LMFDB - Embedded newform 1600.2.s.c.943.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(207,1600)]

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, 1]))

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

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

chi := DirichletCharacter("1600.207");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.s (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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 6x^{12} - 12x^{10} + 36x^{8} - 48x^{6} + 96x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 + 6x^12 - 12x^10 + 36x^8 - 48x^6 + 96x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			943.1
Root			$-1.24570 + 0.669507i$ of defining polynomial
Character	$\chi$	$=$	1600.943
Dual form			1600.2.s.c.207.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.07455 q^{3} +(-1.47763 + 1.47763i) q^{7} +6.45288 q^{9} +O(q^{10})$	$q-3.07455 q^{3} +(-1.47763 + 1.47763i) q^{7} +6.45288 q^{9} +(1.20704 + 1.20704i) q^{11} -5.63329i q^{13} +(-4.22693 + 4.22693i) q^{17} +(-3.11687 - 3.11687i) q^{19} +(4.54305 - 4.54305i) q^{21} +(1.08110 + 1.08110i) q^{23} -10.6161 q^{27} +(-5.32391 + 5.32391i) q^{29} -4.67202i q^{31} +(-3.71111 - 3.71111i) q^{33} -1.51171i q^{37} +17.3198i q^{39} +3.19494i q^{41} -2.42405i q^{43} +(0.827129 + 0.827129i) q^{47} +2.63322i q^{49} +(12.9959 - 12.9959i) q^{51} +8.17664 q^{53} +(9.58299 + 9.58299i) q^{57} +(7.78889 - 7.78889i) q^{59} +(-3.03880 - 3.03880i) q^{61} +(-9.53497 + 9.53497i) q^{63} +2.93200i q^{67} +(-3.32391 - 3.32391i) q^{69} +0.180339 q^{71} +(2.19941 - 2.19941i) q^{73} -3.56712 q^{77} +12.4917 q^{79} +13.2810 q^{81} +8.33457 q^{83} +(16.3687 - 16.3687i) q^{87} +9.08610 q^{89} +(8.32391 + 8.32391i) q^{91} +14.3644i q^{93} +(6.04376 - 6.04376i) q^{97} +(7.78889 + 7.78889i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^9	$ 16 q + 16 q^{9} - 8 q^{11} - 8 q^{19} - 16 q^{29} + 48 q^{51} - 8 q^{59} - 16 q^{61} + 16 q^{69} + 32 q^{71} + 80 q^{79} + 16 q^{81} + 64 q^{91} - 8 q^{99}+O(q^{100}) $ 16 * q + 16 * q^9 - 8 * q^11 - 8 * q^19 - 16 * q^29 + 48 * q^51 - 8 * q^59 - 16 * q^61 + 16 * q^69 + 32 * q^71 + 80 * q^79 + 16 * q^81 + 64 * q^91 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−3.07455			−1.77509			−0.887547	−	0.460717i	$-0.847592\pi$
$3$	−3.07455			−1.77509			−0.887547	+	0.460717i	$0.847592\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.47763	+	1.47763i	−0.558491	+	0.558491i	−0.928878	−	0.370386i	$-0.879225\pi$
$7$	−1.47763	+	1.47763i	−0.558491	+	0.558491i	0.370386	+	0.928878i	$0.379225\pi$
$8$		0			0
$9$	6.45288			2.15096
$10$		0			0
$11$	1.20704	+	1.20704i	0.363937	+	0.363937i	0.865260	−	0.501323i	$-0.167153\pi$
$11$	1.20704	+	1.20704i	0.363937	+	0.363937i	−0.501323	+	0.865260i	$0.667153\pi$
$12$		0			0
$13$		−	5.63329i		−	1.56239i	−0.624285	−	0.781196i	$-0.714610\pi$
$13$		−	5.63329i		−	1.56239i	0.624285	−	0.781196i	$-0.285390\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.22693	+	4.22693i	−1.02518	+	1.02518i	−0.0255073	+	0.999675i	$0.508120\pi$
$17$	−4.22693	+	4.22693i	−1.02518	+	1.02518i	−0.999675	+	0.0255073i	$0.991880\pi$
$18$		0			0
$19$	−3.11687	−	3.11687i	−0.715059	−	0.715059i	0.252530	−	0.967589i	$-0.418737\pi$
$19$	−3.11687	−	3.11687i	−0.715059	−	0.715059i	−0.967589	+	0.252530i	$0.918737\pi$
$20$		0			0
$21$	4.54305	−	4.54305i	0.991375	−	0.991375i
$22$		0			0
$23$	1.08110	+	1.08110i	0.225426	+	0.225426i	0.810779	−	0.585353i	$-0.199044\pi$
$23$	1.08110	+	1.08110i	0.225426	+	0.225426i	−0.585353	+	0.810779i	$0.699044\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−10.6161			−2.04306
$28$		0			0
$29$	−5.32391	+	5.32391i	−0.988626	+	0.988626i	−0.999936	−	0.0113103i	$-0.996400\pi$
$29$	−5.32391	+	5.32391i	−0.988626	+	0.988626i	0.0113103	+	0.999936i	$0.496400\pi$
$30$		0			0
$31$		−	4.67202i		−	0.839120i	−0.907728	−	0.419560i	$-0.862184\pi$
$31$		−	4.67202i		−	0.839120i	0.907728	−	0.419560i	$-0.137816\pi$
$32$		0			0
$33$	−3.71111	−	3.71111i	−0.646022	−	0.646022i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	1.51171i		−	0.248523i	−0.992249	−	0.124262i	$-0.960344\pi$
$37$		−	1.51171i		−	0.248523i	0.992249	−	0.124262i	$-0.0396562\pi$
$38$		0			0
$39$			17.3198i			2.77340i
$40$		0			0
$41$			3.19494i			0.498966i	0.968379	+	0.249483i	$0.0802607\pi$
$41$			3.19494i			0.498966i	−0.968379	+	0.249483i	$0.919739\pi$
$42$		0			0
$43$		−	2.42405i		−	0.369665i	−0.982770	−	0.184832i	$-0.940826\pi$
$43$		−	2.42405i		−	0.369665i	0.982770	−	0.184832i	$-0.0591742\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.827129	+	0.827129i	0.120649	+	0.120649i	0.764853	−	0.644204i	$-0.222811\pi$
$47$	0.827129	+	0.827129i	0.120649	+	0.120649i	−0.644204	+	0.764853i	$0.722811\pi$
$48$		0			0
$49$			2.63322i			0.376175i
$50$		0			0
$51$	12.9959	−	12.9959i	1.81979	−	1.81979i
$52$		0			0
$53$	8.17664			1.12315			0.561574	−	0.827427i	$-0.310196\pi$
$53$	8.17664			1.12315			0.561574	+	0.827427i	$0.310196\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	9.58299	+	9.58299i	1.26930	+	1.26930i
$58$		0			0
$59$	7.78889	−	7.78889i	1.01403	−	1.01403i	0.0141274	−	0.999900i	$-0.495503\pi$
$59$	7.78889	−	7.78889i	1.01403	−	1.01403i	0.999900	−	0.0141274i	$-0.00449704\pi$
$60$		0			0
$61$	−3.03880	−	3.03880i	−0.389079	−	0.389079i	0.485280	−	0.874359i	$-0.338718\pi$
$61$	−3.03880	−	3.03880i	−0.389079	−	0.389079i	−0.874359	+	0.485280i	$0.838718\pi$
$62$		0			0
$63$	−9.53497	+	9.53497i	−1.20129	+	1.20129i
$64$		0			0
$65$		0			0
$66$		0			0
$67$			2.93200i			0.358201i	0.983831	+	0.179101i	$0.0573188\pi$
$67$			2.93200i			0.358201i	−0.983831	+	0.179101i	$0.942681\pi$
$68$		0			0
$69$	−3.32391	−	3.32391i	−0.400152	−	0.400152i
$70$		0			0
$71$	0.180339			0.0214023			0.0107011	−	0.999943i	$-0.496594\pi$
$71$	0.180339			0.0214023			0.0107011	+	0.999943i	$0.496594\pi$
$72$		0			0
$73$	2.19941	−	2.19941i	0.257421	−	0.257421i	−0.566583	−	0.824004i	$-0.691735\pi$
$73$	2.19941	−	2.19941i	0.257421	−	0.257421i	0.824004	+	0.566583i	$0.191735\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.56712			−0.406511
$78$		0			0
$79$	12.4917			1.40542			0.702712	−	0.711474i	$-0.251972\pi$
$79$	12.4917			1.40542			0.702712	+	0.711474i	$0.251972\pi$
$80$		0			0
$81$	13.2810			1.47567
$82$		0			0
$83$	8.33457			0.914838			0.457419	−	0.889251i	$-0.348774\pi$
$83$	8.33457			0.914838			0.457419	+	0.889251i	$0.348774\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	16.3687	−	16.3687i	1.75490	−	1.75490i
$88$		0			0
$89$	9.08610			0.963125			0.481563	−	0.876412i	$-0.340069\pi$
$89$	9.08610			0.963125			0.481563	+	0.876412i	$0.340069\pi$
$90$		0			0
$91$	8.32391	+	8.32391i	0.872583	+	0.872583i
$92$		0			0
$93$			14.3644i			1.48952i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	6.04376	−	6.04376i	0.613650	−	0.613650i	−0.330245	−	0.943895i	$-0.607131\pi$
$97$	6.04376	−	6.04376i	0.613650	−	0.613650i	0.943895	+	0.330245i	$0.107131\pi$
$98$		0			0
$99$	7.78889	+	7.78889i	0.782813	+	0.782813i
$100$		0			0
$101$	9.58185	−	9.58185i	0.953430	−	0.953430i	−0.0455329	−	0.998963i	$-0.514499\pi$
$101$	9.58185	−	9.58185i	0.953430	−	0.953430i	0.998963	+	0.0455329i	$0.0144986\pi$
$102$		0			0
$103$	6.57971	+	6.57971i	0.648318	+	0.648318i	0.952586	−	0.304268i	$-0.0984119\pi$
$103$	6.57971	+	6.57971i	0.648318	+	0.648318i	−0.304268	+	0.952586i	$0.598412\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.980501			−0.0947886			−0.0473943	−	0.998876i	$-0.515092\pi$
$107$	−0.980501			−0.0947886			−0.0473943	+	0.998876i	$0.515092\pi$
$108$		0			0
$109$	−2.00000	+	2.00000i	−0.191565	+	0.191565i	−0.796372	−	0.604807i	$-0.793250\pi$
$109$	−2.00000	+	2.00000i	−0.191565	+	0.191565i	0.604807	+	0.796372i	$0.293250\pi$
$110$		0			0
$111$			4.64783i			0.441152i
$112$		0			0
$113$	−2.54335	−	2.54335i	−0.239258	−	0.239258i	0.577285	−	0.816543i	$-0.304112\pi$
$113$	−2.54335	−	2.54335i	−0.239258	−	0.239258i	−0.816543	+	0.577285i	$0.804112\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		−	36.3509i		−	3.36065i
$118$		0			0
$119$		−	12.4917i		−	1.14511i
$120$		0			0
$121$		−	8.08610i		−	0.735100i
$122$		0			0
$123$		−	9.82302i		−	0.885712i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	14.0019	+	14.0019i	1.24247	+	1.24247i	0.958973	+	0.283498i	$0.0914950\pi$
$127$	14.0019	+	14.0019i	1.24247	+	1.24247i	0.283498	+	0.958973i	$0.408505\pi$
$128$		0			0
$129$			7.45288i			0.656190i
$130$		0			0
$131$	−7.11687	+	7.11687i	−0.621804	+	0.621804i	−0.945992	−	0.324189i	$-0.894909\pi$
$131$	−7.11687	+	7.11687i	−0.621804	+	0.621804i	0.324189	+	0.945992i	$0.394909\pi$
$132$		0			0
$133$	9.21116			0.798709
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.995887	+	0.995887i	0.0850843	+	0.0850843i	0.748368	−	0.663284i	$-0.230838\pi$
$137$	0.995887	+	0.995887i	0.0850843	+	0.0850843i	−0.663284	+	0.748368i	$0.730838\pi$
$138$		0			0
$139$	−12.1128	+	12.1128i	−1.02739	+	1.02739i	−0.0277808	+	0.999614i	$0.508844\pi$
$139$	−12.1128	+	12.1128i	−1.02739	+	1.02739i	−0.999614	+	0.0277808i	$0.991156\pi$
$140$		0			0
$141$	−2.54305	−	2.54305i	−0.214164	−	0.214164i
$142$		0			0
$143$	6.79961	−	6.79961i	0.568612	−	0.568612i
$144$		0			0
$145$		0			0
$146$		0			0
$147$		−	8.09598i		−	0.667745i
$148$		0			0
$149$	9.86696	+	9.86696i	0.808333	+	0.808333i	0.984382	−	0.176048i	$-0.0563315\pi$
$149$	9.86696	+	9.86696i	0.808333	+	0.808333i	−0.176048	+	0.984382i	$0.556331\pi$
$150$		0			0
$151$	9.31985			0.758438			0.379219	−	0.925307i	$-0.376193\pi$
$151$	9.31985			0.758438			0.379219	+	0.925307i	$0.376193\pi$
$152$		0			0
$153$	−27.2759	+	27.2759i	−2.20513	+	2.20513i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	17.9394			1.43172			0.715859	−	0.698245i	$-0.246035\pi$
$157$	17.9394			1.43172			0.715859	+	0.698245i	$0.246035\pi$
$158$		0			0
$159$	−25.1395			−1.99369
$160$		0			0
$161$	−3.19494			−0.251797
$162$		0			0
$163$	−7.39897			−0.579532			−0.289766	−	0.957098i	$-0.593577\pi$
$163$	−7.39897			−0.579532			−0.289766	+	0.957098i	$0.593577\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.74192	−	8.74192i	0.676470	−	0.676470i	−0.282730	−	0.959200i	$-0.591240\pi$
$167$	8.74192	−	8.74192i	0.676470	−	0.676470i	0.959200	+	0.282730i	$0.0912399\pi$
$168$		0			0
$169$	−18.7339			−1.44107
$170$		0			0
$171$	−20.1128	−	20.1128i	−1.53806	−	1.53806i
$172$		0			0
$173$		−	10.7865i		−	0.820083i	−0.912067	−	0.410042i	$-0.865514\pi$
$173$		−	10.7865i		−	0.820083i	0.912067	−	0.410042i	$-0.134486\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−23.9474	+	23.9474i	−1.79999	+	1.79999i
$178$		0			0
$179$	0.535019	+	0.535019i	0.0399892	+	0.0399892i	0.726819	−	0.686829i	$-0.240998\pi$
$179$	0.535019	+	0.535019i	0.0399892	+	0.0399892i	−0.686829	+	0.726819i	$0.740998\pi$
$180$		0			0
$181$	−7.58185	+	7.58185i	−0.563555	+	0.563555i	−0.930315	−	0.366761i	$-0.880467\pi$
$181$	−7.58185	+	7.58185i	−0.563555	+	0.563555i	0.366761	+	0.930315i	$0.380467\pi$
$182$		0			0
$183$	9.34296	+	9.34296i	0.690651	+	0.690651i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−10.2042			−0.746202
$188$		0			0
$189$	15.6866	−	15.6866i	1.14103	−	1.14103i
$190$		0			0
$191$		−	4.46749i		−	0.323256i	−0.986852	−	0.161628i	$-0.948326\pi$
$191$		−	4.46749i		−	0.323256i	0.986852	−	0.161628i	$-0.0516745\pi$
$192$		0			0
$193$	12.9115	+	12.9115i	0.929391	+	0.929391i	0.997667	−	0.0682750i	$-0.0217495\pi$
$193$	12.9115	+	12.9115i	0.929391	+	0.929391i	−0.0682750	+	0.997667i	$0.521750\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			13.8764i			0.988656i	0.869275	+	0.494328i	$0.164586\pi$
$197$			13.8764i			0.988656i	−0.869275	+	0.494328i	$0.835414\pi$
$198$		0			0
$199$		−	9.47599i		−	0.671735i	−0.941909	−	0.335868i	$-0.890971\pi$
$199$		−	9.47599i		−	0.671735i	0.941909	−	0.335868i	$-0.109029\pi$
$200$		0			0
$201$		−	9.01460i		−	0.635841i
$202$		0			0
$203$		−	15.7335i		−	1.10428i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	6.97624	+	6.97624i	0.484882	+	0.484882i
$208$		0			0
$209$		−	7.52438i		−	0.520472i
$210$		0			0
$211$	−6.20298	+	6.20298i	−0.427030	+	0.427030i	−0.887616	−	0.460585i	$-0.847640\pi$
$211$	−6.20298	+	6.20298i	−0.427030	+	0.427030i	0.460585	+	0.887616i	$0.347640\pi$
$212$		0			0
$213$	−0.554462			−0.0379911
$214$		0			0
$215$		0			0
$216$		0			0
$217$	6.90352	+	6.90352i	0.468641	+	0.468641i
$218$		0			0
$219$	−6.76219	+	6.76219i	−0.456947	+	0.456947i
$220$		0			0
$221$	23.8115	+	23.8115i	1.60174	+	1.60174i
$222$		0			0
$223$	13.3793	−	13.3793i	0.895946	−	0.895946i	−0.0991290	−	0.995075i	$-0.531606\pi$
$223$	13.3793	−	13.3793i	0.895946	−	0.895946i	0.995075	+	0.0991290i	$0.0316057\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			9.22366i			0.612196i	0.952000	+	0.306098i	$0.0990235\pi$
$227$			9.22366i			0.612196i	−0.952000	+	0.306098i	$0.900976\pi$
$228$		0			0
$229$	12.2297	+	12.2297i	0.808160	+	0.808160i	0.984355	−	0.176195i	$-0.0563790\pi$
$229$	12.2297	+	12.2297i	0.808160	+	0.808160i	−0.176195	+	0.984355i	$0.556379\pi$
$230$		0			0
$231$	10.9673			0.721595
$232$		0			0
$233$	10.6533	−	10.6533i	0.697919	−	0.697919i	−0.266042	−	0.963961i	$-0.585716\pi$
$233$	10.6533	−	10.6533i	0.697919	−	0.697919i	0.963961	+	0.266042i	$0.0857161\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−38.4064			−2.49476
$238$		0			0
$239$	22.3284			1.44430			0.722150	−	0.691736i	$-0.243154\pi$
$239$	22.3284			1.44430			0.722150	+	0.691736i	$0.243154\pi$
$240$		0			0
$241$	−27.1868			−1.75126			−0.875628	−	0.482986i	$-0.839552\pi$
$241$	−27.1868			−1.75126			−0.875628	+	0.482986i	$0.839552\pi$
$242$		0			0
$243$	−8.98507			−0.576393
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−17.5582	+	17.5582i	−1.11720	+	1.11720i
$248$		0			0
$249$	−25.6251			−1.62392
$250$		0			0
$251$	11.4650	+	11.4650i	0.723663	+	0.723663i	0.969349	−	0.245686i	$-0.0790133\pi$
$251$	11.4650	+	11.4650i	0.723663	+	0.723663i	−0.245686	+	0.969349i	$0.579013\pi$
$252$		0			0
$253$			2.60987i			0.164081i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.36017	−	4.36017i	0.271980	−	0.271980i	−0.557917	−	0.829897i	$-0.688399\pi$
$257$	4.36017	−	4.36017i	0.271980	−	0.271980i	0.829897	+	0.557917i	$0.188399\pi$
$258$		0			0
$259$	2.23374	+	2.23374i	0.138798	+	0.138798i
$260$		0			0
$261$	−34.3546	+	34.3546i	−2.12650	+	2.12650i
$262$		0			0
$263$	−9.93150	−	9.93150i	−0.612402	−	0.612402i	0.331169	−	0.943571i	$-0.392557\pi$
$263$	−9.93150	−	9.93150i	−0.612402	−	0.612402i	−0.943571	+	0.331169i	$0.892557\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−27.9357			−1.70964
$268$		0			0
$269$	15.8670	−	15.8670i	0.967426	−	0.967426i	−0.0320600	−	0.999486i	$-0.510207\pi$
$269$	15.8670	−	15.8670i	0.967426	−	0.967426i	0.999486	+	0.0320600i	$0.0102068\pi$
$270$		0			0
$271$		−	20.8040i		−	1.26375i	−0.775070	−	0.631875i	$-0.782285\pi$
$271$		−	20.8040i		−	1.26375i	0.775070	−	0.631875i	$-0.217715\pi$
$272$		0			0
$273$	−25.5923	−	25.5923i	−1.54892	−	1.54892i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		−	20.4670i		−	1.22974i	−0.788628	−	0.614871i	$-0.789208\pi$
$277$		−	20.4670i		−	1.22974i	0.788628	−	0.614871i	$-0.210792\pi$
$278$		0			0
$279$		−	30.1480i		−	1.80491i
$280$		0			0
$281$			5.89116i			0.351437i	0.984440	+	0.175719i	$0.0562249\pi$
$281$			5.89116i			0.351437i	−0.984440	+	0.175719i	$0.943775\pi$
$282$		0			0
$283$		−	14.6262i		−	0.869439i	−0.900566	−	0.434720i	$-0.856847\pi$
$283$		−	14.6262i		−	0.869439i	0.900566	−	0.434720i	$-0.143153\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.72094	−	4.72094i	−0.278668	−	0.278668i
$288$		0			0
$289$		−	18.7339i		−	1.10200i
$290$		0			0
$291$	−18.5819	+	18.5819i	−1.08929	+	1.08929i
$292$		0			0
$293$	−12.2982			−0.718469			−0.359235	−	0.933247i	$-0.616962\pi$
$293$	−12.2982			−0.718469			−0.359235	+	0.933247i	$0.616962\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−12.8140	−	12.8140i	−0.743546	−	0.743546i
$298$		0			0
$299$	6.09017	−	6.09017i	0.352204	−	0.352204i
$300$		0			0
$301$	3.58185	+	3.58185i	0.206455	+	0.206455i
$302$		0			0
$303$	−29.4599	+	29.4599i	−1.69243	+	1.69243i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			20.6636i			1.17933i	0.807647	+	0.589666i	$0.200741\pi$
$307$			20.6636i			1.17933i	−0.807647	+	0.589666i	$0.799259\pi$
$308$		0			0
$309$	−20.2297	−	20.2297i	−1.15083	−	1.15083i
$310$		0			0
$311$	−16.1561			−0.916131			−0.458065	−	0.888919i	$-0.651457\pi$
$311$	−16.1561			−0.916131			−0.458065	+	0.888919i	$0.651457\pi$
$312$		0			0
$313$	2.29689	−	2.29689i	0.129828	−	0.129828i	−0.639207	−	0.769035i	$-0.720737\pi$
$313$	2.29689	−	2.29689i	0.129828	−	0.129828i	0.769035	+	0.639207i	$0.220737\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.05541			0.115443			0.0577217	−	0.998333i	$-0.481616\pi$
$317$	2.05541			0.115443			0.0577217	+	0.998333i	$0.481616\pi$
$318$		0			0
$319$	−12.8524			−0.719594
$320$		0			0
$321$	3.01460			0.168259
$322$		0			0
$323$	26.3496			1.46613
$324$		0			0
$325$		0			0
$326$		0			0
$327$	6.14911	−	6.14911i	0.340046	−	0.340046i
$328$		0			0
$329$	−2.44438			−0.134763
$330$		0			0
$331$	−13.7113	−	13.7113i	−0.753641	−	0.753641i	0.221516	−	0.975157i	$-0.428900\pi$
$331$	−13.7113	−	13.7113i	−0.753641	−	0.753641i	−0.975157	+	0.221516i	$0.928900\pi$
$332$		0			0
$333$		−	9.75487i		−	0.534563i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−12.8140	+	12.8140i	−0.698025	+	0.698025i	−0.963984	−	0.265959i	$-0.914311\pi$
$337$	−12.8140	+	12.8140i	−0.698025	+	0.698025i	0.265959	+	0.963984i	$0.414311\pi$
$338$		0			0
$339$	7.81966	+	7.81966i	0.424706	+	0.424706i
$340$		0			0
$341$	5.63932	−	5.63932i	0.305386	−	0.305386i
$342$		0			0
$343$	−14.2343	−	14.2343i	−0.768582	−	0.768582i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.81175			0.473040			0.236520	−	0.971627i	$-0.423993\pi$
$347$	8.81175			0.473040			0.236520	+	0.971627i	$0.423993\pi$
$348$		0			0
$349$	−15.8398	+	15.8398i	−0.847885	+	0.847885i	−0.989869	−	0.141984i	$-0.954652\pi$
$349$	−15.8398	+	15.8398i	−0.847885	+	0.847885i	0.141984	+	0.989869i	$0.454652\pi$
$350$		0			0
$351$			59.8034i			3.19207i
$352$		0			0
$353$	−10.2349	−	10.2349i	−0.544751	−	0.544751i	0.380167	−	0.924918i	$-0.375866\pi$
$353$	−10.2349	−	10.2349i	−0.544751	−	0.544751i	−0.924918	+	0.380167i	$0.875866\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			38.4064i			2.03268i
$358$		0			0
$359$		−	9.18790i		−	0.484919i	−0.970162	−	0.242459i	$-0.922046\pi$
$359$		−	9.18790i		−	0.484919i	0.970162	−	0.242459i	$-0.0779541\pi$
$360$		0			0
$361$			0.429776i			0.0226198i
$362$		0			0
$363$			24.8612i			1.30487i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−8.40440	−	8.40440i	−0.438706	−	0.438706i	0.452870	−	0.891576i	$-0.350400\pi$
$367$	−8.40440	−	8.40440i	−0.438706	−	0.438706i	−0.891576	+	0.452870i	$0.850400\pi$
$368$		0			0
$369$			20.6166i			1.07326i
$370$		0			0
$371$	−12.0820	+	12.0820i	−0.627268	+	0.627268i
$372$		0			0
$373$	27.6942			1.43395			0.716977	−	0.697097i	$-0.245525\pi$
$373$	27.6942			1.43395			0.716977	+	0.697097i	$0.245525\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	29.9911	+	29.9911i	1.54462	+	1.54462i
$378$		0			0
$379$	−17.6987	+	17.6987i	−0.909122	+	0.909122i	−0.996201	−	0.0870790i	$-0.972247\pi$
$379$	−17.6987	+	17.6987i	−0.909122	+	0.909122i	0.0870790	+	0.996201i	$0.472247\pi$
$380$		0			0
$381$	−43.0497	−	43.0497i	−2.20550	−	2.20550i
$382$		0			0
$383$	−8.11930	+	8.11930i	−0.414877	+	0.414877i	−0.883434	−	0.468557i	$-0.844774\pi$
$383$	−8.11930	+	8.11930i	−0.414877	+	0.414877i	0.468557	+	0.883434i	$0.344774\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	15.6421i		−	0.795134i
$388$		0			0
$389$	−6.38285	−	6.38285i	−0.323623	−	0.323623i	0.526532	−	0.850155i	$-0.323492\pi$
$389$	−6.38285	−	6.38285i	−0.323623	−	0.323623i	−0.850155	+	0.526532i	$0.823492\pi$
$390$		0			0
$391$	−9.13951			−0.462205
$392$		0			0
$393$	21.8812	−	21.8812i	1.10376	−	1.10376i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	8.65670			0.434467			0.217234	−	0.976120i	$-0.430297\pi$
$397$	8.65670			0.434467			0.217234	+	0.976120i	$0.430297\pi$
$398$		0			0
$399$	−28.3202			−1.41778
$400$		0			0
$401$	−6.57022			−0.328101			−0.164051	−	0.986452i	$-0.552456\pi$
$401$	−6.57022			−0.328101			−0.164051	+	0.986452i	$0.552456\pi$
$402$		0			0
$403$	−26.3188			−1.31104
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.82469	−	1.82469i	0.0904466	−	0.0904466i
$408$		0			0
$409$	3.19494			0.157980			0.0789899	−	0.996875i	$-0.474831\pi$
$409$	3.19494			0.157980			0.0789899	+	0.996875i	$0.474831\pi$
$410$		0			0
$411$	−3.06191	−	3.06191i	−0.151033	−	0.151033i
$412$		0			0
$413$			23.0182i			1.13265i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	37.2415	−	37.2415i	1.82372	−	1.82372i
$418$		0			0
$419$	−26.3707	−	26.3707i	−1.28830	−	1.28830i	−0.935822	−	0.352473i	$-0.885341\pi$
$419$	−26.3707	−	26.3707i	−1.28830	−	1.28830i	−0.352473	−	0.935822i	$-0.614659\pi$
$420$		0			0
$421$	28.3345	−	28.3345i	1.38094	−	1.38094i	0.537977	−	0.842959i	$-0.319189\pi$
$421$	28.3345	−	28.3345i	1.38094	−	1.38094i	0.842959	−	0.537977i	$-0.180811\pi$
$422$		0			0
$423$	5.33736	+	5.33736i	0.259512	+	0.259512i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	8.98044			0.434594
$428$		0			0
$429$	−20.9058	+	20.9058i	−1.00934	+	1.00934i
$430$		0			0
$431$		−	6.49981i		−	0.313085i	−0.987671	−	0.156543i	$-0.949965\pi$
$431$		−	6.49981i		−	0.313085i	0.987671	−	0.156543i	$-0.0500348\pi$
$432$		0			0
$433$	19.5486	+	19.5486i	0.939444	+	0.939444i	0.998268	−	0.0588243i	$-0.0187352\pi$
$433$	19.5486	+	19.5486i	0.939444	+	0.939444i	−0.0588243	+	0.998268i	$0.518735\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	6.73932i		−	0.322386i
$438$		0			0
$439$			23.3117i			1.11261i	0.830979	+	0.556304i	$0.187781\pi$
$439$			23.3117i			1.11261i	−0.830979	+	0.556304i	$0.812219\pi$
$440$		0			0
$441$			16.9919i			0.809137i
$442$		0			0
$443$			35.3347i			1.67880i	0.543513	+	0.839401i	$0.317094\pi$
$443$			35.3347i			1.67880i	−0.543513	+	0.839401i	$0.682906\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−30.3365	−	30.3365i	−1.43487	−	1.43487i
$448$		0			0
$449$		−	17.5305i		−	0.827315i	−0.910433	−	0.413657i	$-0.864251\pi$
$449$		−	17.5305i		−	0.827315i	0.910433	−	0.413657i	$-0.135749\pi$
$450$		0			0
$451$	−3.85643	+	3.85643i	−0.181592	+	0.181592i
$452$		0			0
$453$	−28.6544			−1.34630
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−27.1040	−	27.1040i	−1.26787	−	1.26787i	−0.947185	−	0.320688i	$-0.896086\pi$
$457$	−27.1040	−	27.1040i	−1.26787	−	1.26787i	−0.320688	−	0.947185i	$-0.603914\pi$
$458$		0			0
$459$	44.8734	−	44.8734i	2.09451	−	2.09451i
$460$		0			0
$461$	3.94253	+	3.94253i	0.183622	+	0.183622i	0.792932	−	0.609310i	$-0.208554\pi$
$461$	3.94253	+	3.94253i	0.183622	+	0.183622i	−0.609310	+	0.792932i	$0.708554\pi$
$462$		0			0
$463$	18.8625	−	18.8625i	0.876617	−	0.876617i	−0.116566	−	0.993183i	$-0.537189\pi$
$463$	18.8625	−	18.8625i	0.876617	−	0.876617i	0.993183	+	0.116566i	$0.0371887\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	17.2282i		−	0.797228i	−0.917119	−	0.398614i	$-0.869491\pi$
$467$		−	17.2282i		−	0.797228i	0.917119	−	0.398614i	$-0.130509\pi$
$468$		0			0
$469$	−4.33242	−	4.33242i	−0.200052	−	0.200052i
$470$		0			0
$471$	−55.1556			−2.54143
$472$		0			0
$473$	2.92593	−	2.92593i	0.134534	−	0.134534i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	52.7629			2.41585
$478$		0			0
$479$	39.2875			1.79509			0.897546	−	0.440920i	$-0.145348\pi$
$479$	39.2875			1.79509			0.897546	+	0.440920i	$0.145348\pi$
$480$		0			0
$481$	−8.51588			−0.388291
$482$		0			0
$483$	9.82302			0.446963
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−5.39013	+	5.39013i	−0.244250	+	0.244250i	−0.818606	−	0.574356i	$-0.805253\pi$
$487$	−5.39013	+	5.39013i	−0.244250	+	0.244250i	0.574356	+	0.818606i	$0.305253\pi$
$488$		0			0
$489$	22.7485			1.02872
$490$		0			0
$491$	28.0145	+	28.0145i	1.26428	+	1.26428i	0.949000	+	0.315277i	$0.102098\pi$
$491$	28.0145	+	28.0145i	1.26428	+	1.26428i	0.315277	+	0.949000i	$0.397902\pi$
$492$		0			0
$493$		−	45.0076i		−	2.02704i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.266474	+	0.266474i	−0.0119530	+	0.0119530i
$498$		0			0
$499$	−1.18284	−	1.18284i	−0.0529514	−	0.0529514i	0.680135	−	0.733087i	$-0.261921\pi$
$499$	−1.18284	−	1.18284i	−0.0529514	−	0.0529514i	−0.733087	+	0.680135i	$0.761921\pi$
$500$		0			0
$501$	−26.8775	+	26.8775i	−1.20080	+	1.20080i
$502$		0			0
$503$	30.0763	+	30.0763i	1.34104	+	1.34104i	0.895028	+	0.446010i	$0.147155\pi$
$503$	30.0763	+	30.0763i	1.34104	+	1.34104i	0.446010	+	0.895028i	$0.352845\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	57.5985			2.55804
$508$		0			0
$509$	23.1062	−	23.1062i	1.02417	−	1.02417i	0.0244652	−	0.999701i	$-0.492212\pi$
$509$	23.1062	−	23.1062i	1.02417	−	1.02417i	0.999701	−	0.0244652i	$-0.00778830\pi$
$510$		0			0
$511$			6.49981i			0.287535i
$512$		0			0
$513$	33.0889	+	33.0889i	1.46091	+	1.46091i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			1.99676i			0.0878173i
$518$		0			0
$519$			33.1637i			1.45573i
$520$		0			0
$521$			31.3733i			1.37449i	0.726427	+	0.687244i	$0.241179\pi$
$521$			31.3733i			1.37449i	−0.726427	+	0.687244i	$0.758821\pi$
$522$		0			0
$523$			11.6926i			0.511282i	0.966772	+	0.255641i	$0.0822866\pi$
$523$			11.6926i			0.511282i	−0.966772	+	0.255641i	$0.917713\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	19.7483	+	19.7483i	0.860251	+	0.860251i
$528$		0			0
$529$		−	20.6624i		−	0.898366i
$530$		0			0
$531$	50.2608	−	50.2608i	2.18113	−	2.18113i
$532$		0			0
$533$	17.9980			0.779581
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.64494	−	1.64494i	−0.0709846	−	0.0709846i
$538$		0			0
$539$	−3.17841	+	3.17841i	−0.136904	+	0.136904i
$540$		0			0
$541$	16.4876	+	16.4876i	0.708858	+	0.708858i	0.966295	−	0.257437i	$-0.0828780\pi$
$541$	16.4876	+	16.4876i	0.708858	+	0.708858i	−0.257437	+	0.966295i	$0.582878\pi$
$542$		0			0
$543$	23.3108	−	23.3108i	1.00036	−	1.00036i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	36.0505i		−	1.54141i	−0.637194	−	0.770703i	$-0.719905\pi$
$547$		−	36.0505i		−	1.54141i	0.637194	−	0.770703i	$-0.280095\pi$
$548$		0			0
$549$	−19.6090	−	19.6090i	−0.836893	−	0.836893i
$550$		0			0
$551$	33.1879			1.41385
$552$		0			0
$553$	−18.4581	+	18.4581i	−0.784917	+	0.784917i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−5.64116			−0.239024			−0.119512	−	0.992833i	$-0.538133\pi$
$557$	−5.64116			−0.239024			−0.119512	+	0.992833i	$0.538133\pi$
$558$		0			0
$559$	−13.6554			−0.577561
$560$		0			0
$561$	31.3733			1.32458
$562$		0			0
$563$	−4.69143			−0.197720			−0.0988601	−	0.995101i	$-0.531520\pi$
$563$	−4.69143			−0.197720			−0.0988601	+	0.995101i	$0.531520\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−19.6245	+	19.6245i	−0.824150	+	0.824150i
$568$		0			0
$569$	46.3505			1.94311			0.971557	−	0.236804i	$-0.0761000\pi$
$569$	46.3505			1.94311			0.971557	+	0.236804i	$0.0761000\pi$
$570$		0			0
$571$	6.27708	+	6.27708i	0.262688	+	0.262688i	0.826145	−	0.563457i	$-0.190529\pi$
$571$	6.27708	+	6.27708i	0.262688	+	0.262688i	−0.563457	+	0.826145i	$0.690529\pi$
$572$		0			0
$573$			13.7355i			0.573810i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	12.5833	−	12.5833i	0.523850	−	0.523850i	−0.394882	−	0.918732i	$-0.629214\pi$
$577$	12.5833	−	12.5833i	0.523850	−	0.523850i	0.918732	+	0.394882i	$0.129214\pi$
$578$		0			0
$579$	−39.6972	−	39.6972i	−1.64976	−	1.64976i
$580$		0			0
$581$	−12.3154	+	12.3154i	−0.510929	+	0.510929i
$582$		0			0
$583$	9.86953	+	9.86953i	0.408754	+	0.408754i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.4298			0.719405			0.359703	−	0.933067i	$-0.382878\pi$
$587$	17.4298			0.719405			0.359703	+	0.933067i	$0.382878\pi$
$588$		0			0
$589$	−14.5621	+	14.5621i	−0.600021	+	0.600021i
$590$		0			0
$591$		−	42.6639i		−	1.75496i
$592$		0			0
$593$	−1.81682	−	1.81682i	−0.0746079	−	0.0746079i	0.668818	−	0.743426i	$-0.266800\pi$
$593$	−1.81682	−	1.81682i	−0.0746079	−	0.0746079i	−0.743426	+	0.668818i	$0.766800\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			29.1344i			1.19239i
$598$		0			0
$599$			34.2790i			1.40060i	0.713847	+	0.700301i	$0.246951\pi$
$599$			34.2790i			1.40060i	−0.713847	+	0.700301i	$0.753049\pi$
$600$		0			0
$601$			18.6709i			0.761603i	0.924657	+	0.380802i	$0.124352\pi$
$601$			18.6709i			0.761603i	−0.924657	+	0.380802i	$0.875648\pi$
$602$		0			0
$603$			18.9199i			0.770477i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	21.9446	+	21.9446i	0.890704	+	0.890704i	0.994589	−	0.103885i	$-0.0331274\pi$
$607$	21.9446	+	21.9446i	0.890704	+	0.890704i	−0.103885	+	0.994589i	$0.533127\pi$
$608$		0			0
$609$			48.3736i			1.96020i
$610$		0			0
$611$	4.65945	−	4.65945i	0.188501	−	0.188501i
$612$		0			0
$613$	−32.7731			−1.32369			−0.661846	−	0.749640i	$-0.730227\pi$
$613$	−32.7731			−1.32369			−0.661846	+	0.749640i	$0.730227\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−30.6044	−	30.6044i	−1.23209	−	1.23209i	−0.963160	−	0.268928i	$-0.913331\pi$
$617$	−30.6044	−	30.6044i	−1.23209	−	1.23209i	−0.268928	−	0.963160i	$-0.586669\pi$
$618$		0			0
$619$	10.9365	−	10.9365i	0.439576	−	0.439576i	−0.452293	−	0.891869i	$-0.649394\pi$
$619$	10.9365	−	10.9365i	0.439576	−	0.439576i	0.891869	+	0.452293i	$0.149394\pi$
$620$		0			0
$621$	−11.4771	−	11.4771i	−0.460559	−	0.460559i
$622$		0			0
$623$	−13.4259	+	13.4259i	−0.537897	+	0.537897i
$624$		0			0
$625$		0			0
$626$		0			0
$627$			23.1341i			0.923888i
$628$		0			0
$629$	6.38988	+	6.38988i	0.254781	+	0.254781i
$630$		0			0
$631$	−42.6639			−1.69842			−0.849211	−	0.528053i	$-0.822922\pi$
$631$	−42.6639			−1.69842			−0.849211	+	0.528053i	$0.822922\pi$
$632$		0			0
$633$	19.0714	−	19.0714i	0.758019	−	0.758019i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	14.8337			0.587732
$638$		0			0
$639$	1.16371			0.0460355
$640$		0			0
$641$	−13.4821			−0.532511			−0.266255	−	0.963903i	$-0.585786\pi$
$641$	−13.4821			−0.532511			−0.266255	+	0.963903i	$0.585786\pi$
$642$		0			0
$643$	−36.4066			−1.43574			−0.717868	−	0.696179i	$-0.754882\pi$
$643$	−36.4066			−1.43574			−0.717868	+	0.696179i	$0.754882\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.88954	−	1.88954i	0.0742855	−	0.0742855i	−0.668988	−	0.743273i	$-0.733272\pi$
$647$	1.88954	−	1.88954i	0.0742855	−	0.0742855i	0.743273	+	0.668988i	$0.233272\pi$
$648$		0			0
$649$	18.8030			0.738083
$650$		0			0
$651$	−21.2252	−	21.2252i	−0.831883	−	0.831883i
$652$		0			0
$653$			29.2010i			1.14272i	0.820699	+	0.571361i	$0.193584\pi$
$653$			29.2010i			1.14272i	−0.820699	+	0.571361i	$0.806416\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	14.1925	−	14.1925i	0.553702	−	0.553702i
$658$		0			0
$659$	33.1213	+	33.1213i	1.29022	+	1.29022i	0.934648	+	0.355575i	$0.115715\pi$
$659$	33.1213	+	33.1213i	1.29022	+	1.29022i	0.355575	+	0.934648i	$0.384285\pi$
$660$		0			0
$661$	31.0780	−	31.0780i	1.20879	−	1.20879i	0.237375	−	0.971418i	$-0.423713\pi$
$661$	31.0780	−	31.0780i	1.20879	−	1.20879i	0.971418	−	0.237375i	$-0.0762870\pi$
$662$		0			0
$663$	−73.2098	−	73.2098i	−2.84323	−	2.84323i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−11.5114			−0.445723
$668$		0			0
$669$	−41.1354	+	41.1354i	−1.59039	+	1.59039i
$670$		0			0
$671$		−	7.33591i		−	0.283200i
$672$		0			0
$673$	12.6450	+	12.6450i	0.487431	+	0.487431i	0.907495	−	0.420064i	$-0.137992\pi$
$673$	12.6450	+	12.6450i	0.487431	+	0.487431i	−0.420064	+	0.907495i	$0.637992\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			25.5644i			0.982521i	0.871013	+	0.491261i	$0.163464\pi$
$677$			25.5644i			0.982521i	−0.871013	+	0.491261i	$0.836536\pi$
$678$		0			0
$679$			17.8609i			0.685437i
$680$		0			0
$681$		−	28.3586i		−	1.08671i
$682$		0			0
$683$		−	26.4968i		−	1.01387i	−0.861984	−	0.506936i	$-0.830778\pi$
$683$		−	26.4968i		−	1.01387i	0.861984	−	0.506936i	$-0.169222\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−37.6008	−	37.6008i	−1.43456	−	1.43456i
$688$		0			0
$689$		−	46.0613i		−	1.75480i
$690$		0			0
$691$	−1.84230	+	1.84230i	−0.0700843	+	0.0700843i	−0.741280	−	0.671196i	$-0.765781\pi$
$691$	−1.84230	+	1.84230i	−0.0700843	+	0.0700843i	0.671196	+	0.741280i	$0.265781\pi$
$692$		0			0
$693$	−23.0182			−0.874389
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−13.5048	−	13.5048i	−0.511531	−	0.511531i
$698$		0			0
$699$	−32.7541	+	32.7541i	−1.23887	+	1.23887i
$700$		0			0
$701$	0.360678	+	0.360678i	0.0136226	+	0.0136226i	0.713885	−	0.700263i	$-0.246934\pi$
$701$	0.360678	+	0.360678i	0.0136226	+	0.0136226i	−0.700263	+	0.713885i	$0.746934\pi$
$702$		0			0
$703$	−4.71180	+	4.71180i	−0.177709	+	0.177709i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			28.3169i			1.06497i
$708$		0			0
$709$	3.03677	+	3.03677i	0.114048	+	0.114048i	0.761828	−	0.647780i	$-0.224302\pi$
$709$	3.03677	+	3.03677i	0.114048	+	0.114048i	−0.647780	+	0.761828i	$0.724302\pi$
$710$		0			0
$711$	80.6074			3.02301
$712$		0			0
$713$	5.05094	−	5.05094i	0.189159	−	0.189159i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−68.6497			−2.56377
$718$		0			0
$719$	8.02420			0.299252			0.149626	−	0.988743i	$-0.452193\pi$
$719$	8.02420			0.299252			0.149626	+	0.988743i	$0.452193\pi$
$720$		0			0
$721$	−19.4448			−0.724160
$722$		0			0
$723$	83.5873			3.10865
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−8.46006	+	8.46006i	−0.313766	+	0.313766i	−0.846367	−	0.532601i	$-0.821215\pi$
$727$	−8.46006	+	8.46006i	−0.313766	+	0.313766i	0.532601	+	0.846367i	$0.321215\pi$
$728$		0			0
$729$	−12.2180			−0.452520
$730$		0			0
$731$	10.2463	+	10.2463i	0.378974	+	0.378974i
$732$		0			0
$733$		−	15.3403i		−	0.566605i	−0.959031	−	0.283303i	$-0.908570\pi$
$733$		−	15.3403i		−	0.566605i	0.959031	−	0.283303i	$-0.0914301\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.53905	+	3.53905i	−0.130363	+	0.130363i
$738$		0			0
$739$	−24.9410	−	24.9410i	−0.917468	−	0.917468i	0.0793763	−	0.996845i	$-0.474707\pi$
$739$	−24.9410	−	24.9410i	−0.917468	−	0.917468i	−0.996845	+	0.0793763i	$0.974707\pi$
$740$		0			0
$741$	53.9837	−	53.9837i	1.98314	−	1.98314i
$742$		0			0
$743$	−24.4908	−	24.4908i	−0.898482	−	0.898482i	0.0968199	−	0.995302i	$-0.469133\pi$
$743$	−24.4908	−	24.4908i	−0.898482	−	0.898482i	−0.995302	+	0.0968199i	$0.969133\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	53.7820			1.96778
$748$		0			0
$749$	1.44882	−	1.44882i	0.0529386	−	0.0529386i
$750$		0			0
$751$		−	28.3355i		−	1.03398i	−0.855992	−	0.516989i	$-0.827053\pi$
$751$		−	28.3355i		−	1.03398i	0.855992	−	0.516989i	$-0.172947\pi$
$752$		0			0
$753$	−35.2497	−	35.2497i	−1.28457	−	1.28457i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			23.5834i			0.857154i	0.903505	+	0.428577i	$0.140985\pi$
$757$			23.5834i			0.857154i	−0.903505	+	0.428577i	$0.859015\pi$
$758$		0			0
$759$		−	8.02420i		−	0.291260i
$760$		0			0
$761$		−	21.8891i		−	0.793480i	−0.917931	−	0.396740i	$-0.870141\pi$
$761$		−	21.8891i		−	0.793480i	0.917931	−	0.396740i	$-0.129859\pi$
$762$		0			0
$763$		−	5.91052i		−	0.213975i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−43.8771	−	43.8771i	−1.58431	−	1.58431i
$768$		0			0
$769$			29.2413i			1.05447i	0.849720	+	0.527234i	$0.176771\pi$
$769$			29.2413i			1.05447i	−0.849720	+	0.527234i	$0.823229\pi$
$770$		0			0
$771$	−13.4056	+	13.4056i	−0.482790	+	0.482790i
$772$		0			0
$773$	−37.4599			−1.34734			−0.673669	−	0.739033i	$-0.735283\pi$
$773$	−37.4599			−1.34734			−0.673669	+	0.739033i	$0.735283\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−6.86776	−	6.86776i	−0.246380	−	0.246380i
$778$		0			0
$779$	9.95822	−	9.95822i	0.356790	−	0.356790i
$780$		0			0
$781$	0.217676	+	0.217676i	0.00778907	+	0.00778907i
$782$		0			0
$783$	56.5191	−	56.5191i	2.01983	−	2.01983i
$784$		0			0
$785$		0			0
$786$		0			0
$787$		−	5.74760i		−	0.204880i	−0.994739	−	0.102440i	$-0.967335\pi$
$787$		−	5.74760i		−	0.204880i	0.994739	−	0.102440i	$-0.0326649\pi$
$788$		0			0
$789$	30.5349	+	30.5349i	1.08707	+	1.08707i
$790$		0			0
$791$	7.51625			0.267247
$792$		0			0
$793$	−17.1184	+	17.1184i	−0.607894	+	0.607894i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−48.1720			−1.70634			−0.853170	−	0.521634i	$-0.825323\pi$
$797$	−48.1720			−1.70634			−0.853170	+	0.521634i	$0.825323\pi$
$798$		0			0
$799$	−6.99244			−0.247375
$800$		0			0
$801$	58.6316			2.07164
$802$		0			0
$803$	5.30955			0.187370
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−48.7838	+	48.7838i	−1.71727	+	1.71727i
$808$		0			0
$809$	20.0946			0.706489			0.353244	−	0.935531i	$-0.385078\pi$
$809$	20.0946			0.706489			0.353244	+	0.935531i	$0.385078\pi$
$810$		0			0
$811$	−2.14513	−	2.14513i	−0.0753258	−	0.0753258i	0.668440	−	0.743766i	$-0.266962\pi$
$811$	−2.14513	−	2.14513i	−0.0753258	−	0.0753258i	−0.743766	+	0.668440i	$0.766962\pi$
$812$		0			0
$813$			63.9629i			2.24328i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−7.55546	+	7.55546i	−0.264332	+	0.264332i
$818$		0			0
$819$	53.7132	+	53.7132i	1.87689	+	1.87689i
$820$		0			0
$821$	6.00000	−	6.00000i	0.209401	−	0.209401i	−0.594612	−	0.804013i	$-0.702694\pi$
$821$	6.00000	−	6.00000i	0.209401	−	0.209401i	0.804013	+	0.594612i	$0.202694\pi$
$822$		0			0
$823$	29.2525	+	29.2525i	1.01968	+	1.01968i	0.999802	+	0.0198765i	$0.00632730\pi$
$823$	29.2525	+	29.2525i	1.01968	+	1.01968i	0.0198765	+	0.999802i	$0.493673\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−15.2302			−0.529607			−0.264803	−	0.964302i	$-0.585307\pi$
$827$	−15.2302			−0.529607			−0.264803	+	0.964302i	$0.585307\pi$
$828$		0			0
$829$	14.6005	−	14.6005i	0.507097	−	0.507097i	−0.406537	−	0.913634i	$-0.633264\pi$
$829$	14.6005	−	14.6005i	0.507097	−	0.507097i	0.913634	+	0.406537i	$0.133264\pi$
$830$		0			0
$831$			62.9268i			2.18291i
$832$		0			0
$833$	−11.1305	−	11.1305i	−0.385647	−	0.385647i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			49.5985i			1.71438i
$838$		0			0
$839$		−	48.4754i		−	1.67356i	−0.547541	−	0.836779i	$-0.684436\pi$
$839$		−	48.4754i		−	1.67356i	0.547541	−	0.836779i	$-0.315564\pi$
$840$		0			0
$841$		−	27.6881i		−	0.954762i
$842$		0			0
$843$		−	18.1127i		−	0.623834i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	11.9483	+	11.9483i	0.410547	+	0.410547i
$848$		0			0
$849$			44.9691i			1.54334i
$850$		0			0
$851$	1.63431	−	1.63431i	0.0560235	−	0.0560235i
$852$		0			0
$853$	−27.0575			−0.926432			−0.463216	−	0.886246i	$-0.653305\pi$
$853$	−27.0575			−0.926432			−0.463216	+	0.886246i	$0.653305\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.28577	−	4.28577i	−0.146399	−	0.146399i	0.630108	−	0.776507i	$-0.283011\pi$
$857$	−4.28577	−	4.28577i	−0.146399	−	0.146399i	−0.776507	+	0.630108i	$0.783011\pi$
$858$		0			0
$859$	1.19447	−	1.19447i	0.0407549	−	0.0407549i	−0.686436	−	0.727191i	$-0.740826\pi$
$859$	1.19447	−	1.19447i	0.0407549	−	0.0407549i	0.727191	+	0.686436i	$0.240826\pi$
$860$		0			0
$861$	14.5148	+	14.5148i	0.494663	+	0.494663i
$862$		0			0
$863$	−14.7360	+	14.7360i	−0.501619	+	0.501619i	−0.911941	−	0.410322i	$-0.865416\pi$
$863$	−14.7360	+	14.7360i	−0.501619	+	0.501619i	0.410322	+	0.911941i	$0.365416\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			57.5985i			1.95615i
$868$		0			0
$869$	15.0780	+	15.0780i	0.511485	+	0.511485i
$870$		0			0
$871$	16.5168			0.559651
$872$		0			0
$873$	38.9996	−	38.9996i	1.31994	−	1.31994i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	19.8539			0.670417			0.335209	−	0.942144i	$-0.391193\pi$
$877$	19.8539			0.670417			0.335209	+	0.942144i	$0.391193\pi$
$878$		0			0
$879$	37.8115			1.27535
$880$		0			0
$881$	31.0235			1.04521			0.522604	−	0.852576i	$-0.324961\pi$
$881$	31.0235			1.04521			0.522604	+	0.852576i	$0.324961\pi$
$882$		0			0
$883$	−26.5836			−0.894609			−0.447304	−	0.894382i	$-0.647616\pi$
$883$	−26.5836			−0.894609			−0.447304	+	0.894382i	$0.647616\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.53715	+	2.53715i	−0.0851893	+	0.0851893i	−0.748417	−	0.663228i	$-0.769186\pi$
$887$	−2.53715	+	2.53715i	−0.0851893	+	0.0851893i	0.663228	+	0.748417i	$0.269186\pi$
$888$		0			0
$889$	−41.3794			−1.38782
$890$		0			0
$891$	16.0308	+	16.0308i	0.537051	+	0.537051i
$892$		0			0
$893$		−	5.15611i		−	0.172543i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−18.7246	+	18.7246i	−0.625195	+	0.625195i
$898$		0			0
$899$	24.8734	+	24.8734i	0.829576	+	0.829576i
$900$		0			0
$901$	−34.5621	+	34.5621i	−1.15143	+	1.15143i
$902$		0			0
$903$	−11.0126	−	11.0126i	−0.366476	−	0.366476i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.472551			0.0156908			0.00784539	−	0.999969i	$-0.497503\pi$
$907$	0.472551			0.0156908			0.00784539	+	0.999969i	$0.497503\pi$
$908$		0			0
$909$	61.8306	−	61.8306i	2.05079	−	2.05079i
$910$		0			0
$911$		−	2.03233i		−	0.0673340i	−0.999433	−	0.0336670i	$-0.989281\pi$
$911$		−	2.03233i		−	0.0673340i	0.999433	−	0.0336670i	$-0.0107186\pi$
$912$		0			0
$913$	10.0602	+	10.0602i	0.332943	+	0.332943i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	21.0322i		−	0.694544i
$918$		0			0
$919$		−	19.1234i		−	0.630824i	−0.948955	−	0.315412i	$-0.897857\pi$
$919$		−	19.1234i		−	0.630824i	0.948955	−	0.315412i	$-0.102143\pi$
$920$		0			0
$921$		−	63.5312i		−	2.09343i
$922$		0			0
$923$		−	1.01590i		−	0.0334388i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	42.4581	+	42.4581i	1.39451	+	1.39451i
$928$		0			0
$929$		−	33.7803i		−	1.10830i	−0.832418	−	0.554148i	$-0.813044\pi$
$929$		−	33.7803i		−	1.10830i	0.832418	−	0.554148i	$-0.186956\pi$
$930$		0			0
$931$	8.20741	−	8.20741i	0.268987	−	0.268987i
$932$		0			0
$933$	49.6729			1.62622
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−1.41422	−	1.41422i	−0.0462007	−	0.0462007i	0.683629	−	0.729830i	$-0.260401\pi$
$937$	−1.41422	−	1.41422i	−0.0462007	−	0.0462007i	−0.729830	+	0.683629i	$0.760401\pi$
$938$		0			0
$939$	−7.06191	+	7.06191i	−0.230457	+	0.230457i
$940$		0			0
$941$	17.4961	+	17.4961i	0.570357	+	0.570357i	0.932228	−	0.361871i	$-0.117862\pi$
$941$	17.4961	+	17.4961i	0.570357	+	0.570357i	−0.361871	+	0.932228i	$0.617862\pi$
$942$		0			0
$943$	−3.45406	+	3.45406i	−0.112480	+	0.112480i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	13.6441i		−	0.443374i	−0.975118	−	0.221687i	$-0.928844\pi$
$947$		−	13.6441i		−	0.443374i	0.975118	−	0.221687i	$-0.0711564\pi$
$948$		0			0
$949$	−12.3899	−	12.3899i	−0.402193	−	0.402193i
$950$		0			0
$951$	−6.31948			−0.204923
$952$		0			0
$953$	−5.39470	+	5.39470i	−0.174751	+	0.174751i	−0.789063	−	0.614312i	$-0.789434\pi$
$953$	−5.39470	+	5.39470i	−0.174751	+	0.174751i	0.614312	+	0.789063i	$0.289434\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	39.5153			1.27735
$958$		0			0
$959$	−2.94310			−0.0950377
$960$		0			0
$961$	9.17221			0.295878
$962$		0			0
$963$	−6.32706			−0.203887
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−9.15383	+	9.15383i	−0.294367	+	0.294367i	−0.838803	−	0.544435i	$-0.816744\pi$
$967$	−9.15383	+	9.15383i	−0.294367	+	0.294367i	0.544435	+	0.838803i	$0.316744\pi$
$968$		0			0
$969$	−81.0133			−2.60252
$970$		0			0
$971$	−10.5637	−	10.5637i	−0.339004	−	0.339004i	0.516989	−	0.855992i	$-0.327053\pi$
$971$	−10.5637	−	10.5637i	−0.339004	−	0.339004i	−0.855992	+	0.516989i	$0.827053\pi$
$972$		0			0
$973$		−	35.7965i		−	1.14758i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	16.0480	−	16.0480i	0.513420	−	0.513420i	−0.402153	−	0.915573i	$-0.631738\pi$
$977$	16.0480	−	16.0480i	0.513420	−	0.513420i	0.915573	+	0.402153i	$0.131738\pi$
$978$		0			0
$979$	10.9673	+	10.9673i	0.350516	+	0.350516i
$980$		0			0
$981$	−12.9058	+	12.9058i	−0.412049	+	0.412049i
$982$		0			0
$983$	−32.9855	−	32.9855i	−1.05207	−	1.05207i	−0.998568	−	0.0535049i	$-0.982961\pi$
$983$	−32.9855	−	32.9855i	−1.05207	−	1.05207i	−0.0535049	−	0.998568i	$-0.517039\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	7.51538			0.239217
$988$		0			0
$989$	2.62065	−	2.62065i	0.0833319	−	0.0833319i
$990$		0			0
$991$		−	33.9183i		−	1.07745i	−0.842481	−	0.538726i	$-0.818906\pi$
$991$		−	33.9183i		−	1.07745i	0.842481	−	0.538726i	$-0.181094\pi$
$992$		0			0
$993$	42.1561	+	42.1561i	1.33778	+	1.33778i
$994$		0			0
$995$		0			0
$996$		0			0
$997$		−	29.7497i		−	0.942181i	−0.882085	−	0.471090i	$-0.843861\pi$
$997$		−	29.7497i		−	0.942181i	0.882085	−	0.471090i	$-0.156139\pi$
$998$		0			0
$999$			16.0484i			0.507749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.s.c.943.1		16
4.3	odd	2		400.2.s.c.243.3	yes	16
5.2	odd	4		1600.2.j.c.1007.8		16
5.3	odd	4		1600.2.j.c.1007.1		16
5.4	even	2	inner	1600.2.s.c.943.8		16
16.5	even	4		400.2.j.c.43.2	✓	16
16.11	odd	4		1600.2.j.c.143.1		16
20.3	even	4		400.2.j.c.307.7	yes	16
20.7	even	4		400.2.j.c.307.2	yes	16
20.19	odd	2		400.2.s.c.243.6	yes	16
80.27	even	4	inner	1600.2.s.c.207.1		16
80.37	odd	4		400.2.s.c.107.3	yes	16
80.43	even	4	inner	1600.2.s.c.207.8		16
80.53	odd	4		400.2.s.c.107.6	yes	16
80.59	odd	4		1600.2.j.c.143.8		16
80.69	even	4		400.2.j.c.43.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.c.43.2	✓	16	16.5	even	4
400.2.j.c.43.7	yes	16	80.69	even	4
400.2.j.c.307.2	yes	16	20.7	even	4
400.2.j.c.307.7	yes	16	20.3	even	4
400.2.s.c.107.3	yes	16	80.37	odd	4
400.2.s.c.107.6	yes	16	80.53	odd	4
400.2.s.c.243.3	yes	16	4.3	odd	2
400.2.s.c.243.6	yes	16	20.19	odd	2
1600.2.j.c.143.1		16	16.11	odd	4
1600.2.j.c.143.8		16	80.59	odd	4
1600.2.j.c.1007.1		16	5.3	odd	4
1600.2.j.c.1007.8		16	5.2	odd	4
1600.2.s.c.207.1		16	80.27	even	4	inner
1600.2.s.c.207.8		16	80.43	even	4	inner
1600.2.s.c.943.1		16	1.1	even	1	trivial
1600.2.s.c.943.8		16	5.4	even	2	inner

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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.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.07455 q^{3} +(-1.47763 + 1.47763i) q^{7} +6.45288 q^{9} +O(q^{10})\)	\(q-3.07455 q^{3} +(-1.47763 + 1.47763i) q^{7} +6.45288 q^{9} +(1.20704 + 1.20704i) q^{11} -5.63329i q^{13} +(-4.22693 + 4.22693i) q^{17} +(-3.11687 - 3.11687i) q^{19} +(4.54305 - 4.54305i) q^{21} +(1.08110 + 1.08110i) q^{23} -10.6161 q^{27} +(-5.32391 + 5.32391i) q^{29} -4.67202i q^{31} +(-3.71111 - 3.71111i) q^{33} -1.51171i q^{37} +17.3198i q^{39} +3.19494i q^{41} -2.42405i q^{43} +(0.827129 + 0.827129i) q^{47} +2.63322i q^{49} +(12.9959 - 12.9959i) q^{51} +8.17664 q^{53} +(9.58299 + 9.58299i) q^{57} +(7.78889 - 7.78889i) q^{59} +(-3.03880 - 3.03880i) q^{61} +(-9.53497 + 9.53497i) q^{63} +2.93200i q^{67} +(-3.32391 - 3.32391i) q^{69} +0.180339 q^{71} +(2.19941 - 2.19941i) q^{73} -3.56712 q^{77} +12.4917 q^{79} +13.2810 q^{81} +8.33457 q^{83} +(16.3687 - 16.3687i) q^{87} +9.08610 q^{89} +(8.32391 + 8.32391i) q^{91} +14.3644i q^{93} +(6.04376 - 6.04376i) q^{97} +(7.78889 + 7.78889i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^9	\( 16 q + 16 q^{9} - 8 q^{11} - 8 q^{19} - 16 q^{29} + 48 q^{51} - 8 q^{59} - 16 q^{61} + 16 q^{69} + 32 q^{71} + 80 q^{79} + 16 q^{81} + 64 q^{91} - 8 q^{99}+O(q^{100}) \) 16 * q + 16 * q^9 - 8 * q^11 - 8 * q^19 - 16 * q^29 + 48 * q^51 - 8 * q^59 - 16 * q^61 + 16 * q^69 + 32 * q^71 + 80 * q^79 + 16 * q^81 + 64 * q^91 - 8 * q^99

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