LMFDB - Embedded newform 1600.2.s.c.207.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1600.207");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 6x^{12} - 12x^{10} + 36x^{8} - 48x^{6} + 96x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 + 6x^12 - 12x^10 + 36x^8 - 48x^6 + 96x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			207.5
Root			$-1.35949 + 0.389597i$ of defining polynomial
Character	$\chi$	$=$	1600.207
Dual form			1600.2.s.c.943.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.207468 q^{3} +(1.32185 + 1.32185i) q^{7} -2.95696 q^{9} +O(q^{10})$	$q+0.207468 q^{3} +(1.32185 + 1.32185i) q^{7} -2.95696 q^{9} +(2.39286 - 2.39286i) q^{11} -4.20208i q^{13} +(-3.29071 - 3.29071i) q^{17} +(0.838342 - 0.838342i) q^{19} +(0.274241 + 0.274241i) q^{21} +(-2.67277 + 2.67277i) q^{23} -1.23588 q^{27} +(-2.55451 - 2.55451i) q^{29} -6.23723i q^{31} +(0.496441 - 0.496441i) q^{33} +4.29451i q^{37} -0.871798i q^{39} -7.06598i q^{41} +9.43258i q^{43} +(8.31820 - 8.31820i) q^{47} -3.50544i q^{49} +(-0.682716 - 0.682716i) q^{51} +7.66672 q^{53} +(0.173929 - 0.173929i) q^{57} +(-7.07557 - 7.07557i) q^{59} +(8.74267 - 8.74267i) q^{61} +(-3.90865 - 3.90865i) q^{63} +12.5494i q^{67} +(-0.554514 + 0.554514i) q^{69} +10.4624 q^{71} +(-4.79095 - 4.79095i) q^{73} +6.32598 q^{77} -8.69963 q^{79} +8.61447 q^{81} +4.14519 q^{83} +(-0.529980 - 0.529980i) q^{87} +0.548482 q^{89} +(5.55451 - 5.55451i) q^{91} -1.29403i q^{93} +(-12.2022 - 12.2022i) q^{97} +(-7.07557 + 7.07557i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

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

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
$3$	0.207468			0.119782			0.0598908	−	0.998205i	$-0.480925\pi$
$3$	0.207468			0.119782			0.0598908	+	0.998205i	$0.480925\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.32185	+	1.32185i	0.499611	+	0.499611i	0.911317	−	0.411706i	$-0.135067\pi$
$7$	1.32185	+	1.32185i	0.499611	+	0.499611i	−0.411706	+	0.911317i	$0.635067\pi$
$8$		0			0
$9$	−2.95696			−0.985652
$10$		0			0
$11$	2.39286	−	2.39286i	0.721473	−	0.721473i	−0.247432	−	0.968905i	$-0.579587\pi$
$11$	2.39286	−	2.39286i	0.721473	−	0.721473i	0.968905	+	0.247432i	$0.0795867\pi$
$12$		0			0
$13$		−	4.20208i		−	1.16545i	−0.812670	−	0.582724i	$-0.801987\pi$
$13$		−	4.20208i		−	1.16545i	0.812670	−	0.582724i	$-0.198013\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.29071	−	3.29071i	−0.798114	−	0.798114i	0.184684	−	0.982798i	$-0.440874\pi$
$17$	−3.29071	−	3.29071i	−0.798114	−	0.798114i	−0.982798	+	0.184684i	$0.940874\pi$
$18$		0			0
$19$	0.838342	−	0.838342i	0.192329	−	0.192329i	−0.604373	−	0.796702i	$-0.706576\pi$
$19$	0.838342	−	0.838342i	0.192329	−	0.192329i	0.796702	+	0.604373i	$0.206576\pi$
$20$		0			0
$21$	0.274241	+	0.274241i	0.0598443	+	0.0598443i
$22$		0			0
$23$	−2.67277	+	2.67277i	−0.557311	+	0.557311i	−0.928541	−	0.371230i	$-0.878936\pi$
$23$	−2.67277	+	2.67277i	−0.557311	+	0.557311i	0.371230	+	0.928541i	$0.378936\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.23588			−0.237845
$28$		0			0
$29$	−2.55451	−	2.55451i	−0.474361	−	0.474361i	0.428961	−	0.903323i	$-0.358880\pi$
$29$	−2.55451	−	2.55451i	−0.474361	−	0.474361i	−0.903323	+	0.428961i	$0.858880\pi$
$30$		0			0
$31$		−	6.23723i		−	1.12024i	−0.828412	−	0.560120i	$-0.810755\pi$
$31$		−	6.23723i		−	1.12024i	0.828412	−	0.560120i	$-0.189245\pi$
$32$		0			0
$33$	0.496441	−	0.496441i	0.0864192	−	0.0864192i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			4.29451i			0.706013i	0.935621	+	0.353006i	$0.114841\pi$
$37$			4.29451i			0.706013i	−0.935621	+	0.353006i	$0.885159\pi$
$38$		0			0
$39$		−	0.871798i		−	0.139599i
$40$		0			0
$41$		−	7.06598i		−	1.10352i	−0.834002	−	0.551761i	$-0.813956\pi$
$41$		−	7.06598i		−	1.10352i	0.834002	−	0.551761i	$-0.186044\pi$
$42$		0			0
$43$			9.43258i			1.43845i	0.694775	+	0.719227i	$0.255504\pi$
$43$			9.43258i			1.43845i	−0.694775	+	0.719227i	$0.744496\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	8.31820	−	8.31820i	1.21333	−	1.21333i	0.243410	−	0.969923i	$-0.421734\pi$
$47$	8.31820	−	8.31820i	1.21333	−	1.21333i	0.969923	−	0.243410i	$-0.0782662\pi$
$48$		0			0
$49$		−	3.50544i		−	0.500777i
$50$		0			0
$51$	−0.682716	−	0.682716i	−0.0955994	−	0.0955994i
$52$		0			0
$53$	7.66672			1.05311			0.526553	−	0.850143i	$-0.323484\pi$
$53$	7.66672			1.05311			0.526553	+	0.850143i	$0.323484\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.173929	−	0.173929i	0.0230375	−	0.0230375i
$58$		0			0
$59$	−7.07557	−	7.07557i	−0.921161	−	0.921161i	0.0759506	−	0.997112i	$-0.475801\pi$
$59$	−7.07557	−	7.07557i	−0.921161	−	0.921161i	−0.997112	+	0.0759506i	$0.975801\pi$
$60$		0			0
$61$	8.74267	−	8.74267i	1.11938	−	1.11938i	0.127552	−	0.991832i	$-0.459288\pi$
$61$	8.74267	−	8.74267i	1.11938	−	1.11938i	0.991832	−	0.127552i	$-0.0407120\pi$
$62$		0			0
$63$	−3.90865	−	3.90865i	−0.492443	−	0.492443i
$64$		0			0
$65$		0			0
$66$		0			0
$67$			12.5494i			1.53315i	0.642156	+	0.766574i	$0.278040\pi$
$67$			12.5494i			1.53315i	−0.642156	+	0.766574i	$0.721960\pi$
$68$		0			0
$69$	−0.554514	+	0.554514i	−0.0667556	+	0.0667556i
$70$		0			0
$71$	10.4624			1.24166			0.620829	−	0.783946i	$-0.286796\pi$
$71$	10.4624			1.24166			0.620829	+	0.783946i	$0.286796\pi$
$72$		0			0
$73$	−4.79095	−	4.79095i	−0.560738	−	0.560738i	0.368779	−	0.929517i	$-0.379776\pi$
$73$	−4.79095	−	4.79095i	−0.560738	−	0.560738i	−0.929517	+	0.368779i	$0.879776\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.32598			0.720912
$78$		0			0
$79$	−8.69963			−0.978784			−0.489392	−	0.872064i	$-0.662781\pi$
$79$	−8.69963			−0.978784			−0.489392	+	0.872064i	$0.662781\pi$
$80$		0			0
$81$	8.61447			0.957163
$82$		0			0
$83$	4.14519			0.454993			0.227497	−	0.973779i	$-0.426946\pi$
$83$	4.14519			0.454993			0.227497	+	0.973779i	$0.426946\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.529980	−	0.529980i	−0.0568198	−	0.0568198i
$88$		0			0
$89$	0.548482			0.0581390			0.0290695	−	0.999577i	$-0.490746\pi$
$89$	0.548482			0.0581390			0.0290695	+	0.999577i	$0.490746\pi$
$90$		0			0
$91$	5.55451	−	5.55451i	0.582271	−	0.582271i
$92$		0			0
$93$		−	1.29403i		−	0.134184i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−12.2022	−	12.2022i	−1.23895	−	1.23895i	−0.960431	−	0.278518i	$-0.910157\pi$
$97$	−12.2022	−	12.2022i	−1.23895	−	1.23895i	−0.278518	−	0.960431i	$-0.589843\pi$
$98$		0			0
$99$	−7.07557	+	7.07557i	−0.711122	+	0.711122i
$100$		0			0
$101$	−6.46843	−	6.46843i	−0.643633	−	0.643633i	0.307814	−	0.951447i	$-0.400403\pi$
$101$	−6.46843	−	6.46843i	−0.643633	−	0.643633i	−0.951447	+	0.307814i	$0.900403\pi$
$102$		0			0
$103$	6.55234	−	6.55234i	0.645621	−	0.645621i	−0.306310	−	0.951932i	$-0.599095\pi$
$103$	6.55234	−	6.55234i	0.645621	−	0.645621i	0.951932	+	0.306310i	$0.0990945\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−16.3708			−1.58262			−0.791312	−	0.611413i	$-0.790601\pi$
$107$	−16.3708			−1.58262			−0.791312	+	0.611413i	$0.790601\pi$
$108$		0			0
$109$	−2.00000	−	2.00000i	−0.191565	−	0.191565i	0.604807	−	0.796372i	$-0.293250\pi$
$109$	−2.00000	−	2.00000i	−0.191565	−	0.191565i	−0.796372	+	0.604807i	$0.793250\pi$
$110$		0			0
$111$			0.890973i			0.0845674i
$112$		0			0
$113$	−11.8688	+	11.8688i	−1.11652	+	1.11652i	−0.124275	+	0.992248i	$0.539661\pi$
$113$	−11.8688	+	11.8688i	−1.11652	+	1.11652i	−0.992248	+	0.124275i	$0.960339\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$			12.4254i			1.14873i
$118$		0			0
$119$		−	8.69963i		−	0.797493i
$120$		0			0
$121$		−	0.451518i		−	0.0410471i
$122$		0			0
$123$		−	1.46597i		−	0.132182i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	5.55946	−	5.55946i	0.493322	−	0.493322i	−0.416029	−	0.909351i	$-0.636579\pi$
$127$	5.55946	−	5.55946i	0.493322	−	0.493322i	0.909351	+	0.416029i	$0.136579\pi$
$128$		0			0
$129$			1.95696i			0.172300i
$130$		0			0
$131$	−3.16166	−	3.16166i	−0.276235	−	0.276235i	0.555369	−	0.831604i	$-0.312577\pi$
$131$	−3.16166	−	3.16166i	−0.276235	−	0.276235i	−0.831604	+	0.555369i	$0.812577\pi$
$132$		0			0
$133$	2.21632			0.192179
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.507360	−	0.507360i	0.0433467	−	0.0433467i	−0.685101	−	0.728448i	$-0.740242\pi$
$137$	0.507360	−	0.507360i	0.0433467	−	0.0433467i	0.728448	+	0.685101i	$0.240242\pi$
$138$		0			0
$139$	5.52106	+	5.52106i	0.468290	+	0.468290i	0.901360	−	0.433070i	$-0.142570\pi$
$139$	5.52106	+	5.52106i	0.468290	+	0.468290i	−0.433070	+	0.901360i	$0.642570\pi$
$140$		0			0
$141$	1.72576	−	1.72576i	0.145335	−	0.145335i
$142$		0			0
$143$	−10.0550	−	10.0550i	−0.840840	−	0.840840i
$144$		0			0
$145$		0			0
$146$		0			0
$147$		−	0.727266i		−	0.0599839i
$148$		0			0
$149$	2.82875	−	2.82875i	0.231741	−	0.231741i	−0.581678	−	0.813419i	$-0.697604\pi$
$149$	2.82875	−	2.82875i	0.231741	−	0.231741i	0.813419	+	0.581678i	$0.197604\pi$
$150$		0			0
$151$	−7.12820			−0.580085			−0.290042	−	0.957014i	$-0.593669\pi$
$151$	−7.12820			−0.580085			−0.290042	+	0.957014i	$0.593669\pi$
$152$		0			0
$153$	9.73048	+	9.73048i	0.786663	+	0.786663i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	20.7371			1.65500			0.827501	−	0.561464i	$-0.189762\pi$
$157$	20.7371			1.65500			0.827501	+	0.561464i	$0.189762\pi$
$158$		0			0
$159$	1.59060			0.126143
$160$		0			0
$161$	−7.06598			−0.556878
$162$		0			0
$163$	10.8985			0.853640			0.426820	−	0.904337i	$-0.359634\pi$
$163$	10.8985			0.853640			0.426820	+	0.904337i	$0.359634\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.20680	+	1.20680i	0.0933853	+	0.0933853i	0.752256	−	0.658871i	$-0.228966\pi$
$167$	1.20680	+	1.20680i	0.0933853	+	0.0933853i	−0.658871	+	0.752256i	$0.728966\pi$
$168$		0			0
$169$	−4.65751			−0.358270
$170$		0			0
$171$	−2.47894	+	2.47894i	−0.189569	+	0.189569i
$172$		0			0
$173$		−	5.12438i		−	0.389599i	−0.980843	−	0.194800i	$-0.937594\pi$
$173$		−	5.12438i		−	0.389599i	0.980843	−	0.194800i	$-0.0624057\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.46795	−	1.46795i	−0.110338	−	0.110338i
$178$		0			0
$179$	12.6301	−	12.6301i	0.944017	−	0.944017i	−0.0544970	−	0.998514i	$-0.517356\pi$
$179$	12.6301	−	12.6301i	0.944017	−	0.944017i	0.998514	+	0.0544970i	$0.0173555\pi$
$180$		0			0
$181$	8.46843	+	8.46843i	0.629453	+	0.629453i	0.947931	−	0.318477i	$-0.103171\pi$
$181$	8.46843	+	8.46843i	0.629453	+	0.629453i	−0.318477	+	0.947931i	$0.603171\pi$
$182$		0			0
$183$	1.81382	−	1.81382i	0.134082	−	0.134082i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−15.7484			−1.15164
$188$		0			0
$189$	−1.63364	−	1.63364i	−0.118830	−	0.118830i
$190$		0			0
$191$		−	11.3534i		−	0.821501i	−0.911748	−	0.410750i	$-0.865267\pi$
$191$		−	11.3534i		−	0.821501i	0.911748	−	0.410750i	$-0.134733\pi$
$192$		0			0
$193$	−11.0245	+	11.0245i	−0.793561	+	0.793561i	−0.982071	−	0.188510i	$-0.939634\pi$
$193$	−11.0245	+	11.0245i	−0.793561	+	0.793561i	0.188510	+	0.982071i	$0.439634\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			21.1953i			1.51010i	0.655667	+	0.755050i	$0.272388\pi$
$197$			21.1953i			1.51010i	−0.655667	+	0.755050i	$0.727612\pi$
$198$		0			0
$199$			8.68045i			0.615341i	0.951493	+	0.307670i	$0.0995494\pi$
$199$			8.68045i			0.615341i	−0.951493	+	0.307670i	$0.900451\pi$
$200$		0			0
$201$			2.60359i			0.183643i
$202$		0			0
$203$		−	6.75335i		−	0.473993i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	7.90326	−	7.90326i	0.549315	−	0.549315i
$208$		0			0
$209$		−	4.01206i		−	0.277520i
$210$		0			0
$211$	6.28986	+	6.28986i	0.433012	+	0.433012i	0.889652	−	0.456640i	$-0.150947\pi$
$211$	6.28986	+	6.28986i	0.433012	+	0.433012i	−0.456640	+	0.889652i	$0.650947\pi$
$212$		0			0
$213$	2.17061			0.148728
$214$		0			0
$215$		0			0
$216$		0			0
$217$	8.24467	−	8.24467i	0.559684	−	0.559684i
$218$		0			0
$219$	−0.993968	−	0.993968i	−0.0671661	−	0.0671661i
$220$		0			0
$221$	−13.8278	+	13.8278i	−0.930160	+	0.930160i
$222$		0			0
$223$	−3.50264	−	3.50264i	−0.234554	−	0.234554i	0.580036	−	0.814591i	$-0.303038\pi$
$223$	−3.50264	−	3.50264i	−0.234554	−	0.234554i	−0.814591	+	0.580036i	$0.803038\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			0.622404i			0.0413104i	0.999787	+	0.0206552i	$0.00657522\pi$
$227$			0.622404i			0.0413104i	−0.999787	+	0.0206552i	$0.993425\pi$
$228$		0			0
$229$	−9.35940	+	9.35940i	−0.618487	+	0.618487i	−0.945143	−	0.326657i	$-0.894078\pi$
$229$	−9.35940	+	9.35940i	−0.618487	+	0.618487i	0.326657	+	0.945143i	$0.394078\pi$
$230$		0			0
$231$	1.31244			0.0863521
$232$		0			0
$233$	1.79047	+	1.79047i	0.117297	+	0.117297i	0.763319	−	0.646022i	$-0.223568\pi$
$233$	1.79047	+	1.79047i	0.117297	+	0.117297i	−0.646022	+	0.763319i	$0.723568\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.80489			−0.117240
$238$		0			0
$239$	20.9056			1.35227			0.676136	−	0.736777i	$-0.263653\pi$
$239$	20.9056			1.35227			0.676136	+	0.736777i	$0.263653\pi$
$240$		0			0
$241$	−3.70055			−0.238374			−0.119187	−	0.992872i	$-0.538029\pi$
$241$	−3.70055			−0.238374			−0.119187	+	0.992872i	$0.538029\pi$
$242$		0			0
$243$	5.49486			0.352495
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.52278	−	3.52278i	−0.224149	−	0.224149i
$248$		0			0
$249$	0.859993			0.0544999
$250$		0			0
$251$	−0.630086	+	0.630086i	−0.0397707	+	0.0397707i	−0.726712	−	0.686942i	$-0.758953\pi$
$251$	−0.630086	+	0.630086i	−0.0397707	+	0.0397707i	0.686942	+	0.726712i	$0.258953\pi$
$252$		0			0
$253$			12.7911i			0.804170i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.62414	−	3.62414i	−0.226068	−	0.226068i	0.584980	−	0.811048i	$-0.301102\pi$
$257$	−3.62414	−	3.62414i	−0.226068	−	0.226068i	−0.811048	+	0.584980i	$0.801102\pi$
$258$		0			0
$259$	−5.67668	+	5.67668i	−0.352732	+	0.352732i
$260$		0			0
$261$	7.55359	+	7.55359i	0.467555	+	0.467555i
$262$		0			0
$263$	−5.25957	+	5.25957i	−0.324319	+	0.324319i	−0.850421	−	0.526102i	$-0.823653\pi$
$263$	−5.25957	+	5.25957i	−0.324319	+	0.324319i	0.526102	+	0.850421i	$0.323653\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.113792			0.00696398
$268$		0			0
$269$	8.82875	+	8.82875i	0.538299	+	0.538299i	0.923029	−	0.384730i	$-0.125706\pi$
$269$	8.82875	+	8.82875i	0.538299	+	0.538299i	−0.384730	+	0.923029i	$0.625706\pi$
$270$		0			0
$271$			30.9177i			1.87812i	0.343760	+	0.939058i	$0.388299\pi$
$271$			30.9177i			1.87812i	−0.343760	+	0.939058i	$0.611701\pi$
$272$		0			0
$273$	1.15238	−	1.15238i	0.0697454	−	0.0697454i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		−	18.9322i		−	1.13753i	−0.822501	−	0.568764i	$-0.807422\pi$
$277$		−	18.9322i		−	1.13753i	0.822501	−	0.568764i	$-0.192578\pi$
$278$		0			0
$279$			18.4432i			1.10417i
$280$		0			0
$281$			6.51750i			0.388802i	0.980922	+	0.194401i	$0.0622762\pi$
$281$			6.51750i			0.388802i	−0.980922	+	0.194401i	$0.937724\pi$
$282$		0			0
$283$			16.0721i			0.955390i	0.878526	+	0.477695i	$0.158528\pi$
$283$			16.0721i			0.955390i	−0.878526	+	0.477695i	$0.841472\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.34015	−	9.34015i	0.551332	−	0.551332i
$288$		0			0
$289$			4.65751i			0.273971i
$290$		0			0
$291$	−2.53157	−	2.53157i	−0.148403	−	0.148403i
$292$		0			0
$293$	0.829872			0.0484816			0.0242408	−	0.999706i	$-0.492283\pi$
$293$	0.829872			0.0484816			0.0242408	+	0.999706i	$0.492283\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.95728	+	2.95728i	−0.171599	+	0.171599i
$298$		0			0
$299$	11.2312	+	11.2312i	0.649517	+	0.649517i
$300$		0			0
$301$	−12.4684	+	12.4684i	−0.718668	+	0.718668i
$302$		0			0
$303$	−1.34199	−	1.34199i	−0.0770954	−	0.0770954i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			28.4115i			1.62153i	0.585371	+	0.810766i	$0.300949\pi$
$307$			28.4115i			1.62153i	−0.585371	+	0.810766i	$0.699051\pi$
$308$		0			0
$309$	1.35940	−	1.35940i	0.0773336	−	0.0773336i
$310$		0			0
$311$	−31.8087			−1.80370			−0.901852	−	0.432046i	$-0.857792\pi$
$311$	−31.8087			−1.80370			−0.901852	+	0.432046i	$0.857792\pi$
$312$		0			0
$313$	−18.7727	−	18.7727i	−1.06110	−	1.06110i	−0.998008	−	0.0630896i	$-0.979905\pi$
$313$	−18.7727	−	18.7727i	−1.06110	−	1.06110i	−0.0630896	−	0.998008i	$-0.520095\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.6205			−0.596506			−0.298253	−	0.954487i	$-0.596404\pi$
$317$	−10.6205			−0.596506			−0.298253	+	0.954487i	$0.596404\pi$
$318$		0			0
$319$	−12.2252			−0.684478
$320$		0			0
$321$	−3.39641			−0.189569
$322$		0			0
$323$	−5.51748			−0.307001
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.414936	−	0.414936i	−0.0229460	−	0.0229460i
$328$		0			0
$329$	21.9908			1.21239
$330$		0			0
$331$	−22.4098	+	22.4098i	−1.23175	+	1.23175i	−0.268462	+	0.963290i	$0.586515\pi$
$331$	−22.4098	+	22.4098i	−1.23175	+	1.23175i	−0.963290	+	0.268462i	$0.913485\pi$
$332$		0			0
$333$		−	12.6987i		−	0.695883i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−2.95728	−	2.95728i	−0.161093	−	0.161093i	0.621958	−	0.783051i	$-0.286338\pi$
$337$	−2.95728	−	2.95728i	−0.161093	−	0.161093i	−0.783051	+	0.621958i	$0.786338\pi$
$338$		0			0
$339$	−2.46240	+	2.46240i	−0.133739	+	0.133739i
$340$		0			0
$341$	−14.9248	−	14.9248i	−0.808223	−	0.808223i
$342$		0			0
$343$	13.8866	−	13.8866i	0.749805	−	0.749805i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	13.8901			0.745659			0.372830	−	0.927900i	$-0.378388\pi$
$347$	13.8901			0.745659			0.372830	+	0.927900i	$0.378388\pi$
$348$		0			0
$349$	13.4914	+	13.4914i	0.722176	+	0.722176i	0.969048	−	0.246872i	$-0.0794026\pi$
$349$	13.4914	+	13.4914i	0.722176	+	0.722176i	−0.246872	+	0.969048i	$0.579403\pi$
$350$		0			0
$351$			5.19326i			0.277196i
$352$		0			0
$353$	15.9785	−	15.9785i	0.850448	−	0.850448i	−0.139740	−	0.990188i	$-0.544627\pi$
$353$	15.9785	−	15.9785i	0.850448	−	0.850448i	0.990188	+	0.139740i	$0.0446268\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	1.80489i		−	0.0955251i
$358$		0			0
$359$		−	28.2831i		−	1.49273i	−0.665539	−	0.746363i	$-0.731798\pi$
$359$		−	28.2831i		−	1.49273i	0.665539	−	0.746363i	$-0.268202\pi$
$360$		0			0
$361$			17.5944i			0.926019i
$362$		0			0
$363$		−	0.0936755i		−	0.00491669i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−16.8285	+	16.8285i	−0.878439	+	0.878439i	−0.993373	−	0.114934i	$-0.963334\pi$
$367$	−16.8285	+	16.8285i	−0.878439	+	0.878439i	0.114934	+	0.993373i	$0.463334\pi$
$368$		0			0
$369$			20.8938i			1.08769i
$370$		0			0
$371$	10.1342	+	10.1342i	0.526143	+	0.526143i
$372$		0			0
$373$	8.03845			0.416215			0.208108	−	0.978106i	$-0.433270\pi$
$373$	8.03845			0.416215			0.208108	+	0.978106i	$0.433270\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.7343	+	10.7343i	−0.552844	+	0.552844i
$378$		0			0
$379$	2.30677	+	2.30677i	0.118491	+	0.118491i	0.763866	−	0.645375i	$-0.223299\pi$
$379$	2.30677	+	2.30677i	0.118491	+	0.118491i	−0.645375	+	0.763866i	$0.723299\pi$
$380$		0			0
$381$	1.15341	−	1.15341i	0.0590910	−	0.0590910i
$382$		0			0
$383$	7.85530	+	7.85530i	0.401387	+	0.401387i	0.878722	−	0.477335i	$-0.158397\pi$
$383$	7.85530	+	7.85530i	0.401387	+	0.401387i	−0.477335	+	0.878722i	$0.658397\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	27.8917i		−	1.41782i
$388$		0			0
$389$	27.2171	−	27.2171i	1.37996	−	1.37996i	0.535303	−	0.844660i	$-0.320197\pi$
$389$	27.2171	−	27.2171i	1.37996	−	1.37996i	0.844660	−	0.535303i	$-0.179803\pi$
$390$		0			0
$391$	17.5906			0.889595
$392$		0			0
$393$	−0.655943	−	0.655943i	−0.0330879	−	0.0330879i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	4.38693			0.220174			0.110087	−	0.993922i	$-0.464887\pi$
$397$	4.38693			0.220174			0.110087	+	0.993922i	$0.464887\pi$
$398$		0			0
$399$	0.459815			0.0230196
$400$		0			0
$401$	−24.5944			−1.22818			−0.614092	−	0.789234i	$-0.710478\pi$
$401$	−24.5944			−1.22818			−0.614092	+	0.789234i	$0.710478\pi$
$402$		0			0
$403$	−26.2094			−1.30558
$404$		0			0
$405$		0			0
$406$		0			0
$407$	10.2761	+	10.2761i	0.509369	+	0.509369i
$408$		0			0
$409$	7.06598			0.349390			0.174695	−	0.984623i	$-0.444106\pi$
$409$	7.06598			0.349390			0.174695	+	0.984623i	$0.444106\pi$
$410$		0			0
$411$	0.105261	−	0.105261i	0.00519214	−	0.00519214i
$412$		0			0
$413$		−	18.7057i		−	0.920445i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.14544	+	1.14544i	0.0560926	+	0.0560926i
$418$		0			0
$419$	4.54400	−	4.54400i	0.221989	−	0.221989i	−0.587347	−	0.809336i	$-0.699827\pi$
$419$	4.54400	−	4.54400i	0.221989	−	0.221989i	0.809336	+	0.587347i	$0.199827\pi$
$420$		0			0
$421$	5.47539	+	5.47539i	0.266854	+	0.266854i	0.827831	−	0.560977i	$-0.189574\pi$
$421$	5.47539	+	5.47539i	0.266854	+	0.266854i	−0.560977	+	0.827831i	$0.689574\pi$
$422$		0			0
$423$	−24.5966	+	24.5966i	−1.19593	+	1.19593i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	23.1129			1.11851
$428$		0			0
$429$	−2.08609	−	2.08609i	−0.100717	−	0.100717i
$430$		0			0
$431$			12.6658i			0.610090i	0.952338	+	0.305045i	$0.0986716\pi$
$431$			12.6658i			0.610090i	−0.952338	+	0.305045i	$0.901328\pi$
$432$		0			0
$433$	11.0499	−	11.0499i	0.531022	−	0.531022i	−0.389854	−	0.920876i	$-0.627475\pi$
$433$	11.0499	−	11.0499i	0.531022	−	0.531022i	0.920876	+	0.389854i	$0.127475\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			4.48139i			0.214374i
$438$		0			0
$439$			20.4936i			0.978108i	0.872254	+	0.489054i	$0.162658\pi$
$439$			20.4936i			0.978108i	−0.872254	+	0.489054i	$0.837342\pi$
$440$		0			0
$441$			10.3654i			0.493592i
$442$		0			0
$443$			11.0123i			0.523212i	0.965175	+	0.261606i	$0.0842521\pi$
$443$			11.0123i			0.523212i	−0.965175	+	0.261606i	$0.915748\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.586876	−	0.586876i	0.0277583	−	0.0277583i
$448$		0			0
$449$		−	15.4423i		−	0.728767i	−0.931249	−	0.364383i	$-0.881280\pi$
$449$		−	15.4423i		−	0.728767i	0.931249	−	0.364383i	$-0.118720\pi$
$450$		0			0
$451$	−16.9079	−	16.9079i	−0.796161	−	0.796161i
$452$		0			0
$453$	−1.47887			−0.0694835
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.14212	+	3.14212i	−0.146982	+	0.146982i	−0.776769	−	0.629786i	$-0.783143\pi$
$457$	−3.14212	+	3.14212i	−0.146982	+	0.146982i	0.629786	+	0.776769i	$0.283143\pi$
$458$		0			0
$459$	4.06691	+	4.06691i	0.189827	+	0.189827i
$460$		0			0
$461$	8.45636	−	8.45636i	0.393852	−	0.393852i	−0.482206	−	0.876058i	$-0.660164\pi$
$461$	8.45636	−	8.45636i	0.393852	−	0.393852i	0.876058	+	0.482206i	$0.160164\pi$
$462$		0			0
$463$	21.5859	+	21.5859i	1.00318	+	1.00318i	0.999995	+	0.00318643i	$0.00101428\pi$
$463$	21.5859	+	21.5859i	1.00318	+	1.00318i	0.00318643	+	0.999995i	$0.498986\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	22.4880i		−	1.04062i	−0.853977	−	0.520311i	$-0.825816\pi$
$467$		−	22.4880i		−	1.04062i	0.853977	−	0.520311i	$-0.174184\pi$
$468$		0			0
$469$	−16.5883	+	16.5883i	−0.765978	+	0.765978i
$470$		0			0
$471$	4.30229			0.198239
$472$		0			0
$473$	22.5708	+	22.5708i	1.03781	+	1.03781i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−22.6702			−1.03800
$478$		0			0
$479$	0.852623			0.0389573			0.0194787	−	0.999810i	$-0.493799\pi$
$479$	0.852623			0.0389573			0.0194787	+	0.999810i	$0.493799\pi$
$480$		0			0
$481$	18.0459			0.822821
$482$		0			0
$483$	−1.46597			−0.0667037
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−2.49958	−	2.49958i	−0.113267	−	0.113267i	0.648202	−	0.761469i	$-0.275521\pi$
$487$	−2.49958	−	2.49958i	−0.113267	−	0.113267i	−0.761469	+	0.648202i	$0.775521\pi$
$488$		0			0
$489$	2.26110			0.102250
$490$		0			0
$491$	−22.1177	+	22.1177i	−0.998157	+	0.998157i	−0.999998	−	0.00184099i	$-0.999414\pi$
$491$	−22.1177	+	22.1177i	−0.998157	+	0.998157i	0.00184099	+	0.999998i	$0.499414\pi$
$492$		0			0
$493$			16.8123i			0.757189i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	13.8297	+	13.8297i	0.620346	+	0.620346i
$498$		0			0
$499$	−7.73911	+	7.73911i	−0.346450	+	0.346450i	−0.858786	−	0.512335i	$-0.828781\pi$
$499$	−7.73911	+	7.73911i	−0.346450	+	0.346450i	0.512335	+	0.858786i	$0.328781\pi$
$500$		0			0
$501$	0.250373	+	0.250373i	0.0111858	+	0.0111858i
$502$		0			0
$503$	−13.9144	+	13.9144i	−0.620413	+	0.620413i	−0.945637	−	0.325224i	$-0.894560\pi$
$503$	−13.9144	+	13.9144i	−0.620413	+	0.620413i	0.325224	+	0.945637i	$0.394560\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.966284			−0.0429142
$508$		0			0
$509$	−4.48049	−	4.48049i	−0.198594	−	0.198594i	0.600803	−	0.799397i	$-0.294848\pi$
$509$	−4.48049	−	4.48049i	−0.198594	−	0.198594i	−0.799397	+	0.600803i	$0.794848\pi$
$510$		0			0
$511$		−	12.6658i		−	0.560302i
$512$		0			0
$513$	−1.03609	+	1.03609i	−0.0457444	+	0.0457444i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	39.8085i		−	1.75078i
$518$		0			0
$519$		−	1.06314i		−	0.0466669i
$520$		0			0
$521$			3.26728i			0.143142i	0.997435	+	0.0715711i	$0.0228013\pi$
$521$			3.26728i			0.143142i	−0.997435	+	0.0715711i	$0.977199\pi$
$522$		0			0
$523$		−	10.1372i		−	0.443270i	−0.975130	−	0.221635i	$-0.928861\pi$
$523$		−	10.1372i		−	0.443270i	0.975130	−	0.221635i	$-0.0711393\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−20.5249	+	20.5249i	−0.894079	+	0.894079i
$528$		0			0
$529$			8.71262i			0.378809i
$530$		0			0
$531$	20.9222	+	20.9222i	0.907945	+	0.907945i
$532$		0			0
$533$	−29.6919			−1.28610
$534$		0			0
$535$		0			0
$536$		0			0
$537$	2.62034	−	2.62034i	0.113076	−	0.113076i
$538$		0			0
$539$	−8.38801	−	8.38801i	−0.361297	−	0.361297i
$540$		0			0
$541$	−18.3823	+	18.3823i	−0.790319	+	0.790319i	−0.981546	−	0.191227i	$-0.938753\pi$
$541$	−18.3823	+	18.3823i	−0.790319	+	0.790319i	0.191227	+	0.981546i	$0.438753\pi$
$542$		0			0
$543$	1.75693	+	1.75693i	0.0753970	+	0.0753970i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			3.60503i			0.154140i	0.997026	+	0.0770699i	$0.0245565\pi$
$547$			3.60503i			0.154140i	−0.997026	+	0.0770699i	$0.975444\pi$
$548$		0			0
$549$	−25.8517	+	25.8517i	−1.10332	+	1.10332i
$550$		0			0
$551$	−4.28311			−0.182467
$552$		0			0
$553$	−11.4996	−	11.4996i	−0.489012	−	0.489012i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−21.5670			−0.913823			−0.456911	−	0.889512i	$-0.651044\pi$
$557$	−21.5670			−0.913823			−0.456911	+	0.889512i	$0.651044\pi$
$558$		0			0
$559$	39.6365			1.67644
$560$		0			0
$561$	−3.26728			−0.137945
$562$		0			0
$563$	26.5306			1.11813			0.559066	−	0.829123i	$-0.311160\pi$
$563$	26.5306			1.11813			0.559066	+	0.829123i	$0.311160\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	11.3870	+	11.3870i	0.478209	+	0.478209i
$568$		0			0
$569$	−9.23630			−0.387206			−0.193603	−	0.981080i	$-0.562017\pi$
$569$	−9.23630			−0.387206			−0.193603	+	0.981080i	$0.562017\pi$
$570$		0			0
$571$	31.6530	−	31.6530i	1.32464	−	1.32464i	0.414663	−	0.909975i	$-0.363900\pi$
$571$	31.6530	−	31.6530i	1.32464	−	1.32464i	0.909975	−	0.414663i	$-0.136100\pi$
$572$		0			0
$573$		−	2.35546i		−	0.0984007i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	23.8539	+	23.8539i	0.993051	+	0.993051i	0.999976	−	0.00692502i	$-0.00220432\pi$
$577$	23.8539	+	23.8539i	0.993051	+	0.993051i	−0.00692502	+	0.999976i	$0.502204\pi$
$578$		0			0
$579$	−2.28723	+	2.28723i	−0.0950541	+	0.0950541i
$580$		0			0
$581$	5.47931	+	5.47931i	0.227320	+	0.227320i
$582$		0			0
$583$	18.3454	−	18.3454i	0.759787	−	0.759787i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	24.2348			1.00028			0.500138	−	0.865946i	$-0.333282\pi$
$587$	24.2348			1.00028			0.500138	+	0.865946i	$0.333282\pi$
$588$		0			0
$589$	−5.22893	−	5.22893i	−0.215454	−	0.215454i
$590$		0			0
$591$			4.39734i			0.180882i
$592$		0			0
$593$	15.4929	−	15.4929i	0.636219	−	0.636219i	−0.313402	−	0.949621i	$-0.601469\pi$
$593$	15.4929	−	15.4929i	0.636219	−	0.636219i	0.949621	+	0.313402i	$0.101469\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			1.80091i			0.0737065i
$598$		0			0
$599$			19.1812i			0.783722i	0.920024	+	0.391861i	$0.128169\pi$
$599$			19.1812i			0.783722i	−0.920024	+	0.391861i	$0.871831\pi$
$600$		0			0
$601$		−	21.7464i		−	0.887056i	−0.896261	−	0.443528i	$-0.853727\pi$
$601$		−	21.7464i		−	0.887056i	0.896261	−	0.443528i	$-0.146273\pi$
$602$		0			0
$603$		−	37.1079i		−	1.51115i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−20.2541	+	20.2541i	−0.822088	+	0.822088i	−0.986407	−	0.164319i	$-0.947457\pi$
$607$	−20.2541	+	20.2541i	−0.822088	+	0.822088i	0.164319	+	0.986407i	$0.447457\pi$
$608$		0			0
$609$		−	1.40110i		−	0.0567756i
$610$		0			0
$611$	−34.9538	−	34.9538i	−1.41408	−	1.41408i
$612$		0			0
$613$	−6.00698			−0.242620			−0.121310	−	0.992615i	$-0.538709\pi$
$613$	−6.00698			−0.242620			−0.121310	+	0.992615i	$0.538709\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	20.9289	−	20.9289i	0.842566	−	0.842566i	−0.146626	−	0.989192i	$-0.546841\pi$
$617$	20.9289	−	20.9289i	0.842566	−	0.842566i	0.989192	+	0.146626i	$0.0468413\pi$
$618$		0			0
$619$	−3.30074	−	3.30074i	−0.132668	−	0.132668i	0.637655	−	0.770322i	$-0.279905\pi$
$619$	−3.30074	−	3.30074i	−0.132668	−	0.132668i	−0.770322	+	0.637655i	$0.779905\pi$
$620$		0			0
$621$	3.30321	−	3.30321i	0.132553	−	0.132553i
$622$		0			0
$623$	0.725009	+	0.725009i	0.0290469	+	0.0290469i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		−	0.832374i		−	0.0332418i
$628$		0			0
$629$	14.1320	−	14.1320i	0.563479	−	0.563479i
$630$		0			0
$631$	−4.39734			−0.175055			−0.0875276	−	0.996162i	$-0.527897\pi$
$631$	−4.39734			−0.175055			−0.0875276	+	0.996162i	$0.527897\pi$
$632$		0			0
$633$	1.30494	+	1.30494i	0.0518669	+	0.0518669i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−14.7301			−0.583630
$638$		0			0
$639$	−30.9369			−1.22384
$640$		0			0
$641$	8.74978			0.345596			0.172798	−	0.984957i	$-0.444719\pi$
$641$	8.74978			0.345596			0.172798	+	0.984957i	$0.444719\pi$
$642$		0			0
$643$	−26.4968			−1.04493			−0.522466	−	0.852660i	$-0.674988\pi$
$643$	−26.4968			−1.04493			−0.522466	+	0.852660i	$0.674988\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−15.8343	−	15.8343i	−0.622512	−	0.622512i	0.323661	−	0.946173i	$-0.395086\pi$
$647$	−15.8343	−	15.8343i	−0.622512	−	0.622512i	−0.946173	+	0.323661i	$0.895086\pi$
$648$		0			0
$649$	−33.8616			−1.32919
$650$		0			0
$651$	1.71050	−	1.71050i	0.0670399	−	0.0670399i
$652$		0			0
$653$			26.4608i			1.03549i	0.855534	+	0.517746i	$0.173229\pi$
$653$			26.4608i			1.03549i	−0.855534	+	0.517746i	$0.826771\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	14.1666	+	14.1666i	0.552693	+	0.552693i
$658$		0			0
$659$	30.5128	−	30.5128i	1.18861	−	1.18861i	0.211156	−	0.977452i	$-0.432277\pi$
$659$	30.5128	−	30.5128i	1.18861	−	1.18861i	0.977452	−	0.211156i	$-0.0677228\pi$
$660$		0			0
$661$	−4.81695	−	4.81695i	−0.187358	−	0.187358i	0.607195	−	0.794553i	$-0.292295\pi$
$661$	−4.81695	−	4.81695i	−0.187358	−	0.187358i	−0.794553	+	0.607195i	$0.792295\pi$
$662$		0			0
$663$	−2.86883	+	2.86883i	−0.111416	+	0.111416i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	13.6552			0.528733
$668$		0			0
$669$	−0.726685	−	0.726685i	−0.0280953	−	0.0280953i
$670$		0			0
$671$		−	41.8399i		−	1.61521i
$672$		0			0
$673$	2.80519	−	2.80519i	0.108132	−	0.108132i	−0.650971	−	0.759103i	$-0.725638\pi$
$673$	2.80519	−	2.80519i	0.108132	−	0.108132i	0.759103	+	0.650971i	$0.225638\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	17.5498i		−	0.674492i	−0.941417	−	0.337246i	$-0.890505\pi$
$677$		−	17.5498i		−	0.674492i	0.941417	−	0.337246i	$-0.109495\pi$
$678$		0			0
$679$		−	32.2590i		−	1.23799i
$680$		0			0
$681$			0.129129i			0.00494823i
$682$		0			0
$683$		−	21.7834i		−	0.833518i	−0.909017	−	0.416759i	$-0.863166\pi$
$683$		−	21.7834i		−	0.833518i	0.909017	−	0.416759i	$-0.136834\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−1.94178	+	1.94178i	−0.0740833	+	0.0740833i
$688$		0			0
$689$		−	32.2162i		−	1.22734i
$690$		0			0
$691$	31.2147	+	31.2147i	1.18746	+	1.18746i	0.977767	+	0.209694i	$0.0672469\pi$
$691$	31.2147	+	31.2147i	1.18746	+	1.18746i	0.209694	+	0.977767i	$0.432753\pi$
$692$		0			0
$693$	−18.7057			−0.710569
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−23.2521	+	23.2521i	−0.880736	+	0.880736i
$698$		0			0
$699$	0.371464	+	0.371464i	0.0140501	+	0.0140501i
$700$		0			0
$701$	20.9248	−	20.9248i	0.790318	−	0.790318i	−0.191227	−	0.981546i	$-0.561247\pi$
$701$	20.9248	−	20.9248i	0.790318	−	0.790318i	0.981546	+	0.191227i	$0.0612468\pi$
$702$		0			0
$703$	3.60027	+	3.60027i	0.135787	+	0.135787i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	17.1005i		−	0.643132i
$708$		0			0
$709$	26.3703	−	26.3703i	0.990357	−	0.990357i	−0.00959736	−	0.999954i	$-0.503055\pi$
$709$	26.3703	−	26.3703i	0.990357	−	0.990357i	0.999954	+	0.00959736i	$0.00305498\pi$
$710$		0			0
$711$	25.7244			0.964741
$712$		0			0
$713$	16.6707	+	16.6707i	0.624322	+	0.624322i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	4.33724			0.161977
$718$		0			0
$719$	2.65374			0.0989679			0.0494840	−	0.998775i	$-0.484242\pi$
$719$	2.65374			0.0989679			0.0494840	+	0.998775i	$0.484242\pi$
$720$		0			0
$721$	17.3224			0.645119
$722$		0			0
$723$	−0.767746			−0.0285528
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−30.8999	−	30.8999i	−1.14601	−	1.14601i	−0.987329	−	0.158685i	$-0.949275\pi$
$727$	−30.8999	−	30.8999i	−1.14601	−	1.14601i	−0.158685	−	0.987329i	$-0.550725\pi$
$728$		0			0
$729$	−24.7034			−0.914940
$730$		0			0
$731$	31.0399	−	31.0399i	1.14805	−	1.14805i
$732$		0			0
$733$			46.2726i			1.70912i	0.519354	+	0.854559i	$0.326172\pi$
$733$			46.2726i			1.70912i	−0.519354	+	0.854559i	$0.673828\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	30.0288	+	30.0288i	1.10613	+	1.10613i
$738$		0			0
$739$	−12.0504	+	12.0504i	−0.443280	+	0.443280i	−0.893113	−	0.449833i	$-0.851484\pi$
$739$	−12.0504	+	12.0504i	−0.443280	+	0.443280i	0.449833	+	0.893113i	$0.351484\pi$
$740$		0			0
$741$	−0.730865	−	0.730865i	−0.0268490	−	0.0268490i
$742$		0			0
$743$	21.4100	−	21.4100i	0.785456	−	0.785456i	−0.195290	−	0.980746i	$-0.562565\pi$
$743$	21.4100	−	21.4100i	0.785456	−	0.785456i	0.980746	+	0.195290i	$0.0625648\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−12.2571			−0.448465
$748$		0			0
$749$	−21.6397	−	21.6397i	−0.790696	−	0.790696i
$750$		0			0
$751$		−	8.50828i		−	0.310472i	−0.987877	−	0.155236i	$-0.950386\pi$
$751$		−	8.50828i		−	0.310472i	0.987877	−	0.155236i	$-0.0496137\pi$
$752$		0			0
$753$	−0.130723	+	0.130723i	−0.00476379	+	0.00476379i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	29.2794i		−	1.06418i	−0.846688	−	0.532089i	$-0.821407\pi$
$757$		−	29.2794i		−	1.06418i	0.846688	−	0.532089i	$-0.178593\pi$
$758$		0			0
$759$			2.65374i			0.0963248i
$760$		0			0
$761$		−	39.3132i		−	1.42510i	−0.701621	−	0.712551i	$-0.747540\pi$
$761$		−	39.3132i		−	1.42510i	0.701621	−	0.712551i	$-0.252460\pi$
$762$		0			0
$763$		−	5.28739i		−	0.191416i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−29.7321	+	29.7321i	−1.07357	+	1.07357i
$768$		0			0
$769$			26.4222i			0.952809i	0.879226	+	0.476404i	$0.158060\pi$
$769$			26.4222i			0.952809i	−0.879226	+	0.476404i	$0.841940\pi$
$770$		0			0
$771$	−0.751892	−	0.751892i	−0.0270787	−	0.0270787i
$772$		0			0
$773$	−8.08416			−0.290767			−0.145383	−	0.989375i	$-0.546442\pi$
$773$	−8.08416			−0.290767			−0.145383	+	0.989375i	$0.546442\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.17773	+	1.17773i	−0.0422508	+	0.0422508i
$778$		0			0
$779$	−5.92371	−	5.92371i	−0.212239	−	0.212239i
$780$		0			0
$781$	25.0350	−	25.0350i	0.895823	−	0.895823i
$782$		0			0
$783$	3.15707	+	3.15707i	0.112824	+	0.112824i
$784$		0			0
$785$		0			0
$786$		0			0
$787$		−	40.5596i		−	1.44579i	−0.690955	−	0.722897i	$-0.742810\pi$
$787$		−	40.5596i		−	1.44579i	0.690955	−	0.722897i	$-0.257190\pi$
$788$		0			0
$789$	−1.09119	+	1.09119i	−0.0388474	+	0.0388474i
$790$		0			0
$791$	−31.3775			−1.11566
$792$		0			0
$793$	−36.7374	−	36.7374i	−1.30458	−	1.30458i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.85060			−0.0655517			−0.0327759	−	0.999463i	$-0.510435\pi$
$797$	−1.85060			−0.0655517			−0.0327759	+	0.999463i	$0.510435\pi$
$798$		0			0
$799$	−54.7455			−1.93676
$800$		0			0
$801$	−1.62184			−0.0573048
$802$		0			0
$803$	−22.9281			−0.809115
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.83168	+	1.83168i	0.0644783	+	0.0644783i
$808$		0			0
$809$	26.5823			0.934584			0.467292	−	0.884103i	$-0.345230\pi$
$809$	26.5823			0.934584			0.467292	+	0.884103i	$0.345230\pi$
$810$		0			0
$811$	−6.49812	+	6.49812i	−0.228180	+	0.228180i	−0.811932	−	0.583752i	$-0.801584\pi$
$811$	−6.49812	+	6.49812i	−0.228180	+	0.228180i	0.583752	+	0.811932i	$0.301584\pi$
$812$		0			0
$813$			6.41443i			0.224964i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	7.90773	+	7.90773i	0.276656	+	0.276656i
$818$		0			0
$819$	−16.4245	+	16.4245i	−0.573917	+	0.573917i
$820$		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
$823$	15.1106	−	15.1106i	0.526722	−	0.526722i	−0.392871	−	0.919593i	$-0.628518\pi$
$823$	15.1106	−	15.1106i	0.526722	−	0.526722i	0.919593	+	0.392871i	$0.128518\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.3792			0.465241			0.232621	−	0.972568i	$-0.425270\pi$
$827$	13.3792			0.465241			0.232621	+	0.972568i	$0.425270\pi$
$828$		0			0
$829$	5.81788	+	5.81788i	0.202063	+	0.202063i	0.800883	−	0.598820i	$-0.204364\pi$
$829$	5.81788	+	5.81788i	0.202063	+	0.202063i	−0.598820	+	0.800883i	$0.704364\pi$
$830$		0			0
$831$		−	3.92783i		−	0.136255i
$832$		0			0
$833$	−11.5354	+	11.5354i	−0.399677	+	0.399677i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			7.70845i			0.266443i
$838$		0			0
$839$		−	27.4305i		−	0.947006i	−0.880792	−	0.473503i	$-0.842989\pi$
$839$		−	27.4305i		−	0.947006i	0.880792	−	0.473503i	$-0.157011\pi$
$840$		0			0
$841$		−	15.9489i		−	0.549963i
$842$		0			0
$843$			1.35217i			0.0465713i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.596838	−	0.596838i	0.0205076	−	0.0205076i
$848$		0			0
$849$			3.33445i			0.114438i
$850$		0			0
$851$	−11.4782	−	11.4782i	−0.393469	−	0.393469i
$852$		0			0
$853$	16.6692			0.570742			0.285371	−	0.958417i	$-0.407883\pi$
$853$	16.6692			0.570742			0.285371	+	0.958417i	$0.407883\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.73331	−	4.73331i	0.161687	−	0.161687i	−0.621627	−	0.783314i	$-0.713528\pi$
$857$	4.73331	−	4.73331i	0.161687	−	0.161687i	0.783314	+	0.621627i	$0.213528\pi$
$858$		0			0
$859$	−26.3237	−	26.3237i	−0.898152	−	0.898152i	0.0971203	−	0.995273i	$-0.469037\pi$
$859$	−26.3237	−	26.3237i	−0.898152	−	0.898152i	−0.995273	+	0.0971203i	$0.969037\pi$
$860$		0			0
$861$	1.93778	−	1.93778i	0.0660394	−	0.0660394i
$862$		0			0
$863$	8.71130	+	8.71130i	0.296536	+	0.296536i	0.839655	−	0.543119i	$-0.182757\pi$
$863$	8.71130	+	8.71130i	0.296536	+	0.296536i	−0.543119	+	0.839655i	$0.682757\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			0.966284i			0.0328167i
$868$		0			0
$869$	−20.8170	+	20.8170i	−0.706167	+	0.706167i
$870$		0			0
$871$	52.7334			1.78680
$872$		0			0
$873$	36.0815	+	36.0815i	1.22117	+	1.22117i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	33.6674			1.13687			0.568433	−	0.822730i	$-0.307550\pi$
$877$	33.6674			1.13687			0.568433	+	0.822730i	$0.307550\pi$
$878$		0			0
$879$	0.172172			0.00580721
$880$		0			0
$881$	27.3058			0.919956			0.459978	−	0.887930i	$-0.347857\pi$
$881$	27.3058			0.919956			0.459978	+	0.887930i	$0.347857\pi$
$882$		0			0
$883$	−27.9628			−0.941023			−0.470511	−	0.882394i	$-0.655930\pi$
$883$	−27.9628			−0.941023			−0.470511	+	0.882394i	$0.655930\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.4497	+	12.4497i	0.418020	+	0.418020i	0.884521	−	0.466501i	$-0.154486\pi$
$887$	12.4497	+	12.4497i	0.418020	+	0.418020i	−0.466501	+	0.884521i	$0.654486\pi$
$888$		0			0
$889$	14.6975			0.492939
$890$		0			0
$891$	20.6132	−	20.6132i	0.690567	−	0.690567i
$892$		0			0
$893$		−	13.9470i		−	0.466718i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2.33011	+	2.33011i	0.0778002	+	0.0778002i
$898$		0			0
$899$	−15.9331	+	15.9331i	−0.531398	+	0.531398i
$900$		0			0
$901$	−25.2289	−	25.2289i	−0.840498	−	0.840498i
$902$		0			0
$903$	−2.58680	+	2.58680i	−0.0860833	+	0.0860833i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	38.3527			1.27348			0.636740	−	0.771078i	$-0.280282\pi$
$907$	38.3527			1.27348			0.636740	+	0.771078i	$0.280282\pi$
$908$		0			0
$909$	19.1269	+	19.1269i	0.634398	+	0.634398i
$910$		0			0
$911$			24.0192i			0.795791i	0.917431	+	0.397895i	$0.130259\pi$
$911$			24.0192i			0.795791i	−0.917431	+	0.397895i	$0.869741\pi$
$912$		0			0
$913$	9.91884	−	9.91884i	0.328266	−	0.328266i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	8.35846i		−	0.276021i
$918$		0			0
$919$			25.1211i			0.828668i	0.910125	+	0.414334i	$0.135986\pi$
$919$			25.1211i			0.828668i	−0.910125	+	0.414334i	$0.864014\pi$
$920$		0			0
$921$			5.89448i			0.194230i
$922$		0			0
$923$		−	43.9639i		−	1.44709i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−19.3750	+	19.3750i	−0.636358	+	0.636358i
$928$		0			0
$929$		−	39.8307i		−	1.30680i	−0.757012	−	0.653401i	$-0.773342\pi$
$929$		−	39.8307i		−	1.30680i	0.757012	−	0.653401i	$-0.226658\pi$
$930$		0			0
$931$	−2.93876	−	2.93876i	−0.0963139	−	0.0963139i
$932$		0			0
$933$	−6.59927			−0.216051
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−18.2763	+	18.2763i	−0.597060	+	0.597060i	−0.939529	−	0.342469i	$-0.888737\pi$
$937$	−18.2763	+	18.2763i	−0.597060	+	0.597060i	0.342469	+	0.939529i	$0.388737\pi$
$938$		0			0
$939$	−3.89474	−	3.89474i	−0.127100	−	0.127100i
$940$		0			0
$941$	−2.34852	+	2.34852i	−0.0765597	+	0.0765597i	−0.744350	−	0.667790i	$-0.767240\pi$
$941$	−2.34852	+	2.34852i	−0.0765597	+	0.0765597i	0.667790	+	0.744350i	$0.267240\pi$
$942$		0			0
$943$	18.8857	+	18.8857i	0.615004	+	0.615004i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	18.7829i		−	0.610363i	−0.952294	−	0.305181i	$-0.901283\pi$
$947$		−	18.7829i		−	0.610363i	0.952294	−	0.305181i	$-0.0987171\pi$
$948$		0			0
$949$	−20.1320	+	20.1320i	−0.653511	+	0.653511i
$950$		0			0
$951$	−2.20341			−0.0714505
$952$		0			0
$953$	9.07454	+	9.07454i	0.293953	+	0.293953i	0.838640	−	0.544687i	$-0.183351\pi$
$953$	9.07454	+	9.07454i	0.293953	+	0.293953i	−0.544687	+	0.838640i	$0.683351\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−2.53633			−0.0819879
$958$		0			0
$959$	1.34130			0.0433130
$960$		0			0
$961$	−7.90304			−0.254937
$962$		0			0
$963$	48.4077			1.55992
$964$		0			0
$965$		0			0
$966$		0			0
$967$	13.3057	+	13.3057i	0.427882	+	0.427882i	0.887906	−	0.460024i	$-0.152159\pi$
$967$	13.3057	+	13.3057i	0.427882	+	0.427882i	−0.460024	+	0.887906i	$0.652159\pi$
$968$		0			0
$969$	−1.14470			−0.0367730
$970$		0			0
$971$	−18.6349	+	18.6349i	−0.598023	+	0.598023i	−0.939786	−	0.341763i	$-0.888976\pi$
$971$	−18.6349	+	18.6349i	−0.598023	+	0.598023i	0.341763	+	0.939786i	$0.388976\pi$
$972$		0			0
$973$			14.5960i			0.467926i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.28407	−	7.28407i	−0.233038	−	0.233038i	0.580921	−	0.813960i	$-0.302692\pi$
$977$	−7.28407	−	7.28407i	−0.233038	−	0.233038i	−0.813960	+	0.580921i	$0.802692\pi$
$978$		0			0
$979$	1.31244	−	1.31244i	0.0419457	−	0.0419457i
$980$		0			0
$981$	5.91391	+	5.91391i	0.188817	+	0.188817i
$982$		0			0
$983$	−31.0322	+	31.0322i	−0.989772	+	0.989772i	−0.999948	−	0.0101761i	$-0.996761\pi$
$983$	−31.0322	+	31.0322i	−0.989772	+	0.989772i	0.0101761	+	0.999948i	$0.496761\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	4.56238			0.145222
$988$		0			0
$989$	−25.2111	−	25.2111i	−0.801666	−	0.801666i
$990$		0			0
$991$		−	40.1060i		−	1.27401i	−0.770860	−	0.637004i	$-0.780173\pi$
$991$		−	40.1060i		−	1.27401i	0.770860	−	0.637004i	$-0.219827\pi$
$992$		0			0
$993$	−4.64931	+	4.64931i	−0.147541	+	0.147541i
$994$		0			0
$995$		0			0
$996$		0			0
$997$		−	2.58204i		−	0.0817740i	−0.999164	−	0.0408870i	$-0.986982\pi$
$997$		−	2.58204i		−	0.0817740i	0.999164	−	0.0408870i	$-0.0130184\pi$
$998$		0			0
$999$		−	5.30749i		−	0.167921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.s.c.207.5		16
4.3	odd	2		400.2.s.c.107.5	yes	16
5.2	odd	4		1600.2.j.c.143.4		16
5.3	odd	4		1600.2.j.c.143.5		16
5.4	even	2	inner	1600.2.s.c.207.4		16
16.3	odd	4		1600.2.j.c.1007.4		16
16.13	even	4		400.2.j.c.307.1	yes	16
20.3	even	4		400.2.j.c.43.1	✓	16
20.7	even	4		400.2.j.c.43.8	yes	16
20.19	odd	2		400.2.s.c.107.4	yes	16
80.3	even	4	inner	1600.2.s.c.943.5		16
80.13	odd	4		400.2.s.c.243.5	yes	16
80.19	odd	4		1600.2.j.c.1007.5		16
80.29	even	4		400.2.j.c.307.8	yes	16
80.67	even	4	inner	1600.2.s.c.943.4		16
80.77	odd	4		400.2.s.c.243.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.c.43.1	✓	16	20.3	even	4
400.2.j.c.43.8	yes	16	20.7	even	4
400.2.j.c.307.1	yes	16	16.13	even	4
400.2.j.c.307.8	yes	16	80.29	even	4
400.2.s.c.107.4	yes	16	20.19	odd	2
400.2.s.c.107.5	yes	16	4.3	odd	2
400.2.s.c.243.4	yes	16	80.77	odd	4
400.2.s.c.243.5	yes	16	80.13	odd	4
1600.2.j.c.143.4		16	5.2	odd	4
1600.2.j.c.143.5		16	5.3	odd	4
1600.2.j.c.1007.4		16	16.3	odd	4
1600.2.j.c.1007.5		16	80.19	odd	4
1600.2.s.c.207.4		16	5.4	even	2	inner
1600.2.s.c.207.5		16	1.1	even	1	trivial
1600.2.s.c.943.4		16	80.67	even	4	inner
1600.2.s.c.943.5		16	80.3	even	4	inner

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Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.207468 q^{3} +(1.32185 + 1.32185i) q^{7} -2.95696 q^{9} +O(q^{10})\)	\(q+0.207468 q^{3} +(1.32185 + 1.32185i) q^{7} -2.95696 q^{9} +(2.39286 - 2.39286i) q^{11} -4.20208i q^{13} +(-3.29071 - 3.29071i) q^{17} +(0.838342 - 0.838342i) q^{19} +(0.274241 + 0.274241i) q^{21} +(-2.67277 + 2.67277i) q^{23} -1.23588 q^{27} +(-2.55451 - 2.55451i) q^{29} -6.23723i q^{31} +(0.496441 - 0.496441i) q^{33} +4.29451i q^{37} -0.871798i q^{39} -7.06598i q^{41} +9.43258i q^{43} +(8.31820 - 8.31820i) q^{47} -3.50544i q^{49} +(-0.682716 - 0.682716i) q^{51} +7.66672 q^{53} +(0.173929 - 0.173929i) q^{57} +(-7.07557 - 7.07557i) q^{59} +(8.74267 - 8.74267i) q^{61} +(-3.90865 - 3.90865i) q^{63} +12.5494i q^{67} +(-0.554514 + 0.554514i) q^{69} +10.4624 q^{71} +(-4.79095 - 4.79095i) q^{73} +6.32598 q^{77} -8.69963 q^{79} +8.61447 q^{81} +4.14519 q^{83} +(-0.529980 - 0.529980i) q^{87} +0.548482 q^{89} +(5.55451 - 5.55451i) q^{91} -1.29403i q^{93} +(-12.2022 - 12.2022i) q^{97} +(-7.07557 + 7.07557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{9}+O(q^{10}) \) 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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