LMFDB - Embedded newform 900.3.y.a.809.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(89,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("900.89");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.y (of order $10$, degree $4$, 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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			809.2
Character	$\chi$	$=$	900.809
Dual form			900.3.y.a.89.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.98426 + 0.396382i) q^{5} -2.05133i q^{7} +O(q^{10})$	$q+(-4.98426 + 0.396382i) q^{5} -2.05133i q^{7} +(-3.20226 + 4.40754i) q^{11} +(-8.49111 - 11.6870i) q^{13} +(-3.07013 + 9.44890i) q^{17} +(-0.491549 + 1.51283i) q^{19} +(24.6338 + 17.8975i) q^{23} +(24.6858 - 3.95134i) q^{25} +(14.1695 - 4.60394i) q^{29} +(7.49004 - 23.0520i) q^{31} +(0.813109 + 10.2244i) q^{35} +(-10.4512 - 14.3848i) q^{37} +(0.622089 + 0.856233i) q^{41} +39.1512i q^{43} +(5.02223 + 15.4568i) q^{47} +44.7921 q^{49} +(10.5064 + 32.3353i) q^{53} +(14.2139 - 23.2377i) q^{55} +(18.6182 + 25.6258i) q^{59} +(43.0338 + 31.2659i) q^{61} +(46.9544 + 54.8854i) q^{65} +(42.1147 + 13.6839i) q^{67} +(119.863 - 38.9457i) q^{71} +(39.3118 - 54.1080i) q^{73} +(9.04131 + 6.56889i) q^{77} +(-4.27671 - 13.1624i) q^{79} +(-21.0918 + 64.9140i) q^{83} +(11.5570 - 48.3128i) q^{85} +(-20.5399 + 28.2707i) q^{89} +(-23.9739 + 17.4181i) q^{91} +(1.85035 - 7.73520i) q^{95} +(76.8092 - 24.9568i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q+O(q^{10}) $ 80 * q	$ 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) $ 80 * q + 60 * q^19 + 56 * q^25 - 120 * q^31 + 20 * q^37 - 680 * q^49 - 56 * q^55 - 80 * q^61 - 280 * q^67 - 360 * q^73 + 40 * q^79 + 192 * q^85 + 140 * q^91 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$

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
$5$	−4.98426	+	0.396382i	−0.996853	+	0.0792764i
$5$	−4.98426	+	0.396382i	−0.996853	+	0.0792764i
$6$		0			0
$7$		−	2.05133i		−	0.293047i	−0.989207	−	0.146523i	$-0.953192\pi$
$7$		−	2.05133i		−	0.293047i	0.989207	−	0.146523i	$-0.0468084\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.20226	+	4.40754i	−0.291115	+	0.400685i	−0.929376	−	0.369135i	$-0.879654\pi$
$11$	−3.20226	+	4.40754i	−0.291115	+	0.400685i	0.638261	+	0.769820i	$0.279654\pi$
$12$		0			0
$13$	−8.49111	−	11.6870i	−0.653162	−	0.899001i	0.346069	−	0.938209i	$-0.387516\pi$
$13$	−8.49111	−	11.6870i	−0.653162	−	0.899001i	−0.999231	+	0.0392084i	$0.987516\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.07013	+	9.44890i	−0.180596	+	0.555818i	−0.999845	−	0.0176208i	$-0.994391\pi$
$17$	−3.07013	+	9.44890i	−0.180596	+	0.555818i	0.819249	+	0.573439i	$0.194391\pi$
$18$		0			0
$19$	−0.491549	+	1.51283i	−0.0258710	+	0.0796228i	−0.963158	−	0.268935i	$-0.913328\pi$
$19$	−0.491549	+	1.51283i	−0.0258710	+	0.0796228i	0.937287	+	0.348558i	$0.113328\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	24.6338	+	17.8975i	1.07103	+	0.778152i	0.976098	−	0.217331i	$-0.0697352\pi$
$23$	24.6338	+	17.8975i	1.07103	+	0.778152i	0.0949365	+	0.995483i	$0.469735\pi$
$24$		0			0
$25$	24.6858	−	3.95134i	0.987431	−	0.158054i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	14.1695	−	4.60394i	0.488603	−	0.158757i	−0.0543465	−	0.998522i	$-0.517308\pi$
$29$	14.1695	−	4.60394i	0.488603	−	0.158757i	0.542949	+	0.839765i	$0.317308\pi$
$30$		0			0
$31$	7.49004	−	23.0520i	0.241614	−	0.743612i	−0.754561	−	0.656230i	$-0.772150\pi$
$31$	7.49004	−	23.0520i	0.241614	−	0.743612i	0.996175	−	0.0873818i	$-0.0278500\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.813109	+	10.2244i	0.0232317	+	0.292125i
$36$		0			0
$37$	−10.4512	−	14.3848i	−0.282464	−	0.388778i	0.644084	−	0.764955i	$-0.277239\pi$
$37$	−10.4512	−	14.3848i	−0.282464	−	0.388778i	−0.926548	+	0.376177i	$0.877239\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.622089	+	0.856233i	0.0151729	+	0.0208837i	0.816536	−	0.577294i	$-0.195892\pi$
$41$	0.622089	+	0.856233i	0.0151729	+	0.0208837i	−0.801363	+	0.598178i	$0.795892\pi$
$42$		0			0
$43$			39.1512i			0.910494i	0.890365	+	0.455247i	$0.150449\pi$
$43$			39.1512i			0.910494i	−0.890365	+	0.455247i	$0.849551\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.02223	+	15.4568i	0.106856	+	0.328869i	0.990162	−	0.139929i	$-0.0446873\pi$
$47$	5.02223	+	15.4568i	0.106856	+	0.328869i	−0.883306	+	0.468798i	$0.844687\pi$
$48$		0			0
$49$	44.7921			0.914124
$50$		0			0
$51$		0			0
$52$		0			0
$53$	10.5064	+	32.3353i	0.198233	+	0.610099i	0.999924	+	0.0123597i	$0.00393433\pi$
$53$	10.5064	+	32.3353i	0.198233	+	0.610099i	−0.801690	+	0.597740i	$0.796066\pi$
$54$		0			0
$55$	14.2139	−	23.2377i	0.258434	−	0.422503i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	18.6182	+	25.6258i	0.315563	+	0.434336i	0.937106	−	0.349044i	$-0.113494\pi$
$59$	18.6182	+	25.6258i	0.315563	+	0.434336i	−0.621543	+	0.783380i	$0.713494\pi$
$60$		0			0
$61$	43.0338	+	31.2659i	0.705473	+	0.512556i	0.881710	−	0.471792i	$-0.156393\pi$
$61$	43.0338	+	31.2659i	0.705473	+	0.512556i	−0.176237	+	0.984348i	$0.556393\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	46.9544	+	54.8854i	0.722376	+	0.844391i
$66$		0			0
$67$	42.1147	+	13.6839i	0.628578	+	0.204237i	0.605945	−	0.795507i	$-0.292795\pi$
$67$	42.1147	+	13.6839i	0.628578	+	0.204237i	0.0226328	+	0.999744i	$0.492795\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	119.863	−	38.9457i	1.68821	−	0.548531i	0.701730	−	0.712443i	$-0.252411\pi$
$71$	119.863	−	38.9457i	1.68821	−	0.548531i	0.986475	+	0.163912i	$0.0524113\pi$
$72$		0			0
$73$	39.3118	−	54.1080i	0.538518	−	0.741206i	−0.449881	−	0.893089i	$-0.648534\pi$
$73$	39.3118	−	54.1080i	0.538518	−	0.741206i	0.988399	+	0.151883i	$0.0485335\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.04131	+	6.56889i	0.117420	+	0.0853103i
$78$		0			0
$79$	−4.27671	−	13.1624i	−0.0541356	−	0.166612i	0.920333	−	0.391135i	$-0.127918\pi$
$79$	−4.27671	−	13.1624i	−0.0541356	−	0.166612i	−0.974469	+	0.224523i	$0.927918\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−21.0918	+	64.9140i	−0.254119	+	0.782096i	0.739883	+	0.672735i	$0.234881\pi$
$83$	−21.0918	+	64.9140i	−0.254119	+	0.782096i	−0.994002	+	0.109361i	$0.965119\pi$
$84$		0			0
$85$	11.5570	−	48.3128i	0.135965	−	0.568385i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−20.5399	+	28.2707i	−0.230785	+	0.317649i	−0.908666	−	0.417523i	$-0.862898\pi$
$89$	−20.5399	+	28.2707i	−0.230785	+	0.317649i	0.677881	+	0.735171i	$0.262898\pi$
$90$		0			0
$91$	−23.9739	+	17.4181i	−0.263449	+	0.191407i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.85035	−	7.73520i	0.0194774	−	0.0814232i
$96$		0			0
$97$	76.8092	−	24.9568i	0.791847	−	0.257287i	0.114957	−	0.993371i	$-0.463327\pi$
$97$	76.8092	−	24.9568i	0.791847	−	0.257287i	0.676890	+	0.736084i	$0.263327\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			179.542i			1.77765i	0.458249	+	0.888824i	$0.348477\pi$
$101$			179.542i			1.77765i	−0.458249	+	0.888824i	$0.651523\pi$
$102$		0			0
$103$	−65.6376	+	21.3269i	−0.637258	+	0.207058i	−0.609787	−	0.792565i	$-0.708745\pi$
$103$	−65.6376	+	21.3269i	−0.637258	+	0.207058i	−0.0274704	+	0.999623i	$0.508745\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	47.0450			0.439673			0.219836	−	0.975537i	$-0.429448\pi$
$107$	47.0450			0.439673			0.219836	+	0.975537i	$0.429448\pi$
$108$		0			0
$109$	95.5599	−	69.4283i	0.876696	−	0.636957i	−0.0556793	−	0.998449i	$-0.517732\pi$
$109$	95.5599	−	69.4283i	0.876696	−	0.636957i	0.932375	+	0.361492i	$0.117732\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.47884	−	1.07444i	0.0130871	−	0.00950831i	−0.581222	−	0.813745i	$-0.697425\pi$
$113$	1.47884	−	1.07444i	0.0130871	−	0.00950831i	0.594310	+	0.804236i	$0.297425\pi$
$114$		0			0
$115$	−129.876	−	79.4414i	−1.12935	−	0.690795i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	19.3828	+	6.29785i	0.162881	+	0.0529231i
$120$		0			0
$121$	28.2192	+	86.8496i	0.233216	+	0.717766i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−121.474	+	29.4795i	−0.971793	+	0.235836i
$126$		0			0
$127$	82.7252	−	113.861i	0.651379	−	0.896546i	−0.347779	−	0.937577i	$-0.613064\pi$
$127$	82.7252	−	113.861i	0.651379	−	0.896546i	0.999158	+	0.0410302i	$0.0130640\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5.33914	+	1.73479i	0.0407568	+	0.0132427i	0.329324	−	0.944217i	$-0.393179\pi$
$131$	5.33914	+	1.73479i	0.0407568	+	0.0132427i	−0.288568	+	0.957460i	$0.593179\pi$
$132$		0			0
$133$	3.10332	+	1.00833i	0.0233332	+	0.00758142i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−73.8739	+	53.6725i	−0.539225	+	0.391770i	−0.823797	−	0.566885i	$-0.808149\pi$
$137$	−73.8739	+	53.6725i	−0.539225	+	0.391770i	0.284572	+	0.958655i	$0.408149\pi$
$138$		0			0
$139$	15.6006	+	11.3345i	0.112235	+	0.0815433i	0.642487	−	0.766297i	$-0.277903\pi$
$139$	15.6006	+	11.3345i	0.112235	+	0.0815433i	−0.530252	+	0.847840i	$0.677903\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	78.7017			0.550362
$144$		0			0
$145$	−68.7995	+	28.5638i	−0.474479	+	0.196992i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	113.967i		−	0.764882i	−0.923980	−	0.382441i	$-0.875083\pi$
$149$		−	113.967i		−	0.764882i	0.923980	−	0.382441i	$-0.124917\pi$
$150$		0			0
$151$	59.5217			0.394183			0.197092	−	0.980385i	$-0.436850\pi$
$151$	59.5217			0.394183			0.197092	+	0.980385i	$0.436850\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−28.1949	+	117.866i	−0.181903	+	0.760426i
$156$		0			0
$157$		−	108.076i		−	0.688379i	−0.938900	−	0.344190i	$-0.888154\pi$
$157$		−	108.076i		−	0.688379i	0.938900	−	0.344190i	$-0.111846\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	36.7136	−	50.5320i	0.228035	−	0.313863i
$162$		0			0
$163$	−103.594	−	142.585i	−0.635548	−	0.874757i	0.362820	−	0.931859i	$-0.381814\pi$
$163$	−103.594	−	142.585i	−0.635548	−	0.874757i	−0.998368	+	0.0571021i	$0.981814\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	35.9581	−	110.668i	0.215318	−	0.662680i	−0.783813	−	0.620997i	$-0.786728\pi$
$167$	35.9581	−	110.668i	0.215318	−	0.662680i	0.999131	−	0.0416831i	$-0.0132720\pi$
$168$		0			0
$169$	−12.2634	+	37.7428i	−0.0725644	+	0.223330i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	28.3258	+	20.5799i	0.163733	+	0.118959i	0.666635	−	0.745385i	$-0.267734\pi$
$173$	28.3258	+	20.5799i	0.163733	+	0.118959i	−0.502902	+	0.864344i	$0.667734\pi$
$174$		0			0
$175$	−8.10550	−	50.6386i	−0.0463172	−	0.289363i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	81.2722	−	26.4069i	0.454035	−	0.147525i	−0.0730670	−	0.997327i	$-0.523279\pi$
$179$	81.2722	−	26.4069i	0.454035	−	0.147525i	0.527102	+	0.849802i	$0.323279\pi$
$180$		0			0
$181$	−68.8759	+	211.978i	−0.380530	+	1.17115i	0.559141	+	0.829072i	$0.311131\pi$
$181$	−68.8759	+	211.978i	−0.380530	+	1.17115i	−0.939671	+	0.342079i	$0.888869\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	57.7932	+	67.5549i	0.312396	+	0.365162i
$186$		0			0
$187$	−31.8150	−	43.7896i	−0.170134	−	0.234169i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−48.7407	−	67.0859i	−0.255187	−	0.351235i	0.662132	−	0.749387i	$-0.269652\pi$
$191$	−48.7407	−	67.0859i	−0.255187	−	0.351235i	−0.917319	+	0.398152i	$0.869652\pi$
$192$		0			0
$193$			212.949i			1.10336i	0.834056	+	0.551680i	$0.186013\pi$
$193$			212.949i			1.10336i	−0.834056	+	0.551680i	$0.813987\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−22.7002	−	69.8641i	−0.115230	−	0.354640i	0.876765	−	0.480919i	$-0.159697\pi$
$197$	−22.7002	−	69.8641i	−0.115230	−	0.354640i	−0.991995	+	0.126278i	$0.959697\pi$
$198$		0			0
$199$	288.811			1.45131			0.725655	−	0.688059i	$-0.241537\pi$
$199$	288.811			1.45131			0.725655	+	0.688059i	$0.241537\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−9.44420	−	29.0663i	−0.0465231	−	0.143184i
$204$		0			0
$205$	−3.44005	−	4.02110i	−0.0167807	−	0.0196151i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.09380	−	7.01102i	−0.0243723	−	0.0335455i
$210$		0			0
$211$	34.2306	+	24.8700i	0.162230	+	0.117867i	0.665939	−	0.746007i	$-0.268031\pi$
$211$	34.2306	+	24.8700i	0.162230	+	0.117867i	−0.503708	+	0.863874i	$0.668031\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−15.5188	−	195.140i	−0.0721807	−	0.907628i
$216$		0			0
$217$	−47.2872	−	15.3645i	−0.217913	−	0.0708043i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	136.498	−	44.3510i	0.617639	−	0.200683i
$222$		0			0
$223$	−225.021	+	309.714i	−1.00906	+	1.38885i	−0.0894651	+	0.995990i	$0.528516\pi$
$223$	−225.021	+	309.714i	−1.00906	+	1.38885i	−0.919597	+	0.392864i	$0.871484\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−318.423	−	231.348i	−1.40274	−	1.01915i	−0.994328	−	0.106355i	$-0.966082\pi$
$227$	−318.423	−	231.348i	−1.40274	−	1.01915i	−0.408414	−	0.912797i	$-0.633918\pi$
$228$		0			0
$229$	123.150	+	379.017i	0.537773	+	1.65509i	0.737580	+	0.675260i	$0.235968\pi$
$229$	123.150	+	379.017i	0.537773	+	1.65509i	−0.199807	+	0.979835i	$0.564032\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−110.999	+	341.620i	−0.476391	+	1.46618i	0.367681	+	0.929952i	$0.380152\pi$
$233$	−110.999	+	341.620i	−0.476391	+	1.46618i	−0.844072	+	0.536230i	$0.819848\pi$
$234$		0			0
$235$	−31.1590	−	75.0503i	−0.132591	−	0.319363i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	207.960	−	286.233i	0.870128	−	1.19763i	−0.108931	−	0.994049i	$-0.534743\pi$
$239$	207.960	−	286.233i	0.870128	−	1.19763i	0.979059	−	0.203579i	$-0.0652572\pi$
$240$		0			0
$241$	−222.025	+	161.311i	−0.921267	+	0.669340i	−0.943839	−	0.330406i	$-0.892814\pi$
$241$	−222.025	+	161.311i	−0.921267	+	0.669340i	0.0225722	+	0.999745i	$0.492814\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−223.255	+	17.7548i	−0.911246	+	0.0724684i
$246$		0			0
$247$	21.8543	−	7.10089i	0.0884789	−	0.0287486i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	219.804i		−	0.875712i	−0.899045	−	0.437856i	$-0.855738\pi$
$251$		−	219.804i		−	0.875712i	0.899045	−	0.437856i	$-0.144262\pi$
$252$		0			0
$253$	−157.768	+	51.2619i	−0.623588	+	0.202616i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−374.482			−1.45713			−0.728564	−	0.684978i	$-0.759812\pi$
$257$	−374.482			−1.45713			−0.728564	+	0.684978i	$0.759812\pi$
$258$		0			0
$259$	−29.5079	+	21.4388i	−0.113930	+	0.0827751i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	171.870	−	124.871i	0.653497	−	0.474793i	−0.210964	−	0.977494i	$-0.567660\pi$
$263$	171.870	−	124.871i	0.653497	−	0.474793i	0.864461	+	0.502700i	$0.167660\pi$
$264$		0			0
$265$	−65.1836	−	157.003i	−0.245976	−	0.592464i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−258.977	−	84.1467i	−0.962740	−	0.312813i	−0.214858	−	0.976645i	$-0.568929\pi$
$269$	−258.977	−	84.1467i	−0.962740	−	0.312813i	−0.747882	+	0.663832i	$0.768929\pi$
$270$		0			0
$271$	−37.1986	−	114.485i	−0.137264	−	0.422455i	0.858671	−	0.512527i	$-0.171290\pi$
$271$	−37.1986	−	114.485i	−0.137264	−	0.422455i	−0.995935	+	0.0900714i	$0.971290\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−61.6346	+	121.457i	−0.224126	+	0.441661i
$276$		0			0
$277$	88.5679	−	121.903i	0.319740	−	0.440084i	−0.618648	−	0.785668i	$-0.712319\pi$
$277$	88.5679	−	121.903i	0.319740	−	0.440084i	0.938388	+	0.345584i	$0.112319\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	150.839	+	49.0106i	0.536794	+	0.174415i	0.564853	−	0.825191i	$-0.308933\pi$
$281$	150.839	+	49.0106i	0.536794	+	0.174415i	−0.0280595	+	0.999606i	$0.508933\pi$
$282$		0			0
$283$	−413.859	−	134.471i	−1.46240	−	0.475162i	−0.533596	−	0.845739i	$-0.679160\pi$
$283$	−413.859	−	134.471i	−1.46240	−	0.475162i	−0.928802	+	0.370578i	$0.879160\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.75641	−	1.27611i	0.00611991	−	0.00444637i
$288$		0			0
$289$	153.950	+	111.851i	0.532699	+	0.387028i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−48.8663			−0.166779			−0.0833896	−	0.996517i	$-0.526575\pi$
$293$	−48.8663			−0.166779			−0.0833896	+	0.996517i	$0.526575\pi$
$294$		0			0
$295$	−102.956	−	120.346i	−0.349003	−	0.407952i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		−	439.865i		−	1.47112i
$300$		0			0
$301$	80.3120			0.266817
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−226.885	−	138.780i	−0.743886	−	0.455015i
$306$		0			0
$307$		−	362.825i		−	1.18184i	−0.806731	−	0.590920i	$-0.798765\pi$
$307$		−	362.825i		−	1.18184i	0.806731	−	0.590920i	$-0.201235\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	52.7404	−	72.5909i	0.169583	−	0.233411i	−0.715763	−	0.698343i	$-0.753921\pi$
$311$	52.7404	−	72.5909i	0.169583	−	0.233411i	0.885347	+	0.464932i	$0.153921\pi$
$312$		0			0
$313$	32.5543	+	44.8072i	0.104007	+	0.143154i	0.857848	−	0.513903i	$-0.171801\pi$
$313$	32.5543	+	44.8072i	0.104007	+	0.143154i	−0.753841	+	0.657057i	$0.771801\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.19358	+	28.2949i	−0.0290018	+	0.0892585i	−0.964510	−	0.264047i	$-0.914942\pi$
$317$	−9.19358	+	28.2949i	−0.0290018	+	0.0892585i	0.935508	+	0.353306i	$0.114942\pi$
$318$		0			0
$319$	−25.0824	+	77.1956i	−0.0786281	+	0.241992i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−12.7855	−	9.28920i	−0.0395836	−	0.0287591i
$324$		0			0
$325$	−255.789	−	254.951i	−0.787043	−	0.784466i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	31.7071	−	10.3023i	0.0963741	−	0.0313138i
$330$		0			0
$331$	−170.982	+	526.227i	−0.516561	+	1.58981i	0.263863	+	0.964560i	$0.415003\pi$
$331$	−170.982	+	526.227i	−0.516561	+	1.58981i	−0.780424	+	0.625251i	$0.784997\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−215.335	−	51.5107i	−0.642791	−	0.153763i
$336$		0			0
$337$	21.4423	+	29.5128i	0.0636269	+	0.0875750i	0.839645	−	0.543136i	$-0.182763\pi$
$337$	21.4423	+	29.5128i	0.0636269	+	0.0875750i	−0.776018	+	0.630711i	$0.782763\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	77.6174	+	106.831i	0.227617	+	0.313288i
$342$		0			0
$343$		−	192.398i		−	0.560928i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−94.5031	−	290.851i	−0.272343	−	0.838186i	−0.989910	−	0.141697i	$-0.954744\pi$
$347$	−94.5031	−	290.851i	−0.272343	−	0.838186i	0.717567	−	0.696490i	$-0.245256\pi$
$348$		0			0
$349$	−112.309			−0.321803			−0.160901	−	0.986970i	$-0.551440\pi$
$349$	−112.309			−0.321803			−0.160901	+	0.986970i	$0.551440\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	35.4236	+	109.023i	0.100350	+	0.308846i	0.988611	−	0.150493i	$-0.0480862\pi$
$353$	35.4236	+	109.023i	0.100350	+	0.308846i	−0.888261	+	0.459339i	$0.848086\pi$
$354$		0			0
$355$	−581.989	+	241.627i	−1.63941	+	0.680639i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−202.980	−	279.378i	−0.565403	−	0.778211i	0.426597	−	0.904442i	$-0.359712\pi$
$359$	−202.980	−	279.378i	−0.565403	−	0.778211i	−0.992001	+	0.126231i	$0.959712\pi$
$360$		0			0
$361$	290.008	+	210.703i	0.803347	+	0.583665i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−174.493	+	285.271i	−0.478063	+	0.781565i
$366$		0			0
$367$	81.5574	+	26.4996i	0.222227	+	0.0722060i	0.418014	−	0.908440i	$-0.362726\pi$
$367$	81.5574	+	26.4996i	0.222227	+	0.0722060i	−0.195787	+	0.980646i	$0.562726\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	66.3302	−	21.5520i	0.178788	−	0.0580916i
$372$		0			0
$373$	−285.062	+	392.355i	−0.764242	+	1.05189i	0.232607	+	0.972571i	$0.425274\pi$
$373$	−285.062	+	392.355i	−0.764242	+	1.05189i	−0.996849	+	0.0793182i	$0.974726\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−174.121	−	126.506i	−0.461859	−	0.335560i
$378$		0			0
$379$	−115.620	−	355.843i	−0.305067	−	0.938899i	−0.979652	−	0.200702i	$-0.935678\pi$
$379$	−115.620	−	355.843i	−0.305067	−	0.938899i	0.674586	−	0.738197i	$-0.264322\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−71.4740	+	219.974i	−0.186616	+	0.574346i	−0.999972	−	0.00742012i	$-0.997638\pi$
$383$	−71.4740	+	219.974i	−0.186616	+	0.574346i	0.813356	+	0.581766i	$0.197638\pi$
$384$		0			0
$385$	−47.6680	−	29.1573i	−0.123813	−	0.0757332i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	61.9335	−	85.2441i	0.159212	−	0.219137i	−0.721957	−	0.691938i	$-0.756757\pi$
$389$	61.9335	−	85.2441i	0.159212	−	0.219137i	0.881169	+	0.472801i	$0.156757\pi$
$390$		0			0
$391$	−244.741	+	177.815i	−0.625935	+	0.454769i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	26.5336	+	63.9095i	0.0671736	+	0.161796i
$396$		0			0
$397$	534.778	−	173.760i	1.34705	−	0.437683i	0.455350	−	0.890313i	$-0.349514\pi$
$397$	534.778	−	173.760i	1.34705	−	0.437683i	0.891698	+	0.452630i	$0.149514\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	286.946i		−	0.715575i	−0.933803	−	0.357788i	$-0.883531\pi$
$401$		−	286.946i		−	0.715575i	0.933803	−	0.357788i	$-0.116469\pi$
$402$		0			0
$403$	−333.007	+	108.201i	−0.826321	+	0.268488i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	96.8689			0.238007
$408$		0			0
$409$	404.745	−	294.065i	0.989597	−	0.718984i	0.0297640	−	0.999557i	$-0.490524\pi$
$409$	404.745	−	294.065i	0.989597	−	0.718984i	0.959833	+	0.280573i	$0.0905244\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	52.5669	−	38.1921i	0.127281	−	0.0924749i
$414$		0			0
$415$	79.3965	−	331.909i	0.191317	−	0.799781i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−287.204	−	93.3183i	−0.685451	−	0.222717i	−0.0544709	−	0.998515i	$-0.517347\pi$
$419$	−287.204	−	93.3183i	−0.685451	−	0.222717i	−0.630980	+	0.775799i	$0.717347\pi$
$420$		0			0
$421$	244.958	+	753.903i	0.581848	+	1.79074i	0.611576	+	0.791186i	$0.290536\pi$
$421$	244.958	+	753.903i	0.581848	+	1.79074i	−0.0297280	+	0.999558i	$0.509464\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−38.4527	+	245.385i	−0.0904770	+	0.577375i
$426$		0			0
$427$	64.1366	−	88.2765i	0.150203	−	0.206737i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	509.183	+	165.444i	1.18140	+	0.383860i	0.832887	−	0.553444i	$-0.186687\pi$
$431$	509.183	+	165.444i	1.18140	+	0.383860i	0.348513	+	0.937304i	$0.386687\pi$
$432$		0			0
$433$	36.2033	+	11.7632i	0.0836104	+	0.0271667i	0.350523	−	0.936554i	$-0.386004\pi$
$433$	36.2033	+	11.7632i	0.0836104	+	0.0271667i	−0.266913	+	0.963721i	$0.586004\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−39.1847	+	28.4693i	−0.0896674	+	0.0651472i
$438$		0			0
$439$	678.560	+	493.002i	1.54569	+	1.12301i	0.946635	+	0.322307i	$0.104458\pi$
$439$	678.560	+	493.002i	1.54569	+	1.12301i	0.599059	+	0.800705i	$0.295542\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	124.912			0.281968			0.140984	−	0.990012i	$-0.454973\pi$
$443$	124.912			0.281968			0.140984	+	0.990012i	$0.454973\pi$
$444$		0			0
$445$	91.1702	−	149.050i	0.204877	−	0.334945i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			90.2818i			0.201073i	0.994933	+	0.100537i	$0.0320559\pi$
$449$			90.2818i			0.201073i	−0.994933	+	0.100537i	$0.967944\pi$
$450$		0			0
$451$	−5.76597			−0.0127849
$452$		0			0
$453$		0			0
$454$		0			0
$455$	112.588	−	96.3190i	0.247446	−	0.211690i
$456$		0			0
$457$		−	46.8085i		−	0.102426i	−0.998688	−	0.0512128i	$-0.983691\pi$
$457$		−	46.8085i		−	0.102426i	0.998688	−	0.0512128i	$-0.0163087\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	90.1004	−	124.013i	0.195446	−	0.269008i	−0.700035	−	0.714109i	$-0.746832\pi$
$461$	90.1004	−	124.013i	0.195446	−	0.269008i	0.895480	+	0.445101i	$0.146832\pi$
$462$		0			0
$463$	−172.110	−	236.890i	−0.371729	−	0.511641i	0.581641	−	0.813446i	$-0.302411\pi$
$463$	−172.110	−	236.890i	−0.371729	−	0.511641i	−0.953370	+	0.301805i	$0.902411\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	125.913	−	387.520i	0.269621	−	0.829807i	−0.720972	−	0.692964i	$-0.756304\pi$
$467$	125.913	−	387.520i	0.269621	−	0.829807i	0.990593	−	0.136843i	$-0.0436956\pi$
$468$		0			0
$469$	28.0702	−	86.3911i	0.0598511	−	0.184203i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−172.561	−	125.373i	−0.364821	−	0.265058i
$474$		0			0
$475$	−6.15655	+	39.2877i	−0.0129611	+	0.0827110i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	605.960	−	196.888i	1.26505	−	0.411040i	0.401760	−	0.915745i	$-0.368399\pi$
$479$	605.960	−	196.888i	1.26505	−	0.411040i	0.863292	+	0.504704i	$0.168399\pi$
$480$		0			0
$481$	−79.3732	+	244.286i	−0.165017	+	0.507870i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−372.945	+	154.837i	−0.768958	+	0.319252i
$486$		0			0
$487$	−58.3510	−	80.3132i	−0.119817	−	0.164914i	0.744895	−	0.667181i	$-0.232499\pi$
$487$	−58.3510	−	80.3132i	−0.119817	−	0.164914i	−0.864712	+	0.502267i	$0.832499\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	242.967	+	334.415i	0.494840	+	0.681089i	0.981272	−	0.192630i	$-0.0617016\pi$
$491$	242.967	+	334.415i	0.494840	+	0.681089i	−0.486431	+	0.873719i	$0.661702\pi$
$492$		0			0
$493$			148.021i			0.300245i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−79.8904	−	245.877i	−0.160745	−	0.494723i
$498$		0			0
$499$	438.011			0.877778			0.438889	−	0.898541i	$-0.355372\pi$
$499$	438.011			0.877778			0.438889	+	0.898541i	$0.355372\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	298.017	+	917.202i	0.592479	+	1.82346i	0.566896	+	0.823790i	$0.308144\pi$
$503$	298.017	+	917.202i	0.592479	+	1.82346i	0.0255832	+	0.999673i	$0.491856\pi$
$504$		0			0
$505$	−71.1674	−	894.887i	−0.140926	−	1.77205i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	511.890	+	704.557i	1.00568	+	1.38420i	0.921775	+	0.387724i	$0.126739\pi$
$509$	511.890	+	704.557i	1.00568	+	1.38420i	0.0839033	+	0.996474i	$0.473261\pi$
$510$		0			0
$511$	−110.993	−	80.6414i	−0.217208	−	0.157811i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	318.701	−	132.317i	0.618837	−	0.256925i
$516$		0			0
$517$	−84.2092	−	27.3612i	−0.162880	−	0.0529231i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−20.2982	+	6.59529i	−0.0389601	+	0.0126589i	−0.328432	−	0.944528i	$-0.606520\pi$
$521$	−20.2982	+	6.59529i	−0.0389601	+	0.0126589i	0.289472	+	0.957186i	$0.406520\pi$
$522$		0			0
$523$	−260.381	+	358.384i	−0.497860	+	0.685246i	−0.981813	−	0.189848i	$-0.939200\pi$
$523$	−260.381	+	358.384i	−0.497860	+	0.685246i	0.483953	+	0.875094i	$0.339200\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	194.820	+	141.545i	0.369678	+	0.268587i
$528$		0			0
$529$	123.033	+	378.657i	0.232577	+	0.715799i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.72457	−	14.5407i	0.00886411	−	0.0272809i
$534$		0			0
$535$	−234.485	+	18.6478i	−0.438289	+	0.0348557i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−143.436	+	197.423i	−0.266115	+	0.366276i
$540$		0			0
$541$	473.315	−	343.884i	0.874890	−	0.635645i	−0.0570047	−	0.998374i	$-0.518155\pi$
$541$	473.315	−	343.884i	0.874890	−	0.635645i	0.931895	+	0.362729i	$0.118155\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−448.775	+	383.927i	−0.823441	+	0.704454i
$546$		0			0
$547$	261.467	−	84.9558i	0.478002	−	0.155312i	−0.0600995	−	0.998192i	$-0.519142\pi$
$547$	261.467	−	84.9558i	0.478002	−	0.155312i	0.538101	+	0.842880i	$0.319142\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			23.6991i			0.0430111i
$552$		0			0
$553$	−27.0003	+	8.77293i	−0.0488252	+	0.0158643i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−429.452			−0.771009			−0.385504	−	0.922706i	$-0.625972\pi$
$557$	−429.452			−0.771009			−0.385504	+	0.922706i	$0.625972\pi$
$558$		0			0
$559$	457.561	−	332.437i	0.818534	−	0.594700i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−316.374	+	229.859i	−0.561943	+	0.408276i	−0.832170	−	0.554521i	$-0.812901\pi$
$563$	−316.374	+	229.859i	−0.561943	+	0.408276i	0.270226	+	0.962797i	$0.412901\pi$
$564$		0			0
$565$	−6.94503	+	5.94147i	−0.0122921	+	0.0105159i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−96.4412	−	31.3357i	−0.169493	−	0.0550715i	0.223041	−	0.974809i	$-0.428401\pi$
$569$	−96.4412	−	31.3357i	−0.169493	−	0.0550715i	−0.392534	+	0.919738i	$0.628401\pi$
$570$		0			0
$571$	222.246	+	684.003i	0.389223	+	1.19790i	0.933370	+	0.358915i	$0.116853\pi$
$571$	222.246	+	684.003i	0.389223	+	1.19790i	−0.544148	+	0.838990i	$0.683147\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	678.823	+	344.477i	1.18056	+	0.599090i
$576$		0			0
$577$	457.281	−	629.394i	0.792515	−	1.09080i	−0.201275	−	0.979535i	$-0.564509\pi$
$577$	457.281	−	629.394i	0.792515	−	1.09080i	0.993790	−	0.111269i	$-0.0354914\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	133.160	+	43.2663i	0.229191	+	0.0744686i
$582$		0			0
$583$	−176.163	−	57.2388i	−0.302166	−	0.0981798i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−232.300	+	168.776i	−0.395741	+	0.287523i	−0.767804	−	0.640685i	$-0.778651\pi$
$587$	−232.300	+	168.776i	−0.395741	+	0.287523i	0.372063	+	0.928207i	$0.378651\pi$
$588$		0			0
$589$	31.1921	+	22.6624i	0.0529577	+	0.0384760i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	742.051			1.25135			0.625675	−	0.780084i	$-0.284823\pi$
$593$	742.051			1.25135			0.625675	+	0.780084i	$0.284823\pi$
$594$		0			0
$595$	−99.1053	−	23.7072i	−0.166564	−	0.0398440i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	540.081i		−	0.901638i	−0.892616	−	0.450819i	$-0.851132\pi$
$599$		−	540.081i		−	0.901638i	0.892616	−	0.450819i	$-0.148868\pi$
$600$		0			0
$601$	−441.008			−0.733790			−0.366895	−	0.930262i	$-0.619579\pi$
$601$	−441.008			−0.733790			−0.366895	+	0.930262i	$0.619579\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−175.077	−	421.696i	−0.289384	−	0.697018i
$606$		0			0
$607$		−	566.768i		−	0.933720i	−0.884331	−	0.466860i	$-0.845385\pi$
$607$		−	566.768i		−	0.933720i	0.884331	−	0.466860i	$-0.154615\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	138.000	−	189.941i	0.225859	−	0.310869i
$612$		0			0
$613$	−192.132	−	264.447i	−0.313429	−	0.431398i	0.623018	−	0.782208i	$-0.285906\pi$
$613$	−192.132	−	264.447i	−0.313429	−	0.431398i	−0.936447	+	0.350809i	$0.885906\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−229.928	+	707.647i	−0.372655	+	1.14692i	0.572391	+	0.819980i	$0.306016\pi$
$617$	−229.928	+	707.647i	−0.372655	+	1.14692i	−0.945047	+	0.326935i	$0.893984\pi$
$618$		0			0
$619$	−11.3534	+	34.9420i	−0.0183414	+	0.0564492i	−0.959808	−	0.280656i	$-0.909448\pi$
$619$	−11.3534	+	34.9420i	−0.0183414	+	0.0564492i	0.941467	+	0.337105i	$0.109448\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	57.9925	+	42.1340i	0.0930859	+	0.0676309i
$624$		0			0
$625$	593.774	−	195.084i	0.950038	−	0.312134i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	168.007	−	54.5887i	0.267102	−	0.0867866i
$630$		0			0
$631$	363.832	−	1119.76i	0.576596	−	1.77458i	−0.0540832	−	0.998536i	$-0.517224\pi$
$631$	363.832	−	1119.76i	0.576596	−	1.77458i	0.630679	−	0.776044i	$-0.282776\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−367.191	+	600.306i	−0.578254	+	0.945364i
$636$		0			0
$637$	−380.334	−	523.485i	−0.597071	−	0.821798i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	461.804	+	635.619i	0.720443	+	0.991605i	0.999509	+	0.0313333i	$0.00997534\pi$
$641$	461.804	+	635.619i	0.720443	+	0.991605i	−0.279066	+	0.960272i	$0.590025\pi$
$642$		0			0
$643$		−	235.295i		−	0.365933i	−0.983119	−	0.182967i	$-0.941430\pi$
$643$		−	235.295i		−	0.365933i	0.983119	−	0.182967i	$-0.0585700\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	172.197	+	529.967i	0.266147	+	0.819115i	0.991427	+	0.130661i	$0.0417101\pi$
$647$	172.197	+	529.967i	0.266147	+	0.819115i	−0.725280	+	0.688453i	$0.758290\pi$
$648$		0			0
$649$	−172.567			−0.265897
$650$		0			0
$651$		0			0
$652$		0			0
$653$	317.263	+	976.435i	0.485855	+	1.49531i	0.830739	+	0.556662i	$0.187918\pi$
$653$	317.263	+	976.435i	0.485855	+	1.49531i	−0.344885	+	0.938645i	$0.612082\pi$
$654$		0			0
$655$	−27.2993	−	6.53032i	−0.0416783	−	0.00996995i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−208.299	−	286.699i	−0.316084	−	0.435052i	0.621183	−	0.783666i	$-0.286652\pi$
$659$	−208.299	−	286.699i	−0.316084	−	0.435052i	−0.937266	+	0.348614i	$0.886652\pi$
$660$		0			0
$661$	285.049	+	207.100i	0.431239	+	0.313314i	0.782144	−	0.623097i	$-0.214126\pi$
$661$	285.049	+	207.100i	0.431239	+	0.313314i	−0.350905	+	0.936411i	$0.614126\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−15.8674	−	3.79568i	−0.0238608	−	0.00570779i
$666$		0			0
$667$	431.447	+	140.186i	0.646847	+	0.210173i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−275.611	+	89.5515i	−0.410747	+	0.133460i
$672$		0			0
$673$	−287.332	+	395.479i	−0.426943	+	0.587636i	−0.967248	−	0.253833i	$-0.918309\pi$
$673$	−287.332	+	395.479i	−0.426943	+	0.587636i	0.540305	+	0.841469i	$0.318309\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	234.956	+	170.705i	0.347054	+	0.252150i	0.747632	−	0.664113i	$-0.231191\pi$
$677$	234.956	+	170.705i	0.347054	+	0.252150i	−0.400578	+	0.916263i	$0.631191\pi$
$678$		0			0
$679$	−51.1946	−	157.561i	−0.0753971	−	0.232048i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−110.905	+	341.332i	−0.162380	+	0.499753i	−0.998834	−	0.0482838i	$-0.984625\pi$
$683$	−110.905	+	341.332i	−0.162380	+	0.499753i	0.836454	+	0.548037i	$0.184625\pi$
$684$		0			0
$685$	346.932	−	296.800i	0.506470	−	0.433285i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	288.692	−	397.350i	0.419001	−	0.576706i
$690$		0			0
$691$	167.737	−	121.868i	0.242746	−	0.176365i	−0.459760	−	0.888043i	$-0.652065\pi$
$691$	167.737	−	121.868i	0.242746	−	0.176365i	0.702506	+	0.711678i	$0.252065\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−82.2505	−	50.3104i	−0.118346	−	0.0723891i
$696$		0			0
$697$	−10.0004	+	3.24931i	−0.0143477	+	0.00466185i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			634.998i			0.905846i	0.891550	+	0.452923i	$0.149619\pi$
$701$			634.998i			0.905846i	−0.891550	+	0.452923i	$0.850381\pi$
$702$		0			0
$703$	26.8990	−	8.74003i	0.0382632	−	0.0124325i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	368.300			0.520934
$708$		0			0
$709$	139.720	−	101.513i	0.197067	−	0.143178i	−0.484876	−	0.874583i	$-0.661135\pi$
$709$	139.720	−	101.513i	0.197067	−	0.143178i	0.681943	+	0.731405i	$0.261135\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	597.081	−	433.805i	0.837420	−	0.608422i
$714$		0			0
$715$	−392.270	+	31.1959i	−0.548629	+	0.0436307i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	395.152	+	128.393i	0.549586	+	0.178571i	0.570630	−	0.821207i	$-0.306699\pi$
$719$	395.152	+	128.393i	0.549586	+	0.178571i	−0.0210442	+	0.999779i	$0.506699\pi$
$720$		0			0
$721$	43.7485	+	134.644i	0.0606776	+	0.186746i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	331.593	−	169.640i	0.457369	−	0.233987i
$726$		0			0
$727$	−60.8119	+	83.7004i	−0.0836477	+	0.115131i	−0.848790	−	0.528730i	$-0.822668\pi$
$727$	−60.8119	+	83.7004i	−0.0836477	+	0.115131i	0.765143	+	0.643861i	$0.222668\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−369.936	−	120.200i	−0.506069	−	0.164432i
$732$		0			0
$733$	1137.30	+	369.530i	1.55157	+	0.504134i	0.954539	−	0.298087i	$-0.0963487\pi$
$733$	1137.30	+	369.530i	1.55157	+	0.504134i	0.597027	+	0.802221i	$0.296349\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−195.175	+	141.803i	−0.264823	+	0.192405i
$738$		0			0
$739$	727.911	+	528.858i	0.984995	+	0.715641i	0.958819	−	0.284017i	$-0.0916672\pi$
$739$	727.911	+	528.858i	0.984995	+	0.715641i	0.0261754	+	0.999657i	$0.491667\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	39.4286			0.0530667			0.0265334	−	0.999648i	$-0.491553\pi$
$743$	39.4286			0.0530667			0.0265334	+	0.999648i	$0.491553\pi$
$744$		0			0
$745$	45.1747	+	568.044i	0.0606371	+	0.762475i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	96.5047i		−	0.128845i
$750$		0			0
$751$	−197.135			−0.262497			−0.131248	−	0.991350i	$-0.541899\pi$
$751$	−197.135			−0.262497			−0.131248	+	0.991350i	$0.541899\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−296.672	+	23.5933i	−0.392943	+	0.0312494i
$756$		0			0
$757$		−	232.670i		−	0.307358i	−0.988121	−	0.153679i	$-0.950888\pi$
$757$		−	232.670i		−	0.307358i	0.988121	−	0.153679i	$-0.0491121\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	344.143	−	473.672i	0.452224	−	0.622433i	−0.520649	−	0.853771i	$-0.674310\pi$
$761$	344.143	−	473.672i	0.452224	−	0.622433i	0.972874	+	0.231337i	$0.0743101\pi$
$762$		0			0
$763$	−142.420	−	196.025i	−0.186658	−	0.256913i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	141.400	−	435.183i	0.184354	−	0.567383i
$768$		0			0
$769$	−358.777	+	1104.20i	−0.466550	+	1.43589i	0.390473	+	0.920615i	$0.372312\pi$
$769$	−358.777	+	1104.20i	−0.466550	+	1.43589i	−0.857023	+	0.515279i	$0.827688\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−947.468	−	688.376i	−1.22570	−	0.890525i	−0.229142	−	0.973393i	$-0.573592\pi$
$773$	−947.468	−	688.376i	−1.22570	−	0.890525i	−0.996561	+	0.0828679i	$0.973592\pi$
$774$		0			0
$775$	93.8111	−	598.651i	0.121047	−	0.772453i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.60112	+	0.520237i	−0.00205536	+	0.000667827i
$780$		0			0
$781$	−212.177	+	653.013i	−0.271673	+	0.836124i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	42.8392	+	538.677i	0.0545722	+	0.686213i
$786$		0			0
$787$	743.066	+	1022.74i	0.944176	+	1.29955i	0.954066	+	0.299595i	$0.0968516\pi$
$787$	743.066	+	1022.74i	0.944176	+	1.29955i	−0.00989081	+	0.999951i	$0.503148\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.20403	−	3.03358i	−0.00278638	−	0.00383512i
$792$		0			0
$793$		−	768.419i		−	0.969002i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−89.8487	−	276.526i	−0.112734	−	0.346958i	0.878734	−	0.477312i	$-0.158389\pi$
$797$	−89.8487	−	276.526i	−0.112734	−	0.346958i	−0.991468	+	0.130354i	$0.958389\pi$
$798$		0			0
$799$	−161.469			−0.202089
$800$		0			0
$801$		0			0
$802$		0			0
$803$	112.597	+	346.536i	0.140220	+	0.431552i
$804$		0			0
$805$	−162.960	+	266.417i	−0.202435	+	0.330953i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	138.231	+	190.258i	0.170866	+	0.235177i	0.885859	−	0.463955i	$-0.153570\pi$
$809$	138.231	+	190.258i	0.170866	+	0.235177i	−0.714993	+	0.699132i	$0.753570\pi$
$810$		0			0
$811$	−118.793	−	86.3083i	−0.146477	−	0.106422i	0.512133	−	0.858906i	$-0.328855\pi$
$811$	−118.793	−	86.3083i	−0.146477	−	0.106422i	−0.658610	+	0.752484i	$0.728855\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	572.860	+	669.620i	0.702896	+	0.821620i
$816$		0			0
$817$	−59.2293	−	19.2448i	−0.0724961	−	0.0235554i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1089.13	−	353.880i	1.32659	−	0.431035i	0.441837	−	0.897095i	$-0.354327\pi$
$821$	1089.13	−	353.880i	1.32659	−	0.431035i	0.884753	+	0.466060i	$0.154327\pi$
$822$		0			0
$823$	−207.402	+	285.464i	−0.252007	+	0.346858i	−0.916213	−	0.400692i	$-0.868770\pi$
$823$	−207.402	+	285.464i	−0.252007	+	0.346858i	0.664206	+	0.747550i	$0.268770\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1187.70	−	862.913i	−1.43615	−	1.04343i	−0.988829	−	0.149053i	$-0.952378\pi$
$827$	−1187.70	−	862.913i	−1.43615	−	1.04343i	−0.447323	−	0.894373i	$-0.647622\pi$
$828$		0			0
$829$	−305.680	−	940.787i	−0.368733	−	1.13484i	−0.947610	−	0.319430i	$-0.896509\pi$
$829$	−305.680	−	940.787i	−0.368733	−	1.13484i	0.578876	−	0.815415i	$-0.303491\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−137.518	+	423.236i	−0.165087	+	0.508086i
$834$		0			0
$835$	−135.358	+	565.849i	−0.162105	+	0.677664i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−754.096	+	1037.92i	−0.898803	+	1.23710i	0.0720449	+	0.997401i	$0.477047\pi$
$839$	−754.096	+	1037.92i	−0.898803	+	1.23710i	−0.970848	+	0.239695i	$0.922953\pi$
$840$		0			0
$841$	−500.805	+	363.856i	−0.595488	+	0.432647i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	46.1634	−	192.981i	0.0546312	−	0.228380i
$846$		0			0
$847$	178.157	−	57.8867i	0.210339	−	0.0683433i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	541.401i		−	0.636194i
$852$		0			0
$853$	248.068	−	80.6021i	0.290818	−	0.0944925i	−0.159975	−	0.987121i	$-0.551141\pi$
$853$	248.068	−	80.6021i	0.290818	−	0.0944925i	0.450793	+	0.892629i	$0.351141\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−109.541			−0.127819			−0.0639093	−	0.997956i	$-0.520357\pi$
$857$	−109.541			−0.127819			−0.0639093	+	0.997956i	$0.520357\pi$
$858$		0			0
$859$	453.169	−	329.247i	0.527554	−	0.383291i	−0.291888	−	0.956453i	$-0.594283\pi$
$859$	453.169	−	329.247i	0.527554	−	0.383291i	0.819442	+	0.573162i	$0.194283\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	900.930	−	654.564i	1.04395	−	0.758475i	0.0728985	−	0.997339i	$-0.476775\pi$
$863$	900.930	−	654.564i	1.04395	−	0.758475i	0.971053	+	0.238864i	$0.0767751\pi$
$864$		0			0
$865$	−149.341	−	91.3478i	−0.172648	−	0.105604i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	71.7088	+	23.2996i	0.0825187	+	0.0268120i
$870$		0			0
$871$	−197.677	−	608.387i	−0.226954	−	0.698492i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	60.4722	+	249.183i	0.0691111	+	0.284781i
$876$		0			0
$877$	−188.027	+	258.797i	−0.214398	+	0.295094i	−0.902648	−	0.430380i	$-0.858379\pi$
$877$	−188.027	+	258.797i	−0.214398	+	0.295094i	0.688249	+	0.725474i	$0.258379\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	309.821	+	100.667i	0.351670	+	0.114264i	0.479525	−	0.877528i	$-0.340809\pi$
$881$	309.821	+	100.667i	0.351670	+	0.114264i	−0.127855	+	0.991793i	$0.540809\pi$
$882$		0			0
$883$	610.017	+	198.206i	0.690846	+	0.224469i	0.633338	−	0.773876i	$-0.281685\pi$
$883$	610.017	+	198.206i	0.690846	+	0.224469i	0.0575081	+	0.998345i	$0.481685\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	980.399	−	712.302i	1.10530	−	0.803046i	0.123381	−	0.992359i	$-0.460626\pi$
$887$	980.399	−	712.302i	1.10530	−	0.803046i	0.981917	+	0.189314i	$0.0606263\pi$
$888$		0			0
$889$	−233.567	−	169.696i	−0.262730	−	0.190885i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−25.8523			−0.0289500
$894$		0			0
$895$	−394.615	+	163.834i	−0.440910	+	0.183055i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	361.118i		−	0.401689i
$900$		0			0
$901$	−337.789			−0.374904
$902$		0			0
$903$		0			0
$904$		0			0
$905$	259.271	−	1083.86i	0.286488	−	1.19763i
$906$		0			0
$907$			1376.74i			1.51790i	0.651148	+	0.758951i	$0.274288\pi$
$907$			1376.74i			1.51790i	−0.651148	+	0.758951i	$0.725712\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−731.341	+	1006.60i	−0.802789	+	1.10494i	0.189608	+	0.981860i	$0.439278\pi$
$911$	−731.341	+	1006.60i	−0.802789	+	1.10494i	−0.992396	+	0.123084i	$0.960722\pi$
$912$		0			0
$913$	−218.569	−	300.835i	−0.239397	−	0.329502i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.55863	−	10.9523i	0.00388073	−	0.0119436i
$918$		0			0
$919$	268.155	−	825.295i	0.291789	−	0.898036i	−0.692491	−	0.721426i	$-0.743487\pi$
$919$	268.155	−	825.295i	0.291789	−	0.898036i	0.984281	−	0.176610i	$-0.0565130\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1472.92	−	1070.14i	−1.59580	−	1.15942i
$924$		0			0
$925$	−314.834	−	313.803i	−0.340361	−	0.339247i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	27.2022	−	8.83852i	0.0292811	−	0.00951402i	−0.294340	−	0.955701i	$-0.595100\pi$
$929$	27.2022	−	8.83852i	0.0292811	−	0.00951402i	0.323621	+	0.946187i	$0.395100\pi$
$930$		0			0
$931$	−22.0175	+	67.7629i	−0.0236493	+	0.0727851i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	175.932	+	205.648i	0.188162	+	0.219944i
$936$		0			0
$937$	−970.825	−	1336.23i	−1.03610	−	1.42607i	−0.900268	−	0.435337i	$-0.856629\pi$
$937$	−970.825	−	1336.23i	−1.03610	−	1.42607i	−0.135832	−	0.990732i	$-0.543371\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−783.812	−	1078.82i	−0.832956	−	1.14647i	−0.987366	−	0.158459i	$-0.949347\pi$
$941$	−783.812	−	1078.82i	−0.832956	−	1.14647i	0.154409	−	0.988007i	$-0.450653\pi$
$942$		0			0
$943$			32.2261i			0.0341740i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.64433	+	29.6822i	0.0101841	+	0.0313434i	0.956019	−	0.293303i	$-0.0947546\pi$
$947$	9.64433	+	29.6822i	0.0101841	+	0.0313434i	−0.945835	+	0.324647i	$0.894755\pi$
$948$		0			0
$949$	−966.162			−1.01808
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−537.860	−	1655.36i	−0.564387	−	1.73700i	−0.669767	−	0.742571i	$-0.733606\pi$
$953$	−537.860	−	1655.36i	−0.564387	−	1.73700i	0.105381	−	0.994432i	$-0.466394\pi$
$954$		0			0
$955$	269.528	+	315.054i	0.282229	+	0.329899i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	110.100	+	151.540i	0.114807	+	0.158018i
$960$		0			0
$961$	302.173	+	219.541i	0.314436	+	0.228451i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−84.4090	−	1061.39i	−0.0874704	−	1.09989i
$966$		0			0
$967$	129.567	+	42.0987i	0.133988	+	0.0435354i	0.375243	−	0.926926i	$-0.377559\pi$
$967$	129.567	+	42.0987i	0.133988	+	0.0435354i	−0.241255	+	0.970462i	$0.577559\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1285.89	+	417.810i	−1.32429	+	0.430288i	−0.883966	−	0.467550i	$-0.845137\pi$
$971$	−1285.89	+	417.810i	−1.32429	+	0.430288i	−0.440325	+	0.897839i	$0.645137\pi$
$972$		0			0
$973$	23.2508	−	32.0020i	0.0238960	−	0.0328900i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	740.590	+	538.070i	0.758024	+	0.550737i	0.898304	−	0.439375i	$-0.144800\pi$
$977$	740.590	+	538.070i	0.758024	+	0.550737i	−0.140279	+	0.990112i	$0.544800\pi$
$978$		0			0
$979$	−58.8302	−	181.061i	−0.0600921	−	0.184945i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−519.879	+	1600.02i	−0.528870	+	1.62770i	0.227663	+	0.973740i	$0.426892\pi$
$983$	−519.879	+	1600.02i	−0.528870	+	1.62770i	−0.756533	+	0.653955i	$0.773108\pi$
$984$		0			0
$985$	140.837	+	339.223i	0.142982	+	0.344389i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−700.709	+	964.443i	−0.708502	+	0.975170i
$990$		0			0
$991$	102.185	−	74.2417i	0.103113	−	0.0749159i	−0.535034	−	0.844831i	$-0.679701\pi$
$991$	102.185	−	74.2417i	0.103113	−	0.0749159i	0.638147	+	0.769915i	$0.279701\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1439.51	+	114.479i	−1.44674	+	0.115055i
$996$		0			0
$997$	−1630.20	+	529.685i	−1.63511	+	0.531279i	−0.975438	−	0.220275i	$-0.929304\pi$
$997$	−1630.20	+	529.685i	−1.63511	+	0.531279i	−0.659671	+	0.751554i	$0.729304\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.y.a.809.2	yes	80
3.2	odd	2	inner	900.3.y.a.809.19	yes	80
25.14	even	10	inner	900.3.y.a.89.19	yes	80
75.14	odd	10	inner	900.3.y.a.89.2	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.y.a.89.2	✓	80	75.14	odd	10	inner
900.3.y.a.89.19	yes	80	25.14	even	10	inner
900.3.y.a.809.2	yes	80	1.1	even	1	trivial
900.3.y.a.809.19	yes	80	3.2	odd	2	inner

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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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.98426 + 0.396382i) q^{5} -2.05133i q^{7} +O(q^{10})\)	\(q+(-4.98426 + 0.396382i) q^{5} -2.05133i q^{7} +(-3.20226 + 4.40754i) q^{11} +(-8.49111 - 11.6870i) q^{13} +(-3.07013 + 9.44890i) q^{17} +(-0.491549 + 1.51283i) q^{19} +(24.6338 + 17.8975i) q^{23} +(24.6858 - 3.95134i) q^{25} +(14.1695 - 4.60394i) q^{29} +(7.49004 - 23.0520i) q^{31} +(0.813109 + 10.2244i) q^{35} +(-10.4512 - 14.3848i) q^{37} +(0.622089 + 0.856233i) q^{41} +39.1512i q^{43} +(5.02223 + 15.4568i) q^{47} +44.7921 q^{49} +(10.5064 + 32.3353i) q^{53} +(14.2139 - 23.2377i) q^{55} +(18.6182 + 25.6258i) q^{59} +(43.0338 + 31.2659i) q^{61} +(46.9544 + 54.8854i) q^{65} +(42.1147 + 13.6839i) q^{67} +(119.863 - 38.9457i) q^{71} +(39.3118 - 54.1080i) q^{73} +(9.04131 + 6.56889i) q^{77} +(-4.27671 - 13.1624i) q^{79} +(-21.0918 + 64.9140i) q^{83} +(11.5570 - 48.3128i) q^{85} +(-20.5399 + 28.2707i) q^{89} +(-23.9739 + 17.4181i) q^{91} +(1.85035 - 7.73520i) q^{95} +(76.8092 - 24.9568i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 80 * q	\( 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) \) 80 * q + 60 * q^19 + 56 * q^25 - 120 * q^31 + 20 * q^37 - 680 * q^49 - 56 * q^55 - 80 * q^61 - 280 * q^67 - 360 * q^73 + 40 * q^79 + 192 * q^85 + 140 * q^91 - 40 * q^97

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