LMFDB - Embedded newform 2268.2.t.c.1781.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(1781,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("2268.1781");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.t (of order $6$, degree $2$, 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:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1781.8
Character	$\chi$	$=$	2268.1781
Dual form			2268.2.t.c.2105.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0292047 - 0.0505839i) q^{5} +(-1.38105 + 2.25670i) q^{7} +O(q^{10})$	$q+(-0.0292047 - 0.0505839i) q^{5} +(-1.38105 + 2.25670i) q^{7} +(-0.578326 - 0.333897i) q^{11} +2.60428i q^{13} +(3.62609 - 6.28057i) q^{17} +(-4.49254 + 2.59377i) q^{19} +(-4.90844 + 2.83389i) q^{23} +(2.49829 - 4.32717i) q^{25} +9.41272i q^{29} +(-4.53293 - 2.61709i) q^{31} +(0.154486 + 0.00395308i) q^{35} +(-2.32058 - 4.01937i) q^{37} +5.04275 q^{41} -5.66799 q^{43} +(2.25897 + 3.91265i) q^{47} +(-3.18538 - 6.23325i) q^{49} +(-6.72339 - 3.88175i) q^{53} +0.0390053i q^{55} +(2.45029 - 4.24402i) q^{59} +(-8.86787 + 5.11987i) q^{61} +(0.131735 - 0.0760572i) q^{65} +(-2.26654 + 3.92576i) q^{67} -10.2441i q^{71} +(-3.61968 - 2.08982i) q^{73} +(1.55220 - 0.843978i) q^{77} +(-4.68652 - 8.11728i) q^{79} -7.84087 q^{83} -0.423595 q^{85} +(-4.29809 - 7.44451i) q^{89} +(-5.87708 - 3.59666i) q^{91} +(0.262406 + 0.151500i) q^{95} +2.33159i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{7}+O(q^{10}) $ 32 * q - 8 * q^7	$ 32 q - 8 q^{7} - 16 q^{25} + 24 q^{31} - 4 q^{37} + 8 q^{43} - 4 q^{49} + 12 q^{61} + 4 q^{67} - 36 q^{73} + 28 q^{79} - 24 q^{85} - 36 q^{91}+O(q^{100}) $ 32 * q - 8 * q^7 - 16 * q^25 + 24 * q^31 - 4 * q^37 + 8 * q^43 - 4 * q^49 + 12 * q^61 + 4 * q^67 - 36 * q^73 + 28 * q^79 - 24 * q^85 - 36 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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
$5$	−0.0292047	−	0.0505839i	−0.0130607	−	0.0226218i	0.859421	−	0.511268i	$-0.170824\pi$
$5$	−0.0292047	−	0.0505839i	−0.0130607	−	0.0226218i	−0.872482	+	0.488646i	$0.837491\pi$
$6$		0			0
$7$	−1.38105	+	2.25670i	−0.521990	+	0.852952i
$7$	−1.38105	+	2.25670i	−0.521990	+	0.852952i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.578326	−	0.333897i	−0.174372	−	0.100674i	0.410274	−	0.911962i	$-0.365433\pi$
$11$	−0.578326	−	0.333897i	−0.174372	−	0.100674i	−0.584646	+	0.811289i	$0.698766\pi$
$12$		0			0
$13$			2.60428i			0.722298i	0.932508	+	0.361149i	$0.117615\pi$
$13$			2.60428i			0.722298i	−0.932508	+	0.361149i	$0.882385\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.62609	−	6.28057i	0.879455	−	1.52326i	0.0275159	−	0.999621i	$-0.491240\pi$
$17$	3.62609	−	6.28057i	0.879455	−	1.52326i	0.851940	−	0.523640i	$-0.175426\pi$
$18$		0			0
$19$	−4.49254	+	2.59377i	−1.03066	+	0.595052i	−0.917174	−	0.398487i	$-0.869535\pi$
$19$	−4.49254	+	2.59377i	−1.03066	+	0.595052i	−0.113487	+	0.993540i	$0.536202\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.90844	+	2.83389i	−1.02348	+	0.590907i	−0.915110	−	0.403203i	$-0.867897\pi$
$23$	−4.90844	+	2.83389i	−1.02348	+	0.590907i	−0.108371	+	0.994111i	$0.534563\pi$
$24$		0			0
$25$	2.49829	−	4.32717i	0.499659	−	0.865434i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			9.41272i			1.74790i	0.486018	+	0.873949i	$0.338449\pi$
$29$			9.41272i			1.74790i	−0.486018	+	0.873949i	$0.661551\pi$
$30$		0			0
$31$	−4.53293	−	2.61709i	−0.814138	−	0.470043i	0.0342530	−	0.999413i	$-0.489095\pi$
$31$	−4.53293	−	2.61709i	−0.814138	−	0.470043i	−0.848391	+	0.529371i	$0.822428\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.154486	+	0.00395308i	0.0261129	+	0.000668192i
$36$		0			0
$37$	−2.32058	−	4.01937i	−0.381501	−	0.660780i	0.609776	−	0.792574i	$-0.291259\pi$
$37$	−2.32058	−	4.01937i	−0.381501	−	0.660780i	−0.991277	+	0.131794i	$0.957926\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.04275			0.787545			0.393772	−	0.919208i	$-0.371170\pi$
$41$	5.04275			0.787545			0.393772	+	0.919208i	$0.371170\pi$
$42$		0			0
$43$	−5.66799			−0.864361			−0.432180	−	0.901787i	$-0.642256\pi$
$43$	−5.66799			−0.864361			−0.432180	+	0.901787i	$0.642256\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.25897	+	3.91265i	0.329504	+	0.570718i	0.982414	−	0.186718i	$-0.0597851\pi$
$47$	2.25897	+	3.91265i	0.329504	+	0.570718i	−0.652909	+	0.757436i	$0.726452\pi$
$48$		0			0
$49$	−3.18538	−	6.23325i	−0.455054	−	0.890464i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.72339	−	3.88175i	−0.923528	−	0.533199i	−0.0387695	−	0.999248i	$-0.512344\pi$
$53$	−6.72339	−	3.88175i	−0.923528	−	0.533199i	−0.884759	+	0.466049i	$0.845677\pi$
$54$		0			0
$55$			0.0390053i			0.00525948i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.45029	−	4.24402i	0.319000	−	0.552525i	−0.661279	−	0.750140i	$-0.729986\pi$
$59$	2.45029	−	4.24402i	0.319000	−	0.552525i	0.980280	+	0.197615i	$0.0633195\pi$
$60$		0			0
$61$	−8.86787	+	5.11987i	−1.13541	+	0.655532i	−0.945291	−	0.326229i	$-0.894222\pi$
$61$	−8.86787	+	5.11987i	−1.13541	+	0.655532i	−0.190123	+	0.981760i	$0.560889\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.131735	−	0.0760572i	0.0163397	−	0.00943374i
$66$		0			0
$67$	−2.26654	+	3.92576i	−0.276902	+	0.479608i	−0.970613	−	0.240645i	$-0.922641\pi$
$67$	−2.26654	+	3.92576i	−0.276902	+	0.479608i	0.693712	+	0.720253i	$0.255974\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	10.2441i		−	1.21575i	−0.794031	−	0.607877i	$-0.792021\pi$
$71$		−	10.2441i		−	1.21575i	0.794031	−	0.607877i	$-0.207979\pi$
$72$		0			0
$73$	−3.61968	−	2.08982i	−0.423652	−	0.244595i	0.272987	−	0.962018i	$-0.411988\pi$
$73$	−3.61968	−	2.08982i	−0.423652	−	0.244595i	−0.696638	+	0.717422i	$0.745322\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.55220	−	0.843978i	0.176890	−	0.0961802i
$78$		0			0
$79$	−4.68652	−	8.11728i	−0.527274	−	0.913266i	−0.999495	−	0.0317854i	$-0.989881\pi$
$79$	−4.68652	−	8.11728i	−0.527274	−	0.913266i	0.472220	−	0.881480i	$-0.343453\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.84087			−0.860647			−0.430323	−	0.902675i	$-0.641600\pi$
$83$	−7.84087			−0.860647			−0.430323	+	0.902675i	$0.641600\pi$
$84$		0			0
$85$	−0.423595			−0.0459453
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.29809	−	7.44451i	−0.455597	−	0.789117i	0.543125	−	0.839652i	$-0.317241\pi$
$89$	−4.29809	−	7.44451i	−0.455597	−	0.789117i	−0.998722	+	0.0505347i	$0.983907\pi$
$90$		0			0
$91$	−5.87708	−	3.59666i	−0.616086	−	0.377032i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.262406	+	0.151500i	0.0269223	+	0.0155436i
$96$		0			0
$97$			2.33159i			0.236737i	0.992970	+	0.118369i	$0.0377665\pi$
$97$			2.33159i			0.236737i	−0.992970	+	0.118369i	$0.962234\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.51708	+	14.7520i	−0.847481	+	1.46788i	0.0359672	+	0.999353i	$0.488549\pi$
$101$	−8.51708	+	14.7520i	−0.847481	+	1.46788i	−0.883449	+	0.468528i	$0.844785\pi$
$102$		0			0
$103$	−12.2865	+	7.09362i	−1.21063	+	0.698955i	−0.962896	−	0.269874i	$-0.913018\pi$
$103$	−12.2865	+	7.09362i	−1.21063	+	0.698955i	−0.247730	+	0.968829i	$0.579685\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.9452	−	7.47393i	1.25146	−	0.722532i	0.280063	−	0.959982i	$-0.409645\pi$
$107$	12.9452	−	7.47393i	1.25146	−	0.722532i	0.971400	+	0.237450i	$0.0763115\pi$
$108$		0			0
$109$	−3.01921	+	5.22942i	−0.289188	+	0.500888i	−0.973616	−	0.228192i	$-0.926718\pi$
$109$	−3.01921	+	5.22942i	−0.289188	+	0.500888i	0.684428	+	0.729080i	$0.260052\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			3.14051i			0.295435i	0.989030	+	0.147717i	$0.0471926\pi$
$113$			3.14051i			0.295435i	−0.989030	+	0.147717i	$0.952807\pi$
$114$		0			0
$115$	0.286699	+	0.165526i	0.0267348	+	0.0154353i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	9.16552	+	16.8568i	0.840202	+	1.54526i
$120$		0			0
$121$	−5.27703	−	9.14008i	−0.479730	−	0.830916i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.583894			−0.0522251
$126$		0			0
$127$	−12.5307			−1.11192			−0.555961	−	0.831208i	$-0.687650\pi$
$127$	−12.5307			−1.11192			−0.555961	+	0.831208i	$0.687650\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.03967	+	6.99691i	0.352947	+	0.611322i	0.986764	−	0.162160i	$-0.0518462\pi$
$131$	4.03967	+	6.99691i	0.352947	+	0.611322i	−0.633817	+	0.773483i	$0.718513\pi$
$132$		0			0
$133$	0.351087	−	13.7205i	0.0304431	−	1.18971i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.97686	+	4.60544i	0.681509	+	0.393469i	0.800423	−	0.599435i	$-0.204608\pi$
$137$	7.97686	+	4.60544i	0.681509	+	0.393469i	−0.118914	+	0.992905i	$0.537941\pi$
$138$		0			0
$139$		−	5.86793i		−	0.497711i	−0.968541	−	0.248856i	$-0.919946\pi$
$139$		−	5.86793i		−	0.497711i	0.968541	−	0.248856i	$-0.0800545\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.869562	−	1.50612i	0.0727164	−	0.125948i
$144$		0			0
$145$	0.476132	−	0.274895i	0.0395406	−	0.0228288i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.10695	+	2.94850i	−0.418378	+	0.241550i	−0.694383	−	0.719606i	$-0.744323\pi$
$149$	−5.10695	+	2.94850i	−0.418378	+	0.241550i	0.276005	+	0.961156i	$0.410989\pi$
$150$		0			0
$151$	−10.8457	+	18.7854i	−0.882614	+	1.52873i	−0.0341909	+	0.999415i	$0.510885\pi$
$151$	−10.8457	+	18.7854i	−0.882614	+	1.52873i	−0.848424	+	0.529318i	$0.822448\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			0.305724i			0.0245564i
$156$		0			0
$157$	6.96201	+	4.01952i	0.555629	+	0.320793i	0.751389	−	0.659859i	$-0.229384\pi$
$157$	6.96201	+	4.01952i	0.555629	+	0.320793i	−0.195760	+	0.980652i	$0.562717\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.383589	−	14.9906i	0.0302311	−	1.18143i
$162$		0			0
$163$	0.862658	+	1.49417i	0.0675686	+	0.117032i	0.897831	−	0.440341i	$-0.145143\pi$
$163$	0.862658	+	1.49417i	0.0675686	+	0.117032i	−0.830262	+	0.557373i	$0.811809\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−13.3616			−1.03395			−0.516976	−	0.856000i	$-0.672942\pi$
$167$	−13.3616			−1.03395			−0.516976	+	0.856000i	$0.672942\pi$
$168$		0			0
$169$	6.21770			0.478285
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.32072	−	14.4119i	−0.632613	−	1.09572i	−0.987016	−	0.160624i	$-0.948649\pi$
$173$	−8.32072	−	14.4119i	−0.632613	−	1.09572i	0.354403	−	0.935093i	$-0.384684\pi$
$174$		0			0
$175$	6.31484	+	11.6140i	0.477357	+	0.877933i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.23927	+	4.75694i	0.615832	+	0.355551i	0.775244	−	0.631661i	$-0.217627\pi$
$179$	8.23927	+	4.75694i	0.615832	+	0.355551i	−0.159413	+	0.987212i	$0.550960\pi$
$180$		0			0
$181$			0.562001i			0.0417732i	0.999782	+	0.0208866i	$0.00664890\pi$
$181$			0.562001i			0.0417732i	−0.999782	+	0.0208866i	$0.993351\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.135544	+	0.234768i	−0.00996536	+	0.0172605i
$186$		0			0
$187$	−4.19412	+	2.42148i	−0.306704	+	0.177076i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.30108	−	4.21528i	0.528287	−	0.305007i	−0.212031	−	0.977263i	$-0.568008\pi$
$191$	7.30108	−	4.21528i	0.528287	−	0.305007i	0.740319	+	0.672256i	$0.234675\pi$
$192$		0			0
$193$	0.842451	−	1.45917i	0.0606410	−	0.105033i	−0.834111	−	0.551596i	$-0.814019\pi$
$193$	0.842451	−	1.45917i	0.0606410	−	0.105033i	0.894752	+	0.446563i	$0.147352\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	14.2930i		−	1.01833i	−0.860668	−	0.509167i	$-0.829954\pi$
$197$		−	14.2930i		−	1.01833i	0.860668	−	0.509167i	$-0.170046\pi$
$198$		0			0
$199$	9.59032	+	5.53697i	0.679839	+	0.392505i	0.799795	−	0.600274i	$-0.204942\pi$
$199$	9.59032	+	5.53697i	0.679839	+	0.392505i	−0.119955	+	0.992779i	$0.538275\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−21.2417	−	12.9995i	−1.49087	−	0.912384i
$204$		0			0
$205$	−0.147272	−	0.255082i	−0.0102859	−	0.0178157i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.46421			0.239624
$210$		0			0
$211$	−13.9624			−0.961212			−0.480606	−	0.876937i	$-0.659583\pi$
$211$	−13.9624			−0.961212			−0.480606	+	0.876937i	$0.659583\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.165532	+	0.286709i	0.0112892	+	0.0195534i
$216$		0			0
$217$	12.1662	−	6.61511i	0.825895	−	0.449063i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	16.3564	+	9.44336i	1.10025	+	0.635229i
$222$		0			0
$223$		−	0.190741i		−	0.0127730i	−0.999980	−	0.00638648i	$-0.997967\pi$
$223$		−	0.190741i		−	0.0127730i	0.999980	−	0.00638648i	$-0.00203289\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.9292	+	18.9300i	−0.725399	+	1.25643i	0.233411	+	0.972378i	$0.425011\pi$
$227$	−10.9292	+	18.9300i	−0.725399	+	1.25643i	−0.958810	+	0.284049i	$0.908322\pi$
$228$		0			0
$229$	−3.98341	+	2.29982i	−0.263231	+	0.151977i	−0.625808	−	0.779977i	$-0.715230\pi$
$229$	−3.98341	+	2.29982i	−0.263231	+	0.151977i	0.362577	+	0.931954i	$0.381897\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−17.9899	+	10.3865i	−1.17856	+	0.680442i	−0.955681	−	0.294404i	$-0.904879\pi$
$233$	−17.9899	+	10.3865i	−1.17856	+	0.680442i	−0.222879	+	0.974846i	$0.571545\pi$
$234$		0			0
$235$	0.131945	−	0.228535i	0.00860712	−	0.0149080i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	20.1311i		−	1.30217i	−0.759003	−	0.651087i	$-0.774313\pi$
$239$		−	20.1311i		−	1.30217i	0.759003	−	0.651087i	$-0.225687\pi$
$240$		0			0
$241$	−8.34784	−	4.81963i	−0.537732	−	0.310460i	0.206427	−	0.978462i	$-0.433816\pi$
$241$	−8.34784	−	4.81963i	−0.537732	−	0.310460i	−0.744159	+	0.668002i	$0.767150\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.222274	+	0.343169i	−0.0142006	+	0.0219242i
$246$		0			0
$247$	−6.75492	−	11.6999i	−0.429805	−	0.744444i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.6713			0.799808			0.399904	−	0.916557i	$-0.369043\pi$
$251$	12.6713			0.799808			0.399904	+	0.916557i	$0.369043\pi$
$252$		0			0
$253$	3.78491			0.237955
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.3339	+	26.5591i	0.956501	+	1.65671i	0.730895	+	0.682490i	$0.239103\pi$
$257$	15.3339	+	26.5591i	0.956501	+	1.65671i	0.225606	+	0.974219i	$0.427564\pi$
$258$		0			0
$259$	12.2753	+	0.314109i	0.762753	+	0.0195178i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−8.86090	−	5.11584i	−0.546386	−	0.315456i	0.201277	−	0.979534i	$-0.435491\pi$
$263$	−8.86090	−	5.11584i	−0.546386	−	0.315456i	−0.747663	+	0.664078i	$0.768824\pi$
$264$		0			0
$265$			0.453461i			0.0278559i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.91248	+	3.31251i	−0.116606	+	0.201967i	−0.918421	−	0.395605i	$-0.870535\pi$
$269$	−1.91248	+	3.31251i	−0.116606	+	0.201967i	0.801815	+	0.597573i	$0.203868\pi$
$270$		0			0
$271$	−26.5090	+	15.3050i	−1.61030	+	0.929710i	−0.621006	+	0.783806i	$0.713276\pi$
$271$	−26.5090	+	15.3050i	−1.61030	+	0.929710i	−0.989299	+	0.145903i	$0.953391\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.88966	+	1.66834i	−0.174253	+	0.100605i
$276$		0			0
$277$	2.46368	−	4.26721i	0.148028	−	0.256392i	−0.782471	−	0.622688i	$-0.786041\pi$
$277$	2.46368	−	4.26721i	0.148028	−	0.256392i	0.930499	+	0.366296i	$0.119374\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	0.115392i		−	0.00688372i	−0.999994	−	0.00344186i	$-0.998904\pi$
$281$		−	0.115392i		−	0.00688372i	0.999994	−	0.00344186i	$-0.00109558\pi$
$282$		0			0
$283$	17.7629	+	10.2554i	1.05589	+	0.609620i	0.924293	−	0.381683i	$-0.124656\pi$
$283$	17.7629	+	10.2554i	1.05589	+	0.609620i	0.131599	+	0.991303i	$0.457989\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.96431	+	11.3800i	−0.411090	+	0.671738i
$288$		0			0
$289$	−17.7970	−	30.8253i	−1.04688	−	1.81326i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	33.7933			1.97423			0.987113	−	0.160025i	$-0.0511575\pi$
$293$	33.7933			1.97423			0.987113	+	0.160025i	$0.0511575\pi$
$294$		0			0
$295$	−0.286239			−0.0166655
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.38026	−	12.7830i	−0.426811	−	0.739259i
$300$		0			0
$301$	7.82781	−	12.7910i	0.451187	−	0.737258i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.517966	+	0.299048i	0.0296586	+	0.0171234i
$306$		0			0
$307$			8.91366i			0.508730i	0.967108	+	0.254365i	$0.0818664\pi$
$307$			8.91366i			0.508730i	−0.967108	+	0.254365i	$0.918134\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	10.2332	−	17.7244i	0.580271	−	1.00506i	−0.415175	−	0.909741i	$-0.636280\pi$
$311$	10.2332	−	17.7244i	0.580271	−	1.00506i	0.995447	−	0.0953182i	$-0.0303869\pi$
$312$		0			0
$313$	9.69540	−	5.59764i	0.548017	−	0.316398i	−0.200305	−	0.979734i	$-0.564193\pi$
$313$	9.69540	−	5.59764i	0.548017	−	0.316398i	0.748322	+	0.663336i	$0.230860\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	24.4965	−	14.1431i	1.37586	−	0.794354i	0.384203	−	0.923249i	$-0.374476\pi$
$317$	24.4965	−	14.1431i	1.37586	−	0.794354i	0.991658	+	0.128895i	$0.0411429\pi$
$318$		0			0
$319$	3.14287	−	5.44362i	0.175967	−	0.304784i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			37.6210i			2.09329i
$324$		0			0
$325$	11.2692	+	6.50627i	0.625102	+	0.360903i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−11.9494	−	0.305769i	−0.658793	−	0.0168576i
$330$		0			0
$331$	−2.79898	−	4.84797i	−0.153846	−	0.266469i	0.778792	−	0.627282i	$-0.215833\pi$
$331$	−2.79898	−	4.84797i	−0.153846	−	0.266469i	−0.932638	+	0.360813i	$0.882499\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.264774			0.0144661
$336$		0			0
$337$	13.3104			0.725061			0.362531	−	0.931972i	$-0.381913\pi$
$337$	13.3104			0.725061			0.362531	+	0.931972i	$0.381913\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.74767	+	3.02706i	0.0946418	+	0.163924i
$342$		0			0
$343$	18.4657	+	1.42002i	0.997056	+	0.0766737i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−22.8179	−	13.1739i	−1.22493	−	0.707214i	−0.258965	−	0.965887i	$-0.583381\pi$
$347$	−22.8179	−	13.1739i	−1.22493	−	0.707214i	−0.965965	+	0.258673i	$0.916715\pi$
$348$		0			0
$349$			4.97890i			0.266514i	0.991082	+	0.133257i	$0.0425436\pi$
$349$			4.97890i			0.266514i	−0.991082	+	0.133257i	$0.957456\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.09023	−	8.81654i	0.270926	−	0.469257i	−0.698174	−	0.715929i	$-0.746004\pi$
$353$	5.09023	−	8.81654i	0.270926	−	0.469257i	0.969099	+	0.246672i	$0.0793369\pi$
$354$		0			0
$355$	−0.518188	+	0.299176i	−0.0275026	+	0.0158786i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.22567	+	4.74910i	−0.434134	+	0.250648i	−0.701106	−	0.713057i	$-0.747310\pi$
$359$	−8.22567	+	4.74910i	−0.434134	+	0.250648i	0.266972	+	0.963704i	$0.413977\pi$
$360$		0			0
$361$	3.95531	−	6.85079i	0.208174	−	0.360568i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			0.244130i			0.0127784i
$366$		0			0
$367$	21.2588	+	12.2738i	1.10970	+	0.640686i	0.938752	−	0.344594i	$-0.111984\pi$
$367$	21.2588	+	12.2738i	1.10970	+	0.640686i	0.170948	+	0.985280i	$0.445317\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	18.0453	−	9.81175i	0.936866	−	0.509401i
$372$		0			0
$373$	−4.03812	−	6.99422i	−0.209086	−	0.362147i	0.742341	−	0.670022i	$-0.233715\pi$
$373$	−4.03812	−	6.99422i	−0.209086	−	0.362147i	−0.951427	+	0.307875i	$0.900382\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−24.5134			−1.26250
$378$		0			0
$379$	36.8197			1.89130			0.945650	−	0.325187i	$-0.105427\pi$
$379$	36.8197			1.89130			0.945650	+	0.325187i	$0.105427\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.54530	+	2.67654i	0.0789611	+	0.136765i	0.902802	−	0.430057i	$-0.141506\pi$
$383$	1.54530	+	2.67654i	0.0789611	+	0.136765i	−0.823841	+	0.566821i	$0.808173\pi$
$384$		0			0
$385$	−0.0880233	−	0.0538685i	−0.00448608	−	0.00274539i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−20.1168	−	11.6145i	−1.01996	−	0.588876i	−0.105870	−	0.994380i	$-0.533763\pi$
$389$	−20.1168	−	11.6145i	−1.01996	−	0.588876i	−0.914093	+	0.405504i	$0.867096\pi$
$390$		0			0
$391$			41.1037i			2.07871i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.273736	+	0.474125i	−0.0137732	+	0.0238558i
$396$		0			0
$397$	16.4726	−	9.51047i	0.826737	−	0.477317i	−0.0259970	−	0.999662i	$-0.508276\pi$
$397$	16.4726	−	9.51047i	0.826737	−	0.477317i	0.852734	+	0.522345i	$0.174943\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−30.8461	+	17.8090i	−1.54038	+	0.889340i	−0.541567	+	0.840657i	$0.682169\pi$
$401$	−30.8461	+	17.8090i	−1.54038	+	0.889340i	−0.998814	+	0.0486823i	$0.984498\pi$
$402$		0			0
$403$	6.81564	−	11.8050i	0.339511	−	0.588050i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			3.09934i			0.153628i
$408$		0			0
$409$	0.686855	+	0.396556i	0.0339628	+	0.0196084i	0.516885	−	0.856055i	$-0.327091\pi$
$409$	0.686855	+	0.396556i	0.0339628	+	0.0196084i	−0.482922	+	0.875663i	$0.660425\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	6.19350	+	11.3908i	0.304762	+	0.560504i
$414$		0			0
$415$	0.228990	+	0.396622i	0.0112407	+	0.0194694i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.19615			0.204995			0.102498	−	0.994733i	$-0.467317\pi$
$419$	4.19615			0.204995			0.102498	+	0.994733i	$0.467317\pi$
$420$		0			0
$421$	17.4739			0.851626			0.425813	−	0.904811i	$-0.359988\pi$
$421$	17.4739			0.851626			0.425813	+	0.904811i	$0.359988\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−18.1181	−	31.3814i	−0.878855	−	1.52222i
$426$		0			0
$427$	0.693014	−	27.0829i	0.0335373	−	1.31063i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	12.1533	+	7.01674i	0.585406	+	0.337984i	0.763279	−	0.646069i	$-0.223588\pi$
$431$	12.1533	+	7.01674i	0.585406	+	0.337984i	−0.177873	+	0.984053i	$0.556922\pi$
$432$		0			0
$433$			18.7989i			0.903420i	0.892165	+	0.451710i	$0.149186\pi$
$433$			18.7989i			0.903420i	−0.892165	+	0.451710i	$0.850814\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	14.7009	−	25.4628i	0.703241	−	1.21805i
$438$		0			0
$439$	−26.5225	+	15.3128i	−1.26585	+	0.730839i	−0.974200	−	0.225685i	$-0.927538\pi$
$439$	−26.5225	+	15.3128i	−1.26585	+	0.730839i	−0.291651	+	0.956525i	$0.594205\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	34.4280	−	19.8770i	1.63572	−	0.944386i	0.653443	−	0.756976i	$-0.273324\pi$
$443$	34.4280	−	19.8770i	1.63572	−	0.944386i	0.982282	−	0.187410i	$-0.0600095\pi$
$444$		0			0
$445$	−0.251049	+	0.434829i	−0.0119008	+	0.0206129i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			2.63319i			0.124268i	0.998068	+	0.0621339i	$0.0197906\pi$
$449$			2.63319i			0.124268i	−0.998068	+	0.0621339i	$0.980209\pi$
$450$		0			0
$451$	−2.91635	−	1.68376i	−0.137326	−	0.0792850i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.0102949	+	0.402325i	−0.000482634	+	0.0188613i
$456$		0			0
$457$	−18.8692	−	32.6824i	−0.882663	−	1.52882i	−0.848369	−	0.529405i	$-0.822415\pi$
$457$	−18.8692	−	32.6824i	−0.882663	−	1.52882i	−0.0342933	−	0.999412i	$-0.510918\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−35.4403			−1.65062			−0.825311	−	0.564679i	$-0.809000\pi$
$461$	−35.4403			−1.65062			−0.825311	+	0.564679i	$0.809000\pi$
$462$		0			0
$463$	35.2188			1.63676			0.818378	−	0.574680i	$-0.194874\pi$
$463$	35.2188			1.63676			0.818378	+	0.574680i	$0.194874\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	13.7710	+	23.8521i	0.637246	+	1.10374i	0.986035	+	0.166540i	$0.0532596\pi$
$467$	13.7710	+	23.8521i	0.637246	+	1.10374i	−0.348789	+	0.937201i	$0.613407\pi$
$468$		0			0
$469$	−5.72904	−	10.5366i	−0.264542	−	0.486534i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.27795	+	1.89252i	0.150720	+	0.0870183i
$474$		0			0
$475$			25.9200i			1.18929i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.66290	−	2.88023i	0.0759800	−	0.131601i	−0.825532	−	0.564355i	$-0.809125\pi$
$479$	1.66290	−	2.88023i	0.0759800	−	0.131601i	0.901512	+	0.432754i	$0.142458\pi$
$480$		0			0
$481$	10.4676	−	6.04345i	0.477280	−	0.275558i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.117941	−	0.0680933i	0.00535543	−	0.00309196i
$486$		0			0
$487$	−9.00297	+	15.5936i	−0.407963	+	0.706613i	−0.994661	−	0.103193i	$-0.967094\pi$
$487$	−9.00297	+	15.5936i	−0.407963	+	0.706613i	0.586698	+	0.809806i	$0.300428\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			7.82047i			0.352933i	0.984307	+	0.176466i	$0.0564667\pi$
$491$			7.82047i			0.352933i	−0.984307	+	0.176466i	$0.943533\pi$
$492$		0			0
$493$	59.1172	+	34.1313i	2.66251	+	1.53720i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	23.1179	+	14.1477i	1.03698	+	0.634611i
$498$		0			0
$499$	9.35207	+	16.1983i	0.418656	+	0.725133i	0.995805	−	0.0915057i	$-0.0291680\pi$
$499$	9.35207	+	16.1983i	0.418656	+	0.725133i	−0.577149	+	0.816639i	$0.695835\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	34.4553			1.53628			0.768142	−	0.640280i	$-0.221182\pi$
$503$	34.4553			1.53628			0.768142	+	0.640280i	$0.221182\pi$
$504$		0			0
$505$	0.994954			0.0442749
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10.5400	+	18.2559i	0.467179	+	0.809177i	0.999297	−	0.0374928i	$-0.0119371\pi$
$509$	10.5400	+	18.2559i	0.467179	+	0.809177i	−0.532118	+	0.846670i	$0.678604\pi$
$510$		0			0
$511$	9.71508	−	5.28237i	0.429770	−	0.233678i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.717646	+	0.414333i	0.0316233	+	0.0182577i
$516$		0			0
$517$		−	3.01705i		−	0.132690i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−14.0593	+	24.3514i	−0.615949	+	1.06686i	0.374268	+	0.927321i	$0.377894\pi$
$521$	−14.0593	+	24.3514i	−0.615949	+	1.06686i	−0.990217	+	0.139535i	$0.955439\pi$
$522$		0			0
$523$	−5.84493	+	3.37457i	−0.255581	+	0.147560i	−0.622317	−	0.782765i	$-0.713809\pi$
$523$	−5.84493	+	3.37457i	−0.255581	+	0.147560i	0.366736	+	0.930325i	$0.380475\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−32.8736	+	18.9796i	−1.43200	+	0.826763i
$528$		0			0
$529$	4.56188	−	7.90140i	0.198342	−	0.343539i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			13.1327i			0.568842i
$534$		0			0
$535$	−0.756122	−	0.436547i	−0.0326900	−	0.0188736i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.239074	+	4.66843i	−0.0102976	+	0.201084i
$540$		0			0
$541$	21.0990	+	36.5445i	0.907116	+	1.57117i	0.818052	+	0.575145i	$0.195054\pi$
$541$	21.0990	+	36.5445i	0.907116	+	1.57117i	0.0890639	+	0.996026i	$0.471612\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.352700			0.0151080
$546$		0			0
$547$	21.0471			0.899910			0.449955	−	0.893051i	$-0.351440\pi$
$547$	21.0471			0.899910			0.449955	+	0.893051i	$0.351440\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−24.4144	−	42.2871i	−1.04009	−	1.80149i
$552$		0			0
$553$	24.7906	+	0.634357i	1.05420	+	0.0269756i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−14.8109	−	8.55106i	−0.627557	−	0.362320i	0.152248	−	0.988342i	$-0.451349\pi$
$557$	−14.8109	−	8.55106i	−0.627557	−	0.362320i	−0.779805	+	0.626022i	$0.784682\pi$
$558$		0			0
$559$		−	14.7611i		−	0.624326i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	3.41616	−	5.91697i	0.143974	−	0.249371i	−0.785016	−	0.619476i	$-0.787345\pi$
$563$	3.41616	−	5.91697i	0.143974	−	0.249371i	0.928990	+	0.370105i	$0.120678\pi$
$564$		0			0
$565$	0.158859	−	0.0917176i	0.00668327	−	0.00385859i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	39.7950	−	22.9757i	1.66829	−	0.963190i	0.699735	−	0.714402i	$-0.253301\pi$
$569$	39.7950	−	22.9757i	1.66829	−	0.963190i	0.968558	−	0.248787i	$-0.0800319\pi$
$570$		0			0
$571$	−23.4434	+	40.6051i	−0.981074	+	1.69927i	−0.322845	+	0.946452i	$0.604639\pi$
$571$	−23.4434	+	40.6051i	−0.981074	+	1.69927i	−0.658228	+	0.752818i	$0.728694\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			28.3196i			1.18101i
$576$		0			0
$577$	31.1736	+	17.9981i	1.29778	+	0.749271i	0.980020	−	0.198901i	$-0.0637373\pi$
$577$	31.1736	+	17.9981i	1.29778	+	0.749271i	0.317756	+	0.948172i	$0.397071\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	10.8287	−	17.6945i	0.449249	−	0.734090i
$582$		0			0
$583$	2.59221	+	4.48983i	0.107358	+	0.185950i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−24.5601			−1.01370			−0.506852	−	0.862033i	$-0.669191\pi$
$587$	−24.5601			−1.01370			−0.506852	+	0.862033i	$0.669191\pi$
$588$		0			0
$589$	27.1525			1.11880
$590$		0			0
$591$		0			0
$592$		0			0
$593$	11.9637	+	20.7217i	0.491289	+	0.850937i	0.999950	−	0.0100297i	$-0.00319261\pi$
$593$	11.9637	+	20.7217i	0.491289	+	0.850937i	−0.508661	+	0.860967i	$0.669859\pi$
$594$		0			0
$595$	0.585007	−	0.955925i	0.0239830	−	0.0391891i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.80257	+	1.04071i	0.0736508	+	0.0425223i	0.536373	−	0.843981i	$-0.319794\pi$
$599$	1.80257	+	1.04071i	0.0736508	+	0.0425223i	−0.462722	+	0.886503i	$0.653127\pi$
$600$		0			0
$601$		−	10.6005i		−	0.432403i	−0.976349	−	0.216202i	$-0.930633\pi$
$601$		−	10.6005i		−	0.432403i	0.976349	−	0.216202i	$-0.0693669\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.308227	+	0.533866i	−0.0125312	+	0.0217047i
$606$		0			0
$607$	−26.6704	+	15.3982i	−1.08252	+	0.624993i	−0.931575	−	0.363549i	$-0.881565\pi$
$607$	−26.6704	+	15.3982i	−1.08252	+	0.624993i	−0.150945	+	0.988542i	$0.548232\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−10.1896	+	5.88299i	−0.412229	+	0.238000i
$612$		0			0
$613$	18.6380	−	32.2820i	0.752784	−	1.30386i	−0.193685	−	0.981064i	$-0.562044\pi$
$613$	18.6380	−	32.2820i	0.752784	−	1.30386i	0.946469	−	0.322796i	$-0.104623\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	17.9704i		−	0.723460i	−0.932283	−	0.361730i	$-0.882186\pi$
$617$		−	17.9704i		−	0.723460i	0.932283	−	0.361730i	$-0.117814\pi$
$618$		0			0
$619$	−14.6914	−	8.48207i	−0.590496	−	0.340923i	0.174797	−	0.984604i	$-0.444073\pi$
$619$	−14.6914	−	8.48207i	−0.590496	−	0.340923i	−0.765294	+	0.643681i	$0.777406\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	22.7359	+	0.581781i	0.910895	+	0.0233085i
$624$		0			0
$625$	−12.4744	−	21.6063i	−0.498977	−	0.864253i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−33.6585			−1.34205
$630$		0			0
$631$	3.99470			0.159026			0.0795132	−	0.996834i	$-0.474663\pi$
$631$	3.99470			0.159026			0.0795132	+	0.996834i	$0.474663\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.365955	+	0.633853i	0.0145225	+	0.0251537i
$636$		0			0
$637$	16.2331	−	8.29563i	0.643181	−	0.328685i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10.9944	−	6.34762i	−0.434253	−	0.250716i	0.266904	−	0.963723i	$-0.413999\pi$
$641$	−10.9944	−	6.34762i	−0.434253	−	0.250716i	−0.701157	+	0.713007i	$0.747333\pi$
$642$		0			0
$643$		−	40.8134i		−	1.60952i	−0.593598	−	0.804762i	$-0.702293\pi$
$643$		−	40.8134i		−	1.60952i	0.593598	−	0.804762i	$-0.297707\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−3.11504	+	5.39540i	−0.122465	+	0.212115i	−0.920739	−	0.390179i	$-0.872413\pi$
$647$	−3.11504	+	5.39540i	−0.122465	+	0.212115i	0.798274	+	0.602294i	$0.205747\pi$
$648$		0			0
$649$	−2.83413	+	1.63629i	−0.111249	+	0.0642298i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.85839	+	1.07294i	−0.0727244	+	0.0419875i	−0.535921	−	0.844268i	$-0.680036\pi$
$653$	−1.85839	+	1.07294i	−0.0727244	+	0.0419875i	0.463197	+	0.886255i	$0.346702\pi$
$654$		0			0
$655$	0.235954	−	0.408684i	0.00921949	−	0.0159686i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	31.6468i		−	1.23279i	−0.787439	−	0.616393i	$-0.788593\pi$
$659$		−	31.6468i		−	1.23279i	0.787439	−	0.616393i	$-0.211407\pi$
$660$		0			0
$661$	29.0476	+	16.7706i	1.12982	+	0.652301i	0.943889	−	0.330262i	$-0.107137\pi$
$661$	29.0476	+	16.7706i	1.12982	+	0.652301i	0.185930	+	0.982563i	$0.440470\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.704288	+	0.382942i	−0.0273111	+	0.0148499i
$666$		0			0
$667$	−26.6746	−	46.2018i	−1.03285	−	1.78894i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	6.83802			0.263979
$672$		0			0
$673$	−24.1521			−0.930994			−0.465497	−	0.885049i	$-0.654124\pi$
$673$	−24.1521			−0.930994			−0.465497	+	0.885049i	$0.654124\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10.9047	−	18.8876i	−0.419104	−	0.725909i	0.576746	−	0.816924i	$-0.304322\pi$
$677$	−10.9047	−	18.8876i	−0.419104	−	0.725909i	−0.995850	+	0.0910149i	$0.970989\pi$
$678$		0			0
$679$	−5.26170	−	3.22006i	−0.201926	−	0.123574i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−10.2822	−	5.93644i	−0.393438	−	0.227151i	0.290211	−	0.956963i	$-0.406275\pi$
$683$	−10.2822	−	5.93644i	−0.393438	−	0.227151i	−0.683649	+	0.729811i	$0.739608\pi$
$684$		0			0
$685$		−	0.538001i		−	0.0205560i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	10.1092	−	17.5096i	0.385129	−	0.667063i
$690$		0			0
$691$	−28.8023	+	16.6290i	−1.09569	+	0.632599i	−0.935086	−	0.354420i	$-0.884678\pi$
$691$	−28.8023	+	16.6290i	−1.09569	+	0.632599i	−0.160606	+	0.987019i	$0.551345\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.296823	+	0.171371i	−0.0112591	+	0.00650047i
$696$		0			0
$697$	18.2854	−	31.6713i	0.692611	−	1.19964i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	26.6399i		−	1.00617i	−0.864236	−	0.503087i	$-0.832198\pi$
$701$		−	26.6399i		−	1.00617i	0.864236	−	0.503087i	$-0.167802\pi$
$702$		0			0
$703$	20.8506	+	12.0381i	0.786397	+	0.454026i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−21.5283	−	39.5938i	−0.809655	−	1.48908i
$708$		0			0
$709$	2.26565	+	3.92422i	0.0850882	+	0.147377i	0.905429	−	0.424498i	$-0.139549\pi$
$709$	2.26565	+	3.92422i	0.0850882	+	0.147377i	−0.820341	+	0.571875i	$0.806216\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	29.6662			1.11101
$714$		0			0
$715$	−0.101581			−0.00379891
$716$		0			0
$717$		0			0
$718$		0			0
$719$	4.41658	+	7.64974i	0.164711	+	0.285287i	0.936553	−	0.350527i	$-0.113998\pi$
$719$	4.41658	+	7.64974i	0.164711	+	0.285287i	−0.771842	+	0.635815i	$0.780664\pi$
$720$		0			0
$721$	0.960177	−	37.5236i	0.0357589	−	1.39745i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	40.7305	+	23.5157i	1.51269	+	0.873353i
$726$		0			0
$727$		−	20.6495i		−	0.765849i	−0.923780	−	0.382924i	$-0.874917\pi$
$727$		−	20.6495i		−	0.765849i	0.923780	−	0.382924i	$-0.125083\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−20.5526	+	35.5982i	−0.760167	+	1.31665i
$732$		0			0
$733$	−18.1849	+	10.4991i	−0.671676	+	0.387792i	−0.796711	−	0.604360i	$-0.793429\pi$
$733$	−18.1849	+	10.4991i	−0.671676	+	0.387792i	0.125036	+	0.992152i	$0.460095\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.62159	−	1.51358i	0.0965676	−	0.0557534i
$738$		0			0
$739$	−18.6194	+	32.2498i	−0.684927	+	1.18633i	0.288533	+	0.957470i	$0.406832\pi$
$739$	−18.6194	+	32.2498i	−0.684927	+	1.18633i	−0.973460	+	0.228858i	$0.926501\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	17.6405i		−	0.647167i	−0.946200	−	0.323584i	$-0.895112\pi$
$743$		−	17.6405i		−	0.647167i	0.946200	−	0.323584i	$-0.104888\pi$
$744$		0			0
$745$	0.298293	+	0.172220i	0.0109286	+	0.00630964i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.01166	+	39.5354i	−0.0369651	+	1.44459i
$750$		0			0
$751$	−18.3147	−	31.7220i	−0.668313	−	1.15755i	−0.978376	−	0.206836i	$-0.933683\pi$
$751$	−18.3147	−	31.7220i	−0.668313	−	1.15755i	0.310063	−	0.950716i	$-0.399650\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.26699			0.0461103
$756$		0			0
$757$	−0.390544			−0.0141946			−0.00709728	−	0.999975i	$-0.502259\pi$
$757$	−0.390544			−0.0141946			−0.00709728	+	0.999975i	$0.502259\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	24.2297	+	41.9671i	0.878327	+	1.52131i	0.853175	+	0.521624i	$0.174674\pi$
$761$	24.2297	+	41.9671i	0.878327	+	1.52131i	0.0251519	+	0.999684i	$0.491993\pi$
$762$		0			0
$763$	−7.63154	−	14.0356i	−0.276280	−	0.508121i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	11.0526	+	6.38125i	0.399088	+	0.230413i
$768$		0			0
$769$			21.9672i			0.792158i	0.918216	+	0.396079i	$0.129629\pi$
$769$			21.9672i			0.792158i	−0.918216	+	0.396079i	$0.870371\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.432172	−	0.748544i	0.0155441	−	0.0269233i	−0.858149	−	0.513401i	$-0.828385\pi$
$773$	0.432172	−	0.748544i	0.0155441	−	0.0269233i	0.873693	+	0.486478i	$0.161719\pi$
$774$		0			0
$775$	−22.6492	+	13.0765i	−0.813582	+	0.469722i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−22.6548	+	13.0797i	−0.811691	+	0.468630i
$780$		0			0
$781$	−3.42048	+	5.92444i	−0.122394	+	0.211993i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	0.469555i		−	0.0167591i
$786$		0			0
$787$	22.3812	+	12.9218i	0.797803	+	0.460612i	0.842702	−	0.538380i	$-0.180963\pi$
$787$	22.3812	+	12.9218i	0.797803	+	0.460612i	−0.0448992	+	0.998992i	$0.514297\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−7.08719	−	4.33722i	−0.251991	−	0.154214i
$792$		0			0
$793$	−13.3336	−	23.0944i	−0.473489	−	0.820108i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.0591311			0.00209453			0.00104726	−	0.999999i	$-0.499667\pi$
$797$	0.0591311			0.00209453			0.00104726	+	0.999999i	$0.499667\pi$
$798$		0			0
$799$	32.7649			1.15914
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.39557	+	2.41720i	0.0492486	+	0.0853011i
$804$		0			0
$805$	−0.769488	+	0.418393i	−0.0271209	+	0.0147464i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	25.6967	+	14.8360i	0.903447	+	0.521605i	0.878317	−	0.478079i	$-0.158667\pi$
$809$	25.6967	+	14.8360i	0.903447	+	0.521605i	0.0251298	+	0.999684i	$0.492000\pi$
$810$		0			0
$811$			43.3023i			1.52055i	0.649603	+	0.760274i	$0.274935\pi$
$811$			43.3023i			1.52055i	−0.649603	+	0.760274i	$0.725065\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.0503873	−	0.0872733i	0.00176499	−	0.00305705i
$816$		0			0
$817$	25.4637	−	14.7015i	0.890862	−	0.514340i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−13.2772	+	7.66560i	−0.463378	+	0.267531i	−0.713463	−	0.700692i	$-0.752875\pi$
$821$	−13.2772	+	7.66560i	−0.463378	+	0.267531i	0.250086	+	0.968224i	$0.419541\pi$
$822$		0			0
$823$	10.9630	−	18.9885i	0.382147	−	0.661898i	−0.609222	−	0.793000i	$-0.708518\pi$
$823$	10.9630	−	18.9885i	0.382147	−	0.661898i	0.991369	+	0.131102i	$0.0418514\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			8.21020i			0.285497i	0.989759	+	0.142748i	$0.0455939\pi$
$827$			8.21020i			0.285497i	−0.989759	+	0.142748i	$0.954406\pi$
$828$		0			0
$829$	9.09310	+	5.24990i	0.315816	+	0.182337i	0.649526	−	0.760339i	$-0.274967\pi$
$829$	9.09310	+	5.24990i	0.315816	+	0.182337i	−0.333710	+	0.942676i	$0.608301\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−50.6988	−	2.59632i	−1.75661	−	0.0899572i
$834$		0			0
$835$	0.390221	+	0.675882i	0.0135041	+	0.0233899i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−2.65347			−0.0916081			−0.0458040	−	0.998950i	$-0.514585\pi$
$839$	−2.65347			−0.0916081			−0.0458040	+	0.998950i	$0.514585\pi$
$840$		0			0
$841$	−59.5993			−2.05515
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.181586	−	0.314516i	−0.00624675	−	0.0108197i
$846$		0			0
$847$	27.9143	+	0.714287i	0.959145	+	0.0245432i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	22.7809	+	13.1526i	0.780919	+	0.450864i
$852$		0			0
$853$			36.8437i			1.26150i	0.775985	+	0.630751i	$0.217253\pi$
$853$			36.8437i			1.26150i	−0.775985	+	0.630751i	$0.782747\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7.50704	+	13.0026i	−0.256436	+	0.444159i	−0.965284	−	0.261201i	$-0.915881\pi$
$857$	−7.50704	+	13.0026i	−0.256436	+	0.444159i	0.708849	+	0.705360i	$0.249215\pi$
$858$		0			0
$859$	−28.3399	+	16.3621i	−0.966945	+	0.558266i	−0.898304	−	0.439375i	$-0.855200\pi$
$859$	−28.3399	+	16.3621i	−0.966945	+	0.558266i	−0.0686417	+	0.997641i	$0.521867\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.26566	+	0.730729i	−0.0430836	+	0.0248743i	−0.521387	−	0.853320i	$-0.674585\pi$
$863$	−1.26566	+	0.730729i	−0.0430836	+	0.0248743i	0.478303	+	0.878195i	$0.341252\pi$
$864$		0			0
$865$	−0.486007	+	0.841790i	−0.0165247	+	0.0286217i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			6.25925i			0.212330i
$870$		0			0
$871$	−10.2238	−	5.90271i	−0.346420	−	0.200006i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.806389	−	1.31767i	0.0272609	−	0.0445455i
$876$		0			0
$877$	17.1700	+	29.7393i	0.579789	+	1.00422i	0.995503	+	0.0947283i	$0.0301982\pi$
$877$	17.1700	+	29.7393i	0.579789	+	1.00422i	−0.415714	+	0.909495i	$0.636468\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−4.01790			−0.135366			−0.0676832	−	0.997707i	$-0.521561\pi$
$881$	−4.01790			−0.135366			−0.0676832	+	0.997707i	$0.521561\pi$
$882$		0			0
$883$	−11.2420			−0.378323			−0.189162	−	0.981946i	$-0.560577\pi$
$883$	−11.2420			−0.378323			−0.189162	+	0.981946i	$0.560577\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.98204	+	6.89710i	0.133704	+	0.231582i	0.925102	−	0.379720i	$-0.123980\pi$
$887$	3.98204	+	6.89710i	0.133704	+	0.231582i	−0.791398	+	0.611302i	$0.790646\pi$
$888$		0			0
$889$	17.3056	−	28.2781i	0.580412	−	0.948416i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−20.2970	−	11.7185i	−0.679214	−	0.392144i
$894$		0			0
$895$		−	0.555699i		−	0.0185750i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	24.6339	−	42.6672i	0.821586	−	1.42303i
$900$		0			0
$901$	−48.7592	+	28.1511i	−1.62440	+	0.937850i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.0284282	−	0.0164131i	0.000944987	−	0.000545588i
$906$		0			0
$907$	−18.8777	+	32.6972i	−0.626825	+	1.08569i	0.361360	+	0.932426i	$0.382313\pi$
$907$	−18.8777	+	32.6972i	−0.626825	+	1.08569i	−0.988185	+	0.153266i	$0.951021\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	6.05830i		−	0.200720i	−0.994951	−	0.100360i	$-0.968001\pi$
$911$		−	6.05830i		−	0.200720i	0.994951	−	0.100360i	$-0.0319995\pi$
$912$		0			0
$913$	4.53458	+	2.61804i	0.150073	+	0.0866444i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−21.3689	−	0.546800i	−0.705663	−	0.0180569i
$918$		0			0
$919$	−4.63028	−	8.01988i	−0.152739	−	0.264552i	0.779495	−	0.626409i	$-0.215476\pi$
$919$	−4.63028	−	8.01988i	−0.152739	−	0.264552i	−0.932233	+	0.361858i	$0.882143\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	26.6786			0.878137
$924$		0			0
$925$	−23.1900			−0.762482
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.539524	−	0.934483i	−0.0177012	−	0.0306594i	0.857039	−	0.515251i	$-0.172301\pi$
$929$	−0.539524	−	0.934483i	−0.0177012	−	0.0306594i	−0.874740	+	0.484592i	$0.838968\pi$
$930$		0			0
$931$	30.4781	+	19.7410i	0.998878	+	0.646985i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.244976	+	0.141437i	0.00801156	+	0.00462548i
$936$		0			0
$937$		−	21.7717i		−	0.711250i	−0.934629	−	0.355625i	$-0.884268\pi$
$937$		−	21.7717i		−	0.711250i	0.934629	−	0.355625i	$-0.115732\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	12.7550	−	22.0923i	0.415801	−	0.720188i	−0.579711	−	0.814822i	$-0.696835\pi$
$941$	12.7550	−	22.0923i	0.415801	−	0.720188i	0.995512	+	0.0946337i	$0.0301680\pi$
$942$		0			0
$943$	−24.7520	+	14.2906i	−0.806037	+	0.465366i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	26.8304	−	15.4905i	0.871870	−	0.503375i	0.00390103	−	0.999992i	$-0.498758\pi$
$947$	26.8304	−	15.4905i	0.871870	−	0.503375i	0.867969	+	0.496618i	$0.165425\pi$
$948$		0			0
$949$	5.44249	−	9.42668i	0.176671	−	0.306003i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	49.7253i		−	1.61076i	−0.592759	−	0.805380i	$-0.701961\pi$
$953$		−	49.7253i		−	1.61076i	0.592759	−	0.805380i	$-0.298039\pi$
$954$		0			0
$955$	−0.426451	−	0.246212i	−0.0137996	−	0.00796722i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−21.4096	+	11.6410i	−0.691351	+	0.375908i
$960$		0			0
$961$	−1.80172	−	3.12066i	−0.0581198	−	0.100667i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.0984140			−0.00316806
$966$		0			0
$967$	−4.80990			−0.154676			−0.0773380	−	0.997005i	$-0.524642\pi$
$967$	−4.80990			−0.154676			−0.0773380	+	0.997005i	$0.524642\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−29.7587	−	51.5437i	−0.955004	−	1.65411i	−0.734360	−	0.678760i	$-0.762517\pi$
$971$	−29.7587	−	51.5437i	−0.955004	−	1.65411i	−0.220644	−	0.975354i	$-0.570816\pi$
$972$		0			0
$973$	13.2421	+	8.10393i	0.424524	+	0.259800i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−39.7949	−	22.9756i	−1.27315	−	0.735054i	−0.297571	−	0.954700i	$-0.596177\pi$
$977$	−39.7949	−	22.9756i	−1.27315	−	0.735054i	−0.975580	+	0.219646i	$0.929510\pi$
$978$		0			0
$979$			5.74047i			0.183466i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−28.0437	+	48.5732i	−0.894456	+	1.54924i	−0.0599806	+	0.998200i	$0.519104\pi$
$983$	−28.0437	+	48.5732i	−0.894456	+	1.54924i	−0.834476	+	0.551044i	$0.814229\pi$
$984$		0			0
$985$	−0.722996	+	0.417422i	−0.0230366	+	0.0133002i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	27.8210	−	16.0625i	0.884657	−	0.510757i
$990$		0			0
$991$	5.13896	−	8.90094i	0.163244	−	0.282748i	−0.772786	−	0.634667i	$-0.781137\pi$
$991$	5.13896	−	8.90094i	0.163244	−	0.282748i	0.936030	+	0.351919i	$0.114471\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	0.646821i		−	0.0205056i
$996$		0			0
$997$	−44.3341	−	25.5963i	−1.40407	−	0.810642i	−0.409266	−	0.912415i	$-0.634215\pi$
$997$	−44.3341	−	25.5963i	−1.40407	−	0.810642i	−0.994808	+	0.101773i	$0.967549\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.t.c.1781.8	✓	32
3.2	odd	2	inner	2268.2.t.c.1781.9	yes	32
7.5	odd	6	inner	2268.2.t.c.2105.9	yes	32
9.2	odd	6		2268.2.bm.j.1025.8		32
9.4	even	3		2268.2.w.j.269.8		32
9.5	odd	6		2268.2.w.j.269.9		32
9.7	even	3		2268.2.bm.j.1025.9		32
21.5	even	6	inner	2268.2.t.c.2105.8	yes	32
63.5	even	6		2268.2.bm.j.593.9		32
63.40	odd	6		2268.2.bm.j.593.8		32
63.47	even	6		2268.2.w.j.1349.8		32
63.61	odd	6		2268.2.w.j.1349.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.t.c.1781.8	✓	32	1.1	even	1	trivial
2268.2.t.c.1781.9	yes	32	3.2	odd	2	inner
2268.2.t.c.2105.8	yes	32	21.5	even	6	inner
2268.2.t.c.2105.9	yes	32	7.5	odd	6	inner
2268.2.w.j.269.8		32	9.4	even	3
2268.2.w.j.269.9		32	9.5	odd	6
2268.2.w.j.1349.8		32	63.47	even	6
2268.2.w.j.1349.9		32	63.61	odd	6
2268.2.bm.j.593.8		32	63.40	odd	6
2268.2.bm.j.593.9		32	63.5	even	6
2268.2.bm.j.1025.8		32	9.2	odd	6
2268.2.bm.j.1025.9		32	9.7	even	3

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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0292047 - 0.0505839i) q^{5} +(-1.38105 + 2.25670i) q^{7} +O(q^{10})\)	\(q+(-0.0292047 - 0.0505839i) q^{5} +(-1.38105 + 2.25670i) q^{7} +(-0.578326 - 0.333897i) q^{11} +2.60428i q^{13} +(3.62609 - 6.28057i) q^{17} +(-4.49254 + 2.59377i) q^{19} +(-4.90844 + 2.83389i) q^{23} +(2.49829 - 4.32717i) q^{25} +9.41272i q^{29} +(-4.53293 - 2.61709i) q^{31} +(0.154486 + 0.00395308i) q^{35} +(-2.32058 - 4.01937i) q^{37} +5.04275 q^{41} -5.66799 q^{43} +(2.25897 + 3.91265i) q^{47} +(-3.18538 - 6.23325i) q^{49} +(-6.72339 - 3.88175i) q^{53} +0.0390053i q^{55} +(2.45029 - 4.24402i) q^{59} +(-8.86787 + 5.11987i) q^{61} +(0.131735 - 0.0760572i) q^{65} +(-2.26654 + 3.92576i) q^{67} -10.2441i q^{71} +(-3.61968 - 2.08982i) q^{73} +(1.55220 - 0.843978i) q^{77} +(-4.68652 - 8.11728i) q^{79} -7.84087 q^{83} -0.423595 q^{85} +(-4.29809 - 7.44451i) q^{89} +(-5.87708 - 3.59666i) q^{91} +(0.262406 + 0.151500i) q^{95} +2.33159i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{7}+O(q^{10}) \) 32 * q - 8 * q^7	\( 32 q - 8 q^{7} - 16 q^{25} + 24 q^{31} - 4 q^{37} + 8 q^{43} - 4 q^{49} + 12 q^{61} + 4 q^{67} - 36 q^{73} + 28 q^{79} - 24 q^{85} - 36 q^{91}+O(q^{100}) \) 32 * q - 8 * q^7 - 16 * q^25 + 24 * q^31 - 4 * q^37 + 8 * q^43 - 4 * q^49 + 12 * q^61 + 4 * q^67 - 36 * q^73 + 28 * q^79 - 24 * q^85 - 36 * q^91

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