LMFDB - Embedded newform 864.2.s.a.575.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(287,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("864.287");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			575.5
Character	$\chi$	$=$	864.575
Dual form			864.2.s.a.287.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.135038 - 0.0779642i) q^{5} +(-0.349281 - 0.201658i) q^{7} +O(q^{10})$	$q+(0.135038 - 0.0779642i) q^{5} +(-0.349281 - 0.201658i) q^{7} +(-2.28556 + 3.95871i) q^{11} +(2.14257 + 3.71104i) q^{13} -2.84030i q^{17} -0.958898i q^{19} +(2.71342 + 4.69978i) q^{23} +(-2.48784 + 4.30907i) q^{25} +(4.88928 + 2.82283i) q^{29} +(-8.53685 + 4.92876i) q^{31} -0.0628883 q^{35} +9.89523 q^{37} +(7.79267 - 4.49910i) q^{41} +(2.59514 + 1.49831i) q^{43} +(1.22684 - 2.12495i) q^{47} +(-3.41867 - 5.92131i) q^{49} +9.45890i q^{53} +0.712769i q^{55} +(1.18560 + 2.05352i) q^{59} +(-4.10147 + 7.10395i) q^{61} +(0.578657 + 0.334088i) q^{65} +(-11.4813 + 6.62872i) q^{67} -2.19993 q^{71} -4.53280 q^{73} +(1.59661 - 0.921804i) q^{77} +(2.84683 + 1.64362i) q^{79} +(-0.812395 + 1.40711i) q^{83} +(-0.221442 - 0.383548i) q^{85} -9.45890i q^{89} -1.72826i q^{91} +(-0.0747597 - 0.129488i) q^{95} +(-0.162474 + 0.281413i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 12 q^{25} - 24 q^{29} + 36 q^{41} + 12 q^{49} + 48 q^{65} + 24 q^{73} + 48 q^{77} + 12 q^{97}+O(q^{100}) $ 24 * q + 12 * q^25 - 24 * q^29 + 36 * q^41 + 12 * q^49 + 48 * q^65 + 24 * q^73 + 48 * q^77 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.135038	−	0.0779642i	0.0603908	−	0.0348667i	−0.469501	−	0.882932i	$-0.655566\pi$
$5$	0.135038	−	0.0779642i	0.0603908	−	0.0348667i	0.529891	+	0.848066i	$0.322233\pi$
$6$		0			0
$7$	−0.349281	−	0.201658i	−0.132016	−	0.0762195i	0.432538	−	0.901616i	$-0.357618\pi$
$7$	−0.349281	−	0.201658i	−0.132016	−	0.0762195i	−0.564554	+	0.825396i	$0.690952\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.28556	+	3.95871i	−0.689124	+	1.19360i	0.282998	+	0.959121i	$0.408671\pi$
$11$	−2.28556	+	3.95871i	−0.689124	+	1.19360i	−0.972122	+	0.234477i	$0.924662\pi$
$12$		0			0
$13$	2.14257	+	3.71104i	0.594242	+	1.02926i	0.993653	+	0.112486i	$0.0358812\pi$
$13$	2.14257	+	3.71104i	0.594242	+	1.02926i	−0.399411	+	0.916772i	$0.630785\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	2.84030i		−	0.688874i	−0.938810	−	0.344437i	$-0.888070\pi$
$17$		−	2.84030i		−	0.688874i	0.938810	−	0.344437i	$-0.111930\pi$
$18$		0			0
$19$		−	0.958898i		−	0.219986i	−0.993932	−	0.109993i	$-0.964917\pi$
$19$		−	0.958898i		−	0.219986i	0.993932	−	0.109993i	$-0.0350829\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.71342	+	4.69978i	0.565787	+	0.979972i	0.996976	+	0.0777105i	$0.0247610\pi$
$23$	2.71342	+	4.69978i	0.565787	+	0.979972i	−0.431189	+	0.902262i	$0.641906\pi$
$24$		0			0
$25$	−2.48784	+	4.30907i	−0.497569	+	0.861814i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.88928	+	2.82283i	0.907917	+	0.524186i	0.879760	−	0.475417i	$-0.157703\pi$
$29$	4.88928	+	2.82283i	0.907917	+	0.524186i	0.0281566	+	0.999604i	$0.491036\pi$
$30$		0			0
$31$	−8.53685	+	4.92876i	−1.53326	+	0.885231i	−0.534056	+	0.845449i	$0.679333\pi$
$31$	−8.53685	+	4.92876i	−1.53326	+	0.885231i	−0.999208	+	0.0397815i	$0.987334\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.0628883			−0.0106301
$36$		0			0
$37$	9.89523			1.62677			0.813383	−	0.581729i	$-0.197624\pi$
$37$	9.89523			1.62677			0.813383	+	0.581729i	$0.197624\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	7.79267	−	4.49910i	1.21701	−	0.702642i	0.252733	−	0.967536i	$-0.418670\pi$
$41$	7.79267	−	4.49910i	1.21701	−	0.702642i	0.964277	+	0.264894i	$0.0853371\pi$
$42$		0			0
$43$	2.59514	+	1.49831i	0.395756	+	0.228490i	0.684651	−	0.728871i	$-0.259955\pi$
$43$	2.59514	+	1.49831i	0.395756	+	0.228490i	−0.288895	+	0.957361i	$0.593288\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.22684	−	2.12495i	0.178953	−	0.309956i	−0.762569	−	0.646907i	$-0.776062\pi$
$47$	1.22684	−	2.12495i	0.178953	−	0.309956i	0.941522	+	0.336951i	$0.109396\pi$
$48$		0			0
$49$	−3.41867	−	5.92131i	−0.488381	−	0.845901i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			9.45890i			1.29928i	0.760242	+	0.649640i	$0.225080\pi$
$53$			9.45890i			1.29928i	−0.760242	+	0.649640i	$0.774920\pi$
$54$		0			0
$55$			0.712769i			0.0961098i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.18560	+	2.05352i	0.154352	+	0.267346i	0.932823	−	0.360335i	$-0.117338\pi$
$59$	1.18560	+	2.05352i	0.154352	+	0.267346i	−0.778471	+	0.627681i	$0.784004\pi$
$60$		0			0
$61$	−4.10147	+	7.10395i	−0.525139	+	0.909568i	0.474432	+	0.880292i	$0.342653\pi$
$61$	−4.10147	+	7.10395i	−0.525139	+	0.909568i	−0.999571	+	0.0292756i	$0.990680\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.578657	+	0.334088i	0.0717735	+	0.0414385i
$66$		0			0
$67$	−11.4813	+	6.62872i	−1.40266	+	0.809827i	−0.994665	−	0.103156i	$-0.967106\pi$
$67$	−11.4813	+	6.62872i	−1.40266	+	0.809827i	−0.407997	+	0.912983i	$0.633772\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.19993			−0.261083			−0.130542	−	0.991443i	$-0.541672\pi$
$71$	−2.19993			−0.261083			−0.130542	+	0.991443i	$0.541672\pi$
$72$		0			0
$73$	−4.53280			−0.530524			−0.265262	−	0.964176i	$-0.585459\pi$
$73$	−4.53280			−0.530524			−0.265262	+	0.964176i	$0.585459\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.59661	−	0.921804i	0.181951	−	0.105049i
$78$		0			0
$79$	2.84683	+	1.64362i	0.320293	+	0.184921i	0.651523	−	0.758629i	$-0.274130\pi$
$79$	2.84683	+	1.64362i	0.320293	+	0.184921i	−0.331230	+	0.943550i	$0.607464\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.812395	+	1.40711i	−0.0891720	+	0.154450i	−0.907161	−	0.420783i	$-0.861755\pi$
$83$	−0.812395	+	1.40711i	−0.0891720	+	0.154450i	0.817989	+	0.575233i	$0.195089\pi$
$84$		0			0
$85$	−0.221442	−	0.383548i	−0.0240187	−	0.0416016i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	9.45890i		−	1.00264i	−0.865261	−	0.501321i	$-0.832848\pi$
$89$		−	9.45890i		−	1.00264i	0.865261	−	0.501321i	$-0.167152\pi$
$90$		0			0
$91$		−	1.72826i		−	0.181171i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0747597	−	0.129488i	−0.00767018	−	0.0132851i
$96$		0			0
$97$	−0.162474	+	0.281413i	−0.0164967	+	0.0285732i	−0.874156	−	0.485645i	$-0.838585\pi$
$97$	−0.162474	+	0.281413i	−0.0164967	+	0.0285732i	0.857659	+	0.514219i	$0.171918\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.03402	+	2.90639i	0.500903	+	0.289197i	0.729087	−	0.684421i	$-0.239945\pi$
$101$	5.03402	+	2.90639i	0.500903	+	0.289197i	−0.228183	+	0.973618i	$0.573278\pi$
$102$		0			0
$103$	6.03931	−	3.48680i	0.595071	−	0.343564i	−0.172029	−	0.985092i	$-0.555032\pi$
$103$	6.03931	−	3.48680i	0.595071	−	0.343564i	0.767100	+	0.641527i	$0.221699\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	14.2022			1.37298			0.686490	−	0.727139i	$-0.259150\pi$
$107$	14.2022			1.37298			0.686490	+	0.727139i	$0.259150\pi$
$108$		0			0
$109$	11.8130			1.13148			0.565741	−	0.824583i	$-0.308590\pi$
$109$	11.8130			1.13148			0.565741	+	0.824583i	$0.308590\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.06455	+	4.07872i	−0.664577	+	0.383694i	−0.794019	−	0.607893i	$-0.792015\pi$
$113$	−7.06455	+	4.07872i	−0.664577	+	0.383694i	0.129442	+	0.991587i	$0.458681\pi$
$114$		0			0
$115$	0.732830	+	0.423099i	0.0683367	+	0.0394542i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.572768	+	0.992063i	−0.0525056	+	0.0909423i
$120$		0			0
$121$	−4.94761	−	8.56952i	−0.449783	−	0.779047i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			1.55549i			0.139128i
$126$		0			0
$127$		−	15.6814i		−	1.39150i	−0.718282	−	0.695752i	$-0.755071\pi$
$127$		−	15.6814i		−	1.39150i	0.718282	−	0.695752i	$-0.244929\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−10.2084	−	17.6815i	−0.891913	−	1.54484i	−0.837579	−	0.546316i	$-0.816030\pi$
$131$	−10.2084	−	17.6815i	−0.891913	−	1.54484i	−0.0543338	−	0.998523i	$-0.517304\pi$
$132$		0			0
$133$	−0.193369	+	0.334925i	−0.0167672	+	0.0290417i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.9617	−	7.48346i	−1.10740	−	0.639355i	−0.169242	−	0.985575i	$-0.554132\pi$
$137$	−12.9617	−	7.48346i	−1.10740	−	0.639355i	−0.938153	+	0.346220i	$0.887465\pi$
$138$		0			0
$139$	7.32288	−	4.22786i	0.621118	−	0.358603i	−0.156186	−	0.987728i	$-0.549920\pi$
$139$	7.32288	−	4.22786i	0.621118	−	0.358603i	0.777304	+	0.629125i	$0.216587\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−19.5879			−1.63803
$144$		0			0
$145$	0.880318			0.0731065
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−17.3267	+	10.0036i	−1.41946	+	0.819524i	−0.996251	−	0.0865089i	$-0.972429\pi$
$149$	−17.3267	+	10.0036i	−1.41946	+	0.819524i	−0.423207	+	0.906033i	$0.639096\pi$
$150$		0			0
$151$	16.6516	+	9.61383i	1.35509	+	0.782362i	0.988957	−	0.148200i	$-0.0473481\pi$
$151$	16.6516	+	9.61383i	1.35509	+	0.782362i	0.366133	+	0.930562i	$0.380681\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.768533	+	1.33114i	−0.0617301	+	0.106920i
$156$		0			0
$157$	−4.61167	−	7.98765i	−0.368052	−	0.637484i	0.621209	−	0.783645i	$-0.286642\pi$
$157$	−4.61167	−	7.98765i	−0.368052	−	0.637484i	−0.989261	+	0.146161i	$0.953308\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	2.18873i		−	0.172496i
$162$		0			0
$163$		−	13.7636i		−	1.07805i	−0.842289	−	0.539026i	$-0.818792\pi$
$163$		−	13.7636i		−	1.07805i	0.842289	−	0.539026i	$-0.181208\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.48611	+	9.50223i	0.424528	+	0.735304i	0.996376	−	0.0850551i	$-0.0271066\pi$
$167$	5.48611	+	9.50223i	0.424528	+	0.735304i	−0.571848	+	0.820360i	$0.693773\pi$
$168$		0			0
$169$	−2.68121	+	4.64400i	−0.206247	+	0.357230i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−17.1614	−	9.90813i	−1.30476	−	0.753302i	−0.323541	−	0.946214i	$-0.604873\pi$
$173$	−17.1614	−	9.90813i	−1.30476	−	0.753302i	−0.981216	+	0.192913i	$0.938207\pi$
$174$		0			0
$175$	1.73791	−	1.00339i	0.131374	−	0.0758488i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	2.71217			0.202717			0.101359	−	0.994850i	$-0.467681\pi$
$179$	2.71217			0.202717			0.101359	+	0.994850i	$0.467681\pi$
$180$		0			0
$181$	0.0561450			0.00417323			0.00208661	−	0.999998i	$-0.499336\pi$
$181$	0.0561450			0.00417323			0.00208661	+	0.999998i	$0.499336\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.33623	−	0.771474i	0.0982417	−	0.0567199i
$186$		0			0
$187$	11.2439	+	6.49169i	0.822238	+	0.474719i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	10.3810	−	17.9804i	0.751141	−	1.30101i	−0.196129	−	0.980578i	$-0.562837\pi$
$191$	10.3810	−	17.9804i	0.751141	−	1.30101i	0.947270	−	0.320436i	$-0.103829\pi$
$192$		0			0
$193$	−5.81321	−	10.0688i	−0.418444	−	0.724767i	0.577339	−	0.816505i	$-0.304091\pi$
$193$	−5.81321	−	10.0688i	−0.418444	−	0.724767i	−0.995783	+	0.0917380i	$0.970758\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5.65685i		−	0.403034i	−0.979485	−	0.201517i	$-0.935413\pi$
$197$		−	5.65685i		−	0.403034i	0.979485	−	0.201517i	$-0.0645872\pi$
$198$		0			0
$199$		−	10.3363i		−	0.732718i	−0.930474	−	0.366359i	$-0.880604\pi$
$199$		−	10.3363i		−	0.732718i	0.930474	−	0.366359i	$-0.119396\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.13849	−	1.97192i	−0.0799064	−	0.138402i
$204$		0			0
$205$	0.701538	−	1.21510i	0.0489975	−	0.0848662i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.79600	+	2.19162i	0.262575	+	0.151598i
$210$		0			0
$211$	−3.02408	+	1.74596i	−0.208187	+	0.120197i	−0.600468	−	0.799649i	$-0.705019\pi$
$211$	−3.02408	+	1.74596i	−0.208187	+	0.120197i	0.392282	+	0.919845i	$0.371686\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.467257			0.0318667
$216$		0			0
$217$	3.97569			0.269887
$218$		0			0
$219$		0			0
$220$		0			0
$221$	10.5405	−	6.08554i	0.709028	−	0.409358i
$222$		0			0
$223$	−8.87018	−	5.12120i	−0.593991	−	0.342941i	0.172683	−	0.984977i	$-0.444756\pi$
$223$	−8.87018	−	5.12120i	−0.593991	−	0.342941i	−0.766674	+	0.642037i	$0.778090\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.779959	+	1.35093i	−0.0517677	+	0.0896643i	−0.890748	−	0.454497i	$-0.849819\pi$
$227$	−0.779959	+	1.35093i	−0.0517677	+	0.0896643i	0.838980	+	0.544162i	$0.183152\pi$
$228$		0			0
$229$	−7.09018	−	12.2806i	−0.468533	−	0.811522i	0.530821	−	0.847484i	$-0.321884\pi$
$229$	−7.09018	−	12.2806i	−0.468533	−	0.811522i	−0.999353	+	0.0359620i	$0.988550\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			17.3465i			1.13641i	0.822888	+	0.568204i	$0.192361\pi$
$233$			17.3465i			1.13641i	−0.822888	+	0.568204i	$0.807639\pi$
$234$		0			0
$235$		−	0.382599i		−	0.0249580i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.74548	−	11.6835i	−0.436329	−	0.755744i	0.561074	−	0.827766i	$-0.310388\pi$
$239$	−6.74548	−	11.6835i	−0.436329	−	0.755744i	−0.997403	+	0.0720215i	$0.977055\pi$
$240$		0			0
$241$	1.71016	−	2.96208i	0.110161	−	0.190804i	−0.805674	−	0.592359i	$-0.798197\pi$
$241$	1.71016	−	2.96208i	0.110161	−	0.190804i	0.915835	+	0.401555i	$0.131530\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.923300	−	0.533068i	−0.0589875	−	0.0340564i
$246$		0			0
$247$	3.55851	−	2.05451i	0.226422	−	0.130725i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	8.10511			0.511590			0.255795	−	0.966731i	$-0.417663\pi$
$251$	8.10511			0.511590			0.255795	+	0.966731i	$0.417663\pi$
$252$		0			0
$253$	−24.8068			−1.55959
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.0484	+	8.11087i	−0.876318	+	0.505942i	−0.869443	−	0.494034i	$-0.835522\pi$
$257$	−14.0484	+	8.11087i	−0.876318	+	0.505942i	−0.00687532	+	0.999976i	$0.502188\pi$
$258$		0			0
$259$	−3.45622	−	1.99545i	−0.214759	−	0.123991i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	13.4734	−	23.3366i	0.830805	−	1.43900i	−0.0665964	−	0.997780i	$-0.521214\pi$
$263$	13.4734	−	23.3366i	0.830805	−	1.43900i	0.897401	−	0.441216i	$-0.145453\pi$
$264$		0			0
$265$	0.737456	+	1.27731i	0.0453016	+	0.0784646i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			9.15987i			0.558487i	0.960220	+	0.279243i	$0.0900836\pi$
$269$			9.15987i			0.558487i	−0.960220	+	0.279243i	$0.909916\pi$
$270$		0			0
$271$			23.7150i			1.44058i	0.693670	+	0.720292i	$0.255992\pi$
$271$			23.7150i			1.44058i	−0.693670	+	0.720292i	$0.744008\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−11.3723	−	19.6973i	−0.685773	−	1.18779i
$276$		0			0
$277$	4.07340	−	7.05533i	0.244747	−	0.423914i	−0.717314	−	0.696750i	$-0.754629\pi$
$277$	4.07340	−	7.05533i	0.244747	−	0.423914i	0.962060	+	0.272837i	$0.0879619\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.27676	+	3.62389i	0.374440	+	0.216183i	0.675397	−	0.737455i	$-0.263972\pi$
$281$	6.27676	+	3.62389i	0.374440	+	0.216183i	−0.300956	+	0.953638i	$0.597306\pi$
$282$		0			0
$283$	10.8055	−	6.23858i	0.642323	−	0.370845i	−0.143186	−	0.989696i	$-0.545735\pi$
$283$	10.8055	−	6.23858i	0.642323	−	0.370845i	0.785509	+	0.618851i	$0.212401\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.62911			−0.214220
$288$		0			0
$289$	8.93270			0.525453
$290$		0			0
$291$		0			0
$292$		0			0
$293$	7.93127	−	4.57912i	0.463350	−	0.267515i	−0.250102	−	0.968220i	$-0.580464\pi$
$293$	7.93127	−	4.57912i	0.463350	−	0.267515i	0.713452	+	0.700704i	$0.247131\pi$
$294$		0			0
$295$	0.320203	+	0.184869i	0.0186429	+	0.0107635i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−11.6274	+	20.1392i	−0.672429	+	1.16468i
$300$		0			0
$301$	−0.604290	−	1.04666i	−0.0348307	−	0.0603286i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			1.27907i			0.0732394i
$306$		0			0
$307$			8.99247i			0.513228i	0.966514	+	0.256614i	$0.0826069\pi$
$307$			8.99247i			0.513228i	−0.966514	+	0.256614i	$0.917393\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	17.0122	+	29.4659i	0.964671	+	1.67086i	0.710496	+	0.703701i	$0.248470\pi$
$311$	17.0122	+	29.4659i	0.964671	+	1.67086i	0.254175	+	0.967158i	$0.418196\pi$
$312$		0			0
$313$	0.190546	−	0.330036i	0.0107703	−	0.0186547i	−0.860590	−	0.509298i	$-0.829905\pi$
$313$	0.190546	−	0.330036i	0.0107703	−	0.0186547i	0.871360	+	0.490644i	$0.163238\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.76598	+	4.48369i	0.436181	+	0.251829i	0.701976	−	0.712200i	$-0.252301\pi$
$317$	7.76598	+	4.48369i	0.436181	+	0.251829i	−0.265796	+	0.964029i	$0.585635\pi$
$318$		0			0
$319$	−22.3495	+	12.9035i	−1.25133	+	0.722458i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−2.72356			−0.151543
$324$		0			0
$325$	−21.3215			−1.18270
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.857025	+	0.494804i	−0.0472493	+	0.0272794i
$330$		0			0
$331$	11.8854	+	6.86204i	0.653281	+	0.377172i	0.789712	−	0.613478i	$-0.210230\pi$
$331$	11.8854	+	6.86204i	0.653281	+	0.377172i	−0.136431	+	0.990650i	$0.543563\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.03361	+	1.79026i	−0.0564719	+	0.0978122i
$336$		0			0
$337$	13.2393	+	22.9312i	0.721193	+	1.24914i	0.960522	+	0.278204i	$0.0897390\pi$
$337$	13.2393	+	22.9312i	0.721193	+	1.24914i	−0.239330	+	0.970938i	$0.576928\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	45.0600i		−	2.44013i
$342$		0			0
$343$			5.58081i			0.301335i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.11490	+	7.12721i	0.220899	+	0.382609i	0.955081	−	0.296344i	$-0.0957674\pi$
$347$	4.11490	+	7.12721i	0.220899	+	0.382609i	−0.734182	+	0.678953i	$0.762434\pi$
$348$		0			0
$349$	0.635988	−	1.10156i	0.0340437	−	0.0589654i	−0.848502	−	0.529193i	$-0.822495\pi$
$349$	0.635988	−	1.10156i	0.0340437	−	0.0589654i	0.882545	+	0.470227i	$0.155828\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	11.2765	+	6.51051i	0.600189	+	0.346519i	0.769116	−	0.639109i	$-0.220697\pi$
$353$	11.2765	+	6.51051i	0.600189	+	0.346519i	−0.168927	+	0.985629i	$0.554030\pi$
$354$		0			0
$355$	−0.297073	+	0.171515i	−0.0157670	+	0.00910310i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.69181			0.458736			0.229368	−	0.973340i	$-0.426334\pi$
$359$	8.69181			0.458736			0.229368	+	0.973340i	$0.426334\pi$
$360$		0			0
$361$	18.0805			0.951606
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.612101	+	0.353396i	−0.0320388	+	0.0184976i
$366$		0			0
$367$	−28.6395	−	16.5350i	−1.49497	−	0.863120i	−0.494985	−	0.868902i	$-0.664826\pi$
$367$	−28.6395	−	16.5350i	−1.49497	−	0.863120i	−0.999983	+	0.00578127i	$0.998160\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.90746	−	3.30382i	0.0990304	−	0.171526i
$372$		0			0
$373$	5.02649	+	8.70613i	0.260262	+	0.450786i	0.966311	−	0.257376i	$-0.0828579\pi$
$373$	5.02649	+	8.70613i	0.260262	+	0.450786i	−0.706050	+	0.708162i	$0.749525\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			24.1924i			1.24597i
$378$		0			0
$379$		−	10.2627i		−	0.527160i	−0.964638	−	0.263580i	$-0.915097\pi$
$379$		−	10.2627i		−	0.527160i	0.964638	−	0.263580i	$-0.0849033\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.97279	−	6.88107i	−0.203000	−	0.351607i	0.746494	−	0.665393i	$-0.231736\pi$
$383$	−3.97279	−	6.88107i	−0.203000	−	0.351607i	−0.949494	+	0.313786i	$0.898403\pi$
$384$		0			0
$385$	0.143735	−	0.248957i	0.00732543	−	0.0126880i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.19438	+	1.26692i	0.111259	+	0.0642356i	0.554597	−	0.832119i	$-0.312872\pi$
$389$	2.19438	+	1.26692i	0.111259	+	0.0642356i	−0.443338	+	0.896355i	$0.646206\pi$
$390$		0			0
$391$	13.3488	−	7.70692i	0.675077	−	0.389756i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.512573			0.0257903
$396$		0			0
$397$	16.8586			0.846109			0.423054	−	0.906104i	$-0.360958\pi$
$397$	16.8586			0.846109			0.423054	+	0.906104i	$0.360958\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	20.3709	−	11.7612i	1.01728	−	0.587324i	0.103962	−	0.994581i	$-0.466848\pi$
$401$	20.3709	−	11.7612i	1.01728	−	0.587324i	0.913314	+	0.407257i	$0.133515\pi$
$402$		0			0
$403$	−36.5816	−	21.1204i	−1.82226	−	1.05208i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−22.6162	+	39.1724i	−1.12104	+	1.94170i
$408$		0			0
$409$	15.6804	+	27.1592i	0.775344	+	1.34294i	0.934601	+	0.355698i	$0.115757\pi$
$409$	15.6804	+	27.1592i	0.775344	+	1.34294i	−0.159257	+	0.987237i	$0.550910\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	0.956343i		−	0.0470586i
$414$		0			0
$415$			0.253351i			0.0124365i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.53096	+	14.7761i	0.416765	+	0.721858i	0.995612	−	0.0935782i	$-0.0298305\pi$
$419$	8.53096	+	14.7761i	0.416765	+	0.721858i	−0.578847	+	0.815436i	$0.696497\pi$
$420$		0			0
$421$	−10.2100	+	17.6843i	−0.497606	+	0.861879i	−0.999996	−	0.00276183i	$-0.999121\pi$
$421$	−10.2100	+	17.6843i	−0.497606	+	0.861879i	0.502390	+	0.864641i	$0.332454\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.2390	+	7.06622i	0.593681	+	0.342762i
$426$		0			0
$427$	2.86513	−	1.65419i	0.138653	−	0.0800516i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.66939			0.128580			0.0642899	−	0.997931i	$-0.479522\pi$
$431$	2.66939			0.128580			0.0642899	+	0.997931i	$0.479522\pi$
$432$		0			0
$433$	−5.41857			−0.260400			−0.130200	−	0.991488i	$-0.541562\pi$
$433$	−5.41857			−0.260400			−0.130200	+	0.991488i	$0.541562\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.50661	−	2.60189i	0.215580	−	0.124465i
$438$		0			0
$439$	19.2837	+	11.1334i	0.920360	+	0.531370i	0.883750	−	0.467960i	$-0.155011\pi$
$439$	19.2837	+	11.1334i	0.920360	+	0.531370i	0.0366099	+	0.999330i	$0.488344\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.2064	+	21.1421i	−0.579944	+	1.00449i	0.415541	+	0.909574i	$0.363592\pi$
$443$	−12.2064	+	21.1421i	−0.579944	+	1.00449i	−0.995485	+	0.0949180i	$0.969741\pi$
$444$		0			0
$445$	−0.737456	−	1.27731i	−0.0349588	−	0.0605504i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	8.22186i		−	0.388013i	−0.981000	−	0.194007i	$-0.937852\pi$
$449$		−	8.22186i		−	0.388013i	0.981000	−	0.194007i	$-0.0621484\pi$
$450$		0			0
$451$			41.1320i			1.93683i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.134743	−	0.233381i	−0.00631683	−	0.0109411i
$456$		0			0
$457$	8.59988	−	14.8954i	0.402285	−	0.696779i	−0.591716	−	0.806147i	$-0.701549\pi$
$457$	8.59988	−	14.8954i	0.402285	−	0.696779i	0.994001	+	0.109368i	$0.0348826\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−29.5488	−	17.0600i	−1.37622	−	0.794563i	−0.384521	−	0.923116i	$-0.625633\pi$
$461$	−29.5488	−	17.0600i	−1.37622	−	0.794563i	−0.991703	+	0.128554i	$0.958967\pi$
$462$		0			0
$463$	3.40301	−	1.96473i	0.158151	−	0.0913086i	−0.418836	−	0.908062i	$-0.637562\pi$
$463$	3.40301	−	1.96473i	0.158151	−	0.0913086i	0.576987	+	0.816753i	$0.304228\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.80148			−0.361010			−0.180505	−	0.983574i	$-0.557773\pi$
$467$	−7.80148			−0.361010			−0.180505	+	0.983574i	$0.557773\pi$
$468$		0			0
$469$	5.34693			0.246898
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−11.8627	+	6.84896i	−0.545449	+	0.314915i
$474$		0			0
$475$	4.13196	+	2.38559i	0.189587	+	0.109458i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	5.16002	−	8.93741i	0.235767	−	0.408361i	−0.723728	−	0.690085i	$-0.757573\pi$
$479$	5.16002	−	8.93741i	0.235767	−	0.408361i	0.959495	+	0.281724i	$0.0909064\pi$
$480$		0			0
$481$	21.2012	+	36.7216i	0.966692	+	1.67436i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			0.0506686i			0.00230074i
$486$		0			0
$487$		−	2.25172i		−	0.102035i	−0.998698	−	0.0510177i	$-0.983754\pi$
$487$		−	2.25172i		−	0.102035i	0.998698	−	0.0510177i	$-0.0162465\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.3393	+	21.3722i	0.556863	+	0.964516i	0.997756	+	0.0669558i	$0.0213287\pi$
$491$	12.3393	+	21.3722i	0.556863	+	0.964516i	−0.440893	+	0.897560i	$0.645338\pi$
$492$		0			0
$493$	8.01768	−	13.8870i	0.361098	−	0.625440i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.768393	+	0.443632i	0.0344671	+	0.0198996i
$498$		0			0
$499$	−20.0746	+	11.5901i	−0.898663	+	0.518843i	−0.876766	−	0.480917i	$-0.840304\pi$
$499$	−20.0746	+	11.5901i	−0.898663	+	0.518843i	−0.0218966	+	0.999760i	$0.506970\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−27.8228			−1.24056			−0.620279	−	0.784381i	$-0.712981\pi$
$503$	−27.8228			−1.24056			−0.620279	+	0.784381i	$0.712981\pi$
$504$		0			0
$505$	0.906378			0.0403333
$506$		0			0
$507$		0			0
$508$		0			0
$509$	30.8321	−	17.8009i	1.36661	−	0.789013i	0.376117	−	0.926572i	$-0.377259\pi$
$509$	30.8321	−	17.8009i	1.36661	−	0.789013i	0.990493	+	0.137560i	$0.0439258\pi$
$510$		0			0
$511$	1.58322	+	0.914075i	0.0700377	+	0.0404363i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.543691	−	0.941700i	0.0239579	−	0.0414963i
$516$		0			0
$517$	5.60805	+	9.71343i	0.246642	+	0.427196i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			9.35452i			0.409829i	0.978780	+	0.204914i	$0.0656916\pi$
$521$			9.35452i			0.409829i	−0.978780	+	0.204914i	$0.934308\pi$
$522$		0			0
$523$			3.18845i			0.139421i	0.997567	+	0.0697106i	$0.0222076\pi$
$523$			3.18845i			0.139421i	−0.997567	+	0.0697106i	$0.977792\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.9991	+	24.2472i	0.609812	+	1.05623i
$528$		0			0
$529$	−3.22530	+	5.58638i	−0.140230	+	0.242886i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	33.3927	+	19.2793i	1.44640	+	0.835078i
$534$		0			0
$535$	1.91784	−	1.10726i	0.0829154	−	0.0478712i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	31.2544			1.34622
$540$		0			0
$541$	−17.5925			−0.756359			−0.378180	−	0.925732i	$-0.623450\pi$
$541$	−17.5925			−0.756359			−0.378180	+	0.925732i	$0.623450\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.59521	−	0.920993i	0.0683312	−	0.0394510i
$546$		0			0
$547$	−15.6730	−	9.04882i	−0.670130	−	0.386900i	0.125996	−	0.992031i	$-0.459787\pi$
$547$	−15.6730	−	9.04882i	−0.670130	−	0.386900i	−0.796126	+	0.605131i	$0.793121\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.70680	−	4.68832i	0.115314	−	0.199729i
$552$		0			0
$553$	−0.662895	−	1.14817i	−0.0281892	−	0.0488251i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			20.5638i			0.871318i	0.900112	+	0.435659i	$0.143485\pi$
$557$			20.5638i			0.871318i	−0.900112	+	0.435659i	$0.856515\pi$
$558$		0			0
$559$			12.8409i			0.543113i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−15.1630	−	26.2631i	−0.639043	−	1.10686i	−0.985643	−	0.168842i	$-0.945997\pi$
$563$	−15.1630	−	26.2631i	−0.639043	−	1.10686i	0.346600	−	0.938013i	$-0.387336\pi$
$564$		0			0
$565$	−0.635988	+	1.10156i	−0.0267562	+	0.0463432i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−12.6128	−	7.28198i	−0.528755	−	0.305277i	0.211755	−	0.977323i	$-0.432082\pi$
$569$	−12.6128	−	7.28198i	−0.528755	−	0.305277i	−0.740509	+	0.672046i	$0.765416\pi$
$570$		0			0
$571$	−2.25820	+	1.30377i	−0.0945028	+	0.0545612i	−0.546507	−	0.837455i	$-0.684043\pi$
$571$	−2.25820	+	1.30377i	−0.0945028	+	0.0545612i	0.452004	+	0.892016i	$0.350709\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−27.0023			−1.12607
$576$		0			0
$577$	−20.1253			−0.837826			−0.418913	−	0.908026i	$-0.637589\pi$
$577$	−20.1253			−0.837826			−0.418913	+	0.908026i	$0.637589\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.567509	−	0.327652i	0.0235442	−	0.0135933i
$582$		0			0
$583$	−37.4451	−	21.6189i	−1.55082	−	0.895365i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.4379	−	35.3995i	0.843564	−	1.46110i	−0.0432988	−	0.999062i	$-0.513787\pi$
$587$	20.4379	−	35.3995i	0.843564	−	1.46110i	0.886863	−	0.462033i	$-0.152880\pi$
$588$		0			0
$589$	4.72617	+	8.18597i	0.194739	+	0.337297i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			3.73552i			0.153399i	0.997054	+	0.0766997i	$0.0244383\pi$
$593$			3.73552i			0.153399i	−0.997054	+	0.0766997i	$0.975562\pi$
$594$		0			0
$595$			0.178622i			0.00732277i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.77394	+	4.80461i	0.113340	+	0.196311i	0.917115	−	0.398623i	$-0.130512\pi$
$599$	2.77394	+	4.80461i	0.113340	+	0.196311i	−0.803775	+	0.594934i	$0.797178\pi$
$600$		0			0
$601$	17.1869	−	29.7687i	0.701070	−	1.21429i	−0.267021	−	0.963691i	$-0.586039\pi$
$601$	17.1869	−	29.7687i	0.701070	−	1.21429i	0.968091	−	0.250599i	$-0.0806274\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.33623	−	0.771474i	−0.0543255	−	0.0313649i
$606$		0			0
$607$	23.5586	−	13.6016i	0.956216	−	0.552071i	0.0612094	−	0.998125i	$-0.480504\pi$
$607$	23.5586	−	13.6016i	0.956216	−	0.552071i	0.895006	+	0.446054i	$0.147171\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	10.5144			0.425366
$612$		0			0
$613$	−37.5348			−1.51602			−0.758008	−	0.652245i	$-0.773827\pi$
$613$	−37.5348			−1.51602			−0.758008	+	0.652245i	$0.773827\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	20.2495	−	11.6910i	0.815213	−	0.470663i	−0.0335499	−	0.999437i	$-0.510681\pi$
$617$	20.2495	−	11.6910i	0.815213	−	0.470663i	0.848763	+	0.528774i	$0.177348\pi$
$618$		0			0
$619$	−18.7503	−	10.8255i	−0.753637	−	0.435113i	0.0733695	−	0.997305i	$-0.476625\pi$
$619$	−18.7503	−	10.8255i	−0.753637	−	0.435113i	−0.827007	+	0.562192i	$0.809958\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.90746	+	3.30382i	−0.0764208	+	0.132365i
$624$		0			0
$625$	−12.3179	−	21.3353i	−0.492718	−	0.853412i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	28.1054i		−	1.12064i
$630$		0			0
$631$			36.5039i			1.45320i	0.687062	+	0.726599i	$0.258900\pi$
$631$			36.5039i			1.45320i	−0.687062	+	0.726599i	$0.741100\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.22259	−	2.11759i	−0.0485171	−	0.0840340i
$636$		0			0
$637$	14.6495	−	25.3736i	0.580433	−	1.00534i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	35.4336	+	20.4576i	1.39954	+	0.808027i	0.994345	−	0.106201i	$-0.0338687\pi$
$641$	35.4336	+	20.4576i	1.39954	+	0.808027i	0.405199	+	0.914228i	$0.367202\pi$
$642$		0			0
$643$	25.3014	−	14.6078i	0.997791	−	0.576075i	0.0901973	−	0.995924i	$-0.471250\pi$
$643$	25.3014	−	14.6078i	0.997791	−	0.576075i	0.907594	+	0.419849i	$0.137917\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	45.9293			1.80567			0.902834	−	0.429988i	$-0.141482\pi$
$647$	45.9293			1.80567			0.902834	+	0.429988i	$0.141482\pi$
$648$		0			0
$649$	−10.8391			−0.425471
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−27.3513	+	15.7913i	−1.07034	+	0.617961i	−0.928274	−	0.371896i	$-0.878708\pi$
$653$	−27.3513	+	15.7913i	−1.07034	+	0.617961i	−0.142066	+	0.989857i	$0.545374\pi$
$654$		0			0
$655$	−2.75705	−	1.59178i	−0.107727	−	0.0621961i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−5.19029	+	8.98985i	−0.202185	+	0.350195i	−0.949232	−	0.314576i	$-0.898138\pi$
$659$	−5.19029	+	8.98985i	−0.202185	+	0.350195i	0.747047	+	0.664771i	$0.231471\pi$
$660$		0			0
$661$	8.73963	+	15.1375i	0.339932	+	0.588780i	0.984420	−	0.175835i	$-0.0562626\pi$
$661$	8.73963	+	15.1375i	0.339932	+	0.588780i	−0.644488	+	0.764615i	$0.722929\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			0.0603035i			0.00233847i
$666$		0			0
$667$			30.6381i			1.18631i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−18.7483	−	32.4731i	−0.723772	−	1.25361i
$672$		0			0
$673$	−10.9029	+	18.8843i	−0.420275	+	0.727937i	−0.995966	−	0.0897298i	$-0.971400\pi$
$673$	−10.9029	+	18.8843i	−0.420275	+	0.727937i	0.575691	+	0.817667i	$0.304733\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.62547	+	0.938463i	0.0624717	+	0.0360681i	0.530911	−	0.847428i	$-0.321850\pi$
$677$	1.62547	+	0.938463i	0.0624717	+	0.0360681i	−0.468439	+	0.883496i	$0.655183\pi$
$678$		0			0
$679$	0.113498	−	0.0655282i	0.00435566	−	0.00251474i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−25.5634			−0.978157			−0.489078	−	0.872240i	$-0.662667\pi$
$683$	−25.5634			−0.978157			−0.489078	+	0.872240i	$0.662667\pi$
$684$		0			0
$685$	−2.33377			−0.0891687
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−35.1024	+	20.2664i	−1.33729	+	0.772087i
$690$		0			0
$691$	26.6721	+	15.3992i	1.01466	+	0.585811i	0.912551	−	0.408962i	$-0.134109\pi$
$691$	26.6721	+	15.3992i	1.01466	+	0.585811i	0.102104	+	0.994774i	$0.467443\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.659244	−	1.14184i	0.0250066	−	0.0433126i
$696$		0			0
$697$	−12.7788	−	22.1335i	−0.484031	−	0.838367i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			26.4594i			0.999356i	0.866211	+	0.499678i	$0.166548\pi$
$701$			26.4594i			0.999356i	−0.866211	+	0.499678i	$0.833452\pi$
$702$		0			0
$703$		−	9.48851i		−	0.357866i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.17219	−	2.03030i	−0.0440848	−	0.0763572i
$708$		0			0
$709$	6.22853	−	10.7881i	0.233917	−	0.405157i	−0.725040	−	0.688707i	$-0.758179\pi$
$709$	6.22853	−	10.7881i	0.233917	−	0.405157i	0.958958	+	0.283550i	$0.0915121\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−46.3281	−	26.7476i	−1.73500	−	1.00170i
$714$		0			0
$715$	−2.64511	+	1.52716i	−0.0989217	+	0.0571125i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	10.9461			0.408222			0.204111	−	0.978948i	$-0.434570\pi$
$719$	10.9461			0.408222			0.204111	+	0.978948i	$0.434570\pi$
$720$		0			0
$721$	−2.81256			−0.104745
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−24.3275	+	14.0455i	−0.903502	+	0.521637i
$726$		0			0
$727$	41.4945	+	23.9569i	1.53895	+	0.888511i	0.998901	+	0.0468743i	$0.0149260\pi$
$727$	41.4945	+	23.9569i	1.53895	+	0.888511i	0.540045	+	0.841636i	$0.318407\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.25564	−	7.37098i	0.157401	−	0.272626i
$732$		0			0
$733$	0.392838	+	0.680415i	0.0145098	+	0.0251317i	0.873189	−	0.487382i	$-0.162048\pi$
$733$	0.392838	+	0.680415i	0.0145098	+	0.0251317i	−0.858679	+	0.512513i	$0.828715\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	60.6015i		−	2.23228i
$738$		0			0
$739$		−	34.1281i		−	1.25542i	−0.778446	−	0.627711i	$-0.783992\pi$
$739$		−	34.1281i		−	1.25542i	0.778446	−	0.627711i	$-0.216008\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−20.1056	−	34.8239i	−0.737603	−	1.27757i	−0.953572	−	0.301165i	$-0.902624\pi$
$743$	−20.1056	−	34.8239i	−0.737603	−	1.27757i	0.215969	−	0.976400i	$-0.430709\pi$
$744$		0			0
$745$	−1.55984	+	2.70172i	−0.0571481	+	0.0989835i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−4.96057	−	2.86399i	−0.181255	−	0.104648i
$750$		0			0
$751$	−1.65200	+	0.953783i	−0.0602824	+	0.0348040i	−0.529838	−	0.848099i	$-0.677747\pi$
$751$	−1.65200	+	0.953783i	−0.0602824	+	0.0348040i	0.469556	+	0.882903i	$0.344414\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.99814			0.109113
$756$		0			0
$757$	24.7403			0.899201			0.449600	−	0.893230i	$-0.351566\pi$
$757$	24.7403			0.899201			0.449600	+	0.893230i	$0.351566\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	21.8526	−	12.6166i	0.792158	−	0.457353i	−0.0485638	−	0.998820i	$-0.515464\pi$
$761$	21.8526	−	12.6166i	0.792158	−	0.457353i	0.840722	+	0.541468i	$0.182131\pi$
$762$		0			0
$763$	−4.12607	−	2.38219i	−0.149374	−	0.0862410i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.08047	+	8.79963i	−0.183445	+	0.317736i
$768$		0			0
$769$	−20.2057	−	34.9973i	−0.728636	−	1.26203i	−0.957460	−	0.288566i	$-0.906821\pi$
$769$	−20.2057	−	34.9973i	−0.728636	−	1.26203i	0.228824	−	0.973468i	$-0.426512\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			37.0731i			1.33343i	0.745314	+	0.666714i	$0.232300\pi$
$773$			37.0731i			1.33343i	−0.745314	+	0.666714i	$0.767700\pi$
$774$		0			0
$775$		−	49.0479i		−	1.76185i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.31418	−	7.47238i	−0.154571	−	0.267726i
$780$		0			0
$781$	5.02807	−	8.70888i	0.179919	−	0.311628i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.24550	−	0.719091i	−0.0444539	−	0.0256655i
$786$		0			0
$787$	22.5009	−	12.9909i	0.802072	−	0.463076i	−0.0421234	−	0.999112i	$-0.513412\pi$
$787$	22.5009	−	12.9909i	0.802072	−	0.463076i	0.844195	+	0.536036i	$0.180079\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	3.29002			0.116980
$792$		0			0
$793$	−35.1507			−1.24824
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.84705	+	4.53050i	−0.277957	+	0.160479i	−0.632498	−	0.774562i	$-0.717970\pi$
$797$	−7.84705	+	4.53050i	−0.277957	+	0.160479i	0.354541	+	0.935040i	$0.384637\pi$
$798$		0			0
$799$	−6.03549	−	3.48459i	−0.213520	−	0.123276i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	10.3600	−	17.9441i	0.365597	−	0.633233i
$804$		0			0
$805$	−0.170643	−	0.295561i	−0.00601436	−	0.0104172i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			25.2651i			0.888274i	0.895959	+	0.444137i	$0.146490\pi$
$809$			25.2651i			0.888274i	−0.895959	+	0.444137i	$0.853510\pi$
$810$		0			0
$811$		−	4.43725i		−	0.155813i	−0.996961	−	0.0779064i	$-0.975176\pi$
$811$		−	4.43725i		−	0.155813i	0.996961	−	0.0779064i	$-0.0248235\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.07307	−	1.85862i	−0.0375881	−	0.0651045i
$816$		0			0
$817$	1.43672	−	2.48848i	0.0502646	−	0.0870608i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−14.2690	−	8.23820i	−0.497991	−	0.287515i	0.229893	−	0.973216i	$-0.426163\pi$
$821$	−14.2690	−	8.23820i	−0.497991	−	0.287515i	−0.727883	+	0.685701i	$0.759496\pi$
$822$		0			0
$823$	25.6912	−	14.8328i	0.895540	−	0.517040i	0.0197897	−	0.999804i	$-0.493700\pi$
$823$	25.6912	−	14.8328i	0.895540	−	0.517040i	0.875751	+	0.482764i	$0.160367\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−49.6179			−1.72538			−0.862692	−	0.505730i	$-0.831223\pi$
$827$	−49.6179			−1.72538			−0.862692	+	0.505730i	$0.831223\pi$
$828$		0			0
$829$	21.6521			0.752009			0.376004	−	0.926618i	$-0.377298\pi$
$829$	21.6521			0.752009			0.376004	+	0.926618i	$0.377298\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−16.8183	+	9.71004i	−0.582719	+	0.336433i
$834$		0			0
$835$	1.48167	+	0.855441i	0.0512752	+	0.0296038i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.7930	−	27.3543i	0.545235	−	0.944375i	−0.453357	−	0.891329i	$-0.649774\pi$
$839$	15.7930	−	27.3543i	0.545235	−	0.944375i	0.998592	−	0.0530461i	$-0.0168930\pi$
$840$		0			0
$841$	1.43672	+	2.48848i	0.0495422	+	0.0858096i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			0.836154i			0.0287646i
$846$		0			0
$847$			3.99090i			0.137129i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	26.8499	+	46.5054i	0.920403	+	1.59418i
$852$		0			0
$853$	4.33029	−	7.50029i	0.148266	−	0.256805i	−0.782320	−	0.622876i	$-0.785964\pi$
$853$	4.33029	−	7.50029i	0.148266	−	0.256805i	0.930587	+	0.366071i	$0.119297\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−25.6931	−	14.8339i	−0.877658	−	0.506716i	−0.00777246	−	0.999970i	$-0.502474\pi$
$857$	−25.6931	−	14.8339i	−0.877658	−	0.506716i	−0.869885	+	0.493254i	$0.835807\pi$
$858$		0			0
$859$	41.4164	−	23.9118i	1.41311	−	0.815859i	0.417429	−	0.908709i	$-0.362931\pi$
$859$	41.4164	−	23.9118i	1.41311	−	0.815859i	0.995680	+	0.0928504i	$0.0295978\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	35.2409			1.19961			0.599807	−	0.800144i	$-0.295244\pi$
$863$	35.2409			1.19961			0.599807	+	0.800144i	$0.295244\pi$
$864$		0			0
$865$	−3.08992			−0.105060
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−13.0132	+	7.51318i	−0.441443	+	0.254867i
$870$		0			0
$871$	−49.1989	−	28.4050i	−1.66704	−	0.962467i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.313677	−	0.543305i	0.0106042	−	0.0183671i
$876$		0			0
$877$	9.49592	+	16.4474i	0.320654	+	0.555390i	0.980623	−	0.195903i	$-0.0627638\pi$
$877$	9.49592	+	16.4474i	0.320654	+	0.555390i	−0.659969	+	0.751293i	$0.729431\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	54.0736i		−	1.82178i	−0.412644	−	0.910892i	$-0.635395\pi$
$881$		−	54.0736i		−	1.82178i	0.412644	−	0.910892i	$-0.364605\pi$
$882$		0			0
$883$		−	32.2679i		−	1.08590i	−0.839764	−	0.542951i	$-0.817307\pi$
$883$		−	32.2679i		−	1.08590i	0.839764	−	0.542951i	$-0.182693\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.01404	−	12.1487i	−0.235508	−	0.407913i	0.723912	−	0.689892i	$-0.242342\pi$
$887$	−7.01404	−	12.1487i	−0.235508	−	0.407913i	−0.959420	+	0.281980i	$0.909009\pi$
$888$		0			0
$889$	−3.16228	+	5.47724i	−0.106060	+	0.183701i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.03761	−	1.17641i	−0.0681860	−	0.0393672i
$894$		0			0
$895$	0.366246	−	0.211452i	0.0122423	−	0.00706807i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−55.6521			−1.85610
$900$		0			0
$901$	26.8661			0.895040
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.00758171	−	0.00437730i	0.000252025	−	0.000145507i
$906$		0			0
$907$	17.0198	+	9.82640i	0.565134	+	0.326280i	0.755204	−	0.655490i	$-0.227538\pi$
$907$	17.0198	+	9.82640i	0.565134	+	0.326280i	−0.190070	+	0.981771i	$0.560871\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−7.57865	+	13.1266i	−0.251092	+	0.434904i	−0.963827	−	0.266530i	$-0.914123\pi$
$911$	−7.57865	+	13.1266i	−0.251092	+	0.434904i	0.712735	+	0.701434i	$0.247456\pi$
$912$		0			0
$913$	−3.71356	−	6.43208i	−0.122901	−	0.212871i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			8.23442i			0.271924i
$918$		0			0
$919$			42.4353i			1.39981i	0.714236	+	0.699905i	$0.246774\pi$
$919$			42.4353i			1.39981i	−0.714236	+	0.699905i	$0.753226\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.71349	−	8.16401i	−0.155147	−	0.268722i
$924$		0			0
$925$	−24.6178	+	42.6392i	−0.809427	+	1.40197i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−41.1480	−	23.7568i	−1.35002	−	0.779435i	−0.361770	−	0.932267i	$-0.617827\pi$
$929$	−41.1480	−	23.7568i	−1.35002	−	0.779435i	−0.988252	+	0.152832i	$0.951161\pi$
$930$		0			0
$931$	−5.67793	+	3.27815i	−0.186087	+	0.107437i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.02448			0.0662075
$936$		0			0
$937$	−25.9106			−0.846462			−0.423231	−	0.906022i	$-0.639104\pi$
$937$	−25.9106			−0.846462			−0.423231	+	0.906022i	$0.639104\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	26.9910	−	15.5833i	0.879882	−	0.508000i	0.00926245	−	0.999957i	$-0.497052\pi$
$941$	26.9910	−	15.5833i	0.879882	−	0.508000i	0.870619	+	0.491957i	$0.163718\pi$
$942$		0			0
$943$	42.2896	+	24.4159i	1.37714	+	0.795091i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	8.56333	−	14.8321i	0.278271	−	0.481979i	−0.692684	−	0.721241i	$-0.743572\pi$
$947$	8.56333	−	14.8321i	0.278271	−	0.481979i	0.970955	+	0.239262i	$0.0769054\pi$
$948$		0			0
$949$	−9.71185	−	16.8214i	−0.315260	−	0.546046i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			5.85610i			0.189698i	0.995492	+	0.0948489i	$0.0302368\pi$
$953$			5.85610i			0.189698i	−0.995492	+	0.0948489i	$0.969763\pi$
$954$		0			0
$955$		−	3.23738i		−	0.104759i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	3.01819	+	5.22766i	0.0974626	+	0.168810i
$960$		0			0
$961$	33.0853	−	57.3054i	1.06727	−	1.84856i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.57001	−	0.906445i	−0.0505404	−	0.0291795i
$966$		0			0
$967$	−29.0101	+	16.7490i	−0.932903	+	0.538612i	−0.887728	−	0.460368i	$-0.847718\pi$
$967$	−29.0101	+	16.7490i	−0.932903	+	0.538612i	−0.0451742	+	0.998979i	$0.514384\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	15.6302			0.501596			0.250798	−	0.968039i	$-0.419307\pi$
$971$	15.6302			0.501596			0.250798	+	0.968039i	$0.419307\pi$
$972$		0			0
$973$	−3.41033			−0.109330
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.7594	+	7.36663i	−0.408209	+	0.235679i	−0.690020	−	0.723791i	$-0.742398\pi$
$977$	−12.7594	+	7.36663i	−0.408209	+	0.235679i	0.281811	+	0.959470i	$0.409065\pi$
$978$		0			0
$979$	37.4451	+	21.6189i	1.19675	+	0.690944i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−20.7082	+	35.8676i	−0.660488	+	1.14400i	0.320000	+	0.947418i	$0.396317\pi$
$983$	−20.7082	+	35.8676i	−0.660488	+	1.14400i	−0.980488	+	0.196581i	$0.937016\pi$
$984$		0			0
$985$	−0.441032	−	0.763890i	−0.0140525	−	0.0243396i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			16.2621i			0.517106i
$990$		0			0
$991$		−	23.1798i		−	0.736331i	−0.929760	−	0.368166i	$-0.879986\pi$
$991$		−	23.1798i		−	0.736331i	0.929760	−	0.368166i	$-0.120014\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.805858	−	1.39579i	−0.0255474	−	0.0442494i
$996$		0			0
$997$	9.17878	−	15.8981i	0.290695	−	0.503498i	−0.683279	−	0.730157i	$-0.739447\pi$
$997$	9.17878	−	15.8981i	0.290695	−	0.503498i	0.973974	+	0.226659i	$0.0727802\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.s.a.575.5		24
3.2	odd	2		288.2.s.a.191.12	yes	24
4.3	odd	2	inner	864.2.s.a.575.6		24
8.3	odd	2		1728.2.s.g.575.8		24
8.5	even	2		1728.2.s.g.575.7		24
9.2	odd	6		2592.2.c.c.2591.12		24
9.4	even	3		288.2.s.a.95.1	✓	24
9.5	odd	6	inner	864.2.s.a.287.6		24
9.7	even	3		2592.2.c.c.2591.14		24
12.11	even	2		288.2.s.a.191.1	yes	24
24.5	odd	2		576.2.s.g.191.1		24
24.11	even	2		576.2.s.g.191.12		24
36.7	odd	6		2592.2.c.c.2591.13		24
36.11	even	6		2592.2.c.c.2591.11		24
36.23	even	6	inner	864.2.s.a.287.5		24
36.31	odd	6		288.2.s.a.95.12	yes	24
72.5	odd	6		1728.2.s.g.1151.8		24
72.11	even	6		5184.2.c.m.5183.13		24
72.13	even	6		576.2.s.g.383.12		24
72.29	odd	6		5184.2.c.m.5183.14		24
72.43	odd	6		5184.2.c.m.5183.11		24
72.59	even	6		1728.2.s.g.1151.7		24
72.61	even	6		5184.2.c.m.5183.12		24
72.67	odd	6		576.2.s.g.383.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.s.a.95.1	✓	24	9.4	even	3
288.2.s.a.95.12	yes	24	36.31	odd	6
288.2.s.a.191.1	yes	24	12.11	even	2
288.2.s.a.191.12	yes	24	3.2	odd	2
576.2.s.g.191.1		24	24.5	odd	2
576.2.s.g.191.12		24	24.11	even	2
576.2.s.g.383.1		24	72.67	odd	6
576.2.s.g.383.12		24	72.13	even	6
864.2.s.a.287.5		24	36.23	even	6	inner
864.2.s.a.287.6		24	9.5	odd	6	inner
864.2.s.a.575.5		24	1.1	even	1	trivial
864.2.s.a.575.6		24	4.3	odd	2	inner
1728.2.s.g.575.7		24	8.5	even	2
1728.2.s.g.575.8		24	8.3	odd	2
1728.2.s.g.1151.7		24	72.59	even	6
1728.2.s.g.1151.8		24	72.5	odd	6
2592.2.c.c.2591.11		24	36.11	even	6
2592.2.c.c.2591.12		24	9.2	odd	6
2592.2.c.c.2591.13		24	36.7	odd	6
2592.2.c.c.2591.14		24	9.7	even	3
5184.2.c.m.5183.11		24	72.43	odd	6
5184.2.c.m.5183.12		24	72.61	even	6
5184.2.c.m.5183.13		24	72.11	even	6
5184.2.c.m.5183.14		24	72.29	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.135038 - 0.0779642i) q^{5} +(-0.349281 - 0.201658i) q^{7} +O(q^{10})\)	\(q+(0.135038 - 0.0779642i) q^{5} +(-0.349281 - 0.201658i) q^{7} +(-2.28556 + 3.95871i) q^{11} +(2.14257 + 3.71104i) q^{13} -2.84030i q^{17} -0.958898i q^{19} +(2.71342 + 4.69978i) q^{23} +(-2.48784 + 4.30907i) q^{25} +(4.88928 + 2.82283i) q^{29} +(-8.53685 + 4.92876i) q^{31} -0.0628883 q^{35} +9.89523 q^{37} +(7.79267 - 4.49910i) q^{41} +(2.59514 + 1.49831i) q^{43} +(1.22684 - 2.12495i) q^{47} +(-3.41867 - 5.92131i) q^{49} +9.45890i q^{53} +0.712769i q^{55} +(1.18560 + 2.05352i) q^{59} +(-4.10147 + 7.10395i) q^{61} +(0.578657 + 0.334088i) q^{65} +(-11.4813 + 6.62872i) q^{67} -2.19993 q^{71} -4.53280 q^{73} +(1.59661 - 0.921804i) q^{77} +(2.84683 + 1.64362i) q^{79} +(-0.812395 + 1.40711i) q^{83} +(-0.221442 - 0.383548i) q^{85} -9.45890i q^{89} -1.72826i q^{91} +(-0.0747597 - 0.129488i) q^{95} +(-0.162474 + 0.281413i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 12 q^{25} - 24 q^{29} + 36 q^{41} + 12 q^{49} + 48 q^{65} + 24 q^{73} + 48 q^{77} + 12 q^{97}+O(q^{100}) \) 24 * q + 12 * q^25 - 24 * q^29 + 36 * q^41 + 12 * q^49 + 48 * q^65 + 24 * q^73 + 48 * q^77 + 12 * q^97

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