LMFDB - Embedded newform 2646.2.e.q.2125.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2646,2,Mod(1549,2646)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2646, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2646.1549"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-8,0,8,0,0,0,-8,0,0,-8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2125.3
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	2646.2125
Dual form			2646.2.e.q.1549.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.517638 - 0.896575i) q^{5} -1.00000 q^{8} +(-0.517638 + 0.896575i) q^{10} +(-0.133975 - 0.232051i) q^{11} +(0.896575 + 1.55291i) q^{13} +1.00000 q^{16} +(3.41542 - 5.91567i) q^{17} +(2.19067 + 3.79435i) q^{19} +(0.517638 - 0.896575i) q^{20} +(0.133975 + 0.232051i) q^{22} +(2.73205 - 4.73205i) q^{23} +(1.96410 + 3.40192i) q^{25} +(-0.896575 - 1.55291i) q^{26} +(-2.00000 + 3.46410i) q^{29} -6.69213 q^{31} -1.00000 q^{32} +(-3.41542 + 5.91567i) q^{34} +(-3.73205 - 6.46410i) q^{37} +(-2.19067 - 3.79435i) q^{38} +(-0.517638 + 0.896575i) q^{40} +(4.31199 + 7.46859i) q^{41} +(-0.133975 + 0.232051i) q^{43} +(-0.133975 - 0.232051i) q^{44} +(-2.73205 + 4.73205i) q^{46} +0.757875 q^{47} +(-1.96410 - 3.40192i) q^{50} +(0.896575 + 1.55291i) q^{52} +(5.46410 - 9.46410i) q^{53} -0.277401 q^{55} +(2.00000 - 3.46410i) q^{58} -1.27551 q^{59} +12.6264 q^{61} +6.69213 q^{62} +1.00000 q^{64} +1.85641 q^{65} +12.4641 q^{67} +(3.41542 - 5.91567i) q^{68} -9.46410 q^{71} +(2.70831 - 4.69093i) q^{73} +(3.73205 + 6.46410i) q^{74} +(2.19067 + 3.79435i) q^{76} +8.92820 q^{79} +(0.517638 - 0.896575i) q^{80} +(-4.31199 - 7.46859i) q^{82} +(-3.29530 + 5.70762i) q^{83} +(-3.53590 - 6.12436i) q^{85} +(0.133975 - 0.232051i) q^{86} +(0.133975 + 0.232051i) q^{88} +(-3.53553 - 6.12372i) q^{89} +(2.73205 - 4.73205i) q^{92} -0.757875 q^{94} +4.53590 q^{95} +(-9.07227 + 15.7136i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 8 q^{11} + 8 q^{16} + 8 q^{22} + 8 q^{23} - 12 q^{25} - 16 q^{29} - 8 q^{32} - 16 q^{37} - 8 q^{43} - 8 q^{44} - 8 q^{46} + 12 q^{50} + 16 q^{53} + 16 q^{58} + 8 q^{64}+ \cdots + 64 q^{95}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 8 * q^11 + 8 * q^16 + 8 * q^22 + 8 * q^23 - 12 * q^25 - 16 * q^29 - 8 * q^32 - 16 * q^37 - 8 * q^43 - 8 * q^44 - 8 * q^46 + 12 * q^50 + 16 * q^53 + 16 * q^58 + 8 * q^64 - 96 * q^65 + 72 * q^67 - 48 * q^71 + 16 * q^74 + 16 * q^79 - 56 * q^85 + 8 * q^86 + 8 * q^88 + 8 * q^92 + 64 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	0.517638	−	0.896575i	0.231495	−	0.400961i	−0.726753	−	0.686898i	$-0.758972\pi$
$5$	0.517638	−	0.896575i	0.231495	−	0.400961i	0.958248	+	0.285938i	$0.0923050\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.517638	+	0.896575i	−0.163692	+	0.283522i
$11$	−0.133975	−	0.232051i	−0.0403949	−	0.0699660i	0.845121	−	0.534575i	$-0.179528\pi$
$11$	−0.133975	−	0.232051i	−0.0403949	−	0.0699660i	−0.885516	+	0.464609i	$0.846195\pi$
$12$		0			0
$13$	0.896575	+	1.55291i	0.248665	+	0.430701i	0.963156	−	0.268944i	$-0.0866747\pi$
$13$	0.896575	+	1.55291i	0.248665	+	0.430701i	−0.714490	+	0.699645i	$0.753341\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	3.41542	−	5.91567i	0.828360	−	1.43476i	−0.0709642	−	0.997479i	$-0.522608\pi$
$17$	3.41542	−	5.91567i	0.828360	−	1.43476i	0.899324	−	0.437283i	$-0.144059\pi$
$18$		0			0
$19$	2.19067	+	3.79435i	0.502574	+	0.870484i	0.999996	+	0.00297513i	$0.000947015\pi$
$19$	2.19067	+	3.79435i	0.502574	+	0.870484i	−0.497421	+	0.867509i	$0.665720\pi$
$20$	0.517638	−	0.896575i	0.115747	−	0.200480i
$21$		0			0
$22$	0.133975	+	0.232051i	0.0285635	+	0.0494734i
$23$	2.73205	−	4.73205i	0.569672	−	0.986701i	−0.426926	−	0.904286i	$-0.640404\pi$
$23$	2.73205	−	4.73205i	0.569672	−	0.986701i	0.996598	−	0.0824143i	$-0.0262631\pi$
$24$		0			0
$25$	1.96410	+	3.40192i	0.392820	+	0.680385i
$26$	−0.896575	−	1.55291i	−0.175833	−	0.304552i
$27$		0			0
$28$		0			0
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	−0.989780	−	0.142605i	$-0.954452\pi$
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	0.618389	+	0.785872i	$0.287786\pi$
$30$		0			0
$31$	−6.69213			−1.20194			−0.600971	−	0.799271i	$-0.705219\pi$
$31$	−6.69213			−1.20194			−0.600971	+	0.799271i	$0.705219\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−3.41542	+	5.91567i	−0.585739	+	1.01453i
$35$		0			0
$36$		0			0
$37$	−3.73205	−	6.46410i	−0.613545	−	1.06269i	−0.990638	−	0.136516i	$-0.956409\pi$
$37$	−3.73205	−	6.46410i	−0.613545	−	1.06269i	0.377092	−	0.926176i	$-0.376924\pi$
$38$	−2.19067	−	3.79435i	−0.355374	−	0.615525i
$39$		0			0
$40$	−0.517638	+	0.896575i	−0.0818458	+	0.141761i
$41$	4.31199	+	7.46859i	0.673420	+	1.16640i	0.976928	+	0.213569i	$0.0685087\pi$
$41$	4.31199	+	7.46859i	0.673420	+	1.16640i	−0.303508	+	0.952829i	$0.598158\pi$
$42$		0			0
$43$	−0.133975	+	0.232051i	−0.0204309	+	0.0353874i	−0.876060	−	0.482202i	$-0.839837\pi$
$43$	−0.133975	+	0.232051i	−0.0204309	+	0.0353874i	0.855629	+	0.517589i	$0.173170\pi$
$44$	−0.133975	−	0.232051i	−0.0201974	−	0.0349830i
$45$		0			0
$46$	−2.73205	+	4.73205i	−0.402819	+	0.697703i
$47$	0.757875			0.110547			0.0552737	−	0.998471i	$-0.482397\pi$
$47$	0.757875			0.110547			0.0552737	+	0.998471i	$0.482397\pi$
$48$		0			0
$49$		0			0
$50$	−1.96410	−	3.40192i	−0.277766	−	0.481105i
$51$		0			0
$52$	0.896575	+	1.55291i	0.124333	+	0.215350i
$53$	5.46410	−	9.46410i	0.750552	−	1.29999i	−0.197003	−	0.980403i	$-0.563121\pi$
$53$	5.46410	−	9.46410i	0.750552	−	1.29999i	0.947555	−	0.319592i	$-0.103546\pi$
$54$		0			0
$55$	−0.277401			−0.0374048
$56$		0			0
$57$		0			0
$58$	2.00000	−	3.46410i	0.262613	−	0.454859i
$59$	−1.27551			−0.166058			−0.0830288	−	0.996547i	$-0.526459\pi$
$59$	−1.27551			−0.166058			−0.0830288	+	0.996547i	$0.526459\pi$
$60$		0			0
$61$	12.6264			1.61664			0.808322	−	0.588741i	$-0.200376\pi$
$61$	12.6264			1.61664			0.808322	+	0.588741i	$0.200376\pi$
$62$	6.69213			0.849901
$63$		0			0
$64$	1.00000			0.125000
$65$	1.85641			0.230259
$66$		0			0
$67$	12.4641			1.52273			0.761366	−	0.648322i	$-0.224529\pi$
$67$	12.4641			1.52273			0.761366	+	0.648322i	$0.224529\pi$
$68$	3.41542	−	5.91567i	0.414180	−	0.717381i
$69$		0			0
$70$		0			0
$71$	−9.46410			−1.12318			−0.561591	−	0.827415i	$-0.689811\pi$
$71$	−9.46410			−1.12318			−0.561591	+	0.827415i	$0.689811\pi$
$72$		0			0
$73$	2.70831	−	4.69093i	0.316984	−	0.549032i	−0.662874	−	0.748731i	$-0.730663\pi$
$73$	2.70831	−	4.69093i	0.316984	−	0.549032i	0.979857	+	0.199700i	$0.0639967\pi$
$74$	3.73205	+	6.46410i	0.433842	+	0.751437i
$75$		0			0
$76$	2.19067	+	3.79435i	0.251287	+	0.435242i
$77$		0			0
$78$		0			0
$79$	8.92820			1.00450			0.502251	−	0.864722i	$-0.332505\pi$
$79$	8.92820			1.00450			0.502251	+	0.864722i	$0.332505\pi$
$80$	0.517638	−	0.896575i	0.0578737	−	0.100240i
$81$		0			0
$82$	−4.31199	−	7.46859i	−0.476180	−	0.824768i
$83$	−3.29530	+	5.70762i	−0.361706	+	0.626493i	−0.988242	−	0.152900i	$-0.951139\pi$
$83$	−3.29530	+	5.70762i	−0.361706	+	0.626493i	0.626536	+	0.779393i	$0.284472\pi$
$84$		0			0
$85$	−3.53590	−	6.12436i	−0.383522	−	0.664280i
$86$	0.133975	−	0.232051i	0.0144469	−	0.0250227i
$87$		0			0
$88$	0.133975	+	0.232051i	0.0142817	+	0.0247367i
$89$	−3.53553	−	6.12372i	−0.374766	−	0.649113i	0.615526	−	0.788116i	$-0.288944\pi$
$89$	−3.53553	−	6.12372i	−0.374766	−	0.649113i	−0.990292	+	0.139003i	$0.955610\pi$
$90$		0			0
$91$		0			0
$92$	2.73205	−	4.73205i	0.284836	−	0.493350i
$93$		0			0
$94$	−0.757875			−0.0781688
$95$	4.53590			0.465373
$96$		0			0
$97$	−9.07227	+	15.7136i	−0.921149	+	1.59548i	−0.123510	+	0.992343i	$0.539415\pi$
$97$	−9.07227	+	15.7136i	−0.921149	+	1.59548i	−0.797640	+	0.603134i	$0.793918\pi$
$98$		0			0
$99$		0			0
$100$	1.96410	+	3.40192i	0.196410	+	0.340192i
$101$	2.44949	+	4.24264i	0.243733	+	0.422159i	0.961775	−	0.273842i	$-0.0882945\pi$
$101$	2.44949	+	4.24264i	0.243733	+	0.422159i	−0.718041	+	0.696000i	$0.754961\pi$
$102$		0			0
$103$	6.17449	−	10.6945i	0.608391	−	1.05376i	−0.383115	−	0.923701i	$-0.625149\pi$
$103$	6.17449	−	10.6945i	0.608391	−	1.05376i	0.991506	−	0.130063i	$-0.0415180\pi$
$104$	−0.896575	−	1.55291i	−0.0879165	−	0.152276i
$105$		0			0
$106$	−5.46410	+	9.46410i	−0.530720	+	0.919235i
$107$	−8.69615	−	15.0622i	−0.840689	−	1.45612i	−0.889313	−	0.457299i	$-0.848817\pi$
$107$	−8.69615	−	15.0622i	−0.840689	−	1.45612i	0.0486244	−	0.998817i	$-0.484516\pi$
$108$		0			0
$109$	−2.46410	+	4.26795i	−0.236018	+	0.408795i	−0.959568	−	0.281477i	$-0.909176\pi$
$109$	−2.46410	+	4.26795i	−0.236018	+	0.408795i	0.723550	+	0.690272i	$0.242509\pi$
$110$	0.277401			0.0264492
$111$		0			0
$112$		0			0
$113$	−3.46410	−	6.00000i	−0.325875	−	0.564433i	0.655814	−	0.754923i	$-0.272326\pi$
$113$	−3.46410	−	6.00000i	−0.325875	−	0.564433i	−0.981689	+	0.190490i	$0.938992\pi$
$114$		0			0
$115$	−2.82843	−	4.89898i	−0.263752	−	0.456832i
$116$	−2.00000	+	3.46410i	−0.185695	+	0.321634i
$117$		0			0
$118$	1.27551			0.117420
$119$		0			0
$120$		0			0
$121$	5.46410	−	9.46410i	0.496737	−	0.860373i
$122$	−12.6264			−1.14314
$123$		0			0
$124$	−6.69213			−0.600971
$125$	9.24316			0.826733
$126$		0			0
$127$	13.4641			1.19475			0.597373	−	0.801964i	$-0.296211\pi$
$127$	13.4641			1.19475			0.597373	+	0.801964i	$0.296211\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−1.85641			−0.162818
$131$	−5.46739	+	9.46979i	−0.477688	+	0.827379i	−0.999673	−	0.0255752i	$-0.991858\pi$
$131$	−5.46739	+	9.46979i	−0.477688	+	0.827379i	0.521985	+	0.852955i	$0.325192\pi$
$132$		0			0
$133$		0			0
$134$	−12.4641			−1.07673
$135$		0			0
$136$	−3.41542	+	5.91567i	−0.292869	+	0.507265i
$137$	4.33013	+	7.50000i	0.369948	+	0.640768i	0.989557	−	0.144142i	$-0.0460423\pi$
$137$	4.33013	+	7.50000i	0.369948	+	0.640768i	−0.619609	+	0.784910i	$0.712709\pi$
$138$		0			0
$139$	0.397520	+	0.688524i	0.0337172	+	0.0583999i	0.882392	−	0.470516i	$-0.155932\pi$
$139$	0.397520	+	0.688524i	0.0337172	+	0.0583999i	−0.848674	+	0.528916i	$0.822599\pi$
$140$		0			0
$141$		0			0
$142$	9.46410			0.794210
$143$	0.240237	−	0.416102i	0.0200896	−	0.0347962i
$144$		0			0
$145$	2.07055	+	3.58630i	0.171950	+	0.297826i
$146$	−2.70831	+	4.69093i	−0.224141	+	0.388224i
$147$		0			0
$148$	−3.73205	−	6.46410i	−0.306773	−	0.531346i
$149$	11.4641	−	19.8564i	0.939176	−	1.62670i	0.172163	−	0.985068i	$-0.444924\pi$
$149$	11.4641	−	19.8564i	0.939176	−	1.62670i	0.767013	−	0.641632i	$-0.221742\pi$
$150$		0			0
$151$	−9.19615	−	15.9282i	−0.748372	−	1.29622i	−0.948603	−	0.316470i	$-0.897502\pi$
$151$	−9.19615	−	15.9282i	−0.748372	−	1.29622i	0.200230	−	0.979749i	$-0.435831\pi$
$152$	−2.19067	−	3.79435i	−0.177687	−	0.307763i
$153$		0			0
$154$		0			0
$155$	−3.46410	+	6.00000i	−0.278243	+	0.481932i
$156$		0			0
$157$	−9.52056			−0.759823			−0.379912	−	0.925023i	$-0.624046\pi$
$157$	−9.52056			−0.759823			−0.379912	+	0.925023i	$0.624046\pi$
$158$	−8.92820			−0.710290
$159$		0			0
$160$	−0.517638	+	0.896575i	−0.0409229	+	0.0708805i
$161$		0			0
$162$		0			0
$163$	6.66025	+	11.5359i	0.521671	+	0.903561i	0.999682	+	0.0252074i	$0.00802461\pi$
$163$	6.66025	+	11.5359i	0.521671	+	0.903561i	−0.478011	+	0.878354i	$0.658642\pi$
$164$	4.31199	+	7.46859i	0.336710	+	0.583199i
$165$		0			0
$166$	3.29530	−	5.70762i	0.255765	−	0.442997i
$167$	−0.757875	−	1.31268i	−0.0586461	−	0.101578i	0.835212	−	0.549928i	$-0.185345\pi$
$167$	−0.757875	−	1.31268i	−0.0586461	−	0.101578i	−0.893858	+	0.448350i	$0.852012\pi$
$168$		0			0
$169$	4.89230	−	8.47372i	0.376331	−	0.651825i
$170$	3.53590	+	6.12436i	0.271191	+	0.469717i
$171$		0			0
$172$	−0.133975	+	0.232051i	−0.0102155	+	0.0176937i
$173$	6.69213			0.508793			0.254397	−	0.967100i	$-0.418123\pi$
$173$	6.69213			0.508793			0.254397	+	0.967100i	$0.418123\pi$
$174$		0			0
$175$		0			0
$176$	−0.133975	−	0.232051i	−0.0100987	−	0.0174915i
$177$		0			0
$178$	3.53553	+	6.12372i	0.264999	+	0.458993i
$179$	2.53590	−	4.39230i	0.189542	−	0.328296i	−0.755556	−	0.655084i	$-0.772633\pi$
$179$	2.53590	−	4.39230i	0.189542	−	0.328296i	0.945098	+	0.326788i	$0.105966\pi$
$180$		0			0
$181$	16.9706			1.26141			0.630706	−	0.776022i	$-0.282765\pi$
$181$	16.9706			1.26141			0.630706	+	0.776022i	$0.282765\pi$
$182$		0			0
$183$		0			0
$184$	−2.73205	+	4.73205i	−0.201409	+	0.348851i
$185$	−7.72741			−0.568130
$186$		0			0
$187$	−1.83032			−0.133846
$188$	0.757875			0.0552737
$189$		0			0
$190$	−4.53590			−0.329069
$191$	−14.9282			−1.08017			−0.540083	−	0.841611i	$-0.681607\pi$
$191$	−14.9282			−1.08017			−0.540083	+	0.841611i	$0.681607\pi$
$192$		0			0
$193$	15.0526			1.08351			0.541753	−	0.840537i	$-0.317761\pi$
$193$	15.0526			1.08351			0.541753	+	0.840537i	$0.317761\pi$
$194$	9.07227	−	15.7136i	0.651351	−	1.12817i
$195$		0			0
$196$		0			0
$197$	16.9282			1.20608			0.603042	−	0.797709i	$-0.293955\pi$
$197$	16.9282			1.20608			0.603042	+	0.797709i	$0.293955\pi$
$198$		0			0
$199$	13.1440	−	22.7661i	0.931755	−	1.61385i	0.151435	−	0.988467i	$-0.451611\pi$
$199$	13.1440	−	22.7661i	0.931755	−	1.61385i	0.780320	−	0.625380i	$-0.215056\pi$
$200$	−1.96410	−	3.40192i	−0.138883	−	0.240552i
$201$		0			0
$202$	−2.44949	−	4.24264i	−0.172345	−	0.298511i
$203$		0			0
$204$		0			0
$205$	8.92820			0.623573
$206$	−6.17449	+	10.6945i	−0.430197	+	0.745124i
$207$		0			0
$208$	0.896575	+	1.55291i	0.0621663	+	0.107675i
$209$	0.586988	−	1.01669i	0.0406028	−	0.0703262i
$210$		0			0
$211$	−9.46410	−	16.3923i	−0.651536	−	1.12849i	−0.982750	−	0.184937i	$-0.940792\pi$
$211$	−9.46410	−	16.3923i	−0.651536	−	1.12849i	0.331215	−	0.943555i	$-0.392542\pi$
$212$	5.46410	−	9.46410i	0.375276	−	0.649997i
$213$		0			0
$214$	8.69615	+	15.0622i	0.594457	+	1.02963i
$215$	0.138701	+	0.240237i	0.00945931	+	0.0163840i
$216$		0			0
$217$		0			0
$218$	2.46410	−	4.26795i	0.166890	−	0.289062i
$219$		0			0
$220$	−0.277401			−0.0187024
$221$	12.2487			0.823937
$222$		0			0
$223$	−3.58630	+	6.21166i	−0.240157	+	0.415963i	−0.960759	−	0.277385i	$-0.910532\pi$
$223$	−3.58630	+	6.21166i	−0.240157	+	0.415963i	0.720602	+	0.693349i	$0.243865\pi$
$224$		0			0
$225$		0			0
$226$	3.46410	+	6.00000i	0.230429	+	0.399114i
$227$	13.8325	+	23.9587i	0.918098	+	1.59019i	0.802300	+	0.596920i	$0.203609\pi$
$227$	13.8325	+	23.9587i	0.918098	+	1.59019i	0.115798	+	0.993273i	$0.463057\pi$
$228$		0			0
$229$	0.240237	−	0.416102i	0.0158753	−	0.0274968i	−0.857979	−	0.513685i	$-0.828280\pi$
$229$	0.240237	−	0.416102i	0.0158753	−	0.0274968i	0.873854	+	0.486189i	$0.161613\pi$
$230$	2.82843	+	4.89898i	0.186501	+	0.323029i
$231$		0			0
$232$	2.00000	−	3.46410i	0.131306	−	0.227429i
$233$	0.0621778	+	0.107695i	0.00407340	+	0.00705534i	0.868055	−	0.496468i	$-0.165370\pi$
$233$	0.0621778	+	0.107695i	0.00407340	+	0.00705534i	−0.863982	+	0.503524i	$0.832037\pi$
$234$		0			0
$235$	0.392305	−	0.679492i	0.0255911	−	0.0443252i
$236$	−1.27551			−0.0830288
$237$		0			0
$238$		0			0
$239$	0.464102	+	0.803848i	0.0300202	+	0.0519966i	0.880645	−	0.473776i	$-0.157109\pi$
$239$	0.464102	+	0.803848i	0.0300202	+	0.0519966i	−0.850625	+	0.525773i	$0.823776\pi$
$240$		0			0
$241$	3.13801	+	5.43520i	0.202137	+	0.350112i	0.949217	−	0.314623i	$-0.101878\pi$
$241$	3.13801	+	5.43520i	0.202137	+	0.350112i	−0.747080	+	0.664735i	$0.768545\pi$
$242$	−5.46410	+	9.46410i	−0.351246	+	0.608375i
$243$		0			0
$244$	12.6264			0.808322
$245$		0			0
$246$		0			0
$247$	−3.92820	+	6.80385i	−0.249946	+	0.432918i
$248$	6.69213			0.424951
$249$		0			0
$250$	−9.24316			−0.584589
$251$	0.795040			0.0501824			0.0250912	−	0.999685i	$-0.492012\pi$
$251$	0.795040			0.0501824			0.0250912	+	0.999685i	$0.492012\pi$
$252$		0			0
$253$	−1.46410			−0.0920473
$254$	−13.4641			−0.844813
$255$		0			0
$256$	1.00000			0.0625000
$257$	−5.01910	+	8.69333i	−0.313083	+	0.542275i	−0.979028	−	0.203725i	$-0.934695\pi$
$257$	−5.01910	+	8.69333i	−0.313083	+	0.542275i	0.665945	+	0.746001i	$0.268028\pi$
$258$		0			0
$259$		0			0
$260$	1.85641			0.115129
$261$		0			0
$262$	5.46739	−	9.46979i	0.337776	−	0.585046i
$263$	−4.26795	−	7.39230i	−0.263173	−	0.455829i	0.703910	−	0.710289i	$-0.251436\pi$
$263$	−4.26795	−	7.39230i	−0.263173	−	0.455829i	−0.967083	+	0.254460i	$0.918102\pi$
$264$		0			0
$265$	−5.65685	−	9.79796i	−0.347498	−	0.601884i
$266$		0			0
$267$		0			0
$268$	12.4641			0.761366
$269$	2.82843	−	4.89898i	0.172452	−	0.298696i	−0.766824	−	0.641857i	$-0.778164\pi$
$269$	2.82843	−	4.89898i	0.172452	−	0.298696i	0.939277	+	0.343161i	$0.111498\pi$
$270$		0			0
$271$	6.55343	+	11.3509i	0.398093	+	0.689516i	0.993491	−	0.113914i	$-0.0363390\pi$
$271$	6.55343	+	11.3509i	0.398093	+	0.689516i	−0.595398	+	0.803431i	$0.703006\pi$
$272$	3.41542	−	5.91567i	0.207090	−	0.358690i
$273$		0			0
$274$	−4.33013	−	7.50000i	−0.261593	−	0.453092i
$275$	0.526279	−	0.911543i	0.0317358	−	0.0549681i
$276$		0			0
$277$	−15.7321	−	27.2487i	−0.945247	−	1.63722i	−0.755255	−	0.655431i	$-0.772487\pi$
$277$	−15.7321	−	27.2487i	−0.945247	−	1.63722i	−0.189992	−	0.981786i	$-0.560846\pi$
$278$	−0.397520	−	0.688524i	−0.0238417	−	0.0412949i
$279$		0			0
$280$		0			0
$281$	8.92820	−	15.4641i	0.532612	−	0.922511i	−0.466663	−	0.884435i	$-0.654544\pi$
$281$	8.92820	−	15.4641i	0.532612	−	0.922511i	0.999275	−	0.0380757i	$-0.0121228\pi$
$282$		0			0
$283$	15.0759			0.896168			0.448084	−	0.893992i	$-0.352107\pi$
$283$	15.0759			0.896168			0.448084	+	0.893992i	$0.352107\pi$
$284$	−9.46410			−0.561591
$285$		0			0
$286$	−0.240237	+	0.416102i	−0.0142055	+	0.0246046i
$287$		0			0
$288$		0			0
$289$	−14.8301	−	25.6865i	−0.872360	−	1.51097i
$290$	−2.07055	−	3.58630i	−0.121587	−	0.210595i
$291$		0			0
$292$	2.70831	−	4.69093i	0.158492	−	0.274516i
$293$	4.62158	+	8.00481i	0.269995	+	0.467646i	0.968860	−	0.247608i	$-0.0796445\pi$
$293$	4.62158	+	8.00481i	0.269995	+	0.467646i	−0.698865	+	0.715254i	$0.746311\pi$
$294$		0			0
$295$	−0.660254	+	1.14359i	−0.0384415	+	0.0665826i
$296$	3.73205	+	6.46410i	0.216921	+	0.375718i
$297$		0			0
$298$	−11.4641	+	19.8564i	−0.664098	+	1.15025i
$299$	9.79796			0.566631
$300$		0			0
$301$		0			0
$302$	9.19615	+	15.9282i	0.529179	+	0.916565i
$303$		0			0
$304$	2.19067	+	3.79435i	0.125644	+	0.217621i
$305$	6.53590	−	11.3205i	0.374244	−	0.648210i
$306$		0			0
$307$	−1.17398			−0.0670024			−0.0335012	−	0.999439i	$-0.510666\pi$
$307$	−1.17398			−0.0670024			−0.0335012	+	0.999439i	$0.510666\pi$
$308$		0			0
$309$		0			0
$310$	3.46410	−	6.00000i	0.196748	−	0.340777i
$311$	−7.45001			−0.422451			−0.211226	−	0.977437i	$-0.567745\pi$
$311$	−7.45001			−0.422451			−0.211226	+	0.977437i	$0.567745\pi$
$312$		0			0
$313$	−6.27603			−0.354742			−0.177371	−	0.984144i	$-0.556759\pi$
$313$	−6.27603			−0.354742			−0.177371	+	0.984144i	$0.556759\pi$
$314$	9.52056			0.537276
$315$		0			0
$316$	8.92820			0.502251
$317$	26.0000			1.46031			0.730153	−	0.683284i	$-0.239449\pi$
$317$	26.0000			1.46031			0.730153	+	0.683284i	$0.239449\pi$
$318$		0			0
$319$	1.07180			0.0600091
$320$	0.517638	−	0.896575i	0.0289368	−	0.0501201i
$321$		0			0
$322$		0			0
$323$	29.9282			1.66525
$324$		0			0
$325$	−3.52193	+	6.10016i	−0.195362	+	0.338376i
$326$	−6.66025	−	11.5359i	−0.368877	−	0.638914i
$327$		0			0
$328$	−4.31199	−	7.46859i	−0.238090	−	0.412384i
$329$		0			0
$330$		0			0
$331$	−11.4641			−0.630124			−0.315062	−	0.949071i	$-0.602025\pi$
$331$	−11.4641			−0.630124			−0.315062	+	0.949071i	$0.602025\pi$
$332$	−3.29530	+	5.70762i	−0.180853	+	0.313246i
$333$		0			0
$334$	0.757875	+	1.31268i	0.0414691	+	0.0718265i
$335$	6.45189	−	11.1750i	0.352505	−	0.610556i
$336$		0			0
$337$	3.50000	+	6.06218i	0.190657	+	0.330228i	0.945468	−	0.325714i	$-0.105605\pi$
$337$	3.50000	+	6.06218i	0.190657	+	0.330228i	−0.754811	+	0.655942i	$0.772271\pi$
$338$	−4.89230	+	8.47372i	−0.266106	+	0.460910i
$339$		0			0
$340$	−3.53590	−	6.12436i	−0.191761	−	0.332140i
$341$	0.896575	+	1.55291i	0.0485523	+	0.0840950i
$342$		0			0
$343$		0			0
$344$	0.133975	−	0.232051i	0.00722343	−	0.0125113i
$345$		0			0
$346$	−6.69213			−0.359771
$347$	9.58846			0.514735			0.257368	−	0.966314i	$-0.417145\pi$
$347$	9.58846			0.514735			0.257368	+	0.966314i	$0.417145\pi$
$348$		0			0
$349$	−4.00240	+	6.93237i	−0.214244	+	0.371081i	−0.953038	−	0.302850i	$-0.902062\pi$
$349$	−4.00240	+	6.93237i	−0.214244	+	0.371081i	0.738795	+	0.673931i	$0.235395\pi$
$350$		0			0
$351$		0			0
$352$	0.133975	+	0.232051i	0.00714087	+	0.0123683i
$353$	−12.5063	−	21.6615i	−0.665641	−	1.15292i	−0.979111	−	0.203327i	$-0.934825\pi$
$353$	−12.5063	−	21.6615i	−0.665641	−	1.15292i	0.313470	−	0.949598i	$-0.398509\pi$
$354$		0			0
$355$	−4.89898	+	8.48528i	−0.260011	+	0.450352i
$356$	−3.53553	−	6.12372i	−0.187383	−	0.324557i
$357$		0			0
$358$	−2.53590	+	4.39230i	−0.134026	+	0.232141i
$359$	3.73205	+	6.46410i	0.196970	+	0.341162i	0.947545	−	0.319624i	$-0.103556\pi$
$359$	3.73205	+	6.46410i	0.196970	+	0.341162i	−0.750574	+	0.660786i	$0.770223\pi$
$360$		0			0
$361$	−0.0980762	+	0.169873i	−0.00516191	+	0.00894068i
$362$	−16.9706			−0.891953
$363$		0			0
$364$		0			0
$365$	−2.80385	−	4.85641i	−0.146760	−	0.254196i
$366$		0			0
$367$	9.28032	+	16.0740i	0.484429	+	0.839055i	0.999840	−	0.0178877i	$-0.00569413\pi$
$367$	9.28032	+	16.0740i	0.484429	+	0.839055i	−0.515411	+	0.856943i	$0.672361\pi$
$368$	2.73205	−	4.73205i	0.142418	−	0.246675i
$369$		0			0
$370$	7.72741			0.401729
$371$		0			0
$372$		0			0
$373$	5.39230	−	9.33975i	0.279203	−	0.483594i	−0.691984	−	0.721913i	$-0.743263\pi$
$373$	5.39230	−	9.33975i	0.279203	−	0.483594i	0.971187	+	0.238319i	$0.0765964\pi$
$374$	1.83032			0.0946434
$375$		0			0
$376$	−0.757875			−0.0390844
$377$	−7.17260			−0.369408
$378$		0			0
$379$	13.5885			0.697992			0.348996	−	0.937124i	$-0.386523\pi$
$379$	13.5885			0.697992			0.348996	+	0.937124i	$0.386523\pi$
$380$	4.53590			0.232687
$381$		0			0
$382$	14.9282			0.763793
$383$	−13.6617	+	23.6627i	−0.698078	+	1.20911i	0.271054	+	0.962564i	$0.412628\pi$
$383$	−13.6617	+	23.6627i	−0.698078	+	1.20911i	−0.969132	+	0.246543i	$0.920705\pi$
$384$		0			0
$385$		0			0
$386$	−15.0526			−0.766155
$387$		0			0
$388$	−9.07227	+	15.7136i	−0.460575	+	0.797739i
$389$	4.00000	+	6.92820i	0.202808	+	0.351274i	0.949432	−	0.313972i	$-0.101660\pi$
$389$	4.00000	+	6.92820i	0.202808	+	0.351274i	−0.746624	+	0.665246i	$0.768327\pi$
$390$		0			0
$391$	−18.6622	−	32.3238i	−0.943787	−	1.63469i
$392$		0			0
$393$		0			0
$394$	−16.9282			−0.852831
$395$	4.62158	−	8.00481i	0.232537	−	0.402766i
$396$		0			0
$397$	6.55343	+	11.3509i	0.328907	+	0.569684i	0.982295	−	0.187339i	$-0.0599863\pi$
$397$	6.55343	+	11.3509i	0.328907	+	0.569684i	−0.653388	+	0.757023i	$0.726653\pi$
$398$	−13.1440	+	22.7661i	−0.658850	+	1.14116i
$399$		0			0
$400$	1.96410	+	3.40192i	0.0982051	+	0.170096i
$401$	−11.8923	+	20.5981i	−0.593873	+	1.02862i	0.399831	+	0.916589i	$0.369069\pi$
$401$	−11.8923	+	20.5981i	−0.593873	+	1.02862i	−0.993705	+	0.112030i	$0.964265\pi$
$402$		0			0
$403$	−6.00000	−	10.3923i	−0.298881	−	0.517678i
$404$	2.44949	+	4.24264i	0.121867	+	0.211079i
$405$		0			0
$406$		0			0
$407$	−1.00000	+	1.73205i	−0.0495682	+	0.0858546i
$408$		0			0
$409$	−4.48288			−0.221664			−0.110832	−	0.993839i	$-0.535352\pi$
$409$	−4.48288			−0.221664			−0.110832	+	0.993839i	$0.535352\pi$
$410$	−8.92820			−0.440933
$411$		0			0
$412$	6.17449	−	10.6945i	0.304195	−	0.526882i
$413$		0			0
$414$		0			0
$415$	3.41154	+	5.90897i	0.167466	+	0.290060i
$416$	−0.896575	−	1.55291i	−0.0439582	−	0.0761379i
$417$		0			0
$418$	−0.586988	+	1.01669i	−0.0287105	+	0.0497281i
$419$	−18.0938	−	31.3393i	−0.883939	−	1.53103i	−0.846925	−	0.531712i	$-0.821549\pi$
$419$	−18.0938	−	31.3393i	−0.883939	−	1.53103i	−0.0370132	−	0.999315i	$-0.511784\pi$
$420$		0			0
$421$	−3.80385	+	6.58846i	−0.185388	+	0.321102i	−0.943707	−	0.330782i	$-0.892688\pi$
$421$	−3.80385	+	6.58846i	−0.185388	+	0.321102i	0.758319	+	0.651884i	$0.226021\pi$
$422$	9.46410	+	16.3923i	0.460705	+	0.797965i
$423$		0			0
$424$	−5.46410	+	9.46410i	−0.265360	+	0.459617i
$425$	26.8329			1.30159
$426$		0			0
$427$		0			0
$428$	−8.69615	−	15.0622i	−0.420344	−	0.728058i
$429$		0			0
$430$	−0.138701	−	0.240237i	−0.00668874	−	0.0115852i
$431$	−5.07180	+	8.78461i	−0.244300	+	0.423140i	−0.961935	−	0.273280i	$-0.911891\pi$
$431$	−5.07180	+	8.78461i	−0.244300	+	0.423140i	0.717635	+	0.696420i	$0.245225\pi$
$432$		0			0
$433$	19.8362			0.953265			0.476632	−	0.879103i	$-0.341857\pi$
$433$	19.8362			0.953265			0.476632	+	0.879103i	$0.341857\pi$
$434$		0			0
$435$		0			0
$436$	−2.46410	+	4.26795i	−0.118009	+	0.204398i
$437$	23.9401			1.14521
$438$		0			0
$439$	−19.5959			−0.935262			−0.467631	−	0.883924i	$-0.654892\pi$
$439$	−19.5959			−0.935262			−0.467631	+	0.883924i	$0.654892\pi$
$440$	0.277401			0.0132246
$441$		0			0
$442$	−12.2487			−0.582612
$443$	−16.3205			−0.775411			−0.387705	−	0.921783i	$-0.626732\pi$
$443$	−16.3205			−0.775411			−0.387705	+	0.921783i	$0.626732\pi$
$444$		0			0
$445$	−7.32051			−0.347025
$446$	3.58630	−	6.21166i	0.169816	−	0.294130i
$447$		0			0
$448$		0			0
$449$	−23.7846			−1.12247			−0.561233	−	0.827658i	$-0.689673\pi$
$449$	−23.7846			−1.12247			−0.561233	+	0.827658i	$0.689673\pi$
$450$		0			0
$451$	1.15539	−	2.00120i	0.0544054	−	0.0942329i
$452$	−3.46410	−	6.00000i	−0.162938	−	0.282216i
$453$		0			0
$454$	−13.8325	−	23.9587i	−0.649194	−	1.12444i
$455$		0			0
$456$		0			0
$457$	−31.0526			−1.45258			−0.726289	−	0.687390i	$-0.758756\pi$
$457$	−31.0526			−1.45258			−0.726289	+	0.687390i	$0.758756\pi$
$458$	−0.240237	+	0.416102i	−0.0112255	+	0.0194432i
$459$		0			0
$460$	−2.82843	−	4.89898i	−0.131876	−	0.228416i
$461$	5.51815	−	9.55772i	0.257006	−	0.445148i	−0.708432	−	0.705779i	$-0.750597\pi$
$461$	5.51815	−	9.55772i	0.257006	−	0.445148i	0.965438	+	0.260631i	$0.0839306\pi$
$462$		0			0
$463$	15.3205	+	26.5359i	0.712004	+	1.23323i	0.964104	+	0.265526i	$0.0855457\pi$
$463$	15.3205	+	26.5359i	0.712004	+	1.23323i	−0.252099	+	0.967701i	$0.581121\pi$
$464$	−2.00000	+	3.46410i	−0.0928477	+	0.160817i
$465$		0			0
$466$	−0.0621778	−	0.107695i	−0.00288033	−	0.00498888i
$467$	−4.58939	−	7.94906i	−0.212372	−	0.367839i	0.740085	−	0.672514i	$-0.234785\pi$
$467$	−4.58939	−	7.94906i	−0.212372	−	0.367839i	−0.952456	+	0.304675i	$0.901452\pi$
$468$		0			0
$469$		0			0
$470$	−0.392305	+	0.679492i	−0.0180957	+	0.0313426i
$471$		0			0
$472$	1.27551			0.0587102
$473$	0.0717968			0.00330122
$474$		0			0
$475$	−8.60540	+	14.9050i	−0.394843	+	0.683888i
$476$		0			0
$477$		0			0
$478$	−0.464102	−	0.803848i	−0.0212275	−	0.0367671i
$479$	2.07055	+	3.58630i	0.0946060	+	0.163862i	0.909444	−	0.415826i	$-0.136508\pi$
$479$	2.07055	+	3.58630i	0.0946060	+	0.163862i	−0.814838	+	0.579689i	$0.803174\pi$
$480$		0			0
$481$	6.69213	−	11.5911i	0.305135	−	0.528509i
$482$	−3.13801	−	5.43520i	−0.142933	−	0.247567i
$483$		0			0
$484$	5.46410	−	9.46410i	0.248368	−	0.430186i
$485$	9.39230	+	16.2679i	0.426483	+	0.738690i
$486$		0			0
$487$	1.39230	−	2.41154i	0.0630914	−	0.109277i	−0.832754	−	0.553643i	$-0.813237\pi$
$487$	1.39230	−	2.41154i	0.0630914	−	0.109277i	0.895846	+	0.444365i	$0.146571\pi$
$488$	−12.6264			−0.571570
$489$		0			0
$490$		0			0
$491$	9.69615	+	16.7942i	0.437581	+	0.757913i	0.997502	−	0.0706330i	$-0.0225019\pi$
$491$	9.69615	+	16.7942i	0.437581	+	0.757913i	−0.559921	+	0.828546i	$0.689169\pi$
$492$		0			0
$493$	13.6617	+	23.6627i	0.615290	+	1.06571i
$494$	3.92820	−	6.80385i	0.176738	−	0.306120i
$495$		0			0
$496$	−6.69213			−0.300486
$497$		0			0
$498$		0			0
$499$	−16.6962	+	28.9186i	−0.747422	+	1.29457i	0.201632	+	0.979461i	$0.435376\pi$
$499$	−16.6962	+	28.9186i	−0.747422	+	1.29457i	−0.949054	+	0.315112i	$0.897958\pi$
$500$	9.24316			0.413367
$501$		0			0
$502$	−0.795040			−0.0354843
$503$	−12.3490			−0.550614			−0.275307	−	0.961356i	$-0.588780\pi$
$503$	−12.3490			−0.550614			−0.275307	+	0.961356i	$0.588780\pi$
$504$		0			0
$505$	5.07180			0.225692
$506$	1.46410			0.0650873
$507$		0			0
$508$	13.4641			0.597373
$509$	−10.7961	+	18.6993i	−0.478527	+	0.828834i	−0.999697	−	0.0246194i	$-0.992163\pi$
$509$	−10.7961	+	18.6993i	−0.478527	+	0.828834i	0.521169	+	0.853453i	$0.325496\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	5.01910	−	8.69333i	0.221383	−	0.383446i
$515$	−6.39230	−	11.0718i	−0.281679	−	0.487882i
$516$		0			0
$517$	−0.101536	−	0.175865i	−0.00446555	−	0.00773455i
$518$		0			0
$519$		0			0
$520$	−1.85641			−0.0814088
$521$	16.8876	−	29.2502i	0.739860	−	1.28147i	−0.212699	−	0.977118i	$-0.568225\pi$
$521$	16.8876	−	29.2502i	0.739860	−	1.28147i	0.952558	−	0.304357i	$-0.0984414\pi$
$522$		0			0
$523$	10.3664	+	17.9551i	0.453289	+	0.785120i	0.998588	−	0.0531215i	$-0.0169170\pi$
$523$	10.3664	+	17.9551i	0.453289	+	0.785120i	−0.545299	+	0.838242i	$0.683584\pi$
$524$	−5.46739	+	9.46979i	−0.238844	+	0.413690i
$525$		0			0
$526$	4.26795	+	7.39230i	0.186091	+	0.322320i
$527$	−22.8564	+	39.5885i	−0.995641	+	1.72450i
$528$		0			0
$529$	−3.42820	−	5.93782i	−0.149052	−	0.258166i
$530$	5.65685	+	9.79796i	0.245718	+	0.425596i
$531$		0			0
$532$		0			0
$533$	−7.73205	+	13.3923i	−0.334912	+	0.580085i
$534$		0			0
$535$	−18.0058			−0.778460
$536$	−12.4641			−0.538367
$537$		0			0
$538$	−2.82843	+	4.89898i	−0.121942	+	0.211210i
$539$		0			0
$540$		0			0
$541$	−7.66025	−	13.2679i	−0.329340	−	0.570434i	0.653041	−	0.757323i	$-0.273493\pi$
$541$	−7.66025	−	13.2679i	−0.329340	−	0.570434i	−0.982381	+	0.186889i	$0.940160\pi$
$542$	−6.55343	−	11.3509i	−0.281494	−	0.487562i
$543$		0			0
$544$	−3.41542	+	5.91567i	−0.146435	+	0.253632i
$545$	2.55103	+	4.41851i	0.109274	+	0.189268i
$546$		0			0
$547$	−17.1865	+	29.7679i	−0.734843	+	1.27279i	0.219949	+	0.975511i	$0.429411\pi$
$547$	−17.1865	+	29.7679i	−0.734843	+	1.27279i	−0.954792	+	0.297274i	$0.903922\pi$
$548$	4.33013	+	7.50000i	0.184974	+	0.320384i
$549$		0			0
$550$	−0.526279	+	0.911543i	−0.0224406	+	0.0388683i
$551$	−17.5254			−0.746606
$552$		0			0
$553$		0			0
$554$	15.7321	+	27.2487i	0.668391	+	1.15769i
$555$		0			0
$556$	0.397520	+	0.688524i	0.0168586	+	0.0291999i
$557$	−3.46410	+	6.00000i	−0.146779	+	0.254228i	−0.930035	−	0.367471i	$-0.880224\pi$
$557$	−3.46410	+	6.00000i	−0.146779	+	0.254228i	0.783256	+	0.621699i	$0.213557\pi$
$558$		0			0
$559$	−0.480473			−0.0203219
$560$		0			0
$561$		0			0
$562$	−8.92820	+	15.4641i	−0.376614	+	0.652314i
$563$	−18.2461			−0.768980			−0.384490	−	0.923129i	$-0.625623\pi$
$563$	−18.2461			−0.768980			−0.384490	+	0.923129i	$0.625623\pi$
$564$		0			0
$565$	−7.17260			−0.301754
$566$	−15.0759			−0.633686
$567$		0			0
$568$	9.46410			0.397105
$569$	25.7846			1.08095			0.540474	−	0.841361i	$-0.318245\pi$
$569$	25.7846			1.08095			0.540474	+	0.841361i	$0.318245\pi$
$570$		0			0
$571$	−33.0526			−1.38321			−0.691603	−	0.722278i	$-0.743095\pi$
$571$	−33.0526			−1.38321			−0.691603	+	0.722278i	$0.743095\pi$
$572$	0.240237	−	0.416102i	0.0100448	−	0.0173981i
$573$		0			0
$574$		0			0
$575$	21.4641			0.895115
$576$		0			0
$577$	−13.7446	+	23.8064i	−0.572196	+	0.991072i	0.424144	+	0.905595i	$0.360575\pi$
$577$	−13.7446	+	23.8064i	−0.572196	+	0.991072i	−0.996340	+	0.0854776i	$0.972758\pi$
$578$	14.8301	+	25.6865i	0.616852	+	1.06842i
$579$		0			0
$580$	2.07055	+	3.58630i	0.0859750	+	0.148913i
$581$		0			0
$582$		0			0
$583$	−2.92820			−0.121274
$584$	−2.70831	+	4.69093i	−0.112071	+	0.194112i
$585$		0			0
$586$	−4.62158	−	8.00481i	−0.190916	−	0.330676i
$587$	20.9408	−	36.2705i	0.864319	−	1.49704i	−0.00340370	−	0.999994i	$-0.501083\pi$
$587$	20.9408	−	36.2705i	0.864319	−	1.49704i	0.867722	−	0.497049i	$-0.165583\pi$
$588$		0			0
$589$	−14.6603	−	25.3923i	−0.604065	−	1.04627i
$590$	0.660254	−	1.14359i	0.0271822	−	0.0470810i
$591$		0			0
$592$	−3.73205	−	6.46410i	−0.153386	−	0.265673i
$593$	−8.43451	−	14.6090i	−0.346364	−	0.599920i	0.639237	−	0.769010i	$-0.279250\pi$
$593$	−8.43451	−	14.6090i	−0.346364	−	0.599920i	−0.985601	+	0.169090i	$0.945917\pi$
$594$		0			0
$595$		0			0
$596$	11.4641	−	19.8564i	0.469588	−	0.813350i
$597$		0			0
$598$	−9.79796			−0.400668
$599$	−4.78461			−0.195494			−0.0977469	−	0.995211i	$-0.531164\pi$
$599$	−4.78461			−0.195494			−0.0977469	+	0.995211i	$0.531164\pi$
$600$		0			0
$601$	−1.67303	+	2.89778i	−0.0682444	+	0.118203i	−0.898129	−	0.439733i	$-0.855073\pi$
$601$	−1.67303	+	2.89778i	−0.0682444	+	0.118203i	0.829884	+	0.557936i	$0.188406\pi$
$602$		0			0
$603$		0			0
$604$	−9.19615	−	15.9282i	−0.374186	−	0.648109i
$605$	−5.65685	−	9.79796i	−0.229984	−	0.398344i
$606$		0			0
$607$	−1.13681	+	1.96902i	−0.0461418	+	0.0799199i	−0.888174	−	0.459507i	$-0.848026\pi$
$607$	−1.13681	+	1.96902i	−0.0461418	+	0.0799199i	0.842032	+	0.539427i	$0.181359\pi$
$608$	−2.19067	−	3.79435i	−0.0888434	−	0.153881i
$609$		0			0
$610$	−6.53590	+	11.3205i	−0.264631	+	0.458354i
$611$	0.679492	+	1.17691i	0.0274893	+	0.0476129i
$612$		0			0
$613$	−12.4641	+	21.5885i	−0.503420	+	0.871950i	0.496572	+	0.867996i	$0.334592\pi$
$613$	−12.4641	+	21.5885i	−0.503420	+	0.871950i	−0.999992	+	0.00395396i	$0.998741\pi$
$614$	1.17398			0.0473779
$615$		0			0
$616$		0			0
$617$	−1.57180	−	2.72243i	−0.0632782	−	0.109601i	0.832651	−	0.553798i	$-0.186822\pi$
$617$	−1.57180	−	2.72243i	−0.0632782	−	0.109601i	−0.895929	+	0.444197i	$0.853489\pi$
$618$		0			0
$619$	−15.8523	−	27.4570i	−0.637159	−	1.10359i	−0.986053	−	0.166430i	$-0.946776\pi$
$619$	−15.8523	−	27.4570i	−0.637159	−	1.10359i	0.348894	−	0.937162i	$-0.386557\pi$
$620$	−3.46410	+	6.00000i	−0.139122	+	0.240966i
$621$		0			0
$622$	7.45001			0.298718
$623$		0			0
$624$		0			0
$625$	−5.03590	+	8.72243i	−0.201436	+	0.348897i
$626$	6.27603			0.250841
$627$		0			0
$628$	−9.52056			−0.379912
$629$	−50.9860			−2.03295
$630$		0			0
$631$	−19.7128			−0.784755			−0.392377	−	0.919804i	$-0.628347\pi$
$631$	−19.7128			−0.784755			−0.392377	+	0.919804i	$0.628347\pi$
$632$	−8.92820			−0.355145
$633$		0			0
$634$	−26.0000			−1.03259
$635$	6.96953	−	12.0716i	0.276577	−	0.479046i
$636$		0			0
$637$		0			0
$638$	−1.07180			−0.0424328
$639$		0			0
$640$	−0.517638	+	0.896575i	−0.0204614	+	0.0354403i
$641$	2.03590	+	3.52628i	0.0804132	+	0.139280i	0.903427	−	0.428741i	$-0.141043\pi$
$641$	2.03590	+	3.52628i	0.0804132	+	0.139280i	−0.823014	+	0.568021i	$0.807709\pi$
$642$		0			0
$643$	−22.4565	−	38.8959i	−0.885599	−	1.53390i	−0.845025	−	0.534726i	$-0.820415\pi$
$643$	−22.4565	−	38.8959i	−0.885599	−	1.53390i	−0.0405737	−	0.999177i	$-0.512919\pi$
$644$		0			0
$645$		0			0
$646$	−29.9282			−1.17751
$647$	−10.9348	+	18.9396i	−0.429890	+	0.744592i	−0.996863	−	0.0791447i	$-0.974781\pi$
$647$	−10.9348	+	18.9396i	−0.429890	+	0.744592i	0.566973	+	0.823736i	$0.308114\pi$
$648$		0			0
$649$	0.170886	+	0.295984i	0.00670787	+	0.0116184i
$650$	3.52193	−	6.10016i	0.138141	−	0.239268i
$651$		0			0
$652$	6.66025	+	11.5359i	0.260836	+	0.451781i
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$		0			0
$655$	5.66025	+	9.80385i	0.221164	+	0.383068i
$656$	4.31199	+	7.46859i	0.168355	+	0.291599i
$657$		0			0
$658$		0			0
$659$	−24.1244	+	41.7846i	−0.939751	+	1.62770i	−0.173818	+	0.984778i	$0.555610\pi$
$659$	−24.1244	+	41.7846i	−0.939751	+	1.62770i	−0.765934	+	0.642919i	$0.777723\pi$
$660$		0			0
$661$		0			0			−	1.00000i	$-0.5\pi$
$661$		0			0				1.00000i	$0.5\pi$
$662$	11.4641			0.445565
$663$		0			0
$664$	3.29530	−	5.70762i	0.127882	−	0.221499i
$665$		0			0
$666$		0			0
$667$	10.9282	+	18.9282i	0.423142	+	0.732903i
$668$	−0.757875	−	1.31268i	−0.0293231	−	0.0507890i
$669$		0			0
$670$	−6.45189	+	11.1750i	−0.249258	+	0.431728i
$671$	−1.69161	−	2.92996i	−0.0653041	−	0.113110i
$672$		0			0
$673$	−20.7846	+	36.0000i	−0.801188	+	1.38770i	0.117647	+	0.993055i	$0.462465\pi$
$673$	−20.7846	+	36.0000i	−0.801188	+	1.38770i	−0.918835	+	0.394643i	$0.870868\pi$
$674$	−3.50000	−	6.06218i	−0.134815	−	0.233506i
$675$		0			0
$676$	4.89230	−	8.47372i	0.188166	−	0.325912i
$677$	−5.37945			−0.206749			−0.103375	−	0.994642i	$-0.532964\pi$
$677$	−5.37945			−0.206749			−0.103375	+	0.994642i	$0.532964\pi$
$678$		0			0
$679$		0			0
$680$	3.53590	+	6.12436i	0.135596	+	0.234858i
$681$		0			0
$682$	−0.896575	−	1.55291i	−0.0343316	−	0.0594642i
$683$	−19.1603	+	33.1865i	−0.733147	+	1.26985i	0.222385	+	0.974959i	$0.428616\pi$
$683$	−19.1603	+	33.1865i	−0.733147	+	1.26985i	−0.955532	+	0.294888i	$0.904718\pi$
$684$		0			0
$685$	8.96575			0.342564
$686$		0			0
$687$		0			0
$688$	−0.133975	+	0.232051i	−0.00510773	+	0.00884685i
$689$	19.5959			0.746545
$690$		0			0
$691$	−24.3190			−0.925140			−0.462570	−	0.886583i	$-0.653073\pi$
$691$	−24.3190			−0.925140			−0.462570	+	0.886583i	$0.653073\pi$
$692$	6.69213			0.254397
$693$		0			0
$694$	−9.58846			−0.363973
$695$	0.823085			0.0312214
$696$		0			0
$697$	58.9090			2.23134
$698$	4.00240	−	6.93237i	0.151493	−	0.262394i
$699$		0			0
$700$		0			0
$701$	20.7846			0.785024			0.392512	−	0.919747i	$-0.371606\pi$
$701$	20.7846			0.785024			0.392512	+	0.919747i	$0.371606\pi$
$702$		0			0
$703$	16.3514	−	28.3214i	0.616704	−	1.06816i
$704$	−0.133975	−	0.232051i	−0.00504936	−	0.00874574i
$705$		0			0
$706$	12.5063	+	21.6615i	0.470680	+	0.815241i
$707$		0			0
$708$		0			0
$709$	−12.3923			−0.465403			−0.232701	−	0.972548i	$-0.574756\pi$
$709$	−12.3923			−0.465403			−0.232701	+	0.972548i	$0.574756\pi$
$710$	4.89898	−	8.48528i	0.183855	−	0.318447i
$711$		0			0
$712$	3.53553	+	6.12372i	0.132500	+	0.229496i
$713$	−18.2832	+	31.6675i	−0.684713	+	1.18596i
$714$		0			0
$715$	−0.248711	−	0.430781i	−0.00930128	−	0.0161103i
$716$	2.53590	−	4.39230i	0.0947710	−	0.164148i
$717$		0			0
$718$	−3.73205	−	6.46410i	−0.139279	−	0.241238i
$719$	24.8367	+	43.0184i	0.926251	+	1.60431i	0.789536	+	0.613704i	$0.210321\pi$
$719$	24.8367	+	43.0184i	0.926251	+	1.60431i	0.136716	+	0.990610i	$0.456345\pi$
$720$		0			0
$721$		0			0
$722$	0.0980762	−	0.169873i	0.00365002	−	0.00632202i
$723$		0			0
$724$	16.9706			0.630706
$725$	−15.7128			−0.583559
$726$		0			0
$727$	16.3514	−	28.3214i	0.606439	−	1.05038i	−0.385383	−	0.922757i	$-0.625931\pi$
$727$	16.3514	−	28.3214i	0.606439	−	1.05038i	0.991822	−	0.127627i	$-0.0407361\pi$
$728$		0			0
$729$		0			0
$730$	2.80385	+	4.85641i	0.103775	+	0.179744i
$731$	0.915158	+	1.58510i	0.0338483	+	0.0586270i
$732$		0			0
$733$	4.00240	−	6.93237i	0.147832	−	0.256053i	−0.782594	−	0.622533i	$-0.786104\pi$
$733$	4.00240	−	6.93237i	0.147832	−	0.256053i	0.930426	+	0.366480i	$0.119437\pi$
$734$	−9.28032	−	16.0740i	−0.342543	−	0.593302i
$735$		0			0
$736$	−2.73205	+	4.73205i	−0.100705	+	0.174426i
$737$	−1.66987	−	2.89230i	−0.0615106	−	0.106539i
$738$		0			0
$739$	−3.06218	+	5.30385i	−0.112644	+	0.195105i	−0.916836	−	0.399265i	$-0.869265\pi$
$739$	−3.06218	+	5.30385i	−0.112644	+	0.195105i	0.804191	+	0.594370i	$0.202599\pi$
$740$	−7.72741			−0.284065
$741$		0			0
$742$		0			0
$743$	−15.7846	−	27.3397i	−0.579081	−	1.00300i	−0.995585	−	0.0938641i	$-0.970078\pi$
$743$	−15.7846	−	27.3397i	−0.579081	−	1.00300i	0.416504	−	0.909134i	$-0.363255\pi$
$744$		0			0
$745$	−11.8685	−	20.5569i	−0.434829	−	0.753145i
$746$	−5.39230	+	9.33975i	−0.197426	+	0.341952i
$747$		0			0
$748$	−1.83032			−0.0669230
$749$		0			0
$750$		0			0
$751$	−17.3923	+	30.1244i	−0.634654	+	1.09925i	0.351934	+	0.936025i	$0.385524\pi$
$751$	−17.3923	+	30.1244i	−0.634654	+	1.09925i	−0.986588	+	0.163229i	$0.947809\pi$
$752$	0.757875			0.0276368
$753$		0			0
$754$	7.17260			0.261211
$755$	−19.0411			−0.692977
$756$		0			0
$757$	19.3205			0.702216			0.351108	−	0.936335i	$-0.385805\pi$
$757$	19.3205			0.702216			0.351108	+	0.936335i	$0.385805\pi$
$758$	−13.5885			−0.493555
$759$		0			0
$760$	−4.53590			−0.164534
$761$	20.1272	−	34.8613i	0.729609	−	1.26372i	−0.227440	−	0.973792i	$-0.573035\pi$
$761$	20.1272	−	34.8613i	0.729609	−	1.26372i	0.957049	−	0.289928i	$-0.0936312\pi$
$762$		0			0
$763$		0			0
$764$	−14.9282			−0.540083
$765$		0			0
$766$	13.6617	−	23.6627i	0.493616	−	0.854968i
$767$	−1.14359	−	1.98076i	−0.0412928	−	0.0715212i
$768$		0			0
$769$	19.0919	+	33.0681i	0.688471	+	1.19247i	0.972332	+	0.233601i	$0.0750511\pi$
$769$	19.0919	+	33.0681i	0.688471	+	1.19247i	−0.283862	+	0.958865i	$0.591616\pi$
$770$		0			0
$771$		0			0
$772$	15.0526			0.541753
$773$	−19.6975	+	34.1170i	−0.708468	+	1.22710i	0.256957	+	0.966423i	$0.417280\pi$
$773$	−19.6975	+	34.1170i	−0.708468	+	1.22710i	−0.965425	+	0.260680i	$0.916053\pi$
$774$		0			0
$775$	−13.1440	−	22.7661i	−0.472147	−	0.817783i
$776$	9.07227	−	15.7136i	0.325676	−	0.564087i
$777$		0			0
$778$	−4.00000	−	6.92820i	−0.143407	−	0.248388i
$779$	−18.8923	+	32.7224i	−0.676887	+	1.17240i
$780$		0			0
$781$	1.26795	+	2.19615i	0.0453708	+	0.0785845i
$782$	18.6622	+	32.3238i	0.667358	+	1.15590i
$783$		0			0
$784$		0			0
$785$	−4.92820	+	8.53590i	−0.175895	+	0.304659i
$786$		0			0
$787$	−7.14540			−0.254706			−0.127353	−	0.991857i	$-0.540648\pi$
$787$	−7.14540			−0.254706			−0.127353	+	0.991857i	$0.540648\pi$
$788$	16.9282			0.603042
$789$		0			0
$790$	−4.62158	+	8.00481i	−0.164428	+	0.284798i
$791$		0			0
$792$		0			0
$793$	11.3205	+	19.6077i	0.402003	+	0.696290i
$794$	−6.55343	−	11.3509i	−0.232573	−	0.402827i
$795$		0			0
$796$	13.1440	−	22.7661i	0.465878	−	0.806924i
$797$	18.9396	+	32.8043i	0.670874	+	1.16199i	0.977657	+	0.210209i	$0.0674143\pi$
$797$	18.9396	+	32.8043i	0.670874	+	1.16199i	−0.306782	+	0.951780i	$0.599252\pi$
$798$		0			0
$799$	2.58846	−	4.48334i	0.0915730	−	0.158609i
$800$	−1.96410	−	3.40192i	−0.0694415	−	0.120276i
$801$		0			0
$802$	11.8923	−	20.5981i	0.419932	−	0.727343i
$803$	−1.45138			−0.0512180
$804$		0			0
$805$		0			0
$806$	6.00000	+	10.3923i	0.211341	+	0.366053i
$807$		0			0
$808$	−2.44949	−	4.24264i	−0.0861727	−	0.149256i
$809$	−14.8660	+	25.7487i	−0.522662	+	0.905276i	0.476991	+	0.878908i	$0.341728\pi$
$809$	−14.8660	+	25.7487i	−0.522662	+	0.905276i	−0.999652	+	0.0263681i	$0.991606\pi$
$810$		0			0
$811$	24.9110			0.874744			0.437372	−	0.899281i	$-0.355909\pi$
$811$	24.9110			0.874744			0.437372	+	0.899281i	$0.355909\pi$
$812$		0			0
$813$		0			0
$814$	1.00000	−	1.73205i	0.0350500	−	0.0607083i
$815$	13.7904			0.483057
$816$		0			0
$817$	−1.17398			−0.0410723
$818$	4.48288			0.156740
$819$		0			0
$820$	8.92820			0.311786
$821$	−10.3923			−0.362694			−0.181347	−	0.983419i	$-0.558046\pi$
$821$	−10.3923			−0.362694			−0.181347	+	0.983419i	$0.558046\pi$
$822$		0			0
$823$	−10.7846			−0.375928			−0.187964	−	0.982176i	$-0.560189\pi$
$823$	−10.7846			−0.375928			−0.187964	+	0.982176i	$0.560189\pi$
$824$	−6.17449	+	10.6945i	−0.215099	+	0.372562i
$825$		0			0
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	3.96524	−	6.86800i	0.137718	−	0.238535i	−0.788914	−	0.614503i	$-0.789356\pi$
$829$	3.96524	−	6.86800i	0.137718	−	0.238535i	0.926633	+	0.375968i	$0.122690\pi$
$830$	−3.41154	−	5.90897i	−0.118416	−	0.205103i
$831$		0			0
$832$	0.896575	+	1.55291i	0.0310832	+	0.0538376i
$833$		0			0
$834$		0			0
$835$	−1.56922			−0.0543051
$836$	0.586988	−	1.01669i	0.0203014	−	0.0351631i
$837$		0			0
$838$	18.0938	+	31.3393i	0.625039	+	1.08260i
$839$	−11.3137	+	19.5959i	−0.390593	+	0.676526i	−0.992528	−	0.122019i	$-0.961063\pi$
$839$	−11.3137	+	19.5959i	−0.390593	+	0.676526i	0.601935	+	0.798545i	$0.294397\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$	3.80385	−	6.58846i	0.131089	−	0.227053i
$843$		0			0
$844$	−9.46410	−	16.3923i	−0.325768	−	0.564246i
$845$	−5.06489	−	8.77264i	−0.174237	−	0.301788i
$846$		0			0
$847$		0			0
$848$	5.46410	−	9.46410i	0.187638	−	0.324999i
$849$		0			0
$850$	−26.8329			−0.920361
$851$	−40.7846			−1.39808
$852$		0			0
$853$	16.4901	−	28.5617i	0.564610	−	0.977933i	−0.432476	−	0.901645i	$-0.642360\pi$
$853$	16.4901	−	28.5617i	0.564610	−	0.977933i	0.997086	−	0.0762876i	$-0.0243067\pi$
$854$		0			0
$855$		0			0
$856$	8.69615	+	15.0622i	0.297228	+	0.514815i
$857$	5.60609	+	9.71003i	0.191500	+	0.331688i	0.945748	−	0.324902i	$-0.105331\pi$
$857$	5.60609	+	9.71003i	0.191500	+	0.331688i	−0.754247	+	0.656590i	$0.771998\pi$
$858$		0			0
$859$	−20.8021	+	36.0303i	−0.709758	+	1.22934i	0.255189	+	0.966891i	$0.417862\pi$
$859$	−20.8021	+	36.0303i	−0.709758	+	1.22934i	−0.964947	+	0.262445i	$0.915471\pi$
$860$	0.138701	+	0.240237i	0.00472965	+	0.00819200i
$861$		0			0
$862$	5.07180	−	8.78461i	0.172746	−	0.299205i
$863$	−27.0526	−	46.8564i	−0.920880	−	1.59501i	−0.798057	−	0.602582i	$-0.794139\pi$
$863$	−27.0526	−	46.8564i	−0.920880	−	1.59501i	−0.122823	−	0.992429i	$-0.539195\pi$
$864$		0			0
$865$	3.46410	−	6.00000i	0.117783	−	0.204006i
$866$	−19.8362			−0.674060
$867$		0			0
$868$		0			0
$869$	−1.19615	−	2.07180i	−0.0405767	−	0.0702809i
$870$		0			0
$871$	11.1750	+	19.3557i	0.378651	+	0.655842i
$872$	2.46410	−	4.26795i	0.0834450	−	0.144531i
$873$		0			0
$874$	−23.9401			−0.809786
$875$		0			0
$876$		0			0
$877$	14.5885	−	25.2679i	0.492617	−	0.853238i	−0.507347	−	0.861742i	$-0.669374\pi$
$877$	14.5885	−	25.2679i	0.492617	−	0.853238i	0.999964	+	0.00850405i	$0.00270695\pi$
$878$	19.5959			0.661330
$879$		0			0
$880$	−0.277401			−0.00935120
$881$	−12.7279			−0.428815			−0.214407	−	0.976744i	$-0.568782\pi$
$881$	−12.7279			−0.428815			−0.214407	+	0.976744i	$0.568782\pi$
$882$		0			0
$883$	14.4641			0.486756			0.243378	−	0.969932i	$-0.421744\pi$
$883$	14.4641			0.486756			0.243378	+	0.969932i	$0.421744\pi$
$884$	12.2487			0.411969
$885$		0			0
$886$	16.3205			0.548298
$887$	−26.6298	+	46.1242i	−0.894142	+	1.54870i	−0.0592788	+	0.998241i	$0.518880\pi$
$887$	−26.6298	+	46.1242i	−0.894142	+	1.54870i	−0.834863	+	0.550458i	$0.814453\pi$
$888$		0			0
$889$		0			0
$890$	7.32051			0.245384
$891$		0			0
$892$	−3.58630	+	6.21166i	−0.120078	+	0.207982i
$893$	1.66025	+	2.87564i	0.0555583	+	0.0962298i
$894$		0			0
$895$	−2.62536	−	4.54725i	−0.0877559	−	0.151998i
$896$		0			0
$897$		0			0
$898$	23.7846			0.793703
$899$	13.3843	−	23.1822i	0.446390	−	0.773170i
$900$		0			0
$901$	−37.3244	−	64.6477i	−1.24345	−	2.15373i
$902$	−1.15539	+	2.00120i	−0.0384704	+	0.0666327i
$903$		0			0
$904$	3.46410	+	6.00000i	0.115214	+	0.199557i
$905$	8.78461	−	15.2154i	0.292010	−	0.505777i
$906$		0			0
$907$	2.62436	+	4.54552i	0.0871403	+	0.150931i	0.906301	−	0.422632i	$-0.138894\pi$
$907$	2.62436	+	4.54552i	0.0871403	+	0.150931i	−0.819161	+	0.573564i	$0.805560\pi$
$908$	13.8325	+	23.9587i	0.459049	+	0.795097i
$909$		0			0
$910$		0			0
$911$	−16.5359	+	28.6410i	−0.547859	+	0.948919i	0.450562	+	0.892745i	$0.351224\pi$
$911$	−16.5359	+	28.6410i	−0.547859	+	0.948919i	−0.998421	+	0.0561742i	$0.982110\pi$
$912$		0			0
$913$	1.76594			0.0584442
$914$	31.0526			1.02713
$915$		0			0
$916$	0.240237	−	0.416102i	0.00793764	−	0.0137484i
$917$		0			0
$918$		0			0
$919$	−4.53590	−	7.85641i	−0.149625	−	0.259159i	0.781464	−	0.623951i	$-0.214473\pi$
$919$	−4.53590	−	7.85641i	−0.149625	−	0.259159i	−0.931089	+	0.364792i	$0.881140\pi$
$920$	2.82843	+	4.89898i	0.0932505	+	0.161515i
$921$		0			0
$922$	−5.51815	+	9.55772i	−0.181731	+	0.314767i
$923$	−8.48528	−	14.6969i	−0.279296	−	0.483756i
$924$		0			0
$925$	14.6603	−	25.3923i	0.482026	−	0.834894i
$926$	−15.3205	−	26.5359i	−0.503463	−	0.872024i
$927$		0			0
$928$	2.00000	−	3.46410i	0.0656532	−	0.113715i
$929$	30.8081			1.01078			0.505390	−	0.862891i	$-0.331349\pi$
$929$	30.8081			1.01078			0.505390	+	0.862891i	$0.331349\pi$
$930$		0			0
$931$		0			0
$932$	0.0621778	+	0.107695i	0.00203670	+	0.00352767i
$933$		0			0
$934$	4.58939	+	7.94906i	0.150170	+	0.260101i
$935$	−0.947441	+	1.64102i	−0.0309846	+	0.0536670i
$936$		0			0
$937$	9.89949			0.323402			0.161701	−	0.986840i	$-0.448302\pi$
$937$	9.89949			0.323402			0.161701	+	0.986840i	$0.448302\pi$
$938$		0			0
$939$		0			0
$940$	0.392305	−	0.679492i	0.0127956	−	0.0221626i
$941$	−47.8802			−1.56085			−0.780425	−	0.625250i	$-0.784997\pi$
$941$	−47.8802			−1.56085			−0.780425	+	0.625250i	$0.784997\pi$
$942$		0			0
$943$	47.1223			1.53451
$944$	−1.27551			−0.0415144
$945$		0			0
$946$	−0.0717968			−0.00233431
$947$	18.1244			0.588962			0.294481	−	0.955657i	$-0.404853\pi$
$947$	18.1244			0.588962			0.294481	+	0.955657i	$0.404853\pi$
$948$		0			0
$949$	9.71281			0.315291
$950$	8.60540	−	14.9050i	0.279196	−	0.483582i
$951$		0			0
$952$		0			0
$953$	−19.0000			−0.615470			−0.307735	−	0.951472i	$-0.599571\pi$
$953$	−19.0000			−0.615470			−0.307735	+	0.951472i	$0.599571\pi$
$954$		0			0
$955$	−7.72741	+	13.3843i	−0.250053	+	0.433105i
$956$	0.464102	+	0.803848i	0.0150101	+	0.0259983i
$957$		0			0
$958$	−2.07055	−	3.58630i	−0.0668965	−	0.115868i
$959$		0			0
$960$		0			0
$961$	13.7846			0.444665
$962$	−6.69213	+	11.5911i	−0.215763	+	0.373712i
$963$		0			0
$964$	3.13801	+	5.43520i	0.101069	+	0.175056i
$965$	7.79178	−	13.4958i	0.250826	−	0.434444i
$966$		0			0
$967$	23.7846	+	41.1962i	0.764861	+	1.32478i	0.940320	+	0.340292i	$0.110526\pi$
$967$	23.7846	+	41.1962i	0.764861	+	1.32478i	−0.175458	+	0.984487i	$0.556141\pi$
$968$	−5.46410	+	9.46410i	−0.175623	+	0.304188i
$969$		0			0
$970$	−9.39230	−	16.2679i	−0.301569	−	0.522332i
$971$	−15.6443	−	27.0967i	−0.502049	−	0.869574i	−0.999997	−	0.00236748i	$-0.999246\pi$
$971$	−15.6443	−	27.0967i	−0.502049	−	0.869574i	0.497948	−	0.867207i	$-0.334087\pi$
$972$		0			0
$973$		0			0
$974$	−1.39230	+	2.41154i	−0.0446123	+	0.0772708i
$975$		0			0
$976$	12.6264			0.404161
$977$	−1.98076			−0.0633702			−0.0316851	−	0.999498i	$-0.510087\pi$
$977$	−1.98076			−0.0633702			−0.0316851	+	0.999498i	$0.510087\pi$
$978$		0			0
$979$	−0.947343	+	1.64085i	−0.0302772	+	0.0524417i
$980$		0			0
$981$		0			0
$982$	−9.69615	−	16.7942i	−0.309417	−	0.535925i
$983$	−6.31319	−	10.9348i	−0.201360	−	0.348765i	0.747607	−	0.664141i	$-0.231203\pi$
$983$	−6.31319	−	10.9348i	−0.201360	−	0.348765i	−0.948967	+	0.315376i	$0.897869\pi$
$984$		0			0
$985$	8.76268	−	15.1774i	0.279202	−	0.483593i
$986$	−13.6617	−	23.6627i	−0.435076	−	0.753574i
$987$		0			0
$988$	−3.92820	+	6.80385i	−0.124973	+	0.216459i
$989$	0.732051	+	1.26795i	0.0232779	+	0.0403184i
$990$		0			0
$991$	−25.1244	+	43.5167i	−0.798101	+	1.38235i	0.122750	+	0.992438i	$0.460829\pi$
$991$	−25.1244	+	43.5167i	−0.798101	+	1.38235i	−0.920851	+	0.389915i	$0.872505\pi$
$992$	6.69213			0.212475
$993$		0			0
$994$		0			0
$995$	−13.6077	−	23.5692i	−0.431393	−	0.747194i
$996$		0			0
$997$	−18.8009	−	32.5641i	−0.595430	−	1.03131i	−0.993486	−	0.113954i	$-0.963648\pi$
$997$	−18.8009	−	32.5641i	−0.595430	−	1.03131i	0.398056	−	0.917361i	$-0.369685\pi$
$998$	16.6962	−	28.9186i	0.528507	−	0.915402i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.e.q.2125.3		8
3.2	odd	2		882.2.e.s.655.2		8
7.2	even	3		2646.2.h.t.667.2		8
7.3	odd	6		2646.2.f.r.883.2		8
7.4	even	3		2646.2.f.r.883.3		8
7.5	odd	6		2646.2.h.t.667.3		8
7.6	odd	2	inner	2646.2.e.q.2125.2		8
9.4	even	3		2646.2.h.t.361.2		8
9.5	odd	6		882.2.h.q.67.2		8
21.2	odd	6		882.2.h.q.79.1		8
21.5	even	6		882.2.h.q.79.4		8
21.11	odd	6		882.2.f.q.295.4	yes	8
21.17	even	6		882.2.f.q.295.1	✓	8
21.20	even	2		882.2.e.s.655.3		8
63.4	even	3		2646.2.f.r.1765.3		8
63.5	even	6		882.2.e.s.373.3		8
63.11	odd	6		7938.2.a.cp.1.3		4
63.13	odd	6		2646.2.h.t.361.3		8
63.23	odd	6		882.2.e.s.373.2		8
63.25	even	3		7938.2.a.ci.1.2		4
63.31	odd	6		2646.2.f.r.1765.2		8
63.32	odd	6		882.2.f.q.589.4	yes	8
63.38	even	6		7938.2.a.cp.1.2		4
63.40	odd	6	inner	2646.2.e.q.1549.2		8
63.41	even	6		882.2.h.q.67.3		8
63.52	odd	6		7938.2.a.ci.1.3		4
63.58	even	3	inner	2646.2.e.q.1549.3		8
63.59	even	6		882.2.f.q.589.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.s.373.2		8	63.23	odd	6
882.2.e.s.373.3		8	63.5	even	6
882.2.e.s.655.2		8	3.2	odd	2
882.2.e.s.655.3		8	21.20	even	2
882.2.f.q.295.1	✓	8	21.17	even	6
882.2.f.q.295.4	yes	8	21.11	odd	6
882.2.f.q.589.1	yes	8	63.59	even	6
882.2.f.q.589.4	yes	8	63.32	odd	6
882.2.h.q.67.2		8	9.5	odd	6
882.2.h.q.67.3		8	63.41	even	6
882.2.h.q.79.1		8	21.2	odd	6
882.2.h.q.79.4		8	21.5	even	6
2646.2.e.q.1549.2		8	63.40	odd	6	inner
2646.2.e.q.1549.3		8	63.58	even	3	inner
2646.2.e.q.2125.2		8	7.6	odd	2	inner
2646.2.e.q.2125.3		8	1.1	even	1	trivial
2646.2.f.r.883.2		8	7.3	odd	6
2646.2.f.r.883.3		8	7.4	even	3
2646.2.f.r.1765.2		8	63.31	odd	6
2646.2.f.r.1765.3		8	63.4	even	3
2646.2.h.t.361.2		8	9.4	even	3
2646.2.h.t.361.3		8	63.13	odd	6
2646.2.h.t.667.2		8	7.2	even	3
2646.2.h.t.667.3		8	7.5	odd	6
7938.2.a.ci.1.2		4	63.25	even	3
7938.2.a.ci.1.3		4	63.52	odd	6
7938.2.a.cp.1.2		4	63.38	even	6
7938.2.a.cp.1.3		4	63.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.517638 - 0.896575i) q^{5} -1.00000 q^{8} +(-0.517638 + 0.896575i) q^{10} +(-0.133975 - 0.232051i) q^{11} +(0.896575 + 1.55291i) q^{13} +1.00000 q^{16} +(3.41542 - 5.91567i) q^{17} +(2.19067 + 3.79435i) q^{19} +(0.517638 - 0.896575i) q^{20} +(0.133975 + 0.232051i) q^{22} +(2.73205 - 4.73205i) q^{23} +(1.96410 + 3.40192i) q^{25} +(-0.896575 - 1.55291i) q^{26} +(-2.00000 + 3.46410i) q^{29} -6.69213 q^{31} -1.00000 q^{32} +(-3.41542 + 5.91567i) q^{34} +(-3.73205 - 6.46410i) q^{37} +(-2.19067 - 3.79435i) q^{38} +(-0.517638 + 0.896575i) q^{40} +(4.31199 + 7.46859i) q^{41} +(-0.133975 + 0.232051i) q^{43} +(-0.133975 - 0.232051i) q^{44} +(-2.73205 + 4.73205i) q^{46} +0.757875 q^{47} +(-1.96410 - 3.40192i) q^{50} +(0.896575 + 1.55291i) q^{52} +(5.46410 - 9.46410i) q^{53} -0.277401 q^{55} +(2.00000 - 3.46410i) q^{58} -1.27551 q^{59} +12.6264 q^{61} +6.69213 q^{62} +1.00000 q^{64} +1.85641 q^{65} +12.4641 q^{67} +(3.41542 - 5.91567i) q^{68} -9.46410 q^{71} +(2.70831 - 4.69093i) q^{73} +(3.73205 + 6.46410i) q^{74} +(2.19067 + 3.79435i) q^{76} +8.92820 q^{79} +(0.517638 - 0.896575i) q^{80} +(-4.31199 - 7.46859i) q^{82} +(-3.29530 + 5.70762i) q^{83} +(-3.53590 - 6.12436i) q^{85} +(0.133975 - 0.232051i) q^{86} +(0.133975 + 0.232051i) q^{88} +(-3.53553 - 6.12372i) q^{89} +(2.73205 - 4.73205i) q^{92} -0.757875 q^{94} +4.53590 q^{95} +(-9.07227 + 15.7136i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 8 q^{11} + 8 q^{16} + 8 q^{22} + 8 q^{23} - 12 q^{25} - 16 q^{29} - 8 q^{32} - 16 q^{37} - 8 q^{43} - 8 q^{44} - 8 q^{46} + 12 q^{50} + 16 q^{53} + 16 q^{58} + 8 q^{64}+ \cdots + 64 q^{95}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 8 * q^11 + 8 * q^16 + 8 * q^22 + 8 * q^23 - 12 * q^25 - 16 * q^29 - 8 * q^32 - 16 * q^37 - 8 * q^43 - 8 * q^44 - 8 * q^46 + 12 * q^50 + 16 * q^53 + 16 * q^58 + 8 * q^64 - 96 * q^65 + 72 * q^67 - 48 * q^71 + 16 * q^74 + 16 * q^79 - 56 * q^85 + 8 * q^86 + 8 * q^88 + 8 * q^92 + 64 * q^95

Introduction

L-functions

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Database

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