LMFDB - Embedded newform 1323.2.i.d.1097.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1323,2,Mod(521,1323)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			1097.18
Character	$\chi$	$=$	1323.1097
Dual form			1323.2.i.d.521.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.981621i q^{2} +1.03642 q^{4} +(0.940599 + 1.62916i) q^{5} +2.98061i q^{8} +(-1.59922 + 0.923312i) q^{10} +(3.54040 + 2.04405i) q^{11} +(3.51415 + 2.02890i) q^{13} -0.852996 q^{16} +(0.810727 + 1.40422i) q^{17} +(-7.03722 - 4.06294i) q^{19} +(0.974855 + 1.68850i) q^{20} +(-2.00648 + 3.47533i) q^{22} +(3.73318 - 2.15535i) q^{23} +(0.730548 - 1.26535i) q^{25} +(-1.99161 + 3.44957i) q^{26} +(0.542317 - 0.313107i) q^{29} -4.27047i q^{31} +5.12391i q^{32} +(-1.37841 + 0.795827i) q^{34} +(-3.97076 + 6.87757i) q^{37} +(3.98827 - 6.90789i) q^{38} +(-4.85591 + 2.80356i) q^{40} +(-0.912023 + 1.57967i) q^{41} +(-3.53614 - 6.12477i) q^{43} +(3.66933 + 2.11849i) q^{44} +(2.11574 + 3.66457i) q^{46} -7.93736 q^{47} +(1.24209 + 0.717122i) q^{50} +(3.64214 + 2.10279i) q^{52} +(7.24978 - 4.18567i) q^{53} +7.69052i q^{55} +(0.307352 + 0.532350i) q^{58} -8.17430 q^{59} +3.74415i q^{61} +4.19198 q^{62} -6.73573 q^{64} +7.63351i q^{65} +12.5312 q^{67} +(0.840253 + 1.45536i) q^{68} +14.4969i q^{71} +(3.28167 - 1.89468i) q^{73} +(-6.75117 - 3.89779i) q^{74} +(-7.29351 - 4.21091i) q^{76} +8.36133 q^{79} +(-0.802327 - 1.38967i) q^{80} +(-1.55064 - 0.895261i) q^{82} +(-4.38300 - 7.59159i) q^{83} +(-1.52514 + 2.64162i) q^{85} +(6.01221 - 3.47115i) q^{86} +(-6.09252 + 10.5526i) q^{88} +(-4.90379 + 8.49362i) q^{89} +(3.86914 - 2.23385i) q^{92} -7.79148i q^{94} -15.2864i q^{95} +(11.4579 - 6.61525i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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

Character values

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

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

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 $

$2$			0.981621i			0.694111i	0.937845	+	0.347056i	$0.112818\pi$
$2$			0.981621i			0.694111i	−0.937845	+	0.347056i	$0.887182\pi$
$3$		0			0
$3$		0			0
$4$	1.03642			0.518210
$5$	0.940599	+	1.62916i	0.420648	+	0.728585i	0.996003	−	0.0893196i	$-0.0284692\pi$
$5$	0.940599	+	1.62916i	0.420648	+	0.728585i	−0.575355	+	0.817904i	$0.695136\pi$
$6$		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
$11$	3.54040	+	2.04405i	1.06747	+	0.616304i	0.927489	−	0.373850i	$-0.121963\pi$
$11$	3.54040	+	2.04405i	1.06747	+	0.616304i	0.139980	+	0.990154i	$0.455296\pi$
$12$		0			0
$13$	3.51415	+	2.02890i	0.974651	+	0.562715i	0.900651	−	0.434544i	$-0.143090\pi$
$13$	3.51415	+	2.02890i	0.974651	+	0.562715i	0.0739997	+	0.997258i	$0.476424\pi$
$14$		0			0
$15$		0			0
$16$	−0.852996			−0.213249
$17$	0.810727	+	1.40422i	0.196630	+	0.340574i	0.947434	−	0.319952i	$-0.103667\pi$
$17$	0.810727	+	1.40422i	0.196630	+	0.340574i	−0.750803	+	0.660526i	$0.770333\pi$
$18$		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
$23$	3.73318	−	2.15535i	0.778423	−	0.449423i	−0.0574484	−	0.998348i	$-0.518296\pi$
$23$	3.73318	−	2.15535i	0.778423	−	0.449423i	0.835871	+	0.548926i	$0.184963\pi$
$24$		0			0
$25$	0.730548	−	1.26535i	0.146110	−	0.253069i
$26$	−1.99161	+	3.44957i	−0.390587	+	0.676516i
$27$		0			0
$28$		0			0
$29$	0.542317	−	0.313107i	0.100706	−	0.0581425i	−0.448801	−	0.893632i	$-0.648149\pi$
$29$	0.542317	−	0.313107i	0.100706	−	0.0581425i	0.549507	+	0.835489i	$0.314816\pi$
$30$		0			0
$31$		−	4.27047i		−	0.766999i	−0.923541	−	0.383499i	$-0.874719\pi$
$31$		−	4.27047i		−	0.766999i	0.923541	−	0.383499i	$-0.125281\pi$
$32$			5.12391i			0.905788i
$33$		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	$0.940265\pi$
$38$	3.98827	−	6.90789i	0.646983	−	1.12061i
$39$		0			0
$40$	−4.85591	+	2.80356i	−0.767787	+	0.443282i
$41$	−0.912023	+	1.57967i	−0.142434	+	0.246703i	−0.928413	−	0.371551i	$-0.878826\pi$
$41$	−0.912023	+	1.57967i	−0.142434	+	0.246703i	0.785979	+	0.618254i	$0.212160\pi$
$42$		0			0
$43$	−3.53614	−	6.12477i	−0.539256	−	0.934019i	−0.998944	−	0.0459387i	$-0.985372\pi$
$43$	−3.53614	−	6.12477i	−0.539256	−	0.934019i	0.459688	−	0.888080i	$-0.347961\pi$
$44$	3.66933	+	2.11849i	0.553173	+	0.319375i
$45$		0			0
$46$	2.11574	+	3.66457i	0.311949	+	0.540312i
$47$	−7.93736			−1.15778			−0.578891	−	0.815405i	$-0.696515\pi$
$47$	−7.93736			−1.15778			−0.578891	+	0.815405i	$0.696515\pi$
$48$		0			0
$49$		0			0
$50$	1.24209	+	0.717122i	0.175658	+	0.101416i
$51$		0			0
$52$	3.64214	+	2.10279i	0.505073	+	0.291604i
$53$	7.24978	−	4.18567i	0.995835	−	0.574945i	0.0888214	−	0.996048i	$-0.471690\pi$
$53$	7.24978	−	4.18567i	0.995835	−	0.574945i	0.907013	+	0.421102i	$0.138357\pi$
$54$		0			0
$55$			7.69052i			1.03699i
$56$		0			0
$57$		0			0
$58$	0.307352	+	0.532350i	0.0403573	+	0.0699009i
$59$	−8.17430			−1.06420			−0.532101	−	0.846681i	$-0.678598\pi$
$59$	−8.17430			−1.06420			−0.532101	+	0.846681i	$0.678598\pi$
$60$		0			0
$61$			3.74415i			0.479390i	0.970848	+	0.239695i	$0.0770474\pi$
$61$			3.74415i			0.479390i	−0.970848	+	0.239695i	$0.922953\pi$
$62$	4.19198			0.532382
$63$		0			0
$64$	−6.73573			−0.841966
$65$			7.63351i			0.946820i
$66$		0			0
$67$	12.5312			1.53093			0.765464	−	0.643479i	$-0.222510\pi$
$67$	12.5312			1.53093			0.765464	+	0.643479i	$0.222510\pi$
$68$	0.840253	+	1.45536i	0.101896	+	0.176489i
$69$		0			0
$70$		0			0
$71$			14.4969i			1.72047i	0.509898	+	0.860235i	$0.329683\pi$
$71$			14.4969i			1.72047i	−0.509898	+	0.860235i	$0.670317\pi$
$72$		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	$0.262155\pi$
$74$	−6.75117	−	3.89779i	−0.784807	−	0.453109i
$75$		0			0
$76$	−7.29351	−	4.21091i	−0.836623	−	0.483025i
$77$		0			0
$78$		0			0
$79$	8.36133			0.940723			0.470361	−	0.882474i	$-0.344124\pi$
$79$	8.36133			0.940723			0.470361	+	0.882474i	$0.344124\pi$
$80$	−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	$-0.326428\pi$
$83$	−4.38300	−	7.59159i	−0.481097	−	0.833285i	−0.999765	+	0.0216912i	$0.993095\pi$
$84$		0			0
$85$	−1.52514	+	2.64162i	−0.165424	+	0.286524i
$86$	6.01221	−	3.47115i	0.648313	−	0.374304i
$87$		0			0
$88$	−6.09252	+	10.5526i	−0.649465	+	1.12491i
$89$	−4.90379	+	8.49362i	−0.519801	+	0.900322i	0.479934	+	0.877305i	$0.340661\pi$
$89$	−4.90379	+	8.49362i	−0.519801	+	0.900322i	−0.999735	+	0.0230174i	$0.992673\pi$
$90$		0			0
$91$		0			0
$92$	3.86914	−	2.23385i	0.403386	−	0.232895i
$93$		0			0
$94$		−	7.79148i		−	0.803630i
$95$		−	15.2864i		−	1.56835i
$96$		0			0
$97$	11.4579	−	6.61525i	1.16338	−	0.671677i	0.211267	−	0.977428i	$-0.432241\pi$
$97$	11.4579	−	6.61525i	1.16338	−	0.671677i	0.952111	+	0.305752i	$0.0989077\pi$
$98$		0			0
$99$		0			0
$100$	0.757155	−	1.31143i	0.0757155	−	0.131143i
$101$	0.524900	−	0.909154i	0.0522295	−	0.0904642i	−0.838729	−	0.544550i	$-0.816701\pi$
$101$	0.524900	−	0.909154i	0.0522295	−	0.0904642i	0.890958	+	0.454085i	$0.150034\pi$
$102$		0			0
$103$	1.41937	−	0.819472i	0.139854	−	0.0807449i	−0.428440	−	0.903570i	$-0.640937\pi$
$103$	1.41937	−	0.819472i	0.139854	−	0.0807449i	0.568295	+	0.822825i	$0.307603\pi$
$104$	−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	0.349245	−	0.937031i	$-0.386438\pi$
$107$	−2.97522	−	1.71775i	−0.287626	−	0.166061i	−0.636871	+	0.770971i	$0.719771\pi$
$108$		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	$0.889891\pi$
$110$	−7.54918			−0.719786
$111$		0			0
$112$		0			0
$113$	−15.0858	−	8.70977i	−1.41915	−	0.819346i	−0.422925	−	0.906165i	$-0.638997\pi$
$113$	−15.0858	−	8.70977i	−1.41915	−	0.819346i	−0.996224	+	0.0868183i	$0.972330\pi$
$114$		0			0
$115$	7.02285	+	4.05465i	0.654885	+	0.378098i
$116$	0.562068	−	0.324510i	0.0521867	−	0.0301300i
$117$		0			0
$118$		−	8.02407i		−	0.738675i
$119$		0			0
$120$		0			0
$121$	2.85627	+	4.94720i	0.259661	+	0.449746i
$122$	−3.67534			−0.332750
$123$		0			0
$124$		−	4.42600i		−	0.397466i
$125$	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	$0.648359\pi$
$128$			3.63588i			0.321369i
$129$		0			0
$130$	−7.49322			−0.657199
$131$	2.48851	+	4.31022i	0.217422	+	0.376586i	0.954019	−	0.299746i	$-0.0969019\pi$
$131$	2.48851	+	4.31022i	0.217422	+	0.376586i	−0.736597	+	0.676332i	$0.763569\pi$
$132$		0			0
$133$		0			0
$134$			12.3009i			1.06263i
$135$		0			0
$136$	−4.18544	+	2.41647i	−0.358899	+	0.207210i
$137$	0.728035	+	0.420331i	0.0622003	+	0.0359113i	0.530778	−	0.847511i	$-0.321900\pi$
$137$	0.728035	+	0.420331i	0.0622003	+	0.0359113i	−0.468577	+	0.883422i	$0.655233\pi$
$138$		0			0
$139$	−5.74392	−	3.31626i	−0.487193	−	0.281281i	0.236216	−	0.971701i	$-0.424093\pi$
$139$	−5.74392	−	3.31626i	−0.487193	−	0.281281i	−0.723409	+	0.690419i	$0.757426\pi$
$140$		0			0
$141$		0			0
$142$	−14.2305			−1.19420
$143$	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
$149$	−14.7023	+	8.48838i	−1.20446	+	0.695395i	−0.961544	−	0.274652i	$-0.911437\pi$
$149$	−14.7023	+	8.48838i	−1.20446	+	0.695395i	−0.242916	+	0.970047i	$0.578104\pi$
$150$		0			0
$151$	−0.975709	+	1.68998i	−0.0794021	+	0.137528i	−0.902992	−	0.429657i	$-0.858634\pi$
$151$	−0.975709	+	1.68998i	−0.0794021	+	0.137528i	0.823590	+	0.567186i	$0.191968\pi$
$152$	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
$157$			9.52118i			0.759873i	0.925013	+	0.379936i	$0.124054\pi$
$157$			9.52118i			0.759873i	−0.925013	+	0.379936i	$0.875946\pi$
$158$			8.20766i			0.652966i
$159$		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	$0.180511\pi$
$164$	−0.945238	+	1.63720i	−0.0738107	+	0.127844i
$165$		0			0
$166$	7.45206	−	4.30245i	0.578392	−	0.333935i
$167$	7.00830	−	12.1387i	0.542319	−	0.939324i	−0.456452	−	0.889748i	$-0.650880\pi$
$167$	7.00830	−	12.1387i	0.542319	−	0.939324i	0.998770	−	0.0495754i	$-0.0157868\pi$
$168$		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
$173$	7.11768			0.541147			0.270574	−	0.962699i	$-0.412787\pi$
$173$	7.11768			0.541147			0.270574	+	0.962699i	$0.412787\pi$
$174$		0			0
$175$		0			0
$176$	−3.01994	−	1.74357i	−0.227637	−	0.131426i
$177$		0			0
$178$	−8.33752	−	4.81367i	−0.624924	−	0.360800i
$179$	−5.19845	+	3.00133i	−0.388550	+	0.224330i	−0.681532	−	0.731788i	$-0.738686\pi$
$179$	−5.19845	+	3.00133i	−0.388550	+	0.224330i	0.292981	+	0.956118i	$0.405353\pi$
$180$		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
$184$	6.42428	+	11.1272i	0.473604	+	0.820307i
$185$	−14.9396			−1.09838
$186$		0			0
$187$			6.62866i			0.484736i
$188$	−8.22643			−0.599974
$189$		0			0
$190$	15.0054			1.08861
$191$		−	5.73288i		−	0.414817i	−0.978254	−	0.207408i	$-0.933497\pi$
$191$		−	5.73288i		−	0.414817i	0.978254	−	0.207408i	$-0.0665029\pi$
$192$		0			0
$193$	1.55904			0.112222			0.0561109	−	0.998425i	$-0.482130\pi$
$193$	1.55904			0.112222			0.0561109	+	0.998425i	$0.482130\pi$
$194$	6.49367	+	11.2474i	0.466218	+	0.807514i
$195$		0			0
$196$		0			0
$197$		−	19.5504i		−	1.39291i	−0.717602	−	0.696454i	$-0.754760\pi$
$197$		−	19.5504i		−	1.39291i	0.717602	−	0.696454i	$-0.245240\pi$
$198$		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	$0.344352\pi$
$200$	3.77151	+	2.17748i	0.266686	+	0.153971i
$201$		0			0
$202$	0.892445	+	0.515253i	0.0627922	+	0.0362531i
$203$		0			0
$204$		0			0
$205$	−3.43139			−0.239659
$206$	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	−0.0779625	−	0.996956i	$-0.524841\pi$
$211$	11.9752	−	20.7417i	0.824408	−	1.42792i	0.902371	−	0.430961i	$-0.141825\pi$
$212$	7.51382	−	4.33810i	0.516051	−	0.297942i
$213$		0			0
$214$	1.68618	−	2.92054i	0.115265	−	0.199644i
$215$	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
$220$			7.97060i			0.537378i
$221$			6.57953i			0.442587i
$222$		0			0
$223$	−2.68394	+	1.54957i	−0.179730	+	0.103767i	−0.587166	−	0.809467i	$-0.699756\pi$
$223$	−2.68394	+	1.54957i	−0.179730	+	0.103767i	0.407436	+	0.913234i	$0.366423\pi$
$224$		0			0
$225$		0			0
$226$	8.54970	−	14.8085i	0.568717	−	0.985047i
$227$	10.8991	−	18.8779i	0.723401	−	1.25297i	−0.236228	−	0.971698i	$-0.575911\pi$
$227$	10.8991	−	18.8779i	0.723401	−	1.25297i	0.959629	−	0.281269i	$-0.0907554\pi$
$228$		0			0
$229$	11.1810	−	6.45536i	0.738862	−	0.426582i	−0.0827937	−	0.996567i	$-0.526384\pi$
$229$	11.1810	−	6.45536i	0.738862	−	0.426582i	0.821655	+	0.569985i	$0.193051\pi$
$230$	−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	0.522746	−	0.852488i	$-0.324908\pi$
$233$	0.699758	+	0.404005i	0.0458427	+	0.0264673i	−0.476904	+	0.878956i	$0.658241\pi$
$234$		0			0
$235$	−7.46587	−	12.9313i	−0.487020	−	0.843543i
$236$	−8.47200			−0.551480
$237$		0			0
$238$		0			0
$239$	−12.2032	−	7.04552i	−0.789360	−	0.455737i	0.0503775	−	0.998730i	$-0.483958\pi$
$239$	−12.2032	−	7.04552i	−0.789360	−	0.455737i	−0.839737	+	0.542993i	$0.817291\pi$
$240$		0			0
$241$	−16.0205	−	9.24943i	−1.03197	−	0.595808i	−0.114422	−	0.993432i	$-0.536502\pi$
$241$	−16.0205	−	9.24943i	−1.03197	−	0.595808i	−0.917549	+	0.397624i	$0.869835\pi$
$242$	−4.85628	+	2.80377i	−0.312173	+	0.180233i
$243$		0			0
$244$			3.88051i			0.248424i
$245$		0			0
$246$		0			0
$247$	−16.4866	−	28.5556i	−1.04902	−	1.81695i
$248$	12.7286			0.808268
$249$		0			0
$250$			11.9312i			0.754596i
$251$	22.1733			1.39957			0.699783	−	0.714355i	$-0.253280\pi$
$251$	22.1733			1.39957			0.699783	+	0.714355i	$0.253280\pi$
$252$		0			0
$253$	17.6226			1.10792
$254$		−	9.94262i		−	0.623855i
$255$		0			0
$256$	−17.0405			−1.06503
$257$	2.02896	+	3.51427i	0.126563	+	0.219214i	0.922343	−	0.386372i	$-0.126272\pi$
$257$	2.02896	+	3.51427i	0.126563	+	0.219214i	−0.795780	+	0.605586i	$0.792939\pi$
$258$		0			0
$259$		0			0
$260$			7.91152i			0.490652i
$261$		0			0
$262$	−4.23100	+	2.44277i	−0.261392	+	0.150915i
$263$	−8.62617	−	4.98032i	−0.531913	−	0.307100i	0.209882	−	0.977727i	$-0.432692\pi$
$263$	−8.62617	−	4.98032i	−0.531913	−	0.307100i	−0.741795	+	0.670627i	$0.766025\pi$
$264$		0			0
$265$	13.6383	+	7.87406i	0.837793	+	0.483700i
$266$		0			0
$267$		0			0
$268$	12.9876			0.793341
$269$	4.98399	+	8.63253i	0.303880	+	0.526335i	0.977011	−	0.213188i	$-0.0683846\pi$
$269$	4.98399	+	8.63253i	0.303880	+	0.526335i	−0.673132	+	0.739523i	$0.735051\pi$
$270$		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
$275$	5.17286	−	2.98655i	0.311935	−	0.180096i
$276$		0			0
$277$	7.81184	−	13.5305i	0.469368	−	0.812969i	−0.530019	−	0.847986i	$-0.677815\pi$
$277$	7.81184	−	13.5305i	0.469368	−	0.812969i	0.999387	+	0.0350166i	$0.0111484\pi$
$278$	3.25531	−	5.63836i	0.195240	−	0.338166i
$279$		0			0
$280$		0			0
$281$	20.8780	−	12.0539i	1.24547	−	0.719075i	0.275271	−	0.961367i	$-0.411232\pi$
$281$	20.8780	−	12.0539i	1.24547	−	0.719075i	0.970203	+	0.242292i	$0.0778991\pi$
$282$		0			0
$283$			3.01779i			0.179389i	0.995969	+	0.0896946i	$0.0285891\pi$
$283$			3.01779i			0.179389i	−0.995969	+	0.0896946i	$0.971411\pi$
$284$			15.0249i			0.891564i
$285$		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
$290$	−0.578190	+	1.00145i	−0.0339525	+	0.0588074i
$291$		0			0
$292$	3.40119	−	1.96368i	0.199040	−	0.114916i
$293$	−14.9237	+	25.8485i	−0.871849	+	1.51009i	−0.0117671	+	0.999931i	$0.503746\pi$
$293$	−14.9237	+	25.8485i	−0.871849	+	1.51009i	−0.860082	+	0.510156i	$0.829588\pi$
$294$		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
$299$	17.4920			1.01159
$300$		0			0
$301$		0			0
$302$	−1.65892	−	0.957777i	−0.0954600	−	0.0551139i
$303$		0			0
$304$	6.00272	+	3.46567i	0.344280	+	0.198770i
$305$	−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
$310$	3.94297	+	6.82943i	0.223946	+	0.387886i
$311$	11.0753			0.628020			0.314010	−	0.949420i	$-0.398327\pi$
$311$	11.0753			0.628020			0.314010	+	0.949420i	$0.398327\pi$
$312$		0			0
$313$		−	16.7397i		−	0.946186i	−0.881013	−	0.473093i	$-0.843137\pi$
$313$		−	16.7397i		−	0.946186i	0.881013	−	0.473093i	$-0.156863\pi$
$314$	−9.34619			−0.527436
$315$		0			0
$316$	8.66584			0.487492
$317$			2.94187i			0.165232i	0.996581	+	0.0826160i	$0.0263275\pi$
$317$			2.94187i			0.165232i	−0.996581	+	0.0826160i	$0.973672\pi$
$318$		0			0
$319$	2.56002			0.143334
$320$	−6.33562	−	10.9736i	−0.354172	−	0.613444i
$321$		0			0
$322$		0			0
$323$		−	13.1758i		−	0.733118i
$324$		0			0
$325$	5.13452	−	2.96442i	0.284812	−	0.164436i
$326$	−0.943801	−	0.544904i	−0.0522723	−	0.0301794i
$327$		0			0
$328$	−4.70839	−	2.71839i	−0.259977	−	0.150098i
$329$		0			0
$330$		0			0
$331$	4.88153			0.268313			0.134157	−	0.990960i	$-0.457167\pi$
$331$	4.88153			0.268313			0.134157	+	0.990960i	$0.457167\pi$
$332$	−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	−0.632241	−	0.774772i	$-0.717865\pi$
$337$	6.51421	−	11.2830i	0.354852	−	0.614621i	0.987093	+	0.160151i	$0.0511980\pi$
$338$	−2.94622	+	1.70100i	−0.160253	+	0.0925221i
$339$		0			0
$340$	−1.58068	+	2.73782i	−0.0857245	+	0.148479i
$341$	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
$346$			6.98687i			0.375617i
$347$		−	2.15180i		−	0.115515i	−0.998331	−	0.0577573i	$-0.981605\pi$
$347$		−	2.15180i		−	0.115515i	0.998331	−	0.0577573i	$-0.0183949\pi$
$348$		0			0
$349$	25.2919	−	14.6023i	1.35384	−	0.781642i	0.365058	−	0.930985i	$-0.381049\pi$
$349$	25.2919	−	14.6023i	1.35384	−	0.781642i	0.988785	+	0.149343i	$0.0477159\pi$
$350$		0			0
$351$		0			0
$352$	−10.4735	+	18.1407i	−0.558240	+	0.966901i
$353$	−5.41764	+	9.38362i	−0.288352	+	0.499440i	−0.973416	−	0.229042i	$-0.926441\pi$
$353$	−5.41764	+	9.38362i	−0.288352	+	0.499440i	0.685065	+	0.728482i	$0.259774\pi$
$354$		0			0
$355$	−23.6179	+	13.6358i	−1.25351	+	0.723713i
$356$	−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	−0.0621161	−	0.998069i	$-0.519785\pi$
$359$	−18.1425	−	10.4746i	−0.957527	−	0.552829i	−0.895411	+	0.445240i	$0.853118\pi$
$360$		0			0
$361$	23.5150	+	40.7292i	1.23763	+	2.14364i
$362$	−1.27888			−0.0672167
$363$		0			0
$364$		0			0
$365$	6.17348	+	3.56426i	0.323135	+	0.186562i
$366$		0			0
$367$	4.97835	+	2.87425i	0.259868	+	0.150035i	0.624274	−	0.781205i	$-0.285395\pi$
$367$	4.97835	+	2.87425i	0.259868	+	0.150035i	−0.364407	+	0.931240i	$0.618728\pi$
$368$	−3.18439	+	1.83851i	−0.165998	+	0.0958389i
$369$		0			0
$370$		−	14.6650i		−	0.762398i
$371$		0			0
$372$		0			0
$373$	−14.4467	−	25.0224i	−0.748023	−	1.29561i	−0.948769	−	0.315970i	$-0.897670\pi$
$373$	−14.4467	−	25.0224i	−0.748023	−	1.29561i	0.200747	−	0.979643i	$-0.435663\pi$
$374$	−6.50684			−0.336461
$375$		0			0
$376$		−	23.6582i		−	1.22008i
$377$	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	$0.503364\pi$
$380$		−	15.8431i		−	0.812734i
$381$		0			0
$382$	5.62752			0.287929
$383$	−12.4007	−	21.4787i	−0.633648	−	1.09751i	−0.986800	−	0.161944i	$-0.948223\pi$
$383$	−12.4007	−	21.4787i	−0.633648	−	1.09751i	0.353152	−	0.935566i	$-0.385110\pi$
$384$		0			0
$385$		0			0
$386$			1.53038i			0.0778944i
$387$		0			0
$388$	11.8752	−	6.85617i	0.602874	−	0.348069i
$389$	3.82694	+	2.20948i	0.194033	+	0.112025i	0.593869	−	0.804561i	$-0.297600\pi$
$389$	3.82694	+	2.20948i	0.194033	+	0.112025i	−0.399836	+	0.916587i	$0.630933\pi$
$390$		0			0
$391$	6.05319	+	3.49481i	0.306123	+	0.176740i
$392$		0			0
$393$		0			0
$394$	19.1911			0.966833
$395$	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
$401$	−5.31899	+	3.07092i	−0.265617	+	0.153354i	−0.626894	−	0.779104i	$-0.715674\pi$
$401$	−5.31899	+	3.07092i	−0.265617	+	0.153354i	0.361277	+	0.932459i	$0.382341\pi$
$402$		0			0
$403$	8.66434	−	15.0071i	0.431602	−	0.747556i
$404$	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
$409$		−	0.884369i		−	0.0437293i	−0.999761	−	0.0218646i	$-0.993040\pi$
$409$		−	0.884369i		−	0.0437293i	0.999761	−	0.0218646i	$-0.00696028\pi$
$410$		−	3.36833i		−	0.166350i
$411$		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
$416$	−10.3959	+	18.0062i	−0.509700	+	0.882827i
$417$		0			0
$418$	28.2401	−	16.3044i	1.38127	−	0.797476i
$419$	7.59365	−	13.1526i	0.370974	−	0.642546i	−0.618742	−	0.785595i	$-0.712357\pi$
$419$	7.59365	−	13.1526i	0.370974	−	0.642546i	0.989716	+	0.143049i	$0.0456905\pi$
$420$		0			0
$421$	13.3318	+	23.0914i	0.649753	+	1.12541i	0.983182	+	0.182630i	$0.0584611\pi$
$421$	13.3318	+	23.0914i	0.649753	+	1.12541i	−0.333428	+	0.942775i	$0.608206\pi$
$422$	20.3605	+	11.7551i	0.991133	+	0.572231i
$423$		0			0
$424$	12.4759	+	21.6088i	0.605881	+	1.04942i
$425$	2.36910			0.114918
$426$		0			0
$427$		0			0
$428$	−3.08358	−	1.78031i	−0.149050	−	0.0860543i
$429$		0			0
$430$	11.3102	+	6.52992i	0.545424	+	0.314901i
$431$	−4.06785	+	2.34857i	−0.195941	+	0.113127i	−0.594761	−	0.803903i	$-0.702753\pi$
$431$	−4.06785	+	2.34857i	−0.195941	+	0.113127i	0.398820	+	0.917029i	$0.369420\pi$
$432$		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
$436$	−1.91250	−	3.31254i	−0.0915919	−	0.158642i
$437$	−35.0283			−1.67563
$438$		0			0
$439$			16.5136i			0.788151i	0.919078	+	0.394075i	$0.128935\pi$
$439$			16.5136i			0.788151i	−0.919078	+	0.394075i	$0.871065\pi$
$440$	−22.9225			−1.09279
$441$		0			0
$442$	−6.45861			−0.307205
$443$		−	1.06368i		−	0.0505368i	−0.999681	−	0.0252684i	$-0.991956\pi$
$443$		−	1.06368i		−	0.0505368i	0.999681	−	0.0252684i	$-0.00804404\pi$
$444$		0			0
$445$	−18.4500			−0.874614
$446$	−1.52110	−	2.63461i	−0.0720260	−	0.124753i
$447$		0			0
$448$		0			0
$449$			15.9081i			0.750749i	0.926873	+	0.375374i	$0.122486\pi$
$449$			15.9081i			0.750749i	−0.926873	+	0.375374i	$0.877514\pi$
$450$		0			0
$451$	−6.45785	+	3.72844i	−0.304088	+	0.175565i
$452$	−15.6352	−	9.02697i	−0.735417	−	0.424593i
$453$		0			0
$454$	18.5309	+	10.6988i	0.869698	+	0.502121i
$455$		0			0
$456$		0			0
$457$	−32.7925			−1.53397			−0.766985	−	0.641666i	$-0.778244\pi$
$457$	−32.7925			−1.53397			−0.766985	+	0.641666i	$0.778244\pi$
$458$	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	$-0.0251078\pi$
$461$	9.23690	+	15.9988i	0.430205	+	0.745138i	−0.566685	+	0.823934i	$0.691774\pi$
$462$		0			0
$463$	−0.201921	+	0.349738i	−0.00938408	+	0.0162537i	−0.870679	−	0.491851i	$-0.836320\pi$
$463$	−0.201921	+	0.349738i	−0.00938408	+	0.0162537i	0.861295	+	0.508105i	$0.169654\pi$
$464$	−0.462594	+	0.267079i	−0.0214754	+	0.0123988i
$465$		0			0
$466$	−0.396580	+	0.686897i	−0.0183712	+	0.0318199i
$467$	−7.51283	+	13.0126i	−0.347652	+	0.602151i	−0.985832	−	0.167736i	$-0.946354\pi$
$467$	−7.51283	+	13.0126i	−0.347652	+	0.602151i	0.638180	+	0.769887i	$0.279688\pi$
$468$		0			0
$469$		0			0
$470$	12.6936	−	7.32866i	0.585512	−	0.338046i
$471$		0			0
$472$		−	24.3644i		−	1.12146i
$473$		−	28.9122i		−	1.32938i
$474$		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
$479$	15.5400	−	26.9161i	0.710041	−	1.22983i	−0.254800	−	0.966994i	$-0.582010\pi$
$479$	15.5400	−	26.9161i	0.710041	−	1.22983i	0.964841	−	0.262833i	$-0.0846569\pi$
$480$		0			0
$481$	−27.9077	+	16.1125i	−1.27248	+	0.734669i
$482$	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	$0.932248\pi$
$488$	−11.1599			−0.505184
$489$		0			0
$490$		0			0
$491$	7.07098	+	4.08243i	0.319109	+	0.184238i	0.650995	−	0.759082i	$-0.274352\pi$
$491$	7.07098	+	4.08243i	0.319109	+	0.184238i	−0.331886	+	0.943319i	$0.607685\pi$
$492$		0			0
$493$	0.879342	+	0.507688i	0.0396036	+	0.0228651i
$494$	28.0308	−	16.1836i	1.26116	−	0.728134i
$495$		0			0
$496$			3.64269i			0.163562i
$497$		0			0
$498$		0			0
$499$	14.0097	+	24.2655i	0.627159	+	1.08627i	0.988119	+	0.153690i	$0.0491158\pi$
$499$	14.0097	+	24.2655i	0.627159	+	1.08627i	−0.360960	+	0.932581i	$0.617551\pi$
$500$	12.5973			0.563367
$501$		0			0
$502$			21.7658i			0.971455i
$503$	5.89656			0.262915			0.131457	−	0.991322i	$-0.458034\pi$
$503$	5.89656			0.262915			0.131457	+	0.991322i	$0.458034\pi$
$504$		0			0
$505$	1.97488			0.0878811
$506$			17.2987i			0.769022i
$507$		0			0
$508$	−10.4977			−0.465758
$509$	7.01957	+	12.1582i	0.311137	+	0.538905i	0.978609	−	0.205730i	$-0.0659569\pi$
$509$	7.01957	+	12.1582i	0.311137	+	0.538905i	−0.667472	+	0.744635i	$0.732624\pi$
$510$		0			0
$511$		0			0
$512$		−	9.45558i		−	0.417882i
$513$		0			0
$514$	−3.44968	+	1.99168i	−0.152159	+	0.0878490i
$515$	2.67011	+	1.54159i	0.117659	+	0.0679305i
$516$		0			0
$517$	−28.1014	−	16.2243i	−1.23590	−	0.713546i
$518$		0			0
$519$		0			0
$520$	−22.7526			−0.997765
$521$	−19.2229	−	33.2950i	−0.842170	−	1.45868i	−0.888057	−	0.459734i	$-0.847945\pi$
$521$	−19.2229	−	33.2950i	−0.842170	−	1.45868i	0.0458870	−	0.998947i	$-0.485389\pi$
$522$		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
$527$	5.99668	−	3.46219i	0.261220	−	0.150815i
$528$		0			0
$529$	−2.20889	+	3.82591i	−0.0960388	+	0.166344i
$530$	−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
$535$		−	6.46284i		−	0.279413i
$536$			37.3506i			1.61330i
$537$		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	$0.743890\pi$
$542$	−9.34112	+	16.1793i	−0.401236	+	0.694960i
$543$		0			0
$544$	−7.19510	+	4.15409i	−0.308487	+	0.178105i
$545$	3.47136	−	6.01257i	0.148697	−	0.257550i
$546$		0			0
$547$	−4.05733	−	7.02751i	−0.173479	−	0.300475i	0.766155	−	0.642656i	$-0.222168\pi$
$547$	−4.05733	−	7.02751i	−0.173479	−	0.300475i	−0.939634	+	0.342181i	$0.888834\pi$
$548$	0.754550	+	0.435640i	0.0322328	+	0.0186096i
$549$		0			0
$550$	2.93166	+	5.07779i	0.125007	+	0.216518i
$551$	−5.08854			−0.216779
$552$		0			0
$553$		0			0
$554$	13.2818	+	7.66827i	0.564291	+	0.325794i
$555$		0			0
$556$	−5.95311	−	3.43703i	−0.252468	−	0.145763i
$557$	−14.0925	+	8.13633i	−0.597120	+	0.344747i	−0.767908	−	0.640561i	$-0.778702\pi$
$557$	−14.0925	+	8.13633i	−0.597120	+	0.344747i	0.170788	+	0.985308i	$0.445369\pi$
$558$		0			0
$559$		−	28.6978i		−	1.21379i
$560$		0			0
$561$		0			0
$562$	11.8324	+	20.4942i	0.499118	+	0.864498i
$563$	10.2719			0.432908			0.216454	−	0.976293i	$-0.430551\pi$
$563$	10.2719			0.432908			0.216454	+	0.976293i	$0.430551\pi$
$564$		0			0
$565$		−	32.7696i		−	1.37863i
$566$	−2.96233			−0.124516
$567$		0			0
$568$	−43.2098			−1.81304
$569$			20.6157i			0.864256i	0.901812	+	0.432128i	$0.142237\pi$
$569$			20.6157i			0.864256i	−0.901812	+	0.432128i	$0.857763\pi$
$570$		0			0
$571$	4.25655			0.178131			0.0890656	−	0.996026i	$-0.471612\pi$
$571$	4.25655			0.178131			0.0890656	+	0.996026i	$0.471612\pi$
$572$	8.59640	+	14.8894i	0.359434	+	0.622557i
$573$		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	$0.447961\pi$
$578$	12.2168	+	7.05338i	0.508153	+	0.293382i
$579$		0			0
$580$	1.05736	+	0.610467i	0.0439045	+	0.0253483i
$581$		0			0
$582$		0			0
$583$	34.2228			1.41736
$584$	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	$-0.332450\pi$
$587$	−12.0558	−	20.8812i	−0.497594	−	0.861858i	−0.999996	+	0.00277589i	$0.999116\pi$
$588$		0			0
$589$	−17.3507	+	30.0522i	−0.714922	+	1.23828i
$590$	13.0725	−	7.54743i	0.538187	−	0.310723i
$591$		0			0
$592$	3.38705	−	5.86654i	0.139207	−	0.241113i
$593$	−19.2908	+	33.4126i	−0.792178	+	1.37209i	0.132437	+	0.991191i	$0.457720\pi$
$593$	−19.2908	+	33.4126i	−0.792178	+	1.37209i	−0.924616	+	0.380902i	$0.875614\pi$
$594$		0			0
$595$		0			0
$596$	−15.2378	+	8.79752i	−0.624163	+	0.360360i
$597$		0			0
$598$			17.1705i			0.702154i
$599$		−	33.8236i		−	1.38199i	−0.722857	−	0.690997i	$-0.757172\pi$
$599$		−	33.8236i		−	1.38199i	0.722857	−	0.690997i	$-0.242828\pi$
$600$		0			0
$601$	−27.4855	+	15.8688i	−1.12116	+	0.647300i	−0.941696	−	0.336465i	$-0.890769\pi$
$601$	−27.4855	+	15.8688i	−1.12116	+	0.647300i	−0.179461	+	0.983765i	$0.557435\pi$
$602$		0			0
$603$		0			0
$604$	−1.01124	+	1.75153i	−0.0411469	+	0.0712686i
$605$	−5.37320	+	9.30666i	−0.218452	+	0.378370i
$606$		0			0
$607$	0.169355	−	0.0977772i	0.00687391	−	0.00396865i	−0.496559	−	0.868003i	$-0.665403\pi$
$607$	0.169355	−	0.0977772i	0.00687391	−	0.00396865i	0.503433	+	0.864034i	$0.332070\pi$
$608$	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	$0.852200\pi$
$614$	2.63912			0.106506
$615$		0			0
$616$		0			0
$617$	7.86982	+	4.54365i	0.316827	+	0.182920i	0.649977	−	0.759953i	$-0.274778\pi$
$617$	7.86982	+	4.54365i	0.316827	+	0.182920i	−0.333150	+	0.942874i	$0.608112\pi$
$618$		0			0
$619$	−24.8586	−	14.3521i	−0.999152	−	0.576861i	−0.0911550	−	0.995837i	$-0.529056\pi$
$619$	−24.8586	−	14.3521i	−0.999152	−	0.576861i	−0.907997	+	0.418976i	$0.862389\pi$
$620$	7.21068	−	4.16309i	0.289588	−	0.167194i
$621$		0			0
$622$			10.8717i			0.435916i
$623$		0			0
$624$		0			0
$625$	7.77986	+	13.4751i	0.311194	+	0.539004i
$626$	16.4321			0.656758
$627$		0			0
$628$			9.86793i			0.393773i
$629$	−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	$0.635660\pi$
$632$			24.9219i			0.991340i
$633$		0			0
$634$	−2.88781			−0.114689
$635$	−9.52711	−	16.5014i	−0.378072	−	0.654839i
$636$		0			0
$637$		0			0
$638$			2.51297i			0.0994895i
$639$		0			0
$640$	−5.92345	+	3.41990i	−0.234145	+	0.135184i
$641$	39.7733	+	22.9632i	1.57095	+	0.906990i	0.996052	+	0.0887664i	$0.0282925\pi$
$641$	39.7733	+	22.9632i	1.57095	+	0.906990i	0.574900	+	0.818224i	$0.305041\pi$
$642$		0			0
$643$	9.15428	+	5.28523i	0.361010	+	0.208429i	0.669524	−	0.742791i	$-0.266498\pi$
$643$	9.15428	+	5.28523i	0.361010	+	0.208429i	−0.308514	+	0.951220i	$0.599832\pi$
$644$		0			0
$645$		0			0
$646$	12.9336			0.508866
$647$	−19.2562	−	33.3526i	−0.757038	−	1.31123i	−0.944355	−	0.328928i	$-0.893313\pi$
$647$	−19.2562	−	33.3526i	−0.757038	−	1.31123i	0.187317	−	0.982299i	$-0.440021\pi$
$648$		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
$653$	−11.0867	+	6.40089i	−0.433855	+	0.250486i	−0.700988	−	0.713173i	$-0.747257\pi$
$653$	−11.0867	+	6.40089i	−0.433855	+	0.250486i	0.267133	+	0.963660i	$0.413924\pi$
$654$		0			0
$655$	−4.68137	+	8.10837i	−0.182916	+	0.316820i
$656$	0.777952	−	1.34745i	0.0303739	−	0.0526092i
$657$		0			0
$658$		0			0
$659$	−41.5777	+	24.0049i	−1.61964	+	0.935097i	−0.632622	+	0.774461i	$0.718021\pi$
$659$	−41.5777	+	24.0049i	−1.61964	+	0.935097i	−0.987014	+	0.160636i	$0.948645\pi$
$660$		0			0
$661$			10.8312i			0.421285i	0.977563	+	0.210643i	$0.0675557\pi$
$661$			10.8312i			0.421285i	−0.977563	+	0.210643i	$0.932444\pi$
$662$			4.79182i			0.186239i
$663$		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
$668$	7.26354	−	12.5808i	0.281035	−	0.486767i
$669$		0			0
$670$	−20.0402	+	11.5702i	−0.774219	+	0.446995i
$671$	−7.65323	+	13.2558i	−0.295450	+	0.511734i
$672$		0			0
$673$	−6.19553	−	10.7310i	−0.238820	−	0.413649i	0.721556	−	0.692356i	$-0.243427\pi$
$673$	−6.19553	−	10.7310i	−0.238820	−	0.413649i	−0.960376	+	0.278707i	$0.910094\pi$
$674$	11.0756	+	6.39449i	0.426616	+	0.246307i
$675$		0			0
$676$	1.79595	+	3.11068i	0.0690752	+	0.119642i
$677$	28.9895			1.11416			0.557078	−	0.830460i	$-0.311922\pi$
$677$	28.9895			1.11416			0.557078	+	0.830460i	$0.311922\pi$
$678$		0			0
$679$		0			0
$680$	−7.87364	−	4.54585i	−0.301940	−	0.174325i
$681$		0			0
$682$	14.8413	+	8.56862i	0.568302	+	0.328109i
$683$	0.132048	−	0.0762380i	0.00505268	−	0.00291717i	−0.497472	−	0.867480i	$-0.665738\pi$
$683$	0.132048	−	0.0762380i	0.00505268	−	0.00291717i	0.502524	+	0.864563i	$0.332405\pi$
$684$		0			0
$685$			1.58145i			0.0604242i
$686$		0			0
$687$		0			0
$688$	3.01631	+	5.22441i	0.114996	+	0.199179i
$689$	33.9691			1.29412
$690$		0			0
$691$		−	43.2353i		−	1.64475i	−0.568948	−	0.822373i	$-0.692650\pi$
$691$		−	43.2353i		−	1.64475i	0.568948	−	0.822373i	$-0.307350\pi$
$692$	7.37691			0.280428
$693$		0			0
$694$	2.11225			0.0801799
$695$		−	12.4771i		−	0.473282i
$696$		0			0
$697$	−2.95761			−0.112027
$698$	14.3339	+	24.8271i	0.542546	+	0.939718i
$699$		0			0
$700$		0			0
$701$		−	11.5821i		−	0.437451i	−0.975786	−	0.218726i	$-0.929810\pi$
$701$		−	11.5821i		−	0.437451i	0.975786	−	0.218726i	$-0.0701900\pi$
$702$		0			0
$703$	55.8863	−	32.2660i	2.10779	−	1.21693i
$704$	−23.8472	−	13.7682i	−0.898774	−	0.518907i
$705$		0			0
$706$	−9.21116	−	5.31807i	−0.346667	−	0.200148i
$707$		0			0
$708$		0			0
$709$	−37.8948			−1.42317			−0.711584	−	0.702601i	$-0.752022\pi$
$709$	−37.8948			−1.42317			−0.711584	+	0.702601i	$0.752022\pi$
$710$	−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
$716$	−5.38777	+	3.11063i	−0.201351	+	0.116250i
$717$		0			0
$718$	10.2821	−	17.8091i	0.383724	−	0.664630i
$719$	−23.3158	+	40.3842i	−0.869534	+	1.50608i	−0.00706058	+	0.999975i	$0.502247\pi$
$719$	−23.3158	+	40.3842i	−0.869534	+	1.50608i	−0.862474	+	0.506102i	$0.831086\pi$
$720$		0			0
$721$		0			0
$722$	−39.9806	+	23.0828i	−1.48792	+	0.859054i
$723$		0			0
$724$			1.35028i			0.0501826i
$725$		−	0.914958i		−	0.0339807i
$726$		0			0
$727$	−3.72659	+	2.15155i	−0.138212	+	0.0797965i	−0.567511	−	0.823366i	$-0.692094\pi$
$727$	−3.72659	+	2.15155i	−0.138212	+	0.0797965i	0.429300	+	0.903162i	$0.358760\pi$
$728$		0			0
$729$		0			0
$730$	−3.49875	+	6.06002i	−0.129495	+	0.224291i
$731$	5.73369	−	9.93104i	0.212068	−	0.367313i
$732$		0			0
$733$	−12.1337	+	7.00539i	−0.448168	+	0.258750i	−0.707056	−	0.707157i	$-0.749977\pi$
$733$	−12.1337	+	7.00539i	−0.448168	+	0.258750i	0.258888	+	0.965907i	$0.416644\pi$
$734$	−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	$-0.411883\pi$
$740$	−15.4837			−0.569191
$741$		0			0
$742$		0			0
$743$	24.0489	+	13.8847i	0.882269	+	0.509378i	0.871406	−	0.490563i	$-0.163209\pi$
$743$	24.0489	+	13.8847i	0.882269	+	0.509378i	0.0108634	+	0.999941i	$0.496542\pi$
$744$		0			0
$745$	−27.6579	−	15.9683i	−1.01331	−	0.585034i
$746$	24.5626	−	14.1812i	0.899300	−	0.519211i
$747$		0			0
$748$			6.87007i			0.251195i
$749$		0			0
$750$		0			0
$751$	8.67540	+	15.0262i	0.316570	+	0.548315i	0.979770	−	0.200127i	$-0.0641355\pi$
$751$	8.67540	+	15.0262i	0.316570	+	0.548315i	−0.663200	+	0.748442i	$0.730802\pi$
$752$	6.77054			0.246896
$753$		0			0
$754$			2.49434i			0.0908387i
$755$	−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	$0.388946\pi$
$758$		−	0.403872i		−	0.0146693i
$759$		0			0
$760$	45.5628			1.65274
$761$	−4.22520	−	7.31825i	−0.153163	−	0.265286i	0.779225	−	0.626744i	$-0.215613\pi$
$761$	−4.22520	−	7.31825i	−0.153163	−	0.265286i	−0.932389	+	0.361457i	$0.882279\pi$
$762$		0			0
$763$		0			0
$764$		−	5.94167i		−	0.214962i
$765$		0			0
$766$	21.0840	−	12.1728i	0.761794	−	0.439822i
$767$	−28.7257	−	16.5848i	−1.03723	−	0.598843i
$768$		0			0
$769$	19.8100	+	11.4373i	0.714366	+	0.412440i	0.812676	−	0.582716i	$-0.198010\pi$
$769$	19.8100	+	11.4373i	0.714366	+	0.412440i	−0.0983092	+	0.995156i	$0.531343\pi$
$770$		0			0
$771$		0			0
$772$	1.61581			0.0581544
$773$	18.8374	+	32.6273i	0.677533	+	1.17352i	0.975722	+	0.219015i	$0.0702843\pi$
$773$	18.8374	+	32.6273i	0.677533	+	1.17352i	−0.298189	+	0.954507i	$0.596382\pi$
$774$		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
$779$	12.8362	−	7.41099i	0.459905	−	0.265526i
$780$		0			0
$781$	−29.6324	+	51.3249i	−1.06033	+	1.83655i
$782$	−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
$787$			23.4661i			0.836475i	0.908338	+	0.418237i	$0.137352\pi$
$787$			23.4661i			0.836475i	−0.908338	+	0.418237i	$0.862648\pi$
$788$		−	20.2624i		−	0.721818i
$789$		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
$794$	−10.9256	+	18.9237i	−0.387734	+	0.671575i
$795$		0			0
$796$	−0.876386	+	0.505981i	−0.0310627	+	0.0179340i
$797$	22.8856	−	39.6390i	0.810648	−	1.40408i	−0.101763	−	0.994809i	$-0.532448\pi$
$797$	22.8856	−	39.6390i	0.810648	−	1.40408i	0.912411	−	0.409275i	$-0.134218\pi$
$798$		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
$803$	15.4912			0.546674
$804$		0			0
$805$		0			0
$806$	14.7313	+	8.50510i	0.518887	+	0.299579i
$807$		0			0
$808$	2.70984	+	1.56453i	0.0953317	+	0.0550398i
$809$	−11.4669	+	6.62041i	−0.403154	+	0.232761i	−0.687844	−	0.725858i	$-0.741443\pi$
$809$	−11.4669	+	6.62041i	−0.403154	+	0.232761i	0.284690	+	0.958620i	$0.408109\pi$
$810$		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
$814$	−15.9345	−	27.5994i	−0.558505	−	0.967359i
$815$	−2.08853			−0.0731579
$816$		0			0
$817$			57.4685i			2.01057i
$818$	0.868116			0.0303530
$819$		0			0
$820$	−3.55636			−0.124193
$821$		−	56.3224i		−	1.96567i	−0.184499	−	0.982833i	$-0.559066\pi$
$821$		−	56.3224i		−	1.96567i	0.184499	−	0.982833i	$-0.440934\pi$
$822$		0			0
$823$	17.0436			0.594103			0.297051	−	0.954862i	$-0.403997\pi$
$823$	17.0436			0.594103			0.297051	+	0.954862i	$0.403997\pi$
$824$	2.44253	+	4.23058i	0.0850895	+	0.147379i
$825$		0			0
$826$		0			0
$827$			45.7715i			1.59163i	0.605539	+	0.795816i	$0.292958\pi$
$827$			45.7715i			1.59163i	−0.605539	+	0.795816i	$0.707042\pi$
$828$		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	$0.543262\pi$
$830$	14.0188	+	8.09376i	0.486600	+	0.280938i
$831$		0			0
$832$	−23.6704	−	13.6661i	−0.820623	−	0.473787i
$833$		0			0
$834$		0			0
$835$	26.3680			0.912502
$836$	−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	0.937259	+	0.348634i	$0.113354\pi$
$839$	22.3195	+	38.6585i	0.770555	+	1.33464i	−0.166704	+	0.986007i	$0.553312\pi$
$840$		0			0
$841$	−14.3039	+	24.7751i	−0.493239	+	0.854315i
$842$	−22.6670	+	13.0868i	−0.781157	+	0.451001i
$843$		0			0
$844$	12.4114	−	21.4971i	0.427216	−	0.739960i
$845$	−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
$850$			2.32556i			0.0797661i
$851$			34.2336i			1.17351i
$852$		0			0
$853$	47.7652	−	27.5772i	1.63545	−	0.944227i	0.653077	−	0.757292i	$-0.273478\pi$
$853$	47.7652	−	27.5772i	1.63545	−	0.944227i	0.982372	−	0.186935i	$-0.0598554\pi$
$854$		0			0
$855$		0			0
$856$	5.11994	−	8.86800i	0.174996	−	0.303102i
$857$	−19.0771	+	33.0425i	−0.651660	+	1.12871i	0.331059	+	0.943610i	$0.392594\pi$
$857$	−19.0771	+	33.0425i	−0.651660	+	1.12871i	−0.982720	+	0.185099i	$0.940739\pi$
$858$		0			0
$859$	35.0465	−	20.2341i	1.19577	−	0.690378i	0.236160	−	0.971714i	$-0.424111\pi$
$859$	35.0465	−	20.2341i	1.19577	−	0.690378i	0.959609	+	0.281336i	$0.0907776\pi$
$860$	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	0.927424	−	0.374012i	$-0.122018\pi$
$863$	31.3519	+	18.1011i	1.06723	+	0.616167i	0.139808	+	0.990179i	$0.455351\pi$
$864$		0			0
$865$	6.69488	+	11.5959i	0.227633	+	0.394272i
$866$	−8.81216			−0.299449
$867$		0			0
$868$		0			0
$869$	29.6024	+	17.0910i	1.00419	+	0.579771i
$870$		0			0
$871$	44.0365	+	25.4245i	1.49212	+	0.861475i
$872$	9.52645	−	5.50010i	0.322606	−	0.186257i
$873$		0			0
$874$		−	34.3846i		−	1.16307i
$875$		0			0
$876$		0			0
$877$	5.53439	+	9.58584i	0.186883	+	0.323691i	0.944209	−	0.329346i	$-0.106828\pi$
$877$	5.53439	+	9.58584i	0.186883	+	0.323691i	−0.757326	+	0.653036i	$0.773495\pi$
$878$	−16.2101			−0.547064
$879$		0			0
$880$		−	6.55998i		−	0.221137i
$881$	−8.87036			−0.298850			−0.149425	−	0.988773i	$-0.547742\pi$
$881$	−8.87036			−0.298850			−0.149425	+	0.988773i	$0.547742\pi$
$882$		0			0
$883$	−14.1903			−0.477540			−0.238770	−	0.971076i	$-0.576744\pi$
$883$	−14.1903			−0.477540			−0.238770	+	0.971076i	$0.576744\pi$
$884$			6.81915i			0.229353i
$885$		0			0
$886$	1.04413			0.0350782
$887$	−19.5180	−	33.8062i	−0.655350	−	1.13510i	−0.981806	−	0.189887i	$-0.939188\pi$
$887$	−19.5180	−	33.8062i	−0.655350	−	1.13510i	0.326456	−	0.945213i	$-0.394146\pi$
$888$		0			0
$889$		0			0
$890$		−	18.1109i		−	0.607080i
$891$		0			0
$892$	−2.78169	+	1.60601i	−0.0931378	+	0.0537732i
$893$	55.8570	+	32.2490i	1.86918	+	1.07917i
$894$		0			0
$895$	−9.77931	−	5.64609i	−0.326886	−	0.188728i
$896$		0			0
$897$		0			0
$898$	−15.6157			−0.521103
$899$	−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
$905$	−2.12252	+	1.22544i	−0.0705550	+	0.0407350i
$906$		0			0
$907$	−4.93487	+	8.54745i	−0.163860	+	0.283813i	−0.936250	−	0.351335i	$-0.885728\pi$
$907$	−4.93487	+	8.54745i	−0.163860	+	0.283813i	0.772390	+	0.635148i	$0.219061\pi$
$908$	11.2961	−	19.5654i	0.374873	−	0.649300i
$909$		0			0
$910$		0			0
$911$	46.6335	−	26.9239i	1.54504	−	0.892028i	0.546529	−	0.837440i	$-0.315949\pi$
$911$	46.6335	−	26.9239i	1.54504	−	0.892028i	0.998509	−	0.0545881i	$-0.0173846\pi$
$912$		0			0
$913$		−	35.8363i		−	1.18601i
$914$		−	32.1898i		−	1.06475i
$915$		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	$0.285879\pi$
$920$	−12.0853	+	20.9324i	−0.398442	+	0.690122i
$921$		0			0
$922$	−15.7047	+	9.06714i	−0.517208	+	0.298610i
$923$	−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
$929$	−54.9907			−1.80419			−0.902093	−	0.431541i	$-0.857970\pi$
$929$	−54.9907			−1.80419			−0.902093	+	0.431541i	$0.857970\pi$
$930$		0			0
$931$		0			0
$932$	0.725243	+	0.418719i	0.0237561	+	0.0137156i
$933$		0			0
$934$	−12.7734	−	7.37475i	−0.417960	−	0.241309i
$935$	−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
$940$	−7.73777	−	13.4022i	−0.252378	−	0.437132i
$941$	−15.1752			−0.494696			−0.247348	−	0.968927i	$-0.579559\pi$
$941$	−15.1752			−0.494696			−0.247348	+	0.968927i	$0.579559\pi$
$942$		0			0
$943$			7.86293i			0.256052i
$944$	6.97265			0.226940
$945$		0			0
$946$	28.3808			0.922739
$947$		−	2.62670i		−	0.0853561i	−0.999089	−	0.0426781i	$-0.986411\pi$
$947$		−	2.62670i		−	0.0853561i	0.999089	−	0.0426781i	$-0.0135890\pi$
$948$		0			0
$949$	15.3764			0.499139
$950$	−5.82725	−	10.0931i	−0.189061	−	0.327463i
$951$		0			0
$952$		0			0
$953$		−	40.5520i		−	1.31361i	−0.754061	−	0.656805i	$-0.771908\pi$
$953$		−	40.5520i		−	1.31361i	0.754061	−	0.656805i	$-0.228092\pi$
$954$		0			0
$955$	9.33981	−	5.39234i	0.302229	−	0.174492i
$956$	−12.6476	−	7.30212i	−0.409054	−	0.236167i
$957$		0			0
$958$	26.4214	+	15.2544i	0.853637	+	0.492847i
$959$		0			0
$960$		0			0
$961$	12.7631			0.411713
$962$	−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	−0.742939	−	0.669359i	$-0.766569\pi$
$967$	6.47468	−	11.2145i	0.208212	−	0.360633i	0.951151	+	0.308725i	$0.0999023\pi$
$968$	−14.7457	+	8.51343i	−0.473945	+	0.273632i
$969$		0			0
$970$	−12.2159	+	21.1585i	−0.392228	+	0.679359i
$971$	−8.26077	+	14.3081i	−0.265101	+	0.459168i	−0.967590	−	0.252526i	$-0.918739\pi$
$971$	−8.26077	+	14.3081i	−0.265101	+	0.459168i	0.702489	+	0.711694i	$0.252072\pi$
$972$		0			0
$973$		0			0
$974$	11.4728	−	6.62381i	0.367611	−	0.212240i
$975$		0			0
$976$		−	3.19375i		−	0.102229i
$977$			6.35928i			0.203451i	0.994812	+	0.101726i	$0.0324364\pi$
$977$			6.35928i			0.203451i	−0.994812	+	0.101726i	$0.967564\pi$
$978$		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
$983$	1.11487	−	1.93102i	0.0355590	−	0.0615899i	−0.847698	−	0.530479i	$-0.822012\pi$
$983$	1.11487	−	1.93102i	0.0355590	−	0.0615899i	0.883257	+	0.468889i	$0.155346\pi$
$984$		0			0
$985$	31.8508	−	18.3891i	1.01485	−	0.585924i
$986$	−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	$0.545726\pi$
$992$	21.8815			0.694738
$993$		0			0
$994$		0			0
$995$	−1.59072	−	0.918403i	−0.0504293	−	0.0291153i
$996$		0			0
$997$	−7.28219	−	4.20437i	−0.230629	−	0.133154i	0.380233	−	0.924891i	$-0.375844\pi$
$997$	−7.28219	−	4.20437i	−0.230629	−	0.133154i	−0.610862	+	0.791737i	$0.709177\pi$
$998$	−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.i.d.1097.18		48
3.2	odd	2		441.2.i.d.68.9		48
7.2	even	3		1323.2.o.e.881.15		48
7.3	odd	6		1323.2.s.d.962.10		48
7.4	even	3		1323.2.s.d.962.9		48
7.5	odd	6		1323.2.o.e.881.16		48
7.6	odd	2	inner	1323.2.i.d.1097.8		48
9.2	odd	6		1323.2.s.d.656.10		48
9.7	even	3		441.2.s.d.362.15		48
21.2	odd	6		441.2.o.e.293.10	yes	48
21.5	even	6		441.2.o.e.293.9	yes	48
21.11	odd	6		441.2.s.d.374.16		48
21.17	even	6		441.2.s.d.374.15		48
21.20	even	2		441.2.i.d.68.10		48
63.2	odd	6		1323.2.o.e.440.16		48
63.11	odd	6	inner	1323.2.i.d.521.8		48
63.16	even	3		441.2.o.e.146.9	✓	48
63.20	even	6		1323.2.s.d.656.9		48
63.25	even	3		441.2.i.d.227.16		48
63.34	odd	6		441.2.s.d.362.16		48
63.38	even	6	inner	1323.2.i.d.521.18		48
63.47	even	6		1323.2.o.e.440.15		48
63.52	odd	6		441.2.i.d.227.15		48
63.61	odd	6		441.2.o.e.146.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.9		48	3.2	odd	2
441.2.i.d.68.10		48	21.20	even	2
441.2.i.d.227.15		48	63.52	odd	6
441.2.i.d.227.16		48	63.25	even	3
441.2.o.e.146.9	✓	48	63.16	even	3
441.2.o.e.146.10	yes	48	63.61	odd	6
441.2.o.e.293.9	yes	48	21.5	even	6
441.2.o.e.293.10	yes	48	21.2	odd	6
441.2.s.d.362.15		48	9.7	even	3
441.2.s.d.362.16		48	63.34	odd	6
441.2.s.d.374.15		48	21.17	even	6
441.2.s.d.374.16		48	21.11	odd	6
1323.2.i.d.521.8		48	63.11	odd	6	inner
1323.2.i.d.521.18		48	63.38	even	6	inner
1323.2.i.d.1097.8		48	7.6	odd	2	inner
1323.2.i.d.1097.18		48	1.1	even	1	trivial
1323.2.o.e.440.15		48	63.47	even	6
1323.2.o.e.440.16		48	63.2	odd	6
1323.2.o.e.881.15		48	7.2	even	3
1323.2.o.e.881.16		48	7.5	odd	6
1323.2.s.d.656.9		48	63.20	even	6
1323.2.s.d.656.10		48	9.2	odd	6
1323.2.s.d.962.9		48	7.4	even	3
1323.2.s.d.962.10		48	7.3	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+0.981621i q^{2} +1.03642 q^{4} +(0.940599 + 1.62916i) q^{5} +2.98061i q^{8} +(-1.59922 + 0.923312i) q^{10} +(3.54040 + 2.04405i) q^{11} +(3.51415 + 2.02890i) q^{13} -0.852996 q^{16} +(0.810727 + 1.40422i) q^{17} +(-7.03722 - 4.06294i) q^{19} +(0.974855 + 1.68850i) q^{20} +(-2.00648 + 3.47533i) q^{22} +(3.73318 - 2.15535i) q^{23} +(0.730548 - 1.26535i) q^{25} +(-1.99161 + 3.44957i) q^{26} +(0.542317 - 0.313107i) q^{29} -4.27047i q^{31} +5.12391i q^{32} +(-1.37841 + 0.795827i) q^{34} +(-3.97076 + 6.87757i) q^{37} +(3.98827 - 6.90789i) q^{38} +(-4.85591 + 2.80356i) q^{40} +(-0.912023 + 1.57967i) q^{41} +(-3.53614 - 6.12477i) q^{43} +(3.66933 + 2.11849i) q^{44} +(2.11574 + 3.66457i) q^{46} -7.93736 q^{47} +(1.24209 + 0.717122i) q^{50} +(3.64214 + 2.10279i) q^{52} +(7.24978 - 4.18567i) q^{53} +7.69052i q^{55} +(0.307352 + 0.532350i) q^{58} -8.17430 q^{59} +3.74415i q^{61} +4.19198 q^{62} -6.73573 q^{64} +7.63351i q^{65} +12.5312 q^{67} +(0.840253 + 1.45536i) q^{68} +14.4969i q^{71} +(3.28167 - 1.89468i) q^{73} +(-6.75117 - 3.89779i) q^{74} +(-7.29351 - 4.21091i) q^{76} +8.36133 q^{79} +(-0.802327 - 1.38967i) q^{80} +(-1.55064 - 0.895261i) q^{82} +(-4.38300 - 7.59159i) q^{83} +(-1.52514 + 2.64162i) q^{85} +(6.01221 - 3.47115i) q^{86} +(-6.09252 + 10.5526i) q^{88} +(-4.90379 + 8.49362i) q^{89} +(3.86914 - 2.23385i) q^{92} -7.79148i q^{94} -15.2864i q^{95} +(11.4579 - 6.61525i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) \) 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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