534i		−	0.424529i
$188$	16.9587			1.23684
$189$		0			0
$190$	0.0393482			0.00285462
$191$			13.8034i			0.998776i	0.866379	+	0.499388i	$0.166442\pi$
$191$			13.8034i			0.998776i	−0.866379	+	0.499388i	$0.833558\pi$
$192$		0			0
$193$	−21.0774			−1.51719			−0.758593	−	0.651565i	$-0.774113\pi$
$193$	−21.0774			−1.51719			−0.758593	+	0.651565i	$0.774113\pi$
$194$	−2.59868	+	4.50104i	−0.186574	+	0.323156i
$195$		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	0.766957	−	0.641698i	$-0.221770\pi$
$199$	8.38940	+	4.84362i	0.594709	+	0.343355i	−0.172249	+	0.985054i	$0.555103\pi$
$200$	−10.2349	+	5.90915i	−0.723720	+	0.417840i
$201$		0			0
$202$	−0.261097	+	0.150745i	−0.0183707	+	0.0106064i
$203$		0			0
$204$		0			0
$205$	0.199750			0.0139512
$206$	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	$0.994874\pi$
$212$	15.6579	+	9.04010i	1.07539	+	0.620877i
$213$		0			0
$214$	3.01177	+	5.21654i	0.205880	+	0.356595i
$215$	−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
$220$		−	0.0451007i		−	0.00304069i
$221$		−	31.9895i		−	2.15185i
$222$		0			0
$223$	−2.58777	−	1.49405i	−0.173290	−	0.100049i	0.410846	−	0.911705i	$-0.365233\pi$
$223$	−2.58777	−	1.49405i	−0.173290	−	0.100049i	−0.584136	+	0.811656i	$0.698567\pi$
$224$		0			0
$225$		0			0
$226$	3.14921	+	5.45459i	0.209482	+	0.362834i
$227$	14.3867	+	24.9184i	0.954876	+	1.65389i	0.734652	+	0.678444i	$0.237346\pi$
$227$	14.3867	+	24.9184i	0.954876	+	1.65389i	0.220224	+	0.975449i	$0.429321\pi$
$228$		0			0
$229$	7.67401	+	4.43059i	0.507113	+	0.292782i	0.731646	−	0.681685i	$-0.238752\pi$
$229$	7.67401	+	4.43059i	0.507113	+	0.292782i	−0.224533	+	0.974466i	$0.572086\pi$
$230$	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	$-0.527706\pi$
$233$	11.1789	−	6.45412i	0.732351	−	0.422823i	0.819282	+	0.573391i	$0.194372\pi$
$234$		0			0
$235$	−0.153973	+	0.266688i	−0.0100441	+	0.0173968i
$236$	−9.38690			−0.611035
$237$		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
$241$	9.51481	−	5.49338i	0.612903	−	0.353860i	−0.161198	−	0.986922i	$-0.551536\pi$
$241$	9.51481	−	5.49338i	0.612903	−	0.353860i	0.774101	+	0.633063i	$0.218202\pi$
$242$	−5.72705	−	3.30652i	−0.368149	−	0.212551i
$243$		0			0
$244$		−	3.69364i		−	0.236461i
$245$		0			0
$246$		0			0
$247$	5.89436	−	10.2093i	0.375049	−	0.649604i
$248$	−7.84435			−0.498117
$249$		0			0
$250$		−	0.188007i		−	0.0118906i
$251$	24.2241			1.52901			0.764505	−	0.644618i	$-0.222984\pi$
$251$	24.2241			1.52901			0.764505	+	0.644618i	$0.222984\pi$
$252$		0			0
$253$	7.42314			0.466689
$254$			2.90495i			0.182273i
$255$		0			0
$256$	−8.78416			−0.549010
$257$	−8.86142	+	15.3484i	−0.552760	+	0.957409i	0.445314	+	0.895375i	$0.353092\pi$
$257$	−8.86142	+	15.3484i	−0.552760	+	0.957409i	−0.998074	+	0.0620341i	$0.980241\pi$
$258$		0			0
$259$		0			0
$260$		−	0.248521i		−	0.0154126i
$261$		0			0
$262$	−1.46392	−	0.845193i	−0.0904411	−	0.0522162i
$263$	2.51031	−	1.44933i	0.154793	−	0.0893695i	−0.420603	−	0.907245i	$-0.638181\pi$
$263$	2.51031	−	1.44933i	0.154793	−	0.0893695i	0.575396	+	0.817875i	$0.304848\pi$
$264$		0			0
$265$	−0.284325	+	0.164155i	−0.0174660	+	0.0100840i
$266$		0			0
$267$		0			0
$268$	19.9202			1.21682
$269$	10.9469	−	18.9606i	0.667444	−	1.15605i	−0.311172	−	0.950354i	$-0.600722\pi$
$269$	10.9469	−	18.9606i	0.667444	−	1.15605i	0.978616	−	0.205694i	$-0.0659451\pi$
$270$		0			0
$271$	7.77992	−	4.49174i	0.472596	−	0.272854i	−0.244730	−	0.969591i	$-0.578699\pi$
$271$	7.77992	−	4.49174i	0.472596	−	0.272854i	0.717326	+	0.696738i	$0.245366\pi$
$272$	−4.39254	+	7.60811i	−0.266337	+	0.461309i
$273$		0			0
$274$	−3.76834	−	6.52695i	−0.227654	−	0.394308i
$275$	−4.42591	−	2.55530i	−0.266892	−	0.154090i
$276$		0			0
$277$	−7.95091	−	13.7714i	−0.477724	−	0.827442i	0.521950	−	0.852976i	$-0.325205\pi$
$277$	−7.95091	−	13.7714i	−0.477724	−	0.827442i	−0.999674	+	0.0255339i	$0.991871\pi$
$278$	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
$283$		−	18.7739i		−	1.11599i	−0.829844	−	0.557995i	$-0.811571\pi$
$283$		−	18.7739i		−	1.11599i	0.829844	−	0.557995i	$-0.188429\pi$
$284$		−	12.3670i		−	0.733848i
$285$		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
$290$	−0.0382738	−	0.0662922i	−0.00224751	−	0.00389281i
$291$		0			0
$292$	14.7125	+	8.49426i	0.860983	+	0.497089i
$293$	11.4201	+	19.7802i	0.667169	+	1.15557i	0.978692	+	0.205332i	$0.0658274\pi$
$293$	11.4201	+	19.7802i	0.667169	+	1.15557i	−0.311523	+	0.950238i	$0.600839\pi$
$294$		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
$299$	40.9041			2.36554
$300$		0			0
$301$		0			0
$302$	1.99062	−	1.14929i	0.114548	−	0.0661341i
$303$		0			0
$304$	−2.80373	+	1.61873i	−0.160805	+	0.0928407i
$305$	0.0580853	+	0.0335356i	0.00332596	+	0.00192024i
$306$		0			0
$307$		−	18.6325i		−	1.06341i	−0.846928	−	0.531707i	$-0.821551\pi$
$307$		−	18.6325i		−	1.06341i	0.846928	−	0.531707i	$-0.178449\pi$
$308$		0			0
$309$		0			0
$310$	0.0311947	−	0.0540308i	0.00177174	−	0.00306875i
$311$	20.5495			1.16526			0.582628	−	0.812739i	$-0.302025\pi$
$311$	20.5495			1.16526			0.582628	+	0.812739i	$0.302025\pi$
$312$		0			0
$313$		−	0.721071i		−	0.0407574i	−0.999792	−	0.0203787i	$-0.993513\pi$
$313$		−	0.721071i		−	0.0407574i	0.999792	−	0.0203787i	$-0.00648718\pi$
$314$	10.8605			0.612893
$315$		0			0
$316$	−24.3164			−1.36791
$317$		−	21.9295i		−	1.23168i	−0.787871	−	0.615841i	$-0.788816\pi$
$317$		−	21.9295i		−	1.23168i	0.787871	−	0.615841i	$-0.211184\pi$
$318$		0			0
$319$	−4.16193			−0.233023
$320$	0.0103242	−	0.0178821i	0.000577143	−	0.000999641i
$321$		0			0
$322$		0			0
$323$		−	11.8843i		−	0.661258i
$324$		0			0
$325$	−24.3883	−	14.0806i	−1.35282	−	0.781051i
$326$	5.95757	−	3.43961i	0.329959	−	0.190502i
$327$		0			0
$328$	14.4486	−	8.34191i	0.797791	−	0.460605i
$329$		0			0
$330$		0			0
$331$	21.6676			1.19096			0.595480	−	0.803370i	$-0.296962\pi$
$331$	21.6676			1.19096			0.595480	+	0.803370i	$0.296962\pi$
$332$	−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	$0.591452\pi$
$338$	10.7766	+	6.22190i	0.586172	+	0.338427i
$339$		0			0
$340$	−0.125268	−	0.216970i	−0.00679358	−	0.0117668i
$341$	−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
$346$			3.23215i			0.173761i
$347$			5.68598i			0.305239i	0.988285	+	0.152620i	$0.0487709\pi$
$347$			5.68598i			0.305239i	−0.988285	+	0.152620i	$0.951229\pi$
$348$		0			0
$349$	9.68412	+	5.59113i	0.518379	+	0.299286i	0.736271	−	0.676687i	$-0.236585\pi$
$349$	9.68412	+	5.59113i	0.518379	+	0.299286i	−0.217892	+	0.975973i	$0.569918\pi$
$350$		0			0
$351$		0			0
$352$	−2.94200	−	5.09570i	−0.156809	−	0.271601i
$353$	7.02111	+	12.1609i	0.373696	+	0.647260i	0.990131	−	0.140146i	$-0.0447571\pi$
$353$	7.02111	+	12.1609i	0.373696	+	0.647260i	−0.616435	+	0.787406i	$0.711424\pi$
$354$		0			0
$355$	0.194481	+	0.112284i	0.0103220	+	0.00595940i
$356$	−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	$-0.412531\pi$
$359$	23.5052	−	13.5707i	1.24056	−	0.716235i	0.969207	+	0.246246i	$0.0791973\pi$
$360$		0			0
$361$	−7.31022	+	12.6617i	−0.384748	+	0.666403i
$362$	−4.16031			−0.218661
$363$		0			0
$364$		0			0
$365$	−0.267158	+	0.154244i	−0.0139837	+	0.00807347i
$366$		0			0
$367$	5.95891	−	3.44038i	0.311053	−	0.179586i	−0.336345	−	0.941739i	$-0.609191\pi$
$367$	5.95891	−	3.44038i	0.311053	−	0.179586i	0.647397	+	0.762153i	$0.275857\pi$
$368$	−9.72828	−	5.61662i	−0.507122	−	0.292787i
$369$		0			0
$370$		−	0.0464912i		−	0.00241696i
$371$		0			0
$372$		0			0
$373$	0.123926	−	0.214645i	0.00641662	−	0.0111139i	−0.862799	−	0.505547i	$-0.831291\pi$
$373$	0.123926	−	0.214645i	0.00641662	−	0.0111139i	0.869216	+	0.494433i	$0.164624\pi$
$374$	3.85647			0.199413
$375$		0			0
$376$			25.7206i			1.32644i
$377$	−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	$0.573565\pi$
$380$		−	0.0923268i		−	0.00473626i
$381$		0			0
$382$	−9.16952			−0.469154
$383$	0.163545	−	0.283268i	0.00835675	−	0.0144743i	−0.861817	−	0.507220i	$-0.830673\pi$
$383$	0.163545	−	0.283268i	0.00835675	−	0.0144743i	0.870174	+	0.492745i	$0.164007\pi$
$384$		0			0
$385$		0			0
$386$		−	14.0017i		−	0.712665i
$387$		0			0
$388$	10.5613	+	6.09755i	0.536167	+	0.309556i
$389$	−5.72348	+	3.30445i	−0.290192	+	0.167542i	−0.638028	−	0.770013i	$-0.720250\pi$
$389$	−5.72348	+	3.30445i	−0.290192	+	0.167542i	0.347837	+	0.937555i	$0.386916\pi$
$390$		0			0
$391$	35.7111	−	20.6178i	1.80599	−	1.04269i
$392$		0			0
$393$		0			0
$394$	−10.0760			−0.507621
$395$	0.220776	−	0.382394i	0.0111084	−	0.0192404i
$396$		0			0
$397$	6.50435	−	3.75529i	0.326444	−	0.188472i	−0.327817	−	0.944741i	$-0.606313\pi$
$397$	6.50435	−	3.75529i	0.326444	−	0.188472i	0.654261	+	0.756269i	$0.272980\pi$
$398$	−3.21760	+	5.57305i	−0.161284	+	0.279352i
$399$		0			0
$400$	3.86687	+	6.69762i	0.193344	+	0.334881i
$401$	−5.48595	−	3.16732i	−0.273956	−	0.158168i	0.356728	−	0.934208i	$-0.383892\pi$
$401$	−5.48595	−	3.16732i	−0.273956	−	0.158168i	−0.630684	+	0.776040i	$0.717226\pi$
$402$		0			0
$403$	−9.34594	−	16.1876i	−0.465555	−	0.806364i
$404$	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
$409$			33.4915i			1.65605i	0.560693	+	0.828024i	$0.310535\pi$
$409$			33.4915i			1.65605i	−0.560693	+	0.828024i	$0.689465\pi$
$410$			0.132693i			0.00655326i
$411$		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
$416$	−16.2115	−	28.0791i	−0.794832	−	1.37669i
$417$		0			0
$418$	1.23078	+	0.710590i	0.0601993	+	0.0347561i
$419$	0.896459	+	1.55271i	0.0437949	+	0.0758550i	0.887092	−	0.461593i	$-0.152722\pi$
$419$	0.896459	+	1.55271i	0.0437949	+	0.0758550i	−0.843297	+	0.537448i	$0.819389\pi$
$420$		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
$425$	−28.3894			−1.37709
$426$		0			0
$427$		0			0
$428$	12.2401	−	7.06684i	0.591649	−	0.341589i
$429$		0			0
$430$	0.0377751	−	0.0218095i	0.00182168	−	0.00105175i
$431$	1.15145	+	0.664787i	0.0554632	+	0.0320217i	0.527475	−	0.849570i	$-0.323139\pi$
$431$	1.15145	+	0.664787i	0.0554632	+	0.0320217i	−0.472012	+	0.881592i	$0.656472\pi$
$432$		0			0
$433$			37.4292i			1.79873i	0.437194	+	0.899367i	$0.355972\pi$
$433$			37.4292i			1.79873i	−0.437194	+	0.899367i	$0.644028\pi$
$434$		0			0
$435$		0			0
$436$	−3.68656	+	6.38531i	−0.176554	+	0.305801i
$437$	15.1961			0.726927
$438$		0			0
$439$		−	23.7388i		−	1.13299i	−0.824064	−	0.566496i	$-0.808298\pi$
$439$		−	23.7388i		−	1.13299i	0.824064	−	0.566496i	$-0.191702\pi$
$440$	0.0684026			0.00326097
$441$		0			0
$442$	21.2505			1.01078
$443$			11.2504i			0.534525i	0.963624	+	0.267262i	$0.0861191\pi$
$443$			11.2504i			0.534525i	−0.963624	+	0.267262i	$0.913881\pi$
$444$		0			0
$445$	0.341109			0.0161701
$446$	0.992491	−	1.71904i	0.0469958	−	0.0813991i
$447$		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
$452$	12.7987	−	7.38933i	0.602000	−	0.347565i
$453$		0			0
$454$	−16.5532	+	9.55701i	−0.776881	+	0.448533i
$455$		0			0
$456$		0			0
$457$	−20.6269			−0.964888			−0.482444	−	0.875927i	$-0.660251\pi$
$457$	−20.6269			−0.964888			−0.482444	+	0.875927i	$0.660251\pi$
$458$	−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	−0.884761	−	0.466045i	$-0.845679\pi$
$461$	−0.832511	+	1.44195i	−0.0387739	+	0.0671584i	0.845987	+	0.533203i	$0.179012\pi$
$462$		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	$0.824395\pi$
$464$	5.45435	+	3.14907i	0.253212	+	0.146192i
$465$		0			0
$466$	4.28745	+	7.42608i	0.198612	+	0.344006i
$467$	4.61994	+	8.00197i	0.213785	+	0.370287i	0.952896	−	0.303297i	$-0.0980874\pi$
$467$	4.61994	+	8.00197i	0.213785	+	0.370287i	−0.739111	+	0.673584i	$0.764754\pi$
$468$		0			0
$469$		0			0
$470$	−0.177160	−	0.102283i	−0.00817179	−	0.00471798i
$471$		0			0
$472$		−	14.2368i		−	0.655300i
$473$		−	2.37158i		−	0.109045i
$474$		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
$479$	−8.77241	−	15.1943i	−0.400822	−	0.694243i	0.593004	−	0.805200i	$-0.297942\pi$
$479$	−8.77241	−	15.1943i	−0.400822	−	0.694243i	−0.993825	+	0.110956i	$0.964609\pi$
$480$		0			0
$481$	−12.0627	−	6.96438i	−0.550010	−	0.317549i
$482$	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	0.310900	−	0.950442i	$-0.399369\pi$
$487$	21.5949	−	37.4034i	0.978558	−	1.69491i	0.667657	−	0.744469i	$-0.267297\pi$
$488$	5.60201			0.253591
$489$		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
$493$	−20.0221	+	11.5598i	−0.901751	+	0.520626i
$494$	6.78202	+	3.91560i	0.305138	+	0.176171i
$495$		0			0
$496$			5.13324i			0.230489i
$497$		0			0
$498$		0			0
$499$	−2.65759	+	4.60308i	−0.118970	+	0.206062i	−0.919360	−	0.393418i	$-0.871293\pi$
$499$	−2.65759	+	4.60308i	−0.118970	+	0.206062i	0.800390	+	0.599480i	$0.204626\pi$
$500$	−0.441141			−0.0197284
$501$		0			0
$502$			16.0920i			0.718220i
$503$	−35.5334			−1.58436			−0.792178	−	0.610290i	$-0.791053\pi$
$503$	−35.5334			−1.58436			−0.792178	+	0.610290i	$0.791053\pi$
$504$		0			0
$505$	−0.0128457			−0.000571624
$506$			4.93116i			0.219217i
$507$		0			0
$508$	6.81620			0.302420
$509$	6.81654	−	11.8066i	0.302138	−	0.523318i	−0.674482	−	0.738291i	$-0.735633\pi$
$509$	6.81654	−	11.8066i	0.302138	−	0.523318i	0.976620	+	0.214973i	$0.0689663\pi$
$510$		0			0
$511$		0			0
$512$			16.2184i			0.716760i
$513$		0			0
$514$	−10.1959	−	5.88661i	−0.449722	−	0.259647i
$515$	0.129721	−	0.0748947i	0.00571621	−	0.00330025i
$516$		0			0
$517$	−9.63227	+	5.56120i	−0.423627	+	0.244581i
$518$		0			0
$519$		0			0
$520$	0.376922			0.0165291
$521$	5.11259	−	8.85526i	0.223987	−	0.387956i	−0.732028	−	0.681274i	$-0.761426\pi$
$521$	5.11259	−	8.85526i	0.223987	−	0.387956i	0.956015	+	0.293318i	$0.0947595\pi$
$522$		0			0
$523$	−4.48150	+	2.58740i	−0.195962	+	0.113139i	−0.594771	−	0.803895i	$-0.702757\pi$
$523$	−4.48150	+	2.58740i	−0.195962	+	0.113139i	0.398808	+	0.917034i	$0.369424\pi$
$524$	−1.98317	+	3.43495i	−0.0866350	+	0.150056i
$525$		0			0
$526$	0.962785	+	1.66759i	0.0419794	+	0.0727105i
$527$	−16.3189	−	9.42169i	−0.710860	−	0.410415i
$528$		0			0
$529$	14.8634	+	25.7442i	0.646236	+	1.11931i
$530$	−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
$535$			0.256647i			0.0110958i
$536$			30.2122i			1.30497i
$537$		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	0.998487	+	0.0549871i	$0.0175118\pi$
$541$	12.7197	+	22.0312i	0.546864	+	0.947196i	−0.451623	+	0.892209i	$0.649155\pi$
$542$	2.98385	+	5.16817i	0.128167	+	0.221992i
$543$		0			0
$544$	−28.3067	−	16.3429i	−1.21364	−	0.700694i
$545$	−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
$551$	−8.51998			−0.362963
$552$		0			0
$553$		0			0
$554$	9.14828	−	5.28176i	0.388673	−	0.224401i
$555$		0			0
$556$	4.75237	−	2.74378i	0.201545	−	0.116362i
$557$	−16.9788	−	9.80269i	−0.719413	−	0.415353i	0.0951237	−	0.995465i	$-0.469675\pi$
$557$	−16.9788	−	9.80269i	−0.719413	−	0.415353i	−0.814537	+	0.580112i	$0.803009\pi$
$558$		0			0
$559$		−	13.0683i		−	0.552728i
$560$		0			0
$561$		0			0
$562$	−1.72714	+	2.99149i	−0.0728548	+	0.126188i
$563$	−14.4759			−0.610087			−0.305044	−	0.952338i	$-0.598671\pi$
$563$	−14.4759			−0.610087			−0.305044	+	0.952338i	$0.598671\pi$
$564$		0			0
$565$			0.268359i			0.0112899i
$566$	12.4714			0.524213
$567$		0			0
$568$	18.7566			0.787011
$569$			7.74769i			0.324800i	0.986725	+	0.162400i	$0.0519235\pi$
$569$			7.74769i			0.324800i	−0.986725	+	0.162400i	$0.948076\pi$
$570$		0			0
$571$	16.1371			0.675318			0.337659	−	0.941269i	$-0.390365\pi$
$571$	16.1371			0.675318			0.337659	+	0.941269i	$0.390365\pi$
$572$	4.48805	−	7.77353i	0.187655	−	0.325027i
$573$		0			0
$574$		0			0
$575$		−	36.3008i		−	1.51385i
$576$		0			0
$577$	10.5403	+	6.08542i	0.438797	+	0.253339i	0.703087	−	0.711104i	$-0.251804\pi$
$577$	10.5403	+	6.08542i	0.438797	+	0.253339i	−0.264290	+	0.964443i	$0.585138\pi$
$578$	8.77258	−	5.06485i	0.364891	−	0.210670i
$579$		0			0
$580$	−0.155548	+	0.0898059i	−0.00645879	+	0.00372899i
$581$		0			0
$582$		0			0
$583$	−11.8579			−0.491106
$584$	−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	$-0.588051\pi$
$587$	16.8761	−	29.2302i	0.696550	−	1.20646i	0.969655	−	0.244476i	$-0.0786158\pi$
$588$		0			0
$589$	−3.47207	−	6.01380i	−0.143064	−	0.247794i
$590$	0.0980610	+	0.0566155i	0.00403711	+	0.00233082i
$591$		0			0
$592$	1.91259	+	3.31270i	0.0786069	+	0.136151i
$593$	−9.15123	−	15.8504i	−0.375796	−	0.650897i	0.614650	−	0.788800i	$-0.289297\pi$
$593$	−9.15123	−	15.8504i	−0.375796	−	0.650897i	−0.990446	+	0.137903i	$0.955964\pi$
$594$		0			0
$595$		0			0
$596$	−21.4799	−	12.4015i	−0.879853	−	0.507983i
$597$		0			0
$598$			27.1724i			1.11116i
$599$			39.4798i			1.61310i	0.591165	+	0.806551i	$0.298668\pi$
$599$			39.4798i			1.61310i	−0.591165	+	0.806551i	$0.701332\pi$
$600$		0			0
$601$	−34.4865	−	19.9108i	−1.40673	−	0.812177i	−0.411661	−	0.911337i	$-0.635051\pi$
$601$	−34.4865	−	19.9108i	−1.40673	−	0.812177i	−0.995072	+	0.0991600i	$0.968384\pi$
$602$		0			0
$603$		0			0
$604$	−2.69670	−	4.67082i	−0.109727	−	0.190053i
$605$	−0.140882	−	0.244015i	−0.00572766	−	0.00992060i
$606$		0			0
$607$	21.6104	+	12.4768i	0.877140	+	0.506417i	0.869714	−	0.493555i	$-0.164303\pi$
$607$	21.6104	+	12.4768i	0.877140	+	0.506417i	0.00742570	+	0.999972i	$0.497636\pi$
$608$	−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	0.430294	+	0.902689i	$0.358410\pi$
$613$	−14.0285	+	24.2980i	−0.566605	+	0.981388i	−0.996898	+	0.0786994i	$0.974923\pi$
$614$	12.3775			0.499516
$615$		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
$619$	17.2889	−	9.98173i	0.694898	−	0.401200i	−0.110546	−	0.993871i	$-0.535260\pi$
$619$	17.2889	−	9.98173i	0.694898	−	0.401200i	0.805444	+	0.592671i	$0.201927\pi$
$620$	−0.126778	−	0.0731955i	−0.00509154	−	0.00293960i
$621$		0			0
$622$			13.6510i			0.547354i
$623$		0			0
$624$		0			0
$625$	−12.4940	+	21.6402i	−0.499760	+	0.865609i
$626$	0.479005			0.0191449
$627$		0			0
$628$		−	25.4831i		−	1.01689i
$629$	−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	$0.882314\pi$
$632$		−	36.8798i		−	1.46700i
$633$		0			0
$634$	14.5677			0.578556
$635$	−0.0618862	+	0.107190i	−0.00245588	+	0.00425370i
$636$		0			0
$637$		0			0
$638$		−	2.76475i		−	0.109458i
$639$		0			0
$640$	−0.270290	−	0.156052i	−0.0106841	−	0.00616849i
$641$	−3.34281	+	1.92997i	−0.132033	+	0.0762293i	−0.564562	−	0.825391i	$-0.690955\pi$
$641$	−3.34281	+	1.92997i	−0.132033	+	0.0762293i	0.432529	+	0.901620i	$0.357621\pi$
$642$		0			0
$643$	−31.0233	+	17.9113i	−1.22344	+	0.706352i	−0.965649	−	0.259849i	$-0.916327\pi$
$643$	−31.0233	+	17.9113i	−1.22344	+	0.706352i	−0.257789	+	0.966201i	$0.582994\pi$
$644$		0			0
$645$		0			0
$646$	7.89468			0.310612
$647$	−21.8246	+	37.8013i	−0.858013	+	1.48612i	0.0158075	+	0.999875i	$0.494968\pi$
$647$	−21.8246	+	37.8013i	−0.858013	+	1.48612i	−0.873821	+	0.486248i	$0.838365\pi$
$648$		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
$653$	6.45191	+	3.72501i	0.252483	+	0.145771i	0.620901	−	0.783889i	$-0.286767\pi$
$653$	6.45191	+	3.72501i	0.252483	+	0.145771i	−0.368418	+	0.929660i	$0.620100\pi$
$654$		0			0
$655$	−0.0360114	−	0.0623736i	−0.00140708	−	0.00243714i
$656$	−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
$661$		−	28.8505i		−	1.12215i	−0.827763	−	0.561077i	$-0.810387\pi$
$661$		−	28.8505i		−	1.12215i	0.827763	−	0.561077i	$-0.189613\pi$
$662$			14.3937i			0.559428i
$663$		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
$668$	4.58724	+	7.94534i	0.177486	+	0.307414i
$669$		0			0
$670$	−0.208097	−	0.120145i	−0.00803950	−	0.00464161i
$671$	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
$677$	−36.3821			−1.39828			−0.699140	−	0.714985i	$-0.746433\pi$
$677$	−36.3821			−1.39828			−0.699140	+	0.714985i	$0.746433\pi$
$678$		0			0
$679$		0			0
$680$	0.329070	−	0.189989i	0.0126193	−	0.00728573i
$681$		0			0
$682$	1.95149	−	1.12669i	0.0747265	−	0.0431433i
$683$	20.5530	+	11.8663i	0.786438	+	0.454050i	0.838707	−	0.544583i	$-0.183312\pi$
$683$	20.5530	+	11.8663i	0.786438	+	0.454050i	−0.0522688	+	0.998633i	$0.516645\pi$
$684$		0			0
$685$		−	0.321118i		−	0.0122693i
$686$		0			0
$687$		0			0
$688$	−1.79443	+	3.10804i	−0.0684119	+	0.118493i
$689$	−65.3415			−2.48931
$690$		0			0
$691$		−	3.30391i		−	0.125687i	−0.998023	−	0.0628433i	$-0.979983\pi$
$691$		−	3.30391i		−	0.125687i	0.998023	−	0.0628433i	$-0.0200168\pi$
$692$	7.58393			0.288298
$693$		0			0
$694$	−3.77718			−0.143380
$695$			0.0996463i			0.00377980i
$696$		0			0
$697$	40.0772			1.51803
$698$	−3.71417	+	6.43313i	−0.140583	+	0.243498i
$699$		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
$704$	0.645868	−	0.372892i	0.0243421	−	0.0140539i
$705$		0			0
$706$	−8.07845	+	4.66410i	−0.304037	+	0.175536i
$707$		0			0
$708$		0			0
$709$	16.1553			0.606727			0.303363	−	0.952875i	$-0.401890\pi$
$709$	16.1553			0.606727			0.303363	+	0.952875i	$0.401890\pi$
$710$	−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
$716$	0.273546	+	0.157932i	0.0102229	+	0.00590220i
$717$		0			0
$718$	9.01498	+	15.6144i	0.336436	+	0.582724i
$719$	22.5953	+	39.1361i	0.842661	+	1.45953i	0.887637	+	0.460543i	$0.152345\pi$
$719$	22.5953	+	39.1361i	0.842661	+	1.45953i	−0.0449767	+	0.998988i	$0.514321\pi$
$720$		0			0
$721$		0			0
$722$	−8.41110	−	4.85615i	−0.313029	−	0.180727i
$723$		0			0
$724$			9.76178i			0.362794i
$725$			20.3528i			0.755883i
$726$		0			0
$727$	7.15775	+	4.13253i	0.265466	+	0.153267i	0.626826	−	0.779160i	$-0.284354\pi$
$727$	7.15775	+	4.13253i	0.265466	+	0.153267i	−0.361359	+	0.932427i	$0.617687\pi$
$728$		0			0
$729$		0			0
$730$	−0.102463	−	0.177472i	−0.00379234	−	0.00656853i
$731$	−6.58709	−	11.4092i	−0.243632	−	0.421983i
$732$		0			0
$733$	−10.5799	−	6.10830i	−0.390777	−	0.225615i	0.291720	−	0.956504i	$-0.405773\pi$
$733$	−10.5799	−	6.10830i	−0.390777	−	0.225615i	−0.682497	+	0.730889i	$0.739106\pi$
$734$	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	−0.610323	−	0.792153i	$-0.708960\pi$
$739$	10.3536	−	17.9330i	0.380863	−	0.659674i	0.991186	+	0.132478i	$0.0422935\pi$
$740$	−0.109087			−0.00401013
$741$		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
$745$	0.390045	−	0.225192i	0.0142901	−	0.00825041i
$746$	0.142588	+	0.0823233i	0.00522053	+	0.00301407i
$747$		0			0
$748$		−	9.04885i		−	0.330859i
$749$		0			0
$750$		0			0
$751$	−11.8554	+	20.5342i	−0.432610	+	0.749303i	−0.997097	−	0.0761390i	$-0.975741\pi$
$751$	−11.8554	+	20.5342i	−0.432610	+	0.749303i	0.564487	+	0.825442i	$0.309074\pi$
$752$	16.8312			0.613772
$753$		0			0
$754$		−	15.2348i		−	0.554817i
$755$	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	$0.202628\pi$
$758$		−	5.92462i		−	0.215192i
$759$		0			0
$760$	0.140029			0.00507937
$761$	24.3767	−	42.2217i	0.883656	−	1.53054i	0.0364098	−	0.999337i	$-0.488408\pi$
$761$	24.3767	−	42.2217i	0.883656	−	1.53054i	0.847246	−	0.531200i	$-0.178259\pi$
$762$		0			0
$763$		0			0
$764$			21.5154i			0.778401i
$765$		0			0
$766$	0.188174	+	0.108642i	0.00679900	+	0.00392540i
$767$	29.3791	−	16.9620i	1.06082	−	0.612463i
$768$		0			0
$769$	−23.3870	+	13.5025i	−0.843357	+	0.486912i	−0.858404	−	0.512975i	$-0.828543\pi$
$769$	−23.3870	+	13.5025i	−0.843357	+	0.486912i	0.0150472	+	0.999887i	$0.495210\pi$
$770$		0			0
$771$		0			0
$772$	−32.8536			−1.18243
$773$	13.3567	−	23.1345i	0.480408	−	0.832092i	−0.519339	−	0.854568i	$-0.673822\pi$
$773$	13.3567	−	23.1345i	0.480408	−	0.832092i	0.999747	+	0.0224765i	$0.00715509\pi$
$774$		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
$779$	12.7905	+	7.38459i	0.458267	+	0.264580i
$780$		0			0
$781$	4.05547	+	7.02429i	0.145116	+	0.251349i
$782$	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
$787$			47.3534i			1.68797i	0.536369	+	0.843983i	$0.319795\pi$
$787$			47.3534i			1.68797i	−0.536369	+	0.843983i	$0.680205\pi$
$788$			23.6424i			0.842224i
$789$		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
$794$	2.49462	+	4.32082i	0.0885309	+	0.153340i
$795$		0			0
$796$	13.0766	+	7.54980i	0.463489	+	0.267596i
$797$	−4.42781	−	7.66919i	−0.156841	−	0.271657i	0.776887	−	0.629640i	$-0.216798\pi$
$797$	−4.42781	−	7.66919i	−0.156841	−	0.271657i	−0.933728	+	0.357984i	$0.883464\pi$
$798$		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
$803$	−11.1420			−0.393191
$804$		0			0
$805$		0			0
$806$	10.7534	−	6.20848i	0.378772	−	0.218684i
$807$		0			0
$808$	−0.929170	+	0.536456i	−0.0326881	+	0.0188725i
$809$	6.40871	+	3.70007i	0.225318	+	0.130087i	0.608410	−	0.793623i	$-0.291808\pi$
$809$	6.40871	+	3.70007i	0.225318	+	0.130087i	−0.383092	+	0.923710i	$0.625141\pi$
$810$		0			0
$811$		−	25.0843i		−	0.880829i	−0.897794	−	0.440415i	$-0.854831\pi$
$811$		−	25.0843i		−	0.880829i	0.897794	−	0.440415i	$-0.145169\pi$
$812$		0			0
$813$		0			0
$814$	0.839587	−	1.45421i	0.0294275	−	0.0509699i
$815$	0.293105			0.0102670
$816$		0			0
$817$		−	4.85492i		−	0.169852i
$818$	−22.2483			−0.777893
$819$		0			0
$820$	0.311353			0.0108729
$821$			21.2212i			0.740627i	0.928907	+	0.370313i	$0.120750\pi$
$821$			21.2212i			0.740627i	−0.928907	+	0.370313i	$0.879250\pi$
$822$		0			0
$823$	16.9538			0.590972			0.295486	−	0.955347i	$-0.404518\pi$
$823$	16.9538			0.590972			0.295486	+	0.955347i	$0.404518\pi$
$824$	6.25546	−	10.8348i	0.217919	−	0.377447i
$825$		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	0.970927	−	0.239378i	$-0.0769434\pi$
$829$	35.9640	+	20.7638i	1.24908	+	0.721158i	0.278156	+	0.960536i	$0.410277\pi$
$830$	0.100111	−	0.0577990i	0.00347490	−	0.00200623i
$831$		0			0
$832$	3.55896	−	2.05477i	0.123385	−	0.0712362i
$833$		0			0
$834$		0			0
$835$	−0.166595			−0.00576527
$836$	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	−0.728884	−	0.684638i	$-0.759960\pi$
$839$	6.61780	−	11.4624i	0.228472	−	0.395725i	0.957355	+	0.288913i	$0.0932938\pi$
$840$		0			0
$841$	−6.21265	−	10.7606i	−0.214229	−	0.371056i
$842$	2.18914	+	1.26390i	0.0754428	+	0.0435569i
$843$		0			0
$844$	−11.0036	−	19.0588i	−0.378759	−	0.656030i
$845$	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
$850$		−	18.8590i		−	0.646859i
$851$		−	17.9547i		−	0.615479i
$852$		0			0
$853$	15.3814	+	8.88048i	0.526651	+	0.304062i	0.739651	−	0.672990i	$-0.234990\pi$
$853$	15.3814	+	8.88048i	0.526651	+	0.304062i	−0.213001	+	0.977052i	$0.568324\pi$
$854$		0			0
$855$		0			0
$856$	10.7180	+	18.5642i	0.366334	+	0.634510i
$857$	9.17157	+	15.8856i	0.313295	+	0.542643i	0.979074	−	0.203507i	$-0.0652338\pi$
$857$	9.17157	+	15.8856i	0.313295	+	0.542643i	−0.665779	+	0.746149i	$0.731900\pi$
$858$		0			0
$859$	−2.69126	−	1.55380i	−0.0918246	−	0.0530150i	0.453385	−	0.891315i	$-0.350216\pi$
$859$	−2.69126	−	1.55380i	−0.0918246	−	0.0530150i	−0.545209	+	0.838300i	$0.683550\pi$
$860$	−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	$-0.417731\pi$
$863$	35.8587	−	20.7030i	1.22064	−	0.704739i	0.965055	+	0.262047i	$0.0843974\pi$
$864$		0			0
$865$	−0.0688566	+	0.119263i	−0.00234119	+	0.00405507i
$866$	−24.8641			−0.844917
$867$		0			0
$868$		0			0
$869$	13.8114	−	7.97399i	0.468518	−	0.270499i
$870$		0			0
$871$	−62.3460	+	35.9955i	−2.11251	+	1.21966i
$872$	−9.68438	−	5.59128i	−0.327954	−	0.189345i
$873$		0			0
$874$			10.0947i			0.341459i
$875$		0			0
$876$		0			0
$877$	11.3979	−	19.7417i	0.384878	−	0.666628i	−0.606874	−	0.794798i	$-0.707577\pi$
$877$	11.3979	−	19.7417i	0.384878	−	0.666628i	0.991752	+	0.128170i	$0.0409102\pi$
$878$	15.7696			0.532199
$879$		0			0
$880$		−	0.0447618i		−	0.00150892i
$881$	−43.4050			−1.46235			−0.731175	−	0.682190i	$-0.761028\pi$
$881$	−43.4050			−1.46235			−0.731175	+	0.682190i	$0.761028\pi$
$882$		0			0
$883$	−29.9309			−1.00725			−0.503627	−	0.863921i	$-0.668001\pi$
$883$	−29.9309			−1.00725			−0.503627	+	0.863921i	$0.668001\pi$
$884$		−	49.8623i		−	1.67705i
$885$		0			0
$886$	−7.47363			−0.251082
$887$	19.4788	−	33.7382i	0.654033	−	1.13282i	−0.328102	−	0.944642i	$-0.606409\pi$
$887$	19.4788	−	33.7382i	0.654033	−	1.13282i	0.982135	−	0.188176i	$-0.0602576\pi$
$888$		0			0
$889$		0			0
$890$			0.226597i			0.00759556i
$891$		0			0
$892$	−4.03358	−	2.32879i	−0.135054	−	0.0779736i
$893$	−19.7185	+	11.3845i	−0.659853	+	0.380966i
$894$		0			0
$895$	−0.00496721	+	0.00286782i	−0.000166035	+	9.58606e-5i
$896$		0			0
$897$		0			0
$898$	−9.56277			−0.319114
$899$	−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
$905$	−0.153512	−	0.0886299i	−0.00510290	−	0.00294616i
$906$		0			0
$907$	14.0526	+	24.3399i	0.466610	+	0.808192i	0.999273	−	0.0381355i	$-0.0121419\pi$
$907$	14.0526	+	24.3399i	0.466610	+	0.808192i	−0.532663	+	0.846328i	$0.678809\pi$
$908$	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
$913$		−	6.28511i		−	0.208007i
$914$		−	13.7024i		−	0.453235i
$915$		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	0.996505	−	0.0835328i	$-0.0266203\pi$
$919$	12.9115	+	22.3634i	0.425911	+	0.737699i	−0.570594	+	0.821232i	$0.693287\pi$
$920$	0.242933	+	0.420773i	0.00800928	+	0.0138725i
$921$		0			0
$922$	−0.957884	−	0.553034i	−0.0315462	−	0.0182132i
$923$	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
$929$	−15.9419			−0.523036			−0.261518	−	0.965199i	$-0.584223\pi$
$929$	−15.9419			−0.523036			−0.261518	+	0.965199i	$0.584223\pi$
$930$		0			0
$931$		0			0
$932$	17.4246	−	10.0601i	0.570762	−	0.329529i
$933$		0			0
$934$	−5.31568	+	3.06901i	−0.173934	+	0.100421i
$935$	0.142300	+	0.0821570i	0.00465371	+	0.00268682i
$936$		0			0
$937$			15.0698i			0.492308i	0.969231	+	0.246154i	$0.0791668\pi$
$937$			15.0698i			0.492308i	−0.969231	+	0.246154i	$0.920833\pi$
$938$		0			0
$939$		0			0
$940$	−0.239999	+	0.415690i	−0.00782789	+	0.0135583i
$941$	−11.5372			−0.376102			−0.188051	−	0.982159i	$-0.560217\pi$
$941$	−11.5372			−0.376102			−0.188051	+	0.982159i	$0.560217\pi$
$942$		0			0
$943$			51.2456i			1.66879i
$944$	−9.31636			−0.303222
$945$		0			0
$946$	1.57543			0.0512218
$947$		−	28.3321i		−	0.920671i	−0.887745	−	0.460336i	$-0.847729\pi$
$947$		−	28.3321i		−	0.920671i	0.887745	−	0.460336i	$-0.152271\pi$
$948$		0			0
$949$	−61.3961			−1.99300
$950$	3.47495	−	6.01879i	0.112742	−	0.195275i
$951$		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
$956$	7.57084	−	4.37102i	0.244858	−	0.141369i
$957$		0			0
$958$	10.0935	−	5.82748i	0.326106	−	0.188277i
$959$		0			0
$960$		0			0
$961$	19.9896			0.644824
$962$	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	$0.748619\pi$
$968$	−20.3809	−	11.7669i	−0.655068	−	0.378203i
$969$		0			0
$970$	−0.0735528	−	0.127397i	−0.00236164	−	0.00409048i
$971$	−10.7315	−	18.5875i	−0.344390	−	0.596500i	0.640853	−	0.767663i	$-0.278581\pi$
$971$	−10.7315	−	18.5875i	−0.344390	−	0.596500i	−0.985243	+	0.171163i	$0.945247\pi$
$972$		0			0
$973$		0			0
$974$	24.8470	+	14.3454i	0.796148	+	0.459657i
$975$		0			0
$976$		−	3.66588i		−	0.117342i
$977$			21.5027i			0.687932i	0.938982	+	0.343966i	$0.111770\pi$
$977$			21.5027i			0.687932i	−0.938982	+	0.343966i	$0.888230\pi$
$978$		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
$983$	−12.7097	−	22.0138i	−0.405376	−	0.702131i	0.588989	−	0.808141i	$-0.299526\pi$
$983$	−12.7097	−	22.0138i	−0.405376	−	0.702131i	−0.994365	+	0.106009i	$0.966193\pi$
$984$		0			0
$985$	−0.371794	−	0.214656i	−0.0118464	−	0.00683949i
$986$	−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	−0.990665	−	0.136315i	$-0.956474\pi$
$991$	−11.8768	+	20.5713i	−0.377280	+	0.653468i	0.613385	+	0.789784i	$0.289807\pi$
$992$	−19.0987			−0.606384
$993$		0			0
$994$		0			0
$995$	−0.237453	+	0.137093i	−0.00752776	+	0.00434615i
$996$		0			0
$997$	10.5366	−	6.08329i	0.333697	−	0.192660i	−0.323785	−	0.946131i	$-0.604955\pi$
$997$	10.5366	−	6.08329i	0.333697	−	0.192660i	0.657481	+	0.753471i	$0.271622\pi$
$998$	−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.i.d.521.9		48
3.2	odd	2		441.2.i.d.227.10		48
7.2	even	3		1323.2.s.d.656.15		48
7.3	odd	6		1323.2.o.e.440.10		48
7.4	even	3		1323.2.o.e.440.9		48
7.5	odd	6		1323.2.s.d.656.16		48
7.6	odd	2	inner	1323.2.i.d.521.10		48
9.4	even	3		441.2.s.d.374.9		48
9.5	odd	6		1323.2.s.d.962.16		48
21.2	odd	6		441.2.s.d.362.10		48
21.5	even	6		441.2.s.d.362.9		48
21.11	odd	6		441.2.o.e.146.15	✓	48
21.17	even	6		441.2.o.e.146.16	yes	48
21.20	even	2		441.2.i.d.227.9		48
63.4	even	3		441.2.o.e.293.16	yes	48
63.5	even	6	inner	1323.2.i.d.1097.9		48
63.13	odd	6		441.2.s.d.374.10		48
63.23	odd	6	inner	1323.2.i.d.1097.10		48
63.31	odd	6		441.2.o.e.293.15	yes	48
63.32	odd	6		1323.2.o.e.881.10		48
63.40	odd	6		441.2.i.d.68.16		48
63.41	even	6		1323.2.s.d.962.15		48
63.58	even	3		441.2.i.d.68.15		48
63.59	even	6		1323.2.o.e.881.9		48

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.664297i q^{2} +1.55871 q^{4} +(-0.0141520 + 0.0245119i) q^{5} +2.36404i q^{8} +O(q^{10})\)	\(q+0.664297i q^{2} +1.55871 q^{4} +(-0.0141520 + 0.0245119i) q^{5} +2.36404i q^{8} +(-0.0162832 - 0.00940110i) q^{10} +(-0.885324 + 0.511142i) q^{11} +(-4.87844 + 2.81657i) q^{13} +1.54700 q^{16} +(-2.83940 + 4.91798i) q^{17} +(-1.81237 + 1.04637i) q^{19} +(-0.0220588 + 0.0382070i) q^{20} +(-0.339550 - 0.588118i) q^{22} +(-6.28849 - 3.63066i) q^{23} +(2.49960 + 4.32943i) q^{25} +(-1.87104 - 3.24073i) q^{26} +(3.52577 + 2.03560i) q^{29} +3.31820i q^{31} +5.75574i q^{32} +(-3.26700 - 1.88620i) q^{34} +(1.23632 + 2.14137i) q^{37} +(-0.695101 - 1.20395i) q^{38} +(-0.0579471 - 0.0334558i) q^{40} +(-3.52867 - 6.11183i) q^{41} +(-1.15994 + 2.00908i) q^{43} +(-1.37996 + 0.796722i) q^{44} +(2.41184 - 4.17742i) q^{46} +10.8799 q^{47} +(-2.87603 + 1.66048i) q^{50} +(-7.60408 + 4.39022i) q^{52} +(10.0454 + 5.79973i) q^{53} -0.0289346i q^{55} +(-1.35224 + 2.34215i) q^{58} -6.02222 q^{59} -2.36968i q^{61} -2.20427 q^{62} -0.729528 q^{64} -0.159440i q^{65} +12.7799 q^{67} +(-4.42580 + 7.66571i) q^{68} -7.93415i q^{71} +(9.43889 + 5.44955i) q^{73} +(-1.42251 + 0.821285i) q^{74} +(-2.82496 + 1.63099i) q^{76} -15.6004 q^{79} +(-0.0218930 + 0.0379198i) q^{80} +(4.06007 - 2.34408i) q^{82} +(-3.07406 + 5.32442i) q^{83} +(-0.0803661 - 0.139198i) q^{85} +(-1.33463 - 0.770546i) q^{86} +(-1.20836 - 2.09294i) q^{88} +(-6.02582 - 10.4370i) q^{89} +(-9.80194 - 5.65915i) q^{92} +7.22751i q^{94} -0.0592328i q^{95} +(6.77565 + 3.91192i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4}+O(q^{10}) \) 48 * q - 48 * q^4	\( 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) \) 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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