LMFDB - Embedded newform 1512.2.t.d.289.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(289,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))

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

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

chi := DirichletCharacter("1512.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.t (of order $3$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.7
Character	$\chi$	$=$	1512.289
Dual form			1512.2.t.d.361.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.58188 q^{5} +(-1.80922 - 1.93047i) q^{7} +O(q^{10})$	$q+1.58188 q^{5} +(-1.80922 - 1.93047i) q^{7} -5.17139 q^{11} +(-0.681985 - 1.18123i) q^{13} +(2.30781 + 3.99724i) q^{17} +(0.0321742 - 0.0557274i) q^{19} -6.74395 q^{23} -2.49767 q^{25} +(-4.70787 + 8.15427i) q^{29} +(1.33139 - 2.30604i) q^{31} +(-2.86196 - 3.05376i) q^{35} +(0.880766 - 1.52553i) q^{37} +(0.858924 + 1.48770i) q^{41} +(-5.12012 + 8.86831i) q^{43} +(2.60417 + 4.51056i) q^{47} +(-0.453429 + 6.98530i) q^{49} +(0.479996 + 0.831377i) q^{53} -8.18049 q^{55} +(-4.66676 + 8.08307i) q^{59} +(-7.19512 - 12.4623i) q^{61} +(-1.07882 - 1.86856i) q^{65} +(6.24903 - 10.8236i) q^{67} +4.49160 q^{71} +(-0.941655 - 1.63099i) q^{73} +(9.35619 + 9.98321i) q^{77} +(-3.26752 - 5.65951i) q^{79} +(5.08661 - 8.81026i) q^{83} +(3.65066 + 6.32314i) q^{85} +(4.12369 - 7.14243i) q^{89} +(-1.04647 + 3.45366i) q^{91} +(0.0508957 - 0.0881539i) q^{95} +(-7.26638 + 12.5857i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 6 q^{5} + 7 q^{7}+O(q^{10}) $ 22 * q + 6 * q^5 + 7 * q^7	$ 22 q + 6 q^{5} + 7 q^{7} - 6 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} + 4 q^{23} + 20 q^{25} - 9 q^{29} - 4 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} - 5 q^{47} - 15 q^{49} - 11 q^{53} + 22 q^{55} + 19 q^{59} - 13 q^{61} - 13 q^{65} + 26 q^{67} + 48 q^{71} - 35 q^{73} + 4 q^{77} + 10 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} - 12 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q + 6 * q^5 + 7 * q^7 - 6 * q^11 - 3 * q^13 - 7 * q^17 - q^19 + 4 * q^23 + 20 * q^25 - 9 * q^29 - 4 * q^31 - 14 * q^35 + 2 * q^37 - 16 * q^41 - 5 * q^47 - 15 * q^49 - 11 * q^53 + 22 * q^55 + 19 * q^59 - 13 * q^61 - 13 * q^65 + 26 * q^67 + 48 * q^71 - 35 * q^73 + 4 * q^77 + 10 * q^79 + 28 * q^83 - 20 * q^85 - 6 * q^89 - 37 * q^91 - 12 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.58188			0.707436			0.353718	−	0.935352i	$-0.384917\pi$
$5$	1.58188			0.707436			0.353718	+	0.935352i	$0.384917\pi$
$6$		0			0
$7$	−1.80922	−	1.93047i	−0.683822	−	0.729649i
$7$	−1.80922	−	1.93047i	−0.683822	−	0.729649i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−5.17139			−1.55923			−0.779616	−	0.626258i	$-0.784586\pi$
$11$	−5.17139			−1.55923			−0.779616	+	0.626258i	$0.784586\pi$
$12$		0			0
$13$	−0.681985	−	1.18123i	−0.189149	−	0.327615i	0.755818	−	0.654782i	$-0.227239\pi$
$13$	−0.681985	−	1.18123i	−0.189149	−	0.327615i	−0.944967	+	0.327167i	$0.893906\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.30781	+	3.99724i	0.559726	+	0.969473i	0.997519	+	0.0703975i	$0.0224268\pi$
$17$	2.30781	+	3.99724i	0.559726	+	0.969473i	−0.437794	+	0.899076i	$0.644240\pi$
$18$		0			0
$19$	0.0321742	−	0.0557274i	0.00738128	−	0.0127847i	−0.862311	−	0.506379i	$-0.830984\pi$
$19$	0.0321742	−	0.0557274i	0.00738128	−	0.0127847i	0.869692	+	0.493594i	$0.164317\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.74395			−1.40621			−0.703105	−	0.711086i	$-0.748204\pi$
$23$	−6.74395			−1.40621			−0.703105	+	0.711086i	$0.748204\pi$
$24$		0			0
$25$	−2.49767			−0.499534
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.70787	+	8.15427i	−0.874229	+	1.51421i	−0.0166475	+	0.999861i	$0.505299\pi$
$29$	−4.70787	+	8.15427i	−0.874229	+	1.51421i	−0.857582	+	0.514348i	$0.828034\pi$
$30$		0			0
$31$	1.33139	−	2.30604i	0.239125	−	0.414177i	−0.721339	−	0.692583i	$-0.756473\pi$
$31$	1.33139	−	2.30604i	0.239125	−	0.414177i	0.960463	+	0.278406i	$0.0898061\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.86196	−	3.05376i	−0.483760	−	0.516180i
$36$		0			0
$37$	0.880766	−	1.52553i	0.144797	−	0.250796i	−0.784500	−	0.620129i	$-0.787080\pi$
$37$	0.880766	−	1.52553i	0.144797	−	0.250796i	0.929297	+	0.369333i	$0.120414\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.858924	+	1.48770i	0.134141	+	0.232340i	0.925269	−	0.379311i	$-0.123839\pi$
$41$	0.858924	+	1.48770i	0.134141	+	0.232340i	−0.791128	+	0.611651i	$0.790506\pi$
$42$		0			0
$43$	−5.12012	+	8.86831i	−0.780811	+	1.35240i	0.150658	+	0.988586i	$0.451861\pi$
$43$	−5.12012	+	8.86831i	−0.780811	+	1.35240i	−0.931470	+	0.363819i	$0.881473\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.60417	+	4.51056i	0.379857	+	0.657932i	0.991041	−	0.133556i	$-0.0426397\pi$
$47$	2.60417	+	4.51056i	0.379857	+	0.657932i	−0.611184	+	0.791489i	$0.709306\pi$
$48$		0			0
$49$	−0.453429	+	6.98530i	−0.0647756	+	0.997900i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.479996	+	0.831377i	0.0659325	+	0.114198i	0.897107	−	0.441813i	$-0.145664\pi$
$53$	0.479996	+	0.831377i	0.0659325	+	0.114198i	−0.831175	+	0.556011i	$0.812331\pi$
$54$		0			0
$55$	−8.18049			−1.10306
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.66676	+	8.08307i	−0.607561	+	1.05233i	0.384080	+	0.923300i	$0.374519\pi$
$59$	−4.66676	+	8.08307i	−0.607561	+	1.05233i	−0.991641	+	0.129027i	$0.958815\pi$
$60$		0			0
$61$	−7.19512	−	12.4623i	−0.921241	−	1.59564i	−0.797498	−	0.603321i	$-0.793844\pi$
$61$	−7.19512	−	12.4623i	−0.921241	−	1.59564i	−0.123742	−	0.992314i	$-0.539490\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.07882	−	1.86856i	−0.133811	−	0.231767i
$66$		0			0
$67$	6.24903	−	10.8236i	0.763441	−	1.32232i	−0.177626	−	0.984098i	$-0.556842\pi$
$67$	6.24903	−	10.8236i	0.763441	−	1.32232i	0.941067	−	0.338220i	$-0.109825\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.49160			0.533055			0.266527	−	0.963827i	$-0.414124\pi$
$71$	4.49160			0.533055			0.266527	+	0.963827i	$0.414124\pi$
$72$		0			0
$73$	−0.941655	−	1.63099i	−0.110212	−	0.190893i	0.805643	−	0.592401i	$-0.201820\pi$
$73$	−0.941655	−	1.63099i	−0.110212	−	0.190893i	−0.915856	+	0.401507i	$0.868486\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.35619	+	9.98321i	1.06624	+	1.13769i
$78$		0			0
$79$	−3.26752	−	5.65951i	−0.367625	−	0.636745i	0.621569	−	0.783360i	$-0.286496\pi$
$79$	−3.26752	−	5.65951i	−0.367625	−	0.636745i	−0.989194	+	0.146615i	$0.953162\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.08661	−	8.81026i	0.558328	−	0.967052i	−0.439309	−	0.898336i	$-0.644777\pi$
$83$	5.08661	−	8.81026i	0.558328	−	0.967052i	0.997636	−	0.0687156i	$-0.0218901\pi$
$84$		0			0
$85$	3.65066	+	6.32314i	0.395970	+	0.685840i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.12369	−	7.14243i	0.437110	−	0.757096i	−0.560355	−	0.828252i	$-0.689335\pi$
$89$	4.12369	−	7.14243i	0.437110	−	0.757096i	0.997465	+	0.0711559i	$0.0226688\pi$
$90$		0			0
$91$	−1.04647	+	3.45366i	−0.109700	+	0.362042i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.0508957	−	0.0881539i	0.00522178	−	0.00904440i
$96$		0			0
$97$	−7.26638	+	12.5857i	−0.737789	+	1.27789i	0.215700	+	0.976460i	$0.430797\pi$
$97$	−7.26638	+	12.5857i	−0.737789	+	1.27789i	−0.953489	+	0.301428i	$0.902537\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.24620			−0.621520			−0.310760	−	0.950488i	$-0.600584\pi$
$101$	−6.24620			−0.621520			−0.310760	+	0.950488i	$0.600584\pi$
$102$		0			0
$103$	−5.77762			−0.569286			−0.284643	−	0.958634i	$-0.591875\pi$
$103$	−5.77762			−0.569286			−0.284643	+	0.958634i	$0.591875\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.251126	−	0.434963i	0.0242773	−	0.0420494i	−0.853632	−	0.520877i	$-0.825605\pi$
$107$	0.251126	−	0.434963i	0.0242773	−	0.0420494i	0.877909	+	0.478828i	$0.158938\pi$
$108$		0			0
$109$	−2.37218	−	4.10874i	−0.227214	−	0.393546i	0.729767	−	0.683696i	$-0.239628\pi$
$109$	−2.37218	−	4.10874i	−0.227214	−	0.393546i	−0.956981	+	0.290149i	$0.906295\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.11328	+	1.92825i	0.104728	+	0.181395i	0.913627	−	0.406553i	$-0.133269\pi$
$113$	1.11328	+	1.92825i	0.104728	+	0.181395i	−0.808899	+	0.587948i	$0.799936\pi$
$114$		0			0
$115$	−10.6681			−0.994804
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.54121	−	11.6870i	0.324623	−	1.07135i
$120$		0			0
$121$	15.7432			1.43120
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.8604			−1.06082
$126$		0			0
$127$	−18.6057			−1.65099			−0.825494	−	0.564410i	$-0.809104\pi$
$127$	−18.6057			−1.65099			−0.825494	+	0.564410i	$0.809104\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−13.5404			−1.18303			−0.591515	−	0.806294i	$-0.701470\pi$
$131$	−13.5404			−1.18303			−0.591515	+	0.806294i	$0.701470\pi$
$132$		0			0
$133$	−0.165791	+	0.0387119i	−0.0143759	+	0.00335675i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−13.7420			−1.17406			−0.587029	−	0.809566i	$-0.699702\pi$
$137$	−13.7420			−1.17406			−0.587029	+	0.809566i	$0.699702\pi$
$138$		0			0
$139$	6.79328	+	11.7663i	0.576198	+	0.998005i	0.995910	+	0.0903476i	$0.0287978\pi$
$139$	6.79328	+	11.7663i	0.576198	+	0.998005i	−0.419712	+	0.907657i	$0.637869\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.52681	+	6.10861i	0.294927	+	0.510828i
$144$		0			0
$145$	−7.44726	+	12.8990i	−0.618461	+	1.07121i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.96066			−0.488317			−0.244158	−	0.969735i	$-0.578512\pi$
$149$	−5.96066			−0.488317			−0.244158	+	0.969735i	$0.578512\pi$
$150$		0			0
$151$	8.54142			0.695091			0.347546	−	0.937663i	$-0.387015\pi$
$151$	8.54142			0.695091			0.347546	+	0.937663i	$0.387015\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.10610	−	3.64786i	0.169166	−	0.293004i
$156$		0			0
$157$	1.31996	−	2.28623i	0.105344	−	0.182461i	−0.808535	−	0.588449i	$-0.799739\pi$
$157$	1.31996	−	2.28623i	0.105344	−	0.182461i	0.913879	+	0.405987i	$0.133072\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	12.2013	+	13.0190i	0.961597	+	1.02604i
$162$		0			0
$163$	−8.87875	+	15.3785i	−0.695438	+	1.20453i	0.274595	+	0.961560i	$0.411456\pi$
$163$	−8.87875	+	15.3785i	−0.695438	+	1.20453i	−0.970033	+	0.242973i	$0.921877\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.98937	−	6.90979i	−0.308706	−	0.534695i	0.669373	−	0.742926i	$-0.266563\pi$
$167$	−3.98937	−	6.90979i	−0.308706	−	0.534695i	−0.978080	+	0.208231i	$0.933229\pi$
$168$		0			0
$169$	5.56979	−	9.64716i	0.428446	−	0.742090i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.83170	+	6.63670i	0.291319	+	0.504579i	0.974122	−	0.226023i	$-0.0725726\pi$
$173$	3.83170	+	6.63670i	0.291319	+	0.504579i	−0.682803	+	0.730603i	$0.739239\pi$
$174$		0			0
$175$	4.51884	+	4.82168i	0.341592	+	0.364485i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−11.7864	−	20.4147i	−0.880958	−	1.52586i	−0.850277	−	0.526335i	$-0.823566\pi$
$179$	−11.7864	−	20.4147i	−0.880958	−	1.52586i	−0.0306808	−	0.999529i	$-0.509768\pi$
$180$		0			0
$181$	17.3700			1.29110			0.645551	−	0.763717i	$-0.276628\pi$
$181$	17.3700			1.29110			0.645551	+	0.763717i	$0.276628\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.39326	−	2.41320i	0.102435	−	0.177422i
$186$		0			0
$187$	−11.9346	−	20.6713i	−0.872742	−	1.51163i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.42330	+	4.19728i	0.175344	+	0.303704i	0.940280	−	0.340402i	$-0.110563\pi$
$191$	2.42330	+	4.19728i	0.175344	+	0.303704i	−0.764936	+	0.644106i	$0.777230\pi$
$192$		0			0
$193$	7.32091	−	12.6802i	0.526970	−	0.912739i	−0.472536	−	0.881312i	$-0.656661\pi$
$193$	7.32091	−	12.6802i	0.526970	−	0.912739i	0.999506	−	0.0314278i	$-0.0100054\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	19.1996			1.36791			0.683957	−	0.729522i	$-0.260257\pi$
$197$	19.1996			1.36791			0.683957	+	0.729522i	$0.260257\pi$
$198$		0			0
$199$	6.50796	+	11.2721i	0.461337	+	0.799060i	0.999028	−	0.0440825i	$-0.0140364\pi$
$199$	6.50796	+	11.2721i	0.461337	+	0.799060i	−0.537691	+	0.843142i	$0.680703\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	24.2591	−	5.66448i	1.70266	−	0.397569i
$204$		0			0
$205$	1.35871	+	2.35336i	0.0948965	+	0.164366i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.166385	+	0.288188i	−0.0115091	+	0.0199344i
$210$		0			0
$211$	−7.43389	−	12.8759i	−0.511770	−	0.886412i	−0.999907	−	0.0136450i	$-0.995657\pi$
$211$	−7.43389	−	12.8759i	−0.511770	−	0.886412i	0.488137	−	0.872767i	$-0.337677\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.09940	+	14.0286i	−0.552374	+	0.956740i
$216$		0			0
$217$	−6.86052	+	1.60192i	−0.465722	+	0.108746i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.14778	−	5.45212i	0.211743	−	0.366749i
$222$		0			0
$223$	11.2085	−	19.4136i	0.750574	−	1.30003i	−0.196971	−	0.980409i	$-0.563110\pi$
$223$	11.2085	−	19.4136i	0.750574	−	1.30003i	0.947545	−	0.319623i	$-0.103556\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.89450			−0.258487			−0.129243	−	0.991613i	$-0.541255\pi$
$227$	−3.89450			−0.258487			−0.129243	+	0.991613i	$0.541255\pi$
$228$		0			0
$229$	−1.38717			−0.0916669			−0.0458334	−	0.998949i	$-0.514594\pi$
$229$	−1.38717			−0.0916669			−0.0458334	+	0.998949i	$0.514594\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−8.99057	+	15.5721i	−0.588992	+	1.02016i	0.405373	+	0.914151i	$0.367142\pi$
$233$	−8.99057	+	15.5721i	−0.588992	+	1.02016i	−0.994365	+	0.106013i	$0.966192\pi$
$234$		0			0
$235$	4.11947	+	7.13514i	0.268725	+	0.465445i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.68043	+	4.64264i	0.173382	+	0.300307i	0.939600	−	0.342274i	$-0.111197\pi$
$239$	2.68043	+	4.64264i	0.173382	+	0.300307i	−0.766218	+	0.642581i	$0.777864\pi$
$240$		0			0
$241$	0.416592			0.0268351			0.0134175	−	0.999910i	$-0.495729\pi$
$241$	0.416592			0.0268351			0.0134175	+	0.999910i	$0.495729\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.717269	+	11.0499i	−0.0458246	+	0.705951i
$246$		0			0
$247$	−0.0877694			−0.00558464
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−22.5606			−1.42401			−0.712006	−	0.702173i	$-0.752213\pi$
$251$	−22.5606			−1.42401			−0.712006	+	0.702173i	$0.752213\pi$
$252$		0			0
$253$	34.8756			2.19261
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.0461			0.689039			0.344520	−	0.938779i	$-0.388042\pi$
$257$	11.0461			0.689039			0.344520	+	0.938779i	$0.388042\pi$
$258$		0			0
$259$	−4.53850	+	1.05973i	−0.282008	+	0.0658486i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	25.4620			1.57006			0.785028	−	0.619460i	$-0.212648\pi$
$263$	25.4620			1.57006			0.785028	+	0.619460i	$0.212648\pi$
$264$		0			0
$265$	0.759294	+	1.31514i	0.0466430	+	0.0807881i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.78957	−	4.83168i	−0.170083	−	0.294593i	0.768366	−	0.640011i	$-0.221070\pi$
$269$	−2.78957	−	4.83168i	−0.170083	−	0.294593i	−0.938449	+	0.345419i	$0.887737\pi$
$270$		0			0
$271$	−1.46645	+	2.53997i	−0.0890806	+	0.154292i	−0.907123	−	0.420866i	$-0.861726\pi$
$271$	−1.46645	+	2.53997i	−0.0890806	+	0.154292i	0.818042	+	0.575158i	$0.195060\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	12.9164			0.778889
$276$		0			0
$277$	22.0917			1.32736			0.663680	−	0.748016i	$-0.268993\pi$
$277$	22.0917			1.32736			0.663680	+	0.748016i	$0.268993\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.81009	−	4.86721i	0.167636	−	0.290354i	−0.769952	−	0.638101i	$-0.779720\pi$
$281$	2.81009	−	4.86721i	0.167636	−	0.290354i	0.937588	+	0.347748i	$0.113053\pi$
$282$		0			0
$283$	−10.6502	+	18.4466i	−0.633086	+	1.09654i	0.353831	+	0.935309i	$0.384879\pi$
$283$	−10.6502	+	18.4466i	−0.633086	+	1.09654i	−0.986917	+	0.161228i	$0.948455\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.31798	−	4.34971i	0.0777977	−	0.256755i
$288$		0			0
$289$	−2.15195	+	3.72729i	−0.126585	+	0.219252i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−14.1128	−	24.4440i	−0.824477	−	1.42804i	−0.902319	−	0.431070i	$-0.858136\pi$
$293$	−14.1128	−	24.4440i	−0.824477	−	1.42804i	0.0778418	−	0.996966i	$-0.475197\pi$
$294$		0			0
$295$	−7.38224	+	12.7864i	−0.429811	+	0.744454i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.59927	+	7.96617i	0.265983	+	0.460696i
$300$		0			0
$301$	26.3834	−	6.16050i	1.52072	−	0.355086i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−11.3818	−	19.7138i	−0.651719	−	1.12881i
$306$		0			0
$307$	−2.41329			−0.137734			−0.0688669	−	0.997626i	$-0.521938\pi$
$307$	−2.41329			−0.137734			−0.0688669	+	0.997626i	$0.521938\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.76840	−	8.25911i	0.270391	−	0.468331i	−0.698571	−	0.715541i	$-0.746180\pi$
$311$	4.76840	−	8.25911i	0.270391	−	0.468331i	0.968962	+	0.247210i	$0.0795137\pi$
$312$		0			0
$313$	−16.3010	−	28.2341i	−0.921386	−	1.59589i	−0.797273	−	0.603619i	$-0.793725\pi$
$313$	−16.3010	−	28.2341i	−0.921386	−	1.59589i	−0.124112	−	0.992268i	$-0.539608\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.54977	−	2.68428i	−0.0870438	−	0.150764i	0.819216	−	0.573484i	$-0.194409\pi$
$317$	−1.54977	−	2.68428i	−0.0870438	−	0.150764i	−0.906260	+	0.422720i	$0.861075\pi$
$318$		0			0
$319$	24.3462	−	42.1689i	1.36313	−	2.36100i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.297008			0.0165260
$324$		0			0
$325$	1.70337	+	2.95033i	0.0944862	+	0.163655i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.99597	−	13.1879i	0.220305	−	0.727071i
$330$		0			0
$331$	1.83825	+	3.18394i	0.101039	+	0.175005i	0.912113	−	0.409939i	$-0.134450\pi$
$331$	1.83825	+	3.18394i	0.101039	+	0.175005i	−0.811074	+	0.584944i	$0.801117\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	9.88519	−	17.1216i	0.540086	−	0.935456i
$336$		0			0
$337$	6.15866	+	10.6671i	0.335483	+	0.581074i	0.983578	−	0.180486i	$-0.0577670\pi$
$337$	6.15866	+	10.6671i	0.335483	+	0.581074i	−0.648094	+	0.761560i	$0.724434\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−6.88514	+	11.9254i	−0.372851	+	0.645797i
$342$		0			0
$343$	14.3053	−	11.7626i	0.772412	−	0.635122i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.85078	+	15.3300i	−0.475135	+	0.822958i	−0.999594	−	0.0284778i	$-0.990934\pi$
$347$	−8.85078	+	15.3300i	−0.475135	+	0.822958i	0.524460	+	0.851435i	$0.324267\pi$
$348$		0			0
$349$	0.562639	−	0.974519i	0.0301174	−	0.0521648i	−0.850574	−	0.525856i	$-0.823745\pi$
$349$	0.562639	−	0.974519i	0.0301174	−	0.0521648i	0.880691	+	0.473691i	$0.157079\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	10.9625			0.583475			0.291738	−	0.956498i	$-0.405767\pi$
$353$	10.9625			0.583475			0.291738	+	0.956498i	$0.405767\pi$
$354$		0			0
$355$	7.10515			0.377102
$356$		0			0
$357$		0			0
$358$		0			0
$359$	13.4733	−	23.3364i	0.711092	−	1.23165i	−0.253356	−	0.967373i	$-0.581534\pi$
$359$	13.4733	−	23.3364i	0.711092	−	1.23165i	0.964448	−	0.264274i	$-0.0851324\pi$
$360$		0			0
$361$	9.49793	+	16.4509i	0.499891	+	0.865837i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.48958	−	2.58003i	−0.0779682	−	0.135045i
$366$		0			0
$367$	34.8273			1.81797			0.908986	−	0.416826i	$-0.136858\pi$
$367$	34.8273			1.81797			0.908986	+	0.416826i	$0.136858\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.736530	−	2.43076i	0.0382387	−	0.126199i
$372$		0			0
$373$	−23.1585			−1.19910			−0.599551	−	0.800336i	$-0.704654\pi$
$373$	−23.1585			−1.19910			−0.599551	+	0.800336i	$0.704654\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.8428			0.661437
$378$		0			0
$379$	22.7259			1.16735			0.583676	−	0.811987i	$-0.301614\pi$
$379$	22.7259			1.16735			0.583676	+	0.811987i	$0.301614\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−23.2041			−1.18567			−0.592837	−	0.805322i	$-0.701992\pi$
$383$	−23.2041			−1.18567			−0.592837	+	0.805322i	$0.701992\pi$
$384$		0			0
$385$	14.8003	+	15.7922i	0.754294	+	0.804844i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	9.13474			0.463149			0.231575	−	0.972817i	$-0.425612\pi$
$389$	9.13474			0.463149			0.231575	+	0.972817i	$0.425612\pi$
$390$		0			0
$391$	−15.5637	−	26.9572i	−0.787092	−	1.36328i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−5.16881	−	8.95265i	−0.260071	−	0.450456i
$396$		0			0
$397$	−19.2126	+	33.2773i	−0.964255	+	1.67014i	−0.252652	+	0.967557i	$0.581303\pi$
$397$	−19.2126	+	33.2773i	−0.964255	+	1.67014i	−0.711603	+	0.702582i	$0.752031\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.94696			−0.147164			−0.0735821	−	0.997289i	$-0.523443\pi$
$401$	−2.94696			−0.147164			−0.0735821	+	0.997289i	$0.523443\pi$
$402$		0			0
$403$	−3.63196			−0.180921
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.55478	+	7.88912i	−0.225772	+	0.391049i
$408$		0			0
$409$	−3.30296	+	5.72089i	−0.163321	+	0.282880i	−0.936058	−	0.351847i	$-0.885554\pi$
$409$	−3.30296	+	5.72089i	−0.163321	+	0.282880i	0.772737	+	0.634726i	$0.218887\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	24.0473	−	5.61503i	1.18329	−	0.276297i
$414$		0			0
$415$	8.04638	−	13.9367i	0.394981	−	0.684127i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.381961	+	0.661576i	0.0186600	+	0.0323201i	0.875205	−	0.483753i	$-0.160727\pi$
$419$	0.381961	+	0.661576i	0.0186600	+	0.0323201i	−0.856545	+	0.516073i	$0.827393\pi$
$420$		0			0
$421$	−2.48798	+	4.30931i	−0.121257	+	0.210023i	−0.920264	−	0.391299i	$-0.872026\pi$
$421$	−2.48798	+	4.30931i	−0.121257	+	0.210023i	0.799007	+	0.601322i	$0.205359\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−5.76414	−	9.98378i	−0.279602	−	0.484285i
$426$		0			0
$427$	−11.0406	+	36.4371i	−0.534290	+	1.76331i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	4.01856	+	6.96035i	0.193567	+	0.335268i	0.946430	−	0.322909i	$-0.104661\pi$
$431$	4.01856	+	6.96035i	0.193567	+	0.335268i	−0.752863	+	0.658178i	$0.771328\pi$
$432$		0			0
$433$	−10.8006			−0.519043			−0.259522	−	0.965737i	$-0.583565\pi$
$433$	−10.8006			−0.519043			−0.259522	+	0.965737i	$0.583565\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.216981	+	0.375823i	−0.0103796	+	0.0179780i
$438$		0			0
$439$	10.0597	+	17.4239i	0.480122	+	0.831596i	0.999740	−	0.0228028i	$-0.00725899\pi$
$439$	10.0597	+	17.4239i	0.480122	+	0.831596i	−0.519618	+	0.854399i	$0.673926\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.60623	−	7.97822i	−0.218848	−	0.379057i	0.735608	−	0.677408i	$-0.236897\pi$
$443$	−4.60623	−	7.97822i	−0.218848	−	0.379057i	−0.954456	+	0.298351i	$0.903563\pi$
$444$		0			0
$445$	6.52316	−	11.2984i	0.309227	−	0.535597i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	22.4840			1.06109			0.530544	−	0.847658i	$-0.321988\pi$
$449$	22.4840			1.06109			0.530544	+	0.847658i	$0.321988\pi$
$450$		0			0
$451$	−4.44183	−	7.69347i	−0.209158	−	0.362271i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.65539	+	5.46327i	−0.0776058	+	0.256122i
$456$		0			0
$457$	−9.39776	−	16.2774i	−0.439609	−	0.761425i	0.558050	−	0.829807i	$-0.311550\pi$
$457$	−9.39776	−	16.2774i	−0.439609	−	0.761425i	−0.997659	+	0.0683823i	$0.978216\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.3773	+	17.9739i	−0.483317	+	0.837129i	−0.999816	−	0.0191582i	$-0.993901\pi$
$461$	−10.3773	+	17.9739i	−0.483317	+	0.837129i	0.516500	+	0.856287i	$0.327235\pi$
$462$		0			0
$463$	10.0414	+	17.3922i	0.466663	+	0.808284i	0.999275	−	0.0380753i	$-0.0121227\pi$
$463$	10.0414	+	17.3922i	0.466663	+	0.808284i	−0.532612	+	0.846360i	$0.678789\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−14.6015	+	25.2905i	−0.675676	+	1.17030i	0.300595	+	0.953752i	$0.402815\pi$
$467$	−14.6015	+	25.2905i	−0.675676	+	1.17030i	−0.976271	+	0.216553i	$0.930519\pi$
$468$		0			0
$469$	−32.2006	+	7.51880i	−1.48689	+	0.347186i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	26.4781	−	45.8615i	1.21747	−	2.10871i
$474$		0			0
$475$	−0.0803606	+	0.139189i	−0.00368720	+	0.00638642i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	40.0654			1.83064			0.915319	−	0.402731i	$-0.131939\pi$
$479$	40.0654			1.83064			0.915319	+	0.402731i	$0.131939\pi$
$480$		0			0
$481$	−2.40268			−0.109553
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−11.4945	+	19.9091i	−0.521939	+	0.904024i
$486$		0			0
$487$	9.32801	+	16.1566i	0.422692	+	0.732125i	0.996202	−	0.0870742i	$-0.0277517\pi$
$487$	9.32801	+	16.1566i	0.422692	+	0.732125i	−0.573509	+	0.819199i	$0.694418\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.285132	+	0.493864i	0.0128678	+	0.0222878i	0.872388	−	0.488815i	$-0.162571\pi$
$491$	0.285132	+	0.493864i	0.0128678	+	0.0222878i	−0.859520	+	0.511102i	$0.829237\pi$
$492$		0			0
$493$	−43.4594			−1.95731
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.12630	−	8.67090i	−0.364514	−	0.388943i
$498$		0			0
$499$	−0.928593			−0.0415695			−0.0207848	−	0.999784i	$-0.506616\pi$
$499$	−0.928593			−0.0415695			−0.0207848	+	0.999784i	$0.506616\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	3.27170			0.145878			0.0729389	−	0.997336i	$-0.476762\pi$
$503$	3.27170			0.145878			0.0729389	+	0.997336i	$0.476762\pi$
$504$		0			0
$505$	−9.88071			−0.439686
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−8.96781			−0.397491			−0.198746	−	0.980051i	$-0.563687\pi$
$509$	−8.96781			−0.397491			−0.198746	+	0.980051i	$0.563687\pi$
$510$		0			0
$511$	−1.44492	+	4.76867i	−0.0639196	+	0.210953i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.13948			−0.402734
$516$		0			0
$517$	−13.4672	−	23.3258i	−0.592286	−	1.02587i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5.37649	+	9.31235i	0.235548	+	0.407982i	0.959432	−	0.281940i	$-0.0909781\pi$
$521$	5.37649	+	9.31235i	0.235548	+	0.407982i	−0.723884	+	0.689922i	$0.757645\pi$
$522$		0			0
$523$	−16.2796	+	28.1970i	−0.711856	+	1.23297i	0.252304	+	0.967648i	$0.418812\pi$
$523$	−16.2796	+	28.1970i	−0.711856	+	1.23297i	−0.964160	+	0.265322i	$0.914522\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	12.2904			0.535377
$528$		0			0
$529$	22.4808			0.977427
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.17155	−	2.02918i	0.0507453	−	0.0878935i
$534$		0			0
$535$	0.397250	−	0.688057i	0.0171746	−	0.0297473i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.34486	−	36.1237i	0.101000	−	1.55596i
$540$		0			0
$541$	−3.46359	+	5.99911i	−0.148911	+	0.257922i	−0.930825	−	0.365464i	$-0.880910\pi$
$541$	−3.46359	+	5.99911i	−0.148911	+	0.257922i	0.781914	+	0.623386i	$0.214244\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.75250	−	6.49952i	−0.160739	−	0.278409i
$546$		0			0
$547$	−15.8974	+	27.5351i	−0.679725	+	1.17732i	0.295339	+	0.955392i	$0.404567\pi$
$547$	−15.8974	+	27.5351i	−0.679725	+	1.17732i	−0.975064	+	0.221925i	$0.928766\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.302944	+	0.524715i	0.0129059	+	0.0223536i
$552$		0			0
$553$	−5.01385	+	16.5472i	−0.213211	+	0.703657i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−14.1679	−	24.5395i	−0.600314	−	1.03977i	−0.992773	−	0.120005i	$-0.961709\pi$
$557$	−14.1679	−	24.5395i	−0.600314	−	1.03977i	0.392460	−	0.919769i	$-0.371624\pi$
$558$		0			0
$559$	13.9674			0.590758
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−22.3270	+	38.6715i	−0.940972	+	1.62981i	−0.177350	+	0.984148i	$0.556752\pi$
$563$	−22.3270	+	38.6715i	−0.940972	+	1.62981i	−0.763622	+	0.645664i	$0.776581\pi$
$564$		0			0
$565$	1.76106	+	3.05025i	0.0740885	+	0.128325i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.6102	−	18.3775i	−0.444804	−	0.770423i	0.553235	−	0.833025i	$-0.313393\pi$
$569$	−10.6102	−	18.3775i	−0.444804	−	0.770423i	−0.998039	+	0.0626026i	$0.980060\pi$
$570$		0			0
$571$	−5.94786	+	10.3020i	−0.248910	+	0.431125i	−0.963224	−	0.268701i	$-0.913406\pi$
$571$	−5.94786	+	10.3020i	−0.248910	+	0.431125i	0.714313	+	0.699826i	$0.246739\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	16.8442			0.702450
$576$		0			0
$577$	−19.3490	−	33.5135i	−0.805511	−	1.39519i	−0.915946	−	0.401302i	$-0.868558\pi$
$577$	−19.3490	−	33.5135i	−0.805511	−	1.39519i	0.110435	−	0.993883i	$-0.464776\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−26.2107	+	6.12018i	−1.08741	+	0.253908i
$582$		0			0
$583$	−2.48224	−	4.29937i	−0.102804	−	0.178062i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.92138	+	17.1843i	−0.409499	+	0.709274i	−0.994834	−	0.101518i	$-0.967630\pi$
$587$	−9.92138	+	17.1843i	−0.409499	+	0.709274i	0.585334	+	0.810792i	$0.300963\pi$
$588$		0			0
$589$	−0.0856730	−	0.148390i	−0.00353010	−	0.00611431i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−10.9566	+	18.9774i	−0.449933	+	0.779307i	−0.998381	−	0.0568775i	$-0.981886\pi$
$593$	−10.9566	+	18.9774i	−0.449933	+	0.779307i	0.548448	+	0.836185i	$0.315219\pi$
$594$		0			0
$595$	5.60176	−	18.4875i	0.229650	−	0.757912i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	16.5223	−	28.6174i	0.675081	−	1.16928i	−0.301364	−	0.953509i	$-0.597442\pi$
$599$	16.5223	−	28.6174i	0.675081	−	1.16928i	0.976445	−	0.215766i	$-0.0692248\pi$
$600$		0			0
$601$	11.4951	−	19.9100i	0.468893	−	0.812147i	−0.530475	−	0.847701i	$-0.677986\pi$
$601$	11.4951	−	19.9100i	0.468893	−	0.812147i	0.999368	+	0.0355541i	$0.0113196\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	24.9038			1.01248
$606$		0			0
$607$	27.6564			1.12254			0.561269	−	0.827634i	$-0.310314\pi$
$607$	27.6564			1.12254			0.561269	+	0.827634i	$0.310314\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.55201	−	6.15226i	0.143699	−	0.248894i
$612$		0			0
$613$	−15.7684	−	27.3116i	−0.636879	−	1.10311i	−0.986114	−	0.166072i	$-0.946892\pi$
$613$	−15.7684	−	27.3116i	−0.636879	−	1.10311i	0.349235	−	0.937035i	$-0.386442\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	10.7513	+	18.6217i	0.432830	+	0.749683i	0.997116	−	0.0758961i	$-0.0241817\pi$
$617$	10.7513	+	18.6217i	0.432830	+	0.749683i	−0.564286	+	0.825580i	$0.690848\pi$
$618$		0			0
$619$	28.2522			1.13555			0.567776	−	0.823183i	$-0.307804\pi$
$619$	28.2522			1.13555			0.567776	+	0.823183i	$0.307804\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−21.2489	+	4.96160i	−0.851320	+	0.198782i
$624$		0			0
$625$	−6.27330			−0.250932
$626$		0			0
$627$		0			0
$628$		0			0
$629$	8.13056			0.324187
$630$		0			0
$631$	−9.12550			−0.363281			−0.181640	−	0.983365i	$-0.558141\pi$
$631$	−9.12550			−0.363281			−0.181640	+	0.983365i	$0.558141\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−29.4319			−1.16797
$636$		0			0
$637$	8.56050	−	4.22826i	0.339179	−	0.167530i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−32.8978			−1.29939			−0.649693	−	0.760197i	$-0.725103\pi$
$641$	−32.8978			−1.29939			−0.649693	+	0.760197i	$0.725103\pi$
$642$		0			0
$643$	10.1276	+	17.5415i	0.399392	+	0.691767i	0.993651	−	0.112506i	$-0.0358879\pi$
$643$	10.1276	+	17.5415i	0.399392	+	0.691767i	−0.594259	+	0.804274i	$0.702555\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.67441	+	9.82837i	0.223084	+	0.386393i	0.955743	−	0.294203i	$-0.0950542\pi$
$647$	5.67441	+	9.82837i	0.223084	+	0.386393i	−0.732659	+	0.680596i	$0.761721\pi$
$648$		0			0
$649$	24.1336	−	41.8007i	0.947328	−	1.64082i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.58036			−0.140110			−0.0700552	−	0.997543i	$-0.522318\pi$
$653$	−3.58036			−0.140110			−0.0700552	+	0.997543i	$0.522318\pi$
$654$		0			0
$655$	−21.4192			−0.836918
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−9.13582	+	15.8237i	−0.355881	+	0.616404i	−0.987268	−	0.159064i	$-0.949152\pi$
$659$	−9.13582	+	15.8237i	−0.355881	+	0.616404i	0.631387	+	0.775468i	$0.282486\pi$
$660$		0			0
$661$	−1.11696	+	1.93462i	−0.0434446	+	0.0752482i	−0.886930	−	0.461904i	$-0.847167\pi$
$661$	−1.11696	+	1.93462i	−0.0434446	+	0.0752482i	0.843485	+	0.537152i	$0.180500\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.262260	+	0.0612374i	−0.0101700	+	0.00237468i
$666$		0			0
$667$	31.7496	−	54.9919i	1.22935	−	2.12930i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	37.2087	+	64.4474i	1.43643	+	2.48797i
$672$		0			0
$673$	−12.4804	+	21.6166i	−0.481083	+	0.833260i	−0.999764	−	0.0217074i	$-0.993090\pi$
$673$	−12.4804	+	21.6166i	−0.481083	+	0.833260i	0.518681	+	0.854968i	$0.326423\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.90633	−	17.1583i	−0.380731	−	0.659446i	0.610436	−	0.792066i	$-0.290994\pi$
$677$	−9.90633	−	17.1583i	−0.380731	−	0.659446i	−0.991167	+	0.132620i	$0.957661\pi$
$678$		0			0
$679$	37.4429	−	8.74287i	1.43693	−	0.335521i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−5.72871	−	9.92242i	−0.219203	−	0.379671i	0.735361	−	0.677675i	$-0.237012\pi$
$683$	−5.72871	−	9.92242i	−0.219203	−	0.379671i	−0.954565	+	0.298004i	$0.903679\pi$
$684$		0			0
$685$	−21.7381			−0.830571
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.654700	−	1.13397i	0.0249421	−	0.0432010i
$690$		0			0
$691$	−20.2552	−	35.0831i	−0.770545	−	1.33462i	−0.937265	−	0.348619i	$-0.886651\pi$
$691$	−20.2552	−	35.0831i	−0.770545	−	1.33462i	0.166719	−	0.986004i	$-0.446683\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	10.7461	+	18.6128i	0.407624	+	0.706025i
$696$		0			0
$697$	−3.96446	+	6.86665i	−0.150165	+	0.260093i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	29.5416			1.11577			0.557885	−	0.829918i	$-0.311613\pi$
$701$	29.5416			1.11577			0.557885	+	0.829918i	$0.311613\pi$
$702$		0			0
$703$	−0.0566760	−	0.0981657i	−0.00213758	−	0.00370239i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	11.3008	+	12.0581i	0.425009	+	0.453492i
$708$		0			0
$709$	18.7407	+	32.4599i	0.703822	+	1.21906i	0.967115	+	0.254340i	$0.0818581\pi$
$709$	18.7407	+	32.4599i	0.703822	+	1.21906i	−0.263293	+	0.964716i	$0.584809\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−8.97883	+	15.5518i	−0.336260	+	0.582419i
$714$		0			0
$715$	5.57897	+	9.66306i	0.208642	+	0.361378i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6.35418	+	11.0058i	−0.236971	+	0.410445i	−0.959844	−	0.280536i	$-0.909488\pi$
$719$	−6.35418	+	11.0058i	−0.236971	+	0.410445i	0.722873	+	0.690981i	$0.242821\pi$
$720$		0			0
$721$	10.4530	+	11.1535i	0.389290	+	0.415379i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	11.7587	−	20.3667i	0.436707	−	0.756399i
$726$		0			0
$727$	19.9463	−	34.5480i	0.739768	−	1.28132i	−0.212832	−	0.977089i	$-0.568269\pi$
$727$	19.9463	−	34.5480i	0.739768	−	1.28132i	0.952600	−	0.304227i	$-0.0983980\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−47.2650			−1.74816
$732$		0			0
$733$	−44.8182			−1.65540			−0.827699	−	0.561172i	$-0.810350\pi$
$733$	−44.8182			−1.65540			−0.827699	+	0.561172i	$0.810350\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−32.3162	+	55.9732i	−1.19038	+	2.06180i
$738$		0			0
$739$	−6.64954	−	11.5173i	−0.244607	−	0.423672i	0.717414	−	0.696647i	$-0.245326\pi$
$739$	−6.64954	−	11.5173i	−0.244607	−	0.423672i	−0.962021	+	0.272975i	$0.911992\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−2.15562	−	3.73365i	−0.0790822	−	0.136974i	0.823772	−	0.566921i	$-0.191866\pi$
$743$	−2.15562	−	3.73365i	−0.0790822	−	0.136974i	−0.902854	+	0.429947i	$0.858532\pi$
$744$		0			0
$745$	−9.42903			−0.345453
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.29402	+	0.302153i	−0.0472826	+	0.0110404i
$750$		0			0
$751$	−43.5303			−1.58844			−0.794221	−	0.607629i	$-0.792121\pi$
$751$	−43.5303			−1.58844			−0.794221	+	0.607629i	$0.792121\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	13.5115			0.491733
$756$		0			0
$757$	34.6790			1.26043			0.630215	−	0.776420i	$-0.282967\pi$
$757$	34.6790			1.26043			0.630215	+	0.776420i	$0.282967\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.51946			0.127580			0.0637902	−	0.997963i	$-0.479681\pi$
$761$	3.51946			0.127580			0.0637902	+	0.997963i	$0.479681\pi$
$762$		0			0
$763$	−3.64000	+	12.0131i	−0.131777	+	0.434902i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.7307			0.459677
$768$		0			0
$769$	−19.5075	−	33.7879i	−0.703457	−	1.21842i	−0.967245	−	0.253843i	$-0.918305\pi$
$769$	−19.5075	−	33.7879i	−0.703457	−	1.21842i	0.263788	−	0.964581i	$-0.415028\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−23.2169	−	40.2128i	−0.835054	−	1.44636i	−0.893987	−	0.448094i	$-0.852103\pi$
$773$	−23.2169	−	40.2128i	−0.835054	−	1.44636i	0.0589329	−	0.998262i	$-0.481230\pi$
$774$		0			0
$775$	−3.32538	+	5.75972i	−0.119451	+	0.206895i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.110541			0.00396054
$780$		0			0
$781$	−23.2278			−0.831156
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.08801	−	3.61654i	0.0745242	−	0.129080i
$786$		0			0
$787$	−23.7212	+	41.0863i	−0.845569	+	1.46457i	0.0395575	+	0.999217i	$0.487405\pi$
$787$	−23.7212	+	41.0863i	−0.845569	+	1.46457i	−0.885126	+	0.465351i	$0.845928\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.70827	−	5.63778i	0.0607390	−	0.200456i
$792$		0			0
$793$	−9.81393	+	16.9982i	−0.348503	+	0.603625i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.69773	−	13.3329i	−0.272668	−	0.472274i	0.696876	−	0.717191i	$-0.254573\pi$
$797$	−7.69773	−	13.3329i	−0.272668	−	0.472274i	−0.969544	+	0.244917i	$0.921239\pi$
$798$		0			0
$799$	−12.0198	+	20.8190i	−0.425232	+	0.736523i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.86966	+	8.43450i	0.171847	+	0.297647i
$804$		0			0
$805$	19.3009	+	20.5944i	0.680269	+	0.725858i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	15.0433	+	26.0557i	0.528893	+	0.916069i	0.999432	+	0.0336903i	$0.0107260\pi$
$809$	15.0433	+	26.0557i	0.528893	+	0.916069i	−0.470539	+	0.882379i	$0.655941\pi$
$810$		0			0
$811$	−11.2821			−0.396170			−0.198085	−	0.980185i	$-0.563472\pi$
$811$	−11.2821			−0.396170			−0.198085	+	0.980185i	$0.563472\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−14.0451	+	24.3268i	−0.491978	+	0.852130i
$816$		0			0
$817$	0.329472	+	0.570662i	0.0115268	+	0.0199650i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.62633	+	2.81688i	0.0567593	+	0.0983099i	0.893009	−	0.450039i	$-0.148590\pi$
$821$	1.62633	+	2.81688i	0.0567593	+	0.0983099i	−0.836250	+	0.548349i	$0.815257\pi$
$822$		0			0
$823$	−7.29842	+	12.6412i	−0.254407	+	0.440645i	−0.964734	−	0.263226i	$-0.915214\pi$
$823$	−7.29842	+	12.6412i	−0.254407	+	0.440645i	0.710327	+	0.703871i	$0.248547\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−42.7500			−1.48656			−0.743282	−	0.668978i	$-0.766732\pi$
$827$	−42.7500			−1.48656			−0.743282	+	0.668978i	$0.766732\pi$
$828$		0			0
$829$	−17.6799	−	30.6225i	−0.614049	−	1.06356i	−0.990551	−	0.137148i	$-0.956207\pi$
$829$	−17.6799	−	30.6225i	−0.614049	−	1.06356i	0.376502	−	0.926416i	$-0.377127\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−28.9683	+	14.3083i	−1.00369	+	0.495752i
$834$		0			0
$835$	−6.31068	−	10.9304i	−0.218390	−	0.378263i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−15.0886	+	26.1343i	−0.520917	+	0.902255i	0.478787	+	0.877931i	$0.341077\pi$
$839$	−15.0886	+	26.1343i	−0.520917	+	0.902255i	−0.999704	+	0.0243242i	$0.992257\pi$
$840$		0			0
$841$	−29.8280	−	51.6637i	−1.02855	−	1.78151i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	8.81072	−	15.2606i	0.303098	−	0.524981i
$846$		0			0
$847$	−28.4830	−	30.3918i	−0.978688	−	1.04428i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.93984	+	10.2881i	−0.203615	+	0.352672i
$852$		0			0
$853$	−20.4789	+	35.4705i	−0.701184	+	1.21449i	0.266867	+	0.963733i	$0.414011\pi$
$853$	−20.4789	+	35.4705i	−0.701184	+	1.21449i	−0.968051	+	0.250753i	$0.919322\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−30.4566			−1.04038			−0.520190	−	0.854051i	$-0.674139\pi$
$857$	−30.4566			−1.04038			−0.520190	+	0.854051i	$0.674139\pi$
$858$		0			0
$859$	3.18935			0.108819			0.0544096	−	0.998519i	$-0.482672\pi$
$859$	3.18935			0.108819			0.0544096	+	0.998519i	$0.482672\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−11.5498	+	20.0049i	−0.393161	+	0.680975i	−0.992865	−	0.119247i	$-0.961952\pi$
$863$	−11.5498	+	20.0049i	−0.393161	+	0.680975i	0.599703	+	0.800222i	$0.295285\pi$
$864$		0			0
$865$	6.06128	+	10.4984i	0.206090	+	0.356958i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	16.8976	+	29.2675i	0.573212	+	0.992833i
$870$		0			0
$871$	−17.0470			−0.577615
$872$		0			0
$873$		0			0
$874$		0			0
$875$	21.4581	+	22.8961i	0.725415	+	0.774030i
$876$		0			0
$877$	−3.28938			−0.111074			−0.0555372	−	0.998457i	$-0.517687\pi$
$877$	−3.28938			−0.111074			−0.0555372	+	0.998457i	$0.517687\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−51.4835			−1.73452			−0.867262	−	0.497852i	$-0.834122\pi$
$881$	−51.4835			−1.73452			−0.867262	+	0.497852i	$0.834122\pi$
$882$		0			0
$883$	0.359433			0.0120959			0.00604794	−	0.999982i	$-0.498075\pi$
$883$	0.359433			0.0120959			0.00604794	+	0.999982i	$0.498075\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−11.6000			−0.389488			−0.194744	−	0.980854i	$-0.562388\pi$
$887$	−11.6000			−0.389488			−0.194744	+	0.980854i	$0.562388\pi$
$888$		0			0
$889$	33.6618	+	35.9177i	1.12898	+	1.20464i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.335149			0.0112153
$894$		0			0
$895$	−18.6446	−	32.2935i	−0.623222	−	1.07945i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	12.5360	+	21.7130i	0.418100	+	0.724170i
$900$		0			0
$901$	−2.21548	+	3.83732i	−0.0738082	+	0.127840i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	27.4772			0.913373
$906$		0			0
$907$	24.5791			0.816135			0.408067	−	0.912952i	$-0.366203\pi$
$907$	24.5791			0.816135			0.408067	+	0.912952i	$0.366203\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	20.1678	−	34.9317i	0.668190	−	1.15734i	−0.310219	−	0.950665i	$-0.600402\pi$
$911$	20.1678	−	34.9317i	0.668190	−	1.15734i	0.978410	−	0.206675i	$-0.0662642\pi$
$912$		0			0
$913$	−26.3048	+	45.5613i	−0.870562	+	1.50786i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	24.4976	+	26.1393i	0.808981	+	0.863197i
$918$		0			0
$919$	10.8377	−	18.7714i	0.357501	−	0.619210i	−0.630041	−	0.776562i	$-0.716962\pi$
$919$	10.8377	−	18.7714i	0.357501	−	0.619210i	0.987543	+	0.157351i	$0.0502954\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.06320	−	5.30562i	−0.100827	−	0.174637i
$924$		0			0
$925$	−2.19986	+	3.81028i	−0.0723311	+	0.125281i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−3.96409	−	6.86601i	−0.130058	−	0.225266i	0.793641	−	0.608386i	$-0.208183\pi$
$929$	−3.96409	−	6.86601i	−0.130058	−	0.225266i	−0.923699	+	0.383120i	$0.874850\pi$
$930$		0			0
$931$	0.374684	+	0.250015i	0.0122798	+	0.00819392i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−18.8790	−	32.6994i	−0.617409	−	1.06938i
$936$		0			0
$937$	5.84549			0.190964			0.0954819	−	0.995431i	$-0.469561\pi$
$937$	5.84549			0.190964			0.0954819	+	0.995431i	$0.469561\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−19.5046	+	33.7829i	−0.635831	+	1.10129i	0.350508	+	0.936560i	$0.386009\pi$
$941$	−19.5046	+	33.7829i	−0.635831	+	1.10129i	−0.986339	+	0.164731i	$0.947324\pi$
$942$		0			0
$943$	−5.79254	−	10.0330i	−0.188631	−	0.326719i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.52185	−	6.10003i	−0.114445	−	0.198224i	0.803113	−	0.595827i	$-0.203176\pi$
$947$	−3.52185	−	6.10003i	−0.114445	−	0.198224i	−0.917558	+	0.397603i	$0.869842\pi$
$948$		0			0
$949$	−1.28439	+	2.22463i	−0.0416930	+	0.0722145i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−28.2379			−0.914716			−0.457358	−	0.889283i	$-0.651204\pi$
$953$	−28.2379			−0.914716			−0.457358	+	0.889283i	$0.651204\pi$
$954$		0			0
$955$	3.83336	+	6.63957i	0.124044	+	0.214851i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	24.8623	+	26.5285i	0.802846	+	0.856650i
$960$		0			0
$961$	11.9548	+	20.7063i	0.385639	+	0.667946i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	11.5808	−	20.0585i	0.372798	−	0.645705i
$966$		0			0
$967$	−0.430925	−	0.746384i	−0.0138576	−	0.0240021i	0.859013	−	0.511953i	$-0.171078\pi$
$967$	−0.430925	−	0.746384i	−0.0138576	−	0.0240021i	−0.872871	+	0.487951i	$0.837744\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	19.6403	−	34.0181i	0.630288	−	1.09169i	−0.357204	−	0.934026i	$-0.616270\pi$
$971$	19.6403	−	34.0181i	0.630288	−	1.09169i	0.987493	−	0.157665i	$-0.0503967\pi$
$972$		0			0
$973$	10.4239	−	34.4021i	0.334176	−	1.10288i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−17.2739	+	29.9193i	−0.552641	+	0.957202i	0.445442	+	0.895311i	$0.353047\pi$
$977$	−17.2739	+	29.9193i	−0.552641	+	0.957202i	−0.998083	+	0.0618913i	$0.980287\pi$
$978$		0			0
$979$	−21.3252	+	36.9363i	−0.681555	+	1.18049i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	20.0193			0.638516			0.319258	−	0.947668i	$-0.396566\pi$
$983$	20.0193			0.638516			0.319258	+	0.947668i	$0.396566\pi$
$984$		0			0
$985$	30.3714			0.967712
$986$		0			0
$987$		0			0
$988$		0			0
$989$	34.5298	−	59.8074i	1.09798	−	1.90177i
$990$		0			0
$991$	2.27853	+	3.94653i	0.0723799	+	0.125366i	0.899944	−	0.436006i	$-0.143607\pi$
$991$	2.27853	+	3.94653i	0.0723799	+	0.125366i	−0.827564	+	0.561371i	$0.810274\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	10.2948	+	17.8311i	0.326367	+	0.565284i
$996$		0			0
$997$	21.7323			0.688270			0.344135	−	0.938920i	$-0.388172\pi$
$997$	21.7323			0.688270			0.344135	+	0.938920i	$0.388172\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.t.d.289.7		22
3.2	odd	2		504.2.t.d.457.4	yes	22
4.3	odd	2		3024.2.t.l.289.7		22
7.4	even	3		1512.2.q.c.1369.5		22
9.4	even	3		1512.2.q.c.793.5		22
9.5	odd	6		504.2.q.d.121.11	yes	22
12.11	even	2		1008.2.t.k.961.8		22
21.11	odd	6		504.2.q.d.25.11	✓	22
28.11	odd	6		3024.2.q.k.2881.5		22
36.23	even	6		1008.2.q.k.625.1		22
36.31	odd	6		3024.2.q.k.2305.5		22
63.4	even	3	inner	1512.2.t.d.361.7		22
63.32	odd	6		504.2.t.d.193.4	yes	22
84.11	even	6		1008.2.q.k.529.1		22
252.67	odd	6		3024.2.t.l.1873.7		22
252.95	even	6		1008.2.t.k.193.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.11	✓	22	21.11	odd	6
504.2.q.d.121.11	yes	22	9.5	odd	6
504.2.t.d.193.4	yes	22	63.32	odd	6
504.2.t.d.457.4	yes	22	3.2	odd	2
1008.2.q.k.529.1		22	84.11	even	6
1008.2.q.k.625.1		22	36.23	even	6
1008.2.t.k.193.8		22	252.95	even	6
1008.2.t.k.961.8		22	12.11	even	2
1512.2.q.c.793.5		22	9.4	even	3
1512.2.q.c.1369.5		22	7.4	even	3
1512.2.t.d.289.7		22	1.1	even	1	trivial
1512.2.t.d.361.7		22	63.4	even	3	inner
3024.2.q.k.2305.5		22	36.31	odd	6
3024.2.q.k.2881.5		22	28.11	odd	6
3024.2.t.l.289.7		22	4.3	odd	2
3024.2.t.l.1873.7		22	252.67	odd	6

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.58188 q^{5} +(-1.80922 - 1.93047i) q^{7} +O(q^{10})\)	\(q+1.58188 q^{5} +(-1.80922 - 1.93047i) q^{7} -5.17139 q^{11} +(-0.681985 - 1.18123i) q^{13} +(2.30781 + 3.99724i) q^{17} +(0.0321742 - 0.0557274i) q^{19} -6.74395 q^{23} -2.49767 q^{25} +(-4.70787 + 8.15427i) q^{29} +(1.33139 - 2.30604i) q^{31} +(-2.86196 - 3.05376i) q^{35} +(0.880766 - 1.52553i) q^{37} +(0.858924 + 1.48770i) q^{41} +(-5.12012 + 8.86831i) q^{43} +(2.60417 + 4.51056i) q^{47} +(-0.453429 + 6.98530i) q^{49} +(0.479996 + 0.831377i) q^{53} -8.18049 q^{55} +(-4.66676 + 8.08307i) q^{59} +(-7.19512 - 12.4623i) q^{61} +(-1.07882 - 1.86856i) q^{65} +(6.24903 - 10.8236i) q^{67} +4.49160 q^{71} +(-0.941655 - 1.63099i) q^{73} +(9.35619 + 9.98321i) q^{77} +(-3.26752 - 5.65951i) q^{79} +(5.08661 - 8.81026i) q^{83} +(3.65066 + 6.32314i) q^{85} +(4.12369 - 7.14243i) q^{89} +(-1.04647 + 3.45366i) q^{91} +(0.0508957 - 0.0881539i) q^{95} +(-7.26638 + 12.5857i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 6 q^{5} + 7 q^{7}+O(q^{10}) \) 22 * q + 6 * q^5 + 7 * q^7	\( 22 q + 6 q^{5} + 7 q^{7} - 6 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} + 4 q^{23} + 20 q^{25} - 9 q^{29} - 4 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} - 5 q^{47} - 15 q^{49} - 11 q^{53} + 22 q^{55} + 19 q^{59} - 13 q^{61} - 13 q^{65} + 26 q^{67} + 48 q^{71} - 35 q^{73} + 4 q^{77} + 10 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} - 12 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q + 6 * q^5 + 7 * q^7 - 6 * q^11 - 3 * q^13 - 7 * q^17 - q^19 + 4 * q^23 + 20 * q^25 - 9 * q^29 - 4 * q^31 - 14 * q^35 + 2 * q^37 - 16 * q^41 - 5 * q^47 - 15 * q^49 - 11 * q^53 + 22 * q^55 + 19 * q^59 - 13 * q^61 - 13 * q^65 + 26 * q^67 + 48 * q^71 - 35 * q^73 + 4 * q^77 + 10 * q^79 + 28 * q^83 - 20 * q^85 - 6 * q^89 - 37 * q^91 - 12 * q^95 - 29 * q^97

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