LMFDB - Embedded newform 3024.2.bf.i.1711.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(1711,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 2, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.1711"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.bf (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 1008)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1711.5
Character	$\chi$	$=$	3024.1711
Dual form			3024.2.bf.i.2287.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-1.09736i q^{5} +(1.10288 + 2.40492i) q^{7} -0.100798i q^{11} +(4.27107 + 2.46590i) q^{13} +(-3.23648 - 1.86858i) q^{17} +(-2.54669 - 4.41100i) q^{19} -9.20757i q^{23} +3.79579 q^{25} +(3.96297 + 6.86407i) q^{29} +(2.41787 + 4.18787i) q^{31} +(2.63908 - 1.21026i) q^{35} +(-2.77437 - 4.80534i) q^{37} +(3.91138 + 2.25823i) q^{41} +(-1.73626 + 1.00243i) q^{43} +(3.17534 - 5.49984i) q^{47} +(-4.56733 + 5.30467i) q^{49} +(6.53502 - 11.3190i) q^{53} -0.110612 q^{55} +(1.44382 + 2.50077i) q^{59} +(8.21186 + 4.74112i) q^{61} +(2.70599 - 4.68692i) q^{65} +(-10.8779 + 6.28036i) q^{67} +14.5863i q^{71} +(5.92115 + 3.41858i) q^{73} +(0.242411 - 0.111167i) q^{77} +(2.31531 + 1.33675i) q^{79} +(0.112583 + 0.195000i) q^{83} +(-2.05051 + 3.55159i) q^{85} +(4.90756 - 2.83338i) q^{89} +(-1.21985 + 12.9912i) q^{91} +(-4.84048 + 2.79465i) q^{95} +(6.47632 - 3.73911i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 6 q^{13} + 18 q^{17} - 32 q^{25} + 12 q^{29} + 2 q^{37} - 36 q^{41} + 2 q^{49} + 12 q^{53} + 42 q^{61} - 18 q^{65} + 66 q^{77} - 12 q^{85} + 18 q^{89} - 6 q^{97}+O(q^{100}) $ 32 * q - 6 * q^13 + 18 * q^17 - 32 * q^25 + 12 * q^29 + 2 * q^37 - 36 * q^41 + 2 * q^49 + 12 * q^53 + 42 * q^61 - 18 * q^65 + 66 * q^77 - 12 * q^85 + 18 * q^89 - 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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
$5$		−	1.09736i		−	0.490756i	−0.969427	−	0.245378i	$-0.921088\pi$
$5$		−	1.09736i		−	0.490756i	0.969427	−	0.245378i	$-0.0789121\pi$
$6$		0			0
$7$	1.10288	+	2.40492i	0.416848	+	0.908976i
$7$	1.10288	+	2.40492i	0.416848	+	0.908976i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	0.100798i		−	0.0303917i	−0.999885	−	0.0151958i	$-0.995163\pi$
$11$		−	0.100798i		−	0.0303917i	0.999885	−	0.0151958i	$-0.00483717\pi$
$12$		0			0
$13$	4.27107	+	2.46590i	1.18458	+	0.683918i	0.957070	−	0.289857i	$-0.0936078\pi$
$13$	4.27107	+	2.46590i	1.18458	+	0.683918i	0.227511	+	0.973775i	$0.426941\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.23648	−	1.86858i	−0.784961	−	0.453197i	0.0532247	−	0.998583i	$-0.483050\pi$
$17$	−3.23648	−	1.86858i	−0.784961	−	0.453197i	−0.838185	+	0.545385i	$0.816383\pi$
$18$		0			0
$19$	−2.54669	−	4.41100i	−0.584252	−	1.01195i	−0.994968	−	0.100191i	$-0.968055\pi$
$19$	−2.54669	−	4.41100i	−0.584252	−	1.01195i	0.410716	−	0.911763i	$-0.365279\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	9.20757i		−	1.91991i	−0.280151	−	0.959956i	$-0.590385\pi$
$23$		−	9.20757i		−	1.91991i	0.280151	−	0.959956i	$-0.409615\pi$
$24$		0			0
$25$	3.79579			0.759158
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.96297	+	6.86407i	0.735905	+	1.27463i	0.954325	+	0.298770i	$0.0965764\pi$
$29$	3.96297	+	6.86407i	0.735905	+	1.27463i	−0.218420	+	0.975855i	$0.570090\pi$
$30$		0			0
$31$	2.41787	+	4.18787i	0.434262	+	0.752164i	0.997235	−	0.0743115i	$-0.0236759\pi$
$31$	2.41787	+	4.18787i	0.434262	+	0.752164i	−0.562973	+	0.826475i	$0.690343\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.63908	−	1.21026i	0.446086	−	0.204571i
$36$		0			0
$37$	−2.77437	−	4.80534i	−0.456103	−	0.789993i	0.542648	−	0.839960i	$-0.317422\pi$
$37$	−2.77437	−	4.80534i	−0.456103	−	0.789993i	−0.998751	+	0.0499669i	$0.984088\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.91138	+	2.25823i	0.610854	+	0.352677i	0.773300	−	0.634041i	$-0.218605\pi$
$41$	3.91138	+	2.25823i	0.610854	+	0.352677i	−0.162446	+	0.986718i	$0.551938\pi$
$42$		0			0
$43$	−1.73626	+	1.00243i	−0.264777	+	0.152869i	−0.626512	−	0.779412i	$-0.715518\pi$
$43$	−1.73626	+	1.00243i	−0.264777	+	0.152869i	0.361735	+	0.932281i	$0.382185\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.17534	−	5.49984i	0.463170	−	0.802235i	−0.535947	−	0.844252i	$-0.680045\pi$
$47$	3.17534	−	5.49984i	0.463170	−	0.802235i	0.999117	+	0.0420174i	$0.0133785\pi$
$48$		0			0
$49$	−4.56733	+	5.30467i	−0.652475	+	0.757810i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.53502	−	11.3190i	0.897655	−	1.55478i	0.0671703	−	0.997742i	$-0.478603\pi$
$53$	6.53502	−	11.3190i	0.897655	−	1.55478i	0.830484	−	0.557042i	$-0.188064\pi$
$54$		0			0
$55$	−0.110612			−0.0149149
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.44382	+	2.50077i	0.187969	+	0.325572i	0.944573	−	0.328301i	$-0.106476\pi$
$59$	1.44382	+	2.50077i	0.187969	+	0.325572i	−0.756604	+	0.653874i	$0.773143\pi$
$60$		0			0
$61$	8.21186	+	4.74112i	1.05142	+	0.607038i	0.923047	−	0.384687i	$-0.125691\pi$
$61$	8.21186	+	4.74112i	1.05142	+	0.607038i	0.128374	+	0.991726i	$0.459024\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.70599	−	4.68692i	0.335637	−	0.581341i
$66$		0			0
$67$	−10.8779	+	6.28036i	−1.32895	+	0.767268i	−0.985137	−	0.171771i	$-0.945051\pi$
$67$	−10.8779	+	6.28036i	−1.32895	+	0.767268i	−0.343810	+	0.939039i	$0.611718\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			14.5863i			1.73107i	0.500848	+	0.865535i	$0.333022\pi$
$71$			14.5863i			1.73107i	−0.500848	+	0.865535i	$0.666978\pi$
$72$		0			0
$73$	5.92115	+	3.41858i	0.693018	+	0.400114i	0.804742	−	0.593625i	$-0.202304\pi$
$73$	5.92115	+	3.41858i	0.693018	+	0.400114i	−0.111724	+	0.993739i	$0.535637\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.242411	−	0.111167i	0.0276253	−	0.0126687i
$78$		0			0
$79$	2.31531	+	1.33675i	0.260493	+	0.150396i	0.624559	−	0.780977i	$-0.285279\pi$
$79$	2.31531	+	1.33675i	0.260493	+	0.150396i	−0.364066	+	0.931373i	$0.618612\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.112583	+	0.195000i	0.0123576	+	0.0214040i	0.872138	−	0.489260i	$-0.162733\pi$
$83$	0.112583	+	0.195000i	0.0123576	+	0.0214040i	−0.859780	+	0.510664i	$0.829400\pi$
$84$		0			0
$85$	−2.05051	+	3.55159i	−0.222409	+	0.385224i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.90756	−	2.83338i	0.520200	−	0.300338i	−0.216817	−	0.976212i	$-0.569567\pi$
$89$	4.90756	−	2.83338i	0.520200	−	0.300338i	0.737016	+	0.675875i	$0.236234\pi$
$90$		0			0
$91$	−1.21985	+	12.9912i	−0.127875	+	1.36185i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.84048	+	2.79465i	−0.496623	+	0.286725i
$96$		0			0
$97$	6.47632	−	3.73911i	0.657571	−	0.379649i	−0.133780	−	0.991011i	$-0.542712\pi$
$97$	6.47632	−	3.73911i	0.657571	−	0.379649i	0.791351	+	0.611362i	$0.209378\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		−	1.69404i		−	0.168564i	−0.996442	−	0.0842818i	$-0.973140\pi$
$101$		−	1.69404i		−	0.168564i	0.996442	−	0.0842818i	$-0.0268596\pi$
$102$		0			0
$103$	5.92861			0.584164			0.292082	−	0.956393i	$-0.405652\pi$
$103$	5.92861			0.584164			0.292082	+	0.956393i	$0.405652\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.25250	−	2.45518i	0.411104	−	0.237351i	−0.280160	−	0.959953i	$-0.590387\pi$
$107$	4.25250	−	2.45518i	0.411104	−	0.237351i	0.691264	+	0.722602i	$0.257054\pi$
$108$		0			0
$109$	−5.22573	+	9.05124i	−0.500535	+	0.866951i	0.499465	+	0.866334i	$0.333530\pi$
$109$	−5.22573	+	9.05124i	−0.500535	+	0.866951i	−1.00000		0.000617375i	$0.999803\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.15634	−	8.93104i	0.485068	−	0.840162i	−0.514785	−	0.857319i	$-0.672128\pi$
$113$	5.15634	−	8.93104i	0.485068	−	0.840162i	0.999853	+	0.0171575i	$0.00546166\pi$
$114$		0			0
$115$	−10.1041			−0.942209
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.924363	−	9.84430i	0.0847362	−	0.902425i
$120$		0			0
$121$	10.9898			0.999076
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	9.65219i		−	0.863318i
$126$		0			0
$127$		−	8.87104i		−	0.787177i	−0.919287	−	0.393589i	$-0.871233\pi$
$127$		−	8.87104i		−	0.787177i	0.919287	−	0.393589i	$-0.128767\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.89886			−0.515386			−0.257693	−	0.966227i	$-0.582962\pi$
$131$	−5.89886			−0.515386			−0.257693	+	0.966227i	$0.582962\pi$
$132$		0			0
$133$	7.79945	−	10.9894i	0.676298	−	0.952902i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	17.4326			1.48937			0.744683	−	0.667418i	$-0.232600\pi$
$137$	17.4326			1.48937			0.744683	+	0.667418i	$0.232600\pi$
$138$		0			0
$139$	8.09773	−	14.0257i	0.686840	−	1.18964i	−0.286014	−	0.958225i	$-0.592331\pi$
$139$	8.09773	−	14.0257i	0.686840	−	1.18964i	0.972855	−	0.231417i	$-0.0743362\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.248558	−	0.430514i	0.0207854	−	0.0360014i
$144$		0			0
$145$	7.53238	−	4.34882i	0.625530	−	0.361150i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.4411			−0.855370			−0.427685	−	0.903928i	$-0.640671\pi$
$149$	−10.4411			−0.855370			−0.427685	+	0.903928i	$0.640671\pi$
$150$		0			0
$151$		−	8.91419i		−	0.725427i	−0.931901	−	0.362713i	$-0.881850\pi$
$151$		−	8.91419i		−	0.725427i	0.931901	−	0.362713i	$-0.118150\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.59562	−	2.65328i	0.369129	−	0.213117i
$156$		0			0
$157$	5.54621	−	3.20210i	0.442635	−	0.255556i	−0.262079	−	0.965046i	$-0.584408\pi$
$157$	5.54621	−	3.20210i	0.442635	−	0.255556i	0.704715	+	0.709491i	$0.251075\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	22.1435	−	10.1548i	1.74515	−	0.800311i
$162$		0			0
$163$	7.19404	−	4.15348i	0.563481	−	0.325326i	−0.191061	−	0.981578i	$-0.561193\pi$
$163$	7.19404	−	4.15348i	0.563481	−	0.325326i	0.754541	+	0.656253i	$0.227859\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.92799	+	13.7317i	−0.613487	+	1.06259i	0.377161	+	0.926148i	$0.376900\pi$
$167$	−7.92799	+	13.7317i	−0.613487	+	1.06259i	−0.990648	+	0.136442i	$0.956433\pi$
$168$		0			0
$169$	5.66135	+	9.80575i	0.435488	+	0.754288i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.20209	+	1.84873i	0.243450	+	0.140556i	0.616762	−	0.787150i	$-0.288444\pi$
$173$	3.20209	+	1.84873i	0.243450	+	0.140556i	−0.373311	+	0.927706i	$0.621778\pi$
$174$		0			0
$175$	4.18629	+	9.12859i	0.316454	+	0.690057i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.20657	+	4.16072i	0.538645	+	0.310987i	0.744529	−	0.667590i	$-0.232674\pi$
$179$	7.20657	+	4.16072i	0.538645	+	0.310987i	−0.205885	+	0.978576i	$0.566007\pi$
$180$		0			0
$181$		−	25.2442i		−	1.87638i	−0.346115	−	0.938192i	$-0.612499\pi$
$181$		−	25.2442i		−	1.87638i	0.346115	−	0.938192i	$-0.387501\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.27321	+	3.04449i	−0.387694	+	0.223835i
$186$		0			0
$187$	−0.188349	+	0.326230i	−0.0137734	+	0.0238563i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.65606	−	2.11082i	−0.264543	−	0.152734i	0.361862	−	0.932232i	$-0.382141\pi$
$191$	−3.65606	−	2.11082i	−0.264543	−	0.152734i	−0.626405	+	0.779498i	$0.715474\pi$
$192$		0			0
$193$	11.6625	+	20.2001i	0.839487	+	1.45403i	0.890324	+	0.455327i	$0.150478\pi$
$193$	11.6625	+	20.2001i	0.839487	+	1.45403i	−0.0508376	+	0.998707i	$0.516189\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.9348			−1.06406			−0.532030	−	0.846725i	$-0.678571\pi$
$197$	−14.9348			−1.06406			−0.532030	+	0.846725i	$0.678571\pi$
$198$		0			0
$199$	6.05559	−	10.4886i	0.429269	−	0.743516i	−0.567539	−	0.823346i	$-0.692105\pi$
$199$	6.05559	−	10.4886i	0.429269	−	0.743516i	0.996808	+	0.0798303i	$0.0254378\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−12.1369	+	17.1009i	−0.851843	+	1.20025i
$204$		0			0
$205$	2.47811	−	4.29220i	0.173078	−	0.299781i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.444619	+	0.256701i	−0.0307550	+	0.0177564i
$210$		0			0
$211$	0.912360	+	0.526751i	0.0628095	+	0.0362631i	0.531076	−	0.847324i	$-0.321788\pi$
$211$	0.912360	+	0.526751i	0.0628095	+	0.0362631i	−0.468266	+	0.883587i	$0.655121\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.10003	+	1.90531i	0.0750213	+	0.129941i
$216$		0			0
$217$	−7.40490	+	10.4335i	−0.502678	+	0.708272i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−9.21547	−	15.9617i	−0.619900	−	1.07370i
$222$		0			0
$223$	5.36823	+	9.29804i	0.359483	+	0.622643i	0.987875	−	0.155254i	$-0.0496197\pi$
$223$	5.36823	+	9.29804i	0.359483	+	0.622643i	−0.628392	+	0.777897i	$0.716286\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.51369			0.100467			0.0502334	−	0.998738i	$-0.484003\pi$
$227$	1.51369			0.100467			0.0502334	+	0.998738i	$0.484003\pi$
$228$		0			0
$229$			14.4501i			0.954893i	0.878661	+	0.477446i	$0.158438\pi$
$229$			14.4501i			0.954893i	−0.878661	+	0.477446i	$0.841562\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.37435	+	16.2368i	0.614134	+	1.06371i	0.990536	+	0.137254i	$0.0438278\pi$
$233$	9.37435	+	16.2368i	0.614134	+	1.06371i	−0.376402	+	0.926456i	$0.622839\pi$
$234$		0			0
$235$	−6.03533	−	3.48450i	−0.393702	−	0.227304i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−20.4105	−	11.7840i	−1.32025	−	0.762244i	−0.336478	−	0.941691i	$-0.609236\pi$
$239$	−20.4105	−	11.7840i	−1.32025	−	0.762244i	−0.983768	+	0.179447i	$0.942569\pi$
$240$		0			0
$241$			14.8848i			0.958815i	0.877592	+	0.479407i	$0.159148\pi$
$241$			14.8848i			0.958815i	−0.877592	+	0.479407i	$0.840852\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.82116	+	5.01202i	0.371900	+	0.320206i
$246$		0			0
$247$		−	25.1196i		−	1.59832i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.87937			0.434222			0.217111	−	0.976147i	$-0.430337\pi$
$251$	6.87937			0.434222			0.217111	+	0.976147i	$0.430337\pi$
$252$		0			0
$253$	−0.928103			−0.0583493
$254$		0			0
$255$		0			0
$256$		0			0
$257$			17.9963i			1.12258i	0.827619	+	0.561290i	$0.189695\pi$
$257$			17.9963i			1.12258i	−0.827619	+	0.561290i	$0.810305\pi$
$258$		0			0
$259$	8.49670	−	11.9718i	0.527960	−	0.743894i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			8.87717i			0.547390i	0.961817	+	0.273695i	$0.0882458\pi$
$263$			8.87717i			0.547390i	−0.961817	+	0.273695i	$0.911754\pi$
$264$		0			0
$265$	−12.4211	−	7.17130i	−0.763020	−	0.440530i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.95646	−	5.74836i	−0.607056	−	0.350484i	0.164756	−	0.986334i	$-0.447316\pi$
$269$	−9.95646	−	5.74836i	−0.607056	−	0.350484i	−0.771812	+	0.635850i	$0.780650\pi$
$270$		0			0
$271$	12.3583	+	21.4052i	0.750713	+	1.30027i	0.947478	+	0.319822i	$0.103623\pi$
$271$	12.3583	+	21.4052i	0.750713	+	1.30027i	−0.196765	+	0.980451i	$0.563044\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	0.382607i		−	0.0230721i
$276$		0			0
$277$	1.03433			0.0621466			0.0310733	−	0.999517i	$-0.490107\pi$
$277$	1.03433			0.0621466			0.0310733	+	0.999517i	$0.490107\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.51917	+	2.63128i	0.0906262	+	0.156969i	0.907775	−	0.419458i	$-0.137780\pi$
$281$	1.51917	+	2.63128i	0.0906262	+	0.156969i	−0.817149	+	0.576427i	$0.804446\pi$
$282$		0			0
$283$	−7.02389	−	12.1657i	−0.417527	−	0.723177i	0.578163	−	0.815921i	$-0.303770\pi$
$283$	−7.02389	−	12.1657i	−0.417527	−	0.723177i	−0.995690	+	0.0927436i	$0.970436\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.11712	+	11.8971i	−0.0659415	+	0.702265i
$288$		0			0
$289$	−1.51681	−	2.62720i	−0.0892244	−	0.154541i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.747160	+	0.431373i	0.0436496	+	0.0252011i	0.521666	−	0.853150i	$-0.325311\pi$
$293$	0.747160	+	0.431373i	0.0436496	+	0.0252011i	−0.478016	+	0.878351i	$0.658644\pi$
$294$		0			0
$295$	2.74425	−	1.58440i	0.159777	−	0.0922470i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	22.7050	−	39.3262i	1.31306	−	2.27429i
$300$		0			0
$301$	−4.32564	−	3.07001i	−0.249326	−	0.176953i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	5.20274	−	9.01141i	0.297908	−	0.515992i
$306$		0			0
$307$	0.799801			0.0456471			0.0228235	−	0.999740i	$-0.492734\pi$
$307$	0.799801			0.0456471			0.0228235	+	0.999740i	$0.492734\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−13.1501	−	22.7767i	−0.745674	−	1.29155i	−0.949879	−	0.312618i	$-0.898794\pi$
$311$	−13.1501	−	22.7767i	−0.745674	−	1.29155i	0.204205	−	0.978928i	$-0.434539\pi$
$312$		0			0
$313$	−6.76366	−	3.90500i	−0.382305	−	0.220724i	0.296516	−	0.955028i	$-0.404175\pi$
$313$	−6.76366	−	3.90500i	−0.382305	−	0.220724i	−0.678821	+	0.734304i	$0.737509\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.66835	−	11.5499i	0.374532	−	0.648708i	−0.615725	−	0.787961i	$-0.711137\pi$
$317$	6.66835	−	11.5499i	0.374532	−	0.648708i	0.990257	+	0.139253i	$0.0444701\pi$
$318$		0			0
$319$	0.691883	−	0.399459i	0.0387380	−	0.0223654i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			19.0348i			1.05913i
$324$		0			0
$325$	16.2121	+	9.36005i	0.899285	+	0.519202i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	16.7287	+	1.57080i	0.922284	+	0.0866009i
$330$		0			0
$331$	−12.6057	−	7.27788i	−0.692870	−	0.400029i	0.111816	−	0.993729i	$-0.464333\pi$
$331$	−12.6057	−	7.27788i	−0.692870	−	0.400029i	−0.804686	+	0.593700i	$0.797666\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	6.89184	+	11.9370i	0.376542	+	0.652189i
$336$		0			0
$337$	7.67592	−	13.2951i	0.418134	−	0.724229i	−0.577618	−	0.816307i	$-0.696018\pi$
$337$	7.67592	−	13.2951i	0.418134	−	0.724229i	0.995752	+	0.0920783i	$0.0293510\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.422128	−	0.243716i	0.0228595	−	0.0131979i
$342$		0			0
$343$	−17.7945	−	5.13369i	−0.960814	−	0.277193i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−20.1653	+	11.6424i	−1.08253	+	0.624999i	−0.931578	−	0.363542i	$-0.881567\pi$
$347$	−20.1653	+	11.6424i	−1.08253	+	0.624999i	−0.150952	+	0.988541i	$0.548234\pi$
$348$		0			0
$349$	12.0364	−	6.94922i	0.644294	−	0.371983i	−0.141973	−	0.989871i	$-0.545345\pi$
$349$	12.0364	−	6.94922i	0.644294	−	0.371983i	0.786267	+	0.617887i	$0.212011\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	26.6932i		−	1.42074i	−0.703830	−	0.710368i	$-0.748529\pi$
$353$		−	26.6932i		−	1.42074i	0.703830	−	0.710368i	$-0.251471\pi$
$354$		0			0
$355$	16.0064			0.849534
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−27.9838	+	16.1564i	−1.47693	+	0.852705i	−0.999661	−	0.0260534i	$-0.991706\pi$
$359$	−27.9838	+	16.1564i	−1.47693	+	0.852705i	−0.477267	+	0.878758i	$0.658373\pi$
$360$		0			0
$361$	−3.47131	+	6.01248i	−0.182700	+	0.316446i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.75143	−	6.49766i	0.196359	−	0.340103i
$366$		0			0
$367$	7.83398			0.408931			0.204465	−	0.978874i	$-0.434454\pi$
$367$	7.83398			0.408931			0.204465	+	0.978874i	$0.434454\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	34.4287	+	3.23279i	1.78745	+	0.167838i
$372$		0			0
$373$	−19.2030			−0.994293			−0.497146	−	0.867667i	$-0.665619\pi$
$373$	−19.2030			−0.994293			−0.497146	+	0.867667i	$0.665619\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			39.0892i			2.01320i
$378$		0			0
$379$			17.4093i			0.894254i	0.894470	+	0.447127i	$0.147553\pi$
$379$			17.4093i			0.894254i	−0.894470	+	0.447127i	$0.852447\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	18.3013			0.935151			0.467575	−	0.883953i	$-0.345128\pi$
$383$	18.3013			0.935151			0.467575	+	0.883953i	$0.345128\pi$
$384$		0			0
$385$	−0.121991	−	0.266013i	−0.00621725	−	0.0135573i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.17302			0.110176			0.0550882	−	0.998481i	$-0.482456\pi$
$389$	2.17302			0.110176			0.0550882	+	0.998481i	$0.482456\pi$
$390$		0			0
$391$	−17.2051	+	29.8001i	−0.870099	+	1.50706i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.46690	−	2.54074i	0.0738076	−	0.127839i
$396$		0			0
$397$	5.63167	−	3.25144i	0.282645	−	0.163185i	−0.351975	−	0.936009i	$-0.614490\pi$
$397$	5.63167	−	3.25144i	0.282645	−	0.163185i	0.634620	+	0.772824i	$0.281156\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.97927			0.248653			0.124326	−	0.992241i	$-0.460323\pi$
$401$	4.97927			0.248653			0.124326	+	0.992241i	$0.460323\pi$
$402$		0			0
$403$			23.8489i			1.18800i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.484368	+	0.279650i	−0.0240092	+	0.0138617i
$408$		0			0
$409$	−0.175666	+	0.101421i	−0.00868614	+	0.00501494i	−0.504337	−	0.863507i	$-0.668263\pi$
$409$	−0.175666	+	0.101421i	−0.00868614	+	0.00501494i	0.495651	+	0.868522i	$0.334930\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4.42180	+	6.23031i	−0.217583	+	0.306574i
$414$		0			0
$415$	0.213986	−	0.123545i	0.0105042	−	0.00606458i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.38038	−	9.31910i	0.262849	−	0.455268i	−0.704149	−	0.710052i	$-0.748671\pi$
$419$	5.38038	−	9.31910i	0.262849	−	0.455268i	0.966998	+	0.254785i	$0.0820046\pi$
$420$		0			0
$421$	0.428103	+	0.741496i	0.0208645	+	0.0361383i	0.876269	−	0.481822i	$-0.160025\pi$
$421$	0.428103	+	0.741496i	0.0208645	+	0.0361383i	−0.855405	+	0.517960i	$0.826691\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−12.2850	−	7.09274i	−0.595909	−	0.344048i
$426$		0			0
$427$	−2.34537	+	24.9778i	−0.113501	+	1.20876i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	9.19956	+	5.31137i	0.443127	+	0.255840i	0.704923	−	0.709284i	$-0.250981\pi$
$431$	9.19956	+	5.31137i	0.443127	+	0.255840i	−0.261796	+	0.965123i	$0.584315\pi$
$432$		0			0
$433$			27.8825i			1.33995i	0.742384	+	0.669974i	$0.233695\pi$
$433$			27.8825i			1.33995i	−0.742384	+	0.669974i	$0.766305\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−40.6146	+	23.4489i	−1.94286	+	1.12171i
$438$		0			0
$439$	1.71469	−	2.96993i	0.0818377	−	0.141747i	−0.822202	−	0.569196i	$-0.807254\pi$
$439$	1.71469	−	2.96993i	0.0818377	−	0.141747i	0.904039	+	0.427449i	$0.140588\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−35.8001	−	20.6692i	−1.70092	−	0.982025i	−0.944835	−	0.327547i	$-0.893778\pi$
$443$	−35.8001	−	20.6692i	−1.70092	−	0.982025i	−0.756082	−	0.654477i	$-0.772889\pi$
$444$		0			0
$445$	−3.10925	−	5.38538i	−0.147393	−	0.255291i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−7.99114			−0.377125			−0.188563	−	0.982061i	$-0.560383\pi$
$449$	−7.99114			−0.377125			−0.188563	+	0.982061i	$0.560383\pi$
$450$		0			0
$451$	0.227625	−	0.394258i	0.0107184	−	0.0185649i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	14.2561	+	1.33862i	0.668335	+	0.0627555i
$456$		0			0
$457$	−9.99811	+	17.3172i	−0.467692	+	0.810066i	−0.999318	−	0.0369130i	$-0.988248\pi$
$457$	−9.99811	+	17.3172i	−0.467692	+	0.810066i	0.531627	+	0.846979i	$0.321581\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−21.1665	+	12.2205i	−0.985824	+	0.569166i	−0.904023	−	0.427483i	$-0.859400\pi$
$461$	−21.1665	+	12.2205i	−0.985824	+	0.569166i	−0.0818005	+	0.996649i	$0.526067\pi$
$462$		0			0
$463$	−19.5574	−	11.2915i	−0.908909	−	0.524759i	−0.0288289	−	0.999584i	$-0.509178\pi$
$463$	−19.5574	−	11.2915i	−0.908909	−	0.524759i	−0.880080	+	0.474826i	$0.842511\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.8560	+	34.3915i	0.918824	+	1.59145i	0.801204	+	0.598391i	$0.204193\pi$
$467$	19.8560	+	34.3915i	0.918824	+	1.59145i	0.117620	+	0.993059i	$0.462474\pi$
$468$		0			0
$469$	−27.1008	−	19.2341i	−1.25140	−	0.888147i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.101043	+	0.175011i	0.00464594	+	0.00804700i
$474$		0			0
$475$	−9.66672	−	16.7433i	−0.443540	−	0.768233i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.44014			0.111493			0.0557465	−	0.998445i	$-0.482246\pi$
$479$	2.44014			0.111493			0.0557465	+	0.998445i	$0.482246\pi$
$480$		0			0
$481$		−	27.3653i		−	1.24775i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.10316	−	7.10689i	−0.186315	−	0.322707i
$486$		0			0
$487$	−19.1445	−	11.0531i	−0.867519	−	0.500862i	−0.000996023	−	1.00000i	$-0.500317\pi$
$487$	−19.1445	−	11.0531i	−0.867519	−	0.500862i	−0.866523	+	0.499137i	$0.833650\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−24.5750	−	14.1884i	−1.10906	−	0.640314i	−0.170472	−	0.985363i	$-0.554529\pi$
$491$	−24.5750	−	14.1884i	−1.10906	−	0.640314i	−0.938585	+	0.345049i	$0.887862\pi$
$492$		0			0
$493$		−	29.6205i		−	1.33404i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−35.0789	+	16.0868i	−1.57350	+	0.721593i
$498$		0			0
$499$		−	9.08596i		−	0.406743i	−0.979102	−	0.203372i	$-0.934810\pi$
$499$		−	9.08596i		−	0.406743i	0.979102	−	0.203372i	$-0.0651900\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	35.9302			1.60205			0.801025	−	0.598631i	$-0.204288\pi$
$503$	35.9302			1.60205			0.801025	+	0.598631i	$0.204288\pi$
$504$		0			0
$505$	−1.85898			−0.0827236
$506$		0			0
$507$		0			0
$508$		0			0
$509$		−	15.0086i		−	0.665243i	−0.943060	−	0.332621i	$-0.892067\pi$
$509$		−	15.0086i		−	0.665243i	0.943060	−	0.332621i	$-0.107933\pi$
$510$		0			0
$511$	−1.69113	+	18.0102i	−0.0748111	+	0.796724i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	6.50585i		−	0.286682i
$516$		0			0
$517$	−0.554372	−	0.320067i	−0.0243813	−	0.0140765i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9.05431	+	5.22751i	0.396677	+	0.229021i	0.685049	−	0.728497i	$-0.259781\pi$
$521$	9.05431	+	5.22751i	0.396677	+	0.229021i	−0.288372	+	0.957518i	$0.593114\pi$
$522$		0			0
$523$	13.6688	+	23.6751i	0.597697	+	1.03524i	0.993160	+	0.116759i	$0.0372507\pi$
$523$	13.6688	+	23.6751i	0.597697	+	1.03524i	−0.395463	+	0.918482i	$0.629416\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	18.0719i		−	0.787225i
$528$		0			0
$529$	−61.7794			−2.68606
$530$		0			0
$531$		0			0
$532$		0			0
$533$	11.1372	+	19.2901i	0.482404	+	0.835549i
$534$		0			0
$535$	−2.69423	−	4.66654i	−0.116482	−	0.201752i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.534699	+	0.460377i	0.0230311	+	0.0198298i
$540$		0			0
$541$	−11.1507	−	19.3135i	−0.479405	−	0.830354i	0.520316	−	0.853974i	$-0.325814\pi$
$541$	−11.1507	−	19.3135i	−0.479405	−	0.830354i	−0.999721	+	0.0236197i	$0.992481\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	9.93251	+	5.73454i	0.425462	+	0.245640i
$546$		0			0
$547$	5.02929	−	2.90366i	0.215037	−	0.124152i	−0.388613	−	0.921401i	$-0.627046\pi$
$547$	5.02929	−	2.90366i	0.215037	−	0.124152i	0.603650	+	0.797249i	$0.293712\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	20.1849	−	34.9614i	0.859908	−	1.48940i
$552$		0			0
$553$	−0.661272	+	7.04242i	−0.0281201	+	0.299474i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.23031	−	2.13096i	0.0521300	−	0.0902919i	−0.838783	−	0.544466i	$-0.816732\pi$
$557$	1.23031	−	2.13096i	0.0521300	−	0.0902919i	0.890913	+	0.454174i	$0.150066\pi$
$558$		0			0
$559$	−9.88756			−0.418199
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.01921	+	3.49737i	0.0850995	+	0.147397i	0.905434	−	0.424488i	$-0.139546\pi$
$563$	2.01921	+	3.49737i	0.0850995	+	0.147397i	−0.820334	+	0.571885i	$0.806213\pi$
$564$		0			0
$565$	−9.80061	−	5.65838i	−0.412315	−	0.238050i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−12.6809	+	21.9640i	−0.531612	+	0.920780i	0.467707	+	0.883884i	$0.345080\pi$
$569$	−12.6809	+	21.9640i	−0.531612	+	0.920780i	−0.999319	+	0.0368960i	$0.988253\pi$
$570$		0			0
$571$	−26.2507	+	15.1558i	−1.09856	+	0.634252i	−0.935842	−	0.352421i	$-0.885359\pi$
$571$	−26.2507	+	15.1558i	−1.09856	+	0.634252i	−0.162716	+	0.986673i	$0.552025\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	34.9500i		−	1.45752i
$576$		0			0
$577$	25.7567	+	14.8707i	1.07227	+	0.619073i	0.928800	−	0.370582i	$-0.120842\pi$
$577$	25.7567	+	14.8707i	1.07227	+	0.619073i	0.143467	+	0.989655i	$0.454175\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.344795	+	0.485815i	−0.0143045	+	0.0201550i
$582$		0			0
$583$	−1.14093	−	0.658716i	−0.0472525	−	0.0272812i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−18.1453	−	31.4286i	−0.748938	−	1.29720i	−0.948332	−	0.317280i	$-0.897231\pi$
$587$	−18.1453	−	31.4286i	−0.748938	−	1.29720i	0.199394	−	0.979919i	$-0.436103\pi$
$588$		0			0
$589$	12.3151	−	21.3304i	0.507437	−	0.878906i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−28.4608	+	16.4319i	−1.16875	+	0.674776i	−0.953384	−	0.301758i	$-0.902426\pi$
$593$	−28.4608	+	16.4319i	−1.16875	+	0.674776i	−0.215362	+	0.976534i	$0.569093\pi$
$594$		0			0
$595$	−10.8028	−	1.01436i	−0.442871	−	0.0415848i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−29.9350	+	17.2830i	−1.22311	+	0.706164i	−0.965580	−	0.260105i	$-0.916243\pi$
$599$	−29.9350	+	17.2830i	−1.22311	+	0.706164i	−0.257532	+	0.966270i	$0.582909\pi$
$600$		0			0
$601$	−18.6933	+	10.7926i	−0.762514	+	0.440238i	−0.830198	−	0.557469i	$-0.811772\pi$
$601$	−18.6933	+	10.7926i	−0.762514	+	0.440238i	0.0676837	+	0.997707i	$0.478439\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		−	12.0599i		−	0.490303i
$606$		0			0
$607$	26.7002			1.08373			0.541864	−	0.840466i	$-0.317719\pi$
$607$	26.7002			1.08373			0.541864	+	0.840466i	$0.317719\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	27.1242	−	15.6601i	1.09733	−	0.633541i
$612$		0			0
$613$	1.36963	−	2.37228i	0.0553190	−	0.0958153i	−0.837040	−	0.547142i	$-0.815716\pi$
$613$	1.36963	−	2.37228i	0.0553190	−	0.0958153i	0.892359	+	0.451327i	$0.149049\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.00455	−	5.20403i	0.120959	−	0.209506i	−0.799187	−	0.601082i	$-0.794737\pi$
$617$	3.00455	−	5.20403i	0.120959	−	0.209506i	0.920146	+	0.391576i	$0.128070\pi$
$618$		0			0
$619$	45.7252			1.83785			0.918925	−	0.394432i	$-0.129059\pi$
$619$	45.7252			1.83785			0.918925	+	0.394432i	$0.129059\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	12.2265	+	8.67744i	0.489844	+	0.347654i
$624$		0			0
$625$	8.38699			0.335479
$626$		0			0
$627$		0			0
$628$		0			0
$629$			20.7365i			0.826818i
$630$		0			0
$631$		−	16.5841i		−	0.660204i	−0.943945	−	0.330102i	$-0.892917\pi$
$631$		−	16.5841i		−	0.660204i	0.943945	−	0.330102i	$-0.107083\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−9.73476			−0.386312
$636$		0			0
$637$	−32.5882	+	11.3940i	−1.29119	+	0.451447i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−33.5325			−1.32446			−0.662228	−	0.749303i	$-0.730389\pi$
$641$	−33.5325			−1.32446			−0.662228	+	0.749303i	$0.730389\pi$
$642$		0			0
$643$	−15.7710	+	27.3162i	−0.621949	+	1.07725i	0.367174	+	0.930152i	$0.380325\pi$
$643$	−15.7710	+	27.3162i	−0.621949	+	1.07725i	−0.989122	+	0.147094i	$0.953008\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.1055	+	33.0917i	−0.751114	+	1.30097i	0.196169	+	0.980570i	$0.437150\pi$
$647$	−19.1055	+	33.0917i	−0.751114	+	1.30097i	−0.947283	+	0.320398i	$0.896183\pi$
$648$		0			0
$649$	0.252072	−	0.145534i	0.00989468	−	0.00571270i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	23.6928			0.927171			0.463586	−	0.886052i	$-0.346563\pi$
$653$	23.6928			0.927171			0.463586	+	0.886052i	$0.346563\pi$
$654$		0			0
$655$			6.47320i			0.252929i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−17.6819	+	10.2086i	−0.688788	+	0.397672i	−0.803158	−	0.595766i	$-0.796849\pi$
$659$	−17.6819	+	10.2086i	−0.688788	+	0.397672i	0.114370	+	0.993438i	$0.463515\pi$
$660$		0			0
$661$	−17.3778	+	10.0331i	−0.675919	+	0.390242i	−0.798315	−	0.602239i	$-0.794275\pi$
$661$	−17.3778	+	10.0331i	−0.675919	+	0.390242i	0.122397	+	0.992481i	$0.460942\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−12.0594	−	8.55883i	−0.467643	−	0.331897i
$666$		0			0
$667$	63.2014	−	36.4893i	2.44717	−	1.41287i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.477895	−	0.827738i	0.0184489	−	0.0319545i
$672$		0			0
$673$	−0.955003	−	1.65411i	−0.0368127	−	0.0637614i	0.847032	−	0.531542i	$-0.178387\pi$
$673$	−0.955003	−	1.65411i	−0.0368127	−	0.0637614i	−0.883845	+	0.467780i	$0.845054\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−37.3961	−	21.5907i	−1.43725	−	0.829796i	−0.439592	−	0.898198i	$-0.644877\pi$
$677$	−37.3961	−	21.5907i	−1.43725	−	0.829796i	−0.997658	+	0.0684014i	$0.978210\pi$
$678$		0			0
$679$	16.1349	+	11.4513i	0.619199	+	0.439460i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	21.2100	+	12.2456i	0.811579	+	0.468565i	0.847504	−	0.530789i	$-0.178104\pi$
$683$	21.2100	+	12.2456i	0.811579	+	0.468565i	−0.0359249	+	0.999354i	$0.511438\pi$
$684$		0			0
$685$		−	19.1299i		−	0.730916i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	55.8231	−	32.2295i	2.12669	−	1.22784i
$690$		0			0
$691$	5.83616	−	10.1085i	0.222018	−	0.384547i	−0.733403	−	0.679795i	$-0.762069\pi$
$691$	5.83616	−	10.1085i	0.222018	−	0.384547i	0.955421	+	0.295248i	$0.0954022\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−15.3913	−	8.88616i	−0.583824	−	0.337071i
$696$		0			0
$697$	−8.43938	−	14.6174i	−0.319664	−	0.553675i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−32.0967			−1.21227			−0.606137	−	0.795360i	$-0.707282\pi$
$701$	−32.0967			−1.21227			−0.606137	+	0.795360i	$0.707282\pi$
$702$		0			0
$703$	−14.1309	+	24.4755i	−0.532958	+	0.923110i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.07405	−	1.86832i	0.153220	−	0.0702654i
$708$		0			0
$709$	6.81367	−	11.8016i	0.255893	−	0.443220i	−0.709245	−	0.704962i	$-0.750964\pi$
$709$	6.81367	−	11.8016i	0.255893	−	0.443220i	0.965138	+	0.261743i	$0.0842972\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	38.5601	−	22.2627i	1.44409	−	0.833744i
$714$		0			0
$715$	−0.472431	−	0.272758i	−0.0176679	−	0.0102006i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−17.9410	−	31.0748i	−0.669088	−	1.15889i	−0.978160	−	0.207855i	$-0.933352\pi$
$719$	−17.9410	−	31.0748i	−0.669088	−	1.15889i	0.309072	−	0.951039i	$-0.399982\pi$
$720$		0			0
$721$	6.53853	+	14.2579i	0.243507	+	0.530991i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	15.0426	+	26.0546i	0.558668	+	0.967642i
$726$		0			0
$727$	−1.54920	−	2.68329i	−0.0574565	−	0.0995176i	0.835866	−	0.548933i	$-0.184966\pi$
$727$	−1.54920	−	2.68329i	−0.0574565	−	0.0995176i	−0.893323	+	0.449415i	$0.851632\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	7.49247			0.277119
$732$		0			0
$733$		−	38.4588i		−	1.42051i	−0.703946	−	0.710254i	$-0.748580\pi$
$733$		−	38.4588i		−	1.42051i	0.703946	−	0.710254i	$-0.251420\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.633046	+	1.09647i	0.0233186	+	0.0403889i
$738$		0			0
$739$	−28.0000	−	16.1658i	−1.03000	−	0.594668i	−0.113012	−	0.993594i	$-0.536050\pi$
$739$	−28.0000	−	16.1658i	−1.03000	−	0.594668i	−0.916983	+	0.398926i	$0.869383\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	14.1763	+	8.18468i	0.520077	+	0.300267i	0.736966	−	0.675930i	$-0.236258\pi$
$743$	14.1763	+	8.18468i	0.520077	+	0.300267i	−0.216889	+	0.976196i	$0.569591\pi$
$744$		0			0
$745$			11.4577i			0.419778i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	10.5945	+	7.51917i	0.387115	+	0.274745i
$750$		0			0
$751$		−	47.7607i		−	1.74281i	−0.490562	−	0.871406i	$-0.663209\pi$
$751$		−	47.7607i		−	1.74281i	0.490562	−	0.871406i	$-0.336791\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−9.78212			−0.356008
$756$		0			0
$757$	−32.5248			−1.18213			−0.591066	−	0.806623i	$-0.701293\pi$
$757$	−32.5248			−1.18213			−0.591066	+	0.806623i	$0.701293\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			31.1794i			1.13025i	0.825004	+	0.565127i	$0.191173\pi$
$761$			31.1794i			1.13025i	−0.825004	+	0.565127i	$0.808827\pi$
$762$		0			0
$763$	−27.5309	−	2.58511i	−0.996685	−	0.0935871i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			14.2413i			0.514222i
$768$		0			0
$769$	−24.4724	−	14.1292i	−0.882498	−	0.509510i	−0.0110165	−	0.999939i	$-0.503507\pi$
$769$	−24.4724	−	14.1292i	−0.882498	−	0.509510i	−0.871481	+	0.490429i	$0.836840\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−11.2626	−	6.50244i	−0.405086	−	0.233876i	0.283590	−	0.958946i	$-0.408474\pi$
$773$	−11.2626	−	6.50244i	−0.405086	−	0.233876i	−0.688676	+	0.725069i	$0.741808\pi$
$774$		0			0
$775$	9.17772	+	15.8963i	0.329673	+	0.571011i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	23.0041i		−	0.824208i
$780$		0			0
$781$	1.47026			0.0526101
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.51387	−	6.08621i	−0.125416	−	0.217226i
$786$		0			0
$787$	−12.1694	−	21.0780i	−0.433791	−	0.751348i	0.563405	−	0.826181i	$-0.309491\pi$
$787$	−12.1694	−	21.0780i	−0.433791	−	0.751348i	−0.997196	+	0.0748328i	$0.976158\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	27.1653	+	2.55078i	0.965886	+	0.0906952i
$792$		0			0
$793$	23.3823	+	40.4993i	0.830329	+	1.43817i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−38.8453	−	22.4273i	−1.37597	−	0.794416i	−0.384298	−	0.923209i	$-0.625556\pi$
$797$	−38.8453	−	22.4273i	−1.37597	−	0.794416i	−0.991672	+	0.128793i	$0.958890\pi$
$798$		0			0
$799$	−20.5538	+	11.8667i	−0.727141	+	0.419815i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.344585	−	0.596839i	0.0121601	−	0.0210620i
$804$		0			0
$805$	−11.1435	−	24.2995i	−0.392758	−	0.856445i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−16.1308	+	27.9394i	−0.567130	+	0.982297i	0.429719	+	0.902963i	$0.358613\pi$
$809$	−16.1308	+	27.9394i	−0.567130	+	0.982297i	−0.996848	+	0.0793342i	$0.974721\pi$
$810$		0			0
$811$	−34.7632			−1.22070			−0.610350	−	0.792132i	$-0.708971\pi$
$811$	−34.7632			−1.22070			−0.610350	+	0.792132i	$0.708971\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4.55788	−	7.89448i	−0.159656	−	0.276532i
$816$		0			0
$817$	8.84343	+	5.10576i	0.309392	+	0.178628i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−20.0987	+	34.8119i	−0.701448	+	1.21494i	0.266510	+	0.963832i	$0.414130\pi$
$821$	−20.0987	+	34.8119i	−0.701448	+	1.21494i	−0.967958	+	0.251112i	$0.919204\pi$
$822$		0			0
$823$	−2.85246	+	1.64687i	−0.0994305	+	0.0574062i	−0.548891	−	0.835894i	$-0.684950\pi$
$823$	−2.85246	+	1.64687i	−0.0994305	+	0.0574062i	0.449460	+	0.893300i	$0.351616\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			21.5704i			0.750075i	0.927010	+	0.375038i	$0.122370\pi$
$827$			21.5704i			0.750075i	−0.927010	+	0.375038i	$0.877630\pi$
$828$		0			0
$829$	−6.97609	−	4.02765i	−0.242290	−	0.139886i	0.373939	−	0.927453i	$-0.378007\pi$
$829$	−6.97609	−	4.02765i	−0.242290	−	0.139886i	−0.616229	+	0.787567i	$0.711340\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	24.6942	−	8.63401i	0.855605	−	0.299151i
$834$		0			0
$835$	15.0687	+	8.69990i	0.521473	+	0.301072i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	23.8904	+	41.3793i	0.824787	+	1.42857i	0.902082	+	0.431564i	$0.142038\pi$
$839$	23.8904	+	41.3793i	0.824787	+	1.42857i	−0.0772954	+	0.997008i	$0.524628\pi$
$840$		0			0
$841$	−16.9103	+	29.2894i	−0.583113	+	1.00998i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	10.7605	−	6.21256i	0.370172	−	0.213719i
$846$		0			0
$847$	12.1204	+	26.4297i	0.416463	+	0.908137i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−44.2455	+	25.5452i	−1.51672	+	0.875677i
$852$		0			0
$853$	−23.5845	+	13.6165i	−0.807518	+	0.466221i	−0.846093	−	0.533035i	$-0.821051\pi$
$853$	−23.5845	+	13.6165i	−0.807518	+	0.466221i	0.0385754	+	0.999256i	$0.487718\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			40.4731i			1.38253i	0.722599	+	0.691267i	$0.242947\pi$
$857$			40.4731i			1.38253i	−0.722599	+	0.691267i	$0.757053\pi$
$858$		0			0
$859$	53.7041			1.83236			0.916180	−	0.400766i	$-0.131256\pi$
$859$	53.7041			1.83236			0.916180	+	0.400766i	$0.131256\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−16.5769	+	9.57068i	−0.564285	+	0.325790i	−0.754863	−	0.655882i	$-0.772297\pi$
$863$	−16.5769	+	9.57068i	−0.564285	+	0.325790i	0.190579	+	0.981672i	$0.438964\pi$
$864$		0			0
$865$	2.02873	−	3.51386i	0.0689788	−	0.119475i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.134741	−	0.233378i	0.00457078	−	0.00791682i
$870$		0			0
$871$	−61.9470			−2.09899
$872$		0			0
$873$		0			0
$874$		0			0
$875$	23.2128	−	10.6452i	0.784736	−	0.359872i
$876$		0			0
$877$	−12.0902			−0.408258			−0.204129	−	0.978944i	$-0.565436\pi$
$877$	−12.0902			−0.408258			−0.204129	+	0.978944i	$0.565436\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			41.0338i			1.38246i	0.722633	+	0.691232i	$0.242932\pi$
$881$			41.0338i			1.38246i	−0.722633	+	0.691232i	$0.757068\pi$
$882$		0			0
$883$		−	39.1631i		−	1.31794i	−0.752168	−	0.658971i	$-0.770992\pi$
$883$		−	39.1631i		−	1.31794i	0.752168	−	0.658971i	$-0.229008\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	33.1869			1.11431			0.557154	−	0.830409i	$-0.311893\pi$
$887$	33.1869			1.11431			0.557154	+	0.830409i	$0.311893\pi$
$888$		0			0
$889$	21.3342	−	9.78366i	0.715525	−	0.328133i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−32.3464			−1.08243
$894$		0			0
$895$	4.56582	−	7.90824i	0.152619	−	0.264343i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−19.1639	+	33.1928i	−0.639151	+	1.10704i
$900$		0			0
$901$	−42.3009	+	24.4224i	−1.40925	+	0.813629i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−27.7020			−0.920847
$906$		0			0
$907$			17.5768i			0.583628i	0.956475	+	0.291814i	$0.0942589\pi$
$907$			17.5768i			0.583628i	−0.956475	+	0.291814i	$0.905741\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	28.9644	−	16.7226i	0.959635	−	0.554045i	0.0635741	−	0.997977i	$-0.479750\pi$
$911$	28.9644	−	16.7226i	0.959635	−	0.554045i	0.896061	+	0.443932i	$0.146417\pi$
$912$		0			0
$913$	0.0196556	−	0.0113482i	0.000650505	−	0.000375569i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−6.50571	−	14.1863i	−0.214838	−	0.468473i
$918$		0			0
$919$	17.9607	−	10.3696i	0.592470	−	0.342062i	−0.173604	−	0.984816i	$-0.555541\pi$
$919$	17.9607	−	10.3696i	0.592470	−	0.342062i	0.766073	+	0.642753i	$0.222208\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−35.9683	+	62.2989i	−1.18391	+	2.05059i
$924$		0			0
$925$	−10.5309	−	18.2401i	−0.346254	−	0.599730i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	2.35262	+	1.35829i	0.0771870	+	0.0445639i	0.538097	−	0.842883i	$-0.319143\pi$
$929$	2.35262	+	1.35829i	0.0771870	+	0.0445639i	−0.460910	+	0.887447i	$0.652477\pi$
$930$		0			0
$931$	35.0305	+	6.63713i	1.14808	+	0.217523i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.357993	+	0.206687i	0.0117076	+	0.00675940i
$936$		0			0
$937$		−	20.7924i		−	0.679258i	−0.940559	−	0.339629i	$-0.889698\pi$
$937$		−	20.7924i		−	0.679258i	0.940559	−	0.339629i	$-0.110302\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−44.3702	+	25.6172i	−1.44643	+	0.835096i	−0.998266	−	0.0588569i	$-0.981254\pi$
$941$	−44.3702	+	25.6172i	−1.44643	+	0.835096i	−0.448162	+	0.893953i	$0.647921\pi$
$942$		0			0
$943$	20.7929	−	36.0143i	0.677108	−	1.17279i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−37.0086	−	21.3669i	−1.20262	−	0.694332i	−0.241481	−	0.970406i	$-0.577633\pi$
$947$	−37.0086	−	21.3669i	−1.20262	−	0.694332i	−0.961136	+	0.276074i	$0.910967\pi$
$948$		0			0
$949$	16.8598	+	29.2020i	0.547291	+	0.947936i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−5.14510			−0.166666			−0.0833331	−	0.996522i	$-0.526557\pi$
$953$	−5.14510			−0.166666			−0.0833331	+	0.996522i	$0.526557\pi$
$954$		0			0
$955$	−2.31634	+	4.01203i	−0.0749551	+	0.129826i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	19.2260	+	41.9241i	0.620840	+	1.35380i
$960$		0			0
$961$	3.80783	−	6.59536i	0.122833	−	0.212753i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	22.1669	−	12.7980i	0.713576	−	0.411983i
$966$		0			0
$967$	8.18515	+	4.72570i	0.263217	+	0.151968i	0.625801	−	0.779983i	$-0.284772\pi$
$967$	8.18515	+	4.72570i	0.263217	+	0.151968i	−0.362584	+	0.931951i	$0.618106\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.24445	−	12.5478i	−0.232485	−	0.402677i	0.726053	−	0.687638i	$-0.241352\pi$
$971$	−7.24445	−	12.5478i	−0.232485	−	0.402677i	−0.958539	+	0.284962i	$0.908019\pi$
$972$		0			0
$973$	42.6615	+	4.00584i	1.36766	+	0.128421i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	9.99130	+	17.3054i	0.319650	+	0.553650i	0.980415	−	0.196943i	$-0.0631013\pi$
$977$	9.99130	+	17.3054i	0.319650	+	0.553650i	−0.660765	+	0.750593i	$0.729768\pi$
$978$		0			0
$979$	−0.285598	−	0.494671i	−0.00912776	−	0.0158097i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.64389			0.211907			0.105954	−	0.994371i	$-0.466211\pi$
$983$	6.64389			0.211907			0.105954	+	0.994371i	$0.466211\pi$
$984$		0			0
$985$			16.3889i			0.522194i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	9.22993	+	15.9867i	0.293495	+	0.508348i
$990$		0			0
$991$	0.701316	+	0.404905i	0.0222780	+	0.0128622i	0.511098	−	0.859523i	$-0.329239\pi$
$991$	0.701316	+	0.404905i	0.0222780	+	0.0128622i	−0.488820	+	0.872385i	$0.662572\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−11.5098	−	6.64519i	−0.364885	−	0.210667i
$996$		0			0
$997$		−	15.2446i		−	0.482802i	−0.970425	−	0.241401i	$-0.922393\pi$
$997$		−	15.2446i		−	0.482802i	0.970425	−	0.241401i	$-0.0776069\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.bf.i.1711.5		32
3.2	odd	2		1008.2.bf.i.31.3	✓	32
4.3	odd	2	inner	3024.2.bf.i.1711.6		32
7.5	odd	6		3024.2.cz.i.1279.12		32
9.2	odd	6		1008.2.cz.i.367.8	yes	32
9.7	even	3		3024.2.cz.i.2719.11		32
12.11	even	2		1008.2.bf.i.31.14	yes	32
21.5	even	6		1008.2.cz.i.607.9	yes	32
28.19	even	6		3024.2.cz.i.1279.11		32
36.7	odd	6		3024.2.cz.i.2719.12		32
36.11	even	6		1008.2.cz.i.367.9	yes	32
63.47	even	6		1008.2.bf.i.943.14	yes	32
63.61	odd	6	inner	3024.2.bf.i.2287.11		32
84.47	odd	6		1008.2.cz.i.607.8	yes	32
252.47	odd	6		1008.2.bf.i.943.3	yes	32
252.187	even	6	inner	3024.2.bf.i.2287.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.i.31.3	✓	32	3.2	odd	2
1008.2.bf.i.31.14	yes	32	12.11	even	2
1008.2.bf.i.943.3	yes	32	252.47	odd	6
1008.2.bf.i.943.14	yes	32	63.47	even	6
1008.2.cz.i.367.8	yes	32	9.2	odd	6
1008.2.cz.i.367.9	yes	32	36.11	even	6
1008.2.cz.i.607.8	yes	32	84.47	odd	6
1008.2.cz.i.607.9	yes	32	21.5	even	6
3024.2.bf.i.1711.5		32	1.1	even	1	trivial
3024.2.bf.i.1711.6		32	4.3	odd	2	inner
3024.2.bf.i.2287.11		32	63.61	odd	6	inner
3024.2.bf.i.2287.12		32	252.187	even	6	inner
3024.2.cz.i.1279.11		32	28.19	even	6
3024.2.cz.i.1279.12		32	7.5	odd	6
3024.2.cz.i.2719.11		32	9.7	even	3
3024.2.cz.i.2719.12		32	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.bf (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.09736i q^{5} +(1.10288 + 2.40492i) q^{7} -0.100798i q^{11} +(4.27107 + 2.46590i) q^{13} +(-3.23648 - 1.86858i) q^{17} +(-2.54669 - 4.41100i) q^{19} -9.20757i q^{23} +3.79579 q^{25} +(3.96297 + 6.86407i) q^{29} +(2.41787 + 4.18787i) q^{31} +(2.63908 - 1.21026i) q^{35} +(-2.77437 - 4.80534i) q^{37} +(3.91138 + 2.25823i) q^{41} +(-1.73626 + 1.00243i) q^{43} +(3.17534 - 5.49984i) q^{47} +(-4.56733 + 5.30467i) q^{49} +(6.53502 - 11.3190i) q^{53} -0.110612 q^{55} +(1.44382 + 2.50077i) q^{59} +(8.21186 + 4.74112i) q^{61} +(2.70599 - 4.68692i) q^{65} +(-10.8779 + 6.28036i) q^{67} +14.5863i q^{71} +(5.92115 + 3.41858i) q^{73} +(0.242411 - 0.111167i) q^{77} +(2.31531 + 1.33675i) q^{79} +(0.112583 + 0.195000i) q^{83} +(-2.05051 + 3.55159i) q^{85} +(4.90756 - 2.83338i) q^{89} +(-1.21985 + 12.9912i) q^{91} +(-4.84048 + 2.79465i) q^{95} +(6.47632 - 3.73911i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 6 q^{13} + 18 q^{17} - 32 q^{25} + 12 q^{29} + 2 q^{37} - 36 q^{41} + 2 q^{49} + 12 q^{53} + 42 q^{61} - 18 q^{65} + 66 q^{77} - 12 q^{85} + 18 q^{89} - 6 q^{97}+O(q^{100}) \) 32 * q - 6 * q^13 + 18 * q^17 - 32 * q^25 + 12 * q^29 + 2 * q^37 - 36 * q^41 + 2 * q^49 + 12 * q^53 + 42 * q^61 - 18 * q^65 + 66 * q^77 - 12 * q^85 + 18 * q^89 - 6 * q^97

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