LMFDB - Embedded newform 1600.2.s.c.943.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1600.207");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			943.7
Root			$-0.601202 - 1.28006i$ of defining polynomial
Character	$\chi$	$=$	1600.943
Dual form			1600.2.s.c.207.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.02856 q^{3} +(-3.26957 + 3.26957i) q^{7} +1.11507 q^{9} +O(q^{10})$	$q+2.02856 q^{3} +(-3.26957 + 3.26957i) q^{7} +1.11507 q^{9} +(-3.55423 - 3.55423i) q^{11} -1.41889i q^{13} +(-1.73396 + 1.73396i) q^{17} +(-4.19337 - 4.19337i) q^{19} +(-6.63253 + 6.63253i) q^{21} +(0.177886 + 0.177886i) q^{23} -3.82369 q^{27} +(-1.63915 + 1.63915i) q^{29} +8.15660i q^{31} +(-7.20998 - 7.20998i) q^{33} -1.34169i q^{37} -2.87831i q^{39} +1.16322i q^{41} +1.04265i q^{43} +(4.25549 + 4.25549i) q^{47} -14.3801i q^{49} +(-3.51745 + 3.51745i) q^{51} -8.19145 q^{53} +(-8.50653 - 8.50653i) q^{57} +(-3.96323 + 3.96323i) q^{59} +(-7.22353 - 7.22353i) q^{61} +(-3.64581 + 3.64581i) q^{63} -9.19784i q^{67} +(0.360853 + 0.360853i) q^{69} -11.4952 q^{71} +(5.86829 - 5.86829i) q^{73} +23.2416 q^{77} +11.3386 q^{79} -11.1018 q^{81} +12.0356 q^{83} +(-3.32512 + 3.32512i) q^{87} -13.2651 q^{89} +(4.63915 + 4.63915i) q^{91} +16.5462i q^{93} +(-5.71389 + 5.71389i) q^{97} +(-3.96323 - 3.96323i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^9	$ 16 q + 16 q^{9} - 8 q^{11} - 8 q^{19} - 16 q^{29} + 48 q^{51} - 8 q^{59} - 16 q^{61} + 16 q^{69} + 32 q^{71} + 80 q^{79} + 16 q^{81} + 64 q^{91} - 8 q^{99}+O(q^{100}) $ 16 * q + 16 * q^9 - 8 * q^11 - 8 * q^19 - 16 * q^29 + 48 * q^51 - 8 * q^59 - 16 * q^61 + 16 * q^69 + 32 * q^71 + 80 * q^79 + 16 * q^81 + 64 * q^91 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.02856			1.17119			0.585596	−	0.810603i	$-0.300860\pi$
$3$	2.02856			1.17119			0.585596	+	0.810603i	$0.300860\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.26957	+	3.26957i	−1.23578	+	1.23578i	−0.274070	+	0.961710i	$0.588370\pi$
$7$	−3.26957	+	3.26957i	−1.23578	+	1.23578i	−0.961710	+	0.274070i	$0.911630\pi$
$8$		0			0
$9$	1.11507			0.371691
$10$		0			0
$11$	−3.55423	−	3.55423i	−1.07164	−	1.07164i	−0.997228	−	0.0744120i	$-0.976292\pi$
$11$	−3.55423	−	3.55423i	−1.07164	−	1.07164i	−0.0744120	−	0.997228i	$-0.523708\pi$
$12$		0			0
$13$		−	1.41889i		−	0.393529i	−0.980451	−	0.196764i	$-0.936957\pi$
$13$		−	1.41889i		−	0.393529i	0.980451	−	0.196764i	$-0.0630434\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.73396	+	1.73396i	−0.420547	+	0.420547i	−0.885392	−	0.464845i	$-0.846110\pi$
$17$	−1.73396	+	1.73396i	−0.420547	+	0.420547i	0.464845	+	0.885392i	$0.346110\pi$
$18$		0			0
$19$	−4.19337	−	4.19337i	−0.962026	−	0.962026i	0.0372791	−	0.999305i	$-0.488131\pi$
$19$	−4.19337	−	4.19337i	−0.962026	−	0.962026i	−0.999305	+	0.0372791i	$0.988131\pi$
$20$		0			0
$21$	−6.63253	+	6.63253i	−1.44734	+	1.44734i
$22$		0			0
$23$	0.177886	+	0.177886i	0.0370918	+	0.0370918i	0.725409	−	0.688318i	$-0.241650\pi$
$23$	0.177886	+	0.177886i	0.0370918	+	0.0370918i	−0.688318	+	0.725409i	$0.741650\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.82369			−0.735870
$28$		0			0
$29$	−1.63915	+	1.63915i	−0.304382	+	0.304382i	−0.842725	−	0.538344i	$-0.819050\pi$
$29$	−1.63915	+	1.63915i	−0.304382	+	0.304382i	0.538344	+	0.842725i	$0.319050\pi$
$30$		0			0
$31$			8.15660i			1.46497i	0.680784	+	0.732484i	$0.261639\pi$
$31$			8.15660i			1.46497i	−0.680784	+	0.732484i	$0.738361\pi$
$32$		0			0
$33$	−7.20998	−	7.20998i	−1.25510	−	1.25510i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	1.34169i		−	0.220573i	−0.993900	−	0.110286i	$-0.964823\pi$
$37$		−	1.34169i		−	0.220573i	0.993900	−	0.110286i	$-0.0351768\pi$
$38$		0			0
$39$		−	2.87831i		−	0.460898i
$40$		0			0
$41$			1.16322i			0.181664i	0.995866	+	0.0908322i	$0.0289527\pi$
$41$			1.16322i			0.181664i	−0.995866	+	0.0908322i	$0.971047\pi$
$42$		0			0
$43$			1.04265i			0.159002i	0.996835	+	0.0795010i	$0.0253327\pi$
$43$			1.04265i			0.159002i	−0.996835	+	0.0795010i	$0.974667\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.25549	+	4.25549i	0.620726	+	0.620726i	0.945717	−	0.324991i	$-0.105361\pi$
$47$	4.25549	+	4.25549i	0.620726	+	0.620726i	−0.324991	+	0.945717i	$0.605361\pi$
$48$		0			0
$49$		−	14.3801i		−	2.05430i
$50$		0			0
$51$	−3.51745	+	3.51745i	−0.492542	+	0.492542i
$52$		0			0
$53$	−8.19145			−1.12518			−0.562591	−	0.826735i	$-0.690196\pi$
$53$	−8.19145			−1.12518			−0.562591	+	0.826735i	$0.690196\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−8.50653	−	8.50653i	−1.12672	−	1.12672i
$58$		0			0
$59$	−3.96323	+	3.96323i	−0.515968	+	0.515968i	−0.916349	−	0.400381i	$-0.868878\pi$
$59$	−3.96323	+	3.96323i	−0.515968	+	0.515968i	0.400381	+	0.916349i	$0.368878\pi$
$60$		0			0
$61$	−7.22353	−	7.22353i	−0.924878	−	0.924878i	0.0724912	−	0.997369i	$-0.476905\pi$
$61$	−7.22353	−	7.22353i	−0.924878	−	0.924878i	−0.997369	+	0.0724912i	$0.976905\pi$
$62$		0			0
$63$	−3.64581	+	3.64581i	−0.459329	+	0.459329i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	9.19784i		−	1.12370i	−0.827241	−	0.561848i	$-0.810091\pi$
$67$		−	9.19784i		−	1.12370i	0.827241	−	0.561848i	$-0.189909\pi$
$68$		0			0
$69$	0.360853	+	0.360853i	0.0434416	+	0.0434416i
$70$		0			0
$71$	−11.4952			−1.36423			−0.682115	−	0.731245i	$-0.738939\pi$
$71$	−11.4952			−1.36423			−0.682115	+	0.731245i	$0.738939\pi$
$72$		0			0
$73$	5.86829	−	5.86829i	0.686831	−	0.686831i	−0.274699	−	0.961530i	$-0.588578\pi$
$73$	5.86829	−	5.86829i	0.686831	−	0.686831i	0.961530	+	0.274699i	$0.0885783\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	23.2416			2.64862
$78$		0			0
$79$	11.3386			1.27569			0.637846	−	0.770164i	$-0.279826\pi$
$79$	11.3386			1.27569			0.637846	+	0.770164i	$0.279826\pi$
$80$		0			0
$81$	−11.1018			−1.23354
$82$		0			0
$83$	12.0356			1.32108			0.660540	−	0.750790i	$-0.270327\pi$
$83$	12.0356			1.32108			0.660540	+	0.750790i	$0.270327\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−3.32512	+	3.32512i	−0.356490	+	0.356490i
$88$		0			0
$89$	−13.2651			−1.40609			−0.703046	−	0.711144i	$-0.748177\pi$
$89$	−13.2651			−1.40609			−0.703046	+	0.711144i	$0.748177\pi$
$90$		0			0
$91$	4.63915	+	4.63915i	0.486315	+	0.486315i
$92$		0			0
$93$			16.5462i			1.71576i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.71389	+	5.71389i	−0.580158	+	0.580158i	−0.934947	−	0.354789i	$-0.884553\pi$
$97$	−5.71389	+	5.71389i	−0.580158	+	0.580158i	0.354789	+	0.934947i	$0.384553\pi$
$98$		0			0
$99$	−3.96323	−	3.96323i	−0.398319	−	0.398319i
$100$		0			0
$101$	2.59100	−	2.59100i	0.257814	−	0.257814i	−0.566350	−	0.824165i	$-0.691645\pi$
$101$	2.59100	−	2.59100i	0.257814	−	0.257814i	0.824165	+	0.566350i	$0.191645\pi$
$102$		0			0
$103$	−2.89332	−	2.89332i	−0.285088	−	0.285088i	0.550046	−	0.835134i	$-0.314610\pi$
$103$	−2.89332	−	2.89332i	−0.285088	−	0.285088i	−0.835134	+	0.550046i	$0.814610\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.24009			0.603252			0.301626	−	0.953426i	$-0.402471\pi$
$107$	6.24009			0.603252			0.301626	+	0.953426i	$0.402471\pi$
$108$		0			0
$109$	−2.00000	+	2.00000i	−0.191565	+	0.191565i	−0.796372	−	0.604807i	$-0.793250\pi$
$109$	−2.00000	+	2.00000i	−0.191565	+	0.191565i	0.604807	+	0.796372i	$0.293250\pi$
$110$		0			0
$111$		−	2.72171i		−	0.258333i
$112$		0			0
$113$	9.61034	+	9.61034i	0.904065	+	0.904065i	0.995785	−	0.0917199i	$-0.0292364\pi$
$113$	9.61034	+	9.61034i	0.904065	+	0.904065i	−0.0917199	+	0.995785i	$0.529236\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		−	1.58216i		−	0.146271i
$118$		0			0
$119$		−	11.3386i		−	1.03941i
$120$		0			0
$121$			14.2651i			1.29682i
$122$		0			0
$123$			2.35967i			0.212764i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	11.5266	+	11.5266i	1.02282	+	1.02282i	0.999733	+	0.0230897i	$0.00735034\pi$
$127$	11.5266	+	11.5266i	1.02282	+	1.02282i	0.0230897	+	0.999733i	$0.492650\pi$
$128$		0			0
$129$			2.11507i			0.186222i
$130$		0			0
$131$	−8.19337	+	8.19337i	−0.715858	+	0.715858i	−0.967754	−	0.251896i	$-0.918946\pi$
$131$	−8.19337	+	8.19337i	−0.715858	+	0.715858i	0.251896	+	0.967754i	$0.418946\pi$
$132$		0			0
$133$	27.4210			2.37770
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.81771	+	6.81771i	0.582476	+	0.582476i	0.935583	−	0.353107i	$-0.114875\pi$
$137$	6.81771	+	6.81771i	0.582476	+	0.582476i	−0.353107	+	0.935583i	$0.614875\pi$
$138$		0			0
$139$	3.32408	−	3.32408i	0.281945	−	0.281945i	−0.551939	−	0.833884i	$-0.686112\pi$
$139$	3.32408	−	3.32408i	0.281945	−	0.281945i	0.833884	+	0.551939i	$0.186112\pi$
$140$		0			0
$141$	8.63253	+	8.63253i	0.726990	+	0.726990i
$142$		0			0
$143$	−5.04305	+	5.04305i	−0.421721	+	0.421721i
$144$		0			0
$145$		0			0
$146$		0			0
$147$		−	29.1710i		−	2.40598i
$148$		0			0
$149$	−4.99338	−	4.99338i	−0.409074	−	0.409074i	0.472342	−	0.881415i	$-0.343409\pi$
$149$	−4.99338	−	4.99338i	−0.409074	−	0.409074i	−0.881415	+	0.472342i	$0.843409\pi$
$150$		0			0
$151$	−10.8783			−0.885264			−0.442632	−	0.896703i	$-0.645955\pi$
$151$	−10.8783			−0.885264			−0.442632	+	0.896703i	$0.645955\pi$
$152$		0			0
$153$	−1.93349	+	1.93349i	−0.156314	+	0.156314i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−4.01619			−0.320527			−0.160263	−	0.987074i	$-0.551234\pi$
$157$	−4.01619			−0.320527			−0.160263	+	0.987074i	$0.551234\pi$
$158$		0			0
$159$	−16.6169			−1.31781
$160$		0			0
$161$	−1.16322			−0.0916746
$162$		0			0
$163$	1.31702			0.103157			0.0515785	−	0.998669i	$-0.483575\pi$
$163$	1.31702			0.103157			0.0515785	+	0.998669i	$0.483575\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.53755	+	2.53755i	−0.196362	+	0.196362i	−0.798438	−	0.602077i	$-0.794340\pi$
$167$	−2.53755	+	2.53755i	−0.196362	+	0.196362i	0.602077	+	0.798438i	$0.294340\pi$
$168$		0			0
$169$	10.9868			0.845135
$170$		0			0
$171$	−4.67592	−	4.67592i	−0.357577	−	0.357577i
$172$		0			0
$173$			9.45595i			0.718922i	0.933160	+	0.359461i	$0.117040\pi$
$173$			9.45595i			0.718922i	−0.933160	+	0.359461i	$0.882960\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−8.03966	+	8.03966i	−0.604298	+	0.604298i
$178$		0			0
$179$	8.60237	+	8.60237i	0.642971	+	0.642971i	0.951285	−	0.308313i	$-0.0997645\pi$
$179$	8.60237	+	8.60237i	0.642971	+	0.642971i	−0.308313	+	0.951285i	$0.599765\pi$
$180$		0			0
$181$	−0.591001	+	0.591001i	−0.0439288	+	0.0439288i	−0.728730	−	0.684801i	$-0.759889\pi$
$181$	−0.591001	+	0.591001i	−0.0439288	+	0.0439288i	0.684801	+	0.728730i	$0.259889\pi$
$182$		0			0
$183$	−14.6534	−	14.6534i	−1.08321	−	1.08321i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	12.3258			0.901350
$188$		0			0
$189$	12.5018	−	12.5018i	0.909374	−	0.909374i
$190$		0			0
$191$		−	8.77349i		−	0.634828i	−0.948287	−	0.317414i	$-0.897186\pi$
$191$		−	8.77349i		−	0.634828i	0.948287	−	0.317414i	$-0.102814\pi$
$192$		0			0
$193$	−14.6127	−	14.6127i	−1.05184	−	1.05184i	−0.998580	−	0.0532641i	$-0.983037\pi$
$193$	−14.6127	−	14.6127i	−1.05184	−	1.05184i	−0.0532641	−	0.998580i	$-0.516963\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			1.57328i			0.112092i	0.998428	+	0.0560458i	$0.0178493\pi$
$197$			1.57328i			0.112092i	−0.998428	+	0.0560458i	$0.982151\pi$
$198$		0			0
$199$			16.9386i			1.20075i	0.799720	+	0.600373i	$0.204981\pi$
$199$			16.9386i			1.20075i	−0.799720	+	0.600373i	$0.795019\pi$
$200$		0			0
$201$		−	18.6584i		−	1.31606i
$202$		0			0
$203$		−	10.7186i		−	0.752298i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.198356	+	0.198356i	0.0137867	+	0.0137867i
$208$		0			0
$209$			29.8084i			2.06189i
$210$		0			0
$211$	15.0717	−	15.0717i	1.03758	−	1.03758i	0.0383113	−	0.999266i	$-0.487802\pi$
$211$	15.0717	−	15.0717i	1.03758	−	1.03758i	0.999266	−	0.0383113i	$-0.0121978\pi$
$212$		0			0
$213$	−23.3188			−1.59777
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−26.6685	−	26.6685i	−1.81038	−	1.81038i
$218$		0			0
$219$	11.9042	−	11.9042i	0.804411	−	0.804411i
$220$		0			0
$221$	2.46030	+	2.46030i	0.165497	+	0.165497i
$222$		0			0
$223$	−7.93637	+	7.93637i	−0.531459	+	0.531459i	−0.921006	−	0.389548i	$-0.872631\pi$
$223$	−7.93637	+	7.93637i	−0.531459	+	0.531459i	0.389548	+	0.921006i	$0.372631\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	6.08569i		−	0.403922i	−0.979394	−	0.201961i	$-0.935269\pi$
$227$		−	6.08569i		−	0.403922i	0.979394	−	0.201961i	$-0.0647314\pi$
$228$		0			0
$229$	−2.13071	−	2.13071i	−0.140801	−	0.140801i	0.633193	−	0.773994i	$-0.281744\pi$
$229$	−2.13071	−	2.13071i	−0.140801	−	0.140801i	−0.773994	+	0.633193i	$0.781744\pi$
$230$		0			0
$231$	47.1470			3.10204
$232$		0			0
$233$	9.33621	−	9.33621i	0.611635	−	0.611635i	−0.331737	−	0.943372i	$-0.607635\pi$
$233$	9.33621	−	9.33621i	0.611635	−	0.611635i	0.943372	+	0.331737i	$0.107635\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	23.0011			1.49408
$238$		0			0
$239$	−28.5904			−1.84936			−0.924680	−	0.380745i	$-0.875667\pi$
$239$	−28.5904			−1.84936			−0.924680	+	0.380745i	$0.875667\pi$
$240$		0			0
$241$	7.87168			0.507060			0.253530	−	0.967328i	$-0.418408\pi$
$241$	7.87168			0.507060			0.253530	+	0.967328i	$0.418408\pi$
$242$		0			0
$243$	−11.0497			−0.708839
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5.94993	+	5.94993i	−0.378585	+	0.378585i
$248$		0			0
$249$	24.4150			1.54724
$250$		0			0
$251$	3.39763	+	3.39763i	0.214456	+	0.214456i	0.806157	−	0.591701i	$-0.201543\pi$
$251$	3.39763	+	3.39763i	0.214456	+	0.214456i	−0.591701	+	0.806157i	$0.701543\pi$
$252$		0			0
$253$		−	1.26449i		−	0.0794981i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−17.0582	+	17.0582i	−1.06406	+	1.06406i	−0.0662586	+	0.997802i	$0.521106\pi$
$257$	−17.0582	+	17.0582i	−1.06406	+	1.06406i	−0.997802	+	0.0662586i	$0.978894\pi$
$258$		0			0
$259$	4.38675	+	4.38675i	0.272579	+	0.272579i
$260$		0			0
$261$	−1.82777	+	1.82777i	−0.113136	+	0.113136i
$262$		0			0
$263$	−6.73749	−	6.73749i	−0.415451	−	0.415451i	0.468181	−	0.883632i	$-0.344909\pi$
$263$	−6.73749	−	6.73749i	−0.415451	−	0.415451i	−0.883632	+	0.468181i	$0.844909\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−26.9090			−1.64680
$268$		0			0
$269$	1.00662	−	1.00662i	0.0613748	−	0.0613748i	−0.675753	−	0.737128i	$-0.736181\pi$
$269$	1.00662	−	1.00662i	0.0613748	−	0.0613748i	0.737128	+	0.675753i	$0.236181\pi$
$270$		0			0
$271$		−	7.21799i		−	0.438461i	−0.975673	−	0.219231i	$-0.929645\pi$
$271$		−	7.21799i		−	0.438461i	0.975673	−	0.219231i	$-0.0703547\pi$
$272$		0			0
$273$	9.41081	+	9.41081i	0.569568	+	0.569568i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			18.9849i			1.14069i	0.821405	+	0.570346i	$0.193191\pi$
$277$			18.9849i			1.14069i	−0.821405	+	0.570346i	$0.806809\pi$
$278$		0			0
$279$			9.09521i			0.544516i
$280$		0			0
$281$		−	14.4283i		−	0.860719i	−0.902658	−	0.430359i	$-0.858387\pi$
$281$		−	14.4283i		−	0.860719i	0.902658	−	0.430359i	$-0.141613\pi$
$282$		0			0
$283$		−	15.1478i		−	0.900441i	−0.892917	−	0.450221i	$-0.851345\pi$
$283$		−	15.1478i		−	0.900441i	0.892917	−	0.450221i	$-0.148655\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.80322	−	3.80322i	−0.224497	−	0.224497i
$288$		0			0
$289$			10.9868i			0.646280i
$290$		0			0
$291$	−11.5910	+	11.5910i	−0.679477	+	0.679477i
$292$		0			0
$293$	8.11426			0.474040			0.237020	−	0.971505i	$-0.423829\pi$
$293$	8.11426			0.474040			0.237020	+	0.971505i	$0.423829\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	13.5903	+	13.5903i	0.788588	+	0.788588i
$298$		0			0
$299$	0.252400	−	0.252400i	0.0145967	−	0.0145967i
$300$		0			0
$301$	−3.40900	−	3.40900i	−0.196491	−	0.196491i
$302$		0			0
$303$	5.25601	−	5.25601i	0.301950	−	0.301950i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			30.0370i			1.71430i	0.515067	+	0.857150i	$0.327767\pi$
$307$			30.0370i			1.71430i	−0.515067	+	0.857150i	$0.672233\pi$
$308$		0			0
$309$	−5.86929	−	5.86929i	−0.333893	−	0.333893i
$310$		0			0
$311$	−9.93969			−0.563628			−0.281814	−	0.959469i	$-0.590936\pi$
$311$	−9.93969			−0.563628			−0.281814	+	0.959469i	$0.590936\pi$
$312$		0			0
$313$	4.84587	−	4.84587i	0.273905	−	0.273905i	−0.556765	−	0.830670i	$-0.687958\pi$
$313$	4.84587	−	4.84587i	0.273905	−	0.273905i	0.830670	+	0.556765i	$0.187958\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−24.5832			−1.38073			−0.690366	−	0.723460i	$-0.742551\pi$
$317$	−24.5832			−1.38073			−0.690366	+	0.723460i	$0.742551\pi$
$318$		0			0
$319$	11.6518			0.652375
$320$		0			0
$321$	12.6584			0.706524
$322$		0			0
$323$	14.5423			0.809155
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−4.05713	+	4.05713i	−0.224360	+	0.224360i
$328$		0			0
$329$	−27.8272			−1.53416
$330$		0			0
$331$	6.41028	+	6.41028i	0.352341	+	0.352341i	0.860980	−	0.508639i	$-0.169851\pi$
$331$	6.41028	+	6.41028i	0.352341	+	0.352341i	−0.508639	+	0.860980i	$0.669851\pi$
$332$		0			0
$333$		−	1.49608i		−	0.0819849i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	13.5903	−	13.5903i	0.740309	−	0.740309i	−0.232328	−	0.972637i	$-0.574634\pi$
$337$	13.5903	−	13.5903i	0.740309	−	0.740309i	0.972637	+	0.232328i	$0.0746343\pi$
$338$		0			0
$339$	19.4952	+	19.4952i	1.05883	+	1.05883i
$340$		0			0
$341$	28.9904	−	28.9904i	1.56992	−	1.56992i
$342$		0			0
$343$	24.1298	+	24.1298i	1.30289	+	1.30289i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−22.2352			−1.19365			−0.596823	−	0.802373i	$-0.703571\pi$
$347$	−22.2352			−1.19365			−0.596823	+	0.802373i	$0.703571\pi$
$348$		0			0
$349$	−5.54286	+	5.54286i	−0.296702	+	0.296702i	−0.839721	−	0.543018i	$-0.817281\pi$
$349$	−5.54286	+	5.54286i	−0.296702	+	0.296702i	0.543018	+	0.839721i	$0.317281\pi$
$350$		0			0
$351$			5.42539i			0.289586i
$352$		0			0
$353$	−13.7898	−	13.7898i	−0.733957	−	0.733957i	0.237444	−	0.971401i	$-0.423690\pi$
$353$	−13.7898	−	13.7898i	−0.733957	−	0.733957i	−0.971401	+	0.237444i	$0.923690\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	23.0011i		−	1.21735i
$358$		0			0
$359$			10.2529i			0.541127i	0.962702	+	0.270563i	$0.0872100\pi$
$359$			10.2529i			0.541127i	−0.962702	+	0.270563i	$0.912790\pi$
$360$		0			0
$361$			16.1688i			0.850987i
$362$		0			0
$363$			28.9376i			1.51883i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	7.66200	+	7.66200i	0.399953	+	0.399953i	0.878216	−	0.478263i	$-0.158734\pi$
$367$	7.66200	+	7.66200i	0.399953	+	0.399953i	−0.478263	+	0.878216i	$0.658734\pi$
$368$		0			0
$369$			1.29708i			0.0675231i
$370$		0			0
$371$	26.7825	−	26.7825i	1.39048	−	1.39048i
$372$		0			0
$373$	−2.52010			−0.130486			−0.0652430	−	0.997869i	$-0.520782\pi$
$373$	−2.52010			−0.130486			−0.0652430	+	0.997869i	$0.520782\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.32577	+	2.32577i	0.119783	+	0.119783i
$378$		0			0
$379$	−11.7844	+	11.7844i	−0.605323	+	0.605323i	−0.941720	−	0.336397i	$-0.890791\pi$
$379$	−11.7844	+	11.7844i	−0.605323	+	0.605323i	0.336397	+	0.941720i	$0.390791\pi$
$380$		0			0
$381$	23.3825	+	23.3825i	1.19792	+	1.19792i
$382$		0			0
$383$	22.0006	−	22.0006i	1.12418	−	1.12418i	0.133069	−	0.991107i	$-0.457517\pi$
$383$	22.0006	−	22.0006i	1.12418	−	1.12418i	0.991107	−	0.133069i	$-0.0424832\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			1.16263i			0.0590997i
$388$		0			0
$389$	15.0897	+	15.0897i	0.765077	+	0.765077i	0.977235	−	0.212159i	$-0.0680493\pi$
$389$	15.0897	+	15.0897i	0.765077	+	0.765077i	−0.212159	+	0.977235i	$0.568049\pi$
$390$		0			0
$391$	−0.616895			−0.0311977
$392$		0			0
$393$	−16.6208	+	16.6208i	−0.838408	+	0.838408i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	4.10227			0.205887			0.102943	−	0.994687i	$-0.467174\pi$
$397$	4.10227			0.205887			0.102943	+	0.994687i	$0.467174\pi$
$398$		0			0
$399$	55.6253			2.78475
$400$		0			0
$401$	9.16876			0.457866			0.228933	−	0.973442i	$-0.426476\pi$
$401$	9.16876			0.457866			0.228933	+	0.973442i	$0.426476\pi$
$402$		0			0
$403$	11.5733			0.576507
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.76867	+	4.76867i	−0.236374	+	0.236374i
$408$		0			0
$409$	1.16322			0.0575175			0.0287588	−	0.999586i	$-0.490845\pi$
$409$	1.16322			0.0575175			0.0287588	+	0.999586i	$0.490845\pi$
$410$		0			0
$411$	13.8302	+	13.8302i	0.682191	+	0.682191i
$412$		0			0
$413$		−	25.9161i		−	1.27525i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	6.74311	−	6.74311i	0.330211	−	0.330211i
$418$		0			0
$419$	−7.62778	−	7.62778i	−0.372641	−	0.372641i	0.495797	−	0.868438i	$-0.334876\pi$
$419$	−7.62778	−	7.62778i	−0.372641	−	0.372641i	−0.868438	+	0.495797i	$0.834876\pi$
$420$		0			0
$421$	17.7801	−	17.7801i	0.866550	−	0.866550i	−0.125539	−	0.992089i	$-0.540066\pi$
$421$	17.7801	−	17.7801i	0.866550	−	0.866550i	0.992089	+	0.125539i	$0.0400660\pi$
$422$		0			0
$423$	4.74518	+	4.74518i	0.230719	+	0.230719i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	47.2356			2.28589
$428$		0			0
$429$	−10.2301	+	10.2301i	−0.493916	+	0.493916i
$430$		0			0
$431$		−	38.3735i		−	1.84839i	−0.381925	−	0.924193i	$-0.624739\pi$
$431$		−	38.3735i		−	1.84839i	0.381925	−	0.924193i	$-0.375261\pi$
$432$		0			0
$433$	−3.69692	−	3.69692i	−0.177662	−	0.177662i	0.612674	−	0.790336i	$-0.290094\pi$
$433$	−3.69692	−	3.69692i	−0.177662	−	0.177662i	−0.790336	+	0.612674i	$0.790094\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	1.49188i		−	0.0713665i
$438$		0			0
$439$		−	29.9132i		−	1.42768i	−0.700309	−	0.713840i	$-0.746954\pi$
$439$		−	29.9132i		−	1.42768i	0.700309	−	0.713840i	$-0.253046\pi$
$440$		0			0
$441$		−	16.0349i		−	0.763567i
$442$		0			0
$443$			25.5920i			1.21591i	0.793971	+	0.607956i	$0.208010\pi$
$443$			25.5920i			1.21591i	−0.793971	+	0.607956i	$0.791990\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−10.1294	−	10.1294i	−0.479104	−	0.479104i
$448$		0			0
$449$		−	20.5621i		−	0.970387i	−0.874407	−	0.485193i	$-0.838749\pi$
$449$		−	20.5621i		−	0.970387i	0.874407	−	0.485193i	$-0.161251\pi$
$450$		0			0
$451$	4.13435	−	4.13435i	0.194679	−	0.194679i
$452$		0			0
$453$	−22.0673			−1.03681
$454$		0			0
$455$		0			0
$456$		0			0
$457$	8.06912	+	8.06912i	0.377457	+	0.377457i	0.870184	−	0.492727i	$-0.164000\pi$
$457$	8.06912	+	8.06912i	0.377457	+	0.377457i	−0.492727	+	0.870184i	$0.664000\pi$
$458$		0			0
$459$	6.63014	−	6.63014i	0.309468	−	0.309468i
$460$		0			0
$461$	−26.3994	−	26.3994i	−1.22954	−	1.22954i	−0.964137	−	0.265406i	$-0.914494\pi$
$461$	−26.3994	−	26.3994i	−1.22954	−	1.22954i	−0.265406	−	0.964137i	$-0.585506\pi$
$462$		0			0
$463$	−24.0654	+	24.0654i	−1.11841	+	1.11841i	−0.126438	+	0.991974i	$0.540355\pi$
$463$	−24.0654	+	24.0654i	−1.11841	+	1.11841i	−0.991974	+	0.126438i	$0.959645\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	11.2041i		−	0.518464i	−0.965815	−	0.259232i	$-0.916531\pi$
$467$		−	11.2041i		−	0.518464i	0.965815	−	0.259232i	$-0.0834694\pi$
$468$		0			0
$469$	30.0730	+	30.0730i	1.38864	+	1.38864i
$470$		0			0
$471$	−8.14710			−0.375398
$472$		0			0
$473$	3.70580	−	3.70580i	0.170393	−	0.170393i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−9.13408			−0.418221
$478$		0			0
$479$	−8.47832			−0.387384			−0.193692	−	0.981062i	$-0.562046\pi$
$479$	−8.47832			−0.387384			−0.193692	+	0.981062i	$0.562046\pi$
$480$		0			0
$481$	−1.90371			−0.0868016
$482$		0			0
$483$	−2.35967			−0.107369
$484$		0			0
$485$		0			0
$486$		0			0
$487$	12.1684	−	12.1684i	0.551401	−	0.551401i	−0.375444	−	0.926845i	$-0.622510\pi$
$487$	12.1684	−	12.1684i	0.551401	−	0.551401i	0.926845	+	0.375444i	$0.122510\pi$
$488$		0			0
$489$	2.67166			0.120817
$490$		0			0
$491$	−14.6114	−	14.6114i	−0.659402	−	0.659402i	0.295836	−	0.955239i	$-0.404402\pi$
$491$	−14.6114	−	14.6114i	−0.659402	−	0.659402i	−0.955239	+	0.295836i	$0.904402\pi$
$492$		0			0
$493$		−	5.68443i		−	0.256014i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	37.5843	−	37.5843i	1.68589	−	1.68589i
$498$		0			0
$499$	−1.88067	−	1.88067i	−0.0841902	−	0.0841902i	0.663758	−	0.747948i	$-0.268961\pi$
$499$	−1.88067	−	1.88067i	−0.0841902	−	0.0841902i	−0.747948	+	0.663758i	$0.768961\pi$
$500$		0			0
$501$	−5.14759	+	5.14759i	−0.229977	+	0.229977i
$502$		0			0
$503$	−4.31406	−	4.31406i	−0.192354	−	0.192354i	0.604358	−	0.796713i	$-0.293430\pi$
$503$	−4.31406	−	4.31406i	−0.192354	−	0.192354i	−0.796713	+	0.604358i	$0.793430\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	22.2873			0.989816
$508$		0			0
$509$	−21.2174	+	21.2174i	−0.940445	+	0.940445i	−0.998324	−	0.0578791i	$-0.981566\pi$
$509$	−21.2174	+	21.2174i	−0.940445	+	0.940445i	0.0578791	+	0.998324i	$0.481566\pi$
$510$		0			0
$511$			38.3735i			1.69754i
$512$		0			0
$513$	16.0342	+	16.0342i	0.707926	+	0.707926i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	30.2499i		−	1.33039i
$518$		0			0
$519$			19.1820i			0.841996i
$520$		0			0
$521$			25.0036i			1.09543i	0.836665	+	0.547715i	$0.184502\pi$
$521$			25.0036i			1.09543i	−0.836665	+	0.547715i	$0.815498\pi$
$522$		0			0
$523$		−	26.7211i		−	1.16843i	−0.811599	−	0.584215i	$-0.801402\pi$
$523$		−	26.7211i		−	1.16843i	0.811599	−	0.584215i	$-0.198598\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−14.1432	−	14.1432i	−0.616089	−	0.616089i
$528$		0			0
$529$		−	22.9367i		−	0.997248i
$530$		0			0
$531$	−4.41929	+	4.41929i	−0.191781	+	0.191781i
$532$		0			0
$533$	1.65048			0.0714901
$534$		0			0
$535$		0			0
$536$		0			0
$537$	17.4505	+	17.4505i	0.753043	+	0.753043i
$538$		0			0
$539$	−51.1102	+	51.1102i	−2.20147	+	2.20147i
$540$		0			0
$541$	−1.17885	−	1.17885i	−0.0506828	−	0.0506828i	0.681311	−	0.731994i	$-0.261410\pi$
$541$	−1.17885	−	1.17885i	−0.0506828	−	0.0506828i	−0.731994	+	0.681311i	$0.761410\pi$
$542$		0			0
$543$	−1.19888	+	1.19888i	−0.0514490	+	0.0514490i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			25.8142i			1.10373i	0.833932	+	0.551867i	$0.186085\pi$
$547$			25.8142i			1.10373i	−0.833932	+	0.551867i	$0.813915\pi$
$548$		0			0
$549$	−8.05477	−	8.05477i	−0.343769	−	0.343769i
$550$		0			0
$551$	13.7471			0.585647
$552$		0			0
$553$	−37.0723	+	37.0723i	−1.57647	+	1.57647i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.09807			−0.173641			−0.0868204	−	0.996224i	$-0.527671\pi$
$557$	−4.09807			−0.173641			−0.0868204	+	0.996224i	$0.527671\pi$
$558$		0			0
$559$	1.47940			0.0625718
$560$		0			0
$561$	25.0036			1.05565
$562$		0			0
$563$	−36.4537			−1.53634			−0.768171	−	0.640245i	$-0.778833\pi$
$563$	−36.4537			−1.53634			−0.768171	+	0.640245i	$0.778833\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	36.2982	−	36.2982i	1.52438	−	1.52438i
$568$		0			0
$569$	−2.68968			−0.112757			−0.0563787	−	0.998409i	$-0.517955\pi$
$569$	−2.68968			−0.112757			−0.0563787	+	0.998409i	$0.517955\pi$
$570$		0			0
$571$	17.6505	+	17.6505i	0.738651	+	0.738651i	0.972317	−	0.233666i	$-0.0750722\pi$
$571$	17.6505	+	17.6505i	0.738651	+	0.738651i	−0.233666	+	0.972317i	$0.575072\pi$
$572$		0			0
$573$		−	17.7976i		−	0.743505i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	6.22430	−	6.22430i	0.259121	−	0.259121i	−0.565576	−	0.824697i	$-0.691346\pi$
$577$	6.22430	−	6.22430i	0.259121	−	0.259121i	0.824697	+	0.565576i	$0.191346\pi$
$578$		0			0
$579$	−29.6428	−	29.6428i	−1.23191	−	1.23191i
$580$		0			0
$581$	−39.3513	+	39.3513i	−1.63257	+	1.63257i
$582$		0			0
$583$	29.1143	+	29.1143i	1.20579	+	1.20579i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−46.9277			−1.93691			−0.968456	−	0.249184i	$-0.919838\pi$
$587$	−46.9277			−1.93691			−0.968456	+	0.249184i	$0.919838\pi$
$588$		0			0
$589$	34.2037	−	34.2037i	1.40934	−	1.40934i
$590$		0			0
$591$			3.19150i			0.131281i
$592$		0			0
$593$	7.44785	+	7.44785i	0.305847	+	0.305847i	0.843296	−	0.537449i	$-0.180612\pi$
$593$	7.44785	+	7.44785i	0.305847	+	0.305847i	−0.537449	+	0.843296i	$0.680612\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			34.3611i			1.40630i
$598$		0			0
$599$			17.2338i			0.704154i	0.935971	+	0.352077i	$0.114524\pi$
$599$			17.2338i			0.704154i	−0.935971	+	0.352077i	$0.885476\pi$
$600$		0			0
$601$		−	9.77539i		−	0.398747i	−0.979924	−	0.199373i	$-0.936109\pi$
$601$		−	9.77539i		−	0.398747i	0.979924	−	0.199373i	$-0.0638906\pi$
$602$		0			0
$603$		−	10.2563i		−	0.417668i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−15.7153	−	15.7153i	−0.637865	−	0.637865i	0.312163	−	0.950029i	$-0.398946\pi$
$607$	−15.7153	−	15.7153i	−0.637865	−	0.637865i	−0.950029	+	0.312163i	$0.898946\pi$
$608$		0			0
$609$		−	21.7434i		−	0.881086i
$610$		0			0
$611$	6.03805	−	6.03805i	0.244274	−	0.244274i
$612$		0			0
$613$	24.4200			0.986313			0.493157	−	0.869941i	$-0.335843\pi$
$613$	24.4200			0.986313			0.493157	+	0.869941i	$0.335843\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.17267	+	4.17267i	0.167985	+	0.167985i	0.786093	−	0.618108i	$-0.212101\pi$
$617$	4.17267	+	4.17267i	0.167985	+	0.167985i	−0.618108	+	0.786093i	$0.712101\pi$
$618$		0			0
$619$	23.6886	−	23.6886i	0.952124	−	0.952124i	−0.0467810	−	0.998905i	$-0.514896\pi$
$619$	23.6886	−	23.6886i	0.952124	−	0.952124i	0.998905	+	0.0467810i	$0.0148963\pi$
$620$		0			0
$621$	−0.680181	−	0.680181i	−0.0272947	−	0.0272947i
$622$		0			0
$623$	43.3710	−	43.3710i	1.73762	−	1.73762i
$624$		0			0
$625$		0			0
$626$		0			0
$627$			60.4683i			2.41487i
$628$		0			0
$629$	2.32644	+	2.32644i	0.0927612	+	0.0927612i
$630$		0			0
$631$	3.19150			0.127052			0.0635259	−	0.997980i	$-0.479765\pi$
$631$	3.19150			0.127052			0.0635259	+	0.997980i	$0.479765\pi$
$632$		0			0
$633$	30.5739	−	30.5739i	1.21520	−	1.21520i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−20.4038			−0.808427
$638$		0			0
$639$	−12.8180			−0.507072
$640$		0			0
$641$	−27.4319			−1.08350			−0.541748	−	0.840541i	$-0.682237\pi$
$641$	−27.4319			−1.08350			−0.541748	+	0.840541i	$0.682237\pi$
$642$		0			0
$643$	−31.2331			−1.23171			−0.615857	−	0.787858i	$-0.711190\pi$
$643$	−31.2331			−1.23171			−0.615857	+	0.787858i	$0.711190\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	19.4190	−	19.4190i	0.763441	−	0.763441i	−0.213501	−	0.976943i	$-0.568487\pi$
$647$	19.4190	−	19.4190i	0.763441	−	0.763441i	0.976943	+	0.213501i	$0.0684868\pi$
$648$		0			0
$649$	28.1724			1.10586
$650$		0			0
$651$	−54.0989	−	54.0989i	−2.12030	−	2.12030i
$652$		0			0
$653$			42.7069i			1.67125i	0.549300	+	0.835625i	$0.314895\pi$
$653$			42.7069i			1.67125i	−0.549300	+	0.835625i	$0.685105\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	6.54357	−	6.54357i	0.255289	−	0.255289i
$658$		0			0
$659$	−13.0362	−	13.0362i	−0.507818	−	0.507818i	0.406038	−	0.913856i	$-0.366910\pi$
$659$	−13.0362	−	13.0362i	−0.507818	−	0.507818i	−0.913856	+	0.406038i	$0.866910\pi$
$660$		0			0
$661$	−24.3000	+	24.3000i	−0.945159	+	0.945159i	−0.998572	−	0.0534137i	$-0.982990\pi$
$661$	−24.3000	+	24.3000i	−0.945159	+	0.945159i	0.0534137	+	0.998572i	$0.482990\pi$
$662$		0			0
$663$	4.99087	+	4.99087i	0.193829	+	0.193829i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.583162			−0.0225801
$668$		0			0
$669$	−16.0994	+	16.0994i	−0.622440	+	0.622440i
$670$		0			0
$671$			51.3481i			1.98227i
$672$		0			0
$673$	22.9716	+	22.9716i	0.885491	+	0.885491i	0.994086	−	0.108595i	$-0.0346352\pi$
$673$	22.9716	+	22.9716i	0.885491	+	0.885491i	−0.108595	+	0.994086i	$0.534635\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			11.0381i			0.424229i	0.977245	+	0.212115i	$0.0680350\pi$
$677$			11.0381i			0.424229i	−0.977245	+	0.212115i	$0.931965\pi$
$678$		0			0
$679$		−	37.3639i		−	1.43390i
$680$		0			0
$681$		−	12.3452i		−	0.473070i
$682$		0			0
$683$			14.4743i			0.553845i	0.960892	+	0.276922i	$0.0893145\pi$
$683$			14.4743i			0.553845i	−0.960892	+	0.276922i	$0.910686\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−4.32227	−	4.32227i	−0.164905	−	0.164905i
$688$		0			0
$689$			11.6228i			0.442792i
$690$		0			0
$691$	−3.91872	+	3.91872i	−0.149075	+	0.149075i	−0.777705	−	0.628630i	$-0.783616\pi$
$691$	−3.91872	+	3.91872i	−0.149075	+	0.149075i	0.628630	+	0.777705i	$0.283616\pi$
$692$		0			0
$693$	25.9161			0.984470
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−2.01698	−	2.01698i	−0.0763985	−	0.0763985i
$698$		0			0
$699$	18.9391	−	18.9391i	0.716343	−	0.716343i
$700$		0			0
$701$	−22.9904	−	22.9904i	−0.868335	−	0.868335i	0.123953	−	0.992288i	$-0.460443\pi$
$701$	−22.9904	−	22.9904i	−0.868335	−	0.868335i	−0.992288	+	0.123953i	$0.960443\pi$
$702$		0			0
$703$	−5.62621	+	5.62621i	−0.212197	+	0.212197i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			16.9429i			0.637203i
$708$		0			0
$709$	−16.6295	−	16.6295i	−0.624536	−	0.624536i	0.322152	−	0.946688i	$-0.395594\pi$
$709$	−16.6295	−	16.6295i	−0.624536	−	0.624536i	−0.946688	+	0.322152i	$0.895594\pi$
$710$		0			0
$711$	12.6434			0.474164
$712$		0			0
$713$	−1.45094	+	1.45094i	−0.0543383	+	0.0543383i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−57.9975			−2.16596
$718$		0			0
$719$	2.56511			0.0956624			0.0478312	−	0.998855i	$-0.484769\pi$
$719$	2.56511			0.0956624			0.0478312	+	0.998855i	$0.484769\pi$
$720$		0			0
$721$	18.9198			0.704611
$722$		0			0
$723$	15.9682			0.593864
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−21.9890	+	21.9890i	−0.815526	+	0.815526i	−0.985456	−	0.169930i	$-0.945646\pi$
$727$	−21.9890	+	21.9890i	−0.815526	+	0.815526i	0.169930	+	0.985456i	$0.445646\pi$
$728$		0			0
$729$	10.8905			0.403351
$730$		0			0
$731$	−1.80791	−	1.80791i	−0.0668679	−	0.0668679i
$732$		0			0
$733$		−	46.4920i		−	1.71722i	−0.512628	−	0.858611i	$-0.671328\pi$
$733$		−	46.4920i		−	1.71722i	0.512628	−	0.858611i	$-0.328672\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−32.6912	+	32.6912i	−1.20420	+	1.20420i
$738$		0			0
$739$	9.54098	+	9.54098i	0.350971	+	0.350971i	0.860471	−	0.509500i	$-0.170170\pi$
$739$	9.54098	+	9.54098i	0.350971	+	0.350971i	−0.509500	+	0.860471i	$0.670170\pi$
$740$		0			0
$741$	−12.0698	+	12.0698i	−0.443395	+	0.443395i
$742$		0			0
$743$	−21.2388	−	21.2388i	−0.779177	−	0.779177i	0.200513	−	0.979691i	$-0.435739\pi$
$743$	−21.2388	−	21.2388i	−0.779177	−	0.779177i	−0.979691	+	0.200513i	$0.935739\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	13.4206			0.491034
$748$		0			0
$749$	−20.4024	+	20.4024i	−0.745487	+	0.745487i
$750$		0			0
$751$		−	33.3989i		−	1.21874i	−0.792885	−	0.609372i	$-0.791422\pi$
$751$		−	33.3989i		−	1.21874i	0.792885	−	0.609372i	$-0.208578\pi$
$752$		0			0
$753$	6.89231	+	6.89231i	0.251170	+	0.251170i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			46.6464i			1.69539i	0.530482	+	0.847696i	$0.322011\pi$
$757$			46.6464i			1.69539i	−0.530482	+	0.847696i	$0.677989\pi$
$758$		0			0
$759$		−	2.56511i		−	0.0931075i
$760$		0			0
$761$		−	8.90735i		−	0.322891i	−0.986882	−	0.161446i	$-0.948384\pi$
$761$		−	8.90735i		−	0.322891i	0.986882	−	0.161446i	$-0.0516156\pi$
$762$		0			0
$763$		−	13.0783i		−	0.473465i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	5.62337	+	5.62337i	0.203048	+	0.203048i
$768$		0			0
$769$			23.6291i			0.852086i	0.904703	+	0.426043i	$0.140093\pi$
$769$			23.6291i			0.852086i	−0.904703	+	0.426043i	$0.859907\pi$
$770$		0			0
$771$	−34.6037	+	34.6037i	−1.24622	+	1.24622i
$772$		0			0
$773$	−48.2197			−1.73434			−0.867171	−	0.498011i	$-0.834064\pi$
$773$	−48.2197			−1.73434			−0.867171	+	0.498011i	$0.834064\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	8.89880	+	8.89880i	0.319243	+	0.319243i
$778$		0			0
$779$	4.87781	−	4.87781i	0.174766	−	0.174766i
$780$		0			0
$781$	40.8565	+	40.8565i	1.46196	+	1.46196i
$782$		0			0
$783$	6.26760	−	6.26760i	0.223986	−	0.223986i
$784$		0			0
$785$		0			0
$786$		0			0
$787$		−	36.7365i		−	1.30952i	−0.755839	−	0.654758i	$-0.772771\pi$
$787$		−	36.7365i		−	1.30952i	0.755839	−	0.654758i	$-0.227229\pi$
$788$		0			0
$789$	−13.6674	−	13.6674i	−0.486573	−	0.486573i
$790$		0			0
$791$	−62.8433			−2.23445
$792$		0			0
$793$	−10.2494	+	10.2494i	−0.363966	+	0.363966i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−27.7387			−0.982555			−0.491277	−	0.871003i	$-0.663470\pi$
$797$	−27.7387			−0.982555			−0.491277	+	0.871003i	$0.663470\pi$
$798$		0			0
$799$	−14.7577			−0.522090
$800$		0			0
$801$	−14.7915			−0.522632
$802$		0			0
$803$	−41.7144			−1.47207
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.04200	−	2.04200i	0.0718817	−	0.0718817i
$808$		0			0
$809$	−32.9772			−1.15942			−0.579708	−	0.814825i	$-0.696833\pi$
$809$	−32.9772			−1.15942			−0.579708	+	0.814825i	$0.696833\pi$
$810$		0			0
$811$	−14.2759	−	14.2759i	−0.501296	−	0.501296i	0.410545	−	0.911840i	$-0.365339\pi$
$811$	−14.2759	−	14.2759i	−0.501296	−	0.501296i	−0.911840	+	0.410545i	$0.865339\pi$
$812$		0			0
$813$		−	14.6422i		−	0.513523i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	4.37220	−	4.37220i	0.152964	−	0.152964i
$818$		0			0
$819$	5.17299	+	5.17299i	0.180759	+	0.180759i
$820$		0			0
$821$	6.00000	−	6.00000i	0.209401	−	0.209401i	−0.594612	−	0.804013i	$-0.702694\pi$
$821$	6.00000	−	6.00000i	0.209401	−	0.209401i	0.804013	+	0.594612i	$0.202694\pi$
$822$		0			0
$823$	−36.6130	−	36.6130i	−1.27625	−	1.27625i	−0.942751	−	0.333499i	$-0.891771\pi$
$823$	−36.6130	−	36.6130i	−1.27625	−	1.27625i	−0.333499	−	0.942751i	$-0.608229\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	17.3121			0.602001			0.301000	−	0.953624i	$-0.402679\pi$
$827$	17.3121			0.602001			0.301000	+	0.953624i	$0.402679\pi$
$828$		0			0
$829$	33.7669	−	33.7669i	1.17277	−	1.17277i	0.191226	−	0.981546i	$-0.438754\pi$
$829$	33.7669	−	33.7669i	1.17277	−	1.17277i	0.981546	−	0.191226i	$-0.0612463\pi$
$830$		0			0
$831$			38.5121i			1.33597i
$832$		0			0
$833$	24.9346	+	24.9346i	0.863932	+	0.863932i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	31.1883i		−	1.07803i
$838$		0			0
$839$			18.7312i			0.646673i	0.946284	+	0.323337i	$0.104805\pi$
$839$			18.7312i			0.646673i	−0.946284	+	0.323337i	$0.895195\pi$
$840$		0			0
$841$			23.6264i			0.814703i
$842$		0			0
$843$		−	29.2687i		−	1.00807i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−46.6405	−	46.6405i	−1.60259	−	1.60259i
$848$		0			0
$849$		−	30.7282i		−	1.05459i
$850$		0			0
$851$	0.238668	−	0.238668i	0.00818143	−	0.00818143i
$852$		0			0
$853$	39.5431			1.35393			0.676964	−	0.736016i	$-0.263295\pi$
$853$	39.5431			1.35393			0.676964	+	0.736016i	$0.263295\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	28.0832	+	28.0832i	0.959305	+	0.959305i	0.999204	−	0.0398990i	$-0.0127036\pi$
$857$	28.0832	+	28.0832i	0.959305	+	0.959305i	−0.0398990	+	0.999204i	$0.512704\pi$
$858$		0			0
$859$	10.6404	−	10.6404i	0.363047	−	0.363047i	−0.501887	−	0.864933i	$-0.667361\pi$
$859$	10.6404	−	10.6404i	0.363047	−	0.363047i	0.864933	+	0.501887i	$0.167361\pi$
$860$		0			0
$861$	−7.71509	−	7.71509i	−0.262929	−	0.262929i
$862$		0			0
$863$	−19.7428	+	19.7428i	−0.672051	+	0.672051i	−0.958189	−	0.286137i	$-0.907629\pi$
$863$	−19.7428	+	19.7428i	−0.672051	+	0.672051i	0.286137	+	0.958189i	$0.407629\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			22.2873i			0.756918i
$868$		0			0
$869$	−40.3000	−	40.3000i	−1.36708	−	1.36708i
$870$		0			0
$871$	−13.0507			−0.442206
$872$		0			0
$873$	−6.37141	+	6.37141i	−0.215640	+	0.215640i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−47.9703			−1.61984			−0.809921	−	0.586539i	$-0.800490\pi$
$877$	−47.9703			−1.61984			−0.809921	+	0.586539i	$0.800490\pi$
$878$		0			0
$879$	16.4603			0.555192
$880$		0			0
$881$	−53.8007			−1.81259			−0.906296	−	0.422644i	$-0.861102\pi$
$881$	−53.8007			−1.81259			−0.906296	+	0.422644i	$0.861102\pi$
$882$		0			0
$883$	−33.5928			−1.13049			−0.565244	−	0.824924i	$-0.691218\pi$
$883$	−33.5928			−1.13049			−0.565244	+	0.824924i	$0.691218\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	28.1314	−	28.1314i	0.944560	−	0.944560i	−0.0539823	−	0.998542i	$-0.517191\pi$
$887$	28.1314	−	28.1314i	0.944560	−	0.944560i	0.998542	+	0.0539823i	$0.0171915\pi$
$888$		0			0
$889$	−75.3742			−2.52797
$890$		0			0
$891$	39.4584	+	39.4584i	1.32191	+	1.32191i
$892$		0			0
$893$		−	35.6897i		−	1.19431i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.512010	−	0.512010i	0.0170955	−	0.0170955i
$898$		0			0
$899$	−13.3699	−	13.3699i	−0.445910	−	0.445910i
$900$		0			0
$901$	14.2037	−	14.2037i	0.473193	−	0.473193i
$902$		0			0
$903$	−6.91537	−	6.91537i	−0.230129	−	0.230129i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.91511			0.0635902			0.0317951	−	0.999494i	$-0.489878\pi$
$907$	1.91511			0.0635902			0.0317951	+	0.999494i	$0.489878\pi$
$908$		0			0
$909$	2.88916	−	2.88916i	0.0958273	−	0.0958273i
$910$		0			0
$911$		−	29.6000i		−	0.980692i	−0.871528	−	0.490346i	$-0.836870\pi$
$911$		−	29.6000i		−	0.980692i	0.871528	−	0.490346i	$-0.163130\pi$
$912$		0			0
$913$	−42.7773	−	42.7773i	−1.41572	−	1.41572i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	53.5776i		−	1.76929i
$918$		0			0
$919$		−	49.0867i		−	1.61922i	−0.586968	−	0.809610i	$-0.699678\pi$
$919$		−	49.0867i		−	1.61922i	0.586968	−	0.809610i	$-0.300322\pi$
$920$		0			0
$921$			60.9319i			2.00777i
$922$		0			0
$923$			16.3104i			0.536863i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−3.22627	−	3.22627i	−0.105965	−	0.105965i
$928$		0			0
$929$		−	0.479078i		−	0.0157180i	−0.999969	−	0.00785902i	$-0.997498\pi$
$929$		−	0.479078i		−	0.0157180i	0.999969	−	0.00785902i	$-0.00250163\pi$
$930$		0			0
$931$	−60.3012	+	60.3012i	−1.97629	+	1.97629i
$932$		0			0
$933$	−20.1633			−0.660117
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−2.36411	−	2.36411i	−0.0772320	−	0.0772320i	0.667436	−	0.744668i	$-0.267392\pi$
$937$	−2.36411	−	2.36411i	−0.0772320	−	0.0772320i	−0.744668	+	0.667436i	$0.767392\pi$
$938$		0			0
$939$	9.83016	−	9.83016i	0.320795	−	0.320795i
$940$		0			0
$941$	−30.8910	−	30.8910i	−1.00702	−	1.00702i	−0.999975	−	0.00704119i	$-0.997759\pi$
$941$	−30.8910	−	30.8910i	−1.00702	−	1.00702i	−0.00704119	−	0.999975i	$-0.502241\pi$
$942$		0			0
$943$	−0.206920	+	0.206920i	−0.00673826	+	0.00673826i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			29.6788i			0.964432i	0.876052	+	0.482216i	$0.160168\pi$
$947$			29.6788i			0.964432i	−0.876052	+	0.482216i	$0.839832\pi$
$948$		0			0
$949$	−8.32644	−	8.32644i	−0.270288	−	0.270288i
$950$		0			0
$951$	−49.8687			−1.61710
$952$		0			0
$953$	−18.5543	+	18.5543i	−0.601032	+	0.601032i	−0.940586	−	0.339554i	$-0.889724\pi$
$953$	−18.5543	+	18.5543i	−0.601032	+	0.601032i	0.339554	+	0.940586i	$0.389724\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	23.6364			0.764057
$958$		0			0
$959$	−44.5819			−1.43962
$960$		0			0
$961$	−35.5301			−1.14613
$962$		0			0
$963$	6.95816			0.224224
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−13.6119	+	13.6119i	−0.437730	+	0.437730i	−0.891247	−	0.453517i	$-0.850169\pi$
$967$	−13.6119	+	13.6119i	−0.437730	+	0.437730i	0.453517	+	0.891247i	$0.350169\pi$
$968$		0			0
$969$	29.5000			0.947676
$970$		0			0
$971$	34.0621	+	34.0621i	1.09310	+	1.09310i	0.995195	+	0.0979087i	$0.0312153\pi$
$971$	34.0621	+	34.0621i	1.09310	+	1.09310i	0.0979087	+	0.995195i	$0.468785\pi$
$972$		0			0
$973$			21.7366i			0.696843i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	27.8905	−	27.8905i	0.892296	−	0.892296i	−0.102443	−	0.994739i	$-0.532666\pi$
$977$	27.8905	−	27.8905i	0.892296	−	0.892296i	0.994739	+	0.102443i	$0.0326659\pi$
$978$		0			0
$979$	47.1470	+	47.1470i	1.50682	+	1.50682i
$980$		0			0
$981$	−2.23015	+	2.23015i	−0.0712031	+	0.0712031i
$982$		0			0
$983$	36.9483	+	36.9483i	1.17847	+	1.17847i	0.980135	+	0.198333i	$0.0635529\pi$
$983$	36.9483	+	36.9483i	1.17847	+	1.17847i	0.198333	+	0.980135i	$0.436447\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−56.4492			−1.79680
$988$		0			0
$989$	−0.185472	+	0.185472i	−0.00589767	+	0.00589767i
$990$		0			0
$991$		−	40.2242i		−	1.27776i	−0.769305	−	0.638882i	$-0.779397\pi$
$991$		−	40.2242i		−	1.27776i	0.769305	−	0.638882i	$-0.220603\pi$
$992$		0			0
$993$	13.0037	+	13.0037i	0.412659	+	0.412659i
$994$		0			0
$995$		0			0
$996$		0			0
$997$			27.1034i			0.858372i	0.903216	+	0.429186i	$0.141199\pi$
$997$			27.1034i			0.858372i	−0.903216	+	0.429186i	$0.858801\pi$
$998$		0			0
$999$			5.13021i			0.162313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.s.c.943.7		16
4.3	odd	2		400.2.s.c.243.8	yes	16
5.2	odd	4		1600.2.j.c.1007.2		16
5.3	odd	4		1600.2.j.c.1007.7		16
5.4	even	2	inner	1600.2.s.c.943.2		16
16.5	even	4		400.2.j.c.43.4	✓	16
16.11	odd	4		1600.2.j.c.143.7		16
20.3	even	4		400.2.j.c.307.5	yes	16
20.7	even	4		400.2.j.c.307.4	yes	16
20.19	odd	2		400.2.s.c.243.1	yes	16
80.27	even	4	inner	1600.2.s.c.207.7		16
80.37	odd	4		400.2.s.c.107.8	yes	16
80.43	even	4	inner	1600.2.s.c.207.2		16
80.53	odd	4		400.2.s.c.107.1	yes	16
80.59	odd	4		1600.2.j.c.143.2		16
80.69	even	4		400.2.j.c.43.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.c.43.4	✓	16	16.5	even	4
400.2.j.c.43.5	yes	16	80.69	even	4
400.2.j.c.307.4	yes	16	20.7	even	4
400.2.j.c.307.5	yes	16	20.3	even	4
400.2.s.c.107.1	yes	16	80.53	odd	4
400.2.s.c.107.8	yes	16	80.37	odd	4
400.2.s.c.243.1	yes	16	20.19	odd	2
400.2.s.c.243.8	yes	16	4.3	odd	2
1600.2.j.c.143.2		16	80.59	odd	4
1600.2.j.c.143.7		16	16.11	odd	4
1600.2.j.c.1007.2		16	5.2	odd	4
1600.2.j.c.1007.7		16	5.3	odd	4
1600.2.s.c.207.2		16	80.43	even	4	inner
1600.2.s.c.207.7		16	80.27	even	4	inner
1600.2.s.c.943.2		16	5.4	even	2	inner
1600.2.s.c.943.7		16	1.1	even	1	trivial

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Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.02856 q^{3} +(-3.26957 + 3.26957i) q^{7} +1.11507 q^{9} +O(q^{10})\)	\(q+2.02856 q^{3} +(-3.26957 + 3.26957i) q^{7} +1.11507 q^{9} +(-3.55423 - 3.55423i) q^{11} -1.41889i q^{13} +(-1.73396 + 1.73396i) q^{17} +(-4.19337 - 4.19337i) q^{19} +(-6.63253 + 6.63253i) q^{21} +(0.177886 + 0.177886i) q^{23} -3.82369 q^{27} +(-1.63915 + 1.63915i) q^{29} +8.15660i q^{31} +(-7.20998 - 7.20998i) q^{33} -1.34169i q^{37} -2.87831i q^{39} +1.16322i q^{41} +1.04265i q^{43} +(4.25549 + 4.25549i) q^{47} -14.3801i q^{49} +(-3.51745 + 3.51745i) q^{51} -8.19145 q^{53} +(-8.50653 - 8.50653i) q^{57} +(-3.96323 + 3.96323i) q^{59} +(-7.22353 - 7.22353i) q^{61} +(-3.64581 + 3.64581i) q^{63} -9.19784i q^{67} +(0.360853 + 0.360853i) q^{69} -11.4952 q^{71} +(5.86829 - 5.86829i) q^{73} +23.2416 q^{77} +11.3386 q^{79} -11.1018 q^{81} +12.0356 q^{83} +(-3.32512 + 3.32512i) q^{87} -13.2651 q^{89} +(4.63915 + 4.63915i) q^{91} +16.5462i q^{93} +(-5.71389 + 5.71389i) q^{97} +(-3.96323 - 3.96323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{9}+O(q^{10}) \) 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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