LMFDB - Embedded newform 1323.2.s.d.656.10

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			656.10
Character	$\chi$	$=$	1323.656
Dual form			1323.2.s.d.962.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.850109 + 0.490811i) q^{2} +(-0.518210 + 0.897565i) q^{4} +1.88120 q^{5} -2.98061i q^{8} +O(q^{10})$	\(q+(-0.850109 + 0.490811i) q^{2} +(-0.518210 + 0.897565i) q^{4} +1.88120 q^{5} -2.98061i q^{8} +(-1.59922 + 0.923312i) q^{10} +4.08810i q^{11} +(-3.51415 + 2.02890i) q^{13} +(0.426498 + 0.738716i) q^{16} +(-0.810727 - 1.40422i) q^{17} +(-7.03722 - 4.06294i) q^{19} +(-0.974855 + 1.68850i) q^{20} +(-2.00648 - 3.47533i) q^{22} -4.31071i q^{23} -1.46110 q^{25} +(1.99161 - 3.44957i) q^{26} +(0.542317 + 0.313107i) q^{29} +(3.69833 + 2.13523i) q^{31} +(4.43744 + 2.56195i) q^{32} +(1.37841 + 0.795827i) q^{34} +(-3.97076 + 6.87757i) q^{37} +7.97654 q^{38} -5.60712i q^{40} +(0.912023 + 1.57967i) q^{41} +(-3.53614 + 6.12477i) q^{43} +(-3.66933 - 2.11849i) q^{44} +(2.11574 + 3.66457i) q^{46} +(-3.96868 - 6.87396i) q^{47} +(1.24209 - 0.717122i) q^{50} -4.20558i q^{52} +(-7.24978 + 4.18567i) q^{53} +7.69052i q^{55} -0.614704 q^{58} +(-4.08715 + 7.07915i) q^{59} +(3.24253 - 1.87208i) q^{61} -4.19198 q^{62} -6.73573 q^{64} +(-6.61081 + 3.81676i) q^{65} +(-6.26559 + 10.8523i) q^{67} +1.68051 q^{68} -14.4969i q^{71} +(3.28167 - 1.89468i) q^{73} -7.79557i q^{74} +(7.29351 - 4.21091i) q^{76} +(-4.18066 - 7.24112i) q^{79} +(0.802327 + 1.38967i) q^{80} +(-1.55064 - 0.895261i) q^{82} +(4.38300 - 7.59159i) q^{83} +(-1.52514 - 2.64162i) q^{85} -6.94230i q^{86} +12.1850 q^{88} +(4.90379 - 8.49362i) q^{89} +(3.86914 + 2.23385i) q^{92} +(6.74762 + 3.89574i) q^{94} +(-13.2384 - 7.64320i) q^{95} +(-11.4579 - 6.61525i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.850109	+	0.490811i	−0.601118	+	0.347056i	−0.769481	−	0.638669i	$-0.779485\pi$
$2$	−0.850109	+	0.490811i	−0.601118	+	0.347056i	0.168363	+	0.985725i	$0.446152\pi$
$3$		0			0
$3$		0			0
$4$	−0.518210	+	0.897565i	−0.259105	+	0.448783i
$5$	1.88120			0.841297			0.420648	−	0.907224i	$-0.361803\pi$
$5$	1.88120			0.841297			0.420648	+	0.907224i	$0.361803\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	2.98061i		−	1.05381i
$9$		0			0
$10$	−1.59922	+	0.923312i	−0.505719	+	0.291977i
$11$			4.08810i			1.23261i	0.787508	+	0.616304i	$0.211371\pi$
$11$			4.08810i			1.23261i	−0.787508	+	0.616304i	$0.788629\pi$
$12$		0			0
$13$	−3.51415	+	2.02890i	−0.974651	+	0.562715i	−0.900651	−	0.434544i	$-0.856910\pi$
$13$	−3.51415	+	2.02890i	−0.974651	+	0.562715i	−0.0739997	+	0.997258i	$0.523576\pi$
$14$		0			0
$15$		0			0
$16$	0.426498	+	0.738716i	0.106625	+	0.184679i
$17$	−0.810727	−	1.40422i	−0.196630	−	0.340574i	0.750803	−	0.660526i	$-0.229667\pi$
$17$	−0.810727	−	1.40422i	−0.196630	−	0.340574i	−0.947434	+	0.319952i	$0.896333\pi$
$18$		0			0
$19$	−7.03722	−	4.06294i	−1.61445	−	0.932103i	−0.988322	−	0.152382i	$-0.951305\pi$
$19$	−7.03722	−	4.06294i	−1.61445	−	0.932103i	−0.626128	−	0.779720i	$-0.715361\pi$
$20$	−0.974855	+	1.68850i	−0.217984	+	0.377560i
$21$		0			0
$22$	−2.00648	−	3.47533i	−0.427783	−	0.740943i
$23$		−	4.31071i		−	0.898845i	−0.893319	−	0.449423i	$-0.851630\pi$
$23$		−	4.31071i		−	0.898845i	0.893319	−	0.449423i	$-0.148370\pi$
$24$		0			0
$25$	−1.46110			−0.292219
$26$	1.99161	−	3.44957i	0.390587	−	0.676516i
$27$		0			0
$28$		0			0
$29$	0.542317	+	0.313107i	0.100706	+	0.0581425i	0.549507	−	0.835489i	$-0.314816\pi$
$29$	0.542317	+	0.313107i	0.100706	+	0.0581425i	−0.448801	+	0.893632i	$0.648149\pi$
$30$		0			0
$31$	3.69833	+	2.13523i	0.664240	+	0.383499i	0.793891	−	0.608060i	$-0.208052\pi$
$31$	3.69833	+	2.13523i	0.664240	+	0.383499i	−0.129650	+	0.991560i	$0.541385\pi$
$32$	4.43744	+	2.56195i	0.784435	+	0.452894i
$33$		0			0
$34$	1.37841	+	0.795827i	0.236396	+	0.136483i
$35$		0			0
$36$		0			0
$37$	−3.97076	+	6.87757i	−0.652790	+	1.13066i	0.329653	+	0.944102i	$0.393068\pi$
$37$	−3.97076	+	6.87757i	−0.652790	+	1.13066i	−0.982443	+	0.186563i	$0.940265\pi$
$38$	7.97654			1.29397
$39$		0			0
$40$		−	5.60712i		−	0.886564i
$41$	0.912023	+	1.57967i	0.142434	+	0.246703i	0.928413	−	0.371551i	$-0.121174\pi$
$41$	0.912023	+	1.57967i	0.142434	+	0.246703i	−0.785979	+	0.618254i	$0.787840\pi$
$42$		0			0
$43$	−3.53614	+	6.12477i	−0.539256	+	0.934019i	0.459688	+	0.888080i	$0.347961\pi$
$43$	−3.53614	+	6.12477i	−0.539256	+	0.934019i	−0.998944	+	0.0459387i	$0.985372\pi$
$44$	−3.66933	−	2.11849i	−0.553173	−	0.319375i
$45$		0			0
$46$	2.11574	+	3.66457i	0.311949	+	0.540312i
$47$	−3.96868	−	6.87396i	−0.578891	−	1.00267i	−0.995607	−	0.0936324i	$-0.970152\pi$
$47$	−3.96868	−	6.87396i	−0.578891	−	1.00267i	0.416715	−	0.909037i	$-0.363181\pi$
$48$		0			0
$49$		0			0
$50$	1.24209	−	0.717122i	0.175658	−	0.101416i
$51$		0			0
$52$		−	4.20558i		−	0.583208i
$53$	−7.24978	+	4.18567i	−0.995835	+	0.574945i	−0.907013	−	0.421102i	$-0.861643\pi$
$53$	−7.24978	+	4.18567i	−0.995835	+	0.574945i	−0.0888214	+	0.996048i	$0.528310\pi$
$54$		0			0
$55$			7.69052i			1.03699i
$56$		0			0
$57$		0			0
$58$	−0.614704			−0.0807147
$59$	−4.08715	+	7.07915i	−0.532101	+	0.921627i	0.467196	+	0.884154i	$0.345264\pi$
$59$	−4.08715	+	7.07915i	−0.532101	+	0.921627i	−0.999298	+	0.0374731i	$0.988069\pi$
$60$		0			0
$61$	3.24253	−	1.87208i	0.415164	−	0.239695i	−0.277842	−	0.960627i	$-0.589619\pi$
$61$	3.24253	−	1.87208i	0.415164	−	0.239695i	0.693006	+	0.720932i	$0.256286\pi$
$62$	−4.19198			−0.532382
$63$		0			0
$64$	−6.73573			−0.841966
$65$	−6.61081	+	3.81676i	−0.819971	+	0.473410i
$66$		0			0
$67$	−6.26559	+	10.8523i	−0.765464	+	1.32582i	0.174537	+	0.984651i	$0.444157\pi$
$67$	−6.26559	+	10.8523i	−0.765464	+	1.32582i	−0.940001	+	0.341171i	$0.889176\pi$
$68$	1.68051			0.203791
$69$		0			0
$70$		0			0
$71$		−	14.4969i		−	1.72047i	−0.509898	−	0.860235i	$-0.670317\pi$
$71$		−	14.4969i		−	1.72047i	0.509898	−	0.860235i	$-0.329683\pi$
$72$		0			0
$73$	3.28167	−	1.89468i	0.384091	−	0.221755i	−0.295506	−	0.955341i	$-0.595488\pi$
$73$	3.28167	−	1.89468i	0.384091	−	0.221755i	0.679597	+	0.733586i	$0.262155\pi$
$74$		−	7.79557i		−	0.906217i
$75$		0			0
$76$	7.29351	−	4.21091i	0.836623	−	0.483025i
$77$		0			0
$78$		0			0
$79$	−4.18066	−	7.24112i	−0.470361	−	0.814690i	0.529064	−	0.848582i	$-0.322543\pi$
$79$	−4.18066	−	7.24112i	−0.470361	−	0.814690i	−0.999426	+	0.0338919i	$0.989210\pi$
$80$	0.802327	+	1.38967i	0.0897029	+	0.155370i
$81$		0			0
$82$	−1.55064	−	0.895261i	−0.171239	−	0.0988651i
$83$	4.38300	−	7.59159i	0.481097	−	0.833285i	−0.518668	−	0.854976i	$-0.673572\pi$
$83$	4.38300	−	7.59159i	0.481097	−	0.833285i	0.999765	+	0.0216912i	$0.00690508\pi$
$84$		0			0
$85$	−1.52514	−	2.64162i	−0.165424	−	0.286524i
$86$		−	6.94230i		−	0.748608i
$87$		0			0
$88$	12.1850			1.29893
$89$	4.90379	−	8.49362i	0.519801	−	0.900322i	−0.479934	−	0.877305i	$-0.659339\pi$
$89$	4.90379	−	8.49362i	0.519801	−	0.900322i	0.999735	−	0.0230174i	$-0.00732730\pi$
$90$		0			0
$91$		0			0
$92$	3.86914	+	2.23385i	0.403386	+	0.232895i
$93$		0			0
$94$	6.74762	+	3.89574i	0.695964	+	0.401815i
$95$	−13.2384	−	7.64320i	−1.35823	−	0.784175i
$96$		0			0
$97$	−11.4579	−	6.61525i	−1.16338	−	0.671677i	−0.211267	−	0.977428i	$-0.567759\pi$
$97$	−11.4579	−	6.61525i	−1.16338	−	0.671677i	−0.952111	+	0.305752i	$0.901092\pi$
$98$		0			0
$99$		0			0
$100$	0.757155	−	1.31143i	0.0757155	−	0.131143i
$101$	1.04980			0.104459			0.0522295	−	0.998635i	$-0.483367\pi$
$101$	1.04980			0.104459			0.0522295	+	0.998635i	$0.483367\pi$
$102$		0			0
$103$			1.63894i			0.161490i	0.996735	+	0.0807449i	$0.0257299\pi$
$103$			1.63894i			0.161490i	−0.996735	+	0.0807449i	$0.974270\pi$
$104$	6.04736	+	10.4743i	0.592992	+	1.02709i
$105$		0			0
$106$	4.10874	−	7.11654i	0.399076	−	0.691220i
$107$	2.97522	+	1.71775i	0.287626	+	0.166061i	0.636871	−	0.770971i	$-0.280229\pi$
$107$	2.97522	+	1.71775i	0.287626	+	0.166061i	−0.349245	+	0.937031i	$0.613562\pi$
$108$		0			0
$109$	−1.84529	−	3.19614i	−0.176747	−	0.306134i	0.764018	−	0.645195i	$-0.223224\pi$
$109$	−1.84529	−	3.19614i	−0.176747	−	0.306134i	−0.940764	+	0.339061i	$0.889891\pi$
$110$	−3.77459	−	6.53778i	−0.359893	−	0.623353i
$111$		0			0
$112$		0			0
$113$	−15.0858	+	8.70977i	−1.41915	+	0.819346i	−0.996224	−	0.0868183i	$-0.972330\pi$
$113$	−15.0858	+	8.70977i	−1.41915	+	0.819346i	−0.422925	+	0.906165i	$0.638997\pi$
$114$		0			0
$115$		−	8.10929i		−	0.756196i
$116$	−0.562068	+	0.324510i	−0.0521867	+	0.0301300i
$117$		0			0
$118$		−	8.02407i		−	0.738675i
$119$		0			0
$120$		0			0
$121$	−5.71254			−0.519321
$122$	−1.83767	+	3.18294i	−0.166375	+	0.288170i
$123$		0			0
$124$	−3.83303	+	2.21300i	−0.344216	+	0.198733i
$125$	−12.1546			−1.08714
$126$		0			0
$127$	−10.1288			−0.898783			−0.449391	−	0.893335i	$-0.648359\pi$
$127$	−10.1288			−0.898783			−0.449391	+	0.893335i	$0.648359\pi$
$128$	−3.14876	+	1.81794i	−0.278314	+	0.160685i
$129$		0			0
$130$	3.74661	−	6.48932i	0.328599	−	0.569151i
$131$	4.97701			0.434844			0.217422	−	0.976078i	$-0.430235\pi$
$131$	4.97701			0.434844			0.217422	+	0.976078i	$0.430235\pi$
$132$		0			0
$133$		0			0
$134$		−	12.3009i		−	1.06263i
$135$		0			0
$136$	−4.18544	+	2.41647i	−0.358899	+	0.207210i
$137$			0.840663i			0.0718227i	0.999355	+	0.0359113i	$0.0114334\pi$
$137$			0.840663i			0.0718227i	−0.999355	+	0.0359113i	$0.988567\pi$
$138$		0			0
$139$	5.74392	−	3.31626i	0.487193	−	0.281281i	−0.236216	−	0.971701i	$-0.575907\pi$
$139$	5.74392	−	3.31626i	0.487193	−	0.281281i	0.723409	+	0.690419i	$0.242574\pi$
$140$		0			0
$141$		0			0
$142$	7.11525	+	12.3240i	0.597098	+	1.03420i
$143$	−8.29433	−	14.3662i	−0.693606	−	1.20136i
$144$		0			0
$145$	1.02020	+	0.589015i	0.0847234	+	0.0489151i
$146$	−1.85985	+	3.22136i	−0.153923	+	0.266602i
$147$		0			0
$148$	−4.11538	−	7.12804i	−0.338282	−	0.585921i
$149$			16.9768i			1.39079i	0.718628	+	0.695395i	$0.244771\pi$
$149$			16.9768i			1.39079i	−0.718628	+	0.695395i	$0.755229\pi$
$150$		0			0
$151$	1.95142			0.158804			0.0794021	−	0.996843i	$-0.474699\pi$
$151$	1.95142			0.158804			0.0794021	+	0.996843i	$0.474699\pi$
$152$	−12.1101	+	20.9752i	−0.982256	+	1.70132i
$153$		0			0
$154$		0			0
$155$	6.95730	+	4.01680i	0.558823	+	0.322637i
$156$		0			0
$157$	−8.24558	−	4.76059i	−0.658069	−	0.379936i	0.133472	−	0.991053i	$-0.457387\pi$
$157$	−8.24558	−	4.76059i	−0.658069	−	0.379936i	−0.791541	+	0.611116i	$0.790721\pi$
$158$	7.10804	+	4.10383i	0.565485	+	0.326483i
$159$		0			0
$160$	8.34769	+	4.81954i	0.659943	+	0.381018i
$161$		0			0
$162$		0			0
$163$	−0.555106	+	0.961472i	−0.0434793	+	0.0753083i	−0.886946	−	0.461873i	$-0.847178\pi$
$163$	−0.555106	+	0.961472i	−0.0434793	+	0.0753083i	0.843467	+	0.537181i	$0.180511\pi$
$164$	−1.89048			−0.147621
$165$		0			0
$166$			8.60490i			0.667870i
$167$	−7.00830	−	12.1387i	−0.542319	−	0.939324i	−0.998770	−	0.0495754i	$-0.984213\pi$
$167$	−7.00830	−	12.1387i	−0.542319	−	0.939324i	0.456452	−	0.889748i	$-0.349120\pi$
$168$		0			0
$169$	1.73285	−	3.00138i	0.133296	−	0.230875i
$170$	2.59307	+	1.49711i	0.198879	+	0.114823i
$171$		0			0
$172$	−3.66492	−	6.34783i	−0.279448	−	0.484018i
$173$	3.55884	+	6.16410i	0.270574	+	0.468647i	0.969009	−	0.247026i	$-0.0794533\pi$
$173$	3.55884	+	6.16410i	0.270574	+	0.468647i	−0.698435	+	0.715673i	$0.746120\pi$
$174$		0			0
$175$		0			0
$176$	−3.01994	+	1.74357i	−0.227637	+	0.131426i
$177$		0			0
$178$			9.62734i			0.721600i
$179$	5.19845	−	3.00133i	0.388550	−	0.224330i	−0.292981	−	0.956118i	$-0.594647\pi$
$179$	5.19845	−	3.00133i	0.388550	−	0.224330i	0.681532	+	0.731788i	$0.261314\pi$
$180$		0			0
$181$			1.30283i			0.0968385i	0.998827	+	0.0484192i	$0.0154184\pi$
$181$			1.30283i			0.0968385i	−0.998827	+	0.0484192i	$0.984582\pi$
$182$		0			0
$183$		0			0
$184$	−12.8486			−0.947209
$185$	−7.46979	+	12.9381i	−0.549190	+	0.951225i
$186$		0			0
$187$	5.74059	−	3.31433i	0.419794	−	0.242368i
$188$	8.22643			0.599974
$189$		0			0
$190$	15.0054			1.08861
$191$	4.96482	−	2.86644i	0.359242	−	0.207408i	−0.309506	−	0.950897i	$-0.600164\pi$
$191$	4.96482	−	2.86644i	0.359242	−	0.207408i	0.668748	+	0.743489i	$0.266830\pi$
$192$		0			0
$193$	−0.779518	+	1.35016i	−0.0561109	+	0.0971869i	−0.892716	−	0.450619i	$-0.851203\pi$
$193$	−0.779518	+	1.35016i	−0.0561109	+	0.0971869i	0.836606	+	0.547806i	$0.184537\pi$
$194$	12.9873			0.932437
$195$		0			0
$196$		0			0
$197$			19.5504i			1.39291i	0.717602	+	0.696454i	$0.245240\pi$
$197$			19.5504i			1.39291i	−0.717602	+	0.696454i	$0.754760\pi$
$198$		0			0
$199$	−0.845590	+	0.488202i	−0.0599423	+	0.0346077i	−0.529672	−	0.848203i	$-0.677685\pi$
$199$	−0.845590	+	0.488202i	−0.0599423	+	0.0346077i	0.469729	+	0.882810i	$0.344352\pi$
$200$			4.35497i			0.307943i
$201$		0			0
$202$	−0.892445	+	0.515253i	−0.0627922	+	0.0362531i
$203$		0			0
$204$		0			0
$205$	1.71570	+	2.97167i	0.119829	+	0.207551i
$206$	−0.804411	−	1.39328i	−0.0560460	−	0.0970745i
$207$		0			0
$208$	−2.99756	−	1.73064i	−0.207843	−	0.119998i
$209$	16.6097	−	28.7688i	1.14892	−	1.98998i
$210$		0			0
$211$	11.9752	+	20.7417i	0.824408	+	1.42792i	0.902371	+	0.430961i	$0.141825\pi$
$211$	11.9752	+	20.7417i	0.824408	+	1.42792i	−0.0779625	+	0.996956i	$0.524841\pi$
$212$		−	8.67621i		−	0.595884i
$213$		0			0
$214$	−3.37235			−0.230529
$215$	−6.65218	+	11.5219i	−0.453675	+	0.785787i
$216$		0			0
$217$		0			0
$218$	3.13740	+	1.81138i	0.212491	+	0.122682i
$219$		0			0
$220$	−6.90274	−	3.98530i	−0.465383	−	0.268689i
$221$	5.69804	+	3.28976i	0.383292	+	0.221293i
$222$		0			0
$223$	2.68394	+	1.54957i	0.179730	+	0.103767i	0.587166	−	0.809467i	$-0.300244\pi$
$223$	2.68394	+	1.54957i	0.179730	+	0.103767i	−0.407436	+	0.913234i	$0.633577\pi$
$224$		0			0
$225$		0			0
$226$	8.54970	−	14.8085i	0.568717	−	0.985047i
$227$	21.7983			1.44680			0.723401	−	0.690428i	$-0.242578\pi$
$227$	21.7983			1.44680			0.723401	+	0.690428i	$0.242578\pi$
$228$		0			0
$229$			12.9107i			0.853164i	0.904449	+	0.426582i	$0.140282\pi$
$229$			12.9107i			0.853164i	−0.904449	+	0.426582i	$0.859718\pi$
$230$	3.98013	+	6.89378i	0.262442	+	0.454563i
$231$		0			0
$232$	0.933250	−	1.61644i	0.0612709	−	0.106124i
$233$	−0.699758	−	0.404005i	−0.0458427	−	0.0264673i	0.476904	−	0.878956i	$-0.341759\pi$
$233$	−0.699758	−	0.404005i	−0.0458427	−	0.0264673i	−0.522746	+	0.852488i	$0.675092\pi$
$234$		0			0
$235$	−7.46587	−	12.9313i	−0.487020	−	0.843543i
$236$	−4.23600	−	7.33697i	−0.275740	−	0.477596i
$237$		0			0
$238$		0			0
$239$	−12.2032	+	7.04552i	−0.789360	+	0.455737i	−0.839737	−	0.542993i	$-0.817291\pi$
$239$	−12.2032	+	7.04552i	−0.789360	+	0.455737i	0.0503775	+	0.998730i	$0.483958\pi$
$240$		0			0
$241$			18.4989i			1.19162i	0.803127	+	0.595808i	$0.203168\pi$
$241$			18.4989i			1.19162i	−0.803127	+	0.595808i	$0.796832\pi$
$242$	4.85628	−	2.80377i	0.312173	−	0.180233i
$243$		0			0
$244$			3.88051i			0.248424i
$245$		0			0
$246$		0			0
$247$	32.9732			2.09803
$248$	6.36431	−	11.0233i	0.404134	−	0.699981i
$249$		0			0
$250$	10.3327	−	5.96561i	0.653499	−	0.377298i
$251$	−22.1733			−1.39957			−0.699783	−	0.714355i	$-0.746720\pi$
$251$	−22.1733			−1.39957			−0.699783	+	0.714355i	$0.746720\pi$
$252$		0			0
$253$	17.6226			1.10792
$254$	8.61056	−	4.97131i	0.540274	−	0.311928i
$255$		0			0
$256$	8.52026	−	14.7575i	0.532516	−	0.922345i
$257$	4.05793			0.253127			0.126563	−	0.991959i	$-0.459605\pi$
$257$	4.05793			0.253127			0.126563	+	0.991959i	$0.459605\pi$
$258$		0			0
$259$		0			0
$260$		−	7.91152i		−	0.490652i
$261$		0			0
$262$	−4.23100	+	2.44277i	−0.261392	+	0.150915i
$263$		−	9.96065i		−	0.614200i	−0.951677	−	0.307100i	$-0.900641\pi$
$263$		−	9.96065i		−	0.614200i	0.951677	−	0.307100i	$-0.0993586\pi$
$264$		0			0
$265$	−13.6383	+	7.87406i	−0.837793	+	0.483700i
$266$		0			0
$267$		0			0
$268$	−6.49378	−	11.2476i	−0.396671	−	0.687054i
$269$	−4.98399	−	8.63253i	−0.303880	−	0.526335i	0.673132	−	0.739523i	$-0.264949\pi$
$269$	−4.98399	−	8.63253i	−0.303880	−	0.526335i	−0.977011	+	0.213188i	$0.931615\pi$
$270$		0			0
$271$	16.4822	+	9.51601i	1.00122	+	0.578057i	0.908610	−	0.417646i	$-0.137145\pi$
$271$	16.4822	+	9.51601i	1.00122	+	0.578057i	0.0926133	+	0.995702i	$0.470478\pi$
$272$	0.691547	−	1.19780i	0.0419312	−	0.0726270i
$273$		0			0
$274$	−0.412606	−	0.714655i	−0.0249265	−	0.0431739i
$275$		−	5.97311i		−	0.360192i
$276$		0			0
$277$	−15.6237			−0.938736			−0.469368	−	0.883003i	$-0.655518\pi$
$277$	−15.6237			−0.938736			−0.469368	+	0.883003i	$0.655518\pi$
$278$	−3.25531	+	5.63836i	−0.195240	+	0.338166i
$279$		0			0
$280$		0			0
$281$	20.8780	+	12.0539i	1.24547	+	0.719075i	0.970203	−	0.242292i	$-0.0778991\pi$
$281$	20.8780	+	12.0539i	1.24547	+	0.719075i	0.275271	+	0.961367i	$0.411232\pi$
$282$		0			0
$283$	−2.61349	−	1.50890i	−0.155356	−	0.0896946i	0.420307	−	0.907382i	$-0.361922\pi$
$283$	−2.61349	−	1.50890i	−0.155356	−	0.0896946i	−0.575662	+	0.817687i	$0.695256\pi$
$284$	13.0119	+	7.51245i	0.772117	+	0.445782i
$285$		0			0
$286$	14.1022	+	8.14189i	0.833879	+	0.481440i
$287$		0			0
$288$		0			0
$289$	7.18544	−	12.4456i	0.422673	−	0.732091i
$290$	−1.15638			−0.0679050
$291$		0			0
$292$			3.92736i			0.229831i
$293$	14.9237	+	25.8485i	0.871849	+	1.51009i	0.860082	+	0.510156i	$0.170412\pi$
$293$	14.9237	+	25.8485i	0.871849	+	1.51009i	0.0117671	+	0.999931i	$0.496254\pi$
$294$		0			0
$295$	−7.68873	+	13.3173i	−0.447655	+	0.775362i
$296$	20.4994	+	11.8353i	1.19150	+	0.687914i
$297$		0			0
$298$	−8.33238	−	14.4321i	−0.482682	−	0.836029i
$299$	8.74598	+	15.1485i	0.505793	+	0.876060i
$300$		0			0
$301$		0			0
$302$	−1.65892	+	0.957777i	−0.0954600	+	0.0551139i
$303$		0			0
$304$		−	6.93135i		−	0.397540i
$305$	6.09984	−	3.52175i	0.349276	−	0.201655i
$306$		0			0
$307$		−	2.68853i		−	0.153442i	−0.997053	−	0.0767212i	$-0.975555\pi$
$307$		−	2.68853i		−	0.153442i	0.997053	−	0.0767212i	$-0.0244451\pi$
$308$		0			0
$309$		0			0
$310$	−7.88595			−0.447892
$311$	5.53763	−	9.59145i	0.314010	−	0.543881i	−0.665217	−	0.746650i	$-0.731661\pi$
$311$	5.53763	−	9.59145i	0.314010	−	0.543881i	0.979227	+	0.202769i	$0.0649941\pi$
$312$		0			0
$313$	−14.4970	+	8.36987i	−0.819421	+	0.473093i	−0.850217	−	0.526433i	$-0.823529\pi$
$313$	−14.4970	+	8.36987i	−0.819421	+	0.473093i	0.0307957	+	0.999526i	$0.490196\pi$
$314$	9.34619			0.527436
$315$		0			0
$316$	8.66584			0.487492
$317$	−2.54774	+	1.47094i	−0.143095	+	0.0826160i	−0.569838	−	0.821757i	$-0.692994\pi$
$317$	−2.54774	+	1.47094i	−0.143095	+	0.0826160i	0.426743	+	0.904373i	$0.359661\pi$
$318$		0			0
$319$	−1.28001	+	2.21704i	−0.0716668	+	0.124131i
$320$	−12.6712			−0.708344
$321$		0			0
$322$		0			0
$323$			13.1758i			0.733118i
$324$		0			0
$325$	5.13452	−	2.96442i	0.284812	−	0.164436i
$326$		−	1.08981i		−	0.0603589i
$327$		0			0
$328$	4.70839	−	2.71839i	0.259977	−	0.150098i
$329$		0			0
$330$		0			0
$331$	−2.44077	−	4.22753i	−0.134157	−	0.232366i	0.791118	−	0.611663i	$-0.209499\pi$
$331$	−2.44077	−	4.22753i	−0.134157	−	0.232366i	−0.925275	+	0.379297i	$0.876166\pi$
$332$	4.54263	+	7.86807i	0.249309	+	0.431816i
$333$		0			0
$334$	11.9156	+	6.87950i	0.651995	+	0.376429i
$335$	−11.7868	+	20.4154i	−0.643982	+	1.11541i
$336$		0			0
$337$	6.51421	+	11.2830i	0.354852	+	0.614621i	0.987093	−	0.160151i	$-0.0511980\pi$
$337$	6.51421	+	11.2830i	0.354852	+	0.614621i	−0.632241	+	0.774772i	$0.717865\pi$
$338$			3.40200i			0.185044i
$339$		0			0
$340$	3.16136			0.171449
$341$	−8.72904	+	15.1191i	−0.472704	+	0.818748i
$342$		0			0
$343$		0			0
$344$	18.2556	+	10.5399i	0.984275	+	0.568272i
$345$		0			0
$346$	−6.05081	−	3.49344i	−0.325293	−	0.187808i
$347$	−1.86351	−	1.07590i	−0.100039	−	0.0577573i	0.449146	−	0.893458i	$-0.351728\pi$
$347$	−1.86351	−	1.07590i	−0.100039	−	0.0577573i	−0.549185	+	0.835701i	$0.685062\pi$
$348$		0			0
$349$	−25.2919	−	14.6023i	−1.35384	−	0.781642i	−0.365058	−	0.930985i	$-0.618951\pi$
$349$	−25.2919	−	14.6023i	−1.35384	−	0.781642i	−0.988785	+	0.149343i	$0.952284\pi$
$350$		0			0
$351$		0			0
$352$	−10.4735	+	18.1407i	−0.558240	+	0.966901i
$353$	−10.8353			−0.576703			−0.288352	−	0.957525i	$-0.593107\pi$
$353$	−10.8353			−0.576703			−0.288352	+	0.957525i	$0.593107\pi$
$354$		0			0
$355$		−	27.2716i		−	1.44743i
$356$	5.08239	+	8.80295i	0.269366	+	0.466556i
$357$		0			0
$358$	−2.94617	+	5.10291i	−0.155710	+	0.269697i
$359$	18.1425	+	10.4746i	0.957527	+	0.552829i	0.895411	−	0.445240i	$-0.146882\pi$
$359$	18.1425	+	10.4746i	0.957527	+	0.552829i	0.0621161	+	0.998069i	$0.480215\pi$
$360$		0			0
$361$	23.5150	+	40.7292i	1.23763	+	2.14364i
$362$	−0.639442	−	1.10755i	−0.0336083	−	0.0582113i
$363$		0			0
$364$		0			0
$365$	6.17348	−	3.56426i	0.323135	−	0.186562i
$366$		0			0
$367$		−	5.74850i		−	0.300069i	−0.988681	−	0.150035i	$-0.952061\pi$
$367$		−	5.74850i		−	0.300069i	0.988681	−	0.150035i	$-0.0479385\pi$
$368$	3.18439	−	1.83851i	0.165998	−	0.0958389i
$369$		0			0
$370$		−	14.6650i		−	0.762398i
$371$		0			0
$372$		0			0
$373$	28.8934			1.49605			0.748023	−	0.663673i	$-0.231003\pi$
$373$	28.8934			1.49605			0.748023	+	0.663673i	$0.231003\pi$
$374$	−3.25342	+	5.63509i	−0.168230	+	0.291383i
$375$		0			0
$376$	−20.4886	+	11.8291i	−1.05662	+	0.610039i
$377$	−2.54104			−0.130870
$378$		0			0
$379$	−0.411434			−0.0211339			−0.0105670	−	0.999944i	$-0.503364\pi$
$379$	−0.411434			−0.0211339			−0.0105670	+	0.999944i	$0.503364\pi$
$380$	13.7205	−	7.92156i	0.703849	−	0.406367i
$381$		0			0
$382$	−2.81376	+	4.87358i	−0.143965	+	0.249354i
$383$	−24.8015			−1.26730			−0.633648	−	0.773622i	$-0.718443\pi$
$383$	−24.8015			−1.26730			−0.633648	+	0.773622i	$0.718443\pi$
$384$		0			0
$385$		0			0
$386$		−	1.53038i		−	0.0778944i
$387$		0			0
$388$	11.8752	−	6.85617i	0.602874	−	0.348069i
$389$			4.41896i			0.224050i	0.993705	+	0.112025i	$0.0357337\pi$
$389$			4.41896i			0.224050i	−0.993705	+	0.112025i	$0.964266\pi$
$390$		0			0
$391$	−6.05319	+	3.49481i	−0.306123	+	0.176740i
$392$		0			0
$393$		0			0
$394$	−9.59554	−	16.6200i	−0.483416	−	0.837302i
$395$	−7.86465	−	13.6220i	−0.395714	−	0.685396i
$396$		0			0
$397$	19.2780	+	11.1301i	0.967533	+	0.558605i	0.898483	−	0.439008i	$-0.144670\pi$
$397$	19.2780	+	11.1301i	0.967533	+	0.558605i	0.0690495	+	0.997613i	$0.478003\pi$
$398$	0.479229	−	0.830049i	0.0240216	−	0.0416066i
$399$		0			0
$400$	−0.623155	−	1.07934i	−0.0311578	−	0.0539668i
$401$			6.14184i			0.306709i	0.988171	+	0.153354i	$0.0490076\pi$
$401$			6.14184i			0.306709i	−0.988171	+	0.153354i	$0.950992\pi$
$402$		0			0
$403$	−17.3287			−0.863203
$404$	−0.544017	+	0.942265i	−0.0270658	+	0.0468794i
$405$		0			0
$406$		0			0
$407$	−28.1162	−	16.2329i	−1.39367	−	0.804633i
$408$		0			0
$409$	0.765886	+	0.442185i	0.0378706	+	0.0218646i	0.518816	−	0.854886i	$-0.326373\pi$
$409$	0.765886	+	0.442185i	0.0378706	+	0.0218646i	−0.480945	+	0.876751i	$0.659706\pi$
$410$	−2.91706	−	1.68416i	−0.144063	−	0.0831749i
$411$		0			0
$412$	−1.47106	−	0.849316i	−0.0724739	−	0.0418428i
$413$		0			0
$414$		0			0
$415$	8.24530	−	14.2813i	0.404746	−	0.701040i
$416$	−20.7918			−1.01940
$417$		0			0
$418$			32.6089i			1.59495i
$419$	−7.59365	−	13.1526i	−0.370974	−	0.642546i	0.618742	−	0.785595i	$-0.287643\pi$
$419$	−7.59365	−	13.1526i	−0.370974	−	0.642546i	−0.989716	+	0.143049i	$0.954309\pi$
$420$		0			0
$421$	13.3318	−	23.0914i	0.649753	−	1.12541i	−0.333428	−	0.942775i	$-0.608206\pi$
$421$	13.3318	−	23.0914i	0.649753	−	1.12541i	0.983182	−	0.182630i	$-0.0584611\pi$
$422$	−20.3605	−	11.7551i	−0.991133	−	0.572231i
$423$		0			0
$424$	12.4759	+	21.6088i	0.605881	+	1.04942i
$425$	1.18455	+	2.05170i	0.0574592	+	0.0995222i
$426$		0			0
$427$		0			0
$428$	−3.08358	+	1.78031i	−0.149050	+	0.0860543i
$429$		0			0
$430$		−	13.0598i		−	0.629801i
$431$	4.06785	−	2.34857i	0.195941	−	0.113127i	−0.398820	−	0.917029i	$-0.630580\pi$
$431$	4.06785	−	2.34857i	0.195941	−	0.113127i	0.594761	+	0.803903i	$0.297247\pi$
$432$		0			0
$433$			8.97714i			0.431414i	0.976458	+	0.215707i	$0.0692056\pi$
$433$			8.97714i			0.431414i	−0.976458	+	0.215707i	$0.930794\pi$
$434$		0			0
$435$		0			0
$436$	3.82499			0.183184
$437$	−17.5142	+	30.3354i	−0.837816	+	1.45114i
$438$		0			0
$439$	14.3012	−	8.25679i	0.682558	−	0.394075i	−0.118260	−	0.992983i	$-0.537732\pi$
$439$	14.3012	−	8.25679i	0.682558	−	0.394075i	0.800818	+	0.598907i	$0.204398\pi$
$440$	22.9225			1.09279
$441$		0			0
$442$	−6.45861			−0.307205
$443$	0.921171	−	0.531838i	0.0437661	−	0.0252684i	−0.477957	−	0.878383i	$-0.658623\pi$
$443$	0.921171	−	0.531838i	0.0437661	−	0.0252684i	0.521723	+	0.853115i	$0.325289\pi$
$444$		0			0
$445$	9.22500	−	15.9782i	0.437307	−	0.757438i
$446$	−3.04219			−0.144052
$447$		0			0
$448$		0			0
$449$		−	15.9081i		−	0.750749i	−0.926873	−	0.375374i	$-0.877514\pi$
$449$		−	15.9081i		−	0.750749i	0.926873	−	0.375374i	$-0.122486\pi$
$450$		0			0
$451$	−6.45785	+	3.72844i	−0.304088	+	0.175565i
$452$		−	18.0539i		−	0.849186i
$453$		0			0
$454$	−18.5309	+	10.6988i	−0.869698	+	0.502121i
$455$		0			0
$456$		0			0
$457$	16.3963	+	28.3992i	0.766985	+	1.32846i	0.939191	+	0.343395i	$0.111577\pi$
$457$	16.3963	+	28.3992i	0.766985	+	1.32846i	−0.172206	+	0.985061i	$0.555090\pi$
$458$	−6.33672	−	10.9755i	−0.296095	−	0.512852i
$459$		0			0
$460$	7.27862	+	4.20231i	0.339368	+	0.195934i
$461$	−9.23690	+	15.9988i	−0.430205	+	0.745138i	−0.996891	−	0.0787967i	$-0.974892\pi$
$461$	−9.23690	+	15.9988i	−0.430205	+	0.745138i	0.566685	+	0.823934i	$0.308226\pi$
$462$		0			0
$463$	−0.201921	−	0.349738i	−0.00938408	−	0.0162537i	0.861295	−	0.508105i	$-0.169654\pi$
$463$	−0.201921	−	0.349738i	−0.00938408	−	0.0162537i	−0.870679	+	0.491851i	$0.836320\pi$
$464$			0.534158i			0.0247976i
$465$		0			0
$466$	0.793161			0.0367425
$467$	7.51283	−	13.0126i	0.347652	−	0.602151i	−0.638180	−	0.769887i	$-0.720312\pi$
$467$	7.51283	−	13.0126i	0.347652	−	0.602151i	0.985832	+	0.167736i	$0.0536457\pi$
$468$		0			0
$469$		0			0
$470$	12.6936	+	7.32866i	0.585512	+	0.338046i
$471$		0			0
$472$	21.1002	+	12.1822i	0.971216	+	0.560732i
$473$	−25.0387	−	14.4561i	−1.15128	−	0.664691i
$474$		0			0
$475$	10.2821	+	5.93635i	0.471773	+	0.272379i
$476$		0			0
$477$		0			0
$478$	6.91604	−	11.9789i	0.316332	−	0.547903i
$479$	31.0800			1.42008			0.710041	−	0.704160i	$-0.248676\pi$
$479$	31.0800			1.42008			0.710041	+	0.704160i	$0.248676\pi$
$480$		0			0
$481$		−	32.2251i		−	1.46934i
$482$	−9.07944	−	15.7261i	−0.413557	−	0.716302i
$483$		0			0
$484$	2.96029	−	5.12738i	0.134559	−	0.233063i
$485$	−21.5547	−	12.4446i	−0.978747	−	0.565080i
$486$		0			0
$487$	−6.74782	−	11.6876i	−0.305773	−	0.529614i	0.671660	−	0.740859i	$-0.265582\pi$
$487$	−6.74782	−	11.6876i	−0.305773	−	0.529614i	−0.977433	+	0.211245i	$0.932248\pi$
$488$	−5.57994	−	9.66474i	−0.252592	−	0.437502i
$489$		0			0
$490$		0			0
$491$	7.07098	−	4.08243i	0.319109	−	0.184238i	−0.331886	−	0.943319i	$-0.607685\pi$
$491$	7.07098	−	4.08243i	0.319109	−	0.184238i	0.650995	+	0.759082i	$0.274352\pi$
$492$		0			0
$493$		−	1.01538i		−	0.0457303i
$494$	−28.0308	+	16.1836i	−1.26116	+	0.728134i
$495$		0			0
$496$			3.64269i			0.163562i
$497$		0			0
$498$		0			0
$499$	−28.0194			−1.25432			−0.627159	−	0.778891i	$-0.715782\pi$
$499$	−28.0194			−1.25432			−0.627159	+	0.778891i	$0.715782\pi$
$500$	6.29863	−	10.9095i	0.281683	−	0.487890i
$501$		0			0
$502$	18.8497	−	10.8829i	0.841305	−	0.485727i
$503$	−5.89656			−0.262915			−0.131457	−	0.991322i	$-0.541966\pi$
$503$	−5.89656			−0.262915			−0.131457	+	0.991322i	$0.541966\pi$
$504$		0			0
$505$	1.97488			0.0878811
$506$	−14.9811	+	8.64936i	−0.665992	+	0.384511i
$507$		0			0
$508$	5.24883	−	9.09123i	0.232879	−	0.403358i
$509$	14.0391			0.622274			0.311137	−	0.950365i	$-0.399290\pi$
$509$	14.0391			0.622274			0.311137	+	0.950365i	$0.399290\pi$
$510$		0			0
$511$		0			0
$512$			9.45558i			0.417882i
$513$		0			0
$514$	−3.44968	+	1.99168i	−0.152159	+	0.0878490i
$515$			3.08318i			0.135861i
$516$		0			0
$517$	28.1014	−	16.2243i	1.23590	−	0.713546i
$518$		0			0
$519$		0			0
$520$	11.3763	+	19.7043i	0.498883	+	0.864090i
$521$	19.2229	+	33.2950i	0.842170	+	1.45868i	0.888057	+	0.459734i	$0.152055\pi$
$521$	19.2229	+	33.2950i	0.842170	+	1.45868i	−0.0458870	+	0.998947i	$0.514611\pi$
$522$		0			0
$523$	−9.08734	−	5.24658i	−0.397362	−	0.229417i	0.287983	−	0.957635i	$-0.407015\pi$
$523$	−9.08734	−	5.24658i	−0.397362	−	0.229417i	−0.685345	+	0.728219i	$0.740349\pi$
$524$	−2.57914	+	4.46720i	−0.112670	+	0.195150i
$525$		0			0
$526$	4.88879	+	8.46764i	0.213161	+	0.369207i
$527$		−	6.92437i		−	0.301630i
$528$		0			0
$529$	4.41779			0.192078
$530$	7.72935	−	13.3876i	0.335741	−	0.581521i
$531$		0			0
$532$		0			0
$533$	−6.40998	−	3.70080i	−0.277647	−	0.160300i
$534$		0			0
$535$	5.59698	+	3.23142i	0.241979	+	0.139706i
$536$	32.3466	+	18.6753i	1.39716	+	0.806650i
$537$		0			0
$538$	8.47388	+	4.89240i	0.365335	+	0.210926i
$539$		0			0
$540$		0			0
$541$	−22.5783	+	39.1067i	−0.970715	+	1.68133i	−0.277311	+	0.960780i	$0.589443\pi$
$541$	−22.5783	+	39.1067i	−0.970715	+	1.68133i	−0.693405	+	0.720548i	$0.743890\pi$
$542$	−18.6822			−0.802471
$543$		0			0
$544$		−	8.30819i		−	0.356211i
$545$	−3.47136	−	6.01257i	−0.148697	−	0.257550i
$546$		0			0
$547$	−4.05733	+	7.02751i	−0.173479	+	0.300475i	−0.939634	−	0.342181i	$-0.888834\pi$
$547$	−4.05733	+	7.02751i	−0.173479	+	0.300475i	0.766155	+	0.642656i	$0.222168\pi$
$548$	−0.754550	−	0.435640i	−0.0322328	−	0.0186096i
$549$		0			0
$550$	2.93166	+	5.07779i	0.125007	+	0.216518i
$551$	−2.54427	−	4.40680i	−0.108389	−	0.187736i
$552$		0			0
$553$		0			0
$554$	13.2818	−	7.66827i	0.564291	−	0.325794i
$555$		0			0
$556$			6.87406i			0.291525i
$557$	14.0925	−	8.13633i	0.597120	−	0.344747i	−0.170788	−	0.985308i	$-0.554631\pi$
$557$	14.0925	−	8.13633i	0.597120	−	0.344747i	0.767908	+	0.640561i	$0.221298\pi$
$558$		0			0
$559$		−	28.6978i		−	1.21379i
$560$		0			0
$561$		0			0
$562$	−23.6647			−0.998236
$563$	5.13594	−	8.89572i	0.216454	−	0.374910i	−0.737267	−	0.675601i	$-0.763884\pi$
$563$	5.13594	−	8.89572i	0.216454	−	0.374910i	0.953721	+	0.300692i	$0.0972175\pi$
$564$		0			0
$565$	−28.3793	+	16.3848i	−1.19393	+	0.689314i
$566$	2.96233			0.124516
$567$		0			0
$568$	−43.2098			−1.81304
$569$	−17.8537	+	10.3079i	−0.748468	+	0.432128i	−0.825140	−	0.564928i	$-0.808904\pi$
$569$	−17.8537	+	10.3079i	−0.748468	+	0.432128i	0.0766722	+	0.997056i	$0.475571\pi$
$570$		0			0
$571$	−2.12828	+	3.68628i	−0.0890656	+	0.154266i	−0.907116	−	0.420880i	$-0.861721\pi$
$571$	−2.12828	+	3.68628i	−0.0890656	+	0.154266i	0.818051	+	0.575146i	$0.195055\pi$
$572$	17.1928			0.718867
$573$		0			0
$574$		0			0
$575$			6.29836i			0.262660i
$576$		0			0
$577$	−14.6609	+	8.46446i	−0.610340	+	0.352380i	−0.773099	−	0.634286i	$-0.781294\pi$
$577$	−14.6609	+	8.46446i	−0.610340	+	0.352380i	0.162758	+	0.986666i	$0.447961\pi$
$578$			14.1068i			0.586764i
$579$		0			0
$580$	−1.05736	+	0.610467i	−0.0439045	+	0.0253483i
$581$		0			0
$582$		0			0
$583$	−17.1114	−	29.6378i	−0.708682	−	1.22747i
$584$	−5.64730	−	9.78141i	−0.233687	−	0.404758i
$585$		0			0
$586$	−25.3735	−	14.6494i	−1.04817	−	0.605160i
$587$	12.0558	−	20.8812i	0.497594	−	0.861858i	−0.502402	−	0.864634i	$-0.667550\pi$
$587$	12.0558	−	20.8812i	0.497594	−	0.861858i	0.999996	+	0.00277589i	$0.000883594\pi$
$588$		0			0
$589$	−17.3507	−	30.0522i	−0.714922	−	1.23828i
$590$		−	15.0949i		−	0.621445i
$591$		0			0
$592$	−6.77409			−0.278414
$593$	19.2908	−	33.4126i	0.792178	−	1.37209i	−0.132437	−	0.991191i	$-0.542280\pi$
$593$	19.2908	−	33.4126i	0.792178	−	1.37209i	0.924616	−	0.380902i	$-0.124386\pi$
$594$		0			0
$595$		0			0
$596$	−15.2378	−	8.79752i	−0.624163	−	0.360360i
$597$		0			0
$598$	−14.8701	−	8.58525i	−0.608083	−	0.351077i
$599$	−29.2921	−	16.9118i	−1.19684	−	0.690997i	−0.236992	−	0.971511i	$-0.576162\pi$
$599$	−29.2921	−	16.9118i	−1.19684	−	0.690997i	−0.959850	+	0.280514i	$0.909495\pi$
$600$		0			0
$601$	27.4855	+	15.8688i	1.12116	+	0.647300i	0.941696	−	0.336465i	$-0.109231\pi$
$601$	27.4855	+	15.8688i	1.12116	+	0.647300i	0.179461	+	0.983765i	$0.442565\pi$
$602$		0			0
$603$		0			0
$604$	−1.01124	+	1.75153i	−0.0411469	+	0.0712686i
$605$	−10.7464			−0.436904
$606$		0			0
$607$			0.195554i			0.00793731i	0.999992	+	0.00396865i	$0.00126327\pi$
$607$			0.195554i			0.00793731i	−0.999992	+	0.00396865i	$0.998737\pi$
$608$	−20.8181	−	36.0581i	−0.844287	−	1.46235i
$609$		0			0
$610$	−3.45702	+	5.98774i	−0.139971	+	0.242436i
$611$	27.8931	+	16.1041i	1.12843	+	0.651502i
$612$		0			0
$613$	−1.46664	−	2.54029i	−0.0592370	−	0.102602i	0.834886	−	0.550423i	$-0.185533\pi$
$613$	−1.46664	−	2.54029i	−0.0592370	−	0.102602i	−0.894123	+	0.447821i	$0.852200\pi$
$614$	1.31956	+	2.28554i	0.0532530	+	0.0922370i
$615$		0			0
$616$		0			0
$617$	7.86982	−	4.54365i	0.316827	−	0.182920i	−0.333150	−	0.942874i	$-0.608112\pi$
$617$	7.86982	−	4.54365i	0.316827	−	0.182920i	0.649977	+	0.759953i	$0.274778\pi$
$618$		0			0
$619$			28.7043i			1.15372i	0.816842	+	0.576861i	$0.195723\pi$
$619$			28.7043i			1.15372i	−0.816842	+	0.576861i	$0.804277\pi$
$620$	−7.21068	+	4.16309i	−0.289588	+	0.167194i
$621$		0			0
$622$			10.8717i			0.435916i
$623$		0			0
$624$		0			0
$625$	−15.5597			−0.622388
$626$	8.21604	−	14.2306i	0.328379	−	0.568769i
$627$		0			0
$628$	8.54588	−	4.93397i	0.341018	−	0.196887i
$629$	12.8768			0.513433
$630$		0			0
$631$	−20.7691			−0.826805			−0.413403	−	0.910548i	$-0.635660\pi$
$631$	−20.7691			−0.826805			−0.413403	+	0.910548i	$0.635660\pi$
$632$	−21.5830	+	12.4609i	−0.858525	+	0.495670i
$633$		0			0
$634$	1.44390	−	2.50091i	0.0573447	−	0.0993240i
$635$	−19.0542			−0.756143
$636$		0			0
$637$		0			0
$638$		−	2.51297i		−	0.0994895i
$639$		0			0
$640$	−5.92345	+	3.41990i	−0.234145	+	0.135184i
$641$			45.9263i			1.81398i	0.421152	+	0.906990i	$0.361626\pi$
$641$			45.9263i			1.81398i	−0.421152	+	0.906990i	$0.638374\pi$
$642$		0			0
$643$	−9.15428	+	5.28523i	−0.361010	+	0.208429i	−0.669524	−	0.742791i	$-0.733502\pi$
$643$	−9.15428	+	5.28523i	−0.361010	+	0.208429i	0.308514	+	0.951220i	$0.400168\pi$
$644$		0			0
$645$		0			0
$646$	−6.46680	−	11.2008i	−0.254433	−	0.440691i
$647$	19.2562	+	33.3526i	0.757038	+	1.31123i	0.944355	+	0.328928i	$0.106687\pi$
$647$	19.2562	+	33.3526i	0.757038	+	1.31123i	−0.187317	+	0.982299i	$0.559979\pi$
$648$		0			0
$649$	−28.9402	−	16.7087i	−1.13600	−	0.655872i
$650$	−2.90993	+	5.04015i	−0.114137	+	0.197691i
$651$		0			0
$652$	−0.575323	−	0.996488i	−0.0225314	−	0.0390255i
$653$			12.8018i			0.500973i	0.968120	+	0.250486i	$0.0805905\pi$
$653$			12.8018i			0.500973i	−0.968120	+	0.250486i	$0.919409\pi$
$654$		0			0
$655$	9.36274			0.365833
$656$	−0.777952	+	1.34745i	−0.0303739	+	0.0526092i
$657$		0			0
$658$		0			0
$659$	−41.5777	−	24.0049i	−1.61964	−	0.935097i	−0.987014	−	0.160636i	$-0.948645\pi$
$659$	−41.5777	−	24.0049i	−1.61964	−	0.935097i	−0.632622	−	0.774461i	$-0.718021\pi$
$660$		0			0
$661$	−9.38011	−	5.41561i	−0.364844	−	0.210643i	0.306360	−	0.951916i	$-0.400889\pi$
$661$	−9.38011	−	5.41561i	−0.364844	−	0.210643i	−0.671204	+	0.741273i	$0.734222\pi$
$662$	4.14983	+	2.39591i	0.161288	+	0.0931196i
$663$		0			0
$664$	−22.6276	−	13.0640i	−0.878121	−	0.506983i
$665$		0			0
$666$		0			0
$667$	1.34971	−	2.33777i	0.0522611	−	0.0905188i
$668$	14.5271			0.562070
$669$		0			0
$670$		−	23.1404i		−	0.893991i
$671$	7.65323	+	13.2558i	0.295450	+	0.511734i
$672$		0			0
$673$	−6.19553	+	10.7310i	−0.238820	+	0.413649i	−0.960376	−	0.278707i	$-0.910094\pi$
$673$	−6.19553	+	10.7310i	−0.238820	+	0.413649i	0.721556	+	0.692356i	$0.243427\pi$
$674$	−11.0756	−	6.39449i	−0.426616	−	0.246307i
$675$		0			0
$676$	1.79595	+	3.11068i	0.0690752	+	0.119642i
$677$	14.4947	+	25.1056i	0.557078	+	0.964888i	0.997739	+	0.0672139i	$0.0214110\pi$
$677$	14.4947	+	25.1056i	0.557078	+	0.964888i	−0.440660	+	0.897674i	$0.645256\pi$
$678$		0			0
$679$		0			0
$680$	−7.87364	+	4.54585i	−0.301940	+	0.174325i
$681$		0			0
$682$		−	17.1372i		−	0.656219i
$683$	−0.132048	+	0.0762380i	−0.00505268	+	0.00291717i	−0.502524	−	0.864563i	$-0.667595\pi$
$683$	−0.132048	+	0.0762380i	−0.00505268	+	0.00291717i	0.497472	+	0.867480i	$0.334262\pi$
$684$		0			0
$685$			1.58145i			0.0604242i
$686$		0			0
$687$		0			0
$688$	−6.03263			−0.229992
$689$	16.9846	−	29.4181i	0.647060	−	1.12074i
$690$		0			0
$691$	−37.4428	+	21.6176i	−1.42439	+	0.822373i	−0.996670	−	0.0815369i	$-0.974017\pi$
$691$	−37.4428	+	21.6176i	−1.42439	+	0.822373i	−0.427722	+	0.903910i	$0.640684\pi$
$692$	−7.37691			−0.280428
$693$		0			0
$694$	2.11225			0.0801799
$695$	10.8055	−	6.23853i	0.409874	−	0.236641i
$696$		0			0
$697$	1.47880	−	2.56136i	0.0560137	−	0.0970186i
$698$	28.6678			1.08509
$699$		0			0
$700$		0			0
$701$			11.5821i			0.437451i	0.975786	+	0.218726i	$0.0701900\pi$
$701$			11.5821i			0.437451i	−0.975786	+	0.218726i	$0.929810\pi$
$702$		0			0
$703$	55.8863	−	32.2660i	2.10779	−	1.21693i
$704$		−	27.5363i		−	1.03781i
$705$		0			0
$706$	9.21116	−	5.31807i	0.346667	−	0.200148i
$707$		0			0
$708$		0			0
$709$	18.9474	+	32.8178i	0.711584	+	1.23250i	0.964262	+	0.264949i	$0.0853552\pi$
$709$	18.9474	+	32.8178i	0.711584	+	1.23250i	−0.252678	+	0.967550i	$0.581311\pi$
$710$	13.3852	+	23.1838i	0.502337	+	0.870073i
$711$		0			0
$712$	−25.3162	−	14.6163i	−0.948765	−	0.547770i
$713$	9.20437	−	15.9424i	0.344707	−	0.597049i
$714$		0			0
$715$	−15.6033	−	27.0256i	−0.583529	−	1.01070i
$716$			6.22127i			0.232500i
$717$		0			0
$718$	−20.5642			−0.767449
$719$	23.3158	−	40.3842i	0.869534	−	1.50608i	0.00706058	−	0.999975i	$-0.497753\pi$
$719$	23.3158	−	40.3842i	0.869534	−	1.50608i	0.862474	−	0.506102i	$-0.168914\pi$
$720$		0			0
$721$		0			0
$722$	−39.9806	−	23.0828i	−1.48792	−	0.859054i
$723$		0			0
$724$	−1.16937	−	0.675138i	−0.0434594	−	0.0250913i
$725$	−0.792377	−	0.457479i	−0.0294282	−	0.0169904i
$726$		0			0
$727$	3.72659	+	2.15155i	0.138212	+	0.0797965i	0.567511	−	0.823366i	$-0.307906\pi$
$727$	3.72659	+	2.15155i	0.138212	+	0.0797965i	−0.429300	+	0.903162i	$0.641240\pi$
$728$		0			0
$729$		0			0
$730$	−3.49875	+	6.06002i	−0.129495	+	0.224291i
$731$	11.4674			0.424136
$732$		0			0
$733$		−	14.0108i		−	0.517500i	−0.965944	−	0.258750i	$-0.916689\pi$
$733$		−	14.0108i		−	0.517500i	0.965944	−	0.258750i	$-0.0833105\pi$
$734$	2.82143	+	4.88685i	0.104141	+	0.180377i
$735$		0			0
$736$	11.0438	−	19.1285i	0.407081	−	0.705086i
$737$	−44.3653	−	25.6143i	−1.63422	−	0.943516i
$738$		0			0
$739$	−18.9313	−	32.7901i	−0.696401	−	1.20620i	−0.969706	−	0.244274i	$-0.921450\pi$
$739$	−18.9313	−	32.7901i	−0.696401	−	1.20620i	0.273305	−	0.961927i	$-0.411883\pi$
$740$	−7.74184	−	13.4093i	−0.284596	−	0.492934i
$741$		0			0
$742$		0			0
$743$	24.0489	−	13.8847i	0.882269	−	0.509378i	0.0108634	−	0.999941i	$-0.496542\pi$
$743$	24.0489	−	13.8847i	0.882269	−	0.509378i	0.871406	+	0.490563i	$0.163209\pi$
$744$		0			0
$745$			31.9366i			1.17007i
$746$	−24.5626	+	14.1812i	−0.899300	+	0.519211i
$747$		0			0
$748$			6.87007i			0.251195i
$749$		0			0
$750$		0			0
$751$	−17.3508			−0.633140			−0.316570	−	0.948569i	$-0.602531\pi$
$751$	−17.3508			−0.633140			−0.316570	+	0.948569i	$0.602531\pi$
$752$	3.38527	−	5.86346i	0.123448	−	0.213818i
$753$		0			0
$754$	2.16017	−	1.24717i	0.0786686	−	0.0454193i
$755$	3.67100			0.133601
$756$		0			0
$757$	18.8111			0.683701			0.341850	−	0.939754i	$-0.388946\pi$
$757$	18.8111			0.683701			0.341850	+	0.939754i	$0.388946\pi$
$758$	0.349764	−	0.201936i	0.0127040	−	0.00733465i
$759$		0			0
$760$	−22.7814	+	39.4586i	−0.826369	+	1.43131i
$761$	−8.45039			−0.306326			−0.153163	−	0.988201i	$-0.548946\pi$
$761$	−8.45039			−0.306326			−0.153163	+	0.988201i	$0.548946\pi$
$762$		0			0
$763$		0			0
$764$			5.94167i			0.214962i
$765$		0			0
$766$	21.0840	−	12.1728i	0.761794	−	0.439822i
$767$		−	33.1696i		−	1.19769i
$768$		0			0
$769$	−19.8100	+	11.4373i	−0.714366	+	0.412440i	−0.812676	−	0.582716i	$-0.801990\pi$
$769$	−19.8100	+	11.4373i	−0.714366	+	0.412440i	0.0983092	+	0.995156i	$0.468657\pi$
$770$		0			0
$771$		0			0
$772$	−0.807907	−	1.39934i	−0.0290772	−	0.0503632i
$773$	−18.8374	−	32.6273i	−0.677533	−	1.17352i	−0.975722	−	0.219015i	$-0.929716\pi$
$773$	−18.8374	−	32.6273i	−0.677533	−	1.17352i	0.298189	−	0.954507i	$-0.403618\pi$
$774$		0			0
$775$	−5.40363	−	3.11978i	−0.194104	−	0.112066i
$776$	−19.7175	+	34.1517i	−0.707817	+	1.22598i
$777$		0			0
$778$	−2.16888	−	3.75660i	−0.0777579	−	0.134681i
$779$		−	14.8220i		−	0.531053i
$780$		0			0
$781$	59.2649			2.12066
$782$	3.43058	−	5.94194i	0.122677	−	0.212483i
$783$		0			0
$784$		0			0
$785$	−15.5116	−	8.95561i	−0.553632	−	0.319639i
$786$		0			0
$787$	−20.3222	−	11.7330i	−0.724408	−	0.418237i	0.0919648	−	0.995762i	$-0.470685\pi$
$787$	−20.3222	−	11.7330i	−0.724408	−	0.418237i	−0.816373	+	0.577525i	$0.804019\pi$
$788$	−17.5478	−	10.1312i	−0.625113	−	0.360909i
$789$		0			0
$790$	13.3716	+	7.72011i	0.475741	+	0.274669i
$791$		0			0
$792$		0			0
$793$	−7.59650	+	13.1575i	−0.269760	+	0.467237i
$794$	−21.8511			−0.775468
$795$		0			0
$796$		−	1.01196i		−	0.0358681i
$797$	−22.8856	−	39.6390i	−0.810648	−	1.40408i	−0.912411	−	0.409275i	$-0.865782\pi$
$797$	−22.8856	−	39.6390i	−0.810648	−	1.40408i	0.101763	−	0.994809i	$-0.467552\pi$
$798$		0			0
$799$	−6.43503	+	11.1458i	−0.227655	+	0.394310i
$800$	−6.48352	−	3.74326i	−0.229227	−	0.132344i
$801$		0			0
$802$	−3.01448	−	5.22123i	−0.106445	−	0.184368i
$803$	7.74562	+	13.4158i	0.273337	+	0.473433i
$804$		0			0
$805$		0			0
$806$	14.7313	−	8.50510i	0.518887	−	0.299579i
$807$		0			0
$808$		−	3.12905i		−	0.110080i
$809$	11.4669	−	6.62041i	0.403154	−	0.232761i	−0.284690	−	0.958620i	$-0.591891\pi$
$809$	11.4669	−	6.62041i	0.403154	−	0.232761i	0.687844	+	0.725858i	$0.258557\pi$
$810$		0			0
$811$			56.0437i			1.96796i	0.178275	+	0.983981i	$0.442948\pi$
$811$			56.0437i			1.96796i	−0.178275	+	0.983981i	$0.557052\pi$
$812$		0			0
$813$		0			0
$814$	31.8691			1.11701
$815$	−1.04426	+	1.80872i	−0.0365790	+	0.0633566i
$816$		0			0
$817$	49.7692	−	28.7343i	1.74120	−	1.00528i
$818$	−0.868116			−0.0303530
$819$		0			0
$820$	−3.55636			−0.124193
$821$	48.7766	−	28.1612i	1.70232	−	0.982833i	0.758909	−	0.651197i	$-0.225733\pi$
$821$	48.7766	−	28.1612i	1.70232	−	0.982833i	0.943407	−	0.331636i	$-0.107601\pi$
$822$		0			0
$823$	−8.52180	+	14.7602i	−0.297051	+	0.514508i	−0.975460	−	0.220177i	$-0.929337\pi$
$823$	−8.52180	+	14.7602i	−0.297051	+	0.514508i	0.678409	+	0.734685i	$0.262670\pi$
$824$	4.88506			0.170179
$825$		0			0
$826$		0			0
$827$		−	45.7715i		−	1.59163i	−0.605539	−	0.795816i	$-0.707042\pi$
$827$		−	45.7715i		−	1.59163i	0.605539	−	0.795816i	$-0.292958\pi$
$828$		0			0
$829$	−30.5567	+	17.6419i	−1.06128	+	0.612730i	−0.925786	−	0.378049i	$-0.876595\pi$
$829$	−30.5567	+	17.6419i	−1.06128	+	0.612730i	−0.135493	+	0.990778i	$0.543262\pi$
$830$			16.1875i			0.561877i
$831$		0			0
$832$	23.6704	−	13.6661i	0.820623	−	0.473787i
$833$		0			0
$834$		0			0
$835$	−13.1840	−	22.8354i	−0.456251	−	0.790250i
$836$	17.2146	+	29.8166i	0.595380	+	1.03123i
$837$		0			0
$838$	12.9109	+	7.45409i	0.445998	+	0.257497i
$839$	−22.3195	+	38.6585i	−0.770555	+	1.33464i	0.166704	+	0.986007i	$0.446688\pi$
$839$	−22.3195	+	38.6585i	−0.770555	+	1.33464i	−0.937259	+	0.348634i	$0.886646\pi$
$840$		0			0
$841$	−14.3039	−	24.7751i	−0.493239	−	0.854315i
$842$			26.1736i			0.902002i
$843$		0			0
$844$	−24.8227			−0.854433
$845$	3.25982	−	5.64618i	0.112141	−	0.194235i
$846$		0			0
$847$		0			0
$848$	−6.18404	−	3.57036i	−0.212361	−	0.122607i
$849$		0			0
$850$	−2.01400	−	1.16278i	−0.0690795	−	0.0398831i
$851$	29.6472	+	17.1168i	1.01629	+	0.586757i
$852$		0			0
$853$	−47.7652	−	27.5772i	−1.63545	−	0.944227i	−0.982372	−	0.186935i	$-0.940145\pi$
$853$	−47.7652	−	27.5772i	−1.63545	−	0.944227i	−0.653077	−	0.757292i	$-0.726522\pi$
$854$		0			0
$855$		0			0
$856$	5.11994	−	8.86800i	0.174996	−	0.303102i
$857$	−38.1541			−1.30332			−0.651660	−	0.758511i	$-0.725927\pi$
$857$	−38.1541			−1.30332			−0.651660	+	0.758511i	$0.725927\pi$
$858$		0			0
$859$			40.4682i			1.38076i	0.723449	+	0.690378i	$0.242556\pi$
$859$			40.4682i			1.38076i	−0.723449	+	0.690378i	$0.757444\pi$
$860$	−6.89444	−	11.9415i	−0.235099	−	0.407203i
$861$		0			0
$862$	−2.30541	+	3.99309i	−0.0785226	+	0.136005i
$863$	−31.3519	−	18.1011i	−1.06723	−	0.616167i	−0.139808	−	0.990179i	$-0.544649\pi$
$863$	−31.3519	−	18.1011i	−1.06723	−	0.616167i	−0.927424	+	0.374012i	$0.877982\pi$
$864$		0			0
$865$	6.69488	+	11.5959i	0.227633	+	0.394272i
$866$	−4.40608	−	7.63155i	−0.149725	−	0.259331i
$867$		0			0
$868$		0			0
$869$	29.6024	−	17.0910i	1.00419	−	0.579771i
$870$		0			0
$871$		−	50.8489i		−	1.72295i
$872$	−9.52645	+	5.50010i	−0.322606	+	0.186257i
$873$		0			0
$874$		−	34.3846i		−	1.16307i
$875$		0			0
$876$		0			0
$877$	−11.0688			−0.373766			−0.186883	−	0.982382i	$-0.559839\pi$
$877$	−11.0688			−0.373766			−0.186883	+	0.982382i	$0.559839\pi$
$878$	−8.10505	+	14.0384i	−0.273532	+	0.473771i
$879$		0			0
$880$	−5.68111	+	3.27999i	−0.191510	+	0.110568i
$881$	8.87036			0.298850			0.149425	−	0.988773i	$-0.452258\pi$
$881$	8.87036			0.298850			0.149425	+	0.988773i	$0.452258\pi$
$882$		0			0
$883$	−14.1903			−0.477540			−0.238770	−	0.971076i	$-0.576744\pi$
$883$	−14.1903			−0.477540			−0.238770	+	0.971076i	$0.576744\pi$
$884$	−5.90556	+	3.40958i	−0.198625	+	0.114676i
$885$		0			0
$886$	−0.522064	+	0.904241i	−0.0175391	+	0.0303786i
$887$	−39.0360			−1.31070			−0.655350	−	0.755325i	$-0.727479\pi$
$887$	−39.0360			−1.31070			−0.655350	+	0.755325i	$0.727479\pi$
$888$		0			0
$889$		0			0
$890$			18.1109i			0.607080i
$891$		0			0
$892$	−2.78169	+	1.60601i	−0.0931378	+	0.0537732i
$893$			64.4981i			2.15835i
$894$		0			0
$895$	9.77931	−	5.64609i	0.326886	−	0.188728i
$896$		0			0
$897$		0			0
$898$	7.80786	+	13.5236i	0.260552	+	0.451288i
$899$	1.33711	+	2.31595i	0.0445952	+	0.0772411i
$900$		0			0
$901$	11.7552	+	6.78687i	0.391622	+	0.226103i
$902$	3.65992	−	6.33916i	0.121862	−	0.211071i
$903$		0			0
$904$	25.9605	+	44.9648i	0.863432	+	1.49551i
$905$			2.45088i			0.0814699i
$906$		0			0
$907$	9.86974			0.327719			0.163860	−	0.986484i	$-0.447606\pi$
$907$	9.86974			0.327719			0.163860	+	0.986484i	$0.447606\pi$
$908$	−11.2961	+	19.5654i	−0.374873	+	0.649300i
$909$		0			0
$910$		0			0
$911$	46.6335	+	26.9239i	1.54504	+	0.892028i	0.998509	+	0.0545881i	$0.0173846\pi$
$911$	46.6335	+	26.9239i	1.54504	+	0.892028i	0.546529	+	0.837440i	$0.315949\pi$
$912$		0			0
$913$	31.0351	+	17.9181i	1.02711	+	0.593004i
$914$	−27.8772	−	16.0949i	−0.922096	−	0.532373i
$915$		0			0
$916$	−11.5882	−	6.69046i	−0.382885	−	0.221059i
$917$		0			0
$918$		0			0
$919$	−11.0899	+	19.2084i	−0.365824	+	0.633625i	−0.988908	−	0.148530i	$-0.952546\pi$
$919$	−11.0899	+	19.2084i	−0.365824	+	0.633625i	0.623084	+	0.782155i	$0.285879\pi$
$920$	−24.1707			−0.796884
$921$		0			0
$922$		−	18.1343i		−	0.597221i
$923$	29.4128	+	50.9444i	0.968133	+	1.67686i
$924$		0			0
$925$	5.80167	−	10.0488i	0.190758	−	0.330402i
$926$	0.343310	+	0.198210i	0.0112819	+	0.00651359i
$927$		0			0
$928$	1.60433	+	2.77878i	0.0526647	+	0.0912180i
$929$	−27.4954	−	47.6234i	−0.902093	−	1.56247i	−0.824772	−	0.565466i	$-0.808697\pi$
$929$	−27.4954	−	47.6234i	−0.902093	−	1.56247i	−0.0773215	−	0.997006i	$-0.524637\pi$
$930$		0			0
$931$		0			0
$932$	0.725243	−	0.418719i	0.0237561	−	0.0137156i
$933$		0			0
$934$			14.7495i			0.482618i
$935$	10.7992	−	6.23491i	0.353171	−	0.203903i
$936$		0			0
$937$		−	29.3132i		−	0.957622i	−0.877918	−	0.478811i	$-0.841068\pi$
$937$		−	29.3132i		−	0.957622i	0.877918	−	0.478811i	$-0.158932\pi$
$938$		0			0
$939$		0			0
$940$	15.4755			0.504757
$941$	−7.58758	+	13.1421i	−0.247348	+	0.428419i	−0.962789	−	0.270254i	$-0.912892\pi$
$941$	−7.58758	+	13.1421i	−0.247348	+	0.428419i	0.715441	+	0.698673i	$0.246226\pi$
$942$		0			0
$943$	6.80950	−	3.93147i	0.221748	−	0.128026i
$944$	−6.97265			−0.226940
$945$		0			0
$946$	28.3808			0.922739
$947$	2.27478	−	1.31335i	0.0739206	−	0.0426781i	−0.462584	−	0.886575i	$-0.653078\pi$
$947$	2.27478	−	1.31335i	0.0739206	−	0.0426781i	0.536505	+	0.843897i	$0.319744\pi$
$948$		0			0
$949$	−7.68820	+	13.3164i	−0.249570	+	0.432267i
$950$	−11.6545			−0.378122
$951$		0			0
$952$		0			0
$953$			40.5520i			1.31361i	0.754061	+	0.656805i	$0.228092\pi$
$953$			40.5520i			1.31361i	−0.754061	+	0.656805i	$0.771908\pi$
$954$		0			0
$955$	9.33981	−	5.39234i	0.302229	−	0.174492i
$956$		−	14.6042i		−	0.472335i
$957$		0			0
$958$	−26.4214	+	15.2544i	−0.853637	+	0.492847i
$959$		0			0
$960$		0			0
$961$	−6.38155	−	11.0532i	−0.205856	−	0.356554i
$962$	15.8164	+	27.3948i	0.509942	+	0.883245i
$963$		0			0
$964$	−16.6039	−	9.58629i	−0.534777	−	0.308754i
$965$	−1.46643	+	2.53993i	−0.0472059	+	0.0817631i
$966$		0			0
$967$	6.47468	+	11.2145i	0.208212	+	0.360633i	0.951151	−	0.308725i	$-0.0999023\pi$
$967$	6.47468	+	11.2145i	0.208212	+	0.360633i	−0.742939	+	0.669359i	$0.766569\pi$
$968$			17.0269i			0.547264i
$969$		0			0
$970$	24.4317			0.784456
$971$	8.26077	−	14.3081i	0.265101	−	0.459168i	−0.702489	−	0.711694i	$-0.747928\pi$
$971$	8.26077	−	14.3081i	0.265101	−	0.459168i	0.967590	+	0.252526i	$0.0812614\pi$
$972$		0			0
$973$		0			0
$974$	11.4728	+	6.62381i	0.367611	+	0.212240i
$975$		0			0
$976$	2.76587	+	1.59687i	0.0885333	+	0.0511147i
$977$	5.50730	+	3.17964i	0.176194	+	0.101726i	0.585503	−	0.810670i	$-0.300897\pi$
$977$	5.50730	+	3.17964i	0.176194	+	0.101726i	−0.409309	+	0.912396i	$0.634230\pi$
$978$		0			0
$979$	34.7227	+	20.0472i	1.10974	+	0.640711i
$980$		0			0
$981$		0			0
$982$	−4.00740	+	6.94103i	−0.127881	+	0.221497i
$983$	2.22975			0.0711179			0.0355590	−	0.999368i	$-0.488679\pi$
$983$	2.22975			0.0711179			0.0355590	+	0.999368i	$0.488679\pi$
$984$		0			0
$985$			36.7781i			1.17185i
$986$	0.498358	+	0.863181i	0.0158709	+	0.0274893i
$987$		0			0
$988$	−17.0870	+	29.5956i	−0.543610	+	0.941561i
$989$	26.4021	+	15.2433i	0.839538	+	0.484708i
$990$		0			0
$991$	24.7285	+	42.8310i	0.785527	+	1.36057i	0.928684	+	0.370872i	$0.120941\pi$
$991$	24.7285	+	42.8310i	0.785527	+	1.36057i	−0.143157	+	0.989700i	$0.545726\pi$
$992$	10.9407	+	18.9499i	0.347369	+	0.601661i
$993$		0			0
$994$		0			0
$995$	−1.59072	+	0.918403i	−0.0504293	+	0.0291153i
$996$		0			0
$997$			8.40875i			0.266308i	0.991095	+	0.133154i	$0.0425104\pi$
$997$			8.40875i			0.266308i	−0.991095	+	0.133154i	$0.957490\pi$
$998$	23.8195	−	13.7522i	0.753993	−	0.435318i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.d.656.10		48
3.2	odd	2		441.2.s.d.362.15		48
7.2	even	3		1323.2.o.e.440.16		48
7.3	odd	6		1323.2.i.d.521.18		48
7.4	even	3		1323.2.i.d.521.8		48
7.5	odd	6		1323.2.o.e.440.15		48
7.6	odd	2	inner	1323.2.s.d.656.9		48
9.4	even	3		441.2.i.d.68.9		48
9.5	odd	6		1323.2.i.d.1097.18		48
21.2	odd	6		441.2.o.e.146.9	✓	48
21.5	even	6		441.2.o.e.146.10	yes	48
21.11	odd	6		441.2.i.d.227.16		48
21.17	even	6		441.2.i.d.227.15		48
21.20	even	2		441.2.s.d.362.16		48
63.4	even	3		441.2.s.d.374.16		48
63.5	even	6		1323.2.o.e.881.16		48
63.13	odd	6		441.2.i.d.68.10		48
63.23	odd	6		1323.2.o.e.881.15		48
63.31	odd	6		441.2.s.d.374.15		48
63.32	odd	6	inner	1323.2.s.d.962.9		48
63.40	odd	6		441.2.o.e.293.9	yes	48
63.41	even	6		1323.2.i.d.1097.8		48
63.58	even	3		441.2.o.e.293.10	yes	48
63.59	even	6	inner	1323.2.s.d.962.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.9		48	9.4	even	3
441.2.i.d.68.10		48	63.13	odd	6
441.2.i.d.227.15		48	21.17	even	6
441.2.i.d.227.16		48	21.11	odd	6
441.2.o.e.146.9	✓	48	21.2	odd	6
441.2.o.e.146.10	yes	48	21.5	even	6
441.2.o.e.293.9	yes	48	63.40	odd	6
441.2.o.e.293.10	yes	48	63.58	even	3
441.2.s.d.362.15		48	3.2	odd	2
441.2.s.d.362.16		48	21.20	even	2
441.2.s.d.374.15		48	63.31	odd	6
441.2.s.d.374.16		48	63.4	even	3
1323.2.i.d.521.8		48	7.4	even	3
1323.2.i.d.521.18		48	7.3	odd	6
1323.2.i.d.1097.8		48	63.41	even	6
1323.2.i.d.1097.18		48	9.5	odd	6
1323.2.o.e.440.15		48	7.5	odd	6
1323.2.o.e.440.16		48	7.2	even	3
1323.2.o.e.881.15		48	63.23	odd	6
1323.2.o.e.881.16		48	63.5	even	6
1323.2.s.d.656.9		48	7.6	odd	2	inner
1323.2.s.d.656.10		48	1.1	even	1	trivial
1323.2.s.d.962.9		48	63.32	odd	6	inner
1323.2.s.d.962.10		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)

\(f(q)\)	\(=\)	\(q+(-0.850109 + 0.490811i) q^{2} +(-0.518210 + 0.897565i) q^{4} +1.88120 q^{5} -2.98061i q^{8} +O(q^{10})\)	\(q+(-0.850109 + 0.490811i) q^{2} +(-0.518210 + 0.897565i) q^{4} +1.88120 q^{5} -2.98061i q^{8} +(-1.59922 + 0.923312i) q^{10} +4.08810i q^{11} +(-3.51415 + 2.02890i) q^{13} +(0.426498 + 0.738716i) q^{16} +(-0.810727 - 1.40422i) q^{17} +(-7.03722 - 4.06294i) q^{19} +(-0.974855 + 1.68850i) q^{20} +(-2.00648 - 3.47533i) q^{22} -4.31071i q^{23} -1.46110 q^{25} +(1.99161 - 3.44957i) q^{26} +(0.542317 + 0.313107i) q^{29} +(3.69833 + 2.13523i) q^{31} +(4.43744 + 2.56195i) q^{32} +(1.37841 + 0.795827i) q^{34} +(-3.97076 + 6.87757i) q^{37} +7.97654 q^{38} -5.60712i q^{40} +(0.912023 + 1.57967i) q^{41} +(-3.53614 + 6.12477i) q^{43} +(-3.66933 - 2.11849i) q^{44} +(2.11574 + 3.66457i) q^{46} +(-3.96868 - 6.87396i) q^{47} +(1.24209 - 0.717122i) q^{50} -4.20558i q^{52} +(-7.24978 + 4.18567i) q^{53} +7.69052i q^{55} -0.614704 q^{58} +(-4.08715 + 7.07915i) q^{59} +(3.24253 - 1.87208i) q^{61} -4.19198 q^{62} -6.73573 q^{64} +(-6.61081 + 3.81676i) q^{65} +(-6.26559 + 10.8523i) q^{67} +1.68051 q^{68} -14.4969i q^{71} +(3.28167 - 1.89468i) q^{73} -7.79557i q^{74} +(7.29351 - 4.21091i) q^{76} +(-4.18066 - 7.24112i) q^{79} +(0.802327 + 1.38967i) q^{80} +(-1.55064 - 0.895261i) q^{82} +(4.38300 - 7.59159i) q^{83} +(-1.52514 - 2.64162i) q^{85} -6.94230i q^{86} +12.1850 q^{88} +(4.90379 - 8.49362i) q^{89} +(3.86914 + 2.23385i) q^{92} +(6.74762 + 3.89574i) q^{94} +(-13.2384 - 7.64320i) q^{95} +(-11.4579 - 6.61525i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 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

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