LMFDB - Embedded newform 729.2.g.c.55.1

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			55.1
Character	$\chi$	$=$	729.55
Dual form			729.2.g.c.676.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.964822 + 2.23671i) q^{2} +(-2.69950 - 2.86130i) q^{4} +(-0.171598 - 2.94623i) q^{5} +(2.22815 + 0.528081i) q^{7} +(4.42639 - 1.61107i) q^{8} +(6.75541 + 2.45877i) q^{10} +(-1.97872 - 1.30142i) q^{11} +(-0.609623 - 0.0712547i) q^{13} +(-3.33093 + 4.47422i) q^{14} +(-0.209720 + 3.60075i) q^{16} +(-5.54151 + 4.64988i) q^{17} +(-3.45309 - 2.89749i) q^{19} +(-7.96681 + 8.44433i) q^{20} +(4.82002 - 3.17018i) q^{22} +(-7.28714 + 1.72708i) q^{23} +(-3.68461 + 0.430669i) q^{25} +(0.747554 - 1.29480i) q^{26} +(-4.50389 - 7.80096i) q^{28} +(-1.29693 - 1.74208i) q^{29} +(-0.890466 + 2.97436i) q^{31} +(0.567355 + 0.284936i) q^{32} +(-5.05386 - 16.8811i) q^{34} +(1.17350 - 6.65525i) q^{35} +(0.740274 + 4.19830i) q^{37} +(9.81244 - 4.92800i) q^{38} +(-5.50614 - 12.7647i) q^{40} +(-2.55020 - 5.91203i) q^{41} +(-3.63470 + 1.82541i) q^{43} +(1.61778 + 9.17491i) q^{44} +(3.16781 - 17.9655i) q^{46} +(0.248155 + 0.828895i) q^{47} +(-1.56965 - 0.788307i) q^{49} +(2.59171 - 8.65691i) q^{50} +(1.44180 + 1.93667i) q^{52} +(-1.55323 - 2.69028i) q^{53} +(-3.49475 + 6.05308i) q^{55} +(10.7134 - 1.25222i) q^{56} +(5.14783 - 1.22006i) q^{58} +(-0.512703 + 0.337210i) q^{59} +(3.75166 - 3.97653i) q^{61} +(-5.79364 - 4.86144i) q^{62} +(-6.71074 + 5.63098i) q^{64} +(-0.105322 + 1.80831i) q^{65} +(0.168582 - 0.226445i) q^{67} +(28.2640 + 3.30359i) q^{68} +(13.7536 + 9.04591i) q^{70} +(7.71930 + 2.80960i) q^{71} +(-14.3245 + 5.21369i) q^{73} +(-10.1046 - 2.39484i) q^{74} +(1.03103 + 17.7021i) q^{76} +(-3.72163 - 3.94469i) q^{77} +(2.95265 - 6.84501i) q^{79} +10.6446 q^{80} +15.6840 q^{82} +(-2.16942 + 5.02929i) q^{83} +(14.6505 + 15.5286i) q^{85} +(-0.576083 - 9.89096i) q^{86} +(-10.8553 - 2.57274i) q^{88} +(8.64084 - 3.14501i) q^{89} +(-1.32070 - 0.480697i) q^{91} +(24.6133 + 16.1885i) q^{92} +(-2.09342 - 0.244686i) q^{94} +(-7.94410 + 10.6708i) q^{95} +(0.0995190 - 1.70867i) q^{97} +(3.27764 - 2.75027i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

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 $

$2$	−0.964822	+	2.23671i	−0.682232	+	1.58159i	0.125535	+	0.992089i	$0.459935\pi$
$2$	−0.964822	+	2.23671i	−0.682232	+	1.58159i	−0.807767	+	0.589502i	$0.799324\pi$
$3$		0			0
$3$		0			0
$4$	−2.69950	−	2.86130i	−1.34975	−	1.43065i
$5$	−0.171598	−	2.94623i	−0.0767410	−	1.31759i	−0.788442	−	0.615109i	$-0.789112\pi$
$5$	−0.171598	−	2.94623i	−0.0767410	−	1.31759i	0.711701	−	0.702483i	$-0.247925\pi$
$6$		0			0
$7$	2.22815	+	0.528081i	0.842161	+	0.199596i	0.628985	−	0.777418i	$-0.283471\pi$
$7$	2.22815	+	0.528081i	0.842161	+	0.199596i	0.213177	+	0.977014i	$0.431619\pi$
$8$	4.42639	−	1.61107i	1.56496	−	0.569600i
$9$		0			0
$10$	6.75541	+	2.45877i	2.13625	+	0.777531i
$11$	−1.97872	−	1.30142i	−0.596606	−	0.392394i	0.214987	−	0.976617i	$-0.431029\pi$
$11$	−1.97872	−	1.30142i	−0.596606	−	0.392394i	−0.811593	+	0.584223i	$0.801399\pi$
$12$		0			0
$13$	−0.609623	−	0.0712547i	−0.169079	−	0.0197625i	0.0311321	−	0.999515i	$-0.490089\pi$
$13$	−0.609623	−	0.0712547i	−0.169079	−	0.0197625i	−0.200211	+	0.979753i	$0.564163\pi$
$14$	−3.33093	+	4.47422i	−0.890229	+	1.19578i
$15$		0			0
$16$	−0.209720	+	3.60075i	−0.0524300	+	0.900188i
$17$	−5.54151	+	4.64988i	−1.34401	+	1.12776i	−0.363439	+	0.931618i	$0.618398\pi$
$17$	−5.54151	+	4.64988i	−1.34401	+	1.12776i	−0.980575	+	0.196144i	$0.937158\pi$
$18$		0			0
$19$	−3.45309	−	2.89749i	−0.792193	−	0.664729i	0.154094	−	0.988056i	$-0.450754\pi$
$19$	−3.45309	−	2.89749i	−0.792193	−	0.664729i	−0.946287	+	0.323327i	$0.895199\pi$
$20$	−7.96681	+	8.44433i	−1.78143	+	1.88821i
$21$		0			0
$22$	4.82002	−	3.17018i	1.02763	−	0.675884i
$23$	−7.28714	+	1.72708i	−1.51947	+	0.360122i	−0.903826	−	0.427899i	$-0.859254\pi$
$23$	−7.28714	+	1.72708i	−1.51947	+	0.360122i	−0.615648	+	0.788021i	$0.711106\pi$
$24$		0			0
$25$	−3.68461	+	0.430669i	−0.736922	+	0.0861338i
$26$	0.747554	−	1.29480i	0.146607	−	0.253931i
$27$		0			0
$28$	−4.50389	−	7.80096i	−0.851155	−	1.47424i
$29$	−1.29693	−	1.74208i	−0.240834	−	0.323496i	0.665229	−	0.746640i	$-0.268334\pi$
$29$	−1.29693	−	1.74208i	−0.240834	−	0.323496i	−0.906063	+	0.423143i	$0.860927\pi$
$30$		0			0
$31$	−0.890466	+	2.97436i	−0.159932	+	0.534212i	−0.999965	−	0.00832388i	$-0.997350\pi$
$31$	−0.890466	+	2.97436i	−0.159932	+	0.534212i	0.840033	+	0.542535i	$0.182536\pi$
$32$	0.567355	+	0.284936i	0.100295	+	0.0503701i
$33$		0			0
$34$	−5.05386	−	16.8811i	−0.866729	−	2.89508i
$35$	1.17350	−	6.65525i	0.198358	−	1.12494i
$36$		0			0
$37$	0.740274	+	4.19830i	0.121700	+	0.690197i	0.983213	+	0.182461i	$0.0584063\pi$
$37$	0.740274	+	4.19830i	0.121700	+	0.690197i	−0.861513	+	0.507736i	$0.830483\pi$
$38$	9.81244	−	4.92800i	1.59179	−	0.799426i
$39$		0			0
$40$	−5.50614	−	12.7647i	−0.870598	−	2.01827i
$41$	−2.55020	−	5.91203i	−0.398275	−	0.923305i	−0.992861	−	0.119273i	$-0.961944\pi$
$41$	−2.55020	−	5.91203i	−0.398275	−	0.923305i	0.594587	−	0.804031i	$-0.297316\pi$
$42$		0			0
$43$	−3.63470	+	1.82541i	−0.554286	+	0.278373i	−0.703814	−	0.710385i	$-0.748521\pi$
$43$	−3.63470	+	1.82541i	−0.554286	+	0.278373i	0.149527	+	0.988758i	$0.452225\pi$
$44$	1.61778	+	9.17491i	0.243890	+	1.38317i
$45$		0			0
$46$	3.16781	−	17.9655i	0.467068	−	2.64887i
$47$	0.248155	+	0.828895i	0.0361971	+	0.120907i	0.974179	−	0.225778i	$-0.0724925\pi$
$47$	0.248155	+	0.828895i	0.0361971	+	0.120907i	−0.937982	+	0.346685i	$0.887307\pi$
$48$		0			0
$49$	−1.56965	−	0.788307i	−0.224235	−	0.112615i
$50$	2.59171	−	8.65691i	0.366523	−	1.22427i
$51$		0			0
$52$	1.44180	+	1.93667i	0.199941	+	0.268568i
$53$	−1.55323	−	2.69028i	−0.213353	−	0.369538i	0.739409	−	0.673257i	$-0.235105\pi$
$53$	−1.55323	−	2.69028i	−0.213353	−	0.369538i	−0.952762	+	0.303718i	$0.901772\pi$
$54$		0			0
$55$	−3.49475	+	6.05308i	−0.471231	+	0.816197i
$56$	10.7134	−	1.25222i	1.43164	−	0.167335i
$57$		0			0
$58$	5.14783	−	1.22006i	0.675943	−	0.160202i
$59$	−0.512703	+	0.337210i	−0.0667483	+	0.0439010i	−0.582445	−	0.812870i	$-0.697904\pi$
$59$	−0.512703	+	0.337210i	−0.0667483	+	0.0439010i	0.515696	+	0.856771i	$0.327533\pi$
$60$		0			0
$61$	3.75166	−	3.97653i	0.480351	−	0.509142i	−0.441195	−	0.897411i	$-0.645445\pi$
$61$	3.75166	−	3.97653i	0.480351	−	0.509142i	0.921546	+	0.388269i	$0.126927\pi$
$62$	−5.79364	−	4.86144i	−0.735793	−	0.617404i
$63$		0			0
$64$	−6.71074	+	5.63098i	−0.838842	+	0.703872i
$65$	−0.105322	+	1.80831i	−0.0130636	+	0.224294i
$66$		0			0
$67$	0.168582	−	0.226445i	0.0205956	−	0.0276647i	−0.791706	−	0.610902i	$-0.790807\pi$
$67$	0.168582	−	0.226445i	0.0205956	−	0.0276647i	0.812302	+	0.583237i	$0.198214\pi$
$68$	28.2640	+	3.30359i	3.42752	+	0.400619i
$69$		0			0
$70$	13.7536	+	9.04591i	1.64387	+	1.08119i
$71$	7.71930	+	2.80960i	0.916113	+	0.333438i	0.756691	−	0.653773i	$-0.226815\pi$
$71$	7.71930	+	2.80960i	0.916113	+	0.333438i	0.159422	+	0.987211i	$0.449037\pi$
$72$		0			0
$73$	−14.3245	+	5.21369i	−1.67656	+	0.610216i	−0.992831	−	0.119525i	$-0.961863\pi$
$73$	−14.3245	+	5.21369i	−1.67656	+	0.610216i	−0.683724	+	0.729741i	$0.739641\pi$
$74$	−10.1046	−	2.39484i	−1.17464	−	0.278394i
$75$		0			0
$76$	1.03103	+	17.7021i	0.118267	+	2.03057i
$77$	−3.72163	−	3.94469i	−0.424119	−	0.449539i
$78$		0			0
$79$	2.95265	−	6.84501i	0.332199	−	0.770123i	−0.667476	−	0.744631i	$-0.732625\pi$
$79$	2.95265	−	6.84501i	0.332199	−	0.770123i	0.999675	−	0.0254922i	$-0.00811529\pi$
$80$	10.6446			1.19010
$81$		0			0
$82$	15.6840			1.73201
$83$	−2.16942	+	5.02929i	−0.238125	+	0.552036i	−0.994811	−	0.101743i	$-0.967558\pi$
$83$	−2.16942	+	5.02929i	−0.238125	+	0.552036i	0.756686	+	0.653779i	$0.226817\pi$
$84$		0			0
$85$	14.6505	+	15.5286i	1.58907	+	1.68432i
$86$	−0.576083	−	9.89096i	−0.0621206	−	1.06657i
$87$		0			0
$88$	−10.8553	−	2.57274i	−1.15717	−	0.274255i
$89$	8.64084	−	3.14501i	0.915927	−	0.333370i	0.159310	−	0.987229i	$-0.449073\pi$
$89$	8.64084	−	3.14501i	0.915927	−	0.333370i	0.756617	+	0.653858i	$0.226851\pi$
$90$		0			0
$91$	−1.32070	−	0.480697i	−0.138447	−	0.0503907i
$92$	24.6133	+	16.1885i	2.56612	+	1.68776i
$93$		0			0
$94$	−2.09342	−	0.244686i	−0.215920	−	0.0252374i
$95$	−7.94410	+	10.6708i	−0.815048	+	1.09480i
$96$		0			0
$97$	0.0995190	−	1.70867i	0.0101046	−	0.173490i	−0.989480	−	0.144670i	$-0.953788\pi$
$97$	0.0995190	−	1.70867i	0.0101046	−	0.173490i	0.999585	−	0.0288199i	$-0.00917493\pi$
$98$	3.27764	−	2.75027i	0.331092	−	0.277819i
$99$		0			0
$100$	11.1789	+	9.38019i	1.11789	+	0.938019i
$101$	5.81634	−	6.16496i	0.578747	−	0.613436i	−0.370169	−	0.928964i	$-0.620700\pi$
$101$	5.81634	−	6.16496i	0.578747	−	0.613436i	0.948916	+	0.315528i	$0.102182\pi$
$102$		0			0
$103$	1.51566	−	0.996863i	0.149342	−	0.0982238i	−0.472639	−	0.881256i	$-0.656698\pi$
$103$	1.51566	−	0.996863i	0.149342	−	0.0982238i	0.621981	+	0.783032i	$0.286328\pi$
$104$	−2.81322	+	0.666746i	−0.275859	+	0.0653798i
$105$		0			0
$106$	7.51596	−	0.878490i	0.730015	−	0.0853265i
$107$	2.26668	−	3.92601i	0.219129	−	0.379542i	−0.735413	−	0.677619i	$-0.763012\pi$
$107$	2.26668	−	3.92601i	0.219129	−	0.379542i	0.954542	+	0.298077i	$0.0963452\pi$
$108$		0			0
$109$	−6.62630	−	11.4771i	−0.634684	−	1.09931i	−0.986582	−	0.163267i	$-0.947797\pi$
$109$	−6.62630	−	11.4771i	−0.634684	−	1.09931i	0.351898	−	0.936039i	$-0.385537\pi$
$110$	−10.1672	−	13.6569i	−0.969401	−	1.30213i
$111$		0			0
$112$	−2.36878	+	7.91226i	−0.223828	+	0.747639i
$113$	−3.83584	−	1.92643i	−0.360845	−	0.181223i	0.259134	−	0.965841i	$-0.416563\pi$
$113$	−3.83584	−	1.92643i	−0.360845	−	0.181223i	−0.619979	+	0.784618i	$0.712859\pi$
$114$		0			0
$115$	6.33884	+	21.1732i	0.591100	+	1.97441i
$116$	−1.48355	+	8.41365i	−0.137745	+	0.781188i
$117$		0			0
$118$	−0.259574	−	1.47211i	−0.0238957	−	0.135519i
$119$	−14.8028	+	7.43426i	−1.35697	+	0.681498i
$120$		0			0
$121$	−2.13525	−	4.95007i	−0.194114	−	0.450006i
$122$	5.27465	+	12.2280i	0.477544	+	1.10707i
$123$		0			0
$124$	10.9144	−	5.48140i	0.980139	−	0.492244i
$125$	−0.661249	−	3.75013i	−0.0591439	−	0.335422i
$126$		0			0
$127$	−1.02230	+	5.79777i	−0.0907147	+	0.514469i	0.905262	+	0.424854i	$0.139675\pi$
$127$	−1.02230	+	5.79777i	−0.0907147	+	0.514469i	−0.995977	+	0.0896144i	$0.971437\pi$
$128$	−5.75601	−	19.2264i	−0.508764	−	1.69939i
$129$		0			0
$130$	−3.94305	−	1.98028i	−0.345829	−	0.173682i
$131$	3.74549	−	12.5108i	0.327245	−	1.09307i	−0.623169	−	0.782087i	$-0.714155\pi$
$131$	3.74549	−	12.5108i	0.327245	−	1.09307i	0.950414	−	0.310987i	$-0.100660\pi$
$132$		0			0
$133$	−6.16389	−	8.27954i	−0.534477	−	0.717927i
$134$	0.343840	+	0.595549i	0.0297033	+	0.0514476i
$135$		0			0
$136$	−17.0376	+	29.5099i	−1.46096	+	2.53046i
$137$	−4.49660	+	0.525577i	−0.384170	+	0.0449030i	−0.305986	−	0.952036i	$-0.598986\pi$
$137$	−4.49660	+	0.525577i	−0.384170	+	0.0449030i	−0.0781838	+	0.996939i	$0.524912\pi$
$138$		0			0
$139$	−4.66352	+	1.10527i	−0.395555	+	0.0937482i	−0.423579	−	0.905859i	$-0.639226\pi$
$139$	−4.66352	+	1.10527i	−0.395555	+	0.0937482i	0.0280246	+	0.999607i	$0.491078\pi$
$140$	−22.2105	+	14.6081i	−1.87713	+	1.23461i
$141$		0			0
$142$	−13.7320	+	14.5551i	−1.15236	+	1.22143i
$143$	1.11354	+	0.934372i	0.0931189	+	0.0781361i
$144$		0			0
$145$	−4.91001	+	4.11999i	−0.407754	+	0.342146i
$146$	2.15908	−	37.0700i	0.178687	−	3.06793i
$147$		0			0
$148$	10.0142	−	13.4515i	0.823166	−	1.10570i
$149$	9.74923	+	1.13952i	0.798688	+	0.0933532i	0.505640	−	0.862745i	$-0.331256\pi$
$149$	9.74923	+	1.13952i	0.798688	+	0.0933532i	0.293048	+	0.956098i	$0.405331\pi$
$150$		0			0
$151$	−11.1565	−	7.33774i	−0.907902	−	0.597137i	0.00736985	−	0.999973i	$-0.497654\pi$
$151$	−11.1565	−	7.33774i	−0.907902	−	0.597137i	−0.915272	+	0.402836i	$0.868024\pi$
$152$	−19.9528	−	7.26221i	−1.61838	−	0.589043i
$153$		0			0
$154$	12.4138	−	4.51826i	1.00033	−	0.364092i
$155$	8.91595	+	2.11312i	0.716146	+	0.169730i
$156$		0			0
$157$	0.174383	+	2.99403i	0.0139172	+	0.238950i	0.998092	+	0.0617480i	$0.0196675\pi$
$157$	0.174383	+	2.99403i	0.0139172	+	0.238950i	−0.984175	+	0.177202i	$0.943295\pi$
$158$	12.4615	+	13.2084i	0.991384	+	1.05081i
$159$		0			0
$160$	0.742130	−	1.72045i	0.0586705	−	0.136014i
$161$	−17.1489			−1.35152
$162$		0			0
$163$	17.7302			1.38874			0.694370	−	0.719618i	$-0.255683\pi$
$163$	17.7302			1.38874			0.694370	+	0.719618i	$0.255683\pi$
$164$	−10.0318	+	23.2564i	−0.783355	+	1.81602i
$165$		0			0
$166$	−9.15595	−	9.70474i	−0.710639	−	0.753234i
$167$	1.27868	+	21.9542i	0.0989476	+	1.69886i	0.573958	+	0.818885i	$0.305407\pi$
$167$	1.27868	+	21.9542i	0.0989476	+	1.69886i	−0.475011	+	0.879980i	$0.657556\pi$
$168$		0			0
$169$	−12.2830	−	2.91113i	−0.944848	−	0.223933i
$170$	−48.8682	+	17.7866i	−3.74802	+	1.36417i
$171$		0			0
$172$	15.0349	+	5.47227i	1.14640	+	0.417256i
$173$	−9.04414	−	5.94843i	−0.687614	−	0.452251i	0.157020	−	0.987595i	$-0.449811\pi$
$173$	−9.04414	−	5.94843i	−0.687614	−	0.452251i	−0.844634	+	0.535345i	$0.820182\pi$
$174$		0			0
$175$	−8.43729	−	0.986177i	−0.637799	−	0.0745480i
$176$	5.10108	−	6.85194i	0.384509	−	0.516485i
$177$		0			0
$178$	−1.30240	+	22.3614i	−0.0976193	+	1.67606i
$179$	−6.84973	+	5.74761i	−0.511973	+	0.429596i	−0.861823	−	0.507210i	$-0.830677\pi$
$179$	−6.84973	+	5.74761i	−0.511973	+	0.429596i	0.349850	+	0.936806i	$0.386233\pi$
$180$		0			0
$181$	3.31310	+	2.78002i	0.246261	+	0.206637i	0.757560	−	0.652765i	$-0.226391\pi$
$181$	3.31310	+	2.78002i	0.246261	+	0.206637i	−0.511299	+	0.859403i	$0.670836\pi$
$182$	2.34942	−	2.49024i	0.174151	−	0.184589i
$183$		0			0
$184$	−29.4732	+	19.3849i	−2.17280	+	1.42907i
$185$	12.2421	−	2.90144i	0.900059	−	0.213318i
$186$		0			0
$187$	17.0166	−	1.98895i	1.24437	−	0.145447i
$188$	1.70182	−	2.94765i	0.124118	−	0.214979i
$189$		0			0
$190$	−16.2028	−	28.0640i	−1.17547	−	2.03598i
$191$	12.6673	+	17.0151i	0.916570	+	1.23117i	0.972540	+	0.232735i	$0.0747675\pi$
$191$	12.6673	+	17.0151i	0.916570	+	1.23117i	−0.0559700	+	0.998432i	$0.517825\pi$
$192$		0			0
$193$	5.20688	−	17.3922i	0.374799	−	1.25192i	−0.537804	−	0.843070i	$-0.680746\pi$
$193$	5.20688	−	17.3922i	0.374799	−	1.25192i	0.912603	−	0.408847i	$-0.134069\pi$
$194$	3.72579	+	1.87116i	0.267496	+	0.134342i
$195$		0			0
$196$	1.98168	+	6.61927i	0.141548	+	0.472805i
$197$	1.23957	−	7.02994i	0.0883155	−	0.500862i	−0.908276	−	0.418371i	$-0.862601\pi$
$197$	1.23957	−	7.02994i	0.0883155	−	0.500862i	0.996592	−	0.0824914i	$-0.0262877\pi$
$198$		0			0
$199$	−0.634860	−	3.60047i	−0.0450040	−	0.255231i	0.954002	−	0.299799i	$-0.0969197\pi$
$199$	−0.634860	−	3.60047i	−0.0450040	−	0.255231i	−0.999006	+	0.0445688i	$0.985809\pi$
$200$	−15.6157	+	7.84248i	−1.10419	+	0.554547i
$201$		0			0
$202$	8.17748	+	18.9575i	0.575366	+	1.33385i
$203$	−1.96980	−	4.56650i	−0.138253	−	0.320505i
$204$		0			0
$205$	−16.9806	+	8.52797i	−1.18597	+	0.595619i
$206$	0.767353	+	4.35187i	0.0534640	+	0.303209i
$207$		0			0
$208$	0.384421	−	2.18016i	0.0266548	−	0.151167i
$209$	3.06184	+	10.2272i	0.211792	+	0.707433i
$210$		0			0
$211$	−15.9532	−	8.01201i	−1.09827	−	0.551570i	−0.195066	−	0.980790i	$-0.562492\pi$
$211$	−15.9532	−	8.01201i	−1.09827	−	0.551570i	−0.903200	+	0.429220i	$0.858788\pi$
$212$	−3.50475	+	11.7067i	−0.240707	+	0.804018i
$213$		0			0
$214$	6.59440	+	8.85781i	0.450784	+	0.605508i
$215$	6.00179	+	10.3954i	0.409319	+	0.708961i
$216$		0			0
$217$	−3.55480	+	6.15709i	−0.241315	+	0.417970i
$218$	32.0641	−	3.74775i	2.17165	−	0.253830i
$219$		0			0
$220$	26.7537	−	6.34075i	1.80374	−	0.427493i
$221$	3.70956	−	2.43982i	0.249532	−	0.164120i
$222$		0			0
$223$	9.68032	−	10.2605i	0.648242	−	0.687096i	−0.317008	−	0.948423i	$-0.602678\pi$
$223$	9.68032	−	10.2605i	0.648242	−	0.687096i	0.965251	+	0.261326i	$0.0841598\pi$
$224$	1.11368	+	0.934490i	0.0744110	+	0.0624383i
$225$		0			0
$226$	8.00976	−	6.72099i	0.532801	−	0.447073i
$227$	0.334510	−	5.74332i	0.0222022	−	0.381197i	−0.968843	−	0.247674i	$-0.920334\pi$
$227$	0.334510	−	5.74332i	0.0222022	−	0.381197i	0.991046	−	0.133523i	$-0.0426292\pi$
$228$		0			0
$229$	−14.6753	+	19.7124i	−0.969772	+	1.30263i	−0.0167077	+	0.999860i	$0.505318\pi$
$229$	−14.6753	+	19.7124i	−0.969772	+	1.30263i	−0.953064	+	0.302769i	$0.902089\pi$
$230$	−53.4741	−	6.25023i	−3.52598	−	0.412128i
$231$		0			0
$232$	−8.54733	−	5.62167i	−0.561160	−	0.369081i
$233$	11.9802	+	4.36045i	0.784852	+	0.285663i	0.703194	−	0.710998i	$-0.251756\pi$
$233$	11.9802	+	4.36045i	0.784852	+	0.285663i	0.0816576	+	0.996660i	$0.473979\pi$
$234$		0			0
$235$	2.39953	−	0.873357i	0.156528	−	0.0569715i
$236$	2.34890	+	0.556700i	0.152900	+	0.0362381i
$237$		0			0
$238$	−2.34618	−	40.2824i	−0.152080	−	2.61112i
$239$	−16.7115	−	17.7132i	−1.08098	−	1.14577i	−0.988680	−	0.150038i	$-0.952060\pi$
$239$	−16.7115	−	17.7132i	−1.08098	−	1.14577i	−0.0922975	−	0.995731i	$-0.529421\pi$
$240$		0			0
$241$	−11.5147	+	26.6940i	−0.741725	+	1.71951i	−0.0484641	+	0.998825i	$0.515433\pi$
$241$	−11.5147	+	26.6940i	−0.741725	+	1.71951i	−0.693261	+	0.720687i	$0.743827\pi$
$242$	13.1320			0.844157
$243$		0			0
$244$	−21.5057			−1.37676
$245$	−2.05318	+	4.75981i	−0.131173	+	0.304093i
$246$		0			0
$247$	1.89862	+	2.01242i	0.120807	+	0.128047i
$248$	0.850370	+	14.6003i	0.0539985	+	0.927119i
$249$		0			0
$250$	9.02593	+	2.13918i	0.570850	+	0.135294i
$251$	22.4049	−	8.15471i	1.41418	−	0.514721i	0.481828	−	0.876266i	$-0.339973\pi$
$251$	22.4049	−	8.15471i	1.41418	−	0.514721i	0.932355	+	0.361545i	$0.117751\pi$
$252$		0			0
$253$	16.6669	+	6.06625i	1.04784	+	0.381382i
$254$	−11.9816	−	7.88040i	−0.751791	−	0.494460i
$255$		0			0
$256$	31.1554	+	3.64154i	1.94721	+	0.227596i
$257$	7.24789	−	9.73561i	0.452111	−	0.607291i	−0.516374	−	0.856363i	$-0.672718\pi$
$257$	7.24789	−	9.73561i	0.452111	−	0.607291i	0.968485	+	0.249073i	$0.0801258\pi$
$258$		0			0
$259$	−0.567604	+	9.74538i	−0.0352692	+	0.605548i
$260$	5.45845	−	4.58018i	0.338519	−	0.284051i
$261$		0			0
$262$	24.3693	+	20.4483i	1.50554	+	1.26330i
$263$	−5.49109	+	5.82022i	−0.338595	+	0.358890i	−0.874189	−	0.485586i	$-0.838606\pi$
$263$	−5.49109	+	5.82022i	−0.338595	+	0.358890i	0.535594	+	0.844476i	$0.320088\pi$
$264$		0			0
$265$	−7.65964	+	5.03782i	−0.470528	+	0.309471i
$266$	24.4660	−	5.79854i	1.50011	−	0.355531i
$267$		0			0
$268$	−1.10302	+	0.128924i	−0.0673774	+	0.00787529i
$269$	−11.2578	+	19.4990i	−0.686397	+	1.18887i	0.286598	+	0.958051i	$0.407476\pi$
$269$	−11.2578	+	19.4990i	−0.686397	+	1.18887i	−0.972995	+	0.230824i	$0.925858\pi$
$270$		0			0
$271$	15.1514	+	26.2430i	0.920381	+	1.59415i	0.798826	+	0.601562i	$0.205455\pi$
$271$	15.1514	+	26.2430i	0.920381	+	1.59415i	0.121555	+	0.992585i	$0.461212\pi$
$272$	−15.5809	−	20.9288i	−0.944731	−	1.26899i
$273$		0			0
$274$	3.16285	−	10.5647i	0.191075	−	0.638234i
$275$	7.85129	+	3.94307i	0.473451	+	0.237776i
$276$		0			0
$277$	1.26874	+	4.23789i	0.0762312	+	0.254630i	0.987607	−	0.156944i	$-0.0501643\pi$
$277$	1.26874	+	4.23789i	0.0762312	+	0.254630i	−0.911376	+	0.411574i	$0.864979\pi$
$278$	2.02729	−	11.4973i	0.121589	−	0.689564i
$279$		0			0
$280$	−5.52773	−	31.3493i	−0.330345	−	1.87348i
$281$	5.06519	−	2.54383i	0.302164	−	0.151752i	−0.291257	−	0.956645i	$-0.594073\pi$
$281$	5.06519	−	2.54383i	0.302164	−	0.151752i	0.593421	+	0.804893i	$0.297777\pi$
$282$		0			0
$283$	11.4164	+	26.4661i	0.678632	+	1.57324i	0.812968	+	0.582309i	$0.197851\pi$
$283$	11.4164	+	26.4661i	0.678632	+	1.57324i	−0.134336	+	0.990936i	$0.542890\pi$
$284$	−12.7991	−	29.6718i	−0.759490	−	1.76069i
$285$		0			0
$286$	−3.16428	+	1.58916i	−0.187108	+	0.0939692i
$287$	−2.56020	−	14.5196i	−0.151124	−	0.857065i
$288$		0			0
$289$	6.13495	−	34.7930i	0.360879	−	2.04665i
$290$	−4.47793	−	14.9573i	−0.262953	−	0.878324i
$291$		0			0
$292$	53.5869	+	26.9123i	3.13594	+	1.57493i
$293$	−0.620892	+	2.07392i	−0.0362729	+	0.121160i	−0.974209	−	0.225649i	$-0.927550\pi$
$293$	−0.620892	+	2.07392i	−0.0362729	+	0.121160i	0.937936	+	0.346809i	$0.112735\pi$
$294$		0			0
$295$	1.08148	+	1.45267i	0.0629660	+	0.0845780i
$296$	10.0405	+	17.3907i	0.583593	+	1.01081i
$297$		0			0
$298$	−11.9550	+	20.7067i	−0.692537	+	1.19951i
$299$	4.56548	−	0.533627i	0.264028	−	0.0308605i
$300$		0			0
$301$	−9.06262	+	2.14788i	−0.522361	+	0.123802i
$302$	27.1764	−	17.8742i	1.56383	−	1.02854i
$303$		0			0
$304$	11.1573	−	11.8261i	0.639915	−	0.678271i
$305$	−12.3595	−	10.3709i	−0.707704	−	0.593835i
$306$		0			0
$307$	3.63465	−	3.04984i	0.207441	−	0.174063i	−0.533148	−	0.846022i	$-0.678991\pi$
$307$	3.63465	−	3.04984i	0.207441	−	0.174063i	0.740589	+	0.671959i	$0.234547\pi$
$308$	−1.24043	+	21.2974i	−0.0706801	+	1.21353i
$309$		0			0
$310$	−13.3287	+	17.9036i	−0.757021	+	1.01686i
$311$	−23.4449	−	2.74032i	−1.32944	−	0.155389i	−0.578458	−	0.815713i	$-0.696345\pi$
$311$	−23.4449	−	2.74032i	−1.32944	−	0.155389i	−0.750981	+	0.660323i	$0.770419\pi$
$312$		0			0
$313$	−19.7427	−	12.9850i	−1.11592	−	0.733955i	−0.148955	−	0.988844i	$-0.547591\pi$
$313$	−19.7427	−	12.9850i	−1.11592	−	0.733955i	−0.966970	+	0.254889i	$0.917961\pi$
$314$	−6.86503	−	2.49867i	−0.387416	−	0.141008i
$315$		0			0
$316$	−27.5563	+	10.0297i	−1.55016	+	0.564213i
$317$	33.1557	+	7.85805i	1.86221	+	0.441352i	0.998081	−	0.0619179i	$-0.0197217\pi$
$317$	33.1557	+	7.85805i	1.86221	+	0.441352i	0.864129	+	0.503270i	$0.167870\pi$
$318$		0			0
$319$	0.299076	+	5.13494i	0.0167451	+	0.287502i
$320$	17.7417	+	18.8051i	0.991790	+	1.05124i
$321$		0			0
$322$	16.5456	−	38.3571i	0.922051	−	2.13756i
$323$	32.6083			1.81437
$324$		0			0
$325$	2.27691			0.126300
$326$	−17.1065	+	39.6574i	−0.947443	+	2.19642i
$327$		0			0
$328$	−20.8129	−	22.0604i	−1.14920	−	1.21808i
$329$	0.115202	+	1.97795i	0.00635131	+	0.109048i
$330$		0			0
$331$	25.2281	+	5.97918i	1.38666	+	0.328645i	0.855140	−	0.518398i	$-0.173471\pi$
$331$	25.2281	+	5.97918i	1.38666	+	0.328645i	0.531524	+	0.847043i	$0.321619\pi$
$332$	20.2467	−	7.36919i	1.11118	−	0.404437i
$333$		0			0
$334$	−50.3388	−	18.3218i	−2.75441	−	1.00252i
$335$	−0.696087	−	0.457824i	−0.0380313	−	0.0250136i
$336$		0			0
$337$	−22.0017	−	2.57162i	−1.19851	−	0.140085i	−0.506670	−	0.862140i	$-0.669124\pi$
$337$	−22.0017	−	2.57162i	−1.19851	−	0.140085i	−0.691836	+	0.722055i	$0.743198\pi$
$338$	18.3623	−	24.6648i	0.998776	−	1.34159i
$339$		0			0
$340$	4.88307	−	83.8391i	0.264822	−	4.54681i
$341$	5.63289	−	4.72656i	0.305038	−	0.255957i
$342$		0			0
$343$	−15.3601	−	12.8887i	−0.829369	−	0.695923i
$344$	−13.1477	+	13.9357i	−0.708877	+	0.751365i
$345$		0			0
$346$	22.0309	−	14.4899i	1.18439	−	0.778984i
$347$	1.74506	−	0.413587i	0.0936797	−	0.0222025i	−0.183509	−	0.983018i	$-0.558746\pi$
$347$	1.74506	−	0.413587i	0.0936797	−	0.0222025i	0.277188	+	0.960816i	$0.410597\pi$
$348$		0			0
$349$	−0.174688	+	0.0204181i	−0.00935083	+	0.00109295i	−0.120767	−	0.992681i	$-0.538535\pi$
$349$	−0.174688	+	0.0204181i	−0.00935083	+	0.00109295i	0.111416	+	0.993774i	$0.464461\pi$
$350$	10.3463	−	17.9203i	0.553031	−	0.957878i
$351$		0			0
$352$	−0.751813	−	1.30218i	−0.0400718	−	0.0694064i
$353$	−18.1618	−	24.3956i	−0.966656	−	1.29844i	−0.954404	−	0.298520i	$-0.903507\pi$
$353$	−18.1618	−	24.3956i	−0.966656	−	1.29844i	−0.0122526	−	0.999925i	$-0.503900\pi$
$354$		0			0
$355$	6.95309	−	23.2249i	0.369032	−	1.23265i
$356$	−32.3247	−	16.2341i	−1.71321	−	0.860406i
$357$		0			0
$358$	−6.24695	−	20.8663i	−0.330161	−	1.10282i
$359$	−1.11991	+	6.35130i	−0.0591064	+	0.335209i	−0.999994	−	0.00351034i	$-0.998883\pi$
$359$	−1.11991	+	6.35130i	−0.0591064	+	0.335209i	0.940887	+	0.338719i	$0.109994\pi$
$360$		0			0
$361$	0.229085	+	1.29920i	0.0120571	+	0.0683792i
$362$	−9.41464	+	4.72821i	−0.494823	+	0.248509i
$363$		0			0
$364$	2.18982	+	5.07657i	0.114778	+	0.266085i
$365$	17.8188	+	41.3085i	0.932677	+	2.16219i
$366$		0			0
$367$	16.4470	−	8.26000i	0.858527	−	0.431169i	0.0356343	−	0.999365i	$-0.488655\pi$
$367$	16.4470	−	8.26000i	0.858527	−	0.431169i	0.822893	+	0.568196i	$0.192359\pi$
$368$	−4.69054	−	26.6014i	−0.244512	−	1.38669i
$369$		0			0
$370$	−5.32180	+	30.1814i	−0.276667	+	1.56906i
$371$	−2.04015	−	6.81458i	−0.105919	−	0.353795i
$372$		0			0
$373$	−28.8505	−	14.4893i	−1.49382	−	0.750227i	−0.500517	−	0.865727i	$-0.666857\pi$
$373$	−28.8505	−	14.4893i	−1.49382	−	0.750227i	−0.993307	+	0.115500i	$0.963153\pi$
$374$	−11.9693	+	39.9801i	−0.618915	+	2.06732i
$375$		0			0
$376$	2.43384	+	3.26921i	0.125516	+	0.168597i
$377$	0.666508	+	1.15442i	0.0343269	+	0.0594559i
$378$		0			0
$379$	11.0163	−	19.0808i	0.565870	−	0.980116i	−0.431098	−	0.902305i	$-0.641874\pi$
$379$	11.0163	−	19.0808i	0.565870	−	0.980116i	0.996968	−	0.0778111i	$-0.0247931\pi$
$380$	51.9774	−	6.07529i	2.66639	−	0.311656i
$381$		0			0
$382$	−50.2794	+	11.9164i	−2.57252	+	0.609698i
$383$	11.8857	−	7.81734i	0.607330	−	0.399447i	−0.208263	−	0.978073i	$-0.566781\pi$
$383$	11.8857	−	7.81734i	0.607330	−	0.399447i	0.815593	+	0.578626i	$0.196411\pi$
$384$		0			0
$385$	−10.9833	+	11.6417i	−0.559762	+	0.593313i
$386$	33.8775	+	28.4266i	1.72432	+	1.44688i
$387$		0			0
$388$	−5.15768	+	4.32781i	−0.261842	+	0.219711i
$389$	−0.713209	+	12.2453i	−0.0361612	+	0.620863i	0.930735	+	0.365694i	$0.119168\pi$
$389$	−0.713209	+	12.2453i	−0.0361612	+	0.620863i	−0.966896	+	0.255169i	$0.917869\pi$
$390$		0			0
$391$	32.3511	−	43.4550i	1.63606	−	2.19761i
$392$	−8.21788	−	0.960533i	−0.415066	−	0.0485142i
$393$		0			0
$394$	14.5280	+	9.55519i	0.731908	+	0.481383i
$395$	−20.6736	−	7.52457i	−1.04020	−	0.378602i
$396$		0			0
$397$	−9.12859	+	3.32254i	−0.458151	+	0.166753i	−0.560777	−	0.827967i	$-0.689498\pi$
$397$	−9.12859	+	3.32254i	−0.458151	+	0.166753i	0.102626	+	0.994720i	$0.467275\pi$
$398$	8.66573	+	2.05382i	0.434374	+	0.102948i
$399$		0			0
$400$	−0.777996	−	13.3577i	−0.0388998	−	0.667884i
$401$	−0.802397	−	0.850491i	−0.0400698	−	0.0424715i	0.707029	−	0.707185i	$-0.250035\pi$
$401$	−0.802397	−	0.850491i	−0.0400698	−	0.0424715i	−0.747098	+	0.664713i	$0.768554\pi$
$402$		0			0
$403$	0.754786	−	1.74979i	0.0375986	−	0.0871633i
$404$	−33.3410			−1.65878
$405$		0			0
$406$	12.1144			0.601229
$407$	3.99898	−	9.27068i	0.198222	−	0.459530i
$408$		0			0
$409$	18.8448	+	19.9743i	0.931816	+	0.987668i	0.999950	−	0.0100086i	$-0.00318588\pi$
$409$	18.8448	+	19.9743i	0.931816	+	0.987668i	−0.0681336	+	0.997676i	$0.521704\pi$
$410$	−2.69134	−	46.2086i	−0.132916	−	2.28208i
$411$		0			0
$412$	−6.94384	−	1.64572i	−0.342098	−	0.0810788i
$413$	−1.32045	+	0.480606i	−0.0649753	+	0.0236491i
$414$		0			0
$415$	15.1897	+	5.52860i	0.745633	+	0.271388i
$416$	−0.325570	−	0.214131i	−0.0159624	−	0.0104986i
$417$		0			0
$418$	−25.8295	−	3.01903i	−1.26336	−	0.147666i
$419$	14.6886	−	19.7303i	0.717587	−	0.963886i	−0.282403	−	0.959296i	$-0.591131\pi$
$419$	14.6886	−	19.7303i	0.717587	−	0.963886i	0.999989	−	0.00459033i	$-0.00146115\pi$
$420$		0			0
$421$	0.715310	−	12.2814i	0.0348621	−	0.598559i	−0.934961	−	0.354750i	$-0.884566\pi$
$421$	0.715310	−	12.2814i	0.0348621	−	0.598559i	0.969823	−	0.243809i	$-0.0783970\pi$
$422$	33.3126	−	27.9526i	1.62163	−	1.36071i
$423$		0			0
$424$	−11.2094	−	9.40584i	−0.544379	−	0.456788i
$425$	18.4157	−	19.5196i	0.893295	−	0.946837i
$426$		0			0
$427$	10.4592	−	6.87912i	0.506156	−	0.332904i
$428$	−17.3524	+	4.11260i	−0.838761	+	0.198790i
$429$		0			0
$430$	−29.0421	+	3.39454i	−1.40054	+	0.163699i
$431$	3.97831	−	6.89064i	0.191628	−	0.331910i	−0.754162	−	0.656689i	$-0.771956\pi$
$431$	3.97831	−	6.89064i	0.191628	−	0.331910i	0.945790	+	0.324779i	$0.105290\pi$
$432$		0			0
$433$	−5.95735	−	10.3184i	−0.286292	−	0.495872i	0.686630	−	0.727007i	$-0.259089\pi$
$433$	−5.95735	−	10.3184i	−0.286292	−	0.495872i	−0.972922	+	0.231135i	$0.925756\pi$
$434$	−10.3419	−	13.8915i	−0.496425	−	0.666815i
$435$		0			0
$436$	−14.9517	+	49.9422i	−0.716058	+	2.39180i
$437$	30.1674	+	15.1506i	1.44310	+	0.724752i
$438$		0			0
$439$	−1.98064	−	6.61580i	−0.0945308	−	0.315755i	0.897625	−	0.440759i	$-0.145291\pi$
$439$	−1.98064	−	6.61580i	−0.0945308	−	0.315755i	−0.992156	+	0.125004i	$0.960106\pi$
$440$	−5.71714	+	32.4235i	−0.272554	+	1.54573i
$441$		0			0
$442$	1.87809	+	10.6512i	0.0893318	+	0.506626i
$443$	6.47445	−	3.25159i	0.307610	−	0.154488i	−0.288297	−	0.957541i	$-0.593089\pi$
$443$	6.47445	−	3.25159i	0.307610	−	0.154488i	0.595907	+	0.803053i	$0.296793\pi$
$444$		0			0
$445$	−10.7487	−	24.9182i	−0.509535	−	1.18124i
$446$	13.6100	+	31.5516i	0.644454	+	1.49401i
$447$		0			0
$448$	−17.9261	+	9.00284i	−0.846930	+	0.425344i
$449$	5.97095	+	33.8630i	0.281787	+	1.59809i	0.716542	+	0.697543i	$0.245724\pi$
$449$	5.97095	+	33.8630i	0.281787	+	1.59809i	−0.434756	+	0.900548i	$0.643165\pi$
$450$		0			0
$451$	−2.64793	+	15.0172i	−0.124686	+	0.707130i
$452$	4.84274	+	16.1759i	0.227783	+	0.760850i
$453$		0			0
$454$	12.5234	+	6.28948i	0.587752	+	0.295180i
$455$	−1.18961	+	3.97358i	−0.0557698	+	0.186284i
$456$		0			0
$457$	9.94490	+	13.3583i	0.465203	+	0.624876i	0.971374	−	0.237557i	$-0.0763468\pi$
$457$	9.94490	+	13.3583i	0.465203	+	0.624876i	−0.506170	+	0.862433i	$0.668939\pi$
$458$	−29.9317	−	51.8433i	−1.39862	−	2.42248i
$459$		0			0
$460$	43.4712	−	75.2944i	2.02686	−	3.51062i
$461$	−13.6903	+	1.60016i	−0.637619	+	0.0745270i	−0.428760	−	0.903419i	$-0.641049\pi$
$461$	−13.6903	+	1.60016i	−0.637619	+	0.0745270i	−0.208860	+	0.977946i	$0.566975\pi$
$462$		0			0
$463$	11.9128	−	2.82340i	0.553637	−	0.131214i	0.0557317	−	0.998446i	$-0.482251\pi$
$463$	11.9128	−	2.82340i	0.553637	−	0.131214i	0.497905	+	0.867231i	$0.334103\pi$
$464$	6.54479	−	4.30458i	0.303834	−	0.199835i
$465$		0			0
$466$	−21.3119	+	22.5893i	−0.987253	+	1.04643i
$467$	−11.7925	−	9.89507i	−0.545691	−	0.457889i	0.327788	−	0.944751i	$-0.393697\pi$
$467$	−11.7925	−	9.89507i	−0.545691	−	0.457889i	−0.873479	+	0.486862i	$0.838141\pi$
$468$		0			0
$469$	0.495208	−	0.415529i	0.0228666	−	0.0191873i
$470$	−0.361672	+	6.20968i	−0.0166827	+	0.286431i
$471$		0			0
$472$	−1.72615	+	2.31862i	−0.0794526	+	0.106723i
$473$	9.56769	+	1.11830i	0.439923	+	0.0514196i
$474$		0			0
$475$	13.9711	+	9.18896i	0.641040	+	0.421619i
$476$	61.2319	+	22.2866i	2.80656	+	1.02150i
$477$		0			0
$478$	55.7428	−	20.2887i	2.54962	−	0.927985i
$479$	−14.7420	−	3.49392i	−0.673579	−	0.159641i	−0.120428	−	0.992722i	$-0.538427\pi$
$479$	−14.7420	−	3.49392i	−0.673579	−	0.159641i	−0.553151	+	0.833081i	$0.686575\pi$
$480$		0			0
$481$	−0.152139	−	2.61213i	−0.00693696	−	0.119103i
$482$	−48.5971	−	51.5099i	−2.21354	−	2.34621i
$483$		0			0
$484$	−8.39953	+	19.4723i	−0.381797	+	0.885105i
$485$	−5.05122			−0.229364
$486$		0			0
$487$	−9.74343			−0.441517			−0.220758	−	0.975329i	$-0.570853\pi$
$487$	−9.74343			−0.441517			−0.220758	+	0.975329i	$0.570853\pi$
$488$	10.1998	−	23.6458i	0.461724	−	1.07040i
$489$		0			0
$490$	−8.66535	−	9.18473i	−0.391460	−	0.414924i
$491$	1.11256	+	19.1020i	0.0502093	+	0.862060i	0.925567	+	0.378584i	$0.123589\pi$
$491$	1.11256	+	19.1020i	0.0502093	+	0.862060i	−0.875358	+	0.483476i	$0.839374\pi$
$492$		0			0
$493$	15.2874	+	3.62319i	0.688511	+	0.163180i
$494$	−6.33304	+	2.30504i	−0.284937	+	0.103709i
$495$		0			0
$496$	−10.5232	−	3.83013i	−0.472506	−	0.171978i
$497$	15.7161	+	10.3366i	0.704962	+	0.463661i
$498$		0			0
$499$	25.9471	+	3.03278i	1.16155	+	0.135766i	0.674953	−	0.737861i	$-0.264164\pi$
$499$	25.9471	+	3.03278i	1.16155	+	0.135766i	0.486597	+	0.873627i	$0.338238\pi$
$500$	−8.94521	+	12.0155i	−0.400042	+	0.537350i
$501$		0			0
$502$	−3.37701	+	57.9810i	−0.150723	+	2.58782i
$503$	0.849443	−	0.712768i	0.0378748	−	0.0317807i	−0.623654	−	0.781701i	$-0.714352\pi$
$503$	0.849443	−	0.712768i	0.0378748	−	0.0317807i	0.661529	+	0.749920i	$0.269908\pi$
$504$		0			0
$505$	−19.1614	−	16.0784i	−0.852673	−	0.715477i
$506$	−29.6490	+	31.4261i	−1.31806	+	1.39706i
$507$		0			0
$508$	19.3489	−	12.7259i	0.858467	−	0.564623i
$509$	−16.5171	+	3.91463i	−0.732109	+	0.173513i	−0.579729	−	0.814809i	$-0.696842\pi$
$509$	−16.5171	+	3.91463i	−0.732109	+	0.173513i	−0.152379	+	0.988322i	$0.548694\pi$
$510$		0			0
$511$	−34.6704	+	4.05238i	−1.53373	+	0.179267i
$512$	−18.1349	+	31.4106i	−0.801458	+	1.38817i
$513$		0			0
$514$	14.7828	+	25.6045i	0.652041	+	1.12937i
$515$	−3.19707	−	4.29441i	−0.140880	−	0.189234i
$516$		0			0
$517$	0.587715	−	1.96310i	0.0258477	−	0.0863372i
$518$	−21.2499	−	10.6721i	−0.933668	−	0.468906i
$519$		0			0
$520$	2.44713	+	8.17398i	0.107314	+	0.358453i
$521$	−5.42618	+	30.7734i	−0.237725	+	1.34821i	0.599072	+	0.800695i	$0.295536\pi$
$521$	−5.42618	+	30.7734i	−0.237725	+	1.34821i	−0.836798	+	0.547512i	$0.815575\pi$
$522$		0			0
$523$	−2.23807	−	12.6927i	−0.0978638	−	0.555013i	−0.993832	−	0.110895i	$-0.964628\pi$
$523$	−2.23807	−	12.6927i	−0.0978638	−	0.555013i	0.895968	−	0.444118i	$-0.146483\pi$
$524$	−45.9082	+	23.0559i	−2.00551	+	1.00720i
$525$		0			0
$526$	−7.72021	−	17.8974i	−0.336617	−	0.780366i
$527$	−8.89591	−	20.6230i	−0.387512	−	0.898354i
$528$		0			0
$529$	29.5661	−	14.8487i	1.28548	−	0.645594i
$530$	−3.87796	−	21.9930i	−0.168448	−	0.955314i
$531$		0			0
$532$	−7.05085	+	39.9874i	−0.305693	+	1.73367i
$533$	1.13340	+	3.78583i	0.0490931	+	0.163982i
$534$		0			0
$535$	−11.9559	−	6.00447i	−0.516898	−	0.259596i
$536$	0.381390	−	1.27393i	0.0164736	−	0.0550255i
$537$		0			0
$538$	−32.7518	−	43.9934i	−1.41203	−	1.89669i
$539$	2.07997	+	3.60261i	0.0895907	+	0.155176i
$540$		0			0
$541$	−3.97103	+	6.87802i	−0.170728	+	0.295709i	−0.938675	−	0.344804i	$-0.887945\pi$
$541$	−3.97103	+	6.87802i	−0.170728	+	0.295709i	0.767947	+	0.640514i	$0.221279\pi$
$542$	−73.3162	+	8.56944i	−3.14920	+	0.368089i
$543$		0			0
$544$	−4.46893	+	1.05915i	−0.191604	+	0.0454109i
$545$	−32.6770	+	21.4920i	−1.39973	+	0.920617i
$546$		0			0
$547$	7.43375	−	7.87931i	0.317844	−	0.336895i	−0.548678	−	0.836034i	$-0.684869\pi$
$547$	7.43375	−	7.87931i	0.317844	−	0.336895i	0.866522	+	0.499139i	$0.166350\pi$
$548$	13.6424	+	11.4473i	0.582774	+	0.489005i
$549$		0			0
$550$	−16.3946	+	13.7567i	−0.699067	+	0.586587i
$551$	−0.569235	+	9.77340i	−0.0242502	+	0.416361i
$552$		0			0
$553$	10.1937	−	13.6925i	0.433478	−	0.582263i
$554$	−10.7030	−	1.25100i	−0.454728	−	0.0531501i
$555$		0			0
$556$	15.7517	+	10.3601i	0.668020	+	0.439364i
$557$	1.66135	+	0.604682i	0.0703937	+	0.0256212i	0.376977	−	0.926223i	$-0.376964\pi$
$557$	1.66135	+	0.604682i	0.0703937	+	0.0256212i	−0.306583	+	0.951844i	$0.599186\pi$
$558$		0			0
$559$	2.34587	−	0.853825i	0.0992196	−	0.0361130i
$560$	23.7178	+	5.62122i	1.00226	+	0.237540i
$561$		0			0
$562$	0.802809	+	13.7837i	0.0338644	+	0.581430i
$563$	5.25025	+	5.56494i	0.221272	+	0.234534i	0.828494	−	0.559997i	$-0.189198\pi$
$563$	5.25025	+	5.56494i	0.221272	+	0.234534i	−0.607223	+	0.794532i	$0.707716\pi$
$564$		0			0
$565$	−5.01748	+	11.6318i	−0.211087	+	0.489354i
$566$	−70.2116			−2.95121
$567$		0			0
$568$	38.6951			1.62361
$569$	7.88133	−	18.2710i	0.330402	−	0.765959i	−0.669333	−	0.742962i	$-0.733420\pi$
$569$	7.88133	−	18.2710i	0.330402	−	0.765959i	0.999736	−	0.0229964i	$-0.00732062\pi$
$570$		0			0
$571$	31.6143	+	33.5092i	1.32302	+	1.40232i	0.855028	+	0.518582i	$0.173540\pi$
$571$	31.6143	+	33.5092i	1.32302	+	1.40232i	0.467990	+	0.883734i	$0.344978\pi$
$572$	−0.332483	−	5.70851i	−0.0139018	−	0.238685i
$573$		0			0
$574$	34.9463	+	8.28242i	1.45863	+	0.345701i
$575$	26.1065	−	9.50198i	1.08872	−	0.396260i
$576$		0			0
$577$	−24.3829	−	8.87465i	−1.01507	−	0.369457i	−0.219695	−	0.975569i	$-0.570506\pi$
$577$	−24.3829	−	8.87465i	−1.01507	−	0.369457i	−0.795379	+	0.606112i	$0.792728\pi$
$578$	71.9027	+	47.2912i	2.99076	+	1.96705i
$579$		0			0
$580$	25.0431	+	2.92712i	1.03986	+	0.121542i
$581$	−7.48967	+	10.0604i	−0.310724	+	0.417375i
$582$		0			0
$583$	−0.427782	+	7.34472i	−0.0177169	+	0.304187i
$584$	−55.0061	+	46.1556i	−2.27617	+	1.90993i
$585$		0			0
$586$	−4.03971	−	3.38972i	−0.166879	−	0.140028i
$587$	−14.4213	+	15.2857i	−0.595231	+	0.630908i	−0.953025	−	0.302893i	$-0.902048\pi$
$587$	−14.4213	+	15.2857i	−0.595231	+	0.630908i	0.357794	+	0.933801i	$0.383529\pi$
$588$		0			0
$589$	11.6930	−	7.69063i	0.481803	−	0.316887i
$590$	−4.29264	+	1.01737i	−0.176725	+	0.0418846i
$591$		0			0
$592$	−15.2723	+	1.78508i	−0.627688	+	0.0733662i
$593$	−12.9024	+	22.3476i	−0.529837	+	0.917705i	0.469557	+	0.882902i	$0.344414\pi$
$593$	−12.9024	+	22.3476i	−0.529837	+	0.917705i	−0.999394	+	0.0348027i	$0.988920\pi$
$594$		0			0
$595$	24.4432	+	42.3368i	1.00207	+	1.73564i
$596$	−23.0575	−	30.9716i	−0.944472	−	1.26865i
$597$		0			0
$598$	−3.21130	+	10.7265i	−0.131320	+	0.438639i
$599$	−24.5346	−	12.3217i	−1.00246	−	0.503453i	−0.129671	−	0.991557i	$-0.541392\pi$
$599$	−24.5346	−	12.3217i	−1.00246	−	0.503453i	−0.872785	+	0.488105i	$0.837688\pi$
$600$		0			0
$601$	−0.109405	−	0.365437i	−0.00446271	−	0.0149065i	0.955729	−	0.294248i	$-0.0950691\pi$
$601$	−0.109405	−	0.365437i	−0.00446271	−	0.0149065i	−0.960192	+	0.279341i	$0.909884\pi$
$602$	3.93963	−	22.3428i	0.160567	−	0.910623i
$603$		0			0
$604$	9.12145	+	51.7303i	0.371146	+	2.10488i
$605$	−14.2176	+	7.14036i	−0.578028	+	0.290297i
$606$		0			0
$607$	2.44005	+	5.65667i	0.0990386	+	0.229597i	0.960531	−	0.278173i	$-0.0897290\pi$
$607$	2.44005	+	5.65667i	0.0990386	+	0.229597i	−0.861492	+	0.507771i	$0.830470\pi$
$608$	−1.13353	−	2.62781i	−0.0459706	−	0.106572i
$609$		0			0
$610$	35.1214	−	17.6386i	1.42202	−	0.714166i
$611$	−0.0922182	−	0.522996i	−0.00373075	−	0.0211581i
$612$		0			0
$613$	−4.86771	+	27.6062i	−0.196605	+	1.11500i	0.713509	+	0.700646i	$0.247105\pi$
$613$	−4.86771	+	27.6062i	−0.196605	+	1.11500i	−0.910114	+	0.414357i	$0.864006\pi$
$614$	3.31480	+	11.0722i	0.133775	+	0.446838i
$615$		0			0
$616$	−22.8285	−	11.4649i	−0.919788	−	0.461935i
$617$	4.27981	−	14.2956i	0.172299	−	0.575518i	−0.827600	−	0.561318i	$-0.810295\pi$
$617$	4.27981	−	14.2956i	0.172299	−	0.575518i	0.999899	−	0.0142003i	$-0.00452023\pi$
$618$		0			0
$619$	−2.49285	−	3.34848i	−0.100196	−	0.134587i	0.749197	−	0.662347i	$-0.230439\pi$
$619$	−2.49285	−	3.34848i	−0.100196	−	0.134587i	−0.849394	+	0.527760i	$0.823032\pi$
$620$	−18.0223	−	31.2156i	−0.723794	−	1.25365i
$621$		0			0
$622$	28.7494	−	49.7955i	1.15275	−	1.99662i
$623$	20.9139	−	2.44448i	0.837898	−	0.0979362i
$624$		0			0
$625$	−28.9837	+	6.86927i	−1.15935	+	0.274771i
$626$	48.0919	−	31.6305i	1.92214	−	1.26421i
$627$		0			0
$628$	8.09609	−	8.58135i	0.323069	−	0.342433i
$629$	−23.6239	−	19.8228i	−0.941945	−	0.790386i
$630$		0			0
$631$	24.5789	−	20.6241i	0.978470	−	0.821034i	−0.00538805	−	0.999985i	$-0.501715\pi$
$631$	24.5789	−	20.6241i	0.978470	−	0.821034i	0.983858	+	0.178952i	$0.0572706\pi$
$632$	2.04175	−	35.0556i	0.0812166	−	1.39444i
$633$		0			0
$634$	−49.5655	+	66.5780i	−1.96850	+	2.64415i
$635$	17.2570	+	2.01705i	0.684821	+	0.0800441i
$636$		0			0
$637$	0.900723	+	0.592415i	0.0356879	+	0.0234723i
$638$	−11.7739	−	4.28536i	−0.466134	−	0.169659i
$639$		0			0
$640$	−55.6576	+	20.2577i	−2.20006	+	0.800757i
$641$	−38.3438	−	9.08765i	−1.51449	−	0.358941i	−0.612421	−	0.790532i	$-0.709804\pi$
$641$	−38.3438	−	9.08765i	−1.51449	−	0.358941i	−0.902069	+	0.431591i	$0.857952\pi$
$642$		0			0
$643$	1.65969	+	28.4958i	0.0654519	+	1.12376i	0.857897	+	0.513822i	$0.171771\pi$
$643$	1.65969	+	28.4958i	0.0654519	+	1.12376i	−0.792445	+	0.609943i	$0.791192\pi$
$644$	46.2934	+	49.0681i	1.82422	+	1.93356i
$645$		0			0
$646$	−31.4612	+	72.9353i	−1.23782	+	2.86960i
$647$	3.61582			0.142153			0.0710764	−	0.997471i	$-0.477357\pi$
$647$	3.61582			0.142153			0.0710764	+	0.997471i	$0.477357\pi$
$648$		0			0
$649$	1.45335			0.0570489
$650$	−2.19681	+	5.09278i	−0.0861661	+	0.199755i
$651$		0			0
$652$	−47.8628	−	50.7316i	−1.87445	−	1.98680i
$653$	−0.689989	−	11.8467i	−0.0270014	−	0.463595i	−0.984525	−	0.175242i	$-0.943929\pi$
$653$	−0.689989	−	11.8467i	−0.0270014	−	0.463595i	0.957524	−	0.288353i	$-0.0931078\pi$
$654$		0			0
$655$	−37.5024	−	8.88823i	−1.46534	−	0.347292i
$656$	21.8226	−	7.94277i	0.852029	−	0.310113i
$657$		0			0
$658$	−4.53524	−	1.65069i	−0.176802	−	0.0643507i
$659$	2.19931	+	1.44651i	0.0856730	+	0.0563481i	0.591623	−	0.806215i	$-0.298488\pi$
$659$	2.19931	+	1.44651i	0.0856730	+	0.0563481i	−0.505950	+	0.862563i	$0.668858\pi$
$660$		0			0
$661$	−25.6714	−	3.00056i	−0.998503	−	0.116708i	−0.398890	−	0.916999i	$-0.630605\pi$
$661$	−25.6714	−	3.00056i	−0.998503	−	0.116708i	−0.599613	+	0.800290i	$0.704679\pi$
$662$	−37.7143	+	50.6591i	−1.46581	+	1.96892i
$663$		0			0
$664$	−1.50016	+	25.7567i	−0.0582173	+	0.999553i
$665$	−23.3357	+	19.5810i	−0.904919	+	0.759317i
$666$		0			0
$667$	12.4596	+	10.4549i	0.482439	+	0.404815i
$668$	59.3657	−	62.9240i	2.29693	−	2.43460i
$669$		0			0
$670$	1.69562	−	1.11523i	0.0655075	−	0.0430849i
$671$	−12.5986	+	2.98593i	−0.486365	+	0.115271i
$672$		0			0
$673$	−1.19536	+	0.139717i	−0.0460776	+	0.00538570i	−0.139100	−	0.990278i	$-0.544421\pi$
$673$	−1.19536	+	0.139717i	−0.0460776	+	0.00538570i	0.0930229	+	0.995664i	$0.470347\pi$
$674$	26.9796	−	46.7301i	1.03922	−	1.79998i
$675$		0			0
$676$	24.8284	+	43.0040i	0.954938	+	1.65400i
$677$	−23.4105	−	31.4457i	−0.899737	−	1.20856i	−0.977362	−	0.211574i	$-0.932141\pi$
$677$	−23.4105	−	31.4457i	−0.899737	−	1.20856i	0.0776247	−	0.996983i	$-0.475266\pi$
$678$		0			0
$679$	1.12406	−	3.75463i	0.0431375	−	0.144089i
$680$	89.8666	+	45.1327i	3.44623	+	1.73076i
$681$		0			0
$682$	5.13719	+	17.1594i	0.196713	+	0.657068i
$683$	1.15437	−	6.54674i	0.0441706	−	0.250504i	−0.954725	−	0.297490i	$-0.903851\pi$
$683$	1.15437	−	6.54674i	0.0441706	−	0.250504i	0.998896	+	0.0469860i	$0.0149616\pi$
$684$		0			0
$685$	2.32008	+	13.1578i	0.0886455	+	0.502734i
$686$	43.6480	−	21.9209i	1.66649	−	0.836942i
$687$		0			0
$688$	−5.81059	−	13.4705i	−0.221527	−	0.513557i
$689$	0.755192	+	1.75073i	0.0287705	+	0.0666976i
$690$		0			0
$691$	−10.1591	+	5.10207i	−0.386469	+	0.194092i	−0.631416	−	0.775445i	$-0.717526\pi$
$691$	−10.1591	+	5.10207i	−0.386469	+	0.194092i	0.244947	+	0.969536i	$0.421229\pi$
$692$	7.39441	+	41.9358i	0.281093	+	1.59416i
$693$		0			0
$694$	−0.758598	+	4.30222i	−0.0287960	+	0.163310i
$695$	4.05664	+	13.5501i	0.153877	+	0.513985i
$696$		0			0
$697$	41.6222	+	20.9035i	1.57655	+	0.791776i
$698$	0.122873	−	0.410425i	0.00465082	−	0.0155348i
$699$		0			0
$700$	19.9547	+	26.8038i	0.754217	+	1.01309i
$701$	−14.2748	−	24.7247i	−0.539152	−	0.933838i	−0.998950	−	0.0458147i	$-0.985412\pi$
$701$	−14.2748	−	24.7247i	−0.539152	−	0.933838i	0.459798	−	0.888023i	$-0.347922\pi$
$702$		0			0
$703$	9.60829	−	16.6421i	0.362384	−	0.627667i
$704$	20.6070	−	2.40861i	0.776654	−	0.0907778i
$705$		0			0
$706$	72.0887	−	17.0853i	2.71309	−	0.643015i
$707$	16.2153	−	10.6650i	0.609838	−	0.401097i
$708$		0			0
$709$	29.9559	−	31.7514i	1.12502	−	1.19245i	0.145870	−	0.989304i	$-0.453402\pi$
$709$	29.9559	−	31.7514i	1.12502	−	1.19245i	0.979148	−	0.203146i	$-0.0651166\pi$
$710$	45.2389	+	37.9599i	1.69779	+	1.42461i
$711$		0			0
$712$	33.1808	−	27.8420i	1.24350	−	1.04342i
$713$	1.35198	−	23.2125i	0.0506319	−	0.869316i
$714$		0			0
$715$	2.56179	−	3.44108i	0.0958054	−	0.128689i
$716$	34.9365	+	4.08349i	1.30564	+	0.152607i
$717$		0			0
$718$	−13.1255	−	8.63278i	−0.489839	−	0.322173i
$719$	−28.1797	−	10.2566i	−1.05093	−	0.382506i	−0.241914	−	0.970298i	$-0.577775\pi$
$719$	−28.1797	−	10.2566i	−1.05093	−	0.382506i	−0.809012	+	0.587792i	$0.799998\pi$
$720$		0			0
$721$	3.90353	−	1.42077i	0.145375	−	0.0529122i
$722$	−3.12697	−	0.741105i	−0.116374	−	0.0275811i
$723$		0			0
$724$	−0.989230	−	16.9844i	−0.0367645	−	0.631221i
$725$	5.52894	+	5.86034i	0.205340	+	0.217647i
$726$		0			0
$727$	15.8758	−	36.8042i	0.588800	−	1.36499i	−0.319865	−	0.947463i	$-0.603637\pi$
$727$	15.8758	−	36.8042i	0.588800	−	1.36499i	0.908664	−	0.417528i	$-0.137103\pi$
$728$	−6.62038			−0.245368
$729$		0			0
$730$	−109.587			−4.05600
$731$	11.6538	−	27.0165i	0.431030	−	0.999240i
$732$		0			0
$733$	−18.8469	−	19.9765i	−0.696125	−	0.737849i	0.278808	−	0.960347i	$-0.410061\pi$
$733$	−18.8469	−	19.9765i	−0.696125	−	0.737849i	−0.974933	+	0.222497i	$0.928579\pi$
$734$	2.60678	+	44.7566i	0.0962178	+	1.65200i
$735$		0			0
$736$	−4.62651	−	1.09650i	−0.170535	−	0.0404176i
$737$	−0.628278	+	0.228675i	−0.0231429	+	0.00842334i
$738$		0			0
$739$	−29.1919	−	10.6250i	−1.07384	−	0.390846i	−0.256229	−	0.966616i	$-0.582480\pi$
$739$	−29.1919	−	10.6250i	−1.07384	−	0.390846i	−0.817612	+	0.575770i	$0.804702\pi$
$740$	−41.3495	−	27.1960i	−1.52004	−	0.999744i
$741$		0			0
$742$	17.2106	+	2.01163i	0.631821	+	0.0738493i
$743$	−3.86766	+	5.19517i	−0.141891	+	0.190592i	−0.867388	−	0.497633i	$-0.834203\pi$
$743$	−3.86766	+	5.19517i	−0.141891	+	0.190592i	0.725497	+	0.688226i	$0.241610\pi$
$744$		0			0
$745$	1.68434	−	28.9190i	0.0617094	−	1.05951i
$746$	60.2439	−	50.5507i	2.20569	−	1.85079i
$747$		0			0
$748$	−51.6272	−	43.3204i	−1.88768	−	1.58395i
$749$	7.12377	−	7.55075i	0.260297	−	0.275898i
$750$		0			0
$751$	6.19254	−	4.07290i	0.225969	−	0.148622i	−0.431477	−	0.902124i	$-0.642007\pi$
$751$	6.19254	−	4.07290i	0.225969	−	0.148622i	0.657446	+	0.753502i	$0.271637\pi$
$752$	−3.03669	+	0.719708i	−0.110737	+	0.0262450i
$753$		0			0
$754$	−3.22517	+	0.376969i	−0.117454	+	0.0137284i
$755$	−19.7042	+	34.1287i	−0.717109	+	1.24207i
$756$		0			0
$757$	−22.2841	−	38.5972i	−0.809930	−	1.40284i	−0.912912	−	0.408157i	$-0.866172\pi$
$757$	−22.2841	−	38.5972i	−0.809930	−	1.40284i	0.102981	−	0.994683i	$-0.467162\pi$
$758$	32.0495	+	43.0499i	1.16409	+	1.56364i
$759$		0			0
$760$	−17.9723	+	60.0315i	−0.651922	+	2.17757i
$761$	−17.8901	−	8.98475i	−0.648516	−	0.325697i	0.0939538	−	0.995577i	$-0.470049\pi$
$761$	−17.8901	−	8.98475i	−0.648516	−	0.325697i	−0.742470	+	0.669880i	$0.766346\pi$
$762$		0			0
$763$	−8.70355	−	29.0719i	−0.315090	−	1.05247i
$764$	14.4900	−	82.1770i	0.524231	−	2.97306i
$765$		0			0
$766$	6.01753	+	34.1271i	0.217422	+	1.23306i
$767$	0.336584	−	0.169039i	0.0121533	−	0.00610363i
$768$		0			0
$769$	−1.97582	−	4.58046i	−0.0712499	−	0.165176i	0.878870	−	0.477062i	$-0.158298\pi$
$769$	−1.97582	−	4.58046i	−0.0712499	−	0.165176i	−0.950119	+	0.311887i	$0.899039\pi$
$770$	−15.4420	−	35.7986i	−0.556492	−	1.29009i
$771$		0			0
$772$	−63.8202	+	32.0517i	−2.29694	+	1.15357i
$773$	−4.06522	−	23.0550i	−0.146216	−	0.829232i	−0.966383	−	0.257108i	$-0.917231\pi$
$773$	−4.06522	−	23.0550i	−0.146216	−	0.829232i	0.820167	−	0.572124i	$-0.193881\pi$
$774$		0			0
$775$	2.00005	−	11.3429i	0.0718440	−	0.407448i
$776$	−2.31229	−	7.72358i	−0.0830063	−	0.277260i
$777$		0			0
$778$	−26.7011	−	13.4098i	−0.957281	−	0.480765i
$779$	−8.32396	+	27.8040i	−0.298237	+	0.996180i
$780$		0			0
$781$	−11.6179	−	15.6055i	−0.415720	−	0.558408i
$782$	65.9832	+	114.286i	2.35955	+	4.08687i
$783$		0			0
$784$	3.16768	−	5.48659i	0.113132	−	0.195950i
$785$	8.79117	−	1.02754i	0.313770	−	0.0366745i
$786$		0			0
$787$	−48.5708	+	11.5115i	−1.73136	+	0.410340i	−0.970984	−	0.239143i	$-0.923134\pi$
$787$	−48.5708	+	11.5115i	−1.73136	+	0.410340i	−0.760376	+	0.649483i	$0.774985\pi$
$788$	−23.4610	+	15.4305i	−0.835763	+	0.549690i
$789$		0			0
$790$	36.7766	−	38.9809i	1.30845	−	1.38688i
$791$	−7.52951	−	6.31801i	−0.267719	−	0.224642i
$792$		0			0
$793$	−2.57045	+	2.15686i	−0.0912792	+	0.0765923i
$794$	1.37592	−	23.6236i	0.0488296	−	0.838372i
$795$		0			0
$796$	−8.58823	+	11.5360i	−0.304402	+	0.408882i
$797$	39.9343	+	4.66765i	1.41454	+	0.165337i	0.788780	−	0.614676i	$-0.210713\pi$
$797$	39.9343	+	4.66765i	1.41454	+	0.165337i	0.625764	+	0.780012i	$0.284787\pi$
$798$		0			0
$799$	−5.22942	−	3.43944i	−0.185003	−	0.121679i
$800$	−2.21319	−	0.805537i	−0.0782482	−	0.0284800i
$801$		0			0
$802$	2.67647	−	0.974155i	0.0945094	−	0.0343986i
$803$	35.1294	+	8.32581i	1.23969	+	0.293812i
$804$		0			0
$805$	2.94272	+	50.5245i	0.103717	+	1.78075i
$806$	3.18554	+	3.37647i	0.112206	+	0.118931i
$807$		0			0
$808$	15.8132	−	36.6590i	0.556305	−	1.28966i
$809$	44.4490			1.56274			0.781371	−	0.624066i	$-0.214521\pi$
$809$	44.4490			1.56274			0.781371	+	0.624066i	$0.214521\pi$
$810$		0			0
$811$	−38.6494			−1.35716			−0.678582	−	0.734524i	$-0.737405\pi$
$811$	−38.6494			−1.35716			−0.678582	+	0.734524i	$0.737405\pi$
$812$	−7.74867	+	17.9634i	−0.271925	+	0.630393i
$813$		0			0
$814$	16.8775	+	17.8891i	0.591556	+	0.627013i
$815$	−3.04248	−	52.2373i	−0.106573	−	1.82979i
$816$		0			0
$817$	17.8400	+	4.22817i	0.624144	+	0.147925i
$818$	−62.8587	+	22.8787i	−2.19780	+	0.799934i
$819$		0			0
$820$	70.2401	+	25.5653i	2.45289	+	0.892780i
$821$	−36.1767	−	23.7938i	−1.26257	−	0.830408i	−0.271335	−	0.962485i	$-0.587465\pi$
$821$	−36.1767	−	23.7938i	−1.26257	−	0.830408i	−0.991240	+	0.132076i	$0.957836\pi$
$822$		0			0
$823$	29.9006	+	3.49488i	1.04227	+	0.121824i	0.619965	−	0.784629i	$-0.287147\pi$
$823$	29.9006	+	3.49488i	1.04227	+	0.121824i	0.422306	+	0.906453i	$0.361221\pi$
$824$	5.10286	−	6.85433i	0.177767	−	0.238782i
$825$		0			0
$826$	0.199027	−	3.41717i	0.00692505	−	0.118898i
$827$	−12.5660	+	10.5441i	−0.436963	+	0.366655i	−0.834571	−	0.550900i	$-0.814285\pi$
$827$	−12.5660	+	10.5441i	−0.436963	+	0.366655i	0.397609	+	0.917555i	$0.369840\pi$
$828$		0			0
$829$	22.2396	+	18.6612i	0.772413	+	0.648132i	0.941326	−	0.337500i	$-0.109581\pi$
$829$	22.2396	+	18.6612i	0.772413	+	0.648132i	−0.168913	+	0.985631i	$0.554026\pi$
$830$	−27.0212	+	28.6408i	−0.937920	+	0.994137i
$831$		0			0
$832$	4.49225	−	2.95460i	0.155741	−	0.102432i
$833$	12.3638	−	2.93026i	0.428379	−	0.101528i
$834$		0			0
$835$	64.4625	−	7.53459i	2.23082	−	0.260745i
$836$	20.9978	−	36.3693i	0.726224	−	1.25786i
$837$		0			0
$838$	29.9589	+	51.8904i	1.03491	+	1.79252i
$839$	21.2010	+	28.4779i	0.731940	+	0.983166i	0.999806	+	0.0197096i	$0.00627416\pi$
$839$	21.2010	+	28.4779i	0.731940	+	0.983166i	−0.267866	+	0.963456i	$0.586318\pi$
$840$		0			0
$841$	6.96448	−	23.2630i	0.240154	−	0.802172i
$842$	26.7798	+	13.4493i	0.922891	+	0.463493i
$843$		0			0
$844$	20.1409	+	67.2754i	0.693280	+	2.31572i
$845$	−6.46910	+	36.6881i	−0.222544	+	1.26211i
$846$		0			0
$847$	−2.14362	−	12.1571i	−0.0736557	−	0.417722i
$848$	10.0128	−	5.02860i	0.343840	−	0.172683i
$849$		0			0
$850$	25.8916	+	60.0235i	0.888076	+	2.05879i
$851$	−12.6453	−	29.3151i	−0.433476	−	1.00491i
$852$		0			0
$853$	−0.860025	+	0.431921i	−0.0294467	+	0.0147887i	−0.463462	−	0.886117i	$-0.653393\pi$
$853$	−0.860025	+	0.431921i	−0.0294467	+	0.0147887i	0.434015	+	0.900906i	$0.357097\pi$
$854$	5.29532	+	30.0313i	0.181202	+	1.02765i
$855$		0			0
$856$	3.70813	−	21.0298i	0.126741	−	0.718785i
$857$	−0.162781	−	0.543725i	−0.00556048	−	0.0185733i	0.955164	−	0.296076i	$-0.0956783\pi$
$857$	−0.162781	−	0.543725i	−0.00556048	−	0.0185733i	−0.960725	+	0.277503i	$0.910493\pi$
$858$		0			0
$859$	17.9700	+	9.02486i	0.613128	+	0.307924i	0.728128	−	0.685441i	$-0.240391\pi$
$859$	17.9700	+	9.02486i	0.613128	+	0.307924i	−0.115000	+	0.993365i	$0.536687\pi$
$860$	13.5426	−	45.2353i	0.461798	−	1.54251i
$861$		0			0
$862$	11.5740	+	15.5466i	0.394211	+	0.529518i
$863$	−18.8153	−	32.5891i	−0.640481	−	1.10935i	−0.985326	−	0.170686i	$-0.945402\pi$
$863$	−18.8153	−	32.5891i	−0.640481	−	1.10935i	0.344845	−	0.938660i	$-0.387932\pi$
$864$		0			0
$865$	−15.9735	+	27.6668i	−0.543114	+	0.940700i
$866$	28.8271	−	3.36941i	0.979585	−	0.114497i
$867$		0			0
$868$	27.2135	−	6.44971i	0.923685	−	0.218917i
$869$	−14.7507	+	9.70170i	−0.500384	+	0.329108i
$870$		0			0
$871$	−0.118907	+	0.126034i	−0.00402901	+	0.00427050i
$872$	−47.8210	−	40.1266i	−1.61942	−	1.35886i
$873$		0			0
$874$	−62.9936	+	52.8579i	−2.13079	+	1.78795i
$875$	0.507011	−	8.70504i	0.0171401	−	0.294284i
$876$		0			0
$877$	16.3657	−	21.9830i	0.552632	−	0.742313i	−0.434771	−	0.900541i	$-0.643171\pi$
$877$	16.3657	−	21.9830i	0.552632	−	0.742313i	0.987403	+	0.158228i	$0.0505780\pi$
$878$	16.7086	+	1.95295i	0.563887	+	0.0659090i
$879$		0			0
$880$	−21.0627	−	13.8532i	−0.710024	−	0.466990i
$881$	−31.5862	−	11.4964i	−1.06417	−	0.387324i	−0.250174	−	0.968201i	$-0.580488\pi$
$881$	−31.5862	−	11.4964i	−1.06417	−	0.387324i	−0.813992	+	0.580877i	$0.802710\pi$
$882$		0			0
$883$	40.4061	−	14.7066i	1.35977	−	0.494917i	0.443789	−	0.896131i	$-0.353634\pi$
$883$	40.4061	−	14.7066i	1.35977	−	0.494917i	0.915984	+	0.401214i	$0.131412\pi$
$884$	−16.9950	−	4.02789i	−0.571604	−	0.135473i
$885$		0			0
$886$	1.02617	+	17.6187i	0.0344748	+	0.591910i
$887$	21.2743	+	22.5495i	0.714322	+	0.757137i	0.978255	−	0.207404i	$-0.0665015\pi$
$887$	21.2743	+	22.5495i	0.714322	+	0.757137i	−0.263934	+	0.964541i	$0.585020\pi$
$888$		0			0
$889$	−5.33953	+	12.3784i	−0.179082	+	0.415159i
$890$	66.1052			2.21585
$891$		0			0
$892$	−55.4905			−1.85796
$893$	1.54481	−	3.58127i	0.0516951	−	0.119843i
$894$		0			0
$895$	18.1091	+	19.1946i	0.605322	+	0.641604i
$896$	−2.67215	−	45.8790i	−0.0892701	−	1.53271i
$897$		0			0
$898$	−81.5025	−	19.3164i	−2.71977	−	0.644598i
$899$	6.33645	−	2.30628i	0.211333	−	0.0769188i
$900$		0			0
$901$	21.1167	+	7.68587i	0.703501	+	0.256053i
$902$	−31.0342	−	20.4115i	−1.03333	−	0.679629i
$903$		0			0
$904$	−20.0825	−	2.34731i	−0.667934	−	0.0780703i
$905$	7.62204	−	10.2382i	0.253365	−	0.340329i
$906$		0			0
$907$	0.227537	−	3.90667i	0.00755526	−	0.129719i	−0.992421	−	0.122881i	$-0.960787\pi$
$907$	0.227537	−	3.90667i	0.00755526	−	0.129719i	0.999977	−	0.00683739i	$-0.00217643\pi$
$908$	−17.3364	+	14.5469i	−0.575328	+	0.482757i
$909$		0			0
$910$	−7.73997	−	6.49461i	−0.256577	−	0.215294i
$911$	−26.7414	+	28.3443i	−0.885983	+	0.939087i	−0.998510	−	0.0545616i	$-0.982624\pi$
$911$	−26.7414	+	28.3443i	−0.885983	+	0.939087i	0.112528	+	0.993649i	$0.464105\pi$
$912$		0			0
$913$	10.8379	−	7.12821i	0.358683	−	0.235909i
$914$	−39.4737	+	9.35545i	−1.30568	+	0.309451i
$915$		0			0
$916$	96.0190	−	11.2230i	3.17256	−	0.370819i
$917$	14.9522	−	25.8980i	0.493766	−	0.855228i
$918$		0			0
$919$	10.6253	+	18.4036i	0.350497	+	0.607078i	0.986337	−	0.164743i	$-0.0526794\pi$
$919$	10.6253	+	18.4036i	0.350497	+	0.607078i	−0.635840	+	0.771821i	$0.719346\pi$
$920$	62.1697	+	83.5084i	2.04968	+	2.75319i
$921$		0			0
$922$	9.62957	−	32.1650i	0.317133	−	1.05930i
$923$	−4.50567	−	2.26283i	−0.148306	−	0.0744820i
$924$		0			0
$925$	−4.53570	−	15.1503i	−0.149133	−	0.498139i
$926$	−5.17866	+	29.3696i	−0.170181	+	0.965146i
$927$		0			0
$928$	−0.239438	−	1.35792i	−0.00785994	−	0.0445759i
$929$	14.6055	−	7.33516i	0.479191	−	0.240659i	−0.192772	−	0.981244i	$-0.561748\pi$
$929$	14.6055	−	7.33516i	0.479191	−	0.240659i	0.671963	+	0.740585i	$0.265451\pi$
$930$		0			0
$931$	3.13603	+	7.27012i	0.102779	+	0.238269i
$932$	−19.8641	−	46.0501i	−0.650670	−	1.50842i
$933$		0			0
$934$	33.5100	−	16.8294i	1.09648	−	0.550674i
$935$	−8.77991	−	49.7934i	−0.287134	−	1.62842i
$936$		0			0
$937$	−3.94626	+	22.3803i	−0.128919	+	0.731134i	0.849984	+	0.526808i	$0.176611\pi$
$937$	−3.94626	+	22.3803i	−0.128919	+	0.731134i	−0.978903	+	0.204326i	$0.934500\pi$
$938$	0.451629	+	1.50855i	0.0147462	+	0.0492558i
$939$		0			0
$940$	−8.97646	−	4.50815i	−0.292780	−	0.147040i
$941$	3.75885	−	12.5554i	0.122535	−	0.409295i	−0.874608	−	0.484830i	$-0.838881\pi$
$941$	3.75885	−	12.5554i	0.122535	−	0.409295i	0.997143	+	0.0755352i	$0.0240665\pi$
$942$		0			0
$943$	28.7943	+	38.6774i	0.937671	+	1.25951i
$944$	−1.10669	−	1.91684i	−0.0360196	−	0.0623877i
$945$		0			0
$946$	−11.7324	+	20.3212i	−0.381454	+	0.660698i
$947$	−21.4807	+	2.51073i	−0.698029	+	0.0815879i	−0.457704	−	0.889105i	$-0.651328\pi$
$947$	−21.4807	+	2.51073i	−0.698029	+	0.0815879i	−0.240325	+	0.970692i	$0.577254\pi$
$948$		0			0
$949$	9.10404	−	2.15770i	0.295530	−	0.0700418i
$950$	−34.0327	+	22.3836i	−1.10417	+	0.726221i
$951$		0			0
$952$	−53.5459	+	56.7554i	−1.73543	+	1.83945i
$953$	16.8450	+	14.1347i	0.545665	+	0.457867i	0.873470	−	0.486878i	$-0.161865\pi$
$953$	16.8450	+	14.1347i	0.545665	+	0.457867i	−0.327805	+	0.944745i	$0.606309\pi$
$954$		0			0
$955$	47.9566	−	40.2403i	1.55184	−	1.30215i
$956$	−5.57001	+	95.6333i	−0.180147	+	3.09300i
$957$		0			0
$958$	22.0383	−	29.6025i	0.712024	−	0.956415i
$959$	−10.2966	−	1.20350i	−0.332496	−	0.0388632i
$960$		0			0
$961$	17.8462	+	11.7376i	0.575684	+	0.378633i
$962$	5.98936	+	2.17995i	0.193105	+	0.0702844i
$963$		0			0
$964$	107.463	−	39.1135i	3.46116	−	1.25976i
$965$	−52.1348	−	12.3562i	−1.67828	−	0.397759i
$966$		0			0
$967$	−1.38226	−	23.7325i	−0.0444505	−	0.763185i	−0.944725	−	0.327863i	$-0.893672\pi$
$967$	−1.38226	−	23.7325i	−0.0444505	−	0.763185i	0.900275	−	0.435322i	$-0.143366\pi$
$968$	−17.4264	−	18.4709i	−0.560105	−	0.593676i
$969$		0			0
$970$	4.87352	−	11.2981i	0.156479	−	0.362760i
$971$	−16.4980			−0.529445			−0.264723	−	0.964325i	$-0.585280\pi$
$971$	−16.4980			−0.529445			−0.264723	+	0.964325i	$0.585280\pi$
$972$		0			0
$973$	−10.9747			−0.351833
$974$	9.40067	−	21.7932i	0.301217	−	0.698299i
$975$		0			0
$976$	13.5317	+	14.3428i	0.433139	+	0.459100i
$977$	0.357579	+	6.13940i	0.0114400	+	0.196417i	0.999186	+	0.0403456i	$0.0128459\pi$
$977$	0.357579	+	6.13940i	0.0114400	+	0.196417i	−0.987746	+	0.156071i	$0.950117\pi$
$978$		0			0
$979$	−21.1908	−	5.02231i	−0.677260	−	0.160514i
$980$	19.1618	−	6.97433i	0.612101	−	0.222787i
$981$		0			0
$982$	−43.7990	−	15.9415i	−1.39768	−	0.508714i
$983$	−9.73833	−	6.40500i	−0.310604	−	0.204288i	0.384630	−	0.923071i	$-0.374329\pi$
$983$	−9.73833	−	6.40500i	−0.310604	−	0.204288i	−0.695234	+	0.718783i	$0.744699\pi$
$984$		0			0
$985$	−20.9245	−	2.44572i	−0.666710	−	0.0779272i
$986$	−22.8536	+	30.6978i	−0.727808	+	0.977616i
$987$		0			0
$988$	0.632818	−	10.8651i	0.0201326	−	0.345664i
$989$	23.3339	−	19.5795i	0.741976	−	0.622592i
$990$		0			0
$991$	−20.9608	−	17.5882i	−0.665840	−	0.558706i	0.245991	−	0.969272i	$-0.420887\pi$
$991$	−20.9608	−	17.5882i	−0.665840	−	0.558706i	−0.911831	+	0.410566i	$0.865331\pi$
$992$	−1.35271	+	1.43379i	−0.0429487	+	0.0455230i
$993$		0			0
$994$	−38.2832	+	25.1793i	−1.21427	+	0.798638i
$995$	−10.4989	+	2.48828i	−0.332836	+	0.0788836i
$996$		0			0
$997$	−54.2532	+	6.34129i	−1.71822	+	0.200831i	−0.917369	−	0.398037i	$-0.869691\pi$
$997$	−54.2532	+	6.34129i	−1.71822	+	0.200831i	−0.800848	+	0.598868i	$0.795617\pi$
$998$	−31.8177	+	55.1099i	−1.00717	+	1.74447i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.c.55.1		144
3.2	odd	2		729.2.g.b.55.8		144
9.2	odd	6		729.2.g.a.298.1		144
9.4	even	3		81.2.g.a.7.1	✓	144
9.5	odd	6		243.2.g.a.100.8		144
9.7	even	3		729.2.g.d.298.8		144
81.4	even	27		81.2.g.a.58.1	yes	144
81.23	odd	54		729.2.g.a.433.1		144
81.29	odd	54		6561.2.a.d.1.65		72
81.31	even	27	inner	729.2.g.c.676.1		144
81.50	odd	54		729.2.g.b.676.8		144
81.52	even	27		6561.2.a.c.1.8		72
81.58	even	27		729.2.g.d.433.8		144
81.77	odd	54		243.2.g.a.226.8		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.1	✓	144	9.4	even	3
81.2.g.a.58.1	yes	144	81.4	even	27
243.2.g.a.100.8		144	9.5	odd	6
243.2.g.a.226.8		144	81.77	odd	54
729.2.g.a.298.1		144	9.2	odd	6
729.2.g.a.433.1		144	81.23	odd	54
729.2.g.b.55.8		144	3.2	odd	2
729.2.g.b.676.8		144	81.50	odd	54
729.2.g.c.55.1		144	1.1	even	1	trivial
729.2.g.c.676.1		144	81.31	even	27	inner
729.2.g.d.298.8		144	9.7	even	3
729.2.g.d.433.8		144	81.58	even	27
6561.2.a.c.1.8		72	81.52	even	27
6561.2.a.d.1.65		72	81.29	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)

\(f(q)\)	\(=\)	\(q+(-0.964822 + 2.23671i) q^{2} +(-2.69950 - 2.86130i) q^{4} +(-0.171598 - 2.94623i) q^{5} +(2.22815 + 0.528081i) q^{7} +(4.42639 - 1.61107i) q^{8} +(6.75541 + 2.45877i) q^{10} +(-1.97872 - 1.30142i) q^{11} +(-0.609623 - 0.0712547i) q^{13} +(-3.33093 + 4.47422i) q^{14} +(-0.209720 + 3.60075i) q^{16} +(-5.54151 + 4.64988i) q^{17} +(-3.45309 - 2.89749i) q^{19} +(-7.96681 + 8.44433i) q^{20} +(4.82002 - 3.17018i) q^{22} +(-7.28714 + 1.72708i) q^{23} +(-3.68461 + 0.430669i) q^{25} +(0.747554 - 1.29480i) q^{26} +(-4.50389 - 7.80096i) q^{28} +(-1.29693 - 1.74208i) q^{29} +(-0.890466 + 2.97436i) q^{31} +(0.567355 + 0.284936i) q^{32} +(-5.05386 - 16.8811i) q^{34} +(1.17350 - 6.65525i) q^{35} +(0.740274 + 4.19830i) q^{37} +(9.81244 - 4.92800i) q^{38} +(-5.50614 - 12.7647i) q^{40} +(-2.55020 - 5.91203i) q^{41} +(-3.63470 + 1.82541i) q^{43} +(1.61778 + 9.17491i) q^{44} +(3.16781 - 17.9655i) q^{46} +(0.248155 + 0.828895i) q^{47} +(-1.56965 - 0.788307i) q^{49} +(2.59171 - 8.65691i) q^{50} +(1.44180 + 1.93667i) q^{52} +(-1.55323 - 2.69028i) q^{53} +(-3.49475 + 6.05308i) q^{55} +(10.7134 - 1.25222i) q^{56} +(5.14783 - 1.22006i) q^{58} +(-0.512703 + 0.337210i) q^{59} +(3.75166 - 3.97653i) q^{61} +(-5.79364 - 4.86144i) q^{62} +(-6.71074 + 5.63098i) q^{64} +(-0.105322 + 1.80831i) q^{65} +(0.168582 - 0.226445i) q^{67} +(28.2640 + 3.30359i) q^{68} +(13.7536 + 9.04591i) q^{70} +(7.71930 + 2.80960i) q^{71} +(-14.3245 + 5.21369i) q^{73} +(-10.1046 - 2.39484i) q^{74} +(1.03103 + 17.7021i) q^{76} +(-3.72163 - 3.94469i) q^{77} +(2.95265 - 6.84501i) q^{79} +10.6446 q^{80} +15.6840 q^{82} +(-2.16942 + 5.02929i) q^{83} +(14.6505 + 15.5286i) q^{85} +(-0.576083 - 9.89096i) q^{86} +(-10.8553 - 2.57274i) q^{88} +(8.64084 - 3.14501i) q^{89} +(-1.32070 - 0.480697i) q^{91} +(24.6133 + 16.1885i) q^{92} +(-2.09342 - 0.244686i) q^{94} +(-7.94410 + 10.6708i) q^{95} +(0.0995190 - 1.70867i) q^{97} +(3.27764 - 2.75027i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more