LMFDB - Embedded newform 216.3.m.b.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(17,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("216.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.m (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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.19269881856.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 $ x^8 - 2x^7 + 15x^6 - 2x^5 + 133x^4 - 84x^3 + 276x^2 + 144*x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.1
Root			$0.831167 - 1.43962i$ of defining polynomial
Character	$\chi$	$=$	216.89
Dual form			216.3.m.b.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.44299 + 1.98781i) q^{5} +(-1.80469 + 3.12582i) q^{7} +O(q^{10})$	$q+(-3.44299 + 1.98781i) q^{5} +(-1.80469 + 3.12582i) q^{7} +(-11.8326 - 6.83153i) q^{11} +(-8.96435 - 15.5267i) q^{13} +21.6750i q^{17} -23.4245 q^{19} +(-13.0662 + 7.54376i) q^{23} +(-4.59721 + 7.96260i) q^{25} +(20.4862 + 11.8277i) q^{29} +(-23.5016 - 40.7060i) q^{31} -14.3495i q^{35} +54.6126 q^{37} +(-24.6459 + 14.2293i) q^{41} +(-23.8753 + 41.3532i) q^{43} +(-30.5323 - 17.6278i) q^{47} +(17.9862 + 31.1530i) q^{49} -65.0193i q^{53} +54.3192 q^{55} +(76.0156 - 43.8876i) q^{59} +(-6.46852 + 11.2038i) q^{61} +(61.7284 + 35.6389i) q^{65} +(1.55595 + 2.69499i) q^{67} +49.5089i q^{71} +102.151 q^{73} +(42.7082 - 24.6576i) q^{77} +(-18.7220 + 32.4275i) q^{79} +(-14.6999 - 8.48702i) q^{83} +(-43.0859 - 74.6270i) q^{85} +14.1990i q^{89} +64.7115 q^{91} +(80.6505 - 46.5636i) q^{95} +(-24.1484 + 41.8262i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{5} + 6 q^{7}+O(q^{10}) $ 8 * q + 6 * q^5 + 6 * q^7	$ 8 q + 6 q^{5} + 6 q^{7} - 36 q^{11} + 14 q^{13} + 4 q^{19} + 102 q^{23} + 10 q^{25} + 114 q^{29} - 50 q^{31} + 120 q^{37} - 264 q^{41} - 28 q^{43} - 150 q^{47} + 94 q^{49} - 244 q^{55} + 108 q^{59} + 14 q^{61} + 198 q^{65} - 20 q^{67} - 76 q^{73} - 66 q^{77} + 26 q^{79} - 246 q^{83} - 224 q^{85} + 108 q^{91} + 456 q^{95} - 236 q^{97}+O(q^{100}) $ 8 * q + 6 * q^5 + 6 * q^7 - 36 * q^11 + 14 * q^13 + 4 * q^19 + 102 * q^23 + 10 * q^25 + 114 * q^29 - 50 * q^31 + 120 * q^37 - 264 * q^41 - 28 * q^43 - 150 * q^47 + 94 * q^49 - 244 * q^55 + 108 * q^59 + 14 * q^61 + 198 * q^65 - 20 * q^67 - 76 * q^73 - 66 * q^77 + 26 * q^79 - 246 * q^83 - 224 * q^85 + 108 * q^91 + 456 * q^95 - 236 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−3.44299	+	1.98781i	−0.688598	+	0.397562i	−0.803087	−	0.595862i	$-0.796810\pi$
$5$	−3.44299	+	1.98781i	−0.688598	+	0.397562i	0.114488	+	0.993425i	$0.463477\pi$
$6$		0			0
$7$	−1.80469	+	3.12582i	−0.257813	+	0.446545i	−0.965656	−	0.259825i	$-0.916335\pi$
$7$	−1.80469	+	3.12582i	−0.257813	+	0.446545i	0.707843	+	0.706370i	$0.249669\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−11.8326	−	6.83153i	−1.07569	−	0.621048i	−0.145957	−	0.989291i	$-0.546626\pi$
$11$	−11.8326	−	6.83153i	−1.07569	−	0.621048i	−0.929730	+	0.368243i	$0.879959\pi$
$12$		0			0
$13$	−8.96435	−	15.5267i	−0.689565	−	1.19436i	−0.971979	−	0.235070i	$-0.924468\pi$
$13$	−8.96435	−	15.5267i	−0.689565	−	1.19436i	0.282413	−	0.959293i	$-0.408865\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			21.6750i			1.27500i	0.770449	+	0.637501i	$0.220032\pi$
$17$			21.6750i			1.27500i	−0.770449	+	0.637501i	$0.779968\pi$
$18$		0			0
$19$	−23.4245			−1.23287			−0.616435	−	0.787406i	$-0.711424\pi$
$19$	−23.4245			−1.23287			−0.616435	+	0.787406i	$0.711424\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−13.0662	+	7.54376i	−0.568095	+	0.327990i	−0.756388	−	0.654123i	$-0.773038\pi$
$23$	−13.0662	+	7.54376i	−0.568095	+	0.327990i	0.188293	+	0.982113i	$0.439704\pi$
$24$		0			0
$25$	−4.59721	+	7.96260i	−0.183888	+	0.318504i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	20.4862	+	11.8277i	0.706420	+	0.407852i	0.809734	−	0.586797i	$-0.199611\pi$
$29$	20.4862	+	11.8277i	0.706420	+	0.407852i	−0.103314	+	0.994649i	$0.532945\pi$
$30$		0			0
$31$	−23.5016	−	40.7060i	−0.758117	−	1.31310i	−0.943810	−	0.330489i	$-0.892786\pi$
$31$	−23.5016	−	40.7060i	−0.758117	−	1.31310i	0.185693	−	0.982608i	$-0.440547\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	14.3495i		−	0.409987i
$36$		0			0
$37$	54.6126			1.47602			0.738009	−	0.674791i	$-0.235766\pi$
$37$	54.6126			1.47602			0.738009	+	0.674791i	$0.235766\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−24.6459	+	14.2293i	−0.601118	+	0.347056i	−0.769481	−	0.638669i	$-0.779485\pi$
$41$	−24.6459	+	14.2293i	−0.601118	+	0.347056i	0.168363	+	0.985725i	$0.446152\pi$
$42$		0			0
$43$	−23.8753	+	41.3532i	−0.555239	+	0.961702i	0.442646	+	0.896696i	$0.354040\pi$
$43$	−23.8753	+	41.3532i	−0.555239	+	0.961702i	−0.997885	+	0.0650055i	$0.979294\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−30.5323	−	17.6278i	−0.649623	−	0.375060i	0.138689	−	0.990336i	$-0.455711\pi$
$47$	−30.5323	−	17.6278i	−0.649623	−	0.375060i	−0.788312	+	0.615276i	$0.789045\pi$
$48$		0			0
$49$	17.9862	+	31.1530i	0.367065	+	0.635775i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	65.0193i		−	1.22678i	−0.789780	−	0.613390i	$-0.789805\pi$
$53$		−	65.0193i		−	1.22678i	0.789780	−	0.613390i	$-0.210195\pi$
$54$		0			0
$55$	54.3192			0.987621
$56$		0			0
$57$		0			0
$58$		0			0
$59$	76.0156	−	43.8876i	1.28840	−	0.743858i	0.310031	−	0.950726i	$-0.399661\pi$
$59$	76.0156	−	43.8876i	1.28840	−	0.743858i	0.978369	+	0.206869i	$0.0663272\pi$
$60$		0			0
$61$	−6.46852	+	11.2038i	−0.106041	+	0.183669i	−0.914163	−	0.405346i	$-0.867151\pi$
$61$	−6.46852	+	11.2038i	−0.106041	+	0.183669i	0.808122	+	0.589015i	$0.200484\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	61.7284	+	35.6389i	0.949667	+	0.548291i
$66$		0			0
$67$	1.55595	+	2.69499i	0.0232232	+	0.0402237i	0.877403	−	0.479753i	$-0.159274\pi$
$67$	1.55595	+	2.69499i	0.0232232	+	0.0402237i	−0.854180	+	0.519977i	$0.825941\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			49.5089i			0.697308i	0.937251	+	0.348654i	$0.113361\pi$
$71$			49.5089i			0.697308i	−0.937251	+	0.348654i	$0.886639\pi$
$72$		0			0
$73$	102.151			1.39932			0.699662	−	0.714474i	$-0.253334\pi$
$73$	102.151			1.39932			0.699662	+	0.714474i	$0.253334\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	42.7082	−	24.6576i	0.554652	−	0.320228i
$78$		0			0
$79$	−18.7220	+	32.4275i	−0.236988	+	0.410475i	−0.959849	−	0.280519i	$-0.909494\pi$
$79$	−18.7220	+	32.4275i	−0.236988	+	0.410475i	0.722861	+	0.690994i	$0.242827\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−14.6999	−	8.48702i	−0.177108	−	0.102253i	0.408825	−	0.912613i	$-0.365939\pi$
$83$	−14.6999	−	8.48702i	−0.177108	−	0.102253i	−0.585933	+	0.810359i	$0.699272\pi$
$84$		0			0
$85$	−43.0859	−	74.6270i	−0.506893	−	0.877964i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			14.1990i			0.159540i	0.996813	+	0.0797698i	$0.0254185\pi$
$89$			14.1990i			0.159540i	−0.996813	+	0.0797698i	$0.974581\pi$
$90$		0			0
$91$	64.7115			0.711116
$92$		0			0
$93$		0			0
$94$		0			0
$95$	80.6505	−	46.5636i	0.848952	−	0.490143i
$96$		0			0
$97$	−24.1484	+	41.8262i	−0.248952	+	0.431198i	−0.963235	−	0.268659i	$-0.913420\pi$
$97$	−24.1484	+	41.8262i	−0.248952	+	0.431198i	0.714283	+	0.699857i	$0.246753\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	34.5980	+	19.9752i	0.342554	+	0.197774i	0.661401	−	0.750032i	$-0.269962\pi$
$101$	34.5980	+	19.9752i	0.342554	+	0.197774i	−0.318847	+	0.947806i	$0.603296\pi$
$102$		0			0
$103$	10.9749	+	19.0091i	0.106552	+	0.184554i	0.914371	−	0.404876i	$-0.132685\pi$
$103$	10.9749	+	19.0091i	0.106552	+	0.184554i	−0.807819	+	0.589431i	$0.799352\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	0.521299i		−	0.00487195i	−0.999997	−	0.00243598i	$-0.999225\pi$
$107$		−	0.521299i		−	0.00487195i	0.999997	−	0.00243598i	$-0.000775396\pi$
$108$		0			0
$109$	−198.784			−1.82371			−0.911855	−	0.410513i	$-0.865350\pi$
$109$	−198.784			−1.82371			−0.911855	+	0.410513i	$0.865350\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−115.971	+	66.9557i	−1.02629	+	0.592528i	−0.915919	−	0.401363i	$-0.868537\pi$
$113$	−115.971	+	66.9557i	−1.02629	+	0.592528i	−0.110369	+	0.993891i	$0.535203\pi$
$114$		0			0
$115$	29.9912	−	51.9462i	0.260793	−	0.451706i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−67.7522	−	39.1168i	−0.569346	−	0.328712i
$120$		0			0
$121$	32.8395	+	56.8797i	0.271401	+	0.470080i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	135.944i		−	1.08755i
$126$		0			0
$127$	45.8769			0.361235			0.180618	−	0.983553i	$-0.442190\pi$
$127$	45.8769			0.361235			0.180618	+	0.983553i	$0.442190\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−167.914	+	96.9453i	−1.28179	+	0.740040i	−0.977175	−	0.212436i	$-0.931860\pi$
$131$	−167.914	+	96.9453i	−1.28179	+	0.740040i	−0.304612	+	0.952476i	$0.598527\pi$
$132$		0			0
$133$	42.2741	−	73.2208i	0.317850	−	0.550532i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−149.798	−	86.4859i	−1.09342	−	0.631284i	−0.158932	−	0.987289i	$-0.550805\pi$
$137$	−149.798	−	86.4859i	−1.09342	−	0.631284i	−0.934484	+	0.356005i	$0.884138\pi$
$138$		0			0
$139$	0.803631	+	1.39193i	0.00578151	+	0.0100139i	0.868902	−	0.494985i	$-0.164826\pi$
$139$	0.803631	+	1.39193i	0.00578151	+	0.0100139i	−0.863120	+	0.504999i	$0.831493\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			244.961i			1.71301i
$144$		0			0
$145$	−94.0450			−0.648586
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−76.1133	+	43.9441i	−0.510828	+	0.294927i	−0.733174	−	0.680041i	$-0.761962\pi$
$149$	−76.1133	+	43.9441i	−0.510828	+	0.294927i	0.222346	+	0.974968i	$0.428629\pi$
$150$		0			0
$151$	6.64118	−	11.5029i	0.0439813	−	0.0761778i	−0.843197	−	0.537605i	$-0.819329\pi$
$151$	6.64118	−	11.5029i	0.0439813	−	0.0761778i	0.887178	+	0.461427i	$0.152662\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	161.832	+	93.4336i	1.04408	+	0.602798i
$156$		0			0
$157$	−93.8926	−	162.627i	−0.598042	−	1.03584i	−0.993110	−	0.117188i	$-0.962612\pi$
$157$	−93.8926	−	162.627i	−0.598042	−	1.03584i	0.395068	−	0.918652i	$-0.370721\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	54.4566i		−	0.338240i
$162$		0			0
$163$	−131.235			−0.805123			−0.402562	−	0.915393i	$-0.631880\pi$
$163$	−131.235			−0.805123			−0.402562	+	0.915393i	$0.631880\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	158.636	−	91.5887i	0.949918	−	0.548436i	0.0568627	−	0.998382i	$-0.481890\pi$
$167$	158.636	−	91.5887i	0.949918	−	0.548436i	0.893056	+	0.449946i	$0.148557\pi$
$168$		0			0
$169$	−76.2192	+	132.015i	−0.451001	+	0.781157i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−22.6730	−	13.0903i	−0.131058	−	0.0756662i	0.433038	−	0.901376i	$-0.357442\pi$
$173$	−22.6730	−	13.0903i	−0.131058	−	0.0756662i	−0.564095	+	0.825710i	$0.690775\pi$
$174$		0			0
$175$	−16.5931	−	28.7401i	−0.0948176	−	0.164229i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			175.092i			0.978165i	0.872238	+	0.489083i	$0.162668\pi$
$179$			175.092i			0.978165i	−0.872238	+	0.489083i	$0.837332\pi$
$180$		0			0
$181$	−172.814			−0.954772			−0.477386	−	0.878694i	$-0.658416\pi$
$181$	−172.814			−0.954772			−0.477386	+	0.878694i	$0.658416\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−188.031	+	108.560i	−1.01638	+	0.586809i
$186$		0			0
$187$	148.074	−	256.471i	0.791838	−	1.37150i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−76.1098	−	43.9420i	−0.398481	−	0.230063i	0.287348	−	0.957826i	$-0.407227\pi$
$191$	−76.1098	−	43.9420i	−0.398481	−	0.230063i	−0.685828	+	0.727764i	$0.740560\pi$
$192$		0			0
$193$	68.6377	+	118.884i	0.355636	+	0.615979i	0.987227	−	0.159323i	$-0.0509310\pi$
$193$	68.6377	+	118.884i	0.355636	+	0.615979i	−0.631591	+	0.775302i	$0.717598\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	239.073i		−	1.21357i	−0.794867	−	0.606784i	$-0.792459\pi$
$197$		−	239.073i		−	1.21357i	0.794867	−	0.606784i	$-0.207541\pi$
$198$		0			0
$199$	−250.574			−1.25916			−0.629582	−	0.776934i	$-0.716774\pi$
$199$	−250.574			−1.25916			−0.629582	+	0.776934i	$0.716774\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−73.9425	+	42.6907i	−0.364249	+	0.210299i
$204$		0			0
$205$	56.5703	−	97.9826i	0.275953	−	0.477964i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	277.172	+	160.025i	1.32618	+	0.765671i
$210$		0			0
$211$	118.043	+	204.456i	0.559445	+	0.968988i	0.997543	+	0.0700601i	$0.0223191\pi$
$211$	118.043	+	204.456i	0.559445	+	0.968988i	−0.438098	+	0.898927i	$0.644348\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	189.838i		−	0.882968i
$216$		0			0
$217$	169.653			0.781810
$218$		0			0
$219$		0			0
$220$		0			0
$221$	336.542	−	194.303i	1.52282	−	0.879198i
$222$		0			0
$223$	42.8742	−	74.2603i	0.192261	−	0.333006i	−0.753738	−	0.657175i	$-0.771751\pi$
$223$	42.8742	−	74.2603i	0.192261	−	0.333006i	0.945999	+	0.324169i	$0.105085\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−160.187	−	92.4841i	−0.705671	−	0.407419i	0.103785	−	0.994600i	$-0.466905\pi$
$227$	−160.187	−	92.4841i	−0.705671	−	0.407419i	−0.809456	+	0.587181i	$0.800238\pi$
$228$		0			0
$229$	128.199	+	222.048i	0.559822	+	0.969640i	0.997511	+	0.0705135i	$0.0224638\pi$
$229$	128.199	+	222.048i	0.559822	+	0.969640i	−0.437689	+	0.899126i	$0.644203\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			403.712i			1.73267i	0.499464	+	0.866335i	$0.333530\pi$
$233$			403.712i			1.73267i	−0.499464	+	0.866335i	$0.666470\pi$
$234$		0			0
$235$	140.163			0.596439
$236$		0			0
$237$		0			0
$238$		0			0
$239$	215.728	−	124.551i	0.902630	−	0.521133i	0.0245772	−	0.999698i	$-0.492176\pi$
$239$	215.728	−	124.551i	0.902630	−	0.521133i	0.878052	+	0.478565i	$0.158843\pi$
$240$		0			0
$241$	85.7023	−	148.441i	0.355611	−	0.615937i	−0.631611	−	0.775285i	$-0.717606\pi$
$241$	85.7023	−	148.441i	0.355611	−	0.615937i	0.987222	+	0.159349i	$0.0509394\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−123.852	−	71.5063i	−0.505520	−	0.291862i
$246$		0			0
$247$	209.986	+	363.706i	0.850145	+	1.47249i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	287.980i		−	1.14733i	−0.819089	−	0.573666i	$-0.805521\pi$
$251$		−	287.980i		−	1.14733i	0.819089	−	0.573666i	$-0.194479\pi$
$252$		0			0
$253$	206.142			0.814789
$254$		0			0
$255$		0			0
$256$		0			0
$257$	60.1268	−	34.7142i	0.233957	−	0.135075i	−0.378439	−	0.925626i	$-0.623539\pi$
$257$	60.1268	−	34.7142i	0.233957	−	0.135075i	0.612396	+	0.790551i	$0.290206\pi$
$258$		0			0
$259$	−98.5590	+	170.709i	−0.380537	+	0.659109i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−68.7357	−	39.6845i	−0.261352	−	0.150892i	0.363599	−	0.931556i	$-0.381548\pi$
$263$	−68.7357	−	39.6845i	−0.261352	−	0.150892i	−0.624951	+	0.780664i	$0.714881\pi$
$264$		0			0
$265$	129.246	+	223.861i	0.487722	+	0.844758i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			41.6217i			0.154728i	0.997003	+	0.0773638i	$0.0246503\pi$
$269$			41.6217i			0.154728i	−0.997003	+	0.0773638i	$0.975350\pi$
$270$		0			0
$271$	98.0065			0.361648			0.180824	−	0.983516i	$-0.442124\pi$
$271$	98.0065			0.361648			0.180824	+	0.983516i	$0.442124\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	108.793	−	62.8119i	0.395612	−	0.228407i
$276$		0			0
$277$	153.400	−	265.696i	0.553790	−	0.959193i	−0.444206	−	0.895924i	$-0.646514\pi$
$277$	153.400	−	265.696i	0.553790	−	0.959193i	0.997997	−	0.0632681i	$-0.0201523\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	54.8876	+	31.6894i	0.195330	+	0.112774i	0.594475	−	0.804114i	$-0.297360\pi$
$281$	54.8876	+	31.6894i	0.195330	+	0.112774i	−0.399146	+	0.916888i	$0.630693\pi$
$282$		0			0
$283$	−163.299	−	282.842i	−0.577027	−	0.999440i	−0.995818	−	0.0913578i	$-0.970879\pi$
$283$	−163.299	−	282.842i	−0.577027	−	0.999440i	0.418791	−	0.908083i	$-0.362454\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	102.718i		−	0.357902i
$288$		0			0
$289$	−180.808			−0.625632
$290$		0			0
$291$		0			0
$292$		0			0
$293$	62.3120	−	35.9759i	0.212669	−	0.122784i	−0.389882	−	0.920865i	$-0.627484\pi$
$293$	62.3120	−	35.9759i	0.212669	−	0.122784i	0.602551	+	0.798080i	$0.294151\pi$
$294$		0			0
$295$	−174.481	+	302.209i	−0.591460	+	1.02444i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	234.260	+	135.250i	0.783477	+	0.452341i
$300$		0			0
$301$	−86.1750	−	149.259i	−0.286296	−	0.495879i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	51.4328i		−	0.168632i
$306$		0			0
$307$	−161.023			−0.524504			−0.262252	−	0.964999i	$-0.584465\pi$
$307$	−161.023			−0.524504			−0.262252	+	0.964999i	$0.584465\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−352.553	+	203.547i	−1.13361	+	0.654491i	−0.944841	−	0.327530i	$-0.893784\pi$
$311$	−352.553	+	203.547i	−1.13361	+	0.654491i	−0.188771	+	0.982021i	$0.560451\pi$
$312$		0			0
$313$	79.7548	−	138.139i	0.254808	−	0.441340i	−0.710035	−	0.704166i	$-0.751321\pi$
$313$	79.7548	−	138.139i	0.254808	−	0.441340i	0.964843	+	0.262826i	$0.0846545\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	364.877	+	210.662i	1.15103	+	0.664549i	0.949139	−	0.314859i	$-0.101957\pi$
$317$	364.877	+	210.662i	1.15103	+	0.664549i	0.201894	+	0.979407i	$0.435290\pi$
$318$		0			0
$319$	−161.602	−	279.904i	−0.506591	−	0.877441i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	507.728i		−	1.57191i
$324$		0			0
$325$	164.844			0.507212
$326$		0			0
$327$		0			0
$328$		0			0
$329$	110.203	−	63.6256i	0.334963	−	0.193391i
$330$		0			0
$331$	−64.9715	+	112.534i	−0.196289	+	0.339982i	−0.947322	−	0.320282i	$-0.896222\pi$
$331$	−64.9715	+	112.534i	−0.196289	+	0.339982i	0.751034	+	0.660264i	$0.229556\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−10.7143	−	6.18588i	−0.0319828	−	0.0184653i
$336$		0			0
$337$	53.6006	+	92.8389i	0.159052	+	0.275486i	0.934527	−	0.355892i	$-0.115823\pi$
$337$	53.6006	+	92.8389i	0.159052	+	0.275486i	−0.775475	+	0.631378i	$0.782490\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			642.208i			1.88331i
$342$		0			0
$343$	−306.698			−0.894163
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−347.832	+	200.821i	−1.00240	+	0.578735i	−0.908957	−	0.416890i	$-0.863120\pi$
$347$	−347.832	+	200.821i	−1.00240	+	0.578735i	−0.0934416	+	0.995625i	$0.529787\pi$
$348$		0			0
$349$	−218.729	+	378.849i	−0.626730	+	1.08553i	0.361474	+	0.932382i	$0.382274\pi$
$349$	−218.729	+	378.849i	−0.626730	+	1.08553i	−0.988204	+	0.153146i	$0.951060\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−303.639	−	175.306i	−0.860167	−	0.496618i	0.00390098	−	0.999992i	$-0.498758\pi$
$353$	−303.639	−	175.306i	−0.860167	−	0.496618i	−0.864068	+	0.503375i	$0.832092\pi$
$354$		0			0
$355$	−98.4143	−	170.459i	−0.277223	−	0.480165i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			529.816i			1.47581i	0.674904	+	0.737906i	$0.264185\pi$
$359$			529.816i			1.47581i	−0.674904	+	0.737906i	$0.735815\pi$
$360$		0			0
$361$	187.709			0.519969
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−351.704	+	203.056i	−0.963572	+	0.556319i
$366$		0			0
$367$	361.971	−	626.953i	0.986298	−	1.70832i	0.350278	−	0.936646i	$-0.386087\pi$
$367$	361.971	−	626.953i	0.986298	−	1.70832i	0.636020	−	0.771673i	$-0.280580\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	203.239	+	117.340i	0.547813	+	0.316280i
$372$		0			0
$373$	−29.6005	−	51.2696i	−0.0793580	−	0.137452i	0.823615	−	0.567149i	$-0.191954\pi$
$373$	−29.6005	−	51.2696i	−0.0793580	−	0.137452i	−0.902973	+	0.429697i	$0.858620\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	424.111i		−	1.12496i
$378$		0			0
$379$	32.5366			0.0858485			0.0429243	−	0.999078i	$-0.486333\pi$
$379$	32.5366			0.0858485			0.0429243	+	0.999078i	$0.486333\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	188.264	−	108.694i	0.491551	−	0.283797i	−0.233666	−	0.972317i	$-0.575072\pi$
$383$	188.264	−	108.694i	0.491551	−	0.283797i	0.725218	+	0.688519i	$0.241739\pi$
$384$		0			0
$385$	−98.0293	+	169.792i	−0.254622	+	0.441017i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−579.712	−	334.697i	−1.49026	−	0.860403i	−0.490324	−	0.871540i	$-0.663122\pi$
$389$	−579.712	−	334.697i	−1.49026	−	0.860403i	−0.999938	+	0.0111369i	$0.996455\pi$
$390$		0			0
$391$	−163.511	−	283.210i	−0.418188	−	0.724322i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	148.864i		−	0.376870i
$396$		0			0
$397$	22.3088			0.0561935			0.0280967	−	0.999605i	$-0.491055\pi$
$397$	22.3088			0.0561935			0.0280967	+	0.999605i	$0.491055\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	77.7666	−	44.8986i	0.193932	−	0.111967i	−0.399890	−	0.916563i	$-0.630952\pi$
$401$	77.7666	−	44.8986i	0.193932	−	0.111967i	0.593822	+	0.804597i	$0.297618\pi$
$402$		0			0
$403$	−421.354	+	729.806i	−1.04554	+	1.81093i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−646.207	−	373.088i	−1.58773	−	0.916677i
$408$		0			0
$409$	−308.464	−	534.276i	−0.754191	−	1.30630i	−0.945775	−	0.324821i	$-0.894696\pi$
$409$	−308.464	−	534.276i	−0.754191	−	1.30630i	0.191584	−	0.981476i	$-0.438637\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			316.814i			0.767105i
$414$		0			0
$415$	67.4824			0.162608
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−566.501	+	327.069i	−1.35203	+	0.780595i	−0.988534	−	0.151001i	$-0.951750\pi$
$419$	−566.501	+	327.069i	−1.35203	+	0.780595i	−0.363496	+	0.931596i	$0.618417\pi$
$420$		0			0
$421$	−209.287	+	362.495i	−0.497118	+	0.861033i	−0.999994	−	0.00332489i	$-0.998942\pi$
$421$	−209.287	+	362.495i	−0.497118	+	0.861033i	0.502877	+	0.864358i	$0.332275\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−172.590	−	99.6447i	−0.406093	−	0.234458i
$426$		0			0
$427$	−23.3474	−	40.4388i	−0.0546777	−	0.0947045i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			111.970i			0.259792i	0.991528	+	0.129896i	$0.0414644\pi$
$431$			111.970i			0.259792i	−0.991528	+	0.129896i	$0.958536\pi$
$432$		0			0
$433$	−158.770			−0.366673			−0.183337	−	0.983050i	$-0.558690\pi$
$433$	−158.770			−0.366673			−0.183337	+	0.983050i	$0.558690\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	306.069	−	176.709i	0.700387	−	0.404369i
$438$		0			0
$439$	61.8211	−	107.077i	0.140823	−	0.243912i	−0.786984	−	0.616973i	$-0.788359\pi$
$439$	61.8211	−	107.077i	0.140823	−	0.243912i	0.927807	+	0.373061i	$0.121692\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	680.397	+	392.827i	1.53588	+	0.886743i	0.999073	+	0.0430402i	$0.0137044\pi$
$443$	680.397	+	392.827i	1.53588	+	0.886743i	0.536811	+	0.843703i	$0.319629\pi$
$444$		0			0
$445$	−28.2250	−	48.8871i	−0.0634269	−	0.109859i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			387.277i			0.862533i	0.902225	+	0.431266i	$0.141933\pi$
$449$			387.277i			0.862533i	−0.902225	+	0.431266i	$0.858067\pi$
$450$		0			0
$451$	388.831			0.862153
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−222.801	+	128.634i	−0.489673	+	0.282713i
$456$		0			0
$457$	160.668	−	278.284i	0.351570	−	0.608938i	−0.634954	−	0.772550i	$-0.718981\pi$
$457$	160.668	−	278.284i	0.351570	−	0.608938i	0.986525	+	0.163612i	$0.0523145\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−61.0565	−	35.2510i	−0.132444	−	0.0764663i	0.432314	−	0.901723i	$-0.357697\pi$
$461$	−61.0565	−	35.2510i	−0.132444	−	0.0764663i	−0.564758	+	0.825257i	$0.691030\pi$
$462$		0			0
$463$	181.170	+	313.796i	0.391297	+	0.677746i	0.992621	−	0.121259i	$-0.0386933\pi$
$463$	181.170	+	313.796i	0.391297	+	0.677746i	−0.601324	+	0.799005i	$0.705360\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	478.151i		−	1.02388i	−0.859022	−	0.511939i	$-0.828927\pi$
$467$		−	478.151i		−	1.02388i	0.859022	−	0.511939i	$-0.171073\pi$
$468$		0			0
$469$	−11.2320			−0.0239489
$470$		0			0
$471$		0			0
$472$		0			0
$473$	565.011	−	326.209i	1.19453	−	0.689660i
$474$		0			0
$475$	107.687	−	186.520i	0.226710	−	0.392674i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	790.996	+	456.682i	1.65135	+	0.953407i	0.976518	+	0.215434i	$0.0691166\pi$
$479$	790.996	+	456.682i	1.65135	+	0.953407i	0.674830	+	0.737973i	$0.264217\pi$
$480$		0			0
$481$	−489.567	−	847.955i	−1.01781	−	1.76290i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	192.010i		−	0.395896i
$486$		0			0
$487$	700.870			1.43916			0.719579	−	0.694411i	$-0.244335\pi$
$487$	700.870			1.43916			0.719579	+	0.694411i	$0.244335\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	479.646	−	276.924i	0.976876	−	0.564000i	0.0755505	−	0.997142i	$-0.475929\pi$
$491$	479.646	−	276.924i	0.976876	−	0.564000i	0.901326	+	0.433142i	$0.142595\pi$
$492$		0			0
$493$	−256.366	+	444.039i	−0.520012	+	0.900687i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−154.756	−	89.3482i	−0.311380	−	0.179775i
$498$		0			0
$499$	162.874	+	282.107i	0.326401	+	0.565344i	0.981795	−	0.189944i	$-0.0608306\pi$
$499$	162.874	+	282.107i	0.326401	+	0.565344i	−0.655394	+	0.755287i	$0.727497\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			610.492i			1.21370i	0.794816	+	0.606851i	$0.207567\pi$
$503$			610.492i			1.21370i	−0.794816	+	0.606851i	$0.792433\pi$
$504$		0			0
$505$	−158.827			−0.314510
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−774.630	+	447.233i	−1.52187	+	0.878650i	−0.522200	+	0.852823i	$0.674889\pi$
$509$	−774.630	+	447.233i	−1.52187	+	0.878650i	−0.999666	+	0.0258270i	$0.991778\pi$
$510$		0			0
$511$	−184.350	+	319.304i	−0.360764	+	0.624862i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−75.5729	−	43.6320i	−0.146744	−	0.0847224i
$516$		0			0
$517$	240.850	+	417.164i	0.465860	+	0.806894i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	244.209i		−	0.468732i	−0.972148	−	0.234366i	$-0.924699\pi$
$521$		−	244.209i		−	0.468732i	0.972148	−	0.234366i	$-0.0753014\pi$
$522$		0			0
$523$	−4.79146			−0.00916150			−0.00458075	−	0.999990i	$-0.501458\pi$
$523$	−4.79146			−0.00916150			−0.00458075	+	0.999990i	$0.501458\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	882.305	−	509.399i	1.67420	−	0.966601i
$528$		0			0
$529$	−150.683	+	260.991i	−0.284846	+	0.493367i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	441.868	+	255.113i	0.829021	+	0.478636i
$534$		0			0
$535$	1.03624	+	1.79483i	0.00193690	+	0.00335482i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	491.492i		−	0.911859i
$540$		0			0
$541$	406.633			0.751633			0.375816	−	0.926694i	$-0.377362\pi$
$541$	406.633			0.751633			0.375816	+	0.926694i	$0.377362\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	684.413	−	395.146i	1.25580	−	0.725038i
$546$		0			0
$547$	250.283	−	433.503i	0.457556	−	0.792509i	−0.541276	−	0.840845i	$-0.682058\pi$
$547$	250.283	−	433.503i	0.457556	−	0.792509i	0.998831	+	0.0483358i	$0.0153918\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−479.879	−	277.058i	−0.870924	−	0.502828i
$552$		0			0
$553$	−67.5750	−	117.043i	−0.122197	−	0.211652i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	549.645i		−	0.986796i	−0.869804	−	0.493398i	$-0.835755\pi$
$557$		−	549.645i		−	0.986796i	0.869804	−	0.493398i	$-0.164245\pi$
$558$		0			0
$559$	856.105			1.53149
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−799.025	+	461.317i	−1.41923	+	0.819391i	−0.996231	−	0.0867404i	$-0.972355\pi$
$563$	−799.025	+	461.317i	−1.41923	+	0.819391i	−0.422996	+	0.906132i	$0.639022\pi$
$564$		0			0
$565$	266.191	−	461.056i	0.471134	−	0.816027i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−281.820	−	162.709i	−0.495289	−	0.285955i	0.231477	−	0.972840i	$-0.425644\pi$
$569$	−281.820	−	162.709i	−0.495289	−	0.285955i	−0.726766	+	0.686885i	$0.758978\pi$
$570$		0			0
$571$	64.8487	+	112.321i	0.113570	+	0.196710i	0.917207	−	0.398410i	$-0.130438\pi$
$571$	64.8487	+	112.321i	0.113570	+	0.196710i	−0.803637	+	0.595120i	$0.797105\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	138.721i		−	0.241254i
$576$		0			0
$577$	401.374			0.695621			0.347811	−	0.937565i	$-0.386925\pi$
$577$	401.374			0.695621			0.347811	+	0.937565i	$0.386925\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	53.0577	−	30.6329i	0.0913214	−	0.0527244i
$582$		0			0
$583$	−444.181	+	769.345i	−0.761889	+	1.31963i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	650.079	+	375.323i	1.10746	+	0.639392i	0.938170	−	0.346174i	$-0.112519\pi$
$587$	650.079	+	375.323i	1.10746	+	0.639392i	0.169290	+	0.985566i	$0.445853\pi$
$588$		0			0
$589$	550.515	+	953.519i	0.934660	+	1.61888i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	969.193i		−	1.63439i	−0.576362	−	0.817195i	$-0.695528\pi$
$593$		−	969.193i		−	1.63439i	0.576362	−	0.817195i	$-0.304472\pi$
$594$		0			0
$595$	311.027			0.522735
$596$		0			0
$597$		0			0
$598$		0			0
$599$	9.76897	−	5.64012i	0.0163088	−	0.00941589i	−0.491823	−	0.870695i	$-0.663669\pi$
$599$	9.76897	−	5.64012i	0.0163088	−	0.00941589i	0.508132	+	0.861279i	$0.330336\pi$
$600$		0			0
$601$	−425.209	+	736.483i	−0.707502	+	1.22543i	0.258279	+	0.966070i	$0.416845\pi$
$601$	−425.209	+	736.483i	−0.707502	+	1.22543i	−0.965781	+	0.259359i	$0.916489\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−226.132	−	130.557i	−0.373772	−	0.215797i
$606$		0			0
$607$	−91.2085	−	157.978i	−0.150261	−	0.260260i	0.781062	−	0.624453i	$-0.214678\pi$
$607$	−91.2085	−	157.978i	−0.150261	−	0.260260i	−0.931323	+	0.364193i	$0.881345\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			632.088i			1.03451i
$612$		0			0
$613$	−334.345			−0.545425			−0.272712	−	0.962096i	$-0.587921\pi$
$613$	−334.345			−0.545425			−0.272712	+	0.962096i	$0.587921\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	154.140	−	88.9929i	0.249822	−	0.144235i	−0.369861	−	0.929087i	$-0.620595\pi$
$617$	154.140	−	88.9929i	0.249822	−	0.144235i	0.619683	+	0.784852i	$0.287261\pi$
$618$		0			0
$619$	529.724	−	917.510i	0.855775	−	1.48225i	−0.0201500	−	0.999797i	$-0.506414\pi$
$619$	529.724	−	917.510i	0.855775	−	1.48225i	0.875925	−	0.482448i	$-0.160252\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−44.3836	−	25.6249i	−0.0712417	−	0.0411314i
$624$		0			0
$625$	155.301	+	268.989i	0.248482	+	0.430383i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			1183.73i			1.88193i
$630$		0			0
$631$	−950.275			−1.50598			−0.752991	−	0.658031i	$-0.771390\pi$
$631$	−950.275			−1.50598			−0.752991	+	0.658031i	$0.771390\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−157.954	+	91.1946i	−0.248746	+	0.143614i
$636$		0			0
$637$	322.469	−	558.532i	0.506230	−	0.876817i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	74.1661	+	42.8198i	0.115704	+	0.0668016i	0.556735	−	0.830690i	$-0.312054\pi$
$641$	74.1661	+	42.8198i	0.115704	+	0.0668016i	−0.441031	+	0.897492i	$0.645387\pi$
$642$		0			0
$643$	139.447	+	241.529i	0.216869	+	0.375629i	0.953849	−	0.300286i	$-0.0970821\pi$
$643$	139.447	+	241.529i	0.216869	+	0.375629i	−0.736980	+	0.675915i	$0.763749\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	654.758i		−	1.01199i	−0.862536	−	0.505995i	$-0.831125\pi$
$647$		−	654.758i		−	1.01199i	0.862536	−	0.505995i	$-0.168875\pi$
$648$		0			0
$649$	−1199.28			−1.84789
$650$		0			0
$651$		0			0
$652$		0			0
$653$	159.696	−	92.2004i	0.244557	−	0.141195i	−0.372712	−	0.927947i	$-0.621572\pi$
$653$	159.696	−	92.2004i	0.244557	−	0.141195i	0.617269	+	0.786752i	$0.288239\pi$
$654$		0			0
$655$	385.418	−	667.563i	0.588424	−	1.01918i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	165.641	+	95.6328i	0.251352	+	0.145118i	0.620383	−	0.784299i	$-0.286977\pi$
$659$	165.641	+	95.6328i	0.251352	+	0.145118i	−0.369031	+	0.929417i	$0.620310\pi$
$660$		0			0
$661$	66.6012	+	115.357i	0.100758	+	0.174518i	0.911997	−	0.410196i	$-0.134540\pi$
$661$	66.6012	+	115.357i	0.100758	+	0.174518i	−0.811239	+	0.584715i	$0.801206\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			336.131i			0.505461i
$666$		0			0
$667$	−356.901			−0.535085
$668$		0			0
$669$		0			0
$670$		0			0
$671$	153.078	−	88.3797i	0.228134	−	0.131713i
$672$		0			0
$673$	661.521	−	1145.79i	0.982943	−	1.70251i	0.332201	−	0.943208i	$-0.392209\pi$
$673$	661.521	−	1145.79i	0.982943	−	1.70251i	0.650742	−	0.759299i	$-0.274458\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−288.213	−	166.400i	−0.425720	−	0.245790i	0.271801	−	0.962353i	$-0.412381\pi$
$677$	−288.213	−	166.400i	−0.425720	−	0.245790i	−0.697522	+	0.716564i	$0.745714\pi$
$678$		0			0
$679$	−87.1607	−	150.967i	−0.128366	−	0.222337i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			190.785i			0.279333i	0.990199	+	0.139667i	$0.0446031\pi$
$683$			190.785i			0.279333i	−0.990199	+	0.139667i	$0.955397\pi$
$684$		0			0
$685$	687.671			1.00390
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1009.54	+	582.856i	−1.46522	+	0.845945i
$690$		0			0
$691$	−360.135	+	623.771i	−0.521179	+	0.902708i	0.478518	+	0.878078i	$0.341174\pi$
$691$	−360.135	+	623.771i	−0.521179	+	0.902708i	−0.999697	+	0.0246304i	$0.992159\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.53379	−	3.19493i	−0.00796228	−	0.00459703i
$696$		0			0
$697$	−308.421	−	534.200i	−0.442497	−	0.766428i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			145.736i			0.207897i	0.994583	+	0.103949i	$0.0331477\pi$
$701$			145.736i			0.207897i	−0.994583	+	0.103949i	$0.966852\pi$
$702$		0			0
$703$	−1279.28			−1.81974
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−124.877	+	72.0980i	−0.176630	+	0.101977i
$708$		0			0
$709$	−394.430	+	683.173i	−0.556319	+	0.963572i	0.441481	+	0.897271i	$0.354453\pi$
$709$	−394.430	+	683.173i	−0.556319	+	0.963572i	−0.997800	+	0.0663017i	$0.978880\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	614.153	+	354.581i	0.861365	+	0.497309i
$714$		0			0
$715$	−486.936	−	843.398i	−0.681029	−	1.17958i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			721.671i			1.00372i	0.864950	+	0.501858i	$0.167350\pi$
$719$			721.671i			1.00372i	−0.864950	+	0.501858i	$0.832650\pi$
$720$		0			0
$721$	−79.2252			−0.109882
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−188.358	+	108.749i	−0.259805	+	0.149998i
$726$		0			0
$727$	−543.433	+	941.253i	−0.747500	+	1.29471i	0.201518	+	0.979485i	$0.435413\pi$
$727$	−543.433	+	941.253i	−0.747500	+	1.29471i	−0.949018	+	0.315223i	$0.897921\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−896.332	−	517.498i	−1.22617	−	0.707931i
$732$		0			0
$733$	−352.753	−	610.985i	−0.481245	−	0.833541i	0.518523	−	0.855063i	$-0.326482\pi$
$733$	−352.753	−	610.985i	−0.481245	−	0.833541i	−0.999768	+	0.0215227i	$0.993149\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	42.5181i		−	0.0576908i
$738$		0			0
$739$	−1183.74			−1.60182			−0.800909	−	0.598786i	$-0.795650\pi$
$739$	−1183.74			−1.60182			−0.800909	+	0.598786i	$0.795650\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−187.727	+	108.384i	−0.252661	+	0.145874i	−0.620982	−	0.783825i	$-0.713266\pi$
$743$	−187.727	+	108.384i	−0.252661	+	0.145874i	0.368321	+	0.929699i	$0.379933\pi$
$744$		0			0
$745$	174.705	−	302.598i	0.234503	−	0.406172i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.62949	+	0.940784i	0.00217555	+	0.00125605i
$750$		0			0
$751$	76.7045	+	132.856i	0.102137	+	0.176906i	0.912565	−	0.408932i	$-0.134099\pi$
$751$	76.7045	+	132.856i	0.102137	+	0.176906i	−0.810428	+	0.585838i	$0.800765\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			52.8056i			0.0699412i
$756$		0			0
$757$	−585.893			−0.773967			−0.386983	−	0.922087i	$-0.626483\pi$
$757$	−585.893			−0.773967			−0.386983	+	0.922087i	$0.626483\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	290.563	−	167.757i	0.381817	−	0.220442i	−0.296791	−	0.954942i	$-0.595917\pi$
$761$	290.563	−	167.757i	0.381817	−	0.220442i	0.678609	+	0.734500i	$0.262583\pi$
$762$		0			0
$763$	358.744	−	621.364i	0.470176	−	0.814369i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1362.86	−	786.848i	−1.77687	−	1.02588i
$768$		0			0
$769$	613.797	+	1063.13i	0.798175	+	1.38248i	0.920803	+	0.390028i	$0.127535\pi$
$769$	613.797	+	1063.13i	0.798175	+	1.38248i	−0.122628	+	0.992453i	$0.539132\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			512.944i			0.663576i	0.943354	+	0.331788i	$0.107652\pi$
$773$			512.944i			0.663576i	−0.943354	+	0.331788i	$0.892348\pi$
$774$		0			0
$775$	432.168			0.557636
$776$		0			0
$777$		0			0
$778$		0			0
$779$	577.318	−	333.315i	0.741101	−	0.427875i
$780$		0			0
$781$	338.221	−	585.816i	0.433062	−	0.750085i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	646.543	+	373.282i	0.823622	+	0.475518i
$786$		0			0
$787$	284.387	+	492.573i	0.361356	+	0.625886i	0.988184	−	0.153271i	$-0.0489807\pi$
$787$	284.387	+	492.573i	0.361356	+	0.625886i	−0.626828	+	0.779157i	$0.715647\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	483.337i		−	0.611046i
$792$		0			0
$793$	231.944			0.292490
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1026.79	+	592.819i	−1.28832	+	0.743813i	−0.978355	−	0.206934i	$-0.933651\pi$
$797$	−1026.79	+	592.819i	−1.28832	+	0.743813i	−0.309967	+	0.950747i	$0.600318\pi$
$798$		0			0
$799$	382.084	−	661.789i	0.478203	−	0.828271i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1208.70	−	697.845i	−1.50523	−	0.869047i
$804$		0			0
$805$	108.250	+	187.494i	0.134471	+	0.232911i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			185.707i			0.229552i	0.993391	+	0.114776i	$0.0366150\pi$
$809$			185.707i			0.229552i	−0.993391	+	0.114776i	$0.963385\pi$
$810$		0			0
$811$	451.817			0.557111			0.278555	−	0.960420i	$-0.410144\pi$
$811$	451.817			0.557111			0.278555	+	0.960420i	$0.410144\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	451.841	−	260.871i	0.554406	−	0.320087i
$816$		0			0
$817$	559.267	−	968.679i	0.684537	−	1.18565i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1029.67	+	594.478i	1.25416	+	0.724090i	0.971933	−	0.235257i	$-0.0755932\pi$
$821$	1029.67	+	594.478i	1.25416	+	0.724090i	0.282228	+	0.959347i	$0.408927\pi$
$822$		0			0
$823$	329.832	+	571.286i	0.400768	+	0.694151i	0.993819	−	0.111014i	$-0.0354099\pi$
$823$	329.832	+	571.286i	0.400768	+	0.694151i	−0.593051	+	0.805165i	$0.702077\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			291.986i			0.353067i	0.984295	+	0.176533i	$0.0564883\pi$
$827$			291.986i			0.353067i	−0.984295	+	0.176533i	$0.943512\pi$
$828$		0			0
$829$	−452.809			−0.546212			−0.273106	−	0.961984i	$-0.588051\pi$
$829$	−452.809			−0.546212			−0.273106	+	0.961984i	$0.588051\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−675.242	+	389.851i	−0.810615	+	0.468009i
$834$		0			0
$835$	−364.122	+	630.678i	−0.436075	+	0.755303i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−62.7098	−	36.2055i	−0.0747435	−	0.0431532i	0.462162	−	0.886795i	$-0.347074\pi$
$839$	−62.7098	−	36.2055i	−0.0747435	−	0.0431532i	−0.536906	+	0.843642i	$0.680407\pi$
$840$		0			0
$841$	−140.711	−	243.719i	−0.167314	−	0.289796i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	606.037i		−	0.717204i
$846$		0			0
$847$	−237.061			−0.279883
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−713.578	+	411.985i	−0.838518	+	0.484118i
$852$		0			0
$853$	−165.809	+	287.189i	−0.194383	+	0.336681i	−0.946698	−	0.322122i	$-0.895604\pi$
$853$	−165.809	+	287.189i	−0.194383	+	0.336681i	0.752315	+	0.658803i	$0.228937\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	426.279	+	246.112i	0.497408	+	0.287179i	0.727643	−	0.685956i	$-0.240616\pi$
$857$	426.279	+	246.112i	0.497408	+	0.287179i	−0.230234	+	0.973135i	$0.573949\pi$
$858$		0			0
$859$	379.885	+	657.980i	0.442241	+	0.765984i	0.997855	−	0.0654561i	$-0.0208502\pi$
$859$	379.885	+	657.980i	0.442241	+	0.765984i	−0.555614	+	0.831440i	$0.687517\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	263.506i		−	0.305337i	−0.988277	−	0.152668i	$-0.951213\pi$
$863$		−	263.506i		−	0.305337i	0.988277	−	0.152668i	$-0.0487867\pi$
$864$		0			0
$865$	104.084			0.120328
$866$		0			0
$867$		0			0
$868$		0			0
$869$	443.059	−	255.800i	0.509849	−	0.294362i
$870$		0			0
$871$	27.8962	−	48.3176i	0.0320278	−	0.0554737i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	424.936	+	245.337i	0.485642	+	0.280385i
$876$		0			0
$877$	707.946	+	1226.20i	0.807236	+	1.39817i	0.914771	+	0.403973i	$0.132371\pi$
$877$	707.946	+	1226.20i	0.807236	+	1.39817i	−0.107534	+	0.994201i	$0.534296\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	992.699i		−	1.12679i	−0.826189	−	0.563393i	$-0.809496\pi$
$881$		−	992.699i		−	1.12679i	0.826189	−	0.563393i	$-0.190504\pi$
$882$		0			0
$883$	−800.265			−0.906303			−0.453151	−	0.891434i	$-0.649700\pi$
$883$	−800.265			−0.906303			−0.453151	+	0.891434i	$0.649700\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	522.975	−	301.940i	0.589600	−	0.340405i	−0.175340	−	0.984508i	$-0.556102\pi$
$887$	522.975	−	301.940i	0.589600	−	0.340405i	0.764939	+	0.644103i	$0.222769\pi$
$888$		0			0
$889$	−82.7936	+	143.403i	−0.0931312	+	0.161308i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	715.205	+	412.924i	0.800901	+	0.462400i
$894$		0			0
$895$	−348.049	−	602.839i	−0.388882	−	0.673563i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	1111.88i		−	1.23680i
$900$		0			0
$901$	1409.30			1.56415
$902$		0			0
$903$		0			0
$904$		0			0
$905$	594.996	−	343.521i	0.657454	−	0.379581i
$906$		0			0
$907$	327.494	−	567.237i	0.361074	−	0.625399i	−0.627064	−	0.778968i	$-0.715743\pi$
$907$	327.494	−	567.237i	0.361074	−	0.625399i	0.988138	+	0.153569i	$0.0490767\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1475.55	+	851.907i	1.61970	+	0.935134i	0.986997	+	0.160740i	$0.0513880\pi$
$911$	1475.55	+	851.907i	1.61970	+	0.935134i	0.632703	+	0.774394i	$0.281945\pi$
$912$		0			0
$913$	115.959	+	200.846i	0.127008	+	0.219985i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	699.825i		−	0.763168i
$918$		0			0
$919$	−412.015			−0.448330			−0.224165	−	0.974551i	$-0.571965\pi$
$919$	−412.015			−0.448330			−0.224165	+	0.974551i	$0.571965\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	768.710	−	443.815i	0.832839	−	0.480840i
$924$		0			0
$925$	−251.066	+	434.859i	−0.271422	+	0.470117i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−645.658	−	372.771i	−0.695003	−	0.401260i	0.110480	−	0.993878i	$-0.464761\pi$
$929$	−645.658	−	372.771i	−0.695003	−	0.401260i	−0.805484	+	0.592618i	$0.798094\pi$
$930$		0			0
$931$	−421.318	−	729.744i	−0.452543	−	0.783828i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			1177.37i			1.25922i
$936$		0			0
$937$	227.643			0.242948			0.121474	−	0.992595i	$-0.461238\pi$
$937$	227.643			0.242948			0.121474	+	0.992595i	$0.461238\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	108.079	−	62.3995i	0.114856	−	0.0663119i	−0.441472	−	0.897275i	$-0.645543\pi$
$941$	108.079	−	62.3995i	0.114856	−	0.0663119i	0.556327	+	0.830963i	$0.312210\pi$
$942$		0			0
$943$	214.685	−	371.845i	0.227661	−	0.394321i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	508.817	+	293.766i	0.537294	+	0.310207i	0.743981	−	0.668200i	$-0.232935\pi$
$947$	508.817	+	293.766i	0.537294	+	0.310207i	−0.206688	+	0.978407i	$0.566268\pi$
$948$		0			0
$949$	−915.715	−	1586.06i	−0.964926	−	1.67130i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			413.855i			0.434266i	0.976142	+	0.217133i	$0.0696705\pi$
$953$			413.855i			0.434266i	−0.976142	+	0.217133i	$0.930330\pi$
$954$		0			0
$955$	349.394			0.365857
$956$		0			0
$957$		0			0
$958$		0			0
$959$	540.678	−	312.161i	0.563794	−	0.325507i
$960$		0			0
$961$	−624.153	+	1081.07i	−0.649483	+	1.12494i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−472.638	−	272.878i	−0.489780	−	0.282775i
$966$		0			0
$967$	512.963	+	888.477i	0.530468	+	0.918798i	0.999368	+	0.0355464i	$0.0113172\pi$
$967$	512.963	+	888.477i	0.530468	+	0.918798i	−0.468900	+	0.883251i	$0.655350\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			610.884i			0.629129i	0.949236	+	0.314564i	$0.101858\pi$
$971$			610.884i			0.629129i	−0.949236	+	0.314564i	$0.898142\pi$
$972$		0			0
$973$	−5.80122			−0.00596220
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−408.200	+	235.674i	−0.417809	+	0.241222i	−0.694140	−	0.719840i	$-0.744215\pi$
$977$	−408.200	+	235.674i	−0.417809	+	0.241222i	0.276330	+	0.961063i	$0.410882\pi$
$978$		0			0
$979$	97.0010	−	168.011i	0.0990817	−	0.171615i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−828.578	−	478.380i	−0.842908	−	0.486653i	0.0153438	−	0.999882i	$-0.495116\pi$
$983$	−828.578	−	478.380i	−0.842908	−	0.486653i	−0.858252	+	0.513229i	$0.828449\pi$
$984$		0			0
$985$	475.232	+	823.126i	0.482469	+	0.835661i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	720.437i		−	0.728450i
$990$		0			0
$991$	1743.95			1.75978			0.879892	−	0.475174i	$-0.157615\pi$
$991$	1743.95			1.75978			0.879892	+	0.475174i	$0.157615\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	862.723	−	498.093i	0.867058	−	0.500596i
$996$		0			0
$997$	81.8646	−	141.794i	0.0821109	−	0.142220i	−0.822046	−	0.569422i	$-0.807167\pi$
$997$	81.8646	−	141.794i	0.0821109	−	0.142220i	0.904156	+	0.427201i	$0.140500\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.m.b.89.1		8
3.2	odd	2		72.3.m.b.65.3	yes	8
4.3	odd	2		432.3.q.e.305.1		8
8.3	odd	2		1728.3.q.i.1601.4		8
8.5	even	2		1728.3.q.j.1601.4		8
9.2	odd	6		648.3.e.c.161.7		8
9.4	even	3		72.3.m.b.41.3	✓	8
9.5	odd	6	inner	216.3.m.b.17.1		8
9.7	even	3		648.3.e.c.161.2		8
12.11	even	2		144.3.q.e.65.2		8
24.5	odd	2		576.3.q.i.65.2		8
24.11	even	2		576.3.q.j.65.3		8
36.7	odd	6		1296.3.e.i.161.2		8
36.11	even	6		1296.3.e.i.161.7		8
36.23	even	6		432.3.q.e.17.1		8
36.31	odd	6		144.3.q.e.113.2		8
72.5	odd	6		1728.3.q.j.449.4		8
72.13	even	6		576.3.q.i.257.2		8
72.59	even	6		1728.3.q.i.449.4		8
72.67	odd	6		576.3.q.j.257.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.m.b.41.3	✓	8	9.4	even	3
72.3.m.b.65.3	yes	8	3.2	odd	2
144.3.q.e.65.2		8	12.11	even	2
144.3.q.e.113.2		8	36.31	odd	6
216.3.m.b.17.1		8	9.5	odd	6	inner
216.3.m.b.89.1		8	1.1	even	1	trivial
432.3.q.e.17.1		8	36.23	even	6
432.3.q.e.305.1		8	4.3	odd	2
576.3.q.i.65.2		8	24.5	odd	2
576.3.q.i.257.2		8	72.13	even	6
576.3.q.j.65.3		8	24.11	even	2
576.3.q.j.257.3		8	72.67	odd	6
648.3.e.c.161.2		8	9.7	even	3
648.3.e.c.161.7		8	9.2	odd	6
1296.3.e.i.161.2		8	36.7	odd	6
1296.3.e.i.161.7		8	36.11	even	6
1728.3.q.i.449.4		8	72.59	even	6
1728.3.q.i.1601.4		8	8.3	odd	2
1728.3.q.j.449.4		8	72.5	odd	6
1728.3.q.j.1601.4		8	8.5	even	2

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.44299 + 1.98781i) q^{5} +(-1.80469 + 3.12582i) q^{7} +O(q^{10})\)	\(q+(-3.44299 + 1.98781i) q^{5} +(-1.80469 + 3.12582i) q^{7} +(-11.8326 - 6.83153i) q^{11} +(-8.96435 - 15.5267i) q^{13} +21.6750i q^{17} -23.4245 q^{19} +(-13.0662 + 7.54376i) q^{23} +(-4.59721 + 7.96260i) q^{25} +(20.4862 + 11.8277i) q^{29} +(-23.5016 - 40.7060i) q^{31} -14.3495i q^{35} +54.6126 q^{37} +(-24.6459 + 14.2293i) q^{41} +(-23.8753 + 41.3532i) q^{43} +(-30.5323 - 17.6278i) q^{47} +(17.9862 + 31.1530i) q^{49} -65.0193i q^{53} +54.3192 q^{55} +(76.0156 - 43.8876i) q^{59} +(-6.46852 + 11.2038i) q^{61} +(61.7284 + 35.6389i) q^{65} +(1.55595 + 2.69499i) q^{67} +49.5089i q^{71} +102.151 q^{73} +(42.7082 - 24.6576i) q^{77} +(-18.7220 + 32.4275i) q^{79} +(-14.6999 - 8.48702i) q^{83} +(-43.0859 - 74.6270i) q^{85} +14.1990i q^{89} +64.7115 q^{91} +(80.6505 - 46.5636i) q^{95} +(-24.1484 + 41.8262i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{5} + 6 q^{7}+O(q^{10}) \) 8 * q + 6 * q^5 + 6 * q^7	\( 8 q + 6 q^{5} + 6 q^{7} - 36 q^{11} + 14 q^{13} + 4 q^{19} + 102 q^{23} + 10 q^{25} + 114 q^{29} - 50 q^{31} + 120 q^{37} - 264 q^{41} - 28 q^{43} - 150 q^{47} + 94 q^{49} - 244 q^{55} + 108 q^{59} + 14 q^{61} + 198 q^{65} - 20 q^{67} - 76 q^{73} - 66 q^{77} + 26 q^{79} - 246 q^{83} - 224 q^{85} + 108 q^{91} + 456 q^{95} - 236 q^{97}+O(q^{100}) \) 8 * q + 6 * q^5 + 6 * q^7 - 36 * q^11 + 14 * q^13 + 4 * q^19 + 102 * q^23 + 10 * q^25 + 114 * q^29 - 50 * q^31 + 120 * q^37 - 264 * q^41 - 28 * q^43 - 150 * q^47 + 94 * q^49 - 244 * q^55 + 108 * q^59 + 14 * q^61 + 198 * q^65 - 20 * q^67 - 76 * q^73 - 66 * q^77 + 26 * q^79 - 246 * q^83 - 224 * q^85 + 108 * q^91 + 456 * q^95 - 236 * q^97

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