LMFDB - Embedded newform 648.2.t.a.253.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] 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("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.6
Character	$\chi$	$=$	648.253
Dual form			648.2.t.a.397.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.15171 + 0.820715i) q^{2} +(0.652854 - 1.89044i) q^{4} +(-2.15975 + 2.57389i) q^{5} +(-1.78453 - 0.649515i) q^{7} +(0.799620 + 2.71304i) q^{8} +(0.374968 - 4.73691i) q^{10} +(-3.21944 - 3.83678i) q^{11} +(3.61424 + 0.637289i) q^{13} +(2.58832 - 0.716539i) q^{14} +(-3.14756 - 2.46837i) q^{16} +(1.74380 - 3.02034i) q^{17} +(-2.73085 + 1.57666i) q^{19} +(3.45580 + 5.76327i) q^{20} +(6.85676 + 1.77660i) q^{22} +(2.93428 - 1.06799i) q^{23} +(-1.09215 - 6.19390i) q^{25} +(-4.68558 + 2.23229i) q^{26} +(-2.39291 + 2.94951i) q^{28} +(6.61611 - 1.16660i) q^{29} +(0.842639 - 0.306695i) q^{31} +(5.65090 + 0.259585i) q^{32} +(0.470500 + 4.90971i) q^{34} +(5.52592 - 3.19039i) q^{35} +(6.21485 + 3.58815i) q^{37} +(1.85115 - 4.05710i) q^{38} +(-8.71007 - 3.80137i) q^{40} +(0.341649 - 1.93759i) q^{41} +(-5.36405 - 6.39263i) q^{43} +(-9.35505 + 3.58132i) q^{44} +(-2.50291 + 3.63822i) q^{46} +(-2.63733 - 0.959909i) q^{47} +(-2.59964 - 2.18135i) q^{49} +(6.34127 + 6.23721i) q^{50} +(3.56433 - 6.41647i) q^{52} -9.52536i q^{53} +16.8287 q^{55} +(0.335219 - 5.36087i) q^{56} +(-6.66237 + 6.77352i) q^{58} +(6.13695 - 7.31373i) q^{59} +(2.92540 - 8.03747i) q^{61} +(-0.718763 + 1.04479i) q^{62} +(-6.72122 + 4.33881i) q^{64} +(-9.44618 + 7.92629i) q^{65} +(13.7512 + 2.42470i) q^{67} +(-4.57135 - 5.26839i) q^{68} +(-3.74584 + 8.20960i) q^{70} +(-1.50109 + 2.59997i) q^{71} +(0.472663 + 0.818676i) q^{73} +(-10.1025 + 0.968131i) q^{74} +(1.19774 + 6.19185i) q^{76} +(3.25314 + 8.93793i) q^{77} +(-0.803209 - 4.55523i) q^{79} +(13.1513 - 2.77042i) q^{80} +(1.19673 + 2.51193i) q^{82} +(-2.12803 + 0.375229i) q^{83} +(4.00787 + 11.0115i) q^{85} +(11.4243 + 2.96007i) q^{86} +(7.83503 - 11.8025i) q^{88} +(7.83712 + 13.5743i) q^{89} +(-6.03579 - 3.48477i) q^{91} +(-0.103320 - 6.24433i) q^{92} +(3.82524 - 1.05896i) q^{94} +(1.83982 - 10.4341i) q^{95} +(1.68619 - 1.41488i) q^{97} +(4.78429 + 0.378719i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−1.15171	+	0.820715i	−0.814379	+	0.580333i
$2$	−1.15171	+	0.820715i	−0.814379	+	0.580333i
$3$		0			0
$3$		0			0
$4$	0.652854	−	1.89044i	0.326427	−	0.945222i
$5$	−2.15975	+	2.57389i	−0.965871	+	1.15108i	0.0226118	+	0.999744i	$0.492802\pi$
$5$	−2.15975	+	2.57389i	−0.965871	+	1.15108i	−0.988482	+	0.151335i	$0.951643\pi$
$6$		0			0
$7$	−1.78453	−	0.649515i	−0.674489	−	0.245494i	−0.0180093	−	0.999838i	$-0.505733\pi$
$7$	−1.78453	−	0.649515i	−0.674489	−	0.245494i	−0.656479	+	0.754344i	$0.727955\pi$
$8$	0.799620	+	2.71304i	0.282708	+	0.959206i
$9$		0			0
$10$	0.374968	−	4.73691i	0.118575	−	1.49794i
$11$	−3.21944	−	3.83678i	−0.970699	−	1.15683i	−0.987602	−	0.156977i	$-0.949825\pi$
$11$	−3.21944	−	3.83678i	−0.970699	−	1.15683i	0.0169036	−	0.999857i	$-0.494619\pi$
$12$		0			0
$13$	3.61424	+	0.637289i	1.00241	+	0.176752i	0.650682	−	0.759350i	$-0.274483\pi$
$13$	3.61424	+	0.637289i	1.00241	+	0.176752i	0.351728	+	0.936102i	$0.385594\pi$
$14$	2.58832	−	0.716539i	0.691758	−	0.191503i
$15$		0			0
$16$	−3.14756	−	2.46837i	−0.786891	−	0.617092i
$17$	1.74380	−	3.02034i	0.422932	−	0.732541i	−0.573292	−	0.819351i	$-0.694334\pi$
$17$	1.74380	−	3.02034i	0.422932	−	0.732541i	0.996225	+	0.0868103i	$0.0276674\pi$
$18$		0			0
$19$	−2.73085	+	1.57666i	−0.626501	+	0.361710i	−0.779396	−	0.626532i	$-0.784474\pi$
$19$	−2.73085	+	1.57666i	−0.626501	+	0.361710i	0.152895	+	0.988242i	$0.451140\pi$
$20$	3.45580	+	5.76327i	0.772740	+	1.28871i
$21$		0			0
$22$	6.85676	+	1.77660i	1.46187	+	0.378773i
$23$	2.93428	−	1.06799i	0.611839	−	0.222691i	−0.0174685	−	0.999847i	$-0.505561\pi$
$23$	2.93428	−	1.06799i	0.611839	−	0.222691i	0.629308	+	0.777156i	$0.283338\pi$
$24$		0			0
$25$	−1.09215	−	6.19390i	−0.218430	−	1.23878i
$26$	−4.68558	+	2.23229i	−0.918918	+	0.437789i
$27$		0			0
$28$	−2.39291	+	2.94951i	−0.452218	+	0.557406i
$29$	6.61611	−	1.16660i	1.22858	−	0.216632i	0.478565	−	0.878052i	$-0.341157\pi$
$29$	6.61611	−	1.16660i	1.22858	−	0.216632i	0.750015	+	0.661420i	$0.230046\pi$
$30$		0			0
$31$	0.842639	−	0.306695i	0.151342	−	0.0550841i	−0.265238	−	0.964183i	$-0.585451\pi$
$31$	0.842639	−	0.306695i	0.151342	−	0.0550841i	0.416581	+	0.909099i	$0.363228\pi$
$32$	5.65090	+	0.259585i	0.998947	+	0.0458885i
$33$		0			0
$34$	0.470500	+	4.90971i	0.0806901	+	0.842008i
$35$	5.52592	−	3.19039i	0.934052	−	0.539275i
$36$		0			0
$37$	6.21485	+	3.58815i	1.02172	+	0.589887i	0.914600	−	0.404359i	$-0.132505\pi$
$37$	6.21485	+	3.58815i	1.02172	+	0.589887i	0.107115	+	0.994247i	$0.465839\pi$
$38$	1.85115	−	4.05710i	0.300297	−	0.658148i
$39$		0			0
$40$	−8.71007	−	3.80137i	−1.37718	−	0.601049i
$41$	0.341649	−	1.93759i	0.0533567	−	0.302601i	−0.946438	−	0.322887i	$-0.895347\pi$
$41$	0.341649	−	1.93759i	0.0533567	−	0.302601i	0.999794	+	0.0202862i	$0.00645776\pi$
$42$		0			0
$43$	−5.36405	−	6.39263i	−0.818010	−	0.974867i	0.181954	−	0.983307i	$-0.441758\pi$
$43$	−5.36405	−	6.39263i	−0.818010	−	0.974867i	−0.999964	+	0.00844018i	$0.997313\pi$
$44$	−9.35505	+	3.58132i	−1.41033	+	0.539904i
$45$		0			0
$46$	−2.50291	+	3.63822i	−0.369034	+	0.536426i
$47$	−2.63733	−	0.959909i	−0.384694	−	0.140017i	0.142432	−	0.989805i	$-0.454508\pi$
$47$	−2.63733	−	0.959909i	−0.384694	−	0.140017i	−0.527125	+	0.849788i	$0.676730\pi$
$48$		0			0
$49$	−2.59964	−	2.18135i	−0.371377	−	0.311622i
$50$	6.34127	+	6.23721i	0.896791	+	0.882075i
$51$		0			0
$52$	3.56433	−	6.41647i	0.494284	−	0.889804i
$53$		−	9.52536i		−	1.30841i	−0.756318	−	0.654205i	$-0.773004\pi$
$53$		−	9.52536i		−	1.30841i	0.756318	−	0.654205i	$-0.226996\pi$
$54$		0			0
$55$	16.8287			2.26918
$56$	0.335219	−	5.36087i	0.0447955	−	0.716377i
$57$		0			0
$58$	−6.66237	+	6.77352i	−0.874812	+	0.889406i
$59$	6.13695	−	7.31373i	0.798963	−	0.952167i	−0.200659	−	0.979661i	$-0.564308\pi$
$59$	6.13695	−	7.31373i	0.798963	−	0.952167i	0.999622	+	0.0274946i	$0.00875290\pi$
$60$		0			0
$61$	2.92540	−	8.03747i	0.374559	−	1.02909i	−0.599018	−	0.800735i	$-0.704442\pi$
$61$	2.92540	−	8.03747i	0.374559	−	1.02909i	0.973577	−	0.228358i	$-0.0733355\pi$
$62$	−0.718763	+	1.04479i	−0.0912830	+	0.132688i
$63$		0			0
$64$	−6.72122	+	4.33881i	−0.840152	+	0.542351i
$65$	−9.44618	+	7.92629i	−1.17165	+	0.983135i
$66$		0			0
$67$	13.7512	+	2.42470i	1.67997	+	0.296224i	0.930631	−	0.365960i	$-0.119259\pi$
$67$	13.7512	+	2.42470i	1.67997	+	0.296224i	0.749341	+	0.662184i	$0.230370\pi$
$68$	−4.57135	−	5.26839i	−0.554357	−	0.638886i
$69$		0			0
$70$	−3.74584	+	8.20960i	−0.447713	+	0.981235i
$71$	−1.50109	+	2.59997i	−0.178147	+	0.308560i	−0.941246	−	0.337722i	$-0.890344\pi$
$71$	−1.50109	+	2.59997i	−0.178147	+	0.308560i	0.763099	+	0.646282i	$0.223677\pi$
$72$		0			0
$73$	0.472663	+	0.818676i	0.0553210	+	0.0958187i	0.892360	−	0.451325i	$-0.149048\pi$
$73$	0.472663	+	0.818676i	0.0553210	+	0.0958187i	−0.837039	+	0.547144i	$0.815715\pi$
$74$	−10.1025	+	0.968131i	−1.17439	+	0.112543i
$75$		0			0
$76$	1.19774	+	6.19185i	0.137390	+	0.710254i
$77$	3.25314	+	8.93793i	0.370730	+	1.01857i
$78$		0			0
$79$	−0.803209	−	4.55523i	−0.0903681	−	0.512503i	−0.996069	−	0.0885849i	$-0.971766\pi$
$79$	−0.803209	−	4.55523i	−0.0903681	−	0.512503i	0.905701	−	0.423918i	$-0.139346\pi$
$80$	13.1513	−	2.77042i	1.47036	−	0.309743i
$81$		0			0
$82$	1.19673	+	2.51193i	0.132157	+	0.277396i
$83$	−2.12803	+	0.375229i	−0.233582	+	0.0411868i	−0.289214	−	0.957265i	$-0.593394\pi$
$83$	−2.12803	+	0.375229i	−0.233582	+	0.0411868i	0.0556319	+	0.998451i	$0.482283\pi$
$84$		0			0
$85$	4.00787	+	11.0115i	0.434715	+	1.19437i
$86$	11.4243	+	2.96007i	1.23192	+	0.319193i
$87$		0			0
$88$	7.83503	−	11.8025i	0.835217	−	1.25815i
$89$	7.83712	+	13.5743i	0.830733	+	1.43887i	0.897458	+	0.441101i	$0.145412\pi$
$89$	7.83712	+	13.5743i	0.830733	+	1.43887i	−0.0667245	+	0.997771i	$0.521255\pi$
$90$		0			0
$91$	−6.03579	−	3.48477i	−0.632723	−	0.365303i
$92$	−0.103320	−	6.24433i	−0.0107719	−	0.651017i
$93$		0			0
$94$	3.82524	−	1.05896i	0.394543	−	0.109223i
$95$	1.83982	−	10.4341i	0.188761	−	1.07052i
$96$		0			0
$97$	1.68619	−	1.41488i	0.171207	−	0.143659i	−0.553158	−	0.833076i	$-0.686578\pi$
$97$	1.68619	−	1.41488i	0.171207	−	0.143659i	0.724365	+	0.689417i	$0.242133\pi$
$98$	4.78429	+	0.378719i	0.483286	+	0.0382564i
$99$		0			0
$100$	−12.4222	−	1.97906i	−1.24222	−	0.197906i
$101$	−6.12830	+	16.8374i	−0.609789	+	1.67538i	0.120895	+	0.992665i	$0.461424\pi$
$101$	−6.12830	+	16.8374i	−0.609789	+	1.67538i	−0.730684	+	0.682716i	$0.760799\pi$
$102$		0			0
$103$	−10.6973	−	8.97613i	−1.05404	−	0.884444i	−0.0605268	−	0.998167i	$-0.519278\pi$
$103$	−10.6973	−	8.97613i	−1.05404	−	0.884444i	−0.993513	+	0.113723i	$0.963723\pi$
$104$	1.16103	+	10.3152i	0.113848	+	1.01149i
$105$		0			0
$106$	7.81761	+	10.9704i	0.759313	+	1.06554i
$107$		−	12.3518i		−	1.19409i	−0.802207	−	0.597046i	$-0.796341\pi$
$107$		−	12.3518i		−	1.19409i	0.802207	−	0.597046i	$-0.203659\pi$
$108$		0			0
$109$		−	2.18468i		−	0.209255i	−0.994511	−	0.104627i	$-0.966635\pi$
$109$		−	2.18468i		−	0.209255i	0.994511	−	0.104627i	$-0.0333650\pi$
$110$	−19.3817	+	13.8115i	−1.84797	+	1.31688i
$111$		0			0
$112$	4.01367	+	6.44927i	0.379256	+	0.609399i
$113$	−12.1210	−	10.1708i	−1.14025	−	0.956785i	−0.140805	−	0.990037i	$-0.544969\pi$
$113$	−12.1210	−	10.1708i	−1.14025	−	0.956785i	−0.999447	+	0.0332523i	$0.989413\pi$
$114$		0			0
$115$	−3.58842	+	9.85911i	−0.334622	+	0.919367i
$116$	2.11396	−	13.2690i	0.196277	−	1.23200i
$117$		0			0
$118$	−1.06547	+	13.4600i	−0.0980848	+	1.23909i
$119$	−5.07361	+	4.25727i	−0.465097	+	0.390263i
$120$		0			0
$121$	−2.44596	+	13.8717i	−0.222360	+	1.26107i
$122$	3.22727	+	11.6577i	0.292183	+	1.05544i
$123$		0			0
$124$	−0.0296705	−	1.79319i	−0.00266449	−	0.161033i
$125$	3.75209	+	2.16627i	0.335597	+	0.193757i
$126$		0			0
$127$	−5.17381	−	8.96131i	−0.459102	−	0.795187i	0.539812	−	0.841786i	$-0.318495\pi$
$127$	−5.17381	−	8.96131i	−0.459102	−	0.795187i	−0.998914	+	0.0465982i	$0.985162\pi$
$128$	4.17994	−	10.5132i	0.369458	−	0.929247i
$129$		0			0
$130$	4.37400	−	16.8814i	0.383626	−	1.48059i
$131$	3.07414	+	8.44614i	0.268589	+	0.737942i	0.998518	+	0.0544195i	$0.0173308\pi$
$131$	3.07414	+	8.44614i	0.268589	+	0.737942i	−0.729929	+	0.683523i	$0.760447\pi$
$132$		0			0
$133$	5.89735	−	1.03986i	0.511365	−	0.0901675i
$134$	−17.8273	+	8.49324i	−1.54004	+	0.733704i
$135$		0			0
$136$	9.58869	+	2.31587i	0.822224	+	0.198584i
$137$	−2.92683	−	16.5989i	−0.250056	−	1.41814i	−0.808451	−	0.588563i	$-0.799694\pi$
$137$	−2.92683	−	16.5989i	−0.250056	−	1.41814i	0.558395	−	0.829575i	$-0.311417\pi$
$138$		0			0
$139$	−3.76833	−	10.3534i	−0.319626	−	0.878164i	−0.990613	−	0.136695i	$-0.956352\pi$
$139$	−3.76833	−	10.3534i	−0.319626	−	0.878164i	0.670988	−	0.741469i	$-0.265870\pi$
$140$	−2.42364	−	12.5293i	−0.204835	−	1.05892i
$141$		0			0
$142$	−0.405016	−	4.22637i	−0.0339882	−	0.354669i
$143$	−9.19071	−	15.9188i	−0.768566	−	1.33120i
$144$		0			0
$145$	−11.2865	+	19.5487i	−0.937289	+	1.62343i
$146$	−1.21627	−	0.554953i	−0.100659	−	0.0459282i
$147$		0			0
$148$	10.8406	−	9.40629i	0.891090	−	0.773193i
$149$	−10.6491	−	1.87772i	−0.872406	−	0.153829i	−0.280518	−	0.959849i	$-0.590506\pi$
$149$	−10.6491	−	1.87772i	−0.872406	−	0.153829i	−0.591888	+	0.806020i	$0.701617\pi$
$150$		0			0
$151$	−0.489785	+	0.410979i	−0.0398582	+	0.0334450i	−0.662499	−	0.749063i	$-0.730504\pi$
$151$	−0.489785	+	0.410979i	−0.0398582	+	0.0334450i	0.622641	+	0.782508i	$0.286060\pi$
$152$	−6.46119	−	6.14820i	−0.524072	−	0.498685i
$153$		0			0
$154$	−11.0822	−	7.62397i	−0.893025	−	0.614357i
$155$	−1.03049	+	2.83125i	−0.0827709	+	0.227411i
$156$		0			0
$157$	−5.93021	+	7.06735i	−0.473282	+	0.564036i	−0.948884	−	0.315625i	$-0.897786\pi$
$157$	−5.93021	+	7.06735i	−0.473282	+	0.564036i	0.475602	+	0.879661i	$0.342230\pi$
$158$	4.66360	+	4.58708i	0.371016	+	0.364928i
$159$		0			0
$160$	−12.8727	+	13.9842i	−1.01767	+	1.10554i
$161$	−5.92998			−0.467348
$162$		0			0
$163$		−	8.36032i		−	0.654831i	−0.944881	−	0.327415i	$-0.893822\pi$
$163$		−	8.36032i		−	0.654831i	0.944881	−	0.327415i	$-0.106178\pi$
$164$	−3.43986	−	1.91083i	−0.268608	−	0.149211i
$165$		0			0
$166$	2.14291	−	2.17866i	0.166322	−	0.169097i
$167$	4.77570	+	4.00729i	0.369555	+	0.310094i	0.808586	−	0.588379i	$-0.200234\pi$
$167$	4.77570	+	4.00729i	0.369555	+	0.310094i	−0.439030	+	0.898472i	$0.644678\pi$
$168$		0			0
$169$	0.440614	+	0.160370i	0.0338934	+	0.0123362i
$170$	−13.6532	−	9.39273i	−1.04715	−	0.720390i
$171$		0			0
$172$	−15.5869	+	5.96699i	−1.18849	+	0.454979i
$173$	5.72780	+	6.82613i	0.435477	+	0.518981i	0.938494	−	0.345295i	$-0.112221\pi$
$173$	5.72780	+	6.82613i	0.435477	+	0.518981i	−0.503017	+	0.864276i	$0.667777\pi$
$174$		0			0
$175$	−2.07406	+	11.7626i	−0.156784	+	0.889167i
$176$	0.662802	+	20.0233i	0.0499605	+	1.50931i
$177$		0			0
$178$	−20.1667	−	9.20155i	−1.51156	−	0.689686i
$179$	−12.5035	−	7.21893i	−0.934559	−	0.539568i	−0.0463085	−	0.998927i	$-0.514746\pi$
$179$	−12.5035	−	7.21893i	−0.934559	−	0.539568i	−0.888251	+	0.459359i	$0.848079\pi$
$180$		0			0
$181$	4.19806	−	2.42375i	0.312039	−	0.180156i	−0.335799	−	0.941934i	$-0.609006\pi$
$181$	4.19806	−	2.42375i	0.312039	−	0.180156i	0.647839	+	0.761778i	$0.275673\pi$
$182$	9.81146	−	0.940238i	0.727274	−	0.0696951i
$183$		0			0
$184$	5.24381	+	7.10684i	0.386579	+	0.523923i
$185$	−22.6580	+	8.24685i	−1.66585	+	0.606321i
$186$		0			0
$187$	−17.2024	+	3.03326i	−1.25797	+	0.221814i
$188$	−3.53644	+	4.35904i	−0.257922	+	0.317916i
$189$		0			0
$190$	6.44451	+	13.5270i	0.467534	+	0.981352i
$191$	4.56335	+	25.8800i	0.330192	+	1.87261i	0.470345	+	0.882483i	$0.344129\pi$
$191$	4.56335	+	25.8800i	0.330192	+	1.87261i	−0.140153	+	0.990130i	$0.544759\pi$
$192$		0			0
$193$	3.82953	−	1.39383i	0.275655	−	0.100330i	−0.200494	−	0.979695i	$-0.564255\pi$
$193$	3.82953	−	1.39383i	0.275655	−	0.100330i	0.476149	+	0.879365i	$0.342032\pi$
$194$	−0.780781	+	3.01341i	−0.0560568	+	0.216350i
$195$		0			0
$196$	−5.82091	+	3.49036i	−0.415780	+	0.249312i
$197$	−8.91014	+	5.14427i	−0.634821	+	0.366514i	−0.782617	−	0.622504i	$-0.786116\pi$
$197$	−8.91014	+	5.14427i	−0.634821	+	0.366514i	0.147796	+	0.989018i	$0.452782\pi$
$198$		0			0
$199$	0.690545	−	1.19606i	0.0489514	−	0.0847864i	−0.840511	−	0.541794i	$-0.817745\pi$
$199$	0.690545	−	1.19606i	0.0489514	−	0.0847864i	0.889463	+	0.457007i	$0.151079\pi$
$200$	15.9310	−	7.91583i	1.12649	−	0.559733i
$201$		0			0
$202$	−6.76068	−	24.4213i	−0.475680	−	1.71828i
$203$	−12.5644	−	2.21544i	−0.881845	−	0.155493i
$204$		0			0
$205$	4.24927	+	5.06408i	0.296782	+	0.353691i
$206$	19.6870	+	1.55840i	1.37166	+	0.108579i
$207$		0			0
$208$	−9.80299	−	10.9272i	−0.679715	−	0.757665i
$209$	14.8411	+	5.40173i	1.02658	+	0.373645i
$210$		0			0
$211$	−7.42731	+	8.85152i	−0.511317	+	0.609364i	−0.958505	−	0.285076i	$-0.907981\pi$
$211$	−7.42731	+	8.85152i	−0.511317	+	0.609364i	0.447188	+	0.894440i	$0.352426\pi$
$212$	−18.0072	−	6.21867i	−1.23674	−	0.427100i
$213$		0			0
$214$	10.1373	+	14.2256i	0.692971	+	0.972444i
$215$	28.0390			1.91224
$216$		0			0
$217$	−1.70292			−0.115602
$218$	1.79300	+	2.51611i	0.121437	+	0.170413i
$219$		0			0
$220$	10.9867	−	31.8137i	0.740721	−	2.14488i
$221$	8.22733	−	9.80495i	0.553430	−	0.659552i
$222$		0			0
$223$	2.85912	+	1.04063i	0.191461	+	0.0696860i	0.435971	−	0.899961i	$-0.356405\pi$
$223$	2.85912	+	1.04063i	0.191461	+	0.0696860i	−0.244510	+	0.969647i	$0.578627\pi$
$224$	−9.91558	−	4.13358i	−0.662513	−	0.276186i
$225$		0			0
$226$	22.3072	+	1.76581i	1.48385	+	0.117460i
$227$	−0.641654	−	0.764693i	−0.0425881	−	0.0507545i	0.744330	−	0.667812i	$-0.232769\pi$
$227$	−0.641654	−	0.764693i	−0.0425881	−	0.0507545i	−0.786918	+	0.617058i	$0.788325\pi$
$228$		0			0
$229$	0.846018	+	0.149176i	0.0559064	+	0.00985781i	0.201531	−	0.979482i	$-0.435408\pi$
$229$	0.846018	+	0.149176i	0.0559064	+	0.00985781i	−0.145625	+	0.989340i	$0.546519\pi$
$230$	−3.95871	−	14.2999i	−0.261030	−	0.942906i
$231$		0			0
$232$	8.45541	+	17.0170i	0.555125	+	1.11722i
$233$	5.17379	−	8.96127i	0.338946	−	0.587072i	−0.645288	−	0.763939i	$-0.723263\pi$
$233$	5.17379	−	8.96127i	0.338946	−	0.587072i	0.984235	+	0.176867i	$0.0565961\pi$
$234$		0			0
$235$	8.16668	−	4.71503i	0.532735	−	0.307575i
$236$	−9.81967	−	16.3764i	−0.639206	−	1.06601i
$237$		0			0
$238$	2.34931	−	9.06711i	0.152283	−	0.587733i
$239$	11.5092	−	4.18901i	0.744469	−	0.270965i	0.0581928	−	0.998305i	$-0.481466\pi$
$239$	11.5092	−	4.18901i	0.744469	−	0.270965i	0.686277	+	0.727341i	$0.259244\pi$
$240$		0			0
$241$	−2.60278	−	14.7611i	−0.167660	−	0.950846i	−0.946279	−	0.323350i	$-0.895191\pi$
$241$	−2.60278	−	14.7611i	−0.167660	−	0.950846i	0.778620	−	0.627496i	$-0.215920\pi$
$242$	−8.56771	−	17.9836i	−0.550753	−	1.15603i
$243$		0			0
$244$	−13.2845	−	10.7776i	−0.850455	−	0.689966i
$245$	11.2291	−	1.98000i	0.717404	−	0.126498i
$246$		0			0
$247$	−10.8748	+	3.95809i	−0.691944	+	0.251847i
$248$	1.50587	+	2.04088i	0.0956228	+	0.129596i
$249$		0			0
$250$	−6.09919	+	0.584489i	−0.385747	+	0.0369663i
$251$	13.8356	−	7.98801i	0.873298	−	0.504199i	0.00485525	−	0.999988i	$-0.498455\pi$
$251$	13.8356	−	7.98801i	0.873298	−	0.504199i	0.868443	+	0.495789i	$0.165121\pi$
$252$		0			0
$253$	−13.5444	−	7.81986i	−0.851528	−	0.491630i
$254$	13.3134	+	6.07457i	0.835356	+	0.381152i
$255$		0			0
$256$	3.81430	+	15.5387i	0.238394	+	0.971169i
$257$	1.36142	−	7.72098i	0.0849229	−	0.481622i	−0.912450	−	0.409187i	$-0.865812\pi$
$257$	1.36142	−	7.72098i	0.0849229	−	0.481622i	0.997373	−	0.0724341i	$-0.0230767\pi$
$258$		0			0
$259$	−8.76002	−	10.4398i	−0.544321	−	0.648697i
$260$	8.81723	+	23.0322i	0.546821	+	1.42840i
$261$		0			0
$262$	−10.4724	−	7.20447i	−0.646986	−	0.445094i
$263$	19.3707	+	7.05037i	1.19445	+	0.434744i	0.861284	−	0.508124i	$-0.169661\pi$
$263$	19.3707	+	7.05037i	1.19445	+	0.434744i	0.333166	+	0.942868i	$0.391883\pi$
$264$		0			0
$265$	24.5173	+	20.5724i	1.50608	+	1.26375i
$266$	−5.93858	+	6.03766i	−0.364118	+	0.370193i
$267$		0			0
$268$	13.5613	−	24.4128i	0.828386	−	1.49125i
$269$			15.9724i			0.973852i	0.873443	+	0.486926i	$0.161882\pi$
$269$			15.9724i			0.973852i	−0.873443	+	0.486926i	$0.838118\pi$
$270$		0			0
$271$	7.19443			0.437031			0.218515	−	0.975834i	$-0.429879\pi$
$271$	7.19443			0.437031			0.218515	+	0.975834i	$0.429879\pi$
$272$	−12.9440	+	5.20239i	−0.784847	+	0.315441i
$273$		0			0
$274$	16.9938	+	16.7149i	1.02663	+	1.00979i
$275$	−20.2485	+	24.1313i	−1.22103	+	1.45517i
$276$		0			0
$277$	−6.45750	+	17.7418i	−0.387993	+	1.06600i	0.579910	+	0.814680i	$0.303088\pi$
$277$	−6.45750	+	17.7418i	−0.387993	+	1.06600i	−0.967903	+	0.251322i	$0.919135\pi$
$278$	12.8372	+	8.83135i	0.769924	+	0.529669i
$279$		0			0
$280$	13.0743	+	12.4410i	0.781340	+	0.743490i
$281$	14.1133	−	11.8425i	0.841932	−	0.706465i	−0.116066	−	0.993242i	$-0.537028\pi$
$281$	14.1133	−	11.8425i	0.841932	−	0.706465i	0.957997	+	0.286777i	$0.0925839\pi$
$282$		0			0
$283$	−8.62324	−	1.52051i	−0.512599	−	0.0903850i	−0.0886349	−	0.996064i	$-0.528250\pi$
$283$	−8.62324	−	1.52051i	−0.512599	−	0.0903850i	−0.423964	+	0.905679i	$0.639362\pi$
$284$	3.93511	+	4.53514i	0.233506	+	0.269111i
$285$		0			0
$286$	23.6498	+	10.7908i	1.39844	+	0.638074i
$287$	−1.86818	+	3.23578i	−0.110275	+	0.191002i
$288$		0			0
$289$	2.41836	+	4.18872i	0.142256	+	0.246395i
$290$	−3.04524	−	31.7773i	−0.178823	−	1.86603i
$291$		0			0
$292$	1.85624	−	0.359067i	0.108628	−	0.0210128i
$293$	−4.67724	−	12.8506i	−0.273247	−	0.750741i	−0.998087	−	0.0618236i	$-0.980308\pi$
$293$	−4.67724	−	12.8506i	−0.273247	−	0.750741i	0.724840	−	0.688918i	$-0.241914\pi$
$294$		0			0
$295$	5.57047	+	31.5917i	0.324325	+	1.83934i
$296$	−4.76528	+	19.7303i	−0.276976	+	1.14680i
$297$		0			0
$298$	13.8057	−	6.57727i	0.799742	−	0.381011i
$299$	11.2858	−	1.98999i	0.652675	−	0.115084i
$300$		0			0
$301$	5.42020	+	14.8919i	0.312415	+	0.858353i
$302$	0.226792	−	0.875301i	0.0130504	−	0.0503679i
$303$		0			0
$304$	12.4873	+	1.77812i	0.716196	+	0.101982i
$305$	14.3695	+	24.8886i	0.822792	+	1.42512i
$306$		0			0
$307$	21.3532	+	12.3283i	1.21869	+	0.703612i	0.964638	−	0.263578i	$-0.0849028\pi$
$307$	21.3532	+	12.3283i	1.21869	+	0.703612i	0.254053	+	0.967190i	$0.418236\pi$
$308$	19.0205	−	0.314717i	1.08379	−	0.0179327i
$309$		0			0
$310$	−1.13683	−	4.10650i	−0.0645674	−	0.233234i
$311$	−0.221479	+	1.25607i	−0.0125589	+	0.0712250i	−0.990443	−	0.137922i	$-0.955958\pi$
$311$	−0.221479	+	1.25607i	−0.0125589	+	0.0712250i	0.977884	+	0.209147i	$0.0670688\pi$
$312$		0			0
$313$	15.3438	−	12.8749i	0.867280	−	0.727735i	−0.0962433	−	0.995358i	$-0.530683\pi$
$313$	15.3438	−	12.8749i	0.867280	−	0.727735i	0.963524	+	0.267623i	$0.0862382\pi$
$314$	1.02958	−	13.0065i	0.0581026	−	0.734001i
$315$		0			0
$316$	−9.13578	−	1.45548i	−0.513928	−	0.0818769i
$317$	2.05364	−	5.64232i	0.115344	−	0.316904i	−0.868565	−	0.495575i	$-0.834957\pi$
$317$	2.05364	−	5.64232i	0.115344	−	0.316904i	0.983909	+	0.178671i	$0.0571796\pi$
$318$		0			0
$319$	−25.7762	−	21.6288i	−1.44319	−	1.21098i
$320$	3.34853	−	26.6704i	0.187189	−	1.49092i
$321$		0			0
$322$	6.82960	−	4.86682i	0.380598	−	0.271217i
$323$			10.9975i			0.611916i
$324$		0			0
$325$		−	23.0823i		−	1.28038i
$326$	6.86144	+	9.62863i	0.380020	+	0.533280i
$327$		0			0
$328$	5.52996	−	0.622426i	0.305341	−	0.0343677i
$329$	4.08291	+	3.42597i	0.225098	+	0.188880i
$330$		0			0
$331$	6.69009	−	18.3809i	0.367721	−	1.01030i	−0.608505	−	0.793550i	$-0.708231\pi$
$331$	6.69009	−	18.3809i	0.367721	−	1.01030i	0.976226	−	0.216755i	$-0.0695472\pi$
$332$	−0.679944	+	4.26790i	−0.0373168	+	0.234231i
$333$		0			0
$334$	−8.78905	−	0.695731i	−0.480916	−	0.0380687i
$335$	−35.9400	+	30.1573i	−1.96361	+	1.64767i
$336$		0			0
$337$	3.82769	−	21.7079i	0.208508	−	1.18251i	−0.683316	−	0.730123i	$-0.739463\pi$
$337$	3.82769	−	21.7079i	0.208508	−	1.18251i	0.891824	−	0.452383i	$-0.149426\pi$
$338$	−0.639077	+	0.176919i	−0.0347612	+	0.00962313i
$339$		0			0
$340$	23.4332	−	0.387732i	1.27085	−	0.0210277i
$341$	−3.88955	−	2.24563i	−0.210631	−	0.121608i
$342$		0			0
$343$	9.86900	+	17.0936i	0.532876	+	0.922968i
$344$	13.0543	−	19.6646i	0.703840	−	1.06024i
$345$		0			0
$346$	−12.1990	−	3.16080i	−0.655825	−	0.169926i
$347$	−0.0110975	−	0.0304900i	−0.000595743	−	0.00163679i	0.939394	−	0.342838i	$-0.111388\pi$
$347$	−0.0110975	−	0.0304900i	−0.000595743	−	0.00163679i	−0.939990	+	0.341202i	$0.889166\pi$
$348$		0			0
$349$	−32.0493	+	5.65116i	−1.71556	+	0.302500i	−0.943087	−	0.332546i	$-0.892092\pi$
$349$	−32.0493	+	5.65116i	−1.71556	+	0.302500i	−0.772474	+	0.635046i	$0.780981\pi$
$350$	−7.26501	−	15.2492i	−0.388331	−	0.815106i
$351$		0			0
$352$	−17.1968	−	22.5170i	−0.916591	−	1.20016i
$353$	0.185474	+	1.05188i	0.00987180	+	0.0559857i	0.989346	−	0.145585i	$-0.0465065\pi$
$353$	0.185474	+	1.05188i	0.00987180	+	0.0559857i	−0.979474	+	0.201571i	$0.935395\pi$
$354$		0			0
$355$	−3.45005	−	9.47895i	−0.183110	−	0.503090i
$356$	30.7779	−	5.95361i	1.63123	−	0.315541i
$357$		0			0
$358$	20.3251	−	1.94777i	1.07421	−	0.102943i
$359$	−5.68242	−	9.84224i	−0.299907	−	0.519453i	0.676208	−	0.736711i	$-0.263622\pi$
$359$	−5.68242	−	9.84224i	−0.299907	−	0.519453i	−0.976114	+	0.217258i	$0.930289\pi$
$360$		0			0
$361$	−4.52830	+	7.84324i	−0.238331	+	0.412802i
$362$	−2.84572	+	6.23686i	−0.149568	+	0.327802i
$363$		0			0
$364$	−10.5283	+	9.13529i	−0.551830	+	0.478819i
$365$	−3.12802	−	0.551554i	−0.163728	−	0.0288697i
$366$		0			0
$367$	6.59453	−	5.53346i	0.344231	−	0.288844i	−0.454237	−	0.890881i	$-0.650088\pi$
$367$	6.59453	−	5.53346i	0.344231	−	0.288844i	0.798469	+	0.602036i	$0.205644\pi$
$368$	−11.8720	−	3.88132i	−0.618872	−	0.202328i
$369$		0			0
$370$	19.3271	−	28.0937i	1.00477	−	1.46052i
$371$	−6.18687	+	16.9983i	−0.321206	+	0.882507i
$372$		0			0
$373$	24.5912	−	29.3067i	1.27328	−	1.51744i	0.530966	−	0.847393i	$-0.321829\pi$
$373$	24.5912	−	29.3067i	1.27328	−	1.51744i	0.742318	−	0.670048i	$-0.233726\pi$
$374$	17.3227	−	17.6117i	0.895737	−	0.910681i
$375$		0			0
$376$	0.495415	−	7.92275i	0.0255491	−	0.408584i
$377$	24.6557			1.26983
$378$		0			0
$379$			22.1132i			1.13588i	0.823071	+	0.567939i	$0.192259\pi$
$379$			22.1132i			1.13588i	−0.823071	+	0.567939i	$0.807741\pi$
$380$	−18.5240	−	10.2900i	−0.950260	−	0.527867i
$381$		0			0
$382$	−26.4958	−	26.0610i	−1.35564	−	1.33340i
$383$	1.25391	+	1.05215i	0.0640717	+	0.0537626i	0.674261	−	0.738493i	$-0.264462\pi$
$383$	1.25391	+	1.05215i	0.0640717	+	0.0537626i	−0.610189	+	0.792256i	$0.708907\pi$
$384$		0			0
$385$	−30.0312	−	10.9305i	−1.53053	−	0.557069i
$386$	−3.26655	+	4.74824i	−0.166263	+	0.241679i
$387$		0			0
$388$	−1.57392	−	4.11136i	−0.0799036	−	0.208723i
$389$	−7.37158	−	8.78511i	−0.373754	−	0.445423i	0.546079	−	0.837734i	$-0.316120\pi$
$389$	−7.37158	−	8.78511i	−0.373754	−	0.445423i	−0.919832	+	0.392311i	$0.871676\pi$
$390$		0			0
$391$	1.89109	−	10.7249i	0.0956363	−	0.542380i
$392$	3.83939	−	8.79719i	0.193918	−	0.444325i
$393$		0			0
$394$	6.03988	−	13.2374i	0.304285	−	0.666889i
$395$	13.4594	+	7.77079i	0.677216	+	0.390991i
$396$		0			0
$397$	−2.58188	+	1.49065i	−0.129581	+	0.0748137i	−0.563389	−	0.826192i	$-0.690503\pi$
$397$	−2.58188	+	1.49065i	−0.129581	+	0.0748137i	0.433808	+	0.901005i	$0.357170\pi$
$398$	0.186319	+	1.94425i	0.00933930	+	0.0974564i
$399$		0			0
$400$	−11.8512	+	22.1915i	−0.592561	+	1.10958i
$401$	8.85877	−	3.22433i	0.442386	−	0.161015i	−0.111217	−	0.993796i	$-0.535475\pi$
$401$	8.85877	−	3.22433i	0.442386	−	0.161015i	0.553603	+	0.832781i	$0.313253\pi$
$402$		0			0
$403$	3.24096	−	0.571468i	0.161443	−	0.0284668i
$404$	27.8292	+	22.5776i	1.38456	+	1.12328i
$405$		0			0
$406$	16.2887	−	7.76023i	0.808394	−	0.385134i
$407$	−6.24142	−	35.3969i	−0.309376	−	1.75456i
$408$		0			0
$409$	−24.0695	+	8.76058i	−1.19016	+	0.433183i	−0.859779	−	0.510665i	$-0.829399\pi$
$409$	−24.0695	+	8.76058i	−1.19016	+	0.433183i	−0.330380	+	0.943848i	$0.607177\pi$
$410$	−9.05008	−	2.34490i	−0.446952	−	0.115806i
$411$		0			0
$412$	−23.9527	+	14.3626i	−1.18006	+	0.707595i
$413$	−15.7019	+	9.06552i	−0.772642	+	0.446085i
$414$		0			0
$415$	3.63022	−	6.28773i	0.178201	−	0.308652i
$416$	20.2583	+	4.53945i	0.993244	+	0.222565i
$417$		0			0
$418$	−21.5259	+	5.95913i	−1.05287	+	0.291470i
$419$	2.41298	+	0.425474i	0.117882	+	0.0207858i	0.232278	−	0.972649i	$-0.425382\pi$
$419$	2.41298	+	0.425474i	0.117882	+	0.0207858i	−0.114396	+	0.993435i	$0.536493\pi$
$420$		0			0
$421$	8.35420	+	9.95615i	0.407159	+	0.485233i	0.930189	−	0.367081i	$-0.119643\pi$
$421$	8.35420	+	9.95615i	0.407159	+	0.485233i	−0.523030	+	0.852314i	$0.675198\pi$
$422$	1.28950	−	16.2901i	0.0627720	−	0.792988i
$423$		0			0
$424$	25.8427	−	7.61667i	1.25503	−	0.369898i
$425$	−20.6122	−	7.50223i	−0.999838	−	0.363911i
$426$		0			0
$427$	−10.4409	+	12.4430i	−0.505272	+	0.602160i
$428$	−23.3504	−	8.06391i	−1.12868	−	0.389784i
$429$		0			0
$430$	−32.2927	+	23.0120i	−1.55729	+	1.10974i
$431$	−26.6357			−1.28300			−0.641499	−	0.767124i	$-0.721687\pi$
$431$	−26.6357			−1.28300			−0.641499	+	0.767124i	$0.721687\pi$
$432$		0			0
$433$	27.8356			1.33769			0.668846	−	0.743401i	$-0.266788\pi$
$433$	27.8356			1.33769			0.668846	+	0.743401i	$0.266788\pi$
$434$	1.96126	−	1.39761i	0.0941435	−	0.0670874i
$435$		0			0
$436$	−4.13003	−	1.42628i	−0.197792	−	0.0683064i
$437$	−6.32923	+	7.54288i	−0.302768	+	0.360825i
$438$		0			0
$439$	15.2198	+	5.53956i	0.726402	+	0.264389i	0.678641	−	0.734470i	$-0.262569\pi$
$439$	15.2198	+	5.53956i	0.726402	+	0.264389i	0.0477612	+	0.998859i	$0.484791\pi$
$440$	13.4565	+	45.6569i	0.641515	+	2.17661i
$441$		0			0
$442$	−1.42840	+	18.0447i	−0.0679420	+	0.858300i
$443$	−11.8910	−	14.1711i	−0.564957	−	0.673290i	0.405631	−	0.914037i	$-0.367052\pi$
$443$	−11.8910	−	14.1711i	−0.564957	−	0.673290i	−0.970588	+	0.240747i	$0.922607\pi$
$444$		0			0
$445$	−51.8650	−	9.14520i	−2.45864	−	0.433524i
$446$	−4.14693	+	1.14802i	−0.196363	+	0.0543601i
$447$		0			0
$448$	14.8123	−	3.37720i	0.699817	−	0.159558i
$449$	−3.76662	+	6.52398i	−0.177758	+	0.307886i	−0.941112	−	0.338094i	$-0.890218\pi$
$449$	−3.76662	+	6.52398i	−0.177758	+	0.307886i	0.763354	+	0.645980i	$0.223551\pi$
$450$		0			0
$451$	−8.53403	+	4.92713i	−0.401852	+	0.232009i
$452$	−27.1405	+	16.2741i	−1.27658	+	0.765471i
$453$		0			0
$454$	1.36659	+	0.354087i	0.0641373	+	0.0166181i
$455$	22.0052	−	8.00925i	1.03162	−	0.375479i
$456$		0			0
$457$	−2.46966	−	14.0062i	−0.115526	−	0.655180i	−0.986488	−	0.163831i	$-0.947615\pi$
$457$	−2.46966	−	14.0062i	−0.115526	−	0.655180i	0.870962	−	0.491350i	$-0.163496\pi$
$458$	−1.09679	+	0.522533i	−0.0512499	+	0.0244164i
$459$		0			0
$460$	16.2954	+	13.2203i	0.759776	+	0.616399i
$461$	12.3225	−	2.17278i	0.573914	−	0.101197i	0.120844	−	0.992672i	$-0.461440\pi$
$461$	12.3225	−	2.17278i	0.573914	−	0.101197i	0.453070	+	0.891475i	$0.350329\pi$
$462$		0			0
$463$	−5.11858	+	1.86301i	−0.237881	+	0.0865815i	−0.458210	−	0.888844i	$-0.651509\pi$
$463$	−5.11858	+	1.86301i	−0.237881	+	0.0865815i	0.220329	+	0.975426i	$0.429287\pi$
$464$	−23.7042	−	12.6591i	−1.10044	−	0.587682i
$465$		0			0
$466$	1.39596	+	14.5670i	0.0646666	+	0.674801i
$467$	6.32947	−	3.65432i	0.292893	−	0.169102i	−0.346353	−	0.938104i	$-0.612580\pi$
$467$	6.32947	−	3.65432i	0.292893	−	0.169102i	0.639246	+	0.769003i	$0.279247\pi$
$468$		0			0
$469$	−22.9645	−	13.2585i	−1.06040	−	0.612222i
$470$	−5.53591	+	12.1328i	−0.255353	+	0.559646i
$471$		0			0
$472$	24.7497	+	10.8016i	1.13920	+	0.497184i
$473$	−7.25787	+	41.1614i	−0.333717	+	1.89260i
$474$		0			0
$475$	12.7482	+	15.1927i	0.584926	+	0.697088i
$476$	4.73580	+	12.3708i	0.217065	+	0.567013i
$477$		0			0
$478$	−9.81725	+	14.2703i	−0.449031	+	0.652708i
$479$	−6.51285	−	2.37048i	−0.297580	−	0.108310i	0.188916	−	0.981993i	$-0.439503\pi$
$479$	−6.51285	−	2.37048i	−0.297580	−	0.108310i	−0.486495	+	0.873683i	$0.661725\pi$
$480$		0			0
$481$	20.1753	+	16.9291i	0.919914	+	0.771900i
$482$	15.1123	+	14.8643i	0.688346	+	0.677051i
$483$		0			0
$484$	24.6269	+	13.6802i	1.11940	+	0.621826i
$485$			7.39586i			0.335829i
$486$		0			0
$487$	29.6823			1.34503			0.672517	−	0.740081i	$-0.265213\pi$
$487$	29.6823			1.34503			0.672517	+	0.740081i	$0.265213\pi$
$488$	24.1452	+	1.50982i	1.09300	+	0.0683462i
$489$		0			0
$490$	−11.3077	+	11.4963i	−0.510828	+	0.519350i
$491$	−5.65695	+	6.74169i	−0.255295	+	0.304248i	−0.878435	−	0.477862i	$-0.841412\pi$
$491$	−5.65695	+	6.74169i	−0.255295	+	0.304248i	0.623140	+	0.782110i	$0.285856\pi$
$492$		0			0
$493$	8.01361	−	22.0172i	0.360915	−	0.991606i
$494$	9.27606	−	13.4836i	0.417350	−	0.606657i
$495$		0			0
$496$	−3.40930	−	1.11460i	−0.153082	−	0.0500471i
$497$	4.36747	−	3.66474i	0.195908	−	0.164386i
$498$		0			0
$499$	14.6580	+	2.58460i	0.656181	+	0.115702i	0.491819	−	0.870698i	$-0.336332\pi$
$499$	14.6580	+	2.58460i	0.656181	+	0.115702i	0.164362	+	0.986400i	$0.447443\pi$
$500$	6.54478	−	5.67886i	0.292691	−	0.253966i
$501$		0			0
$502$	−9.37872	+	20.5550i	−0.418593	+	0.917413i
$503$	5.25851	−	9.10801i	0.234465	−	0.406106i	−0.724652	−	0.689115i	$-0.757999\pi$
$503$	5.25851	−	9.10801i	0.234465	−	0.406106i	0.959117	+	0.283009i	$0.0913327\pi$
$504$		0			0
$505$	−30.1020	−	52.1381i	−1.33952	−	2.32012i
$506$	22.0170	−	2.10990i	0.978776	−	0.0937967i
$507$		0			0
$508$	−20.3186	+	3.93038i	−0.901492	+	0.174382i
$509$	−8.68462	−	23.8608i	−0.384939	−	1.05761i	−0.969249	−	0.246081i	$-0.920857\pi$
$509$	−8.68462	−	23.8608i	−0.384939	−	1.05761i	0.584310	−	0.811531i	$-0.301365\pi$
$510$		0			0
$511$	−0.311738	−	1.76795i	−0.0137905	−	0.0782096i
$512$	−17.1458	−	14.7656i	−0.757744	−	0.652552i
$513$		0			0
$514$	4.76877	+	10.0096i	0.210341	+	0.441506i
$515$	46.2072	−	8.14757i	2.03613	−	0.359025i
$516$		0			0
$517$	4.80776	+	13.2092i	0.211445	+	0.580941i
$518$	18.6571	+	4.83409i	0.819744	+	0.212398i
$519$		0			0
$520$	−29.0577	−	19.2899i	−1.27427	−	0.845918i
$521$	5.54892	+	9.61101i	0.243103	+	0.421066i	0.961596	−	0.274467i	$-0.0885015\pi$
$521$	5.54892	+	9.61101i	0.243103	+	0.421066i	−0.718494	+	0.695533i	$0.755168\pi$
$522$		0			0
$523$	21.2339	+	12.2594i	0.928493	+	0.536066i	0.886335	−	0.463045i	$-0.153243\pi$
$523$	21.2339	+	12.2594i	0.928493	+	0.536066i	0.0421586	+	0.999111i	$0.486577\pi$
$524$	17.9739	−	0.297401i	0.785194	−	0.0129920i
$525$		0			0
$526$	−28.0957	+	7.77789i	−1.22503	+	0.339132i
$527$	0.543064	−	3.07987i	0.0236563	−	0.134161i
$528$		0			0
$529$	−10.1496	+	8.51656i	−0.441289	+	0.370285i
$530$	−45.1208	−	3.57171i	−1.95992	−	0.155145i
$531$		0			0
$532$	1.88431	−	11.8275i	0.0816951	−	0.512787i
$533$	2.46961	−	6.78519i	0.106971	−	0.293899i
$534$		0			0
$535$	31.7922	+	26.6768i	1.37450	+	1.15334i
$536$	4.41738	+	39.2463i	0.190802	+	1.69518i
$537$		0			0
$538$	−13.1088	−	18.3955i	−0.565158	−	0.793085i
$539$			16.9970i			0.732112i
$540$		0			0
$541$		−	10.1117i		−	0.434737i	−0.976090	−	0.217369i	$-0.930253\pi$
$541$		−	10.1117i		−	0.434737i	0.976090	−	0.217369i	$-0.0697474\pi$
$542$	−8.28587	+	5.90458i	−0.355909	+	0.253623i
$543$		0			0
$544$	10.6380	−	16.6150i	0.456102	−	0.712361i
$545$	5.62314	+	4.71838i	0.240869	+	0.202113i
$546$		0			0
$547$	−9.82775	+	27.0015i	−0.420204	+	1.15450i	0.531386	+	0.847130i	$0.321672\pi$
$547$	−9.82775	+	27.0015i	−0.420204	+	1.15450i	−0.951590	+	0.307371i	$0.900551\pi$
$548$	−33.2901	−	5.30364i	−1.42208	−	0.226560i
$549$		0			0
$550$	3.51548	−	44.4104i	0.149900	−	1.89367i
$551$	−16.2283	+	13.6172i	−0.691348	+	0.580110i
$552$		0			0
$553$	−1.52534	+	8.65063i	−0.0648640	+	0.367862i
$554$	−7.12384	−	25.7331i	−0.302663	−	1.09330i
$555$		0			0
$556$	−22.0327	+	0.364558i	−0.934395	+	0.0154607i
$557$	10.4290	+	6.02119i	0.441891	+	0.255126i	0.704400	−	0.709804i	$-0.251216\pi$
$557$	10.4290	+	6.02119i	0.441891	+	0.255126i	−0.262508	+	0.964930i	$0.584550\pi$
$558$		0			0
$559$	−15.3130	−	26.5230i	−0.647673	−	1.12180i
$560$	−25.2683	−	3.59806i	−1.06778	−	0.152046i
$561$		0			0
$562$	−6.53511	+	25.2221i	−0.275667	+	1.06393i
$563$	−1.52700	−	4.19539i	−0.0643553	−	0.176815i	0.903347	−	0.428910i	$-0.141102\pi$
$563$	−1.52700	−	4.19539i	−0.0643553	−	0.176815i	−0.967702	+	0.252096i	$0.918880\pi$
$564$		0			0
$565$	52.3569	−	9.23194i	2.20267	−	0.388390i
$566$	11.1793	−	5.32604i	0.469903	−	0.223870i
$567$		0			0
$568$	−8.25414	−	1.99354i	−0.346336	−	0.0836473i
$569$	−5.31792	−	30.1594i	−0.222939	−	1.26435i	−0.866586	−	0.499027i	$-0.833691\pi$
$569$	−5.31792	−	30.1594i	−0.222939	−	1.26435i	0.643648	−	0.765322i	$-0.277420\pi$
$570$		0			0
$571$	−4.43557	−	12.1866i	−0.185623	−	0.509994i	0.811621	−	0.584184i	$-0.198585\pi$
$571$	−4.43557	−	12.1866i	−0.185623	−	0.509994i	−0.997244	+	0.0741895i	$0.976363\pi$
$572$	−36.0938	+	6.98189i	−1.50916	+	0.291928i
$573$		0			0
$574$	−0.504060	−	5.25991i	−0.0210391	−	0.219544i
$575$	−9.81971	−	17.0082i	−0.409510	−	0.709292i
$576$		0			0
$577$	−9.34815	+	16.1915i	−0.389169	+	0.674060i	−0.992338	−	0.123553i	$-0.960571\pi$
$577$	−9.34815	+	16.1915i	−0.389169	+	0.674060i	0.603169	+	0.797613i	$0.293904\pi$
$578$	−6.22298	−	2.83939i	−0.258842	−	0.118103i
$579$		0			0
$580$	29.5874	+	34.0989i	1.22855	+	1.41588i
$581$	4.04125	+	0.712582i	0.167659	+	0.0295629i
$582$		0			0
$583$	−36.5468	+	30.6664i	−1.51361	+	1.27007i
$584$	−1.84315	+	1.93698i	−0.0762702	+	0.0801530i
$585$		0			0
$586$	15.9335	+	10.9615i	0.658207	+	0.452814i
$587$	−9.91990	+	27.2547i	−0.409438	+	1.12492i	0.548049	+	0.836446i	$0.315371\pi$
$587$	−9.91990	+	27.2547i	−0.409438	+	1.12492i	−0.957487	+	0.288475i	$0.906852\pi$
$588$		0			0
$589$	−1.81757	+	2.16609i	−0.0748916	+	0.0892523i
$590$	−32.3433	−	31.8126i	−1.33155	−	1.30970i
$591$		0			0
$592$	−10.7048	−	26.6345i	−0.439963	−	1.09467i
$593$	−12.4895			−0.512883			−0.256441	−	0.966560i	$-0.582550\pi$
$593$	−12.4895			−0.512883			−0.256441	+	0.966560i	$0.582550\pi$
$594$		0			0
$595$		−	22.2536i		−	0.912308i
$596$	−10.5020	+	18.9056i	−0.430179	+	0.774404i
$597$		0			0
$598$	−11.3647	+	11.5543i	−0.464738	+	0.472491i
$599$	−7.49705	−	6.29078i	−0.306321	−	0.257034i	0.476648	−	0.879094i	$-0.341852\pi$
$599$	−7.49705	−	6.29078i	−0.306321	−	0.257034i	−0.782970	+	0.622060i	$0.786296\pi$
$600$		0			0
$601$	27.8247	+	10.1274i	1.13499	+	0.413103i	0.840102	−	0.542428i	$-0.182495\pi$
$601$	27.8247	+	10.1274i	1.13499	+	0.413103i	0.294890	+	0.955531i	$0.404717\pi$
$602$	−18.4645	−	12.7026i	−0.752555	−	0.517720i
$603$		0			0
$604$	0.457174	+	1.19422i	0.0186022	+	0.0485922i
$605$	−30.4217	−	36.2551i	−1.23682	−	1.47398i
$606$		0			0
$607$	1.41051	−	7.99939i	0.0572507	−	0.324685i	−0.942709	−	0.333615i	$-0.891731\pi$
$607$	1.41051	−	7.99939i	0.0572507	−	0.324685i	0.999960	+	0.00892998i	$0.00284254\pi$
$608$	−15.8410	+	8.20064i	−0.642439	+	0.332580i
$609$		0			0
$610$	−36.9758	−	16.8712i	−1.49711	−	0.683093i
$611$	−8.92020	−	5.15008i	−0.360873	−	0.208350i
$612$		0			0
$613$	−10.1533	+	5.86202i	−0.410088	+	0.236765i	−0.690828	−	0.723019i	$-0.742754\pi$
$613$	−10.1533	+	5.86202i	−0.410088	+	0.236765i	0.280739	+	0.959784i	$0.409420\pi$
$614$	−34.7106	+	3.32634i	−1.40081	+	0.134240i
$615$		0			0
$616$	−21.6477	+	15.9729i	−0.872212	+	0.643565i
$617$	1.24227	−	0.452149i	0.0500118	−	0.0182028i	−0.316893	−	0.948461i	$-0.602640\pi$
$617$	1.24227	−	0.452149i	0.0500118	−	0.0182028i	0.366905	+	0.930258i	$0.380417\pi$
$618$		0			0
$619$	25.4782	−	4.49249i	1.02405	−	0.180568i	0.363695	−	0.931518i	$-0.381515\pi$
$619$	25.4782	−	4.49249i	1.02405	−	0.180568i	0.660359	+	0.750950i	$0.270404\pi$
$620$	4.67956	+	3.79648i	0.187936	+	0.152470i
$621$		0			0
$622$	−0.775795	−	1.62839i	−0.0311065	−	0.0652925i
$623$	−5.16886	−	29.3141i	−0.207086	−	1.17444i
$624$		0			0
$625$	15.8714	−	5.77673i	0.634858	−	0.231069i
$626$	−7.10484	+	27.4210i	−0.283967	+	1.09596i
$627$		0			0
$628$	9.48887	+	15.8247i	0.378647	+	0.631474i
$629$	21.6749	−	12.5140i	0.864233	−	0.498965i
$630$		0			0
$631$	−6.70635	+	11.6157i	−0.266976	+	0.462415i	−0.968079	−	0.250644i	$-0.919358\pi$
$631$	−6.70635	+	11.6157i	−0.266976	+	0.462415i	0.701104	+	0.713059i	$0.252691\pi$
$632$	11.7163	−	5.82159i	0.466048	−	0.231571i
$633$		0			0
$634$	2.26555	+	8.18375i	0.0899765	+	0.325018i
$635$	34.2396	+	6.03736i	1.35876	+	0.239585i
$636$		0			0
$637$	−8.00557	−	9.54067i	−0.317192	−	0.378015i
$638$	47.4376	+	3.75511i	1.87807	+	0.148666i
$639$		0			0
$640$	18.0323	+	33.4647i	0.712789	+	1.32281i
$641$	30.4904	+	11.0976i	1.20430	+	0.438328i	0.864722	−	0.502251i	$-0.167495\pi$
$641$	30.4904	+	11.0976i	1.20430	+	0.438328i	0.339575	+	0.940579i	$0.389717\pi$
$642$		0			0
$643$	17.3052	−	20.6235i	0.682449	−	0.813312i	−0.307971	−	0.951396i	$-0.599650\pi$
$643$	17.3052	−	20.6235i	0.682449	−	0.813312i	0.990420	+	0.138084i	$0.0440944\pi$
$644$	−3.87141	+	11.2103i	−0.152555	+	0.441748i
$645$		0			0
$646$	−9.02579	−	12.6659i	−0.355115	−	0.498332i
$647$	−25.1491			−0.988713			−0.494356	−	0.869259i	$-0.664596\pi$
$647$	−25.1491			−0.988713			−0.494356	+	0.869259i	$0.664596\pi$
$648$		0			0
$649$	−47.8188			−1.87705
$650$	18.9440	+	26.5840i	0.743044	+	1.04271i
$651$		0			0
$652$	−15.8047	−	5.45807i	−0.618960	−	0.213754i
$653$	13.3995	−	15.9689i	0.524363	−	0.624912i	−0.437243	−	0.899343i	$-0.644045\pi$
$653$	13.3995	−	15.9689i	0.524363	−	0.624912i	0.961607	+	0.274431i	$0.0884896\pi$
$654$		0			0
$655$	−28.3788	−	10.3291i	−1.10885	−	0.403589i
$656$	−5.85805	+	5.25537i	−0.228718	+	0.205188i
$657$		0			0
$658$	−7.51406	−	0.594804i	−0.292929	−	0.0231879i
$659$	−18.1622	−	21.6448i	−0.707497	−	0.843162i	0.285856	−	0.958273i	$-0.407722\pi$
$659$	−18.1622	−	21.6448i	−0.707497	−	0.843162i	−0.993353	+	0.115110i	$0.963278\pi$
$660$		0			0
$661$	−37.0880	−	6.53962i	−1.44256	−	0.254362i	−0.603046	−	0.797706i	$-0.706047\pi$
$661$	−37.0880	−	6.53962i	−1.44256	−	0.254362i	−0.839510	+	0.543344i	$0.817158\pi$
$662$	7.38044	+	26.6600i	0.286849	+	1.03617i
$663$		0			0
$664$	−2.71963	−	5.47340i	−0.105542	−	0.212409i
$665$	−10.0603	+	17.4250i	−0.390123	+	0.675712i
$666$		0			0
$667$	18.1676	−	10.4891i	0.703452	−	0.406138i
$668$	10.6934	−	6.41203i	0.413740	−	0.248089i
$669$		0			0
$670$	16.6418	−	64.2288i	0.642930	−	2.48138i
$671$	−40.2562	+	14.6521i	−1.55407	+	0.565636i
$672$		0			0
$673$	0.887037	+	5.03064i	0.0341928	+	0.193917i	0.997120	−	0.0758462i	$-0.0241658\pi$
$673$	0.887037	+	5.03064i	0.0341928	+	0.193917i	−0.962927	+	0.269763i	$0.913055\pi$
$674$	13.4076	+	28.1426i	0.516443	+	1.08401i
$675$		0			0
$676$	0.590828	−	0.728258i	0.0227242	−	0.0280099i
$677$	29.3482	−	5.17487i	1.12794	−	0.198887i	0.421617	−	0.906774i	$-0.361463\pi$
$677$	29.3482	−	5.17487i	1.12794	−	0.198887i	0.706325	+	0.707888i	$0.250352\pi$
$678$		0			0
$679$	−3.92804	+	1.42969i	−0.150744	+	0.0548665i
$680$	−26.6700	+	19.6786i	−1.02275	+	0.754639i
$681$		0			0
$682$	6.32265	−	0.605903i	0.242107	−	0.0232012i
$683$	−41.0964	+	23.7270i	−1.57251	+	0.907889i	−0.576650	+	0.816991i	$0.695640\pi$
$683$	−41.0964	+	23.7270i	−1.57251	+	0.907889i	−0.995860	+	0.0908981i	$0.971026\pi$
$684$		0			0
$685$	49.0450	+	28.3161i	1.87391	+	1.08190i
$686$	−25.3952	−	11.5872i	−0.969592	−	0.442401i
$687$		0			0
$688$	1.10432	+	33.3617i	0.0421019	+	1.27190i
$689$	6.07041	−	34.4270i	0.231264	−	1.31156i
$690$		0			0
$691$	19.5742	+	23.3276i	0.744637	+	0.887424i	0.996773	−	0.0802677i	$-0.0255775\pi$
$691$	19.5742	+	23.3276i	0.744637	+	0.887424i	−0.252136	+	0.967692i	$0.581133\pi$
$692$	16.6438	−	6.37163i	0.632704	−	0.242213i
$693$		0			0
$694$	0.0378046	+	0.0260077i	0.00143504	+	0.000987239i
$695$	34.7872	+	12.6615i	1.31955	+	0.480278i
$696$		0			0
$697$	−5.25642	−	4.41066i	−0.199101	−	0.167066i
$698$	32.2734	−	32.8118i	1.22157	−	1.24195i
$699$		0			0
$700$	20.8824	+	11.6001i	0.789282	+	0.438444i
$701$		−	22.9653i		−	0.867386i	−0.901061	−	0.433693i	$-0.857210\pi$
$701$		−	22.9653i		−	0.867386i	0.901061	−	0.433693i	$-0.142790\pi$
$702$		0			0
$703$	−22.6291			−0.853473
$704$	38.2856	+	11.8193i	1.44294	+	0.445457i
$705$		0			0
$706$	−1.07690	−	1.05923i	−0.0405298	−	0.0398647i
$707$	21.8723	−	26.0664i	0.822591	−	0.980326i
$708$		0			0
$709$	−12.4178	+	34.1176i	−0.466361	+	1.28132i	0.454264	+	0.890867i	$0.349902\pi$
$709$	−12.4178	+	34.1176i	−0.466361	+	1.28132i	−0.920625	+	0.390448i	$0.872320\pi$
$710$	11.7530	+	8.08545i	0.441081	+	0.303442i
$711$		0			0
$712$	−30.5609	+	32.1167i	−1.14532	+	1.20363i
$713$	2.14499	−	1.79986i	0.0803305	−	0.0674053i
$714$		0			0
$715$	60.8229	+	10.7247i	2.27465	+	0.401082i
$716$	−21.8100	+	18.9244i	−0.815077	+	0.707237i
$717$		0			0
$718$	14.6221	+	6.67172i	0.545694	+	0.248986i
$719$	−13.7419	+	23.8016i	−0.512485	+	0.887651i	0.487410	+	0.873173i	$0.337942\pi$
$719$	−13.7419	+	23.8016i	−0.512485	+	0.887651i	−0.999895	+	0.0144775i	$0.995392\pi$
$720$		0			0
$721$	13.2596	+	22.9662i	0.493812	+	0.855308i
$722$	−1.22180	−	12.7495i	−0.0454706	−	0.474489i
$723$		0			0
$724$	−1.84125	−	9.51855i	−0.0684294	−	0.353754i
$725$	−14.4516	−	39.7054i	−0.536719	−	1.47462i
$726$		0			0
$727$	−0.612001	−	3.47083i	−0.0226979	−	0.128726i	0.971353	−	0.237640i	$-0.0763738\pi$
$727$	−0.612001	−	3.47083i	−0.0226979	−	0.128726i	−0.994051	+	0.108914i	$0.965263\pi$
$728$	4.62799	−	19.1619i	0.171525	−	0.710186i
$729$		0			0
$730$	4.05523	−	1.93198i	0.150091	−	0.0715059i
$731$	−28.6617	+	5.05384i	−1.06009	+	0.186923i
$732$		0			0
$733$	4.83027	+	13.2711i	0.178410	+	0.490178i	0.996373	−	0.0850933i	$-0.0271188\pi$
$733$	4.83027	+	13.2711i	0.178410	+	0.490178i	−0.817963	+	0.575271i	$0.804897\pi$
$734$	−3.05356	+	11.7851i	−0.112709	+	0.434998i
$735$		0			0
$736$	16.8585	−	5.27341i	0.621414	−	0.194380i
$737$	−34.9680	−	60.5664i	−1.28806	−	2.23099i
$738$		0			0
$739$	−2.52352	−	1.45695i	−0.0928291	−	0.0535949i	0.452867	−	0.891578i	$-0.350401\pi$
$739$	−2.52352	−	1.45695i	−0.0928291	−	0.0535949i	−0.545696	+	0.837983i	$0.683735\pi$
$740$	0.797822	+	48.2178i	0.0293285	+	1.77252i
$741$		0			0
$742$	−6.82529	−	24.6547i	−0.250564	−	0.905102i
$743$	−0.918280	+	5.20783i	−0.0336884	+	0.191057i	−0.997008	−	0.0773010i	$-0.975370\pi$
$743$	−0.918280	+	5.20783i	−0.0336884	+	0.191057i	0.963319	+	0.268358i	$0.0864809\pi$
$744$		0			0
$745$	27.8324	−	23.3542i	1.01970	−	0.855631i
$746$	−4.26943	+	53.9350i	−0.156315	+	1.97470i
$747$		0			0
$748$	−5.49649	+	34.5006i	−0.200971	+	1.26147i
$749$	−8.02267	+	22.0421i	−0.293142	+	0.805401i
$750$		0			0
$751$	−27.0071	−	22.6616i	−0.985502	−	0.826935i	−0.000591865	−	1.00000i	$-0.500188\pi$
$751$	−27.0071	−	22.6616i	−0.985502	−	0.826935i	−0.984910	+	0.173065i	$0.944633\pi$
$752$	5.93174	+	9.53127i	0.216308	+	0.347570i
$753$		0			0
$754$	−28.3961	+	20.2353i	−1.03413	+	0.736926i
$755$		−	2.14827i		−	0.0781834i
$756$		0			0
$757$			38.9874i			1.41702i	0.705700	+	0.708511i	$0.250633\pi$
$757$			38.9874i			1.41702i	−0.705700	+	0.708511i	$0.749367\pi$
$758$	−18.1486	−	25.4679i	−0.659187	−	0.925035i
$759$		0			0
$760$	29.7794	−	3.35182i	1.08021	−	0.121583i
$761$	−31.7399	−	26.6329i	−1.15057	−	0.965443i	−0.150837	−	0.988559i	$-0.548197\pi$
$761$	−31.7399	−	26.6329i	−1.15057	−	0.965443i	−0.999733	+	0.0231155i	$0.992641\pi$
$762$		0			0
$763$	−1.41899	+	3.89863i	−0.0513708	+	0.141140i
$764$	51.9039	+	8.26913i	1.87782	+	0.299166i
$765$		0			0
$766$	−2.30765	−	0.182671i	−0.0833789	−	0.00660017i
$767$	26.8414	−	22.5226i	0.969186	−	0.813244i
$768$		0			0
$769$	8.75977	−	49.6791i	0.315886	−	1.79148i	−0.251325	−	0.967903i	$-0.580866\pi$
$769$	8.75977	−	49.6791i	0.315886	−	1.79148i	0.567210	−	0.823573i	$-0.308023\pi$
$770$	43.5580	−	12.0584i	1.56972	−	0.434554i
$771$		0			0
$772$	−0.134843	−	8.14948i	−0.00485311	−	0.293306i
$773$	−26.2565	−	15.1592i	−0.944379	−	0.545238i	−0.0530488	−	0.998592i	$-0.516894\pi$
$773$	−26.2565	−	15.1592i	−0.944379	−	0.545238i	−0.891330	+	0.453354i	$0.850227\pi$
$774$		0			0
$775$	−2.81993	−	4.88427i	−0.101295	−	0.175448i
$776$	5.18695	+	3.44334i	0.186201	+	0.123609i
$777$		0			0
$778$	15.7000	+	4.06790i	0.562871	+	0.145841i
$779$	2.12192	+	5.82994i	0.0760258	+	0.208879i
$780$		0			0
$781$	14.8082	−	2.61109i	0.529879	−	0.0934320i
$782$	6.62409	+	13.9040i	0.236877	+	0.497204i
$783$		0			0
$784$	2.79813	+	13.2828i	0.0999333	+	0.474386i
$785$	−5.38281	−	30.5275i	−0.192121	−	1.08957i
$786$		0			0
$787$	−9.23473	−	25.3722i	−0.329182	−	0.904421i	−0.988319	−	0.152398i	$-0.951300\pi$
$787$	−9.23473	−	25.3722i	−0.329182	−	0.904421i	0.659137	−	0.752023i	$-0.270922\pi$
$788$	3.90794	+	20.2026i	0.139215	+	0.719687i
$789$		0			0
$790$	−21.8789	+	2.09666i	−0.778415	+	0.0745960i
$791$	15.0243	+	26.0228i	0.534202	+	0.925265i
$792$		0			0
$793$	15.6953	−	27.1851i	0.557356	−	0.965370i
$794$	1.75017	−	3.83578i	0.0621113	−	0.136127i
$795$		0			0
$796$	−1.81026	−	2.08629i	−0.0641629	−	0.0739466i
$797$	52.0759	+	9.18239i	1.84462	+	0.325257i	0.983186	−	0.182608i	$-0.0584538\pi$
$797$	52.0759	+	9.18239i	1.84462	+	0.325257i	0.861437	+	0.507864i	$0.169565\pi$
$798$		0			0
$799$	−7.49821	+	6.29175i	−0.265268	+	0.222586i
$800$	−4.56380	−	35.2846i	−0.161355	−	1.24750i
$801$		0			0
$802$	−7.55644	+	10.9840i	−0.266827	+	0.387858i
$803$	1.61937	−	4.44918i	0.0571463	−	0.157008i
$804$		0			0
$805$	12.8073	−	15.2631i	0.451398	−	0.537955i
$806$	−3.26362	+	3.31806i	−0.114956	+	0.116874i
$807$		0			0
$808$	−50.5808	−	3.16286i	−1.77943	−	0.111269i
$809$	18.3017			0.643453			0.321727	−	0.946833i	$-0.395737\pi$
$809$	18.3017			0.643453			0.321727	+	0.946833i	$0.395737\pi$
$810$		0			0
$811$			34.2759i			1.20359i	0.798650	+	0.601795i	$0.205548\pi$
$811$			34.2759i			1.20359i	−0.798650	+	0.601795i	$0.794452\pi$
$812$	−12.3909	+	22.3059i	−0.434834	+	0.782783i
$813$		0			0
$814$	36.2390	+	35.6444i	1.27018	+	1.24933i
$815$	21.5186	+	18.0562i	0.753762	+	0.632482i
$816$		0			0
$817$	24.7274	+	9.00005i	0.865103	+	0.314872i
$818$	20.5310	−	29.8438i	0.717851	−	1.04346i
$819$		0			0
$820$	12.3475	−	4.72690i	0.431194	−	0.165071i
$821$	16.1380	+	19.2325i	0.563221	+	0.671220i	0.970225	−	0.242206i	$-0.0778710\pi$
$821$	16.1380	+	19.2325i	0.563221	+	0.671220i	−0.407004	+	0.913426i	$0.633427\pi$
$822$		0			0
$823$	−5.65012	+	32.0434i	−0.196951	+	1.11696i	0.712662	+	0.701507i	$0.247489\pi$
$823$	−5.65012	+	32.0434i	−0.196951	+	1.11696i	−0.909613	+	0.415456i	$0.863622\pi$
$824$	15.7988	−	36.1998i	0.550378	−	1.26108i
$825$		0			0
$826$	10.6438	−	23.3276i	0.370346	−	0.811672i
$827$	39.6695	+	22.9032i	1.37944	+	0.796423i	0.992092	−	0.125509i	$-0.0400565\pi$
$827$	39.6695	+	22.9032i	1.37944	+	0.796423i	0.387352	+	0.921932i	$0.373390\pi$
$828$		0			0
$829$	17.0001	−	9.81500i	0.590437	−	0.340889i	−0.174833	−	0.984598i	$-0.555939\pi$
$829$	17.0001	−	9.81500i	0.590437	−	0.340889i	0.765270	+	0.643709i	$0.222605\pi$
$830$	0.979483	+	10.2210i	0.0339984	+	0.354776i
$831$		0			0
$832$	−27.0572	+	11.3982i	−0.938039	+	0.395160i
$833$	−11.1217	+	4.04796i	−0.385343	+	0.140253i
$834$		0			0
$835$	−20.6287	+	3.63739i	−0.713885	+	0.125877i
$836$	19.9008	−	24.5298i	0.688282	−	0.848380i
$837$		0			0
$838$	−3.12824	+	1.49035i	−0.108063	+	0.0514833i
$839$	8.40287	+	47.6550i	0.290099	+	1.64523i	0.686480	+	0.727149i	$0.259155\pi$
$839$	8.40287	+	47.6550i	0.290099	+	1.64523i	−0.396381	+	0.918086i	$0.629734\pi$
$840$		0			0
$841$	15.1609	−	5.51810i	0.522788	−	0.190279i
$842$	−17.7928	−	4.61014i	−0.613179	−	0.158876i
$843$		0			0
$844$	11.8844	+	19.8197i	0.409077	+	0.682221i
$845$	−1.36439	+	0.787733i	−0.0469366	+	0.0270989i
$846$		0			0
$847$	13.3748	−	23.1658i	0.459563	−	0.795987i
$848$	−23.5121	+	29.9817i	−0.807409	+	1.02958i
$849$		0			0
$850$	29.8964	−	8.27638i	1.02544	−	0.283877i
$851$	22.0682	+	3.89122i	0.756488	+	0.133389i
$852$		0			0
$853$	−30.1220	−	35.8980i	−1.03136	−	1.22912i	−0.972995	−	0.230828i	$-0.925857\pi$
$853$	−30.1220	−	35.8980i	−1.03136	−	1.22912i	−0.0583624	−	0.998295i	$-0.518588\pi$
$854$	1.81271	−	22.8997i	0.0620298	−	0.783612i
$855$		0			0
$856$	33.5109	−	9.87673i	1.14538	−	0.337580i
$857$	5.93538	+	2.16030i	0.202749	+	0.0737946i	0.441399	−	0.897311i	$-0.354483\pi$
$857$	5.93538	+	2.16030i	0.202749	+	0.0737946i	−0.238650	+	0.971106i	$0.576705\pi$
$858$		0			0
$859$	−19.3877	+	23.1054i	−0.661501	+	0.788346i	−0.987600	−	0.156990i	$-0.949821\pi$
$859$	−19.3877	+	23.1054i	−0.661501	+	0.788346i	0.326100	+	0.945335i	$0.394266\pi$
$860$	18.3054	−	53.0061i	0.624208	−	1.80749i
$861$		0			0
$862$	30.6765	−	21.8603i	1.04485	−	0.744566i
$863$	−48.6885			−1.65737			−0.828687	−	0.559712i	$-0.810912\pi$
$863$	−48.6885			−1.65737			−0.828687	+	0.559712i	$0.810912\pi$
$864$		0			0
$865$	−29.9404			−1.01800
$866$	−32.0584	+	22.8451i	−1.08939	+	0.776307i
$867$		0			0
$868$	−1.11176	+	3.21927i	−0.0377355	+	0.109269i
$869$	−14.8915	+	17.7470i	−0.505161	+	0.602027i
$870$		0			0
$871$	48.1548	+	17.5269i	1.63166	+	0.593877i
$872$	5.92715	−	1.74692i	0.200718	−	0.0591581i
$873$		0			0
$874$	1.09886	−	13.8817i	0.0371694	−	0.469554i
$875$	−5.28869	−	6.30281i	−0.178790	−	0.213074i
$876$		0			0
$877$	−34.7601	−	6.12915i	−1.17377	−	0.206967i	−0.447438	−	0.894315i	$-0.647664\pi$
$877$	−34.7601	−	6.12915i	−1.17377	−	0.206967i	−0.726328	+	0.687348i	$0.758775\pi$
$878$	−22.0752	+	6.11119i	−0.745001	+	0.206243i
$879$		0			0
$880$	−52.9693	−	41.5394i	−1.78559	−	1.40029i
$881$	−7.22906	+	12.5211i	−0.243553	+	0.421847i	−0.961724	−	0.274020i	$-0.911646\pi$
$881$	−7.22906	+	12.5211i	−0.243553	+	0.421847i	0.718171	+	0.695867i	$0.244980\pi$
$882$		0			0
$883$	−30.6193	+	17.6781i	−1.03042	+	0.594915i	−0.917106	−	0.398644i	$-0.869481\pi$
$883$	−30.6193	+	17.6781i	−1.03042	+	0.594915i	−0.113317	+	0.993559i	$0.536148\pi$
$884$	−13.1645	−	21.9545i	−0.442769	−	0.738410i
$885$		0			0
$886$	25.3253	+	6.56186i	0.850822	+	0.220450i
$887$	33.6657	−	12.2533i	1.13038	−	0.411426i	0.291952	−	0.956433i	$-0.405695\pi$
$887$	33.6657	−	12.2533i	1.13038	−	0.411426i	0.838432	+	0.545007i	$0.183473\pi$
$888$		0			0
$889$	3.41231	+	19.3522i	0.114445	+	0.649051i
$890$	67.2389	−	32.0338i	2.25385	−	1.07378i
$891$		0			0
$892$	3.83385	−	4.72562i	0.128367	−	0.158225i
$893$	8.71560	−	1.53680i	0.291656	−	0.0514269i
$894$		0			0
$895$	45.5853	−	16.5917i	1.52375	−	0.554599i
$896$	−14.2877	+	16.0462i	−0.477320	+	0.536067i
$897$		0			0
$898$	−1.01629	−	10.6050i	−0.0339139	−	0.353894i
$899$	5.21720	−	3.01215i	0.174003	−	0.100461i
$900$		0			0
$901$	−28.7699	−	16.6103i	−0.958463	−	0.553369i
$902$	5.78493	−	12.6786i	0.192617	−	0.422151i
$903$		0			0
$904$	17.9015	−	41.0177i	0.595395	−	1.36423i
$905$	−2.82829	+	16.0401i	−0.0940157	+	0.533189i
$906$		0			0
$907$	5.65021	+	6.73365i	0.187612	+	0.223587i	0.851649	−	0.524112i	$-0.175603\pi$
$907$	5.65021	+	6.73365i	0.187612	+	0.223587i	−0.664037	+	0.747700i	$0.731158\pi$
$908$	−1.86452	+	0.713778i	−0.0618762	+	0.0236876i
$909$		0			0
$910$	−18.7703	+	27.2843i	−0.622228	+	0.904467i
$911$	−13.4129	−	4.88190i	−0.444389	−	0.161744i	0.110127	−	0.993918i	$-0.464874\pi$
$911$	−13.4129	−	4.88190i	−0.444389	−	0.161744i	−0.554516	+	0.832173i	$0.687097\pi$
$912$		0			0
$913$	8.29075	+	6.95676i	0.274384	+	0.230235i
$914$	14.3394	+	14.1041i	0.474305	+	0.466522i
$915$		0			0
$916$	0.834335	−	1.50196i	0.0275672	−	0.0496262i
$917$		−	17.0691i		−	0.563671i
$918$		0			0
$919$	−54.9336			−1.81209			−0.906046	−	0.423179i	$-0.860914\pi$
$919$	−54.9336			−1.81209			−0.906046	+	0.423179i	$0.860914\pi$
$920$	−29.6176	−	1.85201i	−0.976463	−	0.0610589i
$921$		0			0
$922$	−12.4086	+	12.6156i	−0.408656	+	0.415474i
$923$	−7.08225	+	8.44030i	−0.233115	+	0.277816i
$924$		0			0
$925$	15.4371	−	42.4130i	0.507567	−	1.39453i
$926$	4.36610	−	6.34654i	0.143479	−	0.208560i
$927$		0			0
$928$	37.6898	−	4.87488i	1.23723	−	0.160026i
$929$	−20.0336	+	16.8102i	−0.657282	+	0.551525i	−0.909271	−	0.416205i	$-0.863360\pi$
$929$	−20.0336	+	16.8102i	−0.657282	+	0.551525i	0.251989	+	0.967730i	$0.418915\pi$
$930$		0			0
$931$	10.5385	+	1.85822i	0.345385	+	0.0609006i
$932$	−13.5631	−	15.6312i	−0.444273	−	0.512016i
$933$		0			0
$934$	−4.29053	+	9.40339i	−0.140390	+	0.307688i
$935$	29.3458	−	50.8283i	0.959709	−	1.66226i
$936$		0			0
$937$	30.0604	+	52.0662i	0.982031	+	1.70093i	0.654451	+	0.756105i	$0.272900\pi$
$937$	30.0604	+	52.0662i	0.982031	+	1.70093i	0.327580	+	0.944823i	$0.393767\pi$
$938$	37.3298	−	3.57734i	1.21886	−	0.116804i
$939$		0			0
$940$	−3.58186	−	18.5169i	−0.116827	−	0.603954i
$941$	19.3533	+	53.1728i	0.630900	+	1.73338i	0.678585	+	0.734522i	$0.262594\pi$
$941$	19.3533	+	53.1728i	0.630900	+	1.73338i	−0.0476846	+	0.998862i	$0.515184\pi$
$942$		0			0
$943$	−1.06683	−	6.05031i	−0.0347408	−	0.197025i
$944$	−37.3694	+	7.87217i	−1.21627	+	0.256217i
$945$		0			0
$946$	−25.4229	−	53.3625i	−0.826568	−	1.73496i
$947$	−45.6408	+	8.04770i	−1.48313	+	0.261515i	−0.855826	−	0.517263i	$-0.826951\pi$
$947$	−45.6408	+	8.04770i	−1.48313	+	0.261515i	−0.627299	+	0.778778i	$0.715840\pi$
$948$		0			0
$949$	1.18659	+	3.26012i	0.0385182	+	0.105828i
$950$	−27.1510	−	7.03489i	−0.880895	−	0.228242i
$951$		0			0
$952$	−15.6071	−	10.3607i	−0.505829	−	0.335793i
$953$	2.93376	+	5.08142i	0.0950338	+	0.164603i	0.909623	−	0.415435i	$-0.136371\pi$
$953$	2.93376	+	5.08142i	0.0950338	+	0.164603i	−0.814589	+	0.580039i	$0.803037\pi$
$954$		0			0
$955$	−76.4681	−	44.1489i	−2.47445	−	1.42862i
$956$	−0.405256	−	24.4924i	−0.0131069	−	0.792139i
$957$		0			0
$958$	9.44638	−	2.61509i	0.305199	−	0.0844898i
$959$	−5.55822	+	31.5222i	−0.179484	+	1.01791i
$960$		0			0
$961$	−23.1314	+	19.4095i	−0.746174	+	0.626114i
$962$	−37.1300	−	2.93916i	−1.19712	−	0.0947625i
$963$		0			0
$964$	−29.6043	−	4.71643i	−0.953490	−	0.151906i
$965$	−4.68325	+	12.8671i	−0.150759	+	0.414207i
$966$		0			0
$967$	−17.2553	−	14.4789i	−0.554893	−	0.465610i	0.321701	−	0.946841i	$-0.395745\pi$
$967$	−17.2553	−	14.4789i	−0.554893	−	0.465610i	−0.876594	+	0.481231i	$0.840190\pi$
$968$	−39.5904	+	4.45611i	−1.27249	+	0.143225i
$969$		0			0
$970$	−6.06990	−	8.51786i	−0.194893	−	0.273492i
$971$		−	21.9521i		−	0.704475i	−0.935911	−	0.352238i	$-0.885421\pi$
$971$		−	21.9521i		−	0.704475i	0.935911	−	0.352238i	$-0.114579\pi$
$972$		0			0
$973$			20.9235i			0.670778i
$974$	−34.1853	+	24.3607i	−1.09537	+	0.780568i
$975$		0			0
$976$	−29.0473	+	18.0775i	−0.929783	+	0.578646i
$977$	36.9729	+	31.0239i	1.18287	+	0.992543i	0.999956	+	0.00941403i	$0.00299662\pi$
$977$	36.9729	+	31.0239i	1.18287	+	0.992543i	0.182911	+	0.983129i	$0.441448\pi$
$978$		0			0
$979$	26.8504	−	73.7710i	0.858144	−	2.35773i
$980$	3.58791	−	22.5207i	0.114612	−	0.719398i
$981$		0			0
$982$	0.982139	−	12.4072i	0.0313413	−	0.395929i
$983$	35.0417	−	29.4034i	1.11766	−	0.937824i	0.119172	−	0.992874i	$-0.461976\pi$
$983$	35.0417	−	29.4034i	1.11766	−	0.937824i	0.998484	+	0.0550493i	$0.0175316\pi$
$984$		0			0
$985$	6.00289	−	34.0441i	0.191268	−	1.08474i
$986$	8.84053	+	31.9343i	0.281540	+	1.01699i
$987$		0			0
$988$	0.382916	+	23.1422i	0.0121822	+	0.736251i
$989$	−22.5669	−	13.0290i	−0.717585	−	0.414298i
$990$		0			0
$991$	6.44420	+	11.1617i	0.204707	+	0.354562i	0.950039	−	0.312130i	$-0.101043\pi$
$991$	6.44420	+	11.1617i	0.204707	+	0.354562i	−0.745333	+	0.666693i	$0.767709\pi$
$992$	4.84128	−	1.51437i	0.153711	−	0.0480812i
$993$		0			0
$994$	−2.02233	+	7.80515i	−0.0641445	+	0.247564i
$995$	1.58712	+	4.36058i	0.0503151	+	0.138240i
$996$		0			0
$997$	−4.83400	+	0.852365i	−0.153094	+	0.0269947i	−0.249670	−	0.968331i	$-0.580322\pi$
$997$	−4.83400	+	0.852365i	−0.153094	+	0.0269947i	0.0965756	+	0.995326i	$0.469211\pi$
$998$	−19.0029	+	9.05332i	−0.601526	+	0.286578i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.253.6		204
3.2	odd	2		216.2.t.a.13.29	yes	204
8.5	even	2	inner	648.2.t.a.253.32		204
12.11	even	2		864.2.bf.a.337.20		204
24.5	odd	2		216.2.t.a.13.3	✓	204
24.11	even	2		864.2.bf.a.337.15		204
27.2	odd	18		216.2.t.a.133.3	yes	204
27.25	even	9	inner	648.2.t.a.397.32		204
108.83	even	18		864.2.bf.a.241.15		204
216.29	odd	18		216.2.t.a.133.29	yes	204
216.83	even	18		864.2.bf.a.241.20		204
216.133	even	18	inner	648.2.t.a.397.6		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.3	✓	204	24.5	odd	2
216.2.t.a.13.29	yes	204	3.2	odd	2
216.2.t.a.133.3	yes	204	27.2	odd	18
216.2.t.a.133.29	yes	204	216.29	odd	18
648.2.t.a.253.6		204	1.1	even	1	trivial
648.2.t.a.253.32		204	8.5	even	2	inner
648.2.t.a.397.6		204	216.133	even	18	inner
648.2.t.a.397.32		204	27.25	even	9	inner
864.2.bf.a.241.15		204	108.83	even	18
864.2.bf.a.241.20		204	216.83	even	18
864.2.bf.a.337.15		204	24.11	even	2
864.2.bf.a.337.20		204	12.11	even	2

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.15171 + 0.820715i) q^{2} +(0.652854 - 1.89044i) q^{4} +(-2.15975 + 2.57389i) q^{5} +(-1.78453 - 0.649515i) q^{7} +(0.799620 + 2.71304i) q^{8} +(0.374968 - 4.73691i) q^{10} +(-3.21944 - 3.83678i) q^{11} +(3.61424 + 0.637289i) q^{13} +(2.58832 - 0.716539i) q^{14} +(-3.14756 - 2.46837i) q^{16} +(1.74380 - 3.02034i) q^{17} +(-2.73085 + 1.57666i) q^{19} +(3.45580 + 5.76327i) q^{20} +(6.85676 + 1.77660i) q^{22} +(2.93428 - 1.06799i) q^{23} +(-1.09215 - 6.19390i) q^{25} +(-4.68558 + 2.23229i) q^{26} +(-2.39291 + 2.94951i) q^{28} +(6.61611 - 1.16660i) q^{29} +(0.842639 - 0.306695i) q^{31} +(5.65090 + 0.259585i) q^{32} +(0.470500 + 4.90971i) q^{34} +(5.52592 - 3.19039i) q^{35} +(6.21485 + 3.58815i) q^{37} +(1.85115 - 4.05710i) q^{38} +(-8.71007 - 3.80137i) q^{40} +(0.341649 - 1.93759i) q^{41} +(-5.36405 - 6.39263i) q^{43} +(-9.35505 + 3.58132i) q^{44} +(-2.50291 + 3.63822i) q^{46} +(-2.63733 - 0.959909i) q^{47} +(-2.59964 - 2.18135i) q^{49} +(6.34127 + 6.23721i) q^{50} +(3.56433 - 6.41647i) q^{52} -9.52536i q^{53} +16.8287 q^{55} +(0.335219 - 5.36087i) q^{56} +(-6.66237 + 6.77352i) q^{58} +(6.13695 - 7.31373i) q^{59} +(2.92540 - 8.03747i) q^{61} +(-0.718763 + 1.04479i) q^{62} +(-6.72122 + 4.33881i) q^{64} +(-9.44618 + 7.92629i) q^{65} +(13.7512 + 2.42470i) q^{67} +(-4.57135 - 5.26839i) q^{68} +(-3.74584 + 8.20960i) q^{70} +(-1.50109 + 2.59997i) q^{71} +(0.472663 + 0.818676i) q^{73} +(-10.1025 + 0.968131i) q^{74} +(1.19774 + 6.19185i) q^{76} +(3.25314 + 8.93793i) q^{77} +(-0.803209 - 4.55523i) q^{79} +(13.1513 - 2.77042i) q^{80} +(1.19673 + 2.51193i) q^{82} +(-2.12803 + 0.375229i) q^{83} +(4.00787 + 11.0115i) q^{85} +(11.4243 + 2.96007i) q^{86} +(7.83503 - 11.8025i) q^{88} +(7.83712 + 13.5743i) q^{89} +(-6.03579 - 3.48477i) q^{91} +(-0.103320 - 6.24433i) q^{92} +(3.82524 - 1.05896i) q^{94} +(1.83982 - 10.4341i) q^{95} +(1.68619 - 1.41488i) q^{97} +(4.78429 + 0.378719i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

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