LMFDB - Embedded newform 2016.2.cp.b.17.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2016,2,Mod(17,2016)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2016, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))

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

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

chi := DirichletCharacter("2016.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2016 = 2^{5} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2016.cp (of order $6$, 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:	$16.0978410475$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.10
Character	$\chi$	$=$	2016.17
Dual form			2016.2.cp.b.593.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00441 + 0.579896i) q^{5} +(-1.24394 - 2.33508i) q^{7} +O(q^{10})$	$q+(-1.00441 + 0.579896i) q^{5} +(-1.24394 - 2.33508i) q^{7} +(1.41560 - 2.45188i) q^{11} +3.11725 q^{13} +(-0.782206 + 1.35482i) q^{17} +(-2.15042 - 3.72463i) q^{19} +(-4.05782 + 2.34278i) q^{23} +(-1.82744 + 3.16522i) q^{25} -4.08861 q^{29} +(-2.40452 - 1.38825i) q^{31} +(2.60353 + 1.62402i) q^{35} +(4.96358 - 2.86572i) q^{37} +2.19421 q^{41} -6.52977i q^{43} +(5.34609 + 9.25971i) q^{47} +(-3.90521 + 5.80942i) q^{49} +(-5.61902 + 9.73242i) q^{53} +3.28359i q^{55} +(-11.9042 - 6.87289i) q^{59} +(-5.09458 - 8.82407i) q^{61} +(-3.13100 + 1.80768i) q^{65} +(-5.01037 - 2.89274i) q^{67} -4.72781i q^{71} +(-14.0619 - 8.11863i) q^{73} +(-7.48627 - 0.255528i) q^{77} +(-2.89324 - 5.01124i) q^{79} -5.93150i q^{83} -1.81439i q^{85} +(-1.33902 - 2.31925i) q^{89} +(-3.87769 - 7.27904i) q^{91} +(4.31980 + 2.49404i) q^{95} -11.2024i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 20 q^{7}+O(q^{10}) $ 56 * q + 20 * q^7	$ 56 q + 20 q^{7} + 8 q^{25} + 36 q^{31} - 28 q^{49} + 72 q^{73} + 12 q^{79}+O(q^{100}) $ 56 * q + 20 * q^7 + 8 * q^25 + 36 * q^31 - 28 * q^49 + 72 * q^73 + 12 * q^79

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$1765$	$1793$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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
$5$	−1.00441	+	0.579896i	−0.449185	+	0.259337i	−0.707486	−	0.706727i	$-0.750171\pi$
$5$	−1.00441	+	0.579896i	−0.449185	+	0.259337i	0.258301	+	0.966065i	$0.416837\pi$
$6$		0			0
$7$	−1.24394	−	2.33508i	−0.470166	−	0.882578i
$7$	−1.24394	−	2.33508i	−0.470166	−	0.882578i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.41560	−	2.45188i	0.426818	−	0.739271i	−0.569770	−	0.821804i	$-0.692968\pi$
$11$	1.41560	−	2.45188i	0.426818	−	0.739271i	0.996588	+	0.0825332i	$0.0263011\pi$
$12$		0			0
$13$	3.11725			0.864571			0.432285	−	0.901737i	$-0.357707\pi$
$13$	3.11725			0.864571			0.432285	+	0.901737i	$0.357707\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.782206	+	1.35482i	−0.189713	+	0.328592i	−0.945154	−	0.326624i	$-0.894089\pi$
$17$	−0.782206	+	1.35482i	−0.189713	+	0.328592i	0.755442	+	0.655216i	$0.227422\pi$
$18$		0			0
$19$	−2.15042	−	3.72463i	−0.493340	−	0.854489i	0.506631	−	0.862163i	$-0.330891\pi$
$19$	−2.15042	−	3.72463i	−0.493340	−	0.854489i	−0.999971	+	0.00767364i	$0.997557\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.05782	+	2.34278i	−0.846114	+	0.488504i	−0.859338	−	0.511408i	$-0.829124\pi$
$23$	−4.05782	+	2.34278i	−0.846114	+	0.488504i	0.0132237	+	0.999913i	$0.495791\pi$
$24$		0			0
$25$	−1.82744	+	3.16522i	−0.365488	+	0.633044i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.08861			−0.759235			−0.379618	−	0.925143i	$-0.623944\pi$
$29$	−4.08861			−0.759235			−0.379618	+	0.925143i	$0.623944\pi$
$30$		0			0
$31$	−2.40452	−	1.38825i	−0.431865	−	0.249337i	0.268276	−	0.963342i	$-0.413546\pi$
$31$	−2.40452	−	1.38825i	−0.431865	−	0.249337i	−0.700141	+	0.714005i	$0.746879\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.60353	+	1.62402i	0.440077	+	0.274509i
$36$		0			0
$37$	4.96358	−	2.86572i	0.816008	−	0.471122i	−0.0330302	−	0.999454i	$-0.510516\pi$
$37$	4.96358	−	2.86572i	0.816008	−	0.471122i	0.849038	+	0.528332i	$0.177182\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.19421			0.342678			0.171339	−	0.985212i	$-0.445191\pi$
$41$	2.19421			0.342678			0.171339	+	0.985212i	$0.445191\pi$
$42$		0			0
$43$		−	6.52977i		−	0.995781i	−0.867240	−	0.497891i	$-0.834108\pi$
$43$		−	6.52977i		−	0.995781i	0.867240	−	0.497891i	$-0.165892\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.34609	+	9.25971i	0.779808	+	1.35067i	0.932052	+	0.362324i	$0.118017\pi$
$47$	5.34609	+	9.25971i	0.779808	+	1.35067i	−0.152244	+	0.988343i	$0.548650\pi$
$48$		0			0
$49$	−3.90521	+	5.80942i	−0.557887	+	0.829917i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.61902	+	9.73242i	−0.771831	+	1.33685i	0.164727	+	0.986339i	$0.447326\pi$
$53$	−5.61902	+	9.73242i	−0.771831	+	1.33685i	−0.936558	+	0.350512i	$0.886008\pi$
$54$		0			0
$55$			3.28359i			0.442760i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−11.9042	−	6.87289i	−1.54980	−	0.894775i	−0.998157	−	0.0606912i	$-0.980670\pi$
$59$	−11.9042	−	6.87289i	−1.54980	−	0.894775i	−0.551638	−	0.834083i	$-0.685997\pi$
$60$		0			0
$61$	−5.09458	−	8.82407i	−0.652294	−	1.12981i	−0.982565	−	0.185920i	$-0.940474\pi$
$61$	−5.09458	−	8.82407i	−0.652294	−	1.12981i	0.330271	−	0.943886i	$-0.392860\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.13100	+	1.80768i	−0.388352	+	0.224215i
$66$		0			0
$67$	−5.01037	−	2.89274i	−0.612114	−	0.353404i	0.161678	−	0.986844i	$-0.448309\pi$
$67$	−5.01037	−	2.89274i	−0.612114	−	0.353404i	−0.773793	+	0.633439i	$0.781643\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	4.72781i		−	0.561088i	−0.959841	−	0.280544i	$-0.909485\pi$
$71$		−	4.72781i		−	0.561088i	0.959841	−	0.280544i	$-0.0905149\pi$
$72$		0			0
$73$	−14.0619	−	8.11863i	−1.64582	−	0.950213i	−0.978709	−	0.205254i	$-0.934198\pi$
$73$	−14.0619	−	8.11863i	−1.64582	−	0.950213i	−0.667109	−	0.744960i	$-0.732469\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.48627	−	0.255528i	−0.853140	−	0.0291201i
$78$		0			0
$79$	−2.89324	−	5.01124i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$79$	−2.89324	−	5.01124i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	5.93150i		−	0.651066i	−0.945531	−	0.325533i	$-0.894456\pi$
$83$		−	5.93150i		−	0.651066i	0.945531	−	0.325533i	$-0.105544\pi$
$84$		0			0
$85$		−	1.81439i		−	0.196798i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.33902	−	2.31925i	−0.141936	−	0.245840i	0.786290	−	0.617858i	$-0.211999\pi$
$89$	−1.33902	−	2.31925i	−0.141936	−	0.245840i	−0.928226	+	0.372018i	$0.878666\pi$
$90$		0			0
$91$	−3.87769	−	7.27904i	−0.406492	−	0.763051i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.31980	+	2.49404i	0.443202	+	0.255883i
$96$		0			0
$97$		−	11.2024i		−	1.13743i	−0.822534	−	0.568716i	$-0.807440\pi$
$97$		−	11.2024i		−	1.13743i	0.822534	−	0.568716i	$-0.192560\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.473259	+	0.273236i	0.0470911	+	0.0271880i	0.523361	−	0.852111i	$-0.324678\pi$
$101$	0.473259	+	0.273236i	0.0470911	+	0.0271880i	−0.476270	+	0.879299i	$0.658011\pi$
$102$		0			0
$103$	−13.0391	+	7.52810i	−1.28478	+	0.741766i	−0.977718	−	0.209925i	$-0.932678\pi$
$103$	−13.0391	+	7.52810i	−1.28478	+	0.741766i	−0.307059	+	0.951691i	$0.599345\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.42284	+	2.46443i	0.137551	+	0.238246i	0.926569	−	0.376125i	$-0.122744\pi$
$107$	1.42284	+	2.46443i	0.137551	+	0.238246i	−0.789018	+	0.614370i	$0.789410\pi$
$108$		0			0
$109$	0.806006	+	0.465348i	0.0772014	+	0.0445722i	0.538104	−	0.842879i	$-0.319141\pi$
$109$	0.806006	+	0.465348i	0.0772014	+	0.0445722i	−0.460902	+	0.887451i	$0.652474\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			13.9228i			1.30974i	0.755741	+	0.654871i	$0.227277\pi$
$113$			13.9228i			1.30974i	−0.755741	+	0.654871i	$0.772723\pi$
$114$		0			0
$115$	2.71714	−	4.70623i	0.253375	−	0.438858i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.13663	+	0.141195i	0.379205	+	0.0129434i
$120$		0			0
$121$	1.49218	+	2.58452i	0.135652	+	0.234957i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	10.0379i		−	0.897813i
$126$		0			0
$127$	2.15135			0.190901			0.0954506	−	0.995434i	$-0.469571\pi$
$127$	2.15135			0.190901			0.0954506	+	0.995434i	$0.469571\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−10.5792	+	6.10788i	−0.924306	+	0.533648i	−0.885006	−	0.465579i	$-0.845846\pi$
$131$	−10.5792	+	6.10788i	−0.924306	+	0.533648i	−0.0392997	+	0.999227i	$0.512513\pi$
$132$		0			0
$133$	−6.02233	+	9.65463i	−0.522202	+	0.837163i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.51773	−	4.91771i	−0.727718	−	0.420148i	0.0898684	−	0.995954i	$-0.471355\pi$
$137$	−8.51773	−	4.91771i	−0.727718	−	0.420148i	−0.817587	+	0.575805i	$0.804689\pi$
$138$		0			0
$139$	17.6445			1.49658			0.748292	−	0.663369i	$-0.230874\pi$
$139$	17.6445			1.49658			0.748292	+	0.663369i	$0.230874\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.41277	−	7.64315i	0.369015	−	0.639152i
$144$		0			0
$145$	4.10663	−	2.37097i	0.341037	−	0.196898i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.88010	−	8.45259i	−0.399794	−	0.692463i	0.593906	−	0.804534i	$-0.297585\pi$
$149$	−4.88010	−	8.45259i	−0.399794	−	0.692463i	−0.993700	+	0.112071i	$0.964252\pi$
$150$		0			0
$151$	−2.13984	+	3.70631i	−0.174138	+	0.301615i	−0.939862	−	0.341553i	$-0.889047\pi$
$151$	−2.13984	+	3.70631i	−0.174138	+	0.301615i	0.765725	+	0.643168i	$0.222380\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.22016			0.258650
$156$		0			0
$157$	12.1053	−	20.9671i	0.966111	−	1.67335i	0.259512	−	0.965740i	$-0.416438\pi$
$157$	12.1053	−	20.9671i	0.966111	−	1.67335i	0.706599	−	0.707614i	$-0.250228\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	10.5183	+	6.56105i	0.828957	+	0.517083i
$162$		0			0
$163$	7.81820	−	4.51384i	0.612369	−	0.353551i	−0.161523	−	0.986869i	$-0.551641\pi$
$163$	7.81820	−	4.51384i	0.612369	−	0.353551i	0.773892	+	0.633318i	$0.218307\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−16.2972			−1.26112			−0.630559	−	0.776142i	$-0.717174\pi$
$167$	−16.2972			−1.26112			−0.630559	+	0.776142i	$0.717174\pi$
$168$		0			0
$169$	−3.28273			−0.252518
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.0240052	+	0.0138594i	−0.00182508	+	0.00105371i	−0.500912	−	0.865498i	$-0.667002\pi$
$173$	−0.0240052	+	0.0138594i	−0.00182508	+	0.00105371i	0.499087	+	0.866552i	$0.333669\pi$
$174$		0			0
$175$	9.66429	+	0.329870i	0.730551	+	0.0249358i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.39577	+	4.14959i	−0.179068	+	0.310155i	−0.941562	−	0.336841i	$-0.890642\pi$
$179$	−2.39577	+	4.14959i	−0.179068	+	0.310155i	0.762493	+	0.646996i	$0.223975\pi$
$180$		0			0
$181$	−7.03270			−0.522736			−0.261368	−	0.965239i	$-0.584174\pi$
$181$	−7.03270			−0.522736			−0.261368	+	0.965239i	$0.584174\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.32364	+	5.75672i	−0.244359	+	0.423242i
$186$		0			0
$187$	2.21457	+	3.83576i	0.161946	+	0.280498i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.9817	+	6.91767i	−0.866969	+	0.500545i	−0.866340	−	0.499455i	$-0.833534\pi$
$191$	−11.9817	+	6.91767i	−0.866969	+	0.500545i	−0.000629171		1.00000i	$0.500200\pi$
$192$		0			0
$193$	−2.10467	+	3.64540i	−0.151498	+	0.262402i	−0.931778	−	0.363028i	$-0.881743\pi$
$193$	−2.10467	+	3.64540i	−0.151498	+	0.262402i	0.780280	+	0.625430i	$0.215076\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	24.3528			1.73507			0.867534	−	0.497378i	$-0.165704\pi$
$197$	24.3528			1.73507			0.867534	+	0.497378i	$0.165704\pi$
$198$		0			0
$199$	1.63996	+	0.946831i	0.116254	+	0.0671191i	0.556999	−	0.830513i	$-0.311953\pi$
$199$	1.63996	+	0.946831i	0.116254	+	0.0671191i	−0.440746	+	0.897632i	$0.645286\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.08600	+	9.54723i	0.356967	+	0.670084i
$204$		0			0
$205$	−2.20389	+	1.27241i	−0.153926	+	0.0888692i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−12.1765			−0.842266
$210$		0			0
$211$			25.0597i			1.72518i	0.505901	+	0.862592i	$0.331160\pi$
$211$			25.0597i			1.72518i	−0.505901	+	0.862592i	$0.668840\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.78659	+	6.55856i	0.258243	+	0.447290i
$216$		0			0
$217$	−0.250592	+	7.34166i	−0.0170113	+	0.498384i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.43833	+	4.22332i	−0.164020	+	0.284091i
$222$		0			0
$223$		−	9.42532i		−	0.631166i	−0.948898	−	0.315583i	$-0.897800\pi$
$223$		−	9.42532i		−	0.631166i	0.948898	−	0.315583i	$-0.102200\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−16.0967	−	9.29346i	−1.06838	−	0.616829i	−0.140641	−	0.990061i	$-0.544916\pi$
$227$	−16.0967	−	9.29346i	−1.06838	−	0.616829i	−0.927738	+	0.373232i	$0.878250\pi$
$228$		0			0
$229$	−13.7016	−	23.7319i	−0.905428	−	1.56825i	−0.820342	−	0.571874i	$-0.806217\pi$
$229$	−13.7016	−	23.7319i	−0.905428	−	1.56825i	−0.0850862	−	0.996374i	$-0.527117\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	21.0326	−	12.1432i	1.37789	−	0.795526i	0.385987	−	0.922504i	$-0.373861\pi$
$233$	21.0326	−	12.1432i	1.37789	−	0.795526i	0.991906	+	0.126978i	$0.0405278\pi$
$234$		0			0
$235$	−10.7393	−	6.20035i	−0.700556	−	0.404466i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			2.35413i			0.152276i	0.997097	+	0.0761380i	$0.0242590\pi$
$239$			2.35413i			0.152276i	−0.997097	+	0.0761380i	$0.975741\pi$
$240$		0			0
$241$	11.2904	+	6.51850i	0.727277	+	0.419893i	0.817425	−	0.576035i	$-0.195401\pi$
$241$	11.2904	+	6.51850i	0.727277	+	0.419893i	−0.0901483	+	0.995928i	$0.528734\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.553574	−	8.09964i	0.0353665	−	0.517467i
$246$		0			0
$247$	−6.70340	−	11.6106i	−0.426527	−	0.738767i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			24.0484i			1.51792i	0.651136	+	0.758961i	$0.274293\pi$
$251$			24.0484i			1.51792i	−0.651136	+	0.758961i	$0.725707\pi$
$252$		0			0
$253$			13.2657i			0.834010i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.72517	+	11.6483i	0.419504	+	0.726603i	0.995890	−	0.0905752i	$-0.0288706\pi$
$257$	6.72517	+	11.6483i	0.419504	+	0.726603i	−0.576385	+	0.817178i	$0.695537\pi$
$258$		0			0
$259$	−12.8661	−	8.02557i	−0.799461	−	0.498684i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.35260	−	0.780923i	−0.0834048	−	0.0481538i	0.457718	−	0.889098i	$-0.348667\pi$
$263$	−1.35260	−	0.780923i	−0.0834048	−	0.0481538i	−0.541122	+	0.840944i	$0.682000\pi$
$264$		0			0
$265$		−	13.0338i		−	0.800658i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	14.3499	+	8.28490i	0.874927	+	0.505139i	0.868982	−	0.494843i	$-0.164774\pi$
$269$	14.3499	+	8.28490i	0.874927	+	0.505139i	0.00594471	+	0.999982i	$0.498108\pi$
$270$		0			0
$271$	−11.9658	+	6.90846i	−0.726871	+	0.419659i	−0.817276	−	0.576246i	$-0.804517\pi$
$271$	−11.9658	+	6.90846i	−0.726871	+	0.419659i	0.0904054	+	0.995905i	$0.471184\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.17384	+	8.96135i	0.311994	+	0.540390i
$276$		0			0
$277$	11.6351	+	6.71750i	0.699083	+	0.403616i	0.807006	−	0.590544i	$-0.201087\pi$
$277$	11.6351	+	6.71750i	0.699083	+	0.403616i	−0.107923	+	0.994159i	$0.534420\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	27.9830i		−	1.66933i	−0.550761	−	0.834663i	$-0.685662\pi$
$281$		−	27.9830i		−	1.66933i	0.550761	−	0.834663i	$-0.314338\pi$
$282$		0			0
$283$	−9.68568	+	16.7761i	−0.575754	+	0.997235i	0.420205	+	0.907429i	$0.361958\pi$
$283$	−9.68568	+	16.7761i	−0.575754	+	0.997235i	−0.995959	+	0.0898063i	$0.971375\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.72947	−	5.12366i	−0.161116	−	0.302440i
$288$		0			0
$289$	7.27631	+	12.6029i	0.428018	+	0.741349i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	24.4475i		−	1.42824i	−0.700024	−	0.714119i	$-0.746827\pi$
$293$		−	24.4475i		−	1.42824i	0.700024	−	0.714119i	$-0.253173\pi$
$294$		0			0
$295$	15.9422			0.928193
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−12.6493	+	7.30305i	−0.731525	+	0.422346i
$300$		0			0
$301$	−15.2476	+	8.12267i	−0.878855	+	0.468183i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	10.2341	+	5.90865i	0.586001	+	0.338328i
$306$		0			0
$307$	27.0446			1.54352			0.771758	−	0.635917i	$-0.219378\pi$
$307$	27.0446			1.54352			0.771758	+	0.635917i	$0.219378\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.276139	−	0.478286i	0.0156584	−	0.0271211i	−0.858090	−	0.513499i	$-0.828349\pi$
$311$	0.276139	−	0.478286i	0.0156584	−	0.0271211i	0.873748	+	0.486378i	$0.161682\pi$
$312$		0			0
$313$	−13.5478	+	7.82183i	−0.765768	+	0.442116i	−0.831363	−	0.555730i	$-0.812439\pi$
$313$	−13.5478	+	7.82183i	−0.765768	+	0.442116i	0.0655951	+	0.997846i	$0.479105\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.33699	−	10.9760i	−0.355921	−	0.616472i	0.631355	−	0.775494i	$-0.282499\pi$
$317$	−6.33699	−	10.9760i	−0.355921	−	0.616472i	−0.987275	+	0.159022i	$0.949166\pi$
$318$		0			0
$319$	−5.78782	+	10.0248i	−0.324056	+	0.561281i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	6.72828			0.374371
$324$		0			0
$325$	−5.69660	+	9.86680i	−0.315991	+	0.547312i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	14.9719	−	24.0021i	0.825429	−	1.32328i
$330$		0			0
$331$	−2.26793	+	1.30939i	−0.124657	+	0.0719706i	−0.561032	−	0.827794i	$-0.689595\pi$
$331$	−2.26793	+	1.30939i	−0.124657	+	0.0719706i	0.436375	+	0.899765i	$0.356262\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	6.70995			0.366604
$336$		0			0
$337$	34.9446			1.90356			0.951778	−	0.306788i	$-0.0992542\pi$
$337$	34.9446			1.90356			0.951778	+	0.306788i	$0.0992542\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−6.80766	+	3.93040i	−0.368656	+	0.212843i
$342$		0			0
$343$	18.4233	+	1.89241i	0.994766	+	0.102180i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	16.7205	−	28.9607i	0.897602	−	1.55469i	0.0670515	−	0.997750i	$-0.478641\pi$
$347$	16.7205	−	28.9607i	0.897602	−	1.55469i	0.830551	−	0.556943i	$-0.188026\pi$
$348$		0			0
$349$	7.32611			0.392158			0.196079	−	0.980588i	$-0.437179\pi$
$349$	7.32611			0.392158			0.196079	+	0.980588i	$0.437179\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.9297	+	24.1269i	−0.741402	+	1.28415i	0.210454	+	0.977604i	$0.432506\pi$
$353$	−13.9297	+	24.1269i	−0.741402	+	1.28415i	−0.951857	+	0.306543i	$0.900828\pi$
$354$		0			0
$355$	2.74164	+	4.74866i	0.145511	+	0.252033i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	15.6201	−	9.01825i	0.824396	−	0.475965i	−0.0275343	−	0.999621i	$-0.508766\pi$
$359$	15.6201	−	9.01825i	0.824396	−	0.475965i	0.851930	+	0.523656i	$0.175432\pi$
$360$		0			0
$361$	0.251405	−	0.435447i	0.0132319	−	0.0229182i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	18.8318			0.985703
$366$		0			0
$367$	−4.16683	−	2.40572i	−0.217507	−	0.125578i	0.387288	−	0.921959i	$-0.373412\pi$
$367$	−4.16683	−	2.40572i	−0.217507	−	0.125578i	−0.604795	+	0.796381i	$0.706745\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	29.7157	+	1.01428i	1.54276	+	0.0526590i
$372$		0			0
$373$	0.589575	−	0.340391i	0.0305270	−	0.0176248i	−0.484659	−	0.874703i	$-0.661056\pi$
$373$	0.589575	−	0.340391i	0.0305270	−	0.0176248i	0.515186	+	0.857078i	$0.327723\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−12.7452			−0.656413
$378$		0			0
$379$			23.7081i			1.21780i	0.793245	+	0.608902i	$0.208390\pi$
$379$			23.7081i			1.21780i	−0.793245	+	0.608902i	$0.791610\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−16.7429	−	28.9996i	−0.855522	−	1.48181i	−0.876160	−	0.482021i	$-0.839903\pi$
$383$	−16.7429	−	28.9996i	−0.855522	−	1.48181i	0.0206373	−	0.999787i	$-0.493430\pi$
$384$		0			0
$385$	7.66746	−	4.08460i	0.390770	−	0.208171i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−11.7772	+	20.3988i	−0.597130	+	1.03426i	0.396113	+	0.918202i	$0.370359\pi$
$389$	−11.7772	+	20.3988i	−0.597130	+	1.03426i	−0.993243	+	0.116057i	$0.962974\pi$
$390$		0			0
$391$		−	7.33015i		−	0.370702i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.81200	+	3.35556i	0.292433	+	0.168836i
$396$		0			0
$397$	12.7489	+	22.0817i	0.639849	+	1.10825i	0.985466	+	0.169875i	$0.0543364\pi$
$397$	12.7489	+	22.0817i	0.639849	+	1.10825i	−0.345617	+	0.938376i	$0.612330\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.2818	+	5.93623i	−0.513451	+	0.296441i	−0.734251	−	0.678878i	$-0.762467\pi$
$401$	−10.2818	+	5.93623i	−0.513451	+	0.296441i	0.220800	+	0.975319i	$0.429133\pi$
$402$		0			0
$403$	−7.49550	−	4.32753i	−0.373378	−	0.215570i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	16.2268i		−	0.804334i
$408$		0			0
$409$	−4.46727	−	2.57918i	−0.220892	−	0.127532i	0.385471	−	0.922720i	$-0.374039\pi$
$409$	−4.46727	−	2.57918i	−0.220892	−	0.127532i	−0.606363	+	0.795188i	$0.707372\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.24062	+	36.3468i	−0.0610469	+	1.78851i
$414$		0			0
$415$	3.43965	+	5.95765i	0.168846	+	0.292449i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	8.63546i		−	0.421870i	−0.977500	−	0.210935i	$-0.932349\pi$
$419$		−	8.63546i		−	0.421870i	0.977500	−	0.210935i	$-0.0676508\pi$
$420$		0			0
$421$			37.2303i			1.81449i	0.420599	+	0.907247i	$0.361820\pi$
$421$			37.2303i			1.81449i	−0.420599	+	0.907247i	$0.638180\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.85887	−	4.95171i	−0.138676	−	0.240193i
$426$		0			0
$427$	−14.2676	+	22.8729i	−0.690455	+	1.10690i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.24374	+	4.18217i	0.348919	+	0.201448i	0.664209	−	0.747547i	$-0.268769\pi$
$431$	7.24374	+	4.18217i	0.348919	+	0.201448i	−0.315290	+	0.948995i	$0.602102\pi$
$432$		0			0
$433$		−	7.63673i		−	0.366998i	−0.983020	−	0.183499i	$-0.941258\pi$
$433$		−	7.63673i		−	0.366998i	0.983020	−	0.183499i	$-0.0587424\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	17.4520	+	10.0759i	0.834843	+	0.481997i
$438$		0			0
$439$	8.42793	−	4.86587i	0.402243	−	0.232235i	−0.285208	−	0.958466i	$-0.592063\pi$
$439$	8.42793	−	4.86587i	0.402243	−	0.232235i	0.687451	+	0.726230i	$0.258729\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.9352	−	18.9404i	−0.519549	−	0.899885i	−0.999742	−	0.0227221i	$-0.992767\pi$
$443$	−10.9352	−	18.9404i	−0.519549	−	0.899885i	0.480193	−	0.877163i	$-0.340567\pi$
$444$		0			0
$445$	2.68985	+	1.55299i	0.127511	+	0.0736186i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	16.6555i		−	0.786020i	−0.919534	−	0.393010i	$-0.871434\pi$
$449$		−	16.6555i		−	0.786020i	0.919534	−	0.393010i	$-0.128566\pi$
$450$		0			0
$451$	3.10612	−	5.37995i	0.146261	−	0.253332i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	8.11587	+	5.06248i	0.380478	+	0.237333i
$456$		0			0
$457$	−10.3145	−	17.8652i	−0.482490	−	0.835698i	0.517307	−	0.855800i	$-0.326934\pi$
$457$	−10.3145	−	17.8652i	−0.482490	−	0.835698i	−0.999798	+	0.0201016i	$0.993601\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	31.5292i		−	1.46846i	−0.678901	−	0.734230i	$-0.737543\pi$
$461$		−	31.5292i		−	1.46846i	0.678901	−	0.734230i	$-0.262457\pi$
$462$		0			0
$463$	40.3843			1.87682			0.938409	−	0.345526i	$-0.112299\pi$
$463$	40.3843			1.87682			0.938409	+	0.345526i	$0.112299\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.1585	−	5.86499i	0.470077	−	0.271399i	−0.246195	−	0.969220i	$-0.579180\pi$
$467$	10.1585	−	5.86499i	0.470077	−	0.271399i	0.716272	+	0.697821i	$0.245847\pi$
$468$		0			0
$469$	−0.522166	+	15.2980i	−0.0241114	+	0.706398i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−16.0103	−	9.24352i	−0.736152	−	0.425018i
$474$		0			0
$475$	15.7191			0.721240
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−0.299198	+	0.518227i	−0.0136707	+	0.0236784i	−0.872780	−	0.488114i	$-0.837685\pi$
$479$	−0.299198	+	0.518227i	−0.0136707	+	0.0236784i	0.859109	+	0.511792i	$0.171018\pi$
$480$		0			0
$481$	15.4727	−	8.93319i	0.705496	−	0.407318i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.49623	+	11.2518i	0.294979	+	0.510918i
$486$		0			0
$487$	10.3961	−	18.0065i	0.471090	−	0.815952i	−0.528363	−	0.849019i	$-0.677194\pi$
$487$	10.3961	−	18.0065i	0.471090	−	0.815952i	0.999453	+	0.0330665i	$0.0105273\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	22.4435			1.01286			0.506430	−	0.862281i	$-0.330965\pi$
$491$	22.4435			1.01286			0.506430	+	0.862281i	$0.330965\pi$
$492$		0			0
$493$	3.19813	−	5.53933i	0.144037	−	0.249479i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−11.0398	+	5.88113i	−0.495204	+	0.263805i
$498$		0			0
$499$	−10.2264	+	5.90424i	−0.457799	+	0.264310i	−0.711118	−	0.703072i	$-0.751811\pi$
$499$	−10.2264	+	5.90424i	−0.457799	+	0.264310i	0.253320	+	0.967383i	$0.418478\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	3.08281			0.137456			0.0687278	−	0.997635i	$-0.478106\pi$
$503$	3.08281			0.137456			0.0687278	+	0.997635i	$0.478106\pi$
$504$		0			0
$505$	−0.633794			−0.0282035
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.99141	−	2.30444i	0.176916	−	0.102143i	−0.408927	−	0.912567i	$-0.634097\pi$
$509$	3.99141	−	2.30444i	0.176916	−	0.102143i	0.585843	+	0.810425i	$0.300764\pi$
$510$		0			0
$511$	−1.46549	+	42.9347i	−0.0648293	+	1.89932i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.73103	−	15.1226i	0.384735	−	0.666381i
$516$		0			0
$517$	30.2716			1.33135
$518$		0			0
$519$		0			0
$520$		0			0
$521$	19.2542	−	33.3493i	0.843542	−	1.46106i	−0.0433388	−	0.999060i	$-0.513799\pi$
$521$	19.2542	−	33.3493i	0.843542	−	1.46106i	0.886881	−	0.461998i	$-0.152867\pi$
$522$		0			0
$523$	−19.3439	−	33.5046i	−0.845849	−	1.46505i	−0.884882	−	0.465815i	$-0.845761\pi$
$523$	−19.3439	−	33.5046i	−0.845849	−	1.46505i	0.0390332	−	0.999238i	$-0.487572\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.76166	−	2.17180i	0.163860	−	0.0946049i
$528$		0			0
$529$	−0.522727	+	0.905390i	−0.0227273	+	0.0393648i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.83991			0.296270
$534$		0			0
$535$	−2.85823	−	1.65020i	−0.123572	−	0.0713443i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	8.71582	+	17.7989i	0.375417	+	0.766654i
$540$		0			0
$541$	−24.9474	+	14.4034i	−1.07257	+	0.619249i	−0.928883	−	0.370374i	$-0.879230\pi$
$541$	−24.9474	+	14.4034i	−1.07257	+	0.619249i	−0.143688	+	0.989623i	$0.545896\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.07941			−0.0462370
$546$		0			0
$547$			26.0874i			1.11541i	0.830038	+	0.557707i	$0.188319\pi$
$547$			26.0874i			1.11541i	−0.830038	+	0.557707i	$0.811681\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	8.79222	+	15.2286i	0.374561	+	0.648759i
$552$		0			0
$553$	−8.10263	+	12.9897i	−0.344559	+	0.552377i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.2896	+	19.5542i	−0.478357	+	0.828538i	−0.999692	−	0.0248137i	$-0.992101\pi$
$557$	−11.2896	+	19.5542i	−0.478357	+	0.828538i	0.521335	+	0.853352i	$0.325434\pi$
$558$		0			0
$559$		−	20.3550i		−	0.860923i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−15.9160	−	9.18909i	−0.670778	−	0.387274i	0.125593	−	0.992082i	$-0.459917\pi$
$563$	−15.9160	−	9.18909i	−0.670778	−	0.387274i	−0.796371	+	0.604808i	$0.793250\pi$
$564$		0			0
$565$	−8.07374	−	13.9841i	−0.339665	−	0.588317i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−16.3033	+	9.41272i	−0.683470	+	0.394602i	−0.801161	−	0.598449i	$-0.795784\pi$
$569$	−16.3033	+	9.41272i	−0.683470	+	0.394602i	0.117691	+	0.993050i	$0.462451\pi$
$570$		0			0
$571$	−2.34839	−	1.35584i	−0.0982770	−	0.0567403i	0.450056	−	0.893000i	$-0.351404\pi$
$571$	−2.34839	−	1.35584i	−0.0982770	−	0.0567403i	−0.548333	+	0.836260i	$0.684737\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	17.1252i		−	0.714170i
$576$		0			0
$577$	15.8080	+	9.12677i	0.658097	+	0.379952i	0.791551	−	0.611103i	$-0.209274\pi$
$577$	15.8080	+	9.12677i	0.658097	+	0.379952i	−0.133455	+	0.991055i	$0.542607\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−13.8505	+	7.37844i	−0.574617	+	0.306109i
$582$		0			0
$583$	15.9085	+	27.5544i	0.658863	+	1.14119i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	32.5679i		−	1.34422i	−0.740451	−	0.672110i	$-0.765388\pi$
$587$		−	32.5679i		−	1.34422i	0.740451	−	0.672110i	$-0.234612\pi$
$588$		0			0
$589$			11.9413i			0.492032i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	15.3152	+	26.5267i	0.628920	+	1.08932i	0.987769	+	0.155925i	$0.0498359\pi$
$593$	15.3152	+	26.5267i	0.628920	+	1.08932i	−0.358849	+	0.933396i	$0.616831\pi$
$594$		0			0
$595$	−4.23675	+	2.25700i	−0.173690	+	0.0925279i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	28.4250	+	16.4112i	1.16141	+	0.670543i	0.951643	−	0.307207i	$-0.0993944\pi$
$599$	28.4250	+	16.4112i	1.16141	+	0.670543i	0.209772	+	0.977750i	$0.432728\pi$
$600$		0			0
$601$			5.73393i			0.233892i	0.993138	+	0.116946i	$0.0373104\pi$
$601$			5.73393i			0.233892i	−0.993138	+	0.116946i	$0.962690\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.99751	−	1.73061i	−0.121866	−	0.0703594i
$606$		0			0
$607$	−4.62054	+	2.66767i	−0.187542	+	0.108277i	−0.590831	−	0.806795i	$-0.701200\pi$
$607$	−4.62054	+	2.66767i	−0.187542	+	0.108277i	0.403289	+	0.915073i	$0.367867\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	16.6651	+	28.8649i	0.674199	+	1.16775i
$612$		0			0
$613$	0.763004	+	0.440521i	0.0308174	+	0.0177925i	0.515330	−	0.856992i	$-0.327670\pi$
$613$	0.763004	+	0.440521i	0.0308174	+	0.0177925i	−0.484512	+	0.874785i	$0.661003\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	33.3940i		−	1.34439i	−0.740373	−	0.672196i	$-0.765351\pi$
$617$		−	33.3940i		−	1.34439i	0.740373	−	0.672196i	$-0.234649\pi$
$618$		0			0
$619$	0.347094	−	0.601184i	0.0139509	−	0.0241636i	−0.858966	−	0.512033i	$-0.828892\pi$
$619$	0.347094	−	0.601184i	0.0139509	−	0.0241636i	0.872917	+	0.487870i	$0.162226\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.74998	+	6.01174i	−0.150240	+	0.240855i
$624$		0			0
$625$	−3.31630	−	5.74400i	−0.132652	−	0.229760i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			8.96634i			0.357511i
$630$		0			0
$631$	−3.67584			−0.146333			−0.0731664	−	0.997320i	$-0.523310\pi$
$631$	−3.67584			−0.146333			−0.0731664	+	0.997320i	$0.523310\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.16083	+	1.24756i	−0.0857500	+	0.0495078i
$636$		0			0
$637$	−12.1735	+	18.1094i	−0.482333	+	0.717522i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	20.9407	+	12.0901i	0.827108	+	0.477531i	0.852862	−	0.522137i	$-0.174865\pi$
$641$	20.9407	+	12.0901i	0.827108	+	0.477531i	−0.0257532	+	0.999668i	$0.508198\pi$
$642$		0			0
$643$	−7.82797			−0.308705			−0.154352	−	0.988016i	$-0.549329\pi$
$643$	−7.82797			−0.308705			−0.154352	+	0.988016i	$0.549329\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.30976	+	14.3929i	−0.326690	+	0.565844i	−0.981853	−	0.189644i	$-0.939267\pi$
$647$	−8.30976	+	14.3929i	−0.326690	+	0.565844i	0.655163	+	0.755488i	$0.272600\pi$
$648$		0			0
$649$	−33.7031	+	19.4585i	−1.32296	+	0.763812i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	10.0211	+	17.3571i	0.392158	+	0.679237i	0.992734	−	0.120331i	$-0.0383954\pi$
$653$	10.0211	+	17.3571i	0.392158	+	0.679237i	−0.600576	+	0.799568i	$0.705062\pi$
$654$		0			0
$655$	7.08387	−	12.2696i	0.276790	−	0.479414i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	5.53973			0.215797			0.107899	−	0.994162i	$-0.465588\pi$
$659$	5.53973			0.215797			0.107899	+	0.994162i	$0.465588\pi$
$660$		0			0
$661$	14.8650	−	25.7470i	0.578183	−	1.00144i	−0.417505	−	0.908675i	$-0.637095\pi$
$661$	14.8650	−	25.7470i	0.578183	−	1.00144i	0.995688	−	0.0927674i	$-0.0295713\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.450196	−	13.1895i	0.0174579	−	0.511468i
$666$		0			0
$667$	16.5908	−	9.57873i	0.642400	−	0.370890i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−28.8475			−1.11364
$672$		0			0
$673$	28.0307			1.08050			0.540252	−	0.841503i	$-0.318329\pi$
$673$	28.0307			1.08050			0.540252	+	0.841503i	$0.318329\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10.2739	+	5.93164i	−0.394858	+	0.227971i	−0.684263	−	0.729235i	$-0.739876\pi$
$677$	−10.2739	+	5.93164i	−0.394858	+	0.227971i	0.289405	+	0.957207i	$0.406543\pi$
$678$		0			0
$679$	−26.1585	+	13.9352i	−1.00387	+	0.534782i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−7.62606	+	13.2087i	−0.291803	+	0.505418i	−0.974236	−	0.225530i	$-0.927589\pi$
$683$	−7.62606	+	13.2087i	−0.291803	+	0.505418i	0.682433	+	0.730948i	$0.260922\pi$
$684$		0			0
$685$	11.4070			0.435841
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−17.5159	+	30.3384i	−0.667303	+	1.15580i
$690$		0			0
$691$	−3.24122	−	5.61395i	−0.123302	−	0.213565i	0.797766	−	0.602967i	$-0.206015\pi$
$691$	−3.24122	−	5.61395i	−0.123302	−	0.213565i	−0.921068	+	0.389402i	$0.872682\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−17.7223	+	10.2320i	−0.672244	+	0.388120i
$696$		0			0
$697$	−1.71632	+	2.97276i	−0.0650104	+	0.112601i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	4.86157			0.183619			0.0918096	−	0.995777i	$-0.470735\pi$
$701$	4.86157			0.183619			0.0918096	+	0.995777i	$0.470735\pi$
$702$		0			0
$703$	−21.3475	−	12.3250i	−0.805138	−	0.464847i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.0493217	−	1.44499i	0.00185493	−	0.0543444i
$708$		0			0
$709$	21.3747	−	12.3407i	0.802744	−	0.463464i	−0.0416860	−	0.999131i	$-0.513273\pi$
$709$	21.3747	−	12.3407i	0.802744	−	0.463464i	0.844430	+	0.535667i	$0.179940\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	13.0095			0.487209
$714$		0			0
$715$			10.2358i			0.382797i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	10.2912	+	17.8248i	0.383796	+	0.664754i	0.991601	−	0.129332i	$-0.0412833\pi$
$719$	10.2912	+	17.8248i	0.383796	+	0.664754i	−0.607806	+	0.794086i	$0.707950\pi$
$720$		0			0
$721$	33.7986	+	21.0827i	1.25872	+	0.785162i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	7.47169	−	12.9414i	0.277492	−	0.480630i
$726$		0			0
$727$		−	27.0889i		−	1.00467i	−0.864673	−	0.502336i	$-0.832474\pi$
$727$		−	27.0889i		−	1.00467i	0.864673	−	0.502336i	$-0.167526\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	8.84667	+	5.10763i	0.327206	+	0.188912i
$732$		0			0
$733$	−8.48261	−	14.6923i	−0.313312	−	0.542673i	0.665765	−	0.746162i	$-0.268105\pi$
$733$	−8.48261	−	14.6923i	−0.313312	−	0.542673i	−0.979077	+	0.203488i	$0.934772\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−14.1853	+	8.18990i	−0.522523	+	0.301679i
$738$		0			0
$739$	−38.1107	−	22.0032i	−1.40193	−	0.809402i	−0.407336	−	0.913278i	$-0.633542\pi$
$739$	−38.1107	−	22.0032i	−1.40193	−	0.809402i	−0.994590	+	0.103876i	$0.966875\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	30.5441i		−	1.12056i	−0.828305	−	0.560278i	$-0.810694\pi$
$743$		−	30.5441i		−	1.12056i	0.828305	−	0.560278i	$-0.189306\pi$
$744$		0			0
$745$	9.80324	+	5.65990i	0.359163	+	0.207363i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.98472	−	6.38806i	0.145598	−	0.233415i
$750$		0			0
$751$	−8.35120	−	14.4647i	−0.304739	−	0.527824i	0.672464	−	0.740130i	$-0.265236\pi$
$751$	−8.35120	−	14.4647i	−0.304739	−	0.527824i	−0.977203	+	0.212306i	$0.931903\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	4.96353i		−	0.180641i
$756$		0			0
$757$			1.36258i			0.0495237i	0.999693	+	0.0247618i	$0.00788275\pi$
$757$			1.36258i			0.0495237i	−0.999693	+	0.0247618i	$0.992117\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.30823	−	12.6582i	−0.264923	−	0.458860i	0.702620	−	0.711565i	$-0.252013\pi$
$761$	−7.30823	−	12.6582i	−0.264923	−	0.458860i	−0.967543	+	0.252705i	$0.918680\pi$
$762$		0			0
$763$	0.0839995	−	2.46096i	0.00304099	−	0.0890926i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−37.1084	−	21.4246i	−1.33991	−	0.773596i
$768$		0			0
$769$			1.23072i			0.0443809i	0.999754	+	0.0221904i	$0.00706402\pi$
$769$			1.23072i			0.0443809i	−0.999754	+	0.0221904i	$0.992936\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−17.4450	−	10.0719i	−0.627452	−	0.362259i	0.152313	−	0.988332i	$-0.451328\pi$
$773$	−17.4450	−	10.0719i	−0.627452	−	0.362259i	−0.779765	+	0.626073i	$0.784661\pi$
$774$		0			0
$775$	8.78824	−	5.07390i	0.315683	−	0.182260i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.71847	−	8.17263i	−0.169057	−	0.292815i
$780$		0			0
$781$	−11.5921	−	6.69268i	−0.414796	−	0.239483i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			28.0793i			1.00219i
$786$		0			0
$787$	−0.411250	+	0.712307i	−0.0146595	+	0.0253910i	−0.873262	−	0.487251i	$-0.838000\pi$
$787$	−0.411250	+	0.712307i	−0.0146595	+	0.0253910i	0.858603	+	0.512642i	$0.171333\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	32.5108	−	17.3191i	1.15595	−	0.615797i
$792$		0			0
$793$	−15.8811	−	27.5069i	−0.563954	−	0.976797i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	16.0328i		−	0.567911i	−0.958838	−	0.283955i	$-0.908353\pi$
$797$		−	16.0328i		−	0.567911i	0.958838	−	0.283955i	$-0.0916468\pi$
$798$		0			0
$799$	−16.7270			−0.591758
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−39.8119	+	22.9854i	−1.40493	+	0.811137i
$804$		0			0
$805$	−14.3694	−	0.490469i	−0.506454	−	0.0172868i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	19.0060	+	10.9731i	0.668215	+	0.385794i	0.795400	−	0.606085i	$-0.207261\pi$
$809$	19.0060	+	10.9731i	0.668215	+	0.385794i	−0.127185	+	0.991879i	$0.540594\pi$
$810$		0			0
$811$	40.5865			1.42518			0.712592	−	0.701579i	$-0.247521\pi$
$811$	40.5865			1.42518			0.712592	+	0.701579i	$0.247521\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.23511	+	9.06748i	−0.183378	+	0.317620i
$816$		0			0
$817$	−24.3210	+	14.0417i	−0.850885	+	0.491258i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−21.9753	−	38.0623i	−0.766942	−	1.32838i	−0.939214	−	0.343333i	$-0.888444\pi$
$821$	−21.9753	−	38.0623i	−0.766942	−	1.32838i	0.172272	−	0.985049i	$-0.444889\pi$
$822$		0			0
$823$	0.112859	−	0.195478i	0.00393403	−	0.00681394i	−0.864052	−	0.503403i	$-0.832081\pi$
$823$	0.112859	−	0.195478i	0.00393403	−	0.00681394i	0.867986	+	0.496589i	$0.165414\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	7.35761			0.255849			0.127925	−	0.991784i	$-0.459168\pi$
$827$	7.35761			0.255849			0.127925	+	0.991784i	$0.459168\pi$
$828$		0			0
$829$	8.03760	−	13.9215i	0.279157	−	0.483515i	−0.692018	−	0.721880i	$-0.743278\pi$
$829$	8.03760	−	13.9215i	0.279157	−	0.483515i	0.971176	+	0.238365i	$0.0766116\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.81603	−	9.83502i	−0.166866	−	0.340763i
$834$		0			0
$835$	16.3691	−	9.45069i	0.566475	−	0.327055i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−50.6405			−1.74831			−0.874153	−	0.485651i	$-0.838583\pi$
$839$	−50.6405			−1.74831			−0.874153	+	0.485651i	$0.838583\pi$
$840$		0			0
$841$	−12.2833			−0.423562
$842$		0			0
$843$		0			0
$844$		0			0
$845$	3.29720	−	1.90364i	0.113427	−	0.0654872i
$846$		0			0
$847$	4.17889	−	6.69935i	0.143588	−	0.230192i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−13.4275	+	23.2572i	−0.460290	+	0.797246i
$852$		0			0
$853$	8.65855			0.296463			0.148232	−	0.988953i	$-0.452642\pi$
$853$	8.65855			0.296463			0.148232	+	0.988953i	$0.452642\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	17.1294	−	29.6691i	0.585130	−	1.01348i	−0.409729	−	0.912207i	$-0.634377\pi$
$857$	17.1294	−	29.6691i	0.585130	−	1.01348i	0.994859	−	0.101268i	$-0.0322900\pi$
$858$		0			0
$859$	−6.28537	−	10.8866i	−0.214454	−	0.371445i	0.738649	−	0.674090i	$-0.235464\pi$
$859$	−6.28537	−	10.8866i	−0.214454	−	0.371445i	−0.953104	+	0.302644i	$0.902131\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	36.2622	−	20.9360i	1.23438	−	0.712669i	0.266440	−	0.963852i	$-0.414153\pi$
$863$	36.2622	−	20.9360i	1.23438	−	0.712669i	0.967940	+	0.251182i	$0.0808193\pi$
$864$		0			0
$865$	0.0160741	−	0.0278411i	0.000546534	−	0.000946625i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−16.3827			−0.555744
$870$		0			0
$871$	−15.6186	−	9.01741i	−0.529216	−	0.305543i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−23.4392	+	12.4865i	−0.792390	+	0.422122i
$876$		0			0
$877$	4.04807	−	2.33716i	0.136694	−	0.0789201i	−0.430094	−	0.902784i	$-0.641519\pi$
$877$	4.04807	−	2.33716i	0.136694	−	0.0789201i	0.566787	+	0.823864i	$0.308186\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	13.7595			0.463569			0.231785	−	0.972767i	$-0.425544\pi$
$881$	13.7595			0.463569			0.231785	+	0.972767i	$0.425544\pi$
$882$		0			0
$883$			31.7680i			1.06908i	0.845144	+	0.534539i	$0.179515\pi$
$883$			31.7680i			1.06908i	−0.845144	+	0.534539i	$0.820485\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	9.28571	+	16.0833i	0.311784	+	0.540025i	0.978749	−	0.205064i	$-0.0657403\pi$
$887$	9.28571	+	16.0833i	0.311784	+	0.540025i	−0.666965	+	0.745089i	$0.732407\pi$
$888$		0			0
$889$	−2.67615	−	5.02357i	−0.0897553	−	0.168485i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	22.9927	−	39.8245i	0.769420	−	1.33268i
$894$		0			0
$895$		−	5.55718i		−	0.185756i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	9.83114	+	5.67601i	0.327887	+	0.189306i
$900$		0			0
$901$	−8.79045	−	15.2255i	−0.292852	−	0.507235i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.06371	−	4.07823i	0.234806	−	0.135565i
$906$		0			0
$907$	18.8054	+	10.8573i	0.624423	+	0.360511i	0.778589	−	0.627534i	$-0.215936\pi$
$907$	18.8054	+	10.8573i	0.624423	+	0.360511i	−0.154166	+	0.988045i	$0.549269\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			34.1200i			1.13044i	0.824939	+	0.565222i	$0.191210\pi$
$911$			34.1200i			1.13044i	−0.824939	+	0.565222i	$0.808790\pi$
$912$		0			0
$913$	−14.5433	−	8.39660i	−0.481314	−	0.277887i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	27.4223	+	17.1054i	0.905564	+	0.564869i
$918$		0			0
$919$	5.92493	+	10.2623i	0.195445	+	0.338521i	0.947046	−	0.321097i	$-0.104051\pi$
$919$	5.92493	+	10.2623i	0.195445	+	0.338521i	−0.751601	+	0.659618i	$0.770718\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	14.7378i		−	0.485101i
$924$		0			0
$925$			20.9478i			0.688759i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	29.2652	+	50.6888i	0.960161	+	1.66305i	0.722090	+	0.691799i	$0.243182\pi$
$929$	29.2652	+	50.6888i	0.960161	+	1.66305i	0.238071	+	0.971248i	$0.423485\pi$
$930$		0			0
$931$	30.0358	+	2.05281i	0.984383	+	0.0672781i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−4.44868	−	2.56844i	−0.145487	−	0.0839971i
$936$		0			0
$937$		−	58.2795i		−	1.90391i	−0.306242	−	0.951954i	$-0.599072\pi$
$937$		−	58.2795i		−	1.90391i	0.306242	−	0.951954i	$-0.400928\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−47.2322	−	27.2695i	−1.53973	−	0.888961i	−0.998854	−	0.0478564i	$-0.984761\pi$
$941$	−47.2322	−	27.2695i	−1.53973	−	0.888961i	−0.540872	−	0.841105i	$-0.681906\pi$
$942$		0			0
$943$	−8.90372	+	5.14056i	−0.289945	+	0.167400i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−30.3559	−	52.5780i	−0.986435	−	1.70856i	−0.635379	−	0.772200i	$-0.719156\pi$
$947$	−30.3559	−	52.5780i	−0.986435	−	1.70856i	−0.351056	−	0.936355i	$-0.614177\pi$
$948$		0			0
$949$	−43.8344	−	25.3078i	−1.42293	−	0.821527i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	15.3879i		−	0.498463i	−0.968444	−	0.249232i	$-0.919822\pi$
$953$		−	15.3879i		−	0.498463i	0.968444	−	0.249232i	$-0.0801781\pi$
$954$		0			0
$955$	8.02305	−	13.8963i	0.259620	−	0.449675i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.887692	+	26.0069i	−0.0286651	+	0.839808i
$960$		0			0
$961$	−11.6455	−	20.1706i	−0.375662	−	0.650666i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		−	4.88197i		−	0.157156i
$966$		0			0
$967$	−34.1030			−1.09668			−0.548339	−	0.836256i	$-0.684740\pi$
$967$	−34.1030			−1.09668			−0.548339	+	0.836256i	$0.684740\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−33.1725	+	19.1521i	−1.06456	+	0.614621i	−0.926689	−	0.375830i	$-0.877358\pi$
$971$	−33.1725	+	19.1521i	−1.06456	+	0.614621i	−0.137866	+	0.990451i	$0.544024\pi$
$972$		0			0
$973$	−21.9487	−	41.2013i	−0.703644	−	1.32085i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−19.4340	−	11.2202i	−0.621749	−	0.358967i	0.155801	−	0.987788i	$-0.450204\pi$
$977$	−19.4340	−	11.2202i	−0.621749	−	0.358967i	−0.777550	+	0.628822i	$0.783538\pi$
$978$		0			0
$979$	−7.58205			−0.242323
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−14.0698	+	24.3695i	−0.448756	+	0.777268i	−0.998305	−	0.0581932i	$-0.981466\pi$
$983$	−14.0698	+	24.3695i	−0.448756	+	0.777268i	0.549550	+	0.835461i	$0.314799\pi$
$984$		0			0
$985$	−24.4602	+	14.1221i	−0.779367	+	0.449968i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	15.2979	+	26.4967i	0.486443	+	0.842545i
$990$		0			0
$991$	−17.8187	+	30.8629i	−0.566029	+	0.980391i	0.430924	+	0.902388i	$0.358188\pi$
$991$	−17.8187	+	30.8629i	−0.566029	+	0.980391i	−0.996953	+	0.0780029i	$0.975146\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.19625			−0.0696259
$996$		0			0
$997$	12.1376	−	21.0230i	0.384402	−	0.665804i	−0.607284	−	0.794485i	$-0.707741\pi$
$997$	12.1376	−	21.0230i	0.384402	−	0.665804i	0.991686	+	0.128681i	$0.0410742\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2016.2.cp.b.17.10		56
3.2	odd	2	inner	2016.2.cp.b.17.20		56
4.3	odd	2		504.2.ch.b.269.16	yes	56
7.5	odd	6	inner	2016.2.cp.b.593.9		56
8.3	odd	2		504.2.ch.b.269.25	yes	56
8.5	even	2	inner	2016.2.cp.b.17.19		56
12.11	even	2		504.2.ch.b.269.13	yes	56
21.5	even	6	inner	2016.2.cp.b.593.19		56
24.5	odd	2	inner	2016.2.cp.b.17.9		56
24.11	even	2		504.2.ch.b.269.4	✓	56
28.19	even	6		504.2.ch.b.341.4	yes	56
56.5	odd	6	inner	2016.2.cp.b.593.20		56
56.19	even	6		504.2.ch.b.341.13	yes	56
84.47	odd	6		504.2.ch.b.341.25	yes	56
168.5	even	6	inner	2016.2.cp.b.593.10		56
168.131	odd	6		504.2.ch.b.341.16	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.4	✓	56	24.11	even	2
504.2.ch.b.269.13	yes	56	12.11	even	2
504.2.ch.b.269.16	yes	56	4.3	odd	2
504.2.ch.b.269.25	yes	56	8.3	odd	2
504.2.ch.b.341.4	yes	56	28.19	even	6
504.2.ch.b.341.13	yes	56	56.19	even	6
504.2.ch.b.341.16	yes	56	168.131	odd	6
504.2.ch.b.341.25	yes	56	84.47	odd	6
2016.2.cp.b.17.9		56	24.5	odd	2	inner
2016.2.cp.b.17.10		56	1.1	even	1	trivial
2016.2.cp.b.17.19		56	8.5	even	2	inner
2016.2.cp.b.17.20		56	3.2	odd	2	inner
2016.2.cp.b.593.9		56	7.5	odd	6	inner
2016.2.cp.b.593.10		56	168.5	even	6	inner
2016.2.cp.b.593.19		56	21.5	even	6	inner
2016.2.cp.b.593.20		56	56.5	odd	6	inner

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:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2016.cp (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00441 + 0.579896i) q^{5} +(-1.24394 - 2.33508i) q^{7} +O(q^{10})\)	\(q+(-1.00441 + 0.579896i) q^{5} +(-1.24394 - 2.33508i) q^{7} +(1.41560 - 2.45188i) q^{11} +3.11725 q^{13} +(-0.782206 + 1.35482i) q^{17} +(-2.15042 - 3.72463i) q^{19} +(-4.05782 + 2.34278i) q^{23} +(-1.82744 + 3.16522i) q^{25} -4.08861 q^{29} +(-2.40452 - 1.38825i) q^{31} +(2.60353 + 1.62402i) q^{35} +(4.96358 - 2.86572i) q^{37} +2.19421 q^{41} -6.52977i q^{43} +(5.34609 + 9.25971i) q^{47} +(-3.90521 + 5.80942i) q^{49} +(-5.61902 + 9.73242i) q^{53} +3.28359i q^{55} +(-11.9042 - 6.87289i) q^{59} +(-5.09458 - 8.82407i) q^{61} +(-3.13100 + 1.80768i) q^{65} +(-5.01037 - 2.89274i) q^{67} -4.72781i q^{71} +(-14.0619 - 8.11863i) q^{73} +(-7.48627 - 0.255528i) q^{77} +(-2.89324 - 5.01124i) q^{79} -5.93150i q^{83} -1.81439i q^{85} +(-1.33902 - 2.31925i) q^{89} +(-3.87769 - 7.27904i) q^{91} +(4.31980 + 2.49404i) q^{95} -11.2024i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 20 q^{7}+O(q^{10}) \) 56 * q + 20 * q^7	\( 56 q + 20 q^{7} + 8 q^{25} + 36 q^{31} - 28 q^{49} + 72 q^{73} + 12 q^{79}+O(q^{100}) \) 56 * q + 20 * q^7 + 8 * q^25 + 36 * q^31 - 28 * q^49 + 72 * q^73 + 12 * q^79

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