LMFDB - Embedded newform 900.3.ba.a.161.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(161,900)]

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, 8]))

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

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

chi := DirichletCharacter("900.161");

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.ba (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			161.19
Character	$\chi$	$=$	900.161
Dual form			900.3.ba.a.341.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.41393 - 2.34888i) q^{5} -11.9145 q^{7} +O(q^{10})$	$q+(4.41393 - 2.34888i) q^{5} -11.9145 q^{7} +(1.89659 + 2.61044i) q^{11} +(2.54800 + 1.85123i) q^{13} +(15.0552 - 4.89175i) q^{17} +(2.23284 + 6.87198i) q^{19} +(-7.74116 - 10.6548i) q^{23} +(13.9655 - 20.7356i) q^{25} +(-31.8564 - 10.3508i) q^{29} +(-17.7395 - 54.5966i) q^{31} +(-52.5896 + 27.9856i) q^{35} +(-12.3573 - 8.97809i) q^{37} +(7.25806 - 9.98986i) q^{41} -28.5757 q^{43} +(-65.3014 - 21.2177i) q^{47} +92.9544 q^{49} +(-79.6592 - 25.8829i) q^{53} +(14.5030 + 7.06742i) q^{55} +(-46.8919 + 64.5412i) q^{59} +(73.8159 - 53.6304i) q^{61} +(15.5950 + 2.18626i) q^{65} +(-17.8502 - 54.9372i) q^{67} +(4.57632 + 1.48694i) q^{71} +(-59.5675 + 43.2783i) q^{73} +(-22.5969 - 31.1020i) q^{77} +(-26.2947 + 80.9267i) q^{79} +(-13.4088 + 4.35677i) q^{83} +(54.9627 - 56.9548i) q^{85} +(16.6620 + 22.9333i) q^{89} +(-30.3580 - 22.0564i) q^{91} +(25.9971 + 25.0878i) q^{95} +(-18.2310 + 56.1091i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{7}+O(q^{10}) $ 80 * q + 16 * q^7	$ 80 q + 16 q^{7} - 8 q^{13} + 60 q^{19} - 120 q^{25} + 120 q^{31} + 116 q^{37} - 80 q^{43} + 440 q^{49} + 120 q^{55} + 80 q^{61} + 24 q^{67} + 128 q^{73} + 40 q^{79} + 40 q^{85} - 140 q^{91} + 384 q^{97}+O(q^{100}) $ 80 * q + 16 * q^7 - 8 * q^13 + 60 * q^19 - 120 * q^25 + 120 * q^31 + 116 * q^37 - 80 * q^43 + 440 * q^49 + 120 * q^55 + 80 * q^61 + 24 * q^67 + 128 * q^73 + 40 * q^79 + 40 * q^85 - 140 * q^91 + 384 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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
$5$	4.41393	−	2.34888i	0.882786	−	0.469776i
$5$	4.41393	−	2.34888i	0.882786	−	0.469776i
$6$		0			0
$7$	−11.9145			−1.70207			−0.851033	−	0.525112i	$-0.824023\pi$
$7$	−11.9145			−1.70207			−0.851033	+	0.525112i	$0.824023\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.89659	+	2.61044i	0.172418	+	0.237313i	0.886477	−	0.462773i	$-0.153145\pi$
$11$	1.89659	+	2.61044i	0.172418	+	0.237313i	−0.714059	+	0.700085i	$0.753145\pi$
$12$		0			0
$13$	2.54800	+	1.85123i	0.196000	+	0.142402i	0.681457	−	0.731858i	$-0.261347\pi$
$13$	2.54800	+	1.85123i	0.196000	+	0.142402i	−0.485457	+	0.874261i	$0.661347\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	15.0552	−	4.89175i	0.885603	−	0.287750i	0.169321	−	0.985561i	$-0.445843\pi$
$17$	15.0552	−	4.89175i	0.885603	−	0.287750i	0.716282	+	0.697811i	$0.245843\pi$
$18$		0			0
$19$	2.23284	+	6.87198i	0.117518	+	0.361683i	0.992464	−	0.122537i	$-0.0391032\pi$
$19$	2.23284	+	6.87198i	0.117518	+	0.361683i	−0.874946	+	0.484221i	$0.839103\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.74116	−	10.6548i	−0.336572	−	0.463252i	0.606864	−	0.794805i	$-0.292427\pi$
$23$	−7.74116	−	10.6548i	−0.336572	−	0.463252i	−0.943436	+	0.331554i	$0.892427\pi$
$24$		0			0
$25$	13.9655	−	20.7356i	0.558622	−	0.829422i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−31.8564	−	10.3508i	−1.09850	−	0.356923i	−0.296972	−	0.954886i	$-0.595977\pi$
$29$	−31.8564	−	10.3508i	−1.09850	−	0.356923i	−0.801523	+	0.597963i	$0.795977\pi$
$30$		0			0
$31$	−17.7395	−	54.5966i	−0.572243	−	1.76118i	−0.645382	−	0.763860i	$-0.723302\pi$
$31$	−17.7395	−	54.5966i	−0.572243	−	1.76118i	0.0731390	−	0.997322i	$-0.476698\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−52.5896	+	27.9856i	−1.50256	+	0.799589i
$36$		0			0
$37$	−12.3573	−	8.97809i	−0.333980	−	0.242651i	0.408137	−	0.912921i	$-0.366178\pi$
$37$	−12.3573	−	8.97809i	−0.333980	−	0.242651i	−0.742118	+	0.670270i	$0.766178\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	7.25806	−	9.98986i	0.177026	−	0.243655i	−0.711279	−	0.702910i	$-0.751884\pi$
$41$	7.25806	−	9.98986i	0.177026	−	0.243655i	0.888304	+	0.459255i	$0.151884\pi$
$42$		0			0
$43$	−28.5757			−0.664552			−0.332276	−	0.943182i	$-0.607817\pi$
$43$	−28.5757			−0.664552			−0.332276	+	0.943182i	$0.607817\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−65.3014	−	21.2177i	−1.38939	−	0.451441i	−0.483646	−	0.875263i	$-0.660688\pi$
$47$	−65.3014	−	21.2177i	−1.38939	−	0.451441i	−0.905745	+	0.423823i	$0.860688\pi$
$48$		0			0
$49$	92.9544			1.89703
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−79.6592	−	25.8829i	−1.50300	−	0.488356i	−0.562112	−	0.827061i	$-0.690011\pi$
$53$	−79.6592	−	25.8829i	−1.50300	−	0.488356i	−0.940892	+	0.338705i	$0.890011\pi$
$54$		0			0
$55$	14.5030	+	7.06742i	0.263692	+	0.128499i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−46.8919	+	64.5412i	−0.794778	+	1.09392i	0.198719	+	0.980057i	$0.436322\pi$
$59$	−46.8919	+	64.5412i	−0.794778	+	1.09392i	−0.993497	+	0.113862i	$0.963678\pi$
$60$		0			0
$61$	73.8159	−	53.6304i	1.21010	−	0.879186i	0.214857	−	0.976646i	$-0.431072\pi$
$61$	73.8159	−	53.6304i	1.21010	−	0.879186i	0.995240	+	0.0974594i	$0.0310716\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	15.5950	+	2.18626i	0.239923	+	0.0336347i
$66$		0			0
$67$	−17.8502	−	54.9372i	−0.266420	−	0.819958i	−0.991363	−	0.131148i	$-0.958134\pi$
$67$	−17.8502	−	54.9372i	−0.266420	−	0.819958i	0.724942	−	0.688810i	$-0.241866\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.57632	+	1.48694i	0.0644552	+	0.0209427i	0.341067	−	0.940039i	$-0.389212\pi$
$71$	4.57632	+	1.48694i	0.0644552	+	0.0209427i	−0.276612	+	0.960982i	$0.589212\pi$
$72$		0			0
$73$	−59.5675	+	43.2783i	−0.815993	+	0.592854i	−0.915562	−	0.402177i	$-0.868254\pi$
$73$	−59.5675	+	43.2783i	−0.815993	+	0.592854i	0.0995687	+	0.995031i	$0.468254\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−22.5969	−	31.1020i	−0.293466	−	0.403922i
$78$		0			0
$79$	−26.2947	+	80.9267i	−0.332844	+	1.02439i	0.634930	+	0.772570i	$0.281029\pi$
$79$	−26.2947	+	80.9267i	−0.332844	+	1.02439i	−0.967774	+	0.251819i	$0.918971\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−13.4088	+	4.35677i	−0.161551	+	0.0524912i	−0.388676	−	0.921374i	$-0.627068\pi$
$83$	−13.4088	+	4.35677i	−0.161551	+	0.0524912i	0.227125	+	0.973866i	$0.427068\pi$
$84$		0			0
$85$	54.9627	−	56.9548i	0.646620	−	0.670056i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	16.6620	+	22.9333i	0.187213	+	0.257677i	0.892299	−	0.451445i	$-0.149091\pi$
$89$	16.6620	+	22.9333i	0.187213	+	0.257677i	−0.705086	+	0.709122i	$0.749091\pi$
$90$		0			0
$91$	−30.3580	−	22.0564i	−0.333605	−	0.242378i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	25.9971	+	25.0878i	0.273653	+	0.264082i
$96$		0			0
$97$	−18.2310	+	56.1091i	−0.187948	+	0.578445i	−0.999987	−	0.00515897i	$-0.998358\pi$
$97$	−18.2310	+	56.1091i	−0.187948	+	0.578445i	0.812039	+	0.583604i	$0.198358\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		−	2.99226i		−	0.0296264i	−0.999890	−	0.0148132i	$-0.995285\pi$
$101$		−	2.99226i		−	0.0296264i	0.999890	−	0.0148132i	$-0.00471536\pi$
$102$		0			0
$103$	43.5421	−	134.009i	0.422739	−	1.30106i	−0.482403	−	0.875949i	$-0.660236\pi$
$103$	43.5421	−	134.009i	0.422739	−	1.30106i	0.905143	−	0.425108i	$-0.139764\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	116.428i		−	1.08811i	−0.839048	−	0.544057i	$-0.816888\pi$
$107$		−	116.428i		−	1.08811i	0.839048	−	0.544057i	$-0.183112\pi$
$108$		0			0
$109$	−44.4707	−	32.3098i	−0.407988	−	0.296420i	0.364799	−	0.931086i	$-0.381138\pi$
$109$	−44.4707	−	32.3098i	−0.407988	−	0.296420i	−0.772787	+	0.634666i	$0.781138\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	53.4890	−	73.6213i	0.473354	−	0.651516i	−0.503857	−	0.863787i	$-0.668086\pi$
$113$	53.4890	−	73.6213i	0.473354	−	0.651516i	0.977211	+	0.212272i	$0.0680861\pi$
$114$		0			0
$115$	−59.1957	−	28.8464i	−0.514745	−	0.250839i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−179.375	+	58.2825i	−1.50735	+	0.489769i
$120$		0			0
$121$	34.1737	−	105.176i	0.282428	−	0.869223i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.9376	−	124.329i	0.103501	−	0.994629i
$126$		0			0
$127$	−75.1752	+	54.6180i	−0.591931	+	0.430063i	−0.843006	−	0.537905i	$-0.819216\pi$
$127$	−75.1752	+	54.6180i	−0.591931	+	0.430063i	0.251075	+	0.967968i	$0.419216\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−52.0012	+	16.8962i	−0.396955	+	0.128979i	−0.500691	−	0.865626i	$-0.666921\pi$
$131$	−52.0012	+	16.8962i	−0.396955	+	0.128979i	0.103735	+	0.994605i	$0.466921\pi$
$132$		0			0
$133$	−26.6031	−	81.8760i	−0.200023	−	0.615609i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−157.519	+	216.806i	−1.14977	+	1.58253i	−0.406338	+	0.913723i	$0.633194\pi$
$137$	−157.519	+	216.806i	−1.14977	+	1.58253i	−0.743437	+	0.668806i	$0.766806\pi$
$138$		0			0
$139$	157.072	−	114.119i	1.13001	−	0.821003i	0.144317	−	0.989531i	$-0.453901\pi$
$139$	157.072	−	114.119i	1.13001	−	0.821003i	0.985697	+	0.168528i	$0.0539015\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			10.1624i			0.0710659i
$144$		0			0
$145$	−164.924	+	29.1392i	−1.13741	+	0.200960i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	153.954i		−	1.03325i	−0.856212	−	0.516624i	$-0.827188\pi$
$149$		−	153.954i		−	1.03325i	0.856212	−	0.516624i	$-0.172812\pi$
$150$		0			0
$151$	48.4441			0.320822			0.160411	−	0.987050i	$-0.448718\pi$
$151$	48.4441			0.320822			0.160411	+	0.987050i	$0.448718\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−206.542	−	199.318i	−1.33253	−	1.28592i
$156$		0			0
$157$	204.609			1.30324			0.651622	−	0.758544i	$-0.274089\pi$
$157$	204.609			1.30324			0.651622	+	0.758544i	$0.274089\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	92.2317	+	126.946i	0.572868	+	0.788485i
$162$		0			0
$163$	−103.971	−	75.5395i	−0.637860	−	0.463433i	0.221254	−	0.975216i	$-0.428985\pi$
$163$	−103.971	−	75.5395i	−0.637860	−	0.463433i	−0.859114	+	0.511784i	$0.828985\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−20.5159	+	6.66603i	−0.122850	+	0.0399163i	−0.369797	−	0.929113i	$-0.620573\pi$
$167$	−20.5159	+	6.66603i	−0.122850	+	0.0399163i	0.246947	+	0.969029i	$0.420573\pi$
$168$		0			0
$169$	−49.1586	−	151.295i	−0.290879	−	0.895235i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−13.5474	−	18.6464i	−0.0783085	−	0.107782i	0.768066	−	0.640371i	$-0.221219\pi$
$173$	−13.5474	−	18.6464i	−0.0783085	−	0.107782i	−0.846374	+	0.532588i	$0.821219\pi$
$174$		0			0
$175$	−166.392	+	247.053i	−0.950811	+	1.41173i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	316.172	+	102.731i	1.76633	+	0.573914i	0.997824	−	0.0659323i	$-0.0210021\pi$
$179$	316.172	+	102.731i	1.76633	+	0.573914i	0.768503	+	0.639847i	$0.221002\pi$
$180$		0			0
$181$	28.4234	+	87.4783i	0.157036	+	0.483306i	0.998361	−	0.0572225i	$-0.0182245\pi$
$181$	28.4234	+	87.4783i	0.157036	+	0.483306i	−0.841326	+	0.540528i	$0.818224\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−75.6326	−	10.6029i	−0.408825	−	0.0573130i
$186$		0			0
$187$	41.3233	+	30.0231i	0.220980	+	0.160552i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.68690	+	11.9565i	−0.0454812	+	0.0625995i	−0.831152	−	0.556045i	$-0.812318\pi$
$191$	−8.68690	+	11.9565i	−0.0454812	+	0.0625995i	0.785671	+	0.618645i	$0.212318\pi$
$192$		0			0
$193$	−15.8975			−0.0823703			−0.0411852	−	0.999152i	$-0.513113\pi$
$193$	−15.8975			−0.0823703			−0.0411852	+	0.999152i	$0.513113\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−173.974	−	56.5275i	−0.883115	−	0.286941i	−0.167865	−	0.985810i	$-0.553687\pi$
$197$	−173.974	−	56.5275i	−0.883115	−	0.286941i	−0.715250	+	0.698869i	$0.753687\pi$
$198$		0			0
$199$	232.984			1.17077			0.585387	−	0.810754i	$-0.300943\pi$
$199$	232.984			1.17077			0.585387	+	0.810754i	$0.300943\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	379.552	+	123.324i	1.86971	+	0.607506i
$204$		0			0
$205$	8.57159	−	61.1428i	0.0418126	−	0.298258i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−13.7041	+	18.8621i	−0.0655698	+	0.0902491i
$210$		0			0
$211$	−37.5861	+	27.3079i	−0.178133	+	0.129421i	−0.673279	−	0.739389i	$-0.735115\pi$
$211$	−37.5861	+	27.3079i	−0.178133	+	0.129421i	0.495146	+	0.868810i	$0.335115\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−126.131	+	67.1209i	−0.586657	+	0.312190i
$216$		0			0
$217$	211.357	+	650.490i	0.973995	+	2.99765i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	47.4165	+	15.4065i	0.214554	+	0.0697129i
$222$		0			0
$223$	222.697	−	161.799i	0.998643	−	0.725557i	0.0368463	−	0.999321i	$-0.488269\pi$
$223$	222.697	−	161.799i	0.998643	−	0.725557i	0.961797	+	0.273764i	$0.0882688\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	229.722	+	316.185i	1.01199	+	1.39289i	0.917670	+	0.397344i	$0.130068\pi$
$227$	229.722	+	316.185i	1.01199	+	1.39289i	0.0943211	+	0.995542i	$0.469932\pi$
$228$		0			0
$229$	−114.392	+	352.061i	−0.499527	+	1.53739i	0.310254	+	0.950654i	$0.399586\pi$
$229$	−114.392	+	352.061i	−0.499527	+	1.53739i	−0.809781	+	0.586732i	$0.800414\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	432.919	−	140.664i	1.85802	−	0.603708i	0.862864	−	0.505436i	$-0.168668\pi$
$233$	432.919	−	140.664i	1.85802	−	0.603708i	0.995160	−	0.0982722i	$-0.0313316\pi$
$234$		0			0
$235$	−338.074	+	59.7315i	−1.43861	+	0.254177i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	115.824	+	159.418i	0.484618	+	0.667019i	0.979384	−	0.202007i	$-0.0647464\pi$
$239$	115.824	+	159.418i	0.484618	+	0.667019i	−0.494766	+	0.869026i	$0.664746\pi$
$240$		0			0
$241$	162.750	+	118.245i	0.675312	+	0.490643i	0.871799	−	0.489863i	$-0.162953\pi$
$241$	162.750	+	118.245i	0.675312	+	0.490643i	−0.196487	+	0.980506i	$0.562953\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	410.294	−	218.339i	1.67467	−	0.891178i
$246$		0			0
$247$	−7.03233	+	21.6433i	−0.0284710	+	0.0876247i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			206.579i			0.823025i	0.911404	+	0.411512i	$0.134999\pi$
$251$			206.579i			0.823025i	−0.911404	+	0.411512i	$0.865001\pi$
$252$		0			0
$253$	13.1318	−	40.4156i	0.0519045	−	0.159746i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	144.454i		−	0.562077i	−0.959697	−	0.281038i	$-0.909321\pi$
$257$		−	144.454i		−	0.562077i	0.959697	−	0.281038i	$-0.0906788\pi$
$258$		0			0
$259$	147.230	+	106.969i	0.568457	+	0.413008i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−85.6082	+	117.830i	−0.325506	+	0.448021i	−0.940138	−	0.340793i	$-0.889305\pi$
$263$	−85.6082	+	117.830i	−0.325506	+	0.448021i	0.614632	+	0.788814i	$0.289305\pi$
$264$		0			0
$265$	−412.406	+	72.8647i	−1.55625	+	0.274961i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−235.641	+	76.5643i	−0.875987	+	0.284626i	−0.712290	−	0.701885i	$-0.752342\pi$
$269$	−235.641	+	76.5643i	−0.875987	+	0.284626i	−0.163697	+	0.986511i	$0.552342\pi$
$270$		0			0
$271$	11.7830	−	36.2643i	0.0434796	−	0.133817i	−0.926960	−	0.375160i	$-0.877588\pi$
$271$	11.7830	−	36.2643i	0.0434796	−	0.133817i	0.970440	+	0.241343i	$0.0775879\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	80.6159	−	2.87075i	0.293149	−	0.0104391i
$276$		0			0
$277$	−92.4897	+	67.1977i	−0.333898	+	0.242591i	−0.742083	−	0.670308i	$-0.766162\pi$
$277$	−92.4897	+	67.1977i	−0.333898	+	0.242591i	0.408185	+	0.912899i	$0.366162\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	261.020	−	84.8105i	0.928896	−	0.301817i	0.194785	−	0.980846i	$-0.437599\pi$
$281$	261.020	−	84.8105i	0.928896	−	0.301817i	0.734111	+	0.679029i	$0.237599\pi$
$282$		0			0
$283$	−106.974	−	329.233i	−0.378001	−	1.16337i	−0.941432	−	0.337204i	$-0.890519\pi$
$283$	−106.974	−	329.233i	−0.378001	−	1.16337i	0.563430	−	0.826164i	$-0.309481\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−86.4758	+	119.024i	−0.301310	+	0.414717i
$288$		0			0
$289$	−31.0747	+	22.5771i	−0.107525	+	0.0781213i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	233.496i		−	0.796916i	−0.917187	−	0.398458i	$-0.869546\pi$
$293$		−	233.496i		−	0.796916i	0.917187	−	0.398458i	$-0.130454\pi$
$294$		0			0
$295$	−55.3782	+	395.024i	−0.187723	+	1.33906i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		−	41.4790i		−	0.138726i
$300$		0			0
$301$	340.464			1.13111
$302$		0			0
$303$		0			0
$304$		0			0
$305$	199.847	−	410.105i	0.655236	−	1.34461i
$306$		0			0
$307$	−244.602			−0.796749			−0.398374	−	0.917223i	$-0.630425\pi$
$307$	−244.602			−0.796749			−0.398374	+	0.917223i	$0.630425\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−39.6994	−	54.6416i	−0.127651	−	0.175696i	0.740408	−	0.672158i	$-0.234632\pi$
$311$	−39.6994	−	54.6416i	−0.127651	−	0.175696i	−0.868059	+	0.496461i	$0.834632\pi$
$312$		0			0
$313$	−224.263	−	162.937i	−0.716497	−	0.520565i	0.168766	−	0.985656i	$-0.446022\pi$
$313$	−224.263	−	162.937i	−0.716497	−	0.520565i	−0.885263	+	0.465091i	$0.846022\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	129.580	−	42.1030i	0.408768	−	0.132817i	−0.0974127	−	0.995244i	$-0.531057\pi$
$317$	129.580	−	42.1030i	0.408768	−	0.132817i	0.506181	+	0.862427i	$0.331057\pi$
$318$		0			0
$319$	−33.3986	−	102.790i	−0.104698	−	0.322227i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	67.2320	+	92.5369i	0.208149	+	0.286492i
$324$		0			0
$325$	73.9704	−	26.9807i	0.227601	−	0.0830177i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	778.031	+	252.798i	2.36484	+	0.768382i
$330$		0			0
$331$	−144.833	−	445.750i	−0.437561	−	1.34668i	−0.890439	−	0.455103i	$-0.849603\pi$
$331$	−144.833	−	445.750i	−0.437561	−	1.34668i	0.452878	−	0.891573i	$-0.350397\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−207.830	−	200.561i	−0.620388	−	0.598689i
$336$		0			0
$337$	168.789	+	122.632i	0.500858	+	0.363895i	0.809345	−	0.587334i	$-0.199823\pi$
$337$	168.789	+	122.632i	0.500858	+	0.363895i	−0.308487	+	0.951229i	$0.599823\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	108.876	−	149.856i	0.319286	−	0.439459i
$342$		0			0
$343$	−523.693			−1.52680
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−504.819	−	164.026i	−1.45481	−	0.472697i	−0.528330	−	0.849039i	$-0.677182\pi$
$347$	−504.819	−	164.026i	−1.45481	−	0.472697i	−0.926481	+	0.376342i	$0.877182\pi$
$348$		0			0
$349$	671.891			1.92519			0.962594	−	0.270947i	$-0.0873369\pi$
$349$	671.891			1.92519			0.962594	+	0.270947i	$0.0873369\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−268.888	−	87.3671i	−0.761723	−	0.247499i	−0.0977052	−	0.995215i	$-0.531150\pi$
$353$	−268.888	−	87.3671i	−0.761723	−	0.247499i	−0.664018	+	0.747717i	$0.731150\pi$
$354$		0			0
$355$	23.6922	−	4.18598i	0.0667385	−	0.0117915i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−417.069	+	574.047i	−1.16175	+	1.59902i	−0.457200	+	0.889364i	$0.651147\pi$
$359$	−417.069	+	574.047i	−1.16175	+	1.59902i	−0.704553	+	0.709651i	$0.748853\pi$
$360$		0			0
$361$	249.817	−	181.502i	0.692013	−	0.502777i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−161.271	+	330.944i	−0.441839	+	0.906697i
$366$		0			0
$367$	100.038	+	307.885i	0.272583	+	0.838925i	0.989849	+	0.142125i	$0.0453934\pi$
$367$	100.038	+	307.885i	0.272583	+	0.838925i	−0.717266	+	0.696800i	$0.754607\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	949.097	+	308.380i	2.55821	+	0.831214i
$372$		0			0
$373$	−426.760	+	310.059i	−1.14413	+	0.831259i	−0.987689	−	0.156429i	$-0.950002\pi$
$373$	−426.760	+	310.059i	−1.14413	+	0.831259i	−0.156440	+	0.987687i	$0.550002\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−62.0083	−	85.3471i	−0.164478	−	0.226385i
$378$		0			0
$379$	−89.1159	+	274.270i	−0.235134	+	0.723669i	0.761969	+	0.647613i	$0.224233\pi$
$379$	−89.1159	+	274.270i	−0.235134	+	0.723669i	−0.997104	+	0.0760556i	$0.975767\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	287.354	−	93.3668i	0.750270	−	0.243778i	0.0911728	−	0.995835i	$-0.470938\pi$
$383$	287.354	−	93.3668i	0.750270	−	0.243778i	0.659098	+	0.752057i	$0.270938\pi$
$384$		0			0
$385$	−172.796	−	84.2045i	−0.448820	−	0.218713i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−170.210	−	234.274i	−0.437557	−	0.602246i	0.532110	−	0.846675i	$-0.321399\pi$
$389$	−170.210	−	234.274i	−0.437557	−	0.602246i	−0.969667	+	0.244430i	$0.921399\pi$
$390$		0			0
$391$	−168.666	−	122.543i	−0.431370	−	0.313408i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	74.0241	+	418.968i	0.187403	+	1.06068i
$396$		0			0
$397$	−60.9490	+	187.582i	−0.153524	+	0.472498i	−0.998008	−	0.0630822i	$-0.979907\pi$
$397$	−60.9490	+	187.582i	−0.153524	+	0.472498i	0.844485	+	0.535580i	$0.179907\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			68.4386i			0.170670i	0.996352	+	0.0853349i	$0.0271960\pi$
$401$			68.4386i			0.170670i	−0.996352	+	0.0853349i	$0.972804\pi$
$402$		0			0
$403$	55.8706	−	171.952i	0.138637	−	0.426680i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	49.2857i		−	0.121095i
$408$		0			0
$409$	642.747	+	466.983i	1.57151	+	1.14177i	0.925693	+	0.378275i	$0.123483\pi$
$409$	642.747	+	466.983i	1.57151	+	1.14177i	0.645816	+	0.763493i	$0.276517\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	558.692	−	768.973i	1.35276	−	1.86192i
$414$		0			0
$415$	−48.9518	+	50.7261i	−0.117956	+	0.122231i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−453.508	+	147.354i	−1.08236	+	0.351679i	−0.795289	−	0.606231i	$-0.792681\pi$
$419$	−453.508	+	147.354i	−1.08236	+	0.351679i	−0.287069	+	0.957910i	$0.592681\pi$
$420$		0			0
$421$	219.345	−	675.075i	0.521010	−	1.60350i	−0.251063	−	0.967971i	$-0.580780\pi$
$421$	219.345	−	675.075i	0.521010	−	1.60350i	0.772073	−	0.635534i	$-0.219220\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	108.822	−	380.495i	0.256051	−	0.895282i
$426$		0			0
$427$	−879.476	+	638.977i	−2.05966	+	1.49643i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	268.193	−	87.1412i	0.622258	−	0.202184i	0.0191154	−	0.999817i	$-0.493915\pi$
$431$	268.193	−	87.1412i	0.622258	−	0.202184i	0.603142	+	0.797633i	$0.293915\pi$
$432$		0			0
$433$	59.3167	+	182.558i	0.136990	+	0.421612i	0.995894	−	0.0905242i	$-0.0288542\pi$
$433$	59.3167	+	182.558i	0.136990	+	0.421612i	−0.858904	+	0.512136i	$0.828854\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	55.9347	−	76.9875i	0.127997	−	0.176173i
$438$		0			0
$439$	220.698	−	160.347i	0.502729	−	0.365254i	−0.307329	−	0.951603i	$-0.599435\pi$
$439$	220.698	−	160.347i	0.502729	−	0.365254i	0.810059	+	0.586349i	$0.199435\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			491.849i			1.11027i	0.831761	+	0.555134i	$0.187333\pi$
$443$			491.849i			1.11027i	−0.831761	+	0.555134i	$0.812667\pi$
$444$		0			0
$445$	127.412	+	62.0888i	0.286320	+	0.139525i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			64.9462i			0.144646i	0.997381	+	0.0723232i	$0.0230413\pi$
$449$			64.9462i			0.144646i	−0.997381	+	0.0723232i	$0.976959\pi$
$450$		0			0
$451$	39.8435			0.0883448
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−185.806	−	26.0481i	−0.408365	−	0.0572485i
$456$		0			0
$457$	408.723			0.894361			0.447180	−	0.894444i	$-0.352428\pi$
$457$	408.723			0.894361			0.447180	+	0.894444i	$0.352428\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	509.694	+	701.534i	1.10563	+	1.52176i	0.827707	+	0.561161i	$0.189645\pi$
$461$	509.694	+	701.534i	1.10563	+	1.52176i	0.277920	+	0.960604i	$0.410355\pi$
$462$		0			0
$463$	286.350	+	208.045i	0.618465	+	0.449341i	0.852385	−	0.522914i	$-0.175155\pi$
$463$	286.350	+	208.045i	0.618465	+	0.449341i	−0.233920	+	0.972256i	$0.575155\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−30.8819	+	10.0342i	−0.0661284	+	0.0214864i	−0.341894	−	0.939738i	$-0.611069\pi$
$467$	−30.8819	+	10.0342i	−0.0661284	+	0.0214864i	0.275766	+	0.961225i	$0.411069\pi$
$468$		0			0
$469$	212.675	+	654.547i	0.453465	+	1.39562i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−54.1966	−	74.5952i	−0.114580	−	0.157707i
$474$		0			0
$475$	173.677	+	49.6717i	0.365636	+	0.104572i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−103.116	−	33.5043i	−0.215273	−	0.0699465i	0.199395	−	0.979919i	$-0.436102\pi$
$479$	−103.116	−	33.5043i	−0.215273	−	0.0699465i	−0.414668	+	0.909973i	$0.636102\pi$
$480$		0			0
$481$	−14.8658	−	45.7523i	−0.0309061	−	0.0951191i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	51.3233	+	290.484i	0.105821	+	0.598936i
$486$		0			0
$487$	−430.451	−	312.741i	−0.883883	−	0.642178i	0.0503931	−	0.998729i	$-0.483953\pi$
$487$	−430.451	−	312.741i	−0.883883	−	0.642178i	−0.934276	+	0.356551i	$0.883953\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−370.811	+	510.377i	−0.755215	+	1.03946i	0.242382	+	0.970181i	$0.422071\pi$
$491$	−370.811	+	510.377i	−0.755215	+	1.03946i	−0.997597	+	0.0692836i	$0.977929\pi$
$492$		0			0
$493$	−530.239			−1.07554
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−54.5243	−	17.7160i	−0.109707	−	0.0356459i
$498$		0			0
$499$	181.279			0.363285			0.181642	−	0.983365i	$-0.441859\pi$
$499$	181.279			0.363285			0.181642	+	0.983365i	$0.441859\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−795.285	−	258.404i	−1.58108	−	0.513725i	−0.618748	−	0.785589i	$-0.712360\pi$
$503$	−795.285	−	258.404i	−1.58108	−	0.513725i	−0.962336	+	0.271864i	$0.912360\pi$
$504$		0			0
$505$	−7.02846	−	13.2076i	−0.0139177	−	0.0261537i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−321.549	+	442.574i	−0.631726	+	0.869497i	−0.998140	−	0.0609553i	$-0.980585\pi$
$509$	−321.549	+	442.574i	−0.631726	+	0.869497i	0.366414	+	0.930452i	$0.380585\pi$
$510$		0			0
$511$	709.715	−	515.638i	1.38887	−	1.00908i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−122.579	−	693.781i	−0.238017	−	1.34715i
$516$		0			0
$517$	−68.4628	−	210.707i	−0.132423	−	0.407556i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−937.706	−	304.679i	−1.79982	−	0.584797i	−0.799936	−	0.600085i	$-0.795133\pi$
$521$	−937.706	−	304.679i	−1.79982	−	0.584797i	−0.999883	+	0.0152883i	$0.995133\pi$
$522$		0			0
$523$	−26.5860	+	19.3158i	−0.0508336	+	0.0369327i	−0.612912	−	0.790151i	$-0.710002\pi$
$523$	−26.5860	+	19.3158i	−0.0508336	+	0.0369327i	0.562078	+	0.827084i	$0.310002\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−534.146	−	735.189i	−1.01356	−	1.39504i
$528$		0			0
$529$	109.871	−	338.148i	0.207696	−	0.639221i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	36.9870	−	12.0178i	0.0693940	−	0.0225475i
$534$		0			0
$535$	−273.476	−	513.906i	−0.511169	−	0.960572i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	176.297	+	242.652i	0.327081	+	0.450189i
$540$		0			0
$541$	−244.691	−	177.778i	−0.452293	−	0.328610i	0.338207	−	0.941072i	$-0.390179\pi$
$541$	−244.691	−	177.778i	−0.452293	−	0.328610i	−0.790501	+	0.612461i	$0.790179\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−272.182	−	38.1571i	−0.499417	−	0.0700131i
$546$		0			0
$547$	−79.2470	+	243.897i	−0.144876	+	0.445881i	−0.996995	−	0.0774661i	$-0.975317\pi$
$547$	−79.2470	+	243.897i	−0.144876	+	0.445881i	0.852119	+	0.523348i	$0.175317\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	242.028i		−	0.439252i
$552$		0			0
$553$	313.287	−	964.199i	0.566523	−	1.74358i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	10.8654i		−	0.0195070i	−0.999952	−	0.00975349i	$-0.996895\pi$
$557$		−	10.8654i		−	0.0195070i	0.999952	−	0.00975349i	$-0.00310468\pi$
$558$		0			0
$559$	−72.8109	−	52.9002i	−0.130252	−	0.0946336i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	489.932	−	674.334i	0.870217	−	1.19775i	−0.108819	−	0.994062i	$-0.534707\pi$
$563$	489.932	−	674.334i	0.870217	−	1.19775i	0.979036	−	0.203689i	$-0.0652931\pi$
$564$		0			0
$565$	63.1692	−	450.598i	0.111804	−	0.797519i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−883.681	+	287.126i	−1.55304	+	0.504614i	−0.954938	−	0.296804i	$-0.904079\pi$
$569$	−883.681	+	287.126i	−1.55304	+	0.504614i	−0.598105	+	0.801418i	$0.704079\pi$
$570$		0			0
$571$	239.044	−	735.700i	0.418640	−	1.28844i	−0.490314	−	0.871546i	$-0.663118\pi$
$571$	239.044	−	735.700i	0.418640	−	1.28844i	0.908954	−	0.416896i	$-0.136882\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−329.042	+	11.7173i	−0.572248	+	0.0203779i
$576$		0			0
$577$	107.327	−	77.9775i	0.186008	−	0.135143i	−0.490884	−	0.871225i	$-0.663326\pi$
$577$	107.327	−	77.9775i	0.186008	−	0.135143i	0.676893	+	0.736082i	$0.263326\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	159.758	−	51.9086i	0.274971	−	0.0893436i
$582$		0			0
$583$	−83.5157	−	257.035i	−0.143252	−	0.440883i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−345.054	+	474.926i	−0.587826	+	0.809073i	−0.994526	−	0.104489i	$-0.966679\pi$
$587$	−345.054	+	474.926i	−0.587826	+	0.809073i	0.406700	+	0.913562i	$0.366679\pi$
$588$		0			0
$589$	335.578	−	243.811i	0.569741	−	0.413941i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			287.360i			0.484586i	0.970203	+	0.242293i	$0.0778996\pi$
$593$			287.360i			0.484586i	−0.970203	+	0.242293i	$0.922100\pi$
$594$		0			0
$595$	−654.851	+	678.585i	−1.10059	+	1.14048i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			43.5828i			0.0727593i	0.999338	+	0.0363797i	$0.0115826\pi$
$599$			43.5828i			0.0727593i	−0.999338	+	0.0363797i	$0.988417\pi$
$600$		0			0
$601$	−382.293			−0.636095			−0.318047	−	0.948075i	$-0.603027\pi$
$601$	−382.293			−0.636095			−0.318047	+	0.948075i	$0.603027\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−96.2050	−	544.509i	−0.159017	−	0.900015i
$606$		0			0
$607$	628.339			1.03516			0.517578	−	0.855636i	$-0.326834\pi$
$607$	628.339			1.03516			0.517578	+	0.855636i	$0.326834\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−127.109	−	174.951i	−0.208034	−	0.286335i
$612$		0			0
$613$	−856.078	−	621.977i	−1.39654	−	1.01464i	−0.995112	−	0.0987524i	$-0.968515\pi$
$613$	−856.078	−	621.977i	−1.39654	−	1.01464i	−0.401426	−	0.915892i	$-0.631485\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−886.727	+	288.115i	−1.43716	+	0.466961i	−0.921010	−	0.389538i	$-0.872635\pi$
$617$	−886.727	+	288.115i	−1.43716	+	0.466961i	−0.516148	+	0.856499i	$0.672635\pi$
$618$		0			0
$619$	−89.1122	−	274.259i	−0.143962	−	0.443068i	0.852914	−	0.522051i	$-0.174833\pi$
$619$	−89.1122	−	274.259i	−0.143962	−	0.443068i	−0.996876	+	0.0789826i	$0.974833\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−198.519	−	273.237i	−0.318649	−	0.438583i
$624$		0			0
$625$	−234.927	−	579.167i	−0.375883	−	0.926667i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−229.960	−	74.7186i	−0.365597	−	0.118790i
$630$		0			0
$631$	−53.9097	−	165.917i	−0.0854354	−	0.262943i	0.899208	−	0.437522i	$-0.144144\pi$
$631$	−53.9097	−	165.917i	−0.0854354	−	0.262943i	−0.984643	+	0.174579i	$0.944144\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−203.527	+	417.657i	−0.320515	+	0.657728i
$636$		0			0
$637$	236.848	+	172.080i	0.371817	+	0.270141i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	473.841	−	652.186i	0.739221	−	1.01745i	−0.259442	−	0.965759i	$-0.583539\pi$
$641$	473.841	−	652.186i	0.739221	−	1.01745i	0.998663	−	0.0516917i	$-0.0164613\pi$
$642$		0			0
$643$	−432.726			−0.672980			−0.336490	−	0.941687i	$-0.609240\pi$
$643$	−432.726			−0.672980			−0.336490	+	0.941687i	$0.609240\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−258.114	−	83.8662i	−0.398939	−	0.129623i	0.102674	−	0.994715i	$-0.467260\pi$
$647$	−258.114	−	83.8662i	−0.398939	−	0.129623i	−0.501614	+	0.865092i	$0.667260\pi$
$648$		0			0
$649$	−257.416			−0.396634
$650$		0			0
$651$		0			0
$652$		0			0
$653$	87.2243	+	28.3409i	0.133575	+	0.0434011i	0.375041	−	0.927008i	$-0.377628\pi$
$653$	87.2243	+	28.3409i	0.133575	+	0.0434011i	−0.241467	+	0.970409i	$0.577628\pi$
$654$		0			0
$655$	−189.842	+	196.723i	−0.289836	+	0.300340i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	532.584	−	733.039i	0.808170	−	1.11235i	−0.183434	−	0.983032i	$-0.558721\pi$
$659$	532.584	−	733.039i	0.808170	−	1.11235i	0.991603	−	0.129318i	$-0.0412788\pi$
$660$		0			0
$661$	−135.869	+	98.7147i	−0.205551	+	0.149342i	−0.685798	−	0.727792i	$-0.740547\pi$
$661$	−135.869	+	98.7147i	−0.205551	+	0.149342i	0.480247	+	0.877133i	$0.340547\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−309.741	−	298.907i	−0.465776	−	0.449485i
$666$		0			0
$667$	136.320	+	419.550i	0.204378	+	0.629010i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	279.997	+	90.9767i	0.417284	+	0.135584i
$672$		0			0
$673$	797.667	−	579.539i	1.18524	−	0.861128i	0.192488	−	0.981299i	$-0.438344\pi$
$673$	797.667	−	579.539i	1.18524	−	0.861128i	0.992753	+	0.120171i	$0.0383444\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	375.334	+	516.603i	0.554408	+	0.763077i	0.990602	−	0.136776i	$-0.0436739\pi$
$677$	375.334	+	516.603i	0.554408	+	0.763077i	−0.436194	+	0.899853i	$0.643674\pi$
$678$		0			0
$679$	217.212	−	668.510i	0.319900	−	0.984551i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−16.6588	+	5.41279i	−0.0243907	+	0.00792502i	−0.321187	−	0.947016i	$-0.604082\pi$
$683$	−16.6588	+	5.41279i	−0.0243907	+	0.00792502i	0.296796	+	0.954941i	$0.404082\pi$
$684$		0			0
$685$	−186.026	+	1326.96i	−0.271571	+	1.93717i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−155.056	−	213.417i	−0.225046	−	0.309749i
$690$		0			0
$691$	365.306	+	265.410i	0.528663	+	0.384096i	0.819857	−	0.572568i	$-0.194053\pi$
$691$	365.306	+	265.410i	0.528663	+	0.384096i	−0.291195	+	0.956664i	$0.594053\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	425.252	−	872.658i	0.611873	−	1.25562i
$696$		0			0
$697$	60.4040	−	185.904i	0.0866628	−	0.266721i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			580.105i			0.827539i	0.910382	+	0.413770i	$0.135788\pi$
$701$			580.105i			0.827539i	−0.910382	+	0.413770i	$0.864212\pi$
$702$		0			0
$703$	34.1054	−	104.966i	0.0485141	−	0.149311i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			35.6512i			0.0504261i
$708$		0			0
$709$	440.848	+	320.295i	0.621788	+	0.451756i	0.853546	−	0.521018i	$-0.174448\pi$
$709$	440.848	+	320.295i	0.621788	+	0.451756i	−0.231757	+	0.972774i	$0.574448\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−444.391	+	611.652i	−0.623270	+	0.857857i
$714$		0			0
$715$	23.8703	+	44.8562i	0.0333850	+	0.0627360i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	846.494	−	275.043i	1.17732	−	0.382535i	0.345951	−	0.938253i	$-0.387556\pi$
$719$	846.494	−	275.043i	1.17732	−	0.382535i	0.831371	+	0.555718i	$0.187556\pi$
$720$		0			0
$721$	−518.781	+	1596.64i	−0.719530	+	2.21449i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−659.521	+	516.006i	−0.909683	+	0.711732i
$726$		0			0
$727$	791.045	−	574.728i	1.08809	−	0.790547i	0.109018	−	0.994040i	$-0.465229\pi$
$727$	791.045	−	574.728i	1.08809	−	0.790547i	0.979077	+	0.203492i	$0.0652292\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−430.215	+	139.785i	−0.588529	+	0.191225i
$732$		0			0
$733$	−89.2303	−	274.623i	−0.121733	−	0.374656i	0.871559	−	0.490291i	$-0.163110\pi$
$733$	−89.2303	−	274.623i	−0.121733	−	0.374656i	−0.993292	+	0.115636i	$0.963110\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	109.556	−	150.790i	0.148651	−	0.204600i
$738$		0			0
$739$	−26.6125	+	19.3351i	−0.0360115	+	0.0261639i	−0.605645	−	0.795735i	$-0.707085\pi$
$739$	−26.6125	+	19.3351i	−0.0360115	+	0.0261639i	0.569634	+	0.821899i	$0.307085\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			1003.13i			1.35010i	0.737770	+	0.675052i	$0.235879\pi$
$743$			1003.13i			1.35010i	−0.737770	+	0.675052i	$0.764121\pi$
$744$		0			0
$745$	−361.619	−	679.543i	−0.485395	−	0.912138i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			1387.18i			1.85204i
$750$		0			0
$751$	1152.46			1.53457			0.767285	−	0.641306i	$-0.221607\pi$
$751$	1152.46			1.53457			0.767285	+	0.641306i	$0.221607\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	213.829	−	113.789i	0.283217	−	0.150714i
$756$		0			0
$757$	−777.148			−1.02662			−0.513308	−	0.858204i	$-0.671580\pi$
$757$	−777.148			−1.02662			−0.513308	+	0.858204i	$0.671580\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−624.584	−	859.666i	−0.820741	−	1.12965i	−0.989576	−	0.144009i	$-0.954000\pi$
$761$	−624.584	−	859.666i	−0.820741	−	1.12965i	0.168835	−	0.985644i	$-0.446000\pi$
$762$		0			0
$763$	529.844	+	384.954i	0.694422	+	0.504527i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−238.961	+	77.6431i	−0.311553	+	0.101230i
$768$		0			0
$769$	−239.773	−	737.944i	−0.311798	−	0.959615i	−0.977052	−	0.212999i	$-0.931677\pi$
$769$	−239.773	−	737.944i	−0.311798	−	0.959615i	0.665255	−	0.746617i	$-0.268323\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	169.962	+	233.933i	0.219874	+	0.302630i	0.904677	−	0.426098i	$-0.140112\pi$
$773$	169.962	+	233.933i	0.219874	+	0.302630i	−0.684803	+	0.728728i	$0.740112\pi$
$774$		0			0
$775$	−1379.83	−	394.633i	−1.78043	−	0.509204i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	84.8562	+	27.5714i	0.108930	+	0.0353934i
$780$		0			0
$781$	4.79786	+	14.7663i	0.00614323	+	0.0189069i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	903.131	−	480.602i	1.15049	−	0.612232i
$786$		0			0
$787$	909.311	+	660.653i	1.15541	+	0.839458i	0.989191	−	0.146630i	$-0.0468427\pi$
$787$	909.311	+	660.653i	1.15541	+	0.839458i	0.166223	+	0.986088i	$0.446843\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−637.292	+	877.158i	−0.805679	+	1.10892i
$792$		0			0
$793$	287.365			0.362377
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−76.7053	−	24.9231i	−0.0962426	−	0.0312711i	0.260500	−	0.965474i	$-0.416113\pi$
$797$	−76.7053	−	24.9231i	−0.0962426	−	0.0312711i	−0.356742	+	0.934203i	$0.616113\pi$
$798$		0			0
$799$	−1086.92			−1.36035
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−225.951	−	73.4159i	−0.281383	−	0.0914270i
$804$		0			0
$805$	705.285	+	343.690i	0.876131	+	0.426944i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	660.739	−	909.429i	0.816736	−	1.12414i	−0.173513	−	0.984832i	$-0.555512\pi$
$809$	660.739	−	909.429i	0.816736	−	1.12414i	0.990249	−	0.139309i	$-0.0444880\pi$
$810$		0			0
$811$	536.738	−	389.963i	0.661822	−	0.480842i	−0.205456	−	0.978666i	$-0.565868\pi$
$811$	536.738	−	389.963i	0.661822	−	0.480842i	0.867278	+	0.497825i	$0.165868\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−636.355	−	89.2104i	−0.780803	−	0.109461i
$816$		0			0
$817$	−63.8051	−	196.372i	−0.0780968	−	0.240357i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−610.248	−	198.282i	−0.743299	−	0.241512i	−0.0872035	−	0.996191i	$-0.527793\pi$
$821$	−610.248	−	198.282i	−0.743299	−	0.241512i	−0.656095	+	0.754678i	$0.727793\pi$
$822$		0			0
$823$	837.890	−	608.763i	1.01809	−	0.739687i	0.0522012	−	0.998637i	$-0.483376\pi$
$823$	837.890	−	608.763i	1.01809	−	0.739687i	0.965891	+	0.258949i	$0.0833763\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−264.610	−	364.204i	−0.319964	−	0.440392i	0.618492	−	0.785791i	$-0.287744\pi$
$827$	−264.610	−	364.204i	−0.319964	−	0.440392i	−0.938456	+	0.345399i	$0.887744\pi$
$828$		0			0
$829$	−357.984	+	1101.76i	−0.431826	+	1.32902i	0.464479	+	0.885584i	$0.346242\pi$
$829$	−357.984	+	1101.76i	−0.431826	+	1.32902i	−0.896305	+	0.443439i	$0.853758\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1399.45	−	454.709i	1.68001	−	0.545870i
$834$		0			0
$835$	−74.8981	+	77.6128i	−0.0896984	+	0.0929494i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−929.734	−	1279.67i	−1.10815	−	1.52523i	−0.824120	−	0.566415i	$-0.808330\pi$
$839$	−929.734	−	1279.67i	−1.10815	−	1.52523i	−0.284025	−	0.958817i	$-0.591670\pi$
$840$		0			0
$841$	227.307	+	165.148i	0.270282	+	0.196371i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−572.355	−	552.337i	−0.677344	−	0.653653i
$846$		0			0
$847$	−407.162	+	1253.11i	−0.480710	+	1.47947i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			201.165i			0.236386i
$852$		0			0
$853$	258.858	−	796.683i	0.303468	−	0.933978i	−0.676777	−	0.736188i	$-0.736624\pi$
$853$	258.858	−	796.683i	0.303468	−	0.933978i	0.980245	−	0.197789i	$-0.0633762\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			1193.16i			1.39225i	0.717919	+	0.696127i	$0.245095\pi$
$857$			1193.16i			1.39225i	−0.717919	+	0.696127i	$0.754905\pi$
$858$		0			0
$859$	−658.982	−	478.778i	−0.767150	−	0.557367i	0.133945	−	0.990989i	$-0.457235\pi$
$859$	−658.982	−	478.778i	−0.767150	−	0.557367i	−0.901095	+	0.433622i	$0.857235\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	306.150	−	421.379i	0.354751	−	0.488273i	−0.593926	−	0.804520i	$-0.702423\pi$
$863$	306.150	−	421.379i	0.354751	−	0.488273i	0.948677	+	0.316247i	$0.102423\pi$
$864$		0			0
$865$	−103.595	−	50.4826i	−0.119763	−	0.0583614i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−261.125	+	84.8445i	−0.300489	+	0.0976347i
$870$		0			0
$871$	56.2191	−	173.024i	0.0645454	−	0.198650i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−154.145	+	1481.31i	−0.176166	+	1.69292i
$876$		0			0
$877$	822.866	−	597.847i	0.938274	−	0.681696i	−0.00973056	−	0.999953i	$-0.503097\pi$
$877$	822.866	−	597.847i	0.938274	−	0.681696i	0.948005	+	0.318257i	$0.103097\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1030.33	+	334.775i	−1.16950	+	0.379994i	−0.828457	−	0.560052i	$-0.810781\pi$
$881$	−1030.33	+	334.775i	−1.16950	+	0.379994i	−0.341045	+	0.940047i	$0.610781\pi$
$882$		0			0
$883$	355.288	+	1093.46i	0.402365	+	1.23835i	0.923076	+	0.384618i	$0.125667\pi$
$883$	355.288	+	1093.46i	0.402365	+	1.23835i	−0.520711	+	0.853733i	$0.674333\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	30.2899	−	41.6904i	0.0341487	−	0.0470016i	−0.791601	−	0.611038i	$-0.790752\pi$
$887$	30.2899	−	41.6904i	0.0341487	−	0.0470016i	0.825750	+	0.564036i	$0.190752\pi$
$888$		0			0
$889$	895.672	−	650.744i	1.00751	−	0.731995i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	496.126i		−	0.555572i
$894$		0			0
$895$	1636.86	−	289.205i	1.82890	−	0.323134i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			1922.87i			2.13890i
$900$		0			0
$901$	−1325.90			−1.47159
$902$		0			0
$903$		0			0
$904$		0			0
$905$	330.935	+	319.360i	0.365674	+	0.352884i
$906$		0			0
$907$	−1215.93			−1.34060			−0.670302	−	0.742088i	$-0.733836\pi$
$907$	−1215.93			−1.34060			−0.670302	+	0.742088i	$0.733836\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	249.456	+	343.347i	0.273827	+	0.376891i	0.923677	−	0.383172i	$-0.125168\pi$
$911$	249.456	+	343.347i	0.273827	+	0.376891i	−0.649850	+	0.760062i	$0.725168\pi$
$912$		0			0
$913$	−36.8041	−	26.7397i	−0.0403112	−	0.0292878i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	619.566	−	201.309i	0.675644	−	0.219530i
$918$		0			0
$919$	−192.744	−	593.204i	−0.209732	−	0.645488i	−0.999486	−	0.0320644i	$-0.989792\pi$
$919$	−192.744	−	593.204i	−0.209732	−	0.645488i	0.789754	−	0.613424i	$-0.210208\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	8.90778	+	12.2605i	0.00965090	+	0.0132833i
$924$		0			0
$925$	−358.742	+	130.851i	−0.387829	+	0.141461i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−420.792	−	136.724i	−0.452951	−	0.147173i	0.0736519	−	0.997284i	$-0.476535\pi$
$929$	−420.792	−	136.724i	−0.452951	−	0.147173i	−0.526603	+	0.850111i	$0.676535\pi$
$930$		0			0
$931$	207.553	+	638.781i	0.222935	+	0.686124i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	252.919	+	35.4566i	0.270501	+	0.0379215i
$936$		0			0
$937$	580.044	+	421.427i	0.619044	+	0.449762i	0.852587	−	0.522585i	$-0.175032\pi$
$937$	580.044	+	421.427i	0.619044	+	0.449762i	−0.233544	+	0.972346i	$0.575032\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	793.683	−	1092.41i	0.843447	−	1.16090i	−0.141822	−	0.989892i	$-0.545296\pi$
$941$	793.683	−	1092.41i	0.843447	−	1.16090i	0.985269	−	0.171013i	$-0.0547039\pi$
$942$		0			0
$943$	−162.626			−0.172455
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1548.79	+	503.234i	1.63547	+	0.531398i	0.975520	−	0.219909i	$-0.0705760\pi$
$947$	1548.79	+	503.234i	1.63547	+	0.531398i	0.659953	+	0.751307i	$0.270576\pi$
$948$		0			0
$949$	−231.896			−0.244358
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−794.354	−	258.101i	−0.833530	−	0.270830i	−0.138998	−	0.990293i	$-0.544388\pi$
$953$	−794.354	−	258.101i	−0.833530	−	0.270830i	−0.694531	+	0.719462i	$0.744388\pi$
$954$		0			0
$955$	−10.2590	+	73.1796i	−0.0107424	+	0.0766279i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1876.76	−	2583.13i	1.95699	−	2.69357i
$960$		0			0
$961$	−1888.64	+	1372.18i	−1.96528	+	1.42786i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−70.1703	+	37.3412i	−0.0727154	+	0.0386956i
$966$		0			0
$967$	−185.710	−	571.556i	−0.192047	−	0.591061i	−0.999998	−	0.00181148i	$-0.999423\pi$
$967$	−185.710	−	571.556i	−0.192047	−	0.591061i	0.807951	−	0.589250i	$-0.200577\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1774.51	+	576.572i	1.82751	+	0.593792i	0.999451	+	0.0331453i	$0.0105524\pi$
$971$	1774.51	+	576.572i	1.82751	+	0.593792i	0.828055	+	0.560647i	$0.189448\pi$
$972$		0			0
$973$	−1871.43	+	1359.67i	−1.92336	+	1.39740i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	93.4305	+	128.596i	0.0956300	+	0.131623i	0.854151	−	0.520025i	$-0.174078\pi$
$977$	93.4305	+	128.596i	0.0956300	+	0.131623i	−0.758521	+	0.651649i	$0.774078\pi$
$978$		0			0
$979$	−28.2648	+	86.9902i	−0.0288711	+	0.0888561i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−61.4874	+	19.9785i	−0.0625508	+	0.0203240i	−0.340125	−	0.940380i	$-0.610469\pi$
$983$	−61.4874	+	19.9785i	−0.0625508	+	0.0203240i	0.277574	+	0.960704i	$0.410469\pi$
$984$		0			0
$985$	−900.683	+	159.135i	−0.914399	+	0.161558i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	221.209	+	304.468i	0.223670	+	0.307855i
$990$		0			0
$991$	−1108.37	−	805.277i	−1.11844	−	0.812591i	−0.134464	−	0.990918i	$-0.542931\pi$
$991$	−1108.37	−	805.277i	−1.11844	−	0.812591i	−0.983971	+	0.178328i	$0.942931\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1028.37	−	547.251i	1.03354	−	0.550001i
$996$		0			0
$997$	307.970	−	947.835i	0.308897	−	0.950687i	−0.669297	−	0.742995i	$-0.733405\pi$
$997$	307.970	−	947.835i	0.308897	−	0.950687i	0.978194	−	0.207692i	$-0.0665952\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.ba.a.161.19	yes	80
3.2	odd	2	inner	900.3.ba.a.161.2	✓	80
25.16	even	5	inner	900.3.ba.a.341.2	yes	80
75.41	odd	10	inner	900.3.ba.a.341.19	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.ba.a.161.2	✓	80	3.2	odd	2	inner
900.3.ba.a.161.19	yes	80	1.1	even	1	trivial
900.3.ba.a.341.2	yes	80	25.16	even	5	inner
900.3.ba.a.341.19	yes	80	75.41	odd	10	inner

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

\(f(q)\)	\(=\)	\(q+(4.41393 - 2.34888i) q^{5} -11.9145 q^{7} +O(q^{10})\)	\(q+(4.41393 - 2.34888i) q^{5} -11.9145 q^{7} +(1.89659 + 2.61044i) q^{11} +(2.54800 + 1.85123i) q^{13} +(15.0552 - 4.89175i) q^{17} +(2.23284 + 6.87198i) q^{19} +(-7.74116 - 10.6548i) q^{23} +(13.9655 - 20.7356i) q^{25} +(-31.8564 - 10.3508i) q^{29} +(-17.7395 - 54.5966i) q^{31} +(-52.5896 + 27.9856i) q^{35} +(-12.3573 - 8.97809i) q^{37} +(7.25806 - 9.98986i) q^{41} -28.5757 q^{43} +(-65.3014 - 21.2177i) q^{47} +92.9544 q^{49} +(-79.6592 - 25.8829i) q^{53} +(14.5030 + 7.06742i) q^{55} +(-46.8919 + 64.5412i) q^{59} +(73.8159 - 53.6304i) q^{61} +(15.5950 + 2.18626i) q^{65} +(-17.8502 - 54.9372i) q^{67} +(4.57632 + 1.48694i) q^{71} +(-59.5675 + 43.2783i) q^{73} +(-22.5969 - 31.1020i) q^{77} +(-26.2947 + 80.9267i) q^{79} +(-13.4088 + 4.35677i) q^{83} +(54.9627 - 56.9548i) q^{85} +(16.6620 + 22.9333i) q^{89} +(-30.3580 - 22.0564i) q^{91} +(25.9971 + 25.0878i) q^{95} +(-18.2310 + 56.1091i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{7}+O(q^{10}) \) 80 * q + 16 * q^7	\( 80 q + 16 q^{7} - 8 q^{13} + 60 q^{19} - 120 q^{25} + 120 q^{31} + 116 q^{37} - 80 q^{43} + 440 q^{49} + 120 q^{55} + 80 q^{61} + 24 q^{67} + 128 q^{73} + 40 q^{79} + 40 q^{85} - 140 q^{91} + 384 q^{97}+O(q^{100}) \) 80 * q + 16 * q^7 - 8 * q^13 + 60 * q^19 - 120 * q^25 + 120 * q^31 + 116 * q^37 - 80 * q^43 + 440 * q^49 + 120 * q^55 + 80 * q^61 + 24 * q^67 + 128 * q^73 + 40 * q^79 + 40 * q^85 - 140 * q^91 + 384 * q^97

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