LMFDB - Embedded newform 2736.2.dc.f.1889.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(449,2736)]

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([0, 0, 3, 5]))

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

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

chi := DirichletCharacter("2736.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.dc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} - 18 x^{18} + 232 x^{17} + 208 x^{16} - 3152 x^{15} - 2732 x^{14} + 24552 x^{13} + \cdots + 414864 $ x^20 - 8x^19 - 18x^18 + 232x^17 + 208x^16 - 3152x^15 - 2732x^14 + 24552x^13 + 30728x^12 - 110512x^11 - 211368x^10 + 231024x^9 + 827916x^8 + 179664x^7 - 1551960x^6 - 1894880x^5 + 305564x^4 + 2772832x^3 + 3072904x^2 + 1645728*x + 414864
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 1368)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1889.4
Root			$2.25091 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2736.1889
Dual form			2736.2.dc.f.449.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.967070 - 0.558338i) q^{5} +1.95123 q^{7} +O(q^{10})$	$q+(-0.967070 - 0.558338i) q^{5} +1.95123 q^{7} +2.27059i q^{11} +(-1.53204 + 0.884525i) q^{13} +(3.94434 + 2.27726i) q^{17} +(2.17718 - 3.77623i) q^{19} +(-0.852585 + 0.492240i) q^{23} +(-1.87652 - 3.25022i) q^{25} +(3.73673 + 6.47220i) q^{29} -5.02043i q^{31} +(-1.88698 - 1.08945i) q^{35} +6.12206i q^{37} +(-1.26471 + 2.19054i) q^{41} +(1.64669 - 2.85216i) q^{43} +(-1.16976 + 0.675363i) q^{47} -3.19269 q^{49} +(4.63387 + 8.02610i) q^{53} +(1.26776 - 2.19582i) q^{55} +(-4.40143 + 7.62351i) q^{59} +(5.69761 + 9.86855i) q^{61} +1.97545 q^{65} +(7.67610 - 4.43180i) q^{67} +(5.61562 - 9.72654i) q^{71} +(-0.554969 + 0.961235i) q^{73} +4.43045i q^{77} +(8.63739 + 4.98680i) q^{79} +3.51085i q^{83} +(-2.54297 - 4.40455i) q^{85} +(-0.860336 - 1.49015i) q^{89} +(-2.98937 + 1.72591i) q^{91} +(-4.21389 + 2.43628i) q^{95} +(-2.29601 - 1.32560i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{7}+O(q^{10}) $ 20 * q + 4 * q^7	$ 20 q + 4 q^{7} + 6 q^{13} + 12 q^{17} - 4 q^{19} + 14 q^{25} + 12 q^{35} + 8 q^{41} + 2 q^{43} + 36 q^{47} + 32 q^{49} - 8 q^{53} - 12 q^{55} - 8 q^{59} - 2 q^{61} + 8 q^{65} - 30 q^{67} + 4 q^{71} - 22 q^{73} - 54 q^{79} - 4 q^{85} - 32 q^{89} - 18 q^{91} + 32 q^{95} + 12 q^{97}+O(q^{100}) $ 20 * q + 4 * q^7 + 6 * q^13 + 12 * q^17 - 4 * q^19 + 14 * q^25 + 12 * q^35 + 8 * q^41 + 2 * q^43 + 36 * q^47 + 32 * q^49 - 8 * q^53 - 12 * q^55 - 8 * q^59 - 2 * q^61 + 8 * q^65 - 30 * q^67 + 4 * q^71 - 22 * q^73 - 54 * q^79 - 4 * q^85 - 32 * q^89 - 18 * q^91 + 32 * q^95 + 12 * 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
$5$	−0.967070	−	0.558338i	−0.432487	−	0.249696i	0.267919	−	0.963442i	$-0.413664\pi$
$5$	−0.967070	−	0.558338i	−0.432487	−	0.249696i	−0.700405	+	0.713745i	$0.746997\pi$
$6$		0			0
$7$	1.95123			0.737497			0.368748	−	0.929529i	$-0.379786\pi$
$7$	1.95123			0.737497			0.368748	+	0.929529i	$0.379786\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$			2.27059i			0.684609i	0.939589	+	0.342305i	$0.111207\pi$
$11$			2.27059i			0.684609i	−0.939589	+	0.342305i	$0.888793\pi$
$12$		0			0
$13$	−1.53204	+	0.884525i	−0.424912	+	0.245323i	−0.697177	−	0.716899i	$-0.745561\pi$
$13$	−1.53204	+	0.884525i	−0.424912	+	0.245323i	0.272265	+	0.962222i	$0.412227\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.94434	+	2.27726i	0.956643	+	0.552318i	0.895138	−	0.445789i	$-0.147077\pi$
$17$	3.94434	+	2.27726i	0.956643	+	0.552318i	0.0615044	+	0.998107i	$0.480410\pi$
$18$		0			0
$19$	2.17718	−	3.77623i	0.499478	−	0.866326i
$19$	2.17718	−	3.77623i	0.499478	−	0.866326i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.852585	+	0.492240i	−0.177776	+	0.102639i	−0.586247	−	0.810132i	$-0.699395\pi$
$23$	−0.852585	+	0.492240i	−0.177776	+	0.102639i	0.408471	+	0.912771i	$0.366062\pi$
$24$		0			0
$25$	−1.87652	−	3.25022i	−0.375304	−	0.650045i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.73673	+	6.47220i	0.693893	+	1.20186i	0.970552	+	0.240890i	$0.0774392\pi$
$29$	3.73673	+	6.47220i	0.693893	+	1.20186i	−0.276660	+	0.960968i	$0.589227\pi$
$30$		0			0
$31$		−	5.02043i		−	0.901696i	−0.892601	−	0.450848i	$-0.851122\pi$
$31$		−	5.02043i		−	0.901696i	0.892601	−	0.450848i	$-0.148878\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.88698	−	1.08945i	−0.318957	−	0.184150i
$36$		0			0
$37$			6.12206i			1.00646i	0.864152	+	0.503230i	$0.167855\pi$
$37$			6.12206i			1.00646i	−0.864152	+	0.503230i	$0.832145\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.26471	+	2.19054i	−0.197514	+	0.342105i	−0.947722	−	0.319098i	$-0.896620\pi$
$41$	−1.26471	+	2.19054i	−0.197514	+	0.342105i	0.750208	+	0.661202i	$0.229954\pi$
$42$		0			0
$43$	1.64669	−	2.85216i	0.251118	−	0.434950i	−0.712716	−	0.701453i	$-0.752535\pi$
$43$	1.64669	−	2.85216i	0.251118	−	0.434950i	0.963834	+	0.266503i	$0.0858683\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.16976	+	0.675363i	−0.170627	+	0.0985118i	−0.582882	−	0.812557i	$-0.698075\pi$
$47$	−1.16976	+	0.675363i	−0.170627	+	0.0985118i	0.412254	+	0.911069i	$0.364742\pi$
$48$		0			0
$49$	−3.19269			−0.456099
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.63387	+	8.02610i	0.636511	+	1.10247i	0.986193	+	0.165601i	$0.0529565\pi$
$53$	4.63387	+	8.02610i	0.636511	+	1.10247i	−0.349681	+	0.936869i	$0.613710\pi$
$54$		0			0
$55$	1.26776	−	2.19582i	0.170944	−	0.296084i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.40143	+	7.62351i	−0.573018	+	0.992496i	0.423236	+	0.906019i	$0.360894\pi$
$59$	−4.40143	+	7.62351i	−0.573018	+	0.992496i	−0.996254	+	0.0864767i	$0.972439\pi$
$60$		0			0
$61$	5.69761	+	9.86855i	0.729504	+	1.26354i	0.957093	+	0.289781i	$0.0935826\pi$
$61$	5.69761	+	9.86855i	0.729504	+	1.26354i	−0.227589	+	0.973757i	$0.573084\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.97545			0.245025
$66$		0			0
$67$	7.67610	−	4.43180i	0.937784	−	0.541430i	0.0485194	−	0.998822i	$-0.484550\pi$
$67$	7.67610	−	4.43180i	0.937784	−	0.541430i	0.889265	+	0.457392i	$0.151216\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.61562	−	9.72654i	0.666451	−	1.15433i	−0.312438	−	0.949938i	$-0.601146\pi$
$71$	5.61562	−	9.72654i	0.666451	−	1.15433i	0.978890	−	0.204390i	$-0.0655210\pi$
$72$		0			0
$73$	−0.554969	+	0.961235i	−0.0649542	+	0.112504i	−0.896674	−	0.442692i	$-0.854023\pi$
$73$	−0.554969	+	0.961235i	−0.0649542	+	0.112504i	0.831719	+	0.555196i	$0.187357\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			4.43045i			0.504897i
$78$		0			0
$79$	8.63739	+	4.98680i	0.971782	+	0.561059i	0.899779	−	0.436346i	$-0.143728\pi$
$79$	8.63739	+	4.98680i	0.971782	+	0.561059i	0.0720030	+	0.997404i	$0.477061\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			3.51085i			0.385365i	0.981261	+	0.192683i	$0.0617188\pi$
$83$			3.51085i			0.385365i	−0.981261	+	0.192683i	$0.938281\pi$
$84$		0			0
$85$	−2.54297	−	4.40455i	−0.275823	−	0.477740i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.860336	−	1.49015i	−0.0911955	−	0.157955i	0.816819	−	0.576894i	$-0.195735\pi$
$89$	−0.860336	−	1.49015i	−0.0911955	−	0.157955i	−0.908014	+	0.418939i	$0.862402\pi$
$90$		0			0
$91$	−2.98937	+	1.72591i	−0.313371	+	0.180925i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.21389	+	2.43628i	−0.432336	+	0.249957i
$96$		0			0
$97$	−2.29601	−	1.32560i	−0.233125	−	0.134595i	0.378888	−	0.925443i	$-0.376307\pi$
$97$	−2.29601	−	1.32560i	−0.233125	−	0.134595i	−0.612013	+	0.790848i	$0.709640\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.89597	−	2.24934i	0.387664	−	0.223818i	−0.293484	−	0.955964i	$-0.594815\pi$
$101$	3.89597	−	2.24934i	0.387664	−	0.223818i	0.681147	+	0.732146i	$0.261481\pi$
$102$		0			0
$103$		−	9.67418i		−	0.953225i	−0.879114	−	0.476612i	$-0.841865\pi$
$103$		−	9.67418i		−	0.953225i	0.879114	−	0.476612i	$-0.158135\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.79570			0.656965			0.328482	−	0.944510i	$-0.393463\pi$
$107$	6.79570			0.656965			0.328482	+	0.944510i	$0.393463\pi$
$108$		0			0
$109$	8.82811	+	5.09691i	0.845579	+	0.488195i	0.859157	−	0.511712i	$-0.170989\pi$
$109$	8.82811	+	5.09691i	0.845579	+	0.488195i	−0.0135776	+	0.999908i	$0.504322\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	12.4535			1.17152			0.585762	−	0.810483i	$-0.300795\pi$
$113$	12.4535			1.17152			0.585762	+	0.810483i	$0.300795\pi$
$114$		0			0
$115$	1.09935			0.102514
$116$		0			0
$117$		0			0
$118$		0			0
$119$	7.69632	+	4.44347i	0.705521	+	0.407333i
$120$		0			0
$121$	5.84441			0.531310
$122$		0			0
$123$		0			0
$124$		0			0
$125$			9.77430i			0.874240i
$126$		0			0
$127$	2.11424	−	1.22066i	0.187608	−	0.108316i	−0.403254	−	0.915088i	$-0.632121\pi$
$127$	2.11424	−	1.22066i	0.187608	−	0.108316i	0.590862	+	0.806772i	$0.298788\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.96181	−	4.59676i	−0.695627	−	0.401620i	0.110090	−	0.993922i	$-0.464886\pi$
$131$	−7.96181	−	4.59676i	−0.695627	−	0.401620i	−0.805717	+	0.592301i	$0.798220\pi$
$132$		0			0
$133$	4.24818	−	7.36830i	0.368364	−	0.638913i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.78036	−	1.60524i	0.237542	−	0.137145i	−0.376504	−	0.926415i	$-0.622874\pi$
$137$	2.78036	−	1.60524i	0.237542	−	0.137145i	0.614047	+	0.789270i	$0.289541\pi$
$138$		0			0
$139$	3.18883	+	5.52322i	0.270473	+	0.468474i	0.968983	−	0.247127i	$-0.0794865\pi$
$139$	3.18883	+	5.52322i	0.270473	+	0.468474i	−0.698510	+	0.715601i	$0.746153\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.00840	−	3.47864i	−0.167950	−	0.290899i
$144$		0			0
$145$		−	8.34543i		−	0.693050i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.52578	−	5.49971i	−0.780382	−	0.450554i	0.0561834	−	0.998420i	$-0.482107\pi$
$149$	−9.52578	−	5.49971i	−0.780382	−	0.450554i	−0.836566	+	0.547866i	$0.815440\pi$
$150$		0			0
$151$		−	3.70278i		−	0.301328i	−0.988585	−	0.150664i	$-0.951859\pi$
$151$		−	3.70278i		−	0.301328i	0.988585	−	0.150664i	$-0.0481412\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.80310	+	4.85511i	−0.225150	+	0.389972i
$156$		0			0
$157$	0.0643034	−	0.111377i	0.00513197	−	0.00888883i	−0.863448	−	0.504438i	$-0.831700\pi$
$157$	0.0643034	−	0.111377i	0.00513197	−	0.00888883i	0.868580	+	0.495549i	$0.165033\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.66359	+	0.960475i	−0.131109	+	0.0756960i
$162$		0			0
$163$	24.8863			1.94925			0.974624	−	0.223850i	$-0.0718624\pi$
$163$	24.8863			1.94925			0.974624	+	0.223850i	$0.0718624\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.0969	+	17.4883i	0.781322	+	1.35329i	0.931172	+	0.364580i	$0.118788\pi$
$167$	10.0969	+	17.4883i	0.781322	+	1.35329i	−0.149850	+	0.988709i	$0.547879\pi$
$168$		0			0
$169$	−4.93523	+	8.54807i	−0.379633	+	0.657544i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.76244	+	4.78469i	−0.210025	+	0.363774i	−0.951722	−	0.306961i	$-0.900688\pi$
$173$	−2.76244	+	4.78469i	−0.210025	+	0.363774i	0.741697	+	0.670735i	$0.234021\pi$
$174$		0			0
$175$	−3.66152	−	6.34194i	−0.276785	−	0.479406i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.61036			0.269851			0.134925	−	0.990856i	$-0.456921\pi$
$179$	3.61036			0.269851			0.134925	+	0.990856i	$0.456921\pi$
$180$		0			0
$181$	5.12473	−	2.95877i	0.380919	−	0.219923i	−0.297299	−	0.954784i	$-0.596086\pi$
$181$	5.12473	−	2.95877i	0.380919	−	0.219923i	0.678218	+	0.734861i	$0.262753\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.41818	−	5.92046i	0.251309	−	0.435281i
$186$		0			0
$187$	−5.17074	+	8.95598i	−0.378122	+	0.654926i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			16.8258i			1.21747i	0.793374	+	0.608735i	$0.208323\pi$
$191$			16.8258i			1.21747i	−0.793374	+	0.608735i	$0.791677\pi$
$192$		0			0
$193$	−0.333446	−	0.192515i	−0.0240020	−	0.0138576i	0.487951	−	0.872871i	$-0.337744\pi$
$193$	−0.333446	−	0.192515i	−0.0240020	−	0.0138576i	−0.511953	+	0.859013i	$0.671078\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			22.5074i			1.60359i	0.597601	+	0.801794i	$0.296121\pi$
$197$			22.5074i			1.60359i	−0.597601	+	0.801794i	$0.703879\pi$
$198$		0			0
$199$	2.14454	+	3.71444i	0.152022	+	0.263310i	0.931971	−	0.362534i	$-0.118088\pi$
$199$	2.14454	+	3.71444i	0.152022	+	0.263310i	−0.779949	+	0.625844i	$0.784755\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	7.29122	+	12.6288i	0.511744	+	0.886366i
$204$		0			0
$205$	2.44612	−	1.41227i	0.170845	−	0.0986372i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8.57428	+	4.94348i	0.593095	+	0.341947i
$210$		0			0
$211$	−19.5719	−	11.2999i	−1.34739	−	0.777914i	−0.359508	−	0.933142i	$-0.617055\pi$
$211$	−19.5719	−	11.2999i	−1.34739	−	0.777914i	−0.987879	+	0.155228i	$0.950389\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.18493	+	1.83882i	−0.217211	+	0.125407i
$216$		0			0
$217$		−	9.79603i		−	0.664998i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−8.05719			−0.541985
$222$		0			0
$223$	1.36459	+	0.787848i	0.0913799	+	0.0527582i	0.544994	−	0.838440i	$-0.316532\pi$
$223$	1.36459	+	0.787848i	0.0913799	+	0.0527582i	−0.453614	+	0.891198i	$0.649865\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.6162			0.704623			0.352311	−	0.935883i	$-0.385396\pi$
$227$	10.6162			0.704623			0.352311	+	0.935883i	$0.385396\pi$
$228$		0			0
$229$	16.9778			1.12193			0.560963	−	0.827841i	$-0.310431\pi$
$229$	16.9778			1.12193			0.560963	+	0.827841i	$0.310431\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.256478	+	0.148078i	0.0168024	+	0.00970089i	0.508378	−	0.861134i	$-0.330245\pi$
$233$	0.256478	+	0.148078i	0.0168024	+	0.00970089i	−0.491575	+	0.870835i	$0.663579\pi$
$234$		0			0
$235$	1.50832			0.0983921
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	10.9976i		−	0.711377i	−0.934605	−	0.355688i	$-0.884246\pi$
$239$		−	10.9976i		−	0.711377i	0.934605	−	0.355688i	$-0.115754\pi$
$240$		0			0
$241$	16.5596	−	9.56069i	1.06670	−	0.615858i	0.139420	−	0.990233i	$-0.455476\pi$
$241$	16.5596	−	9.56069i	1.06670	−	0.615858i	0.927277	+	0.374375i	$0.122143\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.08755	+	1.78260i	0.197257	+	0.113886i
$246$		0			0
$247$	0.00464381	+	7.71111i	0.000295479	+	0.490646i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	4.95771	−	2.86233i	0.312928	−	0.180669i	−0.335308	−	0.942108i	$-0.608840\pi$
$251$	4.95771	−	2.86233i	0.312928	−	0.180669i	0.648236	+	0.761440i	$0.275507\pi$
$252$		0			0
$253$	−1.11768	−	1.93587i	−0.0702677	−	0.121707i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.86017	+	3.22192i	0.116034	+	0.200978i	0.918193	−	0.396134i	$-0.129648\pi$
$257$	1.86017	+	3.22192i	0.116034	+	0.200978i	−0.802158	+	0.597111i	$0.796315\pi$
$258$		0			0
$259$			11.9456i			0.742261i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.904992	−	0.522497i	−0.0558042	−	0.0322186i	0.471838	−	0.881685i	$-0.343591\pi$
$263$	−0.904992	−	0.522497i	−0.0558042	−	0.0322186i	−0.527643	+	0.849467i	$0.676924\pi$
$264$		0			0
$265$		−	10.3491i		−	0.635738i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.31034	+	10.9298i	−0.384749	+	0.666404i	−0.991734	−	0.128309i	$-0.959045\pi$
$269$	−6.31034	+	10.9298i	−0.384749	+	0.666404i	0.606986	+	0.794713i	$0.292378\pi$
$270$		0			0
$271$	−14.3098	+	24.7853i	−0.869259	+	1.50560i	−0.00650350	+	0.999979i	$0.502070\pi$
$271$	−14.3098	+	24.7853i	−0.869259	+	1.50560i	−0.862755	+	0.505622i	$0.831263\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.37993	−	4.26081i	0.445027	−	0.256936i
$276$		0			0
$277$	−5.54571			−0.333210			−0.166605	−	0.986024i	$-0.553280\pi$
$277$	−5.54571			−0.333210			−0.166605	+	0.986024i	$0.553280\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−12.7550	−	22.0922i	−0.760897	−	1.31791i	−0.942389	−	0.334520i	$-0.891426\pi$
$281$	−12.7550	−	22.0922i	−0.760897	−	1.31791i	0.181492	−	0.983392i	$-0.441907\pi$
$282$		0			0
$283$	−7.56049	+	13.0952i	−0.449425	+	0.778426i	−0.998349	−	0.0574459i	$-0.981704\pi$
$283$	−7.56049	+	13.0952i	−0.449425	+	0.778426i	0.548924	+	0.835872i	$0.315038\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.46774	+	4.27425i	−0.145666	+	0.252301i
$288$		0			0
$289$	1.87187	+	3.24217i	0.110110	+	0.190716i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−13.9388			−0.814314			−0.407157	−	0.913358i	$-0.633480\pi$
$293$	−13.9388			−0.814314			−0.407157	+	0.913358i	$0.633480\pi$
$294$		0			0
$295$	8.51299	−	4.91497i	0.495645	−	0.286161i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.870797	−	1.50827i	0.0503595	−	0.0872252i
$300$		0			0
$301$	3.21308	−	5.56522i	0.185199	−	0.320774i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	12.7248i		−	0.728618i
$306$		0			0
$307$	−12.7032	−	7.33419i	−0.725010	−	0.418584i	0.0915842	−	0.995797i	$-0.470807\pi$
$307$	−12.7032	−	7.33419i	−0.725010	−	0.418584i	−0.816594	+	0.577213i	$0.804140\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			19.7801i			1.12163i	0.827943	+	0.560813i	$0.189511\pi$
$311$			19.7801i			1.12163i	−0.827943	+	0.560813i	$0.810489\pi$
$312$		0			0
$313$	−9.03691	−	15.6524i	−0.510796	−	0.884725i	−0.999922	−	0.0125118i	$-0.996017\pi$
$313$	−9.03691	−	15.6524i	−0.510796	−	0.884725i	0.489125	−	0.872214i	$-0.337316\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−12.4299	−	21.5291i	−0.698130	−	1.20920i	−0.969114	−	0.246613i	$-0.920682\pi$
$317$	−12.4299	−	21.5291i	−0.698130	−	1.20920i	0.270984	−	0.962584i	$-0.412651\pi$
$318$		0			0
$319$	−14.6957	+	8.48458i	−0.822803	+	0.475045i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	17.1870	−	9.93672i	0.956310	−	0.552894i
$324$		0			0
$325$	5.74981	+	3.31965i	0.318942	+	0.184141i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.28248	+	1.31779i	−0.125837	+	0.0726521i
$330$		0			0
$331$		−	15.8687i		−	0.872224i	−0.899892	−	0.436112i	$-0.856355\pi$
$331$		−	15.8687i		−	0.872224i	0.899892	−	0.436112i	$-0.143645\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.89776			−0.540772
$336$		0			0
$337$	−20.4987	−	11.8349i	−1.11663	−	0.644688i	−0.176094	−	0.984373i	$-0.556346\pi$
$337$	−20.4987	−	11.8349i	−1.11663	−	0.644688i	−0.940539	+	0.339685i	$0.889680\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	11.3994			0.617309
$342$		0			0
$343$	−19.8883			−1.07387
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−14.8066	−	8.54858i	−0.794859	−	0.458912i	0.0468116	−	0.998904i	$-0.485094\pi$
$347$	−14.8066	−	8.54858i	−0.794859	−	0.458912i	−0.841670	+	0.539992i	$0.818427\pi$
$348$		0			0
$349$	22.3350			1.19556			0.597782	−	0.801659i	$-0.296049\pi$
$349$	22.3350			1.19556			0.597782	+	0.801659i	$0.296049\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	20.6318i		−	1.09812i	−0.835782	−	0.549061i	$-0.814985\pi$
$353$		−	20.6318i		−	1.09812i	0.835782	−	0.549061i	$-0.185015\pi$
$354$		0			0
$355$	−10.8614	+	6.27083i	−0.576463	+	0.332821i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.21561	−	1.27918i	−0.116936	−	0.0675128i	0.440391	−	0.897806i	$-0.354840\pi$
$359$	−2.21561	−	1.27918i	−0.116936	−	0.0675128i	−0.557327	+	0.830293i	$0.688173\pi$
$360$		0			0
$361$	−9.51981	−	16.4430i	−0.501043	−	0.865423i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.07339	−	0.619721i	0.0561837	−	0.0324377i
$366$		0			0
$367$	5.14184	+	8.90593i	0.268402	+	0.464886i	0.968449	−	0.249211i	$-0.0801712\pi$
$367$	5.14184	+	8.90593i	0.268402	+	0.464886i	−0.700047	+	0.714096i	$0.746838\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	9.04176	+	15.6608i	0.469425	+	0.813068i
$372$		0			0
$373$		−	0.644737i		−	0.0333832i	−0.999861	−	0.0166916i	$-0.994687\pi$
$373$		−	0.644737i		−	0.0333832i	0.999861	−	0.0166916i	$-0.00531335\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−11.4496	−	6.61046i	−0.589687	−	0.340456i
$378$		0			0
$379$		−	14.3674i		−	0.738006i	−0.929428	−	0.369003i	$-0.879699\pi$
$379$		−	14.3674i		−	0.738006i	0.929428	−	0.369003i	$-0.120301\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.5460	−	21.7304i	0.641072	−	1.11037i	−0.344122	−	0.938925i	$-0.611823\pi$
$383$	12.5460	−	21.7304i	0.641072	−	1.11037i	0.985194	−	0.171444i	$-0.0548433\pi$
$384$		0			0
$385$	2.47369	−	4.28456i	0.126071	−	0.218361i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−25.5716	+	14.7637i	−1.29653	+	0.748552i	−0.979803	−	0.199965i	$-0.935917\pi$
$389$	−25.5716	+	14.7637i	−1.29653	+	0.748552i	−0.316727	+	0.948517i	$0.602584\pi$
$390$		0			0
$391$	−4.48384			−0.226758
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−5.56864	−	9.64516i	−0.280189	−	0.485301i
$396$		0			0
$397$	−12.3368	+	21.3679i	−0.619164	+	1.07242i	0.370474	+	0.928843i	$0.379195\pi$
$397$	−12.3368	+	21.3679i	−0.619164	+	1.07242i	−0.989639	+	0.143581i	$0.954138\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.2098	−	19.4160i	0.559792	−	0.969588i	−0.437722	−	0.899111i	$-0.644214\pi$
$401$	11.2098	−	19.4160i	0.559792	−	0.969588i	0.997513	−	0.0704772i	$-0.0224522\pi$
$402$		0			0
$403$	4.44070	+	7.69151i	0.221207	+	0.383142i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−13.9007			−0.689032
$408$		0			0
$409$	−33.0779	+	19.0975i	−1.63560	+	0.944312i	−0.653273	+	0.757122i	$0.726605\pi$
$409$	−33.0779	+	19.0975i	−1.63560	+	0.944312i	−0.982324	+	0.187190i	$0.940062\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.58822	+	14.8752i	−0.422599	+	0.731963i
$414$		0			0
$415$	1.96024	−	3.39523i	0.0962243	−	0.166665i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			10.9902i			0.536906i	0.963293	+	0.268453i	$0.0865124\pi$
$419$			10.9902i			0.536906i	−0.963293	+	0.268453i	$0.913488\pi$
$420$		0			0
$421$	12.7768	+	7.37668i	0.622702	+	0.359517i	0.777920	−	0.628363i	$-0.216275\pi$
$421$	12.7768	+	7.37668i	0.622702	+	0.359517i	−0.155218	+	0.987880i	$0.549608\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		−	17.0933i		−	0.829147i
$426$		0			0
$427$	11.1174	+	19.2558i	0.538007	+	0.931856i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6.98046	−	12.0905i	−0.336237	−	0.582380i	0.647485	−	0.762079i	$-0.275821\pi$
$431$	−6.98046	−	12.0905i	−0.336237	−	0.582380i	−0.983722	+	0.179699i	$0.942488\pi$
$432$		0			0
$433$	−6.49979	+	3.75266i	−0.312360	+	0.180341i	−0.647982	−	0.761656i	$-0.724387\pi$
$433$	−6.49979	+	3.75266i	−0.312360	+	0.180341i	0.335622	+	0.941997i	$0.391054\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.00258429	+	4.29125i	0.000123623	+	0.205278i
$438$		0			0
$439$	16.8069	+	9.70345i	0.802148	+	0.463121i	0.844222	−	0.535994i	$-0.180063\pi$
$439$	16.8069	+	9.70345i	0.802148	+	0.463121i	−0.0420735	+	0.999115i	$0.513396\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.34367	−	1.35312i	0.111351	−	0.0642885i	−0.443290	−	0.896378i	$-0.646189\pi$
$443$	2.34367	−	1.35312i	0.111351	−	0.0642885i	0.554641	+	0.832090i	$0.312856\pi$
$444$		0			0
$445$			1.92143i			0.0910847i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	15.9451			0.752497			0.376249	−	0.926519i	$-0.377214\pi$
$449$	15.9451			0.752497			0.376249	+	0.926519i	$0.377214\pi$
$450$		0			0
$451$	−4.97382	−	2.87164i	−0.234208	−	0.135220i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.85457			0.180705
$456$		0			0
$457$	23.1412			1.08250			0.541250	−	0.840862i	$-0.317951\pi$
$457$	23.1412			1.08250			0.541250	+	0.840862i	$0.317951\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.46820	−	3.73442i	−0.301254	−	0.173929i	0.341752	−	0.939790i	$-0.388980\pi$
$461$	−6.46820	−	3.73442i	−0.301254	−	0.173929i	−0.643006	+	0.765861i	$0.722313\pi$
$462$		0			0
$463$	28.5624			1.32741			0.663703	−	0.747996i	$-0.268984\pi$
$463$	28.5624			1.32741			0.663703	+	0.747996i	$0.268984\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	23.6393i		−	1.09389i	−0.837167	−	0.546947i	$-0.815790\pi$
$467$		−	23.6393i		−	1.09389i	0.837167	−	0.546947i	$-0.184210\pi$
$468$		0			0
$469$	14.9779	−	8.64747i	0.691613	−	0.399303i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	6.47608	+	3.73897i	0.297771	+	0.171918i
$474$		0			0
$475$	−16.3591	+	0.00985184i	−0.750607	+	0.000452033i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−24.4901	+	14.1394i	−1.11898	+	0.646044i	−0.941141	−	0.338015i	$-0.890245\pi$
$479$	−24.4901	+	14.1394i	−1.11898	+	0.646044i	−0.177841	+	0.984059i	$0.556911\pi$
$480$		0			0
$481$	−5.41511	−	9.37925i	−0.246908	−	0.427657i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.48027	+	2.56390i	0.0672156	+	0.116421i
$486$		0			0
$487$		−	5.90227i		−	0.267457i	−0.991018	−	0.133729i	$-0.957305\pi$
$487$		−	5.90227i		−	0.267457i	0.991018	−	0.133729i	$-0.0426950\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−20.8764	−	12.0530i	−0.942138	−	0.543943i	−0.0515078	−	0.998673i	$-0.516403\pi$
$491$	−20.8764	−	12.0530i	−0.942138	−	0.543943i	−0.890630	+	0.454729i	$0.849736\pi$
$492$		0			0
$493$			34.0381i			1.53300i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.9574	−	18.9787i	0.491506	−	0.851313i
$498$		0			0
$499$	0.140704	−	0.243706i	0.00629876	−	0.0109098i	−0.862859	−	0.505445i	$-0.831328\pi$
$499$	0.140704	−	0.243706i	0.00629876	−	0.0109098i	0.869158	+	0.494535i	$0.164662\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	16.2478	−	9.38070i	0.724455	−	0.418265i	−0.0919349	−	0.995765i	$-0.529305\pi$
$503$	16.2478	−	9.38070i	0.724455	−	0.418265i	0.816390	+	0.577500i	$0.195972\pi$
$504$		0			0
$505$	−5.02357			−0.223546
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.7118	−	23.7496i	−0.607767	−	1.05268i	−0.991608	−	0.129283i	$-0.958732\pi$
$509$	−13.7118	−	23.7496i	−0.607767	−	1.05268i	0.383841	−	0.923399i	$-0.374601\pi$
$510$		0			0
$511$	−1.08287	+	1.87559i	−0.0479035	+	0.0829714i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−5.40146	+	9.35560i	−0.238017	+	0.412257i
$516$		0			0
$517$	−1.53347	−	2.65605i	−0.0674421	−	0.116813i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	26.5154			1.16166			0.580830	−	0.814025i	$-0.302728\pi$
$521$	26.5154			1.16166			0.580830	+	0.814025i	$0.302728\pi$
$522$		0			0
$523$	−16.4861	+	9.51823i	−0.720885	+	0.416203i	−0.815078	−	0.579351i	$-0.803306\pi$
$523$	−16.4861	+	9.51823i	−0.720885	+	0.416203i	0.0941935	+	0.995554i	$0.469973\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	11.4329	−	19.8023i	0.498023	−	0.862601i
$528$		0			0
$529$	−11.0154	+	19.0792i	−0.478930	+	0.829532i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	4.47467i		−	0.193819i
$534$		0			0
$535$	−6.57191	−	3.79429i	−0.284128	−	0.164042i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	7.24930i		−	0.312249i
$540$		0			0
$541$	−8.07769	−	13.9910i	−0.347287	−	0.601519i	0.638479	−	0.769639i	$-0.279564\pi$
$541$	−8.07769	−	13.9910i	−0.347287	−	0.601519i	−0.985767	+	0.168120i	$0.946230\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−5.69159	−	9.85813i	−0.243801	−	0.422276i
$546$		0			0
$547$	−3.72666	+	2.15159i	−0.159341	+	0.0919953i	−0.577550	−	0.816355i	$-0.695991\pi$
$547$	−3.72666	+	2.15159i	−0.159341	+	0.0919953i	0.418209	+	0.908351i	$0.362658\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	32.5760	−	0.0196181i	1.38779	−	0.000835757i
$552$		0			0
$553$	16.8536	+	9.73040i	0.716686	+	0.413779i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−32.5547	+	18.7955i	−1.37939	+	0.796390i	−0.992086	−	0.125562i	$-0.959927\pi$
$557$	−32.5547	+	18.7955i	−1.37939	+	0.796390i	−0.387303	+	0.921953i	$0.626593\pi$
$558$		0			0
$559$			5.82616i			0.246420i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.74144			−0.326263			−0.163131	−	0.986604i	$-0.552159\pi$
$563$	−7.74144			−0.326263			−0.163131	+	0.986604i	$0.552159\pi$
$564$		0			0
$565$	−12.0434	−	6.95324i	−0.506668	−	0.292525i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	35.7614			1.49919			0.749597	−	0.661894i	$-0.230247\pi$
$569$	35.7614			1.49919			0.749597	+	0.661894i	$0.230247\pi$
$570$		0			0
$571$	−25.8561			−1.08204			−0.541022	−	0.841008i	$-0.681963\pi$
$571$	−25.8561			−1.08204			−0.541022	+	0.841008i	$0.681963\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.19978	+	1.84739i	0.133440	+	0.0770417i
$576$		0			0
$577$	−36.8743			−1.53510			−0.767549	−	0.640990i	$-0.778524\pi$
$577$	−36.8743			−1.53510			−0.767549	+	0.640990i	$0.778524\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$			6.85048i			0.284206i
$582$		0			0
$583$	−18.2240	+	10.5216i	−0.754761	+	0.435762i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−30.7090	−	17.7298i	−1.26750	−	0.731789i	−0.292982	−	0.956118i	$-0.594648\pi$
$587$	−30.7090	−	17.7298i	−1.26750	−	0.731789i	−0.974513	+	0.224329i	$0.927981\pi$
$588$		0			0
$589$	−18.9583	−	10.9304i	−0.781163	−	0.450378i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−16.4275	+	9.48442i	−0.674596	+	0.389478i	−0.797816	−	0.602901i	$-0.794011\pi$
$593$	−16.4275	+	9.48442i	−0.674596	+	0.389478i	0.123220	+	0.992379i	$0.460678\pi$
$594$		0			0
$595$	−4.96192	−	8.59430i	−0.203419	−	0.352332i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4.50181	−	7.79736i	−0.183939	−	0.318591i	0.759280	−	0.650765i	$-0.225551\pi$
$599$	−4.50181	−	7.79736i	−0.183939	−	0.318591i	−0.943218	+	0.332173i	$0.892218\pi$
$600$		0			0
$601$			36.2544i			1.47885i	0.673241	+	0.739423i	$0.264902\pi$
$601$			36.2544i			1.47885i	−0.673241	+	0.739423i	$0.735098\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.65195	−	3.26316i	−0.229785	−	0.132666i
$606$		0			0
$607$		−	43.9561i		−	1.78412i	−0.451915	−	0.892061i	$-0.649259\pi$
$607$		−	43.9561i		−	1.78412i	0.451915	−	0.892061i	$-0.350741\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.19475	−	2.06937i	0.0483344	−	0.0837177i
$612$		0			0
$613$	4.67971	−	8.10549i	0.189012	−	0.327378i	−0.755909	−	0.654676i	$-0.772805\pi$
$613$	4.67971	−	8.10549i	0.189012	−	0.327378i	0.944921	+	0.327299i	$0.106138\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.43241	−	4.29110i	0.299218	−	0.172753i	−0.342874	−	0.939381i	$-0.611400\pi$
$617$	7.43241	−	4.29110i	0.299218	−	0.172753i	0.642091	+	0.766628i	$0.278067\pi$
$618$		0			0
$619$	38.6541			1.55364			0.776820	−	0.629723i	$-0.216831\pi$
$619$	38.6541			1.55364			0.776820	+	0.629723i	$0.216831\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.67872	−	2.90762i	−0.0672564	−	0.116491i
$624$		0			0
$625$	−3.92523	+	6.79869i	−0.157009	+	0.271948i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−13.9415	+	24.1475i	−0.555886	+	0.962823i
$630$		0			0
$631$	−13.9346	−	24.1355i	−0.554729	−	0.960820i	−0.997925	−	0.0643944i	$-0.979488\pi$
$631$	−13.9346	−	24.1355i	−0.554729	−	0.960820i	0.443195	−	0.896425i	$-0.353845\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.72615			−0.108184
$636$		0			0
$637$	4.89134	−	2.82401i	0.193802	−	0.111892i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	18.1750	−	31.4800i	0.717868	−	1.24338i	−0.243974	−	0.969782i	$-0.578451\pi$
$641$	18.1750	−	31.4800i	0.717868	−	1.24338i	0.961843	−	0.273603i	$-0.0882154\pi$
$642$		0			0
$643$	3.55829	−	6.16313i	0.140325	−	0.243050i	−0.787294	−	0.616578i	$-0.788519\pi$
$643$	3.55829	−	6.16313i	0.140325	−	0.243050i	0.927619	+	0.373528i	$0.121852\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	41.4785i		−	1.63069i	−0.578977	−	0.815344i	$-0.696548\pi$
$647$		−	41.4785i		−	1.63069i	0.578977	−	0.815344i	$-0.303452\pi$
$648$		0			0
$649$	−17.3099	−	9.99386i	−0.679472	−	0.392293i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			26.0851i			1.02079i	0.859940	+	0.510395i	$0.170501\pi$
$653$			26.0851i			1.02079i	−0.859940	+	0.510395i	$0.829499\pi$
$654$		0			0
$655$	5.13308	+	8.89076i	0.200566	+	0.347391i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.23497	+	5.60313i	0.126016	+	0.218267i	0.922130	−	0.386881i	$-0.126447\pi$
$659$	3.23497	+	5.60313i	0.126016	+	0.218267i	−0.796113	+	0.605148i	$0.793114\pi$
$660$		0			0
$661$	−6.51046	+	3.75881i	−0.253227	+	0.146201i	−0.621241	−	0.783619i	$-0.713371\pi$
$661$	−6.51046	+	3.75881i	−0.253227	+	0.146201i	0.368014	+	0.929820i	$0.380038\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.22228	+	4.75374i	−0.318846	+	0.184342i
$666$		0			0
$667$	−6.37175	−	3.67873i	−0.246715	−	0.142441i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−22.4075	+	12.9370i	−0.865030	+	0.499425i
$672$		0			0
$673$			45.0530i			1.73666i	0.495983	+	0.868332i	$0.334808\pi$
$673$			45.0530i			1.73666i	−0.495983	+	0.868332i	$0.665192\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.9432			0.728048			0.364024	−	0.931390i	$-0.381403\pi$
$677$	18.9432			0.728048			0.364024	+	0.931390i	$0.381403\pi$
$678$		0			0
$679$	−4.48005	−	2.58656i	−0.171929	−	0.0992631i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−33.9541			−1.29922			−0.649608	−	0.760269i	$-0.725067\pi$
$683$	−33.9541			−1.29922			−0.649608	+	0.760269i	$0.725067\pi$
$684$		0			0
$685$	−3.58507			−0.136978
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−14.1986	−	8.19755i	−0.540923	−	0.312302i
$690$		0			0
$691$	28.6390			1.08948			0.544739	−	0.838606i	$-0.316629\pi$
$691$	28.6390			1.08948			0.544739	+	0.838606i	$0.316629\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	7.12179i		−	0.270145i
$696$		0			0
$697$	−9.97688	+	5.76015i	−0.377901	+	0.218181i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−9.10417	−	5.25629i	−0.343860	−	0.198527i	0.318118	−	0.948051i	$-0.396949\pi$
$701$	−9.10417	−	5.25629i	−0.343860	−	0.198527i	−0.661977	+	0.749524i	$0.730283\pi$
$702$		0			0
$703$	23.1183	+	13.3288i	0.871923	+	0.502705i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.60195	−	4.38899i	0.285901	−	0.165065i
$708$		0			0
$709$	14.6209	+	25.3241i	0.549099	+	0.951067i	0.998337	+	0.0576544i	$0.0183622\pi$
$709$	14.6209	+	25.3241i	0.549099	+	0.951067i	−0.449238	+	0.893412i	$0.648305\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	2.47126	+	4.28034i	0.0925493	+	0.160300i
$714$		0			0
$715$			4.48545i			0.167746i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−40.3216	−	23.2797i	−1.50374	−	0.868185i	−0.999991	−	0.00433630i	$-0.998620\pi$
$719$	−40.3216	−	23.2797i	−1.50374	−	0.868185i	−0.503751	−	0.863849i	$-0.668047\pi$
$720$		0			0
$721$		−	18.8766i		−	0.703000i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	14.0241	−	24.2904i	0.520841	−	0.902123i
$726$		0			0
$727$	−5.39092	+	9.33735i	−0.199938	+	0.346303i	−0.948508	−	0.316753i	$-0.897407\pi$
$727$	−5.39092	+	9.33735i	−0.199938	+	0.346303i	0.748570	+	0.663056i	$0.230741\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	12.9902	−	7.49991i	0.480461	−	0.277394i
$732$		0			0
$733$	−4.09677			−0.151318			−0.0756588	−	0.997134i	$-0.524106\pi$
$733$	−4.09677			−0.151318			−0.0756588	+	0.997134i	$0.524106\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.0628	+	17.4293i	0.370668	+	0.642016i
$738$		0			0
$739$	21.6495	−	37.4981i	0.796390	−	1.37939i	−0.125562	−	0.992086i	$-0.540073\pi$
$739$	21.6495	−	37.4981i	0.796390	−	1.37939i	0.921953	−	0.387303i	$-0.126593\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−9.48370	+	16.4263i	−0.347923	+	0.602621i	−0.985880	−	0.167451i	$-0.946446\pi$
$743$	−9.48370	+	16.4263i	−0.347923	+	0.602621i	0.637957	+	0.770072i	$0.279780\pi$
$744$		0			0
$745$	6.14139	+	10.6372i	0.225003	+	0.389717i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	13.2600			0.484509
$750$		0			0
$751$	7.00131	−	4.04221i	0.255481	−	0.147502i	−0.366790	−	0.930304i	$-0.619543\pi$
$751$	7.00131	−	4.04221i	0.255481	−	0.147502i	0.622272	+	0.782801i	$0.286210\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.06740	+	3.58085i	−0.0752405	+	0.130320i
$756$		0			0
$757$	−24.7540	+	42.8751i	−0.899698	+	1.55832i	−0.0718180	+	0.997418i	$0.522880\pi$
$757$	−24.7540	+	42.8751i	−0.899698	+	1.55832i	−0.827880	+	0.560905i	$0.810453\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	49.9715i		−	1.81147i	−0.423847	−	0.905734i	$-0.639321\pi$
$761$		−	49.9715i		−	1.81147i	0.423847	−	0.905734i	$-0.360679\pi$
$762$		0			0
$763$	17.2257	+	9.94526i	0.623612	+	0.360042i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	15.5727i		−	0.562298i
$768$		0			0
$769$	−25.8290	−	44.7371i	−0.931417	−	1.61326i	−0.780902	−	0.624653i	$-0.785240\pi$
$769$	−25.8290	−	44.7371i	−0.931417	−	1.61326i	−0.150514	−	0.988608i	$-0.548093\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−8.77157	−	15.1928i	−0.315491	−	0.546447i	0.664050	−	0.747688i	$-0.268836\pi$
$773$	−8.77157	−	15.1928i	−0.315491	−	0.546447i	−0.979542	+	0.201241i	$0.935503\pi$
$774$		0			0
$775$	−16.3175	+	9.42093i	−0.586143	+	0.338410i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.51849	+	9.54502i	0.197720	+	0.341986i
$780$		0			0
$781$	22.0850	+	12.7508i	0.790263	+	0.456259i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.124372	+	0.0718060i	−0.00443902	+	0.00256287i
$786$		0			0
$787$		−	42.2049i		−	1.50444i	−0.658911	−	0.752221i	$-0.728983\pi$
$787$		−	42.2049i		−	1.50444i	0.658911	−	0.752221i	$-0.271017\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	24.2996			0.863995
$792$		0			0
$793$	−17.4580	−	10.0794i	−0.619950	−	0.357929i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	24.7303			0.875993			0.437996	−	0.898977i	$-0.355688\pi$
$797$	24.7303			0.875993			0.437996	+	0.898977i	$0.355688\pi$
$798$		0			0
$799$	−6.15192			−0.217639
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.18257	−	1.26011i	−0.0770213	−	0.0444683i
$804$		0			0
$805$	2.14508			0.0756041
$806$		0			0
$807$		0			0
$808$		0			0
$809$			45.9928i			1.61702i	0.588483	+	0.808510i	$0.299725\pi$
$809$			45.9928i			1.61702i	−0.588483	+	0.808510i	$0.700275\pi$
$810$		0			0
$811$	−46.5242	+	26.8608i	−1.63369	+	0.943209i	−0.650742	+	0.759299i	$0.725542\pi$
$811$	−46.5242	+	26.8608i	−1.63369	+	0.943209i	−0.982943	+	0.183910i	$0.941125\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−24.0668	−	13.8950i	−0.843023	−	0.486720i
$816$		0			0
$817$	−7.18525	−	12.4279i	−0.251380	−	0.434798i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.42433	+	0.822339i	−0.0497096	+	0.0286998i	−0.524649	−	0.851319i	$-0.675803\pi$
$821$	−1.42433	+	0.822339i	−0.0497096	+	0.0286998i	0.474939	+	0.880019i	$0.342470\pi$
$822$		0			0
$823$	−20.4603	−	35.4382i	−0.713200	−	1.23530i	−0.963650	−	0.267169i	$-0.913912\pi$
$823$	−20.4603	−	35.4382i	−0.713200	−	1.23530i	0.250450	−	0.968130i	$-0.419422\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−18.4987	−	32.0407i	−0.643264	−	1.11417i	−0.984700	−	0.174261i	$-0.944246\pi$
$827$	−18.4987	−	32.0407i	−0.643264	−	1.11417i	0.341436	−	0.939905i	$-0.389087\pi$
$828$		0			0
$829$			4.00435i			0.139077i	0.997579	+	0.0695384i	$0.0221526\pi$
$829$			4.00435i			0.139077i	−0.997579	+	0.0695384i	$0.977847\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−12.5931	−	7.27060i	−0.436323	−	0.251911i
$834$		0			0
$835$		−	22.5499i		−	0.780373i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.90631	−	8.49798i	0.169385	−	0.293383i	−0.768819	−	0.639466i	$-0.779155\pi$
$839$	4.90631	−	8.49798i	0.169385	−	0.293383i	0.938204	+	0.346084i	$0.112489\pi$
$840$		0			0
$841$	−13.4263	+	23.2550i	−0.462975	+	0.801896i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	9.54542	−	5.51105i	0.328373	−	0.189586i
$846$		0			0
$847$	11.4038			0.391840
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.01352	−	5.21957i	−0.103302	−	0.178925i
$852$		0			0
$853$	−14.6217	+	25.3255i	−0.500636	+	0.867128i	0.499363	+	0.866393i	$0.333567\pi$
$853$	−14.6217	+	25.3255i	−0.500636	+	0.867128i	−1.00000		0.000734914i	$0.999766\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.34426	+	2.32832i	−0.0459189	+	0.0795339i	−0.888071	−	0.459706i	$-0.847955\pi$
$857$	−1.34426	+	2.32832i	−0.0459189	+	0.0795339i	0.842152	+	0.539240i	$0.181288\pi$
$858$		0			0
$859$	13.4880	+	23.3619i	0.460205	+	0.797099i	0.998971	−	0.0453571i	$-0.0144426\pi$
$859$	13.4880	+	23.3619i	0.460205	+	0.797099i	−0.538766	+	0.842456i	$0.681109\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−49.7658			−1.69405			−0.847024	−	0.531555i	$-0.821608\pi$
$863$	−49.7658			−1.69405			−0.847024	+	0.531555i	$0.821608\pi$
$864$		0			0
$865$	5.34295	−	3.08475i	0.181666	−	0.104885i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−11.3230	+	19.6120i	−0.384106	+	0.665291i
$870$		0			0
$871$	−7.84007	+	13.5794i	−0.265651	+	0.460120i
$872$		0			0
$873$		0			0
$874$		0			0
$875$			19.0719i			0.644749i
$876$		0			0
$877$	−20.5354	−	11.8561i	−0.693430	−	0.400352i	0.111465	−	0.993768i	$-0.464446\pi$
$877$	−20.5354	−	11.8561i	−0.693430	−	0.400352i	−0.804896	+	0.593416i	$0.797779\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			14.0400i			0.473018i	0.971629	+	0.236509i	$0.0760033\pi$
$881$			14.0400i			0.473018i	−0.971629	+	0.236509i	$0.923997\pi$
$882$		0			0
$883$	3.14734	+	5.45135i	0.105916	+	0.183452i	0.914112	−	0.405461i	$-0.132889\pi$
$883$	3.14734	+	5.45135i	0.105916	+	0.183452i	−0.808196	+	0.588914i	$0.799556\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.9577	+	29.3716i	0.569385	+	0.986203i	0.996627	+	0.0820661i	$0.0261518\pi$
$887$	16.9577	+	29.3716i	0.569385	+	0.986203i	−0.427242	+	0.904137i	$0.640515\pi$
$888$		0			0
$889$	4.12537	−	2.38178i	0.138361	−	0.0798825i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.00354570	+	5.88767i	0.000118652	+	0.197023i
$894$		0			0
$895$	−3.49147	−	2.01580i	−0.116707	−	0.0673807i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	32.4932	−	18.7600i	1.08371	−	0.625680i
$900$		0			0
$901$			42.2102i			1.40623i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.60797			−0.219656
$906$		0			0
$907$	26.1500	+	15.0977i	0.868297	+	0.501312i	0.866782	−	0.498687i	$-0.166184\pi$
$907$	26.1500	+	15.0977i	0.868297	+	0.501312i	0.00151535	+	0.999999i	$0.499518\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−10.0276			−0.332229			−0.166115	−	0.986106i	$-0.553122\pi$
$911$	−10.0276			−0.332229			−0.166115	+	0.986106i	$0.553122\pi$
$912$		0			0
$913$	−7.97170			−0.263825
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.5354	−	8.96934i	−0.513022	−	0.296194i
$918$		0			0
$919$	10.4899			0.346030			0.173015	−	0.984919i	$-0.444649\pi$
$919$	10.4899			0.346030			0.173015	+	0.984919i	$0.444649\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			19.8686i			0.653984i
$924$		0			0
$925$	19.8981	−	11.4881i	0.654244	−	0.377728i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−46.8802	−	27.0663i	−1.53809	−	0.888017i	−0.998951	−	0.0458003i	$-0.985416\pi$
$929$	−46.8802	−	27.0663i	−1.53809	−	0.888017i	−0.539140	−	0.842216i	$-0.681250\pi$
$930$		0			0
$931$	−6.95105	+	12.0563i	−0.227811	+	0.395130i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	10.0009	−	5.77404i	0.327065	−	0.188831i
$936$		0			0
$937$	−28.2897	−	48.9992i	−0.924184	−	1.60073i	−0.792868	−	0.609394i	$-0.791413\pi$
$937$	−28.2897	−	48.9992i	−0.924184	−	1.60073i	−0.131317	−	0.991340i	$-0.541921\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.48494	+	7.76815i	0.146205	+	0.253234i	0.929822	−	0.368010i	$-0.119961\pi$
$941$	4.48494	+	7.76815i	0.146205	+	0.253234i	−0.783617	+	0.621244i	$0.786627\pi$
$942$		0			0
$943$		−	2.49016i		−	0.0810908i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	29.0808	+	16.7898i	0.944998	+	0.545595i	0.891524	−	0.452974i	$-0.149637\pi$
$947$	29.0808	+	16.7898i	0.944998	+	0.545595i	0.0534744	+	0.998569i	$0.482970\pi$
$948$		0			0
$949$		−	1.96354i		−	0.0637391i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	18.2674	−	31.6400i	0.591739	−	1.02492i	−0.402259	−	0.915526i	$-0.631775\pi$
$953$	18.2674	−	31.6400i	0.591739	−	1.02492i	0.993998	−	0.109396i	$-0.0348917\pi$
$954$		0			0
$955$	9.39447	−	16.2717i	0.303998	−	0.526540i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	5.42513	−	3.13220i	0.175187	−	0.101144i
$960$		0			0
$961$	5.79527			0.186944
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.214977	+	0.372351i	0.00692036	+	0.0119864i
$966$		0			0
$967$	8.00421	−	13.8637i	0.257398	−	0.445827i	−0.708146	−	0.706066i	$-0.750468\pi$
$967$	8.00421	−	13.8637i	0.257398	−	0.445827i	0.965544	+	0.260239i	$0.0838015\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−17.5887	+	30.4646i	−0.564449	+	0.977654i	0.432652	+	0.901561i	$0.357578\pi$
$971$	−17.5887	+	30.4646i	−0.564449	+	0.977654i	−0.997101	+	0.0760931i	$0.975755\pi$
$972$		0			0
$973$	6.22216	+	10.7771i	0.199473	+	0.345498i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	31.2663			1.00030			0.500148	−	0.865940i	$-0.333279\pi$
$977$	31.2663			1.00030			0.500148	+	0.865940i	$0.333279\pi$
$978$		0			0
$979$	3.38351	−	1.95347i	0.108138	−	0.0624333i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	2.56959	−	4.45066i	0.0819571	−	0.141954i	−0.822133	−	0.569295i	$-0.807216\pi$
$983$	2.56959	−	4.45066i	0.0819571	−	0.141954i	0.904091	+	0.427341i	$0.140550\pi$
$984$		0			0
$985$	12.5667	−	21.7662i	0.400410	−	0.693530i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			3.24227i			0.103098i
$990$		0			0
$991$	−23.9339	−	13.8183i	−0.760287	−	0.438952i	0.0691119	−	0.997609i	$-0.477983\pi$
$991$	−23.9339	−	13.8183i	−0.760287	−	0.438952i	−0.829399	+	0.558657i	$0.811317\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	4.78950i		−	0.151837i
$996$		0			0
$997$	−22.3943	−	38.7881i	−0.709235	−	1.22843i	−0.965141	−	0.261730i	$-0.915707\pi$
$997$	−22.3943	−	38.7881i	−0.709235	−	1.22843i	0.255906	−	0.966702i	$-0.417626\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.dc.f.1889.4		20
3.2	odd	2		2736.2.dc.e.1889.7		20
4.3	odd	2		1368.2.cu.b.521.4	yes	20
12.11	even	2		1368.2.cu.a.521.7	yes	20
19.12	odd	6		2736.2.dc.e.449.7		20
57.50	even	6	inner	2736.2.dc.f.449.4		20
76.31	even	6		1368.2.cu.a.449.7	✓	20
228.107	odd	6		1368.2.cu.b.449.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.cu.a.449.7	✓	20	76.31	even	6
1368.2.cu.a.521.7	yes	20	12.11	even	2
1368.2.cu.b.449.4	yes	20	228.107	odd	6
1368.2.cu.b.521.4	yes	20	4.3	odd	2
2736.2.dc.e.449.7		20	19.12	odd	6
2736.2.dc.e.1889.7		20	3.2	odd	2
2736.2.dc.f.449.4		20	57.50	even	6	inner
2736.2.dc.f.1889.4		20	1.1	even	1	trivial

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.dc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.967070 - 0.558338i) q^{5} +1.95123 q^{7} +O(q^{10})\)	\(q+(-0.967070 - 0.558338i) q^{5} +1.95123 q^{7} +2.27059i q^{11} +(-1.53204 + 0.884525i) q^{13} +(3.94434 + 2.27726i) q^{17} +(2.17718 - 3.77623i) q^{19} +(-0.852585 + 0.492240i) q^{23} +(-1.87652 - 3.25022i) q^{25} +(3.73673 + 6.47220i) q^{29} -5.02043i q^{31} +(-1.88698 - 1.08945i) q^{35} +6.12206i q^{37} +(-1.26471 + 2.19054i) q^{41} +(1.64669 - 2.85216i) q^{43} +(-1.16976 + 0.675363i) q^{47} -3.19269 q^{49} +(4.63387 + 8.02610i) q^{53} +(1.26776 - 2.19582i) q^{55} +(-4.40143 + 7.62351i) q^{59} +(5.69761 + 9.86855i) q^{61} +1.97545 q^{65} +(7.67610 - 4.43180i) q^{67} +(5.61562 - 9.72654i) q^{71} +(-0.554969 + 0.961235i) q^{73} +4.43045i q^{77} +(8.63739 + 4.98680i) q^{79} +3.51085i q^{83} +(-2.54297 - 4.40455i) q^{85} +(-0.860336 - 1.49015i) q^{89} +(-2.98937 + 1.72591i) q^{91} +(-4.21389 + 2.43628i) q^{95} +(-2.29601 - 1.32560i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{7}+O(q^{10}) \) 20 * q + 4 * q^7	\( 20 q + 4 q^{7} + 6 q^{13} + 12 q^{17} - 4 q^{19} + 14 q^{25} + 12 q^{35} + 8 q^{41} + 2 q^{43} + 36 q^{47} + 32 q^{49} - 8 q^{53} - 12 q^{55} - 8 q^{59} - 2 q^{61} + 8 q^{65} - 30 q^{67} + 4 q^{71} - 22 q^{73} - 54 q^{79} - 4 q^{85} - 32 q^{89} - 18 q^{91} + 32 q^{95} + 12 q^{97}+O(q^{100}) \) 20 * q + 4 * q^7 + 6 * q^13 + 12 * q^17 - 4 * q^19 + 14 * q^25 + 12 * q^35 + 8 * q^41 + 2 * q^43 + 36 * q^47 + 32 * q^49 - 8 * q^53 - 12 * q^55 - 8 * q^59 - 2 * q^61 + 8 * q^65 - 30 * q^67 + 4 * q^71 - 22 * q^73 - 54 * q^79 - 4 * q^85 - 32 * q^89 - 18 * q^91 + 32 * q^95 + 12 * q^97

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