LMFDB - Embedded newform 2160.2.br.b.719.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2160,2,Mod(719,2160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2160, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("2160.719");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2160 = 2^{4} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2160.br (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:	$17.2476868366$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 42x^{12} - 239x^{10} + 1858x^{8} + 26493x^{6} + 128697x^{4} + 265752x^{2} + 197136 $ x^16 + x^14 - 42x^12 - 239x^10 + 1858x^8 + 26493x^6 + 128697x^4 + 265752x^2 + 197136
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 720)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			719.1
Root			$2.90064 - 0.687839i$ of defining polynomial
Character	$\chi$	$=$	2160.719
Dual form			2160.2.br.b.1439.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44342 + 1.70779i) q^{5} +(-1.71352 - 2.96790i) q^{7} +O(q^{10})$	$q+(-1.44342 + 1.70779i) q^{5} +(-1.71352 - 2.96790i) q^{7} +(1.40385 + 2.43154i) q^{11} +(4.81103 + 2.77765i) q^{13} -5.22067 q^{17} -7.08757i q^{19} +(-4.26516 - 2.46249i) q^{23} +(-0.833082 - 4.93011i) q^{25} +(-0.127719 + 0.0737384i) q^{29} +(4.21154 + 2.43154i) q^{31} +(7.54187 + 1.35760i) q^{35} -2.06814i q^{37} +(5.87228 + 3.39036i) q^{41} +(2.35143 + 4.07279i) q^{43} +(-0.437696 + 0.252704i) q^{47} +(-2.37228 + 4.10891i) q^{49} +(-6.17889 - 1.11225i) q^{55} +(4.73417 - 8.19982i) q^{59} +(3.87228 + 6.70699i) q^{61} +(-11.6880 + 4.20691i) q^{65} +(2.58891 - 4.48412i) q^{67} +12.2760 q^{71} -11.1106i q^{73} +(4.81103 - 8.33296i) q^{77} +(10.3496 - 5.97532i) q^{79} +(6.89134 - 3.97871i) q^{83} +(7.53562 - 8.91581i) q^{85} -17.6704i q^{89} -19.0382i q^{91} +(12.1041 + 10.2303i) q^{95} +(-6.60209 + 3.81172i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5}+O(q^{10}) $ 16 * q + 6 * q^5	$ 16 q + 6 q^{5} - 26 q^{25} - 48 q^{29} + 48 q^{41} + 8 q^{49} + 16 q^{61} - 66 q^{65}+O(q^{100}) $ 16 * q + 6 * q^5 - 26 * q^25 - 48 * q^29 + 48 * q^41 + 8 * q^49 + 16 * q^61 - 66 * q^65

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times$.

$n$	$271$	$1297$	$1621$	$2081$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.44342	+	1.70779i	−0.645517	+	0.763746i
$5$	−1.44342	+	1.70779i	−0.645517	+	0.763746i
$6$		0			0
$7$	−1.71352	−	2.96790i	−0.647649	−	1.12176i	−0.983683	−	0.179911i	$-0.942419\pi$
$7$	−1.71352	−	2.96790i	−0.647649	−	1.12176i	0.336034	−	0.941850i	$-0.390914\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.40385	+	2.43154i	0.423276	+	0.733136i	0.996258	−	0.0864325i	$-0.0275467\pi$
$11$	1.40385	+	2.43154i	0.423276	+	0.733136i	−0.572982	+	0.819568i	$0.694213\pi$
$12$		0			0
$13$	4.81103	+	2.77765i	1.33434	+	0.770382i	0.985962	−	0.166972i	$-0.0533988\pi$
$13$	4.81103	+	2.77765i	1.33434	+	0.770382i	0.348379	+	0.937354i	$0.386732\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.22067			−1.26620			−0.633100	−	0.774070i	$-0.718218\pi$
$17$	−5.22067			−1.26620			−0.633100	+	0.774070i	$0.718218\pi$
$18$		0			0
$19$		−	7.08757i		−	1.62600i	−0.582263	−	0.813000i	$-0.697833\pi$
$19$		−	7.08757i		−	1.62600i	0.582263	−	0.813000i	$-0.302167\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.26516	−	2.46249i	−0.889347	−	0.513465i	−0.0156182	−	0.999878i	$-0.504972\pi$
$23$	−4.26516	−	2.46249i	−0.889347	−	0.513465i	−0.873729	+	0.486413i	$0.838305\pi$
$24$		0			0
$25$	−0.833082	−	4.93011i	−0.166616	−	0.986022i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.127719	+	0.0737384i	−0.0237168	+	0.0136929i	−0.511812	−	0.859098i	$-0.671025\pi$
$29$	−0.127719	+	0.0737384i	−0.0237168	+	0.0136929i	0.488095	+	0.872791i	$0.337692\pi$
$30$		0			0
$31$	4.21154	+	2.43154i	0.756416	+	0.436717i	0.828007	−	0.560717i	$-0.189475\pi$
$31$	4.21154	+	2.43154i	0.756416	+	0.436717i	−0.0715917	+	0.997434i	$0.522808\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	7.54187	+	1.35760i	1.27481	+	0.229476i
$36$		0			0
$37$		−	2.06814i		−	0.339999i	−0.985444	−	0.170000i	$-0.945623\pi$
$37$		−	2.06814i		−	0.339999i	0.985444	−	0.170000i	$-0.0543767\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.87228	+	3.39036i	0.917096	+	0.529486i	0.882708	−	0.469923i	$-0.155718\pi$
$41$	5.87228	+	3.39036i	0.917096	+	0.529486i	0.0343887	+	0.999409i	$0.489052\pi$
$42$		0			0
$43$	2.35143	+	4.07279i	0.358589	+	0.621095i	0.987725	−	0.156200i	$-0.0499245\pi$
$43$	2.35143	+	4.07279i	0.358589	+	0.621095i	−0.629136	+	0.777295i	$0.716591\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.437696	+	0.252704i	−0.0638446	+	0.0368607i	−0.531582	−	0.847007i	$-0.678402\pi$
$47$	−0.437696	+	0.252704i	−0.0638446	+	0.0368607i	0.467738	+	0.883867i	$0.345069\pi$
$48$		0			0
$49$	−2.37228	+	4.10891i	−0.338897	+	0.586987i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$	−6.17889	−	1.11225i	−0.833161	−	0.149976i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.73417	−	8.19982i	0.616336	−	1.06753i	−0.373812	−	0.927504i	$-0.621949\pi$
$59$	4.73417	−	8.19982i	0.616336	−	1.06753i	0.990148	−	0.140022i	$-0.0447172\pi$
$60$		0			0
$61$	3.87228	+	6.70699i	0.495795	+	0.858742i	0.999988	−	0.00484894i	$-0.00154347\pi$
$61$	3.87228	+	6.70699i	0.495795	+	0.858742i	−0.504193	+	0.863591i	$0.668210\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−11.6880	+	4.20691i	−1.44972	+	0.521803i
$66$		0			0
$67$	2.58891	−	4.48412i	0.316286	−	0.547823i	−0.663424	−	0.748243i	$-0.730898\pi$
$67$	2.58891	−	4.48412i	0.316286	−	0.547823i	0.979710	+	0.200421i	$0.0642309\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	12.2760			1.45690			0.728449	−	0.685100i	$-0.240242\pi$
$71$	12.2760			1.45690			0.728449	+	0.685100i	$0.240242\pi$
$72$		0			0
$73$		−	11.1106i		−	1.30040i	−0.759764	−	0.650199i	$-0.774685\pi$
$73$		−	11.1106i		−	1.30040i	0.759764	−	0.650199i	$-0.225315\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.81103	−	8.33296i	0.548268	−	0.949629i
$78$		0			0
$79$	10.3496	−	5.97532i	1.16442	−	0.672276i	0.212058	−	0.977257i	$-0.431983\pi$
$79$	10.3496	−	5.97532i	1.16442	−	0.672276i	0.952359	+	0.304981i	$0.0986500\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.89134	−	3.97871i	0.756422	−	0.436721i	−0.0715874	−	0.997434i	$-0.522806\pi$
$83$	6.89134	−	3.97871i	0.756422	−	0.436721i	0.828010	+	0.560714i	$0.189473\pi$
$84$		0			0
$85$	7.53562	−	8.91581i	0.817353	−	0.967055i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	17.6704i		−	1.87305i	−0.350594	−	0.936527i	$-0.614020\pi$
$89$		−	17.6704i		−	1.87305i	0.350594	−	0.936527i	$-0.385980\pi$
$90$		0			0
$91$		−	19.0382i		−	1.99575i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	12.1041	+	10.2303i	1.24185	+	1.04961i
$96$		0			0
$97$	−6.60209	+	3.81172i	−0.670341	+	0.387022i	−0.796206	−	0.605026i	$-0.793163\pi$
$97$	−6.60209	+	3.81172i	−0.670341	+	0.387022i	0.125865	+	0.992047i	$0.459829\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.31386	−	3.06796i	0.528749	−	0.305273i	−0.211758	−	0.977322i	$-0.567919\pi$
$101$	5.31386	−	3.06796i	0.528749	−	0.305273i	0.740507	+	0.672049i	$0.234586\pi$
$102$		0			0
$103$	−2.35143	+	4.07279i	−0.231693	+	0.401304i	−0.958306	−	0.285742i	$-0.907760\pi$
$103$	−2.35143	+	4.07279i	−0.231693	+	0.401304i	0.726613	+	0.687047i	$0.241093\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	19.5118i		−	1.88627i	−0.332404	−	0.943137i	$-0.607860\pi$
$107$		−	19.5118i		−	1.88627i	0.332404	−	0.943137i	$-0.392140\pi$
$108$		0			0
$109$	−11.8614			−1.13612			−0.568058	−	0.822988i	$-0.692305\pi$
$109$	−11.8614			−1.13612			−0.568058	+	0.822988i	$0.692305\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.20070	+	3.81172i	−0.207024	+	0.358576i	−0.950776	−	0.309880i	$-0.899711\pi$
$113$	−2.20070	+	3.81172i	−0.207024	+	0.358576i	0.743752	+	0.668456i	$0.233045\pi$
$114$		0			0
$115$	10.3618	−	3.72958i	0.966245	−	0.347785i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	8.94571	+	15.4944i	0.820052	+	1.42037i
$120$		0			0
$121$	1.55842	−	2.69927i	0.141675	−	0.245388i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.62207	+	5.69349i	0.860624	+	0.509241i
$126$		0			0
$127$	10.6815			0.947833			0.473916	−	0.880570i	$-0.342840\pi$
$127$	10.6815			0.947833			0.473916	+	0.880570i	$0.342840\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.73417	−	8.19982i	0.413626	−	0.716422i	−0.581657	−	0.813434i	$-0.697595\pi$
$131$	4.73417	−	8.19982i	0.413626	−	0.716422i	0.995283	+	0.0970124i	$0.0309287\pi$
$132$		0			0
$133$	−21.0352	+	12.1447i	−1.82398	+	1.05308i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.42137	+	12.8542i	0.634051	+	1.09821i	0.986715	+	0.162458i	$0.0519422\pi$
$137$	7.42137	+	12.8542i	0.634051	+	1.09821i	−0.352665	+	0.935750i	$0.614724\pi$
$138$		0			0
$139$	−1.92647	−	1.11225i	−0.163401	−	0.0943399i	0.416069	−	0.909333i	$-0.363407\pi$
$139$	−1.92647	−	1.11225i	−0.163401	−	0.0943399i	−0.579471	+	0.814993i	$0.696741\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			15.5976i			1.30434i
$144$		0			0
$145$	0.0584220	−	0.324552i	0.00485168	−	0.0269526i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.127719	−	0.0737384i	−0.0104631	−	0.00604089i	0.494759	−	0.869030i	$-0.335256\pi$
$149$	−0.127719	−	0.0737384i	−0.0104631	−	0.00604089i	−0.505222	+	0.862989i	$0.668590\pi$
$150$		0			0
$151$	8.06449	−	4.65604i	0.656279	−	0.378903i	−0.134579	−	0.990903i	$-0.542968\pi$
$151$	8.06449	−	4.65604i	0.656279	−	0.378903i	0.790858	+	0.612000i	$0.209635\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−10.2316	+	3.68270i	−0.821820	+	0.295802i
$156$		0			0
$157$	10.1842	+	5.87986i	0.812788	+	0.469264i	0.847923	−	0.530119i	$-0.177853\pi$
$157$	10.1842	+	5.87986i	0.812788	+	0.469264i	−0.0351349	+	0.999383i	$0.511186\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			16.8781i			1.33018i
$162$		0			0
$163$	−7.65492			−0.599580			−0.299790	−	0.954005i	$-0.596917\pi$
$163$	−7.65492			−0.599580			−0.299790	+	0.954005i	$0.596917\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−16.2970	−	9.40910i	−1.26110	−	0.728098i	−0.287815	−	0.957686i	$-0.592929\pi$
$167$	−16.2970	−	9.40910i	−1.26110	−	0.728098i	−0.973288	+	0.229588i	$0.926262\pi$
$168$		0			0
$169$	8.93070	+	15.4684i	0.686977	+	1.18988i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.20070	−	3.81172i	−0.167316	−	0.289800i	0.770159	−	0.637852i	$-0.220177\pi$
$173$	−2.20070	−	3.81172i	−0.167316	−	0.289800i	−0.937475	+	0.348052i	$0.886843\pi$
$174$		0			0
$175$	−13.2046	+	10.9203i	−0.998171	+	0.825499i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	17.8914			1.33727			0.668634	−	0.743592i	$-0.266879\pi$
$179$	17.8914			1.33727			0.668634	+	0.743592i	$0.266879\pi$
$180$		0			0
$181$	6.37228			0.473648			0.236824	−	0.971553i	$-0.423894\pi$
$181$	6.37228			0.473648			0.236824	+	0.971553i	$0.423894\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.53194	+	2.98519i	0.259673	+	0.219475i
$186$		0			0
$187$	−7.32903	−	12.6943i	−0.535952	−	0.928296i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.40385	−	2.43154i	−0.101579	−	0.175940i	0.810756	−	0.585384i	$-0.199056\pi$
$191$	−1.40385	−	2.43154i	−0.101579	−	0.175940i	−0.912335	+	0.409444i	$0.865723\pi$
$192$		0			0
$193$	8.39315	+	4.84579i	0.604152	+	0.348807i	0.770673	−	0.637230i	$-0.219920\pi$
$193$	8.39315	+	4.84579i	0.604152	+	0.348807i	−0.166521	+	0.986038i	$0.553253\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.63856			0.116742			0.0583712	−	0.998295i	$-0.481409\pi$
$197$	1.63856			0.116742			0.0583712	+	0.998295i	$0.481409\pi$
$198$		0			0
$199$			16.8137i			1.19189i	0.803024	+	0.595946i	$0.203223\pi$
$199$			16.8137i			1.19189i	−0.803024	+	0.595946i	$0.796777\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.437696	+	0.252704i	0.0307203	+	0.0177363i
$204$		0			0
$205$	−14.2662	+	5.13490i	−0.996394	+	0.358637i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	17.2337	−	9.94987i	1.19208	−	0.688247i
$210$		0			0
$211$	−8.06449	−	4.65604i	−0.555183	−	0.320535i	0.196027	−	0.980598i	$-0.437196\pi$
$211$	−8.06449	−	4.65604i	−0.555183	−	0.320535i	−0.751210	+	0.660064i	$0.770529\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−10.3496	−	1.86301i	−0.705834	−	0.127056i
$216$		0			0
$217$		−	16.6659i		−	1.13136i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−25.1168	−	14.5012i	−1.68954	−	0.975457i
$222$		0			0
$223$	−6.81680	−	11.8070i	−0.456487	−	0.790658i	0.542286	−	0.840194i	$-0.317559\pi$
$223$	−6.81680	−	11.8070i	−0.456487	−	0.790658i	−0.998772	+	0.0495360i	$0.984226\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.85300	+	3.37923i	−0.388477	+	0.224287i	−0.681500	−	0.731818i	$-0.738672\pi$
$227$	−5.85300	+	3.37923i	−0.388477	+	0.224287i	0.293023	+	0.956105i	$0.405339\pi$
$228$		0			0
$229$	−9.87228	+	17.0993i	−0.652379	+	1.12995i	0.330165	+	0.943923i	$0.392895\pi$
$229$	−9.87228	+	17.0993i	−0.652379	+	1.12995i	−0.982544	+	0.186030i	$0.940438\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	14.0235			0.918708			0.459354	−	0.888253i	$-0.348081\pi$
$233$	14.0235			0.918708			0.459354	+	0.888253i	$0.348081\pi$
$234$		0			0
$235$	0.200214	−	1.11225i	0.0130605	−	0.0725552i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.73417	+	8.19982i	−0.306228	+	0.530402i	−0.977534	−	0.210778i	$-0.932400\pi$
$239$	−4.73417	+	8.19982i	−0.306228	+	0.530402i	0.671306	+	0.741180i	$0.265734\pi$
$240$		0			0
$241$	−12.2446	−	21.2082i	−0.788742	−	1.36614i	−0.926738	−	0.375708i	$-0.877400\pi$
$241$	−12.2446	−	21.2082i	−0.788742	−	1.36614i	0.137997	−	0.990433i	$-0.455934\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.59296	−	9.98224i	−0.229545	−	0.637742i
$246$		0			0
$247$	19.6868	−	34.0986i	1.25264	−	2.16964i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.66064			−0.420416			−0.210208	−	0.977657i	$-0.567414\pi$
$251$	−6.66064			−0.420416			−0.210208	+	0.977657i	$0.567414\pi$
$252$		0			0
$253$		−	13.8278i		−	0.869349i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.20070	+	3.81172i	−0.137276	+	0.237769i	−0.926465	−	0.376382i	$-0.877168\pi$
$257$	−2.20070	+	3.81172i	−0.137276	+	0.237769i	0.789189	+	0.614151i	$0.210501\pi$
$258$		0			0
$259$	−6.13802	+	3.54379i	−0.381398	+	0.220200i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	10.8817	−	6.28258i	0.670997	−	0.387400i	−0.125457	−	0.992099i	$-0.540040\pi$
$263$	10.8817	−	6.28258i	0.670997	−	0.387400i	0.796454	+	0.604699i	$0.206706\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$			2.52434i			0.153912i	0.997035	+	0.0769558i	$0.0245200\pi$
$269$			2.52434i			0.153912i	−0.997035	+	0.0769558i	$0.975480\pi$
$270$		0			0
$271$			21.2627i			1.29162i	0.763499	+	0.645809i	$0.223480\pi$
$271$			21.2627i			1.29162i	−0.763499	+	0.645809i	$0.776520\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	10.8182	−	8.94679i	0.652363	−	0.539512i
$276$		0			0
$277$	−11.9753	+	6.91392i	−0.719524	+	0.415417i	−0.814578	−	0.580055i	$-0.803031\pi$
$277$	−11.9753	+	6.91392i	−0.719524	+	0.415417i	0.0950534	+	0.995472i	$0.469698\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.98913	+	2.30312i	−0.237971	+	0.137393i	−0.614244	−	0.789116i	$-0.710539\pi$
$281$	−3.98913	+	2.30312i	−0.237971	+	0.137393i	0.376273	+	0.926509i	$0.377206\pi$
$282$		0			0
$283$	−6.41637	+	11.1135i	−0.381414	+	0.660628i	−0.991265	−	0.131888i	$-0.957896\pi$
$283$	−6.41637	+	11.1135i	−0.381414	+	0.660628i	0.609851	+	0.792516i	$0.291229\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	23.2378i		−	1.37168i
$288$		0			0
$289$	10.2554			0.603261
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.99176	−	6.91392i	0.233201	−	0.403916i	−0.725547	−	0.688172i	$-0.758413\pi$
$293$	3.99176	−	6.91392i	0.233201	−	0.403916i	0.958748	+	0.284256i	$0.0917467\pi$
$294$		0			0
$295$	7.17017	+	19.9207i	0.417463	+	1.15983i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−13.6799	−	23.6943i	−0.791128	−	1.37027i
$300$		0			0
$301$	8.05842	−	13.9576i	0.464480	−	0.804502i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−17.0434	−	3.06796i	−0.975905	−	0.175671i
$306$		0			0
$307$	4.62832			0.264152			0.132076	−	0.991240i	$-0.457836\pi$
$307$	4.62832			0.264152			0.132076	+	0.991240i	$0.457836\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−13.6799	+	23.6943i	−0.775715	+	1.34358i	0.158677	+	0.987331i	$0.449277\pi$
$311$	−13.6799	+	23.6943i	−0.775715	+	1.34358i	−0.934392	+	0.356247i	$0.884056\pi$
$312$		0			0
$313$	10.8510	−	6.26482i	0.613334	−	0.354109i	−0.160935	−	0.986965i	$-0.551451\pi$
$313$	10.8510	−	6.26482i	0.613334	−	0.354109i	0.774269	+	0.632856i	$0.218118\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.63031	−	9.75199i	−0.316230	−	0.547726i	0.663468	−	0.748204i	$-0.269084\pi$
$317$	−5.63031	−	9.75199i	−0.316230	−	0.547726i	−0.979698	+	0.200478i	$0.935750\pi$
$318$		0			0
$319$	−0.358595	−	0.207035i	−0.0200775	−	0.0115917i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			37.0019i			2.05884i
$324$		0			0
$325$	9.68614	−	26.0329i	0.537290	−	1.44405i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.50000	+	0.866025i	0.0826977	+	0.0477455i
$330$		0			0
$331$	−14.2025	+	8.19982i	−0.780641	+	0.450703i	−0.836657	−	0.547727i	$-0.815493\pi$
$331$	−14.2025	+	8.19982i	−0.780641	+	0.450703i	0.0560167	+	0.998430i	$0.482160\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3.92105	+	10.8938i	0.214230	+	0.595191i
$336$		0			0
$337$	22.2641	+	12.8542i	1.21280	+	0.700213i	0.963369	−	0.268179i	$-0.0864219\pi$
$337$	22.2641	+	12.8542i	1.21280	+	0.700213i	0.249435	+	0.968392i	$0.419755\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			13.6540i			0.739407i
$342$		0			0
$343$	−7.72946			−0.417352
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−16.1341	−	9.31503i	−0.866124	−	0.500057i	−6.56364e−5	−	1.00000i	$-0.500021\pi$
$347$	−16.1341	−	9.31503i	−0.866124	−	0.500057i	−0.866058	+	0.499943i	$0.833354\pi$
$348$		0			0
$349$	−1.12772	−	1.95327i	−0.0603654	−	0.104556i	0.834263	−	0.551366i	$-0.185893\pi$
$349$	−1.12772	−	1.95327i	−0.0603654	−	0.104556i	−0.894629	+	0.446810i	$0.852560\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.01998	−	5.23075i	−0.160737	−	0.278405i	0.774396	−	0.632701i	$-0.218054\pi$
$353$	−3.01998	−	5.23075i	−0.160737	−	0.278405i	−0.935133	+	0.354296i	$0.884720\pi$
$354$		0			0
$355$	−17.7195	+	20.9649i	−0.940452	+	1.11270i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−29.1222			−1.53701			−0.768506	−	0.639843i	$-0.778999\pi$
$359$	−29.1222			−1.53701			−0.768506	+	0.639843i	$0.778999\pi$
$360$		0			0
$361$	−31.2337			−1.64388
$362$		0			0
$363$		0			0
$364$		0			0
$365$	18.9746	+	16.0373i	0.993174	+	0.839429i
$366$		0			0
$367$	5.30350	+	9.18593i	0.276840	+	0.479501i	0.970598	−	0.240707i	$-0.0773794\pi$
$367$	5.30350	+	9.18593i	0.276840	+	0.479501i	−0.693757	+	0.720209i	$0.744046\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	19.8063	+	11.4352i	1.02553	+	0.592090i	0.915701	−	0.401860i	$-0.131636\pi$
$373$	19.8063	+	11.4352i	1.02553	+	0.592090i	0.109829	+	0.993950i	$0.464970\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.819279			−0.0421950
$378$		0			0
$379$		−	19.4523i		−	0.999197i	−0.866257	−	0.499598i	$-0.833481\pi$
$379$		−	19.4523i		−	0.999197i	0.866257	−	0.499598i	$-0.166519\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	10.8817	+	6.28258i	0.556031	+	0.321025i	0.751551	−	0.659675i	$-0.229306\pi$
$383$	10.8817	+	6.28258i	0.556031	+	0.321025i	−0.195520	+	0.980700i	$0.562639\pi$
$384$		0			0
$385$	7.28659	+	20.2442i	0.371359	+	1.03174i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−5.87228	+	3.39036i	−0.297736	+	0.171898i	−0.641426	−	0.767185i	$-0.721657\pi$
$389$	−5.87228	+	3.39036i	−0.297736	+	0.171898i	0.343689	+	0.939083i	$0.388323\pi$
$390$		0			0
$391$	22.2670	+	12.8559i	1.12609	+	0.650149i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.73417	+	26.2998i	−0.238202	+	1.32328i
$396$		0			0
$397$		−	19.3832i		−	0.972813i	−0.873733	−	0.486406i	$-0.838308\pi$
$397$		−	19.3832i		−	0.972813i	0.873733	−	0.486406i	$-0.161692\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−17.3139	−	9.99616i	−0.864613	−	0.499184i	0.000941430	−	1.00000i	$-0.499700\pi$
$401$	−17.3139	−	9.99616i	−0.864613	−	0.499184i	−0.865554	+	0.500815i	$0.833034\pi$
$402$		0			0
$403$	13.5079	+	23.3964i	0.672878	+	1.16546i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.02875	−	2.90335i	0.249266	−	0.143914i
$408$		0			0
$409$	7.68614	−	13.3128i	0.380055	−	0.658275i	−0.611015	−	0.791619i	$-0.709238\pi$
$409$	7.68614	−	13.3128i	0.380055	−	0.658275i	0.991070	+	0.133344i	$0.0425717\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−32.4483			−1.59668
$414$		0			0
$415$	−3.15228	+	17.5119i	−0.154740	+	0.859625i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−8.06449	+	13.9681i	−0.393976	+	0.682387i	−0.992970	−	0.118367i	$-0.962234\pi$
$419$	−8.06449	+	13.9681i	−0.393976	+	0.682387i	0.598994	+	0.800754i	$0.295567\pi$
$420$		0			0
$421$	5.80298	+	10.0511i	0.282820	+	0.489859i	0.972078	−	0.234657i	$-0.0753967\pi$
$421$	5.80298	+	10.0511i	0.282820	+	0.489859i	−0.689258	+	0.724516i	$0.742063\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.34925	+	25.7385i	0.210970	+	1.24850i
$426$		0			0
$427$	13.2704	−	22.9851i	0.642202	−	1.11233i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−35.7829			−1.72360			−0.861800	−	0.507249i	$-0.830663\pi$
$431$	−35.7829			−1.72360			−0.861800	+	0.507249i	$0.830663\pi$
$432$		0			0
$433$			20.1531i			0.968495i	0.874931	+	0.484248i	$0.160907\pi$
$433$			20.1531i			0.968495i	−0.874931	+	0.484248i	$0.839093\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−17.4531	+	30.2296i	−0.834894	+	1.44608i
$438$		0			0
$439$	−18.7726	+	10.8384i	−0.895970	+	0.517288i	−0.875890	−	0.482510i	$-0.839725\pi$
$439$	−18.7726	+	10.8384i	−0.895970	+	0.517288i	−0.0200792	+	0.999798i	$0.506392\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.64212	−	4.98953i	0.410600	−	0.237060i	−0.280448	−	0.959869i	$-0.590483\pi$
$443$	8.64212	−	4.98953i	0.410600	−	0.237060i	0.691047	+	0.722810i	$0.257150\pi$
$444$		0			0
$445$	30.1772	+	25.5057i	1.43054	+	1.20909i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	8.51278i		−	0.401743i	−0.979618	−	0.200871i	$-0.935623\pi$
$449$		−	8.51278i		−	0.401743i	0.979618	−	0.200871i	$-0.0643773\pi$
$450$		0			0
$451$			19.0382i			0.896475i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	32.5132	+	27.4801i	1.52424	+	1.28829i
$456$		0			0
$457$	−7.26887	+	4.19668i	−0.340023	+	0.196313i	−0.660282	−	0.751017i	$-0.729563\pi$
$457$	−7.26887	+	4.19668i	−0.340023	+	0.196313i	0.320259	+	0.947330i	$0.396230\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	18.9891	−	10.9634i	0.884412	−	0.510615i	0.0123012	−	0.999924i	$-0.496084\pi$
$461$	18.9891	−	10.9634i	0.884412	−	0.510615i	0.872110	+	0.489309i	$0.162751\pi$
$462$		0			0
$463$	−4.97760	+	8.62146i	−0.231329	+	0.400673i	−0.958199	−	0.286101i	$-0.907641\pi$
$463$	−4.97760	+	8.62146i	−0.231329	+	0.400673i	0.726871	+	0.686775i	$0.240974\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	40.0344i		−	1.85257i	−0.376825	−	0.926285i	$-0.622984\pi$
$467$		−	40.0344i		−	1.85257i	0.376825	−	0.926285i	$-0.377016\pi$
$468$		0			0
$469$	−17.7446			−0.819368
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.60209	+	11.4352i	−0.303565	+	0.525789i
$474$		0			0
$475$	−34.9425	+	5.90453i	−1.60327	+	0.270918i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−18.7726	−	32.5152i	−0.857744	−	1.48566i	−0.874076	−	0.485790i	$-0.838532\pi$
$479$	−18.7726	−	32.5152i	−0.857744	−	1.48566i	0.0163313	−	0.999867i	$-0.494801\pi$
$480$		0			0
$481$	5.74456	−	9.94987i	0.261930	−	0.453675i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.01998	−	16.7769i	0.137130	−	0.761799i
$486$		0			0
$487$	37.6228			1.70485			0.852427	−	0.522847i	$-0.175130\pi$
$487$	37.6228			1.70485			0.852427	+	0.522847i	$0.175130\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	15.9650	−	27.6521i	0.720488	−	1.24792i	−0.240316	−	0.970695i	$-0.577251\pi$
$491$	15.9650	−	27.6521i	0.720488	−	1.24792i	0.960804	−	0.277228i	$-0.0894156\pi$
$492$		0			0
$493$	0.666778	−	0.384964i	0.0300302	−	0.0173379i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−21.0352	−	36.4340i	−0.943558	−	1.63429i
$498$		0			0
$499$	−1.92647	−	1.11225i	−0.0862408	−	0.0497912i	0.456259	−	0.889847i	$-0.349189\pi$
$499$	−1.92647	−	1.11225i	−0.0862408	−	0.0497912i	−0.542500	+	0.840056i	$0.682522\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	10.0381i		−	0.447577i	−0.974638	−	0.223789i	$-0.928157\pi$
$503$		−	10.0381i		−	0.447577i	0.974638	−	0.223789i	$-0.0718426\pi$
$504$		0			0
$505$	−2.43070	+	13.5033i	−0.108165	+	0.600889i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	21.1277	+	12.1981i	0.936470	+	0.540671i	0.888852	−	0.458195i	$-0.151504\pi$
$509$	21.1277	+	12.1981i	0.936470	+	0.540671i	0.0476178	+	0.998866i	$0.484837\pi$
$510$		0			0
$511$	−32.9752	+	19.0382i	−1.45874	+	0.842201i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.56137	−	9.89449i	−0.156933	−	0.436003i
$516$		0			0
$517$	−1.22892	−	0.709516i	−0.0540478	−	0.0312045i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			24.3036i			1.06476i	0.846505	+	0.532380i	$0.178702\pi$
$521$			24.3036i			1.06476i	−0.846505	+	0.532380i	$0.821298\pi$
$522$		0			0
$523$	12.4323			0.543627			0.271814	−	0.962350i	$-0.412377\pi$
$523$	12.4323			0.543627			0.271814	+	0.962350i	$0.412377\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−21.9871	−	12.6943i	−0.957773	−	0.552970i
$528$		0			0
$529$	0.627719	+	1.08724i	0.0272921	+	0.0472713i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	18.8345	+	32.6223i	0.815813	+	1.41303i
$534$		0			0
$535$	33.3220	+	28.1637i	1.44063	+	1.21762i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−13.3213			−0.573789
$540$		0			0
$541$	15.6277			0.671888			0.335944	−	0.941882i	$-0.390945\pi$
$541$	15.6277			0.671888			0.335944	+	0.941882i	$0.390945\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	17.1210	−	20.2568i	0.733382	−	0.867705i
$546$		0			0
$547$	−13.7454	−	23.8077i	−0.587711	−	1.01795i	−0.994531	−	0.104437i	$-0.966696\pi$
$547$	−13.7454	−	23.8077i	−0.587711	−	1.01795i	0.406820	−	0.913508i	$-0.366637\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.522626	+	0.905215i	0.0222646	+	0.0385635i
$552$		0			0
$553$	−35.4683	−	20.4776i	−1.50827	−	0.870798i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	24.7698			1.04953			0.524765	−	0.851247i	$-0.324153\pi$
$557$	24.7698			1.04953			0.524765	+	0.851247i	$0.324153\pi$
$558$		0			0
$559$			26.1258i			1.10500i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.89134	+	3.97871i	0.290435	+	0.167683i	0.638138	−	0.769922i	$-0.279705\pi$
$563$	6.89134	+	3.97871i	0.290435	+	0.167683i	−0.347703	+	0.937605i	$0.613038\pi$
$564$		0			0
$565$	−3.33308	−	9.26024i	−0.140224	−	0.389581i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−29.6644	+	17.1267i	−1.24360	+	0.717990i	−0.969824	−	0.243804i	$-0.921605\pi$
$569$	−29.6644	+	17.1267i	−1.24360	+	0.717990i	−0.273772	+	0.961795i	$0.588271\pi$
$570$		0			0
$571$	−27.1957	−	15.7015i	−1.13811	−	0.657086i	−0.192145	−	0.981367i	$-0.561544\pi$
$571$	−27.1957	−	15.7015i	−1.13811	−	0.657086i	−0.945961	+	0.324281i	$0.894878\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−8.58712	+	23.0792i	−0.358108	+	0.962467i
$576$		0			0
$577$			11.1106i			0.462541i	0.972890	+	0.231270i	$0.0742882\pi$
$577$			11.1106i			0.462541i	−0.972890	+	0.231270i	$0.925712\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−23.6168	−	13.6352i	−0.979792	−	0.565683i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−18.9232	+	10.9253i	−0.781045	+	0.450937i	−0.836801	−	0.547508i	$-0.815577\pi$
$587$	−18.9232	+	10.9253i	−0.781045	+	0.450937i	0.0557555	+	0.998444i	$0.482243\pi$
$588$		0			0
$589$	17.2337	−	29.8496i	0.710102	−	1.22993i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	5.22067			0.214387			0.107194	−	0.994238i	$-0.465814\pi$
$593$	5.22067			0.214387			0.107194	+	0.994238i	$0.465814\pi$
$594$		0			0
$595$	−39.3736	−	7.08757i	−1.61416	−	0.290562i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−13.1573	+	22.7890i	−0.537591	+	0.931135i	0.461442	+	0.887170i	$0.347332\pi$
$599$	−13.1573	+	22.7890i	−0.537591	+	0.931135i	−0.999033	+	0.0439646i	$0.986001\pi$
$600$		0			0
$601$	3.56930	+	6.18220i	0.145595	+	0.252177i	0.929595	−	0.368583i	$-0.120157\pi$
$601$	3.56930	+	6.18220i	0.145595	+	0.252177i	−0.784000	+	0.620761i	$0.786824\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.36032	+	6.55763i	0.0959606	+	0.266605i
$606$		0			0
$607$	7.29176	−	12.6297i	0.295964	−	0.512624i	−0.679245	−	0.733912i	$-0.737693\pi$
$607$	7.29176	−	12.6297i	0.295964	−	0.512624i	0.975209	+	0.221288i	$0.0710260\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.80770			−0.113587
$612$		0			0
$613$		−	42.3743i		−	1.71148i	−0.517405	−	0.855741i	$-0.673102\pi$
$613$		−	42.3743i		−	1.71148i	0.517405	−	0.855741i	$-0.326898\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	21.4448	−	37.1435i	0.863337	−	1.49534i	−0.00535277	−	0.999986i	$-0.501704\pi$
$617$	21.4448	−	37.1435i	0.863337	−	1.49534i	0.868689	−	0.495357i	$-0.164963\pi$
$618$		0			0
$619$	−16.4876	+	9.51911i	−0.662692	+	0.382605i	−0.793302	−	0.608829i	$-0.791640\pi$
$619$	−16.4876	+	9.51911i	−0.662692	+	0.382605i	0.130610	+	0.991434i	$0.458306\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−52.4438	+	30.2785i	−2.10112	+	1.21308i
$624$		0			0
$625$	−23.6119	+	8.21437i	−0.944478	+	0.328575i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			10.7971i			0.430507i
$630$		0			0
$631$		−	4.44900i		−	0.177112i	−0.996071	−	0.0885560i	$-0.971775\pi$
$631$		−	4.44900i		−	0.177112i	0.996071	−	0.0885560i	$-0.0282252\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−15.4179	+	18.2418i	−0.611842	+	0.723903i
$636$		0			0
$637$	−22.8263	+	13.1787i	−0.904409	+	0.522161i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	31.2446	−	18.0391i	1.23409	−	0.712500i	0.266207	−	0.963916i	$-0.414230\pi$
$641$	31.2446	−	18.0391i	1.23409	−	0.712500i	0.967879	+	0.251416i	$0.0808962\pi$
$642$		0			0
$643$	−8.56759	+	14.8395i	−0.337873	+	0.585212i	−0.984032	−	0.177990i	$-0.943041\pi$
$643$	−8.56759	+	14.8395i	−0.337873	+	0.585212i	0.646160	+	0.763202i	$0.276374\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			10.6726i			0.419584i	0.977746	+	0.209792i	$0.0672787\pi$
$647$			10.6726i			0.419584i	−0.977746	+	0.209792i	$0.932721\pi$
$648$		0			0
$649$	26.5842			1.04352
$650$		0			0
$651$		0			0
$652$		0			0
$653$	10.8510	−	18.7945i	0.424632	−	0.735484i	−0.571754	−	0.820425i	$-0.693737\pi$
$653$	10.8510	−	18.7945i	0.424632	−	0.735484i	0.996386	+	0.0849410i	$0.0270702\pi$
$654$		0			0
$655$	7.17017	+	19.9207i	0.280162	+	0.778368i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	15.9650	+	27.6521i	0.621906	+	1.07717i	0.989130	+	0.147041i	$0.0469749\pi$
$659$	15.9650	+	27.6521i	0.621906	+	1.07717i	−0.367224	+	0.930132i	$0.619692\pi$
$660$		0			0
$661$	−24.5475	+	42.5176i	−0.954789	+	1.65374i	−0.219939	+	0.975514i	$0.570586\pi$
$661$	−24.5475	+	42.5176i	−0.954789	+	1.65374i	−0.734850	+	0.678229i	$0.762748\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	9.62207	−	53.4535i	0.373128	−	2.07284i
$666$		0			0
$667$	0.726321			0.0281232
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−10.8722	+	18.8312i	−0.419716	+	0.726970i
$672$		0			0
$673$	−26.5130	+	15.3073i	−1.02200	+	0.590053i	−0.914683	−	0.404172i	$-0.867560\pi$
$673$	−26.5130	+	15.3073i	−1.02200	+	0.590053i	−0.107318	+	0.994225i	$0.534226\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.8510	+	18.7945i	0.417037	+	0.722330i	0.995640	−	0.0932798i	$-0.0297351\pi$
$677$	10.8510	+	18.7945i	0.417037	+	0.722330i	−0.578603	+	0.815610i	$0.696402\pi$
$678$		0			0
$679$	22.6256	+	13.0629i	0.868291	+	0.501308i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	22.3561i		−	0.855431i	−0.903913	−	0.427716i	$-0.859319\pi$
$683$		−	22.3561i		−	0.855431i	0.903913	−	0.427716i	$-0.140681\pi$
$684$		0			0
$685$	−32.6644	−	5.87986i	−1.24804	−	0.224658i
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	43.3247	−	25.0135i	1.64815	−	0.951560i	0.670343	−	0.742051i	$-0.266147\pi$
$691$	43.3247	−	25.0135i	1.64815	−	0.951560i	0.977807	−	0.209509i	$-0.0671865\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.68020	−	1.68457i	0.177530	−	0.0638993i
$696$		0			0
$697$	−30.6573	−	17.7000i	−1.16123	−	0.670435i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	22.1291i		−	0.835806i	−0.908492	−	0.417903i	$-0.862765\pi$
$701$		−	22.1291i		−	0.835806i	0.908492	−	0.417903i	$-0.137235\pi$
$702$		0			0
$703$	−14.6581			−0.552839
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−18.2108	−	10.5140i	−0.684887	−	0.395420i
$708$		0			0
$709$	−16.9891	−	29.4260i	−0.638040	−	1.10512i	−0.985862	−	0.167557i	$-0.946412\pi$
$709$	−16.9891	−	29.4260i	−0.638040	−	1.10512i	0.347822	−	0.937560i	$-0.386921\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−11.9753	−	20.7418i	−0.448477	−	0.776786i
$714$		0			0
$715$	−26.6374	−	22.5139i	−0.996183	−	0.841971i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	11.2308			0.418838			0.209419	−	0.977826i	$-0.432843\pi$
$719$	11.2308			0.418838			0.209419	+	0.977826i	$0.432843\pi$
$720$		0			0
$721$	16.1168			0.600223
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.469939	+	0.568237i	0.0174531	+	0.0211038i
$726$		0			0
$727$	−22.6761	−	39.2762i	−0.841012	−	1.45668i	−0.889040	−	0.457829i	$-0.848627\pi$
$727$	−22.6761	−	39.2762i	−0.841012	−	1.45668i	0.0480283	−	0.998846i	$-0.484706\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−12.2760	−	21.2627i	−0.454046	−	0.786430i
$732$		0			0
$733$	19.8063	+	11.4352i	0.731562	+	0.422367i	0.818993	−	0.573803i	$-0.194533\pi$
$733$	19.8063	+	11.4352i	0.731562	+	0.422367i	−0.0874316	+	0.996171i	$0.527866\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	14.5377			0.535505
$738$		0			0
$739$			14.1751i			0.521441i	0.965414	+	0.260721i	$0.0839601\pi$
$739$			14.1751i			0.521441i	−0.965414	+	0.260721i	$0.916040\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−5.46644	−	3.15605i	−0.200544	−	0.115784i	0.396365	−	0.918093i	$-0.370271\pi$
$743$	−5.46644	−	3.15605i	−0.200544	−	0.115784i	−0.596909	+	0.802309i	$0.703605\pi$
$744$		0			0
$745$	0.310281	−	0.111681i	0.0113678	−	0.00409168i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−57.9090	+	33.4338i	−2.11595	+	1.22164i
$750$		0			0
$751$	−28.7636	−	16.6067i	−1.04960	−	0.605986i	−0.127062	−	0.991895i	$-0.540555\pi$
$751$	−28.7636	−	16.6067i	−1.04960	−	0.605986i	−0.922537	+	0.385908i	$0.873888\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−3.68892	+	20.4931i	−0.134253	+	0.745819i
$756$		0			0
$757$		−	9.04247i		−	0.328654i	−0.986406	−	0.164327i	$-0.947455\pi$
$757$		−	9.04247i		−	0.328654i	0.986406	−	0.164327i	$-0.0525453\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	38.7119	+	22.3503i	1.40331	+	0.810199i	0.994730	−	0.102525i	$-0.0326921\pi$
$761$	38.7119	+	22.3503i	1.40331	+	0.810199i	0.408576	+	0.912724i	$0.366025\pi$
$762$		0			0
$763$	20.3247	+	35.2035i	0.735804	+	1.27445i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	45.5525	−	26.2998i	1.64481	−	0.949629i
$768$		0			0
$769$	−2.75544	+	4.77256i	−0.0993636	+	0.172103i	−0.911421	−	0.411474i	$-0.865014\pi$
$769$	−2.75544	+	4.77256i	−0.0993636	+	0.172103i	0.812058	+	0.583577i	$0.198347\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	35.2112			1.26646			0.633229	−	0.773965i	$-0.281729\pi$
$773$	35.2112			1.26646			0.633229	+	0.773965i	$0.281729\pi$
$774$		0			0
$775$	8.47918	−	22.7890i	0.304581	−	0.818606i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	24.0294	−	41.6202i	0.860944	−	1.49120i
$780$		0			0
$781$	17.2337	+	29.8496i	0.616670	+	1.06810i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−24.7416	+	8.90538i	−0.883067	+	0.317847i
$786$		0			0
$787$	19.9616	−	34.5744i	0.711553	−	1.23245i	−0.252721	−	0.967539i	$-0.581326\pi$
$787$	19.9616	−	34.5744i	0.711553	−	1.23245i	0.964274	−	0.264907i	$-0.0853411\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	15.0837			0.536316
$792$		0			0
$793$			43.0234i			1.52781i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−12.7945	+	22.1608i	−0.453206	+	0.784976i	−0.998583	−	0.0532149i	$-0.983053\pi$
$797$	−12.7945	+	22.1608i	−0.453206	+	0.784976i	0.545377	+	0.838191i	$0.316387\pi$
$798$		0			0
$799$	2.28507	−	1.31929i	0.0808399	−	0.0466730i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	27.0158	−	15.5976i	0.953368	−	0.550428i
$804$		0			0
$805$	−28.8242	−	24.3621i	−1.01592	−	0.858653i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			16.7306i			0.588217i	0.955772	+	0.294108i	$0.0950226\pi$
$809$			16.7306i			0.588217i	−0.955772	+	0.294108i	$0.904977\pi$
$810$		0			0
$811$			23.9013i			0.839288i	0.907689	+	0.419644i	$0.137845\pi$
$811$			23.9013i			0.839288i	−0.907689	+	0.419644i	$0.862155\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	11.0493	−	13.0730i	0.387039	−	0.457927i
$816$		0			0
$817$	28.8662	−	16.6659i	1.00990	−	0.583066i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	40.2446	−	23.2352i	1.40454	−	0.810914i	0.409690	−	0.912225i	$-0.365637\pi$
$821$	40.2446	−	23.2352i	1.40454	−	0.810914i	0.994855	+	0.101310i	$0.0323035\pi$
$822$		0			0
$823$	10.2438	−	17.7428i	0.357078	−	0.618477i	−0.630394	−	0.776276i	$-0.717106\pi$
$823$	10.2438	−	17.7428i	0.357078	−	0.618477i	0.987471	+	0.157799i	$0.0504398\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	4.23142i		−	0.147141i	−0.997290	−	0.0735704i	$-0.976561\pi$
$827$		−	4.23142i		−	0.147141i	0.997290	−	0.0735704i	$-0.0234394\pi$
$828$		0			0
$829$	19.8614			0.689815			0.344908	−	0.938637i	$-0.387910\pi$
$829$	19.8614			0.689815			0.344908	+	0.938637i	$0.387910\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	12.3849	−	21.4513i	0.429112	−	0.743243i
$834$		0			0
$835$	39.5922	−	14.2506i	1.37015	−	0.493163i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	28.7636	+	49.8200i	0.993030	+	1.71998i	0.598584	+	0.801060i	$0.295730\pi$
$839$	28.7636	+	49.8200i	0.993030	+	1.71998i	0.394446	+	0.918919i	$0.370937\pi$
$840$		0			0
$841$	−14.4891	+	25.0959i	−0.499625	+	0.865376i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−39.3076	−	7.07568i	−1.35222	−	0.243411i
$846$		0			0
$847$	−10.6815			−0.367022
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.09277	+	8.82093i	−0.174578	+	0.302378i
$852$		0			0
$853$	11.9753	−	6.91392i	0.410025	−	0.236728i	−0.280775	−	0.959774i	$-0.590592\pi$
$853$	11.9753	−	6.91392i	0.410025	−	0.236728i	0.690801	+	0.723045i	$0.257258\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	17.1959	+	29.7842i	0.587402	+	1.01741i	0.994571	+	0.104058i	$0.0331826\pi$
$857$	17.1959	+	29.7842i	0.587402	+	1.01741i	−0.407169	+	0.913353i	$0.633484\pi$
$858$		0			0
$859$	−8.06449	−	4.65604i	−0.275157	−	0.158862i	0.356072	−	0.934459i	$-0.384116\pi$
$859$	−8.06449	−	4.65604i	−0.275157	−	0.158862i	−0.631229	+	0.775597i	$0.717449\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	8.65099i		−	0.294483i	−0.989101	−	0.147242i	$-0.952961\pi$
$863$		−	8.65099i		−	0.294483i	0.989101	−	0.147242i	$-0.0470395\pi$
$864$		0			0
$865$	9.68614	+	1.74358i	0.329339	+	0.0592836i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	29.0584	+	16.7769i	0.985739	+	0.569117i
$870$		0			0
$871$	24.9107	−	14.3822i	0.844066	−	0.487322i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.410108	−	38.3132i	0.0138642	−	1.29522i
$876$		0			0
$877$	24.0552	+	13.8883i	0.812285	+	0.468973i	0.847749	−	0.530398i	$-0.177957\pi$
$877$	24.0552	+	13.8883i	0.812285	+	0.468973i	−0.0354634	+	0.999371i	$0.511291\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			22.0193i			0.741850i	0.928663	+	0.370925i	$0.120959\pi$
$881$			22.0193i			0.741850i	−0.928663	+	0.370925i	$0.879041\pi$
$882$		0			0
$883$	10.0297			0.337528			0.168764	−	0.985657i	$-0.446022\pi$
$883$	10.0297			0.337528			0.168764	+	0.985657i	$0.446022\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10.8817	−	6.28258i	−0.365373	−	0.210948i	0.306062	−	0.952012i	$-0.400989\pi$
$887$	−10.8817	−	6.28258i	−0.365373	−	0.210948i	−0.671435	+	0.741063i	$0.734322\pi$
$888$		0			0
$889$	−18.3030	−	31.7017i	−0.613862	−	1.06324i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.79106	+	3.10220i	0.0599355	+	0.103811i
$894$		0			0
$895$	−25.8248	+	30.5548i	−0.863229	+	1.02133i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.717190			−0.0239196
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−9.19787	+	10.8825i	−0.305748	+	0.361747i
$906$		0			0
$907$	6.41637	+	11.1135i	0.213052	+	0.369017i	0.952668	−	0.304012i	$-0.0983262\pi$
$907$	6.41637	+	11.1135i	0.213052	+	0.369017i	−0.739616	+	0.673029i	$0.764993\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	3.68892	+	6.38939i	0.122219	+	0.211690i	0.920643	−	0.390407i	$-0.127666\pi$
$911$	3.68892	+	6.38939i	0.122219	+	0.211690i	−0.798423	+	0.602097i	$0.794332\pi$
$912$		0			0
$913$	19.3488	+	11.1710i	0.640351	+	0.369707i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−32.4483			−1.07154
$918$		0			0
$919$		−	18.6241i		−	0.614354i	−0.951652	−	0.307177i	$-0.900616\pi$
$919$		−	18.6241i		−	0.614354i	0.951652	−	0.307177i	$-0.0993844\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	59.0604	+	34.0986i	1.94400	+	1.12237i
$924$		0			0
$925$	−10.1961	+	1.72293i	−0.335247	+	0.0566495i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−7.54755	+	4.35758i	−0.247627	+	0.142968i	−0.618677	−	0.785645i	$-0.712331\pi$
$929$	−7.54755	+	4.35758i	−0.247627	+	0.142968i	0.371050	+	0.928613i	$0.378998\pi$
$930$		0			0
$931$	29.1222	+	16.8137i	0.954442	+	0.551047i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	32.2580	+	5.80670i	1.05495	+	0.189899i
$936$		0			0
$937$			49.8769i			1.62941i	0.579877	+	0.814704i	$0.303101\pi$
$937$			49.8769i			1.62941i	−0.579877	+	0.814704i	$0.696899\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−30.9891	−	17.8916i	−1.01022	−	0.583249i	−0.0989615	−	0.995091i	$-0.531552\pi$
$941$	−30.9891	−	17.8916i	−1.01022	−	0.583249i	−0.911255	+	0.411842i	$0.864885\pi$
$942$		0			0
$943$	−16.6975	−	28.9209i	−0.543745	−	0.941793i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.5463	+	8.39829i	−0.472690	+	0.272908i	−0.717365	−	0.696697i	$-0.754652\pi$
$947$	−14.5463	+	8.39829i	−0.472690	+	0.272908i	0.244675	+	0.969605i	$0.421319\pi$
$948$		0			0
$949$	30.8614	−	53.4535i	1.00180	−	1.73517i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−33.2676			−1.07764			−0.538822	−	0.842420i	$-0.681130\pi$
$953$	−33.2676			−1.07764			−0.538822	+	0.842420i	$0.681130\pi$
$954$		0			0
$955$	6.17889	+	1.11225i	0.199944	+	0.0359916i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	25.4333	−	44.0518i	0.821284	−	1.42251i
$960$		0			0
$961$	−3.67527	−	6.36575i	−0.118557	−	0.205347i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−20.3904	+	7.33922i	−0.656391	+	0.236258i
$966$		0			0
$967$	−24.3524	+	42.1796i	−0.783120	+	1.35640i	0.146995	+	0.989137i	$0.453040\pi$
$967$	−24.3524	+	42.1796i	−0.783120	+	1.35640i	−0.930116	+	0.367267i	$0.880294\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	48.0589			1.54228			0.771142	−	0.636664i	$-0.219686\pi$
$971$	48.0589			1.54228			0.771142	+	0.636664i	$0.219686\pi$
$972$		0			0
$973$			7.62344i			0.244396i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−24.0552	+	41.6648i	−0.769593	+	1.33297i	0.168191	+	0.985755i	$0.446208\pi$
$977$	−24.0552	+	41.6648i	−0.769593	+	1.33297i	−0.937784	+	0.347220i	$0.887126\pi$
$978$		0			0
$979$	42.9661	−	24.8065i	1.37320	−	0.792819i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−33.0318	+	19.0709i	−1.05355	+	0.608268i	−0.923641	−	0.383258i	$-0.874802\pi$
$983$	−33.0318	+	19.0709i	−1.05355	+	0.608268i	−0.129909	+	0.991526i	$0.541469\pi$
$984$		0			0
$985$	−2.36513	+	2.79831i	−0.0753591	+	0.0891615i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	23.1615i		−	0.736492i
$990$		0			0
$991$		−	23.9013i		−	0.759249i	−0.925141	−	0.379625i	$-0.876053\pi$
$991$		−	23.9013i		−	0.759249i	0.925141	−	0.379625i	$-0.123947\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−28.7143	−	24.2692i	−0.910304	−	0.769387i
$996$		0			0
$997$	41.5083	−	23.9648i	1.31458	−	0.758973i	0.331729	−	0.943375i	$-0.392368\pi$
$997$	41.5083	−	23.9648i	1.31458	−	0.758973i	0.982851	+	0.184402i	$0.0590348\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2160.2.br.b.719.1		16
3.2	odd	2		720.2.br.b.239.6	yes	16
4.3	odd	2	inner	2160.2.br.b.719.2		16
5.4	even	2	inner	2160.2.br.b.719.6		16
9.2	odd	6	inner	2160.2.br.b.1439.5		16
9.7	even	3		720.2.br.b.479.5	yes	16
12.11	even	2		720.2.br.b.239.4	yes	16
15.14	odd	2		720.2.br.b.239.3	✓	16
20.19	odd	2	inner	2160.2.br.b.719.5		16
36.7	odd	6		720.2.br.b.479.3	yes	16
36.11	even	6	inner	2160.2.br.b.1439.6		16
45.29	odd	6	inner	2160.2.br.b.1439.2		16
45.34	even	6		720.2.br.b.479.4	yes	16
60.59	even	2		720.2.br.b.239.5	yes	16
180.79	odd	6		720.2.br.b.479.6	yes	16
180.119	even	6	inner	2160.2.br.b.1439.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.br.b.239.3	✓	16	15.14	odd	2
720.2.br.b.239.4	yes	16	12.11	even	2
720.2.br.b.239.5	yes	16	60.59	even	2
720.2.br.b.239.6	yes	16	3.2	odd	2
720.2.br.b.479.3	yes	16	36.7	odd	6
720.2.br.b.479.4	yes	16	45.34	even	6
720.2.br.b.479.5	yes	16	9.7	even	3
720.2.br.b.479.6	yes	16	180.79	odd	6
2160.2.br.b.719.1		16	1.1	even	1	trivial
2160.2.br.b.719.2		16	4.3	odd	2	inner
2160.2.br.b.719.5		16	20.19	odd	2	inner
2160.2.br.b.719.6		16	5.4	even	2	inner
2160.2.br.b.1439.1		16	180.119	even	6	inner
2160.2.br.b.1439.2		16	45.29	odd	6	inner
2160.2.br.b.1439.5		16	9.2	odd	6	inner
2160.2.br.b.1439.6		16	36.11	even	6	inner

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:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2160.br (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.44342 + 1.70779i) q^{5} +(-1.71352 - 2.96790i) q^{7} +O(q^{10})\)	\(q+(-1.44342 + 1.70779i) q^{5} +(-1.71352 - 2.96790i) q^{7} +(1.40385 + 2.43154i) q^{11} +(4.81103 + 2.77765i) q^{13} -5.22067 q^{17} -7.08757i q^{19} +(-4.26516 - 2.46249i) q^{23} +(-0.833082 - 4.93011i) q^{25} +(-0.127719 + 0.0737384i) q^{29} +(4.21154 + 2.43154i) q^{31} +(7.54187 + 1.35760i) q^{35} -2.06814i q^{37} +(5.87228 + 3.39036i) q^{41} +(2.35143 + 4.07279i) q^{43} +(-0.437696 + 0.252704i) q^{47} +(-2.37228 + 4.10891i) q^{49} +(-6.17889 - 1.11225i) q^{55} +(4.73417 - 8.19982i) q^{59} +(3.87228 + 6.70699i) q^{61} +(-11.6880 + 4.20691i) q^{65} +(2.58891 - 4.48412i) q^{67} +12.2760 q^{71} -11.1106i q^{73} +(4.81103 - 8.33296i) q^{77} +(10.3496 - 5.97532i) q^{79} +(6.89134 - 3.97871i) q^{83} +(7.53562 - 8.91581i) q^{85} -17.6704i q^{89} -19.0382i q^{91} +(12.1041 + 10.2303i) q^{95} +(-6.60209 + 3.81172i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5}+O(q^{10}) \) 16 * q + 6 * q^5	\( 16 q + 6 q^{5} - 26 q^{25} - 48 q^{29} + 48 q^{41} + 8 q^{49} + 16 q^{61} - 66 q^{65}+O(q^{100}) \) 16 * q + 6 * q^5 - 26 * q^25 - 48 * q^29 + 48 * q^41 + 8 * q^49 + 16 * q^61 - 66 * q^65

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