LMFDB - Embedded newform 648.2.v.b.611.11

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			611.11
Character	$\chi$	$=$	648.611
Dual form			648.2.v.b.35.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.821807 + 1.15093i) q^{2} +(-0.649266 - 1.89168i) q^{4} +(-0.426624 + 0.155279i) q^{5} +(-1.28150 + 0.225962i) q^{7} +(2.71076 + 0.807339i) q^{8} +(0.171889 - 0.618623i) q^{10} +(-0.00602720 + 0.0165596i) q^{11} +(-1.43581 + 1.71113i) q^{13} +(0.793076 - 1.66060i) q^{14} +(-3.15691 + 2.45641i) q^{16} +(-1.27216 - 0.734483i) q^{17} +(0.677841 + 1.17406i) q^{19} +(0.570730 + 0.706220i) q^{20} +(-0.0141057 - 0.0205456i) q^{22} +(0.369486 - 2.09546i) q^{23} +(-3.67233 + 3.08145i) q^{25} +(-0.789428 - 3.05873i) q^{26} +(1.25948 + 2.27747i) q^{28} +(-5.56933 + 4.67322i) q^{29} +(-8.87753 - 1.56535i) q^{31} +(-0.232774 - 5.65206i) q^{32} +(1.89081 - 0.860562i) q^{34} +(0.511630 - 0.295390i) q^{35} +(4.58718 + 2.64841i) q^{37} +(-1.90831 - 0.184701i) q^{38} +(-1.28184 + 0.0764919i) q^{40} +(-1.56527 + 1.86542i) q^{41} +(-10.1956 - 3.71089i) q^{43} +(0.0352387 + 0.000649957i) q^{44} +(2.10807 + 2.14731i) q^{46} +(-0.791397 - 4.48824i) q^{47} +(-4.98668 + 1.81500i) q^{49} +(-0.528577 - 6.75893i) q^{50} +(4.16913 + 1.60511i) q^{52} -10.4085 q^{53} -0.00800062i q^{55} +(-3.65625 - 0.422073i) q^{56} +(-0.801622 - 10.2504i) q^{58} +(3.75319 + 10.3118i) q^{59} +(8.87057 - 1.56412i) q^{61} +(9.09722 - 8.93098i) q^{62} +(6.69641 + 4.37700i) q^{64} +(0.346849 - 0.952961i) q^{65} +(3.70041 + 3.10502i) q^{67} +(-0.563436 + 2.88340i) q^{68} +(-0.0804893 + 0.831602i) q^{70} +(5.03714 - 8.72458i) q^{71} +(-0.339460 - 0.587962i) q^{73} +(-6.81790 + 3.10303i) q^{74} +(1.78084 - 2.04453i) q^{76} +(0.00398198 - 0.0225829i) q^{77} +(-5.19665 - 6.19313i) q^{79} +(0.965387 - 1.53816i) q^{80} +(-0.860607 - 3.33452i) q^{82} +(-1.29122 - 1.53881i) q^{83} +(0.656785 + 0.115809i) q^{85} +(12.6498 - 8.68475i) q^{86} +(-0.0297075 + 0.0400230i) q^{88} +(0.103744 - 0.0598964i) q^{89} +(1.45333 - 2.51724i) q^{91} +(-4.20383 + 0.661560i) q^{92} +(5.81601 + 2.77762i) q^{94} +(-0.471489 - 0.395626i) q^{95} +(-10.4801 - 3.81446i) q^{97} +(2.00915 - 7.23088i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.821807	+	1.15093i	−0.581105	+	0.813828i
$2$	−0.821807	+	1.15093i	−0.581105	+	0.813828i
$3$		0			0
$3$		0			0
$4$	−0.649266	−	1.89168i	−0.324633	−	0.945840i
$5$	−0.426624	+	0.155279i	−0.190792	+	0.0694427i	−0.435649	−	0.900116i	$-0.643481\pi$
$5$	−0.426624	+	0.155279i	−0.190792	+	0.0694427i	0.244857	+	0.969559i	$0.421259\pi$
$6$		0			0
$7$	−1.28150	+	0.225962i	−0.484360	+	0.0854057i	−0.410495	−	0.911863i	$-0.634644\pi$
$7$	−1.28150	+	0.225962i	−0.484360	+	0.0854057i	−0.0738642	+	0.997268i	$0.523533\pi$
$8$	2.71076	+	0.807339i	0.958397	+	0.285437i
$9$		0			0
$10$	0.171889	−	0.618623i	0.0543560	−	0.195626i
$11$	−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	−0.927477	−	0.373881i	$-0.878027\pi$
$13$	−1.43581	+	1.71113i	−0.398222	+	0.474582i	0.529255	+	0.848463i	$0.322471\pi$
$14$	0.793076	−	1.66060i	0.211959	−	0.443815i
$15$		0			0
$16$	−3.15691	+	2.45641i	−0.789227	+	0.614102i
$17$	−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	$0.783632\pi$
$20$	0.570730	+	0.706220i	0.127619	+	0.157916i
$21$		0			0
$22$	−0.0141057	−	0.0205456i	−0.00300734	−	0.00438035i
$23$	0.369486	−	2.09546i	0.0770432	−	0.436933i	−0.921748	−	0.387788i	$-0.873239\pi$
$23$	0.369486	−	2.09546i	0.0770432	−	0.436933i	0.998792	−	0.0491452i	$-0.0156497\pi$
$24$		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	−0.991345	−	0.131286i	$-0.958089\pi$
$29$	−5.56933	+	4.67322i	−1.03420	+	0.867796i	−0.0428540	+	0.999081i	$0.513645\pi$
$30$		0			0
$31$	−8.87753	−	1.56535i	−1.59445	−	0.281145i	−0.695279	−	0.718740i	$-0.744719\pi$
$31$	−8.87753	−	1.56535i	−1.59445	−	0.281145i	−0.899172	+	0.437595i	$0.855830\pi$
$32$	−0.232774	−	5.65206i	−0.0411490	−	0.999153i
$33$		0			0
$34$	1.89081	−	0.860562i	0.324271	−	0.147585i
$35$	0.511630	−	0.295390i	0.0864813	−	0.0499300i
$36$		0			0
$37$	4.58718	+	2.64841i	0.754128	+	0.435396i	0.827183	−	0.561932i	$-0.189942\pi$
$37$	4.58718	+	2.64841i	0.754128	+	0.435396i	−0.0730557	+	0.997328i	$0.523275\pi$
$38$	−1.90831	−	0.184701i	−0.309568	−	0.0299625i
$39$		0			0
$40$	−1.28184	+	0.0764919i	−0.202676	+	0.0120944i
$41$	−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	$0.921235\pi$
$44$	0.0352387		0.000649957i	0.00531243		9.79847e-5i
$45$		0			0
$46$	2.10807	+	2.14731i	0.310819	+	0.316604i
$47$	−0.791397	−	4.48824i	−0.115437	−	0.654676i	−0.986533	−	0.163563i	$-0.947701\pi$
$47$	−0.791397	−	4.48824i	−0.115437	−	0.654676i	0.871096	−	0.491113i	$-0.163410\pi$
$48$		0			0
$49$	−4.98668	+	1.81500i	−0.712382	+	0.259286i
$50$	−0.528577	−	6.75893i	−0.0747520	−	0.955858i
$51$		0			0
$52$	4.16913	+	1.60511i	0.578155	+	0.222589i
$53$	−10.4085			−1.42972			−0.714860	−	0.699267i	$-0.753510\pi$
$53$	−10.4085			−1.42972			−0.714860	+	0.699267i	$0.753510\pi$
$54$		0			0
$55$		−	0.00800062i		−	0.00107880i
$56$	−3.65625	−	0.422073i	−0.488587	−	0.0564018i
$57$		0			0
$58$	−0.801622	−	10.2504i	−0.105258	−	1.34594i
$59$	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	0.426010	−	0.904718i	$-0.359919\pi$
$61$	8.87057	−	1.56412i	1.13576	−	0.200265i	0.709750	+	0.704453i	$0.248808\pi$
$62$	9.09722	−	8.93098i	1.15535	−	1.13424i
$63$		0			0
$64$	6.69641	+	4.37700i	0.837051	+	0.547125i
$65$	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	$0.626878\pi$
$68$	−0.563436	+	2.88340i	−0.0683266	+	0.349663i
$69$		0			0
$70$	−0.0804893	+	0.831602i	−0.00962031	+	0.0993955i
$71$	5.03714	−	8.72458i	0.597799	−	1.03542i	−0.395347	−	0.918532i	$-0.629376\pi$
$71$	5.03714	−	8.72458i	0.597799	−	1.03542i	0.993145	−	0.116886i	$-0.0372911\pi$
$72$		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	$0.845983\pi$
$74$	−6.81790	+	3.10303i	−0.792565	+	0.360720i
$75$		0			0
$76$	1.78084	−	2.04453i	0.204276	−	0.234524i
$77$	0.00398198	−	0.0225829i	0.000453789	−	0.00257357i
$78$		0			0
$79$	−5.19665	−	6.19313i	−0.584669	−	0.696782i	0.389903	−	0.920856i	$-0.372509\pi$
$79$	−5.19665	−	6.19313i	−0.584669	−	0.696782i	−0.974572	+	0.224074i	$0.928064\pi$
$80$	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
$86$	12.6498	−	8.68475i	1.36406	−	0.936501i
$87$		0			0
$88$	−0.0297075	+	0.0400230i	−0.00316683	+	0.00426647i
$89$	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
$92$	−4.20383	+	0.661560i	−0.438280	+	0.0689724i
$93$		0			0
$94$	5.81601	+	2.77762i	0.599875	+	0.286490i
$95$	−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	$0.802696\pi$
$98$	2.00915	−	7.23088i	0.202955	−	0.730429i
$99$		0			0
$100$	8.21343	+	4.94619i	0.821343	+	0.494619i
$101$	2.89743	+	16.4321i	0.288305	+	1.63506i	0.693237	+	0.720710i	$0.256184\pi$
$101$	2.89743	+	16.4321i	0.288305	+	1.63506i	−0.404932	+	0.914347i	$0.632705\pi$
$102$		0			0
$103$	−5.45676	−	14.9923i	−0.537670	−	1.47724i	−0.849753	−	0.527182i	$-0.823249\pi$
$103$	−5.45676	−	14.9923i	−0.537670	−	1.47724i	0.312082	−	0.950055i	$-0.398974\pi$
$104$	−5.27359	+	3.47927i	−0.517118	+	0.341171i
$105$		0			0
$106$	8.55380	−	11.9794i	0.830818	−	1.16355i
$107$			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	$-0.955387\pi$
$109$		−	2.91699i		−	0.279397i	0.990194	−	0.139699i	$-0.0446134\pi$
$110$	0.00920813	+	0.00657497i	0.000877961	+	0.000626898i
$111$		0			0
$112$	3.49051	−	3.86121i	0.329822	−	0.364850i
$113$	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
$116$	12.4562	+	7.50123i	1.15653	+	0.696471i
$117$		0			0
$118$	−14.9525	−	4.15467i	−1.37649	−	0.382469i
$119$	1.79623	+	0.653776i	0.164661	+	0.0599315i
$120$		0			0
$121$	8.42625	+	7.07046i	0.766023	+	0.642769i
$122$	−5.48971	+	11.4948i	−0.497015	+	1.04069i
$123$		0			0
$124$	2.80274	+	17.8098i	0.251693	+	1.59937i
$125$	2.22323	−	3.85075i	0.198852	−	0.344422i
$126$		0			0
$127$	14.9938	−	8.65666i	1.33048	−	0.768154i	0.345108	−	0.938563i	$-0.387842\pi$
$127$	14.9938	−	8.65666i	1.33048	−	0.768154i	0.985373	+	0.170409i	$0.0545088\pi$
$128$	−10.5408	+	4.11002i	−0.931681	+	0.363278i
$129$		0			0
$130$	0.811745	+	1.18235i	0.0711947	+	0.103699i
$131$	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	$0.982591\pi$
$140$	−0.890967	−	0.776054i	−0.0753005	−	0.0655885i
$141$		0			0
$142$	5.90180	+	12.9673i	0.495268	+	1.08819i
$143$	−0.0196817	−	0.0340897i	−0.00164587	−	0.00285073i
$144$		0			0
$145$	1.65036	−	2.85851i	0.137055	−	0.237386i
$146$	0.955672	+	0.0924978i	0.0790920	+	0.00765517i
$147$		0			0
$148$	2.03165	−	10.3970i	0.167000	−	0.854628i
$149$	10.9918	+	9.22325i	0.900486	+	0.755598i	0.970285	−	0.241963i	$-0.0777914\pi$
$149$	10.9918	+	9.22325i	0.900486	+	0.755598i	−0.0697991	+	0.997561i	$0.522236\pi$
$150$		0			0
$151$	−4.06790	+	11.1765i	−0.331041	+	0.909528i	0.656800	+	0.754065i	$0.271909\pi$
$151$	−4.06790	+	11.1765i	−0.331041	+	0.909528i	−0.987842	+	0.155464i	$0.950313\pi$
$152$	0.889602	+	3.72983i	0.0721562	+	0.302529i
$153$		0			0
$154$	0.0227189	+	0.0231418i	0.00183074	+	0.00186482i
$155$	4.03044	−	0.710675i	0.323733	−	0.0570828i
$156$		0			0
$157$	5.75062	+	15.7997i	0.458950	+	1.26095i	0.926268	+	0.376865i	$0.122998\pi$
$157$	5.75062	+	15.7997i	0.458950	+	1.26095i	−0.467319	+	0.884089i	$0.654780\pi$
$158$	11.3985	−	0.891409i	0.906815	−	0.0709167i
$159$		0			0
$160$	0.976952	+	2.37516i	0.0772348	+	0.187773i
$161$			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	$0.369502\pi$
$164$	4.54505	+	1.74984i	0.354909	+	0.136640i
$165$		0			0
$166$	2.83219	−	0.221489i	0.219821	−	0.0171909i
$167$	−15.0723	+	5.48587i	−1.16633	+	0.424509i	−0.851355	−	0.524591i	$-0.824218\pi$
$167$	−15.0723	+	5.48587i	−1.16633	+	0.424509i	−0.314975	+	0.949100i	$0.601996\pi$
$168$		0			0
$169$	1.39101	+	7.88879i	0.107000	+	0.606830i
$170$	−0.673038	+	0.660739i	−0.0516197	+	0.0506764i
$171$		0			0
$172$	−0.400173	+	21.6962i	−0.0305129	+	1.65432i
$173$	12.7203	+	4.62982i	0.967109	+	0.351999i	0.776815	−	0.629729i	$-0.216834\pi$
$173$	12.7203	+	4.62982i	0.967109	+	0.351999i	0.190293	+	0.981727i	$0.439056\pi$
$174$		0			0
$175$	4.00978	−	4.77867i	0.303111	−	0.361233i
$176$	−0.0216498	−	0.0670823i	−0.00163191	−	0.00505652i
$177$		0			0
$178$	−0.0163209	+	0.168625i	−0.00122330	+	0.0126390i
$179$	−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	−0.894370	−	0.447327i	$-0.852376\pi$
$181$	−12.8369	+	7.41138i	−0.954159	+	0.550884i	−0.0597883	+	0.998211i	$0.519043\pi$
$182$	1.70281	+	3.74137i	0.126220	+	0.277329i
$183$		0			0
$184$	2.69333	−	5.38198i	0.198555	−	0.396765i
$185$	−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	0.0522283	−	0.998635i	$-0.483368\pi$
$191$	14.4389	−	12.1157i	1.04476	−	0.876659i	0.992533	+	0.121976i	$0.0389232\pi$
$192$		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	$0.0797556\pi$
$194$	13.0028	−	8.92712i	0.933547	−	0.640930i
$195$		0			0
$196$	6.67108	+	8.25478i	0.476506	+	0.589627i
$197$	−5.72884	−	9.92264i	−0.408163	−	0.706959i	0.586521	−	0.809934i	$-0.300497\pi$
$197$	−5.72884	−	9.92264i	−0.408163	−	0.706959i	−0.994684	+	0.102975i	$0.967164\pi$
$198$		0			0
$199$	4.92181	+	2.84161i	0.348898	+	0.201436i	0.664200	−	0.747555i	$-0.268772\pi$
$199$	4.92181	+	2.84161i	0.348898	+	0.201436i	−0.315302	+	0.948991i	$0.602106\pi$
$200$	−12.4426	+	5.38824i	−0.879821	+	0.381006i
$201$		0			0
$202$	−21.2933	−	10.1693i	−1.49819	−	0.715510i
$203$	6.08110	−	7.24717i	0.426809	−	0.508652i
$204$		0			0
$205$	0.378123	−	1.03889i	0.0264093	−	0.0725589i
$206$	21.7395	+	6.04047i	1.51466	+	0.420859i
$207$		0			0
$208$	0.329486	−	8.92881i	0.0228457	−	0.619102i
$209$	−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	$0.194689\pi$
$212$	6.75790	+	19.6896i	0.464134	+	1.35229i
$213$		0			0
$214$	−7.75272	−	5.53575i	−0.529965	−	0.378416i
$215$	4.92591			0.335945
$216$		0			0
$217$	11.7302			0.796300
$218$	3.35725	+	2.39721i	0.227382	+	0.162359i
$219$		0			0
$220$	−0.0151346	+	0.00519453i	−0.00102038	+	0.000350215i
$221$	3.08338	−	1.12226i	0.207410	−	0.0754912i
$222$		0			0
$223$	−2.73564	+	0.482367i	−0.183192	+	0.0323017i	−0.264491	−	0.964388i	$-0.585204\pi$
$223$	−2.73564	+	0.482367i	−0.183192	+	0.0323017i	0.0812995	+	0.996690i	$0.474093\pi$
$224$	1.57545	+	7.19049i	0.105264	+	0.480435i
$225$		0			0
$226$	−26.5789	−	7.38512i	−1.76800	−	0.491251i
$227$	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	−0.988197	−	0.153190i	$-0.951045\pi$
$229$	−10.0744	+	12.0062i	−0.665736	+	0.793393i	0.322461	+	0.946583i	$0.395490\pi$
$230$	−1.23279	−	0.588758i	−0.0812876	−	0.0388216i
$231$		0			0
$232$	−18.8700	+	8.17163i	−1.23887	+	0.536494i
$233$	−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
$236$	17.0698	−	13.7949i	1.11115	−	0.897975i
$237$		0			0
$238$	−2.22861	+	1.53006i	−0.144459	+	0.0991789i
$239$	−1.48780	+	8.43773i	−0.0962378	+	0.545791i	0.898123	+	0.439744i	$0.144931\pi$
$239$	−1.48780	+	8.43773i	−0.0962378	+	0.545791i	−0.994361	+	0.106048i	$0.966180\pi$
$240$		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
$248$	−22.8011	−	11.4105i	−1.44787	−	0.724565i
$249$		0			0
$250$	2.60486	+	5.72335i	0.164746	+	0.361977i
$251$	−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
$254$	−2.35881	+	24.3708i	−0.148005	+	1.52916i
$255$		0			0
$256$	3.93214	−	15.5093i	0.245759	−	0.969331i
$257$	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
$260$	−2.02789	−	0.0374033i	−0.125765	−	0.00231966i
$261$		0			0
$262$	−3.11002	+	3.05318i	−0.192138	+	0.188626i
$263$	−3.07511	−	17.4398i	−0.189620	−	1.07539i	−0.919875	−	0.392212i	$-0.871710\pi$
$263$	−3.07511	−	17.4398i	−0.189620	−	1.07539i	0.730255	−	0.683175i	$-0.239401\pi$
$264$		0			0
$265$	4.44053	−	1.61622i	0.272780	−	0.0992836i
$266$	2.48722	−	0.194511i	0.152501	−	0.0119262i
$267$		0			0
$268$	3.47115	−	9.01598i	0.212034	−	0.550739i
$269$	−10.2475			−0.624803			−0.312402	−	0.949950i	$-0.601133\pi$
$269$	−10.2475			−0.624803			−0.312402	+	0.949950i	$0.601133\pi$
$270$		0			0
$271$			18.7315i			1.13786i	0.822386	+	0.568929i	$0.192642\pi$
$271$			18.7315i			1.13786i	−0.822386	+	0.568929i	$0.807358\pi$
$272$	5.82029	−	0.806251i	0.352907	−	0.0488861i
$273$		0			0
$274$	16.6136	−	1.29925i	1.00366	−	0.0784906i
$275$	−0.0288937	−	0.0793847i	−0.00174235	−	0.00478708i
$276$		0			0
$277$	21.4560	−	3.78327i	1.28917	−	0.227315i	0.513299	−	0.858210i	$-0.328423\pi$
$277$	21.4560	−	3.78327i	1.28917	−	0.227315i	0.775868	+	0.630895i	$0.217312\pi$
$278$	−5.30823	−	5.40704i	−0.318366	−	0.324293i
$279$		0			0
$280$	1.62538	−	0.387671i	0.0971353	−	0.0231678i
$281$	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	$0.762939\pi$
$284$	−19.7746	−	3.86409i	−1.17340	−	0.229291i
$285$		0			0
$286$	0.0554093	+	0.00536297i	0.00327642	+	0.000317119i
$287$	1.58437	−	2.74421i	0.0935226	−	0.161986i
$288$		0			0
$289$	−7.42107	−	12.8537i	−0.436533	−	0.756098i
$290$	1.93366	+	4.24859i	0.113548	+	0.249486i
$291$		0			0
$292$	−0.891837	+	1.02389i	−0.0521908	+	0.0599189i
$293$	2.18285	−	12.3796i	0.127523	−	0.723221i	−0.852254	−	0.523129i	$-0.824765\pi$
$293$	2.18285	−	12.3796i	0.127523	−	0.723221i	0.979777	−	0.200092i	$-0.0641242\pi$
$294$		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
$302$	−9.52027	−	13.8668i	−0.547830	−	0.797943i
$303$		0			0
$304$	−5.02384	−	2.04133i	−0.288137	−	0.117078i
$305$	−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	$0.0265176\pi$
$308$	−0.0453051	+	0.00712969i	−0.00258150	+	0.000406252i
$309$		0			0
$310$	−2.49431	+	5.22278i	−0.141667	+	0.296634i
$311$	−0.935160	−	0.784692i	−0.0530280	−	0.0444958i	0.615888	−	0.787833i	$-0.288797\pi$
$311$	−0.935160	−	0.784692i	−0.0530280	−	0.0444958i	−0.668916	+	0.743338i	$0.733242\pi$
$312$		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	$0.647009\pi$
$314$	−22.9102	−	6.36576i	−1.29290	−	0.359241i
$315$		0			0
$316$	−8.34141	+	13.8514i	−0.469241	+	0.779202i
$317$	1.28552	+	7.29053i	0.0722018	+	0.409477i	0.999391	+	0.0348844i	$0.0111063\pi$
$317$	1.28552	+	7.29053i	0.0722018	+	0.409477i	−0.927190	+	0.374593i	$0.877783\pi$
$318$		0			0
$319$	−0.0438192	−	0.120392i	−0.00245340	−	0.00674067i
$320$	−3.53651	−	0.827527i	−0.197697	−	0.0462601i
$321$		0			0
$322$	−3.18670	−	2.27543i	−0.177588	−	0.126805i
$323$		−	1.99145i		−	0.110807i
$324$		0			0
$325$		−	10.7082i		−	0.593984i
$326$	−8.36400	+	11.7136i	−0.463239	+	0.648759i
$327$		0			0
$328$	−5.74909	+	3.79299i	−0.317440	+	0.209433i
$329$	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	$0.918196\pi$
$332$	−2.07260	+	3.44167i	−0.113749	+	0.188886i
$333$		0			0
$334$	6.07269	−	21.8554i	0.332283	−	1.19588i
$335$	−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	$0.838883\pi$
$338$	−10.2226	−	4.88212i	−0.556034	−	0.265552i
$339$		0			0
$340$	−0.207355	−	1.31762i	−0.0112454	−	0.0714579i
$341$	0.0794281	−	0.137574i	0.00430127	−	0.00745003i
$342$		0			0
$343$	13.8688	−	8.00714i	0.748844	−	0.432345i
$344$	−24.6418	−	18.2906i	−1.32860	−	0.986165i
$345$		0			0
$346$	−15.7822	+	10.8353i	−0.848459	+	0.582512i
$347$	−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	0.273380	−	0.961906i	$-0.411859\pi$
$349$	−13.4766	−	16.0608i	−0.721385	−	0.859713i	−0.994765	+	0.102193i	$0.967414\pi$
$350$	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
$356$	−0.180662	−	0.157361i	−0.00957507	−	0.00834013i
$357$		0			0
$358$	14.6385	−	6.66240i	0.773667	−	0.352119i
$359$	15.2950	+	26.4917i	0.807240	+	1.39818i	0.914768	+	0.403979i	$0.132373\pi$
$359$	15.2950	+	26.4917i	0.807240	+	1.39818i	−0.107529	+	0.994202i	$0.534294\pi$
$360$		0			0
$361$	8.58106	−	14.8628i	0.451635	−	0.782255i
$362$	2.01949	−	20.8651i	0.106142	−	1.09664i
$363$		0			0
$364$	−5.70542	−	1.11488i	−0.299045	−	0.0584355i
$365$	0.236120	+	0.198128i	0.0123591	+	0.0103705i
$366$		0			0
$367$	−7.65245	+	21.0249i	−0.399455	+	1.09749i	0.563096	+	0.826391i	$0.309610\pi$
$367$	−7.65245	+	21.0249i	−0.399455	+	1.09749i	−0.962551	+	0.271101i	$0.912612\pi$
$368$	3.98087	+	7.52278i	0.207517	+	0.392152i
$369$		0			0
$370$	2.42685	−	2.38250i	0.126166	−	0.123860i
$371$	13.3385	−	2.35193i	0.692499	−	0.122106i
$372$		0			0
$373$	3.91132	+	10.7463i	0.202521	+	0.556421i	0.998824	−	0.0484764i	$-0.0154366\pi$
$373$	3.91132	+	10.7463i	0.202521	+	0.556421i	−0.796304	+	0.604897i	$0.793214\pi$
$374$	0.00285428	+	0.0364978i	0.000147591	+	0.00188725i
$375$		0			0
$376$	1.47824	−	12.8054i	0.0762346	−	0.660390i
$377$		−	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	$0.688177\pi$
$380$	−0.442277	+	1.14877i	−0.0226883	+	0.0589308i
$381$		0			0
$382$	2.07826	+	26.5748i	0.106333	+	1.35969i
$383$	−31.1726	+	11.3459i	−1.59285	+	0.579749i	−0.977946	−	0.208856i	$-0.933026\pi$
$383$	−31.1726	+	11.3459i	−1.59285	+	0.579749i	−0.614900	+	0.788605i	$0.710804\pi$
$384$		0			0
$385$	0.00180784	+	0.0102528i	9.21359e−5	+	0.000522529i
$386$	−2.09081	−	2.12973i	−0.106419	−	0.108400i
$387$		0			0
$388$	−0.411341	+	22.3017i	−0.0208827	+	1.13220i
$389$	−6.54404	−	2.38183i	−0.331796	−	0.120764i	0.170750	−	0.985314i	$-0.445381\pi$
$389$	−6.54404	−	2.38183i	−0.331796	−	0.120764i	−0.502546	+	0.864551i	$0.667603\pi$
$390$		0			0
$391$	−2.00913	+	2.39438i	−0.101606	+	0.121089i
$392$	−14.9830	+	0.894090i	−0.756755	+	0.0451584i
$393$		0			0
$394$	16.1282	+	1.56102i	0.812529	+	0.0786432i
$395$	3.17868	+	1.83521i	0.159937	+	0.0923395i
$396$		0			0
$397$	−31.8597	+	18.3942i	−1.59899	+	0.923178i	−0.607308	+	0.794466i	$0.707751\pi$
$397$	−31.8597	+	18.3942i	−1.59899	+	0.923178i	−0.991682	+	0.128712i	$0.958916\pi$
$398$	−7.31526	+	3.32939i	−0.366681	+	0.166887i
$399$		0			0
$400$	4.02391	−	18.7486i	0.201195	−	0.937428i
$401$	−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	$0.852511\pi$
$410$	0.884936	+	1.28896i	0.0437039	+	0.0636570i
$411$		0			0
$412$	−24.8178	+	20.0564i	−1.22268	+	0.988110i
$413$	−7.13978	−	12.3665i	−0.351326	−	0.608514i
$414$		0			0
$415$	0.789809	+	0.455997i	0.0387702	+	0.0223840i
$416$	10.0056	+	7.71698i	0.490567	+	0.378356i
$417$		0			0
$418$	0.0145603	−	0.0304875i	0.000712168	−	0.00149119i
$419$	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	$-0.642208\pi$
$421$	9.82045	−	26.9815i	0.478619	−	1.31500i	0.910666	−	0.413144i	$-0.135570\pi$
$422$	−6.30192	+	22.6804i	−0.306773	+	1.10407i
$423$		0			0
$424$	−28.2150	−	8.40321i	−1.37024	−	0.408096i
$425$	6.93506	−	1.22284i	0.336400	−	0.0593164i
$426$		0			0
$427$	−11.0142	+	4.00883i	−0.533013	+	0.194001i
$428$	12.7425	−	4.37350i	0.615931	−	0.211401i
$429$		0			0
$430$	−4.04815	+	5.66937i	−0.195219	+	0.273401i
$431$	26.5585			1.27928			0.639639	−	0.768675i	$-0.279084\pi$
$431$	26.5585			1.27928			0.639639	+	0.768675i	$0.279084\pi$
$432$		0			0
$433$	−1.55270			−0.0746180			−0.0373090	−	0.999304i	$-0.511879\pi$
$433$	−1.55270			−0.0746180			−0.0373090	+	0.999304i	$0.511879\pi$
$434$	−9.63998	+	13.5006i	−0.462734	+	0.648051i
$435$		0			0
$436$	−5.51802	+	1.89390i	−0.264265	+	0.0907016i
$437$	2.71064	−	0.986591i	0.129667	−	0.0471951i
$438$		0			0
$439$	1.13120	−	0.199460i	0.0539891	−	0.00951973i	−0.146588	−	0.989198i	$-0.546829\pi$
$439$	1.13120	−	0.199460i	0.0539891	−	0.00951973i	0.200577	+	0.979678i	$0.435718\pi$
$440$	0.00645921	−	0.0216877i	0.000307931	−	0.00103392i
$441$		0			0
$442$	−1.24231	+	4.47102i	−0.0590904	+	0.212665i
$443$	−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
$446$	1.69300	−	3.54493i	0.0801658	−	0.167857i
$447$		0			0
$448$	−9.57045	−	4.09597i	−0.452161	−	0.193516i
$449$	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
$452$	30.3424	−	24.5212i	1.42719	−	1.15338i
$453$		0			0
$454$	19.7921	+	28.8282i	0.928889	+	1.35297i
$455$	−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	−0.778550	−	0.627582i	$-0.784045\pi$
$461$	−6.34887	+	5.32733i	−0.295696	+	0.248119i	0.482854	+	0.875701i	$0.339600\pi$
$462$		0			0
$463$	0.381159	+	0.0672086i	0.0177140	+	0.00312345i	0.182498	−	0.983206i	$-0.441582\pi$
$463$	0.381159	+	0.0672086i	0.0177140	+	0.00312345i	−0.164784	+	0.986330i	$0.552693\pi$
$464$	6.10253	−	28.4335i	0.283303	−	1.31999i
$465$		0			0
$466$	26.0396	−	11.8514i	1.20626	−	0.549004i
$467$	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
$470$	−2.91256	−	0.281901i	−0.134346	−	0.0130031i
$471$		0			0
$472$	1.84886	+	30.9829i	0.0851009	+	1.42610i
$473$	0.122902	−	0.146469i	0.00565103	−	0.00673463i
$474$		0			0
$475$	−6.10704	−	2.22278i	−0.280210	−	0.101988i
$476$	0.0705015	−	3.82238i	0.00323143	−	0.175198i
$477$		0			0
$478$	−8.48853	−	8.64654i	−0.388256	−	0.395483i
$479$	0.196814	+	1.11619i	0.00899268	+	0.0510000i	0.988974	−	0.148090i	$-0.0473125\pi$
$479$	0.196814	+	1.11619i	0.00899268	+	0.0510000i	−0.979981	+	0.199090i	$0.936201\pi$
$480$		0			0
$481$	−11.1181	+	4.04665i	−0.506941	+	0.184511i
$482$	1.59375	+	20.3794i	0.0725934	+	0.928255i
$483$		0			0
$484$	7.90418	−	20.5304i	0.359281	−	0.933199i
$485$	5.06338			0.229916
$486$		0			0
$487$			41.9634i			1.90154i	0.309896	+	0.950771i	$0.399706\pi$
$487$			41.9634i			1.90154i	−0.309896	+	0.950771i	$0.600294\pi$
$488$	25.3087	+	2.92161i	1.14567	+	0.132255i
$489$		0			0
$490$	0.265648	+	3.39685i	0.0120007	+	0.153454i
$491$	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
$494$	3.05601	−	3.00016i	0.137496	−	0.134984i
$495$		0			0
$496$	31.8707	−	16.8652i	1.43104	−	0.757268i
$497$	−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	$0.650169\pi$
$500$	−8.72786	−	1.70548i	−0.390322	−	0.0762715i
$501$		0			0
$502$	1.99997	−	20.6634i	0.0892632	−	0.922253i
$503$	−12.3849	+	21.4513i	−0.552216	+	0.956466i	0.445898	+	0.895084i	$0.352884\pi$
$503$	−12.3849	+	21.4513i	−0.552216	+	0.956466i	−0.998114	+	0.0613824i	$0.980449\pi$
$504$		0			0
$505$	−3.78767	−	6.56044i	−0.168549	−	0.291936i
$506$	−0.0482644	+	0.0219665i	−0.00214562	+	0.000976532i
$507$		0			0
$508$	−26.1106	−	22.7429i	−1.15847	−	1.00906i
$509$	5.29018	−	30.0021i	0.234483	−	1.32982i	−0.609217	−	0.793004i	$-0.708516\pi$
$509$	5.29018	−	30.0021i	0.234483	−	1.32982i	0.843700	−	0.536816i	$-0.180373\pi$
$510$		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
$518$	8.03594	−	5.51710i	0.353079	−	0.242408i
$519$		0			0
$520$	1.70959	−	2.30322i	0.0749703	−	0.101003i
$521$	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	$0.254664\pi$
$524$	−0.958157	−	6.08853i	−0.0418573	−	0.265979i
$525$		0			0
$526$	22.5991	+	10.7930i	0.985369	+	0.470595i
$527$	10.1439	+	8.51177i	0.441877	+	0.370779i
$528$		0			0
$529$	17.3585	+	6.31798i	0.754717	+	0.274695i
$530$	−1.78911	+	6.43895i	−0.0777139	+	0.279690i
$531$		0			0
$532$	−1.82015	+	3.02246i	−0.0789134	+	0.131040i
$533$	−0.944542	−	5.35676i	−0.0409126	−	0.232027i
$534$		0			0
$535$	−1.04597	−	2.87377i	−0.0452211	−	0.124244i
$536$	7.52412	+	11.4044i	0.324993	+	0.492596i
$537$		0			0
$538$	8.42150	−	11.7942i	0.363076	−	0.508482i
$539$		−	0.0935167i		−	0.00402805i
$540$		0			0
$541$		−	35.0866i		−	1.50849i	−0.656592	−	0.754246i	$-0.728003\pi$
$541$		−	35.0866i		−	1.50849i	0.656592	−	0.754246i	$-0.271997\pi$
$542$	−21.5586	−	15.3937i	−0.926021	−	0.661216i
$543$		0			0
$544$	−3.85522	+	7.36131i	−0.165291	+	0.315613i
$545$	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	$0.961066\pi$
$548$	−12.1578	+	20.1888i	−0.519356	+	0.862421i
$549$		0			0
$550$	0.115111	+	0.0319844i	0.00490835	+	0.00136382i
$551$	−9.26174	−	3.37100i	−0.394563	−	0.143609i
$552$		0			0
$553$	8.05890	+	6.76222i	0.342699	+	0.287559i
$554$	−13.2784	+	27.8034i	−0.564147	+	1.18125i
$555$		0			0
$556$	10.5854	−	1.66584i	0.448923	−	0.0706473i
$557$	−3.41195	+	5.90968i	−0.144569	+	0.250401i	−0.929212	−	0.369547i	$-0.879513\pi$
$557$	−3.41195	+	5.90968i	−0.144569	+	0.250401i	0.784643	+	0.619948i	$0.212846\pi$
$558$		0			0
$559$	20.9888	−	12.1179i	0.887730	−	0.512531i
$560$	−0.889572	+	2.18929i	−0.0375913	+	0.0925144i
$561$		0			0
$562$	9.25046	+	13.4738i	0.390207	+	0.568357i
$563$	−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	$0.0707711\pi$
$572$	−0.0517082	+	0.0593648i	−0.00216203	+	0.00248217i
$573$		0			0
$574$	1.85634	+	4.07871i	0.0774822	+	0.170242i
$575$	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	$0.314207\pi$
$578$	20.8923	+	2.02213i	0.869006	+	0.0841095i
$579$		0			0
$580$	−6.47891	−	1.26602i	−0.269022	−	0.0525688i
$581$	2.00240	+	1.68021i	0.0830736	+	0.0697070i
$582$		0			0
$583$	0.0627342	−	0.172361i	0.00259818	−	0.00713845i
$584$	−0.445509	−	1.86788i	−0.0184353	−	0.0772935i
$585$		0			0
$586$	12.4541	+	12.6859i	0.514473	+	0.524050i
$587$	−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
$590$	7.02425	−	0.549326i	0.289184	−	0.0226154i
$591$		0			0
$592$	−20.9869	+	2.90719i	−0.862555	+	0.119485i
$593$			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
$596$	10.3108	−	26.7814i	0.422347	−	1.09701i
$597$		0			0
$598$	−6.70113	+	0.524056i	−0.274029	+	0.0214302i
$599$	−8.37844	+	3.04950i	−0.342334	+	0.124599i	−0.507465	−	0.861672i	$-0.669417\pi$
$599$	−8.37844	+	3.04950i	−0.342334	+	0.124599i	0.165131	+	0.986272i	$0.447195\pi$
$600$		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	$0.769412\pi$
$602$	−14.2482	+	13.9878i	−0.580714	+	0.570102i
$603$		0			0
$604$	23.7835	+	0.438672i	0.967735	+	0.0178493i
$605$	−4.69274	−	1.70802i	−0.190787	−	0.0694407i
$606$		0			0
$607$	8.91382	−	10.6231i	0.361801	−	0.431177i	−0.554182	−	0.832396i	$-0.686969\pi$
$607$	8.91382	−	10.6231i	0.361801	−	0.431177i	0.915982	+	0.401218i	$0.131413\pi$
$608$	6.47805	−	4.10449i	0.262720	−	0.166459i
$609$		0			0
$610$	0.557151	−	5.75639i	0.0225584	−	0.233070i
$611$	8.81625	+	5.09007i	0.356667	+	0.205922i
$612$		0			0
$613$	−17.7329	+	10.2381i	−0.716224	+	0.413512i	−0.813361	−	0.581759i	$-0.802365\pi$
$613$	−17.7329	+	10.2381i	−0.716224	+	0.413512i	0.0971374	+	0.995271i	$0.469031\pi$
$614$	8.74955	+	19.2243i	0.353103	+	0.775831i
$615$		0			0
$616$	0.0290263	−	0.0580021i	0.00116950	−	0.00233697i
$617$	−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
$626$	4.64249	−	3.18732i	0.185551	−	0.127391i
$627$		0			0
$628$	26.1543	−	21.1365i	1.04367	−	0.843440i
$629$	−3.89042	−	6.73841i	−0.155121	−	0.268678i
$630$		0			0
$631$	−24.6191	−	14.2138i	−0.980071	−	0.565844i	−0.0777793	−	0.996971i	$-0.524783\pi$
$631$	−24.6191	−	14.2138i	−0.980071	−	0.565844i	−0.902292	+	0.431126i	$0.858116\pi$
$632$	−9.08691	−	20.9835i	−0.361458	−	0.834680i
$633$		0			0
$634$	−9.44732	−	4.51187i	−0.375201	−	0.179189i
$635$	−5.05252	+	6.02135i	−0.200503	+	0.238950i
$636$		0			0
$637$	4.05421	−	11.1389i	0.160634	−	0.441337i
$638$	0.174574	+	0.0485065i	0.00691143	+	0.00192039i
$639$		0			0
$640$	3.85875	−	3.39019i	0.152530	−	0.134009i
$641$	−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	$0.457765\pi$
$644$	5.23770	−	1.79769i	0.206394	−	0.0708391i
$645$		0			0
$646$	2.29201	+	1.63659i	0.0901781	+	0.0643907i
$647$	19.0202			0.747763			0.373881	−	0.927477i	$-0.378027\pi$
$647$	19.0202			0.747763			0.373881	+	0.927477i	$0.378027\pi$
$648$		0			0
$649$	−0.193381			−0.00759085
$650$	12.3244	+	8.80007i	0.483401	+	0.345167i
$651$		0			0
$652$	−6.60795	−	19.2527i	−0.258787	−	0.753995i
$653$	11.7763	−	4.28623i	0.460843	−	0.167733i	−0.101157	−	0.994871i	$-0.532254\pi$
$653$	11.7763	−	4.28623i	0.460843	−	0.167733i	0.562000	+	0.827137i	$0.310032\pi$
$654$		0			0
$655$	−1.37786	+	0.242955i	−0.0538376	+	0.00949302i
$656$	0.359194	−	9.73389i	0.0140242	−	0.380044i
$657$		0			0
$658$	−8.08082	−	2.24531i	−0.315023	−	0.0875315i
$659$	−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	−0.517427	−	0.855727i	$-0.673110\pi$
$661$	10.6735	−	12.7202i	0.415150	−	0.494757i	0.932577	+	0.360971i	$0.117555\pi$
$662$	−3.82482	−	1.82667i	−0.148656	−	0.0709955i
$663$		0			0
$664$	−2.25783	−	5.21379i	−0.0876208	−	0.202334i
$665$	0.693608	+	0.400455i	0.0268970	+	0.0155290i
$666$		0			0
$667$	7.73476	+	13.3970i	0.299491	+	0.518734i
$668$	20.1634	+	24.9502i	0.780147	+	0.965352i
$669$		0			0
$670$	2.55689	−	1.75544i	0.0987814	−	0.0678187i
$671$	−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	−0.534274	−	0.845311i	$-0.679415\pi$
$677$	5.34485	−	4.48486i	0.205419	−	0.172367i	0.739693	+	0.672944i	$0.234971\pi$
$678$		0			0
$679$	14.2922	+	2.52009i	0.548483	+	0.0967123i
$680$	1.68689	+	0.844178i	0.0646892	+	0.0323727i
$681$		0			0
$682$	0.0930625	+	0.204475i	0.00356355	+	0.00782975i
$683$	−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
$686$	−2.18183	+	22.5423i	−0.0833025	+	0.860668i
$687$		0			0
$688$	41.3020	−	13.3296i	1.57463	−	0.508185i
$689$	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	$0.394220\pi$
$692$	0.499268	−	27.0688i	0.0189793	−	1.02900i
$693$		0			0
$694$	29.5505	−	29.0105i	1.12172	−	1.10122i
$695$	−0.422398	−	2.39554i	−0.0160225	−	0.0908679i
$696$		0			0
$697$	3.36139	−	1.22345i	0.127322	−	0.0463414i
$698$	29.5599	−	2.31171i	1.11886	−	0.0874995i
$699$		0			0
$700$	−11.6431	−	4.48259i	−0.440069	−	0.169426i
$701$	9.68894			0.365946			0.182973	−	0.983118i	$-0.441428\pi$
$701$	9.68894			0.365946			0.182973	+	0.983118i	$0.441428\pi$
$702$		0			0
$703$			7.18080i			0.270829i
$704$	−0.112842	+	0.0845087i	−0.00425289	+	0.00318504i
$705$		0			0
$706$	4.44740	−	0.347805i	0.167380	−	0.0130898i
$707$	−7.42607	−	20.4030i	−0.279286	−	0.767333i
$708$		0			0
$709$	−24.6853	+	4.35269i	−0.927077	+	0.163469i	−0.616748	−	0.787161i	$-0.711550\pi$
$709$	−24.6853	+	4.35269i	−0.927077	+	0.163469i	−0.310329	+	0.950629i	$0.600439\pi$
$710$	−4.53140	−	4.61575i	−0.170060	−	0.173226i
$711$		0			0
$712$	0.329581	−	0.0786084i	0.0123516	−	0.00294597i
$713$	−6.56025	+	18.0241i	−0.245683	+	0.675009i
$714$		0			0
$715$	0.0136901	+	0.0114874i	0.000511981	+	0.000429603i
$716$	−4.36207	+	22.3230i	−0.163018	+	0.834250i
$717$		0			0
$718$	−43.0596	−	4.16766i	−1.60697	−	0.155536i
$719$	−16.4482	+	28.4892i	−0.613415	+	1.06247i	0.377245	+	0.926113i	$0.376871\pi$
$719$	−16.4482	+	28.4892i	−0.613415	+	1.06247i	−0.990660	+	0.136353i	$0.956462\pi$
$720$		0			0
$721$	10.3805	+	17.9796i	0.386590	+	0.669594i
$722$	10.0541	+	22.0906i	0.374173	+	0.822126i
$723$		0			0
$724$	22.3545	+	19.4713i	0.830799	+	0.723647i
$725$	6.05210	−	34.3232i	0.224769	−	1.27473i
$726$		0			0
$727$	20.0843	+	23.9355i	0.744884	+	0.887719i	0.996792	−	0.0800327i	$-0.0255025\pi$
$727$	20.0843	+	23.9355i	0.744884	+	0.887719i	−0.251908	+	0.967751i	$0.581058\pi$
$728$	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	−0.134630	−	0.990896i	$-0.542984\pi$
$733$	−16.2456	−	2.86454i	−0.600046	−	0.105804i	−0.465417	+	0.885092i	$0.654096\pi$
$734$	−17.9093	−	26.0858i	−0.661045	−	0.962846i
$735$		0			0
$736$	−11.9297	−	1.60059i	−0.439734	−	0.0589985i
$737$	−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	$0.306835\pi$
$740$	0.747682	+	4.75108i	0.0274853	+	0.174653i
$741$		0			0
$742$	−8.25475	+	17.2844i	−0.303041	+	0.634532i
$743$	−2.55778	−	2.14623i	−0.0938358	−	0.0787376i	0.594663	−	0.803975i	$-0.297286\pi$
$743$	−2.55778	−	2.14623i	−0.0938358	−	0.0787376i	−0.688499	+	0.725238i	$0.741730\pi$
$744$		0			0
$745$	−6.12156	−	2.22807i	−0.224277	−	0.0816300i
$746$	−15.5825	−	4.32971i	−0.570517	−	0.158522i
$747$		0			0
$748$	−0.0443519	−	0.0267091i	−0.00162167	−	0.000976580i
$749$	−1.52210	−	8.63224i	−0.0556162	−	0.315415i
$750$		0			0
$751$	0.701648	+	1.92776i	0.0256035	+	0.0703450i	0.951836	−	0.306608i	$-0.0991940\pi$
$751$	0.701648	+	1.92776i	0.0256035	+	0.0703450i	−0.926232	+	0.376953i	$0.876972\pi$
$752$	13.5233	+	12.2250i	0.493144	+	0.445798i
$753$		0			0
$754$	18.6907	+	13.3459i	0.680676	+	0.486029i
$755$		−	5.39982i		−	0.196519i
$756$		0			0
$757$		−	41.6394i		−	1.51341i	−0.653756	−	0.756705i	$-0.726808\pi$
$757$		−	41.6394i		−	1.51341i	0.653756	−	0.756705i	$-0.273192\pi$
$758$	17.8336	−	24.9756i	0.647744	−	0.907154i
$759$		0			0
$760$	−0.958688	−	1.45310i	−0.0347753	−	0.0527094i
$761$	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
$764$	−32.2936	−	19.4475i	−1.16834	−	0.703585i
$765$		0			0
$766$	12.5596	−	45.2016i	0.453796	−	1.63320i
$767$	−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	$-0.565861\pi$
$770$	−0.0132859	−	0.00634510i	−0.000478789	−	0.000228662i
$771$		0			0
$772$	4.16940	−	0.656142i	0.150060	−	0.0236151i
$773$	3.52468	−	6.10492i	0.126774	−	0.219579i	−0.795651	−	0.605755i	$-0.792871\pi$
$773$	3.52468	−	6.10492i	0.126774	−	0.219579i	0.922425	+	0.386176i	$0.126204\pi$
$774$		0			0
$775$	37.4247	−	21.6072i	1.34434	−	0.776153i
$776$	−25.3295	−	18.8011i	−0.909277	−	0.674920i
$777$		0			0
$778$	8.11926	−	5.57430i	0.291089	−	0.199848i
$779$	−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	$-0.253241\pi$
$788$	−15.0509	+	17.2796i	−0.536167	+	0.615559i
$789$		0			0
$790$	−4.72446	+	2.15024i	−0.168089	+	0.0765021i
$791$	−12.6913	−	21.9820i	−0.451250	−	0.781589i
$792$		0			0
$793$	−10.0600	+	17.4245i	−0.357242	+	0.618762i
$794$	5.01214	−	51.7846i	0.177874	−	1.83777i
$795$		0			0
$796$	2.17985	−	11.1554i	0.0772628	−	0.395394i
$797$	10.7323	+	9.00550i	0.380159	+	0.318991i	0.812765	−	0.582592i	$-0.197961\pi$
$797$	10.7323	+	9.00550i	0.380159	+	0.318991i	−0.432606	+	0.901583i	$0.642406\pi$
$798$		0			0
$799$	−2.28975	+	6.29103i	−0.0810054	+	0.222561i
$800$	18.2714	+	20.0389i	0.645990	+	0.708483i
$801$		0			0
$802$	3.08050	−	3.02421i	0.108776	−	0.106789i
$803$	0.0117824	−	0.00207756i	0.000415792	−	7.33153e-5i
$804$		0			0
$805$	−0.429937	−	1.18124i	−0.0151533	−	0.0416333i
$806$	2.22019	+	28.3897i	0.0782030	+	0.999985i
$807$		0			0
$808$	−5.41207	+	46.8827i	−0.190396	+	1.64933i
$809$		−	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	$0.724774\pi$
$812$	−17.6576	−	6.79815i	−0.619659	−	0.238568i
$813$		0			0
$814$	−0.0102920	−	0.131604i	−0.000360734	−	0.00461272i
$815$	−4.34200	+	1.58036i	−0.152094	+	0.0553576i
$816$		0			0
$817$	−2.55420	−	14.4856i	−0.0893602	−	0.506787i
$818$	−23.8633	−	24.3075i	−0.834359	−	0.849890i
$819$		0			0
$820$	−2.21074	−	0.0407758i	−0.0772024	−	0.00142395i
$821$	5.42437	+	1.97431i	0.189312	+	0.0689038i	0.434936	−	0.900461i	$-0.356771\pi$
$821$	5.42437	+	1.97431i	0.189312	+	0.0689038i	−0.245625	+	0.969365i	$0.578993\pi$
$822$		0			0
$823$	12.2571	−	14.6074i	0.427254	−	0.509182i	−0.508874	−	0.860841i	$-0.669938\pi$
$823$	12.2571	−	14.6074i	0.427254	−	0.509182i	0.936128	+	0.351659i	$0.114382\pi$
$824$	−2.68806	−	45.0460i	−0.0936430	−	1.56925i
$825$		0			0
$826$	20.1004	+	1.94548i	0.699383	+	0.0676920i
$827$	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	−0.853535	−	0.521035i	$-0.825546\pi$
$829$	−23.8710	+	13.7819i	−0.829073	+	0.478666i	0.0244622	+	0.999701i	$0.492213\pi$
$830$	−1.17389	+	0.534271i	−0.0407463	+	0.0185448i
$831$		0			0
$832$	−17.1044	+	5.17389i	−0.592988	+	0.179372i
$833$	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	−0.944816	−	0.327600i	$-0.893760\pi$
$839$	−22.7744	+	19.1100i	−0.786259	+	0.659750i	0.158558	+	0.987350i	$0.449316\pi$
$840$		0			0
$841$	4.14263	−	23.4940i	0.142849	−	0.810138i
$842$	22.9832	+	33.4762i	0.792052	+	1.15367i
$843$		0			0
$844$	−20.9246	−	25.8920i	−0.720253	−	0.891240i
$845$	−1.81840	−	3.14956i	−0.0625548	−	0.108348i
$846$		0			0
$847$	−12.3959	−	7.15675i	−0.425927	−	0.245909i
$848$	32.8587	−	25.5676i	1.12837	−	0.877993i
$849$		0			0
$850$	−4.29189	+	8.98669i	−0.147210	+	0.308241i
$851$	7.24453	−	8.63370i	0.248339	−	0.295959i
$852$		0			0
$853$	−14.9845	+	41.1697i	−0.513061	+	1.40962i	0.364970	+	0.931019i	$0.381079\pi$
$853$	−14.9845	+	41.1697i	−0.513061	+	1.40962i	−0.878031	+	0.478604i	$0.841143\pi$
$854$	4.43765	−	15.9710i	0.151853	−	0.546516i
$855$		0			0
$856$	−5.43829	+	18.2598i	−0.185877	+	0.624109i
$857$	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	$0.550335\pi$
$860$	−3.19823	−	9.31826i	−0.109059	−	0.317750i
$861$		0			0
$862$	−21.8260	+	30.5669i	−0.743396	+	1.04111i
$863$	−46.6170			−1.58686			−0.793431	−	0.608660i	$-0.791707\pi$
$863$	−46.6170			−1.58686			−0.793431	+	0.608660i	$0.791707\pi$
$864$		0			0
$865$	−6.14571			−0.208961
$866$	1.27602	−	1.78704i	0.0433609	−	0.0607262i
$867$		0			0
$868$	−7.61603	−	22.1898i	−0.258505	−	0.753172i
$869$	0.133877	−	0.0487272i	0.00454146	−	0.00165296i
$870$		0			0
$871$	−10.6262	+	1.87368i	−0.360054	+	0.0634873i
$872$	2.35500	−	7.90726i	0.0797505	−	0.267774i
$873$		0			0
$874$	−1.09213	+	3.93053i	−0.0369417	+	0.132952i
$875$	−1.97894	+	5.43708i	−0.0669003	+	0.183807i
$876$		0			0
$877$	−3.98303	+	4.74679i	−0.134497	+	0.160288i	−0.829089	−	0.559116i	$-0.811141\pi$
$877$	−3.98303	+	4.74679i	−0.134497	+	0.160288i	0.694592	+	0.719404i	$0.255585\pi$
$878$	−0.700061	+	1.46584i	−0.0236259	+	0.0494698i
$879$		0			0
$880$	0.0196528	+	0.0252572i	0.000662495	+	0.000851421i
$881$	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	$0.655610\pi$
$884$	−4.12488	−	5.10412i	−0.138735	−	0.171670i
$885$		0			0
$886$	−13.5627	−	19.7547i	−0.455647	−	0.663674i
$887$	−0.0310073	+	0.175851i	−0.00104112	+	0.00590451i	−0.985324	−	0.170695i	$-0.945399\pi$
$887$	−0.0310073	+	0.175851i	−0.00104112	+	0.00590451i	0.984283	+	0.176600i	$0.0565098\pi$
$888$		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
$896$	12.5792	−	7.64879i	0.420243	−	0.255528i
$897$		0			0
$898$	−39.4946	+	17.9751i	−1.31795	+	0.599838i
$899$	56.7571	−	32.7687i	1.89296	−	1.09290i
$900$		0			0
$901$	13.2413	+	7.64488i	0.441132	+	0.254688i
$902$	0.0604054	+	0.00584653i	0.00201128	+	0.000194668i
$903$		0			0
$904$	3.28644	+	55.0736i	0.109305	+	1.83172i
$905$	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	$0.715657\pi$
$908$	−49.4444	−	0.911974i	−1.64087	−	0.0302649i
$909$		0			0
$910$	−1.30741	−	1.33175i	−0.0433403	−	0.0441471i
$911$	0.423720	+	2.40304i	0.0140385	+	0.0796161i	0.991022	−	0.133698i	$-0.0426853\pi$
$911$	0.423720	+	2.40304i	0.0140385	+	0.0796161i	−0.976984	+	0.213314i	$0.931574\pi$
$912$		0			0
$913$	0.0332645	−	0.0121073i	0.00110089	−	0.000400693i
$914$	0.789808	+	10.0993i	0.0261245	+	0.334055i
$915$		0			0
$916$	29.2529	+	11.2623i	0.966542	+	0.372118i
$917$	−4.01015			−0.132427
$918$		0			0
$919$			2.20402i			0.0727038i	0.999339	+	0.0363519i	$0.0115737\pi$
$919$			2.20402i			0.0727038i	−0.999339	+	0.0363519i	$0.988426\pi$
$920$	−0.313335	+	2.71430i	−0.0103304	+	0.0894879i
$921$		0			0
$922$	−0.913825	−	11.6851i	−0.0300952	−	0.384829i
$923$	7.69653	+	21.1460i	0.253334	+	0.696030i
$924$		0			0
$925$	−25.0065	+	4.40933i	−0.822210	+	0.144978i
$926$	−0.390591	+	0.383454i	−0.0128356	+	0.0126011i
$927$		0			0
$928$	27.7097	+	30.3904i	0.909617	+	0.997614i
$929$	−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
$932$	−7.75945	+	39.7092i	−0.254169	+	1.30072i
$933$		0			0
$934$	−0.907587	+	9.37704i	−0.0296972	+	0.306826i
$935$	−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	$-0.425243\pi$
$938$	8.09091	−	3.68241i	0.264178	−	0.120235i
$939$		0			0
$940$	2.71801	−	3.12047i	0.0886516	−	0.101779i
$941$	−7.38960	+	41.9085i	−0.240894	+	1.36618i	0.588944	+	0.808174i	$0.299544\pi$
$941$	−7.38960	+	41.9085i	−0.240894	+	1.36618i	−0.829838	+	0.558004i	$0.811567\pi$
$942$		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
$950$	7.57707	−	5.20206i	0.245833	−	0.168777i
$951$		0			0
$952$	4.34134	+	3.22240i	0.140704	+	0.104439i
$953$	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
$956$	16.9275	−	2.66389i	0.547473	−	0.0861563i
$957$		0			0
$958$	−1.44640	−	0.690774i	−0.0467309	−	0.0223179i
$959$	11.7461	+	9.85611i	0.379300	+	0.318270i
$960$		0			0
$961$	47.2298	+	17.1902i	1.52354	+	0.554524i
$962$	4.47952	−	16.1217i	0.144426	−	0.519784i
$963$		0			0
$964$	−24.7649	−	14.9136i	−0.797624	−	0.480335i
$965$	−0.166374	−	0.943555i	−0.00535578	−	0.0303741i
$966$		0			0
$967$	−0.543982	−	1.49458i	−0.0174933	−	0.0480624i	0.930639	−	0.365939i	$-0.119252\pi$
$967$	−0.543982	−	1.49458i	−0.0174933	−	0.0480624i	−0.948132	+	0.317877i	$0.897030\pi$
$968$	17.1333	+	25.9692i	0.550684	+	0.834680i
$969$		0			0
$970$	−4.16113	+	5.82759i	−0.133606	+	0.187113i
$971$			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
$974$	−48.2968	−	34.4858i	−1.54753	−	1.10500i
$975$		0			0
$976$	−24.1615	+	26.7275i	−0.773390	+	0.855527i
$977$	−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
$980$	−4.12784	−	2.48581i	−0.131859	−	0.0794064i
$981$		0			0
$982$	−28.0622	−	7.79730i	−0.895502	−	0.248822i
$983$	30.2880	+	11.0239i	0.966036	+	0.351608i	0.776396	−	0.630245i	$-0.217046\pi$
$983$	30.2880	+	11.0239i	0.966036	+	0.351608i	0.189640	+	0.981854i	$0.439268\pi$
$984$		0			0
$985$	3.98484	+	3.34368i	0.126967	+	0.106538i
$986$	−6.50894	+	13.6289i	−0.207287	+	0.434033i
$987$		0			0
$988$	0.941518	+	5.98280i	0.0299537	+	0.190338i
$989$	−11.5432	+	19.9933i	−0.367051	+	0.635751i
$990$		0			0
$991$	2.66599	−	1.53921i	0.0846881	−	0.0488947i	−0.457058	−	0.889437i	$-0.651097\pi$
$991$	2.66599	−	1.53921i	0.0846881	−	0.0488947i	0.541746	+	0.840542i	$0.317763\pi$
$992$	−6.78099	+	50.5407i	−0.215297	+	1.60467i
$993$		0			0
$994$	−10.4932	−	15.2840i	−0.332826	−	0.484778i
$995$	−2.54100	−	0.448048i	−0.0805553	−	0.0142041i
$996$		0			0
$997$	27.9424	+	33.3004i	0.884944	+	1.05464i	0.998134	+	0.0610619i	$0.0194487\pi$
$997$	27.9424	+	33.3004i	0.884944	+	1.05464i	−0.113190	+	0.993573i	$0.536107\pi$
$998$	−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.611.11		192
3.2	odd	2		216.2.v.b.59.22	yes	192
8.3	odd	2	inner	648.2.v.b.611.28		192
12.11	even	2		864.2.bh.b.815.2		192
24.5	odd	2		864.2.bh.b.815.1		192
24.11	even	2		216.2.v.b.59.5	yes	192
27.11	odd	18	inner	648.2.v.b.35.28		192
27.16	even	9		216.2.v.b.11.5	✓	192
108.43	odd	18		864.2.bh.b.335.1		192
216.11	even	18	inner	648.2.v.b.35.11		192
216.43	odd	18		216.2.v.b.11.22	yes	192
216.205	even	18		864.2.bh.b.335.2		192

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.821807 + 1.15093i) q^{2} +(-0.649266 - 1.89168i) q^{4} +(-0.426624 + 0.155279i) q^{5} +(-1.28150 + 0.225962i) q^{7} +(2.71076 + 0.807339i) q^{8} +(0.171889 - 0.618623i) q^{10} +(-0.00602720 + 0.0165596i) q^{11} +(-1.43581 + 1.71113i) q^{13} +(0.793076 - 1.66060i) q^{14} +(-3.15691 + 2.45641i) q^{16} +(-1.27216 - 0.734483i) q^{17} +(0.677841 + 1.17406i) q^{19} +(0.570730 + 0.706220i) q^{20} +(-0.0141057 - 0.0205456i) q^{22} +(0.369486 - 2.09546i) q^{23} +(-3.67233 + 3.08145i) q^{25} +(-0.789428 - 3.05873i) q^{26} +(1.25948 + 2.27747i) q^{28} +(-5.56933 + 4.67322i) q^{29} +(-8.87753 - 1.56535i) q^{31} +(-0.232774 - 5.65206i) q^{32} +(1.89081 - 0.860562i) q^{34} +(0.511630 - 0.295390i) q^{35} +(4.58718 + 2.64841i) q^{37} +(-1.90831 - 0.184701i) q^{38} +(-1.28184 + 0.0764919i) q^{40} +(-1.56527 + 1.86542i) q^{41} +(-10.1956 - 3.71089i) q^{43} +(0.0352387 + 0.000649957i) q^{44} +(2.10807 + 2.14731i) q^{46} +(-0.791397 - 4.48824i) q^{47} +(-4.98668 + 1.81500i) q^{49} +(-0.528577 - 6.75893i) q^{50} +(4.16913 + 1.60511i) q^{52} -10.4085 q^{53} -0.00800062i q^{55} +(-3.65625 - 0.422073i) q^{56} +(-0.801622 - 10.2504i) q^{58} +(3.75319 + 10.3118i) q^{59} +(8.87057 - 1.56412i) q^{61} +(9.09722 - 8.93098i) q^{62} +(6.69641 + 4.37700i) q^{64} +(0.346849 - 0.952961i) q^{65} +(3.70041 + 3.10502i) q^{67} +(-0.563436 + 2.88340i) q^{68} +(-0.0804893 + 0.831602i) q^{70} +(5.03714 - 8.72458i) q^{71} +(-0.339460 - 0.587962i) q^{73} +(-6.81790 + 3.10303i) q^{74} +(1.78084 - 2.04453i) q^{76} +(0.00398198 - 0.0225829i) q^{77} +(-5.19665 - 6.19313i) q^{79} +(0.965387 - 1.53816i) q^{80} +(-0.860607 - 3.33452i) q^{82} +(-1.29122 - 1.53881i) q^{83} +(0.656785 + 0.115809i) q^{85} +(12.6498 - 8.68475i) q^{86} +(-0.0297075 + 0.0400230i) q^{88} +(0.103744 - 0.0598964i) q^{89} +(1.45333 - 2.51724i) q^{91} +(-4.20383 + 0.661560i) q^{92} +(5.81601 + 2.77762i) q^{94} +(-0.471489 - 0.395626i) q^{95} +(-10.4801 - 3.81446i) q^{97} +(2.00915 - 7.23088i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40}+ \cdots - 162 q^{98}+O(q^{100}) \) 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

L-functions

Modular forms

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Database

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