LMFDB - Embedded newform 729.2.g.a.352.5

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

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0693332 - 0.231589i) q^{2} +(1.62215 + 1.06690i) q^{4} +(1.68251 - 3.90051i) q^{5} +(0.0669917 + 1.15020i) q^{7} +(0.729927 - 0.612481i) q^{8} +(-0.786660 - 0.660086i) q^{10} +(-1.17914 + 1.58386i) q^{11} +(2.74852 - 2.91326i) q^{13} +(0.271019 + 0.0642327i) q^{14} +(1.44679 + 3.35403i) q^{16} +(0.731666 - 4.14948i) q^{17} +(0.525049 + 2.97770i) q^{19} +(6.89075 - 4.53212i) q^{20} +(0.285051 + 0.382890i) q^{22} +(-0.0709339 + 1.21789i) q^{23} +(-8.95188 - 9.48844i) q^{25} +(-0.484116 - 0.838513i) q^{26} +(-1.11849 + 1.93728i) q^{28} +(0.580763 - 0.137643i) q^{29} +(-1.73853 + 0.873122i) q^{31} +(2.76989 - 0.323753i) q^{32} +(-0.910246 - 0.457143i) q^{34} +(4.59909 + 1.67393i) q^{35} +(-4.95333 + 1.80287i) q^{37} +(0.726006 + 0.0848579i) q^{38} +(-1.16087 - 3.87759i) q^{40} +(1.64295 + 5.48784i) q^{41} +(-7.24960 - 0.847356i) q^{43} +(-3.60257 + 1.31123i) q^{44} +(0.277132 + 0.100868i) q^{46} +(0.390214 + 0.195973i) q^{47} +(5.63419 - 0.658542i) q^{49} +(-2.81808 + 1.41529i) q^{50} +(7.56669 - 1.79334i) q^{52} +(2.23695 - 3.87450i) q^{53} +(4.19394 + 7.26412i) q^{55} +(0.753377 + 0.798533i) q^{56} +(0.00838947 - 0.144042i) q^{58} +(-4.97611 - 6.68408i) q^{59} +(8.81180 - 5.79561i) q^{61} +(0.0816677 + 0.463161i) q^{62} +(-1.15153 + 6.53063i) q^{64} +(-6.73877 - 15.6222i) q^{65} +(7.12830 + 1.68944i) q^{67} +(5.61397 - 5.95046i) q^{68} +(0.706534 - 0.949039i) q^{70} +(3.66891 + 3.07858i) q^{71} +(5.52198 - 4.63349i) q^{73} +(0.0740935 + 1.27214i) q^{74} +(-2.32521 + 5.39045i) q^{76} +(-1.90076 - 1.25015i) q^{77} +(-3.61455 + 12.0734i) q^{79} +15.5167 q^{80} +1.38483 q^{82} +(-3.32012 + 11.0900i) q^{83} +(-14.9540 - 9.83543i) q^{85} +(-0.698876 + 1.62018i) q^{86} +(0.109399 + 1.87830i) q^{88} +(-8.43420 + 7.07713i) q^{89} +(3.53497 + 2.96620i) q^{91} +(-1.41444 + 1.89992i) q^{92} +(0.0724400 - 0.0767819i) q^{94} +(12.4979 + 2.96206i) q^{95} +(2.49045 + 5.77351i) q^{97} +(0.238125 - 1.35047i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0693332	−	0.231589i	0.0490260	−	0.163758i	−0.929971	−	0.367633i	$-0.880168\pi$
$2$	0.0693332	−	0.231589i	0.0490260	−	0.163758i	0.978997	+	0.203875i	$0.0653535\pi$
$3$		0			0
$3$		0			0
$4$	1.62215	+	1.06690i	0.811075	+	0.533452i
$5$	1.68251	−	3.90051i	0.752443	−	1.74436i	0.0891264	−	0.996020i	$-0.471593\pi$
$5$	1.68251	−	3.90051i	0.752443	−	1.74436i	0.663317	−	0.748339i	$-0.269148\pi$
$6$		0			0
$7$	0.0669917	+	1.15020i	0.0253205	+	0.434736i	0.987017	+	0.160618i	$0.0513488\pi$
$7$	0.0669917	+	1.15020i	0.0253205	+	0.434736i	−0.961696	+	0.274118i	$0.911614\pi$
$8$	0.729927	−	0.612481i	0.258068	−	0.216545i
$9$		0			0
$10$	−0.786660	−	0.660086i	−0.248764	−	0.208738i
$11$	−1.17914	+	1.58386i	−0.355524	+	0.477552i	−0.943522	−	0.331311i	$-0.892509\pi$
$11$	−1.17914	+	1.58386i	−0.355524	+	0.477552i	0.587997	+	0.808863i	$0.299917\pi$
$12$		0			0
$13$	2.74852	−	2.91326i	0.762303	−	0.807994i	−0.223711	−	0.974655i	$-0.571817\pi$
$13$	2.74852	−	2.91326i	0.762303	−	0.807994i	0.986014	+	0.166661i	$0.0532987\pi$
$14$	0.271019	+	0.0642327i	0.0724329	+	0.0171669i
$15$		0			0
$16$	1.44679	+	3.35403i	0.361697	+	0.838509i
$17$	0.731666	−	4.14948i	0.177455	−	1.00640i	−0.757817	−	0.652467i	$-0.773734\pi$
$17$	0.731666	−	4.14948i	0.177455	−	1.00640i	0.935272	−	0.353930i	$-0.115155\pi$
$18$		0			0
$19$	0.525049	+	2.97770i	0.120454	+	0.683131i	0.983904	+	0.178696i	$0.0571880\pi$
$19$	0.525049	+	2.97770i	0.120454	+	0.683131i	−0.863450	+	0.504435i	$0.831701\pi$
$20$	6.89075	−	4.53212i	1.54082	−	1.01341i
$21$		0			0
$22$	0.285051	+	0.382890i	0.0607731	+	0.0816325i
$23$	−0.0709339	+	1.21789i	−0.0147907	+	0.253947i	0.982805	+	0.184646i	$0.0591139\pi$
$23$	−0.0709339	+	1.21789i	−0.0147907	+	0.253947i	−0.997596	+	0.0693011i	$0.977923\pi$
$24$		0			0
$25$	−8.95188	−	9.48844i	−1.79038	−	1.89769i
$26$	−0.484116	−	0.838513i	−0.0949430	−	0.164446i
$27$		0			0
$28$	−1.11849	+	1.93728i	−0.211374	+	0.366111i
$29$	0.580763	−	0.137643i	0.107845	−	0.0255597i	−0.176339	−	0.984329i	$-0.556425\pi$
$29$	0.580763	−	0.137643i	0.107845	−	0.0255597i	0.284184	+	0.958770i	$0.408277\pi$
$30$		0			0
$31$	−1.73853	+	0.873122i	−0.312249	+	0.156817i	−0.598021	−	0.801480i	$-0.704046\pi$
$31$	−1.73853	+	0.873122i	−0.312249	+	0.156817i	0.285772	+	0.958298i	$0.407750\pi$
$32$	2.76989	−	0.323753i	0.489651	−	0.0572320i
$33$		0			0
$34$	−0.910246	−	0.457143i	−0.156106	−	0.0783993i
$35$	4.59909	+	1.67393i	0.777388	+	0.282946i
$36$		0			0
$37$	−4.95333	+	1.80287i	−0.814323	+	0.296389i	−0.715408	−	0.698706i	$-0.753759\pi$
$37$	−4.95333	+	1.80287i	−0.814323	+	0.296389i	−0.0989148	+	0.995096i	$0.531537\pi$
$38$	0.726006	+	0.0848579i	0.117774	+	0.0137658i
$39$		0			0
$40$	−1.16087	−	3.87759i	−0.183550	−	0.613101i
$41$	1.64295	+	5.48784i	0.256586	+	0.857057i	0.985094	+	0.172019i	$0.0550291\pi$
$41$	1.64295	+	5.48784i	0.256586	+	0.857057i	−0.728508	+	0.685038i	$0.759786\pi$
$42$		0			0
$43$	−7.24960	−	0.847356i	−1.10555	−	0.129221i	−0.456324	−	0.889814i	$-0.650834\pi$
$43$	−7.24960	−	0.847356i	−1.10555	−	0.129221i	−0.649229	+	0.760593i	$0.724908\pi$
$44$	−3.60257	+	1.31123i	−0.543108	+	0.197675i
$45$		0			0
$46$	0.277132	+	0.100868i	0.0408608	+	0.0148721i
$47$	0.390214	+	0.195973i	0.0569186	+	0.0285856i	0.477031	−	0.878887i	$-0.341713\pi$
$47$	0.390214	+	0.195973i	0.0569186	+	0.0285856i	−0.420112	+	0.907472i	$0.638009\pi$
$48$		0			0
$49$	5.63419	−	0.658542i	0.804884	−	0.0940775i
$50$	−2.81808	+	1.41529i	−0.398537	+	0.200153i
$51$		0			0
$52$	7.56669	−	1.79334i	1.04931	−	0.248691i
$53$	2.23695	−	3.87450i	0.307268	−	0.532204i	−0.670496	−	0.741913i	$-0.733919\pi$
$53$	2.23695	−	3.87450i	0.307268	−	0.532204i	0.977764	+	0.209710i	$0.0672518\pi$
$54$		0			0
$55$	4.19394	+	7.26412i	0.565511	+	0.979493i
$56$	0.753377	+	0.798533i	0.100674	+	0.106708i
$57$		0			0
$58$	0.00838947	−	0.144042i	0.00110159	−	0.0189136i
$59$	−4.97611	−	6.68408i	−0.647835	−	0.870193i	0.349947	−	0.936770i	$-0.386200\pi$
$59$	−4.97611	−	6.68408i	−0.647835	−	0.870193i	−0.997781	+	0.0665767i	$0.978792\pi$
$60$		0			0
$61$	8.81180	−	5.79561i	1.12823	−	0.742052i	0.158778	−	0.987314i	$-0.449245\pi$
$61$	8.81180	−	5.79561i	1.12823	−	0.742052i	0.969457	+	0.245263i	$0.0788742\pi$
$62$	0.0816677	+	0.463161i	0.0103718	+	0.0588215i
$63$		0			0
$64$	−1.15153	+	6.53063i	−0.143941	+	0.816329i
$65$	−6.73877	−	15.6222i	−0.835842	−	1.93770i
$66$		0			0
$67$	7.12830	+	1.68944i	0.870861	+	0.206398i	0.641667	−	0.766983i	$-0.278243\pi$
$67$	7.12830	+	1.68944i	0.870861	+	0.206398i	0.229194	+	0.973381i	$0.426391\pi$
$68$	5.61397	−	5.95046i	0.680794	−	0.721600i
$69$		0			0
$70$	0.706534	−	0.949039i	0.0844469	−	0.113432i
$71$	3.66891	+	3.07858i	0.435420	+	0.365361i	0.833992	−	0.551776i	$-0.186050\pi$
$71$	3.66891	+	3.07858i	0.435420	+	0.365361i	−0.398572	+	0.917137i	$0.630494\pi$
$72$		0			0
$73$	5.52198	−	4.63349i	0.646298	−	0.542309i	−0.259647	−	0.965704i	$-0.583606\pi$
$73$	5.52198	−	4.63349i	0.646298	−	0.542309i	0.905945	+	0.423395i	$0.139162\pi$
$74$	0.0740935	+	1.27214i	0.00861319	+	0.147883i
$75$		0			0
$76$	−2.32521	+	5.39045i	−0.266720	+	0.618327i
$77$	−1.90076	−	1.25015i	−0.216611	−	0.142467i
$78$		0			0
$79$	−3.61455	+	12.0734i	−0.406668	+	1.35837i	0.472280	+	0.881449i	$0.343431\pi$
$79$	−3.61455	+	12.0734i	−0.406668	+	1.35837i	−0.878948	+	0.476918i	$0.841754\pi$
$80$	15.5167			1.73482
$81$		0			0
$82$	1.38483			0.152929
$83$	−3.32012	+	11.0900i	−0.364431	+	1.21728i	0.557581	+	0.830122i	$0.311730\pi$
$83$	−3.32012	+	11.0900i	−0.364431	+	1.21728i	−0.922012	+	0.387161i	$0.873456\pi$
$84$		0			0
$85$	−14.9540	−	9.83543i	−1.62199	−	1.06680i
$86$	−0.698876	+	1.62018i	−0.0753617	+	0.174708i
$87$		0			0
$88$	0.109399	+	1.87830i	0.0116619	+	0.200228i
$89$	−8.43420	+	7.07713i	−0.894023	+	0.750174i	−0.969013	−	0.247010i	$-0.920552\pi$
$89$	−8.43420	+	7.07713i	−0.894023	+	0.750174i	0.0749899	+	0.997184i	$0.476108\pi$
$90$		0			0
$91$	3.53497	+	2.96620i	0.370566	+	0.310942i
$92$	−1.41444	+	1.89992i	−0.147465	+	0.198080i
$93$		0			0
$94$	0.0724400	−	0.0767819i	0.00747161	−	0.00791945i
$95$	12.4979	+	2.96206i	1.28226	+	0.303901i
$96$		0			0
$97$	2.49045	+	5.77351i	0.252867	+	0.586211i	0.996612	−	0.0822525i	$-0.0262114\pi$
$97$	2.49045	+	5.77351i	0.252867	+	0.586211i	−0.743745	+	0.668464i	$0.766952\pi$
$98$	0.238125	−	1.35047i	0.0240543	−	0.136419i
$99$		0			0
$100$	−4.39803	−	24.9425i	−0.439803	−	2.49425i
$101$	−3.38189	+	2.22431i	−0.336511	+	0.221327i	−0.706506	−	0.707707i	$-0.749730\pi$
$101$	−3.38189	+	2.22431i	−0.336511	+	0.221327i	0.369995	+	0.929034i	$0.379359\pi$
$102$		0			0
$103$	4.94733	+	6.64542i	0.487475	+	0.654793i	0.976003	−	0.217755i	$-0.0698734\pi$
$103$	4.94733	+	6.64542i	0.487475	+	0.654793i	−0.488528	+	0.872548i	$0.662466\pi$
$104$	0.221901	−	3.80989i	0.0217592	−	0.373590i
$105$		0			0
$106$	−0.742198	−	0.786684i	−0.0720886	−	0.0764095i
$107$	−7.95369	−	13.7762i	−0.768912	−	1.33179i	−0.938153	−	0.346220i	$-0.887465\pi$
$107$	−7.95369	−	13.7762i	−0.768912	−	1.33179i	0.169241	−	0.985575i	$-0.445868\pi$
$108$		0			0
$109$	1.81056	−	3.13598i	0.173420	−	0.300372i	−0.766193	−	0.642610i	$-0.777852\pi$
$109$	1.81056	−	3.13598i	0.173420	−	0.300372i	0.939613	+	0.342238i	$0.111185\pi$
$110$	1.97307	−	0.467626i	0.188125	−	0.0445864i
$111$		0			0
$112$	−3.76090	+	1.88879i	−0.355372	+	0.178474i
$113$	−9.43092	+	1.10232i	−0.887187	+	0.103697i	−0.547465	−	0.836829i	$-0.684407\pi$
$113$	−9.43092	+	1.10232i	−0.887187	+	0.103697i	−0.339722	+	0.940526i	$0.610333\pi$
$114$		0			0
$115$	4.63103	+	2.32579i	0.431846	+	0.216881i
$116$	1.08894	+	0.396341i	0.101105	+	0.0367993i
$117$		0			0
$118$	−1.89297	+	0.688984i	−0.174262	+	0.0634261i
$119$	4.82177	+	0.563584i	0.442011	+	0.0516636i
$120$		0			0
$121$	2.03659	+	6.80269i	0.185145	+	0.618426i
$122$	−0.731249	−	2.44254i	−0.0662042	−	0.221137i
$123$		0			0
$124$	−3.75169	−	0.438510i	−0.336912	−	0.0393794i
$125$	−32.1127	+	11.6881i	−2.87225	+	1.04541i
$126$		0			0
$127$	−10.4753	−	3.81269i	−0.929532	−	0.338322i	−0.167508	−	0.985871i	$-0.553572\pi$
$127$	−10.4753	−	3.81269i	−0.929532	−	0.338322i	−0.762024	+	0.647549i	$0.775794\pi$
$128$	6.41681	+	3.22264i	0.567171	+	0.284844i
$129$		0			0
$130$	−4.08516	+	0.477487i	−0.358292	+	0.0418783i
$131$	−10.8409	+	5.44450i	−0.947174	+	0.475689i	−0.854180	−	0.519978i	$-0.825940\pi$
$131$	−10.8409	+	5.44450i	−0.947174	+	0.475689i	−0.0929942	+	0.995667i	$0.529644\pi$
$132$		0			0
$133$	−3.38979	+	0.803394i	−0.293932	+	0.0696631i
$134$	0.885484	−	1.53370i	0.0764941	−	0.132492i
$135$		0			0
$136$	−2.00742	−	3.47695i	−0.172135	−	0.298146i
$137$	−0.205335	−	0.217643i	−0.0175430	−	0.0185945i	0.718543	−	0.695483i	$-0.244809\pi$
$137$	−0.205335	−	0.217643i	−0.0175430	−	0.0185945i	−0.736086	+	0.676888i	$0.763328\pi$
$138$		0			0
$139$	0.326168	−	5.60010i	0.0276652	−	0.474994i	−0.955814	−	0.293972i	$-0.905023\pi$
$139$	0.326168	−	5.60010i	0.0276652	−	0.474994i	0.983479	−	0.181021i	$-0.0579404\pi$
$140$	5.67448	+	7.62216i	0.479581	+	0.644190i
$141$		0			0
$142$	0.967343	−	0.636232i	0.0811777	−	0.0533914i
$143$	1.37331	+	7.78843i	0.114842	+	0.651301i
$144$		0			0
$145$	0.440263	−	2.49686i	0.0365619	−	0.207353i
$146$	−0.690209	−	1.60008i	−0.0571221	−	0.132424i
$147$		0			0
$148$	−9.95853	−	2.36022i	−0.818586	−	0.194009i
$149$	−9.35092	+	9.91140i	−0.766057	+	0.811973i	−0.986558	−	0.163413i	$-0.947750\pi$
$149$	−9.35092	+	9.91140i	−0.766057	+	0.811973i	0.220500	+	0.975387i	$0.429231\pi$
$150$		0			0
$151$	−5.64512	+	7.58271i	−0.459393	+	0.617072i	−0.970107	−	0.242679i	$-0.921974\pi$
$151$	−5.64512	+	7.58271i	−0.459393	+	0.617072i	0.510714	+	0.859751i	$0.329381\pi$
$152$	2.20703	+	1.85192i	0.179014	+	0.150211i
$153$		0			0
$154$	−0.421306	+	0.353517i	−0.0339498	+	0.0284872i
$155$	0.480519	+	8.25019i	0.0385962	+	0.662671i
$156$		0			0
$157$	−3.61315	+	8.37622i	−0.288361	+	0.668495i	−0.999399	−	0.0346581i	$-0.988966\pi$
$157$	−3.61315	+	8.37622i	−0.288361	+	0.668495i	0.711039	+	0.703153i	$0.248225\pi$
$158$	2.54546	+	1.67418i	0.202506	+	0.133190i
$159$		0			0
$160$	3.39757	−	11.3487i	0.268601	−	0.897191i
$161$	−1.40557			−0.110775
$162$		0			0
$163$	7.94158			0.622033			0.311016	−	0.950405i	$-0.399331\pi$
$163$	7.94158			0.622033			0.311016	+	0.950405i	$0.399331\pi$
$164$	−3.18989	+	10.6550i	−0.249088	+	0.832013i
$165$		0			0
$166$	2.33812	+	1.53781i	0.181474	+	0.119357i
$167$	1.76055	−	4.08141i	0.136235	−	0.315829i	−0.836418	−	0.548093i	$-0.815354\pi$
$167$	1.76055	−	4.08141i	0.136235	−	0.315829i	0.972653	+	0.232264i	$0.0746133\pi$
$168$		0			0
$169$	−0.176847	−	3.03634i	−0.0136036	−	0.233564i
$170$	−3.31459	+	2.78127i	−0.254217	+	0.213314i
$171$		0			0
$172$	−10.8559	−	9.10916i	−0.827753	−	0.694567i
$173$	−1.86223	+	2.50141i	−0.141583	+	0.190178i	−0.867258	−	0.497859i	$-0.834120\pi$
$173$	−1.86223	+	2.50141i	−0.141583	+	0.190178i	0.725676	+	0.688037i	$0.241527\pi$
$174$		0			0
$175$	10.3139	−	10.9321i	0.779660	−	0.826392i
$176$	−7.01829	−	1.66337i	−0.529024	−	0.125381i
$177$		0			0
$178$	1.05422	+	2.44395i	0.0790168	+	0.183182i
$179$	2.47200	−	14.0194i	0.184766	−	1.04786i	−0.741489	−	0.670965i	$-0.765880\pi$
$179$	2.47200	−	14.0194i	0.184766	−	1.04786i	0.926255	−	0.376897i	$-0.123009\pi$
$180$		0			0
$181$	2.75966	+	15.6508i	0.205124	+	1.16332i	0.897244	+	0.441535i	$0.145566\pi$
$181$	2.75966	+	15.6508i	0.205124	+	1.16332i	−0.692120	+	0.721783i	$0.743323\pi$
$182$	0.932029	−	0.613005i	0.0690866	−	0.0454390i
$183$		0			0
$184$	0.694157	+	0.932415i	0.0511740	+	0.0687386i
$185$	−1.30196	+	22.3539i	−0.0957223	+	1.64349i
$186$		0			0
$187$	5.70947	+	6.05168i	0.417518	+	0.442543i
$188$	0.423901	+	0.734219i	0.0309162	+	0.0535484i
$189$		0			0
$190$	1.55250	−	2.68901i	0.112630	−	0.195082i
$191$	−19.7601	+	4.68324i	−1.42979	+	0.338867i	−0.871344	−	0.490672i	$-0.836751\pi$
$191$	−19.7601	+	4.68324i	−1.42979	+	0.338867i	−0.558449	+	0.829539i	$0.688603\pi$
$192$		0			0
$193$	−2.38819	+	1.19939i	−0.171906	+	0.0863342i	−0.532671	−	0.846322i	$-0.678812\pi$
$193$	−2.38819	+	1.19939i	−0.171906	+	0.0863342i	0.360766	+	0.932657i	$0.382515\pi$
$194$	1.50975	−	0.176465i	0.108394	−	0.0126694i
$195$		0			0
$196$	9.84210	+	4.94289i	0.703007	+	0.353063i
$197$	15.7132	+	5.71915i	1.11952	+	0.407473i	0.834478	−	0.551042i	$-0.185770\pi$
$197$	15.7132	+	5.71915i	1.11952	+	0.407473i	0.285044	+	0.958514i	$0.407992\pi$
$198$		0			0
$199$	−1.83812	+	0.669021i	−0.130301	+	0.0474257i	−0.406348	−	0.913719i	$-0.633198\pi$
$199$	−1.83812	+	0.669021i	−0.130301	+	0.0474257i	0.276047	+	0.961144i	$0.410976\pi$
$200$	−12.3457	−	1.44301i	−0.872973	−	0.102036i
$201$		0			0
$202$	0.280647	+	0.937427i	0.0197463	+	0.0659572i
$203$	0.197224	+	0.658775i	0.0138424	+	0.0462369i
$204$		0			0
$205$	24.1696	+	2.82503i	1.68808	+	0.197308i
$206$	1.88202	−	0.685000i	0.131127	−	0.0477262i
$207$		0			0
$208$	13.7477	+	5.00376i	0.953233	+	0.346948i
$209$	−5.33537	−	2.67952i	−0.369055	−	0.185347i
$210$		0			0
$211$	−10.2942	+	1.20322i	−0.708684	+	0.0828333i	−0.462796	−	0.886465i	$-0.653154\pi$
$211$	−10.2942	+	1.20322i	−0.708684	+	0.0828333i	−0.245888	+	0.969298i	$0.579080\pi$
$212$	7.76238	−	3.89842i	0.533123	−	0.267744i
$213$		0			0
$214$	−3.74187	+	0.886839i	−0.255789	+	0.0606231i
$215$	−15.5027	+	26.8514i	−1.05727	+	1.83125i
$216$		0			0
$217$	−1.12074	−	1.94117i	−0.0760805	−	0.131775i
$218$	−0.600726	−	0.636732i	−0.0406863	−	0.0431249i
$219$		0			0
$220$	−0.946921	+	16.2580i	−0.0638414	+	1.09612i
$221$	−10.0775	−	13.5365i	−0.677889	−	0.910563i
$222$		0			0
$223$	−6.12253	+	4.02685i	−0.409995	+	0.269658i	−0.737709	−	0.675119i	$-0.764092\pi$
$223$	−6.12253	+	4.02685i	−0.409995	+	0.269658i	0.327714	+	0.944777i	$0.393722\pi$
$224$	0.557941	+	3.16424i	0.0372790	+	0.211420i
$225$		0			0
$226$	−0.398592	+	2.26052i	−0.0265139	+	0.150368i
$227$	9.21984	+	21.3740i	0.611942	+	1.41864i	0.889053	+	0.457804i	$0.151364\pi$
$227$	9.21984	+	21.3740i	0.611942	+	1.41864i	−0.277111	+	0.960838i	$0.589377\pi$
$228$		0			0
$229$	−0.0485690	−	0.0115111i	−0.00320953	−	0.000760672i	0.229011	−	0.973424i	$-0.426451\pi$
$229$	−0.0485690	−	0.0115111i	−0.00320953	−	0.000760672i	−0.232220	+	0.972663i	$0.574599\pi$
$230$	0.859712	−	0.911242i	0.0566878	−	0.0600855i
$231$		0			0
$232$	0.339610	−	0.456176i	0.0222965	−	0.0299494i
$233$	17.1664	+	14.4043i	1.12461	+	0.943660i	0.998828	−	0.0483977i	$-0.0154115\pi$
$233$	17.1664	+	14.4043i	1.12461	+	0.943660i	0.125782	+	0.992058i	$0.459856\pi$
$234$		0			0
$235$	1.42093	−	1.19231i	0.0926916	−	0.0777775i
$236$	−0.940724	−	16.1516i	−0.0612359	−	1.05138i
$237$		0			0
$238$	0.464828	−	1.07759i	0.0301303	−	0.0698500i
$239$	−17.1551	−	11.2831i	−1.10967	−	0.729844i	−0.143994	−	0.989579i	$-0.545994\pi$
$239$	−17.1551	−	11.2831i	−1.10967	−	0.729844i	−0.965680	+	0.259735i	$0.916365\pi$
$240$		0			0
$241$	8.25619	−	27.5776i	0.531828	−	1.77643i	−0.0930005	−	0.995666i	$-0.529646\pi$
$241$	8.25619	−	27.5776i	0.531828	−	1.77643i	0.624828	−	0.780762i	$-0.285169\pi$
$242$	1.71663			0.110349
$243$		0			0
$244$	20.4774			1.31093
$245$	6.91095	−	23.0842i	0.441525	−	1.47479i
$246$		0			0
$247$	10.1179	+	6.65467i	0.643789	+	0.423426i
$248$	−0.734228	+	1.70213i	−0.0466235	+	0.108085i
$249$		0			0
$250$	0.480352	+	8.24732i	0.0303801	+	0.521606i
$251$	7.80826	−	6.55190i	0.492853	−	0.413553i	−0.362195	−	0.932102i	$-0.617972\pi$
$251$	7.80826	−	6.55190i	0.492853	−	0.413553i	0.855047	+	0.518550i	$0.173528\pi$
$252$		0			0
$253$	−1.84533	−	1.54841i	−0.116015	−	0.0973479i
$254$	−1.60926	+	2.16162i	−0.100974	+	0.135632i
$255$		0			0
$256$	−7.91023	+	8.38436i	−0.494390	+	0.524022i
$257$	−5.89713	−	1.39764i	−0.367853	−	0.0871827i	0.0425323	−	0.999095i	$-0.486457\pi$
$257$	−5.89713	−	1.39764i	−0.367853	−	0.0871827i	−0.410385	+	0.911912i	$0.634606\pi$
$258$		0			0
$259$	−2.40550	−	5.57657i	−0.149470	−	0.346511i
$260$	5.73613	−	32.5312i	0.355740	−	2.01750i
$261$		0			0
$262$	0.509253	+	2.88812i	0.0314618	+	0.178429i
$263$	11.2105	−	7.37325i	0.691268	−	0.454654i	−0.154648	−	0.987970i	$-0.549424\pi$
$263$	11.2105	−	7.37325i	0.691268	−	0.454654i	0.845916	+	0.533315i	$0.179054\pi$
$264$		0			0
$265$	−11.3488	−	15.2441i	−0.697153	−	0.936439i
$266$	−0.0489675	+	0.840739i	−0.00300239	+	0.0515490i
$267$		0			0
$268$	9.76070	+	10.3457i	0.596230	+	0.631967i
$269$	−1.44120	−	2.49623i	−0.0878715	−	0.152198i	0.818740	−	0.574165i	$-0.194673\pi$
$269$	−1.44120	−	2.49623i	−0.0878715	−	0.152198i	−0.906611	+	0.421967i	$0.861340\pi$
$270$		0			0
$271$	−1.60573	+	2.78120i	−0.0975410	+	0.168946i	−0.910666	−	0.413143i	$-0.864431\pi$
$271$	−1.60573	+	2.78120i	−0.0975410	+	0.168946i	0.813125	+	0.582089i	$0.197764\pi$
$272$	14.9761	−	3.54940i	0.908058	−	0.215214i
$273$		0			0
$274$	−0.0646403	+	0.0324636i	−0.00390506	+	0.00196120i
$275$	25.5839	−	2.99033i	1.54277	−	0.180324i
$276$		0			0
$277$	−3.04397	−	1.52874i	−0.182894	−	0.0918529i	0.354996	−	0.934868i	$-0.384482\pi$
$277$	−3.04397	−	1.52874i	−0.182894	−	0.0918529i	−0.537890	+	0.843015i	$0.680779\pi$
$278$	−1.27431	−	0.463810i	−0.0764278	−	0.0278174i
$279$		0			0
$280$	4.38225	−	1.59501i	0.261889	−	0.0953200i
$281$	−11.4072	−	1.33331i	−0.680497	−	0.0795387i	−0.231180	−	0.972911i	$-0.574259\pi$
$281$	−11.4072	−	1.33331i	−0.680497	−	0.0795387i	−0.449317	+	0.893372i	$0.648333\pi$
$282$		0			0
$283$	−7.26806	−	24.2770i	−0.432041	−	1.44312i	−0.846176	−	0.532903i	$-0.821101\pi$
$283$	−7.26806	−	24.2770i	−0.432041	−	1.44312i	0.414135	−	0.910216i	$-0.364084\pi$
$284$	2.66697	+	8.90830i	0.158256	+	0.528610i
$285$		0			0
$286$	1.89893	+	0.221953i	0.112286	+	0.0131244i
$287$	−6.20207	+	2.25737i	−0.366097	+	0.133248i
$288$		0			0
$289$	−0.708104	−	0.257729i	−0.0416532	−	0.0151605i
$290$	−0.547720	−	0.275075i	−0.0321632	−	0.0161530i
$291$		0			0
$292$	13.9010	−	1.62479i	0.813492	−	0.0950836i
$293$	3.58895	−	1.80244i	0.209669	−	0.105300i	−0.340866	−	0.940112i	$-0.610720\pi$
$293$	3.58895	−	1.80244i	0.209669	−	0.105300i	0.550535	+	0.834812i	$0.314424\pi$
$294$		0			0
$295$	−34.4437	+	8.16330i	−2.00539	+	0.475286i
$296$	−2.51135	+	4.34978i	−0.145969	+	0.252826i
$297$		0			0
$298$	1.64704	+	2.85276i	0.0954106	+	0.165256i
$299$	3.35307	+	3.55404i	0.193913	+	0.205536i
$300$		0			0
$301$	0.488969	−	8.39528i	0.0281837	−	0.483896i
$302$	1.36468	+	1.83308i	0.0785284	+	0.105482i
$303$		0			0
$304$	−9.22767	+	6.06913i	−0.529243	+	0.348089i
$305$	−7.77984	−	44.1216i	−0.445472	−	2.52640i
$306$		0			0
$307$	3.45206	−	19.5776i	0.197020	−	1.11735i	−0.712493	−	0.701679i	$-0.752434\pi$
$307$	3.45206	−	19.5776i	0.197020	−	1.11735i	0.909513	−	0.415675i	$-0.136455\pi$
$308$	−1.74952	−	4.05585i	−0.0996883	−	0.231103i
$309$		0			0
$310$	1.94397	+	0.460729i	0.110410	+	0.0261676i
$311$	1.05969	−	1.12320i	0.0600893	−	0.0636909i	−0.696632	−	0.717429i	$-0.745319\pi$
$311$	1.05969	−	1.12320i	0.0600893	−	0.0636909i	0.756721	+	0.653738i	$0.226800\pi$
$312$		0			0
$313$	−10.4498	+	14.0365i	−0.590656	+	0.793389i	−0.992490	−	0.122324i	$-0.960965\pi$
$313$	−10.4498	+	14.0365i	−0.590656	+	0.793389i	0.401834	+	0.915712i	$0.368373\pi$
$314$	1.68933	+	1.41751i	0.0953343	+	0.0799950i
$315$		0			0
$316$	−18.7445	+	15.7285i	−1.05446	+	0.884799i
$317$	0.114225	+	1.96117i	0.00641553	+	0.110150i	0.999996	−	0.00298109i	$-0.000948911\pi$
$317$	0.114225	+	1.96117i	0.00641553	+	0.110150i	−0.993580	+	0.113131i	$0.963912\pi$
$318$		0			0
$319$	−0.466794	+	1.08215i	−0.0261354	+	0.0605887i
$320$	23.5353	+	15.4794i	1.31566	+	0.865326i
$321$		0			0
$322$	−0.0974528	+	0.325515i	−0.00543083	+	0.0181402i
$323$	12.7401			0.708877
$324$		0			0
$325$	−52.2468			−2.89813
$326$	0.550615	−	1.83918i	0.0304958	−	0.101863i
$327$		0			0
$328$	4.56043	+	2.99944i	0.251808	+	0.165617i
$329$	−0.199268	+	0.461954i	−0.0109860	+	0.0254684i
$330$		0			0
$331$	−2.00496	−	34.4239i	−0.110203	−	1.89211i	−0.373849	−	0.927490i	$-0.621962\pi$
$331$	−2.00496	−	34.4239i	−0.110203	−	1.89211i	0.263646	−	0.964619i	$-0.415075\pi$
$332$	−17.2177	+	14.4474i	−0.944943	+	0.792901i
$333$		0			0
$334$	−0.823144	−	0.690700i	−0.0450405	−	0.0377934i
$335$	18.5831	−	24.9615i	1.01531	−	1.36379i
$336$		0			0
$337$	−11.1007	+	11.7661i	−0.604694	+	0.640938i	−0.955319	−	0.295578i	$-0.904488\pi$
$337$	−11.1007	+	11.7661i	−0.604694	+	0.640938i	0.350625	+	0.936516i	$0.385969\pi$
$338$	−0.715444	−	0.169563i	−0.0389150	−	0.00922303i
$339$		0			0
$340$	−13.7642	−	31.9091i	−0.746470	−	1.73051i
$341$	0.667067	−	3.78313i	0.0361237	−	0.204868i
$342$		0			0
$343$	2.53539	+	14.3789i	0.136898	+	0.776387i
$344$	−5.81066	+	3.82173i	−0.313290	+	0.206054i
$345$		0			0
$346$	0.450184	+	0.604702i	0.0242020	+	0.0325090i
$347$	1.84987	−	31.7610i	0.0993060	−	1.70502i	−0.469815	−	0.882765i	$-0.655679\pi$
$347$	1.84987	−	31.7610i	0.0993060	−	1.70502i	0.569121	−	0.822254i	$-0.307284\pi$
$348$		0			0
$349$	11.8962	+	12.6092i	0.636789	+	0.674957i	0.962740	−	0.270430i	$-0.0871658\pi$
$349$	11.8962	+	12.6092i	0.636789	+	0.674957i	−0.325950	+	0.945387i	$0.605684\pi$
$350$	−1.81666	−	3.14655i	−0.0971048	−	0.168190i
$351$		0			0
$352$	−2.75331	+	4.76887i	−0.146752	+	0.254181i
$353$	3.30817	−	0.784050i	0.176076	−	0.0417308i	−0.141632	−	0.989919i	$-0.545235\pi$
$353$	3.30817	−	0.784050i	0.176076	−	0.0417308i	0.317708	+	0.948189i	$0.397087\pi$
$354$		0			0
$355$	18.1810	−	9.13085i	0.964949	−	0.484615i
$356$	−21.2321	+	2.48168i	−1.12530	+	0.131529i
$357$		0			0
$358$	−3.07535	−	1.54450i	−0.162538	−	0.0816294i
$359$	−9.53489	−	3.47042i	−0.503232	−	0.183162i	0.0779150	−	0.996960i	$-0.475174\pi$
$359$	−9.53489	−	3.47042i	−0.503232	−	0.183162i	−0.581147	+	0.813798i	$0.697396\pi$
$360$		0			0
$361$	9.26314	−	3.37151i	0.487534	−	0.177448i
$362$	3.81590	+	0.446015i	0.200559	+	0.0234420i
$363$		0			0
$364$	2.56961	+	8.58309i	0.134684	+	0.449876i
$365$	−8.78215	−	29.3344i	−0.459678	−	1.53543i
$366$		0			0
$367$	−14.7635	−	1.72560i	−0.770646	−	0.0900756i	−0.278322	−	0.960488i	$-0.589778\pi$
$367$	−14.7635	−	1.72560i	−0.770646	−	0.0900756i	−0.492324	+	0.870412i	$0.663852\pi$
$368$	−4.18747	+	1.52411i	−0.218287	+	0.0794499i
$369$		0			0
$370$	5.08664	+	1.85138i	0.264442	+	0.0962489i
$371$	4.60632	+	2.31338i	0.239148	+	0.120105i
$372$		0			0
$373$	20.9383	−	2.44734i	1.08415	−	0.126718i	0.444794	−	0.895633i	$-0.353277\pi$
$373$	20.9383	−	2.44734i	1.08415	−	0.126718i	0.639351	+	0.768915i	$0.279203\pi$
$374$	1.79736	−	0.902668i	0.0929392	−	0.0466758i
$375$		0			0
$376$	0.404858	−	0.0959530i	0.0208789	−	0.00494840i
$377$	1.19525	−	2.07023i	0.0615585	−	0.106622i
$378$		0			0
$379$	−3.47462	−	6.01822i	−0.178479	−	0.309135i	0.762880	−	0.646540i	$-0.223784\pi$
$379$	−3.47462	−	6.01822i	−0.178479	−	0.309135i	−0.941360	+	0.337404i	$0.890451\pi$
$380$	17.1133	+	18.1390i	0.877893	+	0.930512i
$381$		0			0
$382$	−0.285447	+	4.90093i	−0.0146047	+	0.250754i
$383$	21.0990	+	28.3409i	1.07811	+	1.44815i	0.884187	+	0.467134i	$0.154713\pi$
$383$	21.0990	+	28.3409i	1.07811	+	1.44815i	0.193922	+	0.981017i	$0.437879\pi$
$384$		0			0
$385$	−8.07425	+	5.31052i	−0.411502	+	0.270649i
$386$	0.112186	+	0.636236i	0.00571010	+	0.0323836i
$387$		0			0
$388$	−2.11990	+	12.0226i	−0.107622	+	0.610354i
$389$	10.1886	+	23.6198i	0.516582	+	1.19757i	0.954406	+	0.298512i	$0.0964902\pi$
$389$	10.1886	+	23.6198i	0.516582	+	1.19757i	−0.437823	+	0.899061i	$0.644251\pi$
$390$		0			0
$391$	5.00171	+	1.18543i	0.252947	+	0.0599496i
$392$	3.70920	−	3.93152i	0.187343	−	0.198572i
$393$		0			0
$394$	2.41394	−	3.24249i	0.121613	−	0.163354i
$395$	41.0109	+	34.4123i	2.06348	+	1.73147i
$396$		0			0
$397$	14.2470	−	11.9547i	0.715038	−	0.599988i	−0.210970	−	0.977493i	$-0.567662\pi$
$397$	14.2470	−	11.9547i	0.715038	−	0.599988i	0.926008	+	0.377504i	$0.123218\pi$
$398$	0.0274952	+	0.472074i	0.00137821	+	0.0236629i
$399$		0			0
$400$	18.8731	−	43.7527i	0.943653	−	2.18763i
$401$	−3.86305	−	2.54077i	−0.192912	−	0.126880i	0.449379	−	0.893341i	$-0.351645\pi$
$401$	−3.86305	−	2.54077i	−0.192912	−	0.126880i	−0.642290	+	0.766461i	$0.722016\pi$
$402$		0			0
$403$	−2.23475	+	7.46459i	−0.111321	+	0.371838i
$404$	−7.85906			−0.391003
$405$		0			0
$406$	0.166239			0.00825031
$407$	2.98519	−	9.97123i	0.147970	−	0.494256i
$408$		0			0
$409$	9.13943	+	6.01109i	0.451916	+	0.297230i	0.754989	−	0.655738i	$-0.227642\pi$
$409$	9.13943	+	6.01109i	0.451916	+	0.297230i	−0.303073	+	0.952967i	$0.598013\pi$
$410$	2.33000	−	5.40156i	0.115071	−	0.266764i
$411$		0			0
$412$	0.935284	+	16.0582i	0.0460781	+	0.791131i
$413$	7.35469	−	6.17132i	0.361901	−	0.303671i
$414$		0			0
$415$	37.6704	+	31.6092i	1.84917	+	1.55163i
$416$	6.66991	−	8.95925i	0.327019	−	0.439263i
$417$		0			0
$418$	−0.990466	+	1.04983i	−0.0484453	+	0.0513490i
$419$	32.6371	+	7.73513i	1.59443	+	0.377886i	0.929441	−	0.368971i	$-0.120290\pi$
$419$	32.6371	+	7.73513i	1.59443	+	0.377886i	0.664985	+	0.746857i	$0.268438\pi$
$420$		0			0
$421$	0.656955	+	1.52299i	0.0320180	+	0.0742262i	0.933475	−	0.358643i	$-0.116760\pi$
$421$	0.656955	+	1.52299i	0.0320180	+	0.0742262i	−0.901457	+	0.432869i	$0.857501\pi$
$422$	−0.435079	+	2.46745i	−0.0211793	+	0.120114i
$423$		0			0
$424$	−0.740254	−	4.19819i	−0.0359499	−	0.203882i
$425$	−45.9219	+	30.2033i	−2.22754	+	1.46508i
$426$		0			0
$427$	7.25645	+	9.74710i	0.351164	+	0.471695i
$428$	1.79581	−	30.8329i	0.0868037	−	1.49036i
$429$		0			0
$430$	5.14364	+	5.45194i	0.248048	+	0.262916i
$431$	−7.55425	−	13.0843i	−0.363876	−	0.630251i	0.624720	−	0.780849i	$-0.285213\pi$
$431$	−7.55425	−	13.0843i	−0.363876	−	0.630251i	−0.988595	+	0.150598i	$0.951880\pi$
$432$		0			0
$433$	−2.46655	+	4.27218i	−0.118535	+	0.205308i	−0.919187	−	0.393821i	$-0.871153\pi$
$433$	−2.46655	+	4.27218i	−0.118535	+	0.205308i	0.800653	+	0.599129i	$0.204486\pi$
$434$	−0.527258	+	0.124962i	−0.0253092	+	0.00599839i
$435$		0			0
$436$	6.28278	−	3.15533i	0.300891	−	0.151113i
$437$	−3.66375	+	0.428231i	−0.175261	+	0.0204851i
$438$		0			0
$439$	−18.0341	−	9.05705i	−0.860719	−	0.432269i	−0.0370321	−	0.999314i	$-0.511790\pi$
$439$	−18.0341	−	9.05705i	−0.860719	−	0.432269i	−0.823687	+	0.567045i	$0.808087\pi$
$440$	7.51040	+	2.73356i	0.358044	+	0.130318i
$441$		0			0
$442$	−3.83361	+	1.39532i	−0.182346	+	0.0663686i
$443$	27.9957	+	3.27223i	1.33012	+	0.155468i	0.751285	−	0.659978i	$-0.229434\pi$
$443$	27.9957	+	3.27223i	1.33012	+	0.155468i	0.578833	+	0.815446i	$0.303508\pi$
$444$		0			0
$445$	13.4137	+	44.8050i	0.635872	+	2.12396i
$446$	0.508080	+	1.69711i	0.0240583	+	0.0803603i
$447$		0			0
$448$	−7.58870	−	0.886992i	−0.358532	−	0.0419064i
$449$	0.407937	−	0.148477i	0.0192517	−	0.00700706i	−0.332376	−	0.943147i	$-0.607850\pi$
$449$	0.407937	−	0.148477i	0.0192517	−	0.00700706i	0.351628	+	0.936140i	$0.385628\pi$
$450$		0			0
$451$	−10.6293	−	3.86873i	−0.500512	−	0.182171i
$452$	−16.4744	−	8.27377i	−0.774892	−	0.389165i
$453$		0			0
$454$	5.58922	−	0.653286i	0.262315	−	0.0306602i
$455$	17.5173	−	8.79752i	0.821224	−	0.412434i
$456$		0			0
$457$	26.3714	−	6.25014i	1.23360	−	0.292369i	0.438437	−	0.898762i	$-0.355532\pi$
$457$	26.3714	−	6.25014i	1.23360	−	0.292369i	0.795165	+	0.606393i	$0.207384\pi$
$458$	−0.00603328	+	0.0104499i	−0.000281917	+	0.000488294i
$459$		0			0
$460$	5.03083	+	8.71365i	0.234564	+	0.406276i
$461$	−29.3205	−	31.0779i	−1.36559	−	1.44744i	−0.755590	−	0.655045i	$-0.772650\pi$
$461$	−29.3205	−	31.0779i	−1.36559	−	1.44744i	−0.610003	−	0.792399i	$-0.708832\pi$
$462$		0			0
$463$	1.76421	−	30.2903i	0.0819897	−	1.40771i	−0.666966	−	0.745088i	$-0.732407\pi$
$463$	1.76421	−	30.2903i	0.0819897	−	1.40771i	0.748956	−	0.662620i	$-0.230556\pi$
$464$	1.30190	+	1.74876i	0.0604393	+	0.0811841i
$465$		0			0
$466$	4.52609	−	2.97686i	0.209667	−	0.137900i
$467$	−2.33662	−	13.2516i	−0.108126	−	0.613212i	−0.989926	−	0.141588i	$-0.954779\pi$
$467$	−2.33662	−	13.2516i	−0.108126	−	0.613212i	0.881800	−	0.471624i	$-0.156332\pi$
$468$		0			0
$469$	−1.46566	+	8.31218i	−0.0676779	+	0.383821i
$470$	−0.177607	−	0.411739i	−0.00819240	−	0.0189921i
$471$		0			0
$472$	−7.72607	−	1.83111i	−0.355621	−	0.0842838i
$473$	9.89039	−	10.4832i	0.454761	−	0.482018i
$474$		0			0
$475$	23.5536	−	31.6379i	1.08071	−	1.45165i
$476$	7.22033	+	6.05858i	0.330943	+	0.277695i
$477$		0			0
$478$	−3.80246	+	3.19065i	−0.173921	+	0.145937i
$479$	−1.51040	−	25.9325i	−0.0690118	−	1.18489i	−0.838017	−	0.545644i	$-0.816285\pi$
$479$	−1.51040	−	25.9325i	−0.0690118	−	1.18489i	0.769005	−	0.639243i	$-0.220752\pi$
$480$		0			0
$481$	−8.36213	+	19.3856i	−0.381280	+	0.883907i
$482$	−5.81424	−	3.82408i	−0.264831	−	0.174182i
$483$		0			0
$484$	−3.95416	+	13.2078i	−0.179735	+	0.600356i
$485$	26.7098			1.21283
$486$		0			0
$487$	2.70578			0.122611			0.0613053	−	0.998119i	$-0.480474\pi$
$487$	2.70578			0.122611			0.0613053	+	0.998119i	$0.480474\pi$
$488$	2.88226	−	9.62743i	0.130474	−	0.435813i
$489$		0			0
$490$	−4.86689	−	3.20100i	−0.219863	−	0.144606i
$491$	−15.7670	+	36.5520i	−0.711554	+	1.64957i	0.0477722	+	0.998858i	$0.484788\pi$
$491$	−15.7670	+	36.5520i	−0.711554	+	1.64957i	−0.759326	+	0.650710i	$0.774471\pi$
$492$		0			0
$493$	−0.146224	−	2.51058i	−0.00658561	−	0.113071i
$494$	2.24266	−	1.88181i	0.100902	−	0.0846667i
$495$		0			0
$496$	−5.44377	−	4.56786i	−0.244432	−	0.205103i
$497$	−3.29521	+	4.42624i	−0.147810	+	0.198544i
$498$		0			0
$499$	−1.70556	+	1.80779i	−0.0763516	+	0.0809279i	−0.764423	−	0.644715i	$-0.776976\pi$
$499$	−1.70556	+	1.80779i	−0.0763516	+	0.0809279i	0.688071	+	0.725643i	$0.258458\pi$
$500$	−64.5616	−	15.3014i	−2.88728	−	0.684299i
$501$		0			0
$502$	−0.975978	−	2.26257i	−0.0435600	−	0.100983i
$503$	2.56729	−	14.5598i	0.114470	−	0.649191i	−0.872541	−	0.488540i	$-0.837530\pi$
$503$	2.56729	−	14.5598i	0.114470	−	0.649191i	0.987011	−	0.160651i	$-0.0513594\pi$
$504$		0			0
$505$	2.98584	+	16.9335i	0.132868	+	0.753532i
$506$	−0.486538	+	0.320001i	−0.0216292	+	0.0142258i
$507$		0			0
$508$	−12.9247	−	17.3609i	−0.573441	−	0.770265i
$509$	−1.39600	+	23.9683i	−0.0618764	+	1.06238i	0.814318	+	0.580419i	$0.197111\pi$
$509$	−1.39600	+	23.9683i	−0.0618764	+	1.06238i	−0.876194	+	0.481958i	$0.839926\pi$
$510$		0			0
$511$	5.69938	+	6.04099i	0.252126	+	0.267238i
$512$	8.57387	+	14.8504i	0.378915	+	0.656300i
$513$		0			0
$514$	−0.732546	+	1.26881i	−0.0323112	+	0.0559646i
$515$	34.2445	−	8.11609i	1.50899	−	0.357638i
$516$		0			0
$517$	−0.770512	+	0.386966i	−0.0338871	+	0.0170187i
$518$	−1.45825	+	0.170445i	−0.0640719	+	0.00748893i
$519$		0			0
$520$	−14.4871	−	7.27571i	−0.635303	−	0.319061i
$521$	−18.5919	−	6.76690i	−0.814526	−	0.296463i	−0.0990342	−	0.995084i	$-0.531575\pi$
$521$	−18.5919	−	6.76690i	−0.814526	−	0.296463i	−0.715492	+	0.698621i	$0.753798\pi$
$522$		0			0
$523$	32.2975	−	11.7553i	1.41227	−	0.514025i	0.480477	−	0.877007i	$-0.340464\pi$
$523$	32.2975	−	11.7553i	1.41227	−	0.514025i	0.931796	+	0.362982i	$0.118241\pi$
$524$	−23.3943	−	2.73440i	−1.02199	−	0.119453i
$525$		0			0
$526$	−0.930305	−	3.10744i	−0.0405632	−	0.135491i
$527$	2.35098	+	7.85283i	0.102410	+	0.342075i
$528$		0			0
$529$	21.3663	+	2.49736i	0.928968	+	0.108581i
$530$	−4.31722	+	1.57134i	−0.187528	+	0.0682547i
$531$		0			0
$532$	−6.35588	−	2.31335i	−0.275563	−	0.100297i
$533$	20.5032	+	10.2971i	0.888093	+	0.446017i
$534$		0			0
$535$	−67.1163	+	7.84477i	−2.90169	+	0.339159i
$536$	6.23789	−	3.13279i	0.269436	−	0.135316i
$537$		0			0
$538$	−0.678023	+	0.160694i	−0.0292316	+	0.00692803i
$539$	−5.60046	+	9.70029i	−0.241229	+	0.417821i
$540$		0			0
$541$	−18.0270	−	31.2237i	−0.775042	−	1.34241i	−0.934771	−	0.355252i	$-0.884395\pi$
$541$	−18.0270	−	31.2237i	−0.775042	−	1.34241i	0.159728	−	0.987161i	$-0.448938\pi$
$542$	0.532766	+	0.564699i	0.0228842	+	0.0242559i
$543$		0			0
$544$	0.683222	−	11.7305i	0.0292929	−	0.502940i
$545$	−9.18560	−	12.3384i	−0.393468	−	0.528519i
$546$		0			0
$547$	−7.21874	+	4.74784i	−0.308651	+	0.203003i	−0.694379	−	0.719610i	$-0.744321\pi$
$547$	−7.21874	+	4.74784i	−0.308651	+	0.203003i	0.385728	+	0.922613i	$0.373950\pi$
$548$	−0.100881	−	0.572123i	−0.00430941	−	0.0244399i
$549$		0			0
$550$	1.08129	−	6.13228i	0.0461062	−	0.261481i
$551$	0.714789	+	1.65707i	0.0304511	+	0.0705935i
$552$		0			0
$553$	−14.1290	−	3.34864i	−0.600828	−	0.142399i
$554$	−0.565086	+	0.598957i	−0.0240082	+	0.0254472i
$555$		0			0
$556$	6.50386	−	8.73620i	0.275825	−	0.370497i
$557$	−16.3664	−	13.7330i	−0.693466	−	0.581887i	0.226441	−	0.974025i	$-0.427291\pi$
$557$	−16.3664	−	13.7330i	−0.693466	−	0.581887i	−0.919906	+	0.392138i	$0.871736\pi$
$558$		0			0
$559$	−22.3943	+	18.7910i	−0.947176	+	0.794775i
$560$	1.03949	+	17.8473i	0.0439264	+	0.754187i
$561$		0			0
$562$	−1.09968	+	2.54934i	−0.0463871	+	0.107537i
$563$	23.1111	+	15.2004i	0.974018	+	0.640621i	0.933508	−	0.358558i	$-0.116731\pi$
$563$	23.1111	+	15.2004i	0.974018	+	0.640621i	0.0405100	+	0.999179i	$0.487102\pi$
$564$		0			0
$565$	−11.5681	+	38.6400i	−0.486672	+	1.62560i
$566$	−6.12621			−0.257504
$567$		0			0
$568$	4.56361			0.191485
$569$	6.34020	−	21.1777i	0.265795	−	0.887817i	−0.716037	−	0.698063i	$-0.754046\pi$
$569$	6.34020	−	21.1777i	0.265795	−	0.887817i	0.981832	−	0.189754i	$-0.0607691\pi$
$570$		0			0
$571$	−1.77808	−	1.16946i	−0.0744104	−	0.0489405i	0.511759	−	0.859129i	$-0.328994\pi$
$571$	−1.77808	−	1.16946i	−0.0744104	−	0.0489405i	−0.586169	+	0.810189i	$0.699365\pi$
$572$	−6.08179	+	14.0992i	−0.254293	+	0.589517i
$573$		0			0
$574$	0.0927725	+	1.59284i	0.00387225	+	0.0664839i
$575$	12.1909	−	10.2293i	0.508394	−	0.426593i
$576$		0			0
$577$	−15.8954	−	13.3378i	−0.661733	−	0.555260i	0.248872	−	0.968536i	$-0.419940\pi$
$577$	−15.8954	−	13.3378i	−0.661733	−	0.555260i	−0.910606	+	0.413276i	$0.864384\pi$
$578$	−0.108782	+	0.146120i	−0.00452475	+	0.00607779i
$579$		0			0
$580$	3.37808	−	3.58056i	0.140267	−	0.148674i
$581$	−12.9782	−	3.07588i	−0.538425	−	0.127609i
$582$		0			0
$583$	3.49900	+	8.11160i	0.144914	+	0.335948i
$584$	1.19271	−	6.76421i	0.0493548	−	0.279905i
$585$		0			0
$586$	−0.168592	−	0.956131i	−0.00696446	−	0.0394974i
$587$	9.81262	−	6.45386i	0.405010	−	0.266379i	−0.330618	−	0.943765i	$-0.607257\pi$
$587$	9.81262	−	6.45386i	0.405010	−	0.266379i	0.735629	+	0.677385i	$0.236887\pi$
$588$		0			0
$589$	−3.51271	−	4.71839i	−0.144739	−	0.194418i
$590$	−0.497559	+	8.54276i	−0.0204842	+	0.351700i
$591$		0			0
$592$	−13.2133	−	14.0053i	−0.543064	−	0.575614i
$593$	−10.8840	−	18.8516i	−0.446952	−	0.774144i	0.551234	−	0.834351i	$-0.314157\pi$
$593$	−10.8840	−	18.8516i	−0.446952	−	0.774144i	−0.998186	+	0.0602070i	$0.980824\pi$
$594$		0			0
$595$	10.3109	−	17.8591i	0.422708	−	0.732151i
$596$	−25.7431	+	6.10123i	−1.05448	+	0.249916i
$597$		0			0
$598$	1.05556	−	0.530120i	0.0431649	−	0.0216782i
$599$	10.1747	−	1.18926i	0.415728	−	0.0485917i	0.0943421	−	0.995540i	$-0.469925\pi$
$599$	10.1747	−	1.18926i	0.415728	−	0.0485917i	0.321386	+	0.946948i	$0.395851\pi$
$600$		0			0
$601$	2.52233	+	1.26676i	0.102888	+	0.0516723i	0.499499	−	0.866315i	$-0.333517\pi$
$601$	2.52233	+	1.26676i	0.102888	+	0.0516723i	−0.396611	+	0.917987i	$0.629814\pi$
$602$	−1.91035	−	0.695311i	−0.0778601	−	0.0283388i
$603$		0			0
$604$	−17.2472	+	6.27748i	−0.701780	+	0.255427i
$605$	29.9605	+	3.50188i	1.21807	+	0.142372i
$606$		0			0
$607$	−3.90167	−	13.0325i	−0.158364	−	0.528972i	0.841574	−	0.540142i	$-0.181630\pi$
$607$	−3.90167	−	13.0325i	−0.158364	−	0.528972i	−0.999938	+	0.0111702i	$0.996444\pi$
$608$	2.41836	+	8.07790i	0.0980776	+	0.327602i
$609$		0			0
$610$	−10.7575	−	1.25737i	−0.435558	−	0.0509094i
$611$	1.64343	−	0.598161i	0.0664862	−	0.0241990i
$612$		0			0
$613$	15.3111	+	5.57278i	0.618410	+	0.225083i	0.632179	−	0.774823i	$-0.282161\pi$
$613$	15.3111	+	5.57278i	0.618410	+	0.225083i	−0.0137693	+	0.999905i	$0.504383\pi$
$614$	−4.29462	−	2.15684i	−0.173317	−	0.0870429i
$615$		0			0
$616$	−2.15310	+	0.251662i	−0.0867510	+	0.0101397i
$617$	6.93552	−	3.48315i	0.279214	−	0.140226i	−0.303682	−	0.952774i	$-0.598216\pi$
$617$	6.93552	−	3.48315i	0.279214	−	0.140226i	0.582896	+	0.812547i	$0.301920\pi$
$618$		0			0
$619$	42.6421	−	10.1064i	1.71393	−	0.406209i	0.747730	−	0.664002i	$-0.231144\pi$
$619$	42.6421	−	10.1064i	1.71393	−	0.406209i	0.966200	+	0.257793i	$0.0829954\pi$
$620$	−8.02269	+	13.8957i	−0.322199	+	0.558065i
$621$		0			0
$622$	−0.186650	−	0.323287i	−0.00748397	−	0.0129626i
$623$	−8.70516	−	9.22693i	−0.348765	−	0.369669i
$624$		0			0
$625$	−4.64826	+	79.8075i	−0.185930	+	3.19230i
$626$	2.52618	+	3.39325i	0.100966	+	0.135621i
$627$		0			0
$628$	−14.7977	+	9.73259i	−0.590492	+	0.388373i
$629$	3.85678	+	21.8729i	0.153780	+	0.872129i
$630$		0			0
$631$	3.55734	−	20.1747i	0.141615	−	0.803141i	−0.828407	−	0.560126i	$-0.810753\pi$
$631$	3.55734	−	20.1747i	0.141615	−	0.803141i	0.970023	−	0.243015i	$-0.0781363\pi$
$632$	4.75639	+	11.0266i	0.189199	+	0.438613i
$633$		0			0
$634$	0.462105	+	0.109521i	0.0183526	+	0.00434963i
$635$	−32.4963	+	34.4440i	−1.28957	+	1.36687i
$636$		0			0
$637$	13.5672	−	18.2239i	0.537552	−	0.722057i
$638$	0.218250	+	0.183133i	0.00864058	+	0.00725031i
$639$		0			0
$640$	23.3663	−	19.6066i	0.923634	−	0.775021i
$641$	2.00940	+	34.5001i	0.0793667	+	1.36267i	0.769340	+	0.638839i	$0.220585\pi$
$641$	2.00940	+	34.5001i	0.0793667	+	1.36267i	−0.689974	+	0.723835i	$0.742378\pi$
$642$		0			0
$643$	11.7800	−	27.3091i	0.464558	−	1.07697i	−0.511466	−	0.859304i	$-0.670897\pi$
$643$	11.7800	−	27.3091i	0.464558	−	1.07697i	0.976024	−	0.217663i	$-0.0698435\pi$
$644$	−2.28005	−	1.49961i	−0.0898464	−	0.0590929i
$645$		0			0
$646$	0.883310	−	2.95046i	0.0347534	−	0.116084i
$647$	−43.1443			−1.69618			−0.848089	−	0.529853i	$-0.822247\pi$
$647$	−43.1443			−1.69618			−0.848089	+	0.529853i	$0.822247\pi$
$648$		0			0
$649$	16.4542			0.645884
$650$	−3.62244	+	12.0998i	−0.142084	+	0.474592i
$651$		0			0
$652$	12.8824	+	8.47291i	0.504515	+	0.331825i
$653$	12.3536	−	28.6388i	0.483433	−	1.12072i	−0.485686	−	0.874133i	$-0.661430\pi$
$653$	12.3536	−	28.6388i	0.483433	−	1.12072i	0.969120	−	0.246591i	$-0.0793105\pi$
$654$		0			0
$655$	2.99636	+	51.4454i	0.117077	+	2.01014i
$656$	−16.0294	+	13.4503i	−0.625843	+	0.525145i
$657$		0			0
$658$	0.0931677	+	0.0781770i	0.00363205	+	0.00304766i
$659$	−24.2845	+	32.6198i	−0.945992	+	1.27069i	0.0166368	+	0.999862i	$0.494704\pi$
$659$	−24.2845	+	32.6198i	−0.945992	+	1.27069i	−0.962628	+	0.270826i	$0.912703\pi$
$660$		0			0
$661$	−11.9150	+	12.6291i	−0.463439	+	0.491217i	−0.916372	−	0.400328i	$-0.868896\pi$
$661$	−11.9150	+	12.6291i	−0.463439	+	0.491217i	0.452933	+	0.891545i	$0.350378\pi$
$662$	−8.11121	−	1.92239i	−0.315251	−	0.0747159i
$663$		0			0
$664$	4.36896	+	10.1284i	0.169548	+	0.393058i
$665$	−2.56972	+	14.5736i	−0.0996494	+	0.565140i
$666$		0			0
$667$	0.126439	+	0.717068i	0.00489572	+	0.0277650i
$668$	7.21034	−	4.74232i	0.278976	−	0.183486i
$669$		0			0
$670$	−4.49238	−	6.03431i	−0.173556	−	0.233126i
$671$	−1.21091	+	20.7905i	−0.0467466	+	0.802609i
$672$		0			0
$673$	−30.2553	−	32.0688i	−1.16626	−	1.23616i	−0.966598	−	0.256296i	$-0.917498\pi$
$673$	−30.2553	−	32.0688i	−1.16626	−	1.23616i	−0.199659	−	0.979865i	$-0.563984\pi$
$674$	1.95524	+	3.38658i	0.0753131	+	0.130446i
$675$		0			0
$676$	2.95261	−	5.11407i	0.113562	−	0.196695i
$677$	−33.7584	+	8.00088i	−1.29744	+	0.307499i	−0.820606	−	0.571494i	$-0.806364\pi$
$677$	−33.7584	+	8.00088i	−1.29744	+	0.307499i	−0.476834	+	0.878993i	$0.658216\pi$
$678$		0			0
$679$	−6.47387	+	3.25130i	−0.248445	+	0.124774i
$680$	−16.9394	+	1.97993i	−0.649595	+	0.0759268i
$681$		0			0
$682$	−0.829880	−	0.416782i	−0.0317778	−	0.0159594i
$683$	40.1564	+	14.6157i	1.53654	+	0.559256i	0.965213	−	0.261465i	$-0.0842057\pi$
$683$	40.1564	+	14.6157i	1.53654	+	0.559256i	0.571329	+	0.820721i	$0.306428\pi$
$684$		0			0
$685$	−1.19440	+	0.434725i	−0.0456356	+	0.0166100i
$686$	3.50578	+	0.409767i	0.133851	+	0.0156450i
$687$		0			0
$688$	−7.64657	−	25.5413i	−0.291523	−	0.973754i
$689$	−5.13915	−	17.1660i	−0.195786	−	0.653971i
$690$		0			0
$691$	15.9237	+	1.86121i	0.605764	+	0.0708037i	0.413446	−	0.910529i	$-0.364325\pi$
$691$	15.9237	+	1.86121i	0.605764	+	0.0708037i	0.192319	+	0.981333i	$0.438399\pi$
$692$	−5.68957	+	2.07083i	−0.216285	+	0.0787213i
$693$		0			0
$694$	−7.22724	−	2.63050i	−0.274342	−	0.0998524i
$695$	−21.2944	−	10.6945i	−0.807743	−	0.405664i
$696$		0			0
$697$	23.9738	−	2.80214i	0.908072	−	0.106138i
$698$	3.74496	−	1.88079i	0.141749	−	0.0711890i
$699$		0			0
$700$	28.3943	−	6.72957i	1.07320	−	0.254354i
$701$	−20.8919	+	36.1858i	−0.789075	+	1.36672i	0.137459	+	0.990507i	$0.456106\pi$
$701$	−20.8919	+	36.1858i	−0.789075	+	1.36672i	−0.926534	+	0.376211i	$0.877227\pi$
$702$		0			0
$703$	−7.96914	−	13.8029i	−0.300562	−	0.520588i
$704$	−8.98581	−	9.52440i	−0.338665	−	0.358964i
$705$		0			0
$706$	0.0477884	−	0.820496i	0.00179854	−	0.0308798i
$707$	−2.78496	−	3.74085i	−0.104739	−	0.140689i
$708$		0			0
$709$	14.1161	−	9.28427i	0.530140	−	0.348678i	−0.256050	−	0.966663i	$-0.582421\pi$
$709$	14.1161	−	9.28427i	0.530140	−	0.348678i	0.786190	+	0.617985i	$0.212051\pi$
$710$	−0.854057	−	4.84360i	−0.0320522	−	0.181777i
$711$		0			0
$712$	−1.82174	+	10.3316i	−0.0682724	+	0.387192i
$713$	−0.940045	−	2.17927i	−0.0352050	−	0.0816143i
$714$		0			0
$715$	32.6894	+	7.74754i	1.22252	+	0.289741i
$716$	18.9674	−	20.1042i	0.708843	−	0.751330i
$717$		0			0
$718$	−1.46479	+	1.96756i	−0.0546656	+	0.0734287i
$719$	12.7933	+	10.7349i	0.477111	+	0.400344i	0.849381	−	0.527781i	$-0.176976\pi$
$719$	12.7933	+	10.7349i	0.477111	+	0.400344i	−0.372269	+	0.928125i	$0.621420\pi$
$720$		0			0
$721$	−7.31216	+	6.13563i	−0.272319	+	0.228503i
$722$	−0.138561	−	2.37900i	−0.00515670	−	0.0885372i
$723$		0			0
$724$	−12.2214	+	28.3323i	−0.454203	+	1.05296i
$725$	−6.50494	−	4.27837i	−0.241588	−	0.158895i
$726$		0			0
$727$	−6.34386	+	21.1900i	−0.235281	+	0.785893i	0.756051	+	0.654513i	$0.227126\pi$
$727$	−6.34386	+	21.1900i	−0.235281	+	0.785893i	−0.991332	+	0.131380i	$0.958059\pi$
$728$	4.39701			0.162964
$729$		0			0
$730$	−7.40242			−0.273976
$731$	−8.82037	+	29.4621i	−0.326233	+	1.08970i
$732$		0			0
$733$	10.9756	+	7.21876i	0.405393	+	0.266631i	0.735788	−	0.677212i	$-0.236812\pi$
$733$	10.9756	+	7.21876i	0.405393	+	0.266631i	−0.330396	+	0.943842i	$0.607182\pi$
$734$	−1.42323	+	3.29941i	−0.0525323	+	0.121784i
$735$		0			0
$736$	0.197816	+	3.39638i	0.00729161	+	0.125192i
$737$	−11.0811	+	9.29816i	−0.408178	+	0.342502i
$738$		0			0
$739$	−34.4177	−	28.8799i	−1.26608	−	1.06236i	−0.995007	−	0.0998052i	$-0.968178\pi$
$739$	−34.4177	−	28.8799i	−1.26608	−	1.06236i	−0.271070	−	0.962560i	$-0.587378\pi$
$740$	−25.9614	+	34.8722i	−0.954360	+	1.28193i
$741$		0			0
$742$	0.855125	−	0.906380i	0.0313926	−	0.0332742i
$743$	21.7667	+	5.15881i	0.798545	+	0.189259i	0.609579	−	0.792725i	$-0.291338\pi$
$743$	21.7667	+	5.15881i	0.798545	+	0.189259i	0.188965	+	0.981984i	$0.439487\pi$
$744$		0			0
$745$	22.9264	+	53.1494i	0.839959	+	1.94724i
$746$	0.884944	−	5.01877i	0.0324001	−	0.183750i
$747$		0			0
$748$	2.80504	+	15.9082i	0.102563	+	0.581661i
$749$	15.3126	−	10.0712i	0.559510	−	0.367995i
$750$		0			0
$751$	7.09785	+	9.53407i	0.259004	+	0.347903i	0.912536	−	0.408996i	$-0.134121\pi$
$751$	7.09785	+	9.53407i	0.259004	+	0.347903i	−0.653532	+	0.756899i	$0.726714\pi$
$752$	−0.0927423	+	1.59232i	−0.00338196	+	0.0580661i
$753$		0			0
$754$	−0.396573	−	0.420342i	−0.0144423	−	0.0153080i
$755$	20.0784	+	34.7768i	0.730728	+	1.26566i
$756$		0			0
$757$	−2.60890	+	4.51875i	−0.0948221	+	0.164237i	−0.909534	−	0.415629i	$-0.863562\pi$
$757$	−2.60890	+	4.51875i	−0.0948221	+	0.164237i	0.814712	+	0.579865i	$0.196895\pi$
$758$	−1.63466	+	0.387422i	−0.0593736	+	0.0140718i
$759$		0			0
$760$	10.9368	−	5.49266i	0.396719	−	0.199240i
$761$	−0.693685	+	0.0810801i	−0.0251461	+	0.00293915i	−0.128657	−	0.991689i	$-0.541067\pi$
$761$	−0.693685	+	0.0810801i	−0.0251461	+	0.00293915i	0.103511	+	0.994628i	$0.466992\pi$
$762$		0			0
$763$	3.72830	+	1.87242i	0.134974	+	0.0677863i
$764$	−37.0505	−	13.4853i	−1.34044	−	0.487880i
$765$		0			0
$766$	8.02630	−	2.92133i	0.290002	−	0.105552i
$767$	−33.1494	−	3.87461i	−1.19696	−	0.139904i
$768$		0			0
$769$	−3.19114	−	10.6591i	−0.115075	−	0.384379i	0.880976	−	0.473162i	$-0.156887\pi$
$769$	−3.19114	−	10.6591i	−0.115075	−	0.384379i	−0.996051	+	0.0887831i	$0.971702\pi$
$770$	0.670044	+	2.23810i	0.0241467	+	0.0806556i
$771$		0			0
$772$	−5.15364	−	0.602374i	−0.185483	−	0.0216799i
$773$	14.5554	−	5.29774i	0.523522	−	0.190546i	−0.0667217	−	0.997772i	$-0.521254\pi$
$773$	14.5554	−	5.29774i	0.523522	−	0.190546i	0.590243	+	0.807225i	$0.299032\pi$
$774$		0			0
$775$	23.8477	+	8.67985i	0.856634	+	0.311789i
$776$	5.35401	+	2.68889i	0.192198	+	0.0965254i
$777$		0			0
$778$	6.17650	−	0.721929i	0.221438	−	0.0258824i
$779$	−15.4785	+	7.77360i	−0.554575	+	0.278518i
$780$		0			0
$781$	−9.20222	+	2.18097i	−0.329281	+	0.0780411i
$782$	0.621316	−	1.07615i	0.0222182	−	0.0384831i
$783$		0			0
$784$	10.3603	+	17.9445i	0.370009	+	0.640875i
$785$	26.5923	+	28.1862i	0.949120	+	1.00601i
$786$		0			0
$787$	2.04878	−	35.1762i	0.0730312	−	1.25390i	−0.740372	−	0.672197i	$-0.765351\pi$
$787$	2.04878	−	35.1762i	0.0730312	−	1.25390i	0.813403	−	0.581700i	$-0.197612\pi$
$788$	19.3874	+	26.0418i	0.690648	+	0.927702i
$789$		0			0
$790$	10.8129	−	7.11177i	0.384707	−	0.253025i
$791$	−1.89968	−	10.7736i	−0.0675449	−	0.383066i
$792$		0			0
$793$	7.33528	−	41.6004i	0.260483	−	1.47728i
$794$	−1.78078	−	4.12831i	−0.0631975	−	0.146508i
$795$		0			0
$796$	−3.69549	−	0.875847i	−0.130983	−	0.0310436i
$797$	−18.1942	+	19.2847i	−0.644471	+	0.683099i	−0.964432	−	0.264332i	$-0.914849\pi$
$797$	−18.1942	+	19.2847i	−0.644471	+	0.683099i	0.319961	+	0.947431i	$0.396330\pi$
$798$		0			0
$799$	1.09869	−	1.47580i	0.0388690	−	0.0522101i
$800$	−27.8676	−	23.3837i	−0.985268	−	0.826738i
$801$		0			0
$802$	−0.856252	+	0.718481i	−0.0302353	+	0.0253704i
$803$	0.827614	+	14.2096i	0.0292059	+	0.501445i
$804$		0			0
$805$	−2.36489	+	5.48244i	−0.0833516	+	0.193231i
$806$	1.57378	+	1.03509i	0.0554339	+	0.0364594i
$807$		0			0
$808$	−1.10619	+	3.69493i	−0.0389156	+	0.129987i
$809$	4.72350			0.166070			0.0830348	−	0.996547i	$-0.473539\pi$
$809$	4.72350			0.166070			0.0830348	+	0.996547i	$0.473539\pi$
$810$		0			0
$811$	−14.2884			−0.501733			−0.250866	−	0.968022i	$-0.580716\pi$
$811$	−14.2884			−0.501733			−0.250866	+	0.968022i	$0.580716\pi$
$812$	−0.382922	+	1.27905i	−0.0134379	+	0.0448859i
$813$		0			0
$814$	−2.10225	−	1.38267i	−0.0736840	−	0.0484627i
$815$	13.3618	−	30.9762i	0.468044	−	1.08505i
$816$		0			0
$817$	−1.28322	−	22.0320i	−0.0448942	−	0.770803i
$818$	2.02577	−	1.69982i	0.0708294	−	0.0594329i
$819$		0			0
$820$	36.1927	+	30.3693i	1.26391	+	1.06054i
$821$	13.0600	−	17.5427i	0.455799	−	0.612244i	−0.513512	−	0.858082i	$-0.671656\pi$
$821$	13.0600	−	17.5427i	0.455799	−	0.612244i	0.969311	+	0.245839i	$0.0790633\pi$
$822$		0			0
$823$	−16.1321	+	17.0990i	−0.562329	+	0.596034i	−0.944684	−	0.327981i	$-0.893632\pi$
$823$	−16.1321	+	17.0990i	−0.562329	+	0.596034i	0.382355	+	0.924016i	$0.375113\pi$
$824$	7.68139	+	1.82052i	0.267594	+	0.0634209i
$825$		0			0
$826$	−0.919285	−	2.13114i	−0.0319860	−	0.0741519i
$827$	−3.09330	+	17.5430i	−0.107565	+	0.610030i	0.882600	+	0.470124i	$0.155791\pi$
$827$	−3.09330	+	17.5430i	−0.107565	+	0.610030i	−0.990165	+	0.139905i	$0.955320\pi$
$828$		0			0
$829$	−9.35023	−	53.0278i	−0.324747	−	1.84173i	−0.511447	−	0.859315i	$-0.670890\pi$
$829$	−9.35023	−	53.0278i	−0.324747	−	1.84173i	0.186700	−	0.982417i	$-0.440221\pi$
$830$	9.93215	−	6.53248i	0.344750	−	0.226746i
$831$		0			0
$832$	15.8605	+	21.3043i	0.549863	+	0.738594i
$833$	1.38973	−	23.8608i	0.0481514	−	0.826728i
$834$		0			0
$835$	−12.9574	−	13.7340i	−0.448409	−	0.475286i
$836$	−5.79597	−	10.0389i	−0.200458	−	0.347203i
$837$		0			0
$838$	4.05420	−	7.02209i	0.140050	−	0.242574i
$839$	50.6792	−	12.0112i	1.74964	−	0.414672i	0.773848	−	0.633371i	$-0.218329\pi$
$839$	50.6792	−	12.0112i	1.74964	−	0.414672i	0.975792	+	0.218699i	$0.0701811\pi$
$840$		0			0
$841$	−25.5970	+	12.8553i	−0.882655	+	0.443286i
$842$	0.398257	−	0.0465496i	0.0137249	−	0.00160421i
$843$		0			0
$844$	−17.9825	−	9.03115i	−0.618983	−	0.310865i
$845$	−12.1408	−	4.41889i	−0.417656	−	0.152014i
$846$		0			0
$847$	−7.68804	+	2.79822i	−0.264164	+	0.0961480i
$848$	16.2316	+	1.89720i	0.557396	+	0.0651502i
$849$		0			0
$850$	3.81084	+	12.7291i	0.130711	+	0.436605i
$851$	−1.84433	−	6.16050i	−0.0632229	−	0.211179i
$852$		0			0
$853$	−48.2344	−	5.63779i	−1.65151	−	0.193034i	−0.761244	−	0.648466i	$-0.775411\pi$
$853$	−48.2344	−	5.63779i	−1.65151	−	0.193034i	−0.890271	+	0.455431i	$0.849485\pi$
$854$	2.76043	−	1.00472i	0.0944601	−	0.0343807i
$855$		0			0
$856$	−14.2433	−	5.18412i	−0.486825	−	0.177190i
$857$	−38.9620	−	19.5675i	−1.33092	−	0.668412i	−0.365914	−	0.930648i	$-0.619244\pi$
$857$	−38.9620	−	19.5675i	−1.33092	−	0.668412i	−0.965004	+	0.262236i	$0.915540\pi$
$858$		0			0
$859$	−16.1938	+	1.89278i	−0.552524	+	0.0645808i	−0.387774	−	0.921755i	$-0.626756\pi$
$859$	−16.1938	+	1.89278i	−0.552524	+	0.0645808i	−0.164750	+	0.986335i	$0.552682\pi$
$860$	−53.7955	+	27.0171i	−1.83441	+	0.921276i
$861$		0			0
$862$	−3.55395	+	0.842302i	−0.121048	+	0.0286889i
$863$	25.0920	−	43.4607i	0.854142	−	1.47942i	−0.0232963	−	0.999729i	$-0.507416\pi$
$863$	25.0920	−	43.4607i	0.854142	−	1.47942i	0.877439	−	0.479689i	$-0.159251\pi$
$864$		0			0
$865$	6.62352	+	11.4723i	0.225207	+	0.390069i
$866$	0.818377	+	0.867429i	0.0278096	+	0.0294764i
$867$		0			0
$868$	0.253043	−	4.34459i	0.00858885	−	0.147465i
$869$	−14.8606	−	19.9612i	−0.504111	−	0.677138i
$870$		0			0
$871$	24.5141	−	16.1232i	0.830628	−	0.546313i
$872$	−0.599153	−	3.39796i	−0.0202899	−	0.115070i
$873$		0			0
$874$	−0.154846	+	0.878175i	−0.00523774	+	0.0297047i
$875$	−15.5949	−	36.1531i	−0.527205	−	1.22220i
$876$		0			0
$877$	−43.6563	−	10.3467i	−1.47417	−	0.349385i	−0.586531	−	0.809926i	$-0.699507\pi$
$877$	−43.6563	−	10.3467i	−1.47417	−	0.349385i	−0.887638	+	0.460542i	$0.847655\pi$
$878$	−3.34787	+	3.54854i	−0.112985	+	0.119757i
$879$		0			0
$880$	−18.2963	+	24.5763i	−0.616770	+	0.828466i
$881$	−13.9661	−	11.7190i	−0.470531	−	0.394822i	0.376457	−	0.926434i	$-0.377142\pi$
$881$	−13.9661	−	11.7190i	−0.470531	−	0.394822i	−0.846988	+	0.531612i	$0.821587\pi$
$882$		0			0
$883$	−13.4700	+	11.3026i	−0.453300	+	0.380364i	−0.840659	−	0.541565i	$-0.817832\pi$
$883$	−13.4700	+	11.3026i	−0.453300	+	0.380364i	0.387359	+	0.921929i	$0.373388\pi$
$884$	−1.90514	−	32.7100i	−0.0640768	−	1.10016i
$885$		0			0
$886$	2.69885	−	6.25663i	0.0906696	−	0.210196i
$887$	−27.5435	−	18.1156i	−0.924820	−	0.608264i	−0.00473763	−	0.999989i	$-0.501508\pi$
$887$	−27.5435	−	18.1156i	−0.924820	−	0.608264i	−0.920082	+	0.391725i	$0.871878\pi$
$888$		0			0
$889$	3.68362	−	12.3041i	0.123545	−	0.412667i
$890$	11.3064			0.378990
$891$		0			0
$892$	−14.2279			−0.476386
$893$	−0.378667	+	1.26484i	−0.0126716	+	0.0423261i
$894$		0			0
$895$	−50.5237	−	33.2300i	−1.68882	−	1.11076i
$896$	−3.27682	+	7.59652i	−0.109471	+	0.253782i
$897$		0			0
$898$	−0.00610205	−	0.104768i	−0.000203628	−	0.00349616i
$899$	−0.889494	+	0.746374i	−0.0296663	+	0.0248930i
$900$		0			0
$901$	−14.4405	−	12.1170i	−0.481082	−	0.403676i
$902$	−1.63292	+	2.19339i	−0.0543702	+	0.0730318i
$903$		0			0
$904$	−6.20873	+	6.58087i	−0.206499	+	0.218877i
$905$	65.6894	+	15.5687i	2.18359	+	0.517520i
$906$		0			0
$907$	−15.5485	−	36.0455i	−0.516280	−	1.19687i	−0.954556	−	0.298031i	$-0.903670\pi$
$907$	−15.5485	−	36.0455i	−0.516280	−	1.19687i	0.438277	−	0.898840i	$-0.355589\pi$
$908$	−7.84805	+	44.5085i	−0.260447	+	1.47707i
$909$		0			0
$910$	−0.822878	−	4.66678i	−0.0272782	−	0.154702i
$911$	12.7242	−	8.36883i	0.421571	−	0.277272i	−0.320948	−	0.947097i	$-0.604001\pi$
$911$	12.7242	−	8.36883i	0.421571	−	0.277272i	0.742519	+	0.669825i	$0.233631\pi$
$912$		0			0
$913$	−13.6501	−	18.3353i	−0.451752	−	0.606809i
$914$	0.380951	−	6.54067i	0.0126007	−	0.216346i
$915$		0			0
$916$	−0.0665050	−	0.0704911i	−0.00219739	−	0.00232909i
$917$	−6.98854	−	12.1045i	−0.230782	−	0.399726i
$918$		0			0
$919$	−7.39953	+	12.8164i	−0.244088	+	0.422773i	−0.961875	−	0.273490i	$-0.911822\pi$
$919$	−7.39953	+	12.8164i	−0.244088	+	0.422773i	0.717787	+	0.696263i	$0.245155\pi$
$920$	4.80482	−	1.13876i	0.158410	−	0.0375439i
$921$		0			0
$922$	−9.23020	+	4.63558i	−0.303980	+	0.152665i
$923$	19.0528	−	2.22695i	0.627131	−	0.0733011i
$924$		0			0
$925$	61.4481	+	30.8604i	2.02040	+	1.01468i
$926$	−6.89258	−	2.50869i	−0.226504	−	0.0824407i
$927$		0			0
$928$	1.56408	−	0.569280i	0.0513436	−	0.0186875i
$929$	30.4001	+	3.55326i	0.997395	+	0.116579i	0.599096	−	0.800677i	$-0.295527\pi$
$929$	30.4001	+	3.55326i	0.997395	+	0.116579i	0.398299	+	0.917256i	$0.369601\pi$
$930$		0			0
$931$	4.91916	+	16.4312i	0.161219	+	0.538509i
$932$	12.4785	+	41.6809i	0.408745	+	1.36530i
$933$		0			0
$934$	−3.23094	−	0.377642i	−0.105719	−	0.0123568i
$935$	33.2109	−	12.0878i	1.08611	−	0.395313i
$936$		0			0
$937$	3.22880	+	1.17519i	0.105480	+	0.0383917i	0.394221	−	0.919016i	$-0.371014\pi$
$937$	3.22880	+	1.17519i	0.105480	+	0.0383917i	−0.288741	+	0.957407i	$0.593237\pi$
$938$	1.82339	+	0.915741i	0.0595358	+	0.0299000i
$939$		0			0
$940$	3.57704	−	0.418097i	0.116670	−	0.0136368i
$941$	17.3110	−	8.69390i	0.564321	−	0.283413i	−0.143680	−	0.989624i	$-0.545893\pi$
$941$	17.3110	−	8.69390i	0.564321	−	0.283413i	0.708001	+	0.706211i	$0.249597\pi$
$942$		0			0
$943$	−6.80012	+	1.61166i	−0.221442	+	0.0524828i
$944$	15.2192	−	26.3605i	0.495344	−	0.857961i
$945$		0			0
$946$	−1.74206	−	3.01734i	−0.0566393	−	0.0981022i
$947$	9.46263	+	10.0298i	0.307494	+	0.325925i	0.862630	−	0.505835i	$-0.168815\pi$
$947$	9.46263	+	10.0298i	0.307494	+	0.325925i	−0.555136	+	0.831759i	$0.687334\pi$
$948$		0			0
$949$	1.67870	−	28.8222i	0.0544930	−	0.935609i
$950$	−5.69395	−	7.64830i	−0.184736	−	0.248144i
$951$		0			0
$952$	3.86472	−	2.54187i	0.125256	−	0.0823824i
$953$	6.51937	+	36.9732i	0.211183	+	1.19768i	0.887408	+	0.460984i	$0.152503\pi$
$953$	6.51937	+	36.9732i	0.211183	+	1.19768i	−0.676225	+	0.736695i	$0.736385\pi$
$954$		0			0
$955$	−14.9797	+	84.9541i	−0.484732	+	2.74905i
$956$	−15.7902	−	36.6058i	−0.510691	−	1.18392i
$957$		0			0
$958$	−6.11041	−	1.44819i	−0.197418	−	0.0467890i
$959$	0.236578	−	0.250758i	0.00763950	−	0.00809739i
$960$		0			0
$961$	−16.2518	+	21.8299i	−0.524251	+	0.704191i
$962$	3.90972	+	3.28064i	0.126054	+	0.105772i
$963$		0			0
$964$	42.8154	−	35.9264i	1.37899	−	1.15711i
$965$	0.660080	+	11.3331i	0.0212487	+	0.364827i
$966$		0			0
$967$	9.73644	−	22.5716i	0.313103	−	0.725854i	−0.686897	−	0.726755i	$-0.741028\pi$
$967$	9.73644	−	22.5716i	0.313103	−	0.725854i	1.00000		0.000900887i	$0.000286761\pi$
$968$	5.65308	+	3.71809i	0.181697	+	0.119504i
$969$		0			0
$970$	1.85188	−	6.18570i	0.0594602	−	0.198611i
$971$	−13.0415			−0.418522			−0.209261	−	0.977860i	$-0.567106\pi$
$971$	−13.0415			−0.418522			−0.209261	+	0.977860i	$0.567106\pi$
$972$		0			0
$973$	6.46310			0.207197
$974$	0.187601	−	0.626629i	0.00601111	−	0.0200785i
$975$		0			0
$976$	32.1875	+	21.1700i	1.03030	+	0.677636i
$977$	−19.1859	+	44.4779i	−0.613812	+	1.42298i	0.273530	+	0.961863i	$0.411809\pi$
$977$	−19.1859	+	44.4779i	−0.613812	+	1.42298i	−0.887342	+	0.461112i	$0.847451\pi$
$978$		0			0
$979$	−1.26409	−	21.7035i	−0.0404004	−	0.693648i
$980$	35.8392	−	30.0727i	1.14484	−	0.960636i
$981$		0			0
$982$	7.37186	+	6.18573i	0.235246	+	0.197394i
$983$	19.7673	−	26.5520i	0.630477	−	0.846878i	−0.366011	−	0.930611i	$-0.619277\pi$
$983$	19.7673	−	26.5520i	0.630477	−	0.846878i	0.996488	+	0.0837324i	$0.0266841\pi$
$984$		0			0
$985$	48.7453	−	51.6670i	1.55315	−	1.64625i
$986$	−0.591560	−	0.140202i	−0.0188391	−	0.00446495i
$987$		0			0
$988$	9.31290	+	21.5897i	0.296283	+	0.686861i
$989$	1.54623	−	8.76910i	0.0491672	−	0.278841i
$990$		0			0
$991$	−3.02007	−	17.1276i	−0.0959355	−	0.544078i	−0.994457	−	0.105147i	$-0.966469\pi$
$991$	−3.02007	−	17.1276i	−0.0959355	−	0.544078i	0.898521	−	0.438930i	$-0.144642\pi$
$992$	−4.53285	+	2.98130i	−0.143918	+	0.0946565i
$993$		0			0
$994$	0.796600	+	1.07002i	0.0252666	+	0.0339390i
$995$	−0.483143	+	8.29524i	−0.0153166	+	0.262977i
$996$		0			0
$997$	11.8606	+	12.5715i	0.375628	+	0.398142i	0.887416	−	0.460969i	$-0.152498\pi$
$997$	11.8606	+	12.5715i	0.375628	+	0.398142i	−0.511788	+	0.859112i	$0.671017\pi$
$998$	0.300413	+	0.520330i	0.00950940	+	0.0164708i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.352.5		144
3.2	odd	2		729.2.g.d.352.4		144
9.2	odd	6		729.2.g.c.595.5		144
9.4	even	3		243.2.g.a.199.5		144
9.5	odd	6		81.2.g.a.22.4	✓	144
9.7	even	3		729.2.g.b.595.4		144
81.11	odd	54		729.2.g.c.136.5		144
81.16	even	27		243.2.g.a.127.5		144
81.23	odd	54		6561.2.a.c.1.41		72
81.38	odd	54		729.2.g.d.379.4		144
81.43	even	27	inner	729.2.g.a.379.5		144
81.58	even	27		6561.2.a.d.1.32		72
81.65	odd	54		81.2.g.a.70.4	yes	144
81.70	even	27		729.2.g.b.136.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.22.4	✓	144	9.5	odd	6
81.2.g.a.70.4	yes	144	81.65	odd	54
243.2.g.a.127.5		144	81.16	even	27
243.2.g.a.199.5		144	9.4	even	3
729.2.g.a.352.5		144	1.1	even	1	trivial
729.2.g.a.379.5		144	81.43	even	27	inner
729.2.g.b.136.4		144	81.70	even	27
729.2.g.b.595.4		144	9.7	even	3
729.2.g.c.136.5		144	81.11	odd	54
729.2.g.c.595.5		144	9.2	odd	6
729.2.g.d.352.4		144	3.2	odd	2
729.2.g.d.379.4		144	81.38	odd	54
6561.2.a.c.1.41		72	81.23	odd	54
6561.2.a.d.1.32		72	81.58	even	27

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.0693332 - 0.231589i) q^{2} +(1.62215 + 1.06690i) q^{4} +(1.68251 - 3.90051i) q^{5} +(0.0669917 + 1.15020i) q^{7} +(0.729927 - 0.612481i) q^{8} +(-0.786660 - 0.660086i) q^{10} +(-1.17914 + 1.58386i) q^{11} +(2.74852 - 2.91326i) q^{13} +(0.271019 + 0.0642327i) q^{14} +(1.44679 + 3.35403i) q^{16} +(0.731666 - 4.14948i) q^{17} +(0.525049 + 2.97770i) q^{19} +(6.89075 - 4.53212i) q^{20} +(0.285051 + 0.382890i) q^{22} +(-0.0709339 + 1.21789i) q^{23} +(-8.95188 - 9.48844i) q^{25} +(-0.484116 - 0.838513i) q^{26} +(-1.11849 + 1.93728i) q^{28} +(0.580763 - 0.137643i) q^{29} +(-1.73853 + 0.873122i) q^{31} +(2.76989 - 0.323753i) q^{32} +(-0.910246 - 0.457143i) q^{34} +(4.59909 + 1.67393i) q^{35} +(-4.95333 + 1.80287i) q^{37} +(0.726006 + 0.0848579i) q^{38} +(-1.16087 - 3.87759i) q^{40} +(1.64295 + 5.48784i) q^{41} +(-7.24960 - 0.847356i) q^{43} +(-3.60257 + 1.31123i) q^{44} +(0.277132 + 0.100868i) q^{46} +(0.390214 + 0.195973i) q^{47} +(5.63419 - 0.658542i) q^{49} +(-2.81808 + 1.41529i) q^{50} +(7.56669 - 1.79334i) q^{52} +(2.23695 - 3.87450i) q^{53} +(4.19394 + 7.26412i) q^{55} +(0.753377 + 0.798533i) q^{56} +(0.00838947 - 0.144042i) q^{58} +(-4.97611 - 6.68408i) q^{59} +(8.81180 - 5.79561i) q^{61} +(0.0816677 + 0.463161i) q^{62} +(-1.15153 + 6.53063i) q^{64} +(-6.73877 - 15.6222i) q^{65} +(7.12830 + 1.68944i) q^{67} +(5.61397 - 5.95046i) q^{68} +(0.706534 - 0.949039i) q^{70} +(3.66891 + 3.07858i) q^{71} +(5.52198 - 4.63349i) q^{73} +(0.0740935 + 1.27214i) q^{74} +(-2.32521 + 5.39045i) q^{76} +(-1.90076 - 1.25015i) q^{77} +(-3.61455 + 12.0734i) q^{79} +15.5167 q^{80} +1.38483 q^{82} +(-3.32012 + 11.0900i) q^{83} +(-14.9540 - 9.83543i) q^{85} +(-0.698876 + 1.62018i) q^{86} +(0.109399 + 1.87830i) q^{88} +(-8.43420 + 7.07713i) q^{89} +(3.53497 + 2.96620i) q^{91} +(-1.41444 + 1.89992i) q^{92} +(0.0724400 - 0.0767819i) q^{94} +(12.4979 + 2.96206i) q^{95} +(2.49045 + 5.77351i) q^{97} +(0.238125 - 1.35047i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) \) 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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