LMFDB - Embedded newform 864.2.r.b.721.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(145,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("864.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.r (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:	$6.89907473464$
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^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 $ x^16 - x^15 + x^14 + 2x^12 - 4x^11 - 8x^9 + 4x^8 - 16x^7 - 32x^5 + 32x^4 + 64x^2 - 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			721.6
Root			$-1.12494 - 0.857038i$ of defining polynomial
Character	$\chi$	$=$	864.721
Dual form			864.2.r.b.145.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19115 - 0.687709i) q^{5} +(-1.80469 + 3.12581i) q^{7} +O(q^{10})$	$q+(1.19115 - 0.687709i) q^{5} +(-1.80469 + 3.12581i) q^{7} +(1.83294 + 1.05825i) q^{11} +(-0.887751 + 0.512543i) q^{13} -0.808822 q^{17} +7.43122i q^{19} +(-1.65498 - 2.86652i) q^{23} +(-1.55411 + 2.69180i) q^{25} +(7.71083 + 4.45185i) q^{29} +(-3.26436 - 5.65403i) q^{31} +4.96439i q^{35} +4.01531i q^{37} +(3.45852 + 5.99034i) q^{41} +(0.245957 + 0.142003i) q^{43} +(-3.61351 + 6.25878i) q^{47} +(-3.01378 - 5.22003i) q^{49} -3.86330i q^{53} +2.91107 q^{55} +(7.06904 - 4.08131i) q^{59} +(6.31237 + 3.64445i) q^{61} +(-0.704961 + 1.22103i) q^{65} +(2.43973 - 1.40858i) q^{67} +4.69830 q^{71} +0.409922 q^{73} +(-6.61576 + 3.81961i) q^{77} +(0.0456121 - 0.0790024i) q^{79} +(-2.40891 - 1.39079i) q^{83} +(-0.963426 + 0.556234i) q^{85} -8.91934 q^{89} -3.69992i q^{91} +(5.11052 + 8.85168i) q^{95} +(-2.76022 + 4.78084i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{7}+O(q^{10}) $ 16 * q - 6 * q^7	$ 16 q - 6 q^{7} + 28 q^{17} - 10 q^{23} + 2 q^{25} + 10 q^{31} + 8 q^{41} + 6 q^{47} + 18 q^{49} + 4 q^{55} + 14 q^{65} + 72 q^{71} - 44 q^{73} + 30 q^{79} - 64 q^{89} + 44 q^{95}+O(q^{100}) $ 16 * q - 6 * q^7 + 28 * q^17 - 10 * q^23 + 2 * q^25 + 10 * q^31 + 8 * q^41 + 6 * q^47 + 18 * q^49 + 4 * q^55 + 14 * q^65 + 72 * q^71 - 44 * q^73 + 30 * q^79 - 64 * q^89 + 44 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	1.19115	−	0.687709i	0.532697	−	0.307553i	−0.209417	−	0.977826i	$-0.567157\pi$
$5$	1.19115	−	0.687709i	0.532697	−	0.307553i	0.742114	+	0.670274i	$0.233823\pi$
$6$		0			0
$7$	−1.80469	+	3.12581i	−0.682107	+	1.18144i	0.292229	+	0.956348i	$0.405603\pi$
$7$	−1.80469	+	3.12581i	−0.682107	+	1.18144i	−0.974337	+	0.225096i	$0.927730\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.83294	+	1.05825i	0.552652	+	0.319074i	0.750191	−	0.661221i	$-0.229961\pi$
$11$	1.83294	+	1.05825i	0.552652	+	0.319074i	−0.197539	+	0.980295i	$0.563295\pi$
$12$		0			0
$13$	−0.887751	+	0.512543i	−0.246218	+	0.142154i	−0.618031	−	0.786154i	$-0.712069\pi$
$13$	−0.887751	+	0.512543i	−0.246218	+	0.142154i	0.371813	+	0.928307i	$0.378736\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.808822			−0.196168			−0.0980841	−	0.995178i	$-0.531271\pi$
$17$	−0.808822			−0.196168			−0.0980841	+	0.995178i	$0.531271\pi$
$18$		0			0
$19$			7.43122i			1.70484i	0.522858	+	0.852420i	$0.324866\pi$
$19$			7.43122i			1.70484i	−0.522858	+	0.852420i	$0.675134\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.65498	−	2.86652i	−0.345088	−	0.597710i	0.640282	−	0.768140i	$-0.278818\pi$
$23$	−1.65498	−	2.86652i	−0.345088	−	0.597710i	−0.985370	+	0.170430i	$0.945484\pi$
$24$		0			0
$25$	−1.55411	+	2.69180i	−0.310823	+	0.538361i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	7.71083	+	4.45185i	1.43187	+	0.826688i	0.997263	−	0.0739344i	$-0.0235555\pi$
$29$	7.71083	+	4.45185i	1.43187	+	0.826688i	0.434603	+	0.900622i	$0.356889\pi$
$30$		0			0
$31$	−3.26436	−	5.65403i	−0.586296	−	1.01549i	−0.994713	−	0.102698i	$-0.967252\pi$
$31$	−3.26436	−	5.65403i	−0.586296	−	1.01549i	0.408417	−	0.912796i	$-0.366081\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			4.96439i			0.839136i
$36$		0			0
$37$			4.01531i			0.660113i	0.943961	+	0.330057i	$0.107068\pi$
$37$			4.01531i			0.660113i	−0.943961	+	0.330057i	$0.892932\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.45852	+	5.99034i	0.540131	+	0.935534i	0.998896	+	0.0469764i	$0.0149585\pi$
$41$	3.45852	+	5.99034i	0.540131	+	0.935534i	−0.458765	+	0.888557i	$0.651708\pi$
$42$		0			0
$43$	0.245957	+	0.142003i	0.0375081	+	0.0216553i	0.518637	−	0.854995i	$-0.326440\pi$
$43$	0.245957	+	0.142003i	0.0375081	+	0.0216553i	−0.481129	+	0.876650i	$0.659773\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.61351	+	6.25878i	−0.527084	+	0.912937i	0.472417	+	0.881375i	$0.343381\pi$
$47$	−3.61351	+	6.25878i	−0.527084	+	0.912937i	−0.999502	+	0.0315619i	$0.989952\pi$
$48$		0			0
$49$	−3.01378	−	5.22003i	−0.430540	−	0.745718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	3.86330i		−	0.530666i	−0.964157	−	0.265333i	$-0.914518\pi$
$53$		−	3.86330i		−	0.530666i	0.964157	−	0.265333i	$-0.0854818\pi$
$54$		0			0
$55$	2.91107			0.392528
$56$		0			0
$57$		0			0
$58$		0			0
$59$	7.06904	−	4.08131i	0.920310	−	0.531341i	0.0365764	−	0.999331i	$-0.488355\pi$
$59$	7.06904	−	4.08131i	0.920310	−	0.531341i	0.883734	+	0.467989i	$0.155021\pi$
$60$		0			0
$61$	6.31237	+	3.64445i	0.808216	+	0.466624i	0.846336	−	0.532650i	$-0.178804\pi$
$61$	6.31237	+	3.64445i	0.808216	+	0.466624i	−0.0381201	+	0.999273i	$0.512137\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.704961	+	1.22103i	−0.0874396	+	0.151450i
$66$		0			0
$67$	2.43973	−	1.40858i	0.298061	−	0.172085i	−0.343511	−	0.939149i	$-0.611616\pi$
$67$	2.43973	−	1.40858i	0.298061	−	0.172085i	0.641571	+	0.767063i	$0.278283\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.69830			0.557586			0.278793	−	0.960351i	$-0.410066\pi$
$71$	4.69830			0.557586			0.278793	+	0.960351i	$0.410066\pi$
$72$		0			0
$73$	0.409922			0.0479777			0.0239889	−	0.999712i	$-0.492363\pi$
$73$	0.409922			0.0479777			0.0239889	+	0.999712i	$0.492363\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.61576	+	3.81961i	−0.753936	+	0.435285i
$78$		0			0
$79$	0.0456121	−	0.0790024i	0.00513176	−	0.00888847i	−0.863448	−	0.504438i	$-0.831700\pi$
$79$	0.0456121	−	0.0790024i	0.00513176	−	0.00888847i	0.868580	+	0.495549i	$0.165033\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.40891	−	1.39079i	−0.264412	−	0.152659i	0.361933	−	0.932204i	$-0.382117\pi$
$83$	−2.40891	−	1.39079i	−0.264412	−	0.152659i	−0.626346	+	0.779545i	$0.715450\pi$
$84$		0			0
$85$	−0.963426	+	0.556234i	−0.104498	+	0.0603321i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−8.91934			−0.945448			−0.472724	−	0.881210i	$-0.656729\pi$
$89$	−8.91934			−0.945448			−0.472724	+	0.881210i	$0.656729\pi$
$90$		0			0
$91$		−	3.69992i		−	0.387857i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.11052	+	8.85168i	0.524328	+	0.908163i
$96$		0			0
$97$	−2.76022	+	4.78084i	−0.280258	+	0.485421i	−0.971448	−	0.237252i	$-0.923753\pi$
$97$	−2.76022	+	4.78084i	−0.280258	+	0.485421i	0.691190	+	0.722673i	$0.257087\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.63193	−	3.25160i	−0.560398	−	0.323546i	0.192907	−	0.981217i	$-0.438208\pi$
$101$	−5.63193	−	3.25160i	−0.560398	−	0.323546i	−0.753305	+	0.657671i	$0.771542\pi$
$102$		0			0
$103$	1.50528	+	2.60723i	0.148320	+	0.256898i	0.930607	−	0.366021i	$-0.119280\pi$
$103$	1.50528	+	2.60723i	0.148320	+	0.256898i	−0.782287	+	0.622918i	$0.785947\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			0.447393i			0.0432511i	0.999766	+	0.0216256i	$0.00688417\pi$
$107$			0.447393i			0.0432511i	−0.999766	+	0.0216256i	$0.993116\pi$
$108$		0			0
$109$			9.36497i			0.897002i	0.893782	+	0.448501i	$0.148042\pi$
$109$			9.36497i			0.897002i	−0.893782	+	0.448501i	$0.851958\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.66349	−	9.80944i	−0.532776	−	0.922795i	−0.999267	−	0.0382692i	$-0.987816\pi$
$113$	−5.66349	−	9.80944i	−0.532776	−	0.922795i	0.466492	−	0.884526i	$-0.345518\pi$
$114$		0			0
$115$	−3.94266	−	2.27629i	−0.367655	−	0.212266i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.45967	−	2.52822i	0.133808	−	0.231762i
$120$		0			0
$121$	−3.26022	−	5.64687i	−0.296384	−	0.513351i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			11.1522i			0.997483i
$126$		0			0
$127$	11.8341			1.05011			0.525053	−	0.851069i	$-0.324045\pi$
$127$	11.8341			1.05011			0.525053	+	0.851069i	$0.324045\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.40891	−	1.39079i	0.210468	−	0.121514i	−0.391061	−	0.920365i	$-0.627892\pi$
$131$	2.40891	−	1.39079i	0.210468	−	0.121514i	0.601529	+	0.798851i	$0.294559\pi$
$132$		0			0
$133$	−23.2286	−	13.4110i	−2.01417	−	1.16288i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.17841	−	14.1654i	0.698729	−	1.21023i	−0.270178	−	0.962810i	$-0.587083\pi$
$137$	8.17841	−	14.1654i	0.698729	−	1.21023i	0.968907	−	0.247424i	$-0.0795840\pi$
$138$		0			0
$139$	−1.22979	+	0.710017i	−0.104309	+	0.0602229i	−0.551247	−	0.834342i	$-0.685848\pi$
$139$	−1.22979	+	0.710017i	−0.104309	+	0.0602229i	0.446938	+	0.894565i	$0.352514\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.16959			−0.181430
$144$		0			0
$145$	12.2463			1.01700
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.91390	−	2.83704i	0.402563	−	0.232420i	−0.285027	−	0.958520i	$-0.592002\pi$
$149$	4.91390	−	2.83704i	0.402563	−	0.232420i	0.687589	+	0.726100i	$0.258669\pi$
$150$		0			0
$151$	−7.07318	+	12.2511i	−0.575607	+	0.996981i	0.420368	+	0.907354i	$0.361901\pi$
$151$	−7.07318	+	12.2511i	−0.575607	+	0.996981i	−0.995975	+	0.0896271i	$0.971432\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−7.77665	−	4.48985i	−0.624636	−	0.360634i
$156$		0			0
$157$	18.6713	−	10.7799i	1.49013	−	0.860328i	0.490196	−	0.871612i	$-0.336925\pi$
$157$	18.6713	−	10.7799i	1.49013	−	0.860328i	0.999936	+	0.0112838i	$0.00359181\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	11.9469			0.941548
$162$		0			0
$163$		−	14.9239i		−	1.16893i	−0.811418	−	0.584466i	$-0.801304\pi$
$163$		−	14.9239i		−	1.16893i	0.811418	−	0.584466i	$-0.198696\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−11.0234	−	19.0931i	−0.853019	−	1.47747i	−0.878471	−	0.477796i	$-0.841436\pi$
$167$	−11.0234	−	19.0931i	−0.853019	−	1.47747i	0.0254524	−	0.999676i	$-0.491897\pi$
$168$		0			0
$169$	−5.97460	+	10.3483i	−0.459585	+	0.796024i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−10.9052	−	6.29612i	−0.829107	−	0.478685i	0.0244397	−	0.999701i	$-0.492220\pi$
$173$	−10.9052	−	6.29612i	−0.829107	−	0.478685i	−0.853547	+	0.521016i	$0.825553\pi$
$174$		0			0
$175$	−5.60937	−	9.71572i	−0.424029	−	0.734439i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	12.1116i		−	0.905264i	−0.891697	−	0.452632i	$-0.850485\pi$
$179$		−	12.1116i		−	0.905264i	0.891697	−	0.452632i	$-0.149515\pi$
$180$		0			0
$181$		−	17.6790i		−	1.31407i	−0.753862	−	0.657033i	$-0.771811\pi$
$181$		−	17.6790i		−	1.31407i	0.753862	−	0.657033i	$-0.228189\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.76137	+	4.78283i	0.203020	+	0.351640i
$186$		0			0
$187$	−1.48252	−	0.855935i	−0.108413	−	0.0625922i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.72173	−	16.8385i	0.703440	−	1.21839i	−0.263812	−	0.964574i	$-0.584980\pi$
$191$	9.72173	−	16.8385i	0.703440	−	1.21839i	0.967252	−	0.253820i	$-0.0816870\pi$
$192$		0			0
$193$	0.159120	+	0.275604i	0.0114537	+	0.0198384i	0.871695	−	0.490048i	$-0.163021\pi$
$193$	0.159120	+	0.275604i	0.0114537	+	0.0198384i	−0.860242	+	0.509886i	$0.829687\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	24.5066i		−	1.74602i	−0.487701	−	0.873011i	$-0.662164\pi$
$197$		−	24.5066i		−	1.74602i	0.487701	−	0.873011i	$-0.337836\pi$
$198$		0			0
$199$	7.13579			0.505843			0.252921	−	0.967487i	$-0.418609\pi$
$199$	7.13579			0.505843			0.252921	+	0.967487i	$0.418609\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−27.8313	+	16.0684i	−1.95337	+	1.12778i
$204$		0			0
$205$	8.23922	+	4.75692i	0.575452	+	0.332237i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−7.86408	+	13.6210i	−0.543970	+	0.942183i
$210$		0			0
$211$	7.00175	−	4.04246i	0.482020	−	0.278294i	−0.239238	−	0.970961i	$-0.576898\pi$
$211$	7.00175	−	4.04246i	0.482020	−	0.278294i	0.721258	+	0.692667i	$0.243564\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.390628			0.0266406
$216$		0			0
$217$	23.5646			1.59967
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.718032	−	0.414556i	0.0483001	−	0.0278861i
$222$		0			0
$223$	2.11236	−	3.65872i	0.141454	−	0.245006i	−0.786590	−	0.617475i	$-0.788156\pi$
$223$	2.11236	−	3.65872i	0.141454	−	0.245006i	0.928044	+	0.372469i	$0.121489\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.09451	+	0.631913i	0.0726449	+	0.0419415i	0.535882	−	0.844293i	$-0.319979\pi$
$227$	1.09451	+	0.631913i	0.0726449	+	0.0419415i	−0.463238	+	0.886234i	$0.653312\pi$
$228$		0			0
$229$	−6.29196	+	3.63267i	−0.415785	+	0.240053i	−0.693272	−	0.720676i	$-0.743832\pi$
$229$	−6.29196	+	3.63267i	−0.415785	+	0.240053i	0.277487	+	0.960729i	$0.410498\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.91061			0.387217			0.193608	−	0.981079i	$-0.437981\pi$
$233$	5.91061			0.387217			0.193608	+	0.981079i	$0.437981\pi$
$234$		0			0
$235$			9.94017i			0.648425i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	5.96266	+	10.3276i	0.385692	+	0.668039i	0.991865	−	0.127294i	$-0.0406293\pi$
$239$	5.96266	+	10.3276i	0.385692	+	0.668039i	−0.606173	+	0.795333i	$0.707296\pi$
$240$		0			0
$241$	1.80170	−	3.12063i	0.116057	−	0.201017i	−0.802145	−	0.597130i	$-0.796308\pi$
$241$	1.80170	−	3.12063i	0.116057	−	0.201017i	0.918202	+	0.396113i	$0.129641\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.17972	−	4.14521i	−0.458695	−	0.264828i
$246$		0			0
$247$	−3.80882	−	6.59707i	−0.242350	−	0.419762i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	0.641516i		−	0.0404922i	−0.999795	−	0.0202461i	$-0.993555\pi$
$251$		−	0.641516i		−	0.0404922i	0.999795	−	0.0202461i	$-0.00644497\pi$
$252$		0			0
$253$		−	7.00554i		−	0.440434i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.99885	+	3.46212i	0.124685	+	0.215961i	0.921610	−	0.388118i	$-0.126875\pi$
$257$	1.99885	+	3.46212i	0.124685	+	0.215961i	−0.796925	+	0.604079i	$0.793541\pi$
$258$		0			0
$259$	−12.5511	−	7.24638i	−0.779887	−	0.450268i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.64671	+	9.78039i	−0.348191	+	0.603085i	−0.985928	−	0.167169i	$-0.946537\pi$
$263$	−5.64671	+	9.78039i	−0.348191	+	0.603085i	0.637737	+	0.770254i	$0.279871\pi$
$264$		0			0
$265$	−2.65683	−	4.60176i	−0.163208	−	0.282684i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			24.2695i			1.47974i	0.672750	+	0.739870i	$0.265113\pi$
$269$			24.2695i			1.47974i	−0.672750	+	0.739870i	$0.734887\pi$
$270$		0			0
$271$	−12.2330			−0.743102			−0.371551	−	0.928413i	$-0.621174\pi$
$271$	−12.2330			−0.743102			−0.371551	+	0.928413i	$0.621174\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.69719	+	3.28928i	−0.343554	+	0.198351i
$276$		0			0
$277$	−10.9249	−	6.30750i	−0.656414	−	0.378981i	0.134495	−	0.990914i	$-0.457059\pi$
$277$	−10.9249	−	6.30750i	−0.656414	−	0.378981i	−0.790909	+	0.611933i	$0.790392\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.54364	+	16.5301i	−0.569326	+	0.986101i	0.427307	+	0.904107i	$0.359462\pi$
$281$	−9.54364	+	16.5301i	−0.569326	+	0.986101i	−0.996633	+	0.0819947i	$0.973871\pi$
$282$		0			0
$283$	1.01045	−	0.583382i	0.0600649	−	0.0346785i	−0.469667	−	0.882844i	$-0.655626\pi$
$283$	1.01045	−	0.583382i	0.0600649	−	0.0346785i	0.529732	+	0.848165i	$0.322293\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−24.9662			−1.47371
$288$		0			0
$289$	−16.3458			−0.961518
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2.11446	+	1.22079i	−0.123528	+	0.0713191i	−0.560491	−	0.828161i	$-0.689388\pi$
$293$	−2.11446	+	1.22079i	−0.123528	+	0.0713191i	0.436963	+	0.899480i	$0.356054\pi$
$294$		0			0
$295$	5.61351	−	9.72288i	0.326831	−	0.566088i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.93843	+	1.69650i	0.169934	+	0.0981112i
$300$		0			0
$301$	−0.887751	+	0.512543i	−0.0511691	+	0.0295425i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	10.0253			0.574046
$306$		0			0
$307$			15.7452i			0.898626i	0.893374	+	0.449313i	$0.148331\pi$
$307$			15.7452i			0.898626i	−0.893374	+	0.449313i	$0.851669\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	9.90129	+	17.1495i	0.561451	+	0.972461i	0.997370	+	0.0724757i	$0.0230900\pi$
$311$	9.90129	+	17.1495i	0.561451	+	0.972461i	−0.435919	+	0.899986i	$0.643577\pi$
$312$		0			0
$313$	16.2557	−	28.1557i	0.918828	−	1.59146i	0.117630	−	0.993057i	$-0.462470\pi$
$313$	16.2557	−	28.1557i	0.918828	−	1.59146i	0.801198	−	0.598399i	$-0.204196\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.9271	+	8.04083i	0.782225	+	0.451618i	0.837218	−	0.546869i	$-0.184180\pi$
$317$	13.9271	+	8.04083i	0.782225	+	0.451618i	−0.0549932	+	0.998487i	$0.517514\pi$
$318$		0			0
$319$	9.42233	+	16.3200i	0.527549	+	0.913742i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	6.01054i		−	0.334435i
$324$		0			0
$325$		−	3.18620i		−	0.176739i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−13.0425	−	22.5903i	−0.719056	−	1.24544i
$330$		0			0
$331$	17.7569	+	10.2520i	0.976010	+	0.563499i	0.901063	−	0.433688i	$-0.142788\pi$
$331$	17.7569	+	10.2520i	0.976010	+	0.563499i	0.0749465	+	0.997188i	$0.476121\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.93739	−	3.35565i	0.105851	−	0.183339i
$336$		0			0
$337$	6.21760	+	10.7692i	0.338694	+	0.586635i	0.984187	−	0.177131i	$-0.0566815\pi$
$337$	6.21760	+	10.7692i	0.338694	+	0.586635i	−0.645493	+	0.763766i	$0.723348\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	13.8180i		−	0.748287i
$342$		0			0
$343$	−3.50988			−0.189515
$344$		0			0
$345$		0			0
$346$		0			0
$347$	24.1550	−	13.9459i	1.29671	−	0.748654i	0.316873	−	0.948468i	$-0.397367\pi$
$347$	24.1550	−	13.9459i	1.29671	−	0.748654i	0.979834	+	0.199814i	$0.0640339\pi$
$348$		0			0
$349$	26.0103	+	15.0171i	1.39230	+	0.803846i	0.993570	−	0.113222i	$-0.0361171\pi$
$349$	26.0103	+	15.0171i	1.39230	+	0.803846i	0.398732	+	0.917068i	$0.369450\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.48011	−	16.4200i	0.504575	−	0.873950i	−0.495411	−	0.868659i	$-0.664982\pi$
$353$	9.48011	−	16.4200i	0.504575	−	0.873950i	0.999986	−	0.00529122i	$-0.00168426\pi$
$354$		0			0
$355$	5.59637	−	3.23107i	0.297024	−	0.171487i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	28.6420			1.51167			0.755833	−	0.654765i	$-0.227232\pi$
$359$	28.6420			1.51167			0.755833	+	0.654765i	$0.227232\pi$
$360$		0			0
$361$	−36.2231			−1.90648
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.488277	−	0.281907i	0.0255576	−	0.0147557i
$366$		0			0
$367$	−5.77148	+	9.99650i	−0.301269	+	0.521813i	−0.976424	−	0.215863i	$-0.930744\pi$
$367$	−5.77148	+	9.99650i	−0.301269	+	0.521813i	0.675155	+	0.737676i	$0.264077\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	12.0759	+	6.97205i	0.626952	+	0.361971i
$372$		0			0
$373$	−19.4301	+	11.2180i	−1.00605	+	0.580846i	−0.910034	−	0.414533i	$-0.863945\pi$
$373$	−19.4301	+	11.2180i	−1.00605	+	0.580846i	−0.0960206	+	0.995379i	$0.530611\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−9.12706			−0.470068
$378$		0			0
$379$		−	22.6668i		−	1.16431i	−0.813077	−	0.582157i	$-0.802209\pi$
$379$		−	22.6668i		−	1.16431i	0.813077	−	0.582157i	$-0.197791\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.94277	−	3.36498i	−0.0992709	−	0.171942i	0.812112	−	0.583501i	$-0.198318\pi$
$383$	−1.94277	−	3.36498i	−0.0992709	−	0.171942i	−0.911383	+	0.411559i	$0.864984\pi$
$384$		0			0
$385$	−5.25356	+	9.09944i	−0.267746	+	0.463750i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−11.9463	−	6.89722i	−0.605703	−	0.349703i	0.165579	−	0.986197i	$-0.447051\pi$
$389$	−11.9463	−	6.89722i	−0.605703	−	0.349703i	−0.771282	+	0.636494i	$0.780384\pi$
$390$		0			0
$391$	1.33859	+	2.31850i	0.0676953	+	0.117252i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	0.125471i		−	0.00631315i
$396$		0			0
$397$			23.7680i			1.19288i	0.802657	+	0.596441i	$0.203419\pi$
$397$			23.7680i			1.19288i	−0.802657	+	0.596441i	$0.796581\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.47782	+	7.75581i	0.223612	+	0.387307i	0.955902	−	0.293686i	$-0.0948820\pi$
$401$	4.47782	+	7.75581i	0.223612	+	0.387307i	−0.732290	+	0.680992i	$0.761549\pi$
$402$		0			0
$403$	5.79587	+	3.34625i	0.288713	+	0.166688i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.24920	+	7.35983i	−0.210625	+	0.364813i
$408$		0			0
$409$	10.4170	+	18.0429i	0.515090	+	0.892162i	0.999847	+	0.0175128i	$0.00557480\pi$
$409$	10.4170	+	18.0429i	0.515090	+	0.892162i	−0.484757	+	0.874649i	$0.661092\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			29.4619i			1.44973i
$414$		0			0
$415$	−3.82582			−0.187802
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.74372	−	5.04819i	0.427159	−	0.246620i	−0.270977	−	0.962586i	$-0.587347\pi$
$419$	8.74372	−	5.04819i	0.427159	−	0.246620i	0.698135	+	0.715966i	$0.254013\pi$
$420$		0			0
$421$	20.2218	+	11.6751i	0.985551	+	0.569008i	0.903941	−	0.427656i	$-0.140661\pi$
$421$	20.2218	+	11.6751i	0.985551	+	0.569008i	0.0816096	+	0.996664i	$0.473994\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.25700	−	2.17719i	0.0609735	−	0.105609i
$426$		0			0
$427$	−22.7837	+	13.1542i	−1.10258	+	0.636575i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6.40348			−0.308445			−0.154222	−	0.988036i	$-0.549287\pi$
$431$	−6.40348			−0.308445			−0.154222	+	0.988036i	$0.549287\pi$
$432$		0			0
$433$	−9.82857			−0.472331			−0.236166	−	0.971713i	$-0.575891\pi$
$433$	−9.82857			−0.472331			−0.236166	+	0.971713i	$0.575891\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	21.3017	−	12.2986i	1.01900	−	0.588320i
$438$		0			0
$439$	12.3831	−	21.4482i	0.591015	−	1.02367i	−0.403081	−	0.915164i	$-0.632061\pi$
$439$	12.3831	−	21.4482i	0.591015	−	1.02367i	0.994096	−	0.108504i	$-0.0346061\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	23.5518	+	13.5976i	1.11898	+	0.646044i	0.941140	−	0.338016i	$-0.109756\pi$
$443$	23.5518	+	13.5976i	1.11898	+	0.646044i	0.177840	+	0.984059i	$0.443089\pi$
$444$		0			0
$445$	−10.6242	+	6.13391i	−0.503637	+	0.290775i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−32.6861			−1.54255			−0.771276	−	0.636501i	$-0.780381\pi$
$449$	−32.6861			−1.54255			−0.771276	+	0.636501i	$0.780381\pi$
$450$		0			0
$451$			14.6399i			0.689367i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.54447	−	4.40714i	−0.119286	−	0.206610i
$456$		0			0
$457$	−10.3779	+	17.9750i	−0.485456	+	0.840834i	−0.999860	−	0.0167133i	$-0.994680\pi$
$457$	−10.3779	+	17.9750i	−0.485456	+	0.840834i	0.514404	+	0.857548i	$0.328013\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	32.4695	+	18.7463i	1.51226	+	0.873101i	0.999897	+	0.0143300i	$0.00456153\pi$
$461$	32.4695	+	18.7463i	1.51226	+	0.873101i	0.512359	+	0.858771i	$0.328772\pi$
$462$		0			0
$463$	7.97597	+	13.8148i	0.370675	+	0.642028i	0.989670	−	0.143367i	$-0.0457931\pi$
$463$	7.97597	+	13.8148i	0.370675	+	0.642028i	−0.618995	+	0.785395i	$0.712460\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			27.0476i			1.25161i	0.779979	+	0.625806i	$0.215230\pi$
$467$			27.0476i			1.25161i	−0.779979	+	0.625806i	$0.784770\pi$
$468$		0			0
$469$			10.1682i			0.469523i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.300550	+	0.520568i	0.0138193	+	0.0239357i
$474$		0			0
$475$	−20.0034	−	11.5490i	−0.917818	−	0.529903i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	13.6550	−	23.6511i	0.623912	−	1.08065i	−0.364838	−	0.931071i	$-0.618876\pi$
$479$	13.6550	−	23.6511i	0.623912	−	1.08065i	0.988750	−	0.149577i	$-0.0477910\pi$
$480$		0			0
$481$	−2.05802	−	3.56460i	−0.0938377	−	0.162532i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			7.59291i			0.344776i
$486$		0			0
$487$	−19.1126			−0.866073			−0.433036	−	0.901376i	$-0.642558\pi$
$487$	−19.1126			−0.866073			−0.433036	+	0.901376i	$0.642558\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	11.1131	−	6.41614i	0.501526	−	0.289556i	−0.227817	−	0.973704i	$-0.573159\pi$
$491$	11.1131	−	6.41614i	0.501526	−	0.289556i	0.729344	+	0.684147i	$0.239826\pi$
$492$		0			0
$493$	−6.23669	−	3.60076i	−0.280886	−	0.162170i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.47896	+	14.6860i	−0.380334	+	0.658757i
$498$		0			0
$499$	−15.3846	+	8.88232i	−0.688711	+	0.397627i	−0.803129	−	0.595805i	$-0.796833\pi$
$499$	−15.3846	+	8.88232i	−0.688711	+	0.397627i	0.114418	+	0.993433i	$0.463500\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−24.0108			−1.07059			−0.535294	−	0.844666i	$-0.679799\pi$
$503$	−24.0108			−1.07059			−0.535294	+	0.844666i	$0.679799\pi$
$504$		0			0
$505$	−8.94461			−0.398030
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6.91916	+	3.99478i	−0.306686	+	0.177065i	−0.645443	−	0.763809i	$-0.723327\pi$
$509$	−6.91916	+	3.99478i	−0.306686	+	0.177065i	0.338756	+	0.940874i	$0.389994\pi$
$510$		0			0
$511$	−0.739780	+	1.28134i	−0.0327259	+	0.0566830i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.58602	+	2.07039i	0.158019	+	0.0912324i
$516$		0			0
$517$	−13.2467	+	7.64798i	−0.582589	+	0.336358i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	36.9809			1.62016			0.810082	−	0.586317i	$-0.199423\pi$
$521$	36.9809			1.62016			0.810082	+	0.586317i	$0.199423\pi$
$522$		0			0
$523$			18.4217i			0.805526i	0.915304	+	0.402763i	$0.131950\pi$
$523$			18.4217i			0.805526i	−0.915304	+	0.402763i	$0.868050\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.64028	+	4.57311i	0.115013	+	0.199208i
$528$		0			0
$529$	6.02206	−	10.4305i	0.261828	−	0.453500i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−6.14061	−	3.54529i	−0.265980	−	0.153563i
$534$		0			0
$535$	0.307676	+	0.532911i	0.0133020	+	0.0230397i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	12.7573i		−	0.549497i
$540$		0			0
$541$			13.5032i			0.580549i	0.956943	+	0.290275i	$0.0937467\pi$
$541$			13.5032i			0.580549i	−0.956943	+	0.290275i	$0.906253\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	6.44038	+	11.1551i	0.275875	+	0.477830i
$546$		0			0
$547$	32.2252	+	18.6052i	1.37785	+	0.795501i	0.991900	−	0.127019i	$-0.0405410\pi$
$547$	32.2252	+	18.6052i	1.37785	+	0.795501i	0.385948	+	0.922520i	$0.373874\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−33.0827	+	57.3009i	−1.40937	+	2.44110i
$552$		0			0
$553$	0.164631	+	0.285149i	0.00700082	+	0.0121258i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	16.9602i		−	0.718628i	−0.933217	−	0.359314i	$-0.883011\pi$
$557$		−	16.9602i		−	0.718628i	0.933217	−	0.359314i	$-0.116989\pi$
$558$		0			0
$559$	−0.291131			−0.0123135
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−25.0083	+	14.4385i	−1.05397	+	0.608512i	−0.923759	−	0.382974i	$-0.874900\pi$
$563$	−25.0083	+	14.4385i	−1.05397	+	0.608512i	−0.130214	+	0.991486i	$0.541566\pi$
$564$		0			0
$565$	−13.4921	−	7.78966i	−0.567616	−	0.327713i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.20060	+	3.81154i	−0.0922538	+	0.159788i	−0.908459	−	0.417974i	$-0.862740\pi$
$569$	−2.20060	+	3.81154i	−0.0922538	+	0.159788i	0.816205	+	0.577762i	$0.196074\pi$
$570$		0			0
$571$	28.6730	−	16.5544i	1.19993	−	0.692779i	0.239390	−	0.970924i	$-0.423053\pi$
$571$	28.6730	−	16.5544i	1.19993	−	0.692779i	0.960539	+	0.278144i	$0.0897193\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	10.2881			0.429045
$576$		0			0
$577$	11.4122			0.475097			0.237548	−	0.971376i	$-0.423656\pi$
$577$	11.4122			0.475097			0.237548	+	0.971376i	$0.423656\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	8.69466	−	5.01986i	0.360715	−	0.208259i
$582$		0			0
$583$	4.08834	−	7.08121i	0.169322	−	0.293274i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−22.5512	−	13.0200i	−0.930788	−	0.537391i	−0.0437275	−	0.999043i	$-0.513923\pi$
$587$	−22.5512	−	13.0200i	−0.930788	−	0.537391i	−0.887061	+	0.461653i	$0.847257\pi$
$588$		0			0
$589$	42.0164	−	24.2582i	1.73125	−	0.999540i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−5.75114			−0.236171			−0.118086	−	0.993003i	$-0.537676\pi$
$593$	−5.75114			−0.236171			−0.118086	+	0.993003i	$0.537676\pi$
$594$		0			0
$595$		−	4.01531i		−	0.164612i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−8.10409	−	14.0367i	−0.331124	−	0.573524i	0.651608	−	0.758556i	$-0.274095\pi$
$599$	−8.10409	−	14.0367i	−0.331124	−	0.573524i	−0.982733	+	0.185032i	$0.940761\pi$
$600$		0			0
$601$	9.78181	−	16.9426i	0.399008	−	0.691102i	−0.594596	−	0.804025i	$-0.702688\pi$
$601$	9.78181	−	16.9426i	0.399008	−	0.691102i	0.993604	+	0.112922i	$0.0360212\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.76680	−	4.48416i	−0.315765	−	0.182307i
$606$		0			0
$607$	3.82627	+	6.62730i	0.155304	+	0.268994i	0.933170	−	0.359437i	$-0.117031\pi$
$607$	3.82627	+	6.62730i	0.155304	+	0.268994i	−0.777866	+	0.628430i	$0.783698\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	7.40831i		−	0.299708i
$612$		0			0
$613$		−	27.6512i		−	1.11682i	−0.829565	−	0.558410i	$-0.811412\pi$
$613$		−	27.6512i		−	1.11682i	0.829565	−	0.558410i	$-0.188588\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	12.6938	+	21.9863i	0.511034	+	0.885136i	0.999918	+	0.0127878i	$0.00407059\pi$
$617$	12.6938	+	21.9863i	0.511034	+	0.885136i	−0.488885	+	0.872348i	$0.662596\pi$
$618$		0			0
$619$	19.8583	+	11.4652i	0.798171	+	0.460824i	0.842831	−	0.538178i	$-0.180887\pi$
$619$	19.8583	+	11.4652i	0.798171	+	0.460824i	−0.0446605	+	0.999002i	$0.514221\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	16.0966	−	27.8801i	0.644897	−	1.11699i
$624$		0			0
$625$	−0.101100	−	0.175110i	−0.00404398	−	0.00700439i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	3.24767i		−	0.129493i
$630$		0			0
$631$	−23.2785			−0.926701			−0.463350	−	0.886175i	$-0.653353\pi$
$631$	−23.2785			−0.926701			−0.463350	+	0.886175i	$0.653353\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	14.0961	−	8.13841i	0.559388	−	0.322963i
$636$		0			0
$637$	5.35098	+	3.08939i	0.212013	+	0.122406i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	17.4170	−	30.1672i	0.687932	−	1.19153i	−0.284574	−	0.958654i	$-0.591852\pi$
$641$	17.4170	−	30.1672i	0.687932	−	1.19153i	0.972506	−	0.232879i	$-0.0748146\pi$
$642$		0			0
$643$	−34.0047	+	19.6326i	−1.34102	+	0.774236i	−0.986956	−	0.160987i	$-0.948532\pi$
$643$	−34.0047	+	19.6326i	−1.34102	+	0.774236i	−0.354059	+	0.935223i	$0.615199\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	44.5092			1.74984			0.874918	−	0.484271i	$-0.160915\pi$
$647$	44.5092			1.74984			0.874918	+	0.484271i	$0.160915\pi$
$648$		0			0
$649$	17.2762			0.678149
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−15.7763	+	9.10843i	−0.617373	+	0.356440i	−0.775845	−	0.630923i	$-0.782676\pi$
$653$	−15.7763	+	9.10843i	−0.617373	+	0.356440i	0.158473	+	0.987363i	$0.449343\pi$
$654$		0			0
$655$	1.91291	−	3.31326i	0.0747437	−	0.129460i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−36.2085	−	20.9050i	−1.41048	−	0.814343i	−0.415049	−	0.909799i	$-0.636236\pi$
$659$	−36.2085	−	20.9050i	−1.41048	−	0.814343i	−0.995434	+	0.0954566i	$0.969569\pi$
$660$		0			0
$661$	9.78973	−	5.65210i	0.380776	−	0.219841i	−0.297380	−	0.954759i	$-0.596113\pi$
$661$	9.78973	−	5.65210i	0.380776	−	0.219841i	0.678156	+	0.734918i	$0.262779\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−36.8915			−1.43059
$666$		0			0
$667$		−	29.4710i		−	1.14112i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	7.71346	+	13.3601i	0.297775	+	0.515761i
$672$		0			0
$673$	17.6390	−	30.5517i	0.679934	−	1.17768i	−0.295066	−	0.955477i	$-0.595342\pi$
$673$	17.6390	−	30.5517i	0.679934	−	1.17768i	0.975000	−	0.222203i	$-0.0713249\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.5026	+	10.1051i	0.672679	+	0.388372i	0.797091	−	0.603859i	$-0.206371\pi$
$677$	17.5026	+	10.1051i	0.672679	+	0.388372i	−0.124412	+	0.992231i	$0.539704\pi$
$678$		0			0
$679$	−9.96266	−	17.2558i	−0.382332	−	0.662218i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			43.6659i			1.67083i	0.549621	+	0.835414i	$0.314772\pi$
$683$			43.6659i			1.67083i	−0.549621	+	0.835414i	$0.685228\pi$
$684$		0			0
$685$		−	22.4975i		−	0.859584i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.98011	+	3.42965i	0.0754362	+	0.130659i
$690$		0			0
$691$	7.91193	+	4.56796i	0.300984	+	0.173773i	0.642885	−	0.765963i	$-0.277737\pi$
$691$	7.91193	+	4.56796i	0.300984	+	0.173773i	−0.341901	+	0.939736i	$0.611071\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.976570	+	1.69147i	−0.0370434	+	0.0641611i
$696$		0			0
$697$	−2.79733	−	4.84512i	−0.105956	−	0.183522i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	44.8665i		−	1.69458i	−0.531127	−	0.847292i	$-0.678231\pi$
$701$		−	44.8665i		−	1.69458i	0.531127	−	0.847292i	$-0.321769\pi$
$702$		0			0
$703$	−29.8387			−1.12539
$704$		0			0
$705$		0			0
$706$		0			0
$707$	20.3277	−	11.7362i	0.764504	−	0.441386i
$708$		0			0
$709$	−23.1529	−	13.3673i	−0.869525	−	0.502021i	−0.00233491	−	0.999997i	$-0.500743\pi$
$709$	−23.1529	−	13.3673i	−0.869525	−	0.502021i	−0.867190	+	0.497977i	$0.834077\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−10.8049	+	18.7147i	−0.404647	+	0.700870i
$714$		0			0
$715$	−2.58430	+	1.49205i	−0.0966474	+	0.0557994i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−37.4738			−1.39754			−0.698768	−	0.715348i	$-0.746268\pi$
$719$	−37.4738			−1.39754			−0.698768	+	0.715348i	$0.746268\pi$
$720$		0			0
$721$	−10.8662			−0.404680
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−23.9670	+	13.8374i	−0.890112	+	0.513907i
$726$		0			0
$727$	9.18140	−	15.9027i	0.340519	−	0.589797i	−0.644010	−	0.765017i	$-0.722730\pi$
$727$	9.18140	−	15.9027i	0.340519	−	0.589797i	0.984529	+	0.175220i	$0.0560638\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.198936	−	0.114856i	−0.00735790	−	0.00424808i
$732$		0			0
$733$	−35.6508	+	20.5830i	−1.31679	+	0.760249i	−0.983211	−	0.182472i	$-0.941590\pi$
$733$	−35.6508	+	20.5830i	−1.31679	+	0.760249i	−0.333580	+	0.942722i	$0.608257\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.96251			0.219632
$738$		0			0
$739$		−	45.1004i		−	1.65905i	−0.558473	−	0.829523i	$-0.688613\pi$
$739$		−	45.1004i		−	1.65905i	0.558473	−	0.829523i	$-0.311387\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21.7217	−	37.6231i	−0.796893	−	1.38026i	−0.921630	−	0.388070i	$-0.873142\pi$
$743$	−21.7217	−	37.6231i	−0.796893	−	1.38026i	0.124737	−	0.992190i	$-0.460191\pi$
$744$		0			0
$745$	3.90212	−	6.75867i	0.142963	−	0.247618i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.39846	−	0.807404i	−0.0510988	−	0.0295019i
$750$		0			0
$751$	15.3394	+	26.5686i	0.559742	+	0.969501i	0.997518	+	0.0704172i	$0.0224330\pi$
$751$	15.3394	+	26.5686i	0.559742	+	0.969501i	−0.437776	+	0.899084i	$0.644234\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			19.4571i			0.708118i
$756$		0			0
$757$		−	2.84137i		−	0.103271i	−0.998666	−	0.0516357i	$-0.983557\pi$
$757$		−	2.84137i		−	0.103271i	0.998666	−	0.0516357i	$-0.0164435\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−6.52480	−	11.3013i	−0.236524	−	0.409672i	0.723191	−	0.690649i	$-0.242675\pi$
$761$	−6.52480	−	11.3013i	−0.236524	−	0.409672i	−0.959714	+	0.280977i	$0.909342\pi$
$762$		0			0
$763$	−29.2731	−	16.9008i	−1.05976	−	0.611851i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.18370	+	7.24637i	−0.151065	+	0.261651i
$768$		0			0
$769$	13.7846	+	23.8756i	0.497084	+	0.860975i	0.999994	−	0.00336360i	$-0.00107067\pi$
$769$	13.7846	+	23.8756i	0.497084	+	0.860975i	−0.502910	+	0.864339i	$0.667737\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	15.7109i		−	0.565082i	−0.959255	−	0.282541i	$-0.908823\pi$
$773$		−	15.7109i		−	0.565082i	0.959255	−	0.282541i	$-0.0911774\pi$
$774$		0			0
$775$	20.2927			0.728936
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−44.5155	+	25.7011i	−1.59494	+	0.920836i
$780$		0			0
$781$	8.61171	+	4.97197i	0.308151	+	0.177911i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	14.8268	−	25.6808i	0.529193	−	0.916589i
$786$		0			0
$787$	12.2138	−	7.05164i	0.435375	−	0.251364i	−0.266259	−	0.963902i	$-0.585788\pi$
$787$	12.2138	−	7.05164i	0.435375	−	0.251364i	0.701634	+	0.712538i	$0.252454\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	40.8832			1.45364
$792$		0			0
$793$	−7.47175			−0.265329
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−22.7555	+	13.1379i	−0.806040	+	0.465367i	−0.845579	−	0.533851i	$-0.820744\pi$
$797$	−22.7555	+	13.1379i	−0.806040	+	0.465367i	0.0395390	+	0.999218i	$0.487411\pi$
$798$		0			0
$799$	2.92269	−	5.06224i	0.103397	−	0.179089i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.751362	+	0.433799i	0.0265150	+	0.0153084i
$804$		0			0
$805$	14.2305	−	8.21599i	0.501560	−	0.289576i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	37.5390			1.31980			0.659901	−	0.751353i	$-0.270598\pi$
$809$	37.5390			1.31980			0.659901	+	0.751353i	$0.270598\pi$
$810$		0			0
$811$			37.7228i			1.32463i	0.749227	+	0.662314i	$0.230425\pi$
$811$			37.7228i			1.32463i	−0.749227	+	0.662314i	$0.769575\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−10.2633	−	17.7766i	−0.359508	−	0.622686i
$816$		0			0
$817$	−1.05526	+	1.82776i	−0.0369188	+	0.0639453i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.06427	−	0.614456i	−0.0371432	−	0.0214446i	0.481313	−	0.876549i	$-0.340160\pi$
$821$	−1.06427	−	0.614456i	−0.0371432	−	0.0214446i	−0.518457	+	0.855104i	$0.673493\pi$
$822$		0			0
$823$	17.4937	+	30.2999i	0.609791	+	1.05619i	0.991275	+	0.131813i	$0.0420799\pi$
$823$	17.4937	+	30.2999i	0.609791	+	1.05619i	−0.381484	+	0.924376i	$0.624587\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	48.7311i		−	1.69455i	−0.531157	−	0.847273i	$-0.678243\pi$
$827$		−	48.7311i		−	1.69455i	0.531157	−	0.847273i	$-0.321757\pi$
$828$		0			0
$829$		−	28.9573i		−	1.00573i	−0.864366	−	0.502863i	$-0.832280\pi$
$829$		−	28.9573i		−	1.00573i	0.864366	−	0.502863i	$-0.167720\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	2.43761	+	4.22207i	0.0844583	+	0.146286i
$834$		0			0
$835$	−26.2610	−	15.1618i	−0.908801	−	0.524696i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	7.66037	−	13.2681i	0.264465	−	0.458067i	−0.702958	−	0.711231i	$-0.748138\pi$
$839$	7.66037	−	13.2681i	0.264465	−	0.458067i	0.967423	+	0.253164i	$0.0814712\pi$
$840$		0			0
$841$	25.1380	+	43.5402i	0.866826	+	1.50139i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			16.4351i			0.565386i
$846$		0			0
$847$	23.5347			0.808662
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.5100	−	6.64528i	0.394556	−	0.227797i
$852$		0			0
$853$	5.67204	+	3.27476i	0.194207	+	0.112126i	0.593951	−	0.804502i	$-0.297567\pi$
$853$	5.67204	+	3.27476i	0.194207	+	0.112126i	−0.399743	+	0.916627i	$0.630901\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.71094	−	11.6237i	0.229241	−	0.397058i	−0.728342	−	0.685214i	$-0.759709\pi$
$857$	6.71094	−	11.6237i	0.229241	−	0.397058i	0.957583	+	0.288156i	$0.0930421\pi$
$858$		0			0
$859$	2.57865	−	1.48878i	0.0879824	−	0.0507967i	−0.455363	−	0.890306i	$-0.650491\pi$
$859$	2.57865	−	1.48878i	0.0879824	−	0.0507967i	0.543346	+	0.839509i	$0.317157\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−24.3897			−0.830236			−0.415118	−	0.909768i	$-0.636260\pi$
$863$	−24.3897			−0.830236			−0.415118	+	0.909768i	$0.636260\pi$
$864$		0			0
$865$	−17.3196			−0.588884
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.167208	−	0.0965378i	0.00567216	−	0.00327482i
$870$		0			0
$871$	−1.44392	+	2.50094i	−0.0489252	+	0.0847410i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−34.8596	−	20.1262i	−1.17847	−	0.680390i
$876$		0			0
$877$	4.38552	−	2.53198i	0.148088	−	0.0854988i	−0.424125	−	0.905604i	$-0.639418\pi$
$877$	4.38552	−	2.53198i	0.148088	−	0.0854988i	0.572213	+	0.820105i	$0.306085\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−28.2318			−0.951154			−0.475577	−	0.879674i	$-0.657761\pi$
$881$	−28.2318			−0.951154			−0.475577	+	0.879674i	$0.657761\pi$
$882$		0			0
$883$		−	28.0994i		−	0.945619i	−0.881165	−	0.472809i	$-0.843240\pi$
$883$		−	28.0994i		−	0.945619i	0.881165	−	0.472809i	$-0.156760\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.666005	+	1.15356i	0.0223623	+	0.0387326i	0.876990	−	0.480509i	$-0.159548\pi$
$887$	0.666005	+	1.15356i	0.0223623	+	0.0387326i	−0.854628	+	0.519241i	$0.826215\pi$
$888$		0			0
$889$	−21.3568	+	36.9911i	−0.716285	+	1.24064i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−46.5104	−	26.8528i	−1.55641	−	0.898594i
$894$		0			0
$895$	−8.32926	−	14.4267i	−0.278417	−	0.482232i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	58.1297i		−	1.93873i
$900$		0			0
$901$			3.12473i			0.104100i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−12.1580	−	21.0582i	−0.404145	−	0.699999i
$906$		0			0
$907$	−0.778677	−	0.449569i	−0.0258555	−	0.0149277i	0.487017	−	0.873393i	$-0.338085\pi$
$907$	−0.778677	−	0.449569i	−0.0258555	−	0.0149277i	−0.512872	+	0.858465i	$0.671418\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	7.53390	−	13.0491i	0.249609	−	0.432336i	−0.713808	−	0.700341i	$-0.753031\pi$
$911$	7.53390	−	13.0491i	0.249609	−	0.432336i	0.963417	+	0.268005i	$0.0863645\pi$
$912$		0			0
$913$	−2.94360	−	5.09846i	−0.0974188	−	0.168734i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			10.0397i			0.331541i
$918$		0			0
$919$	28.4761			0.939339			0.469670	−	0.882842i	$-0.344373\pi$
$919$	28.4761			0.939339			0.469670	+	0.882842i	$0.344373\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.17092	+	2.40808i	−0.137288	+	0.0792630i
$924$		0			0
$925$	−10.8084	−	6.24025i	−0.355379	−	0.205178i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−2.12086	+	3.67344i	−0.0695833	+	0.120522i	−0.898718	−	0.438527i	$-0.855500\pi$
$929$	−2.12086	+	3.67344i	−0.0695833	+	0.120522i	0.829135	+	0.559049i	$0.188834\pi$
$930$		0			0
$931$	38.7912	−	22.3961i	1.27133	−	0.734002i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.35454			−0.0770016
$936$		0			0
$937$	−15.1569			−0.495155			−0.247578	−	0.968868i	$-0.579634\pi$
$937$	−15.1569			−0.495155			−0.247578	+	0.968868i	$0.579634\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	36.9463	−	21.3310i	1.20442	−	0.695370i	0.242882	−	0.970056i	$-0.421907\pi$
$941$	36.9463	−	21.3310i	1.20442	−	0.695370i	0.961534	+	0.274686i	$0.0885738\pi$
$942$		0			0
$943$	11.4476	−	19.8278i	0.372785	−	0.645683i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	24.7629	+	14.2969i	0.804686	+	0.464585i	0.845107	−	0.534597i	$-0.179537\pi$
$947$	24.7629	+	14.2969i	0.804686	+	0.464585i	−0.0404213	+	0.999183i	$0.512870\pi$
$948$		0			0
$949$	−0.363908	+	0.210103i	−0.0118130	+	0.00682022i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	28.1424			0.911622			0.455811	−	0.890077i	$-0.349349\pi$
$953$	28.1424			0.911622			0.455811	+	0.890077i	$0.349349\pi$
$954$		0			0
$955$		−	26.7429i		−	0.865380i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	29.5189	+	51.1283i	0.953216	+	1.65102i
$960$		0			0
$961$	−5.81204	+	10.0668i	−0.187485	+	0.324734i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.379071	+	0.218857i	0.0122027	+	0.00704525i
$966$		0			0
$967$	6.99023	+	12.1074i	0.224791	+	0.389349i	0.956257	−	0.292529i	$-0.0944969\pi$
$967$	6.99023	+	12.1074i	0.224791	+	0.389349i	−0.731466	+	0.681878i	$0.761164\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			17.5426i			0.562969i	0.959566	+	0.281484i	$0.0908268\pi$
$971$			17.5426i			0.562969i	−0.959566	+	0.281484i	$0.909173\pi$
$972$		0			0
$973$		−	5.12543i		−	0.164314i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−22.7380	−	39.3834i	−0.727454	−	1.25999i	−0.957956	−	0.286916i	$-0.907370\pi$
$977$	−22.7380	−	39.3834i	−0.727454	−	1.25999i	0.230502	−	0.973072i	$-0.425963\pi$
$978$		0			0
$979$	−16.3486	−	9.43888i	−0.522504	−	0.301668i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5.04836	+	8.74402i	−0.161018	+	0.278891i	−0.935234	−	0.354030i	$-0.884811\pi$
$983$	−5.04836	+	8.74402i	−0.161018	+	0.278891i	0.774216	+	0.632921i	$0.218144\pi$
$984$		0			0
$985$	−16.8534	−	29.1909i	−0.536994	−	0.930100i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	0.940054i		−	0.0298920i
$990$		0			0
$991$	17.6057			0.559263			0.279631	−	0.960107i	$-0.409788\pi$
$991$	17.6057			0.559263			0.279631	+	0.960107i	$0.409788\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	8.49978	−	4.90735i	0.269461	−	0.155573i
$996$		0			0
$997$	26.1168	+	15.0786i	0.827128	+	0.477543i	0.852868	−	0.522126i	$-0.174861\pi$
$997$	26.1168	+	15.0786i	0.827128	+	0.477543i	−0.0257404	+	0.999669i	$0.508194\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.r.b.721.6		16
3.2	odd	2		288.2.r.b.241.3		16
4.3	odd	2		216.2.n.b.181.5		16
8.3	odd	2		216.2.n.b.181.7		16
8.5	even	2	inner	864.2.r.b.721.3		16
9.2	odd	6		2592.2.d.j.1297.3		8
9.4	even	3	inner	864.2.r.b.145.3		16
9.5	odd	6		288.2.r.b.49.6		16
9.7	even	3		2592.2.d.k.1297.6		8
12.11	even	2		72.2.n.b.61.4	yes	16
24.5	odd	2		288.2.r.b.241.6		16
24.11	even	2		72.2.n.b.61.2	yes	16
36.7	odd	6		648.2.d.k.325.2		8
36.11	even	6		648.2.d.j.325.7		8
36.23	even	6		72.2.n.b.13.2	✓	16
36.31	odd	6		216.2.n.b.37.7		16
72.5	odd	6		288.2.r.b.49.3		16
72.11	even	6		648.2.d.j.325.8		8
72.13	even	6	inner	864.2.r.b.145.6		16
72.29	odd	6		2592.2.d.j.1297.6		8
72.43	odd	6		648.2.d.k.325.1		8
72.59	even	6		72.2.n.b.13.4	yes	16
72.61	even	6		2592.2.d.k.1297.3		8
72.67	odd	6		216.2.n.b.37.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.2	✓	16	36.23	even	6
72.2.n.b.13.4	yes	16	72.59	even	6
72.2.n.b.61.2	yes	16	24.11	even	2
72.2.n.b.61.4	yes	16	12.11	even	2
216.2.n.b.37.5		16	72.67	odd	6
216.2.n.b.37.7		16	36.31	odd	6
216.2.n.b.181.5		16	4.3	odd	2
216.2.n.b.181.7		16	8.3	odd	2
288.2.r.b.49.3		16	72.5	odd	6
288.2.r.b.49.6		16	9.5	odd	6
288.2.r.b.241.3		16	3.2	odd	2
288.2.r.b.241.6		16	24.5	odd	2
648.2.d.j.325.7		8	36.11	even	6
648.2.d.j.325.8		8	72.11	even	6
648.2.d.k.325.1		8	72.43	odd	6
648.2.d.k.325.2		8	36.7	odd	6
864.2.r.b.145.3		16	9.4	even	3	inner
864.2.r.b.145.6		16	72.13	even	6	inner
864.2.r.b.721.3		16	8.5	even	2	inner
864.2.r.b.721.6		16	1.1	even	1	trivial
2592.2.d.j.1297.3		8	9.2	odd	6
2592.2.d.j.1297.6		8	72.29	odd	6
2592.2.d.k.1297.3		8	72.61	even	6
2592.2.d.k.1297.6		8	9.7	even	3

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.19115 - 0.687709i) q^{5} +(-1.80469 + 3.12581i) q^{7} +O(q^{10})\)	\(q+(1.19115 - 0.687709i) q^{5} +(-1.80469 + 3.12581i) q^{7} +(1.83294 + 1.05825i) q^{11} +(-0.887751 + 0.512543i) q^{13} -0.808822 q^{17} +7.43122i q^{19} +(-1.65498 - 2.86652i) q^{23} +(-1.55411 + 2.69180i) q^{25} +(7.71083 + 4.45185i) q^{29} +(-3.26436 - 5.65403i) q^{31} +4.96439i q^{35} +4.01531i q^{37} +(3.45852 + 5.99034i) q^{41} +(0.245957 + 0.142003i) q^{43} +(-3.61351 + 6.25878i) q^{47} +(-3.01378 - 5.22003i) q^{49} -3.86330i q^{53} +2.91107 q^{55} +(7.06904 - 4.08131i) q^{59} +(6.31237 + 3.64445i) q^{61} +(-0.704961 + 1.22103i) q^{65} +(2.43973 - 1.40858i) q^{67} +4.69830 q^{71} +0.409922 q^{73} +(-6.61576 + 3.81961i) q^{77} +(0.0456121 - 0.0790024i) q^{79} +(-2.40891 - 1.39079i) q^{83} +(-0.963426 + 0.556234i) q^{85} -8.91934 q^{89} -3.69992i q^{91} +(5.11052 + 8.85168i) q^{95} +(-2.76022 + 4.78084i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{7}+O(q^{10}) \) 16 * q - 6 * q^7	\( 16 q - 6 q^{7} + 28 q^{17} - 10 q^{23} + 2 q^{25} + 10 q^{31} + 8 q^{41} + 6 q^{47} + 18 q^{49} + 4 q^{55} + 14 q^{65} + 72 q^{71} - 44 q^{73} + 30 q^{79} - 64 q^{89} + 44 q^{95}+O(q^{100}) \) 16 * q - 6 * q^7 + 28 * q^17 - 10 * q^23 + 2 * q^25 + 10 * q^31 + 8 * q^41 + 6 * q^47 + 18 * q^49 + 4 * q^55 + 14 * q^65 + 72 * q^71 - 44 * q^73 + 30 * q^79 - 64 * q^89 + 44 * q^95

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