LMFDB - Embedded newform 729.2.g.c.379.5

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,-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			379.5
Character	$\chi$	$=$	729.379
Dual form			729.2.g.c.352.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.189684 + 0.633587i) q^{2} +(1.30552 - 0.858656i) q^{4} +(-0.995544 - 2.30793i) q^{5} +(-0.239094 + 4.10508i) q^{7} +(1.80495 + 1.51453i) q^{8} +(1.27344 - 1.06854i) q^{10} +(1.76794 + 2.37476i) q^{11} +(2.22560 + 2.35899i) q^{13} +(-2.64628 + 0.627180i) q^{14} +(0.620599 - 1.43871i) q^{16} +(-0.572741 - 3.24818i) q^{17} +(-0.571121 + 3.23899i) q^{19} +(-3.28142 - 2.15823i) q^{20} +(-1.16927 + 1.57060i) q^{22} +(-0.145137 - 2.49190i) q^{23} +(-0.904231 + 0.958429i) q^{25} +(-1.07247 + 1.85757i) q^{26} +(3.21271 + 5.56458i) q^{28} +(5.41695 + 1.28384i) q^{29} +(5.73952 + 2.88249i) q^{31} +(5.70979 + 0.667379i) q^{32} +(1.94936 - 0.979008i) q^{34} +(9.71228 - 3.53498i) q^{35} +(-2.56937 - 0.935175i) q^{37} +(-2.16052 + 0.252528i) q^{38} +(1.69853 - 5.67349i) q^{40} +(2.59515 - 8.66839i) q^{41} +(7.76471 - 0.907565i) q^{43} +(4.34719 + 1.58225i) q^{44} +(1.55131 - 0.564629i) q^{46} +(-9.04350 + 4.54182i) q^{47} +(-9.84186 - 1.15035i) q^{49} +(-0.778766 - 0.391111i) q^{50} +(4.93113 + 1.16870i) q^{52} +(0.00494432 + 0.00856381i) q^{53} +(3.72072 - 6.44448i) q^{55} +(-6.64883 + 7.04735i) q^{56} +(0.214081 + 3.67563i) q^{58} +(-6.79150 + 9.12257i) q^{59} +(-7.52933 - 4.95212i) q^{61} +(-0.737619 + 4.18325i) q^{62} +(0.116049 + 0.658144i) q^{64} +(3.22872 - 7.48500i) q^{65} +(5.68771 - 1.34801i) q^{67} +(-3.53679 - 3.74878i) q^{68} +(4.08198 + 5.48305i) q^{70} +(-1.81817 + 1.52563i) q^{71} +(3.61987 + 3.03743i) q^{73} +(0.105147 - 1.80531i) q^{74} +(2.03557 + 4.71897i) q^{76} +(-10.1713 + 6.68977i) q^{77} +(-2.58181 - 8.62383i) q^{79} -3.93828 q^{80} +5.98444 q^{82} +(1.06156 + 3.54585i) q^{83} +(-6.92638 + 4.55555i) q^{85} +(2.04786 + 4.74747i) q^{86} +(-0.405603 + 6.96394i) q^{88} +(-9.57258 - 8.03235i) q^{89} +(-10.2160 + 8.57223i) q^{91} +(-2.32916 - 3.12861i) q^{92} +(-4.59304 - 4.86834i) q^{94} +(8.04395 - 1.90645i) q^{95} +(-2.83273 + 6.56702i) q^{97} +(-1.13799 - 6.45388i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{27}\right)$

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 $

$2$	0.189684	+	0.633587i	0.134127	+	0.448014i	0.998495	−	0.0548454i	$-0.0174666\pi$
$2$	0.189684	+	0.633587i	0.134127	+	0.448014i	−0.864368	+	0.502859i	$0.832281\pi$
$3$		0			0
$3$		0			0
$4$	1.30552	−	0.858656i	0.652761	−	0.429328i
$5$	−0.995544	−	2.30793i	−0.445221	−	1.03214i	−0.982080	−	0.188466i	$-0.939648\pi$
$5$	−0.995544	−	2.30793i	−0.445221	−	1.03214i	0.536859	−	0.843672i	$-0.319611\pi$
$6$		0			0
$7$	−0.239094	+	4.10508i	−0.0903689	+	1.55157i	0.583125	+	0.812382i	$0.301830\pi$
$7$	−0.239094	+	4.10508i	−0.0903689	+	1.55157i	−0.673494	+	0.739193i	$0.735207\pi$
$8$	1.80495	+	1.51453i	0.638146	+	0.535468i
$9$		0			0
$10$	1.27344	−	1.06854i	0.402696	−	0.337902i
$11$	1.76794	+	2.37476i	0.533055	+	0.716018i	0.984324	−	0.176371i	$-0.0564357\pi$
$11$	1.76794	+	2.37476i	0.533055	+	0.716018i	−0.451268	+	0.892388i	$0.649028\pi$
$12$		0			0
$13$	2.22560	+	2.35899i	0.617269	+	0.654267i	0.958293	−	0.285788i	$-0.0922552\pi$
$13$	2.22560	+	2.35899i	0.617269	+	0.654267i	−0.341024	+	0.940055i	$0.610774\pi$
$14$	−2.64628	+	0.627180i	−0.707248	+	0.167621i
$15$		0			0
$16$	0.620599	−	1.43871i	0.155150	−	0.359678i
$17$	−0.572741	−	3.24818i	−0.138910	−	0.787799i	−0.972057	−	0.234746i	$-0.924574\pi$
$17$	−0.572741	−	3.24818i	−0.138910	−	0.787799i	0.833146	−	0.553052i	$-0.186537\pi$
$18$		0			0
$19$	−0.571121	+	3.23899i	−0.131024	+	0.743075i	0.846522	+	0.532354i	$0.178692\pi$
$19$	−0.571121	+	3.23899i	−0.131024	+	0.743075i	−0.977546	+	0.210722i	$0.932419\pi$
$20$	−3.28142	−	2.15823i	−0.733749	−	0.482594i
$21$		0			0
$22$	−1.16927	+	1.57060i	−0.249289	+	0.334853i
$23$	−0.145137	−	2.49190i	−0.0302631	−	0.519597i	−0.979042	−	0.203657i	$-0.934717\pi$
$23$	−0.145137	−	2.49190i	−0.0302631	−	0.519597i	0.948779	−	0.315940i	$-0.102320\pi$
$24$		0			0
$25$	−0.904231	+	0.958429i	−0.180846	+	0.191686i
$26$	−1.07247	+	1.85757i	−0.210329	+	0.364300i
$27$		0			0
$28$	3.21271	+	5.56458i	0.607145	+	1.05161i
$29$	5.41695	+	1.28384i	1.00590	+	0.238403i	0.700371	−	0.713779i	$-0.253018\pi$
$29$	5.41695	+	1.28384i	1.00590	+	0.238403i	0.305531	+	0.952182i	$0.401166\pi$
$30$		0			0
$31$	5.73952	+	2.88249i	1.03085	+	0.517711i	0.882050	−	0.471157i	$-0.156163\pi$
$31$	5.73952	+	2.88249i	1.03085	+	0.517711i	0.148798	+	0.988868i	$0.452460\pi$
$32$	5.70979	+	0.667379i	1.00936	+	0.117977i
$33$		0			0
$34$	1.94936	−	0.979008i	0.334313	−	0.167898i
$35$	9.71228	−	3.53498i	1.64167	−	0.597521i
$36$		0			0
$37$	−2.56937	−	0.935175i	−0.422402	−	0.153742i	0.122069	−	0.992522i	$-0.461047\pi$
$37$	−2.56937	−	0.935175i	−0.422402	−	0.153742i	−0.544471	+	0.838780i	$0.683269\pi$
$38$	−2.16052	+	0.252528i	−0.350482	+	0.0409655i
$39$		0			0
$40$	1.69853	−	5.67349i	0.268561	−	0.897057i
$41$	2.59515	−	8.66839i	0.405294	−	1.35378i	−0.475267	−	0.879842i	$-0.657648\pi$
$41$	2.59515	−	8.66839i	0.405294	−	1.35378i	0.880560	−	0.473934i	$-0.157166\pi$
$42$		0			0
$43$	7.76471	−	0.907565i	1.18411	−	0.138402i	0.498840	−	0.866694i	$-0.333759\pi$
$43$	7.76471	−	0.907565i	1.18411	−	0.138402i	0.685267	+	0.728292i	$0.259685\pi$
$44$	4.34719	+	1.58225i	0.655364	+	0.238533i
$45$		0			0
$46$	1.55131	−	0.564629i	0.228728	−	0.0832500i
$47$	−9.04350	+	4.54182i	−1.31913	+	0.662492i	−0.962380	−	0.271708i	$-0.912412\pi$
$47$	−9.04350	+	4.54182i	−1.31913	+	0.662492i	−0.356750	+	0.934200i	$0.616115\pi$
$48$		0			0
$49$	−9.84186	−	1.15035i	−1.40598	−	0.164335i
$50$	−0.778766	−	0.391111i	−0.110134	−	0.0553115i
$51$		0			0
$52$	4.93113	+	1.16870i	0.683824	+	0.162069i
$53$	0.00494432	+	0.00856381i	0.000679154	+	0.00117633i	0.866365	−	0.499412i	$-0.166450\pi$
$53$	0.00494432	+	0.00856381i	0.000679154	+	0.00117633i	−0.865686	+	0.500588i	$0.833117\pi$
$54$		0			0
$55$	3.72072	−	6.44448i	0.501702	−	0.868973i
$56$	−6.64883	+	7.04735i	−0.888488	+	0.941742i
$57$		0			0
$58$	0.214081	+	3.67563i	0.0281102	+	0.482634i
$59$	−6.79150	+	9.12257i	−0.884178	+	1.18766i	0.0971408	+	0.995271i	$0.469030\pi$
$59$	−6.79150	+	9.12257i	−0.884178	+	1.18766i	−0.981319	+	0.192387i	$0.938377\pi$
$60$		0			0
$61$	−7.52933	−	4.95212i	−0.964032	−	0.634054i	−0.0331796	−	0.999449i	$-0.510563\pi$
$61$	−7.52933	−	4.95212i	−0.964032	−	0.634054i	−0.930852	+	0.365396i	$0.880934\pi$
$62$	−0.737619	+	4.18325i	−0.0936777	+	0.531273i
$63$		0			0
$64$	0.116049	+	0.658144i	0.0145061	+	0.0822680i
$65$	3.22872	−	7.48500i	0.400473	−	0.928400i
$66$		0			0
$67$	5.68771	−	1.34801i	0.694864	−	0.164686i	0.132018	−	0.991247i	$-0.457854\pi$
$67$	5.68771	−	1.34801i	0.694864	−	0.164686i	0.562846	+	0.826562i	$0.309706\pi$
$68$	−3.53679	−	3.74878i	−0.428899	−	0.454607i
$69$		0			0
$70$	4.08198	+	5.48305i	0.487890	+	0.655349i
$71$	−1.81817	+	1.52563i	−0.215777	+	0.181058i	−0.744269	−	0.667880i	$-0.767202\pi$
$71$	−1.81817	+	1.52563i	−0.215777	+	0.181058i	0.528492	+	0.848938i	$0.322758\pi$
$72$		0			0
$73$	3.61987	+	3.03743i	0.423674	+	0.355505i	0.829559	−	0.558420i	$-0.188592\pi$
$73$	3.61987	+	3.03743i	0.423674	+	0.355505i	−0.405885	+	0.913924i	$0.633037\pi$
$74$	0.105147	−	1.80531i	0.0122231	−	0.209863i
$75$		0			0
$76$	2.03557	+	4.71897i	0.233495	+	0.541303i
$77$	−10.1713	+	6.68977i	−1.15913	+	0.762370i
$78$		0			0
$79$	−2.58181	−	8.62383i	−0.290476	−	0.970257i	−0.971310	−	0.237819i	$-0.923568\pi$
$79$	−2.58181	−	8.62383i	−0.290476	−	0.970257i	0.680834	−	0.732438i	$-0.261618\pi$
$80$	−3.93828			−0.440313
$81$		0			0
$82$	5.98444			0.660871
$83$	1.06156	+	3.54585i	0.116521	+	0.389207i	0.996276	−	0.0862198i	$-0.0274787\pi$
$83$	1.06156	+	3.54585i	0.116521	+	0.389207i	−0.879755	+	0.475427i	$0.842294\pi$
$84$		0			0
$85$	−6.92638	+	4.55555i	−0.751272	+	0.494119i
$86$	2.04786	+	4.74747i	0.220826	+	0.511933i
$87$		0			0
$88$	−0.405603	+	6.96394i	−0.0432374	+	0.742358i
$89$	−9.57258	−	8.03235i	−1.01469	−	0.851427i	−0.0257399	−	0.999669i	$-0.508194\pi$
$89$	−9.57258	−	8.03235i	−1.01469	−	0.851427i	−0.988951	+	0.148242i	$0.952639\pi$
$90$		0			0
$91$	−10.2160	+	8.57223i	−1.07093	+	0.898614i
$92$	−2.32916	−	3.12861i	−0.242832	−	0.326180i
$93$		0			0
$94$	−4.59304	−	4.86834i	−0.473736	−	0.502131i
$95$	8.04395	−	1.90645i	0.825291	−	0.195598i
$96$		0			0
$97$	−2.83273	+	6.56702i	−0.287621	+	0.666780i	−0.999364	−	0.0356601i	$-0.988647\pi$
$97$	−2.83273	+	6.56702i	−0.287621	+	0.666780i	0.711743	+	0.702440i	$0.247906\pi$
$98$	−1.13799	−	6.45388i	−0.114955	−	0.651940i
$99$		0			0
$100$	−0.357534	+	2.02767i	−0.0357534	+	0.202767i
$101$	1.75962	+	1.15732i	0.175089	+	0.115158i	0.634029	−	0.773310i	$-0.281400\pi$
$101$	1.75962	+	1.15732i	0.175089	+	0.115158i	−0.458939	+	0.888468i	$0.651771\pi$
$102$		0			0
$103$	−1.23334	+	1.65666i	−0.121524	+	0.163235i	−0.858722	−	0.512442i	$-0.828741\pi$
$103$	−1.23334	+	1.65666i	−0.121524	+	0.163235i	0.737198	+	0.675677i	$0.236149\pi$
$104$	0.444315	+	7.62860i	0.0435687	+	0.748046i
$105$		0			0
$106$	−0.00448806	+	0.00475707i	−0.000435919	+	0.000462048i
$107$	−7.13179	+	12.3526i	−0.689456	+	1.19417i	0.282558	+	0.959250i	$0.408817\pi$
$107$	−7.13179	+	12.3526i	−0.689456	+	1.19417i	−0.972014	+	0.234923i	$0.924516\pi$
$108$		0			0
$109$	−6.70237	−	11.6088i	−0.641970	−	1.11193i	−0.984992	−	0.172598i	$-0.944784\pi$
$109$	−6.70237	−	11.6088i	−0.641970	−	1.11193i	0.343022	−	0.939327i	$-0.388549\pi$
$110$	4.78890	+	1.13499i	0.456604	+	0.108217i
$111$		0			0
$112$	5.75764	+	2.89160i	0.544046	+	0.273230i
$113$	2.94032	+	0.343674i	0.276602	+	0.0323301i	0.253263	−	0.967398i	$-0.418496\pi$
$113$	2.94032	+	0.343674i	0.276602	+	0.0323301i	0.0233389	+	0.999728i	$0.492570\pi$
$114$		0			0
$115$	−5.60664	+	2.81576i	−0.522822	+	0.262571i
$116$	8.17432	−	2.97521i	0.758967	−	0.276241i
$117$		0			0
$118$	−7.06818	−	2.57261i	−0.650679	−	0.236828i
$119$	13.4710	−	1.57453i	1.23488	−	0.144337i
$120$		0			0
$121$	0.640970	−	2.14099i	0.0582700	−	0.194635i
$122$	1.70941	−	5.70982i	0.154763	−	0.516943i
$123$		0			0
$124$	9.96814	−	1.16511i	0.895165	−	0.104630i
$125$	−8.69737	−	3.16558i	−0.777917	−	0.283139i
$126$		0			0
$127$	−11.3063	+	4.11514i	−1.00327	+	0.365160i	−0.790844	−	0.612017i	$-0.790358\pi$
$127$	−11.3063	+	4.11514i	−1.00327	+	0.365160i	−0.212425	+	0.977177i	$0.568136\pi$
$128$	9.87941	−	4.96162i	0.873224	−	0.438550i
$129$		0			0
$130$	5.35484	+	0.625891i	0.469650	+	0.0548943i
$131$	−4.58993	−	2.30515i	−0.401024	−	0.201402i	0.236844	−	0.971548i	$-0.423887\pi$
$131$	−4.58993	−	2.30515i	−0.401024	−	0.201402i	−0.637868	+	0.770146i	$0.720183\pi$
$132$		0			0
$133$	−13.1598	−	3.11892i	−1.14110	−	0.270445i
$134$	1.93295	+	3.34796i	0.166981	+	0.289220i
$135$		0			0
$136$	3.88570	−	6.73023i	0.333196	−	0.577113i
$137$	−1.30458	+	1.38277i	−0.111458	+	0.118138i	−0.780700	−	0.624906i	$-0.785137\pi$
$137$	−1.30458	+	1.38277i	−0.111458	+	0.118138i	0.669242	+	0.743044i	$0.266619\pi$
$138$		0			0
$139$	−0.544109	−	9.34199i	−0.0461507	−	0.792377i	−0.939402	−	0.342819i	$-0.888618\pi$
$139$	−0.544109	−	9.34199i	−0.0461507	−	0.792377i	0.893251	−	0.449559i	$-0.148419\pi$
$140$	9.64426	−	12.9545i	0.815089	−	1.09485i
$141$		0			0
$142$	−1.31149	−	0.862583i	−0.110058	−	0.0723864i
$143$	−1.66732	+	9.45583i	−0.139428	+	0.790736i
$144$		0			0
$145$	−2.42980	−	13.7801i	−0.201784	−	1.14437i
$146$	−1.23785	+	2.86966i	−0.102445	+	0.237494i
$147$		0			0
$148$	−4.15737	+	0.985314i	−0.341733	+	0.0809923i
$149$	0.609823	+	0.646375i	0.0499587	+	0.0529531i	0.751871	−	0.659310i	$-0.229152\pi$
$149$	0.609823	+	0.646375i	0.0499587	+	0.0529531i	−0.701912	+	0.712263i	$0.747670\pi$
$150$		0			0
$151$	−4.81223	−	6.46395i	−0.391614	−	0.526029i	0.561969	−	0.827158i	$-0.310044\pi$
$151$	−4.81223	−	6.46395i	−0.391614	−	0.526029i	−0.953583	+	0.301129i	$0.902636\pi$
$152$	−5.93640	+	4.98123i	−0.481506	+	0.404031i
$153$		0			0
$154$	−6.16788	−	5.17546i	−0.497022	−	0.417051i
$155$	0.938654	−	16.1161i	0.0753945	−	1.29447i
$156$		0			0
$157$	−5.73149	−	13.2871i	−0.457423	−	1.06042i	−0.978375	−	0.206839i	$-0.933682\pi$
$157$	−5.73149	−	13.2871i	−0.457423	−	1.06042i	0.520952	−	0.853586i	$-0.325577\pi$
$158$	4.97422	−	3.27160i	0.395728	−	0.260274i
$159$		0			0
$160$	−4.14409	−	13.8422i	−0.327619	−	1.09432i
$161$	10.2641			0.808928
$162$		0			0
$163$	8.05495			0.630912			0.315456	−	0.948940i	$-0.397843\pi$
$163$	8.05495			0.630912			0.315456	+	0.948940i	$0.397843\pi$
$164$	−4.05514	−	13.5451i	−0.316654	−	1.05770i
$165$		0			0
$166$	−2.04524	+	1.34518i	−0.158742	+	0.104406i
$167$	6.68676	+	15.5017i	0.517437	+	1.19955i	0.953980	+	0.299870i	$0.0969435\pi$
$167$	6.68676	+	15.5017i	0.517437	+	1.19955i	−0.436543	+	0.899683i	$0.643797\pi$
$168$		0			0
$169$	0.144308	−	2.47768i	0.0111006	−	0.190591i
$170$	−4.20016	−	3.52435i	−0.322138	−	0.270306i
$171$		0			0
$172$	9.35772	−	7.85206i	0.713520	−	0.598714i
$173$	4.01480	+	5.39281i	0.305239	+	0.410008i	0.928103	−	0.372322i	$-0.121438\pi$
$173$	4.01480	+	5.39281i	0.305239	+	0.410008i	−0.622864	+	0.782330i	$0.714031\pi$
$174$		0			0
$175$	−3.71823	−	3.94110i	−0.281072	−	0.297919i
$176$	4.51378	−	1.06979i	0.340239	−	0.0806381i
$177$		0			0
$178$	3.27343	−	7.58867i	0.245354	−	0.568795i
$179$	−2.64043	−	14.9746i	−0.197355	−	1.11926i	−0.909024	−	0.416743i	$-0.863172\pi$
$179$	−2.64043	−	14.9746i	−0.197355	−	1.11926i	0.711669	−	0.702515i	$-0.247940\pi$
$180$		0			0
$181$	−0.973297	+	5.51984i	−0.0723446	+	0.410287i	0.927032	+	0.374982i	$0.122351\pi$
$181$	−0.973297	+	5.51984i	−0.0723446	+	0.410287i	−0.999377	+	0.0353044i	$0.988760\pi$
$182$	−7.36906	−	4.84671i	−0.546231	−	0.359262i
$183$		0			0
$184$	3.51210	−	4.71757i	0.258915	−	0.347784i
$185$	0.399604	+	6.86094i	0.0293795	+	0.504427i
$186$		0			0
$187$	6.70107	−	7.10272i	0.490031	−	0.519403i
$188$	−7.90664	+	13.6947i	−0.576651	+	0.998788i
$189$		0			0
$190$	2.73371	+	4.73492i	0.198324	+	0.343507i
$191$	−4.17988	−	0.990651i	−0.302446	−	0.0716810i	0.0765910	−	0.997063i	$-0.475596\pi$
$191$	−4.17988	−	0.990651i	−0.302446	−	0.0716810i	−0.379037	+	0.925382i	$0.623745\pi$
$192$		0			0
$193$	2.53227	+	1.27175i	0.182277	+	0.0915427i	0.537597	−	0.843202i	$-0.319332\pi$
$193$	2.53227	+	1.27175i	0.182277	+	0.0915427i	−0.355321	+	0.934744i	$0.615628\pi$
$194$	−4.69810	−	0.549129i	−0.337304	−	0.0394252i
$195$		0			0
$196$	−13.8365	+	6.94896i	−0.988323	+	0.496354i
$197$	19.9667	−	7.26729i	1.42257	−	0.517773i	0.487777	−	0.872968i	$-0.337808\pi$
$197$	19.9667	−	7.26729i	1.42257	−	0.517773i	0.934792	+	0.355195i	$0.115586\pi$
$198$		0			0
$199$	−9.14529	−	3.32862i	−0.648293	−	0.235959i	−0.00311899	−	0.999995i	$-0.500993\pi$
$199$	−9.14529	−	3.32862i	−0.648293	−	0.235959i	−0.645174	+	0.764036i	$0.723215\pi$
$200$	−3.08366	+	0.360429i	−0.218048	+	0.0254861i
$201$		0			0
$202$	−0.399493	+	1.33440i	−0.0281082	+	0.0938881i
$203$	−6.56543	+	21.9301i	−0.460803	+	1.53919i
$204$		0			0
$205$	−22.5896	+	2.64035i	−1.57773	+	0.184410i
$206$	−1.28358	−	0.467185i	−0.0894313	−	0.0325503i
$207$		0			0
$208$	4.77511	−	1.73800i	0.331094	−	0.120508i
$209$	−8.70154	+	4.37008i	−0.601898	+	0.302285i
$210$		0			0
$211$	−19.4458	−	2.27289i	−1.33870	−	0.156472i	−0.583581	−	0.812055i	$-0.698349\pi$
$211$	−19.4458	−	2.27289i	−1.33870	−	0.156472i	−0.755123	+	0.655583i	$0.772423\pi$
$212$	0.0138083	+	0.00693478i	0.000948357	+	0.000476283i
$213$		0			0
$214$	−9.17925	−	2.17552i	−0.627481	−	0.148716i
$215$	−9.82471	−	17.0169i	−0.670040	−	1.16054i
$216$		0			0
$217$	−13.2052	+	22.8720i	−0.896424	+	1.55265i
$218$	6.08388	−	6.44854i	0.412053	−	0.436750i
$219$		0			0
$220$	−0.676102	−	11.6082i	−0.0455828	−	0.782627i
$221$	6.38774	−	8.58022i	0.429686	−	0.577168i
$222$		0			0
$223$	13.5067	+	8.88352i	0.904478	+	0.594885i	0.914287	−	0.405067i	$-0.132752\pi$
$223$	13.5067	+	8.88352i	0.904478	+	0.594885i	−0.00980880	+	0.999952i	$0.503122\pi$
$224$	−4.10482	+	23.2796i	−0.274265	+	1.55543i
$225$		0			0
$226$	0.339982	+	1.92814i	0.0226153	+	0.128258i
$227$	8.40893	−	19.4941i	0.558121	−	1.29387i	−0.372551	−	0.928012i	$-0.621517\pi$
$227$	8.40893	−	19.4941i	0.558121	−	1.29387i	0.930671	−	0.365857i	$-0.119224\pi$
$228$		0			0
$229$	−8.39688	+	1.99010i	−0.554881	+	0.131509i	−0.498484	−	0.866899i	$-0.666110\pi$
$229$	−8.39688	+	1.99010i	−0.554881	+	0.131509i	−0.0563976	+	0.998408i	$0.517961\pi$
$230$	−2.84752	−	3.01819i	−0.187760	−	0.199014i
$231$		0			0
$232$	7.83290	+	10.5214i	0.514255	+	0.690765i
$233$	−11.4634	+	9.61890i	−0.750989	+	0.630155i	−0.935764	−	0.352626i	$-0.885289\pi$
$233$	−11.4634	+	9.61890i	−0.750989	+	0.630155i	0.184775	+	0.982781i	$0.440844\pi$
$234$		0			0
$235$	19.4854	+	16.3502i	1.27109	+	1.06657i
$236$	−1.03331	+	17.7413i	−0.0672629	+	1.15486i
$237$		0			0
$238$	3.55282	+	8.23637i	0.230295	+	0.533885i
$239$	3.01654	−	1.98401i	0.195124	−	0.128335i	−0.448188	−	0.893939i	$-0.647930\pi$
$239$	3.01654	−	1.98401i	0.195124	−	0.128335i	0.643311	+	0.765605i	$0.277560\pi$
$240$		0			0
$241$	6.56533	+	21.9297i	0.422910	+	1.41262i	0.858658	+	0.512550i	$0.171299\pi$
$241$	6.56533	+	21.9297i	0.422910	+	1.41262i	−0.435747	+	0.900069i	$0.643516\pi$
$242$	1.47808			0.0950149
$243$		0			0
$244$	−14.0819			−0.901500
$245$	7.14308	+	23.8596i	0.456355	+	1.52433i
$246$		0			0
$247$	−8.91184	+	5.86141i	−0.567047	+	0.372953i
$248$	5.99391	+	13.8954i	0.380614	+	0.882361i
$249$		0			0
$250$	0.355925	−	6.11100i	0.0225107	−	0.386494i
$251$	−16.2193	−	13.6096i	−1.02375	−	0.859031i	−0.0336587	−	0.999433i	$-0.510716\pi$
$251$	−16.2193	−	13.6096i	−1.02375	−	0.859031i	−0.990095	+	0.140402i	$0.955160\pi$
$252$		0			0
$253$	5.66107	−	4.75020i	0.355909	−	0.298643i
$254$	−4.75192	−	6.38293i	−0.298162	−	0.400501i
$255$		0			0
$256$	5.93481	+	6.29053i	0.370926	+	0.393158i
$257$	−7.57713	+	1.79581i	−0.472649	+	0.112020i	−0.460035	−	0.887901i	$-0.652163\pi$
$257$	−7.57713	+	1.79581i	−0.472649	+	0.112020i	−0.0126134	+	0.999920i	$0.504015\pi$
$258$		0			0
$259$	4.45329	−	10.3239i	0.276714	−	0.641495i
$260$	−2.21188	−	12.5442i	−0.137175	−	0.777958i
$261$		0			0
$262$	0.589879	−	3.34537i	0.0364428	−	0.206678i
$263$	−1.27536	−	0.838814i	−0.0786418	−	0.0517235i	0.509579	−	0.860424i	$-0.329801\pi$
$263$	−1.27536	−	0.838814i	−0.0786418	−	0.0517235i	−0.588221	+	0.808700i	$0.700171\pi$
$264$		0			0
$265$	0.0148424	−	0.0199368i	0.000911761	−	0.00122471i
$266$	−0.520082	−	8.92947i	−0.0318883	−	0.547501i
$267$		0			0
$268$	6.26795	−	6.64364i	0.382876	−	0.405825i
$269$	14.7193	−	25.4946i	0.897454	−	1.55444i	0.0667154	−	0.997772i	$-0.478748\pi$
$269$	14.7193	−	25.4946i	0.897454	−	1.55444i	0.830738	−	0.556663i	$-0.187919\pi$
$270$		0			0
$271$	−7.28643	−	12.6205i	−0.442619	−	0.766639i	0.555264	−	0.831674i	$-0.312617\pi$
$271$	−7.28643	−	12.6205i	−0.442619	−	0.766639i	−0.997883	+	0.0650354i	$0.979284\pi$
$272$	−5.02863	−	1.19181i	−0.304905	−	0.0722639i
$273$		0			0
$274$	−1.12356	−	0.564275i	−0.0678769	−	0.0340891i
$275$	−3.87467	−	0.452884i	−0.233651	−	0.0273099i
$276$		0			0
$277$	9.13881	−	4.58968i	0.549098	−	0.275767i	−0.152545	−	0.988297i	$-0.548747\pi$
$277$	9.13881	−	4.58968i	0.549098	−	0.275767i	0.701642	+	0.712529i	$0.252450\pi$
$278$	5.81576	−	2.11676i	0.348806	−	0.126955i
$279$		0			0
$280$	22.8840	+	8.32910i	1.36758	+	0.497759i
$281$	−6.97618	+	0.815398i	−0.416164	+	0.0486426i	−0.321599	−	0.946876i	$-0.604220\pi$
$281$	−6.97618	+	0.815398i	−0.416164	+	0.0486426i	−0.0945653	+	0.995519i	$0.530146\pi$
$282$		0			0
$283$	6.20135	−	20.7140i	0.368632	−	1.23132i	−0.549651	−	0.835394i	$-0.685239\pi$
$283$	6.20135	−	20.7140i	0.368632	−	1.23132i	0.918284	−	0.395923i	$-0.129575\pi$
$284$	−1.06367	+	3.55292i	−0.0631175	+	0.210827i
$285$		0			0
$286$	−6.30736	+	0.737224i	−0.372962	+	0.0435930i
$287$	34.9640	+	12.7258i	2.06386	+	0.751183i
$288$		0			0
$289$	5.75215	−	2.09361i	0.338362	−	0.123154i
$290$	8.26998	−	4.15334i	0.485630	−	0.243893i
$291$		0			0
$292$	7.33393	+	0.857214i	0.429186	+	0.0501647i
$293$	−9.76463	−	4.90398i	−0.570456	−	0.286494i	0.140097	−	0.990138i	$-0.455259\pi$
$293$	−9.76463	−	4.90398i	−0.570456	−	0.286494i	−0.710553	+	0.703644i	$0.751555\pi$
$294$		0			0
$295$	27.8155	+	6.59240i	1.61948	+	0.383824i
$296$	−3.22124	−	5.57934i	−0.187230	−	0.324293i
$297$		0			0
$298$	−0.293862	+	0.508983i	−0.0170229	+	0.0294846i
$299$	5.55536	−	5.88833i	0.321275	−	0.340531i
$300$		0			0
$301$	1.86913	+	32.0918i	0.107735	+	1.84974i
$302$	3.18268	−	4.27508i	0.183142	−	0.246003i
$303$		0			0
$304$	4.30553	+	2.83179i	0.246939	+	0.162414i
$305$	−3.93337	+	22.3072i	−0.225224	+	1.27731i
$306$		0			0
$307$	0.798574	+	4.52894i	0.0455770	+	0.258480i	0.999079	−	0.0429063i	$-0.0136617\pi$
$307$	0.798574	+	4.52894i	0.0455770	+	0.258480i	−0.953502	+	0.301386i	$0.902551\pi$
$308$	−7.53465	+	17.4673i	−0.429327	+	0.995291i
$309$		0			0
$310$	10.3890	−	2.46223i	0.590054	−	0.139845i
$311$	11.9674	+	12.6847i	0.678610	+	0.719285i	0.971547	−	0.236847i	$-0.0761140\pi$
$311$	11.9674	+	12.6847i	0.678610	+	0.719285i	−0.292937	+	0.956132i	$0.594632\pi$
$312$		0			0
$313$	−9.45127	−	12.6953i	−0.534217	−	0.717579i	0.450298	−	0.892879i	$-0.351318\pi$
$313$	−9.45127	−	12.6953i	−0.534217	−	0.717579i	−0.984515	+	0.175300i	$0.943910\pi$
$314$	7.33136	−	6.15174i	0.413732	−	0.347163i
$315$		0			0
$316$	−10.7755	−	9.04173i	−0.606170	−	0.508637i
$317$	−1.13979	+	19.5694i	−0.0640169	+	1.09913i	0.801418	+	0.598105i	$0.204080\pi$
$317$	−1.13979	+	19.5694i	−0.0640169	+	1.09913i	−0.865434	+	0.501022i	$0.832957\pi$
$318$		0			0
$319$	6.52805	+	15.1337i	0.365501	+	0.847326i
$320$	1.40342	−	0.923043i	0.0784535	−	0.0515997i
$321$		0			0
$322$	1.94694	+	6.50323i	0.108499	+	0.362411i
$323$	10.8479			0.603594
$324$		0			0
$325$	−4.27338			−0.237044
$326$	1.52789	+	5.10351i	0.0846221	+	0.282657i
$327$		0			0
$328$	17.8127	−	11.7156i	0.983541	−	0.646885i
$329$	−16.4823	−	38.2102i	−0.908698	−	2.10660i
$330$		0			0
$331$	1.27212	−	21.8415i	0.0699221	−	1.20052i	−0.762729	−	0.646719i	$-0.776141\pi$
$331$	1.27212	−	21.8415i	0.0699221	−	1.20052i	0.832651	−	0.553798i	$-0.186822\pi$
$332$	4.43055	+	3.71767i	0.243158	+	0.204034i
$333$		0			0
$334$	−8.55328	+	7.17706i	−0.468015	+	0.392711i
$335$	−8.77348	−	11.7848i	−0.479346	−	0.643874i
$336$		0			0
$337$	6.15073	+	6.51940i	0.335052	+	0.355134i	0.872893	−	0.487912i	$-0.162241\pi$
$337$	6.15073	+	6.51940i	0.335052	+	0.355134i	−0.537841	+	0.843046i	$0.680760\pi$
$338$	1.59720	−	0.378543i	0.0868761	−	0.0205900i
$339$		0			0
$340$	−5.13090	+	11.8948i	−0.278262	+	0.645084i
$341$	3.30191	+	18.7261i	0.178809	+	1.01407i
$342$		0			0
$343$	2.07706	−	11.7796i	0.112151	−	0.636040i
$344$	15.3895	+	10.1218i	0.829744	+	0.545731i
$345$		0			0
$346$	−2.65527	+	3.56665i	−0.142748	+	0.191744i
$347$	−1.11823	−	19.1993i	−0.0600299	−	1.03067i	−0.885028	−	0.465538i	$-0.845861\pi$
$347$	−1.11823	−	19.1993i	−0.0600299	−	1.03067i	0.824998	−	0.565135i	$-0.191176\pi$
$348$		0			0
$349$	−14.6541	+	15.5324i	−0.784414	+	0.831430i	−0.989077	−	0.147402i	$-0.952909\pi$
$349$	−14.6541	+	15.5324i	−0.784414	+	0.831430i	0.204662	+	0.978833i	$0.434390\pi$
$350$	1.79174	−	3.10339i	0.0957726	−	0.165883i
$351$		0			0
$352$	8.50973	+	14.7393i	0.453570	+	0.785607i
$353$	−14.3157	−	3.39287i	−0.761946	−	0.180584i	−0.168768	−	0.985656i	$-0.553979\pi$
$353$	−14.3157	−	3.39287i	−0.761946	−	0.180584i	−0.593178	+	0.805071i	$0.702127\pi$
$354$		0			0
$355$	5.33111	+	2.67738i	0.282946	+	0.142101i
$356$	−19.3942	−	2.26686i	−1.02789	−	0.120143i
$357$		0			0
$358$	8.98690	−	4.51339i	0.474972	−	0.238540i
$359$	−10.0637	+	3.66289i	−0.531142	+	0.193320i	−0.593648	−	0.804725i	$-0.702313\pi$
$359$	−10.0637	+	3.66289i	−0.531142	+	0.193320i	0.0625063	+	0.998045i	$0.480091\pi$
$360$		0			0
$361$	7.68928	+	2.79867i	0.404699	+	0.147298i
$362$	−3.68192	+	0.430355i	−0.193517	+	0.0226189i
$363$		0			0
$364$	−5.97661	+	19.9633i	−0.313259	+	1.04636i
$365$	3.40644	−	11.3783i	0.178301	−	0.595568i
$366$		0			0
$367$	3.93885	−	0.460386i	0.205606	−	0.0240319i	−0.0126662	−	0.999920i	$-0.504032\pi$
$367$	3.93885	−	0.460386i	0.205606	−	0.0240319i	0.218273	+	0.975888i	$0.429958\pi$
$368$	−3.67519	−	1.33766i	−0.191583	−	0.0697304i
$369$		0			0
$370$	−4.27121	+	1.55459i	−0.222050	+	0.0808194i
$371$	−0.0363373	+	0.0182493i	−0.00188654	+	0.000947455i
$372$		0			0
$373$	23.5625	+	2.75406i	1.22002	+	0.142600i	0.701628	−	0.712544i	$-0.252457\pi$
$373$	23.5625	+	2.75406i	1.22002	+	0.142600i	0.518392	+	0.855143i	$0.326531\pi$
$374$	5.77128	+	2.89845i	0.298426	+	0.149875i
$375$		0			0
$376$	−23.2018	−	5.49893i	−1.19654	−	0.283586i
$377$	9.02736	+	15.6359i	0.464933	+	0.805287i
$378$		0			0
$379$	13.0094	−	22.5330i	0.668249	−	1.15744i	−0.310145	−	0.950689i	$-0.600377\pi$
$379$	13.0094	−	22.5330i	0.668249	−	1.15744i	0.978393	−	0.206752i	$-0.0662892\pi$
$380$	8.86457	−	9.39589i	0.454743	−	0.481999i
$381$		0			0
$382$	−0.165192	−	2.83623i	−0.00845194	−	0.145114i
$383$	−17.5716	+	23.6027i	−0.897864	+	1.20604i	0.0799988	+	0.996795i	$0.474508\pi$
$383$	−17.5716	+	23.6027i	−0.897864	+	1.20604i	−0.977863	+	0.209246i	$0.932899\pi$
$384$		0			0
$385$	25.5655	+	16.8147i	1.30294	+	0.856956i
$386$	−0.325437	+	1.84564i	−0.0165643	+	0.0939407i
$387$		0			0
$388$	1.94061	+	11.0057i	0.0985194	+	0.558731i
$389$	−10.4976	+	24.3363i	−0.532252	+	1.23390i	0.413943	+	0.910303i	$0.364151\pi$
$389$	−10.4976	+	24.3363i	−0.532252	+	1.23390i	−0.946195	+	0.323596i	$0.895108\pi$
$390$		0			0
$391$	−8.01100	+	1.89864i	−0.405134	+	0.0960185i
$392$	−16.0218	−	16.9821i	−0.809224	−	0.857728i
$393$		0			0
$394$	8.39182	+	11.2722i	0.422774	+	0.567884i
$395$	−17.3329	+	14.5440i	−0.872114	+	0.731790i
$396$		0			0
$397$	−21.8020	−	18.2941i	−1.09421	−	0.918154i	−0.0971903	−	0.995266i	$-0.530986\pi$
$397$	−21.8020	−	18.2941i	−1.09421	−	0.918154i	−0.997022	+	0.0771123i	$0.975430\pi$
$398$	0.374256	−	6.42573i	0.0187598	−	0.322093i
$399$		0			0
$400$	0.817736	+	1.89573i	0.0408868	+	0.0947863i
$401$	11.8828	−	7.81543i	0.593398	−	0.390284i	−0.216993	−	0.976173i	$-0.569625\pi$
$401$	11.8828	−	7.81543i	0.593398	−	0.390284i	0.810391	+	0.585889i	$0.199255\pi$
$402$		0			0
$403$	5.97406	+	19.9547i	0.297589	+	0.994017i
$404$	3.29097			0.163732
$405$		0			0
$406$	−15.1400			−0.751383
$407$	−2.32169	−	7.75499i	−0.115082	−	0.384400i
$408$		0			0
$409$	−2.60169	+	1.71116i	−0.128645	+	0.0846114i	−0.612201	−	0.790702i	$-0.709716\pi$
$409$	−2.60169	+	1.71116i	−0.128645	+	0.0846114i	0.483555	+	0.875314i	$0.339345\pi$
$410$	−5.95778	−	13.8117i	−0.294234	−	0.682110i
$411$		0			0
$412$	−0.187649	+	3.22181i	−0.00924482	+	0.158727i
$413$	−35.8251	−	30.0608i	−1.76284	−	1.47920i
$414$		0			0
$415$	7.12674	−	5.98005i	0.349838	−	0.293549i
$416$	11.1333	+	14.9547i	0.545857	+	0.733213i
$417$		0			0
$418$	−4.41937	−	4.68425i	−0.216158	−	0.229114i
$419$	−6.66640	+	1.57997i	−0.325675	+	0.0771864i	−0.390201	−	0.920730i	$-0.627595\pi$
$419$	−6.66640	+	1.57997i	−0.325675	+	0.0771864i	0.0645262	+	0.997916i	$0.479446\pi$
$420$		0			0
$421$	−5.91445	+	13.7112i	−0.288253	+	0.668245i	−0.999394	−	0.0348039i	$-0.988919\pi$
$421$	−5.91445	+	13.7112i	−0.288253	+	0.668245i	0.711141	+	0.703049i	$0.248179\pi$
$422$	−2.24848	−	12.7517i	−0.109454	−	0.620745i
$423$		0			0
$424$	−0.00404592	+	0.0229456i	−0.000196487	+	0.00111434i
$425$	3.63104	+	2.38817i	0.176131	+	0.115843i
$426$		0			0
$427$	22.1291	−	29.7245i	1.07090	−	1.43847i
$428$	1.29594	+	22.2504i	0.0626415	+	1.07551i
$429$		0			0
$430$	8.91811	−	9.45264i	0.430069	−	0.455847i
$431$	−15.4334	+	26.7314i	−0.743399	+	1.28760i	0.207540	+	0.978227i	$0.433454\pi$
$431$	−15.4334	+	26.7314i	−0.743399	+	1.28760i	−0.950939	+	0.309378i	$0.899879\pi$
$432$		0			0
$433$	14.3849	+	24.9154i	0.691295	+	1.19736i	0.971414	+	0.237393i	$0.0762928\pi$
$433$	14.3849	+	24.9154i	0.691295	+	1.19736i	−0.280119	+	0.959965i	$0.590374\pi$
$434$	−16.9962	−	4.02817i	−0.815844	−	0.193359i
$435$		0			0
$436$	−18.7181	−	9.40058i	−0.896434	−	0.450206i
$437$	8.15413	+	0.953081i	0.390065	+	0.0455920i
$438$		0			0
$439$	−3.95327	+	1.98541i	−0.188679	+	0.0947582i	−0.540631	−	0.841260i	$-0.681814\pi$
$439$	−3.95327	+	1.98541i	−0.188679	+	0.0947582i	0.351952	+	0.936018i	$0.385518\pi$
$440$	16.4761	−	5.99681i	0.785467	−	0.285886i
$441$		0			0
$442$	6.64797	+	2.41966i	0.316212	+	0.115092i
$443$	2.64954	−	0.309687i	0.125884	−	0.0147137i	−0.0529177	−	0.998599i	$-0.516852\pi$
$443$	2.64954	−	0.309687i	0.125884	−	0.0147137i	0.178801	+	0.983885i	$0.442778\pi$
$444$		0			0
$445$	−9.00818	+	30.0894i	−0.427029	+	1.42637i
$446$	−3.06648	+	10.2428i	−0.145202	+	0.485009i
$447$		0			0
$448$	−2.72948	+	0.319030i	−0.128956	+	0.0150728i
$449$	39.1256	+	14.2405i	1.84645	+	0.672053i	0.986975	+	0.160874i	$0.0514312\pi$
$449$	39.1256	+	14.2405i	1.84645	+	0.672053i	0.859474	+	0.511179i	$0.170791\pi$
$450$		0			0
$451$	25.1735	−	9.16239i	1.18537	−	0.431440i
$452$	4.13375	−	2.07605i	0.194435	−	0.0976490i
$453$		0			0
$454$	13.9463	+	1.63008i	0.654530	+	0.0765036i
$455$	29.9546	+	15.0438i	1.40429	+	0.705262i
$456$		0			0
$457$	7.45826	+	1.76764i	0.348883	+	0.0826867i	0.401321	−	0.915937i	$-0.368551\pi$
$457$	7.45826	+	1.76764i	0.348883	+	0.0826867i	−0.0524384	+	0.998624i	$0.516699\pi$
$458$	−2.85365	−	4.94267i	−0.133342	−	0.230956i
$459$		0			0
$460$	−4.90183	+	8.49022i	−0.228549	+	0.395858i
$461$	−15.1269	+	16.0335i	−0.704528	+	0.746756i	−0.976493	−	0.215551i	$-0.930845\pi$
$461$	−15.1269	+	16.0335i	−0.704528	+	0.746756i	0.271965	+	0.962307i	$0.412327\pi$
$462$		0			0
$463$	−2.16064	−	37.0967i	−0.100413	−	1.72403i	−0.553744	−	0.832687i	$-0.686801\pi$
$463$	−2.16064	−	37.0967i	−0.100413	−	1.72403i	0.453331	−	0.891342i	$-0.350236\pi$
$464$	5.20883	−	6.99667i	0.241814	−	0.324812i
$465$		0			0
$466$	−8.26882	−	5.43849i	−0.383046	−	0.251933i
$467$	1.44385	−	8.18848i	0.0668134	−	0.378918i	−0.933005	−	0.359863i	$-0.882823\pi$
$467$	1.44385	−	8.18848i	0.0668134	−	0.378918i	0.999818	−	0.0190543i	$-0.00606555\pi$
$468$		0			0
$469$	4.17380	+	23.6708i	0.192728	+	1.09302i
$470$	−6.66322	+	15.4471i	−0.307351	+	0.712520i
$471$		0			0
$472$	−26.0748	+	6.17983i	−1.20019	+	0.284450i
$473$	15.8828	+	16.8348i	0.730293	+	0.774066i
$474$		0			0
$475$	−2.58792	−	3.47617i	−0.118742	−	0.159498i
$476$	16.2347	−	13.6225i	0.744115	−	0.624387i
$477$		0			0
$478$	1.82923	+	1.53491i	0.0836671	+	0.0702050i
$479$	−0.148442	+	2.54865i	−0.00678248	+	0.116451i	0.993218	+	0.116271i	$0.0370942\pi$
$479$	−0.148442	+	2.54865i	−0.00678248	+	0.116451i	−1.00000		0.000179474i	$0.999943\pi$
$480$		0			0
$481$	−3.51231	−	8.14245i	−0.160148	−	0.371264i
$482$	−12.6491	+	8.31942i	−0.576149	+	0.378939i
$483$		0			0
$484$	−1.00157	−	3.34548i	−0.0455260	−	0.152067i
$485$	17.9763			0.816263
$486$		0			0
$487$	16.3628			0.741468			0.370734	−	0.928739i	$-0.379106\pi$
$487$	16.3628			0.741468			0.370734	+	0.928739i	$0.379106\pi$
$488$	−6.08992	−	20.3417i	−0.275678	−	0.920827i
$489$		0			0
$490$	−13.7622	+	9.05153i	−0.621712	+	0.408907i
$491$	−14.4509	−	33.5009i	−0.652159	−	1.51187i	−0.847308	−	0.531101i	$-0.821778\pi$
$491$	−14.4509	−	33.5009i	−0.652159	−	1.51187i	0.195149	−	0.980774i	$-0.437481\pi$
$492$		0			0
$493$	1.06763	−	18.3305i	0.0480837	−	0.825565i
$494$	−5.40415	−	4.53462i	−0.243144	−	0.204022i
$495$		0			0
$496$	7.70901	−	6.46863i	0.346145	−	0.290450i
$497$	−5.82811	−	7.82850i	−0.261426	−	0.351156i
$498$		0			0
$499$	21.7797	+	23.0851i	0.974993	+	1.03343i	0.999431	+	0.0337308i	$0.0107389\pi$
$499$	21.7797	+	23.0851i	0.974993	+	1.03343i	−0.0244380	+	0.999701i	$0.507780\pi$
$500$	−14.0728	+	3.33531i	−0.629353	+	0.149159i
$501$		0			0
$502$	5.54634	−	12.8579i	0.247545	−	0.573875i
$503$	1.04817	+	5.94449i	0.0467358	+	0.265052i	0.999218	−	0.0395428i	$-0.0125902\pi$
$503$	1.04817	+	5.94449i	0.0467358	+	0.265052i	−0.952482	+	0.304595i	$0.901479\pi$
$504$		0			0
$505$	0.919238	−	5.21326i	0.0409055	−	0.231987i
$506$	4.08348	+	2.68575i	0.181533	+	0.119396i
$507$		0			0
$508$	−11.2271	+	15.0806i	−0.498122	+	0.669094i
$509$	−1.52941	−	26.2590i	−0.0677899	−	1.16391i	−0.845035	−	0.534710i	$-0.820421\pi$
$509$	−1.52941	−	26.2590i	−0.0677899	−	1.16391i	0.777245	−	0.629198i	$-0.216616\pi$
$510$		0			0
$511$	−13.3344	+	14.1336i	−0.589879	+	0.625235i
$512$	8.19547	−	14.1950i	0.362192	−	0.627335i
$513$		0			0
$514$	−2.57506	−	4.46014i	−0.113581	−	0.196728i
$515$	5.05129	+	1.19718i	0.222586	+	0.0527540i
$516$		0			0
$517$	−26.7741	−	13.4465i	−1.17753	−	0.591376i
$518$	7.38580	+	0.863276i	0.324513	+	0.0379302i
$519$		0			0
$520$	17.1640	−	8.62006i	0.752689	−	0.378015i
$521$	23.7819	−	8.65589i	1.04190	−	0.379221i	0.236301	−	0.971680i	$-0.424065\pi$
$521$	23.7819	−	8.65589i	1.04190	−	0.379221i	0.805601	+	0.592459i	$0.201843\pi$
$522$		0			0
$523$	2.76727	+	1.00720i	0.121004	+	0.0440420i	0.401813	−	0.915722i	$-0.368380\pi$
$523$	2.76727	+	1.00720i	0.121004	+	0.0440420i	−0.280808	+	0.959764i	$0.590603\pi$
$524$	−7.97159	+	0.931745i	−0.348240	+	0.0407035i
$525$		0			0
$526$	0.289548	−	0.967158i	0.0126249	−	0.0421701i
$527$	6.07559	−	20.2939i	0.264657	−	0.884016i
$528$		0			0
$529$	16.6560	−	1.94681i	0.724173	−	0.0846437i
$530$	0.0154471	+	0.00562227i	0.000670977	+	0.000244216i
$531$		0			0
$532$	−19.8585	+	7.22789i	−0.860973	+	0.313369i
$533$	26.2244	−	13.1704i	1.13591	−	0.570474i
$534$		0			0
$535$	35.6090	+	4.16210i	1.53951	+	0.179943i
$536$	12.3076	+	6.18112i	0.531609	+	0.266984i
$537$		0			0
$538$	18.9451	+	4.49007i	0.816781	+	0.193581i
$539$	−14.6681	−	25.4058i	−0.631798	−	1.09431i
$540$		0			0
$541$	−8.84669	+	15.3229i	−0.380349	+	0.658784i	−0.991112	−	0.133030i	$-0.957529\pi$
$541$	−8.84669	+	15.3229i	−0.380349	+	0.658784i	0.610763	+	0.791813i	$0.290863\pi$
$542$	6.61405	−	7.01049i	0.284098	−	0.301126i
$543$		0			0
$544$	−1.10247	−	18.9287i	−0.0472679	−	0.811559i
$545$	−20.1199	+	27.0257i	−0.861842	+	1.15765i
$546$		0			0
$547$	−34.0467	−	22.3929i	−1.45573	−	0.957449i	−0.997648	−	0.0685400i	$-0.978166\pi$
$547$	−34.0467	−	22.3929i	−1.45573	−	0.957449i	−0.458083	−	0.888910i	$-0.651464\pi$
$548$	−0.515831	+	2.92542i	−0.0220352	+	0.124968i
$549$		0			0
$550$	−0.448020	−	2.54085i	−0.0191036	−	0.108342i
$551$	−7.25208	+	16.8122i	−0.308949	+	0.716224i
$552$		0			0
$553$	36.0188	−	8.53662i	1.53168	−	0.363014i
$554$	4.64144	+	4.91964i	0.197196	+	0.209016i
$555$		0			0
$556$	−8.73190	−	11.7290i	−0.370315	−	0.497419i
$557$	−23.1644	+	19.4372i	−0.981505	+	0.823581i	−0.984316	−	0.176415i	$-0.943550\pi$
$557$	−23.1644	+	19.4372i	−0.981505	+	0.823581i	0.00281036	+	0.999996i	$0.499105\pi$
$558$		0			0
$559$	19.4220	+	16.2970i	0.821465	+	0.689291i
$560$	0.941618	−	16.1670i	0.0397906	−	0.683178i
$561$		0			0
$562$	−1.83989	−	4.26535i	−0.0776112	−	0.179923i
$563$	15.4390	−	10.1544i	0.650676	−	0.427956i	−0.180798	−	0.983520i	$-0.557868\pi$
$563$	15.4390	−	10.1544i	0.650676	−	0.427956i	0.831474	+	0.555564i	$0.187498\pi$
$564$		0			0
$565$	−2.13404	−	7.12819i	−0.0897797	−	0.299885i
$566$	14.3004			0.601091
$567$		0			0
$568$	−5.59232			−0.234648
$569$	−2.58058	−	8.61972i	−0.108183	−	0.361358i	0.886705	−	0.462335i	$-0.152988\pi$
$569$	−2.58058	−	8.61972i	−0.108183	−	0.361358i	−0.994889	+	0.100977i	$0.967803\pi$
$570$		0			0
$571$	14.1014	−	9.27464i	0.590125	−	0.388132i	−0.219037	−	0.975717i	$-0.570292\pi$
$571$	14.1014	−	9.27464i	0.590125	−	0.388132i	0.809162	+	0.587585i	$0.199921\pi$
$572$	5.94258	+	13.7765i	0.248472	+	0.576022i
$573$		0			0
$574$	−1.43084	+	24.5666i	−0.0597222	+	1.02539i
$575$	2.51954	+	2.11415i	0.105072	+	0.0881661i
$576$		0			0
$577$	−24.0567	+	20.1860i	−1.00149	+	0.840352i	−0.987191	−	0.159545i	$-0.948997\pi$
$577$	−24.0567	+	20.1860i	−1.00149	+	0.840352i	−0.0143022	+	0.999898i	$0.504553\pi$
$578$	2.41757	+	3.24737i	0.100558	+	0.135073i
$579$		0			0
$580$	−15.0045	−	15.9038i	−0.623027	−	0.660370i
$581$	−14.8098	+	3.50999i	−0.614414	+	0.145619i
$582$		0			0
$583$	−0.0115957	+	0.0268819i	−0.000480246	+	0.00111334i
$584$	1.93340	+	10.9648i	0.0800045	+	0.453728i
$585$		0			0
$586$	1.25491	−	7.11695i	0.0518399	−	0.293999i
$587$	1.15028	+	0.756551i	0.0474771	+	0.0312262i	0.573026	−	0.819537i	$-0.305770\pi$
$587$	1.15028	+	0.756551i	0.0474771	+	0.0312262i	−0.525549	+	0.850764i	$0.676140\pi$
$588$		0			0
$589$	−12.6143	+	16.9440i	−0.519764	+	0.698165i
$590$	1.09929	+	18.8740i	0.0452569	+	0.777031i
$591$		0			0
$592$	−2.94000	+	3.11621i	−0.120833	+	0.128076i
$593$	15.4929	−	26.8346i	0.636219	−	1.10196i	−0.350037	−	0.936736i	$-0.613831\pi$
$593$	15.4929	−	26.8346i	0.636219	−	1.10196i	0.986256	−	0.165227i	$-0.0528358\pi$
$594$		0			0
$595$	−17.0449	−	29.5226i	−0.698771	−	1.21031i
$596$	1.35115	+	0.320229i	0.0553453	+	0.0131171i
$597$		0			0
$598$	4.78453	+	2.40288i	0.195654	+	0.0982612i
$599$	24.0874	+	2.81541i	0.984185	+	0.115035i	0.592935	−	0.805250i	$-0.297969\pi$
$599$	24.0874	+	2.81541i	0.984185	+	0.115035i	0.391249	+	0.920285i	$0.372043\pi$
$600$		0			0
$601$	6.77942	−	3.40476i	0.276539	−	0.138883i	−0.305125	−	0.952312i	$-0.598698\pi$
$601$	6.77942	−	3.40476i	0.276539	−	0.138883i	0.581664	+	0.813429i	$0.302402\pi$
$602$	−19.9784	+	7.27154i	−0.814258	+	0.296366i
$603$		0			0
$604$	−11.8328	−	4.30678i	−0.481469	−	0.175241i
$605$	−5.57937	+	0.652135i	−0.226834	+	0.0265130i
$606$		0			0
$607$	−8.59397	+	28.7059i	−0.348819	+	1.16514i	0.586090	+	0.810246i	$0.300667\pi$
$607$	−8.59397	+	28.7059i	−0.348819	+	1.16514i	−0.934908	+	0.354889i	$0.884519\pi$
$608$	−5.42262	+	18.1128i	−0.219916	+	0.734571i
$609$		0			0
$610$	−14.8797	+	1.73918i	−0.602460	+	0.0704175i
$611$	−30.8413	−	11.2253i	−1.24770	−	0.454127i
$612$		0			0
$613$	11.4606	−	4.17132i	0.462890	−	0.168478i	−0.100039	−	0.994984i	$-0.531897\pi$
$613$	11.4606	−	4.17132i	0.462890	−	0.168478i	0.562929	+	0.826505i	$0.309675\pi$
$614$	−2.71800	+	1.36503i	−0.109690	+	0.0550882i
$615$		0			0
$616$	−28.4906	−	3.33007i	−1.14792	−	0.134172i
$617$	−14.2000	−	7.13150i	−0.571670	−	0.287103i	0.139387	−	0.990238i	$-0.455487\pi$
$617$	−14.2000	−	7.13150i	−0.571670	−	0.287103i	−0.711057	+	0.703135i	$0.751783\pi$
$618$		0			0
$619$	22.6313	+	5.36373i	0.909630	+	0.215586i	0.658688	−	0.752416i	$-0.271112\pi$
$619$	22.6313	+	5.36373i	0.909630	+	0.215586i	0.250942	+	0.968002i	$0.419260\pi$
$620$	−12.6127	−	21.8459i	−0.506539	−	0.877351i
$621$		0			0
$622$	−5.76686	+	9.98849i	−0.231230	+	0.400502i
$623$	35.2622	−	37.3757i	1.41275	−	1.49743i
$624$		0			0
$625$	1.73574	+	29.8016i	0.0694297	+	1.19206i
$626$	6.25081	−	8.39629i	0.249832	−	0.335583i
$627$		0			0
$628$	−18.8916	−	12.4252i	−0.753858	−	0.495820i
$629$	−1.56603	+	8.88139i	−0.0624417	+	0.354124i
$630$		0			0
$631$	2.13182	+	12.0902i	0.0848665	+	0.481302i	0.997385	+	0.0722670i	$0.0230234\pi$
$631$	2.13182	+	12.0902i	0.0848665	+	0.481302i	−0.912519	+	0.409035i	$0.865866\pi$
$632$	8.40105	−	19.4758i	0.334176	−	0.774706i
$633$		0			0
$634$	−12.6151	+	2.98984i	−0.501011	+	0.118742i
$635$	20.7534	+	21.9973i	0.823572	+	0.872935i
$636$		0			0
$637$	−19.1903	−	25.7771i	−0.760349	−	1.02133i
$638$	−8.35027	+	7.00671i	−0.330590	+	0.277398i
$639$		0			0
$640$	−21.2865	−	17.8615i	−0.841422	−	0.706037i
$641$	0.544496	−	9.34864i	0.0215063	−	0.369249i	−0.970335	−	0.241766i	$-0.922273\pi$
$641$	0.544496	−	9.34864i	0.0215063	−	0.369249i	0.991841	−	0.127483i	$-0.0406897\pi$
$642$		0			0
$643$	−7.78874	−	18.0563i	−0.307158	−	0.712072i	0.692801	−	0.721129i	$-0.256376\pi$
$643$	−7.78874	−	18.0563i	−0.307158	−	0.712072i	−0.999959	+	0.00905647i	$0.997117\pi$
$644$	13.4001	−	8.81337i	0.528037	−	0.347295i
$645$		0			0
$646$	2.05767	+	6.87311i	0.0809580	+	0.270419i
$647$	−14.2593			−0.560591			−0.280295	−	0.959914i	$-0.590432\pi$
$647$	−14.2593			−0.560591			−0.280295	+	0.959914i	$0.590432\pi$
$648$		0			0
$649$	−33.6709			−1.32170
$650$	−0.810590	−	2.70756i	−0.0317940	−	0.106199i
$651$		0			0
$652$	10.5159	−	6.91643i	0.411835	−	0.270868i
$653$	16.1557	+	37.4532i	0.632223	+	1.46566i	0.869359	+	0.494181i	$0.164532\pi$
$653$	16.1557	+	37.4532i	0.632223	+	1.46566i	−0.237137	+	0.971476i	$0.576209\pi$
$654$		0			0
$655$	−0.750648	+	12.8881i	−0.0293302	+	0.503581i
$656$	−10.8608	−	9.11326i	−0.424042	−	0.355813i
$657$		0			0
$658$	21.0831	−	17.6908i	0.821905	−	0.689660i
$659$	1.54612	+	2.07679i	0.0602281	+	0.0809004i	0.831217	−	0.555949i	$-0.187645\pi$
$659$	1.54612	+	2.07679i	0.0602281	+	0.0809004i	−0.770989	+	0.636849i	$0.780237\pi$
$660$		0			0
$661$	−20.6098	−	21.8451i	−0.801628	−	0.849676i	0.189597	−	0.981862i	$-0.439282\pi$
$661$	−20.6098	−	21.8451i	−0.801628	−	0.849676i	−0.991225	+	0.132186i	$0.957800\pi$
$662$	14.0798	−	3.33697i	0.547227	−	0.129695i
$663$		0			0
$664$	−3.45424	+	8.00784i	−0.134051	+	0.310764i
$665$	5.90288	+	33.4769i	0.228904	+	1.29818i
$666$		0			0
$667$	2.41300	−	13.6848i	0.0934318	−	0.529878i
$668$	22.0403	+	14.4961i	0.852765	+	0.560872i
$669$		0			0
$670$	5.80253	−	7.79415i	0.224171	−	0.301114i
$671$	−1.55134	−	26.6354i	−0.0598887	−	1.02825i
$672$		0			0
$673$	−9.51681	+	10.0872i	−0.366846	+	0.388834i	−0.884333	−	0.466857i	$-0.845386\pi$
$673$	−9.51681	+	10.0872i	−0.366846	+	0.388834i	0.517487	+	0.855691i	$0.326868\pi$
$674$	−2.96391	+	5.13365i	−0.114166	+	0.197741i
$675$		0			0
$676$	−1.93907	−	3.35858i	−0.0745798	−	0.129176i
$677$	19.4975	+	4.62100i	0.749352	+	0.177600i	0.587510	−	0.809217i	$-0.300108\pi$
$677$	19.4975	+	4.62100i	0.749352	+	0.177600i	0.161842	+	0.986817i	$0.448257\pi$
$678$		0			0
$679$	−26.2808	−	13.1987i	−1.00857	−	0.506521i
$680$	−19.4013	−	2.26769i	−0.744006	−	0.0869619i
$681$		0			0
$682$	−11.2383	+	5.64408i	−0.430336	+	0.216123i
$683$	−29.9877	+	10.9146i	−1.14745	+	0.417636i	−0.844597	−	0.535402i	$-0.820160\pi$
$683$	−29.9877	+	10.9146i	−1.14745	+	0.417636i	−0.302849	+	0.953039i	$0.597938\pi$
$684$		0			0
$685$	4.49011	+	1.63426i	0.171558	+	0.0624421i
$686$	7.85740	−	0.918398i	0.299997	−	0.0350646i
$687$		0			0
$688$	3.51305	−	11.7344i	0.133934	−	0.447370i
$689$	−0.00919792	+	0.0307232i	−0.000350413	+	0.00117046i
$690$		0			0
$691$	−37.1904	+	4.34694i	−1.41479	+	0.165365i	−0.788888	−	0.614537i	$-0.789343\pi$
$691$	−37.1904	+	4.34694i	−1.41479	+	0.165365i	−0.625902	+	0.779902i	$0.715269\pi$
$692$	9.87198	+	3.59311i	0.375276	+	0.136589i
$693$		0			0
$694$	11.9523	−	4.35029i	0.453704	−	0.165135i
$695$	−21.0190	+	10.5561i	−0.797296	+	0.400417i
$696$		0			0
$697$	−29.6428	−	3.46475i	−1.12280	−	0.131237i
$698$	−12.6208	−	6.33839i	−0.477703	−	0.239912i
$699$		0			0
$700$	−8.23828	−	1.95251i	−0.311378	−	0.0737979i
$701$	11.5923	+	20.0785i	0.437836	+	0.758355i	0.997522	−	0.0703498i	$-0.0224116\pi$
$701$	11.5923	+	20.0785i	0.437836	+	0.758355i	−0.559686	+	0.828705i	$0.689078\pi$
$702$		0			0
$703$	4.49645	−	7.78807i	0.169587	−	0.293733i
$704$	−1.35777	+	1.43915i	−0.0511728	+	0.0542400i
$705$		0			0
$706$	−0.565764	−	9.71379i	−0.0212928	−	0.365583i
$707$	−5.17162	+	6.94669i	−0.194499	+	0.261257i
$708$		0			0
$709$	−4.16080	−	2.73660i	−0.156262	−	0.102775i	0.468970	−	0.883214i	$-0.344625\pi$
$709$	−4.16080	−	2.73660i	−0.156262	−	0.102775i	−0.625232	+	0.780439i	$0.714996\pi$
$710$	−0.685132	+	3.88558i	−0.0257126	+	0.145823i
$711$		0			0
$712$	−5.11277	−	28.9960i	−0.191609	−	1.08667i
$713$	6.34987	−	14.7206i	0.237804	−	0.551293i
$714$		0			0
$715$	23.4833	−	5.56564i	0.878225	−	0.208143i
$716$	−16.3052	−	17.2825i	−0.609354	−	0.645878i
$717$		0			0
$718$	−4.22968	−	5.68144i	−0.157850	−	0.212030i
$719$	13.4111	−	11.2533i	0.500151	−	0.419677i	−0.357497	−	0.933914i	$-0.616370\pi$
$719$	13.4111	−	11.2533i	0.500151	−	0.419677i	0.857648	+	0.514238i	$0.171925\pi$
$720$		0			0
$721$	−6.50583	−	5.45904i	−0.242290	−	0.203305i
$722$	−0.314671	+	5.40269i	−0.0117108	+	0.201067i
$723$		0			0
$724$	3.46898	+	8.04201i	0.128924	+	0.298879i
$725$	−6.12864	+	4.03087i	−0.227612	+	0.149703i
$726$		0			0
$727$	−2.30311	−	7.69291i	−0.0854175	−	0.285314i	0.904599	−	0.426263i	$-0.140170\pi$
$727$	−2.30311	−	7.69291i	−0.0854175	−	0.285314i	−0.990017	+	0.140948i	$0.954985\pi$
$728$	−31.4223			−1.16459
$729$		0			0
$730$	7.85530			0.290738
$731$	−7.39510	−	24.7014i	−0.273518	−	0.913613i
$732$		0			0
$733$	25.1300	−	16.5282i	0.928197	−	0.610485i	0.00716600	−	0.999974i	$-0.497719\pi$
$733$	25.1300	−	16.5282i	0.928197	−	0.610485i	0.921031	+	0.389490i	$0.127349\pi$
$734$	1.03883	+	2.40828i	0.0383439	+	0.0888912i
$735$		0			0
$736$	0.834341	−	14.3251i	0.0307542	−	0.528030i
$737$	13.2568	+	11.1237i	0.488319	+	0.409748i
$738$		0			0
$739$	1.84741	−	1.55016i	0.0679580	−	0.0570236i	−0.608176	−	0.793802i	$-0.708098\pi$
$739$	1.84741	−	1.55016i	0.0679580	−	0.0570236i	0.676134	+	0.736779i	$0.263654\pi$
$740$	6.41288	+	8.61399i	0.235742	+	0.316657i
$741$		0			0
$742$	−0.0184551	−	0.0195613i	−0.000677508	−	0.000718116i
$743$	19.1318	−	4.53432i	0.701878	−	0.166348i	0.135844	−	0.990730i	$-0.456625\pi$
$743$	19.1318	−	4.53432i	0.701878	−	0.166348i	0.566034	+	0.824382i	$0.308477\pi$
$744$		0			0
$745$	0.884683	−	2.05093i	0.0324123	−	0.0751401i
$746$	2.72448	+	15.4513i	0.0997503	+	0.565712i
$747$		0			0
$748$	2.64961	−	15.0267i	0.0968793	−	0.549430i
$749$	−49.0034	−	32.2300i	−1.79054	−	1.17766i
$750$		0			0
$751$	−4.10222	+	5.51024i	−0.149692	+	0.201071i	−0.870644	−	0.491914i	$-0.836298\pi$
$751$	−4.10222	+	5.51024i	−0.149692	+	0.201071i	0.720952	+	0.692985i	$0.243705\pi$
$752$	0.921971	+	15.8296i	0.0336208	+	0.577247i
$753$		0			0
$754$	−8.19433	+	8.68549i	−0.298420	+	0.316307i
$755$	−10.1276	+	17.5415i	−0.368580	+	0.638399i
$756$		0			0
$757$	−6.50209	−	11.2620i	−0.236323	−	0.409323i	0.723334	−	0.690499i	$-0.242609\pi$
$757$	−6.50209	−	11.2620i	−0.236323	−	0.409323i	−0.959656	+	0.281176i	$0.909276\pi$
$758$	16.7443	+	3.96847i	0.608180	+	0.144141i
$759$		0			0
$760$	17.4063	+	8.74177i	0.631393	+	0.317097i
$761$	−17.2877	−	2.02065i	−0.626680	−	0.0732484i	−0.203175	−	0.979142i	$-0.565126\pi$
$761$	−17.2877	−	2.02065i	−0.626680	−	0.0732484i	−0.423504	+	0.905894i	$0.639200\pi$
$762$		0			0
$763$	49.2577	−	24.7382i	1.78325	−	0.895581i
$764$	−6.30756	+	2.29576i	−0.228200	+	0.0830578i
$765$		0			0
$766$	−18.2874	−	6.65607i	−0.660751	−	0.240494i
$767$	−36.6352	+	4.28204i	−1.32282	+	0.154616i
$768$		0			0
$769$	5.34304	−	17.8470i	0.192675	−	0.643579i	−0.805990	−	0.591929i	$-0.798367\pi$
$769$	5.34304	−	17.8470i	0.192675	−	0.643579i	0.998665	−	0.0516502i	$-0.0164481\pi$
$770$	−5.80422	+	19.3874i	−0.209170	+	0.698675i
$771$		0			0
$772$	4.39793	−	0.514044i	0.158285	−	0.0185009i
$773$	−27.2264	−	9.90961i	−0.979267	−	0.356424i	−0.197712	−	0.980260i	$-0.563351\pi$
$773$	−27.2264	−	9.90961i	−0.979267	−	0.356424i	−0.781555	+	0.623836i	$0.785573\pi$
$774$		0			0
$775$	−7.95251	+	2.89448i	−0.285663	+	0.103973i
$776$	−15.0589	+	7.56287i	−0.540583	+	0.271491i
$777$		0			0
$778$	−17.4104	−	2.03498i	−0.624193	−	0.0729577i
$779$	26.5947	+	13.3564i	0.952854	+	0.478541i
$780$		0			0
$781$	−6.83742	−	1.62050i	−0.244662	−	0.0579860i
$782$	−2.72251	−	4.71553i	−0.0973568	−	0.168627i
$783$		0			0
$784$	−7.76286	+	13.4457i	−0.277245	+	0.480203i
$785$	−24.9597	+	26.4558i	−0.890851	+	0.944247i
$786$		0			0
$787$	0.861390	+	14.7895i	0.0307052	+	0.527188i	0.978232	+	0.207513i	$0.0665369\pi$
$787$	0.861390	+	14.7895i	0.0307052	+	0.527188i	−0.947527	+	0.319676i	$0.896426\pi$
$788$	19.8269	−	26.6321i	0.706304	−	0.948731i
$789$		0			0
$790$	−12.5027	−	8.22315i	−0.444826	−	0.292566i
$791$	−2.11382	+	11.9881i	−0.0751588	+	0.426247i
$792$		0			0
$793$	−5.07523	−	28.7830i	−0.180227	−	1.02212i
$794$	7.45541	−	17.2836i	0.264583	−	0.613371i
$795$		0			0
$796$	−14.7975	+	3.50708i	−0.524484	+	0.124305i
$797$	−12.0822	−	12.8064i	−0.427975	−	0.453627i	0.477119	−	0.878839i	$-0.341681\pi$
$797$	−12.0822	−	12.8064i	−0.427975	−	0.453627i	−0.905094	+	0.425212i	$0.860200\pi$
$798$		0			0
$799$	19.9322	+	26.7736i	0.705151	+	0.947182i
$800$	−5.80261	+	4.86896i	−0.205153	+	0.172144i
$801$		0			0
$802$	7.20573	+	6.04632i	0.254443	+	0.213503i
$803$	−0.813447	+	13.9663i	−0.0287059	+	0.492862i
$804$		0			0
$805$	−10.2184	−	23.6890i	−0.360152	−	0.834926i
$806$	−11.5099	+	7.57017i	−0.405419	+	0.266648i
$807$		0			0
$808$	1.42323	+	4.75392i	0.0500690	+	0.167242i
$809$	−13.3577			−0.469632			−0.234816	−	0.972040i	$-0.575449\pi$
$809$	−13.3577			−0.469632			−0.234816	+	0.972040i	$0.575449\pi$
$810$		0			0
$811$	13.6700			0.480017			0.240009	−	0.970771i	$-0.422850\pi$
$811$	13.6700			0.480017			0.240009	+	0.970771i	$0.422850\pi$
$812$	10.2591	+	34.2676i	0.360022	+	1.20256i
$813$		0			0
$814$	4.47307	−	2.94199i	0.156781	−	0.103117i
$815$	−8.01906	−	18.5903i	−0.280895	−	0.651189i
$816$		0			0
$817$	−1.49500	+	25.6682i	−0.0523034	+	0.898015i
$818$	−1.57767	−	1.32382i	−0.0551619	−	0.0462863i
$819$		0			0
$820$	−27.2241	+	22.8438i	−0.950708	+	0.797739i
$821$	5.99568	+	8.05360i	0.209251	+	0.281073i	0.894341	−	0.447385i	$-0.147645\pi$
$821$	5.99568	+	8.05360i	0.209251	+	0.281073i	−0.685090	+	0.728458i	$0.740237\pi$
$822$		0			0
$823$	20.7580	+	22.0022i	0.723579	+	0.766949i	0.979867	−	0.199652i	$-0.0639811\pi$
$823$	20.7580	+	22.0022i	0.723579	+	0.766949i	−0.256288	+	0.966600i	$0.582500\pi$
$824$	−4.73517	+	1.12226i	−0.164957	+	0.0390956i
$825$		0			0
$826$	12.2507	−	28.4004i	0.426257	−	0.988175i
$827$	−8.16805	−	46.3233i	−0.284031	−	1.61082i	−0.708726	−	0.705483i	$-0.750730\pi$
$827$	−8.16805	−	46.3233i	−0.284031	−	1.61082i	0.424695	−	0.905336i	$-0.360381\pi$
$828$		0			0
$829$	−0.608907	+	3.45328i	−0.0211482	+	0.119938i	−0.993554	−	0.113357i	$-0.963840\pi$
$829$	−0.608907	+	3.45328i	−0.0211482	+	0.119938i	0.972406	+	0.233295i	$0.0749507\pi$
$830$	5.14071	+	3.38110i	0.178437	+	0.117360i
$831$		0			0
$832$	−1.29428	+	1.73852i	−0.0448711	+	0.0602723i
$833$	1.90030	+	32.6270i	0.0658416	+	1.13046i
$834$		0			0
$835$	29.1198	−	30.8652i	1.00773	−	1.06813i
$836$	−7.60767	+	13.1769i	−0.263117	+	0.455731i
$837$		0			0
$838$	−2.26555	−	3.92405i	−0.0782622	−	0.135554i
$839$	35.8223	+	8.49004i	1.23672	+	0.293109i	0.796422	−	0.604742i	$-0.206724\pi$
$839$	35.8223	+	8.49004i	1.23672	+	0.293109i	0.440301	+	0.897850i	$0.354872\pi$
$840$		0			0
$841$	1.77973	+	0.893813i	0.0613699	+	0.0308211i
$842$	−9.80915	−	1.14652i	−0.338046	−	0.0395119i
$843$		0			0
$844$	−27.3386	+	13.7299i	−0.941032	+	0.472604i
$845$	−5.86198	+	2.13359i	−0.201658	+	0.0733976i
$846$		0			0
$847$	8.63568	+	3.14313i	0.296725	+	0.107999i
$848$	0.0153893	−	0.00179875i	0.000528470	−	6.17693e-5i
$849$		0			0
$850$	−0.824367	+	2.75358i	−0.0282755	+	0.0944469i
$851$	−1.95745	+	6.53834i	−0.0671006	+	0.224132i
$852$		0			0
$853$	36.6614	−	4.28510i	1.25526	−	0.146719i	0.537654	−	0.843166i	$-0.319311\pi$
$853$	36.6614	−	4.28510i	1.25526	−	0.146719i	0.717609	+	0.696447i	$0.245237\pi$
$854$	23.0306	+	8.38245i	0.788090	+	0.286841i
$855$		0			0
$856$	−31.5810	+	11.4945i	−1.07942	+	0.392875i
$857$	26.8999	−	13.5096i	0.918882	−	0.461480i	0.0744999	−	0.997221i	$-0.476264\pi$
$857$	26.8999	−	13.5096i	0.918882	−	0.461480i	0.844382	+	0.535741i	$0.179968\pi$
$858$		0			0
$859$	19.3157	+	2.25768i	0.659043	+	0.0770311i	0.439039	−	0.898468i	$-0.355319\pi$
$859$	19.3157	+	2.25768i	0.659043	+	0.0770311i	0.220004	+	0.975499i	$0.429393\pi$
$860$	−27.4380	−	13.7799i	−0.935630	−	0.469891i
$861$		0			0
$862$	−19.8641	−	4.70788i	−0.676574	−	0.160351i
$863$	14.3566	+	24.8664i	0.488706	+	0.846463i	0.999916	−	0.0129930i	$-0.00413590\pi$
$863$	14.3566	+	24.8664i	0.488706	+	0.846463i	−0.511210	+	0.859456i	$0.670803\pi$
$864$		0			0
$865$	8.44932	−	14.6347i	0.287286	−	0.497593i
$866$	−13.0575	+	13.8401i	−0.443712	+	0.470307i
$867$		0			0
$868$	2.39954	+	41.1986i	0.0814458	+	1.39837i
$869$	15.9151	−	21.3776i	0.539881	−	0.725187i
$870$		0			0
$871$	15.8385	+	10.4171i	0.536666	+	0.352971i
$872$	5.48453	−	31.1043i	0.185730	−	1.05333i
$873$		0			0
$874$	0.942844	+	5.34714i	0.0318922	+	0.180870i
$875$	15.0745	−	34.9466i	0.509610	−	1.18141i
$876$		0			0
$877$	−18.6086	+	4.41032i	−0.628368	+	0.148926i	−0.532447	−	0.846463i	$-0.678728\pi$
$877$	−18.6086	+	4.41032i	−0.628368	+	0.148926i	−0.0959205	+	0.995389i	$0.530579\pi$
$878$	−2.00780	−	2.12814i	−0.0677599	−	0.0718213i
$879$		0			0
$880$	−6.96266	−	9.35247i	−0.234711	−	0.315272i
$881$	35.7695	−	30.0142i	1.20510	−	1.01120i	0.205635	−	0.978629i	$-0.434074\pi$
$881$	35.7695	−	30.0142i	1.20510	−	1.01120i	0.999469	−	0.0325741i	$-0.0103705\pi$
$882$		0			0
$883$	−10.7311	−	9.00449i	−0.361131	−	0.303025i	0.444110	−	0.895972i	$-0.353520\pi$
$883$	−10.7311	−	9.00449i	−0.361131	−	0.303025i	−0.805241	+	0.592947i	$0.797964\pi$
$884$	0.971880	−	16.6865i	0.0326879	−	0.561229i
$885$		0			0
$886$	0.698789	+	1.61998i	0.0234763	+	0.0544241i
$887$	8.66156	−	5.69680i	0.290827	−	0.191280i	−0.395709	−	0.918376i	$-0.629501\pi$
$887$	8.66156	−	5.69680i	0.290827	−	0.191280i	0.686535	+	0.727096i	$0.259131\pi$
$888$		0			0
$889$	−14.1897	−	47.3970i	−0.475909	−	1.58965i
$890$	−20.7730			−0.696312
$891$		0			0
$892$	25.2612			0.845809
$893$	−9.54596	−	31.8857i	−0.319444	−	1.06702i
$894$		0			0
$895$	−31.9318	+	21.0019i	−1.06736	+	0.702015i
$896$	18.0058	+	41.7421i	0.601530	+	1.39450i
$897$		0			0
$898$	−1.60115	+	27.4907i	−0.0534310	+	0.917375i
$899$	27.3900	+	22.9829i	0.913508	+	0.766524i
$900$		0			0
$901$	0.0249850	−	0.0209649i	0.000832370	−	0.000698441i
$902$	10.5802	+	14.2116i	0.352281	+	0.473195i
$903$		0			0
$904$	4.78662	+	5.07352i	0.159201	+	0.168743i
$905$	13.7084	−	3.24895i	0.455682	−	0.107999i
$906$		0			0
$907$	−14.2455	+	33.0247i	−0.473013	+	1.09657i	0.500043	+	0.866001i	$0.333318\pi$
$907$	−14.2455	+	33.0247i	−0.473013	+	1.09657i	−0.973056	+	0.230568i	$0.925942\pi$
$908$	−5.76067	−	32.6704i	−0.191174	−	1.08420i
$909$		0			0
$910$	−3.84964	+	21.8324i	−0.127614	+	0.723737i
$911$	5.31457	+	3.49545i	0.176079	+	0.115809i	0.634489	−	0.772932i	$-0.281210\pi$
$911$	5.31457	+	3.49545i	0.176079	+	0.115809i	−0.458410	+	0.888741i	$0.651581\pi$
$912$		0			0
$913$	−6.54377	+	8.78981i	−0.216567	+	0.290900i
$914$	0.294755	+	5.06075i	0.00974963	+	0.167395i
$915$		0			0
$916$	−9.25351	+	9.80814i	−0.305744	+	0.324070i
$917$	10.5602	−	18.2909i	0.348730	−	0.604018i
$918$		0			0
$919$	23.2884	+	40.3367i	0.768213	+	1.33058i	0.938531	+	0.345194i	$0.112187\pi$
$919$	23.2884	+	40.3367i	0.768213	+	1.33058i	−0.170318	+	0.985389i	$0.554480\pi$
$920$	−14.3843	−	3.40914i	−0.474235	−	0.112396i
$921$		0			0
$922$	−13.0280	−	6.54289i	−0.429053	−	0.215479i
$923$	−7.64545	−	0.893625i	−0.251653	−	0.0294140i
$924$		0			0
$925$	3.21960	−	1.61695i	0.105860	−	0.0531649i
$926$	23.0942	−	8.40558i	0.758921	−	0.276225i
$927$		0			0
$928$	30.0728	+	10.9456i	0.987189	+	0.359307i
$929$	44.6011	−	5.21312i	1.46331	−	0.171037i	0.653145	−	0.757233i	$-0.273449\pi$
$929$	44.6011	−	5.21312i	1.46331	−	0.171037i	0.810169	+	0.586196i	$0.199375\pi$
$930$		0			0
$931$	9.34686	−	31.2207i	0.306331	−	1.02322i
$932$	−6.70635	+	22.4008i	−0.219674	+	0.733762i
$933$		0			0
$934$	5.46199	−	0.638415i	0.178722	−	0.0208896i
$935$	−23.0638	−	8.39454i	−0.754267	−	0.274531i
$936$		0			0
$937$	−48.3251	+	17.5889i	−1.57871	+	0.574605i	−0.974924	−	0.222539i	$-0.928565\pi$
$937$	−48.3251	+	17.5889i	−1.57871	+	0.574605i	−0.603790	+	0.797144i	$0.706343\pi$
$938$	−14.2058	+	7.13443i	−0.463836	+	0.232947i
$939$		0			0
$940$	39.4778	+	4.61430i	1.28762	+	0.150502i
$941$	9.31783	+	4.67959i	0.303753	+	0.152550i	0.594146	−	0.804357i	$-0.297490\pi$
$941$	9.31783	+	4.67959i	0.303753	+	0.152550i	−0.290394	+	0.956907i	$0.593786\pi$
$942$		0			0
$943$	−21.9774	−	5.20874i	−0.715683	−	0.169620i
$944$	8.90994	+	15.4325i	0.289994	+	0.502284i
$945$		0			0
$946$	−7.65361	+	13.2564i	−0.248840	+	0.431004i
$947$	−30.9820	+	32.8390i	−1.00678	+	1.06713i	−0.00903943	+	0.999959i	$0.502877\pi$
$947$	−30.9820	+	32.8390i	−1.00678	+	1.06713i	−0.997742	+	0.0671666i	$0.978604\pi$
$948$		0			0
$949$	0.891086	+	15.2994i	0.0289259	+	0.496638i
$950$	1.71157	−	2.29904i	0.0555308	−	0.0745908i
$951$		0			0
$952$	26.6991	+	17.5603i	0.865323	+	0.569132i
$953$	5.08752	−	28.8527i	0.164801	−	0.934632i	−0.784469	−	0.620168i	$-0.787064\pi$
$953$	5.08752	−	28.8527i	0.164801	−	0.934632i	0.949270	−	0.314463i	$-0.101825\pi$
$954$		0			0
$955$	1.87491	+	10.6331i	0.0606705	+	0.344080i
$956$	2.23458	−	5.18034i	0.0722715	−	0.167544i
$957$		0			0
$958$	−1.64295	+	0.389386i	−0.0530812	+	0.0125805i
$959$	−5.36447	−	5.68601i	−0.173228	−	0.183611i
$960$		0			0
$961$	6.12136	+	8.22241i	0.197463	+	0.265239i
$962$	4.49273	−	3.76985i	0.144851	−	0.121545i
$963$		0			0
$964$	27.4013	+	22.9924i	0.882536	+	0.740536i
$965$	0.414133	−	7.11039i	0.0133314	−	0.228891i
$966$		0			0
$967$	18.5707	+	43.0518i	0.597195	+	1.38445i	0.901875	+	0.431998i	$0.142191\pi$
$967$	18.5707	+	43.0518i	0.597195	+	1.38445i	−0.304680	+	0.952455i	$0.598549\pi$
$968$	4.39952	−	2.89361i	0.141406	−	0.0930040i
$969$		0			0
$970$	3.40982	+	11.3896i	0.109483	+	0.365697i
$971$	45.6691			1.46559			0.732795	−	0.680449i	$-0.238215\pi$
$971$	45.6691			1.46559			0.732795	+	0.680449i	$0.238215\pi$
$972$		0			0
$973$	38.4797			1.23360
$974$	3.10375	+	10.3673i	0.0994506	+	0.332188i
$975$		0			0
$976$	−11.7974	+	7.75924i	−0.377624	+	0.248367i
$977$	−0.491028	−	1.13833i	−0.0157094	−	0.0364184i	0.910181	−	0.414211i	$-0.135942\pi$
$977$	−0.491028	−	1.13833i	−0.0157094	−	0.0364184i	−0.925890	+	0.377793i	$0.876683\pi$
$978$		0			0
$979$	2.15112	−	36.9333i	0.0687501	−	1.18039i
$980$	29.8126	+	25.0157i	0.952329	+	0.799099i
$981$		0			0
$982$	18.4847	−	15.5105i	0.589869	−	0.494959i
$983$	−21.8473	−	29.3460i	−0.696821	−	0.935993i	0.303035	−	0.952979i	$-0.402000\pi$
$983$	−21.8473	−	29.3460i	−0.696821	−	0.935993i	−0.999856	+	0.0169868i	$0.994593\pi$
$984$		0			0
$985$	−36.6502	−	38.8469i	−1.16777	−	1.23777i
$986$	11.8165	−	2.80056i	0.376314	−	0.0891880i
$987$		0			0
$988$	−6.60168	+	15.3044i	−0.210027	+	0.486898i
$989$	−3.38850	−	19.2172i	−0.107748	−	0.611070i
$990$		0			0
$991$	−7.21791	+	40.9348i	−0.229285	+	1.30034i	0.625038	+	0.780594i	$0.285083\pi$
$991$	−7.21791	+	40.9348i	−0.229285	+	1.30034i	−0.854323	+	0.519743i	$0.826028\pi$
$992$	30.8477	+	20.2889i	0.979416	+	0.644172i
$993$		0			0
$994$	3.85454	−	5.17755i	0.122259	−	0.164222i
$995$	1.42233	+	24.4205i	0.0450910	+	0.774182i
$996$		0			0
$997$	−14.5232	+	15.3937i	−0.459954	+	0.487523i	−0.915289	−	0.402797i	$-0.868038\pi$
$997$	−14.5232	+	15.3937i	−0.459954	+	0.487523i	0.455335	+	0.890320i	$0.349520\pi$
$998$	−10.4952	+	18.1782i	−0.332220	+	0.575421i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.c.379.5		144
3.2	odd	2		729.2.g.b.379.4		144
9.2	odd	6		729.2.g.a.622.4		144
9.4	even	3		81.2.g.a.16.4	✓	144
9.5	odd	6		243.2.g.a.208.5		144
9.7	even	3		729.2.g.d.622.5		144
81.5	odd	54		729.2.g.a.109.4		144
81.7	even	27		6561.2.a.c.1.31		72
81.22	even	27		81.2.g.a.76.4	yes	144
81.32	odd	54		729.2.g.b.352.4		144
81.49	even	27	inner	729.2.g.c.352.5		144
81.59	odd	54		243.2.g.a.118.5		144
81.74	odd	54		6561.2.a.d.1.42		72
81.76	even	27		729.2.g.d.109.5		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.4	✓	144	9.4	even	3
81.2.g.a.76.4	yes	144	81.22	even	27
243.2.g.a.118.5		144	81.59	odd	54
243.2.g.a.208.5		144	9.5	odd	6
729.2.g.a.109.4		144	81.5	odd	54
729.2.g.a.622.4		144	9.2	odd	6
729.2.g.b.352.4		144	81.32	odd	54
729.2.g.b.379.4		144	3.2	odd	2
729.2.g.c.352.5		144	81.49	even	27	inner
729.2.g.c.379.5		144	1.1	even	1	trivial
729.2.g.d.109.5		144	81.76	even	27
729.2.g.d.622.5		144	9.7	even	3
6561.2.a.c.1.31		72	81.7	even	27
6561.2.a.d.1.42		72	81.74	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)

\(f(q)\)	\(=\)	\(q+(0.189684 + 0.633587i) q^{2} +(1.30552 - 0.858656i) q^{4} +(-0.995544 - 2.30793i) q^{5} +(-0.239094 + 4.10508i) q^{7} +(1.80495 + 1.51453i) q^{8} +(1.27344 - 1.06854i) q^{10} +(1.76794 + 2.37476i) q^{11} +(2.22560 + 2.35899i) q^{13} +(-2.64628 + 0.627180i) q^{14} +(0.620599 - 1.43871i) q^{16} +(-0.572741 - 3.24818i) q^{17} +(-0.571121 + 3.23899i) q^{19} +(-3.28142 - 2.15823i) q^{20} +(-1.16927 + 1.57060i) q^{22} +(-0.145137 - 2.49190i) q^{23} +(-0.904231 + 0.958429i) q^{25} +(-1.07247 + 1.85757i) q^{26} +(3.21271 + 5.56458i) q^{28} +(5.41695 + 1.28384i) q^{29} +(5.73952 + 2.88249i) q^{31} +(5.70979 + 0.667379i) q^{32} +(1.94936 - 0.979008i) q^{34} +(9.71228 - 3.53498i) q^{35} +(-2.56937 - 0.935175i) q^{37} +(-2.16052 + 0.252528i) q^{38} +(1.69853 - 5.67349i) q^{40} +(2.59515 - 8.66839i) q^{41} +(7.76471 - 0.907565i) q^{43} +(4.34719 + 1.58225i) q^{44} +(1.55131 - 0.564629i) q^{46} +(-9.04350 + 4.54182i) q^{47} +(-9.84186 - 1.15035i) q^{49} +(-0.778766 - 0.391111i) q^{50} +(4.93113 + 1.16870i) q^{52} +(0.00494432 + 0.00856381i) q^{53} +(3.72072 - 6.44448i) q^{55} +(-6.64883 + 7.04735i) q^{56} +(0.214081 + 3.67563i) q^{58} +(-6.79150 + 9.12257i) q^{59} +(-7.52933 - 4.95212i) q^{61} +(-0.737619 + 4.18325i) q^{62} +(0.116049 + 0.658144i) q^{64} +(3.22872 - 7.48500i) q^{65} +(5.68771 - 1.34801i) q^{67} +(-3.53679 - 3.74878i) q^{68} +(4.08198 + 5.48305i) q^{70} +(-1.81817 + 1.52563i) q^{71} +(3.61987 + 3.03743i) q^{73} +(0.105147 - 1.80531i) q^{74} +(2.03557 + 4.71897i) q^{76} +(-10.1713 + 6.68977i) q^{77} +(-2.58181 - 8.62383i) q^{79} -3.93828 q^{80} +5.98444 q^{82} +(1.06156 + 3.54585i) q^{83} +(-6.92638 + 4.55555i) q^{85} +(2.04786 + 4.74747i) q^{86} +(-0.405603 + 6.96394i) q^{88} +(-9.57258 - 8.03235i) q^{89} +(-10.2160 + 8.57223i) q^{91} +(-2.32916 - 3.12861i) q^{92} +(-4.59304 - 4.86834i) q^{94} +(8.04395 - 1.90645i) q^{95} +(-2.83273 + 6.56702i) q^{97} +(-1.13799 - 6.45388i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Introduction

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