LMFDB - Embedded newform 729.2.g.a.514.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(28,729)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("729.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [144,-9,0,9,-9,0,9,18,0,-18,-9,0,9,-9,0,9,18,0,-18,-45] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(20)] == traces)

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			514.2
Character	$\chi$	$=$	729.514
Dual form			729.2.g.a.217.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.123020 - 2.11218i) q^{2} +(-2.45968 + 0.287495i) q^{4} +(-3.78800 - 0.897774i) q^{5} +(-1.99164 + 2.67524i) q^{7} +(0.175036 + 0.992677i) q^{8} +(-1.43025 + 8.11138i) q^{10} +(0.519303 + 0.550429i) q^{11} +(2.22178 - 1.11582i) q^{13} +(5.89558 + 3.87759i) q^{14} +(-2.74416 + 0.650378i) q^{16} +(0.700932 - 0.255119i) q^{17} +(4.21736 + 1.53499i) q^{19} +(9.57537 + 1.11920i) q^{20} +(1.09872 - 1.16457i) q^{22} +(1.36553 + 1.83423i) q^{23} +(9.07482 + 4.55755i) q^{25} +(-2.63013 - 4.55552i) q^{26} +(4.12967 - 7.15280i) q^{28} +(0.387661 - 0.254968i) q^{29} +(-1.56139 + 3.61971i) q^{31} +(2.28949 + 7.64743i) q^{32} +(-0.625084 - 1.44911i) q^{34} +(9.94610 - 8.34577i) q^{35} +(-3.64375 - 3.05747i) q^{37} +(2.72336 - 9.09665i) q^{38} +(0.228163 - 3.91741i) q^{40} +(0.284474 - 4.88423i) q^{41} +(-1.70392 + 5.69149i) q^{43} +(-1.43556 - 1.20458i) q^{44} +(3.70623 - 3.10990i) q^{46} +(4.26433 + 9.88583i) q^{47} +(-1.18264 - 3.95029i) q^{49} +(8.50995 - 19.7283i) q^{50} +(-5.14406 + 3.38330i) q^{52} +(-5.75294 + 9.96438i) q^{53} +(-1.47296 - 2.55124i) q^{55} +(-3.00425 - 1.50879i) q^{56} +(-0.586228 - 0.787441i) q^{58} +(-2.84735 + 3.01801i) q^{59} +(-0.265410 - 0.0310220i) q^{61} +(7.83755 + 2.85264i) q^{62} +(10.5709 - 3.84748i) q^{64} +(-9.41786 + 2.23207i) q^{65} +(1.60209 + 1.05371i) q^{67} +(-1.65072 + 0.829024i) q^{68} +(-18.8513 - 19.9812i) q^{70} +(-1.17278 + 6.65118i) q^{71} +(1.37723 + 7.81064i) q^{73} +(-6.00966 + 8.07238i) q^{74} +(-10.8147 - 2.56312i) q^{76} +(-2.50679 + 0.293002i) q^{77} +(-0.250999 - 4.30948i) q^{79} +10.9788 q^{80} -10.3513 q^{82} +(-0.148089 - 2.54258i) q^{83} +(-2.88417 + 0.337112i) q^{85} +(12.2310 + 2.89881i) q^{86} +(-0.455501 + 0.611845i) q^{88} +(0.935549 + 5.30576i) q^{89} +(-1.43990 + 8.16609i) q^{91} +(-3.88610 - 4.11903i) q^{92} +(20.3560 - 10.2232i) q^{94} +(-14.5973 - 9.60081i) q^{95} +(9.23262 - 2.18817i) q^{97} +(-8.19821 + 2.98391i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{27}\right)$

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 $

$2$	−0.123020	−	2.11218i	−0.0869884	−	1.49353i	−0.706034	−	0.708178i	$-0.749517\pi$
$2$	−0.123020	−	2.11218i	−0.0869884	−	1.49353i	0.619045	−	0.785355i	$-0.287520\pi$
$3$		0			0
$3$		0			0
$4$	−2.45968	+	0.287495i	−1.22984	+	0.143747i
$5$	−3.78800	−	0.897774i	−1.69405	−	0.401497i	−0.733517	−	0.679671i	$-0.762122\pi$
$5$	−3.78800	−	0.897774i	−1.69405	−	0.401497i	−0.960530	+	0.278175i	$0.910271\pi$
$6$		0			0
$7$	−1.99164	+	2.67524i	−0.752769	+	1.01114i	0.246350	+	0.969181i	$0.420769\pi$
$7$	−1.99164	+	2.67524i	−0.752769	+	1.01114i	−0.999119	+	0.0419634i	$0.986639\pi$
$8$	0.175036	+	0.992677i	0.0618845	+	0.350964i
$9$		0			0
$10$	−1.43025	+	8.11138i	−0.452286	+	2.56504i
$11$	0.519303	+	0.550429i	0.156576	+	0.165961i	0.800913	−	0.598781i	$-0.204348\pi$
$11$	0.519303	+	0.550429i	0.156576	+	0.165961i	−0.644337	+	0.764742i	$0.722867\pi$
$12$		0			0
$13$	2.22178	−	1.11582i	0.616210	−	0.309472i	−0.113176	−	0.993575i	$-0.536102\pi$
$13$	2.22178	−	1.11582i	0.616210	−	0.309472i	0.729386	+	0.684103i	$0.239806\pi$
$14$	5.89558	+	3.87759i	1.57566	+	1.03633i
$15$		0			0
$16$	−2.74416	+	0.650378i	−0.686041	+	0.162595i
$17$	0.700932	−	0.255119i	0.170001	−	0.0618753i	−0.255617	−	0.966778i	$-0.582279\pi$
$17$	0.700932	−	0.255119i	0.170001	−	0.0618753i	0.425619	+	0.904903i	$0.360057\pi$
$18$		0			0
$19$	4.21736	+	1.53499i	0.967530	+	0.352152i	0.776980	−	0.629526i	$-0.216751\pi$
$19$	4.21736	+	1.53499i	0.967530	+	0.352152i	0.190550	+	0.981678i	$0.438973\pi$
$20$	9.57537	+	1.11920i	2.14112	+	0.250261i
$21$		0			0
$22$	1.09872	−	1.16457i	0.234247	−	0.248288i
$23$	1.36553	+	1.83423i	0.284733	+	0.382463i	0.921361	−	0.388708i	$-0.127079\pi$
$23$	1.36553	+	1.83423i	0.284733	+	0.382463i	−0.636628	+	0.771171i	$0.719671\pi$
$24$		0			0
$25$	9.07482	+	4.55755i	1.81496	+	0.911509i
$26$	−2.63013	−	4.55552i	−0.515811	−	0.893410i
$27$		0			0
$28$	4.12967	−	7.15280i	0.780435	−	1.35175i
$29$	0.387661	−	0.254968i	0.0719868	−	0.0473464i	−0.513005	−	0.858385i	$-0.671468\pi$
$29$	0.387661	−	0.254968i	0.0719868	−	0.0473464i	0.584992	+	0.811039i	$0.301098\pi$
$30$		0			0
$31$	−1.56139	+	3.61971i	−0.280434	+	0.650120i	−0.998970	−	0.0453702i	$-0.985553\pi$
$31$	−1.56139	+	3.61971i	−0.280434	+	0.650120i	0.718536	+	0.695490i	$0.244813\pi$
$32$	2.28949	+	7.64743i	0.404729	+	1.35189i
$33$		0			0
$34$	−0.625084	−	1.44911i	−0.107201	−	0.248520i
$35$	9.94610	−	8.34577i	1.68120	−	1.41069i
$36$		0			0
$37$	−3.64375	−	3.05747i	−0.599029	−	0.502645i	0.292104	−	0.956387i	$-0.405645\pi$
$37$	−3.64375	−	3.05747i	−0.599029	−	0.502645i	−0.891134	+	0.453741i	$0.850089\pi$
$38$	2.72336	−	9.09665i	0.441787	−	1.47567i
$39$		0			0
$40$	0.228163	−	3.91741i	0.0360757	−	0.619396i
$41$	0.284474	−	4.88423i	0.0444273	−	0.762788i	−0.900368	−	0.435128i	$-0.856703\pi$
$41$	0.284474	−	4.88423i	0.0444273	−	0.762788i	0.944796	−	0.327660i	$-0.106260\pi$
$42$		0			0
$43$	−1.70392	+	5.69149i	−0.259845	+	0.867944i	0.724134	+	0.689660i	$0.242240\pi$
$43$	−1.70392	+	5.69149i	−0.259845	+	0.867944i	−0.983979	+	0.178284i	$0.942945\pi$
$44$	−1.43556	−	1.20458i	−0.216419	−	0.181597i
$45$		0			0
$46$	3.70623	−	3.10990i	0.546454	−	0.458529i
$47$	4.26433	+	9.88583i	0.622017	+	1.44200i	0.879587	+	0.475738i	$0.157819\pi$
$47$	4.26433	+	9.88583i	0.622017	+	1.44200i	−0.257570	+	0.966260i	$0.582922\pi$
$48$		0			0
$49$	−1.18264	−	3.95029i	−0.168948	−	0.564327i
$50$	8.50995	−	19.7283i	1.20349	−	2.79000i
$51$		0			0
$52$	−5.14406	+	3.38330i	−0.713353	+	0.469180i
$53$	−5.75294	+	9.96438i	−0.790227	+	1.36871i	0.135600	+	0.990764i	$0.456704\pi$
$53$	−5.75294	+	9.96438i	−0.790227	+	1.36871i	−0.925826	+	0.377949i	$0.876629\pi$
$54$		0			0
$55$	−1.47296	−	2.55124i	−0.198614	−	0.344010i
$56$	−3.00425	−	1.50879i	−0.401460	−	0.201621i
$57$		0			0
$58$	−0.586228	−	0.787441i	−0.0769755	−	0.103396i
$59$	−2.84735	+	3.01801i	−0.370693	+	0.392911i	−0.885687	−	0.464282i	$-0.846312\pi$
$59$	−2.84735	+	3.01801i	−0.370693	+	0.392911i	0.514995	+	0.857193i	$0.327794\pi$
$60$		0			0
$61$	−0.265410	−	0.0310220i	−0.0339823	−	0.00397196i	0.0990848	−	0.995079i	$-0.468408\pi$
$61$	−0.265410	−	0.0310220i	−0.0339823	−	0.00397196i	−0.133067	+	0.991107i	$0.542483\pi$
$62$	7.83755	+	2.85264i	0.995370	+	0.362285i
$63$		0			0
$64$	10.5709	−	3.84748i	1.32136	−	0.480935i
$65$	−9.41786	+	2.23207i	−1.16814	+	0.276855i
$66$		0			0
$67$	1.60209	+	1.05371i	0.195726	+	0.128731i	0.643589	−	0.765371i	$-0.277444\pi$
$67$	1.60209	+	1.05371i	0.195726	+	0.128731i	−0.447863	+	0.894102i	$0.647815\pi$
$68$	−1.65072	+	0.829024i	−0.200179	+	0.100534i
$69$		0			0
$70$	−18.8513	−	19.9812i	−2.25316	−	2.38821i
$71$	−1.17278	+	6.65118i	−0.139184	+	0.789350i	0.832671	+	0.553768i	$0.186811\pi$
$71$	−1.17278	+	6.65118i	−0.139184	+	0.789350i	−0.971855	+	0.235582i	$0.924300\pi$
$72$		0			0
$73$	1.37723	+	7.81064i	0.161192	+	0.914167i	0.952904	+	0.303272i	$0.0980791\pi$
$73$	1.37723	+	7.81064i	0.161192	+	0.914167i	−0.791712	+	0.610895i	$0.790810\pi$
$74$	−6.00966	+	8.07238i	−0.698609	+	0.938395i
$75$		0			0
$76$	−10.8147	−	2.56312i	−1.24053	−	0.294010i
$77$	−2.50679	+	0.293002i	−0.285675	+	0.0333907i
$78$		0			0
$79$	−0.250999	−	4.30948i	−0.0282396	−	0.484855i	−0.982545	−	0.186023i	$-0.940440\pi$
$79$	−0.250999	−	4.30948i	−0.0282396	−	0.484855i	0.954306	−	0.298832i	$-0.0965970\pi$
$80$	10.9788			1.22747
$81$		0			0
$82$	−10.3513			−1.14311
$83$	−0.148089	−	2.54258i	−0.0162548	−	0.279085i	−0.996635	−	0.0819684i	$-0.973879\pi$
$83$	−0.148089	−	2.54258i	−0.0162548	−	0.279085i	0.980380	−	0.197116i	$-0.0631577\pi$
$84$		0			0
$85$	−2.88417	+	0.337112i	−0.312833	+	0.0365649i
$86$	12.2310	+	2.89881i	1.31891	+	0.312587i
$87$		0			0
$88$	−0.455501	+	0.611845i	−0.0485566	+	0.0652229i
$89$	0.935549	+	5.30576i	0.0991680	+	0.562410i	0.993390	+	0.114786i	$0.0366184\pi$
$89$	0.935549	+	5.30576i	0.0991680	+	0.562410i	−0.894222	+	0.447623i	$0.852271\pi$
$90$		0			0
$91$	−1.43990	+	8.16609i	−0.150943	+	0.856039i
$92$	−3.88610	−	4.11903i	−0.405154	−	0.429438i
$93$		0			0
$94$	20.3560	−	10.2232i	2.09956	−	1.05444i
$95$	−14.5973	−	9.60081i	−1.49765	−	0.985022i
$96$		0			0
$97$	9.23262	−	2.18817i	0.937431	−	0.222175i	0.266618	−	0.963802i	$-0.414094\pi$
$97$	9.23262	−	2.18817i	0.937431	−	0.222175i	0.670812	+	0.741627i	$0.265946\pi$
$98$	−8.19821	+	2.98391i	−0.828145	+	0.301420i
$99$		0			0
$100$	−23.6314	−	8.60112i	−2.36314	−	0.860112i
$101$	−12.2244	−	1.42883i	−1.21638	−	0.142174i	−0.516406	−	0.856344i	$-0.672730\pi$
$101$	−12.2244	−	1.42883i	−1.21638	−	0.142174i	−0.699972	+	0.714170i	$0.746804\pi$
$102$		0			0
$103$	−11.4398	+	12.1255i	−1.12720	+	1.19476i	−0.148623	+	0.988894i	$0.547484\pi$
$103$	−11.4398	+	12.1255i	−1.12720	+	1.19476i	−0.978579	+	0.205870i	$0.933998\pi$
$104$	1.49654	+	2.01020i	0.146748	+	0.197116i
$105$		0			0
$106$	21.7542	+	10.9254i	2.11296	+	1.06117i
$107$	−1.84694	−	3.19899i	−0.178550	−	0.309258i	0.762834	−	0.646595i	$-0.223807\pi$
$107$	−1.84694	−	3.19899i	−0.178550	−	0.309258i	−0.941384	+	0.337336i	$0.890474\pi$
$108$		0			0
$109$	8.66961	−	15.0162i	0.830398	−	1.43829i	−0.0673245	−	0.997731i	$-0.521446\pi$
$109$	8.66961	−	15.0162i	0.830398	−	1.43829i	0.897723	−	0.440561i	$-0.145220\pi$
$110$	−5.20747	+	3.42501i	−0.496513	+	0.326562i
$111$		0			0
$112$	3.72547	−	8.63660i	0.352024	−	0.816082i
$113$	−2.95666	−	9.87594i	−0.278139	−	0.929051i	−0.976900	−	0.213695i	$-0.931450\pi$
$113$	−2.95666	−	9.87594i	−0.278139	−	0.929051i	0.698761	−	0.715355i	$-0.253735\pi$
$114$		0			0
$115$	−3.52593	−	8.17401i	−0.328794	−	0.762231i
$116$	−0.880217	+	0.738590i	−0.0817261	+	0.0685764i
$117$		0			0
$118$	6.72485	+	5.64282i	0.619072	+	0.519464i
$119$	−0.713503	+	2.38326i	−0.0654067	+	0.218473i
$120$		0			0
$121$	0.606297	−	10.4097i	0.0551179	−	0.946337i
$122$	−0.0328731	+	0.564409i	−0.00297619	+	0.0510992i
$123$		0			0
$124$	2.79987	−	9.35221i	0.251436	−	0.839854i
$125$	−15.3730	−	12.8995i	−1.37500	−	1.15376i
$126$		0			0
$127$	−10.1217	+	8.49315i	−0.898159	+	0.753645i	−0.969830	−	0.243783i	$-0.921611\pi$
$127$	−10.1217	+	8.49315i	−0.898159	+	0.753645i	0.0716705	+	0.997428i	$0.477167\pi$
$128$	−3.10334	−	7.19434i	−0.274299	−	0.635896i
$129$		0			0
$130$	5.87312	+	19.6176i	0.515107	+	1.72058i
$131$	−3.98509	+	9.23849i	−0.348179	+	0.807170i	0.650677	+	0.759355i	$0.274485\pi$
$131$	−3.98509	+	9.23849i	−0.348179	+	0.807170i	−0.998856	+	0.0478157i	$0.984774\pi$
$132$		0			0
$133$	−12.5059	+	8.22529i	−1.08440	+	0.713223i
$134$	2.02853	−	3.51352i	0.175238	−	0.303522i
$135$		0			0
$136$	0.375938	+	0.651145i	0.0322365	+	0.0558352i
$137$	8.46148	+	4.24951i	0.722913	+	0.363061i	0.771904	−	0.635739i	$-0.219304\pi$
$137$	8.46148	+	4.24951i	0.722913	+	0.363061i	−0.0489914	+	0.998799i	$0.515601\pi$
$138$		0			0
$139$	−6.27037	−	8.42257i	−0.531846	−	0.714393i	0.452278	−	0.891877i	$-0.350612\pi$
$139$	−6.27037	−	8.42257i	−0.531846	−	0.714393i	−0.984124	+	0.177484i	$0.943204\pi$
$140$	−22.0648	+	23.3873i	−1.86482	+	1.97659i
$141$		0			0
$142$	14.1927	+	1.65889i	1.19103	+	0.139211i
$143$	1.76795	+	0.643483i	0.147844	+	0.0538107i
$144$		0			0
$145$	−1.69736	+	0.617790i	−0.140958	+	0.0513047i
$146$	16.3280	−	3.86981i	1.35132	−	0.320268i
$147$		0			0
$148$	9.84146	+	6.47283i	0.808963	+	0.532063i
$149$	−11.1073	+	5.57830i	−0.909947	+	0.456992i	−0.841251	−	0.540645i	$-0.818180\pi$
$149$	−11.1073	+	5.57830i	−0.909947	+	0.456992i	−0.0686960	+	0.997638i	$0.521884\pi$
$150$		0			0
$151$	12.5081	+	13.2578i	1.01790	+	1.07891i	0.996864	+	0.0791296i	$0.0252141\pi$
$151$	12.5081	+	13.2578i	1.01790	+	1.07891i	0.0210332	+	0.999779i	$0.493304\pi$
$152$	−0.785565	+	4.45516i	−0.0637177	+	0.361361i
$153$		0			0
$154$	0.927258	+	5.25874i	0.0747206	+	0.423761i
$155$	9.16424	−	12.3097i	0.736090	−	0.988740i
$156$		0			0
$157$	22.7419	+	5.38993i	1.81500	+	0.430163i	0.990709	−	0.136002i	$-0.0434254\pi$
$157$	22.7419	+	5.38993i	1.81500	+	0.430163i	0.824292	+	0.566165i	$0.191574\pi$
$158$	−9.07151	+	1.06031i	−0.721691	+	0.0843536i
$159$		0			0
$160$	−1.80694	−	31.0240i	−0.142851	−	2.45266i
$161$	−7.62665			−0.601064
$162$		0			0
$163$	11.7238			0.918278			0.459139	−	0.888364i	$-0.348158\pi$
$163$	11.7238			0.918278			0.459139	+	0.888364i	$0.348158\pi$
$164$	0.704477	+	12.0954i	0.0550104	+	0.944492i
$165$		0			0
$166$	−5.35217	+	0.625579i	−0.415409	+	0.0485543i
$167$	23.5604	+	5.58392i	1.82316	+	0.432097i	0.992244	−	0.124304i	$-0.0396697\pi$
$167$	23.5604	+	5.58392i	1.82316	+	0.432097i	0.830914	+	0.556400i	$0.187818\pi$
$168$		0			0
$169$	−4.07182	+	5.46940i	−0.313217	+	0.420723i
$170$	1.06685	+	6.05041i	0.0818237	+	0.464045i
$171$		0			0
$172$	2.55482	−	14.4891i	0.194803	−	1.10478i
$173$	−10.6453	−	11.2833i	−0.809346	−	0.857857i	0.182773	−	0.983155i	$-0.441493\pi$
$173$	−10.6453	−	11.2833i	−0.809346	−	0.857857i	−0.992119	+	0.125298i	$0.960011\pi$
$174$		0			0
$175$	−30.2663	+	15.2003i	−2.28792	+	1.14903i
$176$	−1.78304	−	1.17272i	−0.134402	−	0.0883973i
$177$		0			0
$178$	11.0916	−	2.62876i	0.831352	−	0.197034i
$179$	−6.75474	+	2.45852i	−0.504873	+	0.183759i	−0.581884	−	0.813271i	$-0.697684\pi$
$179$	−6.75474	+	2.45852i	−0.504873	+	0.183759i	0.0770114	+	0.997030i	$0.475462\pi$
$180$		0			0
$181$	7.27112	+	2.64647i	0.540458	+	0.196711i	0.597802	−	0.801644i	$-0.296041\pi$
$181$	7.27112	+	2.64647i	0.540458	+	0.196711i	−0.0573439	+	0.998354i	$0.518263\pi$
$182$	17.4254	+	2.03673i	1.29165	+	0.150973i
$183$		0			0
$184$	−1.58178	+	1.67659i	−0.116610	+	0.123600i
$185$	11.0576	+	14.8530i	0.812974	+	1.09201i
$186$		0			0
$187$	0.504421	+	0.253330i	0.0368869	+	0.0185253i
$188$	−13.3310	−	23.0900i	−0.972264	−	1.68401i
$189$		0			0
$190$	−18.4828	+	32.0132i	−1.34089	+	2.32248i
$191$	−8.42018	+	5.53804i	−0.609263	+	0.400719i	−0.816311	−	0.577612i	$-0.803985\pi$
$191$	−8.42018	+	5.53804i	−0.609263	+	0.400719i	0.207048	+	0.978331i	$0.433614\pi$
$192$		0			0
$193$	−6.33422	+	14.6844i	−0.455947	+	1.05700i	0.522897	+	0.852396i	$0.324851\pi$
$193$	−6.33422	+	14.6844i	−0.455947	+	1.05700i	−0.978844	+	0.204608i	$0.934408\pi$
$194$	−5.75760	−	19.2317i	−0.413372	−	1.38076i
$195$		0			0
$196$	4.04460	+	9.37643i	0.288900	+	0.669745i
$197$	−8.40349	+	7.05136i	−0.598724	+	0.502389i	−0.891035	−	0.453934i	$-0.850020\pi$
$197$	−8.40349	+	7.05136i	−0.598724	+	0.502389i	0.292311	+	0.956323i	$0.405576\pi$
$198$		0			0
$199$	2.68937	+	2.25665i	0.190644	+	0.159970i	0.733114	−	0.680106i	$-0.238066\pi$
$199$	2.68937	+	2.25665i	0.190644	+	0.159970i	−0.542470	+	0.840075i	$0.682511\pi$
$200$	−2.93575	+	9.80609i	−0.207589	+	0.693396i
$201$		0			0
$202$	−1.51409	+	25.9960i	−0.106531	+	1.82907i
$203$	−0.0899795	+	1.54489i	−0.00631532	+	0.108430i
$204$		0			0
$205$	−5.46252	+	18.2461i	−0.381519	+	1.27436i
$206$	27.0186	+	22.6713i	1.88247	+	1.57958i
$207$		0			0
$208$	−5.37122	+	4.50698i	−0.372427	+	0.312503i
$209$	1.34518	+	3.11849i	0.0930483	+	0.215710i
$210$		0			0
$211$	2.20372	+	7.36094i	0.151710	+	0.506748i	0.999730	−	0.0232159i	$-0.00739053\pi$
$211$	2.20372	+	7.36094i	0.151710	+	0.506748i	−0.848020	+	0.529964i	$0.822205\pi$
$212$	11.2857	−	26.1631i	0.775102	−	1.79689i
$213$		0			0
$214$	−6.52962	+	4.29460i	−0.446356	+	0.293573i
$215$	11.5641	−	20.0297i	0.788667	−	1.36601i
$216$		0			0
$217$	−6.57386	−	11.3863i	−0.446262	−	0.772949i
$218$	−32.7834	−	16.4644i	−2.22037	−	1.11511i
$219$		0			0
$220$	4.35648	+	5.85177i	0.293714	+	0.394526i
$221$	1.27265	−	1.34893i	0.0856077	−	0.0907389i
$222$		0			0
$223$	−10.7710	−	1.25894i	−0.721276	−	0.0843051i	−0.252468	−	0.967605i	$-0.581242\pi$
$223$	−10.7710	−	1.25894i	−0.721276	−	0.0843051i	−0.468808	+	0.883300i	$0.655316\pi$
$224$	−25.0185	−	9.10600i	−1.67162	−	0.608420i
$225$		0			0
$226$	−20.4960	+	7.45993i	−1.36337	+	0.496227i
$227$	10.5686	−	2.50480i	0.701461	−	0.166249i	0.135617	−	0.990761i	$-0.456698\pi$
$227$	10.5686	−	2.50480i	0.701461	−	0.166249i	0.565844	+	0.824512i	$0.308550\pi$
$228$		0			0
$229$	−1.91282	−	1.25808i	−0.126403	−	0.0831363i	0.484733	−	0.874662i	$-0.338917\pi$
$229$	−1.91282	−	1.25808i	−0.126403	−	0.0831363i	−0.611136	+	0.791526i	$0.709287\pi$
$230$	−16.8312	+	8.45294i	−1.10982	+	0.557371i
$231$		0			0
$232$	0.320956	+	0.340193i	0.0210718	+	0.0223348i
$233$	−3.09286	+	17.5405i	−0.202620	+	1.14912i	0.698521	+	0.715590i	$0.253842\pi$
$233$	−3.09286	+	17.5405i	−0.202620	+	1.14912i	−0.901141	+	0.433526i	$0.857269\pi$
$234$		0			0
$235$	−7.27807	−	41.2760i	−0.474769	−	2.69255i
$236$	6.13589	−	8.24192i	0.399412	−	0.536504i
$237$		0			0
$238$	5.12165	+	1.21385i	0.331987	+	0.0786824i
$239$	−12.1833	+	1.42403i	−0.788073	+	0.0921126i	−0.500603	−	0.865677i	$-0.666888\pi$
$239$	−12.1833	+	1.42403i	−0.788073	+	0.0921126i	−0.287470	+	0.957790i	$0.592814\pi$
$240$		0			0
$241$	−1.01750	−	17.4699i	−0.0655432	−	1.12533i	−0.857408	−	0.514637i	$-0.827927\pi$
$241$	−1.01750	−	17.4699i	−0.0655432	−	1.12533i	0.791865	−	0.610696i	$-0.209110\pi$
$242$	−22.0617			−1.41818
$243$		0			0
$244$	0.661742			0.0423637
$245$	0.933376	+	16.0254i	0.0596312	+	1.02383i
$246$		0			0
$247$	11.0828	−	1.29540i	0.705183	−	0.0824241i
$248$	−3.86650	−	0.916378i	−0.245523	−	0.0581901i
$249$		0			0
$250$	−25.3548	+	34.0574i	−1.60358	+	2.15398i
$251$	−3.26810	−	18.5343i	−0.206281	−	1.16988i	−0.895412	−	0.445239i	$-0.853119\pi$
$251$	−3.26810	−	18.5343i	−0.206281	−	1.16988i	0.689131	−	0.724637i	$-0.257992\pi$
$252$		0			0
$253$	−0.300488	+	1.70415i	−0.0188915	+	0.107139i
$254$	19.1842	+	20.3341i	1.20372	+	1.27587i
$255$		0			0
$256$	5.29150	−	2.65749i	0.330718	−	0.166093i
$257$	14.4064	+	9.47524i	0.898646	+	0.591049i	0.912600	−	0.408854i	$-0.134071\pi$
$257$	14.4064	+	9.47524i	0.898646	+	0.591049i	−0.0139536	+	0.999903i	$0.504442\pi$
$258$		0			0
$259$	15.4365	−	3.65852i	0.959178	−	0.227329i
$260$	22.5232	−	8.19776i	1.39683	−	0.508404i
$261$		0			0
$262$	20.0036	+	7.28070i	1.23582	+	0.449803i
$263$	−24.4451	−	2.85722i	−1.50735	−	0.176184i	−0.678062	−	0.735005i	$-0.737180\pi$
$263$	−24.4451	−	2.85722i	−1.50735	−	0.176184i	−0.829288	+	0.558821i	$0.811254\pi$
$264$		0			0
$265$	30.7379	−	32.5803i	1.88821	−	2.00139i
$266$	18.9117	+	25.4029i	1.15955	+	1.55755i
$267$		0			0
$268$	−4.24356	−	2.13119i	−0.259216	−	0.130183i
$269$	5.32448	+	9.22227i	0.324639	+	0.562292i	0.981439	−	0.191773i	$-0.0614238\pi$
$269$	5.32448	+	9.22227i	0.324639	+	0.562292i	−0.656800	+	0.754065i	$0.728090\pi$
$270$		0			0
$271$	2.35817	−	4.08447i	0.143249	−	0.248114i	−0.785469	−	0.618900i	$-0.787578\pi$
$271$	2.35817	−	4.08447i	0.143249	−	0.248114i	0.928718	+	0.370786i	$0.120912\pi$
$272$	−1.75755	+	1.15596i	−0.106567	+	0.0700903i
$273$		0			0
$274$	7.93479	−	18.3949i	0.479358	−	1.11128i
$275$	2.20398	+	7.36179i	0.132905	+	0.443933i
$276$		0			0
$277$	−2.61873	−	6.07089i	−0.157344	−	0.364765i	0.821249	−	0.570570i	$-0.193278\pi$
$277$	−2.61873	−	6.07089i	−0.157344	−	0.364765i	−0.978593	+	0.205806i	$0.934019\pi$
$278$	−17.0186	+	14.2803i	−1.02071	+	0.856474i
$279$		0			0
$280$	10.0256	+	8.41245i	0.599142	+	0.502740i
$281$	−0.710180	+	2.37217i	−0.0423658	+	0.141512i	−0.976556	−	0.215264i	$-0.930939\pi$
$281$	−0.710180	+	2.37217i	−0.0423658	+	0.141512i	0.934190	+	0.356776i	$0.116124\pi$
$282$		0			0
$283$	−0.0539093	+	0.925587i	−0.00320457	+	0.0550204i	−0.999531	−	0.0306125i	$-0.990254\pi$
$283$	−0.0539093	+	0.925587i	−0.00320457	+	0.0550204i	0.996327	+	0.0856330i	$0.0272912\pi$
$284$	0.972485	−	16.6969i	0.0577064	−	0.990780i
$285$		0			0
$286$	1.14165	−	3.81339i	0.0675075	−	0.225491i
$287$	12.4999	+	10.4887i	0.737845	+	0.619126i
$288$		0			0
$289$	−12.5965	+	10.5697i	−0.740973	+	0.621750i
$290$	1.51369	+	3.50913i	0.0888870	+	0.206063i
$291$		0			0
$292$	−5.63305	−	18.8157i	−0.329650	−	1.10111i
$293$	−0.928830	+	2.15327i	−0.0542628	+	0.125795i	−0.943191	−	0.332252i	$-0.892192\pi$
$293$	−0.928830	+	2.15327i	−0.0542628	+	0.125795i	0.888928	+	0.458047i	$0.151451\pi$
$294$		0			0
$295$	13.4952	−	8.87596i	0.785724	−	0.516779i
$296$	2.39729	−	4.15224i	0.139340	−	0.241344i
$297$		0			0
$298$	13.1488	+	22.7744i	0.761688	+	1.31928i
$299$	5.08058	+	2.55156i	0.293818	+	0.147561i
$300$		0			0
$301$	−11.8325	−	15.8938i	−0.682013	−	0.916103i
$302$	26.4642	−	28.0504i	1.52284	−	1.61412i
$303$		0			0
$304$	−12.5715	−	1.46939i	−0.721023	−	0.0842755i
$305$	0.977524	+	0.355790i	0.0559729	+	0.0203725i
$306$		0			0
$307$	14.3376	−	5.21846i	0.818289	−	0.297833i	0.101246	−	0.994861i	$-0.467717\pi$
$307$	14.3376	−	5.21846i	0.818289	−	0.297833i	0.717043	+	0.697028i	$0.245495\pi$
$308$	6.08166	−	1.44138i	0.346535	−	0.0821302i
$309$		0			0
$310$	−27.1277	−	17.8421i	−1.54075	−	1.01337i
$311$	14.9627	−	7.51453i	0.848455	−	0.426110i	0.0292231	−	0.999573i	$-0.490697\pi$
$311$	14.9627	−	7.51453i	0.848455	−	0.426110i	0.819231	+	0.573463i	$0.194400\pi$
$312$		0			0
$313$	−22.3532	−	23.6930i	−1.26348	−	1.33921i	−0.915822	−	0.401584i	$-0.868460\pi$
$313$	−22.3532	−	23.6930i	−1.26348	−	1.33921i	−0.347654	−	0.937623i	$-0.613022\pi$
$314$	8.58676	−	48.6979i	0.484579	−	2.74818i
$315$		0			0
$316$	1.85633	+	10.5278i	0.104427	+	0.592234i
$317$	−12.9409	+	17.3827i	−0.726835	+	0.976309i	0.273063	+	0.961996i	$0.411963\pi$
$317$	−12.9409	+	17.3827i	−0.726835	+	0.976309i	−0.999898	+	0.0143125i	$0.995444\pi$
$318$		0			0
$319$	0.341655	+	0.0809738i	0.0191290	+	0.00453366i
$320$	−43.4966	+	5.08403i	−2.43154	+	0.284206i
$321$		0			0
$322$	0.938232	+	16.1088i	0.0522856	+	0.897710i
$323$	3.34769			0.186271
$324$		0			0
$325$	25.2476			1.40049
$326$	−1.44226	−	24.7627i	−0.0798796	−	1.37148i
$327$		0			0
$328$	4.89825	−	0.572523i	0.270461	−	0.0316123i
$329$	−34.9400	−	8.28092i	−1.92630	−	0.456542i
$330$		0			0
$331$	14.2197	−	19.1003i	0.781583	−	1.04985i	−0.215720	−	0.976455i	$-0.569210\pi$
$331$	14.2197	−	19.1003i	0.781583	−	1.04985i	0.997303	−	0.0733934i	$-0.0233829\pi$
$332$	1.09523	+	6.21136i	0.0601086	+	0.340893i
$333$		0			0
$334$	8.89581	−	50.4507i	0.486757	−	2.76054i
$335$	−5.12273	−	5.42977i	−0.279884	−	0.296660i
$336$		0			0
$337$	−16.4386	+	8.25578i	−0.895468	+	0.449721i	−0.836139	−	0.548517i	$-0.815192\pi$
$337$	−16.4386	+	8.25578i	−0.895468	+	0.449721i	−0.0593292	+	0.998238i	$0.518896\pi$
$338$	12.0532	+	7.92755i	0.655610	+	0.431202i
$339$		0			0
$340$	6.99722	−	1.65837i	0.379477	−	0.0899378i
$341$	−2.80323	+	1.02029i	−0.151803	+	0.0552519i
$342$		0			0
$343$	−9.01506	−	3.28121i	−0.486767	−	0.177169i
$344$	−5.94806	−	0.695228i	−0.320698	−	0.0374842i
$345$		0			0
$346$	−22.5228	+	23.8728i	−1.21083	+	1.28341i
$347$	10.0986	+	13.5648i	0.542122	+	0.728196i	0.985788	−	0.167996i	$-0.0537296\pi$
$347$	10.0986	+	13.5648i	0.542122	+	0.728196i	−0.443665	+	0.896192i	$0.646322\pi$
$348$		0			0
$349$	7.29849	+	3.66544i	0.390679	+	0.196206i	0.633285	−	0.773918i	$-0.281706\pi$
$349$	7.29849	+	3.66544i	0.390679	+	0.196206i	−0.242606	+	0.970125i	$0.578002\pi$
$350$	35.8291	+	62.0578i	1.91514	+	3.31713i
$351$		0			0
$352$	−3.02043	+	5.23154i	−0.160989	+	0.278842i
$353$	20.5651	−	13.5258i	1.09457	−	0.719908i	0.132081	−	0.991239i	$-0.457834\pi$
$353$	20.5651	−	13.5258i	1.09457	−	0.719908i	0.962486	+	0.271331i	$0.0874637\pi$
$354$		0			0
$355$	10.4138	−	24.1418i	0.552705	−	1.28131i
$356$	−3.82653	−	12.7815i	−0.202806	−	0.677418i
$357$		0			0
$358$	6.02381	+	13.9648i	0.318368	+	0.738060i
$359$	9.68682	−	8.12821i	0.511251	−	0.428990i	−0.350318	−	0.936631i	$-0.613927\pi$
$359$	9.68682	−	8.12821i	0.511251	−	0.428990i	0.861569	+	0.507640i	$0.169482\pi$
$360$		0			0
$361$	0.875105	+	0.734300i	0.0460582	+	0.0386474i
$362$	4.69532	−	15.6835i	0.246780	−	0.824304i
$363$		0			0
$364$	1.19398	−	20.4999i	0.0625817	−	1.07449i
$365$	1.79525	−	30.8232i	0.0939675	−	1.61336i
$366$		0			0
$367$	3.00976	−	10.0533i	0.157108	−	0.524777i	−0.842802	−	0.538224i	$-0.819095\pi$
$367$	3.00976	−	10.0533i	0.157108	−	0.524777i	0.999910	+	0.0134470i	$0.00428046\pi$
$368$	−4.94019	−	4.14531i	−0.257525	−	0.216089i
$369$		0			0
$370$	30.0118	−	25.1829i	1.56024	−	1.30920i
$371$	−15.1993	−	35.2359i	−0.789108	−	1.82936i
$372$		0			0
$373$	−3.38324	−	11.3008i	−0.175178	−	0.585135i	−0.999811	−	0.0194660i	$-0.993803\pi$
$373$	−3.38324	−	11.3008i	−0.175178	−	0.585135i	0.824633	−	0.565668i	$-0.191382\pi$
$374$	0.473023	−	1.09659i	0.0244594	−	0.0567033i
$375$		0			0
$376$	−9.06703	+	5.96348i	−0.467596	+	0.307543i
$377$	0.576797	−	0.999042i	0.0297066	−	0.0514533i
$378$		0			0
$379$	−9.06853	−	15.7072i	−0.465819	−	0.806823i	0.533419	−	0.845851i	$-0.320907\pi$
$379$	−9.06853	−	15.7072i	−0.465819	−	0.806823i	−0.999238	+	0.0390286i	$0.987574\pi$
$380$	38.6649	+	19.4182i	1.98347	+	0.996134i
$381$		0			0
$382$	12.7332	+	17.1036i	0.651486	+	0.875097i
$383$	10.6488	−	11.2871i	0.544131	−	0.576745i	−0.395702	−	0.918379i	$-0.629499\pi$
$383$	10.6488	−	11.2871i	0.544131	−	0.576745i	0.939833	+	0.341634i	$0.110980\pi$
$384$		0			0
$385$	9.75879	+	1.14064i	0.497354	+	0.0581323i
$386$	31.7952	+	11.5725i	1.61833	+	0.589025i
$387$		0			0
$388$	−22.0802	+	8.03653i	−1.12095	+	0.407993i
$389$	15.0183	−	3.55940i	0.761457	−	0.180469i	0.168499	−	0.985702i	$-0.446108\pi$
$389$	15.0183	−	3.55940i	0.761457	−	0.180469i	0.592958	+	0.805233i	$0.297960\pi$
$390$		0			0
$391$	1.42509	+	0.937299i	0.0720701	+	0.0474012i
$392$	3.71435	−	1.86542i	0.187603	−	0.0942179i
$393$		0			0
$394$	15.9275	+	16.8822i	0.802417	+	0.850512i
$395$	−2.91816	+	16.5497i	−0.146828	+	0.832705i
$396$		0			0
$397$	0.354695	+	2.01157i	0.0178016	+	0.100958i	0.992414	−	0.122941i	$-0.0392326\pi$
$397$	0.354695	+	2.01157i	0.0178016	+	0.100958i	−0.974612	+	0.223899i	$0.928121\pi$
$398$	4.43559	−	5.95804i	0.222336	−	0.298649i
$399$		0			0
$400$	−27.8669	−	6.60458i	−1.39335	−	0.330229i
$401$	14.8530	−	1.73607i	0.741725	−	0.0866952i	0.263166	−	0.964751i	$-0.415233\pi$
$401$	14.8530	−	1.73607i	0.741725	−	0.0866952i	0.478559	+	0.878055i	$0.341159\pi$
$402$		0			0
$403$	0.569878	+	9.78443i	0.0283876	+	0.487397i
$404$	30.4790			1.51639
$405$		0			0
$406$	3.27415			0.162493
$407$	−0.209291	−	3.59338i	−0.0103742	−	0.178117i
$408$		0			0
$409$	−10.3183	+	1.20604i	−0.510208	+	0.0596348i	−0.367302	−	0.930102i	$-0.619719\pi$
$409$	−10.3183	+	1.20604i	−0.510208	+	0.0596348i	−0.142906	+	0.989736i	$0.545645\pi$
$410$	39.2109	+	9.29316i	1.93649	+	0.458957i
$411$		0			0
$412$	24.6523	−	33.1138i	1.21453	−	1.63140i
$413$	−2.40300	−	13.6281i	−0.118244	−	0.670595i
$414$		0			0
$415$	−1.72170	+	9.76427i	−0.0845151	+	0.479309i
$416$	13.6199	+	14.4362i	0.667770	+	0.707795i
$417$		0			0
$418$	6.42131	−	3.22490i	0.314076	−	0.157735i
$419$	0.442896	+	0.291298i	0.0216369	+	0.0142308i	0.560281	−	0.828302i	$-0.310693\pi$
$419$	0.442896	+	0.291298i	0.0216369	+	0.0142308i	−0.538644	+	0.842533i	$0.681063\pi$
$420$		0			0
$421$	−31.2014	+	7.39486i	−1.52066	+	0.360403i	−0.904244	−	0.427017i	$-0.859565\pi$
$421$	−31.2014	+	7.39486i	−1.52066	+	0.360403i	−0.616417	+	0.787420i	$0.711416\pi$
$422$	15.2765	−	5.56019i	0.743649	−	0.270666i
$423$		0			0
$424$	−10.8984	−	3.96668i	−0.529272	−	0.192639i
$425$	7.52355	+	0.879377i	0.364946	+	0.0426560i
$426$		0			0
$427$	0.611593	−	0.648250i	0.0295970	−	0.0313710i
$428$	5.46257	+	7.33750i	0.264043	+	0.354671i
$429$		0			0
$430$	−43.7288	−	21.9614i	−2.10879	−	1.05907i
$431$	2.69146	+	4.66175i	0.129643	+	0.224549i	0.923538	−	0.383506i	$-0.125283\pi$
$431$	2.69146	+	4.66175i	0.129643	+	0.224549i	−0.793895	+	0.608055i	$0.791950\pi$
$432$		0			0
$433$	−16.6465	+	28.8325i	−0.799978	+	1.38560i	0.119652	+	0.992816i	$0.461822\pi$
$433$	−16.6465	+	28.8325i	−0.799978	+	1.38560i	−0.919630	+	0.392787i	$0.871511\pi$
$434$	−23.2411	+	15.2859i	−1.11561	+	0.733746i
$435$		0			0
$436$	−17.0074	+	39.4275i	−0.814505	+	1.88823i
$437$	2.94342	+	9.83170i	0.140803	+	0.470314i
$438$		0			0
$439$	−7.39954	−	17.1541i	−0.353161	−	0.818719i	−0.998496	−	0.0548196i	$-0.982542\pi$
$439$	−7.39954	−	17.1541i	−0.353161	−	0.818719i	0.645335	−	0.763899i	$-0.276718\pi$
$440$	2.27474	−	1.90873i	0.108444	−	0.0909953i
$441$		0			0
$442$	−3.00574	−	2.52212i	−0.142968	−	0.119965i
$443$	−5.41212	+	18.0777i	−0.257138	+	0.858900i	0.727770	+	0.685821i	$0.240557\pi$
$443$	−5.41212	+	18.0777i	−0.257138	+	0.858900i	−0.984908	+	0.173079i	$0.944628\pi$
$444$		0			0
$445$	1.21951	−	20.9382i	0.0578103	−	0.992565i
$446$	−1.33407	+	22.9050i	−0.0631698	+	1.08458i
$447$		0			0
$448$	−10.7604	+	35.9424i	−0.508383	+	1.69812i
$449$	5.33643	+	4.47780i	0.251842	+	0.211320i	0.759965	−	0.649964i	$-0.225216\pi$
$449$	5.33643	+	4.47780i	0.251842	+	0.211320i	−0.508123	+	0.861284i	$0.669661\pi$
$450$		0			0
$451$	2.83615	−	2.37981i	0.133549	−	0.112061i
$452$	10.1117	+	23.4416i	0.475615	+	1.10260i
$453$		0			0
$454$	−6.59072	−	22.0146i	−0.309318	−	1.03319i
$455$	12.7857	−	29.6405i	0.599401	−	1.38957i
$456$		0			0
$457$	−31.4124	+	20.6603i	−1.46941	+	0.966447i	−0.473066	+	0.881027i	$0.656853\pi$
$457$	−31.4124	+	20.6603i	−1.46941	+	0.966447i	−0.996345	+	0.0854197i	$0.972777\pi$
$458$	−2.42197	+	4.19498i	−0.113171	+	0.196018i
$459$		0			0
$460$	11.0226	+	19.0917i	0.513932	+	0.890157i
$461$	24.6974	+	12.4035i	1.15027	+	0.577688i	0.918632	−	0.395114i	$-0.129295\pi$
$461$	24.6974	+	12.4035i	1.15027	+	0.577688i	0.231639	+	0.972802i	$0.425591\pi$
$462$		0			0
$463$	14.6706	+	19.7060i	0.681800	+	0.915817i	0.999476	−	0.0323827i	$-0.0103095\pi$
$463$	14.6706	+	19.7060i	0.681800	+	0.915817i	−0.317675	+	0.948200i	$0.602902\pi$
$464$	−0.897978	+	0.951801i	−0.0416876	+	0.0441862i
$465$		0			0
$466$	37.4291	+	4.37484i	1.73387	+	0.202660i
$467$	7.38677	+	2.68856i	0.341819	+	0.124412i	0.507225	−	0.861814i	$-0.330671\pi$
$467$	7.38677	+	2.68856i	0.341819	+	0.124412i	−0.165406	+	0.986226i	$0.552893\pi$
$468$		0			0
$469$	−6.00971	+	2.18735i	−0.277503	+	0.101003i
$470$	−86.2868	+	20.4503i	−3.98011	+	0.943304i
$471$		0			0
$472$	−3.49430	−	2.29823i	−0.160838	−	0.105785i
$473$	−4.01761	+	2.01772i	−0.184730	+	0.0927749i
$474$		0			0
$475$	31.2760	+	33.1506i	1.43504	+	1.52106i
$476$	1.06981	−	6.06719i	0.0490346	−	0.278089i
$477$		0			0
$478$	4.50659	+	25.5581i	0.206127	+	1.16900i
$479$	10.5766	−	14.2069i	0.483258	−	0.649129i	−0.491896	−	0.870654i	$-0.663696\pi$
$479$	10.5766	−	14.2069i	0.483258	−	0.649129i	0.975155	+	0.221525i	$0.0711035\pi$
$480$		0			0
$481$	−11.5072	−	2.72726i	−0.524683	−	0.124352i
$482$	−36.7743	+	4.29829i	−1.67502	+	0.195782i
$483$		0			0
$484$	1.50145	+	25.7788i	0.0682475	+	1.17176i
$485$	−36.9377			−1.67725
$486$		0			0
$487$	−42.1146			−1.90840			−0.954198	−	0.299175i	$-0.903289\pi$
$487$	−42.1146			−1.90840			−0.954198	+	0.299175i	$0.903289\pi$
$488$	−0.0156614	−	0.268897i	−0.000708960	−	0.0121724i
$489$		0			0
$490$	33.7337	−	3.94291i	1.52394	−	0.178122i
$491$	7.08138	+	1.67832i	0.319578	+	0.0757415i	0.387274	−	0.921965i	$-0.373417\pi$
$491$	7.08138	+	1.67832i	0.319578	+	0.0757415i	−0.0676959	+	0.997706i	$0.521565\pi$
$492$		0			0
$493$	0.206677	−	0.277615i	0.00930825	−	0.0125032i
$494$	−4.09952	−	23.2495i	−0.184446	−	1.04604i
$495$		0			0
$496$	1.93053	−	10.9486i	0.0866833	−	0.491606i
$497$	−15.4577	−	16.3842i	−0.693374	−	0.734933i
$498$		0			0
$499$	14.4143	−	7.23914i	0.645273	−	0.324068i	−0.0958915	−	0.995392i	$-0.530570\pi$
$499$	14.4143	−	7.23914i	0.645273	−	0.324068i	0.741164	+	0.671324i	$0.234274\pi$
$500$	41.5211	+	27.3089i	1.85688	+	1.22129i
$501$		0			0
$502$	−38.7457	+	9.18290i	−1.72931	+	0.409853i
$503$	−34.7114	+	12.6339i	−1.54771	+	0.563319i	−0.967878	−	0.251421i	$-0.919102\pi$
$503$	−34.7114	+	12.6339i	−1.54771	+	0.563319i	−0.579827	+	0.814739i	$0.696880\pi$
$504$		0			0
$505$	45.0235	+	16.3872i	2.00352	+	0.729221i
$506$	3.63643	+	0.425038i	0.161659	+	0.0188952i
$507$		0			0
$508$	22.4545	−	23.8003i	0.996256	−	1.05597i
$509$	−6.97597	−	9.37035i	−0.309204	−	0.415333i	0.620173	−	0.784465i	$-0.287062\pi$
$509$	−6.97597	−	9.37035i	−0.309204	−	0.415333i	−0.929377	+	0.369132i	$0.879655\pi$
$510$		0			0
$511$	−23.6383	−	11.8716i	−1.04570	−	0.525168i
$512$	−14.0992	−	24.4205i	−0.623101	−	1.07924i
$513$		0			0
$514$	18.2411	−	31.5945i	0.804580	−	1.39357i
$515$	54.2202	−	35.6612i	2.38923	−	1.57142i
$516$		0			0
$517$	−3.22697	+	7.48095i	−0.141922	+	0.329012i
$518$	−9.62644	−	32.1545i	−0.422961	−	1.41279i
$519$		0			0
$520$	−3.86419	−	8.95820i	−0.169456	−	0.392843i
$521$	0.659940	−	0.553755i	0.0289125	−	0.0242605i	−0.628217	−	0.778038i	$-0.716215\pi$
$521$	0.659940	−	0.553755i	0.0289125	−	0.0242605i	0.657129	+	0.753778i	$0.271771\pi$
$522$		0			0
$523$	−6.06895	−	5.09246i	−0.265377	−	0.222678i	0.500383	−	0.865804i	$-0.333192\pi$
$523$	−6.06895	−	5.09246i	−0.265377	−	0.222678i	−0.765760	+	0.643126i	$0.777637\pi$
$524$	7.14602	−	23.8694i	0.312176	−	1.04274i
$525$		0			0
$526$	−3.02772	+	51.9839i	−0.132015	+	2.26660i
$527$	−0.170974	+	2.93551i	−0.00744775	+	0.127873i
$528$		0			0
$529$	5.09676	−	17.0244i	0.221598	−	0.740189i
$530$	−72.5967	−	60.9158i	−3.15340	−	2.64601i
$531$		0			0
$532$	28.3958	−	23.8269i	1.23112	−	1.03303i
$533$	−4.81787	−	11.1691i	−0.208685	−	0.483787i
$534$		0			0
$535$	4.12424	+	13.7759i	0.178307	+	0.595585i
$536$	−0.765571	+	1.77479i	−0.0330676	+	0.0766594i
$537$		0			0
$538$	18.8240	−	12.3808i	0.811562	−	0.533773i
$539$	1.56020	−	2.70235i	0.0672028	−	0.116399i
$540$		0			0
$541$	6.01461	+	10.4176i	0.258588	+	0.447888i	0.965864	−	0.259050i	$-0.0834094\pi$
$541$	6.01461	+	10.4176i	0.258588	+	0.447888i	−0.707276	+	0.706938i	$0.750076\pi$
$542$	−8.91723	−	4.47840i	−0.383028	−	0.192364i
$543$		0			0
$544$	3.55578	+	4.77624i	0.152453	+	0.204780i
$545$	−46.3217	+	49.0981i	−1.98420	+	2.10313i
$546$		0			0
$547$	6.33792	+	0.740797i	0.270990	+	0.0316742i	0.250503	−	0.968116i	$-0.419404\pi$
$547$	6.33792	+	0.740797i	0.270990	+	0.0316742i	0.0204874	+	0.999790i	$0.493478\pi$
$548$	−22.0342	−	8.01980i	−0.941255	−	0.342589i
$549$		0			0
$550$	15.2783	−	5.56083i	0.651467	−	0.237115i
$551$	2.02628	−	0.480237i	0.0863225	−	0.0204588i
$552$		0			0
$553$	12.0288	+	7.91146i	0.511516	+	0.336429i
$554$	−12.5006	+	6.27805i	−0.531101	+	0.266729i
$555$		0			0
$556$	17.8445	+	18.9141i	0.756776	+	0.802136i
$557$	6.99671	−	39.6803i	0.296460	−	1.68131i	−0.364747	−	0.931107i	$-0.618844\pi$
$557$	6.99671	−	39.6803i	0.296460	−	1.68131i	0.661207	−	0.750203i	$-0.270044\pi$
$558$		0			0
$559$	2.56494	+	14.5465i	0.108485	+	0.615251i
$560$	−21.8658	+	29.3709i	−0.923999	+	1.24115i
$561$		0			0
$562$	5.09780	+	1.20820i	0.215038	+	0.0509649i
$563$	−1.57494	+	0.184085i	−0.0663760	+	0.00775824i	−0.149216	−	0.988805i	$-0.547675\pi$
$563$	−1.57494	+	0.184085i	−0.0663760	+	0.00775824i	0.0828401	+	0.996563i	$0.473601\pi$
$564$		0			0
$565$	2.33349	+	40.0645i	0.0981708	+	1.68553i
$566$	1.96163			0.0824536
$567$		0			0
$568$	−6.80775			−0.285647
$569$	0.642162	+	11.0255i	0.0269208	+	0.462213i	0.984650	+	0.174541i	$0.0558442\pi$
$569$	0.642162	+	11.0255i	0.0269208	+	0.462213i	−0.957729	+	0.287672i	$0.907119\pi$
$570$		0			0
$571$	−7.85448	+	0.918056i	−0.328700	+	0.0384195i	−0.278842	−	0.960337i	$-0.589951\pi$
$571$	−7.85448	+	0.918056i	−0.328700	+	0.0384195i	−0.0498572	+	0.998756i	$0.515877\pi$
$572$	−4.53359	−	1.07448i	−0.189559	−	0.0449263i
$573$		0			0
$574$	20.6161	−	27.6923i	0.860501	−	1.15585i
$575$	4.03238	+	22.8688i	0.168162	+	0.953695i
$576$		0			0
$577$	−8.01656	+	45.4642i	−0.333734	+	1.89270i	0.105658	+	0.994402i	$0.466305\pi$
$577$	−8.01656	+	45.4642i	−0.333734	+	1.89270i	−0.439392	+	0.898295i	$0.644806\pi$
$578$	23.8748	+	25.3058i	0.993061	+	1.05258i
$579$		0			0
$580$	3.99735	−	2.00755i	0.165981	−	0.0833588i
$581$	7.09695	+	4.66774i	0.294431	+	0.193650i
$582$		0			0
$583$	−8.47220	+	2.00795i	−0.350883	+	0.0831607i
$584$	−7.51238	+	2.73428i	−0.310865	+	0.113145i
$585$		0			0
$586$	4.66235	+	1.69696i	0.192600	+	0.0701007i
$587$	36.5119	+	4.26763i	1.50701	+	0.176144i	0.829140	−	0.559041i	$-0.188830\pi$
$587$	36.5119	+	4.26763i	1.50701	+	0.176144i	0.677867	+	0.735184i	$0.262904\pi$
$588$		0			0
$589$	−12.1412	+	12.8689i	−0.500269	+	0.530254i
$590$	−20.4078	−	27.4124i	−0.840175	−	1.12855i
$591$		0			0
$592$	11.9876	+	6.02038i	0.492686	+	0.247436i
$593$	7.17407	+	12.4258i	0.294604	+	0.510268i	0.974893	−	0.222676i	$-0.0714791\pi$
$593$	7.17407	+	12.4258i	0.294604	+	0.510268i	−0.680289	+	0.732944i	$0.738146\pi$
$594$		0			0
$595$	4.84238	−	8.38725i	0.198518	−	0.343844i
$596$	25.7167	−	16.9141i	1.05340	−	0.692829i
$597$		0			0
$598$	4.76434	−	11.0450i	0.194828	−	0.451663i
$599$	−3.73299	−	12.4691i	−0.152526	−	0.509472i	0.847238	−	0.531214i	$-0.178264\pi$
$599$	−3.73299	−	12.4691i	−0.152526	−	0.509472i	−0.999764	+	0.0217420i	$0.993079\pi$
$600$		0			0
$601$	−2.49445	−	5.78278i	−0.101751	−	0.235885i	0.859735	−	0.510741i	$-0.170629\pi$
$601$	−2.49445	−	5.78278i	−0.101751	−	0.235885i	−0.961485	+	0.274857i	$0.911370\pi$
$602$	−32.1148	+	26.9476i	−1.30890	+	1.09830i
$603$		0			0
$604$	−34.5775	−	29.0140i	−1.40694	−	1.18056i
$605$	−11.6422	+	38.8877i	−0.473323	+	1.58101i
$606$		0			0
$607$	−0.764581	+	13.1274i	−0.0310334	+	0.532823i	0.946587	+	0.322448i	$0.104506\pi$
$607$	−0.764581	+	13.1274i	−0.0310334	+	0.532823i	−0.977621	+	0.210375i	$0.932531\pi$
$608$	−2.08315	+	35.7664i	−0.0844830	+	1.45052i
$609$		0			0
$610$	0.631235	−	2.10847i	0.0255580	−	0.0853696i
$611$	20.5052	+	17.2059i	0.829552	+	0.696076i
$612$		0			0
$613$	−28.3321	+	23.7734i	−1.14432	+	0.960200i	−0.999572	−	0.0292684i	$-0.990682\pi$
$613$	−28.3321	+	23.7734i	−1.14432	+	0.960200i	−0.144750	+	0.989468i	$0.546238\pi$
$614$	−12.7861	−	29.6415i	−0.516005	−	1.19623i
$615$		0			0
$616$	−0.729634	−	2.43715i	−0.0293978	−	0.0981955i
$617$	−12.8638	+	29.8216i	−0.517877	+	1.20057i	0.435883	+	0.900003i	$0.356436\pi$
$617$	−12.8638	+	29.8216i	−0.517877	+	1.20057i	−0.953760	+	0.300570i	$0.902823\pi$
$618$		0			0
$619$	35.8601	−	23.5855i	1.44134	−	0.947982i	0.442653	−	0.896693i	$-0.354037\pi$
$619$	35.8601	−	23.5855i	1.44134	−	0.947982i	0.998684	−	0.0512897i	$-0.0163332\pi$
$620$	−19.0021	+	32.9126i	−0.763142	+	1.32180i
$621$		0			0
$622$	−17.7127	−	30.6793i	−0.710215	−	1.23013i
$623$	−16.0575	−	8.06436i	−0.643328	−	0.323092i
$624$		0			0
$625$	16.3315	+	21.9370i	0.653260	+	0.877480i
$626$	−47.2939	+	50.1286i	−1.89024	+	2.00354i
$627$		0			0
$628$	−57.4873	−	6.71930i	−2.29399	−	0.268129i
$629$	−3.33404	−	1.21349i	−0.132937	−	0.0483851i
$630$		0			0
$631$	13.0635	−	4.75472i	0.520049	−	0.189282i	−0.0686408	−	0.997641i	$-0.521866\pi$
$631$	13.0635	−	4.75472i	0.520049	−	0.189282i	0.588690	+	0.808359i	$0.299644\pi$
$632$	4.23399	−	1.00347i	0.168419	−	0.0399161i
$633$		0			0
$634$	38.3073	+	25.1951i	1.52138	+	1.00063i
$635$	45.9661	−	23.0851i	1.82411	−	0.916102i
$636$		0			0
$637$	−7.03536	−	7.45705i	−0.278751	−	0.295459i
$638$	0.129000	−	0.731597i	0.00510717	−	0.0289642i
$639$		0			0
$640$	5.29656	+	30.0383i	0.209365	+	1.18737i
$641$	1.56433	−	2.10126i	0.0617874	−	0.0829948i	−0.770155	−	0.637856i	$-0.779821\pi$
$641$	1.56433	−	2.10126i	0.0617874	−	0.0829948i	0.831943	+	0.554862i	$0.187229\pi$
$642$		0			0
$643$	−0.0997430	−	0.0236395i	−0.00393348	−	0.000932252i	0.228649	−	0.973509i	$-0.426569\pi$
$643$	−0.0997430	−	0.0236395i	−0.00393348	−	0.000932252i	−0.232582	+	0.972577i	$0.574717\pi$
$644$	18.7591	−	2.19262i	0.739212	−	0.0864015i
$645$		0			0
$646$	−0.411834	−	7.07092i	−0.0162034	−	0.278202i
$647$	25.1564			0.988998			0.494499	−	0.869178i	$-0.335351\pi$
$647$	25.1564			0.988998			0.494499	+	0.869178i	$0.335351\pi$
$648$		0			0
$649$	−3.13983			−0.123249
$650$	−3.10597	−	53.3274i	−0.121826	−	2.09167i
$651$		0			0
$652$	−28.8367	+	3.37053i	−1.12933	+	0.132000i
$653$	7.25844	+	1.72028i	0.284045	+	0.0673198i	0.370169	−	0.928965i	$-0.379300\pi$
$653$	7.25844	+	1.72028i	0.284045	+	0.0673198i	−0.0861238	+	0.996284i	$0.527448\pi$
$654$		0			0
$655$	23.3896	−	31.4177i	0.913908	−	1.22759i
$656$	2.39595	+	13.5881i	0.0935463	+	0.530527i
$657$		0			0
$658$	−13.1924	+	74.8181i	−0.514295	+	2.91671i
$659$	11.1583	+	11.8271i	0.434664	+	0.460717i	0.907265	−	0.420559i	$-0.138166\pi$
$659$	11.1583	+	11.8271i	0.434664	+	0.460717i	−0.472601	+	0.881277i	$0.656685\pi$
$660$		0			0
$661$	16.8629	−	8.46886i	0.655890	−	0.329401i	−0.0895407	−	0.995983i	$-0.528540\pi$
$661$	16.8629	−	8.46886i	0.655890	−	0.329401i	0.745431	+	0.666583i	$0.232244\pi$
$662$	−42.0925	−	27.6847i	−1.63597	−	1.07600i
$663$		0			0
$664$	2.49804	−	0.592047i	0.0969429	−	0.0229759i
$665$	54.7570	−	19.9299i	2.12339	−	0.772849i
$666$		0			0
$667$	0.997034	+	0.362891i	0.0386053	+	0.0140512i
$668$	−59.5563	−	6.96113i	−2.30430	−	0.269334i
$669$		0			0
$670$	−10.8384	+	11.4881i	−0.418725	+	0.443823i
$671$	−0.120753	−	0.162199i	−0.00466161	−	0.00626163i
$672$		0			0
$673$	−7.31091	−	3.67168i	−0.281815	−	0.141533i	0.302277	−	0.953220i	$-0.402253\pi$
$673$	−7.31091	−	3.67168i	−0.281815	−	0.141533i	−0.584092	+	0.811687i	$0.698549\pi$
$674$	19.4599	+	33.7056i	0.749569	+	1.29829i
$675$		0			0
$676$	8.44293	−	14.6236i	0.324728	−	0.562445i
$677$	−19.2931	+	12.6892i	−0.741493	+	0.487687i	−0.863190	−	0.504880i	$-0.831537\pi$
$677$	−19.2931	+	12.6892i	−0.741493	+	0.487687i	0.121697	+	0.992567i	$0.461166\pi$
$678$		0			0
$679$	−12.5342	+	29.0575i	−0.481018	+	1.11512i
$680$	−0.839476	−	2.80405i	−0.0321924	−	0.107530i
$681$		0			0
$682$	2.49989	+	5.79540i	0.0957257	+	0.221917i
$683$	14.3566	−	12.0466i	0.549340	−	0.460951i	−0.325378	−	0.945584i	$-0.605491\pi$
$683$	14.3566	−	12.0466i	0.549340	−	0.460951i	0.874717	+	0.484633i	$0.161047\pi$
$684$		0			0
$685$	−28.2370	−	23.6937i	−1.07888	−	0.905289i
$686$	−5.82146	+	19.4450i	−0.222265	+	0.742415i
$687$		0			0
$688$	0.974212	−	16.7266i	0.0371415	−	0.637695i
$689$	−1.66331	+	28.5579i	−0.0633669	+	1.08797i
$690$		0			0
$691$	1.90704	−	6.36996i	0.0725472	−	0.242325i	−0.914023	−	0.405662i	$-0.867041\pi$
$691$	1.90704	−	6.36996i	0.0725472	−	0.242325i	0.986570	+	0.163338i	$0.0522261\pi$
$692$	29.4279	+	24.6929i	1.11868	+	0.938684i
$693$		0			0
$694$	27.4089	−	22.9988i	1.04043	−	0.873023i
$695$	16.1906	+	37.5341i	0.614146	+	1.42375i
$696$		0			0
$697$	−1.04666	−	3.49609i	−0.0396451	−	0.132424i
$698$	6.84419	−	15.8666i	0.259056	−	0.600560i
$699$		0			0
$700$	70.0752	−	46.0892i	2.64860	−	1.74201i
$701$	−12.1477	+	21.0405i	−0.458813	+	0.794687i	−0.998899	−	0.0469230i	$-0.985058\pi$
$701$	−12.1477	+	21.0405i	−0.458813	+	0.794687i	0.540086	+	0.841610i	$0.318392\pi$
$702$		0			0
$703$	−10.6738	−	18.4876i	−0.402571	−	0.697274i
$704$	7.60724	+	3.82050i	0.286709	+	0.143991i
$705$		0			0
$706$	−31.0989	−	41.7731i	−1.17042	−	1.57215i
$707$	28.1692	−	29.8576i	1.05941	−	1.12291i
$708$		0			0
$709$	−29.7197	−	3.47374i	−1.11615	−	0.130459i	−0.462039	−	0.886860i	$-0.652882\pi$
$709$	−29.7197	−	3.47374i	−1.11615	−	0.130459i	−0.654108	+	0.756401i	$0.726956\pi$
$710$	−52.2729	−	19.0258i	−1.96177	−	0.714024i
$711$		0			0
$712$	−5.10315	+	1.85740i	−0.191249	+	0.0696089i
$713$	−8.77152	+	2.07889i	−0.328496	+	0.0778550i
$714$		0			0
$715$	−6.11932	−	4.02474i	−0.228850	−	0.150517i
$716$	15.9077	−	7.98913i	0.594497	−	0.298568i
$717$		0			0
$718$	−18.3599	−	19.4603i	−0.685185	−	0.726253i
$719$	2.12889	−	12.0735i	0.0793943	−	0.450267i	−0.919032	−	0.394183i	$-0.871027\pi$
$719$	2.12889	−	12.0735i	0.0793943	−	0.450267i	0.998426	−	0.0560838i	$-0.0178614\pi$
$720$		0			0
$721$	−9.65461	−	54.7540i	−0.359556	−	2.03915i
$722$	1.44332	−	1.93871i	0.0537146	−	0.0721513i
$723$		0			0
$724$	−18.6454	−	4.41905i	−0.692953	−	0.164233i
$725$	4.67998	−	0.547011i	0.173810	−	0.0203155i
$726$		0			0
$727$	2.85025	+	48.9370i	0.105710	+	1.81497i	0.468895	+	0.883254i	$0.344652\pi$
$727$	2.85025	+	48.9370i	0.105710	+	1.81497i	−0.363185	+	0.931717i	$0.618311\pi$
$728$	−8.35832			−0.309780
$729$		0			0
$730$	−65.3249			−2.41778
$731$	0.257672	+	4.42405i	0.00953033	+	0.163630i
$732$		0			0
$733$	20.0628	−	2.34500i	0.741035	−	0.0866146i	0.262805	−	0.964849i	$-0.415352\pi$
$733$	20.0628	−	2.34500i	0.741035	−	0.0866146i	0.478230	+	0.878234i	$0.341278\pi$
$734$	−21.6046	−	5.12038i	−0.797439	−	0.188997i
$735$		0			0
$736$	−10.9008	+	14.6423i	−0.401808	+	0.539722i
$737$	0.251977	+	1.42903i	0.00928168	+	0.0526390i
$738$		0			0
$739$	0.349401	−	1.98155i	0.0128529	−	0.0728925i	−0.977707	−	0.209975i	$-0.932662\pi$
$739$	0.349401	−	1.98155i	0.0128529	−	0.0728925i	0.990560	+	0.137083i	$0.0437727\pi$
$740$	−31.4684	−	33.3545i	−1.15680	−	1.22614i
$741$		0			0
$742$	−72.5546	+	36.4383i	−2.66356	+	1.33769i
$743$	18.0232	+	11.8540i	0.661207	+	0.434883i	0.835261	−	0.549853i	$-0.185316\pi$
$743$	18.0232	+	11.8540i	0.661207	+	0.434883i	−0.174054	+	0.984736i	$0.555687\pi$
$744$		0			0
$745$	47.0826	−	11.1588i	1.72497	−	0.408826i
$746$	−23.4531	+	8.53624i	−0.858680	+	0.312534i
$747$		0			0
$748$	−1.31354	−	0.478091i	−0.0480279	−	0.0174807i
$749$	12.2365	+	1.43024i	0.447112	+	0.0522599i
$750$		0			0
$751$	9.93510	−	10.5306i	0.362537	−	0.384267i	−0.520271	−	0.854001i	$-0.674169\pi$
$751$	9.93510	−	10.5306i	0.362537	−	0.384267i	0.882808	+	0.469735i	$0.155650\pi$
$752$	−18.1316	−	24.3549i	−0.661190	−	0.888132i
$753$		0			0
$754$	−2.18111	−	1.09539i	−0.0794313	−	0.0398919i
$755$	−35.4783	−	61.4503i	−1.29119	−	2.23640i
$756$		0			0
$757$	−5.26451	+	9.11840i	−0.191342	+	0.331414i	−0.945695	−	0.325055i	$-0.894617\pi$
$757$	−5.26451	+	9.11840i	−0.191342	+	0.331414i	0.754353	+	0.656469i	$0.227951\pi$
$758$	−32.0607	+	21.0866i	−1.16450	+	0.765901i
$759$		0			0
$760$	6.97545	−	16.1709i	0.253026	−	0.586580i
$761$	−12.1247	−	40.4993i	−0.439520	−	1.46810i	−0.835321	−	0.549763i	$-0.814718\pi$
$761$	−12.1247	−	40.4993i	−0.439520	−	1.46810i	0.395801	−	0.918336i	$-0.370467\pi$
$762$		0			0
$763$	22.9052	+	53.1001i	0.829223	+	1.92235i
$764$	19.1188	−	16.0425i	0.691693	−	0.580399i
$765$		0			0
$766$	−25.1504	−	21.1037i	−0.908721	−	0.762507i
$767$	−2.95862	+	9.88247i	−0.106829	+	0.356835i
$768$		0			0
$769$	0.524422	−	9.00399i	0.0189112	−	0.324692i	−0.975564	−	0.219717i	$-0.929487\pi$
$769$	0.524422	−	9.00399i	0.0189112	−	0.324692i	0.994475	−	0.104975i	$-0.0334763\pi$
$770$	1.20870	−	20.7526i	0.0435586	−	0.747872i
$771$		0			0
$772$	11.3584	−	37.9399i	0.408799	−	1.36549i
$773$	−0.551231	−	0.462537i	−0.0198264	−	0.0166363i	0.632821	−	0.774298i	$-0.281897\pi$
$773$	−0.551231	−	0.462537i	−0.0198264	−	0.0166363i	−0.652647	+	0.757662i	$0.726342\pi$
$774$		0			0
$775$	−30.6663	+	25.7321i	−1.10157	+	0.924325i
$776$	3.78819	+	8.78200i	0.135988	+	0.315255i
$777$		0			0
$778$	−9.36562	−	31.2834i	−0.335774	−	1.12156i
$779$	8.69699	−	20.1619i	0.311602	−	0.722375i
$780$		0			0
$781$	−4.27003	+	2.80844i	−0.152794	+	0.100494i
$782$	1.80442	−	3.12535i	0.0645261	−	0.111762i
$783$		0			0
$784$	5.81453	+	10.0711i	0.207662	+	0.359681i
$785$	−81.3075	−	40.8341i	−2.90199	−	1.45743i
$786$		0			0
$787$	9.21263	+	12.3747i	0.328395	+	0.441111i	0.935402	−	0.353585i	$-0.115038\pi$
$787$	9.21263	+	12.3747i	0.328395	+	0.441111i	−0.607008	+	0.794696i	$0.707630\pi$
$788$	18.6426	−	19.7600i	0.664116	−	0.703922i
$789$		0			0
$790$	35.3148	+	4.12771i	1.25645	+	0.146857i
$791$	32.3091	+	11.7595i	1.14878	+	0.418121i
$792$		0			0
$793$	−0.624297	+	0.227226i	−0.0221695	+	0.00806902i
$794$	4.20516	−	0.996642i	0.149236	−	0.0353695i
$795$		0			0
$796$	−7.26376	−	4.77745i	−0.257457	−	0.169332i
$797$	−12.4488	+	6.25200i	−0.440957	+	0.221457i	−0.655404	−	0.755279i	$-0.727502\pi$
$797$	−12.4488	+	6.25200i	−0.440957	+	0.221457i	0.214446	+	0.976736i	$0.431205\pi$
$798$		0			0
$799$	5.51107	+	5.84139i	0.194968	+	0.206654i
$800$	−14.0768	+	79.8335i	−0.497690	+	2.82254i
$801$		0			0
$802$	−5.49411	−	31.1586i	−0.194004	−	1.10025i
$803$	−3.58401	+	4.81416i	−0.126477	+	0.169888i
$804$		0			0
$805$	28.8898	+	6.84701i	1.01823	+	0.241325i
$806$	20.5963	−	2.40736i	0.725475	−	0.0847958i
$807$		0			0
$808$	−0.721345	−	12.3850i	−0.0253768	−	0.435704i
$809$	40.8781			1.43720			0.718599	−	0.695424i	$-0.244784\pi$
$809$	40.8781			1.43720			0.718599	+	0.695424i	$0.244784\pi$
$810$		0			0
$811$	51.1039			1.79450			0.897250	−	0.441524i	$-0.145562\pi$
$811$	51.1039			1.79450			0.897250	+	0.441524i	$0.145562\pi$
$812$	−0.222827	−	3.82580i	−0.00781970	−	0.134259i
$813$		0			0
$814$	−7.56411	+	0.884117i	−0.265122	+	0.0309883i
$815$	−44.4098	−	10.5253i	−1.55561	−	0.368685i
$816$		0			0
$817$	−15.9225	+	21.3876i	−0.557057	+	0.748257i
$818$	3.81673	+	21.6457i	0.133449	+	0.756825i
$819$		0			0
$820$	8.19037	−	46.4499i	0.286020	−	1.62210i
$821$	−33.3316	−	35.3295i	−1.16328	−	1.23301i	−0.967641	−	0.252331i	$-0.918803\pi$
$821$	−33.3316	−	35.3295i	−1.16328	−	1.23301i	−0.195641	−	0.980676i	$-0.562679\pi$
$822$		0			0
$823$	24.1523	−	12.1298i	0.841898	−	0.422817i	0.0250611	−	0.999686i	$-0.492022\pi$
$823$	24.1523	−	12.1298i	0.841898	−	0.422817i	0.816837	+	0.576869i	$0.195726\pi$
$824$	−14.0391	−	9.23367i	−0.489076	−	0.321670i
$825$		0			0
$826$	−28.4893	+	6.75210i	−0.991271	+	0.234936i
$827$	14.9793	−	5.45201i	0.520880	−	0.189585i	−0.0681816	−	0.997673i	$-0.521720\pi$
$827$	14.9793	−	5.45201i	0.520880	−	0.189585i	0.589062	+	0.808088i	$0.299497\pi$
$828$		0			0
$829$	1.59698	+	0.581253i	0.0554654	+	0.0201877i	0.369604	−	0.929189i	$-0.379493\pi$
$829$	1.59698	+	0.581253i	0.0554654	+	0.0201877i	−0.314138	+	0.949377i	$0.601716\pi$
$830$	20.8357	+	2.43534i	0.723216	+	0.0845319i
$831$		0			0
$832$	19.1930	−	20.3434i	0.665398	−	0.705281i
$833$	−1.83674	−	2.46717i	−0.0636393	−	0.0854824i
$834$		0			0
$835$	−84.2338	−	42.3038i	−2.91503	−	1.46398i
$836$	−4.20527	−	7.28373i	−0.145442	−	0.251913i
$837$		0			0
$838$	0.560786	−	0.971310i	0.0193720	−	0.0335534i
$839$	−38.7261	+	25.4706i	−1.33697	+	0.879342i	−0.998108	−	0.0614919i	$-0.980414\pi$
$839$	−38.7261	+	25.4706i	−1.33697	+	0.879342i	−0.338867	+	0.940834i	$0.610044\pi$
$840$		0			0
$841$	−11.4010	+	26.4306i	−0.393139	+	0.911399i
$842$	19.4576	+	64.9930i	0.670554	+	2.23981i
$843$		0			0
$844$	−7.53668	−	17.4720i	−0.259423	−	0.601410i
$845$	20.3343	−	17.0625i	0.699523	−	0.586969i
$846$		0			0
$847$	26.6409	+	22.3544i	0.915393	+	0.768106i
$848$	9.30638	−	31.0855i	0.319582	−	1.06748i
$849$		0			0
$850$	0.931850	−	15.9992i	0.0319622	−	0.548769i
$851$	0.632439	−	10.8586i	0.0216797	−	0.372227i
$852$		0			0
$853$	6.93914	−	23.1783i	0.237592	−	0.793611i	−0.753150	−	0.657849i	$-0.771466\pi$
$853$	6.93914	−	23.1783i	0.237592	−	0.793611i	0.990741	−	0.135762i	$-0.0433483\pi$
$854$	−1.44446	−	1.21204i	−0.0494283	−	0.0414753i
$855$		0			0
$856$	2.85228	−	2.39335i	0.0974891	−	0.0818031i
$857$	5.08115	+	11.7794i	0.173569	+	0.402378i	0.982688	−	0.185266i	$-0.0593148\pi$
$857$	5.08115	+	11.7794i	0.173569	+	0.402378i	−0.809119	+	0.587644i	$0.800055\pi$
$858$		0			0
$859$	−5.88521	−	19.6580i	−0.200801	−	0.670721i	−0.997773	−	0.0667049i	$-0.978751\pi$
$859$	−5.88521	−	19.6580i	−0.200801	−	0.670721i	0.796972	−	0.604016i	$-0.206434\pi$
$860$	−22.6856	+	52.5911i	−0.773572	+	1.79334i
$861$		0			0
$862$	9.51534	−	6.25834i	0.324094	−	0.213160i
$863$	−18.5110	+	32.0620i	−0.630121	+	1.09140i	0.357405	+	0.933949i	$0.383662\pi$
$863$	−18.5110	+	32.0620i	−0.630121	+	1.09140i	−0.987527	+	0.157453i	$0.949672\pi$
$864$		0			0
$865$	30.1945	+	52.2984i	1.02664	+	1.77820i
$866$	62.9472	+	31.6133i	2.13903	+	1.07426i
$867$		0			0
$868$	19.4431	+	26.1165i	0.659940	+	0.886453i
$869$	2.24172	−	2.37609i	0.0760452	−	0.0806032i
$870$		0			0
$871$	4.73524	+	0.553470i	0.160447	+	0.0187536i
$872$	16.4237	+	5.97775i	0.556178	+	0.202432i
$873$		0			0
$874$	20.4042	−	7.42652i	0.690182	−	0.251206i
$875$	65.1266	−	15.4353i	2.20168	−	0.521808i
$876$		0			0
$877$	−36.2333	−	23.8310i	−1.22351	−	0.804715i	−0.237498	−	0.971388i	$-0.576327\pi$
$877$	−36.2333	−	23.8310i	−1.22351	−	0.804715i	−0.986012	+	0.166673i	$0.946698\pi$
$878$	−35.3221	+	17.7394i	−1.19206	+	0.598677i
$879$		0			0
$880$	5.70132	+	6.04305i	0.192191	+	0.203711i
$881$	−1.78531	+	10.1250i	−0.0601486	+	0.341120i	−1.00000		0.000464198i	$-0.999852\pi$
$881$	−1.78531	+	10.1250i	−0.0601486	+	0.341120i	0.939851	+	0.341584i	$0.110963\pi$
$882$		0			0
$883$	1.36337	+	7.73205i	0.0458810	+	0.260204i	0.999117	−	0.0420240i	$-0.0133806\pi$
$883$	1.36337	+	7.73205i	0.0458810	+	0.260204i	−0.953236	+	0.302228i	$0.902269\pi$
$884$	−2.74250	+	3.68381i	−0.0922402	+	0.123900i
$885$		0			0
$886$	38.8492	+	9.20743i	1.30516	+	0.309330i
$887$	−34.7570	+	4.06251i	−1.16703	+	0.136406i	−0.677459	−	0.735560i	$-0.736919\pi$
$887$	−34.7570	+	4.06251i	−1.16703	+	0.136406i	−0.489566	+	0.871966i	$0.662845\pi$
$888$		0			0
$889$	−2.56232	−	43.9933i	−0.0859375	−	1.47549i
$890$	−44.3751			−1.48746
$891$		0			0
$892$	26.8550			0.899172
$893$	2.80954	+	48.2379i	0.0940176	+	1.61422i
$894$		0			0
$895$	27.7942	−	3.24867i	0.929057	−	0.108591i
$896$	25.4273	+	6.02638i	0.849467	+	0.201327i
$897$		0			0
$898$	8.80140	−	11.8223i	0.293707	−	0.394516i
$899$	0.317622	+	1.80133i	0.0105933	+	0.0600776i
$900$		0			0
$901$	−1.49032	+	8.45204i	−0.0496498	+	0.281578i
$902$	−5.37548	−	5.69768i	−0.178984	−	0.189712i
$903$		0			0
$904$	9.28610	−	4.66365i	0.308851	−	0.155111i
$905$	−25.1671	−	16.5527i	−0.836583	−	0.550229i
$906$		0			0
$907$	−48.8847	+	11.5859i	−1.62319	+	0.384703i	−0.938813	−	0.344427i	$-0.888073\pi$
$907$	−48.8847	+	11.5859i	−1.62319	+	0.384703i	−0.684375	+	0.729130i	$0.739925\pi$
$908$	−25.2752	+	9.19941i	−0.838786	+	0.305293i
$909$		0			0
$910$	−64.1788	−	23.3592i	−2.12751	−	0.774349i
$911$	−24.4948	−	2.86303i	−0.811548	−	0.0948564i	−0.299811	−	0.953999i	$-0.596924\pi$
$911$	−24.4948	−	2.86303i	−0.811548	−	0.0948564i	−0.511737	+	0.859142i	$0.670998\pi$
$912$		0			0
$913$	1.32261	−	1.40188i	0.0437720	−	0.0463956i
$914$	47.5025	+	63.8069i	1.57124	+	2.11055i
$915$		0			0
$916$	5.06661	+	2.54455i	0.167405	+	0.0840741i
$917$	−16.7783	−	29.0608i	−0.554067	−	0.959672i
$918$		0			0
$919$	−4.12738	+	7.14883i	−0.136150	+	0.235818i	−0.926036	−	0.377435i	$-0.876806\pi$
$919$	−4.12738	+	7.14883i	−0.136150	+	0.235818i	0.789886	+	0.613253i	$0.210139\pi$
$920$	7.49699	−	4.93085i	0.247168	−	0.162565i
$921$		0			0
$922$	23.1601	−	53.6911i	0.762736	−	1.76822i
$923$	4.81585	+	16.0861i	0.158516	+	0.529479i
$924$		0			0
$925$	−19.1318	−	44.3526i	−0.629051	−	1.45830i
$926$	39.8178	−	33.4111i	1.30849	−	1.09796i
$927$		0			0
$928$	2.83740	+	2.38086i	0.0931422	+	0.0781556i
$929$	−2.81291	+	9.39578i	−0.0922886	+	0.308266i	−0.991653	−	0.128934i	$-0.958844\pi$
$929$	−2.81291	+	9.39578i	−0.0922886	+	0.308266i	0.899365	+	0.437200i	$0.144030\pi$
$930$		0			0
$931$	1.07605	−	18.4751i	0.0352663	−	0.605498i
$932$	2.56464	−	44.0331i	0.0840075	−	1.44235i
$933$		0			0
$934$	4.77000	−	15.9329i	0.156079	−	0.521341i
$935$	−1.68332	−	1.41247i	−0.0550503	−	0.0461927i
$936$		0			0
$937$	33.8490	−	28.4027i	1.10580	−	0.927875i	0.107997	−	0.994151i	$-0.465556\pi$
$937$	33.8490	−	28.4027i	1.10580	−	0.927875i	0.997801	+	0.0662763i	$0.0211119\pi$
$938$	5.35939	+	12.4245i	0.174990	+	0.405673i
$939$		0			0
$940$	29.7683	+	99.4332i	0.970936	+	3.24315i
$941$	4.21441	−	9.77010i	0.137386	−	0.318496i	−0.835608	−	0.549326i	$-0.814885\pi$
$941$	4.21441	−	9.77010i	0.137386	−	0.318496i	0.972994	+	0.230829i	$0.0741440\pi$
$942$		0			0
$943$	9.34725	−	6.14779i	0.304388	−	0.200199i
$944$	5.85073	−	10.1338i	0.190425	−	0.329826i
$945$		0			0
$946$	4.75603	+	8.23768i	0.154632	+	0.267830i
$947$	9.82476	+	4.93418i	0.319262	+	0.160339i	0.601212	−	0.799090i	$-0.294685\pi$
$947$	9.82476	+	4.93418i	0.319262	+	0.160339i	−0.281950	+	0.959429i	$0.590981\pi$
$948$		0			0
$949$	11.7752	+	15.8168i	0.382238	+	0.513434i
$950$	66.1724	−	70.1386i	2.14692	−	2.27560i
$951$		0			0
$952$	−2.49070	−	0.291121i	−0.0807240	−	0.00943529i
$953$	−39.7723	−	14.4759i	−1.28835	−	0.468921i	−0.395165	−	0.918610i	$-0.629313\pi$
$953$	−39.7723	−	14.4759i	−1.28835	−	0.468921i	−0.893185	+	0.449689i	$0.851535\pi$
$954$		0			0
$955$	36.8676	−	13.4187i	1.19301	−	0.434219i
$956$	29.5576	−	7.00528i	0.955962	−	0.226567i
$957$		0			0
$958$	−31.3086	−	20.5920i	−1.01153	−	0.665296i
$959$	−28.2207	+	14.1730i	−0.911293	+	0.457669i
$960$		0			0
$961$	10.6091	+	11.2450i	0.342230	+	0.362742i
$962$	−4.34483	+	24.6407i	−0.140083	+	0.794449i
$963$		0			0
$964$	7.52523	+	42.6777i	0.242371	+	1.37456i
$965$	37.1773	−	49.9378i	1.19678	−	1.60755i
$966$		0			0
$967$	−8.08740	−	1.91675i	−0.260073	−	0.0616385i	0.0985107	−	0.995136i	$-0.468592\pi$
$967$	−8.08740	−	1.91675i	−0.260073	−	0.0616385i	−0.358584	+	0.933498i	$0.616740\pi$
$968$	10.4396	−	1.22021i	0.335541	−	0.0392192i
$969$		0			0
$970$	4.54408	+	78.0189i	0.145902	+	2.50504i
$971$	17.9539			0.576169			0.288084	−	0.957605i	$-0.406982\pi$
$971$	17.9539			0.576169			0.288084	+	0.957605i	$0.406982\pi$
$972$		0			0
$973$	35.0207			1.12271
$974$	5.18095	+	88.9535i	0.166008	+	2.85026i
$975$		0			0
$976$	0.748505	−	0.0874877i	0.0239591	−	0.00280041i
$977$	23.7522	+	5.62938i	0.759901	+	0.180100i	0.592259	−	0.805748i	$-0.298236\pi$
$977$	23.7522	+	5.62938i	0.759901	+	0.180100i	0.167643	+	0.985848i	$0.446385\pi$
$978$		0			0
$979$	−2.43461	+	3.27025i	−0.0778106	+	0.104518i
$980$	−6.90304	−	39.1491i	−0.220509	−	1.25057i
$981$		0			0
$982$	2.67375	−	15.1636i	0.0853228	−	0.483890i
$983$	31.9879	+	33.9052i	1.02026	+	1.08141i	0.996658	+	0.0816861i	$0.0260305\pi$
$983$	31.9879	+	33.9052i	1.02026	+	1.08141i	0.0235974	+	0.999722i	$0.492488\pi$
$984$		0			0
$985$	38.1630	−	19.1662i	1.21597	−	0.610685i
$986$	−0.611797	−	0.402385i	−0.0194836	−	0.0128146i
$987$		0			0
$988$	−26.8877	+	6.37251i	−0.855413	+	0.202737i
$989$	−12.7663	+	4.64654i	−0.405944	+	0.147751i
$990$		0			0
$991$	−55.3339	−	20.1399i	−1.75774	−	0.639765i	−0.757820	−	0.652464i	$-0.773735\pi$
$991$	−55.3339	−	20.1399i	−1.75774	−	0.639765i	−0.999919	+	0.0126995i	$0.995958\pi$
$992$	−31.2563	−	3.65334i	−0.992388	−	0.115994i
$993$		0			0
$994$	−32.7048	+	34.6650i	−1.03733	+	1.09951i
$995$	−8.16139	−	10.9626i	−0.258733	−	0.347539i
$996$		0			0
$997$	53.8777	+	27.0584i	1.70632	+	0.856948i	0.986694	+	0.162590i	$0.0519847\pi$
$997$	53.8777	+	27.0584i	1.70632	+	0.856948i	0.719630	+	0.694358i	$0.244312\pi$
$998$	−17.0636	−	29.5550i	−0.540138	−	0.935547i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.514.2		144
3.2	odd	2		729.2.g.d.514.7		144
9.2	odd	6		729.2.g.c.28.7		144
9.4	even	3		243.2.g.a.10.7		144
9.5	odd	6		81.2.g.a.13.2	✓	144
9.7	even	3		729.2.g.b.28.2		144
81.2	odd	54		729.2.g.d.217.7		144
81.22	even	27		6561.2.a.d.1.61		72
81.25	even	27		729.2.g.b.703.2		144
81.29	odd	54		81.2.g.a.25.2	yes	144
81.52	even	27		243.2.g.a.73.7		144
81.56	odd	54		729.2.g.c.703.7		144
81.59	odd	54		6561.2.a.c.1.12		72
81.79	even	27	inner	729.2.g.a.217.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.2	✓	144	9.5	odd	6
81.2.g.a.25.2	yes	144	81.29	odd	54
243.2.g.a.10.7		144	9.4	even	3
243.2.g.a.73.7		144	81.52	even	27
729.2.g.a.217.2		144	81.79	even	27	inner
729.2.g.a.514.2		144	1.1	even	1	trivial
729.2.g.b.28.2		144	9.7	even	3
729.2.g.b.703.2		144	81.25	even	27
729.2.g.c.28.7		144	9.2	odd	6
729.2.g.c.703.7		144	81.56	odd	54
729.2.g.d.217.7		144	81.2	odd	54
729.2.g.d.514.7		144	3.2	odd	2
6561.2.a.c.1.12		72	81.59	odd	54
6561.2.a.d.1.61		72	81.22	even	27

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.123020 - 2.11218i) q^{2} +(-2.45968 + 0.287495i) q^{4} +(-3.78800 - 0.897774i) q^{5} +(-1.99164 + 2.67524i) q^{7} +(0.175036 + 0.992677i) q^{8} +(-1.43025 + 8.11138i) q^{10} +(0.519303 + 0.550429i) q^{11} +(2.22178 - 1.11582i) q^{13} +(5.89558 + 3.87759i) q^{14} +(-2.74416 + 0.650378i) q^{16} +(0.700932 - 0.255119i) q^{17} +(4.21736 + 1.53499i) q^{19} +(9.57537 + 1.11920i) q^{20} +(1.09872 - 1.16457i) q^{22} +(1.36553 + 1.83423i) q^{23} +(9.07482 + 4.55755i) q^{25} +(-2.63013 - 4.55552i) q^{26} +(4.12967 - 7.15280i) q^{28} +(0.387661 - 0.254968i) q^{29} +(-1.56139 + 3.61971i) q^{31} +(2.28949 + 7.64743i) q^{32} +(-0.625084 - 1.44911i) q^{34} +(9.94610 - 8.34577i) q^{35} +(-3.64375 - 3.05747i) q^{37} +(2.72336 - 9.09665i) q^{38} +(0.228163 - 3.91741i) q^{40} +(0.284474 - 4.88423i) q^{41} +(-1.70392 + 5.69149i) q^{43} +(-1.43556 - 1.20458i) q^{44} +(3.70623 - 3.10990i) q^{46} +(4.26433 + 9.88583i) q^{47} +(-1.18264 - 3.95029i) q^{49} +(8.50995 - 19.7283i) q^{50} +(-5.14406 + 3.38330i) q^{52} +(-5.75294 + 9.96438i) q^{53} +(-1.47296 - 2.55124i) q^{55} +(-3.00425 - 1.50879i) q^{56} +(-0.586228 - 0.787441i) q^{58} +(-2.84735 + 3.01801i) q^{59} +(-0.265410 - 0.0310220i) q^{61} +(7.83755 + 2.85264i) q^{62} +(10.5709 - 3.84748i) q^{64} +(-9.41786 + 2.23207i) q^{65} +(1.60209 + 1.05371i) q^{67} +(-1.65072 + 0.829024i) q^{68} +(-18.8513 - 19.9812i) q^{70} +(-1.17278 + 6.65118i) q^{71} +(1.37723 + 7.81064i) q^{73} +(-6.00966 + 8.07238i) q^{74} +(-10.8147 - 2.56312i) q^{76} +(-2.50679 + 0.293002i) q^{77} +(-0.250999 - 4.30948i) q^{79} +10.9788 q^{80} -10.3513 q^{82} +(-0.148089 - 2.54258i) q^{83} +(-2.88417 + 0.337112i) q^{85} +(12.2310 + 2.89881i) q^{86} +(-0.455501 + 0.611845i) q^{88} +(0.935549 + 5.30576i) q^{89} +(-1.43990 + 8.16609i) q^{91} +(-3.88610 - 4.11903i) q^{92} +(20.3560 - 10.2232i) q^{94} +(-14.5973 - 9.60081i) q^{95} +(9.23262 - 2.18817i) q^{97} +(-8.19821 + 2.98391i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) \) 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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