LMFDB - Embedded newform 1044.2.z.c.613.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1044,2,Mod(109,1044)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1044, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("1044.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1044 = 2^{2} \cdot 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1044.z (of order $14$, degree $6$, 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:	$8.33638197102$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			613.1
Character	$\chi$	$=$	1044.613
Dual form			1044.2.z.c.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.700940 + 3.07102i) q^{5} +(2.15220 - 1.03645i) q^{7} +O(q^{10})$	$q+(-0.700940 + 3.07102i) q^{5} +(2.15220 - 1.03645i) q^{7} +(-2.67834 + 2.13590i) q^{11} +(2.48071 + 3.11071i) q^{13} -0.723153i q^{17} +(-0.261864 + 0.543766i) q^{19} +(-0.402398 - 1.76302i) q^{23} +(-4.43499 - 2.13578i) q^{25} +(-0.849902 + 5.31767i) q^{29} +(-8.55480 - 1.95258i) q^{31} +(1.67438 + 7.33594i) q^{35} +(3.03686 + 2.42181i) q^{37} +8.84460i q^{41} +(2.91552 - 0.665448i) q^{43} +(0.0107504 - 0.00857319i) q^{47} +(-0.806668 + 1.01153i) q^{49} +(0.486882 - 2.13317i) q^{53} +(-4.68204 - 9.72235i) q^{55} -5.86354 q^{59} +(0.0283153 + 0.0587974i) q^{61} +(-11.2919 + 5.43787i) q^{65} +(-7.75785 + 9.72804i) q^{67} +(3.03947 + 3.81138i) q^{71} +(9.14236 - 2.08668i) q^{73} +(-3.55058 + 7.37285i) q^{77} +(-4.06431 - 3.24118i) q^{79} +(9.47260 + 4.56176i) q^{83} +(2.22081 + 0.506887i) q^{85} +(-16.2177 - 3.70159i) q^{89} +(8.56307 + 4.12376i) q^{91} +(-1.48636 - 1.18534i) q^{95} +(-3.71825 + 7.72103i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7}+O(q^{10}) $ 24 * q - 4 * q^7	$ 24 q - 4 q^{7} - 10 q^{13} - 10 q^{25} - 28 q^{31} + 28 q^{37} - 14 q^{43} - 4 q^{49} + 14 q^{55} - 56 q^{61} - 20 q^{67} + 14 q^{79} + 14 q^{85} + 46 q^{91} + 28 q^{97}+O(q^{100}) $ 24 * q - 4 * q^7 - 10 * q^13 - 10 * q^25 - 28 * q^31 + 28 * q^37 - 14 * q^43 - 4 * q^49 + 14 * q^55 - 56 * q^61 - 20 * q^67 + 14 * q^79 + 14 * q^85 + 46 * q^91 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1044\mathbb{Z}\right)^\times$.

$n$	$523$	$901$	$929$
$\chi(n)$	$1$	$e\left(\frac{1}{14}\right)$	$1$

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
$5$	−0.700940	+	3.07102i	−0.313470	+	1.37340i	0.535311	+	0.844655i	$0.320195\pi$
$5$	−0.700940	+	3.07102i	−0.313470	+	1.37340i	−0.848780	+	0.528746i	$0.822663\pi$
$6$		0			0
$7$	2.15220	−	1.03645i	0.813457	−	0.391740i	0.0195720	−	0.999808i	$-0.493770\pi$
$7$	2.15220	−	1.03645i	0.813457	−	0.391740i	0.793885	+	0.608068i	$0.208055\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.67834	+	2.13590i	−0.807548	+	0.643998i	−0.937681	−	0.347498i	$-0.887031\pi$
$11$	−2.67834	+	2.13590i	−0.807548	+	0.643998i	0.130132	+	0.991497i	$0.458460\pi$
$12$		0			0
$13$	2.48071	+	3.11071i	0.688024	+	0.862755i	0.996066	−	0.0886181i	$-0.0282451\pi$
$13$	2.48071	+	3.11071i	0.688024	+	0.862755i	−0.308042	+	0.951373i	$0.599674\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	0.723153i		−	0.175390i	−0.996147	−	0.0876951i	$-0.972050\pi$
$17$		−	0.723153i		−	0.175390i	0.996147	−	0.0876951i	$-0.0279501\pi$
$18$		0			0
$19$	−0.261864	+	0.543766i	−0.0600757	+	0.124748i	−0.928845	−	0.370469i	$-0.879197\pi$
$19$	−0.261864	+	0.543766i	−0.0600757	+	0.124748i	0.868769	+	0.495217i	$0.164911\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.402398	−	1.76302i	−0.0839057	−	0.367615i	0.915491	−	0.402338i	$-0.131802\pi$
$23$	−0.402398	−	1.76302i	−0.0839057	−	0.367615i	−0.999397	+	0.0347228i	$0.988945\pi$
$24$		0			0
$25$	−4.43499	−	2.13578i	−0.886998	−	0.427156i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.849902	+	5.31767i	−0.157823	+	0.987467i
$29$	−0.849902	+	5.31767i	−0.157823	+	0.987467i
$30$		0			0
$31$	−8.55480	−	1.95258i	−1.53649	−	0.350693i	−0.631243	−	0.775585i	$-0.717455\pi$
$31$	−8.55480	−	1.95258i	−1.53649	−	0.350693i	−0.905244	+	0.424892i	$0.860312\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.67438	+	7.33594i	0.283022	+	1.24000i
$36$		0			0
$37$	3.03686	+	2.42181i	0.499256	+	0.398144i	0.840483	−	0.541837i	$-0.182271\pi$
$37$	3.03686	+	2.42181i	0.499256	+	0.398144i	−0.341227	+	0.939981i	$0.610843\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			8.84460i			1.38129i	0.723192	+	0.690647i	$0.242674\pi$
$41$			8.84460i			1.38129i	−0.723192	+	0.690647i	$0.757326\pi$
$42$		0			0
$43$	2.91552	−	0.665448i	0.444612	−	0.101480i	0.00564740	−	0.999984i	$-0.498202\pi$
$43$	2.91552	−	0.665448i	0.444612	−	0.101480i	0.438965	+	0.898504i	$0.355345\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.0107504	−	0.00857319i	0.00156811	−	0.00125053i	−0.622705	−	0.782456i	$-0.713966\pi$
$47$	0.0107504	−	0.00857319i	0.00156811	−	0.00125053i	0.624274	+	0.781206i	$0.285395\pi$
$48$		0			0
$49$	−0.806668	+	1.01153i	−0.115238	+	0.144504i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.486882	−	2.13317i	0.0668784	−	0.293013i	−0.930418	−	0.366501i	$-0.880556\pi$
$53$	0.486882	−	2.13317i	0.0668784	−	0.293013i	0.997296	+	0.0734874i	$0.0234129\pi$
$54$		0			0
$55$	−4.68204	−	9.72235i	−0.631326	−	1.31096i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.86354			−0.763368			−0.381684	−	0.924293i	$-0.624656\pi$
$59$	−5.86354			−0.763368			−0.381684	+	0.924293i	$0.624656\pi$
$60$		0			0
$61$	0.0283153	+	0.0587974i	0.00362540	+	0.00752823i	0.902774	−	0.430116i	$-0.141527\pi$
$61$	0.0283153	+	0.0587974i	0.00362540	+	0.00752823i	−0.899148	+	0.437644i	$0.855813\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−11.2919	+	5.43787i	−1.40058	+	0.674485i
$66$		0			0
$67$	−7.75785	+	9.72804i	−0.947772	+	1.18847i	0.0341946	+	0.999415i	$0.489113\pi$
$67$	−7.75785	+	9.72804i	−0.947772	+	1.18847i	−0.981967	+	0.189054i	$0.939458\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.03947	+	3.81138i	0.360719	+	0.452327i	0.928765	−	0.370670i	$-0.120872\pi$
$71$	3.03947	+	3.81138i	0.360719	+	0.452327i	−0.568046	+	0.822997i	$0.692300\pi$
$72$		0			0
$73$	9.14236	−	2.08668i	1.07003	−	0.244228i	0.348995	−	0.937124i	$-0.386523\pi$
$73$	9.14236	−	2.08668i	1.07003	−	0.244228i	0.721037	+	0.692897i	$0.243666\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.55058	+	7.37285i	−0.404626	+	0.840214i
$78$		0			0
$79$	−4.06431	−	3.24118i	−0.457271	−	0.364661i	0.367599	−	0.929984i	$-0.380180\pi$
$79$	−4.06431	−	3.24118i	−0.457271	−	0.364661i	−0.824869	+	0.565323i	$0.808751\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	9.47260	+	4.56176i	1.03975	+	0.500719i	0.874243	−	0.485489i	$-0.161359\pi$
$83$	9.47260	+	4.56176i	1.03975	+	0.500719i	0.165510	+	0.986208i	$0.447073\pi$
$84$		0			0
$85$	2.22081	+	0.506887i	0.240881	+	0.0549796i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−16.2177	−	3.70159i	−1.71908	−	0.392368i	−0.754527	−	0.656268i	$-0.772134\pi$
$89$	−16.2177	−	3.70159i	−1.71908	−	0.392368i	−0.964550	+	0.263900i	$0.914991\pi$
$90$		0			0
$91$	8.56307	+	4.12376i	0.897653	+	0.432287i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.48636	−	1.18534i	−0.152498	−	0.121613i
$96$		0			0
$97$	−3.71825	+	7.72103i	−0.377531	+	0.783951i	0.622468	+	0.782645i	$0.286130\pi$
$97$	−3.71825	+	7.72103i	−0.377531	+	0.783951i	−0.999999	+	0.00130623i	$0.999584\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.56340	−	1.04157i	0.454075	−	0.103640i	0.0106344	−	0.999943i	$-0.496615\pi$
$101$	4.56340	−	1.04157i	0.454075	−	0.103640i	0.443440	+	0.896304i	$0.353758\pi$
$102$		0			0
$103$	1.45537	+	1.82498i	0.143402	+	0.179821i	0.848346	−	0.529443i	$-0.177599\pi$
$103$	1.45537	+	1.82498i	0.143402	+	0.179821i	−0.704943	+	0.709264i	$0.749028\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.23025	−	9.06644i	0.698974	−	0.876486i	−0.297972	−	0.954575i	$-0.596310\pi$
$107$	7.23025	−	9.06644i	0.698974	−	0.876486i	0.996946	+	0.0780885i	$0.0248817\pi$
$108$		0			0
$109$	8.81525	−	4.24520i	0.844347	−	0.406616i	0.0388710	−	0.999244i	$-0.487624\pi$
$109$	8.81525	−	4.24520i	0.844347	−	0.406616i	0.805476	+	0.592628i	$0.201910\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.94126	+	10.2606i	0.464834	+	0.965238i	0.993222	+	0.116235i	$0.0370826\pi$
$113$	4.94126	+	10.2606i	0.464834	+	0.965238i	−0.528387	+	0.849003i	$0.677203\pi$
$114$		0			0
$115$	5.69632			0.531185
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.749509	−	1.55637i	−0.0687074	−	0.142672i
$120$		0			0
$121$	0.163676	−	0.717110i	0.0148796	−	0.0651918i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.152273	+	0.190944i	−0.0136197	+	0.0170785i
$126$		0			0
$127$	13.9958	−	11.1613i	1.24192	−	0.990402i	0.242128	−	0.970244i	$-0.422155\pi$
$127$	13.9958	−	11.1613i	1.24192	−	0.990402i	0.999797	−	0.0201578i	$-0.00641686\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	19.2615	−	4.39631i	1.68288	−	0.384107i	0.729054	−	0.684456i	$-0.239960\pi$
$131$	19.2615	−	4.39631i	1.68288	−	0.384107i	0.953829	+	0.300349i	$0.0971030\pi$
$132$		0			0
$133$			1.44170i			0.125012i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−11.2000	−	8.93167i	−0.956877	−	0.763084i	0.0146797	−	0.999892i	$-0.495327\pi$
$137$	−11.2000	−	8.93167i	−0.956877	−	0.763084i	−0.971556	+	0.236809i	$0.923899\pi$
$138$		0			0
$139$	2.71154	+	11.8800i	0.229990	+	1.00765i	0.949647	+	0.313322i	$0.101442\pi$
$139$	2.71154	+	11.8800i	0.229990	+	1.00765i	−0.719657	+	0.694330i	$0.755701\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−13.2883	−	3.03297i	−1.11123	−	0.253630i
$144$		0			0
$145$	−15.7349	−	6.33743i	−1.30672	−	0.526295i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	15.6974	+	7.55948i	1.28598	+	0.619297i	0.946921	−	0.321467i	$-0.104176\pi$
$149$	15.6974	+	7.55948i	1.28598	+	0.619297i	0.339063	+	0.940764i	$0.389890\pi$
$150$		0			0
$151$	2.47857	+	10.8593i	0.201703	+	0.883721i	0.969899	+	0.243506i	$0.0782975\pi$
$151$	2.47857	+	10.8593i	0.201703	+	0.883721i	−0.768196	+	0.640215i	$0.778845\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	11.9928	−	24.9033i	0.963285	−	2.00028i
$156$		0			0
$157$		−	18.5071i		−	1.47703i	−0.674237	−	0.738515i	$-0.735527\pi$
$157$		−	18.5071i		−	1.47703i	0.674237	−	0.738515i	$-0.264473\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.69332	−	3.37732i	−0.212263	−	0.266170i
$162$		0			0
$163$	4.52326	−	3.60718i	0.354289	−	0.282536i	−0.430131	−	0.902767i	$-0.641533\pi$
$163$	4.52326	−	3.60718i	0.354289	−	0.282536i	0.784419	+	0.620231i	$0.212961\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	19.6087	−	9.44307i	1.51737	−	0.730726i	0.524666	−	0.851308i	$-0.324190\pi$
$167$	19.6087	−	9.44307i	1.51737	−	0.730726i	0.992703	+	0.120582i	$0.0384761\pi$
$168$		0			0
$169$	−0.629822	+	2.75943i	−0.0484479	+	0.212264i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−20.0791			−1.52659			−0.763294	−	0.646052i	$-0.776419\pi$
$173$	−20.0791			−1.52659			−0.763294	+	0.646052i	$0.776419\pi$
$174$		0			0
$175$	−11.7586			−0.888869
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.16107	−	18.2308i	0.311013	−	1.36264i	−0.541839	−	0.840482i	$-0.682272\pi$
$179$	4.16107	−	18.2308i	0.311013	−	1.36264i	0.852852	−	0.522153i	$-0.174871\pi$
$180$		0			0
$181$	−18.0581	+	8.69630i	−1.34224	+	0.646391i	−0.960604	−	0.277920i	$-0.910355\pi$
$181$	−18.0581	+	8.69630i	−1.34224	+	0.646391i	−0.381640	+	0.924311i	$0.624641\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−9.56609	+	7.62870i	−0.703313	+	0.560873i
$186$		0			0
$187$	1.54458	+	1.93685i	0.112951	+	0.141636i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	21.5182i		−	1.55700i	−0.627644	−	0.778501i	$-0.715980\pi$
$191$		−	21.5182i		−	1.55700i	0.627644	−	0.778501i	$-0.284020\pi$
$192$		0			0
$193$	1.41647	−	2.94133i	0.101960	−	0.211722i	−0.843748	−	0.536739i	$-0.819656\pi$
$193$	1.41647	−	2.94133i	0.101960	−	0.211722i	0.945708	+	0.325017i	$0.105370\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−0.397926	−	1.74343i	−0.0283511	−	0.124214i	0.958772	−	0.284176i	$-0.0917200\pi$
$197$	−0.397926	−	1.74343i	−0.0283511	−	0.124214i	−0.987123	+	0.159962i	$0.948863\pi$
$198$		0			0
$199$	1.16436	+	0.560728i	0.0825395	+	0.0397489i	0.474698	−	0.880149i	$-0.342557\pi$
$199$	1.16436	+	0.560728i	0.0825395	+	0.0397489i	−0.392159	+	0.919898i	$0.628272\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.68233	+	12.3256i	0.258449	+	0.865088i
$204$		0			0
$205$	−27.1619	−	6.19953i	−1.89707	−	0.432994i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.460071	−	2.01570i	−0.0318238	−	0.139429i
$210$		0			0
$211$	1.44665	+	1.15367i	0.0995918	+	0.0794218i	0.672020	−	0.740533i	$-0.265427\pi$
$211$	1.44665	+	1.15367i	0.0995918	+	0.0794218i	−0.572428	+	0.819955i	$0.693998\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			9.42005i			0.642442i
$216$		0			0
$217$	−20.4354	+	4.66425i	−1.38725	+	0.316630i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.24952	−	1.79393i	0.151319	−	0.120673i
$222$		0			0
$223$	−2.47015	+	3.09747i	−0.165414	+	0.207422i	−0.857629	−	0.514269i	$-0.828063\pi$
$223$	−2.47015	+	3.09747i	−0.165414	+	0.207422i	0.692215	+	0.721691i	$0.256635\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.95662	−	21.7164i	0.328983	−	1.44137i	−0.492091	−	0.870544i	$-0.663767\pi$
$227$	4.95662	−	21.7164i	0.328983	−	1.44137i	0.821073	−	0.570823i	$-0.193376\pi$
$228$		0			0
$229$	2.89281	+	6.00698i	0.191162	+	0.396953i	0.974417	−	0.224749i	$-0.0721561\pi$
$229$	2.89281	+	6.00698i	0.191162	+	0.396953i	−0.783254	+	0.621701i	$0.786442\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	20.6217			1.35098			0.675488	−	0.737371i	$-0.263933\pi$
$233$	20.6217			1.35098			0.675488	+	0.737371i	$0.263933\pi$
$234$		0			0
$235$	0.0187930	+	0.0390241i	0.00122592	+	0.00254565i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−12.3039	+	5.92523i	−0.795871	+	0.383271i	−0.787205	−	0.616691i	$-0.788473\pi$
$239$	−12.3039	+	5.92523i	−0.795871	+	0.383271i	−0.00866604	+	0.999962i	$0.502759\pi$
$240$		0			0
$241$	15.7436	−	19.7418i	1.01413	−	1.27168i	0.0521299	−	0.998640i	$-0.483399\pi$
$241$	15.7436	−	19.7418i	1.01413	−	1.27168i	0.962002	−	0.273041i	$-0.0880296\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.54100	−	3.18631i	−0.162339	−	0.203566i
$246$		0			0
$247$	−2.34110	+	0.534341i	−0.148961	+	0.0339993i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.09004	−	2.26348i	0.0688025	−	0.142870i	−0.863731	−	0.503953i	$-0.831879\pi$
$251$	1.09004	−	2.26348i	0.0688025	−	0.142870i	0.932534	+	0.361083i	$0.117593\pi$
$252$		0			0
$253$	4.84339	+	3.86248i	0.304501	+	0.242832i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.11101	+	1.49818i	0.194059	+	0.0934540i	0.528390	−	0.849002i	$-0.322796\pi$
$257$	3.11101	+	1.49818i	0.194059	+	0.0934540i	−0.334331	+	0.942456i	$0.608510\pi$
$258$		0			0
$259$	9.04602	+	2.06469i	0.562092	+	0.128294i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−7.54012	−	1.72098i	−0.464944	−	0.106120i	−0.0163695	−	0.999866i	$-0.505211\pi$
$263$	−7.54012	−	1.72098i	−0.464944	−	0.106120i	−0.448574	+	0.893746i	$0.648068\pi$
$264$		0			0
$265$	6.20973	+	2.99045i	0.381460	+	0.183702i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.9573	−	8.73815i	−0.668078	−	0.532775i	0.229678	−	0.973267i	$-0.426233\pi$
$269$	−10.9573	−	8.73815i	−0.668078	−	0.532775i	−0.897757	+	0.440492i	$0.854804\pi$
$270$		0			0
$271$	3.79779	−	7.88620i	0.230699	−	0.479052i	−0.753196	−	0.657796i	$-0.771489\pi$
$271$	3.79779	−	7.88620i	0.230699	−	0.479052i	0.983896	+	0.178744i	$0.0572032\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	16.4402	−	3.75237i	0.991381	−	0.226276i
$276$		0			0
$277$	13.8813	+	17.4066i	0.834044	+	1.04586i	0.998233	+	0.0594295i	$0.0189281\pi$
$277$	13.8813	+	17.4066i	0.834044	+	1.04586i	−0.164188	+	0.986429i	$0.552500\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	19.9164	−	24.9744i	1.18812	−	1.48985i	0.356681	−	0.934226i	$-0.383908\pi$
$281$	19.9164	−	24.9744i	1.18812	−	1.48985i	0.831434	−	0.555623i	$-0.187520\pi$
$282$		0			0
$283$	9.97541	−	4.80390i	0.592976	−	0.285562i	−0.113230	−	0.993569i	$-0.536120\pi$
$283$	9.97541	−	4.80390i	0.592976	−	0.285562i	0.706206	+	0.708007i	$0.250405\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.16696	+	19.0354i	0.541109	+	1.12362i
$288$		0			0
$289$	16.4771			0.969238
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−8.07777	−	16.7737i	−0.471908	−	0.979928i	−0.992050	−	0.125848i	$-0.959835\pi$
$293$	−8.07777	−	16.7737i	−0.471908	−	0.979928i	0.520141	−	0.854080i	$-0.325879\pi$
$294$		0			0
$295$	4.10999	−	18.0070i	0.239293	−	1.04841i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.48601	−	5.62528i	0.259433	−	0.325318i
$300$		0			0
$301$	5.58509	−	4.45396i	0.321919	−	0.256722i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.200415	+	0.0457434i	−0.0114757	+	0.00261926i
$306$		0			0
$307$			13.0736i			0.746150i	0.927801	+	0.373075i	$0.121697\pi$
$307$			13.0736i			0.746150i	−0.927801	+	0.373075i	$0.878303\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.83866	−	3.06123i	−0.217670	−	0.173586i	0.508584	−	0.861012i	$-0.330169\pi$
$311$	−3.83866	−	3.06123i	−0.217670	−	0.173586i	−0.726254	+	0.687426i	$0.758741\pi$
$312$		0			0
$313$	4.71283	+	20.6483i	0.266385	+	1.16711i	0.914184	+	0.405299i	$0.132832\pi$
$313$	4.71283	+	20.6483i	0.266385	+	1.16711i	−0.647799	+	0.761811i	$0.724310\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.25465	−	2.11231i	−0.519793	−	0.118639i	−0.0454279	−	0.998968i	$-0.514465\pi$
$317$	−9.25465	−	2.11231i	−0.519793	−	0.118639i	−0.474365	+	0.880328i	$0.657322\pi$
$318$		0			0
$319$	−9.08171	−	16.0578i	−0.508478	−	0.899065i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.393226	+	0.189368i	0.0218797	+	0.0105367i
$324$		0			0
$325$	−4.35812	−	19.0942i	−0.241745	−	1.05916i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.0142515	−	0.0295935i	0.000785710	−	0.00163154i
$330$		0			0
$331$			23.7025i			1.30281i	0.758731	+	0.651404i	$0.225820\pi$
$331$			23.7025i			1.30281i	−0.758731	+	0.651404i	$0.774180\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−24.4372	−	30.6433i	−1.33515	−	1.67422i
$336$		0			0
$337$	20.4992	−	16.3476i	1.11666	−	0.890510i	0.121884	−	0.992544i	$-0.461106\pi$
$337$	20.4992	−	16.3476i	1.11666	−	0.890510i	0.994781	+	0.102034i	$0.0325350\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	27.0831	−	13.0426i	1.46663	−	0.706294i
$342$		0			0
$343$	−4.40857	+	19.3152i	−0.238040	+	1.04292i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	17.9464			0.963414			0.481707	−	0.876332i	$-0.340017\pi$
$347$	17.9464			0.963414			0.481707	+	0.876332i	$0.340017\pi$
$348$		0			0
$349$	−10.7832			−0.577210			−0.288605	−	0.957448i	$-0.593191\pi$
$349$	−10.7832			−0.577210			−0.288605	+	0.957448i	$0.593191\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.873212	−	3.82579i	0.0464764	−	0.203626i	−0.946359	−	0.323117i	$-0.895269\pi$
$353$	0.873212	−	3.82579i	0.0464764	−	0.203626i	0.992835	+	0.119491i	$0.0381263\pi$
$354$		0			0
$355$	−13.8353	+	6.66272i	−0.734301	+	0.353621i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.16265	+	1.72466i	−0.114140	+	0.0910239i	−0.678897	−	0.734234i	$-0.737542\pi$
$359$	−2.16265	+	1.72466i	−0.114140	+	0.0910239i	0.564756	+	0.825258i	$0.308970\pi$
$360$		0			0
$361$	11.6192	+	14.5700i	0.611537	+	0.766843i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			29.5390i			1.54614i
$366$		0			0
$367$	9.32557	−	19.3648i	0.486791	−	1.01083i	−0.502460	−	0.864601i	$-0.667571\pi$
$367$	9.32557	−	19.3648i	0.486791	−	1.01083i	0.989250	−	0.146231i	$-0.0467143\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.16305	−	5.09564i	−0.0603824	−	0.264553i
$372$		0			0
$373$	9.66818	+	4.65595i	0.500599	+	0.241076i	0.667104	−	0.744965i	$-0.267534\pi$
$373$	9.66818	+	4.65595i	0.500599	+	0.241076i	−0.166505	+	0.986041i	$0.553248\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−18.6501	+	10.5478i	−0.960528	+	0.543239i
$378$		0			0
$379$	−5.18154	−	1.18265i	−0.266158	−	0.0607488i	0.0873591	−	0.996177i	$-0.472157\pi$
$379$	−5.18154	−	1.18265i	−0.266158	−	0.0607488i	−0.353517	+	0.935428i	$0.615014\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.68325	+	33.6625i	0.392596	+	1.72007i	0.655450	+	0.755238i	$0.272479\pi$
$383$	7.68325	+	33.6625i	0.392596	+	1.72007i	−0.262855	+	0.964835i	$0.584664\pi$
$384$		0			0
$385$	−20.1534	−	16.0718i	−1.02711	−	0.819095i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			31.8661i			1.61567i	0.589406	+	0.807837i	$0.299362\pi$
$389$			31.8661i			1.61567i	−0.589406	+	0.807837i	$0.700638\pi$
$390$		0			0
$391$	−1.27493	+	0.290995i	−0.0644761	+	0.0147163i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	12.8026	−	10.2097i	0.644166	−	0.513706i
$396$		0			0
$397$	−14.5684	+	18.2682i	−0.731166	+	0.916853i	−0.998912	−	0.0466365i	$-0.985150\pi$
$397$	−14.5684	+	18.2682i	−0.731166	+	0.916853i	0.267746	+	0.963490i	$0.413721\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−4.28265	+	18.7635i	−0.213865	+	0.937004i	0.748047	+	0.663646i	$0.230992\pi$
$401$	−4.28265	+	18.7635i	−0.213865	+	0.937004i	−0.961912	+	0.273359i	$0.911865\pi$
$402$		0			0
$403$	−15.1480	−	31.4552i	−0.754578	−	1.56690i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−13.3065			−0.659577
$408$		0			0
$409$	13.8827	+	28.8278i	0.686457	+	1.42544i	0.894385	+	0.447299i	$0.147614\pi$
$409$	13.8827	+	28.8278i	0.686457	+	1.42544i	−0.207927	+	0.978144i	$0.566672\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−12.6195	+	6.07725i	−0.620967	+	0.299042i
$414$		0			0
$415$	−20.6490	+	25.8930i	−1.01362	+	1.27104i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	13.0851	+	16.4082i	0.639248	+	0.801592i	0.990909	−	0.134536i	$-0.0429543\pi$
$419$	13.0851	+	16.4082i	0.639248	+	0.801592i	−0.351661	+	0.936128i	$0.614383\pi$
$420$		0			0
$421$	8.92950	−	2.03810i	0.435197	−	0.0993309i	0.000690993	−	1.00000i	$-0.499780\pi$
$421$	8.92950	−	2.03810i	0.435197	−	0.0993309i	0.434506	+	0.900669i	$0.356923\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.54449	+	3.20718i	−0.0749190	+	0.155571i
$426$		0			0
$427$	0.121881	+	0.0971966i	0.00589822	+	0.00470367i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−19.7125	−	9.49302i	−0.949516	−	0.457263i	−0.106000	−	0.994366i	$-0.533804\pi$
$431$	−19.7125	−	9.49302i	−0.949516	−	0.457263i	−0.843516	+	0.537103i	$0.819518\pi$
$432$		0			0
$433$	−14.4516	−	3.29848i	−0.694499	−	0.158515i	−0.139322	−	0.990247i	$-0.544492\pi$
$433$	−14.4516	−	3.29848i	−0.694499	−	0.158515i	−0.555177	+	0.831732i	$0.687349\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.06404	+	0.242861i	0.0509001	+	0.0116176i
$438$		0			0
$439$	−11.2578	−	5.42148i	−0.537307	−	0.258753i	0.145492	−	0.989359i	$-0.453523\pi$
$439$	−11.2578	−	5.42148i	−0.537307	−	0.258753i	−0.682799	+	0.730606i	$0.739238\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14.3662	−	11.4567i	−0.682560	−	0.544323i	0.219672	−	0.975574i	$-0.429501\pi$
$443$	−14.3662	−	11.4567i	−0.682560	−	0.544323i	−0.902232	+	0.431250i	$0.858073\pi$
$444$		0			0
$445$	22.7353	−	47.2104i	1.07776	−	2.23799i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−3.76621	+	0.859614i	−0.177739	+	0.0405677i	−0.310464	−	0.950585i	$-0.600484\pi$
$449$	−3.76621	+	0.859614i	−0.177739	+	0.0405677i	0.132725	+	0.991153i	$0.457627\pi$
$450$		0			0
$451$	−18.8912	−	23.6888i	−0.889552	−	1.11546i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−18.6663	+	23.4068i	−0.875091	+	1.09733i
$456$		0			0
$457$	−0.814695	+	0.392337i	−0.0381098	+	0.0183527i	−0.452842	−	0.891591i	$-0.649590\pi$
$457$	−0.814695	+	0.392337i	−0.0381098	+	0.0183527i	0.414732	+	0.909944i	$0.363875\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.03521	−	6.30267i	−0.141364	−	0.293545i	0.818252	−	0.574860i	$-0.194944\pi$
$461$	−3.03521	−	6.30267i	−0.141364	−	0.293545i	−0.959615	+	0.281315i	$0.909229\pi$
$462$		0			0
$463$	−13.6822			−0.635865			−0.317933	−	0.948113i	$-0.602989\pi$
$463$	−13.6822			−0.635865			−0.317933	+	0.948113i	$0.602989\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.2410	+	29.5718i	0.658996	+	1.36842i	0.915674	+	0.401922i	$0.131658\pi$
$467$	14.2410	+	29.5718i	0.658996	+	1.36842i	−0.256678	+	0.966497i	$0.582628\pi$
$468$		0			0
$469$	−6.61388	+	28.9773i	−0.305401	+	1.33805i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.38740	+	8.00955i	−0.293693	+	0.368280i
$474$		0			0
$475$	2.32273	−	1.85231i	0.106574	−	0.0849899i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.42724	−	1.01049i	0.202286	−	0.0461704i	−0.120177	−	0.992752i	$-0.538346\pi$
$479$	4.42724	−	1.01049i	0.202286	−	0.0461704i	0.322463	+	0.946582i	$0.395489\pi$
$480$		0			0
$481$			15.4546i			0.704668i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−21.1051	−	16.8308i	−0.958335	−	0.764247i
$486$		0			0
$487$	1.89382	+	8.29735i	0.0858170	+	0.375989i	0.999539	−	0.0303503i	$-0.00966228\pi$
$487$	1.89382	+	8.29735i	0.0858170	+	0.375989i	−0.913722	+	0.406339i	$0.866805\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−10.5567	−	2.40950i	−0.476419	−	0.108739i	−0.0224328	−	0.999748i	$-0.507141\pi$
$491$	−10.5567	−	2.40950i	−0.476419	−	0.108739i	−0.453986	+	0.891009i	$0.649998\pi$
$492$		0			0
$493$	3.84549	+	0.614609i	0.173192	+	0.0276806i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.4918	+	5.05261i	0.470624	+	0.226640i
$498$		0			0
$499$	−9.87575	−	43.2685i	−0.442099	−	1.93696i	−0.332980	−	0.942934i	$-0.608054\pi$
$499$	−9.87575	−	43.2685i	−0.442099	−	1.93696i	−0.109119	−	0.994029i	$-0.534803\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−15.0759	+	31.3055i	−0.672203	+	1.39584i	0.233679	+	0.972314i	$0.424924\pi$
$503$	−15.0759	+	31.3055i	−0.672203	+	1.39584i	−0.905882	+	0.423530i	$0.860791\pi$
$504$		0			0
$505$			14.7443i			0.656115i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.81007	+	6.03163i	0.213202	+	0.267347i	0.876921	−	0.480635i	$-0.159594\pi$
$509$	4.81007	+	6.03163i	0.213202	+	0.267347i	−0.663718	+	0.747983i	$0.731023\pi$
$510$		0			0
$511$	17.5135	−	13.9665i	0.774751	−	0.617843i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.62468	+	3.19028i	−0.291918	+	0.140580i
$516$		0			0
$517$	−0.0104818	+	0.0459237i	−0.000460989	+	0.00201972i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	22.8223			0.999865			0.499932	−	0.866064i	$-0.333358\pi$
$521$	22.8223			0.999865			0.499932	+	0.866064i	$0.333358\pi$
$522$		0			0
$523$	−33.7737			−1.47682			−0.738410	−	0.674352i	$-0.764423\pi$
$523$	−33.7737			−1.47682			−0.738410	+	0.674352i	$0.764423\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.41201	+	6.18643i	−0.0615082	+	0.269485i
$528$		0			0
$529$	17.7760	−	8.56046i	0.772868	−	0.372194i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−27.5130	+	21.9409i	−1.19172	+	0.950364i
$534$		0			0
$535$	22.7752	+	28.5592i	0.984660	+	1.23472i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	4.43218i		−	0.190907i
$540$		0			0
$541$	−0.0284360	+	0.0590479i	−0.00122256	+	0.00253867i	−0.901579	−	0.432614i	$-0.857591\pi$
$541$	−0.0284360	+	0.0590479i	−0.00122256	+	0.00253867i	0.900357	+	0.435153i	$0.143306\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	6.85812	+	30.0474i	0.293770	+	1.28709i
$546$		0			0
$547$	38.2698	+	18.4298i	1.63630	+	0.788001i	0.999861	+	0.0166738i	$0.00530767\pi$
$547$	38.2698	+	18.4298i	1.63630	+	0.788001i	0.636439	+	0.771327i	$0.280407\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.66901	−	1.85465i	−0.113704	−	0.0790109i
$552$		0			0
$553$	−12.1065	−	2.76324i	−0.514822	−	0.117505i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.57234	−	11.2701i	−0.108993	−	0.477531i	−0.999735	−	0.0230212i	$-0.992671\pi$
$557$	−2.57234	−	11.2701i	−0.108993	−	0.477531i	0.890742	−	0.454510i	$-0.150186\pi$
$558$		0			0
$559$	9.30256	+	7.41854i	0.393456	+	0.313771i
$560$		0			0
$561$		0			0
$562$		0			0
$563$			11.6060i			0.489135i	0.969632	+	0.244568i	$0.0786460\pi$
$563$			11.6060i			0.489135i	−0.969632	+	0.244568i	$0.921354\pi$
$564$		0			0
$565$	−34.9741	+	7.98261i	−1.47137	+	0.335831i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.18710	+	4.13657i	−0.217455	+	0.173414i	−0.726159	−	0.687527i	$-0.758696\pi$
$569$	−5.18710	+	4.13657i	−0.217455	+	0.173414i	0.508704	+	0.860941i	$0.330125\pi$
$570$		0			0
$571$	−3.21843	+	4.03578i	−0.134687	+	0.168892i	−0.844601	−	0.535396i	$-0.820162\pi$
$571$	−3.21843	+	4.03578i	−0.134687	+	0.168892i	0.709914	+	0.704288i	$0.248734\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.98079	+	8.67841i	−0.0826047	+	0.361915i
$576$		0			0
$577$	−3.04594	−	6.32496i	−0.126804	−	0.263312i	0.827896	−	0.560882i	$-0.189538\pi$
$577$	−3.04594	−	6.32496i	−0.126804	−	0.263312i	−0.954700	+	0.297571i	$0.903824\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	25.1150			1.04195
$582$		0			0
$583$	3.25221	+	6.75327i	0.134693	+	0.279692i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	24.1426	−	11.6264i	0.996470	−	0.479875i	0.136731	−	0.990608i	$-0.456340\pi$
$587$	24.1426	−	11.6264i	0.996470	−	0.479875i	0.859739	+	0.510734i	$0.170626\pi$
$588$		0			0
$589$	3.30194	−	4.14050i	0.136054	−	0.170606i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	3.73226	+	4.68011i	0.153266	+	0.192189i	0.852536	−	0.522668i	$-0.175063\pi$
$593$	3.73226	+	4.68011i	0.153266	+	0.192189i	−0.699271	+	0.714857i	$0.746492\pi$
$594$		0			0
$595$	5.30501	−	1.21083i	0.217484	−	0.0496393i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	12.8387	−	26.6599i	0.524577	−	1.08929i	−0.455419	−	0.890277i	$-0.650511\pi$
$599$	12.8387	−	26.6599i	0.524577	−	1.08929i	0.979996	−	0.199017i	$-0.0637750\pi$
$600$		0			0
$601$	3.63713	+	2.90051i	0.148362	+	0.118314i	0.694858	−	0.719147i	$-0.255467\pi$
$601$	3.63713	+	2.90051i	0.148362	+	0.118314i	−0.546496	+	0.837462i	$0.684039\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.08753	+	1.00530i	0.0848702	+	0.0408713i
$606$		0			0
$607$	11.9675	+	2.73151i	0.485747	+	0.110869i	0.458379	−	0.888757i	$-0.348430\pi$
$607$	11.9675	+	2.73151i	0.485747	+	0.110869i	0.0273682	+	0.999625i	$0.491287\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.0533373	+	0.0121739i	0.00215780	+	0.000492503i
$612$		0			0
$613$	5.52704	+	2.66168i	0.223235	+	0.107504i	0.542159	−	0.840276i	$-0.317607\pi$
$613$	5.52704	+	2.66168i	0.223235	+	0.107504i	−0.318924	+	0.947780i	$0.603321\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.76610	−	3.00336i	−0.151617	−	0.120911i	0.544743	−	0.838603i	$-0.316627\pi$
$617$	−3.76610	−	3.00336i	−0.151617	−	0.120911i	−0.696361	+	0.717692i	$0.745199\pi$
$618$		0			0
$619$	6.31581	−	13.1149i	0.253854	−	0.527133i	−0.734628	−	0.678470i	$-0.762643\pi$
$619$	6.31581	−	13.1149i	0.253854	−	0.527133i	0.988482	+	0.151336i	$0.0483577\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−38.7404	+	8.84224i	−1.55210	+	0.354257i
$624$		0			0
$625$	−15.8252	−	19.8442i	−0.633008	−	0.793767i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.75134	−	2.19611i	0.0698305	−	0.0875647i
$630$		0			0
$631$	38.7440	−	18.6581i	1.54237	−	0.742769i	0.546847	−	0.837233i	$-0.315828\pi$
$631$	38.7440	−	18.6581i	1.54237	−	0.742769i	0.995528	+	0.0944641i	$0.0301138\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	24.4662	+	50.8047i	0.970913	+	2.01612i
$636$		0			0
$637$	−5.14768			−0.203958
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−6.73253	−	13.9803i	−0.265919	−	0.552187i	0.724664	−	0.689103i	$-0.241995\pi$
$641$	−6.73253	−	13.9803i	−0.265919	−	0.552187i	−0.990583	+	0.136916i	$0.956281\pi$
$642$		0			0
$643$	−2.23184	+	9.77832i	−0.0880151	+	0.385619i	−0.999679	−	0.0253163i	$-0.991941\pi$
$643$	−2.23184	+	9.77832i	−0.0880151	+	0.385619i	0.911664	+	0.410935i	$0.134798\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−20.6425	+	25.8848i	−0.811539	+	1.01764i	0.187833	+	0.982201i	$0.439854\pi$
$647$	−20.6425	+	25.8848i	−0.811539	+	1.01764i	−0.999372	+	0.0354366i	$0.988718\pi$
$648$		0			0
$649$	15.7045	−	12.5239i	0.616457	−	0.491608i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−27.3991	+	6.25366i	−1.07221	+	0.244725i	−0.721962	−	0.691933i	$-0.756759\pi$
$653$	−27.3991	+	6.25366i	−1.07221	+	0.244725i	−0.350247	+	0.936657i	$0.613902\pi$
$654$		0			0
$655$			62.2339i			2.43168i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	32.0298	+	25.5429i	1.24771	+	0.995012i	0.999655	+	0.0262645i	$0.00836120\pi$
$659$	32.0298	+	25.5429i	1.24771	+	0.995012i	0.248050	+	0.968747i	$0.420210\pi$
$660$		0			0
$661$	8.61809	+	37.7583i	0.335205	+	1.46863i	0.808904	+	0.587941i	$0.200061\pi$
$661$	8.61809	+	37.7583i	0.335205	+	1.46863i	−0.473699	+	0.880687i	$0.657081\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−4.42750	−	1.01055i	−0.171691	−	0.0391873i
$666$		0			0
$667$	9.71717	−	0.641427i	0.376250	−	0.0248362i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.201423	−	0.0970003i	−0.00777586	−	0.00374466i
$672$		0			0
$673$	−8.21417	−	35.9887i	−0.316633	−	1.38726i	−0.843416	−	0.537261i	$-0.819459\pi$
$673$	−8.21417	−	35.9887i	−0.316633	−	1.38726i	0.526783	−	0.850000i	$-0.323398\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.38226	+	17.4059i	−0.322156	+	0.668964i	−0.997658	−	0.0683936i	$-0.978213\pi$
$677$	−8.38226	+	17.4059i	−0.322156	+	0.668964i	0.675502	+	0.737358i	$0.263927\pi$
$678$		0			0
$679$			20.4710i			0.785605i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.09073	−	10.1455i	−0.309583	−	0.388205i	0.602562	−	0.798072i	$-0.294147\pi$
$683$	−8.09073	−	10.1455i	−0.309583	−	0.388205i	−0.912145	+	0.409867i	$0.865575\pi$
$684$		0			0
$685$	35.2798	−	28.1347i	1.34797	−	1.07497i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.84348	−	3.77722i	0.298813	−	0.143901i
$690$		0			0
$691$	5.79342	−	25.3826i	0.220392	−	0.965600i	−0.736792	−	0.676119i	$-0.763660\pi$
$691$	5.79342	−	25.3826i	0.220392	−	0.965600i	0.957184	−	0.289481i	$-0.0934825\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−38.3844			−1.45601
$696$		0			0
$697$	6.39600			0.242266
$698$		0			0
$699$		0			0
$700$		0			0
$701$	6.75158	−	29.5806i	0.255004	−	1.11724i	−0.671514	−	0.740992i	$-0.734355\pi$
$701$	6.75158	−	29.5806i	0.255004	−	1.11724i	0.926517	−	0.376252i	$-0.122787\pi$
$702$		0			0
$703$	−2.11214	+	1.01715i	−0.0796610	+	0.0383627i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.74183	−	6.97138i	0.328770	−	0.262186i
$708$		0			0
$709$	10.6551	+	13.3611i	0.400161	+	0.501786i	0.940562	−	0.339622i	$-0.110299\pi$
$709$	10.6551	+	13.3611i	0.400161	+	0.501786i	−0.540401	+	0.841407i	$0.681728\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			15.8680i			0.594261i
$714$		0			0
$715$	18.6286	−	38.6827i	0.696671	−	1.44665i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−2.09161	−	9.16395i	−0.0780040	−	0.341758i	0.920834	−	0.389955i	$-0.127509\pi$
$719$	−2.09161	−	9.16395i	−0.0780040	−	0.341758i	−0.998838	+	0.0481974i	$0.984652\pi$
$720$		0			0
$721$	5.02376	+	2.41931i	0.187094	+	0.0901000i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	15.1267	−	21.7686i	0.561791	−	0.808467i
$726$		0			0
$727$	−34.5989	−	7.89697i	−1.28320	−	0.292882i	−0.474058	−	0.880493i	$-0.657211\pi$
$727$	−34.5989	−	7.89697i	−1.28320	−	0.292882i	−0.809144	+	0.587611i	$0.800069\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.481221	−	2.10836i	−0.0177986	−	0.0779807i
$732$		0			0
$733$	4.49188	+	3.58216i	0.165911	+	0.132310i	0.702926	−	0.711263i	$-0.251877\pi$
$733$	4.49188	+	3.58216i	0.165911	+	0.132310i	−0.537015	+	0.843573i	$0.680448\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	42.6249i		−	1.57011i
$738$		0			0
$739$	−37.6980	+	8.60431i	−1.38674	+	0.316515i	−0.849800	−	0.527105i	$-0.823278\pi$
$739$	−37.6980	+	8.60431i	−1.38674	+	0.316515i	−0.536942	+	0.843619i	$0.680420\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−33.5891	+	26.7865i	−1.23227	+	0.982700i	−0.232317	+	0.972640i	$0.574631\pi$
$743$	−33.5891	+	26.7865i	−1.23227	+	0.982700i	−0.999949	+	0.0100595i	$0.996798\pi$
$744$		0			0
$745$	−34.2183	+	42.9083i	−1.25366	+	1.57204i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.16408	−	27.0066i	0.225231	−	0.986800i
$750$		0			0
$751$	−5.64926	−	11.7308i	−0.206145	−	0.428064i	0.772105	−	0.635495i	$-0.219204\pi$
$751$	−5.64926	−	11.7308i	−0.206145	−	0.428064i	−0.978250	+	0.207431i	$0.933490\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−35.0866			−1.27693
$756$		0			0
$757$	−15.1729	−	31.5068i	−0.551468	−	1.14513i	−0.971371	−	0.237566i	$-0.923650\pi$
$757$	−15.1729	−	31.5068i	−0.551468	−	1.14513i	0.419904	−	0.907569i	$-0.362064\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	16.9153	−	8.14599i	0.613180	−	0.295292i	−0.101400	−	0.994846i	$-0.532332\pi$
$761$	16.9153	−	8.14599i	0.613180	−	0.295292i	0.714580	+	0.699554i	$0.246618\pi$
$762$		0			0
$763$	14.5723	−	18.2731i	0.527552	−	0.661529i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−14.5457	−	18.2398i	−0.525216	−	0.658600i
$768$		0			0
$769$	−50.3766	+	11.4981i	−1.81663	+	0.414633i	−0.989155	−	0.146873i	$-0.953079\pi$
$769$	−50.3766	+	11.4981i	−1.81663	+	0.414633i	−0.827472	+	0.561506i	$0.810222\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−15.0368	+	31.2241i	−0.540834	+	1.12305i	0.434162	+	0.900835i	$0.357044\pi$
$773$	−15.0368	+	31.2241i	−0.540834	+	1.12305i	−0.974997	+	0.222220i	$0.928670\pi$
$774$		0			0
$775$	33.7702	+	26.9308i	1.21306	+	0.967384i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.80939	−	2.31608i	−0.172314	−	0.0829822i
$780$		0			0
$781$	−16.2814	−	3.71613i	−0.582596	−	0.132974i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	56.8358	+	12.9724i	2.02856	+	0.463004i
$786$		0			0
$787$	−11.2005	−	5.39387i	−0.399254	−	0.192271i	0.223472	−	0.974710i	$-0.428261\pi$
$787$	−11.2005	−	5.39387i	−0.399254	−	0.192271i	−0.622727	+	0.782440i	$0.713975\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	21.2692	+	16.9616i	0.756245	+	0.603085i
$792$		0			0
$793$	−0.112659	+	0.233940i	−0.00400065	+	0.00830744i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	32.5945	−	7.43948i	1.15456	−	0.263520i	0.397960	−	0.917403i	$-0.369718\pi$
$797$	32.5945	−	7.43948i	1.15456	−	0.263520i	0.756596	+	0.653883i	$0.226861\pi$
$798$		0			0
$799$	−0.00619972	−	0.00777421i	−0.000219330	−	0.000275032i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−20.0294	+	25.1160i	−0.706821	+	0.886325i
$804$		0			0
$805$	12.2596	−	5.90394i	0.432096	−	0.208086i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−13.9469	−	28.9609i	−0.490345	−	1.01821i	−0.988514	−	0.151132i	$-0.951708\pi$
$809$	−13.9469	−	28.9609i	−0.490345	−	1.01821i	0.498168	−	0.867080i	$-0.334006\pi$
$810$		0			0
$811$	−32.4360			−1.13898			−0.569491	−	0.821998i	$-0.692859\pi$
$811$	−32.4360			−1.13898			−0.569491	+	0.821998i	$0.692859\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	7.90717	+	16.4194i	0.276976	+	0.575147i
$816$		0			0
$817$	−0.401621	+	1.75962i	−0.0140509	+	0.0615612i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	18.4990	−	23.1970i	0.645619	−	0.809580i	−0.346075	−	0.938207i	$-0.612486\pi$
$821$	18.4990	−	23.1970i	0.645619	−	0.809580i	0.991693	+	0.128627i	$0.0410570\pi$
$822$		0			0
$823$	9.08309	−	7.24352i	0.316617	−	0.252493i	−0.452266	−	0.891883i	$-0.649384\pi$
$823$	9.08309	−	7.24352i	0.316617	−	0.252493i	0.768883	+	0.639390i	$0.220813\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	12.5181	−	2.85717i	0.435297	−	0.0993537i	0.000743518	−	1.00000i	$-0.499763\pi$
$827$	12.5181	−	2.85717i	0.435297	−	0.0993537i	0.434554	+	0.900646i	$0.356906\pi$
$828$		0			0
$829$		−	44.4069i		−	1.54232i	−0.636643	−	0.771158i	$-0.719678\pi$
$829$		−	44.4069i		−	1.54232i	0.636643	−	0.771158i	$-0.280322\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.731490	+	0.583344i	0.0253446	+	0.0202117i
$834$		0			0
$835$	15.2553	+	66.8378i	0.527931	+	2.31302i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.70848	+	1.98765i	0.300650	+	0.0686214i	0.370185	−	0.928958i	$-0.379294\pi$
$839$	8.70848	+	1.98765i	0.300650	+	0.0686214i	−0.0695348	+	0.997580i	$0.522152\pi$
$840$		0			0
$841$	−27.5553	−	9.03900i	−0.950184	−	0.311690i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−8.03280	−	3.86839i	−0.276337	−	0.133077i
$846$		0			0
$847$	−0.390983	−	1.71301i	−0.0134343	−	0.0588596i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.04768	−	6.32857i	0.104473	−	0.216941i
$852$		0			0
$853$			47.6105i			1.63015i	0.579354	+	0.815076i	$0.303305\pi$
$853$			47.6105i			1.63015i	−0.579354	+	0.815076i	$0.696695\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.28714	+	1.61403i	0.0439680	+	0.0551341i	0.803329	−	0.595535i	$-0.203060\pi$
$857$	1.28714	+	1.61403i	0.0439680	+	0.0551341i	−0.759361	+	0.650669i	$0.774488\pi$
$858$		0			0
$859$	−40.4789	+	32.2808i	−1.38112	+	1.10141i	−0.398217	+	0.917291i	$0.630371\pi$
$859$	−40.4789	+	32.2808i	−1.38112	+	1.10141i	−0.982904	+	0.184116i	$0.941058\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−37.3780	+	18.0003i	−1.27236	+	0.612737i	−0.943416	−	0.331611i	$-0.892408\pi$
$863$	−37.3780	+	18.0003i	−1.27236	+	0.612737i	−0.328946	+	0.944349i	$0.606694\pi$
$864$		0			0
$865$	14.0743	−	61.6633i	0.478539	−	2.09662i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	17.8084			0.604109
$870$		0			0
$871$	−49.5060			−1.67745
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.129819	+	0.568773i	−0.00438867	+	0.0192280i
$876$		0			0
$877$	−34.7552	+	16.7372i	−1.17360	+	0.565175i	−0.916040	−	0.401088i	$-0.868632\pi$
$877$	−34.7552	+	16.7372i	−1.17360	+	0.565175i	−0.257558	+	0.966263i	$0.582918\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	42.0663	−	33.5468i	1.41725	−	1.13022i	0.445205	−	0.895429i	$-0.353131\pi$
$881$	42.0663	−	33.5468i	1.41725	−	1.13022i	0.972046	−	0.234791i	$-0.0754406\pi$
$882$		0			0
$883$	−10.3602	−	12.9913i	−0.348649	−	0.437192i	0.576326	−	0.817220i	$-0.304486\pi$
$883$	−10.3602	−	12.9913i	−0.348649	−	0.437192i	−0.924975	+	0.380028i	$0.875914\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		−	30.2123i		−	1.01443i	−0.861820	−	0.507214i	$-0.830675\pi$
$887$		−	30.2123i		−	1.01443i	0.861820	−	0.507214i	$-0.169325\pi$
$888$		0			0
$889$	18.5537	−	38.5272i	0.622272	−	1.29216i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.00184666	+	0.00809073i	6.17960e−5	+	0.000270746i
$894$		0			0
$895$	53.0705	+	25.5574i	1.77395	+	0.854290i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	17.6539	−	43.8322i	0.588791	−	1.46188i
$900$		0			0
$901$	−1.54261	−	0.352090i	−0.0513917	−	0.0117298i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−14.0489	−	61.5522i	−0.467001	−	2.04606i
$906$		0			0
$907$	−22.1209	−	17.6408i	−0.734512	−	0.585754i	0.183164	−	0.983082i	$-0.441366\pi$
$907$	−22.1209	−	17.6408i	−0.734512	−	0.585754i	−0.917677	+	0.397328i	$0.869937\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	24.0212i		−	0.795857i	−0.917417	−	0.397928i	$-0.869729\pi$
$911$		−	24.0212i		−	0.795857i	0.917417	−	0.397928i	$-0.130271\pi$
$912$		0			0
$913$	−35.1143	+	8.01460i	−1.16211	+	0.265245i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	36.8981	−	29.4253i	1.21848	−	0.971708i
$918$		0			0
$919$	13.2144	−	16.5703i	0.435903	−	0.546605i	−0.514555	−	0.857457i	$-0.672043\pi$
$919$	13.2144	−	16.5703i	0.435903	−	0.546605i	0.950458	+	0.310852i	$0.100614\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.31604	+	18.9098i	−0.142064	+	0.622424i
$924$		0			0
$925$	−8.29598	−	17.2268i	−0.272770	−	0.566413i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	53.6266			1.75943			0.879716	−	0.475499i	$-0.157733\pi$
$929$	53.6266			1.75943			0.879716	+	0.475499i	$0.157733\pi$
$930$		0			0
$931$	−0.338798	−	0.703521i	−0.0111037	−	0.0230570i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.03075	+	3.38583i	−0.229930	+	0.110728i
$936$		0			0
$937$	−7.35260	+	9.21986i	−0.240199	+	0.301200i	−0.887289	−	0.461214i	$-0.847414\pi$
$937$	−7.35260	+	9.21986i	−0.240199	+	0.301200i	0.647090	+	0.762413i	$0.275986\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−4.48497	−	5.62397i	−0.146206	−	0.183336i	0.703336	−	0.710857i	$-0.251693\pi$
$941$	−4.48497	−	5.62397i	−0.146206	−	0.183336i	−0.849542	+	0.527521i	$0.823121\pi$
$942$		0			0
$943$	15.5932	−	3.55905i	0.507785	−	0.115899i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20.6116	−	42.8004i	0.669787	−	1.39083i	−0.237947	−	0.971278i	$-0.576474\pi$
$947$	20.6116	−	42.8004i	0.669787	−	1.39083i	0.907733	−	0.419548i	$-0.137811\pi$
$948$		0			0
$949$	29.1706	+	23.2628i	0.946917	+	0.755141i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−13.2233	−	6.36803i	−0.428346	−	0.206281i	0.207273	−	0.978283i	$-0.433541\pi$
$953$	−13.2233	−	6.36803i	−0.428346	−	0.206281i	−0.635620	+	0.772002i	$0.719255\pi$
$954$		0			0
$955$	66.0828	+	15.0830i	2.13839	+	0.488073i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−33.3618	−	7.61461i	−1.07731	−	0.245889i
$960$		0			0
$961$	41.4420	+	19.9574i	1.33684	+	0.643788i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	8.04003	+	6.41171i	0.258818	+	0.206400i
$966$		0			0
$967$	10.7119	−	22.2435i	0.344472	−	0.715303i	−0.654704	−	0.755885i	$-0.727207\pi$
$967$	10.7119	−	22.2435i	0.344472	−	0.715303i	0.999176	+	0.0405817i	$0.0129211\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	11.4230	−	2.60723i	0.366582	−	0.0836699i	−0.0352620	−	0.999378i	$-0.511227\pi$
$971$	11.4230	−	2.60723i	0.366582	−	0.0836699i	0.401844	+	0.915708i	$0.368369\pi$
$972$		0			0
$973$	18.1488	+	22.7579i	0.581825	+	0.729585i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	7.93279	−	9.94741i	0.253792	−	0.318246i	−0.638571	−	0.769563i	$-0.720474\pi$
$977$	7.93279	−	9.94741i	0.253792	−	0.318246i	0.892364	+	0.451317i	$0.149046\pi$
$978$		0			0
$979$	51.3428	−	24.7254i	1.64092	−	0.790227i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−26.5433	−	55.1178i	−0.846601	−	1.75799i	−0.621079	−	0.783748i	$-0.713306\pi$
$983$	−26.5433	−	55.1178i	−0.846601	−	1.75799i	−0.225522	−	0.974238i	$-0.572409\pi$
$984$		0			0
$985$	5.63302			0.179483
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.34640	−	4.87234i	−0.0746111	−	0.154931i
$990$		0			0
$991$	−2.24343	+	9.82910i	−0.0712648	+	0.312232i	−0.997980	−	0.0635337i	$-0.979763\pi$
$991$	−2.24343	+	9.82910i	−0.0712648	+	0.312232i	0.926715	+	0.375765i	$0.122620\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.53815	+	3.18274i	−0.0804649	+	0.100900i
$996$		0			0
$997$	28.1322	−	22.4347i	0.890957	−	0.710515i	−0.0668999	−	0.997760i	$-0.521311\pi$
$997$	28.1322	−	22.4347i	0.890957	−	0.710515i	0.957857	+	0.287245i	$0.0927394\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1044.2.z.c.613.1	yes	24
3.2	odd	2	inner	1044.2.z.c.613.4	yes	24
29.22	even	14	inner	1044.2.z.c.109.1	✓	24
87.80	odd	14	inner	1044.2.z.c.109.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1044.2.z.c.109.1	✓	24	29.22	even	14	inner
1044.2.z.c.109.4	yes	24	87.80	odd	14	inner
1044.2.z.c.613.1	yes	24	1.1	even	1	trivial
1044.2.z.c.613.4	yes	24	3.2	odd	2	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:	\( N \)	\(=\)	\( 1044 = 2^{2} \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1044.z (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.700940 + 3.07102i) q^{5} +(2.15220 - 1.03645i) q^{7} +O(q^{10})\)	\(q+(-0.700940 + 3.07102i) q^{5} +(2.15220 - 1.03645i) q^{7} +(-2.67834 + 2.13590i) q^{11} +(2.48071 + 3.11071i) q^{13} -0.723153i q^{17} +(-0.261864 + 0.543766i) q^{19} +(-0.402398 - 1.76302i) q^{23} +(-4.43499 - 2.13578i) q^{25} +(-0.849902 + 5.31767i) q^{29} +(-8.55480 - 1.95258i) q^{31} +(1.67438 + 7.33594i) q^{35} +(3.03686 + 2.42181i) q^{37} +8.84460i q^{41} +(2.91552 - 0.665448i) q^{43} +(0.0107504 - 0.00857319i) q^{47} +(-0.806668 + 1.01153i) q^{49} +(0.486882 - 2.13317i) q^{53} +(-4.68204 - 9.72235i) q^{55} -5.86354 q^{59} +(0.0283153 + 0.0587974i) q^{61} +(-11.2919 + 5.43787i) q^{65} +(-7.75785 + 9.72804i) q^{67} +(3.03947 + 3.81138i) q^{71} +(9.14236 - 2.08668i) q^{73} +(-3.55058 + 7.37285i) q^{77} +(-4.06431 - 3.24118i) q^{79} +(9.47260 + 4.56176i) q^{83} +(2.22081 + 0.506887i) q^{85} +(-16.2177 - 3.70159i) q^{89} +(8.56307 + 4.12376i) q^{91} +(-1.48636 - 1.18534i) q^{95} +(-3.71825 + 7.72103i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7}+O(q^{10}) \) 24 * q - 4 * q^7	\( 24 q - 4 q^{7} - 10 q^{13} - 10 q^{25} - 28 q^{31} + 28 q^{37} - 14 q^{43} - 4 q^{49} + 14 q^{55} - 56 q^{61} - 20 q^{67} + 14 q^{79} + 14 q^{85} + 46 q^{91} + 28 q^{97}+O(q^{100}) \) 24 * q - 4 * q^7 - 10 * q^13 - 10 * q^25 - 28 * q^31 + 28 * q^37 - 14 * q^43 - 4 * q^49 + 14 * q^55 - 56 * q^61 - 20 * q^67 + 14 * q^79 + 14 * q^85 + 46 * q^91 + 28 * q^97

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