LMFDB - Embedded newform 729.2.g.c.28.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			28.3
Character	$\chi$	$=$	729.28
Dual form			729.2.g.c.703.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.695972 + 0.457748i) q^{2} +(-0.517316 + 1.19927i) q^{4} +(0.827713 - 0.877324i) q^{5} +(1.30600 + 0.152650i) q^{7} +(-0.478230 - 2.71217i) q^{8} +O(q^{10})$	\(q+(-0.695972 + 0.457748i) q^{2} +(-0.517316 + 1.19927i) q^{4} +(0.827713 - 0.877324i) q^{5} +(1.30600 + 0.152650i) q^{7} +(-0.478230 - 2.71217i) q^{8} +(-0.174471 + 0.989477i) q^{10} +(-0.623332 + 2.08207i) q^{11} +(-0.264847 + 4.54725i) q^{13} +(-0.978817 + 0.491580i) q^{14} +(-0.218261 - 0.231343i) q^{16} +(3.54217 - 1.28924i) q^{17} +(-2.50517 - 0.911807i) q^{19} +(0.623962 + 1.44651i) q^{20} +(-0.519243 - 1.73439i) q^{22} +(5.99251 - 0.700424i) q^{23} +(0.206135 + 3.53920i) q^{25} +(-1.89717 - 3.28599i) q^{26} +(-0.858686 + 1.48729i) q^{28} +(-3.71556 - 1.86603i) q^{29} +(4.45311 + 5.98156i) q^{31} +(5.61736 + 1.33134i) q^{32} +(-1.87510 + 2.51870i) q^{34} +(1.21492 - 1.01944i) q^{35} +(7.47819 + 6.27494i) q^{37} +(2.16090 - 0.512144i) q^{38} +(-2.77529 - 1.82534i) q^{40} +(-4.83588 - 3.18061i) q^{41} +(-4.91887 + 1.16579i) q^{43} +(-2.17451 - 1.82463i) q^{44} +(-3.85000 + 3.23053i) q^{46} +(-1.79025 + 2.40472i) q^{47} +(-5.12897 - 1.21559i) q^{49} +(-1.76352 - 2.36882i) q^{50} +(-5.31638 - 2.66999i) q^{52} +(-6.22987 + 10.7905i) q^{53} +(1.31071 + 2.27022i) q^{55} +(-0.210556 - 3.61511i) q^{56} +(3.44010 - 0.402090i) q^{58} +(3.12841 + 10.4496i) q^{59} +(4.67102 + 10.8287i) q^{61} +(-5.83728 - 2.12460i) q^{62} +(-3.92120 + 1.42720i) q^{64} +(3.77019 + 3.99617i) q^{65} +(-0.741811 + 0.372552i) q^{67} +(-0.286265 + 4.91497i) q^{68} +(-0.378904 + 1.26563i) q^{70} +(1.25916 - 7.14107i) q^{71} +(-1.41006 - 7.99685i) q^{73} +(-8.07695 - 0.944060i) q^{74} +(2.38947 - 2.53269i) q^{76} +(-1.13190 + 2.62404i) q^{77} +(9.60774 - 6.31911i) q^{79} -0.383620 q^{80} +4.82155 q^{82} +(3.98931 - 2.62381i) q^{83} +(1.80081 - 4.17475i) q^{85} +(2.88975 - 3.06296i) q^{86} +(5.94504 + 0.694876i) q^{88} +(0.578632 + 3.28158i) q^{89} +(-1.04003 + 5.89829i) q^{91} +(-2.26002 + 7.54900i) q^{92} +(0.145207 - 2.49310i) q^{94} +(-2.87351 + 1.44313i) q^{95} +(-0.935521 - 0.991594i) q^{97} +(4.12605 - 1.50176i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{22}{27}\right)$

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 $

$2$	−0.695972	+	0.457748i	−0.492126	+	0.323677i	−0.771200	−	0.636593i	$-0.780343\pi$
$2$	−0.695972	+	0.457748i	−0.492126	+	0.323677i	0.279073	+	0.960270i	$0.409973\pi$
$3$		0			0
$3$		0			0
$4$	−0.517316	+	1.19927i	−0.258658	+	0.599637i
$5$	0.827713	−	0.877324i	0.370164	−	0.392351i	−0.515337	−	0.856987i	$-0.672333\pi$
$5$	0.827713	−	0.877324i	0.370164	−	0.392351i	0.885502	+	0.464636i	$0.153815\pi$
$6$		0			0
$7$	1.30600	+	0.152650i	0.493623	+	0.0576963i	0.359263	−	0.933236i	$-0.383028\pi$
$7$	1.30600	+	0.152650i	0.493623	+	0.0576963i	0.134360	+	0.990933i	$0.457102\pi$
$8$	−0.478230	−	2.71217i	−0.169080	−	0.958899i
$9$		0			0
$10$	−0.174471	+	0.989477i	−0.0551727	+	0.312900i
$11$	−0.623332	+	2.08207i	−0.187942	+	0.627769i	0.811137	+	0.584856i	$0.198849\pi$
$11$	−0.623332	+	2.08207i	−0.187942	+	0.627769i	−0.999079	+	0.0429127i	$0.986336\pi$
$12$		0			0
$13$	−0.264847	+	4.54725i	−0.0734553	+	1.26118i	0.737208	+	0.675666i	$0.236144\pi$
$13$	−0.264847	+	4.54725i	−0.0734553	+	1.26118i	−0.810663	+	0.585513i	$0.800893\pi$
$14$	−0.978817	+	0.491580i	−0.261600	+	0.131380i
$15$		0			0
$16$	−0.218261	−	0.231343i	−0.0545652	−	0.0578357i
$17$	3.54217	−	1.28924i	0.859102	−	0.312688i	0.125356	−	0.992112i	$-0.459993\pi$
$17$	3.54217	−	1.28924i	0.859102	−	0.312688i	0.733746	+	0.679424i	$0.237770\pi$
$18$		0			0
$19$	−2.50517	−	0.911807i	−0.574725	−	0.209183i	0.0382728	−	0.999267i	$-0.487814\pi$
$19$	−2.50517	−	0.911807i	−0.574725	−	0.209183i	−0.612998	+	0.790084i	$0.710037\pi$
$20$	0.623962	+	1.44651i	0.139522	+	0.323449i
$21$		0			0
$22$	−0.519243	−	1.73439i	−0.110703	−	0.369774i
$23$	5.99251	−	0.700424i	1.24952	−	0.146049i	0.534513	−	0.845160i	$-0.320495\pi$
$23$	5.99251	−	0.700424i	1.24952	−	0.146049i	0.715012	+	0.699112i	$0.246421\pi$
$24$		0			0
$25$	0.206135	+	3.53920i	0.0412269	+	0.707839i
$26$	−1.89717	−	3.28599i	−0.372065	−	0.644435i
$27$		0			0
$28$	−0.858686	+	1.48729i	−0.162276	+	0.281071i
$29$	−3.71556	−	1.86603i	−0.689963	−	0.346512i	0.0690270	−	0.997615i	$-0.478011\pi$
$29$	−3.71556	−	1.86603i	−0.689963	−	0.346512i	−0.758990	+	0.651102i	$0.774307\pi$
$30$		0			0
$31$	4.45311	+	5.98156i	0.799801	+	1.07432i	0.995603	+	0.0936762i	$0.0298618\pi$
$31$	4.45311	+	5.98156i	0.799801	+	1.07432i	−0.195801	+	0.980644i	$0.562731\pi$
$32$	5.61736	+	1.33134i	0.993018	+	0.235350i
$33$		0			0
$34$	−1.87510	+	2.51870i	−0.321577	+	0.431953i
$35$	1.21492	−	1.01944i	0.205359	−	0.172317i
$36$		0			0
$37$	7.47819	+	6.27494i	1.22941	+	1.03159i	0.998277	+	0.0586711i	$0.0186863\pi$
$37$	7.47819	+	6.27494i	1.22941	+	1.03159i	0.231129	+	0.972923i	$0.425758\pi$
$38$	2.16090	−	0.512144i	0.350545	−	0.0830807i
$39$		0			0
$40$	−2.77529	−	1.82534i	−0.438812	−	0.288611i
$41$	−4.83588	−	3.18061i	−0.755237	−	0.496727i	0.112561	−	0.993645i	$-0.464095\pi$
$41$	−4.83588	−	3.18061i	−0.755237	−	0.496727i	−0.867798	+	0.496918i	$0.834465\pi$
$42$		0			0
$43$	−4.91887	+	1.16579i	−0.750120	+	0.177782i	−0.587856	−	0.808966i	$-0.700028\pi$
$43$	−4.91887	+	1.16579i	−0.750120	+	0.177782i	−0.162264	+	0.986747i	$0.551880\pi$
$44$	−2.17451	−	1.82463i	−0.327820	−	0.275074i
$45$		0			0
$46$	−3.85000	+	3.23053i	−0.567652	+	0.476316i
$47$	−1.79025	+	2.40472i	−0.261135	+	0.350765i	−0.913282	−	0.407327i	$-0.866461\pi$
$47$	−1.79025	+	2.40472i	−0.261135	+	0.350765i	0.652148	+	0.758092i	$0.273868\pi$
$48$		0			0
$49$	−5.12897	−	1.21559i	−0.732710	−	0.173655i
$50$	−1.76352	−	2.36882i	−0.249400	−	0.335002i
$51$		0			0
$52$	−5.31638	−	2.66999i	−0.737249	−	0.370261i
$53$	−6.22987	+	10.7905i	−0.855739	+	1.48218i	0.0202187	+	0.999796i	$0.493564\pi$
$53$	−6.22987	+	10.7905i	−0.855739	+	1.48218i	−0.875958	+	0.482388i	$0.839770\pi$
$54$		0			0
$55$	1.31071	+	2.27022i	0.176737	+	0.306117i
$56$	−0.210556	−	3.61511i	−0.0281368	−	0.483090i
$57$		0			0
$58$	3.44010	−	0.402090i	0.451707	−	0.0527970i
$59$	3.12841	+	10.4496i	0.407284	+	1.36042i	0.878221	+	0.478256i	$0.158731\pi$
$59$	3.12841	+	10.4496i	0.407284	+	1.36042i	−0.470937	+	0.882167i	$0.656084\pi$
$60$		0			0
$61$	4.67102	+	10.8287i	0.598063	+	1.38647i	0.901152	+	0.433504i	$0.142723\pi$
$61$	4.67102	+	10.8287i	0.598063	+	1.38647i	−0.303088	+	0.952962i	$0.598018\pi$
$62$	−5.83728	−	2.12460i	−0.741336	−	0.269824i
$63$		0			0
$64$	−3.92120	+	1.42720i	−0.490150	+	0.178400i
$65$	3.77019	+	3.99617i	0.467635	+	0.495664i
$66$		0			0
$67$	−0.741811	+	0.372552i	−0.0906267	+	0.0455144i	−0.493535	−	0.869726i	$-0.664296\pi$
$67$	−0.741811	+	0.372552i	−0.0906267	+	0.0455144i	0.402909	+	0.915240i	$0.367999\pi$
$68$	−0.286265	+	4.91497i	−0.0347147	+	0.596028i
$69$		0			0
$70$	−0.378904	+	1.26563i	−0.0452877	+	0.151271i
$71$	1.25916	−	7.14107i	0.149435	−	0.847489i	−0.814263	−	0.580496i	$-0.802859\pi$
$71$	1.25916	−	7.14107i	0.149435	−	0.847489i	0.963698	−	0.266993i	$-0.0860301\pi$
$72$		0			0
$73$	−1.41006	−	7.99685i	−0.165035	−	0.935960i	−0.949028	−	0.315191i	$-0.897931\pi$
$73$	−1.41006	−	7.99685i	−0.165035	−	0.935960i	0.783993	−	0.620769i	$-0.213180\pi$
$74$	−8.07695	−	0.944060i	−0.938926	−	0.109745i
$75$		0			0
$76$	2.38947	−	2.53269i	0.274091	−	0.290519i
$77$	−1.13190	+	2.62404i	−0.128992	+	0.299037i
$78$		0			0
$79$	9.60774	−	6.31911i	1.08096	−	0.710955i	0.121436	−	0.992599i	$-0.461250\pi$
$79$	9.60774	−	6.31911i	1.08096	−	0.710955i	0.959519	+	0.281644i	$0.0908797\pi$
$80$	−0.383620			−0.0428900
$81$		0			0
$82$	4.82155			0.532451
$83$	3.98931	−	2.62381i	0.437884	−	0.288001i	−0.311364	−	0.950291i	$-0.600786\pi$
$83$	3.98931	−	2.62381i	0.437884	−	0.288001i	0.749248	+	0.662290i	$0.230415\pi$
$84$		0			0
$85$	1.80081	−	4.17475i	0.195326	−	0.452816i
$86$	2.88975	−	3.06296i	0.311610	−	0.330288i
$87$		0			0
$88$	5.94504	+	0.694876i	0.633743	+	0.0740740i
$89$	0.578632	+	3.28158i	0.0613348	+	0.347847i	0.999995	+	0.00300484i	$0.000956472\pi$
$89$	0.578632	+	3.28158i	0.0613348	+	0.347847i	−0.938661	+	0.344842i	$0.887932\pi$
$90$		0			0
$91$	−1.04003	+	5.89829i	−0.109025	+	0.618309i
$92$	−2.26002	+	7.54900i	−0.235624	+	0.787037i
$93$		0			0
$94$	0.145207	−	2.49310i	0.0149769	−	0.257144i
$95$	−2.87351	+	1.44313i	−0.294816	+	0.148062i
$96$		0			0
$97$	−0.935521	−	0.991594i	−0.0949877	−	0.100681i	0.678136	−	0.734937i	$-0.262788\pi$
$97$	−0.935521	−	0.991594i	−0.0949877	−	0.100681i	−0.773123	+	0.634256i	$0.781307\pi$
$98$	4.12605	−	1.50176i	0.416794	−	0.151701i
$99$		0			0
$100$	−4.35110	−	1.58367i	−0.435110	−	0.158367i
$101$	0.916862	+	2.12552i	0.0912311	+	0.211498i	0.957722	−	0.287695i	$-0.0928891\pi$
$101$	0.916862	+	2.12552i	0.0912311	+	0.211498i	−0.866491	+	0.499193i	$0.833630\pi$
$102$		0			0
$103$	−1.30483	−	4.35843i	−0.128569	−	0.429449i	0.869331	−	0.494230i	$-0.164550\pi$
$103$	−1.30483	−	4.35843i	−0.128569	−	0.429449i	−0.997899	+	0.0647816i	$0.979365\pi$
$104$	12.4596	−	1.45632i	1.22176	−	0.142804i
$105$		0			0
$106$	−0.603492	−	10.3616i	−0.0586164	−	1.00640i
$107$	6.14665	+	10.6463i	0.594219	+	1.02922i	0.993657	+	0.112457i	$0.0358721\pi$
$107$	6.14665	+	10.6463i	0.594219	+	1.02922i	−0.399438	+	0.916760i	$0.630795\pi$
$108$		0			0
$109$	4.45327	−	7.71330i	0.426546	−	0.738800i	−0.570017	−	0.821633i	$-0.693063\pi$
$109$	4.45327	−	7.71330i	0.426546	−	0.738800i	0.996563	+	0.0828329i	$0.0263968\pi$
$110$	−1.95141	−	0.980034i	−0.186060	−	0.0934426i
$111$		0			0
$112$	−0.249735	−	0.335452i	−0.0235977	−	0.0316973i
$113$	−16.9220	−	4.01058i	−1.59188	−	0.377284i	−0.663285	−	0.748367i	$-0.730838\pi$
$113$	−16.9220	−	4.01058i	−1.59188	−	0.377284i	−0.928600	+	0.371083i	$0.878986\pi$
$114$		0			0
$115$	4.34558	−	5.83713i	0.405227	−	0.544315i
$116$	4.16000	−	3.49065i	0.386246	−	0.324099i
$117$		0			0
$118$	−6.96056	−	5.84061i	−0.640772	−	0.537671i
$119$	4.82289	−	1.14305i	0.442113	−	0.104783i
$120$		0			0
$121$	5.24388	+	3.44896i	0.476717	+	0.313541i
$122$	−8.20769	−	5.39828i	−0.743089	−	0.488738i
$123$		0			0
$124$	−9.47719	+	2.24613i	−0.851076	+	0.201709i
$125$	7.89548	+	6.62509i	0.706193	+	0.592566i
$126$		0			0
$127$	4.35255	−	3.65222i	0.386226	−	0.324082i	−0.428915	−	0.903345i	$-0.641104\pi$
$127$	4.35255	−	3.65222i	0.386226	−	0.324082i	0.815141	+	0.579263i	$0.196660\pi$
$128$	−4.81901	+	6.47306i	−0.425945	+	0.572143i
$129$		0			0
$130$	−4.45319	−	1.05542i	−0.390570	−	0.0925669i
$131$	−11.6556	−	15.6562i	−1.01836	−	1.36789i	−0.928250	−	0.371958i	$-0.878687\pi$
$131$	−11.6556	−	15.6562i	−1.01836	−	1.36789i	−0.0901070	−	0.995932i	$-0.528721\pi$
$132$		0			0
$133$	−3.13257	−	1.57324i	−0.271628	−	0.136417i
$134$	0.345745	−	0.598848i	0.0298678	−	0.0517326i
$135$		0			0
$136$	−5.19062	−	8.99042i	−0.445092	−	0.770922i
$137$	−0.921841	−	15.8274i	−0.0787582	−	1.35223i	−0.773879	−	0.633333i	$-0.781686\pi$
$137$	−0.921841	−	15.8274i	−0.0787582	−	1.35223i	0.695121	−	0.718893i	$-0.255351\pi$
$138$		0			0
$139$	10.3686	−	1.21192i	0.879457	−	0.102794i	0.335633	−	0.941993i	$-0.391050\pi$
$139$	10.3686	−	1.21192i	0.879457	−	0.102794i	0.543824	+	0.839199i	$0.316976\pi$
$140$	0.594088	+	1.98439i	0.0502096	+	0.167712i
$141$		0			0
$142$	2.39247	+	5.54636i	0.200771	+	0.465440i
$143$	−9.30261	−	3.38587i	−0.777923	−	0.283141i
$144$		0			0
$145$	−4.71253	+	1.71522i	−0.391354	+	0.142441i
$146$	4.64190	+	4.92013i	0.384166	+	0.407193i
$147$		0			0
$148$	−11.3940	+	5.72226i	−0.936577	+	0.470367i
$149$	0.169499	−	2.91018i	0.0138859	−	0.238411i	−0.984223	−	0.176935i	$-0.943382\pi$
$149$	0.169499	−	2.91018i	0.0138859	−	0.238411i	0.998109	−	0.0614769i	$-0.0195810\pi$
$150$		0			0
$151$	3.65956	−	12.2238i	0.297811	−	0.994758i	−0.669849	−	0.742498i	$-0.733641\pi$
$151$	3.65956	−	12.2238i	0.297811	−	0.994758i	0.967659	−	0.252260i	$-0.0811738\pi$
$152$	−1.27493	+	7.23051i	−0.103411	+	0.586472i
$153$		0			0
$154$	−0.413378	−	2.34439i	−0.0333110	−	0.188916i
$155$	8.93366	+	1.04420i	0.717569	+	0.0838718i
$156$		0			0
$157$	0.871963	−	0.924227i	0.0695902	−	0.0737613i	−0.691643	−	0.722240i	$-0.743113\pi$
$157$	0.871963	−	0.924227i	0.0695902	−	0.0737613i	0.761233	+	0.648478i	$0.224594\pi$
$158$	−3.79416	+	8.79584i	−0.301847	+	0.699760i
$159$		0			0
$160$	5.81758	−	3.82628i	0.459920	−	0.302494i
$161$	7.93316			0.625221
$162$		0			0
$163$	12.3636			0.968391			0.484195	−	0.874960i	$-0.339112\pi$
$163$	12.3636			0.968391			0.484195	+	0.874960i	$0.339112\pi$
$164$	6.31609	−	4.15416i	0.493204	−	0.324385i
$165$		0			0
$166$	−1.57541	+	3.65220i	−0.122275	+	0.283466i
$167$	−2.61701	+	2.77387i	−0.202511	+	0.214649i	−0.820667	−	0.571406i	$-0.806398\pi$
$167$	−2.61701	+	2.77387i	−0.202511	+	0.214649i	0.618157	+	0.786055i	$0.287880\pi$
$168$		0			0
$169$	−7.69521	−	0.899441i	−0.591939	−	0.0691877i
$170$	0.657669	+	3.72983i	0.0504409	+	0.286065i
$171$		0			0
$172$	1.14650	−	6.50215i	0.0874201	−	0.495784i
$173$	6.90339	−	23.0589i	0.524855	−	1.75314i	−0.124056	−	0.992275i	$-0.539590\pi$
$173$	6.90339	−	23.0589i	0.524855	−	1.75314i	0.648912	−	0.760864i	$-0.275224\pi$
$174$		0			0
$175$	−0.271045	+	4.65367i	−0.0204891	+	0.351784i
$176$	0.617722	−	0.310231i	0.0465625	−	0.0233846i
$177$		0			0
$178$	−1.90485	−	2.01902i	−0.142774	−	0.151332i
$179$	5.95691	−	2.16814i	0.445240	−	0.162054i	−0.109664	−	0.993969i	$-0.534977\pi$
$179$	5.95691	−	2.16814i	0.445240	−	0.162054i	0.554904	+	0.831915i	$0.312755\pi$
$180$		0			0
$181$	−5.82014	−	2.11836i	−0.432608	−	0.157456i	0.116532	−	0.993187i	$-0.462822\pi$
$181$	−5.82014	−	2.11836i	−0.432608	−	0.157456i	−0.549140	+	0.835731i	$0.685045\pi$
$182$	−1.97610	−	4.58112i	−0.146478	−	0.339575i
$183$		0			0
$184$	−4.76547	−	15.9178i	−0.351315	−	1.17347i
$185$	11.6950	−	1.36694i	0.859830	−	0.100500i
$186$		0			0
$187$	0.476354	+	8.17868i	0.0348344	+	0.598084i
$188$	−1.95779	−	3.39100i	−0.142787	−	0.247314i
$189$		0			0
$190$	1.33929	−	2.31972i	0.0971625	−	0.168290i
$191$	6.03439	+	3.03058i	0.436633	+	0.219285i	0.653517	−	0.756912i	$-0.273293\pi$
$191$	6.03439	+	3.03058i	0.436633	+	0.219285i	−0.216884	+	0.976197i	$0.569589\pi$
$192$		0			0
$193$	−9.50172	−	12.7630i	−0.683949	−	0.918703i	0.315595	−	0.948894i	$-0.397796\pi$
$193$	−9.50172	−	12.7630i	−0.683949	−	0.918703i	−0.999544	+	0.0301912i	$0.990388\pi$
$194$	1.10500	+	0.261889i	0.0793341	+	0.0188025i
$195$		0			0
$196$	4.11112	−	5.52219i	0.293651	−	0.394442i
$197$	−8.88023	+	7.45140i	−0.632690	+	0.530890i	−0.901764	−	0.432229i	$-0.857727\pi$
$197$	−8.88023	+	7.45140i	−0.632690	+	0.530890i	0.269073	+	0.963120i	$0.413283\pi$
$198$		0			0
$199$	3.29385	+	2.76387i	0.233495	+	0.195925i	0.752026	−	0.659133i	$-0.229077\pi$
$199$	3.29385	+	2.76387i	0.233495	+	0.195925i	−0.518531	+	0.855059i	$0.673521\pi$
$200$	9.50034	−	2.25162i	0.671775	−	0.159214i
$201$		0			0
$202$	−1.61106	−	1.05961i	−0.113354	−	0.0745541i
$203$	−4.56769	−	3.00422i	−0.320589	−	0.210855i
$204$		0			0
$205$	−6.79314	+	1.61000i	−0.474453	+	0.112448i
$206$	2.90318	+	2.43606i	0.202274	+	0.169728i
$207$		0			0
$208$	1.10978	−	0.931215i	0.0769493	−	0.0645682i
$209$	3.46000	−	4.64759i	0.239333	−	0.321480i
$210$		0			0
$211$	13.8963	+	3.29348i	0.956660	+	0.226733i	0.679158	−	0.733992i	$-0.262345\pi$
$211$	13.8963	+	3.29348i	0.956660	+	0.226733i	0.277502	+	0.960725i	$0.410493\pi$
$212$	−9.71789	−	13.0534i	−0.667428	−	0.896511i
$213$		0			0
$214$	−9.15122	−	4.59591i	−0.625564	−	0.314170i
$215$	−3.04863	+	5.28038i	−0.207915	+	0.360119i
$216$		0			0
$217$	4.90269	+	8.49171i	0.332816	+	0.576455i
$218$	0.431392	+	7.40671i	0.0292175	+	0.501646i
$219$		0			0
$220$	−3.40067	+	0.397481i	−0.229273	+	0.0267982i
$221$	4.92438	+	16.4486i	0.331249	+	1.10645i
$222$		0			0
$223$	−7.99694	−	18.5390i	−0.535515	−	1.24146i	−0.944376	−	0.328866i	$-0.893333\pi$
$223$	−7.99694	−	18.5390i	−0.535515	−	1.24146i	0.408862	−	0.912596i	$-0.365926\pi$
$224$	7.13306	+	2.59622i	0.476598	+	0.173467i
$225$		0			0
$226$	13.6130	−	4.95474i	0.905526	−	0.329585i
$227$	−1.86894	−	1.98096i	−0.124046	−	0.131481i	0.662374	−	0.749173i	$-0.269549\pi$
$227$	−1.86894	−	1.98096i	−0.124046	−	0.131481i	−0.786420	+	0.617693i	$0.788068\pi$
$228$		0			0
$229$	1.36418	−	0.685117i	0.0901476	−	0.0452738i	−0.403154	−	0.915132i	$-0.632086\pi$
$229$	1.36418	−	0.685117i	0.0901476	−	0.0452738i	0.493302	+	0.869858i	$0.335790\pi$
$230$	−0.352469	+	6.05165i	−0.0232411	+	0.399034i
$231$		0			0
$232$	−3.28410	+	10.9696i	−0.215612	+	0.720193i
$233$	−1.13347	+	6.42825i	−0.0742563	+	0.421128i	0.924906	+	0.380197i	$0.124144\pi$
$233$	−1.13347	+	6.42825i	−0.0742563	+	0.421128i	−0.999162	+	0.0409317i	$0.986967\pi$
$234$		0			0
$235$	0.627909	+	3.56105i	0.0409602	+	0.232297i
$236$	−14.1503	−	1.65393i	−0.921106	−	0.107662i
$237$		0			0
$238$	−2.83337	+	3.00319i	−0.183660	+	0.194668i
$239$	−6.69279	+	15.5156i	−0.432921	+	1.00362i	0.552504	+	0.833510i	$0.313672\pi$
$239$	−6.69279	+	15.5156i	−0.432921	+	1.00362i	−0.985425	+	0.170112i	$0.945587\pi$
$240$		0			0
$241$	10.5263	−	6.92323i	0.678056	−	0.445964i	−0.163206	−	0.986592i	$-0.552184\pi$
$241$	10.5263	−	6.92323i	0.678056	−	0.445964i	0.841262	+	0.540628i	$0.181813\pi$
$242$	−5.22835			−0.336091
$243$		0			0
$244$	−15.4029			−0.986070
$245$	−5.31178	+	3.49361i	−0.339357	+	0.223199i
$246$		0			0
$247$	4.80970	−	11.1501i	0.306034	−	0.709466i
$248$	14.0934	−	14.9382i	0.894934	−	0.948574i
$249$		0			0
$250$	−8.52765	−	0.996740i	−0.539336	−	0.0630393i
$251$	−4.48052	−	25.4103i	−0.282808	−	1.60388i	−0.713012	−	0.701152i	$-0.752669\pi$
$251$	−4.48052	−	25.4103i	−0.282808	−	1.60388i	0.430204	−	0.902732i	$-0.358442\pi$
$252$		0			0
$253$	−2.27699	+	12.9134i	−0.143153	+	0.811861i
$254$	−1.35745	+	4.53421i	−0.0851742	+	0.284502i
$255$		0			0
$256$	0.876128	−	15.0425i	0.0547580	−	0.940159i
$257$	12.9329	−	6.49515i	0.806733	−	0.405156i	0.00288824	−	0.999996i	$-0.499081\pi$
$257$	12.9329	−	6.49515i	0.806733	−	0.405156i	0.803845	+	0.594839i	$0.202784\pi$
$258$		0			0
$259$	8.80867	+	9.33664i	0.547344	+	0.580151i
$260$	−6.74288	+	2.45421i	−0.418176	+	0.152204i
$261$		0			0
$262$	15.2786	+	5.56095i	0.943914	+	0.343557i
$263$	−4.14086	−	9.59959i	−0.255336	−	0.591936i	0.741541	−	0.670908i	$-0.234095\pi$
$263$	−4.14086	−	9.59959i	−0.255336	−	0.591936i	−0.996877	+	0.0789721i	$0.974836\pi$
$264$		0			0
$265$	4.31019	+	14.3970i	0.264773	+	0.884402i
$266$	2.90033	−	0.339000i	0.177831	−	0.0207854i
$267$		0			0
$268$	−0.0630404	−	1.08236i	−0.00385080	−	0.0661157i
$269$	0.105374	+	0.182513i	0.00642476	+	0.0111280i	0.869220	−	0.494426i	$-0.164622\pi$
$269$	0.105374	+	0.182513i	0.00642476	+	0.0111280i	−0.862795	+	0.505554i	$0.831288\pi$
$270$		0			0
$271$	5.70846	−	9.88735i	0.346765	−	0.600614i	−0.638908	−	0.769283i	$-0.720614\pi$
$271$	5.70846	−	9.88735i	0.346765	−	0.600614i	0.985673	+	0.168669i	$0.0539470\pi$
$272$	−1.07137	−	0.538064i	−0.0649616	−	0.0326249i
$273$		0			0
$274$	7.88653	+	10.5935i	0.476443	+	0.639974i
$275$	−7.49735	−	1.77691i	−0.452107	−	0.107151i
$276$		0			0
$277$	−6.65798	+	8.94322i	−0.400039	+	0.537346i	−0.955808	−	0.293991i	$-0.905017\pi$
$277$	−6.65798	+	8.94322i	−0.400039	+	0.537346i	0.555769	+	0.831337i	$0.312424\pi$
$278$	−6.66153	+	5.58969i	−0.399532	+	0.335247i
$279$		0			0
$280$	−3.34591	−	2.80755i	−0.199956	−	0.167783i
$281$	−21.1181	+	5.00509i	−1.25980	+	0.298579i	−0.805675	−	0.592358i	$-0.798197\pi$
$281$	−21.1181	+	5.00509i	−1.25980	+	0.298579i	−0.454128	+	0.890937i	$0.650049\pi$
$282$		0			0
$283$	0.247741	+	0.162942i	0.0147267	+	0.00968587i	0.556851	−	0.830612i	$-0.312009\pi$
$283$	0.247741	+	0.162942i	0.0147267	+	0.00968587i	−0.542124	+	0.840298i	$0.682380\pi$
$284$	7.91270	+	5.20427i	0.469533	+	0.308816i
$285$		0			0
$286$	8.02423	−	1.90178i	0.474483	−	0.112454i
$287$	−5.83015	−	4.89208i	−0.344143	−	0.288770i
$288$		0			0
$289$	−2.13795	+	1.79396i	−0.125762	+	0.105527i
$290$	2.49465	−	3.35090i	0.146491	−	0.196771i
$291$		0			0
$292$	10.3199	+	2.44585i	0.603924	+	0.143133i
$293$	−8.66275	−	11.6361i	−0.506083	−	0.679788i	0.473508	−	0.880790i	$-0.342988\pi$
$293$	−8.66275	−	11.6361i	−0.506083	−	0.679788i	−0.979591	+	0.201002i	$0.935580\pi$
$294$		0			0
$295$	11.7571	+	5.90464i	0.684526	+	0.343782i
$296$	13.4425	−	23.2830i	0.781327	−	1.35330i
$297$		0			0
$298$	1.21416	+	2.10299i	0.0703346	+	0.121823i
$299$	1.59790	+	27.4349i	0.0924091	+	1.58660i
$300$		0			0
$301$	−6.60202	+	0.771665i	−0.380534	+	0.0444781i
$302$	3.04846	+	10.1826i	0.175419	+	0.585941i
$303$		0			0
$304$	0.335840	+	0.778565i	0.0192617	+	0.0446538i
$305$	13.3665	+	4.86501i	0.765364	+	0.278570i
$306$		0			0
$307$	−3.56052	+	1.29592i	−0.203210	+	0.0739622i	−0.441620	−	0.897202i	$-0.645596\pi$
$307$	−3.56052	+	1.29592i	−0.203210	+	0.0739622i	0.238410	+	0.971165i	$0.423374\pi$
$308$	−2.56139	−	2.71492i	−0.145949	−	0.154697i
$309$		0			0
$310$	−6.69555	+	3.36263i	−0.380282	+	0.190985i
$311$	−0.716898	+	12.3087i	−0.0406516	+	0.697961i	0.914999	+	0.403457i	$0.132191\pi$
$311$	−0.716898	+	12.3087i	−0.0406516	+	0.697961i	−0.955650	+	0.294504i	$0.904846\pi$
$312$		0			0
$313$	−1.95193	+	6.51991i	−0.110330	+	0.368527i	−0.995266	−	0.0971844i	$-0.969016\pi$
$313$	−1.95193	+	6.51991i	−0.110330	+	0.368527i	0.884937	+	0.465711i	$0.154202\pi$
$314$	−0.183799	+	1.04238i	−0.0103724	+	0.0588246i
$315$		0			0
$316$	2.60810	+	14.7913i	0.146717	+	0.832074i
$317$	14.8355	+	1.73402i	0.833246	+	0.0973925i	0.522009	−	0.852940i	$-0.325183\pi$
$317$	14.8355	+	1.73402i	0.833246	+	0.0973925i	0.311237	+	0.950332i	$0.399257\pi$
$318$		0			0
$319$	6.20123	−	6.57292i	0.347202	−	0.368013i
$320$	−1.99351	+	4.62147i	−0.111441	+	0.258348i
$321$		0			0
$322$	−5.52126	+	3.63139i	−0.307688	+	0.202369i
$323$	−10.0493			−0.559156
$324$		0			0
$325$	−16.1482			−0.895740
$326$	−8.60471	+	5.65940i	−0.476571	+	0.313445i
$327$		0			0
$328$	−6.31370	+	14.6368i	−0.348616	+	0.808182i
$329$	−2.70515	+	2.86729i	−0.149140	+	0.158079i
$330$		0			0
$331$	3.66884	+	0.428825i	0.201657	+	0.0235704i	0.216322	−	0.976322i	$-0.430594\pi$
$331$	3.66884	+	0.428825i	0.201657	+	0.0235704i	−0.0146645	+	0.999892i	$0.504668\pi$
$332$	1.08293	+	6.14162i	0.0594337	+	0.337065i
$333$		0			0
$334$	0.551633	−	3.12847i	0.0301840	−	0.171182i
$335$	−0.287158	+	0.959175i	−0.0156891	+	0.0524053i
$336$		0			0
$337$	−1.07246	+	18.4134i	−0.0584206	+	1.00304i	0.833979	+	0.551796i	$0.186057\pi$
$337$	−1.07246	+	18.4134i	−0.0584206	+	1.00304i	−0.892400	+	0.451246i	$0.850980\pi$
$338$	5.76736	−	2.89648i	0.313703	−	0.157548i
$339$		0			0
$340$	4.07508	+	4.31933i	0.221002	+	0.234249i
$341$	−15.2298	+	5.54319i	−0.824740	+	0.300181i
$342$		0			0
$343$	−15.1621	−	5.51854i	−0.818675	−	0.297973i
$344$	5.51418	+	12.7833i	0.297305	+	0.689230i
$345$		0			0
$346$	5.75061	+	19.2084i	0.309155	+	1.03265i
$347$	33.3689	−	3.90026i	1.79133	−	0.209377i	0.845488	−	0.533994i	$-0.179309\pi$
$347$	33.3689	−	3.90026i	1.79133	−	0.209377i	0.945846	+	0.324617i	$0.105235\pi$
$348$		0			0
$349$	1.91515	+	32.8819i	0.102516	+	1.76013i	0.522541	+	0.852614i	$0.324984\pi$
$349$	1.91515	+	32.8819i	0.102516	+	1.76013i	−0.420026	+	0.907512i	$0.637979\pi$
$350$	−1.94157	−	3.36289i	−0.103781	−	0.179754i
$351$		0			0
$352$	−6.27342	+	10.8659i	−0.334374	+	0.579154i
$353$	11.9223	+	5.98761i	0.634561	+	0.318688i	0.736840	−	0.676067i	$-0.236317\pi$
$353$	11.9223	+	5.98761i	0.634561	+	0.318688i	−0.102279	+	0.994756i	$0.532613\pi$
$354$		0			0
$355$	−5.22281	−	7.01545i	−0.277198	−	0.372341i
$356$	−4.23485	−	1.00368i	−0.224447	−	0.0531948i
$357$		0			0
$358$	−3.15338	+	4.23572i	−0.166661	+	0.223865i
$359$	6.91454	−	5.80199i	0.364936	−	0.306217i	−0.441819	−	0.897104i	$-0.645667\pi$
$359$	6.91454	−	5.80199i	0.364936	−	0.306217i	0.806754	+	0.590887i	$0.201222\pi$
$360$		0			0
$361$	−9.11037	−	7.64450i	−0.479493	−	0.402342i
$362$	5.02033	−	1.18984i	0.263863	−	0.0625366i
$363$		0			0
$364$	−6.53564	−	4.29856i	−0.342561	−	0.225306i
$365$	−8.18295	−	5.38201i	−0.428315	−	0.281707i
$366$		0			0
$367$	24.9138	−	5.90467i	1.30049	−	0.308221i	0.478682	−	0.877988i	$-0.341115\pi$
$367$	24.9138	−	5.90467i	1.30049	−	0.308221i	0.821806	+	0.569767i	$0.192967\pi$
$368$	−1.46997	−	1.23345i	−0.0766274	−	0.0642980i
$369$		0			0
$370$	−7.51364	+	6.30469i	−0.390616	+	0.327765i
$371$	−9.78340	+	13.1414i	−0.507929	+	0.682267i
$372$		0			0
$373$	−21.2782	−	5.04304i	−1.10175	−	0.261118i	−0.360773	−	0.932654i	$-0.617487\pi$
$373$	−21.2782	−	5.04304i	−1.10175	−	0.261118i	−0.740973	+	0.671535i	$0.765635\pi$
$374$	−4.07530	−	5.47408i	−0.210729	−	0.283058i
$375$		0			0
$376$	7.37817	+	3.70546i	0.380500	+	0.191094i
$377$	9.46934	−	16.4014i	0.487696	−	0.844714i
$378$		0			0
$379$	−5.26717	−	9.12300i	−0.270556	−	0.468617i	0.698448	−	0.715661i	$-0.253874\pi$
$379$	−5.26717	−	9.12300i	−0.270556	−	0.468617i	−0.969004	+	0.247043i	$0.920541\pi$
$380$	−0.244196	−	4.19268i	−0.0125270	−	0.215080i
$381$		0			0
$382$	−5.58701	+	0.653027i	−0.285856	+	0.0334118i
$383$	−6.27198	−	20.9499i	−0.320483	−	1.07049i	−0.954759	−	0.297382i	$-0.903887\pi$
$383$	−6.27198	−	20.9499i	−0.320483	−	1.07049i	0.634275	−	0.773107i	$-0.281299\pi$
$384$		0			0
$385$	1.36525	+	3.16500i	0.0695794	+	0.161303i
$386$	12.4552	+	4.53331i	0.633952	+	0.230740i
$387$		0			0
$388$	1.67315	−	0.608977i	0.0849414	−	0.0309161i
$389$	−16.7379	−	17.7411i	−0.848643	−	0.899510i	0.147336	−	0.989086i	$-0.452930\pi$
$389$	−16.7379	−	17.7411i	−0.848643	−	0.899510i	−0.995980	+	0.0895769i	$0.971449\pi$
$390$		0			0
$391$	20.3235	−	10.2068i	1.02780	−	0.516181i
$392$	−0.844062	+	14.4920i	−0.0426316	+	0.731956i
$393$		0			0
$394$	2.76953	−	9.25087i	0.139527	−	0.466052i
$395$	2.40854	−	13.6595i	0.121187	−	0.687285i
$396$		0			0
$397$	4.16728	+	23.6338i	0.209150	+	1.18615i	0.890775	+	0.454445i	$0.150163\pi$
$397$	4.16728	+	23.6338i	0.209150	+	1.18615i	−0.681625	+	0.731702i	$0.738726\pi$
$398$	−3.55758	−	0.415822i	−0.178325	−	0.0208433i
$399$		0			0
$400$	0.773777	−	0.820155i	0.0386888	−	0.0410078i
$401$	−14.6208	+	33.8948i	−0.730127	+	1.69263i	−0.00886741	+	0.999961i	$0.502823\pi$
$401$	−14.6208	+	33.8948i	−0.730127	+	1.69263i	−0.721260	+	0.692665i	$0.756437\pi$
$402$		0			0
$403$	−28.3790	+	18.6652i	−1.41366	+	0.929778i
$404$	−3.02339			−0.150419
$405$		0			0
$406$	4.55416			0.226019
$407$	−17.7263	+	11.6588i	−0.878659	+	0.577903i
$408$		0			0
$409$	−1.13089	+	2.62170i	−0.0559190	+	0.129635i	−0.943885	−	0.330274i	$-0.892859\pi$
$409$	−1.13089	+	2.62170i	−0.0559190	+	0.129635i	0.887966	+	0.459909i	$0.152118\pi$
$410$	3.99086	−	4.23006i	0.197094	−	0.208908i
$411$		0			0
$412$	5.90196	+	0.689840i	0.290768	+	0.0339860i
$413$	2.49058	+	14.1248i	0.122553	+	0.695035i
$414$		0			0
$415$	1.00007	−	5.67169i	0.0490916	−	0.278412i
$416$	−7.54166	+	25.1909i	−0.369761	+	1.23509i
$417$		0			0
$418$	−0.280640	+	4.81839i	−0.0137265	+	0.235675i
$419$	30.7184	−	15.4274i	1.50069	−	0.753677i	0.506598	−	0.862182i	$-0.330903\pi$
$419$	30.7184	−	15.4274i	1.50069	−	0.753677i	0.994096	+	0.108505i	$0.0346064\pi$
$420$		0			0
$421$	−4.29013	−	4.54727i	−0.209088	−	0.221620i	0.614339	−	0.789042i	$-0.289423\pi$
$421$	−4.29013	−	4.54727i	−0.209088	−	0.221620i	−0.823428	+	0.567421i	$0.807941\pi$
$422$	−11.1790	+	4.06883i	−0.544186	+	0.198067i
$423$		0			0
$424$	32.2449	+	11.7362i	1.56595	+	0.569960i
$425$	5.29305	+	12.2707i	0.256751	+	0.595215i
$426$		0			0
$427$	4.44738	+	14.8553i	0.215224	+	0.718898i
$428$	−15.9476	+	1.86401i	−0.770856	+	0.0901001i
$429$		0			0
$430$	−0.295323	−	5.07050i	−0.0142417	−	0.244521i
$431$	−1.50862	−	2.61301i	−0.0726679	−	0.125864i	0.827402	−	0.561610i	$-0.189818\pi$
$431$	−1.50862	−	2.61301i	−0.0726679	−	0.125864i	−0.900070	+	0.435746i	$0.856485\pi$
$432$		0			0
$433$	−15.3659	+	26.6146i	−0.738439	+	1.27901i	0.214759	+	0.976667i	$0.431104\pi$
$433$	−15.3659	+	26.6146i	−0.738439	+	1.27901i	−0.953198	+	0.302347i	$0.902230\pi$
$434$	−7.29919	−	3.66579i	−0.350372	−	0.175964i
$435$		0			0
$436$	6.94660	+	9.33090i	0.332682	+	0.446869i
$437$	−15.6509	−	3.70933i	−0.748684	−	0.177441i
$438$		0			0
$439$	0.273278	−	0.367076i	0.0130428	−	0.0175196i	−0.795554	−	0.605883i	$-0.792820\pi$
$439$	0.273278	−	0.367076i	0.0130428	−	0.0175196i	0.808597	+	0.588363i	$0.200227\pi$
$440$	5.53042	−	4.64057i	0.263652	−	0.221231i
$441$		0			0
$442$	−10.9565	−	9.19361i	−0.521148	−	0.437296i
$443$	−33.9676	+	8.05047i	−1.61385	+	0.382489i	−0.935801	−	0.352528i	$-0.885322\pi$
$443$	−33.9676	+	8.05047i	−1.61385	+	0.382489i	−0.678048	+	0.735018i	$0.737174\pi$
$444$		0			0
$445$	3.35795	+	2.20856i	0.159182	+	0.104696i
$446$	14.0518	+	9.24203i	0.665373	+	0.437623i
$447$		0			0
$448$	−5.33896	+	1.26536i	−0.252242	+	0.0597825i
$449$	−5.48196	−	4.59991i	−0.258710	−	0.217083i	0.504202	−	0.863586i	$-0.331787\pi$
$449$	−5.48196	−	4.59991i	−0.258710	−	0.217083i	−0.762912	+	0.646502i	$0.776231\pi$
$450$		0			0
$451$	9.63661	−	8.08607i	0.453770	−	0.380758i
$452$	13.5638	−	18.2193i	0.637987	−	0.856965i
$453$		0			0
$454$	2.20751	+	0.523189i	0.103603	+	0.0245545i
$455$	4.31387	+	5.79453i	0.202237	+	0.271652i
$456$		0			0
$457$	−11.3334	−	5.69186i	−0.530155	−	0.266254i	0.163522	−	0.986540i	$-0.447714\pi$
$457$	−11.3334	−	5.69186i	−0.530155	−	0.266254i	−0.693677	+	0.720286i	$0.744011\pi$
$458$	−0.635820	+	1.10127i	−0.0297099	+	0.0514591i
$459$		0			0
$460$	4.75227	+	8.23117i	0.221576	+	0.383780i
$461$	−0.0268522	−	0.461034i	−0.00125063	−	0.0214725i	0.997625	−	0.0688777i	$-0.0219418\pi$
$461$	−0.0268522	−	0.461034i	−0.00125063	−	0.0214725i	−0.998876	+	0.0474052i	$0.984905\pi$
$462$		0			0
$463$	−36.8501	+	4.30715i	−1.71257	+	0.200170i	−0.915110	−	0.403205i	$-0.867896\pi$
$463$	−36.8501	+	4.30715i	−1.71257	+	0.200170i	−0.797457	+	0.603375i	$0.793822\pi$
$464$	0.379270	+	1.26685i	0.0176072	+	0.0588120i
$465$		0			0
$466$	−2.15365	−	4.99272i	−0.0997659	−	0.231283i
$467$	−25.8480	−	9.40792i	−1.19611	−	0.435347i	−0.334242	−	0.942487i	$-0.608480\pi$
$467$	−25.8480	−	9.40792i	−1.19611	−	0.435347i	−0.861863	+	0.507141i	$0.830702\pi$
$468$		0			0
$469$	−1.02568	+	0.373316i	−0.0473614	+	0.0172381i
$470$	−2.06707	−	2.19096i	−0.0953467	−	0.101062i
$471$		0			0
$472$	26.8451	−	13.4821i	1.23564	−	0.620564i
$473$	0.638820	−	10.9681i	0.0293730	−	0.504315i
$474$		0			0
$475$	2.71066	−	9.05424i	0.124374	−	0.415437i
$476$	−1.12413	+	6.37527i	−0.0515245	+	0.292210i
$477$		0			0
$478$	−2.44425	−	13.8620i	−0.111798	−	0.634035i
$479$	14.1641	+	1.65554i	0.647173	+	0.0756436i	0.433346	−	0.901228i	$-0.357333\pi$
$479$	14.1641	+	1.65554i	0.647173	+	0.0756436i	0.213827	+	0.976871i	$0.431407\pi$
$480$		0			0
$481$	−30.5143	+	32.3433i	−1.39133	+	1.47473i
$482$	−4.15689	+	9.63674i	−0.189341	+	0.438942i
$483$		0			0
$484$	−6.84898	+	4.50465i	−0.311317	+	0.204757i
$485$	−1.64429			−0.0746634
$486$		0			0
$487$	9.07752			0.411342			0.205671	−	0.978621i	$-0.434062\pi$
$487$	9.07752			0.411342			0.205671	+	0.978621i	$0.434062\pi$
$488$	27.1354	−	17.8472i	1.22836	−	0.807905i
$489$		0			0
$490$	2.09766	−	4.86291i	0.0947624	−	0.219684i
$491$	19.1344	−	20.2813i	0.863524	−	0.915282i	−0.133602	−	0.991035i	$-0.542654\pi$
$491$	19.1344	−	20.2813i	0.863524	−	0.915282i	0.997127	+	0.0757527i	$0.0241359\pi$
$492$		0			0
$493$	−15.5669	−	1.81951i	−0.701098	−	0.0819467i
$494$	1.75653	+	9.96180i	0.0790302	+	0.448203i
$495$		0			0
$496$	0.411853	−	2.33573i	0.0184927	−	0.104878i
$497$	2.73455	−	9.13405i	0.122662	−	0.409718i
$498$		0			0
$499$	1.38333	−	23.7509i	0.0619266	−	1.06324i	−0.814022	−	0.580834i	$-0.802727\pi$
$499$	1.38333	−	23.7509i	0.0619266	−	1.06324i	0.875949	−	0.482404i	$-0.160236\pi$
$500$	−12.0298	+	6.04157i	−0.537987	+	0.270187i
$501$		0			0
$502$	14.7498	+	15.6339i	0.658317	+	0.697775i
$503$	7.57016	−	2.75531i	0.337537	−	0.122853i	−0.167690	−	0.985840i	$-0.553631\pi$
$503$	7.57016	−	2.75531i	0.337537	−	0.122853i	0.505227	+	0.862986i	$0.331409\pi$
$504$		0			0
$505$	2.62367	+	0.954939i	0.116752	+	0.0424942i
$506$	−4.32638	−	10.0297i	−0.192331	−	0.445873i
$507$		0			0
$508$	2.12837	+	7.10924i	0.0944310	+	0.315422i
$509$	19.1743	−	2.24115i	0.849884	−	0.0993372i	0.320011	−	0.947414i	$-0.396313\pi$
$509$	19.1743	−	2.24115i	0.849884	−	0.0993372i	0.529874	+	0.848077i	$0.322239\pi$
$510$		0			0
$511$	−0.620825	−	10.6592i	−0.0274637	−	0.471533i
$512$	−1.79397	−	3.10725i	−0.0792832	−	0.137323i
$513$		0			0
$514$	−6.02780	+	10.4405i	−0.265875	+	0.460509i
$515$	−4.90378	−	2.46277i	−0.216086	−	0.108523i
$516$		0			0
$517$	−3.89088	−	5.22637i	−0.171121	−	0.229855i
$518$	−10.4044	−	2.46589i	−0.457144	−	0.108345i
$519$		0			0
$520$	9.03530	−	12.1365i	0.396224	−	0.532221i
$521$	2.04454	−	1.71557i	0.0895727	−	0.0751604i	−0.596902	−	0.802314i	$-0.703602\pi$
$521$	2.04454	−	1.71557i	0.0895727	−	0.0751604i	0.686474	+	0.727154i	$0.259157\pi$
$522$		0			0
$523$	11.7693	+	9.87562i	0.514636	+	0.431831i	0.862757	−	0.505619i	$-0.168736\pi$
$523$	11.7693	+	9.87562i	0.514636	+	0.431831i	−0.348121	+	0.937450i	$0.613180\pi$
$524$	24.8057	−	5.87906i	1.08364	−	0.256828i
$525$		0			0
$526$	7.27611	+	4.78557i	0.317253	+	0.208661i
$527$	23.4853	+	15.4465i	1.02304	+	0.672862i
$528$		0			0
$529$	13.0396	−	3.09043i	0.566938	−	0.134367i
$530$	−9.58997	−	8.04694i	−0.416562	−	0.349537i
$531$		0			0
$532$	3.50727	−	2.94295i	0.152059	−	0.127593i
$533$	15.7438	−	21.1475i	0.681938	−	0.916002i
$534$		0			0
$535$	14.4279	+	3.41948i	0.623774	+	0.147837i
$536$	1.36518	+	1.83376i	0.0589668	+	0.0792062i
$537$		0			0
$538$	−0.156882	−	0.0787892i	−0.00676368	−	0.00339685i
$539$	5.72799	−	9.92117i	0.246722	−	0.427335i
$540$		0			0
$541$	9.39421	+	16.2713i	0.403889	+	0.699556i	0.994191	−	0.107626i	$-0.0343250\pi$
$541$	9.39421	+	16.2713i	0.403889	+	0.699556i	−0.590303	+	0.807182i	$0.700992\pi$
$542$	0.552983	+	9.49435i	0.0237527	+	0.407817i
$543$		0			0
$544$	21.6140	−	2.52632i	0.926695	−	0.108315i
$545$	−3.08103	−	10.2914i	−0.131977	−	0.440833i
$546$		0			0
$547$	−4.53941	−	10.5235i	−0.194091	−	0.449954i	0.793182	−	0.608984i	$-0.208423\pi$
$547$	−4.53941	−	10.5235i	−0.194091	−	0.449954i	−0.987274	+	0.159030i	$0.949163\pi$
$548$	19.4583	+	7.08223i	0.831216	+	0.302538i
$549$		0			0
$550$	6.03132	−	2.19522i	0.257176	−	0.0936045i
$551$	7.60666	+	8.06259i	0.324055	+	0.343478i
$552$		0			0
$553$	13.5124	−	6.78616i	0.574604	−	0.288577i
$554$	0.540027	−	9.27191i	0.0229436	−	0.393926i
$555$		0			0
$556$	−3.91044	+	13.0618i	−0.165840	+	0.553943i
$557$	4.33665	−	24.5943i	0.183750	−	1.04210i	−0.743802	−	0.668400i	$-0.766979\pi$
$557$	4.33665	−	24.5943i	0.183750	−	1.04210i	0.927551	−	0.373695i	$-0.121909\pi$
$558$		0			0
$559$	−3.99840	−	22.6761i	−0.169114	−	0.959095i
$560$	−0.501009	−	0.0585596i	−0.0211715	−	0.00247459i
$561$		0			0
$562$	12.4066	−	13.1502i	0.523339	−	0.554707i
$563$	−6.96357	+	16.1434i	−0.293479	+	0.680362i	−0.999616	−	0.0277141i	$-0.991177\pi$
$563$	−6.96357	+	16.1434i	−0.293479	+	0.680362i	0.706137	+	0.708076i	$0.250436\pi$
$564$		0			0
$565$	−17.5251	+	11.5264i	−0.737287	+	0.484921i
$566$	−0.247007			−0.0103825
$567$		0			0
$568$	−19.9700			−0.837922
$569$	−13.3587	+	8.78615i	−0.560026	+	0.368335i	−0.797741	−	0.603000i	$-0.793972\pi$
$569$	−13.3587	+	8.78615i	−0.560026	+	0.368335i	0.237715	+	0.971335i	$0.423601\pi$
$570$		0			0
$571$	4.09156	−	9.48530i	0.171226	−	0.396947i	−0.810896	−	0.585190i	$-0.801020\pi$
$571$	4.09156	−	9.48530i	0.171226	−	0.396947i	0.982123	+	0.188243i	$0.0602791\pi$
$572$	8.87297	−	9.40480i	0.370998	−	0.393235i
$573$		0			0
$574$	6.29696	+	0.736009i	0.262830	+	0.0307204i
$575$	3.71420	+	21.0643i	0.154893	+	0.878441i
$576$		0			0
$577$	6.79785	−	38.5525i	0.282998	−	1.60496i	−0.429351	−	0.903138i	$-0.641258\pi$
$577$	6.79785	−	38.5525i	0.282998	−	1.60496i	0.712349	−	0.701825i	$-0.247631\pi$
$578$	0.666776	−	2.22719i	0.0277342	−	0.0926387i
$579$		0			0
$580$	0.380849	−	6.53892i	0.0158139	−	0.271514i
$581$	5.61058	−	2.81774i	0.232766	−	0.116900i
$582$		0			0
$583$	−18.5832	−	19.6971i	−0.769639	−	0.815770i
$584$	−21.0145	+	7.64866i	−0.869587	+	0.316504i
$585$		0			0
$586$	11.3554	+	4.13304i	0.469088	+	0.170734i
$587$	−7.05091	−	16.3458i	−0.291022	−	0.674665i	0.708496	−	0.705715i	$-0.249374\pi$
$587$	−7.05091	−	16.3458i	−0.291022	−	0.674665i	−0.999518	+	0.0310501i	$0.990115\pi$
$588$		0			0
$589$	−5.70176	−	19.0452i	−0.234937	−	0.784743i
$590$	−10.8855	+	1.27233i	−0.448147	+	0.0523809i
$591$		0			0
$592$	−0.180531	−	3.09960i	−0.00741978	−	0.127393i
$593$	6.92687	+	11.9977i	0.284452	+	0.492686i	0.972476	−	0.233002i	$-0.0748549\pi$
$593$	6.92687	+	11.9977i	0.284452	+	0.492686i	−0.688024	+	0.725688i	$0.741522\pi$
$594$		0			0
$595$	2.98914	−	5.17735i	0.122543	−	0.212251i
$596$	3.40242	+	1.70876i	0.139369	+	0.0699935i
$597$		0			0
$598$	−13.6704	−	18.3625i	−0.559023	−	0.750898i
$599$	3.52152	+	0.834615i	0.143885	+	0.0341014i	0.301927	−	0.953331i	$-0.402370\pi$
$599$	3.52152	+	0.834615i	0.143885	+	0.0341014i	−0.158042	+	0.987432i	$0.550518\pi$
$600$		0			0
$601$	−6.20029	+	8.32844i	−0.252915	+	0.339724i	−0.910389	−	0.413753i	$-0.864218\pi$
$601$	−6.20029	+	8.32844i	−0.252915	+	0.339724i	0.657474	+	0.753477i	$0.271625\pi$
$602$	4.24159	−	3.55912i	0.172874	−	0.145059i
$603$		0			0
$604$	12.7665	+	10.7124i	0.519462	+	0.435880i
$605$	7.36628	−	1.74584i	0.299482	−	0.0709785i
$606$		0			0
$607$	−11.2230	−	7.38148i	−0.455527	−	0.299605i	0.300932	−	0.953646i	$-0.402702\pi$
$607$	−11.2230	−	7.38148i	−0.455527	−	0.299605i	−0.756459	+	0.654041i	$0.773073\pi$
$608$	−12.8585	−	8.45717i	−0.521481	−	0.342984i
$609$		0			0
$610$	−11.5297	+	2.73258i	−0.466822	+	0.110639i
$611$	−10.4607	−	8.77758i	−0.423195	−	0.355103i
$612$		0			0
$613$	22.2652	−	18.6827i	0.899281	−	0.754587i	−0.0707686	−	0.997493i	$-0.522545\pi$
$613$	22.2652	−	18.6827i	0.899281	−	0.754587i	0.970050	+	0.242906i	$0.0781007\pi$
$614$	1.88481	−	2.53175i	0.0760649	−	0.102173i
$615$		0			0
$616$	7.65817	+	1.81502i	0.308557	+	0.0731292i
$617$	7.42289	+	9.97068i	0.298834	+	0.401404i	0.926025	−	0.377461i	$-0.123203\pi$
$617$	7.42289	+	9.97068i	0.298834	+	0.401404i	−0.627191	+	0.778866i	$0.715795\pi$
$618$		0			0
$619$	30.8888	+	15.5129i	1.24153	+	0.623518i	0.943605	−	0.331073i	$-0.107411\pi$
$619$	30.8888	+	15.5129i	1.24153	+	0.623518i	0.297921	+	0.954591i	$0.403707\pi$
$620$	−5.87380	+	10.1737i	−0.235898	+	0.408586i
$621$		0			0
$622$	−5.13533	−	8.89464i	−0.205908	−	0.356643i
$623$	0.254762	+	4.37409i	0.0102068	+	0.175244i
$624$		0			0
$625$	−5.25856	+	0.614638i	−0.210343	+	0.0245855i
$626$	−1.62598	−	5.43116i	−0.0649874	−	0.217073i
$627$		0			0
$628$	0.657320	+	1.52384i	0.0262299	+	0.0608078i
$629$	34.5789	+	12.5857i	1.37875	+	0.501825i
$630$		0			0
$631$	12.4258	−	4.52262i	0.494663	−	0.180042i	−0.0826292	−	0.996580i	$-0.526332\pi$
$631$	12.4258	−	4.52262i	0.494663	−	0.180042i	0.577292	+	0.816538i	$0.304109\pi$
$632$	−21.7332	−	23.0359i	−0.864502	−	0.916318i
$633$		0			0
$634$	−11.1189	+	5.58410i	−0.441586	+	0.221773i
$635$	0.398477	−	6.84158i	0.0158131	−	0.271500i
$636$		0			0
$637$	6.88597	−	23.0007i	0.272832	−	0.911323i
$638$	−1.30714	+	7.41317i	−0.0517502	+	0.293490i
$639$		0			0
$640$	1.69021	+	9.58567i	0.0668115	+	0.378907i
$641$	5.23723	+	0.612144i	0.206858	+	0.0241782i	0.218891	−	0.975749i	$-0.429756\pi$
$641$	5.23723	+	0.612144i	0.206858	+	0.0241782i	−0.0120327	+	0.999928i	$0.503830\pi$
$642$		0			0
$643$	−3.00341	+	3.18343i	−0.118443	+	0.125542i	−0.783882	−	0.620910i	$-0.786763\pi$
$643$	−3.00341	+	3.18343i	−0.118443	+	0.125542i	0.665439	+	0.746453i	$0.268245\pi$
$644$	−4.10395	+	9.51403i	−0.161718	+	0.374905i
$645$		0			0
$646$	6.99401	−	4.60003i	0.275176	−	0.180986i
$647$	5.42624			0.213327			0.106664	−	0.994295i	$-0.465983\pi$
$647$	5.42624			0.213327			0.106664	+	0.994295i	$0.465983\pi$
$648$		0			0
$649$	−23.7069			−0.930576
$650$	11.2387	−	7.39180i	0.440817	−	0.289930i
$651$		0			0
$652$	−6.39588	+	14.8273i	−0.250482	+	0.580683i
$653$	−7.61797	+	8.07457i	−0.298114	+	0.315982i	−0.859065	−	0.511867i	$-0.828954\pi$
$653$	−7.61797	+	8.07457i	−0.298114	+	0.315982i	0.560951	+	0.827849i	$0.310436\pi$
$654$		0			0
$655$	−23.3831	−	2.73309i	−0.913653	−	0.106791i
$656$	0.319672	+	1.81295i	0.0124811	+	0.0707837i
$657$		0			0
$658$	0.570212	−	3.23383i	0.0222292	−	0.126068i
$659$	2.13247	−	7.12294i	0.0830691	−	0.277470i	−0.906356	−	0.422515i	$-0.861147\pi$
$659$	2.13247	−	7.12294i	0.0830691	−	0.277470i	0.989425	+	0.145045i	$0.0463326\pi$
$660$		0			0
$661$	0.222789	−	3.82514i	0.00866548	−	0.148781i	−0.991200	−	0.132373i	$-0.957740\pi$
$661$	0.222789	−	3.82514i	0.00866548	−	0.148781i	0.999865	−	0.0164071i	$-0.00522278\pi$
$662$	−2.74970	+	1.38095i	−0.106870	+	0.0536722i
$663$		0			0
$664$	−9.02405	−	9.56493i	−0.350201	−	0.371191i
$665$	−3.97311	+	1.44609i	−0.154071	+	0.0560771i
$666$		0			0
$667$	−23.5726	−	8.57971i	−0.912733	−	0.332208i
$668$	−1.97281	−	4.57348i	−0.0763302	−	0.176953i
$669$		0			0
$670$	−0.239206	−	0.799005i	−0.00924134	−	0.0308682i
$671$	−25.4576	+	2.97557i	−0.982781	+	0.114871i
$672$		0			0
$673$	−2.44739	−	42.0201i	−0.0943400	−	1.61975i	−0.630880	−	0.775880i	$-0.717306\pi$
$673$	−2.44739	−	42.0201i	−0.0943400	−	1.61975i	0.536540	−	0.843875i	$-0.319731\pi$
$674$	−7.68230	−	13.3061i	−0.295911	−	0.512533i
$675$		0			0
$676$	5.05953	−	8.76336i	0.194597	−	0.337052i
$677$	−2.22728	−	1.11858i	−0.0856012	−	0.0429906i	0.405484	−	0.914102i	$-0.367103\pi$
$677$	−2.22728	−	1.11858i	−0.0856012	−	0.0429906i	−0.491085	+	0.871112i	$0.663399\pi$
$678$		0			0
$679$	−1.07043	−	1.43783i	−0.0410792	−	0.0551789i
$680$	−12.1839	−	2.88763i	−0.467230	−	0.110735i
$681$		0			0
$682$	8.06213	−	10.8293i	0.308715	−	0.414676i
$683$	−11.7411	+	9.85194i	−0.449260	+	0.376974i	−0.839161	−	0.543883i	$-0.816954\pi$
$683$	−11.7411	+	9.85194i	−0.449260	+	0.376974i	0.389901	+	0.920857i	$0.372509\pi$
$684$		0			0
$685$	−14.6488	−	12.2918i	−0.559701	−	0.469645i
$686$	13.0785	−	3.09966i	0.499338	−	0.118345i
$687$		0			0
$688$	1.34329	+	0.883498i	0.0512126	+	0.0336831i
$689$	−47.4169	−	31.1866i	−1.80644	−	1.18811i
$690$		0			0
$691$	36.1088	−	8.55795i	1.37364	−	0.325560i	0.523462	−	0.852049i	$-0.324640\pi$
$691$	36.1088	−	8.55795i	1.37364	−	0.325560i	0.850182	+	0.526489i	$0.176492\pi$
$692$	24.0827	+	20.2078i	0.915488	+	0.768186i
$693$		0			0
$694$	−21.4384	+	17.9890i	−0.813792	+	0.682853i
$695$	7.51902	−	10.0998i	0.285213	−	0.383107i
$696$		0			0
$697$	−21.2301	−	5.03162i	−0.804146	−	0.190586i
$698$	−16.3845	−	22.0082i	−0.620162	−	0.833023i
$699$		0			0
$700$	−5.44080	−	2.73247i	−0.205643	−	0.103278i
$701$	−3.35489	+	5.81083i	−0.126712	+	0.219472i	−0.922401	−	0.386234i	$-0.873776\pi$
$701$	−3.35489	+	5.81083i	−0.126712	+	0.219472i	0.795689	+	0.605706i	$0.207109\pi$
$702$		0			0
$703$	−13.0126	−	22.5385i	−0.490779	−	0.850054i
$704$	−0.527326	−	9.05384i	−0.0198743	−	0.341229i
$705$		0			0
$706$	−11.0384	+	1.29021i	−0.415436	+	0.0485575i
$707$	0.872964	+	2.91590i	0.0328312	+	0.109664i
$708$		0			0
$709$	−9.41920	−	21.8362i	−0.353745	−	0.820074i	−0.998451	−	0.0556428i	$-0.982279\pi$
$709$	−9.41920	−	21.8362i	−0.353745	−	0.820074i	0.644705	−	0.764431i	$-0.276980\pi$
$710$	6.84623	+	2.49182i	0.256934	+	0.0935165i
$711$		0			0
$712$	8.62351	−	3.13870i	0.323180	−	0.117628i
$713$	30.8749	+	32.7255i	1.15627	+	1.22558i
$714$		0			0
$715$	−10.6704	+	5.35888i	−0.399050	+	0.200411i
$716$	−0.481415	+	8.26557i	−0.0179913	+	0.308899i
$717$		0			0
$718$	−2.15648	+	7.20314i	−0.0804790	+	0.268819i
$719$	−7.41202	+	42.0356i	−0.276422	+	1.56766i	0.457988	+	0.888958i	$0.348570\pi$
$719$	−7.41202	+	42.0356i	−0.276422	+	1.56766i	−0.734410	+	0.678706i	$0.762541\pi$
$720$		0			0
$721$	−1.03880	−	5.89131i	−0.0386868	−	0.219404i
$722$	9.83981	+	1.15011i	0.366200	+	0.0428026i
$723$		0			0
$724$	5.55134	−	5.88408i	0.206314	−	0.218680i
$725$	5.83833	−	13.5348i	0.216830	−	0.502668i
$726$		0			0
$727$	−15.9209	+	10.4713i	−0.590472	+	0.388360i	−0.809293	−	0.587405i	$-0.800149\pi$
$727$	−15.9209	+	10.4713i	−0.590472	+	0.388360i	0.218821	+	0.975765i	$0.429779\pi$
$728$	16.4946			0.611329
$729$		0			0
$730$	8.15871			0.301967
$731$	−15.9205	+	10.4711i	−0.588840	+	0.387286i
$732$		0			0
$733$	−7.11488	+	16.4941i	−0.262794	+	0.609225i	−0.997614	−	0.0690370i	$-0.978007\pi$
$733$	−7.11488	+	16.4941i	−0.262794	+	0.609225i	0.734820	+	0.678262i	$0.237267\pi$
$734$	−14.6364	+	15.5137i	−0.540240	+	0.572621i
$735$		0			0
$736$	34.5946	+	4.04353i	1.27517	+	0.149046i
$737$	−0.313285	−	1.77673i	−0.0115400	−	0.0654466i
$738$		0			0
$739$	2.16602	−	12.2841i	0.0796782	−	0.451878i	−0.918700	−	0.394955i	$-0.870760\pi$
$739$	2.16602	−	12.2841i	0.0796782	−	0.451878i	0.998379	−	0.0569224i	$-0.0181288\pi$
$740$	−4.41065	+	14.7326i	−0.162139	+	0.541580i
$741$		0			0
$742$	0.793529	−	13.6244i	0.0291314	−	0.500166i
$743$	−23.1603	+	11.6315i	−0.849668	+	0.426719i	−0.819674	−	0.572831i	$-0.805845\pi$
$743$	−23.1603	+	11.6315i	−0.849668	+	0.426719i	−0.0299942	+	0.999550i	$0.509549\pi$
$744$		0			0
$745$	−2.41288	−	2.55750i	−0.0884010	−	0.0936996i
$746$	17.1175	−	6.23026i	0.626716	−	0.228106i
$747$		0			0
$748$	−10.0549	−	3.65968i	−0.367643	−	0.133811i
$749$	6.40239	+	14.8424i	0.233938	+	0.542330i
$750$		0			0
$751$	−3.01027	−	10.0550i	−0.109846	−	0.366913i	0.885336	−	0.464951i	$-0.153928\pi$
$751$	−3.01027	−	10.0550i	−0.109846	−	0.366913i	−0.995183	+	0.0980389i	$0.968743\pi$
$752$	0.947056	−	0.110695i	0.0345356	−	0.00403663i
$753$		0			0
$754$	0.917302	+	15.7495i	0.0334062	+	0.573562i
$755$	−7.69516	−	13.3284i	−0.280056	−	0.485070i
$756$		0			0
$757$	−0.0864170	+	0.149679i	−0.00314088	+	0.00544016i	−0.867592	−	0.497277i	$-0.834333\pi$
$757$	−0.0864170	+	0.149679i	−0.00314088	+	0.00544016i	0.864451	+	0.502718i	$0.167666\pi$
$758$	7.84184	+	3.93832i	0.284828	+	0.143046i
$759$		0			0
$760$	5.28822	+	7.10331i	0.191824	+	0.257664i
$761$	1.82265	+	0.431977i	0.0660711	+	0.0156591i	0.263518	−	0.964654i	$-0.415117\pi$
$761$	1.82265	+	0.431977i	0.0660711	+	0.0156591i	−0.197447	+	0.980313i	$0.563265\pi$
$762$		0			0
$763$	6.99343	−	9.39380i	0.253179	−	0.340079i
$764$	−6.75618	+	5.66911i	−0.244430	+	0.205101i
$765$		0			0
$766$	13.9549	+	11.7095i	0.504211	+	0.423083i
$767$	−48.3455	+	11.4581i	−1.74565	+	0.413728i
$768$		0			0
$769$	23.3184	+	15.3368i	0.840885	+	0.553059i	0.895302	−	0.445460i	$-0.146960\pi$
$769$	23.3184	+	15.3368i	0.840885	+	0.553059i	−0.0544173	+	0.998518i	$0.517330\pi$
$770$	−2.39895	−	1.57781i	−0.0864520	−	0.0568604i
$771$		0			0
$772$	20.2217	−	4.79264i	0.727797	−	0.172491i
$773$	0.0418155	+	0.0350873i	0.00150400	+	0.00126200i	0.643539	−	0.765413i	$-0.277465\pi$
$773$	0.0418155	+	0.0350873i	0.00150400	+	0.00126200i	−0.642035	+	0.766675i	$0.721910\pi$
$774$		0			0
$775$	−20.2520	+	16.9934i	−0.727472	+	0.610422i
$776$	−2.24198	+	3.01150i	−0.0804825	+	0.108107i
$777$		0			0
$778$	19.7700	+	4.68558i	0.708790	+	0.167986i
$779$	9.21459	+	12.3773i	0.330147	+	0.443464i
$780$		0			0
$781$	14.0833	+	7.07292i	0.503942	+	0.253089i

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.695972 + 0.457748i) q^{2} +(-0.517316 + 1.19927i) q^{4} +(0.827713 - 0.877324i) q^{5} +(1.30600 + 0.152650i) q^{7} +(-0.478230 - 2.71217i) q^{8} +O(q^{10})\)	\(q+(-0.695972 + 0.457748i) q^{2} +(-0.517316 + 1.19927i) q^{4} +(0.827713 - 0.877324i) q^{5} +(1.30600 + 0.152650i) q^{7} +(-0.478230 - 2.71217i) q^{8} +(-0.174471 + 0.989477i) q^{10} +(-0.623332 + 2.08207i) q^{11} +(-0.264847 + 4.54725i) q^{13} +(-0.978817 + 0.491580i) q^{14} +(-0.218261 - 0.231343i) q^{16} +(3.54217 - 1.28924i) q^{17} +(-2.50517 - 0.911807i) q^{19} +(0.623962 + 1.44651i) q^{20} +(-0.519243 - 1.73439i) q^{22} +(5.99251 - 0.700424i) q^{23} +(0.206135 + 3.53920i) q^{25} +(-1.89717 - 3.28599i) q^{26} +(-0.858686 + 1.48729i) q^{28} +(-3.71556 - 1.86603i) q^{29} +(4.45311 + 5.98156i) q^{31} +(5.61736 + 1.33134i) q^{32} +(-1.87510 + 2.51870i) q^{34} +(1.21492 - 1.01944i) q^{35} +(7.47819 + 6.27494i) q^{37} +(2.16090 - 0.512144i) q^{38} +(-2.77529 - 1.82534i) q^{40} +(-4.83588 - 3.18061i) q^{41} +(-4.91887 + 1.16579i) q^{43} +(-2.17451 - 1.82463i) q^{44} +(-3.85000 + 3.23053i) q^{46} +(-1.79025 + 2.40472i) q^{47} +(-5.12897 - 1.21559i) q^{49} +(-1.76352 - 2.36882i) q^{50} +(-5.31638 - 2.66999i) q^{52} +(-6.22987 + 10.7905i) q^{53} +(1.31071 + 2.27022i) q^{55} +(-0.210556 - 3.61511i) q^{56} +(3.44010 - 0.402090i) q^{58} +(3.12841 + 10.4496i) q^{59} +(4.67102 + 10.8287i) q^{61} +(-5.83728 - 2.12460i) q^{62} +(-3.92120 + 1.42720i) q^{64} +(3.77019 + 3.99617i) q^{65} +(-0.741811 + 0.372552i) q^{67} +(-0.286265 + 4.91497i) q^{68} +(-0.378904 + 1.26563i) q^{70} +(1.25916 - 7.14107i) q^{71} +(-1.41006 - 7.99685i) q^{73} +(-8.07695 - 0.944060i) q^{74} +(2.38947 - 2.53269i) q^{76} +(-1.13190 + 2.62404i) q^{77} +(9.60774 - 6.31911i) q^{79} -0.383620 q^{80} +4.82155 q^{82} +(3.98931 - 2.62381i) q^{83} +(1.80081 - 4.17475i) q^{85} +(2.88975 - 3.06296i) q^{86} +(5.94504 + 0.694876i) q^{88} +(0.578632 + 3.28158i) q^{89} +(-1.04003 + 5.89829i) q^{91} +(-2.26002 + 7.54900i) q^{92} +(0.145207 - 2.49310i) q^{94} +(-2.87351 + 1.44313i) q^{95} +(-0.935521 - 0.991594i) q^{97} +(4.12605 - 1.50176i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Introduction

L-functions

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