LMFDB - Embedded newform 648.2.v.b.611.28

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(35,648)] 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("648.35"); 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([9, 9, 13])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			611.28
Character	$\chi$	$=$	648.611
Dual form			648.2.v.b.35.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.27615 - 0.609466i) q^{2} +(1.25710 - 1.55554i) q^{4} +(0.426624 - 0.155279i) q^{5} +(1.28150 - 0.225962i) q^{7} +(0.656202 - 2.75125i) q^{8} +(0.449799 - 0.458171i) q^{10} +(-0.00602720 + 0.0165596i) q^{11} +(1.43581 - 1.71113i) q^{13} +(1.49766 - 1.06939i) q^{14} +(-0.839384 - 3.91094i) q^{16} +(-1.27216 - 0.734483i) q^{17} +(0.677841 + 1.17406i) q^{19} +(0.294769 - 0.858831i) q^{20} +(0.00240091 + 0.0248058i) q^{22} +(-0.369486 + 2.09546i) q^{23} +(-3.67233 + 3.08145i) q^{25} +(0.789428 - 3.05873i) q^{26} +(1.25948 - 2.27747i) q^{28} +(5.56933 - 4.67322i) q^{29} +(8.87753 + 1.56535i) q^{31} +(-3.45476 - 4.47936i) q^{32} +(-2.07111 - 0.161969i) q^{34} +(0.511630 - 0.295390i) q^{35} +(-4.58718 - 2.64841i) q^{37} +(1.58057 + 1.08515i) q^{38} +(-0.147259 - 1.27565i) q^{40} +(-1.56527 + 1.86542i) q^{41} +(-10.1956 - 3.71089i) q^{43} +(0.0181822 + 0.0301926i) q^{44} +(0.805592 + 2.89930i) q^{46} +(0.791397 + 4.48824i) q^{47} +(-4.98668 + 1.81500i) q^{49} +(-2.80839 + 6.17054i) q^{50} +(-0.856765 - 4.38452i) q^{52} +10.4085 q^{53} +0.00800062i q^{55} +(0.219241 - 3.67400i) q^{56} +(4.25911 - 9.35804i) q^{58} +(3.75319 + 10.3118i) q^{59} +(-8.87057 + 1.56412i) q^{61} +(12.2831 - 3.41294i) q^{62} +(-7.13880 - 3.61076i) q^{64} +(0.346849 - 0.952961i) q^{65} +(3.70041 + 3.10502i) q^{67} +(-2.74175 + 1.05557i) q^{68} +(0.472885 - 0.688782i) q^{70} +(-5.03714 + 8.72458i) q^{71} +(-0.339460 - 0.587962i) q^{73} +(-7.46803 - 0.584031i) q^{74} +(2.67840 + 0.421502i) q^{76} +(-0.00398198 + 0.0225829i) q^{77} +(5.19665 + 6.19313i) q^{79} +(-0.965387 - 1.53816i) q^{80} +(-0.860607 + 3.33452i) q^{82} +(-1.29122 - 1.53881i) q^{83} +(-0.656785 - 0.115809i) q^{85} +(-15.2727 + 1.47822i) q^{86} +(0.0416046 + 0.0274488i) q^{88} +(0.103744 - 0.0598964i) q^{89} +(1.45333 - 2.51724i) q^{91} +(2.79508 + 3.20896i) q^{92} +(3.74536 + 5.24532i) q^{94} +(0.471489 + 0.395626i) q^{95} +(-10.4801 - 3.81446i) q^{97} +(-5.25755 + 5.35542i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40}+ \cdots - 162 q^{98}+O(q^{100}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Character values

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

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	1.27615	−	0.609466i	0.902372	−	0.430957i
$2$	1.27615	−	0.609466i	0.902372	−	0.430957i
$3$		0			0
$3$		0			0
$4$	1.25710	−	1.55554i	0.628551	−	0.777768i
$5$	0.426624	−	0.155279i	0.190792	−	0.0694427i	−0.244857	−	0.969559i	$-0.578741\pi$
$5$	0.426624	−	0.155279i	0.190792	−	0.0694427i	0.435649	+	0.900116i	$0.356519\pi$
$6$		0			0
$7$	1.28150	−	0.225962i	0.484360	−	0.0854057i	0.0738642	−	0.997268i	$-0.476467\pi$
$7$	1.28150	−	0.225962i	0.484360	−	0.0854057i	0.410495	+	0.911863i	$0.365356\pi$
$8$	0.656202	−	2.75125i	0.232003	−	0.972715i
$9$		0			0
$10$	0.449799	−	0.458171i	0.142239	−	0.144887i
$11$	−0.00602720	+	0.0165596i	−0.00181727	+	0.00499290i	−0.940598	−	0.339522i	$-0.889735\pi$
$11$	−0.00602720	+	0.0165596i	−0.00181727	+	0.00499290i	0.938781	+	0.344515i	$0.111957\pi$
$12$		0			0
$13$	1.43581	−	1.71113i	0.398222	−	0.474582i	−0.529255	−	0.848463i	$-0.677529\pi$
$13$	1.43581	−	1.71113i	0.398222	−	0.474582i	0.927477	+	0.373881i	$0.121973\pi$
$14$	1.49766	−	1.06939i	0.400267	−	0.285806i
$15$		0			0
$16$	−0.839384	−	3.91094i	−0.209846	−	0.977734i
$17$	−1.27216	−	0.734483i	−0.308545	−	0.178138i	0.337730	−	0.941243i	$-0.390341\pi$
$17$	−1.27216	−	0.734483i	−0.308545	−	0.178138i	−0.646275	+	0.763105i	$0.723674\pi$
$18$		0			0
$19$	0.677841	+	1.17406i	0.155507	+	0.269347i	0.933244	−	0.359244i	$-0.116965\pi$
$19$	0.677841	+	1.17406i	0.155507	+	0.269347i	−0.777736	+	0.628591i	$0.783632\pi$
$20$	0.294769	−	0.858831i	0.0659124	−	0.192040i
$21$		0			0
$22$	0.00240091	+	0.0248058i	0.000511876	+	0.00528862i
$23$	−0.369486	+	2.09546i	−0.0770432	+	0.436933i	0.921748	+	0.387788i	$0.126761\pi$
$23$	−0.369486	+	2.09546i	−0.0770432	+	0.436933i	−0.998792	+	0.0491452i	$0.984350\pi$
$24$		0			0
$25$	−3.67233	+	3.08145i	−0.734465	+	0.616289i
$26$	0.789428	−	3.05873i	0.154820	−	0.599866i
$27$		0			0
$28$	1.25948	−	2.27747i	0.238019	−	0.430401i
$29$	5.56933	−	4.67322i	1.03420	−	0.867796i	0.0428540	−	0.999081i	$-0.486355\pi$
$29$	5.56933	−	4.67322i	1.03420	−	0.867796i	0.991345	+	0.131286i	$0.0419105\pi$
$30$		0			0
$31$	8.87753	+	1.56535i	1.59445	+	0.281145i	0.899172	−	0.437595i	$-0.144170\pi$
$31$	8.87753	+	1.56535i	1.59445	+	0.281145i	0.695279	+	0.718740i	$0.255281\pi$
$32$	−3.45476	−	4.47936i	−0.610721	−	0.791846i
$33$		0			0
$34$	−2.07111	−	0.161969i	−0.355192	−	0.0277775i
$35$	0.511630	−	0.295390i	0.0864813	−	0.0499300i
$36$		0			0
$37$	−4.58718	−	2.64841i	−0.754128	−	0.435396i	0.0730557	−	0.997328i	$-0.476725\pi$
$37$	−4.58718	−	2.64841i	−0.754128	−	0.435396i	−0.827183	+	0.561932i	$0.810058\pi$
$38$	1.58057	+	1.08515i	0.256403	+	0.176034i
$39$		0			0
$40$	−0.147259	−	1.27565i	−0.0232837	−	0.201697i
$41$	−1.56527	+	1.86542i	−0.244454	+	0.291329i	−0.874295	−	0.485395i	$-0.838676\pi$
$41$	−1.56527	+	1.86542i	−0.244454	+	0.291329i	0.629841	+	0.776724i	$0.283120\pi$
$42$		0			0
$43$	−10.1956	−	3.71089i	−1.55481	−	0.565906i	−0.585273	−	0.810836i	$-0.699013\pi$
$43$	−10.1956	−	3.71089i	−1.55481	−	0.565906i	−0.969541	+	0.244930i	$0.921235\pi$
$44$	0.0181822	+	0.0301926i	0.00274107	+	0.00455171i
$45$		0			0
$46$	0.805592	+	2.89930i	0.118778	+	0.427479i
$47$	0.791397	+	4.48824i	0.115437	+	0.654676i	0.986533	+	0.163563i	$0.0522988\pi$
$47$	0.791397	+	4.48824i	0.115437	+	0.654676i	−0.871096	+	0.491113i	$0.836590\pi$
$48$		0			0
$49$	−4.98668	+	1.81500i	−0.712382	+	0.259286i
$50$	−2.80839	+	6.17054i	−0.397166	+	0.872646i
$51$		0			0
$52$	−0.856765	−	4.38452i	−0.118812	−	0.608023i
$53$	10.4085			1.42972			0.714860	−	0.699267i	$-0.246490\pi$
$53$	10.4085			1.42972			0.714860	+	0.699267i	$0.246490\pi$
$54$		0			0
$55$			0.00800062i			0.00107880i
$56$	0.219241	−	3.67400i	0.0292973	−	0.490958i
$57$		0			0
$58$	4.25911	−	9.35804i	0.559249	−	1.22877i
$59$	3.75319	+	10.3118i	0.488624	+	1.34248i	0.901926	+	0.431890i	$0.142153\pi$
$59$	3.75319	+	10.3118i	0.488624	+	1.34248i	−0.413302	+	0.910594i	$0.635625\pi$
$60$		0			0
$61$	−8.87057	+	1.56412i	−1.13576	+	0.200265i	−0.709750	−	0.704453i	$-0.751192\pi$
$61$	−8.87057	+	1.56412i	−1.13576	+	0.200265i	−0.426010	+	0.904718i	$0.640081\pi$
$62$	12.2831	−	3.41294i	1.55995	−	0.433443i
$63$		0			0
$64$	−7.13880	−	3.61076i	−0.892350	−	0.451345i
$65$	0.346849	−	0.952961i	0.0430214	−	0.118200i
$66$		0			0
$67$	3.70041	+	3.10502i	0.452078	+	0.379338i	0.840206	−	0.542267i	$-0.182434\pi$
$67$	3.70041	+	3.10502i	0.452078	+	0.379338i	−0.388129	+	0.921605i	$0.626878\pi$
$68$	−2.74175	+	1.05557i	−0.332486	+	0.128007i
$69$		0			0
$70$	0.472885	−	0.688782i	0.0565206	−	0.0823252i
$71$	−5.03714	+	8.72458i	−0.597799	+	1.03542i	0.395347	+	0.918532i	$0.370624\pi$
$71$	−5.03714	+	8.72458i	−0.597799	+	1.03542i	−0.993145	+	0.116886i	$0.962709\pi$
$72$		0			0
$73$	−0.339460	−	0.587962i	−0.0397308	−	0.0688158i	0.845476	−	0.534013i	$-0.179317\pi$
$73$	−0.339460	−	0.587962i	−0.0397308	−	0.0688158i	−0.885207	+	0.465197i	$0.845983\pi$
$74$	−7.46803	−	0.584031i	−0.868141	−	0.0678922i
$75$		0			0
$76$	2.67840	+	0.421502i	0.307234	+	0.0483496i
$77$	−0.00398198	+	0.0225829i	−0.000453789	+	0.00257357i
$78$		0			0
$79$	5.19665	+	6.19313i	0.584669	+	0.696782i	0.974572	−	0.224074i	$-0.0719358\pi$
$79$	5.19665	+	6.19313i	0.584669	+	0.696782i	−0.389903	+	0.920856i	$0.627491\pi$
$80$	−0.965387	−	1.53816i	−0.107934	−	0.171972i
$81$		0			0
$82$	−0.860607	+	3.33452i	−0.0950382	+	0.368237i
$83$	−1.29122	−	1.53881i	−0.141729	−	0.168907i	0.690510	−	0.723323i	$-0.257386\pi$
$83$	−1.29122	−	1.53881i	−0.141729	−	0.168907i	−0.832240	+	0.554416i	$0.812942\pi$
$84$		0			0
$85$	−0.656785	−	0.115809i	−0.0712383	−	0.0125612i
$86$	−15.2727	+	1.47822i	−1.64690	+	0.159401i
$87$		0			0
$88$	0.0416046	+	0.0274488i	0.00443506	+	0.00292605i
$89$	0.103744	−	0.0598964i	0.0109968	−	0.00634901i	−0.494492	−	0.869182i	$-0.664646\pi$
$89$	0.103744	−	0.0598964i	0.0109968	−	0.00634901i	0.505488	+	0.862833i	$0.331312\pi$
$90$		0			0
$91$	1.45333	−	2.51724i	0.152351	−	0.263879i
$92$	2.79508	+	3.20896i	0.291407	+	0.334557i
$93$		0			0
$94$	3.74536	+	5.24532i	0.386305	+	0.541013i
$95$	0.471489	+	0.395626i	0.0483738	+	0.0405904i
$96$		0			0
$97$	−10.4801	−	3.81446i	−1.06410	−	0.387299i	−0.250130	−	0.968212i	$-0.580474\pi$
$97$	−10.4801	−	3.81446i	−1.06410	−	0.387299i	−0.813966	+	0.580913i	$0.802696\pi$
$98$	−5.25755	+	5.35542i	−0.531093	+	0.540979i
$99$		0			0
$100$	0.176811	+	9.58613i	0.0176811	+	0.958613i
$101$	−2.89743	−	16.4321i	−0.288305	−	1.63506i	−0.693237	−	0.720710i	$-0.743816\pi$
$101$	−2.89743	−	16.4321i	−0.288305	−	1.63506i	0.404932	−	0.914347i	$-0.367295\pi$
$102$		0			0
$103$	5.45676	+	14.9923i	0.537670	+	1.47724i	0.849753	+	0.527182i	$0.176751\pi$
$103$	5.45676	+	14.9923i	0.537670	+	1.47724i	−0.312082	+	0.950055i	$0.601026\pi$
$104$	−3.76557	−	5.07312i	−0.369245	−	0.497461i
$105$		0			0
$106$	13.2828	−	6.34364i	1.29014	−	0.616149i
$107$			6.73607i			0.651200i	0.945508	+	0.325600i	$0.105566\pi$
$107$			6.73607i			0.651200i	−0.945508	+	0.325600i	$0.894434\pi$
$108$		0			0
$109$			2.91699i			0.279397i	0.990194	+	0.139699i	$0.0446134\pi$
$109$			2.91699i			0.279397i	−0.990194	+	0.139699i	$0.955387\pi$
$110$	0.00487610	+	0.0102100i	0.000464918	+	0.000973482i
$111$		0			0
$112$	−1.95939	−	4.82218i	−0.185145	−	0.455653i
$113$	6.67148	+	18.3297i	0.627600	+	1.72432i	0.687572	+	0.726116i	$0.258677\pi$
$113$	6.67148	+	18.3297i	0.627600	+	1.72432i	−0.0599724	+	0.998200i	$0.519101\pi$
$114$		0			0
$115$	0.167748	+	0.951347i	0.0156426	+	0.0887136i
$116$	−0.268145	−	14.5380i	−0.0248967	−	1.34982i
$117$		0			0
$118$	11.0743	+	10.8719i	1.01947	+	1.00084i
$119$	−1.79623	−	0.653776i	−0.164661	−	0.0599315i
$120$		0			0
$121$	8.42625	+	7.07046i	0.766023	+	0.642769i
$122$	−10.3669	+	7.40236i	−0.938573	+	0.670178i
$123$		0			0
$124$	13.5949	−	11.8415i	1.22086	−	1.06340i
$125$	−2.22323	+	3.85075i	−0.198852	+	0.344422i
$126$		0			0
$127$	−14.9938	+	8.65666i	−1.33048	+	0.768154i	−0.985373	−	0.170409i	$-0.945491\pi$
$127$	−14.9938	+	8.65666i	−1.33048	+	0.768154i	−0.345108	+	0.938563i	$0.612158\pi$
$128$	−11.3108	−	0.257006i	−0.999742	−	0.0227164i
$129$		0			0
$130$	−0.138166	−	1.42751i	−0.0121180	−	0.125201i
$131$	3.03491	+	0.535137i	0.265162	+	0.0467552i	0.304648	−	0.952465i	$-0.401461\pi$
$131$	3.03491	+	0.535137i	0.265162	+	0.0467552i	−0.0394865	+	0.999220i	$0.512572\pi$
$132$		0			0
$133$	1.13394	+	1.35138i	0.0983252	+	0.117179i
$134$	6.61467	+	1.70718i	0.571421	+	0.147478i
$135$		0			0
$136$	−2.85554	+	3.01807i	−0.244861	+	0.258797i
$137$	−7.57425	−	9.02665i	−0.647112	−	0.771198i	0.338363	−	0.941016i	$-0.390127\pi$
$137$	−7.57425	−	9.02665i	−0.647112	−	0.771198i	−0.985476	+	0.169817i	$0.945682\pi$
$138$		0			0
$139$	−0.930383	+	5.27646i	−0.0789140	+	0.447544i	0.919591	+	0.392878i	$0.128520\pi$
$139$	−0.930383	+	5.27646i	−0.0789140	+	0.447544i	−0.998505	+	0.0546659i	$0.982591\pi$
$140$	0.183682	−	1.16719i	0.0155240	−	0.0986459i
$141$		0			0
$142$	−1.11080	+	14.2038i	−0.0932160	+	1.19196i
$143$	0.0196817	+	0.0340897i	0.00164587	+	0.00285073i
$144$		0			0
$145$	1.65036	−	2.85851i	0.137055	−	0.237386i
$146$	−0.791544	−	0.543437i	−0.0655086	−	0.0449752i
$147$		0			0
$148$	−9.88625	+	3.80620i	−0.812645	+	0.312868i
$149$	−10.9918	−	9.22325i	−0.900486	−	0.755598i	0.0697991	−	0.997561i	$-0.477764\pi$
$149$	−10.9918	−	9.22325i	−0.900486	−	0.755598i	−0.970285	+	0.241963i	$0.922209\pi$
$150$		0			0
$151$	4.06790	−	11.1765i	0.331041	−	0.909528i	−0.656800	−	0.754065i	$-0.728091\pi$
$151$	4.06790	−	11.1765i	0.331041	−	0.909528i	0.987842	−	0.155464i	$-0.0496872\pi$
$152$	3.67492	−	1.09450i	0.298076	−	0.0887753i
$153$		0			0
$154$	0.00868194	+	0.0312460i	0.000699610	+	0.00251788i
$155$	4.03044	−	0.710675i	0.323733	−	0.0570828i
$156$		0			0
$157$	−5.75062	−	15.7997i	−0.458950	−	1.26095i	−0.926268	−	0.376865i	$-0.877002\pi$
$157$	−5.75062	−	15.7997i	−0.458950	−	1.26095i	0.467319	−	0.884089i	$-0.345220\pi$
$158$	10.4062	+	4.73616i	0.827873	+	0.376789i
$159$		0			0
$160$	−2.16943	−	1.37455i	−0.171509	−	0.108668i
$161$			2.76881i			0.218213i
$162$		0			0
$163$	10.1776			0.797169			0.398585	−	0.917132i	$-0.369502\pi$
$163$	10.1776			0.797169			0.398585	+	0.917132i	$0.369502\pi$
$164$	0.934016	+	4.77985i	0.0729344	+	0.373244i
$165$		0			0
$166$	−2.58564	−	1.17680i	−0.200684	−	0.0913372i
$167$	15.0723	−	5.48587i	1.16633	−	0.424509i	0.314975	−	0.949100i	$-0.398004\pi$
$167$	15.0723	−	5.48587i	1.16633	−	0.424509i	0.851355	+	0.524591i	$0.175782\pi$
$168$		0			0
$169$	1.39101	+	7.88879i	0.107000	+	0.606830i
$170$	−0.908736	+	0.252499i	−0.0696968	+	0.0193658i
$171$		0			0
$172$	−18.5893	+	11.1946i	−1.41742	+	0.853584i
$173$	−12.7203	−	4.62982i	−0.967109	−	0.351999i	−0.190293	−	0.981727i	$-0.560944\pi$
$173$	−12.7203	−	4.62982i	−0.967109	−	0.351999i	−0.776815	+	0.629729i	$0.783166\pi$
$174$		0			0
$175$	−4.00978	+	4.77867i	−0.303111	+	0.361233i
$176$	0.0698226	+	0.00967213i	0.00526308	+	0.000729064i
$177$		0			0
$178$	0.0958874	−	0.139665i	0.00718706	−	0.0104683i
$179$	−9.84897	−	5.68630i	−0.736146	−	0.425014i	0.0845201	−	0.996422i	$-0.473064\pi$
$179$	−9.84897	−	5.68630i	−0.736146	−	0.425014i	−0.820667	+	0.571407i	$0.806398\pi$
$180$		0			0
$181$	12.8369	−	7.41138i	0.954159	−	0.550884i	0.0597883	−	0.998211i	$-0.480957\pi$
$181$	12.8369	−	7.41138i	0.954159	−	0.550884i	0.894370	+	0.447327i	$0.147624\pi$
$182$	0.320491	−	4.09813i	0.0237564	−	0.303774i
$183$		0			0
$184$	5.52268	+	2.39159i	0.407138	+	0.176311i
$185$	−2.36824	−	0.417585i	−0.174117	−	0.0307015i
$186$		0			0
$187$	0.0198303	−	0.0166396i	0.00145014	−	0.00121681i
$188$	7.97648	+	4.41113i	0.581745	+	0.321715i
$189$		0			0
$190$	0.842810	+	0.217521i	0.0611439	+	0.0157806i
$191$	−14.4389	+	12.1157i	−1.04476	+	0.876659i	−0.992533	−	0.121976i	$-0.961077\pi$
$191$	−14.4389	+	12.1157i	−1.04476	+	0.876659i	−0.0522283	+	0.998635i	$0.516632\pi$
$192$		0			0
$193$	−0.366460	+	2.07830i	−0.0263783	+	0.149599i	−0.995152	−	0.0983471i	$-0.968644\pi$
$193$	−0.366460	+	2.07830i	−0.0263783	+	0.149599i	0.968774	+	0.247946i	$0.0797556\pi$
$194$	−15.6990	+	1.51947i	−1.12712	+	0.109092i
$195$		0			0
$196$	−3.44547	+	10.0386i	−0.246105	+	0.717043i
$197$	5.72884	+	9.92264i	0.408163	+	0.706959i	0.994684	−	0.102975i	$-0.0328362\pi$
$197$	5.72884	+	9.92264i	0.408163	+	0.706959i	−0.586521	+	0.809934i	$0.699503\pi$
$198$		0			0
$199$	−4.92181	−	2.84161i	−0.348898	−	0.201436i	0.315302	−	0.948991i	$-0.397894\pi$
$199$	−4.92181	−	2.84161i	−0.348898	−	0.201436i	−0.664200	+	0.747555i	$0.731228\pi$
$200$	6.06805	+	12.1256i	0.429076	+	0.857406i
$201$		0			0
$202$	−13.7124	−	19.2039i	−0.964798	−	1.35118i
$203$	6.08110	−	7.24717i	0.426809	−	0.508652i
$204$		0			0
$205$	−0.378123	+	1.03889i	−0.0264093	+	0.0725589i
$206$	16.1009	+	15.8067i	1.12180	+	1.10130i
$207$		0			0
$208$	−7.89732	−	4.17906i	−0.547581	−	0.289766i
$209$	−0.0235273	+	0.00414851i	−0.00162742	+	0.000286958i
$210$		0			0
$211$	15.6412	−	5.69295i	1.07679	−	0.391919i	0.258077	−	0.966124i	$-0.416911\pi$
$211$	15.6412	−	5.69295i	1.07679	−	0.391919i	0.818711	+	0.574206i	$0.194689\pi$
$212$	13.0846	−	16.1908i	0.898653	−	1.11199i
$213$		0			0
$214$	4.10540	+	8.59621i	0.280640	+	0.587625i
$215$	−4.92591			−0.335945
$216$		0			0
$217$	11.7302			0.796300
$218$	1.77781	+	3.72251i	0.120408	+	0.252120i
$219$		0			0
$220$	0.0124453	+	0.0100576i	0.000839059	+	0.000678083i
$221$	−3.08338	+	1.12226i	−0.207410	+	0.0754912i
$222$		0			0
$223$	2.73564	−	0.482367i	0.183192	−	0.0323017i	−0.0812995	−	0.996690i	$-0.525907\pi$
$223$	2.73564	−	0.482367i	0.183192	−	0.0323017i	0.264491	+	0.964388i	$0.414796\pi$
$224$	−5.43942	−	4.95963i	−0.363437	−	0.331379i
$225$		0			0
$226$	19.6851	+	19.3254i	1.30944	+	1.28551i
$227$	8.45693	−	23.2352i	0.561306	−	1.54218i	−0.256418	−	0.966566i	$-0.582542\pi$
$227$	8.45693	−	23.2352i	0.561306	−	1.54218i	0.817724	−	0.575611i	$-0.195236\pi$
$228$		0			0
$229$	10.0744	−	12.0062i	0.665736	−	0.793393i	−0.322461	−	0.946583i	$-0.604510\pi$
$229$	10.0744	−	12.0062i	0.665736	−	0.793393i	0.988197	+	0.153190i	$0.0489546\pi$
$230$	0.793885	+	1.11182i	0.0523472	+	0.0733114i
$231$		0			0
$232$	−9.20261	−	18.3892i	−0.604181	−	1.20731i
$233$	−17.5198	−	10.1151i	−1.14776	−	0.662659i	−0.199419	−	0.979914i	$-0.563906\pi$
$233$	−17.5198	−	10.1151i	−1.14776	−	0.662659i	−0.948340	+	0.317255i	$0.897239\pi$
$234$		0			0
$235$	1.03456	+	1.79190i	0.0674870	+	0.116891i
$236$	20.7585	+	7.12478i	1.35127	+	0.463784i
$237$		0			0
$238$	−2.69071	+	0.260429i	−0.174413	+	0.0168811i
$239$	1.48780	−	8.43773i	0.0962378	−	0.545791i	−0.898123	−	0.439744i	$-0.855069\pi$
$239$	1.48780	−	8.43773i	0.0962378	−	0.545791i	0.994361	−	0.106048i	$-0.0338196\pi$
$240$		0			0
$241$	11.0727	−	9.29110i	0.713255	−	0.598492i	−0.212255	−	0.977214i	$-0.568081\pi$
$241$	11.0727	−	9.29110i	0.713255	−	0.598492i	0.925510	+	0.378722i	$0.123636\pi$
$242$	15.0623	+	3.88744i	0.968244	+	0.249894i
$243$		0			0
$244$	−8.71818	+	15.7648i	−0.558124	+	1.00924i
$245$	−1.84561	+	1.54865i	−0.117912	+	0.0989395i
$246$		0			0
$247$	2.98221	+	0.525844i	0.189754	+	0.0334587i
$248$	10.1321	−	23.3972i	0.643391	−	1.48572i
$249$		0			0
$250$	−0.490270	+	6.26911i	−0.0310074	+	0.396493i
$251$	−12.7128	+	7.33976i	−0.802427	+	0.463281i	−0.844319	−	0.535841i	$-0.819995\pi$
$251$	−12.7128	+	7.33976i	−0.802427	+	0.463281i	0.0418921	+	0.999122i	$0.486661\pi$
$252$		0			0
$253$	−0.0324730	−	0.0187483i	−0.00204156	−	0.00117869i
$254$	−13.8583	+	20.1854i	−0.869548	+	1.26654i
$255$		0			0
$256$	−14.5909	+	6.56556i	−0.911929	+	0.410348i
$257$	14.4703	−	17.2450i	0.902633	−	1.07572i	−0.0941497	−	0.995558i	$-0.530013\pi$
$257$	14.4703	−	17.2450i	0.902633	−	1.07572i	0.996782	−	0.0801575i	$-0.0255423\pi$
$258$		0			0
$259$	−6.47689	−	2.35739i	−0.402454	−	0.146481i
$260$	−1.04634	−	1.73751i	−0.0648912	−	0.107756i
$261$		0			0
$262$	4.19914	−	1.16676i	0.259424	−	0.0720828i
$263$	3.07511	+	17.4398i	0.189620	+	1.07539i	0.919875	+	0.392212i	$0.128290\pi$
$263$	3.07511	+	17.4398i	0.189620	+	1.07539i	−0.730255	+	0.683175i	$0.760599\pi$
$264$		0			0
$265$	4.44053	−	1.61622i	0.272780	−	0.0992836i
$266$	2.27070	+	1.03346i	0.139225	+	0.0633655i
$267$		0			0
$268$	9.48177	−	1.85280i	0.579191	−	0.113178i
$269$	10.2475			0.624803			0.312402	−	0.949950i	$-0.398867\pi$
$269$	10.2475			0.624803			0.312402	+	0.949950i	$0.398867\pi$
$270$		0			0
$271$		−	18.7315i		−	1.13786i	−0.822386	−	0.568929i	$-0.807358\pi$
$271$		−	18.7315i		−	1.13786i	0.822386	−	0.568929i	$-0.192642\pi$
$272$	−1.80468	+	5.59186i	−0.109425	+	0.339056i
$273$		0			0
$274$	−15.1673	−	6.90308i	−0.916290	−	0.417030i
$275$	−0.0288937	−	0.0793847i	−0.00174235	−	0.00478708i
$276$		0			0
$277$	−21.4560	+	3.78327i	−1.28917	+	0.227315i	−0.775868	−	0.630895i	$-0.782688\pi$
$277$	−21.4560	+	3.78327i	−1.28917	+	0.227315i	−0.513299	+	0.858210i	$0.671577\pi$
$278$	2.02852	+	7.30058i	0.121662	+	0.437860i
$279$		0			0
$280$	−0.476959	−	1.60146i	−0.0285038	−	0.0957055i
$281$	3.95262	−	10.8597i	0.235793	−	0.647837i	−0.764203	−	0.644976i	$-0.776867\pi$
$281$	3.95262	−	10.8597i	0.235793	−	0.647837i	0.999996	−	0.00286067i	$-0.000910580\pi$
$282$		0			0
$283$	−3.28791	−	2.75888i	−0.195446	−	0.163998i	0.539813	−	0.841785i	$-0.318495\pi$
$283$	−3.28791	−	2.75888i	−0.195446	−	0.163998i	−0.735259	+	0.677786i	$0.762939\pi$
$284$	7.23920	+	18.8032i	0.429567	+	1.11576i
$285$		0			0
$286$	0.0458933	+	0.0315082i	0.00271373	+	0.00186312i
$287$	−1.58437	+	2.74421i	−0.0935226	+	0.161986i
$288$		0			0
$289$	−7.42107	−	12.8537i	−0.436533	−	0.756098i
$290$	0.363940	−	4.65372i	0.0213713	−	0.273276i
$291$		0			0
$292$	−1.34133	−	0.211087i	−0.0784956	−	0.0123529i
$293$	−2.18285	+	12.3796i	−0.127523	+	0.723221i	0.852254	+	0.523129i	$0.175235\pi$
$293$	−2.18285	+	12.3796i	−0.127523	+	0.723221i	−0.979777	+	0.200092i	$0.935876\pi$
$294$		0			0
$295$	3.20241	+	3.81648i	0.186451	+	0.222204i
$296$	−10.2966	+	10.8826i	−0.598476	+	0.632538i
$297$		0			0
$298$	−19.6485	−	5.07107i	−1.13820	−	0.293759i
$299$	3.05509	+	3.64092i	0.176681	+	0.210560i
$300$		0			0
$301$	−13.9041	−	2.45167i	−0.801421	−	0.141312i
$302$	−1.62043	−	16.7421i	−0.0932455	−	0.963398i
$303$		0			0
$304$	4.02269	−	3.63648i	0.230717	−	0.208566i
$305$	−3.54153	+	2.04470i	−0.202787	+	0.117079i
$306$		0			0
$307$	7.46768	−	12.9344i	0.426203	−	0.738205i	−0.570329	−	0.821416i	$-0.693184\pi$
$307$	7.46768	−	12.9344i	0.426203	−	0.738205i	0.996532	+	0.0832113i	$0.0265176\pi$
$308$	0.0301228	+	0.0345832i	0.00171641	+	0.00197056i
$309$		0			0
$310$	4.71030	−	3.36334i	0.267527	−	0.191025i
$311$	0.935160	+	0.784692i	0.0530280	+	0.0444958i	0.668916	−	0.743338i	$-0.266758\pi$
$311$	0.935160	+	0.784692i	0.0530280	+	0.0444958i	−0.615888	+	0.787833i	$0.711203\pi$
$312$		0			0
$313$	−3.74180	−	1.36190i	−0.211499	−	0.0769794i	0.234098	−	0.972213i	$-0.424786\pi$
$313$	−3.74180	−	1.36190i	−0.211499	−	0.0769794i	−0.445597	+	0.895234i	$0.647009\pi$
$314$	−16.9680	−	16.6579i	−0.957561	−	0.940062i
$315$		0			0
$316$	16.1664	−	0.298179i	0.909429	−	0.0167739i
$317$	−1.28552	−	7.29053i	−0.0722018	−	0.409477i	−0.999391	−	0.0348844i	$-0.988894\pi$
$317$	−1.28552	−	7.29053i	−0.0722018	−	0.409477i	0.927190	−	0.374593i	$-0.122217\pi$
$318$		0			0
$319$	0.0438192	+	0.120392i	0.00245340	+	0.00674067i
$320$	−3.60626	−	0.431935i	−0.201596	−	0.0241459i
$321$		0			0
$322$	1.68750	+	3.53341i	0.0940404	+	0.196909i
$323$		−	1.99145i		−	0.110807i
$324$		0			0
$325$			10.7082i			0.593984i
$326$	12.9881	−	6.20288i	0.719343	−	0.343546i
$327$		0			0
$328$	4.10510	+	5.53055i	0.226666	+	0.305373i
$329$	2.02834	+	5.57283i	0.111826	+	0.307240i
$330$		0			0
$331$	0.520452	+	2.95163i	0.0286066	+	0.162236i	0.995765	−	0.0919400i	$-0.0293068\pi$
$331$	0.520452	+	2.95163i	0.0286066	+	0.162236i	−0.967158	+	0.254176i	$0.918196\pi$
$332$	−4.01687	+	0.0740888i	−0.220454	+	0.00406615i
$333$		0			0
$334$	15.8910	−	16.1868i	0.869518	−	0.885704i
$335$	2.06083	+	0.750081i	0.112595	+	0.0409813i
$336$		0			0
$337$	−10.0788	−	8.45709i	−0.549025	−	0.460687i	0.325586	−	0.945513i	$-0.394439\pi$
$337$	−10.0788	−	8.45709i	−0.549025	−	0.460687i	−0.874611	+	0.484826i	$0.838883\pi$
$338$	6.58307	+	9.21948i	0.358072	+	0.501474i
$339$		0			0
$340$	−1.00579	+	0.876069i	−0.0545467	+	0.0475115i
$341$	−0.0794281	+	0.137574i	−0.00430127	+	0.00745003i
$342$		0			0
$343$	−13.8688	+	8.00714i	−0.748844	+	0.432345i
$344$	−16.9000	+	25.6156i	−0.911186	+	1.38110i
$345$		0			0
$346$	−19.0547	+	1.84427i	−1.02439	+	0.0991487i
$347$	−28.8369	−	5.08472i	−1.54804	−	0.272962i	−0.666660	−	0.745362i	$-0.732277\pi$
$347$	−28.8369	−	5.08472i	−1.54804	−	0.272962i	−0.881385	+	0.472400i	$0.843388\pi$
$348$		0			0
$349$	13.4766	+	16.0608i	0.721385	+	0.859713i	0.994765	−	0.102193i	$-0.0325859\pi$
$349$	13.4766	+	16.0608i	0.721385	+	0.859713i	−0.273380	+	0.961906i	$0.588141\pi$
$350$	−2.20463	+	8.54210i	−0.117843	+	0.456595i
$351$		0			0
$352$	0.0949988	−	0.0302114i	0.00506345	−	0.00161028i
$353$	−2.02760	−	2.41640i	−0.107918	−	0.128612i	0.709381	−	0.704825i	$-0.248974\pi$
$353$	−2.02760	−	2.41640i	−0.107918	−	0.128612i	−0.817300	+	0.576213i	$0.804530\pi$
$354$		0			0
$355$	−0.794226	+	4.50428i	−0.0421532	+	0.239062i
$356$	0.0372454	−	0.236673i	0.00197400	−	0.0125436i
$357$		0			0
$358$	−16.0343	−	1.25395i	−0.847441	−	0.0662734i
$359$	−15.2950	−	26.4917i	−0.807240	−	1.39818i	−0.914768	−	0.403979i	$-0.867627\pi$
$359$	−15.2950	−	26.4917i	−0.807240	−	1.39818i	0.107529	−	0.994202i	$-0.465706\pi$
$360$		0			0
$361$	8.58106	−	14.8628i	0.451635	−	0.782255i
$362$	11.8648	−	17.2817i	0.623599	−	0.908304i
$363$		0			0
$364$	−2.08868	−	5.42514i	−0.109476	−	0.284355i
$365$	−0.236120	−	0.198128i	−0.0123591	−	0.0103705i
$366$		0			0
$367$	7.65245	−	21.0249i	0.399455	−	1.09749i	−0.563096	−	0.826391i	$-0.690390\pi$
$367$	7.65245	−	21.0249i	0.399455	−	1.09749i	0.962551	−	0.271101i	$-0.0873878\pi$
$368$	8.50535	−	0.313859i	0.443372	−	0.0163610i
$369$		0			0
$370$	−3.27673	+	0.910464i	−0.170349	+	0.0473327i
$371$	13.3385	−	2.35193i	0.692499	−	0.122106i
$372$		0			0
$373$	−3.91132	−	10.7463i	−0.202521	−	0.556421i	0.796304	−	0.604897i	$-0.206786\pi$
$373$	−3.91132	−	10.7463i	−0.202521	−	0.556421i	−0.998824	+	0.0484764i	$0.984563\pi$
$374$	0.0151651	−	0.0333205i	0.000784170	−	0.00172296i
$375$		0			0
$376$	12.8676	+	0.767856i	0.663595	+	0.0395992i
$377$		−	16.2397i		−	0.836387i
$378$		0			0
$379$	−21.7004			−1.11468			−0.557338	−	0.830286i	$-0.688177\pi$
$379$	−21.7004			−1.11468			−0.557338	+	0.830286i	$0.688177\pi$
$380$	1.20812	−	0.236075i	0.0619753	−	0.0121104i
$381$		0			0
$382$	−11.0421	+	24.2614i	−0.564961	+	1.24132i
$383$	31.1726	−	11.3459i	1.59285	−	0.579749i	0.614900	−	0.788605i	$-0.289196\pi$
$383$	31.1726	−	11.3459i	1.59285	−	0.579749i	0.977946	+	0.208856i	$0.0669740\pi$
$384$		0			0
$385$	0.00180784	+	0.0102528i	9.21359e−5	+	0.000522529i
$386$	0.798994	+	2.87556i	0.0406677	+	0.146362i
$387$		0			0
$388$	−19.1081	+	11.5071i	−0.970068	+	0.584182i
$389$	6.54404	+	2.38183i	0.331796	+	0.120764i	0.502546	−	0.864551i	$-0.332397\pi$
$389$	6.54404	+	2.38183i	0.331796	+	0.120764i	−0.170750	+	0.985314i	$0.554619\pi$
$390$		0			0
$391$	2.00913	−	2.39438i	0.101606	−	0.121089i
$392$	1.72126	+	14.9106i	0.0869369	+	0.753100i
$393$		0			0
$394$	13.3584	+	9.17122i	0.672984	+	0.462039i
$395$	3.17868	+	1.83521i	0.159937	+	0.0923395i
$396$		0			0
$397$	31.8597	−	18.3942i	1.59899	−	0.923178i	0.607308	−	0.794466i	$-0.292249\pi$
$397$	31.8597	−	18.3942i	1.59899	−	0.923178i	0.991682	−	0.128712i	$-0.0410841\pi$
$398$	−8.01281	−	0.626635i	−0.401646	−	0.0314104i
$399$		0			0
$400$	15.1338	+	11.7757i	0.756692	+	0.588786i
$401$	−3.00611	−	0.530059i	−0.150118	−	0.0264699i	0.0980840	−	0.995178i	$-0.468729\pi$
$401$	−3.00611	−	0.530059i	−0.150118	−	0.0264699i	−0.248202	+	0.968708i	$0.579840\pi$
$402$		0			0
$403$	15.4250	−	12.9431i	0.768372	−	0.644740i
$404$	−29.2031	−	16.1498i	−1.45291	−	0.803483i
$405$		0			0
$406$	3.34347	−	12.9547i	0.165934	−	0.642930i
$407$	0.0715044	−	0.0599993i	0.00354434	−	0.00297406i
$408$		0			0
$409$	−4.18256	+	23.7205i	−0.206814	+	1.17290i	0.687745	+	0.725952i	$0.258601\pi$
$409$	−4.18256	+	23.7205i	−0.206814	+	1.17290i	−0.894559	+	0.446949i	$0.852511\pi$
$410$	0.150624	+	1.55622i	0.00743879	+	0.0768564i
$411$		0			0
$412$	30.1808	+	10.3587i	1.48690	+	0.510337i
$413$	7.13978	+	12.3665i	0.351326	+	0.608514i
$414$		0			0
$415$	−0.789809	−	0.455997i	−0.0387702	−	0.0223840i
$416$	−12.6251	−	0.519953i	−0.618998	−	0.0254928i
$417$		0			0
$418$	−0.0274960	+	0.0196332i	−0.00134487	+	0.000960292i
$419$	19.0854	−	22.7451i	0.932383	−	1.11117i	−0.0612068	−	0.998125i	$-0.519495\pi$
$419$	19.0854	−	22.7451i	0.932383	−	1.11117i	0.993590	−	0.113046i	$-0.0360607\pi$
$420$		0			0
$421$	−9.82045	+	26.9815i	−0.478619	+	1.31500i	0.432046	+	0.901851i	$0.357792\pi$
$421$	−9.82045	+	26.9815i	−0.478619	+	1.31500i	−0.910666	+	0.413144i	$0.864430\pi$
$422$	16.4909	−	16.7978i	0.802763	−	0.817706i
$423$		0			0
$424$	6.83010	−	28.6365i	0.331699	−	1.39071i
$425$	6.93506	−	1.22284i	0.336400	−	0.0593164i
$426$		0			0
$427$	−11.0142	+	4.00883i	−0.533013	+	0.194001i
$428$	10.4782	+	8.46793i	0.506483	+	0.409313i
$429$		0			0
$430$	−6.28619	+	3.00218i	−0.303147	+	0.144778i
$431$	−26.5585			−1.27928			−0.639639	−	0.768675i	$-0.720916\pi$
$431$	−26.5585			−1.27928			−0.639639	+	0.768675i	$0.720916\pi$
$432$		0			0
$433$	−1.55270			−0.0746180			−0.0373090	−	0.999304i	$-0.511879\pi$
$433$	−1.55270			−0.0746180			−0.0373090	+	0.999304i	$0.511879\pi$
$434$	14.9695	−	7.14917i	0.718559	−	0.343171i
$435$		0			0
$436$	4.53749	+	3.66696i	0.217306	+	0.175616i
$437$	−2.71064	+	0.986591i	−0.129667	+	0.0471951i
$438$		0			0
$439$	−1.13120	+	0.199460i	−0.0539891	+	0.00951973i	−0.200577	−	0.979678i	$-0.564282\pi$
$439$	−1.13120	+	0.199460i	−0.0539891	+	0.00951973i	0.146588	+	0.989198i	$0.453171\pi$
$440$	0.0220117	+	0.00525002i	0.00104937	+	0.000250285i
$441$		0			0
$442$	−3.25087	+	3.31138i	−0.154628	+	0.157506i
$443$	−5.79518	+	15.9221i	−0.275337	+	0.756483i	0.722538	+	0.691331i	$0.242975\pi$
$443$	−5.79518	+	15.9221i	−0.275337	+	0.756483i	−0.997875	+	0.0651518i	$0.979247\pi$
$444$		0			0
$445$	0.0349590	−	0.0416625i	0.00165721	−	0.00197499i
$446$	3.19709	−	2.28285i	0.151387	−	0.108096i
$447$		0			0
$448$	−9.96423	−	3.01407i	−0.470766	−	0.142401i
$449$	26.5725	+	15.3416i	1.25403	+	0.724017i	0.971908	−	0.235361i	$-0.0756272\pi$
$449$	26.5725	+	15.3416i	1.25403	+	0.724017i	0.282126	+	0.959377i	$0.408961\pi$
$450$		0			0
$451$	−0.0214563	−	0.0371634i	−0.00101034	−	0.00174996i
$452$	36.8993	+	12.6646i	1.73560	+	0.595694i
$453$		0			0
$454$	−3.36879	−	34.8058i	−0.158105	−	1.63352i
$455$	0.229153	−	1.29959i	0.0107428	−	0.0609257i
$456$		0			0
$457$	5.48725	−	4.60435i	0.256683	−	0.215382i	−0.505361	−	0.862908i	$-0.668641\pi$
$457$	5.48725	−	4.60435i	0.256683	−	0.215382i	0.762044	+	0.647526i	$0.224196\pi$
$458$	5.53905	−	21.4617i	0.258823	−	1.00284i
$459$		0			0
$460$	1.69073	+	0.935003i	0.0788308	+	0.0435948i
$461$	6.34887	−	5.32733i	0.295696	−	0.248119i	−0.482854	−	0.875701i	$-0.660400\pi$
$461$	6.34887	−	5.32733i	0.295696	−	0.248119i	0.778550	+	0.627582i	$0.215955\pi$
$462$		0			0
$463$	−0.381159	−	0.0672086i	−0.0177140	−	0.00312345i	0.164784	−	0.986330i	$-0.447307\pi$
$463$	−0.381159	−	0.0672086i	−0.0177140	−	0.00312345i	−0.182498	+	0.983206i	$0.558418\pi$
$464$	−22.9515	−	17.8587i	−1.06550	−	0.829068i
$465$		0			0
$466$	−28.5226	−	2.23059i	−1.32128	−	0.103330i
$467$	5.76908	−	3.33078i	0.266961	−	0.154130i	−0.360545	−	0.932742i	$-0.617409\pi$
$467$	5.76908	−	3.33078i	0.266961	−	0.154130i	0.627506	+	0.778612i	$0.284076\pi$
$468$		0			0
$469$	5.44368	+	3.14291i	0.251366	+	0.145126i
$470$	2.41235	+	1.65621i	0.111273	+	0.0763951i
$471$		0			0
$472$	30.8333	−	3.55935i	1.41922	−	0.163832i
$473$	0.122902	−	0.146469i	0.00565103	−	0.00673463i
$474$		0			0
$475$	−6.10704	−	2.22278i	−0.280210	−	0.101988i
$476$	−3.27502	+	1.97224i	−0.150110	+	0.0903977i
$477$		0			0
$478$	−3.24386	−	11.6745i	−0.148371	−	0.533981i
$479$	−0.196814	−	1.11619i	−0.00899268	−	0.0510000i	0.979981	−	0.199090i	$-0.0637986\pi$
$479$	−0.196814	−	1.11619i	−0.00899268	−	0.0510000i	−0.988974	+	0.148090i	$0.952687\pi$
$480$		0			0
$481$	−11.1181	+	4.04665i	−0.506941	+	0.184511i
$482$	8.46779	−	18.6052i	0.385697	−	0.847446i
$483$		0			0
$484$	21.5910	−	4.21904i	0.981410	−	0.191774i
$485$	−5.06338			−0.229916
$486$		0			0
$487$		−	41.9634i		−	1.90154i	−0.309896	−	0.950771i	$-0.600294\pi$
$487$		−	41.9634i		−	1.90154i	0.309896	−	0.950771i	$-0.399706\pi$
$488$	−1.51760	+	25.4316i	−0.0686983	+	1.15123i
$489$		0			0
$490$	−1.41142	+	3.10114i	−0.0637614	+	0.140095i
$491$	7.04382	+	19.3527i	0.317883	+	0.873377i	0.991003	+	0.133843i	$0.0427317\pi$
$491$	7.04382	+	19.3527i	0.317883	+	0.873377i	−0.673119	+	0.739534i	$0.735046\pi$
$492$		0			0
$493$	−10.5175	+	1.85452i	−0.473684	+	0.0835233i
$494$	4.12622	−	1.14650i	0.185648	−	0.0515835i
$495$		0			0
$496$	−1.32968	−	36.0334i	−0.0597045	−	1.61795i
$497$	−4.48365	+	12.3187i	−0.201119	+	0.552570i
$498$		0			0
$499$	7.68110	+	6.44521i	0.343853	+	0.288527i	0.798316	−	0.602239i	$-0.205724\pi$
$499$	7.68110	+	6.44521i	0.343853	+	0.288527i	−0.454463	+	0.890766i	$0.650169\pi$
$500$	3.19515	+	8.29911i	0.142891	+	0.371147i
$501$		0			0
$502$	−11.7501	+	17.1146i	−0.524433	+	0.763864i
$503$	12.3849	−	21.4513i	0.552216	−	0.956466i	−0.445898	−	0.895084i	$-0.647116\pi$
$503$	12.3849	−	21.4513i	0.552216	−	0.956466i	0.998114	−	0.0613824i	$-0.0195509\pi$
$504$		0			0
$505$	−3.78767	−	6.56044i	−0.168549	−	0.291936i
$506$	−0.0528667	−	0.00413440i	−0.00235021	−	0.000183796i
$507$		0			0
$508$	−5.38297	+	34.2057i	−0.238831	+	1.51763i
$509$	−5.29018	+	30.0021i	−0.234483	+	1.32982i	0.609217	+	0.793004i	$0.291484\pi$
$509$	−5.29018	+	30.0021i	−0.234483	+	1.32982i	−0.843700	+	0.536816i	$0.819627\pi$
$510$		0			0
$511$	−0.567874	−	0.676766i	−0.0251213	−	0.0299383i
$512$	−14.6186	+	17.2713i	−0.646057	+	0.763289i
$513$		0			0
$514$	7.95597	−	30.8264i	0.350923	−	1.35969i
$515$	4.65597	+	5.54877i	0.205167	+	0.244508i
$516$		0			0
$517$	−0.0790932	−	0.0139463i	−0.00347852	−	0.000613356i
$518$	−9.70221	+	0.939060i	−0.426291	+	0.0412599i
$519$		0			0
$520$	−2.39423	−	1.57961i	−0.104994	−	0.0692703i
$521$	2.67309	−	1.54331i	0.117110	−	0.0676136i	−0.440301	−	0.897850i	$-0.645128\pi$
$521$	2.67309	−	1.54331i	0.117110	−	0.0676136i	0.557411	+	0.830237i	$0.311795\pi$
$522$		0			0
$523$	−6.24198	+	10.8114i	−0.272943	+	0.472750i	−0.969614	−	0.244640i	$-0.921330\pi$
$523$	−6.24198	+	10.8114i	−0.272943	+	0.472750i	0.696671	+	0.717390i	$0.254664\pi$
$524$	4.64762	−	4.04820i	0.203032	−	0.176846i
$525$		0			0
$526$	14.5533	+	20.3816i	0.634553	+	0.888681i
$527$	−10.1439	−	8.51177i	−0.441877	−	0.370779i
$528$		0			0
$529$	17.3585	+	6.31798i	0.754717	+	0.274695i
$530$	4.68174	−	4.76889i	0.203362	−	0.207147i
$531$		0			0
$532$	3.52760	−	0.0650645i	0.152941	−	0.00282091i
$533$	0.944542	+	5.35676i	0.0409126	+	0.232027i
$534$		0			0
$535$	1.04597	+	2.87377i	0.0452211	+	0.124244i
$536$	10.9709	−	8.14326i	0.473871	−	0.351735i
$537$		0			0
$538$	13.0774	−	6.24552i	0.563805	−	0.269264i
$539$		−	0.0935167i		−	0.00402805i
$540$		0			0
$541$			35.0866i			1.50849i	0.656592	+	0.754246i	$0.271997\pi$
$541$			35.0866i			1.50849i	−0.656592	+	0.754246i	$0.728003\pi$
$542$	−11.4162	−	23.9042i	−0.490368	−	1.02677i
$543$		0			0
$544$	1.10500	+	8.23593i	0.0473767	+	0.353113i
$545$	0.452947	+	1.24446i	0.0194021	+	0.0533069i
$546$		0			0
$547$	−0.423952	−	2.40435i	−0.0181269	−	0.102803i	0.974402	−	0.224813i	$-0.0721771\pi$
$547$	−0.423952	−	2.40435i	−0.0181269	−	0.102803i	−0.992529	+	0.122010i	$0.961066\pi$
$548$	−23.5629	+	0.434604i	−1.00656	+	0.0185654i
$549$		0			0
$550$	−0.0852548	−	0.0836968i	−0.00363528	−	0.00356884i
$551$	9.26174	+	3.37100i	0.394563	+	0.143609i
$552$		0			0
$553$	8.05890	+	6.76222i	0.342699	+	0.287559i
$554$	−25.0752	+	17.9047i	−1.06535	+	0.760699i
$555$		0			0
$556$	7.03814	+	8.08030i	0.298484	+	0.342681i
$557$	3.41195	−	5.90968i	0.144569	−	0.250401i	−0.784643	−	0.619948i	$-0.787154\pi$
$557$	3.41195	−	5.90968i	0.144569	−	0.250401i	0.929212	+	0.369547i	$0.120487\pi$
$558$		0			0
$559$	−20.9888	+	12.1179i	−0.887730	+	0.512531i
$560$	−1.58471	−	1.75301i	−0.0669660	−	0.0740781i
$561$		0			0
$562$	−1.57451	−	16.2676i	−0.0664167	−	0.686207i
$563$	−20.6520	−	3.64150i	−0.870377	−	0.153471i	−0.279415	−	0.960170i	$-0.590141\pi$
$563$	−20.6520	−	3.64150i	−0.870377	−	0.153471i	−0.590962	+	0.806699i	$0.701252\pi$
$564$		0			0
$565$	5.69243	+	6.78397i	0.239482	+	0.285404i
$566$	−5.87730	−	1.51687i	−0.247041	−	0.0637589i
$567$		0			0
$568$	20.6982	+	19.5835i	0.868476	+	0.821707i
$569$	20.8313	+	24.8258i	0.873295	+	1.04075i	0.998815	+	0.0486610i	$0.0154954\pi$
$569$	20.8313	+	24.8258i	0.873295	+	1.04075i	−0.125521	+	0.992091i	$0.540060\pi$
$570$		0			0
$571$	−0.396543	+	2.24891i	−0.0165948	+	0.0941139i	−0.991980	−	0.126393i	$-0.959660\pi$
$571$	−0.396543	+	2.24891i	−0.0165948	+	0.0941139i	0.975385	+	0.220507i	$0.0707711\pi$
$572$	0.0777697	+	0.0122387i	0.00325172	+	0.000511725i
$573$		0			0
$574$	−0.349388	+	4.46764i	−0.0145832	+	0.186476i
$575$	−5.10017	−	8.83376i	−0.212692	−	0.368393i
$576$		0			0
$577$	−10.7395	+	18.6014i	−0.447092	+	0.774387i	−0.998195	−	0.0600507i	$-0.980874\pi$
$577$	−10.7395	+	18.6014i	−0.447092	+	0.774387i	0.551103	+	0.834437i	$0.314207\pi$
$578$	−17.3042	−	11.8803i	−0.719762	−	0.494155i
$579$		0			0
$580$	−2.37184	−	6.16064i	−0.0984853	−	0.255806i
$581$	−2.00240	−	1.68021i	−0.0830736	−	0.0697070i
$582$		0			0
$583$	−0.0627342	+	0.172361i	−0.00259818	+	0.00713845i
$584$	−1.84039	+	0.548119i	−0.0761558	+	0.0226813i
$585$		0			0
$586$	4.75928	+	17.1285i	0.196604	+	0.707572i
$587$	−18.6609	+	3.29041i	−0.770216	+	0.135810i	−0.544928	−	0.838483i	$-0.683443\pi$
$587$	−18.6609	+	3.29041i	−0.770216	+	0.135810i	−0.225287	+	0.974292i	$0.572332\pi$
$588$		0			0
$589$	4.17975	+	11.4838i	0.172224	+	0.473180i
$590$	6.41276	+	2.91863i	0.264009	+	0.120158i
$591$		0			0
$592$	−6.50736	+	20.1632i	−0.267451	+	0.828703i
$593$			23.6650i			0.971804i	0.874013	+	0.485902i	$0.161509\pi$
$593$			23.6650i			0.971804i	−0.874013	+	0.485902i	$0.838491\pi$
$594$		0			0
$595$	−0.867835			−0.0355778
$596$	−28.1650	+	5.50363i	−1.15368	+	0.225437i
$597$		0			0
$598$	6.11776	+	2.78437i	0.250174	+	0.113861i
$599$	8.37844	−	3.04950i	0.342334	−	0.124599i	−0.165131	−	0.986272i	$-0.552805\pi$
$599$	8.37844	−	3.04950i	0.342334	−	0.124599i	0.507465	+	0.861672i	$0.330583\pi$
$600$		0			0
$601$	4.44934	+	25.2334i	0.181492	+	1.02929i	0.930380	+	0.366597i	$0.119477\pi$
$601$	4.44934	+	25.2334i	0.181492	+	1.02929i	−0.748888	+	0.662697i	$0.769412\pi$
$602$	−19.2379	+	5.34540i	−0.784080	+	0.217862i
$603$		0			0
$604$	−12.2716	−	20.3777i	−0.499326	−	0.829159i
$605$	4.69274	+	1.70802i	0.190787	+	0.0694407i
$606$		0			0
$607$	−8.91382	+	10.6231i	−0.361801	+	0.431177i	−0.915982	−	0.401218i	$-0.868587\pi$
$607$	−8.91382	+	10.6231i	−0.361801	+	0.431177i	0.554182	+	0.832396i	$0.313031\pi$
$608$	2.91723	−	7.09237i	0.118309	−	0.287634i
$609$		0			0
$610$	−3.27334	+	4.76778i	−0.132533	+	0.193042i
$611$	8.81625	+	5.09007i	0.356667	+	0.205922i
$612$		0			0
$613$	17.7329	−	10.2381i	0.716224	−	0.413512i	−0.0971374	−	0.995271i	$-0.530969\pi$
$613$	17.7329	−	10.2381i	0.716224	−	0.413512i	0.813361	+	0.581759i	$0.197635\pi$
$614$	1.64678	−	21.0575i	0.0664587	−	0.849811i
$615$		0			0
$616$	0.0595184	+	0.0257744i	0.00239807	+	0.00103848i
$617$	−45.9610	−	8.10416i	−1.85032	−	0.326261i	−0.865644	−	0.500660i	$-0.833091\pi$
$617$	−45.9610	−	8.10416i	−1.85032	−	0.326261i	−0.984675	+	0.174399i	$0.944202\pi$
$618$		0			0
$619$	−20.3900	+	17.1092i	−0.819542	+	0.687678i	−0.952865	−	0.303395i	$-0.901880\pi$
$619$	−20.3900	+	17.1092i	−0.819542	+	0.687678i	0.133323	+	0.991073i	$0.457435\pi$
$620$	3.96119	−	7.16288i	0.159085	−	0.287668i
$621$		0			0
$622$	1.67164	+	0.431435i	0.0670268	+	0.0172990i
$623$	0.119413	−	0.100199i	0.00478417	−	0.00401439i
$624$		0			0
$625$	3.81170	−	21.6172i	0.152468	−	0.864688i
$626$	−5.60513	+	0.542510i	−0.224026	+	0.0216831i
$627$		0			0
$628$	−31.8061	−	10.9166i	−1.26920	−	0.435618i
$629$	3.89042	+	6.73841i	0.155121	+	0.268678i
$630$		0			0
$631$	24.6191	+	14.2138i	0.980071	+	0.565844i	0.902292	−	0.431126i	$-0.141884\pi$
$631$	24.6191	+	14.2138i	0.980071	+	0.565844i	0.0777793	+	0.996971i	$0.475217\pi$
$632$	20.4489	−	10.2334i	0.813415	−	0.407062i
$633$		0			0
$634$	−6.08384	−	8.52031i	−0.241620	−	0.338385i
$635$	−5.05252	+	6.02135i	−0.200503	+	0.238950i
$636$		0			0
$637$	−4.05421	+	11.1389i	−0.160634	+	0.441337i
$638$	0.129295	+	0.126932i	0.00511882	+	0.00502528i
$639$		0			0
$640$	−4.86537	+	1.64668i	−0.192321	+	0.0650907i
$641$	−19.2764	+	3.39896i	−0.761373	+	0.134251i	−0.540836	−	0.841128i	$-0.681892\pi$
$641$	−19.2764	+	3.39896i	−0.761373	+	0.134251i	−0.220537	+	0.975379i	$0.570781\pi$
$642$		0			0
$643$	−10.2317	+	3.72402i	−0.403497	+	0.146861i	−0.535793	−	0.844349i	$-0.679987\pi$
$643$	−10.2317	+	3.72402i	−0.403497	+	0.146861i	0.132296	+	0.991210i	$0.457765\pi$
$644$	4.30698	+	3.48068i	0.169719	+	0.137158i
$645$		0			0
$646$	−1.21372	−	2.54138i	−0.0477532	−	0.0999894i
$647$	−19.0202			−0.747763			−0.373881	−	0.927477i	$-0.621973\pi$
$647$	−19.0202			−0.747763			−0.373881	+	0.927477i	$0.621973\pi$
$648$		0			0
$649$	−0.193381			−0.00759085
$650$	6.52628	+	13.6652i	0.255982	+	0.535995i
$651$		0			0
$652$	12.7943	−	15.8316i	0.501062	−	0.620013i
$653$	−11.7763	+	4.28623i	−0.460843	+	0.167733i	−0.562000	−	0.827137i	$-0.689968\pi$
$653$	−11.7763	+	4.28623i	−0.460843	+	0.167733i	0.101157	+	0.994871i	$0.467746\pi$
$654$		0			0
$655$	1.37786	−	0.242955i	0.0538376	−	0.00949302i
$656$	8.60939	+	4.55587i	0.336140	+	0.177877i
$657$		0			0
$658$	5.98491	+	5.87554i	0.233316	+	0.229052i
$659$	−9.65592	+	26.5294i	−0.376141	+	1.03344i	0.596801	+	0.802389i	$0.296438\pi$
$659$	−9.65592	+	26.5294i	−0.376141	+	1.03344i	−0.972942	+	0.231050i	$0.925784\pi$
$660$		0			0
$661$	−10.6735	+	12.7202i	−0.415150	+	0.494757i	−0.932577	−	0.360971i	$-0.882445\pi$
$661$	−10.6735	+	12.7202i	−0.415150	+	0.494757i	0.517427	+	0.855727i	$0.326890\pi$
$662$	2.46309	+	3.44952i	0.0957307	+	0.134069i
$663$		0			0
$664$	−5.08096	+	2.54269i	−0.197180	+	0.0986756i
$665$	0.693608	+	0.400455i	0.0268970	+	0.0155290i
$666$		0			0
$667$	7.73476	+	13.3970i	0.299491	+	0.518734i
$668$	10.4140	−	30.3418i	0.402929	−	1.17396i
$669$		0			0
$670$	3.08707	−	0.298792i	0.119264	−	0.0115433i
$671$	0.0275635	−	0.156320i	0.00106408	−	0.00603468i
$672$		0			0
$673$	4.64214	−	3.89522i	0.178941	−	0.150150i	−0.548918	−	0.835876i	$-0.684960\pi$
$673$	4.64214	−	3.89522i	0.178941	−	0.150150i	0.727859	+	0.685727i	$0.240516\pi$
$674$	−18.0163	−	4.64982i	−0.693962	−	0.179105i
$675$		0			0
$676$	14.0199	+	7.75326i	0.539228	+	0.298202i
$677$	−5.34485	+	4.48486i	−0.205419	+	0.172367i	−0.739693	−	0.672944i	$-0.765029\pi$
$677$	−5.34485	+	4.48486i	−0.205419	+	0.172367i	0.534274	+	0.845311i	$0.320585\pi$
$678$		0			0
$679$	−14.2922	−	2.52009i	−0.548483	−	0.0967123i
$680$	−0.749603	+	1.73099i	−0.0287460	+	0.0663804i
$681$		0			0
$682$	−0.0175156	+	0.223973i	−0.000670707	+	0.00857636i
$683$	−25.8624	+	14.9317i	−0.989597	+	0.571344i	−0.905154	−	0.425084i	$-0.860244\pi$
$683$	−25.8624	+	14.9317i	−0.989597	+	0.571344i	−0.0844432	+	0.996428i	$0.526911\pi$
$684$		0			0
$685$	−4.63301	−	2.67487i	−0.177018	−	0.102201i
$686$	−12.8185	+	18.6708i	−0.489413	+	0.712856i
$687$		0			0
$688$	−5.95505	+	42.9892i	−0.227034	+	1.63895i
$689$	14.9446	−	17.8103i	0.569346	−	0.678520i
$690$		0			0
$691$	31.1175	+	11.3259i	1.18377	+	0.430856i	0.857531	−	0.514432i	$-0.171997\pi$
$691$	31.1175	+	11.3259i	1.18377	+	0.430856i	0.326236	+	0.945288i	$0.394220\pi$
$692$	−23.1926	+	13.9668i	−0.881651	+	0.530937i
$693$		0			0
$694$	−39.8991	+	11.0862i	−1.51455	+	0.420828i
$695$	0.422398	+	2.39554i	0.0160225	+	0.0908679i
$696$		0			0
$697$	3.36139	−	1.22345i	0.127322	−	0.0463414i
$698$	26.9866	+	12.2824i	1.02146	+	0.464895i
$699$		0			0
$700$	2.39268	+	12.2446i	0.0904350	+	0.462803i
$701$	−9.68894			−0.365946			−0.182973	−	0.983118i	$-0.558572\pi$
$701$	−9.68894			−0.365946			−0.182973	+	0.983118i	$0.558572\pi$
$702$		0			0
$703$		−	7.18080i		−	0.270829i
$704$	0.102820	−	0.0964528i	0.00387516	−	0.00363520i
$705$		0			0
$706$	−4.06024	−	1.84793i	−0.152809	−	0.0695478i
$707$	−7.42607	−	20.4030i	−0.279286	−	0.767333i
$708$		0			0
$709$	24.6853	−	4.35269i	0.927077	−	0.163469i	0.310329	−	0.950629i	$-0.399561\pi$
$709$	24.6853	−	4.35269i	0.927077	−	0.163469i	0.616748	+	0.787161i	$0.288450\pi$
$710$	1.73166	+	6.23218i	0.0649879	+	0.233890i
$711$		0			0
$712$	−0.0967135	−	0.324729i	−0.00362449	−	0.0121697i
$713$	−6.56025	+	18.0241i	−0.245683	+	0.675009i
$714$		0			0
$715$	0.0136901	+	0.0114874i	0.000511981	+	0.000429603i
$716$	−21.2264	+	8.17215i	−0.793268	+	0.305408i
$717$		0			0
$718$	−35.6645	−	24.4856i	−1.33099	−	0.913793i
$719$	16.4482	−	28.4892i	0.613415	−	1.06247i	−0.377245	−	0.926113i	$-0.623129\pi$
$719$	16.4482	−	28.4892i	0.613415	−	1.06247i	0.990660	−	0.136353i	$-0.0435381\pi$
$720$		0			0
$721$	10.3805	+	17.9796i	0.386590	+	0.669594i
$722$	1.89231	−	24.1970i	0.0704244	−	0.900520i
$723$		0			0
$724$	4.60862	−	29.2851i	0.171278	−	1.08837i
$725$	−6.05210	+	34.3232i	−0.224769	+	1.27473i
$726$		0			0
$727$	−20.0843	−	23.9355i	−0.744884	−	0.887719i	0.251908	−	0.967751i	$-0.418942\pi$
$727$	−20.0843	−	23.9355i	−0.744884	−	0.887719i	−0.996792	+	0.0800327i	$0.974498\pi$
$728$	−5.97190	−	5.65031i	−0.221333	−	0.209414i
$729$		0			0
$730$	−0.422076	−	0.108934i	−0.0156217	−	0.00403182i
$731$	10.2449	+	12.2094i	0.378920	+	0.451579i
$732$		0			0
$733$	16.2456	+	2.86454i	0.600046	+	0.105804i	0.465417	−	0.885092i	$-0.345904\pi$
$733$	16.2456	+	2.86454i	0.600046	+	0.105804i	0.134630	+	0.990896i	$0.457016\pi$
$734$	−3.04832	−	31.4948i	−0.112516	−	1.16249i
$735$		0			0
$736$	10.6628	−	5.58425i	0.393036	−	0.205838i
$737$	−0.0737209	+	0.0425628i	−0.00271554	+	0.00156782i
$738$		0			0
$739$	−11.5876	+	20.0704i	−0.426258	+	0.738301i	−0.996537	−	0.0831501i	$-0.973502\pi$
$739$	−11.5876	+	20.0704i	−0.426258	+	0.738301i	0.570279	+	0.821451i	$0.306835\pi$
$740$	−3.62670	+	3.15894i	−0.133320	+	0.116125i
$741$		0			0
$742$	15.5884	−	11.1308i	0.572269	−	0.408623i
$743$	2.55778	+	2.14623i	0.0938358	+	0.0787376i	0.688499	−	0.725238i	$-0.258270\pi$
$743$	2.55778	+	2.14623i	0.0938358	+	0.0787376i	−0.594663	+	0.803975i	$0.702714\pi$
$744$		0			0
$745$	−6.12156	−	2.22807i	−0.224277	−	0.0816300i
$746$	−11.5409	−	11.3300i	−0.422542	−	0.414821i
$747$		0			0
$748$	−0.000954765	−	0.0517644i	−3.49097e−5	−	0.00189270i
$749$	1.52210	+	8.63224i	0.0556162	+	0.315415i
$750$		0			0
$751$	−0.701648	−	1.92776i	−0.0256035	−	0.0703450i	0.926232	−	0.376953i	$-0.123028\pi$
$751$	−0.701648	−	1.92776i	−0.0256035	−	0.0703450i	−0.951836	+	0.306608i	$0.900806\pi$
$752$	16.8889	−	6.86246i	0.615876	−	0.250248i
$753$		0			0
$754$	−9.89754	−	20.7243i	−0.360447	−	0.754733i
$755$		−	5.39982i		−	0.196519i
$756$		0			0
$757$			41.6394i			1.51341i	0.653756	+	0.756705i	$0.273192\pi$
$757$			41.6394i			1.51341i	−0.653756	+	0.756705i	$0.726808\pi$
$758$	−27.6929	+	13.2257i	−1.00585	+	0.480377i
$759$		0			0
$760$	1.39786	−	1.03758i	0.0507057	−	0.0376368i
$761$	14.1101	+	38.7671i	0.511490	+	1.40531i	0.879684	+	0.475558i	$0.157754\pi$
$761$	14.1101	+	38.7671i	0.511490	+	1.40531i	−0.368195	+	0.929749i	$0.620024\pi$
$762$		0			0
$763$	0.659130	+	3.73811i	0.0238621	+	0.135329i
$764$	0.695186	+	37.6909i	0.0251509	+	1.36361i
$765$		0			0
$766$	32.8659	−	33.4777i	1.18749	−	1.20960i
$767$	23.0337	+	8.38359i	0.831700	+	0.302714i
$768$		0			0
$769$	−33.4132	−	28.0370i	−1.20491	−	1.01104i	−0.999476	−	0.0323712i	$-0.989694\pi$
$769$	−33.4132	−	28.0370i	−1.20491	−	1.01104i	−0.205437	−	0.978670i	$-0.565861\pi$
$770$	0.00855577	+	0.0119822i	0.000308329	+	0.000431809i
$771$		0			0
$772$	2.77219	+	3.18267i	0.0997732	+	0.114547i
$773$	−3.52468	+	6.10492i	−0.126774	+	0.219579i	−0.922425	−	0.386176i	$-0.873796\pi$
$773$	−3.52468	+	6.10492i	−0.126774	+	0.219579i	0.795651	+	0.605755i	$0.207129\pi$
$774$		0			0
$775$	−37.4247	+	21.6072i	−1.34434	+	0.776153i
$776$	−17.3716	+	26.3305i	−0.623605	+	0.945208i
$777$		0			0
$778$	9.80280	−	0.948795i	0.351447	−	0.0340160i
$779$	−3.25111	−	0.573258i	−0.116483	−	0.0205391i
$780$		0			0
$781$	−0.114116	−	0.135998i	−0.00408338	−	0.00486638i
$782$	1.10465	−	4.28008i	0.0395020	−	0.153055i
$783$		0			0
$784$	11.2841	+	17.9791i	0.403004	+	0.642111i
$785$	−4.90671	−	5.84759i	−0.175128	−	0.208709i
$786$		0			0
$787$	8.03739	−	45.5823i	0.286502	−	1.62483i	−0.413369	−	0.910564i	$-0.635648\pi$
$787$	8.03739	−	45.5823i	0.286502	−	1.62483i	0.699871	−	0.714270i	$-0.253241\pi$
$788$	22.6368	+	3.56237i	0.806402	+	0.126904i
$789$		0			0
$790$	5.17496	+	0.404704i	0.184117	+	0.0143987i
$791$	12.6913	+	21.9820i	0.451250	+	0.781589i
$792$		0			0
$793$	−10.0600	+	17.4245i	−0.357242	+	0.618762i
$794$	29.4470	−	42.8911i	1.04503	−	1.52215i
$795$		0			0
$796$	−10.6074	+	4.08386i	−0.375971	+	0.144748i
$797$	−10.7323	−	9.00550i	−0.380159	−	0.318991i	0.432606	−	0.901583i	$-0.357594\pi$
$797$	−10.7323	−	9.00550i	−0.380159	−	0.318991i	−0.812765	+	0.582592i	$0.802039\pi$
$798$		0			0
$799$	2.28975	−	6.29103i	0.0810054	−	0.222561i
$800$	26.4899	+	5.80399i	0.936559	+	0.205202i
$801$		0			0
$802$	−4.15930	+	1.15569i	−0.146870	+	0.0408088i
$803$	0.0117824	−	0.00207756i	0.000415792	−	7.33153e-5i
$804$		0			0
$805$	0.429937	+	1.18124i	0.0151533	+	0.0416333i
$806$	11.7962	−	25.9182i	0.415502	−	0.912931i
$807$		0			0
$808$	−47.1102	−	2.81124i	−1.65733	−	0.0988991i
$809$		−	25.2574i		−	0.888002i	−0.896026	−	0.444001i	$-0.853559\pi$
$809$		−	25.2574i		−	0.888002i	0.896026	−	0.444001i	$-0.146441\pi$
$810$		0			0
$811$	−36.9593			−1.29782			−0.648908	−	0.760867i	$-0.724774\pi$
$811$	−36.9593			−1.29782			−0.648908	+	0.760867i	$0.724774\pi$
$812$	−3.62867	−	18.5698i	−0.127341	−	0.651672i
$813$		0			0
$814$	0.0546826	−	0.120147i	0.00191662	−	0.00421116i
$815$	4.34200	−	1.58036i	0.152094	−	0.0553576i
$816$		0			0
$817$	−2.55420	−	14.4856i	−0.0893602	−	0.506787i
$818$	9.11925	+	32.8199i	0.318847	+	1.14752i
$819$		0			0
$820$	1.14068	+	1.89417i	0.0398344	+	0.0661473i
$821$	−5.42437	−	1.97431i	−0.189312	−	0.0689038i	0.245625	−	0.969365i	$-0.421007\pi$
$821$	−5.42437	−	1.97431i	−0.189312	−	0.0689038i	−0.434936	+	0.900461i	$0.643229\pi$
$822$		0			0
$823$	−12.2571	+	14.6074i	−0.427254	+	0.509182i	−0.936128	−	0.351659i	$-0.885618\pi$
$823$	−12.2571	+	14.6074i	−0.427254	+	0.509182i	0.508874	+	0.860841i	$0.330062\pi$
$824$	44.8284	−	5.17493i	1.56167	−	0.180277i
$825$		0			0
$826$	16.6483	+	11.4300i	0.579270	+	0.397700i
$827$	23.7503	+	13.7122i	0.825878	+	0.476821i	0.852439	−	0.522826i	$-0.175122\pi$
$827$	23.7503	+	13.7122i	0.825878	+	0.476821i	−0.0265613	+	0.999647i	$0.508456\pi$
$828$		0			0
$829$	23.8710	−	13.7819i	0.829073	−	0.478666i	−0.0244622	−	0.999701i	$-0.507787\pi$
$829$	23.8710	−	13.7819i	0.829073	−	0.478666i	0.853535	+	0.521035i	$0.174454\pi$
$830$	−1.28583	−	0.100557i	−0.0446317	−	0.00349038i
$831$		0			0
$832$	−16.4284	+	7.03105i	−0.569553	+	0.243758i
$833$	7.67695	+	1.35365i	0.265991	+	0.0469013i
$834$		0			0
$835$	5.57837	−	4.68081i	0.193048	−	0.161986i
$836$	−0.0231231	+	0.0418127i	−0.000799731	+	0.00144612i
$837$		0			0
$838$	10.4934	−	40.6580i	0.362489	−	1.40451i
$839$	22.7744	−	19.1100i	0.786259	−	0.659750i	−0.158558	−	0.987350i	$-0.550684\pi$
$839$	22.7744	−	19.1100i	0.786259	−	0.659750i	0.944816	+	0.327600i	$0.106240\pi$
$840$		0			0
$841$	4.14263	−	23.4940i	0.142849	−	0.810138i
$842$	3.91194	+	40.4175i	0.134814	+	1.39288i
$843$		0			0
$844$	10.8071	−	31.4871i	0.371995	−	1.08383i
$845$	1.81840	+	3.14956i	0.0625548	+	0.108348i
$846$		0			0
$847$	12.3959	+	7.15675i	0.425927	+	0.245909i
$848$	−8.73675	−	40.7071i	−0.300021	−	1.39789i
$849$		0			0
$850$	8.10488	−	5.78721i	0.277995	−	0.198500i
$851$	7.24453	−	8.63370i	0.248339	−	0.295959i
$852$		0			0
$853$	14.9845	−	41.1697i	0.513061	−	1.40962i	−0.364970	−	0.931019i	$-0.618921\pi$
$853$	14.9845	−	41.1697i	0.513061	−	1.40962i	0.878031	−	0.478604i	$-0.158857\pi$
$854$	−11.6124	+	11.8286i	−0.397370	+	0.404767i
$855$		0			0
$856$	18.5326	+	4.42022i	0.633432	+	0.151080i
$857$	12.6966	−	2.23875i	0.433708	−	0.0764744i	0.0474680	−	0.998873i	$-0.484885\pi$
$857$	12.6966	−	2.23875i	0.433708	−	0.0764744i	0.386240	+	0.922398i	$0.373774\pi$
$858$		0			0
$859$	−26.7551	+	9.73806i	−0.912872	+	0.332258i	−0.755399	−	0.655265i	$-0.772557\pi$
$859$	−26.7551	+	9.73806i	−0.912872	+	0.332258i	−0.157473	+	0.987523i	$0.550335\pi$
$860$	−6.19238	+	7.66244i	−0.211158	+	0.261287i
$861$		0			0
$862$	−33.8926	+	16.1865i	−1.15439	+	0.551315i
$863$	46.6170			1.58686			0.793431	−	0.608660i	$-0.208293\pi$
$863$	46.6170			1.58686			0.793431	+	0.608660i	$0.208293\pi$
$864$		0			0
$865$	−6.14571			−0.208961
$866$	−1.98147	+	0.946317i	−0.0673332	+	0.0321572i
$867$		0			0
$868$	14.7461	−	18.2468i	0.500515	−	0.619336i
$869$	−0.133877	+	0.0487272i	−0.00454146	+	0.00165296i
$870$		0			0
$871$	10.6262	−	1.87368i	0.360054	−	0.0634873i
$872$	8.02539	+	1.91414i	0.271774	+	0.0648209i
$873$		0			0
$874$	−2.85788	+	2.91108i	−0.0966692	+	0.0984686i
$875$	−1.97894	+	5.43708i	−0.0669003	+	0.183807i
$876$		0			0
$877$	3.98303	−	4.74679i	0.134497	−	0.160288i	−0.694592	−	0.719404i	$-0.744415\pi$
$877$	3.98303	−	4.74679i	0.134497	−	0.160288i	0.829089	+	0.559116i	$0.188859\pi$
$878$	−1.32201	+	0.943966i	−0.0446156	+	0.0318573i
$879$		0			0
$880$	0.0312899	−	0.00671560i	0.00105478	−	0.000226383i
$881$	21.9173	+	12.6539i	0.738412	+	0.426322i	0.821492	−	0.570221i	$-0.193142\pi$
$881$	21.9173	+	12.6539i	0.738412	+	0.426322i	−0.0830799	+	0.996543i	$0.526476\pi$
$882$		0			0
$883$	15.7424	+	27.2667i	0.529775	+	0.917597i	0.999397	+	0.0347290i	$0.0110568\pi$
$883$	15.7424	+	27.2667i	0.529775	+	0.917597i	−0.469622	+	0.882868i	$0.655610\pi$
$884$	−2.13041	+	6.20710i	−0.0716535	+	0.208767i
$885$		0			0
$886$	2.30849	+	23.8509i	0.0775552	+	0.801288i
$887$	0.0310073	−	0.175851i	0.00104112	−	0.00590451i	−0.984283	−	0.176600i	$-0.943490\pi$
$887$	0.0310073	−	0.175851i	0.00104112	−	0.00590451i	0.985324	+	0.170695i	$0.0546013\pi$
$888$		0			0
$889$	−17.2584	+	14.4815i	−0.578827	+	0.485694i
$890$	0.0192209	−	0.0744737i	0.000644287	−	0.00249636i
$891$		0			0
$892$	2.68864	−	4.86177i	0.0900223	−	0.162784i
$893$	−4.73299	+	3.97145i	−0.158384	+	0.132900i
$894$		0			0
$895$	−5.08477	−	0.896582i	−0.169965	−	0.0299694i
$896$	−14.5528	+	2.22646i	−0.486175	+	0.0743807i
$897$		0			0
$898$	43.2606	+	3.38316i	1.44363	+	0.112898i
$899$	56.7571	−	32.7687i	1.89296	−	1.09290i
$900$		0			0
$901$	−13.2413	−	7.64488i	−0.441132	−	0.254688i
$902$	−0.0500313	−	0.0343491i	−0.00166586	−	0.00114370i
$903$		0			0
$904$	54.8076	−	6.32691i	1.82287	−	0.210430i
$905$	4.32570	−	5.15517i	0.143791	−	0.171364i
$906$		0			0
$907$	−18.2575	−	6.64519i	−0.606231	−	0.220650i	0.0206225	−	0.999787i	$-0.493435\pi$
$907$	−18.2575	−	6.64519i	−0.606231	−	0.220650i	−0.626853	+	0.779137i	$0.715657\pi$
$908$	−25.5120	−	42.3641i	−0.846646	−	1.40590i
$909$		0			0
$910$	−0.499623	−	1.79813i	−0.0165623	−	0.0596074i
$911$	−0.423720	−	2.40304i	−0.0140385	−	0.0796161i	0.976984	−	0.213314i	$-0.0684258\pi$
$911$	−0.423720	−	2.40304i	−0.0140385	−	0.0796161i	−0.991022	+	0.133698i	$0.957315\pi$
$912$		0			0
$913$	0.0332645	−	0.0121073i	0.00110089	−	0.000400693i
$914$	4.19634	−	9.22011i	0.138803	−	0.304974i
$915$		0			0
$916$	−6.01153	−	30.7641i	−0.198626	−	1.01648i
$917$	4.01015			0.132427
$918$		0			0
$919$		−	2.20402i		−	0.0727038i	−0.999339	−	0.0363519i	$-0.988426\pi$
$919$		−	2.20402i		−	0.0727038i	0.999339	−	0.0363519i	$-0.0115737\pi$
$920$	2.72748	+	0.162758i	0.0899222	+	0.00536599i
$921$		0			0
$922$	4.85526	−	10.6679i	0.159900	−	0.351328i
$923$	7.69653	+	21.1460i	0.253334	+	0.696030i
$924$		0			0
$925$	25.0065	−	4.40933i	0.822210	−	0.144978i
$926$	−0.527376	+	0.146535i	−0.0173307	+	0.00481545i
$927$		0			0
$928$	−40.1737	−	8.80214i	−1.31877	−	0.288944i
$929$	−3.30889	+	9.09111i	−0.108561	+	0.298270i	−0.982063	−	0.188551i	$-0.939621\pi$
$929$	−3.30889	+	9.09111i	−0.108561	+	0.298270i	0.873502	+	0.486820i	$0.161843\pi$
$930$		0			0
$931$	−5.51109	−	4.62435i	−0.180619	−	0.151557i
$932$	−37.7585	+	14.5370i	−1.23682	+	0.476175i
$933$		0			0
$934$	5.33220	−	7.76662i	0.174475	−	0.254131i
$935$	0.00587632	−	0.0101781i	0.000192176	−	0.000332859i
$936$		0			0
$937$	−22.2202	−	38.4864i	−0.725901	−	1.25730i	−0.958602	−	0.284749i	$-0.908090\pi$
$937$	−22.2202	−	38.4864i	−0.725901	−	1.25730i	0.232701	−	0.972548i	$-0.425243\pi$
$938$	8.86243	+	0.693079i	0.289369	+	0.0226298i
$939$		0			0
$940$	4.08792	+	0.643318i	0.133333	+	0.0209827i
$941$	7.38960	−	41.9085i	0.240894	−	1.36618i	−0.588944	−	0.808174i	$-0.700456\pi$
$941$	7.38960	−	41.9085i	0.240894	−	1.36618i	0.829838	−	0.558004i	$-0.188433\pi$
$942$		0			0
$943$	−3.33056	−	3.96920i	−0.108458	−	0.129255i
$944$	37.1785	−	23.3341i	1.21006	−	0.759460i
$945$		0			0
$946$	0.0675731	−	0.261820i	0.00219699	−	0.00851250i
$947$	−30.3650	−	36.1877i	−0.986731	−	1.17594i	−0.984400	−	0.175943i	$-0.943702\pi$
$947$	−30.3650	−	36.1877i	−0.986731	−	1.17594i	−0.00233119	−	0.999997i	$-0.500742\pi$
$948$		0			0
$949$	−1.49348	−	0.263341i	−0.0484804	−	0.00854841i
$950$	−9.14819	+	0.885437i	−0.296807	+	0.0287274i
$951$		0			0
$952$	−2.97740	+	4.51289i	−0.0964980	+	0.146264i
$953$	23.8540	−	13.7721i	0.772707	−	0.446123i	−0.0611321	−	0.998130i	$-0.519471\pi$
$953$	23.8540	−	13.7721i	0.772707	−	0.446123i	0.833840	+	0.552007i	$0.186138\pi$
$954$		0			0
$955$	−4.27868	+	7.41089i	−0.138455	+	0.239811i
$956$	−11.2549	−	12.9214i	−0.364009	−	0.417909i
$957$		0			0
$958$	−0.931443	−	1.30447i	−0.0300936	−	0.0421455i
$959$	−11.7461	−	9.85611i	−0.379300	−	0.318270i
$960$		0			0
$961$	47.2298	+	17.1902i	1.52354	+	0.554524i
$962$	−11.7220	+	11.9402i	−0.377933	+	0.384968i
$963$		0			0
$964$	−0.533115	−	28.9039i	−0.0171705	−	0.930930i
$965$	0.166374	+	0.943555i	0.00535578	+	0.0303741i
$966$		0			0
$967$	0.543982	+	1.49458i	0.0174933	+	0.0480624i	0.948132	−	0.317877i	$-0.102970\pi$
$967$	0.543982	+	1.49458i	0.0174933	+	0.0480624i	−0.930639	+	0.365939i	$0.880748\pi$
$968$	24.9820	−	18.5431i	0.802951	−	0.595998i
$969$		0			0
$970$	−6.46162	+	3.08596i	−0.207470	+	0.0990842i
$971$			9.93969i			0.318980i	0.987200	+	0.159490i	$0.0509849\pi$
$971$			9.93969i			0.318980i	−0.987200	+	0.159490i	$0.949015\pi$
$972$		0			0
$973$			6.97199i			0.223512i
$974$	−25.5752	−	53.5514i	−0.819483	−	1.71590i
$975$		0			0
$976$	13.5630	+	33.3794i	0.434141	+	1.06845i
$977$	−13.5121	−	37.1242i	−0.432290	−	1.18771i	−0.944403	−	0.328789i	$-0.893359\pi$
$977$	−13.5121	−	37.1242i	−0.432290	−	1.18771i	0.512113	−	0.858918i	$-0.328863\pi$
$978$		0			0
$979$	0.000366577		0.00207896i	1.17158e−5		6.64438e-5i
$980$	0.0888600	+	4.81772i	0.00283853	+	0.153896i
$981$		0			0
$982$	20.7838	+	20.4040i	0.663237	+	0.651117i
$983$	−30.2880	−	11.0239i	−0.966036	−	0.351608i	−0.189640	−	0.981854i	$-0.560732\pi$
$983$	−30.2880	−	11.0239i	−0.966036	−	0.351608i	−0.776396	+	0.630245i	$0.782954\pi$
$984$		0			0
$985$	3.98484	+	3.34368i	0.126967	+	0.106538i
$986$	−12.2916	+	8.77669i	−0.391444	+	0.279507i
$987$		0			0
$988$	4.56692	−	3.97790i	0.145293	−	0.126554i
$989$	11.5432	−	19.9933i	0.367051	−	0.635751i
$990$		0			0
$991$	−2.66599	+	1.53921i	−0.0846881	+	0.0488947i	−0.541746	−	0.840542i	$-0.682237\pi$
$991$	−2.66599	+	1.53921i	−0.0846881	+	0.0488947i	0.457058	+	0.889437i	$0.348903\pi$
$992$	−23.6580	−	45.1735i	−0.751142	−	1.43426i
$993$		0			0
$994$	1.78604	+	18.4531i	0.0566499	+	0.585297i
$995$	−2.54100	−	0.448048i	−0.0805553	−	0.0142041i
$996$		0			0
$997$	−27.9424	−	33.3004i	−0.884944	−	1.05464i	−0.998134	−	0.0610619i	$-0.980551\pi$
$997$	−27.9424	−	33.3004i	−0.884944	−	1.05464i	0.113190	−	0.993573i	$-0.463893\pi$
$998$	13.7303	+	3.54367i	0.434626	+	0.112173i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.v.b.611.28		192
3.2	odd	2		216.2.v.b.59.5	yes	192
8.3	odd	2	inner	648.2.v.b.611.11		192
12.11	even	2		864.2.bh.b.815.1		192
24.5	odd	2		864.2.bh.b.815.2		192
24.11	even	2		216.2.v.b.59.22	yes	192
27.11	odd	18	inner	648.2.v.b.35.11		192
27.16	even	9		216.2.v.b.11.22	yes	192
108.43	odd	18		864.2.bh.b.335.2		192
216.11	even	18	inner	648.2.v.b.35.28		192
216.43	odd	18		216.2.v.b.11.5	✓	192
216.205	even	18		864.2.bh.b.335.1		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.5	✓	192	216.43	odd	18
216.2.v.b.11.22	yes	192	27.16	even	9
216.2.v.b.59.5	yes	192	3.2	odd	2
216.2.v.b.59.22	yes	192	24.11	even	2
648.2.v.b.35.11		192	27.11	odd	18	inner
648.2.v.b.35.28		192	216.11	even	18	inner
648.2.v.b.611.11		192	8.3	odd	2	inner
648.2.v.b.611.28		192	1.1	even	1	trivial
864.2.bh.b.335.1		192	216.205	even	18
864.2.bh.b.335.2		192	108.43	odd	18
864.2.bh.b.815.1		192	12.11	even	2
864.2.bh.b.815.2		192	24.5	odd	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.v (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.27615 - 0.609466i) q^{2} +(1.25710 - 1.55554i) q^{4} +(0.426624 - 0.155279i) q^{5} +(1.28150 - 0.225962i) q^{7} +(0.656202 - 2.75125i) q^{8} +(0.449799 - 0.458171i) q^{10} +(-0.00602720 + 0.0165596i) q^{11} +(1.43581 - 1.71113i) q^{13} +(1.49766 - 1.06939i) q^{14} +(-0.839384 - 3.91094i) q^{16} +(-1.27216 - 0.734483i) q^{17} +(0.677841 + 1.17406i) q^{19} +(0.294769 - 0.858831i) q^{20} +(0.00240091 + 0.0248058i) q^{22} +(-0.369486 + 2.09546i) q^{23} +(-3.67233 + 3.08145i) q^{25} +(0.789428 - 3.05873i) q^{26} +(1.25948 - 2.27747i) q^{28} +(5.56933 - 4.67322i) q^{29} +(8.87753 + 1.56535i) q^{31} +(-3.45476 - 4.47936i) q^{32} +(-2.07111 - 0.161969i) q^{34} +(0.511630 - 0.295390i) q^{35} +(-4.58718 - 2.64841i) q^{37} +(1.58057 + 1.08515i) q^{38} +(-0.147259 - 1.27565i) q^{40} +(-1.56527 + 1.86542i) q^{41} +(-10.1956 - 3.71089i) q^{43} +(0.0181822 + 0.0301926i) q^{44} +(0.805592 + 2.89930i) q^{46} +(0.791397 + 4.48824i) q^{47} +(-4.98668 + 1.81500i) q^{49} +(-2.80839 + 6.17054i) q^{50} +(-0.856765 - 4.38452i) q^{52} +10.4085 q^{53} +0.00800062i q^{55} +(0.219241 - 3.67400i) q^{56} +(4.25911 - 9.35804i) q^{58} +(3.75319 + 10.3118i) q^{59} +(-8.87057 + 1.56412i) q^{61} +(12.2831 - 3.41294i) q^{62} +(-7.13880 - 3.61076i) q^{64} +(0.346849 - 0.952961i) q^{65} +(3.70041 + 3.10502i) q^{67} +(-2.74175 + 1.05557i) q^{68} +(0.472885 - 0.688782i) q^{70} +(-5.03714 + 8.72458i) q^{71} +(-0.339460 - 0.587962i) q^{73} +(-7.46803 - 0.584031i) q^{74} +(2.67840 + 0.421502i) q^{76} +(-0.00398198 + 0.0225829i) q^{77} +(5.19665 + 6.19313i) q^{79} +(-0.965387 - 1.53816i) q^{80} +(-0.860607 + 3.33452i) q^{82} +(-1.29122 - 1.53881i) q^{83} +(-0.656785 - 0.115809i) q^{85} +(-15.2727 + 1.47822i) q^{86} +(0.0416046 + 0.0274488i) q^{88} +(0.103744 - 0.0598964i) q^{89} +(1.45333 - 2.51724i) q^{91} +(2.79508 + 3.20896i) q^{92} +(3.74536 + 5.24532i) q^{94} +(0.471489 + 0.395626i) q^{95} +(-10.4801 - 3.81446i) q^{97} +(-5.25755 + 5.35542i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40}+ \cdots - 162 q^{98}+O(q^{100}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Introduction

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