LMFDB - Embedded newform 1512.2.t.c.289.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(289,1512)]

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, 4, 2]))

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

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

chi := DirichletCharacter("1512.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.t (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			289.11
Character	$\chi$	$=$	1512.289
Dual form			1512.2.t.c.361.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.22296 q^{5} +(-2.37802 - 1.15974i) q^{7} +O(q^{10})$	$q+4.22296 q^{5} +(-2.37802 - 1.15974i) q^{7} -1.92915 q^{11} +(-0.291529 - 0.504943i) q^{13} +(-3.61082 - 6.25412i) q^{17} +(2.10268 - 3.64194i) q^{19} -1.27988 q^{23} +12.8334 q^{25} +(4.20305 - 7.27990i) q^{29} +(0.476061 - 0.824561i) q^{31} +(-10.0423 - 4.89755i) q^{35} +(3.03329 - 5.25381i) q^{37} +(-1.31299 - 2.27416i) q^{41} +(0.442349 - 0.766171i) q^{43} +(2.88201 + 4.99178i) q^{47} +(4.30999 + 5.51579i) q^{49} +(0.962456 + 1.66702i) q^{53} -8.14673 q^{55} +(-2.27614 + 3.94240i) q^{59} +(5.29008 + 9.16268i) q^{61} +(-1.23112 - 2.13236i) q^{65} +(2.43191 - 4.21220i) q^{67} -11.5443 q^{71} +(0.446138 + 0.772734i) q^{73} +(4.58756 + 2.23732i) q^{77} +(5.93520 + 10.2801i) q^{79} +(5.24250 - 9.08028i) q^{83} +(-15.2484 - 26.4109i) q^{85} +(-3.87906 + 6.71874i) q^{89} +(0.107659 + 1.53887i) q^{91} +(8.87953 - 15.3798i) q^{95} +(-1.98651 + 3.44073i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q + 2 * q^5 - q^7	$ 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	4.22296			1.88857			0.944283	−	0.329134i	$-0.106757\pi$
$5$	4.22296			1.88857			0.944283	+	0.329134i	$0.106757\pi$
$6$		0			0
$7$	−2.37802	−	1.15974i	−0.898809	−	0.438341i
$7$	−2.37802	−	1.15974i	−0.898809	−	0.438341i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.92915			−0.581660			−0.290830	−	0.956775i	$-0.593931\pi$
$11$	−1.92915			−0.581660			−0.290830	+	0.956775i	$0.593931\pi$
$12$		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	−0.855959	−	0.517044i	$-0.827032\pi$
$17$	−3.61082	−	6.25412i	−0.875753	−	1.51685i	−0.0197936	−	0.999804i	$-0.506301\pi$
$18$		0			0
$19$	2.10268	−	3.64194i	0.482387	−	0.835519i	−0.517408	−	0.855739i	$-0.673103\pi$
$19$	2.10268	−	3.64194i	0.482387	−	0.835519i	0.999796	+	0.0202194i	$0.00643646\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.27988			−0.266873			−0.133437	−	0.991057i	$-0.542601\pi$
$23$	−1.27988			−0.266873			−0.133437	+	0.991057i	$0.542601\pi$
$24$		0			0
$25$	12.8334			2.56668
$26$		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
$31$	0.476061	−	0.824561i	0.0855030	−	0.148096i	−0.820102	−	0.572217i	$-0.806084\pi$
$31$	0.476061	−	0.824561i	0.0855030	−	0.148096i	0.905605	+	0.424121i	$0.139417\pi$
$32$		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	−0.501330	−	0.865256i	$-0.667156\pi$
$37$	3.03329	−	5.25381i	0.498669	−	0.863721i	0.999999	+	0.00153588i	$0.000488885\pi$
$38$		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
$47$	2.88201	+	4.99178i	0.420384	+	0.728126i	0.995977	−	0.0896103i	$-0.0285622\pi$
$47$	2.88201	+	4.99178i	0.420384	+	0.728126i	−0.575593	+	0.817736i	$0.695229\pi$
$48$		0			0
$49$	4.30999	+	5.51579i	0.615713	+	0.787970i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.962456	+	1.66702i	0.132204	+	0.228983i	0.924526	−	0.381120i	$-0.124461\pi$
$53$	0.962456	+	1.66702i	0.132204	+	0.228983i	−0.792322	+	0.610103i	$0.791128\pi$
$54$		0			0
$55$	−8.14673			−1.09850
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.27614	+	3.94240i	−0.296329	+	0.513256i	−0.975293	−	0.220915i	$-0.929096\pi$
$59$	−2.27614	+	3.94240i	−0.296329	+	0.513256i	0.678964	+	0.734171i	$0.262429\pi$
$60$		0			0
$61$	5.29008	+	9.16268i	0.677325	+	1.17316i	0.975783	+	0.218739i	$0.0701943\pi$
$61$	5.29008	+	9.16268i	0.677325	+	1.17316i	−0.298458	+	0.954423i	$0.596472\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.23112	−	2.13236i	−0.152701	−	0.264486i
$66$		0			0
$67$	2.43191	−	4.21220i	0.297106	−	0.514602i	−0.678367	−	0.734723i	$-0.737312\pi$
$67$	2.43191	−	4.21220i	0.297106	−	0.514602i	0.975473	+	0.220121i	$0.0706453\pi$
$68$		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	0.890952	−	0.454097i	$-0.150038\pi$
$73$	0.446138	+	0.772734i	0.0522165	+	0.0904417i	−0.838736	+	0.544539i	$0.816705\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.58756	+	2.23732i	0.522801	+	0.254966i
$78$		0			0
$79$	5.93520	+	10.2801i	0.667763	+	1.15660i	0.978528	+	0.206112i	$0.0660812\pi$
$79$	5.93520	+	10.2801i	0.667763	+	1.15660i	−0.310766	+	0.950487i	$0.600585\pi$
$80$		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	−0.995019	−	0.0996849i	$-0.968217\pi$
$89$	−3.87906	+	6.71874i	−0.411180	+	0.712185i	0.583839	+	0.811869i	$0.301550\pi$
$90$		0			0
$91$	0.107659	+	1.53887i	0.0112857	+	0.161317i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.87953	−	15.3798i	0.911020	−	1.57793i
$96$		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
$101$	−16.7707			−1.66874			−0.834372	−	0.551202i	$-0.814169\pi$
$101$	−16.7707			−1.66874			−0.834372	+	0.551202i	$0.814169\pi$
$102$		0			0
$103$	11.6114			1.14410			0.572052	−	0.820218i	$-0.306148\pi$
$103$	11.6114			1.14410			0.572052	+	0.820218i	$0.306148\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.2454	−	17.7455i	0.990460	−	1.71553i	0.375890	−	0.926664i	$-0.377337\pi$
$107$	10.2454	−	17.7455i	0.990460	−	1.71553i	0.614570	−	0.788862i	$-0.289329\pi$
$108$		0			0
$109$	2.46965	+	4.27756i	0.236550	+	0.409716i	0.959722	−	0.280951i	$-0.0906500\pi$
$109$	2.46965	+	4.27756i	0.236550	+	0.409716i	−0.723172	+	0.690668i	$0.757317\pi$
$110$		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
$115$	−5.40488			−0.504008
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.33344	+	19.0601i	0.122236	+	1.74723i
$120$		0			0
$121$	−7.27838			−0.661671
$122$		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
$131$	2.34684			0.205045			0.102522	−	0.994731i	$-0.467309\pi$
$131$	2.34684			0.205045			0.102522	+	0.994731i	$0.467309\pi$
$132$		0			0
$133$	−9.22393	+	6.22207i	−0.799817	+	0.539522i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.28363			−0.109668			−0.0548340	−	0.998495i	$-0.517463\pi$
$137$	−1.28363			−0.109668			−0.0548340	+	0.998495i	$0.517463\pi$
$138$		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
$149$	−6.29459			−0.515673			−0.257836	−	0.966189i	$-0.583010\pi$
$149$	−6.29459			−0.515673			−0.257836	+	0.966189i	$0.583010\pi$
$150$		0			0
$151$	2.35453			0.191609			0.0958044	−	0.995400i	$-0.469458\pi$
$151$	2.35453			0.191609			0.0958044	+	0.995400i	$0.469458\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.01039	−	3.48209i	0.161478	−	0.279688i
$156$		0			0
$157$	1.44437	−	2.50172i	0.115273	−	0.199659i	−0.802616	−	0.596496i	$-0.796559\pi$
$157$	1.44437	−	2.50172i	0.115273	−	0.199659i	0.917889	+	0.396838i	$0.129892\pi$
$158$		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	−0.745767	−	0.666207i	$-0.767917\pi$
$163$	2.60538	−	4.51265i	0.204069	−	0.353458i	0.949836	+	0.312749i	$0.101250\pi$
$164$		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
$173$	−2.03653	−	3.52737i	−0.154834	−	0.268181i	0.778164	−	0.628061i	$-0.216151\pi$
$173$	−2.03653	−	3.52737i	−0.154834	−	0.268181i	−0.932999	+	0.359880i	$0.882818\pi$
$174$		0			0
$175$	−30.5182	−	14.8835i	−2.30696	−	1.12508i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.11088	+	5.38821i	0.232518	+	0.402733i	0.958549	−	0.284929i	$-0.0919701\pi$
$179$	3.11088	+	5.38821i	0.232518	+	0.402733i	−0.726030	+	0.687663i	$0.758637\pi$
$180$		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
$185$	12.8095	−	22.1866i	0.941770	−	1.63119i
$186$		0			0
$187$	6.96581	+	12.0651i	0.509391	+	0.882290i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.69298	−	6.39644i	−0.267215	−	0.462830i	0.700927	−	0.713233i	$-0.252770\pi$
$191$	−3.69298	−	6.39644i	−0.267215	−	0.462830i	−0.968142	+	0.250404i	$0.919437\pi$
$192$		0			0
$193$	−9.75908	+	16.9032i	−0.702474	+	1.21672i	0.265121	+	0.964215i	$0.414588\pi$
$193$	−9.75908	+	16.9032i	−0.702474	+	1.21672i	−0.967595	+	0.252506i	$0.918745\pi$
$194$		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	0.696301	−	0.717750i	$-0.254828\pi$
$199$	−3.85734	−	6.68110i	−0.273439	−	0.473611i	−0.969740	+	0.244139i	$0.921495\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−18.4378	+	12.4373i	−1.29408	+	0.872928i
$204$		0			0
$205$	−5.54469	−	9.60368i	−0.387258	−	0.670750i
$206$		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
$221$	−2.10532	+	3.64652i	−0.141619	+	0.245291i
$222$		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
$227$	−17.9718			−1.19283			−0.596417	−	0.802675i	$-0.703409\pi$
$227$	−17.9718			−1.19283			−0.596417	+	0.802675i	$0.703409\pi$
$228$		0			0
$229$	−7.91668			−0.523149			−0.261574	−	0.965183i	$-0.584242\pi$
$229$	−7.91668			−0.523149			−0.261574	+	0.965183i	$0.584242\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.27796	+	5.67759i	−0.214746	+	0.371951i	−0.953194	−	0.302359i	$-0.902226\pi$
$233$	−3.27796	+	5.67759i	−0.214746	+	0.371951i	0.738448	+	0.674311i	$0.235559\pi$
$234$		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
$241$	11.1791			0.720112			0.360056	−	0.932931i	$-0.382758\pi$
$241$	11.1791			0.720112			0.360056	+	0.932931i	$0.382758\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	18.2009	+	23.2930i	1.16282	+	1.48813i
$246$		0			0
$247$	−2.45197			−0.156015
$248$		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
$257$	−14.9187			−0.930605			−0.465302	−	0.885152i	$-0.654054\pi$
$257$	−14.9187			−0.930605			−0.465302	+	0.885152i	$0.654054\pi$
$258$		0			0
$259$	−13.3063	+	8.97585i	−0.826813	+	0.557732i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	22.2114			1.36962			0.684808	−	0.728724i	$-0.259886\pi$
$263$	22.2114			1.36962			0.684808	+	0.728724i	$0.259886\pi$
$264$		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	0.973512	−	0.228635i	$-0.0734261\pi$
$269$	4.73590	+	8.20281i	0.288753	+	0.500134i	−0.684760	+	0.728769i	$0.740093\pi$
$270$		0			0
$271$	8.78188	−	15.2107i	0.533461	−	0.923982i	−0.465775	−	0.884903i	$-0.654224\pi$
$271$	8.78188	−	15.2107i	0.533461	−	0.923982i	0.999236	−	0.0390786i	$-0.0124423\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−24.7576			−1.49294
$276$		0			0
$277$	13.5530			0.814322			0.407161	−	0.913356i	$-0.366519\pi$
$277$	13.5530			0.814322			0.407161	+	0.913356i	$0.366519\pi$
$278$		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
$283$	−7.02415	+	12.1662i	−0.417542	+	0.723204i	−0.995692	−	0.0927267i	$-0.970442\pi$
$283$	−7.02415	+	12.1662i	−0.417542	+	0.723204i	0.578149	+	0.815931i	$0.303775\pi$
$284$		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
$299$	0.373122	+	0.646266i	0.0215782	+	0.0373746i
$300$		0			0
$301$	−1.94048	+	1.30896i	−0.111847	+	0.0754473i
$302$		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
$311$	−4.17980	+	7.23963i	−0.237015	+	0.410522i	−0.959856	−	0.280492i	$-0.909502\pi$
$311$	−4.17980	+	7.23963i	−0.237015	+	0.410522i	0.722841	+	0.691014i	$0.242836\pi$
$312$		0			0
$313$	−13.0542	−	22.6105i	−0.737864	−	1.27802i	−0.953455	−	0.301535i	$-0.902501\pi$
$313$	−13.0542	−	22.6105i	−0.737864	−	1.27802i	0.215591	−	0.976484i	$-0.430832\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.60741	+	9.71231i	0.314943	+	0.545498i	0.979425	−	0.201806i	$-0.0646812\pi$
$317$	5.60741	+	9.71231i	0.314943	+	0.545498i	−0.664482	+	0.747304i	$0.731348\pi$
$318$		0			0
$319$	−8.10831	+	14.0440i	−0.453978	+	0.786314i
$320$		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
$329$	−1.06430	−	15.2130i	−0.0586766	−	0.838717i
$330$		0			0
$331$	9.11645	+	15.7902i	0.501086	+	0.867906i	0.999999	+	0.00125391i	$0.000399132\pi$
$331$	9.11645	+	15.7902i	0.501086	+	0.867906i	−0.498914	+	0.866652i	$0.666268\pi$
$332$		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
$347$	−15.8325	+	27.4226i	−0.849931	+	1.47212i	0.0313384	+	0.999509i	$0.490023\pi$
$347$	−15.8325	+	27.4226i	−0.849931	+	1.47212i	−0.881269	+	0.472615i	$0.843310\pi$
$348$		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
$353$	−7.19777			−0.383098			−0.191549	−	0.981483i	$-0.561351\pi$
$353$	−7.19777			−0.383098			−0.191549	+	0.981483i	$0.561351\pi$
$354$		0			0
$355$	−48.7510			−2.58744
$356$		0			0
$357$		0			0
$358$		0			0
$359$	7.39891	−	12.8153i	0.390499	−	0.676365i	−0.602016	−	0.798484i	$-0.705636\pi$
$359$	7.39891	−	12.8153i	0.390499	−	0.676365i	0.992515	+	0.122119i	$0.0389690\pi$
$360$		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
$367$	4.19100			0.218768			0.109384	−	0.994000i	$-0.465112\pi$
$367$	4.19100			0.218768			0.109384	+	0.994000i	$0.465112\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.355426	−	5.08042i	−0.0184528	−	0.263762i
$372$		0			0
$373$	17.4175			0.901844			0.450922	−	0.892563i	$-0.351095\pi$
$373$	17.4175			0.901844			0.450922	+	0.892563i	$0.351095\pi$
$374$		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
$383$	25.1016			1.28263			0.641316	−	0.767276i	$-0.278389\pi$
$383$	25.1016			1.28263			0.641316	+	0.767276i	$0.278389\pi$
$384$		0			0
$385$	19.3731	+	9.44811i	0.987345	+	0.481520i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.46402			−0.0742289			−0.0371144	−	0.999311i	$-0.511817\pi$
$389$	−1.46402			−0.0742289			−0.0371144	+	0.999311i	$0.511817\pi$
$390$		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	−0.901120	−	0.433570i	$-0.857254\pi$
$397$	−1.49591	+	2.59100i	−0.0750778	+	0.130039i	0.826042	+	0.563608i	$0.190587\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	26.3371			1.31521			0.657605	−	0.753363i	$-0.271570\pi$
$401$	26.3371			1.31521			0.657605	+	0.753363i	$0.271570\pi$
$402$		0			0
$403$	−0.555142			−0.0276536
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.85166	+	10.1354i	−0.290056	+	0.502392i
$408$		0			0
$409$	−1.50392	+	2.60487i	−0.0743642	+	0.128803i	−0.900810	−	0.434214i	$-0.857026\pi$
$409$	−1.50392	+	2.60487i	−0.0743642	+	0.128803i	0.826445	+	0.563017i	$0.190359\pi$
$410$		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
$425$	−46.3392	−	80.2618i	−2.24778	−	3.89327i
$426$		0			0
$427$	−1.95358	−	27.9242i	−0.0945402	−	1.35135i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.4257	−	18.0578i	−0.502188	−	0.869816i	−0.999997	−	0.00252883i	$-0.999195\pi$
$431$	−10.4257	−	18.0578i	−0.502188	−	0.869816i	0.497808	−	0.867287i	$-0.334138\pi$
$432$		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
$437$	−2.69117	+	4.66125i	−0.128736	+	0.222978i
$438$		0			0
$439$	−17.8495	−	30.9162i	−0.851909	−	1.47555i	−0.879483	−	0.475930i	$-0.842112\pi$
$439$	−17.8495	−	30.9162i	−0.851909	−	1.47555i	0.0275746	−	0.999620i	$-0.491222\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.05787	+	15.6887i	0.430352	+	0.745392i	0.996904	−	0.0786344i	$-0.0250560\pi$
$443$	9.05787	+	15.6887i	0.430352	+	0.745392i	−0.566551	+	0.824027i	$0.691723\pi$
$444$		0			0
$445$	−16.3811	+	28.3730i	−0.776541	+	1.34501i
$446$		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
$455$	0.454640	+	6.49858i	0.0213139	+	0.304658i
$456$		0			0
$457$	−7.67918	−	13.3007i	−0.359217	−	0.622182i	0.628613	−	0.777718i	$-0.283623\pi$
$457$	−7.67918	−	13.3007i	−0.359217	−	0.622182i	−0.987830	+	0.155536i	$0.950290\pi$
$458$		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	−0.486135	−	0.873884i	$-0.661594\pi$
$467$	11.1020	−	19.2292i	0.513738	−	0.889820i	0.999873	−	0.0159363i	$-0.00507290\pi$
$468$		0			0
$469$	−10.6682	+	7.19631i	−0.492612	+	0.332295i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.853358	+	1.47806i	−0.0392374	+	0.0679612i
$474$		0			0
$475$	26.9845	−	46.7386i	1.23814	−	2.14451i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	34.5938			1.58063			0.790317	−	0.612699i	$-0.209916\pi$
$479$	34.5938			1.58063			0.790317	+	0.612699i	$0.209916\pi$
$480$		0			0
$481$	−3.53717			−0.161281
$482$		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	0.977934	−	0.208915i	$-0.0669931\pi$
$487$	6.79789	+	11.7743i	0.308042	+	0.533544i	−0.669892	+	0.742458i	$0.733660\pi$
$488$		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
$493$	−60.7058			−2.73405
$494$		0			0
$495$		0			0
$496$		0			0
$497$	27.4526	+	13.3884i	1.23142	+	0.600551i
$498$		0			0
$499$	−30.2816			−1.35559			−0.677794	−	0.735251i	$-0.737064\pi$
$499$	−30.2816			−1.35559			−0.677794	+	0.735251i	$0.737064\pi$
$500$		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
$509$	6.47349			0.286932			0.143466	−	0.989655i	$-0.454175\pi$
$509$	6.47349			0.286932			0.143466	+	0.989655i	$0.454175\pi$
$510$		0			0
$511$	−0.164755	−	2.35499i	−0.00728832	−	0.104178i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	49.0344			2.16072
$516$		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	0.697982	−	0.716116i	$-0.254082\pi$
$521$	−6.18988	−	10.7212i	−0.271184	−	0.469704i	−0.969165	+	0.246412i	$0.920748\pi$
$522$		0			0
$523$	11.0290	−	19.1028i	0.482265	−	0.835308i	−0.517527	−	0.855667i	$-0.673147\pi$
$523$	11.0290	−	19.1028i	0.482265	−	0.835308i	0.999793	+	0.0203585i	$0.00648074\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.87588			−0.299518
$528$		0			0
$529$	−21.3619			−0.928779
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.765547	+	1.32597i	−0.0331595	+	0.0574340i
$534$		0			0
$535$	43.2659	−	74.9388i	1.87055	−	3.23989i
$536$		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	−0.667033	−	0.745028i	$-0.732436\pi$
$541$	7.24989	−	12.5572i	0.311697	−	0.539875i	0.978730	+	0.205153i	$0.0657693\pi$
$542$		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
$551$	−17.6753	−	30.6146i	−0.752994	−	1.30422i
$552$		0			0
$553$	−2.19182	−	31.3296i	−0.0932055	−	1.33227i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.02336	−	15.6289i	−0.382332	−	0.662219i	0.609063	−	0.793122i	$-0.291546\pi$
$557$	−9.02336	−	15.6289i	−0.382332	−	0.662219i	−0.991395	+	0.130903i	$0.958212\pi$
$558$		0			0
$559$	−0.515831			−0.0218173
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.51748	−	16.4848i	0.401114	−	0.694749i	−0.592747	−	0.805389i	$-0.701957\pi$
$563$	9.51748	−	16.4848i	0.401114	−	0.694749i	0.993861	+	0.110639i	$0.0352899\pi$
$564$		0			0
$565$	31.3399	+	54.2823i	1.31848	+	2.28367i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.68018	+	8.10631i	0.196203	+	0.339834i	0.947294	−	0.320364i	$-0.103805\pi$
$569$	4.68018	+	8.10631i	0.196203	+	0.339834i	−0.751091	+	0.660199i	$0.770472\pi$
$570$		0			0
$571$	−17.6805	+	30.6236i	−0.739907	+	1.28156i	0.212630	+	0.977133i	$0.431797\pi$
$571$	−17.6805	+	30.6236i	−0.739907	+	1.28156i	−0.952537	+	0.304424i	$0.901536\pi$
$572$		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	0.995061	+	0.0992610i	$0.0316479\pi$
$577$	14.0160	+	24.2764i	0.583493	+	1.01064i	−0.411568	+	0.911379i	$0.635019\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−22.9976	+	15.5132i	−0.954100	+	0.643595i
$582$		0			0
$583$	−1.85672	−	3.21594i	−0.0768976	−	0.133190i
$584$		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	−0.541879	−	0.840457i	$-0.682287\pi$
$593$	11.1267	−	19.2719i	0.456917	−	0.791404i	0.998796	+	0.0490525i	$0.0156202\pi$
$594$		0			0
$595$	5.63108	+	80.4900i	0.230852	+	3.29977i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.37059	−	5.83804i	0.137719	−	0.238536i	−0.788914	−	0.614504i	$-0.789356\pi$
$599$	3.37059	−	5.83804i	0.137719	−	0.238536i	0.926633	+	0.375968i	$0.122690\pi$
$600$		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
$605$	−30.7363			−1.24961
$606$		0			0
$607$	31.6039			1.28276			0.641382	−	0.767222i	$-0.278361\pi$
$607$	31.6039			1.28276			0.641382	+	0.767222i	$0.278361\pi$
$608$		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	0.796458	−	0.604693i	$-0.206704\pi$
$613$	−3.10601	−	5.37977i	−0.125451	−	0.217287i	−0.921909	+	0.387407i	$0.873371\pi$
$614$		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
$619$	40.0206			1.60857			0.804283	−	0.594247i	$-0.202550\pi$
$619$	40.0206			1.60857			0.804283	+	0.594247i	$0.202550\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	17.0165	−	11.4786i	0.681752	−	0.459880i
$624$		0			0
$625$	75.5295			3.02118
$626$		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
$635$	−36.0492			−1.43057
$636$		0			0
$637$	1.52867	−	3.78432i	0.0605682	−	0.149940i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.274587			0.0108455			0.00542277	−	0.999985i	$-0.498274\pi$
$641$	0.274587			0.0108455			0.00542277	+	0.999985i	$0.498274\pi$
$642$		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	0.517271	−	0.855822i	$-0.326948\pi$
$647$	−12.2737	−	21.2586i	−0.482528	−	0.835763i	−0.999799	+	0.0200588i	$0.993615\pi$
$648$		0			0
$649$	4.39102	−	7.60547i	0.172363	−	0.298541i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−33.0308			−1.29260			−0.646298	−	0.763085i	$-0.723684\pi$
$653$	−33.0308			−1.29260			−0.646298	+	0.763085i	$0.723684\pi$
$654$		0			0
$655$	9.91064			0.387241
$656$		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
$661$	9.55416	−	16.5483i	0.371614	−	0.643654i	−0.618200	−	0.786021i	$-0.712138\pi$
$661$	9.55416	−	16.5483i	0.371614	−	0.643654i	0.989814	+	0.142367i	$0.0454713\pi$
$662$		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
$677$	0.946686	+	1.63971i	0.0363841	+	0.0630191i	0.883644	−	0.468159i	$-0.155083\pi$
$677$	0.946686	+	1.63971i	0.0363841	+	0.0630191i	−0.847260	+	0.531178i	$0.821749\pi$
$678$		0			0
$679$	8.71432	−	5.87830i	0.334425	−	0.225589i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	6.39573	+	11.0777i	0.244726	+	0.423878i	0.962055	−	0.272857i	$-0.0879687\pi$
$683$	6.39573	+	11.0777i	0.244726	+	0.423878i	−0.717329	+	0.696735i	$0.754635\pi$
$684$		0			0
$685$	−5.42072			−0.207115
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.561168	−	0.971972i	0.0213788	−	0.0370292i
$690$		0			0
$691$	18.0349	+	31.2373i	0.686079	+	1.18832i	0.973096	+	0.230399i	$0.0740030\pi$
$691$	18.0349	+	31.2373i	0.686079	+	1.18832i	−0.287017	+	0.957925i	$0.592664\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.57834	+	4.46582i	0.0978022	+	0.169398i
$696$		0			0
$697$	−9.48191	+	16.4231i	−0.359153	+	0.622071i
$698$		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
$707$	39.8811	+	19.4497i	1.49988	+	0.731480i
$708$		0			0
$709$	3.38318	+	5.85984i	0.127058	+	0.220071i	0.922536	−	0.385912i	$-0.126113\pi$
$709$	3.38318	+	5.85984i	0.127058	+	0.220071i	−0.795478	+	0.605983i	$0.792780\pi$
$710$		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	−0.960738	−	0.277457i	$-0.910508\pi$
$719$	−6.43767	+	11.1504i	−0.240084	+	0.415839i	0.720654	+	0.693295i	$0.243842\pi$
$720$		0			0
$721$	−27.6121	−	13.4662i	−1.02833	−	0.501508i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	53.9395	−	93.4260i	2.00326	−	3.46975i
$726$		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
$731$	−6.38897			−0.236305
$732$		0			0
$733$	4.66050			0.172139			0.0860697	−	0.996289i	$-0.472569\pi$
$733$	4.66050			0.172139			0.0860697	+	0.996289i	$0.472569\pi$
$734$		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	0.985919	−	0.167227i	$-0.0534811\pi$
$739$	9.46395	+	16.3920i	0.348137	+	0.602991i	−0.637782	+	0.770217i	$0.720148\pi$
$740$		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
$745$	−26.5818			−0.973882
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−44.9441	+	30.3173i	−1.64222	+	1.10777i
$750$		0			0
$751$	−15.2353			−0.555945			−0.277972	−	0.960589i	$-0.589662\pi$
$751$	−15.2353			−0.555945			−0.277972	+	0.960589i	$0.589662\pi$
$752$		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
$761$	−7.09595			−0.257228			−0.128614	−	0.991695i	$-0.541053\pi$
$761$	−7.09595			−0.257228			−0.128614	+	0.991695i	$0.541053\pi$
$762$		0			0
$763$	−0.912020	−	13.0363i	−0.0330173	−	0.471946i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.65425			0.0958394
$768$		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	0.701674	−	0.712498i	$-0.252436\pi$
$773$	−7.40125	−	12.8193i	−0.266204	−	0.461080i	−0.967878	+	0.251418i	$0.919103\pi$
$774$		0			0
$775$	6.10949	−	10.5819i	0.219459	−	0.380114i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−11.0431			−0.395661
$780$		0			0
$781$	22.2706			0.796906
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.09951	−	10.5647i	0.217701	−	0.377069i
$786$		0			0
$787$	9.85887	−	17.0761i	0.351431	−	0.608696i	−0.635070	−	0.772455i	$-0.719029\pi$
$787$	9.85887	−	17.0761i	0.351431	−	0.608696i	0.986500	+	0.163759i	$0.0523619\pi$
$788$		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
$803$	−0.860667	−	1.49072i	−0.0303723	−	0.0526063i
$804$		0			0
$805$	12.8529	+	6.26827i	0.453007	+	0.220928i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	5.34657	+	9.26053i	0.187975	+	0.325583i	0.944575	−	0.328296i	$-0.106474\pi$
$809$	5.34657	+	9.26053i	0.187975	+	0.325583i	−0.756600	+	0.653878i	$0.773141\pi$
$810$		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
$815$	11.0024	−	19.0567i	0.385398	−	0.667529i
$816$		0			0
$817$	−1.86024	−	3.22202i	−0.0650814	−	0.112724i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.31404	+	2.27598i	0.0458602	+	0.0794323i	0.888044	−	0.459758i	$-0.152064\pi$
$821$	1.31404	+	2.27598i	0.0458602	+	0.0794323i	−0.842184	+	0.539190i	$0.818730\pi$
$822$		0			0
$823$	23.1960	−	40.1767i	0.808563	−	1.40047i	−0.105296	−	0.994441i	$-0.533579\pi$
$823$	23.1960	−	40.1767i	0.808563	−	1.40047i	0.913859	−	0.406031i	$-0.133088\pi$
$824$		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	0.979926	+	0.199361i	$0.0638867\pi$
$829$	19.0782	+	33.0445i	0.662615	+	1.14768i	−0.317311	+	0.948322i	$0.602780\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	18.9338	−	46.8718i	0.656018	−	1.62401i
$834$		0			0
$835$	−44.5101	−	77.0937i	−1.54033	−	2.66794i
$836$		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
$851$	−3.88224	+	6.72424i	−0.133081	+	0.230504i
$852$		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
$857$	−6.09527			−0.208211			−0.104105	−	0.994566i	$-0.533198\pi$
$857$	−6.09527			−0.208211			−0.104105	+	0.994566i	$0.533198\pi$
$858$		0			0
$859$	30.2137			1.03088			0.515438	−	0.856927i	$-0.327629\pi$
$859$	30.2137			1.03088			0.515438	+	0.856927i	$0.327629\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	21.3315	−	36.9472i	0.726131	−	1.25770i	−0.232375	−	0.972626i	$-0.574650\pi$
$863$	21.3315	−	36.9472i	0.726131	−	1.25770i	0.958507	−	0.285070i	$-0.0920169\pi$
$864$		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
$871$	−2.83590			−0.0960907
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−78.6656	−	38.3645i	−2.65938	−	1.29696i
$876$		0			0
$877$	20.6751			0.698147			0.349074	−	0.937095i	$-0.386496\pi$
$877$	20.6751			0.698147			0.349074	+	0.937095i	$0.386496\pi$
$878$		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
$887$	10.0863			0.338666			0.169333	−	0.985559i	$-0.445839\pi$
$887$	10.0863			0.338666			0.169333	+	0.985559i	$0.445839\pi$
$888$		0			0
$889$	20.3000	+	9.90012i	0.680839	+	0.332039i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	24.2397			0.811151
$894$		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
$905$	77.0249			2.56040
$906$		0			0
$907$	−23.8637			−0.792380			−0.396190	−	0.918169i	$-0.629668\pi$
$907$	−23.8637			−0.792380			−0.396190	+	0.918169i	$0.629668\pi$
$908$		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
$913$	−10.1136	+	17.5172i	−0.334710	+	0.579735i
$914$		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	0.0654498	+	0.997856i	$0.479152\pi$
$919$	−25.2052	+	43.6567i	−0.831444	+	1.44010i	−0.896893	+	0.442247i	$0.854182\pi$
$920$		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
$929$	21.1465	+	36.6267i	0.693793	+	1.20168i	0.970586	+	0.240755i	$0.0773950\pi$
$929$	21.1465	+	36.6267i	0.693793	+	1.20168i	−0.276793	+	0.960930i	$0.589272\pi$
$930$		0			0
$931$	29.1507	−	4.09883i	0.955377	−	0.134334i
$932$		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
$941$	−17.1646	+	29.7300i	−0.559550	+	0.969170i	0.437983	+	0.898983i	$0.355693\pi$
$941$	−17.1646	+	29.7300i	−0.559550	+	0.969170i	−0.997534	+	0.0701867i	$0.977640\pi$
$942$		0			0
$943$	1.68046	+	2.91065i	0.0547234	+	0.0947837i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13.8650	−	24.0149i	−0.450551	−	0.780378i	0.547869	−	0.836564i	$-0.315439\pi$
$947$	−13.8650	−	24.0149i	−0.450551	−	0.780378i	−0.998420	+	0.0561863i	$0.982106\pi$
$948$		0			0
$949$	0.260125	−	0.450549i	0.00844400	−	0.0146254i
$950$		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
$959$	3.05250	+	1.48868i	0.0985705	+	0.0480720i
$960$		0			0
$961$	15.0467	+	26.0617i	0.485378	+	0.840700i
$962$		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	−0.351174	−	0.936310i	$-0.614218\pi$
$971$	19.7959	−	34.2875i	0.635281	−	1.10034i	0.986455	−	0.164029i	$-0.0524491\pi$
$972$		0			0
$973$	−0.225472	−	3.22287i	−0.00722829	−	0.103320i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−22.8724	+	39.6161i	−0.731752	+	1.26743i	0.224382	+	0.974501i	$0.427964\pi$
$977$	−22.8724	+	39.6161i	−0.731752	+	1.26743i	−0.956134	+	0.292930i	$0.905370\pi$
$978$		0			0
$979$	7.48329	−	12.9614i	0.239167	−	0.414250i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−15.0498			−0.480014			−0.240007	−	0.970771i	$-0.577150\pi$
$983$	−15.0498			−0.480014			−0.240007	+	0.970771i	$0.577150\pi$
$984$		0			0
$985$	−32.8363			−1.04625
$986$		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	0.627463	−	0.778646i	$-0.284093\pi$
$991$	−11.3516	−	19.6616i	−0.360596	−	0.624570i	−0.988059	+	0.154076i	$0.950760\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−16.2894	−	28.2140i	−0.516408	−	0.894445i
$996$		0			0
$997$	−55.5352			−1.75882			−0.879408	−	0.476069i	$-0.842061\pi$
$997$	−55.5352			−1.75882			−0.879408	+	0.476069i	$0.842061\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.t.c.289.11		22
3.2	odd	2		504.2.t.c.457.1	yes	22
4.3	odd	2		3024.2.t.k.289.11		22
7.4	even	3		1512.2.q.d.1369.1		22
9.4	even	3		1512.2.q.d.793.1		22
9.5	odd	6		504.2.q.c.121.7	yes	22
12.11	even	2		1008.2.t.l.961.11		22
21.11	odd	6		504.2.q.c.25.7	✓	22
28.11	odd	6		3024.2.q.l.2881.1		22
36.23	even	6		1008.2.q.l.625.5		22
36.31	odd	6		3024.2.q.l.2305.1		22
63.4	even	3	inner	1512.2.t.c.361.11		22
63.32	odd	6		504.2.t.c.193.1	yes	22
84.11	even	6		1008.2.q.l.529.5		22
252.67	odd	6		3024.2.t.k.1873.11		22
252.95	even	6		1008.2.t.l.193.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.7	✓	22	21.11	odd	6
504.2.q.c.121.7	yes	22	9.5	odd	6
504.2.t.c.193.1	yes	22	63.32	odd	6
504.2.t.c.457.1	yes	22	3.2	odd	2
1008.2.q.l.529.5		22	84.11	even	6
1008.2.q.l.625.5		22	36.23	even	6
1008.2.t.l.193.11		22	252.95	even	6
1008.2.t.l.961.11		22	12.11	even	2
1512.2.q.d.793.1		22	9.4	even	3
1512.2.q.d.1369.1		22	7.4	even	3
1512.2.t.c.289.11		22	1.1	even	1	trivial
1512.2.t.c.361.11		22	63.4	even	3	inner
3024.2.q.l.2305.1		22	36.31	odd	6
3024.2.q.l.2881.1		22	28.11	odd	6
3024.2.t.k.289.11		22	4.3	odd	2
3024.2.t.k.1873.11		22	252.67	odd	6

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Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+4.22296 q^{5} +(-2.37802 - 1.15974i) q^{7} +O(q^{10})\)	\(q+4.22296 q^{5} +(-2.37802 - 1.15974i) q^{7} -1.92915 q^{11} +(-0.291529 - 0.504943i) q^{13} +(-3.61082 - 6.25412i) q^{17} +(2.10268 - 3.64194i) q^{19} -1.27988 q^{23} +12.8334 q^{25} +(4.20305 - 7.27990i) q^{29} +(0.476061 - 0.824561i) q^{31} +(-10.0423 - 4.89755i) q^{35} +(3.03329 - 5.25381i) q^{37} +(-1.31299 - 2.27416i) q^{41} +(0.442349 - 0.766171i) q^{43} +(2.88201 + 4.99178i) q^{47} +(4.30999 + 5.51579i) q^{49} +(0.962456 + 1.66702i) q^{53} -8.14673 q^{55} +(-2.27614 + 3.94240i) q^{59} +(5.29008 + 9.16268i) q^{61} +(-1.23112 - 2.13236i) q^{65} +(2.43191 - 4.21220i) q^{67} -11.5443 q^{71} +(0.446138 + 0.772734i) q^{73} +(4.58756 + 2.23732i) q^{77} +(5.93520 + 10.2801i) q^{79} +(5.24250 - 9.08028i) q^{83} +(-15.2484 - 26.4109i) q^{85} +(-3.87906 + 6.71874i) q^{89} +(0.107659 + 1.53887i) q^{91} +(8.87953 - 15.3798i) q^{95} +(-1.98651 + 3.44073i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q + 2 * q^5 - q^7	\( 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

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