LMFDB - Embedded newform 2736.2.bm.k.559.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(559,2736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2736, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))

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

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

chi := DirichletCharacter("2736.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.bm (of order $6$, degree $2$, 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:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 304)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2736.559
Dual form			2736.2.bm.k.1855.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{5} +2.00000i q^{7} +O(q^{10})$	$q+(-0.500000 + 0.866025i) q^{5} +2.00000i q^{7} -2.00000i q^{11} +(-1.50000 + 0.866025i) q^{13} +(0.500000 - 0.866025i) q^{17} +(-1.73205 + 4.00000i) q^{19} +(-0.866025 + 0.500000i) q^{23} +(2.00000 + 3.46410i) q^{25} +(1.50000 - 0.866025i) q^{29} +3.46410 q^{31} +(-1.73205 - 1.00000i) q^{35} -3.46410i q^{37} +(-4.50000 - 2.59808i) q^{41} +(-7.79423 - 4.50000i) q^{43} +(-9.52628 + 5.50000i) q^{47} +3.00000 q^{49} +(-7.50000 + 4.33013i) q^{53} +(1.73205 + 1.00000i) q^{55} +(-4.33013 + 7.50000i) q^{59} +(4.50000 + 7.79423i) q^{61} -1.73205i q^{65} +(-2.59808 - 4.50000i) q^{67} +(-7.79423 + 13.5000i) q^{71} +(0.500000 - 0.866025i) q^{73} +4.00000 q^{77} +(0.866025 - 1.50000i) q^{79} -8.00000i q^{83} +(0.500000 + 0.866025i) q^{85} +(13.5000 - 7.79423i) q^{89} +(-1.73205 - 3.00000i) q^{91} +(-2.59808 - 3.50000i) q^{95} +(-13.5000 - 7.79423i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5}+O(q^{10}) $ 4 * q - 2 * q^5	$ 4 q - 2 q^{5} - 6 q^{13} + 2 q^{17} + 8 q^{25} + 6 q^{29} - 18 q^{41} + 12 q^{49} - 30 q^{53} + 18 q^{61} + 2 q^{73} + 16 q^{77} + 2 q^{85} + 54 q^{89} - 54 q^{97}+O(q^{100}) $ 4 * q - 2 * q^5 - 6 * q^13 + 2 * q^17 + 8 * q^25 + 6 * q^29 - 18 * q^41 + 12 * q^49 - 30 * q^53 + 18 * q^61 + 2 * q^73 + 16 * q^77 + 2 * q^85 + 54 * q^89 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$		0			0
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$		0			0
$13$	−1.50000	+	0.866025i	−0.416025	+	0.240192i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−1.50000	+	0.866025i	−0.416025	+	0.240192i	0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	−0.799000	−	0.601331i	$-0.794637\pi$
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	0.920268	+	0.391289i	$0.127971\pi$
$18$		0			0
$19$	−1.73205	+	4.00000i	−0.397360	+	0.917663i
$19$	−1.73205	+	4.00000i	−0.397360	+	0.917663i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.866025	+	0.500000i	−0.180579	+	0.104257i	−0.587565	−	0.809177i	$-0.699913\pi$
$23$	−0.866025	+	0.500000i	−0.180579	+	0.104257i	0.406986	+	0.913434i	$0.366580\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.50000	−	0.866025i	0.278543	−	0.160817i	−0.354221	−	0.935162i	$-0.615254\pi$
$29$	1.50000	−	0.866025i	0.278543	−	0.160817i	0.632764	+	0.774345i	$0.281920\pi$
$30$		0			0
$31$	3.46410			0.622171			0.311086	−	0.950382i	$-0.399307\pi$
$31$	3.46410			0.622171			0.311086	+	0.950382i	$0.399307\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.73205	−	1.00000i	−0.292770	−	0.169031i
$36$		0			0
$37$		−	3.46410i		−	0.569495i	−0.958603	−	0.284747i	$-0.908090\pi$
$37$		−	3.46410i		−	0.569495i	0.958603	−	0.284747i	$-0.0919097\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.50000	−	2.59808i	−0.702782	−	0.405751i	0.105601	−	0.994409i	$-0.466323\pi$
$41$	−4.50000	−	2.59808i	−0.702782	−	0.405751i	−0.808383	+	0.588657i	$0.799657\pi$
$42$		0			0
$43$	−7.79423	−	4.50000i	−1.18861	−	0.686244i	−0.230618	−	0.973044i	$-0.574075\pi$
$43$	−7.79423	−	4.50000i	−1.18861	−	0.686244i	−0.957990	+	0.286801i	$0.907408\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−9.52628	+	5.50000i	−1.38955	+	0.802257i	−0.993264	−	0.115870i	$-0.963035\pi$
$47$	−9.52628	+	5.50000i	−1.38955	+	0.802257i	−0.396286	+	0.918127i	$0.629701\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−7.50000	+	4.33013i	−1.03020	+	0.594789i	−0.917043	−	0.398788i	$-0.869431\pi$
$53$	−7.50000	+	4.33013i	−1.03020	+	0.594789i	−0.113161	+	0.993577i	$0.536098\pi$
$54$		0			0
$55$	1.73205	+	1.00000i	0.233550	+	0.134840i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.33013	+	7.50000i	−0.563735	+	0.976417i	0.433432	+	0.901186i	$0.357303\pi$
$59$	−4.33013	+	7.50000i	−0.563735	+	0.976417i	−0.997166	+	0.0752304i	$0.976031\pi$
$60$		0			0
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	0.995914	+	0.0903080i	$0.0287851\pi$
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	−0.419748	+	0.907641i	$0.637882\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	1.73205i		−	0.214834i
$66$		0			0
$67$	−2.59808	−	4.50000i	−0.317406	−	0.549762i	0.662540	−	0.749026i	$-0.269478\pi$
$67$	−2.59808	−	4.50000i	−0.317406	−	0.549762i	−0.979946	+	0.199264i	$0.936145\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.79423	+	13.5000i	−0.925005	+	1.60216i	−0.133451	+	0.991055i	$0.542606\pi$
$71$	−7.79423	+	13.5000i	−0.925005	+	1.60216i	−0.791554	+	0.611100i	$0.790727\pi$
$72$		0			0
$73$	0.500000	−	0.866025i	0.0585206	−	0.101361i	−0.835281	−	0.549823i	$-0.814695\pi$
$73$	0.500000	−	0.866025i	0.0585206	−	0.101361i	0.893801	+	0.448463i	$0.148028\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.00000			0.455842
$78$		0			0
$79$	0.866025	−	1.50000i	0.0974355	−	0.168763i	−0.813187	−	0.582003i	$-0.802269\pi$
$79$	0.866025	−	1.50000i	0.0974355	−	0.168763i	0.910622	+	0.413239i	$0.135603\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	8.00000i		−	0.878114i	−0.898459	−	0.439057i	$-0.855313\pi$
$83$		−	8.00000i		−	0.878114i	0.898459	−	0.439057i	$-0.144687\pi$
$84$		0			0
$85$	0.500000	+	0.866025i	0.0542326	+	0.0939336i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	13.5000	−	7.79423i	1.43100	−	0.826187i	0.433800	−	0.901009i	$-0.357172\pi$
$89$	13.5000	−	7.79423i	1.43100	−	0.826187i	0.997197	+	0.0748225i	$0.0238390\pi$
$90$		0			0
$91$	−1.73205	−	3.00000i	−0.181568	−	0.314485i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.59808	−	3.50000i	−0.266557	−	0.359092i
$96$		0			0
$97$	−13.5000	−	7.79423i	−1.37072	−	0.791384i	−0.379699	−	0.925110i	$-0.623972\pi$
$97$	−13.5000	−	7.79423i	−1.37072	−	0.791384i	−0.991018	+	0.133726i	$0.957306\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.50000	−	6.06218i	−0.348263	−	0.603209i	0.637678	−	0.770303i	$-0.279895\pi$
$101$	−3.50000	−	6.06218i	−0.348263	−	0.603209i	−0.985941	+	0.167094i	$0.946562\pi$
$102$		0			0
$103$	−13.8564			−1.36531			−0.682656	−	0.730740i	$-0.739175\pi$
$103$	−13.8564			−1.36531			−0.682656	+	0.730740i	$0.739175\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.92820			−0.669775			−0.334887	−	0.942258i	$-0.608698\pi$
$107$	−6.92820			−0.669775			−0.334887	+	0.942258i	$0.608698\pi$
$108$		0			0
$109$	−1.50000	−	0.866025i	−0.143674	−	0.0829502i	0.426440	−	0.904516i	$-0.359768\pi$
$109$	−1.50000	−	0.866025i	−0.143674	−	0.0829502i	−0.570114	+	0.821566i	$0.693101\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			3.46410i			0.325875i	0.986636	+	0.162938i	$0.0520969\pi$
$113$			3.46410i			0.325875i	−0.986636	+	0.162938i	$0.947903\pi$
$114$		0			0
$115$		−	1.00000i		−	0.0932505i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.73205	+	1.00000i	0.158777	+	0.0916698i
$120$		0			0
$121$	7.00000			0.636364
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	6.06218	+	10.5000i	0.537931	+	0.931724i	0.999015	+	0.0443678i	$0.0141274\pi$
$127$	6.06218	+	10.5000i	0.537931	+	0.931724i	−0.461084	+	0.887357i	$0.652539\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−14.7224	−	8.50000i	−1.28630	−	0.742648i	−0.308312	−	0.951285i	$-0.599764\pi$
$131$	−14.7224	−	8.50000i	−1.28630	−	0.742648i	−0.977993	+	0.208637i	$0.933097\pi$
$132$		0			0
$133$	−8.00000	−	3.46410i	−0.693688	−	0.300376i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.50000	−	6.06218i	−0.299025	−	0.517927i	0.676888	−	0.736086i	$-0.263328\pi$
$137$	−3.50000	−	6.06218i	−0.299025	−	0.517927i	−0.975913	+	0.218159i	$0.929995\pi$
$138$		0			0
$139$	−9.52628	+	5.50000i	−0.808008	+	0.466504i	−0.846264	−	0.532764i	$-0.821153\pi$
$139$	−9.52628	+	5.50000i	−0.808008	+	0.466504i	0.0382553	+	0.999268i	$0.487820\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.73205	+	3.00000i	0.144841	+	0.250873i
$144$		0			0
$145$			1.73205i			0.143839i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.50000	+	16.4545i	−0.778270	+	1.34800i	0.154668	+	0.987967i	$0.450569\pi$
$149$	−9.50000	+	16.4545i	−0.778270	+	1.34800i	−0.932938	+	0.360037i	$0.882764\pi$
$150$		0			0
$151$	−6.92820			−0.563809			−0.281905	−	0.959442i	$-0.590966\pi$
$151$	−6.92820			−0.563809			−0.281905	+	0.959442i	$0.590966\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.73205	+	3.00000i	−0.139122	+	0.240966i
$156$		0			0
$157$	10.5000	−	18.1865i	0.837991	−	1.45144i	−0.0535803	−	0.998564i	$-0.517063\pi$
$157$	10.5000	−	18.1865i	0.837991	−	1.45144i	0.891572	−	0.452880i	$-0.149603\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.00000	−	1.73205i	−0.0788110	−	0.136505i
$162$		0			0
$163$			14.0000i			1.09656i	0.836293	+	0.548282i	$0.184718\pi$
$163$			14.0000i			1.09656i	−0.836293	+	0.548282i	$0.815282\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.866025	−	1.50000i	−0.0670151	−	0.116073i	0.830571	−	0.556913i	$-0.188014\pi$
$167$	−0.866025	−	1.50000i	−0.0670151	−	0.116073i	−0.897586	+	0.440839i	$0.854681\pi$
$168$		0			0
$169$	−5.00000	+	8.66025i	−0.384615	+	0.666173i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	16.5000	+	9.52628i	1.25447	+	0.724270i	0.971994	−	0.235004i	$-0.0755104\pi$
$173$	16.5000	+	9.52628i	1.25447	+	0.724270i	0.282477	+	0.959274i	$0.408844\pi$
$174$		0			0
$175$	−6.92820	+	4.00000i	−0.523723	+	0.302372i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−13.8564			−1.03568			−0.517838	−	0.855479i	$-0.673263\pi$
$179$	−13.8564			−1.03568			−0.517838	+	0.855479i	$0.673263\pi$
$180$		0			0
$181$	−4.50000	+	2.59808i	−0.334482	+	0.193113i	−0.657829	−	0.753167i	$-0.728525\pi$
$181$	−4.50000	+	2.59808i	−0.334482	+	0.193113i	0.323347	+	0.946280i	$0.395192\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.00000	+	1.73205i	0.220564	+	0.127343i
$186$		0			0
$187$	−1.73205	−	1.00000i	−0.126660	−	0.0731272i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	10.0000i		−	0.723575i	−0.932261	−	0.361787i	$-0.882167\pi$
$191$		−	10.0000i		−	0.723575i	0.932261	−	0.361787i	$-0.117833\pi$
$192$		0			0
$193$	7.50000	+	4.33013i	0.539862	+	0.311689i	0.745023	−	0.667039i	$-0.232439\pi$
$193$	7.50000	+	4.33013i	0.539862	+	0.311689i	−0.205161	+	0.978728i	$0.565772\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	20.0000			1.42494			0.712470	−	0.701702i	$-0.247576\pi$
$197$	20.0000			1.42494			0.712470	+	0.701702i	$0.247576\pi$
$198$		0			0
$199$	2.59808	−	1.50000i	0.184173	−	0.106332i	−0.405079	−	0.914282i	$-0.632756\pi$
$199$	2.59808	−	1.50000i	0.184173	−	0.106332i	0.589252	+	0.807950i	$0.299423\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.73205	+	3.00000i	0.121566	+	0.210559i
$204$		0			0
$205$	4.50000	−	2.59808i	0.314294	−	0.181458i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8.00000	+	3.46410i	0.553372	+	0.239617i
$210$		0			0
$211$	6.06218	−	10.5000i	0.417338	−	0.722850i	−0.578333	−	0.815801i	$-0.696297\pi$
$211$	6.06218	−	10.5000i	0.417338	−	0.722850i	0.995671	+	0.0929509i	$0.0296300\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	7.79423	−	4.50000i	0.531562	−	0.306897i
$216$		0			0
$217$			6.92820i			0.470317i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			1.73205i			0.116510i
$222$		0			0
$223$	−4.33013	+	7.50000i	−0.289967	+	0.502237i	−0.973801	−	0.227400i	$-0.926978\pi$
$223$	−4.33013	+	7.50000i	−0.289967	+	0.502237i	0.683835	+	0.729637i	$0.260311\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−20.7846			−1.37952			−0.689761	−	0.724037i	$-0.742285\pi$
$227$	−20.7846			−1.37952			−0.689761	+	0.724037i	$0.742285\pi$
$228$		0			0
$229$	−24.0000			−1.58596			−0.792982	−	0.609245i	$-0.791473\pi$
$229$	−24.0000			−1.58596			−0.792982	+	0.609245i	$0.791473\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.50000	+	16.4545i	−0.622366	+	1.07797i	0.366678	+	0.930348i	$0.380495\pi$
$233$	−9.50000	+	16.4545i	−0.622366	+	1.07797i	−0.989044	+	0.147621i	$0.952838\pi$
$234$		0			0
$235$		−	11.0000i		−	0.717561i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			20.0000i			1.29369i	0.762620	+	0.646846i	$0.223912\pi$
$239$			20.0000i			1.29369i	−0.762620	+	0.646846i	$0.776088\pi$
$240$		0			0
$241$	−13.5000	+	7.79423i	−0.869611	+	0.502070i	−0.867219	−	0.497927i	$-0.834095\pi$
$241$	−13.5000	+	7.79423i	−0.869611	+	0.502070i	−0.00239235	+	0.999997i	$0.500762\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.50000	+	2.59808i	−0.0958315	+	0.165985i
$246$		0			0
$247$	−0.866025	−	7.50000i	−0.0551039	−	0.477214i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−11.2583	+	6.50000i	−0.710620	+	0.410276i	−0.811290	−	0.584643i	$-0.801234\pi$
$251$	−11.2583	+	6.50000i	−0.710620	+	0.410276i	0.100671	+	0.994920i	$0.467901\pi$
$252$		0			0
$253$	1.00000	+	1.73205i	0.0628695	+	0.108893i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.5000	−	6.06218i	0.654972	−	0.378148i	−0.135387	−	0.990793i	$-0.543228\pi$
$257$	10.5000	−	6.06218i	0.654972	−	0.378148i	0.790359	+	0.612645i	$0.209894\pi$
$258$		0			0
$259$	6.92820			0.430498
$260$		0			0
$261$		0			0
$262$		0			0
$263$	16.4545	+	9.50000i	1.01463	+	0.585795i	0.912543	−	0.408981i	$-0.134116\pi$
$263$	16.4545	+	9.50000i	1.01463	+	0.585795i	0.102084	+	0.994776i	$0.467449\pi$
$264$		0			0
$265$		−	8.66025i		−	0.531995i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.50000	+	0.866025i	0.0914566	+	0.0528025i	0.545031	−	0.838416i	$-0.316518\pi$
$269$	1.50000	+	0.866025i	0.0914566	+	0.0528025i	−0.453574	+	0.891219i	$0.649851\pi$
$270$		0			0
$271$	18.1865	+	10.5000i	1.10475	+	0.637830i	0.937465	−	0.348079i	$-0.113166\pi$
$271$	18.1865	+	10.5000i	1.10475	+	0.637830i	0.167288	+	0.985908i	$0.446499\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.92820	−	4.00000i	0.417786	−	0.241209i
$276$		0			0
$277$	24.0000			1.44202			0.721010	−	0.692925i	$-0.243678\pi$
$277$	24.0000			1.44202			0.721010	+	0.692925i	$0.243678\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−19.5000	+	11.2583i	−1.16327	+	0.671616i	−0.952086	−	0.305830i	$-0.901066\pi$
$281$	−19.5000	+	11.2583i	−1.16327	+	0.671616i	−0.211186	+	0.977446i	$0.567733\pi$
$282$		0			0
$283$	−12.9904	−	7.50000i	−0.772198	−	0.445829i	0.0614601	−	0.998110i	$-0.480424\pi$
$283$	−12.9904	−	7.50000i	−0.772198	−	0.445829i	−0.833658	+	0.552281i	$0.813758\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.19615	−	9.00000i	0.306719	−	0.531253i
$288$		0			0
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	24.2487i		−	1.41662i	−0.705899	−	0.708312i	$-0.749457\pi$
$293$		−	24.2487i		−	1.41662i	0.705899	−	0.708312i	$-0.250543\pi$
$294$		0			0
$295$	−4.33013	−	7.50000i	−0.252110	−	0.436667i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.866025	−	1.50000i	0.0500835	−	0.0867472i
$300$		0			0
$301$	9.00000	−	15.5885i	0.518751	−	0.898504i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−9.00000			−0.515339
$306$		0			0
$307$	0.866025	−	1.50000i	0.0494267	−	0.0856095i	−0.840254	−	0.542194i	$-0.817594\pi$
$307$	0.866025	−	1.50000i	0.0494267	−	0.0856095i	0.889680	+	0.456584i	$0.150927\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			28.0000i			1.58773i	0.608091	+	0.793867i	$0.291935\pi$
$311$			28.0000i			1.58773i	−0.608091	+	0.793867i	$0.708065\pi$
$312$		0			0
$313$	−4.50000	−	7.79423i	−0.254355	−	0.440556i	0.710365	−	0.703833i	$-0.248530\pi$
$313$	−4.50000	−	7.79423i	−0.254355	−	0.440556i	−0.964720	+	0.263278i	$0.915197\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.50000	−	0.866025i	0.0842484	−	0.0486408i	−0.457284	−	0.889321i	$-0.651178\pi$
$317$	1.50000	−	0.866025i	0.0842484	−	0.0486408i	0.541532	+	0.840680i	$0.317844\pi$
$318$		0			0
$319$	−1.73205	−	3.00000i	−0.0969762	−	0.167968i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.59808	+	3.50000i	0.144561	+	0.194745i
$324$		0			0
$325$	−6.00000	−	3.46410i	−0.332820	−	0.192154i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−11.0000	−	19.0526i	−0.606450	−	1.05040i
$330$		0			0
$331$	20.7846			1.14243			0.571213	−	0.820802i	$-0.306473\pi$
$331$	20.7846			1.14243			0.571213	+	0.820802i	$0.306473\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.19615			0.283896
$336$		0			0
$337$	−7.50000	−	4.33013i	−0.408551	−	0.235877i	0.281616	−	0.959527i	$-0.409130\pi$
$337$	−7.50000	−	4.33013i	−0.408551	−	0.235877i	−0.690167	+	0.723650i	$0.742463\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	6.92820i		−	0.375183i
$342$		0			0
$343$			20.0000i			1.07990i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.06218	−	3.50000i	−0.325435	−	0.187890i	0.328378	−	0.944547i	$-0.393498\pi$
$347$	−6.06218	−	3.50000i	−0.325435	−	0.187890i	−0.653812	+	0.756657i	$0.726831\pi$
$348$		0			0
$349$	8.00000			0.428230			0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000			0.428230			0.214115	+	0.976808i	$0.431313\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	8.00000			0.425797			0.212899	−	0.977074i	$-0.431710\pi$
$353$	8.00000			0.425797			0.212899	+	0.977074i	$0.431710\pi$
$354$		0			0
$355$	−7.79423	−	13.5000i	−0.413675	−	0.716506i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	26.8468	+	15.5000i	1.41692	+	0.818059i	0.996027	−	0.0890519i	$-0.0283837\pi$
$359$	26.8468	+	15.5000i	1.41692	+	0.818059i	0.420892	+	0.907111i	$0.361717\pi$
$360$		0			0
$361$	−13.0000	−	13.8564i	−0.684211	−	0.729285i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.500000	+	0.866025i	0.0261712	+	0.0453298i
$366$		0			0
$367$	12.9904	−	7.50000i	0.678092	−	0.391497i	−0.121044	−	0.992647i	$-0.538624\pi$
$367$	12.9904	−	7.50000i	0.678092	−	0.391497i	0.799136	+	0.601150i	$0.205291\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−8.66025	−	15.0000i	−0.449618	−	0.778761i
$372$		0			0
$373$			6.92820i			0.358729i	0.983783	+	0.179364i	$0.0574041\pi$
$373$			6.92820i			0.358729i	−0.983783	+	0.179364i	$0.942596\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.50000	+	2.59808i	−0.0772539	+	0.133808i
$378$		0			0
$379$	20.7846			1.06763			0.533817	−	0.845600i	$-0.320757\pi$
$379$	20.7846			1.06763			0.533817	+	0.845600i	$0.320757\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	16.4545	−	28.5000i	0.840785	−	1.45628i	−0.0484473	−	0.998826i	$-0.515427\pi$
$383$	16.4545	−	28.5000i	0.840785	−	1.45628i	0.889232	−	0.457456i	$-0.151239\pi$
$384$		0			0
$385$	−2.00000	+	3.46410i	−0.101929	+	0.176547i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.50000	−	11.2583i	−0.329563	−	0.570820i	0.652862	−	0.757477i	$-0.273568\pi$
$389$	−6.50000	−	11.2583i	−0.329563	−	0.570820i	−0.982425	+	0.186657i	$0.940235\pi$
$390$		0			0
$391$			1.00000i			0.0505722i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.866025	+	1.50000i	0.0435745	+	0.0754732i
$396$		0			0
$397$	−9.50000	+	16.4545i	−0.476791	+	0.825827i	−0.999646	−	0.0265948i	$-0.991534\pi$
$397$	−9.50000	+	16.4545i	−0.476791	+	0.825827i	0.522855	+	0.852422i	$0.324867\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	25.5000	+	14.7224i	1.27341	+	0.735203i	0.975628	−	0.219431i	$-0.0704201\pi$
$401$	25.5000	+	14.7224i	1.27341	+	0.735203i	0.297781	+	0.954634i	$0.403753\pi$
$402$		0			0
$403$	−5.19615	+	3.00000i	−0.258839	+	0.149441i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.92820			−0.343418
$408$		0			0
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	−0.302979	−	0.952997i	$-0.597981\pi$
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	0.673830	+	0.738886i	$0.264648\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−15.0000	−	8.66025i	−0.738102	−	0.426143i
$414$		0			0
$415$	6.92820	+	4.00000i	0.340092	+	0.196352i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	26.0000i		−	1.27018i	−0.772437	−	0.635092i	$-0.780962\pi$
$419$		−	26.0000i		−	1.27018i	0.772437	−	0.635092i	$-0.219038\pi$
$420$		0			0
$421$	−4.50000	−	2.59808i	−0.219317	−	0.126622i	0.386317	−	0.922366i	$-0.373747\pi$
$421$	−4.50000	−	2.59808i	−0.219317	−	0.126622i	−0.605634	+	0.795744i	$0.707080\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.00000			0.194029
$426$		0			0
$427$	−15.5885	+	9.00000i	−0.754378	+	0.435541i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.866025	+	1.50000i	0.0417150	+	0.0722525i	0.886129	−	0.463439i	$-0.153385\pi$
$431$	0.866025	+	1.50000i	0.0417150	+	0.0722525i	−0.844414	+	0.535691i	$0.820051\pi$
$432$		0			0
$433$	7.50000	−	4.33013i	0.360427	−	0.208093i	−0.308841	−	0.951114i	$-0.599941\pi$
$433$	7.50000	−	4.33013i	0.360427	−	0.208093i	0.669268	+	0.743021i	$0.266608\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.500000	−	4.33013i	−0.0239182	−	0.207138i
$438$		0			0
$439$	−12.9904	+	22.5000i	−0.619997	+	1.07387i	0.369489	+	0.929235i	$0.379533\pi$
$439$	−12.9904	+	22.5000i	−0.619997	+	1.07387i	−0.989486	+	0.144631i	$0.953800\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	19.9186	−	11.5000i	0.946360	−	0.546381i	0.0544120	−	0.998519i	$-0.482672\pi$
$443$	19.9186	−	11.5000i	0.946360	−	0.546381i	0.891948	+	0.452137i	$0.149338\pi$
$444$		0			0
$445$			15.5885i			0.738964i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	24.2487i		−	1.14437i	−0.820125	−	0.572184i	$-0.806096\pi$
$449$		−	24.2487i		−	1.14437i	0.820125	−	0.572184i	$-0.193904\pi$
$450$		0			0
$451$	−5.19615	+	9.00000i	−0.244677	+	0.423793i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.46410			0.162400
$456$		0			0
$457$	22.0000			1.02912			0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000			1.02912			0.514558	+	0.857455i	$0.327956\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.50000	+	16.4545i	−0.442459	+	0.766362i	−0.997871	−	0.0652135i	$-0.979227\pi$
$461$	−9.50000	+	16.4545i	−0.442459	+	0.766362i	0.555412	+	0.831575i	$0.312560\pi$
$462$		0			0
$463$		−	36.0000i		−	1.67306i	−0.547920	−	0.836531i	$-0.684580\pi$
$463$		−	36.0000i		−	1.67306i	0.547920	−	0.836531i	$-0.315420\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	14.0000i		−	0.647843i	−0.946084	−	0.323921i	$-0.894999\pi$
$467$		−	14.0000i		−	0.647843i	0.946084	−	0.323921i	$-0.105001\pi$
$468$		0			0
$469$	9.00000	−	5.19615i	0.415581	−	0.239936i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−9.00000	+	15.5885i	−0.413820	+	0.716758i
$474$		0			0
$475$	−17.3205	+	2.00000i	−0.794719	+	0.0917663i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	21.6506	−	12.5000i	0.989243	−	0.571140i	0.0841949	−	0.996449i	$-0.473168\pi$
$479$	21.6506	−	12.5000i	0.989243	−	0.571140i	0.905048	+	0.425310i	$0.139835\pi$
$480$		0			0
$481$	3.00000	+	5.19615i	0.136788	+	0.236924i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	13.5000	−	7.79423i	0.613003	−	0.353918i
$486$		0			0
$487$	20.7846			0.941841			0.470920	−	0.882176i	$-0.343922\pi$
$487$	20.7846			0.941841			0.470920	+	0.882176i	$0.343922\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.06218	+	3.50000i	0.273582	+	0.157953i	0.630514	−	0.776178i	$-0.282844\pi$
$491$	6.06218	+	3.50000i	0.273582	+	0.157953i	−0.356932	+	0.934130i	$0.616177\pi$
$492$		0			0
$493$		−	1.73205i		−	0.0780076i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−27.0000	−	15.5885i	−1.21112	−	0.699238i
$498$		0			0
$499$	9.52628	+	5.50000i	0.426455	+	0.246214i	0.697835	−	0.716258i	$-0.254147\pi$
$499$	9.52628	+	5.50000i	0.426455	+	0.246214i	−0.271380	+	0.962472i	$0.587480\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	9.52628	−	5.50000i	0.424756	−	0.245233i	−0.272354	−	0.962197i	$-0.587802\pi$
$503$	9.52628	−	5.50000i	0.424756	−	0.245233i	0.697110	+	0.716964i	$0.254469\pi$
$504$		0			0
$505$	7.00000			0.311496
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.5000	+	9.52628i	−0.731350	+	0.422245i	−0.818916	−	0.573914i	$-0.805424\pi$
$509$	−16.5000	+	9.52628i	−0.731350	+	0.422245i	0.0875661	+	0.996159i	$0.472091\pi$
$510$		0			0
$511$	1.73205	+	1.00000i	0.0766214	+	0.0442374i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.92820	−	12.0000i	0.305293	−	0.528783i
$516$		0			0
$517$	11.0000	+	19.0526i	0.483779	+	0.837931i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			27.7128i			1.21412i	0.794656	+	0.607060i	$0.207651\pi$
$521$			27.7128i			1.21412i	−0.794656	+	0.607060i	$0.792349\pi$
$522$		0			0
$523$	14.7224	+	25.5000i	0.643767	+	1.11504i	0.984585	+	0.174908i	$0.0559627\pi$
$523$	14.7224	+	25.5000i	0.643767	+	1.11504i	−0.340818	+	0.940129i	$0.610704\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.73205	−	3.00000i	0.0754493	−	0.130682i
$528$		0			0
$529$	−11.0000	+	19.0526i	−0.478261	+	0.828372i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	9.00000			0.389833
$534$		0			0
$535$	3.46410	−	6.00000i	0.149766	−	0.259403i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	6.00000i		−	0.258438i
$540$		0			0
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	0.623404	−	0.781900i	$-0.285749\pi$
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	−0.988847	+	0.148933i	$0.952416\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.50000	−	0.866025i	0.0642529	−	0.0370965i
$546$		0			0
$547$	−18.1865	−	31.5000i	−0.777600	−	1.34684i	−0.933322	−	0.359042i	$-0.883104\pi$
$547$	−18.1865	−	31.5000i	−0.777600	−	1.34684i	0.155721	−	0.987801i	$-0.450230\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.866025	+	7.50000i	0.0368939	+	0.319511i
$552$		0			0
$553$	3.00000	+	1.73205i	0.127573	+	0.0736543i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.500000	−	0.866025i	−0.0211857	−	0.0366947i	0.855238	−	0.518235i	$-0.173411\pi$
$557$	−0.500000	−	0.866025i	−0.0211857	−	0.0366947i	−0.876424	+	0.481540i	$0.840077\pi$
$558$		0			0
$559$	15.5885			0.659321
$560$		0			0
$561$		0			0
$562$		0			0
$563$	13.8564			0.583978			0.291989	−	0.956422i	$-0.405683\pi$
$563$	13.8564			0.583978			0.291989	+	0.956422i	$0.405683\pi$
$564$		0			0
$565$	−3.00000	−	1.73205i	−0.126211	−	0.0728679i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	24.2487i		−	1.01656i	−0.861192	−	0.508279i	$-0.830282\pi$
$569$		−	24.2487i		−	1.01656i	0.861192	−	0.508279i	$-0.169718\pi$
$570$		0			0
$571$		−	18.0000i		−	0.753277i	−0.926360	−	0.376638i	$-0.877080\pi$
$571$		−	18.0000i		−	0.753277i	0.926360	−	0.376638i	$-0.122920\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.46410	−	2.00000i	−0.144463	−	0.0834058i
$576$		0			0
$577$	12.0000			0.499567			0.249783	−	0.968302i	$-0.419641\pi$
$577$	12.0000			0.499567			0.249783	+	0.968302i	$0.419641\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	16.0000			0.663792
$582$		0			0
$583$	8.66025	+	15.0000i	0.358671	+	0.621237i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.52628	+	5.50000i	0.393192	+	0.227009i	0.683542	−	0.729911i	$-0.260439\pi$
$587$	9.52628	+	5.50000i	0.393192	+	0.227009i	−0.290350	+	0.956920i	$0.593772\pi$
$588$		0			0
$589$	−6.00000	+	13.8564i	−0.247226	+	0.570943i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.50000	+	11.2583i	0.266923	+	0.462324i	0.968066	−	0.250697i	$-0.0806597\pi$
$593$	6.50000	+	11.2583i	0.266923	+	0.462324i	−0.701143	+	0.713021i	$0.747326\pi$
$594$		0			0
$595$	−1.73205	+	1.00000i	−0.0710072	+	0.0409960i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	18.1865	+	31.5000i	0.743082	+	1.28706i	0.951086	+	0.308927i	$0.0999699\pi$
$599$	18.1865	+	31.5000i	0.743082	+	1.28706i	−0.208004	+	0.978128i	$0.566697\pi$
$600$		0			0
$601$		−	3.46410i		−	0.141304i	−0.997501	−	0.0706518i	$-0.977492\pi$
$601$		−	3.46410i		−	0.141304i	0.997501	−	0.0706518i	$-0.0225079\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$		0			0
$607$	6.92820			0.281207			0.140604	−	0.990066i	$-0.455096\pi$
$607$	6.92820			0.281207			0.140604	+	0.990066i	$0.455096\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	9.52628	−	16.5000i	0.385392	−	0.667519i
$612$		0			0
$613$	1.50000	−	2.59808i	0.0605844	−	0.104935i	−0.834142	−	0.551549i	$-0.814037\pi$
$613$	1.50000	−	2.59808i	0.0605844	−	0.104935i	0.894727	+	0.446614i	$0.147370\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.50000	−	6.06218i	−0.140905	−	0.244054i	0.786933	−	0.617039i	$-0.211668\pi$
$617$	−3.50000	−	6.06218i	−0.140905	−	0.244054i	−0.927838	+	0.372985i	$0.878334\pi$
$618$		0			0
$619$		−	14.0000i		−	0.562708i	−0.959604	−	0.281354i	$-0.909217\pi$
$619$		−	14.0000i		−	0.562708i	0.959604	−	0.281354i	$-0.0907834\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	15.5885	+	27.0000i	0.624538	+	1.08173i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−3.00000	−	1.73205i	−0.119618	−	0.0690614i
$630$		0			0
$631$	30.3109	−	17.5000i	1.20666	−	0.696664i	0.244630	−	0.969617i	$-0.421334\pi$
$631$	30.3109	−	17.5000i	1.20666	−	0.696664i	0.962028	+	0.272953i	$0.0880002\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−12.1244			−0.481140
$636$		0			0
$637$	−4.50000	+	2.59808i	−0.178296	+	0.102940i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	10.5000	+	6.06218i	0.414725	+	0.239442i	0.692818	−	0.721113i	$-0.256369\pi$
$641$	10.5000	+	6.06218i	0.414725	+	0.239442i	−0.278093	+	0.960554i	$0.589702\pi$
$642$		0			0
$643$	−18.1865	−	10.5000i	−0.717207	−	0.414080i	0.0965169	−	0.995331i	$-0.469230\pi$
$643$	−18.1865	−	10.5000i	−0.717207	−	0.414080i	−0.813724	+	0.581252i	$0.802563\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	2.00000i		−	0.0786281i	−0.999227	−	0.0393141i	$-0.987483\pi$
$647$		−	2.00000i		−	0.0786281i	0.999227	−	0.0393141i	$-0.0125173\pi$
$648$		0			0
$649$	15.0000	+	8.66025i	0.588802	+	0.339945i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	20.0000			0.782660			0.391330	−	0.920250i	$-0.372015\pi$
$653$	20.0000			0.782660			0.391330	+	0.920250i	$0.372015\pi$
$654$		0			0
$655$	14.7224	−	8.50000i	0.575253	−	0.332122i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.52628	+	16.5000i	0.371091	+	0.642749i	0.989734	−	0.142924i	$-0.0456504\pi$
$659$	9.52628	+	16.5000i	0.371091	+	0.642749i	−0.618643	+	0.785673i	$0.712317\pi$
$660$		0			0
$661$	−31.5000	+	18.1865i	−1.22521	+	0.707374i	−0.966024	−	0.258454i	$-0.916787\pi$
$661$	−31.5000	+	18.1865i	−1.22521	+	0.707374i	−0.259184	+	0.965828i	$0.583454\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	7.00000	−	5.19615i	0.271448	−	0.201498i
$666$		0			0
$667$	−0.866025	+	1.50000i	−0.0335326	+	0.0580802i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	15.5885	−	9.00000i	0.601786	−	0.347441i
$672$		0			0
$673$		−	31.1769i		−	1.20178i	−0.799331	−	0.600891i	$-0.794813\pi$
$673$		−	31.1769i		−	1.20178i	0.799331	−	0.600891i	$-0.205187\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			24.2487i			0.931954i	0.884797	+	0.465977i	$0.154297\pi$
$677$			24.2487i			0.931954i	−0.884797	+	0.465977i	$0.845703\pi$
$678$		0			0
$679$	15.5885	−	27.0000i	0.598230	−	1.03616i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	3.46410			0.132550			0.0662751	−	0.997801i	$-0.478889\pi$
$683$	3.46410			0.132550			0.0662751	+	0.997801i	$0.478889\pi$
$684$		0			0
$685$	7.00000			0.267456
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.50000	−	12.9904i	0.285727	−	0.494894i
$690$		0			0
$691$		−	6.00000i		−	0.228251i	−0.993466	−	0.114125i	$-0.963593\pi$
$691$		−	6.00000i		−	0.228251i	0.993466	−	0.114125i	$-0.0364066\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	11.0000i		−	0.417254i
$696$		0			0
$697$	−4.50000	+	2.59808i	−0.170450	+	0.0984092i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−11.5000	+	19.9186i	−0.434349	+	0.752315i	−0.997242	−	0.0742151i	$-0.976355\pi$
$701$	−11.5000	+	19.9186i	−0.434349	+	0.752315i	0.562893	+	0.826530i	$0.309688\pi$
$702$		0			0
$703$	13.8564	+	6.00000i	0.522604	+	0.226294i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	12.1244	−	7.00000i	0.455983	−	0.263262i
$708$		0			0
$709$	−5.50000	−	9.52628i	−0.206557	−	0.357767i	0.744071	−	0.668101i	$-0.232892\pi$
$709$	−5.50000	−	9.52628i	−0.206557	−	0.357767i	−0.950628	+	0.310334i	$0.899559\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.00000	+	1.73205i	−0.112351	+	0.0648658i
$714$		0			0
$715$	−3.46410			−0.129550
$716$		0			0
$717$		0			0
$718$		0			0
$719$	16.4545	+	9.50000i	0.613649	+	0.354290i	0.774392	−	0.632706i	$-0.218056\pi$
$719$	16.4545	+	9.50000i	0.613649	+	0.354290i	−0.160743	+	0.986996i	$0.551389\pi$
$720$		0			0
$721$		−	27.7128i		−	1.03208i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	6.00000	+	3.46410i	0.222834	+	0.128654i
$726$		0			0
$727$	7.79423	+	4.50000i	0.289072	+	0.166896i	0.637523	−	0.770431i	$-0.279959\pi$
$727$	7.79423	+	4.50000i	0.289072	+	0.166896i	−0.348451	+	0.937327i	$0.613292\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−7.79423	+	4.50000i	−0.288280	+	0.166439i
$732$		0			0
$733$	8.00000			0.295487			0.147743	−	0.989026i	$-0.452799\pi$
$733$	8.00000			0.295487			0.147743	+	0.989026i	$0.452799\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.00000	+	5.19615i	−0.331519	+	0.191403i
$738$		0			0
$739$	30.3109	+	17.5000i	1.11500	+	0.643748i	0.940121	−	0.340841i	$-0.110712\pi$
$739$	30.3109	+	17.5000i	1.11500	+	0.643748i	0.174883	+	0.984589i	$0.444045\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−6.06218	+	10.5000i	−0.222400	+	0.385208i	−0.955536	−	0.294874i	$-0.904722\pi$
$743$	−6.06218	+	10.5000i	−0.222400	+	0.385208i	0.733136	+	0.680082i	$0.238056\pi$
$744$		0			0
$745$	−9.50000	−	16.4545i	−0.348053	−	0.602846i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	13.8564i		−	0.506302i
$750$		0			0
$751$	−14.7224	−	25.5000i	−0.537229	−	0.930508i	−0.999052	−	0.0435359i	$-0.986138\pi$
$751$	−14.7224	−	25.5000i	−0.537229	−	0.930508i	0.461823	−	0.886972i	$-0.347196\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3.46410	−	6.00000i	0.126072	−	0.218362i
$756$		0			0
$757$	4.50000	−	7.79423i	0.163555	−	0.283286i	−0.772586	−	0.634910i	$-0.781037\pi$
$757$	4.50000	−	7.79423i	0.163555	−	0.283286i	0.936141	+	0.351624i	$0.114370\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−40.0000			−1.45000			−0.724999	−	0.688749i	$-0.758160\pi$
$761$	−40.0000			−1.45000			−0.724999	+	0.688749i	$0.758160\pi$
$762$		0			0
$763$	1.73205	−	3.00000i	0.0627044	−	0.108607i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	15.0000i		−	0.541619i
$768$		0			0
$769$	−7.50000	−	12.9904i	−0.270457	−	0.468445i	0.698522	−	0.715589i	$-0.253841\pi$
$769$	−7.50000	−	12.9904i	−0.270457	−	0.468445i	−0.968979	+	0.247143i	$0.920508\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−25.5000	+	14.7224i	−0.917171	+	0.529529i	−0.882732	−	0.469878i	$-0.844298\pi$
$773$	−25.5000	+	14.7224i	−0.917171	+	0.529529i	−0.0344397	+	0.999407i	$0.510965\pi$
$774$		0			0
$775$	6.92820	+	12.0000i	0.248868	+	0.431053i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	18.1865	−	13.5000i	0.651600	−	0.483688i
$780$		0			0
$781$	27.0000	+	15.5885i	0.966136	+	0.557799i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	10.5000	+	18.1865i	0.374761	+	0.649105i
$786$		0			0
$787$	−41.5692			−1.48178			−0.740891	−	0.671625i	$-0.765597\pi$
$787$	−41.5692			−1.48178			−0.740891	+	0.671625i	$0.765597\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−6.92820			−0.246339
$792$		0			0
$793$	−13.5000	−	7.79423i	−0.479399	−	0.276781i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	51.9615i		−	1.84057i	−0.391247	−	0.920286i	$-0.627956\pi$
$797$		−	51.9615i		−	1.84057i	0.391247	−	0.920286i	$-0.372044\pi$
$798$		0			0
$799$			11.0000i			0.389152i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.73205	−	1.00000i	−0.0611227	−	0.0352892i
$804$		0			0
$805$	2.00000			0.0704907
$806$		0			0
$807$		0			0
$808$		0			0
$809$	44.0000			1.54696			0.773479	−	0.633822i	$-0.218515\pi$
$809$	44.0000			1.54696			0.773479	+	0.633822i	$0.218515\pi$
$810$		0			0
$811$	21.6506	+	37.5000i	0.760257	+	1.31680i	0.942718	+	0.333590i	$0.108260\pi$
$811$	21.6506	+	37.5000i	0.760257	+	1.31680i	−0.182462	+	0.983213i	$0.558407\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−12.1244	−	7.00000i	−0.424698	−	0.245199i
$816$		0			0
$817$	31.5000	−	23.3827i	1.10205	−	0.818057i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	6.50000	+	11.2583i	0.226852	+	0.392918i	0.956873	−	0.290505i	$-0.0938234\pi$
$821$	6.50000	+	11.2583i	0.226852	+	0.392918i	−0.730022	+	0.683424i	$0.760490\pi$
$822$		0			0
$823$	−32.0429	+	18.5000i	−1.11695	+	0.644869i	−0.940620	−	0.339462i	$-0.889755\pi$
$823$	−32.0429	+	18.5000i	−1.11695	+	0.644869i	−0.176327	+	0.984332i	$0.556422\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	4.33013	+	7.50000i	0.150573	+	0.260801i	0.931438	−	0.363899i	$-0.118555\pi$
$827$	4.33013	+	7.50000i	0.150573	+	0.260801i	−0.780865	+	0.624700i	$0.785221\pi$
$828$		0			0
$829$			6.92820i			0.240626i	0.992736	+	0.120313i	$0.0383899\pi$
$829$			6.92820i			0.240626i	−0.992736	+	0.120313i	$0.961610\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.50000	−	2.59808i	0.0519719	−	0.0900180i
$834$		0			0
$835$	1.73205			0.0599401
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−9.52628	+	16.5000i	−0.328884	+	0.569643i	−0.982291	−	0.187364i	$-0.940006\pi$
$839$	−9.52628	+	16.5000i	−0.328884	+	0.569643i	0.653407	+	0.757007i	$0.273339\pi$
$840$		0			0
$841$	−13.0000	+	22.5167i	−0.448276	+	0.776437i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−5.00000	−	8.66025i	−0.172005	−	0.297922i
$846$		0			0
$847$			14.0000i			0.481046i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.73205	+	3.00000i	0.0593739	+	0.102839i
$852$		0			0
$853$	2.50000	−	4.33013i	0.0855984	−	0.148261i	−0.820048	−	0.572295i	$-0.806053\pi$
$853$	2.50000	−	4.33013i	0.0855984	−	0.148261i	0.905646	+	0.424034i	$0.139386\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	22.5000	+	12.9904i	0.768585	+	0.443743i	0.832370	−	0.554221i	$-0.186984\pi$
$857$	22.5000	+	12.9904i	0.768585	+	0.443743i	−0.0637844	+	0.997964i	$0.520317\pi$
$858$		0			0
$859$	−21.6506	+	12.5000i	−0.738710	+	0.426494i	−0.821600	−	0.570064i	$-0.806918\pi$
$859$	−21.6506	+	12.5000i	−0.738710	+	0.426494i	0.0828900	+	0.996559i	$0.473585\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	31.1769			1.06127			0.530637	−	0.847599i	$-0.321953\pi$
$863$	31.1769			1.06127			0.530637	+	0.847599i	$0.321953\pi$
$864$		0			0
$865$	−16.5000	+	9.52628i	−0.561017	+	0.323903i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−3.00000	−	1.73205i	−0.101768	−	0.0587558i
$870$		0			0
$871$	7.79423	+	4.50000i	0.264097	+	0.152477i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		−	18.0000i		−	0.608511i
$876$		0			0
$877$	−49.5000	−	28.5788i	−1.67150	−	0.965039i	−0.966802	−	0.255528i	$-0.917751\pi$
$877$	−49.5000	−	28.5788i	−1.67150	−	0.965039i	−0.704695	−	0.709511i	$-0.748916\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	28.0000			0.943344			0.471672	−	0.881774i	$-0.343651\pi$
$881$	28.0000			0.943344			0.471672	+	0.881774i	$0.343651\pi$
$882$		0			0
$883$	32.0429	−	18.5000i	1.07833	−	0.622575i	0.147885	−	0.989005i	$-0.452753\pi$
$883$	32.0429	−	18.5000i	1.07833	−	0.622575i	0.930446	+	0.366430i	$0.119420\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−21.6506	−	37.5000i	−0.726957	−	1.25913i	−0.958163	−	0.286222i	$-0.907601\pi$
$887$	−21.6506	−	37.5000i	−0.726957	−	1.25913i	0.231206	−	0.972905i	$-0.425733\pi$
$888$		0			0
$889$	−21.0000	+	12.1244i	−0.704317	+	0.406638i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−5.50000	−	47.6314i	−0.184050	−	1.59392i
$894$		0			0
$895$	6.92820	−	12.0000i	0.231584	−	0.401116i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5.19615	−	3.00000i	0.173301	−	0.100056i
$900$		0			0
$901$			8.66025i			0.288515i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	5.19615i		−	0.172726i
$906$		0			0
$907$	18.1865	−	31.5000i	0.603874	−	1.04594i	−0.388354	−	0.921510i	$-0.626956\pi$
$907$	18.1865	−	31.5000i	0.603874	−	1.04594i	0.992228	−	0.124430i	$-0.0397103\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	20.7846			0.688625			0.344312	−	0.938855i	$-0.388112\pi$
$911$	20.7846			0.688625			0.344312	+	0.938855i	$0.388112\pi$
$912$		0			0
$913$	−16.0000			−0.529523
$914$		0			0
$915$		0			0
$916$		0			0
$917$	17.0000	−	29.4449i	0.561389	−	0.972355i
$918$		0			0
$919$			58.0000i			1.91324i	0.291333	+	0.956622i	$0.405901\pi$
$919$			58.0000i			1.91324i	−0.291333	+	0.956622i	$0.594099\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	27.0000i		−	0.888716i
$924$		0			0
$925$	12.0000	−	6.92820i	0.394558	−	0.227798i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−12.5000	+	21.6506i	−0.410112	+	0.710334i	−0.994902	−	0.100851i	$-0.967844\pi$
$929$	−12.5000	+	21.6506i	−0.410112	+	0.710334i	0.584790	+	0.811185i	$0.301177\pi$
$930$		0			0
$931$	−5.19615	+	12.0000i	−0.170297	+	0.393284i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.73205	−	1.00000i	0.0566441	−	0.0327035i
$936$		0			0
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	0.614741	−	0.788729i	$-0.289260\pi$
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	−0.990430	+	0.138017i	$0.955927\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.5000	+	7.79423i	−0.440087	+	0.254085i	−0.703635	−	0.710562i	$-0.748441\pi$
$941$	−13.5000	+	7.79423i	−0.440087	+	0.254085i	0.263547	+	0.964646i	$0.415107\pi$
$942$		0			0
$943$	5.19615			0.169210
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.866025	+	0.500000i	0.0281420	+	0.0162478i	0.514005	−	0.857787i	$-0.328161\pi$
$947$	0.866025	+	0.500000i	0.0281420	+	0.0162478i	−0.485863	+	0.874035i	$0.661495\pi$
$948$		0			0
$949$			1.73205i			0.0562247i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−31.5000	−	18.1865i	−1.02039	−	0.589120i	−0.106170	−	0.994348i	$-0.533859\pi$
$953$	−31.5000	−	18.1865i	−1.02039	−	0.589120i	−0.914215	+	0.405228i	$0.867192\pi$
$954$		0			0
$955$	8.66025	+	5.00000i	0.280239	+	0.161796i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	12.1244	−	7.00000i	0.391516	−	0.226042i
$960$		0			0
$961$	−19.0000			−0.612903
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−7.50000	+	4.33013i	−0.241434	+	0.139392i
$966$		0			0
$967$	−4.33013	−	2.50000i	−0.139247	−	0.0803946i	0.428758	−	0.903419i	$-0.358951\pi$
$967$	−4.33013	−	2.50000i	−0.139247	−	0.0803946i	−0.568005	+	0.823025i	$0.692285\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.79423	+	13.5000i	−0.250129	+	0.433236i	−0.963561	−	0.267488i	$-0.913806\pi$
$971$	−7.79423	+	13.5000i	−0.250129	+	0.433236i	0.713432	+	0.700724i	$0.247140\pi$
$972$		0			0
$973$	−11.0000	−	19.0526i	−0.352644	−	0.610797i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			58.8897i			1.88405i	0.335544	+	0.942025i	$0.391080\pi$
$977$			58.8897i			1.88405i	−0.335544	+	0.942025i	$0.608920\pi$
$978$		0			0
$979$	−15.5885	−	27.0000i	−0.498209	−	0.862924i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−18.1865	+	31.5000i	−0.580060	+	1.00469i	0.415411	+	0.909634i	$0.363638\pi$
$983$	−18.1865	+	31.5000i	−0.580060	+	1.00469i	−0.995472	+	0.0950602i	$0.969696\pi$
$984$		0			0
$985$	−10.0000	+	17.3205i	−0.318626	+	0.551877i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	9.00000			0.286183
$990$		0			0
$991$	−23.3827	+	40.5000i	−0.742775	+	1.28652i	0.208451	+	0.978033i	$0.433158\pi$
$991$	−23.3827	+	40.5000i	−0.742775	+	1.28652i	−0.951227	+	0.308492i	$0.900176\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			3.00000i			0.0951064i
$996$		0			0
$997$	4.50000	+	7.79423i	0.142516	+	0.246846i	0.928444	−	0.371473i	$-0.121147\pi$
$997$	4.50000	+	7.79423i	0.142516	+	0.246846i	−0.785927	+	0.618319i	$0.787814\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.bm.k.559.2		4
3.2	odd	2		304.2.n.c.255.1	yes	4
4.3	odd	2	inner	2736.2.bm.k.559.1		4
12.11	even	2		304.2.n.c.255.2	yes	4
19.12	odd	6	inner	2736.2.bm.k.1855.2		4
24.5	odd	2		1216.2.n.c.255.2		4
24.11	even	2		1216.2.n.c.255.1		4
57.50	even	6		304.2.n.c.31.2	yes	4
76.31	even	6	inner	2736.2.bm.k.1855.1		4
228.107	odd	6		304.2.n.c.31.1	✓	4
456.107	odd	6		1216.2.n.c.639.2		4
456.221	even	6		1216.2.n.c.639.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.n.c.31.1	✓	4	228.107	odd	6
304.2.n.c.31.2	yes	4	57.50	even	6
304.2.n.c.255.1	yes	4	3.2	odd	2
304.2.n.c.255.2	yes	4	12.11	even	2
1216.2.n.c.255.1		4	24.11	even	2
1216.2.n.c.255.2		4	24.5	odd	2
1216.2.n.c.639.1		4	456.221	even	6
1216.2.n.c.639.2		4	456.107	odd	6
2736.2.bm.k.559.1		4	4.3	odd	2	inner
2736.2.bm.k.559.2		4	1.1	even	1	trivial
2736.2.bm.k.1855.1		4	76.31	even	6	inner
2736.2.bm.k.1855.2		4	19.12	odd	6	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:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{5} +2.00000i q^{7} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{5} +2.00000i q^{7} -2.00000i q^{11} +(-1.50000 + 0.866025i) q^{13} +(0.500000 - 0.866025i) q^{17} +(-1.73205 + 4.00000i) q^{19} +(-0.866025 + 0.500000i) q^{23} +(2.00000 + 3.46410i) q^{25} +(1.50000 - 0.866025i) q^{29} +3.46410 q^{31} +(-1.73205 - 1.00000i) q^{35} -3.46410i q^{37} +(-4.50000 - 2.59808i) q^{41} +(-7.79423 - 4.50000i) q^{43} +(-9.52628 + 5.50000i) q^{47} +3.00000 q^{49} +(-7.50000 + 4.33013i) q^{53} +(1.73205 + 1.00000i) q^{55} +(-4.33013 + 7.50000i) q^{59} +(4.50000 + 7.79423i) q^{61} -1.73205i q^{65} +(-2.59808 - 4.50000i) q^{67} +(-7.79423 + 13.5000i) q^{71} +(0.500000 - 0.866025i) q^{73} +4.00000 q^{77} +(0.866025 - 1.50000i) q^{79} -8.00000i q^{83} +(0.500000 + 0.866025i) q^{85} +(13.5000 - 7.79423i) q^{89} +(-1.73205 - 3.00000i) q^{91} +(-2.59808 - 3.50000i) q^{95} +(-13.5000 - 7.79423i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5}+O(q^{10}) \) 4 * q - 2 * q^5	\( 4 q - 2 q^{5} - 6 q^{13} + 2 q^{17} + 8 q^{25} + 6 q^{29} - 18 q^{41} + 12 q^{49} - 30 q^{53} + 18 q^{61} + 2 q^{73} + 16 q^{77} + 2 q^{85} + 54 q^{89} - 54 q^{97}+O(q^{100}) \) 4 * q - 2 * q^5 - 6 * q^13 + 2 * q^17 + 8 * q^25 + 6 * q^29 - 18 * q^41 + 12 * q^49 - 30 * q^53 + 18 * q^61 + 2 * q^73 + 16 * q^77 + 2 * q^85 + 54 * q^89 - 54 * q^97

Introduction

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