LMFDB - Embedded newform 864.2.s.a.287.1

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			287.1
Character	$\chi$	$=$	864.287
Dual form			864.2.s.a.575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.40926 - 1.96834i) q^{5} +(-0.961325 + 0.555021i) q^{7} +O(q^{10})$	$q+(-3.40926 - 1.96834i) q^{5} +(-0.961325 + 0.555021i) q^{7} +(1.63301 + 2.82846i) q^{11} +(0.124912 - 0.216355i) q^{13} +5.86838i q^{17} -2.19827i q^{19} +(2.79320 - 4.83797i) q^{23} +(5.24871 + 9.09103i) q^{25} +(-2.35571 + 1.36007i) q^{29} +(8.96997 + 5.17882i) q^{31} +4.36988 q^{35} -0.333076 q^{37} +(5.28400 + 3.05072i) q^{41} +(8.50982 - 4.91315i) q^{43} +(4.70740 + 8.15346i) q^{47} +(-2.88390 + 4.99507i) q^{49} +4.75157i q^{53} -12.8573i q^{55} +(-3.26523 + 5.65555i) q^{59} +(1.07336 + 1.85911i) q^{61} +(-0.851719 + 0.491740i) q^{65} +(-0.501168 - 0.289349i) q^{67} -3.26444 q^{71} -12.6045 q^{73} +(-3.13971 - 1.81271i) q^{77} +(-7.67063 + 4.42864i) q^{79} +(-2.34056 - 4.05397i) q^{83} +(11.5510 - 20.0069i) q^{85} -4.75157i q^{89} +0.277316i q^{91} +(-4.32693 + 7.49447i) q^{95} +(0.916363 + 1.58719i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$5$	−3.40926	−	1.96834i	−1.52467	−	0.880267i	−0.999573	−	0.0292239i	$-0.990696\pi$
$5$	−3.40926	−	1.96834i	−1.52467	−	0.880267i	−0.525095	−	0.851044i	$-0.675970\pi$
$6$		0			0
$7$	−0.961325	+	0.555021i	−0.363347	+	0.209778i	−0.670548	−	0.741866i	$-0.733941\pi$
$7$	−0.961325	+	0.555021i	−0.363347	+	0.209778i	0.307201	+	0.951645i	$0.400608\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.63301	+	2.82846i	0.492372	+	0.852813i	0.999961	−	0.00878589i	$-0.00279667\pi$
$11$	1.63301	+	2.82846i	0.492372	+	0.852813i	−0.507590	+	0.861599i	$0.669463\pi$
$12$		0			0
$13$	0.124912	−	0.216355i	0.0346445	−	0.0600060i	−0.848183	−	0.529703i	$-0.822303\pi$
$13$	0.124912	−	0.216355i	0.0346445	−	0.0600060i	0.882828	+	0.469697i	$0.155637\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			5.86838i			1.42329i	0.702538	+	0.711646i	$0.252050\pi$
$17$			5.86838i			1.42329i	−0.702538	+	0.711646i	$0.747950\pi$
$18$		0			0
$19$		−	2.19827i		−	0.504317i	−0.967686	−	0.252159i	$-0.918860\pi$
$19$		−	2.19827i		−	0.504317i	0.967686	−	0.252159i	$-0.0811405\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.79320	−	4.83797i	0.582423	−	1.00879i	−0.412768	−	0.910836i	$-0.635438\pi$
$23$	2.79320	−	4.83797i	0.582423	−	1.00879i	0.995191	−	0.0979508i	$-0.0312288\pi$
$24$		0			0
$25$	5.24871	+	9.09103i	1.04974	+	1.81821i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.35571	+	1.36007i	−0.437445	+	0.252559i	−0.702513	−	0.711671i	$-0.747939\pi$
$29$	−2.35571	+	1.36007i	−0.437445	+	0.252559i	0.265068	+	0.964230i	$0.414606\pi$
$30$		0			0
$31$	8.96997	+	5.17882i	1.61105	+	0.930143i	0.989126	+	0.147069i	$0.0469840\pi$
$31$	8.96997	+	5.17882i	1.61105	+	0.930143i	0.621929	+	0.783074i	$0.286349\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.36988			0.738644
$36$		0			0
$37$	−0.333076			−0.0547574			−0.0273787	−	0.999625i	$-0.508716\pi$
$37$	−0.333076			−0.0547574			−0.0273787	+	0.999625i	$0.508716\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.28400	+	3.05072i	0.825222	+	0.476442i	0.852214	−	0.523194i	$-0.175260\pi$
$41$	5.28400	+	3.05072i	0.825222	+	0.476442i	−0.0269919	+	0.999636i	$0.508593\pi$
$42$		0			0
$43$	8.50982	−	4.91315i	1.29773	−	0.749248i	0.317722	−	0.948184i	$-0.397082\pi$
$43$	8.50982	−	4.91315i	1.29773	−	0.749248i	0.980012	+	0.198936i	$0.0637486\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.70740	+	8.15346i	0.686645	+	1.18930i	0.972917	+	0.231156i	$0.0742507\pi$
$47$	4.70740	+	8.15346i	0.686645	+	1.18930i	−0.286272	+	0.958148i	$0.592416\pi$
$48$		0			0
$49$	−2.88390	+	4.99507i	−0.411986	+	0.713581i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			4.75157i			0.652678i	0.945253	+	0.326339i	$0.105815\pi$
$53$			4.75157i			0.652678i	−0.945253	+	0.326339i	$0.894185\pi$
$54$		0			0
$55$		−	12.8573i		−	1.73368i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.26523	+	5.65555i	−0.425097	+	0.736290i	−0.996430	−	0.0844287i	$-0.973093\pi$
$59$	−3.26523	+	5.65555i	−0.425097	+	0.736290i	0.571332	+	0.820719i	$0.306427\pi$
$60$		0			0
$61$	1.07336	+	1.85911i	0.137429	+	0.238034i	0.926523	−	0.376239i	$-0.122783\pi$
$61$	1.07336	+	1.85911i	0.137429	+	0.238034i	−0.789094	+	0.614273i	$0.789449\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.851719	+	0.491740i	−0.105643	+	0.0609928i
$66$		0			0
$67$	−0.501168	−	0.289349i	−0.0612274	−	0.0353497i	0.469074	−	0.883159i	$-0.344588\pi$
$67$	−0.501168	−	0.289349i	−0.0612274	−	0.0353497i	−0.530301	+	0.847809i	$0.677921\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.26444			−0.387418			−0.193709	−	0.981059i	$-0.562052\pi$
$71$	−3.26444			−0.387418			−0.193709	+	0.981059i	$0.562052\pi$
$72$		0			0
$73$	−12.6045			−1.47525			−0.737623	−	0.675213i	$-0.764052\pi$
$73$	−12.6045			−1.47525			−0.737623	+	0.675213i	$0.764052\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.13971	−	1.81271i	−0.357803	−	0.206578i
$78$		0			0
$79$	−7.67063	+	4.42864i	−0.863014	+	0.498261i	−0.865020	−	0.501737i	$-0.832695\pi$
$79$	−7.67063	+	4.42864i	−0.863014	+	0.498261i	0.00200667	+	0.999998i	$0.499361\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.34056	−	4.05397i	−0.256910	−	0.444981i	0.708502	−	0.705708i	$-0.249371\pi$
$83$	−2.34056	−	4.05397i	−0.256910	−	0.444981i	−0.965413	+	0.260727i	$0.916038\pi$
$84$		0			0
$85$	11.5510	−	20.0069i	1.25288	−	2.17005i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	4.75157i		−	0.503665i	−0.967771	−	0.251833i	$-0.918967\pi$
$89$		−	4.75157i		−	0.503665i	0.967771	−	0.251833i	$-0.0810333\pi$
$90$		0			0
$91$			0.277316i			0.0290707i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.32693	+	7.49447i	−0.443934	+	0.768916i
$96$		0			0
$97$	0.916363	+	1.58719i	0.0930426	+	0.161154i	0.908790	−	0.417254i	$-0.137007\pi$
$97$	0.916363	+	1.58719i	0.0930426	+	0.161154i	−0.815747	+	0.578408i	$0.803674\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.30824	+	4.79677i	−0.826701	+	0.477296i	−0.852722	−	0.522365i	$-0.825050\pi$
$101$	−8.30824	+	4.79677i	−0.826701	+	0.477296i	0.0260209	+	0.999661i	$0.491716\pi$
$102$		0			0
$103$	−0.338016	−	0.195154i	−0.0333057	−	0.0192291i	0.483255	−	0.875480i	$-0.339455\pi$
$103$	−0.338016	−	0.195154i	−0.0333057	−	0.0192291i	−0.516560	+	0.856251i	$0.672788\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.67656			0.742121			0.371060	−	0.928609i	$-0.378994\pi$
$107$	7.67656			0.742121			0.371060	+	0.928609i	$0.378994\pi$
$108$		0			0
$109$	−4.72961			−0.453015			−0.226507	−	0.974009i	$-0.572731\pi$
$109$	−4.72961			−0.453015			−0.226507	+	0.974009i	$0.572731\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.34715	+	3.66453i	0.597089	+	0.344730i	0.767896	−	0.640575i	$-0.221304\pi$
$113$	6.34715	+	3.66453i	0.597089	+	0.344730i	−0.170806	+	0.985305i	$0.554637\pi$
$114$		0			0
$115$	−19.0455	+	10.9959i	−1.77600	+	1.02538i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.25708	−	5.64143i	−0.298576	−	0.517149i
$120$		0			0
$121$	0.166538	−	0.288453i	0.0151398	−	0.0262230i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	21.6415i		−	1.93568i
$126$		0			0
$127$		−	0.116971i		−	0.0103795i	−0.999987	−	0.00518973i	$-0.998348\pi$
$127$		−	0.116971i		−	0.0103795i	0.999987	−	0.00518973i	$-0.00165195\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.95887	+	3.39286i	−0.171147	+	0.296436i	−0.938821	−	0.344405i	$-0.888081\pi$
$131$	−1.95887	+	3.39286i	−0.171147	+	0.296436i	0.767674	+	0.640841i	$0.221414\pi$
$132$		0			0
$133$	1.22009	+	2.11325i	0.105795	+	0.183242i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.43350	−	3.71438i	0.549651	−	0.317341i	−0.199330	−	0.979932i	$-0.563877\pi$
$137$	6.43350	−	3.71438i	0.549651	−	0.317341i	0.748981	+	0.662591i	$0.230543\pi$
$138$		0			0
$139$	12.9406	+	7.47128i	1.09761	+	0.633706i	0.935592	−	0.353082i	$-0.114866\pi$
$139$	12.9406	+	7.47128i	1.09761	+	0.633706i	0.162018	+	0.986788i	$0.448200\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.815935			0.0682319
$144$		0			0
$145$	10.7083			0.889278
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.47576	−	0.852029i	−0.120899	−	0.0698010i	0.438331	−	0.898814i	$-0.355570\pi$
$149$	−1.47576	−	0.852029i	−0.120899	−	0.0698010i	−0.559230	+	0.829013i	$0.688903\pi$
$150$		0			0
$151$	5.20887	−	3.00734i	0.423892	−	0.244734i	−0.272849	−	0.962057i	$-0.587966\pi$
$151$	5.20887	−	3.00734i	0.423892	−	0.244734i	0.696741	+	0.717323i	$0.254633\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−20.3873	−	35.3119i	−1.63755	−	2.83632i
$156$		0			0
$157$	−2.92863	+	5.07254i	−0.233731	+	0.404833i	−0.958903	−	0.283734i	$-0.908427\pi$
$157$	−2.92863	+	5.07254i	−0.233731	+	0.404833i	0.725172	+	0.688567i	$0.241760\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			6.20115i			0.488719i
$162$		0			0
$163$			4.27956i			0.335201i	0.985855	+	0.167601i	$0.0536019\pi$
$163$			4.27956i			0.335201i	−0.985855	+	0.167601i	$0.946398\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.31473	−	16.1336i	0.720795	−	1.24845i	−0.239886	−	0.970801i	$-0.577110\pi$
$167$	9.31473	−	16.1336i	0.720795	−	1.24845i	0.960681	−	0.277653i	$-0.0895565\pi$
$168$		0			0
$169$	6.46879	+	11.2043i	0.497600	+	0.861868i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.63503	−	4.40809i	0.580481	−	0.335141i	−0.180844	−	0.983512i	$-0.557883\pi$
$173$	7.63503	−	4.40809i	0.580481	−	0.335141i	0.761325	+	0.648371i	$0.224549\pi$
$174$		0			0
$175$	−10.0914	−	5.82629i	−0.762840	−	0.440426i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.21764			0.464728			0.232364	−	0.972629i	$-0.425354\pi$
$179$	6.21764			0.464728			0.232364	+	0.972629i	$0.425354\pi$
$180$		0			0
$181$	−20.6618			−1.53578			−0.767888	−	0.640584i	$-0.778692\pi$
$181$	−20.6618			−1.53578			−0.767888	+	0.640584i	$0.778692\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.13554	+	0.655607i	0.0834869	+	0.0482012i
$186$		0			0
$187$	−16.5985	+	9.58315i	−1.21380	+	0.700789i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.87216	+	11.9029i	0.497252	+	0.861266i	0.999995	−	0.00317001i	$-0.00100905\pi$
$191$	6.87216	+	11.9029i	0.497252	+	0.861266i	−0.502743	+	0.864436i	$0.667676\pi$
$192$		0			0
$193$	8.58105	−	14.8628i	0.617678	−	1.06985i	−0.372231	−	0.928140i	$-0.621407\pi$
$193$	8.58105	−	14.8628i	0.617678	−	1.06985i	0.989908	−	0.141709i	$-0.0452597\pi$
$194$		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
$199$			10.8015i			0.765700i	0.923811	+	0.382850i	$0.125057\pi$
$199$			10.8015i			0.765700i	−0.923811	+	0.382850i	$0.874943\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.50974	−	2.61494i	0.105963	−	0.183533i
$204$		0			0
$205$	−12.0097	−	20.8014i	−0.838793	−	1.45283i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.21771	−	3.58980i	0.430088	−	0.248312i
$210$		0			0
$211$	6.44593	+	3.72156i	0.443756	+	0.256203i	0.705190	−	0.709019i	$-0.250862\pi$
$211$	6.44593	+	3.72156i	0.443756	+	0.256203i	−0.261433	+	0.965221i	$0.584195\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−38.6829			−2.63815
$216$		0			0
$217$	−11.4974			−0.780495
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.26965	+	0.733035i	0.0854061	+	0.0493092i
$222$		0			0
$223$	−18.5665	+	10.7194i	−1.24330	+	0.717822i	−0.969765	−	0.244040i	$-0.921527\pi$
$223$	−18.5665	+	10.7194i	−1.24330	+	0.717822i	−0.273538	+	0.961861i	$0.588194\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.3957	+	23.2020i	0.889104	+	1.53997i	0.840937	+	0.541134i	$0.182005\pi$
$227$	13.3957	+	23.2020i	0.889104	+	1.53997i	0.0481672	+	0.998839i	$0.484662\pi$
$228$		0			0
$229$	0.0416257	−	0.0720978i	0.00275070	−	0.00476436i	−0.864647	−	0.502380i	$-0.832458\pi$
$229$	0.0416257	−	0.0720978i	0.00275070	−	0.00476436i	0.867397	+	0.497616i	$0.165791\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	9.29262i		−	0.608780i	−0.952548	−	0.304390i	$-0.901547\pi$
$233$		−	9.29262i		−	0.608780i	0.952548	−	0.304390i	$-0.0984526\pi$
$234$		0			0
$235$		−	37.0630i		−	2.41773i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.54478	−	13.0679i	0.488031	−	0.845294i	−0.511874	−	0.859060i	$-0.671049\pi$
$239$	7.54478	−	13.0679i	0.488031	−	0.845294i	0.999905	+	0.0137660i	$0.00438198\pi$
$240$		0			0
$241$	−12.0192	−	20.8179i	−0.774227	−	1.34100i	−0.935228	−	0.354046i	$-0.884806\pi$
$241$	−12.0192	−	20.8179i	−0.774227	−	1.34100i	0.161001	−	0.986954i	$-0.448528\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	19.6640	−	11.3530i	1.25628	−	0.725316i
$246$		0			0
$247$	−0.475606	−	0.274591i	−0.0302621	−	0.0174718i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−18.4712			−1.16589			−0.582947	−	0.812510i	$-0.698101\pi$
$251$	−18.4712			−1.16589			−0.582947	+	0.812510i	$0.698101\pi$
$252$		0			0
$253$	18.2454			1.14708
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−16.5839	−	9.57471i	−1.03447	−	0.597254i	−0.116211	−	0.993225i	$-0.537075\pi$
$257$	−16.5839	−	9.57471i	−1.03447	−	0.597254i	−0.918263	+	0.395971i	$0.870408\pi$
$258$		0			0
$259$	0.320195	−	0.184864i	0.0198959	−	0.0114869i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.89930	+	3.28969i	0.117116	+	0.202851i	0.918624	−	0.395134i	$-0.129302\pi$
$263$	1.89930	+	3.28969i	0.117116	+	0.202851i	−0.801508	+	0.597984i	$0.795968\pi$
$264$		0			0
$265$	9.35270	−	16.1993i	0.574532	−	0.995118i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			22.0593i			1.34498i	0.740106	+	0.672490i	$0.234775\pi$
$269$			22.0593i			1.34498i	−0.740106	+	0.672490i	$0.765225\pi$
$270$		0			0
$271$			16.7153i			1.01538i	0.861540	+	0.507690i	$0.169501\pi$
$271$			16.7153i			1.01538i	−0.861540	+	0.507690i	$0.830499\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−17.1424	+	29.6915i	−1.03373	+	1.79047i
$276$		0			0
$277$	9.25752	+	16.0345i	0.556231	+	0.963420i	0.997807	+	0.0661959i	$0.0210862\pi$
$277$	9.25752	+	16.0345i	0.556231	+	0.963420i	−0.441576	+	0.897224i	$0.645580\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.39881	+	2.53965i	−0.262411	+	0.151503i	−0.625434	−	0.780277i	$-0.715078\pi$
$281$	−4.39881	+	2.53965i	−0.262411	+	0.151503i	0.363023	+	0.931780i	$0.381745\pi$
$282$		0			0
$283$	−19.8035	−	11.4336i	−1.17720	−	0.679656i	−0.221834	−	0.975085i	$-0.571204\pi$
$283$	−19.8035	−	11.4336i	−1.17720	−	0.679656i	−0.955365	+	0.295429i	$0.904538\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.77285			−0.399789
$288$		0			0
$289$	−17.4379			−1.02576
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.160276	+	0.0925356i	0.00936344	+	0.00540599i	0.504674	−	0.863310i	$-0.331613\pi$
$293$	0.160276	+	0.0925356i	0.00936344	+	0.00540599i	−0.495311	+	0.868716i	$0.664946\pi$
$294$		0			0
$295$	22.2641	−	12.8542i	1.29626	−	0.748399i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.697812	−	1.20865i	−0.0403555	−	0.0698978i
$300$		0			0
$301$	−5.45380	+	9.44626i	−0.314352	+	0.544473i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	8.45090i		−	0.483897i
$306$		0			0
$307$			18.7966i			1.07278i	0.843971	+	0.536388i	$0.180212\pi$
$307$			18.7966i			1.07278i	−0.843971	+	0.536388i	$0.819788\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.65208	+	6.32560i	−0.207091	+	0.358692i	−0.950797	−	0.309815i	$-0.899733\pi$
$311$	−3.65208	+	6.32560i	−0.207091	+	0.358692i	0.743706	+	0.668507i	$0.233066\pi$
$312$		0			0
$313$	−11.2472	−	19.4808i	−0.635732	−	1.10112i	−0.986360	−	0.164605i	$-0.947365\pi$
$313$	−11.2472	−	19.4808i	−0.635732	−	1.10112i	0.350628	−	0.936515i	$-0.385968\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.95052	+	5.16758i	−0.502711	+	0.290240i	−0.729832	−	0.683626i	$-0.760402\pi$
$317$	−8.95052	+	5.16758i	−0.502711	+	0.290240i	0.227121	+	0.973866i	$0.427069\pi$
$318$		0			0
$319$	−7.69382	−	4.44203i	−0.430771	−	0.248706i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	12.9003			0.717791
$324$		0			0
$325$	2.62252			0.145471
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−9.05069	−	5.22542i	−0.498981	−	0.288087i
$330$		0			0
$331$	24.6744	−	14.2458i	1.35623	−	0.783018i	0.367114	−	0.930176i	$-0.380346\pi$
$331$	24.6744	−	14.2458i	1.35623	−	0.783018i	0.989113	+	0.147158i	$0.0470125\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.13907	+	1.97294i	0.0622343	+	0.107793i
$336$		0			0
$337$	−11.7179	+	20.2959i	−0.638312	+	1.10559i	0.347491	+	0.937683i	$0.387034\pi$
$337$	−11.7179	+	20.2959i	−0.638312	+	1.10559i	−0.985803	+	0.167906i	$0.946300\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			33.8283i			1.83191i
$342$		0			0
$343$		−	14.1728i		−	0.765260i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.9531	−	18.9714i	0.587995	−	1.01844i	−0.406500	−	0.913651i	$-0.633251\pi$
$347$	10.9531	−	18.9714i	0.587995	−	1.01844i	0.994495	−	0.104786i	$-0.0334159\pi$
$348$		0			0
$349$	14.4261	+	24.9867i	0.772209	+	1.33750i	0.936350	+	0.351068i	$0.114181\pi$
$349$	14.4261	+	24.9867i	0.772209	+	1.33750i	−0.164141	+	0.986437i	$0.552485\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.24937	−	4.18543i	0.385845	−	0.222768i	−0.294513	−	0.955647i	$-0.595158\pi$
$353$	7.24937	−	4.18543i	0.385845	−	0.222768i	0.680358	+	0.732880i	$0.261824\pi$
$354$		0			0
$355$	11.1293	+	6.42553i	0.590684	+	0.341032i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	35.2621			1.86106			0.930532	−	0.366210i	$-0.119345\pi$
$359$	35.2621			1.86106			0.930532	+	0.366210i	$0.119345\pi$
$360$		0			0
$361$	14.1676			0.745664
$362$		0			0
$363$		0			0
$364$		0			0
$365$	42.9721	+	24.8099i	2.24926	+	1.29861i
$366$		0			0
$367$	5.56938	−	3.21548i	0.290719	−	0.167847i	−0.347547	−	0.937663i	$-0.612985\pi$
$367$	5.56938	−	3.21548i	0.290719	−	0.167847i	0.638266	+	0.769816i	$0.279652\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2.63722	−	4.56780i	−0.136918	−	0.237149i
$372$		0			0
$373$	−9.84241	+	17.0476i	−0.509621	+	0.882689i	0.490317	+	0.871544i	$0.336881\pi$
$373$	−9.84241	+	17.0476i	−0.509621	+	0.882689i	−0.999938	+	0.0111451i	$0.996452\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			0.679560i			0.0349991i
$378$		0			0
$379$		−	1.50534i		−	0.0773240i	−0.999252	−	0.0386620i	$-0.987690\pi$
$379$		−	1.50534i		−	0.0773240i	0.999252	−	0.0386620i	$-0.0123096\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	14.0663	−	24.3635i	0.718754	−	1.24492i	−0.242739	−	0.970092i	$-0.578046\pi$
$383$	14.0663	−	24.3635i	0.718754	−	1.24492i	0.961494	−	0.274827i	$-0.0886207\pi$
$384$		0			0
$385$	7.13607	+	12.3600i	0.363688	+	0.629926i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	13.8804	−	8.01387i	0.703766	−	0.406319i	−0.104983	−	0.994474i	$-0.533479\pi$
$389$	13.8804	−	8.01387i	0.703766	−	0.406319i	0.808748	+	0.588155i	$0.200145\pi$
$390$		0			0
$391$	28.3911	+	16.3916i	1.43580	+	0.828959i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	34.8683			1.75441
$396$		0			0
$397$	13.7725			0.691224			0.345612	−	0.938377i	$-0.387671\pi$
$397$	13.7725			0.691224			0.345612	+	0.938377i	$0.387671\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−31.5929	−	18.2402i	−1.57767	−	0.910870i	−0.995183	−	0.0980324i	$-0.968745\pi$
$401$	−31.5929	−	18.2402i	−1.57767	−	0.910870i	−0.582490	−	0.812838i	$-0.697922\pi$
$402$		0			0
$403$	2.24092	−	1.29380i	0.111628	−	0.0644487i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.543918	−	0.942094i	−0.0269610	−	0.0466978i
$408$		0			0
$409$	1.41675	−	2.45388i	0.0700537	−	0.121337i	−0.828871	−	0.559440i	$-0.811016\pi$
$409$	1.41675	−	2.45388i	0.0700537	−	0.121337i	0.898925	+	0.438103i	$0.144350\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	7.24910i		−	0.356705i
$414$		0			0
$415$			18.4281i			0.904599i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.64717	+	11.5132i	−0.324736	+	0.562458i	−0.981459	−	0.191673i	$-0.938609\pi$
$419$	−6.64717	+	11.5132i	−0.324736	+	0.562458i	0.656723	+	0.754132i	$0.271942\pi$
$420$		0			0
$421$	9.90259	+	17.1518i	0.482623	+	0.835927i	0.999801	−	0.0199505i	$-0.00635085\pi$
$421$	9.90259	+	17.1518i	0.482623	+	0.835927i	−0.517178	+	0.855878i	$0.673018\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−53.3497	+	30.8014i	−2.58784	+	1.49409i
$426$		0			0
$427$	−2.06369	−	1.19147i	−0.0998688	−	0.0576593i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−11.7886			−0.567837			−0.283919	−	0.958848i	$-0.591635\pi$
$431$	−11.7886			−0.567837			−0.283919	+	0.958848i	$0.591635\pi$
$432$		0			0
$433$	33.5993			1.61468			0.807341	−	0.590086i	$-0.200906\pi$
$433$	33.5993			1.61468			0.807341	+	0.590086i	$0.200906\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.6352	−	6.14021i	−0.508749	−	0.293726i
$438$		0			0
$439$	3.87174	−	2.23535i	0.184788	−	0.106687i	−0.404752	−	0.914426i	$-0.632642\pi$
$439$	3.87174	−	2.23535i	0.184788	−	0.106687i	0.589540	+	0.807739i	$0.299309\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.03420	−	1.79129i	−0.0491363	−	0.0851066i	0.840411	−	0.541949i	$-0.182314\pi$
$443$	−1.03420	−	1.79129i	−0.0491363	−	0.0851066i	−0.889547	+	0.456843i	$0.848980\pi$
$444$		0			0
$445$	−9.35270	+	16.1993i	−0.443360	+	0.767923i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			0.297420i			0.0140361i	0.999975	+	0.00701807i	$0.00223394\pi$
$449$			0.297420i			0.0140361i	−0.999975	+	0.00701807i	$0.997766\pi$
$450$		0			0
$451$			19.9274i			0.938347i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.545852	−	0.945444i	0.0255900	−	0.0443231i
$456$		0			0
$457$	−1.08489	−	1.87909i	−0.0507491	−	0.0879000i	0.839535	−	0.543306i	$-0.182828\pi$
$457$	−1.08489	−	1.87909i	−0.0507491	−	0.0879000i	−0.890284	+	0.455406i	$0.849494\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−35.9806	+	20.7734i	−1.67578	+	0.967514i	−0.711482	+	0.702704i	$0.751976\pi$
$461$	−35.9806	+	20.7734i	−1.67578	+	0.967514i	−0.964301	+	0.264809i	$0.914691\pi$
$462$		0			0
$463$	−16.8271	−	9.71513i	−0.782022	−	0.451501i	0.0551244	−	0.998479i	$-0.482444\pi$
$463$	−16.8271	−	9.71513i	−0.782022	−	0.451501i	−0.837146	+	0.546979i	$0.815778\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.5573			0.673630			0.336815	−	0.941571i	$-0.390650\pi$
$467$	14.5573			0.673630			0.336815	+	0.941571i	$0.390650\pi$
$468$		0			0
$469$	0.642380			0.0296624
$470$		0			0
$471$		0			0
$472$		0			0
$473$	27.7933	+	16.0465i	1.27794	+	0.737817i
$474$		0			0
$475$	19.9845	−	11.5381i	0.916952	−	0.529403i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	13.1650	+	22.8025i	0.601526	+	1.04187i	0.992590	+	0.121510i	$0.0387735\pi$
$479$	13.1650	+	22.8025i	0.601526	+	1.04187i	−0.391065	+	0.920363i	$0.627893\pi$
$480$		0			0
$481$	−0.0416054	+	0.0720627i	−0.00189704	+	0.00328577i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	7.21485i		−	0.327609i
$486$		0			0
$487$		−	21.6173i		−	0.979574i	−0.871842	−	0.489787i	$-0.837074\pi$
$487$		−	21.6173i		−	0.979574i	0.871842	−	0.489787i	$-0.162926\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−8.66258	+	15.0040i	−0.390937	+	0.677122i	−0.992573	−	0.121648i	$-0.961182\pi$
$491$	−8.66258	+	15.0040i	−0.390937	+	0.677122i	0.601637	+	0.798770i	$0.294516\pi$
$492$		0			0
$493$	−7.98143	−	13.8242i	−0.359465	−	0.622612i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.13819	−	1.81184i	0.140767	−	0.0812720i
$498$		0			0
$499$	−21.4481	−	12.3831i	−0.960148	−	0.554342i	−0.0639294	−	0.997954i	$-0.520363\pi$
$499$	−21.4481	−	12.3831i	−0.960148	−	0.554342i	−0.896219	+	0.443613i	$0.853697\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−11.4045			−0.508500			−0.254250	−	0.967139i	$-0.581829\pi$
$503$	−11.4045			−0.508500			−0.254250	+	0.967139i	$0.581829\pi$
$504$		0			0
$505$	37.7666			1.68059
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−20.3093	−	11.7256i	−0.900192	−	0.519726i	−0.0229294	−	0.999737i	$-0.507299\pi$
$509$	−20.3093	−	11.7256i	−0.900192	−	0.519726i	−0.877262	+	0.480011i	$0.840633\pi$
$510$		0			0
$511$	12.1170	−	6.99577i	0.536026	−	0.309475i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.768257	+	1.33066i	0.0338534	+	0.0586359i
$516$		0			0
$517$	−15.3745	+	26.6294i	−0.676169	+	1.17116i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	12.9913i		−	0.569160i	−0.958652	−	0.284580i	$-0.908146\pi$
$521$		−	12.9913i		−	0.569160i	0.958652	−	0.284580i	$-0.0918541\pi$
$522$		0			0
$523$			18.8040i			0.822243i	0.911581	+	0.411121i	$0.134863\pi$
$523$			18.8040i			0.822243i	−0.911581	+	0.411121i	$0.865137\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−30.3913	+	52.6393i	−1.32387	+	2.29300i
$528$		0			0
$529$	−4.10399	−	7.10832i	−0.178434	−	0.309057i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.32007	−	0.762146i	0.0571788	−	0.0330122i
$534$		0			0
$535$	−26.1714	−	15.1101i	−1.13149	−	0.653265i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−18.8378			−0.811401
$540$		0			0
$541$	−9.13908			−0.392920			−0.196460	−	0.980512i	$-0.562945\pi$
$541$	−9.13908			−0.392920			−0.196460	+	0.980512i	$0.562945\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	16.1245	+	9.30947i	0.690697	+	0.398774i
$546$		0			0
$547$	15.4148	−	8.89976i	0.659091	−	0.380526i	−0.132840	−	0.991138i	$-0.542410\pi$
$547$	15.4148	−	8.89976i	0.659091	−	0.380526i	0.791930	+	0.610611i	$0.209076\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.98980	+	5.17849i	0.127370	+	0.220611i
$552$		0			0
$553$	4.91598	−	8.51473i	0.209049	−	0.362083i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	19.4205i		−	0.822872i	−0.911439	−	0.411436i	$-0.865027\pi$
$557$		−	19.4205i		−	0.822872i	0.911439	−	0.411436i	$-0.134973\pi$
$558$		0			0
$559$		−	2.45485i		−	0.103829i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	15.2077	−	26.3406i	0.640930	−	1.11012i	−0.344295	−	0.938861i	$-0.611882\pi$
$563$	15.2077	−	26.3406i	0.640930	−	1.11012i	0.985226	−	0.171262i	$-0.0547845\pi$
$564$		0			0
$565$	−14.4261	−	24.9867i	−0.606909	−	1.05120i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.38491	+	4.84103i	−0.351514	+	0.202947i	−0.665352	−	0.746530i	$-0.731718\pi$
$569$	−8.38491	+	4.84103i	−0.351514	+	0.202947i	0.313838	+	0.949477i	$0.398385\pi$
$570$		0			0
$571$	4.98471	+	2.87792i	0.208604	+	0.120437i	0.600662	−	0.799503i	$-0.294904\pi$
$571$	4.98471	+	2.87792i	0.208604	+	0.120437i	−0.392059	+	0.919940i	$0.628237\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	58.6429			2.44558
$576$		0			0
$577$	−19.7436			−0.821936			−0.410968	−	0.911650i	$-0.634809\pi$
$577$	−19.7436			−0.821936			−0.410968	+	0.911650i	$0.634809\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4.50008	+	2.59813i	0.186695	+	0.107788i
$582$		0			0
$583$	−13.4396	+	7.75938i	−0.556613	+	0.321361i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−13.6014	−	23.5584i	−0.561392	−	0.972359i	−0.997375	−	0.0724042i	$-0.976933\pi$
$587$	−13.6014	−	23.5584i	−0.561392	−	0.972359i	0.435984	−	0.899955i	$-0.356400\pi$
$588$		0			0
$589$	11.3844	−	19.7184i	0.469087	−	0.812483i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			34.4946i			1.41652i	0.705950	+	0.708261i	$0.250520\pi$
$593$			34.4946i			1.41652i	−0.705950	+	0.708261i	$0.749480\pi$
$594$		0			0
$595$			25.6441i			1.05131i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.09709	−	5.36431i	0.126544	−	0.219180i	−0.795792	−	0.605570i	$-0.792945\pi$
$599$	3.09709	−	5.36431i	0.126544	−	0.219180i	0.922335	+	0.386391i	$0.126278\pi$
$600$		0			0
$601$	−12.8844	−	22.3164i	−0.525565	−	0.910306i	−0.999557	−	0.0297762i	$-0.990521\pi$
$601$	−12.8844	−	22.3164i	−0.525565	−	0.910306i	0.473991	−	0.880529i	$-0.342813\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.13554	+	0.655607i	−0.0461664	+	0.0266542i
$606$		0			0
$607$	37.2241	+	21.4914i	1.51088	+	0.872307i	0.999919	+	0.0127033i	$0.00404369\pi$
$607$	37.2241	+	21.4914i	1.51088	+	0.872307i	0.510961	+	0.859604i	$0.329290\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.35205			0.0951539
$612$		0			0
$613$	33.0975			1.33679			0.668397	−	0.743805i	$-0.266981\pi$
$613$	33.0975			1.33679			0.668397	+	0.743805i	$0.266981\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.02894	+	2.32611i	0.162199	+	0.0936456i	0.578902	−	0.815397i	$-0.303481\pi$
$617$	4.02894	+	2.32611i	0.162199	+	0.0936456i	−0.416703	+	0.909043i	$0.636815\pi$
$618$		0			0
$619$	6.50736	−	3.75703i	0.261553	−	0.151008i	−0.363490	−	0.931598i	$-0.618415\pi$
$619$	6.50736	−	3.75703i	0.261553	−	0.151008i	0.625043	+	0.780591i	$0.285082\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.63722	+	4.56780i	0.105658	+	0.183005i
$624$		0			0
$625$	−16.3543	+	28.3265i	−0.654173	+	1.13306i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	1.95462i		−	0.0779358i
$630$		0			0
$631$		−	41.0242i		−	1.63315i	−0.577241	−	0.816574i	$-0.695871\pi$
$631$		−	41.0242i		−	1.63315i	0.577241	−	0.816574i	$-0.304129\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.230238	+	0.398783i	−0.00913670	+	0.0158252i
$636$		0			0
$637$	0.720471	+	1.24789i	0.0285461	+	0.0494433i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	21.0962	−	12.1799i	0.833249	−	0.481076i	−0.0217149	−	0.999764i	$-0.506913\pi$
$641$	21.0962	−	12.1799i	0.833249	−	0.481076i	0.854964	+	0.518688i	$0.173579\pi$
$642$		0			0
$643$	−24.3082	−	14.0344i	−0.958623	−	0.553461i	−0.0628738	−	0.998021i	$-0.520027\pi$
$643$	−24.3082	−	14.0344i	−0.958623	−	0.553461i	−0.895749	+	0.444560i	$0.853360\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.3596			−0.721791			−0.360895	−	0.932606i	$-0.617529\pi$
$647$	−18.3596			−0.721791			−0.360895	+	0.932606i	$0.617529\pi$
$648$		0			0
$649$	−21.3287			−0.837224
$650$		0			0
$651$		0			0
$652$		0			0
$653$	35.6953	+	20.6087i	1.39687	+	0.806481i	0.994063	−	0.108806i	$-0.0347027\pi$
$653$	35.6953	+	20.6087i	1.39687	+	0.806481i	0.402803	+	0.915287i	$0.368036\pi$
$654$		0			0
$655$	13.3566	−	7.71144i	0.521886	−	0.301311i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	6.77194	+	11.7293i	0.263797	+	0.456910i	0.967248	−	0.253834i	$-0.0816917\pi$
$659$	6.77194	+	11.7293i	0.263797	+	0.456910i	−0.703451	+	0.710744i	$0.748358\pi$
$660$		0			0
$661$	−12.9871	+	22.4944i	−0.505141	+	0.874930i	0.494841	+	0.868983i	$0.335226\pi$
$661$	−12.9871	+	22.4944i	−0.505141	+	0.874930i	−0.999982	+	0.00594652i	$0.998107\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	9.60616i		−	0.372511i
$666$		0			0
$667$			15.1958i			0.588385i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.50561	+	6.07189i	−0.135332	+	0.234403i
$672$		0			0
$673$	7.20522	+	12.4798i	0.277741	+	0.481061i	0.970823	−	0.239797i	$-0.0770810\pi$
$673$	7.20522	+	12.4798i	0.277741	+	0.481061i	−0.693082	+	0.720859i	$0.743748\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	28.6445	−	16.5379i	1.10090	−	0.635604i	0.164442	−	0.986387i	$-0.447418\pi$
$677$	28.6445	−	16.5379i	1.10090	−	0.635604i	0.936457	+	0.350782i	$0.114084\pi$
$678$		0			0
$679$	−1.76185	−	1.01720i	−0.0676134	−	0.0390366i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−31.1501			−1.19193			−0.595963	−	0.803012i	$-0.703229\pi$
$683$	−31.1501			−1.19193			−0.595963	+	0.803012i	$0.703229\pi$
$684$		0			0
$685$	−29.2447			−1.11738
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.02802	+	0.593531i	0.0391646	+	0.0226117i
$690$		0			0
$691$	11.9611	−	6.90572i	0.455020	−	0.262706i	−0.254928	−	0.966960i	$-0.582052\pi$
$691$	11.9611	−	6.90572i	0.455020	−	0.262706i	0.709948	+	0.704254i	$0.248718\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−29.4120	−	50.9431i	−1.11566	−	1.93238i
$696$		0			0
$697$	−17.9028	+	31.0085i	−0.678116	+	1.17453i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			30.8782i			1.16625i	0.812381	+	0.583127i	$0.198171\pi$
$701$			30.8782i			1.16625i	−0.812381	+	0.583127i	$0.801829\pi$
$702$		0			0
$703$			0.732191i			0.0276151i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.32461	−	9.22250i	0.200253	−	0.346848i
$708$		0			0
$709$	−15.3068	−	26.5122i	−0.574861	−	0.995688i	−0.996057	−	0.0887184i	$-0.971723\pi$
$709$	−15.3068	−	26.5122i	−0.574861	−	0.995688i	0.421196	−	0.906970i	$-0.361610\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	50.1100	−	28.9310i	1.87663	−	1.08347i
$714$		0			0
$715$	−2.78173	−	1.60604i	−0.104031	−	0.0600623i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−34.2682			−1.27799			−0.638995	−	0.769211i	$-0.720649\pi$
$719$	−34.2682			−1.27799			−0.638995	+	0.769211i	$0.720649\pi$
$720$		0			0
$721$	0.433258			0.0161354
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−24.7289	−	14.2772i	−0.918409	−	0.530244i
$726$		0			0
$727$	7.19890	−	4.15628i	0.266992	−	0.154148i	−0.360528	−	0.932748i	$-0.617403\pi$
$727$	7.19890	−	4.15628i	0.266992	−	0.154148i	0.627520	+	0.778600i	$0.284070\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	28.8322	+	49.9389i	1.06640	+	1.84706i
$732$		0			0
$733$	17.6922	−	30.6438i	0.653477	−	1.13186i	−0.328796	−	0.944401i	$-0.606643\pi$
$733$	17.6922	−	30.6438i	0.653477	−	1.13186i	0.982273	−	0.187454i	$-0.0600237\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	1.89005i		−	0.0696207i
$738$		0			0
$739$		−	30.3812i		−	1.11759i	−0.829305	−	0.558795i	$-0.811264\pi$
$739$		−	30.3812i		−	1.11759i	0.829305	−	0.558795i	$-0.188736\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	17.2730	−	29.9177i	0.633684	−	1.09757i	−0.353109	−	0.935582i	$-0.614875\pi$
$743$	17.2730	−	29.9177i	0.633684	−	1.09757i	0.986792	−	0.161990i	$-0.0517912\pi$
$744$		0			0
$745$	3.35416	+	5.80958i	0.122887	+	0.212847i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−7.37967	+	4.26065i	−0.269647	+	0.155681i
$750$		0			0
$751$	−8.74633	−	5.04970i	−0.319158	−	0.184266i	0.331859	−	0.943329i	$-0.392324\pi$
$751$	−8.74633	−	5.04970i	−0.319158	−	0.184266i	−0.651017	+	0.759063i	$0.725657\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−23.6779			−0.861725
$756$		0			0
$757$	38.7446			1.40820			0.704099	−	0.710102i	$-0.251351\pi$
$757$	38.7446			1.40820			0.704099	+	0.710102i	$0.251351\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−30.7016	−	17.7256i	−1.11293	−	0.642551i	−0.173345	−	0.984861i	$-0.555457\pi$
$761$	−30.7016	−	17.7256i	−1.11293	−	0.642551i	−0.939587	+	0.342310i	$0.888791\pi$
$762$		0			0
$763$	4.54669	−	2.62504i	0.164601	−	0.0950327i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.815737	+	1.41290i	0.0294546	+	0.0510168i
$768$		0			0
$769$	17.9368	−	31.0675i	0.646818	−	1.12032i	−0.337060	−	0.941483i	$-0.609433\pi$
$769$	17.9368	−	31.0675i	0.646818	−	1.12032i	0.983878	−	0.178839i	$-0.0572341\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			0.214276i			0.00770697i	0.999993	+	0.00385349i	$0.00122661\pi$
$773$			0.214276i			0.00770697i	−0.999993	+	0.00385349i	$0.998773\pi$
$774$		0			0
$775$			108.728i			3.90564i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.70629	−	11.6156i	0.240278	−	0.416174i
$780$		0			0
$781$	−5.33088	−	9.23335i	−0.190754	−	0.330395i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	19.9690	−	11.5291i	0.712723	−	0.411491i
$786$		0			0
$787$	−29.0781	−	16.7883i	−1.03652	−	0.598437i	−0.117677	−	0.993052i	$-0.537545\pi$
$787$	−29.0781	−	16.7883i	−1.03652	−	0.598437i	−0.918847	+	0.394615i	$0.870878\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−8.13556			−0.289267
$792$		0			0
$793$	0.536302			0.0190446
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−31.1529	−	17.9861i	−1.10349	−	0.637102i	−0.166357	−	0.986066i	$-0.553200\pi$
$797$	−31.1529	−	17.9861i	−1.10349	−	0.637102i	−0.937136	+	0.348964i	$0.886534\pi$
$798$		0			0
$799$	−47.8476	+	27.6248i	−1.69273	+	0.977297i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−20.5833	−	35.6514i	−0.726370	−	1.25811i
$804$		0			0
$805$	12.2060	−	21.1414i	0.430204	−	0.745135i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			7.82300i			0.275042i	0.990499	+	0.137521i	$0.0439135\pi$
$809$			7.82300i			0.275042i	−0.990499	+	0.137521i	$0.956087\pi$
$810$		0			0
$811$			40.2969i			1.41502i	0.706705	+	0.707508i	$0.250181\pi$
$811$			40.2969i			1.41502i	−0.706705	+	0.707508i	$0.749819\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	8.42363	−	14.5902i	0.295067	−	0.511071i
$816$		0			0
$817$	−10.8004	−	18.7069i	−0.377858	−	0.654470i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	9.96043	−	5.75066i	0.347621	−	0.200699i	−0.316016	−	0.948754i	$-0.602345\pi$
$821$	9.96043	−	5.75066i	0.347621	−	0.200699i	0.663637	+	0.748055i	$0.269012\pi$
$822$		0			0
$823$	−47.2358	−	27.2716i	−1.64654	−	0.950628i	−0.978435	−	0.206557i	$-0.933774\pi$
$823$	−47.2358	−	27.2716i	−1.64654	−	0.950628i	−0.668101	−	0.744071i	$-0.732893\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	2.34342			0.0814887			0.0407443	−	0.999170i	$-0.487027\pi$
$827$	2.34342			0.0814887			0.0407443	+	0.999170i	$0.487027\pi$
$828$		0			0
$829$	15.5991			0.541778			0.270889	−	0.962611i	$-0.412682\pi$
$829$	15.5991			0.541778			0.270889	+	0.962611i	$0.412682\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−29.3130	−	16.9238i	−1.01563	−	0.586377i
$834$		0			0
$835$	−63.5127	+	36.6691i	−2.19795	+	1.26899i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.79725	+	3.11293i	0.0620481	+	0.107470i	0.895381	−	0.445301i	$-0.146903\pi$
$839$	1.79725	+	3.11293i	0.0620481	+	0.107470i	−0.833333	+	0.552772i	$0.813570\pi$
$840$		0			0
$841$	−10.8004	+	18.7069i	−0.372428	+	0.645064i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	50.9311i		−	1.75208i
$846$		0			0
$847$			0.369729i			0.0127040i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.930351	+	1.61141i	−0.0318920	+	0.0552386i
$852$		0			0
$853$	−19.1495	−	33.1679i	−0.655666	−	1.13565i	−0.981726	−	0.190298i	$-0.939055\pi$
$853$	−19.1495	−	33.1679i	−0.655666	−	1.13565i	0.326061	−	0.945349i	$-0.394279\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−26.8867	+	15.5230i	−0.918432	+	0.530257i	−0.883134	−	0.469120i	$-0.844571\pi$
$857$	−26.8867	+	15.5230i	−0.918432	+	0.530257i	−0.0352975	+	0.999377i	$0.511238\pi$
$858$		0			0
$859$	37.4925	+	21.6463i	1.27923	+	0.738562i	0.976706	−	0.214581i	$-0.0688387\pi$
$859$	37.4925	+	21.6463i	1.27923	+	0.738562i	0.302520	+	0.953143i	$0.402172\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−28.1206			−0.957237			−0.478619	−	0.878023i	$-0.658862\pi$
$863$	−28.1206			−0.957237			−0.478619	+	0.878023i	$0.658862\pi$
$864$		0			0
$865$	−34.7064			−1.18005
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−25.0525	−	14.4641i	−0.849847	−	0.490660i
$870$		0			0
$871$	−0.125204	+	0.0722867i	−0.00424238	+	0.00244934i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	12.0115	+	20.8046i	0.406064	+	0.703323i
$876$		0			0
$877$	26.7964	−	46.4127i	0.904849	−	1.56725i	0.0837301	−	0.996488i	$-0.473317\pi$
$877$	26.7964	−	46.4127i	0.904849	−	1.56725i	0.821119	−	0.570757i	$-0.193350\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	26.3409i		−	0.887449i	−0.896163	−	0.443724i	$-0.853657\pi$
$881$		−	26.3409i		−	0.887449i	0.896163	−	0.443724i	$-0.146343\pi$
$882$		0			0
$883$		−	47.8523i		−	1.61036i	−0.593032	−	0.805179i	$-0.702069\pi$
$883$		−	47.8523i		−	1.61036i	0.593032	−	0.805179i	$-0.297931\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.26690	+	16.0507i	−0.311152	+	0.538931i	−0.978612	−	0.205714i	$-0.934048\pi$
$887$	−9.26690	+	16.0507i	−0.311152	+	0.538931i	0.667460	+	0.744646i	$0.267382\pi$
$888$		0			0
$889$	0.0649212	+	0.112447i	0.00217739	+	0.00377134i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	17.9235	−	10.3481i	0.599786	−	0.346287i
$894$		0			0
$895$	−21.1976	−	12.2384i	−0.708556	−	0.409085i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−28.1743			−0.939664
$900$		0			0
$901$	−27.8840			−0.928952
$902$		0			0
$903$		0			0
$904$		0			0
$905$	70.4413	+	40.6693i	2.34155	+	1.35189i
$906$		0			0
$907$	−37.8891	+	21.8753i	−1.25809	+	0.726357i	−0.972702	−	0.232056i	$-0.925455\pi$
$907$	−37.8891	+	21.8753i	−1.25809	+	0.726357i	−0.285385	+	0.958413i	$0.592121\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−22.4205	−	38.8334i	−0.742823	−	1.28661i	−0.951205	−	0.308559i	$-0.900153\pi$
$911$	−22.4205	−	38.8334i	−0.742823	−	1.28661i	0.208382	−	0.978047i	$-0.433180\pi$
$912$		0			0
$913$	7.64434	−	13.2404i	0.252991	−	0.438193i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	4.34886i		−	0.143612i
$918$		0			0
$919$		−	13.3225i		−	0.439469i	−0.975560	−	0.219734i	$-0.929481\pi$
$919$		−	13.3225i		−	0.439469i	0.975560	−	0.219734i	$-0.0705191\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.407770	+	0.706278i	−0.0134219	+	0.0232474i
$924$		0			0
$925$	−1.74822	−	3.02801i	−0.0574811	−	0.0995603i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	16.5850	−	9.57535i	0.544136	−	0.314157i	−0.202618	−	0.979258i	$-0.564945\pi$
$929$	16.5850	−	9.57535i	0.544136	−	0.314157i	0.746754	+	0.665101i	$0.231611\pi$
$930$		0			0
$931$	10.9805	+	6.33959i	0.359871	+	0.207772i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	75.4515			2.46753
$936$		0			0
$937$	17.6708			0.577281			0.288640	−	0.957438i	$-0.406797\pi$
$937$	17.6708			0.577281			0.288640	+	0.957438i	$0.406797\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−24.1771	−	13.9587i	−0.788152	−	0.455040i	0.0511595	−	0.998690i	$-0.483708\pi$
$941$	−24.1771	−	13.9587i	−0.788152	−	0.455040i	−0.839312	+	0.543651i	$0.817042\pi$
$942$		0			0
$943$	29.5186	−	17.0426i	0.961257	−	0.554982i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.15200	+	5.45942i	0.102426	+	0.177407i	0.912684	−	0.408667i	$-0.134006\pi$
$947$	3.15200	+	5.45942i	0.102426	+	0.177407i	−0.810258	+	0.586074i	$0.800673\pi$
$948$		0			0
$949$	−1.57446	+	2.72705i	−0.0511092	+	0.0885237i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	8.17205i		−	0.264719i	−0.991202	−	0.132359i	$-0.957745\pi$
$953$		−	8.17205i		−	0.264719i	0.991202	−	0.132359i	$-0.0422553\pi$
$954$		0			0
$955$		−	54.1069i		−	1.75086i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.12313	+	7.14146i	−0.133143	+	0.230610i
$960$		0			0
$961$	38.1403	+	66.0609i	1.23033	+	2.13100i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−58.5101	+	33.7808i	−1.88351	+	1.08744i
$966$		0			0
$967$	23.0033	+	13.2810i	0.739736	+	0.427087i	0.821973	−	0.569526i	$-0.192873\pi$
$967$	23.0033	+	13.2810i	0.739736	+	0.427087i	−0.0822375	+	0.996613i	$0.526207\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−46.2192			−1.48324			−0.741622	−	0.670818i	$-0.765943\pi$
$971$	−46.2192			−1.48324			−0.741622	+	0.670818i	$0.765943\pi$
$972$		0			0
$973$	−16.5869			−0.531751
$974$		0			0
$975$		0			0
$976$		0			0
$977$	31.1382	+	17.9776i	0.996198	+	0.575155i	0.907121	−	0.420870i	$-0.138275\pi$
$977$	31.1382	+	17.9776i	0.996198	+	0.575155i	0.0890768	+	0.996025i	$0.471608\pi$
$978$		0			0
$979$	13.4396	−	7.75938i	0.429533	−	0.247991i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−11.0687	−	19.1716i	−0.353038	−	0.611479i	0.633742	−	0.773544i	$-0.281518\pi$
$983$	−11.0687	−	19.1716i	−0.353038	−	0.611479i	−0.986780	+	0.162065i	$0.948185\pi$
$984$		0			0
$985$	−11.1346	+	19.2857i	−0.354778	+	0.614493i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	54.8937i		−	1.74552i
$990$		0			0
$991$			49.0851i			1.55924i	0.626254	+	0.779619i	$0.284587\pi$
$991$			49.0851i			1.55924i	−0.626254	+	0.779619i	$0.715413\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	21.2610	−	36.8252i	0.674021	−	1.16744i
$996$		0			0
$997$	−9.59479	−	16.6187i	−0.303870	−	0.526318i	0.673139	−	0.739516i	$-0.264946\pi$
$997$	−9.59479	−	16.6187i	−0.303870	−	0.526318i	−0.977009	+	0.213198i	$0.931612\pi$
$998$		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.287.1		24
3.2	odd	2		288.2.s.a.95.8	yes	24
4.3	odd	2	inner	864.2.s.a.287.2		24
8.3	odd	2		1728.2.s.g.1151.12		24
8.5	even	2		1728.2.s.g.1151.11		24
9.2	odd	6	inner	864.2.s.a.575.2		24
9.4	even	3		2592.2.c.c.2591.23		24
9.5	odd	6		2592.2.c.c.2591.1		24
9.7	even	3		288.2.s.a.191.5	yes	24
12.11	even	2		288.2.s.a.95.5	✓	24
24.5	odd	2		576.2.s.g.383.5		24
24.11	even	2		576.2.s.g.383.8		24
36.7	odd	6		288.2.s.a.191.8	yes	24
36.11	even	6	inner	864.2.s.a.575.1		24
36.23	even	6		2592.2.c.c.2591.2		24
36.31	odd	6		2592.2.c.c.2591.24		24
72.5	odd	6		5184.2.c.m.5183.23		24
72.11	even	6		1728.2.s.g.575.11		24
72.13	even	6		5184.2.c.m.5183.1		24
72.29	odd	6		1728.2.s.g.575.12		24
72.43	odd	6		576.2.s.g.191.5		24
72.59	even	6		5184.2.c.m.5183.24		24
72.61	even	6		576.2.s.g.191.8		24
72.67	odd	6		5184.2.c.m.5183.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.s.a.95.5	✓	24	12.11	even	2
288.2.s.a.95.8	yes	24	3.2	odd	2
288.2.s.a.191.5	yes	24	9.7	even	3
288.2.s.a.191.8	yes	24	36.7	odd	6
576.2.s.g.191.5		24	72.43	odd	6
576.2.s.g.191.8		24	72.61	even	6
576.2.s.g.383.5		24	24.5	odd	2
576.2.s.g.383.8		24	24.11	even	2
864.2.s.a.287.1		24	1.1	even	1	trivial
864.2.s.a.287.2		24	4.3	odd	2	inner
864.2.s.a.575.1		24	36.11	even	6	inner
864.2.s.a.575.2		24	9.2	odd	6	inner
1728.2.s.g.575.11		24	72.11	even	6
1728.2.s.g.575.12		24	72.29	odd	6
1728.2.s.g.1151.11		24	8.5	even	2
1728.2.s.g.1151.12		24	8.3	odd	2
2592.2.c.c.2591.1		24	9.5	odd	6
2592.2.c.c.2591.2		24	36.23	even	6
2592.2.c.c.2591.23		24	9.4	even	3
2592.2.c.c.2591.24		24	36.31	odd	6
5184.2.c.m.5183.1		24	72.13	even	6
5184.2.c.m.5183.2		24	72.67	odd	6
5184.2.c.m.5183.23		24	72.5	odd	6
5184.2.c.m.5183.24		24	72.59	even	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)

\(f(q)\)	\(=\)	\(q+(-3.40926 - 1.96834i) q^{5} +(-0.961325 + 0.555021i) q^{7} +O(q^{10})\)	\(q+(-3.40926 - 1.96834i) q^{5} +(-0.961325 + 0.555021i) q^{7} +(1.63301 + 2.82846i) q^{11} +(0.124912 - 0.216355i) q^{13} +5.86838i q^{17} -2.19827i q^{19} +(2.79320 - 4.83797i) q^{23} +(5.24871 + 9.09103i) q^{25} +(-2.35571 + 1.36007i) q^{29} +(8.96997 + 5.17882i) q^{31} +4.36988 q^{35} -0.333076 q^{37} +(5.28400 + 3.05072i) q^{41} +(8.50982 - 4.91315i) q^{43} +(4.70740 + 8.15346i) q^{47} +(-2.88390 + 4.99507i) q^{49} +4.75157i q^{53} -12.8573i q^{55} +(-3.26523 + 5.65555i) q^{59} +(1.07336 + 1.85911i) q^{61} +(-0.851719 + 0.491740i) q^{65} +(-0.501168 - 0.289349i) q^{67} -3.26444 q^{71} -12.6045 q^{73} +(-3.13971 - 1.81271i) q^{77} +(-7.67063 + 4.42864i) q^{79} +(-2.34056 - 4.05397i) q^{83} +(11.5510 - 20.0069i) q^{85} -4.75157i q^{89} +0.277316i q^{91} +(-4.32693 + 7.49447i) q^{95} +(0.916363 + 1.58719i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 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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