LMFDB - Embedded newform 2592.2.p.f.431.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2592,2,Mod(431,2592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("2592.431");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$20.6972242039$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.534694406811304329216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.7
Root			$0.841995 - 1.13624i$ of defining polynomial
Character	$\chi$	$=$	2592.431
Dual form			2592.2.p.f.2159.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53819 + 2.66422i) q^{5} +(-3.45632 - 1.99551i) q^{7} +O(q^{10})$	$q+(1.53819 + 2.66422i) q^{5} +(-3.45632 - 1.99551i) q^{7} +(1.64492 + 0.949697i) q^{11} +(-0.926118 + 0.534695i) q^{13} -7.08863i q^{17} -3.73205 q^{19} +(0.412157 + 0.713876i) q^{23} +(-2.23205 + 3.86603i) q^{25} +(-2.25207 + 3.90069i) q^{29} +(-5.06040 + 2.92163i) q^{31} -12.2779i q^{35} -6.91264i q^{37} +(-3.28985 + 1.89939i) q^{41} +(1.00000 - 1.73205i) q^{43} +(3.48853 - 6.04232i) q^{47} +(4.46410 + 7.73205i) q^{49} -10.6569 q^{53} +5.84325i q^{55} +(-1.64492 + 0.949697i) q^{59} +(-0.926118 - 0.534695i) q^{61} +(-2.84909 - 1.64492i) q^{65} +(-4.59808 - 7.96410i) q^{67} -10.6569 q^{71} +5.92820 q^{73} +(-3.79025 - 6.56491i) q^{77} +(5.30856 + 3.06490i) q^{79} +(-8.98803 - 5.18924i) q^{83} +(18.8857 - 10.9037i) q^{85} -13.6683i q^{89} +4.26795 q^{91} +(-5.74060 - 9.94301i) q^{95} +(5.69615 - 9.86603i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 32 q^{19} - 8 q^{25} + 16 q^{43} + 16 q^{49} - 32 q^{67} - 16 q^{73} + 96 q^{91} + 8 q^{97}+O(q^{100}) $ 16 * q - 32 * q^19 - 8 * q^25 + 16 * q^43 + 16 * q^49 - 32 * q^67 - 16 * q^73 + 96 * q^91 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.53819	+	2.66422i	0.687899	+	1.19148i	0.972516	+	0.232835i	$0.0748002\pi$
$5$	1.53819	+	2.66422i	0.687899	+	1.19148i	−0.284617	+	0.958641i	$0.591867\pi$
$6$		0			0
$7$	−3.45632	−	1.99551i	−1.30637	−	0.754231i	−0.324879	−	0.945756i	$-0.605323\pi$
$7$	−3.45632	−	1.99551i	−1.30637	−	0.754231i	−0.981488	+	0.191525i	$0.938657\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.64492	+	0.949697i	0.495963	+	0.286344i	0.727045	−	0.686590i	$-0.240893\pi$
$11$	1.64492	+	0.949697i	0.495963	+	0.286344i	−0.231082	+	0.972934i	$0.574227\pi$
$12$		0			0
$13$	−0.926118	+	0.534695i	−0.256859	+	0.148298i	−0.622901	−	0.782301i	$-0.714046\pi$
$13$	−0.926118	+	0.534695i	−0.256859	+	0.148298i	0.366042	+	0.930598i	$0.380713\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	7.08863i		−	1.71925i	−0.510929	−	0.859623i	$-0.670698\pi$
$17$		−	7.08863i		−	1.71925i	0.510929	−	0.859623i	$-0.329302\pi$
$18$		0			0
$19$	−3.73205			−0.856191			−0.428096	−	0.903733i	$-0.640815\pi$
$19$	−3.73205			−0.856191			−0.428096	+	0.903733i	$0.640815\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.412157	+	0.713876i	0.0859406	+	0.148853i	0.905792	−	0.423723i	$-0.139277\pi$
$23$	0.412157	+	0.713876i	0.0859406	+	0.148853i	−0.819851	+	0.572577i	$0.805944\pi$
$24$		0			0
$25$	−2.23205	+	3.86603i	−0.446410	+	0.773205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.25207	+	3.90069i	−0.418198	+	0.724340i	−0.995758	−	0.0920079i	$-0.970672\pi$
$29$	−2.25207	+	3.90069i	−0.418198	+	0.724340i	0.577560	+	0.816348i	$0.304005\pi$
$30$		0			0
$31$	−5.06040	+	2.92163i	−0.908876	+	0.524740i	−0.880069	−	0.474845i	$-0.842504\pi$
$31$	−5.06040	+	2.92163i	−0.908876	+	0.524740i	−0.0288063	+	0.999585i	$0.509171\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	12.2779i		−	2.07534i
$36$		0			0
$37$		−	6.91264i		−	1.13643i	−0.822880	−	0.568216i	$-0.807634\pi$
$37$		−	6.91264i		−	1.13643i	0.822880	−	0.568216i	$-0.192366\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.28985	+	1.89939i	−0.513788	+	0.296635i	−0.734389	−	0.678729i	$-0.762531\pi$
$41$	−3.28985	+	1.89939i	−0.513788	+	0.296635i	0.220602	+	0.975364i	$0.429198\pi$
$42$		0			0
$43$	1.00000	−	1.73205i	0.152499	−	0.264135i	−0.779647	−	0.626219i	$-0.784601\pi$
$43$	1.00000	−	1.73205i	0.152499	−	0.264135i	0.932145	+	0.362084i	$0.117935\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.48853	−	6.04232i	0.508855	−	0.881363i	−0.491092	−	0.871108i	$-0.663402\pi$
$47$	3.48853	−	6.04232i	0.508855	−	0.881363i	0.999947	−	0.0102553i	$-0.00326442\pi$
$48$		0			0
$49$	4.46410	+	7.73205i	0.637729	+	1.10458i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−10.6569			−1.46384			−0.731918	−	0.681393i	$-0.761375\pi$
$53$	−10.6569			−1.46384			−0.731918	+	0.681393i	$0.761375\pi$
$54$		0			0
$55$			5.84325i			0.787904i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.64492	+	0.949697i	−0.214151	+	0.123640i	−0.603239	−	0.797561i	$-0.706123\pi$
$59$	−1.64492	+	0.949697i	−0.214151	+	0.123640i	0.389088	+	0.921201i	$0.372790\pi$
$60$		0			0
$61$	−0.926118	−	0.534695i	−0.118577	−	0.0684606i	0.439538	−	0.898224i	$-0.355142\pi$
$61$	−0.926118	−	0.534695i	−0.118577	−	0.0684606i	−0.558116	+	0.829763i	$0.688475\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.84909	−	1.64492i	−0.353386	−	0.204028i
$66$		0			0
$67$	−4.59808	−	7.96410i	−0.561744	−	0.972970i	−0.997344	−	0.0728295i	$-0.976797\pi$
$67$	−4.59808	−	7.96410i	−0.561744	−	0.972970i	0.435600	−	0.900140i	$-0.356536\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−10.6569			−1.26474			−0.632370	−	0.774667i	$-0.717918\pi$
$71$	−10.6569			−1.26474			−0.632370	+	0.774667i	$0.717918\pi$
$72$		0			0
$73$	5.92820			0.693844			0.346922	−	0.937894i	$-0.387227\pi$
$73$	5.92820			0.693844			0.346922	+	0.937894i	$0.387227\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.79025	−	6.56491i	−0.431940	−	0.748141i
$78$		0			0
$79$	5.30856	+	3.06490i	0.597259	+	0.344828i	0.767963	−	0.640495i	$-0.221271\pi$
$79$	5.30856	+	3.06490i	0.597259	+	0.344828i	−0.170703	+	0.985322i	$0.554604\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.98803	−	5.18924i	−0.986564	−	0.569593i	−0.0823186	−	0.996606i	$-0.526232\pi$
$83$	−8.98803	−	5.18924i	−0.986564	−	0.569593i	−0.904245	+	0.427013i	$0.859566\pi$
$84$		0			0
$85$	18.8857	−	10.9037i	2.04844	−	1.18267i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	13.6683i		−	1.44884i	−0.689359	−	0.724420i	$-0.742108\pi$
$89$		−	13.6683i		−	1.44884i	0.689359	−	0.724420i	$-0.257892\pi$
$90$		0			0
$91$	4.26795			0.447403
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−5.74060	−	9.94301i	−0.588973	−	1.02013i
$96$		0			0
$97$	5.69615	−	9.86603i	0.578357	−	1.00174i	−0.417311	−	0.908764i	$-0.637028\pi$
$97$	5.69615	−	9.86603i	0.578357	−	1.00174i	0.995668	−	0.0929795i	$-0.0296391\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.07638	−	5.32844i	0.306111	−	0.530200i	−0.671397	−	0.741098i	$-0.734305\pi$
$101$	3.07638	−	5.32844i	0.306111	−	0.530200i	0.977508	+	0.210898i	$0.0676388\pi$
$102$		0			0
$103$	−3.45632	+	1.99551i	−0.340561	+	0.196623i	−0.660520	−	0.750808i	$-0.729664\pi$
$103$	−3.45632	+	1.99551i	−0.340561	+	0.196623i	0.319959	+	0.947431i	$0.396331\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	8.47908i		−	0.819704i	−0.912152	−	0.409852i	$-0.865580\pi$
$107$		−	8.47908i		−	0.819704i	0.912152	−	0.409852i	$-0.134420\pi$
$108$		0			0
$109$			10.1208i			0.969398i	0.874681	+	0.484699i	$0.161071\pi$
$109$			10.1208i			0.969398i	−0.874681	+	0.484699i	$0.838929\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.42878	−	5.44371i	0.886985	−	0.512101i	0.0140300	−	0.999902i	$-0.495534\pi$
$113$	9.42878	−	5.44371i	0.886985	−	0.512101i	0.872955	+	0.487800i	$0.162201\pi$
$114$		0			0
$115$	−1.26795	+	2.19615i	−0.118237	+	0.204792i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−14.1454	+	24.5006i	−1.29671	+	2.24597i
$120$		0			0
$121$	−3.69615	−	6.40192i	−0.336014	−	0.581993i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.64863			0.147458
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.98803	−	5.18924i	0.785287	−	0.453386i	−0.0530134	−	0.998594i	$-0.516883\pi$
$131$	8.98803	−	5.18924i	0.785287	−	0.453386i	0.838301	+	0.545208i	$0.183549\pi$
$132$		0			0
$133$	12.8992	+	7.44734i	1.11850	+	0.645766i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−15.1270	−	8.73356i	−1.29238	−	0.746158i	−0.313307	−	0.949652i	$-0.601437\pi$
$137$	−15.1270	−	8.73356i	−1.29238	−	0.746158i	−0.979076	+	0.203494i	$0.934770\pi$
$138$		0			0
$139$	−1.59808	−	2.76795i	−0.135547	−	0.234774i	0.790259	−	0.612773i	$-0.209946\pi$
$139$	−1.59808	−	2.76795i	−0.135547	−	0.234774i	−0.925806	+	0.377998i	$0.876613\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.03119			−0.169857
$144$		0			0
$145$	−13.8564			−1.15071
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.07638	−	5.32844i	−0.252027	−	0.436523i	0.712057	−	0.702122i	$-0.247764\pi$
$149$	−3.07638	−	5.32844i	−0.252027	−	0.436523i	−0.964084	+	0.265599i	$0.914430\pi$
$150$		0			0
$151$	8.51673	+	4.91713i	0.693081	+	0.400151i	0.804765	−	0.593593i	$-0.202291\pi$
$151$	8.51673	+	4.91713i	0.693081	+	0.400151i	−0.111684	+	0.993744i	$0.535624\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−15.5677	−	8.98803i	−1.25043	−	0.721936i
$156$		0			0
$157$	−18.8857	+	10.9037i	−1.50724	+	0.870207i	−0.507277	+	0.861783i	$0.669348\pi$
$157$	−18.8857	+	10.9037i	−1.50724	+	0.870207i	−0.999965	+	0.00842371i	$0.997319\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	3.28985i		−	0.259276i
$162$		0			0
$163$	−8.80385			−0.689571			−0.344785	−	0.938682i	$-0.612048\pi$
$163$	−8.80385			−0.689571			−0.344785	+	0.938682i	$0.612048\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.0690	+	19.1721i	0.856548	+	1.48359i	0.875201	+	0.483759i	$0.160729\pi$
$167$	11.0690	+	19.1721i	0.856548	+	1.48359i	−0.0186530	+	0.999826i	$0.505938\pi$
$168$		0			0
$169$	−5.92820	+	10.2679i	−0.456016	+	0.789842i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.824313	+	1.42775i	−0.0626714	+	0.108550i	−0.895659	−	0.444742i	$-0.853295\pi$
$173$	−0.824313	+	1.42775i	−0.0626714	+	0.108550i	0.832987	+	0.553292i	$0.186629\pi$
$174$		0			0
$175$	15.4294	−	8.90815i	1.16635	−	0.673393i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			3.79879i			0.283935i	0.989871	+	0.141967i	$0.0453428\pi$
$179$			3.79879i			0.283935i	−0.989871	+	0.141967i	$0.954657\pi$
$180$		0			0
$181$		−	3.20817i		−	0.238461i	−0.992867	−	0.119231i	$-0.961957\pi$
$181$		−	3.20817i		−	0.238461i	0.992867	−	0.119231i	$-0.0380428\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	18.4168	−	10.6329i	1.35403	−	0.781750i
$186$		0			0
$187$	6.73205	−	11.6603i	0.492296	−	0.852682i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.48853	−	6.04232i	0.252421	−	0.437207i	−0.711770	−	0.702412i	$-0.752106\pi$
$191$	3.48853	−	6.04232i	0.252421	−	0.437207i	0.964192	+	0.265205i	$0.0854397\pi$
$192$		0			0
$193$	2.69615	+	4.66987i	0.194073	+	0.336145i	0.946596	−	0.322421i	$-0.104497\pi$
$193$	2.69615	+	4.66987i	0.194073	+	0.336145i	−0.752523	+	0.658566i	$0.771163\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.0305			1.21337			0.606687	−	0.794941i	$-0.292498\pi$
$197$	17.0305			1.21337			0.606687	+	0.794941i	$0.292498\pi$
$198$		0			0
$199$		−	15.6775i		−	1.11135i	−0.831400	−	0.555675i	$-0.812460\pi$
$199$		−	15.6775i		−	1.11135i	0.831400	−	0.555675i	$-0.187540\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	15.5677	−	8.98803i	1.09264	−	0.630836i
$204$		0			0
$205$	−10.1208	−	5.84325i	−0.706868	−	0.408110i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.13894	−	3.54432i	−0.424639	−	0.245165i
$210$		0			0
$211$	10.5263	+	18.2321i	0.724659	+	1.25515i	0.959114	+	0.283019i	$0.0913360\pi$
$211$	10.5263	+	18.2321i	0.724659	+	1.25515i	−0.234455	+	0.972127i	$0.575331\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.15276			0.419614
$216$		0			0
$217$	23.3205			1.58310
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.79025	+	6.56491i	0.254960	+	0.441604i
$222$		0			0
$223$	−22.5902	−	13.0424i	−1.51275	−	0.873386i	−0.999889	−	0.0149140i	$-0.995253\pi$
$223$	−22.5902	−	13.0424i	−1.51275	−	0.873386i	−0.512860	−	0.858472i	$-0.671414\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.28985	−	1.89939i	−0.218355	−	0.126067i	0.386833	−	0.922150i	$-0.373569\pi$
$227$	−3.28985	−	1.89939i	−0.218355	−	0.126067i	−0.605188	+	0.796082i	$0.706902\pi$
$228$		0			0
$229$	−10.1208	+	5.84325i	−0.668802	+	0.386133i	−0.795623	−	0.605793i	$-0.792856\pi$
$229$	−10.1208	+	5.84325i	−0.668802	+	0.386133i	0.126821	+	0.991926i	$0.459523\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			14.1773i			0.928784i	0.885630	+	0.464392i	$0.153727\pi$
$233$			14.1773i			0.928784i	−0.885630	+	0.464392i	$0.846273\pi$
$234$		0			0
$235$	21.4641			1.40016
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.15276	−	10.6569i	−0.397989	−	0.689337i	0.595489	−	0.803363i	$-0.296958\pi$
$239$	−6.15276	−	10.6569i	−0.397989	−	0.689337i	−0.993478	+	0.114027i	$0.963625\pi$
$240$		0			0
$241$	2.69615	−	4.66987i	0.173674	−	0.300813i	−0.766027	−	0.642808i	$-0.777769\pi$
$241$	2.69615	−	4.66987i	0.173674	−	0.300813i	0.939702	+	0.341995i	$0.111103\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−13.7333	+	23.7867i	−0.877386	+	1.51968i
$246$		0			0
$247$	3.45632	−	1.99551i	0.219920	−	0.126971i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	14.1773i		−	0.894861i	−0.894319	−	0.447431i	$-0.852339\pi$
$251$		−	14.1773i		−	0.894861i	0.894319	−	0.447431i	$-0.147661\pi$
$252$		0			0
$253$			1.56569i			0.0984344i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.28985	+	1.89939i	−0.205215	+	0.118481i	−0.599086	−	0.800685i	$-0.704469\pi$
$257$	−3.28985	+	1.89939i	−0.205215	+	0.118481i	0.393871	+	0.919166i	$0.371136\pi$
$258$		0			0
$259$	−13.7942	+	23.8923i	−0.857132	+	1.48460i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.64863	+	2.85550i	−0.101659	+	0.176078i	−0.912368	−	0.409371i	$-0.865748\pi$
$263$	−1.64863	+	2.85550i	−0.101659	+	0.176078i	0.810710	+	0.585449i	$0.199082\pi$
$264$		0			0
$265$	−16.3923	−	28.3923i	−1.00697	−	1.74413i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−19.8860			−1.21247			−0.606236	−	0.795285i	$-0.707321\pi$
$269$	−19.8860			−1.21247			−0.606236	+	0.795285i	$0.707321\pi$
$270$		0			0
$271$			11.9730i			0.727311i	0.931534	+	0.363655i	$0.118471\pi$
$271$			11.9730i			0.727311i	−0.931534	+	0.363655i	$0.881529\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.34310	+	4.23954i	−0.442806	+	0.255654i
$276$		0			0
$277$	−18.8857	−	10.9037i	−1.13473	−	0.655137i	−0.189611	−	0.981859i	$-0.560723\pi$
$277$	−18.8857	−	10.9037i	−1.13473	−	0.655137i	−0.945120	+	0.326722i	$0.894056\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	8.98803	+	5.18924i	0.536181	+	0.309564i	0.743530	−	0.668703i	$-0.233150\pi$
$281$	8.98803	+	5.18924i	0.536181	+	0.309564i	−0.207349	+	0.978267i	$0.566484\pi$
$282$		0			0
$283$	13.9282	+	24.1244i	0.827946	+	1.43404i	0.899647	+	0.436618i	$0.143824\pi$
$283$	13.9282	+	24.1244i	0.827946	+	1.43404i	−0.0717013	+	0.997426i	$0.522843\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	15.1610			0.894926
$288$		0			0
$289$	−33.2487			−1.95581
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.79025	−	6.56491i	−0.221429	−	0.383526i	0.733813	−	0.679351i	$-0.237739\pi$
$293$	−3.79025	−	6.56491i	−0.221429	−	0.383526i	−0.955242	+	0.295825i	$0.904405\pi$
$294$		0			0
$295$	−5.06040	−	2.92163i	−0.294628	−	0.170104i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.763411	−	0.440756i	−0.0441492	−	0.0254896i
$300$		0			0
$301$	−6.91264	+	3.99102i	−0.398438	+	0.230038i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	3.28985i		−	0.188376i
$306$		0			0
$307$	−20.9282			−1.19444			−0.597218	−	0.802079i	$-0.703727\pi$
$307$	−20.9282			−1.19444			−0.597218	+	0.802079i	$0.703727\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−10.2447	−	17.7444i	−0.580925	−	1.00619i	−0.995370	−	0.0961176i	$-0.969357\pi$
$311$	−10.2447	−	17.7444i	−0.580925	−	1.00619i	0.414445	−	0.910075i	$-0.363976\pi$
$312$		0			0
$313$	−4.69615	+	8.13397i	−0.265442	+	0.459759i	−0.967679	−	0.252184i	$-0.918851\pi$
$313$	−4.69615	+	8.13397i	−0.265442	+	0.459759i	0.702237	+	0.711943i	$0.252185\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.40482	−	14.5576i	0.472062	−	0.817635i	−0.527427	−	0.849600i	$-0.676843\pi$
$317$	8.40482	−	14.5576i	0.472062	−	0.817635i	0.999489	+	0.0319652i	$0.0101766\pi$
$318$		0			0
$319$	−7.40895	+	4.27756i	−0.414821	+	0.239497i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			26.4551i			1.47200i
$324$		0			0
$325$		−	4.77386i		−	0.264806i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−24.1150	+	13.9228i	−1.32950	+	0.767589i
$330$		0			0
$331$	0.937822	−	1.62436i	0.0515474	−	0.0892827i	−0.839100	−	0.543977i	$-0.816918\pi$
$331$	0.937822	−	1.62436i	0.0515474	−	0.0892827i	0.890648	+	0.454694i	$0.150251\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	14.1454	−	24.5006i	0.772847	−	1.33861i
$336$		0			0
$337$	5.69615	+	9.86603i	0.310289	+	0.537437i	0.978425	−	0.206603i	$-0.0662408\pi$
$337$	5.69615	+	9.86603i	0.310289	+	0.537437i	−0.668136	+	0.744039i	$0.732907\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−11.0986			−0.601025
$342$		0			0
$343$		−	7.69549i		−	0.415517i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.57969	+	3.79879i	−0.353216	+	0.203930i	−0.666101	−	0.745862i	$-0.732038\pi$
$347$	−6.57969	+	3.79879i	−0.353216	+	0.203930i	0.312885	+	0.949791i	$0.398705\pi$
$348$		0			0
$349$	2.28205	+	1.31754i	0.122155	+	0.0705264i	0.559833	−	0.828606i	$-0.310865\pi$
$349$	2.28205	+	1.31754i	0.122155	+	0.0705264i	−0.437677	+	0.899132i	$0.644199\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.57969	−	3.79879i	−0.350202	−	0.202189i	0.314572	−	0.949233i	$-0.398139\pi$
$353$	−6.57969	−	3.79879i	−0.350202	−	0.202189i	−0.664774	+	0.747044i	$0.731472\pi$
$354$		0			0
$355$	−16.3923	−	28.3923i	−0.870013	−	1.50691i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−23.7867			−1.25541			−0.627707	−	0.778449i	$-0.716007\pi$
$359$	−23.7867			−1.25541			−0.627707	+	0.778449i	$0.716007\pi$
$360$		0			0
$361$	−5.07180			−0.266937
$362$		0			0
$363$		0			0
$364$		0			0
$365$	9.11870	+	15.7940i	0.477294	+	0.826698i
$366$		0			0
$367$	32.4628	+	18.7424i	1.69455	+	0.978346i	0.950760	+	0.309927i	$0.100305\pi$
$367$	32.4628	+	18.7424i	1.69455	+	0.978346i	0.743785	+	0.668419i	$0.233029\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	36.8336	+	21.2659i	1.91231	+	1.10407i
$372$		0			0
$373$	−16.1073	+	9.29957i	−0.834006	+	0.481514i	−0.855222	−	0.518261i	$-0.826579\pi$
$373$	−16.1073	+	9.29957i	−0.834006	+	0.481514i	0.0212163	+	0.999775i	$0.493246\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	4.81667i		−	0.248071i
$378$		0			0
$379$	26.2679			1.34929			0.674647	−	0.738141i	$-0.264296\pi$
$379$	26.2679			1.34929			0.674647	+	0.738141i	$0.264296\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.824313	−	1.42775i	−0.0421204	−	0.0729547i	0.844197	−	0.536034i	$-0.180078\pi$
$383$	−0.824313	−	1.42775i	−0.0421204	−	0.0729547i	−0.886317	+	0.463079i	$0.846745\pi$
$384$		0			0
$385$	11.6603	−	20.1962i	0.594262	−	1.02929i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	7.69095	−	13.3211i	0.389946	−	0.675407i	−0.602496	−	0.798122i	$-0.705827\pi$
$389$	7.69095	−	13.3211i	0.389946	−	0.675407i	0.992442	+	0.122715i	$0.0391602\pi$
$390$		0			0
$391$	5.06040	−	2.92163i	0.255916	−	0.147753i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			18.8576i			0.948827i
$396$		0			0
$397$			10.1208i			0.507949i	0.967211	+	0.253974i	$0.0817379\pi$
$397$			10.1208i			0.507949i	−0.967211	+	0.253974i	$0.918262\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.1594	+	7.59757i	−0.657148	+	0.379405i	−0.791190	−	0.611571i	$-0.790538\pi$
$401$	−13.1594	+	7.59757i	−0.657148	+	0.379405i	0.134041	+	0.990976i	$0.457205\pi$
$402$		0			0
$403$	3.12436	−	5.41154i	0.155635	−	0.269568i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.56491	−	11.3708i	0.325411	−	0.563628i
$408$		0			0
$409$	4.30385	+	7.45448i	0.212812	+	0.368600i	0.952593	−	0.304246i	$-0.0984046\pi$
$409$	4.30385	+	7.45448i	0.212812	+	0.368600i	−0.739782	+	0.672847i	$0.765071\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.58051			0.373012
$414$		0			0
$415$		−	31.9281i		−	1.56729i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−22.9108	+	13.2276i	−1.11927	+	0.646209i	−0.941214	−	0.337812i	$-0.890313\pi$
$419$	−22.9108	+	13.2276i	−1.11927	+	0.646209i	−0.178053	+	0.984021i	$0.556980\pi$
$420$		0			0
$421$	−4.13429	−	2.38693i	−0.201493	−	0.116332i	0.395859	−	0.918311i	$-0.370447\pi$
$421$	−4.13429	−	2.38693i	−0.201493	−	0.116332i	−0.597352	+	0.801979i	$0.703780\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	27.4048	+	15.8222i	1.32933	+	0.767489i
$426$		0			0
$427$	2.13397	+	3.69615i	0.103270	+	0.178869i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.382565			0.0184275			0.00921375	−	0.999958i	$-0.497067\pi$
$431$	0.382565			0.0184275			0.00921375	+	0.999958i	$0.497067\pi$
$432$		0			0
$433$	4.53590			0.217981			0.108991	−	0.994043i	$-0.465238\pi$
$433$	4.53590			0.217981			0.108991	+	0.994043i	$0.465238\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.53819	−	2.66422i	−0.0735816	−	0.127447i
$438$		0			0
$439$	12.4694	+	7.19918i	0.595130	+	0.343598i	0.767123	−	0.641500i	$-0.221687\pi$
$439$	12.4694	+	7.19918i	0.595130	+	0.343598i	−0.171994	+	0.985098i	$0.555021\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	23.6742	+	13.6683i	1.12480	+	0.649402i	0.942621	−	0.333864i	$-0.108353\pi$
$443$	23.6742	+	13.6683i	1.12480	+	0.649402i	0.182176	+	0.983266i	$0.441686\pi$
$444$		0			0
$445$	36.4154	−	21.0245i	1.72626	−	0.996655i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			24.0468i			1.13484i	0.823429	+	0.567419i	$0.192058\pi$
$449$			24.0468i			1.13484i	−0.823429	+	0.567419i	$0.807942\pi$
$450$		0			0
$451$	−7.21539			−0.339759
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.56491	+	11.3708i	0.307768	+	0.533070i
$456$		0			0
$457$	−3.19615	+	5.53590i	−0.149510	+	0.258958i	−0.931046	−	0.364901i	$-0.881103\pi$
$457$	−3.19615	+	5.53590i	−0.149510	+	0.258958i	0.781537	+	0.623859i	$0.214436\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.96594	+	5.13716i	−0.138138	+	0.239261i	−0.926792	−	0.375576i	$-0.877445\pi$
$461$	−2.96594	+	5.13716i	−0.138138	+	0.239261i	0.788654	+	0.614837i	$0.210778\pi$
$462$		0			0
$463$	2.10039	−	1.21266i	0.0976134	−	0.0563571i	−0.450399	−	0.892828i	$-0.648718\pi$
$463$	2.10039	−	1.21266i	0.0976134	−	0.0563571i	0.548012	+	0.836470i	$0.315385\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	19.8754i		−	0.919726i	−0.887990	−	0.459863i	$-0.847899\pi$
$467$		−	19.8754i		−	0.919726i	0.887990	−	0.459863i	$-0.152101\pi$
$468$		0			0
$469$			36.7020i			1.69474i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.28985	−	1.89939i	0.151267	−	0.0873342i
$474$		0			0
$475$	8.33013	−	14.4282i	0.382212	−	0.662011i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.07638	+	5.32844i	−0.140563	+	0.243463i	−0.927709	−	0.373304i	$-0.878225\pi$
$479$	−3.07638	+	5.32844i	−0.140563	+	0.243463i	0.787146	+	0.616767i	$0.211558\pi$
$480$		0			0
$481$	3.69615	+	6.40192i	0.168530	+	0.291903i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	35.0470			1.59140
$486$		0			0
$487$			33.2073i			1.50477i	0.658726	+	0.752383i	$0.271096\pi$
$487$			33.2073i			1.50477i	−0.658726	+	0.752383i	$0.728904\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−28.6090	+	16.5174i	−1.29111	+	0.745420i	−0.978850	−	0.204578i	$-0.934418\pi$
$491$	−28.6090	+	16.5174i	−1.29111	+	0.745420i	−0.312256	+	0.949998i	$0.601085\pi$
$492$		0			0
$493$	27.6506	+	15.9641i	1.24532	+	0.718985i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	36.8336	+	21.2659i	1.65221	+	0.953906i
$498$		0			0
$499$	−2.80385	−	4.85641i	−0.125517	−	0.217403i	0.796418	−	0.604747i	$-0.206726\pi$
$499$	−2.80385	−	4.85641i	−0.125517	−	0.217403i	−0.921935	+	0.387344i	$0.873392\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	29.4977			1.31524			0.657619	−	0.753351i	$-0.271564\pi$
$503$	29.4977			1.31524			0.657619	+	0.753351i	$0.271564\pi$
$504$		0			0
$505$	18.9282			0.842294
$506$		0			0
$507$		0			0
$508$		0			0
$509$	0.110437	+	0.191282i	0.00489503	+	0.00847845i	0.868463	−	0.495755i	$-0.165109\pi$
$509$	0.110437	+	0.191282i	0.00489503	+	0.00847845i	−0.863568	+	0.504233i	$0.831775\pi$
$510$		0			0
$511$	−20.4898	−	11.8298i	−0.906414	−	0.523318i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−10.6329	−	6.13894i	−0.468544	−	0.270514i
$516$		0			0
$517$	11.4767	−	6.62610i	0.504746	−	0.291416i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	7.08863i		−	0.310559i	−0.987871	−	0.155279i	$-0.950372\pi$
$521$		−	7.08863i		−	0.310559i	0.987871	−	0.155279i	$-0.0496278\pi$
$522$		0			0
$523$	37.5885			1.64363			0.821814	−	0.569756i	$-0.192962\pi$
$523$	37.5885			1.64363			0.821814	+	0.569756i	$0.192962\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	20.7103	+	35.8713i	0.902156	+	1.56258i
$528$		0			0
$529$	11.1603	−	19.3301i	0.485228	−	0.840440i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.03119	−	3.51813i	0.0879806	−	0.152387i
$534$		0			0
$535$	22.5902	−	13.0424i	0.976658	−	0.563874i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			16.9582i			0.730440i
$540$		0			0
$541$		−	34.5632i		−	1.48599i	−0.669298	−	0.742994i	$-0.733405\pi$
$541$		−	34.5632i		−	1.48599i	0.669298	−	0.742994i	$-0.266595\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−26.9641	+	15.5677i	−1.15501	+	0.666848i
$546$		0			0
$547$	−15.7942	+	27.3564i	−0.675312	+	1.16968i	0.301065	+	0.953604i	$0.402658\pi$
$547$	−15.7942	+	27.3564i	−0.675312	+	1.16968i	−0.976377	+	0.216072i	$0.930675\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	8.40482	−	14.5576i	0.358057	−	0.620174i
$552$		0			0
$553$	−12.2321	−	21.1865i	−0.520160	−	0.900943i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.9401			0.633034			0.316517	−	0.948587i	$-0.397487\pi$
$557$	14.9401			0.633034			0.316517	+	0.948587i	$0.397487\pi$
$558$		0			0
$559$			2.13878i			0.0904607i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	30.2539	−	17.4671i	1.27505	−	0.736151i	0.299117	−	0.954217i	$-0.403308\pi$
$563$	30.2539	−	17.4671i	1.27505	−	0.736151i	0.975934	+	0.218066i	$0.0699747\pi$
$564$		0			0
$565$	29.0065	+	16.7469i	1.22031	+	0.704548i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.25742	−	3.03538i	−0.220403	−	0.127250i	0.385734	−	0.922610i	$-0.373948\pi$
$569$	−5.25742	−	3.03538i	−0.220403	−	0.127250i	−0.606137	+	0.795360i	$0.707282\pi$
$570$		0			0
$571$	−1.59808	−	2.76795i	−0.0668774	−	0.115835i	0.830648	−	0.556798i	$-0.187970\pi$
$571$	−1.59808	−	2.76795i	−0.0668774	−	0.115835i	−0.897525	+	0.440963i	$0.854637\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.67982			−0.153459
$576$		0			0
$577$	11.9282			0.496578			0.248289	−	0.968686i	$-0.420132\pi$
$577$	11.9282			0.496578			0.248289	+	0.968686i	$0.420132\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	20.7103	+	35.8713i	0.859209	+	1.48819i
$582$		0			0
$583$	−17.5298	−	10.1208i	−0.726008	−	0.419161i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	28.6090	+	16.5174i	1.18082	+	0.681747i	0.956204	−	0.292701i	$-0.0945540\pi$
$587$	28.6090	+	16.5174i	1.18082	+	0.681747i	0.224616	+	0.974447i	$0.427887\pi$
$588$		0			0
$589$	18.8857	−	10.9037i	0.778171	−	0.449277i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			38.7330i			1.59057i	0.606233	+	0.795287i	$0.292680\pi$
$593$			38.7330i			1.59057i	−0.606233	+	0.795287i	$0.707320\pi$
$594$		0			0
$595$	−87.0333			−3.56802
$596$		0			0
$597$		0			0
$598$		0			0
$599$	11.2603	+	19.5035i	0.460084	+	0.796890i	0.998965	−	0.0454928i	$-0.0144858\pi$
$599$	11.2603	+	19.5035i	0.460084	+	0.796890i	−0.538880	+	0.842382i	$0.681152\pi$
$600$		0			0
$601$	−15.1962	+	26.3205i	−0.619864	+	1.07364i	0.369646	+	0.929173i	$0.379479\pi$
$601$	−15.1962	+	26.3205i	−0.619864	+	1.07364i	−0.989510	+	0.144463i	$0.953854\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	11.3708	−	19.6947i	0.462287	−	0.800705i
$606$		0			0
$607$	−30.6106	+	17.6730i	−1.24245	+	0.717326i	−0.969591	−	0.244729i	$-0.921301\pi$
$607$	−30.6106	+	17.6730i	−1.24245	+	0.717326i	−0.272854	+	0.962056i	$0.587968\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			7.46120i			0.301848i
$612$		0			0
$613$			6.91264i			0.279199i	0.990208	+	0.139599i	$0.0445815\pi$
$613$			6.91264i			0.279199i	−0.990208	+	0.139599i	$0.955418\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	24.9965	−	14.4317i	1.00632	−	0.581000i	0.0962087	−	0.995361i	$-0.469328\pi$
$617$	24.9965	−	14.4317i	1.00632	−	0.581000i	0.910112	+	0.414361i	$0.135995\pi$
$618$		0			0
$619$	18.5981	−	32.2128i	0.747520	−	1.29474i	−0.201488	−	0.979491i	$-0.564578\pi$
$619$	18.5981	−	32.2128i	0.747520	−	1.29474i	0.949008	−	0.315251i	$-0.102089\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−27.2752	+	47.2421i	−1.09276	+	1.89272i
$624$		0			0
$625$	13.6962	+	23.7224i	0.547846	+	0.948897i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−49.0012			−1.95380
$630$		0			0
$631$			22.0939i			0.879542i	0.898110	+	0.439771i	$0.144940\pi$
$631$			22.0939i			0.879542i	−0.898110	+	0.439771i	$0.855060\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−8.26857	−	4.77386i	−0.327613	−	0.189147i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	30.2539	+	17.4671i	1.19496	+	0.689909i	0.959427	−	0.281957i	$-0.0909837\pi$
$641$	30.2539	+	17.4671i	1.19496	+	0.689909i	0.235531	+	0.971867i	$0.424317\pi$
$642$		0			0
$643$	−9.39230	−	16.2679i	−0.370396	−	0.641545i	0.619230	−	0.785210i	$-0.287445\pi$
$643$	−9.39230	−	16.2679i	−0.370396	−	0.641545i	−0.989626	+	0.143664i	$0.954111\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	39.7720			1.56360			0.781800	−	0.623529i	$-0.214302\pi$
$647$	39.7720			1.56360			0.781800	+	0.623529i	$0.214302\pi$
$648$		0			0
$649$	−3.60770			−0.141614
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−16.2062	−	28.0700i	−0.634198	−	1.09846i	−0.986685	−	0.162646i	$-0.947997\pi$
$653$	−16.2062	−	28.0700i	−0.634198	−	1.09846i	0.352487	−	0.935817i	$-0.385336\pi$
$654$		0			0
$655$	27.6506	+	15.9641i	1.08040	+	0.623767i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−18.8576	−	10.8874i	−0.734586	−	0.424114i	0.0855113	−	0.996337i	$-0.472748\pi$
$659$	−18.8576	−	10.8874i	−0.734586	−	0.424114i	−0.820098	+	0.572224i	$0.806081\pi$
$660$		0			0
$661$	−39.1938	+	22.6285i	−1.52446	+	0.880149i	−0.524882	+	0.851175i	$0.675891\pi$
$661$	−39.1938	+	22.6285i	−1.52446	+	0.880149i	−0.999580	+	0.0289735i	$0.990776\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			45.8216i			1.77689i
$666$		0			0
$667$	−3.71281			−0.143761
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.01560	−	1.75906i	−0.0392066	−	0.0679079i
$672$		0			0
$673$	−17.6244	+	30.5263i	−0.679369	+	1.17670i	0.295802	+	0.955249i	$0.404413\pi$
$673$	−17.6244	+	30.5263i	−0.679369	+	1.17670i	−0.975171	+	0.221452i	$0.928920\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	22.2485	−	38.5356i	0.855080	−	1.48104i	−0.0214905	−	0.999769i	$-0.506841\pi$
$677$	22.2485	−	38.5356i	0.855080	−	1.48104i	0.876571	−	0.481273i	$-0.159826\pi$
$678$		0			0
$679$	−39.3755	+	22.7334i	−1.51109	+	0.872429i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			39.7509i			1.52103i	0.649323	+	0.760513i	$0.275052\pi$
$683$			39.7509i			1.52103i	−0.649323	+	0.760513i	$0.724948\pi$
$684$		0			0
$685$		−	53.7354i		−	2.05313i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	9.86954	−	5.69818i	0.375999	−	0.217083i
$690$		0			0
$691$	1.92820	−	3.33975i	0.0733523	−	0.127050i	−0.827016	−	0.562178i	$-0.809964\pi$
$691$	1.92820	−	3.33975i	0.0733523	−	0.127050i	0.900369	+	0.435128i	$0.143297\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.91629	−	8.51526i	0.186485	−	0.323002i
$696$		0			0
$697$	13.4641	+	23.3205i	0.509989	+	0.883327i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	51.8567			1.95860			0.979300	−	0.202415i	$-0.0648790\pi$
$701$	51.8567			1.95860			0.979300	+	0.202415i	$0.0648790\pi$
$702$		0			0
$703$			25.7983i			0.973002i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−21.2659	+	12.2779i	−0.799786	+	0.461757i
$708$		0			0
$709$	−30.4289	−	17.5681i	−1.14278	−	0.659786i	−0.195664	−	0.980671i	$-0.562686\pi$
$709$	−30.4289	−	17.5681i	−1.14278	−	0.659786i	−0.947118	+	0.320885i	$0.896020\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.17136	−	2.40833i	−0.156219	−	0.0901928i
$714$		0			0
$715$	−3.12436	−	5.41154i	−0.116844	−	0.202380i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−7.80138			−0.290942			−0.145471	−	0.989362i	$-0.546470\pi$
$719$	−7.80138			−0.290942			−0.145471	+	0.989362i	$0.546470\pi$
$720$		0			0
$721$	15.9282			0.593197
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−10.0534	−	17.4131i	−0.373376	−	0.646706i
$726$		0			0
$727$	−22.5902	−	13.0424i	−0.837823	−	0.483717i	0.0187009	−	0.999825i	$-0.494047\pi$
$727$	−22.5902	−	13.0424i	−0.837823	−	0.483717i	−0.856524	+	0.516108i	$0.827380\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−12.2779	−	7.08863i	−0.454113	−	0.262183i
$732$		0			0
$733$	11.4767	−	6.62610i	0.423903	−	0.244741i	−0.272843	−	0.962059i	$-0.587964\pi$
$733$	11.4767	−	6.62610i	0.423903	−	0.244741i	0.696746	+	0.717318i	$0.254631\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	17.4671i		−	0.643409i
$738$		0			0
$739$	20.6410			0.759292			0.379646	−	0.925132i	$-0.376046\pi$
$739$	20.6410			0.759292			0.379646	+	0.925132i	$0.376046\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−25.8475	−	44.7692i	−0.948253	−	1.64242i	−0.749104	−	0.662452i	$-0.769516\pi$
$743$	−25.8475	−	44.7692i	−0.948253	−	1.64242i	−0.199148	−	0.979969i	$-0.563818\pi$
$744$		0			0
$745$	9.46410	−	16.3923i	0.346738	−	0.600568i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−16.9201	+	29.3064i	−0.618246	+	1.07083i
$750$		0			0
$751$	17.2816	−	9.97754i	0.630615	−	0.364086i	−0.150375	−	0.988629i	$-0.548048\pi$
$751$	17.2816	−	9.97754i	0.630615	−	0.364086i	0.780990	+	0.624543i	$0.214715\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			30.2539i			1.10105i
$756$		0			0
$757$		−	52.0930i		−	1.89335i	−0.322189	−	0.946675i	$-0.604419\pi$
$757$		−	52.0930i		−	1.89335i	0.322189	−	0.946675i	$-0.395581\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−37.2744	+	21.5204i	−1.35119	+	0.780113i	−0.988417	−	0.151763i	$-0.951505\pi$
$761$	−37.2744	+	21.5204i	−1.35119	+	0.780113i	−0.362778	+	0.931876i	$0.618172\pi$
$762$		0			0
$763$	20.1962	−	34.9808i	0.731150	−	1.26639i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.01560	−	1.75906i	0.0366710	−	0.0635161i
$768$		0			0
$769$	−2.03590	−	3.52628i	−0.0734164	−	0.127161i	0.826980	−	0.562231i	$-0.190057\pi$
$769$	−2.03590	−	3.52628i	−0.0734164	−	0.127161i	−0.900397	+	0.435070i	$0.856724\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	44.7179			1.60839			0.804196	−	0.594364i	$-0.202596\pi$
$773$	44.7179			1.60839			0.804196	+	0.594364i	$0.202596\pi$
$774$		0			0
$775$		−	26.0849i		−	0.936996i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.2779	−	7.08863i	0.439900	−	0.253977i
$780$		0			0
$781$	−17.5298	−	10.1208i	−0.627264	−	0.362151i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−58.0995	−	33.5438i	−2.07366	−	1.19723i
$786$		0			0
$787$	3.72243	+	6.44744i	0.132690	+	0.229826i	0.924713	−	0.380666i	$-0.124305\pi$
$787$	3.72243	+	6.44744i	0.132690	+	0.229826i	−0.792022	+	0.610492i	$0.790972\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−43.4519			−1.54497
$792$		0			0
$793$	1.14359			0.0406102
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−13.7333	−	23.7867i	−0.486457	−	0.842569i	0.513422	−	0.858136i	$-0.328378\pi$
$797$	−13.7333	−	23.7867i	−0.486457	−	0.842569i	−0.999879	+	0.0155679i	$0.995044\pi$
$798$		0			0
$799$	−42.8318	−	24.7289i	−1.51528	−	0.874847i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9.75144	+	5.62999i	0.344121	+	0.198678i
$804$		0			0
$805$	8.76488	−	5.06040i	0.308921	−	0.178356i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			14.1773i			0.498446i	0.968446	+	0.249223i	$0.0801752\pi$
$809$			14.1773i			0.498446i	−0.968446	+	0.249223i	$0.919825\pi$
$810$		0			0
$811$	27.0718			0.950619			0.475310	−	0.879819i	$-0.342336\pi$
$811$	27.0718			0.950619			0.475310	+	0.879819i	$0.342336\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−13.5420	−	23.4554i	−0.474355	−	0.821607i
$816$		0			0
$817$	−3.73205	+	6.46410i	−0.130568	+	0.226150i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.43888	+	9.42042i	−0.189818	+	0.328775i	−0.945190	−	0.326522i	$-0.894123\pi$
$821$	−5.43888	+	9.42042i	−0.189818	+	0.328775i	0.755371	+	0.655297i	$0.227457\pi$
$822$		0			0
$823$	−20.9861	+	12.1163i	−0.731529	+	0.422348i	−0.818981	−	0.573820i	$-0.805461\pi$
$823$	−20.9861	+	12.1163i	−0.731529	+	0.422348i	0.0874525	+	0.996169i	$0.472127\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			40.6324i			1.41293i	0.707749	+	0.706464i	$0.249711\pi$
$827$			40.6324i			1.41293i	−0.707749	+	0.706464i	$0.750289\pi$
$828$		0			0
$829$			34.5632i			1.20043i	0.799839	+	0.600215i	$0.204918\pi$
$829$			34.5632i			1.20043i	−0.799839	+	0.600215i	$0.795082\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	54.8097	−	31.6444i	1.89904	−	1.09641i
$834$		0			0
$835$	−34.0526	+	58.9808i	−1.17844	+	2.04111i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.5264	−	21.6963i	0.432459	−	0.749041i	−0.564626	−	0.825347i	$-0.690979\pi$
$839$	12.5264	−	21.6963i	0.432459	−	0.749041i	0.997084	+	0.0763065i	$0.0243127\pi$
$840$		0			0
$841$	4.35641	+	7.54552i	0.150221	+	0.260190i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−36.4748			−1.25477
$846$		0			0
$847$			29.5028i			1.01373i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4.93477	−	2.84909i	0.169162	−	0.0976655i
$852$		0			0
$853$	−12.8992	−	7.44734i	−0.441659	−	0.254992i	0.262642	−	0.964893i	$-0.415406\pi$
$853$	−12.8992	−	7.44734i	−0.441659	−	0.254992i	−0.704301	+	0.709901i	$0.748739\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.881512	−	0.508941i	−0.0301119	−	0.0173851i	0.484869	−	0.874587i	$-0.338867\pi$
$857$	−0.881512	−	0.508941i	−0.0301119	−	0.0173851i	−0.514980	+	0.857202i	$0.672201\pi$
$858$		0			0
$859$	5.79423	+	10.0359i	0.197697	+	0.342420i	0.947781	−	0.318921i	$-0.103321\pi$
$859$	5.79423	+	10.0359i	0.197697	+	0.342420i	−0.750085	+	0.661342i	$0.769987\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−15.9853			−0.544147			−0.272073	−	0.962276i	$-0.587709\pi$
$863$	−15.9853			−0.544147			−0.272073	+	0.962276i	$0.587709\pi$
$864$		0			0
$865$	−5.07180			−0.172446
$866$		0			0
$867$		0			0
$868$		0			0
$869$	5.82145	+	10.0830i	0.197479	+	0.342044i
$870$		0			0
$871$	8.51673	+	4.91713i	0.288578	+	0.166611i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.69818	−	3.28985i	−0.192634	−	0.111217i
$876$		0			0
$877$	16.6036	−	9.58611i	0.560665	−	0.323700i	−0.192747	−	0.981248i	$-0.561740\pi$
$877$	16.6036	−	9.58611i	0.560665	−	0.323700i	0.753412	+	0.657548i	$0.228406\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			6.07075i			0.204529i	0.994757	+	0.102264i	$0.0326088\pi$
$881$			6.07075i			0.204529i	−0.994757	+	0.102264i	$0.967391\pi$
$882$		0			0
$883$	−44.1244			−1.48490			−0.742451	−	0.669900i	$-0.766337\pi$
$883$	−44.1244			−1.48490			−0.742451	+	0.669900i	$0.766337\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.9090	−	22.3590i	−0.433440	−	0.750740i	0.563727	−	0.825961i	$-0.309367\pi$
$887$	−12.9090	−	22.3590i	−0.433440	−	0.750740i	−0.997167	+	0.0752210i	$0.976034\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−13.0194	+	22.5502i	−0.435677	+	0.754615i
$894$		0			0
$895$	−10.1208	+	5.84325i	−0.338301	+	0.195318i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	26.3188i		−	0.877780i
$900$		0			0
$901$			75.5427i			2.51669i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	8.54727	−	4.93477i	0.284121	−	0.164037i
$906$		0			0
$907$	−23.1865	+	40.1603i	−0.769896	+	1.33350i	0.167723	+	0.985834i	$0.446359\pi$
$907$	−23.1865	+	40.1603i	−0.769896	+	1.33350i	−0.937619	+	0.347665i	$0.886975\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.220874	+	0.382565i	−0.00731788	+	0.0126749i	−0.869661	−	0.493649i	$-0.835663\pi$
$911$	−0.220874	+	0.382565i	−0.00731788	+	0.0126749i	0.862343	+	0.506324i	$0.168996\pi$
$912$		0			0
$913$	−9.85641	−	17.0718i	−0.326199	−	0.564994i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−41.4207			−1.36783
$918$		0			0
$919$		−	58.0130i		−	1.91367i	−0.290628	−	0.956836i	$-0.593864\pi$
$919$		−	58.0130i		−	1.91367i	0.290628	−	0.956836i	$-0.406136\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	9.86954	−	5.69818i	0.324860	−	0.187558i
$924$		0			0
$925$	26.7244	+	15.4294i	0.878694	+	0.507314i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−17.9761	−	10.3785i	−0.589775	−	0.340507i	0.175233	−	0.984527i	$-0.443932\pi$
$929$	−17.9761	−	10.3785i	−0.589775	−	0.340507i	−0.765009	+	0.644020i	$0.777265\pi$
$930$		0			0
$931$	−16.6603	−	28.8564i	−0.546018	−	0.945731i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	41.4207			1.35460
$936$		0			0
$937$	−23.3923			−0.764193			−0.382097	−	0.924122i	$-0.624798\pi$
$937$	−23.3923			−0.764193			−0.382097	+	0.924122i	$0.624798\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.33957	+	16.1766i	0.304461	+	0.527342i	0.977141	−	0.212591i	$-0.0681902\pi$
$941$	9.33957	+	16.1766i	0.304461	+	0.527342i	−0.672680	+	0.739934i	$0.734857\pi$
$942$		0			0
$943$	−2.71186	−	1.56569i	−0.0883104	−	0.0509860i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−25.3192	−	14.6180i	−0.822762	−	0.475022i	0.0286060	−	0.999591i	$-0.490893\pi$
$947$	−25.3192	−	14.6180i	−0.822762	−	0.475022i	−0.851368	+	0.524569i	$0.824227\pi$
$948$		0			0
$949$	−5.49022	+	3.16978i	−0.178220	+	0.102895i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			15.7041i			0.508705i	0.967112	+	0.254353i	$0.0818624\pi$
$953$			15.7041i			0.508705i	−0.967112	+	0.254353i	$0.918138\pi$
$954$		0			0
$955$	21.4641			0.694562
$956$		0			0
$957$		0			0
$958$		0			0
$959$	34.8558	+	60.3719i	1.12555	+	1.94951i
$960$		0			0
$961$	1.57180	−	2.72243i	0.0507031	−	0.0878204i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−8.29438	+	14.3663i	−0.267006	+	0.462467i
$966$		0			0
$967$	8.51673	−	4.91713i	0.273879	−	0.158124i	−0.356770	−	0.934192i	$-0.616122\pi$
$967$	8.51673	−	4.91713i	0.273879	−	0.158124i	0.630649	+	0.776068i	$0.282789\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	55.8275i		−	1.79159i	−0.444466	−	0.895796i	$-0.646607\pi$
$971$		−	55.8275i		−	1.79159i	0.444466	−	0.895796i	$-0.353393\pi$
$972$		0			0
$973$			12.7559i			0.408935i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.3844	+	11.7689i	−0.652154	+	0.376521i	−0.789281	−	0.614032i	$-0.789547\pi$
$977$	−20.3844	+	11.7689i	−0.652154	+	0.376521i	0.137127	+	0.990554i	$0.456213\pi$
$978$		0			0
$979$	12.9808	−	22.4833i	0.414867	−	0.718571i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	27.6578	−	47.9047i	0.882147	−	1.52792i	0.0331982	−	0.999449i	$-0.489431\pi$
$983$	27.6578	−	47.9047i	0.882147	−	1.52792i	0.848949	−	0.528475i	$-0.177236\pi$
$984$		0			0
$985$	26.1962	+	45.3731i	0.834679	+	1.44571i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.64863			0.0524233
$990$		0			0
$991$		−	25.7983i		−	0.819511i	−0.912195	−	0.409755i	$-0.865614\pi$
$991$		−	25.7983i		−	0.819511i	0.912195	−	0.409755i	$-0.134386\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	41.7684	−	24.1150i	1.32415	−	0.764497i
$996$		0			0
$997$	−1.35593	−	0.782847i	−0.0429428	−	0.0247930i	0.478375	−	0.878156i	$-0.341226\pi$
$997$	−1.35593	−	0.782847i	−0.0429428	−	0.0247930i	−0.521318	+	0.853363i	$0.674559\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.p.f.431.7		16
3.2	odd	2	inner	2592.2.p.f.431.1		16
4.3	odd	2		648.2.l.f.107.6		16
8.3	odd	2	inner	2592.2.p.f.431.2		16
8.5	even	2		648.2.l.f.107.8		16
9.2	odd	6		864.2.f.a.431.8		8
9.4	even	3	inner	2592.2.p.f.2159.8		16
9.5	odd	6	inner	2592.2.p.f.2159.2		16
9.7	even	3		864.2.f.a.431.2		8
12.11	even	2		648.2.l.f.107.3		16
24.5	odd	2		648.2.l.f.107.1		16
24.11	even	2	inner	2592.2.p.f.431.8		16
36.7	odd	6		216.2.f.a.107.5	yes	8
36.11	even	6		216.2.f.a.107.4	yes	8
36.23	even	6		648.2.l.f.539.8		16
36.31	odd	6		648.2.l.f.539.1		16
72.5	odd	6		648.2.l.f.539.6		16
72.11	even	6		864.2.f.a.431.1		8
72.13	even	6		648.2.l.f.539.3		16
72.29	odd	6		216.2.f.a.107.6	yes	8
72.43	odd	6		864.2.f.a.431.7		8
72.59	even	6	inner	2592.2.p.f.2159.7		16
72.61	even	6		216.2.f.a.107.3	✓	8
72.67	odd	6	inner	2592.2.p.f.2159.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.f.a.107.3	✓	8	72.61	even	6
216.2.f.a.107.4	yes	8	36.11	even	6
216.2.f.a.107.5	yes	8	36.7	odd	6
216.2.f.a.107.6	yes	8	72.29	odd	6
648.2.l.f.107.1		16	24.5	odd	2
648.2.l.f.107.3		16	12.11	even	2
648.2.l.f.107.6		16	4.3	odd	2
648.2.l.f.107.8		16	8.5	even	2
648.2.l.f.539.1		16	36.31	odd	6
648.2.l.f.539.3		16	72.13	even	6
648.2.l.f.539.6		16	72.5	odd	6
648.2.l.f.539.8		16	36.23	even	6
864.2.f.a.431.1		8	72.11	even	6
864.2.f.a.431.2		8	9.7	even	3
864.2.f.a.431.7		8	72.43	odd	6
864.2.f.a.431.8		8	9.2	odd	6
2592.2.p.f.431.1		16	3.2	odd	2	inner
2592.2.p.f.431.2		16	8.3	odd	2	inner
2592.2.p.f.431.7		16	1.1	even	1	trivial
2592.2.p.f.431.8		16	24.11	even	2	inner
2592.2.p.f.2159.1		16	72.67	odd	6	inner
2592.2.p.f.2159.2		16	9.5	odd	6	inner
2592.2.p.f.2159.7		16	72.59	even	6	inner
2592.2.p.f.2159.8		16	9.4	even	3	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:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.53819 + 2.66422i) q^{5} +(-3.45632 - 1.99551i) q^{7} +O(q^{10})\)	\(q+(1.53819 + 2.66422i) q^{5} +(-3.45632 - 1.99551i) q^{7} +(1.64492 + 0.949697i) q^{11} +(-0.926118 + 0.534695i) q^{13} -7.08863i q^{17} -3.73205 q^{19} +(0.412157 + 0.713876i) q^{23} +(-2.23205 + 3.86603i) q^{25} +(-2.25207 + 3.90069i) q^{29} +(-5.06040 + 2.92163i) q^{31} -12.2779i q^{35} -6.91264i q^{37} +(-3.28985 + 1.89939i) q^{41} +(1.00000 - 1.73205i) q^{43} +(3.48853 - 6.04232i) q^{47} +(4.46410 + 7.73205i) q^{49} -10.6569 q^{53} +5.84325i q^{55} +(-1.64492 + 0.949697i) q^{59} +(-0.926118 - 0.534695i) q^{61} +(-2.84909 - 1.64492i) q^{65} +(-4.59808 - 7.96410i) q^{67} -10.6569 q^{71} +5.92820 q^{73} +(-3.79025 - 6.56491i) q^{77} +(5.30856 + 3.06490i) q^{79} +(-8.98803 - 5.18924i) q^{83} +(18.8857 - 10.9037i) q^{85} -13.6683i q^{89} +4.26795 q^{91} +(-5.74060 - 9.94301i) q^{95} +(5.69615 - 9.86603i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 32 q^{19} - 8 q^{25} + 16 q^{43} + 16 q^{49} - 32 q^{67} - 16 q^{73} + 96 q^{91} + 8 q^{97}+O(q^{100}) \) 16 * q - 32 * q^19 - 8 * q^25 + 16 * q^43 + 16 * q^49 - 32 * q^67 - 16 * q^73 + 96 * q^91 + 8 * q^97

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