LMFDB - Embedded newform 882.2.e.s.655.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(373,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("882.373"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,0,8,0,0,0,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$7.04280545828$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			655.3
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	882.655
Dual form			882.2.e.s.373.3

$q$-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} +(0.448288 - 1.67303i) q^{3} +1.00000 q^{4} +(0.517638 - 0.896575i) q^{5} +(0.448288 - 1.67303i) q^{6} +1.00000 q^{8} +(-2.59808 - 1.50000i) q^{9} +(0.517638 - 0.896575i) q^{10} +(0.133975 + 0.232051i) q^{11} +(0.448288 - 1.67303i) q^{12} +(-0.896575 - 1.55291i) q^{13} +(-1.26795 - 1.26795i) q^{15} +1.00000 q^{16} +(3.41542 - 5.91567i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(-2.19067 - 3.79435i) q^{19} +(0.517638 - 0.896575i) q^{20} +(0.133975 + 0.232051i) q^{22} +(-2.73205 + 4.73205i) q^{23} +(0.448288 - 1.67303i) q^{24} +(1.96410 + 3.40192i) q^{25} +(-0.896575 - 1.55291i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.00000 - 3.46410i) q^{29} +(-1.26795 - 1.26795i) q^{30} +6.69213 q^{31} +1.00000 q^{32} +(0.448288 - 0.120118i) q^{33} +(3.41542 - 5.91567i) q^{34} +(-2.59808 - 1.50000i) q^{36} +(-3.73205 - 6.46410i) q^{37} +(-2.19067 - 3.79435i) q^{38} +(-3.00000 + 0.803848i) q^{39} +(0.517638 - 0.896575i) q^{40} +(4.31199 + 7.46859i) q^{41} +(-0.133975 + 0.232051i) q^{43} +(0.133975 + 0.232051i) q^{44} +(-2.68973 + 1.55291i) q^{45} +(-2.73205 + 4.73205i) q^{46} +0.757875 q^{47} +(0.448288 - 1.67303i) q^{48} +(1.96410 + 3.40192i) q^{50} +(-8.36603 - 8.36603i) q^{51} +(-0.896575 - 1.55291i) q^{52} +(-5.46410 + 9.46410i) q^{53} +(-3.67423 + 3.67423i) q^{54} +0.277401 q^{55} +(-7.33013 + 1.96410i) q^{57} +(2.00000 - 3.46410i) q^{58} -1.27551 q^{59} +(-1.26795 - 1.26795i) q^{60} -12.6264 q^{61} +6.69213 q^{62} +1.00000 q^{64} -1.85641 q^{65} +(0.448288 - 0.120118i) q^{66} +12.4641 q^{67} +(3.41542 - 5.91567i) q^{68} +(6.69213 + 6.69213i) q^{69} +9.46410 q^{71} +(-2.59808 - 1.50000i) q^{72} +(-2.70831 + 4.69093i) q^{73} +(-3.73205 - 6.46410i) q^{74} +(6.57201 - 1.76097i) q^{75} +(-2.19067 - 3.79435i) q^{76} +(-3.00000 + 0.803848i) q^{78} +8.92820 q^{79} +(0.517638 - 0.896575i) q^{80} +(4.50000 + 7.79423i) q^{81} +(4.31199 + 7.46859i) q^{82} +(-3.29530 + 5.70762i) q^{83} +(-3.53590 - 6.12436i) q^{85} +(-0.133975 + 0.232051i) q^{86} +(-4.89898 - 4.89898i) q^{87} +(0.133975 + 0.232051i) q^{88} +(-3.53553 - 6.12372i) q^{89} +(-2.68973 + 1.55291i) q^{90} +(-2.73205 + 4.73205i) q^{92} +(3.00000 - 11.1962i) q^{93} +0.757875 q^{94} -4.53590 q^{95} +(0.448288 - 1.67303i) q^{96} +(9.07227 - 15.7136i) q^{97} -0.803848i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} + 8 q^{11} - 24 q^{15} + 8 q^{16} + 8 q^{22} - 8 q^{23} - 12 q^{25} + 16 q^{29} - 24 q^{30} + 8 q^{32} - 16 q^{37} - 24 q^{39} - 8 q^{43} + 8 q^{44} - 8 q^{46} - 12 q^{50}+ \cdots - 64 q^{95}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 + 8 * q^11 - 24 * q^15 + 8 * q^16 + 8 * q^22 - 8 * q^23 - 12 * q^25 + 16 * q^29 - 24 * q^30 + 8 * q^32 - 16 * q^37 - 24 * q^39 - 8 * q^43 + 8 * q^44 - 8 * q^46 - 12 * q^50 - 60 * q^51 - 16 * q^53 - 24 * q^57 + 16 * q^58 - 24 * q^60 + 8 * q^64 + 96 * q^65 + 72 * q^67 + 48 * q^71 - 16 * q^74 - 24 * q^78 + 16 * q^79 + 36 * q^81 - 56 * q^85 - 8 * q^86 + 8 * q^88 - 8 * q^92 + 24 * q^93 - 64 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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
$3$	0.448288	−	1.67303i	0.258819	−	0.965926i
$3$	0.448288	−	1.67303i	0.258819	−	0.965926i
$4$	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	$0.0923050\pi$
$6$	0.448288	−	1.67303i	0.183013	−	0.683013i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−2.59808	−	1.50000i	−0.866025	−	0.500000i
$10$	0.517638	−	0.896575i	0.163692	−	0.283522i
$11$	0.133975	+	0.232051i	0.0403949	+	0.0699660i	0.885516	−	0.464609i	$-0.153805\pi$
$11$	0.133975	+	0.232051i	0.0403949	+	0.0699660i	−0.845121	+	0.534575i	$0.820472\pi$
$12$	0.448288	−	1.67303i	0.129410	−	0.482963i
$13$	−0.896575	−	1.55291i	−0.248665	−	0.430701i	0.714490	−	0.699645i	$-0.246659\pi$
$13$	−0.896575	−	1.55291i	−0.248665	−	0.430701i	−0.963156	+	0.268944i	$0.913325\pi$
$14$		0			0
$15$	−1.26795	−	1.26795i	−0.327383	−	0.327383i
$16$	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	$-0.144059\pi$
$18$	−2.59808	−	1.50000i	−0.612372	−	0.353553i
$19$	−2.19067	−	3.79435i	−0.502574	−	0.870484i	−0.999996	−	0.00297513i	$-0.999053\pi$
$19$	−2.19067	−	3.79435i	−0.502574	−	0.870484i	0.497421	−	0.867509i	$-0.334280\pi$
$20$	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	$0.359596\pi$
$23$	−2.73205	+	4.73205i	−0.569672	+	0.986701i	−0.996598	+	0.0824143i	$0.973737\pi$
$24$	0.448288	−	1.67303i	0.0915064	−	0.341506i
$25$	1.96410	+	3.40192i	0.392820	+	0.680385i
$26$	−0.896575	−	1.55291i	−0.175833	−	0.304552i
$27$	−3.67423	+	3.67423i	−0.707107	+	0.707107i
$28$		0			0
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	−0.618389	−	0.785872i	$-0.712214\pi$
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	0.989780	+	0.142605i	$0.0455477\pi$
$30$	−1.26795	−	1.26795i	−0.231495	−	0.231495i
$31$	6.69213			1.20194			0.600971	−	0.799271i	$-0.294781\pi$
$31$	6.69213			1.20194			0.600971	+	0.799271i	$0.294781\pi$
$32$	1.00000			0.176777
$33$	0.448288	−	0.120118i	0.0780369	−	0.0209099i
$34$	3.41542	−	5.91567i	0.585739	−	1.01453i
$35$		0			0
$36$	−2.59808	−	1.50000i	−0.433013	−	0.250000i
$37$	−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
$39$	−3.00000	+	0.803848i	−0.480384	+	0.128719i
$40$	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
$45$	−2.68973	+	1.55291i	−0.400961	+	0.231495i
$46$	−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	$0.482397\pi$
$48$	0.448288	−	1.67303i	0.0647048	−	0.241481i
$49$		0			0
$50$	1.96410	+	3.40192i	0.277766	+	0.481105i
$51$	−8.36603	−	8.36603i	−1.17148	−	1.17148i
$52$	−0.896575	−	1.55291i	−0.124333	−	0.215350i
$53$	−5.46410	+	9.46410i	−0.750552	+	1.29999i	0.197003	+	0.980403i	$0.436879\pi$
$53$	−5.46410	+	9.46410i	−0.750552	+	1.29999i	−0.947555	+	0.319592i	$0.896454\pi$
$54$	−3.67423	+	3.67423i	−0.500000	+	0.500000i
$55$	0.277401			0.0374048
$56$		0			0
$57$	−7.33013	+	1.96410i	−0.970899	+	0.260152i
$58$	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	$0.526459\pi$
$60$	−1.26795	−	1.26795i	−0.163692	−	0.163692i
$61$	−12.6264			−1.61664			−0.808322	−	0.588741i	$-0.799624\pi$
$61$	−12.6264			−1.61664			−0.808322	+	0.588741i	$0.799624\pi$
$62$	6.69213			0.849901
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.85641			−0.230259
$66$	0.448288	−	0.120118i	0.0551804	−	0.0147855i
$67$	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
$69$	6.69213	+	6.69213i	0.805638	+	0.805638i
$70$		0			0
$71$	9.46410			1.12318			0.561591	−	0.827415i	$-0.310189\pi$
$71$	9.46410			1.12318			0.561591	+	0.827415i	$0.310189\pi$
$72$	−2.59808	−	1.50000i	−0.306186	−	0.176777i
$73$	−2.70831	+	4.69093i	−0.316984	+	0.549032i	−0.979857	−	0.199700i	$-0.936003\pi$
$73$	−2.70831	+	4.69093i	−0.316984	+	0.549032i	0.662874	+	0.748731i	$0.269337\pi$
$74$	−3.73205	−	6.46410i	−0.433842	−	0.751437i
$75$	6.57201	−	1.76097i	0.758871	−	0.203339i
$76$	−2.19067	−	3.79435i	−0.251287	−	0.435242i
$77$		0			0
$78$	−3.00000	+	0.803848i	−0.339683	+	0.0910178i
$79$	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
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	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
$87$	−4.89898	−	4.89898i	−0.525226	−	0.525226i
$88$	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	$0.955610\pi$
$90$	−2.68973	+	1.55291i	−0.283522	+	0.163692i
$91$		0			0
$92$	−2.73205	+	4.73205i	−0.284836	+	0.493350i
$93$	3.00000	−	11.1962i	0.311086	−	1.16099i
$94$	0.757875			0.0781688
$95$	−4.53590			−0.465373
$96$	0.448288	−	1.67303i	0.0457532	−	0.170753i
$97$	9.07227	−	15.7136i	0.921149	−	1.59548i	0.123510	−	0.992343i	$-0.460585\pi$
$97$	9.07227	−	15.7136i	0.921149	−	1.59548i	0.797640	−	0.603134i	$-0.206082\pi$
$98$		0			0
$99$		−	0.803848i		−	0.0807897i
$100$	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	$0.754961\pi$
$102$	−8.36603	−	8.36603i	−0.828360	−	0.828360i
$103$	−6.17449	+	10.6945i	−0.608391	+	1.05376i	0.383115	+	0.923701i	$0.374851\pi$
$103$	−6.17449	+	10.6945i	−0.608391	+	1.05376i	−0.991506	+	0.130063i	$0.958482\pi$
$104$	−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	$0.151183\pi$
$107$	8.69615	+	15.0622i	0.840689	+	1.45612i	−0.0486244	+	0.998817i	$0.515484\pi$
$108$	−3.67423	+	3.67423i	−0.353553	+	0.353553i
$109$	−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
$111$	−12.4877	+	3.34607i	−1.18528	+	0.317594i
$112$		0			0
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	0.981689	−	0.190490i	$-0.0610077\pi$
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	−0.655814	+	0.754923i	$0.727674\pi$
$114$	−7.33013	+	1.96410i	−0.686529	+	0.183955i
$115$	2.82843	+	4.89898i	0.263752	+	0.456832i
$116$	2.00000	−	3.46410i	0.185695	−	0.321634i
$117$			5.37945i			0.497331i
$118$	−1.27551			−0.117420
$119$		0			0
$120$	−1.26795	−	1.26795i	−0.115747	−	0.115747i
$121$	5.46410	−	9.46410i	0.496737	−	0.860373i
$122$	−12.6264			−1.14314
$123$	14.4282	−	3.86603i	1.30095	−	0.348588i
$124$	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
$129$	0.328169	+	0.328169i	0.0288937	+	0.0288937i
$130$	−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	$0.325192\pi$
$132$	0.448288	−	0.120118i	0.0390184	−	0.0104550i
$133$		0			0
$134$	12.4641			1.07673
$135$	1.39230	+	5.19615i	0.119831	+	0.447214i
$136$	3.41542	−	5.91567i	0.292869	−	0.507265i
$137$	−4.33013	−	7.50000i	−0.369948	−	0.640768i	0.619609	−	0.784910i	$-0.287291\pi$
$137$	−4.33013	−	7.50000i	−0.369948	−	0.640768i	−0.989557	+	0.144142i	$0.953958\pi$
$138$	6.69213	+	6.69213i	0.569672	+	0.569672i
$139$	−0.397520	−	0.688524i	−0.0337172	−	0.0583999i	0.848674	−	0.528916i	$-0.177401\pi$
$139$	−0.397520	−	0.688524i	−0.0337172	−	0.0583999i	−0.882392	+	0.470516i	$0.844068\pi$
$140$		0			0
$141$	0.339746	−	1.26795i	0.0286118	−	0.106781i
$142$	9.46410			0.794210
$143$	0.240237	−	0.416102i	0.0200896	−	0.0347962i
$144$	−2.59808	−	1.50000i	−0.216506	−	0.125000i
$145$	−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	$0.555076\pi$
$149$	−11.4641	+	19.8564i	−0.939176	+	1.62670i	−0.767013	+	0.641632i	$0.778258\pi$
$150$	6.57201	−	1.76097i	0.536603	−	0.143782i
$151$	−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
$153$	−17.7470	+	10.2462i	−1.43476	+	0.828360i
$154$		0			0
$155$	3.46410	−	6.00000i	0.278243	−	0.481932i
$156$	−3.00000	+	0.803848i	−0.240192	+	0.0643593i
$157$	9.52056			0.759823			0.379912	−	0.925023i	$-0.375954\pi$
$157$	9.52056			0.759823			0.379912	+	0.925023i	$0.375954\pi$
$158$	8.92820			0.710290
$159$	13.3843	+	13.3843i	1.06144	+	1.06144i
$160$	0.517638	−	0.896575i	0.0409229	−	0.0708805i
$161$		0			0
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	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
$165$	0.124356	−	0.464102i	0.00968107	−	0.0361303i
$166$	−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
$171$			13.1440i			1.00515i
$172$	−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	$0.418123\pi$
$174$	−4.89898	−	4.89898i	−0.371391	−	0.371391i
$175$		0			0
$176$	0.133975	+	0.232051i	0.0100987	+	0.0174915i
$177$	−0.571797	+	2.13397i	−0.0429789	+	0.160399i
$178$	−3.53553	−	6.12372i	−0.264999	−	0.458993i
$179$	−2.53590	+	4.39230i	−0.189542	+	0.328296i	−0.945098	−	0.326788i	$-0.894034\pi$
$179$	−2.53590	+	4.39230i	−0.189542	+	0.328296i	0.755556	+	0.655084i	$0.227367\pi$
$180$	−2.68973	+	1.55291i	−0.200480	+	0.115747i
$181$	−16.9706			−1.26141			−0.630706	−	0.776022i	$-0.717235\pi$
$181$	−16.9706			−1.26141			−0.630706	+	0.776022i	$0.717235\pi$
$182$		0			0
$183$	−5.66025	+	21.1244i	−0.418418	+	1.56156i
$184$	−2.73205	+	4.73205i	−0.201409	+	0.348851i
$185$	−7.72741			−0.568130
$186$	3.00000	−	11.1962i	0.219971	−	0.820942i
$187$	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	$-0.318393\pi$
$191$	14.9282			1.08017			0.540083	+	0.841611i	$0.318393\pi$
$192$	0.448288	−	1.67303i	0.0323524	−	0.120741i
$193$	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
$195$	−0.832204	+	3.10583i	−0.0595954	+	0.222413i
$196$		0			0
$197$	−16.9282			−1.20608			−0.603042	−	0.797709i	$-0.706045\pi$
$197$	−16.9282			−1.20608			−0.603042	+	0.797709i	$0.706045\pi$
$198$		−	0.803848i		−	0.0571270i
$199$	−13.1440	+	22.7661i	−0.931755	+	1.61385i	−0.151435	+	0.988467i	$0.548389\pi$
$199$	−13.1440	+	22.7661i	−0.931755	+	1.61385i	−0.780320	+	0.625380i	$0.784944\pi$
$200$	1.96410	+	3.40192i	0.138883	+	0.240552i
$201$	5.58750	−	20.8528i	0.394112	−	1.47085i
$202$	2.44949	+	4.24264i	0.172345	+	0.298511i
$203$		0			0
$204$	−8.36603	−	8.36603i	−0.585739	−	0.585739i
$205$	8.92820			0.623573
$206$	−6.17449	+	10.6945i	−0.430197	+	0.745124i
$207$	14.1962	−	8.19615i	0.986701	−	0.569672i
$208$	−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
$213$	4.24264	−	15.8338i	0.290701	−	1.08491i
$214$	8.69615	+	15.0622i	0.594457	+	1.02963i
$215$	0.138701	+	0.240237i	0.00945931	+	0.0163840i
$216$	−3.67423	+	3.67423i	−0.250000	+	0.250000i
$217$		0			0
$218$	−2.46410	+	4.26795i	−0.166890	+	0.289062i
$219$	6.63397	+	6.63397i	0.448282	+	0.448282i
$220$	0.277401			0.0187024
$221$	−12.2487			−0.823937
$222$	−12.4877	+	3.34607i	−0.838119	+	0.224573i
$223$	3.58630	−	6.21166i	0.240157	−	0.415963i	−0.720602	−	0.693349i	$-0.756135\pi$
$223$	3.58630	−	6.21166i	0.240157	−	0.415963i	0.960759	+	0.277385i	$0.0894679\pi$
$224$		0			0
$225$		−	11.7846i		−	0.785641i
$226$	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	$0.463057\pi$
$228$	−7.33013	+	1.96410i	−0.485450	+	0.130076i
$229$	−0.240237	+	0.416102i	−0.0158753	+	0.0274968i	−0.873854	−	0.486189i	$-0.838387\pi$
$229$	−0.240237	+	0.416102i	−0.0158753	+	0.0274968i	0.857979	+	0.513685i	$0.171720\pi$
$230$	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	0.863982	−	0.503524i	$-0.167963\pi$
$233$	−0.0621778	−	0.107695i	−0.00407340	−	0.00705534i	−0.868055	+	0.496468i	$0.834630\pi$
$234$			5.37945i			0.351666i
$235$	0.392305	−	0.679492i	0.0255911	−	0.0443252i
$236$	−1.27551			−0.0830288
$237$	4.00240	−	14.9372i	0.259984	−	0.970274i
$238$		0			0
$239$	−0.464102	−	0.803848i	−0.0300202	−	0.0519966i	0.850625	−	0.525773i	$-0.176224\pi$
$239$	−0.464102	−	0.803848i	−0.0300202	−	0.0519966i	−0.880645	+	0.473776i	$0.842891\pi$
$240$	−1.26795	−	1.26795i	−0.0818458	−	0.0818458i
$241$	−3.13801	−	5.43520i	−0.202137	−	0.350112i	0.747080	−	0.664735i	$-0.231455\pi$
$241$	−3.13801	−	5.43520i	−0.202137	−	0.350112i	−0.949217	+	0.314623i	$0.898122\pi$
$242$	5.46410	−	9.46410i	0.351246	−	0.608375i
$243$	15.0573	−	4.03459i	0.965926	−	0.258819i
$244$	−12.6264			−0.808322
$245$		0			0
$246$	14.4282	−	3.86603i	0.919909	−	0.246489i
$247$	−3.92820	+	6.80385i	−0.249946	+	0.432918i
$248$	6.69213			0.424951
$249$	8.07180	+	8.07180i	0.511529	+	0.511529i
$250$	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
$255$	−11.8313	+	3.17020i	−0.740908	+	0.198526i
$256$	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	$0.268028\pi$
$258$	0.328169	+	0.328169i	0.0204309	+	0.0204309i
$259$		0			0
$260$	−1.85641			−0.115129
$261$	−10.3923	+	6.00000i	−0.643268	+	0.371391i
$262$	−5.46739	+	9.46979i	−0.337776	+	0.585046i
$263$	4.26795	+	7.39230i	0.263173	+	0.455829i	0.967083	−	0.254460i	$-0.0818977\pi$
$263$	4.26795	+	7.39230i	0.263173	+	0.455829i	−0.703910	+	0.710289i	$0.748564\pi$
$264$	0.448288	−	0.120118i	0.0275902	−	0.00739277i
$265$	5.65685	+	9.79796i	0.347498	+	0.601884i
$266$		0			0
$267$	−11.8301	+	3.16987i	−0.723992	+	0.193993i
$268$	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	$0.111498\pi$
$270$	1.39230	+	5.19615i	0.0847330	+	0.316228i
$271$	−6.55343	−	11.3509i	−0.398093	−	0.689516i	0.595398	−	0.803431i	$-0.296994\pi$
$271$	−6.55343	−	11.3509i	−0.398093	−	0.689516i	−0.993491	+	0.113914i	$0.963661\pi$
$272$	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
$276$	6.69213	+	6.69213i	0.402819	+	0.402819i
$277$	−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
$279$	−17.3867	−	10.0382i	−1.04091	−	0.600971i
$280$		0			0
$281$	−8.92820	+	15.4641i	−0.532612	+	0.922511i	0.466663	+	0.884435i	$0.345456\pi$
$281$	−8.92820	+	15.4641i	−0.532612	+	0.922511i	−0.999275	+	0.0380757i	$0.987877\pi$
$282$	0.339746	−	1.26795i	0.0202316	−	0.0755053i
$283$	−15.0759			−0.896168			−0.448084	−	0.893992i	$-0.647893\pi$
$283$	−15.0759			−0.896168			−0.448084	+	0.893992i	$0.647893\pi$
$284$	9.46410			0.561591
$285$	−2.03339	+	7.58871i	−0.120447	+	0.449516i
$286$	0.240237	−	0.416102i	0.0142055	−	0.0246046i
$287$		0			0
$288$	−2.59808	−	1.50000i	−0.153093	−	0.0883883i
$289$	−14.8301	−	25.6865i	−0.872360	−	1.51097i
$290$	−2.07055	−	3.58630i	−0.121587	−	0.210595i
$291$	−22.2224	−	22.2224i	−1.30270	−	1.30270i
$292$	−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
$297$	−1.34486	−	0.360355i	−0.0780369	−	0.0209099i
$298$	−11.4641	+	19.8564i	−0.664098	+	1.15025i
$299$	9.79796			0.566631
$300$	6.57201	−	1.76097i	0.379435	−	0.101669i
$301$		0			0
$302$	−9.19615	−	15.9282i	−0.529179	−	0.916565i
$303$	8.19615	−	2.19615i	0.470857	−	0.126166i
$304$	−2.19067	−	3.79435i	−0.125644	−	0.217621i
$305$	−6.53590	+	11.3205i	−0.374244	+	0.648210i
$306$	−17.7470	+	10.2462i	−1.01453	+	0.585739i
$307$	1.17398			0.0670024			0.0335012	−	0.999439i	$-0.489334\pi$
$307$	1.17398			0.0670024			0.0335012	+	0.999439i	$0.489334\pi$
$308$		0			0
$309$	15.1244	+	15.1244i	0.860395	+	0.860395i
$310$	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	$0.567745\pi$
$312$	−3.00000	+	0.803848i	−0.169842	+	0.0455089i
$313$	6.27603			0.354742			0.177371	−	0.984144i	$-0.443241\pi$
$313$	6.27603			0.354742			0.177371	+	0.984144i	$0.443241\pi$
$314$	9.52056			0.537276
$315$		0			0
$316$	8.92820			0.502251
$317$	−26.0000			−1.46031			−0.730153	−	0.683284i	$-0.760551\pi$
$317$	−26.0000			−1.46031			−0.730153	+	0.683284i	$0.760551\pi$
$318$	13.3843	+	13.3843i	0.750552	+	0.750552i
$319$	1.07180			0.0600091
$320$	0.517638	−	0.896575i	0.0289368	−	0.0501201i
$321$	29.0979	−	7.79676i	1.62409	−	0.435173i
$322$		0			0
$323$	−29.9282			−1.66525
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$	3.52193	−	6.10016i	0.195362	−	0.338376i
$326$	6.66025	+	11.5359i	0.368877	+	0.638914i
$327$	6.03579	+	6.03579i	0.333780	+	0.333780i
$328$	4.31199	+	7.46859i	0.238090	+	0.412384i
$329$		0			0
$330$	0.124356	−	0.464102i	0.00684555	−	0.0255480i
$331$	−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
$333$			22.3923i			1.22709i
$334$	−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
$339$	11.5911	−	3.10583i	0.629543	−	0.168685i
$340$	−3.53590	−	6.12436i	−0.191761	−	0.332140i
$341$	0.896575	+	1.55291i	0.0485523	+	0.0840950i
$342$			13.1440i			0.710747i
$343$		0			0
$344$	−0.133975	+	0.232051i	−0.00722343	+	0.0125113i
$345$	9.46410	−	2.53590i	0.509530	−	0.136528i
$346$	6.69213			0.359771
$347$	−9.58846			−0.514735			−0.257368	−	0.966314i	$-0.582855\pi$
$347$	−9.58846			−0.514735			−0.257368	+	0.966314i	$0.582855\pi$
$348$	−4.89898	−	4.89898i	−0.262613	−	0.262613i
$349$	4.00240	−	6.93237i	0.214244	−	0.371081i	−0.738795	−	0.673931i	$-0.764605\pi$
$349$	4.00240	−	6.93237i	0.214244	−	0.371081i	0.953038	+	0.302850i	$0.0979380\pi$
$350$		0			0
$351$	9.00000	+	2.41154i	0.480384	+	0.128719i
$352$	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	$-0.398509\pi$
$354$	−0.571797	+	2.13397i	−0.0303907	+	0.113419i
$355$	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	0.750574	−	0.660786i	$-0.229777\pi$
$359$	−3.73205	−	6.46410i	−0.196970	−	0.341162i	−0.947545	+	0.319624i	$0.896444\pi$
$360$	−2.68973	+	1.55291i	−0.141761	+	0.0818458i
$361$	−0.0980762	+	0.169873i	−0.00516191	+	0.00894068i
$362$	−16.9706			−0.891953
$363$	−13.3843	−	13.3843i	−0.702492	−	0.702492i
$364$		0			0
$365$	2.80385	+	4.85641i	0.146760	+	0.254196i
$366$	−5.66025	+	21.1244i	−0.295866	+	1.10419i
$367$	−9.28032	−	16.0740i	−0.484429	−	0.839055i	0.515411	−	0.856943i	$-0.327639\pi$
$367$	−9.28032	−	16.0740i	−0.484429	−	0.839055i	−0.999840	+	0.0178877i	$0.994306\pi$
$368$	−2.73205	+	4.73205i	−0.142418	+	0.246675i
$369$		−	25.8719i		−	1.34684i
$370$	−7.72741			−0.401729
$371$		0			0
$372$	3.00000	−	11.1962i	0.155543	−	0.580493i
$373$	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
$375$	4.14359	−	15.4641i	0.213974	−	0.798563i
$376$	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
$381$	6.03579	−	22.5259i	0.309223	−	1.15404i
$382$	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	$0.920705\pi$
$384$	0.448288	−	1.67303i	0.0228766	−	0.0853766i
$385$		0			0
$386$	15.0526			0.766155
$387$	0.696152	−	0.401924i	0.0353874	−	0.0204309i
$388$	9.07227	−	15.7136i	0.460575	−	0.797739i
$389$	−4.00000	−	6.92820i	−0.202808	−	0.351274i	0.746624	−	0.665246i	$-0.231673\pi$
$389$	−4.00000	−	6.92820i	−0.202808	−	0.351274i	−0.949432	+	0.313972i	$0.898340\pi$
$390$	−0.832204	+	3.10583i	−0.0421403	+	0.157270i
$391$	18.6622	+	32.3238i	0.943787	+	1.63469i
$392$		0			0
$393$	13.3923	+	13.3923i	0.675552	+	0.675552i
$394$	−16.9282			−0.852831
$395$	4.62158	−	8.00481i	0.232537	−	0.402766i
$396$		−	0.803848i		−	0.0403949i
$397$	−6.55343	−	11.3509i	−0.328907	−	0.569684i	0.653388	−	0.757023i	$-0.273347\pi$
$397$	−6.55343	−	11.3509i	−0.328907	−	0.569684i	−0.982295	+	0.187339i	$0.940014\pi$
$398$	−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	$-0.630931\pi$
$401$	11.8923	−	20.5981i	0.593873	−	1.02862i	0.993705	−	0.112030i	$-0.0357353\pi$
$402$	5.58750	−	20.8528i	0.278679	−	1.04005i
$403$	−6.00000	−	10.3923i	−0.298881	−	0.517678i
$404$	2.44949	+	4.24264i	0.121867	+	0.211079i
$405$	9.31749			0.462990
$406$		0			0
$407$	1.00000	−	1.73205i	0.0495682	−	0.0858546i
$408$	−8.36603	−	8.36603i	−0.414180	−	0.414180i
$409$	4.48288			0.221664			0.110832	−	0.993839i	$-0.464648\pi$
$409$	4.48288			0.221664			0.110832	+	0.993839i	$0.464648\pi$
$410$	8.92820			0.440933
$411$	−14.4889	+	3.88229i	−0.714684	+	0.191499i
$412$	−6.17449	+	10.6945i	−0.304195	+	0.526882i
$413$		0			0
$414$	14.1962	−	8.19615i	0.697703	−	0.402819i
$415$	3.41154	+	5.90897i	0.167466	+	0.290060i
$416$	−0.896575	−	1.55291i	−0.0439582	−	0.0761379i
$417$	−1.33013	+	0.356406i	−0.0651366	+	0.0174533i
$418$	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
$423$	−1.96902	−	1.13681i	−0.0957369	−	0.0552737i
$424$	−5.46410	+	9.46410i	−0.265360	+	0.459617i
$425$	26.8329			1.30159
$426$	4.24264	−	15.8338i	0.205557	−	0.767148i
$427$		0			0
$428$	8.69615	+	15.0622i	0.420344	+	0.728058i
$429$	−0.588457	−	0.588457i	−0.0284110	−	0.0284110i
$430$	0.138701	+	0.240237i	0.00668874	+	0.0115852i
$431$	5.07180	−	8.78461i	0.244300	−	0.423140i	−0.717635	−	0.696420i	$-0.754775\pi$
$431$	5.07180	−	8.78461i	0.244300	−	0.423140i	0.961935	+	0.273280i	$0.0881085\pi$
$432$	−3.67423	+	3.67423i	−0.176777	+	0.176777i
$433$	−19.8362			−0.953265			−0.476632	−	0.879103i	$-0.658143\pi$
$433$	−19.8362			−0.953265			−0.476632	+	0.879103i	$0.658143\pi$
$434$		0			0
$435$	−6.92820	+	1.85641i	−0.332182	+	0.0890079i
$436$	−2.46410	+	4.26795i	−0.118009	+	0.204398i
$437$	23.9401			1.14521
$438$	6.63397	+	6.63397i	0.316984	+	0.316984i
$439$	19.5959			0.935262			0.467631	−	0.883924i	$-0.345108\pi$
$439$	19.5959			0.935262			0.467631	+	0.883924i	$0.345108\pi$
$440$	0.277401			0.0132246
$441$		0			0
$442$	−12.2487			−0.582612
$443$	16.3205			0.775411			0.387705	−	0.921783i	$-0.373268\pi$
$443$	16.3205			0.775411			0.387705	+	0.921783i	$0.373268\pi$
$444$	−12.4877	+	3.34607i	−0.592639	+	0.158797i
$445$	−7.32051			−0.347025
$446$	3.58630	−	6.21166i	0.169816	−	0.294130i
$447$	28.0812	+	28.0812i	1.32820	+	1.32820i
$448$		0			0
$449$	23.7846			1.12247			0.561233	−	0.827658i	$-0.310327\pi$
$449$	23.7846			1.12247			0.561233	+	0.827658i	$0.310327\pi$
$450$		−	11.7846i		−	0.555532i
$451$	−1.15539	+	2.00120i	−0.0544054	+	0.0942329i
$452$	3.46410	+	6.00000i	0.162938	+	0.282216i
$453$	−30.7709	+	8.24504i	−1.44574	+	0.387386i
$454$	13.8325	+	23.9587i	0.649194	+	1.12444i
$455$		0			0
$456$	−7.33013	+	1.96410i	−0.343265	+	0.0919775i
$457$	−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
$459$	9.18653	+	34.2846i	0.428791	+	1.60027i
$460$	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
$465$	−8.48528	−	8.48528i	−0.393496	−	0.393496i
$466$	−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	$0.901452\pi$
$468$			5.37945i			0.248665i
$469$		0			0
$470$	0.392305	−	0.679492i	0.0180957	−	0.0313426i
$471$	4.26795	−	15.9282i	0.196657	−	0.733933i
$472$	−1.27551			−0.0587102
$473$	−0.0717968			−0.00330122
$474$	4.00240	−	14.9372i	0.183837	−	0.686087i
$475$	8.60540	−	14.9050i	0.394843	−	0.683888i
$476$		0			0
$477$	28.3923	−	16.3923i	1.29999	−	0.750552i
$478$	−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	$0.803174\pi$
$480$	−1.26795	−	1.26795i	−0.0578737	−	0.0578737i
$481$	−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
$486$	15.0573	−	4.03459i	0.683013	−	0.183013i
$487$	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
$489$	22.2856	−	5.97142i	1.00779	−	0.270037i
$490$		0			0
$491$	−9.69615	−	16.7942i	−0.437581	−	0.757913i	0.559921	−	0.828546i	$-0.310831\pi$
$491$	−9.69615	−	16.7942i	−0.437581	−	0.757913i	−0.997502	+	0.0706330i	$0.977498\pi$
$492$	14.4282	−	3.86603i	0.650474	−	0.174294i
$493$	−13.6617	−	23.6627i	−0.615290	−	1.06571i
$494$	−3.92820	+	6.80385i	−0.176738	+	0.306120i
$495$	−0.720710	−	0.416102i	−0.0323935	−	0.0187024i
$496$	6.69213			0.300486
$497$		0			0
$498$	8.07180	+	8.07180i	0.361706	+	0.361706i
$499$	−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
$501$	−2.53590	+	0.679492i	−0.113296	+	0.0303575i
$502$	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
$507$	−11.9837	−	11.9837i	−0.532213	−	0.532213i
$508$	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	$0.325496\pi$
$510$	−11.8313	+	3.17020i	−0.523901	+	0.140379i
$511$		0			0
$512$	1.00000			0.0441942
$513$	21.9904	+	5.89230i	0.970899	+	0.260152i
$514$	−5.01910	+	8.69333i	−0.221383	+	0.383446i
$515$	6.39230	+	11.0718i	0.281679	+	0.487882i
$516$	0.328169	+	0.328169i	0.0144469	+	0.0144469i
$517$	0.101536	+	0.175865i	0.00446555	+	0.00773455i
$518$		0			0
$519$	3.00000	−	11.1962i	0.131685	−	0.491457i
$520$	−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	$-0.0984414\pi$
$522$	−10.3923	+	6.00000i	−0.454859	+	0.262613i
$523$	−10.3664	−	17.9551i	−0.453289	−	0.785120i	0.545299	−	0.838242i	$-0.316416\pi$
$523$	−10.3664	−	17.9551i	−0.453289	−	0.785120i	−0.998588	+	0.0531215i	$0.983083\pi$
$524$	−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
$528$	0.448288	−	0.120118i	0.0195092	−	0.00522748i
$529$	−3.42820	−	5.93782i	−0.149052	−	0.258166i
$530$	5.65685	+	9.79796i	0.245718	+	0.425596i
$531$	3.31388	+	1.91327i	0.143810	+	0.0830288i
$532$		0			0
$533$	7.73205	−	13.3923i	0.334912	−	0.580085i
$534$	−11.8301	+	3.16987i	−0.511940	+	0.137174i
$535$	18.0058			0.778460
$536$	12.4641			0.538367
$537$	6.21166	+	6.21166i	0.268053	+	0.268053i
$538$	2.82843	−	4.89898i	0.121942	−	0.211210i
$539$		0			0
$540$	1.39230	+	5.19615i	0.0599153	+	0.223607i
$541$	−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
$543$	−7.60770	+	28.3923i	−0.326477	+	1.21843i
$544$	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
$549$	32.8043	+	18.9396i	1.40005	+	0.808322i
$550$	−0.526279	+	0.911543i	−0.0224406	+	0.0388683i
$551$	−17.5254			−0.746606
$552$	6.69213	+	6.69213i	0.284836	+	0.284836i
$553$		0			0
$554$	−15.7321	−	27.2487i	−0.668391	−	1.15769i
$555$	−3.46410	+	12.9282i	−0.147043	+	0.548772i
$556$	−0.397520	−	0.688524i	−0.0168586	−	0.0291999i
$557$	3.46410	−	6.00000i	0.146779	−	0.254228i	−0.783256	−	0.621699i	$-0.786443\pi$
$557$	3.46410	−	6.00000i	0.146779	−	0.254228i	0.930035	+	0.367471i	$0.119776\pi$
$558$	−17.3867	−	10.0382i	−0.736036	−	0.424951i
$559$	0.480473			0.0203219
$560$		0			0
$561$	0.820508	−	3.06218i	0.0346419	−	0.129285i
$562$	−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	$0.625623\pi$
$564$	0.339746	−	1.26795i	0.0143059	−	0.0533903i
$565$	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	$-0.681755\pi$
$569$	−25.7846			−1.08095			−0.540474	+	0.841361i	$0.681755\pi$
$570$	−2.03339	+	7.58871i	−0.0851692	+	0.317856i
$571$	−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
$573$	6.69213	−	24.9754i	0.279568	−	1.04336i
$574$		0			0
$575$	−21.4641			−0.895115
$576$	−2.59808	−	1.50000i	−0.108253	−	0.0625000i
$577$	13.7446	−	23.8064i	0.572196	−	0.991072i	−0.424144	−	0.905595i	$-0.639425\pi$
$577$	13.7446	−	23.8064i	0.572196	−	0.991072i	0.996340	−	0.0854776i	$-0.0272416\pi$
$578$	−14.8301	−	25.6865i	−0.616852	−	1.06842i
$579$	6.74788	−	25.1834i	0.280432	−	1.04659i
$580$	−2.07055	−	3.58630i	−0.0859750	−	0.148913i
$581$		0			0
$582$	−22.2224	−	22.2224i	−0.921149	−	0.921149i
$583$	−2.92820			−0.121274
$584$	−2.70831	+	4.69093i	−0.112071	+	0.194112i
$585$	4.82309	+	2.78461i	0.199410	+	0.115129i
$586$	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
$591$	−7.58871	+	28.3214i	−0.312158	+	1.16499i
$592$	−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	$0.945917\pi$
$594$	−1.34486	−	0.360355i	−0.0551804	−	0.0147855i
$595$		0			0
$596$	−11.4641	+	19.8564i	−0.469588	+	0.813350i
$597$	32.1962	+	32.1962i	1.31770	+	1.31770i
$598$	9.79796			0.400668
$599$	4.78461			0.195494			0.0977469	−	0.995211i	$-0.468836\pi$
$599$	4.78461			0.195494			0.0977469	+	0.995211i	$0.468836\pi$
$600$	6.57201	−	1.76097i	0.268301	−	0.0718911i
$601$	1.67303	−	2.89778i	0.0682444	−	0.118203i	−0.829884	−	0.557936i	$-0.811594\pi$
$601$	1.67303	−	2.89778i	0.0682444	−	0.118203i	0.898129	+	0.439733i	$0.144927\pi$
$602$		0			0
$603$	−32.3827	−	18.6962i	−1.31872	−	0.761366i
$604$	−9.19615	−	15.9282i	−0.374186	−	0.648109i
$605$	−5.65685	−	9.79796i	−0.229984	−	0.398344i
$606$	8.19615	−	2.19615i	0.332946	−	0.0892126i
$607$	1.13681	−	1.96902i	0.0461418	−	0.0799199i	−0.842032	−	0.539427i	$-0.818641\pi$
$607$	1.13681	−	1.96902i	0.0461418	−	0.0799199i	0.888174	+	0.459507i	$0.151974\pi$
$608$	−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
$612$	−17.7470	+	10.2462i	−0.717381	+	0.414180i
$613$	−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
$615$	4.00240	−	14.9372i	0.161393	−	0.602325i
$616$		0			0
$617$	1.57180	+	2.72243i	0.0632782	+	0.109601i	0.895929	−	0.444197i	$-0.146511\pi$
$617$	1.57180	+	2.72243i	0.0632782	+	0.109601i	−0.832651	+	0.553798i	$0.813178\pi$
$618$	15.1244	+	15.1244i	0.608391	+	0.608391i
$619$	15.8523	+	27.4570i	0.637159	+	1.10359i	0.986053	+	0.166430i	$0.0532239\pi$
$619$	15.8523	+	27.4570i	0.637159	+	1.10359i	−0.348894	+	0.937162i	$0.613443\pi$
$620$	3.46410	−	6.00000i	0.139122	−	0.240966i
$621$	−7.34847	−	27.4249i	−0.294884	−	1.10052i
$622$	−7.45001			−0.298718
$623$		0			0
$624$	−3.00000	+	0.803848i	−0.120096	+	0.0321797i
$625$	−5.03590	+	8.72243i	−0.201436	+	0.348897i
$626$	6.27603			0.250841
$627$	−1.43782	−	1.43782i	−0.0574211	−	0.0574211i
$628$	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
$633$	−31.6675	+	8.48528i	−1.25867	+	0.337260i
$634$	−26.0000			−1.03259
$635$	6.96953	−	12.0716i	0.276577	−	0.479046i
$636$	13.3843	+	13.3843i	0.530720	+	0.530720i
$637$		0			0
$638$	1.07180			0.0424328
$639$	−24.5885	−	14.1962i	−0.972704	−	0.561591i
$640$	0.517638	−	0.896575i	0.0204614	−	0.0354403i
$641$	−2.03590	−	3.52628i	−0.0804132	−	0.139280i	0.823014	−	0.568021i	$-0.192291\pi$
$641$	−2.03590	−	3.52628i	−0.0804132	−	0.139280i	−0.903427	+	0.428741i	$0.858957\pi$
$642$	29.0979	−	7.79676i	1.14840	−	0.307713i
$643$	22.4565	+	38.8959i	0.885599	+	1.53390i	0.845025	+	0.534726i	$0.179585\pi$
$643$	22.4565	+	38.8959i	0.885599	+	1.53390i	0.0405737	+	0.999177i	$0.487081\pi$
$644$		0			0
$645$	0.464102	−	0.124356i	0.0182740	−	0.00489650i
$646$	−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	$0.308114\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$	−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	−0.918736	−	0.394872i	$-0.870789\pi$
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	0.801337	+	0.598213i	$0.204122\pi$
$654$	6.03579	+	6.03579i	0.236018	+	0.236018i
$655$	5.66025	+	9.80385i	0.221164	+	0.383068i
$656$	4.31199	+	7.46859i	0.168355	+	0.291599i
$657$	14.0728	−	8.12493i	0.549032	−	0.316984i
$658$		0			0
$659$	24.1244	−	41.7846i	0.939751	−	1.62770i	0.173818	−	0.984778i	$-0.444390\pi$
$659$	24.1244	−	41.7846i	0.939751	−	1.62770i	0.765934	−	0.642919i	$-0.222277\pi$
$660$	0.124356	−	0.464102i	0.00484054	−	0.0180651i
$661$		0			0			−	1.00000i	$-0.5\pi$
$661$		0			0				1.00000i	$0.5\pi$
$662$	−11.4641			−0.445565
$663$	−5.49095	+	20.4925i	−0.213251	+	0.795862i
$664$	−3.29530	+	5.70762i	−0.127882	+	0.221499i
$665$		0			0
$666$			22.3923i			0.867684i
$667$	10.9282	+	18.9282i	0.423142	+	0.732903i
$668$	−0.757875	−	1.31268i	−0.0293231	−	0.0507890i
$669$	−8.78461	−	8.78461i	−0.339633	−	0.339633i
$670$	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
$675$	−19.7160	−	5.28290i	−0.758871	−	0.203339i
$676$	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	$0.532964\pi$
$678$	11.5911	−	3.10583i	0.445154	−	0.119279i
$679$		0			0
$680$	−3.53590	−	6.12436i	−0.135596	−	0.234858i
$681$	46.2846	−	12.4019i	1.77363	−	0.475243i
$682$	0.896575	+	1.55291i	0.0343316	+	0.0594642i
$683$	19.1603	−	33.1865i	0.733147	−	1.26985i	−0.222385	−	0.974959i	$-0.571384\pi$
$683$	19.1603	−	33.1865i	0.733147	−	1.26985i	0.955532	−	0.294888i	$-0.0952825\pi$
$684$			13.1440i			0.502574i
$685$	−8.96575			−0.342564
$686$		0			0
$687$	0.588457	+	0.588457i	0.0224510	+	0.0224510i
$688$	−0.133975	+	0.232051i	−0.00510773	+	0.00884685i
$689$	19.5959			0.746545
$690$	9.46410	−	2.53590i	0.360292	−	0.0965400i
$691$	24.3190			0.925140			0.462570	−	0.886583i	$-0.346927\pi$
$691$	24.3190			0.925140			0.462570	+	0.886583i	$0.346927\pi$
$692$	6.69213			0.254397
$693$		0			0
$694$	−9.58846			−0.363973
$695$	−0.823085			−0.0312214
$696$	−4.89898	−	4.89898i	−0.185695	−	0.185695i
$697$	58.9090			2.23134
$698$	4.00240	−	6.93237i	0.151493	−	0.262394i
$699$	−0.208051	+	0.0557471i	−0.00786921	+	0.00210855i
$700$		0			0
$701$	−20.7846			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$702$	9.00000	+	2.41154i	0.339683	+	0.0910178i
$703$	−16.3514	+	28.3214i	−0.616704	+	1.06816i
$704$	0.133975	+	0.232051i	0.00504936	+	0.00874574i
$705$	−0.960947	−	0.960947i	−0.0361913	−	0.0361913i
$706$	−12.5063	−	21.6615i	−0.470680	−	0.815241i
$707$		0			0
$708$	−0.571797	+	2.13397i	−0.0214894	+	0.0801997i
$709$	−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
$711$	−23.1962	−	13.3923i	−0.869924	−	0.502251i
$712$	−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
$717$	−1.55291	+	0.416102i	−0.0579946	+	0.0155396i
$718$	−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	$0.456345\pi$
$720$	−2.68973	+	1.55291i	−0.100240	+	0.0578737i
$721$		0			0
$722$	−0.0980762	+	0.169873i	−0.00365002	+	0.00632202i
$723$	−10.5000	+	2.81347i	−0.390499	+	0.104634i
$724$	−16.9706			−0.630706
$725$	15.7128			0.583559
$726$	−13.3843	−	13.3843i	−0.496737	−	0.496737i
$727$	−16.3514	+	28.3214i	−0.606439	+	1.05038i	0.385383	+	0.922757i	$0.374069\pi$
$727$	−16.3514	+	28.3214i	−0.606439	+	1.05038i	−0.991822	+	0.127627i	$0.959264\pi$
$728$		0			0
$729$		−	27.0000i		−	1.00000i
$730$	2.80385	+	4.85641i	0.103775	+	0.179744i
$731$	0.915158	+	1.58510i	0.0338483	+	0.0586270i
$732$	−5.66025	+	21.1244i	−0.209209	+	0.780779i
$733$	−4.00240	+	6.93237i	−0.147832	+	0.256053i	−0.930426	−	0.366480i	$-0.880563\pi$
$733$	−4.00240	+	6.93237i	−0.147832	+	0.256053i	0.782594	+	0.622533i	$0.213896\pi$
$734$	−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
$738$		−	25.8719i		−	0.952360i
$739$	−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
$741$	9.62209	+	9.62209i	0.353476	+	0.353476i
$742$		0			0
$743$	15.7846	+	27.3397i	0.579081	+	1.00300i	0.995585	+	0.0938641i	$0.0299219\pi$
$743$	15.7846	+	27.3397i	0.579081	+	1.00300i	−0.416504	+	0.909134i	$0.636745\pi$
$744$	3.00000	−	11.1962i	0.109985	−	0.410471i
$745$	11.8685	+	20.5569i	0.434829	+	0.753145i
$746$	5.39230	−	9.33975i	0.197426	−	0.341952i
$747$	17.1229	−	9.88589i	0.626493	−	0.361706i
$748$	1.83032			0.0669230
$749$		0			0
$750$	4.14359	−	15.4641i	0.151303	−	0.564669i
$751$	−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
$753$	0.356406	−	1.33013i	0.0129882	−	0.0484725i
$754$	−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
$759$	−0.656339	+	2.44949i	−0.0238236	+	0.0889108i
$760$	−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	$-0.0936312\pi$
$762$	6.03579	−	22.5259i	0.218654	−	0.816027i
$763$		0			0
$764$	14.9282			0.540083
$765$			21.2154i			0.767044i
$766$	−13.6617	+	23.6627i	−0.493616	+	0.854968i
$767$	1.14359	+	1.98076i	0.0412928	+	0.0715212i
$768$	0.448288	−	1.67303i	0.0161762	−	0.0603704i
$769$	−19.0919	−	33.0681i	−0.688471	−	1.19247i	−0.972332	−	0.233601i	$-0.924949\pi$
$769$	−19.0919	−	33.0681i	−0.688471	−	1.19247i	0.283862	−	0.958865i	$-0.408384\pi$
$770$		0			0
$771$	12.2942	+	12.2942i	0.442766	+	0.442766i
$772$	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	$0.916053\pi$
$774$	0.696152	−	0.401924i	0.0250227	−	0.0144469i
$775$	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
$780$	−0.832204	+	3.10583i	−0.0297977	+	0.111207i
$781$	1.26795	+	2.19615i	0.0453708	+	0.0785845i
$782$	18.6622	+	32.3238i	0.667358	+	1.15590i
$783$	5.37945	+	20.0764i	0.192246	+	0.717472i
$784$		0			0
$785$	4.92820	−	8.53590i	0.175895	−	0.304659i
$786$	13.3923	+	13.3923i	0.477688	+	0.477688i
$787$	7.14540			0.254706			0.127353	−	0.991857i	$-0.459352\pi$
$787$	7.14540			0.254706			0.127353	+	0.991857i	$0.459352\pi$
$788$	−16.9282			−0.603042
$789$	14.2808	−	3.82654i	0.508411	−	0.136228i
$790$	4.62158	−	8.00481i	0.164428	−	0.284798i
$791$		0			0
$792$		−	0.803848i		−	0.0285635i
$793$	11.3205	+	19.6077i	0.402003	+	0.696290i
$794$	−6.55343	−	11.3509i	−0.232573	−	0.402827i
$795$	18.9282	−	5.07180i	0.671314	−	0.179878i
$796$	−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
$801$			21.2132i			0.749532i
$802$	11.8923	−	20.5981i	0.419932	−	0.727343i
$803$	−1.45138			−0.0512180
$804$	5.58750	−	20.8528i	0.197056	−	0.735423i
$805$		0			0
$806$	−6.00000	−	10.3923i	−0.211341	−	0.366053i
$807$	−6.92820	−	6.92820i	−0.243884	−	0.243884i
$808$	2.44949	+	4.24264i	0.0861727	+	0.149256i
$809$	14.8660	−	25.7487i	0.522662	−	0.905276i	−0.476991	−	0.878908i	$-0.658272\pi$
$809$	14.8660	−	25.7487i	0.522662	−	0.905276i	0.999652	−	0.0263681i	$-0.00839421\pi$
$810$	9.31749			0.327383
$811$	−24.9110			−0.874744			−0.437372	−	0.899281i	$-0.644091\pi$
$811$	−24.9110			−0.874744			−0.437372	+	0.899281i	$0.644091\pi$
$812$		0			0
$813$	−21.9282	+	5.87564i	−0.769056	+	0.206068i
$814$	1.00000	−	1.73205i	0.0350500	−	0.0607083i
$815$	13.7904			0.483057
$816$	−8.36603	−	8.36603i	−0.292869	−	0.292869i
$817$	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	$-0.441954\pi$
$821$	10.3923			0.362694			0.181347	+	0.983419i	$0.441954\pi$
$822$	−14.4889	+	3.88229i	−0.505358	+	0.135410i
$823$	−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
$825$	1.28912	+	1.28912i	0.0448813	+	0.0448813i
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	14.1962	−	8.19615i	0.493350	−	0.284836i
$829$	−3.96524	+	6.86800i	−0.137718	+	0.238535i	−0.926633	−	0.375968i	$-0.877310\pi$
$829$	−3.96524	+	6.86800i	−0.137718	+	0.238535i	0.788914	+	0.614503i	$0.210644\pi$
$830$	3.41154	+	5.90897i	0.118416	+	0.205103i
$831$	−52.6405	+	14.1050i	−1.82608	+	0.489296i
$832$	−0.896575	−	1.55291i	−0.0310832	−	0.0538376i
$833$		0			0
$834$	−1.33013	+	0.356406i	−0.0460585	+	0.0123413i
$835$	−1.56922			−0.0543051
$836$	0.586988	−	1.01669i	0.0203014	−	0.0351631i
$837$	−24.5885	+	24.5885i	−0.849901	+	0.849901i
$838$	−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
$843$	21.8695	+	21.8695i	0.753227	+	0.753227i
$844$	−9.46410	−	16.3923i	−0.325768	−	0.564246i
$845$	−5.06489	−	8.77264i	−0.174237	−	0.301788i
$846$	−1.96902	−	1.13681i	−0.0676962	−	0.0390844i
$847$		0			0
$848$	−5.46410	+	9.46410i	−0.187638	+	0.324999i
$849$	−6.75833	+	25.2224i	−0.231945	+	0.865632i
$850$	26.8329			0.920361
$851$	40.7846			1.39808
$852$	4.24264	−	15.8338i	0.145350	−	0.542455i
$853$	−16.4901	+	28.5617i	−0.564610	+	0.977933i	0.432476	+	0.901645i	$0.357640\pi$
$853$	−16.4901	+	28.5617i	−0.564610	+	0.977933i	−0.997086	+	0.0762876i	$0.975693\pi$
$854$		0			0
$855$	11.7846	+	6.80385i	0.403025	+	0.232687i
$856$	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	$0.771998\pi$
$858$	−0.588457	−	0.588457i	−0.0200896	−	0.0200896i
$859$	20.8021	−	36.0303i	0.709758	−	1.22934i	−0.255189	−	0.966891i	$-0.582138\pi$
$859$	20.8021	−	36.0303i	0.709758	−	1.22934i	0.964947	−	0.262445i	$-0.0845290\pi$
$860$	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	$0.205861\pi$
$863$	27.0526	+	46.8564i	0.920880	+	1.59501i	0.122823	+	0.992429i	$0.460805\pi$
$864$	−3.67423	+	3.67423i	−0.125000	+	0.125000i
$865$	3.46410	−	6.00000i	0.117783	−	0.204006i
$866$	−19.8362			−0.674060
$867$	−49.6226	+	13.2963i	−1.68527	+	0.451567i
$868$		0			0
$869$	1.19615	+	2.07180i	0.0405767	+	0.0702809i
$870$	−6.92820	+	1.85641i	−0.234888	+	0.0629381i
$871$	−11.1750	−	19.3557i	−0.378651	−	0.655842i
$872$	−2.46410	+	4.26795i	−0.0834450	+	0.144531i
$873$	−47.1409	+	27.2168i	−1.59548	+	0.921149i
$874$	23.9401			0.809786
$875$		0			0
$876$	6.63397	+	6.63397i	0.224141	+	0.224141i
$877$	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
$879$	15.4641	−	4.14359i	0.521591	−	0.139760i
$880$	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
$885$	1.61729	+	1.61729i	0.0543645	+	0.0543645i
$886$	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	$0.814453\pi$
$888$	−12.4877	+	3.34607i	−0.419059	+	0.112287i
$889$		0			0
$890$	−7.32051			−0.245384
$891$	−1.20577	+	2.08846i	−0.0403949	+	0.0699660i
$892$	3.58630	−	6.21166i	0.120078	−	0.207982i
$893$	−1.66025	−	2.87564i	−0.0555583	−	0.0962298i
$894$	28.0812	+	28.0812i	0.939176	+	0.939176i
$895$	2.62536	+	4.54725i	0.0877559	+	0.151998i
$896$		0			0
$897$	4.39230	−	16.3923i	0.146655	−	0.547323i
$898$	23.7846			0.793703
$899$	13.3843	−	23.1822i	0.446390	−	0.773170i
$900$		−	11.7846i		−	0.392820i
$901$	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
$906$	−30.7709	+	8.24504i	−1.02230	+	0.273923i
$907$	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
$909$		−	14.6969i		−	0.487467i
$910$		0			0
$911$	16.5359	−	28.6410i	0.547859	−	0.948919i	−0.450562	−	0.892745i	$-0.648776\pi$
$911$	16.5359	−	28.6410i	0.547859	−	0.948919i	0.998421	−	0.0561742i	$-0.0178902\pi$
$912$	−7.33013	+	1.96410i	−0.242725	+	0.0650379i
$913$	−1.76594			−0.0584442
$914$	−31.0526			−1.02713
$915$	16.0096	+	16.0096i	0.529262	+	0.529262i
$916$	−0.240237	+	0.416102i	−0.00793764	+	0.0137484i
$917$		0			0
$918$	9.18653	+	34.2846i	0.303201	+	1.13156i
$919$	−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
$921$	0.526279	−	1.96410i	0.0173415	−	0.0647193i
$922$	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
$927$	32.0836	−	18.5235i	1.05376	−	0.608391i
$928$	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	$0.331349\pi$
$930$	−8.48528	−	8.48528i	−0.278243	−	0.278243i
$931$		0			0
$932$	−0.0621778	−	0.107695i	−0.00203670	−	0.00352767i
$933$	−3.33975	+	12.4641i	−0.109338	+	0.408056i
$934$	−4.58939	−	7.94906i	−0.150170	−	0.260101i
$935$	0.947441	−	1.64102i	0.0309846	−	0.0536670i
$936$			5.37945i			0.175833i
$937$	−9.89949			−0.323402			−0.161701	−	0.986840i	$-0.551698\pi$
$937$	−9.89949			−0.323402			−0.161701	+	0.986840i	$0.551698\pi$
$938$		0			0
$939$	2.81347	−	10.5000i	0.0918140	−	0.342655i
$940$	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	$0.784997\pi$
$942$	4.26795	−	15.9282i	0.139057	−	0.518969i
$943$	−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	$-0.595147\pi$
$947$	−18.1244			−0.588962			−0.294481	+	0.955657i	$0.595147\pi$
$948$	4.00240	−	14.9372i	0.129992	−	0.485137i
$949$	9.71281			0.315291
$950$	8.60540	−	14.9050i	0.279196	−	0.483582i
$951$	−11.6555	+	43.4988i	−0.377955	+	1.41055i
$952$		0			0
$953$	19.0000			0.615470			0.307735	−	0.951472i	$-0.400429\pi$
$953$	19.0000			0.615470			0.307735	+	0.951472i	$0.400429\pi$
$954$	28.3923	−	16.3923i	0.919235	−	0.530720i
$955$	7.72741	−	13.3843i	0.250053	−	0.433105i
$956$	−0.464102	−	0.803848i	−0.0150101	−	0.0259983i
$957$	0.480473	−	1.79315i	0.0155315	−	0.0579643i
$958$	2.07055	+	3.58630i	0.0668965	+	0.115868i
$959$		0			0
$960$	−1.26795	−	1.26795i	−0.0409229	−	0.0409229i
$961$	13.7846			0.444665
$962$	−6.69213	+	11.5911i	−0.215763	+	0.373712i
$963$		−	52.1769i		−	1.68138i
$964$	−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
$969$	−13.4164	+	50.0709i	−0.430998	+	1.60851i
$970$	−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	$-0.334087\pi$
$972$	15.0573	−	4.03459i	0.482963	−	0.129410i
$973$		0			0
$974$	1.39230	−	2.41154i	0.0446123	−	0.0772708i
$975$	−8.62693	−	8.62693i	−0.276283	−	0.276283i
$976$	−12.6264			−0.404161
$977$	1.98076			0.0633702			0.0316851	−	0.999498i	$-0.489913\pi$
$977$	1.98076			0.0633702			0.0316851	+	0.999498i	$0.489913\pi$
$978$	22.2856	−	5.97142i	0.712616	−	0.190945i
$979$	0.947343	−	1.64085i	0.0302772	−	0.0524417i
$980$		0			0
$981$	12.8038	−	7.39230i	0.408795	−	0.236018i
$982$	−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	$0.897869\pi$
$984$	14.4282	−	3.86603i	0.459954	−	0.123244i
$985$	−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
$990$	−0.720710	−	0.416102i	−0.0229057	−	0.0132246i
$991$	−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
$993$	−5.13922	+	19.1798i	−0.163088	+	0.608653i
$994$		0			0
$995$	13.6077	+	23.5692i	0.431393	+	0.747194i
$996$	8.07180	+	8.07180i	0.255765	+	0.255765i
$997$	18.8009	+	32.5641i	0.595430	+	1.03131i	0.993486	+	0.113954i	$0.0363515\pi$
$997$	18.8009	+	32.5641i	0.595430	+	1.03131i	−0.398056	+	0.917361i	$0.630315\pi$
$998$	−16.6962	+	28.9186i	−0.528507	+	0.915402i
$999$	37.4631	+	10.0382i	1.18528	+	0.317594i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.s.373.2		8	63.40	odd	6	inner
882.2.e.s.373.3		8	63.58	even	3	inner
882.2.e.s.655.2		8	7.6	odd	2	inner
882.2.e.s.655.3		8	1.1	even	1	trivial
882.2.f.q.295.1	✓	8	7.4	even	3
882.2.f.q.295.4	yes	8	7.3	odd	6
882.2.f.q.589.1	yes	8	63.4	even	3
882.2.f.q.589.4	yes	8	63.31	odd	6
882.2.h.q.67.2		8	63.13	odd	6
882.2.h.q.67.3		8	9.4	even	3
882.2.h.q.79.1		8	7.5	odd	6
882.2.h.q.79.4		8	7.2	even	3
2646.2.e.q.1549.2		8	63.23	odd	6
2646.2.e.q.1549.3		8	63.5	even	6
2646.2.e.q.2125.2		8	3.2	odd	2
2646.2.e.q.2125.3		8	21.20	even	2
2646.2.f.r.883.2		8	21.11	odd	6
2646.2.f.r.883.3		8	21.17	even	6
2646.2.f.r.1765.2		8	63.32	odd	6
2646.2.f.r.1765.3		8	63.59	even	6
2646.2.h.t.361.2		8	63.41	even	6
2646.2.h.t.361.3		8	9.5	odd	6
2646.2.h.t.667.2		8	21.5	even	6
2646.2.h.t.667.3		8	21.2	odd	6
7938.2.a.ci.1.2		4	63.38	even	6
7938.2.a.ci.1.3		4	63.11	odd	6
7938.2.a.cp.1.2		4	63.25	even	3
7938.2.a.cp.1.3		4	63.52	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.448288 - 1.67303i) q^{3} +1.00000 q^{4} +(0.517638 - 0.896575i) q^{5} +(0.448288 - 1.67303i) q^{6} +1.00000 q^{8} +(-2.59808 - 1.50000i) q^{9} +(0.517638 - 0.896575i) q^{10} +(0.133975 + 0.232051i) q^{11} +(0.448288 - 1.67303i) q^{12} +(-0.896575 - 1.55291i) q^{13} +(-1.26795 - 1.26795i) q^{15} +1.00000 q^{16} +(3.41542 - 5.91567i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(-2.19067 - 3.79435i) q^{19} +(0.517638 - 0.896575i) q^{20} +(0.133975 + 0.232051i) q^{22} +(-2.73205 + 4.73205i) q^{23} +(0.448288 - 1.67303i) q^{24} +(1.96410 + 3.40192i) q^{25} +(-0.896575 - 1.55291i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.00000 - 3.46410i) q^{29} +(-1.26795 - 1.26795i) q^{30} +6.69213 q^{31} +1.00000 q^{32} +(0.448288 - 0.120118i) q^{33} +(3.41542 - 5.91567i) q^{34} +(-2.59808 - 1.50000i) q^{36} +(-3.73205 - 6.46410i) q^{37} +(-2.19067 - 3.79435i) q^{38} +(-3.00000 + 0.803848i) q^{39} +(0.517638 - 0.896575i) q^{40} +(4.31199 + 7.46859i) q^{41} +(-0.133975 + 0.232051i) q^{43} +(0.133975 + 0.232051i) q^{44} +(-2.68973 + 1.55291i) q^{45} +(-2.73205 + 4.73205i) q^{46} +0.757875 q^{47} +(0.448288 - 1.67303i) q^{48} +(1.96410 + 3.40192i) q^{50} +(-8.36603 - 8.36603i) q^{51} +(-0.896575 - 1.55291i) q^{52} +(-5.46410 + 9.46410i) q^{53} +(-3.67423 + 3.67423i) q^{54} +0.277401 q^{55} +(-7.33013 + 1.96410i) q^{57} +(2.00000 - 3.46410i) q^{58} -1.27551 q^{59} +(-1.26795 - 1.26795i) q^{60} -12.6264 q^{61} +6.69213 q^{62} +1.00000 q^{64} -1.85641 q^{65} +(0.448288 - 0.120118i) q^{66} +12.4641 q^{67} +(3.41542 - 5.91567i) q^{68} +(6.69213 + 6.69213i) q^{69} +9.46410 q^{71} +(-2.59808 - 1.50000i) q^{72} +(-2.70831 + 4.69093i) q^{73} +(-3.73205 - 6.46410i) q^{74} +(6.57201 - 1.76097i) q^{75} +(-2.19067 - 3.79435i) q^{76} +(-3.00000 + 0.803848i) q^{78} +8.92820 q^{79} +(0.517638 - 0.896575i) q^{80} +(4.50000 + 7.79423i) q^{81} +(4.31199 + 7.46859i) q^{82} +(-3.29530 + 5.70762i) q^{83} +(-3.53590 - 6.12436i) q^{85} +(-0.133975 + 0.232051i) q^{86} +(-4.89898 - 4.89898i) q^{87} +(0.133975 + 0.232051i) q^{88} +(-3.53553 - 6.12372i) q^{89} +(-2.68973 + 1.55291i) q^{90} +(-2.73205 + 4.73205i) q^{92} +(3.00000 - 11.1962i) q^{93} +0.757875 q^{94} -4.53590 q^{95} +(0.448288 - 1.67303i) q^{96} +(9.07227 - 15.7136i) q^{97} -0.803848i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} + 8 q^{11} - 24 q^{15} + 8 q^{16} + 8 q^{22} - 8 q^{23} - 12 q^{25} + 16 q^{29} - 24 q^{30} + 8 q^{32} - 16 q^{37} - 24 q^{39} - 8 q^{43} + 8 q^{44} - 8 q^{46} - 12 q^{50}+ \cdots - 64 q^{95}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 + 8 * q^11 - 24 * q^15 + 8 * q^16 + 8 * q^22 - 8 * q^23 - 12 * q^25 + 16 * q^29 - 24 * q^30 + 8 * q^32 - 16 * q^37 - 24 * q^39 - 8 * q^43 + 8 * q^44 - 8 * q^46 - 12 * q^50 - 60 * q^51 - 16 * q^53 - 24 * q^57 + 16 * q^58 - 24 * q^60 + 8 * q^64 + 96 * q^65 + 72 * q^67 + 48 * q^71 - 16 * q^74 - 24 * q^78 + 16 * q^79 + 36 * q^81 - 56 * q^85 - 8 * q^86 + 8 * q^88 - 8 * q^92 + 24 * q^93 - 64 * q^95

Introduction

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