LMFDB - Embedded newform 648.2.v.b.35.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(35,648)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			35.11
Character	$\chi$	$=$	648.35
Dual form			648.2.v.b.611.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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	0.244857	−	0.969559i	$-0.421259\pi$
$5$	−0.426624	−	0.155279i	−0.190792	−	0.0694427i	−0.435649	+	0.900116i	$0.643481\pi$
$6$		0			0
$7$	−1.28150	−	0.225962i	−0.484360	−	0.0854057i	−0.0738642	−	0.997268i	$-0.523533\pi$
$7$	−1.28150	−	0.225962i	−0.484360	−	0.0854057i	−0.410495	+	0.911863i	$0.634644\pi$
$8$	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	0.938781	−	0.344515i	$-0.111957\pi$
$11$	−0.00602720	−	0.0165596i	−0.00181727	−	0.00499290i	−0.940598	+	0.339522i	$0.889735\pi$
$12$		0			0
$13$	−1.43581	−	1.71113i	−0.398222	−	0.474582i	0.529255	−	0.848463i	$-0.322471\pi$
$13$	−1.43581	−	1.71113i	−0.398222	−	0.474582i	−0.927477	+	0.373881i	$0.878027\pi$
$14$	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	−0.646275	−	0.763105i	$-0.723674\pi$
$17$	−1.27216	+	0.734483i	−0.308545	+	0.178138i	0.337730	+	0.941243i	$0.390341\pi$
$18$		0			0
$19$	0.677841	−	1.17406i	0.155507	−	0.269347i	−0.777736	−	0.628591i	$-0.783632\pi$
$19$	0.677841	−	1.17406i	0.155507	−	0.269347i	0.933244	+	0.359244i	$0.116965\pi$
$20$	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	0.998792	+	0.0491452i	$0.0156497\pi$
$23$	0.369486	+	2.09546i	0.0770432	+	0.436933i	−0.921748	+	0.387788i	$0.873239\pi$
$24$		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	$-0.513645\pi$
$29$	−5.56933	−	4.67322i	−1.03420	−	0.867796i	−0.991345	+	0.131286i	$0.958089\pi$
$30$		0			0
$31$	−8.87753	+	1.56535i	−1.59445	+	0.281145i	−0.899172	−	0.437595i	$-0.855830\pi$
$31$	−8.87753	+	1.56535i	−1.59445	+	0.281145i	−0.695279	+	0.718740i	$0.744719\pi$
$32$	−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	−0.0730557	−	0.997328i	$-0.523275\pi$
$37$	4.58718	−	2.64841i	0.754128	−	0.435396i	0.827183	+	0.561932i	$0.189942\pi$
$38$	−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	0.629841	−	0.776724i	$-0.283120\pi$
$41$	−1.56527	−	1.86542i	−0.244454	−	0.291329i	−0.874295	+	0.485395i	$0.838676\pi$
$42$		0			0
$43$	−10.1956	+	3.71089i	−1.55481	+	0.565906i	−0.969541	−	0.244930i	$-0.921235\pi$
$43$	−10.1956	+	3.71089i	−1.55481	+	0.565906i	−0.585273	+	0.810836i	$0.699013\pi$
$44$	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	0.871096	+	0.491113i	$0.163410\pi$
$47$	−0.791397	+	4.48824i	−0.115437	+	0.654676i	−0.986533	+	0.163563i	$0.947701\pi$
$48$		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	−0.413302	−	0.910594i	$-0.635625\pi$
$59$	3.75319	−	10.3118i	0.488624	−	1.34248i	0.901926	−	0.431890i	$-0.142153\pi$
$60$		0			0
$61$	8.87057	+	1.56412i	1.13576	+	0.200265i	0.709750	−	0.704453i	$-0.248808\pi$
$61$	8.87057	+	1.56412i	1.13576	+	0.200265i	0.426010	+	0.904718i	$0.359919\pi$
$62$	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	−0.388129	−	0.921605i	$-0.626878\pi$
$67$	3.70041	−	3.10502i	0.452078	−	0.379338i	0.840206	+	0.542267i	$0.182434\pi$
$68$	−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	0.993145	+	0.116886i	$0.0372911\pi$
$71$	5.03714	+	8.72458i	0.597799	+	1.03542i	−0.395347	+	0.918532i	$0.629376\pi$
$72$		0			0
$73$	−0.339460	+	0.587962i	−0.0397308	+	0.0688158i	−0.885207	−	0.465197i	$-0.845983\pi$
$73$	−0.339460	+	0.587962i	−0.0397308	+	0.0688158i	0.845476	+	0.534013i	$0.179317\pi$
$74$	−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	−0.974572	−	0.224074i	$-0.928064\pi$
$79$	−5.19665	+	6.19313i	−0.584669	+	0.696782i	0.389903	+	0.920856i	$0.372509\pi$
$80$	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	−0.832240	−	0.554416i	$-0.812942\pi$
$83$	−1.29122	+	1.53881i	−0.141729	+	0.168907i	0.690510	+	0.723323i	$0.257386\pi$
$84$		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	0.505488	−	0.862833i	$-0.331312\pi$
$89$	0.103744	+	0.0598964i	0.0109968	+	0.00634901i	−0.494492	+	0.869182i	$0.664646\pi$
$90$		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	−0.813966	−	0.580913i	$-0.802696\pi$
$97$	−10.4801	+	3.81446i	−1.06410	+	0.387299i	−0.250130	+	0.968212i	$0.580474\pi$
$98$	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	−0.404932	−	0.914347i	$-0.632705\pi$
$101$	2.89743	−	16.4321i	0.288305	−	1.63506i	0.693237	−	0.720710i	$-0.256184\pi$
$102$		0			0
$103$	−5.45676	+	14.9923i	−0.537670	+	1.47724i	0.312082	+	0.950055i	$0.398974\pi$
$103$	−5.45676	+	14.9923i	−0.537670	+	1.47724i	−0.849753	+	0.527182i	$0.823249\pi$
$104$	−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	$-0.894434\pi$
$107$		−	6.73607i		−	0.651200i	0.945508	−	0.325600i	$-0.105566\pi$
$108$		0			0
$109$			2.91699i			0.279397i	0.990194	+	0.139699i	$0.0446134\pi$
$109$			2.91699i			0.279397i	−0.990194	+	0.139699i	$0.955387\pi$
$110$	0.00920813	−	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	−0.0599724	−	0.998200i	$-0.519101\pi$
$113$	6.67148	−	18.3297i	0.627600	−	1.72432i	0.687572	−	0.726116i	$-0.258677\pi$
$114$		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	0.985373	−	0.170409i	$-0.0545088\pi$
$127$	14.9938	+	8.65666i	1.33048	+	0.768154i	0.345108	+	0.938563i	$0.387842\pi$
$128$	−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	−0.0394865	−	0.999220i	$-0.512572\pi$
$131$	3.03491	−	0.535137i	0.265162	−	0.0467552i	0.304648	+	0.952465i	$0.401461\pi$
$132$		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	−0.985476	−	0.169817i	$-0.945682\pi$
$137$	−7.57425	+	9.02665i	−0.647112	+	0.771198i	0.338363	+	0.941016i	$0.390127\pi$
$138$		0			0
$139$	−0.930383	−	5.27646i	−0.0789140	−	0.447544i	−0.998505	−	0.0546659i	$-0.982591\pi$
$139$	−0.930383	−	5.27646i	−0.0789140	−	0.447544i	0.919591	−	0.392878i	$-0.128520\pi$
$140$	−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	−0.0697991	−	0.997561i	$-0.522236\pi$
$149$	10.9918	−	9.22325i	0.900486	−	0.755598i	0.970285	+	0.241963i	$0.0777914\pi$
$150$		0			0
$151$	−4.06790	−	11.1765i	−0.331041	−	0.909528i	−0.987842	−	0.155464i	$-0.950313\pi$
$151$	−4.06790	−	11.1765i	−0.331041	−	0.909528i	0.656800	−	0.754065i	$-0.271909\pi$
$152$	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	−0.467319	−	0.884089i	$-0.654780\pi$
$157$	5.75062	−	15.7997i	0.458950	−	1.26095i	0.926268	−	0.376865i	$-0.122998\pi$
$158$	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	−0.314975	−	0.949100i	$-0.601996\pi$
$167$	−15.0723	−	5.48587i	−1.16633	−	0.424509i	−0.851355	+	0.524591i	$0.824218\pi$
$168$		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	0.190293	−	0.981727i	$-0.439056\pi$
$173$	12.7203	−	4.62982i	0.967109	−	0.351999i	0.776815	+	0.629729i	$0.216834\pi$
$174$		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	−0.820667	−	0.571407i	$-0.806398\pi$
$179$	−9.84897	+	5.68630i	−0.736146	+	0.425014i	0.0845201	+	0.996422i	$0.473064\pi$
$180$		0			0
$181$	−12.8369	−	7.41138i	−0.954159	−	0.550884i	−0.0597883	−	0.998211i	$-0.519043\pi$
$181$	−12.8369	−	7.41138i	−0.954159	−	0.550884i	−0.894370	+	0.447327i	$0.852376\pi$
$182$	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	0.992533	−	0.121976i	$-0.0389232\pi$
$191$	14.4389	+	12.1157i	1.04476	+	0.876659i	0.0522283	+	0.998635i	$0.483368\pi$
$192$		0			0
$193$	−0.366460	−	2.07830i	−0.0263783	−	0.149599i	0.968774	−	0.247946i	$-0.0797556\pi$
$193$	−0.366460	−	2.07830i	−0.0263783	−	0.149599i	−0.995152	+	0.0983471i	$0.968644\pi$
$194$	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	−0.994684	−	0.102975i	$-0.967164\pi$
$197$	−5.72884	+	9.92264i	−0.408163	+	0.706959i	0.586521	+	0.809934i	$0.300497\pi$
$198$		0			0
$199$	4.92181	−	2.84161i	0.348898	−	0.201436i	−0.315302	−	0.948991i	$-0.602106\pi$
$199$	4.92181	−	2.84161i	0.348898	−	0.201436i	0.664200	+	0.747555i	$0.268772\pi$
$200$	−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	0.818711	−	0.574206i	$-0.194689\pi$
$211$	15.6412	+	5.69295i	1.07679	+	0.391919i	0.258077	+	0.966124i	$0.416911\pi$
$212$	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	0.0812995	−	0.996690i	$-0.474093\pi$
$223$	−2.73564	−	0.482367i	−0.183192	−	0.0323017i	−0.264491	+	0.964388i	$0.585204\pi$
$224$	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	0.817724	+	0.575611i	$0.195236\pi$
$227$	8.45693	+	23.2352i	0.561306	+	1.54218i	−0.256418	+	0.966566i	$0.582542\pi$
$228$		0			0
$229$	−10.0744	−	12.0062i	−0.665736	−	0.793393i	0.322461	−	0.946583i	$-0.395490\pi$
$229$	−10.0744	−	12.0062i	−0.665736	−	0.793393i	−0.988197	+	0.153190i	$0.951045\pi$
$230$	−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	−0.948340	−	0.317255i	$-0.897239\pi$
$233$	−17.5198	+	10.1151i	−1.14776	+	0.662659i	−0.199419	+	0.979914i	$0.563906\pi$
$234$		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	−0.994361	−	0.106048i	$-0.966180\pi$
$239$	−1.48780	−	8.43773i	−0.0962378	−	0.545791i	0.898123	−	0.439744i	$-0.144931\pi$
$240$		0			0
$241$	11.0727	+	9.29110i	0.713255	+	0.598492i	0.925510	−	0.378722i	$-0.123636\pi$
$241$	11.0727	+	9.29110i	0.713255	+	0.598492i	−0.212255	+	0.977214i	$0.568081\pi$
$242$	−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	0.0418921	−	0.999122i	$-0.486661\pi$
$251$	−12.7128	−	7.33976i	−0.802427	−	0.463281i	−0.844319	+	0.535841i	$0.819995\pi$
$252$		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	0.996782	+	0.0801575i	$0.0255423\pi$
$257$	14.4703	+	17.2450i	0.902633	+	1.07572i	−0.0941497	+	0.995558i	$0.530013\pi$
$258$		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	0.730255	+	0.683175i	$0.239401\pi$
$263$	−3.07511	+	17.4398i	−0.189620	+	1.07539i	−0.919875	+	0.392212i	$0.871710\pi$
$264$		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	$-0.807358\pi$
$271$		−	18.7315i		−	1.13786i	0.822386	−	0.568929i	$-0.192642\pi$
$272$	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	0.775868	−	0.630895i	$-0.217312\pi$
$277$	21.4560	+	3.78327i	1.28917	+	0.227315i	0.513299	+	0.858210i	$0.328423\pi$
$278$	−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	0.999996	+	0.00286067i	$0.000910580\pi$
$281$	3.95262	+	10.8597i	0.235793	+	0.647837i	−0.764203	+	0.644976i	$0.776867\pi$
$282$		0			0
$283$	−3.28791	+	2.75888i	−0.195446	+	0.163998i	−0.735259	−	0.677786i	$-0.762939\pi$
$283$	−3.28791	+	2.75888i	−0.195446	+	0.163998i	0.539813	+	0.841785i	$0.318495\pi$
$284$	−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	0.979777	+	0.200092i	$0.0641242\pi$
$293$	2.18285	+	12.3796i	0.127523	+	0.723221i	−0.852254	+	0.523129i	$0.824765\pi$
$294$		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	0.996532	−	0.0832113i	$-0.0265176\pi$
$307$	7.46768	+	12.9344i	0.426203	+	0.738205i	−0.570329	+	0.821416i	$0.693184\pi$
$308$	−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	−0.668916	−	0.743338i	$-0.733242\pi$
$311$	−0.935160	+	0.784692i	−0.0530280	+	0.0444958i	0.615888	+	0.787833i	$0.288797\pi$
$312$		0			0
$313$	−3.74180	+	1.36190i	−0.211499	+	0.0769794i	−0.445597	−	0.895234i	$-0.647009\pi$
$313$	−3.74180	+	1.36190i	−0.211499	+	0.0769794i	0.234098	+	0.972213i	$0.424786\pi$
$314$	−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	−0.927190	−	0.374593i	$-0.877783\pi$
$317$	1.28552	−	7.29053i	0.0722018	−	0.409477i	0.999391	−	0.0348844i	$-0.0111063\pi$
$318$		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	−0.967158	−	0.254176i	$-0.918196\pi$
$331$	0.520452	−	2.95163i	0.0286066	−	0.162236i	0.995765	+	0.0919400i	$0.0293068\pi$
$332$	−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	−0.874611	−	0.484826i	$-0.838883\pi$
$337$	−10.0788	+	8.45709i	−0.549025	+	0.460687i	0.325586	+	0.945513i	$0.394439\pi$
$338$	−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	−0.881385	−	0.472400i	$-0.843388\pi$
$347$	−28.8369	+	5.08472i	−1.54804	+	0.272962i	−0.666660	+	0.745362i	$0.732277\pi$
$348$		0			0
$349$	−13.4766	+	16.0608i	−0.721385	+	0.859713i	−0.994765	−	0.102193i	$-0.967414\pi$
$349$	−13.4766	+	16.0608i	−0.721385	+	0.859713i	0.273380	+	0.961906i	$0.411859\pi$
$350$	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	−0.817300	−	0.576213i	$-0.804530\pi$
$353$	−2.02760	+	2.41640i	−0.107918	+	0.128612i	0.709381	+	0.704825i	$0.248974\pi$
$354$		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	−0.107529	−	0.994202i	$-0.534294\pi$
$359$	15.2950	−	26.4917i	0.807240	−	1.39818i	0.914768	−	0.403979i	$-0.132373\pi$
$360$		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	−0.962551	−	0.271101i	$-0.912612\pi$
$367$	−7.65245	−	21.0249i	−0.399455	−	1.09749i	0.563096	−	0.826391i	$-0.309610\pi$
$368$	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	−0.796304	−	0.604897i	$-0.793214\pi$
$373$	3.91132	−	10.7463i	0.202521	−	0.556421i	0.998824	+	0.0484764i	$0.0154366\pi$
$374$	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	−0.614900	−	0.788605i	$-0.710804\pi$
$383$	−31.1726	−	11.3459i	−1.59285	−	0.579749i	−0.977946	+	0.208856i	$0.933026\pi$
$384$		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	−0.502546	−	0.864551i	$-0.667603\pi$
$389$	−6.54404	+	2.38183i	−0.331796	+	0.120764i	0.170750	+	0.985314i	$0.445381\pi$
$390$		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	−0.991682	−	0.128712i	$-0.958916\pi$
$397$	−31.8597	−	18.3942i	−1.59899	−	0.923178i	−0.607308	−	0.794466i	$-0.707751\pi$
$398$	−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	−0.248202	−	0.968708i	$-0.579840\pi$
$401$	−3.00611	+	0.530059i	−0.150118	+	0.0264699i	0.0980840	+	0.995178i	$0.468729\pi$
$402$		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	−0.894559	−	0.446949i	$-0.852511\pi$
$409$	−4.18256	−	23.7205i	−0.206814	−	1.17290i	0.687745	−	0.725952i	$-0.258601\pi$
$410$	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	0.993590	+	0.113046i	$0.0360607\pi$
$419$	19.0854	+	22.7451i	0.932383	+	1.11117i	−0.0612068	+	0.998125i	$0.519495\pi$
$420$		0			0
$421$	9.82045	+	26.9815i	0.478619	+	1.31500i	0.910666	+	0.413144i	$0.135570\pi$
$421$	9.82045	+	26.9815i	0.478619	+	1.31500i	−0.432046	+	0.901851i	$0.642208\pi$
$422$	−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	0.200577	−	0.979678i	$-0.435718\pi$
$439$	1.13120	+	0.199460i	0.0539891	+	0.00951973i	−0.146588	+	0.989198i	$0.546829\pi$
$440$	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	−0.997875	−	0.0651518i	$-0.979247\pi$
$443$	−5.79518	−	15.9221i	−0.275337	−	0.756483i	0.722538	−	0.691331i	$-0.242975\pi$
$444$		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	0.282126	−	0.959377i	$-0.408961\pi$
$449$	26.5725	−	15.3416i	1.25403	−	0.724017i	0.971908	+	0.235361i	$0.0756272\pi$
$450$		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	0.762044	−	0.647526i	$-0.224196\pi$
$457$	5.48725	+	4.60435i	0.256683	+	0.215382i	−0.505361	+	0.862908i	$0.668641\pi$
$458$	−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	$-0.339600\pi$
$461$	−6.34887	−	5.32733i	−0.295696	−	0.248119i	−0.778550	+	0.627582i	$0.784045\pi$
$462$		0			0
$463$	0.381159	−	0.0672086i	0.0177140	−	0.00312345i	−0.164784	−	0.986330i	$-0.552693\pi$
$463$	0.381159	−	0.0672086i	0.0177140	−	0.00312345i	0.182498	+	0.983206i	$0.441582\pi$
$464$	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	0.627506	−	0.778612i	$-0.284076\pi$
$467$	5.76908	+	3.33078i	0.266961	+	0.154130i	−0.360545	+	0.932742i	$0.617409\pi$
$468$		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	−0.979981	−	0.199090i	$-0.936201\pi$
$479$	0.196814	−	1.11619i	0.00899268	−	0.0510000i	0.988974	+	0.148090i	$0.0473125\pi$
$480$		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	$-0.600294\pi$
$487$		−	41.9634i		−	1.90154i	0.309896	−	0.950771i	$-0.399706\pi$
$488$	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	−0.673119	−	0.739534i	$-0.735046\pi$
$491$	7.04382	−	19.3527i	0.317883	−	0.873377i	0.991003	−	0.133843i	$-0.0427317\pi$
$492$		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	−0.454463	−	0.890766i	$-0.650169\pi$
$499$	7.68110	−	6.44521i	0.343853	−	0.288527i	0.798316	+	0.602239i	$0.205724\pi$
$500$	−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	−0.998114	−	0.0613824i	$-0.980449\pi$
$503$	−12.3849	−	21.4513i	−0.552216	−	0.956466i	0.445898	−	0.895084i	$-0.352884\pi$
$504$		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	0.843700	+	0.536816i	$0.180373\pi$
$509$	5.29018	+	30.0021i	0.234483	+	1.32982i	−0.609217	+	0.793004i	$0.708516\pi$
$510$		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	0.557411	−	0.830237i	$-0.311795\pi$
$521$	2.67309	+	1.54331i	0.117110	+	0.0676136i	−0.440301	+	0.897850i	$0.645128\pi$
$522$		0			0
$523$	−6.24198	−	10.8114i	−0.272943	−	0.472750i	0.696671	−	0.717390i	$-0.254664\pi$
$523$	−6.24198	−	10.8114i	−0.272943	−	0.472750i	−0.969614	+	0.244640i	$0.921330\pi$
$524$	−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	$0.271997\pi$
$541$			35.0866i			1.50849i	−0.656592	+	0.754246i	$0.728003\pi$
$542$	−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	−0.992529	−	0.122010i	$-0.961066\pi$
$547$	−0.423952	+	2.40435i	−0.0181269	+	0.102803i	0.974402	+	0.224813i	$0.0721771\pi$
$548$	−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	0.784643	−	0.619948i	$-0.212846\pi$
$557$	−3.41195	−	5.90968i	−0.144569	−	0.250401i	−0.929212	+	0.369547i	$0.879513\pi$
$558$		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	−0.590962	−	0.806699i	$-0.701252\pi$
$563$	−20.6520	+	3.64150i	−0.870377	+	0.153471i	−0.279415	+	0.960170i	$0.590141\pi$
$564$		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	−0.125521	−	0.992091i	$-0.540060\pi$
$569$	20.8313	−	24.8258i	0.873295	−	1.04075i	0.998815	−	0.0486610i	$-0.0154954\pi$
$570$		0			0
$571$	−0.396543	−	2.24891i	−0.0165948	−	0.0941139i	0.975385	−	0.220507i	$-0.0707711\pi$
$571$	−0.396543	−	2.24891i	−0.0165948	−	0.0941139i	−0.991980	+	0.126393i	$0.959660\pi$
$572$	−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	0.551103	−	0.834437i	$-0.314207\pi$
$577$	−10.7395	−	18.6014i	−0.447092	−	0.774387i	−0.998195	+	0.0600507i	$0.980874\pi$
$578$	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	−0.225287	−	0.974292i	$-0.572332\pi$
$587$	−18.6609	−	3.29041i	−0.770216	−	0.135810i	−0.544928	+	0.838483i	$0.683443\pi$
$588$		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	$-0.838491\pi$
$593$		−	23.6650i		−	0.971804i	0.874013	−	0.485902i	$-0.161509\pi$
$594$		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	0.165131	−	0.986272i	$-0.447195\pi$
$599$	−8.37844	−	3.04950i	−0.342334	−	0.124599i	−0.507465	+	0.861672i	$0.669417\pi$
$600$		0			0
$601$	4.44934	−	25.2334i	0.181492	−	1.02929i	−0.748888	−	0.662697i	$-0.769412\pi$
$601$	4.44934	−	25.2334i	0.181492	−	1.02929i	0.930380	−	0.366597i	$-0.119477\pi$
$602$	−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	0.915982	−	0.401218i	$-0.131413\pi$
$607$	8.91382	+	10.6231i	0.361801	+	0.431177i	−0.554182	+	0.832396i	$0.686969\pi$
$608$	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	0.0971374	−	0.995271i	$-0.469031\pi$
$613$	−17.7329	−	10.2381i	−0.716224	−	0.413512i	−0.813361	+	0.581759i	$0.802365\pi$
$614$	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	−0.984675	−	0.174399i	$-0.944202\pi$
$617$	−45.9610	+	8.10416i	−1.85032	+	0.326261i	−0.865644	+	0.500660i	$0.833091\pi$
$618$		0			0
$619$	−20.3900	−	17.1092i	−0.819542	−	0.687678i	0.133323	−	0.991073i	$-0.457435\pi$
$619$	−20.3900	−	17.1092i	−0.819542	−	0.687678i	−0.952865	+	0.303395i	$0.901880\pi$
$620$	−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	−0.902292	−	0.431126i	$-0.858116\pi$
$631$	−24.6191	+	14.2138i	−0.980071	+	0.565844i	−0.0777793	+	0.996971i	$0.524783\pi$
$632$	−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	−0.220537	−	0.975379i	$-0.570781\pi$
$641$	−19.2764	−	3.39896i	−0.761373	−	0.134251i	−0.540836	+	0.841128i	$0.681892\pi$
$642$		0			0
$643$	−10.2317	−	3.72402i	−0.403497	−	0.146861i	0.132296	−	0.991210i	$-0.457765\pi$
$643$	−10.2317	−	3.72402i	−0.403497	−	0.146861i	−0.535793	+	0.844349i	$0.679987\pi$
$644$	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	0.562000	−	0.827137i	$-0.310032\pi$
$653$	11.7763	+	4.28623i	0.460843	+	0.167733i	−0.101157	+	0.994871i	$0.532254\pi$
$654$		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	−0.972942	−	0.231050i	$-0.925784\pi$
$659$	−9.65592	−	26.5294i	−0.376141	−	1.03344i	0.596801	−	0.802389i	$-0.296438\pi$
$660$		0			0
$661$	10.6735	+	12.7202i	0.415150	+	0.494757i	0.932577	−	0.360971i	$-0.117555\pi$
$661$	10.6735	+	12.7202i	0.415150	+	0.494757i	−0.517427	+	0.855727i	$0.673110\pi$
$662$	−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	0.727859	−	0.685727i	$-0.240516\pi$
$673$	4.64214	+	3.89522i	0.178941	+	0.150150i	−0.548918	+	0.835876i	$0.684960\pi$
$674$	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	$-0.234971\pi$
$677$	5.34485	+	4.48486i	0.205419	+	0.172367i	−0.534274	+	0.845311i	$0.679415\pi$
$678$		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	−0.0844432	−	0.996428i	$-0.526911\pi$
$683$	−25.8624	−	14.9317i	−0.989597	−	0.571344i	−0.905154	+	0.425084i	$0.860244\pi$
$684$		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	0.326236	−	0.945288i	$-0.394220\pi$
$691$	31.1175	−	11.3259i	1.18377	−	0.430856i	0.857531	+	0.514432i	$0.171997\pi$
$692$	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	−0.310329	−	0.950629i	$-0.600439\pi$
$709$	−24.6853	−	4.35269i	−0.927077	−	0.163469i	−0.616748	+	0.787161i	$0.711550\pi$
$710$	−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	−0.990660	−	0.136353i	$-0.956462\pi$
$719$	−16.4482	−	28.4892i	−0.613415	−	1.06247i	0.377245	−	0.926113i	$-0.376871\pi$
$720$		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	−0.251908	−	0.967751i	$-0.581058\pi$
$727$	20.0843	−	23.9355i	0.744884	−	0.887719i	0.996792	+	0.0800327i	$0.0255025\pi$
$728$	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	$-0.654096\pi$
$733$	−16.2456	+	2.86454i	−0.600046	+	0.105804i	−0.134630	+	0.990896i	$0.542984\pi$
$734$	−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	0.570279	−	0.821451i	$-0.306835\pi$
$739$	−11.5876	−	20.0704i	−0.426258	−	0.738301i	−0.996537	+	0.0831501i	$0.973502\pi$
$740$	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	−0.688499	−	0.725238i	$-0.741730\pi$
$743$	−2.55778	+	2.14623i	−0.0938358	+	0.0787376i	0.594663	+	0.803975i	$0.297286\pi$
$744$		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	−0.926232	−	0.376953i	$-0.876972\pi$
$751$	0.701648	−	1.92776i	0.0256035	−	0.0703450i	0.951836	+	0.306608i	$0.0991940\pi$
$752$	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	$0.273192\pi$
$757$			41.6394i			1.51341i	−0.653756	+	0.756705i	$0.726808\pi$
$758$	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	−0.368195	−	0.929749i	$-0.620024\pi$
$761$	14.1101	−	38.7671i	0.511490	−	1.40531i	0.879684	−	0.475558i	$-0.157754\pi$
$762$		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	−0.205437	+	0.978670i	$0.565861\pi$
$769$	−33.4132	+	28.0370i	−1.20491	+	1.01104i	−0.999476	+	0.0323712i	$0.989694\pi$
$770$	−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	0.922425	−	0.386176i	$-0.126204\pi$
$773$	3.52468	+	6.10492i	0.126774	+	0.219579i	−0.795651	+	0.605755i	$0.792871\pi$
$774$		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	0.699871	+	0.714270i	$0.253241\pi$
$787$	8.03739	+	45.5823i	0.286502	+	1.62483i	−0.413369	+	0.910564i	$0.635648\pi$
$788$	−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	−0.432606	−	0.901583i	$-0.642406\pi$
$797$	10.7323	−	9.00550i	0.380159	−	0.318991i	0.812765	+	0.582592i	$0.197961\pi$
$798$		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	$0.146441\pi$
$809$			25.2574i			0.888002i	−0.896026	+	0.444001i	$0.853559\pi$
$810$		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	−0.245625	−	0.969365i	$-0.578993\pi$
$821$	5.42437	−	1.97431i	0.189312	−	0.0689038i	0.434936	+	0.900461i	$0.356771\pi$
$822$		0			0
$823$	12.2571	+	14.6074i	0.427254	+	0.509182i	0.936128	−	0.351659i	$-0.114382\pi$
$823$	12.2571	+	14.6074i	0.427254	+	0.509182i	−0.508874	+	0.860841i	$0.669938\pi$
$824$	−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	−0.0265613	−	0.999647i	$-0.508456\pi$
$827$	23.7503	−	13.7122i	0.825878	−	0.476821i	0.852439	+	0.522826i	$0.175122\pi$
$828$		0			0
$829$	−23.8710	−	13.7819i	−0.829073	−	0.478666i	0.0244622	−	0.999701i	$-0.492213\pi$
$829$	−23.8710	−	13.7819i	−0.829073	−	0.478666i	−0.853535	+	0.521035i	$0.825546\pi$
$830$	−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	0.158558	−	0.987350i	$-0.449316\pi$
$839$	−22.7744	−	19.1100i	−0.786259	−	0.659750i	−0.944816	+	0.327600i	$0.893760\pi$
$840$		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	−0.878031	−	0.478604i	$-0.841143\pi$
$853$	−14.9845	−	41.1697i	−0.513061	−	1.40962i	0.364970	−	0.931019i	$-0.381079\pi$
$854$	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	0.386240	−	0.922398i	$-0.373774\pi$
$857$	12.6966	+	2.23875i	0.433708	+	0.0764744i	0.0474680	+	0.998873i	$0.484885\pi$
$858$		0			0
$859$	−26.7551	−	9.73806i	−0.912872	−	0.332258i	−0.157473	−	0.987523i	$-0.550335\pi$
$859$	−26.7551	−	9.73806i	−0.912872	−	0.332258i	−0.755399	+	0.655265i	$0.772557\pi$
$860$	−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	0.694592	−	0.719404i	$-0.255585\pi$
$877$	−3.98303	−	4.74679i	−0.134497	−	0.160288i	−0.829089	+	0.559116i	$0.811141\pi$
$878$	−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	−0.0830799	−	0.996543i	$-0.526476\pi$
$881$	21.9173	−	12.6539i	0.738412	−	0.426322i	0.821492	+	0.570221i	$0.193142\pi$
$882$		0			0
$883$	15.7424	−	27.2667i	0.529775	−	0.917597i	−0.469622	−	0.882868i	$-0.655610\pi$
$883$	15.7424	−	27.2667i	0.529775	−	0.917597i	0.999397	−	0.0347290i	$-0.0110568\pi$
$884$	−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	0.984283	−	0.176600i	$-0.0565098\pi$
$887$	−0.0310073	−	0.175851i	−0.00104112	−	0.00590451i	−0.985324	+	0.170695i	$0.945399\pi$
$888$		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	−0.626853	−	0.779137i	$-0.715657\pi$
$907$	−18.2575	+	6.64519i	−0.606231	+	0.220650i	0.0206225	+	0.999787i	$0.493435\pi$
$908$	−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	−0.976984	−	0.213314i	$-0.931574\pi$
$911$	0.423720	−	2.40304i	0.0140385	−	0.0796161i	0.991022	+	0.133698i	$0.0426853\pi$
$912$		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	$-0.988426\pi$
$919$		−	2.20402i		−	0.0727038i	0.999339	−	0.0363519i	$-0.0115737\pi$
$920$	−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	0.873502	−	0.486820i	$-0.161843\pi$
$929$	−3.30889	−	9.09111i	−0.108561	−	0.298270i	−0.982063	+	0.188551i	$0.939621\pi$
$930$		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	0.232701	+	0.972548i	$0.425243\pi$
$937$	−22.2202	+	38.4864i	−0.725901	+	1.25730i	−0.958602	+	0.284749i	$0.908090\pi$
$938$	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	−0.829838	−	0.558004i	$-0.811567\pi$
$941$	−7.38960	−	41.9085i	−0.240894	−	1.36618i	0.588944	−	0.808174i	$-0.299544\pi$
$942$		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	−0.00233119	+	0.999997i	$0.500742\pi$
$947$	−30.3650	+	36.1877i	−0.986731	+	1.17594i	−0.984400	+	0.175943i	$0.943702\pi$
$948$		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	0.833840	−	0.552007i	$-0.186138\pi$
$953$	23.8540	+	13.7721i	0.772707	+	0.446123i	−0.0611321	+	0.998130i	$0.519471\pi$
$954$		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	−0.948132	−	0.317877i	$-0.897030\pi$
$967$	−0.543982	+	1.49458i	−0.0174933	+	0.0480624i	0.930639	+	0.365939i	$0.119252\pi$
$968$	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	$-0.949015\pi$
$971$		−	9.93969i		−	0.318980i	0.987200	−	0.159490i	$-0.0509849\pi$
$972$		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	0.512113	+	0.858918i	$0.328863\pi$
$977$	−13.5121	+	37.1242i	−0.432290	+	1.18771i	−0.944403	+	0.328789i	$0.893359\pi$
$978$		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	0.189640	−	0.981854i	$-0.439268\pi$
$983$	30.2880	−	11.0239i	0.966036	−	0.351608i	0.776396	+	0.630245i	$0.217046\pi$
$984$		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	0.541746	−	0.840542i	$-0.317763\pi$
$991$	2.66599	+	1.53921i	0.0846881	+	0.0488947i	−0.457058	+	0.889437i	$0.651097\pi$
$992$	−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	−0.113190	−	0.993573i	$-0.536107\pi$
$997$	27.9424	−	33.3004i	0.884944	−	1.05464i	0.998134	−	0.0610619i	$-0.0194487\pi$
$998$	−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.35.11		192
3.2	odd	2		216.2.v.b.11.22	yes	192
8.3	odd	2	inner	648.2.v.b.35.28		192
12.11	even	2		864.2.bh.b.335.2		192
24.5	odd	2		864.2.bh.b.335.1		192
24.11	even	2		216.2.v.b.11.5	✓	192
27.5	odd	18	inner	648.2.v.b.611.28		192
27.22	even	9		216.2.v.b.59.5	yes	192
108.103	odd	18		864.2.bh.b.815.1		192
216.59	even	18	inner	648.2.v.b.611.11		192
216.157	even	18		864.2.bh.b.815.2		192
216.211	odd	18		216.2.v.b.59.22	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.5	✓	192	24.11	even	2
216.2.v.b.11.22	yes	192	3.2	odd	2
216.2.v.b.59.5	yes	192	27.22	even	9
216.2.v.b.59.22	yes	192	216.211	odd	18
648.2.v.b.35.11		192	1.1	even	1	trivial
648.2.v.b.35.28		192	8.3	odd	2	inner
648.2.v.b.611.11		192	216.59	even	18	inner
648.2.v.b.611.28		192	27.5	odd	18	inner
864.2.bh.b.335.1		192	24.5	odd	2
864.2.bh.b.335.2		192	12.11	even	2
864.2.bh.b.815.1		192	108.103	odd	18
864.2.bh.b.815.2		192	216.157	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.821807 - 1.15093i) q^{2} +(-0.649266 + 1.89168i) q^{4} +(-0.426624 - 0.155279i) q^{5} +(-1.28150 - 0.225962i) q^{7} +(2.71076 - 0.807339i) q^{8} +O(q^{10})\)	\(q+(-0.821807 - 1.15093i) q^{2} +(-0.649266 + 1.89168i) q^{4} +(-0.426624 - 0.155279i) q^{5} +(-1.28150 - 0.225962i) q^{7} +(2.71076 - 0.807339i) q^{8} +(0.171889 + 0.618623i) q^{10} +(-0.00602720 - 0.0165596i) q^{11} +(-1.43581 - 1.71113i) q^{13} +(0.793076 + 1.66060i) q^{14} +(-3.15691 - 2.45641i) q^{16} +(-1.27216 + 0.734483i) q^{17} +(0.677841 - 1.17406i) q^{19} +(0.570730 - 0.706220i) q^{20} +(-0.0141057 + 0.0205456i) q^{22} +(0.369486 + 2.09546i) q^{23} +(-3.67233 - 3.08145i) q^{25} +(-0.789428 + 3.05873i) q^{26} +(1.25948 - 2.27747i) q^{28} +(-5.56933 - 4.67322i) q^{29} +(-8.87753 + 1.56535i) q^{31} +(-0.232774 + 5.65206i) q^{32} +(1.89081 + 0.860562i) q^{34} +(0.511630 + 0.295390i) q^{35} +(4.58718 - 2.64841i) q^{37} +(-1.90831 + 0.184701i) q^{38} +(-1.28184 - 0.0764919i) q^{40} +(-1.56527 - 1.86542i) q^{41} +(-10.1956 + 3.71089i) q^{43} +(0.0352387 - 0.000649957i) q^{44} +(2.10807 - 2.14731i) q^{46} +(-0.791397 + 4.48824i) q^{47} +(-4.98668 - 1.81500i) q^{49} +(-0.528577 + 6.75893i) q^{50} +(4.16913 - 1.60511i) q^{52} -10.4085 q^{53} +0.00800062i q^{55} +(-3.65625 + 0.422073i) q^{56} +(-0.801622 + 10.2504i) q^{58} +(3.75319 - 10.3118i) q^{59} +(8.87057 + 1.56412i) q^{61} +(9.09722 + 8.93098i) q^{62} +(6.69641 - 4.37700i) q^{64} +(0.346849 + 0.952961i) q^{65} +(3.70041 - 3.10502i) q^{67} +(-0.563436 - 2.88340i) q^{68} +(-0.0804893 - 0.831602i) q^{70} +(5.03714 + 8.72458i) q^{71} +(-0.339460 + 0.587962i) q^{73} +(-6.81790 - 3.10303i) q^{74} +(1.78084 + 2.04453i) q^{76} +(0.00398198 + 0.0225829i) q^{77} +(-5.19665 + 6.19313i) q^{79} +(0.965387 + 1.53816i) q^{80} +(-0.860607 + 3.33452i) q^{82} +(-1.29122 + 1.53881i) q^{83} +(0.656785 - 0.115809i) q^{85} +(12.6498 + 8.68475i) q^{86} +(-0.0297075 - 0.0400230i) q^{88} +(0.103744 + 0.0598964i) q^{89} +(1.45333 + 2.51724i) q^{91} +(-4.20383 - 0.661560i) q^{92} +(5.81601 - 2.77762i) q^{94} +(-0.471489 + 0.395626i) q^{95} +(-10.4801 + 3.81446i) q^{97} +(2.00915 + 7.23088i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) \) 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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