LMFDB - Embedded newform 1600.2.j.c.143.8

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:	$16$
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			143.8
Root			$-1.24570 + 0.669507i$ of defining polynomial
Character	$\chi$	$=$	1600.143
Dual form			1600.2.j.c.1007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.07455i q^{3} +(1.47763 - 1.47763i) q^{7} -6.45288 q^{9} +O(q^{10})$	$q+3.07455i q^{3} +(1.47763 - 1.47763i) q^{7} -6.45288 q^{9} +(1.20704 - 1.20704i) q^{11} +5.63329 q^{13} +(4.22693 - 4.22693i) q^{17} +(3.11687 - 3.11687i) q^{19} +(4.54305 + 4.54305i) q^{21} +(-1.08110 - 1.08110i) q^{23} -10.6161i q^{27} +(5.32391 + 5.32391i) q^{29} +4.67202i q^{31} +(3.71111 + 3.71111i) q^{33} -1.51171 q^{37} +17.3198i q^{39} -3.19494i q^{41} +2.42405 q^{43} +(0.827129 + 0.827129i) q^{47} +2.63322i q^{49} +(12.9959 + 12.9959i) q^{51} -8.17664i q^{53} +(9.58299 + 9.58299i) q^{57} +(-7.78889 - 7.78889i) q^{59} +(-3.03880 + 3.03880i) q^{61} +(-9.53497 + 9.53497i) q^{63} +2.93200 q^{67} +(3.32391 - 3.32391i) q^{69} +0.180339 q^{71} +(2.19941 - 2.19941i) q^{73} -3.56712i q^{77} -12.4917 q^{79} +13.2810 q^{81} -8.33457i q^{83} +(-16.3687 + 16.3687i) q^{87} -9.08610 q^{89} +(8.32391 - 8.32391i) q^{91} -14.3644 q^{93} +(-6.04376 + 6.04376i) q^{97} +(-7.78889 + 7.78889i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

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

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
$3$			3.07455i			1.77509i	0.460717	+	0.887547i	$0.347592\pi$
$3$			3.07455i			1.77509i	−0.460717	+	0.887547i	$0.652408\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.47763	−	1.47763i	0.558491	−	0.558491i	−0.370386	−	0.928878i	$-0.620775\pi$
$7$	1.47763	−	1.47763i	0.558491	−	0.558491i	0.928878	+	0.370386i	$0.120775\pi$
$8$		0			0
$9$	−6.45288			−2.15096
$10$		0			0
$11$	1.20704	−	1.20704i	0.363937	−	0.363937i	−0.501323	−	0.865260i	$-0.667153\pi$
$11$	1.20704	−	1.20704i	0.363937	−	0.363937i	0.865260	+	0.501323i	$0.167153\pi$
$12$		0			0
$13$	5.63329			1.56239			0.781196	−	0.624285i	$-0.214610\pi$
$13$	5.63329			1.56239			0.781196	+	0.624285i	$0.214610\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.22693	−	4.22693i	1.02518	−	1.02518i	0.0255073	−	0.999675i	$-0.491880\pi$
$17$	4.22693	−	4.22693i	1.02518	−	1.02518i	0.999675	−	0.0255073i	$-0.00812009\pi$
$18$		0			0
$19$	3.11687	−	3.11687i	0.715059	−	0.715059i	−0.252530	−	0.967589i	$-0.581263\pi$
$19$	3.11687	−	3.11687i	0.715059	−	0.715059i	0.967589	+	0.252530i	$0.0812626\pi$
$20$		0			0
$21$	4.54305	+	4.54305i	0.991375	+	0.991375i
$22$		0			0
$23$	−1.08110	−	1.08110i	−0.225426	−	0.225426i	0.585353	−	0.810779i	$-0.300956\pi$
$23$	−1.08110	−	1.08110i	−0.225426	−	0.225426i	−0.810779	+	0.585353i	$0.800956\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	10.6161i		−	2.04306i
$28$		0			0
$29$	5.32391	+	5.32391i	0.988626	+	0.988626i	0.999936	−	0.0113103i	$-0.00360026\pi$
$29$	5.32391	+	5.32391i	0.988626	+	0.988626i	−0.0113103	+	0.999936i	$0.503600\pi$
$30$		0			0
$31$			4.67202i			0.839120i	0.907728	+	0.419560i	$0.137816\pi$
$31$			4.67202i			0.839120i	−0.907728	+	0.419560i	$0.862184\pi$
$32$		0			0
$33$	3.71111	+	3.71111i	0.646022	+	0.646022i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.51171			−0.248523			−0.124262	−	0.992249i	$-0.539656\pi$
$37$	−1.51171			−0.248523			−0.124262	+	0.992249i	$0.539656\pi$
$38$		0			0
$39$			17.3198i			2.77340i
$40$		0			0
$41$		−	3.19494i		−	0.498966i	−0.968379	−	0.249483i	$-0.919739\pi$
$41$		−	3.19494i		−	0.498966i	0.968379	−	0.249483i	$-0.0802607\pi$
$42$		0			0
$43$	2.42405			0.369665			0.184832	−	0.982770i	$-0.440826\pi$
$43$	2.42405			0.369665			0.184832	+	0.982770i	$0.440826\pi$
$44$		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
$53$		−	8.17664i		−	1.12315i	−0.827427	−	0.561574i	$-0.810196\pi$
$53$		−	8.17664i		−	1.12315i	0.827427	−	0.561574i	$-0.189804\pi$
$54$		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	−0.999900	−	0.0141274i	$-0.995503\pi$
$59$	−7.78889	−	7.78889i	−1.01403	−	1.01403i	−0.0141274	−	0.999900i	$-0.504497\pi$
$60$		0			0
$61$	−3.03880	+	3.03880i	−0.389079	+	0.389079i	−0.874359	−	0.485280i	$-0.838718\pi$
$61$	−3.03880	+	3.03880i	−0.389079	+	0.389079i	0.485280	+	0.874359i	$0.338718\pi$
$62$		0			0
$63$	−9.53497	+	9.53497i	−1.20129	+	1.20129i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.93200			0.358201			0.179101	−	0.983831i	$-0.442681\pi$
$67$	2.93200			0.358201			0.179101	+	0.983831i	$0.442681\pi$
$68$		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
$77$		−	3.56712i		−	0.406511i
$78$		0			0
$79$	−12.4917			−1.40542			−0.702712	−	0.711474i	$-0.748028\pi$
$79$	−12.4917			−1.40542			−0.702712	+	0.711474i	$0.748028\pi$
$80$		0			0
$81$	13.2810			1.47567
$82$		0			0
$83$		−	8.33457i		−	0.914838i	−0.889251	−	0.457419i	$-0.848774\pi$
$83$		−	8.33457i		−	0.914838i	0.889251	−	0.457419i	$-0.151226\pi$
$84$		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	$-0.659931\pi$
$89$	−9.08610			−0.963125			−0.481563	+	0.876412i	$0.659931\pi$
$90$		0			0
$91$	8.32391	−	8.32391i	0.872583	−	0.872583i
$92$		0			0
$93$	−14.3644			−1.48952
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.04376	+	6.04376i	−0.613650	+	0.613650i	−0.943895	−	0.330245i	$-0.892869\pi$
$97$	−6.04376	+	6.04376i	−0.613650	+	0.613650i	0.330245	+	0.943895i	$0.392869\pi$
$98$		0			0
$99$	−7.78889	+	7.78889i	−0.782813	+	0.782813i
$100$		0			0
$101$	9.58185	+	9.58185i	0.953430	+	0.953430i	0.998963	−	0.0455329i	$-0.0144986\pi$
$101$	9.58185	+	9.58185i	0.953430	+	0.953430i	−0.0455329	+	0.998963i	$0.514499\pi$
$102$		0			0
$103$	−6.57971	−	6.57971i	−0.648318	−	0.648318i	0.304268	−	0.952586i	$-0.401588\pi$
$103$	−6.57971	−	6.57971i	−0.648318	−	0.648318i	−0.952586	+	0.304268i	$0.901588\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	0.980501i		−	0.0947886i	−0.998876	−	0.0473943i	$-0.984908\pi$
$107$		−	0.980501i		−	0.0947886i	0.998876	−	0.0473943i	$-0.0150917\pi$
$108$		0			0
$109$	2.00000	+	2.00000i	0.191565	+	0.191565i	0.796372	−	0.604807i	$-0.206750\pi$
$109$	2.00000	+	2.00000i	0.191565	+	0.191565i	−0.604807	+	0.796372i	$0.706750\pi$
$110$		0			0
$111$		−	4.64783i		−	0.441152i
$112$		0			0
$113$	2.54335	+	2.54335i	0.239258	+	0.239258i	0.816543	−	0.577285i	$-0.195888\pi$
$113$	2.54335	+	2.54335i	0.239258	+	0.239258i	−0.577285	+	0.816543i	$0.695888\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−36.3509			−3.36065
$118$		0			0
$119$		−	12.4917i		−	1.14511i
$120$		0			0
$121$			8.08610i			0.735100i
$122$		0			0
$123$	9.82302			0.885712
$124$		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	0.324189	−	0.945992i	$-0.394909\pi$
$131$	−7.11687	−	7.11687i	−0.621804	−	0.621804i	−0.945992	+	0.324189i	$0.894909\pi$
$132$		0			0
$133$		−	9.21116i		−	0.798709i
$134$		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	0.999614	+	0.0277808i	$0.00884403\pi$
$139$	12.1128	+	12.1128i	1.02739	+	1.02739i	0.0277808	+	0.999614i	$0.491156\pi$
$140$		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
$147$	−8.09598			−0.667745
$148$		0			0
$149$	−9.86696	+	9.86696i	−0.808333	+	0.808333i	−0.984382	−	0.176048i	$-0.943669\pi$
$149$	−9.86696	+	9.86696i	−0.808333	+	0.808333i	0.176048	+	0.984382i	$0.443669\pi$
$150$		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
$157$			17.9394i			1.43172i	0.698245	+	0.715859i	$0.253965\pi$
$157$			17.9394i			1.43172i	−0.698245	+	0.715859i	$0.746035\pi$
$158$		0			0
$159$	25.1395			1.99369
$160$		0			0
$161$	−3.19494			−0.251797
$162$		0			0
$163$			7.39897i			0.579532i	0.957098	+	0.289766i	$0.0935775\pi$
$163$			7.39897i			0.579532i	−0.957098	+	0.289766i	$0.906423\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.74192	+	8.74192i	−0.676470	+	0.676470i	−0.959200	−	0.282730i	$-0.908760\pi$
$167$	−8.74192	+	8.74192i	−0.676470	+	0.676470i	0.282730	+	0.959200i	$0.408760\pi$
$168$		0			0
$169$	18.7339			1.44107
$170$		0			0
$171$	−20.1128	+	20.1128i	−1.53806	+	1.53806i
$172$		0			0
$173$	10.7865			0.820083			0.410042	−	0.912067i	$-0.365514\pi$
$173$	10.7865			0.820083			0.410042	+	0.912067i	$0.365514\pi$
$174$		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	$-0.759002\pi$
$179$	−0.535019	+	0.535019i	−0.0399892	+	0.0399892i	0.686829	+	0.726819i	$0.259002\pi$
$180$		0			0
$181$	−7.58185	−	7.58185i	−0.563555	−	0.563555i	0.366761	−	0.930315i	$-0.380467\pi$
$181$	−7.58185	−	7.58185i	−0.563555	−	0.563555i	−0.930315	+	0.366761i	$0.880467\pi$
$182$		0			0
$183$	−9.34296	−	9.34296i	−0.690651	−	0.690651i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	10.2042i		−	0.746202i
$188$		0			0
$189$	−15.6866	−	15.6866i	−1.14103	−	1.14103i
$190$		0			0
$191$			4.46749i			0.323256i	0.986852	+	0.161628i	$0.0516745\pi$
$191$			4.46749i			0.323256i	−0.986852	+	0.161628i	$0.948326\pi$
$192$		0			0
$193$	−12.9115	−	12.9115i	−0.929391	−	0.929391i	0.0682750	−	0.997667i	$-0.478250\pi$
$193$	−12.9115	−	12.9115i	−0.929391	−	0.929391i	−0.997667	+	0.0682750i	$0.978250\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.8764			0.988656			0.494328	−	0.869275i	$-0.335414\pi$
$197$	13.8764			0.988656			0.494328	+	0.869275i	$0.335414\pi$
$198$		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
$203$	15.7335			1.10428
$204$		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	0.460585	−	0.887616i	$-0.347640\pi$
$211$	−6.20298	−	6.20298i	−0.427030	−	0.427030i	−0.887616	+	0.460585i	$0.847640\pi$
$212$		0			0
$213$			0.554462i			0.0379911i
$214$		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
$227$	9.22366			0.612196			0.306098	−	0.952000i	$-0.400976\pi$
$227$	9.22366			0.612196			0.306098	+	0.952000i	$0.400976\pi$
$228$		0			0
$229$	−12.2297	+	12.2297i	−0.808160	+	0.808160i	−0.984355	−	0.176195i	$-0.943621\pi$
$229$	−12.2297	+	12.2297i	−0.808160	+	0.808160i	0.176195	+	0.984355i	$0.443621\pi$
$230$		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
$237$		−	38.4064i		−	2.49476i
$238$		0			0
$239$	−22.3284			−1.44430			−0.722150	−	0.691736i	$-0.756846\pi$
$239$	−22.3284			−1.44430			−0.722150	+	0.691736i	$0.756846\pi$
$240$		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
$243$			8.98507i			0.576393i
$244$		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	−0.245686	−	0.969349i	$-0.579013\pi$
$251$	11.4650	−	11.4650i	0.723663	−	0.723663i	0.969349	+	0.245686i	$0.0790133\pi$
$252$		0			0
$253$	−2.60987			−0.164081
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.36017	+	4.36017i	−0.271980	+	0.271980i	−0.829897	−	0.557917i	$-0.811601\pi$
$257$	−4.36017	+	4.36017i	−0.271980	+	0.271980i	0.557917	+	0.829897i	$0.311601\pi$
$258$		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	0.943571	−	0.331169i	$-0.107443\pi$
$263$	9.93150	+	9.93150i	0.612402	+	0.612402i	−0.331169	+	0.943571i	$0.607443\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	27.9357i		−	1.70964i
$268$		0			0
$269$	−15.8670	−	15.8670i	−0.967426	−	0.967426i	0.0320600	−	0.999486i	$-0.489793\pi$
$269$	−15.8670	−	15.8670i	−0.967426	−	0.967426i	−0.999486	+	0.0320600i	$0.989793\pi$
$270$		0			0
$271$			20.8040i			1.26375i	0.775070	+	0.631875i	$0.217715\pi$
$271$			20.8040i			1.26375i	−0.775070	+	0.631875i	$0.782285\pi$
$272$		0			0
$273$	25.5923	+	25.5923i	1.54892	+	1.54892i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−20.4670			−1.22974			−0.614871	−	0.788628i	$-0.710792\pi$
$277$	−20.4670			−1.22974			−0.614871	+	0.788628i	$0.710792\pi$
$278$		0			0
$279$		−	30.1480i		−	1.80491i
$280$		0			0
$281$		−	5.89116i		−	0.351437i	−0.984440	−	0.175719i	$-0.943775\pi$
$281$		−	5.89116i		−	0.351437i	0.984440	−	0.175719i	$-0.0562249\pi$
$282$		0			0
$283$	14.6262			0.869439			0.434720	−	0.900566i	$-0.356847\pi$
$283$	14.6262			0.869439			0.434720	+	0.900566i	$0.356847\pi$
$284$		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
$293$			12.2982i			0.718469i	0.933247	+	0.359235i	$0.116962\pi$
$293$			12.2982i			0.718469i	−0.933247	+	0.359235i	$0.883038\pi$
$294$		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
$307$	20.6636			1.17933			0.589666	−	0.807647i	$-0.299259\pi$
$307$	20.6636			1.17933			0.589666	+	0.807647i	$0.299259\pi$
$308$		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
$317$			2.05541i			0.115443i	0.998333	+	0.0577217i	$0.0183836\pi$
$317$			2.05541i			0.115443i	−0.998333	+	0.0577217i	$0.981616\pi$
$318$		0			0
$319$	12.8524			0.719594
$320$		0			0
$321$	3.01460			0.168259
$322$		0			0
$323$		−	26.3496i		−	1.46613i
$324$		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	−0.975157	−	0.221516i	$-0.928900\pi$
$331$	−13.7113	+	13.7113i	−0.753641	+	0.753641i	0.221516	+	0.975157i	$0.428900\pi$
$332$		0			0
$333$	9.75487			0.534563
$334$		0			0
$335$		0			0
$336$		0			0
$337$	12.8140	−	12.8140i	0.698025	−	0.698025i	−0.265959	−	0.963984i	$-0.585689\pi$
$337$	12.8140	−	12.8140i	0.698025	−	0.698025i	0.963984	+	0.265959i	$0.0856887\pi$
$338$		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
$347$			8.81175i			0.473040i	0.971627	+	0.236520i	$0.0760068\pi$
$347$			8.81175i			0.473040i	−0.971627	+	0.236520i	$0.923993\pi$
$348$		0			0
$349$	15.8398	+	15.8398i	0.847885	+	0.847885i	0.989869	−	0.141984i	$-0.0453482\pi$
$349$	15.8398	+	15.8398i	0.847885	+	0.847885i	−0.141984	+	0.989869i	$0.545348\pi$
$350$		0			0
$351$		−	59.8034i		−	3.19207i
$352$		0			0
$353$	10.2349	+	10.2349i	0.544751	+	0.544751i	0.924918	−	0.380167i	$-0.124134\pi$
$353$	10.2349	+	10.2349i	0.544751	+	0.544751i	−0.380167	+	0.924918i	$0.624134\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	38.4064			2.03268
$358$		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
$363$	−24.8612			−1.30487
$364$		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
$373$		−	27.6942i		−	1.43395i	−0.697097	−	0.716977i	$-0.745525\pi$
$373$		−	27.6942i		−	1.43395i	0.697097	−	0.716977i	$-0.254475\pi$
$374$		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	$-0.0277533\pi$
$379$	17.6987	+	17.6987i	0.909122	+	0.909122i	−0.0870790	+	0.996201i	$0.527753\pi$
$380$		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
$387$	−15.6421			−0.795134
$388$		0			0
$389$	6.38285	−	6.38285i	0.323623	−	0.323623i	−0.526532	−	0.850155i	$-0.676508\pi$
$389$	6.38285	−	6.38285i	0.323623	−	0.323623i	0.850155	+	0.526532i	$0.176508\pi$
$390$		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
$397$			8.65670i			0.434467i	0.976120	+	0.217234i	$0.0697034\pi$
$397$			8.65670i			0.434467i	−0.976120	+	0.217234i	$0.930297\pi$
$398$		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
$403$			26.3188i			1.31104i
$404$		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	$-0.525169\pi$
$409$	−3.19494			−0.157980			−0.0789899	+	0.996875i	$0.525169\pi$
$410$		0			0
$411$	−3.06191	+	3.06191i	−0.151033	+	0.151033i
$412$		0			0
$413$	−23.0182			−1.13265
$414$		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	0.352473	−	0.935822i	$-0.385341\pi$
$419$	26.3707	−	26.3707i	1.28830	−	1.28830i	0.935822	−	0.352473i	$-0.114659\pi$
$420$		0			0
$421$	28.3345	+	28.3345i	1.38094	+	1.38094i	0.842959	+	0.537977i	$0.180811\pi$
$421$	28.3345	+	28.3345i	1.38094	+	1.38094i	0.537977	+	0.842959i	$0.319189\pi$
$422$		0			0
$423$	−5.33736	−	5.33736i	−0.259512	−	0.259512i
$424$		0			0
$425$		0			0
$426$		0			0
$427$			8.98044i			0.434594i
$428$		0			0
$429$	20.9058	+	20.9058i	1.00934	+	1.00934i
$430$		0			0
$431$			6.49981i			0.313085i	0.987671	+	0.156543i	$0.0500348\pi$
$431$			6.49981i			0.313085i	−0.987671	+	0.156543i	$0.949965\pi$
$432$		0			0
$433$	−19.5486	−	19.5486i	−0.939444	−	0.939444i	0.0588243	−	0.998268i	$-0.481265\pi$
$433$	−19.5486	−	19.5486i	−0.939444	−	0.939444i	−0.998268	+	0.0588243i	$0.981265\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.73932			−0.322386
$438$		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
$443$	−35.3347			−1.67880			−0.839401	−	0.543513i	$-0.817094\pi$
$443$	−35.3347			−1.67880			−0.839401	+	0.543513i	$0.817094\pi$
$444$		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
$453$			28.6544i			1.34630i
$454$		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	−0.609310	−	0.792932i	$-0.708554\pi$
$461$	3.94253	−	3.94253i	0.183622	−	0.183622i	0.792932	+	0.609310i	$0.208554\pi$
$462$		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
$467$	−17.2282			−0.797228			−0.398614	−	0.917119i	$-0.630509\pi$
$467$	−17.2282			−0.797228			−0.398614	+	0.917119i	$0.630509\pi$
$468$		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
$477$			52.7629i			2.41585i
$478$		0			0
$479$	−39.2875			−1.79509			−0.897546	−	0.440920i	$-0.854652\pi$
$479$	−39.2875			−1.79509			−0.897546	+	0.440920i	$0.854652\pi$
$480$		0			0
$481$	−8.51588			−0.388291
$482$		0			0
$483$		−	9.82302i		−	0.446963i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	5.39013	−	5.39013i	0.244250	−	0.244250i	−0.574356	−	0.818606i	$-0.694747\pi$
$487$	5.39013	−	5.39013i	0.244250	−	0.244250i	0.818606	+	0.574356i	$0.194747\pi$
$488$		0			0
$489$	−22.7485			−1.02872
$490$		0			0
$491$	28.0145	−	28.0145i	1.26428	−	1.26428i	0.315277	−	0.949000i	$-0.397902\pi$
$491$	28.0145	−	28.0145i	1.26428	−	1.26428i	0.949000	−	0.315277i	$-0.102098\pi$
$492$		0			0
$493$	45.0076			2.02704
$494$		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	$-0.738079\pi$
$499$	1.18284	−	1.18284i	0.0529514	−	0.0529514i	0.733087	+	0.680135i	$0.238079\pi$
$500$		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	$-0.852845\pi$
$503$	−30.0763	−	30.0763i	−1.34104	−	1.34104i	−0.446010	−	0.895028i	$-0.647155\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			57.5985i			2.55804i
$508$		0			0
$509$	−23.1062	−	23.1062i	−1.02417	−	1.02417i	−0.999701	−	0.0244652i	$-0.992212\pi$
$509$	−23.1062	−	23.1062i	−1.02417	−	1.02417i	−0.0244652	−	0.999701i	$-0.507788\pi$
$510$		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
$517$	1.99676			0.0878173
$518$		0			0
$519$			33.1637i			1.45573i
$520$		0			0
$521$		−	31.3733i		−	1.37449i	−0.726427	−	0.687244i	$-0.758821\pi$
$521$		−	31.3733i		−	1.37449i	0.726427	−	0.687244i	$-0.241179\pi$
$522$		0			0
$523$	−11.6926			−0.511282			−0.255641	−	0.966772i	$-0.582287\pi$
$523$	−11.6926			−0.511282			−0.255641	+	0.966772i	$0.582287\pi$
$524$		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
$533$		−	17.9980i		−	0.779581i
$534$		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	−0.257437	−	0.966295i	$-0.582878\pi$
$541$	16.4876	−	16.4876i	0.708858	−	0.708858i	0.966295	+	0.257437i	$0.0828780\pi$
$542$		0			0
$543$	23.3108	−	23.3108i	1.00036	−	1.00036i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−36.0505			−1.54141			−0.770703	−	0.637194i	$-0.780095\pi$
$547$	−36.0505			−1.54141			−0.770703	+	0.637194i	$0.780095\pi$
$548$		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
$557$		−	5.64116i		−	0.239024i	−0.992833	−	0.119512i	$-0.961867\pi$
$557$		−	5.64116i		−	0.239024i	0.992833	−	0.119512i	$-0.0381329\pi$
$558$		0			0
$559$	13.6554			0.577561
$560$		0			0
$561$	31.3733			1.32458
$562$		0			0
$563$			4.69143i			0.197720i	0.995101	+	0.0988601i	$0.0315196\pi$
$563$			4.69143i			0.197720i	−0.995101	+	0.0988601i	$0.968480\pi$
$564$		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	$-0.923900\pi$
$569$	−46.3505			−1.94311			−0.971557	+	0.236804i	$0.923900\pi$
$570$		0			0
$571$	6.27708	−	6.27708i	0.262688	−	0.262688i	−0.563457	−	0.826145i	$-0.690529\pi$
$571$	6.27708	−	6.27708i	0.262688	−	0.262688i	0.826145	+	0.563457i	$0.190529\pi$
$572$		0			0
$573$	−13.7355			−0.573810
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−12.5833	+	12.5833i	−0.523850	+	0.523850i	−0.918732	−	0.394882i	$-0.870786\pi$
$577$	−12.5833	+	12.5833i	−0.523850	+	0.523850i	0.394882	+	0.918732i	$0.370786\pi$
$578$		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
$587$			17.4298i			0.719405i	0.933067	+	0.359703i	$0.117122\pi$
$587$			17.4298i			0.719405i	−0.933067	+	0.359703i	$0.882878\pi$
$588$		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	0.743426	−	0.668818i	$-0.233200\pi$
$593$	1.81682	+	1.81682i	0.0746079	+	0.0746079i	−0.668818	+	0.743426i	$0.733200\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	29.1344			1.19239
$598$		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	$-0.875648\pi$
$601$		−	18.6709i		−	0.761603i	0.924657	−	0.380802i	$-0.124352\pi$
$602$		0			0
$603$	−18.9199			−0.770477
$604$		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
$613$			32.7731i			1.32369i	0.749640	+	0.661846i	$0.230227\pi$
$613$			32.7731i			1.32369i	−0.749640	+	0.661846i	$0.769773\pi$
$614$		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	$-0.350606\pi$
$619$	−10.9365	−	10.9365i	−0.439576	−	0.439576i	−0.891869	+	0.452293i	$0.850606\pi$
$620$		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
$627$	23.1341			0.923888
$628$		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
$637$			14.8337i			0.587732i
$638$		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
$643$			36.4066i			1.43574i	0.696179	+	0.717868i	$0.254882\pi$
$643$			36.4066i			1.43574i	−0.696179	+	0.717868i	$0.745118\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.88954	+	1.88954i	−0.0742855	+	0.0742855i	−0.743273	−	0.668988i	$-0.766728\pi$
$647$	−1.88954	+	1.88954i	−0.0742855	+	0.0742855i	0.668988	+	0.743273i	$0.266728\pi$
$648$		0			0
$649$	−18.8030			−0.738083
$650$		0			0
$651$	−21.2252	+	21.2252i	−0.831883	+	0.831883i
$652$		0			0
$653$	−29.2010			−1.14272			−0.571361	−	0.820699i	$-0.693584\pi$
$653$	−29.2010			−1.14272			−0.571361	+	0.820699i	$0.693584\pi$
$654$		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	−0.355575	+	0.934648i	$0.615715\pi$
$659$	−33.1213	+	33.1213i	−1.29022	+	1.29022i	−0.934648	+	0.355575i	$0.884285\pi$
$660$		0			0
$661$	31.0780	+	31.0780i	1.20879	+	1.20879i	0.971418	+	0.237375i	$0.0762870\pi$
$661$	31.0780	+	31.0780i	1.20879	+	1.20879i	0.237375	+	0.971418i	$0.423713\pi$
$662$		0			0
$663$	73.2098	+	73.2098i	2.84323	+	2.84323i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		−	11.5114i		−	0.445723i
$668$		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	0.420064	−	0.907495i	$-0.362008\pi$
$673$	−12.6450	−	12.6450i	−0.487431	−	0.487431i	−0.907495	+	0.420064i	$0.862008\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	25.5644			0.982521			0.491261	−	0.871013i	$-0.336536\pi$
$677$	25.5644			0.982521			0.491261	+	0.871013i	$0.336536\pi$
$678$		0			0
$679$			17.8609i			0.685437i
$680$		0			0
$681$			28.3586i			1.08671i
$682$		0			0
$683$	26.4968			1.01387			0.506936	−	0.861984i	$-0.330778\pi$
$683$	26.4968			1.01387			0.506936	+	0.861984i	$0.330778\pi$
$684$		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	0.671196	−	0.741280i	$-0.265781\pi$
$691$	−1.84230	−	1.84230i	−0.0700843	−	0.0700843i	−0.741280	+	0.671196i	$0.765781\pi$
$692$		0			0
$693$			23.0182i			0.874389i
$694$		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	−0.700263	−	0.713885i	$-0.746934\pi$
$701$	0.360678	−	0.360678i	0.0136226	−	0.0136226i	0.713885	+	0.700263i	$0.246934\pi$
$702$		0			0
$703$	−4.71180	+	4.71180i	−0.177709	+	0.177709i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	28.3169			1.06497
$708$		0			0
$709$	−3.03677	+	3.03677i	−0.114048	+	0.114048i	−0.761828	−	0.647780i	$-0.775698\pi$
$709$	−3.03677	+	3.03677i	−0.114048	+	0.114048i	0.647780	+	0.761828i	$0.275698\pi$
$710$		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
$717$		−	68.6497i		−	2.56377i
$718$		0			0
$719$	−8.02420			−0.299252			−0.149626	−	0.988743i	$-0.547807\pi$
$719$	−8.02420			−0.299252			−0.149626	+	0.988743i	$0.547807\pi$
$720$		0			0
$721$	−19.4448			−0.724160
$722$		0			0
$723$		−	83.5873i		−	3.10865i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	8.46006	−	8.46006i	0.313766	−	0.313766i	−0.532601	−	0.846367i	$-0.678785\pi$
$727$	8.46006	−	8.46006i	0.313766	−	0.313766i	0.846367	+	0.532601i	$0.178785\pi$
$728$		0			0
$729$	12.2180			0.452520
$730$		0			0
$731$	10.2463	−	10.2463i	0.378974	−	0.378974i
$732$		0			0
$733$	15.3403			0.566605			0.283303	−	0.959031i	$-0.408570\pi$
$733$	15.3403			0.566605			0.283303	+	0.959031i	$0.408570\pi$
$734$		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	$-0.525293\pi$
$739$	24.9410	−	24.9410i	0.917468	−	0.917468i	0.996845	+	0.0793763i	$0.0252929\pi$
$740$		0			0
$741$	53.9837	+	53.9837i	1.98314	+	1.98314i
$742$		0			0
$743$	24.4908	+	24.4908i	0.898482	+	0.898482i	0.995302	−	0.0968199i	$-0.0308671\pi$
$743$	24.4908	+	24.4908i	0.898482	+	0.898482i	−0.0968199	+	0.995302i	$0.530867\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			53.7820i			1.96778i
$748$		0			0
$749$	−1.44882	−	1.44882i	−0.0529386	−	0.0529386i
$750$		0			0
$751$			28.3355i			1.03398i	0.855992	+	0.516989i	$0.172947\pi$
$751$			28.3355i			1.03398i	−0.855992	+	0.516989i	$0.827053\pi$
$752$		0			0
$753$	35.2497	+	35.2497i	1.28457	+	1.28457i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	23.5834			0.857154			0.428577	−	0.903505i	$-0.359015\pi$
$757$	23.5834			0.857154			0.428577	+	0.903505i	$0.359015\pi$
$758$		0			0
$759$		−	8.02420i		−	0.291260i
$760$		0			0
$761$			21.8891i			0.793480i	0.917931	+	0.396740i	$0.129859\pi$
$761$			21.8891i			0.793480i	−0.917931	+	0.396740i	$0.870141\pi$
$762$		0			0
$763$	5.91052			0.213975
$764$		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
$773$			37.4599i			1.34734i	0.739033	+	0.673669i	$0.235283\pi$
$773$			37.4599i			1.34734i	−0.739033	+	0.673669i	$0.764717\pi$
$774$		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
$787$	−5.74760			−0.204880			−0.102440	−	0.994739i	$-0.532665\pi$
$787$	−5.74760			−0.204880			−0.102440	+	0.994739i	$0.532665\pi$
$788$		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
$797$		−	48.1720i		−	1.70634i	−0.521634	−	0.853170i	$-0.674677\pi$
$797$		−	48.1720i		−	1.70634i	0.521634	−	0.853170i	$-0.325323\pi$
$798$		0			0
$799$	6.99244			0.247375
$800$		0			0
$801$	58.6316			2.07164
$802$		0			0
$803$		−	5.30955i		−	0.187370i
$804$		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	$-0.614922\pi$
$809$	−20.0946			−0.706489			−0.353244	+	0.935531i	$0.614922\pi$
$810$		0			0
$811$	−2.14513	+	2.14513i	−0.0753258	+	0.0753258i	−0.743766	−	0.668440i	$-0.766962\pi$
$811$	−2.14513	+	2.14513i	−0.0753258	+	0.0753258i	0.668440	+	0.743766i	$0.266962\pi$
$812$		0			0
$813$	−63.9629			−2.24328
$814$		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	0.804013	−	0.594612i	$-0.202694\pi$
$821$	6.00000	+	6.00000i	0.209401	+	0.209401i	−0.594612	+	0.804013i	$0.702694\pi$
$822$		0			0
$823$	−29.2525	−	29.2525i	−1.01968	−	1.01968i	−0.999802	−	0.0198765i	$-0.993673\pi$
$823$	−29.2525	−	29.2525i	−1.01968	−	1.01968i	−0.0198765	−	0.999802i	$-0.506327\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	15.2302i		−	0.529607i	−0.964302	−	0.264803i	$-0.914693\pi$
$827$		−	15.2302i		−	0.529607i	0.964302	−	0.264803i	$-0.0853070\pi$
$828$		0			0
$829$	−14.6005	−	14.6005i	−0.507097	−	0.507097i	0.406537	−	0.913634i	$-0.366736\pi$
$829$	−14.6005	−	14.6005i	−0.507097	−	0.507097i	−0.913634	+	0.406537i	$0.866736\pi$
$830$		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
$837$	49.5985			1.71438
$838$		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
$843$	18.1127			0.623834
$844$		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
$853$			27.0575i			0.926432i	0.886246	+	0.463216i	$0.153305\pi$
$853$			27.0575i			0.926432i	−0.886246	+	0.463216i	$0.846695\pi$
$854$		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	$-0.259174\pi$
$859$	−1.19447	−	1.19447i	−0.0407549	−	0.0407549i	−0.727191	+	0.686436i	$0.759174\pi$
$860$		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
$867$	57.5985			1.95615
$868$		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
$877$			19.8539i			0.670417i	0.942144	+	0.335209i	$0.108807\pi$
$877$			19.8539i			0.670417i	−0.942144	+	0.335209i	$0.891193\pi$
$878$		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
$883$			26.5836i			0.894609i	0.894382	+	0.447304i	$0.147616\pi$
$883$			26.5836i			0.894609i	−0.894382	+	0.447304i	$0.852384\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.53715	−	2.53715i	0.0851893	−	0.0851893i	−0.663228	−	0.748417i	$-0.730814\pi$
$887$	2.53715	−	2.53715i	0.0851893	−	0.0851893i	0.748417	+	0.663228i	$0.230814\pi$
$888$		0			0
$889$	41.3794			1.38782
$890$		0			0
$891$	16.0308	−	16.0308i	0.537051	−	0.537051i
$892$		0			0
$893$	5.15611			0.172543
$894$		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
$907$			0.472551i			0.0156908i	0.999969	+	0.00784539i	$0.00249729\pi$
$907$			0.472551i			0.0156908i	−0.999969	+	0.00784539i	$0.997503\pi$
$908$		0			0
$909$	−61.8306	−	61.8306i	−2.05079	−	2.05079i
$910$		0			0
$911$			2.03233i			0.0673340i	0.999433	+	0.0336670i	$0.0107186\pi$
$911$			2.03233i			0.0673340i	−0.999433	+	0.0336670i	$0.989281\pi$
$912$		0			0
$913$	−10.0602	−	10.0602i	−0.332943	−	0.332943i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−21.0322			−0.694544
$918$		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
$923$	1.01590			0.0334388
$924$		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
$933$		−	49.6729i		−	1.62622i
$934$		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	−0.361871	−	0.932228i	$-0.617862\pi$
$941$	17.4961	−	17.4961i	0.570357	−	0.570357i	0.932228	+	0.361871i	$0.117862\pi$
$942$		0			0
$943$	−3.45406	+	3.45406i	−0.112480	+	0.112480i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13.6441			−0.443374			−0.221687	−	0.975118i	$-0.571156\pi$
$947$	−13.6441			−0.443374			−0.221687	+	0.975118i	$0.571156\pi$
$948$		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
$957$			39.5153i			1.27735i
$958$		0			0
$959$	2.94310			0.0950377
$960$		0			0
$961$	9.17221			0.295878
$962$		0			0
$963$			6.32706i			0.203887i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	9.15383	−	9.15383i	0.294367	−	0.294367i	−0.544435	−	0.838803i	$-0.683256\pi$
$967$	9.15383	−	9.15383i	0.294367	−	0.294367i	0.838803	+	0.544435i	$0.183256\pi$
$968$		0			0
$969$	81.0133			2.60252
$970$		0			0
$971$	−10.5637	+	10.5637i	−0.339004	+	0.339004i	−0.855992	−	0.516989i	$-0.827053\pi$
$971$	−10.5637	+	10.5637i	−0.339004	+	0.339004i	0.516989	+	0.855992i	$0.327053\pi$
$972$		0			0
$973$	35.7965			1.14758
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−16.0480	+	16.0480i	−0.513420	+	0.513420i	−0.915573	−	0.402153i	$-0.868262\pi$
$977$	−16.0480	+	16.0480i	−0.513420	+	0.513420i	0.402153	+	0.915573i	$0.368262\pi$
$978$		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	$0.0170393\pi$
$983$	32.9855	+	32.9855i	1.05207	+	1.05207i	0.0535049	+	0.998568i	$0.482961\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			7.51538i			0.239217i
$988$		0			0
$989$	−2.62065	−	2.62065i	−0.0833319	−	0.0833319i
$990$		0			0
$991$			33.9183i			1.07745i	0.842481	+	0.538726i	$0.181094\pi$
$991$			33.9183i			1.07745i	−0.842481	+	0.538726i	$0.818906\pi$
$992$		0			0
$993$	−42.1561	−	42.1561i	−1.33778	−	1.33778i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−29.7497			−0.942181			−0.471090	−	0.882085i	$-0.656139\pi$
$997$	−29.7497			−0.942181			−0.471090	+	0.882085i	$0.656139\pi$
$998$		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.j.c.143.8		16
4.3	odd	2		400.2.j.c.43.7	yes	16
5.2	odd	4		1600.2.s.c.207.8		16
5.3	odd	4		1600.2.s.c.207.1		16
5.4	even	2	inner	1600.2.j.c.143.1		16
16.3	odd	4		1600.2.s.c.943.8		16
16.13	even	4		400.2.s.c.243.6	yes	16
20.3	even	4		400.2.s.c.107.3	yes	16
20.7	even	4		400.2.s.c.107.6	yes	16
20.19	odd	2		400.2.j.c.43.2	✓	16
80.3	even	4	inner	1600.2.j.c.1007.8		16
80.13	odd	4		400.2.j.c.307.2	yes	16
80.19	odd	4		1600.2.s.c.943.1		16
80.29	even	4		400.2.s.c.243.3	yes	16
80.67	even	4	inner	1600.2.j.c.1007.1		16
80.77	odd	4		400.2.j.c.307.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.c.43.2	✓	16	20.19	odd	2
400.2.j.c.43.7	yes	16	4.3	odd	2
400.2.j.c.307.2	yes	16	80.13	odd	4
400.2.j.c.307.7	yes	16	80.77	odd	4
400.2.s.c.107.3	yes	16	20.3	even	4
400.2.s.c.107.6	yes	16	20.7	even	4
400.2.s.c.243.3	yes	16	80.29	even	4
400.2.s.c.243.6	yes	16	16.13	even	4
1600.2.j.c.143.1		16	5.4	even	2	inner
1600.2.j.c.143.8		16	1.1	even	1	trivial
1600.2.j.c.1007.1		16	80.67	even	4	inner
1600.2.j.c.1007.8		16	80.3	even	4	inner
1600.2.s.c.207.1		16	5.3	odd	4
1600.2.s.c.207.8		16	5.2	odd	4
1600.2.s.c.943.1		16	80.19	odd	4
1600.2.s.c.943.8		16	16.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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