LMFDB - Embedded newform 1600.2.j.c.1007.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(143,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("1600.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1007.2
Root			$0.601202 - 1.28006i$ of defining polynomial
Character	$\chi$	$=$	1600.1007
Dual form			1600.2.j.c.143.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02856i q^{3} +(-3.26957 - 3.26957i) q^{7} -1.11507 q^{9} +O(q^{10})$	$q-2.02856i q^{3} +(-3.26957 - 3.26957i) q^{7} -1.11507 q^{9} +(-3.55423 - 3.55423i) q^{11} -1.41889 q^{13} +(-1.73396 - 1.73396i) q^{17} +(4.19337 + 4.19337i) q^{19} +(-6.63253 + 6.63253i) q^{21} +(0.177886 - 0.177886i) q^{23} -3.82369i q^{27} +(1.63915 - 1.63915i) q^{29} +8.15660i q^{31} +(-7.20998 + 7.20998i) q^{33} +1.34169 q^{37} +2.87831i q^{39} +1.16322i q^{41} +1.04265 q^{43} +(-4.25549 + 4.25549i) q^{47} +14.3801i q^{49} +(-3.51745 + 3.51745i) q^{51} +8.19145i q^{53} +(8.50653 - 8.50653i) q^{57} +(3.96323 - 3.96323i) q^{59} +(-7.22353 - 7.22353i) q^{61} +(3.64581 + 3.64581i) q^{63} +9.19784 q^{67} +(-0.360853 - 0.360853i) q^{69} -11.4952 q^{71} +(-5.86829 - 5.86829i) q^{73} +23.2416i q^{77} -11.3386 q^{79} -11.1018 q^{81} -12.0356i q^{83} +(-3.32512 - 3.32512i) q^{87} +13.2651 q^{89} +(4.63915 + 4.63915i) q^{91} +16.5462 q^{93} +(-5.71389 - 5.71389i) q^{97} +(3.96323 + 3.96323i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

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

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
$3$		−	2.02856i		−	1.17119i	−0.810603	−	0.585596i	$-0.800860\pi$
$3$		−	2.02856i		−	1.17119i	0.810603	−	0.585596i	$-0.199140\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.26957	−	3.26957i	−1.23578	−	1.23578i	−0.961710	−	0.274070i	$-0.911630\pi$
$7$	−3.26957	−	3.26957i	−1.23578	−	1.23578i	−0.274070	−	0.961710i	$-0.588370\pi$
$8$		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
$13$	−1.41889			−0.393529			−0.196764	−	0.980451i	$-0.563043\pi$
$13$	−1.41889			−0.393529			−0.196764	+	0.980451i	$0.563043\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.73396	−	1.73396i	−0.420547	−	0.420547i	0.464845	−	0.885392i	$-0.346110\pi$
$17$	−1.73396	−	1.73396i	−0.420547	−	0.420547i	−0.885392	+	0.464845i	$0.846110\pi$
$18$		0			0
$19$	4.19337	+	4.19337i	0.962026	+	0.962026i	0.999305	−	0.0372791i	$-0.0118690\pi$
$19$	4.19337	+	4.19337i	0.962026	+	0.962026i	−0.0372791	+	0.999305i	$0.511869\pi$
$20$		0			0
$21$	−6.63253	+	6.63253i	−1.44734	+	1.44734i
$22$		0			0
$23$	0.177886	−	0.177886i	0.0370918	−	0.0370918i	−0.688318	−	0.725409i	$-0.741650\pi$
$23$	0.177886	−	0.177886i	0.0370918	−	0.0370918i	0.725409	+	0.688318i	$0.241650\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	3.82369i		−	0.735870i
$28$		0			0
$29$	1.63915	−	1.63915i	0.304382	−	0.304382i	−0.538344	−	0.842725i	$-0.680950\pi$
$29$	1.63915	−	1.63915i	0.304382	−	0.304382i	0.842725	+	0.538344i	$0.180950\pi$
$30$		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
$37$	1.34169			0.220573			0.110286	−	0.993900i	$-0.464823\pi$
$37$	1.34169			0.220573			0.110286	+	0.993900i	$0.464823\pi$
$38$		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
$43$	1.04265			0.159002			0.0795010	−	0.996835i	$-0.474667\pi$
$43$	1.04265			0.159002			0.0795010	+	0.996835i	$0.474667\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.25549	+	4.25549i	−0.620726	+	0.620726i	−0.945717	−	0.324991i	$-0.894639\pi$
$47$	−4.25549	+	4.25549i	−0.620726	+	0.620726i	0.324991	+	0.945717i	$0.394639\pi$
$48$		0			0
$49$			14.3801i			2.05430i
$50$		0			0
$51$	−3.51745	+	3.51745i	−0.492542	+	0.492542i
$52$		0			0
$53$			8.19145i			1.12518i	0.826735	+	0.562591i	$0.190196\pi$
$53$			8.19145i			1.12518i	−0.826735	+	0.562591i	$0.809804\pi$
$54$		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	−0.400381	−	0.916349i	$-0.631122\pi$
$59$	3.96323	−	3.96323i	0.515968	−	0.515968i	0.916349	+	0.400381i	$0.131122\pi$
$60$		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
$67$	9.19784			1.12370			0.561848	−	0.827241i	$-0.310091\pi$
$67$	9.19784			1.12370			0.561848	+	0.827241i	$0.310091\pi$
$68$		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	$-0.411422\pi$
$73$	−5.86829	−	5.86829i	−0.686831	−	0.686831i	−0.961530	+	0.274699i	$0.911422\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			23.2416i			2.64862i
$78$		0			0
$79$	−11.3386			−1.27569			−0.637846	−	0.770164i	$-0.720174\pi$
$79$	−11.3386			−1.27569			−0.637846	+	0.770164i	$0.720174\pi$
$80$		0			0
$81$	−11.1018			−1.23354
$82$		0			0
$83$		−	12.0356i		−	1.32108i	−0.750790	−	0.660540i	$-0.770327\pi$
$83$		−	12.0356i		−	1.32108i	0.750790	−	0.660540i	$-0.229673\pi$
$84$		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	$-0.251823\pi$
$89$	13.2651			1.40609			0.703046	+	0.711144i	$0.251823\pi$
$90$		0			0
$91$	4.63915	+	4.63915i	0.486315	+	0.486315i
$92$		0			0
$93$	16.5462			1.71576
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.71389	−	5.71389i	−0.580158	−	0.580158i	0.354789	−	0.934947i	$-0.384553\pi$
$97$	−5.71389	−	5.71389i	−0.580158	−	0.580158i	−0.934947	+	0.354789i	$0.884553\pi$
$98$		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	−0.835134	−	0.550046i	$-0.814610\pi$
$103$	−2.89332	+	2.89332i	−0.285088	+	0.285088i	0.550046	+	0.835134i	$0.314610\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			6.24009i			0.603252i	0.953426	+	0.301626i	$0.0975294\pi$
$107$			6.24009i			0.603252i	−0.953426	+	0.301626i	$0.902471\pi$
$108$		0			0
$109$	2.00000	−	2.00000i	0.191565	−	0.191565i	−0.604807	−	0.796372i	$-0.706750\pi$
$109$	2.00000	−	2.00000i	0.191565	−	0.191565i	0.796372	+	0.604807i	$0.206750\pi$
$110$		0			0
$111$		−	2.72171i		−	0.258333i
$112$		0			0
$113$	9.61034	−	9.61034i	0.904065	−	0.904065i	−0.0917199	−	0.995785i	$-0.529236\pi$
$113$	9.61034	−	9.61034i	0.904065	−	0.904065i	0.995785	+	0.0917199i	$0.0292364\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.58216			0.146271
$118$		0			0
$119$			11.3386i			1.03941i
$120$		0			0
$121$			14.2651i			1.29682i
$122$		0			0
$123$	2.35967			0.212764
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−11.5266	+	11.5266i	−1.02282	+	1.02282i	−0.0230897	+	0.999733i	$0.507350\pi$
$127$	−11.5266	+	11.5266i	−1.02282	+	1.02282i	−0.999733	+	0.0230897i	$0.992650\pi$
$128$		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
$133$		−	27.4210i		−	2.37770i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.81771	+	6.81771i	−0.582476	+	0.582476i	−0.935583	−	0.353107i	$-0.885125\pi$
$137$	−6.81771	+	6.81771i	−0.582476	+	0.582476i	0.353107	+	0.935583i	$0.385125\pi$
$138$		0			0
$139$	−3.32408	+	3.32408i	−0.281945	+	0.281945i	−0.833884	−	0.551939i	$-0.813888\pi$
$139$	−3.32408	+	3.32408i	−0.281945	+	0.281945i	0.551939	+	0.833884i	$0.313888\pi$
$140$		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
$147$	29.1710			2.40598
$148$		0			0
$149$	4.99338	+	4.99338i	0.409074	+	0.409074i	0.881415	−	0.472342i	$-0.156591\pi$
$149$	4.99338	+	4.99338i	0.409074	+	0.409074i	−0.472342	+	0.881415i	$0.656591\pi$
$150$		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
$157$		−	4.01619i		−	0.320527i	−0.987074	−	0.160263i	$-0.948766\pi$
$157$		−	4.01619i		−	0.320527i	0.987074	−	0.160263i	$-0.0512344\pi$
$158$		0			0
$159$	16.6169			1.31781
$160$		0			0
$161$	−1.16322			−0.0916746
$162$		0			0
$163$		−	1.31702i		−	0.103157i	−0.998669	−	0.0515785i	$-0.983575\pi$
$163$		−	1.31702i		−	0.103157i	0.998669	−	0.0515785i	$-0.0164252\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.53755	−	2.53755i	−0.196362	−	0.196362i	0.602077	−	0.798438i	$-0.294340\pi$
$167$	−2.53755	−	2.53755i	−0.196362	−	0.196362i	−0.798438	+	0.602077i	$0.794340\pi$
$168$		0			0
$169$	−10.9868			−0.845135
$170$		0			0
$171$	−4.67592	−	4.67592i	−0.357577	−	0.357577i
$172$		0			0
$173$	9.45595			0.718922			0.359461	−	0.933160i	$-0.382960\pi$
$173$	9.45595			0.718922			0.359461	+	0.933160i	$0.382960\pi$
$174$		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	0.308313	−	0.951285i	$-0.400235\pi$
$179$	−8.60237	−	8.60237i	−0.642971	−	0.642971i	−0.951285	+	0.308313i	$0.900235\pi$
$180$		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
$187$			12.3258i			0.901350i
$188$		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	−0.0532641	+	0.998580i	$0.516963\pi$
$193$	−14.6127	+	14.6127i	−1.05184	+	1.05184i	−0.998580	+	0.0532641i	$0.983037\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.57328			−0.112092			−0.0560458	−	0.998428i	$-0.517849\pi$
$197$	−1.57328			−0.112092			−0.0560458	+	0.998428i	$0.517849\pi$
$198$		0			0
$199$		−	16.9386i		−	1.20075i	−0.799720	−	0.600373i	$-0.795019\pi$
$199$		−	16.9386i		−	1.20075i	0.799720	−	0.600373i	$-0.204981\pi$
$200$		0			0
$201$		−	18.6584i		−	1.31606i
$202$		0			0
$203$	−10.7186			−0.752298
$204$		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
$213$			23.3188i			1.59777i
$214$		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	$-0.127369\pi$
$223$	7.93637	+	7.93637i	0.531459	+	0.531459i	−0.389548	+	0.921006i	$0.627369\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.08569			0.403922			0.201961	−	0.979394i	$-0.435269\pi$
$227$	6.08569			0.403922			0.201961	+	0.979394i	$0.435269\pi$
$228$		0			0
$229$	2.13071	+	2.13071i	0.140801	+	0.140801i	0.773994	−	0.633193i	$-0.218256\pi$
$229$	2.13071	+	2.13071i	0.140801	+	0.140801i	−0.633193	+	0.773994i	$0.718256\pi$
$230$		0			0
$231$	47.1470			3.10204
$232$		0			0
$233$	−9.33621	−	9.33621i	−0.611635	−	0.611635i	0.331737	−	0.943372i	$-0.392365\pi$
$233$	−9.33621	−	9.33621i	−0.611635	−	0.611635i	−0.943372	+	0.331737i	$0.892365\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			23.0011i			1.49408i
$238$		0			0
$239$	28.5904			1.84936			0.924680	−	0.380745i	$-0.124333\pi$
$239$	28.5904			1.84936			0.924680	+	0.380745i	$0.124333\pi$
$240$		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
$243$			11.0497i			0.708839i
$244$		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
$253$	−1.26449			−0.0794981
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−17.0582	−	17.0582i	−1.06406	−	1.06406i	−0.997802	−	0.0662586i	$-0.978894\pi$
$257$	−17.0582	−	17.0582i	−1.06406	−	1.06406i	−0.0662586	−	0.997802i	$-0.521106\pi$
$258$		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	−0.883632	−	0.468181i	$-0.844909\pi$
$263$	−6.73749	+	6.73749i	−0.415451	+	0.415451i	0.468181	+	0.883632i	$0.344909\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	26.9090i		−	1.64680i
$268$		0			0
$269$	−1.00662	+	1.00662i	−0.0613748	+	0.0613748i	−0.737128	−	0.675753i	$-0.763819\pi$
$269$	−1.00662	+	1.00662i	−0.0613748	+	0.0613748i	0.675753	+	0.737128i	$0.263819\pi$
$270$		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
$277$	−18.9849			−1.14069			−0.570346	−	0.821405i	$-0.693191\pi$
$277$	−18.9849			−1.14069			−0.570346	+	0.821405i	$0.693191\pi$
$278$		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
$283$	−15.1478			−0.900441			−0.450221	−	0.892917i	$-0.648655\pi$
$283$	−15.1478			−0.900441			−0.450221	+	0.892917i	$0.648655\pi$
$284$		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
$293$		−	8.11426i		−	0.474040i	−0.971505	−	0.237020i	$-0.923829\pi$
$293$		−	8.11426i		−	0.474040i	0.971505	−	0.237020i	$-0.0761707\pi$
$294$		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
$307$	−30.0370			−1.71430			−0.857150	−	0.515067i	$-0.827767\pi$
$307$	−30.0370			−1.71430			−0.857150	+	0.515067i	$0.827767\pi$
$308$		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	$-0.312042\pi$
$313$	−4.84587	−	4.84587i	−0.273905	−	0.273905i	−0.830670	+	0.556765i	$0.812042\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	24.5832i		−	1.38073i	−0.723460	−	0.690366i	$-0.757449\pi$
$317$		−	24.5832i		−	1.38073i	0.723460	−	0.690366i	$-0.242551\pi$
$318$		0			0
$319$	−11.6518			−0.652375
$320$		0			0
$321$	12.6584			0.706524
$322$		0			0
$323$		−	14.5423i		−	0.809155i
$324$		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
$333$	−1.49608			−0.0819849
$334$		0			0
$335$		0			0
$336$		0			0
$337$	13.5903	+	13.5903i	0.740309	+	0.740309i	0.972637	−	0.232328i	$-0.0746343\pi$
$337$	13.5903	+	13.5903i	0.740309	+	0.740309i	−0.232328	+	0.972637i	$0.574634\pi$
$338$		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
$347$		−	22.2352i		−	1.19365i	−0.802373	−	0.596823i	$-0.796429\pi$
$347$		−	22.2352i		−	1.19365i	0.802373	−	0.596823i	$-0.203571\pi$
$348$		0			0
$349$	5.54286	−	5.54286i	0.296702	−	0.296702i	−0.543018	−	0.839721i	$-0.682719\pi$
$349$	5.54286	−	5.54286i	0.296702	−	0.296702i	0.839721	+	0.543018i	$0.182719\pi$
$350$		0			0
$351$			5.42539i			0.289586i
$352$		0			0
$353$	−13.7898	+	13.7898i	−0.733957	+	0.733957i	−0.971401	−	0.237444i	$-0.923690\pi$
$353$	−13.7898	+	13.7898i	−0.733957	+	0.733957i	0.237444	+	0.971401i	$0.423690\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	23.0011			1.21735
$358$		0			0
$359$		−	10.2529i		−	0.541127i	−0.962702	−	0.270563i	$-0.912790\pi$
$359$		−	10.2529i		−	0.541127i	0.962702	−	0.270563i	$-0.0872100\pi$
$360$		0			0
$361$			16.1688i			0.850987i
$362$		0			0
$363$	28.9376			1.51883
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.66200	+	7.66200i	−0.399953	+	0.399953i	−0.878216	−	0.478263i	$-0.841266\pi$
$367$	−7.66200	+	7.66200i	−0.399953	+	0.399953i	0.478263	+	0.878216i	$0.341266\pi$
$368$		0			0
$369$		−	1.29708i		−	0.0675231i
$370$		0			0
$371$	26.7825	−	26.7825i	1.39048	−	1.39048i
$372$		0			0
$373$			2.52010i			0.130486i	0.997869	+	0.0652430i	$0.0207823\pi$
$373$			2.52010i			0.130486i	−0.997869	+	0.0652430i	$0.979218\pi$
$374$		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	−0.336397	−	0.941720i	$-0.609209\pi$
$379$	11.7844	−	11.7844i	0.605323	−	0.605323i	0.941720	+	0.336397i	$0.109209\pi$
$380$		0			0
$381$	23.3825	+	23.3825i	1.19792	+	1.19792i
$382$		0			0
$383$	−22.0006	−	22.0006i	−1.12418	−	1.12418i	−0.991107	−	0.133069i	$-0.957517\pi$
$383$	−22.0006	−	22.0006i	−1.12418	−	1.12418i	−0.133069	−	0.991107i	$-0.542483\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.16263			−0.0590997
$388$		0			0
$389$	−15.0897	−	15.0897i	−0.765077	−	0.765077i	0.212159	−	0.977235i	$-0.431951\pi$
$389$	−15.0897	−	15.0897i	−0.765077	−	0.765077i	−0.977235	+	0.212159i	$0.931951\pi$
$390$		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
$397$			4.10227i			0.205887i	0.994687	+	0.102943i	$0.0328261\pi$
$397$			4.10227i			0.205887i	−0.994687	+	0.102943i	$0.967174\pi$
$398$		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
$403$		−	11.5733i		−	0.576507i
$404$		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	$-0.509155\pi$
$409$	−1.16322			−0.0575175			−0.0287588	+	0.999586i	$0.509155\pi$
$410$		0			0
$411$	13.8302	+	13.8302i	0.682191	+	0.682191i
$412$		0			0
$413$	−25.9161			−1.27525
$414$		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	0.868438	−	0.495797i	$-0.165124\pi$
$419$	7.62778	+	7.62778i	0.372641	+	0.372641i	−0.495797	+	0.868438i	$0.665124\pi$
$420$		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
$427$			47.2356i			2.28589i
$428$		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	−0.790336	−	0.612674i	$-0.790094\pi$
$433$	−3.69692	+	3.69692i	−0.177662	+	0.177662i	0.612674	+	0.790336i	$0.290094\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.49188			0.0713665
$438$		0			0
$439$			29.9132i			1.42768i	0.700309	+	0.713840i	$0.253046\pi$
$439$			29.9132i			1.42768i	−0.700309	+	0.713840i	$0.746954\pi$
$440$		0			0
$441$		−	16.0349i		−	0.763567i
$442$		0			0
$443$	25.5920			1.21591			0.607956	−	0.793971i	$-0.291990\pi$
$443$	25.5920			1.21591			0.607956	+	0.793971i	$0.291990\pi$
$444$		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	$0.161251\pi$
$449$			20.5621i			0.970387i	−0.874407	+	0.485193i	$0.838749\pi$
$450$		0			0
$451$	4.13435	−	4.13435i	0.194679	−	0.194679i
$452$		0			0
$453$			22.0673i			1.03681i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−8.06912	+	8.06912i	−0.377457	+	0.377457i	−0.870184	−	0.492727i	$-0.836000\pi$
$457$	−8.06912	+	8.06912i	−0.377457	+	0.377457i	0.492727	+	0.870184i	$0.336000\pi$
$458$		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	0.991974	+	0.126438i	$0.0403546\pi$
$463$	24.0654	+	24.0654i	1.11841	+	1.11841i	0.126438	+	0.991974i	$0.459645\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	11.2041			0.518464			0.259232	−	0.965815i	$-0.416531\pi$
$467$	11.2041			0.518464			0.259232	+	0.965815i	$0.416531\pi$
$468$		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
$477$		−	9.13408i		−	0.418221i
$478$		0			0
$479$	8.47832			0.387384			0.193692	−	0.981062i	$-0.437954\pi$
$479$	8.47832			0.387384			0.193692	+	0.981062i	$0.437954\pi$
$480$		0			0
$481$	−1.90371			−0.0868016
$482$		0			0
$483$			2.35967i			0.107369i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	12.1684	+	12.1684i	0.551401	+	0.551401i	0.926845	−	0.375444i	$-0.122510\pi$
$487$	12.1684	+	12.1684i	0.551401	+	0.551401i	−0.375444	+	0.926845i	$0.622510\pi$
$488$		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
$493$	−5.68443			−0.256014
$494$		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	0.747948	−	0.663758i	$-0.231039\pi$
$499$	1.88067	+	1.88067i	0.0841902	+	0.0841902i	−0.663758	+	0.747948i	$0.731039\pi$
$500$		0			0
$501$	−5.14759	+	5.14759i	−0.229977	+	0.229977i
$502$		0			0
$503$	−4.31406	+	4.31406i	−0.192354	+	0.192354i	−0.796713	−	0.604358i	$-0.793430\pi$
$503$	−4.31406	+	4.31406i	−0.192354	+	0.192354i	0.604358	+	0.796713i	$0.293430\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			22.2873i			0.989816i
$508$		0			0
$509$	21.2174	−	21.2174i	0.940445	−	0.940445i	−0.0578791	−	0.998324i	$-0.518434\pi$
$509$	21.2174	−	21.2174i	0.940445	−	0.940445i	0.998324	+	0.0578791i	$0.0184338\pi$
$510$		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
$517$	30.2499			1.33039
$518$		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
$523$	−26.7211			−1.16843			−0.584215	−	0.811599i	$-0.698598\pi$
$523$	−26.7211			−1.16843			−0.584215	+	0.811599i	$0.698598\pi$
$524$		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
$533$		−	1.65048i		−	0.0714901i
$534$		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
$547$	−25.8142			−1.10373			−0.551867	−	0.833932i	$-0.686085\pi$
$547$	−25.8142			−1.10373			−0.551867	+	0.833932i	$0.686085\pi$
$548$		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
$557$		−	4.09807i		−	0.173641i	−0.996224	−	0.0868204i	$-0.972329\pi$
$557$		−	4.09807i		−	0.173641i	0.996224	−	0.0868204i	$-0.0276706\pi$
$558$		0			0
$559$	−1.47940			−0.0625718
$560$		0			0
$561$	25.0036			1.05565
$562$		0			0
$563$			36.4537i			1.53634i	0.640245	+	0.768171i	$0.278833\pi$
$563$			36.4537i			1.53634i	−0.640245	+	0.768171i	$0.721167\pi$
$564$		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	$-0.482045\pi$
$569$	2.68968			0.112757			0.0563787	+	0.998409i	$0.482045\pi$
$570$		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
$573$	−17.7976			−0.743505
$574$		0			0
$575$		0			0
$576$		0			0
$577$	6.22430	+	6.22430i	0.259121	+	0.259121i	0.824697	−	0.565576i	$-0.191346\pi$
$577$	6.22430	+	6.22430i	0.259121	+	0.259121i	−0.565576	+	0.824697i	$0.691346\pi$
$578$		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
$587$		−	46.9277i		−	1.93691i	−0.249184	−	0.968456i	$-0.580162\pi$
$587$		−	46.9277i		−	1.93691i	0.249184	−	0.968456i	$-0.419838\pi$
$588$		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	−0.537449	−	0.843296i	$-0.680612\pi$
$593$	7.44785	−	7.44785i	0.305847	−	0.305847i	0.843296	+	0.537449i	$0.180612\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−34.3611			−1.40630
$598$		0			0
$599$		−	17.2338i		−	0.704154i	−0.935971	−	0.352077i	$-0.885476\pi$
$599$		−	17.2338i		−	0.704154i	0.935971	−	0.352077i	$-0.114524\pi$
$600$		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
$603$	−10.2563			−0.417668
$604$		0			0
$605$		0			0
$606$		0			0
$607$	15.7153	−	15.7153i	0.637865	−	0.637865i	−0.312163	−	0.950029i	$-0.601054\pi$
$607$	15.7153	−	15.7153i	0.637865	−	0.637865i	0.950029	+	0.312163i	$0.101054\pi$
$608$		0			0
$609$			21.7434i			0.881086i
$610$		0			0
$611$	6.03805	−	6.03805i	0.244274	−	0.244274i
$612$		0			0
$613$		−	24.4200i		−	0.986313i	−0.869941	−	0.493157i	$-0.835843\pi$
$613$		−	24.4200i		−	0.986313i	0.869941	−	0.493157i	$-0.164157\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.17267	+	4.17267i	−0.167985	+	0.167985i	−0.786093	−	0.618108i	$-0.787899\pi$
$617$	−4.17267	+	4.17267i	−0.167985	+	0.167985i	0.618108	+	0.786093i	$0.287899\pi$
$618$		0			0
$619$	−23.6886	+	23.6886i	−0.952124	+	0.952124i	−0.998905	−	0.0467810i	$-0.985104\pi$
$619$	−23.6886	+	23.6886i	−0.952124	+	0.952124i	0.0467810	+	0.998905i	$0.485104\pi$
$620$		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
$627$	−60.4683			−2.41487
$628$		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
$637$		−	20.4038i		−	0.808427i
$638$		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
$643$			31.2331i			1.23171i	0.787858	+	0.615857i	$0.211190\pi$
$643$			31.2331i			1.23171i	−0.787858	+	0.615857i	$0.788810\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	19.4190	+	19.4190i	0.763441	+	0.763441i	0.976943	−	0.213501i	$-0.0684868\pi$
$647$	19.4190	+	19.4190i	0.763441	+	0.763441i	−0.213501	+	0.976943i	$0.568487\pi$
$648$		0			0
$649$	−28.1724			−1.10586
$650$		0			0
$651$	−54.0989	−	54.0989i	−2.12030	−	2.12030i
$652$		0			0
$653$	42.7069			1.67125			0.835625	−	0.549300i	$-0.185105\pi$
$653$	42.7069			1.67125			0.835625	+	0.549300i	$0.185105\pi$
$654$		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	0.913856	−	0.406038i	$-0.133090\pi$
$659$	13.0362	+	13.0362i	0.507818	+	0.507818i	−0.406038	+	0.913856i	$0.633090\pi$
$660$		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
$667$		−	0.583162i		−	0.0225801i
$668$		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	−0.108595	−	0.994086i	$-0.534635\pi$
$673$	22.9716	−	22.9716i	0.885491	−	0.885491i	0.994086	+	0.108595i	$0.0346352\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.0381			−0.424229			−0.212115	−	0.977245i	$-0.568035\pi$
$677$	−11.0381			−0.424229			−0.212115	+	0.977245i	$0.568035\pi$
$678$		0			0
$679$			37.3639i			1.43390i
$680$		0			0
$681$		−	12.3452i		−	0.473070i
$682$		0			0
$683$	14.4743			0.553845			0.276922	−	0.960892i	$-0.410686\pi$
$683$	14.4743			0.553845			0.276922	+	0.960892i	$0.410686\pi$
$684$		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
$693$		−	25.9161i		−	0.984470i
$694$		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
$707$	−16.9429			−0.637203
$708$		0			0
$709$	16.6295	+	16.6295i	0.624536	+	0.624536i	0.946688	−	0.322152i	$-0.104406\pi$
$709$	16.6295	+	16.6295i	0.624536	+	0.624536i	−0.322152	+	0.946688i	$0.604406\pi$
$710$		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
$717$		−	57.9975i		−	2.16596i
$718$		0			0
$719$	−2.56511			−0.0956624			−0.0478312	−	0.998855i	$-0.515231\pi$
$719$	−2.56511			−0.0956624			−0.0478312	+	0.998855i	$0.515231\pi$
$720$		0			0
$721$	18.9198			0.704611
$722$		0			0
$723$		−	15.9682i		−	0.593864i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−21.9890	−	21.9890i	−0.815526	−	0.815526i	0.169930	−	0.985456i	$-0.445646\pi$
$727$	−21.9890	−	21.9890i	−0.815526	−	0.815526i	−0.985456	+	0.169930i	$0.945646\pi$
$728$		0			0
$729$	−10.8905			−0.403351
$730$		0			0
$731$	−1.80791	−	1.80791i	−0.0668679	−	0.0668679i
$732$		0			0
$733$	−46.4920			−1.71722			−0.858611	−	0.512628i	$-0.828672\pi$
$733$	−46.4920			−1.71722			−0.858611	+	0.512628i	$0.828672\pi$
$734$		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	0.509500	−	0.860471i	$-0.329830\pi$
$739$	−9.54098	−	9.54098i	−0.350971	−	0.350971i	−0.860471	+	0.509500i	$0.829830\pi$
$740$		0			0
$741$	−12.0698	+	12.0698i	−0.443395	+	0.443395i
$742$		0			0
$743$	−21.2388	+	21.2388i	−0.779177	+	0.779177i	−0.979691	−	0.200513i	$-0.935739\pi$
$743$	−21.2388	+	21.2388i	−0.779177	+	0.779177i	0.200513	+	0.979691i	$0.435739\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			13.4206i			0.491034i
$748$		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
$757$	−46.6464			−1.69539			−0.847696	−	0.530482i	$-0.822011\pi$
$757$	−46.6464			−1.69539			−0.847696	+	0.530482i	$0.822011\pi$
$758$		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
$763$	−13.0783			−0.473465
$764$		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	$-0.859907\pi$
$769$		−	23.6291i		−	0.852086i	0.904703	−	0.426043i	$-0.140093\pi$
$770$		0			0
$771$	−34.6037	+	34.6037i	−1.24622	+	1.24622i
$772$		0			0
$773$			48.2197i			1.73434i	0.498011	+	0.867171i	$0.334064\pi$
$773$			48.2197i			1.73434i	−0.498011	+	0.867171i	$0.665936\pi$
$774$		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
$787$	36.7365			1.30952			0.654758	−	0.755839i	$-0.272771\pi$
$787$	36.7365			1.30952			0.654758	+	0.755839i	$0.272771\pi$
$788$		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
$797$		−	27.7387i		−	0.982555i	−0.871003	−	0.491277i	$-0.836530\pi$
$797$		−	27.7387i		−	0.982555i	0.871003	−	0.491277i	$-0.163470\pi$
$798$		0			0
$799$	14.7577			0.522090
$800$		0			0
$801$	−14.7915			−0.522632
$802$		0			0
$803$			41.7144i			1.47207i
$804$		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	$-0.303167\pi$
$809$	32.9772			1.15942			0.579708	+	0.814825i	$0.303167\pi$
$810$		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
$813$	−14.6422			−0.513523
$814$		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	−0.333499	+	0.942751i	$0.608229\pi$
$823$	−36.6130	+	36.6130i	−1.27625	+	1.27625i	−0.942751	+	0.333499i	$0.891771\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			17.3121i			0.602001i	0.953624	+	0.301000i	$0.0973205\pi$
$827$			17.3121i			0.602001i	−0.953624	+	0.301000i	$0.902679\pi$
$828$		0			0
$829$	−33.7669	+	33.7669i	−1.17277	+	1.17277i	−0.191226	+	0.981546i	$0.561246\pi$
$829$	−33.7669	+	33.7669i	−1.17277	+	1.17277i	−0.981546	+	0.191226i	$0.938754\pi$
$830$		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
$837$	31.1883			1.07803
$838$		0			0
$839$		−	18.7312i		−	0.646673i	−0.946284	−	0.323337i	$-0.895195\pi$
$839$		−	18.7312i		−	0.646673i	0.946284	−	0.323337i	$-0.104805\pi$
$840$		0			0
$841$			23.6264i			0.814703i
$842$		0			0
$843$	−29.2687			−1.00807
$844$		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
$853$		−	39.5431i		−	1.35393i	−0.736016	−	0.676964i	$-0.763295\pi$
$853$		−	39.5431i		−	1.35393i	0.736016	−	0.676964i	$-0.236705\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−28.0832	+	28.0832i	−0.959305	+	0.959305i	−0.999204	−	0.0398990i	$-0.987296\pi$
$857$	−28.0832	+	28.0832i	−0.959305	+	0.959305i	0.0398990	+	0.999204i	$0.487296\pi$
$858$		0			0
$859$	−10.6404	+	10.6404i	−0.363047	+	0.363047i	−0.864933	−	0.501887i	$-0.832639\pi$
$859$	−10.6404	+	10.6404i	−0.363047	+	0.363047i	0.501887	+	0.864933i	$0.332639\pi$
$860$		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	$-0.0923714\pi$
$863$	19.7428	+	19.7428i	0.672051	+	0.672051i	−0.286137	+	0.958189i	$0.592371\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−22.2873			−0.756918
$868$		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
$877$		−	47.9703i		−	1.61984i	−0.586539	−	0.809921i	$-0.699510\pi$
$877$		−	47.9703i		−	1.61984i	0.586539	−	0.809921i	$-0.300490\pi$
$878$		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
$883$			33.5928i			1.13049i	0.824924	+	0.565244i	$0.191218\pi$
$883$			33.5928i			1.13049i	−0.824924	+	0.565244i	$0.808782\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	28.1314	+	28.1314i	0.944560	+	0.944560i	0.998542	−	0.0539823i	$-0.0171915\pi$
$887$	28.1314	+	28.1314i	0.944560	+	0.944560i	−0.0539823	+	0.998542i	$0.517191\pi$
$888$		0			0
$889$	75.3742			2.52797
$890$		0			0
$891$	39.4584	+	39.4584i	1.32191	+	1.32191i
$892$		0			0
$893$	−35.6897			−1.19431
$894$		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
$907$			1.91511i			0.0635902i	0.999494	+	0.0317951i	$0.0101224\pi$
$907$			1.91511i			0.0635902i	−0.999494	+	0.0317951i	$0.989878\pi$
$908$		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
$917$	53.5776			1.76929
$918$		0			0
$919$			49.0867i			1.61922i	0.586968	+	0.809610i	$0.300322\pi$
$919$			49.0867i			1.61922i	−0.586968	+	0.809610i	$0.699678\pi$
$920$		0			0
$921$			60.9319i			2.00777i
$922$		0			0
$923$	16.3104			0.536863
$924$		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	$0.00250163\pi$
$929$			0.479078i			0.0157180i	−0.999969	+	0.00785902i	$0.997498\pi$
$930$		0			0
$931$	−60.3012	+	60.3012i	−1.97629	+	1.97629i
$932$		0			0
$933$			20.1633i			0.660117i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	2.36411	−	2.36411i	0.0772320	−	0.0772320i	−0.667436	−	0.744668i	$-0.732608\pi$
$937$	2.36411	−	2.36411i	0.0772320	−	0.0772320i	0.744668	+	0.667436i	$0.232608\pi$
$938$		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
$947$	−29.6788			−0.964432			−0.482216	−	0.876052i	$-0.660168\pi$
$947$	−29.6788			−0.964432			−0.482216	+	0.876052i	$0.660168\pi$
$948$		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	$-0.110276\pi$
$953$	18.5543	+	18.5543i	0.601032	+	0.601032i	−0.339554	+	0.940586i	$0.610276\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			23.6364i			0.764057i
$958$		0			0
$959$	44.5819			1.43962
$960$		0			0
$961$	−35.5301			−1.14613
$962$		0			0
$963$		−	6.95816i		−	0.224224i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−13.6119	−	13.6119i	−0.437730	−	0.437730i	0.453517	−	0.891247i	$-0.350169\pi$
$967$	−13.6119	−	13.6119i	−0.437730	−	0.437730i	−0.891247	+	0.453517i	$0.850169\pi$
$968$		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
$973$	21.7366			0.696843
$974$		0			0
$975$		0			0
$976$		0			0
$977$	27.8905	+	27.8905i	0.892296	+	0.892296i	0.994739	−	0.102443i	$-0.0326659\pi$
$977$	27.8905	+	27.8905i	0.892296	+	0.892296i	−0.102443	+	0.994739i	$0.532666\pi$
$978$		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	0.198333	−	0.980135i	$-0.436447\pi$
$983$	36.9483	−	36.9483i	1.17847	−	1.17847i	0.980135	−	0.198333i	$-0.0635529\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	56.4492i		−	1.79680i
$988$		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
$997$	−27.1034			−0.858372			−0.429186	−	0.903216i	$-0.641199\pi$
$997$	−27.1034			−0.858372			−0.429186	+	0.903216i	$0.641199\pi$
$998$		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.j.c.1007.2		16
4.3	odd	2		400.2.j.c.307.4	yes	16
5.2	odd	4		1600.2.s.c.943.2		16
5.3	odd	4		1600.2.s.c.943.7		16
5.4	even	2	inner	1600.2.j.c.1007.7		16
16.5	even	4		400.2.s.c.107.8	yes	16
16.11	odd	4		1600.2.s.c.207.7		16
20.3	even	4		400.2.s.c.243.8	yes	16
20.7	even	4		400.2.s.c.243.1	yes	16
20.19	odd	2		400.2.j.c.307.5	yes	16
80.27	even	4	inner	1600.2.j.c.143.2		16
80.37	odd	4		400.2.j.c.43.5	yes	16
80.43	even	4	inner	1600.2.j.c.143.7		16
80.53	odd	4		400.2.j.c.43.4	✓	16
80.59	odd	4		1600.2.s.c.207.2		16
80.69	even	4		400.2.s.c.107.1	yes	16

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

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

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