LMFDB - Embedded newform 441.2.i.d.227.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(68,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.68"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.15
Character	$\chi$	$=$	441.227
Dual form			441.2.i.d.68.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.981621i q^{2} +(-1.73160 + 0.0395255i) q^{3} +1.03642 q^{4} +(-0.940599 + 1.62916i) q^{5} +(-0.0387990 - 1.69978i) q^{6} +2.98061i q^{8} +(2.99688 - 0.136885i) q^{9} +(-1.59922 - 0.923312i) q^{10} +(-3.54040 + 2.04405i) q^{11} +(-1.79466 + 0.0409650i) q^{12} +(3.51415 - 2.02890i) q^{13} +(1.56435 - 2.85824i) q^{15} -0.852996 q^{16} +(-0.810727 + 1.40422i) q^{17} +(0.134369 + 2.94180i) q^{18} +(-7.03722 + 4.06294i) q^{19} +(-0.974855 + 1.68850i) q^{20} +(-2.00648 - 3.47533i) q^{22} +(-3.73318 - 2.15535i) q^{23} +(-0.117810 - 5.16123i) q^{24} +(0.730548 + 1.26535i) q^{25} +(1.99161 + 3.44957i) q^{26} +(-5.18398 + 0.355482i) q^{27} +(-0.542317 - 0.313107i) q^{29} +(2.80571 + 1.53560i) q^{30} +4.27047i q^{31} +5.12391i q^{32} +(6.04976 - 3.67941i) q^{33} +(-1.37841 - 0.795827i) q^{34} +(3.10602 - 0.141870i) q^{36} +(-3.97076 - 6.87757i) q^{37} +(-3.98827 - 6.90789i) q^{38} +(-6.00491 + 3.65214i) q^{39} +(-4.85591 - 2.80356i) q^{40} +(0.912023 + 1.57967i) q^{41} +(-3.53614 + 6.12477i) q^{43} +(-3.66933 + 2.11849i) q^{44} +(-2.59585 + 5.01116i) q^{45} +(2.11574 - 3.66457i) q^{46} +7.93736 q^{47} +(1.47705 - 0.0337151i) q^{48} +(-1.24209 + 0.717122i) q^{50} +(1.34835 - 2.46359i) q^{51} +(3.64214 - 2.10279i) q^{52} +(-7.24978 - 4.18567i) q^{53} +(-0.348949 - 5.08870i) q^{54} -7.69052i q^{55} +(12.0251 - 7.31354i) q^{57} +(0.307352 - 0.532350i) q^{58} +8.17430 q^{59} +(1.62132 - 2.96233i) q^{60} -3.74415i q^{61} -4.19198 q^{62} -6.73573 q^{64} +7.63351i q^{65} +(3.61179 + 5.93857i) q^{66} +12.5312 q^{67} +(-0.840253 + 1.45536i) q^{68} +(6.54957 + 3.58466i) q^{69} +14.4969i q^{71} +(0.408000 + 8.93253i) q^{72} +(3.28167 + 1.89468i) q^{73} +(6.75117 - 3.89779i) q^{74} +(-1.31503 - 2.16220i) q^{75} +(-7.29351 + 4.21091i) q^{76} +(-3.58501 - 5.89455i) q^{78} +8.36133 q^{79} +(0.802327 - 1.38967i) q^{80} +(8.96253 - 0.820452i) q^{81} +(-1.55064 + 0.895261i) q^{82} +(4.38300 - 7.59159i) q^{83} +(-1.52514 - 2.64162i) q^{85} +(-6.01221 - 3.47115i) q^{86} +(0.951451 + 0.520740i) q^{87} +(-6.09252 - 10.5526i) q^{88} +(4.90379 + 8.49362i) q^{89} +(-4.91906 - 2.54814i) q^{90} +(-3.86914 - 2.23385i) q^{92} +(-0.168792 - 7.39474i) q^{93} +7.79148i q^{94} -15.2864i q^{95} +(-0.202525 - 8.87256i) q^{96} +(11.4579 + 6.61525i) q^{97} +(-10.3303 + 6.61038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60}+ \cdots - 72 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			0.981621i			0.694111i	0.937845	+	0.347056i	$0.112818\pi$
$2$			0.981621i			0.694111i	−0.937845	+	0.347056i	$0.887182\pi$
$3$	−1.73160	+	0.0395255i	−0.999740	+	0.0228200i
$3$	−1.73160	+	0.0395255i	−0.999740	+	0.0228200i
$4$	1.03642			0.518210
$5$	−0.940599	+	1.62916i	−0.420648	+	0.728585i	−0.996003	−	0.0893196i	$-0.971531\pi$
$5$	−0.940599	+	1.62916i	−0.420648	+	0.728585i	0.575355	+	0.817904i	$0.304864\pi$
$6$	−0.0387990	−	1.69978i	−0.0158396	−	0.693930i
$7$		0			0
$7$		0			0
$8$			2.98061i			1.05381i
$9$	2.99688	−	0.136885i	0.998958	−	0.0456282i
$10$	−1.59922	−	0.923312i	−0.505719	−	0.291977i
$11$	−3.54040	+	2.04405i	−1.06747	+	0.616304i	−0.927489	−	0.373850i	$-0.878037\pi$
$11$	−3.54040	+	2.04405i	−1.06747	+	0.616304i	−0.139980	+	0.990154i	$0.544704\pi$
$12$	−1.79466	+	0.0409650i	−0.518075	+	0.0118256i
$13$	3.51415	−	2.02890i	0.974651	−	0.562715i	0.0739997	−	0.997258i	$-0.476424\pi$
$13$	3.51415	−	2.02890i	0.974651	−	0.562715i	0.900651	+	0.434544i	$0.143090\pi$
$14$		0			0
$15$	1.56435	−	2.85824i	0.403913	−	0.737994i
$16$	−0.852996			−0.213249
$17$	−0.810727	+	1.40422i	−0.196630	+	0.340574i	−0.947434	−	0.319952i	$-0.896333\pi$
$17$	−0.810727	+	1.40422i	−0.196630	+	0.340574i	0.750803	+	0.660526i	$0.229667\pi$
$18$	0.134369	+	2.94180i	0.0316710	+	0.693388i
$19$	−7.03722	+	4.06294i	−1.61445	+	0.932103i	−0.626128	+	0.779720i	$0.715361\pi$
$19$	−7.03722	+	4.06294i	−1.61445	+	0.932103i	−0.988322	+	0.152382i	$0.951305\pi$
$20$	−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	$-0.481704\pi$
$23$	−3.73318	−	2.15535i	−0.778423	−	0.449423i	−0.835871	+	0.548926i	$0.815037\pi$
$24$	−0.117810	−	5.16123i	−0.0240479	−	1.05353i
$25$	0.730548	+	1.26535i	0.146110	+	0.253069i
$26$	1.99161	+	3.44957i	0.390587	+	0.676516i
$27$	−5.18398	+	0.355482i	−0.997657	+	0.0684126i
$28$		0			0
$29$	−0.542317	−	0.313107i	−0.100706	−	0.0581425i	0.448801	−	0.893632i	$-0.351851\pi$
$29$	−0.542317	−	0.313107i	−0.100706	−	0.0581425i	−0.549507	+	0.835489i	$0.685184\pi$
$30$	2.80571	+	1.53560i	0.512250	+	0.280360i
$31$			4.27047i			0.766999i	0.923541	+	0.383499i	$0.125281\pi$
$31$			4.27047i			0.766999i	−0.923541	+	0.383499i	$0.874719\pi$
$32$			5.12391i			0.905788i
$33$	6.04976	−	3.67941i	1.05313	−	0.640503i
$34$	−1.37841	−	0.795827i	−0.236396	−	0.136483i
$35$		0			0
$36$	3.10602	−	0.141870i	0.517670	−	0.0236450i
$37$	−3.97076	−	6.87757i	−0.652790	−	1.13066i	−0.982443	−	0.186563i	$-0.940265\pi$
$37$	−3.97076	−	6.87757i	−0.652790	−	1.13066i	0.329653	−	0.944102i	$-0.393068\pi$
$38$	−3.98827	−	6.90789i	−0.646983	−	1.12061i
$39$	−6.00491	+	3.65214i	−0.961556	+	0.584810i
$40$	−4.85591	−	2.80356i	−0.767787	−	0.443282i
$41$	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
$45$	−2.59585	+	5.01116i	−0.386966	+	0.747019i
$46$	2.11574	−	3.66457i	0.311949	−	0.540312i
$47$	7.93736			1.15778			0.578891	−	0.815405i	$-0.303485\pi$
$47$	7.93736			1.15778			0.578891	+	0.815405i	$0.303485\pi$
$48$	1.47705	−	0.0337151i	0.213194	−	0.00486635i
$49$		0			0
$50$	−1.24209	+	0.717122i	−0.175658	+	0.101416i
$51$	1.34835	−	2.46359i	0.188807	−	0.344972i
$52$	3.64214	−	2.10279i	0.505073	−	0.291604i
$53$	−7.24978	−	4.18567i	−0.995835	−	0.574945i	−0.0888214	−	0.996048i	$-0.528310\pi$
$53$	−7.24978	−	4.18567i	−0.995835	−	0.574945i	−0.907013	+	0.421102i	$0.861643\pi$
$54$	−0.348949	−	5.08870i	−0.0474859	−	0.692485i
$55$		−	7.69052i		−	1.03699i
$56$		0			0
$57$	12.0251	−	7.31354i	1.59276	−	0.968702i
$58$	0.307352	−	0.532350i	0.0403573	−	0.0699009i
$59$	8.17430			1.06420			0.532101	−	0.846681i	$-0.321402\pi$
$59$	8.17430			1.06420			0.532101	+	0.846681i	$0.321402\pi$
$60$	1.62132	−	2.96233i	0.209311	−	0.382436i
$61$		−	3.74415i		−	0.479390i	−0.970848	−	0.239695i	$-0.922953\pi$
$61$		−	3.74415i		−	0.479390i	0.970848	−	0.239695i	$-0.0770474\pi$
$62$	−4.19198			−0.532382
$63$		0			0
$64$	−6.73573			−0.841966
$65$			7.63351i			0.946820i
$66$	3.61179	+	5.93857i	0.444580	+	0.730988i
$67$	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
$69$	6.54957	+	3.58466i	0.788476	+	0.431542i
$70$		0			0
$71$			14.4969i			1.72047i	0.509898	+	0.860235i	$0.329683\pi$
$71$			14.4969i			1.72047i	−0.509898	+	0.860235i	$0.670317\pi$
$72$	0.408000	+	8.93253i	0.0480833	+	1.05271i
$73$	3.28167	+	1.89468i	0.384091	+	0.221755i	0.679597	−	0.733586i	$-0.262155\pi$
$73$	3.28167	+	1.89468i	0.384091	+	0.221755i	−0.295506	+	0.955341i	$0.595488\pi$
$74$	6.75117	−	3.89779i	0.784807	−	0.453109i
$75$	−1.31503	−	2.16220i	−0.151847	−	0.249669i
$76$	−7.29351	+	4.21091i	−0.836623	+	0.483025i
$77$		0			0
$78$	−3.58501	−	5.89455i	−0.405923	−	0.667426i
$79$	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
$81$	8.96253	−	0.820452i	0.995836	−	0.0911613i
$82$	−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
$86$	−6.01221	−	3.47115i	−0.648313	−	0.374304i
$87$	0.951451	+	0.520740i	0.102006	+	0.0558292i
$88$	−6.09252	−	10.5526i	−0.649465	−	1.12491i
$89$	4.90379	+	8.49362i	0.519801	+	0.900322i	0.999735	+	0.0230174i	$0.00732730\pi$
$89$	4.90379	+	8.49362i	0.519801	+	0.900322i	−0.479934	+	0.877305i	$0.659339\pi$
$90$	−4.91906	−	2.54814i	−0.518514	−	0.268598i
$91$		0			0
$92$	−3.86914	−	2.23385i	−0.403386	−	0.232895i
$93$	−0.168792	−	7.39474i	−0.0175029	−	0.766799i
$94$			7.79148i			0.803630i
$95$		−	15.2864i		−	1.56835i
$96$	−0.202525	−	8.87256i	−0.0206701	−	0.905552i
$97$	11.4579	+	6.61525i	1.16338	+	0.671677i	0.952111	−	0.305752i	$-0.0989077\pi$
$97$	11.4579	+	6.61525i	1.16338	+	0.671677i	0.211267	+	0.977428i	$0.432241\pi$
$98$		0			0
$99$	−10.3303	+	6.61038i	−1.03824	+	0.664369i
$100$	0.757155	+	1.31143i	0.0757155	+	0.131143i
$101$	−0.524900	−	0.909154i	−0.0522295	−	0.0904642i	0.838729	−	0.544550i	$-0.183299\pi$
$101$	−0.524900	−	0.909154i	−0.0522295	−	0.0904642i	−0.890958	+	0.454085i	$0.849966\pi$
$102$	2.41832	+	1.32357i	0.239449	+	0.131053i
$103$	1.41937	+	0.819472i	0.139854	+	0.0807449i	0.568295	−	0.822825i	$-0.307603\pi$
$103$	1.41937	+	0.819472i	0.139854	+	0.0807449i	−0.428440	+	0.903570i	$0.640937\pi$
$104$	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	$-0.613562\pi$
$107$	2.97522	−	1.71775i	0.287626	−	0.166061i	0.636871	+	0.770971i	$0.280229\pi$
$108$	−5.37278	+	0.368429i	−0.516996	+	0.0354521i
$109$	−1.84529	+	3.19614i	−0.176747	+	0.306134i	−0.940764	−	0.339061i	$-0.889891\pi$
$109$	−1.84529	+	3.19614i	−0.176747	+	0.306134i	0.764018	+	0.645195i	$0.223224\pi$
$110$	7.54918			0.719786
$111$	7.14761	+	11.7522i	0.678421	+	1.11547i
$112$		0			0
$113$	15.0858	−	8.70977i	1.41915	−	0.819346i	0.422925	−	0.906165i	$-0.361003\pi$
$113$	15.0858	−	8.70977i	1.41915	−	0.819346i	0.996224	+	0.0868183i	$0.0276699\pi$
$114$	7.17913	+	11.8041i	0.672387	+	1.10555i
$115$	7.02285	−	4.05465i	0.654885	−	0.378098i
$116$	−0.562068	−	0.324510i	−0.0521867	−	0.0301300i
$117$	10.2538	−	6.56138i	0.947960	−	0.606600i
$118$			8.02407i			0.738675i
$119$		0			0
$120$	8.51931	+	4.66271i	0.777703	+	0.425646i
$121$	2.85627	−	4.94720i	0.259661	−	0.449746i
$122$	3.67534			0.332750
$123$	−1.64170	−	2.69931i	−0.148027	−	0.243388i
$124$			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
$129$	5.88109	−	10.7454i	0.517801	−	0.946082i
$130$	−7.49322			−0.657199
$131$	−2.48851	+	4.31022i	−0.217422	+	0.376586i	−0.954019	−	0.299746i	$-0.903098\pi$
$131$	−2.48851	+	4.31022i	−0.217422	+	0.376586i	0.736597	+	0.676332i	$0.236431\pi$
$132$	6.27008	−	3.81341i	0.545741	−	0.331915i
$133$		0			0
$134$			12.3009i			1.06263i
$135$	4.29690	−	8.77992i	0.369819	−	0.755655i
$136$	−4.18544	−	2.41647i	−0.358899	−	0.207210i
$137$	−0.728035	+	0.420331i	−0.0622003	+	0.0359113i	−0.530778	−	0.847511i	$-0.678100\pi$
$137$	−0.728035	+	0.420331i	−0.0622003	+	0.0359113i	0.468577	+	0.883422i	$0.344767\pi$
$138$	−3.51877	+	6.42920i	−0.299538	+	0.547290i
$139$	−5.74392	+	3.31626i	−0.487193	+	0.281281i	−0.723409	−	0.690419i	$-0.757426\pi$
$139$	−5.74392	+	3.31626i	−0.487193	+	0.281281i	0.236216	+	0.971701i	$0.424093\pi$
$140$		0			0
$141$	−13.7443	+	0.313728i	−1.15748	+	0.0264206i
$142$	−14.2305			−1.19420
$143$	−8.29433	+	14.3662i	−0.693606	+	1.20136i
$144$	−2.55632	+	0.116762i	−0.213027	+	0.00973017i
$145$	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	$-0.0885627\pi$
$149$	14.7023	+	8.48838i	1.20446	+	0.695395i	0.242916	+	0.970047i	$0.421896\pi$
$150$	2.12246	−	1.29086i	0.173298	−	0.105398i
$151$	−0.975709	−	1.68998i	−0.0794021	−	0.137528i	0.823590	−	0.567186i	$-0.191968\pi$
$151$	−0.975709	−	1.68998i	−0.0794021	−	0.137528i	−0.902992	+	0.429657i	$0.858634\pi$
$152$	−12.1101	−	20.9752i	−0.982256	−	1.70132i
$153$	−2.23743	+	4.31925i	−0.180886	+	0.349191i
$154$		0			0
$155$	−6.95730	−	4.01680i	−0.558823	−	0.322637i
$156$	−6.22361	+	3.78514i	−0.498287	+	0.303054i
$157$		−	9.52118i		−	0.759873i	−0.925013	−	0.379936i	$-0.875946\pi$
$157$		−	9.52118i		−	0.759873i	0.925013	−	0.379936i	$-0.124054\pi$
$158$			8.20766i			0.652966i
$159$	12.7192	+	6.96135i	1.00870	+	0.552071i
$160$	−8.34769	−	4.81954i	−0.659943	−	0.381018i
$161$		0			0
$162$	0.805373	+	8.79781i	0.0632761	+	0.691221i
$163$	−0.555106	−	0.961472i	−0.0434793	−	0.0753083i	0.843467	−	0.537181i	$-0.180511\pi$
$163$	−0.555106	−	0.961472i	−0.0434793	−	0.0753083i	−0.886946	+	0.461873i	$0.847178\pi$
$164$	0.945238	+	1.63720i	0.0738107	+	0.127844i
$165$	0.303971	+	13.3169i	0.0236641	+	1.03672i
$166$	7.45206	+	4.30245i	0.578392	+	0.333935i
$167$	−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
$171$	−20.5335	+	13.1394i	−1.57024	+	1.00480i
$172$	−3.66492	+	6.34783i	−0.279448	+	0.484018i
$173$	−7.11768			−0.541147			−0.270574	−	0.962699i	$-0.587213\pi$
$173$	−7.11768			−0.541147			−0.270574	+	0.962699i	$0.587213\pi$
$174$	−0.511170	+	0.933965i	−0.0387517	+	0.0708037i
$175$		0			0
$176$	3.01994	−	1.74357i	0.227637	−	0.131426i
$177$	−14.1546	+	0.323093i	−1.06393	+	0.0242851i
$178$	−8.33752	+	4.81367i	−0.624924	+	0.360800i
$179$	5.19845	+	3.00133i	0.388550	+	0.224330i	0.681532	−	0.731788i	$-0.261314\pi$
$179$	5.19845	+	3.00133i	0.388550	+	0.224330i	−0.292981	+	0.956118i	$0.594647\pi$
$180$	−2.69039	+	5.19366i	−0.200530	+	0.387113i
$181$		−	1.30283i		−	0.0968385i	−0.998827	−	0.0484192i	$-0.984582\pi$
$181$		−	1.30283i		−	0.0968385i	0.998827	−	0.0484192i	$-0.0154184\pi$
$182$		0			0
$183$	0.147989	+	6.48337i	0.0109397	+	0.479265i
$184$	6.42428	−	11.1272i	0.473604	−	0.820307i
$185$	14.9396			1.09838
$186$	7.25884	−	0.165690i	0.532244	−	0.0121490i
$187$		−	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	$-0.0665029\pi$
$192$	11.6636	−	0.266233i	0.841747	−	0.0192137i
$193$	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
$195$	−0.301718	−	13.2182i	−0.0216065	−	0.946574i
$196$		0			0
$197$		−	19.5504i		−	1.39291i	−0.717602	−	0.696454i	$-0.754760\pi$
$197$		−	19.5504i		−	1.39291i	0.717602	−	0.696454i	$-0.245240\pi$
$198$	−6.48889	−	10.1405i	−0.461146	−	0.720652i
$199$	−0.845590	−	0.488202i	−0.0599423	−	0.0346077i	0.469729	−	0.882810i	$-0.344352\pi$
$199$	−0.845590	−	0.488202i	−0.0599423	−	0.0346077i	−0.529672	+	0.848203i	$0.677685\pi$
$200$	−3.77151	+	2.17748i	−0.266686	+	0.153971i
$201$	−21.6990	+	0.495301i	−1.53053	+	0.0349358i
$202$	0.892445	−	0.515253i	0.0627922	−	0.0362531i
$203$		0			0
$204$	1.39746	−	2.55332i	0.0978417	−	0.178768i
$205$	−3.43139			−0.239659
$206$	−0.804411	+	1.39328i	−0.0560460	+	0.0970745i
$207$	−11.4829	−	5.94831i	−0.798118	−	0.413436i
$208$	−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	$0.524841\pi$
$212$	−7.51382	−	4.33810i	−0.516051	−	0.297942i
$213$	−0.572998	−	25.1029i	−0.0392612	−	1.72002i
$214$	1.68618	+	2.92054i	0.115265	+	0.199644i
$215$	−6.65218	−	11.5219i	−0.453675	−	0.785787i
$216$	−1.05956	−	15.4514i	−0.0720936	−	1.05134i
$217$		0			0
$218$	−3.13740	−	1.81138i	−0.212491	−	0.122682i
$219$	−5.75744	−	3.15111i	−0.389051	−	0.212932i
$220$		−	7.97060i		−	0.537378i
$221$			6.57953i			0.442587i
$222$	−11.5363	+	7.01625i	−0.774263	+	0.470900i
$223$	−2.68394	−	1.54957i	−0.179730	−	0.103767i	0.407436	−	0.913234i	$-0.366423\pi$
$223$	−2.68394	−	1.54957i	−0.179730	−	0.103767i	−0.587166	+	0.809467i	$0.699756\pi$
$224$		0			0
$225$	2.36257	+	3.69209i	0.157505	+	0.246139i
$226$	8.54970	+	14.8085i	0.568717	+	0.985047i
$227$	−10.8991	−	18.8779i	−0.723401	−	1.25297i	−0.959629	−	0.281269i	$-0.909245\pi$
$227$	−10.8991	−	18.8779i	−0.723401	−	1.25297i	0.236228	−	0.971698i	$-0.424089\pi$
$228$	12.4630	−	7.57989i	0.825383	−	0.501991i
$229$	11.1810	+	6.45536i	0.738862	+	0.426582i	0.821655	−	0.569985i	$-0.193051\pi$
$229$	11.1810	+	6.45536i	0.738862	+	0.426582i	−0.0827937	+	0.996567i	$0.526384\pi$
$230$	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	$-0.675092\pi$
$233$	−0.699758	+	0.404005i	−0.0458427	+	0.0264673i	0.476904	+	0.878956i	$0.341759\pi$
$234$	6.44080	+	10.0653i	0.421048	+	0.657989i
$235$	−7.46587	+	12.9313i	−0.487020	+	0.843543i
$236$	8.47200			0.551480
$237$	−14.4785	+	0.330485i	−0.940478	+	0.0214673i
$238$		0			0
$239$	12.2032	−	7.04552i	0.789360	−	0.455737i	−0.0503775	−	0.998730i	$-0.516042\pi$
$239$	12.2032	−	7.04552i	0.789360	−	0.455737i	0.839737	+	0.542993i	$0.182709\pi$
$240$	−1.33438	+	2.43807i	−0.0861340	+	0.157377i
$241$	−16.0205	+	9.24943i	−1.03197	+	0.595808i	−0.917549	−	0.397624i	$-0.869835\pi$
$241$	−16.0205	+	9.24943i	−1.03197	+	0.595808i	−0.114422	+	0.993432i	$0.536502\pi$
$242$	4.85628	+	2.80377i	0.312173	+	0.180233i
$243$	−15.4871	+	1.77494i	−0.993497	+	0.113863i
$244$		−	3.88051i		−	0.248424i
$245$		0			0
$246$	2.64970	−	1.61152i	0.168939	−	0.102747i
$247$	−16.4866	+	28.5556i	−1.04902	+	1.81695i
$248$	−12.7286			−0.808268
$249$	−7.28955	+	13.3188i	−0.461956	+	0.844046i
$250$		−	11.9312i		−	0.754596i
$251$	−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
$254$		−	9.94262i		−	0.623855i
$255$	2.74534	+	4.51394i	0.171920	+	0.282674i
$256$	−17.0405			−1.06503
$257$	−2.02896	+	3.51427i	−0.126563	+	0.219214i	−0.922343	−	0.386372i	$-0.873728\pi$
$257$	−2.02896	+	3.51427i	−0.126563	+	0.219214i	0.795780	+	0.605586i	$0.207061\pi$
$258$	10.5479	+	5.77301i	0.656686	+	0.359412i
$259$		0			0
$260$			7.91152i			0.490652i
$261$	−1.66812	−	0.864107i	−0.103254	−	0.0534869i
$262$	−4.23100	−	2.44277i	−0.261392	−	0.150915i
$263$	8.62617	−	4.98032i	0.531913	−	0.307100i	−0.209882	−	0.977727i	$-0.567308\pi$
$263$	8.62617	−	4.98032i	0.531913	−	0.307100i	0.741795	+	0.670627i	$0.233975\pi$
$264$	10.9669	+	18.0320i	0.674966	+	1.10979i
$265$	13.6383	−	7.87406i	0.837793	−	0.483700i
$266$		0			0
$267$	−8.82712	−	14.5137i	−0.540211	−	0.888226i
$268$	12.9876			0.793341
$269$	−4.98399	+	8.63253i	−0.303880	+	0.526335i	−0.977011	−	0.213188i	$-0.931615\pi$
$269$	−4.98399	+	8.63253i	−0.303880	+	0.526335i	0.673132	+	0.739523i	$0.264949\pi$
$270$	8.61856	+	4.21793i	0.524509	+	0.256695i
$271$	16.4822	−	9.51601i	1.00122	−	0.578057i	0.0926133	−	0.995702i	$-0.470478\pi$
$271$	16.4822	−	9.51601i	1.00122	−	0.578057i	0.908610	+	0.417646i	$0.137145\pi$
$272$	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
$276$	6.78810	+	3.71521i	0.408596	+	0.223629i
$277$	7.81184	+	13.5305i	0.469368	+	0.812969i	0.999387	−	0.0350166i	$-0.0111484\pi$
$277$	7.81184	+	13.5305i	0.469368	+	0.812969i	−0.530019	+	0.847986i	$0.677815\pi$
$278$	−3.25531	−	5.63836i	−0.195240	−	0.338166i
$279$	0.584561	+	12.7981i	0.0349968	+	0.766200i
$280$		0			0
$281$	−20.8780	−	12.0539i	−1.24547	−	0.719075i	−0.275271	−	0.961367i	$-0.588768\pi$
$281$	−20.8780	−	12.0539i	−1.24547	−	0.719075i	−0.970203	+	0.242292i	$0.922101\pi$
$282$	−0.307962	−	13.4917i	−0.0183389	−	0.803421i
$283$		−	3.01779i		−	0.179389i	−0.995969	−	0.0896946i	$-0.971411\pi$
$283$		−	3.01779i		−	0.179389i	0.995969	−	0.0896946i	$-0.0285891\pi$
$284$			15.0249i			0.891564i
$285$	0.604202	+	26.4699i	0.0357898	+	1.56794i
$286$	−14.1022	−	8.14189i	−0.833879	−	0.481440i
$287$		0			0
$288$	0.701384	+	15.3557i	0.0413295	+	0.904844i
$289$	7.18544	+	12.4456i	0.422673	+	0.732091i
$290$	0.578190	+	1.00145i	0.0339525	+	0.0588074i
$291$	−20.1021	−	11.0021i	−1.17840	−	0.644954i
$292$	3.40119	+	1.96368i	0.199040	+	0.114916i
$293$	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
$297$	17.6267	−	11.8549i	1.02281	−	0.687888i
$298$	−8.33238	+	14.4321i	−0.482682	+	0.836029i
$299$	−17.4920			−1.01159
$300$	−1.36292	−	2.24095i	−0.0786884	−	0.129381i
$301$		0			0
$302$	1.65892	−	0.957777i	0.0954600	−	0.0551139i
$303$	0.944852	+	1.55354i	0.0542803	+	0.0892487i
$304$	6.00272	−	3.46567i	0.344280	−	0.198770i
$305$	6.09984	+	3.52175i	0.349276	+	0.201655i
$306$	−4.23987	−	2.19631i	−0.242377	−	0.125555i
$307$			2.68853i			0.153442i	0.997053	+	0.0767212i	$0.0244451\pi$
$307$			2.68853i			0.153442i	−0.997053	+	0.0767212i	$0.975555\pi$
$308$		0			0
$309$	−2.49016	−	1.36290i	−0.141661	−	0.0775324i
$310$	3.94297	−	6.82943i	0.223946	−	0.387886i
$311$	−11.0753			−0.628020			−0.314010	−	0.949420i	$-0.601673\pi$
$311$	−11.0753			−0.628020			−0.314010	+	0.949420i	$0.601673\pi$
$312$	−10.8856	−	17.8983i	−0.616276	−	1.01329i
$313$			16.7397i			0.946186i	0.881013	+	0.473093i	$0.156863\pi$
$313$			16.7397i			0.946186i	−0.881013	+	0.473093i	$0.843137\pi$
$314$	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	$0.973672\pi$
$318$	−6.83341	+	12.4854i	−0.383198	+	0.700147i
$319$	2.56002			0.143334
$320$	6.33562	−	10.9736i	0.354172	−	0.613444i
$321$	−5.08400	+	3.09205i	−0.283761	+	0.172581i
$322$		0			0
$323$		−	13.1758i		−	0.733118i
$324$	9.28893	−	0.850332i	0.516052	−	0.0472407i
$325$	5.13452	+	2.96442i	0.284812	+	0.164436i
$326$	0.943801	−	0.544904i	0.0522723	−	0.0301794i
$327$	3.06898	−	5.60737i	0.169715	−	0.310088i
$328$	−4.70839	+	2.71839i	−0.259977	+	0.150098i
$329$		0			0
$330$	−13.0722	+	0.298385i	−0.719598	+	0.0164255i
$331$	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
$333$	−12.8413	−	20.0677i	−0.703700	−	1.09970i
$334$	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	$0.717865\pi$
$338$	2.94622	+	1.70100i	0.160253	+	0.0925221i
$339$	−25.7783	+	15.6781i	−1.40008	+	0.851518i
$340$	−1.58068	−	2.73782i	−0.0857245	−	0.148479i
$341$	−8.72904	−	15.1191i	−0.472704	−	0.818748i
$342$	−12.8979	−	20.1561i	−0.697440	−	1.08992i
$343$		0			0
$344$	−18.2556	−	10.5399i	−0.984275	−	0.568272i
$345$	−12.0005	+	7.29861i	−0.646086	+	0.392944i
$346$		−	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	$-0.0183949\pi$
$348$	0.986102	+	0.539705i	0.0528606	+	0.0289312i
$349$	25.2919	+	14.6023i	1.35384	+	0.781642i	0.988785	−	0.149343i	$-0.0477159\pi$
$349$	25.2919	+	14.6023i	1.35384	+	0.781642i	0.365058	+	0.930985i	$0.381049\pi$
$350$		0			0
$351$	−17.4961	+	11.7670i	−0.933870	+	0.628075i
$352$	−10.4735	−	18.1407i	−0.558240	−	0.966901i
$353$	5.41764	+	9.38362i	0.288352	+	0.499440i	0.973416	−	0.229042i	$-0.0735595\pi$
$353$	5.41764	+	9.38362i	0.288352	+	0.499440i	−0.685065	+	0.728482i	$0.740226\pi$
$354$	−0.317155	−	13.8945i	−0.0168566	−	0.738483i
$355$	−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	$-0.480215\pi$
$359$	18.1425	−	10.4746i	0.957527	−	0.552829i	0.895411	+	0.445240i	$0.146882\pi$
$360$	−14.9363	−	7.73723i	−0.787213	−	0.407788i
$361$	23.5150	−	40.7292i	1.23763	−	2.14364i
$362$	1.27888			0.0672167
$363$	−4.75037	+	8.67947i	−0.249330	+	0.455554i
$364$		0			0
$365$	−6.17348	+	3.56426i	−0.323135	+	0.186562i
$366$	−6.36422	+	0.145270i	−0.332663	+	0.00759336i
$367$	4.97835	−	2.87425i	0.259868	−	0.150035i	−0.364407	−	0.931240i	$-0.618728\pi$
$367$	4.97835	−	2.87425i	0.259868	−	0.150035i	0.624274	+	0.781205i	$0.285395\pi$
$368$	3.18439	+	1.83851i	0.165998	+	0.0958389i
$369$	2.94945	+	4.60923i	0.153542	+	0.239947i
$370$			14.6650i			0.762398i
$371$		0			0
$372$	−0.174940	−	7.66405i	−0.00907019	−	0.397363i
$373$	−14.4467	+	25.0224i	−0.748023	+	1.29561i	0.200747	+	0.979643i	$0.435663\pi$
$373$	−14.4467	+	25.0224i	−0.748023	+	1.29561i	−0.948769	+	0.315970i	$0.897670\pi$
$374$	6.50684			0.336461
$375$	21.0469	−	0.480416i	1.08686	−	0.0248086i
$376$			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
$381$	17.5390	−	0.400344i	0.898549	−	0.0205103i
$382$	5.62752			0.287929
$383$	12.4007	−	21.4787i	0.633648	−	1.09751i	−0.353152	−	0.935566i	$-0.614890\pi$
$383$	12.4007	−	21.4787i	0.633648	−	1.09751i	0.986800	−	0.161944i	$-0.0517765\pi$
$384$	−0.143710	−	6.29589i	−0.00733366	−	0.321286i
$385$		0			0
$386$			1.53038i			0.0778944i
$387$	−9.75898	+	18.8392i	−0.496077	+	0.957652i
$388$	11.8752	+	6.85617i	0.602874	+	0.348069i
$389$	−3.82694	+	2.20948i	−0.194033	+	0.112025i	−0.593869	−	0.804561i	$-0.702400\pi$
$389$	−3.82694	+	2.20948i	−0.194033	+	0.112025i	0.399836	+	0.916587i	$0.369067\pi$
$390$	12.9753	−	0.296173i	0.657028	−	0.0149973i
$391$	6.05319	−	3.49481i	0.306123	−	0.176740i
$392$		0			0
$393$	4.13873	−	7.56193i	0.208772	−	0.381449i
$394$	19.1911			0.966833
$395$	−7.86465	+	13.6220i	−0.395714	+	0.685396i
$396$	−10.7066	+	6.85113i	−0.538024	+	0.344282i
$397$	19.2780	−	11.1301i	0.967533	−	0.558605i	0.0690495	−	0.997613i	$-0.478003\pi$
$397$	19.2780	−	11.1301i	0.967533	−	0.558605i	0.898483	+	0.439008i	$0.144670\pi$
$398$	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	$-0.284326\pi$
$401$	5.31899	+	3.07092i	0.265617	+	0.153354i	−0.361277	+	0.932459i	$0.617659\pi$
$402$	−0.486198	−	21.3002i	−0.0242493	−	1.06236i
$403$	8.66434	+	15.0071i	0.431602	+	0.747556i
$404$	−0.544017	−	0.942265i	−0.0270658	−	0.0468794i
$405$	−7.09349	+	15.3731i	−0.352478	+	0.763898i
$406$		0			0
$407$	28.1162	+	16.2329i	1.39367	+	0.804633i
$408$	7.34302	+	4.01892i	0.363534	+	0.198966i
$409$			0.884369i			0.0437293i	0.999761	+	0.0218646i	$0.00696028\pi$
$409$			0.884369i			0.0437293i	−0.999761	+	0.0218646i	$0.993040\pi$
$410$		−	3.36833i		−	0.166350i
$411$	1.24405	−	0.756622i	0.0613646	−	0.0373214i
$412$	1.47106	+	0.849316i	0.0724739	+	0.0418428i
$413$		0			0
$414$	5.83899	−	11.2719i	0.286971	−	0.553983i
$415$	8.24530	+	14.2813i	0.404746	+	0.701040i
$416$	10.3959	+	18.0062i	0.509700	+	0.882827i
$417$	9.81510	−	5.96946i	0.480648	−	0.292326i
$418$	28.2401	+	16.3044i	1.38127	+	0.797476i
$419$	−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
$423$	23.7873	−	1.08650i	1.15658	−	0.0528275i
$424$	12.4759	−	21.6088i	0.605881	−	1.04942i
$425$	−2.36910			−0.114918
$426$	24.6415	−	0.562467i	1.19389	−	0.0272516i
$427$		0			0
$428$	3.08358	−	1.78031i	0.149050	−	0.0860543i
$429$	13.7946	−	25.2043i	0.666011	−	1.21688i
$430$	11.3102	−	6.52992i	0.545424	−	0.314901i
$431$	4.06785	+	2.34857i	0.195941	+	0.113127i	0.594761	−	0.803903i	$-0.297247\pi$
$431$	4.06785	+	2.34857i	0.195941	+	0.113127i	−0.398820	+	0.917029i	$0.630580\pi$
$432$	4.42191	−	0.303225i	0.212749	−	0.0145889i
$433$		−	8.97714i		−	0.431414i	−0.976458	−	0.215707i	$-0.930794\pi$
$433$		−	8.97714i		−	0.431414i	0.976458	−	0.215707i	$-0.0692056\pi$
$434$		0			0
$435$	−1.74331	+	1.06026i	−0.0835851	+	0.0508357i
$436$	−1.91250	+	3.31254i	−0.0915919	+	0.158642i
$437$	35.0283			1.67563
$438$	3.09320	−	5.65162i	0.147799	−	0.270045i
$439$		−	16.5136i		−	0.788151i	−0.919078	−	0.394075i	$-0.871065\pi$
$439$		−	16.5136i		−	0.788151i	0.919078	−	0.394075i	$-0.128935\pi$
$440$	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	$-0.00804404\pi$
$444$	7.40792	+	12.1803i	0.351565	+	0.578049i
$445$	−18.4500			−0.874614
$446$	1.52110	−	2.63461i	0.0720260	−	0.124753i
$447$	−25.7940	−	14.1174i	−1.22002	−	0.667728i
$448$		0			0
$449$			15.9081i			0.750749i	0.926873	+	0.375374i	$0.122486\pi$
$449$			15.9081i			0.750749i	−0.926873	+	0.375374i	$0.877514\pi$
$450$	−3.62423	+	2.31915i	−0.170848	+	0.109326i
$451$	−6.45785	−	3.72844i	−0.304088	−	0.175565i
$452$	15.6352	−	9.02697i	0.735417	−	0.424593i
$453$	1.75634	+	2.88780i	0.0825198	+	0.135681i
$454$	18.5309	−	10.6988i	0.869698	−	0.502121i
$455$		0			0
$456$	21.7988	+	35.8421i	1.02082	+	1.67846i
$457$	−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
$459$	3.70362	−	7.56765i	0.172870	−	0.353228i
$460$	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	$0.836320\pi$
$464$	0.462594	+	0.267079i	0.0214754	+	0.0123988i
$465$	12.2060	+	6.68049i	0.566041	+	0.309801i
$466$	−0.396580	−	0.686897i	−0.0183712	−	0.0318199i
$467$	7.51283	+	13.0126i	0.347652	+	0.602151i	0.985832	−	0.167736i	$-0.0536457\pi$
$467$	7.51283	+	13.0126i	0.347652	+	0.602151i	−0.638180	+	0.769887i	$0.720312\pi$
$468$	10.6272	−	6.80035i	0.491242	−	0.314346i
$469$		0			0
$470$	−12.6936	−	7.32866i	−0.585512	−	0.338046i
$471$	0.376329	+	16.4869i	0.0173403	+	0.759675i
$472$			24.3644i			1.12146i
$473$		−	28.9122i		−	1.32938i
$474$	−0.324412	−	14.2124i	−0.0149007	−	0.652796i
$475$	−10.2821	−	5.93635i	−0.471773	−	0.272379i
$476$		0			0
$477$	−22.2997	−	11.5515i	−1.02103	−	0.528908i
$478$	6.91604	+	11.9789i	0.316332	+	0.547903i
$479$	−15.5400	−	26.9161i	−0.710041	−	1.22983i	−0.964841	−	0.262833i	$-0.915343\pi$
$479$	−15.5400	−	26.9161i	−0.710041	−	1.22983i	0.254800	−	0.966994i	$-0.417990\pi$
$480$	14.6454	+	8.01557i	0.668466	+	0.365859i
$481$	−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
$486$	−1.74232	−	15.2024i	−0.0790333	−	0.689597i
$487$	−6.74782	+	11.6876i	−0.305773	+	0.529614i	−0.977433	−	0.211245i	$-0.932248\pi$
$487$	−6.74782	+	11.6876i	−0.305773	+	0.529614i	0.671660	+	0.740859i	$0.265582\pi$
$488$	11.1599			0.505184
$489$	0.999224	+	1.64294i	0.0451865	+	0.0742965i
$490$		0			0
$491$	−7.07098	+	4.08243i	−0.319109	+	0.184238i	−0.650995	−	0.759082i	$-0.725648\pi$
$491$	−7.07098	+	4.08243i	−0.319109	+	0.184238i	0.331886	+	0.943319i	$0.392315\pi$
$492$	−1.70149	−	2.79762i	−0.0767089	−	0.126126i
$493$	0.879342	−	0.507688i	0.0396036	−	0.0228651i
$494$	−28.0308	−	16.1836i	−1.26116	−	0.728134i
$495$	−1.05271	−	23.0475i	−0.0473159	−	1.03591i
$496$		−	3.64269i		−	0.163562i
$497$		0			0
$498$	−13.0740	−	7.15558i	−0.585862	−	0.320649i
$499$	14.0097	−	24.2655i	0.627159	−	1.08627i	−0.360960	−	0.932581i	$-0.617551\pi$
$499$	14.0097	−	24.2655i	0.627159	−	1.08627i	0.988119	−	0.153690i	$-0.0491158\pi$
$500$	−12.5973			−0.563367
$501$	12.6154	+	20.7424i	0.563613	+	0.926703i
$502$		−	21.7658i		−	0.971455i
$503$	−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
$506$			17.2987i			0.769022i
$507$	−2.88196	+	5.26567i	−0.127993	+	0.233857i
$508$	−10.4977			−0.465758
$509$	−7.01957	+	12.1582i	−0.311137	+	0.538905i	−0.978609	−	0.205730i	$-0.934043\pi$
$509$	−7.01957	+	12.1582i	−0.311137	+	0.538905i	0.667472	+	0.744635i	$0.267376\pi$
$510$	−4.43098	+	2.69488i	−0.196207	+	0.119331i
$511$		0			0
$512$		−	9.45558i		−	0.417882i
$513$	35.0365	−	23.5638i	1.54690	−	1.04037i
$514$	−3.44968	−	1.99168i	−0.152159	−	0.0878490i
$515$	−2.67011	+	1.54159i	−0.117659	+	0.0679305i
$516$	6.09528	−	11.1368i	0.268330	−	0.490269i
$517$	−28.1014	+	16.2243i	−1.23590	+	0.713546i
$518$		0			0
$519$	12.3250	−	0.281330i	0.541007	−	0.0123490i
$520$	−22.7526			−0.997765
$521$	19.2229	−	33.2950i	0.842170	−	1.45868i	−0.0458870	−	0.998947i	$-0.514611\pi$
$521$	19.2229	−	33.2950i	0.842170	−	1.45868i	0.888057	−	0.459734i	$-0.152055\pi$
$522$	0.848226	−	1.63746i	0.0371258	−	0.0716696i
$523$	−9.08734	+	5.24658i	−0.397362	+	0.229417i	−0.685345	−	0.728219i	$-0.740349\pi$
$523$	−9.08734	+	5.24658i	−0.397362	+	0.229417i	0.287983	+	0.957635i	$0.407015\pi$
$524$	−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
$528$	−5.16042	+	3.13852i	−0.224578	+	0.136587i
$529$	−2.20889	−	3.82591i	−0.0960388	−	0.166344i
$530$	7.72935	+	13.3876i	0.335741	+	0.581521i
$531$	24.4974	−	1.11894i	1.06309	−	0.0485576i
$532$		0			0
$533$	6.40998	+	3.70080i	0.277647	+	0.160300i
$534$	14.2470	−	8.66489i	0.616527	−	0.374967i
$535$			6.46284i			0.279413i
$536$			37.3506i			1.61330i
$537$	−9.12026	−	4.99163i	−0.393568	−	0.215405i
$538$	−8.47388	−	4.89240i	−0.365335	−	0.210926i
$539$		0			0
$540$	4.45339	−	9.09968i	0.191644	−	0.391588i
$541$	−22.5783	−	39.1067i	−0.970715	−	1.68133i	−0.693405	−	0.720548i	$-0.743890\pi$
$541$	−22.5783	−	39.1067i	−0.970715	−	1.68133i	−0.277311	−	0.960780i	$-0.589443\pi$
$542$	9.34112	+	16.1793i	0.401236	+	0.694960i
$543$	0.0514949	+	2.25598i	0.00220986	+	0.0968133i
$544$	−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	−0.939634	−	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
$549$	−0.512517	−	11.2208i	−0.0218737	−	0.478890i
$550$	2.93166	−	5.07779i	0.125007	−	0.216518i
$551$	5.08854			0.216779
$552$	−10.6845	+	19.5217i	−0.454762	+	0.830901i
$553$		0			0
$554$	−13.2818	+	7.66827i	−0.564291	+	0.325794i
$555$	−25.8694	+	0.590494i	−1.09809	+	0.0250651i
$556$	−5.95311	+	3.43703i	−0.252468	+	0.145763i
$557$	14.0925	+	8.13633i	0.597120	+	0.344747i	0.767908	−	0.640561i	$-0.221298\pi$
$557$	14.0925	+	8.13633i	0.597120	+	0.344747i	−0.170788	+	0.985308i	$0.554631\pi$
$558$	−12.5629	+	0.573818i	−0.531828	+	0.0242916i
$559$			28.6978i			1.21379i
$560$		0			0
$561$	0.262001	+	11.4782i	0.0110617	+	0.484610i
$562$	11.8324	−	20.4942i	0.499118	−	0.864498i
$563$	−10.2719			−0.432908			−0.216454	−	0.976293i	$-0.569449\pi$
$563$	−10.2719			−0.432908			−0.216454	+	0.976293i	$0.569449\pi$
$564$	−14.2449	+	0.325154i	−0.599818	+	0.0136914i
$565$			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	$0.857763\pi$
$570$	−25.9834	+	0.593097i	−1.08833	+	0.0248421i
$571$	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
$573$	0.226595	+	9.92706i	0.00946614	+	0.414709i
$574$		0			0
$575$		−	6.29836i		−	0.262660i
$576$	−20.1861	+	0.922018i	−0.841090	+	0.0384174i
$577$	−14.6609	−	8.46446i	−0.610340	−	0.352380i	0.162758	−	0.986666i	$-0.447961\pi$
$577$	−14.6609	−	8.46446i	−0.610340	−	0.352380i	−0.773099	+	0.634286i	$0.781294\pi$
$578$	−12.2168	+	7.05338i	−0.508153	+	0.293382i
$579$	−2.69963	+	0.0616216i	−0.112193	+	0.00256091i
$580$	1.05736	−	0.610467i	0.0439045	−	0.0253483i
$581$		0			0
$582$	10.7999	−	19.7326i	0.447669	−	0.817943i
$583$	34.2228			1.41736
$584$	−5.64730	+	9.78141i	−0.233687	+	0.404758i
$585$	1.04491	+	22.8767i	0.0432017	+	0.945834i
$586$	−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
$590$	−13.0725	−	7.54743i	−0.538187	−	0.310723i
$591$	0.772738	+	33.8534i	0.0317862	+	1.39254i
$592$	3.38705	+	5.86654i	0.139207	+	0.241113i
$593$	19.2908	+	33.4126i	0.792178	+	1.37209i	0.924616	+	0.380902i	$0.124386\pi$
$593$	19.2908	+	33.4126i	0.792178	+	1.37209i	−0.132437	+	0.991191i	$0.542280\pi$
$594$	11.6370	+	17.3028i	0.477471	+	0.709941i
$595$		0			0
$596$	15.2378	+	8.79752i	0.624163	+	0.360360i
$597$	1.48352	+	0.811947i	0.0607164	+	0.0332308i
$598$		−	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	$-0.242828\pi$
$600$	6.44468	−	3.91960i	0.263103	−	0.160017i
$601$	−27.4855	−	15.8688i	−1.12116	−	0.647300i	−0.179461	−	0.983765i	$-0.557435\pi$
$601$	−27.4855	−	15.8688i	−1.12116	−	0.647300i	−0.941696	+	0.336465i	$0.890769\pi$
$602$		0			0
$603$	37.5544	−	1.71533i	1.52933	−	0.0698534i
$604$	−1.01124	−	1.75153i	−0.0411469	−	0.0712686i
$605$	5.37320	+	9.30666i	0.218452	+	0.378370i
$606$	−1.52499	+	0.927487i	−0.0619486	+	0.0376766i
$607$	0.169355	+	0.0977772i	0.00687391	+	0.00396865i	0.503433	−	0.864034i	$-0.332070\pi$
$607$	0.169355	+	0.0977772i	0.00687391	+	0.00396865i	−0.496559	+	0.868003i	$0.665403\pi$
$608$	−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
$612$	−2.31892	+	4.47656i	−0.0937367	+	0.180954i
$613$	−1.46664	+	2.54029i	−0.0592370	+	0.102602i	−0.894123	−	0.447821i	$-0.852200\pi$
$613$	−1.46664	+	2.54029i	−0.0592370	+	0.102602i	0.834886	+	0.550423i	$0.185533\pi$
$614$	−2.63912			−0.106506
$615$	5.94180	−	0.135627i	0.239596	−	0.00546902i
$616$		0			0
$617$	−7.86982	+	4.54365i	−0.316827	+	0.182920i	−0.649977	−	0.759953i	$-0.725222\pi$
$617$	−7.86982	+	4.54365i	−0.316827	+	0.182920i	0.333150	+	0.942874i	$0.391888\pi$
$618$	1.33785	−	2.44440i	0.0538161	−	0.0983282i
$619$	−24.8586	+	14.3521i	−0.999152	+	0.576861i	−0.907997	−	0.418976i	$-0.862389\pi$
$619$	−24.8586	+	14.3521i	−0.999152	+	0.576861i	−0.0911550	+	0.995837i	$0.529056\pi$
$620$	−7.21068	−	4.16309i	−0.289588	−	0.167194i
$621$	20.1189	+	9.84623i	0.807345	+	0.395116i
$622$		−	10.8717i		−	0.435916i
$623$		0			0
$624$	5.12217	−	3.11526i	0.205051	−	0.124710i
$625$	7.77986	−	13.4751i	0.311194	−	0.539004i
$626$	−16.4321			−0.656758
$627$	−27.6243	+	50.4726i	−1.10321	+	2.01568i
$628$		−	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
$633$	−21.5561	−	35.4430i	−0.856779	−	1.40873i
$634$	−2.88781			−0.114689
$635$	9.52711	−	16.5014i	0.378072	−	0.654839i
$636$	13.1824	+	7.21487i	0.522716	+	0.286088i
$637$		0			0
$638$			2.51297i			0.0994895i
$639$	1.98441	+	43.4455i	0.0785019	+	1.71868i
$640$	−5.92345	−	3.41990i	−0.234145	−	0.135184i
$641$	−39.7733	+	22.9632i	−1.57095	+	0.906990i	−0.574900	+	0.818224i	$0.694959\pi$
$641$	−39.7733	+	22.9632i	−1.57095	+	0.906990i	−0.996052	+	0.0887664i	$0.971708\pi$
$642$	−3.03522	−	4.99057i	−0.119791	−	0.196962i
$643$	9.15428	−	5.28523i	0.361010	−	0.208429i	−0.308514	−	0.951220i	$-0.599832\pi$
$643$	9.15428	−	5.28523i	0.361010	−	0.208429i	0.669524	+	0.742791i	$0.266498\pi$
$644$		0			0
$645$	11.9743	+	19.6884i	0.471488	+	0.775230i
$646$	12.9336			0.508866
$647$	19.2562	−	33.3526i	0.757038	−	1.31123i	−0.187317	−	0.982299i	$-0.559979\pi$
$647$	19.2562	−	33.3526i	0.757038	−	1.31123i	0.944355	−	0.328928i	$-0.106687\pi$
$648$	2.44545	+	26.7138i	0.0960664	+	1.04942i
$649$	−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	$-0.252743\pi$
$653$	11.0867	+	6.40089i	0.433855	+	0.250486i	−0.267133	+	0.963660i	$0.586076\pi$
$654$	5.50431	+	3.01257i	0.215236	+	0.117801i
$655$	−4.68137	−	8.10837i	−0.182916	−	0.316820i
$656$	−0.777952	−	1.34745i	−0.0303739	−	0.0526092i
$657$	10.0941	+	5.22890i	0.393809	+	0.203999i
$658$		0			0
$659$	41.5777	+	24.0049i	1.61964	+	0.935097i	0.987014	+	0.160636i	$0.0513546\pi$
$659$	41.5777	+	24.0049i	1.61964	+	0.935097i	0.632622	+	0.774461i	$0.281979\pi$
$660$	0.315042	+	13.8019i	0.0122630	+	0.537238i
$661$		−	10.8312i		−	0.421285i	−0.977563	−	0.210643i	$-0.932444\pi$
$661$		−	10.8312i		−	0.421285i	0.977563	−	0.210643i	$-0.0675557\pi$
$662$			4.79182i			0.186239i
$663$	−0.260059	−	11.3931i	−0.0100998	−	0.442472i
$664$	22.6276	+	13.0640i	0.878121	+	0.506983i
$665$		0			0
$666$	19.6989	−	12.6053i	0.763315	−	0.488446i
$667$	1.34971	+	2.33777i	0.0522611	+	0.0905188i
$668$	−7.26354	−	12.5808i	−0.281035	−	0.486767i
$669$	4.70876	+	2.57716i	0.182051	+	0.0996387i
$670$	−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	−0.960376	−	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
$675$	−4.23696	−	6.29983i	−0.163081	−	0.242481i
$676$	1.79595	−	3.11068i	0.0690752	−	0.119642i
$677$	−28.9895			−1.11416			−0.557078	−	0.830460i	$-0.688078\pi$
$677$	−28.9895			−1.11416			−0.557078	+	0.830460i	$0.688078\pi$
$678$	−15.3900	−	25.3045i	−0.591048	−	0.971813i
$679$		0			0
$680$	7.87364	−	4.54585i	0.301940	−	0.174325i
$681$	19.6191	+	32.2581i	0.751805	+	1.23613i
$682$	14.8413	−	8.56862i	0.568302	−	0.328109i
$683$	−0.132048	−	0.0762380i	−0.00505268	−	0.00291717i	0.497472	−	0.867480i	$-0.334262\pi$
$683$	−0.132048	−	0.0762380i	−0.00505268	−	0.00291717i	−0.502524	+	0.864563i	$0.667595\pi$
$684$	−21.2813	+	13.6179i	−0.813712	+	0.520695i
$685$		−	1.58145i		−	0.0604242i
$686$		0			0
$687$	−19.6162	−	10.7362i	−0.748404	−	0.409610i
$688$	3.01631	−	5.22441i	0.114996	−	0.199179i
$689$	−33.9691			−1.29412
$690$	−7.16447	−	11.7800i	−0.272747	−	0.448455i
$691$			43.2353i			1.64475i	0.568948	+	0.822373i	$0.307350\pi$
$691$			43.2353i			1.64475i	−0.568948	+	0.822373i	$0.692650\pi$
$692$	−7.37691			−0.280428
$693$		0			0
$694$	2.11225			0.0801799
$695$		−	12.4771i		−	0.473282i
$696$	−1.55213	+	2.83591i	−0.0588332	+	0.107495i
$697$	−2.95761			−0.112027
$698$	−14.3339	+	24.8271i	−0.542546	+	0.939718i
$699$	1.19573	−	0.727234i	0.0452267	−	0.0275065i
$700$		0			0
$701$		−	11.5821i		−	0.437451i	−0.975786	−	0.218726i	$-0.929810\pi$
$701$		−	11.5821i		−	0.437451i	0.975786	−	0.218726i	$-0.0701900\pi$
$702$	−11.5507	−	17.1745i	−0.435954	−	0.648210i
$703$	55.8863	+	32.2660i	2.10779	+	1.21693i
$704$	23.8472	−	13.7682i	0.898774	−	0.518907i
$705$	12.4168	−	22.6869i	0.467643	−	0.854437i
$706$	−9.21116	+	5.31807i	−0.346667	+	0.200148i
$707$		0			0
$708$	−14.6701	+	0.334860i	−0.551337	+	0.0125848i
$709$	−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
$711$	25.0579	−	1.14454i	0.939743	−	0.0429235i
$712$	−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
$717$	−20.8526	+	12.6824i	−0.778754	+	0.473631i
$718$	10.2821	+	17.8091i	0.383724	+	0.664630i
$719$	23.3158	+	40.3842i	0.869534	+	1.50608i	0.862474	+	0.506102i	$0.168914\pi$
$719$	23.3158	+	40.3842i	0.869534	+	1.50608i	0.00706058	+	0.999975i	$0.497753\pi$
$720$	2.21425	−	4.27450i	0.0825202	−	0.159301i
$721$		0			0
$722$	39.9806	+	23.0828i	1.48792	+	0.859054i
$723$	27.3755	−	16.6495i	1.01811	−	0.619203i
$724$		−	1.35028i		−	0.0501826i
$725$		−	0.914958i		−	0.0339807i
$726$	−8.51995	−	4.66307i	−0.316205	−	0.173063i
$727$	−3.72659	−	2.15155i	−0.138212	−	0.0797965i	0.429300	−	0.903162i	$-0.358760\pi$
$727$	−3.72659	−	2.15155i	−0.138212	−	0.0797965i	−0.567511	+	0.823366i	$0.692094\pi$
$728$		0			0
$729$	26.7473	−	3.68562i	0.990639	−	0.136505i
$730$	−3.49875	−	6.06002i	−0.129495	−	0.224291i
$731$	−5.73369	−	9.93104i	−0.212068	−	0.367313i
$732$	0.153379	+	6.71949i	0.00566905	+	0.248360i
$733$	−12.1337	−	7.00539i	−0.448168	−	0.258750i	0.258888	−	0.965907i	$-0.416644\pi$
$733$	−12.1337	−	7.00539i	−0.448168	−	0.258750i	−0.707056	+	0.707157i	$0.749977\pi$
$734$	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
$738$	−4.52452	+	2.89525i	−0.166550	+	0.106575i
$739$	−18.9313	+	32.7901i	−0.696401	+	1.20620i	0.273305	+	0.961927i	$0.411883\pi$
$739$	−18.9313	+	32.7901i	−0.696401	+	1.20620i	−0.969706	+	0.244274i	$0.921450\pi$
$740$	15.4837			0.569191
$741$	27.4195	−	50.0985i	1.00728	−	1.84041i
$742$		0			0
$743$	−24.0489	+	13.8847i	−0.882269	+	0.509378i	−0.871406	−	0.490563i	$-0.836791\pi$
$743$	−24.0489	+	13.8847i	−0.882269	+	0.509378i	−0.0108634	+	0.999941i	$0.503458\pi$
$744$	22.0409	−	0.503105i	0.808058	−	0.0184447i
$745$	−27.6579	+	15.9683i	−1.01331	+	0.585034i
$746$	−24.5626	−	14.1812i	−0.899300	−	0.519211i
$747$	12.0961	−	23.3510i	0.442575	−	0.854369i
$748$		−	6.87007i		−	0.251195i
$749$		0			0
$750$	0.471587	+	20.6601i	0.0172199	+	0.754400i
$751$	8.67540	−	15.0262i	0.316570	−	0.548315i	−0.663200	−	0.748442i	$-0.730802\pi$
$751$	8.67540	−	15.0262i	0.316570	−	0.548315i	0.979770	+	0.200127i	$0.0641355\pi$
$752$	−6.77054			−0.246896
$753$	38.3953	−	0.876410i	1.39920	−	0.0319382i
$754$		−	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
$759$	−30.5153	+	0.696541i	−1.10763	+	0.0252828i
$760$	45.5628			1.65274
$761$	4.22520	−	7.31825i	0.153163	−	0.265286i	−0.779225	−	0.626744i	$-0.784387\pi$
$761$	4.22520	−	7.31825i	0.153163	−	0.265286i	0.932389	+	0.361457i	$0.117721\pi$
$762$	0.392986	+	17.2166i	0.0142364	+	0.623693i
$763$		0			0
$764$		−	5.94167i		−	0.214962i
$765$	−4.93224	−	7.70783i	−0.178326	−	0.278677i
$766$	21.0840	+	12.1728i	0.761794	+	0.439822i
$767$	28.7257	−	16.5848i	1.03723	−	0.598843i
$768$	29.5074	−	0.673534i	1.06476	−	0.0243041i
$769$	19.8100	−	11.4373i	0.714366	−	0.412440i	−0.0983092	−	0.995156i	$-0.531343\pi$
$769$	19.8100	−	11.4373i	0.714366	−	0.412440i	0.812676	+	0.582716i	$0.198010\pi$
$770$		0			0
$771$	3.37445	−	6.16550i	0.121528	−	0.222045i
$772$	1.61581			0.0581544
$773$	−18.8374	+	32.6273i	−0.677533	+	1.17352i	0.298189	+	0.954507i	$0.403618\pi$
$773$	−18.8374	+	32.6273i	−0.677533	+	1.17352i	−0.975722	+	0.219015i	$0.929716\pi$
$774$	−18.4930	−	9.57963i	−0.664717	−	0.344333i
$775$	−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
$780$	−0.312706	−	13.6996i	−0.0111967	−	0.490524i
$781$	−29.6324	−	51.3249i	−1.06033	−	1.83655i
$782$	3.43058	+	5.94194i	0.122677	+	0.212483i
$783$	2.92266	+	1.43035i	0.104447	+	0.0511167i
$784$		0			0
$785$	15.5116	+	8.95561i	0.553632	+	0.319639i
$786$	7.42296	+	4.06267i	0.264768	+	0.144911i
$787$		−	23.4661i		−	0.836475i	−0.908338	−	0.418237i	$-0.862648\pi$
$787$		−	23.4661i		−	0.836475i	0.908338	−	0.418237i	$-0.137352\pi$
$788$		−	20.2624i		−	0.721818i
$789$	−14.7402	+	8.96488i	−0.524766	+	0.319158i
$790$	−13.3716	−	7.72011i	−0.475741	−	0.274669i
$791$		0			0
$792$	−19.7030	−	30.7907i	−0.700116	−	1.09410i
$793$	−7.59650	−	13.1575i	−0.269760	−	0.467237i
$794$	10.9256	+	18.9237i	0.387734	+	0.671575i
$795$	−23.3048	+	14.1738i	−0.826536	+	0.502692i
$796$	−0.876386	−	0.505981i	−0.0310627	−	0.0179340i
$797$	−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
$801$	15.8587	+	24.7831i	0.560340	+	0.875667i
$802$	−3.01448	+	5.22123i	−0.106445	+	0.184368i
$803$	−15.4912			−0.546674
$804$	−22.4893	+	0.513339i	−0.793135	+	0.0181041i
$805$		0			0
$806$	−14.7313	+	8.50510i	−0.518887	+	0.299579i
$807$	8.28908	−	15.1451i	0.291789	−	0.533132i
$808$	2.70984	−	1.56453i	0.0953317	−	0.0550398i
$809$	11.4669	+	6.62041i	0.403154	+	0.232761i	0.687844	−	0.725858i	$-0.258557\pi$
$809$	11.4669	+	6.62041i	0.403154	+	0.232761i	−0.284690	+	0.958620i	$0.591891\pi$
$810$	−15.0906	−	6.96312i	−0.530230	−	0.244659i
$811$		−	56.0437i		−	1.96796i	−0.178275	−	0.983981i	$-0.557052\pi$
$811$		−	56.0437i		−	1.96796i	0.178275	−	0.983981i	$-0.442948\pi$
$812$		0			0
$813$	−28.1645	+	17.1294i	−0.987771	+	0.600754i
$814$	−15.9345	+	27.5994i	−0.558505	+	0.967359i
$815$	2.08853			0.0731579
$816$	−1.15014	+	2.10144i	−0.0402629	+	0.0735650i
$817$		−	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	$-0.440934\pi$
$822$	0.742716	+	1.22119i	0.0259052	+	0.0425938i
$823$	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
$825$	9.07537	+	4.96705i	0.315964	+	0.172931i
$826$		0			0
$827$			45.7715i			1.59163i	0.605539	+	0.795816i	$0.292958\pi$
$827$			45.7715i			1.59163i	−0.605539	+	0.795816i	$0.707042\pi$
$828$	−11.9011	−	6.16495i	−0.413593	−	0.214247i
$829$	−30.5567	−	17.6419i	−1.06128	−	0.612730i	−0.135493	−	0.990778i	$-0.543262\pi$
$829$	−30.5567	−	17.6419i	−1.06128	−	0.612730i	−0.925786	+	0.378049i	$0.876595\pi$
$830$	−14.0188	+	8.09376i	−0.486600	+	0.280938i
$831$	−14.0618	−	23.1207i	−0.487798	−	0.802047i
$832$	−23.6704	+	13.6661i	−0.820623	+	0.473787i
$833$		0			0
$834$	5.85975	+	9.63472i	0.202907	+	0.333623i
$835$	26.3680			0.912502
$836$	17.2146	−	29.8166i	0.595380	−	1.03123i
$837$	−1.51808	−	22.1380i	−0.0524724	−	0.765202i
$838$	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
$842$	22.6670	+	13.0868i	0.781157	+	0.451001i
$843$	36.6287	+	20.0473i	1.26156	+	0.690466i
$844$	12.4114	+	21.4971i	0.427216	+	0.739960i
$845$	3.25982	+	5.64618i	0.112141	+	0.194235i
$846$	1.06653	+	23.3501i	0.0366682	+	0.802793i
$847$		0			0
$848$	6.18404	+	3.57036i	0.212361	+	0.122607i
$849$	0.119280	+	5.22561i	0.00409367	+	0.179342i
$850$		−	2.32556i		−	0.0797661i
$851$			34.2336i			1.17351i
$852$	−0.593866	−	26.0171i	−0.0203455	−	0.891332i
$853$	47.7652	+	27.5772i	1.63545	+	0.944227i	0.982372	+	0.186935i	$0.0598554\pi$
$853$	47.7652	+	27.5772i	1.63545	+	0.944227i	0.653077	+	0.757292i	$0.273478\pi$
$854$		0			0
$855$	−2.09247	−	45.8114i	−0.0715610	−	1.56672i
$856$	5.11994	+	8.86800i	0.174996	+	0.303102i
$857$	19.0771	+	33.0425i	0.651660	+	1.12871i	0.982720	+	0.185099i	$0.0592606\pi$
$857$	19.0771	+	33.0425i	0.651660	+	1.12871i	−0.331059	+	0.943610i	$0.607406\pi$
$858$	24.7411	+	13.5411i	0.844648	+	0.462286i
$859$	35.0465	+	20.2341i	1.19577	+	0.690378i	0.959609	−	0.281336i	$-0.0907776\pi$
$859$	35.0465	+	20.2341i	1.19577	+	0.690378i	0.236160	+	0.971714i	$0.424111\pi$
$860$	−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	$-0.877982\pi$
$863$	−31.3519	+	18.1011i	−1.06723	+	0.616167i	−0.139808	+	0.990179i	$0.544649\pi$
$864$	−1.82146	−	26.5622i	−0.0619673	−	0.903666i
$865$	6.69488	−	11.5959i	0.227633	−	0.394272i
$866$	8.81216			0.299449
$867$	−12.9342	−	21.2667i	−0.439269	−	0.722255i
$868$		0			0
$869$	−29.6024	+	17.0910i	−1.00419	+	0.579771i
$870$	−1.04078	−	1.71127i	−0.0352856	−	0.0580173i
$871$	44.0365	−	25.4245i	1.49212	−	0.861475i
$872$	−9.52645	−	5.50010i	−0.322606	−	0.186257i
$873$	35.2436	+	18.2567i	1.19281	+	0.617894i
$874$			34.3846i			1.16307i
$875$		0			0
$876$	−5.96712	−	3.26587i	−0.201610	−	0.110344i
$877$	5.53439	−	9.58584i	0.186883	−	0.323691i	−0.757326	−	0.653036i	$-0.773495\pi$
$877$	5.53439	−	9.58584i	0.186883	−	0.323691i	0.944209	+	0.329346i	$0.106828\pi$
$878$	16.2101			0.547064
$879$	−26.8635	−	44.1694i	−0.906082	−	1.48980i
$880$			6.55998i			0.221137i
$881$	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	$0.576744\pi$
$884$			6.81915i			0.229353i
$885$	12.7874	−	23.3641i	0.429845	−	0.785375i
$886$	1.04413			0.0350782
$887$	19.5180	−	33.8062i	0.655350	−	1.13510i	−0.326456	−	0.945213i	$-0.605854\pi$
$887$	19.5180	−	33.8062i	0.655350	−	1.13510i	0.981806	−	0.189887i	$-0.0608123\pi$
$888$	−35.0289	+	21.3043i	−1.17549	+	0.714925i
$889$		0			0
$890$		−	18.1109i		−	0.607080i
$891$	−30.0538	+	21.2246i	−1.00684	+	0.711050i
$892$	−2.78169	−	1.60601i	−0.0931378	−	0.0537732i
$893$	−55.8570	+	32.2490i	−1.86918	+	1.07917i
$894$	13.8579	−	25.3200i	0.463478	−	0.846826i
$895$	−9.77931	+	5.64609i	−0.326886	+	0.188728i
$896$		0			0
$897$	30.2891	−	0.691378i	1.01132	−	0.0230844i
$898$	−15.6157			−0.521103
$899$	1.33711	−	2.31595i	0.0445952	−	0.0772411i
$900$	2.44861	+	3.82655i	0.0816204	+	0.127552i
$901$	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
$906$	−2.83473	+	1.72406i	−0.0941775	+	0.0572779i
$907$	−4.93487	−	8.54745i	−0.163860	−	0.283813i	0.772390	−	0.635148i	$-0.219061\pi$
$907$	−4.93487	−	8.54745i	−0.163860	−	0.283813i	−0.936250	+	0.351335i	$0.885728\pi$
$908$	−11.2961	−	19.5654i	−0.374873	−	0.649300i
$909$	−1.69751	−	2.65277i	−0.0563028	−	0.0879868i
$910$		0			0
$911$	−46.6335	−	26.9239i	−1.54504	−	0.892028i	−0.998509	−	0.0545881i	$-0.982615\pi$
$911$	−46.6335	−	26.9239i	−1.54504	−	0.892028i	−0.546529	−	0.837440i	$-0.684051\pi$
$912$	−10.2573	+	6.23842i	−0.339654	+	0.206575i
$913$			35.8363i			1.18601i
$914$		−	32.1898i		−	1.06475i
$915$	−10.7017	−	5.85715i	−0.353787	−	0.193632i
$916$	11.5882	+	6.69046i	0.382885	+	0.221059i
$917$		0			0
$918$	7.42857	+	3.63555i	0.245179	+	0.119991i
$919$	−11.0899	−	19.2084i	−0.365824	−	0.633625i	0.623084	−	0.782155i	$-0.285879\pi$
$919$	−11.0899	−	19.2084i	−0.365824	−	0.633625i	−0.988908	+	0.148530i	$0.952546\pi$
$920$	12.0853	+	20.9324i	0.398442	+	0.690122i
$921$	−0.106265	−	4.65545i	−0.00350156	−	0.153402i
$922$	−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
$927$	4.36584	+	2.26157i	0.143393	+	0.0742796i
$928$	1.60433	−	2.77878i	0.0526647	−	0.0912180i
$929$	54.9907			1.80419			0.902093	−	0.431541i	$-0.142030\pi$
$929$	54.9907			1.80419			0.902093	+	0.431541i	$0.142030\pi$
$930$	−6.55772	+	11.9817i	−0.215036	+	0.392895i
$931$		0			0
$932$	−0.725243	+	0.418719i	−0.0237561	+	0.0137156i
$933$	19.1779	−	0.437754i	0.627856	−	0.0143314i
$934$	−12.7734	+	7.37475i	−0.417960	+	0.241309i
$935$	10.7992	+	6.23491i	0.353171	+	0.203903i
$936$	19.5570	+	30.5625i	0.639239	+	0.998966i
$937$			29.3132i			0.957622i	0.877918	+	0.478811i	$0.158932\pi$
$937$			29.3132i			0.957622i	−0.877918	+	0.478811i	$0.841068\pi$
$938$		0			0
$939$	−0.661646	−	28.9865i	−0.0215920	−	0.945940i
$940$	−7.73777	+	13.4022i	−0.252378	+	0.437132i
$941$	15.1752			0.494696			0.247348	−	0.968927i	$-0.420441\pi$
$941$	15.1752			0.494696			0.247348	+	0.968927i	$0.420441\pi$
$942$	−16.1839	+	0.369413i	−0.527299	+	0.0120361i
$943$		−	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	$-0.0135890\pi$
$948$	−15.0058	+	0.342521i	−0.487365	+	0.0111246i
$949$	15.3764			0.499139
$950$	5.82725	−	10.0931i	0.189061	−	0.327463i
$951$	−0.116279	−	5.09415i	−0.00377060	−	0.165189i
$952$		0			0
$953$		−	40.5520i		−	1.31361i	−0.754061	−	0.656805i	$-0.771908\pi$
$953$		−	40.5520i		−	1.31361i	0.754061	−	0.656805i	$-0.228092\pi$
$954$	11.3392	−	21.8898i	0.367121	−	0.708709i
$955$	9.33981	+	5.39234i	0.302229	+	0.174492i
$956$	12.6476	−	7.30212i	0.409054	−	0.236167i
$957$	−4.43293	+	0.101186i	−0.143296	+	0.00327088i
$958$	26.4214	−	15.2544i	0.853637	−	0.492847i
$959$		0			0
$960$	−10.5370	+	19.2523i	−0.340081	+	0.621366i
$961$	12.7631			0.411713
$962$	15.8164	−	27.3948i	0.509942	−	0.883245i
$963$	8.68124	−	5.55513i	0.279749	−	0.179012i
$964$	−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	$0.766569\pi$
$968$	14.7457	+	8.51343i	0.473945	+	0.273632i
$969$	0.520778	+	22.8151i	0.0167298	+	0.732927i
$970$	−12.2159	−	21.1585i	−0.392228	−	0.679359i
$971$	8.26077	+	14.3081i	0.265101	+	0.459168i	0.967590	−	0.252526i	$-0.0812614\pi$
$971$	8.26077	+	14.3081i	0.265101	+	0.459168i	−0.702489	+	0.711694i	$0.747928\pi$
$972$	−16.0511	+	1.83958i	−0.514839	+	0.0590047i
$973$		0			0
$974$	−11.4728	−	6.62381i	−0.367611	−	0.212240i
$975$	−9.00810	−	4.93024i	−0.288490	−	0.157894i
$976$			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	$0.967564\pi$
$978$	−1.61275	+	0.980860i	−0.0515700	+	0.0313644i
$979$	−34.7227	−	20.0472i	−1.10974	−	0.640711i
$980$		0			0
$981$	−5.09261	+	9.83102i	−0.162594	+	0.313880i
$982$	−4.00740	−	6.94103i	−0.127881	−	0.221497i
$983$	−1.11487	−	1.93102i	−0.0355590	−	0.0615899i	0.847698	−	0.530479i	$-0.177988\pi$
$983$	−1.11487	−	1.93102i	−0.0355590	−	0.0615899i	−0.883257	+	0.468889i	$0.844654\pi$
$984$	8.04560	−	4.89326i	0.256484	−	0.155992i
$985$	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
$990$	22.6239	−	1.03337i	0.719036	−	0.0328425i
$991$	24.7285	−	42.8310i	0.785527	−	1.36057i	−0.143157	−	0.989700i	$-0.545726\pi$
$991$	24.7285	−	42.8310i	0.785527	−	1.36057i	0.928684	−	0.370872i	$-0.120941\pi$
$992$	−21.8815			−0.694738
$993$	−8.45286	+	0.192945i	−0.268243	+	0.00612292i
$994$		0			0
$995$	1.59072	−	0.918403i	0.0504293	−	0.0291153i
$996$	−7.55503	+	13.8039i	−0.239390	+	0.437393i
$997$	−7.28219	+	4.20437i	−0.230629	+	0.133154i	−0.610862	−	0.791737i	$-0.709177\pi$
$997$	−7.28219	+	4.20437i	−0.230629	+	0.133154i	0.380233	+	0.924891i	$0.375844\pi$
$998$	23.8195	+	13.7522i	0.753993	+	0.435318i
$999$	23.0292	+	34.2416i	0.728612	+	1.08336i

Twists

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

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

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.981621i q^{2} +(-1.73160 + 0.0395255i) q^{3} +1.03642 q^{4} +(-0.940599 + 1.62916i) q^{5} +(-0.0387990 - 1.69978i) q^{6} +2.98061i q^{8} +(2.99688 - 0.136885i) q^{9} +(-1.59922 - 0.923312i) q^{10} +(-3.54040 + 2.04405i) q^{11} +(-1.79466 + 0.0409650i) q^{12} +(3.51415 - 2.02890i) q^{13} +(1.56435 - 2.85824i) q^{15} -0.852996 q^{16} +(-0.810727 + 1.40422i) q^{17} +(0.134369 + 2.94180i) q^{18} +(-7.03722 + 4.06294i) q^{19} +(-0.974855 + 1.68850i) q^{20} +(-2.00648 - 3.47533i) q^{22} +(-3.73318 - 2.15535i) q^{23} +(-0.117810 - 5.16123i) q^{24} +(0.730548 + 1.26535i) q^{25} +(1.99161 + 3.44957i) q^{26} +(-5.18398 + 0.355482i) q^{27} +(-0.542317 - 0.313107i) q^{29} +(2.80571 + 1.53560i) q^{30} +4.27047i q^{31} +5.12391i q^{32} +(6.04976 - 3.67941i) q^{33} +(-1.37841 - 0.795827i) q^{34} +(3.10602 - 0.141870i) q^{36} +(-3.97076 - 6.87757i) q^{37} +(-3.98827 - 6.90789i) q^{38} +(-6.00491 + 3.65214i) q^{39} +(-4.85591 - 2.80356i) q^{40} +(0.912023 + 1.57967i) q^{41} +(-3.53614 + 6.12477i) q^{43} +(-3.66933 + 2.11849i) q^{44} +(-2.59585 + 5.01116i) q^{45} +(2.11574 - 3.66457i) q^{46} +7.93736 q^{47} +(1.47705 - 0.0337151i) q^{48} +(-1.24209 + 0.717122i) q^{50} +(1.34835 - 2.46359i) q^{51} +(3.64214 - 2.10279i) q^{52} +(-7.24978 - 4.18567i) q^{53} +(-0.348949 - 5.08870i) q^{54} -7.69052i q^{55} +(12.0251 - 7.31354i) q^{57} +(0.307352 - 0.532350i) q^{58} +8.17430 q^{59} +(1.62132 - 2.96233i) q^{60} -3.74415i q^{61} -4.19198 q^{62} -6.73573 q^{64} +7.63351i q^{65} +(3.61179 + 5.93857i) q^{66} +12.5312 q^{67} +(-0.840253 + 1.45536i) q^{68} +(6.54957 + 3.58466i) q^{69} +14.4969i q^{71} +(0.408000 + 8.93253i) q^{72} +(3.28167 + 1.89468i) q^{73} +(6.75117 - 3.89779i) q^{74} +(-1.31503 - 2.16220i) q^{75} +(-7.29351 + 4.21091i) q^{76} +(-3.58501 - 5.89455i) q^{78} +8.36133 q^{79} +(0.802327 - 1.38967i) q^{80} +(8.96253 - 0.820452i) q^{81} +(-1.55064 + 0.895261i) q^{82} +(4.38300 - 7.59159i) q^{83} +(-1.52514 - 2.64162i) q^{85} +(-6.01221 - 3.47115i) q^{86} +(0.951451 + 0.520740i) q^{87} +(-6.09252 - 10.5526i) q^{88} +(4.90379 + 8.49362i) q^{89} +(-4.91906 - 2.54814i) q^{90} +(-3.86914 - 2.23385i) q^{92} +(-0.168792 - 7.39474i) q^{93} +7.79148i q^{94} -15.2864i q^{95} +(-0.202525 - 8.87256i) q^{96} +(11.4579 + 6.61525i) q^{97} +(-10.3303 + 6.61038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60}+ \cdots - 72 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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