LMFDB - Embedded newform 1152.2.w.a.431.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(143,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4]))

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

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

chi := DirichletCharacter("1152.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.w (of order $8$, degree $4$, 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:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			431.6
Character	$\chi$	$=$	1152.431
Dual form			1152.2.w.a.719.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64859 - 0.682869i) q^{5} +(-2.51270 - 2.51270i) q^{7} +O(q^{10})$	$q+(1.64859 - 0.682869i) q^{5} +(-2.51270 - 2.51270i) q^{7} +(-2.69097 + 1.11464i) q^{11} +(-1.76057 + 4.25040i) q^{13} -6.10169 q^{17} +(-3.43292 - 1.42196i) q^{19} +(-0.525502 - 0.525502i) q^{23} +(-1.28399 + 1.28399i) q^{25} +(1.46544 - 3.53788i) q^{29} +7.55322i q^{31} +(-5.85826 - 2.42657i) q^{35} +(2.30333 + 5.56073i) q^{37} +(3.04402 - 3.04402i) q^{41} +(3.31422 + 8.00123i) q^{43} +8.59875i q^{47} +5.62732i q^{49} +(-3.78946 - 9.14856i) q^{53} +(-3.67516 + 3.67516i) q^{55} +(-3.73387 - 9.01437i) q^{59} +(3.41173 + 1.41318i) q^{61} +8.20941i q^{65} +(-0.0538792 + 0.130076i) q^{67} +(-1.31641 + 1.31641i) q^{71} +(-10.9226 - 10.9226i) q^{73} +(9.56234 + 3.96085i) q^{77} -11.8735 q^{79} +(4.38490 - 10.5861i) q^{83} +(-10.0592 + 4.16666i) q^{85} +(-5.97566 - 5.97566i) q^{89} +(15.1038 - 6.25618i) q^{91} -6.63051 q^{95} -3.21530 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95}+O(q^{100}) $ 32 * q - 8 * q^11 + 16 * q^29 + 24 * q^35 + 16 * q^53 + 32 * q^55 + 32 * q^59 + 32 * q^61 + 16 * q^67 + 16 * q^71 + 16 * q^77 + 32 * q^79 - 40 * q^83 + 48 * q^91 - 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.64859	−	0.682869i	0.737273	−	0.305388i	0.0177359	−	0.999843i	$-0.494354\pi$
$5$	1.64859	−	0.682869i	0.737273	−	0.305388i	0.719537	+	0.694454i	$0.244354\pi$
$6$		0			0
$7$	−2.51270	−	2.51270i	−0.949711	−	0.949711i	0.0490835	−	0.998795i	$-0.484370\pi$
$7$	−2.51270	−	2.51270i	−0.949711	−	0.949711i	−0.998795	+	0.0490835i	$0.984370\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.69097	+	1.11464i	−0.811357	+	0.336075i	−0.749495	−	0.662010i	$-0.769704\pi$
$11$	−2.69097	+	1.11464i	−0.811357	+	0.336075i	−0.0618618	+	0.998085i	$0.519704\pi$
$12$		0			0
$13$	−1.76057	+	4.25040i	−0.488295	+	1.17885i	0.467283	+	0.884108i	$0.345233\pi$
$13$	−1.76057	+	4.25040i	−0.488295	+	1.17885i	−0.955577	+	0.294740i	$0.904767\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.10169			−1.47988			−0.739939	−	0.672674i	$-0.765146\pi$
$17$	−6.10169			−1.47988			−0.739939	+	0.672674i	$0.765146\pi$
$18$		0			0
$19$	−3.43292	−	1.42196i	−0.787567	−	0.326221i	−0.0476020	−	0.998866i	$-0.515158\pi$
$19$	−3.43292	−	1.42196i	−0.787567	−	0.326221i	−0.739965	+	0.672645i	$0.765158\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.525502	−	0.525502i	−0.109575	−	0.109575i	0.650194	−	0.759768i	$-0.274688\pi$
$23$	−0.525502	−	0.525502i	−0.109575	−	0.109575i	−0.759768	+	0.650194i	$0.774688\pi$
$24$		0			0
$25$	−1.28399	+	1.28399i	−0.256798	+	0.256798i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.46544	−	3.53788i	0.272125	−	0.656967i	−0.727449	−	0.686162i	$-0.759294\pi$
$29$	1.46544	−	3.53788i	0.272125	−	0.656967i	0.999574	+	0.0291945i	$0.00929421\pi$
$30$		0			0
$31$			7.55322i			1.35660i	0.734786	+	0.678299i	$0.237283\pi$
$31$			7.55322i			1.35660i	−0.734786	+	0.678299i	$0.762717\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.85826	−	2.42657i	−0.990227	−	0.410165i
$36$		0			0
$37$	2.30333	+	5.56073i	0.378665	+	0.914178i	0.992217	+	0.124523i	$0.0397402\pi$
$37$	2.30333	+	5.56073i	0.378665	+	0.914178i	−0.613552	+	0.789655i	$0.710260\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.04402	−	3.04402i	0.475396	−	0.475396i	−0.428260	−	0.903656i	$-0.640873\pi$
$41$	3.04402	−	3.04402i	0.475396	−	0.475396i	0.903656	+	0.428260i	$0.140873\pi$
$42$		0			0
$43$	3.31422	+	8.00123i	0.505414	+	1.22018i	0.946498	+	0.322711i	$0.104594\pi$
$43$	3.31422	+	8.00123i	0.505414	+	1.22018i	−0.441084	+	0.897466i	$0.645406\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			8.59875i			1.25426i	0.778916	+	0.627128i	$0.215770\pi$
$47$			8.59875i			1.25426i	−0.778916	+	0.627128i	$0.784230\pi$
$48$		0			0
$49$			5.62732i			0.803903i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.78946	−	9.14856i	−0.520522	−	1.25665i	−0.937580	−	0.347771i	$-0.886939\pi$
$53$	−3.78946	−	9.14856i	−0.520522	−	1.25665i	0.417058	−	0.908880i	$-0.363061\pi$
$54$		0			0
$55$	−3.67516	+	3.67516i	−0.495558	+	0.495558i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.73387	−	9.01437i	−0.486109	−	1.17357i	−0.956662	−	0.291199i	$-0.905946\pi$
$59$	−3.73387	−	9.01437i	−0.486109	−	1.17357i	0.470553	−	0.882372i	$-0.344054\pi$
$60$		0			0
$61$	3.41173	+	1.41318i	0.436827	+	0.180940i	0.590249	−	0.807221i	$-0.299030\pi$
$61$	3.41173	+	1.41318i	0.436827	+	0.180940i	−0.153422	+	0.988161i	$0.549030\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			8.20941i			1.01825i
$66$		0			0
$67$	−0.0538792	+	0.130076i	−0.00658239	+	0.0158913i	−0.927137	−	0.374724i	$-0.877738\pi$
$67$	−0.0538792	+	0.130076i	−0.00658239	+	0.0158913i	0.920554	+	0.390615i	$0.127738\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.31641	+	1.31641i	−0.156229	+	0.156229i	−0.780893	−	0.624664i	$-0.785236\pi$
$71$	−1.31641	+	1.31641i	−0.156229	+	0.156229i	0.624664	+	0.780893i	$0.285236\pi$
$72$		0			0
$73$	−10.9226	−	10.9226i	−1.27839	−	1.27839i	−0.941566	−	0.336829i	$-0.890646\pi$
$73$	−10.9226	−	10.9226i	−1.27839	−	1.27839i	−0.336829	−	0.941566i	$-0.609354\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.56234	+	3.96085i	1.08973	+	0.451381i
$78$		0			0
$79$	−11.8735			−1.33588			−0.667939	−	0.744216i	$-0.732823\pi$
$79$	−11.8735			−1.33588			−0.667939	+	0.744216i	$0.732823\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.38490	−	10.5861i	0.481305	−	1.16197i	−0.477684	−	0.878532i	$-0.658524\pi$
$83$	4.38490	−	10.5861i	0.481305	−	1.16197i	0.958989	−	0.283442i	$-0.0914763\pi$
$84$		0			0
$85$	−10.0592	+	4.16666i	−1.09107	+	0.451937i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.97566	−	5.97566i	−0.633418	−	0.633418i	0.315506	−	0.948924i	$-0.397826\pi$
$89$	−5.97566	−	5.97566i	−0.633418	−	0.633418i	−0.948924	+	0.315506i	$0.897826\pi$
$90$		0			0
$91$	15.1038	−	6.25618i	1.58330	−	0.655826i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−6.63051			−0.680276
$96$		0			0
$97$	−3.21530			−0.326464			−0.163232	−	0.986588i	$-0.552192\pi$
$97$	−3.21530			−0.326464			−0.163232	+	0.986588i	$0.552192\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.62739	−	0.674085i	0.161931	−	0.0670740i	−0.300246	−	0.953862i	$-0.597069\pi$
$101$	1.62739	−	0.674085i	0.161931	−	0.0670740i	0.462177	+	0.886788i	$0.347069\pi$
$102$		0			0
$103$	−0.111372	−	0.111372i	−0.0109738	−	0.0109738i	0.701599	−	0.712572i	$-0.252470\pi$
$103$	−0.111372	−	0.111372i	−0.0109738	−	0.0109738i	−0.712572	+	0.701599i	$0.752470\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.59142	−	1.48762i	0.347196	−	0.143813i	−0.202269	−	0.979330i	$-0.564832\pi$
$107$	3.59142	−	1.48762i	0.347196	−	0.143813i	0.549465	+	0.835517i	$0.314832\pi$
$108$		0			0
$109$	5.90637	−	14.2592i	0.565727	−	1.36579i	−0.339398	−	0.940643i	$-0.610223\pi$
$109$	5.90637	−	14.2592i	0.565727	−	1.36579i	0.905126	−	0.425144i	$-0.139777\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−16.6022			−1.56180			−0.780902	−	0.624653i	$-0.785240\pi$
$113$	−16.6022			−1.56180			−0.780902	+	0.624653i	$0.785240\pi$
$114$		0			0
$115$	−1.22519	−	0.507489i	−0.114249	−	0.0473236i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	15.3317	+	15.3317i	1.40546	+	1.40546i
$120$		0			0
$121$	−1.77928	+	1.77928i	−0.161753	+	0.161753i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.65432	+	11.2365i	−0.416295	+	1.00503i
$126$		0			0
$127$			19.5462i			1.73444i	0.497923	+	0.867221i	$0.334096\pi$
$127$			19.5462i			1.73444i	−0.497923	+	0.867221i	$0.665904\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.97269	−	2.47397i	−0.521837	−	0.216152i	0.106187	−	0.994346i	$-0.466136\pi$
$131$	−5.97269	−	2.47397i	−0.521837	−	0.216152i	−0.628023	+	0.778194i	$0.716136\pi$
$132$		0			0
$133$	5.05294	+	12.1989i	0.438145	+	1.05778i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−13.9438	+	13.9438i	−1.19130	+	1.19130i	−0.214594	+	0.976703i	$0.568843\pi$
$137$	−13.9438	+	13.9438i	−1.19130	+	1.19130i	−0.976703	+	0.214594i	$0.931157\pi$
$138$		0			0
$139$	−5.10923	−	12.3348i	−0.433359	−	1.04622i	−0.978197	−	0.207680i	$-0.933409\pi$
$139$	−5.10923	−	12.3348i	−0.433359	−	1.04622i	0.544838	−	0.838542i	$-0.316591\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	13.4001i		−	1.12057i
$144$		0			0
$145$		−	6.83322i		−	0.567468i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.29028	−	3.11502i	−0.105704	−	0.255192i	0.862174	−	0.506612i	$-0.169102\pi$
$149$	−1.29028	−	3.11502i	−0.105704	−	0.255192i	−0.967878	+	0.251420i	$0.919102\pi$
$150$		0			0
$151$	10.0537	−	10.0537i	0.818159	−	0.818159i	−0.167682	−	0.985841i	$-0.553628\pi$
$151$	10.0537	−	10.0537i	0.818159	−	0.818159i	0.985841	+	0.167682i	$0.0536281\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.15786	+	12.4522i	0.414289	+	1.00018i
$156$		0			0
$157$	15.3765	+	6.36916i	1.22718	+	0.508315i	0.899686	−	0.436539i	$-0.143796\pi$
$157$	15.3765	+	6.36916i	1.22718	+	0.508315i	0.327494	+	0.944853i	$0.393796\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			2.64086i			0.208129i
$162$		0			0
$163$	−4.22080	+	10.1899i	−0.330599	+	0.798136i	0.667946	+	0.744210i	$0.267174\pi$
$163$	−4.22080	+	10.1899i	−0.330599	+	0.798136i	−0.998545	+	0.0539266i	$0.982826\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.1209	−	11.1209i	0.860562	−	0.860562i	−0.130842	−	0.991403i	$-0.541768\pi$
$167$	11.1209	−	11.1209i	0.860562	−	0.860562i	0.991403	+	0.130842i	$0.0417679\pi$
$168$		0			0
$169$	−5.77387	−	5.77387i	−0.444144	−	0.444144i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.66463	+	4.00322i	0.734788	+	0.304359i	0.718518	−	0.695509i	$-0.244821\pi$
$173$	9.66463	+	4.00322i	0.734788	+	0.304359i	0.0162700	+	0.999868i	$0.494821\pi$
$174$		0			0
$175$	6.45256			0.487768
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.65549	−	16.0678i	0.497455	−	1.20096i	−0.453395	−	0.891310i	$-0.649787\pi$
$179$	6.65549	−	16.0678i	0.497455	−	1.20096i	0.950850	−	0.309652i	$-0.100213\pi$
$180$		0			0
$181$	−16.5604	+	6.85953i	−1.23092	+	0.509865i	−0.900867	−	0.434096i	$-0.857068\pi$
$181$	−16.5604	+	6.85953i	−1.23092	+	0.509865i	−0.330056	+	0.943961i	$0.607068\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	7.59450	+	7.59450i	0.558359	+	0.558359i
$186$		0			0
$187$	16.4195	−	6.80116i	1.20071	−	0.497350i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.545506			0.0394715			0.0197357	−	0.999805i	$-0.493718\pi$
$191$	0.545506			0.0394715			0.0197357	+	0.999805i	$0.493718\pi$
$192$		0			0
$193$	13.7484			0.989632			0.494816	−	0.868998i	$-0.335235\pi$
$193$	13.7484			0.989632			0.494816	+	0.868998i	$0.335235\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.74434	−	1.55095i	0.266773	−	0.110501i	−0.245288	−	0.969450i	$-0.578882\pi$
$197$	3.74434	−	1.55095i	0.266773	−	0.110501i	0.512060	+	0.858949i	$0.328882\pi$
$198$		0			0
$199$	−9.72904	−	9.72904i	−0.689673	−	0.689673i	0.272486	−	0.962160i	$-0.412154\pi$
$199$	−9.72904	−	9.72904i	−0.689673	−	0.689673i	−0.962160	+	0.272486i	$0.912154\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−12.5718	+	5.20742i	−0.882369	+	0.365489i
$204$		0			0
$205$	2.93968	−	7.09701i	0.205316	−	0.495677i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	10.8229			0.748633
$210$		0			0
$211$	−12.8221	−	5.31108i	−0.882708	−	0.365630i	−0.105162	−	0.994455i	$-0.533536\pi$
$211$	−12.8221	−	5.31108i	−0.882708	−	0.365630i	−0.777546	+	0.628826i	$0.783536\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	10.9276	+	10.9276i	0.745255	+	0.745255i
$216$		0			0
$217$	18.9790	−	18.9790i	1.28838	−	1.28838i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	10.7425	−	25.9346i	0.722616	−	1.74455i
$222$		0			0
$223$		−	11.9519i		−	0.800361i	−0.916436	−	0.400180i	$-0.868947\pi$
$223$		−	11.9519i		−	0.800361i	0.916436	−	0.400180i	$-0.131053\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.57146	−	3.13620i	−0.502536	−	0.208157i	0.116991	−	0.993133i	$-0.462675\pi$
$227$	−7.57146	−	3.13620i	−0.502536	−	0.208157i	−0.619526	+	0.784976i	$0.712675\pi$
$228$		0			0
$229$	−4.36683	−	10.5425i	−0.288568	−	0.696665i	0.711413	−	0.702774i	$-0.248055\pi$
$229$	−4.36683	−	10.5425i	−0.288568	−	0.696665i	−0.999981	+	0.00610879i	$0.998055\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	16.6048	−	16.6048i	1.08782	−	1.08782i	0.0920662	−	0.995753i	$-0.470653\pi$
$233$	16.6048	−	16.6048i	1.08782	−	1.08782i	0.995753	−	0.0920662i	$-0.0293472\pi$
$234$		0			0
$235$	5.87182	+	14.1758i	0.383035	+	0.924729i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			19.8212i			1.28213i	0.767488	+	0.641063i	$0.221506\pi$
$239$			19.8212i			1.28213i	−0.767488	+	0.641063i	$0.778494\pi$
$240$		0			0
$241$			7.78762i			0.501645i	0.968033	+	0.250823i	$0.0807011\pi$
$241$			7.78762i			0.501645i	−0.968033	+	0.250823i	$0.919299\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.84272	+	9.27715i	0.245503	+	0.592695i
$246$		0			0
$247$	12.0878	−	12.0878i	0.769130	−	0.769130i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	11.1471	+	26.9114i	0.703597	+	1.69863i	0.715412	+	0.698703i	$0.246239\pi$
$251$	11.1471	+	26.9114i	0.703597	+	1.69863i	−0.0118144	+	0.999930i	$0.503761\pi$
$252$		0			0
$253$	1.99985	+	0.828365i	0.125729	+	0.0520789i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			6.18232i			0.385643i	0.981234	+	0.192821i	$0.0617638\pi$
$257$			6.18232i			0.385643i	−0.981234	+	0.192821i	$0.938236\pi$
$258$		0			0
$259$	8.18487	−	19.7600i	0.508583	−	1.22783i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.98771	+	2.98771i	−0.184230	+	0.184230i	−0.793196	−	0.608966i	$-0.791584\pi$
$263$	−2.98771	+	2.98771i	−0.184230	+	0.184230i	0.608966	+	0.793196i	$0.291584\pi$
$264$		0			0
$265$	−12.4945	−	12.4945i	−0.767533	−	0.767533i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	14.2963	+	5.92170i	0.871658	+	0.361053i	0.773256	−	0.634094i	$-0.218627\pi$
$269$	14.2963	+	5.92170i	0.871658	+	0.361053i	0.0984022	+	0.995147i	$0.468627\pi$
$270$		0			0
$271$	4.23625			0.257334			0.128667	−	0.991688i	$-0.458930\pi$
$271$	4.23625			0.257334			0.128667	+	0.991688i	$0.458930\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.02399	−	4.88635i	0.122051	−	0.294658i
$276$		0			0
$277$	1.63206	−	0.676023i	0.0980612	−	0.0406183i	−0.333114	−	0.942887i	$-0.608099\pi$
$277$	1.63206	−	0.676023i	0.0980612	−	0.0406183i	0.431175	+	0.902268i	$0.358099\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.648281	−	0.648281i	−0.0386732	−	0.0386732i	0.687506	−	0.726179i	$-0.258706\pi$
$281$	−0.648281	−	0.648281i	−0.0386732	−	0.0386732i	−0.726179	+	0.687506i	$0.758706\pi$
$282$		0			0
$283$	0.905971	−	0.375265i	0.0538544	−	0.0223072i	−0.355594	−	0.934641i	$-0.615721\pi$
$283$	0.905971	−	0.375265i	0.0538544	−	0.0223072i	0.409448	+	0.912333i	$0.365721\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−15.2974			−0.902978
$288$		0			0
$289$	20.2306			1.19004
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.85498	+	1.59678i	−0.225210	+	0.0932851i	−0.492435	−	0.870349i	$-0.663893\pi$
$293$	−3.85498	+	1.59678i	−0.225210	+	0.0932851i	0.267225	+	0.963634i	$0.413893\pi$
$294$		0			0
$295$	−12.3113	−	12.3113i	−0.716790	−	0.716790i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.15877	−	1.30841i	0.182677	−	0.0756671i
$300$		0			0
$301$	11.7771	−	28.4323i	0.678818	−	1.63881i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6.58956			0.377317
$306$		0			0
$307$	4.77567	+	1.97815i	0.272562	+	0.112899i	0.514778	−	0.857323i	$-0.327874\pi$
$307$	4.77567	+	1.97815i	0.272562	+	0.112899i	−0.242216	+	0.970222i	$0.577874\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.85083	−	5.85083i	−0.331770	−	0.331770i	0.521488	−	0.853258i	$-0.325377\pi$
$311$	−5.85083	−	5.85083i	−0.331770	−	0.331770i	−0.853258	+	0.521488i	$0.825377\pi$
$312$		0			0
$313$	−9.37980	+	9.37980i	−0.530178	+	0.530178i	−0.920625	−	0.390448i	$-0.872320\pi$
$313$	−9.37980	+	9.37980i	−0.530178	+	0.530178i	0.390448	+	0.920625i	$0.372320\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.45951	+	18.0089i	−0.418968	+	1.01148i	0.563679	+	0.825994i	$0.309385\pi$
$317$	−7.45951	+	18.0089i	−0.418968	+	1.01148i	−0.982647	+	0.185484i	$0.940615\pi$
$318$		0			0
$319$			11.1537i			0.624490i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	20.9466	+	8.67638i	1.16550	+	0.482767i
$324$		0			0
$325$	−3.19691	−	7.71802i	−0.177333	−	0.428119i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	21.6061	−	21.6061i	1.19118	−	1.19118i
$330$		0			0
$331$	2.04504	+	4.93715i	0.112405	+	0.271370i	0.970064	−	0.242849i	$-0.0780818\pi$
$331$	2.04504	+	4.93715i	0.112405	+	0.271370i	−0.857659	+	0.514219i	$0.828082\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			0.251234i			0.0137264i
$336$		0			0
$337$			32.7329i			1.78308i	0.452946	+	0.891538i	$0.350373\pi$
$337$			32.7329i			1.78308i	−0.452946	+	0.891538i	$0.649627\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8.41908	−	20.3255i	−0.455919	−	1.10069i
$342$		0			0
$343$	−3.44913	+	3.44913i	−0.186236	+	0.186236i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.0545	−	24.2737i	−0.539755	−	1.30308i	−0.924894	−	0.380225i	$-0.875847\pi$
$347$	−10.0545	−	24.2737i	−0.539755	−	1.30308i	0.385140	−	0.922858i	$-0.374153\pi$
$348$		0			0
$349$	−7.53157	−	3.11968i	−0.403156	−	0.166993i	0.171886	−	0.985117i	$-0.445014\pi$
$349$	−7.53157	−	3.11968i	−0.403156	−	0.166993i	−0.575041	+	0.818124i	$0.695014\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			14.4403i			0.768579i	0.923213	+	0.384290i	$0.125554\pi$
$353$			14.4403i			0.768579i	−0.923213	+	0.384290i	$0.874446\pi$
$354$		0			0
$355$	−1.27128	+	3.06915i	−0.0674728	+	0.162894i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.26776	+	1.26776i	−0.0669099	+	0.0669099i	−0.739770	−	0.672860i	$-0.765066\pi$
$359$	−1.26776	+	1.26776i	−0.0669099	+	0.0669099i	0.672860	+	0.739770i	$0.265066\pi$
$360$		0			0
$361$	−3.67204	−	3.67204i	−0.193265	−	0.193265i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−25.4656	−	10.5482i	−1.33293	−	0.552119i
$366$		0			0
$367$	0.516344			0.0269529			0.0134765	−	0.999909i	$-0.495710\pi$
$367$	0.516344			0.0269529			0.0134765	+	0.999909i	$0.495710\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−13.4658	+	32.5093i	−0.699110	+	1.68780i
$372$		0			0
$373$	15.7829	−	6.53747i	0.817205	−	0.338498i	0.0653805	−	0.997860i	$-0.479174\pi$
$373$	15.7829	−	6.53747i	0.817205	−	0.338498i	0.751825	+	0.659363i	$0.229174\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.4574	+	12.4574i	0.641587	+	0.641587i
$378$		0			0
$379$	−10.1190	+	4.19144i	−0.519780	+	0.215300i	−0.627120	−	0.778922i	$-0.715767\pi$
$379$	−10.1190	+	4.19144i	−0.519780	+	0.215300i	0.107340	+	0.994222i	$0.465767\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−10.5915			−0.541201			−0.270601	−	0.962692i	$-0.587222\pi$
$383$	−10.5915			−0.541201			−0.270601	+	0.962692i	$0.587222\pi$
$384$		0			0
$385$	18.4691			0.941274
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.74428	+	4.03621i	−0.494054	+	0.204644i	−0.615778	−	0.787920i	$-0.711158\pi$
$389$	−9.74428	+	4.03621i	−0.494054	+	0.204644i	0.121723	+	0.992564i	$0.461158\pi$
$390$		0			0
$391$	3.20645	+	3.20645i	0.162157	+	0.162157i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−19.5746	+	8.10808i	−0.984906	+	0.407962i
$396$		0			0
$397$	−6.26413	+	15.1230i	−0.314388	+	0.759000i	0.685144	+	0.728408i	$0.259739\pi$
$397$	−6.26413	+	15.1230i	−0.314388	+	0.759000i	−0.999532	+	0.0305919i	$0.990261\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.54016			−0.476413			−0.238207	−	0.971215i	$-0.576560\pi$
$401$	−9.54016			−0.476413			−0.238207	+	0.971215i	$0.576560\pi$
$402$		0			0
$403$	−32.1042	−	13.2980i	−1.59922	−	0.662420i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−12.3964	−	12.3964i	−0.614465	−	0.614465i
$408$		0			0
$409$	−9.43887	+	9.43887i	−0.466722	+	0.466722i	−0.900851	−	0.434129i	$-0.857056\pi$
$409$	−9.43887	+	9.43887i	−0.466722	+	0.466722i	0.434129	+	0.900851i	$0.357056\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−13.2683	+	32.0325i	−0.652890	+	1.57622i
$414$		0			0
$415$		−	20.4464i		−	1.00368i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	18.2081	+	7.54205i	0.889525	+	0.368453i	0.780183	−	0.625551i	$-0.215126\pi$
$419$	18.2081	+	7.54205i	0.889525	+	0.368453i	0.109342	+	0.994004i	$0.465126\pi$
$420$		0			0
$421$	7.63758	+	18.4387i	0.372233	+	0.898649i	0.993371	+	0.114949i	$0.0366704\pi$
$421$	7.63758	+	18.4387i	0.372233	+	0.898649i	−0.621139	+	0.783701i	$0.713330\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	7.83451	−	7.83451i	0.380029	−	0.380029i
$426$		0			0
$427$	−5.02174	−	12.1235i	−0.243019	−	0.586700i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	15.7171i		−	0.757067i	−0.925588	−	0.378534i	$-0.876428\pi$
$431$		−	15.7171i		−	0.757067i	0.925588	−	0.378534i	$-0.123572\pi$
$432$		0			0
$433$		−	2.04349i		−	0.0982041i	−0.998794	−	0.0491020i	$-0.984364\pi$
$433$		−	2.04349i		−	0.0982041i	0.998794	−	0.0491020i	$-0.0156360\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.05676	+	2.55125i	0.0505518	+	0.122043i
$438$		0			0
$439$	8.47375	−	8.47375i	0.404430	−	0.404430i	−0.475361	−	0.879791i	$-0.657682\pi$
$439$	8.47375	−	8.47375i	0.404430	−	0.404430i	0.879791	+	0.475361i	$0.157682\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	12.8153	+	30.9388i	0.608873	+	1.46995i	0.864228	+	0.503101i	$0.167808\pi$
$443$	12.8153	+	30.9388i	0.608873	+	1.46995i	−0.255355	+	0.966847i	$0.582192\pi$
$444$		0			0
$445$	−13.9320	−	5.77083i	−0.660440	−	0.273563i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	19.7880i		−	0.933851i	−0.884297	−	0.466926i	$-0.845362\pi$
$449$		−	19.7880i		−	0.933851i	0.884297	−	0.466926i	$-0.154638\pi$
$450$		0			0
$451$	−4.79839	+	11.5843i	−0.225947	+	0.545485i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	20.6278	−	20.6278i	0.967045	−	0.967045i
$456$		0			0
$457$	9.46165	+	9.46165i	0.442597	+	0.442597i	0.892884	−	0.450287i	$-0.148678\pi$
$457$	9.46165	+	9.46165i	0.442597	+	0.442597i	−0.450287	+	0.892884i	$0.648678\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	8.16779	+	3.38321i	0.380412	+	0.157572i	0.564691	−	0.825302i	$-0.308995\pi$
$461$	8.16779	+	3.38321i	0.380412	+	0.157572i	−0.184280	+	0.982874i	$0.558995\pi$
$462$		0			0
$463$	39.2301			1.82318			0.911590	−	0.411101i	$-0.134856\pi$
$463$	39.2301			1.82318			0.911590	+	0.411101i	$0.134856\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.94459	−	16.7657i	0.321357	−	0.775825i	−0.677818	−	0.735230i	$-0.737074\pi$
$467$	6.94459	−	16.7657i	0.321357	−	0.775825i	0.999176	−	0.0405959i	$-0.0129256\pi$
$468$		0			0
$469$	0.462224	−	0.191459i	0.0213435	−	0.00884078i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−17.8369	−	17.8369i	−0.820142	−	0.820142i
$474$		0			0
$475$	6.23363	−	2.58205i	0.286018	−	0.118473i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	10.6817			0.488058			0.244029	−	0.969768i	$-0.421531\pi$
$479$	10.6817			0.488058			0.244029	+	0.969768i	$0.421531\pi$
$480$		0			0
$481$	−27.6905			−1.26258
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5.30071	+	2.19563i	−0.240693	+	0.0996983i
$486$		0			0
$487$	7.67417	+	7.67417i	0.347750	+	0.347750i	0.859271	−	0.511521i	$-0.170918\pi$
$487$	7.67417	+	7.67417i	0.347750	+	0.347750i	−0.511521	+	0.859271i	$0.670918\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	38.6885	−	16.0253i	1.74599	−	0.723212i	0.747744	−	0.663987i	$-0.231137\pi$
$491$	38.6885	−	16.0253i	1.74599	−	0.723212i	0.998245	−	0.0592250i	$-0.0188629\pi$
$492$		0			0
$493$	−8.94164	+	21.5870i	−0.402711	+	0.972231i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.61547			0.296745
$498$		0			0
$499$	−18.1565	−	7.52067i	−0.812797	−	0.336671i	−0.0627275	−	0.998031i	$-0.519980\pi$
$499$	−18.1565	−	7.52067i	−0.812797	−	0.336671i	−0.750069	+	0.661359i	$0.769980\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−20.9341	−	20.9341i	−0.933405	−	0.933405i	0.0645124	−	0.997917i	$-0.479451\pi$
$503$	−20.9341	−	20.9341i	−0.933405	−	0.933405i	−0.997917	+	0.0645124i	$0.979451\pi$
$504$		0			0
$505$	2.22258	−	2.22258i	0.0989036	−	0.0989036i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.399075	+	0.963453i	−0.0176887	+	0.0427043i	−0.932477	−	0.361229i	$-0.882357\pi$
$509$	−0.399075	+	0.963453i	−0.0176887	+	0.0427043i	0.914788	+	0.403933i	$0.132357\pi$
$510$		0			0
$511$			54.8905i			2.42821i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.259658	−	0.107554i	−0.0114419	−	0.00473940i
$516$		0			0
$517$	−9.58447	−	23.1390i	−0.421525	−	1.01765i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−3.86359	+	3.86359i	−0.169267	+	0.169267i	−0.786657	−	0.617390i	$-0.788190\pi$
$521$	−3.86359	+	3.86359i	−0.169267	+	0.169267i	0.617390	+	0.786657i	$0.288190\pi$
$522$		0			0
$523$	8.40221	+	20.2847i	0.367403	+	0.886989i	0.994174	+	0.107786i	$0.0343761\pi$
$523$	8.40221	+	20.2847i	0.367403	+	0.886989i	−0.626771	+	0.779203i	$0.715624\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	46.0874i		−	2.00760i
$528$		0			0
$529$		−	22.4477i		−	0.975987i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	7.57908	+	18.2975i	0.328286	+	0.792553i
$534$		0			0
$535$	4.90494	−	4.90494i	0.212059	−	0.212059i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−6.27241	−	15.1429i	−0.270172	−	0.652252i
$540$		0			0
$541$	0.504857	+	0.209119i	0.0217055	+	0.00899071i	0.393510	−	0.919320i	$-0.371261\pi$
$541$	0.504857	+	0.209119i	0.0217055	+	0.00899071i	−0.371804	+	0.928311i	$0.621261\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	27.5409i		−	1.17972i
$546$		0			0
$547$	−11.9972	+	28.9639i	−0.512964	+	1.23841i	0.429186	+	0.903216i	$0.358800\pi$
$547$	−11.9972	+	28.9639i	−0.512964	+	1.23841i	−0.942151	+	0.335190i	$0.891200\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−10.0615	+	10.0615i	−0.428633	+	0.428633i
$552$		0			0
$553$	29.8347	+	29.8347i	1.26870	+	1.26870i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−3.31995	−	1.37517i	−0.140671	−	0.0582677i	0.311238	−	0.950332i	$-0.399257\pi$
$557$	−3.31995	−	1.37517i	−0.140671	−	0.0582677i	−0.451908	+	0.892064i	$0.649257\pi$
$558$		0			0
$559$	−39.8433			−1.68519
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−3.47196	+	8.38204i	−0.146325	+	0.353261i	−0.980001	−	0.198994i	$-0.936233\pi$
$563$	−3.47196	+	8.38204i	−0.146325	+	0.353261i	0.833675	+	0.552255i	$0.186233\pi$
$564$		0			0
$565$	−27.3703	+	11.3371i	−1.15148	+	0.476957i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.72691	+	2.72691i	0.114318	+	0.114318i	0.761952	−	0.647634i	$-0.224241\pi$
$569$	2.72691	+	2.72691i	0.114318	+	0.114318i	−0.647634	+	0.761952i	$0.724241\pi$
$570$		0			0
$571$	−30.8517	+	12.7792i	−1.29110	+	0.534792i	−0.919314	−	0.393525i	$-0.871255\pi$
$571$	−30.8517	+	12.7792i	−1.29110	+	0.534792i	−0.371789	+	0.928317i	$0.621255\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.34948			0.0562771
$576$		0			0
$577$	−45.9313			−1.91214			−0.956072	−	0.293131i	$-0.905303\pi$
$577$	−45.9313			−1.91214			−0.956072	+	0.293131i	$0.905303\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−37.6176	+	15.5817i	−1.56064	+	0.646438i
$582$		0			0
$583$	20.3946	+	20.3946i	0.844658	+	0.844658i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.3774	−	4.71269i	0.469597	−	0.194514i	−0.135320	−	0.990802i	$-0.543206\pi$
$587$	11.3774	−	4.71269i	0.469597	−	0.194514i	0.604917	+	0.796288i	$0.293206\pi$
$588$		0			0
$589$	10.7404	−	25.9296i	0.442551	−	1.06841i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−14.4266			−0.592431			−0.296216	−	0.955121i	$-0.595725\pi$
$593$	−14.4266			−0.592431			−0.296216	+	0.955121i	$0.595725\pi$
$594$		0			0
$595$	35.7453	+	14.8062i	1.46541	+	0.606994i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−11.4738	−	11.4738i	−0.468808	−	0.468808i	0.432720	−	0.901528i	$-0.357554\pi$
$599$	−11.4738	−	11.4738i	−0.468808	−	0.468808i	−0.901528	+	0.432720i	$0.857554\pi$
$600$		0			0
$601$	−5.94470	+	5.94470i	−0.242489	+	0.242489i	−0.817879	−	0.575390i	$-0.804850\pi$
$601$	−5.94470	+	5.94470i	−0.242489	+	0.242489i	0.575390	+	0.817879i	$0.304850\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.71829	+	4.14832i	−0.0698585	+	0.168653i
$606$		0			0
$607$		−	22.8701i		−	0.928269i	−0.885765	−	0.464135i	$-0.846365\pi$
$607$		−	22.8701i		−	0.928269i	0.885765	−	0.464135i	$-0.153635\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−36.5481	−	15.1387i	−1.47858	−	0.612447i
$612$		0			0
$613$	−5.36341	−	12.9484i	−0.216626	−	0.522982i	0.777788	−	0.628526i	$-0.216342\pi$
$613$	−5.36341	−	12.9484i	−0.216626	−	0.522982i	−0.994415	+	0.105544i	$0.966342\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−20.5540	+	20.5540i	−0.827474	+	0.827474i	−0.987167	−	0.159693i	$-0.948950\pi$
$617$	−20.5540	+	20.5540i	−0.827474	+	0.827474i	0.159693	+	0.987167i	$0.448950\pi$
$618$		0			0
$619$	4.42844	+	10.6912i	0.177994	+	0.429716i	0.987546	−	0.157333i	$-0.0502896\pi$
$619$	4.42844	+	10.6912i	0.177994	+	0.429716i	−0.809551	+	0.587049i	$0.800290\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			30.0301i			1.20313i
$624$		0			0
$625$			12.6236i			0.504943i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−14.0542	−	33.9298i	−0.560378	−	1.35287i
$630$		0			0
$631$	−0.402845	+	0.402845i	−0.0160370	+	0.0160370i	−0.715080	−	0.699043i	$-0.753610\pi$
$631$	−0.402845	+	0.402845i	−0.0160370	+	0.0160370i	0.699043	+	0.715080i	$0.253610\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	13.3475	+	32.2237i	0.529678	+	1.27876i
$636$		0			0
$637$	−23.9183	−	9.90730i	−0.947679	−	0.392542i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			11.0551i			0.436649i	0.975876	+	0.218324i	$0.0700591\pi$
$641$			11.0551i			0.436649i	−0.975876	+	0.218324i	$0.929941\pi$
$642$		0			0
$643$	−10.8771	+	26.2596i	−0.428950	+	1.03558i	0.550671	+	0.834722i	$0.314372\pi$
$643$	−10.8771	+	26.2596i	−0.428950	+	1.03558i	−0.979621	+	0.200854i	$0.935628\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−3.60517	+	3.60517i	−0.141734	+	0.141734i	−0.774414	−	0.632680i	$-0.781955\pi$
$647$	−3.60517	+	3.60517i	−0.141734	+	0.141734i	0.632680	+	0.774414i	$0.281955\pi$
$648$		0			0
$649$	20.0955	+	20.0955i	0.788816	+	0.788816i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−34.1322	−	14.1380i	−1.33570	−	0.553264i	−0.403423	−	0.915014i	$-0.632180\pi$
$653$	−34.1322	−	14.1380i	−1.33570	−	0.553264i	−0.932275	+	0.361749i	$0.882180\pi$
$654$		0			0
$655$	−11.5359			−0.450746
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−17.8965	+	43.2060i	−0.697150	+	1.68307i	0.0327038	+	0.999465i	$0.489588\pi$
$659$	−17.8965	+	43.2060i	−0.697150	+	1.68307i	−0.729854	+	0.683603i	$0.760412\pi$
$660$		0			0
$661$	−3.26994	+	1.35446i	−0.127186	+	0.0526822i	−0.445369	−	0.895347i	$-0.646927\pi$
$661$	−3.26994	+	1.35446i	−0.127186	+	0.0526822i	0.318183	+	0.948029i	$0.396927\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	16.6605	+	16.6605i	0.646065	+	0.646065i
$666$		0			0
$667$	−2.62925	+	1.08907i	−0.101805	+	0.0421690i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−10.7560			−0.415232
$672$		0			0
$673$	31.8698			1.22849			0.614245	−	0.789115i	$-0.289461\pi$
$673$	31.8698			1.22849			0.614245	+	0.789115i	$0.289461\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.6153	+	5.63965i	−0.523279	+	0.216749i	−0.628657	−	0.777683i	$-0.716395\pi$
$677$	−13.6153	+	5.63965i	−0.523279	+	0.216749i	0.105378	+	0.994432i	$0.466395\pi$
$678$		0			0
$679$	8.07908	+	8.07908i	0.310047	+	0.310047i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−24.0468	+	9.96050i	−0.920124	+	0.381128i	−0.791923	−	0.610621i	$-0.790920\pi$
$683$	−24.0468	+	9.96050i	−0.920124	+	0.381128i	−0.128200	+	0.991748i	$0.540920\pi$
$684$		0			0
$685$	−13.4658	+	32.5094i	−0.514503	+	1.24212i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	45.5566			1.73557
$690$		0			0
$691$	37.6111	+	15.5790i	1.43079	+	0.592653i	0.957547	−	0.288278i	$-0.0930826\pi$
$691$	37.6111	+	15.5790i	1.43079	+	0.592653i	0.473245	+	0.880931i	$0.343083\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−16.8461	−	16.8461i	−0.639008	−	0.639008i
$696$		0			0
$697$	−18.5737	+	18.5737i	−0.703528	+	0.703528i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	9.53278	−	23.0142i	0.360048	−	0.869233i	−0.635244	−	0.772312i	$-0.719100\pi$
$701$	9.53278	−	23.0142i	0.360048	−	0.869233i	0.995292	−	0.0969216i	$-0.0308996\pi$
$702$		0			0
$703$		−	22.3648i		−	0.843505i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.78290	−	2.39536i	−0.217488	−	0.0900867i
$708$		0			0
$709$	−1.93081	−	4.66140i	−0.0725132	−	0.175062i	0.883467	−	0.468493i	$-0.155203\pi$
$709$	−1.93081	−	4.66140i	−0.0725132	−	0.175062i	−0.955980	+	0.293431i	$0.905203\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.96923	−	3.96923i	0.148649	−	0.148649i
$714$		0			0
$715$	−9.15050	−	22.0913i	−0.342209	−	0.826166i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	39.1090i		−	1.45852i	−0.684237	−	0.729260i	$-0.739865\pi$
$719$		−	39.1090i		−	1.45852i	0.684237	−	0.729260i	$-0.260135\pi$
$720$		0			0
$721$			0.559686i			0.0208438i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.66099	+	6.42420i	0.0988268	+	0.238589i
$726$		0			0
$727$	−17.8274	+	17.8274i	−0.661183	+	0.661183i	−0.955659	−	0.294476i	$-0.904855\pi$
$727$	−17.8274	+	17.8274i	−0.661183	+	0.661183i	0.294476	+	0.955659i	$0.404855\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−20.2223	−	48.8210i	−0.747950	−	1.80571i
$732$		0			0
$733$	3.09283	+	1.28109i	0.114236	+	0.0473182i	0.439070	−	0.898453i	$-0.355308\pi$
$733$	3.09283	+	1.28109i	0.114236	+	0.0473182i	−0.324833	+	0.945771i	$0.605308\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	0.410086i		−	0.0151057i
$738$		0			0
$739$	8.57114	−	20.6926i	0.315295	−	0.761188i	−0.684197	−	0.729297i	$-0.739847\pi$
$739$	8.57114	−	20.6926i	0.315295	−	0.761188i	0.999491	−	0.0318910i	$-0.0101529\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−30.6030	+	30.6030i	−1.12272	+	1.12272i	−0.131384	+	0.991332i	$0.541942\pi$
$743$	−30.6030	+	30.6030i	−1.12272	+	1.12272i	−0.991332	+	0.131384i	$0.958058\pi$
$744$		0			0
$745$	−4.25430	−	4.25430i	−0.155866	−	0.155866i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−12.7621	−	5.28623i	−0.466317	−	0.193155i
$750$		0			0
$751$	9.79523			0.357433			0.178716	−	0.983901i	$-0.442806\pi$
$751$	9.79523			0.357433			0.178716	+	0.983901i	$0.442806\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	9.70910	−	23.4398i	0.353350	−	0.853063i
$756$		0			0
$757$	10.1531	−	4.20556i	0.369021	−	0.152854i	−0.190463	−	0.981694i	$-0.560999\pi$
$757$	10.1531	−	4.20556i	0.369021	−	0.152854i	0.559485	+	0.828841i	$0.310999\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−19.7195	−	19.7195i	−0.714832	−	0.714832i	0.252710	−	0.967542i	$-0.418678\pi$
$761$	−19.7195	−	19.7195i	−0.714832	−	0.714832i	−0.967542	+	0.252710i	$0.918678\pi$
$762$		0			0
$763$	−50.6701	+	20.9882i	−1.83438	+	0.759825i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	44.8884			1.62083
$768$		0			0
$769$	−11.6440			−0.419894			−0.209947	−	0.977713i	$-0.567329\pi$
$769$	−11.6440			−0.419894			−0.209947	+	0.977713i	$0.567329\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	32.6494	−	13.5238i	1.17432	−	0.486418i	0.291700	−	0.956510i	$-0.405779\pi$
$773$	32.6494	−	13.5238i	1.17432	−	0.486418i	0.882617	+	0.470092i	$0.155779\pi$
$774$		0			0
$775$	−9.69825	−	9.69825i	−0.348372	−	0.348372i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−14.7784	+	6.12140i	−0.529490	+	0.219322i
$780$		0			0
$781$	2.07510	−	5.00972i	0.0742528	−	0.179262i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	29.6989			1.06000
$786$		0			0
$787$	−4.72873	−	1.95870i	−0.168561	−	0.0698203i	0.296807	−	0.954937i	$-0.404078\pi$
$787$	−4.72873	−	1.95870i	−0.168561	−	0.0698203i	−0.465368	+	0.885117i	$0.654078\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	41.7164	+	41.7164i	1.48326	+	1.48326i
$792$		0			0
$793$	−12.0132	+	12.0132i	−0.426600	+	0.426600i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.47493	+	3.56079i	−0.0522447	+	0.126130i	−0.947847	−	0.318726i	$-0.896745\pi$
$797$	−1.47493	+	3.56079i	−0.0522447	+	0.126130i	0.895602	+	0.444856i	$0.146745\pi$
$798$		0			0
$799$		−	52.4669i		−	1.85615i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	41.5671	+	17.2177i	1.46687	+	0.607598i
$804$		0			0
$805$	1.80336	+	4.35369i	0.0635600	+	0.153447i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.851642	−	0.851642i	0.0299421	−	0.0299421i	−0.691977	−	0.721919i	$-0.743260\pi$
$809$	0.851642	−	0.851642i	0.0299421	−	0.0299421i	0.721919	+	0.691977i	$0.243260\pi$
$810$		0			0
$811$	−11.0808	−	26.7515i	−0.389100	−	0.939371i	−0.990131	−	0.140145i	$-0.955243\pi$
$811$	−11.0808	−	26.7515i	−0.389100	−	0.939371i	0.601031	−	0.799226i	$-0.294757\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$			19.6813i			0.689405i
$816$		0			0
$817$		−	32.1803i		−	1.12585i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	14.6802	+	35.4411i	0.512342	+	1.23690i	0.942517	+	0.334157i	$0.108452\pi$
$821$	14.6802	+	35.4411i	0.512342	+	1.23690i	−0.430176	+	0.902745i	$0.641548\pi$
$822$		0			0
$823$	−23.7916	+	23.7916i	−0.829322	+	0.829322i	−0.987423	−	0.158101i	$-0.949463\pi$
$823$	−23.7916	+	23.7916i	−0.829322	+	0.829322i	0.158101	+	0.987423i	$0.449463\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.95203	−	16.7837i	−0.241746	−	0.583626i	0.755711	−	0.654906i	$-0.227292\pi$
$827$	−6.95203	−	16.7837i	−0.241746	−	0.583626i	−0.997456	+	0.0712800i	$0.977292\pi$
$828$		0			0
$829$	17.6000	+	7.29015i	0.611272	+	0.253197i	0.666772	−	0.745261i	$-0.267675\pi$
$829$	17.6000	+	7.29015i	0.611272	+	0.253197i	−0.0555001	+	0.998459i	$0.517675\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		−	34.3362i		−	1.18968i
$834$		0			0
$835$	10.7397	−	25.9280i	0.371663	−	0.897274i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.74463	+	4.74463i	−0.163803	+	0.163803i	−0.784249	−	0.620446i	$-0.786952\pi$
$839$	−4.74463	+	4.74463i	−0.163803	+	0.163803i	0.620446	+	0.784249i	$0.286952\pi$
$840$		0			0
$841$	10.1370	+	10.1370i	0.349553	+	0.349553i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−13.4616	−	5.57596i	−0.463092	−	0.191819i
$846$		0			0
$847$	8.94160			0.307237
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.71177	−	4.13257i	0.0586787	−	0.141663i
$852$		0			0
$853$	21.3984	−	8.86349i	0.732666	−	0.303480i	0.0150190	−	0.999887i	$-0.495219\pi$
$853$	21.3984	−	8.86349i	0.732666	−	0.303480i	0.717647	+	0.696407i	$0.245219\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.9755	+	14.9755i	0.511554	+	0.511554i	0.915003	−	0.403448i	$-0.132188\pi$
$857$	14.9755	+	14.9755i	0.511554	+	0.511554i	−0.403448	+	0.915003i	$0.632188\pi$
$858$		0			0
$859$	3.68023	−	1.52440i	0.125568	−	0.0520119i	−0.319015	−	0.947750i	$-0.603352\pi$
$859$	3.68023	−	1.52440i	0.125568	−	0.0520119i	0.444583	+	0.895738i	$0.353352\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−52.6581			−1.79250			−0.896252	−	0.443545i	$-0.853721\pi$
$863$	−52.6581			−1.79250			−0.896252	+	0.443545i	$0.853721\pi$
$864$		0			0
$865$	18.6667			0.634687
$866$		0			0
$867$		0			0
$868$		0			0
$869$	31.9513	−	13.2347i	1.08387	−	0.448955i
$870$		0			0
$871$	−0.458016	−	0.458016i	−0.0155193	−	0.0155193i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	39.9289	−	16.5391i	1.34984	−	0.559124i
$876$		0			0
$877$	−4.99743	+	12.0649i	−0.168751	+	0.407401i	−0.985519	−	0.169565i	$-0.945764\pi$
$877$	−4.99743	+	12.0649i	−0.168751	+	0.407401i	0.816768	+	0.576966i	$0.195764\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−38.6516			−1.30221			−0.651103	−	0.758989i	$-0.725694\pi$
$881$	−38.6516			−1.30221			−0.651103	+	0.758989i	$0.725694\pi$
$882$		0			0
$883$	10.8231	+	4.48306i	0.364226	+	0.150867i	0.557288	−	0.830319i	$-0.311842\pi$
$883$	10.8231	+	4.48306i	0.364226	+	0.150867i	−0.193062	+	0.981186i	$0.561842\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.30593	−	3.30593i	−0.111002	−	0.111002i	0.649424	−	0.760426i	$-0.275010\pi$
$887$	−3.30593	−	3.30593i	−0.111002	−	0.111002i	−0.760426	+	0.649424i	$0.775010\pi$
$888$		0			0
$889$	49.1137	−	49.1137i	1.64722	−	1.64722i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	12.2271	−	29.5189i	0.409165	−	0.987811i
$894$		0			0
$895$		−	31.0340i		−	1.03735i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	26.7224	+	11.0688i	0.891241	+	0.369164i
$900$		0			0
$901$	23.1221	+	55.8217i	0.770309	+	1.85969i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−22.6171	+	22.6171i	−0.751819	+	0.751819i
$906$		0			0
$907$	−14.0586	−	33.9405i	−0.466809	−	1.12698i	−0.965548	−	0.260225i	$-0.916203\pi$
$907$	−14.0586	−	33.9405i	−0.466809	−	1.12698i	0.498739	−	0.866752i	$-0.333797\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			28.5526i			0.945990i	0.881065	+	0.472995i	$0.156827\pi$
$911$			28.5526i			0.945990i	−0.881065	+	0.472995i	$0.843173\pi$
$912$		0			0
$913$			33.3744i			1.10453i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	8.79124	+	21.2239i	0.290312	+	0.700876i
$918$		0			0
$919$	−14.1101	+	14.1101i	−0.465448	+	0.465448i	−0.900436	−	0.434988i	$-0.856753\pi$
$919$	−14.1101	+	14.1101i	−0.465448	+	0.465448i	0.434988	+	0.900436i	$0.356753\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.27762	−	7.91289i	−0.107884	−	0.260456i
$924$		0			0
$925$	−10.0974	−	4.18247i	−0.331999	−	0.137519i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	1.88348i		−	0.0617951i	−0.999523	−	0.0308975i	$-0.990163\pi$
$929$		−	1.88348i		−	0.0617951i	0.999523	−	0.0308975i	$-0.00983656\pi$
$930$		0			0
$931$	8.00185	−	19.3182i	0.262250	−	0.633127i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	22.4247	−	22.4247i	0.733365	−	0.733365i
$936$		0			0
$937$	−15.2871	−	15.2871i	−0.499409	−	0.499409i	0.411845	−	0.911254i	$-0.364885\pi$
$937$	−15.2871	−	15.2871i	−0.499409	−	0.499409i	−0.911254	+	0.411845i	$0.864885\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	35.4271	+	14.6744i	1.15489	+	0.478372i	0.876171	−	0.482000i	$-0.160090\pi$
$941$	35.4271	+	14.6744i	1.15489	+	0.478372i	0.278721	+	0.960372i	$0.410090\pi$
$942$		0			0
$943$	−3.19927			−0.104183
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.28542	+	20.0028i	−0.269240	+	0.650003i	−0.999448	−	0.0332221i	$-0.989423\pi$
$947$	−8.28542	+	20.0028i	−0.269240	+	0.650003i	0.730208	+	0.683225i	$0.239423\pi$
$948$		0			0
$949$	65.6555	−	27.1954i	2.13127	−	0.882800i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−27.6252	−	27.6252i	−0.894867	−	0.894867i	0.100110	−	0.994976i	$-0.468081\pi$
$953$	−27.6252	−	27.6252i	−0.894867	−	0.894867i	−0.994976	+	0.100110i	$0.968081\pi$
$954$		0			0
$955$	0.899317	−	0.372509i	0.0291012	−	0.0120541i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	70.0731			2.26278
$960$		0			0
$961$	−26.0511			−0.840358
$962$		0			0
$963$		0			0
$964$		0			0
$965$	22.6655	−	9.38836i	0.729629	−	0.302222i
$966$		0			0
$967$	32.5133	+	32.5133i	1.04556	+	1.04556i	0.998911	+	0.0466463i	$0.0148534\pi$
$967$	32.5133	+	32.5133i	1.04556	+	1.04556i	0.0466463	+	0.998911i	$0.485147\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−49.5609	+	20.5288i	−1.59048	+	0.658800i	−0.990030	−	0.140859i	$-0.955014\pi$
$971$	−49.5609	+	20.5288i	−1.59048	+	0.658800i	−0.600455	+	0.799659i	$0.705014\pi$
$972$		0			0
$973$	−18.1556	+	43.8315i	−0.582042	+	1.40517i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	29.2129			0.934603			0.467301	−	0.884098i	$-0.345226\pi$
$977$	29.2129			0.934603			0.467301	+	0.884098i	$0.345226\pi$
$978$		0			0
$979$	22.7410	+	9.41962i	0.726805	+	0.301052i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−33.7320	−	33.7320i	−1.07588	−	1.07588i	−0.996874	−	0.0790094i	$-0.974824\pi$
$983$	−33.7320	−	33.7320i	−1.07588	−	1.07588i	−0.0790094	−	0.996874i	$-0.525176\pi$
$984$		0			0
$985$	5.11378	−	5.11378i	0.162939	−	0.162939i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.46303	−	5.94629i	0.0783199	−	0.189081i
$990$		0			0
$991$			2.34392i			0.0744571i	0.999307	+	0.0372285i	$0.0118530\pi$
$991$			2.34392i			0.0744571i	−0.999307	+	0.0372285i	$0.988147\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−22.6829	−	9.39555i	−0.719095	−	0.297859i
$996$		0			0
$997$	−14.7502	−	35.6102i	−0.467145	−	1.12779i	−0.965404	−	0.260759i	$-0.916027\pi$
$997$	−14.7502	−	35.6102i	−0.467145	−	1.12779i	0.498259	−	0.867028i	$-0.333973\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.w.a.431.6		32
3.2	odd	2		1152.2.w.b.431.3		32
4.3	odd	2		288.2.w.b.35.5	yes	32
12.11	even	2		288.2.w.a.35.4	✓	32
32.11	odd	8		1152.2.w.b.719.3		32
32.21	even	8		288.2.w.a.107.4	yes	32
96.11	even	8	inner	1152.2.w.a.719.6		32
96.53	odd	8		288.2.w.b.107.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.4	✓	32	12.11	even	2
288.2.w.a.107.4	yes	32	32.21	even	8
288.2.w.b.35.5	yes	32	4.3	odd	2
288.2.w.b.107.5	yes	32	96.53	odd	8
1152.2.w.a.431.6		32	1.1	even	1	trivial
1152.2.w.a.719.6		32	96.11	even	8	inner
1152.2.w.b.431.3		32	3.2	odd	2
1152.2.w.b.719.3		32	32.11	odd	8

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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.w (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.64859 - 0.682869i) q^{5} +(-2.51270 - 2.51270i) q^{7} +O(q^{10})\)	\(q+(1.64859 - 0.682869i) q^{5} +(-2.51270 - 2.51270i) q^{7} +(-2.69097 + 1.11464i) q^{11} +(-1.76057 + 4.25040i) q^{13} -6.10169 q^{17} +(-3.43292 - 1.42196i) q^{19} +(-0.525502 - 0.525502i) q^{23} +(-1.28399 + 1.28399i) q^{25} +(1.46544 - 3.53788i) q^{29} +7.55322i q^{31} +(-5.85826 - 2.42657i) q^{35} +(2.30333 + 5.56073i) q^{37} +(3.04402 - 3.04402i) q^{41} +(3.31422 + 8.00123i) q^{43} +8.59875i q^{47} +5.62732i q^{49} +(-3.78946 - 9.14856i) q^{53} +(-3.67516 + 3.67516i) q^{55} +(-3.73387 - 9.01437i) q^{59} +(3.41173 + 1.41318i) q^{61} +8.20941i q^{65} +(-0.0538792 + 0.130076i) q^{67} +(-1.31641 + 1.31641i) q^{71} +(-10.9226 - 10.9226i) q^{73} +(9.56234 + 3.96085i) q^{77} -11.8735 q^{79} +(4.38490 - 10.5861i) q^{83} +(-10.0592 + 4.16666i) q^{85} +(-5.97566 - 5.97566i) q^{89} +(15.1038 - 6.25618i) q^{91} -6.63051 q^{95} -3.21530 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95}+O(q^{100}) \) 32 * q - 8 * q^11 + 16 * q^29 + 24 * q^35 + 16 * q^53 + 32 * q^55 + 32 * q^59 + 32 * q^61 + 16 * q^67 + 16 * q^71 + 16 * q^77 + 32 * q^79 - 40 * q^83 + 48 * q^91 - 80 * q^95

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