LMFDB - Embedded newform 2592.2.s.e.1727.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2592,2,Mod(863,2592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2592, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2592.863");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2592 = 2^{5} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2592.s (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:	$20.6972242039$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1727.4
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	2592.1727
Dual form			2592.2.s.e.863.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44949 - 1.41421i) q^{5} +(1.73205 + 1.00000i) q^{7} +O(q^{10})$	$q+(2.44949 - 1.41421i) q^{5} +(1.73205 + 1.00000i) q^{7} +(1.41421 - 2.44949i) q^{11} +(1.00000 + 1.73205i) q^{13} +6.00000i q^{19} +(2.82843 + 4.89898i) q^{23} +(1.50000 - 2.59808i) q^{25} +(2.44949 + 1.41421i) q^{29} +(-1.73205 + 1.00000i) q^{31} +5.65685 q^{35} +6.00000 q^{37} +(4.89898 - 2.82843i) q^{41} +(1.73205 + 1.00000i) q^{43} +(-5.65685 + 9.79796i) q^{47} +(-1.50000 - 2.59808i) q^{49} -8.48528i q^{53} -8.00000i q^{55} +(1.41421 + 2.44949i) q^{59} +(1.00000 - 1.73205i) q^{61} +(4.89898 + 2.82843i) q^{65} +(-1.73205 + 1.00000i) q^{67} +5.65685 q^{71} -6.00000 q^{73} +(4.89898 - 2.82843i) q^{77} +(-12.1244 - 7.00000i) q^{79} +(-1.41421 + 2.44949i) q^{83} -16.9706i q^{89} +4.00000i q^{91} +(8.48528 + 14.6969i) q^{95} +(-5.00000 + 8.66025i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 8 q^{13} + 12 q^{25} + 48 q^{37} - 12 q^{49} + 8 q^{61} - 48 q^{73} - 40 q^{97}+O(q^{100}) $ 8 * q + 8 * q^13 + 12 * q^25 + 48 * q^37 - 12 * q^49 + 8 * q^61 - 48 * q^73 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times$.

$n$	$325$	$1217$	$2431$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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
$5$	2.44949	−	1.41421i	1.09545	−	0.632456i	0.160424	−	0.987048i	$-0.448714\pi$
$5$	2.44949	−	1.41421i	1.09545	−	0.632456i	0.935021	+	0.354593i	$0.115380\pi$
$6$		0			0
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	0.790237	−	0.612801i	$-0.209957\pi$
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	−0.135583	+	0.990766i	$0.543291\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.41421	−	2.44949i	0.426401	−	0.738549i	−0.570149	−	0.821541i	$-0.693114\pi$
$11$	1.41421	−	2.44949i	0.426401	−	0.738549i	0.996550	+	0.0829925i	$0.0264478\pi$
$12$		0			0
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$		0			0
$19$			6.00000i			1.37649i	0.725476	+	0.688247i	$0.241620\pi$
$19$			6.00000i			1.37649i	−0.725476	+	0.688247i	$0.758380\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.82843	+	4.89898i	0.589768	+	1.02151i	0.994263	+	0.106967i	$0.0341141\pi$
$23$	2.82843	+	4.89898i	0.589768	+	1.02151i	−0.404495	+	0.914540i	$0.632553\pi$
$24$		0			0
$25$	1.50000	−	2.59808i	0.300000	−	0.519615i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.44949	+	1.41421i	0.454859	+	0.262613i	0.709880	−	0.704323i	$-0.248749\pi$
$29$	2.44949	+	1.41421i	0.454859	+	0.262613i	−0.255021	+	0.966935i	$0.582082\pi$
$30$		0			0
$31$	−1.73205	+	1.00000i	−0.311086	+	0.179605i	−0.647412	−	0.762140i	$-0.724149\pi$
$31$	−1.73205	+	1.00000i	−0.311086	+	0.179605i	0.336327	+	0.941745i	$0.390815\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.65685			0.956183
$36$		0			0
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.89898	−	2.82843i	0.765092	−	0.441726i	−0.0660290	−	0.997818i	$-0.521033\pi$
$41$	4.89898	−	2.82843i	0.765092	−	0.441726i	0.831121	+	0.556092i	$0.187700\pi$
$42$		0			0
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	0.626219	−	0.779647i	$-0.284601\pi$
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	−0.362084	+	0.932145i	$0.617935\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.65685	+	9.79796i	−0.825137	+	1.42918i	0.0766776	+	0.997056i	$0.475569\pi$
$47$	−5.65685	+	9.79796i	−0.825137	+	1.42918i	−0.901815	+	0.432123i	$0.857765\pi$
$48$		0			0
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	8.48528i		−	1.16554i	−0.812636	−	0.582772i	$-0.801968\pi$
$53$		−	8.48528i		−	1.16554i	0.812636	−	0.582772i	$-0.198032\pi$
$54$		0			0
$55$		−	8.00000i		−	1.07872i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.41421	+	2.44949i	0.184115	+	0.318896i	0.943278	−	0.332004i	$-0.107725\pi$
$59$	1.41421	+	2.44949i	0.184115	+	0.318896i	−0.759163	+	0.650901i	$0.774391\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.89898	+	2.82843i	0.607644	+	0.350823i
$66$		0			0
$67$	−1.73205	+	1.00000i	−0.211604	+	0.122169i	−0.602056	−	0.798454i	$-0.705652\pi$
$67$	−1.73205	+	1.00000i	−0.211604	+	0.122169i	0.390453	+	0.920623i	$0.372318\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.65685			0.671345			0.335673	−	0.941979i	$-0.391036\pi$
$71$	5.65685			0.671345			0.335673	+	0.941979i	$0.391036\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.89898	−	2.82843i	0.558291	−	0.322329i
$78$		0			0
$79$	−12.1244	−	7.00000i	−1.36410	−	0.787562i	−0.373930	−	0.927457i	$-0.621990\pi$
$79$	−12.1244	−	7.00000i	−1.36410	−	0.787562i	−0.990166	+	0.139895i	$0.955323\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.41421	+	2.44949i	−0.155230	+	0.268866i	−0.933143	−	0.359506i	$-0.882945\pi$
$83$	−1.41421	+	2.44949i	−0.155230	+	0.268866i	0.777913	+	0.628372i	$0.216279\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	16.9706i		−	1.79888i	−0.437048	−	0.899438i	$-0.643976\pi$
$89$		−	16.9706i		−	1.79888i	0.437048	−	0.899438i	$-0.356024\pi$
$90$		0			0
$91$			4.00000i			0.419314i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.48528	+	14.6969i	0.870572	+	1.50787i
$96$		0			0
$97$	−5.00000	+	8.66025i	−0.507673	+	0.879316i	0.492287	+	0.870433i	$0.336161\pi$
$97$	−5.00000	+	8.66025i	−0.507673	+	0.879316i	−0.999961	+	0.00888289i	$0.997172\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.44949	−	1.41421i	−0.243733	−	0.140720i	0.373158	−	0.927768i	$-0.378275\pi$
$101$	−2.44949	−	1.41421i	−0.243733	−	0.140720i	−0.616891	+	0.787048i	$0.711608\pi$
$102$		0			0
$103$	12.1244	−	7.00000i	1.19465	−	0.689730i	0.235291	−	0.971925i	$-0.424396\pi$
$103$	12.1244	−	7.00000i	1.19465	−	0.689730i	0.959357	+	0.282194i	$0.0910623\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.48528			0.820303			0.410152	−	0.912017i	$-0.365476\pi$
$107$	8.48528			0.820303			0.410152	+	0.912017i	$0.365476\pi$
$108$		0			0
$109$	−18.0000			−1.72409			−0.862044	−	0.506834i	$-0.830816\pi$
$109$	−18.0000			−1.72409			−0.862044	+	0.506834i	$0.830816\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.79796	−	5.65685i	0.921714	−	0.532152i	0.0375328	−	0.999295i	$-0.488050\pi$
$113$	9.79796	−	5.65685i	0.921714	−	0.532152i	0.884182	+	0.467143i	$0.154717\pi$
$114$		0			0
$115$	13.8564	+	8.00000i	1.29212	+	0.746004i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.50000	+	2.59808i	0.136364	+	0.236189i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			5.65685i			0.505964i
$126$		0			0
$127$		−	18.0000i		−	1.59724i	−0.601834	−	0.798621i	$-0.705563\pi$
$127$		−	18.0000i		−	1.59724i	0.601834	−	0.798621i	$-0.294437\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.89949	+	17.1464i	0.864923	+	1.49809i	0.867124	+	0.498093i	$0.165966\pi$
$131$	9.89949	+	17.1464i	0.864923	+	1.49809i	−0.00220084	+	0.999998i	$0.500701\pi$
$132$		0			0
$133$	−6.00000	+	10.3923i	−0.520266	+	0.901127i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.89898	−	2.82843i	−0.418548	−	0.241649i	0.275908	−	0.961184i	$-0.411022\pi$
$137$	−4.89898	−	2.82843i	−0.418548	−	0.241649i	−0.694456	+	0.719535i	$0.744355\pi$
$138$		0			0
$139$	−8.66025	+	5.00000i	−0.734553	+	0.424094i	−0.820086	−	0.572241i	$-0.806074\pi$
$139$	−8.66025	+	5.00000i	−0.734553	+	0.424094i	0.0855324	+	0.996335i	$0.472741\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.65685			0.473050
$144$		0			0
$145$	8.00000			0.664364
$146$		0			0
$147$		0			0
$148$		0			0
$149$	12.2474	−	7.07107i	1.00335	−	0.579284i	0.0941123	−	0.995562i	$-0.469999\pi$
$149$	12.2474	−	7.07107i	1.00335	−	0.579284i	0.909238	+	0.416277i	$0.136665\pi$
$150$		0			0
$151$	−12.1244	−	7.00000i	−0.986666	−	0.569652i	−0.0823900	−	0.996600i	$-0.526255\pi$
$151$	−12.1244	−	7.00000i	−0.986666	−	0.569652i	−0.904276	+	0.426948i	$0.859589\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.82843	+	4.89898i	−0.227185	+	0.393496i
$156$		0			0
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			11.3137i			0.891645i
$162$		0			0
$163$			6.00000i			0.469956i	0.972001	+	0.234978i	$0.0755019\pi$
$163$			6.00000i			0.469956i	−0.972001	+	0.234978i	$0.924498\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.82843	−	4.89898i	−0.218870	−	0.379094i	0.735593	−	0.677424i	$-0.236904\pi$
$167$	−2.82843	−	4.89898i	−0.218870	−	0.379094i	−0.954463	+	0.298330i	$0.903570\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	12.2474	+	7.07107i	0.931156	+	0.537603i	0.887177	−	0.461429i	$-0.152663\pi$
$173$	12.2474	+	7.07107i	0.931156	+	0.537603i	0.0439792	+	0.999032i	$0.485996\pi$
$174$		0			0
$175$	5.19615	−	3.00000i	0.392792	−	0.226779i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.48528			−0.634220			−0.317110	−	0.948389i	$-0.602712\pi$
$179$	−8.48528			−0.634220			−0.317110	+	0.948389i	$0.602712\pi$
$180$		0			0
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	14.6969	−	8.48528i	1.08054	−	0.623850i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.3137	−	19.5959i	0.818631	−	1.41791i	−0.0880597	−	0.996115i	$-0.528067\pi$
$191$	11.3137	−	19.5959i	0.818631	−	1.41791i	0.906691	−	0.421796i	$-0.138600\pi$
$192$		0			0
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	0.999990	+	0.00447566i	$0.00142465\pi$
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	−0.496119	+	0.868255i	$0.665242\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	19.7990i		−	1.41062i	−0.708899	−	0.705310i	$-0.750808\pi$
$197$		−	19.7990i		−	1.41062i	0.708899	−	0.705310i	$-0.249192\pi$
$198$		0			0
$199$		−	2.00000i		−	0.141776i	−0.997484	−	0.0708881i	$-0.977417\pi$
$199$		−	2.00000i		−	0.141776i	0.997484	−	0.0708881i	$-0.0225833\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.82843	+	4.89898i	0.198517	+	0.343841i
$204$		0			0
$205$	8.00000	−	13.8564i	0.558744	−	0.967773i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	14.6969	+	8.48528i	1.01661	+	0.586939i
$210$		0			0
$211$	−1.73205	+	1.00000i	−0.119239	+	0.0688428i	−0.558433	−	0.829549i	$-0.688597\pi$
$211$	−1.73205	+	1.00000i	−0.119239	+	0.0688428i	0.439194	+	0.898392i	$0.355264\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	5.65685			0.385794
$216$		0			0
$217$	−4.00000			−0.271538
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	1.73205	+	1.00000i	0.115987	+	0.0669650i	0.556871	−	0.830599i	$-0.312002\pi$
$223$	1.73205	+	1.00000i	0.115987	+	0.0669650i	−0.440884	+	0.897564i	$0.645335\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.07107	+	12.2474i	−0.469323	+	0.812892i	−0.999385	−	0.0350674i	$-0.988835\pi$
$227$	−7.07107	+	12.2474i	−0.469323	+	0.812892i	0.530062	+	0.847959i	$0.322169\pi$
$228$		0			0
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	0.982592	−	0.185776i	$-0.0594799\pi$
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	−0.652183	+	0.758062i	$0.726147\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	5.65685i		−	0.370593i	−0.982683	−	0.185296i	$-0.940675\pi$
$233$		−	5.65685i		−	0.370593i	0.982683	−	0.185296i	$-0.0593245\pi$
$234$		0			0
$235$			32.0000i			2.08745i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−5.65685	−	9.79796i	−0.365911	−	0.633777i	0.623011	−	0.782213i	$-0.285909\pi$
$239$	−5.65685	−	9.79796i	−0.365911	−	0.633777i	−0.988922	+	0.148436i	$0.952576\pi$
$240$		0			0
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	−0.896435	−	0.443176i	$-0.853852\pi$
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	0.832019	+	0.554747i	$0.187185\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.34847	−	4.24264i	−0.469476	−	0.271052i
$246$		0			0
$247$	−10.3923	+	6.00000i	−0.661247	+	0.381771i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	8.48528			0.535586			0.267793	−	0.963476i	$-0.413706\pi$
$251$	8.48528			0.535586			0.267793	+	0.963476i	$0.413706\pi$
$252$		0			0
$253$	16.0000			1.00591
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−19.5959	+	11.3137i	−1.22236	+	0.705730i	−0.965420	−	0.260698i	$-0.916047\pi$
$257$	−19.5959	+	11.3137i	−1.22236	+	0.705730i	−0.256939	+	0.966428i	$0.582714\pi$
$258$		0			0
$259$	10.3923	+	6.00000i	0.645746	+	0.372822i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.82843	+	4.89898i	−0.174408	+	0.302084i	−0.939956	−	0.341295i	$-0.889135\pi$
$263$	−2.82843	+	4.89898i	−0.174408	+	0.302084i	0.765548	+	0.643379i	$0.222468\pi$
$264$		0			0
$265$	−12.0000	−	20.7846i	−0.737154	−	1.27679i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			8.48528i			0.517357i	0.965964	+	0.258678i	$0.0832870\pi$
$269$			8.48528i			0.517357i	−0.965964	+	0.258678i	$0.916713\pi$
$270$		0			0
$271$		−	18.0000i		−	1.09342i	−0.837321	−	0.546711i	$-0.815880\pi$
$271$		−	18.0000i		−	1.09342i	0.837321	−	0.546711i	$-0.184120\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.24264	−	7.34847i	−0.255841	−	0.443129i
$276$		0			0
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.89898	−	2.82843i	−0.292249	−	0.168730i	0.346707	−	0.937974i	$-0.387300\pi$
$281$	−4.89898	−	2.82843i	−0.292249	−	0.168730i	−0.638955	+	0.769244i	$0.720633\pi$
$282$		0			0
$283$	−8.66025	+	5.00000i	−0.514799	+	0.297219i	−0.734804	−	0.678280i	$-0.762726\pi$
$283$	−8.66025	+	5.00000i	−0.514799	+	0.297219i	0.220005	+	0.975499i	$0.429393\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	11.3137			0.667827
$288$		0			0
$289$	17.0000			1.00000
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.44949	−	1.41421i	0.143101	−	0.0826192i	−0.426740	−	0.904374i	$-0.640338\pi$
$293$	2.44949	−	1.41421i	0.143101	−	0.0826192i	0.569841	+	0.821755i	$0.307005\pi$
$294$		0			0
$295$	6.92820	+	4.00000i	0.403376	+	0.232889i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−5.65685	+	9.79796i	−0.327144	+	0.566631i
$300$		0			0
$301$	2.00000	+	3.46410i	0.115278	+	0.199667i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	5.65685i		−	0.323911i
$306$		0			0
$307$			30.0000i			1.71219i	0.516818	+	0.856095i	$0.327116\pi$
$307$			30.0000i			1.71219i	−0.516818	+	0.856095i	$0.672884\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.82843	+	4.89898i	0.160385	+	0.277796i	0.935007	−	0.354629i	$-0.115393\pi$
$311$	2.82843	+	4.89898i	0.160385	+	0.277796i	−0.774622	+	0.632425i	$0.782060\pi$
$312$		0			0
$313$	−1.00000	+	1.73205i	−0.0565233	+	0.0979013i	−0.892903	−	0.450250i	$-0.851335\pi$
$313$	−1.00000	+	1.73205i	−0.0565233	+	0.0979013i	0.836379	+	0.548151i	$0.184668\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.44949	+	1.41421i	0.137577	+	0.0794301i	0.567209	−	0.823574i	$-0.308023\pi$
$317$	2.44949	+	1.41421i	0.137577	+	0.0794301i	−0.429632	+	0.903004i	$0.641357\pi$
$318$		0			0
$319$	6.92820	−	4.00000i	0.387905	−	0.223957i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	6.00000			0.332820
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−19.5959	+	11.3137i	−1.08036	+	0.623745i
$330$		0			0
$331$	8.66025	+	5.00000i	0.476011	+	0.274825i	0.718752	−	0.695266i	$-0.244713\pi$
$331$	8.66025	+	5.00000i	0.476011	+	0.274825i	−0.242742	+	0.970091i	$0.578047\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.82843	+	4.89898i	−0.154533	+	0.267660i
$336$		0			0
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	0.992938	+	0.118633i	$0.0378512\pi$
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	−0.393730	+	0.919226i	$0.628816\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			5.65685i			0.306336i
$342$		0			0
$343$		−	20.0000i		−	1.07990i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.07107	+	12.2474i	0.379595	+	0.657477i	0.991003	−	0.133838i	$-0.0427301\pi$
$347$	7.07107	+	12.2474i	0.379595	+	0.657477i	−0.611408	+	0.791315i	$0.709397\pi$
$348$		0			0
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	0.615581	+	0.788074i	$0.288921\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−19.5959	−	11.3137i	−1.04299	−	0.602168i	−0.122308	−	0.992492i	$-0.539030\pi$
$353$	−19.5959	−	11.3137i	−1.04299	−	0.602168i	−0.920677	+	0.390324i	$0.872363\pi$
$354$		0			0
$355$	13.8564	−	8.00000i	0.735422	−	0.424596i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−16.9706			−0.895672			−0.447836	−	0.894116i	$-0.647805\pi$
$359$	−16.9706			−0.895672			−0.447836	+	0.894116i	$0.647805\pi$
$360$		0			0
$361$	−17.0000			−0.894737
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−14.6969	+	8.48528i	−0.769273	+	0.444140i
$366$		0			0
$367$	−12.1244	−	7.00000i	−0.632886	−	0.365397i	0.148983	−	0.988840i	$-0.452400\pi$
$367$	−12.1244	−	7.00000i	−0.632886	−	0.365397i	−0.781869	+	0.623443i	$0.785733\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	8.48528	−	14.6969i	0.440534	−	0.763027i
$372$		0			0
$373$	13.0000	+	22.5167i	0.673114	+	1.16587i	0.977016	+	0.213165i	$0.0683772\pi$
$373$	13.0000	+	22.5167i	0.673114	+	1.16587i	−0.303902	+	0.952703i	$0.598289\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			5.65685i			0.291343i
$378$		0			0
$379$		−	2.00000i		−	0.102733i	−0.998680	−	0.0513665i	$-0.983642\pi$
$379$		−	2.00000i		−	0.102733i	0.998680	−	0.0513665i	$-0.0163577\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−11.3137	−	19.5959i	−0.578103	−	1.00130i	−0.995697	−	0.0926706i	$-0.970460\pi$
$383$	−11.3137	−	19.5959i	−0.578103	−	1.00130i	0.417593	−	0.908634i	$-0.362874\pi$
$384$		0			0
$385$	8.00000	−	13.8564i	0.407718	−	0.706188i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−2.44949	−	1.41421i	−0.124194	−	0.0717035i	0.436616	−	0.899648i	$-0.356177\pi$
$389$	−2.44949	−	1.41421i	−0.124194	−	0.0717035i	−0.560810	+	0.827945i	$0.689510\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−39.5980			−1.99239
$396$		0			0
$397$	−18.0000			−0.903394			−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000			−0.903394			−0.451697	+	0.892171i	$0.649181\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	19.5959	−	11.3137i	0.978573	−	0.564980i	0.0767343	−	0.997052i	$-0.475551\pi$
$401$	19.5959	−	11.3137i	0.978573	−	0.564980i	0.901839	+	0.432072i	$0.142217\pi$
$402$		0			0
$403$	−3.46410	−	2.00000i	−0.172559	−	0.0996271i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	8.48528	−	14.6969i	0.420600	−	0.728500i
$408$		0			0
$409$	−13.0000	−	22.5167i	−0.642809	−	1.11338i	−0.984803	−	0.173675i	$-0.944436\pi$
$409$	−13.0000	−	22.5167i	−0.642809	−	1.11338i	0.341994	−	0.939702i	$-0.388898\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			5.65685i			0.278356i
$414$		0			0
$415$			8.00000i			0.392705i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−18.3848	−	31.8434i	−0.898155	−	1.55565i	−0.829851	−	0.557986i	$-0.811574\pi$
$419$	−18.3848	−	31.8434i	−0.898155	−	1.55565i	−0.0683046	−	0.997665i	$-0.521759\pi$
$420$		0			0
$421$	−11.0000	+	19.0526i	−0.536107	+	0.928565i	0.463002	+	0.886357i	$0.346772\pi$
$421$	−11.0000	+	19.0526i	−0.536107	+	0.928565i	−0.999109	+	0.0422075i	$0.986561\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.46410	−	2.00000i	0.167640	−	0.0967868i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−33.9411			−1.63489			−0.817443	−	0.576009i	$-0.804609\pi$
$431$	−33.9411			−1.63489			−0.817443	+	0.576009i	$0.804609\pi$
$432$		0			0
$433$	−6.00000			−0.288342			−0.144171	−	0.989553i	$-0.546051\pi$
$433$	−6.00000			−0.288342			−0.144171	+	0.989553i	$0.546051\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−29.3939	+	16.9706i	−1.40610	+	0.811812i
$438$		0			0
$439$	−12.1244	−	7.00000i	−0.578664	−	0.334092i	0.181938	−	0.983310i	$-0.441763\pi$
$439$	−12.1244	−	7.00000i	−0.578664	−	0.334092i	−0.760602	+	0.649218i	$0.775096\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.07107	−	12.2474i	0.335957	−	0.581894i	−0.647712	−	0.761886i	$-0.724274\pi$
$443$	7.07107	−	12.2474i	0.335957	−	0.581894i	0.983668	+	0.179992i	$0.0576071\pi$
$444$		0			0
$445$	−24.0000	−	41.5692i	−1.13771	−	1.97057i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			33.9411i			1.60178i	0.598811	+	0.800890i	$0.295640\pi$
$449$			33.9411i			1.60178i	−0.598811	+	0.800890i	$0.704360\pi$
$450$		0			0
$451$		−	16.0000i		−	0.753411i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	5.65685	+	9.79796i	0.265197	+	0.459335i
$456$		0			0
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	0.725059	+	0.688686i	$0.241812\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−26.9444	−	15.5563i	−1.25493	−	0.724531i	−0.282842	−	0.959167i	$-0.591277\pi$
$461$	−26.9444	−	15.5563i	−1.25493	−	0.724531i	−0.972083	+	0.234635i	$0.924610\pi$
$462$		0			0
$463$	−1.73205	+	1.00000i	−0.0804952	+	0.0464739i	−0.539707	−	0.841853i	$-0.681465\pi$
$463$	−1.73205	+	1.00000i	−0.0804952	+	0.0464739i	0.459212	+	0.888327i	$0.348132\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	25.4558			1.17796			0.588978	−	0.808149i	$-0.299530\pi$
$467$	25.4558			1.17796			0.588978	+	0.808149i	$0.299530\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.89898	−	2.82843i	0.225255	−	0.130051i
$474$		0			0
$475$	15.5885	+	9.00000i	0.715247	+	0.412948i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−11.3137	+	19.5959i	−0.516937	+	0.895360i	0.482870	+	0.875692i	$0.339594\pi$
$479$	−11.3137	+	19.5959i	−0.516937	+	0.895360i	−0.999807	+	0.0196683i	$0.993739\pi$
$480$		0			0
$481$	6.00000	+	10.3923i	0.273576	+	0.473848i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			28.2843i			1.28432i
$486$		0			0
$487$		−	18.0000i		−	0.815658i	−0.913058	−	0.407829i	$-0.866286\pi$
$487$		−	18.0000i		−	0.815658i	0.913058	−	0.407829i	$-0.133714\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−15.5563	−	26.9444i	−0.702048	−	1.21598i	−0.967746	−	0.251927i	$-0.918936\pi$
$491$	−15.5563	−	26.9444i	−0.702048	−	1.21598i	0.265698	−	0.964056i	$-0.414398\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	9.79796	+	5.65685i	0.439499	+	0.253745i
$498$		0			0
$499$	−29.4449	+	17.0000i	−1.31813	+	0.761025i	−0.983428	−	0.181298i	$-0.941970\pi$
$499$	−29.4449	+	17.0000i	−1.31813	+	0.761025i	−0.334705	+	0.942323i	$0.608637\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−5.65685			−0.252227			−0.126113	−	0.992016i	$-0.540250\pi$
$503$	−5.65685			−0.252227			−0.126113	+	0.992016i	$0.540250\pi$
$504$		0			0
$505$	−8.00000			−0.355995
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.44949	+	1.41421i	−0.108572	+	0.0626839i	−0.553303	−	0.832980i	$-0.686633\pi$
$509$	−2.44949	+	1.41421i	−0.108572	+	0.0626839i	0.444731	+	0.895664i	$0.353299\pi$
$510$		0			0
$511$	−10.3923	−	6.00000i	−0.459728	−	0.265424i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	19.7990	−	34.2929i	0.872448	−	1.51112i
$516$		0			0
$517$	16.0000	+	27.7128i	0.703679	+	1.21881i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			5.65685i			0.247831i	0.992293	+	0.123916i	$0.0395452\pi$
$521$			5.65685i			0.247831i	−0.992293	+	0.123916i	$0.960455\pi$
$522$		0			0
$523$		−	34.0000i		−	1.48672i	−0.668894	−	0.743358i	$-0.733232\pi$
$523$		−	34.0000i		−	1.48672i	0.668894	−	0.743358i	$-0.266768\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−4.50000	+	7.79423i	−0.195652	+	0.338880i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	9.79796	+	5.65685i	0.424397	+	0.245026i
$534$		0			0
$535$	20.7846	−	12.0000i	0.898597	−	0.518805i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−8.48528			−0.365487
$540$		0			0
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−44.0908	+	25.4558i	−1.88864	+	1.09041i
$546$		0			0
$547$	−32.9090	−	19.0000i	−1.40709	−	0.812381i	−0.411980	−	0.911193i	$-0.635163\pi$
$547$	−32.9090	−	19.0000i	−1.40709	−	0.812381i	−0.995106	+	0.0988117i	$0.968496\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−8.48528	+	14.6969i	−0.361485	+	0.626111i
$552$		0			0
$553$	−14.0000	−	24.2487i	−0.595341	−	1.03116i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			8.48528i			0.359533i	0.983709	+	0.179766i	$0.0575342\pi$
$557$			8.48528i			0.359533i	−0.983709	+	0.179766i	$0.942466\pi$
$558$		0			0
$559$			4.00000i			0.169182i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.41421	−	2.44949i	−0.0596020	−	0.103234i	0.834685	−	0.550728i	$-0.185650\pi$
$563$	−1.41421	−	2.44949i	−0.0596020	−	0.103234i	−0.894287	+	0.447494i	$0.852316\pi$
$564$		0			0
$565$	16.0000	−	27.7128i	0.673125	−	1.16589i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.89898	+	2.82843i	0.205376	+	0.118574i	0.599161	−	0.800629i	$-0.295501\pi$
$569$	4.89898	+	2.82843i	0.205376	+	0.118574i	−0.393785	+	0.919203i	$0.628834\pi$
$570$		0			0
$571$	19.0526	−	11.0000i	0.797325	−	0.460336i	−0.0452101	−	0.998978i	$-0.514396\pi$
$571$	19.0526	−	11.0000i	0.797325	−	0.460336i	0.842535	+	0.538642i	$0.181062\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	16.9706			0.707721
$576$		0			0
$577$	−6.00000			−0.249783			−0.124892	−	0.992170i	$-0.539858\pi$
$577$	−6.00000			−0.249783			−0.124892	+	0.992170i	$0.539858\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.89898	+	2.82843i	−0.203244	+	0.117343i
$582$		0			0
$583$	−20.7846	−	12.0000i	−0.860811	−	0.496989i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.07107	−	12.2474i	0.291854	−	0.505506i	−0.682394	−	0.730985i	$-0.739061\pi$
$587$	7.07107	−	12.2474i	0.291854	−	0.505506i	0.974248	+	0.225478i	$0.0723945\pi$
$588$		0			0
$589$	−6.00000	−	10.3923i	−0.247226	−	0.428207i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	33.9411i		−	1.39379i	−0.717171	−	0.696897i	$-0.754563\pi$
$593$		−	33.9411i		−	1.39379i	0.717171	−	0.696897i	$-0.245437\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−19.7990	−	34.2929i	−0.808965	−	1.40117i	−0.913582	−	0.406656i	$-0.866695\pi$
$599$	−19.7990	−	34.2929i	−0.808965	−	1.40117i	0.104617	−	0.994513i	$-0.466638\pi$
$600$		0			0
$601$	−5.00000	+	8.66025i	−0.203954	+	0.353259i	−0.949799	−	0.312861i	$-0.898713\pi$
$601$	−5.00000	+	8.66025i	−0.203954	+	0.353259i	0.745845	+	0.666120i	$0.232046\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.34847	+	4.24264i	0.298758	+	0.172488i
$606$		0			0
$607$	12.1244	−	7.00000i	0.492112	−	0.284121i	−0.233338	−	0.972396i	$-0.574965\pi$
$607$	12.1244	−	7.00000i	0.492112	−	0.284121i	0.725450	+	0.688274i	$0.241632\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−22.6274			−0.915407
$612$		0			0
$613$	6.00000			0.242338			0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000			0.242338			0.121169	+	0.992632i	$0.461336\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−24.4949	+	14.1421i	−0.986127	+	0.569341i	−0.904114	−	0.427290i	$-0.859468\pi$
$617$	−24.4949	+	14.1421i	−0.986127	+	0.569341i	−0.0820130	+	0.996631i	$0.526135\pi$
$618$		0			0
$619$	8.66025	+	5.00000i	0.348085	+	0.200967i	0.663842	−	0.747873i	$-0.268925\pi$
$619$	8.66025	+	5.00000i	0.348085	+	0.200967i	−0.315757	+	0.948840i	$0.602258\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	16.9706	−	29.3939i	0.679911	−	1.17764i
$624$		0			0
$625$	15.5000	+	26.8468i	0.620000	+	1.07387i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$			30.0000i			1.19428i	0.802137	+	0.597141i	$0.203697\pi$
$631$			30.0000i			1.19428i	−0.802137	+	0.597141i	$0.796303\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−25.4558	−	44.0908i	−1.01018	−	1.74969i
$636$		0			0
$637$	3.00000	−	5.19615i	0.118864	−	0.205879i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.79796	−	5.65685i	−0.386996	−	0.223432i	0.293862	−	0.955848i	$-0.405059\pi$
$641$	−9.79796	−	5.65685i	−0.386996	−	0.223432i	−0.680858	+	0.732416i	$0.738393\pi$
$642$		0			0
$643$	−22.5167	+	13.0000i	−0.887970	+	0.512670i	−0.873278	−	0.487222i	$-0.838010\pi$
$643$	−22.5167	+	13.0000i	−0.887970	+	0.512670i	−0.0146923	+	0.999892i	$0.504677\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−16.9706			−0.667182			−0.333591	−	0.942718i	$-0.608260\pi$
$647$	−16.9706			−0.667182			−0.333591	+	0.942718i	$0.608260\pi$
$648$		0			0
$649$	8.00000			0.314027
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−12.2474	+	7.07107i	−0.479280	+	0.276712i	−0.720116	−	0.693853i	$-0.755912\pi$
$653$	−12.2474	+	7.07107i	−0.479280	+	0.276712i	0.240837	+	0.970566i	$0.422578\pi$
$654$		0			0
$655$	48.4974	+	28.0000i	1.89495	+	1.09405i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7.07107	+	12.2474i	−0.275450	+	0.477093i	−0.970248	−	0.242111i	$-0.922160\pi$
$659$	−7.07107	+	12.2474i	−0.275450	+	0.477093i	0.694799	+	0.719204i	$0.255493\pi$
$660$		0			0
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			33.9411i			1.31618i
$666$		0			0
$667$			16.0000i			0.619522i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.82843	−	4.89898i	−0.109190	−	0.189123i
$672$		0			0
$673$	−5.00000	+	8.66025i	−0.192736	+	0.333828i	−0.946156	−	0.323711i	$-0.895069\pi$
$673$	−5.00000	+	8.66025i	−0.192736	+	0.333828i	0.753420	+	0.657539i	$0.228403\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.44949	−	1.41421i	−0.0941415	−	0.0543526i	0.452190	−	0.891922i	$-0.350643\pi$
$677$	−2.44949	−	1.41421i	−0.0941415	−	0.0543526i	−0.546332	+	0.837569i	$0.683976\pi$
$678$		0			0
$679$	−17.3205	+	10.0000i	−0.664700	+	0.383765i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	42.4264			1.62340			0.811701	−	0.584074i	$-0.198542\pi$
$683$	42.4264			1.62340			0.811701	+	0.584074i	$0.198542\pi$
$684$		0			0
$685$	−16.0000			−0.611329
$686$		0			0
$687$		0			0
$688$		0			0
$689$	14.6969	−	8.48528i	0.559909	−	0.323263i
$690$		0			0
$691$	22.5167	+	13.0000i	0.856574	+	0.494543i	0.862864	−	0.505437i	$-0.168669\pi$
$691$	22.5167	+	13.0000i	0.856574	+	0.494543i	−0.00628943	+	0.999980i	$0.502002\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−14.1421	+	24.4949i	−0.536442	+	0.929144i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	25.4558i		−	0.961454i	−0.876870	−	0.480727i	$-0.840373\pi$
$701$		−	25.4558i		−	0.961454i	0.876870	−	0.480727i	$-0.159627\pi$
$702$		0			0
$703$			36.0000i			1.35777i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.82843	−	4.89898i	−0.106374	−	0.184245i
$708$		0			0
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−9.79796	−	5.65685i	−0.366936	−	0.211851i
$714$		0			0
$715$	13.8564	−	8.00000i	0.518200	−	0.299183i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−33.9411			−1.26579			−0.632895	−	0.774237i	$-0.718134\pi$
$719$	−33.9411			−1.26579			−0.632895	+	0.774237i	$0.718134\pi$
$720$		0			0
$721$	28.0000			1.04277
$722$		0			0
$723$		0			0
$724$		0			0
$725$	7.34847	−	4.24264i	0.272915	−	0.157568i
$726$		0			0
$727$	29.4449	+	17.0000i	1.09205	+	0.630495i	0.934121	−	0.356956i	$-0.116185\pi$
$727$	29.4449	+	17.0000i	1.09205	+	0.630495i	0.157928	+	0.987451i	$0.449519\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−23.0000	−	39.8372i	−0.849524	−	1.47142i	−0.881633	−	0.471935i	$-0.843556\pi$
$733$	−23.0000	−	39.8372i	−0.849524	−	1.47142i	0.0321090	−	0.999484i	$-0.489778\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			5.65685i			0.208373i
$738$		0			0
$739$		−	34.0000i		−	1.25071i	−0.780340	−	0.625355i	$-0.784954\pi$
$739$		−	34.0000i		−	1.25071i	0.780340	−	0.625355i	$-0.215046\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−2.82843	−	4.89898i	−0.103765	−	0.179726i	0.809468	−	0.587164i	$-0.199756\pi$
$743$	−2.82843	−	4.89898i	−0.103765	−	0.179726i	−0.913233	+	0.407438i	$0.866422\pi$
$744$		0			0
$745$	20.0000	−	34.6410i	0.732743	−	1.26915i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	14.6969	+	8.48528i	0.537014	+	0.310045i
$750$		0			0
$751$	−29.4449	+	17.0000i	−1.07446	+	0.620339i	−0.929396	−	0.369084i	$-0.879672\pi$
$751$	−29.4449	+	17.0000i	−1.07446	+	0.620339i	−0.145062	+	0.989423i	$0.546338\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−39.5980			−1.44112
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−24.4949	+	14.1421i	−0.887939	+	0.512652i	−0.873268	−	0.487240i	$-0.838004\pi$
$761$	−24.4949	+	14.1421i	−0.887939	+	0.512652i	−0.0146714	+	0.999892i	$0.504670\pi$
$762$		0			0
$763$	−31.1769	−	18.0000i	−1.12868	−	0.651644i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.82843	+	4.89898i	−0.102129	+	0.176892i
$768$		0			0
$769$	23.0000	+	39.8372i	0.829401	+	1.43657i	0.898509	+	0.438956i	$0.144652\pi$
$769$	23.0000	+	39.8372i	0.829401	+	1.43657i	−0.0691074	+	0.997609i	$0.522015\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			25.4558i			0.915583i	0.889060	+	0.457792i	$0.151359\pi$
$773$			25.4558i			0.915583i	−0.889060	+	0.457792i	$0.848641\pi$
$774$		0			0
$775$			6.00000i			0.215526i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	16.9706	+	29.3939i	0.608034	+	1.05314i
$780$		0			0
$781$	8.00000	−	13.8564i	0.286263	−	0.495821i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−34.2929	−	19.7990i	−1.22396	−	0.706656i
$786$		0			0
$787$	32.9090	−	19.0000i	1.17308	−	0.677277i	0.218675	−	0.975798i	$-0.429827\pi$
$787$	32.9090	−	19.0000i	1.17308	−	0.677277i	0.954403	+	0.298521i	$0.0964933\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	22.6274			0.804538
$792$		0			0
$793$	4.00000			0.142044
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.44949	+	1.41421i	−0.0867654	+	0.0500940i	−0.542755	−	0.839891i	$-0.682619\pi$
$797$	−2.44949	+	1.41421i	−0.0867654	+	0.0500940i	0.455990	+	0.889985i	$0.349285\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−8.48528	+	14.6969i	−0.299439	+	0.518644i
$804$		0			0
$805$	16.0000	+	27.7128i	0.563926	+	0.976748i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			50.9117i			1.78996i	0.446107	+	0.894980i	$0.352810\pi$
$809$			50.9117i			1.78996i	−0.446107	+	0.894980i	$0.647190\pi$
$810$		0			0
$811$			30.0000i			1.05344i	0.850038	+	0.526721i	$0.176579\pi$
$811$			30.0000i			1.05344i	−0.850038	+	0.526721i	$0.823421\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	8.48528	+	14.6969i	0.297226	+	0.514811i
$816$		0			0
$817$	−6.00000	+	10.3923i	−0.209913	+	0.363581i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−12.2474	−	7.07107i	−0.427439	−	0.246782i	0.270816	−	0.962631i	$-0.412706\pi$
$821$	−12.2474	−	7.07107i	−0.427439	−	0.246782i	−0.698255	+	0.715849i	$0.746040\pi$
$822$		0			0
$823$	−1.73205	+	1.00000i	−0.0603755	+	0.0348578i	−0.529884	−	0.848070i	$-0.677765\pi$
$823$	−1.73205	+	1.00000i	−0.0603755	+	0.0348578i	0.469508	+	0.882928i	$0.344431\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−25.4558			−0.885186			−0.442593	−	0.896723i	$-0.645941\pi$
$827$	−25.4558			−0.885186			−0.442593	+	0.896723i	$0.645941\pi$
$828$		0			0
$829$	−18.0000			−0.625166			−0.312583	−	0.949890i	$-0.601194\pi$
$829$	−18.0000			−0.625166			−0.312583	+	0.949890i	$0.601194\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−13.8564	−	8.00000i	−0.479521	−	0.276851i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	19.7990	−	34.2929i	0.683537	−	1.18392i	−0.290357	−	0.956918i	$-0.593774\pi$
$839$	19.7990	−	34.2929i	0.683537	−	1.18392i	0.973894	−	0.227003i	$-0.0728926\pi$
$840$		0			0
$841$	−10.5000	−	18.1865i	−0.362069	−	0.627122i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	25.4558i		−	0.875708i
$846$		0			0
$847$			6.00000i			0.206162i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	16.9706	+	29.3939i	0.581743	+	1.00761i
$852$		0			0
$853$	13.0000	−	22.5167i	0.445112	−	0.770956i	−0.552948	−	0.833215i	$-0.686497\pi$
$853$	13.0000	−	22.5167i	0.445112	−	0.770956i	0.998060	+	0.0622597i	$0.0198307\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	24.4949	+	14.1421i	0.836730	+	0.483086i	0.856151	−	0.516725i	$-0.172849\pi$
$857$	24.4949	+	14.1421i	0.836730	+	0.483086i	−0.0194215	+	0.999811i	$0.506182\pi$
$858$		0			0
$859$	−1.73205	+	1.00000i	−0.0590968	+	0.0341196i	−0.529257	−	0.848461i	$-0.677529\pi$
$859$	−1.73205	+	1.00000i	−0.0590968	+	0.0341196i	0.470160	+	0.882581i	$0.344196\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	40.0000			1.36004
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−34.2929	+	19.7990i	−1.16331	+	0.671635i
$870$		0			0
$871$	−3.46410	−	2.00000i	−0.117377	−	0.0677674i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.65685	+	9.79796i	−0.191237	+	0.331231i
$876$		0			0
$877$	1.00000	+	1.73205i	0.0337676	+	0.0584872i	0.882415	−	0.470471i	$-0.155916\pi$
$877$	1.00000	+	1.73205i	0.0337676	+	0.0584872i	−0.848648	+	0.528958i	$0.822583\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	33.9411i		−	1.14351i	−0.820426	−	0.571753i	$-0.806264\pi$
$881$		−	33.9411i		−	1.14351i	0.820426	−	0.571753i	$-0.193736\pi$
$882$		0			0
$883$			6.00000i			0.201916i	0.994891	+	0.100958i	$0.0321908\pi$
$883$			6.00000i			0.201916i	−0.994891	+	0.100958i	$0.967809\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.82843	+	4.89898i	0.0949693	+	0.164492i	0.909596	−	0.415494i	$-0.136391\pi$
$887$	2.82843	+	4.89898i	0.0949693	+	0.164492i	−0.814627	+	0.579986i	$0.803058\pi$
$888$		0			0
$889$	18.0000	−	31.1769i	0.603701	−	1.04564i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−58.7878	−	33.9411i	−1.96726	−	1.13580i
$894$		0			0
$895$	−20.7846	+	12.0000i	−0.694753	+	0.401116i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−5.65685			−0.188667
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	14.6969	−	8.48528i	0.488543	−	0.282060i
$906$		0			0
$907$	1.73205	+	1.00000i	0.0575118	+	0.0332045i	0.528480	−	0.848946i	$-0.322762\pi$
$907$	1.73205	+	1.00000i	0.0575118	+	0.0332045i	−0.470968	+	0.882150i	$0.656095\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	5.65685	−	9.79796i	0.187420	−	0.324621i	−0.756969	−	0.653450i	$-0.773321\pi$
$911$	5.65685	−	9.79796i	0.187420	−	0.324621i	0.944389	+	0.328830i	$0.106654\pi$
$912$		0			0
$913$	4.00000	+	6.92820i	0.132381	+	0.229290i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			39.5980i			1.30764i
$918$		0			0
$919$			30.0000i			0.989609i	0.869004	+	0.494804i	$0.164760\pi$
$919$			30.0000i			0.989609i	−0.869004	+	0.494804i	$0.835240\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5.65685	+	9.79796i	0.186198	+	0.322504i
$924$		0			0
$925$	9.00000	−	15.5885i	0.295918	−	0.512545i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	9.79796	+	5.65685i	0.321461	+	0.185595i	0.652043	−	0.758182i	$-0.273912\pi$
$929$	9.79796	+	5.65685i	0.321461	+	0.185595i	−0.330583	+	0.943777i	$0.607245\pi$
$930$		0			0
$931$	15.5885	−	9.00000i	0.510891	−	0.294963i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−30.0000			−0.980057			−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000			−0.980057			−0.490029	+	0.871706i	$0.663014\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	46.5403	−	26.8701i	1.51717	−	0.875939i	0.517374	−	0.855759i	$-0.326910\pi$
$941$	46.5403	−	26.8701i	1.51717	−	0.875939i	0.999796	−	0.0201796i	$-0.00642380\pi$
$942$		0			0
$943$	27.7128	+	16.0000i	0.902453	+	0.521032i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.07107	+	12.2474i	−0.229779	+	0.397989i	−0.957742	−	0.287627i	$-0.907134\pi$
$947$	−7.07107	+	12.2474i	−0.229779	+	0.397989i	0.727964	+	0.685616i	$0.240467\pi$
$948$		0			0
$949$	−6.00000	−	10.3923i	−0.194768	−	0.337348i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	50.9117i		−	1.64919i	−0.565723	−	0.824596i	$-0.691403\pi$
$953$		−	50.9117i		−	1.64919i	0.565723	−	0.824596i	$-0.308597\pi$
$954$		0			0
$955$		−	64.0000i		−	2.07099i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.65685	−	9.79796i	−0.182669	−	0.316393i
$960$		0			0
$961$	−13.5000	+	23.3827i	−0.435484	+	0.754280i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	34.2929	+	19.7990i	1.10393	+	0.637352i
$966$		0			0
$967$	−43.3013	+	25.0000i	−1.39247	+	0.803946i	−0.993589	−	0.113055i	$-0.963936\pi$
$967$	−43.3013	+	25.0000i	−1.39247	+	0.803946i	−0.398886	+	0.917000i	$0.630603\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	19.7990			0.635380			0.317690	−	0.948195i	$-0.397093\pi$
$971$	19.7990			0.635380			0.317690	+	0.948195i	$0.397093\pi$
$972$		0			0
$973$	−20.0000			−0.641171
$974$		0			0
$975$		0			0
$976$		0			0
$977$	39.1918	−	22.6274i	1.25386	−	0.723915i	0.281984	−	0.959419i	$-0.409007\pi$
$977$	39.1918	−	22.6274i	1.25386	−	0.723915i	0.971873	+	0.235504i	$0.0756740\pi$
$978$		0			0
$979$	−41.5692	−	24.0000i	−1.32856	−	0.767043i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	14.1421	−	24.4949i	0.451064	−	0.781266i	−0.547388	−	0.836879i	$-0.684378\pi$
$983$	14.1421	−	24.4949i	0.451064	−	0.781266i	0.998452	+	0.0556128i	$0.0177113\pi$
$984$		0			0
$985$	−28.0000	−	48.4974i	−0.892154	−	1.54526i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			11.3137i			0.359755i
$990$		0			0
$991$		−	18.0000i		−	0.571789i	−0.958261	−	0.285894i	$-0.907709\pi$
$991$		−	18.0000i		−	0.571789i	0.958261	−	0.285894i	$-0.0922907\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.82843	−	4.89898i	−0.0896672	−	0.155308i
$996$		0			0
$997$	−19.0000	+	32.9090i	−0.601736	+	1.04224i	0.390822	+	0.920466i	$0.372191\pi$
$997$	−19.0000	+	32.9090i	−0.601736	+	1.04224i	−0.992558	+	0.121771i	$0.961143\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.s.e.1727.4		8
3.2	odd	2	inner	2592.2.s.e.1727.2		8
4.3	odd	2	inner	2592.2.s.e.1727.3		8
9.2	odd	6		96.2.c.a.95.1	✓	4
9.4	even	3	inner	2592.2.s.e.863.1		8
9.5	odd	6	inner	2592.2.s.e.863.3		8
9.7	even	3		96.2.c.a.95.3	yes	4
12.11	even	2	inner	2592.2.s.e.1727.1		8
36.7	odd	6		96.2.c.a.95.2	yes	4
36.11	even	6		96.2.c.a.95.4	yes	4
36.23	even	6	inner	2592.2.s.e.863.4		8
36.31	odd	6	inner	2592.2.s.e.863.2		8
45.2	even	12		2400.2.o.a.2399.4		4
45.7	odd	12		2400.2.o.a.2399.1		4
45.29	odd	6		2400.2.h.c.1151.4		4
45.34	even	6		2400.2.h.c.1151.2		4
45.38	even	12		2400.2.o.h.2399.2		4
45.43	odd	12		2400.2.o.h.2399.3		4
72.11	even	6		192.2.c.b.191.1		4
72.29	odd	6		192.2.c.b.191.4		4
72.43	odd	6		192.2.c.b.191.3		4
72.61	even	6		192.2.c.b.191.2		4
144.11	even	12		768.2.f.g.383.2		4
144.29	odd	12		768.2.f.g.383.1		4
144.43	odd	12		768.2.f.g.383.3		4
144.61	even	12		768.2.f.g.383.4		4
144.83	even	12		768.2.f.a.383.3		4
144.101	odd	12		768.2.f.a.383.4		4
144.115	odd	12		768.2.f.a.383.2		4
144.133	even	12		768.2.f.a.383.1		4
180.7	even	12		2400.2.o.h.2399.4		4
180.43	even	12		2400.2.o.a.2399.2		4
180.47	odd	12		2400.2.o.h.2399.1		4
180.79	odd	6		2400.2.h.c.1151.3		4
180.83	odd	12		2400.2.o.a.2399.3		4
180.119	even	6		2400.2.h.c.1151.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.c.a.95.1	✓	4	9.2	odd	6
96.2.c.a.95.2	yes	4	36.7	odd	6
96.2.c.a.95.3	yes	4	9.7	even	3
96.2.c.a.95.4	yes	4	36.11	even	6
192.2.c.b.191.1		4	72.11	even	6
192.2.c.b.191.2		4	72.61	even	6
192.2.c.b.191.3		4	72.43	odd	6
192.2.c.b.191.4		4	72.29	odd	6
768.2.f.a.383.1		4	144.133	even	12
768.2.f.a.383.2		4	144.115	odd	12
768.2.f.a.383.3		4	144.83	even	12
768.2.f.a.383.4		4	144.101	odd	12
768.2.f.g.383.1		4	144.29	odd	12
768.2.f.g.383.2		4	144.11	even	12
768.2.f.g.383.3		4	144.43	odd	12
768.2.f.g.383.4		4	144.61	even	12
2400.2.h.c.1151.1		4	180.119	even	6
2400.2.h.c.1151.2		4	45.34	even	6
2400.2.h.c.1151.3		4	180.79	odd	6
2400.2.h.c.1151.4		4	45.29	odd	6
2400.2.o.a.2399.1		4	45.7	odd	12
2400.2.o.a.2399.2		4	180.43	even	12
2400.2.o.a.2399.3		4	180.83	odd	12
2400.2.o.a.2399.4		4	45.2	even	12
2400.2.o.h.2399.1		4	180.47	odd	12
2400.2.o.h.2399.2		4	45.38	even	12
2400.2.o.h.2399.3		4	45.43	odd	12
2400.2.o.h.2399.4		4	180.7	even	12
2592.2.s.e.863.1		8	9.4	even	3	inner
2592.2.s.e.863.2		8	36.31	odd	6	inner
2592.2.s.e.863.3		8	9.5	odd	6	inner
2592.2.s.e.863.4		8	36.23	even	6	inner
2592.2.s.e.1727.1		8	12.11	even	2	inner
2592.2.s.e.1727.2		8	3.2	odd	2	inner
2592.2.s.e.1727.3		8	4.3	odd	2	inner
2592.2.s.e.1727.4		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.44949 - 1.41421i) q^{5} +(1.73205 + 1.00000i) q^{7} +O(q^{10})\)	\(q+(2.44949 - 1.41421i) q^{5} +(1.73205 + 1.00000i) q^{7} +(1.41421 - 2.44949i) q^{11} +(1.00000 + 1.73205i) q^{13} +6.00000i q^{19} +(2.82843 + 4.89898i) q^{23} +(1.50000 - 2.59808i) q^{25} +(2.44949 + 1.41421i) q^{29} +(-1.73205 + 1.00000i) q^{31} +5.65685 q^{35} +6.00000 q^{37} +(4.89898 - 2.82843i) q^{41} +(1.73205 + 1.00000i) q^{43} +(-5.65685 + 9.79796i) q^{47} +(-1.50000 - 2.59808i) q^{49} -8.48528i q^{53} -8.00000i q^{55} +(1.41421 + 2.44949i) q^{59} +(1.00000 - 1.73205i) q^{61} +(4.89898 + 2.82843i) q^{65} +(-1.73205 + 1.00000i) q^{67} +5.65685 q^{71} -6.00000 q^{73} +(4.89898 - 2.82843i) q^{77} +(-12.1244 - 7.00000i) q^{79} +(-1.41421 + 2.44949i) q^{83} -16.9706i q^{89} +4.00000i q^{91} +(8.48528 + 14.6969i) q^{95} +(-5.00000 + 8.66025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 8 q^{13} + 12 q^{25} + 48 q^{37} - 12 q^{49} + 8 q^{61} - 48 q^{73} - 40 q^{97}+O(q^{100}) \) 8 * q + 8 * q^13 + 12 * q^25 + 48 * q^37 - 12 * q^49 + 8 * q^61 - 48 * q^73 - 40 * q^97

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