LMFDB - Embedded newform 729.2.g.c.703.7

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,-63] 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			703.7
Character	$\chi$	$=$	729.703
Dual form			729.2.g.c.28.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.76769 + 1.16263i) q^{2} +(0.980860 + 2.27389i) q^{4} +(-2.67150 - 2.83162i) q^{5} +(3.31264 - 0.387192i) q^{7} +(-0.175036 + 0.992677i) q^{8} +(-1.43025 - 8.11138i) q^{10} +(-0.217034 - 0.724944i) q^{11} +(-0.144562 - 2.48203i) q^{13} +(6.30588 + 3.16693i) q^{14} +(1.93533 - 2.05133i) q^{16} +(-0.700932 - 0.255119i) q^{17} +(4.21736 - 1.53499i) q^{19} +(3.81843 - 8.85211i) q^{20} +(0.459191 - 1.53380i) q^{22} +(2.27126 + 0.265472i) q^{23} +(-0.590459 + 10.1378i) q^{25} +(2.63013 - 4.55552i) q^{26} +(4.12967 + 7.15280i) q^{28} +(0.414639 - 0.208240i) q^{29} +(-2.35407 + 3.16206i) q^{31} +(7.76762 - 1.84096i) q^{32} +(-0.942422 - 1.26589i) q^{34} +(-9.94610 - 8.34577i) q^{35} +(-3.64375 + 3.05747i) q^{37} +(9.23961 + 2.18983i) q^{38} +(3.27849 - 2.15630i) q^{40} +(-4.08763 + 2.68847i) q^{41} +(5.78094 + 1.37011i) q^{43} +(1.43556 - 1.20458i) q^{44} +(3.70623 + 3.10990i) q^{46} +(-6.42922 - 8.63594i) q^{47} +(4.01237 - 0.950949i) q^{49} +(-12.8302 + 17.2340i) q^{50} +(5.50206 - 2.76324i) q^{52} +(5.75294 + 9.96438i) q^{53} +(-1.47296 + 2.55124i) q^{55} +(-0.195474 + 3.35616i) q^{56} +(0.975058 + 0.113968i) q^{58} +(1.19000 - 3.97488i) q^{59} +(0.105839 - 0.245363i) q^{61} +(-7.83755 + 2.85264i) q^{62} +(10.5709 + 3.84748i) q^{64} +(-6.64196 + 7.04007i) q^{65} +(-1.71358 - 0.860594i) q^{67} +(-0.107405 - 1.84408i) q^{68} +(-7.87859 - 26.3163i) q^{70} +(1.17278 + 6.65118i) q^{71} +(1.37723 - 7.81064i) q^{73} +(-9.99572 + 1.16833i) q^{74} +(7.62705 + 8.08420i) q^{76} +(-0.999649 - 2.31745i) q^{77} +(-3.60662 - 2.37211i) q^{79} -10.9788 q^{80} -10.3513 q^{82} +(2.12790 + 1.39954i) q^{83} +(1.15014 + 2.66632i) q^{85} +(8.62597 + 9.14299i) q^{86} +(0.757624 - 0.0885535i) q^{88} +(-0.935549 + 5.30576i) q^{89} +(-1.43990 - 8.16609i) q^{91} +(1.62413 + 5.42498i) q^{92} +(-1.32448 - 22.7404i) q^{94} +(-15.6132 - 7.84124i) q^{95} +(-6.51132 + 6.90160i) q^{97} +(8.19821 + 2.98391i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 63 q^{20} + 9 q^{22} + 36 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 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{27}\right)$

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 $

$2$	1.76769	+	1.16263i	1.24994	+	0.822101i	0.989660	−	0.143431i	$-0.0458135\pi$
$2$	1.76769	+	1.16263i	1.24994	+	0.822101i	0.260284	+	0.965532i	$0.416184\pi$
$3$		0			0
$3$		0			0
$4$	0.980860	+	2.27389i	0.490430	+	1.13694i
$5$	−2.67150	−	2.83162i	−1.19473	−	1.26634i	−0.955371	−	0.295408i	$-0.904544\pi$
$5$	−2.67150	−	2.83162i	−1.19473	−	1.26634i	−0.239359	−	0.970931i	$-0.576937\pi$
$6$		0			0
$7$	3.31264	−	0.387192i	1.25206	−	0.146345i	0.535901	−	0.844281i	$-0.319972\pi$
$7$	3.31264	−	0.387192i	1.25206	−	0.146345i	0.716160	+	0.697936i	$0.245898\pi$
$8$	−0.175036	+	0.992677i	−0.0618845	+	0.350964i
$9$		0			0
$10$	−1.43025	−	8.11138i	−0.452286	−	2.56504i
$11$	−0.217034	−	0.724944i	−0.0654382	−	0.218579i	0.919016	−	0.394220i	$-0.128985\pi$
$11$	−0.217034	−	0.724944i	−0.0654382	−	0.218579i	−0.984454	+	0.175641i	$0.943800\pi$
$12$		0			0
$13$	−0.144562	−	2.48203i	−0.0400942	−	0.688390i	−0.957143	−	0.289615i	$-0.906473\pi$
$13$	−0.144562	−	2.48203i	−0.0400942	−	0.688390i	0.917049	−	0.398775i	$-0.130564\pi$
$14$	6.30588	+	3.16693i	1.68532	+	0.846398i
$15$		0			0
$16$	1.93533	−	2.05133i	0.483831	−	0.512831i
$17$	−0.700932	−	0.255119i	−0.170001	−	0.0618753i	0.255617	−	0.966778i	$-0.417721\pi$
$17$	−0.700932	−	0.255119i	−0.170001	−	0.0618753i	−0.425619	+	0.904903i	$0.639943\pi$
$18$		0			0
$19$	4.21736	−	1.53499i	0.967530	−	0.352152i	0.190550	−	0.981678i	$-0.438973\pi$
$19$	4.21736	−	1.53499i	0.967530	−	0.352152i	0.776980	+	0.629526i	$0.216751\pi$
$20$	3.81843	−	8.85211i	0.853827	−	1.97939i
$21$		0			0
$22$	0.459191	−	1.53380i	0.0978998	−	0.327008i
$23$	2.27126	+	0.265472i	0.473590	+	0.0553547i	0.349540	−	0.936921i	$-0.386338\pi$
$23$	2.27126	+	0.265472i	0.473590	+	0.0553547i	0.124049	+	0.992276i	$0.460412\pi$
$24$		0			0
$25$	−0.590459	+	10.1378i	−0.118092	+	2.02756i
$26$	2.63013	−	4.55552i	0.515811	−	0.893410i
$27$		0			0
$28$	4.12967	+	7.15280i	0.780435	+	1.35175i
$29$	0.414639	−	0.208240i	0.0769966	−	0.0386691i	−0.409884	−	0.912138i	$-0.634431\pi$
$29$	0.414639	−	0.208240i	0.0769966	−	0.0386691i	0.486881	+	0.873468i	$0.338135\pi$
$30$		0			0
$31$	−2.35407	+	3.16206i	−0.422803	+	0.567923i	−0.961580	−	0.274526i	$-0.911479\pi$
$31$	−2.35407	+	3.16206i	−0.422803	+	0.567923i	0.538777	+	0.842449i	$0.318887\pi$
$32$	7.76762	−	1.84096i	1.37313	−	0.325439i
$33$		0			0
$34$	−0.942422	−	1.26589i	−0.161624	−	0.217099i
$35$	−9.94610	−	8.34577i	−1.68120	−	1.41069i
$36$		0			0
$37$	−3.64375	+	3.05747i	−0.599029	+	0.502645i	−0.891134	−	0.453741i	$-0.850089\pi$
$37$	−3.64375	+	3.05747i	−0.599029	+	0.502645i	0.292104	+	0.956387i	$0.405645\pi$
$38$	9.23961	+	2.18983i	1.49886	+	0.355237i
$39$		0			0
$40$	3.27849	−	2.15630i	0.518375	−	0.340941i
$41$	−4.08763	+	2.68847i	−0.638380	+	0.419869i	−0.827016	−	0.562178i	$-0.809964\pi$
$41$	−4.08763	+	2.68847i	−0.638380	+	0.419869i	0.188636	+	0.982047i	$0.439593\pi$
$42$		0			0
$43$	5.78094	+	1.37011i	0.881585	+	0.208939i	0.646388	−	0.763009i	$-0.276279\pi$
$43$	5.78094	+	1.37011i	0.881585	+	0.208939i	0.235196	+	0.971948i	$0.424427\pi$
$44$	1.43556	−	1.20458i	0.216419	−	0.181597i
$45$		0			0
$46$	3.70623	+	3.10990i	0.546454	+	0.458529i
$47$	−6.42922	−	8.63594i	−0.937798	−	1.25968i	−0.965590	−	0.260067i	$-0.916255\pi$
$47$	−6.42922	−	8.63594i	−0.937798	−	1.25968i	0.0277927	−	0.999614i	$-0.491152\pi$
$48$		0			0
$49$	4.01237	−	0.950949i	0.573195	−	0.135850i
$50$	−12.8302	+	17.2340i	−1.81447	+	2.43725i
$51$		0			0
$52$	5.50206	−	2.76324i	0.762998	−	0.383192i
$53$	5.75294	+	9.96438i	0.790227	+	1.36871i	0.925826	+	0.377949i	$0.123371\pi$
$53$	5.75294	+	9.96438i	0.790227	+	1.36871i	−0.135600	+	0.990764i	$0.543296\pi$
$54$		0			0
$55$	−1.47296	+	2.55124i	−0.198614	+	0.344010i
$56$	−0.195474	+	3.35616i	−0.0261213	+	0.448485i
$57$		0			0
$58$	0.975058	+	0.113968i	0.128031	+	0.0149647i
$59$	1.19000	−	3.97488i	0.154925	−	0.517485i	−0.844924	−	0.534887i	$-0.820354\pi$
$59$	1.19000	−	3.97488i	0.154925	−	0.517485i	0.999849	+	0.0174017i	$0.00553943\pi$
$60$		0			0
$61$	0.105839	−	0.245363i	0.0135513	−	0.0314155i	−0.911306	−	0.411730i	$-0.864925\pi$
$61$	0.105839	−	0.245363i	0.0135513	−	0.0314155i	0.924857	+	0.380314i	$0.124184\pi$
$62$	−7.83755	+	2.85264i	−0.995370	+	0.362285i
$63$		0			0
$64$	10.5709	+	3.84748i	1.32136	+	0.480935i
$65$	−6.64196	+	7.04007i	−0.823834	+	0.873213i
$66$		0			0
$67$	−1.71358	−	0.860594i	−0.209348	−	0.105138i	0.341036	−	0.940050i	$-0.389222\pi$
$67$	−1.71358	−	0.860594i	−0.209348	−	0.105138i	−0.550384	+	0.834912i	$0.685519\pi$
$68$	−0.107405	−	1.84408i	−0.0130248	−	0.223627i
$69$		0			0
$70$	−7.87859	−	26.3163i	−0.941671	−	3.14540i
$71$	1.17278	+	6.65118i	0.139184	+	0.789350i	0.971855	+	0.235582i	$0.0756996\pi$
$71$	1.17278	+	6.65118i	0.139184	+	0.789350i	−0.832671	+	0.553768i	$0.813189\pi$
$72$		0			0
$73$	1.37723	−	7.81064i	0.161192	−	0.914167i	−0.791712	−	0.610895i	$-0.790810\pi$
$73$	1.37723	−	7.81064i	0.161192	−	0.914167i	0.952904	−	0.303272i	$-0.0980791\pi$
$74$	−9.99572	+	1.16833i	−1.16198	+	0.135816i
$75$		0			0
$76$	7.62705	+	8.08420i	0.874883	+	0.927322i
$77$	−0.999649	−	2.31745i	−0.113921	−	0.264098i
$78$		0			0
$79$	−3.60662	−	2.37211i	−0.405777	−	0.266884i	0.330172	−	0.943921i	$-0.392893\pi$
$79$	−3.60662	−	2.37211i	−0.405777	−	0.266884i	−0.735949	+	0.677037i	$0.763264\pi$
$80$	−10.9788			−1.22747
$81$		0			0
$82$	−10.3513			−1.14311
$83$	2.12790	+	1.39954i	0.233567	+	0.153620i	0.660898	−	0.750476i	$-0.270176\pi$
$83$	2.12790	+	1.39954i	0.233567	+	0.153620i	−0.427331	+	0.904095i	$0.640546\pi$
$84$		0			0
$85$	1.15014	+	2.66632i	0.124750	+	0.289203i
$86$	8.62597	+	9.14299i	0.930162	+	0.985914i
$87$		0			0
$88$	0.757624	−	0.0885535i	0.0807630	−	0.00943984i
$89$	−0.935549	+	5.30576i	−0.0991680	+	0.562410i	0.894222	+	0.447623i	$0.147729\pi$
$89$	−0.935549	+	5.30576i	−0.0991680	+	0.562410i	−0.993390	+	0.114786i	$0.963382\pi$
$90$		0			0
$91$	−1.43990	−	8.16609i	−0.150943	−	0.856039i
$92$	1.62413	+	5.42498i	0.169327	+	0.565593i
$93$		0			0
$94$	−1.32448	−	22.7404i	−0.136610	−	2.34550i
$95$	−15.6132	−	7.84124i	−1.60188	−	0.804495i
$96$		0			0
$97$	−6.51132	+	6.90160i	−0.661125	+	0.700751i	−0.967986	−	0.251003i	$-0.919240\pi$
$97$	−6.51132	+	6.90160i	−0.661125	+	0.700751i	0.306862	+	0.951754i	$0.400721\pi$
$98$	8.19821	+	2.98391i	0.828145	+	0.301420i
$99$		0			0
$100$	−23.6314	+	8.60112i	−2.36314	+	0.860112i
$101$	−4.87482	+	11.3011i	−0.485063	+	1.12450i	0.483413	+	0.875392i	$0.339397\pi$
$101$	−4.87482	+	11.3011i	−0.485063	+	1.12450i	−0.968475	+	0.249109i	$0.919862\pi$
$102$		0			0
$103$	−4.78109	+	15.9700i	−0.471095	+	1.57357i	0.311001	+	0.950410i	$0.399336\pi$
$103$	−4.78109	+	15.9700i	−0.471095	+	1.57357i	−0.782096	+	0.623158i	$0.785849\pi$
$104$	2.48915	+	0.290940i	0.244081	+	0.0285290i
$105$		0			0
$106$	−1.41546	+	24.3024i	−0.137481	+	2.36046i
$107$	1.84694	−	3.19899i	0.178550	−	0.309258i	−0.762834	−	0.646595i	$-0.776193\pi$
$107$	1.84694	−	3.19899i	0.178550	−	0.309258i	0.941384	+	0.337336i	$0.109526\pi$
$108$		0			0
$109$	8.66961	+	15.0162i	0.830398	+	1.43829i	0.897723	+	0.440561i	$0.145220\pi$
$109$	8.66961	+	15.0162i	0.830398	+	1.43829i	−0.0673245	+	0.997731i	$0.521446\pi$
$110$	−5.56988	+	2.79730i	−0.531067	+	0.266712i
$111$		0			0
$112$	5.61678	−	7.54465i	0.530736	−	0.712902i
$113$	−10.0311	+	2.37743i	−0.943651	+	0.223649i	−0.673516	−	0.739173i	$-0.735217\pi$
$113$	−10.0311	+	2.37743i	−0.943651	+	0.223649i	−0.270135	+	0.962822i	$0.587068\pi$
$114$		0			0
$115$	−5.31594	−	7.14055i	−0.495714	−	0.665859i
$116$	0.880217	+	0.738590i	0.0817261	+	0.0685764i
$117$		0			0
$118$	6.72485	−	5.64282i	0.619072	−	0.519464i
$119$	−2.42072	−	0.573721i	−0.221907	−	0.0525929i
$120$		0			0
$121$	8.71193	−	5.72992i	0.791993	−	0.520902i
$122$	0.472356	−	0.310674i	0.0427651	−	0.0281271i
$123$		0			0
$124$	−9.49919	−	2.25135i	−0.853052	−	0.202177i
$125$	15.3730	−	12.8995i	1.37500	−	1.15376i
$126$		0			0
$127$	−10.1217	−	8.49315i	−0.898159	−	0.753645i	0.0716705	−	0.997428i	$-0.477167\pi$
$127$	−10.1217	−	8.49315i	−0.898159	−	0.753645i	−0.969830	+	0.243783i	$0.921611\pi$
$128$	4.67882	+	6.28474i	0.413553	+	0.555498i
$129$		0			0
$130$	−19.9259	+	4.72252i	−1.74762	+	0.414192i
$131$	6.00822	−	8.07044i	0.524940	−	0.705117i	−0.458018	−	0.888943i	$-0.651441\pi$
$131$	6.00822	−	8.07044i	0.524940	−	0.705117i	0.982959	+	0.183825i	$0.0588481\pi$
$132$		0			0
$133$	13.3763	−	6.71782i	1.15987	−	0.582509i
$134$	−2.02853	−	3.51352i	−0.175238	−	0.303522i
$135$		0			0
$136$	0.375938	−	0.651145i	0.0322365	−	0.0558352i
$137$	0.550552	−	9.45261i	0.0470368	−	0.807591i	−0.889481	−	0.456972i	$-0.848934\pi$
$137$	0.550552	−	9.45261i	0.0470368	−	0.807591i	0.936518	−	0.350619i	$-0.114029\pi$
$138$		0			0
$139$	10.4293	+	1.21902i	0.884605	+	0.103396i	0.546249	−	0.837623i	$-0.316055\pi$
$139$	10.4293	+	1.21902i	0.884605	+	0.103396i	0.338356	+	0.941018i	$0.390129\pi$
$140$	9.22162	−	30.8024i	0.779369	−	2.60327i
$141$		0			0
$142$	−5.65973	+	13.1207i	−0.474954	+	1.10107i
$143$	−1.76795	+	0.643483i	−0.147844	+	0.0538107i
$144$		0			0
$145$	−1.69736	−	0.617790i	−0.140958	−	0.0513047i
$146$	11.5154	−	12.2056i	0.953019	−	1.01014i
$147$		0			0
$148$	−10.5264	−	5.28654i	−0.865262	−	0.434551i
$149$	−0.722705	−	12.4084i	−0.0592063	−	1.01653i	−0.888838	−	0.458222i	$-0.848487\pi$
$149$	−0.722705	−	12.4084i	−0.0592063	−	1.01653i	0.829632	−	0.558311i	$-0.188551\pi$
$150$		0			0
$151$	5.22757	+	17.4613i	0.425413	+	1.42098i	0.855317	+	0.518105i	$0.173362\pi$
$151$	5.22757	+	17.4613i	0.425413	+	1.42098i	−0.429904	+	0.902875i	$0.641453\pi$
$152$	0.785565	+	4.45516i	0.0637177	+	0.361361i
$153$		0			0
$154$	0.927258	−	5.25874i	0.0747206	−	0.423761i
$155$	15.2426	−	1.78161i	1.22432	−	0.143102i
$156$		0			0
$157$	−16.0388	−	17.0001i	−1.28003	−	1.35675i	−0.902459	−	0.430775i	$-0.858240\pi$
$157$	−16.0388	−	17.0001i	−1.28003	−	1.35675i	−0.377573	−	0.925980i	$-0.623241\pi$
$158$	−3.61750	−	8.38631i	−0.287793	−	0.667179i
$159$		0			0
$160$	−25.9641	−	17.0768i	−2.05264	−	1.35004i
$161$	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	$0.348158\pi$
$164$	−10.1227	−	6.65780i	−0.790449	−	0.519886i
$165$		0			0
$166$	2.13432	+	4.94790i	0.165655	+	0.384032i
$167$	16.6160	+	17.6119i	1.28579	+	1.36285i	0.897314	+	0.441393i	$0.145516\pi$
$167$	16.6160	+	17.6119i	1.28579	+	1.36285i	0.388472	+	0.921461i	$0.373003\pi$
$168$		0			0
$169$	6.77255	−	0.791597i	0.520965	−	0.0608921i
$170$	−1.06685	+	6.05041i	−0.0818237	+	0.464045i
$171$		0			0
$172$	2.55482	+	14.4891i	0.194803	+	1.10478i
$173$	4.44902	+	14.8608i	0.338253	+	1.12984i	0.942824	+	0.333292i	$0.108159\pi$
$173$	4.44902	+	14.8608i	0.338253	+	1.12984i	−0.604571	+	0.796551i	$0.706655\pi$
$174$		0			0
$175$	1.96930	+	33.8115i	0.148865	+	2.55591i
$176$	−1.90713	−	0.957795i	−0.143755	−	0.0721965i
$177$		0			0
$178$	−7.82238	+	8.29124i	−0.586312	+	0.621455i
$179$	6.75474	+	2.45852i	0.504873	+	0.183759i	0.581884	−	0.813271i	$-0.302316\pi$
$179$	6.75474	+	2.45852i	0.504873	+	0.183759i	−0.0770114	+	0.997030i	$0.524538\pi$
$180$		0			0
$181$	7.27112	−	2.64647i	0.540458	−	0.196711i	−0.0573439	−	0.998354i	$-0.518263\pi$
$181$	7.27112	−	2.64647i	0.540458	−	0.196711i	0.597802	+	0.801644i	$0.296041\pi$
$182$	6.94882	−	16.1092i	0.515081	−	1.19409i
$183$		0			0
$184$	−0.661079	+	2.20816i	−0.0487354	+	0.162787i
$185$	18.3919	+	2.14970i	1.35220	+	0.158049i
$186$		0			0
$187$	−0.0328205	+	0.563506i	−0.00240007	+	0.0412077i
$188$	13.3310	−	23.0900i	0.972264	−	1.68401i
$189$		0			0
$190$	−18.4828	−	32.0132i	−1.34089	−	2.32248i
$191$	−9.00617	+	4.52307i	−0.651664	+	0.327278i	−0.743735	−	0.668475i	$-0.766948\pi$
$191$	−9.00617	+	4.52307i	−0.651664	+	0.327278i	0.0920711	+	0.995752i	$0.470651\pi$
$192$		0			0
$193$	−9.54993	+	12.8278i	−0.687419	+	0.923364i	−0.999645	−	0.0266441i	$-0.991518\pi$
$193$	−9.54993	+	12.8278i	−0.687419	+	0.923364i	0.312226	+	0.950008i	$0.398925\pi$
$194$	−19.5340	+	4.62964i	−1.40246	+	0.332389i
$195$		0			0
$196$	6.09793	+	8.19094i	0.435566	+	0.585067i
$197$	8.40349	+	7.05136i	0.598724	+	0.502389i	0.891035	−	0.453934i	$-0.149980\pi$
$197$	8.40349	+	7.05136i	0.598724	+	0.502389i	−0.292311	+	0.956323i	$0.594424\pi$
$198$		0			0
$199$	2.68937	−	2.25665i	0.190644	−	0.159970i	−0.542470	−	0.840075i	$-0.682511\pi$
$199$	2.68937	−	2.25665i	0.190644	−	0.159970i	0.733114	+	0.680106i	$0.238066\pi$
$200$	−9.96020	−	2.36061i	−0.704293	−	0.166920i
$201$		0			0
$202$	−21.7561	+	14.3092i	−1.53075	+	1.00679i
$203$	1.29292	−	0.850369i	0.0907454	−	0.0596842i
$204$		0			0
$205$	18.5328	+	4.39236i	1.29439	+	0.306776i
$206$	−27.0186	+	22.6713i	−1.88247	+	1.57958i
$207$		0			0
$208$	−5.37122	−	4.50698i	−0.372427	−	0.312503i
$209$	−2.02810	−	2.72421i	−0.140286	−	0.188437i
$210$		0			0
$211$	−7.47663	+	1.77199i	−0.514712	+	0.121989i	−0.479760	−	0.877400i	$-0.659276\pi$
$211$	−7.47663	+	1.77199i	−0.514712	+	0.121989i	−0.0349525	+	0.999389i	$0.511128\pi$
$212$	−17.0151	+	22.8552i	−1.16860	+	1.56970i
$213$		0			0
$214$	6.98404	−	3.50752i	0.477419	−	0.239769i
$215$	−11.5641	−	20.0297i	−0.788667	−	1.36601i
$216$		0			0
$217$	−6.57386	+	11.3863i	−0.446262	+	0.772949i
$218$	−2.13308	+	36.6235i	−0.144470	+	2.48046i
$219$		0			0
$220$	−7.24602	−	0.846938i	−0.488526	−	0.0571005i
$221$	−0.531883	+	1.77661i	−0.0357783	+	0.119508i
$222$		0			0
$223$	4.29520	−	9.95739i	0.287628	−	0.666796i	−0.711737	−	0.702447i	$-0.752091\pi$
$223$	4.29520	−	9.95739i	0.287628	−	0.666796i	0.999364	+	0.0356504i	$0.0113503\pi$
$224$	25.0185	−	9.10600i	1.67162	−	0.608420i
$225$		0			0
$226$	−20.4960	−	7.45993i	−1.36337	−	0.496227i
$227$	7.45351	−	7.90026i	0.494707	−	0.524358i	−0.431126	−	0.902292i	$-0.641884\pi$
$227$	7.45351	−	7.90026i	0.494707	−	0.524358i	0.925833	+	0.377933i	$0.123365\pi$
$228$		0			0
$229$	2.04594	+	1.02751i	0.135199	+	0.0678997i	0.515113	−	0.857122i	$-0.327750\pi$
$229$	2.04594	+	1.02751i	0.135199	+	0.0678997i	−0.379914	+	0.925022i	$0.624046\pi$
$230$	−1.09513	−	18.8027i	−0.0722110	−	1.23981i
$231$		0			0
$232$	0.134138	+	0.448052i	0.00880659	+	0.0294161i
$233$	3.09286	+	17.5405i	0.202620	+	1.14912i	0.901141	+	0.433526i	$0.142731\pi$
$233$	3.09286	+	17.5405i	0.202620	+	1.14912i	−0.698521	+	0.715590i	$0.746158\pi$
$234$		0			0
$235$	−7.27807	+	41.2760i	−0.474769	+	2.69255i
$236$	10.2057	−	1.19287i	0.664332	−	0.0776493i
$237$		0			0
$238$	−3.61205	−	3.82855i	−0.234135	−	0.248168i
$239$	−4.85842	−	11.2631i	−0.314265	−	0.728548i	−1.00000		0.000696435i	$-0.999778\pi$
$239$	−4.85842	−	11.2631i	−0.314265	−	0.728548i	0.685735	−	0.727851i	$-0.259481\pi$
$240$		0			0
$241$	−14.6206	−	9.61612i	−0.941795	−	0.619429i	−0.0169845	−	0.999856i	$-0.505407\pi$
$241$	−14.6206	−	9.61612i	−0.941795	−	0.619429i	−0.924811	+	0.380427i	$0.875777\pi$
$242$	22.0617			1.41818
$243$		0			0
$244$	0.661742			0.0423637
$245$	−13.4118	−	8.82105i	−0.856846	−	0.563556i
$246$		0			0
$247$	−4.41956	−	10.2457i	−0.281210	−	0.651918i
$248$	−2.72686	−	2.89030i	−0.173156	−	0.183534i
$249$		0			0
$250$	42.1719	−	4.92919i	2.66719	−	0.311749i
$251$	3.26810	−	18.5343i	0.206281	−	1.16988i	−0.689131	−	0.724637i	$-0.742008\pi$
$251$	3.26810	−	18.5343i	0.206281	−	1.16988i	0.895412	−	0.445239i	$-0.146881\pi$
$252$		0			0
$253$	−0.300488	−	1.70415i	−0.0188915	−	0.107139i
$254$	−8.01772	−	26.7810i	−0.503076	−	1.68039i
$255$		0			0
$256$	−0.344295	−	5.91131i	−0.0215184	−	0.369457i
$257$	15.4090	+	7.73869i	0.961187	+	0.482726i	0.858964	−	0.512035i	$-0.171108\pi$
$257$	15.4090	+	7.73869i	0.961187	+	0.482726i	0.102222	+	0.994762i	$0.467405\pi$
$258$		0			0
$259$	−10.8866	+	11.5391i	−0.676462	+	0.717008i
$260$	−22.5232	−	8.19776i	−1.39683	−	0.508404i
$261$		0			0
$262$	20.0036	−	7.28070i	1.23582	−	0.449803i
$263$	−9.74813	+	22.5987i	−0.601095	+	1.39350i	0.297502	+	0.954721i	$0.403846\pi$
$263$	−9.74813	+	22.5987i	−0.601095	+	1.39350i	−0.898597	+	0.438774i	$0.855413\pi$
$264$		0			0
$265$	12.8464	−	42.9100i	0.789148	−	2.63594i
$266$	31.4554	+	3.67661i	1.92865	+	0.225427i
$267$		0			0
$268$	0.276110	−	4.74062i	0.0168661	−	0.289580i
$269$	−5.32448	+	9.22227i	−0.324639	+	0.562292i	−0.981439	−	0.191773i	$-0.938576\pi$
$269$	−5.32448	+	9.22227i	−0.324639	+	0.562292i	0.656800	+	0.754065i	$0.271910\pi$
$270$		0			0
$271$	2.35817	+	4.08447i	0.143249	+	0.248114i	0.928718	−	0.370786i	$-0.120912\pi$
$271$	2.35817	+	4.08447i	0.143249	+	0.248114i	−0.785469	+	0.618900i	$0.787578\pi$
$272$	−1.87986	+	0.944103i	−0.113983	+	0.0572447i
$273$		0			0
$274$	11.9631	−	16.0692i	0.722715	−	0.970775i
$275$	7.47748	−	1.77220i	0.450909	−	0.106867i
$276$		0			0
$277$	−3.94818	−	5.30333i	−0.237223	−	0.318646i	0.667529	−	0.744583i	$-0.267352\pi$
$277$	−3.94818	−	5.30333i	−0.237223	−	0.318646i	−0.904753	+	0.425937i	$0.859944\pi$
$278$	17.0186	+	14.2803i	1.02071	+	0.856474i
$279$		0			0
$280$	10.0256	−	8.41245i	0.599142	−	0.502740i
$281$	−2.40945	−	0.571049i	−0.143736	−	0.0340659i	0.158118	−	0.987420i	$-0.449457\pi$
$281$	−2.40945	−	0.571049i	−0.143736	−	0.0340659i	−0.301854	+	0.953354i	$0.597605\pi$
$282$		0			0
$283$	−0.774627	+	0.509480i	−0.0460468	+	0.0302855i	−0.572324	−	0.820028i	$-0.693958\pi$
$283$	−0.774627	+	0.509480i	−0.0460468	+	0.0302855i	0.526277	+	0.850313i	$0.323588\pi$
$284$	−13.9737	+	9.19066i	−0.829188	+	0.545365i
$285$		0			0
$286$	−3.87332	−	0.917994i	−0.229034	−	0.0542821i
$287$	−12.4999	+	10.4887i	−0.737845	+	0.619126i
$288$		0			0
$289$	−12.5965	−	10.5697i	−0.740973	−	0.621750i
$290$	−2.28215	−	3.06546i	−0.134012	−	0.180010i
$291$		0			0
$292$	19.1114	−	4.52949i	1.11841	−	0.265068i
$293$	1.40037	−	1.88103i	0.0818106	−	0.109891i	−0.759334	−	0.650701i	$-0.774475\pi$
$293$	1.40037	−	1.88103i	0.0818106	−	0.109891i	0.841144	+	0.540811i	$0.181882\pi$
$294$		0			0
$295$	−14.4344	+	7.24925i	−0.840405	+	0.422067i
$296$	−2.39729	−	4.15224i	−0.139340	−	0.241344i
$297$		0			0
$298$	13.1488	−	22.7744i	0.761688	−	1.31928i
$299$	0.330572	−	5.67569i	0.0191174	−	0.328234i
$300$		0			0
$301$	19.6807	+	2.30034i	1.13438	+	0.132589i
$302$	−11.0603	+	36.9438i	−0.636446	+	2.12588i
$303$		0			0
$304$	5.01320	−	11.6219i	0.287527	−	0.666562i
$305$	−0.977524	+	0.355790i	−0.0559729	+	0.0203725i
$306$		0			0
$307$	14.3376	+	5.21846i	0.818289	+	0.297833i	0.717043	−	0.697028i	$-0.245495\pi$
$307$	14.3376	+	5.21846i	0.818289	+	0.297833i	0.101246	+	0.994861i	$0.467717\pi$
$308$	4.28910	−	4.54618i	0.244394	−	0.259043i
$309$		0			0
$310$	29.0156	+	14.5722i	1.64797	+	0.827644i
$311$	0.973556	+	16.7153i	0.0552053	+	0.947838i	0.906249	+	0.422744i	$0.138933\pi$
$311$	0.973556	+	16.7153i	0.0552053	+	0.947838i	−0.851044	+	0.525094i	$0.824030\pi$
$312$		0			0
$313$	−9.34214	−	31.2049i	−0.528049	−	1.76381i	−0.638178	−	0.769889i	$-0.720312\pi$
$313$	−9.34214	−	31.2049i	−0.528049	−	1.76381i	0.110129	−	0.993917i	$-0.464873\pi$
$314$	−8.58676	−	48.6979i	−0.484579	−	2.74818i
$315$		0			0
$316$	1.85633	−	10.5278i	0.104427	−	0.592234i
$317$	−21.5243	+	2.51583i	−1.20893	+	0.141303i	−0.696582	−	0.717477i	$-0.745297\pi$
$317$	−21.5243	+	2.51583i	−1.20893	+	0.141303i	−0.512344	+	0.858780i	$0.671223\pi$
$318$		0			0
$319$	−0.240953	−	0.255395i	−0.0134908	−	0.0142994i
$320$	−17.3454	−	40.2112i	−0.969639	−	2.24788i
$321$		0			0
$322$	13.4815	+	8.86695i	0.751297	+	0.494136i
$323$	−3.34769			−0.186271
$324$		0			0
$325$	25.2476			1.40049
$326$	20.7240	+	13.6304i	1.14780	+	0.754917i
$327$		0			0
$328$	−1.95331	−	4.52827i	−0.107853	−	0.250032i
$329$	−24.6415	−	26.1184i	−1.35853	−	1.43996i
$330$		0			0
$331$	−23.6512	+	2.76443i	−1.29999	+	0.151947i	−0.737775	−	0.675046i	$-0.764124\pi$
$331$	−23.6512	+	2.76443i	−1.29999	+	0.151947i	−0.562212	+	0.826993i	$0.690050\pi$
$332$	−1.09523	+	6.21136i	−0.0601086	+	0.340893i
$333$		0			0
$334$	8.89581	+	50.4507i	0.486757	+	2.76054i
$335$	2.14096	+	7.15130i	0.116973	+	0.390717i
$336$		0			0
$337$	1.06959	+	18.3641i	0.0582643	+	1.00036i	0.893100	+	0.449859i	$0.148526\pi$
$337$	1.06959	+	18.3641i	0.0582643	+	1.00036i	−0.834835	+	0.550500i	$0.814437\pi$
$338$	12.8921	+	6.47465i	0.701237	+	0.352174i
$339$		0			0
$340$	−4.93480	+	5.23058i	−0.267627	+	0.283668i
$341$	2.80323	+	1.02029i	0.151803	+	0.0552519i
$342$		0			0
$343$	−9.01506	+	3.28121i	−0.486767	+	0.177169i
$344$	−2.37194	+	5.49878i	−0.127887	+	0.296475i
$345$		0			0
$346$	−9.41304	+	31.4417i	−0.506048	+	1.69032i
$347$	16.7968	+	1.96326i	0.901698	+	0.105393i	0.554293	−	0.832322i	$-0.312989\pi$
$347$	16.7968	+	1.96326i	0.901698	+	0.105393i	0.347405	+	0.937715i	$0.387063\pi$
$348$		0			0
$349$	−0.474881	+	8.15340i	−0.0254198	+	0.436441i	0.961456	+	0.274959i	$0.0886644\pi$
$349$	−0.474881	+	8.15340i	−0.0254198	+	0.436441i	−0.986876	+	0.161482i	$0.948373\pi$
$350$	−35.8291	+	62.0578i	−1.91514	+	3.31713i
$351$		0			0
$352$	−3.02043	−	5.23154i	−0.160989	−	0.278842i
$353$	21.9963	−	11.0469i	1.17074	−	0.587969i	0.246264	−	0.969203i	$-0.420797\pi$
$353$	21.9963	−	11.0469i	1.17074	−	0.587969i	0.924479	+	0.381234i	$0.124501\pi$
$354$		0			0
$355$	15.7005	−	21.0895i	0.833298	−	1.11931i
$356$	−12.9824	+	3.07688i	−0.688064	+	0.163074i
$357$		0			0
$358$	9.08193	+	12.1991i	0.479995	+	0.644745i
$359$	−9.68682	−	8.12821i	−0.511251	−	0.428990i	0.350318	−	0.936631i	$-0.386073\pi$
$359$	−9.68682	−	8.12821i	−0.511251	−	0.428990i	−0.861569	+	0.507640i	$0.830518\pi$
$360$		0			0
$361$	0.875105	−	0.734300i	0.0460582	−	0.0386474i
$362$	15.9299	+	3.77546i	0.837258	+	0.198434i
$363$		0			0
$364$	17.1564	−	11.2840i	0.899242	−	0.591441i
$365$	−25.7960	+	16.9663i	−1.35023	+	0.888058i
$366$		0			0
$367$	−10.2113	−	2.42012i	−0.533025	−	0.126329i	−0.0447153	−	0.999000i	$-0.514238\pi$
$367$	−10.2113	−	2.42012i	−0.533025	−	0.126329i	−0.488309	+	0.872671i	$0.662386\pi$
$368$	4.94019	−	4.14531i	0.257525	−	0.216089i
$369$		0			0
$370$	30.0118	+	25.1829i	1.56024	+	1.30920i
$371$	22.9156	+	30.7809i	1.18972	+	1.59807i
$372$		0			0
$373$	11.4784	−	2.72044i	0.594330	−	0.140859i	0.0775669	−	0.996987i	$-0.475285\pi$
$373$	11.4784	−	2.72044i	0.594330	−	0.140859i	0.516763	+	0.856128i	$0.327137\pi$
$374$	−0.713164	+	0.957945i	−0.0368768	+	0.0495342i
$375$		0			0
$376$	9.69804	−	4.87054i	0.500138	−	0.251179i
$377$	−0.576797	−	0.999042i	−0.0297066	−	0.0514533i
$378$		0			0
$379$	−9.06853	+	15.7072i	−0.465819	+	0.806823i	−0.999238	−	0.0390286i	$-0.987574\pi$
$379$	−9.06853	+	15.7072i	−0.465819	+	0.806823i	0.533419	+	0.845851i	$0.320907\pi$
$380$	2.51576	−	43.1939i	0.129056	−	2.21580i
$381$		0			0
$382$	−21.1787	−	2.47544i	−1.08360	−	0.126655i
$383$	−4.45051	+	14.8657i	−0.227410	+	0.759603i	0.765780	+	0.643102i	$0.222353\pi$
$383$	−4.45051	+	14.8657i	−0.227410	+	0.759603i	−0.993191	+	0.116501i	$0.962832\pi$
$384$		0			0
$385$	−3.89157	+	9.02168i	−0.198333	+	0.459787i
$386$	−31.7952	+	11.5725i	−1.61833	+	0.589025i
$387$		0			0
$388$	−22.0802	−	8.03653i	−1.12095	−	0.407993i
$389$	10.5917	−	11.2265i	0.537019	−	0.569207i	−0.400873	−	0.916133i	$-0.631293\pi$
$389$	10.5917	−	11.2265i	0.537019	−	0.569207i	0.937892	+	0.346927i	$0.112775\pi$
$390$		0			0
$391$	−1.52427	−	0.765518i	−0.0770857	−	0.0387139i
$392$	0.241677	+	4.14943i	0.0122065	+	0.209578i
$393$		0			0
$394$	6.65664	+	22.2347i	0.335357	+	1.12017i
$395$	2.91816	+	16.5497i	0.146828	+	0.832705i
$396$		0			0
$397$	0.354695	−	2.01157i	0.0178016	−	0.100958i	−0.974612	−	0.223899i	$-0.928121\pi$
$397$	0.354695	−	2.01157i	0.0178016	−	0.100958i	0.992414	+	0.122941i	$0.0392326\pi$
$398$	7.37761	−	0.862319i	0.369806	−	0.0432241i
$399$		0			0
$400$	19.6532	+	20.8312i	0.982659	+	1.04156i
$401$	5.92303	+	13.7311i	0.295782	+	0.685700i	0.999698	−	0.0245834i	$-0.00782592\pi$
$401$	5.92303	+	13.7311i	0.295782	+	0.685700i	−0.703916	+	0.710284i	$0.748567\pi$
$402$		0			0
$403$	8.18862	+	5.38574i	0.407904	+	0.268283i
$404$	−30.4790			−1.51639
$405$		0			0
$406$	3.27415			0.162493
$407$	3.00731	+	1.97794i	0.149067	+	0.0980429i
$408$		0			0
$409$	4.11470	+	9.53894i	0.203459	+	0.471670i	0.989143	−	0.146958i	$-0.0469481\pi$
$409$	4.11470	+	9.53894i	0.203459	+	0.471670i	−0.785684	+	0.618628i	$0.787689\pi$
$410$	27.6536	+	29.3111i	1.36571	+	1.44757i
$411$		0			0
$412$	−41.0035	+	4.79262i	−2.02010	+	0.236116i
$413$	2.40300	−	13.6281i	0.118244	−	0.670595i
$414$		0			0
$415$	−1.72170	−	9.76427i	−0.0845151	−	0.479309i
$416$	−5.69221	−	19.0133i	−0.279083	−	0.932203i
$417$		0			0
$418$	−0.417807	−	7.17347i	−0.0204356	−	0.350866i
$419$	0.473719	+	0.237911i	0.0231427	+	0.0116227i	0.460333	−	0.887746i	$-0.347730\pi$
$419$	0.473719	+	0.237911i	0.0231427	+	0.0116227i	−0.437190	+	0.899369i	$0.644026\pi$
$420$		0			0
$421$	22.0048	−	23.3237i	1.07245	−	1.13673i	0.0823146	−	0.996606i	$-0.473769\pi$
$421$	22.0048	−	23.3237i	1.07245	−	1.13673i	0.990134	−	0.140123i	$-0.0447497\pi$
$422$	−15.2765	−	5.56019i	−0.743649	−	0.270666i
$423$		0			0
$424$	−10.8984	+	3.96668i	−0.529272	+	0.192639i
$425$	3.00021	−	6.95527i	0.145532	−	0.337380i
$426$		0			0
$427$	0.255605	−	0.853780i	0.0123696	−	0.0413173i
$428$	9.08574	+	1.06197i	0.439176	+	0.0513323i
$429$		0			0
$430$	2.84524	−	48.8510i	0.137210	−	2.35580i
$431$	−2.69146	+	4.66175i	−0.129643	+	0.224549i	−0.923538	−	0.383506i	$-0.874717\pi$
$431$	−2.69146	+	4.66175i	−0.129643	+	0.224549i	0.793895	+	0.608055i	$0.208050\pi$
$432$		0			0
$433$	−16.6465	−	28.8325i	−0.799978	−	1.38560i	−0.919630	−	0.392787i	$-0.871511\pi$
$433$	−16.6465	−	28.8325i	−0.799978	−	1.38560i	0.119652	−	0.992816i	$-0.461822\pi$
$434$	−24.8585	+	12.4844i	−1.19325	+	0.599270i
$435$		0			0
$436$	−25.6415	+	34.4425i	−1.22801	+	1.64950i
$437$	9.98622	−	2.36678i	0.477705	−	0.113218i
$438$		0			0
$439$	−11.1561	−	14.9852i	−0.532451	−	0.715206i	0.451773	−	0.892133i	$-0.350792\pi$
$439$	−11.1561	−	14.9852i	−0.532451	−	0.715206i	−0.984224	+	0.176927i	$0.943384\pi$
$440$	−2.27474	−	1.90873i	−0.108444	−	0.0909953i
$441$		0			0
$442$	−3.00574	+	2.52212i	−0.142968	+	0.119965i
$443$	−18.3619	−	4.35184i	−0.872398	−	0.206762i	−0.230053	−	0.973178i	$-0.573890\pi$
$443$	−18.3619	−	4.35184i	−0.872398	−	0.206762i	−0.642345	+	0.766416i	$0.722038\pi$
$444$		0			0
$445$	17.5232	−	11.5252i	0.830681	−	0.546348i
$446$	19.1693	−	12.6078i	0.907693	−	0.596999i
$447$		0			0
$448$	36.5072	+	8.65237i	1.72480	+	0.408786i
$449$	−5.33643	+	4.47780i	−0.251842	+	0.211320i	−0.759965	−	0.649964i	$-0.774784\pi$
$449$	−5.33643	+	4.47780i	−0.251842	+	0.211320i	0.508123	+	0.861284i	$0.330339\pi$
$450$		0			0
$451$	2.83615	+	2.37981i	0.133549	+	0.112061i
$452$	−15.2452	−	20.4778i	−0.717072	−	0.963195i
$453$		0			0
$454$	22.3605	−	5.29954i	1.04943	−	0.248720i
$455$	−19.2766	+	25.8929i	−0.903700	+	1.21388i
$456$		0			0
$457$	33.5985	−	16.8738i	1.57167	−	0.789324i	0.572148	−	0.820150i	$-0.306110\pi$
$457$	33.5985	−	16.8738i	1.57167	−	0.789324i	0.999525	+	0.0308265i	$0.00981393\pi$
$458$	2.42197	+	4.19498i	0.113171	+	0.196018i
$459$		0			0
$460$	11.0226	−	19.0917i	0.513932	−	0.890157i
$461$	1.60695	−	27.5903i	0.0748432	−	1.28501i	−0.726652	−	0.687006i	$-0.758925\pi$
$461$	1.60695	−	27.5903i	0.0748432	−	1.28501i	0.801495	−	0.598002i	$-0.204038\pi$
$462$		0			0
$463$	−24.4012	−	2.85209i	−1.13402	−	0.132548i	−0.471694	−	0.881763i	$-0.656357\pi$
$463$	−24.4012	−	2.85209i	−1.13402	−	0.132548i	−0.662327	+	0.749215i	$0.730431\pi$
$464$	0.375295	−	1.25357i	0.0174226	−	0.0581956i
$465$		0			0
$466$	−14.9258	+	34.6020i	−0.691426	+	1.60291i
$467$	−7.38677	+	2.68856i	−0.341819	+	0.124412i	−0.507225	−	0.861814i	$-0.669329\pi$
$467$	−7.38677	+	2.68856i	−0.341819	+	0.124412i	0.165406	+	0.986226i	$0.447107\pi$
$468$		0			0
$469$	−6.00971	−	2.18735i	−0.277503	−	0.101003i
$470$	−60.8539	+	64.5014i	−2.80698	+	2.97523i
$471$		0			0
$472$	3.73748	+	1.87703i	0.172031	+	0.0863974i
$473$	−0.261409	−	4.48821i	−0.0120196	−	0.206368i
$474$		0			0
$475$	13.0713	+	43.6611i	0.599752	+	2.00331i
$476$	−1.06981	−	6.06719i	−0.0490346	−	0.278089i
$477$		0			0
$478$	4.50659	−	25.5581i	0.206127	−	1.16900i
$479$	17.5918	−	2.05619i	0.803791	−	0.0939497i	0.295731	−	0.955271i	$-0.404437\pi$
$479$	17.5918	−	2.05619i	0.803791	−	0.0939497i	0.508060	+	0.861322i	$0.330363\pi$
$480$		0			0
$481$	8.11547	+	8.60190i	0.370034	+	0.392213i
$482$	−14.6647	−	33.9966i	−0.667959	−	1.54850i
$483$		0			0
$484$	21.5744	+	14.1897i	0.980654	+	0.644987i
$485$	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	$0.903289\pi$
$488$	0.225040	+	0.148011i	0.0101871	+	0.00670016i
$489$		0			0
$490$	−13.4522	−	31.1857i	−0.607709	−	1.40883i
$491$	4.99416	+	5.29350i	0.225383	+	0.238892i	0.830191	−	0.557479i	$-0.188231\pi$
$491$	4.99416	+	5.29350i	0.225383	+	0.238892i	−0.604808	+	0.796372i	$0.706750\pi$
$492$		0			0
$493$	−0.343760	+	0.0401798i	−0.0154822	+	0.00180961i
$494$	4.09952	−	23.2495i	0.184446	−	1.04604i
$495$		0			0
$496$	1.93053	+	10.9486i	0.0866833	+	0.491606i
$497$	6.46030	+	21.5789i	0.289784	+	0.967946i
$498$		0			0
$499$	−0.937877	−	16.1027i	−0.0419851	−	0.720857i	−0.951965	−	0.306205i	$-0.900941\pi$
$499$	−0.937877	−	16.1027i	−0.0419851	−	0.720857i	0.909980	−	0.414651i	$-0.136096\pi$
$500$	44.4107	+	22.3039i	1.98611	+	0.997461i
$501$		0			0
$502$	27.3255	−	28.9633i	1.21960	−	1.29270i
$503$	34.7114	+	12.6339i	1.54771	+	0.563319i	0.967878	−	0.251421i	$-0.0808977\pi$
$503$	34.7114	+	12.6339i	1.54771	+	0.563319i	0.579827	+	0.814739i	$0.303120\pi$
$504$		0			0
$505$	45.0235	−	16.3872i	2.00352	−	0.729221i
$506$	1.45012	−	3.36176i	0.0644658	−	0.149449i
$507$		0			0
$508$	9.38447	−	31.3463i	0.416369	−	1.39077i
$509$	−11.6029	−	1.35619i	−0.514291	−	0.0601120i	−0.145011	−	0.989430i	$-0.546322\pi$
$509$	−11.6029	−	1.35619i	−0.514291	−	0.0601120i	−0.369280	+	0.929318i	$0.620396\pi$
$510$		0			0
$511$	1.53804	−	26.4071i	0.0680389	−	1.16818i
$512$	14.0992	−	24.4205i	0.623101	−	1.07924i
$513$		0			0
$514$	18.2411	+	31.5945i	0.804580	+	1.39357i
$515$	57.9936	−	29.1255i	2.55550	−	1.28342i
$516$		0			0
$517$	−4.86521	+	6.53511i	−0.213972	+	0.287414i
$518$	−32.6599	+	7.74053i	−1.43499	+	0.340099i
$519$		0			0
$520$	−5.82593	−	7.82558i	−0.255484	−	0.343175i
$521$	−0.659940	−	0.553755i	−0.0289125	−	0.0242605i	0.628217	−	0.778038i	$-0.283785\pi$
$521$	−0.659940	−	0.553755i	−0.0289125	−	0.0242605i	−0.657129	+	0.753778i	$0.728229\pi$
$522$		0			0
$523$	−6.06895	+	5.09246i	−0.265377	+	0.222678i	−0.765760	−	0.643126i	$-0.777637\pi$
$523$	−6.06895	+	5.09246i	−0.265377	+	0.222678i	0.500383	+	0.865804i	$0.333192\pi$
$524$	24.2445	+	5.74605i	1.05913	+	0.251018i
$525$		0			0
$526$	−43.5055	+	28.6140i	−1.89693	+	1.24763i
$527$	2.45674	−	1.61582i	0.107017	−	0.0703864i
$528$		0			0
$529$	−17.2919	−	4.09826i	−0.751822	−	0.178185i
$530$	72.5967	−	60.9158i	3.15340	−	2.64601i
$531$		0			0
$532$	28.3958	+	23.8269i	1.23112	+	1.03303i
$533$	7.26378	+	9.75694i	0.314629	+	0.422620i
$534$		0			0
$535$	−13.9924	+	3.31627i	−0.604945	+	0.143375i
$536$	1.15423	−	1.55040i	0.0498552	−	0.0669671i
$537$		0			0
$538$	−20.1341	+	10.1117i	−0.868042	+	0.435947i
$539$	−1.56020	−	2.70235i	−0.0672028	−	0.116399i
$540$		0			0
$541$	6.01461	−	10.4176i	0.258588	−	0.447888i	−0.707276	−	0.706938i	$-0.750076\pi$
$541$	6.01461	−	10.4176i	0.258588	−	0.447888i	0.965864	+	0.259050i	$0.0834094\pi$
$542$	−0.580206	+	9.96175i	−0.0249220	+	0.427894i
$543$		0			0
$544$	−5.91424	−	0.691275i	−0.253571	−	0.0296382i
$545$	19.3594	−	64.6648i	0.829265	−	2.76994i
$546$		0			0
$547$	−2.52741	+	5.85920i	−0.108064	+	0.250521i	−0.963664	−	0.267116i	$-0.913929\pi$
$547$	−2.52741	+	5.85920i	−0.108064	+	0.250521i	0.855600	+	0.517638i	$0.173188\pi$
$548$	22.0342	−	8.01980i	0.941255	−	0.342589i
$549$		0			0
$550$	15.2783	+	5.56083i	0.651467	+	0.237115i
$551$	1.42904	−	1.51469i	0.0608791	−	0.0645280i
$552$		0			0
$553$	−12.8659	−	6.46151i	−0.547115	−	0.274771i
$554$	−0.813362	−	13.9649i	−0.0345565	−	0.593311i
$555$		0			0
$556$	7.45782	+	24.9109i	0.316282	+	1.05646i
$557$	−6.99671	−	39.6803i	−0.296460	−	1.68131i	−0.661207	−	0.750203i	$-0.729956\pi$
$557$	−6.99671	−	39.6803i	−0.296460	−	1.68131i	0.364747	−	0.931107i	$-0.381156\pi$
$558$		0			0
$559$	2.56494	−	14.5465i	0.108485	−	0.615251i
$560$	−36.3688	+	4.25091i	−1.53686	+	0.179634i
$561$		0			0
$562$	−3.59523	−	3.81072i	−0.151656	−	0.160746i
$563$	−0.628050	−	1.45598i	−0.0264692	−	0.0613624i	0.904469	−	0.426540i	$-0.140268\pi$
$563$	−0.628050	−	1.45598i	−0.0264692	−	0.0613624i	−0.930938	+	0.365177i	$0.881008\pi$
$564$		0			0
$565$	33.5302	+	22.0531i	1.41062	+	0.927782i
$566$	−1.96163			−0.0824536
$567$		0			0
$568$	−6.80775			−0.285647
$569$	−9.22728	−	6.06888i	−0.386828	−	0.254421i	0.341168	−	0.940002i	$-0.389178\pi$
$569$	−9.22728	−	6.06888i	−0.386828	−	0.254421i	−0.727996	+	0.685582i	$0.759548\pi$
$570$		0			0
$571$	3.13218	+	7.26120i	0.131078	+	0.303872i	0.971097	−	0.238684i	$-0.0767160\pi$
$571$	3.13218	+	7.26120i	0.131078	+	0.303872i	−0.840020	+	0.542556i	$0.817457\pi$
$572$	−3.19733	−	3.38897i	−0.133687	−	0.141700i
$573$		0			0
$574$	−34.2903	+	4.00796i	−1.43125	+	0.167289i
$575$	−4.03238	+	22.8688i	−0.168162	+	0.953695i
$576$		0			0
$577$	−8.01656	−	45.4642i	−0.333734	−	1.89270i	−0.439392	−	0.898295i	$-0.644806\pi$
$577$	−8.01656	−	45.4642i	−0.333734	−	1.89270i	0.105658	−	0.994402i	$-0.466305\pi$
$578$	−9.97807	−	33.3291i	−0.415033	−	1.38631i
$579$		0			0
$580$	−0.260091	−	4.46558i	−0.0107997	−	0.185423i
$581$	7.59086	+	3.81227i	0.314922	+	0.158160i
$582$		0			0
$583$	5.97503	−	6.33317i	0.247461	−	0.262293i
$584$	7.51238	+	2.73428i	0.310865	+	0.113145i
$585$		0			0
$586$	4.66235	−	1.69696i	0.192600	−	0.0701007i
$587$	14.5601	−	33.7540i	0.600959	−	1.39318i	−0.297755	−	0.954642i	$-0.596238\pi$
$587$	14.5601	−	33.7540i	0.600959	−	1.39318i	0.898713	−	0.438536i	$-0.144503\pi$
$588$		0			0
$589$	−5.07421	+	16.9490i	−0.209079	+	0.698373i
$590$	−33.9437	−	3.96745i	−1.39744	−	0.163337i
$591$		0			0
$592$	−0.779979	+	13.3917i	−0.0320570	+	0.550397i
$593$	−7.17407	+	12.4258i	−0.294604	+	0.510268i	−0.974893	−	0.222676i	$-0.928521\pi$
$593$	−7.17407	+	12.4258i	−0.294604	+	0.510268i	0.680289	+	0.732944i	$0.261854\pi$
$594$		0			0
$595$	4.84238	+	8.38725i	0.198518	+	0.343844i
$596$	27.5064	−	13.8142i	1.12671	−	0.565853i
$597$		0			0
$598$	7.18306	−	9.64853i	0.293737	−	0.394558i
$599$	−12.6650	+	3.00166i	−0.517479	+	0.122645i	−0.481053	−	0.876692i	$-0.659745\pi$
$599$	−12.6650	+	3.00166i	−0.517479	+	0.122645i	−0.0364259	+	0.999336i	$0.511597\pi$
$600$		0			0
$601$	−3.76081	−	5.05165i	−0.153407	−	0.206061i	0.718775	−	0.695242i	$-0.244703\pi$
$601$	−3.76081	−	5.05165i	−0.153407	−	0.206061i	−0.872182	+	0.489181i	$0.837296\pi$
$602$	32.1148	+	26.9476i	1.30890	+	1.09830i
$603$		0			0
$604$	−34.5775	+	29.0140i	−1.40694	+	1.18056i
$605$	−39.4989	−	9.36140i	−1.60586	−	0.380595i
$606$		0			0
$607$	−10.9863	+	7.22582i	−0.445921	+	0.293287i	−0.752542	−	0.658545i	$-0.771172\pi$
$607$	−10.9863	+	7.22582i	−0.445921	+	0.293287i	0.306620	+	0.951832i	$0.400802\pi$
$608$	29.9330	−	19.6872i	1.21394	−	0.798423i
$609$		0			0
$610$	−2.14161	−	0.507571i	−0.0867112	−	0.0205509i
$611$	−20.5052	+	17.2059i	−0.829552	+	0.696076i
$612$		0			0
$613$	−28.3321	−	23.7734i	−1.14432	−	0.960200i	−0.144750	−	0.989468i	$-0.546238\pi$
$613$	−28.3321	−	23.7734i	−1.14432	−	0.960200i	−0.999572	+	0.0292684i	$0.990682\pi$
$614$	19.2773	+	25.8939i	0.777967	+	1.04499i
$615$		0			0
$616$	2.47545	−	0.586692i	0.0997387	−	0.0236385i
$617$	19.3944	−	26.0512i	0.780789	−	1.04878i	−0.216579	−	0.976265i	$-0.569490\pi$
$617$	19.3944	−	26.0512i	0.780789	−	1.04878i	0.997367	−	0.0725160i	$-0.0231028\pi$
$618$		0			0
$619$	−38.3557	+	19.2630i	−1.54165	+	0.774243i	−0.997885	−	0.0649972i	$-0.979296\pi$
$619$	−38.3557	+	19.2630i	−1.54165	+	0.774243i	−0.543760	+	0.839241i	$0.683000\pi$
$620$	19.0021	+	32.9126i	0.763142	+	1.32180i
$621$		0			0
$622$	−17.7127	+	30.6793i	−0.710215	+	1.23013i
$623$	−1.04479	+	17.9383i	−0.0418586	+	0.718684i
$624$		0			0
$625$	−27.1638	−	3.17499i	−1.08655	−	0.126999i
$626$	19.7657	−	66.0220i	0.789995	−	2.63877i
$627$		0			0
$628$	22.9245	−	53.1451i	0.914789	−	2.12072i
$629$	3.33404	−	1.21349i	0.132937	−	0.0483851i
$630$		0			0
$631$	13.0635	+	4.75472i	0.520049	+	0.189282i	0.588690	−	0.808359i	$-0.299644\pi$
$631$	13.0635	+	4.75472i	0.520049	+	0.189282i	−0.0686408	+	0.997641i	$0.521866\pi$
$632$	2.98603	−	3.16501i	0.118778	−	0.125897i
$633$		0			0
$634$	−40.9732	−	20.5775i	−1.62725	−	0.817238i
$635$	2.99082	+	51.3504i	0.118687	+	2.03778i
$636$		0			0
$637$	−2.94031	−	9.82133i	−0.116499	−	0.389135i
$638$	−0.129000	−	0.731597i	−0.00510717	−	0.0289642i
$639$		0			0
$640$	5.29656	−	30.0383i	0.209365	−	1.18737i
$641$	2.60191	−	0.304120i	0.102769	−	0.0120120i	−0.0645528	−	0.997914i	$-0.520562\pi$
$641$	2.60191	−	0.304120i	0.102769	−	0.0120120i	0.167322	+	0.985902i	$0.446488\pi$
$642$		0			0
$643$	0.0703439	+	0.0745602i	0.00277409	+	0.00294037i	0.728759	−	0.684770i	$-0.240097\pi$
$643$	0.0703439	+	0.0745602i	0.00277409	+	0.00294037i	−0.725985	+	0.687710i	$0.758616\pi$
$644$	7.48068	+	17.3422i	0.294780	+	0.683377i
$645$		0			0
$646$	−5.91768	−	3.89212i	−0.232828	−	0.153133i
$647$	−25.1564			−0.988998			−0.494499	−	0.869178i	$-0.664649\pi$
$647$	−25.1564			−0.988998			−0.494499	+	0.869178i	$0.664649\pi$
$648$		0			0
$649$	−3.13983			−0.123249
$650$	44.6299	+	29.3536i	1.75053	+	1.15134i
$651$		0			0
$652$	11.4994	+	26.6586i	0.450351	+	1.04403i
$653$	5.11903	+	5.42585i	0.200323	+	0.212330i	0.819746	−	0.572728i	$-0.194115\pi$
$653$	5.11903	+	5.42585i	0.200323	+	0.212330i	−0.619423	+	0.785058i	$0.712633\pi$
$654$		0			0
$655$	−38.9034	+	4.54715i	−1.52008	+	0.177672i
$656$	−2.39595	+	13.5881i	−0.0935463	+	0.530527i
$657$		0			0
$658$	−13.1924	−	74.8181i	−0.514295	−	2.91671i
$659$	−4.66341	−	15.5769i	−0.181661	−	0.606789i	−0.999508	−	0.0313543i	$-0.990018\pi$
$659$	−4.66341	−	15.5769i	−0.181661	−	0.606789i	0.817848	−	0.575435i	$-0.195167\pi$
$660$		0			0
$661$	−1.09720	−	18.8381i	−0.0426760	−	0.732718i	−0.949993	−	0.312271i	$-0.898910\pi$
$661$	−1.09720	−	18.8381i	−0.0426760	−	0.732718i	0.907317	−	0.420447i	$-0.138127\pi$
$662$	−45.0219	−	22.6109i	−1.74983	−	0.878796i
$663$		0			0
$664$	−1.76175	+	1.86735i	−0.0683691	+	0.0724670i
$665$	−54.7570	−	19.9299i	−2.12339	−	0.772849i
$666$		0			0
$667$	0.997034	−	0.362891i	0.0386053	−	0.0140512i
$668$	−23.7496	+	55.0578i	−0.918901	+	2.13025i
$669$		0			0
$670$	−4.52974	+	15.1304i	−0.174999	+	0.584538i
$671$	−0.200845	−	0.0234754i	−0.00775354	−	0.000906259i
$672$		0			0
$673$	0.475690	−	8.16727i	0.0183365	−	0.314825i	−0.976651	−	0.214830i	$-0.931080\pi$
$673$	0.475690	−	8.16727i	0.0183365	−	0.314825i	0.994988	−	0.0999952i	$-0.0318827\pi$
$674$	−19.4599	+	33.7056i	−0.749569	+	1.29829i
$675$		0			0
$676$	8.44293	+	14.6236i	0.324728	+	0.562445i
$677$	−20.6357	+	10.3637i	−0.793096	+	0.398308i	−0.798740	−	0.601676i	$-0.794500\pi$
$677$	−20.6357	+	10.3637i	−0.793096	+	0.398308i	0.00564403	+	0.999984i	$0.498203\pi$
$678$		0			0
$679$	−18.8974	+	25.3837i	−0.725217	+	0.974136i
$680$	−2.84811	+	0.675015i	−0.109220	+	0.0258857i
$681$		0			0
$682$	3.76902	+	5.06267i	0.144323	+	0.193860i
$683$	−14.3566	−	12.0466i	−0.549340	−	0.460951i	0.325378	−	0.945584i	$-0.394509\pi$
$683$	−14.3566	−	12.0466i	−0.549340	−	0.460951i	−0.874717	+	0.484633i	$0.838953\pi$
$684$		0			0
$685$	−28.2370	+	23.6937i	−1.07888	+	0.905289i
$686$	−19.7506	−	4.68099i	−0.754083	−	0.178721i
$687$		0			0
$688$	13.9985	−	9.20698i	0.533689	−	0.351013i
$689$	23.9002	−	15.7194i	0.910525	−	0.598862i
$690$		0			0
$691$	−6.47006	−	1.53343i	−0.246133	−	0.0583345i	0.105698	−	0.994398i	$-0.466292\pi$
$691$	−6.47006	−	1.53343i	−0.246133	−	0.0583345i	−0.351830	+	0.936064i	$0.614441\pi$
$692$	−29.4279	+	24.6929i	−1.11868	+	0.938684i
$693$		0			0
$694$	27.4089	+	22.9988i	1.04043	+	0.873023i
$695$	−24.4102	−	32.7885i	−0.925931	−	1.24374i
$696$		0			0
$697$	3.55103	−	0.841610i	0.134505	−	0.0318782i
$698$	−10.3188	+	13.8605i	−0.390572	+	0.524630i
$699$		0			0
$700$	−74.9521	+	37.6423i	−2.83292	+	1.42275i
$701$	12.1477	+	21.0405i	0.458813	+	0.794687i	0.998899	−	0.0469230i	$-0.0149415\pi$
$701$	12.1477	+	21.0405i	0.458813	+	0.794687i	−0.540086	+	0.841610i	$0.681608\pi$
$702$		0			0
$703$	−10.6738	+	18.4876i	−0.402571	+	0.697274i
$704$	0.494971	−	8.49832i	0.0186549	−	0.320292i
$705$		0			0
$706$	51.7260	+	6.04590i	1.94673	+	0.227540i
$707$	−11.7728	+	39.3240i	−0.442763	+	1.47893i
$708$		0			0
$709$	11.8515	−	27.4749i	0.445093	−	1.03184i	−0.537024	−	0.843567i	$-0.680451\pi$
$709$	11.8515	−	27.4749i	0.445093	−	1.03184i	0.982117	−	0.188274i	$-0.0602893\pi$
$710$	52.2729	−	19.0258i	1.96177	−	0.714024i
$711$		0			0
$712$	−5.10315	−	1.85740i	−0.191249	−	0.0696089i
$713$	−6.18613	+	6.55691i	−0.231672	+	0.245558i
$714$		0			0
$715$	6.54519	+	3.28712i	0.244776	+	0.122931i
$716$	1.03504	+	17.7710i	0.0386814	+	0.664134i
$717$		0			0
$718$	−7.67320	−	25.6303i	−0.286361	−	0.956514i
$719$	−2.12889	−	12.0735i	−0.0793943	−	0.450267i	−0.998426	−	0.0560838i	$-0.982139\pi$
$719$	−2.12889	−	12.0735i	−0.0793943	−	0.450267i	0.919032	−	0.394183i	$-0.128973\pi$
$720$		0			0
$721$	−9.65461	+	54.7540i	−0.359556	+	2.03915i
$722$	2.40063	−	0.280593i	0.0893422	−	0.0104426i
$723$		0			0
$724$	13.1497	+	13.9379i	0.488706	+	0.517998i
$725$	1.86626	+	4.32649i	0.0693113	+	0.160682i
$726$		0			0
$727$	40.9555	+	26.9369i	1.51896	+	0.999033i	0.988483	+	0.151331i	$0.0483560\pi$
$727$	40.9555	+	26.9369i	1.51896	+	0.999033i	0.530473	+	0.847702i	$0.322014\pi$
$728$	8.35832			0.309780
$729$		0			0
$730$	−65.3249			−2.41778
$731$	−3.70251	−	2.43518i	−0.136942	−	0.0900683i
$732$		0			0
$733$	−8.00055	−	18.5474i	−0.295507	−	0.685063i	0.704181	−	0.710020i	$-0.251314\pi$
$733$	−8.00055	−	18.5474i	−0.295507	−	0.685063i	−0.999689	+	0.0249576i	$0.992055\pi$
$734$	−15.2367	−	16.1499i	−0.562396	−	0.596104i
$735$		0			0
$736$	18.1310	−	2.11921i	0.668317	−	0.0781150i
$737$	−0.251977	+	1.42903i	−0.00928168	+	0.0526390i
$738$		0			0
$739$	0.349401	+	1.98155i	0.0128529	+	0.0728925i	0.990560	−	0.137083i	$-0.0437727\pi$
$739$	0.349401	+	1.98155i	0.0128529	+	0.0728925i	−0.977707	+	0.209975i	$0.932662\pi$
$740$	13.1517	+	43.9297i	0.483465	+	1.61489i
$741$		0			0
$742$	4.72082	+	81.0533i	0.173307	+	2.97556i
$743$	19.2775	+	9.68153i	0.707223	+	0.355181i	0.765779	−	0.643103i	$-0.222353\pi$
$743$	19.2775	+	9.68153i	0.707223	+	0.355181i	−0.0585563	+	0.998284i	$0.518650\pi$
$744$		0			0
$745$	−33.2051	+	35.1953i	−1.21654	+	1.28946i
$746$	23.4531	+	8.53624i	0.858680	+	0.312534i
$747$		0			0
$748$	−1.31354	+	0.478091i	−0.0480279	+	0.0174807i
$749$	4.87962	−	11.3122i	0.178298	−	0.413340i
$750$		0			0
$751$	4.15221	−	13.8693i	0.151516	−	0.506099i	−0.848206	−	0.529666i	$-0.822317\pi$
$751$	4.15221	−	13.8693i	0.151516	−	0.506099i	0.999722	+	0.0235670i	$0.00750231\pi$
$752$	−30.1577	−	3.52494i	−1.09974	−	0.128541i
$753$		0			0
$754$	0.141915	−	2.43659i	0.00516826	−	0.0887355i
$755$	35.4783	−	61.4503i	1.29119	−	2.23640i
$756$		0			0
$757$	−5.26451	−	9.11840i	−0.191342	−	0.331414i	0.754353	−	0.656469i	$-0.227951\pi$
$757$	−5.26451	−	9.11840i	−0.191342	−	0.331414i	−0.945695	+	0.325055i	$0.894617\pi$
$758$	−34.2919	+	17.2220i	−1.24554	+	0.625533i
$759$		0			0
$760$	10.5167	−	14.1264i	0.381480	−	0.512417i
$761$	−41.1358	+	9.74936i	−1.49117	+	0.353414i	−0.893769	−	0.448528i	$-0.851949\pi$
$761$	−41.1358	+	9.74936i	−1.49117	+	0.353414i	−0.597402	+	0.801942i	$0.703800\pi$
$762$		0			0
$763$	34.5335	+	46.3865i	1.25020	+	1.67930i
$764$	−19.1188	−	16.0425i	−0.691693	−	0.580399i
$765$		0			0
$766$	−25.1504	+	21.1037i	−0.908721	+	0.762507i
$767$	−10.0378	−	2.37900i	−0.362443	−	0.0859006i
$768$		0			0
$769$	7.53547	−	4.95616i	0.271736	−	0.178724i	−0.406326	−	0.913728i	$-0.633190\pi$
$769$	7.53547	−	4.95616i	0.271736	−	0.178724i	0.678062	+	0.735005i	$0.262820\pi$
$770$	−17.3679	+	11.4231i	−0.625897	+	0.411659i
$771$		0			0
$772$	−38.5361	−	9.13322i	−1.38694	−	0.328712i
$773$	0.551231	−	0.462537i	0.0198264	−	0.0166363i	−0.632821	−	0.774298i	$-0.718103\pi$
$773$	0.551231	−	0.462537i	0.0198264	−	0.0166363i	0.652647	+	0.757662i	$0.273658\pi$
$774$		0			0
$775$	−30.6663	−	25.7321i	−1.10157	−	0.924325i
$776$	−5.71134	−	7.67167i	−0.205025	−	0.275397i
$777$		0			0
$778$	31.7750	−	7.53081i	1.13919	−	0.269993i
$779$	−13.1122	+	17.6128i	−0.469794	+	0.631043i
$780$		0			0
$781$	4.56720	−	2.29373i	0.163427	−	0.0820763i
$782$	−1.80442	−	3.12535i	−0.0645261	−	0.111762i
$783$		0			0
$784$	5.81453	−	10.0711i	0.207662	−	0.359681i
$785$	−5.29033	+	90.8314i	−0.188820	+	3.24191i
$786$		0			0
$787$	−15.3231	−	1.79102i	−0.546210	−	0.0638428i	−0.161487	−	0.986875i	$-0.551629\pi$
$787$	−15.3231	−	1.79102i	−0.546210	−	0.0638428i	−0.384723	+	0.923032i	$0.625703\pi$
$788$	−7.79138	+	26.0250i	−0.277556	+	0.927102i
$789$		0			0
$790$	−14.0827	+	32.6474i	−0.501041	+	1.16154i
$791$	−32.3091	+	11.7595i	−1.14878	+	0.418121i
$792$		0			0
$793$	−0.624297	−	0.227226i	−0.0221695	−	0.00806902i
$794$	2.96570	−	3.14346i	0.105249	−	0.111557i
$795$		0			0
$796$	7.76927	+	3.90187i	0.275374	+	0.138298i
$797$	−0.809987	−	13.9069i	−0.0286912	−	0.492609i	−0.981792	−	0.189957i	$-0.939165\pi$
$797$	−0.809987	−	13.9069i	−0.0286912	−	0.492609i	0.953101	−	0.302652i	$-0.0978719\pi$
$798$		0			0
$799$	2.30326	+	7.69342i	0.0814835	+	0.272174i
$800$	14.0768	+	79.8335i	0.497690	+	2.82254i
$801$		0			0
$802$	−5.49411	+	31.1586i	−0.194004	+	1.10025i
$803$	−5.96118	+	0.696763i	−0.210366	+	0.0245882i
$804$		0			0
$805$	−20.3746	−	21.5958i	−0.718109	−	0.761152i
$806$	8.21332	+	19.0406i	0.289302	+	0.670677i
$807$		0			0
$808$	−10.3651	−	6.81721i	−0.364642	−	0.239829i
$809$	−40.8781			−1.43720			−0.718599	−	0.695424i	$-0.755216\pi$
$809$	−40.8781			−1.43720			−0.718599	+	0.695424i	$0.755216\pi$
$810$		0			0
$811$	51.1039			1.79450			0.897250	−	0.441524i	$-0.145562\pi$
$811$	51.1039			1.79450			0.897250	+	0.441524i	$0.145562\pi$
$812$	3.20182	+	2.10587i	0.112362	+	0.0739016i
$813$		0			0
$814$	3.01639	+	6.99277i	0.105724	+	0.245096i
$815$	−31.3201	−	33.1973i	−1.09709	−	1.16285i
$816$		0			0
$817$	26.4834	−	3.09547i	0.926538	−	0.108297i
$818$	−3.81673	+	21.6457i	−0.133449	+	0.756825i
$819$		0			0
$820$	8.19037	+	46.4499i	0.286020	+	1.62210i
$821$	13.9304	+	46.5308i	0.486174	+	1.62393i	0.751470	+	0.659768i	$0.229345\pi$
$821$	13.9304	+	46.5308i	0.486174	+	1.62393i	−0.265296	+	0.964167i	$0.585470\pi$
$822$		0			0
$823$	−1.57149	−	26.9814i	−0.0547787	−	0.940513i	−0.908002	−	0.418967i	$-0.862392\pi$
$823$	−1.57149	−	26.9814i	−0.0547787	−	0.940513i	0.853223	−	0.521546i	$-0.174645\pi$
$824$	−15.0162	−	7.54139i	−0.523112	−	0.262717i
$825$		0			0
$826$	20.0922	−	21.2964i	0.699096	−	0.740998i
$827$	−14.9793	−	5.45201i	−0.520880	−	0.189585i	0.0681816	−	0.997673i	$-0.478280\pi$
$827$	−14.9793	−	5.45201i	−0.520880	−	0.189585i	−0.589062	+	0.808088i	$0.700503\pi$
$828$		0			0
$829$	1.59698	−	0.581253i	0.0554654	−	0.0201877i	−0.314138	−	0.949377i	$-0.601716\pi$
$829$	1.59698	−	0.581253i	0.0554654	−	0.0201877i	0.369604	+	0.929189i	$0.379493\pi$
$830$	8.30876	−	19.2619i	0.288401	−	0.668590i
$831$		0			0
$832$	8.02140	−	26.7933i	0.278092	−	0.928892i
$833$	−3.05500	−	0.357079i	−0.105850	−	0.0123720i
$834$		0			0
$835$	5.48073	−	94.1005i	0.189669	−	3.25648i
$836$	4.20527	−	7.28373i	0.145442	−	0.251913i
$837$		0			0
$838$	0.560786	+	0.971310i	0.0193720	+	0.0335534i
$839$	−41.4212	+	20.8025i	−1.43002	+	0.718183i	−0.984220	−	0.176949i	$-0.943377\pi$
$839$	−41.4212	+	20.8025i	−1.43002	+	0.718183i	−0.445800	+	0.895132i	$0.647081\pi$
$840$		0			0
$841$	−17.1890	+	23.0889i	−0.592725	+	0.796168i
$842$	66.0144	−	15.6457i	2.27501	−	0.539187i
$843$		0			0
$844$	−11.3628	−	15.2629i	−0.391125	−	0.525372i
$845$	−20.3343	−	17.0625i	−0.699523	−	0.586969i
$846$		0			0
$847$	26.6409	−	22.3544i	0.915393	−	0.768106i
$848$	31.5740	+	7.48317i	1.08426	+	0.256973i
$849$		0			0
$850$	13.3898	−	8.80663i	0.459267	−	0.302065i
$851$	−9.08757	+	5.97699i	−0.311518	+	0.204889i
$852$		0			0
$853$	−23.5426	−	5.57970i	−0.806083	−	0.191045i	−0.193139	−	0.981171i	$-0.561867\pi$
$853$	−23.5426	−	5.57970i	−0.806083	−	0.191045i	−0.612944	+	0.790126i	$0.710015\pi$
$854$	1.44446	−	1.21204i	0.0494283	−	0.0414753i
$855$		0			0
$856$	2.85228	+	2.39335i	0.0974891	+	0.0818031i
$857$	−7.66072	−	10.2901i	−0.261685	−	0.351504i	0.651789	−	0.758400i	$-0.274019\pi$
$857$	−7.66072	−	10.2901i	−0.261685	−	0.351504i	−0.913475	+	0.406896i	$0.866611\pi$
$858$		0			0
$859$	19.9669	−	4.73224i	0.681262	−	0.161462i	0.124607	−	0.992206i	$-0.460233\pi$
$859$	19.9669	−	4.73224i	0.681262	−	0.161462i	0.556654	+	0.830744i	$0.312085\pi$
$860$	34.2024	−	45.9419i	1.16629	−	1.56660i
$861$		0			0
$862$	−10.1775	+	5.11136i	−0.346649	+	0.174093i
$863$	18.5110	+	32.0620i	0.630121	+	1.09140i	0.987527	+	0.157453i	$0.0503282\pi$
$863$	18.5110	+	32.0620i	0.630121	+	1.09140i	−0.357405	+	0.933949i	$0.616338\pi$
$864$		0			0
$865$	30.1945	−	52.2984i	1.02664	−	1.77820i
$866$	4.09570	−	70.3205i	0.139178	−	2.38959i
$867$		0			0
$868$	−32.3391	−	3.77990i	−1.09766	−	0.128298i
$869$	−0.936890	+	3.12943i	−0.0317818	+	0.106159i
$870$		0			0
$871$	−1.88830	+	4.37757i	−0.0639826	+	0.148328i
$872$	−16.4237	+	5.97775i	−0.556178	+	0.202432i
$873$		0			0
$874$	20.4042	+	7.42652i	0.690182	+	0.251206i
$875$	45.9306	−	48.6836i	1.55274	−	1.64581i
$876$		0			0
$877$	38.7549	+	19.4634i	1.30866	+	0.657233i	0.959996	−	0.280015i	$-0.0903394\pi$
$877$	38.7549	+	19.4634i	1.30866	+	0.657233i	0.348663	+	0.937248i	$0.386636\pi$
$878$	−2.29826	−	39.4596i	−0.0775625	−	1.33170i
$879$		0			0
$880$	2.38277	+	7.95901i	0.0803232	+	0.268298i
$881$	1.78531	+	10.1250i	0.0601486	+	0.341120i	1.00000		0.000464198i	$-0.000147759\pi$
$881$	1.78531	+	10.1250i	0.0601486	+	0.341120i	−0.939851	+	0.341584i	$0.889037\pi$
$882$		0			0
$883$	1.36337	−	7.73205i	0.0458810	−	0.260204i	−0.953236	−	0.302228i	$-0.902269\pi$
$883$	1.36337	−	7.73205i	0.0458810	−	0.260204i	0.999117	+	0.0420240i	$0.0133806\pi$
$884$	−4.56152	+	0.533166i	−0.153421	+	0.0179323i
$885$		0			0
$886$	−27.3985	−	29.0407i	−0.920469	−	0.975640i
$887$	−13.8603	−	32.1317i	−0.465382	−	1.07888i	−0.975744	−	0.218917i	$-0.929748\pi$
$887$	−13.8603	−	32.1317i	−0.465382	−	1.07888i	0.510362	−	0.859960i	$-0.329512\pi$
$888$		0			0
$889$	−36.8182	−	24.2157i	−1.23484	−	0.812169i
$890$	44.3751			1.48746
$891$		0			0
$892$	26.8550			0.899172
$893$	−40.3705	−	26.5521i	−1.35095	−	0.888531i
$894$		0			0
$895$	−11.0837	−	25.6948i	−0.370486	−	0.858883i
$896$	17.9327	+	19.0075i	0.599088	+	0.634996i
$897$		0			0
$898$	−14.6391	+	1.71107i	−0.488515	+	0.0570992i
$899$	−0.317622	+	1.80133i	−0.0105933	+	0.0600776i
$900$		0			0
$901$	−1.49032	−	8.45204i	−0.0496498	−	0.281578i
$902$	2.24659	+	7.50414i	0.0748034	+	0.249861i
$903$		0			0
$904$	−0.604206	−	10.3738i	−0.0200956	−	0.345028i
$905$	−26.9186	−	13.5190i	−0.894804	−	0.449387i
$906$		0			0
$907$	34.4760	−	36.5424i	1.14476	−	1.21337i	0.171124	−	0.985250i	$-0.445260\pi$
$907$	34.4760	−	36.5424i	1.14476	−	1.21337i	0.973633	−	0.228122i	$-0.0732584\pi$
$908$	25.2752	+	9.19941i	0.838786	+	0.305293i
$909$		0			0
$910$	−64.1788	+	23.3592i	−2.12751	+	0.774349i
$911$	−9.76794	+	22.6446i	−0.323626	+	0.750250i	0.676281	+	0.736643i	$0.263590\pi$
$911$	−9.76794	+	22.6446i	−0.323626	+	0.750250i	−0.999907	+	0.0136062i	$0.995669\pi$
$912$		0			0
$913$	0.552762	−	1.84635i	0.0182938	−	0.0611054i
$914$	79.0097	+	9.23490i	2.61341	+	0.305463i
$915$		0			0
$916$	−0.329662	+	5.66008i	−0.0108923	+	0.187014i
$917$	16.7783	−	29.0608i	0.554067	−	0.959672i
$918$		0			0
$919$	−4.12738	−	7.14883i	−0.136150	−	0.235818i	0.789886	−	0.613253i	$-0.210139\pi$
$919$	−4.12738	−	7.14883i	−0.136150	−	0.235818i	−0.926036	+	0.377435i	$0.876806\pi$
$920$	8.01873	−	4.02716i	0.264370	−	0.132772i
$921$		0			0
$922$	34.9178	−	46.9027i	1.14996	−	1.54466i
$923$	16.3389	−	3.87238i	0.537800	−	0.127461i
$924$		0			0
$925$	−28.8445	−	38.7449i	−0.948403	−	1.27393i
$926$	−39.8178	−	33.4111i	−1.30849	−	1.09796i
$927$		0			0
$928$	2.83740	−	2.38086i	0.0931422	−	0.0781556i
$929$	−9.54344	−	2.26184i	−0.313110	−	0.0742085i	0.0710563	−	0.997472i	$-0.477363\pi$
$929$	−9.54344	−	2.26184i	−0.313110	−	0.0742085i	−0.384166	+	0.923264i	$0.625511\pi$
$930$		0			0
$931$	15.4619	−	10.1695i	0.506744	−	0.333291i
$932$	−36.8515	+	24.2376i	−1.20711	+	0.793929i
$933$		0			0
$934$	−16.1833	−	3.83551i	−0.529534	−	0.125502i
$935$	1.68332	−	1.41247i	0.0550503	−	0.0461927i
$936$		0			0
$937$	33.8490	+	28.4027i	1.10580	+	0.927875i	0.997801	−	0.0662763i	$-0.0211119\pi$
$937$	33.8490	+	28.4027i	1.10580	+	0.927875i	0.107997	+	0.994151i	$0.465556\pi$
$938$	−8.08021	−	10.8536i	−0.263828	−	0.354383i
$939$		0			0
$940$	−100.996	+	23.9365i	−3.29412	+	0.780721i
$941$	−6.35395	+	8.53483i	−0.207133	+	0.278228i	−0.893534	−	0.448995i	$-0.851782\pi$
$941$	−6.35395	+	8.53483i	−0.207133	+	0.278228i	0.686401	+	0.727223i	$0.259189\pi$
$942$		0			0
$943$	−9.99777	+	5.02107i	−0.325572	+	0.163508i
$944$	−5.85073	−	10.1338i	−0.190425	−	0.329826i
$945$		0			0
$946$	4.75603	−	8.23768i	0.154632	−	0.267830i
$947$	0.639255	−	10.9756i	0.0207730	−	0.356659i	−0.971865	−	0.235539i	$-0.924314\pi$
$947$	0.639255	−	10.9756i	0.0207730	−	0.356659i	0.992638	−	0.121120i	$-0.0386485\pi$
$948$		0			0
$949$	−19.5853	−	2.28919i	−0.635766	−	0.0743104i
$950$	−27.6556	+	92.3763i	−0.897267	+	2.99708i
$951$		0			0
$952$	0.993232	−	2.30257i	0.0321908	−	0.0746267i
$953$	39.7723	−	14.4759i	1.28835	−	0.468921i	0.395165	−	0.918610i	$-0.370687\pi$
$953$	39.7723	−	14.4759i	1.28835	−	0.468921i	0.893185	+	0.449689i	$0.148465\pi$
$954$		0			0
$955$	36.8676	+	13.4187i	1.19301	+	0.434219i
$956$	20.8456	−	22.0950i	0.674194	−	0.714604i
$957$		0			0
$958$	33.4874	+	16.8180i	1.08193	+	0.543366i
$959$	−1.83620	−	31.5263i	−0.0592939	−	1.01804i
$960$		0			0
$961$	4.43390	+	14.8103i	0.143029	+	0.477751i
$962$	4.34483	+	24.6407i	0.140083	+	0.794449i
$963$		0			0
$964$	7.52523	−	42.6777i	0.242371	−	1.37456i
$965$	61.8360	−	7.22759i	1.99057	−	0.232664i
$966$		0			0
$967$	5.70365	+	6.04552i	0.183417	+	0.194411i	0.812558	−	0.582881i	$-0.198075\pi$
$967$	5.70365	+	6.04552i	0.183417	+	0.194411i	−0.629141	+	0.777291i	$0.716593\pi$
$968$	4.16306	+	9.65107i	0.133806	+	0.310197i
$969$		0			0
$970$	65.2943	+	42.9448i	2.09647	+	1.37887i
$971$	−17.9539			−0.576169			−0.288084	−	0.957605i	$-0.593018\pi$
$971$	−17.9539			−0.576169			−0.288084	+	0.957605i	$0.593018\pi$
$972$		0			0
$973$	35.0207			1.12271
$974$	−74.4455	−	48.9636i	−2.38539	−	1.56890i
$975$		0			0
$976$	−0.298486	−	0.691968i	−0.00955430	−	0.0221494i
$977$	16.7513	+	17.7553i	0.535922	+	0.568044i	0.937591	−	0.347741i	$-0.113051\pi$
$977$	16.7513	+	17.7553i	0.535922	+	0.568044i	−0.401669	+	0.915785i	$0.631570\pi$
$978$		0			0
$979$	4.04943	−	0.473310i	0.129420	−	0.0151271i
$980$	6.90304	−	39.1491i	0.220509	−	1.25057i
$981$		0			0
$982$	2.67375	+	15.1636i	0.0853228	+	0.483890i
$983$	−13.3688	−	44.6549i	−0.426399	−	1.42427i	−0.853986	−	0.520297i	$-0.825821\pi$
$983$	−13.3688	−	44.6549i	−0.426399	−	1.42427i	0.427587	−	0.903974i	$-0.359364\pi$
$984$		0			0
$985$	−2.48310	−	42.6332i	−0.0791182	−	1.35841i
$986$	−0.654375	−	0.328639i	−0.0208395	−	0.0104660i
$987$		0			0
$988$	18.9626	−	20.0992i	0.603281	−	0.639441i
$989$	12.7663	+	4.64654i	0.405944	+	0.147751i
$990$		0			0
$991$	−55.3339	+	20.1399i	−1.75774	+	0.639765i	−0.999919	−	0.0126995i	$-0.995958\pi$
$991$	−55.3339	+	20.1399i	−1.75774	+	0.639765i	−0.757820	+	0.652464i	$0.773735\pi$
$992$	−12.4643	+	28.8954i	−0.395741	+	0.917430i
$993$		0			0
$994$	−13.6684	+	45.6557i	−0.433536	+	1.44811i
$995$	−13.5746	−	1.58665i	−0.430344	−	0.0503001i
$996$		0			0
$997$	−3.50559	+	60.1886i	−0.111023	+	1.90619i	0.241517	+	0.970397i	$0.422355\pi$
$997$	−3.50559	+	60.1886i	−0.111023	+	1.90619i	−0.352540	+	0.935797i	$0.614682\pi$
$998$	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.c.703.7		144
3.2	odd	2		729.2.g.b.703.2		144
9.2	odd	6		729.2.g.a.217.2		144
9.4	even	3		81.2.g.a.25.2	yes	144
9.5	odd	6		243.2.g.a.73.7		144
9.7	even	3		729.2.g.d.217.7		144
81.13	even	27		729.2.g.d.514.7		144
81.14	odd	54		729.2.g.b.28.2		144
81.38	odd	54		6561.2.a.d.1.61		72
81.40	even	27		81.2.g.a.13.2	✓	144
81.41	odd	54		243.2.g.a.10.7		144
81.43	even	27		6561.2.a.c.1.12		72
81.67	even	27	inner	729.2.g.c.28.7		144
81.68	odd	54		729.2.g.a.514.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.2	✓	144	81.40	even	27
81.2.g.a.25.2	yes	144	9.4	even	3
243.2.g.a.10.7		144	81.41	odd	54
243.2.g.a.73.7		144	9.5	odd	6
729.2.g.a.217.2		144	9.2	odd	6
729.2.g.a.514.2		144	81.68	odd	54
729.2.g.b.28.2		144	81.14	odd	54
729.2.g.b.703.2		144	3.2	odd	2
729.2.g.c.28.7		144	81.67	even	27	inner
729.2.g.c.703.7		144	1.1	even	1	trivial
729.2.g.d.217.7		144	9.7	even	3
729.2.g.d.514.7		144	81.13	even	27
6561.2.a.c.1.12		72	81.43	even	27
6561.2.a.d.1.61		72	81.38	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.76769 + 1.16263i) q^{2} +(0.980860 + 2.27389i) q^{4} +(-2.67150 - 2.83162i) q^{5} +(3.31264 - 0.387192i) q^{7} +(-0.175036 + 0.992677i) q^{8} +(-1.43025 - 8.11138i) q^{10} +(-0.217034 - 0.724944i) q^{11} +(-0.144562 - 2.48203i) q^{13} +(6.30588 + 3.16693i) q^{14} +(1.93533 - 2.05133i) q^{16} +(-0.700932 - 0.255119i) q^{17} +(4.21736 - 1.53499i) q^{19} +(3.81843 - 8.85211i) q^{20} +(0.459191 - 1.53380i) q^{22} +(2.27126 + 0.265472i) q^{23} +(-0.590459 + 10.1378i) q^{25} +(2.63013 - 4.55552i) q^{26} +(4.12967 + 7.15280i) q^{28} +(0.414639 - 0.208240i) q^{29} +(-2.35407 + 3.16206i) q^{31} +(7.76762 - 1.84096i) q^{32} +(-0.942422 - 1.26589i) q^{34} +(-9.94610 - 8.34577i) q^{35} +(-3.64375 + 3.05747i) q^{37} +(9.23961 + 2.18983i) q^{38} +(3.27849 - 2.15630i) q^{40} +(-4.08763 + 2.68847i) q^{41} +(5.78094 + 1.37011i) q^{43} +(1.43556 - 1.20458i) q^{44} +(3.70623 + 3.10990i) q^{46} +(-6.42922 - 8.63594i) q^{47} +(4.01237 - 0.950949i) q^{49} +(-12.8302 + 17.2340i) q^{50} +(5.50206 - 2.76324i) q^{52} +(5.75294 + 9.96438i) q^{53} +(-1.47296 + 2.55124i) q^{55} +(-0.195474 + 3.35616i) q^{56} +(0.975058 + 0.113968i) q^{58} +(1.19000 - 3.97488i) q^{59} +(0.105839 - 0.245363i) q^{61} +(-7.83755 + 2.85264i) q^{62} +(10.5709 + 3.84748i) q^{64} +(-6.64196 + 7.04007i) q^{65} +(-1.71358 - 0.860594i) q^{67} +(-0.107405 - 1.84408i) q^{68} +(-7.87859 - 26.3163i) q^{70} +(1.17278 + 6.65118i) q^{71} +(1.37723 - 7.81064i) q^{73} +(-9.99572 + 1.16833i) q^{74} +(7.62705 + 8.08420i) q^{76} +(-0.999649 - 2.31745i) q^{77} +(-3.60662 - 2.37211i) q^{79} -10.9788 q^{80} -10.3513 q^{82} +(2.12790 + 1.39954i) q^{83} +(1.15014 + 2.66632i) q^{85} +(8.62597 + 9.14299i) q^{86} +(0.757624 - 0.0885535i) q^{88} +(-0.935549 + 5.30576i) q^{89} +(-1.43990 - 8.16609i) q^{91} +(1.62413 + 5.42498i) q^{92} +(-1.32448 - 22.7404i) q^{94} +(-15.6132 - 7.84124i) q^{95} +(-6.51132 + 6.90160i) q^{97} +(8.19821 + 2.98391i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) \) 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 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Introduction

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