LMFDB - Embedded newform 648.2.t.a.397.6

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			397.6
Character	$\chi$	$=$	648.397
Dual form			648.2.t.a.253.6

$q$-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 $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{9}\right)$

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	−0.988482	−	0.151335i	$-0.951643\pi$
$5$	−2.15975	−	2.57389i	−0.965871	−	1.15108i	0.0226118	−	0.999744i	$-0.492802\pi$
$6$		0			0
$7$	−1.78453	+	0.649515i	−0.674489	+	0.245494i	−0.656479	−	0.754344i	$-0.727955\pi$
$7$	−1.78453	+	0.649515i	−0.674489	+	0.245494i	−0.0180093	+	0.999838i	$0.505733\pi$
$8$	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	0.0169036	+	0.999857i	$0.494619\pi$
$11$	−3.21944	+	3.83678i	−0.970699	+	1.15683i	−0.987602	+	0.156977i	$0.949825\pi$
$12$		0			0
$13$	3.61424	−	0.637289i	1.00241	−	0.176752i	0.351728	−	0.936102i	$-0.385594\pi$
$13$	3.61424	−	0.637289i	1.00241	−	0.176752i	0.650682	+	0.759350i	$0.274483\pi$
$14$	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	0.996225	−	0.0868103i	$-0.0276674\pi$
$17$	1.74380	+	3.02034i	0.422932	+	0.732541i	−0.573292	+	0.819351i	$0.694334\pi$
$18$		0			0
$19$	−2.73085	−	1.57666i	−0.626501	−	0.361710i	0.152895	−	0.988242i	$-0.451140\pi$
$19$	−2.73085	−	1.57666i	−0.626501	−	0.361710i	−0.779396	+	0.626532i	$0.784474\pi$
$20$	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	0.629308	−	0.777156i	$-0.283338\pi$
$23$	2.93428	+	1.06799i	0.611839	+	0.222691i	−0.0174685	+	0.999847i	$0.505561\pi$
$24$		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	0.750015	−	0.661420i	$-0.230046\pi$
$29$	6.61611	+	1.16660i	1.22858	+	0.216632i	0.478565	+	0.878052i	$0.341157\pi$
$30$		0			0
$31$	0.842639	+	0.306695i	0.151342	+	0.0550841i	0.416581	−	0.909099i	$-0.363228\pi$
$31$	0.842639	+	0.306695i	0.151342	+	0.0550841i	−0.265238	+	0.964183i	$0.585451\pi$
$32$	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	0.107115	−	0.994247i	$-0.465839\pi$
$37$	6.21485	−	3.58815i	1.02172	−	0.589887i	0.914600	+	0.404359i	$0.132505\pi$
$38$	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	0.999794	−	0.0202862i	$-0.00645776\pi$
$41$	0.341649	+	1.93759i	0.0533567	+	0.302601i	−0.946438	+	0.322887i	$0.895347\pi$
$42$		0			0
$43$	−5.36405	+	6.39263i	−0.818010	+	0.974867i	−0.999964	−	0.00844018i	$-0.997313\pi$
$43$	−5.36405	+	6.39263i	−0.818010	+	0.974867i	0.181954	+	0.983307i	$0.441758\pi$
$44$	−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	−0.527125	−	0.849788i	$-0.676730\pi$
$47$	−2.63733	+	0.959909i	−0.384694	+	0.140017i	0.142432	+	0.989805i	$0.454508\pi$
$48$		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	$0.226996\pi$
$53$			9.52536i			1.30841i	−0.756318	+	0.654205i	$0.773004\pi$
$54$		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	0.999622	−	0.0274946i	$-0.00875290\pi$
$59$	6.13695	+	7.31373i	0.798963	+	0.952167i	−0.200659	+	0.979661i	$0.564308\pi$
$60$		0			0
$61$	2.92540	+	8.03747i	0.374559	+	1.02909i	0.973577	+	0.228358i	$0.0733355\pi$
$61$	2.92540	+	8.03747i	0.374559	+	1.02909i	−0.599018	+	0.800735i	$0.704442\pi$
$62$	−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	0.749341	−	0.662184i	$-0.230370\pi$
$67$	13.7512	−	2.42470i	1.67997	−	0.296224i	0.930631	+	0.365960i	$0.119259\pi$
$68$	−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	0.763099	−	0.646282i	$-0.223677\pi$
$71$	−1.50109	−	2.59997i	−0.178147	−	0.308560i	−0.941246	+	0.337722i	$0.890344\pi$
$72$		0			0
$73$	0.472663	−	0.818676i	0.0553210	−	0.0958187i	−0.837039	−	0.547144i	$-0.815715\pi$
$73$	0.472663	−	0.818676i	0.0553210	−	0.0958187i	0.892360	+	0.451325i	$0.149048\pi$
$74$	−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	0.905701	+	0.423918i	$0.139346\pi$
$79$	−0.803209	+	4.55523i	−0.0903681	+	0.512503i	−0.996069	+	0.0885849i	$0.971766\pi$
$80$	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	0.0556319	−	0.998451i	$-0.482283\pi$
$83$	−2.12803	−	0.375229i	−0.233582	−	0.0411868i	−0.289214	+	0.957265i	$0.593394\pi$
$84$		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	−0.0667245	−	0.997771i	$-0.521255\pi$
$89$	7.83712	−	13.5743i	0.830733	−	1.43887i	0.897458	−	0.441101i	$-0.145412\pi$
$90$		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	0.724365	−	0.689417i	$-0.242133\pi$
$97$	1.68619	+	1.41488i	0.171207	+	0.143659i	−0.553158	+	0.833076i	$0.686578\pi$
$98$	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	−0.730684	−	0.682716i	$-0.760799\pi$
$101$	−6.12830	−	16.8374i	−0.609789	−	1.67538i	0.120895	−	0.992665i	$-0.461424\pi$
$102$		0			0
$103$	−10.6973	+	8.97613i	−1.05404	+	0.884444i	−0.993513	−	0.113723i	$-0.963723\pi$
$103$	−10.6973	+	8.97613i	−1.05404	+	0.884444i	−0.0605268	+	0.998167i	$0.519278\pi$
$104$	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	$0.203659\pi$
$107$			12.3518i			1.19409i	−0.802207	+	0.597046i	$0.796341\pi$
$108$		0			0
$109$			2.18468i			0.209255i	0.994511	+	0.104627i	$0.0333650\pi$
$109$			2.18468i			0.209255i	−0.994511	+	0.104627i	$0.966635\pi$
$110$	−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	−0.999447	−	0.0332523i	$-0.989413\pi$
$113$	−12.1210	+	10.1708i	−1.14025	+	0.956785i	−0.140805	+	0.990037i	$0.544969\pi$
$114$		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	−0.998914	−	0.0465982i	$-0.985162\pi$
$127$	−5.17381	+	8.96131i	−0.459102	+	0.795187i	0.539812	+	0.841786i	$0.318495\pi$
$128$	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	−0.729929	−	0.683523i	$-0.760447\pi$
$131$	3.07414	−	8.44614i	0.268589	−	0.737942i	0.998518	−	0.0544195i	$-0.0173308\pi$
$132$		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	0.558395	+	0.829575i	$0.311417\pi$
$137$	−2.92683	+	16.5989i	−0.250056	+	1.41814i	−0.808451	+	0.588563i	$0.799694\pi$
$138$		0			0
$139$	−3.76833	+	10.3534i	−0.319626	+	0.878164i	0.670988	+	0.741469i	$0.265870\pi$
$139$	−3.76833	+	10.3534i	−0.319626	+	0.878164i	−0.990613	+	0.136695i	$0.956352\pi$
$140$	−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	−0.591888	−	0.806020i	$-0.701617\pi$
$149$	−10.6491	+	1.87772i	−0.872406	+	0.153829i	−0.280518	+	0.959849i	$0.590506\pi$
$150$		0			0
$151$	−0.489785	−	0.410979i	−0.0398582	−	0.0334450i	0.622641	−	0.782508i	$-0.286060\pi$
$151$	−0.489785	−	0.410979i	−0.0398582	−	0.0334450i	−0.662499	+	0.749063i	$0.730504\pi$
$152$	−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	0.475602	−	0.879661i	$-0.342230\pi$
$157$	−5.93021	−	7.06735i	−0.473282	−	0.564036i	−0.948884	+	0.315625i	$0.897786\pi$
$158$	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	$0.106178\pi$
$163$			8.36032i			0.654831i	−0.944881	+	0.327415i	$0.893822\pi$
$164$	−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	−0.439030	−	0.898472i	$-0.644678\pi$
$167$	4.77570	−	4.00729i	0.369555	−	0.310094i	0.808586	+	0.588379i	$0.200234\pi$
$168$		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	−0.503017	−	0.864276i	$-0.667777\pi$
$173$	5.72780	−	6.82613i	0.435477	−	0.518981i	0.938494	+	0.345295i	$0.112221\pi$
$174$		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	−0.888251	−	0.459359i	$-0.848079\pi$
$179$	−12.5035	+	7.21893i	−0.934559	+	0.539568i	−0.0463085	+	0.998927i	$0.514746\pi$
$180$		0			0
$181$	4.19806	+	2.42375i	0.312039	+	0.180156i	0.647839	−	0.761778i	$-0.275673\pi$
$181$	4.19806	+	2.42375i	0.312039	+	0.180156i	−0.335799	+	0.941934i	$0.609006\pi$
$182$	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	−0.140153	−	0.990130i	$-0.544759\pi$
$191$	4.56335	−	25.8800i	0.330192	−	1.87261i	0.470345	−	0.882483i	$-0.344129\pi$
$192$		0			0
$193$	3.82953	+	1.39383i	0.275655	+	0.100330i	0.476149	−	0.879365i	$-0.342032\pi$
$193$	3.82953	+	1.39383i	0.275655	+	0.100330i	−0.200494	+	0.979695i	$0.564255\pi$
$194$	−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	0.147796	−	0.989018i	$-0.452782\pi$
$197$	−8.91014	−	5.14427i	−0.634821	−	0.366514i	−0.782617	+	0.622504i	$0.786116\pi$
$198$		0			0
$199$	0.690545	+	1.19606i	0.0489514	+	0.0847864i	0.889463	−	0.457007i	$-0.151079\pi$
$199$	0.690545	+	1.19606i	0.0489514	+	0.0847864i	−0.840511	+	0.541794i	$0.817745\pi$
$200$	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	0.447188	−	0.894440i	$-0.352426\pi$
$211$	−7.42731	−	8.85152i	−0.511317	−	0.609364i	−0.958505	+	0.285076i	$0.907981\pi$
$212$	−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	−0.244510	−	0.969647i	$-0.578627\pi$
$223$	2.85912	−	1.04063i	0.191461	−	0.0696860i	0.435971	+	0.899961i	$0.356405\pi$
$224$	−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	−0.786918	−	0.617058i	$-0.788325\pi$
$227$	−0.641654	+	0.764693i	−0.0425881	+	0.0507545i	0.744330	+	0.667812i	$0.232769\pi$
$228$		0			0
$229$	0.846018	−	0.149176i	0.0559064	−	0.00985781i	−0.145625	−	0.989340i	$-0.546519\pi$
$229$	0.846018	−	0.149176i	0.0559064	−	0.00985781i	0.201531	+	0.979482i	$0.435408\pi$
$230$	−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	0.984235	−	0.176867i	$-0.0565961\pi$
$233$	5.17379	+	8.96127i	0.338946	+	0.587072i	−0.645288	+	0.763939i	$0.723263\pi$
$234$		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	0.686277	−	0.727341i	$-0.259244\pi$
$239$	11.5092	+	4.18901i	0.744469	+	0.270965i	0.0581928	+	0.998305i	$0.481466\pi$
$240$		0			0
$241$	−2.60278	+	14.7611i	−0.167660	+	0.950846i	0.778620	+	0.627496i	$0.215920\pi$
$241$	−2.60278	+	14.7611i	−0.167660	+	0.950846i	−0.946279	+	0.323350i	$0.895191\pi$
$242$	−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	0.868443	−	0.495789i	$-0.165121\pi$
$251$	13.8356	+	7.98801i	0.873298	+	0.504199i	0.00485525	+	0.999988i	$0.498455\pi$
$252$		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	0.997373	+	0.0724341i	$0.0230767\pi$
$257$	1.36142	+	7.72098i	0.0849229	+	0.481622i	−0.912450	+	0.409187i	$0.865812\pi$
$258$		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	0.333166	−	0.942868i	$-0.391883\pi$
$263$	19.3707	−	7.05037i	1.19445	−	0.434744i	0.861284	+	0.508124i	$0.169661\pi$
$264$		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	$-0.838118\pi$
$269$		−	15.9724i		−	0.973852i	0.873443	−	0.486926i	$-0.161882\pi$
$270$		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	−0.967903	−	0.251322i	$-0.919135\pi$
$277$	−6.45750	−	17.7418i	−0.387993	−	1.06600i	0.579910	−	0.814680i	$-0.303088\pi$
$278$	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	0.957997	−	0.286777i	$-0.0925839\pi$
$281$	14.1133	+	11.8425i	0.841932	+	0.706465i	−0.116066	+	0.993242i	$0.537028\pi$
$282$		0			0
$283$	−8.62324	+	1.52051i	−0.512599	+	0.0903850i	−0.423964	−	0.905679i	$-0.639362\pi$
$283$	−8.62324	+	1.52051i	−0.512599	+	0.0903850i	−0.0886349	+	0.996064i	$0.528250\pi$
$284$	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	0.724840	+	0.688918i	$0.241914\pi$
$293$	−4.67724	+	12.8506i	−0.273247	+	0.750741i	−0.998087	+	0.0618236i	$0.980308\pi$
$294$		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	0.254053	−	0.967190i	$-0.418236\pi$
$307$	21.3532	−	12.3283i	1.21869	−	0.703612i	0.964638	+	0.263578i	$0.0849028\pi$
$308$	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	0.977884	−	0.209147i	$-0.0670688\pi$
$311$	−0.221479	−	1.25607i	−0.0125589	−	0.0712250i	−0.990443	+	0.137922i	$0.955958\pi$
$312$		0			0
$313$	15.3438	+	12.8749i	0.867280	+	0.727735i	0.963524	−	0.267623i	$-0.0862382\pi$
$313$	15.3438	+	12.8749i	0.867280	+	0.727735i	−0.0962433	+	0.995358i	$0.530683\pi$
$314$	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	0.983909	−	0.178671i	$-0.0571796\pi$
$317$	2.05364	+	5.64232i	0.115344	+	0.316904i	−0.868565	+	0.495575i	$0.834957\pi$
$318$		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	0.976226	+	0.216755i	$0.0695472\pi$
$331$	6.69009	+	18.3809i	0.367721	+	1.01030i	−0.608505	+	0.793550i	$0.708231\pi$
$332$	−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	0.891824	+	0.452383i	$0.149426\pi$
$337$	3.82769	+	21.7079i	0.208508	+	1.18251i	−0.683316	+	0.730123i	$0.739463\pi$
$338$	−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	−0.939990	−	0.341202i	$-0.889166\pi$
$347$	−0.0110975	+	0.0304900i	−0.000595743	+	0.00163679i	0.939394	+	0.342838i	$0.111388\pi$
$348$		0			0
$349$	−32.0493	−	5.65116i	−1.71556	−	0.302500i	−0.772474	−	0.635046i	$-0.780981\pi$
$349$	−32.0493	−	5.65116i	−1.71556	−	0.302500i	−0.943087	+	0.332546i	$0.892092\pi$
$350$	−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	−0.979474	−	0.201571i	$-0.935395\pi$
$353$	0.185474	−	1.05188i	0.00987180	−	0.0559857i	0.989346	+	0.145585i	$0.0465065\pi$
$354$		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	−0.976114	−	0.217258i	$-0.930289\pi$
$359$	−5.68242	+	9.84224i	−0.299907	+	0.519453i	0.676208	+	0.736711i	$0.263622\pi$
$360$		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	0.798469	−	0.602036i	$-0.205644\pi$
$367$	6.59453	+	5.53346i	0.344231	+	0.288844i	−0.454237	+	0.890881i	$0.650088\pi$
$368$	−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	0.742318	+	0.670048i	$0.233726\pi$
$373$	24.5912	+	29.3067i	1.27328	+	1.51744i	0.530966	+	0.847393i	$0.321829\pi$
$374$	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	$-0.807741\pi$
$379$		−	22.1132i		−	1.13588i	0.823071	−	0.567939i	$-0.192259\pi$
$380$	−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	−0.610189	−	0.792256i	$-0.708907\pi$
$383$	1.25391	−	1.05215i	0.0640717	−	0.0537626i	0.674261	+	0.738493i	$0.264462\pi$
$384$		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	−0.919832	−	0.392311i	$-0.871676\pi$
$389$	−7.37158	+	8.78511i	−0.373754	+	0.445423i	0.546079	+	0.837734i	$0.316120\pi$
$390$		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	0.433808	−	0.901005i	$-0.357170\pi$
$397$	−2.58188	−	1.49065i	−0.129581	−	0.0748137i	−0.563389	+	0.826192i	$0.690503\pi$
$398$	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	0.553603	−	0.832781i	$-0.313253\pi$
$401$	8.85877	+	3.22433i	0.442386	+	0.161015i	−0.111217	+	0.993796i	$0.535475\pi$
$402$		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	−0.330380	−	0.943848i	$-0.607177\pi$
$409$	−24.0695	−	8.76058i	−1.19016	−	0.433183i	−0.859779	+	0.510665i	$0.829399\pi$
$410$	−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	−0.114396	−	0.993435i	$-0.536493\pi$
$419$	2.41298	−	0.425474i	0.117882	−	0.0207858i	0.232278	+	0.972649i	$0.425382\pi$
$420$		0			0
$421$	8.35420	−	9.95615i	0.407159	−	0.485233i	−0.523030	−	0.852314i	$-0.675198\pi$
$421$	8.35420	−	9.95615i	0.407159	−	0.485233i	0.930189	+	0.367081i	$0.119643\pi$
$422$	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	0.0477612	−	0.998859i	$-0.484791\pi$
$439$	15.2198	−	5.53956i	0.726402	−	0.264389i	0.678641	+	0.734470i	$0.262569\pi$
$440$	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	−0.970588	−	0.240747i	$-0.922607\pi$
$443$	−11.8910	+	14.1711i	−0.564957	+	0.673290i	0.405631	+	0.914037i	$0.367052\pi$
$444$		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	0.763354	−	0.645980i	$-0.223551\pi$
$449$	−3.76662	−	6.52398i	−0.177758	−	0.307886i	−0.941112	+	0.338094i	$0.890218\pi$
$450$		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	0.870962	+	0.491350i	$0.163496\pi$
$457$	−2.46966	+	14.0062i	−0.115526	+	0.655180i	−0.986488	+	0.163831i	$0.947615\pi$
$458$	−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	0.453070	−	0.891475i	$-0.350329\pi$
$461$	12.3225	+	2.17278i	0.573914	+	0.101197i	0.120844	+	0.992672i	$0.461440\pi$
$462$		0			0
$463$	−5.11858	−	1.86301i	−0.237881	−	0.0865815i	0.220329	−	0.975426i	$-0.429287\pi$
$463$	−5.11858	−	1.86301i	−0.237881	−	0.0865815i	−0.458210	+	0.888844i	$0.651509\pi$
$464$	−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	0.639246	−	0.769003i	$-0.279247\pi$
$467$	6.32947	+	3.65432i	0.292893	+	0.169102i	−0.346353	+	0.938104i	$0.612580\pi$
$468$		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	−0.486495	−	0.873683i	$-0.661725\pi$
$479$	−6.51285	+	2.37048i	−0.297580	+	0.108310i	0.188916	+	0.981993i	$0.439503\pi$
$480$		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	0.623140	−	0.782110i	$-0.285856\pi$
$491$	−5.65695	−	6.74169i	−0.255295	−	0.304248i	−0.878435	+	0.477862i	$0.841412\pi$
$492$		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	0.164362	−	0.986400i	$-0.447443\pi$
$499$	14.6580	−	2.58460i	0.656181	−	0.115702i	0.491819	+	0.870698i	$0.336332\pi$
$500$	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	0.959117	−	0.283009i	$-0.0913327\pi$
$503$	5.25851	+	9.10801i	0.234465	+	0.406106i	−0.724652	+	0.689115i	$0.757999\pi$
$504$		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	0.584310	+	0.811531i	$0.301365\pi$
$509$	−8.68462	+	23.8608i	−0.384939	+	1.05761i	−0.969249	+	0.246081i	$0.920857\pi$
$510$		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	−0.718494	−	0.695533i	$-0.755168\pi$
$521$	5.54892	−	9.61101i	0.243103	−	0.421066i	0.961596	+	0.274467i	$0.0885015\pi$
$522$		0			0
$523$	21.2339	−	12.2594i	0.928493	−	0.536066i	0.0421586	−	0.999111i	$-0.486577\pi$
$523$	21.2339	−	12.2594i	0.928493	−	0.536066i	0.886335	+	0.463045i	$0.153243\pi$
$524$	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	$0.0697474\pi$
$541$			10.1117i			0.434737i	−0.976090	+	0.217369i	$0.930253\pi$
$542$	−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	−0.951590	−	0.307371i	$-0.900551\pi$
$547$	−9.82775	−	27.0015i	−0.420204	−	1.15450i	0.531386	−	0.847130i	$-0.321672\pi$
$548$	−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	−0.262508	−	0.964930i	$-0.584550\pi$
$557$	10.4290	−	6.02119i	0.441891	−	0.255126i	0.704400	+	0.709804i	$0.251216\pi$
$558$		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	−0.967702	−	0.252096i	$-0.918880\pi$
$563$	−1.52700	+	4.19539i	−0.0643553	+	0.176815i	0.903347	+	0.428910i	$0.141102\pi$
$564$		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	0.643648	+	0.765322i	$0.277420\pi$
$569$	−5.31792	+	30.1594i	−0.222939	+	1.26435i	−0.866586	+	0.499027i	$0.833691\pi$
$570$		0			0
$571$	−4.43557	+	12.1866i	−0.185623	+	0.509994i	−0.997244	−	0.0741895i	$-0.976363\pi$
$571$	−4.43557	+	12.1866i	−0.185623	+	0.509994i	0.811621	+	0.584184i	$0.198585\pi$
$572$	−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	0.603169	−	0.797613i	$-0.293904\pi$
$577$	−9.34815	−	16.1915i	−0.389169	−	0.674060i	−0.992338	+	0.123553i	$0.960571\pi$
$578$	−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	−0.957487	−	0.288475i	$-0.906852\pi$
$587$	−9.91990	−	27.2547i	−0.409438	−	1.12492i	0.548049	−	0.836446i	$-0.315371\pi$
$588$		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	−0.782970	−	0.622060i	$-0.786296\pi$
$599$	−7.49705	+	6.29078i	−0.306321	+	0.257034i	0.476648	+	0.879094i	$0.341852\pi$
$600$		0			0
$601$	27.8247	−	10.1274i	1.13499	−	0.413103i	0.294890	−	0.955531i	$-0.404717\pi$
$601$	27.8247	−	10.1274i	1.13499	−	0.413103i	0.840102	+	0.542428i	$0.182495\pi$
$602$	−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	0.999960	−	0.00892998i	$-0.00284254\pi$
$607$	1.41051	+	7.99939i	0.0572507	+	0.324685i	−0.942709	+	0.333615i	$0.891731\pi$
$608$	−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	0.280739	−	0.959784i	$-0.409420\pi$
$613$	−10.1533	−	5.86202i	−0.410088	−	0.236765i	−0.690828	+	0.723019i	$0.742754\pi$
$614$	−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	0.366905	−	0.930258i	$-0.380417\pi$
$617$	1.24227	+	0.452149i	0.0500118	+	0.0182028i	−0.316893	+	0.948461i	$0.602640\pi$
$618$		0			0
$619$	25.4782	+	4.49249i	1.02405	+	0.180568i	0.660359	−	0.750950i	$-0.270404\pi$
$619$	25.4782	+	4.49249i	1.02405	+	0.180568i	0.363695	+	0.931518i	$0.381515\pi$
$620$	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	0.701104	−	0.713059i	$-0.252691\pi$
$631$	−6.70635	−	11.6157i	−0.266976	−	0.462415i	−0.968079	+	0.250644i	$0.919358\pi$
$632$	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	0.339575	−	0.940579i	$-0.389717\pi$
$641$	30.4904	−	11.0976i	1.20430	−	0.438328i	0.864722	+	0.502251i	$0.167495\pi$
$642$		0			0
$643$	17.3052	+	20.6235i	0.682449	+	0.813312i	0.990420	−	0.138084i	$-0.0440944\pi$
$643$	17.3052	+	20.6235i	0.682449	+	0.813312i	−0.307971	+	0.951396i	$0.599650\pi$
$644$	−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	0.961607	−	0.274431i	$-0.0884896\pi$
$653$	13.3995	+	15.9689i	0.524363	+	0.624912i	−0.437243	+	0.899343i	$0.644045\pi$
$654$		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	−0.993353	−	0.115110i	$-0.963278\pi$
$659$	−18.1622	+	21.6448i	−0.707497	+	0.843162i	0.285856	+	0.958273i	$0.407722\pi$
$660$		0			0
$661$	−37.0880	+	6.53962i	−1.44256	+	0.254362i	−0.839510	−	0.543344i	$-0.817158\pi$
$661$	−37.0880	+	6.53962i	−1.44256	+	0.254362i	−0.603046	+	0.797706i	$0.706047\pi$
$662$	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	−0.962927	−	0.269763i	$-0.913055\pi$
$673$	0.887037	−	5.03064i	0.0341928	−	0.193917i	0.997120	+	0.0758462i	$0.0241658\pi$
$674$	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	0.706325	−	0.707888i	$-0.250352\pi$
$677$	29.3482	+	5.17487i	1.12794	+	0.198887i	0.421617	+	0.906774i	$0.361463\pi$
$678$		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	−0.995860	−	0.0908981i	$-0.971026\pi$
$683$	−41.0964	−	23.7270i	−1.57251	−	0.907889i	−0.576650	−	0.816991i	$-0.695640\pi$
$684$		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	−0.252136	−	0.967692i	$-0.581133\pi$
$691$	19.5742	−	23.3276i	0.744637	−	0.887424i	0.996773	+	0.0802677i	$0.0255775\pi$
$692$	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	$0.142790\pi$
$701$			22.9653i			0.867386i	−0.901061	+	0.433693i	$0.857210\pi$
$702$		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	−0.920625	−	0.390448i	$-0.872320\pi$
$709$	−12.4178	−	34.1176i	−0.466361	−	1.28132i	0.454264	−	0.890867i	$-0.349902\pi$
$710$	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	−0.999895	−	0.0144775i	$-0.995392\pi$
$719$	−13.7419	−	23.8016i	−0.512485	−	0.887651i	0.487410	−	0.873173i	$-0.337942\pi$
$720$		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	−0.994051	−	0.108914i	$-0.965263\pi$
$727$	−0.612001	+	3.47083i	−0.0226979	+	0.128726i	0.971353	+	0.237640i	$0.0763738\pi$
$728$	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	−0.817963	−	0.575271i	$-0.804897\pi$
$733$	4.83027	−	13.2711i	0.178410	−	0.490178i	0.996373	+	0.0850933i	$0.0271188\pi$
$734$	−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	−0.545696	−	0.837983i	$-0.683735\pi$
$739$	−2.52352	+	1.45695i	−0.0928291	+	0.0535949i	0.452867	+	0.891578i	$0.350401\pi$
$740$	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	0.963319	−	0.268358i	$-0.0864809\pi$
$743$	−0.918280	−	5.20783i	−0.0336884	−	0.191057i	−0.997008	+	0.0773010i	$0.975370\pi$
$744$		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	−0.984910	−	0.173065i	$-0.944633\pi$
$751$	−27.0071	+	22.6616i	−0.985502	+	0.826935i	−0.000591865		1.00000i	$0.500188\pi$
$752$	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	$-0.749367\pi$
$757$		−	38.9874i		−	1.41702i	0.705700	−	0.708511i	$-0.250633\pi$
$758$	−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	−0.999733	−	0.0231155i	$-0.992641\pi$
$761$	−31.7399	+	26.6329i	−1.15057	+	0.965443i	−0.150837	+	0.988559i	$0.548197\pi$
$762$		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	0.567210	+	0.823573i	$0.308023\pi$
$769$	8.75977	+	49.6791i	0.315886	+	1.79148i	−0.251325	+	0.967903i	$0.580866\pi$
$770$	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	−0.891330	−	0.453354i	$-0.850227\pi$
$773$	−26.2565	+	15.1592i	−0.944379	+	0.545238i	−0.0530488	+	0.998592i	$0.516894\pi$
$774$		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	0.659137	+	0.752023i	$0.270922\pi$
$787$	−9.23473	+	25.3722i	−0.329182	+	0.904421i	−0.988319	+	0.152398i	$0.951300\pi$
$788$	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	0.861437	−	0.507864i	$-0.169565\pi$
$797$	52.0759	−	9.18239i	1.84462	−	0.325257i	0.983186	+	0.182608i	$0.0584538\pi$
$798$		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	$-0.794452\pi$
$811$		−	34.2759i		−	1.20359i	0.798650	−	0.601795i	$-0.205548\pi$
$812$	−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	−0.407004	−	0.913426i	$-0.633427\pi$
$821$	16.1380	−	19.2325i	0.563221	−	0.671220i	0.970225	+	0.242206i	$0.0778710\pi$
$822$		0			0
$823$	−5.65012	−	32.0434i	−0.196951	−	1.11696i	−0.909613	−	0.415456i	$-0.863622\pi$
$823$	−5.65012	−	32.0434i	−0.196951	−	1.11696i	0.712662	−	0.701507i	$-0.247489\pi$
$824$	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	0.387352	−	0.921932i	$-0.373390\pi$
$827$	39.6695	−	22.9032i	1.37944	−	0.796423i	0.992092	+	0.125509i	$0.0400565\pi$
$828$		0			0
$829$	17.0001	+	9.81500i	0.590437	+	0.340889i	0.765270	−	0.643709i	$-0.222605\pi$
$829$	17.0001	+	9.81500i	0.590437	+	0.340889i	−0.174833	+	0.984598i	$0.555939\pi$
$830$	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	−0.396381	−	0.918086i	$-0.629734\pi$
$839$	8.40287	−	47.6550i	0.290099	−	1.64523i	0.686480	−	0.727149i	$-0.259155\pi$
$840$		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	−0.0583624	+	0.998295i	$0.518588\pi$
$853$	−30.1220	+	35.8980i	−1.03136	+	1.22912i	−0.972995	+	0.230828i	$0.925857\pi$
$854$	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	−0.238650	−	0.971106i	$-0.576705\pi$
$857$	5.93538	−	2.16030i	0.202749	−	0.0737946i	0.441399	+	0.897311i	$0.354483\pi$
$858$		0			0
$859$	−19.3877	−	23.1054i	−0.661501	−	0.788346i	0.326100	−	0.945335i	$-0.394266\pi$
$859$	−19.3877	−	23.1054i	−0.661501	−	0.788346i	−0.987600	+	0.156990i	$0.949821\pi$
$860$	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	−0.726328	−	0.687348i	$-0.758775\pi$
$877$	−34.7601	+	6.12915i	−1.17377	+	0.206967i	−0.447438	+	0.894315i	$0.647664\pi$
$878$	−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	0.718171	−	0.695867i	$-0.244980\pi$
$881$	−7.22906	−	12.5211i	−0.243553	−	0.421847i	−0.961724	+	0.274020i	$0.911646\pi$
$882$		0			0
$883$	−30.6193	−	17.6781i	−1.03042	−	0.594915i	−0.113317	−	0.993559i	$-0.536148\pi$
$883$	−30.6193	−	17.6781i	−1.03042	−	0.594915i	−0.917106	+	0.398644i	$0.869481\pi$
$884$	−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	0.838432	−	0.545007i	$-0.183473\pi$
$887$	33.6657	+	12.2533i	1.13038	+	0.411426i	0.291952	+	0.956433i	$0.405695\pi$
$888$		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	−0.664037	−	0.747700i	$-0.731158\pi$
$907$	5.65021	−	6.73365i	0.187612	−	0.223587i	0.851649	+	0.524112i	$0.175603\pi$
$908$	−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	−0.554516	−	0.832173i	$-0.687097\pi$
$911$	−13.4129	+	4.88190i	−0.444389	+	0.161744i	0.110127	+	0.993918i	$0.464874\pi$
$912$		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	0.251989	−	0.967730i	$-0.418915\pi$
$929$	−20.0336	−	16.8102i	−0.657282	−	0.551525i	−0.909271	+	0.416205i	$0.863360\pi$
$930$		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	0.327580	−	0.944823i	$-0.393767\pi$
$937$	30.0604	−	52.0662i	0.982031	−	1.70093i	0.654451	−	0.756105i	$-0.272900\pi$
$938$	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	−0.0476846	−	0.998862i	$-0.515184\pi$
$941$	19.3533	−	53.1728i	0.630900	−	1.73338i	0.678585	−	0.734522i	$-0.262594\pi$
$942$		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	−0.627299	−	0.778778i	$-0.715840\pi$
$947$	−45.6408	−	8.04770i	−1.48313	−	0.261515i	−0.855826	+	0.517263i	$0.826951\pi$
$948$		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	−0.814589	−	0.580039i	$-0.803037\pi$
$953$	2.93376	−	5.08142i	0.0950338	−	0.164603i	0.909623	+	0.415435i	$0.136371\pi$
$954$		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	−0.876594	−	0.481231i	$-0.840190\pi$
$967$	−17.2553	+	14.4789i	−0.554893	+	0.465610i	0.321701	+	0.946841i	$0.395745\pi$
$968$	−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	$0.114579\pi$
$971$			21.9521i			0.704475i	−0.935911	+	0.352238i	$0.885421\pi$
$972$		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	0.182911	−	0.983129i	$-0.441448\pi$
$977$	36.9729	−	31.0239i	1.18287	−	0.992543i	0.999956	−	0.00941403i	$-0.00299662\pi$
$978$		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	0.998484	−	0.0550493i	$-0.0175316\pi$
$983$	35.0417	+	29.4034i	1.11766	+	0.937824i	0.119172	+	0.992874i	$0.461976\pi$
$984$		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	−0.745333	−	0.666693i	$-0.767709\pi$
$991$	6.44420	−	11.1617i	0.204707	−	0.354562i	0.950039	+	0.312130i	$0.101043\pi$
$992$	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	0.0965756	−	0.995326i	$-0.469211\pi$
$997$	−4.83400	−	0.852365i	−0.153094	−	0.0269947i	−0.249670	+	0.968331i	$0.580322\pi$
$998$	−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.397.6		204
3.2	odd	2		216.2.t.a.133.29	yes	204
8.5	even	2	inner	648.2.t.a.397.32		204
12.11	even	2		864.2.bf.a.241.20		204
24.5	odd	2		216.2.t.a.133.3	yes	204
24.11	even	2		864.2.bf.a.241.15		204
27.13	even	9	inner	648.2.t.a.253.32		204
27.14	odd	18		216.2.t.a.13.3	✓	204
108.95	even	18		864.2.bf.a.337.15		204
216.13	even	18	inner	648.2.t.a.253.6		204
216.149	odd	18		216.2.t.a.13.29	yes	204
216.203	even	18		864.2.bf.a.337.20		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.3	✓	204	27.14	odd	18
216.2.t.a.13.29	yes	204	216.149	odd	18
216.2.t.a.133.3	yes	204	24.5	odd	2
216.2.t.a.133.29	yes	204	3.2	odd	2
648.2.t.a.253.6		204	216.13	even	18	inner
648.2.t.a.253.32		204	27.13	even	9	inner
648.2.t.a.397.6		204	1.1	even	1	trivial
648.2.t.a.397.32		204	8.5	even	2	inner
864.2.bf.a.241.15		204	24.11	even	2
864.2.bf.a.241.20		204	12.11	even	2
864.2.bf.a.337.15		204	108.95	even	18
864.2.bf.a.337.20		204	216.203	even	18

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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