LMFDB - Embedded newform 729.2.g.d.352.5

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			352.5
Character	$\chi$	$=$	729.352
Dual form			729.2.g.d.379.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.108562 - 0.362623i) q^{2} +(1.55127 + 1.02028i) q^{4} +(0.507898 - 1.17744i) q^{5} +(-0.111081 - 1.90719i) q^{7} +(1.11832 - 0.938383i) q^{8} +(-0.371828 - 0.312001i) q^{10} +(2.91390 - 3.91405i) q^{11} +(-2.36051 + 2.50200i) q^{13} +(-0.703649 - 0.166768i) q^{14} +(1.25195 + 2.90234i) q^{16} +(0.0728119 - 0.412937i) q^{17} +(-0.626542 - 3.55329i) q^{19} +(1.98921 - 1.30832i) q^{20} +(-1.10299 - 1.48157i) q^{22} +(0.390372 - 6.70243i) q^{23} +(2.30281 + 2.44083i) q^{25} +(0.651020 + 1.12760i) q^{26} +(1.77356 - 3.07189i) q^{28} +(-4.88707 + 1.15826i) q^{29} +(-5.93035 + 2.97833i) q^{31} +(4.08835 - 0.477860i) q^{32} +(-0.141836 - 0.0712326i) q^{34} +(-2.30201 - 0.837864i) q^{35} +(0.465059 - 0.169268i) q^{37} +(-1.35652 - 0.158555i) q^{38} +(-0.536896 - 1.79336i) q^{40} +(1.74088 + 5.81495i) q^{41} +(11.5214 + 1.34666i) q^{43} +(8.51368 - 3.09873i) q^{44} +(-2.38808 - 0.869188i) q^{46} +(5.42033 + 2.72219i) q^{47} +(3.32765 - 0.388946i) q^{49} +(1.13510 - 0.570068i) q^{50} +(-6.21453 + 1.47287i) q^{52} +(2.95007 - 5.10967i) q^{53} +(-3.12859 - 5.41888i) q^{55} +(-1.91390 - 2.02861i) q^{56} +(-0.110540 + 1.89791i) q^{58} +(3.36501 + 4.51999i) q^{59} +(2.32430 - 1.52872i) q^{61} +(0.436200 + 2.47381i) q^{62} +(-0.827191 + 4.69124i) q^{64} +(1.74705 + 4.05012i) q^{65} +(-7.04135 - 1.66883i) q^{67} +(0.534263 - 0.566286i) q^{68} +(-0.553741 + 0.743803i) q^{70} +(-11.9949 - 10.0649i) q^{71} +(-5.04326 + 4.23179i) q^{73} +(-0.0108925 - 0.187017i) q^{74} +(2.65344 - 6.15135i) q^{76} +(-7.78851 - 5.12258i) q^{77} +(-1.09627 + 3.66180i) q^{79} +4.05318 q^{80} +2.29763 q^{82} +(1.39129 - 4.64723i) q^{83} +(-0.449227 - 0.295461i) q^{85} +(1.73912 - 4.03173i) q^{86} +(-0.414199 - 7.11153i) q^{88} +(-7.97723 + 6.69369i) q^{89} +(5.03399 + 4.22402i) q^{91} +(7.44395 - 9.99896i) q^{92} +(1.57557 - 1.67001i) q^{94} +(-4.50201 - 1.06700i) q^{95} +(-0.856906 - 1.98653i) q^{97} +(0.220216 - 1.24891i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 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 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{16}{27}\right)$

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 $

$2$	0.108562	−	0.362623i	0.0767651	−	0.256413i	−0.910989	−	0.412430i	$-0.864680\pi$
$2$	0.108562	−	0.362623i	0.0767651	−	0.256413i	0.987754	+	0.156017i	$0.0498654\pi$
$3$		0			0
$3$		0			0
$4$	1.55127	+	1.02028i	0.775633	+	0.510142i
$5$	0.507898	−	1.17744i	0.227139	−	0.526567i	−0.766091	−	0.642732i	$-0.777801\pi$
$5$	0.507898	−	1.17744i	0.227139	−	0.526567i	0.993230	+	0.116165i	$0.0370602\pi$
$6$		0			0
$7$	−0.111081	−	1.90719i	−0.0419847	−	0.720849i	−0.951967	−	0.306201i	$-0.900942\pi$
$7$	−0.111081	−	1.90719i	−0.0419847	−	0.720849i	0.909982	−	0.414647i	$-0.136095\pi$
$8$	1.11832	−	0.938383i	0.395386	−	0.331768i
$9$		0			0
$10$	−0.371828	−	0.312001i	−0.117582	−	0.0986633i
$11$	2.91390	−	3.91405i	0.878575	−	1.18013i	−0.104058	−	0.994571i	$-0.533183\pi$
$11$	2.91390	−	3.91405i	0.878575	−	1.18013i	0.982633	−	0.185560i	$-0.0594099\pi$
$12$		0			0
$13$	−2.36051	+	2.50200i	−0.654689	+	0.693930i	−0.966631	−	0.256171i	$-0.917539\pi$
$13$	−2.36051	+	2.50200i	−0.654689	+	0.693930i	0.311942	+	0.950101i	$0.399020\pi$
$14$	−0.703649	−	0.166768i	−0.188058	−	0.0445706i
$15$		0			0
$16$	1.25195	+	2.90234i	0.312986	+	0.725584i
$17$	0.0728119	−	0.412937i	0.0176595	−	0.100152i	−0.974704	−	0.223499i	$-0.928252\pi$
$17$	0.0728119	−	0.412937i	0.0176595	−	0.100152i	0.992364	+	0.123348i	$0.0393630\pi$
$18$		0			0
$19$	−0.626542	−	3.55329i	−0.143739	−	0.815182i	−0.968371	−	0.249513i	$-0.919729\pi$
$19$	−0.626542	−	3.55329i	−0.143739	−	0.815182i	0.824633	−	0.565668i	$-0.191382\pi$
$20$	1.98921	−	1.30832i	0.444800	−	0.292550i
$21$		0			0
$22$	−1.10299	−	1.48157i	−0.235157	−	0.315871i
$23$	0.390372	−	6.70243i	0.0813982	−	1.39755i	−0.672274	−	0.740302i	$-0.734682\pi$
$23$	0.390372	−	6.70243i	0.0813982	−	1.39755i	0.753672	−	0.657251i	$-0.228281\pi$
$24$		0			0
$25$	2.30281	+	2.44083i	0.460561	+	0.488166i
$26$	0.651020	+	1.12760i	0.127675	+	0.221140i
$27$		0			0
$28$	1.77356	−	3.07189i	0.335170	−	0.580532i
$29$	−4.88707	+	1.15826i	−0.907506	+	0.215083i	−0.657759	−	0.753228i	$-0.728495\pi$
$29$	−4.88707	+	1.15826i	−0.907506	+	0.215083i	−0.249747	+	0.968311i	$0.580347\pi$
$30$		0			0
$31$	−5.93035	+	2.97833i	−1.06512	+	0.534924i	−0.892956	−	0.450144i	$-0.851373\pi$
$31$	−5.93035	+	2.97833i	−1.06512	+	0.534924i	−0.172166	+	0.985068i	$0.555076\pi$
$32$	4.08835	−	0.477860i	0.722726	−	0.0844745i
$33$		0			0
$34$	−0.141836	−	0.0712326i	−0.0243246	−	0.0122163i
$35$	−2.30201	−	0.837864i	−0.389111	−	0.141625i
$36$		0			0
$37$	0.465059	−	0.169268i	0.0764552	−	0.0278274i	−0.303509	−	0.952828i	$-0.598158\pi$
$37$	0.465059	−	0.169268i	0.0764552	−	0.0278274i	0.379965	+	0.925001i	$0.375936\pi$
$38$	−1.35652	−	0.158555i	−0.220057	−	0.0257210i
$39$		0			0
$40$	−0.536896	−	1.79336i	−0.0848907	−	0.283555i
$41$	1.74088	+	5.81495i	0.271880	+	0.908143i	0.979482	+	0.201531i	$0.0645918\pi$
$41$	1.74088	+	5.81495i	0.271880	+	0.908143i	−0.707602	+	0.706611i	$0.750223\pi$
$42$		0			0
$43$	11.5214	+	1.34666i	1.75700	+	0.205364i	0.932665	−	0.360743i	$-0.117477\pi$
$43$	11.5214	+	1.34666i	1.75700	+	0.205364i	0.824332	+	0.566107i	$0.191551\pi$
$44$	8.51368	−	3.09873i	1.28349	−	0.467151i
$45$		0			0
$46$	−2.38808	−	0.869188i	−0.352102	−	0.128155i
$47$	5.42033	+	2.72219i	0.790636	+	0.397072i	0.797815	−	0.602902i	$-0.205989\pi$
$47$	5.42033	+	2.72219i	0.790636	+	0.397072i	−0.00717941	+	0.999974i	$0.502285\pi$
$48$		0			0
$49$	3.32765	−	0.388946i	0.475378	−	0.0555637i
$50$	1.13510	−	0.570068i	0.160527	−	0.0806198i
$51$		0			0
$52$	−6.21453	+	1.47287i	−0.861801	+	0.204251i
$53$	2.95007	−	5.10967i	0.405223	−	0.701867i	−0.589124	−	0.808043i	$-0.700527\pi$
$53$	2.95007	−	5.10967i	0.405223	−	0.701867i	0.994347	+	0.106175i	$0.0338605\pi$
$54$		0			0
$55$	−3.12859	−	5.41888i	−0.421859	−	0.730682i
$56$	−1.91390	−	2.02861i	−0.255755	−	0.271084i
$57$		0			0
$58$	−0.110540	+	1.89791i	−0.0145147	+	0.249207i
$59$	3.36501	+	4.51999i	0.438087	+	0.588453i	0.965255	−	0.261308i	$-0.0841538\pi$
$59$	3.36501	+	4.51999i	0.438087	+	0.588453i	−0.527169	+	0.849761i	$0.676746\pi$
$60$		0			0
$61$	2.32430	−	1.52872i	0.297596	−	0.195732i	−0.391926	−	0.919997i	$-0.628191\pi$
$61$	2.32430	−	1.52872i	0.297596	−	0.195732i	0.689522	+	0.724265i	$0.257821\pi$
$62$	0.436200	+	2.47381i	0.0553975	+	0.314175i
$63$		0			0
$64$	−0.827191	+	4.69124i	−0.103399	+	0.586404i
$65$	1.74705	+	4.05012i	0.216695	+	0.502356i
$66$		0			0
$67$	−7.04135	−	1.66883i	−0.860238	−	0.203880i	−0.223257	−	0.974760i	$-0.571669\pi$
$67$	−7.04135	−	1.66883i	−0.860238	−	0.203880i	−0.636981	+	0.770880i	$0.719817\pi$
$68$	0.534263	−	0.566286i	0.0647889	−	0.0686722i
$69$		0			0
$70$	−0.553741	+	0.743803i	−0.0661847	+	0.0889014i
$71$	−11.9949	−	10.0649i	−1.42353	−	1.19448i	−0.949418	−	0.314015i	$-0.898326\pi$
$71$	−11.9949	−	10.0649i	−1.42353	−	1.19448i	−0.474109	−	0.880466i	$-0.657230\pi$
$72$		0			0
$73$	−5.04326	+	4.23179i	−0.590268	+	0.495294i	−0.888301	−	0.459262i	$-0.848114\pi$
$73$	−5.04326	+	4.23179i	−0.590268	+	0.495294i	0.298033	+	0.954556i	$0.403670\pi$
$74$	−0.0108925	−	0.187017i	−0.00126623	−	0.0217403i
$75$		0			0
$76$	2.65344	−	6.15135i	0.304370	−	0.705609i
$77$	−7.78851	−	5.12258i	−0.887583	−	0.583772i
$78$		0			0
$79$	−1.09627	+	3.66180i	−0.123340	+	0.411984i	−0.997251	−	0.0741024i	$-0.976391\pi$
$79$	−1.09627	+	3.66180i	−0.123340	+	0.411984i	0.873911	+	0.486087i	$0.161576\pi$
$80$	4.05318			0.453160
$81$		0			0
$82$	2.29763			0.253731
$83$	1.39129	−	4.64723i	0.152714	−	0.510100i	−0.847057	−	0.531502i	$-0.821628\pi$
$83$	1.39129	−	4.64723i	0.152714	−	0.510100i	0.999771	+	0.0214019i	$0.00681295\pi$
$84$		0			0
$85$	−0.449227	−	0.295461i	−0.0487255	−	0.0320473i
$86$	1.73912	−	4.03173i	0.187534	−	0.434753i
$87$		0			0
$88$	−0.414199	−	7.11153i	−0.0441538	−	0.758091i
$89$	−7.97723	+	6.69369i	−0.845585	+	0.709530i	−0.958813	−	0.284039i	$-0.908325\pi$
$89$	−7.97723	+	6.69369i	−0.845585	+	0.709530i	0.113228	+	0.993569i	$0.463881\pi$
$90$		0			0
$91$	5.03399	+	4.22402i	0.527705	+	0.442797i
$92$	7.44395	−	9.99896i	0.776085	−	1.04246i
$93$		0			0
$94$	1.57557	−	1.67001i	0.162508	−	0.172248i
$95$	−4.50201	−	1.06700i	−0.461896	−	0.109471i
$96$		0			0
$97$	−0.856906	−	1.98653i	−0.0870056	−	0.201702i	0.869158	−	0.494534i	$-0.164661\pi$
$97$	−0.856906	−	1.98653i	−0.0870056	−	0.201702i	−0.956164	+	0.292833i	$0.905402\pi$
$98$	0.220216	−	1.24891i	0.0222452	−	0.126159i
$99$		0			0
$100$	1.08192	+	6.13589i	0.108192	+	0.613589i
$101$	−13.6371	+	8.96929i	−1.35695	+	0.892477i	−0.999146	−	0.0413207i	$-0.986843\pi$
$101$	−13.6371	+	8.96929i	−1.35695	+	0.892477i	−0.357800	+	0.933798i	$0.616473\pi$
$102$		0			0
$103$	10.7894	+	14.4927i	1.06311	+	1.42801i	0.897069	+	0.441890i	$0.145692\pi$
$103$	10.7894	+	14.4927i	1.06311	+	1.42801i	0.166043	+	0.986118i	$0.446901\pi$
$104$	−0.291980	+	5.01311i	−0.0286310	+	0.491575i
$105$		0			0
$106$	−1.53262	−	1.62448i	−0.148861	−	0.157783i
$107$	8.06607	+	13.9708i	0.779777	+	1.35061i	0.932070	+	0.362277i	$0.118001\pi$
$107$	8.06607	+	13.9708i	0.779777	+	1.35061i	−0.152294	+	0.988335i	$0.548666\pi$
$108$		0			0
$109$	4.04171	−	7.00045i	0.387126	−	0.670521i	−0.604936	−	0.796274i	$-0.706801\pi$
$109$	4.04171	−	7.00045i	0.387126	−	0.670521i	0.992062	+	0.125753i	$0.0401347\pi$
$110$	−2.30466	+	0.546214i	−0.219741	+	0.0520795i
$111$		0			0
$112$	5.39623	−	2.71009i	0.509896	−	0.256079i
$113$	1.70912	−	0.199768i	0.160781	−	0.0187926i	−0.0353218	−	0.999376i	$-0.511246\pi$
$113$	1.70912	−	0.199768i	0.160781	−	0.0187926i	0.196102	+	0.980583i	$0.437172\pi$
$114$		0			0
$115$	−7.69343	−	3.86379i	−0.717416	−	0.360300i
$116$	−8.76289	−	3.18943i	−0.813614	−	0.296131i
$117$		0			0
$118$	2.00437	−	0.729529i	0.184517	−	0.0671586i
$119$	−0.795635	−	0.0929964i	−0.0729358	−	0.00852497i
$120$		0			0
$121$	−3.67413	−	12.2725i	−0.334012	−	1.11568i
$122$	−0.302017	−	1.00881i	−0.0273433	−	0.0913330i
$123$		0			0
$124$	−12.2383	−	1.43045i	−1.09903	−	0.128458i
$125$	10.0684	−	3.66460i	0.900546	−	0.327772i
$126$		0			0
$127$	−4.79894	−	1.74667i	−0.425837	−	0.154992i	0.120206	−	0.992749i	$-0.461644\pi$
$127$	−4.79894	−	1.74667i	−0.425837	−	0.154992i	−0.546044	+	0.837757i	$0.683867\pi$
$128$	8.96807	+	4.50393i	0.792673	+	0.398095i
$129$		0			0
$130$	1.65833	−	0.193831i	0.145445	−	0.0170001i
$131$	−10.4120	+	5.22912i	−0.909704	+	0.456871i	−0.841165	−	0.540778i	$-0.818130\pi$
$131$	−10.4120	+	5.22912i	−0.909704	+	0.456871i	−0.0685388	+	0.997648i	$0.521834\pi$
$132$		0			0
$133$	−6.70720	+	1.58964i	−0.581588	+	0.137839i
$134$	−1.36958	+	2.37218i	−0.118314	+	0.204925i
$135$		0			0
$136$	−0.306066	−	0.530121i	−0.0262449	−	0.0454575i
$137$	−3.39935	−	3.60310i	−0.290426	−	0.307834i	0.565689	−	0.824619i	$-0.308610\pi$
$137$	−3.39935	−	3.60310i	−0.290426	−	0.307834i	−0.856115	+	0.516785i	$0.827129\pi$
$138$		0			0
$139$	−0.978519	+	16.8005i	−0.0829969	+	1.42500i	0.657759	+	0.753228i	$0.271504\pi$
$139$	−0.978519	+	16.8005i	−0.0829969	+	1.42500i	−0.740756	+	0.671774i	$0.765533\pi$
$140$	−2.71618	−	3.64846i	−0.229559	−	0.308351i
$141$		0			0
$142$	−4.95194	+	3.25694i	−0.415558	+	0.273317i
$143$	2.91464	+	16.5298i	0.243735	+	1.38229i
$144$		0			0
$145$	−1.11835	+	6.34250i	−0.0928742	+	0.526716i
$146$	0.987039	+	2.28821i	0.0816879	+	0.189374i
$147$		0			0
$148$	0.894131	+	0.211913i	0.0734972	+	0.0174191i
$149$	−11.9596	+	12.6764i	−0.979767	+	1.03849i	0.0194845	+	0.999810i	$0.493797\pi$
$149$	−11.9596	+	12.6764i	−0.979767	+	1.03849i	−0.999252	+	0.0386822i	$0.987684\pi$
$150$		0			0
$151$	3.85502	−	5.17818i	0.313717	−	0.421395i	−0.617098	−	0.786886i	$-0.711692\pi$
$151$	3.85502	−	5.17818i	0.313717	−	0.421395i	0.930815	+	0.365492i	$0.119099\pi$
$152$	−4.03503	−	3.38579i	−0.327284	−	0.274624i
$153$		0			0
$154$	−2.70310	+	2.26817i	−0.217822	+	0.182775i
$155$	0.494796	+	8.49531i	0.0397429	+	0.682360i
$156$		0			0
$157$	5.05847	−	11.7269i	0.403710	−	0.935905i	−0.588171	−	0.808736i	$-0.700152\pi$
$157$	5.05847	−	11.7269i	0.403710	−	0.935905i	0.991881	−	0.127168i	$-0.0405889\pi$
$158$	1.20884	+	0.795065i	0.0961700	+	0.0632520i
$159$		0			0
$160$	1.51381	−	5.05649i	0.119678	−	0.399751i
$161$	−12.8261			−1.01084
$162$		0			0
$163$	−0.599869			−0.0469853			−0.0234927	−	0.999724i	$-0.507479\pi$
$163$	−0.599869			−0.0469853			−0.0234927	+	0.999724i	$0.507479\pi$
$164$	−3.23233	+	10.7967i	−0.252402	+	0.843083i
$165$		0			0
$166$	−1.53415	−	1.00903i	−0.119073	−	0.0783158i
$167$	−1.20188	+	2.78626i	−0.0930039	+	0.215607i	−0.958368	−	0.285537i	$-0.907828\pi$
$167$	−1.20188	+	2.78626i	−0.0930039	+	0.215607i	0.865364	+	0.501144i	$0.167087\pi$
$168$		0			0
$169$	0.0679114	+	1.16599i	0.00522396	+	0.0896919i
$170$	−0.155910	+	0.130824i	−0.0119578	+	0.0100337i
$171$		0			0
$172$	16.4988	+	13.8441i	1.25802	+	1.05560i
$173$	−5.76591	+	7.74497i	−0.438374	+	0.588839i	−0.965323	−	0.261058i	$-0.915929\pi$
$173$	−5.76591	+	7.74497i	−0.438374	+	0.588839i	0.526949	+	0.849897i	$0.323336\pi$
$174$		0			0
$175$	4.39932	−	4.66301i	0.332557	−	0.352490i
$176$	15.0079	+	3.55695i	1.13127	+	0.268115i
$177$		0			0
$178$	1.56126	+	3.61941i	0.117021	+	0.271286i
$179$	−4.48229	+	25.4203i	−0.335022	+	1.90001i	0.0919897	+	0.995760i	$0.470677\pi$
$179$	−4.48229	+	25.4203i	−0.335022	+	1.90001i	−0.427012	+	0.904246i	$0.640434\pi$
$180$		0			0
$181$	0.154861	+	0.878259i	0.0115107	+	0.0652805i	0.990022	−	0.140913i	$-0.0450036\pi$
$181$	0.154861	+	0.878259i	0.0115107	+	0.0652805i	−0.978511	+	0.206193i	$0.933893\pi$
$182$	2.07823	−	1.36687i	0.154048	−	0.101319i
$183$		0			0
$184$	−5.85288	−	7.86179i	−0.431480	−	0.579579i
$185$	0.0369001	−	0.633549i	0.00271295	−	0.0465795i
$186$		0			0
$187$	−1.40409	−	1.48825i	−0.102677	−	0.108831i
$188$	5.63096	+	9.75311i	0.410680	+	0.711319i
$189$		0			0
$190$	−0.875665	+	1.51670i	−0.0635274	+	0.110033i
$191$	−7.85677	+	1.86209i	−0.568496	+	0.134736i	−0.504805	−	0.863234i	$-0.668435\pi$
$191$	−7.85677	+	1.86209i	−0.568496	+	0.134736i	−0.0636914	+	0.997970i	$0.520287\pi$
$192$		0			0
$193$	0.174073	−	0.0874229i	0.0125301	−	0.00629284i	−0.442523	−	0.896757i	$-0.645917\pi$
$193$	0.174073	−	0.0874229i	0.0125301	−	0.00629284i	0.455053	+	0.890464i	$0.349620\pi$
$194$	−0.813389	+	0.0950716i	−0.0583979	+	0.00682574i
$195$		0			0
$196$	5.55890	+	2.79179i	0.397064	+	0.199413i
$197$	−10.8405	−	3.94561i	−0.772351	−	0.281113i	−0.0743718	−	0.997231i	$-0.523695\pi$
$197$	−10.8405	−	3.94561i	−0.772351	−	0.281113i	−0.697980	+	0.716118i	$0.745917\pi$
$198$		0			0
$199$	−1.65236	+	0.601410i	−0.117133	+	0.0426328i	−0.399922	−	0.916549i	$-0.630963\pi$
$199$	−1.65236	+	0.601410i	−0.117133	+	0.0426328i	0.282789	+	0.959182i	$0.408740\pi$
$200$	4.86571	+	0.568720i	0.344058	+	0.0402146i
$201$		0			0
$202$	1.77199	+	5.91887i	0.124677	+	0.416450i
$203$	2.75187	+	9.19189i	0.193143	+	0.645144i
$204$		0			0
$205$	7.73094	+	0.903617i	0.539952	+	0.0631114i
$206$	6.42671	−	2.33913i	0.447770	−	0.162975i
$207$		0			0
$208$	−10.2169	−	3.71864i	−0.708413	−	0.257841i
$209$	−15.7335	−	7.90164i	−1.08831	−	0.546568i
$210$		0			0
$211$	3.55247	−	0.415224i	0.244562	−	0.0285852i	0.00707131	−	0.999975i	$-0.497749\pi$
$211$	3.55247	−	0.415224i	0.244562	−	0.0285852i	0.237491	+	0.971390i	$0.423675\pi$
$212$	9.78966	−	4.91655i	0.672356	−	0.337670i
$213$		0			0
$214$	5.94182	−	1.40824i	0.406174	−	0.0962651i
$215$	7.43730	−	12.8818i	0.507220	−	0.878530i
$216$		0			0
$217$	6.33898	+	10.9794i	0.430318	+	0.745333i
$218$	−2.09975	−	2.22560i	−0.142213	−	0.150737i
$219$		0			0
$220$	0.675517	−	11.5982i	0.0455434	−	0.781949i
$221$	0.861294	+	1.15692i	0.0579369	+	0.0778227i
$222$		0			0
$223$	5.48173	−	3.60539i	0.367083	−	0.241435i	−0.352544	−	0.935795i	$-0.614683\pi$
$223$	5.48173	−	3.60539i	0.367083	−	0.241435i	0.719627	+	0.694361i	$0.244313\pi$
$224$	−1.36551	−	7.74417i	−0.0912368	−	0.517429i
$225$		0			0
$226$	0.113106	−	0.641454i	0.00752367	−	0.0426689i
$227$	−3.21943	−	7.46348i	−0.213681	−	0.495369i	0.777339	−	0.629082i	$-0.216569\pi$
$227$	−3.21943	−	7.46348i	−0.213681	−	0.495369i	−0.991020	+	0.133713i	$0.957310\pi$
$228$		0			0
$229$	7.62361	+	1.80683i	0.503782	+	0.119399i	0.474646	−	0.880177i	$-0.342576\pi$
$229$	7.62361	+	1.80683i	0.503782	+	0.119399i	0.0291365	+	0.999575i	$0.490724\pi$
$230$	−2.23631	+	2.37035i	−0.147458	+	0.156297i
$231$		0			0
$232$	−4.37842	+	5.88124i	−0.287458	+	0.386122i
$233$	−19.7955	−	16.6104i	−1.29685	−	1.08818i	−0.990681	−	0.136205i	$-0.956509\pi$
$233$	−19.7955	−	16.6104i	−1.29685	−	1.08818i	−0.306166	−	0.951978i	$-0.599046\pi$
$234$		0			0
$235$	5.95818	−	4.99951i	0.388669	−	0.326132i
$236$	0.608350	+	10.4450i	0.0396002	+	0.679910i
$237$		0			0
$238$	−0.120099	+	0.278420i	−0.00778483	+	0.0180473i
$239$	−0.146694	−	0.0964819i	−0.00948882	−	0.00624090i	0.544756	−	0.838595i	$-0.316622\pi$
$239$	−0.146694	−	0.0964819i	−0.00948882	−	0.00624090i	−0.554245	+	0.832354i	$0.686993\pi$
$240$		0			0
$241$	−5.54360	+	18.5169i	−0.357095	+	1.19278i	0.571161	+	0.820838i	$0.306493\pi$
$241$	−5.54360	+	18.5169i	−0.357095	+	1.19278i	−0.928256	+	0.371942i	$0.878692\pi$
$242$	−4.84915			−0.311715
$243$		0			0
$244$	5.16534			0.330677
$245$	1.23214	−	4.11565i	0.0787188	−	0.262939i
$246$		0			0
$247$	10.3693	+	6.82000i	0.659783	+	0.433946i
$248$	−3.83722	+	8.89567i	−0.243664	+	0.564876i
$249$		0			0
$250$	−0.235820	−	4.04888i	−0.0149146	−	0.256073i
$251$	18.5138	−	15.5349i	1.16858	−	0.980554i	0.168592	−	0.985686i	$-0.446078\pi$
$251$	18.5138	−	15.5349i	1.16858	−	0.980554i	0.999987	+	0.00513137i	$0.00163337\pi$
$252$		0			0
$253$	−25.0962	−	21.0582i	−1.57778	−	1.32392i
$254$	−1.15437	+	1.55058i	−0.0724315	+	0.0972924i
$255$		0			0
$256$	−3.93115	+	4.16677i	−0.245697	+	0.260423i
$257$	−13.3227	−	3.15754i	−0.831049	−	0.196962i	−0.206994	−	0.978342i	$-0.566368\pi$
$257$	−13.3227	−	3.15754i	−0.831049	−	0.196962i	−0.624055	+	0.781380i	$0.714516\pi$
$258$		0			0
$259$	−0.374484	−	0.868152i	−0.0232693	−	0.0539443i
$260$	−1.42213	+	8.06530i	−0.0881968	+	0.500189i
$261$		0			0
$262$	0.765846	+	4.34333i	0.0473141	+	0.268332i
$263$	12.1331	−	7.98009i	0.748162	−	0.492074i	−0.117270	−	0.993100i	$-0.537414\pi$
$263$	12.1331	−	7.98009i	0.748162	−	0.492074i	0.865432	+	0.501026i	$0.167044\pi$
$264$		0			0
$265$	−4.51799	−	6.06872i	−0.277538	−	0.372798i
$266$	−0.151710	+	2.60476i	−0.00930193	+	0.159708i
$267$		0			0
$268$	−9.22032	−	9.77297i	−0.563221	−	0.596979i
$269$	0.0908847	+	0.157417i	0.00554134	+	0.00959788i	0.868783	−	0.495193i	$-0.164903\pi$
$269$	0.0908847	+	0.157417i	0.00554134	+	0.00959788i	−0.863241	+	0.504791i	$0.831569\pi$
$270$		0			0
$271$	−10.1446	+	17.5709i	−0.616239	+	1.06736i	0.373927	+	0.927458i	$0.378011\pi$
$271$	−10.1446	+	17.5709i	−0.616239	+	1.06736i	−0.990166	+	0.139899i	$0.955322\pi$
$272$	1.28964	−	0.305650i	0.0781958	−	0.0185327i
$273$		0			0
$274$	−1.67561	+	0.841522i	−0.101227	+	0.0508382i
$275$	16.2637	−	1.90095i	0.980738	−	0.114632i
$276$		0			0
$277$	−9.95402	−	4.99910i	−0.598079	−	0.300367i	0.123885	−	0.992297i	$-0.460464\pi$
$277$	−9.95402	−	4.99910i	−0.598079	−	0.300367i	−0.721965	+	0.691930i	$0.756761\pi$
$278$	5.98603	+	2.17874i	0.359018	+	0.130672i
$279$		0			0
$280$	−3.36063	+	1.22317i	−0.200836	+	0.0730983i
$281$	−1.98964	−	0.232555i	−0.118692	−	0.0138731i	0.0565396	−	0.998400i	$-0.481993\pi$
$281$	−1.98964	−	0.232555i	−0.118692	−	0.0138731i	−0.175231	+	0.984527i	$0.556067\pi$
$282$		0			0
$283$	−0.656114	−	2.19157i	−0.0390020	−	0.130276i	0.936271	−	0.351277i	$-0.114253\pi$
$283$	−0.656114	−	2.19157i	−0.0390020	−	0.130276i	−0.975273	+	0.221002i	$0.929067\pi$
$284$	−8.33818	−	27.8514i	−0.494780	−	1.65268i
$285$		0			0
$286$	6.31049	+	0.737591i	0.373147	+	0.0436147i
$287$	10.8968	−	3.96612i	0.643219	−	0.234112i
$288$		0			0
$289$	15.8096	+	5.75421i	0.929974	+	0.338483i
$290$	2.17853	+	1.09410i	0.127927	+	0.0642476i
$291$		0			0
$292$	−12.1411	+	1.41909i	−0.710502	+	0.0830458i
$293$	4.48342	−	2.25166i	0.261924	−	0.131543i	−0.312991	−	0.949756i	$-0.601331\pi$
$293$	4.48342	−	2.25166i	0.261924	−	0.131543i	0.574916	+	0.818213i	$0.305035\pi$
$294$		0			0
$295$	7.03109	−	1.66640i	0.409366	−	0.0970216i
$296$	0.361248	−	0.625699i	0.0209971	−	0.0363680i
$297$		0			0
$298$	3.29840	+	5.71300i	0.191071	+	0.330945i
$299$	15.8480	+	16.7979i	0.916513	+	0.971447i
$300$		0			0
$301$	1.28852	−	22.1230i	0.0742691	−	1.27515i
$302$	−1.45922	−	1.96007i	−0.0839687	−	0.112789i
$303$		0			0
$304$	9.52846	−	6.26697i	0.546495	−	0.359435i
$305$	−0.619464	−	3.51316i	−0.0354704	−	0.201163i
$306$		0			0
$307$	3.72532	−	21.1273i	0.212615	−	1.20580i	−0.672382	−	0.740204i	$-0.734729\pi$
$307$	3.72532	−	21.1273i	0.212615	−	1.20580i	0.884997	−	0.465596i	$-0.154160\pi$
$308$	−6.85556	−	15.8930i	−0.390632	−	0.905586i
$309$		0			0
$310$	3.13431	+	0.742845i	0.178017	+	0.0421908i
$311$	8.26246	−	8.75770i	0.468521	−	0.496603i	−0.449420	−	0.893321i	$-0.648369\pi$
$311$	8.26246	−	8.75770i	0.468521	−	0.496603i	0.917941	+	0.396717i	$0.129851\pi$
$312$		0			0
$313$	5.56046	−	7.46899i	0.314296	−	0.422172i	−0.616703	−	0.787196i	$-0.711532\pi$
$313$	5.56046	−	7.46899i	0.314296	−	0.422172i	0.930998	+	0.365024i	$0.118939\pi$
$314$	−3.70327	−	3.10741i	−0.208988	−	0.175361i
$315$		0			0
$316$	−5.43668	+	4.56191i	−0.305837	+	0.256628i
$317$	−0.952314	−	16.3506i	−0.0534873	−	0.918341i	−0.913187	−	0.407541i	$-0.866386\pi$
$317$	−0.952314	−	16.3506i	−0.0534873	−	0.918341i	0.859700	−	0.510800i	$-0.170651\pi$
$318$		0			0
$319$	−9.70697	+	22.5033i	−0.543486	+	1.25994i
$320$	5.10352	+	3.35663i	0.285295	+	0.187642i
$321$		0			0
$322$	−1.39243	+	4.65105i	−0.0775973	+	0.259193i
$323$	−1.51290			−0.0841803
$324$		0			0
$325$	−11.5428			−0.640277
$326$	−0.0651231	+	0.217526i	−0.00360683	+	0.0120477i
$327$		0			0
$328$	7.40351	+	4.86937i	0.408791	+	0.268866i
$329$	4.58963	−	10.6400i	0.253034	−	0.586600i
$330$		0			0
$331$	0.298222	+	5.12027i	0.0163918	+	0.281436i	0.996537	+	0.0831535i	$0.0264992\pi$
$331$	0.298222	+	5.12027i	0.0163918	+	0.281436i	−0.980145	+	0.198282i	$0.936464\pi$
$332$	6.89976	−	5.78959i	0.378673	−	0.317745i
$333$		0			0
$334$	0.879884	+	0.738310i	0.0481451	+	0.0403985i
$335$	−5.54123	+	7.44316i	−0.302750	+	0.406663i
$336$		0			0
$337$	−8.59479	+	9.10995i	−0.468188	+	0.496251i	−0.917838	−	0.396954i	$-0.870067\pi$
$337$	−8.59479	+	9.10995i	−0.468188	+	0.496251i	0.449650	+	0.893205i	$0.351549\pi$
$338$	0.430189	+	0.101957i	0.0233992	+	0.00554571i
$339$		0			0
$340$	−0.395416	−	0.916677i	−0.0214444	−	0.0497138i
$341$	−5.62311	+	31.8903i	−0.304509	+	1.72695i
$342$		0			0
$343$	−3.43362	−	19.4730i	−0.185398	−	1.05144i
$344$	14.1483	−	9.30549i	0.762826	−	0.501718i
$345$		0			0
$346$	2.18254	+	2.93166i	0.117334	+	0.157607i
$347$	0.818471	−	14.0526i	0.0439378	−	0.754383i	−0.902339	−	0.431026i	$-0.858152\pi$
$347$	0.818471	−	14.0526i	0.0439378	−	0.754383i	0.946277	−	0.323357i	$-0.104811\pi$
$348$		0			0
$349$	10.5671	+	11.2004i	0.565642	+	0.599546i	0.945549	−	0.325479i	$-0.105526\pi$
$349$	10.5671	+	11.2004i	0.565642	+	0.599546i	−0.379907	+	0.925025i	$0.624044\pi$
$350$	−1.21331	−	2.10152i	−0.0648544	−	0.112331i
$351$		0			0
$352$	10.0427	−	17.3945i	0.535278	−	0.927129i
$353$	32.6811	−	7.74556i	1.73944	−	0.412254i	0.766301	−	0.642482i	$-0.222095\pi$
$353$	32.6811	−	7.74556i	1.73944	−	0.412254i	0.973137	+	0.230227i	$0.0739469\pi$
$354$		0			0
$355$	−17.9429	+	9.01128i	−0.952312	+	0.478269i
$356$	−19.2043	+	2.24466i	−1.01782	+	0.118967i
$357$		0			0
$358$	8.73139	+	4.38507i	0.461469	+	0.231758i
$359$	11.6368	+	4.23546i	0.614168	+	0.223539i	0.630326	−	0.776330i	$-0.282921\pi$
$359$	11.6368	+	4.23546i	0.614168	+	0.223539i	−0.0161577	+	0.999869i	$0.505143\pi$
$360$		0			0
$361$	5.62081	−	2.04581i	0.295832	−	0.107674i
$362$	0.335289	+	0.0391897i	0.0176224	+	0.00205976i
$363$		0			0
$364$	3.49936	+	11.6887i	0.183416	+	0.612653i
$365$	2.42122	+	8.08745i	0.126733	+	0.423316i
$366$		0			0
$367$	−28.5035	−	3.33158i	−1.48787	−	0.173907i	−0.667015	−	0.745044i	$-0.732428\pi$
$367$	−28.5035	−	3.33158i	−1.48787	−	0.173907i	−0.820855	+	0.571137i	$0.806502\pi$
$368$	19.9414	−	7.25809i	1.03952	−	0.378354i
$369$		0			0
$370$	−0.225734	−	0.0821603i	−0.0117353	−	0.00427131i
$371$	−10.0728	−	5.05875i	−0.522953	−	0.262637i
$372$		0			0
$373$	−18.8589	+	2.20429i	−0.976476	+	0.114134i	−0.589337	−	0.807888i	$-0.700611\pi$
$373$	−18.8589	+	2.20429i	−0.976476	+	0.114134i	−0.387139	+	0.922021i	$0.626537\pi$
$374$	−0.692104	+	0.347587i	−0.0357878	+	0.0179733i
$375$		0			0
$376$	8.61612	−	2.04206i	0.444343	−	0.105311i
$377$	8.63804	−	14.9615i	0.444882	−	0.770557i
$378$		0			0
$379$	−9.40390	−	16.2880i	−0.483046	−	0.836660i	0.516764	−	0.856128i	$-0.327136\pi$
$379$	−9.40390	−	16.2880i	−0.483046	−	0.836660i	−0.999810	+	0.0194673i	$0.993803\pi$
$380$	−5.89517	−	6.24852i	−0.302416	−	0.320542i
$381$		0			0
$382$	−0.177712	+	3.05120i	−0.00909254	+	0.156113i
$383$	3.97760	+	5.34284i	0.203246	+	0.273006i	0.892046	−	0.451945i	$-0.149270\pi$
$383$	3.97760	+	5.34284i	0.203246	+	0.273006i	−0.688800	+	0.724951i	$0.741862\pi$
$384$		0			0
$385$	−9.98729	+	6.56875i	−0.509000	+	0.334774i
$386$	−0.0128038	−	0.0726138i	−0.000651695	−	0.00369595i
$387$		0			0
$388$	0.697536	−	3.95592i	0.0354120	−	0.200832i
$389$	0.346443	+	0.803144i	0.0175653	+	0.0407210i	0.926773	−	0.375622i	$-0.122571\pi$
$389$	0.346443	+	0.803144i	0.0175653	+	0.0407210i	−0.909208	+	0.416343i	$0.863312\pi$
$390$		0			0
$391$	−2.73925	−	0.649215i	−0.138530	−	0.0328322i
$392$	3.35640	−	3.55757i	0.169524	−	0.179685i
$393$		0			0
$394$	−2.60763	+	3.50266i	−0.131371	+	0.176461i
$395$	3.75475	+	3.15061i	0.188922	+	0.158524i
$396$		0			0
$397$	26.1379	−	21.9323i	1.31182	−	1.10075i	0.323854	−	0.946107i	$-0.395021\pi$
$397$	26.1379	−	21.9323i	1.31182	−	1.10075i	0.987970	−	0.154644i	$-0.0494231\pi$
$398$	0.0387012	+	0.664474i	0.00193992	+	0.0333071i
$399$		0			0
$400$	−4.20113	+	9.73930i	−0.210056	+	0.486965i
$401$	3.50874	+	2.30773i	0.175218	+	0.115243i	0.634089	−	0.773260i	$-0.281375\pi$
$401$	3.50874	+	2.30773i	0.175218	+	0.115243i	−0.458871	+	0.888503i	$0.651746\pi$
$402$		0			0
$403$	6.54689	−	21.8681i	0.326124	−	1.08933i
$404$	−30.3060			−1.50778
$405$		0			0
$406$	3.63194			0.180250
$407$	0.692615	−	2.31350i	0.0343317	−	0.114676i
$408$		0			0
$409$	−18.1139	−	11.9137i	−0.895672	−	0.589093i	0.0160629	−	0.999871i	$-0.494887\pi$
$409$	−18.1139	−	11.9137i	−0.895672	−	0.589093i	−0.911735	+	0.410778i	$0.865257\pi$
$410$	1.16696	−	2.70532i	0.0576321	−	0.133606i
$411$		0			0
$412$	1.95059	+	33.4903i	0.0960986	+	1.64995i
$413$	8.24668	−	6.91978i	0.405792	−	0.340500i
$414$		0			0
$415$	−4.76520	−	3.99848i	−0.233915	−	0.196278i
$416$	−8.45502	+	11.3571i	−0.414541	+	0.556826i
$417$		0			0
$418$	−4.57338	+	4.84750i	−0.223691	+	0.237099i
$419$	−4.07282	−	0.965277i	−0.198971	−	0.0471569i	0.129922	−	0.991524i	$-0.458527\pi$
$419$	−4.07282	−	0.965277i	−0.198971	−	0.0471569i	−0.328893	+	0.944367i	$0.606675\pi$
$420$		0			0
$421$	1.96853	+	4.56357i	0.0959403	+	0.222415i	0.959427	−	0.281957i	$-0.0909835\pi$
$421$	1.96853	+	4.56357i	0.0959403	+	0.222415i	−0.863487	+	0.504372i	$0.831724\pi$
$422$	0.235094	−	1.33328i	0.0114442	−	0.0649033i
$423$		0			0
$424$	−1.49570	−	8.48255i	−0.0726377	−	0.411949i
$425$	1.17558	−	0.773191i	0.0570240	−	0.0375053i
$426$		0			0
$427$	−3.17374	−	4.26307i	−0.153588	−	0.206304i
$428$	−1.74160	+	29.9022i	−0.0841836	+	1.44538i
$429$		0			0
$430$	−3.86382	−	4.09541i	−0.186330	−	0.197498i
$431$	−13.2418	−	22.9355i	−0.637837	−	1.10477i	−0.985907	−	0.167297i	$-0.946496\pi$
$431$	−13.2418	−	22.9355i	−0.637837	−	1.10477i	0.348070	−	0.937469i	$-0.386837\pi$
$432$		0			0
$433$	−10.6919	+	18.5189i	−0.513820	+	0.889962i	0.486052	+	0.873930i	$0.338437\pi$
$433$	−10.6919	+	18.5189i	−0.513820	+	0.889962i	−0.999871	+	0.0160319i	$0.994897\pi$
$434$	4.66957	−	1.10671i	0.224147	−	0.0531237i
$435$		0			0
$436$	13.4122	−	6.73586i	0.642328	−	0.322589i
$437$	−24.0603	+	2.81224i	−1.15096	+	0.134528i
$438$		0			0
$439$	28.8729	+	14.5005i	1.37803	+	0.692072i	0.974811	−	0.223031i	$-0.0715953\pi$
$439$	28.8729	+	14.5005i	1.37803	+	0.692072i	0.403218	+	0.915104i	$0.367892\pi$
$440$	−8.58376	−	3.12423i	−0.409215	−	0.148942i
$441$		0			0
$442$	0.513029	−	0.186727i	0.0244023	−	0.00888171i
$443$	32.2960	+	3.77486i	1.53443	+	0.179349i	0.840944	−	0.541122i	$-0.182000\pi$
$443$	32.2960	+	3.77486i	1.53443	+	0.179349i	0.693485	+	0.720471i	$0.256074\pi$
$444$		0			0
$445$	3.82980	+	12.7924i	0.181550	+	0.606418i
$446$	−0.712288	−	2.37921i	−0.0337278	−	0.112659i
$447$		0			0
$448$	9.03895	+	1.05650i	0.427050	+	0.0499150i
$449$	15.0197	−	5.46673i	0.708825	−	0.257991i	0.0376508	−	0.999291i	$-0.488013\pi$
$449$	15.0197	−	5.46673i	0.708825	−	0.257991i	0.671174	+	0.741300i	$0.265790\pi$
$450$		0			0
$451$	27.8328	+	10.1303i	1.31059	+	0.477017i
$452$	2.85512	+	1.43390i	0.134294	+	0.0674448i
$453$		0			0
$454$	−3.05594	+	0.357188i	−0.143422	+	0.0167637i
$455$	7.53027	−	3.78185i	0.353025	−	0.177296i
$456$		0			0
$457$	18.7712	−	4.44886i	0.878081	−	0.208109i	0.233234	−	0.972421i	$-0.425069\pi$
$457$	18.7712	−	4.44886i	0.878081	−	0.208109i	0.644847	+	0.764312i	$0.276921\pi$
$458$	1.48283	−	2.56834i	0.0692883	−	0.120011i
$459$		0			0
$460$	−7.99240	−	13.8432i	−0.372648	−	0.645445i
$461$	−10.1699	−	10.7794i	−0.473658	−	0.502048i	0.445856	−	0.895105i	$-0.352899\pi$
$461$	−10.1699	−	10.7794i	−0.473658	−	0.502048i	−0.919514	+	0.393056i	$0.871418\pi$
$462$		0			0
$463$	−0.161028	+	2.76474i	−0.00748359	+	0.128488i	0.992497	+	0.122268i	$0.0390169\pi$
$463$	−0.161028	+	2.76474i	−0.00748359	+	0.128488i	−0.999981	+	0.00621987i	$0.998020\pi$
$464$	−9.47999	−	12.7338i	−0.440098	−	0.591154i
$465$		0			0
$466$	−8.17236	+	5.37504i	−0.378577	+	0.248994i
$467$	3.42252	+	19.4101i	0.158375	+	0.898191i	0.955635	+	0.294554i	$0.0951712\pi$
$467$	3.42252	+	19.4101i	0.158375	+	0.898191i	−0.797259	+	0.603637i	$0.793718\pi$
$468$		0			0
$469$	−2.40061	+	13.6145i	−0.110850	+	0.628661i
$470$	−1.16610	−	2.70333i	−0.0537884	−	0.124695i
$471$		0			0
$472$	8.00464	+	1.89714i	0.368444	+	0.0873227i
$473$	38.8432	−	41.1713i	1.78601	−	1.89306i
$474$		0			0
$475$	7.23019	−	9.71183i	0.331744	−	0.445609i
$476$	−1.13936	−	0.956036i	−0.0522224	−	0.0438198i
$477$		0			0
$478$	−0.0509120	+	0.0427202i	−0.00232866	+	0.00195398i
$479$	−1.08385	−	18.6089i	−0.0495222	−	0.850263i	−0.928023	−	0.372522i	$-0.878493\pi$
$479$	−1.08385	−	18.6089i	−0.0495222	−	0.850263i	0.878501	−	0.477740i	$-0.158544\pi$
$480$		0			0
$481$	−0.674271	+	1.56314i	−0.0307441	+	0.0712729i
$482$	6.11284	+	4.02048i	0.278432	+	0.183128i
$483$		0			0
$484$	6.82183	−	22.7865i	0.310083	−	1.03575i
$485$	−2.77424			−0.125972
$486$		0			0
$487$	−5.34343			−0.242134			−0.121067	−	0.992644i	$-0.538632\pi$
$487$	−5.34343			−0.242134			−0.121067	+	0.992644i	$0.538632\pi$
$488$	1.16479	−	3.89068i	0.0527277	−	0.176123i
$489$		0			0
$490$	−1.35866	−	0.893607i	−0.0613782	−	0.0403691i
$491$	1.46595	−	3.39844i	0.0661572	−	0.153370i	−0.881930	−	0.471381i	$-0.843756\pi$
$491$	1.46595	−	3.39844i	0.0661572	−	0.153370i	0.948087	+	0.318011i	$0.103015\pi$
$492$		0			0
$493$	0.122450	+	2.10238i	0.00551487	+	0.0946866i
$494$	3.59880	−	3.01975i	0.161918	−	0.135865i
$495$		0			0
$496$	−16.0686	−	13.4832i	−0.721501	−	0.605411i
$497$	−17.8632	+	23.9944i	−0.801274	+	1.07630i
$498$		0			0
$499$	19.1808	−	20.3304i	0.858650	−	0.910116i	−0.138121	−	0.990415i	$-0.544106\pi$
$499$	19.1808	−	20.3304i	0.858650	−	0.910116i	0.996771	+	0.0802996i	$0.0255877\pi$
$500$	19.3577	+	4.58786i	0.865704	+	0.205176i
$501$		0			0
$502$	−3.62342	−	8.40002i	−0.161721	−	0.374911i
$503$	−1.72317	+	9.77258i	−0.0768323	+	0.435738i	0.921990	+	0.387214i	$0.126563\pi$
$503$	−1.72317	+	9.77258i	−0.0768323	+	0.435738i	−0.998822	+	0.0485234i	$0.984548\pi$
$504$		0			0
$505$	3.63452	+	20.6124i	0.161734	+	0.917239i
$506$	−10.3607	+	6.81432i	−0.460588	+	0.302933i
$507$		0			0
$508$	−5.66234	−	7.60584i	−0.251226	−	0.337455i
$509$	0.00164498	−	0.0282431i	7.29123e−5	−	0.00125186i	−0.998272	−	0.0587707i	$-0.981282\pi$
$509$	0.00164498	−	0.0282431i	7.29123e−5	−	0.00125186i	0.998344	+	0.0575189i	$0.0183189\pi$
$510$		0			0
$511$	8.63103	+	9.14836i	0.381814	+	0.404700i
$512$	11.1197	+	19.2599i	0.491426	+	0.851176i
$513$		0			0
$514$	−2.59134	+	4.48834i	−0.114299	+	0.197972i
$515$	22.5442	−	5.34307i	0.993416	−	0.235444i
$516$		0			0
$517$	26.4491	−	13.2832i	1.16323	−	0.584196i
$518$	−0.355467	+	0.0415481i	−0.0156183	+	0.00182552i
$519$		0			0
$520$	5.75433	+	2.88993i	0.252344	+	0.126732i
$521$	−2.11604	−	0.770177i	−0.0927056	−	0.0337421i	0.295251	−	0.955420i	$-0.404597\pi$
$521$	−2.11604	−	0.770177i	−0.0927056	−	0.0337421i	−0.387957	+	0.921678i	$0.626819\pi$
$522$		0			0
$523$	−11.5433	+	4.20142i	−0.504753	+	0.183715i	−0.581831	−	0.813310i	$-0.697663\pi$
$523$	−11.5433	+	4.20142i	−0.504753	+	0.183715i	0.0770775	+	0.997025i	$0.475441\pi$
$524$	−21.4870	−	2.51147i	−0.938665	−	0.109714i
$525$		0			0
$526$	−1.57656	−	5.26609i	−0.0687415	−	0.229613i
$527$	0.798063	+	2.66572i	0.0347642	+	0.116120i
$528$		0			0
$529$	−21.9257	−	2.56274i	−0.953290	−	0.111424i
$530$	−2.69114	+	0.979495i	−0.116896	+	0.0425465i
$531$		0			0
$532$	−12.0265	−	4.37730i	−0.521416	−	0.189780i
$533$	−18.6584	−	9.37059i	−0.808184	−	0.405885i
$534$		0			0
$535$	20.5466	−	2.40155i	0.888305	−	0.103828i
$536$	−9.44049	+	4.74119i	−0.407767	+	0.204788i
$537$		0			0
$538$	0.0669496	−	0.0158674i	0.00288640	−	0.000684090i
$539$	8.17409	−	14.1579i	0.352083	−	0.609826i
$540$		0			0
$541$	19.8474	+	34.3766i	0.853304	+	1.47797i	0.878209	+	0.478277i	$0.158738\pi$
$541$	19.8474	+	34.3766i	0.853304	+	1.47797i	−0.0249047	+	0.999690i	$0.507928\pi$
$542$	5.27030	+	5.58619i	0.226379	+	0.239948i
$543$		0			0
$544$	0.100355	−	1.72303i	0.00430268	−	0.0738741i
$545$	−6.18982	−	8.31438i	−0.265143	−	0.356149i
$546$		0			0
$547$	−6.79505	+	4.46918i	−0.290536	+	0.191088i	−0.686407	−	0.727218i	$-0.740813\pi$
$547$	−6.79505	+	4.46918i	−0.290536	+	0.191088i	0.395871	+	0.918306i	$0.370443\pi$
$548$	−1.59711	−	9.05767i	−0.0682252	−	0.386924i
$549$		0			0
$550$	1.07629	−	6.10396i	0.0458933	−	0.260274i
$551$	7.17758	+	16.6395i	0.305775	+	0.708866i
$552$		0			0
$553$	7.10550	+	1.68403i	0.302157	+	0.0716124i
$554$	−2.89342	+	3.06684i	−0.122930	+	0.130298i
$555$		0			0
$556$	−18.6592	+	25.0637i	−0.791328	+	1.06294i
$557$	−16.2629	−	13.6462i	−0.689081	−	0.578207i	0.229563	−	0.973294i	$-0.426270\pi$
$557$	−16.2629	−	13.6462i	−0.689081	−	0.578207i	−0.918644	+	0.395086i	$0.870715\pi$
$558$		0			0
$559$	−30.5658	+	25.6477i	−1.29279	+	1.08478i
$560$	−0.450232	−	7.73018i	−0.0190258	−	0.326660i
$561$		0			0
$562$	−0.300329	+	0.696241i	−0.0126686	+	0.0293692i
$563$	37.7470	+	24.8266i	1.59085	+	1.04632i	0.963547	+	0.267539i	$0.0862105\pi$
$563$	37.7470	+	24.8266i	1.59085	+	1.04632i	0.627300	+	0.778777i	$0.284160\pi$
$564$		0			0
$565$	0.632844	−	2.11385i	0.0266240	−	0.0889302i
$566$	−0.865945			−0.0363984
$567$		0			0
$568$	−22.8588			−0.959134
$569$	−1.64533	+	5.49580i	−0.0689760	+	0.230396i	−0.985526	−	0.169524i	$-0.945777\pi$
$569$	−1.64533	+	5.49580i	−0.0689760	+	0.230396i	0.916550	+	0.399920i	$0.130962\pi$
$570$		0			0
$571$	−36.2309	−	23.8295i	−1.51622	−	0.997232i	−0.989068	−	0.147458i	$-0.952891\pi$
$571$	−36.2309	−	23.8295i	−1.51622	−	0.997232i	−0.527149	−	0.849773i	$-0.676739\pi$
$572$	−12.3437	+	28.6158i	−0.516114	+	1.19649i
$573$		0			0
$574$	−0.255223	−	4.38201i	−0.0106528	−	0.182901i
$575$	17.2584	−	14.4816i	0.719727	−	0.603923i
$576$		0			0
$577$	10.1857	+	8.54680i	0.424035	+	0.355808i	0.829696	−	0.558216i	$-0.188514\pi$
$577$	10.1857	+	8.54680i	0.424035	+	0.355808i	−0.405660	+	0.914024i	$0.632958\pi$
$578$	3.80293	−	5.10822i	0.158181	−	0.212474i
$579$		0			0
$580$	−8.20601	+	8.69787i	−0.340736	+	0.361159i
$581$	−9.01769	−	2.13723i	−0.374117	−	0.0886673i
$582$		0			0
$583$	−11.4033	−	26.4358i	−0.472276	−	1.09486i
$584$	−1.66894	+	9.46501i	−0.0690611	+	0.391665i
$585$		0			0
$586$	−0.329773	−	1.87024i	−0.0136228	−	0.0772588i
$587$	−10.3345	+	6.79710i	−0.426550	+	0.280546i	−0.744579	−	0.667535i	$-0.767350\pi$
$587$	−10.3345	+	6.79710i	−0.426550	+	0.280546i	0.318029	+	0.948081i	$0.396979\pi$
$588$		0			0
$589$	14.2985	+	19.2062i	0.589160	+	0.791379i
$590$	0.159036	−	2.73054i	0.00654741	−	0.112415i
$591$		0			0
$592$	1.07350	+	1.13784i	0.0441206	+	0.0467651i
$593$	0.572367	+	0.991369i	0.0235043	+	0.0407106i	0.877538	−	0.479507i	$-0.159184\pi$
$593$	0.572367	+	0.991369i	0.0235043	+	0.0407106i	−0.854034	+	0.520217i	$0.825851\pi$
$594$		0			0
$595$	−0.513599	+	0.889579i	−0.0210555	+	0.0364692i
$596$	−31.4860	+	7.46233i	−1.28972	+	0.305669i
$597$		0			0
$598$	7.81179	−	3.92323i	0.319448	−	0.160433i
$599$	−2.40955	+	0.281636i	−0.0984514	+	0.0115073i	−0.165176	−	0.986264i	$-0.552819\pi$
$599$	−2.40955	+	0.281636i	−0.0984514	+	0.0115073i	0.0667245	+	0.997771i	$0.478745\pi$
$600$		0			0
$601$	−35.0541	−	17.6048i	−1.42988	−	0.718115i	−0.445687	−	0.895189i	$-0.647041\pi$
$601$	−35.0541	−	17.6048i	−1.42988	−	0.718115i	−0.984198	+	0.177074i	$0.943337\pi$
$602$	−7.88244	−	2.86897i	−0.321264	−	0.116931i
$603$		0			0
$604$	11.2634	−	4.09953i	0.458300	−	0.166808i
$605$	−16.3162	−	1.90709i	−0.663346	−	0.0775341i
$606$		0			0
$607$	2.03130	+	6.78502i	0.0824480	+	0.275396i	0.989266	−	0.146127i	$-0.0466809\pi$
$607$	2.03130	+	6.78502i	0.0824480	+	0.275396i	−0.906818	+	0.421523i	$0.861496\pi$
$608$	−4.25950	−	14.2277i	−0.172746	−	0.577011i
$609$		0			0
$610$	−1.34120	−	0.156764i	−0.0543037	−	0.00634719i
$611$	−19.6057	+	7.13588i	−0.793161	+	0.288687i
$612$		0			0
$613$	19.4482	+	7.07855i	0.785503	+	0.285900i	0.703466	−	0.710729i	$-0.251635\pi$
$613$	19.4482	+	7.07855i	0.785503	+	0.285900i	0.0820378	+	0.996629i	$0.473857\pi$
$614$	−7.25683	−	3.64452i	−0.292862	−	0.147081i
$615$		0			0
$616$	−13.5170	+	1.57991i	−0.544615	+	0.0636564i
$617$	−21.3037	+	10.6991i	−0.857653	+	0.430730i	−0.822576	−	0.568655i	$-0.807464\pi$
$617$	−21.3037	+	10.6991i	−0.857653	+	0.430730i	−0.0350771	+	0.999385i	$0.511168\pi$
$618$		0			0
$619$	−0.647679	+	0.153503i	−0.0260324	+	0.00616980i	−0.243611	−	0.969873i	$-0.578332\pi$
$619$	−0.647679	+	0.153503i	−0.0260324	+	0.00616980i	0.217579	+	0.976043i	$0.430184\pi$
$620$	−7.90007	+	13.6833i	−0.317274	+	0.549535i
$621$		0			0
$622$	−2.27875	−	3.94691i	−0.0913696	−	0.158257i
$623$	13.6522	+	14.4705i	0.546965	+	0.579749i
$624$		0			0
$625$	−0.176699	+	3.03381i	−0.00706798	+	0.121352i
$626$	−2.10477	−	2.82720i	−0.0841236	−	0.112998i
$627$		0			0
$628$	19.8118	−	13.0304i	0.790575	−	0.519969i
$629$	−0.0360350	−	0.204365i	−0.00143681	−	0.00814855i
$630$		0			0
$631$	4.06193	−	23.0363i	0.161703	−	0.917062i	−0.790696	−	0.612209i	$-0.790281\pi$
$631$	4.06193	−	23.0363i	0.161703	−	0.917062i	0.952399	−	0.304854i	$-0.0986076\pi$
$632$	2.21018	+	5.12378i	0.0879164	+	0.203813i
$633$		0			0
$634$	−6.03249	−	1.42973i	−0.239581	−	0.0567817i
$635$	−4.49397	+	4.76333i	−0.178338	+	0.189027i
$636$		0			0
$637$	−6.88182	+	9.24388i	−0.272668	+	0.366256i
$638$	7.10640	+	5.96298i	0.281345	+	0.236077i
$639$		0			0
$640$	9.85797	−	8.27182i	0.389670	−	0.326972i
$641$	−0.414079	−	7.10947i	−0.0163552	−	0.280807i	−0.996563	−	0.0828367i	$-0.973602\pi$
$641$	−0.414079	−	7.10947i	−0.0163552	−	0.280807i	0.980208	−	0.197970i	$-0.0634350\pi$
$642$		0			0
$643$	6.12929	−	14.2093i	0.241716	−	0.560360i	−0.753568	−	0.657370i	$-0.771669\pi$
$643$	6.12929	−	14.2093i	0.241716	−	0.560360i	0.995283	+	0.0970103i	$0.0309280\pi$
$644$	−19.8968	−	13.0863i	−0.784042	−	0.515673i
$645$		0			0
$646$	−0.164244	+	0.548614i	−0.00646210	+	0.0215849i
$647$	−15.3916			−0.605107			−0.302554	−	0.953132i	$-0.597839\pi$
$647$	−15.3916			−0.605107			−0.302554	+	0.953132i	$0.597839\pi$
$648$		0			0
$649$	27.4968			1.07934
$650$	−1.25311	+	4.18567i	−0.0491509	+	0.164176i
$651$		0			0
$652$	−0.930556	−	0.612036i	−0.0364434	−	0.0239692i
$653$	−0.487882	+	1.13104i	−0.0190923	+	0.0442610i	−0.927496	−	0.373834i	$-0.878043\pi$
$653$	−0.487882	+	1.13104i	−0.0190923	+	0.0442610i	0.908403	+	0.418095i	$0.137302\pi$
$654$		0			0
$655$	0.868723	+	14.9154i	0.0339438	+	0.582793i
$656$	−14.6975	+	12.3326i	−0.573839	+	0.481508i
$657$		0			0
$658$	−3.36003	−	2.81940i	−0.130988	−	0.109912i
$659$	4.12166	−	5.53635i	0.160557	−	0.215665i	−0.714563	−	0.699571i	$-0.753375\pi$
$659$	4.12166	−	5.53635i	0.160557	−	0.215665i	0.875120	+	0.483905i	$0.160782\pi$
$660$		0			0
$661$	24.6651	−	26.1434i	0.959360	−	1.01686i	−0.0404839	−	0.999180i	$-0.512890\pi$
$661$	24.6651	−	26.1434i	0.959360	−	1.01686i	0.999844	−	0.0176818i	$-0.00562858\pi$
$662$	1.88910	+	0.447726i	0.0734221	+	0.0174014i
$663$		0			0
$664$	−2.80498	−	6.50266i	−0.108854	−	0.252352i
$665$	−1.53487	+	8.70469i	−0.0595198	+	0.337553i
$666$		0			0
$667$	5.85536	+	33.2074i	0.226720	+	1.28579i
$668$	−4.70720	+	3.09598i	−0.182127	+	0.119787i
$669$		0			0
$670$	2.09749	+	2.81742i	0.0810333	+	0.108847i
$671$	0.789313	−	13.5520i	0.0304711	−	0.523168i
$672$		0			0
$673$	−5.96965	−	6.32746i	−0.230113	−	0.243906i	0.602021	−	0.798480i	$-0.294362\pi$
$673$	−5.96965	−	6.32746i	−0.230113	−	0.243906i	−0.832134	+	0.554575i	$0.812881\pi$
$674$	2.37041	+	4.10567i	0.0913047	+	0.158144i
$675$		0			0
$676$	−1.08430	+	1.87806i	−0.0417037	+	0.0722329i
$677$	−0.561618	+	0.133106i	−0.0215847	+	0.00511568i	−0.241394	−	0.970427i	$-0.577605\pi$
$677$	−0.561618	+	0.133106i	−0.0215847	+	0.00511568i	0.219809	+	0.975543i	$0.429456\pi$
$678$		0			0
$679$	−3.69350	+	1.85494i	−0.141743	+	0.0711862i
$680$	−0.779635	+	0.0911263i	−0.0298977	+	0.00349453i
$681$		0			0
$682$	10.9537	+	5.50115i	0.419438	+	0.210650i
$683$	33.8572	+	12.3230i	1.29551	+	0.471528i	0.895532	−	0.444997i	$-0.146795\pi$
$683$	33.8572	+	12.3230i	1.29551	+	0.471528i	0.399979	+	0.916524i	$0.369017\pi$
$684$		0			0
$685$	−5.96895	+	2.17252i	−0.228062	+	0.0830078i
$686$	−7.43412	−	0.868924i	−0.283836	−	0.0331757i
$687$		0			0
$688$	10.5157	+	35.1249i	0.400908	+	1.33913i
$689$	5.82071	+	19.4425i	0.221751	+	0.740701i
$690$		0			0
$691$	14.5788	+	1.70402i	0.554603	+	0.0648238i	0.388778	−	0.921331i	$-0.372897\pi$
$691$	14.5788	+	1.70402i	0.554603	+	0.0648238i	0.165825	+	0.986155i	$0.446971\pi$
$692$	−16.8465	+	6.13164i	−0.640409	+	0.233090i
$693$		0			0
$694$	−5.00694	−	1.82238i	−0.190061	−	0.0691765i
$695$	19.2846	+	9.68509i	0.731507	+	0.367377i
$696$		0			0
$697$	2.52796	−	0.295476i	0.0957534	−	0.0111920i
$698$	5.20872	−	2.61592i	0.197153	−	0.0990139i
$699$		0			0
$700$	11.5821	−	2.74501i	0.437763	−	0.103752i
$701$	−15.3027	+	26.5051i	−0.577976	+	1.00108i	0.417735	+	0.908569i	$0.362824\pi$
$701$	−15.3027	+	26.5051i	−0.577976	+	1.00108i	−0.995711	+	0.0925152i	$0.970509\pi$
$702$		0			0
$703$	−0.892837	−	1.54644i	−0.0336740	−	0.0583250i
$704$	15.9514	+	16.9075i	0.601190	+	0.637225i
$705$		0			0
$706$	0.739212	−	12.6918i	0.0278206	−	0.477662i
$707$	18.6209	+	25.0123i	0.700312	+	0.940682i
$708$		0			0
$709$	−38.5157	+	25.3322i	−1.44649	+	0.951370i	−0.448136	+	0.893965i	$0.647912\pi$
$709$	−38.5157	+	25.3322i	−1.44649	+	0.951370i	−0.998351	+	0.0574044i	$0.981718\pi$
$710$	1.31977	+	7.48480i	0.0495302	+	0.280900i
$711$		0			0
$712$	−2.63986	+	14.9714i	−0.0989329	+	0.561077i
$713$	17.6470	+	40.9104i	0.660886	+	1.53211i
$714$		0			0
$715$	20.9431	+	4.96361i	0.783229	+	0.185629i
$716$	−32.8892	+	34.8605i	−1.22913	+	1.30280i
$717$		0			0
$718$	2.79920	−	3.75997i	0.104465	−	0.140321i
$719$	15.5899	+	13.0815i	0.581404	+	0.487856i	0.885408	−	0.464815i	$-0.153879\pi$
$719$	15.5899	+	13.0815i	0.581404	+	0.487856i	−0.304004	+	0.952671i	$0.598324\pi$
$720$		0			0
$721$	26.4418	−	22.1873i	0.984743	−	0.826298i
$722$	−0.131649	−	2.26033i	−0.00489949	−	0.0841209i
$723$		0			0
$724$	−0.655843	+	1.52042i	−0.0243742	+	0.0565058i
$725$	−14.0811	−	9.26127i	−0.522958	−	0.343955i
$726$		0			0
$727$	6.97074	−	23.2839i	0.258530	−	0.863552i	−0.725903	−	0.687797i	$-0.758578\pi$
$727$	6.97074	−	23.2839i	0.258530	−	0.863552i	0.984434	−	0.175755i	$-0.0562367\pi$
$728$	9.59336			0.355554
$729$		0			0
$730$	3.19555			0.118272
$731$	1.39498	−	4.65956i	0.0515952	−	0.172340i
$732$		0			0
$733$	33.3307	+	21.9219i	1.23110	+	0.809704i	0.987105	−	0.160073i	$-0.0511730\pi$
$733$	33.3307	+	21.9219i	1.23110	+	0.809704i	0.243991	+	0.969778i	$0.421543\pi$
$734$	−4.30251	+	9.97433i	−0.158808	+	0.368159i
$735$		0			0
$736$	−1.60684	−	27.5884i	−0.0592291	−	1.01692i
$737$	−27.0497	+	22.6974i	−0.996389	+	0.836069i
$738$		0			0
$739$	6.20932	+	5.21024i	0.228413	+	0.191662i	0.749811	−	0.661652i	$-0.230145\pi$
$739$	6.20932	+	5.21024i	0.228413	+	0.191662i	−0.521397	+	0.853314i	$0.674589\pi$
$740$	0.703642	−	0.945155i	0.0258664	−	0.0347446i
$741$		0			0
$742$	−2.92794	+	3.10344i	−0.107488	+	0.113931i
$743$	−24.1388	−	5.72099i	−0.885565	−	0.209883i	−0.237427	−	0.971405i	$-0.576304\pi$
$743$	−24.1388	−	5.72099i	−0.885565	−	0.209883i	−0.648138	+	0.761523i	$0.724452\pi$
$744$		0			0
$745$	8.85146	+	20.5200i	0.324293	+	0.751795i
$746$	−1.24804	+	7.07796i	−0.0456938	+	0.259143i
$747$		0			0
$748$	−0.659681	−	3.74124i	−0.0241203	−	0.136793i
$749$	25.7490	−	16.9354i	0.940849	−	0.618806i
$750$		0			0
$751$	−18.9074	−	25.3970i	−0.689940	−	0.926750i	0.309770	−	0.950811i	$-0.399748\pi$
$751$	−18.9074	−	25.3970i	−0.689940	−	0.926750i	−0.999710	+	0.0240611i	$0.992340\pi$
$752$	−1.11476	+	19.1396i	−0.0406510	+	0.697951i
$753$		0			0
$754$	−4.48763	−	4.75661i	−0.163430	−	0.173225i
$755$	−4.13904	−	7.16903i	−0.150635	−	0.260908i
$756$		0			0
$757$	−7.21394	+	12.4949i	−0.262195	+	0.454135i	−0.966825	−	0.255440i	$-0.917780\pi$
$757$	−7.21394	+	12.4949i	−0.262195	+	0.454135i	0.704630	+	0.709575i	$0.251113\pi$
$758$	−6.92733	+	1.64181i	−0.251612	+	0.0596331i
$759$		0			0
$760$	−6.03594	+	3.03136i	−0.218947	+	0.109959i
$761$	−22.1774	+	2.59217i	−0.803930	+	0.0939659i	−0.508126	−	0.861283i	$-0.669662\pi$
$761$	−22.1774	+	2.59217i	−0.803930	+	0.0939659i	−0.295804	+	0.955249i	$0.595587\pi$
$762$		0			0
$763$	−13.8001	−	6.93068i	−0.499598	−	0.250907i
$764$	−14.0878	−	5.12754i	−0.509679	−	0.185508i
$765$		0			0
$766$	2.36925	−	0.862338i	0.0856046	−	0.0311575i
$767$	−19.2522	−	2.25026i	−0.695155	−	0.0812520i
$768$		0			0
$769$	−7.82437	−	26.1352i	−0.282154	−	0.942460i	−0.975155	−	0.221524i	$-0.928897\pi$
$769$	−7.82437	−	26.1352i	−0.282154	−	0.942460i	0.693001	−	0.720937i	$-0.256288\pi$
$770$	1.29774	+	4.33474i	0.0467672	+	0.156213i
$771$		0			0
$772$	0.359230	+	0.0419880i	0.0129290	+	0.00151118i
$773$	7.11832	−	2.59086i	0.256028	−	0.0931867i	−0.210817	−	0.977525i	$-0.567613\pi$
$773$	7.11832	−	2.59086i	0.256028	−	0.0931867i	0.466846	+	0.884339i	$0.345390\pi$
$774$		0			0
$775$	−20.9260	−	7.61646i	−0.751686	−	0.273591i
$776$	−2.82242	−	1.41747i	−0.101319	−	0.0508843i
$777$		0			0
$778$	0.328849	−	0.0384370i	0.0117898	−	0.00137803i
$779$	19.5715	−	9.82917i	0.701222	−	0.352167i
$780$		0			0
$781$	−74.3463	+	17.6204i	−2.66032	+	0.630507i
$782$	−0.532800	+	0.922836i	−0.0190529	+	0.0330006i
$783$		0			0
$784$	5.29489	+	9.17101i	0.189103	+	0.327536i
$785$	−11.2385	−	11.9121i	−0.401118	−	0.425161i
$786$		0			0
$787$	0.465741	−	7.99646i	0.0166019	−	0.285043i	−0.979781	−	0.200071i	$-0.935883\pi$
$787$	0.465741	−	7.99646i	0.0166019	−	0.285043i	0.996383	−	0.0849722i	$-0.0270801\pi$
$788$	−12.7908	−	17.1810i	−0.455654	−	0.612049i
$789$		0			0
$790$	1.55011	−	1.01952i	0.0551503	−	0.0362729i
$791$	−0.570845	−	3.23742i	−0.0202969	−	0.115109i
$792$		0			0
$793$	−1.66170	+	9.42396i	−0.0590087	+	0.334655i
$794$	−5.11557	−	11.8592i	−0.181545	−	0.420868i
$795$		0			0
$796$	−3.17686	−	0.752929i	−0.112601	−	0.0266869i
$797$	−9.37990	+	9.94211i	−0.332253	+	0.352168i	−0.871865	−	0.489746i	$-0.837089\pi$
$797$	−9.37990	+	9.94211i	−0.332253	+	0.352168i	0.539612	+	0.841914i	$0.318571\pi$
$798$		0			0
$799$	1.51876	−	2.04004i	0.0537297	−	0.0721715i
$800$	10.5811	+	8.87856i	0.374097	+	0.313905i
$801$		0			0
$802$	1.21775	−	1.02182i	0.0430003	−	0.0360816i
$803$	1.86790	+	32.0706i	0.0659168	+	1.13175i
$804$		0			0
$805$	−6.51437	+	15.1020i	−0.229601	+	0.532276i
$806$	−7.21914	−	4.74810i	−0.254283	−	0.167245i
$807$		0			0
$808$	−6.83408	+	22.8274i	−0.240422	+	0.803065i
$809$	6.31109			0.221886			0.110943	−	0.993827i	$-0.464613\pi$
$809$	6.31109			0.221886			0.110943	+	0.993827i	$0.464613\pi$
$810$		0			0
$811$	−29.8809			−1.04926			−0.524631	−	0.851330i	$-0.675797\pi$
$811$	−29.8809			−1.04926			−0.524631	+	0.851330i	$0.675797\pi$
$812$	−5.10945	+	17.0668i	−0.179307	+	0.598926i
$813$		0			0
$814$	−0.763735	−	0.502316i	−0.0267689	−	0.0176062i
$815$	−0.304672	+	0.706309i	−0.0106722	+	0.0247409i
$816$		0			0
$817$	−2.43356	−	41.7827i	−0.0851396	−	1.46179i
$818$	−6.28665	+	5.27513i	−0.219808	+	0.184440i
$819$		0			0
$820$	11.0708	+	9.28950i	0.386609	+	0.324403i
$821$	18.9709	−	25.4824i	0.662089	−	0.889340i	−0.336541	−	0.941669i	$-0.609257\pi$
$821$	18.9709	−	25.4824i	0.662089	−	0.889340i	0.998630	+	0.0523287i	$0.0166643\pi$
$822$		0			0
$823$	−17.6566	+	18.7149i	−0.615469	+	0.652359i	−0.957872	−	0.287194i	$-0.907278\pi$
$823$	−17.6566	+	18.7149i	−0.615469	+	0.652359i	0.342404	+	0.939553i	$0.388759\pi$
$824$	25.6657	+	6.08289i	0.894108	+	0.211908i
$825$		0			0
$826$	−1.61400	−	3.74166i	−0.0561581	−	0.130189i
$827$	3.15225	−	17.8773i	0.109615	−	0.621655i	−0.879662	−	0.475600i	$-0.842231\pi$
$827$	3.15225	−	17.8773i	0.109615	−	0.621655i	0.989276	−	0.146056i	$-0.0466578\pi$
$828$		0			0
$829$	−4.93669	−	27.9974i	−0.171458	−	0.972389i	−0.942153	−	0.335184i	$-0.891202\pi$
$829$	−4.93669	−	27.9974i	−0.171458	−	0.972389i	0.770694	−	0.637205i	$-0.219910\pi$
$830$	−1.96726	+	1.29389i	−0.0682846	+	0.0449115i
$831$		0			0
$832$	−9.78487	−	13.1434i	−0.339229	−	0.455664i
$833$	0.0816821	−	1.40243i	0.00283012	−	0.0485912i
$834$		0			0
$835$	2.67022	+	2.83027i	0.0924068	+	0.0979455i
$836$	−16.3449	−	28.3101i	−0.565299	−	0.979127i
$837$		0			0
$838$	−0.792187	+	1.37211i	−0.0273656	+	0.0473987i
$839$	−29.0531	+	6.88571i	−1.00302	+	0.237721i	−0.699137	−	0.714987i	$-0.746432\pi$
$839$	−29.0531	+	6.88571i	−1.00302	+	0.237721i	−0.303886	+	0.952708i	$0.598284\pi$
$840$		0			0
$841$	−3.37348	+	1.69422i	−0.116327	+	0.0584215i
$842$	1.86856	−	0.218404i	0.0643949	−	0.00752669i
$843$		0			0
$844$	5.93447	+	2.98040i	0.204273	+	0.102590i
$845$	1.40738	+	0.512244i	0.0484153	+	0.0176217i
$846$		0			0
$847$	−22.9977	+	8.37050i	−0.790212	+	0.287614i
$848$	18.5233	+	2.16506i	0.636093	+	0.0743486i
$849$		0			0
$850$	−0.152753	−	0.510232i	−0.00523940	−	0.0175008i
$851$	−0.952958	−	3.18310i	−0.0326670	−	0.109115i
$852$		0			0
$853$	5.06987	+	0.592583i	0.173589	+	0.0202897i	0.202443	−	0.979294i	$-0.435112\pi$
$853$	5.06987	+	0.592583i	0.173589	+	0.0202897i	−0.0288542	+	0.999584i	$0.509186\pi$
$854$	−1.89043	+	0.688062i	−0.0646893	+	0.0235450i
$855$		0			0
$856$	22.1305	+	8.05483i	0.756403	+	0.275308i
$857$	12.7262	+	6.39134i	0.434719	+	0.218324i	0.652680	−	0.757633i	$-0.273644\pi$
$857$	12.7262	+	6.39134i	0.434719	+	0.218324i	−0.217962	+	0.975957i	$0.569941\pi$
$858$		0			0
$859$	41.6878	−	4.87260i	1.42237	−	0.166251i	0.630143	−	0.776479i	$-0.282996\pi$
$859$	41.6878	−	4.87260i	1.42237	−	0.166251i	0.792226	+	0.610228i	$0.208922\pi$
$860$	24.6803	−	12.3949i	0.841591	−	0.422663i
$861$		0			0
$862$	−9.75451	+	2.31186i	−0.332240	+	0.0787423i
$863$	12.5420	−	21.7234i	0.426934	−	0.739472i	−0.569665	−	0.821877i	$-0.692927\pi$
$863$	12.5420	−	21.7234i	0.426934	−	0.739472i	0.996599	+	0.0824054i	$0.0262602\pi$
$864$		0			0
$865$	6.19073	+	10.7227i	0.210491	+	0.364582i
$866$	5.55465	+	5.88758i	0.188755	+	0.200068i
$867$		0			0
$868$	−1.36870	+	23.4996i	−0.0464566	+	0.797628i
$869$	11.1380	+	14.9610i	0.377832	+	0.507516i
$870$		0			0
$871$	20.7966	−	13.6781i	0.704666	−	0.463466i
$872$	−2.04917	−	11.6214i	−0.0693936	−	0.393551i
$873$		0			0
$874$	−1.59225	+	9.03012i	−0.0538588	+	0.305448i
$875$	−8.10749	−	18.7953i	−0.274083	−	0.635396i
$876$		0			0
$877$	−31.0130	−	7.35023i	−1.04724	−	0.248200i	−0.329240	−	0.944246i	$-0.606792\pi$
$877$	−31.0130	−	7.35023i	−1.04724	−	0.248200i	−0.717996	+	0.696047i	$0.754941\pi$
$878$	8.39273	−	8.89578i	0.283241	−	0.300218i
$879$		0			0
$880$	11.8106	−	15.8644i	0.398135	−	0.534788i
$881$	−4.45428	−	3.73758i	−0.150068	−	0.125922i	0.564662	−	0.825322i	$-0.309006\pi$
$881$	−4.45428	−	3.73758i	−0.150068	−	0.125922i	−0.714731	+	0.699400i	$0.753451\pi$
$882$		0			0
$883$	−0.930865	+	0.781089i	−0.0313261	+	0.0262857i	−0.658316	−	0.752741i	$-0.728731\pi$
$883$	−0.930865	+	0.781089i	−0.0313261	+	0.0262857i	0.626990	+	0.779027i	$0.284287\pi$
$884$	0.155711	+	2.67345i	0.00523712	+	0.0899179i
$885$		0			0
$886$	4.87497	−	11.3015i	0.163778	−	0.379680i
$887$	−2.17614	−	1.43127i	−0.0730675	−	0.0480572i	0.512450	−	0.858717i	$-0.328738\pi$
$887$	−2.17614	−	1.43127i	−0.0730675	−	0.0480572i	−0.585517	+	0.810660i	$0.699109\pi$
$888$		0			0
$889$	−2.79816	+	9.34650i	−0.0938473	+	0.313472i
$890$	5.05459			0.169430
$891$		0			0
$892$	12.1821			0.407888
$893$	6.27668	−	20.9656i	0.210041	−	0.701586i
$894$		0			0
$895$	27.6544	+	18.1886i	0.924383	+	0.607977i
$896$	7.59366	−	17.6041i	0.253686	−	0.588111i
$897$		0			0
$898$	−0.351789	−	6.03998i	−0.0117393	−	0.201557i
$899$	25.5323	−	21.4242i	0.851551	−	0.714536i
$900$		0			0
$901$	−1.89517	−	1.59024i	−0.0631373	−	0.0529785i
$902$	6.69507	−	8.99304i	0.222921	−	0.299435i
$903$		0			0
$904$	1.72389	−	1.82721i	0.0573356	−	0.0607722i
$905$	1.11275	+	0.263727i	0.0369891	+	0.00876657i
$906$		0			0
$907$	5.32533	+	12.3455i	0.176825	+	0.409926i	0.983460	−	0.181123i	$-0.0579732\pi$
$907$	5.32533	+	12.3455i	0.176825	+	0.409926i	−0.806636	+	0.591049i	$0.798714\pi$
$908$	2.62067	−	14.8626i	0.0869701	−	0.493232i
$909$		0			0
$910$	−0.553881	−	3.14122i	−0.0183610	−	0.104130i
$911$	−23.5524	+	15.4906i	−0.780325	+	0.513228i	−0.876073	−	0.482178i	$-0.839846\pi$
$911$	−23.5524	+	15.4906i	−0.780325	+	0.513228i	0.0957484	+	0.995406i	$0.469476\pi$
$912$		0			0
$913$	−14.1354	−	18.9872i	−0.467815	−	0.628384i
$914$	0.424586	−	7.28986i	0.0140441	−	0.241127i
$915$		0			0
$916$	9.98277	+	10.5811i	0.329840	+	0.349610i
$917$	11.1295	+	19.2768i	0.367528	+	0.636578i
$918$		0			0
$919$	13.5339	−	23.4413i	0.446441	−	0.773258i	−0.551710	−	0.834036i	$-0.686025\pi$
$919$	13.5339	−	23.4413i	0.446441	−	0.773258i	0.998151	+	0.0607774i	$0.0193580\pi$
$920$	−12.2294	+	2.89843i	−0.403193	+	0.0955584i
$921$		0			0
$922$	−5.01293	+	2.51759i	−0.165092	+	0.0829124i
$923$	53.4963	−	6.25282i	1.76085	−	0.205814i
$924$		0			0
$925$	1.48409	+	0.745340i	0.0487967	+	0.0245066i
$926$	0.985077	+	0.358539i	0.0323716	+	0.0117823i
$927$		0			0
$928$	−19.4266	+	7.07070i	−0.637709	+	0.232107i
$929$	−47.7953	−	5.58647i	−1.56811	−	0.183286i	−0.712789	−	0.701379i	$-0.752568\pi$
$929$	−47.7953	−	5.58647i	−1.56811	−	0.183286i	−0.855324	+	0.518093i	$0.826642\pi$
$930$		0			0
$931$	−3.46695	−	11.5804i	−0.113625	−	0.379533i
$932$	−13.7608	−	45.9642i	−0.450749	−	1.50561i
$933$		0			0
$934$	7.41009	+	0.866116i	0.242466	+	0.0283402i
$935$	−2.46545	+	0.897352i	−0.0806290	+	0.0293465i
$936$		0			0
$937$	−48.7239	−	17.7340i	−1.59174	−	0.579346i	−0.614026	−	0.789286i	$-0.710451\pi$
$937$	−48.7239	−	17.7340i	−1.59174	−	0.579346i	−0.977714	+	0.209940i	$0.932673\pi$
$938$	4.67633	+	2.34854i	0.152688	+	0.0766826i
$939$		0			0
$940$	14.3436	−	1.67653i	0.467838	−	0.0546824i
$941$	−40.4652	+	20.3224i	−1.31913	+	0.662491i	−0.962380	−	0.271709i	$-0.912411\pi$
$941$	−40.4652	+	20.3224i	−1.31913	+	0.662491i	−0.356749	+	0.934200i	$0.616115\pi$
$942$		0			0
$943$	39.6539	−	9.39814i	1.29131	−	0.306046i
$944$	−8.90573	+	15.4252i	−0.289857	+	0.502047i
$945$		0			0
$946$	−10.7128	−	18.5551i	−0.348302	−	0.603277i
$947$	−14.4175	−	15.2817i	−0.468506	−	0.496587i	0.449430	−	0.893315i	$-0.351627\pi$
$947$	−14.4175	−	15.2817i	−0.468506	−	0.496587i	−0.917936	+	0.396728i	$0.870146\pi$
$948$		0			0
$949$	1.31673	−	22.6074i	0.0427430	−	0.733868i
$950$	−2.73681	−	3.67617i	−0.0887937	−	0.119271i
$951$		0			0
$952$	−0.977042	+	0.642610i	−0.0316661	+	0.0208271i
$953$	−1.52233	−	8.63357i	−0.0493132	−	0.279669i	0.950173	−	0.311723i	$-0.100906\pi$
$953$	−1.52233	−	8.63357i	−0.0493132	−	0.279669i	−0.999486	+	0.0320543i	$0.989795\pi$
$954$		0			0
$955$	−1.79794	+	10.1966i	−0.0581800	+	0.329955i
$956$	−0.129122	−	0.299338i	−0.00417610	−	0.00968129i
$957$		0			0
$958$	−6.86568	−	1.62720i	−0.221820	−	0.0525723i
$959$	−6.49418	+	6.88343i	−0.209708	+	0.222278i
$960$		0			0
$961$	7.78665	−	10.4593i	0.251182	−	0.337396i
$962$	0.493629	+	0.414204i	0.0159152	+	0.0133545i
$963$		0			0
$964$	−27.4921	+	23.0686i	−0.885461	+	0.742990i
$965$	−0.0145237	−	0.249363i	−0.000467535	−	0.00802727i
$966$		0			0
$967$	−8.96620	+	20.7860i	−0.288334	+	0.668433i	−0.999398	−	0.0346944i	$-0.988954\pi$
$967$	−8.96620	+	20.7860i	−0.288334	+	0.668433i	0.711064	+	0.703127i	$0.248213\pi$
$968$	−15.6251	−	10.2768i	−0.502211	−	0.330309i
$969$		0			0
$970$	−0.301178	+	1.00600i	−0.00967023	+	0.0323008i
$971$	13.1781			0.422905			0.211453	−	0.977388i	$-0.432181\pi$
$971$	13.1781			0.422905			0.211453	+	0.977388i	$0.432181\pi$
$972$		0			0
$973$	32.1504			1.03070
$974$	−0.580094	+	1.93765i	−0.0185874	+	0.0620863i
$975$		0			0
$976$	7.34675	+	4.83204i	0.235164	+	0.154670i
$977$	15.7360	−	36.4800i	0.503438	−	1.16710i	−0.457217	−	0.889355i	$-0.651154\pi$
$977$	15.7360	−	36.4800i	0.503438	−	1.16710i	0.960655	−	0.277745i	$-0.0895869\pi$
$978$		0			0
$979$	2.95457	+	50.7281i	0.0944286	+	1.62128i
$980$	6.11051	−	5.12733i	0.195193	−	0.163786i
$981$		0			0
$982$	−1.07321	−	0.900528i	−0.0342474	−	0.0287370i
$983$	35.0323	−	47.0565i	1.11736	−	1.50087i	0.275395	−	0.961331i	$-0.411191\pi$
$983$	35.0323	−	47.0565i	1.11736	−	1.50087i	0.841961	−	0.539538i	$-0.181401\pi$
$984$		0			0
$985$	−10.1516	+	10.7600i	−0.323456	+	0.342843i
$986$	0.775666	+	0.183836i	0.0247022	+	0.00585454i
$987$		0			0
$988$	9.12721	+	21.1593i	0.290375	+	0.673166i
$989$	13.5235	−	76.6957i	0.430023	−	2.43878i
$990$		0			0
$991$	3.30423	+	18.7392i	0.104962	+	0.595270i	0.991235	+	0.132108i	$0.0421744\pi$
$991$	3.30423	+	18.7392i	0.104962	+	0.595270i	−0.886273	+	0.463163i	$0.846714\pi$
$992$	−22.8221	+	15.0104i	−0.724604	+	0.476579i
$993$		0			0
$994$	6.76167	+	9.08249i	0.214467	+	0.288079i
$995$	−0.131106	+	2.25101i	−0.00415635	+	0.0713618i
$996$		0			0
$997$	3.90600	+	4.14012i	0.123704	+	0.131119i	0.786265	−	0.617889i	$-0.212012\pi$
$997$	3.90600	+	4.14012i	0.123704	+	0.131119i	−0.662561	+	0.749008i	$0.730530\pi$
$998$	−5.28998	−	9.16251i	−0.167451	−	0.290034i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.352.5		144
3.2	odd	2		729.2.g.a.352.4		144
9.2	odd	6		729.2.g.b.595.5		144
9.4	even	3		81.2.g.a.22.5	✓	144
9.5	odd	6		243.2.g.a.199.4		144
9.7	even	3		729.2.g.c.595.4		144
81.11	odd	54		729.2.g.b.136.5		144
81.16	even	27		81.2.g.a.70.5	yes	144
81.23	odd	54		6561.2.a.d.1.39		72
81.38	odd	54		729.2.g.a.379.4		144
81.43	even	27	inner	729.2.g.d.379.5		144
81.58	even	27		6561.2.a.c.1.34		72
81.65	odd	54		243.2.g.a.127.4		144
81.70	even	27		729.2.g.c.136.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.22.5	✓	144	9.4	even	3
81.2.g.a.70.5	yes	144	81.16	even	27
243.2.g.a.127.4		144	81.65	odd	54
243.2.g.a.199.4		144	9.5	odd	6
729.2.g.a.352.4		144	3.2	odd	2
729.2.g.a.379.4		144	81.38	odd	54
729.2.g.b.136.5		144	81.11	odd	54
729.2.g.b.595.5		144	9.2	odd	6
729.2.g.c.136.4		144	81.70	even	27
729.2.g.c.595.4		144	9.7	even	3
729.2.g.d.352.5		144	1.1	even	1	trivial
729.2.g.d.379.5		144	81.43	even	27	inner
6561.2.a.c.1.34		72	81.58	even	27
6561.2.a.d.1.39		72	81.23	odd	54

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)

\(f(q)\)	\(=\)	\(q+(0.108562 - 0.362623i) q^{2} +(1.55127 + 1.02028i) q^{4} +(0.507898 - 1.17744i) q^{5} +(-0.111081 - 1.90719i) q^{7} +(1.11832 - 0.938383i) q^{8} +(-0.371828 - 0.312001i) q^{10} +(2.91390 - 3.91405i) q^{11} +(-2.36051 + 2.50200i) q^{13} +(-0.703649 - 0.166768i) q^{14} +(1.25195 + 2.90234i) q^{16} +(0.0728119 - 0.412937i) q^{17} +(-0.626542 - 3.55329i) q^{19} +(1.98921 - 1.30832i) q^{20} +(-1.10299 - 1.48157i) q^{22} +(0.390372 - 6.70243i) q^{23} +(2.30281 + 2.44083i) q^{25} +(0.651020 + 1.12760i) q^{26} +(1.77356 - 3.07189i) q^{28} +(-4.88707 + 1.15826i) q^{29} +(-5.93035 + 2.97833i) q^{31} +(4.08835 - 0.477860i) q^{32} +(-0.141836 - 0.0712326i) q^{34} +(-2.30201 - 0.837864i) q^{35} +(0.465059 - 0.169268i) q^{37} +(-1.35652 - 0.158555i) q^{38} +(-0.536896 - 1.79336i) q^{40} +(1.74088 + 5.81495i) q^{41} +(11.5214 + 1.34666i) q^{43} +(8.51368 - 3.09873i) q^{44} +(-2.38808 - 0.869188i) q^{46} +(5.42033 + 2.72219i) q^{47} +(3.32765 - 0.388946i) q^{49} +(1.13510 - 0.570068i) q^{50} +(-6.21453 + 1.47287i) q^{52} +(2.95007 - 5.10967i) q^{53} +(-3.12859 - 5.41888i) q^{55} +(-1.91390 - 2.02861i) q^{56} +(-0.110540 + 1.89791i) q^{58} +(3.36501 + 4.51999i) q^{59} +(2.32430 - 1.52872i) q^{61} +(0.436200 + 2.47381i) q^{62} +(-0.827191 + 4.69124i) q^{64} +(1.74705 + 4.05012i) q^{65} +(-7.04135 - 1.66883i) q^{67} +(0.534263 - 0.566286i) q^{68} +(-0.553741 + 0.743803i) q^{70} +(-11.9949 - 10.0649i) q^{71} +(-5.04326 + 4.23179i) q^{73} +(-0.0108925 - 0.187017i) q^{74} +(2.65344 - 6.15135i) q^{76} +(-7.78851 - 5.12258i) q^{77} +(-1.09627 + 3.66180i) q^{79} +4.05318 q^{80} +2.29763 q^{82} +(1.39129 - 4.64723i) q^{83} +(-0.449227 - 0.295461i) q^{85} +(1.73912 - 4.03173i) q^{86} +(-0.414199 - 7.11153i) q^{88} +(-7.97723 + 6.69369i) q^{89} +(5.03399 + 4.22402i) q^{91} +(7.44395 - 9.99896i) q^{92} +(1.57557 - 1.67001i) q^{94} +(-4.50201 - 1.06700i) q^{95} +(-0.856906 - 1.98653i) q^{97} +(0.220216 - 1.24891i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) \) 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 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Introduction

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