LMFDB - Embedded newform 720.2.bm.g.109.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(109,720)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("720.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bm (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.9
Character	$\chi$	$=$	720.109
Dual form			720.2.bm.g.469.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.903873 - 1.08766i) q^{2} +(-0.366025 - 1.96622i) q^{4} +(-1.32403 + 1.80193i) q^{5} -3.06349 q^{7} +(-2.46943 - 1.37910i) q^{8} +(0.763129 + 3.06882i) q^{10} +(-0.686732 + 0.686732i) q^{11} +(-1.12131 + 1.12131i) q^{13} +(-2.76901 + 3.33205i) q^{14} +(-3.73205 + 1.43937i) q^{16} +4.85810i q^{17} +(2.73205 + 2.73205i) q^{19} +(4.02761 + 1.94379i) q^{20} +(0.126215 + 1.36765i) q^{22} -3.34641 q^{23} +(-1.49387 - 4.77162i) q^{25} +(0.206087 + 2.23314i) q^{26} +(1.12131 + 6.02350i) q^{28} +(5.00215 + 5.00215i) q^{29} -7.83592 q^{31} +(-1.80775 + 5.36023i) q^{32} +(5.28398 + 4.39111i) q^{34} +(4.05616 - 5.52018i) q^{35} +(-6.35168 - 6.35168i) q^{37} +(5.44098 - 0.502125i) q^{38} +(5.75465 - 2.62375i) q^{40} +10.8286i q^{41} +(-7.14481 - 7.14481i) q^{43} +(1.60163 + 1.09891i) q^{44} +(-3.02473 + 3.63977i) q^{46} +1.22487i q^{47} +2.38496 q^{49} +(-6.54019 - 2.68812i) q^{50} +(2.61518 + 1.79432i) q^{52} +(-6.05342 - 6.05342i) q^{53} +(-0.328183 - 2.14670i) q^{55} +(7.56507 + 4.22486i) q^{56} +(9.96196 - 0.919346i) q^{58} +(2.97509 - 2.97509i) q^{59} +(-0.971033 - 0.971033i) q^{61} +(-7.08268 + 8.52284i) q^{62} +(4.19615 + 6.81119i) q^{64} +(-0.535866 - 3.50518i) q^{65} +(4.97793 - 4.97793i) q^{67} +(9.55211 - 1.77819i) q^{68} +(-2.33784 - 9.40128i) q^{70} -9.70256i q^{71} +9.05926 q^{73} +(-12.6496 + 1.16738i) q^{74} +(4.37182 - 6.37182i) q^{76} +(2.10380 - 2.10380i) q^{77} +9.49307 q^{79} +(2.34772 - 8.63066i) q^{80} +(11.7779 + 9.78772i) q^{82} +(-2.47138 + 2.47138i) q^{83} +(-8.75394 - 6.43230i) q^{85} +(-14.2292 + 1.31315i) q^{86} +(2.64291 - 0.748762i) q^{88} +3.75237i q^{89} +(3.43513 - 3.43513i) q^{91} +(1.22487 + 6.57977i) q^{92} +(1.33225 + 1.10713i) q^{94} +(-8.54028 + 1.30562i) q^{95} -1.58626i q^{97} +(2.15570 - 2.59404i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 24 q^{10} - 64 q^{16} + 32 q^{19} + 32 q^{31} - 72 q^{40} - 32 q^{46} + 128 q^{49} - 32 q^{64} - 104 q^{70} - 32 q^{76} + 224 q^{79} - 48 q^{85} - 32 q^{91} - 48 q^{94}+O(q^{100}) $ 32 * q + 16 * q^4 - 24 * q^10 - 64 * q^16 + 32 * q^19 + 32 * q^31 - 72 * q^40 - 32 * q^46 + 128 * q^49 - 32 * q^64 - 104 * q^70 - 32 * q^76 + 224 * q^79 - 48 * q^85 - 32 * q^91 - 48 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$1$

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 $

$2$	0.903873	−	1.08766i	0.639135	−	0.769095i
$2$	0.903873	−	1.08766i	0.639135	−	0.769095i
$3$		0			0
$3$		0			0
$4$	−0.366025	−	1.96622i	−0.183013	−	0.983111i
$5$	−1.32403	+	1.80193i	−0.592126	+	0.805845i
$5$	−1.32403	+	1.80193i	−0.592126	+	0.805845i
$6$		0			0
$7$	−3.06349			−1.15789			−0.578945	−	0.815367i	$-0.696535\pi$
$7$	−3.06349			−1.15789			−0.578945	+	0.815367i	$0.696535\pi$
$8$	−2.46943	−	1.37910i	−0.873075	−	0.487586i
$9$		0			0
$10$	0.763129	+	3.06882i	0.241323	+	0.970445i
$11$	−0.686732	+	0.686732i	−0.207058	+	0.207058i	−0.803016	−	0.595958i	$-0.796772\pi$
$11$	−0.686732	+	0.686732i	−0.207058	+	0.207058i	0.595958	+	0.803016i	$0.296772\pi$
$12$		0			0
$13$	−1.12131	+	1.12131i	−0.310997	+	0.310997i	−0.845296	−	0.534299i	$-0.820576\pi$
$13$	−1.12131	+	1.12131i	−0.310997	+	0.310997i	0.534299	+	0.845296i	$0.320576\pi$
$14$	−2.76901	+	3.33205i	−0.740048	+	0.890527i
$15$		0			0
$16$	−3.73205	+	1.43937i	−0.933013	+	0.359843i
$17$			4.85810i			1.17826i	0.808037	+	0.589132i	$0.200530\pi$
$17$			4.85810i			1.17826i	−0.808037	+	0.589132i	$0.799470\pi$
$18$		0			0
$19$	2.73205	+	2.73205i	0.626775	+	0.626775i	0.947255	−	0.320480i	$-0.103844\pi$
$19$	2.73205	+	2.73205i	0.626775	+	0.626775i	−0.320480	+	0.947255i	$0.603844\pi$
$20$	4.02761	+	1.94379i	0.900602	+	0.434645i
$21$		0			0
$22$	0.126215	+	1.36765i	0.0269091	+	0.291585i
$23$	−3.34641			−0.697774			−0.348887	−	0.937165i	$-0.613440\pi$
$23$	−3.34641			−0.697774			−0.348887	+	0.937165i	$0.613440\pi$
$24$		0			0
$25$	−1.49387	−	4.77162i	−0.298774	−	0.954324i
$26$	0.206087	+	2.23314i	0.0404170	+	0.437955i
$27$		0			0
$28$	1.12131	+	6.02350i	0.211909	+	1.13833i
$29$	5.00215	+	5.00215i	0.928875	+	0.928875i	0.997633	−	0.0687581i	$-0.0219037\pi$
$29$	5.00215	+	5.00215i	0.928875	+	0.928875i	−0.0687581	+	0.997633i	$0.521904\pi$
$30$		0			0
$31$	−7.83592			−1.40737			−0.703686	−	0.710511i	$-0.748464\pi$
$31$	−7.83592			−1.40737			−0.703686	+	0.710511i	$0.748464\pi$
$32$	−1.80775	+	5.36023i	−0.319568	+	0.947564i
$33$		0			0
$34$	5.28398	+	4.39111i	0.906196	+	0.753069i
$35$	4.05616	−	5.52018i	0.685617	−	0.933080i
$36$		0			0
$37$	−6.35168	−	6.35168i	−1.04421	−	1.04421i	−0.998976	−	0.0452332i	$-0.985597\pi$
$37$	−6.35168	−	6.35168i	−1.04421	−	1.04421i	−0.0452332	−	0.998976i	$-0.514403\pi$
$38$	5.44098	−	0.502125i	0.882644	−	0.0814554i
$39$		0			0
$40$	5.75465	−	2.62375i	0.909890	−	0.414851i
$41$			10.8286i			1.69115i	0.533857	+	0.845575i	$0.320742\pi$
$41$			10.8286i			1.69115i	−0.533857	+	0.845575i	$0.679258\pi$
$42$		0			0
$43$	−7.14481	−	7.14481i	−1.08957	−	1.08957i	−0.995572	−	0.0940013i	$-0.970034\pi$
$43$	−7.14481	−	7.14481i	−1.08957	−	1.08957i	−0.0940013	−	0.995572i	$-0.529966\pi$
$44$	1.60163	+	1.09891i	0.241455	+	0.165666i
$45$		0			0
$46$	−3.02473	+	3.63977i	−0.445972	+	0.536654i
$47$			1.22487i			0.178666i	0.996002	+	0.0893328i	$0.0284735\pi$
$47$			1.22487i			0.178666i	−0.996002	+	0.0893328i	$0.971527\pi$
$48$		0			0
$49$	2.38496			0.340709
$50$	−6.54019	−	2.68812i	−0.924922	−	0.380157i
$51$		0			0
$52$	2.61518	+	1.79432i	0.362661	+	0.248828i
$53$	−6.05342	−	6.05342i	−0.831501	−	0.831501i	0.156221	−	0.987722i	$-0.450069\pi$
$53$	−6.05342	−	6.05342i	−0.831501	−	0.831501i	−0.987722	+	0.156221i	$0.950069\pi$
$54$		0			0
$55$	−0.328183	−	2.14670i	−0.0442522	−	0.289461i
$56$	7.56507	+	4.22486i	1.01092	+	0.564571i
$57$		0			0
$58$	9.96196	−	0.919346i	1.30807	−	0.120716i
$59$	2.97509	−	2.97509i	0.387324	−	0.387324i	−0.486408	−	0.873732i	$-0.661693\pi$
$59$	2.97509	−	2.97509i	0.387324	−	0.387324i	0.873732	+	0.486408i	$0.161693\pi$
$60$		0			0
$61$	−0.971033	−	0.971033i	−0.124328	−	0.124328i	0.642205	−	0.766533i	$-0.278020\pi$
$61$	−0.971033	−	0.971033i	−0.124328	−	0.124328i	−0.766533	+	0.642205i	$0.778020\pi$
$62$	−7.08268	+	8.52284i	−0.899501	+	1.08240i
$63$		0			0
$64$	4.19615	+	6.81119i	0.524519	+	0.851399i
$65$	−0.535866	−	3.50518i	−0.0664660	−	0.434765i
$66$		0			0
$67$	4.97793	−	4.97793i	0.608152	−	0.608152i	−0.334311	−	0.942463i	$-0.608504\pi$
$67$	4.97793	−	4.97793i	0.608152	−	0.608152i	0.942463	+	0.334311i	$0.108504\pi$
$68$	9.55211	−	1.77819i	1.15836	−	0.215637i
$69$		0			0
$70$	−2.33784	−	9.40128i	−0.279425	−	1.12367i
$71$		−	9.70256i		−	1.15148i	−0.817632	−	0.575741i	$-0.804714\pi$
$71$		−	9.70256i		−	1.15148i	0.817632	−	0.575741i	$-0.195286\pi$
$72$		0			0
$73$	9.05926			1.06031			0.530153	−	0.847902i	$-0.322135\pi$
$73$	9.05926			1.06031			0.530153	+	0.847902i	$0.322135\pi$
$74$	−12.6496	+	1.16738i	−1.47049	+	0.135705i
$75$		0			0
$76$	4.37182	−	6.37182i	0.501482	−	0.730897i
$77$	2.10380	−	2.10380i	0.239750	−	0.239750i
$78$		0			0
$79$	9.49307			1.06805			0.534027	−	0.845468i	$-0.320678\pi$
$79$	9.49307			1.06805			0.534027	+	0.845468i	$0.320678\pi$
$80$	2.34772	−	8.63066i	0.262483	−	0.964937i
$81$		0			0
$82$	11.7779	+	9.78772i	1.30065	+	1.08087i
$83$	−2.47138	+	2.47138i	−0.271269	+	0.271269i	−0.829611	−	0.558342i	$-0.811438\pi$
$83$	−2.47138	+	2.47138i	−0.271269	+	0.271269i	0.558342	+	0.829611i	$0.311438\pi$
$84$		0			0
$85$	−8.75394	−	6.43230i	−0.949498	−	0.697680i
$86$	−14.2292	+	1.31315i	−1.53437	+	0.141600i
$87$		0			0
$88$	2.64291	−	0.748762i	0.281735	−	0.0798183i
$89$			3.75237i			0.397751i	0.980025	+	0.198875i	$0.0637289\pi$
$89$			3.75237i			0.397751i	−0.980025	+	0.198875i	$0.936271\pi$
$90$		0			0
$91$	3.43513	−	3.43513i	0.360100	−	0.360100i
$92$	1.22487	+	6.57977i	0.127701	+	0.685989i
$93$		0			0
$94$	1.33225	+	1.10713i	0.137411	+	0.114191i
$95$	−8.54028	+	1.30562i	−0.876214	+	0.133954i
$96$		0			0
$97$		−	1.58626i		−	0.161061i	−0.996752	−	0.0805303i	$-0.974339\pi$
$97$		−	1.58626i		−	0.161061i	0.996752	−	0.0805303i	$-0.0256614\pi$
$98$	2.15570	−	2.59404i	0.217759	−	0.262037i
$99$		0			0
$100$	−8.83527	+	4.68381i	−0.883527	+	0.468381i
$101$	−0.626415	+	0.626415i	−0.0623306	+	0.0623306i	−0.737585	−	0.675254i	$-0.764034\pi$
$101$	−0.626415	+	0.626415i	−0.0623306	+	0.0623306i	0.675254	+	0.737585i	$0.264034\pi$
$102$		0			0
$103$	−13.5242			−1.33258			−0.666290	−	0.745692i	$-0.732119\pi$
$103$	−13.5242			−1.33258			−0.666290	+	0.745692i	$0.732119\pi$
$104$	4.31541	−	1.22260i	0.423161	−	0.119886i
$105$		0			0
$106$	−12.0556	+	1.11256i	−1.17094	+	0.108061i
$107$	9.19102	+	9.19102i	0.888529	+	0.888529i	0.994382	−	0.105852i	$-0.0337571\pi$
$107$	9.19102	+	9.19102i	0.888529	+	0.888529i	−0.105852	+	0.994382i	$0.533757\pi$
$108$		0			0
$109$	4.70732	+	4.70732i	0.450880	+	0.450880i	0.895646	−	0.444767i	$-0.146713\pi$
$109$	4.70732	+	4.70732i	0.450880	+	0.450880i	−0.444767	+	0.895646i	$0.646713\pi$
$110$	−2.63152	−	1.58339i	−0.250906	−	0.150970i
$111$		0			0
$112$	11.4331	−	4.40951i	1.08033	−	0.416659i
$113$			2.18774i			0.205806i	0.994691	+	0.102903i	$0.0328131\pi$
$113$			2.18774i			0.205806i	−0.994691	+	0.102903i	$0.967187\pi$
$114$		0			0
$115$	4.43076	−	6.02997i	0.413170	−	0.562298i
$116$	8.00441	−	11.6662i	0.743191	−	1.08318i
$117$		0			0
$118$	−0.546793	−	5.92501i	−0.0503364	−	0.545441i
$119$		−	14.8827i		−	1.36430i
$120$		0			0
$121$			10.0568i			0.914254i
$122$	−1.93385	+	0.178467i	−0.175082	+	0.0161576i
$123$		0			0
$124$	2.86814	+	15.4071i	0.257567	+	1.38360i
$125$	10.5760	+	3.62595i	0.945949	+	0.324315i
$126$		0			0
$127$			11.3776i			1.00960i	0.863236	+	0.504801i	$0.168434\pi$
$127$			11.3776i			1.00960i	−0.863236	+	0.504801i	$0.831566\pi$
$128$	11.2011	+	1.59245i	0.990045	+	0.140754i
$129$		0			0
$130$	−4.29682	−	2.58540i	−0.376856	−	0.226755i
$131$	−14.1055	−	14.1055i	−1.23240	−	1.23240i	−0.963039	−	0.269361i	$-0.913188\pi$
$131$	−14.1055	−	14.1055i	−1.23240	−	1.23240i	−0.269361	−	0.963039i	$-0.586812\pi$
$132$		0			0
$133$	−8.36961	−	8.36961i	−0.725737	−	0.725737i
$134$	−0.914897	−	9.91374i	−0.0790350	−	0.856417i
$135$		0			0
$136$	6.69982	−	11.9967i	0.574505	−	1.02871i
$137$	−6.86660			−0.586653			−0.293327	−	0.956012i	$-0.594762\pi$
$137$	−6.86660			−0.586653			−0.293327	+	0.956012i	$0.594762\pi$
$138$		0			0
$139$	−1.05441	+	1.05441i	−0.0894340	+	0.0894340i	−0.750408	−	0.660974i	$-0.770143\pi$
$139$	−1.05441	+	1.05441i	−0.0894340	+	0.0894340i	0.660974	+	0.750408i	$0.270143\pi$
$140$	−12.3385	−	5.95479i	−1.04280	−	0.503272i
$141$		0			0
$142$	−10.5531	−	8.76989i	−0.885599	−	0.735953i
$143$		−	1.54009i		−	0.128788i
$144$		0			0
$145$	−15.6365	+	2.39048i	−1.29854	+	0.198519i
$146$	8.18842	−	9.85343i	0.677679	−	0.815475i
$147$		0			0
$148$	−10.1639	+	14.8137i	−0.835470	+	1.21768i
$149$	−5.82649	+	5.82649i	−0.477325	+	0.477325i	−0.904275	−	0.426950i	$-0.859588\pi$
$149$	−5.82649	+	5.82649i	−0.477325	+	0.477325i	0.426950	+	0.904275i	$0.359588\pi$
$150$		0			0
$151$		−	11.1154i		−	0.904562i	−0.891875	−	0.452281i	$-0.850610\pi$
$151$		−	11.1154i		−	0.904562i	0.891875	−	0.452281i	$-0.149390\pi$
$152$	−2.97883	−	10.5144i	−0.241615	−	0.852829i
$153$		0			0
$154$	−0.386657	−	4.18979i	−0.0311577	−	0.337623i
$155$	10.3750	−	14.1197i	0.833342	−	1.13412i
$156$		0			0
$157$	−7.93794	+	7.93794i	−0.633517	+	0.633517i	−0.948948	−	0.315432i	$-0.897851\pi$
$157$	−7.93794	+	7.93794i	−0.633517	+	0.633517i	0.315432	+	0.948948i	$0.397851\pi$
$158$	8.58053	−	10.3253i	0.682631	−	0.821434i
$159$		0			0
$160$	−7.26521	−	10.3545i	−0.574365	−	0.818599i
$161$	10.2517			0.807945
$162$		0			0
$163$	12.7791	−	12.7791i	1.00094	−	1.00094i	0.000937724	−	1.00000i	$-0.499702\pi$
$163$	12.7791	−	12.7791i	1.00094	−	1.00094i	1.00000		0.000937724i	$-0.000298487\pi$
$164$	21.2915	−	3.96356i	1.66259	−	0.309502i
$165$		0			0
$166$	0.454215	+	4.92184i	0.0352539	+	0.382009i
$167$	2.69519			0.208560			0.104280	−	0.994548i	$-0.466746\pi$
$167$	2.69519			0.208560			0.104280	+	0.994548i	$0.466746\pi$
$168$		0			0
$169$			10.4853i			0.806562i
$170$	−14.9086	+	3.70736i	−1.14344	+	0.284342i
$171$		0			0
$172$	−11.4331	+	16.6635i	−0.871765	+	1.27058i
$173$	−15.2031	+	15.2031i	−1.15587	+	1.15587i	−0.170512	+	0.985356i	$0.554542\pi$
$173$	−15.2031	+	15.2031i	−1.15587	+	1.15587i	−0.985356	+	0.170512i	$0.945458\pi$
$174$		0			0
$175$	4.57645	+	14.6178i	0.345947	+	1.10500i
$176$	1.57446	−	3.55138i	0.118679	−	0.267696i
$177$		0			0
$178$	4.08132	+	3.39167i	0.305908	+	0.254217i
$179$	−6.72747	−	6.72747i	−0.502835	−	0.502835i	0.409483	−	0.912318i	$-0.365709\pi$
$179$	−6.72747	−	6.72747i	−0.502835	−	0.502835i	−0.912318	+	0.409483i	$0.865709\pi$
$180$		0			0
$181$	9.45095	−	9.45095i	0.702484	−	0.702484i	−0.262459	−	0.964943i	$-0.584534\pi$
$181$	9.45095	−	9.45095i	0.702484	−	0.702484i	0.964943	+	0.262459i	$0.0845335\pi$
$182$	−0.631345	−	6.84120i	−0.0467984	−	0.507103i
$183$		0			0
$184$	8.26371	+	4.61504i	0.609209	+	0.340225i
$185$	19.8551	−	3.03541i	1.45978	−	0.223168i
$186$		0			0
$187$	−3.33622	−	3.33622i	−0.243968	−	0.243968i
$188$	2.40836	−	0.448333i	0.175648	−	0.0326981i
$189$		0			0
$190$	−6.29925	+	10.4691i	−0.456996	+	0.759506i
$191$	19.2784			1.39493			0.697467	−	0.716617i	$-0.254310\pi$
$191$	19.2784			1.39493			0.697467	+	0.716617i	$0.254310\pi$
$192$		0			0
$193$			19.7269i			1.41998i	0.704213	+	0.709988i	$0.251300\pi$
$193$			19.7269i			1.41998i	−0.704213	+	0.709988i	$0.748700\pi$
$194$	−1.72532	−	1.43378i	−0.123871	−	0.102939i
$195$		0			0
$196$	−0.872957	−	4.68936i	−0.0623541	−	0.334955i
$197$	13.7682	+	13.7682i	0.980945	+	0.980945i	0.999822	−	0.0188769i	$-0.00600906\pi$
$197$	13.7682	+	13.7682i	0.980945	+	0.980945i	−0.0188769	+	0.999822i	$0.506009\pi$
$198$		0			0
$199$			16.3633i			1.15997i	0.814628	+	0.579983i	$0.196941\pi$
$199$			16.3633i			1.15997i	−0.814628	+	0.579983i	$0.803059\pi$
$200$	−2.89155	+	13.8434i	−0.204464	+	0.978874i
$201$		0			0
$202$	0.115129	+	1.24753i	0.00810046	+	0.0877759i
$203$	−15.3240	−	15.3240i	−1.07554	−	1.07554i
$204$		0			0
$205$	−19.5124	−	14.3375i	−1.36280	−	1.00137i
$206$	−12.2242	+	14.7098i	−0.851699	+	1.02488i
$207$		0			0
$208$	2.57081	−	5.79879i	0.178254	−	0.402074i
$209$	−3.75237			−0.259557
$210$		0			0
$211$	−18.0900	−	18.0900i	−1.24537	−	1.24537i	−0.957743	−	0.287624i	$-0.907135\pi$
$211$	−18.0900	−	18.0900i	−1.24537	−	1.24537i	−0.287624	−	0.957743i	$-0.592865\pi$
$212$	−9.68665	+	14.1181i	−0.665282	+	0.969632i
$213$		0			0
$214$	18.3043	−	1.68922i	1.25125	−	0.115473i
$215$	22.3344	−	3.41444i	1.52319	−	0.232863i
$216$		0			0
$217$	24.0052			1.62958
$218$	9.37481	−	0.865161i	0.634942	−	0.0585961i
$219$		0			0
$220$	−4.10076	+	1.43103i	−0.276473	+	0.0964798i
$221$	−5.44746	−	5.44746i	−0.366436	−	0.366436i
$222$		0			0
$223$			21.8384i			1.46241i	0.682160	+	0.731203i	$0.261041\pi$
$223$			21.8384i			1.46241i	−0.682160	+	0.731203i	$0.738959\pi$
$224$	5.53801	−	16.4210i	0.370024	−	1.09717i
$225$		0			0
$226$	2.37953	+	1.97744i	0.158284	+	0.131538i
$227$	−1.08500	+	1.08500i	−0.0720141	+	0.0720141i	−0.742196	−	0.670182i	$-0.766216\pi$
$227$	−1.08500	+	1.08500i	−0.0720141	+	0.0720141i	0.670182	+	0.742196i	$0.266216\pi$
$228$		0			0
$229$	4.22088	−	4.22088i	0.278924	−	0.278924i	−0.553756	−	0.832679i	$-0.686806\pi$
$229$	4.22088	−	4.22088i	0.278924	−	0.278924i	0.832679	+	0.553756i	$0.186806\pi$
$230$	−2.55374	−	10.2695i	−0.168389	−	0.677151i
$231$		0			0
$232$	−5.45397	−	19.2509i	−0.358071	−	1.26388i
$233$	−24.3929			−1.59803			−0.799016	−	0.601309i	$-0.794646\pi$
$233$	−24.3929			−1.59803			−0.799016	+	0.601309i	$0.794646\pi$
$234$		0			0
$235$	−2.20712	−	1.62177i	−0.143977	−	0.105793i
$236$	−6.93865	−	4.76073i	−0.451668	−	0.309897i
$237$		0			0
$238$	−16.1874	−	13.4521i	−1.04927	−	0.871971i
$239$	−17.6297			−1.14037			−0.570184	−	0.821517i	$-0.693128\pi$
$239$	−17.6297			−1.14037			−0.570184	+	0.821517i	$0.693128\pi$
$240$		0			0
$241$	14.3151			0.922118			0.461059	−	0.887369i	$-0.347470\pi$
$241$	14.3151			0.922118			0.461059	+	0.887369i	$0.347470\pi$
$242$	10.9384	+	9.09007i	0.703148	+	0.584332i
$243$		0			0
$244$	−1.55384	+	2.26469i	−0.0994746	+	0.144982i
$245$	−3.15777	+	4.29752i	−0.201743	+	0.274559i
$246$		0			0
$247$	−6.12698			−0.389850
$248$	19.3502	+	10.8065i	1.22874	+	0.686216i
$249$		0			0
$250$	13.5032	−	8.22577i	0.854018	−	0.520243i
$251$	−5.26345	+	5.26345i	−0.332226	+	0.332226i	−0.853431	−	0.521205i	$-0.825483\pi$
$251$	−5.26345	+	5.26345i	−0.332226	+	0.332226i	0.521205	+	0.853431i	$0.325483\pi$
$252$		0			0
$253$	2.29808	−	2.29808i	0.144479	−	0.144479i
$254$	12.3750	+	10.2839i	0.776480	+	0.645272i
$255$		0			0
$256$	11.8564	−	10.7436i	0.741025	−	0.671477i
$257$		−	12.8006i		−	0.798481i	−0.916846	−	0.399240i	$-0.869274\pi$
$257$		−	12.8006i		−	0.798481i	0.916846	−	0.399240i	$-0.130726\pi$
$258$		0			0
$259$	19.4583	+	19.4583i	1.20908	+	1.20908i
$260$	−6.69583	+	2.33662i	−0.415257	+	0.144911i
$261$		0			0
$262$	−28.0916	+	2.59245i	−1.73550	+	0.160162i
$263$	−9.54951			−0.588848			−0.294424	−	0.955675i	$-0.595128\pi$
$263$	−9.54951			−0.588848			−0.294424	+	0.955675i	$0.595128\pi$
$264$		0			0
$265$	18.9227	−	2.89287i	1.16241	−	0.177708i
$266$	−16.6684	+	1.53825i	−1.02200	+	0.0943164i
$267$		0			0
$268$	−11.6098	−	7.96567i	−0.709180	−	0.486581i
$269$	5.82649	+	5.82649i	0.355248	+	0.355248i	0.862058	−	0.506810i	$-0.169175\pi$
$269$	5.82649	+	5.82649i	0.355248	+	0.355248i	−0.506810	+	0.862058i	$0.669175\pi$
$270$		0			0
$271$	−13.9433			−0.846996			−0.423498	−	0.905897i	$-0.639198\pi$
$271$	−13.9433			−0.846996			−0.423498	+	0.905897i	$0.639198\pi$
$272$	−6.99263	−	18.1307i	−0.423990	−	1.09933i
$273$		0			0
$274$	−6.20654	+	7.46856i	−0.374951	+	0.451192i
$275$	4.30271	+	2.25094i	0.259463	+	0.135737i
$276$		0			0
$277$	−7.24829	−	7.24829i	−0.435508	−	0.435508i	0.454989	−	0.890497i	$-0.349643\pi$
$277$	−7.24829	−	7.24829i	−0.435508	−	0.435508i	−0.890497	+	0.454989i	$0.849643\pi$
$278$	0.193791	+	2.09990i	0.0116228	+	0.125944i
$279$		0			0
$280$	−17.6293	+	8.03782i	−1.05355	+	0.480351i
$281$			19.0031i			1.13363i	0.823844	+	0.566816i	$0.191825\pi$
$281$			19.0031i			1.13363i	−0.823844	+	0.566816i	$0.808175\pi$
$282$		0			0
$283$	11.6098	+	11.6098i	0.690129	+	0.690129i	0.962260	−	0.272131i	$-0.0877284\pi$
$283$	11.6098	+	11.6098i	0.690129	+	0.690129i	−0.272131	+	0.962260i	$0.587728\pi$
$284$	−19.0774	+	3.55138i	−1.13203	+	0.210736i
$285$		0			0
$286$	−1.67510	−	1.39204i	−0.0990505	−	0.0823132i
$287$		−	33.1734i		−	1.95816i
$288$		0			0
$289$	−6.60117			−0.388304
$290$	−11.5334	+	19.1680i	−0.677264	+	1.12558i
$291$		0			0
$292$	−3.31592	−	17.8125i	−0.194049	−	1.04240i
$293$	−1.14684	−	1.14684i	−0.0669994	−	0.0669994i	0.672813	−	0.739812i	$-0.265086\pi$
$293$	−1.14684	−	1.14684i	−0.0669994	−	0.0669994i	−0.739812	+	0.672813i	$0.765086\pi$
$294$		0			0
$295$	1.42177	+	9.30002i	0.0827787	+	0.541468i
$296$	6.92540	+	24.4446i	0.402531	+	1.42082i
$297$		0			0
$298$	1.07085	+	11.6037i	0.0620329	+	0.672183i
$299$	3.75237	−	3.75237i	0.217005	−	0.217005i
$300$		0			0
$301$	21.8880	+	21.8880i	1.26161	+	1.26161i
$302$	−12.0899	−	10.0470i	−0.695694	−	0.578138i
$303$		0			0
$304$	−14.1286	−	6.26371i	−0.810330	−	0.359248i
$305$	3.03541	−	0.464048i	0.173807	−	0.0265713i
$306$		0			0
$307$	21.0730	−	21.0730i	1.20270	−	1.20270i	0.229355	−	0.973343i	$-0.426338\pi$
$307$	21.0730	−	21.0730i	1.20270	−	1.20270i	0.973343	−	0.229355i	$-0.0736616\pi$
$308$	−4.90657	−	3.36649i	−0.279578	−	0.191823i
$309$		0			0
$310$	−5.97982	−	24.0470i	−0.339631	−	1.36578i
$311$		−	0.549117i		−	0.0311376i	−0.999879	−	0.0155688i	$-0.995044\pi$
$311$		−	0.549117i		−	0.0311376i	0.999879	−	0.0155688i	$-0.00495590\pi$
$312$		0			0
$313$	24.2122			1.36855			0.684277	−	0.729222i	$-0.260118\pi$
$313$	24.2122			1.36855			0.684277	+	0.729222i	$0.260118\pi$
$314$	1.45892	+	15.8087i	0.0823315	+	0.892137i
$315$		0			0
$316$	−3.47470	−	18.6655i	−0.195467	−	1.05001i
$317$	21.3168	−	21.3168i	1.19727	−	1.19727i	0.222287	−	0.974981i	$-0.428648\pi$
$317$	21.3168	−	21.3168i	1.19727	−	1.19727i	0.974981	−	0.222287i	$-0.0713523\pi$
$318$		0			0
$319$	−6.87027			−0.384661
$320$	−17.8291	−	1.45710i	−0.996677	−	0.0814541i
$321$		0			0
$322$	9.26622	−	11.1504i	0.516386	−	0.621386i
$323$	−13.2726	+	13.2726i	−0.738506	+	0.738506i
$324$		0			0
$325$	7.02558	+	3.67539i	0.389709	+	0.203874i
$326$	−2.34868	−	25.4501i	−0.130081	−	1.40955i
$327$		0			0
$328$	14.9338	−	26.7406i	0.824581	−	1.47650i
$329$		−	3.75237i		−	0.206875i
$330$		0			0
$331$	−19.4552	+	19.4552i	−1.06935	+	1.06935i	−0.0719456	+	0.997409i	$0.522921\pi$
$331$	−19.4552	+	19.4552i	−1.06935	+	1.06935i	−0.997409	+	0.0719456i	$0.977079\pi$
$332$	5.76386	+	3.95469i	0.316333	+	0.217042i
$333$		0			0
$334$	2.43611	−	2.93146i	0.133298	−	0.160403i
$335$	2.37891	+	15.5608i	0.129974	+	0.850178i
$336$		0			0
$337$			31.7739i			1.73084i	0.501050	+	0.865418i	$0.332947\pi$
$337$			31.7739i			1.73084i	−0.501050	+	0.865418i	$0.667053\pi$
$338$	11.4045	+	9.47739i	0.620322	+	0.515502i
$339$		0			0
$340$	−9.44315	+	19.5666i	−0.512127	+	1.06115i
$341$	5.38118	−	5.38118i	0.291407	−	0.291407i
$342$		0			0
$343$	14.1381			0.763386
$344$	7.79017	+	27.4970i	0.420018	+	1.48254i
$345$		0			0
$346$	2.79418	+	30.2775i	0.150216	+	1.62773i
$347$	8.26752	+	8.26752i	0.443824	+	0.443824i	0.893295	−	0.449471i	$-0.148388\pi$
$347$	8.26752	+	8.26752i	0.443824	+	0.443824i	−0.449471	+	0.893295i	$0.648388\pi$
$348$		0			0
$349$	−8.22088	−	8.22088i	−0.440054	−	0.440054i	0.451976	−	0.892030i	$-0.350719\pi$
$349$	−8.22088	−	8.22088i	−0.440054	−	0.440054i	−0.892030	+	0.451976i	$0.850719\pi$
$350$	20.0358	+	8.23501i	1.07096	+	0.440180i
$351$		0			0
$352$	−2.43960	−	4.92248i	−0.130031	−	0.262369i
$353$		−	11.4485i		−	0.609344i	−0.952457	−	0.304672i	$-0.901453\pi$
$353$		−	11.4485i		−	0.609344i	0.952457	−	0.304672i	$-0.0985468\pi$
$354$		0			0
$355$	17.4833	+	12.8465i	0.927916	+	0.681823i
$356$	7.37800	−	1.37346i	0.391033	−	0.0727935i
$357$		0			0
$358$	−13.3980	+	1.23644i	−0.708106	+	0.0653481i
$359$			32.5124i			1.71594i	0.513700	+	0.857970i	$0.328275\pi$
$359$			32.5124i			1.71594i	−0.513700	+	0.857970i	$0.671725\pi$
$360$		0			0
$361$		−	4.07180i		−	0.214305i
$362$	−1.73699	−	18.8219i	−0.0912944	−	0.989259i
$363$		0			0
$364$	−8.01158	−	5.49689i	−0.419921	−	0.288115i
$365$	−11.9948	+	16.3241i	−0.627835	+	0.854443i
$366$		0			0
$367$			23.3286i			1.21774i	0.793269	+	0.608871i	$0.208377\pi$
$367$			23.3286i			1.21774i	−0.793269	+	0.608871i	$0.791623\pi$
$368$	12.4890	−	4.81673i	0.651032	−	0.251089i
$369$		0			0
$370$	14.6450	−	24.3393i	0.761356	−	1.26534i
$371$	18.5446	+	18.5446i	0.962786	+	0.962786i
$372$		0			0
$373$	−9.28396	−	9.28396i	−0.480705	−	0.480705i	0.424652	−	0.905357i	$-0.360397\pi$
$373$	−9.28396	−	9.28396i	−0.480705	−	0.480705i	−0.905357	+	0.424652i	$0.860397\pi$
$374$	−6.64420	+	0.613164i	−0.343563	+	0.0317060i
$375$		0			0
$376$	1.68922	−	3.02473i	0.0871149	−	0.155988i
$377$	−11.2180			−0.577754
$378$		0			0
$379$	12.9398	−	12.9398i	0.664672	−	0.664672i	−0.291806	−	0.956478i	$-0.594256\pi$
$379$	12.9398	−	12.9398i	0.664672	−	0.664672i	0.956478	+	0.291806i	$0.0942560\pi$
$380$	5.69310	+	16.3142i	0.292050	+	0.836900i
$381$		0			0
$382$	17.4252	−	20.9684i	0.891551	−	1.07284i
$383$			37.7317i			1.92800i	0.265902	+	0.964000i	$0.414330\pi$
$383$			37.7317i			1.92800i	−0.265902	+	0.964000i	$0.585670\pi$
$384$		0			0
$385$	1.00539	+	6.57638i	0.0512392	+	0.335163i
$386$	21.4563	+	17.8307i	1.09210	+	0.907557i
$387$		0			0
$388$	−3.11894	+	0.580613i	−0.158340	+	0.0294761i
$389$	−2.30161	+	2.30161i	−0.116696	+	0.116696i	−0.763043	−	0.646347i	$-0.776296\pi$
$389$	−2.30161	+	2.30161i	−0.116696	+	0.116696i	0.646347	+	0.763043i	$0.276296\pi$
$390$		0			0
$391$		−	16.2572i		−	0.822161i
$392$	−5.88949	−	3.28911i	−0.297464	−	0.166125i
$393$		0			0
$394$	27.4199	−	2.53047i	1.38140	−	0.127483i
$395$	−12.5691	+	17.1058i	−0.632422	+	0.860686i
$396$		0			0
$397$	7.99340	−	7.99340i	0.401177	−	0.401177i	−0.477471	−	0.878648i	$-0.658446\pi$
$397$	7.99340	−	7.99340i	0.401177	−	0.401177i	0.878648	+	0.477471i	$0.158446\pi$
$398$	17.7978	+	14.7904i	0.892124	+	0.741375i
$399$		0			0
$400$	12.4433	+	15.6577i	0.622167	+	0.782885i
$401$	−8.17450			−0.408215			−0.204108	−	0.978948i	$-0.565429\pi$
$401$	−8.17450			−0.408215			−0.204108	+	0.978948i	$0.565429\pi$
$402$		0			0
$403$	8.78653	−	8.78653i	0.437688	−	0.437688i
$404$	1.46095	+	1.00239i	0.0726852	+	0.0498706i
$405$		0			0
$406$	−30.5184	+	2.81641i	−1.51460	+	0.139776i
$407$	8.72380			0.432423
$408$		0			0
$409$		−	18.5294i		−	0.916219i	−0.888896	−	0.458109i	$-0.848527\pi$
$409$		−	18.5294i		−	0.916219i	0.888896	−	0.458109i	$-0.151473\pi$
$410$	−33.2311	+	8.26365i	−1.64117	+	0.408113i
$411$		0			0
$412$	4.95021	+	26.5916i	0.243879	+	1.31007i
$413$	−9.11416	+	9.11416i	−0.448479	+	0.448479i
$414$		0			0
$415$	−1.18105	−	7.72542i	−0.0579754	−	0.379226i
$416$	−3.98345	−	8.03756i	−0.195305	−	0.394074i
$417$		0			0
$418$	−3.39167	+	4.08132i	−0.165892	+	0.199624i
$419$	9.01583	+	9.01583i	0.440452	+	0.440452i	0.892164	−	0.451712i	$-0.149186\pi$
$419$	9.01583	+	9.01583i	0.440452	+	0.440452i	−0.451712	+	0.892164i	$0.649186\pi$
$420$		0			0
$421$	−14.8274	+	14.8274i	−0.722645	+	0.722645i	−0.969143	−	0.246498i	$-0.920720\pi$
$421$	−14.8274	+	14.8274i	−0.722645	+	0.722645i	0.246498	+	0.969143i	$0.420720\pi$
$422$	−36.0269	+	3.32477i	−1.75376	+	0.161847i
$423$		0			0
$424$	6.60020	+	23.2968i	0.320534	+	1.13139i
$425$	23.1810	−	7.25736i	1.12444	−	0.352034i
$426$		0			0
$427$	2.97475	+	2.97475i	0.143958	+	0.143958i
$428$	14.7074	−	21.4357i	0.710910	−	1.03613i
$429$		0			0
$430$	16.4737	−	27.3785i	0.794432	−	1.32031i
$431$	−17.0806			−0.822742			−0.411371	−	0.911468i	$-0.634950\pi$
$431$	−17.0806			−0.822742			−0.411371	+	0.911468i	$0.634950\pi$
$432$		0			0
$433$		−	18.3255i		−	0.880666i	−0.897834	−	0.440333i	$-0.854860\pi$
$433$		−	18.3255i		−	0.880666i	0.897834	−	0.440333i	$-0.145140\pi$
$434$	21.6977	−	26.1096i	1.04152	−	1.25330i
$435$		0			0
$436$	7.53264	−	10.9786i	0.360748	−	0.525781i
$437$	−9.14255	−	9.14255i	−0.437348	−	0.437348i
$438$		0			0
$439$		−	13.7865i		−	0.657992i	−0.944331	−	0.328996i	$-0.893290\pi$
$439$		−	13.7865i		−	0.657992i	0.944331	−	0.328996i	$-0.106710\pi$
$440$	−2.15009	+	5.75371i	−0.102502	+	0.274297i
$441$		0			0
$442$	−10.8488	+	1.00119i	−0.516026	+	0.0476218i
$443$	−3.17106	−	3.17106i	−0.150662	−	0.150662i	0.627752	−	0.778413i	$-0.283975\pi$
$443$	−3.17106	−	3.17106i	−0.150662	−	0.150662i	−0.778413	+	0.627752i	$0.783975\pi$
$444$		0			0
$445$	−6.76150	−	4.96827i	−0.320526	−	0.235519i
$446$	23.7528	+	19.7391i	1.12473	+	0.934675i
$447$		0			0
$448$	−12.8549	−	20.8660i	−0.607335	−	0.985826i
$449$	6.43302			0.303593			0.151796	−	0.988412i	$-0.451494\pi$
$449$	6.43302			0.303593			0.151796	+	0.988412i	$0.451494\pi$
$450$		0			0
$451$	−7.43638	−	7.43638i	−0.350165	−	0.350165i
$452$	4.30159	−	0.800770i	0.202330	−	0.0376651i
$453$		0			0
$454$	0.199413	+	2.16082i	0.00935891	+	0.101412i
$455$	1.64162	+	10.7381i	0.0769603	+	0.503409i
$456$		0			0
$457$	18.3255			0.857230			0.428615	−	0.903487i	$-0.359002\pi$
$457$	18.3255			0.857230			0.428615	+	0.903487i	$0.359002\pi$
$458$	−0.775757	−	8.40604i	−0.0362488	−	0.392788i
$459$		0			0
$460$	−13.4780	−	6.50472i	−0.628416	−	0.303284i
$461$	−6.00759	−	6.00759i	−0.279801	−	0.279801i	0.553228	−	0.833030i	$-0.313396\pi$
$461$	−6.00759	−	6.00759i	−0.279801	−	0.279801i	−0.833030	+	0.553228i	$0.813396\pi$
$462$		0			0
$463$			21.1820i			0.984411i	0.870479	+	0.492206i	$0.163809\pi$
$463$			21.1820i			0.984411i	−0.870479	+	0.492206i	$0.836191\pi$
$464$	−25.8682	−	11.4683i	−1.20090	−	0.532403i
$465$		0			0
$466$	−22.0481	+	26.5313i	−1.02136	+	1.22904i
$467$	−7.65179	+	7.65179i	−0.354083	+	0.354083i	−0.861626	−	0.507544i	$-0.830554\pi$
$467$	−7.65179	+	7.65179i	−0.354083	+	0.354083i	0.507544	+	0.861626i	$0.330554\pi$
$468$		0			0
$469$	−15.2498	+	15.2498i	−0.704173	+	0.704173i
$470$	−3.75890	+	0.934734i	−0.173385	+	0.0431161i
$471$		0			0
$472$	−11.4497	+	3.24382i	−0.527017	+	0.149309i
$473$	9.81314			0.451209
$474$		0			0
$475$	8.95499	−	17.1176i	0.410883	−	0.785411i
$476$	−29.2628	+	5.44746i	−1.34126	+	0.249684i
$477$		0			0
$478$	−15.9350	+	19.1752i	−0.728850	+	0.877051i
$479$	33.0615			1.51062			0.755310	−	0.655368i	$-0.227486\pi$
$479$	33.0615			1.51062			0.755310	+	0.655368i	$0.227486\pi$
$480$		0			0
$481$	14.2445			0.649492
$482$	12.9391	−	15.5700i	0.589358	−	0.709196i
$483$		0			0
$484$	19.7739	−	3.68104i	0.898813	−	0.167320i
$485$	2.85833	+	2.10027i	0.129790	+	0.0953682i
$486$		0			0
$487$	−8.05361			−0.364944			−0.182472	−	0.983211i	$-0.558410\pi$
$487$	−8.05361			−0.364944			−0.182472	+	0.983211i	$0.558410\pi$
$488$	1.05874	+	3.73705i	0.0479270	+	0.169168i
$489$		0			0
$490$	1.82004	+	7.31901i	0.0822208	+	0.330639i
$491$	−13.2811	+	13.2811i	−0.599368	+	0.599368i	−0.940145	−	0.340776i	$-0.889310\pi$
$491$	−13.2811	+	13.2811i	−0.599368	+	0.599368i	0.340776	+	0.940145i	$0.389310\pi$
$492$		0			0
$493$	−24.3009	+	24.3009i	−1.09446	+	1.09446i
$494$	−5.53801	+	6.66409i	−0.249167	+	0.299832i
$495$		0			0
$496$	29.2440	−	11.2788i	1.31310	−	0.506434i
$497$			29.7237i			1.33329i
$498$		0			0
$499$	−2.65363	−	2.65363i	−0.118793	−	0.118793i	0.645211	−	0.764004i	$-0.276769\pi$
$499$	−2.65363	−	2.65363i	−0.118793	−	0.118793i	−0.764004	+	0.645211i	$0.776769\pi$
$500$	3.25832	−	22.1220i	0.145717	−	0.989326i
$501$		0			0
$502$	0.967372	+	10.4824i	0.0431759	+	0.467851i
$503$	−39.3687			−1.75536			−0.877682	−	0.479243i	$-0.840911\pi$
$503$	−39.3687			−1.75536			−0.877682	+	0.479243i	$0.840911\pi$
$504$		0			0
$505$	−0.299358	−	1.95815i	−0.0133213	−	0.0871365i
$506$	−0.422366	−	4.57672i	−0.0187765	−	0.203460i
$507$		0			0
$508$	22.3710	−	4.16451i	0.992551	−	0.184770i
$509$	−17.4596	−	17.4596i	−0.773883	−	0.773883i	0.204900	−	0.978783i	$-0.434313\pi$
$509$	−17.4596	−	17.4596i	−0.773883	−	0.773883i	−0.978783	+	0.204900i	$0.934313\pi$
$510$		0			0
$511$	−27.7529			−1.22772
$512$	−0.968769	−	22.6067i	−0.0428139	−	0.999083i
$513$		0			0
$514$	−13.9228	−	11.5701i	−0.614107	−	0.510337i
$515$	17.9065	−	24.3696i	0.789056	−	1.07385i
$516$		0			0
$517$	−0.841157	−	0.841157i	−0.0369941	−	0.0369941i
$518$	38.7519	−	3.57625i	1.70266	−	0.157131i
$519$		0			0
$520$	−3.51072	+	9.39481i	−0.153955	+	0.411990i
$521$		−	40.0835i		−	1.75609i	−0.478580	−	0.878044i	$-0.658848\pi$
$521$		−	40.0835i		−	1.75609i	0.478580	−	0.878044i	$-0.341152\pi$
$522$		0			0
$523$	−2.82324	−	2.82324i	−0.123452	−	0.123452i	0.642682	−	0.766133i	$-0.277822\pi$
$523$	−2.82324	−	2.82324i	−0.123452	−	0.123452i	−0.766133	+	0.642682i	$0.777822\pi$
$524$	−22.5715	+	32.8974i	−0.986041	+	1.43713i
$525$		0			0
$526$	−8.63155	+	10.3867i	−0.376353	+	0.452880i
$527$		−	38.0677i		−	1.65826i
$528$		0			0
$529$	−11.8016			−0.513112
$530$	13.9573	−	23.1964i	0.606266	−	1.00759i
$531$		0			0
$532$	−13.3930	+	19.5200i	−0.580661	+	0.846299i
$533$	−12.1423	−	12.1423i	−0.525942	−	0.525942i
$534$		0			0
$535$	−28.7307	+	4.39230i	−1.24214	+	0.189896i
$536$	−19.1577	+	5.42757i	−0.827488	+	0.234435i
$537$		0			0
$538$	11.6037	−	1.07085i	0.500270	−	0.0461678i
$539$	−1.63783	+	1.63783i	−0.0705464	+	0.0705464i
$540$		0			0
$541$	25.3653	+	25.3653i	1.09054	+	1.09054i	0.995471	+	0.0950685i	$0.0303070\pi$
$541$	25.3653	+	25.3653i	1.09054	+	1.09054i	0.0950685	+	0.995471i	$0.469693\pi$
$542$	−12.6030	+	15.1656i	−0.541345	+	0.651420i
$543$		0			0
$544$	−26.0405	−	8.78222i	−1.11648	−	0.376535i
$545$	−14.7149	+	2.24959i	−0.630317	+	0.0963617i
$546$		0			0
$547$	−17.1007	+	17.1007i	−0.731172	+	0.731172i	−0.970852	−	0.239680i	$-0.922958\pi$
$547$	−17.1007	+	17.1007i	−0.731172	+	0.731172i	0.239680	+	0.970852i	$0.422958\pi$
$548$	2.51335	+	13.5013i	0.107365	+	0.576745i
$549$		0			0
$550$	6.33737	−	2.64534i	0.270226	−	0.112798i
$551$			27.3322i			1.16439i
$552$		0			0
$553$	−29.0819			−1.23669
$554$	−14.4352	+	1.33217i	−0.613295	+	0.0565983i
$555$		0			0
$556$	2.45915	+	1.68726i	0.104291	+	0.0715559i
$557$	31.4151	−	31.4151i	1.33110	−	1.33110i	0.426713	−	0.904387i	$-0.359671\pi$
$557$	31.4151	−	31.4151i	1.33110	−	1.33110i	0.904387	−	0.426713i	$-0.140329\pi$
$558$		0			0
$559$	16.0232			0.677708
$560$	−7.19221	+	26.4399i	−0.303926	+	1.11729i
$561$		0			0
$562$	20.6690	+	17.1764i	0.871870	+	0.724544i
$563$	11.5009	−	11.5009i	0.484705	−	0.484705i	−0.421926	−	0.906630i	$-0.638646\pi$
$563$	11.5009	−	11.5009i	0.484705	−	0.484705i	0.906630	+	0.421926i	$0.138646\pi$
$564$		0			0
$565$	−3.94215	−	2.89665i	−0.165848	−	0.121863i
$566$	23.1213	−	2.13376i	0.971860	−	0.0896888i
$567$		0			0
$568$	−13.3808	+	23.9598i	−0.561447	+	1.00533i
$569$		−	17.3279i		−	0.726425i	−0.931706	−	0.363213i	$-0.881680\pi$
$569$		−	17.3279i		−	0.726425i	0.931706	−	0.363213i	$-0.118320\pi$
$570$		0			0
$571$	9.28844	−	9.28844i	0.388709	−	0.388709i	−0.485518	−	0.874227i	$-0.661369\pi$
$571$	9.28844	−	9.28844i	0.388709	−	0.388709i	0.874227	+	0.485518i	$0.161369\pi$
$572$	−3.02815	+	0.563710i	−0.126613	+	0.0235699i
$573$		0			0
$574$	−36.0815	−	29.9846i	−1.50601	−	1.25153i
$575$	4.99909	+	15.9678i	0.208476	+	0.665902i
$576$		0			0
$577$		−	16.3475i		−	0.680554i	−0.940325	−	0.340277i	$-0.889479\pi$
$577$		−	16.3475i		−	0.680554i	0.940325	−	0.340277i	$-0.110521\pi$
$578$	−5.96663	+	7.17986i	−0.248179	+	0.298643i
$579$		0			0
$580$	10.4236	+	29.8698i	0.432815	+	1.24028i
$581$	7.57104	−	7.57104i	0.314099	−	0.314099i
$582$		0			0
$583$	8.31415			0.344337
$584$	−22.3712	−	12.4936i	−0.925726	−	0.516991i
$585$		0			0
$586$	−2.28398	+	0.210779i	−0.0943505	+	0.00870720i
$587$	23.8984	+	23.8984i	0.986395	+	0.986395i	0.999909	−	0.0135141i	$-0.00430182\pi$
$587$	23.8984	+	23.8984i	0.986395	+	0.986395i	−0.0135141	+	0.999909i	$0.504302\pi$
$588$		0			0
$589$	−21.4081	−	21.4081i	−0.882106	−	0.882106i
$590$	11.4004	+	6.85963i	0.469347	+	0.282407i
$591$		0			0
$592$	32.8472	+	14.5623i	1.35001	+	0.598509i
$593$			14.7736i			0.606681i	0.952882	+	0.303340i	$0.0981019\pi$
$593$			14.7736i			0.606681i	−0.952882	+	0.303340i	$0.901898\pi$
$594$		0			0
$595$	26.8176	+	19.7053i	1.09941	+	0.807837i
$596$	13.5888	+	9.32353i	0.556620	+	0.381907i
$597$		0			0
$598$	−0.689650	−	7.47299i	−0.0282019	−	0.305593i
$599$		−	15.0697i		−	0.615730i	−0.951430	−	0.307865i	$-0.900386\pi$
$599$		−	15.0697i		−	0.615730i	0.951430	−	0.307865i	$-0.0996145\pi$
$600$		0			0
$601$			37.1294i			1.51454i	0.653102	+	0.757270i	$0.273467\pi$
$601$			37.1294i			1.51454i	−0.653102	+	0.757270i	$0.726533\pi$
$602$	43.5909	−	4.02281i	1.77663	−	0.163958i
$603$		0			0
$604$	−21.8554	+	4.06854i	−0.889285	+	0.165546i
$605$	−18.1216	−	13.3155i	−0.736748	−	0.541354i
$606$		0			0
$607$		−	18.3385i		−	0.744335i	−0.928166	−	0.372168i	$-0.878615\pi$
$607$		−	18.3385i		−	0.744335i	0.928166	−	0.372168i	$-0.121385\pi$
$608$	−19.5833	+	9.70556i	−0.794207	+	0.393612i
$609$		0			0
$610$	2.23890	−	3.72095i	0.0906503	−	0.150657i
$611$	−1.37346	−	1.37346i	−0.0555644	−	0.0555644i
$612$		0			0
$613$	−19.3507	−	19.3507i	−0.781569	−	0.781569i	0.198527	−	0.980096i	$-0.436384\pi$
$613$	−19.3507	−	19.3507i	−0.781569	−	0.781569i	−0.980096	+	0.198527i	$0.936384\pi$
$614$	−3.87301	−	41.9676i	−0.156302	−	1.69367i
$615$		0			0
$616$	−8.09652	+	2.29382i	−0.326218	+	0.0924208i
$617$	−24.3361			−0.979736			−0.489868	−	0.871797i	$-0.662955\pi$
$617$	−24.3361			−0.979736			−0.489868	+	0.871797i	$0.662955\pi$
$618$		0			0
$619$	−9.73868	+	9.73868i	−0.391430	+	0.391430i	−0.875197	−	0.483767i	$-0.839268\pi$
$619$	−9.73868	+	9.73868i	−0.391430	+	0.391430i	0.483767	+	0.875197i	$0.339268\pi$
$620$	−31.5600	−	15.2314i	−1.26748	−	0.611708i
$621$		0			0
$622$	−0.597255	−	0.496332i	−0.0239477	−	0.0199011i
$623$		−	11.4954i		−	0.460552i
$624$		0			0
$625$	−20.5367	+	14.2563i	−0.821469	+	0.570253i
$626$	21.8848	−	26.3347i	0.874691	−	1.05255i
$627$		0			0
$628$	18.5132	+	12.7023i	0.738759	+	0.506875i
$629$	30.8571	−	30.8571i	1.23035	−	1.23035i
$630$		0			0
$631$		−	12.0931i		−	0.481419i	−0.970597	−	0.240709i	$-0.922620\pi$
$631$		−	12.0931i		−	0.481419i	0.970597	−	0.240709i	$-0.0773801\pi$
$632$	−23.4425	−	13.0919i	−0.932491	−	0.520768i
$633$		0			0
$634$	−3.91782	−	42.4531i	−0.155596	−	1.68603i
$635$	−20.5017	−	15.0644i	−0.813583	−	0.597812i
$636$		0			0
$637$	−2.67429	+	2.67429i	−0.105959	+	0.105959i
$638$	−6.20985	+	7.47254i	−0.245850	+	0.295841i
$639$		0			0
$640$	−17.7001	+	18.0750i	−0.699657	+	0.714479i
$641$	−23.0912			−0.912048			−0.456024	−	0.889968i	$-0.650727\pi$
$641$	−23.0912			−0.912048			−0.456024	+	0.889968i	$0.650727\pi$
$642$		0			0
$643$	−4.46496	+	4.46496i	−0.176081	+	0.176081i	−0.789645	−	0.613564i	$-0.789735\pi$
$643$	−4.46496	+	4.46496i	−0.176081	+	0.176081i	0.613564	+	0.789645i	$0.289735\pi$
$644$	−3.75237	−	20.1571i	−0.147864	−	0.794300i
$645$		0			0
$646$	2.43937	+	26.4329i	0.0959759	+	1.03999i
$647$	−32.2496			−1.26786			−0.633931	−	0.773390i	$-0.718560\pi$
$647$	−32.2496			−1.26786			−0.633931	+	0.773390i	$0.718560\pi$
$648$		0			0
$649$			4.08618i			0.160397i
$650$	10.3478	−	4.31938i	0.405875	−	0.169420i
$651$		0			0
$652$	−29.8040	−	20.4491i	−1.16722	−	0.800848i
$653$	−10.2610	+	10.2610i	−0.401544	+	0.401544i	−0.878777	−	0.477233i	$-0.841640\pi$
$653$	−10.2610	+	10.2610i	−0.401544	+	0.401544i	0.477233	+	0.878777i	$0.341640\pi$
$654$		0			0
$655$	44.0931	−	6.74087i	1.72286	−	0.263388i
$656$	−15.5865	−	40.4130i	−0.608549	−	1.57786i
$657$		0			0
$658$	−4.08132	−	3.39167i	−0.159106	−	0.132221i
$659$	25.1815	+	25.1815i	0.980932	+	0.980932i	0.999822	−	0.0188900i	$-0.00601323\pi$
$659$	25.1815	+	25.1815i	0.980932	+	0.980932i	−0.0188900	+	0.999822i	$0.506013\pi$
$660$		0			0
$661$	18.5425	−	18.5425i	0.721221	−	0.721221i	−0.247633	−	0.968854i	$-0.579653\pi$
$661$	18.5425	−	18.5425i	0.721221	−	0.721221i	0.968854	+	0.247633i	$0.0796528\pi$
$662$	3.57568	+	38.7457i	0.138973	+	1.50590i
$663$		0			0
$664$	9.51117	−	2.69461i	0.369105	−	0.104571i
$665$	26.1630	−	3.99976i	1.01456	−	0.155104i
$666$		0			0
$667$	−16.7392	−	16.7392i	−0.648145	−	0.648145i
$668$	−0.986509	−	5.29934i	−0.0381692	−	0.205038i
$669$		0			0
$670$	19.0752	+	11.4776i	0.736938	+	0.443417i
$671$	1.33368			0.0514861
$672$		0			0
$673$		−	4.27830i		−	0.164916i	−0.996595	−	0.0824581i	$-0.973723\pi$
$673$		−	4.27830i		−	0.164916i	0.996595	−	0.0824581i	$-0.0262771\pi$
$674$	34.5594	+	28.7196i	1.33118	+	1.10624i
$675$		0			0
$676$	20.6164	−	3.83789i	0.792940	−	0.147611i
$677$	20.2120	+	20.2120i	0.776811	+	0.776811i	0.979287	−	0.202476i	$-0.0648988\pi$
$677$	20.2120	+	20.2120i	0.776811	+	0.776811i	−0.202476	+	0.979287i	$0.564899\pi$
$678$		0			0
$679$			4.85950i			0.186490i
$680$	12.7464	+	27.9567i	0.488803	+	1.07209i
$681$		0			0
$682$	−0.989008	−	10.7168i	−0.0378711	−	0.410368i
$683$	−19.6208	−	19.6208i	−0.750767	−	0.750767i	0.223855	−	0.974622i	$-0.428136\pi$
$683$	−19.6208	−	19.6208i	−0.750767	−	0.750767i	−0.974622	+	0.223855i	$0.928136\pi$
$684$		0			0
$685$	9.09162	−	12.3731i	0.347373	−	0.472752i
$686$	12.7791	−	15.3775i	0.487907	−	0.587116i
$687$		0			0
$688$	36.9488	+	16.3807i	1.40866	+	0.624510i
$689$	13.5756			0.517188
$690$		0			0
$691$	−26.5622	−	26.5622i	−1.01047	−	1.01047i	−0.999945	−	0.0105277i	$-0.996649\pi$
$691$	−26.5622	−	26.5622i	−1.01047	−	1.01047i	−0.0105277	−	0.999945i	$-0.503351\pi$
$692$	35.4573	+	24.3279i	1.34788	+	0.924807i
$693$		0			0
$694$	16.4651	−	1.51949i	0.625006	−	0.0576791i
$695$	−0.503893	−	3.29605i	−0.0191138	−	0.125026i
$696$		0			0
$697$	−52.6067			−1.99262
$698$	−16.3722	+	1.51092i	−0.619697	+	0.0571891i
$699$		0			0
$700$	27.0667	−	14.3488i	1.02303	−	0.542333i
$701$	6.02748	+	6.02748i	0.227655	+	0.227655i	0.811712	−	0.584057i	$-0.198536\pi$
$701$	6.02748	+	6.02748i	0.227655	+	0.227655i	−0.584057	+	0.811712i	$0.698536\pi$
$702$		0			0
$703$		−	34.7062i		−	1.30897i
$704$	−7.55910	−	1.79583i	−0.284894	−	0.0676829i
$705$		0			0
$706$	−12.4521	−	10.3480i	−0.468643	−	0.389453i
$707$	1.91902	−	1.91902i	0.0721720	−	0.0721720i
$708$		0			0
$709$	25.4722	−	25.4722i	0.956627	−	0.956627i	−0.0424707	−	0.999098i	$-0.513523\pi$
$709$	25.4722	−	25.4722i	0.956627	−	0.956627i	0.999098	+	0.0424707i	$0.0135229\pi$
$710$	29.7754	−	7.40431i	1.11745	−	0.277879i
$711$		0			0
$712$	5.17491	−	9.26622i	0.193938	−	0.347266i
$713$	26.2222			0.982028
$714$		0			0
$715$	2.77512	+	2.03913i	0.103784	+	0.0762590i
$716$	−10.7653	+	15.6901i	−0.402317	+	0.586367i
$717$		0			0
$718$	35.3626	+	29.3871i	1.31972	+	1.09672i
$719$	−19.5138			−0.727743			−0.363871	−	0.931449i	$-0.618545\pi$
$719$	−19.5138			−0.727743			−0.363871	+	0.931449i	$0.618545\pi$
$720$		0			0
$721$	41.4313			1.54298
$722$	−4.42875	−	3.68039i	−0.164821	−	0.136970i
$723$		0			0
$724$	−22.0420	−	15.1234i	−0.819183	−	0.562056i
$725$	16.3958	−	31.3409i	0.608925	−	1.16397i
$726$		0			0
$727$	17.5046			0.649210			0.324605	−	0.945850i	$-0.394769\pi$
$727$	17.5046			0.649210			0.324605	+	0.945850i	$0.394769\pi$
$728$	−13.2202	+	3.74542i	−0.489974	+	0.138814i
$729$		0			0
$730$	6.91339	+	27.8012i	0.255876	+	1.02897i
$731$	34.7102	−	34.7102i	1.28380	−	1.28380i
$732$		0			0
$733$	27.1600	−	27.1600i	1.00318	−	1.00318i	0.00318373	−	0.999995i	$-0.498987\pi$
$733$	27.1600	−	27.1600i	1.00318	−	1.00318i	0.999995	−	0.00318373i	$-0.00101341\pi$
$734$	25.3737	+	21.0861i	0.936559	+	0.778302i
$735$		0			0
$736$	6.04946	−	17.9375i	0.222986	−	0.661185i
$737$			6.83702i			0.251845i
$738$		0			0
$739$	−23.2042	−	23.2042i	−0.853581	−	0.853581i	0.136992	−	0.990572i	$-0.456257\pi$
$739$	−23.2042	−	23.2042i	−0.853581	−	0.853581i	−0.990572	+	0.136992i	$0.956257\pi$
$740$	−13.2358	−	37.9285i	−0.486556	−	1.39428i
$741$		0			0
$742$	36.9322	−	3.40831i	1.35582	−	0.125123i
$743$	34.8880			1.27992			0.639958	−	0.768410i	$-0.278952\pi$
$743$	34.8880			1.27992			0.639958	+	0.768410i	$0.278952\pi$
$744$		0			0
$745$	−2.78443	−	18.2134i	−0.102014	−	0.667287i
$746$	−18.4894	+	1.70630i	−0.676943	+	0.0624722i
$747$		0			0
$748$	−5.33860	+	7.78088i	−0.195199	+	0.284497i
$749$	−28.1566	−	28.1566i	−1.02882	−	1.02882i
$750$		0			0
$751$	−10.7811			−0.393407			−0.196704	−	0.980463i	$-0.563024\pi$
$751$	−10.7811			−0.393407			−0.196704	+	0.980463i	$0.563024\pi$
$752$	−1.76305	−	4.57128i	−0.0642916	−	0.166697i
$753$		0			0
$754$	−10.1396	+	12.2014i	−0.369263	+	0.444348i
$755$	20.0292	+	14.7172i	0.728937	+	0.535615i
$756$		0			0
$757$	−5.00566	−	5.00566i	−0.181934	−	0.181934i	0.610264	−	0.792198i	$-0.291063\pi$
$757$	−5.00566	−	5.00566i	−0.181934	−	0.181934i	−0.792198	+	0.610264i	$0.791063\pi$
$758$	−2.37821	−	25.7701i	−0.0863804	−	0.936011i
$759$		0			0
$760$	22.8902	+	8.55378i	0.830315	+	0.310278i
$761$		−	46.5987i		−	1.68920i	−0.535398	−	0.844600i	$-0.679838\pi$
$761$		−	46.5987i		−	1.68920i	0.535398	−	0.844600i	$-0.320162\pi$
$762$		0			0
$763$	−14.4208	−	14.4208i	−0.522069	−	0.522069i
$764$	−7.05637	−	37.9055i	−0.255291	−	1.37137i
$765$		0			0
$766$	41.0394	+	34.1047i	1.48281	+	1.23225i
$767$			6.67203i			0.240913i
$768$		0			0
$769$	−28.9989			−1.04573			−0.522863	−	0.852417i	$-0.675136\pi$
$769$	−28.9989			−1.04573			−0.522863	+	0.852417i	$0.675136\pi$
$770$	8.06163	+	4.85070i	0.290521	+	0.174807i
$771$		0			0
$772$	38.7875	−	7.22056i	1.39599	−	0.259874i
$773$	−20.7786	−	20.7786i	−0.747354	−	0.747354i	0.226628	−	0.973981i	$-0.427230\pi$
$773$	−20.7786	−	20.7786i	−0.747354	−	0.747354i	−0.973981	+	0.226628i	$0.927230\pi$
$774$		0			0
$775$	11.7058	+	37.3900i	0.420486	+	1.34309i
$776$	−2.18762	+	3.91716i	−0.0785310	+	0.140618i
$777$		0			0
$778$	0.423014	+	4.58375i	0.0151658	+	0.164335i
$779$	−29.5844	+	29.5844i	−1.05997	+	1.05997i
$780$		0			0
$781$	6.66306	+	6.66306i	0.238423	+	0.238423i
$782$	−17.6824	−	14.6944i	−0.632320	−	0.525472i
$783$		0			0
$784$	−8.90080	+	3.43285i	−0.317886	+	0.122602i
$785$	−3.79347	−	24.8137i	−0.135395	−	0.885638i
$786$		0			0
$787$	−6.25819	+	6.25819i	−0.223080	+	0.223080i	−0.809794	−	0.586714i	$-0.800421\pi$
$787$	−6.25819	+	6.25819i	−0.223080	+	0.223080i	0.586714	+	0.809794i	$0.300421\pi$
$788$	22.0318	−	32.1109i	0.784852	−	1.14390i
$789$		0			0
$790$	7.24444	+	29.1325i	0.257746	+	1.03649i
$791$		−	6.70213i		−	0.238300i
$792$		0			0
$793$	2.17767			0.0773312
$794$	−1.46911	−	15.9192i	−0.0521367	−	0.564950i
$795$		0			0
$796$	32.1739	−	5.98940i	1.14038	−	0.212289i
$797$	12.0418	−	12.0418i	0.426542	−	0.426542i	−0.460906	−	0.887449i	$-0.652476\pi$
$797$	12.0418	−	12.0418i	0.426542	−	0.426542i	0.887449	+	0.460906i	$0.152476\pi$
$798$		0			0
$799$	−5.95054			−0.210515
$800$	28.2775	+	0.618411i	0.999761	+	0.0218641i
$801$		0			0
$802$	−7.38871	+	8.89111i	−0.260905	+	0.313956i
$803$	−6.22128	+	6.22128i	−0.219544	+	0.219544i
$804$		0			0
$805$	−13.5736	+	18.4728i	−0.478405	+	0.651079i
$806$	−1.61488	−	17.4987i	−0.0568817	−	0.616365i
$807$		0			0
$808$	2.41078	−	0.682997i	0.0848109	−	0.0240277i
$809$			0.0662866i			0.00233051i	0.999999	+	0.00116526i	$0.000370913\pi$
$809$			0.0662866i			0.00233051i	−0.999999	+	0.00116526i	$0.999629\pi$
$810$		0			0
$811$	3.55286	−	3.55286i	0.124758	−	0.124758i	−0.641971	−	0.766729i	$-0.721883\pi$
$811$	3.55286	−	3.55286i	0.124758	−	0.124758i	0.766729	+	0.641971i	$0.221883\pi$
$812$	−24.5214	+	35.7394i	−0.860533	+	1.25421i
$813$		0			0
$814$	7.88522	−	9.48857i	0.276377	−	0.332574i
$815$	6.10702	+	39.9470i	0.213920	+	1.39928i
$816$		0			0
$817$		−	39.0400i		−	1.36584i
$818$	−20.1537	−	16.7482i	−0.704659	−	0.585588i
$819$		0			0
$820$	−21.0486	+	43.6136i	−0.735050	+	1.52305i
$821$	−21.0773	+	21.0773i	−0.735601	+	0.735601i	−0.971723	−	0.236122i	$-0.924123\pi$
$821$	−21.0773	+	21.0773i	−0.735601	+	0.735601i	0.236122	+	0.971723i	$0.424123\pi$
$822$		0			0
$823$	−44.2906			−1.54387			−0.771937	−	0.635699i	$-0.780712\pi$
$823$	−44.2906			−1.54387			−0.771937	+	0.635699i	$0.780712\pi$
$824$	33.3971	+	18.6513i	1.16344	+	0.649748i
$825$		0			0
$826$	1.67510	+	18.1512i	0.0582840	+	0.631561i
$827$	37.6123	+	37.6123i	1.30791	+	1.30791i	0.922923	+	0.384984i	$0.125793\pi$
$827$	37.6123	+	37.6123i	1.30791	+	1.30791i	0.384984	+	0.922923i	$0.374207\pi$
$828$		0			0
$829$	−23.0437	−	23.0437i	−0.800339	−	0.800339i	0.182809	−	0.983148i	$-0.441481\pi$
$829$	−23.0437	−	23.0437i	−0.800339	−	0.800339i	−0.983148	+	0.182809i	$0.941481\pi$
$830$	−9.47018	−	5.69822i	−0.328715	−	0.197788i
$831$		0			0
$832$	−12.3427	−	2.93228i	−0.427906	−	0.101659i
$833$			11.5864i			0.401445i
$834$		0			0
$835$	−3.56853	+	4.85654i	−0.123494	+	0.168067i
$836$	1.37346	+	7.37800i	0.0475023	+	0.255173i
$837$		0			0
$838$	17.9554	−	1.65702i	0.620258	−	0.0572409i
$839$			26.6564i			0.920280i	0.887846	+	0.460140i	$0.152201\pi$
$839$			26.6564i			0.920280i	−0.887846	+	0.460140i	$0.847799\pi$
$840$		0			0
$841$			21.0429i			0.725618i
$842$	2.72514	+	29.5294i	0.0939146	+	1.01765i
$843$		0			0
$844$	−28.9475	+	42.1903i	−0.996416	+	1.45225i
$845$	−18.8937	−	13.8829i	−0.649964	−	0.477586i
$846$		0			0
$847$		−	30.8089i		−	1.05861i
$848$	31.3048	+	13.8785i	1.07501	+	0.476591i
$849$		0			0
$850$	13.0591	−	31.7729i	0.447925	−	1.08980i
$851$	21.2553	+	21.2553i	0.728622	+	0.728622i
$852$		0			0
$853$	40.6085	+	40.6085i	1.39041	+	1.39041i	0.824398	+	0.566010i	$0.191514\pi$
$853$	40.6085	+	40.6085i	1.39041	+	1.39041i	0.566010	+	0.824398i	$0.308486\pi$
$854$	5.92432	−	0.546730i	0.202726	−	0.0187087i
$855$		0			0
$856$	−10.0212	−	35.3719i	−0.342518	−	1.20899i
$857$	−53.2027			−1.81737			−0.908685	−	0.417483i	$-0.862912\pi$
$857$	−53.2027			−1.81737			−0.908685	+	0.417483i	$0.862912\pi$
$858$		0			0
$859$	−16.4533	+	16.4533i	−0.561381	+	0.561381i	−0.929700	−	0.368319i	$-0.879934\pi$
$859$	−16.4533	+	16.4533i	−0.561381	+	0.561381i	0.368319	+	0.929700i	$0.379934\pi$
$860$	−14.8885	−	42.6646i	−0.507694	−	1.45485i
$861$		0			0
$862$	−15.4387	+	18.5779i	−0.525843	+	0.632766i
$863$		−	0.342388i		−	0.0116550i	−0.999983	−	0.00582751i	$-0.998145\pi$
$863$		−	0.342388i		−	0.0116550i	0.999983	−	0.00582751i	$-0.00185497\pi$
$864$		0			0
$865$	−7.26540	−	47.5241i	−0.247031	−	1.61587i
$866$	−19.9320	−	16.5639i	−0.677316	−	0.562865i
$867$		0			0
$868$	−8.78653	−	47.1996i	−0.298234	−	1.60206i
$869$	−6.51920	+	6.51920i	−0.221149	+	0.221149i
$870$		0			0
$871$			11.1637i			0.378266i
$872$	−5.13252	−	18.1163i	−0.173809	−	0.613495i
$873$		0			0
$874$	−18.2077	+	1.68031i	−0.615886	+	0.0568374i
$875$	−32.3996	−	11.1081i	−1.09530	−	0.375521i
$876$		0			0
$877$	3.51545	−	3.51545i	0.118708	−	0.118708i	−0.645257	−	0.763965i	$-0.723250\pi$
$877$	3.51545	−	3.51545i	0.118708	−	0.118708i	0.763965	+	0.645257i	$0.223250\pi$
$878$	−14.9950	−	12.4612i	−0.506058	−	0.420546i
$879$		0			0
$880$	4.31469	+	7.53920i	0.145448	+	0.254146i
$881$	16.7669			0.564891			0.282445	−	0.959283i	$-0.408854\pi$
$881$	16.7669			0.564891			0.282445	+	0.959283i	$0.408854\pi$
$882$		0			0
$883$	−18.2497	+	18.2497i	−0.614152	+	0.614152i	−0.944025	−	0.329873i	$-0.892994\pi$
$883$	−18.2497	+	18.2497i	−0.614152	+	0.614152i	0.329873	+	0.944025i	$0.392994\pi$
$884$	−8.71701	+	12.7048i	−0.293185	+	0.427310i
$885$		0			0
$886$	−6.31528	+	0.582810i	−0.212166	+	0.0195799i
$887$	−22.7350			−0.763368			−0.381684	−	0.924293i	$-0.624656\pi$
$887$	−22.7350			−0.763368			−0.381684	+	0.924293i	$0.624656\pi$
$888$		0			0
$889$		−	34.8553i		−	1.16901i
$890$	−11.5153	+	2.86355i	−0.385995	+	0.0959863i
$891$		0			0
$892$	42.9391	−	7.99340i	1.43771	−	0.267639i
$893$	−3.34641	+	3.34641i	−0.111983	+	0.111983i
$894$		0			0
$895$	21.0298	−	3.21500i	0.702948	−	0.107465i
$896$	−34.3144	−	4.87845i	−1.14636	−	0.162978i
$897$		0			0
$898$	5.81463	−	6.99696i	0.194037	−	0.233492i
$899$	−39.1964	−	39.1964i	−1.30727	−	1.30727i
$900$		0			0
$901$	29.4081	−	29.4081i	0.979727	−	0.979727i
$902$	−14.8098	+	1.36673i	−0.493113	+	0.0455073i
$903$		0			0
$904$	3.01712	−	5.40248i	0.100348	−	0.179684i
$905$	4.51653	+	29.5433i	0.150134	+	0.982052i
$906$		0			0
$907$	−5.61400	−	5.61400i	−0.186410	−	0.186410i	0.607732	−	0.794142i	$-0.292079\pi$
$907$	−5.61400	−	5.61400i	−0.186410	−	0.186410i	−0.794142	+	0.607732i	$0.792079\pi$
$908$	2.53049	+	1.73622i	0.0839773	+	0.0576183i
$909$		0			0
$910$	13.1633	+	7.92035i	0.436357	+	0.262557i
$911$	−25.4300			−0.842535			−0.421267	−	0.906936i	$-0.638415\pi$
$911$	−25.4300			−0.842535			−0.421267	+	0.906936i	$0.638415\pi$
$912$		0			0
$913$		−	3.39435i		−	0.112337i
$914$	16.5639	−	19.9320i	0.547886	−	0.659291i
$915$		0			0
$916$	−9.84413	−	6.75423i	−0.325259	−	0.223166i
$917$	43.2119	+	43.2119i	1.42698	+	1.42698i
$918$		0			0
$919$		−	9.20111i		−	0.303517i	−0.988418	−	0.151758i	$-0.951506\pi$
$919$		−	9.20111i		−	0.303517i	0.988418	−	0.151758i	$-0.0484935\pi$
$920$	−19.2574	+	8.78012i	−0.634897	+	0.289472i
$921$		0			0
$922$	−11.9643	+	1.10414i	−0.394025	+	0.0363628i
$923$	10.8796	+	10.8796i	0.358107	+	0.358107i
$924$		0			0
$925$	−20.8192	+	39.7964i	−0.684532	+	1.30850i
$926$	23.0389	+	19.1459i	0.757105	+	0.629172i
$927$		0			0
$928$	−35.8553	+	17.7700i	−1.17701	+	0.583330i
$929$	−37.9400			−1.24477			−0.622385	−	0.782711i	$-0.713836\pi$
$929$	−37.9400			−1.24477			−0.622385	+	0.782711i	$0.713836\pi$
$930$		0			0
$931$	6.51584	+	6.51584i	0.213548	+	0.213548i
$932$	8.92842	+	47.9619i	0.292460	+	1.57104i
$933$		0			0
$934$	1.40633	+	15.2388i	0.0460164	+	0.498630i
$935$	10.4289	−	1.59435i	0.341061	−	0.0521407i
$936$		0			0
$937$	−7.65779			−0.250169			−0.125084	−	0.992146i	$-0.539920\pi$
$937$	−7.65779			−0.250169			−0.125084	+	0.992146i	$0.539920\pi$
$938$	2.80278	+	30.3706i	0.0915139	+	0.991637i
$939$		0			0
$940$	−2.38089	+	4.93330i	−0.0776562	+	0.160907i
$941$	23.2008	+	23.2008i	0.756325	+	0.756325i	0.975652	−	0.219326i	$-0.0703859\pi$
$941$	23.2008	+	23.2008i	0.756325	+	0.756325i	−0.219326	+	0.975652i	$0.570386\pi$
$942$		0			0
$943$		−	36.2370i		−	1.18004i
$944$	−6.82093	+	15.3855i	−0.222002	+	0.500754i
$945$		0			0
$946$	8.86984	−	10.6734i	0.288383	−	0.347022i
$947$	−41.3933	+	41.3933i	−1.34510	+	1.34510i	−0.454205	+	0.890897i	$0.650077\pi$
$947$	−41.3933	+	41.3933i	−1.34510	+	1.34510i	−0.890897	+	0.454205i	$0.849923\pi$
$948$		0			0
$949$	−10.1583	+	10.1583i	−0.329752	+	0.329752i
$950$	−10.5241	−	25.2122i	−0.341445	−	0.817991i
$951$		0			0
$952$	−20.5248	+	36.7519i	−0.665214	+	1.19114i
$953$	19.1404			0.620018			0.310009	−	0.950734i	$-0.399668\pi$
$953$	19.1404			0.620018			0.310009	+	0.950734i	$0.399668\pi$
$954$		0			0
$955$	−25.5252	+	34.7382i	−0.825977	+	1.12410i
$956$	6.45291	+	34.6638i	0.208702	+	1.12111i
$957$		0			0
$958$	29.8834	−	35.9598i	0.965490	−	1.16181i
$959$	21.0358			0.679280
$960$		0			0
$961$	30.4016			0.980697
$962$	12.8752	−	15.4932i	0.415113	−	0.499520i
$963$		0			0
$964$	−5.23970	−	28.1467i	−0.168759	−	0.906544i
$965$	−35.5465	−	26.1192i	−1.14428	−	0.840805i
$966$		0			0
$967$	−13.5648			−0.436215			−0.218108	−	0.975925i	$-0.569988\pi$
$967$	−13.5648			−0.436215			−0.218108	+	0.975925i	$0.569988\pi$
$968$	13.8694	−	24.8345i	0.445778	−	0.798212i
$969$		0			0
$970$	4.86795	−	1.21052i	0.156300	−	0.0388676i
$971$	−17.8216	+	17.8216i	−0.571924	+	0.571924i	−0.932666	−	0.360742i	$-0.882523\pi$
$971$	−17.8216	+	17.8216i	−0.571924	+	0.571924i	0.360742	+	0.932666i	$0.382523\pi$
$972$		0			0
$973$	3.23018	−	3.23018i	0.103555	−	0.103555i
$974$	−7.27944	+	8.75962i	−0.233248	+	0.280676i
$975$		0			0
$976$	5.02162	+	2.22627i	0.160738	+	0.0712610i
$977$		−	12.5185i		−	0.400504i	−0.979744	−	0.200252i	$-0.935824\pi$
$977$		−	12.5185i		−	0.400504i	0.979744	−	0.200252i	$-0.0641760\pi$
$978$		0			0
$979$	−2.57688	−	2.57688i	−0.0823573	−	0.0823573i
$980$	9.60571	+	4.63587i	0.306843	+	0.148088i
$981$		0			0
$982$	2.44094	+	26.4498i	0.0778936	+	0.844048i
$983$	44.1661			1.40868			0.704340	−	0.709863i	$-0.251243\pi$
$983$	44.1661			1.40868			0.704340	+	0.709863i	$0.251243\pi$
$984$		0			0
$985$	−43.0389	+	6.57971i	−1.37133	+	0.209647i
$986$	4.46628	+	48.3962i	0.142235	+	1.54125i
$987$		0			0
$988$	2.24263	+	12.0470i	0.0713475	+	0.383266i
$989$	23.9094	+	23.9094i	0.760276	+	0.760276i
$990$		0			0
$991$	1.64743			0.0523324			0.0261662	−	0.999658i	$-0.491670\pi$
$991$	1.64743			0.0523324			0.0261662	+	0.999658i	$0.491670\pi$
$992$	14.1654	−	42.0023i	0.449751	−	1.33357i
$993$		0			0
$994$	32.3294	+	26.8665i	1.02543	+	0.852152i
$995$	−29.4855	−	21.6656i	−0.934753	−	0.686846i
$996$		0			0
$997$	28.4173	+	28.4173i	0.899985	+	0.899985i	0.995434	−	0.0954491i	$-0.0304287\pi$
$997$	28.4173	+	28.4173i	0.899985	+	0.899985i	−0.0954491	+	0.995434i	$0.530429\pi$
$998$	−5.28480	+	0.487711i	−0.167287	+	0.0154382i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bm.g.109.9	yes	32
3.2	odd	2	inner	720.2.bm.g.109.8	yes	32
5.4	even	2	inner	720.2.bm.g.109.7	✓	32
15.14	odd	2	inner	720.2.bm.g.109.10	yes	32
16.5	even	4	inner	720.2.bm.g.469.5	yes	32
48.5	odd	4	inner	720.2.bm.g.469.12	yes	32
80.69	even	4	inner	720.2.bm.g.469.11	yes	32
240.149	odd	4	inner	720.2.bm.g.469.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.bm.g.109.7	✓	32	5.4	even	2	inner
720.2.bm.g.109.8	yes	32	3.2	odd	2	inner
720.2.bm.g.109.9	yes	32	1.1	even	1	trivial
720.2.bm.g.109.10	yes	32	15.14	odd	2	inner
720.2.bm.g.469.5	yes	32	16.5	even	4	inner
720.2.bm.g.469.6	yes	32	240.149	odd	4	inner
720.2.bm.g.469.11	yes	32	80.69	even	4	inner
720.2.bm.g.469.12	yes	32	48.5	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.bm (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.903873 - 1.08766i) q^{2} +(-0.366025 - 1.96622i) q^{4} +(-1.32403 + 1.80193i) q^{5} -3.06349 q^{7} +(-2.46943 - 1.37910i) q^{8} +(0.763129 + 3.06882i) q^{10} +(-0.686732 + 0.686732i) q^{11} +(-1.12131 + 1.12131i) q^{13} +(-2.76901 + 3.33205i) q^{14} +(-3.73205 + 1.43937i) q^{16} +4.85810i q^{17} +(2.73205 + 2.73205i) q^{19} +(4.02761 + 1.94379i) q^{20} +(0.126215 + 1.36765i) q^{22} -3.34641 q^{23} +(-1.49387 - 4.77162i) q^{25} +(0.206087 + 2.23314i) q^{26} +(1.12131 + 6.02350i) q^{28} +(5.00215 + 5.00215i) q^{29} -7.83592 q^{31} +(-1.80775 + 5.36023i) q^{32} +(5.28398 + 4.39111i) q^{34} +(4.05616 - 5.52018i) q^{35} +(-6.35168 - 6.35168i) q^{37} +(5.44098 - 0.502125i) q^{38} +(5.75465 - 2.62375i) q^{40} +10.8286i q^{41} +(-7.14481 - 7.14481i) q^{43} +(1.60163 + 1.09891i) q^{44} +(-3.02473 + 3.63977i) q^{46} +1.22487i q^{47} +2.38496 q^{49} +(-6.54019 - 2.68812i) q^{50} +(2.61518 + 1.79432i) q^{52} +(-6.05342 - 6.05342i) q^{53} +(-0.328183 - 2.14670i) q^{55} +(7.56507 + 4.22486i) q^{56} +(9.96196 - 0.919346i) q^{58} +(2.97509 - 2.97509i) q^{59} +(-0.971033 - 0.971033i) q^{61} +(-7.08268 + 8.52284i) q^{62} +(4.19615 + 6.81119i) q^{64} +(-0.535866 - 3.50518i) q^{65} +(4.97793 - 4.97793i) q^{67} +(9.55211 - 1.77819i) q^{68} +(-2.33784 - 9.40128i) q^{70} -9.70256i q^{71} +9.05926 q^{73} +(-12.6496 + 1.16738i) q^{74} +(4.37182 - 6.37182i) q^{76} +(2.10380 - 2.10380i) q^{77} +9.49307 q^{79} +(2.34772 - 8.63066i) q^{80} +(11.7779 + 9.78772i) q^{82} +(-2.47138 + 2.47138i) q^{83} +(-8.75394 - 6.43230i) q^{85} +(-14.2292 + 1.31315i) q^{86} +(2.64291 - 0.748762i) q^{88} +3.75237i q^{89} +(3.43513 - 3.43513i) q^{91} +(1.22487 + 6.57977i) q^{92} +(1.33225 + 1.10713i) q^{94} +(-8.54028 + 1.30562i) q^{95} -1.58626i q^{97} +(2.15570 - 2.59404i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 24 q^{10} - 64 q^{16} + 32 q^{19} + 32 q^{31} - 72 q^{40} - 32 q^{46} + 128 q^{49} - 32 q^{64} - 104 q^{70} - 32 q^{76} + 224 q^{79} - 48 q^{85} - 32 q^{91} - 48 q^{94}+O(q^{100}) \) 32 * q + 16 * q^4 - 24 * q^10 - 64 * q^16 + 32 * q^19 + 32 * q^31 - 72 * q^40 - 32 * q^46 + 128 * q^49 - 32 * q^64 - 104 * q^70 - 32 * q^76 + 224 * q^79 - 48 * q^85 - 32 * q^91 - 48 * q^94

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