LMFDB - Embedded newform 1512.2.q.d.1369.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(793,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))

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

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

chi := DirichletCharacter("1512.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.q (of order $3$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1369.1
Character	$\chi$	$=$	1512.1369
Dual form			1512.2.q.d.793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.11148 + 3.65719i) q^{5} +(2.19338 + 1.47956i) q^{7} +O(q^{10})$	$q+(-2.11148 + 3.65719i) q^{5} +(2.19338 + 1.47956i) q^{7} +(0.964575 + 1.67069i) q^{11} +(-0.291529 - 0.504943i) q^{13} +(-3.61082 + 6.25412i) q^{17} +(2.10268 + 3.64194i) q^{19} +(0.639939 - 1.10841i) q^{23} +(-6.41671 - 11.1141i) q^{25} +(4.20305 - 7.27990i) q^{29} -0.952121 q^{31} +(-10.0423 + 4.89755i) q^{35} +(3.03329 + 5.25381i) q^{37} +(-1.31299 - 2.27416i) q^{41} +(0.442349 - 0.766171i) q^{43} -5.76401 q^{47} +(2.62182 + 6.49046i) q^{49} +(0.962456 - 1.66702i) q^{53} -8.14673 q^{55} +4.55229 q^{59} -10.5802 q^{61} +2.46223 q^{65} -4.86383 q^{67} -11.5443 q^{71} +(0.446138 - 0.772734i) q^{73} +(-0.356209 + 5.09160i) q^{77} -11.8704 q^{79} +(5.24250 - 9.08028i) q^{83} +(-15.2484 - 26.4109i) q^{85} +(-3.87906 - 6.71874i) q^{89} +(0.107659 - 1.53887i) q^{91} -17.7591 q^{95} +(-1.98651 + 3.44073i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{5} + 5 q^{7}+O(q^{10}) $ 22 * q - q^5 + 5 * q^7	$ 22 q - q^{5} + 5 q^{7} - 3 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} - 22 q^{25} + 7 q^{29} - 12 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} + 34 q^{47} - 25 q^{49} - q^{53} + 2 q^{55} - 42 q^{59} - 62 q^{61} - 6 q^{65} + 52 q^{67} + 32 q^{71} + 17 q^{73} + q^{77} + 32 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} - 48 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q - q^5 + 5 * q^7 - 3 * q^11 + 7 * q^13 + q^17 + 13 * q^19 - 22 * q^25 + 7 * q^29 - 12 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 + 34 * q^47 - 25 * q^49 - q^53 + 2 * q^55 - 42 * q^59 - 62 * q^61 - 6 * q^65 + 52 * q^67 + 32 * q^71 + 17 * q^73 + q^77 + 32 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 - 48 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.11148	+	3.65719i	−0.944283	+	1.63555i	−0.187103	+	0.982340i	$0.559910\pi$
$5$	−2.11148	+	3.65719i	−0.944283	+	1.63555i	−0.757180	+	0.653206i	$0.773423\pi$
$6$		0			0
$7$	2.19338	+	1.47956i	0.829019	+	0.559220i
$7$	2.19338	+	1.47956i	0.829019	+	0.559220i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.964575	+	1.67069i	0.290830	+	0.503733i	0.974006	−	0.226521i	$-0.0727352\pi$
$11$	0.964575	+	1.67069i	0.290830	+	0.503733i	−0.683176	+	0.730254i	$0.739402\pi$
$12$		0			0
$13$	−0.291529	−	0.504943i	−0.0808557	−	0.140046i	0.822762	−	0.568386i	$-0.192432\pi$
$13$	−0.291529	−	0.504943i	−0.0808557	−	0.140046i	−0.903618	+	0.428340i	$0.859099\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.61082	+	6.25412i	−0.875753	+	1.51685i	−0.0197936	+	0.999804i	$0.506301\pi$
$17$	−3.61082	+	6.25412i	−0.875753	+	1.51685i	−0.855959	+	0.517044i	$0.827032\pi$
$18$		0			0
$19$	2.10268	+	3.64194i	0.482387	+	0.835519i	0.999796	−	0.0202194i	$-0.00643646\pi$
$19$	2.10268	+	3.64194i	0.482387	+	0.835519i	−0.517408	+	0.855739i	$0.673103\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.639939	−	1.10841i	0.133437	−	0.231119i	−0.791563	−	0.611088i	$-0.790732\pi$
$23$	0.639939	−	1.10841i	0.133437	−	0.231119i	0.924999	+	0.379969i	$0.124065\pi$
$24$		0			0
$25$	−6.41671	−	11.1141i	−1.28334	−	2.22281i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.20305	−	7.27990i	0.780487	−	1.35184i	−0.151171	−	0.988508i	$-0.548305\pi$
$29$	4.20305	−	7.27990i	0.780487	−	1.35184i	0.931658	−	0.363335i	$-0.118362\pi$
$30$		0			0
$31$	−0.952121			−0.171006			−0.0855030	−	0.996338i	$-0.527250\pi$
$31$	−0.952121			−0.171006			−0.0855030	+	0.996338i	$0.527250\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−10.0423	+	4.89755i	−1.69746	+	0.827837i
$36$		0			0
$37$	3.03329	+	5.25381i	0.498669	+	0.863721i	0.999999	−	0.00153588i	$-0.000488885\pi$
$37$	3.03329	+	5.25381i	0.498669	+	0.863721i	−0.501330	+	0.865256i	$0.667156\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.31299	−	2.27416i	−0.205054	−	0.355164i	0.745096	−	0.666957i	$-0.232404\pi$
$41$	−1.31299	−	2.27416i	−0.205054	−	0.355164i	−0.950150	+	0.311794i	$0.899070\pi$
$42$		0			0
$43$	0.442349	−	0.766171i	0.0674576	−	0.116840i	−0.830324	−	0.557281i	$-0.811845\pi$
$43$	0.442349	−	0.766171i	0.0674576	−	0.116840i	0.897782	+	0.440441i	$0.145178\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.76401			−0.840767			−0.420384	−	0.907346i	$-0.638105\pi$
$47$	−5.76401			−0.840767			−0.420384	+	0.907346i	$0.638105\pi$
$48$		0			0
$49$	2.62182	+	6.49046i	0.374545	+	0.927209i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.962456	−	1.66702i	0.132204	−	0.228983i	−0.792322	−	0.610103i	$-0.791128\pi$
$53$	0.962456	−	1.66702i	0.132204	−	0.228983i	0.924526	+	0.381120i	$0.124461\pi$
$54$		0			0
$55$	−8.14673			−1.09850
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.55229			0.592657			0.296329	−	0.955086i	$-0.404238\pi$
$59$	4.55229			0.592657			0.296329	+	0.955086i	$0.404238\pi$
$60$		0			0
$61$	−10.5802			−1.35465			−0.677325	−	0.735684i	$-0.736861\pi$
$61$	−10.5802			−1.35465			−0.677325	+	0.735684i	$0.736861\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.46223			0.305403
$66$		0			0
$67$	−4.86383			−0.594211			−0.297106	−	0.954845i	$-0.596021\pi$
$67$	−4.86383			−0.594211			−0.297106	+	0.954845i	$0.596021\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−11.5443			−1.37005			−0.685027	−	0.728518i	$-0.740209\pi$
$71$	−11.5443			−1.37005			−0.685027	+	0.728518i	$0.740209\pi$
$72$		0			0
$73$	0.446138	−	0.772734i	0.0522165	−	0.0904417i	−0.838736	−	0.544539i	$-0.816705\pi$
$73$	0.446138	−	0.772734i	0.0522165	−	0.0904417i	0.890952	+	0.454097i	$0.150038\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.356209	+	5.09160i	−0.0405937	+	0.580242i
$78$		0			0
$79$	−11.8704			−1.33553			−0.667763	−	0.744374i	$-0.732748\pi$
$79$	−11.8704			−1.33553			−0.667763	+	0.744374i	$0.732748\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.24250	−	9.08028i	0.575439	−	0.996690i	−0.420555	−	0.907267i	$-0.638164\pi$
$83$	5.24250	−	9.08028i	0.575439	−	0.996690i	0.995994	−	0.0894227i	$-0.0285022\pi$
$84$		0			0
$85$	−15.2484	−	26.4109i	−1.65392	−	2.86467i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.87906	−	6.71874i	−0.411180	−	0.712185i	0.583839	−	0.811869i	$-0.301550\pi$
$89$	−3.87906	−	6.71874i	−0.411180	−	0.712185i	−0.995019	+	0.0996849i	$0.968217\pi$
$90$		0			0
$91$	0.107659	−	1.53887i	0.0112857	−	0.161317i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−17.7591			−1.82204
$96$		0			0
$97$	−1.98651	+	3.44073i	−0.201699	+	0.349353i	−0.949076	−	0.315047i	$-0.897980\pi$
$97$	−1.98651	+	3.44073i	−0.201699	+	0.349353i	0.747377	+	0.664400i	$0.231313\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.38533	+	14.5238i	0.834372	+	1.44517i	0.894541	+	0.446986i	$0.147503\pi$
$101$	8.38533	+	14.5238i	0.834372	+	1.44517i	−0.0601687	+	0.998188i	$0.519164\pi$
$102$		0			0
$103$	−5.80569	+	10.0558i	−0.572052	+	0.990823i	0.424303	+	0.905520i	$0.360519\pi$
$103$	−5.80569	+	10.0558i	−0.572052	+	0.990823i	−0.996355	+	0.0853025i	$0.972814\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.2454	+	17.7455i	0.990460	+	1.71553i	0.614570	+	0.788862i	$0.289329\pi$
$107$	10.2454	+	17.7455i	0.990460	+	1.71553i	0.375890	+	0.926664i	$0.377337\pi$
$108$		0			0
$109$	2.46965	−	4.27756i	0.236550	−	0.409716i	−0.723172	−	0.690668i	$-0.757317\pi$
$109$	2.46965	−	4.27756i	0.236550	−	0.409716i	0.959722	+	0.280951i	$0.0906500\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.42131	+	12.8541i	0.698138	+	1.20921i	0.969111	+	0.246623i	$0.0793210\pi$
$113$	7.42131	+	12.8541i	0.698138	+	1.20921i	−0.270974	+	0.962587i	$0.587346\pi$
$114$		0			0
$115$	2.70244	+	4.68076i	0.252004	+	0.436484i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−17.1732	+	8.37524i	−1.57427	+	0.767757i
$120$		0			0
$121$	3.63919	−	6.30326i	0.330836	−	0.573024i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	33.0802			2.95879
$126$		0			0
$127$	−8.53648			−0.757490			−0.378745	−	0.925501i	$-0.623644\pi$
$127$	−8.53648			−0.757490			−0.378745	+	0.925501i	$0.623644\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.17342	+	2.03243i	−0.102522	+	0.177574i	−0.912723	−	0.408578i	$-0.866025\pi$
$131$	−1.17342	+	2.03243i	−0.102522	+	0.177574i	0.810201	+	0.586152i	$0.199358\pi$
$132$		0			0
$133$	−0.776499	+	11.0992i	−0.0673310	+	0.962422i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.641815	+	1.11166i	0.0548340	+	0.0949752i	0.892139	−	0.451760i	$-0.149204\pi$
$137$	0.641815	+	1.11166i	0.0548340	+	0.0949752i	−0.837305	+	0.546735i	$0.815870\pi$
$138$		0			0
$139$	0.610553	+	1.05751i	0.0517865	+	0.0896968i	0.890757	−	0.454481i	$-0.150175\pi$
$139$	0.610553	+	1.05751i	0.0517865	+	0.0896968i	−0.838970	+	0.544177i	$0.816842\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.562403	−	0.974111i	0.0470305	−	0.0814593i
$144$		0			0
$145$	17.7493	+	30.7427i	1.47400	+	2.55305i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.14729	−	5.45127i	0.257836	−	0.446585i	−0.707826	−	0.706387i	$-0.750324\pi$
$149$	3.14729	−	5.45127i	0.257836	−	0.446585i	0.965662	+	0.259802i	$0.0836572\pi$
$150$		0			0
$151$	−1.17726	−	2.03908i	−0.0958044	−	0.165938i	0.814140	−	0.580669i	$-0.197209\pi$
$151$	−1.17726	−	2.03908i	−0.0958044	−	0.165938i	−0.909944	+	0.414731i	$0.863876\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.01039	−	3.48209i	0.161478	−	0.279688i
$156$		0			0
$157$	−2.88873			−0.230546			−0.115273	−	0.993334i	$-0.536774\pi$
$157$	−2.88873			−0.230546			−0.115273	+	0.993334i	$0.536774\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	3.04358	−	1.48433i	0.239868	−	0.116982i
$162$		0			0
$163$	2.60538	+	4.51265i	0.204069	+	0.353458i	0.949836	−	0.312749i	$-0.101250\pi$
$163$	2.60538	+	4.51265i	0.204069	+	0.353458i	−0.745767	+	0.666207i	$0.767917\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.5400	−	18.2558i	−0.815610	−	1.41268i	−0.908889	−	0.417039i	$-0.863068\pi$
$167$	−10.5400	−	18.2558i	−0.815610	−	1.41268i	0.0932784	−	0.995640i	$-0.470265\pi$
$168$		0			0
$169$	6.33002	−	10.9639i	0.486925	−	0.843378i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.07305			0.309669			0.154834	−	0.987940i	$-0.450516\pi$
$173$	4.07305			0.309669			0.154834	+	0.987940i	$0.450516\pi$
$174$		0			0
$175$	2.36963	−	33.8712i	0.179127	−	2.56042i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.11088	−	5.38821i	0.232518	−	0.402733i	−0.726030	−	0.687663i	$-0.758637\pi$
$179$	3.11088	−	5.38821i	0.232518	−	0.402733i	0.958549	+	0.284929i	$0.0919701\pi$
$180$		0			0
$181$	18.2396			1.35574			0.677868	−	0.735184i	$-0.262904\pi$
$181$	18.2396			1.35574			0.677868	+	0.735184i	$0.262904\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−25.6189			−1.88354
$186$		0			0
$187$	−13.9316			−1.01878
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.38597			0.534430			0.267215	−	0.963637i	$-0.413897\pi$
$191$	7.38597			0.534430			0.267215	+	0.963637i	$0.413897\pi$
$192$		0			0
$193$	19.5182			1.40495			0.702474	−	0.711709i	$-0.252079\pi$
$193$	19.5182			1.40495			0.702474	+	0.711709i	$0.252079\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.77564			−0.553992			−0.276996	−	0.960871i	$-0.589339\pi$
$197$	−7.77564			−0.553992			−0.276996	+	0.960871i	$0.589339\pi$
$198$		0			0
$199$	−3.85734	+	6.68110i	−0.273439	+	0.473611i	−0.969740	−	0.244139i	$-0.921495\pi$
$199$	−3.85734	+	6.68110i	−0.273439	+	0.473611i	0.696301	+	0.717750i	$0.254828\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	19.9899	−	9.74891i	1.40302	−	0.684240i
$204$		0			0
$205$	11.0894			0.774515
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.05638	+	7.02585i	−0.280586	+	0.485989i
$210$		0			0
$211$	11.7645	+	20.3767i	0.809899	+	1.40279i	0.912933	+	0.408109i	$0.133812\pi$
$211$	11.7645	+	20.3767i	0.809899	+	1.40279i	−0.103034	+	0.994678i	$0.532855\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.86802	+	3.23551i	0.127398	+	0.220660i
$216$		0			0
$217$	−2.08836	−	1.40872i	−0.141767	−	0.0956301i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.21064			0.283238
$222$		0			0
$223$	−4.83093	+	8.36742i	−0.323503	+	0.560324i	−0.981208	−	0.192952i	$-0.938194\pi$
$223$	−4.83093	+	8.36742i	−0.323503	+	0.560324i	0.657705	+	0.753275i	$0.271527\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.98592	+	15.5641i	0.596417	+	1.03302i	0.993345	+	0.115175i	$0.0367427\pi$
$227$	8.98592	+	15.5641i	0.596417	+	1.03302i	−0.396929	+	0.917850i	$0.629924\pi$
$228$		0			0
$229$	3.95834	−	6.85604i	0.261574	−	0.453060i	−0.705086	−	0.709122i	$-0.749092\pi$
$229$	3.95834	−	6.85604i	0.261574	−	0.453060i	0.966660	+	0.256062i	$0.0824250\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.27796	−	5.67759i	−0.214746	−	0.371951i	0.738448	−	0.674311i	$-0.235559\pi$
$233$	−3.27796	−	5.67759i	−0.214746	−	0.371951i	−0.953194	+	0.302359i	$0.902226\pi$
$234$		0			0
$235$	12.1706	−	21.0801i	0.793922	−	1.37511i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	8.01922	+	13.8897i	0.518720	+	0.898450i	0.999763	+	0.0217529i	$0.00692470\pi$
$239$	8.01922	+	13.8897i	0.518720	+	0.898450i	−0.481043	+	0.876697i	$0.659742\pi$
$240$		0			0
$241$	−5.58957	−	9.68142i	−0.360056	−	0.623635i	0.627914	−	0.778283i	$-0.283909\pi$
$241$	−5.58957	−	9.68142i	−0.360056	−	0.623635i	−0.987970	+	0.154648i	$0.950576\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−29.2728	−	4.11599i	−1.87017	−	0.262961i
$246$		0			0
$247$	1.22598	−	2.12347i	0.0780075	−	0.135113i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−14.6169			−0.922613			−0.461307	−	0.887241i	$-0.652619\pi$
$251$	−14.6169			−0.922613			−0.461307	+	0.887241i	$0.652619\pi$
$252$		0			0
$253$	2.46908			0.155230
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.45936	−	12.9200i	0.465302	−	0.805927i	−0.533913	−	0.845540i	$-0.679279\pi$
$257$	7.45936	−	12.9200i	0.465302	−	0.805927i	0.999215	+	0.0396123i	$0.0126123\pi$
$258$		0			0
$259$	−1.12016	+	16.0115i	−0.0696037	+	0.994907i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−11.1057	−	19.2357i	−0.684808	−	1.18612i	−0.973497	−	0.228699i	$-0.926553\pi$
$263$	−11.1057	−	19.2357i	−0.684808	−	1.18612i	0.288689	−	0.957423i	$-0.406781\pi$
$264$		0			0
$265$	4.06442	+	7.03978i	0.249675	+	0.432450i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.73590	−	8.20281i	0.288753	−	0.500134i	−0.684760	−	0.728769i	$-0.740093\pi$
$269$	4.73590	−	8.20281i	0.288753	−	0.500134i	0.973512	+	0.228635i	$0.0734261\pi$
$270$		0			0
$271$	8.78188	+	15.2107i	0.533461	+	0.923982i	0.999236	+	0.0390786i	$0.0124423\pi$
$271$	8.78188	+	15.2107i	0.533461	+	0.923982i	−0.465775	+	0.884903i	$0.654224\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	12.3788	−	21.4407i	0.746469	−	1.29292i
$276$		0			0
$277$	−6.77651	−	11.7373i	−0.407161	−	0.705224i	0.587409	−	0.809290i	$-0.300148\pi$
$277$	−6.77651	−	11.7373i	−0.407161	−	0.705224i	−0.994570	+	0.104066i	$0.966815\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.14196	+	10.6382i	−0.366398	+	0.634621i	−0.989000	−	0.147919i	$-0.952743\pi$
$281$	−6.14196	+	10.6382i	−0.366398	+	0.634621i	0.622601	+	0.782539i	$0.286076\pi$
$282$		0			0
$283$	14.0483			0.835084			0.417542	−	0.908658i	$-0.362892\pi$
$283$	14.0483			0.835084			0.417542	+	0.908658i	$0.362892\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.484873	−	6.93072i	0.0286212	−	0.409108i
$288$		0			0
$289$	−17.5760	−	30.4426i	−1.03388	−	1.79074i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.05863	−	7.02975i	−0.237108	−	0.410682i	0.722776	−	0.691083i	$-0.242866\pi$
$293$	−4.05863	−	7.02975i	−0.237108	−	0.410682i	−0.959883	+	0.280401i	$0.909533\pi$
$294$		0			0
$295$	−9.61207	+	16.6486i	−0.559636	+	0.969319i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.746244			−0.0431564
$300$		0			0
$301$	2.10383	−	1.02602i	0.121263	−	0.0591390i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	22.3398	−	38.6937i	1.27917	−	2.21559i
$306$		0			0
$307$	6.61556			0.377570			0.188785	−	0.982018i	$-0.439545\pi$
$307$	6.61556			0.377570			0.188785	+	0.982018i	$0.439545\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.35961			0.474030			0.237015	−	0.971506i	$-0.423831\pi$
$311$	8.35961			0.474030			0.237015	+	0.971506i	$0.423831\pi$
$312$		0			0
$313$	26.1083			1.47573			0.737864	−	0.674949i	$-0.235834\pi$
$313$	26.1083			1.47573			0.737864	+	0.674949i	$0.235834\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.2148			−0.629887			−0.314943	−	0.949110i	$-0.601986\pi$
$317$	−11.2148			−0.629887			−0.314943	+	0.949110i	$0.601986\pi$
$318$		0			0
$319$	16.2166			0.907957
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−30.3696			−1.68981
$324$		0			0
$325$	−3.74132	+	6.48015i	−0.207531	+	0.359454i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−12.6427	−	8.52819i	−0.697012	−	0.470174i
$330$		0			0
$331$	−18.2329			−1.00217			−0.501086	−	0.865398i	$-0.667066\pi$
$331$	−18.2329			−1.00217			−0.501086	+	0.865398i	$0.667066\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	10.2699	−	17.7880i	0.561104	−	0.971860i
$336$		0			0
$337$	4.62148	+	8.00465i	0.251748	+	0.436041i	0.964007	−	0.265876i	$-0.0856612\pi$
$337$	4.62148	+	8.00465i	0.251748	+	0.436041i	−0.712259	+	0.701917i	$0.752328\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.918392	−	1.59070i	−0.0497337	−	0.0861413i
$342$		0			0
$343$	−3.85237	+	18.1152i	−0.208009	+	0.978127i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	31.6649			1.69986			0.849931	−	0.526894i	$-0.176644\pi$
$347$	31.6649			1.69986			0.849931	+	0.526894i	$0.176644\pi$
$348$		0			0
$349$	−18.2112	+	31.5427i	−0.974821	+	1.68844i	−0.294296	+	0.955714i	$0.595085\pi$
$349$	−18.2112	+	31.5427i	−0.974821	+	1.68844i	−0.680525	+	0.732725i	$0.738248\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3.59888	+	6.23345i	0.191549	+	0.331773i	0.945764	−	0.324855i	$-0.105316\pi$
$353$	3.59888	+	6.23345i	0.191549	+	0.331773i	−0.754215	+	0.656628i	$0.771982\pi$
$354$		0			0
$355$	24.3755	−	42.2196i	1.29372	−	2.24079i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	7.39891	+	12.8153i	0.390499	+	0.676365i	0.992515	−	0.122119i	$-0.0389690\pi$
$359$	7.39891	+	12.8153i	0.390499	+	0.676365i	−0.602016	+	0.798484i	$0.705636\pi$
$360$		0			0
$361$	0.657495	−	1.13881i	0.0346050	−	0.0599376i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.88402	+	3.26323i	0.0986144	+	0.170805i
$366$		0			0
$367$	−2.09550	−	3.62951i	−0.109384	−	0.189459i	0.806137	−	0.591729i	$-0.201555\pi$
$367$	−2.09550	−	3.62951i	−0.109384	−	0.189459i	−0.915521	+	0.402270i	$0.868221\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.57749	−	2.23240i	0.237651	−	0.115901i
$372$		0			0
$373$	−8.70875	+	15.0840i	−0.450922	+	0.781020i	−0.998444	−	0.0557718i	$-0.982238\pi$
$373$	−8.70875	+	15.0840i	−0.450922	+	0.781020i	0.547522	+	0.836792i	$0.315571\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.90125			−0.252427
$378$		0			0
$379$	−11.1732			−0.573927			−0.286964	−	0.957941i	$-0.592646\pi$
$379$	−11.1732			−0.573927			−0.286964	+	0.957941i	$0.592646\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.5508	+	21.7386i	−0.641316	+	1.11079i	0.343823	+	0.939035i	$0.388278\pi$
$383$	−12.5508	+	21.7386i	−0.641316	+	1.11079i	−0.985139	+	0.171758i	$0.945055\pi$
$384$		0			0
$385$	−17.8689	−	12.0536i	−0.910681	−	0.614306i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.732011	+	1.26788i	0.0371144	+	0.0642841i	0.883986	−	0.467513i	$-0.154850\pi$
$389$	0.732011	+	1.26788i	0.0371144	+	0.0642841i	−0.846872	+	0.531798i	$0.821517\pi$
$390$		0			0
$391$	4.62141	+	8.00452i	0.233715	+	0.404806i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	25.0641	−	43.4124i	1.26111	−	2.18431i
$396$		0			0
$397$	−1.49591	−	2.59100i	−0.0750778	−	0.130039i	0.826042	−	0.563608i	$-0.190587\pi$
$397$	−1.49591	−	2.59100i	−0.0750778	−	0.130039i	−0.901120	+	0.433570i	$0.857254\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.1685	+	22.8086i	−0.657605	+	1.13901i	0.323629	+	0.946184i	$0.395097\pi$
$401$	−13.1685	+	22.8086i	−0.657605	+	1.13901i	−0.981234	+	0.192821i	$0.938236\pi$
$402$		0			0
$403$	0.277571	+	0.480767i	0.0138268	+	0.0239487i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.85166	+	10.1354i	−0.290056	+	0.502392i
$408$		0			0
$409$	3.00784			0.148728			0.0743642	−	0.997231i	$-0.476307\pi$
$409$	3.00784			0.148728			0.0743642	+	0.997231i	$0.476307\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	9.98489	+	6.73537i	0.491324	+	0.331426i
$414$		0			0
$415$	22.1389	+	38.3457i	1.08676	+	1.88232i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	17.2414	+	29.8630i	0.842297	+	1.45890i	0.887948	+	0.459944i	$0.152131\pi$
$419$	17.2414	+	29.8630i	0.842297	+	1.45890i	−0.0456508	+	0.998957i	$0.514536\pi$
$420$		0			0
$421$	9.86151	−	17.0806i	0.480620	−	0.832459i	−0.519132	−	0.854694i	$-0.673745\pi$
$421$	9.86151	−	17.0806i	0.480620	−	0.832459i	0.999753	+	0.0222349i	$0.00707818\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	92.6783			4.49556
$426$		0			0
$427$	−23.2063	−	15.6540i	−1.12303	−	0.757548i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.4257	+	18.0578i	−0.502188	+	0.869816i	0.497808	+	0.867287i	$0.334138\pi$
$431$	−10.4257	+	18.0578i	−0.502188	+	0.869816i	−0.999997	+	0.00252883i	$0.999195\pi$
$432$		0			0
$433$	15.6324			0.751247			0.375624	−	0.926772i	$-0.377429\pi$
$433$	15.6324			0.751247			0.375624	+	0.926772i	$0.377429\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.38235			0.257473
$438$		0			0
$439$	35.6989			1.70382			0.851909	−	0.523690i	$-0.175445\pi$
$439$	35.6989			1.70382			0.851909	+	0.523690i	$0.175445\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−18.1157			−0.860705			−0.430352	−	0.902661i	$-0.641611\pi$
$443$	−18.1157			−0.860705			−0.430352	+	0.902661i	$0.641611\pi$
$444$		0			0
$445$	32.7623			1.55308
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−17.4189			−0.822051			−0.411025	−	0.911624i	$-0.634829\pi$
$449$	−17.4189			−0.822051			−0.411025	+	0.911624i	$0.634829\pi$
$450$		0			0
$451$	2.53294	−	4.38719i	0.119272	−	0.206585i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	5.40061	+	3.64302i	0.253185	+	0.170787i
$456$		0			0
$457$	15.3584			0.718434			0.359217	−	0.933254i	$-0.383044\pi$
$457$	15.3584			0.718434			0.359217	+	0.933254i	$0.383044\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.15140	−	10.6545i	0.286499	−	0.496231i	−0.686472	−	0.727156i	$-0.740842\pi$
$461$	6.15140	−	10.6545i	0.286499	−	0.496231i	0.972972	+	0.230924i	$0.0741750\pi$
$462$		0			0
$463$	9.18922	+	15.9162i	0.427059	+	0.739688i	0.996610	−	0.0822677i	$-0.0262162\pi$
$463$	9.18922	+	15.9162i	0.427059	+	0.739688i	−0.569551	+	0.821956i	$0.692883\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	11.1020	+	19.2292i	0.513738	+	0.889820i	0.999873	+	0.0159363i	$0.00507290\pi$
$467$	11.1020	+	19.2292i	0.513738	+	0.889820i	−0.486135	+	0.873884i	$0.661594\pi$
$468$		0			0
$469$	−10.6682	−	7.19631i	−0.492612	−	0.332295i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.70672			0.0784749
$474$		0			0
$475$	26.9845	−	46.7386i	1.23814	−	2.14451i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−17.2969	−	29.9591i	−0.790317	−	1.36887i	−0.925771	−	0.378085i	$-0.876583\pi$
$479$	−17.2969	−	29.9591i	−0.790317	−	1.36887i	0.135454	−	0.990784i	$-0.456751\pi$
$480$		0			0
$481$	1.76858	−	3.06328i	0.0806405	−	0.139673i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.38895	−	14.5301i	−0.380922	−	0.659777i
$486$		0			0
$487$	6.79789	−	11.7743i	0.308042	−	0.533544i	−0.669892	−	0.742458i	$-0.733660\pi$
$487$	6.79789	−	11.7743i	0.308042	−	0.533544i	0.977934	+	0.208915i	$0.0669931\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7.01841	+	12.1563i	0.316737	+	0.548604i	0.979805	−	0.199955i	$-0.0640795\pi$
$491$	7.01841	+	12.1563i	0.316737	+	0.548604i	−0.663069	+	0.748559i	$0.730746\pi$
$492$		0			0
$493$	30.3529	+	52.5728i	1.36703	+	2.36776i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−25.3210	−	17.0804i	−1.13580	−	0.766161i
$498$		0			0
$499$	15.1408	−	26.2246i	0.677794	−	1.17397i	−0.297849	−	0.954613i	$-0.596269\pi$
$499$	15.1408	−	26.2246i	0.677794	−	1.17397i	0.975644	−	0.219362i	$-0.0703974\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	35.5942			1.58707			0.793533	−	0.608527i	$-0.208239\pi$
$503$	35.5942			1.58707			0.793533	+	0.608527i	$0.208239\pi$
$504$		0			0
$505$	−70.8219			−3.15153
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.23675	+	5.60621i	−0.143466	+	0.248491i	−0.928800	−	0.370582i	$-0.879158\pi$
$509$	−3.23675	+	5.60621i	−0.143466	+	0.248491i	0.785333	+	0.619073i	$0.212492\pi$
$510$		0			0
$511$	2.12185	−	1.03481i	0.0938653	−	0.0457773i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−24.5172	−	42.4651i	−1.08036	−	1.87123i
$516$		0			0
$517$	−5.55982	−	9.62989i	−0.244521	−	0.423522i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.18988	+	10.7212i	−0.271184	+	0.469704i	−0.969165	−	0.246412i	$-0.920748\pi$
$521$	−6.18988	+	10.7212i	−0.271184	+	0.469704i	0.697982	+	0.716116i	$0.254082\pi$
$522$		0			0
$523$	11.0290	+	19.1028i	0.482265	+	0.835308i	0.999793	−	0.0203585i	$-0.00648074\pi$
$523$	11.0290	+	19.1028i	0.482265	+	0.835308i	−0.517527	+	0.855667i	$0.673147\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.43794	−	5.95469i	0.149759	−	0.259390i
$528$		0			0
$529$	10.6810	+	18.5000i	0.464389	+	0.804346i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.765547	+	1.32597i	−0.0331595	+	0.0574340i
$534$		0			0
$535$	−86.5319			−3.74110
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−8.31462	+	10.6408i	−0.358136	+	0.458331i
$540$		0			0
$541$	7.24989	+	12.5572i	0.311697	+	0.539875i	0.978730	−	0.205153i	$-0.0657693\pi$
$541$	7.24989	+	12.5572i	0.311697	+	0.539875i	−0.667033	+	0.745028i	$0.732436\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	10.4293	+	18.0640i	0.446740	+	0.773777i
$546$		0			0
$547$	−12.4034	+	21.4834i	−0.530332	+	0.918562i	0.469042	+	0.883176i	$0.344599\pi$
$547$	−12.4034	+	21.4834i	−0.530332	+	0.918562i	−0.999374	+	0.0353858i	$0.988734\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	35.3506			1.50599
$552$		0			0
$553$	−26.0363	−	17.5630i	−1.10718	−	0.746853i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.02336	+	15.6289i	−0.382332	+	0.662219i	−0.991395	−	0.130903i	$-0.958212\pi$
$557$	−9.02336	+	15.6289i	−0.382332	+	0.662219i	0.609063	+	0.793122i	$0.291546\pi$
$558$		0			0
$559$	−0.515831			−0.0218173
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−19.0350			−0.802228			−0.401114	−	0.916028i	$-0.631377\pi$
$563$	−19.0350			−0.802228			−0.401114	+	0.916028i	$0.631377\pi$
$564$		0			0
$565$	−62.6798			−2.63696
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.36036			−0.392407			−0.196203	−	0.980563i	$-0.562861\pi$
$569$	−9.36036			−0.392407			−0.196203	+	0.980563i	$0.562861\pi$
$570$		0			0
$571$	35.3611			1.47981			0.739907	−	0.672709i	$-0.234869\pi$
$571$	35.3611			1.47981			0.739907	+	0.672709i	$0.234869\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−16.4252			−0.684979
$576$		0			0
$577$	14.0160	−	24.2764i	0.583493	−	1.01064i	−0.411568	−	0.911379i	$-0.635019\pi$
$577$	14.0160	−	24.2764i	0.583493	−	1.01064i	0.995061	−	0.0992610i	$-0.0316479\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	24.9336	−	12.1599i	1.03442	−	0.504478i
$582$		0			0
$583$	3.71344			0.153795
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−13.7305	+	23.7819i	−0.566718	+	0.981585i	0.430169	+	0.902748i	$0.358454\pi$
$587$	−13.7305	+	23.7819i	−0.566718	+	0.981585i	−0.996888	+	0.0788364i	$0.974880\pi$
$588$		0			0
$589$	−2.00200	−	3.46757i	−0.0824912	−	0.142879i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	11.1267	+	19.2719i	0.456917	+	0.791404i	0.998796	−	0.0490525i	$-0.0156202\pi$
$593$	11.1267	+	19.2719i	0.456917	+	0.791404i	−0.541879	+	0.840457i	$0.682287\pi$
$594$		0			0
$595$	5.63108	−	80.4900i	0.230852	−	3.29977i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−6.74118			−0.275437			−0.137719	−	0.990471i	$-0.543977\pi$
$599$	−6.74118			−0.275437			−0.137719	+	0.990471i	$0.543977\pi$
$600$		0			0
$601$	4.04153	−	7.00013i	0.164857	−	0.285541i	−0.771747	−	0.635929i	$-0.780617\pi$
$601$	4.04153	−	7.00013i	0.164857	−	0.285541i	0.936605	+	0.350388i	$0.113950\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	15.3682	+	26.6185i	0.624805	+	1.08219i
$606$		0			0
$607$	−15.8020	+	27.3698i	−0.641382	+	1.11091i	0.343742	+	0.939064i	$0.388305\pi$
$607$	−15.8020	+	27.3698i	−0.641382	+	1.11091i	−0.985124	+	0.171843i	$0.945028\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.68038	+	2.91050i	0.0679808	+	0.117746i
$612$		0			0
$613$	−3.10601	+	5.37977i	−0.125451	+	0.217287i	−0.921909	−	0.387407i	$-0.873371\pi$
$613$	−3.10601	+	5.37977i	−0.125451	+	0.217287i	0.796458	+	0.604693i	$0.206704\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.309009	+	0.535218i	0.0124402	+	0.0215471i	0.872178	−	0.489188i	$-0.162707\pi$
$617$	0.309009	+	0.535218i	0.0124402	+	0.0215471i	−0.859738	+	0.510735i	$0.829373\pi$
$618$		0			0
$619$	−20.0103	−	34.6589i	−0.804283	−	1.39306i	−0.916774	−	0.399406i	$-0.869217\pi$
$619$	−20.0103	−	34.6589i	−0.804283	−	1.39306i	0.112492	−	0.993653i	$-0.464117\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.43250	−	20.4760i	0.0573920	−	0.820355i
$624$		0			0
$625$	−37.7647	+	65.4105i	−1.51059	+	2.61642i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−43.8106			−1.74684
$630$		0			0
$631$	5.20154			0.207070			0.103535	−	0.994626i	$-0.466985\pi$
$631$	5.20154			0.207070			0.103535	+	0.994626i	$0.466985\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	18.0246	−	31.2196i	0.715285	−	1.23891i
$636$		0			0
$637$	2.51298	−	3.21603i	0.0995678	−	0.127424i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.137294	−	0.237799i	−0.00542277	−	0.00939251i	0.863301	−	0.504689i	$-0.168393\pi$
$641$	−0.137294	−	0.237799i	−0.00542277	−	0.00939251i	−0.868724	+	0.495296i	$0.835059\pi$
$642$		0			0
$643$	11.2657	+	19.5128i	0.444277	+	0.769510i	0.998002	−	0.0631900i	$-0.0201274\pi$
$643$	11.2657	+	19.5128i	0.444277	+	0.769510i	−0.553725	+	0.832700i	$0.686794\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.2737	+	21.2586i	−0.482528	+	0.835763i	−0.999799	−	0.0200588i	$-0.993615\pi$
$647$	−12.2737	+	21.2586i	−0.482528	+	0.835763i	0.517271	+	0.855822i	$0.326948\pi$
$648$		0			0
$649$	4.39102	+	7.60547i	0.172363	+	0.298541i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	16.5154	−	28.6055i	0.646298	−	1.11942i	−0.337703	−	0.941253i	$-0.609650\pi$
$653$	16.5154	−	28.6055i	0.646298	−	1.11942i	0.984000	−	0.178167i	$-0.0570169\pi$
$654$		0			0
$655$	−4.95532	−	8.58286i	−0.193620	−	0.335360i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−21.3813	+	37.0335i	−0.832897	+	1.44262i	0.0628336	+	0.998024i	$0.479986\pi$
$659$	−21.3813	+	37.0335i	−0.832897	+	1.44262i	−0.895731	+	0.444596i	$0.853347\pi$
$660$		0			0
$661$	−19.1083			−0.743227			−0.371614	−	0.928387i	$-0.621195\pi$
$661$	−19.1083			−0.743227			−0.371614	+	0.928387i	$0.621195\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−38.9523	−	26.2756i	−1.51051	−	1.01892i
$666$		0			0
$667$	−5.37940	−	9.31739i	−0.208291	−	0.360771i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−10.2054	−	17.6762i	−0.393973	−	0.682382i
$672$		0			0
$673$	−12.9345	+	22.4032i	−0.498588	+	0.863579i	−0.999999	−	0.00162995i	$-0.999481\pi$
$673$	−12.9345	+	22.4032i	−0.498588	+	0.863579i	0.501411	+	0.865209i	$0.332815\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.89337			−0.0727682			−0.0363841	−	0.999338i	$-0.511584\pi$
$677$	−1.89337			−0.0727682			−0.0363841	+	0.999338i	$0.511584\pi$
$678$		0			0
$679$	−9.44792	+	4.60767i	−0.362578	+	0.176826i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	6.39573	−	11.0777i	0.244726	−	0.423878i	−0.717329	−	0.696735i	$-0.754635\pi$
$683$	6.39573	−	11.0777i	0.244726	−	0.423878i	0.962055	+	0.272857i	$0.0879687\pi$
$684$		0			0
$685$	−5.42072			−0.207115
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.12234			−0.0427576
$690$		0			0
$691$	−36.0698			−1.37216			−0.686079	−	0.727527i	$-0.740670\pi$
$691$	−36.0698			−1.37216			−0.686079	+	0.727527i	$0.740670\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.15669			−0.195604
$696$		0			0
$697$	18.9638			0.718306
$698$		0			0
$699$		0			0
$700$		0			0
$701$	20.2524			0.764922			0.382461	−	0.923972i	$-0.375077\pi$
$701$	20.2524			0.764922			0.382461	+	0.923972i	$0.375077\pi$
$702$		0			0
$703$	−12.7560	+	22.0941i	−0.481103	+	0.833296i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.09663	+	44.2628i	−0.116461	+	1.66468i
$708$		0			0
$709$	−6.76636			−0.254116			−0.127058	−	0.991895i	$-0.540553\pi$
$709$	−6.76636			−0.254116			−0.127058	+	0.991895i	$0.540553\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.609300	+	1.05534i	−0.0228185	+	0.0395227i
$714$		0			0
$715$	2.37501	+	4.11364i	0.0888203	+	0.153841i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6.43767	−	11.1504i	−0.240084	−	0.415839i	0.720654	−	0.693295i	$-0.243842\pi$
$719$	−6.43767	−	11.1504i	−0.240084	−	0.415839i	−0.960738	+	0.277457i	$0.910508\pi$
$720$		0			0
$721$	−27.6121	+	13.4662i	−1.02833	+	0.501508i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−107.879			−4.00653
$726$		0			0
$727$	14.3621	−	24.8758i	0.532659	−	0.922593i	−0.466613	−	0.884461i	$-0.654526\pi$
$727$	14.3621	−	24.8758i	0.532659	−	0.922593i	0.999273	−	0.0381316i	$-0.0121406\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.19449	+	5.53301i	0.118152	+	0.204646i
$732$		0			0
$733$	−2.33025	+	4.03611i	−0.0860697	+	0.149077i	−0.905847	−	0.423606i	$-0.860764\pi$
$733$	−2.33025	+	4.03611i	−0.0860697	+	0.149077i	0.819777	+	0.572683i	$0.194097\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.69153	−	8.12596i	−0.172815	−	0.299324i
$738$		0			0
$739$	9.46395	−	16.3920i	0.348137	−	0.602991i	−0.637782	−	0.770217i	$-0.720148\pi$
$739$	9.46395	−	16.3920i	0.348137	−	0.602991i	0.985919	+	0.167227i	$0.0534811\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−6.64732	−	11.5135i	−0.243867	−	0.422389i	0.717946	−	0.696099i	$-0.245083\pi$
$743$	−6.64732	−	11.5135i	−0.243867	−	0.422389i	−0.961812	+	0.273710i	$0.911749\pi$
$744$		0			0
$745$	13.2909	+	23.0205i	0.486941	+	0.843406i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.78353	+	54.0814i	−0.138247	+	1.97609i
$750$		0			0
$751$	7.61766	−	13.1942i	0.277972	−	0.481462i	−0.692908	−	0.721026i	$-0.743671\pi$
$751$	7.61766	−	13.1942i	0.277972	−	0.481462i	0.970881	+	0.239563i	$0.0770043\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	9.94308			0.361866
$756$		0			0
$757$	15.6279			0.568004			0.284002	−	0.958824i	$-0.408338\pi$
$757$	15.6279			0.568004			0.284002	+	0.958824i	$0.408338\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.54797	−	6.14527i	0.128614	−	0.222766i	−0.794526	−	0.607230i	$-0.792281\pi$
$761$	3.54797	−	6.14527i	0.128614	−	0.222766i	0.923140	+	0.384464i	$0.125614\pi$
$762$		0			0
$763$	11.7458	−	5.72832i	0.425226	−	0.207379i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.32712	−	2.29865i	−0.0479197	−	0.0829994i
$768$		0			0
$769$	5.71618	+	9.90071i	0.206131	+	0.357029i	0.950492	−	0.310748i	$-0.100579\pi$
$769$	5.71618	+	9.90071i	0.206131	+	0.357029i	−0.744362	+	0.667777i	$0.767246\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−7.40125	+	12.8193i	−0.266204	+	0.461080i	−0.967878	−	0.251418i	$-0.919103\pi$
$773$	−7.40125	+	12.8193i	−0.266204	+	0.461080i	0.701674	+	0.712498i	$0.252436\pi$
$774$		0			0
$775$	6.10949	+	10.5819i	0.219459	+	0.380114i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.52157	−	9.56364i	0.197831	−	0.342653i
$780$		0			0
$781$	−11.1353	−	19.2869i	−0.398453	−	0.690141i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.09951	−	10.5647i	0.217701	−	0.377069i
$786$		0			0
$787$	−19.7177			−0.702861			−0.351431	−	0.936214i	$-0.614305\pi$
$787$	−19.7177			−0.702861			−0.351431	+	0.936214i	$0.614305\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.74062	+	39.1741i	−0.0974452	+	1.39287i
$792$		0			0
$793$	3.08442	+	5.34238i	0.109531	+	0.189713i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−22.2215	−	38.4887i	−0.787125	−	1.36334i	−0.927722	−	0.373273i	$-0.878236\pi$
$797$	−22.2215	−	38.4887i	−0.787125	−	1.36334i	0.140597	−	0.990067i	$-0.455098\pi$
$798$		0			0
$799$	20.8128	−	36.0488i	0.736304	−	1.27532i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.72133			0.0607446
$804$		0			0
$805$	−0.997986	+	14.2651i	−0.0351744	+	0.502779i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	5.34657	−	9.26053i	0.187975	−	0.325583i	−0.756600	−	0.653878i	$-0.773141\pi$
$809$	5.34657	−	9.26053i	0.187975	−	0.325583i	0.944575	+	0.328296i	$0.106474\pi$
$810$		0			0
$811$	−13.1292			−0.461030			−0.230515	−	0.973069i	$-0.574041\pi$
$811$	−13.1292			−0.461030			−0.230515	+	0.973069i	$0.574041\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−22.0048			−0.770796
$816$		0			0
$817$	3.72047			0.130163
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.62808			−0.0917205			−0.0458602	−	0.998948i	$-0.514603\pi$
$821$	−2.62808			−0.0917205			−0.0458602	+	0.998948i	$0.514603\pi$
$822$		0			0
$823$	−46.3921			−1.61713			−0.808563	−	0.588410i	$-0.799754\pi$
$823$	−46.3921			−1.61713			−0.808563	+	0.588410i	$0.799754\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	15.2072			0.528807			0.264404	−	0.964412i	$-0.414825\pi$
$827$	15.2072			0.528807			0.264404	+	0.964412i	$0.414825\pi$
$828$		0			0
$829$	19.0782	−	33.0445i	0.662615	−	1.14768i	−0.317311	−	0.948322i	$-0.602780\pi$
$829$	19.0782	−	33.0445i	0.662615	−	1.14768i	0.979926	−	0.199361i	$-0.0638867\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−50.0591	−	7.03871i	−1.73444	−	0.243877i
$834$		0			0
$835$	89.0201			3.08067
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.52298	−	9.56608i	0.190674	−	0.330258i	−0.754800	−	0.655955i	$-0.772266\pi$
$839$	5.52298	−	9.56608i	0.190674	−	0.330258i	0.945474	+	0.325698i	$0.105599\pi$
$840$		0			0
$841$	−20.8313	−	36.0808i	−0.718320	−	1.24417i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	26.7314	+	46.3002i	0.919590	+	1.59278i
$846$		0			0
$847$	17.3082	−	8.44105i	0.594716	−	0.290038i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	7.76448			0.266163
$852$		0			0
$853$	22.4259	−	38.8428i	0.767847	−	1.32995i	−0.170881	−	0.985292i	$-0.554661\pi$
$853$	22.4259	−	38.8428i	0.767847	−	1.32995i	0.938728	−	0.344659i	$-0.112005\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.04764	+	5.27866i	0.104105	+	0.180316i	0.913372	−	0.407125i	$-0.133469\pi$
$857$	3.04764	+	5.27866i	0.104105	+	0.180316i	−0.809267	+	0.587441i	$0.800135\pi$
$858$		0			0
$859$	−15.1068	+	26.1658i	−0.515438	+	0.892765i	0.484401	+	0.874846i	$0.339038\pi$
$859$	−15.1068	+	26.1658i	−0.515438	+	0.892765i	−0.999839	+	0.0179194i	$0.994296\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	21.3315	+	36.9472i	0.726131	+	1.25770i	0.958507	+	0.285070i	$0.0920169\pi$
$863$	21.3315	+	36.9472i	0.726131	+	1.25770i	−0.232375	+	0.972626i	$0.574650\pi$
$864$		0			0
$865$	−8.60018	+	14.8959i	−0.292415	+	0.506477i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−11.4499	−	19.8318i	−0.388411	−	0.672748i
$870$		0			0
$871$	1.41795	+	2.45596i	0.0480453	+	0.0832170i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	72.5575	+	48.9441i	2.45289	+	1.65461i
$876$		0			0
$877$	−10.3375	+	17.9051i	−0.349074	+	0.604613i	−0.986085	−	0.166241i	$-0.946837\pi$
$877$	−10.3375	+	17.9051i	−0.349074	+	0.604613i	0.637012	+	0.770854i	$0.280170\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−5.40674			−0.182158			−0.0910789	−	0.995844i	$-0.529032\pi$
$881$	−5.40674			−0.182158			−0.0910789	+	0.995844i	$0.529032\pi$
$882$		0			0
$883$	−3.16348			−0.106460			−0.0532299	−	0.998582i	$-0.516952\pi$
$883$	−3.16348			−0.106460			−0.0532299	+	0.998582i	$0.516952\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.04317	+	8.73502i	−0.169333	+	0.293293i	−0.938186	−	0.346133i	$-0.887495\pi$
$887$	−5.04317	+	8.73502i	−0.169333	+	0.293293i	0.768853	+	0.639426i	$0.220828\pi$
$888$		0			0
$889$	−18.7237	−	12.6302i	−0.627974	−	0.423604i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−12.1199	−	20.9922i	−0.405575	−	0.702477i
$894$		0			0
$895$	13.1371	+	22.7542i	0.439126	+	0.760589i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.00181	+	6.93135i	−0.133468	+	0.231173i
$900$		0			0
$901$	6.95051	+	12.0386i	0.231555	+	0.401065i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−38.5125	+	66.7056i	−1.28020	+	2.21737i
$906$		0			0
$907$	11.9318	+	20.6665i	0.396190	+	0.686221i	0.993252	−	0.115974i	$-0.0369988\pi$
$907$	11.9318	+	20.6665i	0.396190	+	0.686221i	−0.597062	+	0.802195i	$0.703666\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−9.67946	+	16.7653i	−0.320695	+	0.555460i	−0.980632	−	0.195862i	$-0.937250\pi$
$911$	−9.67946	+	16.7653i	−0.320695	+	0.555460i	0.659937	+	0.751321i	$0.270583\pi$
$912$		0			0
$913$	20.2271			0.669420
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.58085	+	2.72174i	−0.184296	+	0.0898796i
$918$		0			0
$919$	−25.2052	−	43.6567i	−0.831444	−	1.44010i	−0.896893	−	0.442247i	$-0.854182\pi$
$919$	−25.2052	−	43.6567i	−0.831444	−	1.44010i	0.0654498	−	0.997856i	$-0.479152\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	3.36549	+	5.82920i	0.110777	+	0.191871i
$924$		0			0
$925$	38.9274	−	67.4243i	1.27993	−	2.21690i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−42.2929			−1.38759			−0.693793	−	0.720175i	$-0.744062\pi$
$929$	−42.2929			−1.38759			−0.693793	+	0.720175i	$0.744062\pi$
$930$		0			0
$931$	−18.1251	+	23.1959i	−0.594025	+	0.760214i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	29.4164	−	50.9506i	0.962018	−	1.66626i
$936$		0			0
$937$	20.6771			0.675490			0.337745	−	0.941238i	$-0.390336\pi$
$937$	20.6771			0.675490			0.337745	+	0.941238i	$0.390336\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	34.3292			1.11910			0.559550	−	0.828796i	$-0.310974\pi$
$941$	34.3292			1.11910			0.559550	+	0.828796i	$0.310974\pi$
$942$		0			0
$943$	−3.36092			−0.109447
$944$		0			0
$945$		0			0
$946$		0			0
$947$	27.7300			0.901103			0.450551	−	0.892751i	$-0.351227\pi$
$947$	27.7300			0.901103			0.450551	+	0.892751i	$0.351227\pi$
$948$		0			0
$949$	−0.520249			−0.0168880
$950$		0			0
$951$		0			0
$952$		0			0
$953$	22.8102			0.738894			0.369447	−	0.929252i	$-0.379547\pi$
$953$	22.8102			0.738894			0.369447	+	0.929252i	$0.379547\pi$
$954$		0			0
$955$	−15.5953	+	27.0119i	−0.504653	+	0.874085i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.237016	+	3.38789i	−0.00765366	+	0.109401i
$960$		0			0
$961$	−30.0935			−0.970757
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−41.2123	+	71.3817i	−1.32667	+	2.29786i
$966$		0			0
$967$	10.8697	+	18.8269i	0.349546	+	0.605432i	0.986169	−	0.165744i	$-0.0530024\pi$
$967$	10.8697	+	18.8269i	0.349546	+	0.605432i	−0.636623	+	0.771175i	$0.719669\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	19.7959	+	34.2875i	0.635281	+	1.10034i	0.986455	+	0.164029i	$0.0524491\pi$
$971$	19.7959	+	34.2875i	0.635281	+	1.10034i	−0.351174	+	0.936310i	$0.614218\pi$
$972$		0			0
$973$	−0.225472	+	3.22287i	−0.00722829	+	0.103320i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	45.7447			1.46350			0.731752	−	0.681571i	$-0.238703\pi$
$977$	45.7447			1.46350			0.731752	+	0.681571i	$0.238703\pi$
$978$		0			0
$979$	7.48329	−	12.9614i	0.239167	−	0.414250i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	7.52490	+	13.0335i	0.240007	+	0.415704i	0.960716	−	0.277534i	$-0.0895170\pi$
$983$	7.52490	+	13.0335i	0.240007	+	0.415704i	−0.720709	+	0.693238i	$0.756184\pi$
$984$		0			0
$985$	16.4181	−	28.4370i	0.523125	−	0.906079i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.566154	−	0.980607i	−0.0180026	−	0.0311815i
$990$		0			0
$991$	−11.3516	+	19.6616i	−0.360596	+	0.624570i	−0.988059	−	0.154076i	$-0.950760\pi$
$991$	−11.3516	+	19.6616i	−0.360596	+	0.624570i	0.627463	+	0.778646i	$0.284093\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−16.2894	−	28.2140i	−0.516408	−	0.894445i
$996$		0			0
$997$	27.7676	+	48.0949i	0.879408	+	1.52318i	0.851992	+	0.523556i	$0.175395\pi$
$997$	27.7676	+	48.0949i	0.879408	+	1.52318i	0.0274166	+	0.999624i	$0.491272\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.q.d.1369.1		22
3.2	odd	2		504.2.q.c.25.7	✓	22
4.3	odd	2		3024.2.q.l.2881.1		22
7.2	even	3		1512.2.t.c.289.11		22
9.4	even	3		1512.2.t.c.361.11		22
9.5	odd	6		504.2.t.c.193.1	yes	22
12.11	even	2		1008.2.q.l.529.5		22
21.2	odd	6		504.2.t.c.457.1	yes	22
28.23	odd	6		3024.2.t.k.289.11		22
36.23	even	6		1008.2.t.l.193.11		22
36.31	odd	6		3024.2.t.k.1873.11		22
63.23	odd	6		504.2.q.c.121.7	yes	22
63.58	even	3	inner	1512.2.q.d.793.1		22
84.23	even	6		1008.2.t.l.961.11		22
252.23	even	6		1008.2.q.l.625.5		22
252.247	odd	6		3024.2.q.l.2305.1		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.7	✓	22	3.2	odd	2
504.2.q.c.121.7	yes	22	63.23	odd	6
504.2.t.c.193.1	yes	22	9.5	odd	6
504.2.t.c.457.1	yes	22	21.2	odd	6
1008.2.q.l.529.5		22	12.11	even	2
1008.2.q.l.625.5		22	252.23	even	6
1008.2.t.l.193.11		22	36.23	even	6
1008.2.t.l.961.11		22	84.23	even	6
1512.2.q.d.793.1		22	63.58	even	3	inner
1512.2.q.d.1369.1		22	1.1	even	1	trivial
1512.2.t.c.289.11		22	7.2	even	3
1512.2.t.c.361.11		22	9.4	even	3
3024.2.q.l.2305.1		22	252.247	odd	6
3024.2.q.l.2881.1		22	4.3	odd	2
3024.2.t.k.289.11		22	28.23	odd	6
3024.2.t.k.1873.11		22	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.11148 + 3.65719i) q^{5} +(2.19338 + 1.47956i) q^{7} +O(q^{10})\)	\(q+(-2.11148 + 3.65719i) q^{5} +(2.19338 + 1.47956i) q^{7} +(0.964575 + 1.67069i) q^{11} +(-0.291529 - 0.504943i) q^{13} +(-3.61082 + 6.25412i) q^{17} +(2.10268 + 3.64194i) q^{19} +(0.639939 - 1.10841i) q^{23} +(-6.41671 - 11.1141i) q^{25} +(4.20305 - 7.27990i) q^{29} -0.952121 q^{31} +(-10.0423 + 4.89755i) q^{35} +(3.03329 + 5.25381i) q^{37} +(-1.31299 - 2.27416i) q^{41} +(0.442349 - 0.766171i) q^{43} -5.76401 q^{47} +(2.62182 + 6.49046i) q^{49} +(0.962456 - 1.66702i) q^{53} -8.14673 q^{55} +4.55229 q^{59} -10.5802 q^{61} +2.46223 q^{65} -4.86383 q^{67} -11.5443 q^{71} +(0.446138 - 0.772734i) q^{73} +(-0.356209 + 5.09160i) q^{77} -11.8704 q^{79} +(5.24250 - 9.08028i) q^{83} +(-15.2484 - 26.4109i) q^{85} +(-3.87906 - 6.71874i) q^{89} +(0.107659 - 1.53887i) q^{91} -17.7591 q^{95} +(-1.98651 + 3.44073i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{5} + 5 q^{7}+O(q^{10}) \) 22 * q - q^5 + 5 * q^7	\( 22 q - q^{5} + 5 q^{7} - 3 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} - 22 q^{25} + 7 q^{29} - 12 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} + 34 q^{47} - 25 q^{49} - q^{53} + 2 q^{55} - 42 q^{59} - 62 q^{61} - 6 q^{65} + 52 q^{67} + 32 q^{71} + 17 q^{73} + q^{77} + 32 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} - 48 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q - q^5 + 5 * q^7 - 3 * q^11 + 7 * q^13 + q^17 + 13 * q^19 - 22 * q^25 + 7 * q^29 - 12 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 + 34 * q^47 - 25 * q^49 - q^53 + 2 * q^55 - 42 * q^59 - 62 * q^61 - 6 * q^65 + 52 * q^67 + 32 * q^71 + 17 * q^73 + q^77 + 32 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 - 48 * q^95 + 19 * q^97

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