LMFDB - Embedded newform 3024.2.cc.d.881.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(881,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3024.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cc (of order $6$, degree $2$, 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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.3
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.d.2897.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79123 + 3.10250i) q^{5} +(2.56863 - 0.634134i) q^{7} +O(q^{10})$	$q+(-1.79123 + 3.10250i) q^{5} +(2.56863 - 0.634134i) q^{7} +(-0.200372 + 0.115685i) q^{11} +(1.16716 + 0.673862i) q^{13} -7.94895 q^{17} +3.06168i q^{19} +(-4.87566 - 2.81497i) q^{23} +(-3.91701 - 6.78446i) q^{25} +(2.33703 - 1.34928i) q^{29} +(-1.85401 - 1.07041i) q^{31} +(-2.63361 + 9.10507i) q^{35} -7.27483 q^{37} +(0.813774 - 1.40950i) q^{41} +(0.927618 + 1.60668i) q^{43} +(-0.0396273 - 0.0686364i) q^{47} +(6.19575 - 3.25771i) q^{49} -11.6845i q^{53} -0.828872i q^{55} +(-6.48614 + 11.2343i) q^{59} +(0.729056 - 0.420921i) q^{61} +(-4.18131 + 2.41408i) q^{65} +(5.05736 - 8.75961i) q^{67} +7.47959i q^{71} -7.97751i q^{73} +(-0.441322 + 0.424214i) q^{77} +(3.30854 + 5.73056i) q^{79} +(6.41792 + 11.1162i) q^{83} +(14.2384 - 24.6616i) q^{85} +3.56067 q^{89} +(3.42533 + 0.990766i) q^{91} +(-9.49885 - 5.48417i) q^{95} +(-13.1326 + 7.58210i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{23} - 24 q^{25} + 36 q^{29} - 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} + 12 q^{79} + 12 q^{91} - 108 q^{95}+O(q^{100}) $ 48 * q + 12 * q^23 - 24 * q^25 + 36 * q^29 - 12 * q^43 + 6 * q^49 - 36 * q^65 + 60 * q^77 + 12 * q^79 + 12 * q^91 - 108 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.79123	+	3.10250i	−0.801063	+	1.38748i	0.117855	+	0.993031i	$0.462398\pi$
$5$	−1.79123	+	3.10250i	−0.801063	+	1.38748i	−0.918917	+	0.394450i	$0.870935\pi$
$6$		0			0
$7$	2.56863	−	0.634134i	0.970852	−	0.239680i
$7$	2.56863	−	0.634134i	0.970852	−	0.239680i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.200372	+	0.115685i	−0.0604144	+	0.0348803i	−0.529903	−	0.848058i	$-0.677772\pi$
$11$	−0.200372	+	0.115685i	−0.0604144	+	0.0348803i	0.469489	+	0.882939i	$0.344438\pi$
$12$		0			0
$13$	1.16716	+	0.673862i	0.323713	+	0.186896i	0.653046	−	0.757318i	$-0.273491\pi$
$13$	1.16716	+	0.673862i	0.323713	+	0.186896i	−0.329334	+	0.944214i	$0.606824\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−7.94895			−1.92790			−0.963952	−	0.266075i	$-0.914273\pi$
$17$	−7.94895			−1.92790			−0.963952	+	0.266075i	$0.914273\pi$
$18$		0			0
$19$			3.06168i			0.702397i	0.936301	+	0.351198i	$0.114226\pi$
$19$			3.06168i			0.702397i	−0.936301	+	0.351198i	$0.885774\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.87566	−	2.81497i	−1.01665	−	0.586961i	−0.103516	−	0.994628i	$-0.533009\pi$
$23$	−4.87566	−	2.81497i	−1.01665	−	0.586961i	−0.913131	+	0.407667i	$0.866342\pi$
$24$		0			0
$25$	−3.91701	−	6.78446i	−0.783402	−	1.35689i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.33703	−	1.34928i	0.433975	−	0.250555i	−0.267064	−	0.963679i	$-0.586053\pi$
$29$	2.33703	−	1.34928i	0.433975	−	0.250555i	0.701038	+	0.713123i	$0.252720\pi$
$30$		0			0
$31$	−1.85401	−	1.07041i	−0.332990	−	0.192252i	0.324178	−	0.945996i	$-0.394912\pi$
$31$	−1.85401	−	1.07041i	−0.332990	−	0.192252i	−0.657168	+	0.753744i	$0.728246\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.63361	+	9.10507i	−0.445162	+	1.53904i
$36$		0			0
$37$	−7.27483			−1.19597			−0.597987	−	0.801506i	$-0.704033\pi$
$37$	−7.27483			−1.19597			−0.597987	+	0.801506i	$0.704033\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.813774	−	1.40950i	0.127090	−	0.220127i	−0.795458	−	0.606009i	$-0.792770\pi$
$41$	0.813774	−	1.40950i	0.127090	−	0.220127i	0.922548	+	0.385882i	$0.126103\pi$
$42$		0			0
$43$	0.927618	+	1.60668i	0.141460	+	0.245017i	0.928047	−	0.372464i	$-0.121487\pi$
$43$	0.927618	+	1.60668i	0.141460	+	0.245017i	−0.786586	+	0.617480i	$0.788154\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.0396273	−	0.0686364i	−0.00578023	−	0.0100117i	0.863121	−	0.504997i	$-0.168507\pi$
$47$	−0.0396273	−	0.0686364i	−0.00578023	−	0.0100117i	−0.868901	+	0.494986i	$0.835173\pi$
$48$		0			0
$49$	6.19575	−	3.25771i	0.885107	−	0.465388i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	11.6845i		−	1.60498i	−0.596663	−	0.802492i	$-0.703507\pi$
$53$		−	11.6845i		−	1.60498i	0.596663	−	0.802492i	$-0.296493\pi$
$54$		0			0
$55$		−	0.828872i		−	0.111765i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.48614	+	11.2343i	−0.844424	+	1.46258i	0.0416970	+	0.999130i	$0.486724\pi$
$59$	−6.48614	+	11.2343i	−0.844424	+	1.46258i	−0.886121	+	0.463454i	$0.846610\pi$
$60$		0			0
$61$	0.729056	−	0.420921i	0.0933461	−	0.0538934i	−0.452600	−	0.891713i	$-0.649504\pi$
$61$	0.729056	−	0.420921i	0.0933461	−	0.0538934i	0.545946	+	0.837820i	$0.316170\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.18131	+	2.41408i	−0.518628	+	0.299430i
$66$		0			0
$67$	5.05736	−	8.75961i	0.617855	−	1.07016i	−0.372021	−	0.928224i	$-0.621335\pi$
$67$	5.05736	−	8.75961i	0.617855	−	1.07016i	0.989876	−	0.141932i	$-0.0453315\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			7.47959i			0.887664i	0.896110	+	0.443832i	$0.146381\pi$
$71$			7.47959i			0.887664i	−0.896110	+	0.443832i	$0.853619\pi$
$72$		0			0
$73$		−	7.97751i		−	0.933697i	−0.884337	−	0.466848i	$-0.845389\pi$
$73$		−	7.97751i		−	0.933697i	0.884337	−	0.466848i	$-0.154611\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.441322	+	0.424214i	−0.0502933	+	0.0483437i
$78$		0			0
$79$	3.30854	+	5.73056i	0.372240	+	0.644738i	0.989910	−	0.141699i	$-0.0452566\pi$
$79$	3.30854	+	5.73056i	0.372240	+	0.644738i	−0.617670	+	0.786437i	$0.711923\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.41792	+	11.1162i	0.704458	+	1.22016i	0.966887	+	0.255206i	$0.0821432\pi$
$83$	6.41792	+	11.1162i	0.704458	+	1.22016i	−0.262429	+	0.964951i	$0.584523\pi$
$84$		0			0
$85$	14.2384	−	24.6616i	1.54437	−	2.67493i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.56067			0.377430			0.188715	−	0.982032i	$-0.439568\pi$
$89$	3.56067			0.377430			0.188715	+	0.982032i	$0.439568\pi$
$90$		0			0
$91$	3.42533	+	0.990766i	0.359072	+	0.103860i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−9.49885	−	5.48417i	−0.974562	−	0.562664i
$96$		0			0
$97$	−13.1326	+	7.58210i	−1.33341	+	0.769845i	−0.985821	−	0.167801i	$-0.946333\pi$
$97$	−13.1326	+	7.58210i	−1.33341	+	0.769845i	−0.347590	+	0.937647i	$0.613000\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.78084	+	6.54861i	0.376208	+	0.651611i	0.990507	−	0.137462i	$-0.0438945\pi$
$101$	3.78084	+	6.54861i	0.376208	+	0.651611i	−0.614299	+	0.789073i	$0.710561\pi$
$102$		0			0
$103$	−10.1520	−	5.86126i	−1.00031	−	0.577527i	−0.0919672	−	0.995762i	$-0.529315\pi$
$103$	−10.1520	−	5.86126i	−1.00031	−	0.577527i	−0.908339	+	0.418235i	$0.862649\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	12.1425i		−	1.17386i	−0.809636	−	0.586932i	$-0.800336\pi$
$107$		−	12.1425i		−	1.17386i	0.809636	−	0.586932i	$-0.199664\pi$
$108$		0			0
$109$	−13.8764			−1.32912			−0.664561	−	0.747234i	$-0.731381\pi$
$109$	−13.8764			−1.32912			−0.664561	+	0.747234i	$0.731381\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−15.6660	−	9.04479i	−1.47374	−	0.850862i	−0.474174	−	0.880431i	$-0.657253\pi$
$113$	−15.6660	−	9.04479i	−1.47374	−	0.850862i	−0.999563	+	0.0295692i	$0.990586\pi$
$114$		0			0
$115$	17.4669	−	10.0845i	1.62879	−	0.940385i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−20.4179	+	5.04070i	−1.87171	+	0.462080i
$120$		0			0
$121$	−5.47323	+	9.47992i	−0.497567	+	0.861811i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.1528			0.908092
$126$		0			0
$127$	−12.1457			−1.07776			−0.538878	−	0.842384i	$-0.681151\pi$
$127$	−12.1457			−1.07776			−0.538878	+	0.842384i	$0.681151\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.27640	−	14.3352i	0.723113	−	1.25247i	−0.236633	−	0.971599i	$-0.576044\pi$
$131$	8.27640	−	14.3352i	0.723113	−	1.25247i	0.959746	−	0.280869i	$-0.0906227\pi$
$132$		0			0
$133$	1.94151	+	7.86432i	0.168350	+	0.681923i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.8250	−	7.98187i	1.18115	−	0.681937i	0.224869	−	0.974389i	$-0.427804\pi$
$137$	13.8250	−	7.98187i	1.18115	−	0.681937i	0.956280	+	0.292452i	$0.0944711\pi$
$138$		0			0
$139$	7.40140	+	4.27320i	0.627779	+	0.362448i	0.779891	−	0.625915i	$-0.215274\pi$
$139$	7.40140	+	4.27320i	0.627779	+	0.362448i	−0.152113	+	0.988363i	$0.548608\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.311822			−0.0260759
$144$		0			0
$145$			9.66750i			0.802842i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.43319	−	3.71421i	−0.527028	−	0.304280i	0.212777	−	0.977101i	$-0.431749\pi$
$149$	−6.43319	−	3.71421i	−0.527028	−	0.304280i	−0.739805	+	0.672821i	$0.765082\pi$
$150$		0			0
$151$	−9.32926	−	16.1587i	−0.759204	−	1.31498i	−0.943257	−	0.332064i	$-0.892255\pi$
$151$	−9.32926	−	16.1587i	−0.759204	−	1.31498i	0.184053	−	0.982916i	$-0.441078\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.64192	−	3.83471i	0.533492	−	0.308012i
$156$		0			0
$157$	−19.9510	−	11.5187i	−1.59226	−	0.919293i	−0.992918	−	0.118801i	$-0.962095\pi$
$157$	−19.9510	−	11.5187i	−1.59226	−	0.919293i	−0.599344	−	0.800492i	$-0.704572\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−14.3089	−	4.13879i	−1.12770	−	0.326182i
$162$		0			0
$163$	9.75747			0.764264			0.382132	−	0.924108i	$-0.375190\pi$
$163$	9.75747			0.764264			0.382132	+	0.924108i	$0.375190\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.15227	−	14.1202i	0.630842	−	1.09265i	−0.356538	−	0.934281i	$-0.616043\pi$
$167$	8.15227	−	14.1202i	0.630842	−	1.09265i	0.987380	−	0.158369i	$-0.0506237\pi$
$168$		0			0
$169$	−5.59182	−	9.68532i	−0.430140	−	0.745025i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.681518	−	1.18042i	−0.0518148	−	0.0897459i	0.838955	−	0.544201i	$-0.183167\pi$
$173$	−0.681518	−	1.18042i	−0.0518148	−	0.0897459i	−0.890769	+	0.454455i	$0.849834\pi$
$174$		0			0
$175$	−14.3636	−	14.9429i	−1.08579	−	1.12958i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	15.5303i		−	1.16079i	−0.814336	−	0.580394i	$-0.802899\pi$
$179$		−	15.5303i		−	1.16079i	0.814336	−	0.580394i	$-0.197101\pi$
$180$		0			0
$181$		−	17.5414i		−	1.30384i	−0.758287	−	0.651920i	$-0.773964\pi$
$181$		−	17.5414i		−	1.30384i	0.758287	−	0.651920i	$-0.226036\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	13.0309	−	22.5702i	0.958050	−	1.65939i
$186$		0			0
$187$	1.59275	−	0.919573i	0.116473	−	0.0672458i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.67352	+	0.966209i	−0.121092	+	0.0699124i	−0.559323	−	0.828950i	$-0.688939\pi$
$191$	−1.67352	+	0.966209i	−0.121092	+	0.0699124i	0.438231	+	0.898863i	$0.355605\pi$
$192$		0			0
$193$	1.95786	−	3.39111i	0.140930	−	0.244098i	−0.786917	−	0.617059i	$-0.788324\pi$
$193$	1.95786	−	3.39111i	0.140930	−	0.244098i	0.927847	+	0.372961i	$0.121657\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			12.5710i			0.895647i	0.894122	+	0.447824i	$0.147801\pi$
$197$			12.5710i			0.895647i	−0.894122	+	0.447824i	$0.852199\pi$
$198$		0			0
$199$			17.0255i			1.20691i	0.797398	+	0.603454i	$0.206209\pi$
$199$			17.0255i			1.20691i	−0.797398	+	0.603454i	$0.793791\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.14733	−	4.94780i	0.361272	−	0.347267i
$204$		0			0
$205$	2.91531	+	5.04947i	0.203614	+	0.352670i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.354189	−	0.613474i	−0.0244998	−	0.0424349i
$210$		0			0
$211$	−1.81881	+	3.15027i	−0.125212	+	0.216874i	−0.921816	−	0.387628i	$-0.873294\pi$
$211$	−1.81881	+	3.15027i	−0.125212	+	0.216874i	0.796604	+	0.604502i	$0.206628\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.64631			−0.453274
$216$		0			0
$217$	−5.44106	−	1.57381i	−0.369363	−	0.106837i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−9.27772	−	5.35649i	−0.624087	−	0.360317i
$222$		0			0
$223$	−10.2325	+	5.90773i	−0.685218	+	0.395611i	−0.801818	−	0.597568i	$-0.796134\pi$
$223$	−10.2325	+	5.90773i	−0.685218	+	0.395611i	0.116600	+	0.993179i	$0.462800\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.97271	+	15.5412i	0.595539	+	1.03150i	0.993471	+	0.114089i	$0.0363950\pi$
$227$	8.97271	+	15.5412i	0.595539	+	1.03150i	−0.397931	+	0.917415i	$0.630272\pi$
$228$		0			0
$229$	16.0434	+	9.26264i	1.06017	+	0.612092i	0.925481	−	0.378795i	$-0.123661\pi$
$229$	16.0434	+	9.26264i	1.06017	+	0.612092i	0.134694	+	0.990887i	$0.456995\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			9.83034i			0.644007i	0.946738	+	0.322004i	$0.104356\pi$
$233$			9.83034i			0.644007i	−0.946738	+	0.322004i	$0.895644\pi$
$234$		0			0
$235$	0.283926			0.0185213
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.28151	−	5.35868i	−0.600371	−	0.346624i	0.168817	−	0.985647i	$-0.446005\pi$
$239$	−9.28151	−	5.35868i	−0.600371	−	0.346624i	−0.769188	+	0.639023i	$0.779339\pi$
$240$		0			0
$241$	−8.99246	+	5.19180i	−0.579256	+	0.334433i	−0.760837	−	0.648942i	$-0.775212\pi$
$241$	−8.99246	+	5.19180i	−0.579256	+	0.334433i	0.181582	+	0.983376i	$0.441878\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.990951	+	25.0576i	−0.0633096	+	1.60087i
$246$		0			0
$247$	−2.06315	+	3.57347i	−0.131275	+	0.227375i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−17.1797			−1.08437			−0.542187	−	0.840258i	$-0.682404\pi$
$251$	−17.1797			−1.08437			−0.542187	+	0.840258i	$0.682404\pi$
$252$		0			0
$253$	1.30259			0.0818934
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.751617	+	1.30184i	−0.0468846	+	0.0812065i	−0.888515	−	0.458847i	$-0.848263\pi$
$257$	−0.751617	+	1.30184i	−0.0468846	+	0.0812065i	0.841631	+	0.540053i	$0.181596\pi$
$258$		0			0
$259$	−18.6864	+	4.61321i	−1.16111	+	0.286651i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	7.80797	−	4.50793i	0.481460	−	0.277971i	−0.239565	−	0.970880i	$-0.577005\pi$
$263$	7.80797	−	4.50793i	0.481460	−	0.277971i	0.721025	+	0.692909i	$0.243671\pi$
$264$		0			0
$265$	36.2510	+	20.9296i	2.22688	+	1.28569i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−21.6914			−1.32255			−0.661273	−	0.750145i	$-0.729984\pi$
$269$	−21.6914			−1.32255			−0.661273	+	0.750145i	$0.729984\pi$
$270$		0			0
$271$			13.5501i			0.823111i	0.911385	+	0.411556i	$0.135014\pi$
$271$			13.5501i			0.823111i	−0.911385	+	0.411556i	$0.864986\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.56972	+	0.906277i	0.0946576	+	0.0546506i
$276$		0			0
$277$	−0.996101	−	1.72530i	−0.0598499	−	0.103663i	0.834548	−	0.550935i	$-0.185729\pi$
$277$	−0.996101	−	1.72530i	−0.0598499	−	0.103663i	−0.894398	+	0.447272i	$0.852396\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−22.9759	+	13.2652i	−1.37063	+	0.791333i	−0.991007	−	0.133809i	$-0.957279\pi$
$281$	−22.9759	+	13.2652i	−1.37063	+	0.791333i	−0.379621	+	0.925142i	$0.623946\pi$
$282$		0			0
$283$	−10.3080	−	5.95134i	−0.612748	−	0.353770i	0.161292	−	0.986907i	$-0.448434\pi$
$283$	−10.3080	−	5.95134i	−0.612748	−	0.353770i	−0.774040	+	0.633136i	$0.781767\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.19648	−	4.13652i	0.0706258	−	0.244171i
$288$		0			0
$289$	46.1859			2.71682
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.36418	+	5.82693i	−0.196537	+	0.340413i	−0.947403	−	0.320042i	$-0.896303\pi$
$293$	−3.36418	+	5.82693i	−0.196537	+	0.340413i	0.750866	+	0.660455i	$0.229636\pi$
$294$		0			0
$295$	−23.2363	−	40.2465i	−1.35287	−	2.34324i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.79379	−	6.57105i	−0.219401	−	0.380013i
$300$		0			0
$301$	3.40156	+	3.53874i	0.196063	+	0.203970i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			3.01586i			0.172688i
$306$		0			0
$307$			14.2812i			0.815069i	0.913190	+	0.407535i	$0.133611\pi$
$307$			14.2812i			0.815069i	−0.913190	+	0.407535i	$0.866389\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.99609	+	8.65348i	−0.283302	+	0.490694i	−0.972196	−	0.234168i	$-0.924763\pi$
$311$	−4.99609	+	8.65348i	−0.283302	+	0.490694i	0.688894	+	0.724862i	$0.258097\pi$
$312$		0			0
$313$	2.05595	−	1.18701i	0.116209	−	0.0670935i	−0.440769	−	0.897621i	$-0.645294\pi$
$313$	2.05595	−	1.18701i	0.116209	−	0.0670935i	0.556978	+	0.830527i	$0.311961\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.48046	+	0.854744i	−0.0831509	+	0.0480072i	−0.540999	−	0.841023i	$-0.681954\pi$
$317$	−1.48046	+	0.854744i	−0.0831509	+	0.0480072i	0.457848	+	0.889030i	$0.348620\pi$
$318$		0			0
$319$	−0.312183	+	0.540716i	−0.0174789	+	0.0302743i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	24.3371i		−	1.35415i
$324$		0			0
$325$		−	10.5581i		−	0.585658i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.145313	−	0.151173i	−0.00801134	−	0.00833443i
$330$		0			0
$331$	10.5054	+	18.1959i	0.577430	+	1.00014i	0.995773	+	0.0918494i	$0.0292778\pi$
$331$	10.5054	+	18.1959i	0.577430	+	1.00014i	−0.418343	+	0.908289i	$0.637389\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	18.1178	+	31.3810i	0.989881	+	1.71452i
$336$		0			0
$337$	−8.04527	+	13.9348i	−0.438254	+	0.759077i	−0.997555	−	0.0698870i	$-0.977736\pi$
$337$	−8.04527	+	13.9348i	−0.438254	+	0.759077i	0.559301	+	0.828964i	$0.311069\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.495322			0.0268232
$342$		0			0
$343$	13.8488	−	12.2968i	0.747764	−	0.663965i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.2415	+	6.49029i	0.603476	+	0.348417i	0.770408	−	0.637551i	$-0.220053\pi$
$347$	11.2415	+	6.49029i	0.603476	+	0.348417i	−0.166932	+	0.985968i	$0.553386\pi$
$348$		0			0
$349$	−12.2260	+	7.05868i	−0.654442	+	0.377842i	−0.790156	−	0.612906i	$-0.790001\pi$
$349$	−12.2260	+	7.05868i	−0.654442	+	0.377842i	0.135714	+	0.990748i	$0.456667\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.3917	−	17.9990i	−0.553096	−	0.957991i	−0.998049	−	0.0624367i	$-0.980113\pi$
$353$	−10.3917	−	17.9990i	−0.553096	−	0.957991i	0.444953	−	0.895554i	$-0.353220\pi$
$354$		0			0
$355$	−23.2054	−	13.3977i	−1.23162	−	0.711074i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			11.2290i			0.592644i	0.955088	+	0.296322i	$0.0957601\pi$
$359$			11.2290i			0.592644i	−0.955088	+	0.296322i	$0.904240\pi$
$360$		0			0
$361$	9.62614			0.506639
$362$		0			0
$363$		0			0
$364$		0			0
$365$	24.7502	+	14.2896i	1.29549	+	0.747950i
$366$		0			0
$367$	−5.16800	+	2.98375i	−0.269768	+	0.155750i	−0.628782	−	0.777582i	$-0.716446\pi$
$367$	−5.16800	+	2.98375i	−0.269768	+	0.155750i	0.359014	+	0.933332i	$0.383113\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.40951	−	30.0131i	−0.384682	−	1.55820i
$372$		0			0
$373$	−11.5890	+	20.0727i	−0.600055	+	1.03933i	0.392757	+	0.919642i	$0.371521\pi$
$373$	−11.5890	+	20.0727i	−0.600055	+	1.03933i	−0.992812	+	0.119684i	$0.961812\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.63692			0.187311
$378$		0			0
$379$	33.7053			1.73132			0.865662	−	0.500629i	$-0.166898\pi$
$379$	33.7053			1.73132			0.865662	+	0.500629i	$0.166898\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.09459	+	1.89589i	−0.0559310	+	0.0968754i	−0.892635	−	0.450780i	$-0.851146\pi$
$383$	−1.09459	+	1.89589i	−0.0559310	+	0.0968754i	0.836704	+	0.547655i	$0.184479\pi$
$384$		0			0
$385$	−0.525616	−	2.12907i	−0.0267879	−	0.108507i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.71424	−	5.03117i	0.441829	−	0.255090i	−0.262544	−	0.964920i	$-0.584561\pi$
$389$	8.71424	−	5.03117i	0.441829	−	0.255090i	0.704373	+	0.709830i	$0.251228\pi$
$390$		0			0
$391$	38.7564	+	22.3760i	1.96000	+	1.13160i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−23.7054			−1.19275
$396$		0			0
$397$			14.7293i			0.739243i	0.929182	+	0.369621i	$0.120513\pi$
$397$			14.7293i			0.739243i	−0.929182	+	0.369621i	$0.879487\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9.40832	+	5.43190i	0.469829	+	0.271256i	0.716168	−	0.697928i	$-0.245894\pi$
$401$	9.40832	+	5.43190i	0.469829	+	0.271256i	−0.246339	+	0.969184i	$0.579228\pi$
$402$		0			0
$403$	−1.44262	−	2.49869i	−0.0718621	−	0.124469i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.45767	−	0.841587i	0.0722541	−	0.0417159i
$408$		0			0
$409$	−19.4688	−	11.2403i	−0.962672	−	0.555799i	−0.0656773	−	0.997841i	$-0.520921\pi$
$409$	−19.4688	−	11.2403i	−0.962672	−	0.555799i	−0.896994	+	0.442042i	$0.854254\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−9.53645	+	32.9699i	−0.469258	+	1.62234i
$414$		0			0
$415$	−45.9839			−2.25726
$416$		0			0
$417$		0			0
$418$		0			0
$419$	14.2135	−	24.6184i	0.694373	−	1.20269i	−0.276018	−	0.961152i	$-0.589015\pi$
$419$	14.2135	−	24.6184i	0.694373	−	1.20269i	0.970392	−	0.241537i	$-0.0776516\pi$
$420$		0			0
$421$	10.7934	+	18.6947i	0.526037	+	0.911123i	0.999540	+	0.0303305i	$0.00965599\pi$
$421$	10.7934	+	18.6947i	0.526037	+	0.911123i	−0.473503	+	0.880792i	$0.657011\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	31.1361	+	53.9294i	1.51033	+	2.61596i
$426$		0			0
$427$	1.60576	−	1.54351i	0.0777081	−	0.0746957i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			19.1530i			0.922567i	0.887253	+	0.461284i	$0.152611\pi$
$431$			19.1530i			0.922567i	−0.887253	+	0.461284i	$0.847389\pi$
$432$		0			0
$433$			3.46577i			0.166554i	0.996526	+	0.0832772i	$0.0265387\pi$
$433$			3.46577i			0.166554i	−0.996526	+	0.0832772i	$0.973461\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	8.61851	−	14.9277i	0.412279	−	0.714089i
$438$		0			0
$439$	21.9087	−	12.6490i	1.04565	−	0.603704i	0.124218	−	0.992255i	$-0.460358\pi$
$439$	21.9087	−	12.6490i	1.04565	−	0.603704i	0.921427	+	0.388551i	$0.127024\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.6599	−	9.61858i	0.791534	−	0.456992i	−0.0489683	−	0.998800i	$-0.515593\pi$
$443$	16.6599	−	9.61858i	0.791534	−	0.456992i	0.840502	+	0.541808i	$0.182260\pi$
$444$		0			0
$445$	−6.37798	+	11.0470i	−0.302345	+	0.523677i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			3.44859i			0.162749i	0.996684	+	0.0813744i	$0.0259309\pi$
$449$			3.44859i			0.162749i	−0.996684	+	0.0813744i	$0.974069\pi$
$450$		0			0
$451$			0.376565i			0.0177318i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−9.20941	+	8.85240i	−0.431744	+	0.415007i
$456$		0			0
$457$	3.88750	+	6.73335i	0.181850	+	0.314973i	0.942510	−	0.334177i	$-0.108458\pi$
$457$	3.88750	+	6.73335i	0.181850	+	0.314973i	−0.760661	+	0.649150i	$0.775125\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.88500	−	3.26492i	−0.0877933	−	0.152062i	0.818785	−	0.574101i	$-0.194648\pi$
$461$	−1.88500	−	3.26492i	−0.0877933	−	0.152062i	−0.906578	+	0.422038i	$0.861315\pi$
$462$		0			0
$463$	1.71692	−	2.97379i	0.0797919	−	0.138204i	−0.823368	−	0.567508i	$-0.807908\pi$
$463$	1.71692	−	2.97379i	0.0797919	−	0.138204i	0.903160	+	0.429304i	$0.141241\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.92981			−0.366948			−0.183474	−	0.983025i	$-0.558734\pi$
$467$	−7.92981			−0.366948			−0.183474	+	0.983025i	$0.558734\pi$
$468$		0			0
$469$	7.43574	−	25.7073i	0.343351	−	1.18705i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.371737	−	0.214623i	−0.0170925	−	0.00986835i
$474$		0			0
$475$	20.7718	−	11.9926i	0.953077	−	0.550259i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.22428	+	7.31666i	0.193012	+	0.334307i	0.946247	−	0.323445i	$-0.104841\pi$
$479$	4.22428	+	7.31666i	0.193012	+	0.334307i	−0.753235	+	0.657752i	$0.771508\pi$
$480$		0			0
$481$	−8.49091	−	4.90223i	−0.387152	−	0.223522i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	54.3251i		−	2.46678i
$486$		0			0
$487$	−13.5361			−0.613377			−0.306689	−	0.951810i	$-0.599221\pi$
$487$	−13.5361			−0.613377			−0.306689	+	0.951810i	$0.599221\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.60993	+	3.81624i	0.298302	+	0.172225i	0.641680	−	0.766973i	$-0.278238\pi$
$491$	6.60993	+	3.81624i	0.298302	+	0.172225i	−0.343378	+	0.939197i	$0.611571\pi$
$492$		0			0
$493$	−18.5769	+	10.7254i	−0.836662	+	0.483047i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.74306	+	19.2123i	0.212755	+	0.861790i
$498$		0			0
$499$	−12.8845	+	22.3165i	−0.576788	+	0.999025i	0.419057	+	0.907960i	$0.362361\pi$
$499$	−12.8845	+	22.3165i	−0.576788	+	0.999025i	−0.995845	+	0.0910656i	$0.970973\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	2.94027			0.131100			0.0655500	−	0.997849i	$-0.479120\pi$
$503$	2.94027			0.131100			0.0655500	+	0.997849i	$0.479120\pi$
$504$		0			0
$505$	−27.0894			−1.20546
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.91221	+	8.50821i	−0.217730	+	0.377120i	−0.954114	−	0.299445i	$-0.903199\pi$
$509$	−4.91221	+	8.50821i	−0.217730	+	0.377120i	0.736384	+	0.676564i	$0.236532\pi$
$510$		0			0
$511$	−5.05881	−	20.4913i	−0.223788	−	0.906481i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	36.3691	−	20.9977i	1.60262	−	0.925270i
$516$		0			0
$517$	0.0158804	+	0.00916854i	0.000698418	+	0.000403232i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.59400			−0.288889			−0.144444	−	0.989513i	$-0.546139\pi$
$521$	−6.59400			−0.288889			−0.144444	+	0.989513i	$0.546139\pi$
$522$		0			0
$523$		−	3.05847i		−	0.133737i	−0.997762	−	0.0668687i	$-0.978699\pi$
$523$		−	3.05847i		−	0.133737i	0.997762	−	0.0668687i	$-0.0213009\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	14.7374	+	8.50867i	0.641973	+	0.370643i
$528$		0			0
$529$	4.34807	+	7.53108i	0.189046	+	0.327438i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.89961	−	1.09674i	0.0822814	−	0.0475052i
$534$		0			0
$535$	37.6723	+	21.7501i	1.62871	+	0.940339i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.864586	+	1.36951i	−0.0372404	+	0.0589889i
$540$		0			0
$541$	−28.2396			−1.21411			−0.607057	−	0.794659i	$-0.707650\pi$
$541$	−28.2396			−1.21411			−0.607057	+	0.794659i	$0.707650\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	24.8559	−	43.0517i	1.06471	−	1.84413i
$546$		0			0
$547$	15.2952	+	26.4921i	0.653976	+	1.13272i	0.982150	+	0.188102i	$0.0602335\pi$
$547$	15.2952	+	26.4921i	0.653976	+	1.13272i	−0.328174	+	0.944617i	$0.606433\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.13106	+	7.15521i	0.175989	+	0.304822i
$552$		0			0
$553$	12.1324	+	12.6216i	0.515920	+	0.536727i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			19.7931i			0.838660i	0.907834	+	0.419330i	$0.137735\pi$
$557$			19.7931i			0.838660i	−0.907834	+	0.419330i	$0.862265\pi$
$558$		0			0
$559$			2.50034i			0.105753i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−3.05934	+	5.29894i	−0.128936	+	0.223324i	−0.923265	−	0.384165i	$-0.874490\pi$
$563$	−3.05934	+	5.29894i	−0.128936	+	0.223324i	0.794329	+	0.607488i	$0.207823\pi$
$564$		0			0
$565$	56.1229	−	32.4026i	2.36111	−	1.36319i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	24.3621	−	14.0655i	1.02131	−	0.589655i	0.106828	−	0.994277i	$-0.465930\pi$
$569$	24.3621	−	14.0655i	1.02131	−	0.589655i	0.914484	+	0.404623i	$0.132597\pi$
$570$		0			0
$571$	−9.64625	+	16.7078i	−0.403683	+	0.699199i	−0.994167	−	0.107850i	$-0.965603\pi$
$571$	−9.64625	+	16.7078i	−0.403683	+	0.699199i	0.590484	+	0.807049i	$0.298937\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			44.1050i			1.83931i
$576$		0			0
$577$		−	19.8248i		−	0.825317i	−0.910886	−	0.412659i	$-0.864600\pi$
$577$		−	19.8248i		−	0.825317i	0.910886	−	0.412659i	$-0.135400\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	23.5344	+	24.4835i	0.976372	+	1.01575i
$582$		0			0
$583$	1.35171	+	2.34124i	0.0559823	+	0.0969641i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.51705	+	4.35967i	0.103890	+	0.179943i	0.913284	−	0.407323i	$-0.133538\pi$
$587$	2.51705	+	4.35967i	0.103890	+	0.179943i	−0.809394	+	0.587266i	$0.800204\pi$
$588$		0			0
$589$	3.27726	−	5.67638i	0.135037	−	0.233891i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−28.7225			−1.17949			−0.589747	−	0.807588i	$-0.700772\pi$
$593$	−28.7225			−1.17949			−0.589747	+	0.807588i	$0.700772\pi$
$594$		0			0
$595$	20.9345	−	72.3758i	0.858229	−	2.96712i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−41.0308	−	23.6892i	−1.67647	−	0.967913i	−0.963880	−	0.266335i	$-0.914187\pi$
$599$	−41.0308	−	23.6892i	−1.67647	−	0.967913i	−0.712593	−	0.701577i	$-0.752480\pi$
$600$		0			0
$601$	19.9885	−	11.5404i	0.815347	−	0.470741i	−0.0334621	−	0.999440i	$-0.510653\pi$
$601$	19.9885	−	11.5404i	0.815347	−	0.470741i	0.848809	+	0.528699i	$0.177320\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−19.6076	−	33.9614i	−0.797164	−	1.38073i
$606$		0			0
$607$	−26.3852	−	15.2335i	−1.07094	−	0.618309i	−0.142504	−	0.989794i	$-0.545515\pi$
$607$	−26.3852	−	15.2335i	−1.07094	−	0.618309i	−0.928439	+	0.371485i	$0.878849\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	0.106813i		−	0.00432120i
$612$		0			0
$613$	27.6918			1.11846			0.559231	−	0.829012i	$-0.311096\pi$
$613$	27.6918			1.11846			0.559231	+	0.829012i	$0.311096\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.04021	+	3.48732i	0.243170	+	0.140394i	0.616633	−	0.787251i	$-0.288496\pi$
$617$	6.04021	+	3.48732i	0.243170	+	0.140394i	−0.373463	+	0.927645i	$0.621830\pi$
$618$		0			0
$619$	13.9319	−	8.04361i	0.559972	−	0.323300i	−0.193162	−	0.981167i	$-0.561874\pi$
$619$	13.9319	−	8.04361i	0.559972	−	0.323300i	0.753134	+	0.657867i	$0.228541\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	9.14605	−	2.25794i	0.366429	−	0.0904625i
$624$		0			0
$625$	1.39910	−	2.42331i	0.0559639	−	0.0969323i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	57.8273			2.30572
$630$		0			0
$631$	21.9346			0.873201			0.436601	−	0.899655i	$-0.356182\pi$
$631$	21.9346			0.873201			0.436601	+	0.899655i	$0.356182\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	21.7557	−	37.6820i	0.863349	−	1.49536i
$636$		0			0
$637$	9.42669	+	0.372796i	0.373499	+	0.0147707i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	5.46275	−	3.15392i	0.215766	−	0.124572i	−0.388222	−	0.921566i	$-0.626911\pi$
$641$	5.46275	−	3.15392i	0.215766	−	0.124572i	0.603988	+	0.796993i	$0.293577\pi$
$642$		0			0
$643$	−5.64446	−	3.25883i	−0.222596	−	0.128516i	0.384556	−	0.923102i	$-0.374355\pi$
$643$	−5.64446	−	3.25883i	−0.222596	−	0.128516i	−0.607152	+	0.794586i	$0.707688\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−14.6209			−0.574806			−0.287403	−	0.957810i	$-0.592792\pi$
$647$	−14.6209			−0.574806			−0.287403	+	0.957810i	$0.592792\pi$
$648$		0			0
$649$		−	3.00139i		−	0.117815i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−15.7716	−	9.10576i	−0.617192	−	0.356336i	0.158583	−	0.987346i	$-0.449307\pi$
$653$	−15.7716	−	9.10576i	−0.617192	−	0.356336i	−0.775775	+	0.631010i	$0.782641\pi$
$654$		0			0
$655$	29.6499	+	51.3551i	1.15852	+	2.00661i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−17.6278	+	10.1774i	−0.686682	+	0.396456i	−0.802368	−	0.596830i	$-0.796427\pi$
$659$	−17.6278	+	10.1774i	−0.686682	+	0.396456i	0.115686	+	0.993286i	$0.463093\pi$
$660$		0			0
$661$	−26.6406	−	15.3810i	−1.03620	−	0.598250i	−0.117445	−	0.993079i	$-0.537470\pi$
$661$	−26.6406	−	15.3810i	−1.03620	−	0.598250i	−0.918754	+	0.394829i	$0.870804\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−27.8768	−	8.06327i	−1.08101	−	0.312680i
$666$		0			0
$667$	−15.1927			−0.588265
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.0973882	+	0.168681i	−0.00375963	+	0.00651187i
$672$		0			0
$673$	−2.27563	−	3.94151i	−0.0877191	−	0.151934i	0.818828	−	0.574040i	$-0.194624\pi$
$673$	−2.27563	−	3.94151i	−0.0877191	−	0.151934i	−0.906547	+	0.422106i	$0.861291\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10.2205	−	17.7025i	−0.392807	−	0.680361i	0.600012	−	0.799991i	$-0.295163\pi$
$677$	−10.2205	−	17.7025i	−0.392807	−	0.680361i	−0.992819	+	0.119630i	$0.961829\pi$
$678$		0			0
$679$	−28.9247	+	27.8034i	−1.11003	+	1.06700i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			44.3113i			1.69553i	0.530376	+	0.847763i	$0.322051\pi$
$683$			44.3113i			1.69553i	−0.530376	+	0.847763i	$0.677949\pi$
$684$		0			0
$685$			57.1895i			2.18510i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.87371	−	13.6377i	0.299964	−	0.519553i
$690$		0			0
$691$	−11.6403	+	6.72051i	−0.442817	+	0.255660i	−0.704792	−	0.709414i	$-0.748960\pi$
$691$	−11.6403	+	6.72051i	−0.442817	+	0.255660i	0.261975	+	0.965075i	$0.415626\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−26.5152	+	15.3086i	−1.00578	+	0.580687i
$696$		0			0
$697$	−6.46865	+	11.2040i	−0.245018	+	0.424383i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			25.5980i			0.966823i	0.875393	+	0.483411i	$0.160602\pi$
$701$			25.5980i			0.966823i	−0.875393	+	0.483411i	$0.839398\pi$
$702$		0			0
$703$		−	22.2732i		−	0.840048i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	13.8643	+	14.4234i	0.521420	+	0.542449i
$708$		0			0
$709$	−20.0523	−	34.7316i	−0.753080	−	1.30437i	−0.946323	−	0.323222i	$-0.895234\pi$
$709$	−20.0523	−	34.7316i	−0.753080	−	1.30437i	0.193243	−	0.981151i	$-0.438099\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	6.02636	+	10.4380i	0.225689	+	0.390904i
$714$		0			0
$715$	0.558545	−	0.967429i	0.0208884	−	0.0361798i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	32.5961			1.21563			0.607815	−	0.794079i	$-0.292046\pi$
$719$	32.5961			1.21563			0.607815	+	0.794079i	$0.292046\pi$
$720$		0			0
$721$	−29.7936	−	8.61770i	−1.10957	−	0.320940i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−18.3083	−	10.5703i	−0.679954	−	0.392571i
$726$		0			0
$727$	−29.2124	+	16.8658i	−1.08343	+	0.625517i	−0.931819	−	0.362924i	$-0.881778\pi$
$727$	−29.2124	+	16.8658i	−1.08343	+	0.625517i	−0.151608	+	0.988441i	$0.548445\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−7.37359	−	12.7714i	−0.272722	−	0.472369i
$732$		0			0
$733$	16.0129	+	9.24503i	0.591448	+	0.341473i	0.765670	−	0.643234i	$-0.222408\pi$
$733$	16.0129	+	9.24503i	0.591448	+	0.341473i	−0.174222	+	0.984706i	$0.555741\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			2.34024i			0.0862038i
$738$		0			0
$739$	−4.77060			−0.175489			−0.0877446	−	0.996143i	$-0.527966\pi$
$739$	−4.77060			−0.175489			−0.0877446	+	0.996143i	$0.527966\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	34.5888	+	19.9698i	1.26894	+	0.732622i	0.974787	−	0.223136i	$-0.0716296\pi$
$743$	34.5888	+	19.9698i	1.26894	+	0.732622i	0.294152	+	0.955759i	$0.404963\pi$
$744$		0			0
$745$	23.0467	−	13.3060i	0.844365	−	0.487494i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−7.70000	−	31.1897i	−0.281352	−	1.13965i
$750$		0			0
$751$	14.3918	−	24.9273i	0.525164	−	0.909611i	−0.474406	−	0.880306i	$-0.657337\pi$
$751$	14.3918	−	24.9273i	0.525164	−	0.909611i	0.999571	−	0.0293052i	$-0.00932948\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	66.8434			2.43268
$756$		0			0
$757$	−3.83374			−0.139340			−0.0696699	−	0.997570i	$-0.522195\pi$
$757$	−3.83374			−0.139340			−0.0696699	+	0.997570i	$0.522195\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.51888	+	2.63077i	−0.0550592	+	0.0953654i	−0.892241	−	0.451559i	$-0.850868\pi$
$761$	−1.51888	+	2.63077i	−0.0550592	+	0.0953654i	0.837182	+	0.546924i	$0.184201\pi$
$762$		0			0
$763$	−35.6435	+	8.79951i	−1.29038	+	0.318564i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−15.1408	+	8.74152i	−0.546701	+	0.315638i
$768$		0			0
$769$	−26.0647	−	15.0484i	−0.939916	−	0.542661i	−0.0499822	−	0.998750i	$-0.515916\pi$
$769$	−26.0647	−	15.0484i	−0.939916	−	0.542661i	−0.889934	+	0.456089i	$0.849250\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−36.9887			−1.33039			−0.665196	−	0.746669i	$-0.731652\pi$
$773$	−36.9887			−1.33039			−0.665196	+	0.746669i	$0.731652\pi$
$774$		0			0
$775$			16.7713i			0.602443i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.31543	+	2.49151i	0.154616	+	0.0892677i
$780$		0			0
$781$	−0.865274	−	1.49870i	−0.0309619	−	0.0536277i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	71.4736	−	41.2653i	2.55100	−	1.47282i
$786$		0			0
$787$	15.7679	+	9.10359i	0.562064	+	0.324508i	0.753974	−	0.656905i	$-0.228135\pi$
$787$	15.7679	+	9.10359i	0.562064	+	0.324508i	−0.191910	+	0.981413i	$0.561468\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−45.9759	−	13.2984i	−1.63471	−	0.472836i
$792$		0			0
$793$	1.13457			0.0402897
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.25236	+	5.63325i	−0.115204	+	0.199540i	−0.917861	−	0.396901i	$-0.870086\pi$
$797$	−3.25236	+	5.63325i	−0.115204	+	0.199540i	0.802657	+	0.596441i	$0.203419\pi$
$798$		0			0
$799$	0.314995	+	0.545588i	0.0111437	+	0.0193015i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.922876	+	1.59847i	0.0325676	+	0.0564087i
$804$		0			0
$805$	38.4711	−	36.9797i	1.35593	−	1.30336i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			53.4736i			1.88003i	0.341129	+	0.940016i	$0.389191\pi$
$809$			53.4736i			1.88003i	−0.341129	+	0.940016i	$0.610809\pi$
$810$		0			0
$811$			26.2305i			0.921078i	0.887640	+	0.460539i	$0.152344\pi$
$811$			26.2305i			0.921078i	−0.887640	+	0.460539i	$0.847656\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−17.4779	+	30.2726i	−0.612224	+	1.06040i
$816$		0			0
$817$	−4.91914	+	2.84006i	−0.172099	+	0.0993613i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.7877	−	6.22830i	0.376495	−	0.217369i	−0.299797	−	0.954003i	$-0.596919\pi$
$821$	10.7877	−	6.22830i	0.376495	−	0.217369i	0.676292	+	0.736634i	$0.263586\pi$
$822$		0			0
$823$	−11.8574	+	20.5376i	−0.413323	+	0.715897i	−0.995251	−	0.0973438i	$-0.968965\pi$
$823$	−11.8574	+	20.5376i	−0.413323	+	0.715897i	0.581928	+	0.813241i	$0.302299\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			13.9408i			0.484770i	0.970180	+	0.242385i	$0.0779298\pi$
$827$			13.9408i			0.484770i	−0.970180	+	0.242385i	$0.922070\pi$
$828$		0			0
$829$		−	13.9568i		−	0.484739i	−0.970184	−	0.242369i	$-0.922075\pi$
$829$		−	13.9568i		−	0.484739i	0.970184	−	0.242369i	$-0.0779246\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−49.2497	+	25.8954i	−1.70640	+	0.897223i
$834$		0			0
$835$	29.2052	+	50.5849i	1.01069	+	1.75056i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	3.81179	+	6.60221i	0.131597	+	0.227933i	0.924293	−	0.381685i	$-0.124656\pi$
$839$	3.81179	+	6.60221i	0.131597	+	0.227933i	−0.792695	+	0.609618i	$0.791323\pi$
$840$		0			0
$841$	−10.8589	+	18.8081i	−0.374444	+	0.648556i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	40.0650			1.37828
$846$		0			0
$847$	−8.04719	+	27.8212i	−0.276505	+	0.955948i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	35.4696	+	20.4784i	1.21588	+	0.701990i
$852$		0			0
$853$	−26.8767	+	15.5173i	−0.920242	+	0.531302i	−0.883712	−	0.468031i	$-0.844964\pi$
$853$	−26.8767	+	15.5173i	−0.920242	+	0.531302i	−0.0365294	+	0.999333i	$0.511630\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	11.1297	+	19.2772i	0.380184	+	0.658497i	0.991088	−	0.133207i	$-0.0425275\pi$
$857$	11.1297	+	19.2772i	0.380184	+	0.658497i	−0.610905	+	0.791704i	$0.709194\pi$
$858$		0			0
$859$	27.9713	+	16.1492i	0.954369	+	0.551005i	0.894435	−	0.447197i	$-0.147578\pi$
$859$	27.9713	+	16.1492i	0.954369	+	0.551005i	0.0599334	+	0.998202i	$0.480911\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	33.0060i		−	1.12354i	−0.827295	−	0.561768i	$-0.810121\pi$
$863$		−	33.0060i		−	1.12354i	0.827295	−	0.561768i	$-0.189879\pi$
$864$		0			0
$865$	4.88302			0.166028
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.32588	−	0.765495i	−0.0449773	−	0.0259676i
$870$		0			0
$871$	11.8055	−	6.81592i	0.400015	−	0.230949i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	26.0788	−	6.43822i	0.881623	−	0.217651i
$876$		0			0
$877$	−16.7520	+	29.0153i	−0.565675	+	0.979778i	0.431311	+	0.902203i	$0.358051\pi$
$877$	−16.7520	+	29.0153i	−0.565675	+	0.979778i	−0.996987	+	0.0775752i	$0.975282\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−18.6150			−0.627156			−0.313578	−	0.949562i	$-0.601528\pi$
$881$	−18.6150			−0.627156			−0.313578	+	0.949562i	$0.601528\pi$
$882$		0			0
$883$	31.6752			1.06595			0.532977	−	0.846130i	$-0.321073\pi$
$883$	31.6752			1.06595			0.532977	+	0.846130i	$0.321073\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	21.8400	−	37.8280i	0.733315	−	1.27014i	−0.222144	−	0.975014i	$-0.571305\pi$
$887$	21.8400	−	37.8280i	0.733315	−	1.27014i	0.955459	−	0.295125i	$-0.0953612\pi$
$888$		0			0
$889$	−31.1978	+	7.70199i	−1.04634	+	0.258316i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.210143	−	0.121326i	0.00703215	−	0.00406001i
$894$		0			0
$895$	48.1827	+	27.8183i	1.61057	+	0.929863i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−5.77716			−0.192679
$900$		0			0
$901$			92.8792i			3.09426i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	54.4222	+	31.4207i	1.80905	+	1.04446i
$906$		0			0
$907$	24.0218	+	41.6070i	0.797631	+	1.38154i	0.921155	+	0.389196i	$0.127247\pi$
$907$	24.0218	+	41.6070i	0.797631	+	1.38154i	−0.123524	+	0.992342i	$0.539420\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−36.8038	+	21.2487i	−1.21937	+	0.704001i	−0.964782	−	0.263050i	$-0.915272\pi$
$911$	−36.8038	+	21.2487i	−1.21937	+	0.704001i	−0.254584	+	0.967051i	$0.581938\pi$
$912$		0			0
$913$	−2.57194	−	1.48491i	−0.0851188	−	0.0491434i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	12.1686	−	42.0701i	0.401844	−	1.38928i
$918$		0			0
$919$	−11.3790			−0.375358			−0.187679	−	0.982230i	$-0.560096\pi$
$919$	−11.3790			−0.375358			−0.187679	+	0.982230i	$0.560096\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−5.04021	+	8.72989i	−0.165900	+	0.287348i
$924$		0			0
$925$	28.4956	+	49.3558i	0.936929	+	1.62281i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.0349888	+	0.0606024i	0.00114795	+	0.00198830i	0.866599	−	0.499006i	$-0.166301\pi$
$929$	0.0349888	+	0.0606024i	0.00114795	+	0.00198830i	−0.865451	+	0.500994i	$0.832968\pi$
$930$		0			0
$931$	9.97406	+	18.9694i	0.326887	+	0.621696i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			6.58867i			0.215472i
$936$		0			0
$937$			21.7954i			0.712026i	0.934481	+	0.356013i	$0.115864\pi$
$937$			21.7954i			0.712026i	−0.934481	+	0.356013i	$0.884136\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−14.4480	+	25.0247i	−0.470993	+	0.815784i	−0.999450	−	0.0331768i	$-0.989438\pi$
$941$	−14.4480	+	25.0247i	−0.470993	+	0.815784i	0.528457	+	0.848960i	$0.322771\pi$
$942$		0			0
$943$	−7.93538	+	4.58149i	−0.258411	+	0.149194i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.77197	−	5.64185i	0.317546	−	0.183335i	−0.332752	−	0.943014i	$-0.607977\pi$
$947$	9.77197	−	5.64185i	0.317546	−	0.183335i	0.650298	+	0.759679i	$0.274644\pi$
$948$		0			0
$949$	5.37574	−	9.31105i	0.174504	−	0.302249i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	40.5950i		−	1.31500i	−0.753454	−	0.657501i	$-0.771614\pi$
$953$		−	40.5950i		−	1.31500i	0.753454	−	0.657501i	$-0.228386\pi$
$954$		0			0
$955$		−	6.92281i		−	0.224017i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	30.4498	−	29.2694i	0.983275	−	0.945158i
$960$		0			0
$961$	−13.2084	−	22.8777i	−0.426078	−	0.737989i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	7.01395	+	12.1485i	0.225787	+	0.391075i
$966$		0			0
$967$	−5.88584	+	10.1946i	−0.189276	+	0.327835i	−0.945009	−	0.327044i	$-0.893947\pi$
$967$	−5.88584	+	10.1946i	−0.189276	+	0.327835i	0.755733	+	0.654880i	$0.227281\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−35.5390			−1.14050			−0.570250	−	0.821471i	$-0.693154\pi$
$971$	−35.5390			−1.14050			−0.570250	+	0.821471i	$0.693154\pi$
$972$		0			0
$973$	21.7213	+	6.28281i	0.696352	+	0.201417i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−8.68968	−	5.01699i	−0.278007	−	0.160508i	0.354514	−	0.935051i	$-0.384646\pi$
$977$	−8.68968	−	5.01699i	−0.278007	−	0.160508i	−0.632521	+	0.774543i	$0.717980\pi$
$978$		0			0
$979$	−0.713458	+	0.411915i	−0.0228022	+	0.0131649i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	16.6532	+	28.8443i	0.531156	+	0.919989i	0.999339	+	0.0363574i	$0.0115755\pi$
$983$	16.6532	+	28.8443i	0.531156	+	0.919989i	−0.468183	+	0.883632i	$0.655091\pi$
$984$		0			0
$985$	−39.0016	−	22.5176i	−1.24269	−	0.717469i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	10.4449i		−	0.332127i
$990$		0			0
$991$	0.563501			0.0179002			0.00895010	−	0.999960i	$-0.497151\pi$
$991$	0.563501			0.0179002			0.00895010	+	0.999960i	$0.497151\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−52.8217	−	30.4966i	−1.67456	−	0.966808i
$996$		0			0
$997$	−17.1879	+	9.92344i	−0.544346	+	0.314278i	−0.746839	−	0.665005i	$-0.768429\pi$
$997$	−17.1879	+	9.92344i	−0.544346	+	0.314278i	0.202492	+	0.979284i	$0.435096\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cc.d.881.3		48
3.2	odd	2		1008.2.cc.d.545.2		48
4.3	odd	2		1512.2.bu.a.881.3		48
7.6	odd	2	inner	3024.2.cc.d.881.22		48
9.2	odd	6	inner	3024.2.cc.d.2897.22		48
9.7	even	3		1008.2.cc.d.209.23		48
12.11	even	2		504.2.bu.a.41.23	yes	48
21.20	even	2		1008.2.cc.d.545.23		48
28.27	even	2		1512.2.bu.a.881.22		48
36.7	odd	6		504.2.bu.a.209.2	yes	48
36.11	even	6		1512.2.bu.a.1385.22		48
36.23	even	6		4536.2.k.a.3401.6		48
36.31	odd	6		4536.2.k.a.3401.43		48
63.20	even	6	inner	3024.2.cc.d.2897.3		48
63.34	odd	6		1008.2.cc.d.209.2		48
84.83	odd	2		504.2.bu.a.41.2	✓	48
252.83	odd	6		1512.2.bu.a.1385.3		48
252.139	even	6		4536.2.k.a.3401.5		48
252.167	odd	6		4536.2.k.a.3401.44		48
252.223	even	6		504.2.bu.a.209.23	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.2	✓	48	84.83	odd	2
504.2.bu.a.41.23	yes	48	12.11	even	2
504.2.bu.a.209.2	yes	48	36.7	odd	6
504.2.bu.a.209.23	yes	48	252.223	even	6
1008.2.cc.d.209.2		48	63.34	odd	6
1008.2.cc.d.209.23		48	9.7	even	3
1008.2.cc.d.545.2		48	3.2	odd	2
1008.2.cc.d.545.23		48	21.20	even	2
1512.2.bu.a.881.3		48	4.3	odd	2
1512.2.bu.a.881.22		48	28.27	even	2
1512.2.bu.a.1385.3		48	252.83	odd	6
1512.2.bu.a.1385.22		48	36.11	even	6
3024.2.cc.d.881.3		48	1.1	even	1	trivial
3024.2.cc.d.881.22		48	7.6	odd	2	inner
3024.2.cc.d.2897.3		48	63.20	even	6	inner
3024.2.cc.d.2897.22		48	9.2	odd	6	inner
4536.2.k.a.3401.5		48	252.139	even	6
4536.2.k.a.3401.6		48	36.23	even	6
4536.2.k.a.3401.43		48	36.31	odd	6
4536.2.k.a.3401.44		48	252.167	odd	6

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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.79123 + 3.10250i) q^{5} +(2.56863 - 0.634134i) q^{7} +O(q^{10})\)	\(q+(-1.79123 + 3.10250i) q^{5} +(2.56863 - 0.634134i) q^{7} +(-0.200372 + 0.115685i) q^{11} +(1.16716 + 0.673862i) q^{13} -7.94895 q^{17} +3.06168i q^{19} +(-4.87566 - 2.81497i) q^{23} +(-3.91701 - 6.78446i) q^{25} +(2.33703 - 1.34928i) q^{29} +(-1.85401 - 1.07041i) q^{31} +(-2.63361 + 9.10507i) q^{35} -7.27483 q^{37} +(0.813774 - 1.40950i) q^{41} +(0.927618 + 1.60668i) q^{43} +(-0.0396273 - 0.0686364i) q^{47} +(6.19575 - 3.25771i) q^{49} -11.6845i q^{53} -0.828872i q^{55} +(-6.48614 + 11.2343i) q^{59} +(0.729056 - 0.420921i) q^{61} +(-4.18131 + 2.41408i) q^{65} +(5.05736 - 8.75961i) q^{67} +7.47959i q^{71} -7.97751i q^{73} +(-0.441322 + 0.424214i) q^{77} +(3.30854 + 5.73056i) q^{79} +(6.41792 + 11.1162i) q^{83} +(14.2384 - 24.6616i) q^{85} +3.56067 q^{89} +(3.42533 + 0.990766i) q^{91} +(-9.49885 - 5.48417i) q^{95} +(-13.1326 + 7.58210i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{23} - 24 q^{25} + 36 q^{29} - 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} + 12 q^{79} + 12 q^{91} - 108 q^{95}+O(q^{100}) \) 48 * q + 12 * q^23 - 24 * q^25 + 36 * q^29 - 12 * q^43 + 6 * q^49 - 36 * q^65 + 60 * q^77 + 12 * q^79 + 12 * q^91 - 108 * q^95

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