LMFDB - Embedded newform 729.2.g.d.298.3

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			298.3
Character	$\chi$	$=$	729.298
Dual form			729.2.g.d.433.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.782176 + 0.0914233i) q^{2} +(-1.34265 + 0.318213i) q^{4} +(-2.48948 - 1.25026i) q^{5} +(-1.42895 - 4.77302i) q^{7} +(2.50111 - 0.910331i) q^{8} +(2.06152 + 0.750330i) q^{10} +(-0.101002 + 1.73414i) q^{11} +(1.29643 - 1.74141i) q^{13} +(1.55406 + 3.60270i) q^{14} +(0.593056 - 0.297844i) q^{16} +(-3.39468 + 2.84848i) q^{17} +(-1.63306 - 1.37030i) q^{19} +(3.74035 + 0.886478i) q^{20} +(-0.0795392 - 1.36564i) q^{22} +(0.194482 - 0.649615i) q^{23} +(1.64856 + 2.21440i) q^{25} +(-0.854835 + 1.48062i) q^{26} +(3.43741 + 5.95378i) q^{28} +(-2.27909 + 5.28353i) q^{29} +(4.03553 + 4.27741i) q^{31} +(-4.88416 + 3.21236i) q^{32} +(2.39482 - 2.53836i) q^{34} +(-2.41020 + 13.6689i) q^{35} +(0.131814 + 0.747552i) q^{37} +(1.40262 + 0.922517i) q^{38} +(-7.36463 - 0.860801i) q^{40} +(-0.122631 - 0.0143335i) q^{41} +(-2.12747 - 1.39926i) q^{43} +(-0.416216 - 2.36048i) q^{44} +(-0.0927292 + 0.525894i) q^{46} +(-1.16557 + 1.23544i) q^{47} +(-14.8914 + 9.79424i) q^{49} +(-1.49191 - 1.58133i) q^{50} +(-1.18651 + 2.75065i) q^{52} +(-5.02192 - 8.69822i) q^{53} +(2.41957 - 4.19082i) q^{55} +(-7.91899 - 10.6371i) q^{56} +(1.29962 - 4.34102i) q^{58} +(0.676232 + 11.6105i) q^{59} +(7.70658 + 1.82649i) q^{61} +(-3.54755 - 2.97675i) q^{62} +(2.50983 - 2.10599i) q^{64} +(-5.40467 + 2.71433i) q^{65} +(-0.184347 - 0.427364i) q^{67} +(3.65144 - 4.90473i) q^{68} +(0.635542 - 10.9118i) q^{70} +(11.4588 + 4.17067i) q^{71} +(-2.01159 + 0.732160i) q^{73} +(-0.171445 - 0.572667i) q^{74} +(2.62867 + 1.32017i) q^{76} +(8.42140 - 1.99591i) q^{77} +(-6.96575 + 0.814179i) q^{79} -1.84879 q^{80} +0.0972297 q^{82} +(3.28752 - 0.384257i) q^{83} +(12.0123 - 2.84698i) q^{85} +(1.79198 + 0.899965i) q^{86} +(1.32602 + 4.42922i) q^{88} +(-4.72182 + 1.71860i) q^{89} +(-10.1643 - 3.69952i) q^{91} +(-0.0544046 + 0.934091i) q^{92} +(0.798737 - 1.07289i) q^{94} +(2.35223 + 5.45309i) q^{95} +(-6.70871 + 3.36924i) q^{97} +(10.7523 - 9.02224i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{26}{27}\right)$

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 $

$2$	−0.782176	+	0.0914233i	−0.553082	+	0.0646460i	−0.388044	−	0.921641i	$-0.626849\pi$
$2$	−0.782176	+	0.0914233i	−0.553082	+	0.0646460i	−0.165039	+	0.986287i	$0.552775\pi$
$3$		0			0
$3$		0			0
$4$	−1.34265	+	0.318213i	−0.671324	+	0.159107i
$5$	−2.48948	−	1.25026i	−1.11333	−	0.559135i	−0.205577	−	0.978641i	$-0.565907\pi$
$5$	−2.48948	−	1.25026i	−1.11333	−	0.559135i	−0.907753	+	0.419506i	$0.862203\pi$
$6$		0			0
$7$	−1.42895	−	4.77302i	−0.540092	−	1.80403i	−0.592708	−	0.805417i	$-0.701941\pi$
$7$	−1.42895	−	4.77302i	−0.540092	−	1.80403i	0.0526165	−	0.998615i	$-0.483244\pi$
$8$	2.50111	−	0.910331i	0.884277	−	0.321851i
$9$		0			0
$10$	2.06152	+	0.750330i	0.651909	+	0.237275i
$11$	−0.101002	+	1.73414i	−0.0304532	+	0.522862i	0.948243	+	0.317547i	$0.102859\pi$
$11$	−0.101002	+	1.73414i	−0.0304532	+	0.522862i	−0.978696	+	0.205315i	$0.934178\pi$
$12$		0			0
$13$	1.29643	−	1.74141i	0.359566	−	0.482981i	−0.585125	−	0.810943i	$-0.698954\pi$
$13$	1.29643	−	1.74141i	0.359566	−	0.482981i	0.944691	+	0.327962i	$0.106362\pi$
$14$	1.55406	+	3.60270i	0.415339	+	0.962863i
$15$		0			0
$16$	0.593056	−	0.297844i	0.148264	−	0.0744610i
$17$	−3.39468	+	2.84848i	−0.823331	+	0.690857i	−0.953750	−	0.300602i	$-0.902812\pi$
$17$	−3.39468	+	2.84848i	−0.823331	+	0.690857i	0.130419	+	0.991459i	$0.458368\pi$
$18$		0			0
$19$	−1.63306	−	1.37030i	−0.374650	−	0.314369i	0.435948	−	0.899972i	$-0.356413\pi$
$19$	−1.63306	−	1.37030i	−0.374650	−	0.314369i	−0.810598	+	0.585603i	$0.800858\pi$
$20$	3.74035	+	0.886478i	0.836367	+	0.198223i
$21$		0			0
$22$	−0.0795392	−	1.36564i	−0.0169578	−	0.291154i
$23$	0.194482	−	0.649615i	0.0405523	−	0.135454i	−0.935316	−	0.353813i	$-0.884885\pi$
$23$	0.194482	−	0.649615i	0.0405523	−	0.135454i	0.975869	+	0.218359i	$0.0700702\pi$
$24$		0			0
$25$	1.64856	+	2.21440i	0.329712	+	0.442880i
$26$	−0.854835	+	1.48062i	−0.167647	+	0.290373i
$27$		0			0
$28$	3.43741	+	5.95378i	0.649610	+	1.12516i
$29$	−2.27909	+	5.28353i	−0.423217	+	0.981127i	0.564580	+	0.825379i	$0.309038\pi$
$29$	−2.27909	+	5.28353i	−0.423217	+	0.981127i	−0.987797	+	0.155749i	$0.950221\pi$
$30$		0			0
$31$	4.03553	+	4.27741i	0.724803	+	0.768246i	0.980076	−	0.198623i	$-0.0636468\pi$
$31$	4.03553	+	4.27741i	0.724803	+	0.768246i	−0.255273	+	0.966869i	$0.582165\pi$
$32$	−4.88416	+	3.21236i	−0.863406	+	0.567871i
$33$		0			0
$34$	2.39482	−	2.53836i	0.410709	−	0.435326i
$35$	−2.41020	+	13.6689i	−0.407397	+	2.31047i
$36$		0			0
$37$	0.131814	+	0.747552i	0.0216700	+	0.122897i	0.993724	−	0.111861i	$-0.0356813\pi$
$37$	0.131814	+	0.747552i	0.0216700	+	0.122897i	−0.972054	+	0.234758i	$0.924570\pi$
$38$	1.40262	+	0.922517i	0.227535	+	0.149652i
$39$		0			0
$40$	−7.36463	−	0.860801i	−1.16445	−	0.136105i
$41$	−0.122631	−	0.0143335i	−0.0191518	−	0.00223852i	0.106512	−	0.994311i	$-0.466032\pi$
$41$	−0.122631	−	0.0143335i	−0.0191518	−	0.00223852i	−0.125663	+	0.992073i	$0.540106\pi$
$42$		0			0
$43$	−2.12747	−	1.39926i	−0.324435	−	0.213385i	0.376834	−	0.926281i	$-0.377013\pi$
$43$	−2.12747	−	1.39926i	−0.324435	−	0.213385i	−0.701270	+	0.712896i	$0.747383\pi$
$44$	−0.416216	−	2.36048i	−0.0627469	−	0.355855i
$45$		0			0
$46$	−0.0927292	+	0.525894i	−0.0136722	+	0.0775388i
$47$	−1.16557	+	1.23544i	−0.170017	+	0.180207i	−0.806780	−	0.590853i	$-0.798791\pi$
$47$	−1.16557	+	1.23544i	−0.170017	+	0.180207i	0.636763	+	0.771060i	$0.280273\pi$
$48$		0			0
$49$	−14.8914	+	9.79424i	−2.12734	+	1.39918i
$50$	−1.49191	−	1.58133i	−0.210988	−	0.223634i
$51$		0			0
$52$	−1.18651	+	2.75065i	−0.164540	+	0.381446i
$53$	−5.02192	−	8.69822i	−0.689814	−	1.19479i	−0.971898	−	0.235403i	$-0.924359\pi$
$53$	−5.02192	−	8.69822i	−0.689814	−	1.19479i	0.282084	−	0.959390i	$-0.408974\pi$
$54$		0			0
$55$	2.41957	−	4.19082i	0.326255	−	0.565090i
$56$	−7.91899	−	10.6371i	−1.05822	−	1.42144i
$57$		0			0
$58$	1.29962	−	4.34102i	0.170648	−	0.570004i
$59$	0.676232	+	11.6105i	0.0880379	+	1.51155i	0.696262	+	0.717788i	$0.254845\pi$
$59$	0.676232	+	11.6105i	0.0880379	+	1.51155i	−0.608224	+	0.793765i	$0.708118\pi$
$60$		0			0
$61$	7.70658	+	1.82649i	0.986727	+	0.233859i	0.692138	−	0.721766i	$-0.256669\pi$
$61$	7.70658	+	1.82649i	0.986727	+	0.233859i	0.294589	+	0.955624i	$0.404817\pi$
$62$	−3.54755	−	2.97675i	−0.450540	−	0.378048i
$63$		0			0
$64$	2.50983	−	2.10599i	0.313728	−	0.263249i
$65$	−5.40467	+	2.71433i	−0.670367	+	0.336671i
$66$		0			0
$67$	−0.184347	−	0.427364i	−0.0225216	−	0.0522108i	0.906584	−	0.422025i	$-0.138681\pi$
$67$	−0.184347	−	0.427364i	−0.0225216	−	0.0522108i	−0.929106	+	0.369814i	$0.879421\pi$
$68$	3.65144	−	4.90473i	0.442802	−	0.594786i
$69$		0			0
$70$	0.635542	−	10.9118i	0.0759618	−	1.30421i
$71$	11.4588	+	4.17067i	1.35991	+	0.494968i	0.916027	−	0.401116i	$-0.131378\pi$
$71$	11.4588	+	4.17067i	1.35991	+	0.494968i	0.443885	+	0.896084i	$0.353600\pi$
$72$		0			0
$73$	−2.01159	+	0.732160i	−0.235439	+	0.0856928i	−0.457045	−	0.889443i	$-0.651092\pi$
$73$	−2.01159	+	0.732160i	−0.235439	+	0.0856928i	0.221606	+	0.975136i	$0.428870\pi$
$74$	−0.171445	−	0.572667i	−0.0199301	−	0.0665712i
$75$		0			0
$76$	2.62867	+	1.32017i	0.301530	+	0.151434i
$77$	8.42140	−	1.99591i	0.959707	−	0.227455i
$78$		0			0
$79$	−6.96575	+	0.814179i	−0.783708	+	0.0916023i	−0.498530	−	0.866872i	$-0.666127\pi$
$79$	−6.96575	+	0.814179i	−0.783708	+	0.0916023i	−0.285178	+	0.958475i	$0.592053\pi$
$80$	−1.84879			−0.206701
$81$		0			0
$82$	0.0972297			0.0107372
$83$	3.28752	−	0.384257i	0.360853	−	0.0421776i	0.0662650	−	0.997802i	$-0.478892\pi$
$83$	3.28752	−	0.384257i	0.360853	−	0.0421776i	0.294588	+	0.955624i	$0.404818\pi$
$84$		0			0
$85$	12.0123	−	2.84698i	1.30292	−	0.308798i
$86$	1.79198	+	0.899965i	0.193234	+	0.0970457i
$87$		0			0
$88$	1.32602	+	4.42922i	0.141354	+	0.472156i
$89$	−4.72182	+	1.71860i	−0.500512	+	0.182171i	−0.579924	−	0.814670i	$-0.696918\pi$
$89$	−4.72182	+	1.71860i	−0.500512	+	0.182171i	0.0794124	+	0.996842i	$0.474696\pi$
$90$		0			0
$91$	−10.1643	−	3.69952i	−1.06551	−	0.387815i
$92$	−0.0544046	+	0.934091i	−0.00567207	+	0.0973857i
$93$		0			0
$94$	0.798737	−	1.07289i	0.0823835	−	0.110660i
$95$	2.35223	+	5.45309i	0.241334	+	0.559476i
$96$		0			0
$97$	−6.70871	+	3.36924i	−0.681166	+	0.342095i	−0.755509	−	0.655138i	$-0.772610\pi$
$97$	−6.70871	+	3.36924i	−0.681166	+	0.342095i	0.0743428	+	0.997233i	$0.476314\pi$
$98$	10.7523	−	9.02224i	1.08615	−	0.911384i
$99$		0			0
$100$	−2.91808	−	2.44856i	−0.291808	−	0.244856i
$101$	2.19888	+	0.521143i	0.218796	+	0.0518557i	0.338552	−	0.940948i	$-0.390063\pi$
$101$	2.19888	+	0.521143i	0.218796	+	0.0518557i	−0.119755	+	0.992803i	$0.538211\pi$
$102$		0			0
$103$	0.0155730	+	0.267378i	0.00153445	+	0.0263456i	0.998988	−	0.0449670i	$-0.0143183\pi$
$103$	0.0155730	+	0.267378i	0.00153445	+	0.0263456i	−0.997454	+	0.0713126i	$0.977281\pi$
$104$	1.65727	−	5.53566i	0.162508	−	0.542816i
$105$		0			0
$106$	4.72325	+	6.34442i	0.458762	+	0.616225i
$107$	4.97987	−	8.62539i	0.481423	−	0.833848i	−0.518350	−	0.855169i	$-0.673454\pi$
$107$	4.97987	−	8.62539i	0.481423	−	0.833848i	0.999773	+	0.0213201i	$0.00678691\pi$
$108$		0			0
$109$	6.70725	+	11.6173i	0.642438	+	1.11273i	0.984887	+	0.173198i	$0.0554102\pi$
$109$	6.70725	+	11.6173i	0.642438	+	1.11273i	−0.342449	+	0.939536i	$0.611256\pi$
$110$	−1.50939	+	3.49917i	−0.143915	+	0.333632i
$111$		0			0
$112$	−2.26906	−	2.40507i	−0.214406	−	0.227257i
$113$	−0.335122	+	0.220413i	−0.0315257	+	0.0207348i	−0.565174	−	0.824972i	$-0.691191\pi$
$113$	−0.335122	+	0.220413i	−0.0315257	+	0.0207348i	0.533648	+	0.845706i	$0.320821\pi$
$114$		0			0
$115$	−1.29635	+	1.37405i	−0.120885	+	0.128131i
$116$	1.37873	−	7.81916i	0.128012	−	0.725991i
$117$		0			0
$118$	−1.59040	−	9.01960i	−0.146408	−	0.830322i
$119$	18.4467	+	12.1326i	1.69100	+	1.11219i
$120$		0			0
$121$	7.92859	+	0.926719i	0.720781	+	0.0842472i
$122$	−6.19489	−	0.724079i	−0.560859	−	0.0655550i
$123$		0			0
$124$	−6.77943	−	4.45890i	−0.608811	−	0.400421i
$125$	1.08327	+	6.14355i	0.0968909	+	0.549495i
$126$		0			0
$127$	−1.81470	+	10.2917i	−0.161029	+	0.913239i	0.792037	+	0.610474i	$0.209021\pi$
$127$	−1.81470	+	10.2917i	−0.161029	+	0.913239i	−0.953065	+	0.302765i	$0.902090\pi$
$128$	6.25278	−	6.62756i	0.552673	−	0.585799i
$129$		0			0
$130$	3.97926	−	2.61720i	0.349004	−	0.229543i
$131$	−9.23051	−	9.78377i	−0.806473	−	0.854812i	0.185318	−	0.982679i	$-0.440668\pi$
$131$	−9.23051	−	9.78377i	−0.806473	−	0.854812i	−0.991791	+	0.127867i	$0.959187\pi$
$132$		0			0
$133$	−4.20691	+	9.75272i	−0.364786	+	0.845668i
$134$	0.183263	+	0.317421i	0.0158315	+	0.0274210i
$135$		0			0
$136$	−5.89743	+	10.2146i	−0.505700	+	0.875898i
$137$	−8.53855	−	11.4693i	−0.729498	−	0.979886i	−0.999853	−	0.0171251i	$-0.994549\pi$
$137$	−8.53855	−	11.4693i	−0.729498	−	0.979886i	0.270355	−	0.962761i	$-0.412859\pi$
$138$		0			0
$139$	0.0928721	−	0.310214i	0.00787731	−	0.0263120i	−0.953961	−	0.299932i	$-0.903036\pi$
$139$	0.0928721	−	0.310214i	0.00787731	−	0.0263120i	0.961838	+	0.273620i	$0.0882211\pi$
$140$	−1.11358	−	19.1195i	−0.0941149	−	1.61589i
$141$		0			0
$142$	−9.34412	−	2.21460i	−0.784141	−	0.185845i
$143$	2.88891	+	2.42408i	0.241583	+	0.202712i
$144$		0			0
$145$	12.2796	−	10.3038i	1.01976	−	0.855682i
$146$	1.50648	−	0.756585i	0.124677	−	0.0626154i
$147$		0			0
$148$	−0.414860	−	0.961755i	−0.0341013	−	0.0790557i
$149$	−1.83804	+	2.46891i	−0.150578	+	0.202261i	−0.871011	−	0.491263i	$-0.836535\pi$
$149$	−1.83804	+	2.46891i	−0.150578	+	0.202261i	0.720434	+	0.693524i	$0.243943\pi$
$150$		0			0
$151$	−0.728324	+	12.5048i	−0.0592702	+	1.01763i	0.829275	+	0.558841i	$0.188754\pi$
$151$	−0.728324	+	12.5048i	−0.0592702	+	1.01763i	−0.888545	+	0.458789i	$0.848283\pi$
$152$	−5.33190	−	1.94065i	−0.432474	−	0.157408i
$153$		0			0
$154$	−6.40455	+	2.33106i	−0.516093	+	0.187843i
$155$	−4.69848	−	15.6940i	−0.377391	−	1.26057i
$156$		0			0
$157$	5.20202	+	2.61255i	0.415166	+	0.208504i	0.644106	−	0.764936i	$-0.277230\pi$
$157$	5.20202	+	2.61255i	0.415166	+	0.208504i	−0.228940	+	0.973441i	$0.573526\pi$
$158$	5.37401	−	1.27366i	0.427533	−	0.101327i
$159$		0			0
$160$	16.1753	−	1.89062i	1.27877	−	0.149467i
$161$	−3.37853			−0.266265
$162$		0			0
$163$	−6.75084			−0.528767			−0.264383	−	0.964418i	$-0.585168\pi$
$163$	−6.75084			−0.528767			−0.264383	+	0.964418i	$0.585168\pi$
$164$	0.169212	−	0.0197780i	0.0132132	−	0.00154440i
$165$		0			0
$166$	−2.53629	+	0.601113i	−0.196855	+	0.0466554i
$167$	−15.5387	−	7.80382i	−1.20242	−	0.603877i	−0.269165	−	0.963094i	$-0.586748\pi$
$167$	−15.5387	−	7.80382i	−1.20242	−	0.603877i	−0.933254	+	0.359217i	$0.883044\pi$
$168$		0			0
$169$	2.37666	+	7.93861i	0.182820	+	0.610662i
$170$	−9.13549	+	3.32504i	−0.700660	+	0.255019i
$171$		0			0
$172$	3.30170	+	1.20172i	0.251752	+	0.0916303i
$173$	0.799204	−	13.7218i	0.0607624	−	1.04325i	−0.820810	−	0.571201i	$-0.806478\pi$
$173$	0.799204	−	13.7218i	0.0607624	−	1.04325i	0.881573	−	0.472049i	$-0.156485\pi$
$174$		0			0
$175$	8.21366	−	11.0329i	0.620894	−	0.834006i
$176$	0.456603	+	1.05852i	0.0344177	+	0.0797892i
$177$		0			0
$178$	3.53618	−	1.77593i	0.265048	−	0.133112i
$179$	1.66053	−	1.39335i	0.124114	−	0.104144i	−0.578618	−	0.815599i	$-0.696408\pi$
$179$	1.66053	−	1.39335i	0.124114	−	0.104144i	0.702732	+	0.711455i	$0.251963\pi$
$180$		0			0
$181$	−17.7173	−	14.8665i	−1.31691	−	1.10502i	−0.986950	−	0.161028i	$-0.948519\pi$
$181$	−17.7173	−	14.8665i	−1.31691	−	1.10502i	−0.329963	−	0.943994i	$-0.607036\pi$
$182$	8.28853	+	1.96442i	0.614387	+	0.145612i
$183$		0			0
$184$	−0.104943	−	1.80180i	−0.00773651	−	0.132831i
$185$	0.606490	−	2.02582i	0.0445900	−	0.148941i
$186$		0			0
$187$	−4.59678	−	6.17454i	−0.336150	−	0.451527i
$188$	1.17182	−	2.02966i	0.0854640	−	0.148028i
$189$		0			0
$190$	−2.33840	−	4.05023i	−0.169646	−	0.293835i
$191$	−8.66905	+	20.0971i	−0.627271	+	1.45418i	0.247135	+	0.968981i	$0.420511\pi$
$191$	−8.66905	+	20.0971i	−0.627271	+	1.45418i	−0.874406	+	0.485196i	$0.838748\pi$
$192$		0			0
$193$	4.95097	+	5.24773i	0.356379	+	0.377740i	0.880614	−	0.473834i	$-0.157130\pi$
$193$	4.95097	+	5.24773i	0.356379	+	0.377740i	−0.524235	+	0.851573i	$0.675649\pi$
$194$	4.93937	−	3.24867i	0.354626	−	0.233241i
$195$		0			0
$196$	16.8773	−	17.8889i	1.20552	−	1.27778i
$197$	2.84835	−	16.1538i	0.202936	−	1.15091i	−0.697718	−	0.716373i	$-0.745801\pi$
$197$	2.84835	−	16.1538i	0.202936	−	1.15091i	0.900654	−	0.434537i	$-0.143088\pi$
$198$		0			0
$199$	−1.40107	−	7.94587i	−0.0993193	−	0.563268i	−0.993338	−	0.115238i	$-0.963237\pi$
$199$	−1.40107	−	7.94587i	−0.0993193	−	0.563268i	0.894019	−	0.448030i	$-0.147874\pi$
$200$	6.13907	+	4.03773i	0.434098	+	0.285510i
$201$		0			0
$202$	−1.76755	−	0.206598i	−0.124365	−	0.0145362i
$203$	28.4751	+	3.32826i	1.99856	+	0.233598i
$204$		0			0
$205$	0.287367	+	0.189004i	0.0200706	+	0.0132006i
$206$	−0.0366255	−	0.207713i	−0.00255182	−	0.0144721i
$207$		0			0
$208$	0.250189	−	1.41889i	0.0173475	−	0.0983824i
$209$	2.54123	−	2.69355i	0.175781	−	0.186317i
$210$		0			0
$211$	19.9870	−	13.1457i	1.37596	−	0.904984i	0.376194	−	0.926541i	$-0.377233\pi$
$211$	19.9870	−	13.1457i	1.37596	−	0.904984i	0.999768	+	0.0215570i	$0.00686233\pi$
$212$	9.51056	+	10.0806i	0.653188	+	0.692339i
$213$		0			0
$214$	−3.10658	+	7.20186i	−0.212361	+	0.492309i
$215$	3.54684	+	6.14331i	0.241893	+	0.418970i
$216$		0			0
$217$	14.6496	−	25.3739i	0.994481	−	1.72249i
$218$	−6.30834	−	8.47357i	−0.427255	−	0.573903i
$219$		0			0
$220$	−1.91506	+	6.39674i	−0.129113	+	0.431268i
$221$	0.559393	+	9.60440i	0.0376288	+	0.646062i
$222$		0			0
$223$	11.6432	+	2.75949i	0.779688	+	0.184789i	0.601142	−	0.799142i	$-0.294713\pi$
$223$	11.6432	+	2.75949i	0.779688	+	0.184789i	0.178546	+	0.983932i	$0.442861\pi$
$224$	22.3119	+	18.7219i	1.49078	+	1.25091i
$225$		0			0
$226$	0.241974	−	0.203040i	0.0160959	−	0.0135060i
$227$	−22.4417	+	11.2706i	−1.48951	+	0.748058i	−0.992791	−	0.119856i	$-0.961757\pi$
$227$	−22.4417	+	11.2706i	−1.48951	+	0.748058i	−0.496715	+	0.867914i	$0.665461\pi$
$228$		0			0
$229$	−10.2084	−	23.6658i	−0.674592	−	1.56388i	−0.818638	−	0.574310i	$-0.805270\pi$
$229$	−10.2084	−	23.6658i	−0.674592	−	1.56388i	0.144045	−	0.989571i	$-0.453989\pi$
$230$	0.888353	−	1.19327i	0.0585763	−	0.0786816i
$231$		0			0
$232$	−0.890509	+	15.2894i	−0.0584648	+	1.00380i
$233$	−8.58260	−	3.12381i	−0.562265	−	0.204648i	0.0452226	−	0.998977i	$-0.485600\pi$
$233$	−8.58260	−	3.12381i	−0.562265	−	0.204648i	−0.607488	+	0.794329i	$0.707823\pi$
$234$		0			0
$235$	4.44630	−	1.61832i	0.290044	−	0.105568i
$236$	−4.60254	−	15.3736i	−0.299600	−	1.00073i
$237$		0			0
$238$	−15.5377	−	7.80334i	−1.00716	−	0.505816i
$239$	−21.1730	+	5.01810i	−1.36957	+	0.324594i	−0.848624	−	0.528997i	$-0.822568\pi$
$239$	−21.1730	+	5.01810i	−1.36957	+	0.324594i	−0.520944	+	0.853591i	$0.674420\pi$
$240$		0			0
$241$	−13.7710	+	1.60960i	−0.887067	+	0.103683i	−0.547408	−	0.836866i	$-0.684386\pi$
$241$	−13.7710	+	1.60960i	−0.887067	+	0.103683i	−0.339659	+	0.940549i	$0.610311\pi$
$242$	−6.28628			−0.404097
$243$		0			0
$244$	−10.9284			−0.699622
$245$	49.3173	−	5.76436i	3.15076	−	0.368271i
$246$		0			0
$247$	−4.50342	+	1.06733i	−0.286546	+	0.0679125i
$248$	13.9872	+	7.02463i	0.888187	+	0.446064i
$249$		0			0
$250$	−1.40897	−	4.70630i	−0.0891113	−	0.297653i
$251$	−10.0143	+	3.64492i	−0.632099	+	0.230065i	−0.638144	−	0.769917i	$-0.720298\pi$
$251$	−10.0143	+	3.64492i	−0.632099	+	0.230065i	0.00604584	+	0.999982i	$0.498076\pi$
$252$		0			0
$253$	1.10688	+	0.402871i	0.0695888	+	0.0253283i
$254$	0.478517	−	8.21582i	0.0300248	−	0.515506i
$255$		0			0
$256$	−8.19786	+	11.0116i	−0.512366	+	0.688228i
$257$	−0.465607	−	1.07940i	−0.0290438	−	0.0673310i	0.903077	−	0.429479i	$-0.141303\pi$
$257$	−0.465607	−	1.07940i	−0.0290438	−	0.0673310i	−0.932121	+	0.362148i	$0.882044\pi$
$258$		0			0
$259$	3.37973	−	1.69736i	0.210006	−	0.105469i
$260$	6.39284	−	5.36423i	0.396467	−	0.332675i
$261$		0			0
$262$	8.11435	+	6.80875i	0.501306	+	0.420646i
$263$	9.08124	+	2.15229i	0.559973	+	0.132716i	0.500849	−	0.865535i	$-0.333021\pi$
$263$	9.08124	+	2.15229i	0.559973	+	0.132716i	0.0591241	+	0.998251i	$0.481169\pi$
$264$		0			0
$265$	1.62690	+	27.9328i	0.0999396	+	1.71590i
$266$	2.39892	−	8.01296i	0.147087	−	0.491306i
$267$		0			0
$268$	0.383506	+	0.515138i	0.0234264	+	0.0314671i
$269$	−1.25116	+	2.16707i	−0.0762845	+	0.132129i	−0.901644	−	0.432479i	$-0.857639\pi$
$269$	−1.25116	+	2.16707i	−0.0762845	+	0.132129i	0.825360	+	0.564607i	$0.190972\pi$
$270$		0			0
$271$	−2.76243	−	4.78467i	−0.167806	−	0.290648i	0.769842	−	0.638234i	$-0.220335\pi$
$271$	−2.76243	−	4.78467i	−0.167806	−	0.290648i	−0.937648	+	0.347586i	$0.887002\pi$
$272$	−1.16484	+	2.70039i	−0.0706285	+	0.163735i
$273$		0			0
$274$	7.72721	+	8.19037i	0.466818	+	0.494798i
$275$	−4.00658	+	2.63517i	−0.241606	+	0.158907i
$276$		0			0
$277$	−18.3318	+	19.4306i	−1.10145	+	1.16747i	−0.116759	+	0.993160i	$0.537251\pi$
$277$	−18.3318	+	19.4306i	−1.10145	+	1.16747i	−0.984691	+	0.174309i	$0.944231\pi$
$278$	−0.0442815	+	0.251133i	−0.00265583	+	0.0150620i
$279$		0			0
$280$	6.41505	+	36.3816i	0.383373	+	2.17421i
$281$	−26.3020	−	17.2991i	−1.56905	−	1.03198i	−0.973508	−	0.228653i	$-0.926568\pi$
$281$	−26.3020	−	17.2991i	−1.56905	−	1.03198i	−0.595540	−	0.803326i	$-0.703062\pi$
$282$		0			0
$283$	−6.64605	−	0.776812i	−0.395067	−	0.0461767i	−0.0837594	−	0.996486i	$-0.526693\pi$
$283$	−6.64605	−	0.776812i	−0.395067	−	0.0461767i	−0.311307	+	0.950309i	$0.600767\pi$
$284$	−16.7123	−	1.95339i	−0.991694	−	0.115912i
$285$		0			0
$286$	−2.48125	−	1.63195i	−0.146720	−	0.0964990i
$287$	0.106819	+	0.605803i	0.00630535	+	0.0357594i
$288$		0			0
$289$	0.458026	−	2.59759i	0.0269427	−	0.152800i
$290$	−8.66278	+	9.18201i	−0.508696	+	0.539186i
$291$		0			0
$292$	2.46788	−	1.62315i	0.144422	−	0.0949876i
$293$	−2.57603	−	2.73044i	−0.150493	−	0.159514i	0.647741	−	0.761861i	$-0.275714\pi$
$293$	−2.57603	−	2.73044i	−0.150493	−	0.159514i	−0.798234	+	0.602347i	$0.794232\pi$
$294$		0			0
$295$	12.8327	−	29.7495i	0.747147	−	1.73208i
$296$	1.01020	+	1.74972i	0.0587167	+	0.101700i
$297$		0			0
$298$	1.21195	−	2.09916i	0.0702066	−	0.121601i
$299$	−0.879115	−	1.18086i	−0.0508405	−	0.0682907i
$300$		0			0
$301$	−3.63864	+	12.1539i	−0.209728	+	0.700539i
$302$	−0.573556	−	9.84758i	−0.0330044	−	0.566664i
$303$		0			0
$304$	−1.37663	−	0.326268i	−0.0789553	−	0.0187128i
$305$	−16.9018	−	14.1823i	−0.967793	−	0.812075i
$306$		0			0
$307$	−22.9491	+	19.2566i	−1.30977	+	1.09903i	−0.321406	+	0.946942i	$0.604155\pi$
$307$	−22.9491	+	19.2566i	−1.30977	+	1.09903i	−0.988367	+	0.152088i	$0.951400\pi$
$308$	−10.6718	+	5.35960i	−0.608085	+	0.305392i
$309$		0			0
$310$	5.10984	+	11.8459i	0.290219	+	0.672804i
$311$	2.65632	−	3.56805i	0.150626	−	0.202326i	−0.720405	−	0.693553i	$-0.756044\pi$
$311$	2.65632	−	3.56805i	0.150626	−	0.202326i	0.871031	+	0.491228i	$0.163452\pi$
$312$		0			0
$313$	1.81546	−	31.1702i	0.102616	−	1.76184i	−0.418369	−	0.908277i	$-0.637398\pi$
$313$	1.81546	−	31.1702i	0.102616	−	1.76184i	0.520985	−	0.853566i	$-0.325565\pi$
$314$	−4.30775	−	1.56789i	−0.243100	−	0.0884812i
$315$		0			0
$316$	9.09346	−	3.30975i	0.511547	−	0.186188i
$317$	7.98146	+	26.6599i	0.448284	+	1.49737i	0.821815	+	0.569754i	$0.192962\pi$
$317$	7.98146	+	26.6599i	0.448284	+	1.49737i	−0.373531	+	0.927618i	$0.621853\pi$
$318$		0			0
$319$	−8.93218	−	4.48591i	−0.500106	−	0.251163i
$320$	−8.88121	+	2.10489i	−0.496475	+	0.117667i
$321$		0			0
$322$	2.64261	−	0.308876i	0.147267	−	0.0172130i
$323$	9.44699			0.525644
$324$		0			0
$325$	5.99343			0.332456
$326$	5.28035	−	0.617185i	0.292452	−	0.0341827i
$327$		0			0
$328$	−0.319763	+	0.0757852i	−0.0176560	+	0.00418454i
$329$	7.56231	+	3.79794i	0.416924	+	0.209387i
$330$		0			0
$331$	−0.0565245	−	0.188805i	−0.00310687	−	0.0103777i	0.956422	−	0.291988i	$-0.0943167\pi$
$331$	−0.0565245	−	0.188805i	−0.00310687	−	0.0103777i	−0.959529	+	0.281610i	$0.909132\pi$
$332$	−4.29171	+	1.56206i	−0.235538	+	0.0857289i
$333$		0			0
$334$	12.8674	+	4.68336i	0.704075	+	0.256262i
$335$	−0.0753900	+	1.29440i	−0.00411900	+	0.0707204i
$336$		0			0
$337$	−10.6919	+	14.3617i	−0.582424	+	0.782331i	−0.991491	−	0.130173i	$-0.958447\pi$
$337$	−10.6919	+	14.3617i	−0.582424	+	0.782331i	0.409068	+	0.912504i	$0.365854\pi$
$338$	−2.58474	−	5.99211i	−0.140592	−	0.325928i
$339$		0			0
$340$	−15.2224	+	7.64497i	−0.825550	+	0.414607i
$341$	−7.82522	+	6.56614i	−0.423759	+	0.355576i
$342$		0			0
$343$	41.3103	+	34.6635i	2.23055	+	1.87165i
$344$	−6.59482	−	1.56300i	−0.355569	−	0.0842714i
$345$		0			0
$346$	0.629374	+	10.8059i	0.0338354	+	0.580931i
$347$	−6.46215	+	21.5851i	−0.346906	+	1.15875i	0.589482	+	0.807782i	$0.299332\pi$
$347$	−6.46215	+	21.5851i	−0.346906	+	1.15875i	−0.936388	+	0.350966i	$0.885853\pi$
$348$		0			0
$349$	−7.07995	−	9.51003i	−0.378981	−	0.509060i	0.571178	−	0.820826i	$-0.306487\pi$
$349$	−7.07995	−	9.51003i	−0.378981	−	0.509060i	−0.950159	+	0.311766i	$0.899079\pi$
$350$	−5.41587	+	9.38056i	−0.289490	+	0.501412i
$351$		0			0
$352$	−5.07737	−	8.79426i	−0.270625	−	0.468736i
$353$	−7.44792	+	17.2662i	−0.396413	+	0.918989i	0.596769	+	0.802413i	$0.296451\pi$
$353$	−7.44792	+	17.2662i	−0.396413	+	0.918989i	−0.993182	+	0.116575i	$0.962808\pi$
$354$		0			0
$355$	−23.3121	−	24.7094i	−1.23728	−	1.31144i
$356$	5.79286	−	3.81002i	0.307021	−	0.201931i
$357$		0			0
$358$	−1.17144	+	1.24166i	−0.0619126	+	0.0656236i
$359$	−1.61227	+	9.14366i	−0.0850926	+	0.482584i	0.912244	+	0.409647i	$0.134348\pi$
$359$	−1.61227	+	9.14366i	−0.0850926	+	0.482584i	−0.997337	+	0.0729368i	$0.976763\pi$
$360$		0			0
$361$	−2.51015	−	14.2358i	−0.132113	−	0.749251i
$362$	15.2172	+	10.0085i	0.799797	+	0.526034i
$363$		0			0
$364$	14.8244	+	1.73272i	0.777008	+	0.0908192i
$365$	5.92321	+	0.692324i	0.310035	+	0.0362379i
$366$		0			0
$367$	24.4128	+	16.0566i	1.27434	+	0.838145i	0.992610	−	0.121349i	$-0.0387221\pi$
$367$	24.4128	+	16.0566i	1.27434	+	0.838145i	0.281728	+	0.959494i	$0.409092\pi$
$368$	−0.0781452	−	0.443183i	−0.00407360	−	0.0231025i
$369$		0			0
$370$	−0.289175	+	1.63999i	−0.0150335	+	0.0852593i
$371$	−34.3407	+	36.3990i	−1.78288	+	1.88974i
$372$		0			0
$373$	−4.64920	+	3.05782i	−0.240726	+	0.158328i	−0.664140	−	0.747608i	$-0.731202\pi$
$373$	−4.64920	+	3.05782i	−0.240726	+	0.158328i	0.423414	+	0.905936i	$0.360832\pi$
$374$	4.15999	+	4.40933i	0.215108	+	0.228001i
$375$		0			0
$376$	−1.79058	+	4.15103i	−0.0923420	+	0.214073i
$377$	6.24612	+	10.8186i	0.321692	+	0.557186i
$378$		0			0
$379$	−14.7919	+	25.6203i	−0.759808	+	1.31603i	0.183140	+	0.983087i	$0.441374\pi$
$379$	−14.7919	+	25.6203i	−0.759808	+	1.31603i	−0.942948	+	0.332940i	$0.891959\pi$
$380$	−4.89347	−	6.57307i	−0.251030	−	0.337191i
$381$		0			0
$382$	4.94338	−	16.5120i	0.252925	−	0.844830i
$383$	0.720228	+	12.3658i	0.0368019	+	0.631865i	0.965399	+	0.260776i	$0.0839784\pi$
$383$	0.720228	+	12.3658i	0.0368019	+	0.631865i	−0.928597	+	0.371089i	$0.878985\pi$
$384$		0			0
$385$	−23.4603	−	5.56020i	−1.19565	−	0.283374i
$386$	−4.35230	−	3.65201i	−0.221526	−	0.185883i
$387$		0			0
$388$	7.93530	−	6.65850i	0.402854	−	0.338034i
$389$	16.6026	−	8.33812i	0.841784	−	0.422760i	0.0249887	−	0.999688i	$-0.492045\pi$
$389$	16.6026	−	8.33812i	0.841784	−	0.422760i	0.816795	+	0.576928i	$0.195749\pi$
$390$		0			0
$391$	1.19021	+	2.75921i	0.0601914	+	0.139539i
$392$	−28.3291	+	38.0526i	−1.43084	+	1.92195i
$393$		0			0
$394$	−0.751078	+	12.8955i	−0.0378388	+	0.649667i
$395$	18.3590	+	6.68214i	0.923743	+	0.336215i
$396$		0			0
$397$	9.59694	−	3.49300i	0.481657	−	0.175309i	−0.0897688	−	0.995963i	$-0.528613\pi$
$397$	9.59694	−	3.49300i	0.481657	−	0.175309i	0.571426	+	0.820654i	$0.306391\pi$
$398$	1.82232	+	6.08698i	0.0913448	+	0.305113i
$399$		0			0
$400$	1.63723	+	0.822249i	0.0818617	+	0.0411125i
$401$	1.96445	−	0.465583i	0.0980998	−	0.0232501i	−0.181273	−	0.983433i	$-0.558022\pi$
$401$	1.96445	−	0.465583i	0.0980998	−	0.0232501i	0.279373	+	0.960183i	$0.409874\pi$
$402$		0			0
$403$	12.6806	−	1.48214i	0.631663	−	0.0738308i
$404$	−3.11815			−0.155134
$405$		0			0
$406$	−22.5768			−1.12047
$407$	−1.30967	+	0.153079i	−0.0649180	+	0.00758783i
$408$		0			0
$409$	−0.846252	+	0.200565i	−0.0418445	+	0.00991732i	−0.251485	−	0.967861i	$-0.580919\pi$
$409$	−0.846252	+	0.200565i	−0.0418445	+	0.00991732i	0.209640	+	0.977779i	$0.432771\pi$
$410$	−0.242051	−	0.121563i	−0.0119541	−	0.00600356i
$411$		0			0
$412$	−0.105992	−	0.354039i	−0.00522187	−	0.0174423i
$413$	54.4506	−	19.8184i	2.67934	−	0.975200i
$414$		0			0
$415$	−8.66465	−	3.15367i	−0.425331	−	0.154808i
$416$	−0.737942	+	12.6700i	−0.0361806	+	0.621196i
$417$		0			0
$418$	−1.74144	+	2.33916i	−0.0851766	+	0.114412i
$419$	−9.99881	−	23.1799i	−0.488474	−	1.13241i	−0.967101	−	0.254392i	$-0.918125\pi$
$419$	−9.99881	−	23.1799i	−0.488474	−	1.13241i	0.478627	−	0.878018i	$-0.341135\pi$
$420$		0			0
$421$	14.9708	−	7.51861i	0.729631	−	0.366435i	−0.0448820	−	0.998992i	$-0.514291\pi$
$421$	14.9708	−	7.51861i	0.729631	−	0.366435i	0.774513	+	0.632558i	$0.217995\pi$
$422$	−14.4315	+	12.1095i	−0.702516	+	0.589481i
$423$		0			0
$424$	−20.4787	−	17.1836i	−0.994532	−	0.834511i
$425$	−11.9040	−	2.82130i	−0.577428	−	0.136853i
$426$		0			0
$427$	−2.29442	−	39.3936i	−0.111035	−	1.90639i
$428$	−3.94150	+	13.1655i	−0.190520	+	0.636380i
$429$		0			0
$430$	−3.33590	−	4.48089i	−0.160871	−	0.216088i
$431$	−13.1811	+	22.8303i	−0.634911	+	1.09970i	0.351623	+	0.936142i	$0.385630\pi$
$431$	−13.1811	+	22.8303i	−0.634911	+	1.09970i	−0.986534	+	0.163556i	$0.947703\pi$
$432$		0			0
$433$	6.29345	+	10.9006i	0.302444	+	0.523848i	0.976689	−	0.214660i	$-0.0688642\pi$
$433$	6.29345	+	10.9006i	0.302444	+	0.523848i	−0.674245	+	0.738508i	$0.735531\pi$
$434$	−9.13882	+	21.1862i	−0.438678	+	1.01697i
$435$		0			0
$436$	−12.7022	−	13.4636i	−0.608327	−	0.644789i
$437$	−1.20777	+	0.794362i	−0.0577754	+	0.0379995i
$438$		0			0
$439$	−6.03805	+	6.39996i	−0.288181	+	0.305454i	−0.855249	−	0.518217i	$-0.826596\pi$
$439$	−6.03805	+	6.39996i	−0.288181	+	0.305454i	0.567069	+	0.823671i	$0.308077\pi$
$440$	2.23659	−	12.6843i	0.106625	−	0.604702i
$441$		0			0
$442$	−1.31561	−	7.46120i	−0.0625772	−	0.354893i
$443$	12.7182	+	8.36487i	0.604258	+	0.397427i	0.814450	−	0.580233i	$-0.197039\pi$
$443$	12.7182	+	8.36487i	0.604258	+	0.397427i	−0.210192	+	0.977660i	$0.567409\pi$
$444$		0			0
$445$	13.9036	+	1.62510i	0.659093	+	0.0770369i
$446$	−9.35933	−	1.09395i	−0.443177	−	0.0518000i
$447$		0			0
$448$	−13.6384	−	8.97010i	−0.644352	−	0.423797i
$449$	−0.214786	−	1.21811i	−0.0101364	−	0.0574862i	0.979320	−	0.202317i	$-0.0648472\pi$
$449$	−0.214786	−	1.21811i	−0.0101364	−	0.0574862i	−0.989456	+	0.144831i	$0.953736\pi$
$450$		0			0
$451$	0.0372423	−	0.211212i	0.00175367	−	0.00994557i
$452$	0.379813	−	0.402578i	0.0178649	−	0.0189357i
$453$		0			0
$454$	16.5230	−	10.8673i	0.775460	−	0.510028i
$455$	20.6785	+	21.9180i	0.969425	+	1.02753i
$456$		0			0
$457$	12.2727	−	28.4513i	0.574092	−	1.33089i	−0.345648	−	0.938364i	$-0.612341\pi$
$457$	12.2727	−	28.4513i	0.574092	−	1.33089i	0.919739	−	0.392530i	$-0.128400\pi$
$458$	10.1484	+	17.5776i	0.474204	+	0.821345i
$459$		0			0
$460$	1.30330	−	2.25738i	0.0607666	−	0.105251i
$461$	−10.1168	−	13.5892i	−0.471185	−	0.632912i	0.501467	−	0.865177i	$-0.332794\pi$
$461$	−10.1168	−	13.5892i	−0.471185	−	0.632912i	−0.972653	+	0.232265i	$0.925386\pi$
$462$		0			0
$463$	−10.2352	+	34.1880i	−0.475671	+	1.58885i	0.297543	+	0.954708i	$0.403833\pi$
$463$	−10.2352	+	34.1880i	−0.475671	+	1.58885i	−0.773215	+	0.634144i	$0.781353\pi$
$464$	0.222038	+	3.81225i	0.0103079	+	0.176979i
$465$		0			0
$466$	6.99870	+	1.65872i	0.324208	+	0.0768388i
$467$	−32.1894	−	27.0101i	−1.48955	−	1.24988i	−0.895195	−	0.445675i	$-0.852964\pi$
$467$	−32.1894	−	27.0101i	−1.48955	−	1.24988i	−0.594353	−	0.804204i	$-0.702592\pi$
$468$		0			0
$469$	−1.77640	+	1.49057i	−0.0820263	+	0.0688282i
$470$	−3.32984	+	1.67231i	−0.153594	+	0.0771378i
$471$		0			0
$472$	12.2607	+	28.4235i	0.564344	+	1.30830i
$473$	2.64138	−	3.54799i	0.121451	−	0.163137i
$474$		0			0
$475$	0.342195	−	5.87527i	0.0157010	−	0.269576i
$476$	−28.6281	−	10.4198i	−1.31217	−	0.477590i
$477$		0			0
$478$	16.1023	−	5.86074i	0.736500	−	0.268064i
$479$	−10.3510	−	34.5748i	−0.472950	−	1.57976i	−0.778537	−	0.627598i	$-0.784038\pi$
$479$	−10.3510	−	34.5748i	−0.472950	−	1.57976i	0.305588	−	0.952164i	$-0.401147\pi$
$480$		0			0
$481$	1.47269	+	0.739610i	0.0671487	+	0.0337233i
$482$	10.6242	−	2.51798i	0.483918	−	0.114691i
$483$		0			0
$484$	−10.9402	+	1.27873i	−0.497282	+	0.0581239i
$485$	20.9136			0.949639
$486$		0			0
$487$	27.8890			1.26377			0.631885	−	0.775062i	$-0.282282\pi$
$487$	27.8890			1.26377			0.631885	+	0.775062i	$0.282282\pi$
$488$	20.9378	−	2.44727i	0.947807	−	0.110783i
$489$		0			0
$490$	−38.0478	+	9.01749i	−1.71882	+	0.407369i
$491$	19.4382	+	9.76222i	0.877233	+	0.440563i	0.829637	−	0.558304i	$-0.188548\pi$
$491$	19.4382	+	9.76222i	0.877233	+	0.440563i	0.0475961	+	0.998867i	$0.484844\pi$
$492$		0			0
$493$	−7.31322	−	24.4278i	−0.329371	−	1.10017i
$494$	3.42489	−	1.24656i	0.154093	−	0.0560853i
$495$		0			0
$496$	3.66730	+	1.33479i	0.164667	+	0.0599338i
$497$	3.53263	−	60.6529i	0.158460	−	2.72065i
$498$		0			0
$499$	−1.78214	+	2.39383i	−0.0797794	+	0.107162i	−0.840221	−	0.542244i	$-0.817575\pi$
$499$	−1.78214	+	2.39383i	−0.0797794	+	0.107162i	0.760442	+	0.649406i	$0.224982\pi$
$500$	−3.40941	−	7.90391i	−0.152474	−	0.353473i
$501$		0			0
$502$	7.49974	−	3.76651i	0.334730	−	0.168108i
$503$	−30.5223	+	25.6113i	−1.36092	+	1.14195i	−0.385227	+	0.922822i	$0.625877\pi$
$503$	−30.5223	+	25.6113i	−1.36092	+	1.14195i	−0.975696	+	0.219128i	$0.929679\pi$
$504$		0			0
$505$	−4.82249	−	4.04655i	−0.214598	−	0.180069i
$506$	−0.902606	−	0.213922i	−0.0401257	−	0.00950997i
$507$		0			0
$508$	−0.838446	−	14.3956i	−0.0372000	−	0.638700i
$509$	5.71537	−	19.0907i	0.253329	−	0.846178i	−0.732835	−	0.680406i	$-0.761803\pi$
$509$	5.71537	−	19.0907i	0.253329	−	0.846178i	0.986164	−	0.165772i	$-0.0530115\pi$
$510$		0			0
$511$	6.36908	+	8.55515i	0.281751	+	0.378458i
$512$	−3.70618	+	6.41930i	−0.163792	+	0.283695i
$513$		0			0
$514$	0.462869	+	0.801713i	0.0204163	+	0.0353620i
$515$	0.295525	−	0.685103i	0.0130224	−	0.0301893i
$516$		0			0
$517$	−2.02469	−	2.14605i	−0.0890459	−	0.0943831i
$518$	−2.48836	+	1.63662i	−0.109332	+	0.0719091i
$519$		0			0
$520$	−11.0468	+	11.7089i	−0.484433	+	0.513469i
$521$	−6.17183	+	35.0022i	−0.270393	+	1.53347i	0.482833	+	0.875713i	$0.339608\pi$
$521$	−6.17183	+	35.0022i	−0.270393	+	1.53347i	−0.753226	+	0.657762i	$0.771503\pi$
$522$		0			0
$523$	4.17875	+	23.6989i	0.182724	+	1.03628i	0.928845	+	0.370469i	$0.120803\pi$
$523$	4.17875	+	23.6989i	0.182724	+	1.03628i	−0.746121	+	0.665810i	$0.768086\pi$
$524$	15.5067	+	10.1989i	0.677411	+	0.445540i
$525$		0			0
$526$	−7.29990	−	0.853236i	−0.318291	−	0.0372029i
$527$	−25.8835	−	3.02534i	−1.12750	−	0.131786i
$528$		0			0
$529$	18.8320	+	12.3860i	0.818784	+	0.538523i
$530$	−3.82623	−	21.6996i	−0.166201	−	0.942571i
$531$		0			0
$532$	2.54496	−	14.4332i	0.110338	−	0.625757i
$533$	−0.183944	+	0.194969i	−0.00796750	+	0.00844505i
$534$		0			0
$535$	−23.1813	+	15.2466i	−1.00222	+	0.659168i
$536$	−0.850115	−	0.901069i	−0.0367194	−	0.0389203i
$537$		0			0
$538$	0.780507	−	1.80942i	0.0336500	−	0.0780095i
$539$	−15.4805	−	26.8130i	−0.666792	−	1.15492i
$540$		0			0
$541$	5.32644	−	9.22567i	0.229002	−	0.396642i	−0.728511	−	0.685034i	$-0.759787\pi$
$541$	5.32644	−	9.22567i	0.229002	−	0.396642i	0.957512	+	0.288392i	$0.0931206\pi$
$542$	2.59814	+	3.48991i	0.111600	+	0.149904i
$543$		0			0
$544$	7.42983	−	24.8174i	0.318551	−	1.06404i
$545$	−2.17288	−	37.3068i	−0.0930758	−	1.59805i
$546$		0			0
$547$	13.2337	+	3.13643i	0.565830	+	0.134104i	0.503568	−	0.863956i	$-0.332020\pi$
$547$	13.2337	+	3.13643i	0.565830	+	0.134104i	0.0622623	+	0.998060i	$0.480168\pi$
$548$	15.1139	+	12.6821i	0.645636	+	0.541753i
$549$		0			0
$550$	2.89293	−	2.42746i	0.123355	−	0.103507i
$551$	10.9619	−	5.50529i	0.466994	−	0.234533i
$552$		0			0
$553$	13.8398	+	32.0842i	0.588527	+	1.36436i
$554$	12.5623	−	16.8741i	0.533720	−	0.716911i
$555$		0			0
$556$	−0.0259801	+	0.446062i	−0.00110180	+	0.0189172i
$557$	4.31357	+	1.57001i	0.182772	+	0.0665235i	0.431785	−	0.901977i	$-0.357884\pi$
$557$	4.31357	+	1.57001i	0.182772	+	0.0665235i	−0.249013	+	0.968500i	$0.580106\pi$
$558$		0			0
$559$	−5.19480	+	1.89075i	−0.219717	+	0.0799704i
$560$	2.64182	+	8.82429i	0.111637	+	0.372894i
$561$		0			0
$562$	22.1544	+	11.1263i	0.934526	+	0.469337i
$563$	0.964385	−	0.228563i	0.0406440	−	0.00963280i	−0.210244	−	0.977649i	$-0.567426\pi$
$563$	0.964385	−	0.228563i	0.0406440	−	0.00963280i	0.250888	+	0.968016i	$0.419278\pi$
$564$		0			0
$565$	1.10986	−	0.129723i	0.0466920	−	0.00545751i
$566$	5.26940			0.221489
$567$		0			0
$568$	32.4565			1.36185
$569$	7.71668	−	0.901950i	0.323500	−	0.0378117i	0.0472068	−	0.998885i	$-0.484968\pi$
$569$	7.71668	−	0.901950i	0.323500	−	0.0378117i	0.276293	+	0.961073i	$0.410894\pi$
$570$		0			0
$571$	20.8205	−	4.93455i	0.871312	−	0.206505i	0.229446	−	0.973321i	$-0.426309\pi$
$571$	20.8205	−	4.93455i	0.871312	−	0.206505i	0.641866	+	0.766817i	$0.278161\pi$
$572$	−4.65016	−	2.33540i	−0.194433	−	0.0976479i
$573$		0			0
$574$	−0.138936	−	0.464079i	−0.00579909	−	0.0193703i
$575$	1.75912	−	0.640267i	0.0733604	−	0.0267010i
$576$		0			0
$577$	−8.13925	−	2.96244i	−0.338841	−	0.123328i	0.166995	−	0.985958i	$-0.446594\pi$
$577$	−8.13925	−	2.96244i	−0.338841	−	0.123328i	−0.505836	+	0.862630i	$0.668816\pi$
$578$	−0.120776	+	2.07365i	−0.00502364	+	0.0862525i
$579$		0			0
$580$	−13.2083	+	17.7419i	−0.548446	+	0.736691i
$581$	−6.53177	−	15.1423i	−0.270983	−	0.628210i
$582$		0			0
$583$	15.5911	−	7.83016i	0.645719	−	0.324292i
$584$	−4.36471	+	3.66243i	−0.180613	+	0.151552i
$585$		0			0
$586$	2.26454	+	1.90017i	0.0935472	+	0.0784954i
$587$	10.2303	+	2.42462i	0.422249	+	0.100075i	0.436247	−	0.899827i	$-0.356307\pi$
$587$	10.2303	+	2.42462i	0.422249	+	0.100075i	−0.0139973	+	0.999902i	$0.504456\pi$
$588$		0			0
$589$	−0.728926	−	12.5152i	−0.0300349	−	0.515679i
$590$	−7.31762	+	24.4425i	−0.301261	+	1.00628i
$591$		0			0
$592$	0.300827	+	0.404081i	0.0123639	+	0.0166076i
$593$	14.0175	−	24.2790i	0.575630	−	0.997020i	−0.420343	−	0.907365i	$-0.638090\pi$
$593$	14.0175	−	24.2790i	0.575630	−	0.997020i	0.995973	−	0.0896551i	$-0.0285765\pi$
$594$		0			0
$595$	−30.7537	−	53.2669i	−1.26078	−	2.18373i
$596$	1.68220	−	3.89977i	0.0689054	−	0.159741i
$597$		0			0
$598$	0.795581	+	0.843266i	0.0325337	+	0.0344837i
$599$	19.4428	−	12.7878i	0.794413	−	0.522494i	−0.0862293	−	0.996275i	$-0.527482\pi$
$599$	19.4428	−	12.7878i	0.794413	−	0.522494i	0.880642	+	0.473782i	$0.157111\pi$
$600$		0			0
$601$	−14.7481	+	15.6320i	−0.601586	+	0.637644i	−0.954570	−	0.297985i	$-0.903685\pi$
$601$	−14.7481	+	15.6320i	−0.601586	+	0.637644i	0.352984	+	0.935629i	$0.385167\pi$
$602$	1.73491	−	9.83915i	0.0707096	−	0.401014i
$603$		0			0
$604$	−3.00133	−	17.0214i	−0.122122	−	0.692589i
$605$	−18.5794	−	12.2199i	−0.755361	−	0.496809i
$606$		0			0
$607$	−4.81123	−	0.562352i	−0.195282	−	0.0228252i	0.0178897	−	0.999840i	$-0.494305\pi$
$607$	−4.81123	−	0.562352i	−0.195282	−	0.0228252i	−0.213171	+	0.977015i	$0.568379\pi$
$608$	12.3780	+	1.44679i	0.501996	+	0.0586749i
$609$		0			0
$610$	14.5168	+	9.54783i	0.587767	+	0.386580i
$611$	0.640316	+	3.63141i	0.0259044	+	0.146911i
$612$		0			0
$613$	2.42381	−	13.7461i	0.0978969	−	0.555201i	−0.895924	−	0.444207i	$-0.853485\pi$
$613$	2.42381	−	13.7461i	0.0978969	−	0.555201i	0.993821	−	0.110994i	$-0.0354034\pi$
$614$	16.1897	−	17.1601i	0.653364	−	0.692525i
$615$		0			0
$616$	19.2459	−	12.6583i	0.775441	−	0.510016i
$617$	−13.8691	−	14.7004i	−0.558351	−	0.591817i	0.385287	−	0.922797i	$-0.374102\pi$
$617$	−13.8691	−	14.7004i	−0.558351	−	0.591817i	−0.943638	+	0.330980i	$0.892621\pi$
$618$		0			0
$619$	−11.4319	+	26.5020i	−0.459485	+	1.06521i	0.518224	+	0.855245i	$0.326593\pi$
$619$	−11.4319	+	26.5020i	−0.459485	+	1.06521i	−0.977710	+	0.209962i	$0.932666\pi$
$620$	11.3025	+	19.5764i	0.453917	+	0.786208i
$621$		0			0
$622$	−1.75151	+	3.03370i	−0.0702290	+	0.121640i
$623$	14.9502	+	20.0815i	0.598965	+	0.804550i
$624$		0			0
$625$	8.94311	−	29.8721i	0.357725	−	1.19488i
$626$	1.42967	+	24.5466i	0.0571413	+	0.981078i
$627$		0			0
$628$	−7.81583	−	1.85239i	−0.311886	−	0.0739182i
$629$	−2.57685	−	2.16223i	−0.102746	−	0.0862139i
$630$		0			0
$631$	−35.3851	+	29.6916i	−1.40866	+	1.18200i	−0.451558	+	0.892242i	$0.649132\pi$
$631$	−35.3851	+	29.6916i	−1.40866	+	1.18200i	−0.957099	+	0.289762i	$0.906424\pi$
$632$	−16.6809	+	8.37749i	−0.663533	+	0.333239i
$633$		0			0
$634$	−8.68025	−	20.1231i	−0.344737	−	0.799190i
$635$	17.3850	−	23.3521i	0.689902	−	0.926699i
$636$		0			0
$637$	−2.24992	+	38.6297i	−0.0891452	+	1.53056i
$638$	7.39666	+	2.69216i	0.292836	+	0.106584i
$639$		0			0
$640$	−23.8524	+	8.68156i	−0.942848	+	0.343169i
$641$	7.13913	+	23.8464i	0.281979	+	0.941874i	0.975233	+	0.221181i	$0.0709912\pi$
$641$	7.13913	+	23.8464i	0.281979	+	0.941874i	−0.693254	+	0.720693i	$0.743824\pi$
$642$		0			0
$643$	1.97867	+	0.993725i	0.0780311	+	0.0391887i	0.487387	−	0.873186i	$-0.337950\pi$
$643$	1.97867	+	0.993725i	0.0780311	+	0.0391887i	−0.409356	+	0.912375i	$0.634246\pi$
$644$	4.53618	−	1.07509i	0.178750	−	0.0423646i
$645$		0			0
$646$	−7.38921	+	0.863675i	−0.290725	+	0.0339808i
$647$	26.5378			1.04331			0.521654	−	0.853157i	$-0.325315\pi$
$647$	26.5378			1.04331			0.521654	+	0.853157i	$0.325315\pi$
$648$		0			0
$649$	−20.2024			−0.793015
$650$	−4.68792	+	0.547939i	−0.183875	+	0.0214919i
$651$		0			0
$652$	9.06401	−	2.14821i	0.354974	−	0.0841304i
$653$	0.189664	+	0.0952529i	0.00742213	+	0.00372753i	0.452506	−	0.891761i	$-0.350530\pi$
$653$	0.189664	+	0.0952529i	0.00742213	+	0.00372753i	−0.445084	+	0.895489i	$0.646826\pi$
$654$		0			0
$655$	10.7469	+	35.8971i	0.419915	+	1.40261i
$656$	−0.0769964	+	0.0280244i	−0.00300620	+	0.00109417i
$657$		0			0
$658$	−6.26228	−	2.27928i	−0.244129	−	0.0888558i
$659$	1.57427	−	27.0291i	0.0613247	−	1.05290i	−0.817552	−	0.575855i	$-0.804669\pi$
$659$	1.57427	−	27.0291i	0.0613247	−	1.05290i	0.878876	−	0.477050i	$-0.158294\pi$
$660$		0			0
$661$	21.3649	−	28.6980i	0.830998	−	1.11622i	−0.160620	−	0.987016i	$-0.551349\pi$
$661$	21.3649	−	28.6980i	0.830998	−	1.11622i	0.991618	−	0.129207i	$-0.0412432\pi$
$662$	0.0614733	+	0.142511i	0.00238923	+	0.00553885i
$663$		0			0
$664$	7.87267	−	3.95381i	0.305519	−	0.153437i
$665$	22.6665	−	19.0195i	0.878969	−	0.737543i
$666$		0			0
$667$	2.98902	+	2.50808i	0.115735	+	0.0971134i
$668$	23.3463	+	5.53316i	0.903294	+	0.214085i
$669$		0			0
$670$	−0.0593697	−	1.01934i	−0.00229365	−	0.0393805i
$671$	−3.94577	+	13.1798i	−0.152325	+	0.508800i
$672$		0			0
$673$	−17.0503	−	22.9025i	−0.657240	−	0.882827i	0.341123	−	0.940019i	$-0.389193\pi$
$673$	−17.0503	−	22.9025i	−0.657240	−	0.882827i	−0.998363	+	0.0571917i	$0.981785\pi$
$674$	7.04994	−	12.2109i	0.271554	−	0.470345i
$675$		0			0
$676$	−5.71719	−	9.90247i	−0.219892	−	0.380864i
$677$	5.83223	−	13.5206i	0.224151	−	0.519640i	−0.768614	−	0.639712i	$-0.779053\pi$
$677$	5.83223	−	13.5206i	0.224151	−	0.519640i	0.992765	+	0.120073i	$0.0383127\pi$
$678$		0			0
$679$	25.6679	+	27.2063i	0.985042	+	1.04408i
$680$	27.4525	−	18.0558i	1.05276	−	0.692409i
$681$		0			0
$682$	5.52041	−	5.85129i	0.211387	−	0.224057i
$683$	0.764140	−	4.33365i	0.0292390	−	0.165823i	−0.966692	−	0.255943i	$-0.917614\pi$
$683$	0.764140	−	4.33365i	0.0292390	−	0.165823i	0.995931	+	0.0901204i	$0.0287252\pi$
$684$		0			0
$685$	6.91695	+	39.2280i	0.264283	+	1.49882i
$686$	−35.4810	−	23.3362i	−1.35467	−	0.890982i
$687$		0			0
$688$	−1.67847	−	0.196185i	−0.0639910	−	0.00747947i
$689$	−21.6578	−	2.53143i	−0.825096	−	0.0964399i
$690$		0			0
$691$	−2.53025	−	1.66417i	−0.0962553	−	0.0633081i	0.500469	−	0.865755i	$-0.333161\pi$
$691$	−2.53025	−	1.66417i	−0.0962553	−	0.0633081i	−0.596724	+	0.802446i	$0.703531\pi$
$692$	3.29341	+	18.6779i	0.125197	+	0.710026i
$693$		0			0
$694$	3.08116	−	17.4741i	0.116959	−	0.663309i
$695$	−0.619053	+	0.656158i	−0.0234820	+	0.0248895i
$696$		0			0
$697$	0.457123	−	0.300654i	0.0173148	−	0.0113881i
$698$	6.40721	+	6.79125i	0.242516	+	0.257052i
$699$		0			0
$700$	−7.51725	+	17.4269i	−0.284125	+	0.658677i
$701$	−21.6147	−	37.4378i	−0.816377	−	1.41401i	−0.908335	−	0.418243i	$-0.862646\pi$
$701$	−21.6147	−	37.4378i	−0.816377	−	1.41401i	0.0919585	−	0.995763i	$-0.470687\pi$
$702$		0			0
$703$	0.809112	−	1.40142i	0.0305162	−	0.0528557i
$704$	3.39859	+	4.56509i	0.128089	+	0.172053i
$705$		0			0
$706$	4.24706	−	14.1862i	0.159840	−	0.533903i
$707$	−0.654654	−	11.2400i	−0.0246208	−	0.422723i
$708$		0			0
$709$	−31.3091	−	7.42039i	−1.17584	−	0.278679i	−0.404157	−	0.914690i	$-0.632435\pi$
$709$	−31.3091	−	7.42039i	−1.17584	−	0.278679i	−0.771680	+	0.636011i	$0.780583\pi$
$710$	20.4932	+	17.1958i	0.769095	+	0.645347i
$711$		0			0
$712$	−10.2453	+	8.59684i	−0.383959	+	0.322180i
$713$	3.56351	−	1.78966i	0.133454	−	0.0670234i
$714$		0			0
$715$	−4.16114	−	9.64660i	−0.155618	−	0.360762i
$716$	−1.78612	+	2.39918i	−0.0667506	+	0.0896616i
$717$		0			0
$718$	0.425139	−	7.29936i	0.0158661	−	0.272410i
$719$	−9.54600	−	3.47446i	−0.356006	−	0.129576i	0.157825	−	0.987467i	$-0.449552\pi$
$719$	−9.54600	−	3.47446i	−0.356006	−	0.129576i	−0.513831	+	0.857892i	$0.671774\pi$
$720$		0			0
$721$	1.25395	−	0.456400i	0.0466995	−	0.0169972i
$722$	3.26486	+	10.9054i	0.121506	+	0.405857i
$723$		0			0
$724$	28.5188	+	14.3227i	1.05989	+	0.532298i
$725$	−15.4571	+	3.66339i	−0.574061	+	0.136055i
$726$		0			0
$727$	−13.9993	+	1.63629i	−0.519206	+	0.0606865i	−0.371660	−	0.928369i	$-0.621211\pi$
$727$	−13.9993	+	1.63629i	−0.519206	+	0.0606865i	−0.147546	+	0.989055i	$0.547137\pi$
$728$	−28.7900			−1.06703
$729$		0			0
$730$	−4.69629			−0.173818
$731$	11.2078	−	1.31001i	0.414536	−	0.0484523i
$732$		0			0
$733$	−15.2752	+	3.62028i	−0.564201	+	0.133718i	−0.502812	−	0.864396i	$-0.667701\pi$
$733$	−15.2752	+	3.62028i	−0.564201	+	0.133718i	−0.0613890	+	0.998114i	$0.519553\pi$
$734$	−20.5631	−	10.3272i	−0.758996	−	0.381182i
$735$		0			0
$736$	1.13692	+	3.79757i	0.0419074	+	0.139980i
$737$	0.759727	−	0.276518i	0.0279849	−	0.0101857i
$738$		0			0
$739$	−3.42025	−	1.24487i	−0.125816	−	0.0457933i	0.278345	−	0.960481i	$-0.410214\pi$
$739$	−3.42025	−	1.24487i	−0.125816	−	0.0457933i	−0.404161	+	0.914688i	$0.632436\pi$
$740$	−0.169660	+	2.91295i	−0.00623683	+	0.107082i
$741$		0			0
$742$	23.5328	−	31.6100i	0.863916	−	1.16044i
$743$	9.22126	+	21.3773i	0.338295	+	0.784257i	0.999422	+	0.0339829i	$0.0108192\pi$
$743$	9.22126	+	21.3773i	0.338295	+	0.784257i	−0.661127	+	0.750274i	$0.729922\pi$
$744$		0			0
$745$	7.66255	−	3.84828i	0.280734	−	0.140990i
$746$	3.35694	−	2.81680i	0.122906	−	0.103130i
$747$		0			0
$748$	8.13668	+	6.82748i	0.297506	+	0.249637i
$749$	−48.2852	−	11.4438i	−1.76430	−	0.418147i
$750$		0			0
$751$	−0.459295	−	7.88578i	−0.0167599	−	0.287756i	−0.996266	−	0.0863404i	$-0.972483\pi$
$751$	−0.459295	−	7.88578i	−0.0167599	−	0.287756i	0.979506	−	0.201416i	$-0.0645543\pi$
$752$	−0.323284	+	1.07984i	−0.0117890	+	0.0393778i
$753$		0			0
$754$	−5.87464	−	7.89101i	−0.213942	−	0.287374i
$755$	17.4475	−	30.2200i	0.634980	−	1.09982i
$756$		0			0
$757$	−2.12074	−	3.67323i	−0.0770795	−	0.133506i	0.824909	−	0.565265i	$-0.191226\pi$
$757$	−2.12074	−	3.67323i	−0.0770795	−	0.133506i	−0.901989	+	0.431760i	$0.857893\pi$
$758$	9.22757	−	21.3919i	0.335161	−	0.776990i
$759$		0			0
$760$	10.8473	+	11.4975i	0.393474	+	0.417058i
$761$	−34.1615	+	22.4684i	−1.23835	+	0.814477i	−0.988116	−	0.153707i	$-0.950879\pi$
$761$	−34.1615	+	22.4684i	−1.23835	+	0.814477i	−0.250236	+	0.968185i	$0.580508\pi$
$762$		0			0
$763$	45.8653	−	48.6143i	1.66043	−	1.75996i
$764$	5.24431	−	29.7420i	0.189733	−	1.07603i
$765$		0			0
$766$	−1.69387	−	9.60642i	−0.0612020	−	0.347094i
$767$	21.0953	+	13.8746i	0.761707	+	0.500983i
$768$		0			0
$769$	−32.4744	−	3.79571i	−1.17106	−	0.136877i	−0.491753	−	0.870735i	$-0.663644\pi$
$769$	−32.4744	−	3.79571i	−1.17106	−	0.136877i	−0.679303	+	0.733858i	$0.737718\pi$
$770$	18.8584	+	2.20424i	0.679611	+	0.0794351i
$771$		0			0
$772$	−8.31731	−	5.47038i	−0.299347	−	0.196883i
$773$	−6.74796	−	38.2696i	−0.242707	−	1.37646i	−0.825757	−	0.564025i	$-0.809252\pi$
$773$	−6.74796	−	38.2696i	−0.242707	−	1.37646i	0.583050	−	0.812436i	$-0.301859\pi$
$774$		0			0
$775$	−2.81909	+	15.9878i	−0.101265	+	0.574300i
$776$	−13.7121	+	14.5340i	−0.492236	+	0.521740i
$777$		0			0
$778$	−12.2238	+	8.03975i	−0.438246	+	0.288239i
$779$	0.180623	+	0.191449i	0.00647149	+	0.00685938i
$780$		0			0
$781$	−8.38988	+	19.4499i	−0.300214	+	0.695973i
$782$	−1.18321	−	2.04938i	−0.0423115	−	0.0732856i
$783$		0			0
$784$	−5.91429	+	10.2439i	−0.211225	+	0.365852i
$785$	−9.68394	−	13.0078i	−0.345635	−	0.464268i
$786$		0			0
$787$	−0.654240	+	2.18531i	−0.0233211	+	0.0778980i	−0.968858	−	0.247617i	$-0.920353\pi$
$787$	−0.654240	+	2.18531i	−0.0233211	+	0.0778980i	0.945537	+	0.325515i	$0.105538\pi$
$788$	1.31602	+	22.5952i	0.0468813	+	0.804922i
$789$		0			0
$790$	−14.9709	−	3.54817i	−0.532641	−	0.126238i
$791$	1.53091	+	1.28459i	0.0544329	+	0.0456746i
$792$		0			0
$793$	13.1718	−	11.0524i	0.467743	−	0.392483i
$794$	−7.18716	+	3.60953i	−0.255063	+	0.128097i
$795$		0			0
$796$	4.40963	+	10.2227i	0.156295	+	0.362333i
$797$	20.4260	−	27.4369i	0.723526	−	0.971864i	−0.276416	−	0.961038i	$-0.589147\pi$
$797$	20.4260	−	27.4369i	0.723526	−	0.971864i	0.999941	−	0.0108254i	$-0.00344591\pi$
$798$		0			0
$799$	0.437642	−	7.51403i	0.0154827	−	0.265827i
$800$	−15.1653	−	5.51971i	−0.536174	−	0.195151i
$801$		0			0
$802$	−1.49398	+	0.543764i	−0.0527543	+	0.0192010i
$803$	−1.06649	−	3.56233i	−0.0376356	−	0.125712i
$804$		0			0
$805$	8.41078	+	4.22405i	0.296441	+	0.148878i
$806$	−9.78293	+	2.31860i	−0.344589	+	0.0816691i
$807$		0			0
$808$	5.97406	−	0.698267i	0.210167	−	0.0245649i
$809$	−22.5844			−0.794027			−0.397013	−	0.917813i	$-0.629953\pi$
$809$	−22.5844			−0.794027			−0.397013	+	0.917813i	$0.629953\pi$
$810$		0			0
$811$	15.6809			0.550631			0.275315	−	0.961354i	$-0.411218\pi$
$811$	15.6809			0.550631			0.275315	+	0.961354i	$0.411218\pi$
$812$	−39.2912	+	4.59248i	−1.37885	+	0.161164i
$813$		0			0
$814$	1.01040	−	0.239469i	0.0354145	−	0.00839339i
$815$	16.8061	+	8.44034i	0.588692	+	0.295652i
$816$		0			0
$817$	1.55688	+	5.20034i	0.0544683	+	0.181937i
$818$	0.643582	−	0.234245i	0.0225023	−	0.00819017i
$819$		0			0
$820$	−0.445977	−	0.162322i	−0.0155742	−	0.00566854i
$821$	−2.97242	+	51.0345i	−0.103738	+	1.78112i	0.399269	+	0.916834i	$0.369264\pi$
$821$	−2.97242	+	51.0345i	−0.103738	+	1.78112i	−0.503007	+	0.864282i	$0.667773\pi$
$822$		0			0
$823$	1.96916	−	2.64504i	0.0686407	−	0.0922004i	−0.766477	−	0.642272i	$-0.777992\pi$
$823$	1.96916	−	2.64504i	0.0686407	−	0.0922004i	0.835118	+	0.550071i	$0.185399\pi$
$824$	0.282353	+	0.654567i	0.00983622	+	0.0228029i
$825$		0			0
$826$	−40.7781	+	20.4796i	−1.41885	+	0.712575i
$827$	15.7734	−	13.2354i	0.548494	−	0.460241i	−0.325937	−	0.945392i	$-0.605680\pi$
$827$	15.7734	−	13.2354i	0.548494	−	0.460241i	0.874431	+	0.485151i	$0.161235\pi$
$828$		0			0
$829$	10.1320	+	8.50174i	0.351898	+	0.295278i	0.801552	−	0.597925i	$-0.204008\pi$
$829$	10.1320	+	8.50174i	0.351898	+	0.295278i	−0.449654	+	0.893203i	$0.648453\pi$
$830$	7.06560	+	1.67458i	0.245251	+	0.0581255i
$831$		0			0
$832$	−0.413582	−	7.10093i	−0.0143384	−	0.246180i
$833$	22.6530	−	75.6661i	0.784878	−	2.62168i
$834$		0			0
$835$	28.9264	+	38.8549i	1.00104	+	1.34463i
$836$	−2.55486	+	4.42514i	−0.0883616	+	0.153047i
$837$		0			0
$838$	9.94002	+	17.2166i	0.343372	+	0.594738i
$839$	2.49892	−	5.79314i	0.0862721	−	0.200001i	−0.869618	−	0.493724i	$-0.835635\pi$
$839$	2.49892	−	5.79314i	0.0862721	−	0.200001i	0.955891	+	0.293723i	$0.0948944\pi$
$840$		0			0
$841$	−2.82044	−	2.98950i	−0.0972567	−	0.103086i
$842$	−11.0224	+	7.24956i	−0.379858	+	0.249836i
$843$		0			0
$844$	−22.6524	+	24.0101i	−0.779727	+	0.826462i
$845$	4.00870	−	22.7345i	0.137903	−	0.782089i
$846$		0			0
$847$	−6.90630	−	39.1676i	−0.237303	−	1.34581i
$848$	−5.56900	−	3.66279i	−0.191240	−	0.125781i
$849$		0			0
$850$	9.56895	+	1.11845i	0.328212	+	0.0383625i
$851$	0.511256	+	0.0597573i	0.0175256	+	0.00204845i
$852$		0			0
$853$	−15.1422	−	9.95918i	−0.518459	−	0.340996i	0.263160	−	0.964752i	$-0.415235\pi$
$853$	−15.1422	−	9.95918i	−0.518459	−	0.340996i	−0.781619	+	0.623756i	$0.785606\pi$
$854$	5.39614	+	30.6030i	0.184652	+	1.04721i
$855$		0			0
$856$	4.60327	−	26.1064i	0.157336	−	0.892299i
$857$	23.3373	−	24.7360i	0.797185	−	0.844967i	−0.193505	−	0.981099i	$-0.561986\pi$
$857$	23.3373	−	24.7360i	0.797185	−	0.844967i	0.990691	+	0.136132i	$0.0434671\pi$
$858$		0			0
$859$	−39.7658	+	26.1544i	−1.35679	+	0.892376i	−0.999139	−	0.0414781i	$-0.986793\pi$
$859$	−39.7658	+	26.1544i	−1.35679	+	0.892376i	−0.357653	+	0.933855i	$0.616423\pi$
$860$	−6.71705	−	7.11965i	−0.229049	−	0.242778i
$861$		0			0
$862$	8.22272	−	19.0624i	0.280067	−	0.649268i
$863$	26.7851	+	46.3932i	0.911777	+	1.57924i	0.811553	+	0.584279i	$0.198623\pi$
$863$	26.7851	+	46.3932i	0.911777	+	1.57924i	0.100224	+	0.994965i	$0.468044\pi$
$864$		0			0
$865$	−19.1455	+	33.1610i	−0.650966	+	1.12751i
$866$	−5.91915	−	7.95080i	−0.201141	−	0.270179i
$867$		0			0
$868$	−11.5950	+	38.7299i	−0.393559	+	1.31458i
$869$	−0.708344	−	12.1618i	−0.0240289	−	0.412561i
$870$		0			0
$871$	−0.983211	−	0.233025i	−0.0333148	−	0.00789576i
$872$	27.3512	+	22.9504i	0.926227	+	0.777197i
$873$		0			0
$874$	0.872065	−	0.731749i	0.0294980	−	0.0247518i
$875$	27.7753	−	13.9493i	0.938977	−	0.471572i
$876$		0			0
$877$	−5.69036	−	13.1917i	−0.192150	−	0.445453i	0.794719	−	0.606977i	$-0.207618\pi$
$877$	−5.69036	−	13.1917i	−0.192150	−	0.445453i	−0.986869	+	0.161524i	$0.948359\pi$
$878$	4.13772	−	5.55792i	0.139641	−	0.187571i
$879$		0			0
$880$	0.186731	−	3.20605i	0.00629470	−	0.108076i
$881$	0.647962	+	0.235839i	0.0218304	+	0.00794561i	0.352912	−	0.935656i	$-0.385191\pi$
$881$	0.647962	+	0.235839i	0.0218304	+	0.00794561i	−0.331082	+	0.943602i	$0.607414\pi$
$882$		0			0
$883$	−23.8383	+	8.67642i	−0.802222	+	0.291985i	−0.710407	−	0.703791i	$-0.751489\pi$
$883$	−23.8383	+	8.67642i	−0.802222	+	0.291985i	−0.0918148	+	0.995776i	$0.529267\pi$
$884$	−3.80732	−	12.7173i	−0.128054	−	0.427730i
$885$		0			0
$886$	−10.7126	−	5.38007i	−0.359897	−	0.180747i
$887$	40.5894	−	9.61987i	1.36286	−	0.323004i	0.516806	−	0.856102i	$-0.327121\pi$
$887$	40.5894	−	9.61987i	1.36286	−	0.323004i	0.846053	+	0.533099i	$0.178973\pi$
$888$		0			0
$889$	51.7155	−	6.04468i	1.73448	−	0.202732i
$890$	−11.0236			−0.369513
$891$		0			0
$892$	−16.5109			−0.552824
$893$	3.59638	−	0.420356i	0.120348	−	0.0140667i
$894$		0			0
$895$	−5.87591	+	1.39262i	−0.196410	+	0.0465500i
$896$	−40.5684	−	20.3742i	−1.35530	−	0.680655i
$897$		0			0
$898$	0.279364	+	0.933141i	0.00932250	+	0.0311393i
$899$	−31.7972	+	11.5732i	−1.06050	+	0.385989i
$900$		0			0
$901$	41.8245	+	15.2229i	1.39338	+	0.507147i
$902$	−0.00982039	+	0.168610i	−0.000326983	+	0.00561409i
$903$		0			0
$904$	−0.637530	+	0.856351i	−0.0212039	+	0.0284818i
$905$	25.5197	+	59.1612i	0.848302	+	1.96658i
$906$		0			0
$907$	−35.4778	+	17.8176i	−1.17802	+	0.591624i	−0.926525	−	0.376234i	$-0.877219\pi$
$907$	−35.4778	+	17.8176i	−1.17802	+	0.591624i	−0.251496	+	0.967858i	$0.580923\pi$
$908$	26.5448	−	22.2737i	0.880920	−	0.739180i
$909$		0			0
$910$	−18.1781	−	15.2532i	−0.602598	−	0.505640i
$911$	38.3314	+	9.08471i	1.26998	+	0.300990i	0.809731	−	0.586802i	$-0.199613\pi$
$911$	38.3314	+	9.08471i	1.26998	+	0.300990i	0.460246	+	0.887792i	$0.347761\pi$
$912$		0			0
$913$	0.334307	+	5.73983i	0.0110639	+	0.189961i
$914$	−6.99829	+	23.3759i	−0.231483	+	0.773207i
$915$		0			0
$916$	21.2371	+	28.5264i	0.701694	+	0.942539i
$917$	−33.5082	+	58.0379i	−1.10654	+	1.91658i
$918$		0			0
$919$	7.97650	+	13.8157i	0.263120	+	0.455738i	0.967069	−	0.254513i	$-0.0819150\pi$
$919$	7.97650	+	13.8157i	0.263120	+	0.455738i	−0.703949	+	0.710250i	$0.748582\pi$
$920$	−1.99148	+	4.61676i	−0.0656570	+	0.152210i
$921$		0			0
$922$	9.15548	+	9.70424i	0.301520	+	0.319592i
$923$	22.1185	−	14.5476i	0.728039	−	0.478838i
$924$		0			0
$925$	−1.43808	+	1.52427i	−0.0472836	+	0.0501177i
$926$	4.88017	−	27.6768i	0.160372	−	0.909516i
$927$		0			0
$928$	−5.84117	−	33.1269i	−0.191746	−	1.08744i
$929$	20.9718	+	13.7934i	0.688064	+	0.452547i	0.844792	−	0.535095i	$-0.179724\pi$
$929$	20.9718	+	13.7934i	0.688064	+	0.452547i	−0.156728	+	0.987642i	$0.550095\pi$
$930$		0			0
$931$	37.7396	+	4.41113i	1.23687	+	0.144569i
$932$	12.5175	+	1.46308i	0.410023	+	0.0479248i
$933$		0			0
$934$	27.6471	+	18.1838i	0.904642	+	0.594993i
$935$	3.72378	+	21.1186i	0.121781	+	0.690652i
$936$		0			0
$937$	−6.76540	+	38.3685i	−0.221016	+	1.25344i	0.649140	+	0.760669i	$0.275129\pi$
$937$	−6.76540	+	38.3685i	−0.221016	+	1.25344i	−0.870156	+	0.492776i	$0.835982\pi$
$938$	1.25318	−	1.32829i	0.0409178	−	0.0433704i
$939$		0			0
$940$	−5.45484	+	3.58771i	−0.177917	+	0.117018i
$941$	−22.6965	−	24.0569i	−0.739884	−	0.784231i	0.242690	−	0.970104i	$-0.421970\pi$
$941$	−22.6965	−	24.0569i	−0.739884	−	0.784231i	−0.982574	+	0.185873i	$0.940489\pi$
$942$		0			0
$943$	−0.0331608	+	0.0768755i	−0.00107987	+	0.00250341i
$944$	3.85915	+	6.68424i	0.125605	+	0.217554i
$945$		0			0
$946$	−1.74166	+	3.01664i	−0.0566261	+	0.0980793i
$947$	8.66134	+	11.6342i	0.281456	+	0.378060i	0.920259	−	0.391309i	$-0.127978\pi$
$947$	8.66134	+	11.6342i	0.281456	+	0.378060i	−0.638804	+	0.769370i	$0.720570\pi$
$948$		0			0
$949$	−1.33290	+	4.45221i	−0.0432679	+	0.144525i
$950$	0.269479	+	4.62678i	0.00874306	+	0.150113i
$951$		0			0
$952$	57.1818	+	13.5523i	1.85327	+	0.439234i
$953$	−4.46031	−	3.74265i	−0.144484	−	0.121236i	0.567681	−	0.823249i	$-0.307841\pi$
$953$	−4.46031	−	3.74265i	−0.144484	−	0.121236i	−0.712165	+	0.702012i	$0.752285\pi$
$954$		0			0
$955$	46.7081	−	39.1928i	1.51144	−	1.26825i
$956$	26.8311	−	13.4751i	0.867779	−	0.435815i
$957$		0			0
$958$	11.2573	+	26.0973i	0.363706	+	0.843164i
$959$	−42.5419	+	57.1437i	−1.37375	+	1.84527i
$960$		0			0
$961$	−0.208263	+	3.57574i	−0.00671816	+	0.115346i
$962$	−1.21952	−	0.443868i	−0.0393188	−	0.0143109i
$963$		0			0
$964$	17.9774	−	6.54323i	0.579013	−	0.210743i
$965$	−5.76431	−	19.2541i	−0.185560	−	0.619813i
$966$		0			0
$967$	−40.8302	−	20.5057i	−1.31301	−	0.659418i	−0.352018	−	0.935993i	$-0.614504\pi$
$967$	−40.8302	−	20.5057i	−1.31301	−	0.659418i	−0.960992	+	0.276575i	$0.910801\pi$
$968$	20.6739	−	4.89981i	0.664485	−	0.157486i
$969$		0			0
$970$	−16.3582	+	1.91199i	−0.525229	+	0.0613904i
$971$	1.52462			0.0489275			0.0244638	−	0.999701i	$-0.492212\pi$
$971$	1.52462			0.0489275			0.0244638	+	0.999701i	$0.492212\pi$
$972$		0			0
$973$	−1.61337			−0.0517222
$974$	−21.8141	+	2.54970i	−0.698969	+	0.0816977i
$975$		0			0
$976$	5.11445	−	1.21215i	0.163709	−	0.0387999i
$977$	18.2252	+	9.15302i	0.583075	+	0.292831i	0.715782	−	0.698324i	$-0.246071\pi$
$977$	18.2252	+	9.15302i	0.583075	+	0.292831i	−0.132707	+	0.991155i	$0.542367\pi$
$978$		0			0
$979$	−2.50338	−	8.36186i	−0.0800083	−	0.267246i
$980$	−64.3814	+	23.4329i	−2.05659	+	0.748537i
$981$		0			0
$982$	−16.0966	−	5.85868i	−0.513662	−	0.186958i
$983$	−2.45164	+	42.0930i	−0.0781952	+	1.34256i	0.699822	+	0.714317i	$0.253262\pi$
$983$	−2.45164	+	42.0930i	−0.0781952	+	1.34256i	−0.778018	+	0.628242i	$0.783775\pi$
$984$		0			0
$985$	−27.2874	+	36.6533i	−0.869449	+	1.16787i
$986$	7.95350	+	18.4383i	0.253291	+	0.587195i
$987$		0			0
$988$	5.70686	−	2.86609i	0.181560	−	0.0911826i
$989$	−1.32273	+	1.10990i	−0.0420604	+	0.0352929i
$990$		0			0
$991$	−1.19365	−	1.00159i	−0.0379176	−	0.0318167i	0.623632	−	0.781718i	$-0.285656\pi$
$991$	−1.19365	−	1.00159i	−0.0379176	−	0.0318167i	−0.661550	+	0.749901i	$0.730101\pi$
$992$	−33.4508	−	7.92799i	−1.06206	−	0.251714i
$993$		0			0
$994$	2.78195	+	47.7642i	0.0882381	+	1.51499i
$995$	−6.44650	+	21.5328i	−0.204368	+	0.682636i
$996$		0			0
$997$	−31.2532	−	41.9803i	−0.989799	−	1.32953i	−0.943774	−	0.330590i	$-0.892752\pi$
$997$	−31.2532	−	41.9803i	−0.989799	−	1.32953i	−0.0460247	−	0.998940i	$-0.514655\pi$
$998$	1.17509	−	2.03532i	0.0371970	−	0.0644270i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.298.3		144
3.2	odd	2		729.2.g.a.298.6		144
9.2	odd	6		243.2.g.a.100.3		144
9.4	even	3		729.2.g.c.55.6		144
9.5	odd	6		729.2.g.b.55.3		144
9.7	even	3		81.2.g.a.7.6	✓	144
81.2	odd	54		6561.2.a.d.1.25		72
81.4	even	27	inner	729.2.g.d.433.3		144
81.23	odd	54		729.2.g.b.676.3		144
81.31	even	27		81.2.g.a.58.6	yes	144
81.50	odd	54		243.2.g.a.226.3		144
81.58	even	27		729.2.g.c.676.6		144
81.77	odd	54		729.2.g.a.433.6		144
81.79	even	27		6561.2.a.c.1.48		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.6	✓	144	9.7	even	3
81.2.g.a.58.6	yes	144	81.31	even	27
243.2.g.a.100.3		144	9.2	odd	6
243.2.g.a.226.3		144	81.50	odd	54
729.2.g.a.298.6		144	3.2	odd	2
729.2.g.a.433.6		144	81.77	odd	54
729.2.g.b.55.3		144	9.5	odd	6
729.2.g.b.676.3		144	81.23	odd	54
729.2.g.c.55.6		144	9.4	even	3
729.2.g.c.676.6		144	81.58	even	27
729.2.g.d.298.3		144	1.1	even	1	trivial
729.2.g.d.433.3		144	81.4	even	27	inner
6561.2.a.c.1.48		72	81.79	even	27
6561.2.a.d.1.25		72	81.2	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)

\(f(q)\)	\(=\)	\(q+(-0.782176 + 0.0914233i) q^{2} +(-1.34265 + 0.318213i) q^{4} +(-2.48948 - 1.25026i) q^{5} +(-1.42895 - 4.77302i) q^{7} +(2.50111 - 0.910331i) q^{8} +(2.06152 + 0.750330i) q^{10} +(-0.101002 + 1.73414i) q^{11} +(1.29643 - 1.74141i) q^{13} +(1.55406 + 3.60270i) q^{14} +(0.593056 - 0.297844i) q^{16} +(-3.39468 + 2.84848i) q^{17} +(-1.63306 - 1.37030i) q^{19} +(3.74035 + 0.886478i) q^{20} +(-0.0795392 - 1.36564i) q^{22} +(0.194482 - 0.649615i) q^{23} +(1.64856 + 2.21440i) q^{25} +(-0.854835 + 1.48062i) q^{26} +(3.43741 + 5.95378i) q^{28} +(-2.27909 + 5.28353i) q^{29} +(4.03553 + 4.27741i) q^{31} +(-4.88416 + 3.21236i) q^{32} +(2.39482 - 2.53836i) q^{34} +(-2.41020 + 13.6689i) q^{35} +(0.131814 + 0.747552i) q^{37} +(1.40262 + 0.922517i) q^{38} +(-7.36463 - 0.860801i) q^{40} +(-0.122631 - 0.0143335i) q^{41} +(-2.12747 - 1.39926i) q^{43} +(-0.416216 - 2.36048i) q^{44} +(-0.0927292 + 0.525894i) q^{46} +(-1.16557 + 1.23544i) q^{47} +(-14.8914 + 9.79424i) q^{49} +(-1.49191 - 1.58133i) q^{50} +(-1.18651 + 2.75065i) q^{52} +(-5.02192 - 8.69822i) q^{53} +(2.41957 - 4.19082i) q^{55} +(-7.91899 - 10.6371i) q^{56} +(1.29962 - 4.34102i) q^{58} +(0.676232 + 11.6105i) q^{59} +(7.70658 + 1.82649i) q^{61} +(-3.54755 - 2.97675i) q^{62} +(2.50983 - 2.10599i) q^{64} +(-5.40467 + 2.71433i) q^{65} +(-0.184347 - 0.427364i) q^{67} +(3.65144 - 4.90473i) q^{68} +(0.635542 - 10.9118i) q^{70} +(11.4588 + 4.17067i) q^{71} +(-2.01159 + 0.732160i) q^{73} +(-0.171445 - 0.572667i) q^{74} +(2.62867 + 1.32017i) q^{76} +(8.42140 - 1.99591i) q^{77} +(-6.96575 + 0.814179i) q^{79} -1.84879 q^{80} +0.0972297 q^{82} +(3.28752 - 0.384257i) q^{83} +(12.0123 - 2.84698i) q^{85} +(1.79198 + 0.899965i) q^{86} +(1.32602 + 4.42922i) q^{88} +(-4.72182 + 1.71860i) q^{89} +(-10.1643 - 3.69952i) q^{91} +(-0.0544046 + 0.934091i) q^{92} +(0.798737 - 1.07289i) q^{94} +(2.35223 + 5.45309i) q^{95} +(-6.70871 + 3.36924i) q^{97} +(10.7523 - 9.02224i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) \) 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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