LMFDB - Embedded newform 2736.2.dc.e.449.7

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			449.7
Root			$2.25091 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2736.449
Dual form			2736.2.dc.e.1889.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.967070 - 0.558338i) q^{5} +1.95123 q^{7} +O(q^{10})$	$q+(0.967070 - 0.558338i) q^{5} +1.95123 q^{7} +2.27059i q^{11} +(-1.53204 - 0.884525i) q^{13} +(-3.94434 + 2.27726i) q^{17} +(2.17718 + 3.77623i) q^{19} +(0.852585 + 0.492240i) q^{23} +(-1.87652 + 3.25022i) q^{25} +(-3.73673 + 6.47220i) q^{29} +5.02043i q^{31} +(1.88698 - 1.08945i) q^{35} -6.12206i q^{37} +(1.26471 + 2.19054i) q^{41} +(1.64669 + 2.85216i) q^{43} +(1.16976 + 0.675363i) q^{47} -3.19269 q^{49} +(-4.63387 + 8.02610i) q^{53} +(1.26776 + 2.19582i) q^{55} +(4.40143 + 7.62351i) q^{59} +(5.69761 - 9.86855i) q^{61} -1.97545 q^{65} +(7.67610 + 4.43180i) q^{67} +(-5.61562 - 9.72654i) q^{71} +(-0.554969 - 0.961235i) q^{73} +4.43045i q^{77} +(8.63739 - 4.98680i) q^{79} +3.51085i q^{83} +(-2.54297 + 4.40455i) q^{85} +(0.860336 - 1.49015i) q^{89} +(-2.98937 - 1.72591i) q^{91} +(4.21389 + 2.43628i) q^{95} +(-2.29601 + 1.32560i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

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	$-0.586336\pi$
$5$	0.967070	−	0.558338i	0.432487	−	0.249696i	0.700405	+	0.713745i	$0.253003\pi$
$6$		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	0.272265	−	0.962222i	$-0.412227\pi$
$13$	−1.53204	−	0.884525i	−0.424912	−	0.245323i	−0.697177	+	0.716899i	$0.745561\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.94434	+	2.27726i	−0.956643	+	0.552318i	−0.895138	−	0.445789i	$-0.852923\pi$
$17$	−3.94434	+	2.27726i	−0.956643	+	0.552318i	−0.0615044	+	0.998107i	$0.519590\pi$
$18$		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	$-0.300605\pi$
$23$	0.852585	+	0.492240i	0.177776	+	0.102639i	−0.408471	+	0.912771i	$0.633938\pi$
$24$		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	0.276660	+	0.960968i	$0.410773\pi$
$29$	−3.73673	+	6.47220i	−0.693893	+	1.20186i	−0.970552	+	0.240890i	$0.922561\pi$
$30$		0			0
$31$			5.02043i			0.901696i	0.892601	+	0.450848i	$0.148878\pi$
$31$			5.02043i			0.901696i	−0.892601	+	0.450848i	$0.851122\pi$
$32$		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	$-0.832145\pi$
$37$		−	6.12206i		−	1.00646i	0.864152	−	0.503230i	$-0.167855\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.26471	+	2.19054i	0.197514	+	0.342105i	0.947722	−	0.319098i	$-0.103380\pi$
$41$	1.26471	+	2.19054i	0.197514	+	0.342105i	−0.750208	+	0.661202i	$0.770046\pi$
$42$		0			0
$43$	1.64669	+	2.85216i	0.251118	+	0.434950i	0.963834	−	0.266503i	$-0.0858683\pi$
$43$	1.64669	+	2.85216i	0.251118	+	0.434950i	−0.712716	+	0.701453i	$0.752535\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.16976	+	0.675363i	0.170627	+	0.0985118i	0.582882	−	0.812557i	$-0.301925\pi$
$47$	1.16976	+	0.675363i	0.170627	+	0.0985118i	−0.412254	+	0.911069i	$0.635258\pi$
$48$		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	0.349681	+	0.936869i	$0.386290\pi$
$53$	−4.63387	+	8.02610i	−0.636511	+	1.10247i	−0.986193	+	0.165601i	$0.947043\pi$
$54$		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	0.996254	+	0.0864767i	$0.0275608\pi$
$59$	4.40143	+	7.62351i	0.573018	+	0.992496i	−0.423236	+	0.906019i	$0.639106\pi$
$60$		0			0
$61$	5.69761	−	9.86855i	0.729504	−	1.26354i	−0.227589	−	0.973757i	$-0.573084\pi$
$61$	5.69761	−	9.86855i	0.729504	−	1.26354i	0.957093	−	0.289781i	$-0.0935826\pi$
$62$		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	0.889265	−	0.457392i	$-0.151216\pi$
$67$	7.67610	+	4.43180i	0.937784	+	0.541430i	0.0485194	+	0.998822i	$0.484550\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.61562	−	9.72654i	−0.666451	−	1.15433i	−0.978890	−	0.204390i	$-0.934479\pi$
$71$	−5.61562	−	9.72654i	−0.666451	−	1.15433i	0.312438	−	0.949938i	$-0.398854\pi$
$72$		0			0
$73$	−0.554969	−	0.961235i	−0.0649542	−	0.112504i	0.831719	−	0.555196i	$-0.187357\pi$
$73$	−0.554969	−	0.961235i	−0.0649542	−	0.112504i	−0.896674	+	0.442692i	$0.854023\pi$
$74$		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	0.0720030	−	0.997404i	$-0.477061\pi$
$79$	8.63739	−	4.98680i	0.971782	−	0.561059i	0.899779	+	0.436346i	$0.143728\pi$
$80$		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	$-0.804265\pi$
$89$	0.860336	−	1.49015i	0.0911955	−	0.157955i	0.908014	+	0.418939i	$0.137598\pi$
$90$		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	−0.612013	−	0.790848i	$-0.709640\pi$
$97$	−2.29601	+	1.32560i	−0.233125	+	0.134595i	0.378888	+	0.925443i	$0.376307\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.89597	−	2.24934i	−0.387664	−	0.223818i	0.293484	−	0.955964i	$-0.405185\pi$
$101$	−3.89597	−	2.24934i	−0.387664	−	0.223818i	−0.681147	+	0.732146i	$0.738519\pi$
$102$		0			0
$103$			9.67418i			0.953225i	0.879114	+	0.476612i	$0.158135\pi$
$103$			9.67418i			0.953225i	−0.879114	+	0.476612i	$0.841865\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.79570			−0.656965			−0.328482	−	0.944510i	$-0.606537\pi$
$107$	−6.79570			−0.656965			−0.328482	+	0.944510i	$0.606537\pi$
$108$		0			0
$109$	8.82811	−	5.09691i	0.845579	−	0.488195i	−0.0135776	−	0.999908i	$-0.504322\pi$
$109$	8.82811	−	5.09691i	0.845579	−	0.488195i	0.859157	+	0.511712i	$0.170989\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−12.4535			−1.17152			−0.585762	−	0.810483i	$-0.699205\pi$
$113$	−12.4535			−1.17152			−0.585762	+	0.810483i	$0.699205\pi$
$114$		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	0.590862	−	0.806772i	$-0.298788\pi$
$127$	2.11424	+	1.22066i	0.187608	+	0.108316i	−0.403254	+	0.915088i	$0.632121\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.96181	−	4.59676i	0.695627	−	0.401620i	−0.110090	−	0.993922i	$-0.535114\pi$
$131$	7.96181	−	4.59676i	0.695627	−	0.401620i	0.805717	+	0.592301i	$0.201780\pi$
$132$		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	$-0.377126\pi$
$137$	−2.78036	−	1.60524i	−0.237542	−	0.137145i	−0.614047	+	0.789270i	$0.710459\pi$
$138$		0			0
$139$	3.18883	−	5.52322i	0.270473	−	0.468474i	−0.698510	−	0.715601i	$-0.746153\pi$
$139$	3.18883	−	5.52322i	0.270473	−	0.468474i	0.968983	+	0.247127i	$0.0794865\pi$
$140$		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	$-0.517893\pi$
$149$	9.52578	−	5.49971i	0.780382	−	0.450554i	0.836566	+	0.547866i	$0.184560\pi$
$150$		0			0
$151$			3.70278i			0.301328i	0.988585	+	0.150664i	$0.0481412\pi$
$151$			3.70278i			0.301328i	−0.988585	+	0.150664i	$0.951859\pi$
$152$		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	0.868580	−	0.495549i	$-0.165033\pi$
$157$	0.0643034	+	0.111377i	0.00513197	+	0.00888883i	−0.863448	+	0.504438i	$0.831700\pi$
$158$		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	0.149850	+	0.988709i	$0.452121\pi$
$167$	−10.0969	+	17.4883i	−0.781322	+	1.35329i	−0.931172	+	0.364580i	$0.881212\pi$
$168$		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	$-0.0993122\pi$
$173$	2.76244	+	4.78469i	0.210025	+	0.363774i	−0.741697	+	0.670735i	$0.765979\pi$
$174$		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	$-0.543079\pi$
$179$	−3.61036			−0.269851			−0.134925	+	0.990856i	$0.543079\pi$
$180$		0			0
$181$	5.12473	+	2.95877i	0.380919	+	0.219923i	0.678218	−	0.734861i	$-0.262753\pi$
$181$	5.12473	+	2.95877i	0.380919	+	0.219923i	−0.297299	+	0.954784i	$0.596086\pi$
$182$		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	−0.511953	−	0.859013i	$-0.671078\pi$
$193$	−0.333446	+	0.192515i	−0.0240020	+	0.0138576i	0.487951	+	0.872871i	$0.337744\pi$
$194$		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	−0.779949	−	0.625844i	$-0.784755\pi$
$199$	2.14454	−	3.71444i	0.152022	−	0.263310i	0.931971	+	0.362534i	$0.118088\pi$
$200$		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	−0.987879	−	0.155228i	$-0.950389\pi$
$211$	−19.5719	+	11.2999i	−1.34739	+	0.777914i	−0.359508	+	0.933142i	$0.617055\pi$
$212$		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	−0.453614	−	0.891198i	$-0.649865\pi$
$223$	1.36459	−	0.787848i	0.0913799	−	0.0527582i	0.544994	+	0.838440i	$0.316532\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.6162			−0.704623			−0.352311	−	0.935883i	$-0.614604\pi$
$227$	−10.6162			−0.704623			−0.352311	+	0.935883i	$0.614604\pi$
$228$		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	$-0.669755\pi$
$233$	−0.256478	+	0.148078i	−0.0168024	+	0.00970089i	0.491575	+	0.870835i	$0.336421\pi$
$234$		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	0.927277	−	0.374375i	$-0.122143\pi$
$241$	16.5596	+	9.56069i	1.06670	+	0.615858i	0.139420	+	0.990233i	$0.455476\pi$
$242$		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	$-0.391160\pi$
$251$	−4.95771	−	2.86233i	−0.312928	−	0.180669i	−0.648236	+	0.761440i	$0.724493\pi$
$252$		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	$-0.870352\pi$
$257$	−1.86017	+	3.22192i	−0.116034	+	0.200978i	0.802158	+	0.597111i	$0.203685\pi$
$258$		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	$-0.656409\pi$
$263$	0.904992	−	0.522497i	0.0558042	−	0.0322186i	0.527643	+	0.849467i	$0.323076\pi$
$264$		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	$-0.0409548\pi$
$269$	6.31034	+	10.9298i	0.384749	+	0.666404i	−0.606986	+	0.794713i	$0.707622\pi$
$270$		0			0
$271$	−14.3098	−	24.7853i	−0.869259	−	1.50560i	−0.862755	−	0.505622i	$-0.831263\pi$
$271$	−14.3098	−	24.7853i	−0.869259	−	1.50560i	−0.00650350	−	0.999979i	$-0.502070\pi$
$272$		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	−0.181492	−	0.983392i	$-0.558093\pi$
$281$	12.7550	−	22.0922i	0.760897	−	1.31791i	0.942389	−	0.334520i	$-0.108574\pi$
$282$		0			0
$283$	−7.56049	−	13.0952i	−0.449425	−	0.778426i	0.548924	−	0.835872i	$-0.315038\pi$
$283$	−7.56049	−	13.0952i	−0.449425	−	0.778426i	−0.998349	+	0.0574459i	$0.981704\pi$
$284$		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	$-0.366520\pi$
$293$	13.9388			0.814314			0.407157	+	0.913358i	$0.366520\pi$
$294$		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	−0.816594	−	0.577213i	$-0.804140\pi$
$307$	−12.7032	+	7.33419i	−0.725010	+	0.418584i	0.0915842	+	0.995797i	$0.470807\pi$
$308$		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	0.489125	+	0.872214i	$0.337316\pi$
$313$	−9.03691	+	15.6524i	−0.510796	+	0.884725i	−0.999922	+	0.0125118i	$0.996017\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.4299	−	21.5291i	0.698130	−	1.20920i	−0.270984	−	0.962584i	$-0.587349\pi$
$317$	12.4299	−	21.5291i	0.698130	−	1.20920i	0.969114	−	0.246613i	$-0.0793177\pi$
$318$		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	$0.143645\pi$
$331$			15.8687i			0.872224i	−0.899892	+	0.436112i	$0.856355\pi$
$332$		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	−0.940539	−	0.339685i	$-0.889680\pi$
$337$	−20.4987	+	11.8349i	−1.11663	+	0.644688i	−0.176094	+	0.984373i	$0.556346\pi$
$338$		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	$-0.514906\pi$
$347$	14.8066	−	8.54858i	0.794859	−	0.458912i	0.841670	+	0.539992i	$0.181573\pi$
$348$		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	$-0.645160\pi$
$359$	2.21561	−	1.27918i	0.116936	−	0.0675128i	0.557327	+	0.830293i	$0.311827\pi$
$360$		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	−0.700047	−	0.714096i	$-0.746838\pi$
$367$	5.14184	−	8.90593i	0.268402	−	0.464886i	0.968449	+	0.249211i	$0.0801712\pi$
$368$		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	$0.00531335\pi$
$373$			0.644737i			0.0333832i	−0.999861	+	0.0166916i	$0.994687\pi$
$374$		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	$0.120301\pi$
$379$			14.3674i			0.738006i	−0.929428	+	0.369003i	$0.879699\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.5460	−	21.7304i	−0.641072	−	1.11037i	−0.985194	−	0.171444i	$-0.945157\pi$
$383$	−12.5460	−	21.7304i	−0.641072	−	1.11037i	0.344122	−	0.938925i	$-0.388177\pi$
$384$		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	$-0.0640829\pi$
$389$	25.5716	+	14.7637i	1.29653	+	0.748552i	0.316727	+	0.948517i	$0.397416\pi$
$390$		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	−0.989639	−	0.143581i	$-0.954138\pi$
$397$	−12.3368	−	21.3679i	−0.619164	−	1.07242i	0.370474	−	0.928843i	$-0.379195\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−11.2098	−	19.4160i	−0.559792	−	0.969588i	−0.997513	−	0.0704772i	$-0.977548\pi$
$401$	−11.2098	−	19.4160i	−0.559792	−	0.969588i	0.437722	−	0.899111i	$-0.355786\pi$
$402$		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	−0.982324	−	0.187190i	$-0.940062\pi$
$409$	−33.0779	−	19.0975i	−1.63560	−	0.944312i	−0.653273	−	0.757122i	$-0.726605\pi$
$410$		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	−0.155218	−	0.987880i	$-0.549608\pi$
$421$	12.7768	−	7.37668i	0.622702	−	0.359517i	0.777920	+	0.628363i	$0.216275\pi$
$422$		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	$-0.724179\pi$
$431$	6.98046	−	12.0905i	0.336237	−	0.582380i	0.983722	+	0.179699i	$0.0575123\pi$
$432$		0			0
$433$	−6.49979	−	3.75266i	−0.312360	−	0.180341i	0.335622	−	0.941997i	$-0.391054\pi$
$433$	−6.49979	−	3.75266i	−0.312360	−	0.180341i	−0.647982	+	0.761656i	$0.724387\pi$
$434$		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	−0.0420735	−	0.999115i	$-0.513396\pi$
$439$	16.8069	−	9.70345i	0.802148	−	0.463121i	0.844222	+	0.535994i	$0.180063\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.34367	−	1.35312i	−0.111351	−	0.0642885i	0.443290	−	0.896378i	$-0.353811\pi$
$443$	−2.34367	−	1.35312i	−0.111351	−	0.0642885i	−0.554641	+	0.832090i	$0.687144\pi$
$444$		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	$-0.622786\pi$
$449$	−15.9451			−0.752497			−0.376249	+	0.926519i	$0.622786\pi$
$450$		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	$-0.611020\pi$
$461$	6.46820	−	3.73442i	0.301254	−	0.173929i	0.643006	+	0.765861i	$0.277687\pi$
$462$		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	$-0.109755\pi$
$479$	24.4901	+	14.1394i	1.11898	+	0.646044i	0.177841	+	0.984059i	$0.443089\pi$
$480$		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	$0.0426950\pi$
$487$			5.90227i			0.267457i	−0.991018	+	0.133729i	$0.957305\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	20.8764	−	12.0530i	0.942138	−	0.543943i	0.0515078	−	0.998673i	$-0.483597\pi$
$491$	20.8764	−	12.0530i	0.942138	−	0.543943i	0.890630	+	0.454729i	$0.150264\pi$
$492$		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	0.869158	−	0.494535i	$-0.164662\pi$
$499$	0.140704	+	0.243706i	0.00629876	+	0.0109098i	−0.862859	+	0.505445i	$0.831328\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−16.2478	−	9.38070i	−0.724455	−	0.418265i	0.0919349	−	0.995765i	$-0.470695\pi$
$503$	−16.2478	−	9.38070i	−0.724455	−	0.418265i	−0.816390	+	0.577500i	$0.804028\pi$
$504$		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	−0.383841	−	0.923399i	$-0.625399\pi$
$509$	13.7118	−	23.7496i	0.607767	−	1.05268i	0.991608	−	0.129283i	$-0.0412677\pi$
$510$		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	$-0.697272\pi$
$521$	−26.5154			−1.16166			−0.580830	+	0.814025i	$0.697272\pi$
$522$		0			0
$523$	−16.4861	−	9.51823i	−0.720885	−	0.416203i	0.0941935	−	0.995554i	$-0.469973\pi$
$523$	−16.4861	−	9.51823i	−0.720885	−	0.416203i	−0.815078	+	0.579351i	$0.803306\pi$
$524$		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	−0.985767	−	0.168120i	$-0.946230\pi$
$541$	−8.07769	+	13.9910i	−0.347287	+	0.601519i	0.638479	+	0.769639i	$0.279564\pi$
$542$		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	0.418209	−	0.908351i	$-0.362658\pi$
$547$	−3.72666	−	2.15159i	−0.159341	−	0.0919953i	−0.577550	+	0.816355i	$0.695991\pi$
$548$		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	$-0.0400735\pi$
$557$	32.5547	+	18.7955i	1.37939	+	0.796390i	0.387303	+	0.921953i	$0.373407\pi$
$558$		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	$-0.447841\pi$
$563$	7.74144			0.326263			0.163131	+	0.986604i	$0.447841\pi$
$564$		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	$-0.769753\pi$
$569$	−35.7614			−1.49919			−0.749597	+	0.661894i	$0.769753\pi$
$570$		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	$-0.405352\pi$
$587$	30.7090	−	17.7298i	1.26750	−	0.731789i	0.974513	+	0.224329i	$0.0720191\pi$
$588$		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	$-0.205989\pi$
$593$	16.4275	+	9.48442i	0.674596	+	0.389478i	−0.123220	+	0.992379i	$0.539322\pi$
$594$		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	$-0.774449\pi$
$599$	4.50181	−	7.79736i	0.183939	−	0.318591i	0.943218	+	0.332173i	$0.107782\pi$
$600$		0			0
$601$		−	36.2544i		−	1.47885i	−0.673241	−	0.739423i	$-0.735098\pi$
$601$		−	36.2544i		−	1.47885i	0.673241	−	0.739423i	$-0.264902\pi$
$602$		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	$0.350741\pi$
$607$			43.9561i			1.78412i	−0.451915	+	0.892061i	$0.649259\pi$
$608$		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	0.944921	−	0.327299i	$-0.106138\pi$
$613$	4.67971	+	8.10549i	0.189012	+	0.327378i	−0.755909	+	0.654676i	$0.772805\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.43241	−	4.29110i	−0.299218	−	0.172753i	0.342874	−	0.939381i	$-0.388600\pi$
$617$	−7.43241	−	4.29110i	−0.299218	−	0.172753i	−0.642091	+	0.766628i	$0.721933\pi$
$618$		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	0.443195	+	0.896425i	$0.353845\pi$
$631$	−13.9346	+	24.1355i	−0.554729	+	0.960820i	−0.997925	+	0.0643944i	$0.979488\pi$
$632$		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	−0.961843	−	0.273603i	$-0.911785\pi$
$641$	−18.1750	−	31.4800i	−0.717868	−	1.24338i	0.243974	−	0.969782i	$-0.421549\pi$
$642$		0			0
$643$	3.55829	+	6.16313i	0.140325	+	0.243050i	0.927619	−	0.373528i	$-0.121852\pi$
$643$	3.55829	+	6.16313i	0.140325	+	0.243050i	−0.787294	+	0.616578i	$0.788519\pi$
$644$		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	$-0.873553\pi$
$659$	−3.23497	+	5.60313i	−0.126016	+	0.218267i	0.796113	+	0.605148i	$0.206886\pi$
$660$		0			0
$661$	−6.51046	−	3.75881i	−0.253227	−	0.146201i	0.368014	−	0.929820i	$-0.380038\pi$
$661$	−6.51046	−	3.75881i	−0.253227	−	0.146201i	−0.621241	+	0.783619i	$0.713371\pi$
$662$		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	$-0.665192\pi$
$673$		−	45.0530i		−	1.73666i	0.495983	−	0.868332i	$-0.334808\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−18.9432			−0.728048			−0.364024	−	0.931390i	$-0.618597\pi$
$677$	−18.9432			−0.728048			−0.364024	+	0.931390i	$0.618597\pi$
$678$		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	$-0.274933\pi$
$683$	33.9541			1.29922			0.649608	+	0.760269i	$0.274933\pi$
$684$		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	$-0.603051\pi$
$701$	9.10417	−	5.25629i	0.343860	−	0.198527i	0.661977	+	0.749524i	$0.269717\pi$
$702$		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	−0.449238	−	0.893412i	$-0.648305\pi$
$709$	14.6209	−	25.3241i	0.549099	−	0.951067i	0.998337	−	0.0576544i	$-0.0183622\pi$
$710$		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	0.503751	−	0.863849i	$-0.331953\pi$
$719$	40.3216	−	23.2797i	1.50374	−	0.868185i	0.999991	−	0.00433630i	$-0.00138029\pi$
$720$		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	0.748570	−	0.663056i	$-0.230741\pi$
$727$	−5.39092	−	9.33735i	−0.199938	−	0.346303i	−0.948508	+	0.316753i	$0.897407\pi$
$728$		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	0.921953	+	0.387303i	$0.126593\pi$
$739$	21.6495	+	37.4981i	0.796390	+	1.37939i	−0.125562	+	0.992086i	$0.540073\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	9.48370	+	16.4263i	0.347923	+	0.602621i	0.985880	−	0.167451i	$-0.0535536\pi$
$743$	9.48370	+	16.4263i	0.347923	+	0.602621i	−0.637957	+	0.770072i	$0.720220\pi$
$744$		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	0.622272	−	0.782801i	$-0.286210\pi$
$751$	7.00131	+	4.04221i	0.255481	+	0.147502i	−0.366790	+	0.930304i	$0.619543\pi$
$752$		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	−0.827880	−	0.560905i	$-0.810453\pi$
$757$	−24.7540	−	42.8751i	−0.899698	−	1.55832i	−0.0718180	−	0.997418i	$-0.522880\pi$
$758$		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	−0.150514	+	0.988608i	$0.548093\pi$
$769$	−25.8290	+	44.7371i	−0.931417	+	1.61326i	−0.780902	+	0.624653i	$0.785240\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	8.77157	−	15.1928i	0.315491	−	0.546447i	−0.664050	−	0.747688i	$-0.731164\pi$
$773$	8.77157	−	15.1928i	0.315491	−	0.546447i	0.979542	+	0.201241i	$0.0644973\pi$
$774$		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	$0.271017\pi$
$787$			42.2049i			1.50444i	−0.658911	+	0.752221i	$0.728983\pi$
$788$		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	$-0.644312\pi$
$797$	−24.7303			−0.875993			−0.437996	+	0.898977i	$0.644312\pi$
$798$		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	−0.982943	−	0.183910i	$-0.941125\pi$
$811$	−46.5242	−	26.8608i	−1.63369	−	0.943209i	−0.650742	−	0.759299i	$-0.725542\pi$
$812$		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	$-0.324197\pi$
$821$	1.42433	+	0.822339i	0.0497096	+	0.0286998i	−0.474939	+	0.880019i	$0.657530\pi$
$822$		0			0
$823$	−20.4603	+	35.4382i	−0.713200	+	1.23530i	0.250450	+	0.968130i	$0.419422\pi$
$823$	−20.4603	+	35.4382i	−0.713200	+	1.23530i	−0.963650	+	0.267169i	$0.913912\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	18.4987	−	32.0407i	0.643264	−	1.11417i	−0.341436	−	0.939905i	$-0.610913\pi$
$827$	18.4987	−	32.0407i	0.643264	−	1.11417i	0.984700	−	0.174261i	$-0.0557536\pi$
$828$		0			0
$829$		−	4.00435i		−	0.139077i	−0.997579	−	0.0695384i	$-0.977847\pi$
$829$		−	4.00435i		−	0.139077i	0.997579	−	0.0695384i	$-0.0221526\pi$
$830$		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	$-0.220845\pi$
$839$	−4.90631	−	8.49798i	−0.169385	−	0.293383i	−0.938204	+	0.346084i	$0.887511\pi$
$840$		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	−1.00000		0.000734914i	$-0.999766\pi$
$853$	−14.6217	−	25.3255i	−0.500636	−	0.867128i	0.499363	−	0.866393i	$-0.333567\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.34426	+	2.32832i	0.0459189	+	0.0795339i	0.888071	−	0.459706i	$-0.152045\pi$
$857$	1.34426	+	2.32832i	0.0459189	+	0.0795339i	−0.842152	+	0.539240i	$0.818712\pi$
$858$		0			0
$859$	13.4880	−	23.3619i	0.460205	−	0.797099i	−0.538766	−	0.842456i	$-0.681109\pi$
$859$	13.4880	−	23.3619i	0.460205	−	0.797099i	0.998971	+	0.0453571i	$0.0144426\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	49.7658			1.69405			0.847024	−	0.531555i	$-0.178392\pi$
$863$	49.7658			1.69405			0.847024	+	0.531555i	$0.178392\pi$
$864$		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	−0.804896	−	0.593416i	$-0.797779\pi$
$877$	−20.5354	+	11.8561i	−0.693430	+	0.400352i	0.111465	+	0.993768i	$0.464446\pi$
$878$		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	−0.808196	−	0.588914i	$-0.799556\pi$
$883$	3.14734	−	5.45135i	0.105916	−	0.183452i	0.914112	+	0.405461i	$0.132889\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.9577	+	29.3716i	−0.569385	+	0.986203i	0.427242	+	0.904137i	$0.359485\pi$
$887$	−16.9577	+	29.3716i	−0.569385	+	0.986203i	−0.996627	+	0.0820661i	$0.973848\pi$
$888$		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	0.00151535	−	0.999999i	$-0.499518\pi$
$907$	26.1500	−	15.0977i	0.868297	−	0.501312i	0.866782	+	0.498687i	$0.166184\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	10.0276			0.332229			0.166115	−	0.986106i	$-0.446878\pi$
$911$	10.0276			0.332229			0.166115	+	0.986106i	$0.446878\pi$
$912$		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	0.539140	−	0.842216i	$-0.318750\pi$
$929$	46.8802	−	27.0663i	1.53809	−	0.888017i	0.998951	−	0.0458003i	$-0.0145838\pi$
$930$		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	−0.131317	+	0.991340i	$0.541921\pi$
$937$	−28.2897	+	48.9992i	−0.924184	+	1.60073i	−0.792868	+	0.609394i	$0.791413\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−4.48494	+	7.76815i	−0.146205	+	0.253234i	−0.929822	−	0.368010i	$-0.880039\pi$
$941$	−4.48494	+	7.76815i	−0.146205	+	0.253234i	0.783617	+	0.621244i	$0.213373\pi$
$942$		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	$-0.850363\pi$
$947$	−29.0808	+	16.7898i	−0.944998	+	0.545595i	−0.0534744	+	0.998569i	$0.517030\pi$
$948$		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	−0.993998	−	0.109396i	$-0.965108\pi$
$953$	−18.2674	−	31.6400i	−0.591739	−	1.02492i	0.402259	−	0.915526i	$-0.368225\pi$
$954$		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	0.965544	−	0.260239i	$-0.0838015\pi$
$967$	8.00421	+	13.8637i	0.257398	+	0.445827i	−0.708146	+	0.706066i	$0.750468\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	17.5887	+	30.4646i	0.564449	+	0.977654i	0.997101	+	0.0760931i	$0.0242446\pi$
$971$	17.5887	+	30.4646i	0.564449	+	0.977654i	−0.432652	+	0.901561i	$0.642422\pi$
$972$		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	$-0.666721\pi$
$977$	−31.2663			−1.00030			−0.500148	+	0.865940i	$0.666721\pi$
$978$		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	$-0.192784\pi$
$983$	−2.56959	−	4.45066i	−0.0819571	−	0.141954i	−0.904091	+	0.427341i	$0.859450\pi$
$984$		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	−0.829399	−	0.558657i	$-0.811317\pi$
$991$	−23.9339	+	13.8183i	−0.760287	+	0.438952i	0.0691119	+	0.997609i	$0.477983\pi$
$992$		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	0.255906	+	0.966702i	$0.417626\pi$
$997$	−22.3943	+	38.7881i	−0.709235	+	1.22843i	−0.965141	+	0.261730i	$0.915707\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.cu.a.449.7	✓	20	4.3	odd	2
1368.2.cu.a.521.7	yes	20	228.179	odd	6
1368.2.cu.b.449.4	yes	20	12.11	even	2
1368.2.cu.b.521.4	yes	20	76.27	even	6
2736.2.dc.e.449.7		20	1.1	even	1	trivial
2736.2.dc.e.1889.7		20	57.8	even	6	inner
2736.2.dc.f.449.4		20	3.2	odd	2
2736.2.dc.f.1889.4		20	19.8	odd	6

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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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