LMFDB - Embedded newform 2340.2.q.a.2161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2340,2,Mod(1621,2340)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2340, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2340.1621");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2340.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.6849940730$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2161.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2340.2161
Dual form			2340.2.q.a.1621.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{5} +(-1.50000 + 2.59808i) q^{7} +O(q^{10})$	$q-1.00000 q^{5} +(-1.50000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{11} +(1.00000 - 3.46410i) q^{13} +(-3.50000 + 6.06218i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-3.50000 - 6.06218i) q^{23} +1.00000 q^{25} +(-2.50000 - 4.33013i) q^{29} -4.00000 q^{31} +(1.50000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{37} +(3.50000 + 6.06218i) q^{41} +(4.50000 - 7.79423i) q^{43} -8.00000 q^{47} +(-1.00000 - 1.73205i) q^{49} +6.00000 q^{53} +(-1.50000 - 2.59808i) q^{55} +(2.50000 - 4.33013i) q^{59} +(2.50000 - 4.33013i) q^{61} +(-1.00000 + 3.46410i) q^{65} +(-6.50000 - 11.2583i) q^{67} +(-1.50000 + 2.59808i) q^{71} -14.0000 q^{73} -9.00000 q^{77} -8.00000 q^{79} -12.0000 q^{83} +(3.50000 - 6.06218i) q^{85} +(3.50000 + 6.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} +(0.500000 - 0.866025i) q^{95} +(5.50000 - 9.52628i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{5} - 3 q^{7}+O(q^{10}) $ 2 * q - 2 * q^5 - 3 * q^7	$ 2 q - 2 q^{5} - 3 q^{7} + 3 q^{11} + 2 q^{13} - 7 q^{17} - q^{19} - 7 q^{23} + 2 q^{25} - 5 q^{29} - 8 q^{31} + 3 q^{35} + 3 q^{37} + 7 q^{41} + 9 q^{43} - 16 q^{47} - 2 q^{49} + 12 q^{53} - 3 q^{55} + 5 q^{59} + 5 q^{61} - 2 q^{65} - 13 q^{67} - 3 q^{71} - 28 q^{73} - 18 q^{77} - 16 q^{79} - 24 q^{83} + 7 q^{85} + 7 q^{89} + 15 q^{91} + q^{95} + 11 q^{97}+O(q^{100}) $ 2 * q - 2 * q^5 - 3 * q^7 + 3 * q^11 + 2 * q^13 - 7 * q^17 - q^19 - 7 * q^23 + 2 * q^25 - 5 * q^29 - 8 * q^31 + 3 * q^35 + 3 * q^37 + 7 * q^41 + 9 * q^43 - 16 * q^47 - 2 * q^49 + 12 * q^53 - 3 * q^55 + 5 * q^59 + 5 * q^61 - 2 * q^65 - 13 * q^67 - 3 * q^71 - 28 * q^73 - 18 * q^77 - 16 * q^79 - 24 * q^83 + 7 * q^85 + 7 * q^89 + 15 * q^91 + q^95 + 11 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times$.

$n$	$937$	$1081$	$1171$	$2081$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	0.429919	+	0.902867i	$0.358542\pi$
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	−0.996866	+	0.0791130i	$0.974791\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	0.0333386	+	0.999444i	$0.489386\pi$
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	−0.882213	+	0.470850i	$0.843947\pi$
$18$		0			0
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.50000	−	6.06218i	−0.729800	−	1.26405i	−0.956967	−	0.290196i	$-0.906280\pi$
$23$	−3.50000	−	6.06218i	−0.729800	−	1.26405i	0.227167	−	0.973856i	$-0.427054\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.50000	−	4.33013i	−0.464238	−	0.804084i	0.534928	−	0.844897i	$-0.320339\pi$
$29$	−2.50000	−	4.33013i	−0.464238	−	0.804084i	−0.999167	+	0.0408130i	$0.987005\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.50000	−	2.59808i	0.253546	−	0.439155i
$36$		0			0
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	0.962580	−	0.270998i	$-0.0873538\pi$
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	−0.715981	+	0.698119i	$0.754020\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.50000	+	6.06218i	0.546608	+	0.946753i	0.998504	+	0.0546823i	$0.0174146\pi$
$41$	3.50000	+	6.06218i	0.546608	+	0.946753i	−0.451896	+	0.892071i	$0.649252\pi$
$42$		0			0
$43$	4.50000	−	7.79423i	0.686244	−	1.18861i	−0.286801	−	0.957990i	$-0.592592\pi$
$43$	4.50000	−	7.79423i	0.686244	−	1.18861i	0.973044	−	0.230618i	$-0.0740749\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$		0			0
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	−1.50000	−	2.59808i	−0.202260	−	0.350325i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.50000	−	4.33013i	0.325472	−	0.563735i	−0.656136	−	0.754643i	$-0.727810\pi$
$59$	2.50000	−	4.33013i	0.325472	−	0.563735i	0.981608	+	0.190909i	$0.0611434\pi$
$60$		0			0
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.00000	+	3.46410i	−0.124035	+	0.429669i
$66$		0			0
$67$	−6.50000	−	11.2583i	−0.794101	−	1.37542i	−0.923408	−	0.383819i	$-0.874609\pi$
$67$	−6.50000	−	11.2583i	−0.794101	−	1.37542i	0.129307	−	0.991605i	$-0.458725\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	−0.941201	−	0.337846i	$-0.890302\pi$
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	0.763184	+	0.646181i	$0.223635\pi$
$72$		0			0
$73$	−14.0000			−1.63858			−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000			−1.63858			−0.819288	+	0.573382i	$0.805631\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−9.00000			−1.02565
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	3.50000	−	6.06218i	0.379628	−	0.657536i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	0.989720	−	0.143022i	$-0.0456819\pi$
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	−0.618720	+	0.785611i	$0.712349\pi$
$90$		0			0
$91$	7.50000	+	7.79423i	0.786214	+	0.817057i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.500000	−	0.866025i	0.0512989	−	0.0888523i
$96$		0			0
$97$	5.50000	−	9.52628i	0.558440	−	0.967247i	−0.439187	−	0.898396i	$-0.644733\pi$
$97$	5.50000	−	9.52628i	0.558440	−	0.967247i	0.997627	−	0.0688512i	$-0.0219334\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$		0			0
$103$	−16.0000			−1.57653			−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000			−1.57653			−0.788263	+	0.615338i	$0.789020\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	0.784366	−	0.620298i	$-0.212988\pi$
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	−0.929377	+	0.369132i	$0.879655\pi$
$108$		0			0
$109$	−14.0000			−1.34096			−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000			−1.34096			−0.670478	+	0.741929i	$0.733911\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.50000	−	11.2583i	0.611469	−	1.05909i	−0.379525	−	0.925182i	$-0.623912\pi$
$113$	6.50000	−	11.2583i	0.611469	−	1.05909i	0.990993	−	0.133913i	$-0.0427543\pi$
$114$		0			0
$115$	3.50000	+	6.06218i	0.326377	+	0.565301i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−10.5000	−	18.1865i	−0.962533	−	1.66716i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−0.500000	−	0.866025i	−0.0443678	−	0.0768473i	0.842989	−	0.537931i	$-0.180794\pi$
$127$	−0.500000	−	0.866025i	−0.0443678	−	0.0768473i	−0.887357	+	0.461084i	$0.847461\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.00000			−0.349482			−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000			−0.349482			−0.174741	+	0.984614i	$0.555909\pi$
$132$		0			0
$133$	−1.50000	−	2.59808i	−0.130066	−	0.225282i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$		0			0
$139$	−6.50000	+	11.2583i	−0.551323	+	0.954919i	0.446857	+	0.894606i	$0.352543\pi$
$139$	−6.50000	+	11.2583i	−0.551323	+	0.954919i	−0.998179	+	0.0603135i	$0.980790\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	10.5000	−	2.59808i	0.878054	−	0.217262i
$144$		0			0
$145$	2.50000	+	4.33013i	0.207614	+	0.359597i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	6.00000			0.478852			0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000			0.478852			0.239426	+	0.970915i	$0.423041\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	21.0000			1.65503
$162$		0			0
$163$	−5.50000	+	9.52628i	−0.430793	+	0.746156i	−0.996942	−	0.0781474i	$-0.975100\pi$
$163$	−5.50000	+	9.52628i	−0.430793	+	0.746156i	0.566149	+	0.824303i	$0.308433\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.500000	+	0.866025i	0.0386912	+	0.0670151i	0.884723	−	0.466118i	$-0.154348\pi$
$167$	0.500000	+	0.866025i	0.0386912	+	0.0670151i	−0.846031	+	0.533133i	$0.821014\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	0.426329	+	0.904568i	$0.359807\pi$
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	−0.996544	+	0.0830722i	$0.973527\pi$
$174$		0			0
$175$	−1.50000	+	2.59808i	−0.113389	+	0.196396i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.50000	+	16.4545i	0.710063	+	1.22987i	0.964833	+	0.262864i	$0.0846670\pi$
$179$	9.50000	+	16.4545i	0.710063	+	1.22987i	−0.254770	+	0.967002i	$0.582000\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.50000	−	2.59808i	−0.110282	−	0.191014i
$186$		0			0
$187$	−21.0000			−1.53567
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	−0.915177	−	0.403051i	$-0.867950\pi$
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	0.806641	+	0.591041i	$0.201283\pi$
$192$		0			0
$193$	7.50000	+	12.9904i	0.539862	+	0.935068i	0.998911	+	0.0466572i	$0.0148568\pi$
$193$	7.50000	+	12.9904i	0.539862	+	0.935068i	−0.459049	+	0.888411i	$0.651810\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−11.5000	−	19.9186i	−0.819341	−	1.41914i	−0.906168	−	0.422917i	$-0.861006\pi$
$197$	−11.5000	−	19.9186i	−0.819341	−	1.41914i	0.0868274	−	0.996223i	$-0.472327\pi$
$198$		0			0
$199$	−4.50000	+	7.79423i	−0.318997	+	0.552518i	−0.980279	−	0.197619i	$-0.936679\pi$
$199$	−4.50000	+	7.79423i	−0.318997	+	0.552518i	0.661282	+	0.750137i	$0.270013\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	15.0000			1.05279
$204$		0			0
$205$	−3.50000	−	6.06218i	−0.244451	−	0.423401i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.00000			−0.207514
$210$		0			0
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.50000	+	7.79423i	−0.306897	+	0.531562i
$216$		0			0
$217$	6.00000	−	10.3923i	0.407307	−	0.705476i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	17.5000	+	18.1865i	1.17718	+	1.22336i
$222$		0			0
$223$	11.5000	+	19.9186i	0.770097	+	1.33385i	0.937509	+	0.347960i	$0.113126\pi$
$223$	11.5000	+	19.9186i	0.770097	+	1.33385i	−0.167412	+	0.985887i	$0.553541\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.500000	+	0.866025i	−0.0331862	+	0.0574801i	−0.882141	−	0.470985i	$-0.843899\pi$
$227$	−0.500000	+	0.866025i	−0.0331862	+	0.0574801i	0.848955	+	0.528465i	$0.177232\pi$
$228$		0			0
$229$	26.0000			1.71813			0.859064	−	0.511868i	$-0.171046\pi$
$229$	26.0000			1.71813			0.859064	+	0.511868i	$0.171046\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$		0			0
$235$	8.00000			0.521862
$236$		0			0
$237$		0			0
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.00000	+	1.73205i	0.0638877	+	0.110657i
$246$		0			0
$247$	2.50000	+	2.59808i	0.159071	+	0.165312i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	2.50000	−	4.33013i	0.157799	−	0.273315i	−0.776276	−	0.630393i	$-0.782894\pi$
$251$	2.50000	−	4.33013i	0.157799	−	0.273315i	0.934075	+	0.357078i	$0.116227\pi$
$252$		0			0
$253$	10.5000	−	18.1865i	0.660129	−	1.14338i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.50000	−	16.4545i	−0.592594	−	1.02640i	−0.993882	−	0.110450i	$-0.964771\pi$
$257$	−9.50000	−	16.4545i	−0.592594	−	1.02640i	0.401288	−	0.915952i	$-0.368563\pi$
$258$		0			0
$259$	−9.00000			−0.559233
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.50000	−	6.06218i	−0.215819	−	0.373810i	0.737706	−	0.675122i	$-0.235909\pi$
$263$	−3.50000	−	6.06218i	−0.215819	−	0.373810i	−0.953526	+	0.301312i	$0.902576\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	−0.816668	−	0.577108i	$-0.804181\pi$
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	0.908124	+	0.418701i	$0.137514\pi$
$270$		0			0
$271$	−11.5000	−	19.9186i	−0.698575	−	1.20997i	−0.968960	−	0.247216i	$-0.920484\pi$
$271$	−11.5000	−	19.9186i	−0.698575	−	1.20997i	0.270385	−	0.962752i	$-0.412849\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$		0			0
$277$	11.5000	−	19.9186i	0.690968	−	1.19679i	−0.280553	−	0.959839i	$-0.590518\pi$
$277$	11.5000	−	19.9186i	0.690968	−	1.19679i	0.971521	−	0.236953i	$-0.0761488\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.0000			0.596550			0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000			0.596550			0.298275	+	0.954480i	$0.403589\pi$
$282$		0			0
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	0.850782	−	0.525519i	$-0.176129\pi$
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	−0.880504	+	0.474039i	$0.842796\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−21.0000			−1.23959
$288$		0			0
$289$	−16.0000	−	27.7128i	−0.941176	−	1.63017i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	−0.704117	−	0.710084i	$-0.748657\pi$
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	0.967009	+	0.254741i	$0.0819901\pi$
$294$		0			0
$295$	−2.50000	+	4.33013i	−0.145556	+	0.252110i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−24.5000	+	6.06218i	−1.41687	+	0.350585i
$300$		0			0
$301$	13.5000	+	23.3827i	0.778127	+	1.34776i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.50000	+	4.33013i	−0.143150	+	0.247942i
$306$		0			0
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.00000			0.112331			0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000			0.112331			0.0561656	+	0.998421i	$0.482113\pi$
$318$		0			0
$319$	7.50000	−	12.9904i	0.419919	−	0.727322i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−3.50000	−	6.06218i	−0.194745	−	0.337309i
$324$		0			0
$325$	1.00000	−	3.46410i	0.0554700	−	0.192154i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	12.0000	−	20.7846i	0.661581	−	1.14589i
$330$		0			0
$331$	−6.50000	+	11.2583i	−0.357272	+	0.618814i	−0.987504	−	0.157593i	$-0.949627\pi$
$331$	−6.50000	+	11.2583i	−0.357272	+	0.618814i	0.630232	+	0.776407i	$0.282960\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	6.50000	+	11.2583i	0.355133	+	0.615108i
$336$		0			0
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$		0			0
$343$	−15.0000			−0.809924
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.50000	+	11.2583i	−0.348938	+	0.604379i	−0.986061	−	0.166383i	$-0.946791\pi$
$347$	−6.50000	+	11.2583i	−0.348938	+	0.604379i	0.637123	+	0.770762i	$0.280124\pi$
$348$		0			0
$349$	12.5000	+	21.6506i	0.669110	+	1.15893i	0.978153	+	0.207884i	$0.0666577\pi$
$349$	12.5000	+	21.6506i	0.669110	+	1.15893i	−0.309044	+	0.951048i	$0.600009\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	0.997592	+	0.0693543i	$0.0220939\pi$
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	−0.438733	+	0.898617i	$0.644573\pi$
$354$		0			0
$355$	1.50000	−	2.59808i	0.0796117	−	0.137892i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.00000			0.422224			0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000			0.422224			0.211112	+	0.977462i	$0.432292\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	14.0000			0.732793
$366$		0			0
$367$	−4.50000	−	7.79423i	−0.234898	−	0.406855i	0.724345	−	0.689438i	$-0.242142\pi$
$367$	−4.50000	−	7.79423i	−0.234898	−	0.406855i	−0.959243	+	0.282582i	$0.908809\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−9.00000	+	15.5885i	−0.467257	+	0.809312i
$372$		0			0
$373$	13.5000	−	23.3827i	0.699004	−	1.21071i	−0.269809	−	0.962914i	$-0.586961\pi$
$373$	13.5000	−	23.3827i	0.699004	−	1.21071i	0.968812	−	0.247796i	$-0.0797062\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−17.5000	+	4.33013i	−0.901296	+	0.223013i
$378$		0			0
$379$	4.50000	+	7.79423i	0.231149	+	0.400363i	0.958147	−	0.286278i	$-0.0924180\pi$
$379$	4.50000	+	7.79423i	0.231149	+	0.400363i	−0.726997	+	0.686640i	$0.759085\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−6.50000	+	11.2583i	−0.332134	+	0.575274i	−0.982930	−	0.183979i	$-0.941102\pi$
$383$	−6.50000	+	11.2583i	−0.332134	+	0.575274i	0.650796	+	0.759253i	$0.274435\pi$
$384$		0			0
$385$	9.00000			0.458682
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−18.0000			−0.912636			−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000			−0.912636			−0.456318	+	0.889817i	$0.650832\pi$
$390$		0			0
$391$	49.0000			2.47804
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.00000			0.402524
$396$		0			0
$397$	−16.5000	+	28.5788i	−0.828111	+	1.43433i	0.0714068	+	0.997447i	$0.477251\pi$
$397$	−16.5000	+	28.5788i	−0.828111	+	1.43433i	−0.899518	+	0.436884i	$0.856082\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$		0			0
$403$	−4.00000	+	13.8564i	−0.199254	+	0.690237i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.50000	+	7.79423i	−0.223057	+	0.386346i
$408$		0			0
$409$	0.500000	−	0.866025i	0.0247234	−	0.0428222i	−0.853399	−	0.521258i	$-0.825463\pi$
$409$	0.500000	−	0.866025i	0.0247234	−	0.0428222i	0.878122	+	0.478436i	$0.158796\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.50000	+	12.9904i	0.369051	+	0.639215i
$414$		0			0
$415$	12.0000			0.589057
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−16.5000	−	28.5788i	−0.806078	−	1.39617i	−0.915561	−	0.402179i	$-0.868253\pi$
$419$	−16.5000	−	28.5788i	−0.806078	−	1.39617i	0.109483	−	0.993989i	$-0.465080\pi$
$420$		0			0
$421$	34.0000			1.65706			0.828529	−	0.559946i	$-0.189178\pi$
$421$	34.0000			1.65706			0.828529	+	0.559946i	$0.189178\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.50000	+	6.06218i	−0.169775	+	0.294059i
$426$		0			0
$427$	7.50000	+	12.9904i	0.362950	+	0.628649i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−4.50000	−	7.79423i	−0.216757	−	0.375435i	0.737057	−	0.675830i	$-0.236215\pi$
$431$	−4.50000	−	7.79423i	−0.216757	−	0.375435i	−0.953815	+	0.300395i	$0.902881\pi$
$432$		0			0
$433$	−0.500000	+	0.866025i	−0.0240285	+	0.0416185i	−0.877790	−	0.479046i	$-0.840983\pi$
$433$	−0.500000	+	0.866025i	−0.0240285	+	0.0416185i	0.853761	+	0.520665i	$0.174316\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	7.00000			0.334855
$438$		0			0
$439$	−1.50000	−	2.59808i	−0.0715911	−	0.123999i	0.828008	−	0.560717i	$-0.189474\pi$
$439$	−1.50000	−	2.59808i	−0.0715911	−	0.123999i	−0.899599	+	0.436717i	$0.856141\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−24.0000			−1.14027			−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000			−1.14027			−0.570137	+	0.821549i	$0.693110\pi$
$444$		0			0
$445$	−3.50000	−	6.06218i	−0.165916	−	0.287375i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−10.5000	+	18.1865i	−0.495526	+	0.858276i	−0.999987	−	0.00515887i	$-0.998358\pi$
$449$	−10.5000	+	18.1865i	−0.495526	+	0.858276i	0.504461	+	0.863434i	$0.331691\pi$
$450$		0			0
$451$	−10.5000	+	18.1865i	−0.494426	+	0.856370i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−7.50000	−	7.79423i	−0.351605	−	0.365399i
$456$		0			0
$457$	11.5000	+	19.9186i	0.537947	+	0.931752i	0.999014	+	0.0443868i	$0.0141334\pi$
$457$	11.5000	+	19.9186i	0.537947	+	0.931752i	−0.461067	+	0.887365i	$0.652533\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5.50000	−	9.52628i	0.256161	−	0.443683i	−0.709050	−	0.705159i	$-0.750876\pi$
$461$	5.50000	−	9.52628i	0.256161	−	0.443683i	0.965210	+	0.261476i	$0.0842091\pi$
$462$		0			0
$463$	−28.0000			−1.30127			−0.650635	−	0.759390i	$-0.725497\pi$
$463$	−28.0000			−1.30127			−0.650635	+	0.759390i	$0.725497\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−20.0000			−0.925490			−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000			−0.925490			−0.462745	+	0.886492i	$0.653135\pi$
$468$		0			0
$469$	39.0000			1.80085
$470$		0			0
$471$		0			0
$472$		0			0
$473$	27.0000			1.24146
$474$		0			0
$475$	−0.500000	+	0.866025i	−0.0229416	+	0.0397360i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−0.500000	−	0.866025i	−0.0228456	−	0.0395697i	0.854377	−	0.519654i	$-0.173939\pi$
$479$	−0.500000	−	0.866025i	−0.0228456	−	0.0395697i	−0.877222	+	0.480085i	$0.840606\pi$
$480$		0			0
$481$	10.5000	−	2.59808i	0.478759	−	0.118462i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5.50000	+	9.52628i	−0.249742	+	0.432566i
$486$		0			0
$487$	8.50000	−	14.7224i	0.385172	−	0.667137i	−0.606621	−	0.794991i	$-0.707476\pi$
$487$	8.50000	−	14.7224i	0.385172	−	0.667137i	0.991793	+	0.127854i	$0.0408089\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	11.5000	+	19.9186i	0.518988	+	0.898913i	0.999757	+	0.0220657i	$0.00702431\pi$
$491$	11.5000	+	19.9186i	0.518988	+	0.898913i	−0.480769	+	0.876847i	$0.659642\pi$
$492$		0			0
$493$	35.0000			1.57632
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.50000	−	7.79423i	−0.201853	−	0.349619i
$498$		0			0
$499$	−16.0000			−0.716258			−0.358129	−	0.933672i	$-0.616585\pi$
$499$	−16.0000			−0.716258			−0.358129	+	0.933672i	$0.616585\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	5.50000	−	9.52628i	0.245233	−	0.424756i	−0.716964	−	0.697110i	$-0.754469\pi$
$503$	5.50000	−	9.52628i	0.245233	−	0.424756i	0.962197	+	0.272354i	$0.0878022\pi$
$504$		0			0
$505$	4.50000	+	7.79423i	0.200247	+	0.346839i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	0.982988	−	0.183669i	$-0.0587976\pi$
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	−0.650556	+	0.759458i	$0.725464\pi$
$510$		0			0
$511$	21.0000	−	36.3731i	0.928985	−	1.60905i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	16.0000			0.705044
$516$		0			0
$517$	−12.0000	−	20.7846i	−0.527759	−	0.914106i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	34.0000			1.48957			0.744784	−	0.667306i	$-0.232553\pi$
$521$	34.0000			1.48957			0.744784	+	0.667306i	$0.232553\pi$
$522$		0			0
$523$	11.5000	+	19.9186i	0.502860	+	0.870979i	0.999995	+	0.00330547i	$0.00105217\pi$
$523$	11.5000	+	19.9186i	0.502860	+	0.870979i	−0.497135	+	0.867673i	$0.665615\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	14.0000	−	24.2487i	0.609850	−	1.05629i
$528$		0			0
$529$	−13.0000	+	22.5167i	−0.565217	+	0.978985i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	24.5000	−	6.06218i	1.06121	−	0.262582i
$534$		0			0
$535$	1.50000	+	2.59808i	0.0648507	+	0.112325i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.00000	−	5.19615i	0.129219	−	0.223814i
$540$		0			0
$541$	10.0000			0.429934			0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000			0.429934			0.214967	+	0.976621i	$0.431036\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	14.0000			0.599694
$546$		0			0
$547$	−16.0000			−0.684111			−0.342055	−	0.939680i	$-0.611123\pi$
$547$	−16.0000			−0.684111			−0.342055	+	0.939680i	$0.611123\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	5.00000			0.213007
$552$		0			0
$553$	12.0000	−	20.7846i	0.510292	−	0.883852i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.50000	−	16.4545i	−0.402528	−	0.697199i	0.591502	−	0.806303i	$-0.298535\pi$
$557$	−9.50000	−	16.4545i	−0.402528	−	0.697199i	−0.994030	+	0.109104i	$0.965202\pi$
$558$		0			0
$559$	−22.5000	−	23.3827i	−0.951649	−	0.988982i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−22.5000	+	38.9711i	−0.948262	+	1.64244i	−0.199177	+	0.979963i	$0.563827\pi$
$563$	−22.5000	+	38.9711i	−0.948262	+	1.64244i	−0.749085	+	0.662474i	$0.769506\pi$
$564$		0			0
$565$	−6.50000	+	11.2583i	−0.273457	+	0.473642i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.50000	+	16.4545i	0.398261	+	0.689808i	0.993511	−	0.113732i	$-0.0362806\pi$
$569$	9.50000	+	16.4545i	0.398261	+	0.689808i	−0.595251	+	0.803540i	$0.702947\pi$
$570$		0			0
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.50000	−	6.06218i	−0.145960	−	0.252810i
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	18.0000	−	31.1769i	0.746766	−	1.29344i
$582$		0			0
$583$	9.00000	+	15.5885i	0.372742	+	0.645608i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.5000	+	32.0429i	0.763577	+	1.32255i	0.940996	+	0.338418i	$0.109892\pi$
$587$	18.5000	+	32.0429i	0.763577	+	1.32255i	−0.177419	+	0.984135i	$0.556775\pi$
$588$		0			0
$589$	2.00000	−	3.46410i	0.0824086	−	0.142736i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−26.0000			−1.06769			−0.533846	−	0.845582i	$-0.679254\pi$
$593$	−26.0000			−1.06769			−0.533846	+	0.845582i	$0.679254\pi$
$594$		0			0
$595$	10.5000	+	18.1865i	0.430458	+	0.745575i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−8.00000			−0.326871			−0.163436	−	0.986554i	$-0.552258\pi$
$599$	−8.00000			−0.326871			−0.163436	+	0.986554i	$0.552258\pi$
$600$		0			0
$601$	6.50000	+	11.2583i	0.265141	+	0.459237i	0.967600	−	0.252486i	$-0.0812483\pi$
$601$	6.50000	+	11.2583i	0.265141	+	0.459237i	−0.702460	+	0.711723i	$0.747915\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$		0			0
$607$	4.50000	−	7.79423i	0.182649	−	0.316358i	−0.760133	−	0.649768i	$-0.774866\pi$
$607$	4.50000	−	7.79423i	0.182649	−	0.316358i	0.942782	+	0.333410i	$0.108199\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8.00000	+	27.7128i	−0.323645	+	1.12114i
$612$		0			0
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	0.988339	+	0.152270i	$0.0486583\pi$
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	−0.362300	+	0.932062i	$0.618008\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	14.5000	−	25.1147i	0.583748	−	1.01108i	−0.411282	−	0.911508i	$-0.634919\pi$
$617$	14.5000	−	25.1147i	0.583748	−	1.01108i	0.995030	−	0.0995732i	$-0.0317477\pi$
$618$		0			0
$619$	12.0000			0.482321			0.241160	−	0.970485i	$-0.422472\pi$
$619$	12.0000			0.482321			0.241160	+	0.970485i	$0.422472\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−21.0000			−0.841347
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−21.0000			−0.837325
$630$		0			0
$631$	7.50000	−	12.9904i	0.298570	−	0.517139i	−0.677239	−	0.735763i	$-0.736824\pi$
$631$	7.50000	−	12.9904i	0.298570	−	0.517139i	0.975809	+	0.218624i	$0.0701569\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.500000	+	0.866025i	0.0198419	+	0.0343672i
$636$		0			0
$637$	−7.00000	+	1.73205i	−0.277350	+	0.0686264i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10.5000	+	18.1865i	−0.414725	+	0.718325i	−0.995400	−	0.0958109i	$-0.969456\pi$
$641$	−10.5000	+	18.1865i	−0.414725	+	0.718325i	0.580674	+	0.814136i	$0.302789\pi$
$642$		0			0
$643$	−3.50000	+	6.06218i	−0.138027	+	0.239069i	−0.926750	−	0.375680i	$-0.877409\pi$
$643$	−3.50000	+	6.06218i	−0.138027	+	0.239069i	0.788723	+	0.614749i	$0.210743\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.50000	+	14.7224i	0.334169	+	0.578799i	0.983325	−	0.181857i	$-0.0582109\pi$
$647$	8.50000	+	14.7224i	0.334169	+	0.578799i	−0.649155	+	0.760656i	$0.724878\pi$
$648$		0			0
$649$	15.0000			0.588802
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.50000	−	9.52628i	−0.215232	−	0.372792i	0.738113	−	0.674678i	$-0.235717\pi$
$653$	−5.50000	−	9.52628i	−0.215232	−	0.372792i	−0.953344	+	0.301885i	$0.902384\pi$
$654$		0			0
$655$	4.00000			0.156293
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	−0.974320	−	0.225168i	$-0.927707\pi$
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	0.682161	+	0.731202i	$0.261040\pi$
$660$		0			0
$661$	8.50000	+	14.7224i	0.330612	+	0.572636i	0.982632	−	0.185565i	$-0.0594116\pi$
$661$	8.50000	+	14.7224i	0.330612	+	0.572636i	−0.652020	+	0.758202i	$0.726078\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.50000	+	2.59808i	0.0581675	+	0.100749i
$666$		0			0
$667$	−17.5000	+	30.3109i	−0.677603	+	1.17364i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	15.0000			0.579069
$672$		0			0
$673$	−6.50000	−	11.2583i	−0.250557	−	0.433977i	0.713123	−	0.701039i	$-0.247280\pi$
$673$	−6.50000	−	11.2583i	−0.250557	−	0.433977i	−0.963679	+	0.267063i	$0.913947\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−22.0000			−0.845529			−0.422764	−	0.906240i	$-0.638940\pi$
$677$	−22.0000			−0.845529			−0.422764	+	0.906240i	$0.638940\pi$
$678$		0			0
$679$	16.5000	+	28.5788i	0.633212	+	1.09676i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	15.5000	−	26.8468i	0.593091	−	1.02726i	−0.400722	−	0.916200i	$-0.631241\pi$
$683$	15.5000	−	26.8468i	0.593091	−	1.02726i	0.993813	−	0.111064i	$-0.0354259\pi$
$684$		0			0
$685$	1.50000	−	2.59808i	0.0573121	−	0.0992674i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6.00000	−	20.7846i	0.228582	−	0.791831i
$690$		0			0
$691$	12.5000	+	21.6506i	0.475522	+	0.823629i	0.999607	−	0.0280373i	$-0.00892572\pi$
$691$	12.5000	+	21.6506i	0.475522	+	0.823629i	−0.524084	+	0.851666i	$0.675592\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.50000	−	11.2583i	0.246559	−	0.427053i
$696$		0			0
$697$	−49.0000			−1.85601
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$		0			0
$703$	−3.00000			−0.113147
$704$		0			0
$705$		0			0
$706$		0			0
$707$	27.0000			1.01544
$708$		0			0
$709$	−17.5000	+	30.3109i	−0.657226	+	1.13835i	0.324104	+	0.946021i	$0.394937\pi$
$709$	−17.5000	+	30.3109i	−0.657226	+	1.13835i	−0.981331	+	0.192328i	$0.938396\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	14.0000	+	24.2487i	0.524304	+	0.908121i
$714$		0			0
$715$	−10.5000	+	2.59808i	−0.392678	+	0.0971625i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.500000	−	0.866025i	0.0186469	−	0.0322973i	−0.856551	−	0.516062i	$-0.827398\pi$
$719$	0.500000	−	0.866025i	0.0186469	−	0.0322973i	0.875198	+	0.483764i	$0.160731\pi$
$720$		0			0
$721$	24.0000	−	41.5692i	0.893807	−	1.54812i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.50000	−	4.33013i	−0.0928477	−	0.160817i
$726$		0			0
$727$	−28.0000			−1.03846			−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	31.5000	+	54.5596i	1.16507	+	2.01796i
$732$		0			0
$733$	14.0000			0.517102			0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000			0.517102			0.258551	+	0.965998i	$0.416755\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	19.5000	−	33.7750i	0.718292	−	1.24412i
$738$		0			0
$739$	−19.5000	−	33.7750i	−0.717319	−	1.24243i	−0.962058	−	0.272844i	$-0.912036\pi$
$739$	−19.5000	−	33.7750i	−0.717319	−	1.24243i	0.244739	−	0.969589i	$-0.421298\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.500000	+	0.866025i	0.0183432	+	0.0317714i	0.875051	−	0.484030i	$-0.160828\pi$
$743$	0.500000	+	0.866025i	0.0183432	+	0.0317714i	−0.856708	+	0.515802i	$0.827494\pi$
$744$		0			0
$745$	−1.50000	+	2.59808i	−0.0549557	+	0.0951861i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	9.00000			0.328853
$750$		0			0
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	0.959906	−	0.280321i	$-0.0904408\pi$
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	−0.722718	+	0.691143i	$0.757107\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	8.00000			0.291150
$756$		0			0
$757$	−0.500000	−	0.866025i	−0.0181728	−	0.0314762i	0.856796	−	0.515656i	$-0.172452\pi$
$757$	−0.500000	−	0.866025i	−0.0181728	−	0.0314762i	−0.874969	+	0.484179i	$0.839118\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	25.5000	−	44.1673i	0.924374	−	1.60106i	0.131810	−	0.991275i	$-0.457921\pi$
$761$	25.5000	−	44.1673i	0.924374	−	1.60106i	0.792564	−	0.609788i	$-0.208745\pi$
$762$		0			0
$763$	21.0000	−	36.3731i	0.760251	−	1.31679i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−12.5000	−	12.9904i	−0.451349	−	0.469055i
$768$		0			0
$769$	2.50000	+	4.33013i	0.0901523	+	0.156148i	0.907575	−	0.419890i	$-0.137931\pi$
$769$	2.50000	+	4.33013i	0.0901523	+	0.156148i	−0.817423	+	0.576038i	$0.804598\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	12.5000	−	21.6506i	0.449594	−	0.778719i	−0.548766	−	0.835976i	$-0.684902\pi$
$773$	12.5000	−	21.6506i	0.449594	−	0.778719i	0.998359	+	0.0572570i	$0.0182354\pi$
$774$		0			0
$775$	−4.00000			−0.143684
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−7.00000			−0.250801
$780$		0			0
$781$	−9.00000			−0.322045
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−6.00000			−0.214149
$786$		0			0
$787$	0.500000	−	0.866025i	0.0178231	−	0.0308705i	−0.856976	−	0.515356i	$-0.827660\pi$
$787$	0.500000	−	0.866025i	0.0178231	−	0.0308705i	0.874799	+	0.484485i	$0.160993\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	19.5000	+	33.7750i	0.693340	+	1.20090i
$792$		0			0
$793$	−12.5000	−	12.9904i	−0.443888	−	0.461302i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.50000	+	6.06218i	−0.123976	+	0.214733i	−0.921332	−	0.388776i	$-0.872898\pi$
$797$	−3.50000	+	6.06218i	−0.123976	+	0.214733i	0.797356	+	0.603509i	$0.206231\pi$
$798$		0			0
$799$	28.0000	−	48.4974i	0.990569	−	1.71572i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−21.0000	−	36.3731i	−0.741074	−	1.28358i
$804$		0			0
$805$	−21.0000			−0.740153
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−12.5000	−	21.6506i	−0.439477	−	0.761196i	0.558173	−	0.829725i	$-0.311503\pi$
$809$	−12.5000	−	21.6506i	−0.439477	−	0.761196i	−0.997649	+	0.0685291i	$0.978169\pi$
$810$		0			0
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	5.50000	−	9.52628i	0.192657	−	0.333691i
$816$		0			0
$817$	4.50000	+	7.79423i	0.157435	+	0.272686i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	0.966708	−	0.255884i	$-0.0823665\pi$
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	−0.704956	+	0.709251i	$0.749033\pi$
$822$		0			0
$823$	−23.5000	+	40.7032i	−0.819159	+	1.41882i	0.0871445	+	0.996196i	$0.472226\pi$
$823$	−23.5000	+	40.7032i	−0.819159	+	1.41882i	−0.906303	+	0.422628i	$0.861108\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	6.50000	+	11.2583i	0.225754	+	0.391018i	0.956545	−	0.291583i	$-0.0941820\pi$
$829$	6.50000	+	11.2583i	0.225754	+	0.391018i	−0.730791	+	0.682601i	$0.760849\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	14.0000			0.485071
$834$		0			0
$835$	−0.500000	−	0.866025i	−0.0173032	−	0.0299700i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	6.50000	−	11.2583i	0.224405	−	0.388681i	−0.731736	−	0.681588i	$-0.761290\pi$
$839$	6.50000	−	11.2583i	0.224405	−	0.388681i	0.956141	+	0.292908i	$0.0946228\pi$
$840$		0			0
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	11.0000	+	6.92820i	0.378412	+	0.238337i
$846$		0			0
$847$	3.00000	+	5.19615i	0.103081	+	0.178542i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	10.5000	−	18.1865i	0.359935	−	0.623426i
$852$		0			0
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−18.0000			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$		0			0
$859$	44.0000			1.50126			0.750630	−	0.660722i	$-0.229750\pi$
$859$	44.0000			1.50126			0.750630	+	0.660722i	$0.229750\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−16.0000			−0.544646			−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000			−0.544646			−0.272323	+	0.962206i	$0.587792\pi$
$864$		0			0
$865$	7.50000	−	12.9904i	0.255008	−	0.441686i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$		0			0
$871$	−45.5000	+	11.2583i	−1.54171	+	0.381474i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.50000	−	2.59808i	0.0507093	−	0.0878310i
$876$		0			0
$877$	−2.50000	+	4.33013i	−0.0844190	+	0.146218i	−0.905143	−	0.425106i	$-0.860237\pi$
$877$	−2.50000	+	4.33013i	−0.0844190	+	0.146218i	0.820724	+	0.571324i	$0.193570\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	5.50000	+	9.52628i	0.185300	+	0.320949i	0.943677	−	0.330867i	$-0.107341\pi$
$881$	5.50000	+	9.52628i	0.185300	+	0.320949i	−0.758378	+	0.651815i	$0.774008\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.50000	−	16.4545i	−0.318979	−	0.552487i	0.661296	−	0.750125i	$-0.270007\pi$
$887$	−9.50000	−	16.4545i	−0.318979	−	0.552487i	−0.980275	+	0.197637i	$0.936673\pi$
$888$		0			0
$889$	3.00000			0.100617
$890$		0			0
$891$		0			0
$892$		0			0
$893$	4.00000	−	6.92820i	0.133855	−	0.231843i
$894$		0			0
$895$	−9.50000	−	16.4545i	−0.317550	−	0.550013i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	10.0000	+	17.3205i	0.333519	+	0.577671i
$900$		0			0
$901$	−21.0000	+	36.3731i	−0.699611	+	1.21176i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	14.0000			0.465376
$906$		0			0
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	0.689698	−	0.724097i	$-0.257743\pi$
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	−0.971936	+	0.235247i	$0.924410\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$	−18.0000	−	31.1769i	−0.595713	−	1.03181i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.00000	−	10.3923i	0.198137	−	0.343184i
$918$		0			0
$919$	21.5000	−	37.2391i	0.709220	−	1.22840i	−0.255927	−	0.966696i	$-0.582381\pi$
$919$	21.5000	−	37.2391i	0.709220	−	1.22840i	0.965147	−	0.261708i	$-0.0842858\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	7.50000	+	7.79423i	0.246866	+	0.256550i
$924$		0			0
$925$	1.50000	+	2.59808i	0.0493197	+	0.0854242i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−26.5000	+	45.8993i	−0.869437	+	1.50591i	−0.00686358	+	0.999976i	$0.502185\pi$
$929$	−26.5000	+	45.8993i	−0.869437	+	1.50591i	−0.862573	+	0.505932i	$0.831149\pi$
$930$		0			0
$931$	2.00000			0.0655474
$932$		0			0
$933$		0			0
$934$		0			0
$935$	21.0000			0.686773
$936$		0			0
$937$	50.0000			1.63343			0.816714	−	0.577042i	$-0.195793\pi$
$937$	50.0000			1.63343			0.816714	+	0.577042i	$0.195793\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−42.0000			−1.36916			−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−42.0000			−1.36916			−0.684580	+	0.728937i	$0.740015\pi$
$942$		0			0
$943$	24.5000	−	42.4352i	0.797830	−	1.38188i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−27.5000	−	47.6314i	−0.893630	−	1.54781i	−0.835491	−	0.549504i	$-0.814817\pi$
$947$	−27.5000	−	47.6314i	−0.893630	−	1.54781i	−0.0581388	−	0.998309i	$-0.518517\pi$
$948$		0			0
$949$	−14.0000	+	48.4974i	−0.454459	+	1.57429i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−15.5000	+	26.8468i	−0.502094	+	0.869653i	0.497903	+	0.867233i	$0.334104\pi$
$953$	−15.5000	+	26.8468i	−0.502094	+	0.869653i	−0.999997	+	0.00241992i	$0.999230\pi$
$954$		0			0
$955$	1.50000	−	2.59808i	0.0485389	−	0.0840718i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.50000	−	7.79423i	−0.145313	−	0.251689i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−7.50000	−	12.9904i	−0.241434	−	0.418175i
$966$		0			0
$967$	−48.0000			−1.54358			−0.771788	−	0.635880i	$-0.780637\pi$
$967$	−48.0000			−1.54358			−0.771788	+	0.635880i	$0.780637\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−21.5000	+	37.2391i	−0.689968	+	1.19506i	0.281880	+	0.959450i	$0.409042\pi$
$971$	−21.5000	+	37.2391i	−0.689968	+	1.19506i	−0.971848	+	0.235610i	$0.924291\pi$
$972$		0			0
$973$	−19.5000	−	33.7750i	−0.625141	−	1.08278i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.50000	−	2.59808i	−0.0479893	−	0.0831198i	0.841033	−	0.540984i	$-0.181948\pi$
$977$	−1.50000	−	2.59808i	−0.0479893	−	0.0831198i	−0.889022	+	0.457864i	$0.848615\pi$
$978$		0			0
$979$	−10.5000	+	18.1865i	−0.335581	+	0.581244i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−36.0000			−1.14822			−0.574111	−	0.818778i	$-0.694652\pi$
$983$	−36.0000			−1.14822			−0.574111	+	0.818778i	$0.694652\pi$
$984$		0			0
$985$	11.5000	+	19.9186i	0.366420	+	0.634659i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−63.0000			−2.00328
$990$		0			0
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	0.950603	−	0.310409i	$-0.100466\pi$
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	−0.744124	+	0.668042i	$0.767133\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	4.50000	−	7.79423i	0.142660	−	0.247094i
$996$		0			0
$997$	−6.50000	+	11.2583i	−0.205857	+	0.356555i	−0.950405	−	0.311014i	$-0.899332\pi$
$997$	−6.50000	+	11.2583i	−0.205857	+	0.356555i	0.744548	+	0.667568i	$0.232665\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2340.2.q.a.2161.1		2
3.2	odd	2		260.2.i.d.81.1	yes	2
12.11	even	2		1040.2.q.b.81.1		2
13.9	even	3	inner	2340.2.q.a.1621.1		2
15.2	even	4		1300.2.bb.e.549.2		4
15.8	even	4		1300.2.bb.e.549.1		4
15.14	odd	2		1300.2.i.a.601.1		2
39.2	even	12		3380.2.f.a.3041.1		2
39.11	even	12		3380.2.f.a.3041.2		2
39.23	odd	6		3380.2.a.a.1.1		1
39.29	odd	6		3380.2.a.b.1.1		1
39.35	odd	6		260.2.i.d.61.1	✓	2
156.35	even	6		1040.2.q.b.321.1		2
195.74	odd	6		1300.2.i.a.1101.1		2
195.113	even	12		1300.2.bb.e.1049.2		4
195.152	even	12		1300.2.bb.e.1049.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.i.d.61.1	✓	2	39.35	odd	6
260.2.i.d.81.1	yes	2	3.2	odd	2
1040.2.q.b.81.1		2	12.11	even	2
1040.2.q.b.321.1		2	156.35	even	6
1300.2.i.a.601.1		2	15.14	odd	2
1300.2.i.a.1101.1		2	195.74	odd	6
1300.2.bb.e.549.1		4	15.8	even	4
1300.2.bb.e.549.2		4	15.2	even	4
1300.2.bb.e.1049.1		4	195.152	even	12
1300.2.bb.e.1049.2		4	195.113	even	12
2340.2.q.a.1621.1		2	13.9	even	3	inner
2340.2.q.a.2161.1		2	1.1	even	1	trivial
3380.2.a.a.1.1		1	39.23	odd	6
3380.2.a.b.1.1		1	39.29	odd	6
3380.2.f.a.3041.1		2	39.2	even	12
3380.2.f.a.3041.2		2	39.11	even	12

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:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{5} +(-1.50000 + 2.59808i) q^{7} +O(q^{10})\)	\(q-1.00000 q^{5} +(-1.50000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{11} +(1.00000 - 3.46410i) q^{13} +(-3.50000 + 6.06218i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-3.50000 - 6.06218i) q^{23} +1.00000 q^{25} +(-2.50000 - 4.33013i) q^{29} -4.00000 q^{31} +(1.50000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{37} +(3.50000 + 6.06218i) q^{41} +(4.50000 - 7.79423i) q^{43} -8.00000 q^{47} +(-1.00000 - 1.73205i) q^{49} +6.00000 q^{53} +(-1.50000 - 2.59808i) q^{55} +(2.50000 - 4.33013i) q^{59} +(2.50000 - 4.33013i) q^{61} +(-1.00000 + 3.46410i) q^{65} +(-6.50000 - 11.2583i) q^{67} +(-1.50000 + 2.59808i) q^{71} -14.0000 q^{73} -9.00000 q^{77} -8.00000 q^{79} -12.0000 q^{83} +(3.50000 - 6.06218i) q^{85} +(3.50000 + 6.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} +(0.500000 - 0.866025i) q^{95} +(5.50000 - 9.52628i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{5} - 3 q^{7}+O(q^{10}) \) 2 * q - 2 * q^5 - 3 * q^7	\( 2 q - 2 q^{5} - 3 q^{7} + 3 q^{11} + 2 q^{13} - 7 q^{17} - q^{19} - 7 q^{23} + 2 q^{25} - 5 q^{29} - 8 q^{31} + 3 q^{35} + 3 q^{37} + 7 q^{41} + 9 q^{43} - 16 q^{47} - 2 q^{49} + 12 q^{53} - 3 q^{55} + 5 q^{59} + 5 q^{61} - 2 q^{65} - 13 q^{67} - 3 q^{71} - 28 q^{73} - 18 q^{77} - 16 q^{79} - 24 q^{83} + 7 q^{85} + 7 q^{89} + 15 q^{91} + q^{95} + 11 q^{97}+O(q^{100}) \) 2 * q - 2 * q^5 - 3 * q^7 + 3 * q^11 + 2 * q^13 - 7 * q^17 - q^19 - 7 * q^23 + 2 * q^25 - 5 * q^29 - 8 * q^31 + 3 * q^35 + 3 * q^37 + 7 * q^41 + 9 * q^43 - 16 * q^47 - 2 * q^49 + 12 * q^53 - 3 * q^55 + 5 * q^59 + 5 * q^61 - 2 * q^65 - 13 * q^67 - 3 * q^71 - 28 * q^73 - 18 * q^77 - 16 * q^79 - 24 * q^83 + 7 * q^85 + 7 * q^89 + 15 * q^91 + q^95 + 11 * q^97

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