LMFDB - Embedded newform 729.2.i.a.685.3

Newspace parameters

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			685.3
Character	$\chi$	$=$	729.685
Dual form			729.2.i.a.613.3

$q$-expansion

$f(q)$	$=$	$q+(-2.26585 - 0.630742i) q^{2} +(3.02391 + 1.82494i) q^{4} +(2.74419 - 0.106487i) q^{5} +(2.01284 + 0.314803i) q^{7} +(-2.47257 - 2.62077i) q^{8} +O(q^{10})$	\(q+(-2.26585 - 0.630742i) q^{2} +(3.02391 + 1.82494i) q^{4} +(2.74419 - 0.106487i) q^{5} +(2.01284 + 0.314803i) q^{7} +(-2.47257 - 2.62077i) q^{8} +(-6.28508 - 1.48959i) q^{10} +(-0.475940 - 3.48450i) q^{11} +(3.06939 - 4.47529i) q^{13} +(-4.36224 - 1.98288i) q^{14} +(0.657389 + 1.24802i) q^{16} +(-6.06937 + 3.04815i) q^{17} +(-0.238916 - 4.10203i) q^{19} +(8.49249 + 4.68596i) q^{20} +(-1.11941 + 8.19555i) q^{22} +(3.06012 - 7.92590i) q^{23} +(2.53425 - 0.196978i) q^{25} +(-9.77754 + 8.20433i) q^{26} +(5.51215 + 4.62524i) q^{28} +(3.45486 + 2.46939i) q^{29} +(-3.03787 + 3.48101i) q^{31} +(0.823198 + 3.80030i) q^{32} +(15.6749 - 3.07845i) q^{34} +(5.55714 + 0.649536i) q^{35} +(-1.71554 - 2.30438i) q^{37} +(-2.04598 + 9.44528i) q^{38} +(-7.06426 - 6.92858i) q^{40} +(-0.270732 + 1.05105i) q^{41} +(2.62829 + 2.38505i) q^{43} +(4.91979 - 11.4054i) q^{44} +(-11.9330 + 16.0288i) q^{46} +(1.07362 + 1.23024i) q^{47} +(-2.71330 - 0.869985i) q^{49} +(-5.86647 - 1.15214i) q^{50} +(17.4487 - 7.93139i) q^{52} +(-0.605884 + 3.43614i) q^{53} +(-1.67712 - 9.51143i) q^{55} +(-4.15187 - 6.05357i) q^{56} +(-6.27065 - 7.77439i) q^{58} +(5.85044 - 2.39017i) q^{59} +(-1.49488 + 0.902167i) q^{61} +(9.07897 - 5.97134i) q^{62} +(0.695806 - 11.9465i) q^{64} +(7.94643 - 12.6079i) q^{65} +(-3.44909 + 2.46526i) q^{67} +(-23.9159 - 1.85889i) q^{68} +(-12.1819 - 4.97687i) q^{70} +(-3.29550 - 11.0077i) q^{71} +(4.93945 - 1.17067i) q^{73} +(2.43370 + 6.30344i) q^{74} +(6.76348 - 12.8402i) q^{76} +(0.138937 - 7.16358i) q^{77} +(2.80526 - 2.75138i) q^{79} +(1.93690 + 3.35480i) q^{80} +(1.27638 - 2.21075i) q^{82} +(3.48933 + 13.5464i) q^{83} +(-16.3309 + 9.01101i) q^{85} +(-4.45097 - 7.06194i) q^{86} +(-7.95527 + 9.86299i) q^{88} +(1.52261 - 5.08586i) q^{89} +(7.58704 - 8.04179i) q^{91} +(23.7178 - 18.3827i) q^{92} +(-1.65671 - 3.46471i) q^{94} +(-1.09244 - 11.2313i) q^{95} +(-8.20755 - 0.318490i) q^{97} +(5.59919 + 3.68265i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{81}\right)$

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 $

$2$	−2.26585	−	0.630742i	−1.60220	−	0.446002i	−0.652146	−	0.758094i	$-0.726131\pi$
$2$	−2.26585	−	0.630742i	−1.60220	−	0.446002i	−0.950052	+	0.312091i	$0.898970\pi$
$3$		0			0
$3$		0			0
$4$	3.02391	+	1.82494i	1.51195	+	0.912468i
$5$	2.74419	−	0.106487i	1.22724	−	0.0476224i	0.583015	−	0.812461i	$-0.301873\pi$
$5$	2.74419	−	0.106487i	1.22724	−	0.0476224i	0.644222	+	0.764839i	$0.277181\pi$
$6$		0			0
$7$	2.01284	+	0.314803i	0.760783	+	0.118984i	0.522998	−	0.852334i	$-0.324813\pi$
$7$	2.01284	+	0.314803i	0.760783	+	0.118984i	0.237785	+	0.971318i	$0.423579\pi$
$8$	−2.47257	−	2.62077i	−0.874185	−	0.926582i
$9$		0			0
$10$	−6.28508	−	1.48959i	−1.98752	−	0.471050i
$11$	−0.475940	−	3.48450i	−0.143501	−	1.05062i	−0.911832	−	0.410563i	$-0.865332\pi$
$11$	−0.475940	−	3.48450i	−0.143501	−	1.05062i	0.768331	−	0.640053i	$-0.221088\pi$
$12$		0			0
$13$	3.06939	−	4.47529i	0.851297	−	1.24122i	−0.117427	−	0.993081i	$-0.537465\pi$
$13$	3.06939	−	4.47529i	0.851297	−	1.24122i	0.968724	−	0.248140i	$-0.0798192\pi$
$14$	−4.36224	−	1.98288i	−1.16586	−	0.529947i
$15$		0			0
$16$	0.657389	+	1.24802i	0.164347	+	0.312006i
$17$	−6.06937	+	3.04815i	−1.47204	+	0.739286i	−0.990548	−	0.137165i	$-0.956201\pi$
$17$	−6.06937	+	3.04815i	−1.47204	+	0.739286i	−0.481491	+	0.876451i	$0.659905\pi$
$18$		0			0
$19$	−0.238916	−	4.10203i	−0.0548111	−	0.941070i	−0.907869	−	0.419254i	$-0.862292\pi$
$19$	−0.238916	−	4.10203i	−0.0548111	−	0.941070i	0.853058	−	0.521816i	$-0.174745\pi$
$20$	8.49249	+	4.68596i	1.89898	+	1.04781i
$21$		0			0
$22$	−1.11941	+	8.19555i	−0.238659	+	1.74730i
$23$	3.06012	−	7.92590i	0.638079	−	1.65267i	−0.113912	−	0.993491i	$-0.536338\pi$
$23$	3.06012	−	7.92590i	0.638079	−	1.65267i	0.751990	−	0.659174i	$-0.229094\pi$
$24$		0			0
$25$	2.53425	−	0.196978i	0.506850	−	0.0393955i
$26$	−9.77754	+	8.20433i	−1.91753	+	1.60900i
$27$		0			0
$28$	5.51215	+	4.62524i	1.04170	+	0.874089i
$29$	3.45486	+	2.46939i	0.641552	+	0.458554i	0.855159	−	0.518366i	$-0.173459\pi$
$29$	3.45486	+	2.46939i	0.641552	+	0.458554i	−0.213607	+	0.976920i	$0.568521\pi$
$30$		0			0
$31$	−3.03787	+	3.48101i	−0.545617	+	0.625208i	−0.958334	−	0.285652i	$-0.907790\pi$
$31$	−3.03787	+	3.48101i	−0.545617	+	0.625208i	0.412716	+	0.910860i	$0.364580\pi$
$32$	0.823198	+	3.80030i	0.145522	+	0.671805i
$33$		0			0
$34$	15.6749	−	3.07845i	2.68822	−	0.527949i
$35$	5.55714	+	0.649536i	0.939328	+	0.109792i
$36$		0			0
$37$	−1.71554	−	2.30438i	−0.282034	−	0.378837i	0.638420	−	0.769688i	$-0.279588\pi$
$37$	−1.71554	−	2.30438i	−0.282034	−	0.378837i	−0.920454	+	0.390851i	$0.872181\pi$
$38$	−2.04598	+	9.44528i	−0.331901	+	1.53223i
$39$		0			0
$40$	−7.06426	−	6.92858i	−1.11696	−	1.09550i
$41$	−0.270732	+	1.05105i	−0.0422813	+	0.164146i	−0.986046	−	0.166471i	$-0.946763\pi$
$41$	−0.270732	+	1.05105i	−0.0422813	+	0.164146i	0.943765	+	0.330617i	$0.107257\pi$
$42$		0			0
$43$	2.62829	+	2.38505i	0.400811	+	0.363717i	0.847338	−	0.531053i	$-0.178204\pi$
$43$	2.62829	+	2.38505i	0.400811	+	0.363717i	−0.446527	+	0.894770i	$0.647339\pi$
$44$	4.91979	−	11.4054i	0.741686	−	1.71942i
$45$		0			0
$46$	−11.9330	+	16.0288i	−1.75942	+	2.36331i
$47$	1.07362	+	1.23024i	0.156604	+	0.179448i	0.826376	−	0.563118i	$-0.190398\pi$
$47$	1.07362	+	1.23024i	0.156604	+	0.179448i	−0.669772	+	0.742567i	$0.733608\pi$
$48$		0			0
$49$	−2.71330	−	0.869985i	−0.387614	−	0.124284i
$50$	−5.86647	−	1.15214i	−0.829645	−	0.162937i
$51$		0			0
$52$	17.4487	−	7.93139i	2.41970	−	1.09989i
$53$	−0.605884	+	3.43614i	−0.0832246	+	0.471990i	0.914501	+	0.404584i	$0.132584\pi$
$53$	−0.605884	+	3.43614i	−0.0832246	+	0.471990i	−0.997726	+	0.0674066i	$0.978528\pi$
$54$		0			0
$55$	−1.67712	−	9.51143i	−0.226143	−	1.28252i
$56$	−4.15187	−	6.05357i	−0.554816	−	0.808942i
$57$		0			0
$58$	−6.27065	−	7.77439i	−0.823377	−	1.02083i
$59$	5.85044	−	2.39017i	0.761662	−	0.311173i	0.0361170	−	0.999348i	$-0.488501\pi$
$59$	5.85044	−	2.39017i	0.761662	−	0.311173i	0.725545	+	0.688174i	$0.241588\pi$
$60$		0			0
$61$	−1.49488	+	0.902167i	−0.191400	+	0.115511i	−0.609161	−	0.793046i	$-0.708494\pi$
$61$	−1.49488	+	0.902167i	−0.191400	+	0.115511i	0.417761	+	0.908557i	$0.362815\pi$
$62$	9.07897	−	5.97134i	1.15303	−	0.758360i
$63$		0			0
$64$	0.695806	−	11.9465i	0.0869757	−	1.49332i
$65$	7.94643	−	12.6079i	0.985633	−	1.56381i
$66$		0			0
$67$	−3.44909	+	2.46526i	−0.421374	+	0.301180i	−0.772341	−	0.635208i	$-0.780914\pi$
$67$	−3.44909	+	2.46526i	−0.421374	+	0.301180i	0.350968	+	0.936388i	$0.385853\pi$
$68$	−23.9159	−	1.85889i	−2.90023	−	0.225424i
$69$		0			0
$70$	−12.1819	−	4.97687i	−1.45602	−	0.594850i
$71$	−3.29550	−	11.0077i	−0.391103	−	1.30638i	−0.896329	−	0.443389i	$-0.853776\pi$
$71$	−3.29550	−	11.0077i	−0.391103	−	1.30638i	0.505226	−	0.862987i	$-0.331409\pi$
$72$		0			0
$73$	4.93945	−	1.17067i	0.578119	−	0.137017i	0.0688543	−	0.997627i	$-0.478066\pi$
$73$	4.93945	−	1.17067i	0.578119	−	0.137017i	0.509264	+	0.860610i	$0.329918\pi$
$74$	2.43370	+	6.30344i	0.282912	+	0.732760i
$75$		0			0
$76$	6.76348	−	12.8402i	0.775825	−	1.47287i
$77$	0.138937	−	7.16358i	0.0158334	−	0.816365i
$78$		0			0
$79$	2.80526	−	2.75138i	0.315617	−	0.309555i	−0.525089	−	0.851048i	$-0.675968\pi$
$79$	2.80526	−	2.75138i	0.315617	−	0.309555i	0.840705	+	0.541493i	$0.182141\pi$
$80$	1.93690	+	3.35480i	0.216552	+	0.375078i
$81$		0			0
$82$	1.27638	−	2.21075i	0.140952	−	0.244137i
$83$	3.48933	+	13.5464i	0.383004	+	1.48691i	0.812027	+	0.583620i	$0.198364\pi$
$83$	3.48933	+	13.5464i	0.383004	+	1.48691i	−0.429023	+	0.903294i	$0.641142\pi$
$84$		0			0
$85$	−16.3309	+	9.01101i	−1.77133	+	0.977381i
$86$	−4.45097	−	7.06194i	−0.479960	−	0.761508i
$87$		0			0
$88$	−7.95527	+	9.86299i	−0.848035	+	1.05140i
$89$	1.52261	−	5.08586i	0.161396	−	0.539100i	−0.838588	−	0.544766i	$-0.816618\pi$
$89$	1.52261	−	5.08586i	0.161396	−	0.539100i	0.999984	+	0.00566589i	$0.00180352\pi$
$90$		0			0
$91$	7.58704	−	8.04179i	0.795338	−	0.843009i
$92$	23.7178	−	18.3827i	2.47275	−	1.91653i
$93$		0			0
$94$	−1.65671	−	3.46471i	−0.170876	−	0.357358i
$95$	−1.09244	−	11.2313i	−0.112082	−	1.15231i
$96$		0			0
$97$	−8.20755	−	0.318490i	−0.833351	−	0.0323378i	−0.381432	−	0.924397i	$-0.624569\pi$
$97$	−8.20755	−	0.318490i	−0.833351	−	0.0323378i	−0.451919	+	0.892059i	$0.649260\pi$
$98$	5.59919	+	3.68265i	0.565604	+	0.372004i
$99$		0			0
$100$	8.02281	+	4.02921i	0.802281	+	0.402921i
$101$	−0.303406	−	15.6435i	−0.0301900	−	1.55659i	−0.642695	−	0.766122i	$-0.722184\pi$
$101$	−0.303406	−	15.6435i	−0.0301900	−	1.55659i	0.612505	−	0.790467i	$-0.290162\pi$
$102$		0			0
$103$	6.82645	+	5.29090i	0.672630	+	0.521327i	0.890692	−	0.454607i	$-0.150220\pi$
$103$	6.82645	+	5.29090i	0.672630	+	0.521327i	−0.218062	+	0.975935i	$0.569974\pi$
$104$	−19.3180	+	3.02128i	−1.89428	+	0.296261i
$105$		0			0
$106$	3.54016	−	7.40362i	0.343851	−	0.719103i
$107$	9.60541	+	3.49608i	0.928590	+	0.337979i	0.761650	−	0.647988i	$-0.224389\pi$
$107$	9.60541	+	3.49608i	0.928590	+	0.337979i	0.166939	+	0.985967i	$0.446612\pi$
$108$		0			0
$109$	−11.9146	+	4.33655i	−1.14121	+	0.415367i	−0.842350	−	0.538930i	$-0.818829\pi$
$109$	−11.9146	+	4.33655i	−1.14121	+	0.415367i	−0.298860	+	0.954297i	$0.596606\pi$
$110$	−2.19916	+	22.6093i	−0.209681	+	2.15571i
$111$		0			0
$112$	0.930340	+	2.71902i	0.0879089	+	0.256923i
$113$	−0.898174	+	0.815050i	−0.0844931	+	0.0766734i	−0.713160	−	0.701001i	$-0.752737\pi$
$113$	−0.898174	+	0.815050i	−0.0844931	+	0.0766734i	0.628667	+	0.777675i	$0.283601\pi$
$114$		0			0
$115$	7.55353	−	22.0760i	0.704370	−	2.05860i
$116$	5.94071	+	13.7721i	0.551581	+	1.27871i
$117$		0			0
$118$	−14.7638	+	1.72564i	−1.35912	+	0.158858i
$119$	−13.1763	+	4.22480i	−1.20787	+	0.387287i
$120$		0			0
$121$	−1.31814	+	0.366928i	−0.119831	+	0.0333571i
$122$	3.95622	−	1.10129i	0.358179	−	0.0997060i
$123$		0			0
$124$	−15.5389	+	4.98233i	−1.39543	+	0.447427i
$125$	−6.70493	+	0.783694i	−0.599707	+	0.0700957i
$126$		0			0
$127$	4.68643	+	10.8644i	0.415853	+	0.964056i	0.989444	+	0.144914i	$0.0462906\pi$
$127$	4.68643	+	10.8644i	0.415853	+	0.964056i	−0.573591	+	0.819142i	$0.694450\pi$
$128$	−6.59413	+	19.2721i	−0.582844	+	1.70343i
$129$		0			0
$130$	−25.9577	+	23.5554i	−2.27664	+	2.06594i
$131$	6.73353	+	19.6795i	0.588311	+	1.71940i	0.689262	+	0.724512i	$0.257935\pi$
$131$	6.73353	+	19.6795i	0.588311	+	1.71940i	−0.100951	+	0.994891i	$0.532189\pi$
$132$		0			0
$133$	0.810430	−	8.33195i	0.0702732	−	0.722472i
$134$	9.37007	−	3.41043i	0.809451	−	0.294616i
$135$		0			0
$136$	22.9955	+	8.36966i	1.97184	+	0.717692i
$137$	−2.07853	+	4.34688i	−0.177581	+	0.371379i	−0.971641	−	0.236460i	$-0.924013\pi$
$137$	−2.07853	+	4.34688i	−0.177581	+	0.371379i	0.794060	+	0.607839i	$0.207963\pi$
$138$		0			0
$139$	18.6595	−	2.91829i	1.58268	−	0.247526i	0.698825	−	0.715293i	$-0.253707\pi$
$139$	18.6595	−	2.91829i	1.58268	−	0.247526i	0.883852	+	0.467766i	$0.154941\pi$
$140$	15.6189	+	12.1056i	1.32004	+	1.02311i
$141$		0			0
$142$	0.524061	+	27.0205i	0.0439782	+	2.26751i
$143$	−17.0550	−	8.56533i	−1.42621	−	0.716269i
$144$		0			0
$145$	9.74375	+	6.40856i	0.809174	+	0.532202i
$146$	−11.9304	−	0.462955i	−0.987370	−	0.0383145i
$147$		0			0
$148$	−0.982305	−	10.0990i	−0.0807449	−	0.830131i
$149$	−1.88833	−	3.94910i	−0.154698	−	0.323523i	0.810198	−	0.586156i	$-0.199360\pi$
$149$	−1.88833	−	3.94910i	−0.154698	−	0.323523i	−0.964896	+	0.262634i	$0.915409\pi$
$150$		0			0
$151$	1.50440	−	1.16600i	0.122426	−	0.0948876i	−0.549547	−	0.835463i	$-0.685200\pi$
$151$	1.50440	−	1.16600i	0.122426	−	0.0948876i	0.671974	+	0.740575i	$0.265447\pi$
$152$	−10.1597	+	10.7687i	−0.824063	+	0.873456i
$153$		0			0
$154$	−4.83318	+	16.1440i	−0.389469	+	1.30092i
$155$	−7.96579	+	9.87603i	−0.639828	+	0.793262i
$156$		0			0
$157$	9.21069	+	14.6138i	0.735093	+	1.16630i	0.980430	+	0.196867i	$0.0630766\pi$
$157$	9.21069	+	14.6138i	0.735093	+	1.16630i	−0.245337	+	0.969438i	$0.578899\pi$
$158$	−8.09172	+	4.46482i	−0.643742	+	0.355202i
$159$		0			0
$160$	2.66369	+	10.3411i	0.210583	+	0.817534i
$161$	8.65463	−	14.9903i	0.682081	−	1.18140i
$162$		0			0
$163$	5.52274	+	9.56566i	0.432574	+	0.749240i	0.997094	−	0.0761790i	$-0.0242720\pi$
$163$	5.52274	+	9.56566i	0.432574	+	0.749240i	−0.564520	+	0.825419i	$0.690939\pi$
$164$	−2.73676	+	2.68420i	−0.213705	+	0.209601i
$165$		0			0
$166$	0.637999	−	32.8950i	0.0495183	−	2.55315i
$167$	11.0801	−	21.0351i	0.857406	−	1.62775i	0.0816955	−	0.996657i	$-0.473967\pi$
$167$	11.0801	−	21.0351i	0.857406	−	1.62775i	0.775711	−	0.631088i	$-0.217392\pi$
$168$		0			0
$169$	−5.92470	−	15.3453i	−0.455746	−	1.18041i
$170$	42.6870	−	10.1170i	3.27394	−	0.775939i
$171$		0			0
$172$	3.59515	+	12.0086i	0.274127	+	0.915649i
$173$	17.4511	+	7.12957i	1.32678	+	0.542051i	0.927173	−	0.374634i	$-0.122232\pi$
$173$	17.4511	+	7.12957i	1.32678	+	0.542051i	0.399611	+	0.916685i	$0.369145\pi$
$174$		0			0
$175$	5.16306	+	0.401305i	0.390290	+	0.0303358i
$176$	4.03586	−	2.88466i	0.304214	−	0.217439i
$177$		0			0
$178$	−6.65787	+	10.5634i	−0.499028	+	0.791763i
$179$	−0.312381	+	5.36337i	−0.0233484	+	0.400877i	0.966305	+	0.257399i	$0.0828656\pi$
$179$	−0.312381	+	5.36337i	−0.0233484	+	0.400877i	−0.989654	+	0.143478i	$0.954171\pi$
$180$		0			0
$181$	−9.95648	+	6.54848i	−0.740059	+	0.486745i	−0.862706	−	0.505706i	$-0.831232\pi$
$181$	−9.95648	+	6.54848i	−0.740059	+	0.486745i	0.122647	+	0.992450i	$0.460862\pi$
$182$	−22.2634	+	13.4360i	−1.65027	+	0.995945i
$183$		0			0
$184$	−28.3383	+	11.5775i	−2.08913	+	0.853503i
$185$	−4.95316	−	6.14095i	−0.364163	−	0.451492i
$186$		0			0
$187$	13.5100	+	19.6980i	0.987945	+	1.44046i
$188$	1.00143	+	5.67941i	0.0730370	+	0.414214i
$189$		0			0
$190$	−4.60874	+	26.1375i	−0.334353	+	1.89621i
$191$	−7.06783	+	3.21272i	−0.511410	+	0.232465i	−0.652857	−	0.757481i	$-0.726430\pi$
$191$	−7.06783	+	3.21272i	−0.511410	+	0.232465i	0.141446	+	0.989946i	$0.454825\pi$
$192$		0			0
$193$	20.0324	+	3.93424i	1.44197	+	0.283193i	0.851706	−	0.524020i	$-0.175568\pi$
$193$	20.0324	+	3.93424i	1.44197	+	0.283193i	0.590261	+	0.807213i	$0.299025\pi$
$194$	18.3962	+	5.89850i	1.32077	+	0.423488i
$195$		0			0
$196$	−6.61710	−	7.58235i	−0.472650	−	0.541597i
$197$	−3.23175	+	4.34100i	−0.230253	+	0.309283i	−0.902202	−	0.431314i	$-0.858050\pi$
$197$	−3.23175	+	4.34100i	−0.230253	+	0.309283i	0.671949	+	0.740597i	$0.265457\pi$
$198$		0			0
$199$	7.85817	−	18.2173i	0.557051	−	1.29139i	−0.374314	−	0.927302i	$-0.622122\pi$
$199$	7.85817	−	18.2173i	0.557051	−	1.29139i	0.931365	−	0.364087i	$-0.118619\pi$
$200$	−6.78234	−	6.15465i	−0.479584	−	0.435199i
$201$		0			0
$202$	−9.17956	+	35.6373i	−0.645872	+	2.50743i
$203$	6.17673	+	6.05809i	0.433521	+	0.425195i
$204$		0			0
$205$	−0.631017	+	2.91310i	−0.0440721	+	0.203460i
$206$	−12.1305	−	16.2941i	−0.845173	−	1.13526i
$207$		0			0
$208$	7.60305	+	0.888669i	0.527177	+	0.0616181i
$209$	−14.1798	+	2.78482i	−0.980838	+	0.192630i
$210$		0			0
$211$	−0.789332	−	3.64396i	−0.0543399	−	0.250861i	0.942082	−	0.335383i	$-0.108866\pi$
$211$	−0.789332	−	3.64396i	−0.0543399	−	0.250861i	−0.996422	+	0.0845228i	$0.973063\pi$
$212$	−8.10288	+	9.28487i	−0.556508	+	0.637687i
$213$		0			0
$214$	−19.5593	−	13.9801i	−1.33705	−	0.955663i
$215$	7.46650	+	6.26514i	0.509211	+	0.427279i
$216$		0			0
$217$	−7.21058	+	6.05040i	−0.489486	+	0.410728i
$218$	29.7319	−	2.31095i	2.01370	−	0.156517i
$219$		0			0
$220$	12.2863	−	31.8223i	0.828342	−	2.14546i
$221$	−4.98794	+	36.5182i	−0.335525	+	2.45648i
$222$		0			0
$223$	5.27169	+	2.90880i	0.353019	+	0.194787i	0.649703	−	0.760188i	$-0.274893\pi$
$223$	5.27169	+	2.90880i	0.353019	+	0.194787i	−0.296684	+	0.954976i	$0.595881\pi$
$224$	0.460621	+	7.90856i	0.0307765	+	0.528413i
$225$		0			0
$226$	2.54921	−	1.28026i	0.169571	−	0.0851619i
$227$	5.09961	+	9.68138i	0.338473	+	0.642576i	0.993602	−	0.112942i	$-0.0360274\pi$
$227$	5.09961	+	9.68138i	0.338473	+	0.642576i	−0.655128	+	0.755518i	$0.727385\pi$
$228$		0			0
$229$	−18.3623	−	8.34671i	−1.21342	−	0.551566i	−0.298191	−	0.954506i	$-0.596383\pi$
$229$	−18.3623	−	8.34671i	−1.21342	−	0.551566i	−0.915226	+	0.402940i	$0.867988\pi$
$230$	−31.0394	+	45.2566i	−2.04668	+	2.98413i
$231$		0			0
$232$	−2.07069	−	15.1601i	−0.135947	−	0.995311i
$233$	−12.4860	−	2.95923i	−0.817984	−	0.193866i	−0.199737	−	0.979850i	$-0.564009\pi$
$233$	−12.4860	−	2.95923i	−0.817984	−	0.193866i	−0.618247	+	0.785984i	$0.712157\pi$
$234$		0			0
$235$	3.07723	+	3.26167i	0.200736	+	0.212768i
$236$	22.0531	+	3.44904i	1.43553	+	0.224513i
$237$		0			0
$238$	32.5202	−	1.26193i	2.10797	−	0.0817989i
$239$	−6.27719	−	3.78831i	−0.406038	−	0.245045i	0.298944	−	0.954271i	$-0.403366\pi$
$239$	−6.27719	−	3.78831i	−0.406038	−	0.245045i	−0.704982	+	0.709226i	$0.749045\pi$
$240$		0			0
$241$	1.28930	+	0.358902i	0.0830513	+	0.0231189i	0.309449	−	0.950916i	$-0.399855\pi$
$241$	1.28930	+	0.358902i	0.0830513	+	0.0231189i	−0.226398	+	0.974035i	$0.572695\pi$
$242$	3.21814			0.206870
$243$		0			0
$244$	−6.16679			−0.394788
$245$	−7.53844	−	2.09847i	−0.481613	−	0.134066i
$246$		0			0
$247$	−19.0911	−	11.5215i	−1.21474	−	0.733097i
$248$	16.6343	−	0.645485i	1.05628	−	0.0409884i
$249$		0			0
$250$	15.6867	+	2.45335i	0.992112	+	0.155164i
$251$	−12.4919	−	13.2406i	−0.788481	−	0.835741i	0.201122	−	0.979566i	$-0.435541\pi$
$251$	−12.4919	−	13.2406i	−0.788481	−	0.835741i	−0.989603	+	0.143826i	$0.954060\pi$
$252$		0			0
$253$	−29.0742	−	6.89072i	−1.82788	−	0.433216i
$254$	−3.76613	−	27.5729i	−0.236308	−	1.73008i
$255$		0			0
$256$	13.5600	−	19.7710i	0.847503	−	1.23569i
$257$	10.3642	+	4.71110i	0.646499	+	0.293870i	0.710095	−	0.704106i	$-0.248652\pi$
$257$	10.3642	+	4.71110i	0.646499	+	0.293870i	−0.0635957	+	0.997976i	$0.520257\pi$
$258$		0			0
$259$	−2.72770	−	5.17840i	−0.169491	−	0.321770i
$260$	47.0378	−	23.6233i	2.91716	−	1.46505i
$261$		0			0
$262$	−2.84448	−	48.8378i	−0.175733	−	3.01721i
$263$	4.60701	+	2.54204i	0.284080	+	0.156749i	0.618753	−	0.785585i	$-0.287638\pi$
$263$	4.60701	+	2.54204i	0.284080	+	0.156749i	−0.334673	+	0.942334i	$0.608626\pi$
$264$		0			0
$265$	−1.29676	+	9.49393i	−0.0796591	+	0.583207i
$266$	−7.09163	+	18.3678i	−0.434816	+	1.12620i
$267$		0			0
$268$	−14.9287	+	1.16035i	−0.911914	+	0.0708795i
$269$	−18.8875	+	15.8485i	−1.15159	+	0.966301i	−0.999756	−	0.0221041i	$-0.992963\pi$
$269$	−18.8875	+	15.8485i	−1.15159	+	0.966301i	−0.151837	+	0.988405i	$0.548519\pi$
$270$		0			0
$271$	3.39725	+	2.85063i	0.206368	+	0.173163i	0.740114	−	0.672482i	$-0.234772\pi$
$271$	3.39725	+	2.85063i	0.206368	+	0.173163i	−0.533746	+	0.845645i	$0.679216\pi$
$272$	−7.79411	−	5.57089i	−0.472587	−	0.337785i
$273$		0			0
$274$	7.45139	−	8.53835i	0.450155	−	0.515821i
$275$	−1.89252	−	8.73685i	−0.114123	−	0.526852i
$276$		0			0
$277$	−1.56079	+	0.306529i	−0.0937788	+	0.0184176i	−0.239382	−	0.970926i	$-0.576945\pi$
$277$	−1.56079	+	0.306529i	−0.0937788	+	0.0184176i	0.145603	+	0.989343i	$0.453488\pi$
$278$	−44.1203	−	5.15692i	−2.64616	−	0.309292i
$279$		0			0
$280$	−12.0381	−	16.1700i	−0.719415	−	0.966342i
$281$	−1.83332	+	8.46357i	−0.109367	+	0.504894i	0.889484	+	0.456967i	$0.151064\pi$
$281$	−1.83332	+	8.46357i	−0.109367	+	0.504894i	−0.998851	+	0.0479275i	$0.984738\pi$
$282$		0			0
$283$	−11.6567	−	11.4328i	−0.692920	−	0.679611i	0.265779	−	0.964034i	$-0.414371\pi$
$283$	−11.6567	−	11.4328i	−0.692920	−	0.679611i	−0.958699	+	0.284423i	$0.908198\pi$
$284$	10.1231	−	39.3004i	0.600697	−	2.33205i
$285$		0			0
$286$	33.2415	+	30.1651i	1.96561	+	1.78370i
$287$	−0.875814	+	2.03036i	−0.0516977	+	0.119849i
$288$		0			0
$289$	17.3944	−	23.3647i	1.02320	−	1.37439i
$290$	−18.0357	−	20.6666i	−1.05909	−	1.21359i
$291$		0			0
$292$	17.0728	+	5.47418i	0.999112	+	0.320352i
$293$	12.6452	+	2.48344i	0.738741	+	0.145084i	0.547908	−	0.836538i	$-0.315424\pi$
$293$	12.6452	+	2.48344i	0.738741	+	0.145084i	0.190833	+	0.981622i	$0.438881\pi$
$294$		0			0
$295$	15.8002	−	7.18206i	0.919922	−	0.418156i
$296$	−1.79744	+	10.1938i	−0.104474	+	0.592501i
$297$		0			0
$298$	1.78780	+	10.1391i	0.103564	+	0.587343i
$299$	−26.0780	−	38.0226i	−1.50813	−	2.19891i
$300$		0			0
$301$	4.53952	+	5.62812i	0.261654	+	0.324400i
$302$	−4.14419	+	1.69309i	−0.238471	+	0.0974262i
$303$		0			0
$304$	4.96237	−	2.99480i	0.284611	−	0.171764i
$305$	−4.00617	+	2.63490i	−0.229393	+	0.150874i
$306$		0			0
$307$	−1.03115	+	17.7042i	−0.0588510	+	1.01043i	0.831606	+	0.555366i	$0.187422\pi$
$307$	−1.03115	+	17.7042i	−0.0588510	+	1.01043i	−0.890457	+	0.455067i	$0.849615\pi$
$308$	13.4932	−	21.4084i	0.768847	−	1.21986i
$309$		0			0
$310$	24.2785	−	17.3532i	1.37893	−	0.985598i
$311$	25.0480	+	1.94689i	1.42034	+	0.110398i	0.764561	−	0.644552i	$-0.222956\pi$
$311$	25.0480	+	1.94689i	1.42034	+	0.110398i	0.655783	+	0.754950i	$0.272339\pi$
$312$		0			0
$313$	1.63062	+	0.666182i	0.0921681	+	0.0376548i	0.423815	−	0.905749i	$-0.360691\pi$
$313$	1.63062	+	0.666182i	0.0921681	+	0.0376548i	−0.331647	+	0.943404i	$0.607604\pi$
$314$	−11.6525	−	38.9221i	−0.657590	−	2.19650i
$315$		0			0
$316$	13.5039	−	3.20049i	0.759656	−	0.180042i
$317$	−9.20980	−	23.8540i	−0.517274	−	1.33977i	−0.907886	−	0.419217i	$-0.862305\pi$
$317$	−9.20980	−	23.8540i	−0.517274	−	1.33977i	0.390612	−	0.920555i	$-0.372263\pi$
$318$		0			0
$319$	6.96027	−	13.2138i	0.389700	−	0.739828i
$320$	0.637272	−	32.8576i	0.0356246	−	1.83679i
$321$		0			0
$322$	−29.0651	+	28.5068i	−1.61973	+	1.58862i
$323$	13.9537	+	24.1685i	0.776404	+	1.34477i
$324$		0			0
$325$	6.89709	−	11.9461i	0.382581	−	0.662650i
$326$	−6.48022	−	25.1578i	−0.358906	−	1.39336i
$327$		0			0
$328$	3.42396	−	1.88926i	0.189056	−	0.104317i
$329$	1.77375	+	2.81425i	0.0977902	+	0.155155i
$330$		0			0
$331$	5.41705	−	6.71609i	0.297748	−	0.369150i	−0.607290	−	0.794480i	$-0.707743\pi$
$331$	5.41705	−	6.71609i	0.297748	−	0.369150i	0.905038	+	0.425331i	$0.139842\pi$
$332$	−14.1700	+	47.3309i	−0.777677	+	2.59762i
$333$		0			0
$334$	−38.3737	+	40.6737i	−2.09971	+	2.22557i
$335$	−9.20243	+	7.13242i	−0.502782	+	0.389686i
$336$		0			0
$337$	11.3603	+	23.7580i	0.618834	+	1.29418i	0.938050	+	0.346499i	$0.112630\pi$
$337$	11.3603	+	23.7580i	0.618834	+	1.29418i	−0.319217	+	0.947682i	$0.603420\pi$
$338$	3.74551	+	38.5072i	0.203729	+	2.09452i
$339$		0			0
$340$	−65.8276	−	2.55441i	−3.57000	−	0.138532i
$341$	13.5754	+	8.92870i	0.735150	+	0.483516i
$342$		0			0
$343$	−17.9318	−	9.00570i	−0.968228	−	0.486262i
$344$	−0.247971	−	12.7853i	−0.0133697	−	0.689340i
$345$		0			0
$346$	−35.0447	−	27.1617i	−1.88401	−	1.46022i
$347$	16.6880	−	2.60996i	0.895861	−	0.140110i	0.310205	−	0.950670i	$-0.399602\pi$
$347$	16.6880	−	2.60996i	0.895861	−	0.140110i	0.585656	+	0.810559i	$0.300837\pi$
$348$		0			0
$349$	−4.02871	+	8.42534i	−0.215652	+	0.450998i	−0.981357	−	0.192194i	$-0.938440\pi$
$349$	−4.02871	+	8.42534i	−0.215652	+	0.450998i	0.765705	+	0.643192i	$0.222390\pi$
$350$	−11.4456	−	4.16586i	−0.611793	−	0.222674i
$351$		0			0
$352$	12.8504	−	4.67715i	0.684927	−	0.249293i
$353$	−1.68470	+	17.3202i	−0.0896675	+	0.921863i	0.837306	+	0.546735i	$0.184129\pi$
$353$	−1.68470	+	17.3202i	−0.0896675	+	0.921863i	−0.926973	+	0.375128i	$0.877599\pi$
$354$		0			0
$355$	−10.2156	−	29.8563i	−0.542189	−	1.58461i
$356$	13.8856	−	12.6005i	0.735935	−	0.667826i
$357$		0			0
$358$	4.09071	−	11.9556i	0.216201	−	0.631871i
$359$	−8.26195	−	19.1533i	−0.436049	−	1.01088i	−0.984610	−	0.174765i	$-0.944084\pi$
$359$	−8.26195	−	19.1533i	−0.436049	−	1.01088i	0.548561	−	0.836110i	$-0.315176\pi$
$360$		0			0
$361$	2.10197	−	0.245685i	0.110630	−	0.0129308i
$362$	26.6903	−	8.55790i	1.40281	−	0.449793i
$363$		0			0
$364$	37.6183	−	10.4718i	1.97173	−	0.548869i
$365$	13.4301	−	3.73852i	0.702964	−	0.195683i
$366$		0			0
$367$	−20.2383	+	6.48916i	−1.05643	+	0.338731i	−0.782262	−	0.622950i	$-0.785934\pi$
$367$	−20.2383	+	6.48916i	−1.05643	+	0.338731i	−0.274170	+	0.961681i	$0.588403\pi$
$368$	11.9034	−	1.39131i	0.620508	−	0.0725269i
$369$		0			0
$370$	7.34975	+	17.0386i	0.382096	+	0.885797i
$371$	−2.30126	+	6.72568i	−0.119475	+	0.349180i
$372$		0			0
$373$	−10.5117	+	9.53883i	−0.544274	+	0.493902i	−0.897125	−	0.441778i	$-0.854348\pi$
$373$	−10.5117	+	9.53883i	−0.544274	+	0.493902i	0.352851	+	0.935680i	$0.385212\pi$
$374$	−18.1872	−	53.1540i	−0.940436	−	2.74853i
$375$		0			0
$376$	0.569557	−	5.85556i	0.0293727	−	0.301978i
$377$	21.6556	−	7.88198i	1.11532	−	0.405943i
$378$		0			0
$379$	17.8430	+	6.49434i	0.916536	+	0.333592i	0.756859	−	0.653578i	$-0.226733\pi$
$379$	17.8430	+	6.49434i	0.916536	+	0.333592i	0.159676	+	0.987169i	$0.448955\pi$
$380$	17.1929	−	35.9560i	0.881979	−	1.84450i
$381$		0			0
$382$	18.0410	−	2.82157i	0.923060	−	0.144364i
$383$	2.89576	+	2.24438i	0.147966	+	0.114683i	0.683894	−	0.729581i	$-0.260285\pi$
$383$	2.89576	+	2.24438i	0.147966	+	0.114683i	−0.535928	+	0.844264i	$0.680038\pi$
$384$		0			0
$385$	−0.381557	−	19.6730i	−0.0194459	−	1.00263i
$386$	−42.9090	−	21.5497i	−2.18401	−	1.09685i
$387$		0			0
$388$	−24.2376	−	15.9413i	−1.23048	−	0.809299i
$389$	14.8910	+	0.577838i	0.755003	+	0.0292976i	0.413403	−	0.910548i	$-0.364340\pi$
$389$	14.8910	+	0.577838i	0.755003	+	0.0292976i	0.341600	+	0.939846i	$0.389031\pi$
$390$		0			0
$391$	5.58638	+	57.4330i	0.282515	+	2.90451i
$392$	4.42879	+	9.26203i	0.223688	+	0.467803i
$393$		0			0
$394$	10.0607	−	7.79764i	0.506851	−	0.392839i
$395$	7.40517	−	7.84903i	0.372595	−	0.394927i
$396$		0			0
$397$	4.94007	−	16.5010i	0.247935	−	0.828160i	−0.739909	−	0.672707i	$-0.765131\pi$
$397$	4.94007	−	16.5010i	0.247935	−	0.828160i	0.987843	−	0.155453i	$-0.0496836\pi$
$398$	−29.2959	+	36.3212i	−1.46847	+	1.82062i
$399$		0			0
$400$	1.91182	+	3.03331i	0.0955911	+	0.151666i
$401$	−17.0499	+	9.40772i	−0.851430	+	0.469799i	−0.847876	−	0.530194i	$-0.822119\pi$
$401$	−17.0499	+	9.40772i	−0.851430	+	0.469799i	−0.00355411	+	0.999994i	$0.501131\pi$
$402$		0			0
$403$	6.25411	+	24.2799i	0.311539	+	1.20947i
$404$	27.6310	−	47.8582i	1.37469	−	2.38104i
$405$		0			0
$406$	−10.1744	−	17.6226i	−0.504949	−	0.874597i
$407$	−7.21310	+	7.07456i	−0.357540	+	0.350673i
$408$		0			0
$409$	−0.655222	+	33.7831i	−0.0323986	+	1.67047i	0.533355	+	0.845892i	$0.320931\pi$
$409$	−0.655222	+	33.7831i	−0.0323986	+	1.67047i	−0.565754	+	0.824574i	$0.691415\pi$
$410$	3.26720	−	6.20263i	0.161356	−	0.306326i
$411$		0			0
$412$	10.9870	+	28.4570i	0.541290	+	1.40198i
$413$	12.5284	−	2.96930i	0.616485	−	0.146110i
$414$		0			0
$415$	11.0179	+	36.8023i	0.540847	+	1.80656i
$416$	19.5342	+	7.98059i	0.957742	+	0.391280i
$417$		0			0
$418$	33.8858	+	2.63381i	1.65741	+	0.128824i
$419$	3.72897	−	2.66531i	0.182172	−	0.130209i	−0.486750	−	0.873541i	$-0.661818\pi$
$419$	3.72897	−	2.66531i	0.182172	−	0.130209i	0.668922	+	0.743333i	$0.266756\pi$
$420$		0			0
$421$	7.16781	−	11.3725i	0.349338	−	0.554262i	−0.624638	−	0.780915i	$-0.714753\pi$
$421$	7.16781	−	11.3725i	0.349338	−	0.554262i	0.973976	+	0.226652i	$0.0727781\pi$
$422$	−0.509894	+	8.75454i	−0.0248212	+	0.426164i
$423$		0			0
$424$	10.5034	−	6.90821i	0.510091	−	0.335492i
$425$	−14.7809	+	8.92032i	−0.716979	+	0.432699i
$426$		0			0
$427$	−3.29297	+	1.34533i	−0.159358	+	0.0651049i
$428$	22.6657	+	28.1011i	1.09559	+	1.35832i
$429$		0			0
$430$	−12.9663	−	18.9053i	−0.625290	−	0.911694i
$431$	2.10249	+	11.9238i	0.101273	+	0.574350i	0.992643	+	0.121074i	$0.0386338\pi$
$431$	2.10249	+	11.9238i	0.101273	+	0.574350i	−0.891370	+	0.453276i	$0.850255\pi$
$432$		0			0
$433$	−6.29503	+	35.7009i	−0.302520	+	1.71568i	0.332435	+	0.943126i	$0.392130\pi$
$433$	−6.29503	+	35.7009i	−0.302520	+	1.71568i	−0.634955	+	0.772549i	$0.718981\pi$
$434$	20.1543	−	9.16127i	0.967439	−	0.439755i
$435$		0			0
$436$	−43.9425	−	8.63003i	−2.10446	−	0.413303i
$437$	−33.2434	−	10.6591i	−1.59025	−	0.509892i
$438$		0			0
$439$	0.118936	+	0.136286i	0.00567652	+	0.00650457i	0.756267	−	0.654263i	$-0.227021\pi$
$439$	0.118936	+	0.136286i	0.00567652	+	0.00650457i	−0.750591	+	0.660768i	$0.770231\pi$
$440$	−20.7805	+	27.9130i	−0.990670	+	1.33070i
$441$		0			0
$442$	34.3355	−	79.5986i	1.63317	−	3.78612i
$443$	−22.1281	−	20.0802i	−1.05134	−	0.954038i	−0.0523323	−	0.998630i	$-0.516666\pi$
$443$	−22.1281	−	20.0802i	−1.05134	−	0.954038i	−0.999005	+	0.0445917i	$0.985801\pi$
$444$		0			0
$445$	3.63674	−	14.1187i	0.172398	−	0.669290i
$446$	−10.1102	−	9.91598i	−0.478730	−	0.469535i
$447$		0			0
$448$	5.16135	−	23.8274i	0.243851	−	1.12574i
$449$	10.4161	+	13.9913i	0.491567	+	0.660289i	0.976814	−	0.214088i	$-0.0686779\pi$
$449$	10.4161	+	13.9913i	0.491567	+	0.660289i	−0.485248	+	0.874377i	$0.661271\pi$
$450$		0			0
$451$	3.79122	+	0.443131i	0.178522	+	0.0208662i
$452$	−4.20341	+	0.825522i	−0.197712	+	0.0388293i
$453$		0			0
$454$	−5.44850	−	25.1531i	−0.255711	−	1.18049i
$455$	19.9639	−	22.8761i	0.935922	−	1.07245i
$456$		0			0
$457$	−14.6293	−	10.4564i	−0.684331	−	0.489131i	0.185396	−	0.982664i	$-0.440643\pi$
$457$	−14.6293	−	10.4564i	−0.684331	−	0.489131i	−0.869727	+	0.493533i	$0.835705\pi$
$458$	36.3417	+	30.4943i	1.69814	+	1.42490i
$459$		0			0
$460$	63.1285	−	52.9711i	2.94338	−	2.46979i
$461$	−23.8883	+	1.85674i	−1.11259	+	0.0864772i	−0.620602	−	0.784126i	$-0.713112\pi$
$461$	−23.8883	+	1.85674i	−1.11259	+	0.0864772i	−0.491986	+	0.870603i	$0.663729\pi$
$462$		0			0
$463$	−9.39527	+	24.3344i	−0.436635	+	1.13091i	0.523660	+	0.851927i	$0.324566\pi$
$463$	−9.39527	+	24.3344i	−0.436635	+	1.13091i	−0.960295	+	0.278986i	$0.910002\pi$
$464$	−0.810663	+	5.93510i	−0.0376341	+	0.275530i
$465$		0			0
$466$	26.4249	+	14.5806i	1.22411	+	0.675434i
$467$	−0.0830352	−	1.42566i	−0.00384241	−	0.0659716i	0.995842	−	0.0910989i	$-0.0290379\pi$
$467$	−0.0830352	−	1.42566i	−0.00384241	−	0.0659716i	−0.999684	+	0.0251273i	$0.992001\pi$
$468$		0			0
$469$	−7.71855	+	3.87640i	−0.356410	+	0.178996i
$470$	−4.91526	−	9.33139i	−0.226724	−	0.430425i
$471$		0			0
$472$	−20.7297	−	9.42280i	−0.954161	−	0.433720i
$473$	7.05979	−	10.2934i	0.324609	−	0.473292i
$474$		0			0
$475$	−1.41348	−	10.3485i	−0.0648549	−	0.474822i
$476$	−47.5538	−	11.2704i	−2.17962	−	0.516580i
$477$		0			0
$478$	11.8337	+	12.5430i	0.541262	+	0.573705i
$479$	19.5312	+	3.05463i	0.892405	+	0.139570i	0.584065	−	0.811707i	$-0.301461\pi$
$479$	19.5312	+	3.05463i	0.892405	+	0.139570i	0.308340	+	0.951276i	$0.400227\pi$
$480$		0			0
$481$	−15.5784	+	0.604514i	−0.710315	+	0.0275635i
$482$	−2.69499	−	1.62644i	−0.122754	−	0.0740822i
$483$		0			0
$484$	−4.65554	−	1.29596i	−0.211616	−	0.0589072i
$485$	−22.5570			−1.02426
$486$		0			0
$487$	−10.6963			−0.484697			−0.242349	−	0.970189i	$-0.577918\pi$
$487$	−10.6963			−0.484697			−0.242349	+	0.970189i	$0.577918\pi$
$488$	6.06057	+	1.68708i	0.274349	+	0.0763704i
$489$		0			0
$490$	15.7574	+	9.50963i	0.711846	+	0.429601i
$491$	−20.1197	+	0.780736i	−0.907989	+	0.0352341i	−0.488537	−	0.872543i	$-0.662469\pi$
$491$	−20.1197	+	0.780736i	−0.907989	+	0.0352341i	−0.419452	+	0.907777i	$0.637778\pi$
$492$		0			0
$493$	−28.4959	−	4.45668i	−1.28339	−	0.200719i
$494$	35.9904	+	38.1476i	1.61929	+	1.71634i
$495$		0			0
$496$	−6.34144	−	1.50295i	−0.284739	−	0.0674844i
$497$	−3.16805	−	23.1942i	−0.142107	−	1.04040i
$498$		0			0
$499$	−14.7346	+	21.4836i	−0.659611	+	0.961736i	0.340161	+	0.940367i	$0.389519\pi$
$499$	−14.7346	+	21.4836i	−0.659611	+	0.961736i	−0.999772	+	0.0213690i	$0.993198\pi$
$500$	−21.7053	−	9.86625i	−0.970689	−	0.441232i
$501$		0			0
$502$	19.9533	+	37.8804i	0.890560	+	1.69069i
$503$	−30.6455	+	15.3907i	−1.36641	+	0.686239i	−0.972499	−	0.232907i	$-0.925176\pi$
$503$	−30.6455	+	15.3907i	−1.36641	+	0.686239i	−0.393916	+	0.919147i	$0.628880\pi$
$504$		0			0
$505$	−2.49843	−	42.8964i	−0.111179	−	1.90887i
$506$	61.5316	+	33.9517i	2.73541	+	1.50934i
$507$		0			0
$508$	−5.65545	+	41.4052i	−0.250920	+	1.83706i
$509$	−7.69506	+	19.9307i	−0.341077	+	0.883413i	0.651147	+	0.758952i	$0.274288\pi$
$509$	−7.69506	+	19.9307i	−0.341077	+	0.883413i	−0.992224	+	0.124461i	$0.960280\pi$
$510$		0			0
$511$	10.3109	−	0.801424i	0.456126	−	0.0354529i
$512$	−11.9884	+	10.0594i	−0.529816	+	0.444569i
$513$		0			0
$514$	−20.5122	−	17.2118i	−0.904753	−	0.759178i
$515$	19.2964	+	13.7923i	0.850303	+	0.607760i
$516$		0			0
$517$	3.77578	−	4.32656i	0.166058	−	0.190282i
$518$	2.91431	+	13.4540i	0.128048	+	0.591133i
$519$		0			0
$520$	−52.6904	+	10.3481i	−2.31063	+	0.453792i
$521$	−4.35729	−	0.509294i	−0.190896	−	0.0223126i	0.0201075	−	0.999798i	$-0.493599\pi$
$521$	−4.35729	−	0.509294i	−0.190896	−	0.0223126i	−0.211004	+	0.977485i	$0.567673\pi$
$522$		0			0
$523$	8.15494	+	10.9540i	0.356590	+	0.478984i	0.943831	−	0.330428i	$-0.107193\pi$
$523$	8.15494	+	10.9540i	0.356590	+	0.478984i	−0.587241	+	0.809412i	$0.699786\pi$
$524$	−15.5522	+	71.7971i	−0.679403	+	3.13647i
$525$		0			0
$526$	−8.83542	−	8.66572i	−0.385243	−	0.377843i
$527$	7.82730	−	30.3874i	0.340963	−	1.32370i
$528$		0			0
$529$	−36.4231	−	33.0522i	−1.58361	−	1.43705i
$530$	8.92648	−	20.6939i	0.387741	−	0.898886i
$531$		0			0
$532$	17.6559	−	23.7160i	0.765482	−	1.02822i
$533$	3.87275	+	4.43768i	0.167748	+	0.192217i
$534$		0			0
$535$	26.7313	+	8.57105i	1.15570	+	0.370559i
$536$	14.9890	+	2.94374i	0.647426	+	0.127150i
$537$		0			0
$538$	52.7926	−	23.9972i	2.27605	−	1.03459i
$539$	−1.74009	+	9.86855i	−0.0749511	+	0.425069i
$540$		0			0
$541$	5.30788	+	30.1025i	0.228204	+	1.29421i	0.856465	+	0.516205i	$0.172656\pi$
$541$	5.30788	+	30.1025i	0.228204	+	1.29421i	−0.628261	+	0.778003i	$0.716233\pi$
$542$	−5.89964	−	8.60189i	−0.253411	−	0.369483i
$543$		0			0
$544$	−16.5802	−	20.5562i	−0.710871	−	0.881341i
$545$	−32.2340	+	13.1691i	−1.38075	+	0.564100i
$546$		0			0
$547$	−4.06531	+	2.45343i	−0.173820	+	0.104901i	−0.600940	−	0.799294i	$-0.705207\pi$
$547$	−4.06531	+	2.45343i	−0.173820	+	0.104901i	0.427120	+	0.904195i	$0.359528\pi$
$548$	−14.2180	+	9.35136i	−0.607365	+	0.399470i
$549$		0			0
$550$	−1.22253	+	20.9901i	−0.0521290	+	0.895020i
$551$	9.30408	−	14.7619i	0.396367	−	0.628879i
$552$		0			0
$553$	6.51269	−	4.65499i	0.276948	−	0.197950i
$554$	3.72986	+	0.289907i	0.158466	+	0.0123170i
$555$		0			0
$556$	61.7502	+	25.2277i	2.61879	+	1.06989i
$557$	9.92217	+	33.1423i	0.420416	+	1.40429i	0.861928	+	0.507031i	$0.169257\pi$
$557$	9.92217	+	33.1423i	0.420416	+	1.40429i	−0.441512	+	0.897255i	$0.645558\pi$
$558$		0			0
$559$	18.7410	−	4.44171i	0.792662	−	0.187864i
$560$	2.84257	+	7.36243i	0.120120	+	0.311120i
$561$		0			0
$562$	9.49237	−	18.0208i	0.400411	−	0.760162i
$563$	−0.0965944	+	4.98038i	−0.00407097	+	0.209898i	0.992253	+	0.124233i	$0.0396471\pi$
$563$	−0.0965944	+	4.98038i	−0.00407097	+	0.209898i	−0.996324	+	0.0856648i	$0.972699\pi$
$564$		0			0
$565$	−2.37796	+	2.33229i	−0.100042	+	0.0981202i
$566$	19.2012	+	33.2575i	0.807087	+	1.39792i
$567$		0			0
$568$	−20.7004	+	35.8541i	−0.868568	+	1.50440i
$569$	2.12779	+	8.26060i	0.0892018	+	0.346303i	0.997385	−	0.0722701i	$-0.0230244\pi$
$569$	2.12779	+	8.26060i	0.0892018	+	0.346303i	−0.908183	+	0.418573i	$0.862531\pi$
$570$		0			0
$571$	2.71811	−	1.49979i	0.113749	−	0.0627642i	−0.425218	−	0.905091i	$-0.639802\pi$
$571$	2.71811	−	1.49979i	0.113749	−	0.0627642i	0.538967	+	0.842327i	$0.318815\pi$
$572$	−35.9415	−	57.0250i	−1.50279	−	2.38434i
$573$		0			0
$574$	3.26510	−	4.04809i	0.136283	−	0.168964i
$575$	6.19388	−	20.6890i	0.258303	−	0.862791i
$576$		0			0
$577$	22.2585	−	23.5926i	0.926633	−	0.982173i	−0.0732528	−	0.997313i	$-0.523338\pi$
$577$	22.2585	−	23.5926i	0.926633	−	0.982173i	0.999885	+	0.0151403i	$0.00481949\pi$
$578$	−54.1501	+	41.9695i	−2.25235	+	1.74570i
$579$		0			0
$580$	17.7689	+	37.1606i	0.737815	+	1.54301i
$581$	2.75903	+	28.3653i	0.114464	+	1.17679i
$582$		0			0
$583$	12.2616	+	0.475806i	0.507823	+	0.0197059i
$584$	−15.2812	−	10.0506i	−0.632340	−	0.415896i
$585$		0			0
$586$	−27.0858	−	13.6030i	−1.11890	−	0.561934i
$587$	−0.577092	−	29.7547i	−0.0238191	−	1.22811i	−0.800935	−	0.598751i	$-0.795664\pi$
$587$	−0.577092	−	29.7547i	−0.0238191	−	1.22811i	0.777116	−	0.629357i	$-0.216682\pi$
$588$		0			0
$589$	15.0050	+	11.6298i	0.618270	+	0.479196i
$590$	−40.3309	+	6.30763i	−1.66039	+	0.259681i
$591$		0			0
$592$	1.74813	−	3.65591i	0.0718479	−	0.150257i
$593$	−17.3860	−	6.32799i	−0.713958	−	0.259860i	−0.0405995	−	0.999176i	$-0.512927\pi$
$593$	−17.3860	−	6.32799i	−0.713958	−	0.259860i	−0.673359	+	0.739316i	$0.735149\pi$
$594$		0			0
$595$	−35.7082	+	12.9967i	−1.46389	+	0.532814i
$596$	1.49673	−	15.3878i	0.0613086	−	0.630308i
$597$		0			0
$598$	35.1063	+	102.602i	1.43560	+	4.19571i
$599$	1.99940	−	1.81436i	0.0816934	−	0.0741328i	−0.630138	−	0.776483i	$-0.717002\pi$
$599$	1.99940	−	1.81436i	0.0816934	−	0.0741328i	0.711832	+	0.702350i	$0.247866\pi$
$600$		0			0
$601$	−7.48402	+	21.8729i	−0.305280	+	0.892214i	0.681737	+	0.731597i	$0.261225\pi$
$601$	−7.48402	+	21.8729i	−0.305280	+	0.892214i	−0.987017	+	0.160616i	$0.948652\pi$
$602$	−6.73598	−	15.6157i	−0.274538	−	0.636450i
$603$		0			0
$604$	6.67704	−	0.780434i	0.271685	−	0.0317554i
$605$	−3.57814	+	1.14728i	−0.145472	+	0.0466437i
$606$		0			0
$607$	−12.6817	+	3.53019i	−0.514734	+	0.143286i	−0.515793	−	0.856714i	$-0.672502\pi$
$607$	−12.6817	+	3.53019i	−0.514734	+	0.143286i	0.00105883	+	0.999999i	$0.499663\pi$
$608$	15.3923	−	4.28474i	0.624240	−	0.173769i
$609$		0			0
$610$	10.7393	−	3.44343i	0.434822	−	0.139420i
$611$	8.80103	−	1.02869i	0.356052	−	0.0416165i
$612$		0			0
$613$	−9.96575	−	23.1032i	−0.402513	−	0.933130i	−0.992103	−	0.125427i	$-0.959970\pi$
$613$	−9.96575	−	23.1032i	−0.402513	−	0.933130i	0.589590	−	0.807703i	$-0.299289\pi$
$614$	13.5032	−	39.4647i	0.544947	−	1.59267i
$615$		0			0
$616$	−19.1176	+	17.3483i	−0.770271	+	0.698983i
$617$	0.271197	+	0.792604i	0.0109180	+	0.0319090i	0.951473	−	0.307733i	$-0.0995705\pi$
$617$	0.271197	+	0.792604i	0.0109180	+	0.0319090i	−0.940555	+	0.339642i	$0.889694\pi$
$618$		0			0
$619$	4.15235	−	42.6899i	0.166897	−	1.71585i	−0.421121	−	0.907004i	$-0.638363\pi$
$619$	4.15235	−	42.6899i	0.166897	−	1.71585i	0.588018	−	0.808848i	$-0.299908\pi$
$620$	−42.1109	+	15.3271i	−1.69122	+	0.615552i
$621$		0			0
$622$	−55.5271	−	20.2102i	−2.22643	−	0.810356i
$623$	4.66581	−	9.75772i	0.186932	−	0.390935i
$624$		0			0
$625$	−30.8729	+	4.82844i	−1.23492	+	0.193138i
$626$	−3.27455	−	2.53797i	−0.130877	−	0.101438i
$627$		0			0
$628$	1.18308	+	60.9995i	0.0472102	+	2.43415i
$629$	17.4364	+	8.75688i	0.695234	+	0.349160i
$630$		0			0
$631$	−18.0503	−	11.8718i	−0.718569	−	0.472610i	0.136820	−	0.990596i	$-0.456312\pi$
$631$	−18.0503	−	11.8718i	−0.718569	−	0.472610i	−0.855389	+	0.517985i	$0.826682\pi$
$632$	−14.1469	−	0.548966i	−0.562735	−	0.0218367i
$633$		0			0
$634$	5.82231	+	59.8585i	0.231233	+	2.37729i
$635$	14.0173	+	29.3148i	0.556261	+	1.16332i
$636$		0			0
$637$	−12.2216	+	9.47247i	−0.484238	+	0.375313i
$638$	−24.1054	+	25.5502i	−0.954342	+	1.01154i
$639$		0			0
$640$	−16.0433	+	53.5883i	−0.634167	+	2.11826i
$641$	−11.0097	+	13.6498i	−0.434855	+	0.539136i	−0.947623	−	0.319392i	$-0.896521\pi$
$641$	−11.0097	+	13.6498i	−0.434855	+	0.539136i	0.512768	+	0.858527i	$0.328620\pi$
$642$		0			0
$643$	−3.65641	−	5.80128i	−0.144195	−	0.228780i	0.766120	−	0.642698i	$-0.222185\pi$
$643$	−3.65641	−	5.80128i	−0.144195	−	0.228780i	−0.910314	+	0.413917i	$0.864160\pi$
$644$	53.5271	−	29.5350i	2.10926	−	1.16384i
$645$		0			0
$646$	−16.3729	−	63.5634i	−0.644182	−	2.50087i
$647$	−14.7935	+	25.6232i	−0.581594	+	1.00735i	0.413697	+	0.910415i	$0.364237\pi$
$647$	−14.7935	+	25.6232i	−0.581594	+	1.00735i	−0.995291	+	0.0969356i	$0.969096\pi$
$648$		0			0
$649$	−11.1130	−	19.2483i	−0.436223	−	0.755561i
$650$	−23.1627	+	22.7178i	−0.908515	+	0.891065i
$651$		0			0
$652$	−0.756488	+	39.0043i	−0.0296263	+	1.52753i
$653$	21.2827	−	40.4042i	0.832856	−	1.58114i	0.0191813	−	0.999816i	$-0.493894\pi$
$653$	21.2827	−	40.4042i	0.832856	−	1.58114i	0.813674	−	0.581321i	$-0.197464\pi$
$654$		0			0
$655$	20.5737	+	53.2871i	0.803879	+	2.08210i
$656$	−1.48971	+	0.353067i	−0.0581633	+	0.0137850i
$657$		0			0
$658$	−2.24399	−	7.49545i	−0.0874799	−	0.292203i
$659$	14.1933	+	5.79858i	0.552891	+	0.225881i	0.637388	−	0.770543i	$-0.280015\pi$
$659$	14.1933	+	5.79858i	0.552891	+	0.225881i	−0.0844974	+	0.996424i	$0.526928\pi$
$660$		0			0
$661$	47.6557	+	3.70409i	1.85359	+	0.144072i	0.955359	−	0.295448i	$-0.0954691\pi$
$661$	47.6557	+	3.70409i	1.85359	+	0.144072i	0.898232	+	0.439521i	$0.144852\pi$
$662$	−16.5103	+	11.8009i	−0.641693	+	0.458654i
$663$		0			0
$664$	26.8744	−	42.6392i	1.04293	−	1.65472i
$665$	1.33673	−	22.9507i	0.0518361	−	0.889991i
$666$		0			0
$667$	30.1444	−	19.8263i	1.16720	−	0.767677i
$668$	71.8930	−	43.3877i	2.78162	−	1.67872i
$669$		0			0
$670$	25.3500	−	10.3566i	0.979358	−	0.400112i
$671$	3.85508	+	4.77954i	0.148824	+	0.184512i
$672$		0			0
$673$	22.4286	+	32.7017i	0.864560	+	1.26056i	0.964104	+	0.265526i	$0.0855456\pi$
$673$	22.4286	+	32.7017i	0.864560	+	1.26056i	−0.0995438	+	0.995033i	$0.531738\pi$
$674$	−10.7555	−	60.9975i	−0.414286	−	2.34953i
$675$		0			0
$676$	10.0886	−	57.2151i	0.388022	−	2.20058i
$677$	−10.1875	+	4.63077i	−0.391536	+	0.177975i	−0.599897	−	0.800077i	$-0.704792\pi$
$677$	−10.1875	+	4.63077i	−0.391536	+	0.177975i	0.208361	+	0.978052i	$0.433187\pi$
$678$		0			0
$679$	−16.4202	−	3.22483i	−0.630151	−	0.123758i
$680$	63.9950	+	20.5192i	2.45410	+	0.786875i
$681$		0			0
$682$	−25.1282	−	28.7937i	−0.962207	−	1.10257i
$683$	−20.0015	+	26.8667i	−0.765338	+	1.02803i	0.233117	+	0.972449i	$0.425108\pi$
$683$	−20.0015	+	26.8667i	−0.765338	+	1.02803i	−0.998454	+	0.0555783i	$0.982300\pi$
$684$		0			0
$685$	−5.24099	+	12.1500i	−0.200248	+	0.464226i
$686$	34.9505	+	31.7159i	1.33442	+	1.21092i
$687$		0			0
$688$	−1.24878	+	4.84808i	−0.0476094	+	0.184831i
$689$	13.5180	+	13.2584i	0.514996	+	0.505104i
$690$		0			0
$691$	1.91763	−	8.85275i	0.0729500	−	0.336774i	−0.926244	−	0.376925i	$-0.876981\pi$
$691$	1.91763	−	8.85275i	0.0729500	−	0.336774i	0.999194	+	0.0401508i	$0.0127838\pi$
$692$	39.7595	+	53.4063i	1.51143	+	2.03020i
$693$		0			0
$694$	−39.4588	−	4.61208i	−1.49784	−	0.175072i
$695$	50.8943	−	9.99532i	1.93053	−	0.379144i
$696$		0			0
$697$	−1.56058	−	7.20443i	−0.0591111	−	0.272887i
$698$	14.4427	−	16.5495i	0.546663	−	0.626407i
$699$		0			0
$700$	14.8802	+	10.6358i	0.562420	+	0.401994i
$701$	−0.828040	−	0.694808i	−0.0312746	−	0.0262425i	0.627016	−	0.779006i	$-0.284276\pi$
$701$	−0.828040	−	0.694808i	−0.0312746	−	0.0262425i	−0.658291	+	0.752764i	$0.728720\pi$
$702$		0			0
$703$	−9.04275	+	7.58777i	−0.341054	+	0.286178i
$704$	−41.9588	+	3.26130i	−1.58138	+	0.122915i
$705$		0			0
$706$	14.7419	−	38.1824i	0.554818	−	1.43701i
$707$	4.31392	−	31.5835i	0.162242	−	1.18782i
$708$		0			0
$709$	−3.19359	−	1.76215i	−0.119938	−	0.0661788i	0.422009	−	0.906592i	$-0.361325\pi$
$709$	−3.19359	−	1.76215i	−0.119938	−	0.0661788i	−0.541947	+	0.840413i	$0.682313\pi$
$710$	4.31545	+	74.0933i	0.161956	+	2.78067i
$711$		0			0
$712$	−17.0936	+	8.58474i	−0.640611	+	0.321727i
$713$	18.2939	+	34.7302i	0.685113	+	1.30065i
$714$		0			0
$715$	−47.7141	−	21.6887i	−1.78441	−	0.811113i
$716$	−10.7324	+	15.6483i	−0.401089	+	0.584803i
$717$		0			0
$718$	6.63950	+	48.6098i	0.247784	+	1.81410i
$719$	28.9896	+	6.87067i	1.08113	+	0.256233i	0.732320	−	0.680961i	$-0.238438\pi$
$719$	28.9896	+	6.87067i	1.08113	+	0.256233i	0.348810	+	0.937193i	$0.386586\pi$
$720$		0			0
$721$	12.0750	+	12.7987i	0.449696	+	0.476649i
$722$	−4.91771	−	0.769116i	−0.183018	−	0.0286235i
$723$		0			0
$724$	−42.0580	+	1.63204i	−1.56307	+	0.0606544i
$725$	9.24191	+	5.57752i	0.343236	+	0.207144i
$726$		0			0
$727$	−7.64608	−	2.12843i	−0.283577	−	0.0789391i	0.123463	−	0.992349i	$-0.460600\pi$
$727$	−7.64608	−	2.12843i	−0.283577	−	0.0789391i	−0.407041	+	0.913410i	$0.633439\pi$
$728$	−39.8352			−1.47639
$729$		0			0
$730$	−32.7886			−1.21356
$731$	−23.2221	−	6.46431i	−0.858900	−	0.239091i
$732$		0			0
$733$	−3.99533	−	2.41119i	−0.147571	−	0.0890595i	0.440992	−	0.897511i	$-0.354627\pi$
$733$	−3.99533	−	2.41119i	−0.147571	−	0.0890595i	−0.588562	+	0.808452i	$0.700306\pi$
$734$	49.9500	−	1.93829i	1.84369	−	0.0715435i
$735$		0			0
$736$	32.6399	+	5.10479i	1.20312	+	0.188165i
$737$	10.2318	+	10.8450i	0.376892	+	0.399482i
$738$		0			0
$739$	34.8218	+	8.25291i	1.28094	+	0.303588i	0.814085	−	0.580746i	$-0.197239\pi$
$739$	34.8218	+	8.25291i	1.28094	+	0.303588i	0.466855	+	0.884334i	$0.345387\pi$
$740$	−3.77104	−	27.6089i	−0.138626	−	1.01492i
$741$		0			0
$742$	9.45647	−	13.7879i	0.347158	−	0.506169i
$743$	−7.32151	−	3.32804i	−0.268600	−	0.122094i	0.274983	−	0.961449i	$-0.411328\pi$
$743$	−7.32151	−	3.32804i	−0.268600	−	0.122094i	−0.543583	+	0.839355i	$0.682933\pi$
$744$		0			0
$745$	−5.60244	−	10.6360i	−0.205258	−	0.389672i
$746$	29.8344	−	14.9834i	1.09232	−	0.548581i
$747$		0			0
$748$	4.90524	+	84.2197i	0.179353	+	3.07938i
$749$	18.2336	+	10.0609i	0.666241	+	0.367616i
$750$		0			0
$751$	4.73356	−	34.6558i	0.172730	−	1.26461i	−0.676444	−	0.736494i	$-0.736480\pi$
$751$	4.73356	−	34.6558i	0.172730	−	1.26461i	0.849174	−	0.528113i	$-0.177100\pi$
$752$	−0.829574	+	2.14865i	−0.0302515	+	0.0783532i
$753$		0			0
$754$	−54.0397	+	4.20030i	−1.96801	+	0.152966i
$755$	4.00419	−	3.35991i	0.145727	−	0.122280i
$756$		0			0
$757$	−20.1696	−	16.9243i	−0.733076	−	0.615123i	0.197893	−	0.980224i	$-0.436590\pi$
$757$	−20.1696	−	16.9243i	−0.733076	−	0.615123i	−0.930968	+	0.365100i	$0.881035\pi$
$758$	−36.3334	−	25.9696i	−1.31969	−	0.943257i
$759$		0			0
$760$	−26.7335	+	30.6332i	−0.969725	+	1.11118i
$761$	5.66582	+	26.1563i	0.205386	+	0.948166i	0.957343	+	0.288954i	$0.0933076\pi$
$761$	5.66582	+	26.1563i	0.205386	+	0.948166i	−0.751957	+	0.659212i	$0.770890\pi$
$762$		0			0
$763$	−25.3473	+	4.97806i	−0.917635	+	0.180218i
$764$	−27.2355	−	3.18337i	−0.985345	−	0.115170i
$765$		0			0
$766$	−5.14573	−	6.91191i	−0.185923	−	0.249737i
$767$	7.26062	−	33.5188i	0.262166	−	1.21029i
$768$		0			0
$769$	−33.2820	−	32.6428i	−1.20018	−	1.17713i	−0.979427	−	0.201798i	$-0.935322\pi$
$769$	−33.2820	−	32.6428i	−1.20018	−	1.17713i	−0.220752	−	0.975330i	$-0.570851\pi$
$770$	−11.5440	+	44.8167i	−0.416018	+	1.61508i
$771$		0			0
$772$	53.3965	+	48.4547i	1.92178	+	1.74392i
$773$	−0.117392	+	0.272145i	−0.00422229	+	0.00978837i	−0.920314	−	0.391180i	$-0.872067\pi$
$773$	−0.117392	+	0.272145i	−0.00422229	+	0.00978837i	0.916092	+	0.400968i	$0.131326\pi$
$774$		0			0
$775$	−7.01304	+	9.42015i	−0.251916	+	0.338382i
$776$	19.4590	+	22.2976i	0.698539	+	0.800437i
$777$		0			0
$778$	−33.3763	−	10.7017i	−1.19660	−	0.383674i
$779$	4.37611	+	0.859439i	0.156790	+	0.0307926i
$780$		0			0
$781$	−36.7879	+	16.7222i	−1.31638	+	0.598366i
$782$	23.5675	−	133.658i	0.842773	−	4.77960i
$783$		0			0
$784$	−0.697934	−	3.95818i	−0.0249262	−	0.141364i
$785$	26.8320	+	39.1220i	0.957676	+	1.39633i
$786$		0			0
$787$	−21.2654	−

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.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.26585 - 0.630742i) q^{2} +(3.02391 + 1.82494i) q^{4} +(2.74419 - 0.106487i) q^{5} +(2.01284 + 0.314803i) q^{7} +(-2.47257 - 2.62077i) q^{8} +O(q^{10})\)	\(q+(-2.26585 - 0.630742i) q^{2} +(3.02391 + 1.82494i) q^{4} +(2.74419 - 0.106487i) q^{5} +(2.01284 + 0.314803i) q^{7} +(-2.47257 - 2.62077i) q^{8} +(-6.28508 - 1.48959i) q^{10} +(-0.475940 - 3.48450i) q^{11} +(3.06939 - 4.47529i) q^{13} +(-4.36224 - 1.98288i) q^{14} +(0.657389 + 1.24802i) q^{16} +(-6.06937 + 3.04815i) q^{17} +(-0.238916 - 4.10203i) q^{19} +(8.49249 + 4.68596i) q^{20} +(-1.11941 + 8.19555i) q^{22} +(3.06012 - 7.92590i) q^{23} +(2.53425 - 0.196978i) q^{25} +(-9.77754 + 8.20433i) q^{26} +(5.51215 + 4.62524i) q^{28} +(3.45486 + 2.46939i) q^{29} +(-3.03787 + 3.48101i) q^{31} +(0.823198 + 3.80030i) q^{32} +(15.6749 - 3.07845i) q^{34} +(5.55714 + 0.649536i) q^{35} +(-1.71554 - 2.30438i) q^{37} +(-2.04598 + 9.44528i) q^{38} +(-7.06426 - 6.92858i) q^{40} +(-0.270732 + 1.05105i) q^{41} +(2.62829 + 2.38505i) q^{43} +(4.91979 - 11.4054i) q^{44} +(-11.9330 + 16.0288i) q^{46} +(1.07362 + 1.23024i) q^{47} +(-2.71330 - 0.869985i) q^{49} +(-5.86647 - 1.15214i) q^{50} +(17.4487 - 7.93139i) q^{52} +(-0.605884 + 3.43614i) q^{53} +(-1.67712 - 9.51143i) q^{55} +(-4.15187 - 6.05357i) q^{56} +(-6.27065 - 7.77439i) q^{58} +(5.85044 - 2.39017i) q^{59} +(-1.49488 + 0.902167i) q^{61} +(9.07897 - 5.97134i) q^{62} +(0.695806 - 11.9465i) q^{64} +(7.94643 - 12.6079i) q^{65} +(-3.44909 + 2.46526i) q^{67} +(-23.9159 - 1.85889i) q^{68} +(-12.1819 - 4.97687i) q^{70} +(-3.29550 - 11.0077i) q^{71} +(4.93945 - 1.17067i) q^{73} +(2.43370 + 6.30344i) q^{74} +(6.76348 - 12.8402i) q^{76} +(0.138937 - 7.16358i) q^{77} +(2.80526 - 2.75138i) q^{79} +(1.93690 + 3.35480i) q^{80} +(1.27638 - 2.21075i) q^{82} +(3.48933 + 13.5464i) q^{83} +(-16.3309 + 9.01101i) q^{85} +(-4.45097 - 7.06194i) q^{86} +(-7.95527 + 9.86299i) q^{88} +(1.52261 - 5.08586i) q^{89} +(7.58704 - 8.04179i) q^{91} +(23.7178 - 18.3827i) q^{92} +(-1.65671 - 3.46471i) q^{94} +(-1.09244 - 11.2313i) q^{95} +(-8.20755 - 0.318490i) q^{97} +(5.59919 + 3.68265i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

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