LMFDB - Embedded newform 441.2.s.d.374.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(362,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.362"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.s (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			374.15
Character	$\chi$	$=$	441.374
Dual form			441.2.s.d.362.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.850109 + 0.490811i) q^{2} +(-0.831570 - 1.51937i) q^{3} +(-0.518210 - 0.897565i) q^{4} -1.88120 q^{5} +(0.0387990 - 1.69978i) q^{6} -2.98061i q^{8} +(-1.61698 + 2.52693i) q^{9} +(-1.59922 - 0.923312i) q^{10} +4.08810i q^{11} +(-0.932808 + 1.53374i) q^{12} +(-3.51415 - 2.02890i) q^{13} +(1.56435 + 2.85824i) q^{15} +(0.426498 - 0.738716i) q^{16} +(0.810727 - 1.40422i) q^{17} +(-2.61486 + 1.35453i) q^{18} +(-7.03722 + 4.06294i) q^{19} +(0.974855 + 1.68850i) q^{20} +(-2.00648 + 3.47533i) q^{22} -4.31071i q^{23} +(-4.52866 + 2.47859i) q^{24} -1.46110 q^{25} +(-1.99161 - 3.44957i) q^{26} +(5.18398 + 0.355482i) q^{27} +(-0.542317 + 0.313107i) q^{29} +(-0.0729886 + 3.19761i) q^{30} +(3.69833 - 2.13523i) q^{31} +(-4.43744 + 2.56195i) q^{32} +(6.21134 - 3.39954i) q^{33} +(1.37841 - 0.795827i) q^{34} +(3.10602 + 0.141870i) q^{36} +(-3.97076 - 6.87757i) q^{37} -7.97654 q^{38} +(-0.160386 + 7.02647i) q^{39} +5.60712i q^{40} +(-0.912023 + 1.57967i) q^{41} +(-3.53614 - 6.12477i) q^{43} +(3.66933 - 2.11849i) q^{44} +(3.04186 - 4.75365i) q^{45} +(2.11574 - 3.66457i) q^{46} +(3.96868 - 6.87396i) q^{47} +(-1.47705 - 0.0337151i) q^{48} +(-1.24209 - 0.717122i) q^{50} +(-2.80771 - 0.0640887i) q^{51} +4.20558i q^{52} +(7.24978 + 4.18567i) q^{53} +(4.23247 + 2.84655i) q^{54} -7.69052i q^{55} +(12.0251 + 7.31354i) q^{57} -0.614704 q^{58} +(4.08715 + 7.07915i) q^{59} +(1.75480 - 2.88527i) q^{60} +(3.24253 + 1.87208i) q^{61} +4.19198 q^{62} -6.73573 q^{64} +(6.61081 + 3.81676i) q^{65} +(6.94885 + 0.158614i) q^{66} +(-6.26559 - 10.8523i) q^{67} -1.68051 q^{68} +(-6.54957 + 3.58466i) q^{69} -14.4969i q^{71} +(7.53180 + 4.81960i) q^{72} +(3.28167 + 1.89468i) q^{73} -7.79557i q^{74} +(1.21500 + 2.21995i) q^{75} +(7.29351 + 4.21091i) q^{76} +(-3.58501 + 5.89455i) q^{78} +(-4.18066 + 7.24112i) q^{79} +(-0.802327 + 1.38967i) q^{80} +(-3.77073 - 8.17200i) q^{81} +(-1.55064 + 0.895261i) q^{82} +(-4.38300 - 7.59159i) q^{83} +(-1.52514 + 2.64162i) q^{85} -6.94230i q^{86} +(0.926700 + 0.563611i) q^{87} +12.1850 q^{88} +(-4.90379 - 8.49362i) q^{89} +(4.91906 - 2.54814i) q^{90} +(-3.86914 + 2.23385i) q^{92} +(-6.31964 - 3.84355i) q^{93} +(6.74762 - 3.89574i) q^{94} +(13.2384 - 7.64320i) q^{95} +(7.58260 + 4.61167i) q^{96} +(-11.4579 + 6.61525i) q^{97} +(-10.3303 - 6.61038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65}+ \cdots - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.850109	+	0.490811i	0.601118	+	0.347056i	0.769481	−	0.638669i	$-0.220515\pi$
$2$	0.850109	+	0.490811i	0.601118	+	0.347056i	−0.168363	+	0.985725i	$0.553848\pi$
$3$	−0.831570	−	1.51937i	−0.480107	−	0.877210i
$3$	−0.831570	−	1.51937i	−0.480107	−	0.877210i
$4$	−0.518210	−	0.897565i	−0.259105	−	0.448783i
$5$	−1.88120			−0.841297			−0.420648	−	0.907224i	$-0.638197\pi$
$5$	−1.88120			−0.841297			−0.420648	+	0.907224i	$0.638197\pi$
$6$	0.0387990	−	1.69978i	0.0158396	−	0.693930i
$7$		0			0
$7$		0			0
$8$		−	2.98061i		−	1.05381i
$9$	−1.61698	+	2.52693i	−0.538994	+	0.842309i
$10$	−1.59922	−	0.923312i	−0.505719	−	0.291977i
$11$			4.08810i			1.23261i	0.787508	+	0.616304i	$0.211371\pi$
$11$			4.08810i			1.23261i	−0.787508	+	0.616304i	$0.788629\pi$
$12$	−0.932808	+	1.53374i	−0.269279	+	0.442753i
$13$	−3.51415	−	2.02890i	−0.974651	−	0.562715i	−0.0739997	−	0.997258i	$-0.523576\pi$
$13$	−3.51415	−	2.02890i	−0.974651	−	0.562715i	−0.900651	+	0.434544i	$0.856910\pi$
$14$		0			0
$15$	1.56435	+	2.85824i	0.403913	+	0.737994i
$16$	0.426498	−	0.738716i	0.106625	−	0.184679i
$17$	0.810727	−	1.40422i	0.196630	−	0.340574i	−0.750803	−	0.660526i	$-0.770333\pi$
$17$	0.810727	−	1.40422i	0.196630	−	0.340574i	0.947434	+	0.319952i	$0.103667\pi$
$18$	−2.61486	+	1.35453i	−0.616327	+	0.319266i
$19$	−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
$23$		−	4.31071i		−	0.898845i	−0.893319	−	0.449423i	$-0.851630\pi$
$23$		−	4.31071i		−	0.898845i	0.893319	−	0.449423i	$-0.148370\pi$
$24$	−4.52866	+	2.47859i	−0.924409	+	0.505940i
$25$	−1.46110			−0.292219
$26$	−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	−0.549507	−	0.835489i	$-0.685184\pi$
$29$	−0.542317	+	0.313107i	−0.100706	+	0.0581425i	0.448801	+	0.893632i	$0.351851\pi$
$30$	−0.0729886	+	3.19761i	−0.0133258	+	0.583802i
$31$	3.69833	−	2.13523i	0.664240	−	0.383499i	−0.129650	−	0.991560i	$-0.541385\pi$
$31$	3.69833	−	2.13523i	0.664240	−	0.383499i	0.793891	+	0.608060i	$0.208052\pi$
$32$	−4.43744	+	2.56195i	−0.784435	+	0.452894i
$33$	6.21134	−	3.39954i	1.08126	−	0.591784i
$34$	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	$-0.393068\pi$
$38$	−7.97654			−1.29397
$39$	−0.160386	+	7.02647i	−0.0256823	+	1.12514i
$40$			5.60712i			0.886564i
$41$	−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
$45$	3.04186	−	4.75365i	0.453454	−	0.708632i
$46$	2.11574	−	3.66457i	0.311949	−	0.540312i
$47$	3.96868	−	6.87396i	0.578891	−	1.00267i	−0.416715	−	0.909037i	$-0.636819\pi$
$47$	3.96868	−	6.87396i	0.578891	−	1.00267i	0.995607	−	0.0936324i	$-0.0298478\pi$
$48$	−1.47705	−	0.0337151i	−0.213194	−	0.00486635i
$49$		0			0
$50$	−1.24209	−	0.717122i	−0.175658	−	0.101416i
$51$	−2.80771	−	0.0640887i	−0.393158	−	0.00897422i
$52$			4.20558i			0.583208i
$53$	7.24978	+	4.18567i	0.995835	+	0.574945i	0.907013	−	0.421102i	$-0.138357\pi$
$53$	7.24978	+	4.18567i	0.995835	+	0.574945i	0.0888214	+	0.996048i	$0.471690\pi$
$54$	4.23247	+	2.84655i	0.575967	+	0.387366i
$55$		−	7.69052i		−	1.03699i
$56$		0			0
$57$	12.0251	+	7.31354i	1.59276	+	0.968702i
$58$	−0.614704			−0.0807147
$59$	4.08715	+	7.07915i	0.532101	+	0.921627i	0.999298	+	0.0374731i	$0.0119308\pi$
$59$	4.08715	+	7.07915i	0.532101	+	0.921627i	−0.467196	+	0.884154i	$0.654736\pi$
$60$	1.75480	−	2.88527i	0.226543	−	0.372487i
$61$	3.24253	+	1.87208i	0.415164	+	0.239695i	0.693006	−	0.720932i	$-0.256286\pi$
$61$	3.24253	+	1.87208i	0.415164	+	0.239695i	−0.277842	+	0.960627i	$0.589619\pi$
$62$	4.19198			0.532382
$63$		0			0
$64$	−6.73573			−0.841966
$65$	6.61081	+	3.81676i	0.819971	+	0.473410i
$66$	6.94885	+	0.158614i	0.855344	+	0.0195241i
$67$	−6.26559	−	10.8523i	−0.765464	−	1.32582i	−0.940001	−	0.341171i	$-0.889176\pi$
$67$	−6.26559	−	10.8523i	−0.765464	−	1.32582i	0.174537	−	0.984651i	$-0.444157\pi$
$68$	−1.68051			−0.203791
$69$	−6.54957	+	3.58466i	−0.788476	+	0.431542i
$70$		0			0
$71$		−	14.4969i		−	1.72047i	−0.509898	−	0.860235i	$-0.670317\pi$
$71$		−	14.4969i		−	1.72047i	0.509898	−	0.860235i	$-0.329683\pi$
$72$	7.53180	+	4.81960i	0.887631	+	0.567996i
$73$	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	$0.595488\pi$
$74$		−	7.79557i		−	0.906217i
$75$	1.21500	+	2.21995i	0.140297	+	0.256338i
$76$	7.29351	+	4.21091i	0.836623	+	0.483025i
$77$		0			0
$78$	−3.58501	+	5.89455i	−0.405923	+	0.667426i
$79$	−4.18066	+	7.24112i	−0.470361	+	0.814690i	−0.999426	−	0.0338919i	$-0.989210\pi$
$79$	−4.18066	+	7.24112i	−0.470361	+	0.814690i	0.529064	+	0.848582i	$0.322543\pi$
$80$	−0.802327	+	1.38967i	−0.0897029	+	0.155370i
$81$	−3.77073	−	8.17200i	−0.418970	−	0.908000i
$82$	−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
$86$		−	6.94230i		−	0.748608i
$87$	0.926700	+	0.563611i	0.0993526	+	0.0604254i
$88$	12.1850			1.29893
$89$	−4.90379	−	8.49362i	−0.519801	−	0.900322i	−0.999735	−	0.0230174i	$-0.992673\pi$
$89$	−4.90379	−	8.49362i	−0.519801	−	0.900322i	0.479934	−	0.877305i	$-0.340661\pi$
$90$	4.91906	−	2.54814i	0.518514	−	0.268598i
$91$		0			0
$92$	−3.86914	+	2.23385i	−0.403386	+	0.232895i
$93$	−6.31964	−	3.84355i	−0.655316	−	0.398558i
$94$	6.74762	−	3.89574i	0.695964	−	0.401815i
$95$	13.2384	−	7.64320i	1.35823	−	0.784175i
$96$	7.58260	+	4.61167i	0.773896	+	0.470677i
$97$	−11.4579	+	6.61525i	−1.16338	+	0.671677i	−0.952111	−	0.305752i	$-0.901092\pi$
$97$	−11.4579	+	6.61525i	−1.16338	+	0.671677i	−0.211267	+	0.977428i	$0.567759\pi$
$98$		0			0
$99$	−10.3303	−	6.61038i	−1.03824	−	0.664369i
$100$	0.757155	+	1.31143i	0.0757155	+	0.131143i
$101$	−1.04980			−0.104459			−0.0522295	−	0.998635i	$-0.516633\pi$
$101$	−1.04980			−0.104459			−0.0522295	+	0.998635i	$0.516633\pi$
$102$	−2.35540	−	1.43254i	−0.233220	−	0.141842i
$103$		−	1.63894i		−	0.161490i	−0.996735	−	0.0807449i	$-0.974270\pi$
$103$		−	1.63894i		−	0.161490i	0.996735	−	0.0807449i	$-0.0257299\pi$
$104$	−6.04736	+	10.4743i	−0.592992	+	1.02709i
$105$		0			0
$106$	4.10874	+	7.11654i	0.399076	+	0.691220i
$107$	−2.97522	+	1.71775i	−0.287626	+	0.166061i	−0.636871	−	0.770971i	$-0.719771\pi$
$107$	−2.97522	+	1.71775i	−0.287626	+	0.166061i	0.349245	+	0.937031i	$0.386438\pi$
$108$	−2.36732	−	4.83717i	−0.227795	−	0.465457i
$109$	−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	$0.223224\pi$
$110$	3.77459	−	6.53778i	0.359893	−	0.623353i
$111$	−7.14761	+	11.7522i	−0.678421	+	1.11547i
$112$		0			0
$113$	15.0858	+	8.70977i	1.41915	+	0.819346i	0.996224	−	0.0868183i	$-0.0276699\pi$
$113$	15.0858	+	8.70977i	1.41915	+	0.819346i	0.422925	+	0.906165i	$0.361003\pi$
$114$	6.63305	+	12.1193i	0.621242	+	1.13508i
$115$			8.10929i			0.756196i
$116$	0.562068	+	0.324510i	0.0521867	+	0.0301300i
$117$	10.8092	−	5.59932i	0.999311	−	0.517657i
$118$			8.02407i			0.738675i
$119$		0			0
$120$	8.51931	−	4.66271i	0.777703	−	0.425646i
$121$	−5.71254			−0.519321
$122$	1.83767	+	3.18294i	0.166375	+	0.288170i
$123$	3.15852	+	0.0720963i	0.284794	+	0.00650070i
$124$	−3.83303	−	2.21300i	−0.344216	−	0.198733i
$125$	12.1546			1.08714
$126$		0			0
$127$	−10.1288			−0.898783			−0.449391	−	0.893335i	$-0.648359\pi$
$127$	−10.1288			−0.898783			−0.449391	+	0.893335i	$0.648359\pi$
$128$	3.14876	+	1.81794i	0.278314	+	0.160685i
$129$	−6.36526	+	10.4659i	−0.560430	+	0.921470i
$130$	3.74661	+	6.48932i	0.328599	+	0.569151i
$131$	−4.97701			−0.434844			−0.217422	−	0.976078i	$-0.569765\pi$
$131$	−4.97701			−0.434844			−0.217422	+	0.976078i	$0.569765\pi$
$132$	−6.27008	−	3.81341i	−0.545741	−	0.331915i
$133$		0			0
$134$		−	12.3009i		−	1.06263i
$135$	−9.75209	−	0.668732i	−0.839326	−	0.0575553i
$136$	−4.18544	−	2.41647i	−0.358899	−	0.207210i
$137$			0.840663i			0.0718227i	0.999355	+	0.0359113i	$0.0114334\pi$
$137$			0.840663i			0.0718227i	−0.999355	+	0.0359113i	$0.988567\pi$
$138$	−7.32724	−	0.167251i	−0.623736	−	0.0142374i
$139$	5.74392	+	3.31626i	0.487193	+	0.281281i	0.723409	−	0.690419i	$-0.242574\pi$
$139$	5.74392	+	3.31626i	0.487193	+	0.281281i	−0.236216	+	0.971701i	$0.575907\pi$
$140$		0			0
$141$	−13.7443	−	0.313728i	−1.15748	−	0.0264206i
$142$	7.11525	−	12.3240i	0.597098	−	1.03420i
$143$	8.29433	−	14.3662i	0.693606	−	1.20136i
$144$	1.17704	+	2.27222i	0.0980869	+	0.189352i
$145$	1.02020	−	0.589015i	0.0847234	−	0.0489151i
$146$	1.85985	+	3.22136i	0.153923	+	0.266602i
$147$		0			0
$148$	−4.11538	+	7.12804i	−0.338282	+	0.585921i
$149$			16.9768i			1.39079i	0.718628	+	0.695395i	$0.244771\pi$
$149$			16.9768i			1.39079i	−0.718628	+	0.695395i	$0.755229\pi$
$150$	−0.0566892	+	2.48354i	−0.00462865	+	0.202780i
$151$	1.95142			0.158804			0.0794021	−	0.996843i	$-0.474699\pi$
$151$	1.95142			0.158804			0.0794021	+	0.996843i	$0.474699\pi$
$152$	12.1101	+	20.9752i	0.982256	+	1.70132i
$153$	2.23743	+	4.31925i	0.180886	+	0.349191i
$154$		0			0
$155$	−6.95730	+	4.01680i	−0.558823	+	0.322637i
$156$	6.38983	−	3.49723i	0.511596	−	0.280003i
$157$	−8.24558	+	4.76059i	−0.658069	+	0.379936i	−0.791541	−	0.611116i	$-0.790721\pi$
$157$	−8.24558	+	4.76059i	−0.658069	+	0.379936i	0.133472	+	0.991053i	$0.457387\pi$
$158$	−7.10804	+	4.10383i	−0.565485	+	0.326483i
$159$	0.330881	−	14.4958i	0.0262405	−	1.14959i
$160$	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	$0.847178\pi$
$164$	1.89048			0.147621
$165$	−11.6848	+	6.39520i	−0.909657	+	0.497866i
$166$		−	8.60490i		−	0.667870i
$167$	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
$171$	1.11231	−	24.3523i	0.0850603	−	1.86226i
$172$	−3.66492	+	6.34783i	−0.279448	+	0.484018i
$173$	−3.55884	+	6.16410i	−0.270574	+	0.468647i	−0.969009	−	0.247026i	$-0.920547\pi$
$173$	−3.55884	+	6.16410i	−0.270574	+	0.468647i	0.698435	+	0.715673i	$0.253880\pi$
$174$	0.511170	+	0.933965i	0.0387517	+	0.0708037i
$175$		0			0
$176$	3.01994	+	1.74357i	0.227637	+	0.131426i
$177$	7.35711	−	12.0967i	0.552994	−	0.909244i
$178$		−	9.62734i		−	0.721600i
$179$	−5.19845	−	3.00133i	−0.388550	−	0.224330i	0.292981	−	0.956118i	$-0.405353\pi$
$179$	−5.19845	−	3.00133i	−0.388550	−	0.224330i	−0.681532	+	0.731788i	$0.738686\pi$
$180$	−5.84304	−	0.266885i	−0.435514	−	0.0198924i
$181$		−	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
$184$	−12.8486			−0.947209
$185$	7.46979	+	12.9381i	0.549190	+	0.951225i
$186$	−3.48593	−	6.36918i	−0.255601	−	0.467011i
$187$	5.74059	+	3.31433i	0.419794	+	0.242368i
$188$	−8.22643			−0.599974
$189$		0			0
$190$	15.0054			1.08861
$191$	−4.96482	−	2.86644i	−0.359242	−	0.207408i	0.309506	−	0.950897i	$-0.399836\pi$
$191$	−4.96482	−	2.86644i	−0.359242	−	0.207408i	−0.668748	+	0.743489i	$0.733170\pi$
$192$	5.60123	+	10.2341i	0.404234	+	0.738581i
$193$	−0.779518	−	1.35016i	−0.0561109	−	0.0971869i	0.836606	−	0.547806i	$-0.184537\pi$
$193$	−0.779518	−	1.35016i	−0.0561109	−	0.0971869i	−0.892716	+	0.450619i	$0.851203\pi$
$194$	−12.9873			−0.932437
$195$	0.301718	−	13.2182i	0.0216065	−	0.946574i
$196$		0			0
$197$			19.5504i			1.39291i	0.717602	+	0.696454i	$0.245240\pi$
$197$			19.5504i			1.39291i	−0.717602	+	0.696454i	$0.754760\pi$
$198$	−5.53746	−	10.6898i	−0.393530	−	0.759690i
$199$	−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	$0.677685\pi$
$200$			4.35497i			0.307943i
$201$	−11.2784	+	18.5442i	−0.795520	+	1.30801i
$202$	−0.892445	−	0.515253i	−0.0627922	−	0.0362531i
$203$		0			0
$204$	1.39746	+	2.55332i	0.0978417	+	0.178768i
$205$	1.71570	−	2.97167i	0.119829	−	0.207551i
$206$	0.804411	−	1.39328i	0.0560460	−	0.0970745i
$207$	10.8929	+	6.97034i	0.757106	+	0.484472i
$208$	−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	$-0.141825\pi$
$212$		−	8.67621i		−	0.595884i
$213$	−22.0262	+	12.0552i	−1.50921	+	0.826009i
$214$	−3.37235			−0.230529
$215$	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
$219$	0.149776	−	6.56164i	0.0101209	−	0.443395i
$220$	−6.90274	+	3.98530i	−0.465383	+	0.268689i
$221$	−5.69804	+	3.28976i	−0.383292	+	0.221293i
$222$	−11.8444	+	6.48256i	−0.794943	+	0.435081i
$223$	2.68394	−	1.54957i	0.179730	−	0.103767i	−0.407436	−	0.913234i	$-0.633577\pi$
$223$	2.68394	−	1.54957i	0.179730	−	0.103767i	0.587166	+	0.809467i	$0.300244\pi$
$224$		0			0
$225$	2.36257	−	3.69209i	0.157505	−	0.246139i
$226$	8.54970	+	14.8085i	0.568717	+	0.985047i
$227$	−21.7983			−1.44680			−0.723401	−	0.690428i	$-0.757422\pi$
$227$	−21.7983			−1.44680			−0.723401	+	0.690428i	$0.757422\pi$
$228$	0.332876	−	14.5832i	0.0220453	−	0.965798i
$229$		−	12.9107i		−	0.853164i	−0.904449	−	0.426582i	$-0.859718\pi$
$229$		−	12.9107i		−	0.853164i	0.904449	−	0.426582i	$-0.140282\pi$
$230$	−3.98013	+	6.89378i	−0.262442	+	0.454563i
$231$		0			0
$232$	0.933250	+	1.61644i	0.0612709	+	0.106124i
$233$	0.699758	−	0.404005i	0.0458427	−	0.0264673i	−0.476904	−	0.878956i	$-0.658241\pi$
$233$	0.699758	−	0.404005i	0.0458427	−	0.0264673i	0.522746	+	0.852488i	$0.324908\pi$
$234$	11.9372	+	0.545241i	0.780360	+	0.0356435i
$235$	−7.46587	+	12.9313i	−0.487020	+	0.843543i
$236$	4.23600	−	7.33697i	0.275740	−	0.477596i
$237$	14.4785	+	0.330485i	0.940478	+	0.0214673i
$238$		0			0
$239$	12.2032	+	7.04552i	0.789360	+	0.455737i	0.839737	−	0.542993i	$-0.182709\pi$
$239$	12.2032	+	7.04552i	0.789360	+	0.455737i	−0.0503775	+	0.998730i	$0.516042\pi$
$240$	2.77862	+	0.0634247i	0.179359	+	0.00409405i
$241$		−	18.4989i		−	1.19162i	−0.803127	−	0.595808i	$-0.796832\pi$
$241$		−	18.4989i		−	1.19162i	0.803127	−	0.595808i	$-0.203168\pi$
$242$	−4.85628	−	2.80377i	−0.312173	−	0.180233i
$243$	−9.28068	+	12.5247i	−0.595356	+	0.803462i
$244$		−	3.88051i		−	0.248424i
$245$		0			0
$246$	2.64970	+	1.61152i	0.168939	+	0.102747i
$247$	32.9732			2.09803
$248$	−6.36431	−	11.0233i	−0.404134	−	0.699981i
$249$	−7.88967	+	12.9723i	−0.499988	+	0.822089i
$250$	10.3327	+	5.96561i	0.653499	+	0.377298i
$251$	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
$254$	−8.61056	−	4.97131i	−0.540274	−	0.311928i
$255$	5.28186	+	0.120564i	0.330763	+	0.00754998i
$256$	8.52026	+	14.7575i	0.532516	+	0.922345i
$257$	−4.05793			−0.253127			−0.126563	−	0.991959i	$-0.540395\pi$
$257$	−4.05793			−0.253127			−0.126563	+	0.991959i	$0.540395\pi$
$258$	−10.5479	+	5.77301i	−0.656686	+	0.359412i
$259$		0			0
$260$		−	7.91152i		−	0.490652i
$261$	0.0857189	−	1.87668i	0.00530587	−	0.116164i
$262$	−4.23100	−	2.44277i	−0.261392	−	0.150915i
$263$		−	9.96065i		−	0.614200i	−0.951677	−	0.307100i	$-0.900641\pi$
$263$		−	9.96065i		−	0.614200i	0.951677	−	0.307100i	$-0.0993586\pi$
$264$	−10.1327	−	18.5136i	−0.623625	−	1.13943i
$265$	−13.6383	−	7.87406i	−0.837793	−	0.483700i
$266$		0			0
$267$	−8.82712	+	14.5137i	−0.540211	+	0.888226i
$268$	−6.49378	+	11.2476i	−0.396671	+	0.687054i
$269$	4.98399	−	8.63253i	0.303880	−	0.526335i	−0.673132	−	0.739523i	$-0.735051\pi$
$269$	4.98399	−	8.63253i	0.303880	−	0.526335i	0.977011	+	0.213188i	$0.0683846\pi$
$270$	−7.96212	−	5.35492i	−0.484559	−	0.325890i
$271$	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
$275$		−	5.97311i		−	0.360192i
$276$	6.61151	+	4.02107i	0.397966	+	0.242040i
$277$	−15.6237			−0.938736			−0.469368	−	0.883003i	$-0.655518\pi$
$277$	−15.6237			−0.938736			−0.469368	+	0.883003i	$0.655518\pi$
$278$	3.25531	+	5.63836i	0.195240	+	0.338166i
$279$	−0.584561	+	12.7981i	−0.0349968	+	0.766200i
$280$		0			0
$281$	−20.8780	+	12.0539i	−1.24547	+	0.719075i	−0.970203	−	0.242292i	$-0.922101\pi$
$281$	−20.8780	+	12.0539i	−1.24547	+	0.719075i	−0.275271	+	0.961367i	$0.588768\pi$
$282$	−11.5302	−	7.01257i	−0.686613	−	0.417592i
$283$	−2.61349	+	1.50890i	−0.155356	+	0.0896946i	−0.575662	−	0.817687i	$-0.695256\pi$
$283$	−2.61349	+	1.50890i	−0.155356	+	0.0896946i	0.420307	+	0.907382i	$0.361922\pi$
$284$	−13.0119	+	7.51245i	−0.772117	+	0.445782i
$285$	−22.6215	−	13.7582i	−1.33998	−	0.814966i
$286$	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
$290$	1.15638			0.0679050
$291$	19.5791	+	11.9078i	1.14775	+	0.698050i
$292$		−	3.92736i		−	0.229831i
$293$	−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
$297$	−1.45325	+	21.1926i	−0.0843259	+	1.22972i
$298$	−8.33238	+	14.4321i	−0.482682	+	0.836029i
$299$	−8.74598	+	15.1485i	−0.505793	+	0.876060i
$300$	1.36292	−	2.24095i	0.0786884	−	0.129381i
$301$		0			0
$302$	1.65892	+	0.957777i	0.0954600	+	0.0551139i
$303$	0.872982	+	1.59504i	0.0501515	+	0.0916325i
$304$			6.93135i			0.397540i
$305$	−6.09984	−	3.52175i	−0.349276	−	0.201655i
$306$	−0.217873	+	4.76999i	−0.0124550	+	0.272682i
$307$			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
$310$	−7.88595			−0.447892
$311$	−5.53763	−	9.59145i	−0.314010	−	0.543881i	0.665217	−	0.746650i	$-0.268339\pi$
$311$	−5.53763	−	9.59145i	−0.314010	−	0.543881i	−0.979227	+	0.202769i	$0.935006\pi$
$312$	20.9432	+	0.478049i	1.18568	+	0.0270642i
$313$	−14.4970	−	8.36987i	−0.819421	−	0.473093i	0.0307957	−	0.999526i	$-0.490196\pi$
$313$	−14.4970	−	8.36987i	−0.819421	−	0.473093i	−0.850217	+	0.526433i	$0.823529\pi$
$314$	−9.34619			−0.527436
$315$		0			0
$316$	8.66584			0.487492
$317$	2.54774	+	1.47094i	0.143095	+	0.0826160i	0.569838	−	0.821757i	$-0.307006\pi$
$317$	2.54774	+	1.47094i	0.143095	+	0.0826160i	−0.426743	+	0.904373i	$0.640339\pi$
$318$	7.39598	−	12.1606i	0.414746	−	0.681933i
$319$	−1.28001	−	2.21704i	−0.0716668	−	0.124131i
$320$	12.6712			0.708344
$321$	5.08400	+	3.09205i	0.283761	+	0.172581i
$322$		0			0
$323$			13.1758i			0.733118i
$324$	−5.38088	+	7.61929i	−0.298938	+	0.423294i
$325$	5.13452	+	2.96442i	0.284812	+	0.164436i
$326$		−	1.08981i		−	0.0603589i
$327$	6.39061	+	0.145872i	0.353402	+	0.00806674i
$328$	4.70839	+	2.71839i	0.259977	+	0.150098i
$329$		0			0
$330$	−13.0722	−	0.298385i	−0.719598	−	0.0164255i
$331$	−2.44077	+	4.22753i	−0.134157	+	0.232366i	−0.925275	−	0.379297i	$-0.876166\pi$
$331$	−2.44077	+	4.22753i	−0.134157	+	0.232366i	0.791118	+	0.611663i	$0.209499\pi$
$332$	−4.54263	+	7.86807i	−0.249309	+	0.431816i
$333$	23.7998	+	1.08707i	1.30422	+	0.0595712i
$334$	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	$0.0511980\pi$
$338$			3.40200i			0.185044i
$339$	0.688515	−	30.1637i	0.0373950	−	1.63827i
$340$	3.16136			0.171449
$341$	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
$345$	12.3210	−	6.74344i	0.663342	−	0.363055i
$346$	−6.05081	+	3.49344i	−0.325293	+	0.187808i
$347$	1.86351	−	1.07590i	0.100039	−	0.0577573i	−0.449146	−	0.893458i	$-0.648272\pi$
$347$	1.86351	−	1.07590i	0.100039	−	0.0577573i	0.549185	+	0.835701i	$0.314938\pi$
$348$	0.0256528	−	1.12384i	0.00137513	−	0.0602443i
$349$	−25.2919	+	14.6023i	−1.35384	+	0.781642i	−0.988785	−	0.149343i	$-0.952284\pi$
$349$	−25.2919	+	14.6023i	−1.35384	+	0.781642i	−0.365058	+	0.930985i	$0.618951\pi$
$350$		0			0
$351$	−17.4961	−	11.7670i	−0.933870	−	0.628075i
$352$	−10.4735	−	18.1407i	−0.558240	−	0.966901i
$353$	10.8353			0.576703			0.288352	−	0.957525i	$-0.406893\pi$
$353$	10.8353			0.576703			0.288352	+	0.957525i	$0.406893\pi$
$354$	12.1915	−	6.67257i	0.647973	−	0.354643i
$355$			27.2716i			1.44743i
$356$	−5.08239	+	8.80295i	−0.269366	+	0.466556i
$357$		0			0
$358$	−2.94617	−	5.10291i	−0.155710	−	0.269697i
$359$	−18.1425	+	10.4746i	−0.957527	+	0.552829i	−0.895411	−	0.445240i	$-0.853118\pi$
$359$	−18.1425	+	10.4746i	−0.957527	+	0.552829i	−0.0621161	+	0.998069i	$0.519785\pi$
$360$	−14.1688	−	9.06662i	−0.746761	−	0.477853i
$361$	23.5150	−	40.7292i	1.23763	−	2.14364i
$362$	0.639442	−	1.10755i	0.0336083	−	0.0582113i
$363$	4.75037	+	8.67947i	0.249330	+	0.455554i
$364$		0			0
$365$	−6.17348	−	3.56426i	−0.323135	−	0.186562i
$366$	3.30792	−	5.43894i	0.172908	−	0.284298i
$367$			5.74850i			0.300069i	0.988681	+	0.150035i	$0.0479385\pi$
$367$			5.74850i			0.300069i	−0.988681	+	0.150035i	$0.952061\pi$
$368$	−3.18439	−	1.83851i	−0.165998	−	0.0958389i
$369$	−2.51699	−	4.85892i	−0.131029	−	0.252945i
$370$			14.6650i			0.762398i
$371$		0			0
$372$	−0.174940	+	7.66405i	−0.00907019	+	0.397363i
$373$	28.8934			1.49605			0.748023	−	0.663673i	$-0.231003\pi$
$373$	28.8934			1.49605			0.748023	+	0.663673i	$0.231003\pi$
$374$	3.25342	+	5.63509i	0.168230	+	0.291383i
$375$	−10.1074	−	18.4674i	−0.521944	−	0.953650i
$376$	−20.4886	−	11.8291i	−1.05662	−	0.610039i
$377$	2.54104			0.130870
$378$		0			0
$379$	−0.411434			−0.0211339			−0.0105670	−	0.999944i	$-0.503364\pi$
$379$	−0.411434			−0.0211339			−0.0105670	+	0.999944i	$0.503364\pi$
$380$	−13.7205	−	7.92156i	−0.703849	−	0.406367i
$381$	8.42278	+	15.3894i	0.431512	+	0.788421i
$382$	−2.81376	−	4.87358i	−0.143965	−	0.249354i
$383$	24.8015			1.26730			0.633648	−	0.773622i	$-0.281557\pi$
$383$	24.8015			1.26730			0.633648	+	0.773622i	$0.281557\pi$
$384$	0.143710	−	6.29589i	0.00733366	−	0.321286i
$385$		0			0
$386$		−	1.53038i		−	0.0778944i
$387$	21.1947	+	0.968086i	1.07739	+	0.0492106i
$388$	11.8752	+	6.85617i	0.602874	+	0.348069i
$389$			4.41896i			0.224050i	0.993705	+	0.112025i	$0.0357337\pi$
$389$			4.41896i			0.224050i	−0.993705	+	0.112025i	$0.964266\pi$
$390$	6.74412	−	11.0888i	0.341502	−	0.561504i
$391$	−6.05319	−	3.49481i	−0.306123	−	0.176740i
$392$		0			0
$393$	4.13873	+	7.56193i	0.208772	+	0.381449i
$394$	−9.59554	+	16.6200i	−0.483416	+	0.837302i
$395$	7.86465	−	13.6220i	0.395714	−	0.685396i
$396$	−0.579977	+	12.6977i	−0.0291450	+	0.638084i
$397$	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
$401$			6.14184i			0.306709i	0.988171	+	0.153354i	$0.0490076\pi$
$401$			6.14184i			0.306709i	−0.988171	+	0.153354i	$0.950992\pi$
$402$	−18.6896	+	10.2290i	−0.932153	+	0.510178i
$403$	−17.3287			−0.863203
$404$	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
$408$	−0.191024	+	8.36870i	−0.00945709	+	0.414312i
$409$	0.765886	−	0.442185i	0.0378706	−	0.0218646i	−0.480945	−	0.876751i	$-0.659706\pi$
$409$	0.765886	−	0.442185i	0.0378706	−	0.0218646i	0.518816	+	0.854886i	$0.326373\pi$
$410$	2.91706	−	1.68416i	0.144063	−	0.0831749i
$411$	1.27728	−	0.699070i	0.0630036	−	0.0344826i
$412$	−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
$416$	20.7918			1.01940
$417$	0.262153	−	11.4849i	0.0128377	−	0.562416i
$418$		−	32.6089i		−	1.59495i
$419$	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
$423$	10.9527	+	21.1436i	0.532539	+	1.02804i
$424$	12.4759	−	21.6088i	0.605881	−	1.04942i
$425$	−1.18455	+	2.05170i	−0.0574592	+	0.0995222i
$426$	−24.6415	−	0.562467i	−1.19389	−	0.0272516i
$427$		0			0
$428$	3.08358	+	1.78031i	0.149050	+	0.0860543i
$429$	−28.7249	−	0.655674i	−1.38685	−	0.0316562i
$430$			13.0598i			0.629801i
$431$	−4.06785	−	2.34857i	−0.195941	−	0.113127i	0.398820	−	0.917029i	$-0.369420\pi$
$431$	−4.06785	−	2.34857i	−0.195941	−	0.113127i	−0.594761	+	0.803903i	$0.702753\pi$
$432$	2.47356	−	3.67788i	0.119009	−	0.176952i
$433$		−	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
$436$	3.82499			0.183184
$437$	17.5142	+	30.3354i	0.837816	+	1.45114i
$438$	3.34785	−	5.50460i	0.159966	−	0.263020i
$439$	14.3012	+	8.25679i	0.682558	+	0.394075i	0.800818	−	0.598907i	$-0.204398\pi$
$439$	14.3012	+	8.25679i	0.682558	+	0.394075i	−0.118260	+	0.992983i	$0.537732\pi$
$440$	−22.9225			−1.09279
$441$		0			0
$442$	−6.45861			−0.307205
$443$	−0.921171	−	0.531838i	−0.0437661	−	0.0252684i	0.477957	−	0.878383i	$-0.341377\pi$
$443$	−0.921171	−	0.531838i	−0.0437661	−	0.0252684i	−0.521723	+	0.853115i	$0.674711\pi$
$444$	14.2524	+	0.325324i	0.676388	+	0.0154392i
$445$	9.22500	+	15.9782i	0.437307	+	0.757438i
$446$	3.04219			0.144052
$447$	25.7940	−	14.1174i	1.22002	−	0.667728i
$448$		0			0
$449$		−	15.9081i		−	0.750749i	−0.926873	−	0.375374i	$-0.877514\pi$
$449$		−	15.9081i		−	0.750749i	0.926873	−	0.375374i	$-0.122486\pi$
$450$	3.82056	−	1.97910i	0.180103	−	0.0932958i
$451$	−6.45785	−	3.72844i	−0.304088	−	0.175565i
$452$		−	18.0539i		−	0.849186i
$453$	−1.62274	−	2.96493i	−0.0762430	−	0.139305i
$454$	−18.5309	−	10.6988i	−0.869698	−	0.502121i
$455$		0			0
$456$	21.7988	−	35.8421i	1.02082	−	1.67846i
$457$	16.3963	−	28.3992i	0.766985	−	1.32846i	−0.172206	−	0.985061i	$-0.555090\pi$
$457$	16.3963	−	28.3992i	0.766985	−	1.32846i	0.939191	−	0.343395i	$-0.111577\pi$
$458$	6.33672	−	10.9755i	0.296095	−	0.512852i
$459$	4.70197	−	6.99125i	0.219469	−	0.326324i
$460$	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	$0.169654\pi$
$464$			0.534158i			0.0247976i
$465$	11.8885	+	7.23048i	0.551315	+	0.335305i
$466$	0.793161			0.0367425
$467$	−7.51283	−	13.0126i	−0.347652	−	0.602151i	0.638180	−	0.769887i	$-0.279688\pi$
$467$	−7.51283	−	13.0126i	−0.347652	−	0.602151i	−0.985832	+	0.167736i	$0.946354\pi$
$468$	−10.6272	−	6.80035i	−0.491242	−	0.314346i
$469$		0			0
$470$	−12.6936	+	7.32866i	−0.585512	+	0.338046i
$471$	14.0899	+	8.56935i	0.649228	+	0.394855i
$472$	21.1002	−	12.1822i	0.971216	−	0.560732i
$473$	25.0387	−	14.4561i	1.15128	−	0.664691i
$474$	12.1461	+	7.38714i	0.557888	+	0.339303i
$475$	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
$479$	−31.0800			−1.42008			−0.710041	−	0.704160i	$-0.751324\pi$
$479$	−31.0800			−1.42008			−0.710041	+	0.704160i	$0.751324\pi$
$480$	−14.2644	−	8.67546i	−0.651076	−	0.395979i
$481$			32.2251i			1.46934i
$482$	9.07944	−	15.7261i	0.413557	−	0.716302i
$483$		0			0
$484$	2.96029	+	5.12738i	0.134559	+	0.233063i
$485$	21.5547	−	12.4446i	0.978747	−	0.565080i
$486$	−14.0369	+	6.09233i	−0.636725	+	0.276354i
$487$	−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	$0.265582\pi$
$488$	5.57994	−	9.66474i	0.252592	−	0.437502i
$489$	−0.999224	+	1.64294i	−0.0451865	+	0.0742965i
$490$		0			0
$491$	−7.07098	−	4.08243i	−0.319109	−	0.184238i	0.331886	−	0.943319i	$-0.392315\pi$
$491$	−7.07098	−	4.08243i	−0.319109	−	0.184238i	−0.650995	+	0.759082i	$0.725648\pi$
$492$	−1.57206	−	2.87234i	−0.0708741	−	0.129495i
$493$			1.01538i			0.0457303i
$494$	28.0308	+	16.1836i	1.26116	+	0.728134i
$495$	19.4334	+	12.4354i	0.873466	+	0.558931i
$496$		−	3.64269i		−	0.163562i
$497$		0			0
$498$	−13.0740	+	7.15558i	−0.585862	+	0.320649i
$499$	−28.0194			−1.25432			−0.627159	−	0.778891i	$-0.715782\pi$
$499$	−28.0194			−1.25432			−0.627159	+	0.778891i	$0.715782\pi$
$500$	−6.29863	−	10.9095i	−0.281683	−	0.487890i
$501$	−24.2711	−	0.554013i	−1.08435	−	0.0247515i
$502$	18.8497	+	10.8829i	0.841305	+	0.485727i
$503$	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
$506$	14.9811	+	8.64936i	0.665992	+	0.384511i
$507$	3.11923	−	5.12869i	0.138530	−	0.227773i
$508$	5.24883	+	9.09123i	0.232879	+	0.403358i
$509$	−14.0391			−0.622274			−0.311137	−	0.950365i	$-0.600710\pi$
$509$	−14.0391			−0.622274			−0.311137	+	0.950365i	$0.600710\pi$
$510$	4.43098	+	2.69488i	0.196207	+	0.119331i
$511$		0			0
$512$			9.45558i			0.417882i
$513$	−37.9251	+	18.5606i	−1.67443	+	0.819470i
$514$	−3.44968	−	1.99168i	−0.152159	−	0.0878490i
$515$			3.08318i			0.135861i
$516$	12.6924	+	0.289716i	0.558750	+	0.0127540i
$517$	28.1014	+	16.2243i	1.23590	+	0.713546i
$518$		0			0
$519$	12.3250	+	0.281330i	0.541007	+	0.0123490i
$520$	11.3763	−	19.7043i	0.498883	−	0.864090i
$521$	−19.2229	+	33.2950i	−0.842170	+	1.45868i	0.0458870	+	0.998947i	$0.485389\pi$
$521$	−19.2229	+	33.2950i	−0.842170	+	1.45868i	−0.888057	+	0.459734i	$0.847945\pi$
$522$	0.993967	−	1.55331i	0.0435047	−	0.0679867i
$523$	−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
$527$		−	6.92437i		−	0.301630i
$528$	0.137830	−	6.03832i	0.00599830	−	0.262784i
$529$	4.41779			0.192078
$530$	−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
$534$	−14.6275	+	8.00580i	−0.632994	+	0.346445i
$535$	5.59698	−	3.23142i	0.241979	−	0.139706i
$536$	−32.3466	+	18.6753i	−1.39716	+	0.806650i
$537$	−0.237258	+	10.3942i	−0.0102384	+	0.448543i
$538$	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	$-0.589443\pi$
$542$	18.6822			0.802471
$543$	−1.97948	+	1.08339i	−0.0849477	+	0.0464928i
$544$			8.30819i			0.356211i
$545$	3.47136	−	6.01257i	0.148697	−	0.257550i
$546$		0			0
$547$	−4.05733	−	7.02751i	−0.173479	−	0.300475i	0.766155	−	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
$549$	−9.97372	+	5.16653i	−0.425668	+	0.220502i
$550$	2.93166	−	5.07779i	0.125007	−	0.216518i
$551$	2.54427	−	4.40680i	0.108389	−	0.187736i
$552$	10.6845	+	19.5217i	0.454762	+	0.830901i
$553$		0			0
$554$	−13.2818	−	7.66827i	−0.564291	−	0.325794i
$555$	13.4461	−	22.1083i	0.570754	−	0.938445i
$556$		−	6.87406i		−	0.291525i
$557$	−14.0925	−	8.13633i	−0.597120	−	0.344747i	0.170788	−	0.985308i	$-0.445369\pi$
$557$	−14.0925	−	8.13633i	−0.597120	−	0.344747i	−0.767908	+	0.640561i	$0.778702\pi$
$558$	−6.77837	+	10.5928i	−0.286951	+	0.448431i
$559$			28.6978i			1.21379i
$560$		0			0
$561$	0.262001	−	11.4782i	0.0110617	−	0.484610i
$562$	−23.6647			−0.998236
$563$	−5.13594	−	8.89572i	−0.216454	−	0.374910i	0.737267	−	0.675601i	$-0.236116\pi$
$563$	−5.13594	−	8.89572i	−0.216454	−	0.374910i	−0.953721	+	0.300692i	$0.902783\pi$
$564$	6.84085	+	12.4990i	0.288052	+	0.526303i
$565$	−28.3793	−	16.3848i	−1.19393	−	0.689314i
$566$	−2.96233			−0.124516
$567$		0			0
$568$	−43.2098			−1.81304
$569$	17.8537	+	10.3079i	0.748468	+	0.432128i	0.825140	−	0.564928i	$-0.191096\pi$
$569$	17.8537	+	10.3079i	0.748468	+	0.432128i	−0.0766722	+	0.997056i	$0.524429\pi$
$570$	−12.4781	−	22.7989i	−0.522649	−	0.954939i
$571$	−2.12828	−	3.68628i	−0.0890656	−	0.154266i	0.818051	−	0.575146i	$-0.195055\pi$
$571$	−2.12828	−	3.68628i	−0.0890656	−	0.154266i	−0.907116	+	0.420880i	$0.861721\pi$
$572$	−17.1928			−0.718867
$573$	−0.226595	+	9.92706i	−0.00946614	+	0.414709i
$574$		0			0
$575$			6.29836i			0.262660i
$576$	10.8916	−	17.0207i	0.453815	−	0.709196i
$577$	−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	$0.781294\pi$
$578$			14.1068i			0.586764i
$579$	−1.40318	+	2.30713i	−0.0583141	+	0.0958812i
$580$	−1.05736	−	0.610467i	−0.0439045	−	0.0253483i
$581$		0			0
$582$	10.7999	+	19.7326i	0.447669	+	0.817943i
$583$	−17.1114	+	29.6378i	−0.708682	+	1.22747i
$584$	5.64730	−	9.78141i	0.233687	−	0.404758i
$585$	−20.3342	+	10.5334i	−0.840717	+	0.435503i
$586$	−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
$590$		−	15.0949i		−	0.621445i
$591$	29.7043	−	16.2575i	1.22187	−	0.668745i
$592$	−6.77409			−0.278414
$593$	−19.2908	−	33.4126i	−0.792178	−	1.37209i	−0.924616	−	0.380902i	$-0.875614\pi$
$593$	−19.2908	−	33.4126i	−0.792178	−	1.37209i	0.132437	−	0.991191i	$-0.457720\pi$
$594$	−11.6370	+	17.3028i	−0.477471	+	0.709941i
$595$		0			0
$596$	15.2378	−	8.79752i	0.624163	−	0.360360i
$597$	−0.0385928	+	1.69074i	−0.00157950	+	0.0691974i
$598$	−14.8701	+	8.58525i	−0.608083	+	0.351077i
$599$	29.2921	−	16.9118i	1.19684	−	0.690997i	0.236992	−	0.971511i	$-0.423838\pi$
$599$	29.2921	−	16.9118i	1.19684	−	0.690997i	0.959850	+	0.280514i	$0.0905050\pi$
$600$	6.61681	−	3.62146i	0.270130	−	0.147845i
$601$	27.4855	−	15.8688i	1.12116	−	0.647300i	0.179461	−	0.983765i	$-0.442565\pi$
$601$	27.4855	−	15.8688i	1.12116	−	0.647300i	0.941696	+	0.336465i	$0.109231\pi$
$602$		0			0
$603$	37.5544	+	1.71533i	1.52933	+	0.0698534i
$604$	−1.01124	−	1.75153i	−0.0411469	−	0.0712686i
$605$	10.7464			0.436904
$606$	−0.0407312	+	1.78442i	−0.00165459	+	0.0724873i
$607$		−	0.195554i		−	0.00793731i	−0.999992	−	0.00396865i	$-0.998737\pi$
$607$		−	0.195554i		−	0.00793731i	0.999992	−	0.00396865i	$-0.00126327\pi$
$608$	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
$612$	2.71735	−	4.24652i	0.109842	−	0.171655i
$613$	−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	$0.185533\pi$
$614$	−1.31956	+	2.28554i	−0.0532530	+	0.0922370i
$615$	−5.94180	−	0.135627i	−0.239596	−	0.00546902i
$616$		0			0
$617$	−7.86982	−	4.54365i	−0.316827	−	0.182920i	0.333150	−	0.942874i	$-0.391888\pi$
$617$	−7.86982	−	4.54365i	−0.316827	−	0.182920i	−0.649977	+	0.759953i	$0.725222\pi$
$618$	−2.78584	−	0.0635894i	−0.112063	−	0.00255794i
$619$		−	28.7043i		−	1.15372i	−0.816842	−	0.576861i	$-0.804277\pi$
$619$		−	28.7043i		−	1.15372i	0.816842	−	0.576861i	$-0.195723\pi$
$620$	7.21068	+	4.16309i	0.289588	+	0.167194i
$621$	1.53238	−	22.3466i	0.0614923	−	0.896739i
$622$		−	10.8717i		−	0.435916i
$623$		0			0
$624$	5.12217	+	3.11526i	0.205051	+	0.124710i
$625$	−15.5597			−0.622388
$626$	−8.21604	−	14.2306i	−0.328379	−	0.568769i
$627$	−29.8985	+	49.1596i	−1.19403	+	1.96325i
$628$	8.54588	+	4.93397i	0.341018	+	0.196887i
$629$	−12.8768			−0.513433
$630$		0			0
$631$	−20.7691			−0.826805			−0.413403	−	0.910548i	$-0.635660\pi$
$631$	−20.7691			−0.826805			−0.413403	+	0.910548i	$0.635660\pi$
$632$	21.5830	+	12.4609i	0.858525	+	0.495670i
$633$	−41.4726	−	0.946652i	−1.64839	−	0.0376260i
$634$	1.44390	+	2.50091i	0.0573447	+	0.0993240i
$635$	19.0542			0.756143
$636$	−13.1824	+	7.21487i	−0.522716	+	0.286088i
$637$		0			0
$638$		−	2.51297i		−	0.0994895i
$639$	36.6327	+	23.4413i	1.44917	+	0.927323i
$640$	−5.92345	−	3.41990i	−0.234145	−	0.135184i
$641$			45.9263i			1.81398i	0.421152	+	0.906990i	$0.361626\pi$
$641$			45.9263i			1.81398i	−0.421152	+	0.906990i	$0.638374\pi$
$642$	2.80435	+	5.12386i	0.110679	+	0.202223i
$643$	−9.15428	−	5.28523i	−0.361010	−	0.208429i	0.308514	−	0.951220i	$-0.400168\pi$
$643$	−9.15428	−	5.28523i	−0.361010	−	0.208429i	−0.669524	+	0.742791i	$0.733502\pi$
$644$		0			0
$645$	11.9743	−	19.6884i	0.471488	−	0.775230i
$646$	−6.46680	+	11.2008i	−0.254433	+	0.440691i
$647$	−19.2562	+	33.3526i	−0.757038	+	1.31123i	0.187317	+	0.982299i	$0.440021\pi$
$647$	−19.2562	+	33.3526i	−0.757038	+	1.31123i	−0.944355	+	0.328928i	$0.893313\pi$
$648$	−24.3576	+	11.2391i	−0.956856	+	0.441513i
$649$	−28.9402	+	16.7087i	−1.13600	+	0.655872i
$650$	2.90993	+	5.04015i	0.114137	+	0.197691i
$651$		0			0
$652$	−0.575323	+	0.996488i	−0.0225314	+	0.0390255i
$653$			12.8018i			0.500973i	0.968120	+	0.250486i	$0.0805905\pi$
$653$			12.8018i			0.500973i	−0.968120	+	0.250486i	$0.919409\pi$
$654$	5.36112	+	3.26059i	0.209636	+	0.127499i
$655$	9.36274			0.365833
$656$	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	0.632622	−	0.774461i	$-0.281979\pi$
$659$	41.5777	−	24.0049i	1.61964	−	0.935097i	0.987014	−	0.160636i	$-0.0513546\pi$
$660$	11.7953	+	7.17378i	0.459130	+	0.279239i
$661$	−9.38011	+	5.41561i	−0.364844	+	0.210643i	−0.671204	−	0.741273i	$-0.734222\pi$
$661$	−9.38011	+	5.41561i	−0.364844	+	0.210643i	0.306360	+	0.951916i	$0.400889\pi$
$662$	−4.14983	+	2.39591i	−0.161288	+	0.0931196i
$663$	9.73669	+	5.92177i	0.378142	+	0.229983i
$664$	−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
$668$	−14.5271			−0.562070
$669$	−4.58627	−	2.78933i	−0.177315	−	0.107842i
$670$			23.1404i			0.893991i
$671$	−7.65323	+	13.2558i	−0.295450	+	0.511734i
$672$		0			0
$673$	−6.19553	−	10.7310i	−0.238820	−	0.413649i	0.721556	−	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
$675$	−7.57430	−	0.519394i	−0.291535	−	0.0199915i
$676$	1.79595	−	3.11068i	0.0690752	−	0.119642i
$677$	−14.4947	+	25.1056i	−0.557078	+	0.964888i	0.440660	+	0.897674i	$0.354744\pi$
$677$	−14.4947	+	25.1056i	−0.557078	+	0.964888i	−0.997739	+	0.0672139i	$0.978589\pi$
$678$	15.3900	−	25.3045i	0.591048	−	0.971813i
$679$		0			0
$680$	7.87364	+	4.54585i	0.301940	+	0.174325i
$681$	18.1268	+	33.1197i	0.694620	+	1.26915i
$682$			17.1372i			0.656219i
$683$	0.132048	+	0.0762380i	0.00505268	+	0.00291717i	0.502524	−	0.864563i	$-0.332405\pi$
$683$	0.132048	+	0.0762380i	0.00505268	+	0.00291717i	−0.497472	+	0.867480i	$0.665738\pi$
$684$	−22.4342	+	11.6212i	−0.857792	+	0.444348i
$685$		−	1.58145i		−	0.0604242i
$686$		0			0
$687$	−19.6162	+	10.7362i	−0.748404	+	0.409610i
$688$	−6.03263			−0.229992
$689$	−16.9846	−	29.4181i	−0.647060	−	1.12074i
$690$	13.7840	+	0.314633i	0.524747	+	0.0119779i
$691$	−37.4428	−	21.6176i	−1.42439	−	0.822373i	−0.427722	−	0.903910i	$-0.640684\pi$
$691$	−37.4428	−	21.6176i	−1.42439	−	0.822373i	−0.996670	+	0.0815369i	$0.974017\pi$
$692$	7.37691			0.280428
$693$		0			0
$694$	2.11225			0.0801799
$695$	−10.8055	−	6.23853i	−0.409874	−	0.236641i
$696$	1.67991	−	2.76213i	0.0636767	−	0.104698i
$697$	1.47880	+	2.56136i	0.0560137	+	0.0970186i
$698$	−28.6678			−1.08509
$699$	−1.19573	−	0.727234i	−0.0452267	−	0.0275065i
$700$		0			0
$701$			11.5821i			0.437451i	0.975786	+	0.218726i	$0.0701900\pi$
$701$			11.5821i			0.437451i	−0.975786	+	0.218726i	$0.929810\pi$
$702$	−9.09820	−	18.5905i	−0.343389	−	0.701652i
$703$	55.8863	+	32.2660i	2.10779	+	1.21693i
$704$		−	27.5363i		−	1.03781i
$705$	25.8558	+	0.590184i	0.973786	+	0.0222276i
$706$	9.21116	+	5.31807i	0.346667	+	0.200148i
$707$		0			0
$708$	−14.6701	−	0.334860i	−0.551337	−	0.0125848i
$709$	18.9474	−	32.8178i	0.711584	−	1.23250i	−0.252678	−	0.967550i	$-0.581311\pi$
$709$	18.9474	−	32.8178i	0.711584	−	1.23250i	0.964262	−	0.264949i	$-0.0853552\pi$
$710$	−13.3852	+	23.1838i	−0.502337	+	0.870073i
$711$	−11.5377	−	22.2730i	−0.432699	−	0.835303i
$712$	−25.3162	+	14.6163i	−0.948765	+	0.547770i
$713$	−9.20437	−	15.9424i	−0.344707	−	0.597049i
$714$		0			0
$715$	−15.6033	+	27.0256i	−0.583529	+	1.01070i
$716$			6.22127i			0.232500i
$717$	0.556955	−	24.4000i	0.0207999	−	0.911237i
$718$	−20.5642			−0.767449
$719$	−23.3158	−	40.3842i	−0.869534	−	1.50608i	−0.862474	−	0.506102i	$-0.831086\pi$
$719$	−23.3158	−	40.3842i	−0.869534	−	1.50608i	−0.00706058	−	0.999975i	$-0.502247\pi$
$720$	−2.21425	−	4.27450i	−0.0825202	−	0.159301i
$721$		0			0
$722$	39.9806	−	23.0828i	1.48792	−	0.859054i
$723$	−28.1067	+	15.3831i	−1.04530	+	0.572104i
$724$	−1.16937	+	0.675138i	−0.0434594	+	0.0250913i
$725$	0.792377	−	0.457479i	0.0294282	−	0.0169904i
$726$	−0.221641	+	9.71003i	−0.00822587	+	0.360373i
$727$	3.72659	−	2.15155i	0.138212	−	0.0797965i	−0.429300	−	0.903162i	$-0.641240\pi$
$727$	3.72659	−	2.15155i	0.138212	−	0.0797965i	0.567511	+	0.823366i	$0.307906\pi$
$728$		0			0
$729$	26.7473	+	3.68562i	0.990639	+	0.136505i
$730$	−3.49875	−	6.06002i	−0.129495	−	0.224291i
$731$	−11.4674			−0.424136
$732$	−5.89594	+	3.22692i	−0.217920	+	0.119270i
$733$			14.0108i			0.517500i	0.965944	+	0.258750i	$0.0833105\pi$
$733$			14.0108i			0.517500i	−0.965944	+	0.258750i	$0.916689\pi$
$734$	−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
$738$	0.245095	−	5.36597i	0.00902207	−	0.197524i
$739$	−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	$0.921450\pi$
$740$	7.74184	−	13.4093i	0.284596	−	0.492934i
$741$	−27.4195	−	50.0985i	−1.00728	−	1.84041i
$742$		0			0
$743$	−24.0489	−	13.8847i	−0.882269	−	0.509378i	−0.0108634	−	0.999941i	$-0.503458\pi$
$743$	−24.0489	−	13.8847i	−0.882269	−	0.509378i	−0.871406	+	0.490563i	$0.836791\pi$
$744$	−11.4561	+	18.8364i	−0.420002	+	0.690576i
$745$		−	31.9366i		−	1.17007i
$746$	24.5626	+	14.1812i	0.899300	+	0.519211i
$747$	26.2706	+	1.19993i	0.961192	+	0.0439032i
$748$		−	6.87007i		−	0.251195i
$749$		0			0
$750$	0.471587	−	20.6601i	0.0172199	−	0.754400i
$751$	−17.3508			−0.633140			−0.316570	−	0.948569i	$-0.602531\pi$
$751$	−17.3508			−0.633140			−0.316570	+	0.948569i	$0.602531\pi$
$752$	−3.38527	−	5.86346i	−0.123448	−	0.213818i
$753$	−18.4387	−	33.6895i	−0.671942	−	1.22771i
$754$	2.16017	+	1.24717i	0.0786686	+	0.0454193i
$755$	−3.67100			−0.133601
$756$		0			0
$757$	18.8111			0.683701			0.341850	−	0.939754i	$-0.388946\pi$
$757$	18.8111			0.683701			0.341850	+	0.939754i	$0.388946\pi$
$758$	−0.349764	−	0.201936i	−0.0127040	−	0.00733465i
$759$	−14.6544	−	26.7753i	−0.531922	−	0.971881i
$760$	−22.7814	−	39.4586i	−0.826369	−	1.43131i
$761$	8.45039			0.306326			0.153163	−	0.988201i	$-0.451054\pi$
$761$	8.45039			0.306326			0.153163	+	0.988201i	$0.451054\pi$
$762$	−0.392986	+	17.2166i	−0.0142364	+	0.623693i
$763$		0			0
$764$			5.94167i			0.214962i
$765$	−4.20905	−	8.12536i	−0.152179	−	0.293773i
$766$	21.0840	+	12.1728i	0.761794	+	0.439822i
$767$		−	33.1696i		−	1.19769i
$768$	15.3370	−	25.2174i	0.553426	−	0.909953i
$769$	−19.8100	−	11.4373i	−0.714366	−	0.412440i	0.0983092	−	0.995156i	$-0.468657\pi$
$769$	−19.8100	−	11.4373i	−0.714366	−	0.412440i	−0.812676	+	0.582716i	$0.801990\pi$
$770$		0			0
$771$	3.37445	+	6.16550i	0.121528	+	0.222045i
$772$	−0.807907	+	1.39934i	−0.0290772	+	0.0503632i
$773$	18.8374	−	32.6273i	0.677533	−	1.17352i	−0.298189	−	0.954507i	$-0.596382\pi$
$773$	18.8374	−	32.6273i	0.677533	−	1.17352i	0.975722	−	0.219015i	$-0.0702843\pi$
$774$	17.5427	+	11.2256i	0.630559	+	0.403495i
$775$	−5.40363	+	3.11978i	−0.194104	+	0.112066i
$776$	19.7175	+	34.1517i	0.707817	+	1.22598i
$777$		0			0
$778$	−2.16888	+	3.75660i	−0.0777579	+	0.134681i
$779$		−	14.8220i		−	0.531053i
$780$	−12.0205	+	6.57898i	−0.430404	+	0.235565i
$781$	59.2649			2.12066
$782$	−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
$786$	−0.193103	+	8.45980i	−0.00688777	+	0.301751i
$787$	−20.3222	+	11.7330i	−0.724408	+	0.418237i	−0.816373	−	0.577525i	$-0.804019\pi$
$787$	−20.3222	+	11.7330i	−0.724408	+	0.418237i	0.0919648	+	0.995762i	$0.470685\pi$
$788$	17.5478	−	10.1312i	0.625113	−	0.360909i
$789$	−15.1339	+	8.28297i	−0.538782	+	0.294882i
$790$	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
$794$	21.8511			0.775468
$795$	−0.622452	+	27.2694i	−0.0220761	+	0.967148i
$796$			1.01196i			0.0358681i
$797$	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
$801$	29.3921	+	1.34251i	1.03852	+	0.0474352i
$802$	−3.01448	+	5.22123i	−0.106445	+	0.184368i
$803$	−7.74562	+	13.4158i	−0.273337	+	0.473433i
$804$	22.4893	+	0.513339i	0.793135	+	0.0181041i
$805$		0			0
$806$	−14.7313	−	8.50510i	−0.518887	−	0.299579i
$807$	−17.2606	−	0.393989i	−0.607601	−	0.0138691i
$808$			3.12905i			0.110080i
$809$	−11.4669	−	6.62041i	−0.403154	−	0.232761i	0.284690	−	0.958620i	$-0.408109\pi$
$809$	−11.4669	−	6.62041i	−0.403154	−	0.232761i	−0.687844	+	0.725858i	$0.741443\pi$
$810$	−1.51507	+	16.5504i	−0.0532340	+	0.581522i
$811$		−	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
$814$	31.8691			1.11701
$815$	1.04426	+	1.80872i	0.0365790	+	0.0633566i
$816$	−1.24483	+	2.04677i	−0.0435776	+	0.0716512i
$817$	49.7692	+	28.7343i	1.74120	+	1.00528i
$818$	0.868116			0.0303530
$819$		0			0
$820$	−3.55636			−0.124193
$821$	−48.7766	−	28.1612i	−1.70232	−	0.982833i	−0.943407	−	0.331636i	$-0.892399\pi$
$821$	−48.7766	−	28.1612i	−1.70232	−	0.982833i	−0.758909	−	0.651197i	$-0.774267\pi$
$822$	1.42894	+	0.0326169i	0.0498399	+	0.00113765i
$823$	−8.52180	−	14.7602i	−0.297051	−	0.514508i	0.678409	−	0.734685i	$-0.262670\pi$
$823$	−8.52180	−	14.7602i	−0.297051	−	0.514508i	−0.975460	+	0.220177i	$0.929337\pi$
$824$	−4.88506			−0.170179
$825$	−9.07537	+	4.96705i	−0.315964	+	0.172931i
$826$		0			0
$827$		−	45.7715i		−	1.59163i	−0.605539	−	0.795816i	$-0.707042\pi$
$827$		−	45.7715i		−	1.59163i	0.605539	−	0.795816i	$-0.292958\pi$
$828$	0.611559	−	13.3891i	0.0212532	−	0.465305i
$829$	−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	$0.876595\pi$
$830$			16.1875i			0.561877i
$831$	12.9922	+	23.7382i	0.450694	+	0.823469i
$832$	23.6704	+	13.6661i	0.820623	+	0.473787i
$833$		0			0
$834$	5.85975	−	9.63472i	0.202907	−	0.333623i
$835$	−13.1840	+	22.8354i	−0.456251	+	0.790250i
$836$	−17.2146	+	29.8166i	−0.595380	+	1.03123i
$837$	19.9311	−	9.75432i	0.688920	−	0.337159i
$838$	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
$842$			26.1736i			0.902002i
$843$	35.6758	+	21.6977i	1.22874	+	0.747309i
$844$	−24.8227			−0.854433
$845$	−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
$849$	4.46587	+	2.71610i	0.153268	+	0.0932164i
$850$	−2.01400	+	1.16278i	−0.0690795	+	0.0398831i
$851$	−29.6472	+	17.1168i	−1.01629	+	0.586757i
$852$	22.2345	+	13.5229i	0.761743	+	0.463286i
$853$	−47.7652	+	27.5772i	−1.63545	+	0.944227i	−0.653077	+	0.757292i	$0.726522\pi$
$853$	−47.7652	+	27.5772i	−1.63545	+	0.944227i	−0.982372	+	0.186935i	$0.940145\pi$
$854$		0			0
$855$	−2.09247	+	45.8114i	−0.0715610	+	1.56672i
$856$	5.11994	+	8.86800i	0.174996	+	0.303102i
$857$	38.1541			1.30332			0.651660	−	0.758511i	$-0.274073\pi$
$857$	38.1541			1.30332			0.651660	+	0.758511i	$0.274073\pi$
$858$	−24.0975	−	14.6559i	−0.822675	−	0.500344i
$859$		−	40.4682i		−	1.38076i	−0.723449	−	0.690378i	$-0.757444\pi$
$859$		−	40.4682i		−	1.38076i	0.723449	−	0.690378i	$-0.242556\pi$
$860$	6.89444	−	11.9415i	0.235099	−	0.407203i
$861$		0			0
$862$	−2.30541	−	3.99309i	−0.0785226	−	0.136005i
$863$	31.3519	−	18.1011i	1.06723	−	0.616167i	0.139808	−	0.990179i	$-0.455351\pi$
$863$	31.3519	−	18.1011i	1.06723	−	0.616167i	0.927424	+	0.374012i	$0.122018\pi$
$864$	−23.9143	+	11.7037i	−0.813581	+	0.398168i
$865$	6.69488	−	11.5959i	0.227633	−	0.394272i
$866$	4.40608	−	7.63155i	0.149725	−	0.259331i
$867$	12.9342	−	21.2667i	0.439269	−	0.722255i
$868$		0			0
$869$	−29.6024	−	17.0910i	−1.00419	−	0.579771i
$870$	−0.961611	−	1.75697i	−0.0326017	−	0.0595669i
$871$			50.8489i			1.72295i
$872$	9.52645	+	5.50010i	0.322606	+	0.186257i
$873$	1.81105	−	39.6502i	0.0612948	−	1.34195i
$874$			34.3846i			1.16307i
$875$		0			0
$876$	−5.96712	+	3.26587i	−0.201610	+	0.110344i
$877$	−11.0688			−0.373766			−0.186883	−	0.982382i	$-0.559839\pi$
$877$	−11.0688			−0.373766			−0.186883	+	0.982382i	$0.559839\pi$
$878$	8.10505	+	14.0384i	0.273532	+	0.473771i
$879$	51.6836	+	1.17973i	1.74324	+	0.0397912i
$880$	−5.68111	−	3.27999i	−0.191510	−	0.110568i
$881$	−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	$0.576744\pi$
$884$	5.90556	+	3.40958i	0.198625	+	0.114676i
$885$	−13.8402	+	22.7563i	−0.465233	+	0.764944i
$886$	−0.522064	−	0.904241i	−0.0175391	−	0.0303786i
$887$	39.0360			1.31070			0.655350	−	0.755325i	$-0.272521\pi$
$887$	39.0360			1.31070			0.655350	+	0.755325i	$0.272521\pi$
$888$	35.0289	+	21.3043i	1.17549	+	0.714925i
$889$		0			0
$890$			18.1109i			0.607080i
$891$	33.4079	−	15.4151i	1.11921	−	0.516426i
$892$	−2.78169	−	1.60601i	−0.0931378	−	0.0537732i
$893$			64.4981i			2.15835i
$894$	28.8567	+	0.658682i	0.965112	+	0.0220296i
$895$	9.77931	+	5.64609i	0.326886	+	0.188728i
$896$		0			0
$897$	30.2891	+	0.691378i	1.01132	+	0.0230844i
$898$	7.80786	−	13.5236i	0.260552	−	0.451288i
$899$	−1.33711	+	2.31595i	−0.0445952	+	0.0772411i
$900$	−4.53820	−	0.207286i	−0.151273	−	0.00690952i
$901$	11.7552	−	6.78687i	0.391622	−	0.226103i
$902$	−3.65992	−	6.33916i	−0.121862	−	0.211071i
$903$		0			0
$904$	25.9605	−	44.9648i	0.863432	−	1.49551i
$905$			2.45088i			0.0814699i
$906$	0.0757132	−	3.31697i	0.00251540	−	0.110199i
$907$	9.86974			0.327719			0.163860	−	0.986484i	$-0.447606\pi$
$907$	9.86974			0.327719			0.163860	+	0.986484i	$0.447606\pi$
$908$	11.2961	+	19.5654i	0.374873	+	0.649300i
$909$	1.69751	−	2.65277i	0.0563028	−	0.0879868i
$910$		0			0
$911$	−46.6335	+	26.9239i	−1.54504	+	0.892028i	−0.546529	+	0.837440i	$0.684051\pi$
$911$	−46.6335	+	26.9239i	−1.54504	+	0.892028i	−0.998509	+	0.0545881i	$0.982615\pi$
$912$	10.5313	−	5.76390i	0.348726	−	0.190862i
$913$	31.0351	−	17.9181i	1.02711	−	0.593004i
$914$	27.8772	−	16.0949i	0.922096	−	0.532373i
$915$	−0.278397	+	12.1965i	−0.00920353	+	0.403204i
$916$	−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	$0.952546\pi$
$920$	24.1707			0.796884
$921$	4.08487	−	2.23570i	0.134601	−	0.0736688i
$922$			18.1343i			0.597221i
$923$	−29.4128	+	50.9444i	−0.968133	+	1.67686i
$924$		0			0
$925$	5.80167	+	10.0488i	0.190758	+	0.330402i
$926$	−0.343310	+	0.198210i	−0.0112819	+	0.00651359i
$927$	4.14149	+	2.65014i	0.136024	+	0.0870422i
$928$	1.60433	−	2.77878i	0.0526647	−	0.0912180i
$929$	27.4954	−	47.6234i	0.902093	−	1.56247i	0.0773215	−	0.997006i	$-0.475363\pi$
$929$	27.4954	−	47.6234i	0.902093	−	1.56247i	0.824772	−	0.565466i	$-0.191303\pi$
$930$	6.55772	+	11.9817i	0.215036	+	0.392895i
$931$		0			0
$932$	−0.725243	−	0.418719i	−0.0237561	−	0.0137156i
$933$	−9.96806	+	16.3897i	−0.326340	+	0.536574i
$934$		−	14.7495i		−	0.482618i
$935$	−10.7992	−	6.23491i	−0.353171	−	0.203903i
$936$	−16.6894	−	32.2181i	−0.545510	−	1.05308i
$937$			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
$940$	15.4755			0.504757
$941$	7.58758	+	13.1421i	0.247348	+	0.428419i	0.962789	−	0.270254i	$-0.0871076\pi$
$941$	7.58758	+	13.1421i	0.247348	+	0.428419i	−0.715441	+	0.698673i	$0.753774\pi$
$942$	7.77201	+	14.2003i	0.253226	+	0.462672i
$943$	6.80950	+	3.93147i	0.221748	+	0.128026i
$944$	6.97265			0.226940
$945$		0			0
$946$	28.3808			0.922739
$947$	−2.27478	−	1.31335i	−0.0739206	−	0.0426781i	0.462584	−	0.886575i	$-0.346922\pi$
$947$	−2.27478	−	1.31335i	−0.0739206	−	0.0426781i	−0.536505	+	0.843897i	$0.680256\pi$
$948$	−7.20625	−	13.1666i	−0.234048	−	0.427633i
$949$	−7.68820	−	13.3164i	−0.249570	−	0.432267i
$950$	11.6545			0.378122
$951$	0.116279	−	5.09415i	0.00377060	−	0.165189i
$952$		0			0
$953$			40.5520i			1.31361i	0.754061	+	0.656805i	$0.228092\pi$
$953$			40.5520i			1.31361i	−0.754061	+	0.656805i	$0.771908\pi$
$954$	−24.6268	−	1.12485i	−0.797321	−	0.0364182i
$955$	9.33981	+	5.39234i	0.302229	+	0.174492i
$956$		−	14.6042i		−	0.472335i
$957$	−2.30410	+	3.78844i	−0.0744808	+	0.122463i
$958$	−26.4214	−	15.2544i	−0.853637	−	0.492847i
$959$		0			0
$960$	−10.5370	−	19.2523i	−0.340081	−	0.621366i
$961$	−6.38155	+	11.0532i	−0.205856	+	0.356554i
$962$	−15.8164	+	27.3948i	−0.509942	+	0.883245i
$963$	0.470266	−	10.2957i	0.0151541	−	0.331776i
$964$	−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	$0.0999023\pi$
$968$			17.0269i			0.547264i
$969$	20.0189	−	10.9566i	0.643099	−	0.351975i
$970$	24.4317			0.784456
$971$	−8.26077	−	14.3081i	−0.265101	−	0.459168i	0.702489	−	0.711694i	$-0.252072\pi$
$971$	−8.26077	−	14.3081i	−0.265101	−	0.459168i	−0.967590	+	0.252526i	$0.918739\pi$
$972$	16.0511	+	1.83958i	0.514839	+	0.0590047i
$973$		0			0
$974$	−11.4728	+	6.62381i	−0.367611	+	0.212240i
$975$	0.234340	−	10.2664i	0.00750488	−	0.328787i
$976$	2.76587	−	1.59687i	0.0885333	−	0.0511147i
$977$	−5.50730	+	3.17964i	−0.176194	+	0.101726i	−0.585503	−	0.810670i	$-0.699103\pi$
$977$	−5.50730	+	3.17964i	−0.176194	+	0.101726i	0.409309	+	0.912396i	$0.365770\pi$
$978$	−1.65582	+	0.906251i	−0.0529474	+	0.0289787i
$979$	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
$983$	−2.22975			−0.0711179			−0.0355590	−	0.999368i	$-0.511321\pi$
$983$	−2.22975			−0.0711179			−0.0355590	+	0.999368i	$0.511321\pi$
$984$	0.214891	−	9.41432i	0.00685048	−	0.300118i
$985$		−	36.7781i		−	1.17185i
$986$	−0.498358	+	0.863181i	−0.0158709	+	0.0274893i
$987$		0			0
$988$	−17.0870	−	29.5956i	−0.543610	−	0.941561i
$989$	−26.4021	+	15.2433i	−0.839538	+	0.484708i
$990$	10.4170	+	20.1096i	0.331076	+	0.639125i
$991$	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	$-0.120941\pi$
$992$	−10.9407	+	18.9499i	−0.347369	+	0.601661i
$993$	8.45286	+	0.192945i	0.268243	+	0.00612292i
$994$		0			0
$995$	1.59072	+	0.918403i	0.0504293	+	0.0291153i
$996$	15.7320	+	0.359099i	0.498489	+	0.0113785i
$997$		−	8.40875i		−	0.266308i	−0.991095	−	0.133154i	$-0.957490\pi$
$997$		−	8.40875i		−	0.266308i	0.991095	−	0.133154i	$-0.0425104\pi$
$998$	−23.8195	−	13.7522i	−0.753993	−	0.435318i
$999$	−18.1395	−	37.0647i	−0.573909	−	1.17267i

Twists

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

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

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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.850109 + 0.490811i) q^{2} +(-0.831570 - 1.51937i) q^{3} +(-0.518210 - 0.897565i) q^{4} -1.88120 q^{5} +(0.0387990 - 1.69978i) q^{6} -2.98061i q^{8} +(-1.61698 + 2.52693i) q^{9} +(-1.59922 - 0.923312i) q^{10} +4.08810i q^{11} +(-0.932808 + 1.53374i) q^{12} +(-3.51415 - 2.02890i) q^{13} +(1.56435 + 2.85824i) q^{15} +(0.426498 - 0.738716i) q^{16} +(0.810727 - 1.40422i) q^{17} +(-2.61486 + 1.35453i) q^{18} +(-7.03722 + 4.06294i) q^{19} +(0.974855 + 1.68850i) q^{20} +(-2.00648 + 3.47533i) q^{22} -4.31071i q^{23} +(-4.52866 + 2.47859i) q^{24} -1.46110 q^{25} +(-1.99161 - 3.44957i) q^{26} +(5.18398 + 0.355482i) q^{27} +(-0.542317 + 0.313107i) q^{29} +(-0.0729886 + 3.19761i) q^{30} +(3.69833 - 2.13523i) q^{31} +(-4.43744 + 2.56195i) q^{32} +(6.21134 - 3.39954i) q^{33} +(1.37841 - 0.795827i) q^{34} +(3.10602 + 0.141870i) q^{36} +(-3.97076 - 6.87757i) q^{37} -7.97654 q^{38} +(-0.160386 + 7.02647i) q^{39} +5.60712i q^{40} +(-0.912023 + 1.57967i) q^{41} +(-3.53614 - 6.12477i) q^{43} +(3.66933 - 2.11849i) q^{44} +(3.04186 - 4.75365i) q^{45} +(2.11574 - 3.66457i) q^{46} +(3.96868 - 6.87396i) q^{47} +(-1.47705 - 0.0337151i) q^{48} +(-1.24209 - 0.717122i) q^{50} +(-2.80771 - 0.0640887i) q^{51} +4.20558i q^{52} +(7.24978 + 4.18567i) q^{53} +(4.23247 + 2.84655i) q^{54} -7.69052i q^{55} +(12.0251 + 7.31354i) q^{57} -0.614704 q^{58} +(4.08715 + 7.07915i) q^{59} +(1.75480 - 2.88527i) q^{60} +(3.24253 + 1.87208i) q^{61} +4.19198 q^{62} -6.73573 q^{64} +(6.61081 + 3.81676i) q^{65} +(6.94885 + 0.158614i) q^{66} +(-6.26559 - 10.8523i) q^{67} -1.68051 q^{68} +(-6.54957 + 3.58466i) q^{69} -14.4969i q^{71} +(7.53180 + 4.81960i) q^{72} +(3.28167 + 1.89468i) q^{73} -7.79557i q^{74} +(1.21500 + 2.21995i) q^{75} +(7.29351 + 4.21091i) q^{76} +(-3.58501 + 5.89455i) q^{78} +(-4.18066 + 7.24112i) q^{79} +(-0.802327 + 1.38967i) q^{80} +(-3.77073 - 8.17200i) q^{81} +(-1.55064 + 0.895261i) q^{82} +(-4.38300 - 7.59159i) q^{83} +(-1.52514 + 2.64162i) q^{85} -6.94230i q^{86} +(0.926700 + 0.563611i) q^{87} +12.1850 q^{88} +(-4.90379 - 8.49362i) q^{89} +(4.91906 - 2.54814i) q^{90} +(-3.86914 + 2.23385i) q^{92} +(-6.31964 - 3.84355i) q^{93} +(6.74762 - 3.89574i) q^{94} +(13.2384 - 7.64320i) q^{95} +(7.58260 + 4.61167i) q^{96} +(-11.4579 + 6.61525i) q^{97} +(-10.3303 - 6.61038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65}+ \cdots - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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