LMFDB - Embedded newform 1600.2.j.b.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(143,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("1600.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.j (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.1
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1600.143
Dual form			1600.2.j.b.1007.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.93185i q^{3} +(-0.896575 + 0.896575i) q^{7} -0.732051 q^{9} +O(q^{10})$	$q-1.93185i q^{3} +(-0.896575 + 0.896575i) q^{7} -0.732051 q^{9} +(-4.09808 + 4.09808i) q^{11} +4.89898 q^{13} +(0.707107 - 0.707107i) q^{17} +(3.09808 - 3.09808i) q^{19} +(1.73205 + 1.73205i) q^{21} +(2.96713 + 2.96713i) q^{23} -4.38134i q^{27} +(-1.26795 - 1.26795i) q^{29} -4.19615i q^{31} +(7.91688 + 7.91688i) q^{33} +10.9348 q^{37} -9.46410i q^{39} +6.46410i q^{41} +9.14162 q^{43} +(-1.41421 - 1.41421i) q^{47} +5.39230i q^{49} +(-1.36603 - 1.36603i) q^{51} -9.89949i q^{53} +(-5.98502 - 5.98502i) q^{57} +(-4.26795 - 4.26795i) q^{59} +(7.19615 - 7.19615i) q^{61} +(0.656339 - 0.656339i) q^{63} +1.55291 q^{67} +(5.73205 - 5.73205i) q^{69} +12.9282 q^{71} +(-3.91447 + 3.91447i) q^{73} -7.34847i q^{77} -8.19615 q^{79} -10.6603 q^{81} +4.65874i q^{83} +(-2.44949 + 2.44949i) q^{87} -13.7321 q^{89} +(-4.39230 + 4.39230i) q^{91} -8.10634 q^{93} +(3.10583 - 3.10583i) q^{97} +(3.00000 - 3.00000i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^9	$ 8 q + 8 q^{9} - 12 q^{11} + 4 q^{19} - 24 q^{29} - 4 q^{51} - 48 q^{59} + 16 q^{61} + 32 q^{69} + 48 q^{71} - 24 q^{79} - 16 q^{81} - 96 q^{89} + 48 q^{91} + 24 q^{99}+O(q^{100}) $ 8 * q + 8 * q^9 - 12 * q^11 + 4 * q^19 - 24 * q^29 - 4 * q^51 - 48 * q^59 + 16 * q^61 + 32 * q^69 + 48 * q^71 - 24 * q^79 - 16 * q^81 - 96 * q^89 + 48 * q^91 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	1.93185i		−	1.11536i	−0.830058	−	0.557678i	$-0.811693\pi$
$3$		−	1.93185i		−	1.11536i	0.830058	−	0.557678i	$-0.188307\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.896575	+	0.896575i	−0.338874	+	0.338874i	−0.855943	−	0.517070i	$-0.827023\pi$
$7$	−0.896575	+	0.896575i	−0.338874	+	0.338874i	0.517070	+	0.855943i	$0.327023\pi$
$8$		0			0
$9$	−0.732051			−0.244017
$10$		0			0
$11$	−4.09808	+	4.09808i	−1.23562	+	1.23562i	−0.273842	+	0.961775i	$0.588294\pi$
$11$	−4.09808	+	4.09808i	−1.23562	+	1.23562i	−0.961775	+	0.273842i	$0.911706\pi$
$12$		0			0
$13$	4.89898			1.35873			0.679366	−	0.733799i	$-0.262255\pi$
$13$	4.89898			1.35873			0.679366	+	0.733799i	$0.262255\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i	−0.616139	−	0.787638i	$-0.711304\pi$
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i	0.787638	+	0.616139i	$0.211304\pi$
$18$		0			0
$19$	3.09808	−	3.09808i	0.710747	−	0.710747i	−0.255944	−	0.966692i	$-0.582386\pi$
$19$	3.09808	−	3.09808i	0.710747	−	0.710747i	0.966692	+	0.255944i	$0.0823863\pi$
$20$		0			0
$21$	1.73205	+	1.73205i	0.377964	+	0.377964i
$22$		0			0
$23$	2.96713	+	2.96713i	0.618689	+	0.618689i	0.945195	−	0.326506i	$-0.105871\pi$
$23$	2.96713	+	2.96713i	0.618689	+	0.618689i	−0.326506	+	0.945195i	$0.605871\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	4.38134i		−	0.843190i
$28$		0			0
$29$	−1.26795	−	1.26795i	−0.235452	−	0.235452i	0.579512	−	0.814964i	$-0.303243\pi$
$29$	−1.26795	−	1.26795i	−0.235452	−	0.235452i	−0.814964	+	0.579512i	$0.803243\pi$
$30$		0			0
$31$		−	4.19615i		−	0.753651i	−0.926284	−	0.376826i	$-0.877016\pi$
$31$		−	4.19615i		−	0.753651i	0.926284	−	0.376826i	$-0.122984\pi$
$32$		0			0
$33$	7.91688	+	7.91688i	1.37815	+	1.37815i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	10.9348			1.79767			0.898833	−	0.438292i	$-0.144416\pi$
$37$	10.9348			1.79767			0.898833	+	0.438292i	$0.144416\pi$
$38$		0			0
$39$		−	9.46410i		−	1.51547i
$40$		0			0
$41$			6.46410i			1.00952i	0.863259	+	0.504762i	$0.168420\pi$
$41$			6.46410i			1.00952i	−0.863259	+	0.504762i	$0.831580\pi$
$42$		0			0
$43$	9.14162			1.39408			0.697042	−	0.717030i	$-0.254499\pi$
$43$	9.14162			1.39408			0.697042	+	0.717030i	$0.254499\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.41421	−	1.41421i	−0.206284	−	0.206284i	0.596402	−	0.802686i	$-0.296597\pi$
$47$	−1.41421	−	1.41421i	−0.206284	−	0.206284i	−0.802686	+	0.596402i	$0.796597\pi$
$48$		0			0
$49$			5.39230i			0.770329i
$50$		0			0
$51$	−1.36603	−	1.36603i	−0.191282	−	0.191282i
$52$		0			0
$53$		−	9.89949i		−	1.35980i	−0.733305	−	0.679900i	$-0.762023\pi$
$53$		−	9.89949i		−	1.35980i	0.733305	−	0.679900i	$-0.237977\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−5.98502	−	5.98502i	−0.792736	−	0.792736i
$58$		0			0
$59$	−4.26795	−	4.26795i	−0.555640	−	0.555640i	0.372423	−	0.928063i	$-0.378527\pi$
$59$	−4.26795	−	4.26795i	−0.555640	−	0.555640i	−0.928063	+	0.372423i	$0.878527\pi$
$60$		0			0
$61$	7.19615	−	7.19615i	0.921373	−	0.921373i	−0.0757537	−	0.997127i	$-0.524136\pi$
$61$	7.19615	−	7.19615i	0.921373	−	0.921373i	0.997127	+	0.0757537i	$0.0241363\pi$
$62$		0			0
$63$	0.656339	−	0.656339i	0.0826909	−	0.0826909i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.55291			0.189719			0.0948593	−	0.995491i	$-0.469760\pi$
$67$	1.55291			0.189719			0.0948593	+	0.995491i	$0.469760\pi$
$68$		0			0
$69$	5.73205	−	5.73205i	0.690058	−	0.690058i
$70$		0			0
$71$	12.9282			1.53430			0.767148	−	0.641470i	$-0.221675\pi$
$71$	12.9282			1.53430			0.767148	+	0.641470i	$0.221675\pi$
$72$		0			0
$73$	−3.91447	+	3.91447i	−0.458154	+	0.458154i	−0.898049	−	0.439895i	$-0.855016\pi$
$73$	−3.91447	+	3.91447i	−0.458154	+	0.458154i	0.439895	+	0.898049i	$0.355016\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	7.34847i		−	0.837436i
$78$		0			0
$79$	−8.19615			−0.922139			−0.461070	−	0.887364i	$-0.652534\pi$
$79$	−8.19615			−0.922139			−0.461070	+	0.887364i	$0.652534\pi$
$80$		0			0
$81$	−10.6603			−1.18447
$82$		0			0
$83$			4.65874i			0.511363i	0.966761	+	0.255682i	$0.0822999\pi$
$83$			4.65874i			0.511363i	−0.966761	+	0.255682i	$0.917700\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.44949	+	2.44949i	−0.262613	+	0.262613i
$88$		0			0
$89$	−13.7321			−1.45559			−0.727797	−	0.685792i	$-0.759456\pi$
$89$	−13.7321			−1.45559			−0.727797	+	0.685792i	$0.759456\pi$
$90$		0			0
$91$	−4.39230	+	4.39230i	−0.460439	+	0.460439i
$92$		0			0
$93$	−8.10634			−0.840589
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.10583	−	3.10583i	0.315349	−	0.315349i	−0.531629	−	0.846978i	$-0.678420\pi$
$97$	3.10583	−	3.10583i	0.315349	−	0.315349i	0.846978	+	0.531629i	$0.178420\pi$
$98$		0			0
$99$	3.00000	−	3.00000i	0.301511	−	0.301511i
$100$		0			0
$101$	3.92820	+	3.92820i	0.390871	+	0.390871i	0.874998	−	0.484127i	$-0.160863\pi$
$101$	3.92820	+	3.92820i	0.390871	+	0.390871i	−0.484127	+	0.874998i	$0.660863\pi$
$102$		0			0
$103$	2.44949	+	2.44949i	0.241355	+	0.241355i	0.817411	−	0.576055i	$-0.195409\pi$
$103$	2.44949	+	2.44949i	0.241355	+	0.241355i	−0.576055	+	0.817411i	$0.695409\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	1.55291i		−	0.150126i	−0.997179	−	0.0750629i	$-0.976084\pi$
$107$		−	1.55291i		−	0.150126i	0.997179	−	0.0750629i	$-0.0239158\pi$
$108$		0			0
$109$	−11.3923	−	11.3923i	−1.09118	−	1.09118i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$	−11.3923	−	11.3923i	−1.09118	−	1.09118i	−0.0957826	−	0.995402i	$-0.530535\pi$
$110$		0			0
$111$		−	21.1244i		−	2.00504i
$112$		0			0
$113$	9.33109	+	9.33109i	0.877795	+	0.877795i	0.993306	−	0.115511i	$-0.0368506\pi$
$113$	9.33109	+	9.33109i	0.877795	+	0.877795i	−0.115511	+	0.993306i	$0.536851\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.58630			−0.331554
$118$		0			0
$119$			1.26795i			0.116233i
$120$		0			0
$121$		−	22.5885i		−	2.05350i
$122$		0			0
$123$	12.4877			1.12598
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−1.55291	−	1.55291i	−0.137799	−	0.137799i	0.634843	−	0.772641i	$-0.281065\pi$
$127$	−1.55291	−	1.55291i	−0.137799	−	0.137799i	−0.772641	+	0.634843i	$0.781065\pi$
$128$		0			0
$129$		−	17.6603i		−	1.55490i
$130$		0			0
$131$	9.92820	+	9.92820i	0.867431	+	0.867431i	0.992187	−	0.124756i	$-0.0398149\pi$
$131$	9.92820	+	9.92820i	0.867431	+	0.867431i	−0.124756	+	0.992187i	$0.539815\pi$
$132$		0			0
$133$			5.55532i			0.481707i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.98262	+	1.98262i	0.169387	+	0.169387i	0.786710	−	0.617323i	$-0.211783\pi$
$137$	1.98262	+	1.98262i	0.169387	+	0.169387i	−0.617323	+	0.786710i	$0.711783\pi$
$138$		0			0
$139$	8.29423	+	8.29423i	0.703507	+	0.703507i	0.965162	−	0.261654i	$-0.0842680\pi$
$139$	8.29423	+	8.29423i	0.703507	+	0.703507i	−0.261654	+	0.965162i	$0.584268\pi$
$140$		0			0
$141$	−2.73205	+	2.73205i	−0.230080	+	0.230080i
$142$		0			0
$143$	−20.0764	+	20.0764i	−1.67887	+	1.67887i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	10.4171			0.859191
$148$		0			0
$149$	9.12436	−	9.12436i	0.747496	−	0.747496i	−0.226512	−	0.974008i	$-0.572732\pi$
$149$	9.12436	−	9.12436i	0.747496	−	0.747496i	0.974008	+	0.226512i	$0.0727323\pi$
$150$		0			0
$151$	0.196152			0.0159627			0.00798133	−	0.999968i	$-0.497459\pi$
$151$	0.196152			0.0159627			0.00798133	+	0.999968i	$0.497459\pi$
$152$		0			0
$153$	−0.517638	+	0.517638i	−0.0418486	+	0.0418486i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			0.656339i			0.0523815i	0.999657	+	0.0261908i	$0.00833773\pi$
$157$			0.656339i			0.0523815i	−0.999657	+	0.0261908i	$0.991662\pi$
$158$		0			0
$159$	−19.1244			−1.51666
$160$		0			0
$161$	−5.32051			−0.419315
$162$		0			0
$163$		−	13.1440i		−	1.02952i	−0.857334	−	0.514760i	$-0.827881\pi$
$163$		−	13.1440i		−	1.02952i	0.857334	−	0.514760i	$-0.172119\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	14.4195	−	14.4195i	1.11582	−	1.11582i	0.123469	−	0.992348i	$-0.460598\pi$
$167$	14.4195	−	14.4195i	1.11582	−	1.11582i	0.992348	−	0.123469i	$-0.0394019\pi$
$168$		0			0
$169$	11.0000			0.846154
$170$		0			0
$171$	−2.26795	+	2.26795i	−0.173434	+	0.173434i
$172$		0			0
$173$	8.76268			0.666214			0.333107	−	0.942889i	$-0.391903\pi$
$173$	8.76268			0.666214			0.333107	+	0.942889i	$0.391903\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−8.24504	+	8.24504i	−0.619736	+	0.619736i
$178$		0			0
$179$	−4.56218	+	4.56218i	−0.340993	+	0.340993i	−0.856741	−	0.515747i	$-0.827514\pi$
$179$	−4.56218	+	4.56218i	−0.340993	+	0.340993i	0.515747	+	0.856741i	$0.327514\pi$
$180$		0			0
$181$	13.1962	+	13.1962i	0.980862	+	0.980862i	0.999820	−	0.0189580i	$-0.00603488\pi$
$181$	13.1962	+	13.1962i	0.980862	+	0.980862i	−0.0189580	+	0.999820i	$0.506035\pi$
$182$		0			0
$183$	−13.9019	−	13.9019i	−1.02766	−	1.02766i
$184$		0			0
$185$		0			0
$186$		0			0
$187$			5.79555i			0.423813i
$188$		0			0
$189$	3.92820	+	3.92820i	0.285735	+	0.285735i
$190$		0			0
$191$			0.339746i			0.0245832i	0.999924	+	0.0122916i	$0.00391263\pi$
$191$			0.339746i			0.0245832i	−0.999924	+	0.0122916i	$0.996087\pi$
$192$		0			0
$193$	−5.22715	−	5.22715i	−0.376258	−	0.376258i	0.493492	−	0.869750i	$-0.335720\pi$
$193$	−5.22715	−	5.22715i	−0.376258	−	0.376258i	−0.869750	+	0.493492i	$0.835720\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−18.9396			−1.34939			−0.674695	−	0.738097i	$-0.735725\pi$
$197$	−18.9396			−1.34939			−0.674695	+	0.738097i	$0.735725\pi$
$198$		0			0
$199$			4.39230i			0.311362i	0.987807	+	0.155681i	$0.0497572\pi$
$199$			4.39230i			0.311362i	−0.987807	+	0.155681i	$0.950243\pi$
$200$		0			0
$201$		−	3.00000i		−	0.211604i
$202$		0			0
$203$	2.27362			0.159577
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−2.17209	−	2.17209i	−0.150971	−	0.150971i
$208$		0			0
$209$			25.3923i			1.75642i
$210$		0			0
$211$	4.29423	+	4.29423i	0.295627	+	0.295627i	0.839298	−	0.543671i	$-0.182966\pi$
$211$	4.29423	+	4.29423i	0.295627	+	0.295627i	−0.543671	+	0.839298i	$0.682966\pi$
$212$		0			0
$213$		−	24.9754i		−	1.71128i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	3.76217	+	3.76217i	0.255393	+	0.255393i
$218$		0			0
$219$	7.56218	+	7.56218i	0.511005	+	0.511005i
$220$		0			0
$221$	3.46410	−	3.46410i	0.233021	−	0.233021i
$222$		0			0
$223$	2.44949	−	2.44949i	0.164030	−	0.164030i	−0.620319	−	0.784349i	$-0.712997\pi$
$223$	2.44949	−	2.44949i	0.164030	−	0.164030i	0.784349	+	0.620319i	$0.212997\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.4543			−0.693876			−0.346938	−	0.937888i	$-0.612779\pi$
$227$	−10.4543			−0.693876			−0.346938	+	0.937888i	$0.612779\pi$
$228$		0			0
$229$	−4.00000	+	4.00000i	−0.264327	+	0.264327i	−0.826809	−	0.562482i	$-0.809847\pi$
$229$	−4.00000	+	4.00000i	−0.264327	+	0.264327i	0.562482	+	0.826809i	$0.309847\pi$
$230$		0			0
$231$	−14.1962			−0.934038
$232$		0			0
$233$	5.65685	−	5.65685i	0.370593	−	0.370593i	−0.497100	−	0.867693i	$-0.665602\pi$
$233$	5.65685	−	5.65685i	0.370593	−	0.370593i	0.867693	+	0.497100i	$0.165602\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			15.8338i			1.02851i
$238$		0			0
$239$	14.5359			0.940249			0.470125	−	0.882600i	$-0.344209\pi$
$239$	14.5359			0.940249			0.470125	+	0.882600i	$0.344209\pi$
$240$		0			0
$241$	−23.1962			−1.49420			−0.747098	−	0.664714i	$-0.768553\pi$
$241$	−23.1962			−1.49420			−0.747098	+	0.664714i	$0.768553\pi$
$242$		0			0
$243$			7.45001i			0.477918i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	15.1774	−	15.1774i	0.965716	−	0.965716i
$248$		0			0
$249$	9.00000			0.570352
$250$		0			0
$251$	−0.169873	+	0.169873i	−0.0107223	+	0.0107223i	−0.712448	−	0.701725i	$-0.752413\pi$
$251$	−0.169873	+	0.169873i	−0.0107223	+	0.0107223i	0.701725	+	0.712448i	$0.252413\pi$
$252$		0			0
$253$	−24.3190			−1.52892
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.1769	+	10.1769i	−0.634817	+	0.634817i	−0.949272	−	0.314455i	$-0.898178\pi$
$257$	−10.1769	+	10.1769i	−0.634817	+	0.634817i	0.314455	+	0.949272i	$0.398178\pi$
$258$		0			0
$259$	−9.80385	+	9.80385i	−0.609181	+	0.609181i
$260$		0			0
$261$	0.928203	+	0.928203i	0.0574543	+	0.0574543i
$262$		0			0
$263$	−1.27551	−	1.27551i	−0.0786515	−	0.0786515i	0.666687	−	0.745338i	$-0.267712\pi$
$263$	−1.27551	−	1.27551i	−0.0786515	−	0.0786515i	−0.745338	+	0.666687i	$0.767712\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			26.5283i			1.62350i
$268$		0			0
$269$	10.7321	+	10.7321i	0.654345	+	0.654345i	0.954036	−	0.299691i	$-0.0968837\pi$
$269$	10.7321	+	10.7321i	0.654345	+	0.654345i	−0.299691	+	0.954036i	$0.596884\pi$
$270$		0			0
$271$			30.5885i			1.85812i	0.369934	+	0.929058i	$0.379380\pi$
$271$			30.5885i			1.85812i	−0.369934	+	0.929058i	$0.620620\pi$
$272$		0			0
$273$	8.48528	+	8.48528i	0.513553	+	0.513553i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0			−	1.00000i	$-0.5\pi$
$277$		0			0				1.00000i	$0.5\pi$
$278$		0			0
$279$			3.07180i			0.183904i
$280$		0			0
$281$			8.53590i			0.509209i	0.967045	+	0.254605i	$0.0819453\pi$
$281$			8.53590i			0.509209i	−0.967045	+	0.254605i	$0.918055\pi$
$282$		0			0
$283$	20.9730			1.24671			0.623357	−	0.781938i	$-0.285768\pi$
$283$	20.9730			1.24671			0.623357	+	0.781938i	$0.285768\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.79555	−	5.79555i	−0.342101	−	0.342101i
$288$		0			0
$289$			16.0000i			0.941176i
$290$		0			0
$291$	−6.00000	−	6.00000i	−0.351726	−	0.351726i
$292$		0			0
$293$			9.89949i			0.578335i	0.957279	+	0.289167i	$0.0933784\pi$
$293$			9.89949i			0.578335i	−0.957279	+	0.289167i	$0.906622\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	17.9551	+	17.9551i	1.04186	+	1.04186i
$298$		0			0
$299$	14.5359	+	14.5359i	0.840633	+	0.840633i
$300$		0			0
$301$	−8.19615	+	8.19615i	−0.472418	+	0.472418i
$302$		0			0
$303$	7.58871	−	7.58871i	0.435960	−	0.435960i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−6.27603			−0.358192			−0.179096	−	0.983832i	$-0.557317\pi$
$307$	−6.27603			−0.358192			−0.179096	+	0.983832i	$0.557317\pi$
$308$		0			0
$309$	4.73205	−	4.73205i	0.269197	−	0.269197i
$310$		0			0
$311$	−5.66025			−0.320964			−0.160482	−	0.987039i	$-0.551305\pi$
$311$	−5.66025			−0.320964			−0.160482	+	0.987039i	$0.551305\pi$
$312$		0			0
$313$	−9.14162	+	9.14162i	−0.516715	+	0.516715i	−0.916576	−	0.399861i	$-0.869058\pi$
$313$	−9.14162	+	9.14162i	−0.516715	+	0.516715i	0.399861	+	0.916576i	$0.369058\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	20.0764i		−	1.12760i	−0.825911	−	0.563801i	$-0.809338\pi$
$317$		−	20.0764i		−	1.12760i	0.825911	−	0.563801i	$-0.190662\pi$
$318$		0			0
$319$	10.3923			0.581857
$320$		0			0
$321$	−3.00000			−0.167444
$322$		0			0
$323$		−	4.38134i		−	0.243784i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−22.0082	+	22.0082i	−1.21706	+	1.21706i
$328$		0			0
$329$	2.53590			0.139809
$330$		0			0
$331$	−6.49038	+	6.49038i	−0.356744	+	0.356744i	−0.862611	−	0.505868i	$-0.831172\pi$
$331$	−6.49038	+	6.49038i	−0.356744	+	0.356744i	0.505868	+	0.862611i	$0.331172\pi$
$332$		0			0
$333$	−8.00481			−0.438661
$334$		0			0
$335$		0			0
$336$		0			0
$337$	9.71003	−	9.71003i	0.528939	−	0.528939i	−0.391317	−	0.920256i	$-0.627980\pi$
$337$	9.71003	−	9.71003i	0.528939	−	0.528939i	0.920256	+	0.391317i	$0.127980\pi$
$338$		0			0
$339$	18.0263	−	18.0263i	0.979053	−	0.979053i
$340$		0			0
$341$	17.1962	+	17.1962i	0.931224	+	0.931224i
$342$		0			0
$343$	−11.1106	−	11.1106i	−0.599918	−	0.599918i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	4.38134i		−	0.235203i	−0.993061	−	0.117601i	$-0.962479\pi$
$347$		−	4.38134i		−	0.235203i	0.993061	−	0.117601i	$-0.0375205\pi$
$348$		0			0
$349$	−7.58846	−	7.58846i	−0.406201	−	0.406201i	0.474211	−	0.880411i	$-0.342734\pi$
$349$	−7.58846	−	7.58846i	−0.406201	−	0.406201i	−0.880411	+	0.474211i	$0.842734\pi$
$350$		0			0
$351$		−	21.4641i		−	1.14567i
$352$		0			0
$353$	−24.5964	−	24.5964i	−1.30914	−	1.30914i	−0.922039	−	0.387097i	$-0.873478\pi$
$353$	−24.5964	−	24.5964i	−1.30914	−	1.30914i	−0.387097	−	0.922039i	$-0.626522\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.44949			0.129641
$358$		0			0
$359$		−	6.58846i		−	0.347725i	−0.984770	−	0.173863i	$-0.944375\pi$
$359$		−	6.58846i		−	0.347725i	0.984770	−	0.173863i	$-0.0556249\pi$
$360$		0			0
$361$		−	0.196152i		−	0.0103238i
$362$		0			0
$363$	−43.6375			−2.29038
$364$		0			0
$365$		0			0
$366$		0			0
$367$	22.5259	+	22.5259i	1.17584	+	1.17584i	0.980794	+	0.195048i	$0.0624862\pi$
$367$	22.5259	+	22.5259i	1.17584	+	1.17584i	0.195048	+	0.980794i	$0.437514\pi$
$368$		0			0
$369$		−	4.73205i		−	0.246341i
$370$		0			0
$371$	8.87564	+	8.87564i	0.460800	+	0.460800i
$372$		0			0
$373$			1.13681i			0.0588619i	0.999567	+	0.0294310i	$0.00936952\pi$
$373$			1.13681i			0.0588619i	−0.999567	+	0.0294310i	$0.990630\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−6.21166	−	6.21166i	−0.319917	−	0.319917i
$378$		0			0
$379$	−5.29423	−	5.29423i	−0.271946	−	0.271946i	0.557937	−	0.829883i	$-0.311593\pi$
$379$	−5.29423	−	5.29423i	−0.271946	−	0.271946i	−0.829883	+	0.557937i	$0.811593\pi$
$380$		0			0
$381$	−3.00000	+	3.00000i	−0.153695	+	0.153695i
$382$		0			0
$383$	−7.20977	+	7.20977i	−0.368402	+	0.368402i	−0.866894	−	0.498492i	$-0.833887\pi$
$383$	−7.20977	+	7.20977i	−0.368402	+	0.368402i	0.498492	+	0.866894i	$0.333887\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−6.69213			−0.340180
$388$		0			0
$389$	−26.3205	+	26.3205i	−1.33450	+	1.33450i	−0.433209	+	0.901293i	$0.642619\pi$
$389$	−26.3205	+	26.3205i	−1.33450	+	1.33450i	−0.901293	+	0.433209i	$0.857381\pi$
$390$		0			0
$391$	4.19615			0.212209
$392$		0			0
$393$	19.1798	−	19.1798i	0.967494	−	0.967494i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			13.3843i			0.671737i	0.941909	+	0.335868i	$0.109030\pi$
$397$			13.3843i			0.671737i	−0.941909	+	0.335868i	$0.890970\pi$
$398$		0			0
$399$	10.7321			0.537275
$400$		0			0
$401$	12.1244			0.605461			0.302731	−	0.953076i	$-0.402102\pi$
$401$	12.1244			0.605461			0.302731	+	0.953076i	$0.402102\pi$
$402$		0			0
$403$		−	20.5569i		−	1.02401i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−44.8115	+	44.8115i	−2.22122	+	2.22122i
$408$		0			0
$409$	−4.60770			−0.227836			−0.113918	−	0.993490i	$-0.536340\pi$
$409$	−4.60770			−0.227836			−0.113918	+	0.993490i	$0.536340\pi$
$410$		0			0
$411$	3.83013	−	3.83013i	0.188926	−	0.188926i
$412$		0			0
$413$	7.65308			0.376583
$414$		0			0
$415$		0			0
$416$		0			0
$417$	16.0232	−	16.0232i	0.784660	−	0.784660i
$418$		0			0
$419$	−16.5622	+	16.5622i	−0.809115	+	0.809115i	−0.984500	−	0.175385i	$-0.943883\pi$
$419$	−16.5622	+	16.5622i	−0.809115	+	0.809115i	0.175385	+	0.984500i	$0.443883\pi$
$420$		0			0
$421$	−26.3923	−	26.3923i	−1.28628	−	1.28628i	−0.937028	−	0.349254i	$-0.886435\pi$
$421$	−26.3923	−	26.3923i	−1.28628	−	1.28628i	−0.349254	−	0.937028i	$-0.613565\pi$
$422$		0			0
$423$	1.03528	+	1.03528i	0.0503369	+	0.0503369i
$424$		0			0
$425$		0			0
$426$		0			0
$427$			12.9038i			0.624458i
$428$		0			0
$429$	38.7846	+	38.7846i	1.87254	+	1.87254i
$430$		0			0
$431$		−	6.58846i		−	0.317355i	−0.987330	−	0.158677i	$-0.949277\pi$
$431$		−	6.58846i		−	0.317355i	0.987330	−	0.158677i	$-0.0507230\pi$
$432$		0			0
$433$	−4.57081	−	4.57081i	−0.219659	−	0.219659i	0.588696	−	0.808355i	$-0.299642\pi$
$433$	−4.57081	−	4.57081i	−0.219659	−	0.219659i	−0.808355	+	0.588696i	$0.799642\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	18.3848			0.879463
$438$		0			0
$439$			40.3923i			1.92782i	0.266229	+	0.963910i	$0.414222\pi$
$439$			40.3923i			1.92782i	−0.266229	+	0.963910i	$0.585778\pi$
$440$		0			0
$441$		−	3.94744i		−	0.187973i
$442$		0			0
$443$	−16.5545			−0.786526			−0.393263	−	0.919426i	$-0.628654\pi$
$443$	−16.5545			−0.786526			−0.393263	+	0.919426i	$0.628654\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−17.6269	−	17.6269i	−0.833724	−	0.833724i
$448$		0			0
$449$			6.12436i			0.289026i	0.989503	+	0.144513i	$0.0461616\pi$
$449$			6.12436i			0.289026i	−0.989503	+	0.144513i	$0.953838\pi$
$450$		0			0
$451$	−26.4904	−	26.4904i	−1.24738	−	1.24738i
$452$		0			0
$453$		−	0.378937i		−	0.0178040i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−18.1953	−	18.1953i	−0.851141	−	0.851141i	0.139133	−	0.990274i	$-0.455568\pi$
$457$	−18.1953	−	18.1953i	−0.851141	−	0.851141i	−0.990274	+	0.139133i	$0.955568\pi$
$458$		0			0
$459$	−3.09808	−	3.09808i	−0.144606	−	0.144606i
$460$		0			0
$461$	−13.2679	+	13.2679i	−0.617950	+	0.617950i	−0.945005	−	0.327055i	$-0.893944\pi$
$461$	−13.2679	+	13.2679i	−0.617950	+	0.617950i	0.327055	+	0.945005i	$0.393944\pi$
$462$		0			0
$463$	−8.00481	+	8.00481i	−0.372015	+	0.372015i	−0.868211	−	0.496196i	$-0.834730\pi$
$463$	−8.00481	+	8.00481i	−0.372015	+	0.372015i	0.496196	+	0.868211i	$0.334730\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.41421			−0.0654420			−0.0327210	−	0.999465i	$-0.510417\pi$
$467$	−1.41421			−0.0654420			−0.0327210	+	0.999465i	$0.510417\pi$
$468$		0			0
$469$	−1.39230	+	1.39230i	−0.0642907	+	0.0642907i
$470$		0			0
$471$	1.26795			0.0584240
$472$		0			0
$473$	−37.4631	+	37.4631i	−1.72255	+	1.72255i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			7.24693i			0.331814i
$478$		0			0
$479$	−24.3397			−1.11211			−0.556056	−	0.831145i	$-0.687686\pi$
$479$	−24.3397			−1.11211			−0.556056	+	0.831145i	$0.687686\pi$
$480$		0			0
$481$	53.5692			2.44255
$482$		0			0
$483$			10.2784i			0.467685i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	23.4225	−	23.4225i	1.06137	−	1.06137i	0.0633836	−	0.997989i	$-0.479811\pi$
$487$	23.4225	−	23.4225i	1.06137	−	1.06137i	0.997989	−	0.0633836i	$-0.0201892\pi$
$488$		0			0
$489$	−25.3923			−1.14828
$490$		0			0
$491$	14.3205	−	14.3205i	0.646275	−	0.646275i	−0.305815	−	0.952091i	$-0.598929\pi$
$491$	14.3205	−	14.3205i	0.646275	−	0.646275i	0.952091	+	0.305815i	$0.0989290\pi$
$492$		0			0
$493$	−1.79315			−0.0807595
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−11.5911	+	11.5911i	−0.519932	+	0.519932i
$498$		0			0
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.0300737	−	0.999548i	$-0.490426\pi$
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.999548	−	0.0300737i	$-0.00957421\pi$
$500$		0			0
$501$	−27.8564	−	27.8564i	−1.24453	−	1.24453i
$502$		0			0
$503$	−7.62587	−	7.62587i	−0.340021	−	0.340021i	0.516354	−	0.856375i	$-0.327289\pi$
$503$	−7.62587	−	7.62587i	−0.340021	−	0.340021i	−0.856375	+	0.516354i	$0.827289\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	21.2504i		−	0.943762i
$508$		0			0
$509$	−15.0000	−	15.0000i	−0.664863	−	0.664863i	0.291659	−	0.956522i	$-0.405793\pi$
$509$	−15.0000	−	15.0000i	−0.664863	−	0.664863i	−0.956522	+	0.291659i	$0.905793\pi$
$510$		0			0
$511$		−	7.01924i		−	0.310513i
$512$		0			0
$513$	−13.5737	−	13.5737i	−0.599295	−	0.599295i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	11.5911			0.509776
$518$		0			0
$519$		−	16.9282i		−	0.743066i
$520$		0			0
$521$			45.2487i			1.98238i	0.132440	+	0.991191i	$0.457719\pi$
$521$			45.2487i			1.98238i	−0.132440	+	0.991191i	$0.542281\pi$
$522$		0			0
$523$	−26.0478			−1.13899			−0.569496	−	0.821994i	$-0.692861\pi$
$523$	−26.0478			−1.13899			−0.569496	+	0.821994i	$0.692861\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.96713	−	2.96713i	−0.129250	−	0.129250i
$528$		0			0
$529$		−	5.39230i		−	0.234448i
$530$		0			0
$531$	3.12436	+	3.12436i	0.135585	+	0.135585i
$532$		0			0
$533$			31.6675i			1.37167i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	8.81345	+	8.81345i	0.380328	+	0.380328i
$538$		0			0
$539$	−22.0981	−	22.0981i	−0.951832	−	0.951832i
$540$		0			0
$541$	30.1962	−	30.1962i	1.29823	−	1.29823i	0.368676	−	0.929558i	$-0.379811\pi$
$541$	30.1962	−	30.1962i	1.29823	−	1.29823i	0.929558	−	0.368676i	$-0.120189\pi$
$542$		0			0
$543$	25.4930	−	25.4930i	1.09401	−	1.09401i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−14.2808			−0.610604			−0.305302	−	0.952256i	$-0.598757\pi$
$547$	−14.2808			−0.610604			−0.305302	+	0.952256i	$0.598757\pi$
$548$		0			0
$549$	−5.26795	+	5.26795i	−0.224831	+	0.224831i
$550$		0			0
$551$	−7.85641			−0.334694
$552$		0			0
$553$	7.34847	−	7.34847i	0.312489	−	0.312489i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			3.38323i			0.143352i	0.997428	+	0.0716760i	$0.0228348\pi$
$557$			3.38323i			0.143352i	−0.997428	+	0.0716760i	$0.977165\pi$
$558$		0			0
$559$	44.7846			1.89419
$560$		0			0
$561$	11.1962			0.472702
$562$		0			0
$563$			38.4612i			1.62094i	0.585777	+	0.810472i	$0.300790\pi$
$563$			38.4612i			1.62094i	−0.585777	+	0.810472i	$0.699210\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	9.55772	−	9.55772i	0.401387	−	0.401387i
$568$		0			0
$569$	14.0718			0.589920			0.294960	−	0.955510i	$-0.404694\pi$
$569$	14.0718			0.589920			0.294960	+	0.955510i	$0.404694\pi$
$570$		0			0
$571$	−0.607695	+	0.607695i	−0.0254313	+	0.0254313i	−0.719708	−	0.694277i	$-0.755724\pi$
$571$	−0.607695	+	0.607695i	−0.0254313	+	0.0254313i	0.694277	+	0.719708i	$0.255724\pi$
$572$		0			0
$573$	0.656339			0.0274189
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−13.4722	+	13.4722i	−0.560855	+	0.560855i	−0.929550	−	0.368695i	$-0.879805\pi$
$577$	−13.4722	+	13.4722i	−0.560855	+	0.560855i	0.368695	+	0.929550i	$0.379805\pi$
$578$		0			0
$579$	−10.0981	+	10.0981i	−0.419662	+	0.419662i
$580$		0			0
$581$	−4.17691	−	4.17691i	−0.173288	−	0.173288i
$582$		0			0
$583$	40.5689	+	40.5689i	1.68019	+	1.68019i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	45.9483i		−	1.89649i	−0.317538	−	0.948245i	$-0.602856\pi$
$587$		−	45.9483i		−	1.89649i	0.317538	−	0.948245i	$-0.397144\pi$
$588$		0			0
$589$	−13.0000	−	13.0000i	−0.535656	−	0.535656i
$590$		0			0
$591$			36.5885i			1.50505i
$592$		0			0
$593$	11.3001	+	11.3001i	0.464040	+	0.464040i	0.899977	−	0.435937i	$-0.143583\pi$
$593$	11.3001	+	11.3001i	0.464040	+	0.464040i	−0.435937	+	0.899977i	$0.643583\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.48528			0.347279
$598$		0			0
$599$		−	26.1962i		−	1.07035i	−0.844743	−	0.535173i	$-0.820246\pi$
$599$		−	26.1962i		−	1.07035i	0.844743	−	0.535173i	$-0.179754\pi$
$600$		0			0
$601$		−	23.1962i		−	0.946191i	−0.881011	−	0.473095i	$-0.843137\pi$
$601$		−	23.1962i		−	0.946191i	0.881011	−	0.473095i	$-0.156863\pi$
$602$		0			0
$603$	−1.13681			−0.0462946
$604$		0			0
$605$		0			0
$606$		0			0
$607$	24.3190	+	24.3190i	0.987079	+	0.987079i	0.999918	−	0.0128385i	$-0.00408674\pi$
$607$	24.3190	+	24.3190i	0.987079	+	0.987079i	−0.0128385	+	0.999918i	$0.504087\pi$
$608$		0			0
$609$		−	4.39230i		−	0.177985i
$610$		0			0
$611$	−6.92820	−	6.92820i	−0.280285	−	0.280285i
$612$		0			0
$613$		−	13.5601i		−	0.547688i	−0.961774	−	0.273844i	$-0.911705\pi$
$613$		−	13.5601i		−	0.547688i	0.961774	−	0.273844i	$-0.0882953\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−22.9048	−	22.9048i	−0.922113	−	0.922113i	0.0750653	−	0.997179i	$-0.476083\pi$
$617$	−22.9048	−	22.9048i	−0.922113	−	0.922113i	−0.997179	+	0.0750653i	$0.976083\pi$
$618$		0			0
$619$	−15.7846	−	15.7846i	−0.634437	−	0.634437i	0.314741	−	0.949178i	$-0.398082\pi$
$619$	−15.7846	−	15.7846i	−0.634437	−	0.634437i	−0.949178	+	0.314741i	$0.898082\pi$
$620$		0			0
$621$	13.0000	−	13.0000i	0.521672	−	0.521672i
$622$		0			0
$623$	12.3118	−	12.3118i	0.493263	−	0.493263i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	49.0542			1.95903
$628$		0			0
$629$	7.73205	−	7.73205i	0.308297	−	0.308297i
$630$		0			0
$631$	18.5885			0.739995			0.369997	−	0.929033i	$-0.379359\pi$
$631$	18.5885			0.739995			0.369997	+	0.929033i	$0.379359\pi$
$632$		0			0
$633$	8.29581	−	8.29581i	0.329729	−	0.329729i
$634$		0			0
$635$		0			0
$636$		0			0
$637$			26.4168i			1.04667i
$638$		0			0
$639$	−9.46410			−0.374394
$640$		0			0
$641$	0.928203			0.0366618			0.0183309	−	0.999832i	$-0.494165\pi$
$641$	0.928203			0.0366618			0.0183309	+	0.999832i	$0.494165\pi$
$642$		0			0
$643$		−	32.3238i		−	1.27473i	−0.770563	−	0.637364i	$-0.780025\pi$
$643$		−	32.3238i		−	1.27473i	0.770563	−	0.637364i	$-0.219975\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−3.96524	+	3.96524i	−0.155890	+	0.155890i	−0.780743	−	0.624853i	$-0.785159\pi$
$647$	−3.96524	+	3.96524i	−0.155890	+	0.155890i	0.624853	+	0.780743i	$0.285159\pi$
$648$		0			0
$649$	34.9808			1.37312
$650$		0			0
$651$	7.26795	−	7.26795i	0.284853	−	0.284853i
$652$		0			0
$653$	7.62587			0.298423			0.149212	−	0.988805i	$-0.452326\pi$
$653$	7.62587			0.298423			0.149212	+	0.988805i	$0.452326\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.86559	−	2.86559i	0.111797	−	0.111797i
$658$		0			0
$659$	−26.4904	+	26.4904i	−1.03192	+	1.03192i	−0.0324452	+	0.999474i	$0.510329\pi$
$659$	−26.4904	+	26.4904i	−1.03192	+	1.03192i	−0.999474	+	0.0324452i	$0.989671\pi$
$660$		0			0
$661$	−8.00000	−	8.00000i	−0.311164	−	0.311164i	0.534196	−	0.845360i	$-0.320614\pi$
$661$	−8.00000	−	8.00000i	−0.311164	−	0.311164i	−0.845360	+	0.534196i	$0.820614\pi$
$662$		0			0
$663$	−6.69213	−	6.69213i	−0.259901	−	0.259901i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		−	7.52433i		−	0.291343i
$668$		0			0
$669$	−4.73205	−	4.73205i	−0.182952	−	0.182952i
$670$		0			0
$671$			58.9808i			2.27693i
$672$		0			0
$673$	−7.17260	−	7.17260i	−0.276484	−	0.276484i	0.555220	−	0.831704i	$-0.312634\pi$
$673$	−7.17260	−	7.17260i	−0.276484	−	0.276484i	−0.831704	+	0.555220i	$0.812634\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−31.1127			−1.19576			−0.597879	−	0.801586i	$-0.703990\pi$
$677$	−31.1127			−1.19576			−0.597879	+	0.801586i	$0.703990\pi$
$678$		0			0
$679$			5.56922i			0.213727i
$680$		0			0
$681$			20.1962i			0.773918i
$682$		0			0
$683$	−26.7314			−1.02285			−0.511423	−	0.859329i	$-0.670882\pi$
$683$	−26.7314			−1.02285			−0.511423	+	0.859329i	$0.670882\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	7.72741	+	7.72741i	0.294819	+	0.294819i
$688$		0			0
$689$		−	48.4974i		−	1.84760i
$690$		0			0
$691$	−25.8827	−	25.8827i	−0.984624	−	0.984624i	0.0152598	−	0.999884i	$-0.495142\pi$
$691$	−25.8827	−	25.8827i	−0.984624	−	0.984624i	−0.999884	+	0.0152598i	$0.995142\pi$
$692$		0			0
$693$			5.37945i			0.204349i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	4.57081	+	4.57081i	0.173132	+	0.173132i
$698$		0			0
$699$	−10.9282	−	10.9282i	−0.413343	−	0.413343i
$700$		0			0
$701$	−12.5885	+	12.5885i	−0.475459	+	0.475459i	−0.903676	−	0.428217i	$-0.859142\pi$
$701$	−12.5885	+	12.5885i	−0.475459	+	0.475459i	0.428217	+	0.903676i	$0.359142\pi$
$702$		0			0
$703$	33.8768	−	33.8768i	1.27769	−	1.27769i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.04386			−0.264912
$708$		0			0
$709$	−2.00000	+	2.00000i	−0.0751116	+	0.0751116i	−0.743665	−	0.668553i	$-0.766914\pi$
$709$	−2.00000	+	2.00000i	−0.0751116	+	0.0751116i	0.668553	+	0.743665i	$0.266914\pi$
$710$		0			0
$711$	6.00000			0.225018
$712$		0			0
$713$	12.4505	−	12.4505i	0.466276	−	0.466276i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		−	28.0812i		−	1.04871i
$718$		0			0
$719$	4.73205			0.176476			0.0882379	−	0.996099i	$-0.471876\pi$
$719$	4.73205			0.176476			0.0882379	+	0.996099i	$0.471876\pi$
$720$		0			0
$721$	−4.39230			−0.163578
$722$		0			0
$723$			44.8115i			1.66656i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−7.34847	+	7.34847i	−0.272540	+	0.272540i	−0.830122	−	0.557582i	$-0.811729\pi$
$727$	−7.34847	+	7.34847i	−0.272540	+	0.272540i	0.557582	+	0.830122i	$0.311729\pi$
$728$		0			0
$729$	−17.5885			−0.651424
$730$		0			0
$731$	6.46410	−	6.46410i	0.239083	−	0.239083i
$732$		0			0
$733$	47.6771			1.76099			0.880497	−	0.474051i	$-0.157209\pi$
$733$	47.6771			1.76099			0.880497	+	0.474051i	$0.157209\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.36396	+	6.36396i	−0.234420	+	0.234420i
$738$		0			0
$739$	−0.607695	+	0.607695i	−0.0223544	+	0.0223544i	−0.718196	−	0.695841i	$-0.755032\pi$
$739$	−0.607695	+	0.607695i	−0.0223544	+	0.0223544i	0.695841	+	0.718196i	$0.255032\pi$
$740$		0			0
$741$	−29.3205	−	29.3205i	−1.07712	−	1.07712i
$742$		0			0
$743$	26.4267	+	26.4267i	0.969503	+	0.969503i	0.999549	−	0.0300451i	$-0.00956511\pi$
$743$	26.4267	+	26.4267i	0.969503	+	0.969503i	−0.0300451	+	0.999549i	$0.509565\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	3.41044i		−	0.124781i
$748$		0			0
$749$	1.39230	+	1.39230i	0.0508737	+	0.0508737i
$750$		0			0
$751$		−	23.6077i		−	0.861457i	−0.902482	−	0.430729i	$-0.858257\pi$
$751$		−	23.6077i		−	0.861457i	0.902482	−	0.430729i	$-0.141743\pi$
$752$		0			0
$753$	0.328169	+	0.328169i	0.0119592	+	0.0119592i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−5.37945			−0.195520			−0.0977598	−	0.995210i	$-0.531168\pi$
$757$	−5.37945			−0.195520			−0.0977598	+	0.995210i	$0.531168\pi$
$758$		0			0
$759$			46.9808i			1.70529i
$760$		0			0
$761$			25.3923i			0.920470i	0.887797	+	0.460235i	$0.152235\pi$
$761$			25.3923i			0.920470i	−0.887797	+	0.460235i	$0.847765\pi$
$762$		0			0
$763$	20.4281			0.739548
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−20.9086	−	20.9086i	−0.754966	−	0.754966i
$768$		0			0
$769$		−	24.8038i		−	0.894450i	−0.894422	−	0.447225i	$-0.852412\pi$
$769$		−	24.8038i		−	0.894450i	0.894422	−	0.447225i	$-0.147588\pi$
$770$		0			0
$771$	19.6603	+	19.6603i	0.708047	+	0.708047i
$772$		0			0
$773$			40.9850i			1.47413i	0.675823	+	0.737064i	$0.263788\pi$
$773$			40.9850i			1.47413i	−0.675823	+	0.737064i	$0.736212\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	18.9396	+	18.9396i	0.679454	+	0.679454i
$778$		0			0
$779$	20.0263	+	20.0263i	0.717516	+	0.717516i
$780$		0			0
$781$	−52.9808	+	52.9808i	−1.89580	+	1.89580i
$782$		0			0
$783$	−5.55532	+	5.55532i	−0.198531	+	0.198531i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−10.1026			−0.360118			−0.180059	−	0.983656i	$-0.557629\pi$
$787$	−10.1026			−0.360118			−0.180059	+	0.983656i	$0.557629\pi$
$788$		0			0
$789$	−2.46410	+	2.46410i	−0.0877243	+	0.0877243i
$790$		0			0
$791$	−16.7321			−0.594923
$792$		0			0
$793$	35.2538	−	35.2538i	1.25190	−	1.25190i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	22.0454i		−	0.780888i	−0.920627	−	0.390444i	$-0.872321\pi$
$797$		−	22.0454i		−	0.780888i	0.920627	−	0.390444i	$-0.127679\pi$
$798$		0			0
$799$	−2.00000			−0.0707549
$800$		0			0
$801$	10.0526			0.355190
$802$		0			0
$803$		−	32.0836i		−	1.13221i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	20.7327	−	20.7327i	0.729827	−	0.729827i
$808$		0			0
$809$	6.24871			0.219693			0.109846	−	0.993949i	$-0.464964\pi$
$809$	6.24871			0.219693			0.109846	+	0.993949i	$0.464964\pi$
$810$		0			0
$811$	3.78461	−	3.78461i	0.132896	−	0.132896i	−0.637530	−	0.770426i	$-0.720044\pi$
$811$	3.78461	−	3.78461i	0.132896	−	0.132896i	0.770426	+	0.637530i	$0.220044\pi$
$812$		0			0
$813$	59.0924			2.07246
$814$		0			0
$815$		0			0
$816$		0			0
$817$	28.3214	−	28.3214i	0.990842	−	0.990842i
$818$		0			0
$819$	3.21539	−	3.21539i	0.112355	−	0.112355i
$820$		0			0
$821$	18.4641	+	18.4641i	0.644402	+	0.644402i	0.951634	−	0.307233i	$-0.0994030\pi$
$821$	18.4641	+	18.4641i	0.644402	+	0.644402i	−0.307233	+	0.951634i	$0.599403\pi$
$822$		0			0
$823$	11.5911	+	11.5911i	0.404041	+	0.404041i	0.879654	−	0.475614i	$-0.157774\pi$
$823$	11.5911	+	11.5911i	0.404041	+	0.404041i	−0.475614	+	0.879654i	$0.657774\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	11.4524i		−	0.398239i	−0.979975	−	0.199120i	$-0.936192\pi$
$827$		−	11.4524i		−	0.398239i	0.979975	−	0.199120i	$-0.0638082\pi$
$828$		0			0
$829$	−14.5885	−	14.5885i	−0.506678	−	0.506678i	0.406827	−	0.913505i	$-0.366635\pi$
$829$	−14.5885	−	14.5885i	−0.506678	−	0.506678i	−0.913505	+	0.406827i	$0.866635\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.81294	+	3.81294i	0.132110	+	0.132110i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−18.3848			−0.635471
$838$		0			0
$839$		−	27.4641i		−	0.948166i	−0.880480	−	0.474083i	$-0.842780\pi$
$839$		−	27.4641i		−	0.948166i	0.880480	−	0.474083i	$-0.157220\pi$
$840$		0			0
$841$		−	25.7846i		−	0.889124i
$842$		0			0
$843$	16.4901			0.567949
$844$		0			0
$845$		0			0
$846$		0			0
$847$	20.2523	+	20.2523i	0.695876	+	0.695876i
$848$		0			0
$849$		−	40.5167i		−	1.39053i
$850$		0			0
$851$	32.4449	+	32.4449i	1.11220	+	1.11220i
$852$		0			0
$853$			21.6937i			0.742777i	0.928477	+	0.371389i	$0.121118\pi$
$853$			21.6937i			0.742777i	−0.928477	+	0.371389i	$0.878882\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.53365	+	4.53365i	0.154866	+	0.154866i	0.780287	−	0.625421i	$-0.215073\pi$
$857$	4.53365	+	4.53365i	0.154866	+	0.154866i	−0.625421	+	0.780287i	$0.715073\pi$
$858$		0			0
$859$	−27.9019	−	27.9019i	−0.952001	−	0.952001i	0.0468983	−	0.998900i	$-0.485066\pi$
$859$	−27.9019	−	27.9019i	−0.952001	−	0.952001i	−0.998900	+	0.0468983i	$0.985066\pi$
$860$		0			0
$861$	−11.1962	+	11.1962i	−0.381564	+	0.381564i
$862$		0			0
$863$	11.8685	−	11.8685i	0.404009	−	0.404009i	−0.475634	−	0.879643i	$-0.657781\pi$
$863$	11.8685	−	11.8685i	0.404009	−	0.404009i	0.879643	+	0.475634i	$0.157781\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	30.9096			1.04975
$868$		0			0
$869$	33.5885	−	33.5885i	1.13941	−	1.13941i
$870$		0			0
$871$	7.60770			0.257777
$872$		0			0
$873$	−2.27362	+	2.27362i	−0.0769505	+	0.0769505i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		−	0.480473i		−	0.0162244i	−0.999967	−	0.00811222i	$-0.997418\pi$
$877$		−	0.480473i		−	0.0162244i	0.999967	−	0.00811222i	$-0.00258223\pi$
$878$		0			0
$879$	19.1244			0.645049
$880$		0			0
$881$	13.8564			0.466834			0.233417	−	0.972377i	$-0.425009\pi$
$881$	13.8564			0.466834			0.233417	+	0.972377i	$0.425009\pi$
$882$		0			0
$883$			33.8768i			1.14004i	0.821630	+	0.570022i	$0.193065\pi$
$883$			33.8768i			1.14004i	−0.821630	+	0.570022i	$0.806935\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.6932	−	16.6932i	0.560502	−	0.560502i	−0.368948	−	0.929450i	$-0.620282\pi$
$887$	16.6932	−	16.6932i	0.560502	−	0.560502i	0.929450	+	0.368948i	$0.120282\pi$
$888$		0			0
$889$	2.78461			0.0933928
$890$		0			0
$891$	43.6865	−	43.6865i	1.46355	−	1.46355i
$892$		0			0
$893$	−8.76268			−0.293232
$894$		0			0
$895$		0			0
$896$		0			0
$897$	28.0812	−	28.0812i	0.937604	−	0.937604i
$898$		0			0
$899$	−5.32051	+	5.32051i	−0.177449	+	0.177449i
$900$		0			0
$901$	−7.00000	−	7.00000i	−0.233204	−	0.233204i
$902$		0			0
$903$	15.8338	+	15.8338i	0.526914	+	0.526914i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			52.8807i			1.75587i	0.478775	+	0.877937i	$0.341081\pi$
$907$			52.8807i			1.75587i	−0.478775	+	0.877937i	$0.658919\pi$
$908$		0			0
$909$	−2.87564	−	2.87564i	−0.0953791	−	0.0953791i
$910$		0			0
$911$			24.2487i			0.803396i	0.915772	+	0.401698i	$0.131580\pi$
$911$			24.2487i			0.803396i	−0.915772	+	0.401698i	$0.868420\pi$
$912$		0			0
$913$	−19.0919	−	19.0919i	−0.631849	−	0.631849i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−17.8028			−0.587899
$918$		0			0
$919$			4.19615i			0.138418i	0.997602	+	0.0692091i	$0.0220476\pi$
$919$			4.19615i			0.138418i	−0.997602	+	0.0692091i	$0.977952\pi$
$920$		0			0
$921$			12.1244i			0.399511i
$922$		0			0
$923$	63.3350			2.08470
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.79315	−	1.79315i	−0.0588948	−	0.0588948i
$928$		0			0
$929$		−	36.0000i		−	1.18112i	−0.806993	−	0.590561i	$-0.798907\pi$
$929$		−	36.0000i		−	1.18112i	0.806993	−	0.590561i	$-0.201093\pi$
$930$		0			0
$931$	16.7058	+	16.7058i	0.547510	+	0.547510i
$932$		0			0
$933$			10.9348i			0.357988i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−19.7482	−	19.7482i	−0.645146	−	0.645146i	0.306670	−	0.951816i	$-0.400785\pi$
$937$	−19.7482	−	19.7482i	−0.645146	−	0.645146i	−0.951816	+	0.306670i	$0.900785\pi$
$938$		0			0
$939$	17.6603	+	17.6603i	0.576321	+	0.576321i
$940$		0			0
$941$	26.7846	−	26.7846i	0.873153	−	0.873153i	−0.119661	−	0.992815i	$-0.538181\pi$
$941$	26.7846	−	26.7846i	0.873153	−	0.873153i	0.992815	+	0.119661i	$0.0381809\pi$
$942$		0			0
$943$	−19.1798	+	19.1798i	−0.624581	+	0.624581i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.8338			−0.514528			−0.257264	−	0.966341i	$-0.582821\pi$
$947$	−15.8338			−0.514528			−0.257264	+	0.966341i	$0.582821\pi$
$948$		0			0
$949$	−19.1769	+	19.1769i	−0.622509	+	0.622509i
$950$		0			0
$951$	−38.7846			−1.25768
$952$		0			0
$953$	1.12321	−	1.12321i	0.0363843	−	0.0363843i	−0.688681	−	0.725065i	$-0.741810\pi$
$953$	1.12321	−	1.12321i	0.0363843	−	0.0363843i	0.725065	+	0.688681i	$0.241810\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	20.0764i		−	0.648978i
$958$		0			0
$959$	−3.55514			−0.114801
$960$		0			0
$961$	13.3923			0.432010
$962$		0			0
$963$			1.13681i			0.0366333i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	27.9053	−	27.9053i	0.897375	−	0.897375i	−0.0978283	−	0.995203i	$-0.531190\pi$
$967$	27.9053	−	27.9053i	0.897375	−	0.897375i	0.995203	+	0.0978283i	$0.0311896\pi$
$968$		0			0
$969$	−8.46410			−0.271906
$970$		0			0
$971$	−0.633975	+	0.633975i	−0.0203452	+	0.0203452i	−0.717206	−	0.696861i	$-0.754579\pi$
$971$	−0.633975	+	0.633975i	−0.0203452	+	0.0203452i	0.696861	+	0.717206i	$0.254579\pi$
$972$		0			0
$973$	−14.8728			−0.476800
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.3292	+	10.3292i	−0.330460	+	0.330460i	−0.852761	−	0.522301i	$-0.825074\pi$
$977$	−10.3292	+	10.3292i	−0.330460	+	0.330460i	0.522301	+	0.852761i	$0.325074\pi$
$978$		0			0
$979$	56.2750	−	56.2750i	1.79856	−	1.79856i
$980$		0			0
$981$	8.33975	+	8.33975i	0.266268	+	0.266268i
$982$		0			0
$983$	−7.48717	−	7.48717i	−0.238804	−	0.238804i	0.577551	−	0.816355i	$-0.304008\pi$
$983$	−7.48717	−	7.48717i	−0.238804	−	0.238804i	−0.816355	+	0.577551i	$0.804008\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	4.89898i		−	0.155936i
$988$		0			0
$989$	27.1244	+	27.1244i	0.862504	+	0.862504i
$990$		0			0
$991$			18.5885i			0.590482i	0.955423	+	0.295241i	$0.0953999\pi$
$991$			18.5885i			0.590482i	−0.955423	+	0.295241i	$0.904600\pi$
$992$		0			0
$993$	12.5385	+	12.5385i	0.397896	+	0.397896i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	54.3692			1.72189			0.860946	−	0.508697i	$-0.169873\pi$
$997$	54.3692			1.72189			0.860946	+	0.508697i	$0.169873\pi$
$998$		0			0
$999$		−	47.9090i		−	1.51577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.j.b.143.1		8
4.3	odd	2		400.2.j.b.43.2	✓	8
5.2	odd	4		1600.2.s.b.207.1		8
5.3	odd	4		1600.2.s.b.207.4		8
5.4	even	2	inner	1600.2.j.b.143.4		8
16.3	odd	4		1600.2.s.b.943.1		8
16.13	even	4		400.2.s.b.243.4	yes	8
20.3	even	4		400.2.s.b.107.3	yes	8
20.7	even	4		400.2.s.b.107.2	yes	8
20.19	odd	2		400.2.j.b.43.3	yes	8
80.3	even	4	inner	1600.2.j.b.1007.1		8
80.13	odd	4		400.2.j.b.307.4	yes	8
80.19	odd	4		1600.2.s.b.943.4		8
80.29	even	4		400.2.s.b.243.1	yes	8
80.67	even	4	inner	1600.2.j.b.1007.4		8
80.77	odd	4		400.2.j.b.307.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.b.43.2	✓	8	4.3	odd	2
400.2.j.b.43.3	yes	8	20.19	odd	2
400.2.j.b.307.1	yes	8	80.77	odd	4
400.2.j.b.307.4	yes	8	80.13	odd	4
400.2.s.b.107.2	yes	8	20.7	even	4
400.2.s.b.107.3	yes	8	20.3	even	4
400.2.s.b.243.1	yes	8	80.29	even	4
400.2.s.b.243.4	yes	8	16.13	even	4
1600.2.j.b.143.1		8	1.1	even	1	trivial
1600.2.j.b.143.4		8	5.4	even	2	inner
1600.2.j.b.1007.1		8	80.3	even	4	inner
1600.2.j.b.1007.4		8	80.67	even	4	inner
1600.2.s.b.207.1		8	5.2	odd	4
1600.2.s.b.207.4		8	5.3	odd	4
1600.2.s.b.943.1		8	16.3	odd	4
1600.2.s.b.943.4		8	80.19	odd	4

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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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.93185i q^{3} +(-0.896575 + 0.896575i) q^{7} -0.732051 q^{9} +O(q^{10})\)	\(q-1.93185i q^{3} +(-0.896575 + 0.896575i) q^{7} -0.732051 q^{9} +(-4.09808 + 4.09808i) q^{11} +4.89898 q^{13} +(0.707107 - 0.707107i) q^{17} +(3.09808 - 3.09808i) q^{19} +(1.73205 + 1.73205i) q^{21} +(2.96713 + 2.96713i) q^{23} -4.38134i q^{27} +(-1.26795 - 1.26795i) q^{29} -4.19615i q^{31} +(7.91688 + 7.91688i) q^{33} +10.9348 q^{37} -9.46410i q^{39} +6.46410i q^{41} +9.14162 q^{43} +(-1.41421 - 1.41421i) q^{47} +5.39230i q^{49} +(-1.36603 - 1.36603i) q^{51} -9.89949i q^{53} +(-5.98502 - 5.98502i) q^{57} +(-4.26795 - 4.26795i) q^{59} +(7.19615 - 7.19615i) q^{61} +(0.656339 - 0.656339i) q^{63} +1.55291 q^{67} +(5.73205 - 5.73205i) q^{69} +12.9282 q^{71} +(-3.91447 + 3.91447i) q^{73} -7.34847i q^{77} -8.19615 q^{79} -10.6603 q^{81} +4.65874i q^{83} +(-2.44949 + 2.44949i) q^{87} -13.7321 q^{89} +(-4.39230 + 4.39230i) q^{91} -8.10634 q^{93} +(3.10583 - 3.10583i) q^{97} +(3.00000 - 3.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^9	\( 8 q + 8 q^{9} - 12 q^{11} + 4 q^{19} - 24 q^{29} - 4 q^{51} - 48 q^{59} + 16 q^{61} + 32 q^{69} + 48 q^{71} - 24 q^{79} - 16 q^{81} - 96 q^{89} + 48 q^{91} + 24 q^{99}+O(q^{100}) \) 8 * q + 8 * q^9 - 12 * q^11 + 4 * q^19 - 24 * q^29 - 4 * q^51 - 48 * q^59 + 16 * q^61 + 32 * q^69 + 48 * q^71 - 24 * q^79 - 16 * q^81 - 96 * q^89 + 48 * q^91 + 24 * q^99

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