LMFDB - Embedded newform 648.3.m.d.377.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,3,Mod(377,648)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("648.377"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	648.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.6567211305$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			377.2
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	648.377
Dual form			648.3.m.d.593.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 + 2.82843i) q^{5} +(3.00000 + 5.19615i) q^{7} +(-4.89898 + 2.82843i) q^{11} +(-5.00000 + 8.66025i) q^{13} +22.6274i q^{17} +2.00000 q^{19} +(-9.79796 - 5.65685i) q^{23} +(3.50000 + 6.06218i) q^{25} +(-14.6969 + 8.48528i) q^{29} +(11.0000 - 19.0526i) q^{31} +33.9411i q^{35} -6.00000 q^{37} +(29.3939 + 16.9706i) q^{41} +(-41.0000 - 71.0141i) q^{43} +(-58.7878 + 33.9411i) q^{47} +(6.50000 - 11.2583i) q^{49} +62.2254i q^{53} -32.0000 q^{55} +(63.6867 + 36.7696i) q^{59} +(43.0000 + 74.4782i) q^{61} +(-48.9898 + 28.2843i) q^{65} +(-1.00000 + 1.73205i) q^{67} +124.451i q^{71} +82.0000 q^{73} +(-29.3939 - 16.9706i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(63.6867 - 36.7696i) q^{83} +(-64.0000 + 110.851i) q^{85} +33.9411i q^{89} -60.0000 q^{91} +(9.79796 + 5.65685i) q^{95} +(47.0000 + 81.4064i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{7} - 20 q^{13} + 8 q^{19} + 14 q^{25} + 44 q^{31} - 24 q^{37} - 164 q^{43} + 26 q^{49} - 128 q^{55} + 172 q^{61} - 4 q^{67} + 328 q^{73} - 20 q^{79} - 256 q^{85} - 240 q^{91} + 188 q^{97}+O(q^{100}) $ 4 * q + 12 * q^7 - 20 * q^13 + 8 * q^19 + 14 * q^25 + 44 * q^31 - 24 * q^37 - 164 * q^43 + 26 * q^49 - 128 * q^55 + 172 * q^61 - 4 * q^67 + 328 * q^73 - 20 * q^79 - 256 * q^85 - 240 * q^91 + 188 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	4.89898	+	2.82843i	0.979796	+	0.565685i	0.902209	−	0.431300i	$-0.141945\pi$
$5$	4.89898	+	2.82843i	0.979796	+	0.565685i	0.0775874	+	0.996986i	$0.475278\pi$
$6$		0			0
$7$	3.00000	+	5.19615i	0.428571	+	0.742307i	0.996747	−	0.0806002i	$-0.0256837\pi$
$7$	3.00000	+	5.19615i	0.428571	+	0.742307i	−0.568175	+	0.822908i	$0.692350\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.89898	+	2.82843i	−0.445362	+	0.257130i	−0.705869	−	0.708342i	$-0.749443\pi$
$11$	−4.89898	+	2.82843i	−0.445362	+	0.257130i	0.260508	+	0.965472i	$0.416110\pi$
$12$		0			0
$13$	−5.00000	+	8.66025i	−0.384615	+	0.666173i	−0.991716	−	0.128452i	$-0.958999\pi$
$13$	−5.00000	+	8.66025i	−0.384615	+	0.666173i	0.607100	+	0.794625i	$0.292333\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			22.6274i			1.33102i	0.746387	+	0.665512i	$0.231787\pi$
$17$			22.6274i			1.33102i	−0.746387	+	0.665512i	$0.768213\pi$
$18$		0			0
$19$	2.00000			0.105263			0.0526316	−	0.998614i	$-0.483239\pi$
$19$	2.00000			0.105263			0.0526316	+	0.998614i	$0.483239\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−9.79796	−	5.65685i	−0.425998	−	0.245950i	0.271642	−	0.962398i	$-0.412433\pi$
$23$	−9.79796	−	5.65685i	−0.425998	−	0.245950i	−0.697640	+	0.716448i	$0.745767\pi$
$24$		0			0
$25$	3.50000	+	6.06218i	0.140000	+	0.242487i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−14.6969	+	8.48528i	−0.506791	+	0.292596i	−0.731514	−	0.681827i	$-0.761186\pi$
$29$	−14.6969	+	8.48528i	−0.506791	+	0.292596i	0.224723	+	0.974423i	$0.427852\pi$
$30$		0			0
$31$	11.0000	−	19.0526i	0.354839	−	0.614599i	−0.632252	−	0.774763i	$-0.717869\pi$
$31$	11.0000	−	19.0526i	0.354839	−	0.614599i	0.987090	+	0.160164i	$0.0512024\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			33.9411i			0.969746i
$36$		0			0
$37$	−6.00000			−0.162162			−0.0810811	−	0.996708i	$-0.525837\pi$
$37$	−6.00000			−0.162162			−0.0810811	+	0.996708i	$0.525837\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	29.3939	+	16.9706i	0.716924	+	0.413916i	0.813619	−	0.581398i	$-0.197494\pi$
$41$	29.3939	+	16.9706i	0.716924	+	0.413916i	−0.0966956	+	0.995314i	$0.530827\pi$
$42$		0			0
$43$	−41.0000	−	71.0141i	−0.953488	−	1.65149i	−0.737790	−	0.675030i	$-0.764131\pi$
$43$	−41.0000	−	71.0141i	−0.953488	−	1.65149i	−0.215698	−	0.976460i	$-0.569203\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−58.7878	+	33.9411i	−1.25080	+	0.722152i	−0.971269	−	0.237984i	$-0.923513\pi$
$47$	−58.7878	+	33.9411i	−1.25080	+	0.722152i	−0.279534	+	0.960136i	$0.590180\pi$
$48$		0			0
$49$	6.50000	−	11.2583i	0.132653	−	0.229762i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			62.2254i			1.17406i	0.809564	+	0.587032i	$0.199704\pi$
$53$			62.2254i			1.17406i	−0.809564	+	0.587032i	$0.800296\pi$
$54$		0			0
$55$	−32.0000			−0.581818
$56$		0			0
$57$		0			0
$58$		0			0
$59$	63.6867	+	36.7696i	1.07944	+	0.623213i	0.930744	−	0.365671i	$-0.119160\pi$
$59$	63.6867	+	36.7696i	1.07944	+	0.623213i	0.148692	+	0.988884i	$0.452494\pi$
$60$		0			0
$61$	43.0000	+	74.4782i	0.704918	+	1.22095i	0.966721	+	0.255833i	$0.0823496\pi$
$61$	43.0000	+	74.4782i	0.704918	+	1.22095i	−0.261803	+	0.965121i	$0.584317\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−48.9898	+	28.2843i	−0.753689	+	0.435143i
$66$		0			0
$67$	−1.00000	+	1.73205i	−0.0149254	+	0.0258515i	−0.873392	−	0.487019i	$-0.838084\pi$
$67$	−1.00000	+	1.73205i	−0.0149254	+	0.0258515i	0.858466	+	0.512870i	$0.171418\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			124.451i			1.75283i	0.481558	+	0.876414i	$0.340071\pi$
$71$			124.451i			1.75283i	−0.481558	+	0.876414i	$0.659929\pi$
$72$		0			0
$73$	82.0000			1.12329			0.561644	−	0.827379i	$-0.310169\pi$
$73$	82.0000			1.12329			0.561644	+	0.827379i	$0.310169\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−29.3939	−	16.9706i	−0.381739	−	0.220397i
$78$		0			0
$79$	−5.00000	−	8.66025i	−0.0632911	−	0.109623i	0.832644	−	0.553809i	$-0.186826\pi$
$79$	−5.00000	−	8.66025i	−0.0632911	−	0.109623i	−0.895935	+	0.444186i	$0.853493\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	63.6867	−	36.7696i	0.767310	−	0.443007i	−0.0646041	−	0.997911i	$-0.520578\pi$
$83$	63.6867	−	36.7696i	0.767310	−	0.443007i	0.831914	+	0.554904i	$0.187245\pi$
$84$		0			0
$85$	−64.0000	+	110.851i	−0.752941	+	1.30413i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			33.9411i			0.381361i	0.981652	+	0.190680i	$0.0610694\pi$
$89$			33.9411i			0.381361i	−0.981652	+	0.190680i	$0.938931\pi$
$90$		0			0
$91$	−60.0000			−0.659341
$92$		0			0
$93$		0			0
$94$		0			0
$95$	9.79796	+	5.65685i	0.103136	+	0.0595458i
$96$		0			0
$97$	47.0000	+	81.4064i	0.484536	+	0.839241i	0.999842	−	0.0177651i	$-0.00565510\pi$
$97$	47.0000	+	81.4064i	0.484536	+	0.839241i	−0.515306	+	0.857006i	$0.672322\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−44.0908	+	25.4558i	−0.436543	+	0.252038i	−0.702130	−	0.712049i	$-0.747767\pi$
$101$	−44.0908	+	25.4558i	−0.436543	+	0.252038i	0.265587	+	0.964087i	$0.414434\pi$
$102$		0			0
$103$	67.0000	−	116.047i	0.650485	−	1.12667i	−0.332520	−	0.943096i	$-0.607899\pi$
$103$	67.0000	−	116.047i	0.650485	−	1.12667i	0.983005	−	0.183578i	$-0.0587678\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	50.9117i		−	0.475810i	−0.971288	−	0.237905i	$-0.923539\pi$
$107$		−	50.9117i		−	0.475810i	0.971288	−	0.237905i	$-0.0764607\pi$
$108$		0			0
$109$	10.0000			0.0917431			0.0458716	−	0.998947i	$-0.485394\pi$
$109$	10.0000			0.0917431			0.0458716	+	0.998947i	$0.485394\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−58.7878	−	33.9411i	−0.520246	−	0.300364i	0.216790	−	0.976218i	$-0.430441\pi$
$113$	−58.7878	−	33.9411i	−0.520246	−	0.300364i	−0.737035	+	0.675854i	$0.763775\pi$
$114$		0			0
$115$	−32.0000	−	55.4256i	−0.278261	−	0.481962i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−117.576	+	67.8823i	−0.988029	+	0.570439i
$120$		0			0
$121$	−44.5000	+	77.0763i	−0.367769	+	0.636994i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	101.823i		−	0.814587i
$126$		0			0
$127$	106.000			0.834646			0.417323	−	0.908758i	$-0.362968\pi$
$127$	106.000			0.834646			0.417323	+	0.908758i	$0.362968\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.89898	−	2.82843i	−0.0373968	−	0.0215910i	0.481185	−	0.876619i	$-0.340207\pi$
$131$	−4.89898	−	2.82843i	−0.0373968	−	0.0215910i	−0.518582	+	0.855028i	$0.673540\pi$
$132$		0			0
$133$	6.00000	+	10.3923i	0.0451128	+	0.0781376i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	88.1816	−	50.9117i	0.643662	−	0.371618i	−0.142362	−	0.989815i	$-0.545470\pi$
$137$	88.1816	−	50.9117i	0.643662	−	0.371618i	0.786024	+	0.618196i	$0.212136\pi$
$138$		0			0
$139$	39.0000	−	67.5500i	0.280576	−	0.485971i	−0.690951	−	0.722902i	$-0.742808\pi$
$139$	39.0000	−	67.5500i	0.280576	−	0.485971i	0.971527	+	0.236930i	$0.0761413\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	56.5685i		−	0.395584i
$144$		0			0
$145$	−96.0000			−0.662069
$146$		0			0
$147$		0			0
$148$		0			0
$149$	142.070	+	82.0244i	0.953493	+	0.550499i	0.894164	−	0.447739i	$-0.147771\pi$
$149$	142.070	+	82.0244i	0.953493	+	0.550499i	0.0593285	+	0.998239i	$0.481104\pi$
$150$		0			0
$151$	−109.000	−	188.794i	−0.721854	−	1.25029i	−0.960256	−	0.279122i	$-0.909957\pi$
$151$	−109.000	−	188.794i	−0.721854	−	1.25029i	0.238401	−	0.971167i	$-0.423377\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	107.778	−	62.2254i	0.695339	−	0.401454i
$156$		0			0
$157$	43.0000	−	74.4782i	0.273885	−	0.474383i	−0.695968	−	0.718073i	$-0.745024\pi$
$157$	43.0000	−	74.4782i	0.273885	−	0.474383i	0.969853	+	0.243690i	$0.0783578\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	67.8823i		−	0.421629i
$162$		0			0
$163$	−222.000			−1.36196			−0.680982	−	0.732301i	$-0.738447\pi$
$163$	−222.000			−1.36196			−0.680982	+	0.732301i	$0.738447\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−146.969	−	84.8528i	−0.880056	−	0.508101i	−0.00937926	−	0.999956i	$-0.502986\pi$
$167$	−146.969	−	84.8528i	−0.880056	−	0.508101i	−0.870677	+	0.491855i	$0.836319\pi$
$168$		0			0
$169$	34.5000	+	59.7558i	0.204142	+	0.353584i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	161.666	−	93.3381i	0.934487	−	0.539527i	0.0462594	−	0.998929i	$-0.485270\pi$
$173$	161.666	−	93.3381i	0.934487	−	0.539527i	0.888228	+	0.459403i	$0.151937\pi$
$174$		0			0
$175$	−21.0000	+	36.3731i	−0.120000	+	0.207846i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	152.735i		−	0.853269i	−0.904424	−	0.426634i	$-0.859699\pi$
$179$		−	152.735i		−	0.853269i	0.904424	−	0.426634i	$-0.140301\pi$
$180$		0			0
$181$	90.0000			0.497238			0.248619	−	0.968601i	$-0.420023\pi$
$181$	90.0000			0.497238			0.248619	+	0.968601i	$0.420023\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−29.3939	−	16.9706i	−0.158886	−	0.0917328i
$186$		0			0
$187$	−64.0000	−	110.851i	−0.342246	−	0.592787i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	235.151	−	135.765i	1.23116	−	0.710809i	0.263886	−	0.964554i	$-0.414996\pi$
$191$	235.151	−	135.765i	1.23116	−	0.710809i	0.967271	+	0.253745i	$0.0816624\pi$
$192$		0			0
$193$	−1.00000	+	1.73205i	−0.00518135	+	0.00897436i	−0.868604	−	0.495506i	$-0.834983\pi$
$193$	−1.00000	+	1.73205i	−0.00518135	+	0.00897436i	0.863423	+	0.504480i	$0.168316\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			84.8528i			0.430725i	0.976534	+	0.215362i	$0.0690933\pi$
$197$			84.8528i			0.430725i	−0.976534	+	0.215362i	$0.930907\pi$
$198$		0			0
$199$	250.000			1.25628			0.628141	−	0.778100i	$-0.283816\pi$
$199$	250.000			1.25628			0.628141	+	0.778100i	$0.283816\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−88.1816	−	50.9117i	−0.434392	−	0.250796i
$204$		0			0
$205$	96.0000	+	166.277i	0.468293	+	0.811107i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−9.79796	+	5.65685i	−0.0468802	+	0.0270663i
$210$		0			0
$211$	−17.0000	+	29.4449i	−0.0805687	+	0.139549i	−0.903494	−	0.428600i	$-0.859007\pi$
$211$	−17.0000	+	29.4449i	−0.0805687	+	0.139549i	0.822926	+	0.568149i	$0.192340\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	463.862i		−	2.15750i
$216$		0			0
$217$	132.000			0.608295
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−195.959	−	113.137i	−0.886693	−	0.511933i
$222$		0			0
$223$	139.000	+	240.755i	0.623318	+	1.07962i	0.988863	+	0.148825i	$0.0475493\pi$
$223$	139.000	+	240.755i	0.623318	+	1.07962i	−0.365545	+	0.930794i	$0.619117\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−191.060	+	110.309i	−0.841675	+	0.485941i	−0.857833	−	0.513928i	$-0.828190\pi$
$227$	−191.060	+	110.309i	−0.841675	+	0.485941i	0.0161583	+	0.999869i	$0.494856\pi$
$228$		0			0
$229$	−29.0000	+	50.2295i	−0.126638	+	0.219343i	−0.922372	−	0.386303i	$-0.873752\pi$
$229$	−29.0000	+	50.2295i	−0.126638	+	0.219343i	0.795734	+	0.605646i	$0.207085\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	395.980i		−	1.69948i	−0.527199	−	0.849742i	$-0.676758\pi$
$233$		−	395.980i		−	1.69948i	0.527199	−	0.849742i	$-0.323242\pi$
$234$		0			0
$235$	−384.000			−1.63404
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−19.5959	−	11.3137i	−0.0819913	−	0.0473377i	0.458444	−	0.888723i	$-0.348407\pi$
$239$	−19.5959	−	11.3137i	−0.0819913	−	0.0473377i	−0.540435	+	0.841386i	$0.681740\pi$
$240$		0			0
$241$	15.0000	+	25.9808i	0.0622407	+	0.107804i	0.895467	−	0.445129i	$-0.146842\pi$
$241$	15.0000	+	25.9808i	0.0622407	+	0.107804i	−0.833226	+	0.552933i	$0.813509\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	63.6867	−	36.7696i	0.259946	−	0.150080i
$246$		0			0
$247$	−10.0000	+	17.3205i	−0.0404858	+	0.0701235i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			107.480i			0.428208i	0.976811	+	0.214104i	$0.0686832\pi$
$251$			107.480i			0.428208i	−0.976811	+	0.214104i	$0.931317\pi$
$252$		0			0
$253$	64.0000			0.252964
$254$		0			0
$255$		0			0
$256$		0			0
$257$	156.767	+	90.5097i	0.609990	+	0.352178i	0.772961	−	0.634453i	$-0.218775\pi$
$257$	156.767	+	90.5097i	0.609990	+	0.352178i	−0.162972	+	0.986631i	$0.552108\pi$
$258$		0			0
$259$	−18.0000	−	31.1769i	−0.0694981	−	0.120374i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	186.161	−	107.480i	0.707837	−	0.408670i	−0.102422	−	0.994741i	$-0.532659\pi$
$263$	186.161	−	107.480i	0.707837	−	0.408670i	0.810260	+	0.586071i	$0.199326\pi$
$264$		0			0
$265$	−176.000	+	304.841i	−0.664151	+	1.15034i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	401.637i		−	1.49307i	−0.665344	−	0.746537i	$-0.731715\pi$
$269$		−	401.637i		−	1.49307i	0.665344	−	0.746537i	$-0.268285\pi$
$270$		0			0
$271$	266.000			0.981550			0.490775	−	0.871286i	$-0.336714\pi$
$271$	266.000			0.981550			0.490775	+	0.871286i	$0.336714\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−34.2929	−	19.7990i	−0.124701	−	0.0719963i
$276$		0			0
$277$	−173.000	−	299.645i	−0.624549	−	1.08175i	−0.988628	−	0.150382i	$-0.951950\pi$
$277$	−173.000	−	299.645i	−0.624549	−	1.08175i	0.364079	−	0.931368i	$-0.381384\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	107.778	−	62.2254i	0.383550	−	0.221443i	−0.295812	−	0.955246i	$-0.595590\pi$
$281$	107.778	−	62.2254i	0.383550	−	0.221443i	0.679362	+	0.733804i	$0.262257\pi$
$282$		0			0
$283$	23.0000	−	39.8372i	0.0812721	−	0.140767i	−0.822525	−	0.568730i	$-0.807435\pi$
$283$	23.0000	−	39.8372i	0.0812721	−	0.140767i	0.903797	+	0.427962i	$0.140768\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			203.647i			0.709571i
$288$		0			0
$289$	−223.000			−0.771626
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−191.060	−	110.309i	−0.652083	−	0.376480i	0.137171	−	0.990547i	$-0.456199\pi$
$293$	−191.060	−	110.309i	−0.652083	−	0.376480i	−0.789254	+	0.614067i	$0.789532\pi$
$294$		0			0
$295$	208.000	+	360.267i	0.705085	+	1.22124i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	97.9796	−	56.5685i	0.327691	−	0.189192i
$300$		0			0
$301$	246.000	−	426.084i	0.817276	−	1.41556i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			486.489i			1.59505i
$306$		0			0
$307$	−30.0000			−0.0977199			−0.0488599	−	0.998806i	$-0.515559\pi$
$307$	−30.0000			−0.0977199			−0.0488599	+	0.998806i	$0.515559\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	499.696	+	288.500i	1.60674	+	0.927651i	0.990093	+	0.140411i	$0.0448423\pi$
$311$	499.696	+	288.500i	1.60674	+	0.927651i	0.616646	+	0.787241i	$0.288491\pi$
$312$		0			0
$313$	−105.000	−	181.865i	−0.335463	−	0.581039i	0.648110	−	0.761546i	$-0.275560\pi$
$313$	−105.000	−	181.865i	−0.335463	−	0.581039i	−0.983574	+	0.180507i	$0.942226\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−132.272	+	76.3675i	−0.417263	+	0.240907i	−0.693906	−	0.720066i	$-0.744112\pi$
$317$	−132.272	+	76.3675i	−0.417263	+	0.240907i	0.276642	+	0.960973i	$0.410778\pi$
$318$		0			0
$319$	48.0000	−	83.1384i	0.150470	−	0.260622i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			45.2548i			0.140108i
$324$		0			0
$325$	−70.0000			−0.215385
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−352.727	−	203.647i	−1.07212	−	0.618987i
$330$		0			0
$331$	−217.000	−	375.855i	−0.655589	−	1.13551i	−0.981746	−	0.190198i	$-0.939087\pi$
$331$	−217.000	−	375.855i	−0.655589	−	1.13551i	0.326157	−	0.945316i	$-0.394246\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.79796	+	5.65685i	−0.0292476	+	0.0168861i
$336$		0			0
$337$	255.000	−	441.673i	0.756677	−	1.31060i	−0.187860	−	0.982196i	$-0.560155\pi$
$337$	255.000	−	441.673i	0.756677	−	1.31060i	0.944537	−	0.328406i	$-0.106512\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			124.451i			0.364958i
$342$		0			0
$343$	372.000			1.08455
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−132.272	−	76.3675i	−0.381189	−	0.220079i	0.297147	−	0.954832i	$-0.403965\pi$
$347$	−132.272	−	76.3675i	−0.381189	−	0.220079i	−0.678335	+	0.734752i	$0.737298\pi$
$348$		0			0
$349$	−213.000	−	368.927i	−0.610315	−	1.05710i	−0.991187	−	0.132469i	$-0.957709\pi$
$349$	−213.000	−	368.927i	−0.610315	−	1.05710i	0.380872	−	0.924628i	$-0.375624\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−39.1918	+	22.6274i	−0.111025	+	0.0641003i	−0.554484	−	0.832194i	$-0.687084\pi$
$353$	−39.1918	+	22.6274i	−0.111025	+	0.0641003i	0.443459	+	0.896295i	$0.353751\pi$
$354$		0			0
$355$	−352.000	+	609.682i	−0.991549	+	1.71741i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			441.235i			1.22907i	0.788891	+	0.614533i	$0.210655\pi$
$359$			441.235i			1.22907i	−0.788891	+	0.614533i	$0.789345\pi$
$360$		0			0
$361$	−357.000			−0.988920
$362$		0			0
$363$		0			0
$364$		0			0
$365$	401.716	+	231.931i	1.10059	+	0.635427i
$366$		0			0
$367$	283.000	+	490.170i	0.771117	+	1.33561i	0.936951	+	0.349460i	$0.113635\pi$
$367$	283.000	+	490.170i	0.771117	+	1.33561i	−0.165834	+	0.986154i	$0.553032\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−323.333	+	186.676i	−0.871517	+	0.503170i
$372$		0			0
$373$	−109.000	+	188.794i	−0.292225	+	0.506149i	−0.974336	−	0.225100i	$-0.927729\pi$
$373$	−109.000	+	188.794i	−0.292225	+	0.506149i	0.682110	+	0.731249i	$0.261062\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	169.706i		−	0.450148i
$378$		0			0
$379$	−142.000			−0.374670			−0.187335	−	0.982296i	$-0.559985\pi$
$379$	−142.000			−0.374670			−0.187335	+	0.982296i	$0.559985\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$383$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$384$		0			0
$385$	−96.0000	−	166.277i	−0.249351	−	0.431888i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−475.201	+	274.357i	−1.22160	+	0.705289i	−0.965258	−	0.261298i	$-0.915849\pi$
$389$	−475.201	+	274.357i	−1.22160	+	0.705289i	−0.256338	+	0.966587i	$0.582516\pi$
$390$		0			0
$391$	128.000	−	221.703i	0.327366	−	0.567014i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	56.5685i		−	0.143211i
$396$		0			0
$397$	−310.000			−0.780856			−0.390428	−	0.920633i	$-0.627673\pi$
$397$	−310.000			−0.780856			−0.390428	+	0.920633i	$0.627673\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	293.939	+	169.706i	0.733014	+	0.423206i	0.819524	−	0.573045i	$-0.194238\pi$
$401$	293.939	+	169.706i	0.733014	+	0.423206i	−0.0865095	+	0.996251i	$0.527571\pi$
$402$		0			0
$403$	110.000	+	190.526i	0.272953	+	0.472768i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	29.3939	−	16.9706i	0.0722208	−	0.0416967i
$408$		0			0
$409$	135.000	−	233.827i	0.330073	−	0.571704i	−0.652453	−	0.757830i	$-0.726260\pi$
$409$	135.000	−	233.827i	0.330073	−	0.571704i	0.982526	+	0.186126i	$0.0595932\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			441.235i			1.06836i
$414$		0			0
$415$	416.000			1.00241
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−44.0908	−	25.4558i	−0.105229	−	0.0607538i	0.446462	−	0.894803i	$-0.352684\pi$
$419$	−44.0908	−	25.4558i	−0.105229	−	0.0607538i	−0.551691	+	0.834049i	$0.686017\pi$
$420$		0			0
$421$	227.000	+	393.176i	0.539192	+	0.933909i	0.998948	+	0.0458630i	$0.0146038\pi$
$421$	227.000	+	393.176i	0.539192	+	0.933909i	−0.459755	+	0.888046i	$0.652063\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−137.171	+	79.1960i	−0.322756	+	0.186343i
$426$		0			0
$427$	−258.000	+	446.869i	−0.604215	+	1.04653i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	248.902i		−	0.577498i	−0.957405	−	0.288749i	$-0.906761\pi$
$431$		−	248.902i		−	0.577498i	0.957405	−	0.288749i	$-0.0932393\pi$
$432$		0			0
$433$	706.000			1.63048			0.815242	−	0.579120i	$-0.196604\pi$
$433$	706.000			1.63048			0.815242	+	0.579120i	$0.196604\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−19.5959	−	11.3137i	−0.0448419	−	0.0258895i
$438$		0			0
$439$	243.000	+	420.888i	0.553531	+	0.958743i	0.998016	+	0.0629573i	$0.0200532\pi$
$439$	243.000	+	420.888i	0.553531	+	0.958743i	−0.444485	+	0.895786i	$0.646613\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−612.372	+	353.553i	−1.38233	+	0.798089i	−0.992435	−	0.122770i	$-0.960822\pi$
$443$	−612.372	+	353.553i	−1.38233	+	0.798089i	−0.389895	+	0.920859i	$0.627489\pi$
$444$		0			0
$445$	−96.0000	+	166.277i	−0.215730	+	0.373656i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			724.077i			1.61264i	0.591477	+	0.806322i	$0.298545\pi$
$449$			724.077i			1.61264i	−0.591477	+	0.806322i	$0.701455\pi$
$450$		0			0
$451$	−192.000			−0.425721
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−293.939	−	169.706i	−0.646019	−	0.372979i
$456$		0			0
$457$	−169.000	−	292.717i	−0.369803	−	0.640518i	0.619731	−	0.784814i	$-0.287242\pi$
$457$	−169.000	−	292.717i	−0.369803	−	0.640518i	−0.989535	+	0.144296i	$0.953908\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	671.160	−	387.495i	1.45588	−	0.840552i	0.457074	−	0.889429i	$-0.348897\pi$
$461$	671.160	−	387.495i	1.45588	−	0.840552i	0.998805	+	0.0488765i	$0.0155641\pi$
$462$		0			0
$463$	−37.0000	+	64.0859i	−0.0799136	+	0.138414i	−0.903212	−	0.429194i	$-0.858798\pi$
$463$	−37.0000	+	64.0859i	−0.0799136	+	0.138414i	0.823299	+	0.567608i	$0.192131\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			797.616i			1.70796i	0.520307	+	0.853979i	$0.325817\pi$
$467$			797.616i			1.70796i	−0.520307	+	0.853979i	$0.674183\pi$
$468$		0			0
$469$	−12.0000			−0.0255864
$470$		0			0
$471$		0			0
$472$		0			0
$473$	401.716	+	231.931i	0.849295	+	0.490340i
$474$		0			0
$475$	7.00000	+	12.1244i	0.0147368	+	0.0255250i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−274.343	+	158.392i	−0.572741	+	0.330672i	−0.758243	−	0.651972i	$-0.773942\pi$
$479$	−274.343	+	158.392i	−0.572741	+	0.330672i	0.185502	+	0.982644i	$0.440609\pi$
$480$		0			0
$481$	30.0000	−	51.9615i	0.0623701	−	0.108028i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			531.744i			1.09638i
$486$		0			0
$487$	−134.000			−0.275154			−0.137577	−	0.990491i	$-0.543931\pi$
$487$	−134.000			−0.275154			−0.137577	+	0.990491i	$0.543931\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	44.0908	+	25.4558i	0.0897980	+	0.0518449i	0.544227	−	0.838938i	$-0.316823\pi$
$491$	44.0908	+	25.4558i	0.0897980	+	0.0518449i	−0.454429	+	0.890783i	$0.650157\pi$
$492$		0			0
$493$	−192.000	−	332.554i	−0.389452	−	0.674551i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−646.665	+	373.352i	−1.30114	+	0.751212i
$498$		0			0
$499$	15.0000	−	25.9808i	0.0300601	−	0.0520657i	−0.850604	−	0.525807i	$-0.823763\pi$
$499$	15.0000	−	25.9808i	0.0300601	−	0.0520657i	0.880664	+	0.473741i	$0.157097\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			237.588i			0.472342i	0.971712	+	0.236171i	$0.0758925\pi$
$503$			237.588i			0.472342i	−0.971712	+	0.236171i	$0.924107\pi$
$504$		0			0
$505$	−288.000			−0.570297
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−102.879	−	59.3970i	−0.202119	−	0.116693i	0.395524	−	0.918455i	$-0.370563\pi$
$509$	−102.879	−	59.3970i	−0.202119	−	0.116693i	−0.597643	+	0.801762i	$0.703896\pi$
$510$		0			0
$511$	246.000	+	426.084i	0.481409	+	0.833825i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	656.463	−	379.009i	1.27469	−	0.735940i
$516$		0			0
$517$	192.000	−	332.554i	0.371373	−	0.643237i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	79.1960i		−	0.152008i	−0.997108	−	0.0760038i	$-0.975784\pi$
$521$		−	79.1960i		−	0.152008i	0.997108	−	0.0760038i	$-0.0242161\pi$
$522$		0			0
$523$	−494.000			−0.944551			−0.472275	−	0.881451i	$-0.656567\pi$
$523$	−494.000			−0.944551			−0.472275	+	0.881451i	$0.656567\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	431.110	+	248.902i	0.818046	+	0.472299i
$528$		0			0
$529$	−200.500	−	347.276i	−0.379017	−	0.656477i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−293.939	+	169.706i	−0.551480	+	0.318397i
$534$		0			0
$535$	144.000	−	249.415i	0.269159	−	0.466197i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			73.5391i			0.136436i
$540$		0			0
$541$	234.000			0.432532			0.216266	−	0.976334i	$-0.430612\pi$
$541$	234.000			0.432532			0.216266	+	0.976334i	$0.430612\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	48.9898	+	28.2843i	0.0898895	+	0.0518977i
$546$		0			0
$547$	−145.000	−	251.147i	−0.265082	−	0.459136i	0.702503	−	0.711681i	$-0.252066\pi$
$547$	−145.000	−	251.147i	−0.265082	−	0.459136i	−0.967585	+	0.252545i	$0.918732\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−29.3939	+	16.9706i	−0.0533464	+	0.0307996i
$552$		0			0
$553$	30.0000	−	51.9615i	0.0542495	−	0.0939630i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	175.362i		−	0.314834i	−0.987532	−	0.157417i	$-0.949683\pi$
$557$		−	175.362i		−	0.314834i	0.987532	−	0.157417i	$-0.0503167\pi$
$558$		0			0
$559$	820.000			1.46691
$560$		0			0
$561$		0			0
$562$		0			0
$563$	210.656	+	121.622i	0.374167	+	0.216026i	0.675277	−	0.737564i	$-0.264024\pi$
$563$	210.656	+	121.622i	0.374167	+	0.216026i	−0.301110	+	0.953589i	$0.597357\pi$
$564$		0			0
$565$	−192.000	−	332.554i	−0.339823	−	0.588591i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	538.888	−	311.127i	0.947079	−	0.546796i	0.0549064	−	0.998492i	$-0.482514\pi$
$569$	538.888	−	311.127i	0.947079	−	0.546796i	0.892172	+	0.451695i	$0.149181\pi$
$570$		0			0
$571$	−201.000	+	348.142i	−0.352014	+	0.609706i	−0.986602	−	0.163144i	$-0.947836\pi$
$571$	−201.000	+	348.142i	−0.352014	+	0.609706i	0.634588	+	0.772850i	$0.281170\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	79.1960i		−	0.137732i
$576$		0			0
$577$	98.0000			0.169844			0.0849220	−	0.996388i	$-0.472936\pi$
$577$	98.0000			0.169844			0.0849220	+	0.996388i	$0.472936\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	382.120	+	220.617i	0.657694	+	0.379720i
$582$		0			0
$583$	−176.000	−	304.841i	−0.301887	−	0.522883i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−475.201	+	274.357i	−0.809542	+	0.467389i	−0.846797	−	0.531917i	$-0.821472\pi$
$587$	−475.201	+	274.357i	−0.809542	+	0.467389i	0.0372550	+	0.999306i	$0.488139\pi$
$588$		0			0
$589$	22.0000	−	38.1051i	0.0373514	−	0.0646946i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	701.450i		−	1.18288i	−0.806348	−	0.591442i	$-0.798559\pi$
$593$		−	701.450i		−	1.18288i	0.806348	−	0.591442i	$-0.201441\pi$
$594$		0			0
$595$	−768.000			−1.29076
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−558.484	−	322.441i	−0.932360	−	0.538298i	−0.0448028	−	0.998996i	$-0.514266\pi$
$599$	−558.484	−	322.441i	−0.932360	−	0.538298i	−0.887557	+	0.460698i	$0.847599\pi$
$600$		0			0
$601$	199.000	+	344.678i	0.331115	+	0.573508i	0.982731	−	0.185041i	$-0.0592419\pi$
$601$	199.000	+	344.678i	0.331115	+	0.573508i	−0.651616	+	0.758549i	$0.725909\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−436.009	+	251.730i	−0.720676	+	0.416083i
$606$		0			0
$607$	−85.0000	+	147.224i	−0.140033	+	0.242544i	−0.927509	−	0.373801i	$-0.878054\pi$
$607$	−85.0000	+	147.224i	−0.140033	+	0.242544i	0.787476	+	0.616346i	$0.211388\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	678.823i		−	1.11100i
$612$		0			0
$613$	−1030.00			−1.68026			−0.840131	−	0.542384i	$-0.817522\pi$
$613$	−1030.00			−1.68026			−0.840131	+	0.542384i	$0.817522\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−911.210	−	526.087i	−1.47684	−	0.852654i	−0.477182	−	0.878805i	$-0.658342\pi$
$617$	−911.210	−	526.087i	−1.47684	−	0.852654i	−0.999658	+	0.0261507i	$0.991675\pi$
$618$		0			0
$619$	7.00000	+	12.1244i	0.0113086	+	0.0195870i	0.871624	−	0.490175i	$-0.163067\pi$
$619$	7.00000	+	12.1244i	0.0113086	+	0.0195870i	−0.860316	+	0.509762i	$0.829734\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−176.363	+	101.823i	−0.283087	+	0.163440i
$624$		0			0
$625$	375.500	−	650.385i	0.600800	−	1.04062i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	135.765i		−	0.215842i
$630$		0			0
$631$	1114.00			1.76545			0.882726	−	0.469888i	$-0.155706\pi$
$631$	1114.00			1.76545			0.882726	+	0.469888i	$0.155706\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	519.292	+	299.813i	0.817782	+	0.472147i
$636$		0			0
$637$	65.0000	+	112.583i	0.102041	+	0.176740i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	391.918	−	226.274i	0.611417	−	0.353002i	−0.162103	−	0.986774i	$-0.551828\pi$
$641$	391.918	−	226.274i	0.611417	−	0.353002i	0.773520	+	0.633772i	$0.218494\pi$
$642$		0			0
$643$	399.000	−	691.088i	0.620529	−	1.07479i	−0.368859	−	0.929486i	$-0.620251\pi$
$643$	399.000	−	691.088i	0.620529	−	1.07479i	0.989387	−	0.145302i	$-0.0464153\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	147.078i		−	0.227323i	−0.993520	−	0.113662i	$-0.963742\pi$
$647$		−	147.078i		−	0.227323i	0.993520	−	0.113662i	$-0.0362580\pi$
$648$		0			0
$649$	−416.000			−0.640986
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−279.242	−	161.220i	−0.427629	−	0.246892i	0.270707	−	0.962662i	$-0.412743\pi$
$653$	−279.242	−	161.220i	−0.427629	−	0.246892i	−0.698336	+	0.715770i	$0.746076\pi$
$654$		0			0
$655$	−16.0000	−	27.7128i	−0.0244275	−	0.0423096i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	690.756	−	398.808i	1.04819	−	0.605172i	0.126047	−	0.992024i	$-0.459771\pi$
$659$	690.756	−	398.808i	1.04819	−	0.605172i	0.922142	+	0.386852i	$0.126438\pi$
$660$		0			0
$661$	−493.000	+	853.901i	−0.745840	+	1.29183i	0.203962	+	0.978979i	$0.434618\pi$
$661$	−493.000	+	853.901i	−0.745840	+	1.29183i	−0.949801	+	0.312853i	$0.898715\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			67.8823i			0.102079i
$666$		0			0
$667$	192.000			0.287856
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−421.312	−	243.245i	−0.627887	−	0.362511i
$672$		0			0
$673$	−17.0000	−	29.4449i	−0.0252600	−	0.0437517i	0.853119	−	0.521716i	$-0.174708\pi$
$673$	−17.0000	−	29.4449i	−0.0252600	−	0.0437517i	−0.878379	+	0.477965i	$0.841375\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	347.828	−	200.818i	0.513778	−	0.296630i	−0.220607	−	0.975363i	$-0.570804\pi$
$677$	347.828	−	200.818i	0.513778	−	0.296630i	0.734385	+	0.678733i	$0.237471\pi$
$678$		0			0
$679$	−282.000	+	488.438i	−0.415317	+	0.719350i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			130.108i			0.190494i	0.995454	+	0.0952472i	$0.0303641\pi$
$683$			130.108i			0.190494i	−0.995454	+	0.0952472i	$0.969636\pi$
$684$		0			0
$685$	576.000			0.840876
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−538.888	−	311.127i	−0.782130	−	0.451563i
$690$		0			0
$691$	−289.000	−	500.563i	−0.418234	−	0.724403i	0.577528	−	0.816371i	$-0.304018\pi$
$691$	−289.000	−	500.563i	−0.418234	−	0.724403i	−0.995762	+	0.0919679i	$0.970684\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	382.120	−	220.617i	0.549814	−	0.317435i
$696$		0			0
$697$	−384.000	+	665.108i	−0.550933	+	0.954243i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	1238.85i		−	1.76726i	−0.468183	−	0.883631i	$-0.655091\pi$
$701$		−	1238.85i		−	1.76726i	0.468183	−	0.883631i	$-0.344909\pi$
$702$		0			0
$703$	−12.0000			−0.0170697
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−264.545	−	152.735i	−0.374179	−	0.216033i
$708$		0			0
$709$	611.000	+	1058.28i	0.861777	+	1.49264i	0.870212	+	0.492677i	$0.163982\pi$
$709$	611.000	+	1058.28i	0.861777	+	1.49264i	−0.00843489	+	0.999964i	$0.502685\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−215.555	+	124.451i	−0.302321	+	0.174545i
$714$		0			0
$715$	160.000	−	277.128i	0.223776	−	0.387592i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			248.902i			0.346177i	0.984906	+	0.173089i	$0.0553747\pi$
$719$			248.902i			0.346177i	−0.984906	+	0.173089i	$0.944625\pi$
$720$		0			0
$721$	804.000			1.11512
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−102.879	−	59.3970i	−0.141901	−	0.0819269i
$726$		0			0
$727$	435.000	+	753.442i	0.598349	+	1.03637i	0.993065	+	0.117568i	$0.0375098\pi$
$727$	435.000	+	753.442i	0.598349	+	1.03637i	−0.394715	+	0.918803i	$0.629157\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1606.87	−	927.724i	2.19817	−	1.26912i
$732$		0			0
$733$	107.000	−	185.329i	0.145975	−	0.252837i	−0.783761	−	0.621063i	$-0.786701\pi$
$733$	107.000	−	185.329i	0.145975	−	0.252837i	0.929736	+	0.368226i	$0.120035\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	11.3137i		−	0.0153510i
$738$		0			0
$739$	−958.000			−1.29635			−0.648173	−	0.761493i	$-0.724467\pi$
$739$	−958.000			−1.29635			−0.648173	+	0.761493i	$0.724467\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	872.018	+	503.460i	1.17365	+	0.677604i	0.954536	−	0.298096i	$-0.0963516\pi$
$743$	872.018	+	503.460i	1.17365	+	0.677604i	0.219109	+	0.975700i	$0.429685\pi$
$744$		0			0
$745$	464.000	+	803.672i	0.622819	+	1.07875i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	264.545	−	152.735i	0.353197	−	0.203919i
$750$		0			0
$751$	315.000	−	545.596i	0.419441	−	0.726493i	−0.576443	−	0.817138i	$-0.695560\pi$
$751$	315.000	−	545.596i	0.419441	−	0.726493i	0.995883	+	0.0906450i	$0.0288929\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	1233.19i		−	1.63337i
$756$		0			0
$757$	602.000			0.795244			0.397622	−	0.917549i	$-0.369835\pi$
$757$	602.000			0.795244			0.397622	+	0.917549i	$0.369835\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	950.402	+	548.715i	1.24889	+	0.721044i	0.970887	−	0.239537i	$-0.0769956\pi$
$761$	950.402	+	548.715i	1.24889	+	0.721044i	0.277998	+	0.960582i	$0.410329\pi$
$762$		0			0
$763$	30.0000	+	51.9615i	0.0393185	+	0.0681016i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−636.867	+	367.696i	−0.830336	+	0.479394i
$768$		0			0
$769$	−385.000	+	666.840i	−0.500650	+	0.867152i	0.499350	+	0.866401i	$0.333572\pi$
$769$	−385.000	+	666.840i	−0.500650	+	0.867152i	−1.00000		0.000750943i	$0.999761\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	186.676i		−	0.241496i	−0.992683	−	0.120748i	$-0.961471\pi$
$773$		−	186.676i		−	0.241496i	0.992683	−	0.120748i	$-0.0385293\pi$
$774$		0			0
$775$	154.000			0.198710
$776$		0			0
$777$		0			0
$778$		0			0
$779$	58.7878	+	33.9411i	0.0754657	+	0.0435701i
$780$		0			0
$781$	−352.000	−	609.682i	−0.450704	−	0.780643i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	421.312	−	243.245i	0.536703	−	0.309866i
$786$		0			0
$787$	−257.000	+	445.137i	−0.326557	+	0.565613i	−0.981826	−	0.189783i	$-0.939222\pi$
$787$	−257.000	+	445.137i	−0.326557	+	0.565613i	0.655270	+	0.755395i	$0.272555\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	407.294i		−	0.514910i
$792$		0			0
$793$	−860.000			−1.08449
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−612.372	−	353.553i	−0.768347	−	0.443605i	0.0639377	−	0.997954i	$-0.479634\pi$
$797$	−612.372	−	353.553i	−0.768347	−	0.443605i	−0.832285	+	0.554349i	$0.812967\pi$
$798$		0			0
$799$	−768.000	−	1330.22i	−0.961202	−	1.66485i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−401.716	+	231.931i	−0.500269	+	0.288831i
$804$		0			0
$805$	192.000	−	332.554i	0.238509	−	0.413110i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	758.018i		−	0.936982i	−0.883468	−	0.468491i	$-0.844798\pi$
$809$		−	758.018i		−	0.936982i	0.883468	−	0.468491i	$-0.155202\pi$
$810$		0			0
$811$	−1454.00			−1.79285			−0.896424	−	0.443197i	$-0.853844\pi$
$811$	−1454.00			−1.79285			−0.896424	+	0.443197i	$0.853844\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1087.57	−	627.911i	−1.33445	−	0.770443i
$816$		0			0
$817$	−82.0000	−	142.028i	−0.100367	−	0.173841i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	837.725	−	483.661i	1.02037	−	0.589112i	0.106160	−	0.994349i	$-0.466144\pi$
$821$	837.725	−	483.661i	1.02037	−	0.589112i	0.914212	+	0.405237i	$0.132811\pi$
$822$		0			0
$823$	83.0000	−	143.760i	0.100851	−	0.174678i	−0.811185	−	0.584790i	$-0.801177\pi$
$823$	83.0000	−	143.760i	0.100851	−	0.174678i	0.912035	+	0.410112i	$0.134510\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	978.636i		−	1.18336i	−0.806174	−	0.591678i	$-0.798466\pi$
$827$		−	978.636i		−	1.18336i	0.806174	−	0.591678i	$-0.201534\pi$
$828$		0			0
$829$	1258.00			1.51749			0.758745	−	0.651387i	$-0.225813\pi$
$829$	1258.00			1.51749			0.758745	+	0.651387i	$0.225813\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	254.747	+	147.078i	0.305819	+	0.176564i
$834$		0			0
$835$	−480.000	−	831.384i	−0.574850	−	0.995670i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1146.36	+	661.852i	−1.36634	+	0.788858i	−0.990459	−	0.137809i	$-0.955994\pi$
$839$	−1146.36	+	661.852i	−1.36634	+	0.788858i	−0.375883	+	0.926667i	$0.622661\pi$
$840$		0			0
$841$	−276.500	+	478.912i	−0.328775	+	0.569455i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			390.323i			0.461921i
$846$		0			0
$847$	−534.000			−0.630460
$848$		0			0
$849$		0			0
$850$		0			0
$851$	58.7878	+	33.9411i	0.0690808	+	0.0398838i
$852$		0			0
$853$	371.000	+	642.591i	0.434936	+	0.753330i	0.997290	−	0.0735656i	$-0.0234378\pi$
$853$	371.000	+	642.591i	0.434936	+	0.753330i	−0.562355	+	0.826896i	$0.690104\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−205.757	+	118.794i	−0.240090	+	0.138616i	−0.615218	−	0.788357i	$-0.710932\pi$
$857$	−205.757	+	118.794i	−0.240090	+	0.138616i	0.375128	+	0.926973i	$0.377599\pi$
$858$		0			0
$859$	615.000	−	1065.21i	0.715949	−	1.24006i	−0.246644	−	0.969106i	$-0.579328\pi$
$859$	615.000	−	1065.21i	0.715949	−	1.24006i	0.962592	−	0.270953i	$-0.0873389\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			45.2548i			0.0524390i	0.999656	+	0.0262195i	$0.00834688\pi$
$863$			45.2548i			0.0524390i	−0.999656	+	0.0262195i	$0.991653\pi$
$864$		0			0
$865$	1056.00			1.22081
$866$		0			0
$867$		0			0
$868$		0			0
$869$	48.9898	+	28.2843i	0.0563749	+	0.0325481i
$870$		0			0
$871$	−10.0000	−	17.3205i	−0.0114811	−	0.0198858i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	529.090	−	305.470i	0.604674	−	0.349109i
$876$		0			0
$877$	411.000	−	711.873i	0.468643	−	0.811714i	−0.530715	−	0.847551i	$-0.678076\pi$
$877$	411.000	−	711.873i	0.468643	−	0.811714i	0.999358	+	0.0358370i	$0.0114097\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	656.195i		−	0.744830i	−0.928066	−	0.372415i	$-0.878530\pi$
$881$		−	656.195i		−	0.744830i	0.928066	−	0.372415i	$-0.121470\pi$
$882$		0			0
$883$	962.000			1.08947			0.544734	−	0.838609i	$-0.316631\pi$
$883$	962.000			1.08947			0.544734	+	0.838609i	$0.316631\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−989.594	−	571.342i	−1.11566	−	0.644129i	−0.175373	−	0.984502i	$-0.556113\pi$
$887$	−989.594	−	571.342i	−1.11566	−	0.644129i	−0.940290	+	0.340373i	$0.889447\pi$
$888$		0			0
$889$	318.000	+	550.792i	0.357705	+	0.619564i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−117.576	+	67.8823i	−0.131664	+	0.0760160i
$894$		0			0
$895$	432.000	−	748.246i	0.482682	−	0.836029i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			373.352i			0.415297i
$900$		0			0
$901$	−1408.00			−1.56271
$902$		0			0
$903$		0			0
$904$		0			0
$905$	440.908	+	254.558i	0.487191	+	0.281280i
$906$		0			0
$907$	−521.000	−	902.398i	−0.574421	−	0.994927i	−0.996104	−	0.0881834i	$-0.971894\pi$
$907$	−521.000	−	902.398i	−0.574421	−	0.994927i	0.421683	−	0.906743i	$-0.361439\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1391.31	−	803.273i	1.52723	−	0.881749i	0.527758	−	0.849395i	$-0.323033\pi$
$911$	1391.31	−	803.273i	1.52723	−	0.881749i	0.999476	−	0.0323539i	$-0.0103004\pi$
$912$		0			0
$913$	−208.000	+	360.267i	−0.227820	+	0.394596i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	33.9411i		−	0.0370132i
$918$		0			0
$919$	−614.000			−0.668118			−0.334059	−	0.942552i	$-0.608418\pi$
$919$	−614.000			−0.668118			−0.334059	+	0.942552i	$0.608418\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1077.78	−	622.254i	−1.16769	−	0.674165i
$924$		0			0
$925$	−21.0000	−	36.3731i	−0.0227027	−	0.0393222i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−39.1918	+	22.6274i	−0.0421871	+	0.0243567i	−0.520945	−	0.853590i	$-0.674420\pi$
$929$	−39.1918	+	22.6274i	−0.0421871	+	0.0243567i	0.478758	+	0.877947i	$0.341087\pi$
$930$		0			0
$931$	13.0000	−	22.5167i	0.0139635	−	0.0241855i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	724.077i		−	0.774414i
$936$		0			0
$937$	−462.000			−0.493063			−0.246531	−	0.969135i	$-0.579291\pi$
$937$	−462.000			−0.493063			−0.246531	+	0.969135i	$0.579291\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	308.636	+	178.191i	0.327987	+	0.189363i	0.654947	−	0.755675i	$-0.272691\pi$
$941$	308.636	+	178.191i	0.327987	+	0.189363i	−0.326960	+	0.945038i	$0.606024\pi$
$942$		0			0
$943$	−192.000	−	332.554i	−0.203606	−	0.352655i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−602.574	+	347.897i	−0.636298	+	0.367367i	−0.783187	−	0.621786i	$-0.786407\pi$
$947$	−602.574	+	347.897i	−0.636298	+	0.367367i	0.146889	+	0.989153i	$0.453074\pi$
$948$		0			0
$949$	−410.000	+	710.141i	−0.432034	+	0.748304i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			1527.35i			1.60268i	0.598212	+	0.801338i	$0.295878\pi$
$953$			1527.35i			1.60268i	−0.598212	+	0.801338i	$0.704122\pi$
$954$		0			0
$955$	1536.00			1.60838
$956$		0			0
$957$		0			0
$958$		0			0
$959$	529.090	+	305.470i	0.551710	+	0.318530i
$960$		0			0
$961$	238.500	+	413.094i	0.248179	+	0.429859i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−9.79796	+	5.65685i	−0.0101533	+	0.00586203i
$966$		0			0
$967$	35.0000	−	60.6218i	0.0361944	−	0.0626906i	−0.847361	−	0.531018i	$-0.821810\pi$
$967$	35.0000	−	60.6218i	0.0361944	−	0.0626906i	0.883555	+	0.468327i	$0.155143\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			627.911i			0.646664i	0.946286	+	0.323332i	$0.104803\pi$
$971$			627.911i			0.646664i	−0.946286	+	0.323332i	$0.895197\pi$
$972$		0			0
$973$	468.000			0.480987
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−881.816	−	509.117i	−0.902576	−	0.521102i	−0.0245406	−	0.999699i	$-0.507812\pi$
$977$	−881.816	−	509.117i	−0.902576	−	0.521102i	−0.878035	+	0.478597i	$0.841146\pi$
$978$		0			0
$979$	−96.0000	−	166.277i	−0.0980592	−	0.169844i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	558.484	−	322.441i	0.568142	−	0.328017i	−0.188265	−	0.982118i	$-0.560286\pi$
$983$	558.484	−	322.441i	0.568142	−	0.328017i	0.756407	+	0.654101i	$0.226953\pi$
$984$		0			0
$985$	−240.000	+	415.692i	−0.243655	+	0.422023i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			927.724i			0.938043i
$990$		0			0
$991$	−854.000			−0.861756			−0.430878	−	0.902410i	$-0.641796\pi$
$991$	−854.000			−0.861756			−0.430878	+	0.902410i	$0.641796\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1224.74	+	707.107i	1.23090	+	0.710660i
$996$		0			0
$997$	259.000	+	448.601i	0.259779	+	0.449951i	0.966183	−	0.257858i	$-0.0830168\pi$
$997$	259.000	+	448.601i	0.259779	+	0.449951i	−0.706403	+	0.707810i	$0.749684\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.3.m.d.377.2		4
3.2	odd	2	inner	648.3.m.d.377.1		4
4.3	odd	2		1296.3.q.e.1025.2		4
9.2	odd	6	inner	648.3.m.d.593.2		4
9.4	even	3		24.3.e.a.17.2	yes	2
9.5	odd	6		24.3.e.a.17.1	✓	2
9.7	even	3	inner	648.3.m.d.593.1		4
12.11	even	2		1296.3.q.e.1025.1		4
36.7	odd	6		1296.3.q.e.593.1		4
36.11	even	6		1296.3.q.e.593.2		4
36.23	even	6		48.3.e.b.17.2		2
36.31	odd	6		48.3.e.b.17.1		2
45.4	even	6		600.3.l.b.401.1		2
45.13	odd	12		600.3.c.a.449.2		4
45.14	odd	6		600.3.l.b.401.2		2
45.22	odd	12		600.3.c.a.449.3		4
45.23	even	12		600.3.c.a.449.4		4
45.32	even	12		600.3.c.a.449.1		4
63.13	odd	6		1176.3.d.a.785.1		2
63.41	even	6		1176.3.d.a.785.2		2
72.5	odd	6		192.3.e.c.65.2		2
72.13	even	6		192.3.e.c.65.1		2
72.59	even	6		192.3.e.d.65.1		2
72.67	odd	6		192.3.e.d.65.2		2
144.5	odd	12		768.3.h.d.641.1		4
144.13	even	12		768.3.h.d.641.2		4
144.59	even	12		768.3.h.c.641.4		4
144.67	odd	12		768.3.h.c.641.3		4
144.77	odd	12		768.3.h.d.641.4		4
144.85	even	12		768.3.h.d.641.3		4
144.131	even	12		768.3.h.c.641.1		4
144.139	odd	12		768.3.h.c.641.2		4
180.23	odd	12		1200.3.c.i.449.1		4
180.59	even	6		1200.3.l.n.401.1		2
180.67	even	12		1200.3.c.i.449.2		4
180.103	even	12		1200.3.c.i.449.3		4
180.139	odd	6		1200.3.l.n.401.2		2
180.167	odd	12		1200.3.c.i.449.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.3.e.a.17.1	✓	2	9.5	odd	6
24.3.e.a.17.2	yes	2	9.4	even	3
48.3.e.b.17.1		2	36.31	odd	6
48.3.e.b.17.2		2	36.23	even	6
192.3.e.c.65.1		2	72.13	even	6
192.3.e.c.65.2		2	72.5	odd	6
192.3.e.d.65.1		2	72.59	even	6
192.3.e.d.65.2		2	72.67	odd	6
600.3.c.a.449.1		4	45.32	even	12
600.3.c.a.449.2		4	45.13	odd	12
600.3.c.a.449.3		4	45.22	odd	12
600.3.c.a.449.4		4	45.23	even	12
600.3.l.b.401.1		2	45.4	even	6
600.3.l.b.401.2		2	45.14	odd	6
648.3.m.d.377.1		4	3.2	odd	2	inner
648.3.m.d.377.2		4	1.1	even	1	trivial
648.3.m.d.593.1		4	9.7	even	3	inner
648.3.m.d.593.2		4	9.2	odd	6	inner
768.3.h.c.641.1		4	144.131	even	12
768.3.h.c.641.2		4	144.139	odd	12
768.3.h.c.641.3		4	144.67	odd	12
768.3.h.c.641.4		4	144.59	even	12
768.3.h.d.641.1		4	144.5	odd	12
768.3.h.d.641.2		4	144.13	even	12
768.3.h.d.641.3		4	144.85	even	12
768.3.h.d.641.4		4	144.77	odd	12
1176.3.d.a.785.1		2	63.13	odd	6
1176.3.d.a.785.2		2	63.41	even	6
1200.3.c.i.449.1		4	180.23	odd	12
1200.3.c.i.449.2		4	180.67	even	12
1200.3.c.i.449.3		4	180.103	even	12
1200.3.c.i.449.4		4	180.167	odd	12
1200.3.l.n.401.1		2	180.59	even	6
1200.3.l.n.401.2		2	180.139	odd	6
1296.3.q.e.593.1		4	36.7	odd	6
1296.3.q.e.593.2		4	36.11	even	6
1296.3.q.e.1025.1		4	12.11	even	2
1296.3.q.e.1025.2		4	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	648.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 + 2.82843i) q^{5} +(3.00000 + 5.19615i) q^{7} +(-4.89898 + 2.82843i) q^{11} +(-5.00000 + 8.66025i) q^{13} +22.6274i q^{17} +2.00000 q^{19} +(-9.79796 - 5.65685i) q^{23} +(3.50000 + 6.06218i) q^{25} +(-14.6969 + 8.48528i) q^{29} +(11.0000 - 19.0526i) q^{31} +33.9411i q^{35} -6.00000 q^{37} +(29.3939 + 16.9706i) q^{41} +(-41.0000 - 71.0141i) q^{43} +(-58.7878 + 33.9411i) q^{47} +(6.50000 - 11.2583i) q^{49} +62.2254i q^{53} -32.0000 q^{55} +(63.6867 + 36.7696i) q^{59} +(43.0000 + 74.4782i) q^{61} +(-48.9898 + 28.2843i) q^{65} +(-1.00000 + 1.73205i) q^{67} +124.451i q^{71} +82.0000 q^{73} +(-29.3939 - 16.9706i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(63.6867 - 36.7696i) q^{83} +(-64.0000 + 110.851i) q^{85} +33.9411i q^{89} -60.0000 q^{91} +(9.79796 + 5.65685i) q^{95} +(47.0000 + 81.4064i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{7} - 20 q^{13} + 8 q^{19} + 14 q^{25} + 44 q^{31} - 24 q^{37} - 164 q^{43} + 26 q^{49} - 128 q^{55} + 172 q^{61} - 4 q^{67} + 328 q^{73} - 20 q^{79} - 256 q^{85} - 240 q^{91} + 188 q^{97}+O(q^{100}) \) 4 * q + 12 * q^7 - 20 * q^13 + 8 * q^19 + 14 * q^25 + 44 * q^31 - 24 * q^37 - 164 * q^43 + 26 * q^49 - 128 * q^55 + 172 * q^61 - 4 * q^67 + 328 * q^73 - 20 * q^79 - 256 * q^85 - 240 * q^91 + 188 * q^97

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